{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.3"
    },
    "colab": {
      "name": "01_Chapter01.ipynb",
      "provenance": [],
      "toc_visible": true,
      "include_colab_link": true
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/saketkc/pyFLGLM/blob/master/Chapters/01_Chapter01.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K7hg0Lj4LbXQ",
        "colab_type": "text"
      },
      "source": [
        "## Chapter 1 - Introduction to Linear and Generalized Linear Models"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JXAhcV0hLbXS",
        "colab_type": "code",
        "colab": {},
        "outputId": "854eb5eb-e67f-429c-998b-ca08d033aff9"
      },
      "source": [
        "import warnings\n",
        "\n",
        "import pandas as pd\n",
        "import proplot as plot\n",
        "import seaborn as sns\n",
        "import statsmodels.api as sm\n",
        "import statsmodels.formula.api as smf\n",
        "from patsy import dmatrices\n",
        "from scipy import stats\n",
        "\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "%pylab inline\n",
        "\n",
        "\n",
        "plt.rcParams[\"axes.labelweight\"] = \"bold\"\n",
        "plt.rcParams[\"font.weight\"] = \"bold\""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Populating the interactive namespace from numpy and matplotlib\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WvkmJrJiLbXf",
        "colab_type": "code",
        "colab": {},
        "outputId": "c8e2db95-1a5d-4ecf-ea09-0f45766a0fd4"
      },
      "source": [
        "crabs_df = pd.read_csv(\"../data/Crabs.tsv.gz\", sep=\"\\t\")\n",
        "crabs_df.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>crab</th>\n",
              "      <th>y</th>\n",
              "      <th>weight</th>\n",
              "      <th>width</th>\n",
              "      <th>color</th>\n",
              "      <th>spine</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>8</td>\n",
              "      <td>3.05</td>\n",
              "      <td>28.3</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1.55</td>\n",
              "      <td>22.5</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>9</td>\n",
              "      <td>2.30</td>\n",
              "      <td>26.0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>2.10</td>\n",
              "      <td>24.8</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>2.60</td>\n",
              "      <td>26.0</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   crab  y  weight  width  color  spine\n",
              "1     1  8    3.05   28.3      2      3\n",
              "2     2  0    1.55   22.5      3      3\n",
              "3     3  9    2.30   26.0      1      1\n",
              "4     4  0    2.10   24.8      3      3\n",
              "5     5  4    2.60   26.0      3      3"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IXmZ6yAdLbXn",
        "colab_type": "text"
      },
      "source": [
        "This data comes from a study of female horseshoe crabs (citation unknown). During spawning session, the females migrate to the shore to brred. The males then attach themselves to females' posterior spine while the females\n",
        "burrows into the sand and lays cluster of eggs. The fertilization of eggs happens externally in the sand beneath the pair. During this spanwing, multulpe males may cluster the pair and may also fertilize the eggs. These males are called satellites.\n",
        "\n",
        "**crab**: observation index\n",
        "\n",
        "**y**: Number of satellites attached\n",
        "\n",
        "**weight**: weight of the female crab\n",
        "\n",
        "**color**: color of the female \n",
        "\n",
        "**spine**:condition of female's spine\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nDq3MNZvLbXp",
        "colab_type": "code",
        "colab": {},
        "outputId": "49acd864-0981-4b1f-e24f-26bd785a4d79"
      },
      "source": [
        "print((crabs_df[\"y\"].mean(), crabs_df[\"y\"].var()))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(2.9190751445086707, 9.912017744320465)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3jIHLGRWLbXx",
        "colab_type": "code",
        "colab": {},
        "outputId": "648c9f0f-7da4-4762-8b32-a2fa6bb57d64"
      },
      "source": [
        "sns.distplot(crabs_df[\"y\"], kde=False, color=\"slateblue\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x2ad246bfca58>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "height": 480,
              "width": 640
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eLbxp8O5LbX6",
        "colab_type": "code",
        "colab": {},
        "outputId": "59196cf1-eb79-45da-9e6d-33e0f3453d08"
      },
      "source": [
        "pd.crosstab(index=crabs_df[\"y\"], columns=\"count\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th>col_0</th>\n",
              "      <th>count</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>y</th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>62</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>16</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>19</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>19</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "col_0  count\n",
              "y           \n",
              "0         62\n",
              "1         16\n",
              "2          9\n",
              "3         19\n",
              "4         19\n",
              "5         15\n",
              "6         13\n",
              "7          4\n",
              "8          6\n",
              "9          3\n",
              "10         3\n",
              "11         1\n",
              "12         1\n",
              "14         1\n",
              "15         1"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JREMguCOLbYC",
        "colab_type": "code",
        "colab": {},
        "outputId": "23a81b7b-38ad-4a70-e66a-7880cbec63ae"
      },
      "source": [
        "formula = \"\"\"y ~ 1\"\"\"\n",
        "response, predictors = dmatrices(formula, crabs_df, return_type=\"dataframe\")\n",
        "fit_pois = sm.GLM(\n",
        "    response, predictors, family=sm.families.Poisson(link=sm.families.links.identity())\n",
        ").fit()\n",
