Credit_Risk_2_Default_Statistic_Ratings_and_Their_Poperties.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/olesyamba/Risk_analysis/blob/main/Credit_Risk_2_Default_Statistic_Ratings_and_Their_Poperties_ipynb%22.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IXx8ZHQe-_ck"
      },
      "source": [
        "# 2. Статистика дефолтов, рейтинги и их свойства"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UnsbMxaVzOmM"
      },
      "source": [
        "Для оценки вероятностей дефолтов требуется дополнительный инструментарий - показатель ранжирования по кредитному риску - рейтинги, скоринг, рыночные меры кредитного риска (например, спрэд облигаций).\n",
        "\n",
        "В этом курсе мы рассматриваем рейтинги - набор категорий или ступеней кредитного качества, по которым распределяются все заемщики.  \n",
        "\n",
        "Обозначать рейтинговую категорию будем $Ri$. Если $i < j$, то $Ri \\succ Rj$, т.е. кредитный риск в категории $Ri$ **ниже**, чем в категрии $Rj$.\n",
        "\n",
        "**Качественный рейтинг**:\n",
        " - монотонно ранжирует по кредитному качеству,\n",
        " - категории как можно сильнее различаются по уровню кредитного качества (что выражается в стремительном росте PD).\n",
        "\n",
        "Рассматриваем риск дефолта на горизонте $h$.\n",
        "\n",
        "| Rating | Rated at t (N) | Defaulted by t+h (D)  | Survived by t+h (S)|\n",
        "|:-------|:-------|:-------|:-------|\n",
        "| R1| 10 | 0 | 10 |\n",
        "|R2 | 20 | 1 | 19|\n",
        "|R3 | 30 | 3 | 27|\n",
        "....\n",
        "\n",
        "<font color='red'>**Важно**</font>\n",
        "\n",
        "В $N$ входят только те заемщики, для которых:\n",
        "\n",
        "* горизонт риска не меньше $h$,\n",
        "* однозначно можно определить допустил или нет дефолт заемщик (т.е. достоверно можно отнести к столбцу $D$ и $S$ на выбранном горизонте.\n",
        "\n",
        "Изменение $h$ может изменять количество наблюдений в $N$: например, рост горизонта приводит к тому, что количество наблюдений в N уменьшается, а дефолтеров растет. Т.е. структура выборки меняется."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "eD3ZUpbXWyfZ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 830
        },
        "id": "YFVk-16ON6u_",
        "outputId": "3d42c9f7-7b68-4691-966b-6d06ae8d9815"
      },
      "source": [
        "k = 8 # количество рейтинговых категорий, исключая дефолт\n",
        "\n",
        "# Зададим рейтинговую шкалу\n",
        "grades = ['R{}'.format(i+1) for i in range(k)]\n",
        "\n",
        "# Пусть каждой рейтинговой категории соответствует своя вероятность дефолта\n",
        "# Профиль PD монотонно возрастает\n",
        "pds = np.array([.01, 0.015, .03, .05, .10, .16, .24, .68 ])\n",
        "plt.plot(grades, 100*pds, '-s')\n",
        "plt.title('Профиль теоритических оценок PD')\n",
        "plt.ylabel('PD, в %')\n",
        "plt.grid(), plt.show()\n",
        "\n",
        "# Рассмотрим распределение заемщиков по рейтинговым категориям\n",
        "N  = np.array([10, 20, 30, 40, 50, 40, 30, 20])\n",
        "\n",
        "# Сгенерируем дефолты\n",
        "np.random.seed(65)\n",
        "D = np.random.binomial(N, pds)\n",
        "S = N - D\n",
        "\n",
        "data = pd.DataFrame({\n",
        "                     'N': N,\n",
        "                     'D': D,\n",
        "                     'S': N - D,\n",
        "                          }, index = grades)\n",
        "display(data)\n",
        "\n",
        "# Вспомогательный код для подписей к осям\n",
        "x_1 = [i-0.25 for i in range(8)]\n",
        "x_2 = [i+0.25 for i in range(8)]\n",
        "\n",
        "# Распределение исходных наблюдения против распределения наблюдений за дефолтерам\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.bar(x_1, (N/N.sum())[::-1],width=0.5, label = 'Rated entities')\n",
        "plt.bar(x_2, (D/D.sum())[::-1], width=0.5, label = 'Defaults')\n",
        "plt.title(r'F(N(t)) vs F(D(t+h))')\n",
        "plt.xticks(range(8), grades[-1::-1]), plt.grid(), plt.legend()\n",
        "# plt.show()\n",
        "\n",
        "# Распределение добросовестных заемщиков против распределения дефолтеров\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.bar(x_1, (S/S.sum())[::-1],width=0.5, label = 'Survivals')\n",
        "plt.bar(x_2, (D/D.sum())[::-1],width=0.5, label = 'Defaults')\n",
        "plt.title(r'$F (S(t+h))$ vs $F( D(t+h))$')\n",
        "plt.xticks(range(8), grades[-1::-1]), plt.grid(), plt.legend()\n",
        "plt.show()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "     N   D   S\n",
              "R1  10   0  10\n",
              "R2  20   0  20\n",
              "R3  30   0  30\n",
              "R4  40   1  39\n",
              "R5  50   4  46\n",
              "R6  40   4  36\n",
              "R7  30   8  22\n",
              "R8  20  12   8"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-b9afb7bb-0c34-4523-b364-77201a9f9cd7\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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>N</th>\n",
              "      <th>D</th>\n",
              "      <th>S</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>R1</th>\n",
              "      <td>10</td>\n",
              "      <td>0</td>\n",
              "      <td>10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>R2</th>\n",
              "      <td>20</td>\n",
              "      <td>0</td>\n",
              "      <td>20</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>R3</th>\n",
              "      <td>30</td>\n",
              "      <td>0</td>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>R4</th>\n",
              "      <td>40</td>\n",
              "      <td>1</td>\n",
              "      <td>39</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>R5</th>\n",
              "      <td>50</td>\n",
              "      <td>4</td>\n",
              "      <td>46</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>R6</th>\n",
              "      <td>40</td>\n",
              "      <td>4</td>\n",
              "      <td>36</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>R7</th>\n",
              "      <td>30</td>\n",
              "      <td>8</td>\n",
              "      <td>22</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>R8</th>\n",
              "      <td>20</td>\n",
              "      <td>12</td>\n",
              "      <td>8</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-b9afb7bb-0c34-4523-b364-77201a9f9cd7')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-b9afb7bb-0c34-4523-b364-77201a9f9cd7 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-b9afb7bb-0c34-4523-b364-77201a9f9cd7');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Дискриминационная способность рейтингов\n",
        "\n",
        "Графические инструменты:\n",
        "\n",
        "- Cumulative Accuracy Profile (CAP)\n",
        "- Receiver Operating Characteristic (ROC)\n",
        "\n",
        "Количественные меры:\n",
        "\n",
        "- Area Under Curve (AUC)\n",
        "- Accuracy Ratio (AR or Gini coefficient)"
      ],
      "metadata": {
        "id": "dGAiR3VyWwOk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def cap_roc_data(data):\n",
        "  '''\n",
        "  data.N - количество заемщиков в каждой категории на начало периода в порядке улучшения рейтинга\n",
        "  data.D - количество дефолтов в каждой категории на конец периода в порядке улучшения рейтинга\n",
        "  data.S - количество \"выживших\" в каждой категории на конец периода в порядке улучшения рейтинга\n",
        "\n",
        "  ppr - Population Positive Rate (доля рейтингов ниже определенного уровня или значение функции распределения заемщиков относительно рейтинговой шкалы F(N))\n",
        "  tpr - True Positive Rate (доля дефолтеров, попавших в рейтинги ниже определенного уровня, или значение функции распределения дефолтеров относительно рейтинговой шкалы F(D))\n",
        "  tpr - False Positive Rate (доля \"выживших\", попавших в рейтинги ниже определенного уровня, или значение функции распределения выживших относительно рейтинговой шкалы F(S))\n",
        "  '''\n",
        "  data = data[::-1]\n",
        "  N, D, S = np.insert(data.N.values, 0, 0), np.insert(data.D.values, 0, 0), np.insert(data.S.values, 0, 0)\n",
        "  ppr, tpr, fpr = N.cumsum()/N.sum(), D.cumsum()/D.sum(), S.cumsum()/S.sum() # F(N), F(D), F(S)\n",
        "  return ppr, tpr, fpr"
      ],
      "metadata": {
        "id": "uwRJ90rDatXj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Обработаем данные для построения\n",
        "display(data)\n",
        "emp_ppr, emp_tpr, emp_fpr = cap_roc_data(data)\n",
        "\n",
        "data_thr = pd.DataFrame({\n",
        "    'N': data.N.values,\n",
        "    'D': data.N.values*pds,\n",
        "    'S': data.N.values*(1 - pds)\n",
        "})\n",
        "thr_ppr, thr_tpr, thr_fpr = cap_roc_data(data_thr)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "id": "DCIhXwX3dTQ5",
        "outputId": "010cbec6-eae7-4eb3-a46a-5de60b3399cc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "     N   D   S\n",
              "R1  10   0  10\n",
              "R2  20   0  20\n",
              "R3  30   0  30\n",
              "R4  40   1  39\n",
              "R5  50   4  46\n",
              "R6  40   4  36\n",
              "R7  30   8  22\n",
              "R8  20  12   8"
            ],
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              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-d4020b94-3893-460a-b328-65279f43da01 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-d4020b94-3893-460a-b328-65279f43da01');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "id": "m7G5RNdHOZ8X",
        "outputId": "67c1cd56-c5b9-4f0c-c01c-acd69355a6e0"
      },
      "source": [
        "# Построим CAP- кривую (эмпирическую и теоретическию):\n",
        "plt.title('CAP - curve')\n",
        "plt.grid()\n",
        "plt.plot(emp_ppr, emp_tpr, '--*b', label = 'EmpCAP')\n",
        "plt.plot(thr_ppr, thr_tpr, '--*m', label = 'ThrCAP')\n",
        "plt.plot([0, 1], [0, 1], '--*r', label = 'RandomCAP')\n",
        "plt.plot([0, data.D.sum()/data.N.sum() ,1], [0, 1, 1], '--*g',label = 'PerfectCAP')\n",
        "plt.xlim([0,1.05]), plt.xlabel('PPR'), plt.ylabel('TPR')\n",
        "plt.ylim([0,1.05])\n",
        "plt.legend()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f4042dac750>"
            ]
          },
          "metadata": {},
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Построим ROC- кривую (эмпирическую и теоретическию):\n",
        "plt.title('ROC - curve')\n",
        "plt.grid()\n",
        "plt.plot(emp_fpr, emp_tpr, '--*b', label = 'EmpROC')\n",
        "plt.plot(thr_fpr, thr_tpr, '--*m', label = 'ThrROC')\n",
        "plt.plot([0, 1], [0, 1], '--*r', label = 'RandomROC')\n",
        "plt.plot([0, 0 ,1], [0, 1, 1], '--*g',label = 'PerfectROC')\n",
        "plt.xlim([0,1.05]), plt.xlabel('FPR'), plt.ylabel('TPR')\n",
        "plt.ylim([0,1.05])\n",
        "plt.legend()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "id": "-ePX0rQmdWOE",
        "outputId": "19a0da11-17d5-4108-e9ac-df034627039d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f4042cd0f90>"
            ]
          },
          "metadata": {},
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XjZiJbD5VIZh"
      },
      "source": [
        "Разделяющую способность можно рейтинговой модели можно оценить с помощью показателей AUC (area under curve) и AR (accuracy ratio, Gini).\n",
        "\n",
        "Для CAP-кривой:\n",
        "\n",
        "$$AUC_{CAP} = 0.5\\sum\\limits_{i=0,..,k-1}(TPR_{i+1} + TPR_i)(PPR_{i+1} -PPR_i)$$\n",
        "$$DR = \\frac{\\sum_i{D_i}}{\\sum_i{N_i}}$$\n",
        "$$ AR_{CAP} = \\frac{AUC_{CAP} - 0.5}{AUC_{PerfectCAP} -0.5} =  \\frac{AUC - 0.5}{0.5(1- DR)} = \\frac{2AUC_{CAP} - 1}{1- DR}$$\n",
        "\n",
        "Для ROC-кривой:\n",
        "\n",
        "$$AUC_{ROC}= 0.5\\sum\\limits_{i=0,..,k-1}(TPR_{i+1} + TPR_i)(FPR_{i+1} -FPR_i)$$\n",
        "$$ AR_{ROC} = \\frac{AUC_{ROC} - 0.5}{AUC_{PerfectROC} -0.5} = 2AUC_{ROC} - 1$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9_oyP9zlVKiZ",
        "outputId": "9e1fd903-c004-43da-9e5e-7ffb6099bdcd"
      },
      "source": [
        "# Вычислим AUC и AR (Gini) по CAP\n",
        "emp_dr, thr_dr  =  D.sum()/N.sum(), (N*pds).sum()/N.sum()\n",
        "\n",
        "emp_auc, thr_auc = 0.5 * (emp_tpr[1:] + emp_tpr[:-1])@(emp_ppr[1:] - emp_ppr[:-1]), 0.5 * (thr_tpr[1:] + thr_tpr[:-1])@(thr_ppr[1:] - thr_ppr[:-1])\n",
        "emp_ar, thr_ar = (2*emp_auc - 1)/(1 - D.sum()/N.sum()), (2*thr_auc - 1)/(1 - (N*pds).sum()/N.sum())\n",
        "\n",
        "print( 'Эмпирический DR = {:.2%},  эмпирический AUC = {:.3f},  эмпирический AR = {:.2%}\\n'.format(emp_dr, emp_auc, emp_ar))\n",
        "print('Теоретический DR = {:.2%}, теоретический AUC = {:.3f}, теоретический AR = {:.2%}'.format(thr_dr, thr_auc, thr_ar))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Эмпирический DR = 12.08%,  эмпирический AUC = 0.813,  эмпирический AR = 71.25%\n",
            "\n",
            "Теоретический DR = 14.79%, теоретический AUC = 0.766, теоретический AR = 62.37%\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Вычислим AUC и AR (Gini) по ROC\n",
        "emp_auc, thr_auc = 0.5 * (emp_tpr[1:] + emp_tpr[:-1])@(emp_fpr[1:] - emp_fpr[:-1]), 0.5 * (thr_tpr[1:] + thr_tpr[:-1])@(thr_fpr[1:] - thr_fpr[:-1])\n",
        "emp_ar, thr_ar = (2*emp_auc - 1), (2*thr_auc - 1)\n",
        "\n",
        "print( 'Эмпирический AUC = {:.3f},  эмпирический AR = {:.2%}\\n'.format(emp_auc, emp_ar))\n",
        "print('Теоретический AUC = {:.3f}, теоретический AR = {:.2%}'.format(thr_auc, thr_ar))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "o_pUu8UhgGWi",
        "outputId": "c1b48669-7eaf-4eb1-fc00-c6c484121a6b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Эмпирический AUC = 0.856,  эмпирический AR = 71.25%\n",
            "\n",
            "Теоретический AUC = 0.812, теоретический AR = 62.37%\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "mIsiBqDmNPSu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Практическое задание**"
      ],
      "metadata": {
        "id": "ahc3GGrRcz1H"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Аналитик исследует качество рейтинговой системы с помощью статистики за два года, представленной в следующей таблице. Для этого он строит ROC (CAP)-кривые и метрики разделяющей способности рейтинговой системы для различных периодов и горизонта риска дефолта.\n",