        "print(fit_pois.summary())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                 Generalized Linear Model Regression Results                  \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   No. Observations:                  173\n",
            "Model:                            GLM   Df Residuals:                      172\n",
            "Model Family:                 Poisson   Df Model:                            0\n",
            "Link Function:               identity   Scale:                          1.0000\n",
            "Method:                          IRLS   Log-Likelihood:                -494.04\n",
            "Date:                Mon, 22 Jun 2020   Deviance:                       632.79\n",
            "Time:                        23:43:22   Pearson chi2:                     584.\n",
            "No. Iterations:                     3                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "Intercept      2.9191      0.130     22.472      0.000       2.664       3.174\n",
            "==============================================================================\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ee_P7HsnLbYK",
        "colab_type": "text"
      },
      "source": [
        "Fitting a Poisson distribution with a GLM containing only an iontercept and using identity link function gives the estimate of intercept which is essentially the mean of `y`. But poisson has the same mean as its variance. The sample variance of 9.92 suggests that a poisson fit is not appropriate here."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v21laxIFLbYM",
        "colab_type": "text"
      },
      "source": [
        "### Linear Model Using Weight to Predict Satellite Counts"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "F_YmmYPdLbYO",
        "colab_type": "code",
        "colab": {},
        "outputId": "728ca1a6-2a45-4db5-bd98-2ce8ea258928"
      },
      "source": [
        "print((crabs_df[\"weight\"].mean(), crabs_df[\"weight\"].var()))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(2.437190751445087, 0.33295809712326924)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xul4X0aNLbYX",
        "colab_type": "code",
        "colab": {},
        "outputId": "605fc848-6bb8-469c-8bca-dcff40111741"
      },
      "source": [
        "print(crabs_df[\"weight\"].quantile(q=[0, 0.25, 0.5, 0.75, 1]))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.00    1.20\n",
            "0.25    2.00\n",
            "0.50    2.35\n",
            "0.75    2.85\n",
            "1.00    5.20\n",
            "Name: weight, dtype: float64\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J-78QcmVLbYe",
        "colab_type": "code",
        "colab": {},
        "outputId": "8a64efe2-a7d7-459e-899c-ddf738836dd2"
      },
      "source": [
        "fig, ax = plt.subplots(figsize=(5, 5))\n",
        "ax.scatter(crabs_df[\"weight\"], crabs_df[\"y\"])\n",
        "ax.set_xlabel(\"weight\")\n",
        "ax.set_ylabel(\"y\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'y')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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bW8ybN2/AsgULFjiCDgAAkCAFvYbl8/nI5/MDljU0NESxWMwoEQAAAEfiUCoAAAAkQEEHAACABCjoAAAAkAAFHQAAABKgoAMAAEACFHQAAABIgIIOAAAACVDQAQAAIAEKOgAAACRAQQcAAIAEKOgAAACQAAUdAAAAEqCgAwAAQAIUdAAAAEiAgg4AAAAJUNABAAAgAQo6AAAAJEBBBwAAgAQo6AAAAJCA+qwDUDnd3d3R09MzYFmhUIi6Ou/LAAAApEZBr2EdHR3R3t5+yPKmpqYM0gAAAHA0CnoNa2tri3nz5g1YtmDBAkfQAQAAEqSg17B8Ph/5fH7AsoaGhigWixklAgAA4EgcSgUAAIAEKOgAAACQAAUdAAAAEqCgAwAAQAIUdAAAAEiAgg4AAAAJUNABAAAgAQo6AAAAJEBBBwAAgAQo6AAAAJAABR0AAAASoKADAABAAhR0AAAASICCDgAAAAlQ0AEAACABCjoAAAAkQEEHAACABCjoAAAAkAAFHQAAABKgoAMAAEAC6rMOQOV0d3dHT0/PgGWFQiHq6rwvAwAAkBoFvYZ1dHREe3v7IcubmpoySAMAAMDRKOg1rK2tLebNmzdg2YIFCxxBBwAASJCCXsPy+Xzk8/kByxoaGqJYLGaUCAAAgCNxKBUAAAASoKADAABAAhR0AAAASICCDgAAAAlQ0AEAACABCjoAAAAkQEEHAACABCjoAAAAkAAFHQAAABKgoAMAAEACFHQAAABIQH3WAWrd6tWr46qrroqIiEsuuSRWrVp12PUee+yx+NKXvhSPPvpodHV1RUNDQ5x11llx1VVXxc033xwnn3zySMYGYJTo2luIZRt2xDPdvfFSoS9ObqiPGflxsXBOSzQ3NmQdDwBGFQW9gnp7e+Ouu+465np33313fOYzn4lisdi/7MCBA/H444/H448/Hvfff398+9vfjtNPP72ScQEYRdZv3x2LV2+JBzftir5i6ZDr71r1VFx37qS4/bIzonXKhAwSAsDo4yPuFfLSSy/F/Pnzo7Oz86jr/eu//mt86lOf6i/nr3vd6+L888+PU089tX+dZ599Nt7//vdXNC8Ao8fSddvionvWxvIndh62nEdE9BVLsfyJnXHRPWtj6bptIxsQAEYpBb0C1q1bFxdffHGsXbv2mOt+/vOf7//79NNPjw0bNsTq1avjF7/4Rfzpn/5p/3Xr16+PRx99tCJ5ARg9lq7bFotWdEbp8L38EKVSxKIVnXGfkg4AFaegl1GhUIirr7463vOe98TWrVsHtf66dev6L//Zn/1ZtLS0RETECSecEJ/85CcHrP/YY4+VNzAAo8r67bvj1pWdkYuIQfbzKEVELiI+vLIz1m/fXblwAIDvoJfTyy+/HI888kj/5SuuuCIiIr773e8edv1XX301Pv/5z8euXbti165dcfHFFw+4fty4cQMuHzhwoMyJARhNFq/eEkf4RPtRleK1I+lL1myN+2/0fXQAqBQFvQKamprizjvvjFtuuSVuueWWI643duzYuOmmm454/Y9+9KMBl9/0pjeVKyIAo8zze/bHg5t2DWuMBzbujMVXz3R2dwCoEB9xL6OTTjoplixZEk8++WQsWrQocrnccY+1d+/e+PSnPz1g7Msvv7wcMQEYhb7y2HNHPCHcYPUVS7Fsw44yJQIAfpcj6GU0duzY+OAHPzjscV5++eW44YYb4plnnulftnDhwpg4ceIRb9Pa2jqosbds2RItLS3R1dU17Jwcqru7O+sINc38Vpb5rays5/eJzdsjeof/HfKNz26Prrc2liFReWU9v7XO/FaW+a08c3x4fX19UVfnmG1KPBqJ6e3tjeuvvz7WrFnTv2zy5Mnxf/7P/8kwFQDVbt+BvrKM01sozzgAwKEcQU/Inj174rrrrouf/OQn/csaGxvj/vvvj/Hjxx/1tuvXrx/UfbS2tkaxWIzm5uZhZeXozG9lmd/KMr+VldX8Tnxjc8S4wrDHyTc3J72PpJytFpjfyjK/lWeOB6qvr49isZh1DH6Lgp6IPXv2xNVXXz3gp9ROOeWUWLFiRZx33nkZJgOgFszIjzv2SoMwfWJ5xgEADuUj7gnYv39/XH/99QPK+Rve8Ib49re/HRdeeGGGyQCoFTe9bXLU1x3/yUsjIurrcrFwTkuZEgEAv0tBT8BHPvKRWLduXf/lpqam+M53vhPnn39+hqkAqCWnnjImrjt30rDGmD/7ND+xBgAVpKBn7Jvf/GZ8/etf779cX18f3/jGN2LmzJkZpgKgFt1+2RlRl4sY6nH0XETU5SJuu3RaJWIBAP/Dd9AzVCqV4m//9m8HLDv55JOPeMb2BQsWxMKFC0ciGgA1qHXKhLj3mlmxaEVn5CJiML+KfnC9f7hmVrROmVDZgAAwyinoGfrZz34WTz755IBlL7zwQqxdu/aw67/jHe8YiVgA1LBb5k6NXER8eGVnlAbR0HO518r5zXOnVjoaAIx6CnqGfvrTn2YdAYBR6Oa5U+OCyeNjyZqt8cDGndFXPLSp19flYv7s0+K2S6c5cg4AIyS3Z8+ewXzCjRpx8HfQn3766ayj1KSurq6I8BublWJ+K8v8Vlaq89u1txDLNuyIzT29sXd/XzSOqY/pE8fFwjktVXVCuFTnt1aY38oyv5Vnjg9v5syZUSwWY/369VlH4X84gg4Ao1hzY0PceflZWccAAMJZ3AEAACAJCjoAAAAkQEEHAACABCjoAAAAkAAFHQAAABKgoAMAAEACFHQAAABIgIIOAAAACVDQAQAAIAEKOgAAACRAQQcAAIAE1GcdgMrp7u6Onp6eAcsKhULU1XlfBgAAIDUKeg3r6OiI9vb2Q5Y3NTVlkAYAAICjUdBrWFtbW8ybN2/AsgULFjiCDgAAkCAFvYbl8/nI5/MDljU0NESxWMwoEQAAAEfiUCoAAAAkQEEHAACABCjoAAAAkAAFHQAAABKgoAMAAEACFHQAAABIgIIOAAAACVDQAQAAIAEKOgAAACRAQQcAAIAEKOgAAACQAAUdAAAAElCfdQAAGO269hZi2YYd8Ux3b7xU6IuTG+pjRn5cLJzTEs2NDVnHAwBGiIIOABlZv313LF69JR7ctCv6iqVDrr9r1VNx3bmT4vbLzojWKRMySAgAjCQfcQeADCxdty0uumdtLH9i52HLeUREX7EUy5/YGRfdszaWrts2sgEBgBGnoAPACFu6blssWtEZpcP38kOUShGLVnTGfUo6ANQ0BR0ARtD67bvj1pWdkYuIQfbzKEVELiI+vLIz1m/fXblwAECmFHQAGEGLV2+JYmnw5fygUkQUSxFL1mytRCwAIAEKOgCMkP+3d388uGnXsMZ4YOPO6NpbKFMiACAlCjoAjJAHNh7+bO1D0VcsxbINO8qUCABIiZ9Zq2Hd3d3R09MzYFmhUIi6Ou/LAGThl7/eV5ZxNvf0lmUcACAtCnoN6+joiPb29kOWNzU1ZZAGgH0H+soyzt795RkHAEiLgl7D2traYt68eQOWLViwwBF0gIyMPak+Iob//fHGMV6+AaAWeYWvYfl8PvL5/IBlDQ0NUSwWM0oEMLqd2TQ2Iob/8fTpE8cNPwwAkByHUgFghMyfPSnq63LDGqO+LhcL57SUKREAkBIFHQBGyBsbx8R1504a1hjzZ58WzY0NZUoEAKREQQeAEXT7ZWdEXS5iqMfRcxFRl4u47dJplYgFACRAQQeAEdQ6ZULce82sKMXgS3ouIkoR8cVrZkXrlAmVCwcAZEpBB4ARdsvcqbH02lmRG2RDz+Uill47K26eO7WiuQCAbDmLOwBk4Oa5U+OCyeNjyZqt8cDGndFXLB2yTn1dLubPPi1uu3SaI+cAMAoo6ACQkdYpE+L+GyfE4qtnxrINO2JzT2/s3d8XjWPqY/rEcbFwTosTwgHAKKKgA0DGmhsb4s7Lz8o6BgCQMd9BBwAAgAQo6AAAAJAABR0AAAASoKADAABAAhR0AAAASICCDgAAAAlQ0AEAACABCjoAAAAkQEEHAACABCjoAAAAkAAFHQAAABJQn3UAKqe7uzt6enoGLCsUClFX530ZAACA1CjoNayjoyPa29sPWd7U1JRBGgAAAI5GQa9hbW1tMW/evAHLFixY4Ag6AABAghT0GpbP5yOfzw9Y1tDQEMViMaNEAAAAHIlDqQAAAJAABR0AAAASoKADAABAAhR0AAAASICCDgAAAAlQ0AEAACABCjoAAAAkQEEHAACABCjoAAAAkAAFHQAAABKgoAMAAEAC6rMOUOtWr14dV111VUREXHLJJbFq1arDrtfd3R2f+9zn4uGHH45du3bFySefHG9/+9vjtttui7lz545kZCirrr2FWLZhRzzT3RsvFfri5Ib6mJEfFwvntERzY0PW8SpiNG4z1cP+CQDpUtArqLe3N+66665jrrd58+a48sor4/nnn+9fVigU4uGHH47vfe97cffdd0dbW1slo0LZrd++Oxav3hIPbtoVfcXSIdffteqpuO7cSXH7ZWdE65QJGSQsv9G4zVQP+ycApM9H3CvkpZdeivnz50dnZ+dR1yuVSvGhD32ov5zX1dXF+eefH69//ev7r//kJz8ZTz75ZMUzQ7ksXbctLrpnbSx/Yudhi0BERF+xFMuf2BkX3bM2lq7bNrIBK2A0bjPVw/4JANVBQa+AdevWxcUXXxxr16495ro//OEPY8OGDf2XH3jggVi9enVs3Lgxpk2bFhERfX198bnPfa5ieaGclq7bFotWdEbp8B3gEKVSxKIVnXFfFReC0bjNVA/7JwBUDwW9jAqFQlx99dXxnve8J7Zu3Tqo23zzm9/s//uCCy6IP/iDP4iIiAkTJsSHPvSh/usefvjh2L9/f3kDQ5mt3747bl3ZGbmIGGQXiFJE5CLiwys7Y/323ZULVyGjcZupHvZPAKguCnoZvfzyy/HII4/0X77iiiviiiuuOOpt/uM//qP/7zlz5gy47h3veEf/3729vfH000+XKSlUxuLVW6JYGnwROKgUEcVSxJI1g3tjKyWjcZupHvZPAKguCnoFNDU1RXt7eyxfvjwmTDjyiXaKxWJs3ry5//KkSZMGXH/66acPuKygk7Ln9+yPBzftGtYYD2zcGV17C2VKVHmjcZupHvZPAKg+CnoZnXTSSbFkyZJ48sknY9GiRZHL5Y66/t69e+PAgQP9l0855ZQB148bN27A5f/+7/8uX1gos6889twRTz41WH3FUizbsKNMiSpvNG4z1cP+CQDVx8+sldHYsWPjgx/84KDX37dv34DLJ5544lEv9/b2HnGs1tbWQd3nli1boqWlJbq6ugaZkqHo7u7OOkJmnti8PaJ3+N9X3fjs9uh6a+Nhr0ttfkdim0dSavNba0Z6fmtt/zwW+29lmd/KMr+VZ44Pr6+vL+rqHLNNiUcjQ6VjnFL3WEfgISX7DvSVZZzeQnnGGQmjcZupHvZPAKg+jqBnaOzYsQMuv/LKK0e9/Lsfef9t69evH9R9tra2RrFYjObm5kGm5HiMxvmd+MbmiHHD/65qvrn5mPOXyvyO5DaPpJSy1KKRmt9a3T+PpZqyViPzW1nmt/LM8UD19fVRLBazjsFvcQQ9Q42NjVFf/5v3SF566aUB1+/du3fA5Te84Q0jkguOx4z8kd9AGorpE8szzkgYjdtM9bB/AkD1UdAzdMIJJ8TUqVP7L+/aNfBsuzt37hxw+c1vfvNIxILjctPbJkd93fC+llFfl4uFc1rKlKjyRuM2Uz3snwBQfRT0jJ133nn9f//0pz8dcN2GDRv6/x43bpyCTtJOPWVMXHfupGOveBTzZ58WzY0NZUpUeaNxm6ke9k8AqD4Kesb+6I/+qP/vxx9/PL73ve9FRMSLL74YX/rSl/qve/e73x1jxowZ8XwwFLdfdkbU5SKGeswuFxF1uYjbLp1WiVgVNRq3meph/wSA6qKgZ+yP//iP4+yzz+6//N73vjcuu+yyOPfcc2Pz5s0R8dpH4T/+8Y9nFREGrXXKhLj3mllRisEXglxElCLii9fMitYpEyoXrkJG4zZTPeyfAFBdFPSM1dfXx1e+8pU49dRTIyKiWCzG448/Hrt3/+a3a//mb/4mzjnnnKwiwpDcMndqLPCOE4cAACAASURBVL12Vgz2VwJzuYil186Km+dOrWiuShqN20z1sH8CQPXwM2sJmDFjRvz4xz+Ov//7v4/vfOc78atf/SpOPvnkePvb3x4f/ehH45JLLsk6IgzJzXOnxgWTx8eSNVvjgY07o69YOmSd+rpczJ99Wtx26bSaOEo3GreZ6mH/BIDqkNuzZ8+hr9LUrIO/g/70009nHaUmdXV1RYTf2PxtXXsLsWzDjtjc0xt79/dF45j6mD5xXCyc0zLkk09Vy/yWc5tHUrXMb7VKZX6rdf88llTmt1aZ38oyv5Vnjg9v5syZUSwWY/369VlH4X84gg5UVHNjQ9x5+VlZxxhRo3GbqR72TwBIl++gAwAAQAIUdAAAAEiAgg4AAAAJUNABAAAgAQo6AAAAJEBBBwAAgAQo6AAAAJAABR0AAAASoKADAABAAhR0AAAASICCDgAAAAlQ0AEAACAB9VkHoHK6u7ujp6dnwLJCoRB1dd6XAQAASI2CXsM6Ojqivb39kOVNTU0ZpAEAAOBoFPQa1tbWFvPmzRuwbMGCBY6gAwAAJEhBr2H5fD7y+fyAZQ0NDVEsFjNKBAAAwJE4lAoAAAAJUNABAAAgAQo6AAAAJEBBBwAAgAQo6AAAAJAABR0AAAASoKADAABAAhR0AAAASICCDgAAAAlQ0AEAACABCjoAAAAkoD7rAACjUdfeQizbsCOe6e6Nlwp9cXJDfczIj4uFc1qiubEh63iU0cHH+onN22Pfgb6Y+MbmpB9r+yYAZEdBBxhB67fvjsWrt8SDm3ZFX7F0yPV3rXoqrjt3Utx+2RnROmVCBgkpl0Me697dr10xrhAR6T3W9k0AyJ6PuAOMkKXrtsVF96yN5U/sPGwBiojoK5Zi+RM746J71sbSddtGNiBlU22PdbXlBYBapaADjICl67bFohWdUTp89zlEqRSxaEVn3KcIVZ1qe6yrLS8A1DIFHaDC1m/fHbeu7IxcRAyyA0UpInIR8eGVnbF+++7KhaOsqu2xrra8AFDrFHSAClu8eksUS4MvQAeVIqJYiliyZmslYlEB1fZYV1teAKh1CjpABT2/Z388uGnXsMZ4YOPO6NpbKFMiKqXaHutqywsAo4GCDlBBX3nsuSOedGuw+oqlWLZhR5kSUSnV9lhXW14AGA38zFoN6+7ujp6engHLCoVC1NV5XwZGyjPdvWUZZ3NPecahcqrtsa62vAAwGijoNayjoyPa29sPWd7U1JRBGhidXir0lWWcvfvLMw6VU22PdbXlBYDRQEGvYW1tbTFv3rwByxYsWOAIOoygkxvK8zTbOMbTdeqq7bGutrwAMBp4Va1h+Xw+8vn8gGUNDQ1RLBYzSgSjz4z8uLKMM31iecahcqrtsa62vAAwGjiUClBBN71tctTX5YY1Rn1dLhbOaSlTIiql2h7rassLAKOBgg5QQaeeMiauO3fSsMaYP/u0aG5sKFMiKqXaHutqywsAo4GCDlBht192RtTlIoZ6rDIXEXW5iNsunVaJWFRAtT3W1ZYXAGqdgg5QYa1TJsS918yKUgy+COUiohQRX7xmVrROmVC5cJRVtT3W1ZYXAGqdgg4wAm6ZOzWWXjsrcoNsQblcxNJrZ8XNc6dWNBflV22PdbXlBYBa5izuACPk5rlT44LJ42PJmq3xwMad0VcsHbJOfV0u5s8+LW67dJqjk1Ws2h7rassLALVKQQcYQa1TJsT9N06IxVfPjGUbdsTmnt7Yu78vGsfUx/SJ42LhnBYn3aoRv/tYb3x2e/QW+iLf3JzkY23fBIDsKegAGWhubIg7Lz8r6xiMgIOPdddbG1+73NyccaKjs28CQHZ8Bx0AAAASoKADAABAAhR0AAAASICCDgAAAAlQ0AEAACABCjoAAAAkQEEHAACABCjoAAAAkAAFHQAAABKgoAMAAEACFHQAAABIQH3WAaic7u7u6OnpGbCsUChEXZ33ZQAAAFKjoNewjo6OaG9vP2R5U1NTBmkAAAA4GgW9hrW1tcW8efMGLFuwYIEj6AAAAAlS0GtYPp+PfD4/YFlDQ0MUi8WMEgEAAHAkDqUCAABAAhR0AAAASICCDgAAAAlQ0AEAACABCjoAAAAkQEEHAACABCjoAAAAkAAFHQAAABKgoAMAAEACFHQAAABIgIIOAAAACVDQAQAAIAH1WQcg4qmnnoovfOELsWbNmnj++eejvr4+pk2bFldeeWXceuutMX78+KwjQqa69hZi2YYd8cTm7bHvQF9MfGNzzMiPi4VzWqK5sWHI4zzT3RsvFfri5Ib64xoHDirXPvWjZ3vilhWbYteeQrzyailOPCEXk05piKXXnhu/d9bECm4BAJASBT1j3/3ud+P9739/7N+/v39ZoVCIn//85/Hzn/88vvGNb8SqVavi9NNPzzAlZGP99t2xePWWeHDTrugrliJ6d792xbhCRETcteqpuO7cSXH7ZWdE65QJgx/ndwx2HDioXPvUX333qfi/q7fEvldeHXjFKxEv7u+Ly5f+OMaeeELccdkZ8ekr3lLuzQAAEuMj7hnavXt3fOhDH+ov57lcLs4555yYOnVq/zpbt26NRYsWZZQQsrN03ba46J61sfyJnYctQBERfcVSLH9iZ1x0z9pYum5bRceBg8q1T81ZvCY+84PNh5bz37HvlVfjMz/YHHMWrxludAAgcQp6hh5++OF44YUXIiKirq4uVq5cGevWrYtNmzbFJz7xif71Hnnkkdi1a1dWMWHELV23LRat6IzS4bvPIUqliEUrOuO+3ylC5RoHDirXPjVn8Zp47LkXh3Tfjz33Yrx9iZIOALVMQc/Qzp07+/+eOXNm/P7v/37/5VtvvXXAujt27BixXJCl9dt3x60rOyMXEYPsQFGKiFxEfHhlZ6zfvrus48BBw92n/uO5196Q/avvPjXkcn7Qhh0vxl9996njui0AkD4FPUNTpkzp/3vv3r0DrnvxxYH/eDvttNNGJBNkbfHqLVEsDb4AHVSKiGIpYsmarWUdBw4a7j71jz/ZHhER/3f1lmHlGO7tAYB0KegZ+sM//MNobm6OiIht27bFX//1X8eLL74Y27dvj9tvv71/vXe9610xefLkrGLCiHl+z/54cNPwvs7xwMad0blzT1nG6dpbGNYY1I5y7Jvf/s/n41/+c9cxv3N+LPteeTV+9GzPsMYAANKkoGdo3LhxsWLFijjzzDMjIqK9vT1aWlrinHPOiR/84AcREXHeeedFR0dHljFhxHzlseeOeNKtweorluL/W/WLsoyzbIOvlvCacuybrxZL8cl/+UVZ8tyyYlNZxgEA0uJn1jI2ffr0mDdvXtx9992HXDd27Nj45Cc/Gfl8/pjjtLa2Dur+tmzZEi0tLdHV1TXkrBxbd3d31hGq2hObt//mp9QOZ9/gvrf79LZCRO++YefZ+Oz26Hpr47DHqRb23yM75r45GPtejBcKuYiGV4ad51c793oe/x3238oyv5VlfivPHB9eX19f1NU5ZpsSj0aG9u/fP6Cc19fXx8yZM/t/Zm3fvn1xww03xKc+9akMU8LI2Xegryzj7H9leEc6D+otlCcP1a9c+2axWJZhhn00HwBIkyPoGfriF78Y69ati4iIxsbG+Jd/+Zc4//zzIyLivvvu6/+ptbvvvjve/e53x4UXXnjEsdavXz+o+2xtbY1isdj/3Xcqw/wen4lvbI4YN4jvfY+bcNSrT37DuIi+3mHnyTc3j8rHcjRu87EMet88hhNOyEXfmNcPe5yTxtR7nI7AvFSW+a0s81t55nig+vr6KJbr3WPKwhH0DH3961/v//v9739/fzmPiLj55pvjvPPO67/8ta99bUSzQRZm5MeVZZwzm8ozzvSJ5RmH6leufXN8Q3neF590SkNZxgEA0qKgZ2jbtm39f0+bNu2Q63972X/913+NRCTI1E1vmxz1dblhjVFfl4v2Pzy7LOMsnNMyrDGoHeXYN0+oy8Xf/tHZZcmz9NpzyzIOAJAWBT1D48b95ojML35x6Jl9n3322f6/x48fPyKZIEunnjImrjt30rDGmD/7tJh12illGae50VFKXlOOffOqmafGH82cFGNPPGFY44w98YT4vbMmDmsMACBNCnqGLrnkkv6///mf/zkeffTR/ssdHR3R2dnZf/niiy8e0WyQldsvOyPqchFDPVaZi4i6XMRtl04r6zhw0HD3qf/9jikREXHHZWcMK8dwbw8ApEtBz9Add9wRJ5zw2pGU/fv3x5VXXhkXXnhhzJ49Oz72sY/1r3f66afHn/zJn2QVE0ZU65QJce81s6IUgy9CuYgoRcQXr5kVrVMmlHUcOGi4+9QFk187Odynr3hLvG3y8X0qak7L+Pj0FW85rtsCAOlT0DN0/vnnxz/90z/FmDFjIiKiWCzGL37xi9i6dWv/Os3NzbF8+fIBH4eHWnfL3Kmx9NpZkRtkC8rlIpZeOytunju1IuPAQeXapzbcfmnMaRlaSZ/TMj5+dtulQ7oNAFBdFPSMXXPNNfGTn/wk2tra4swzz4yGhoZ43eteF2effXbccccd8eMf/zhmz56ddUwYcTfPnRo//vNL4obzTz/iybnq63Jxw/mnx4///JIjlupyjQMHlWuf+tltl8Zf/q/px/xO+tgTT4i//F/TlXMAGAVye/bsKWUdgpFz8HfQn3766ayj1KSurq6I8Bub5da1txDLNuyIjc9uj95CX+Sbm2P6xHGxcE7LkE7kdnCczT29sXd/XzSOqT+ucWqV/XfohrJPHW1+f/RsT9yyYlPs2lOIV14txYkn5GLSKQ2x9NpznRBukOy/lWV+K8v8Vp45PryZM2dGsViM9evXZx2F/1GeH2QFqKDmxoa48/Kzouutja9dPs4X14PjQLmUa5/6vbMmxi8++a4yJAIAqpmPuAMAAEACFHQAAABIgIIOAAAACVDQAQAAIAEKOgAAACRAQQcAAIAE1FRBX7VqVbz66qtZxwAAAIAhq6mCfsMNN8SMGTPiL/7iL2LTpk1ZxwEAAIBBq6mCHhHx61//OpYuXRqXXnppzJ07N+69997o7u7OOhYAAAAcVc0V9FKp1P/fk08+GX/5l38Zb3nLW+L666+Phx56KA4cOJB1RAAAADhETRX0H/7wh/GRj3wkpkyZEhG/Ket9fX3x/e9/Pz7wgQ/E9OnT44477ogNGzZknBYAAAB+oz7rAOU0Z86cmDNnTnzmM5+Jxx57LB566KF46KGHYvv27VEqlSIi4oUXXogvf/nL8eUvfznOPPPMuOGGG+K9731vtLS0ZJy+/Lq7u6Onp2fAskKhEHV1NfW+DAAAQE2o2ab2tre9LT796U9HZ2dn/Nu//Vv8+Z//ebzpTW+KiN8cWX/22WfjM5/5TMyePTs+8IEPxK9+9auMU5dXR0dHXHjhhQP+27p1a7zwwgtZRwMAAOB31NQR9COZMWNGnH322fHkk0/G9u3bD7n+1VdfjYceeih+9rOfxcMPP1wzR9Pb2tpi3rx5A5YtWLDAEXQAAIAE1WxB37dvX6xatSpWrlwZP/zhD6NQKPRfd/Dj7ieddFK88sor/ct+9atfxd/93d/FF77whUwyl1s+n498Pj9gWUNDQxSLxYwSAQAAcCQ1VdD3798f3/ve92LlypXx/e9/P15++eWI+E0hP+i8886Lm266KebPnx89PT3xiU98In7wgx9EqVSKRx99NIvoAAAAjHI1VdDPOOOM2LdvX0S8VspzuVx/OX/DG94Q119/fdx0001xzjnn9N9m/Pjx8bWvfS3OP//8eO6552Lnzp2ZZAcAAGB0q6mC3tvbO6CU53K5eNe73hULFy6MK6+8Mk488cTD3u6kk06Kt771rfHcc8/F2LFjRzIyAAAARESNFfSI146cT506NW688cZ43/veF6eddtqgbnfgwIGYPn16XHTRRRVOCAAAAIeqqYL+3ve+N2666aZ45zvfOeTbfutb36pAIgAAABicmiro//iP/5h1BAAAADgufhAbAAAAEqCgAwAAQAIUdAAAAEiAgg4AAAAJUNABAAAgATV1FncAal/X3kIs27AjnunujZcKfXFyQ33MyI+LhXNaormxYdDrpKTa8gIwdJ7rGQwFHYCqsH777li8eks8uGlX9BVLh1x/16qn4vKzmiJKEY/88tdHXOe6cyfF7ZedEa1TJoxE7KMazDallBeAofNcz1Ao6AAkb+m6bXHrys44zL9r+vUVS/Gvz/QcdZy+YimWP7EzvrFxZ9x7zay4Ze7U8gYdgsFuUyp5ARg6z/UMle+gA5C0peu2xaIVnVE6yj9uhqpUili0ojPuW7etfIMOwVC3Keu8AAyd53qOh4IOQLLWb98dt67sjFxElLGfRykichHx4ZWdsX777jKOfGzHs01Z5gVg6DzXc7wUdACStXj1liiWylvODypFRLEUsWTN1gqMfmTHu01Z5QVg6DzXc7wUdACS9Pye/fHgpl0Vv58HNu6Mrr2Fit9PRMT/2zv8bRrJvAAMXTlevzzXj14KOgBJ+spjzx32bLfl1lcsxbINOyp+PxERD2w8/Bl8h2Ik8wIwdOV4/fJcP3o5i3sN6+7ujp6egWc0LhQKUVfnfRkgfc90947YfW3uGZn7+uWv95VlnJHKC8DQlev1y3P96KSg17COjo5ob28/ZHlTU1MGaQCG5qVC34jd1979I3Nf+w6U535GKi8AQ1eu1y/P9aOTgl7D2traYt68eQOWLViwwBF0oCqc3DByL1GNY0bmvsaeVB8Rw/9O4UjlBWDoyvX65bl+dPKo17B8Ph/5fH7AsoaGhigWixklAhi8GflxI3Zf0yeOzH2d2TQ2Iob/kcWRygvA0JXr9ctz/ejkUCoASbrpbZOjvi5X8fupr8vFwjktFb+fiIj5sycNe5tGMi8AQ1eO1y/P9aOXgg5Akk49ZUxcd+6kit/P/NmnRXNjQ8XvJyLijY3D36aRzAvA0JXj9ctz/eiloAOQrNsvOyPqchGVOI6ei4i6XMRtl06rwOhHdrzblFVeAIbOcz3HS0EHIFmtUybEvdfMilKUt6TnIqIUEV+8Zla0TplQxpGP7Xi2Kcu8AAyd53qOl4IOQNJumTs1ll47K3JlbOi5XMTSa2fFzXOnlm/QIRjqNmWdF4Ch81zP8XAWdwCSd/PcqXHB5PGxZM3WeGDjzugrlg5Zp74uF+86a2JERPzbsz1HXGf+7NPitkunZX50YrDblEpeAIbOcz1DpaADUBVap0yI+2+cEIuvnhnLNuyIzT29sXd/XzSOqY/pE8fFwjkt/SfU6dpbOOY6KRjKNgFQnTzXMxQKOgBVpbmxIe68/Kxhr5OSassLwNB5rmcwfAcdAAAAEqCgAwAAQAIUdAAAAEiAgg4AAAAJUNABAAAgAQo6AAAAJEBBBwAAgAQo6AAAAJAABR0AAAASoKADAABAAhR0AAAASICCDgAAAAmozzoAldPd3f3/s3f30VWVd97/P+fkhBACgZgcIykJFIRKQ0AKjS212nZGHeXu7QDSho4wP7t+6YhVR6bOWDq1MrVd4jxUO2PFabr0t7BV1yh0Oa06beceH6blnkZQHrQYQIRAAzGxgYRADjnZ5/dHTMzDSc7OOdfe+0ryfq3VZdjZ57q++3s99Hyzz4Oam5v7HYvFYgqH+bsMAAAAANiGAn0Mq6mp0ebNmwcdLywsDCAaAAAAAMBwKNDHsOrqaq1YsaLfsaqqKu6gAwAAAICFKNDHsGg0qmg02u9YTk6OHMcJKCIAAAAAwFC4lQoAAAAAgAUo0AEAAAAAsAAFOgAAAAAAFqBABwAAAADAAhToAAAAAABYgAIdAAAAAAALUKADAAAAAGABCnQAAAAAACxAgQ4AAAAAgAUo0AEAAAAAsAAFOgAAAAAAFogEHQC6vfrqq3rkkUe0Y8cONTU1aerUqfrUpz6lO++8UwsXLgw6PIxDjW0xbd15TAea2nUmFtfknIjmRfO0bmmpiqfkjLp+/PTGiVbd9dx+vd3crnOdjnKzw5pTlKf7l8/Xgun5kuy67pcONWv9tr36fcNJxZ2EJuRfoOn5OdqyaqE+c3GR63YGXlM4HNKpc50qyM1Wl5NwdY2m8mJTfv00Xq8bAICxItTa2poIOojxbvPmzbrvvvuUSAweiuzsbG3dulXLly830ldlZaUcx1FdXZ2R9tBfY2OjJKm4uDjgSNJXW9+iB14+rGf2nlDcGTwnI+GQblg4XRuunK3KsgJf+7E9v4/V1mvTLw6o/tS5Ic8pnjxBMwty9drvWz3Nrxt3v/CWvvfyYZ3t7Oo+0N7S/d+8D/qdlJ2lv7pytu699pIh20k1lgMlu0ZT886v+ZsOL+evzdftF9v3h9GO/HqL/HqPHCdXXl4ux3FUW1sbdCh4HwV6wB577DH95V/+Ze+/p02bplmzZunNN99UZ2dn77HXX39dhYWFGfdHge6t0b75b9lxRLdu3ycXNZbCIemhlRVav2yWb/3YnN81j+/SU7sbjLWXSX7dWPrAK9p1/HT/g0kK9B5LZkzVzg1XDDo+krEcqOcaJRmZd37N33R5NX9tv26/2Lw/jAXk11vk13vkODkKdPvwHvQAtbW16Vvf+lbvv//0T/9UBw8e1CuvvKL//M//1IQJEyRJp06d0tNPPx1UmBgntuw4olu27VOSF3IklUhIt2zbp0d2HLGyHz+ZLs4lb687aXGewq7jp/XxB1/pd2ykYzlQzzWamA9jcV65MV6vGwCAsYoCPUD//u//rtOnu58kT5gwQf/8z/+snJzu9wguXrxY69ev17p16/T1r39d5eXlQYaKMa62vkW3bt+nkCS3tVZCUkjSV7fvU219iy/9vHb8lMtH+eex2nrjxbmUXn7duPuFt0ZcnPfYeey07n7hLUnpjeVAiSF+TvWYgXnxa/7aZrxeNwAAYxkFeoBefPHF3p/Ly8s1bdq0fr+/99579dBDD+kb3/iGPv3pT/sdHsaRB14+LCcx8kIrIclJSA++8o4v/fzwf+pH+EjvbfrFAc/aHml+3fjey4eNPD7dsTRhYF78mr+2Ga/XDQDAWEaBHqDf/e53vT+Xlpbq1KlTuu+++3TDDTdo7dq1euSRR3T27NkAI8R4cLK1Q8/sPZFRG0/vaVBjW8zzfn725kk1nRm+Hz/tbTg97AfCmeImv27818GmDz4QLk1nO7u0fU9DxmNpwtN7GrSv4bQv89c2fq1bAADgLwr0AJ048cGTqz/84Q+6/PLLdd999+mXv/ylnn32Wf3N3/yNLrvsMj7QDZ56fNdxV5+8PZy4k9DWncc876fLSejfPHg5ebo2Pv+WL/24ya8bX92+z0A00s3b9mY8libEnYS+/vxbvsxf2/i1bgEAgL/4HvQAnTlzpvfnX//610nPOXr0qFatWqVf//rXg14C31dlZaWrPg8fPqzS0tLeT7KEWU1NTUGHMGK7D9Z/8OndGdhzqF6NH53ibT9nT+vNI8etmb917xyT2v15lUuq/Lrx+4aTUiw+9Aln3b03vaUjJHUFX6BLUt07MSNjYCK/qZjcH/xat6PJaNx/RxPy6y3y6z1ynFw8Hlc4zD1bmzAaAerq6v9S00984hN69dVXdfToUX3729/uPV5fX6+HH37Y7/AwTpw9P0zBNgLtwxV+Bvs5G8vsJdomdcT9K1JT5dcNU3e9HcdIM0aYGgMT+fWTX+sWAAD4izvoAZo8ebJOner+VOpwOKxHH31UM2bMkCTdcccd2rFjh/7jP/5DkvTzn/9c3/jGN4Zsy+13F/Z8DzrfAemt0ZTfoguLpbzM34caLS4e9rpN9VMYjVqT38kFhVK83Ze+UuXXjQn5F+hch4uCLMn3oPeVlRWSY8kd9MkFeUbGwER+3TLRj1/rdjQaa9djG/LrLfLrPXLcXyQSkWPTX97BHfQgFRYW9v5cUlLSW5z3WLZsWe/P77zDp+3CG/OieUbamVs0fDum+pl9wSQj7ZgwJ8U1m5Qqv25Mz88xEIk0baI9f9s1NQYm8usnv9YtAADwFwV6gObPn9/78/nz5wf9Pi/vgydO/GULXlm7ZIYi4VBGbUTCIa1bWup5P1nhkL5waUlGbZh033WX+NKPm/y68YOVFQaikR5ZtTDjsTQhEg5p83WX+DJ/bePXugUAAP6iQA/QJz/5yd6f3333XR0+3P/7ifv+u6yszLe4ML5clD9RNyycnlEbqxeVqHjK8HdnTfTz+fKLFJ1s5i6wCQtLpqpsWq7n/bjJrxufmxvVpOysjNqYlJ2llYtKMh5LE1YvKlFFyVRf5q9t/Fq3AADAXxToAVq1apUikQ9eKnr77bfr9OnuT1E+dOiQfvKTn/T+7qqrrvI9PowfG66crXBIGun9uJCkcEi644oP+9LPVz5h3x+qNl0zz7O2R5pfN/7qytlGHp/uWJowMC9+zV/bjNfrBgBgLKNAD1BJSYluv/323n+/8sorKi8v1xVXXKFPfvKTvR8gN23aNN16661BhYlxoLKsQA+trFBC7p/shyQl1P2y6cqy4T9UzFQ/H5sx9FcNBuWmyjJVefCy+3Ty68a9116iJTOmpvXYpaVTde+13S/rT2csBwoN8XOqxwzMi1/z1zbj9boBABjLKNAD9s1vflOrV6/u/Xdra6t2796tWKz703mnTp2qH//4xyopsed9txib1i+bpS2rKhRy+Uw/FJK2rKrQzctmWdmPn55cu0RrFptdo15e984NV2hp6ciK9KWlU/XqHVf0OzbSsRyo5xpNzIexOK/cGK/XDQDAWJW1cePGTUEHMZ6Fw2Fdf/31+uhHP6pTp07p1KlTchxHpaWlWr16tWpqarRw4UJj/dXU1CiRSOi2224z1iY+0N7e/XVPkydPDjiS9CwtnaZrL7lQ7ee79Na7Z5Tsa7Mj4ZC+eOmH9KMvLNL1C9J7D2y6/dic31ULSzSzIFe7G1p1epivMrtoSo7Ki6eoOA3B5AAAIABJREFU8UzMs/y68ZVPzFSXk9DOY6fV2RNIZ0f3fyd88L76SdlZuutzF+vJtUuStuNmLAcaeI2m5p1f8zddXs1f26/bLzbvD2MB+fUW+fUeOU7u4YcfViKRUHV1ddCh4H2h1tZWO77MFr7o+R70urq6oEMZkxobGyWNje/YbGyLaevOYzrY3K62jrimTIxoblGe1i0tNfrBUiPpZ7Tk940Trbrruf06/F67zp53NGlCWLML83T/8vlaMD1fkn/5deOlQ81av22vft9wUnEnoQn5F2h6fo62rFqoz1xc5LqdgdeUFQ6p5VynLsjNVtxJuLpGU3mxKb+9Mfkwf228br+Mlv1htCK/3iK/3iPHyZWXl8txHNXW1gYdCt5HgT7OUKB7i83fW+TXW+TXW+TXW+TXW+TXW+TXe+Q4OQp0+/AedAAAAAAALECBDgAAAACABSjQAQAAAACwAAU6AAAAAAAWoEAHAAAAAMACFOgAAAAAAFiAAh0AAAAAAAtQoAMAAAAAYAEKdAAAAAAALECBDgAAAACABSjQAQAAAACwQCToAOCdpqYmNTc39zsWi8UUDvN3GQAAAACwDQX6GFZTU6PNmzcPOl5YWBhANAAAAACA4VCgj2HV1dVasWJFv2NVVVXcQQcAAAAAC1Ggj2HRaFTRaLTfsZycHDmOE1BEAAAAAIChcCsVAAAAAAALUKADAAAAAGABCnQAAAAAACxAgQ4AAAAAgAUo0AEAAAAAsAAFOgAAAAAAFqBABwAAAADAAhToAAAAAABYgAIdAAAAAAALUKADAAAAAGABCnQAAAAAACxAgQ4AAAAAgAUiQQcAAKk0tsW0decx7T5Yr7Pn4yq6sFjzonlat7RUxVNy+p1zoKldZ2JxTc6JDDrnjROtuuu5/Xq7uV3nOh3lZoc1pyhP9y+frwXT8123YxM31zSavHSoWeu37dWJ1pg6uxLKzgppen6OtqxaqM9cXOS6HVPjaNN8IBb0xRgAwNgUam1tTQQdBPxTWVkpx3FUV1cXdChjUmNjoySpuLg44EjGhtr6Fj3w8mE9s/eE4k5Cam/p/kVegSQpEg7ps3MKpZD04qH3us8ZIBIO6WMfytfRlnNqPHN+yL6KJ0/QzIJcvfb71iHbuWHhdG24crYqywrMXGAGHqut16ZfHFD9qXNDnlM2LVebrpmnmyrLXLUZ5Py9+4W39L2XD+tsZ9eQ50zKztJfXTlb9157yZDnDJozA7gdR1Pt9JVufr2IJV02xTLQeNl/gxqD8ZLfoJBf75Hj5MrLy+U4jmpra4MOBe+jQB9nKNC9xeZvzpYdR3Tr9n3q9/xzQIEehHBIemhlhdYvmxVYDGse36Wndje4Pr/q0hI9uXZJyvOCmr9LH3hFu46fdn3+khlTtXPDFYOOJ50zQxhuHE21M1A6+fUqlnTYFEsy42H/DXIMxkN+g0R+vUeOk6NAtw/vQQdgnS07juiWbfuUsPDPh4mEdMu2fXpkx5FA+h9pcS5JT+1u0Jd+vMujiDIz0uJcknYdP62PP/hKv2MjnTNDjaOpdkwgFvTFGADA+ECBDsAqtfUtunX7PoUkWVifKyEpJOmr2/eptr7F174fq60fcXHe48nXG/RYbb3hiDJz9wtvjbg477Hz2Gnd/cJbktKbM8nG0VQ7JhAL+mIMAGD8oEAHYJUHXj4sJ2Fncd4jIclJSA++8o6v/W76xYGMHv93v8zs8aZ97+XDRh6f7pwZOI6m2jGBWNAXYwAA4wcFOgBrnGzt0DN7TwQdhmtP72lQY1vMl772Npwe9gPh3Djack5vnGg1FFFm/utg07AfCOfG2c4ubd/bkPGceXpPg/Y1tBppx8R8MLEOxmIs4xVjAADjCwU6AGs8vut40k8ltlXcSWjrzmO+9LXx+beMtHPXc/uNtJOpr27fZ6Sdm5/Zm/GciTsJff35/UbaMTEfTKyDsRjLeMUYAMD4wvegj2FNTU1qbm7udywWiykc5u8ysNOBpvagQxixg83+xPy2oX4Ov2dHjk+0mrmbd6ojbqSdtw3lxcR8MLUOxlos4xVjAADjCwX6GFZTU6PNmzcPOl5YWBhANEBqZ2Jmii0/tRkqEFM51+kYaefseTPtZKqzy8wrJRxDl3POUF5MzAdT62CsxTJeMQYAML5QoI9h1dXVWrFiRb9jVVVV3EGHtSbnjL4tacpEf2LOzTazbidNsGP9Z2eFpM7M2wmHpa7M3souSco1lBcT88HUOhhrsYxXjAEAjC/s1mNYNBpVNBrtdywnJ0eOqVtOgGHzonlBhzBic4v8iXlOUZ7qDLzUdXahHTmenp+j0wbu6E2bGFFTe+aV/pzCPNW9m3l+TcwHU+tgrMUyXjEGADC+2HErBQAkrV0yQ5FwKOgwXIuEQ1q3tNSXvu677hIj7dy/fL6RdjL1g5UVRtp55IaFGc+ZSDikzdfNN9KOiflgYh2MxVjGK8YAAMYXCnQA1rgof6JuWDg96DBcW72oRMVTcnzpa2HJVJVNy82ojZkFuVowPd9QRJn53NyoJmVnZdTGpOwsrVxYkvGcWb2oRBUl+UbaMTEfTKyDsRjLeMUYAMD4QoEOwCobrpytcEiy+T56SFI4JN1xxYd97XfTNfMyevw9V2f2eNP+6srZRh6f7pwZOI6m2jGBWNAXYwAA4wcFOgCrVJYV6KGVFUrIziI9JCmh7pdoV5YV+Nr3TZVlqrq0JK3HrllcopsqywxHlJl7r71ES2ZMTeuxS0un6t5ru1/2n86cSTaOptoxgVjQF2MAAOMHBToA66xfNktbVlUoZGGFHgpJW1ZV6OZlswLp/8m1S7Rm8ciK9DWLS/TEjUs8iigzOzdcoaWlIyvSl5ZO1at3XNHv2EjnzFDjaKodE4gFfTEGADA+UKADsNLNy2bp/95+udYs/tCQH5AUCYd09byorp4XHfacy0qn6aIU77+8aEqOLiudNmw7axZ/SP/39ssDf8L7xI1L9OgXF2lmwfDvSZ9ZkKtHv7jI2uK8x6t3XKFv/vHclO9Jn5SdpW/+8dxBxXkPt3Mm1TiaascEYkFfjAEAjH2h1tbWRNBBwD+VlZVyHEd1dXVBhzImNTY2SpKKi4sDjmRsaWyLaevOY9pzqF7tsbiixcWaW5SndUtLez/4qOecg83tauuIa8rEyKBz3jjRqrue26/D77Xr7HlHkyaENbswT/cvn9/74Wlu2rGJm2tyy4b5+9KhZq3ftlcnWmPq7EooOyuk6fk52rJqoT5zcZHrdkyNo8n5kGl+bZqbNsXSG5MF89dPfo/BeMuv38iv98hxcuXl5XIcR7W1tUGHgvdRoI8zFOjeYvP3Fvn1Fvn1Fvn1Fvn1Fvn1Fvn1HjlOjgLdPrzEHQAAAAAAC1CgAwAAAABgAQp0AAAAAAAsQIEOAAAAAIAFKNABAAAAALAABToAAAAAABagQAcAAAAAwAIU6AAAAAAAWIACHQAAAAAAC1CgAwAAAABgAQp0AAAAAAAsEAk6AHinqalJzc3N/Y7FYjGFw/xdBgAAAABsQ4E+htXU1Gjz5s2DjhcWFgYQDQAAAABgOBToY1h1dbVWrFjR71hVVRV30AEAAADAQhToY1g0GlU0Gu13LCcnR47jBBQRAAAAAGAo3EoFAAAAAMACFOgAAAAAAFiAAh0AAAAAAAtQoAMAAAAAYAEKdAAAAAAALECBDgAAAACABSjQAQAAAACwAAU6AAAAAAAWoEAHAAAAAMACFOgAAAAAAFiAAh0AAAAAAAtEgg4AyR08eFCf+tSn1NHRIUnat2+fZs6cGXBU6NHYFtPWncd0oKldZ2JxTc6JaF40T9eWTVB0co7xdtctLVXxlPTbtdkbJ1p113P79XZzu851OsrNDmtOUZ7uXz5fC6bnG+3Lr/y66cfUOX5xM042xWv7GASZq3T6tmlsh4pt98F6nT0fV9GFxdbE1jc+G3MHALBPqLW1NRF0EOgvkUjouuuu029+85veY6YK9MrKSjmOo7q6uozbGo9q61v0wMuH9czeE4o7g5dO1rlT+vxHi7Xxf39clWUFxtqNhEO6YeF0bbhy9ojatdljtfXa9IsDqj91bshzyqblatM183RTZZkkqbGxUZJUXFw8or78yq+bfj47p1AKSS8eei+jc7yYD8ny62aciqdM0MxpuXrt962Bz19jY3BxoZSQXnzb3Bg0NjbqteOntPV3ZwJZ6+msA5v3pkGxtbd0/yKvIPDYksY3QNDxjVS6+y/cIb/eI8fJlZeXy3Ec1dbWBh0K3keBbqFHH31Ud9xxR79jFOjB27LjiG7dvk9Jnmd94P0niOHJBXpoZYXWL5tlpt33hUNy3a7N1jy+S0/tbnB9ftWlJXpy7ZK0/s/Vr/yOpB9TTM+Hgfkd6Til4vX8tX0M7v/5q9r43H4lJqUuxkznKp11IMnavSnp9Qwo0IOKbcj4hjBa9nWKG2+RX++R4+Qo0O3DS9wtc+LECd1zzz1Bh4EBtuw4olu27VPI5fmJhHrPv3mYJ11etWuzdIq+p3Y3KBSSHrhqxoge51d+R9qPKV7OB9PFueRtvLaPwZYdR/T1n+833q4b6a4DSVbuTbbvm7bHBwCwGx8SZ5k777xTp0+fDjoM9FFb36Jbt3c/eXJ7Yy6h7ie2X92+T7X1Lb62a7PHauvTLvqefL1BT7523PX5fuU3nX5M8Wo+ZDJOw/EqXtvHoCc+0+26ke46SPZzqsf4sTfZvm/aHh8AwH4U6BZ59tln9bOf/UySNG3atICjQY8HXj4sJzHyJ/4JSU5CevCVd3xt12abfnEgo8f/08uHXZ/rV37T7ccUL+ZDpuM0HC/itX0MeuIz3a4bfubGj73J9n3T9vgAAPajQLfEqVOn9Nd//deSpAkTJuhb3/pWwBFBkk62duiZvScyauPpPQ1qbIv50q7N9jacHvaDxtw4fuqc9je2pTzPr/ya6McUU/PhdydbMx4nN0zFa/sYBLnWg8qNV3uT7fum7fEBAEYHCnRL3H333Tp58qQkacOGDfrIRz4ScESQpMd3HU/66bsjEXcS2rrzmC/t2mzj828Zaec7/5n67q5f+TXRjymm5sN3/89BA9GkZipe28cgyLUeVG682pts3zdtjw8AMDrwIXEW+O///m9t3bpVknTxxRfrzjvvHPEnKVZWVro67/DhwyotLe39JEsMb/fB+g8+GdiNs8k/P2DPoXo1fnRK+u0OYWC7Nqt755jUfjazRs6e1tv151POX7/ya6ofUzKdD01NTTp0tEGKTTAY1dBMzF/bx6BffEPsD+m060aQufFib0p5PS7z69W+Odb39aampqBDGNPIr/fIcXLxeFzhMPdsbcJoBKyjo0O33XabEonuv7p///vfV05OTsBRocfZ83Ej7bTH+rfjVbs264ibuZPnph2/8muqH1NMzIdYl393XE3Ea/sYBLnWg8yNF3uT7fum7fEBAEYH7qAH7L777tPhw90ffLV27Vp9+tOfTqsdt3fce74Hne+AdKfowmIpL433Aw74Ht5ocXG/nKfd7gAD27XZ5IJCKd6eeTvTJqW8Zr/ya6ofU0zMh7ypBVKHP38kNBGv7WOQNL681N+DnqpdN4LMjRd7k+vrSZFfr/bN8bKv2xzbWEB+vUeO+4tEInIcJ+gw0Ad30AO0d+9e/cu//IskqaioSPfee2/AEWGgedE8I+3MLerfjlft2myOoVhnXjAp5Tl+5ddUP6aYmA+zClPn1xQT8do+BkGu9SBz48XeZPu+aXt8AIDRgQI9QM8995zi8e6XsjU3N2vWrFnKz89Xfn6+li9f3u/ciooK5efn6yc/+UkQoY5ba5fMUCQcyqiNSDikdUtLfWnXZvddd4mRdr75x/NSnuNXfk30Y4qp+fC3fzTXQDSpmYrX9jEIcq0HlRuv9ibb903b4wMAjA4U6AHqed857HVR/kTdsHB6Rm2sXlSi4in9XzLsVbs2W1gyVWXTcjNqY8a0XM0vTv3hSX7l10Q/ppiaDx+9KD/jcXLDVLy2j0GQaz2o3Hi1N9m+b9oeHwBgdKBAD9DMmTN1+eWXJ/1fRUVFv3OXLl2qyy+/XBdeeGFA0Y5fG66crXBIGul9kZCkcEi644oP+9quzTZdk/ru93C+duVs1+f6ld90+zHFi/mQ6TgNx4t4bR+DnvhMt+uGn7nxY2+yfd+0PT4AgP0o0AP0Z3/2Z3r++eeT/m/z5s39zn3sscf0/PPP66qrrgoo2vGrsqxAD62sUELun3SFJCUk/WBlhSrLkn9gkVft2uymyjJVXVqS1mPXLC7Rmo/NcH2+X/lNpx9TvJoPmYzTcLyK1/Yx6InPdLtupLsOkv2c6jF+7E2275u2xwcAsB8FOuDC+mWztGVVhUIun3GFQtKWVRW6edmsQNq12ZNrl2jN4pEVf2sWl+iJG5eMuC+/8jvSfkzxcj6kM06peBmv7WOwftks3f+/5gey1tNdB7buTbbvm7bHBwCwW9bGjRs3BR0EBquvr9cTTzzR++9bbrlF06ZNy7jdmpoaJRIJ3XbbbRm3Nd4sLZ2may+5UO3nu/TWu2fkJPkIgayumK5fMF3/37pP6PoF7t6L6KbdSDikL176If3oC4tct2uzVQtLNLMgV7sbWnW6Y+jv/J1ZkKsHri/Xd66dL0lqb+/+mrbJkye77suv/Lrt54/nRjWnME9HW85ldI4X82Fgft2O00VTclRePEWNZ2KBzl/bx+DiqRF97uIiOZGJvq/1dNaBzXtT0tg6O7p/OSE30NiGjG+A0bavp7P/wj3y6z1ynNzDDz+sRCKh6urqoEPB+0Ktra18Utk40vM96HV1dUGHMqo1tsW0decxHWxuV1tHXFMmRjS3KE/Xlk1QdHJO2t+xOVS765aWjtkPDnrjRKvuem6/Dr/XrrPnHU2aENbswjzdv3y+FkzP73duY2OjpPS/w9Sv/Lrpx9Q5Jg2XXzfjZNP8tXEM+uY3yFyl07dNYztUbHsO1as9Fle0uNia2PrGZ2PuRiLT/RfDI7/eI8fJlZeXy3Ec1dbWBh0K3keBPs5QoHuLzd9b5Ndb5Ndb5Ndb5Ndb5Ndb5Nd75Dg5CnT78B50AAAAAAAsQIEOAAAAAIAFKNABAAAAALAABToAAAAAABagQAcAAAAAwAIU6AAAAAAAWIACHQAAAAAAC1CgAwAAAABgAQp0AAAAAAAsQIEOAAAAAIAFKNABAAAAALAABToAAAAAABaIBB0AvNPU1KTm5uZ+x2KxmMJh/i4DAAAAALahQB/DampqtHnz5kHHCwsLA4gGAAAAADAcCvQxrLq6WitWrOh3rKqqijvoAAAAAGAhCvQxLBqNKhqN9juWk5Mjx3ECiggAAAAAMBRupQIAAAAAYAEKdAAAAAAALECBDgAAAACABSjQAQAAAACwAAU6AAAAAAAWoEAHAAAAAMACFOgAAAAAAFiAAh0AAAAAAAtQoAMAAAAAYAEKdAAAAAAALECBDgAAAACABSJBBwAAqTS2xbR15zHtPlivs+fjKrqwWPOieVq3tFTFU3ICieVAU7vOxOKanBMZFEuyc6bnd//uRGtMZ2JxdXY5erOxTZ1dCXV2JZSbHdacojzdv3y+FkzPNxaPm3htkm5+vbqmgX2FwyGdOtepgtxsdTkJV32bmr+mcuPVnBltc22g0R4/AGBsCLW2tiaCDgL+qayslOM4qqurCzqUMamxsVGSVFxcHHAkY0NtfYseePmwntl7QnEnIbW3dP8ir0CSFAmHdMPC6dpw5WxVlhX4G8sAkXBIn51TKIWkFw+9l/Qct8qm5WrTNfN0U2VZ2vFkhUP6UP5E/f70OXUlCSVZ7oKcvybya3I+pIrHTd+m5q+r3FxcKCWkF98eOjep8pfOnHEbnx/rNN35a0v8tuP/37xFfr1HjpMrLy+X4ziqra0NOhS8jwJ9nKFA9xabvzlbdhzRrdv3qd/z5QEFTo9wSHpoZYXWL5vlXyw+qLq0RE+uXeJpPH1zF9T8NZ3fTOdDJvH09C3JyPwNau4Np2+8I4nP63Wazvy1KX7b8f9v3iK/3iPHyVGg24eXuAOwzpYdR3TLtn0KuTw/kVDv+TcbfvI80lhMemp3g0Ih6YkbPyjSTcfTN3cr5uQaatU9L/KbyXzINJ6eviVlPH+DnHvD6Yn3lbff656jI3ycF+s0HTbtMwAA9OBD4gBYpba+Rbdu734S7PamYULdxdBXt+9TbX1LoLGY9uTrDXqstt6zePrm7rXjpwy16o5X+U13PpiIJzHEz6keMzBeG+beUHri6SnOg16n6bBpnwEAoC8KdABWeeDlw3ISIy9KEpKchPTgK+8EHotpf/fLA57G05O7H/5PveGWh+dlftOZD0GO98B4bZl7qdiwTtNh0z4DAEBfFOgArHGytUPP7D2RURtP72lQY1vMilhMOdpyTi8davY8np+9eVJNZzLPnRt+5dftfLBlvJ/e06B9DaetiMVLptZpOmzaZwAAGIgCHYA1Ht91PKNPP5ekuJPQ1p3HrIjFpPXb9noeT5eT0L/tbvC0jx5+5dftfLBlvONOQl9//i0rYvGSqXWaDpv2GQAABuJD4sawpqYmNTc39zsWi8UUDvN3GdjpQFO7kXYONmfejqlYTDnR6s/dusN/OOtLP37m1818sGm83zYwf0cDE+s0HTbtMwAADESBPobV1NRo8+bNg44XFhYGEA2Q2plY3Eg7bR2Zt2MqFlM6k30xtQfafbpuP/PrZj7YNN7nOp2gQ/CFiXWaDpv2GQAABqJAH8Oqq6u1YsWKfseqqqq4gw5rTc4xsyVNmZh5O6ZiMSU7KyR1et9Pnk/X7Wd+3cwHm8Y7N3t87NEm1mk6bNpnAAAYiP93GcOi0aii0Wi/Yzk5OXKc8XF3BqPPvGiekXbmFmXejqlYTJmen6PTPtyxm33BJM/7kPzNr5v5YNN4zynKU51FL7n3iol1mg6b9hkAAAYaH3+mBzAqrF0yQ5FwKKM2IuGQ1i0ttSIWk7asWuh5PFnhkL5waYmnffTwK79u54Mt4x0Jh7T5ukusiMVLptZpOmzaZwAAGIgCHYA1LsqfqBsWTs+ojdWLSlQ8JceKWEyZWZCrz1xc5Hk8ny+/SNHJmefODb/y63Y+2DLeqxeVqKJkqhWxeMnUOk2HTfsMAAADUaADsMqGK2crHJJGen8rJCkcku644sOBx2LaPVfP8zSentx95RNlhlsenpf5TWc+BDneA+O1Ze6lYsM6TYdN+wwAAH1RoAOwSmVZgR5aWaGE3D95DklKSPrBygpVlhUEGotpaxaX6KbKMs/i6Zu7j82YZqhVd7zKb7rzwUQ8oSF+TvWYgfHaMPeG0hNP1aUlVqzTdNi0zwAA0BcFOgDrrF82S1tWVSjk8plzKCRtWVWhm5fNCjwWk9YsLtETNy7xNB4vc+eGF/nN5JoyjaenbxPzN8i5N5yeeJ9cu8SadZoOm/YZAAB68CnuAKx087JZ+tiMqXrwlXf09J4GxZ3B3wMeCYe0elGJ7rjiw57e0XIby+cuLpIk/deh5qTnuDWzIFf3XD2v9855OvFkhUOaMXWijp86p2Rfoe5X7twwlV9T1+QmHjd9m5i/JnOT6px05oxN6zQdoz1+AMDYE2ptbU3/WSRGncrKSjmOo7q6uqBDGZMaGxslScXFxQFHMrY0tsW0decx7TlUr/ZYXNHiYs0tytO6paW+f1BTTywHm9vV1hHXlImRQbEkO+ei9393si2mto64Op2E3jzZqriT0Pl4QpMmhDW7ME/3L5+vBdPzjcXjJt7etiyYv+nm16v5MLCvrHBILec6dUFutuJOwlXfpuavqdyYnDMjjc9Lmc7foOO3nQ37w1hGfr1HjpMrLy+X4ziqra0NOhS8jwJ9nKFA9xabv7fIr7fIr7fIr7fIr7fIr7fIr/fIcXIU6PbhPegAAAAAAFiAAh0AAAAAAAtQoAMAAAAAYAEKdAAAAAAALECBDgAAAACABSjQAQAAAACwAAU6AAAAAAAWoEAHAAAAAMACFOgAAAAAAFiAAh0AAAAAAAtQoAMAAAAAYIFI0AHAO01NTWpubu53LBaLKRzm7zIAAAAAYBsK9DGspqZGmzdvHnS8sLAwgGgAAAAAAMOhQB/DqqurtWLFin7HqqqquIMOAAAAABaiQB/DotGootFov2M5OTlyHCegiAAAAAAAQ+FWKgAAAAAAFqBABwAAAADAAhToAAAAAABYgAIdAAAAAAALUKADAAAAAGABCnQAAAAAACxAgQ4AAAAAgAUo0AEAAAAAsAAFOgAAAAAAFqBABwAAAADAAhToAAAAAABYgAIdAAAAAAALRIIOAN0OHjyohx9+WC+++KIaGhqUlZWlmTNn6k/+5E906623qqioKOgQYYHGtpi27jymA03tOhOLa3JORPOieVq3tFTFU3KsjMermNNp16/HjFfkauwKcq0DADCehFpbWxNBBzHePfHEE7r99tt1/vz5pL8vLi7WT3/6Uy1YsCDjviorK+U4jurq6jJuC4M1NjZK6h4zk2rrW/TAy4f1zN4TijuDl2wkHNINC6drw5WzVVlWYLTvdOP57MWFUkJ68e33jMXc2Nio146f0tbfnRlRLtLJn20590O683c85iodXu0PXgpqradjNOZ3NCG/3iK/3iPHyZWXl8txHNXW1gYdCt5HgR6wN998U5/+9KcVj8clSdnZ2Zo/f75Onz6to0eP9p43c+ZMvfrqq5o4cWJG/VGge8uLzX/LjiO6dfs+JXneO0g4JD20skLrl80y1n8m8bgxkpjv//mr2vjcfiUmpX6S39OupBHnL53HeJlzv6Qzf22bnzYbbU8Og1zr6Rht+R1tyK+3yK/3yHFyFOj24SXuAfvBD37QW5xPnjxZv/rVr1ReXi5Juv/++/Xd735XknT06FFt375dX/rSlwKLFf7bsuOIbtm2TyGX5yffc7hsAAAgAElEQVQS6j3/Zg+eBI80HjfcxrxlxxF9/ef7R9yupBHnL53HeJVzm9k2P2FOkGsdAIDxjA+JC9iLL77Y+/Pq1at7i3NJuvPOO/vdMd+1a5evsSFYtfUtunV795NZtzewEuouLL+6fZ9q61sCj8cNNzH39D3SdpP97MVjvMq5zWybnzAnyLUOAMB4R4EesLvvvlv33HOPvvKVr+jqq6/u97usrKx+BXpnZ6ff4SFAD7x8WE5i5E+QE5KchPTgK+9YEY8bqWLu6dtWXuXcZrbNT5gT5FoHAGC8o0AP2Je+9CV97Wtf0z/+4z9q+fLl/X73+uuv69SpU73/njlzpt/hISAnWzv0zN4TGbXx9J4GNbbFrInHjWQx+9W3CSZzbjPb5ifMCXKtAwAACnRrxeNx/e3f/m2/YwPvsGPsenzX8aSfhjwScSehrTuPWROPG8li9qtvE0zm3Ga2zU+YE+RaBwAAfEiclRzH0V/8xV/o17/+de+xq6++WhUVFUM+prKy0lXbhw8fVmlpae8nWcKspqYmI+3sPlgvtWf+Hs09h+rV+NEp1sTjxsCY+/V99rQvMWTCVM6D4Hb+2jY/RwtT+4OXglzrmRoN+R3NyK+3yK/3yHFy8Xhc4TD3bG3CaFimq6tL1dXVevrpp3uP5efn63vf+16AUcFvZ8/HjbTTHjPTjql43BgYs599m2Aq5zazbX7CnCDXOgAA4A66VTo7O/XlL39Zzz77bO+x7OxsPfrooyorKxv2sW6/u7Dne9D5DkhvZZrfoguLpbzM358ZLS42Mtam4nFjYMxJ+85L/T3oQTGV8yClit+2+Tna2HzNQa51U2zO71hAfr1Ffr1HjvuLRCJyHCfoMNAHBbolOjs7deONN+qFF17oPTZhwgQ99thjvPd8HJoXzTPSztwiM+2YiseNgTH72bcJpnJuM9vmJ8wJcq0DAABe4m6FRCKh6urqfsV5bm6unnjiCX3+858PMDIEZe2SGYqEQxm1EQmHtG5pqTXxuJEsZr/6NsFkzm1m2/yEOUGudQAAQIFuhe985zvavn17779zc3P1b//2b9w5H8cuyp+oGxZOz6iN1YtKVDwlx5p43EgWs199m2Ay5zazbX7CnCDXOgAAoEAPXG1trf7pn/6p37Ef/vCHuvLKKwOKCLbYcOVshUPSSO9lhSSFQ9IdV3zYinjcSBVzT9+28irnNrNtfsKcINc6AADjHQV6wP7+7/++3wczTJw4Uf/6r/+q6667btD//uEf/iHASOG3yrICPbSyQgm5f6IckpSQ9IOVFaosM/tBaunE44abmHv6Hmm7yX724jFe5dxmts1PmBPkWgcAYLzjQ+ICdPLkSf3qV7/qd6yjo6Pf95/3VVJS4kdYsMj6ZbMUkvTV7fuUSKQ+PxSSHl5ZoZuXzbIiHjfcxrx+2Sy1/aFJX39uv9x03dOuNPL8pfMYr3JuM9vmJ8wJcq0DADCeUaAH6Le//a0Spp75YMy6edksfWzGVD34yjt6ek+D4s7gORMJh7R6UYnuuOLDnt+ZchvP5y4ukiT916FmYzH/+cfLVDE9X4/vbx9RLtLJn005t5lt8xPmBLnWAQAYr0Ktra1UiONIz/eg19XVBR3KmNTY2CjJu+/YbGyLaevOYzrY3K62jrimTIxoblGe1i0tDeQDl9zEYzLmvvlNp12/HjNaZTp/x1Ou0uH1/uAlv9d6WjGO4vyOBuTXW+TXe+Q4ufLycjmOo9ra2qBDwfso0McZCnRvsfl7i/x6i/x6i/x6i/x6i/x6i/x6jxwnR4FuHz4kDgAAAAAAC1CgAwAAAABgAQp0AAAAAAAsQIEOAAAAAIAFKNABAAAAALAABToAAAAAABagQAcAAAAAwAIU6AAAAAAAWIACHQAAAAAAC1CgAwAAAABgAQp0AAAAAAAsEAk6AHinqalJzc3N/Y7FYjGFw/xdBgAAAABsQ4E+htXU1Gjz5s2DjhcWFgYQDQAAAABgOBToY1h1dbVWrFjR71hVVRV30AEAAADAQhToY1g0GlU0Gu13LCcnR47jBBQRAAAAAGAo3EoFAAAAAMACFOgAAAAAAFiAAh0AAAAAAAtQoAMAAAAAYAEKdAAAAAAALECBDgAAAACABSjQAQAAAACwAAU6AAAAAAAWoEAHAAAAAMACFOgAAAAAAFiAAh0AAAAAAAtEgg4AwAfeONGqu57br7eb23Wu01FudlhzivJ0//L5WjA9X41tMW3deUwHmtp1JhbX5JyI5kXztG5pqYqn5AQdfsaGur6Pl07TP7z0tureOaaOeEKTCwr75cWGGIMaA7/ise26U0m1lgYa6vquveRCvfDWuxldd08smc7f0TYGAABg5EKtra2JoIOAfyorK+U4jurq6oIOZUxqbGyUJBUXF4/ocY/V1mvTLw6o/tS5Ic+ZlJ2ljniXnCQrNhIO6YaF07XhytmqLCsYUd82qK1v0QMvH9Yze08onuwCe7S3dP8374NrLJuWq03XzNNNlWWBxuj3GHgRT7L5a9t1p+JmLfWdM67n3gBurntQLGnO39E2BkFJd/+FO+TXW+TXe+Q4ufLycjmOo9ra2qBDwfso0McZCnRvpbP5r3l8l57a3WCk/3BIemhlhdYvm2WkPT9s2XFEt27fl/QPD4MkKXB6VF1aoifXLjEb3PtGEqMfY+BVPAPnr23XncpI19KSGVP1+u9Pu5t7QxjqupPGksb8HW1jECSefHuL/HqL/HqPHCdHgW4f3oMOBMhkcS5JiYR0y7Z9emTHEWNtemnLjiO6Zds+JQz8mfCp3Q360o93Zd7QACON0esx8Cse2647lXTW0q7jmRXnUvLrTieWZPN3tI0BAADIHAU6EJDHauuNFueSlJAUkvTV7ftUW99itG3TautbdOv2fQqpO24Tnny9QY/V1htqLb0YvRwDv+Kx7bpT8WItuTXwujOJpe/8HW1jAAAAzKBABwKy6RcHPGk3IclJSA++8o4n7ZvywMuH5STMFec9/u6X5vKaboxejYFf8dh23al4tZbc6nvdmcbSM39H2xgAAAAzKNCBAOxtOD3sh1iZ8PSeBjW2xTztI10nWzv0zN4TnrR9tOWc3jjRmnE7JmI0OQZ+xfNum13XnYofa8mtp/c0ZBzL0ZZzeulQ86gaAwAAYA4FOhCAjc+/5XkfcSehrTuPed5POh7fdXxEn5g9Unc9tz/jNkzEaHIM/Irn6T0j+zTzdPsxxY+15JapOb1+295RNQYAAMAcvgd9DGtqalJzc3O/Y7FYTOEwf5cJ2tvN7b70c9CnfkbqQJO3cR1+L/P2TcVoagz8iuft98760o8pfq0lP51oNXPn29b1DwAAhkaBPobV1NRo8+bNg44XFhYGEA36Otfp+NJPW0fcl35G6kzM27jOns88v6ZiNDUGfsVz9rxd152KX2vJT51dZu7E27r+AQDA0CjQx7Dq6mqtWLGi37GqqiruoFsgN9ufMZgy0c4lPjnH27gmTcg8v6ZiNDUGfsUzaUJEUuZ3cP2ae36tJT9lZ4WkzszbsXX9AwCAofH/3mNYNBpVNBrtdywnJ0eOM/buOI02c4ryVOfxy7wlaW5Rnud9pGNe1Nu4Zhdm3r6pGE2NgV/xzCmcJCnzuenX3PNrLflpen6OThu4+23r+gcAAEMbe7cegFHgvusu8byPSDikdUtLPe8nHWuXzFAkHPKs/fuXz8+4DRMxmhwDv+JZvWi6Vdedih9ryS1Tc3rLqoWjagwAAIA5FOhAABaWTFXZtFxP+1i9qETFU3I87SNdF+VP1A0Lp3vS9syCXC2Ynp9xOyZiNDkGfsVz4RS7rjsVP9aSW6sXlWQcy8yCXH3m4qJRNQYAAMAcCnQgIJuumedJuyFJ4ZB0xxUf9qR9UzZcOVvhUHe8Jt1ztbm8phujV2PgVzy2XXcqXq0lt/ped6ax9Mzf0TYGAADADAp0ICA3VZap6tISo22GJCUk/WBlhSrLCoy2bVplWYEeWlmhhMwV6WsWl+imyjJDraUXo5dj4Fc8tl13Kl6sJbcGXncmsfSdv6NtDAAAgBkU6ECAnly7RGsWmyssQiFpy6oK3bxslrE2vbR+2SxtWVWhkIEKfc3iEj1x45LMGxpgpDF6PQZ+xWPbdaeSzlpaWjpVmb5tPNl1pxNLsvk72sYAAABkLmvjxo2bgg4C/qmpqVEikdBtt90WdChjUnt796dJT5482fVjVi0s0cyCXO1uaB32k5snZWepK5FQsm9IjoRD+uKlH9KPvrBI1y/w5r3dXllaOk3XXnKh2s936a13z8gZ7iugOzu6/zvhg/f5zizI1QPXl+s712b+wXCZxOjnGHgVz8D5a9t1p+J2LfXMmYdXLXQ/9wZIdd1JY0lj/o62MQhSOvsv3CO/3iK/3iPHyT388MNKJBKqrq4OOhS8L9Ta2jqCpyQY7SorK+U4jurq6oIOZUxqbGyUJBUXF6f1+DdOtOqu5/br8HvtOnve0aQJYc0uzNP9y+drwfR8NbbFtHXnMR1sbldbR1xTJkY0tyhP65aWjokPhBrq+j5eOk3/8NLbOnDkmM51JjTlgsJ+ebEhxqDGwGQ8w81f2647lVRraaChru/aSy7UC2+9m9F198SS6fwdbWPgt0z3XwyP/HqL/HqPHCdXXl4ux3FUW1sbdCh4HwX6OEOB7i02f2+RX2+RX2+RX2+RX2+RX2+RX++R4+Qo0O3De9ABAAAAALAABToAAAAAABagQAcAAAAAwAIU6AAAAAAAWIACHQAAAAAAC1CgAwAAAABgAQp0AAAAAAAsQIEOAAAAAIAFKNABAAAAALAABToAAAAAABagQAcAAAAAwAIU6AAAAAAAWCASdADwTlNTk5qbm/sdi8ViCof5uwwAAAAA2IYCfQyrqanR5s2bBx0vLCwMIBoAAAAAwHAo0Mew6upqrVixot+xqqoq7qADAAAAgIUo0MewaDSqaDTa71hOTo4cxwkoIgAAAADAULiVCgAAAACABSjQAQAAAACwAAU6AAAAAAAWoEAHAAAAAMACFOgAAAAAAFiAAh0AAAAAAAtQoAMAAAAAYAEKdAAAAAAALECBDgAAAACABSjQAQAAAACwAAU6AAAAAAAWiAQdAKS2tjY9+OCDevbZZ1VfX6+JEydq0aJFuvnmm7V8+fKgwzOusS2mrTuP6UBTu87E4pqcE9G8aJ7WLS1V8ZQc1+28caJVdz23X283t+tcp6Pc7LDmFOXp/uXztWB6vq+xmIo31Tlu4jV1TY/+9qhu/+kbOht3pISkkDQpEtY/r1igL1820/U1pWrHTbzb9zbo5mf2quW9JjmOlDWlQNMmRvTIDQu1cmGJ62vqaedUR1yOI4XDGtTOS4eatX7bXp1ojamzK6HsrJCm5+doy6qF+szFRUl/H508QZ+7uEhOQjoTi6stFldtfYs64o66HA1qw00/bsfSxJxxI535GwpJZ8/HlTchIich5WaHdeHkHCUkNZ2Jpb1uTax9t/zaI2zbiwAAQDBCra2tiaCDGM+ampp03XXXqa6uLunv77jjDn3729821l9lZaUcxxmyPy/V1rfogZcP65m9JxR3Bk+7SDikGxZO14YrZ6uyrGDIdh6rrdemXxxQ/alzQ55TNi1Xm66Zp5sqyzyNZaDGxkZJUnFx8YjivSA3IoVC+sPZziHPmZSdpY54l5KEq0g4pM/OKZRC0ouH3svomj7/o9/quf3vKtXGMDErpI6uoc9K9ftUIuGQSqfm6Oipjg+uub2l+795H8SfFQpp3dIZerTq0iHb+vJTu7V153F1JYaOJyQpHJIyCNmVrLAUUijpGPXIiYQ154JcHWg+O+RYfuxD+Tp66pwa284P2U6qOTNwPqQ9fydlSwnpD+eGnr9upFq3Jta+W17sEcny69VelIyf+QtCsvzCHPLrLfLrPXKcXHl5uRzHUW1tbdCh4H0U6AH78z//c/30pz/t/XdFRYXefffd3k1EkrZt26arrrrKSH9BFehbdhzRrdv3JS0UBgqHpIdWVmj9slmDfrfm8V16aneD636rLi3Rk2uXeBJLMgM3/5HG64fhrumCb76glnNx/4NyK0mB3qNs2kQdvXvwOpl5769Uf6rD68hGrb7zwZb5m2zdmlj7bnm1RwzMr5d70UB+5i8oPPn2Fvn1Fvn1HjlOjgLdPrwHPUAHDhzoV5w/8MAD+s1vfqM33nhDlZWVvcc3b94cRHjGbNlxRLds26dhbl72k0hIt2zbp0d2HOl3PJ1i4andDfrSj3cZj8UNG4tzaehrsr44T6H+VIdmfudX/Y5RnKdmcr2ZMnDdmlj7bvm1R9i+F6WbPwAAkBkK9AD1Lc6Li4t10003SZJycnK0YcOG3t+9+uqrOn78uO/xmVBb36Jbt+9TSEr5kuke779NWV/dvk+19d13TB+rrU+7WHjy9QY9VltvLBY3MonXa8mu6fM/+u2oLs571Ld06MtP7ZbU/bJ2ivPU+s6H146fkmTH/O1ZtybWvlt+7RGjZS8aaf4AAEDmKNAD9Nprr/X+vHjxYoXDHwzHJz7xiX7nvv76677FZdIDLx+Wk3D/JLRHQpKTkB585R1J0qZfHMgojr/75QFjsbiRabxeG3hNz+1/N9iADNq683i//yK1nvnww//pLsZsmb9/98sDRta+W37tEaNpLxpJ/gAAQOYo0APU933g06dP7/e7wsJC5eTkJD13tDjZ2qFn9p7IqI2n9zToxYNNw36okRtHW84ZiaWxLZbyvN+dbM04Xr88vadB//TSwREXCjbrSiR057/vG/YD