        "\n",
        "![image.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA4oAAAGhCAIAAACoG91zAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAADiqADAAQAAAABAAABoQAAAACn2dNdAABAAElEQVR4Aey9B3xcx3UvfLf3XrEL7ALYRe8dBECCvalRlGxLcpHsuOY5yWcnecnLSz7H+dJe7Nhx7JfYsVwky7JsiaRIyuwFnSB677vA7mIXiwWwvdfv3EUhQFICKEv+MeIM90fs3jv3zMx/5sycOXPOuYREIoGhhBBACCAEEAIIAYQAQgAhgBB4OBAgPhzVQLVACCAEEAIIAYQAQgAhgBBACOAIIPEUjQOEAEIAIYAQQAggBBACCIGHCAHyQ1QXVBWEwAMhkIiGvA6vL7ScECsFVDYd7bUeCD6UGSGAEEAIIAQQAg8pAh9t8TQej0bCvmAY7GvJVDKNQScTiAQsEYvEwv5ghEKkUmh0Cukh7RpUrfsikIA+jUbwFI357bPDsxZnH7nxqXJBFp123wfQxZ0gAEwRiYQjkVg0HscwEoFMplCoVAqRRCDs5HGUByGAEMAS8VhydgpHY3Hw6SAQiWQKjUolk4iw7qCEEEAIPBACH23xdGVxvPvq3/30VjQWK9pfcuzF50vZQgbRtzBgvPZPP+3YpWzY9/RnKlMx7KONwgMNiIc7cwyLexcnukd6um93jUws+10eD0WskT+52x97uCv+cNcORH7vXGdP161WQNXkDVFTJNllpY17j5enpXBpFLSyPtzdh2r3cCAQxyLL88O9/R0drQMTVnciyldJ8muePHKoRC2UsR6OOqJaIAT++yDw0RbMwmHv8sLQ0Hgk6vCIPIyx3doSBp0RC7p9lqGpMUUs0x3AMBS54L/HcE0E/HajvvlCS/9435hOP7dgi3I5KZpcdUl9DlvM/miP5A+xixJ+W8Dcf+bslY7uoclZ84I9FCHNccyWJccCl/P5upyUdM6HWDoijRD4SCAQiUWc+hunWtq6mvpnpowLriAWZxg5CysBTBQ7VLqvUEz/SLQTNQIh8HtD4NFY1IkEr3Xe0NUx+ZRWzKWjfezvbXh9gAXFA0t2/e0rb/yyeZm5QhaIM0tkvFR1QXVZdeXBPA6XjFR87xPsiGvePnzq/KURvYcqkBcUqsEAJg7WL4T57mnr81mpGBJP3yey6LFHB4F4IOY3DF5650b/4mBMos0uU5EIWDwaS/gMU7PmYlUQiaePzmBALf2AEHg0xFMKmRg1RRavd089lSEUZH1A2CEyv08EopZxc9+NX0+GxQ0vnDh67ESdWkwn0MlkEolEJiMDyfffFX63zTTe4vMr8xqff+ozzx5UU2iEoMc6bp4Z0Am5DCT2v39o0ZOPDAJhd3xlcsbgX2RXZRz4xLc+VSZlUYgBu9dqaB/wK0WURwYI1FCEwAeGwKMhnuZXqBLBXMfiYO9opYqt4j4wfPapG6O9zRe6l3xhLAquI0QyRhfI1AUFxcUNtblCCkbd3mvc47fr23/wVi+3mF29+6t1crwSzhnr1K0fnOqX1Z6s2tVQK4tjvrGeq+1NVwcNGIabUxIpJAZPnllVVVtSWqiSUDCC9VZLR/fZ7qXSk1+ty5ZpeJApgVnar7V2Xxn14Rcz+emMlfDKyPmf3xg2LtnwYsC6lsGRZKRlVzTuLUoXszlr7mB+63Dr4LWzNwyYJ7yaD/9fXXWo8uDT9QqMTsLigeWgbbT9ZufgtNXoikbJzLT8xtKKkpoyJY+I7cSrLOZb8o+f/3VTwMHNbvzEoXw2xiaF3AsTY+d/1hSplRdUPbM3g4X5jW3netrboCbJRCRSmawUTVHN7vKCnHwJlBNasRrndMagsFzBcUUmfvPazUVHmEyU5qcXVR0/VKZgEFl4baIYtjD4m8u3m/oGVinh/4PLlLr25JGaSmlGEIfFyi+W1R95Io8W0LX19fRc7pnzYyxxbkNJZe2xMgmVCMJuOOgyj53/acvEypR9g5BYkFKw/6UnimRMKRV3sPObewa7+273z+gdoRhNJs4oyK+ubiyQS1hUcsyJecffeeWGgaDm7znxRB6TSyNG7bPusQs/uY4xcysajpfls62Dr77TZYjPVjz5R/VyFZ8SWJ6db3v9fP9KIKW6/NgLDSkYhxLx203W0ebOIcOkybHkiazVhquiZu797BP5uWAculHB9/WFQKIQaRyMYLeYdcMjcyXy3FQuV6QsYPIUMjKPw9wp0YDuek/XxKlu2v7PPlGWJZGFLI6hi6db50ykDFXt8RMVEimbsi2X3DNaoglj90RP+69b57llT1RXlx8sEEA/E4K2FdNUf0dnz8TCgisUo7JZKfmldbXlhZoc/D7mnLw43tn8Vl/Z/k/VVVelSXBmso6evdbZZekvf/YLdYoS1uLKDM56/NLHKxv21qfgzXRNX5vsvHKqv7Tu2braUjrf3P3qb26bWPmp1Qc+XSVh4NWPR4NOc8uPr/X5TKTCxk8/UywkiajvDdHSfE93+0/f6ccw99aMNA6/7ORXd+Uosvj4jZh9fHqot7NzaGzB709QWVJNRtG+xjq1WsxiEkJQ/55XYLQEZwrqnqZNzutn+2btMG41NY9XVxTVZvFwJpnvnRq89XbTmCOIhaDFBCJGYQkUOTmFZbsaylJZGAMyJSJYxK7v7+rvH+qaMPsjGJGVIskoKt/bWJHGkeFGMvdlomTVFbVFVTWfOpIDg4IU8/qWjVPd7R1Der3VFYxTaILM7Mra8vLCylTWDj2B4pHAQvv3b/bMdeg3QwPCnLr82P66faV5bIyAxfw2nXmsq719eGbZZ49RCQyRpqSxqjy3PFvMJEIGSJFocAUYtm1kfmRpg5SAxc8Bhi1RCxSxRWyhHbp7bG5l7TaNx5dpNfl1DbvUaWIm83fchhFJGJVGSRBJVqNntO+2SbtbI1HypHQGq54XoXFZOz6yCyxP94xcOXUD219aXXakQsaMOsZvnL49YBr2qWqfPlGllWZwt2cjDPNPX/t116Sjn974uSfyNaJE0DwxfPnXLUYuKaO65sjBSimJTSFEfSv++f62zp7B6QWTIwajRZxZWlha3libIyDDouZ0GMfbv/9WX8Z+dU31ixUSHLqV0emRTkAy77Ev1JTn5dMsMJO3ONWYetdnH8+DgUEOWexzAzDNevOPaWuqD2ZEpy79uG0gOE8pPvwHx/IENCEMsXgYcw03X2hvHfMtFZ/43O60QgUb59v3SBFn2DF14+3r/TNWk3d1GiRRWEK+Iqu4obFcK8sQ4Dze/n9P9YzqJ+9DJ12WVvnMV+vTOTR2xB1xGfvbO3uH9VMWVwgjM+U5mpLK6tryfBGJQSb4F8esHT841VfGVMmKS8KTV7tnl4JeloKbU39if1F2Cm9tAQ0sLOjG+jt7eiaty75IgiGAWah6T31pjjITZ0csONc63NPxs/VVbaNS0uzy8qc+D3OOiI7Fgi7//EBnV8/ApGl2OYKRWUJ1YU5JxYG6fBGNQNu2q3GiIJEsjL1zs/NCB6x6wL13krw8q7Tus0/ksQkEcswPi9pUV3vn0MyU2e6PEmgCjaakqry6vDKVSQVlP6REFPOO3b7U1nJzBJZioIsnCgtT73/8QMneEgX0LyDT2jV2c2r1Hkai84EdgY2q8tMKZDteLdae3ubPoyGeSnJTBcFKm7N7tH+2XJWj3QaUe28HbONz/RcuXVzxRVbFUxJG44tTdfN2DzElfXcqVQLT5DYpFA0uzrY1d0goQkXZWt6Q3bsw3HTzWqagWlkM1+JY2LYw2X/70pUhmHHhAoindI5EbbaEY24a58lcPsVrNk10X7k+Fyz8RKZcqOFRQDqNuwz64c7rrS5K/ecLwNWL6o/5jJO3WlqGDXOrJZHpLGGactpqZ7CPVWoqFKvVjXiX9PquSzeGMLCQ2kjFVJWoBquBsRlbWdIP9F1953Jb34DeZnbFYhSGQucwOL0rlP1Hs/giYOWNx97lSyLiDy8MDdx2W0SUrBNYFr6yRcMem6X/akeIq2Vrn8AymFjYOT86cevSJWg2nohECoMhU89aMY+XIj6mFRDDXo9rxbYUj4pXDKOBmWXjuNEWIhFEulSzy88SnCiTZ0uYIE5jmGdxfKD/0qXLq5Tw/2FpKGaVVWQVslVJWGZktExN3fHU+dGOpquXmi8MmgIYQzTtXvISVerjWh6BSwmGfZaZm03t/eZe5wahtBQtIfPkUY0YS4ScIZBurly62dLVOTJncIXiVLFQNaO32SKJx8FeU8MKYcH5ma62IaJHnnP8SBYDhORY0BmY7+1sxXgJefbB4tyEa2G4p2coPsBr/EyFJOFZsk11nj9/8bdDdloZk1eHVckwptNgHm07c+Zc3/i8zuJeWZuXMUxSyHBlP7ZXq03Bpe/fJVG5UnHeHk1by8jCUM81KsuRqVAolEqVSp2exqHQdjxDRO1zprHeK9eYaY/tV/F9UWPHtXMXm818SmZGNpWEy/w7SFtGyxMRpXNA33HteutA16K8rhgibQCRGBZzzg919rU0XbnVN6hbsrlDMQqLIZsxLgXcnhj7YJ6YjAVXdPNDN65dpan2FxYAWriFuWdpamigafIyc/9TRRKM7PRbR1qbr8voRfLStZoFHbOW4es3rlLEtQXFZTQeFrJP3Or3OHTh9MMlwhQQ4xPBqN882dLUPsxaUqXv2VGb/G6rbuzSpZsYdkdwShbIEsnJtS/lqKFNQWD8kdbrLU0tN3vGpxcDAYzCFKWnzTrt2GMHKrVVSiIRS46W1rlbM4sYTbdgMA4bnTBu1YtEf4QgktRncrCo07gw3nHhYqczhIVXxVMygy+bmrT5FgWq5wq4aZx4yG0x916/0dzZ0jM+oFvAxVOmTKwyGJcDscf2VOYqU5j3ZaJkjXNYEWHWx7AEPeF3zQ5MdDVfabrdOWowLnlCcTKVp54025edAcbje9K5RM4ONIawx/MaO4dvD1zq3Tw4YEQXE7X5WfVYHshZlqGRnram6623u8dn7QFnjEJgCNQG+5LvUJBSt0fNoeGTUCgWXtS3tt66Ndm+Ln9iWApfFlY/eUijhEXbhzkmejqbWwbm10qicriSjAydLcA6ubc0o3C7Tcbm+t3nO4lFYmXkFCpHnXMDk+1Xz5JsallGqlKWmpGhkjKZ1B2AsUo16neYDL1Xm7E0RqqqLitqG7h282pzn5USSs8mQiSAbdcZnAyM9rBjbmC013KdnfXkfiXXo5/ruH72UpdZUJeZTqWRMNg/xD3zC1N9Ny5fudU7ODJnszhjoMUQqo36RbeTwD5aLFbygkHX/PT1a23lKrcqyUZAO7hkNwxcuXw5mPdUem52NsFlHW3ptpZgkawXMAy3r416Aiu6oZvXHfE8Qlb5wfQE0WeeHZtucTjZ+xokuWQhj5SIhYPzfUNd7c0jVG7WyWB8B9uZmB/8N8fampv79VO+VRmMRGHyufKsWRuLdKJKVMPjYk6YX7ua+m7hINyVSjILxHu+WKuIu+2GkYnmq1c6ervGTXqrO4yRGJIpGFE2J0Y5WpgpZsZ9y87JS7da5v08yYwurGsdNK0EfQw5Z3qFxuNg1dkVcjLMQrPdLV2trde7hgZ1Noc/mqDzGNKZBUfEe6CO2aAVU4AfTZaJjkuXhu+qSoaTyGnEymFW8i4szw5CF3T09A/rLEZ7FLqArwSh2QFdcKxEliECHdG2CbrbuzIzPJhc9dYVGMmnNEQ7K+uFBGwb/M75kZmuJmDYWyOz+gVnIEYAhlXPLS06g9TH9mjFND5ss+MxzKWfHLr120vtwCdr4imNj5Wocws19UmS3vme8e6WS+sQk2hcuiBjxhaIhPZy9xQqGBD2ZdsK7zTDjhefnRJ8KPMR5BI1tSjDxHt5wDBTNsanZT5oNcPuWMDpCbPZAiaEpyIl4omw12XsHqJRKaUnCoWkHYin60WGfCGnzWJJ7jOWl5cc/hgeymc1ETAincEVihUK0ObgLJiIxiNBz3TLDZrYyck8lM2DECWQCJGIdVZvVtEsJBaWSEQsdqc7uE4EtCZkApnFlUilisiaVjQeCvnnDb1Lc7x8qVAAu6CkxieeiEEkFCJGZXMZdCYlngh5HBsCECyarqnpnuuv/PjiLI0bp4pkUKd4xD/b0hYIjYVTiz5fwmOQdzztRiJBt9NqsQaxANlvX7I7AqDG2UigLeVxJSAXrV6BAC3hoH1y6DIbi3JLDmgLabFINB70BRK2kSkPi8Gg0gQp4kQ06J2z9IV+HE7LEjeCCoRNAFEdQrrEYyQqxuCKmGRy3B/2x1ybhO+1IiOeuK2ro3Wwa9hB4cs5Cb9/tm+URG3ad1igpYJ4Ggs7lvUxf4BN5zOFTDKs6j7/RlsTUbfJPnzmrV83D1r9YZZQlkIgAMKLfUPnJpdZ2SwWNyNn7Y0XsZDfb7daF/xhJjG8uGR3hiLRDTobzU9gibDfODBz69ovOpY9oWj2+p2IdUTXffVHZwcpLD6DIUrhgpQXhZF4b4PWn3jgvwyRKq3uub23baHb4309p15tDRJTCrMq9h46dPRQWZpSyEhqDXdONh4NgSA4MtPx9svNK2lHnj16/MALu2TQ5geZtRKwgIU8NlP/mSs3h24uyPKe+fLJgxnlKjY5Hox7J3uvvHPqrebOOJfH5InZoF+LRtyjg5dCAW8ipSKnXrBaFLCVz+NYAmaj4sxkW/EGNjHJdi1i8EmppdXZwtmWBV3v0LSvjE2nUGPOkGNqeDjopJUqSivKxMT1g4jtqEG/0UEVTeOAaAAp6vf7AxvjPxF2RK1tl05fuDEwb6VyOBIeD4tGQxZT+6uvJcREKrdIKWeslrBkCq9Yr3A4DDqVLxRxI35r3/VbLK6wuFqaQ6bFQqFQ0OansQRciLhAJQCDB33L4yMDTF1q4740ehrT5zIP3nz1R2cmQ3MBOkek4ECgvYg/ZOq+Ma4jSRRUsTxFtd4WIpwKsQQcPPjeWt9JBUIOHBQlCBGrrvvKhV++ddpIo9GZPCkHpsRYyGq8dcm97CbmVX88h86B45WdJghjRoeS6CRCsiSYnMRgV0InQQ9Gbf2/vXn+xivNNpAMaEKeghBLxALLA+evRbEVqrokJUtMBpktHI857Iaoz8Ok8tjA+DA/+wObGA3Ou6hckVimUKxNtoloIOSeGmuZ8qgK+ULZ7yyecsmcgtrHqucigekbuqHTY12gwFAVFTQ8fuxwXblWmsZLStE7BQSf+SOBpUXdTO/rL9+YT2OUHT3xuRcOplL4tAdhI1gb4qGg2zQxfKX9nZs37XnHnj15fF/5LpCu4GDM3DvefOpfX+7EuDwqXYwvOYlIwDo40BQYdaVkSutFG8eMQY/fkWQjqP/iyoorCALRzhLYXtEyS6pUgwvEhaneoaU6GVPLo8MyYpscnreHY5Lc4zUahWAnUncUiwX8jkA8RmcL2RwaSLSxSMgfnB/umFdpspRFNXwOvqkTi2AZgYUt6HH7Q0HYNeEDi0AhSqQSFh0e8htn+2++8YNXYfaIUOkiBQu3EfbPz3dds+p9slwlk82QrrVtVDdFN5lYbAaHKWJSg67A4Pl3UorFAnGxhEP0jHacO3P+2uBAgsPliCR86LFw1N53+2w4FiPJijLrBXfGP4MnYtBpG5KmVCzgUDEyMR5aGNK3v/mDn3d6iHQKc7UL4BhgfKzVPeRUpgkbZEI5cOhOEwxyWCc4dMaaLhTDpEIxB48HTojYjAM3L/7ildMGGpxzwFIrIMDcsLzQd+2KdYWkLXmWLuYLgbPjCZd9KeAzU6j4+kkBTocQnJhvUx3ITBEPh3i1Uol4JBTxjI1e8HC4fHlRoZSOxNOddtedfAxpaoqiqoT2a8P0TDdNCCfroFx4wCTGsIbnvn6soVolDdgDo2d+eLprNEYVC5gU8g52OBuFjV8dnu966a3k1BkLRvxu4Pas1btwGMcpqfl4Ru7hz62to36T19jxyr+e6/b6wg6XP5FgMHk8Blvhtevf/tb3rtFeXrUqCLkcLg/GW19YqGJayoHnvlHxRCiytgQ6evuuXnvjF93TK46gH1+kk+KpK+D02s3cWObJZ5+uO5zpj/W++o+npjZqujLTMzM+OImllj7z5UO7cquVcSyov/pfr9zsts+1jpmfz0nFWKKN3Nt8Men6Jn/0tSuvwcYdDsbDILSFnBpcOwK6UgzjZO596YWyk8dDSSpxn8c20fmLb18Y9IQDrmUfFlnbRoFMX9DwiSf37y8qF5KwgL7rzOmrF0bbeofmraXWsFJLiWMehwskW6mWuPuLf35MpV65OHD19R+13F05kH4DJr3Zx+JUPHPypRO1wauX3m5uN9sXbL5gGhHmKxB9ozC3Fxwt3Xf0m4eU3t5XTl823rCs0gk7F2eHm64aXAr1voMHTjY2KOgUZ2/PlWtvvt43O6G3VmX4ctir/u7LYy2D5rFhJgQQhfkrGPM7rc4cGElbUiKGhaeHO25dP9sXAzUZ6c68hsF6TcD3AJkHXzrUuOtoHpNMNLZ+77Vr3Z7BLSR+hx9ENoWbf/DLf5HZ0DN4u6O1pWd0WT95Y3FprHPihT99dnf+7nRQP+8wxRNR3/LQ+auWGfNMTHb86y88VrE7H7e82zS/7YRULLA0NdfyatP57hV+RcXJE195XJPKx6f3eDjgGW0dMc2NszMV9X/wpSOZxUp6wmnSX/nhr1rMxuXRthFXYfmqSYILw66//aPu66/TkswW9q843PS0NfFk+1rQyGRZYVVhu6FryNLdr/+kmobx/QvOofZOF4W1K7uhKptNJOyU8ykMrO6zTx+q/BToTCCZrl66cuNH18yrtQjAfrXj9JgtQMw//vSJjz1ZwOYSLHM9LRd/+Frb0IyjrHABk4OOFU8kDpWn3f2pTx6s0BSyHIGJc995vWtwxXxtdO64WpXUo8O4Kz7yxRcba7Jzqe7IQtupVy7fXiHTxTwGhHh2mu36odMTgXnB3son93/2qWIpGQtNX+lrvvBvZ3Q9ulmNMfuIap2nOanE3JN/+GJFlVa8dmhH5bA4XF48SrSMjEwbrtkEifynn3+2prEohR/1OHpeeeNC3/Wl+Xf6ZhrlGVrQM+00yaTptU//xYs1MrocbwMMFhpbwOeyAwTMON4yqR+KMpWNT//hC7uyxCrScsTW/cr3T9+eXZhvHdM9mU5jkqFKWAT0V/F49t7sfSf+8agqOvrGxatTb66dxsAJihzLeu5P/+Zxf2hV8YaFDC1dzdd+/OsBm9Nn9z/AtuXd2kQg0fjFz50UlBdV9vY032wbMcyZB7rOWiaGZz/2/LETR0tU1J1zQRyLLht6rl4ZMJ8fkRWefGH/od0gm3KoD8hG8QBoHPvPNpl0K/pYxWNf+8rj5an5YpyN4DBhfmpksn/cjynqn/nSwd3FuxQJmFFb3vjV9WZjf3fbjLUwQ8Vc6/fBt9v111/6RZKNov6Azw3KgnfD4e7rRDJZXZqvGqzo6W0eGFmo4AXUHKLfMNSqs0TUwpK6fWriAwU1kJUfKzn2iRcrOHRscfb2lZa3zl2MCxh8JgsDAw1t49f+uvxLQa9vydP76o/P9/f41Hkn/+zFcnaGkE2hccRcWmx8SD812BZmsBpefPZA5bESCR0LzN342ZWbXRdme3omlvLkonXxlMTLrCncf/KT+zMVVPN8R9M733ur+/bkfGHOXKlcOHh9wLIwKyrU7v7klw9nZopIYeu47vKPft5msCxOdE14ysrZq+hB9NvK5//8UF15LYgdyURhsNmiBJfqnddPjHUPeiLiwmdf3L+veq+KBCvs7bdPXb080t7dojfn5WXLcUuaHSamFMt5+qVP1jQWytembAqbzuYKYJpaHJ+a0V+cZ4aznv7YU7uOVKnEhIi9+5Wzl2+f081fHtTVptIKhTxQu4OMHY/EBWnZDV/8x2OaKHnq4q1zb55OziyrtVDs+dMXyvyPrSpI4iGnvguMN37SYfOH7E4vhqvaNi1fO6z4u2V7NLSngBhDxlGQa8pOLc7P6XtWpjIx/443gOvY+TBscqAl4dDz2ZFA1DZuIaalZFfVpFG59AeZNQJOf8A5Y1unetdfIjEeXHYaRkf0lgVnyOe1h52GaZffI4zLoviUkODlaEt2nXhs8eaAbsZmXcD3sVQ41YjGokmJc5UcIUHAIi69YXp2en550R2J++ctM4bFRCIMRGKxtakl4gv4/PYgNZaiVWiy89KXvSYWg0pcU7jCgZnbBsoWb4RiGLzZ4hjR8xJgtQYH2AteXpwUCMdgTdh5CgW9y/DZ8sCd50mEaMC3MjsyprMsuN1+r8+3bJoNLPtiElDvxkAJsPocNFGhUGflFuZqYS6KCn3jnXODA+1Ddm8gAnYXYBCHeezuUCDIZGuzirRauZLRvcDZIu8BIftUpy28+F3S5JAhJaVGW1SuzXbrRlv7uMaIxxeOxBJYKBh1ORfiMaJAkpqRlaVVOK0CAdu6XvloOOi32+zBCNE703XrwtICh0IMms3TBmsi4QuEwpsmb9h+uOGz/mSSd+/aGUXiEdtca9vM2OI0Pf/wXtft/jWpBR6iSPMyK/Z/4QnPmHNy4vqiexgUWa45ndmCbWg27pB+n99AAiYxeSlZ2TSOQJaZXrRvXtfT1zfc3jvd99u+PIkgN10L8vTOhng4FnXNDq34l+IRgrZ+V0VOulTE2t4C5J6a+11L9rFOvc5ATs/OKq/MTxcxaMk3BMSiYAcy4nBaCZyC/Jr6/Hxhroyc8HCk9vwb43a9z+/xwoBZHS6As8u+CJ9N5EFFtNMEkzqdX1CR1WVQ6m1g+1srl3IdhtHO0SVGTo0ms1iNm7bsDBaAj4BxpEJFOm6NAYkwLBXcWXZi4YB/SecPxpcs4yNNZ2LjNBrmdphnp3wY7CWjwfVNJjzIElMya2urS6qK0tJISxFGrvbCiM4ZXvGEYmuthh3eAljQRsx9A6RQ3DM34uMzM0oO5IlgHx1etrutxkVflFOSBfZtZTlqNhGLMi3hlemMs5NGX9ATuMOTGBxBsKTytAyNdkvUTthlBZdM9pUVH5mdVlJTVFBYlC1gxLwBQmn/gHFgIWRxBUORHYsvOBwUCl0gVWvUSkba5vBL0RUQoiw2ly0hoGvKKkrzitUCMVEWVZBLtNcMi6GlFU8QFMRAIByKuRyLMLmJRcp0rUarijhFYu6mGRHykLDIkn5uRj9jXnIEYiH73Lze4k0kAjEYMA9UW7zG90mwj2SJZelwFCWWKLT5FsP0cM/orY7bMzd7R9LT8rJTtYx1LfR9nt5yCc5YPbMmh9+PRaz8+ifzcooyRQ+oN03SC7sirrHBZZ0tkU7OKq8vT0+X0JLsCJg5l00O8xQhjuXnFuaXlOVquSCbSD0FN0xT+t4JjxeM0WLY2hj12T3w2VLFHf+AQCCMNHVWRlH22LXx7rn5HJMiKJ7va5t1h1PTCksL5PQdWliulegxT7hazrylo5Ixr8NkMfvT8vbmZ6WLebhYROcqUmFmjHnYLguHwySTokyWLEOVwdOC30YyWZdm7Ta9j0DJKyjJLy7NzWZRsIjYkaeb1cdnVrx+UAYm1gUsOEkoqm6sKc4TiihCxooxS5UYtHhDvqA/5E8YBhzuFYqwIL9qV36eUM0nxoQEuSPv/EiXA7bQvk1nohiBDYpRYP3UzaDBkHPZLXbTGAy/bG1OfllFrpYP3CgOTneaxwbae9ygtwzctVZsJnDvdzjuYEilqepMbdpdW8PgssWxYnNh9JSCioLC4uJsMQtOcLCSqQlD59SSxR0M4sZAGDCTxwmmRXE6Q6nWajTaCOYVTzO2BIYnJSI+29zk+Myc1eENhDzL88vTXpBpYIu48z3LvXW/75VHRTzFSFw6j1dem3Hr1NLshKmbjG0+DL8vNPdcBPHHsWwxYsFlOkyJsTiJzOETqP5FW0AkitKBW3aW+EqBNKVInmT8kMvvsg7r14W2RDxoG5sAb4Nbwzo/MRCAA3EPhG51hqMb54AYA3i69ig5SpcOj827bH4Y5TQR3TprtBhAfk6mGHiMWvpuXWsaNtotfpC1wrHAitOGH3FvnobDy9YVx4oZIzFlEg6LCRsk79YWwHFdPBYAHaJ3Zd6ccPuZuIc8QZatkaVy+GBRRd20p9r65H1+sTlipkKTBm5kFGIs7HM4DBPm1eUDwAwuG0c6b3f1Ns35Sf5ALBIIBOGQMOq/s1aCfz4RzlYJmDcShRezQAFwJoMlQBML+mM6ePCDejIOhhA+89yyxxWhS/IUQtaq1uyeyriNI3PGkTH8uiiVRAGLRtjhk8HeFYRHAjQxFnKu2A1zhhiDI+anS+7VHcYhRUG5mgj6XTbrXCLKAHsLAsZUZjVkZWWowJdlYzDQ+XK5IiNdQIbzlnjQHXaYJubXJsq1egXsYWNv53DnCrWIVVlzNLfLaFjZ6AiSUCXPdB7Ia548q9P5KbY0Ppvkt7t9vg9MPI2GfD7XkiPBETJZSlWxOr0ENvACIeab7LTMDs0tgBUUHLXeg+G7XEhgYF9BZlDpCTL0lWfJ4+f6ItSdmCFuJRgH82OMQmcwolRQY7vt9iBbBMsYCTYqcIaGSxQkMonJAoUgrPhgEkOiMxnQh9B7+Ivh1mRGGF5ida5cKmUz8IEP7xgzL0axdWbbWuB9fxFJlJRCTXpvPtd8pndsPt9DsRv7h5dZ6c9pMtVq3o5l0/sS33wxEQNHu0SCEPI5Viy6GQ8VRguBwBaV7xZheTnpQhiCa22ic0hSjVrBF3GIMU8kEAoQ4bATWg04rDUblhlQ0ZtMEacLDscTwTCVJ6BTyDabT53CjMI2FpZfcOOh0elUUMYBF4FJL4VOZxAINMJOXxIGRGDbCGohBpNJo5DJuLEjqAAYNKCEgXEodN5O5fbNMNz9HXal0XAEeI1EJ0IHU2EOAMMCcoLMhM0KPvuQ8LcAwolk2O106GaMcFgrEGjlbLB0vjNh4kTjYd+Se7a9/erwqHFpGbY4wXDYs2Rf9sBEsrbzvbvsB/wdCcQDdpOPRqUzBRJtniI7P7pcmEoXLvWO3tJbrBbdYiihYTwAKnGMRIZeIjPDWMjr8bp9ITauPH0wWIEd42C6xWAkqACle8nu54gi4MIFTIpbj8QiQdCkMuk0eLVVkjCBDiXScfsBnJXW+QjDhGqZTJojSRqYBO1O++KIbudsBJXmSTIys4sVkuZhk9EyIaRlG7pHQqIUlaYiF6RTODR8gBTxOjwLel0AXsUFglIswRByqS6YxRzeBAPsfLZL0PmxaAg4Bk7bqRDSB89PpAIzJCEALto0dAUCgTwzXQIH8cQQvFIvHARzGToJ7H+J8CKTsB8GJsw5TJh58JeCAfNQGCw4JiPDBJSEb7uqYLFYOB4OkhKJZBeAGxRUnwBsCXUD7Mm4a+P2Ddq2FDwDzrDRKEyqwEYwGSQZNkGkMagUKuwHgWHxchLheMhhnDU6/XSGUJsuIDGpEf9m8okwFnPPD7R39I62zSzDGSgkv8vuckRD0Q+GjTaXBt83ltG7rn/0fhLBmEJTcVDVcbqtf/BG0wNxxCoasEYffe7rzx3Zq0mLg1qj9+3/76en3vnV30yTvv03B3YXyHAf+p2kvENFT73w849r8byLXTOdb730D5dWn4vHIiu3f3n57MgFs/aJv/q7kyVCLUG3NHrxh998o2VT7zPE2vQG7UsN64XBJD79xo9/ee6HTY7VSwHrhOHid356CmPtev6pP/nkyWxqwnyj/czbP//P5o3DLsjpnhydmZ0eI5OK5UIRrOD3JhIZHAnJVHnVx7/+9P7yRg13e9fre4msXUnTlNd+5u++2CjABBTf8lRHy3f/n5+vHuXHAthi6/WzZ073hbEn//qbT2mrUiJeQ/elH3/jzc6kfxjOo3SwjeXw3QRi87iuMVdfUFFMxexDunFz7wQjLtBIhGBwFo3YHbreLqPFGqanqVJ4O3jLqdXrX5y3xnP8DnfQ7yZT07ngwxh1zM5MdHXOxlS70zUVWuG9liDAzfj7PjFt4d5PPPu540czmJQkg99pfXhNZScu2FP4qf/59QaemEUKWfqXW77/xy/fyYV/W5wJ3TCdCkl2fbLq2BOVBcY+MGfcEE9BLxRwWY29t+axA9onTnzuiw3F7Jmbf/39M9cX2reSeb+/AiumiZ53WsJlB7JyNHkKHqxTJL6EwxXLMGz+gYkyyFT+rmefZOmaxs9d/dU/+4l//hX64fJSwYMS4qdkZx/94i7LD/6+vfvcr5aDvG/8Ub2SmgJ292SKAM672DbPkneof3xZkxcWMhN+58zomHNlBezcQEQCoSVZHqhRDpz40sefeqogHbc9nWn61o9PvT25xmw7qhERI6erc9WlRT1nLgzOV6y4AubhBWbh85UF2jT+jijsLBM+nigYkZNWcuToS5/7RJkENjhbNW3rywQInEnvzBiY79kXJq5fGV5cdApzSvggqa8uZcnD/S99/fEDhaXsEBYxtP3ku2+fPfXtZjfp+586kMbjiOVUInFh1qjTmaz1cgUp6rUYjbrJiXgcZD42dXtrBVjB2SI5k8OP+BamwKmmWlKgZooi/qWpUf2SdYEkAJu1DeO3nbX/XXJRaJhAIWXShZ5F2/TwuHlvqoDNJblCluFxndfskxC0DArUJhFyW2cn2ptnQym5Kk1tjnizdUySdNhtGel97Ruvt1VIG5/91Nef2sWPBCcv3Hzn7L/9tHPpXQp/sMs+a3jm5ttTCkmqdk+xCmcjIovOAV2unEw1PBgpyA07ZfGumipWHXfc/o+/OvcbojNC/9rzpRLYsq128g4pMlLogqMff9wyeaP9XNOv/iHE+8sv1B8uTRHgNikCgZIp1XiwgaHpuWXTQjhHncB8Mwa9UzcHd0GIIVE2pIPSE/Unnvr24+l4seam29dPbaxZO6wIU5mRml9cRr5lNcz2EGIE66BX/FxmTkG5GgS5HdJYyyarOFb/ia98rQGMVaKOyRtD7/zH3/7m2zb3/whwVJ8quHsavpc0V5jGFapiMdM0vIMkXxVMT2FigXm9fsFohqEE8hqIvetbliiYoa1aAYYtI8bh/iujBEc6nyJgsakMlqKAxvQ77K7R4Sl7Th6EvAi5VyYGh70uF5lLhFlok3R/by3gCjSbz5MzU7L9pP5Rvck2Nx8q1JIwv35+DkKUkeIgs1JIO/dMvW8ZGxdZQimLJwTtl254fK4i1Z7NlUMwHN243mo2EQl8JoUOgnrUHXFP9LfPzvtz+bW15QqSgIatzztJSjE3iD3Xf/H6Oxaps+FT3/virixe0DV2s+uNf/v+zQ+GjTYqvPplYwDedf2j+JNMByvK/MyOihTs8sL7aCDsFy+98Z3Baz9nJrWnrkW9eRGDRfyDS6COCzsj0UXngvPSd/+4n01hEvygPZ1fcNjl2LpF2PbFxcAfJ7QEe7up1tdf0d+8CMbfsOW12cwYlrQYCTpN3cOnfvjbHv3tadisFZfniuWiu0YiXoo0vTQjwyS+OjD4m+8Yr3FfXdWewo3UUn71iT9rVKTyth6fbV+1++UA8Rp8WmIRm00XPfv3/+cWxGCKw5u9lk0uq0ugXnuCLFZmZRXtkrb0mq6/8srwhasccIewW002D09Z8MRurSJsv3nqty+fbrbqJgNaRUVtZTrGZWAbhgqbC5aVHc2qrD5OafrlVf1k7+mX/1fnmbjNaiZRFBmqNFPPf72p72nvWFxwOO2tv/nuVMurPHIi6pgzL/rsvoVffeNN2h817lKlFVaXc2fmx5t+8p/T595c1Z7CNpTJyzj6lcPlGZXSzQW+5/dYgkghy49+rKahsl6GkU1bM9v1i9NDpwYiibqC7GIN2CGtqjm2ZvqdfsUDVt/sOxe7b/kITBb4b4CNbNjlstkW6FT2ngI1GEhsqO52Ug6IhvTUwsaD2czI4sudXefegZ07/9lqBbjZPNA6RAY/mLwjn/k4/e3mK71tP/13KeHFvbtL0iRkGkdTli7VKfrHLRf+z7f7WDyIlhTx+6x6Y1ibVlO7r4TBZ98xUNm2yuNXXlsZAh7BM4ac865FrzvY9M4VcZRJ+R+P58NlXqo2vSBfe76j7TQlSJEEZUceyxWmgqTwwSWI+qapeCKt6Vb34OUz3x65xVnVnoKYQsKqXnisvvRjxeu7R7fO3/ej7/3lm3irg27vosHglKrzs/cWydj01ckczmBnL//oG31vcbi49jTgmDfYVmDcJKvLlfHSsg8oSK22pu5fj/1FK49OSEQ9Nofd4ycX7CvQlmlgM7ZdAt2oHE4q5bXMoc6R1371LxeuculUOLlwGOaX6QJVPsQkThGuV3g7Yu95HzQ7qswKpXJx/vZU85v/MnuDTWMQQrGAw6hbJmVXlewvSKfNj7z8dvvlm61WnGM95//T1HuKTwG3TqN10e11cE7/82nqF3fVpEci3kgiOjbU/KPvGs78jJyI+5bsSzaY07fqWd+zOu9xMxGJhZZGrt0wLIfPcehJNoqHvXbXEhyu5TakaoozwVD5PZ6/zy2KqDCzJPurn138eXvX4E3sx1z+5xoVSt6qt8F98t/3EljEMlRHGg/TaYkrP77103MXwCNm97NVEKuPI1Olp+coKAOW3re+bWrivQY9FvUtmYxgn63cvS9PyZdTwpv2yfclv37R0jmmn/2TgZ/AECTGfDB5G5y+SMuvgkSvTPwnjUpMTFNw5XmN++i/njvbPBgbTxCkEKEpQyF+UH0wbOd7L85YRsZ/tqo9tXuWTDZXZMfHOxhDkaVIy84jTJlvvfL6zPkbfFBaQuSy2UUvj566a1eRRAXm2Gu6BeNoy6s/MFz7JfBOYMlhW7KRaGlVeVkaJah8YfhpRbNTupHpM//wdx0sNg2s8txeiH4YKyrOLK/PZzC3cWKD0cCSKNUZ+SrasGXo/A8st19/CyzWYr4V87yTKJQ/fiBXLVZ+EAss3knSTHWqsoF7+/bkm6e/d6PjVQYVDgkdRssyiS0oebw6XR0fuXWu/T/ebLXOLCxFPIQV05+NADSxoN26YvE6sdNnRFQ/seYvyyK+UCJgGlq89N2/HfkZ+AxHYZBbly3OSPb6WPgA/z5K4ilsSVkqbXZ6YY708sLOzyaSaFOYRBqNQTEbRs16UGTCGkxl8wTylOLyrLpcpWDVEf537Rc4HuCqyjMz7Rr9pH7stoXEYUtksjSlXLqSYD8AcTxUUM7ugvRez5hRN2CcpvBlmangbpcRN0/iB8sxEHkXx9qG9Uw3q7ygel+1midnEbdulPDiGPKy7Er/03ORzkn93MTkuG/doCyHIks54E9aqzxAtd4tK/QLPzNLm1k8buqdHRg1kWm8FJFMpkqTeRNJqQF/kMCQ5qnLjj3eGGgbmZsZ182EIcgBX5KanVu5e9+BzEyJbalzTn97cJwu5pZVlNdWZnMxaNN9xVOGKFVZVLc7lai3uB0tY7o+gAiizTVUVFaWS/39MyOTg9OTeKGBxVlwgsK/bSR939zicnWiLCO19ukj1iudvRMzE2AjGIkn1ds0ntSd/3x57oNYDNFEFFlp3d5d5QWpMuq8a8saFnObxwwTQ8MrgpKMDE26lPfB8yuVzZdmFuWJbkwadVNjLjApJlLYIr5cqd6XX3q4uCRTeMdGcgOF9/oC2leWQFUkpQZPGkynB0YGmiFyr/ipSqWCs3aE+F5Pb9wDX1u6UFnc2OBwez1tp7suXFdxyFTqwXwhQ1pSvsvidAWbhqaNQ2EvjAQqi6fI1FTtr2+sLRaTIQLufft9g/bmL06zDj5Tmy9hCyazRW90ARFYsqkCtSSzsFJ14YYpuCSQp9fvyU7hwishtjzxu/0gsyTc7Mf37cew9t5+/eCAMxSOwaYNDq8pGGdfQX5esiLJMqLeqGtmvDeegBCbEE5TlpVTX7d7765aJYMJNnQkCoVC5NPti9N2M4xg2GqQwItfKtWWFBdUZErA4Z9MSis+9sSRxK2h25MzQ3o8rhSZLxOm5tbXNO4rzcyBbeq24MHsx1LnlNUeXXREOsdndEaDLwqxMmgSlTqnurqucX8mF49H+gEkGO681OrGal/CGukfn+2z+KNhCN7KkKhy6iv21jdWy4VUiPU6Ntk/MYYXFwgYnUvGiU0lh+eGDFZrSbxIlla6J3txzD49M9qlJ9HEKVoJTyhRWw137Qc3PfsgX2kckgTiSk25LHr98IodJgSwQOCIJbLi2urGvVX5+aIHVhMS6QJ+qrT66Emj/fTNqYHWizy16KnGfEWG4EFkFlhU2Ep1cQM56DUYTw8NX29mkmXig1VKBje9PHeX82lL09CM0TDkHY3AosaTpGqyK+trjhVrpSwWhPPbIQY+m9Ns6zRuzb2oXzRMz3mwGpgOiSyWIK20rvTKG8MD83GvOP9EkVqj5Gwjwm2hB061NDqbGvXNzY/Mz+O3iGQamyGQp5XnlhVk5Yg3rHq2PHbXD7JAk1m068SxxZsQ/lM/NwtGohiFJ09X5u2qrz1cqeZLGcR1EzhwWdS7l2diEHGLLhKkpOcfKWnYV1CWAYrbGJZSVbvbHAi3to1NTveFIYwomcHjK/IKKg411pVB/FRwmA/eVfbdPyns1KLsXceesDT1jRuMI5MTMONQ+CKFWlNZU/UYhE/lgWn4B5OYqRmF1cePWeOd4+NGS+9oOAobF4kqVVNRV924P0sod/dOmibbu5JsBFosz1L3FsaYM1isE7Y4RkvLLMrOAruYudEhM4kkSJFJeNlq9aJ/S+4Pps4f9cN9MgUiOmi16SkCCRvkMuhqrjKnqGCXRTsPU5hcLmbBZLyTdYbMTROqygpzLe4QbJOTywZTmpZRXFJVu/dwOUQchGVsuwQ2Kyy+Sp0mlPA3bPbBSo8jS8/IVIq5YOACJpCSgsernRSfj3xzwuunpEhyC4tqchTDxKGAPIT7mKwdW95dFpiXSZSZ6RwpmwzuzQxehrr2s4ctNAp9atCCRVmq/MYaLdPOmWq6SIZzfLCzYcPb6lVhRWrmnoZje0olLJB7ImQ6madIVXkicjFo9fG9Pi8rs4L5WSFHePFG9wgoYXC/CXzVVKWIBWBsuyPWIUDoVo5Mnsom8QVwbJ1UIcDKyoIKpIUlMj4DIo9gsrLaXctEMJJtmfSEGVxlsbagcJd8pOlWzMcVcsh4rAoiN0OWz3rhuQDrShdndN7iw8g8VU71wfo9u4+X8GhEj4cnlmbnaLk5BUfq9+/LkydrR2YIODJNhkYpg4hgZAqRyhOnqf1isVTEZ2jr66pNoUCibTYYgWOu+r2791WX8ux6WBNpbApHoOBSN58VQWQxvzexHKGSSEQKN5VbdOITFJpKKmrqnBxbCkaT8imVI0oVMtmg4CCAXQRXqFQpiDI41gdjOICNCAhzFWlqjA22vvglOhsC3RSwc7MeO1qVmZPCJDhpJE6KIi2DIpIKwXyTEPe4Xf5QTKytqshRwYIBCj68ctKUlAyyJoXDot1zjHn3yNj2Nw2m1PIn/8BNvMDrmxgxO7xhMoChLqoqb2jYV5gi4wCL7CgRGXweuIRo6CIWlcaUizOrT3x6ZTna0m5Z6OkzNuRLJSCebkdpy2gBe2BOdmHdHgopZFxsW5wzTeqz6gpkNFZWaWOML2QxWFd7DB6bh0BiSVRl+xoP7q4uzlAmJXgI4MiVZWSC0cedQqlMkUyeHtCKGYAbhJOmsKXq9Ewic7PLB9iUBf0ri64kkbXK0oQMYWpeJrHbTo8pleUHitN4TDiQ2HGi0NhCiUaTIeNChLK1pyDoplipyYjKOFQGXKPyMVn94afJYoWQe7Nr1ABxOmBNTM4zch6ESbpTFoVBgjHGgdCVNCpPIcnfffyxvdX5aWnJ7WuMAYuopqLAYfNhOK/iseI5oFzNr9jVsH9fsZTCB2cuaUH9Cy8RhBc5vL7bU/YgRqap8jPKdz925FBpCi3pQw1to7El8pTMiDaFy75PQCQILiFNL9vLEQhIrPOtQ2YIWh6msji5tSCa7qsqLuThtng7SvD+DV6qLJWnjohBLXjPyTVQIYsLDzdQhHw661zHqAHCTxIENEFu7bHje2tyKjPB4j9ZEpVJYouAYTdXNhZyQ0Ck5QiFSGZAiNO0Y5/e6z9HYM6MrgD/5pQczEkjukPhG50y3p1+2VGl75eJIaGmNz7zeFgu5Lf26fRLgShdJEzJyoHd/+GG/DSedMdsBGsWX6FJx0RiNo3KEnMKTxw9sEwitJ+a6Bk2NGiVkh2Ip4AJicGXSxWkTCYHDI+Y8kJtNeWzduNPWhYXLJM9prpCKY2dUppTx/9DOuP01Z4+nc0aIGFMVW5VY/2e6sO1SohnBKYtZBpXlJmpShHCQF1rNojdfLkGXPzgjJtCBKtvYCNlOkW7eQmEM/Gw27bFmYpAgdlOUypggPstjabZX50jVuEB+neciDQiXaLMzdZEaQl85wgJaicTqgtK9xzaW55RJN9qDvNuhOmpquKGjwlorLevdgybZpbCUfDnKN5duaexcQ++lINYue7JyoQoTQIpixqDl/Bo04vrdx8/vk/LkeCvrsAwdm7N0eN8MYd5obnH4HUESHSBUlW2/8CRhvIchZyEZyFCLDlxmlYblkNggfu1lQqvlakRfJ7MPH+9C96RYYYATkyVtqy+dveu4w0q3rqVEk5rm0RlCmVyjVqr5PHo9zPBI4lTCxq4Aj6Jc07Yb5hc8IXgXSx5tVUNew/sqiyWkKnJc1V8LyNWcJk0fFJaS+ABHXRbloMk2BxwMXZa1aG9EXihQ+uowU+hppcU5qYdVYcI5zoZMiFETn1QU431Uu7/lwCuBve/81G4CjbQ4GLtCtK4NCaDlww7BkH+ghA9DVQuGIPBZrC5+JHYtnNpDLz1gj6vHxdCknjh3hhkMF0HlwImHeb8HUzHcfxF5mC9BtsqBmttyYmFwcIarpGZPHAywJchMLmGyE94UEQI0UAmUaEIWJ294QQlQWFCADco6D61jYKvu98bjNNhLaOS8HiH8D4WrycABt1gP0MkU8GUiBAnRgLwmhlwZmCQY2GP0xclgRcLncVk4VHT8WhP8WTcUygIcAF2ws9543jgVZ8f3NHBq2J9rFDo8LIAkJbBCHz7YQIUQh6XD9zgaSwenIEAVkAVovE5fAkmmc7gsUCaS4A9AvSLJxABBxHYFFOoVDo5HAgmwHGDxcNDt+E1hJimYZ/PD26GuJMgiDLgPAPuMyBtgBt/2Of3u3xBcKBiscF1Au+VpKI47Pe4AlQ6BxwEyNRE0OPwRUh0MpPFpcZDfm8gEAqC6hPM2uksOiPGoenf/MI/nTWxjAdeBFurzdYLy/2v9zSd/r7pxS9/+dDJvZkSCM2JjyX4FwZd1yoOuHk8i88G1yA4V4VmO+EtYxQSC4JQ4gv2OsKgBWAwOQx4jVTQ6Q4E42EKCyYVGqAJAa1Cbqc3HCPR6Rw+C44gQ56g3+8Oklh8HoS6pBKhoGTc02AsBAH9uMmntu+D98wBse7AGc3vA3frMPgwA/5gdQZeGQAtFU7QdjrhwFkmgOn2EyHOIIMGwbBi4Lng9gSDEFiXBvM82ITCqfB26d7REg8BR7jcgRiZBVzMxUcLOHyEI8DaPggTBJGBYSSAGwkDOBGcHVbn5ljIEwr4XAEGm8+EwK1JVwCYZX3gbhhg4OIInRDF2dEd3Oq1jb/N9fbLf3vat1dSc/Kf/nAXGJRTfCbLcNOvvv0vF5dLFI1PfeVPnyliEbd7xc3mZkIAy4Df6Q3QeeB/uDnuqcsfxYML0sBtDs8PHvGhIB72DUK7rCrj8ZmJwWUz6VwabEtmzv/Zd8+0LPeWPvPNz9cUpfLBC4NEhWkDxgVwYpIC+EqBCbUvBONxjVeT0IDnB7AJcAnOr3AjEYFBlRz5kBH8OKgUCF4K8wJ5NewoPsaCLogbGg3eFfd0c7Nwdy7A2AfVhWAXMGqIuIMVA2qDs+MOE8xTfrsvEA8nNsc9vethmDjxMeALADAJcJojgCtLstk0SpCwCktfoH//F/718fRc+TShbwAAQABJREFU6R0pyT52buTqj/59/qWTzx/59GNZUuhvL8TViMCpD1CgQjxA8FQG32MGl8mkr/XLXSU/wE8c8ShMYsEgFIFH/yCAPgKmMWB1YCPcUH1nCRobgJCdXowFD7LxmMMQodXt9wchMklybkmaCW5PC9gR39kGcXak4aqEWDjid3kCEOeaRmNxIW4osDYwPky8gAFEY47FYRkjU2jQhTQwe4T6wkkzHlkU1icqGFsy+KsySywIQflW3AEaOFOCJxURj2cNfIi/pWwjBVew2fP//LMbo/Hc43/+g09kYamscHB5Bl639q1f3B4llBR94n/96WF5unAHls4bNBMQ7zbsdXvx8bbGHqCtAZABYtwpD9q4gXHMY3W1fecfX+tocWeVfe5bYPqfs+65j9ODSQa6ChaS1aELzabScSJAJemM5Na3zPzmpb+/mEcpe/LEF56o5mFMMoVMg7UenDGhX9fKgfoABwAnQZyKWAIqk0QPn4XASRMvJxH24cKGL3JX3FP83nqCtRC6AOoCXRBd7QJgVwhDDlLmfdf69Qe3/o2EPD6/LxyEpYQDfl73U1tALFjwKvUBCwDDAoI4G+FtwutLIMyeP3v2zF/+pL/xj/71eHXuJuM0u2dx5PzX/30y/2T6M5/+3/ulyZU6gGMHtaWAnx0ZwqPCnAOhyxks2AvdTz7ZWted/7ojJO/8mf8+OUlkYMQU1uYYPASQveCz+dIO2gPaPhZ8dur9dF+KqxtN+pZTehI46VFljE1eFsApTC58thS17SvxyEw2Dz4b5UJMHBqTR7vnWPZOKEKykHHXXQKJSoKgxluvAsuRaGwubUutN4rZ0RdwdGQIBHdWDXgIqNKZQrBJ30hQ3yTCm5CAe8ytxcJkRKJzufDZeO7OFwi/zIXPnQvJbyRwW4XPHbLwtoINgwHY+Au29se6Ig10VFyJTJ6iADXyeiKZuHw2ODzARIX7+MOyTqKyWPC5A/t6Vvwv6OeYHNGmJsITdyNMYcCLtzY/RCQTGMJNZnsEIp3Lhs+dPDDtwVObsty59X6/gdBCpoHB75a6PjgxIrxZFD530CARqFyeaOtI3pbsvaMF1IQsmoS11bsKvM0ZVN67szGJhofAZ97pdxw3OpcP+/91QlQSg7pJmFmtmd+VsAkYJBocy/kXQtPnf3hhZAE09SsL03MxZlVlUWV5Dpv4gAf7cIbD4cFnc9vB3xeEoq2jlUCm09nw2Zzvnu/wBlo6XyjFh+a9/UWgwDaUQb8rqMxdNGC7QaDCIem7F5TECtz9t9T4Lir4aCZR4aDgLh69J9t7X4AtJkvM3+DI+2cmghTOgM9WuLbkJdMIHAkofBWrEVGS96g2voUNwZ7A4oFIBcGbzIBXW9xdFPfOENlC8IF/AKrQgWyIM/neHbgdYWgsiyXaPOPjp8Zc+Gz35Nb7wI4C6uaqgKqDIxFtHRvwQmPQjPDvHUlrtEjwXiYOeMFtJk2iU1n0lDv8SGXAefjmDPAdXojg5YCAhfkj4O47ceGNmybj8LzLC3HTXCpFZdXhWpmI/UDRwvHxBkBwhIwtlbmr3PWfMG2yCp/92Od3N4S54hy2/K6XZ8AkQyWzQY2xnv9d/oKszhPIFCkCDF5IeG+C+ZzKhM+78gmBCoEaWYx3vY+ThLUQlPvvMZXdW+79rkBQVz68mvq9EsjVEFrgXhbY/AyRwORJRHCml7JxlerGLFwKzkawj8a7YXWl3rif/EK/m6+23n6/vz7a4un7RQU994giAOzAV5bXVDm5mgzw4d+i7KMJM5R5e/eDLYYYD8KF0kcRARAlhSnF+2q8eQwhiWDtuwHv2dW5aGyROLV2b11VbXEavFoFpYcGAZAaeClFlZXcuEgLJxBbhAgaP1WWd6BRqsmSsxHD/l67DOy1eNrC8np6WKBhexwjV9vaRm6YmXR+iqqkrqa2qlpFA8eADy+BEoqWVl2T9uGV8JGjzEpRaCsPHxSB6ZJoc+xhDCKNyTIaGqmpWSLJ75uNPtqH+x+5MYQahBBACPx+EHBOesdOfflb10YWiBJtVf0zn/t4rTJ/s8b/91ONtVLANEx34a/+7zudrsGKF/7lq/Vl6vtoT3+vNUKFIQS2RwCC+y+2/+B/nro53eFMk5cdf+6FQ3vKM1RbBKDtqfyec3jm2nSnv/ytK4Ws2mc/9kfP1vPvrz39PdfqESwOiaePYKejJiMEEALbIRANxPxL0yaHLwxn5uDJBO+Mot2lUN+OxAd4H5yJA/ZZy4o76uVINQoehJH6MNVPH2DNEalHGQEwFg67zLPLroA7SqOCj6BUwGfTwQPhYU6xoCuwDKzPIkHsBaUE/IbXzU0f5lp/BOuGxNOPYKeiJiEEEAIIAYQAQgAhgBD474vAw72L+e+LK6o5QgAhgBBACCAEEAIIAYTA+0IAiafvCzb0EEIAIYAQQAggBBACCAGEwIeDABJPPxxcEVWEAEIAIYAQQAggBBACCIH3hQAST98XbOghhABCACGAEEAIIAQQAgiBDwcBJJ5+OLgiqggBhABCACGAEEAIIAQQAu8LASSevi/Y0EMIAYQAQgAhgBBACCAEEAIfDgJIPP1wcEVUEQIIAYQAQgAhgBBACCAE3hcCSDx9X7ChhxACCAGEAEIAIYAQQAggBD4cBJB4+uHgiqgiBBACCAGEAEIAIYAQQAi8LwSQePq+YEMPIQQQAggBhABCACGAEEAIfDgIIPH0w8EVUUUIIAQQAggBhABCACGAEHhfCJAf6KloNJpIJB7oEZQZIYAQQAggBBACCAGEAELgEUeATCYTCIQdgvAA4ikIpsvLy8FgcIekUTaEAEIAIYAQQAggBBACCAGEAMimMpmMQqHsEIoHEE+BIoPBgAJ2SBplQwggBBACCAGEAEIAIYAQQAgQk2nnOBAe6LA+HA7H4/GdU0c5EQIIAYQAQgAhgBBACCAEHnEE4FifSqXu/HAfuUY94gMGNR8hgBBACCAEEAIIAYTAw4UAEk8frv5AtUEIIAQQAggBhABCACHwiCOAxNNHfACg5iMEEAIIAYQAQgAhgBB4uBBA4unD1R+oNggBhABCACGAEEAIIAQecQSQePqIDwDUfIQAQgAhgBBACCAEEAIPFwJIPH24+gPVBiGAEEAIIAQQAggBhMAjjgASTx/xAYCajxBACCAEEAIIAYQAQuDhQgCJpw9Xf6DaIAQQAggBhABCACGAEHjEEUDi6SM+AFDzEQIIAYQAQgAhgBBACDxcCCDx9OHqD1QbhABCACGAEEAIIAQQAo84Akg8fcQHAGo+QgAhgBBACCAEEAIIgYcLASSePlz9gWqDEEAIIAQQAggBhABC4BFHAImnj/gAQM1HCCAEEAIIAYQAQgAh8HAhQP5gq+Mx3JozmicX70eVRMeEWcU5igw5h3LP/ZDDYJ/rHpzH6MrCNE1uJhcjEO7JhC4gBD7KCPh9ywuzrYPx3BphmjKVvdbUiMfqnm0D1rD7NzWeLSGlFu3O4IhZ9zLTpmzoK0LgEUMgHnSHF0d7lnlUnrREK6Zi2H1XEt98r8nuHSciJnrExgdq7o4RwMU5V8JIzdudweXSSOvPhd3mGfP02LQdC8cx7MNciT5g8XRl8I2r56++3L7ekM1/GSIs55kvfebQycacNMbWcqMBu77z9lvf/M8WTHroa4+9kKvmYOT7TiqbCaLvCIGPEAKx0IJ1/PrZv/8P4he/VXFsQzxN+JemZi/8vz/r5M/Y6UzKOlekltIbpVoxHYmnH6EhgJryOyOQiIQdBkvLz38+ViQqqNNqxbDSbKyra9QTcSzqN/aeujBseZ3z9f96RoOY6HfGHRH4aCGQiGER/+yt197WEZolf5gnYSTF0wSGJUKeBV3/taazb900kX0RLCbNIVTExSdKKtUCxsby9AGBsVVM/ICI3p9MyIlNnnrrGstL5f/v/coteRa7Rga6v9+ELXsx6ZYb6AdC4FFBwD7aOtr0y2vRSOmWFgdDIf+CGUvZ/YVd+VVHshlrNykMAluo4IBuCCWEAEJgHYGAYVHX+cvXhg0itahg/eJdf8NuzHjl8i39GR0da7jrHvqJEEAIYFhgGTNefrvdfMmeymjcACSKYd7Rs/95YZYwWvI3f/3HaSJmZHGmd/Did1p7/ypCKN2vWV+eNp743b58KOIplcXN3f/xIpU4jbNeu/CS2zrVer7HMDBjTDFY9ivFGAZLazzgCM62XL7ZcrF1aMG1nhn9RQg8UgjE/3/27gO8jePMG/ig9w4CIFjA3imKVaSo3ottyXbiEjux0+sluUu5XC65XMqX7lxyqb5UO45jx1W9F6uREkVS7BR77wTRe/kWpFitOCQNMCL530ePsFjMzs78FsN9MTu76yYjVTfbek52sUS+QLuYMVmdFlN/IxFnR8ckJsfH41T+DBvMQmBagOracQzcrmgovTzEUzqZ3OlPZs1ZbIaeWy81DXUbWUKufdZHeAMBCFACJsNAV9WfmgzDZpZ4BojHSuxNzdVshkC3dWtuSqJUzPaqmWZJn+YXPYNKzWhRfCTV6iZP8M1YcbGzIQlPWVxB/MaDuwvi8qb6Qp0dgw0X9edqDH0Dto6ebhcRMgnDPmLovFVx5o3XzvTW9hikEmK2LLYeWA8Cy1TA5/BaBzuv37g96B+VpMfRhiYHnY7Xx2NxWqz9vTIxRygWIjZdpvsYxQ65gN/nsQ1U1Da2VA/4dOnhraa7duR4bKPtXQ03S1oEPB43SUVuhrxc2AAElpeAxzLU3NFQfbVVLpdx4lSka6r4fj/xuLmqvIxo3dp0OT+wnC6UKOPSki1/0w/1j5hJJCeo4elSXbnPETDFYWo6g08MdvfYgIG4vMTZc6Px/B+//ufKijaRTBqZmkp4d/2TMqWDGQisPAHXkGOg5OU/dHjsEQ/sLopkUpcQzpjsJqfF3U8yBWKhWDBjOWYhAIEZAl6ntff8T8/3uipinngsh6WTzfhsetbWW3n5xpG/de/ZlVCQlCuf/gBzEIAANbSUOn3fWXKm/PKZ3kcfScvWZUpnqLBkRLbhwBcfuP+RrChCprs2fX7SNmobshio8+Ezkr/72elNvPu83ikHw5C1s+GSx91DpCksmUZK2BPj1cXhZOv2j+REJrtrmy/ebn2nLPAZBFaegH24rb762BuWoseyCqNSmS1DNEIN8JmerCaLqbOG1HT+/jvn3xCKJlpN+t6cdcWfLFJPJ8McBFazgLnL0Xb1TxeTmdm5T26OYLXevdvFVn+mosN6kffQo7kaZQO73LSayVB3CMwV8Hsc1rqjpT2MCvF9jxbKBddYHdZ3DjiHe29XX/75RXHmR1OyE6griuZehjh3Cwt7H5Lw1O2wtl5+81Snsn5q7Km5e6SrptXmYMXrItMSotgkMEZBFqvN3P6YLm1XCk/YPjx6cUY8vrBaIDUElqWAa7ChtbXtdI8m7oGU1CSBrLtlzsAdt8VkMRrHCD9cHRUZKVeyqF+3riFjfWel80Xuzu2JEjXO+C/LPY9CB1HArO9srDty0SzfkZOUmRvuYbTNaUaEeG3E2Vt9ublvTBKetyk9QuzuuHsIG8RiISsILCcBj9lt6Kg43zzq0UVkF2VquKPct7WjO/XxuKyjfZWXbw/01lT21TfIkh/UJSfJg356LyThqctqqj7yu+pZe4bJYPGlam3a1uzs4mTtxEeq1FhV6ucD8+au9lmp8QYCK1yAunOHzz5SV367Zaxe/eB7UyISVdaR7rmV9vgYLE5YfHzYnsef2JifkCzwUidf6l//2fGy888MR0S9f42UL+XgODuXDe9XkYDb0tp2u+bMpZG0z2flZMcoScvbekV9HvuQreNcyS2vNz5m/5ZkJY8MryIhVBUC/1DA57b06VsvX6pkSorjC9fHixnk71+s7nXbR7rLjl6sHq0dVLK0uQoxnc9wWr1sPuOevzTqbhJKqSrv4f/44KbU6CQ5RpjeTQjLVpWA10qMZVfODfU4VI99al20gsMh1rcDcGM35mvy/28fEUhFPGrYeeDkiSghc21Kn8v78snqzVFqjTRpfIz629fFEgisBoGhsmNVPX1Xd3zuB+maFGrIKTUCbu7kGOttvvn8c2PpX07Nz88RE/yimyuE96tdwD7cXlf2JjXM7MuZ69asERHG3+s5DUCxebLEvA/+MM3ldY11OVvf+u5fX2tp2fjAEzvzxYQVvO6SkPSecoSStN0fyI4Ni2GNkKHy50/Vt/SY3b7BQSuX0NhCdvCKv9q/Uqj/chXwOW32tqqmgbrSrprmZ7trOIRNsweeGuX2+M691Ggcri3c8v7csDABn8fi82be3YPQ2TKlQipPsHbS3V73Ow8NWq48KDcE5iPgImS4q3qw9WL9KOOV54ZPyXgMv5N6alR903Afq6X75wOdm9+zLU0+Zh5ov3nT2NBxuP12WcOxwFHP2lvRrTe76b//fXdh19689dsTw6jrkOezTaSBwMoTsPfpezvKy4YbO14dbLxYLgkMIrV01bcb/UbWH3/eWrjrYF5ekY5qI+MTjc5g86SqQEejlO0S2XPPP99raW3oKs5O47Ho7xTY3slgfi8hCU+ZHH7Mut1bqBtLCYfIQPiIjX7qal2HoaP+6oUG2VaNMFYb9EEK86stUkHgHhHwE6afoYzMTIwXGojTaHcSO3HYrXan3+9z2KjJ5PT6fMQ+fHtozNhEkrIjhErBZGulUROLSePz2HT25LJ7pF4oBgSWVsDLUaTHRNM2U1t1WYwu4ndZ3Ta32+UgDpvZbHN6/F4fjS0IU2XuTKKOuMRqHD9nabe5HNRnNIvVZLc7PNSgGUwQWL0CfhpHotWkb6Z+8NkJdb1DQMJmczudfp/XYqbaiNPjc1sDv+qaCFMii00Oo4K4wM85toiuSEhR28x+w9Coy+cL5rnxEB/c+CoSd+ATT/hFbM+P/1LScvjH5yQ8rjLqweTAI0uDFmOv3u8Uar5cBRgCpTDnA0/nkKena9DfU/7Wqx/7gXv/h7L27twVHfigr+LwpZu3vuf6/K8fSdoYJxn/XerzGsYMRlsLO0Ig4ohm3YZqOi/MQWAVCFCPsIjOefLjOU9O19U92mK6+vOv3UwRJ6379ydzJIEBMVKSp/t43oPTiQjpPv2NE9Wdz7I+99mH43Mj0V8y0wbzq0+An5C4kfr32Myadxz+3OtN3mPiT3314bg4BZeYO0jH0d/+j5uXmfPUl7anMOkcKobz+/xel9tL99MZzHccEDAz53nOL8nZDO2G/NysjxQTMZfUn6q49mYJdR2UY54FRDIIrGIBpTY5XBxFTh+r6xxuCzzihvpx21V+qrSuciDjye2Jahlu3biKvx2oOgQgAIGlEuCLSUJOLr/Z3Hzjd6e7TfbALRDdo536ay8dq9KZ2enFWQI2K5i9jiHuPZ1w4yoj0nI3GHbU1VytGaypqVX+9Uby+1OkOvHsxzcuFTK2A4HlIsBWZyZmej9RdKPr+pEXangaDvUXQa/v57BT1zyyXRcl46IJLZddiXJCAAIQWMYCDAERJhc9UOC80V1x6Pm/tMi5HIbHZHP02cTZRdmF6UkSZmDIavCmIIenbKlOE5uZTlNGSjmCGY9gFGjTYooe3XHBIRwxdiqcTW0me4yITF/wwWALFcrYzGQ/CYsIk1MXUAUzBA+eFnKCQAgFWGyBQpOe4VGJp3+4iWN1mZzPyqzf+/P1W7eGGsa3Hr35yfWbt+1LwRX7IdwZyHqZCtCYHKYsOiZSJVBMDda+S1XYkgiVhpHO5Atwqe5deLAIAiQQzmm8KQIehzlxmp26d0x4+oH9dOYZ+vMnrl+jRqlSUzibU/iBTxRmp6iUwTaj+annqM57crmooa/vdKmwz2VzUaPSvXQWT8Bi0O9UKpA/dcUHdStXu5saqEBn0lhcPpv6dCoIpT50u5126kmndBaXxebceabUvAuGhBBY/gI+n8fjstkJh89gsaZvz+H3Ea/L6nB7vHeaHoPNZVGNJDB+GxMEIDBbwO/1e5w2D4PGYPDYf7eR+Nx2t9fnJHOORLOzwjsIrGKBQDjnI24ah/oJR5/uMvR5nE63w+UefwRq4PooGovHZzOZ9H84VJS6pJfNZlP/zxM1yOHpPLeKZBCAAAQgAAEIQAACq0RgoeHpP4x3V4kbqgkBCEAAAhCAAAQgcE8IIDy9J3YDCgEBCEAAAhCAAAQgMCGA8BTfBAhAAAIQgAAEIACBe0gA4ek9tDNQFAhAAAIQgAAEIAABhKf4DkAAAhCAAAQgAAEI3EMCCE/voZ2BokAAAhCAAAQgAAEIIDzFdwACEIAABCAAAQhA4B4SQHh6D+0MFAUCEIAABCAAAQhAAOEpvgMQgAAEIAABCEAAAveQAMLTe2hnoCgQgAAEIAABCEAAAghP8R2AAAQgAAEIQAACELiHBBCe3kM7A0WBAAQgAAEIQAACEEB4iu8ABCAAAQhAAAIQgMA9JIDw9B7aGSgKBCAAAQhAAAIQgABzQQQMBoNOR0S7IDMkhgAEIAABCEAAAhBYgADN7/cvIDmSQgACEIAABCAAAQhAIJQC6AoNpS7yhgAEIAABCEAAAhBYoADC0wWCITkEIAABCEAAAhCAQCgFEJ6GUhd5QwACEIAABCAAAQgsUADh6QLBkBwCEIAABCAAAQhAIJQCCE9DqYu8IQABCEAAAhCAAAQWKIDwdIFgSA4BCEAAAhCAAAQgEEoBhKeh1EXeEIAABCAAAQhAAAILFEB4ukAwJIcABCAAAQhAAAIQCKUAwtNQ6iJvCEAAAhCAAAQgAIEFCiA8XSAYkkMAAhCAAAQgAAEIhFIA4WkodZE3BCAAAQhAAAIQgMACBRCeLhAMySEAAQhAAAIQgAAEQimA8DSUusgbAhCAAAQgAAEIQGCBAghPFwiG5BCAAAQgAAEIQAACoRRAeBpKXeQNAQhAAAIQgAAEILBAAeYC0/+D5ANXf3Gp5Obx2rsl40hI7O5H92dvzgznT33uMRNLzfHnz5ZUtHVPLEzamly044ubtCwGbSoVZiCwMgWstxtKrh154a12QuzTNdQlF23Y9tjOTCHhM4hnrMNa+/qvT7U39pgnkkRseLSwePP9qdPNaHpVzEFg9QmYO0s6Lj/7YhnpN86ofFS2vODAFzdrtWL2xNK+S89cKKk503AnjTo5L/+9n9kcQcJ4M9bCLARWqYDb7Riuee3Xb1V1Vw1NE7AEstg9n9yTo8uJ4IwvtfZWnC0/+capdmJ1EyLRsRN2feKhjLQICXd6peDMBTk8tQ3Vt9dcunT5boVjC0mzjS1m+Hn8fQmSQAq33tRXX37i8KkTJTdu9w5OrNRh7TS6Fbz9u5PlOtkEx91ywzIIrAABS39/W8eF66ao3cnhSoHgTo00EWqpiEHoNOIevt1eXX7ycI9BItckqIXEQ4jR2lxeb/Pw2TtytBwZDydAVsD3AFV4NwIum76nq+p6u3ULX66Ok08e1NThEjmHzQg0EJexx9B0+lR5d4dFEpkQRh1XaK5Bt7W94uXn+ft3r0lQRwrfTQGwLgRWgIDT6xrqLCnr0Yvc4VnJ0sABiJqYPJFWzhWw7xxoDE1nKypvnO9kiiMiw5g+h9UxUPv6SR3HSVKLIiaPYEHCmGzJQcpuIhs6gylURoj5LC5jMl+/y+Ow6nsuXrwQRRNHbUuQBH7PWrsHG976y2+OVXl5Lo0uQcik/oqMjtV1XrR83xcb8fRarYzDmswArxBYeQI+85jRxupTbP/YRx8uTteo5tbQq28vqb12/f9urPnq/+zfXhitJk5Cut76/i/fKj36vDxLs1Ml4XERn85lw/vVJWCzWa3Dg9zIrU9uK87Zl/T2vlC3dbCx8dXvnPV+Jm3jvs8cSBERQrfU1Zw9/NwPfnBBG8+QKCKpow8mCKxmAb/D7xod7mIq1uzMf/pjD8cR1pxDi99DvLb2y0cqm9m9yU9/50N5MVKvofb89Rd+9LuraWy2bI0mnjrdF8Sz3iFpk1yJYsPHv7svR7dWObm37W1DjZd/+82XK2o7rVGtbU+m6ag/EMP9w20NtV6PIevgzt27vrZZQdoPP/vSuT+fNZJTFf17Y4bTFdrJDPAKgZUnYDMabDQnPV0t5bHfdqreR4i5r7tj2GpZ8+E9yZFh442J+lkXk74hrZvZ+mZ5zVBhYaya+7YVV54TagSBdxAw2w3moQaaZJ9QJLjrCcYR43DfzRMk8ZMZWelxgdiUyoyfGB6ftnuH/1cjPbr+hN2x6nfYAD6CwMoXcNp9huFhbwydr1JICO3tYaZ7jBivX78mJar09z6YFy7gUEcjpS5t4+Pvq/hui6tKU7Eufp2ETHazBgEsJOEpnc7gy8KUaq12qsl7fEx7dxSLedupt5tHek3+cIHd0t/VWt9k83gT4mLWpqdpI1lElJNxsWGNd6zW4vB4vd4gVBBZQODeFbAYeszuUVpkuIjDettxlfrzwAtfu39jlCU1LDxWwR4/FUEtZHF4HDaX7nQ4PT6//96tHEoGgSURsBvsFt+gOyFGwhfy335Qpcoglset2/bV75LszLDwyaMnnc1kc4QCv8vrcXlwqFmSPYWN3MsCTrtHP9TmkUfxxUrx3cJTl52MdDSbhIyosJhwLpsZ6Chl8JXC6NzUiJIBVl+/gfjEwaxhSMLTuxTQ6/G6HAa/30moA6rP56Ne/DS+ShqTt30HSSxIzqHG/tBchMFk0uksLotoVAI+5+0nae6SMxZBYFkKUIGl2zimNw50up21FZdHRqTUiDhqMIskOj0+XCOTsai2z1HE5yviZ1YvsJbFZDRZbEQoYDHoS9WAZ5YB8xC4lwQsY2aLsc3jp9WX8JytgxO/81RJURGadPXEqQWBODx57WPJswttc1itQ500fgyHz8Ygstk2eLf6BHxOm2Okf9htdLdXV15wDVDjswnhyrWK6JREJYvLpPlcDvdw3whPppCKlVxyZ+Qmg0vjq8NU5iH62PCY2xfJJMG7qD0kRzcq9PQ4HQ67zWab3MlDXaMtNZfdrkGmLIanDJfSOEQgzzsYmXfw/jtJ/H6X3d1W2zgyWCmXMHfnaNXSqaEBk7ngFQIrRoDqsDEZ9C5DQ5Ot5Wc/PU8fH4cuJr7kB7/68X178vIVTKqZz+0L8nt8nuGOtvaOvjFuYriIy8HFgyvmC4GKLE7AbzYYzB1V9qr639UfZ9DGx8v5fRs/eXD/nq/vjuNQHR5zWxG1Hb/P0z/S11d5iROeJNNKgnxJx+IqgrUg8E8UcDnspqEur6eh9OTF8nMTjcavyt6T+/C/fWZTWKSU7XW5TEMDnvBInkYspfpNZ5fVYnO6xyw+P3XV+13a2+y0830XkvDUYRq98uxXG/7KFU39KHWbqYWjJkfEhoy07dlUf9DcU5nOQXt/2cv/d7qszKbR5O3fnhAdhj8Z892LSLcMBahr8EfHup1jngzhwce+ui0iXsEltlHSU/rna2dfHR7zf3BvlogIZv8NcJkGe85/68Qlb59ww78/FB9F/YbFBIHVLWA3jdmNhMsv2P/ZR9elhMfwqJZlrTl/uL5i7AvuJ/5zW2TE+IW4M5CoX4bWpjNvXLhUczHrA58ois/V4VfeDB7MrkoBp21sdKDZ7Vq75eGNex/KjAgM0e7rvF5d/dw3/uL5t52F8VkhiRbfyTokG/S6XSPttSOztisWSKLzDx7I27i5MEs9N/B09PbUll49cuz0zVZn+IZ1u/bsTRCr5xyZZ+WGNxBY7gJU4CmNKd6/O8GflbR+S6ZCLWQR1xgZpZXdeqOyixypyo3LkwsE0y3U2ners+L4oaO9Y/Ltmes3bIoQUD9hMUFglQswwjLSNog/pWLn7ChOjJCGsano06kauaG/MvC30yW1Gfu5fLZiqqOEuJ2Wwa7Sw2dPtty2Rxc/vjsrURVGXW+MCQKrW4Atj9Ose/J9ssTItenZedHyQC/omNpm9laVvXL2VrhMEJ0+fk3hEipNH/yCuFE6kyXVxsmEXCHdSRyjbX1Gs43LlcSuPfDh3emqFMmM2xVQtyrwmIdbykpPnXr5xSvD2rjsHVt33L8xUxLEAQxBrBmygkCwBKgDpjplz4MpM/Nji0h4QV7iK53N3Zfrhj6cISaT4alD39ZefvrqqRNXRjdu3rdl+640zcwVMQ+B1SrAicjNov7tmKo/FWvyo1MzYmqtnHO3Wke3xWqlk+Gp12Hs72u8fv7lQ5WjWYrCbU/dnxZFyJ279k9lgBkIrD4BniolRpXy9NaZNZepdLrMDdHP/rq5uyBBnynUcLg06qp1h4e6H/+cq3KZDAaNxXz7eLSZ2S10PiThKW/8xlIP5MXmcDtI6xuf+cm5a7UDDmdDddNogVaaMvPhAh4LMZQc/8Mrh0+VtwjEWz703wc3Z2+IRGy60P2I9CtDgGqPEpmcKZVSd5WaNfVf+smxI7dPdBc9/I1Pbk8PT8JdxGfx4A0EZguIZHKhNIXcuVBq8jPqgTcnzv/5hefLi/b/64MH3psbP3GTqcmP8QoBCMwUYPOoy/jVdGagS5HF4UjV4cxeq11tHCNENnv4qZC6z5RCeNeB3jMzXNB8SMJTGo3O5ouEYqlUnkAEj/7L+5nqY5eP3OhvePVH59kf5vA2Fty54ZTB0Fdz7WcvXiptHNGkpW1/4v51SWvU1HM+FlQFJIbAMhTwWom18cJrrcM+Zdx7t6UKJoaZUuclbSajl+nhJobJOMxAS7APNQyU/ubPR91mxf6nnti2Pl0dIWJSv1IxQQAClMBwxQs3e8yX2fs/WaiOCtz+Ynyymow2bxdduUvE4AeWUQNSbY3Hf3+2rLNMdN/TX91WUJigE+BQc0cLL6tewD7SXN546Vhb3FMZSbGTzy8l1DXuVqvBFxMnkAvEbA5NqY1mtHupa6jMREeN0aSiVrfJN9bU2qKyJqq0UtrdLkNcPG1IwtPp4rCERJ62bqPZaDT0drVUNV0qOZshEkYnPKCjbo/lHrrdWXHs2LmKOrPDGROltFvby86Z66lDMnVHqYj0wphIrXjuKNXprDEHgWUtQJ0bcenbblbpxY0Z2Zp0kUDI9DlN7sGbNa1sMyN6XZKEz2F4xtq7a8qOvtk4InogY8OW3dvSqSdLhbjRLmtVFH7VCdBs/X232453qTbHbhULORImFYmaOisb+wZtrDXU6TqumEnc5kFTx5m3bja3u6PjN+3bsztZI8TdpFbdVwUV/vsCNJ991NpR9lbrWg8RJkREUk+voLmGBrraqm71qtK2aiMVIhaPKDIzY6oaPK03KnuT89Vsnt852t1z42yNL1ori6GeVT/+COG/v5EFfrIkRzrNupy8Fl/vue+9bmm7WF7C1OZu12ZxibXhet25v112EQtV6I7qSurfndKHE7Lny88+uh/h6QJ3J5IvGwEGl4hT4lLo9TVdpy9XbxfFcsJ4Hn2H6fqbJW0a/prsx7MEQuI1V1+uvnD5FxcLPv+zdYWFKtbwMHVWZXxi0GgcgYTLoe59umzqjIJCIPgCyuisiFq7uOpSZXO8kOtN4lupw8mV0zV9jqj8x9fHSwRiv3usv6HhlW+dGHg8Lr/w8U0att1osE+UhEZYPB6Xw+eOn78MfumQIwSWhQD1rM/IpMw19j/Vt6mkDRmcGKpv1FheU3nr4g1r9r+lp+g0PCpalBTkFb/QfrPh/PGrheGFbqlP31BTcvh8R9KXU9ckpQd7yNmShKfUJcpJ69L2fnzHyd9eMNc29Eh/8Hr2D3YRR6u+/irxuJbFzkMhIRBcAeosgSh5zwf98vPcN7/1y69xTC663yP0WhN3fnzHpu3pMcTDIt0NpQ1lp8qoYT9/fab0qDDwELnJScvmFH/kW7vz0zVhk4vwCoHVKKApLNrBe0Z08qcvfffsL21cBjVCxqXIemz9fVvuzxfLeXRiaxlqrzl8ggy5T3XXldYf4lFt787oGOq5FokHD+zf8Oi2hEB30WrkQ50hEBBgh6WEb/74l90vHb7+3H9+8OfUiBia16pMKsz4/DP35YZHU0NNxyftpk9s8Rx2v/mLH3/hTy6f38NRucOe+vDWnE3p1LX+QZ6CHJ7K0w9uYWeFjQrj0hRRM0JpJl8blrhz/2cEKRa7XqJlxsuVfOJbu23bJ8JjCKH+nMyeqFP6cesSlZLZS/EOAitIgDoUMvmK2ISsTSwvPWKYmAO/06hvfmxBcXJ8uJgbaBZibd727ZyYuLtUW8JgxsXI+Xiy2l1ssGhVCbDFkojUzI20h5nJw5Odosr0jcmJOq04MHqbsGTUQ023foSfTohjjgyNQcJS0yPn3hl1Tiq8hcCKF6CxBRxlXMqGHTZFkrrTNFFfuS41PjdRJyOBrtPxiSONT8jZyWTKIoaIkzpG8ZRMTeaGRE04dWPEYE806glPwc4T+UEAAhCAAAQgAAEIQGCRAhi3tkg4rAYBCEAAAhCAAAQgEAoBhKehUEWeEIAABCAAAQhAAAKLFEB4ukg4rAYBCEAAAhCAAAQgEAoBhKehUEWeEIAABCAAAQhAAAKLFEB4ukg4rAYBCEAAAhCAAAQgEAoBhKehUEWeEIAABCAAAQhAAAKLFEB4ukg4rAYBCEAAAhCAAAQgEAoBhKehUEWeEIAABCAAAQhAAAKLFEB4ukg4rAYBCEAAAhCAAAQgEAoBhKehUEWeEIAABCAAAQhAAAKLFEB4ukg4rAYBCEAAAhCAAAQgEAoBhKehUEWeEIAABCAAAQhAAAKLFEB4ukg4rAYBCEAAAhCAAAQgEAoBhKehUEWeEIAABCAAAQhAAAKLFGAudD2/37/QVZAeAhCAAAQgAAEIQGDVCtBotAXVfWHhqdvtRni6IF8khgAEIAABCEAAAhBgsVjzD1IXFp5SsanP5wMxBCAAAQhAAAIQgAAE5ikw/8B0IkOMPZ0nLJJBAAIQgAAEIAABCCyFAMLTpVDGNiAAAQhAAAIQgAAE5imA8HSeUEgGAQhAAAIQgAAEILAUAghPl0IZ24AABCAAAQhAAAIQmKcAwtN5QiEZBCAAAQhAAAIQgMBSCCA8XQplbAMCEIAABCAAAQhAYJ4CCE/nCYVkEIAABCAAAQhAAAJLIYDwdCmUsQ0IQAACEIAABCAAgXkKIDydJxSSQQACEIAABCAAAQgshQDC06VQxjYgAAEIQAACEIAABOYpgPB0nlBIBgEIQAACEIAABCCwFAIIT5dCGduAAAQgAAEIQAACEJinAMLTeUIhGQQgAAEIQAACEIDAUggwg7uRkaqXKqvqL7fcLVe2iEQU7d6Qkpuo5E5+7rON2lvPHyntrO82EUIVJiJt47qc9RkJAoLAeRIJrytRwGUiQ+WvX6i71Tx0l+ppUqQZW96fGxYmYDlGWoYrnj9ZR7rHZiRUxrLTd74/J0wn48xYilkIrCoBHyH2jqvHqqtqbw68veISvjiu6D3bUrUSFXvup2P1h2t6Ri8x0IjmyuD96hXwe4itpeqt8hult3sJoVqXJDYrrmDPtniehDsVkQ13ltysPFFSR4iTkgrlkSjI4amls6Tm8plXr95t/3LEJGrUzaYxhLzCcEEghUNv7Km+curIofPNVR3G8fA0OsvgMDM43MJ4FZc+DXK3/LAMAstYwO8nXqfNajYaqW/+5OS1E0tvVbPdHUfWRG90eanlHruhu+vaq9c7Mw0kLELMuJOUY+U4vF6ff3JNvEJgFQpQ33+/x2WzWWY2I2qhW99e12+VO7WC5H0e75xW4nURa29t2fmj9YZz2ty9yTL8xluFXx1Uea6Ay+w2dlZUXCyv6G3ptfmExO/W662uARM/nL8hWSuScTyEOj5VlJReqrhc3cOIEBImze1uc3lPXxFscidGJiimOh7n5r2490EOTycKQaPRGCwOk0Gn06ZK5fP77O7WI4fPKW08TcFD8YFP9A09t4597281JoefzeUx6cTn6ag7f9QwZBPEfW6zhh0R5MpOFQYzEPhnC3AkRLfnyU/seXK6IH6/qcvT8MqXfjNkDE97sChKzKc+szgd1r4eoln/1J6ize/JGP9dN70K5iCwmgWoX2vChK1PU/8em2Lwu/ze0SvPfvtYJ7s6ZctajTB81gkGv99l9DSfPHu943iXlKOdWg0zEFjNAn6/udNU8+qPf3mZn/f4ff/xkYNxhGUuu/r6m688/+PTsYl0vrBAZSP+1iu/efmkKdL08Fd+eTBWI2IZW841HfvPH13ijTp5n94UwZgO+YKAGZLwlCuW57/v3zelaVNkk0V09Iy233z1Vyfr67ssUe3tD8VTfxbsg209TaVejztq0weKi9fv1nl6L/7weMlAg635VqNxrUAawWVNro9XCKx4Af1IT92F/zlDj388d3NRvpjwA12lVqfFNFBLBMV8sRA/11b8dwAVfLcCHtOgtfbls7ekdk3mJ/dFK8RzDiJG82j7hd/0OQ226Cjp4LvdGtaHwMoQsA/1tt28WGpJfTA/f/2WCKpjlBBBSnRSwvqiK3/r7k6LUxYILaS3osKaIE5Y88guqvckED0KIpIT7v/cxh92swW3b2VHrBERVvAi1JCEp3QmWxGblpQZl6Oa3HPusCGxpYJzrntgxD462GslVDcwW5miK3jkQ3IiTtmSkpKSKbWIW/ml1Q5is9HoVMGmxjpMZoJXCKxcAUv3rZaaKyetCWsyU9Zlhssmjqous9Pi6DdFa/hCsWDyzP7KRUDNIPCuBFzDhp6ay29cscrui8/JX6fhB85ATE9OfXt1040rtZJklbg9Q0gQnk7bYG5VC1gtoyNdNYbo3ZmJMdFhvHELpkgRn5+732sjEQlyFjUYzdnbPiLWqKIiMtS8ieHcTJ5MpF0bK7w24NL0GEng9F7wDlMhCU/vtpdphMbwEZqPuLxULV3ExyHCqPw06t8uKrnTPjbWV9fc3mc30OQCdVSqViDiBa+WdysQlkHgnhHwE495oPZm/a2arqxPvzczPiN88lIOm8lhNndSv+ZGe/vaODUT138Iw8RSDJi7Z/YeCnLPCLgNLb3N14/ccCZ/LCWvKGGqe2SigF5Lb3ttVcnNZrLtkYThOuFw/7l7puQoCAT+mQJek91k1/eJUsLFEo+hq6aduladGrPNEkiFGU8/IWSwGDTPsNdlt/oFLCafTY2XmewkZRAahyMechL9iMHrCw9m2LZU4alhyNrVcMnj6iUSNVumkRD2rL7Roc7Sk0e++ftzLutA+gOZGx97MJEpnDxA/zP3GbYNgSUQ8LmJuep2bXdDi2Tzp4tiNKLps/hWk9nUVUNqGv7QfPR5xp2RPevev3X3fd/dG70ERcMmILCMBPRtlc0NlTXJj+xJjk6bE5wSYqs/U9Fuvch/8Bu5Gl4le2B4GdUMRYVAKAWsBruVDNGSs6T6ztPHLr567AJ1WS4h6uw9ue/53McKRGohg8nmSFRaZr/VrjZRd5GhRm6Oh6JOv29U3+buFztFeovPJ54OXN91eUMSnjothrIXf9h/SiifGpPu1FtGe4bMjrC85KTizBg6mT4AU3WwjVmNQ90mk4EQV3u3paa+dl9qmoR+5/zmu64kMoDAvSzg93rsnQ2dPuVoXM7BFJ5GNH1JITXw1GpweEhC0cE9a1MjdTzqXh+29sa6/uq/fZX2yEcL1LHTbexeriLKBoFQC1BNY7C/eWSwmbtux4aY8DDhzB4Qj5FYb791athI0+7YUxAl4VlnfhrqoiF/CNzjAn6f32902JvP/aF6TW5q0ddzCqkCW5s7W/obXnrmFfcHt6yNzJCLafFZa9iHa1poL1xM+td1KjmP6RkbNNadKzOM9fL9a4J9J5mQhKcep73n1qWeWfuDzxWo4gt3rt1ctD4vQjrrIyraFkqjUrMeuE9h6qhsNY02lh0rzRMVhItU44Nv5yTGWwisKAGvz2vrb7ptpocLUvNTFAzRzGs5BOHqxPwDB8iG+3auSYmI4lLHYHsnq+/4tZbfHi/bELVJJg6ThqQRryhiVGblC/i9xNTW2efvNMcV5EZp5NwZzYK6O1vvUPnhenMYPyVlS6ZGwiaOlS+CGkJgQQLU6XoGnSFVp2bl7AwMjKHZWhsunnA1nrt+oTZMxNOpZSJZ2rpN1Zaa0fojh04MqIQ8JsNvZbjoPgGNK1zQtuaVeEYTnlf6eSWi0ekcgYTDYrBoXuJxmKwul0ciVGRv/+i/7khWJAgmBi143Ta7w+Z0ESZHEBW9Pu7D6/aQjkO/+MPR35+ve/PV63nazbEqvmheG0QiCCxbAb/L4xptaeiiCXSJSToxPXBV4NTEiczPov7tm1pA9fkIdCkZiR0mxqFLt+/P0unCpCH4uzC1PcxAYHkIeD2eroY2E69Vkv5oNEM6cW3HRNH9NkNf87WXXh/O+q+0xEiNY8TkIGNmh83u9ruNxjGzWc7i8dkz293yqDJKCYFgCojYvNTCp7cV5urUE9ny4+PSs3dtbz75h9q2NO3Q+nARic7/4KPsvx0iv/jrn8uIjRB5clbKA09mRJTq5TQvI8inJELSJKkbSxU9/V/bMiLT2L2k++y3/1RS2TzicDbWNuuzVeIEATWqlOoE6m04fvzCi1dKSOLmjzy8aVNGuoBFIlMSZWV51oGSugGT2WEhBOFpML9+yOseFHAZvPrbjU1aWnZUUoxg5r2C/25hhWKJSJpORnET1L9LhA9WmYCXurChqdQgjubqkmIZ9FlNw95nGuioqCXVbb8rP/3SkfHHvbjNAya7y0X74Y+ubd73+PYH3pcdGcxrjleZPqq7QgWo320ipYrBmBkohifueFS1ZtdD42Eck+tl8ixX3yB+DidMPr/j17ytZm513iv9o4R0BkuijYtOiEuRhJMo0fsNDMnZsqu3extO/qmU/14RPztNTnWgsnyeMauptnlgUNJcEJWSmB5DiGlU77D2sxj+MCGbzcTFUf9IGp8vfwGX1TPa12yWh3OkGjmDNnk95ETFTK0Xm3v7LpItD2cqYqaeX+pyOp2+EZqMx6euoVz+AqgBBN6tgMfnsw71jzEY8RGRYXw6fdb1w0y5Im7djk8I11JPKpzckKHpzO3+seuMosLMzKzkMKofZHbLm0yHVwisBgGuSqTkx0Z1Od1OO/Ws0smfdz632+ly+LVyrpgr8FqoRwhfO97rlGkjizNjeeO3OLX3OPtqmqzRDF5kXDgjuP2nIQlPp/cm9WgcdcGeXXaP09rdc6rr5ptXFTqBJCp6k4JHxPIIVVS6mD7S33n7VoWcpxqgk76Sis7eHhFPnRcfJhPOvmXddK6Yg8CKEfA57M6x4QGuRC0Syblzj5GukfrWyvLfd0lT5PlKcZiQujkbses7ugf6TdbYFLmUT42iwwSBVS/g8nmNI31eroQvk4unLy2ccGGrlAmq3QmBiz2mpu7TXSeqO8tZ9933cHxu5OTReOpjzEBgVQlwVApt2JosZ0nHQJ9akyIXUxev0zymsaG+1uZ+tm6tLEws8jmJe/D2pbPdspTI6Hh1HI/FctmG+3qv3OzmpyRFJcQrgnjP04B+kMcK3H2Hajfm52Z9tJhQNa47WX7tzZJ2QnMQQVRC6toN61hsVvelF1/50ec++sl/+ei3/naitF2mkOzYu16nkc8cPnT3nLEUAstcwO2wm/XDPp1EECaQvK0LR6FNDhdHkVNH6zqG26mRPsRFSFf5qdK6yoGMJ7YnqWVTz2Vb5gwoPgTejYDT5x0dafXQbByFTEA9Vfvd5IV1IbD6BHhh2ricDcW1h8puXmvoHb/pKbE2NFWWHTrUporSRarCBCwRka5JSBwxuRoPlXRbqTvKkOHepupD/3tRnJmYkpMY9OExIe49ndjJNLosibr9/ge3XH2t1Frf2C3/6eHMLxdrkuWpMfnkh/9C++2bN8saBrzjiRM2HCje/8jBZE7EnSuoVt/3BDVeTQJOh3F0+LZbuoEjElF9OHOOq7SwrPT17F/5zr158bc/OOIUB3pPbSx5dvyB9Q+vl2jFgSfPYYLAahdw2X3GkRF3FOGFKSQE0elq/z6g/gsXoImjRekPfPnpqxfqDn37U88FTih4xvxCneCRr9y/OS5dS52nox6uJEl/4NGx49edr/2/71wT+JlOBl/Ff+yb+7dnZEZzg34wCnJ4KorZuHar0pMmSY0Rq2Z0frIluvCMfbsfZkYZLYOKGLaIxaPuMM6hHoeVsWGbe4Qel9A2POEZnbstIy87UUbmnqBZODfWgMC9L8AUhcuTd+wjSZlRc58OHig8VynXpW3hO/toDa291H2BA5MqqzB9TVaGGuf1Jzzw/6oXoPGYvKi0PbsZ8Yk68bzOCQqjCtLpCY8wFGHCIB8EV/3OAMDyFGCJWIqE3GKzmcmwk57xOoRLdJkxeRuyY6ihpxNn2tny2Ly1eTSant5APe2TEKE2MbJgy9o4blgInrlN8/upJ1fNd3K5XD4f1X+DCQIQgAAEIAABCEAAAvMSoEbdsNns+Y+9WZKxp/MqORJBAAIQgAAEIAABCEBgXqdBwAQBCEAAAhCAAAQgAIElEkDv6RJBYzMQgAAEIAABCEAAAvMRQHg6HyWkgQAEIAABCEAAAhBYIgGEp0sEjc1AAAIQgAAEIAABCMxHAOHpfJSQBgIQgAAEIAABCEBgiQQQni4RNDYDAQhAAAIQgAAEIDAfAYSn81FCGghAAAIQgAAEIACBJRJAeLpE0NgMBCAAAQhAAAIQgMB8BBCezkcJaSAAAQhAAAIQgAAElkgA4ekSQWMzEIAABCAAAQhAAALzEUB4Oh8lpIEABCAAAQhAAAIQWCIBhKdLBI3NQAACEIAABCAAAQjMRwDh6XyUkAYCEIAABCAAAQhAYIkEEJ4uETQ2AwEIQAACEIAABCAwHwGa3++fT7qJND6fb0Hp558zUkIAAhCAAAQgAAEIrEgBGo1Gpy+gS3Rh4emKJEOlIAABCEAAAhCAAATuHYEFRLL3TqFREghAAAIQgAAEIACBlSqA8HSl7lnUCwIQgAAEIAABCCxLAYSny3K3odAQgAAEIAABCEBgpQogPF2pexb1ggAEIAABCEAAAstSAOHpstxtKDQEIAABCEAAAhBYqQIIT1fqnkW9IAABCEAAAhCAwLIUQHi6LHcbCg0BCEAAAhCAAARWqgDC05W6Z1EvCEAAAhCAAAQgsCwFEJ4uy92GQkMAAhCAAAQgAIGVKoDwdKXuWdQLAhCAAAQgAAEILEsBhKfLcreh0BCAAAQgAAEIQGClCiA8Xal7FvWCAAQgAAEIQAACy1IA4emy3G0oNAQgAAEIQAACEFipAghPV+qeRb0gAAEIQAACEIDAshRgBrfUzrEO/ZhxyHy3XOkswldqVRK5iMN4++c+p9dpGugaMTtYdKFMGyfn0Wh3Sfb2FbEEAve4gN9LvOaRPqfLx5LGyDmEzPxie+xjdn1Xn5E43FQ1WIRIwmMUUgmXPVUpv5t4zANdw0aLwzG+kCvXSmVytXBmNlOpMQOB1SfgsXtt+rY+g83pmai8WBMjl0okVGObOTn0w6NjfSOW8WVcnlgaFqkWMQmTNjMR5iGwWgX8PuIYHRgxDOptEwQ8sUKijlRwCXNGT6bbOmzV9/UaicdLpeLQ6RJtnEIsYFNHr+BOQQ5PB6798tDxc38quVsheUqS/sTnn9r8YHGM6O2fu4Zs3Zf+8vW/XGkJF+Ts/uKvHkpgMyVvT4YlEFh2Aj47Md4499uubqtq908eiCNEMKMK5s7ShkP/+eOzpGOUWqoiZPtnfnRw1/bEyKk07jFiuPb69/9yrry1fXxh/P2f33Pfgx/Ov0szmloJMxBYRQLmTkvdm9/8ydn6Dv1ErTd96kf37d6+I2q2Qe/F06+dfOalm+NL41OL9zz2Xx9eLyWKoB9XZ28W7yCwPAS8LtJ15vW/nPrd0ZqJAidufmjnR772UBqvwhQAAEAASURBVDyRc6drYGg6XX74GeqYpbdSC6PZ3O1f+OVDG7MjNNNJgjMX5PDU67LaLQaD4W6FszjIrVf+FsG2s/kfz6cOwzMn+3B7bdWbL93o6mw3iHRWl8dP/DM/xzwElqmAc8DQVXH8D6+cvirhpG7YQWZ9se2tFyovVb5wdV3BY+sfVEm5o32DpW9WlcndLMYTm+L4hNCJfqi5/Nr/Ptcl25j7oUeejvQTa0NleXnbUfvRsI8XaQj1uxYTBFa1wHBF+dWzzx26ys977H0H1cky6hzDYNe1882vjfgeerQonIio6NM2RAau/eaFmhZ38kNfvD9FQDijrR29+he+dVTwuaLsBIVsVQui8hAgxDXiGK4+/vypfq9ux8ffQx1cmMM3ajusJ5/9i/rT+/JiZOEc6tSErfH4829VddxyPvT4Z1OkXI67r2Wg4sSFcyq3Z/2B/CjqmBXEUxFBDk8ndjKTw49YU6wLEymnjp0ek93QV1/W0l5aXaZMfG++SkzI9LYt3d1N1Ucv1rWbSCAcxwSBFSHgGqpva6q4UXbjRkVni35Gh2igdlRTN/eUlzTXDxl0B4u2r1sbI+XqmwY1t359rKbjuqwxMy5dTFimjp7WxkM1jMRPFG7akrsh0kesSSL9n6+0NBy53hmzVS3hcqfb0YpAQyUgsCABS095Y2vDBVPsJ4t37MyKSZQ6qfD0Ztevr/U3nyrvSdqm5ktYPsugqe5Q7ViiKG3dgfs3JAsIW19eev7atfNH2/uStFqFjDquYoLAKhbw2kbMneUX22jigqx9D9y/IRCehotPnWs9cvKthjUyES88zEFM9dculVeaNez1B7bvSY4Qsd29pd3i0qrTjW3yqP41UbFswghefBqSQxtXJM1/35feU5hQoJ7c27aW/tozP/3cb6/d7rbGtLf78pJoRBSoBtVJ6nV23LpdV3ekg8X0eDCebpIMr8tagPpiewxVJ88df+uFm2NZKbFsp3x2fVzE11F/vW1kTLblC7uTVSQwlEUeEb3nM0Unv9vQfvNqx8GYFDqno767p+etjMcfzo3Pjh4fSSdam7+pbpTR+Orp6w+v3Rqj4gpn54t3EFhNAr6h7sYRl1+w9WObklWJUqrqVDOJztu3ru1S72sXywfXbVVJWF67pa+jPqb48YS07MyJQTHKpMj41gOJv+nRf6hf70/hB++gupr0UdcVI+AxGYydLa2a4s0JqWvDxy+QUOWlZ7Y80vvadxrb0yLUxQKzv+XcpVYJLTX3vXsz1fzApRIspS52w2M5Z6q8BkOfjUSz7vnw9C47jCtgSlRqOoNPjHb3WP8YiaG6TwMjfqhful0lh65ev9LNSE9PbGoauzMk9y55YBEElo8A9T3uLj9tI6ydH/lOfrHzrWdfdPbPLL3HTUyDY06FkxuRqCCsO78TeYTExecIR4ZdLSNmj1foNvUbrX0kQivgcKjPJiaeVhcuNqXXDnisLupsA8LTSRi8rjYB6tIMs2HM5bdz0xOVvJnXZohkctdQUuOgzeGhmqIsPDPhkT+GsSI4vKlmFLDy+8nImMVMDTwjs5avNkfUFwL/UMDjdFgG+zwRieGxkcnUmb2Ji6XYSpZ6yyNfX0d4Ar5ocuE/zGt+CULSe3qXTdtMzpHeBp9XTzg6OlfIJYzxurnNwyPVz1+t6x0SxO/al8n540A9wtO78GHRshOgfnvJYrdtVfNk0jXqqK5yIdcza9ipx0X0A31OgZ4bppFNhadUq+DxRAz7qKNlaNTpJg6jxW7xxUWqhVz2xF8DCoLO4XKYNIGl32B2mp1EPd6puuyAUGAIvGsBqsuTw+UyaCz7sMXm8c4YQepy2K36QYt7wOKOcxElW8hTp82MQJ29tZ31Hec6c9MOyLXKpToOvusKIwMIhEiAKRSLInRRwxWWLk3DcFqBkjAcnYPdPTW1jPhtao1U6HZ2jPQ3uKTZbDJqL3vx2bJ+i50aoiZnspK3PbImXiMJ+rW6IWmWXrdzuKWqjj3im/pzMdbQW195y+G0h2nDIqMiqZHplLHLaOptuHTkaJ0rR5i14cBmXf2rR9oICdxgBxMElrcAdWModcre8dEtjlHqEqe5k89LLAa9m2kW8qX8GeOwx9NZnO4+o9nt49qpY66DGU0N/GHOaapuPzGYHZ7A7agQns7FxftVIhD4OSdXKbmdhq7Gss5CiUbCkbAD42qMvV39Ax09PtGozUf9zCNT92lzmeym4YZOvaHudGXVUB1n1wFdeKwycCIPEwRWswBDqBDHZq/XNHb215VeCPNGEqatva3FPMrN35AUGafke8Yc5rEuj7XHMORuIYPV1Z1mm9tjY7tNDTQNw70xPSNKSv0CDOIomTnHvODsHbtRf/k3/3GVTptRUL/f5/N6fYkPpqdvz46fqMNoXX/N6WdOuVR7N2/ZtbFI0tmFkafB2QPIBQIQgMCqEFDrMtW32lynnjmdmy6UKNaHUz06xvqbN5qrGwkpnEtguN13/fUvfP9037BJnrZpzdO7kjTSOaPC566C9xBYDQJsFU+79Ykv0d989tWXvvbH39KIl6Tm7T/46Le/tknBlLCIeWxcoeyvdTGPytd+7ls/Ect5dOomU42vffGHv/EPDfkkn99IhXZBjCmDmNXMHej3eT1U99CMSSlRpe38yMHivJwsnZBGfIT0N1wrO/PybVv0QxvXrdmcLKR7gxl3z9g0ZiEAAQhAYGUK0DSFhdtoP2Sx/3LyZ88cJn/kUj04kVlrdbJ0afKVt51akCRq8t//ne/vcbjM5qHOrvKv/tr8xJb8rIPpiFFX5tcDtZqngHu4aaTm5P8dI7zI7U/++rHxSxpsY01tTf/9ldNFjx4oTl430XuY83BW1p4ncqQyAZPFoEl1aSkP/cuGmxdHOmsuV2VHpwuYwXvKRUjCUxZXEJ23PV4tUTONxNByrryrb8RDZzN4utzYyPAYGZNQz9ExtDW1NL1V3+vSRvdUX7pk4tKtveV60yjxegdvnH7Rq8/flq6Lig76cIZ57iskg0BIBegMIhBLWSa7x26yEy91gn7GAAABm6kRCVl0PpfHZHA8vdQDozxzroBi0YhYwGFycFoypLsJmd/7Any1JiF/G4/R668ffyIUFZ5qYqI9PWa2h+YQ8uiz2ghHKtBIizVUrZyG5isNvWdOXb+tEGo2p8upW2fMaIL3frVRQggEUcA81t1YdfRCt/OhgpSCou1xYYFT3CM9HIu7quT1C/VJGkVK0vjmVElhkTEpYXcOPCxhmDRhQ1LUSTN9tG/E7fVRQ2tmnDV/dwUMSXjKEUqyH/5M4MZS/G7ScdTxv8fP3mh12JtrbzXkqXlxEqWQ4SODHd3G4WqHgbSdOEb9m67GCOno/OO3j/Z8SUsTITyddsHcihJgsohcE8FpdrpGBsZImnJieBx1VsHttPkEdEGiWsFhilgSPnXjqOa+IbNT7iO8icOnz+Vye2kOXrhMxBZh4OmK+lqgMgsW8DlNVjfbINvygU/s5bLoE8dGd/0LL9U5uiQRMjFLyPZ5XXa7YcTJUXK4PCFnohlxpMqIrKIC4QW9qWtokKRSPSEITxesjxVWiMDocHdHxbmuuK9mp6+NU92plDIyOWXzwfY//r8+Q9/oaCp1R3sx3Ur1LnqpA9VkY2HSaEKhiiGg0/1M6p6nQYtNqSJMbiJExAINSXrsCx+67307UxyGwYaXvnnqUsnV/hBtDNlCYPkIMFhEqpGxR7jO7gE9cVHj5QITdYObttZKy3ArW60UMZkMoVgrEWhJT5/N4aA+m5js/Z39pr66jHCWgD3z+aiTn+MVAqtIwH775PlDz3361yW1g+apNjLQXjlMBplb1ugEXClx6DtKL/3k6d8fK73YPpVkFRGhqhB49wJ8sTJh7R6+i+40mswkMEBzfHL6faMjrW6/hRMmF9Lv/Dx891sL5BCS3tPpotFZhCNTpW7bWDg42HHrZF1/5akbMnZU+kfXhKkLNj+gkqTeP5nY5qJO7v/5ZG2/wBuTuef9uXn5KWkYDjSpg9eVJkDjEIYuJS+6//roxT+dX/sveXydmDPWN1zx7HWnwhuR/YCOwWcTVnRKZNfQ+pderavSKqTSwnA/sbVUXL3V2OxcuyNfIxNNPZdtpfmgPhCYnwBLIuK6Rmglr9zaFCcWSZK5Y2So/GSps90Xvfu+eLmQwyA+DpunDWO/eaXE7BDERRYm8Ambrh/saCp7oUyQ+J641GjqFhsh7qqZX2WQCgL/HAFFWFRMzvboVy9VKsWCxPDJk/u3Gy+/WW2J2yPVKtQCGSdlb/G1E8P9vtMN8XvjeUI2zT7Y1lv2h+sDCmFiTGIkfeKGocGqQYjD04liShOTs3IfGCpraWtuqau8KVPHbY/bq43PLEzOLJyqiN42WkU7dq2/X+FWF+x632PJHGbgCSCYILAyBaimp9Dlr4s3XL9y9M3Sy/qBFhlvpKv/St2Y+j0pBTnpCkKFnnRlbGTc4IHY82XVNy7ZRqw6PzHXXm+yWrjJ+4vitNS9kVcmDmoFgfkKsJXxMVFtm2WVdWXXnCPtPTwD6a2qs0SLk/P2psnHR78w+JKI2ML9cZ2tfY2Xjp2xpgsJhz483NxeO6BMezR1bXr41C0Q57tVpIPAihIQyaJS1uzbcuWltu5K9yl2e3hgDOlgX01L/VjYml2pqfFKCXWuTrV2Q2pJeVdP49Uz/C4Bl0mz9jb2lrTYYu5LzkxJkI0/ayp4LEEOT2l0BoPJoiYGdVepGYMQJIn5qXT/zle+57E23x6U/++RjZnviddEzrnag05nMZnU83OYgQ7iGWsHr7rICQL/BAFqQA7VMBhMMvfMBy9xV77byRv94nd/fapthCoZ1Ymz+99+vmXftoTJawKVmuS89/7og31feu7UG02/Hy980oNf3n/gvQ9R9/DABAEICJKSCzxq3uiHv//rE4FWRF3jlPm+b3/6vj05udSzCccnpkwnKf7sJ8nPXnjt1P9+ZaIZEWXGluynv/dUsSQR9z3Ft2jVC7DCkjWbIr/I+OmvXn7pO891TXiEFzxQ+MFvfqNYEi6auG5fkn7gk+yzL1j/9OVv1RBDYKRMDIe/9z9++/CWvEgqog3uRPNTj3UL3mQfvj00oh+0suUxaSoxTzx1M2TicttNg/Udoy63jSumK3Spap6YOusyPbm9bstQQ8eIleUXK2NS1Xw6Lcix8/S2MAeBJRTwuYltqK3XYyc8XbKKuq541vfeOmIdau4YJfbA4yioBiOPTlIrFPzps/Y+F/EYupv7R002+3ip+WE6RZgqUoL2sYQ7EZu6lwXcVo+VOnrorYHHVFDtQqCOi1TKRaLZTcRj7B4Y0veMTjQjwhJIReHxVDviU7fBwAQBCFA3BDV29wwZBsbuDNFmi5UStS5KymRTVz3dmTw2/cBYf0+/lXgC40+5dLqciuekIk7QL9MNcng6WQG8QgACEIAABCAAAQhAYDECGA6+GDWsAwEIQAACEIAABCAQIgGEpyGCRbYQgAAEIAABCEAAAosRQHi6GDWsAwEIQAACEIAABCAQIgGEpyGCRbYQgAAEIAABCEAAAosRQHi6GDWsAwEIQAACEIAABCAQIgGEpyGCRbYQgAAEIAABCEAAAosRQHi6GDWsAwEIQAACEIAABCAQIgGEpyGCRbYQgAAEIAABCEAAAosRQHi6GDWsAwEIQAACEIAABCAQIgGEpyGCRbYQgAAEIAABCEAAAosRQHi6GDWsAwEIQAACEIAABCAQIgGEpyGCRbYQgAAEIAABCEAAAosRQHi6GDWsAwEIQAACEIAABCAQIgGEpyGCRbYQgAAEIAABCEAAAosRYC5oJZ/Pt6D0SAwBCEAAAhCAAAQgAAE6fQFdogsLTz0eDyJUfMMgAAEIQAACEIAABOYvQKPR2Gw29f88V1lAJDvPHJEMAhCAAAQgAAEIQAACixZAeLpoOqwIAQhAAAIQgAAEIBB8AYSnwTdFjhCAAAQgAAEIQAACixZAeLpoOqwIAQhAAAIQgAAEIBB8AYSnwTdFjhCAAAQgAAEIQAACixZAeLpoOqwIAQhAAAIQgAAEIBB8AYSnwTdFjhCAAAQgAAEIQAACixZAeLpoOqwIAQhAAAIQgAAEIBB8AYSnwTdFjhCAAAQgAAEIQAACixZAeLpoOqwIAQhAAAIQgAAEIBB8AYSnwTdFjhCAAAQgAAEIQAACixZAeLpoOqwIAQhAAAIQgAAEIBB8AYSnwTdFjhCAAAQgAAEIQAACixZgLnrNu67odZocDpfdfbcPaXTC5Al4bC6bQZv83O/zeB1Gq9Pv9k4uol7pTMIRiLnMGQlnfIpZCCwzAT/xuRxWr9dP54i5DEKmvv+EeD1Op8NscxHiC1SK+rnI4Ys4HA6TSnZn8vuI32Uz251u70QrYXAEHC6Xz5qRzWRavEJgBQv4PQ6qFVh9gWbEmj6MEOL3+n2BNuLy+CbaCJMrpFoRb04b8TrsDqd18vjEYLGp4wyHQWbmtIL1UDUI/AMBv9/nttmpEM51pxmxOBwuFbTRZx6z/F6X3Wm32T3E7w9EazQmTyRgsRj0oB+QghyeDpb85tyl0jdu3Q2BKyMJ9z91MH9HToRg8nPnWGfP2W+9eNV8q2dyEfWqjCVFH/rKDl1BlHDGUsxCYHkKeO3EXHnh+f4Bm6L4K1sjCeFP12Oo6/qlcz99uYQQQ2ChgpCiJ768fUOhTj2VxjNGTLcO/exISW3XRCuJ3vrUxq07Hs6YakZTSTEDgZUsYG+9UNoy8H+G4q/viExXz2hGrmHHYPnLPz1S3jHUPw4Qt/fT2zYW7UuZkYZa3nfl7OlLfzxWO2GkTS8sevLLO6LIzJxWMh/qBoF3FKB+/lmrX37ldPnRm3eaUfqmbbuf3pctIoLp/hJrb+XxG0deOtJCzFS3ijSek7zvXx/PXhMt5b5j5ov4MMjhqcvUO9zd2Nh4t5Kw+GTQ+4aC6eby35MmG0/hdtnH+m43tTQaG2eGpxoaibeZnTM7VO+WIZZB4N4XcI9a+uuvvnH49DkOTZeXc6eXlCo3dYpB33jyVGVZZ0fc1twYDpfH8Frtjs6WmrNC6tu/a2cSFasyiUnfVVfz4t+aHDpZTnKW2kfsHR29ZY1n3Vfk78lUEgn73idACSHwbgV8Touz8+q5M6ePtdNuR+XYXOMnG+7kahhqqqp6/VgLI1ZTkJUjd1NtpKXprXq/UyHdR7URPnWU81qohddOnG/s9Kjy9mcqCNfcNGjSn/jzYdn7inMTFGq0o3e7i7D+8hbwGLuNLddeP9zY7tekbs2J4RG6w2q395T/6STjoeLEcJGSFaigvubIzaraS5bENZtiBBy/Ta/v7njt2A2ezZe+JUYUXIIgh6cThaNOmsijU5Rirmi8PoGFPrvLOtbTWnHrarxAGrMnTcYjhEEcbpd5sMtvt0glSmVknJxaGBgMK9eRaJGMF5KyTZQQ/0NgCQQ8xt6h3pq6ypKzpyqr+5IidDO26XMQW3PF2VvVozLlx596MEOgFTI8pi5b7Ys/+FVFlY0Wvz5JxCM0e09/S/2h4z2yjzyxcWvBNp2PWGpO/e6v19tKjlZtUa2TCOWs6Z+1M7LHLARWioDHPjY02l7Xev3s2dLqcnsEiZpVM6+5s+N2w6nLetlHPrqtOK0o3EEstW/+7LlbzTdO1a2LXCflChk0h8HTV3KxfMCiLdr3xIe3RxCBvqz0wpWqP71WmhsllovUGsSns1TxZpUJeO0jbd03jlxsS0jcsePBh4syhIRhra86XXrqtYtXMhLZPK5S4SceY+u1q7e7+Y70Rx58NDNS7DPdvnLr9V/+4WatjCfPihBJWOMhXJDsQhICcsXy4g9/60B+bI5qspi2loH687/8jxdu1HVZI9ran8qII0RAbG67YbDB5zBmZd5336e+s4daSEWohEYjNEYIRjJMFgavEFgSAVvDoWOHzvz+fG9qcipxyGdt02Ej7TW1Zq1emfp4gVga+FlGmGK5uHBP3ss/azbV13aQlHjib6/v7O45nfnU9wsS82O5gRFAkvyiLU3m680/OHVtd2JxpFwx+/zlrI3gDQSWv4Ctr+rY+ed+/0Jtqiyc6BJI6+wq2ZtvtQ0Zr2U+9oN1ujWRHELjEEnRll01+hvDfzlfdl96sVwoYlpNxvrKFmVBVEp+cTThUu0oLDd5rf6zW1/4SVtzmCp8g0YzO1e8g8CqErAbRvtvN7Rpt30sf92aNaLxwabC1KS1I3RX/VcaujVyca7ERwzXrl+X+CPXPHQgRy2gUz/pFLrUDY8+WvmfNS6p+lZRUrGUUANVgzWFJDwNBJhMJoNFTZPlFEp4Mo2azuD7jQ6nfsBIIgVEYB4w9dx+y+Pt99ePlY0+87kT1GA6esKmxPzNn1mvCf4428my4BUCoRewEzJw66zFR9v4+FdS1pGavx72jc3cKkdKdHvf/2mviyWMoxPOnY9ohE6nEz/N76NGnVPjzq3GfqOl3xexV8Dj8e+MPKfzI3ThEktS3YDL6rLNGsk6cwOYh8CKEOi/1Tjku6p8/GPfWCfs/2v94Nic8NQ81m1yjvjDtSIOOxB3UhONLoyO09b44xqHrE6Pg+oKCTQnn5/QaVT7ono/xtPQaHQmnWpo1D+qqWGCwGoWMNsNpuFGv7RYLBLeaUZUQ+LwBRKFgjSM2c1Wm4vOH+nrcAhYHKlaSrWdABeNLWEq05Piz/QJBkaMxCcJpmGIwtO3FdHlcFsMfX6fhdBFNAZVMaqH1GMeswz29Pi8NjJqGxjVD9QHVmsz95q9meoDayN4yhnDcd+WIxZA4F4WoI6ALHF8VrowTLE+Jr6v57TQOCs8ZXCIOCZ1zewquJ3E2NPr4o5ypFq+n0F3GUwmu9Wp1aqFHPbUSXwmX8hns2X6XrPVZXGTiSFBszPCOwisFAGmOEyXni9QbN0S7yz5/+3dB3xb130v8IO99yQBggT3FklJpAa1ZUmWbFmejeM0iVMnzutL4tRN4ravI23WS7Pal7SxGzvD8Ugcb0m2ZO1NkVpc4t4EN0Fib+AdkOKQLDmWDVoQ8bsffwQQuLg453vu8fnj3HPOfW/0qmpER6D6bZP2gDeYZFAL6ezhmUyzRVIRiyWZGJl0BV1BIqVLXehTNK7u4FBSp7W4UE54wVH7+FBzK0NdKtdIMctwBg6PCSrApFesaaNEl8CIdo3MbPSXW9jnIz0j7kmXzc9ljg5OSjRqpVTFpYMzpzYmj/CUcpm7nzjGJnxhI33jSj/KzDE++uOChKeRcMg1NjBiYffS363T23hzb0N9jd8/IdLkKnTJEkK7hb1Ou8M6RLPPFStFIqGEyyA0hh2vHzrle16/TLLNKBeJFiR9M4nCIwQWTIDOYjSWPEyn6dMT3TrVXfPnvirsD9hGbBfONQdU/mSzURHhsNwuZyDo5mSq5ULuNVXBH4mM21wBl4+GwX/uyHgfArevgKakXEPKp9Lff20uaHjqdtgDET/XrJLx5qLT6f284bB1whny+AlLKBNnLStkv9TVX1d1aYkwlYh8re1tfXUWU+Hdxiy99NoD428IJJaAWCSX6XO4rWMjY2M2j1HFjy4mFXDbJofb+oPtbI/NYwsQjnUspDbx1SI6B+qaa/geD22/PJFILMdwX9PmxaZAvHbrqef+pZbPoUvKXdlCvoDXabV7jRvz8jYsMUenJJNx5+jkWAeNZY3rH960ceP9uUzSs+83rx/90/GJht8fbM3fkZoqwoCgGUE8LnYBb89A0/Hnf3ogUPHlpetXLpcS+j8IbBCAQAwEOAqiWH3P44Hje4/v+e6X3uWQYCTJVLB8w/d+Xp6qNcR4wnEM0otDQOCTFRDIVUk5eel/2HvoHItnytiwVEq7QYf7W1tOvNrisid9som58m0LEp6GQ0HX+KDrqgzJxcqcdZ9bX16xuixbMR1gi1JXFO0QfrOYiNKWmc1pJlWYKEoLT7c2BOqarF2jNtekl+hjvpTWVanCHxCIA4FIkLg7644cPHy08ZTxrl0VS9blKYWzP+3iIIFIAgRua4GQc8TTeeztY66JcN7aL5bSq48MEg7YXLbXXny15I6Kkqz1GehAva1LGIn/mAJMnjrTsOrhv5g4erH33d/86OQ+OsmQJKlYHt2mfPaBWxOHLUh4yuLytRnFeoVQxnQT12Bdx6jVzuIK1aaKHcuKdHnRWcp0cIPb52X7fEatVqozaHQKuiBBkCh0GqHERILNxO72BehFGXJrWD5mSePjEPjQAmFPyD3cVX3k6OnW6jG5efuuihJjdnQ8Kb1wyeFymUxOaNzlDYSuuUUFizCEfC7z2mv+H/prsSMEbn+B6AhvHo8OmwtMuH3B0PzFUGnm2AyGQMBlcFhe11BXxzuvVfesT6lcs+7hYnpRjk3GLDXHTp58+61xPZMvX5YRHX8as0Fzt78scpBoAiyxTpq1dutWW/hkw+H6waFo/jWqTLl5iZHbIGHzOXwWiysQMdyBoMtPx5TNDVCdkuKwWSw+J7ZVaEHCU75EseLRf763PH0Zv5t0vP7XP37vRG2f19fc0DpSbpDlyIRMBs3aYMu+l9/6+Tv7woU7/uHxnXeVl8tpjqODcsM0iwwmI7ol2hmC/CaaQCTiHXb2HXvlF2+ckqzS7vj0T+9NF3CmL+rTf8VSGY8rDjYOjjp8tHdn5rdatJrwCFOvFHMlM68lGhzyC4Ho2tlEIqdX4/iO5uFxT4A2IbND32hLImCytBopW8QbHx9oO/j7RtO3nli2vnhqPDjFUxuyinb+73V7/n10omNwgGSkTw05gyoEElSA3j2bweLl339f4QMPzMRenq4THafr2elpYpVIyWVJdUmcQbdXZ6fTfOlCiVNX+KIhWyTCEAl5PKUotgsuTTeEC1YcQj3JfOCJz29/aGOOb3Kk5U/fPXCy6kw0LKeBp0GfocxZ4WFzmk40tJy8PEJCAdLX3DYxdE4kDheUpCbJDVjRccFKBgeOCwFXa8vJfb/6we6R0s/c8+mHvrXewGNf9ZtMJE2SipKIZdDt883OM/QM9g7ZBy7n6zgiLqpIXJQjEnHrBCTyFAlPHRkccgXoyhdXNndfp8U71pajFfDY0bW0sUEAAh8o4Og92/DqE//06qm9TVM32I7u7LaOWjqaO00ZqUadWsjlEZU+jeuU+uyjdnLlWoXfFrY2tbbp7A69WkbXRfzA77jJN2N6sPd/N5tPJKacsg0bVhatNXsDg43nD507fbJtlDACRKA2Z2ZXFJs4blfDsdNv/P6553773IvvnWzs88qlBWvK0/QKGYbfvZ8UrywSgSAhY50nT16s6upRriypXLWuLCNPK6BXDebnT5CcmaRLLmp7r6N1oG00QMJ+4ulsvtDY3j2ZUlmklonQeTqfC88TUEBoyjUo5FmtR+jVuW5rgIQ89H5s9Wcb+kc9xhX5KiGfRyQShb5obcpYa09HY+84vcVplMlhHew9t/+yQyEV6eS0K2iB28IELBlk+XYSYDNCnKC96dSF2su9fd7o2DL/YH17U//JzpT83OTUJBGbIyXKkuIsByfYerKqe9IbCBK/Y7Sn5fj+el5qRG/OltLxNLHM8oJc3L82gaqigiXtDw6d6h8a6a25WCPQ5603rpTzVMl55tKtq82jnu7zlzvPTK16SoRyjbksb9v6IpOaM3ud5toD4m8I3OYCkZAn7Lpc896Jqg6mb8d9qWJPZLyjmbacUxtHKBUqdGp6Ww59pjFteDvrnaZLtacZYU56mNgvnq4dGAqatq4tSJLNXcu8zT2QfAh8RAGeIc+cMrAufLypuo4TcEUMXuK4eKJ2zKEo2bgyRyOkC6/xZPrMFQ+tOfmHrs5z7OpUN72+zyFDltrGU2cc0s2p5my9+iN+OT4GgUUiIJAnG3I2pB9smmitPVbHK5UQb0NVQ6vHIt54d5YmRUWnQ3CIuHDJSmnvub5jR47UKkqTJGFbW+3FY032/E26QnNGrK/lfSLhKb0RY9by3MhjG3b/4pD9cotF+tM3l/3srjSVPkWbtfaLXxvue/Zwd03PdCFnrr13y0OP3p/NFiM4XSSnPbJxHYGQy+aoOXhxtP9E51jk2b9t5DLnL2asLdlSdu9XHlsu0YpV+uylD/zws7/6yTsH9/3qRVpfw/6ktV9Yt+3uezPI3MJt1/kGvASBBBHQmkoqdv6da+jHL7y5e+xZdoROyjfe8bUtd2zenkb4U5fg2IpU6aqvfTn0mzcOvP6dL/3XVLMXkpmXZn7uB0+s1uclYVn+BDlVkM0bC4hNwrydX39g6Pf73/zFk8/Se5NGAmXLtmz66g82Fcj4szNzkyq/WOl/zf/KM//xdxxXgEQkaYz0z3xrXenKnKvv2n3j7/nw7zBu6n5ufr8/HL5mduRV3+Xsq+7tG+yyC5ILV5rUEtXcpUevzzHWc6bB4vHZRWqWIX9lqkQlZJOghzh6zjdZ+ked0wdSpeUZzNlp9JavMe0lviqV+AMCn6RAyEdP8trWgCMiKagw0TUWaesYoTckHW2q6xwfsM6OKZ1Lk0BlVJsL87RcAYcugOMhvpGmCx0DY47pSiJJKTCaUqdm9899BM8gsOgFXIO1A1ZHM6OANh/q+fdsCdF7Qw03nW8fpjdZm1KQmUtMRkO68qr+l8BIU2fvQLPlSltDb82oTC/N03IkPFzYX/TnDjL45wUi4SCtIy3dw53D09VIr09NySmht1GauUdU9BgB+2DnYEdzxwQJ0GCQJ2MpM5bm0jmIvKsq2/W+jc5253K5H37Oe4zD0+slCa9BAAIQgAAEIAABCCSuwM2Gp/jVmLjnCnIOAQhAAAIQgAAE4lAA4WkcFgqSBAEIQAACEIAABBJXAOFp4pY9cg4BCEAAAhCAAATiUADhaRwWCpIEAQhAAAIQgAAEElcA4Wnilj1yDgEIQAACEIAABOJQAOFpHBYKkgQBCEAAAhCAAAQSVwDhaeKWPXIOAQhAAAIQgAAE4lAA4WkcFgqSBAEIQAACEIAABBJXAOFp4pY9cg4BCEAAAhCAAATiUADhaRwWCpIEAQhAAAIQgAAEElcA4Wnilj1yDgEIQAACEIAABOJQAOFpHBYKkgQBCEAAAhCAAAQSVwDhaeKWPXIOAQhAAAIQgAAE4lAA4WkcFgqSBAEIQAACEIAABBJXgH1TWWdMbTf1EewMAQhAAAIQgAAEIJDIAjR+vKnsMyKRyIf/wE3t/OEPiz0hAAEIQAACEIAABBaxwE1FqDcXni5iNWQNAhCAAAQgAAEIQCAeBDD2NB5KAWmAAAQgAAEIQAACELgigPAUpwIEIAABCEAAAhCAQBwJIDyNo8JAUiAAAQhAAAIQgAAEEJ7iHIAABCAAAQhAAAIQiCMBhKdxVBhICgQgAAEIQAACEIAAwlOcAxCAAAQgAAEIQAACcSSA8DSOCgNJgQAEIAABCEAAAhBAeIpzAAIQgAAEIAABCEAgjgQQnsZRYSApEIAABCAAAQhAAAIIT3EOQAACEIAABCAAAQjEkQDC0zgqDCQFAhCAAAQgAAEIQADhKc4BCEAAAhCAAAQgAIE4EkB4GkeFgaRAAAIQgAAEIAABCCA8xTkAAQhAAAIQgAAEIBBHAuzYpsXeeay9q7dx4HpHZQuIOm9pQUpmspQ7936QEFvXyUtdXQOWqRelqUUpmXklSTwmY24nPIPAIhXwO4a7LPXVTePE6SeEJyWqvJXFyakaMWc2wyE38Q3UnmzqGZ60Tb0oz1ialp5ZpJ9XjWZ3xhMIJKBA0BFwWi6dbLJMOB1T2VfmrMwwp+Zq5qpR9OXJtqa27nPNQ9NCUp3JVLouS07mVbbpd/AvBBJSIBKibU1nfXtrc/8YIRFCRLp0fc7SJUk8EXcuIPOMNA13nDvXQzwBqiRlsU3LNmUZtGJRrM1iHJ6O1f7xwJv7njlxvWQKVCT3gS9//s4HZXlm0dT/NcL+gG98cqz+2PPP7TtYUz31oZR1j6y757PGLRkKPpODvt3rQeK1RSFA637Yax/orj1y6KVfHx0STPqYDJEulLo5xF7DKUszSnisaD6DAeegs+3A/peOVrcNj3MjJORVlz+yerMgZYOZNqts1JFFcTYgEx9DIOi3943Uv7fnt0frBicnOWFasbRr/Js235G02kTrCIs2rLTdDXsmm48ee+fUrw710BeZIbcya3l+KP/hZfJMFYeLevQxCgAfXQwCIX/Yax3uPn3yneMHD1y2cEg47JVkrMzaKFfekZGm5vNZ0TbLMznWU3e45uDzf6wVOL2MSEBJgvl23cPrKzKzRTGuRjEOTz+okLyTpOmVP74ndvAU39mSEt3T2ztcf+zX33upqmuoZ+aTQzV7qgI2renHOzK5ZunMq3iEwGITCBHibNn3m3dPd+0XfemJfynPTZaxbf3OulefO8XsHw985b5CCSEsMjbUXLPnm78e3PDElk8t3ZoVJvaaPc8f73xr9NWU7+xII0kx/8W62JyRn0UvMNxz/vS+f3/LuuGJ+1bkrjV5iK3mlWcOd+y1vp38zbvSiIJHSMBKX3z9hQPd7NyHvv2vO8xEMnLs9OnLP/vRz5P+5QvsZWnZqEeL/jRBBj9YwNHjbN77r7/Y70+9Y9V3vnVHGmE7L5w/dOq9F779rvbHm8pSi9X0Wrej4fUf7ql31Qu/8jf/vjxFKvB1nu448LM/HEjyBdnJW7JpmzXXy/rBX/ch3l2Q8JQnluVv/WypWZ1KEzu9+UdsA02HXzvTdbGtP7mrf0uKhhBfX0NH9dtnuvoCeVvXFhevNBBPx+Gj59rqB/reqetbpkk2SwUzn8cjBBaXQMhH3K2djW6H27Rq16bCvOQ0OY/pFfvFm0sGjo8PRqothSu1ROK0jPQN7e3PWZOXW7osM1UZIT5RZXlfsGHy3cOXSu7LVInEuMa/uM4M5OYmBcZ7LH0TR0Zz1pbmLinNTJUFiFe2vqLjcLf94ImGck2mmMcPTQ6Onn7xvCBTkbP2rqWpWTLC1a3zeII7G1+62LZGo1Vk58lu8luxOwQWk4DXOtRRf+Joh6h0eUHFhpJUs5ww/TzfQN/w5VPHu/rMJmWxyENGTx8+7xjgZC7fuK4gM1ktYIeENkWg8vDzg462/q7V2QVCwo5dfLog4SmHL8qovHvLisxy3Uz5+bqGGg+PvHvROjDk6unv9REpJ2Ab7OlparEE9WXL79i2646daRHXZbFUWy/u5xNhkMcKz3wYjxBYdAIhL5no6BkWejnpW1eZNRISrYp8GT99TYnqzVp7W63FX6rgSJwTrkn3ZZJ/X7IyST01JEaQlp5tahl3Nzd2Tmw1BgjC00V3biBDNyVgH7fZAx3MnIeNMq2CViM2Eabn5Jsu2UfaWrrtPlOQsL220e7zZ+z6OzNzigqUU0eXpKZkZN67ivkPQ3T092QgT3b1MNWbSgF2hsDtLuCaHB5oqu6Wrng8Lz8/RzGVHZ5en12yYktPD+GKWPRSvy3YXXPZrubnF2xYbpLzom0WW56sW7JrbX57WCWIxDpkW5Dw9DoFxRWyJWo1kyUgNq9/csgWyZY7HQ7v2Ig0HNlQkpVWZGYHI4SX/8CDBQ89xGJFRwthg8AiFggGyMRIv483LpfrZIRz5YSn9VGqUHDYXv/QqCMQlBMGg/7HJKFwOBKhI3+iu9EnEfo/AkZ0W8RAyBoEPpzAVD1gknBkXh2J1pdwZKaGeH1e10AfSU6WJUnFswcVybTmwo38rpDPbncSQrtPMQB1FgdPEkzA4Z50jLeylz5oMKuloUBgOtQUpKwuTl1bwoy2PP6h3slhSyC53JhmyBYHGaFIgI5QI3KiXH3f369ZiObokwpPJ4ddPY3HAv4+Ii/gKpLkES7H5hh2j1q44Rz9ZMvze9sGqy5Fz4ek8nuWrd/+QJEYcz4SrHokWHbZHKLUm3iXiX9iyEZSxUQYrYt0cI/Lag10DpBmwbgvKCaaFLWhbRt5oaNxVUNKckoGnS5laTh5ubPWUVRZROdK8hOMDdmFwLUCenOSvnVN8MClS+t0CmWSif6Ms1w81DhoEeevzdfw+Txi9TpsA3VEtFokk1xdY8Jh0jHmNjom6O/Ca4+LvyGQMAKuCY+LjDByc+TjXfuevXTkOJ2qToNPVV5l/h2PPFgkVgmZfp9jdKDOL6kkrvaB3XuefqdzIrrcjJ7LK3/kqQ2lOVpVrLUWJDz1e5wth155u111cfaXqrNvvKe+w+3l55hNRdmpXMIn/qA36Jt0RQQXaquaIs6Buo5o5pRWMuYOiTh3lZuEOvHU3OVY5xnHg8CtF2DxiSIzNfnccF/LwaNt5rUpIiWf43eSiYsXOyYuDKhsBn+I9pfydPqcovsfLz/bVXX+9429SbR/Z8xpk4lKyh9akUSXaEMNufVFiRTcWgF+sqm4eMfDA2drD57qPdOspeHpuCOYoi4tXrZUpxTSjo5gOBjwTNJRcWwO5301xukLegO0maUfwwaBBBUIBkJBl9M/WX+w2axhaYuLC2mN8FlsjvaGN/+gCO+oyNUpQ0GfZzLcW9Xvy68TGszZgpRgyGednOzYfeQNtntT+erlKXRQQAwvQSxMeOqy1+95tv6qcuawuWKVIa1g87Jla3KSZ9/y2Uj3oQ6NQSbNz88LE9/EyNCli+86nfwCxT3pCjHG1c1K4cniEqDhqTgjo0je7ujYf+DARVmZUyflBybJRFPTsGPQo6KzjaNbgMmV6nR3b0t65q2LZ3uqokt7hHI2PFS2fGmeLMhjR0f7xPB/B9PfiX8hcDsJ+Fl8jVF/x9rkp9+82DRyeqqOFN75+bLSomxpkM2M+Yi428kGaYXAhxbwBgMj3dUTGV/avuHTJSm0ZXHU1ux+69Xf/mG3KIPHF6yenj040DgmyreaH3jsPrGMz3R0H+/Y/28/evmAPyzQ5iYvFbNiuGL9goSn1+PQyHUVD/3T4xvyU7IV9PLKVb9Ui3c+fue2rVuSPaTzzf9+6cDz71kbfvteS8m95nSx4XrHwmsQuP0FaC+ONGfbo2zZO/zf/fx3/8od8zAZmnSy7suPpB+XhsnB6RyOXqw/eurr/2nZ9eRnHvx6ZraYXm+xN+157ugfjv2P4KHvPL5iWbpKePtbIAcQ+OgCQ1Vn9lX/4I/2e5984nOFyWYhHSFjr3vl/x168ejz6vu/+/jK3NkZuh/9O/BJCCx6ATlPWLrzb3atWZVJ465or4coP7ds+L6x7n98o7opTWFeNSWw/OGypds+XyYWTi1yKjLmZd//jfUH/ru1r/74pdVFFVLOvAX8PybZgoSnPIm8+O4vLs/QpXNGyPDZX+2ub+mdDIT6+yZYwRBbeGUaiFSkFijTJMy+osy0jPwcjUboI4KSAl1jccha7/AEgqFYzwP7mFb4OARiK8DkCDQpRRu3flGZYSVu2qoKxMSQwj3M9zt4mWopj+Xtba7t6upWbbx3SUFWnlGt5NDfdQrm8mXWiQvn95zv31loSlalXT2aLrZJxNEgEMcC9Neap7P+nGV4VLtuZ1luWo5BJmPTdkNZtLJ8cLKls7q2a7REIxdyRRJdLukKuR0uH70521yO6OxCk1ygFmNe1JwJniWoAJPB5AllQr6AeyUuZHKEMrnWqI/4QwF/kFa26MYT8wRCMe/KRTsmW8QVpyWlMyxsv9cfjkR7HmM2Y3dBwlMOT5i6/I61dGEpyQgZ0o84mXuP17WPdzce31+v3KKTZKZEx6RKxUqB2kSYA7QzmDHVIXzlkUmHBynEPB6dPIINAotVgFZ2h+Vii83HYRXct05CBLQuht3E3733LVHQoy4wyfjcgGVkaNLu1C9falJLldH6QGs+T2UypyQPaYcvO5w+Jw1qsUEgQQVoW+gbGxxw+EJJ5SUmpUgWbdBow8nTpmelqMeUI0MTzqArKFEIJclZ5LzPMWZ3z4anfq9rcrQ7qKsUqCR0XlTMGtUELQtk+3YW4EgFEp5OPRqIBqJXZYTBYhKVkCvkinkMjj6DYyEhn4+O1abN0UyVia6QweOyOQLuzFoZVx3hI/+xwOPWhFqSvuvLn9nx0KZ8lne0/e0fHzh6+lSPP0QYESKUyMS6pACXeaqrr6u5Y3LSOj7ZXNs0OniJRuZFBrmUdiVhg8BiFaAVfKD2j8+89fTv3mj1W710GlQk4rf7hy609cjdwcziTAmfy2ax2SwmM+B209+uoSsjYiJBv98fCATZHCbdFisP8gWBDyXAYNHpTrSOeDz+UHiujvh89PpbiM1m0y4hBp8vEBvShOOO8aFxqy80NbYsHLCPDzZeOhMUcUUKKb1p1Exb+6G+FTtBYFEJCI0qg7y4oMths0/aZjpKI0GPwz46Mkoy1BKNWC/RmEu2yYOhwMT4WCAyXdciIXfA3TvUGQ67hTqViBnTxQ4/kdbNsL5ieemX1xIZnzS+e+7Ea6c66A1N6QWY9CXZFTuLOLzet555+u8effSxLz/6Ly/vOd0pkoiKlhXpFbhn1KI6/5GZqwXoFcY0c7GUrxk5tP+MZdLhI17bcMepF54/r9SElhZXyBlCljgjf0mqQV/33K/PNFs6aL9PdK0Pe9vpI1UXLl4uKk3Si/W4sdrVrPgrkQSiA7hzS5bqpKLa379wunOsl7Yr0dXZbJeP7K9qaekoKE7V8jX0Ni9qY8YdjxZ0HnecOfBOD3EHCBmuab5Y/9NDRUWZ2UszYr4kTiIVAvK6GAQEWmPGsjWV9W+crT7VaKFX8mimnJdbLlS98UaHzpiaotOIRGqSdedW4QWR5cTr5+kwmald+pvbXv/JsdFkpzIrz0TY71sY4+PYsL797W9/nM9f89mJ5r2Xm9vrxySZa3flG5WG6f5PtoAvCIk5Pku1ZWzMPs5m25JzsmVclVjEFUgVgoC1t6+ntb1zeGR43MFNKS3esOsvtiwvShJKZ8Y3XPMt+BMCt78A7azhcPkhv981Wl/d39Ny4VxNVW3bKZs2Y/m69Uuz8tR82u/D4fG5HLbY3dk50FV7oaa+uurMmdMnunx2RcGmzWtW5Gs1ovevlHP72yAHEPhQArQSMbl8Pl07iufsvNzV1nC+urb6DN2O90WC+iUbN6woz1bLefQaBF05Rsu39QyPDBy72NRVe6bm9LF6i8+XueuuDYWFyWJRTJvVD5V27ASBOBJg0irCFyuIfWhkpPnsubOXzpypOn38Uo93UrN60+aVZekKlYhLuBIR2xtxj1saqusu1Jypqjp9sr76nFe2cnv5xtISs1xIR2jGLlMxDk89o81WV8TNNxeu2Jijl2pmuna4EolArmd1jLPk7FCSxinNWWmSaKQyvkSVma8M2YOMCF+UHN0K1+9au/We+wrFUv4n0rMbO0ocCQI3K8BXGcVsIhk4Xds+1N41OOwXeEv/8jOVuZXmmTXCeQqZQlZudp+/2NTc2NLfb+nvH7YZVueu3va1zWaFALHpzZJj/0UnwFeplaKCJMfZqvqO1vbpOmI3b1m2ZuNja00SOkKG5phJW1aNUcOw2ccuVF8cGujvH3Nzk/M2PvK51akCLSYXLrqTAhm6aQGOiC1NKkieHOhrO3mqjrY0/UN2RtKSgrs+u6tEaZDSYd00JOPIjHRtjAnv5UOnLls6e/qHrFw3b9OuxzeuKDWoYz1ChjF1q8SbzsiNPhAO+oLBUDBClz/msVjMefcmpbeYo4u6BoL0++g9GmmczqZDgmicTUfcRcfi0mn60yPr6EgiOt6OO++TN/ouvA6B218gEgmFgrQChKfGw9GqweLw2Myr1o6j6zZGgj5/aKaK0P9LRMek0t1u/+wjBxCIhQC9gSlte+jg0+idf6c2FoeOO722HaGr8wfpf1eWhGFEO4x47Ohtg2ORBhwDAotAIBwI0OlRM8sm0TrC5HC5NFabqyPRUI7e9fTKbU+jvaXReI62WXO7xMghxuFpjFKFw0AAAhCAAAQgAAEIJKgAOmAStOCRbQhAAAIQgAAEIBCfAghP47NckCoIQAACEIAABCCQoAIITxO04JFtCEAAAhCAAAQgEJ8CCE/js1yQKghAAAIQgAAEIJCgAghPE7TgkW0IQAACEIAABCAQnwIIT+OzXJAqCEAAAhCAAAQgkKACCE8TtOCRbQhAAAIQgAAEIBCfAghP47NckCoIQAACEIAABCCQoAIITxO04JFtCEAAAhCAAAQgEJ8CCE/js1yQKghAAAIQgAAEIJCgAghPE7TgkW0IQAACEIAABCAQnwIIT+OzXJAqCEAAAhCAAAQgkKACCE8TtOCRbQhAAAIQgAAEIBCfAuybSlYgEIhEIjf1EewMAQhAAAIQgAAEIJDIAgwGg81m038/JMLNhac0Ng2Hwx/y0NgNAhCAAAQgAAEIQAACHz4wnbbCxX2cMxCAAAQgAAEIQAACcSSA8DSOCgNJgQAEIAABCEAAAhBAeIpzAAIQgAAEIAABCEAgjgQQnsZRYSApEIAABCAAAQhAAAIIT3EOQAACEIAABCAAAQjEkQDC0zgqDCQFAhCAAAQgAAEIQADhKc4BCEAAAhCAAAQgAIE4EkB4GkeFgaRAAAIQgAAEIAABCCA8xTkAAQhAAAIQgAAEIBBHAghP46gwkBQIQAACEIAABCAAAYSnOAcgAAEIQAACEIAABOJIAOFpHBUGkgIBCEAAAhCAAAQggPAU5wAEIAABCEAAAhCAQBwJIDyNo8JAUiAAAQhAAAIQgAAE2LElcA81DA2P9U5c76gsLpEYM0zqJKWQTSKEuCd6+oe6BkcJCV+7O48QTXphkkYtElz7Fv6GwKIQCPmIa7Cpe2TY6r5OfkRqnjZ1SZJIyGWSsI8ErF1N/aOTruldRfoMrT4pVR7jynudZOAlCNxuAhG/KzDR1TIpZosUmUYZrSQM4nVbxwbr2mlb4702Owza1uhT9UazUhTdExsEElggEqKtUlf/SM+QfUpBLNPpDRlGJYewGbQhcgQnui73OSZdgfcbCVRGVXKqWcFhxa7PM8Yt3Ej1r97cfeDZU+9PPCFCNSn4yye/sPH+NekKJg1PB5rfffnN//fKe4T4rt1dT8iWJ39+/7ZNWcZr38LfEFgUAj4b6dn34tPv7T7VMS8/ERIJh0IkkrPBsP2vn77PnK7kRfzW8PiJ3f/58qHznd3R9jOcvuPrW+++74srFEwGGtR5eHgKARIJ2C2Tp5/5rwt5spwVT32mTEYIi1hHmo6+9cSPDhJimSOKRMK0sjEIc9uux+/53FdXp0f3xAaBhBWIkKA32HP47Rf3P7e3IdrURHJK79z5wN98eo2aSX/nhWx99rP/84vfN9S0zeuAjNAtFAozTOv/cv1Dj39lpUzEjdmvvBiHpx9UsF4baXn11YM8F0f0xCrtB+2J9yCw6AX4cmK++wtPrN75ec9cXj2jxHLsF6+OOgx521abaEUnZHyo5dzxH/5uKGvX5q3ZFakR4qw/dbDOstv5huaJdQaiwfWFOT48S3gBT89Ie9WfXqjvERmKc2Y1VPrCzQ/8KnvTVV0hI33nqk8+vXt82/LcskwDIbHr9Jn9XjyBwO0j4Oh1dp78ya9b3Umbv/LTJ4rEhDV48XzT+B++v1fx1LoCg1QmT5Wt+uo30l12T3A2V4Gxtsn6Pb/cr0pPKaxcIubQXtbYbQsSnnIEYnPFtqwkmV44k9LghGus5/yRhoHzLU3a3NFVOjlRGEpXr/8rSTIh03mNBL2TLfvqOsf7fCJNUaFeJZPMfBqPEFhsAkwuERvScwy0z2Zmczp6G1pOW1WmInPJ0vUmkZhDAqOdlu6OvWPGpfeXrVpdtFQbIZ6kiGXsVItl3+m27K1GuUDAmfk8HiGQwAL0ipx/rLO29dzJTq/AJZjftPH4Mr2pXG+ap+Po3msXBCdNleVrcouyFLMt1bxd8BQCCSSpXuygAAAbCklEQVTgnbSMtBwe5C3LyV2+eVVhGp8wJzg+96nmusNdI0v1CqlcKOJocnI180z8wwOXek4NedKWriwuLciRs+fXunn7fcSnsT3alURwhZKC7Z+/tzx92Wwnqbdz+PLRX57rcHdb3G29PcFyPkttqriD/nfn9IdCXt9E75mXaqxOv42RtuKB8kyDgl6XwQaBBBEIuPoGOi6+/U6f5MEHlq0oyqFD4Qix97cNDFrO5d796fyUfD3tTCVElFNUXjQSaHnj2MXRCrlZh/A0qoItwQXodXq/rbW5sbGufUSTZ+J7purPdVHCQeK3ddScrW0fHF752bLilBztVM267s54EQKJIeAPBF3+QPHGlcW5menTF+WUGcaUSyuT6vpGXGP6cIZw/gUG+msw7BlubG2q3VPHKHtiydKyNHWsoRYkPL1OInkitlSjZbKExOYNTAxNEjONPed3+9h73C17fnt0otZXlr16x2dWKYx0AhU2CCSMwETjicaaAwdzHvza8txVGVeu2bvsgzbXIDEkCXl8/gyFIMmUJHXkXx4OuPx0shQuMszA4DFxBcJ+V/+h/zxiMbanPfL3umN9jTemCDhI9979Vb46T9kjf7UqXcehU3GxQSDBBcSmilxdgZkl4bDnR2YkFA6PjjtcHj8hs00QpaIT2h3tVceqmwZb7njy8aKUAlXs/eaHw7E/+twRHRPuwc7zwcAwEXPZEqWYsK8ahT5uaak/8NwxS78iM3/Z5s2lBiGbT+d9YINAIghEgsR5ub2+s6mVvWT9GrNRK+PQk5/+PHXZbR6fk5mTpJHwoy9NbwwWm8UMcvxD9FKD433zCmf2wiMEEkbANeDtPPrKUVWAU3RnZYZcyGTfsGXze10jdSeO9LClwsKytck8BRctTcKcJ8jojQWYbB5HpBLzubyZ8aOezqrmuoEj/RU56Sqj5qqYlQTcpL+qutHT7jRv31BoUInoGjMx3xakhzLo9/RfOlblaB6ZvTxv6xzuuNDk9UWMRn16mpF/VRxOXJb+zub3avpt+q0riwsrC3QCJgaqx7ysccA4FYiEg4GRxo7RUB8jf8OyNKOSN1Uto2PpfL5Q2M/SSYRc1lW/5+iA7UjE6fGFfHSJD3T+xGnBIlmfjIDLbmltO3C4h1Femla82sxgD8z+lHtfAoJOz4TlUvUkN8OQWZqdMr8/6H374gUIJKKAZ9Q60l/TNORsPVjXxbLq1+enKPWSqxqgkM/lbD/R7uF7tcXb8xTKhRm7vSDhqc8xWfPSj2quKlgmgwbnQn7OmqLCtQXzh6jTXqLgQKdlsOsMjdpXrEzLTc+78aihqw6JPyCwGATouhwBR0ezhalz5q+oTGdrMBBuMRQr8vAJCYQDlu6mun2vXs79xpfLlmfpSfv0mo3X/fqId9Qz2tPQlZG+OmtlwfxZHtfdHS9CIPEEbB1959754c+PeHwBTdHG4rsLNVwOLxiJrn16ZYsEvI7uhiqX5m5tXsky6czLsX5ckPD0eolUy2mU/dW/qCzKzpubz093DBHibL10obW2gcvmVGQbzXROPzYIJJBAIBScaGtqZTBLs3Iz5Ezm1RdREggCWYXARxAYqdlb29d9evPX/qFAn6ek0wk/6Bh+68h4f2dTena2QZ2KfpAPosJ7iSqgKshcn/zznIfCEedo24Xms//6g5FH71tdsCNXMSMy6XX1NR4LaldoUtN0My/G/nFBwlM6cz+z8p48o9LAniDWxrdOtvcMecJMt09glMsUWvG8XuKwl3i6OlsHuro4bFZxYZoymd6gABsEEkcg6AjaultbeEyzJjtdSQfCzfxEpY8CoZDNFgS7rXZPgF4+md+tymEwFBIBWzD/tcRBQ04hEBWgQ1sm+mp72k43D7Kl+/7Udl7EDnsmfP3t3QOTvKHJF/zjFVtXZmrFqiutim9yZKC/s0ecvUGjU8nmNUTghAAErghwJCKVZGqqk2+SY+MMXHzzTHtXss6aq6C//qKba8w12HtmNDtVlpydvIBjyxYkPKXrnuZs/tQ9dGEp0SCxHLH73j1Y1Trm7rx87twSNccoSVbNjvgJ+shke8+gvcelZ6euytKLteJpAPwLgcQQ8DtC1q4Wi06aqUtL5s2bpkHDU75EJuGL2L0DI06fMkSE0+1pyOv2BsMOqV4m5koQnibGaYJcXk+ATh92BhkGKXMsP9zV1djVFR0r5g3ZJyadXpaTXcdTmlaWGVTimVVinBMjIwOdYymbDFqFdAHb1eulFa9BII4FQj6H1T4y4JKYZRKxgs7+iW48uVqfmZPNfXPUMWqjt4qaDk/DdqtryHJZUJil1hpme1QXIG8LEp7OpVOoI5kPPvE5hlLI+Okr51te/d5ByT/y1fftSJvZJRgg1uE+n6c/OUm+ocggEeLS/gwNHhNDwOcJWkc7grJcgYQ2o7N9p9OZF0n1UlESaR10e830duHTVyO9g31D9oHL+UvYIu7CDElPDHnk8rYXoBFmWvkXvlb2WXon4CtbwNrhqHr63y7kSDPLn3y4TMnlcOd6SW2ucedEJ1N9n0TIxw+7GTI8QoB4RluOVr38y0tl31tbXrIl64PuRuh3u5zOiXBmqlgpWLBxp9EiWYDFAOaXNIPOwOfwTGsrlhd/tiIiZHob9p8/tbumhxDa1tItFPQ7Rod9Xo9ExM9JVgu5c4Nv5x8GzyGwWAUCXo/TOhowSgVqkZxBZq7sX8kuPzXPZDRsbHyx7nzHhR4vXQiZ2C+cPX6hqdm55o4Kg0I6ex1isfogXxD4QAEmi8vjCedtAoGAy2axOSwuly/gcli0EZrZXFaXmzPByFApuELUnBkVPEKAXqmTytRpabqew0dqqhsanSRMV44hI90N9Uf+cEG3qigzJ0U/w+RxjU1Mdoe1CoFIuKD9IwvcezqdH7EhraBs03hjS0ttc3dd7QXt2w0Z95klBhEnFKCDgbr8HodExE3VyHmcTyQ9M8p4hMAtF6An/8R4d1BbLFCI37/APltmSs7Ivbvi7OmmMyesXcNJEeJua7KwIvqC7UuTdRIy1zF0y3OCBEAgzgUcE5NuxgArZamcLcCl/TgvLCTvExVgC9Vpqcu2Lu1tGGo9+uZrPQ1CwmKMjfeMDwsKV6/LLTQrZ2YS+t1Oh81qV6oVEuFV9w6OeXpjHA6yBAqJMkmv08oF7HmXVIgkdUnmOrL5HQebP9EZ7t1XPbxezY+Gp+Gw2+cUS8UpWnWaTjS93mPMM4kDQiBuBYLhoDfoURpVSjrT6TqplKvNxVufenjwB68d3/3OoakdzFsf37Bl++aU6+yNlyCQ4AJ0BUOmUKGUi8XvXyncGwhwxH6dXCuj42IS3AnZh8BVAmyFWb1M9wXiemHv2dee33d46k3tks2lD/6vu5dJNKLZnhBfIMyNMJJKDGqdZGGvQTAikWgf7ofc/H5/OExHo99wCziG7E6X3ccWqZKkAi5/LvoNhfwe++CYMxjycwQMsTJZwuVzmOGgL2AfsLrCQbZEpNBKueTGd/u44ZfiDQjcvgIhn9PnHB0javpLVHHd36L0nlIht3XERm8rR+8rRzcuHaQqkc6MXr99s46UQyD2ApGQP0yri5fH4gpUMj69sj83YMZvn7QHbB6WOknKZzNn29vYJwJHhMDtKBAJ06Zmwu62uemaGNGNLZAIpCpl9DZss9WI3j/Y5nE6PHydVMgVzt3NcPoTH/Qvg8Hgcrn03w/aad57MQ5P5x0ZTyEAAQhAAAIQgAAEIEAn/t5ceDo3ahx4EIAABCAAAQhAAAIQuOUCCE9veREgARCAAAQgAAEIQAACcwIIT+cs8AwCEIAABCAAAQhA4JYLIDy95UWABEAAAhCAAAQgAAEIzAkgPJ2zwDMIQAACEIAABCAAgVsugPD0lhcBEgABCEAAAhCAAAQgMCeA8HTOAs8gAAEIQAACEIAABG65AMLTW14ESAAEIAABCEAAAhCAwJwAwtM5CzyDAAQgAAEIQAACELjlAghPb3kRIAEQgAAEIAABCEAAAnMCCE/nLPAMAhCAAAQgAAEIQOCWCyA8veVFgARAAAIQgAAEIAABCMwJIDyds8AzCEAAAhCAAAQgAIFbLoDw9JYXARIAAQhAAAIQgAAEIDAnwJ57+iGeMZlMBoPxIXbELhCAAAQgAAEIQAACEIgK3Gz0yIhEIpCDAAQgAAEIQAACEIBAnAjg4n6cFASSAQEIQAACEIAABCAQFUB4ivMAAhCAAAQgAAEIQCCOBBCexlFhICkQgAAEIAABCEAAAghPcQ5AAAIQgAAEIAABCMSRAMLTOCoMJAUCEIAABCAAAQhAAOEpzgEIQAACEIAABCAAgTgSQHgaR4WBpEAAAhCAAAQgAAEIIDzFOQABCEAAAhCAAAQgEEcCCE/jqDCQFAhAAAIQgAAEIAABhKc4ByAAAQhAAAIQgAAE4kgA4WkcFQaSAgEIQAACEIAABCCA8BTnAAQgAAEIQAACEIBAHAkgPI2jwkBSIAABCEAAAhCAAAQQnuIcgAAEIAABCEAAAhCIIwGEp3FUGEgKBCAAAQhAAAIQgAA7tgSj55+vvlB3pOV6R+VJScrau9bnV+RqBTPv+239w2d/ta/W1TJ85SVt8aaC8nXbsoUsRM4zSnhcvAJjlgsXql96r44QRzSTMkKK7/xceUlRkmo2z0EbcbXsf+l4XcfQdC1JWn5XydKKTZmz1Wh2VzyBAARuLDB09njVxbdPtk/vockoLt7+2QodUfJv/BG8AwEIzBdwtTScqjn+3qU+QgL0dYmRm1b5yNacTL2EN3+3WDyPcXjq6K1qOLnv9RPXSxoNT03WEI+wxMI1RjHdI2i3jDSfeHfPG2+eczYPXfmItsPR42DJ+ZX5Or5CgBD1epJ4bTEIhGhEarlYden4xepup1fDDXMZYd9EYLTqzFGePxJZVZxMKwmLuJ0jHb2H3qqus1vcYZ4sQvyjrTUn/V5WsmpNqoQIY1yDF4Ms8gCBawXCXuIfaTl9+Py53uYxrklCOJ7B3qZgdzhPsj23KEUiQz26lgx/Q+BqgSuV6Mj56s6WsQCREMIkAWvfuH33EVXIV5JbaJRxCGFc/aGP89eCVEoGg8kRiLhsFns2vIyEwiG/t2P37oNar8iw6qEsJol4+861nXjll4e97rBQKOFymRES9tuaDp+2j9qk2V/foF9q5Mcwqx+HCZ+FQIwFIl4S7jz7+zfP9onCj33/6yukqXJ2YLzdXvWL//PsUcuAX1+wM5dJ+OGRwZbzf/zOW/Yv/vsdd667PzdMJk+//KMXag4OvpZd8ZkCTqqUgToS46LB4RafgN8aGTvx9utnhjSr73/qqQcyiGT44MF3Tzz1y2eMaX8rUuSUymfbqsWXeeQIArEQmK5Ev3uHVqKS6UrEJba2Ay1vf+t7ewUTHr7pgSVKRtyHp3yZauWj/7yp0JivnEHx9o61n33pZ7vrG3qcpo6OhzJTiHN4oKe1sT0YDBXvenzdurVrdF7Se+CFt0682eiqP1c/WCrwGPnCmQPgEQKLSsDnJr2X6u3JVm3mp1ZI5WIWzR1bppKt2l7+xss9tsb6rp1pKYT0NvT09O8rfvSrK3Iq0gWEFSHyitWbWtwX+p9/99T6pFKdVI5r/IvqxEBmFkAg4LQ7G8+1airU+RVr0gifdvJol+eWTjy5ad/ujhadXlO6VL0AX4tDQmDxCFynEhEi1qVlrX+ksHqM2W1ptS9ZLiXM2PWXLEjvKYvNUZpyMvIzl+hmyiagGBHa0nn7uq1jnvFhi5OhFXCYzBCb5aJ7SPSm1NwlxQanN3BaIWSGGBEHm0O7YBckcTMpwiMEbqUAS0Bkhat2Zrv52kI5e/pnGIPNYSu0cq5vKOiwu0koQlxjPWMTllHzGq1WrhVOdfCw5frsrNR+v/BPHc4Hcz0E4emtLEZ8920hEAkGgw6bm5vFlMiV9FceTTRPJpZK0tV2h9tld/lvi1wgkRC4hQJMvpJn2rj9riS5PsUgINPhGYsrECoNEv9gyONzBUkkEsur+59cBEjTTQfShkkgFPZ7/CTM50u1ScbsNH1Vn3+gq7Ph3LlBt7Ou3TIcEooMKUUpKqmAewuLAl8NgQUV4IiJrvyOnVd/RyhIPJOTQbaLKdByI0xGyGYbd7omZYYkMZ83Wx24So1CKE/ppRXG7wwRZbSxxQYBCNxQgMFmc6QKsc8atlvH3EQiIMyw0+uyD40wxEaBmD9bt254BLwBgQQXYIm1wry77827iiEcDAQck44Qi8ti82g4GbuuU/o1n1R4OjHi7Gk8GvD3E5meq0hSEC6DiPIrCwKhLX/44cG3nnl677O/ohkL+f3BksyydU89kJUjpBdgsEEgkQQ8TtJx4aJTNq41rlBG2CyH3ebzO7nF2RrJXHQ6DeKJkMExh9/hoddXEokIeYXAzQtwxDJZwbKs3704cJl9snujPpNwvG0D7U37DzIyv2HISp5bJ+Pmj41PQCBxBYL2iYmmSy1ubTpfoonplX1quiDhqdduPfObf+t7W6yYXWnAN+Ec7x+xe/Ur8vPWlZgZhC7lwQh4w16HNRJxB3y+6BIF05szGLZPuhgBHoPOC8MGgUQR8PYONp/a/Yv3vEk7l1SuWiYjQlYkeq0kwmAxrzv/ib4bfR8bBCDwZwS4CoZqzT1/5aw601r9/b8+R3/RhQQStaH4n/6jbGl2piqmfT5/Jil4GwKLRWD0Qv3Z/f/9xybF+h1LKwuNjKlhM7HL3IKEp0G/11J30nJVKkUCiT5n3V1lGyorlxvk0bf8k33tnZfOtQUD4oIVK9PSUkUBYuusbXGP2tqOne40rTQq9SL0oF6liD8WpUAkRHxD3RdPnzpavcdqKt+0ZE1ZatLsT7tFmWVkCgKfoEDY5/YPdfZPiHw8fYpp3B4dZiYSCflc22THwLhIyFMLMAv3EywPfNXtLhDy0mit5tTh96o7O8UrP1VZWJqjpitNxXZbkPCUwWQJZCohl81lBEnQPW73+PxSkbJk42Pf3JqnyRbTn6q008fR33ipZv/RZp+gcssju3bt2JbkJl1v/Of/vPk/BxrffOXsihRRBsLT2JY2jhaHApFgJOCw91Ydf+fIW9WuiR1/U7k6a1UqvboQpsvKMWm/KTPiDYZC1/aT0krEpr2qMZwmGYc2SBIEYiEQ8o13DR16+nfv5usq1z/2/co0QjjE0nF4/9v/54e/K/vqzns35OpN6AqJBTWOkQACIX/QPjhe9/Yr+2rOu8yrPvPUlmKpearTMbaZX5DL5zQ2rfzS9//+Z7/97X/94Lf/sK0oXUPImNfXVNdqHbNOz5Gk4anNOeIabZOFQxvNSclmPV2CnENMednKpHKXn1U/aLd7p+6jE9v84mgQiDMB/4jHcvSlH734Vo+cddeXfvlg7jKjaCqJtG5KZDIuR+yvGxh1+q6ZXEyXBE5SS3h0kgc2CEDgAwXGRvtb9j1Xl1pZtmJzqenKmDZtSm7JA09u0gyMWFst/fRq/wceAm9CAAJXBCZbBs6/8rf/8W67aPXmh770lVUyg2xB5ucuSO8pk8WW6k0Gc2amQkOSRY9ZWYr9VUcb+y/vfvqk4BGxcHlxdI25YMgfDnq9EdJutdutNBSVh8jk8Kjb3huKhN3+YChMu4+wQWAxC3h7ey6dOv7WgRZxefHKimWrinJ1QvZcjyhLLNNKREp336DTm+QjV+4a5xsdGnNZuzL0fDFXvCA/MBczOfKWeAIBOt5sYtjNk4glctHMqBkOXRJHlSzj+ANBr983dUUv8WSQYwjcpMDoxbMnD+45Vsda8tCmFWvXlKQlSRYkNqXJWpDwdC67XBldPWfLVo/P6+zr29t5/u0T6gyxzGTepBESoUQl05o4TEtza33VSQkjoPYRy8lzXf19Ap7caJCJBbgT8pwkni02AdpZ4x69XFN78sLxZlbaw9s3r8ypSJlpOmcyK9KmaVTDxqPVAwOpAwaFWUyXZ5vob2rpHhwlFaulEgE6T2eo8AiBGwnw+UKZMVvZPDw2MjDuTFHRcaZM4nXZrD0NA15hBk8qpBcsMD3qRnx4HQJRgbCPtj7d546cPddW5zHd9elPbcxRZcgW0GaBw9PplBvWVSzviPTu/e47pPGdGknYsGrTfZnEmFmSt2pX1h+frat96xn63y9nsilPLy16dGtuqpqOCcAGgUUqQPtruqpe2nOmiy949P8+skaWprhOZeSnF6b1D2yr++75M8UClcFcECa2sycP1TQOKbd8c3WKKroCBjYIQOADBdRqY86djxXvf+6CMyItqdicSQiXjPQ1X3r1J4dGt69UZhvoDdqwQQACHyQQmCATx1///Xv9qsodX/3Hv8gm0gVeL/g6LeIHpe+jvifPrsjf9uXNR18+5Wxs6lf98LUl/7Q2Oce0Iv8O7v8N/e65fc3nOianj61ffnfF1oc+t1aVrsJQ9Y/Kjc/FvUDIaXM17j833Heswx56+qtP/ZFNb6M2m2plzsq8TZ++v1CkFKr1ucs/9bMvvLx3z/5/e2UfXRAnMMFIXpO3a/ODmUSDvtNZMjyBwI0F2Io02Zonv+Lee6z+T//8+Remek89bHGy+LGffGN9UVkW1j29sR3egcCUgHu8f+DQrxvHLI0d+2sH2o+LCHuuySIZq2nkdv86A+HF7lJ/jMNTWebG5VuTmSWy3Ay5ft5KHVxZalLhju2PcNJsrhFlKkfFF3OYLJFGaV5euc3lUPYVW67Mg1Llrc4uKStK4rNwrQW1YvEKMFh8ljizeBOXk3OdGYBSo14nYU1Vfr5QmZq+8a5K+1lVz+jYFIimeH1BcWGadPHqIGcQiKkAkyfm6gpLK8eDElmwcboaEXFSprF83Zp0vkYUuxY1psnGwSAQPwJMnoKfXFm5k5iv9CVelTSDTiXnkbl5E1e9+RH/YGBh748oh49BAAIQgAAEIAABCCyAwLzO2QU4Og4JAQhAAAIQgAAEIACBmxJAeHpTXNgZAhCAAAQgAAEIQGBhBRCeLqwvjg4BCEAAAhCAAAQgcFMCCE9vigs7QwACEIAABCAAAQgsrADC04X1xdEhAAEIQAACEIAABG5KAOHpTXFhZwhAAAIQgAAEIACBhRVAeLqwvjg6BCAAAQhAAAIQgMBNCSA8vSku7AwBCEAAAhCAAAQgsLACCE8X1hdHhwAEIAABCEAAAhC4KQGEpzfFhZ0hAAEIQAACEIAABBZWAOHpwvri6BCAAAQgAAEIQAACNyXw/wFVSFFdcTTGYgAAAABJRU5ErkJggg==)\n",
        "\n",
        "Вопрос 1: Какой из следующих графиков соответствует CAP кривым, построенным для первого года наблюдений (1st_y_CAP) и для всего ДВУХЛЕТНЕГО периода наблюдений (2_ys_CAP)."
      ],
      "metadata": {
        "id": "xQaiG3C3NQhp"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "k = 8 # количество рейтинговых категорий, исключая дефолт\n",
        "\n",
        "# Зададим рейтинговую шкалу\n",
        "grades = ['R{}'.format(i+1) for i in range(k)]\n",
        "\n",
        "\n",
        "# Рассмотрим распределение заемщиков по рейтинговым категориям\n",
        "N  = np.array([45, 52, 75, 100, 120, 98, 70, 20])\n",
        "S1  = np.array([44, 52, 74, 93, 108, 80, 47, 8])\n",
        "S2  = np.array([43, 50, 69, 86, 90, 66, 37, 2])\n",
        "# Сгенерируем дефолты\n",
        "\n",
        "D1 = N - S1\n",
        "D2 = N - S2\n",
        "DD = D2 - D1\n",
        "\n",
        "data_new = pd.DataFrame({\n",
        "                     'N': N,\n",
        "                     'D1': D1,\n",
        "                     'D2': D2,\n",
        "                     'S1': S1,\n",
        "                     'S2': S2,\n",
        "                     'DD': DD\n",
        "                          }, index = grades)\n",
        "display(data_new)\n",
        "\n",
        "# Вспомогательный код для подписей к осям\n",
        "x_1 = [i-0.25 for i in range(8)]\n",
        "x_2 = [i+0.25 for i in range(8)]\n",
        "\n",
        "# Распределение исходных наблюдения против распределения наблюдений за дефолтерам\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.bar(x_1, (N/N.sum())[::-1],width=0.5, label = 'Rated entities')\n",
        "plt.bar(x_2, (D2/D2.sum())[::-1], width=0.5, label = 'Defaults_2')\n",
        "plt.title(r'F(N(t)) vs F(D(t+h))')\n",
        "plt.xticks(range(8), grades[-1::-1]), plt.grid(), plt.legend()\n",
        "plt.show()\n",
        "\n",
        "# Распределение исходных наблюдения против распределения наблюдений за дефолтерам\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.bar(x_1, (N/N.sum())[::-1],width=0.5, label = 'Rated entities')\n",
        "plt.bar(x_2, (D2/D2.sum())[::-1], width=0.5, label = 'Defaults_2')\n",
        "plt.title(r'F(N(t)) vs F(D(t+h))')\n",
        "plt.xticks(range(8), grades[-1::-1]), plt.grid(), plt.legend()\n",
        "plt.show()\n",
        "\n",
        "# Распределение добросовестных заемщиков против распределения дефолтеров\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.bar(x_1, (S1/S1.sum())[::-1],width=0.5, label = 'Survivals_1')\n",
        "plt.bar(x_2, (D1/D1.sum())[::-1],width=0.5, label = 'Defaults_1')\n",
        "plt.title(r'$F (S(t+h))$ vs $F( D(t+h))$')\n",
        "plt.xticks(range(8), grades[-1::-1]), plt.grid(), plt.legend()\n",
        "plt.show()\n",
        "\n",
        "# Распределение добросовестных заемщиков против распределения дефолтеров\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.bar(x_1, (S2/S2.sum())[::-1],width=0.5, label = 'Survivals_2')\n",
        "plt.bar(x_2, (D2/D2.sum())[::-1],width=0.5, label = 'Defaults_2')\n",
        "plt.title(r'$F (S(t+h))$ vs $F( D(t+h))$')\n",
        "plt.xticks(range(8), grades[-1::-1]), plt.grid(), plt.legend()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "fSWACB5ONhIZ",
        "outputId": "cf1dad46-76b1-490d-fbfa-cf50e1404aa5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "      N  D1  D2   S1  S2\n",
              "R1   45   1   2   44  43\n",
              "R2   52   0   2   52  50\n",
              "R3   75   1   6   74  69\n",
              "R4  100   7  14   93  86\n",
              "R5  120  12  30  108  90\n",
              "R6   98  18  32   80  66\n",
              "R7   70  23  33   47  37\n",
              "R8   20  12  18    8   2"
            ],
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              "      <th>R1</th>\n",
              "      <td>45</td>\n",
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              "      <td>43</td>\n",
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              "      <td>69</td>\n",
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              "      <th>R4</th>\n",
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              "      <td>14</td>\n",
              "      <td>93</td>\n",
              "      <td>86</td>\n",
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              "    <tr>\n",
              "      <th>R5</th>\n",
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              "      <td>108</td>\n",
              "      <td>90</td>\n",
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              "      <td>98</td>\n",
              "      <td>18</td>\n",
              "      <td>32</td>\n",
              "      <td>80</td>\n",
              "      <td>66</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>R7</th>\n",
              "      <td>70</td>\n",
              "      <td>23</td>\n",
              "      <td>33</td>\n",
              "      <td>47</td>\n",
              "      <td>37</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>R8</th>\n",
              "      <td>20</td>\n",
              "      <td>12</td>\n",
              "      <td>18</td>\n",
              "      <td>8</td>\n",
              "      <td>2</td>\n",
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              "                                                     [key], {});\n",
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            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMMAAAEKCAYAAACv7+FiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAeRklEQVR4nO3de3SU5b3o8e+PBCHbICIgIlACW+zmIgQIBMXaBBXQY2FvRIIo21goy6NRu1y4y25V8HrAyqparIKiWCoGCudoRKxX4nFVsRCM4XZQbkKAioBGglwC/M4f75M4mUxm3rkQJvD7rJWVmed9nt8888z85r2/r6gqxhhocqo7YEyysGQwxrFkMMaxZDDGsWQwxrFkMMaxZDDGsWQwxjktkkFE/peI/Ppkt4ky/g4R6Rei/B8i0jNS2akQ65icNmOpqo3iD2gFKFAZ8LcTaOv+pwXVvwkoAb4DvgWKgQ5uWp02QDnQN4F9PR7cJzdtDLAkUlkDj6EEj0mIutuBxUCvoJinzVie8i95FIOSC+wLUX4v8HxQWT6wCejvPug2wETgX0K1cdOrgGYR+jANmOajr1cAm+uZ1hzYD1wQrqwhx7CeMckF9gY8bw3cDxwE/i1Mu0Y7lo1pMSkTWB+i/Brgw6CyCcBsVS1Rz15VfUFVfwhuIyIXATvwFhn3icg+EUmNs6+9gU0i8rSIfCMiu0TkagBVPYw3xxpWXTlUWSAR+Y2ILA4qe0pEng6YvlNEDojIRhG5sp5+1TeGUHccM4HPA/q4T1UfBlbjjW+ddo1hLMNpTMnQl9Af5CXAxqCyQ8AvRWSMiLQJ10ZVNwGTgcWqmq6qrVX1WJx9vQTIAt4E2gGzgd8ETN8A9AlqE6qsWiFwrYi0ABCRFLzFgQUi8lOgABigqi3wvgTb6olT3xhW93ljUN3SEPX+H9AhVLtGMpb1akzJkAmMF5Hv3N8aV34ucCCo7n8CbwNPAF+LyBsicn7A9OA2fQj9wceqN/Coqr6tqieo+wU84PoQqQwAVf0K7xf5P1zREOAHVV2BtzzdDOghIk1VdZuqbq6nX/WNIdQdk0xCj0lL4Jsw7ZJ6LMNpFMkgIs2A7sAVqnqu+7vETf4WaBFYX1X/qaq/VtWfAAPxBjTw1yS4Ta1FgqDXXlr95QGmAFMCvkxLQ9QXoBfwRkBxL2p/iC3wVuyJUBZoAXCjezzOPa/+Nf413jL4HhEpFJELQ/Qr3BhCwJgE1P08KEYKcBm1F6ca41iG1CiSAW8ATgBlIaaVARfX11BVS4A1wNmh2ohIExc/5K+Zql5X/eUBpgPTA75M14Vo0sX93xRQFrzIUeeLVk9ZoL8COSLSEW8OsSCgjwtU9XKgM94WoBkh2ocbQ6g9jr3w5jgbgurcBhyl9pezMY5lSI0lGfoCa1X1aIhpy4CfVz8RkSkiMlhEmrm/fCAHeKmeNmnuL1Fj0RtYo27TRkD/P3f9a463levdgD7XKQumqt/gbR5+Cdiqqhtc25+KyBD3a34Yb33pRIgQ4cYQao9JX2C9qla51+gkIo8ADwJjq8tDtGsUY1mfeNf0G0omsKqeaX8GSkUkTVUPAefgfWEuxNsMuBq4UlU/rafNQRF5DlgvIt+rasc4+3oJAb9KbgX+AmCtK/oFUKyquwLahCoLZYHr+38FlDXD+5XtjrdJ82NgUoi24cYQAsbE1e0tIgeAY8Ae4D0gS1W31deukY1lHVI76RonEXkM2KOqT57MNokgIp8CE1R1bbiyUyHWMTldxvK0SAZjEqGxrDMYc9JZMhjjWDIY4/jamiQiw4GngBTgBVWdHjT9HrwD4Y7h7Z38pdtriogcx9vOD7BdVUeEe602bdpoRkZGNO+hloMHD3L22WdHrniSYyRTX5IlRrL0paSkZK+qtq0zwcdRgynAZqArcBbepq4eQXVy+fGI0P8JLAyYVhnNkYP9+/fXeCxfvjyu9omKkag4p1OMRMWJNwawSmM8anUgsElVt6i3w6YQGBmUUMv1xyNCVwDxbl82psFF3LQqIqOB4ao60T0fD2SrakE99WcB/1TVR9zzY3i7z4/h7X5/LUSbSbgdRe3atetfWFgY8xuqrKwkPT095vaJipFMfUmWGMnSl9zc3BJVzaozIdTsQmsvAo3GW0+ofj4emFVP3Zvx5gzNAsqqzy7rindo8b+Gez1bTDp9YyQqzslaTPKzAr0T6BTwvKMrq0VErgJ+B/xcVY8EJNtO93+LiBTjHVtS3yHGp7WqqirKy8s5fPiw7zYtW7Zkw4bg4+WikywxGrovzZs3p2PHjjRt2tRXXD/JsBLoJiJd8JJgLN4hxDVEpC/eSRfDVXVPQHkrvOPuj7jjSgYDj/vq2WmovLycFi1akJGRgXd0cmQHDhygRYsWkSs2ghgN2RdVZd++fZSXl9OlS5ewdatFXIFW70ylAryTZTYAi1R1nYg8JCLVm0l/D6QDfxWRUhEpcuXdgVUi8jmwHG+dob4zrU57hw8fpnXr1r4TwcRORGjdunVUc2Ff+xlUdRneobqBZQ8EPL6qnnYf4x15aBxLhIYT7VjbHmhjnMZyPsNpKWPKmwmNt236/0hovDONJUMou0th2sjwdaZVNExfEuzRRx9lwYIFpKSk0KRJE2bPnk12dnZcMYuKili/fj1TpkyJuu20adNIT09n8uTJvtssXLiQp59+GlWlRYsWPPvss/TpE/XFMOqwZDiDfPLJJyxdupTVq1fTrFkz9u7dy9Gj9Z0FWtuxY/Vf8WXEiBGMGBH2kLOEysjI4MMPP6RVq1a89dZbTJo0iU8//TRywwhsneEMsnv3btq0aUOzZs0AaNOmDRdeeCEZGRns3bsXgFWrVpGTkwN4v9rjx49n8ODB/OpXv2LQoEGsW7euJl5OTg6rVq1i3rx5FBQUUFFRQefOnTlxwjsF++DBg3Tq1Imqqiqef/55BgwYwGWXXcb111/PDz/8QLCnn36aHj160Lt3b8aOHVvv+8jOzqZVq1YADBo0iPLy8oSMjyXDGWTo0KHs2LGDiy++mNtvv50PPwy+EGFd69ev57333uOll14iLy+PRYsWAV5i7d69m6ysH49qaNmyJZmZmTVxly5dyrBhw2jatCmjRo1i5cqVfPzxx3Tv3p25c+fWea3p06fz2WefUVZWxnPPPefrPc2dO5drrrnGV91ILBnOIOnp6ZSUlDBnzhzatm1LXl4e8+bNC9tmxIgRpKWlATBmzBgWL/aucrlo0SJGjx5dp35eXh4LFy4EoLCwkLy8PADWrl3Lz372MwYNGsQrr7xSaw5TrXfv3tx000385S9/ITU18hL88uXLmTt3LjNmhLoyTvQsGc4wKSkp5OTk8OCDDzJr1iyWLFlCampqzaJN8E6qwPMGOnToQOvWrSkrK2PhwoU1X/RAI0aM4G9/+xv79++npKSEIUOGAJCfn8+sWbNYsWIFU6dODbkz7M033+SOO+5g9erVDBgwIOx6SllZGRMnTuT111+ndevWMY1FMFuBPpmCt0oNWwS7fvwS+NkUmqjDIAA2btxIkyZN6NatGwClpaV07tyZQ4cOUVJSwjXXXMOSJUvCxsjLy+Pxxx+noqKC3r1715menp7OgAEDuPvuu7nuuutISUmpeR/t27enqqqKV155hQ4dOtRqd+LECXbs2EFubi6XX345hYWFVFZWcu65da8SuWPHDkaNGsX8+fO5+OJ6rx8XNUuGM0hlZSV33nkn3333HampqVx00UXMmTOHDRs2MGHCBO6///6alef6jB49mrvvvpv777+/3jp5eXnccMMNFBcX15Q9/PDDZGdnc95553HZZZdx4EDty+MeP36cm2++mYqKClSVu+66K2QiAMyYMYN9+/Zx++23A5CamsqqVeEuCeVP0l0qJisrS+N5Y8XFxRE/0IgxXn2SnI1Tw1fysZ8hOM6GYYvo3jng+scX9o0YI1kOsmtsB+pV27BhA927d69VJiIhz2ewdQZjHFtMMknrpZde4qmnnqpVNnjwYKZPn15Pi/hYMpikdeutt3LrrbfWKQ9e30gUW0wyxrFkMMaxZDDGsXWGU2lay4hVotoI2UgPK08WNmc4w6SkpJCZmUnPnj3p06cPM2fOrDkUI5z77ruPnj17cu+998b0utXXOfrqq69YsGBBhNp1Ve+d7tGjBwMHDqyzlSkRbM5whklLS6O01Lsl2p49exg3bhzff/89Dz74YNh28+bNY//+/TWHV8Rq+/btLFiwgHHjxkWuHCA1NZWZM2fSr18/du3aRU5ODldffTU9evSIqz+BbM5wBjv//POZM2cOs2bNQlU5fvw49957LwMGDKB3797Mnj0b8A6+q6yspH///ixcuJA33niD7Oxs+vbty1VXXcXXX38NeOc/PPHEEzXxe/XqxbZt22q95tSpU/noo4/IzMzkD3/4A+vWrWPgwIFkZmbSu3dvvvzyy5B9bd++Pf369QOgRYsWdO/enZ0761y+Ky42ZzjDde3alePHj7Nnzx5ef/11WrZsycqVKzly5AiDBw9m6NChFBUVkZ6eXjNH+fbbb1mxYgUiwgsvvMDjjz/OzJkzfb3egw8+yJ/+9CeWLvXudHvnnXdy9913c9NNN3H06FGOHz8eMcZXX33FZ599FvfpqsEsGUyNd955h7KysppzFioqKvjyyy/rXISrvLycvLw8du/ezdGjR31fpCuUSy+9lEcffZTy8nJGjRpVc0RtfSorKxk/fjxPPvkk55xzTsyvG4otJp3htmzZQkpKCueffz6qyh//+EdKS0spLS1l69atDB06tE6bO++8k4KCAtasWcPs2bNrzk0IPC8C6p4bEcq4ceMoKioiLS2Na6+9lg8++KDeulVVVVx//fWMGTOGUaNGxfBuw7M5w6nkY1PogX1f0+JIhLu4+jj6NZRvvvmG2267jYKCAkSEYcOG8eyzzzJkyBCaNm3KF198QYcOHercGKSioqLmfISXX365pjwjI6Nm8Wf16tVs3bq1zmump6fXOpxiy5YtdO3albvuuovt27dTVlZWc0JQIFVlwoQJdO/enYKCkBeAj5slwxnm0KFDZGZmUlVVRWpqKuPHj+eee+4BYOLEiWzbto1+/fqhqrRt25bXXqtzBwGmTZvGDTfcQKtWrRgyZEjNl/7666/nz3/+Mz179iQ7OzvkiTe9evUiJSWFPn36kJ+fz5EjR5g/fz5Nmzblggsu4Le//W3Ifv/9739n/vz5XHLJJXzwwQc0adKExx57jGuvvTZhY2PJcIYJt4Ja/QV77LHH6kzbvXt3zeORI0cycmTd60qlpaXxzjvvhIxdWVkJQNOmTessCvm53tLll19efYuDhJ79F8jWGYxxbM5gksq+ffu48sor65S///77CTvxvz6WDA3Ku0OMXYm7fq1bt67ZnxGvaE9ptsWkBtS8Ygv7Dh6L+kMy0au+WUnz5s19t7E5QwPquHoG5fyGb1p2BQQqIt+K6fDB72le9V34ShHiHD58OKovxcmK0dB9qb6NlV+WDA2o6dHv6LLiv38s8HmFjb5xXqmjuLiYvn1j2xeRyBjJ1pdgtphkjONrziAiw4GngBS82+BOD5p+DzAR717P3wC/VNWv3LRbgPtc1UdU9WUM4O9mJfPiv+2A8SninEFEUoBngGuAHsCNIhJ8EPlnQJaq9gYW4+7oKSLnAVOBbGAgMNXdAdSYpONnMWkgsElVt6jqUaAQqLX7UVWXq2r1BfdX4N0rGmAY8K6q7lfVb4F3geGJ6boxiRXx8pIiMhrv/s4T3fPxQLaqhjxaSkRmAf9U1UdEZDLQXFUfcdPuBw6p6hNBbSYBkwDatWvXv7CwMOY3VFlZWXOKYcwx9u8hPdLBce0z446z5kTkQ5+7pB2Juy8JGZMExEiWvuTm5oa8vGRCtyaJyM1AFvDzaNqp6hxgDnjXWo3nWqkNdq3VG6O/1mqw/MORzwWe12dr3H1JyJgkIEay9SWYn8WknUCngOcdXVktInIV8DtghKoeiaatMcnATzKsBLqJSBcROQsYCxQFVhCRvsBsvETYEzDpbWCoiLRyK85DXZkxSSfiYpKqHhORArwvcQrwoqquE5GHgFWqWgT8HkgH/uqOu9muqiNUdb+IPIyXUAAPqer+k/JOjImTr3UGVV0GLAsqeyDg8VVh2r4IvBhrB01kkfZXzBt+dtjpxmN7oI1xLBmMcSwZjHEsGYxxLBmMcSwZjHEsGYxxLBmMcSwZjHEsGYxxLBmMcSwZjHEsGYxxLBmMcSwZjHEsGYxxLBmMcSwZjHEsGYxxLBmMcSwZjHEsGYxxLBmMcSwZjHEsGYxxLBmMcSwZjHEsGYxxLBmMcSwZjHEsGYxxLBmMcRJ6g0PTeNkNT2zOYEwNX8kgIsNFZKOIbBKRKSGmXyEiq0XkmLtvdOC04yJS6v6KgtsakywiLiaJSArwDHA1UA6sFJEiVV0fUG07kA9MDhHikKpGvoO4MaeYn3WGgcAmVd0CICKFwEigJhlUdZubduIk9NGYBiGqGr6Ct9gzXFUnuufjgWxVLQhRdx6wVFUXB5QdA0qBY8B0VX0tRLtJwCSAdu3a9S8sLIz5DVVWVpKenh5ze4DK/XtIP7IrfKX2kWd2keKsOdElYowuaUci9iVSnC4tUyKOyZqdFXHH8CMhn0+cMXJzc0tUNSu4vCG2JnVW1Z0i0hX4QETWqOrmwAqqOgeYA5CVlaU5OTkxv1hxcTHxtAcofvVJcjZODVsn4/MFEePM67MrbJz8w35ibI3Yl0hx5g0/O+KY5PvYmhTvuEKCPp8ExAjFzwr0TqBTwPOOrswXVd3p/m8BioG+UfTPmAbjJxlWAt1EpIuInAWMBXxtFRKRViLSzD1uAwwmYF3DmGQSMRlU9RhQALwNbAAWqeo6EXlIREYAiMgAESkHbgBmi8g617w7sEpEPgeW460zWDKYpORrnUFVlwHLgsoeCHi8Em/xKbjdx8AlcfbRmAZhe6CNcSwZjHEsGYxxLBmMcSwZjHEsGYxxLBmMcSwZjHEsGYxxLBmMcU6/CwLsLoVpI8PXmRb+2H1zZrI5gzGOJYMxjiWDMY4lgzGOJYMxjiWDMY4lgzGOJYMxjiWDMY4lgzGOJYMxjiWDMY4lgzGOJYMxjiWDMc7pdz6DOWUi3SQRkvtGiTZnMMaxZDDGsWQwxrFkMMaxZDDGsWQwxrFkMMbxlQwiMlxENorIJhGZEmL6FSKyWkSOuftGB067RUS+dH+3JKrjxiRaxJ1uIpICPANcDZQDK0WkKOhGhduBfGByUNvzgKlAFqBAiWv7bWK6b3zxc2E1It+T+nTnZ84wENikqltU9ShQCNQaWVXdpqplwImgtsOAd1V1v0uAd4HhCei3MQknqhq+grfYM1xVJ7rn44FsVS0IUXcesFRVF7vnk4HmqvqIe34/cEhVnwhqNwmYBNCuXbv+hYWFMb+hyv17SD+yK3yl9plxx1hzokvEvnRJOxI2TiJi+ImTkBgtU0hPTw8fY2fky3b6iRNJZWVlXDFyc3NLVDUruDwpjk1S1TnAHICsrCzNycmJOVbxq0+Ss3Fq+Eo3hv/Q/MTIPxx5sWJen61h4yQihp84CYkx/GwifS75Po9NiufzBSguLo47Rih+kmEn0CngeUdX5sdOICeobbHPtuYMdCoP9vOzzrAS6CYiXUTkLGAsUOQz/tvAUBFpJSKtgKGuzJikEzEZVPUYUID3Jd4ALFLVdSLykIiMABCRASJSDtwAzBaRda7tfuBhvIRaCTzkyoxJOr7WGVR1GbAsqOyBgMcr8RaBQrV9EXgxjj4a0yBsD7QxjiWDMY4lgzGOJYMxjiWDMY4lgzGOJYMxjiWDMU5SHKjX0CId/zKvTwN1xCQVmzMY41gyGONYMhjjWDIY41gyGONYMhjjWDIY41gyGONYMhjjWDIY41gyGONYMhjjWDIY41gyGONYMhjjWDIY41gyGONYMhjjWDIY41gyGONYMhjjWDIY41gyGONYMhjjWDIY4/hKBhEZLiIbRWSTiEwJMb2ZiCx00z8VkQxXniEih0Sk1P09l9juG5M4ES8vKSIpwDPA1UA5sFJEilR1fUC1CcC3qnqRiIwFZgB5btpmVQ1/F3JjkoCfOcNAYJOqblHVo0AhMDKozkjgZfd4MXCliEjiumnMySeqGr6CyGhguKpOdM/HA9mqWhBQZ62rU+6ebwaygXRgHfAF8D1wn6p+FOI1JgGTANq1a9e/sLAw5jdUuX8P6Ud2ha2z5kSXsNO7pB2JO4afOImI4SdOQmK0TCE9PT18jJ0VYaf7iZOIGJHk5uaWqGpWcPnJvgr3buAnqrpPRPoDr4lIT1X9PrCSqs4B5gBkZWVpTk5OzC9Y/OqT5GycGrZO/uEFYafP67M17hh+4iQihp84CYkx/GwifS75Ea5u7idOImLEys9i0k6gU8Dzjq4sZB0RSQVaAvtU9Yiq7gNQ1RJgM3BxvJ025mTwkwwrgW4i0kVEzgLGAkVBdYqAW9zj0cAHqqoi0tatgCMiXYFuwJbEdN2YxIq4mKSqx0SkAHgbSAFeVNV1IvIQsEpVi4C5wHwR2QTsx0sYgCuAh0SkCjgB3Kaq+0/GGzEmXr7WGVR1GbAsqOyBgMeHgRtCtFsCLImzjyYZ7C6FacEbEYNFXgdKZrYH2hjHksEYx5LBGMeSwRjHksEYx5LBGMeSwRjHksEYx5LBGMeSwRjHksEYx5LBGMeSwRjHksEYx5LBGMeSwRjHksEYx5LBGMeSwRjHksEYx5LBGMeSwRjHksEYx5LBGOdkX3jYmNoiXozMx4XI/FzQbFrkq3kHszmDMY4lgzGOJYMxjiWDMY4lgzGOJYMxjiWDMY4lgzFOo9rpluHnTpB9GqAj5rTka84gIsNFZKOIbBKRKSGmNxORhW76pyKSETDtv135RhEZlriuG5NYEZPB3a3zGeAaoAdwo4j0CKo2AfhWVS8C/gDMcG174N3ssCcwHPhT9d0/jUk2fuYMA4FNqrpFVY8ChUDwgSEjgZfd48XAlSIirrzQ3Q96K7DJxTMm6Yiqhq8gMhoYrqoT3fPxQLaqFgTUWevqlLvnm4FsYBqwQlX/4srnAm+p6uKg15gETHJPfwpsjOM9tQH2xtE+UTGSqS/JEiNZ+tJZVdsGFybFCrSqzgHmJCKWiKxS1axTHSOZ+pIsMZKtL8H8LCbtBDoFPO/oykLWEZFUoCWwz2dbY5KCn2RYCXQTkS4ichbeCnFRUJ0i4Bb3eDTwgXrLX0XAWLe1qQvQDfhHYrpuTGJFXExS1WMiUgC8DaQAL6rqOhF5CFilqkXAXGC+iGwC9uMlDK7eImA9cAy4Q1WPn6T3Ui0Ri1sJWWRLUJzTKUai4iSqL7VEXIE25kxhh2MY41gyGOM02mQQkeMiUioia0XkDRE5N2Da4yKyTkQ2iMjTbgdgVHFEJNeVV/8dFpF/j6EvPxGRd1xf1gceqhJFjOMB/QjeeOE7jpt+joiUi8isGMaks4isdtPWichtMcTIFJFPXPsyEcmL5b2IyN9E5DsRWRpuPKKiqo3yD6gMePwy8Dv3+DLg73gr+ynAJ0BOtHGC6pyHt2HgX6KNARQDV7vH6THGqKyv/9G+H+ApvEtQzIphbM8CmgW8l23AhVHGuBjo5h5fCOwGzo1hTK4EfgEsTdR3qtHOGYJ8AnRwjxVojvvggKbA1zHECTQab8/5D9HEcMdmparquwCqWhltjDjViiMi/YF2wDuxxFDVo6p6xJU3w/+SRWCML1T1S/d4F7AHqLM3OFwM1/Z94IDP1/el0SeDO/DvSty+D1X9BFiO94uzG3hbVTdEGyfIWODVGGJcDHwnIv9bRD4Tkd9HOlCxnn40F5FVIrKivkW1SHFEpAkwE5jsp319fRGRTiJSBuwAZrgvdLTvp3raQLwfrc2xxkioRC++NNQfcBwoBb4B/i+Q4sovAt7Em42n4/2i/CzaOAHT27tpTWPoy2igAuiKt09nCTAh2n4AHdz/rniLJv8aQ18KgP9yj/MJv5gUdkz0x0WcfwDt4hjXjcCgOD6bHGwxCYBDqpoJdAYEuMOV/wfewYGVqloJvAVcGkOcamOA/6OqVTHEKAdK1Tvi9xjwGtAv2n6o6k73fwveOkjfGPpyKVAgItuAJ4D/FJHp0fYloE+7gLXAz6KNISLn4P1g/U5VV8TwXk6OU/0LH+sftVeu+gJf4f365gHvucdNgfeBX0QbJ6BsBZAbY19SgM+Btm7aS3h74aOJ0YofV1rbAF8CPWJ9P648H/8r0IF96QikufJWwBfAJVHGOMt9Jr+O9TMOKMvB5gy1qepnQBlwI975FJuBNXhfxM9V9Y0Y4uA2g3YCPoylL+odejIZeF9E1uD9uj0fZT+6A6tE5HO8daHpqro+lvcTixB9+dT15UPgCVVdE2WMMcAVQH7A5uLMaN+LiHwE/BXv3JlyScBZlHY4hjHOaTFnMCYRLBmMcSwZjHEsGYxxLBmMcSwZjHEsGYxx/j9kKXIoFhnFygAAAABJRU5ErkJggg==\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def cap_roc_data_1(data):\n",
        "  '''\n",
        "  data.N - количество заемщиков в каждой категории на начало периода в порядке улучшения рейтинга\n",
        "  data.D - количество дефолтов в каждой категории на конец периода в порядке улучшения рейтинга\n",
        "  data.S - количество \"выживших\" в каждой категории на конец периода в порядке улучшения рейтинга\n",
        "\n",
        "  ppr - Population Positive Rate (доля рейтингов ниже определенного уровня или значение функции распределения заемщиков относительно рейтинговой шкалы F(N))\n",
        "  tpr - True Positive Rate (доля дефолтеров, попавших в рейтинги ниже определенного уровня, или значение функции распределения дефолтеров относительно рейтинговой шкалы F(D))\n",
        "  tpr - False Positive Rate (доля \"выживших\", попавших в рейтинги ниже определенного уровня, или значение функции распределения выживших относительно рейтинговой шкалы F(S))\n",
        "  '''\n",
        "  data = data_new[::-1]\n",
        "  N, D, S = np.insert(data.N.values, 0, 0), np.insert(data.D1.values, 0, 0), np.insert(data.S1.values, 0, 0)\n",
        "  ppr, tpr, fpr = N.cumsum()/N.sum(), D.cumsum()/D.sum(), S.cumsum()/S.sum() # F(N), F(D), F(S)\n",
        "  return ppr, tpr, fpr"
      ],
      "metadata": {
        "id": "DHx9sQkGQtLD"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Обработаем данные для построения\n",
        "display(data_new)\n",
        "emp_ppr_1, emp_tpr_1, emp_fpr_1 = cap_roc_data_1(data)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "id": "jGbEaIh3Q5Z2",
        "outputId": "1b1e326b-c574-420a-bf27-4ef8c2410f63"
      },
      "execution_count": null,
      "outputs": [
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              "      N  D1  D2   S1  S2\n",
              "R1   45   1   2   44  43\n",
              "R2   52   0   2   52  50\n",
              "R3   75   1   6   74  69\n",
              "R4  100   7  14   93  86\n",
              "R5  120  12  30  108  90\n",
              "R6   98  18  32   80  66\n",
              "R7   70  23  33   47  37\n",
              "R8   20  12  18    8   2"
            ],
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    {
      "cell_type": "code",
      "source": [
        "def cap_roc_data_2(data):\n",
        "  '''\n",
        "  data.N - количество заемщиков в каждой категории на начало периода в порядке улучшения рейтинга\n",
        "  data.D - количество дефолтов в каждой категории на конец периода в порядке улучшения рейтинга\n",
        "  data.S - количество \"выживших\" в каждой категории на конец периода в порядке улучшения рейтинга\n",
        "\n",
        "  ppr - Population Positive Rate (доля рейтингов ниже определенного уровня или значение функции распределения заемщиков относительно рейтинговой шкалы F(N))\n",
        "  tpr - True Positive Rate (доля дефолтеров, попавших в рейтинги ниже определенного уровня, или значение функции распределения дефолтеров относительно рейтинговой шкалы F(D))\n",
        "  tpr - False Positive Rate (доля \"выживших\", попавших в рейтинги ниже определенного уровня, или значение функции распределения выживших относительно рейтинговой шкалы F(S))\n",
        "  '''\n",
        "  data = data_new[::-1]\n",
        "  N, D, S = np.insert(data.N.values, 0, 0), np.insert(data.D2.values, 0, 0), np.insert(data.S2.values, 0, 0)\n",
        "  ppr, tpr, fpr = N.cumsum()/N.sum(), D.cumsum()/D.sum(), S.cumsum()/S.sum() # F(N), F(D), F(S)\n",
        "  return ppr, tpr, fpr"
      ],
      "metadata": {
        "id": "0sVD49oeRTvy"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "emp_ppr_2, emp_tpr_2, emp_fpr_2 = cap_roc_data_2(data)"
      ],
      "metadata": {
        "id": "hqeCMXGcRgKk"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def cap_roc_data_DD(data):\n",
        "  '''\n",
        "  data.N - количество заемщиков в каждой категории на начало периода в порядке улучшения рейтинга\n",
        "  data.D - количество дефолтов в каждой категории на конец периода в порядке улучшения рейтинга\n",
        "  data.S - количество \"выживших\" в каждой категории на конец периода в порядке улучшения рейтинга\n",
        "\n",
        "  ppr - Population Positive Rate (доля рейтингов ниже определенного уровня или значение функции распределения заемщиков относительно рейтинговой шкалы F(N))\n",
        "  tpr - True Positive Rate (доля дефолтеров, попавших в рейтинги ниже определенного уровня, или значение функции распределения дефолтеров относительно рейтинговой шкалы F(D))\n",
        "  tpr - False Positive Rate (доля \"выживших\", попавших в рейтинги ниже определенного уровня, или значение функции распределения выживших относительно рейтинговой шкалы F(S))\n",
        "  '''\n",
        "  data = data_new[::-1]\n",
        "  N, D, S = np.insert(data.N.values, 0, 0), np.insert(data.DD.values, 0, 0), np.insert(data.S2.values, 0, 0)\n",
        "  ppr, tpr, fpr = N.cumsum()/N.sum(), D.cumsum()/D.sum(), S.cumsum()/S.sum() # F(N), F(D), F(S)\n",
        "  return ppr, tpr, fpr"
      ],
      "metadata": {
        "id": "k9QS0Iepk2kT"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "emp_ppr_DD, emp_tpr_DD, emp_fpr_DD = cap_roc_data_DD(data)"
      ],
      "metadata": {
        "id": "uz8D1CESk5n3"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Построим CAP- кривую (для t=1, t=2):\n",
        "plt.title('CAP - curve')\n",
        "plt.grid()\n",
        "plt.plot(emp_ppr_1, emp_tpr_1, '--*b', label = 'EmpCAP_1')\n",
        "plt.plot(emp_ppr_2, emp_tpr_2, '--*m', label = 'EmpCAP_2')\n",
        "plt.plot([0, 1], [0, 1], '--*r', label = 'RandomCAP')\n",
        "plt.plot([0, data_new.D1.sum()/data_new.N.sum() ,1], [0, 1, 1], '--*g',label = 'PerfectCAP_1')\n",
        "plt.plot([0, data_new.DD.sum()/data_new.N.sum() ,1], [0, 1, 1], '--*y',label = 'PerfectCAP_2')\n",
        "plt.xlim([0,1.05]), plt.xlabel('PPR'), plt.ylabel('TPR')\n",
        "plt.ylim([0,1.05])\n",
        "plt.legend()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "id": "bRM5drgMRvHV",
        "outputId": "4422f7a8-67a9-4d17-ae3b-4c35672b4971"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f036284bcd0>"
            ]
          },
          "metadata": {},
          "execution_count": 43
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Построим ROC- кривую (эмпирическую и теоретическию):\n",
        "plt.title('ROC - curve')\n",
        "plt.grid()\n",
        "plt.plot(emp_fpr_1, emp_tpr_1, '--*b', label = 'EmpROC_1')\n",
        "plt.plot(emp_fpr_2, emp_tpr_2, '--*m', label = 'EmpROC_2')\n",
        "plt.plot([0, 1], [0, 1], '--*r', label = 'RandomROC')\n",
        "plt.plot([0, 0 ,1], [0, 1, 1], '--*g',label = 'PerfectROC')\n",
        "plt.xlim([0,1.05]), plt.xlabel('FPR'), plt.ylabel('TPR')\n",
        "plt.ylim([0,1.05])\n",
        "plt.legend()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "id": "IOk19tIrUie4",
        "outputId": "bacd2b6d-479e-4b8d-d776-2762395b3bec"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f0362ab6d50>"
            ]
          },
          "metadata": {},
          "execution_count": 26
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Какие значения AUC соответствуют CAP и ROC кривым для первого года наблюдений.\n",
        "\n",
        "a.\n",
        "AUC_cap = 0.702, AUC_roc = 0.758\n",
        "\n",
        "b.\n",
        "AUC_cap = 0.702, AUC_roc = 0.764\n",
        "\n",
        "c.\n",
        "AUC_cap = 0.796, AUC_roc = 0.701\n",
        "\n",
        "d.\n",
        "AUC_cap = 0.758, AUC_roc = 0.796"
      ],
      "metadata": {
        "id": "qylnz92aNho8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Вычислим AUC и AR (Gini) по ROC 1 year\n",
        "emp_auc_1 = 0.5 * (emp_tpr_1[1:] + emp_tpr_1[:-1])@(emp_fpr_1[1:] - emp_fpr_1[:-1])\n",
        "emp_ar_1= (2*emp_auc_1 - 1)\n",
        "\n",
        "print( 'Эмпирический AUC = {:.3f},  эмпирический AR = {:.2%}\\n'.format(emp_auc_1, emp_ar_1))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4c05f7a1-2c86-4d83-8b84-b1b22564b6f4",
        "id": "NG_lpDRAU9Kg"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Эмпирический AUC = 0.796,  эмпирический AR = 59.22%\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Вычислим AUC и AR (Gini) по ROC 2 year\n",
        "emp_auc_2 = 0.5 * (emp_tpr_2[1:] + emp_tpr_2[:-1])@(emp_fpr_2[1:] - emp_fpr_2[:-1])\n",
        "emp_ar_2= (2*emp_auc_2 - 1)\n",
        "\n",
        "print( 'Эмпирический AUC = {:.3f},  эмпирический AR = {:.2%}\\n'.format(emp_auc_2, emp_ar_2))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b16b1079-028b-4efa-e8f4-35be8fb73369",
        "id": "EIUV0aEkVHuk"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Эмпирический AUC = 0.764,  эмпирический AR = 52.82%\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Какие значения AR (или показателя Gini) соответствуют CAP кривым для статистики дефолта ПЕРВОГО года (AR_1st_y) и статистики дефолта ВТОРОГО года наблюдения (AR_2nd_y)?\n",
        "\n",
        "\n",
        "a.\n",
        "AR_1st_y = 51.67%, AR_2nd_y = 35.26%\n",
        "\n",
        "b.\n",
        "AR_1st_y = 59.22%, AR_2nd_y = 40.28%\n",
        "\n",
        "c.\n",
        "AR_1st_y = 51.67%, AR_2nd_y = 40.84%\n",
        "\n",
        "d.\n",
        "AR_1st_y = 59.22%, AR_2nd_y = 46.76%,"
      ],
      "metadata": {
        "id": "eFuJrovTNlZB"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a5144667-b2df-4a76-907a-886e892dbffd",
        "id": "x0MS36YqU9Ke"
      },
      "source": [
        "# Вычислим AUC и AR (Gini) по CAP 1 year\n",
        "emp_dr_1=  D1.sum()/N.sum()\n",
        "\n",
        "emp_auc_1= 0.5 * (emp_tpr_1[1:] + emp_tpr_1[:-1])@(emp_ppr_1[1:] - emp_ppr_1[:-1])\n",
        "emp_ar_1 = (2*emp_auc_1 - 1)/(1 - D1.sum()/N.sum())\n",
        "\n",
        "print( 'Эмпирический DR = {:.2%},  эмпирический AUC = {:.3f},  эмпирический AR = {:.2%}\\n'.format(emp_dr_1, emp_auc_1, emp_ar_1))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Эмпирический DR = 12.76%,  эмпирический AUC = 0.758,  эмпирический AR = 59.22%\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8d2c24da-a6a2-4872-e917-1ab0fadece78",
        "id": "Gcurwl8bVHuj"
      },
      "source": [
        "# Вычислим AUC и AR (Gini) по CAP 2 year\n",
        "emp_dr_DD=  DD.sum()/N.sum()\n",
        "\n",
        "emp_auc_DD= 0.5 * (emp_tpr_DD[1:] + emp_tpr_DD[:-1])@(emp_ppr_DD[1:] - emp_ppr_DD[:-1])\n",
        "emp_ar_DD = (2*emp_auc_DD - 1)/(1 - DD.sum()/N.sum())\n",
        "\n",
        "print( 'Эмпирический DR = {:.2%},  эмпирический AUC = {:.3f},  эмпирический AR = {:.2%}\\n'.format(emp_dr_DD, emp_auc_DD, emp_ar_DD))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Эмпирический DR = 10.86%,  эмпирический AUC = 0.635,  эмпирический AR = 30.34%\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "YqSgqydmNl3N"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Сравните AR и AUC для ROC и CAP кривых для двухлетнего периода наблюдений.\n",
        "\n",
        "a.\n",
        "AUC_cap = 0.654, AUC_roc = 0.701. AR_cap = 40.34%, AR_roc = 40.34%\n",
        "\n",
        "b.\n",
        "AUC_cap = 0.702, AUC_roc = 0.764. AR_cap = 52.82%, , AR_roc = 52.82%,\n",
        "\n",
        "c.\n",
        "AUC_cap = 0.764, AUC_roc = 0.846. AR_cap = 69.16% , AR_roc = 69.16%\n",
        "\n",
        "d.\n",
        "AUC_cap = 0.702, AUC_roc = 0.846 , AR_cap = 40.34%, AR_roc = 69.16%,"
      ],
      "metadata": {
        "id": "sgk8OLhzNns8"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "ClnwlMdKNoPX"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}