4ZDcz948qV8fbrZm/h5tOWdk7b9xojXleab2q1R7xLtt/vQjSXsbTvuWPwAAYAYFeoD+8Ic/9P6cnz/4q23y8vKSnjtaPL7r+LCfVO1G3Enolu37jMRjIpatO4+lPO+7/+dgRv34Ke4ktPG50ffHn1S+9/KRoEMYlbqchL7+3P6gwzDuLhfXZGq/SrVHPL0n+ae1m+5HkjY+/1ZG/fRwkz8AAGAG34MeoPb29t6fs7OzB/2+77G+5ybT90PlhnP48GGVlpb2+5R4r+w+WP/Bp25n4PcNbVLMjvdH7zlUr8aPThny901NTTp0tEGKTfAxqsxk9sVYPjt72tVp3DtP09nTOtHYLmXlpT53FDlwJKbGxlnDnmNqvxpuj2hqatIb7xyX2s962k+PuneOGenLTf5s0NTUFHQIYxr59Rb59R45Ti4ej/d7my2Cx2gEKJHiJbihUMinSLxx9ryZojrTu00mtbv4Q0HM6y/SBjzUZdF6M+VcZ+prMrVfpdojzp3v8qUfSeqImxlLN/kDAABmcAc9QHl5eTp9uvuOYGfn4PuYfY/1fbl7Mm6/u7Dne9D9+A7IoguLpbzU75NMZcLEiM512HEHPVpcnDJ3eVMLpI6cYc9BhpJ8DzrMyM6JqCMy/J3Z0WbKBXkp162p/SrVHnFBUVR6b/hXRJnoR5ImFxRK8cz7cpM/m4ymWEcj8ust8us9ctxfJBKR4zhBh4E+uIMeoIKCD4qMM2fODPp9W1tb788XXHCBLzGZNC9q5mWy0/PtKXbnFqW+plmFk3yIxJzs8Oh+pUYyY++K/FM8ZfS8PcOt2YWp162p/SrVHjHH0P7gZi+a4+IcN9zkDwAAmEGBHqDZs2f3/nziRP9P9X3vvfd0/vz53n9/5CMf8S0uU9YumaFIhsVfJBzSwysrjMRjIpZ1S0tTnve3fzQ3o378FAmHdN/y0Te3UvmrK2cFHcKolBUOafPy+UGHYdz9Lq7J1H6Vao9YvWi6b3vRfdddklE/PdzkDwAAmEGBHqDFixf3/rxz5051dX3w3sRXX311yHNHi4vyJ+qGhdNTnziM1YtK9Nm5UZVNy82onZkFuUZiKZ6S+m7+Ry/Kzzhev6xeVKKvfWbumLrjnBUK6R//d4WyRvlnOATh8+UX6fLZRdbM35kFuUbW/oLpg78lYyBT+1WqPeLCKf70I0kLS6b6lj8AAGAGBXqAli9f3vvzu+++q0cffVSSdP78eX3/+9/v/d3SpUs1Y8YM3+MzYcOVsxUOjfwlxyFJ4ZB0xxUfliRtumZeRnHcc/U8Y7G4kWm8Xht4TcvnXxhsQAatWzqj33+RWs98+MonyiTZM3/vuXqekbXvll97xGjai0aSPwAAkDkK9AAtXbpUf/RHf9T776997Wv61Kc+pQULFug3v/lN7/G77roriPCMqCwr0EMrK5SQ+yejIXV/TdYPVlaosqz7ffo3VZap6tKStGJYs7hEN1WWGYvFjUzi9Vqya/rZ/3uZCnJH/2dGlhVM1KNVl0qSHq26VGXTJgYckf36zoePzZgmyY7527NuTax9t/zaI0bLXjTS/AEAgMxRoAfskUce6ff+8n379unkyZO9/77tttt0zTXXBBGaMeuXzdKWVRVy+4rjUEjasqpCNy+b1e/4k2uXaM3ikT3RXLO4RE/cuMR4LG6kE68fhrqmP3znWhVMGr1FelnBRB395lX9jh29+yqVFVCkD8fkejNl4Lo1sfbd8muPsH0vSjd/AAAgM1kbN27cFHQQ49nkyZN14403asKECWpqatKZM2eUl5enyy67TN/97nd1yy23GO2vpqZGiURCt912m9F2U1laOk3XXnKh2s936a13zyjZVy1HwiF98dIP6UdfWKTrFyR/j+aqhSWaWZCr3Q2tOj3MV6/NLMjVA9eX6zvXDv5wI1OxJNPe3v2VRpMnTx5RvBdMytak7Cyd6xz6ay4mZWepK5FQsm8kjoRD+uO5Uc0pzNPRlnNpX9Ndn5urXcdO6WBz6q9mmpgV0nBfs5zq96lEwiHNnJar1lj8g2vu7Oj+74QP3lebFQrp//l4qV665VNJ29lwxRzVt5zTvhNtSXPXIyQpK6RhzzEhEu6OebivG58YCesjRXlqOdc55Fh+fMY0dSUSOjPM92qnmjMD50O687dwUrZyU8xfN4ZbtybWvlte7RED8+vlXjSQn/kLysD8wizy6y3y6z1ynNzDDz+sRCKh6urqoEPB+0Ktra1ePx+FRXq+B72uri6wGBrbYtq685gONrerrSOuKRMjmluUp3VLS1198FGPN0606q7n9uvwe+06e97RpAlhzS7M0/3L57v+UCNTsfS219goKfl3bLqJN9U5buI1dU2P/vaobv/pGzobd9TzWtxJkbD+ecUCffmyma6vKVU7buLdvrdBNz+zVy3vNclxpKwpBZo2MaJHbliolQvd3xnsaedUR1yOI4XDGtTOS4eatX7bXp1ojamzK6HsrJCm5+doy6qF+szFRUl/H508QZ+7uEgJSW0dcbXF4qqtb1FH3FGXo0FtuOnH7ViamDM9TM/fcFhqj8WVlxOR40iTJoQVzctRQlJzeyztdWti7btlco8YLr+m96Lh+Jk/Pw2XX2SO/HqL/HqPHCdXXl4ux3FUW1sbdCh4HwX6OGNDgT6Wsfl7i/x6i/x6i/x6i/x6i/x6i/x6jxwnR4FuH96DDgAAAACABSjQAQAAAACwAAU6AAAAAAAWoEAHAAAAAMACFOgAAAAAAFiAAh0AAAAAAAtQoAMAAAAAYAEKdAAAAAAALECBDgAAAACABSjQAQAAAACwAAU6AAAAAAAWiAQdALzT1NSk5ubmfsdisZjCYf4uAwAAAAC2oUAfw2pqarR58+ZBxwsLCwOIBgAAAAAwHAr0May6ulorVqzod6yqqoo76AAAAABgIQr0MSwajSoajfY7lpOTI8dxAooIAAAAADAUbqUCAAAAAGABCnQAAAAAACxAgQ4AAAAAgAUo0AEAAAAAsAAFOgAAAAAAFqBABwAAAADAAhToAAAAAABYgAIdAAAAAAALRIIOAP46fvy4zp8/r/Ly8qBDGZPi8bgkKRJhaXmB/HqL/HqL/HqL/HqL/HqL/HqPHCf39ttvKzs7O+gw0AczdJw5d+6cEomEHMfJqJ2uri61tLSooKBAWVlZgbVhWyxHjhyRJM2ePTvtNkzFY1N+TbVDfr1th/x6245N+TXVjk2xkF9v2yG/3rZDfr1vx0SObbomU7FEIhE5jqOmpiZFo9G024E5odbW1kTQQcA/lZWVkqTa2tqM2tm/f78uu+wy/fa3v9X8+fMDa8O2WMivt+2QX2/bIb/etmNTfk21Y1Ms5Nfbdsivt+2QX+/bMZFjm67JplhgFu9BBwAAAADAAhToAAAAAABYgAIdAAAAAAALUKADAAAAAGCBrI0bN24KOoj/v707D6rqvP84/lFkjzcYAbca1IoGQaOIjlFcY9xNZlqXmuhMNGXi3jpiJo0Tk2psa02baidNUupoGyGm0dgs4kSMCwYSTUJdMYoad4gRgygCIvD7gx+n94gGvNzLOcD7NePMPQvP/d5vnsm933Oe8zyoOwkJCZKkuLi4WrcVEBCggQMHKjAw0NI27BQL+fVsO+TXs+2QX8+2Y7f8uqsdu8RCfj3bDvn1bDvk1/PtuCvHdvpMdooF7sMs7o2Mu2YJxZ2RX88iv55Ffj2L/HoW+fUs8utZ5NfzyDHqC4a4AwAAAABgAxToAAAAAADYAAU6AAAAAAA2wDPoAAAAAADYAHfQAQAAAACwAQp0AAAAAABsgAIdAAAAAAAboEAHAAAAAMAGKNABAAAAALABCvRGaPfu3XI4HHI4HBozZozV4dQbtc3btWvXdP/99xtt3O3fd99954Ho67esrCwtWLBAPXv2VGhoqNq0aaN+/frp5Zdf1uXLl60Oz5bcmTP6bu2cOXNG8fHxxn+L9u3ba9SoUUpMTFRZWZnV4dmWu/PWsWPHavvwvn37PPBJGpasrCyFhoYaOTtz5ozVIdULtc0b/dc1gwcPrjZvGzdutDpMwKSZ1QGgbhUUFOiFF16wOox6xx15O3LkiMrLWdXwXiUlJWn+/Pm6efOmaX9mZqYyMzOVmJiozZs3KyoqyqII7cfdOc3fgWwAABUOSURBVKPvum7btm2aNm2aCgsLjX1FRUVKT09Xenq6PvroI7399tvy9va2MEr7cXfeLl68qNzcXE+F22iUl5dr/vz5KioqsjqUeqW2eaP/uqa0tFRHjx61OgzgnlGgNyLXr1/XpEmTdOjQIatDqVfclTfnv2/VqpXCw8PveB4/1P/nyJEjmjt3rm7duiWpIjcRERG6evWqcffhu+++05QpU/Tll1/Kz8/PynBtwRM5o++65ocfftAzzzxjFJk+Pj7q1q2bzp07Z/zYTk5O1vLly/Xyyy9bGKm9eCJvzn04KCjorhenHA5H7YJv4NauXau0tDSrw6h3aps3+q9rsrKyjIsifn5+iomJueN5ISEhdRkWUC0K9EYiPT1ds2bN0rfffmt1KPWKO/N2+PBh4/WUKVO0dOnSWrfZ0L3++utGoXnfffcpJSVFkZGRkqQVK1Zo+fLlkiqGwr7//vt68sknLYvVLjyRM/quaxITE3X16lVJFT+cU1JSFBERoRs3buiJJ57Q3r17JUkJCQlavHgxFzj+nyfy5tyHhw0bpnXr1nkk9oYsOztbL730ktVh1DvuyBv91zXOFzYiIyOVnJxsYTRAzfEMegNXXFysJ554QqNGjaI4vweeyJvzF0WnTp3c0mZDt3PnTuP1xIkTjUJTkuLj4013f7/++us6jc2uPJEz+q7roqOjFRgYqGnTpikiIkKSFBAQoJ///OfGOdeuXdP3339vVYi25O680YdrLz4+3rhwgppzR97ov65xvrBB3lCfcAe9gSssLDT9YB89erQkaevWrVaFVC+4O29lZWXKzMw0tjt27Fi7ABuJF198UdnZ2crOztbQoUNNx7y8vOTn52cMXyspKbEiRNtxd87ou66bO3eu5s6dq/LychUXF5uOnTp1ynjt5+en0NDQug7PtjyRN+cf6vThe/fBBx/oo48+klQxxDovL8/iiOoHd+WN/usa5wsb5A31CXfQG4mWLVvqD3/4gzZs2KAWLVpYHU694a68nTx5Ujdu3DC2161bp6ioKAUHBysqKkoLFy5Udna2O0JuUJ588kktXLhQr776qsaOHWs69t///tf0YycsLKyuw7Mld+eMvlt7TZo0MUYuXLp0SW+++abWrFljHI+Li1OzZlwvv5278lZYWKiTJ08a28nJyYqOjlZISIi6dOmiZ599VidOnHD/B2gg8vLytGjRIkkV8wEsWbLE4ojqB3fljf7rOucLG19++aX69++v0NBQdezYUVOnTlVGRoaF0QF3R4HewPn4+Ogvf/mLMjMzNXv2bDVp0sTqkOoFd+fN+UtCkjZt2qSzZ8/q5s2bOnv2rBISEjRgwAC+LGro1q1bWrx4sWnfiBEjLIqmfnA1Z/Rd99m6das6d+6s5557zhi9MGnSJP32t7+1ODJ7q23eMjMzVVpaamxv2bJFJ06cUHFxsXJycvTOO+8oNjZW27Zt80j89d2LL76onJwcSdKCBQvUtWtXiyOqH9yVN/qvay5fvmzkX6p4/Ovw4cMqKipSbm6uPvzwQw0fPlz/+te/LIwSuDMK9AYuICBAM2bMkL+/v9Wh1CvuztvtM8AHBgaqd+/eat26tbHv8uXLmjJlCs/4VaOsrEzPPvusPvvsM2PfiBEj1L17dwujsrfa5Iy+6z5nz541bXfo0EGTJk3i7nk1apu32y8y+fj4KDo62jSC5MaNG3r66ad1+vTpWsfbkOzZs8coYDp37qz4+HiLI6of3Jk3+q9rbv/uatq0qR5++GF17tzZuOly69Yt/epXv2L9eNgOBTpQB1q2bKmYmBg98MADmjp1qo4dO6adO3fq2LFj+s1vfmOcl52drbVr11oYqb2VlpYqLi5O7733nrHP4XDoz3/+s4VR2Vttc0bfdZ/Lly+rV69exmRFp0+f1oQJEzRv3jzWmf8Rtc2bv7+/+vXrp9DQUI0cOVKZmZnatWuXDh06pDfeeMM47/r161q1apXHPkd9U1RUZMrxqlWr5Ovra3FU9ufuvNF/XTdw4EC1a9dOffr0UUZGhvbs2aOMjAxt3rzZWP2htLRUK1assDhSwKxJfn4+vwoamZkzZyopKUmSFBsby7ITNeSpvJWVlalXr17GbPGDBg3Sxx9/7Ja2G5KSkhLNmDFDH3zwgbHP29tb77zzDsPb78LTOaPvui4hIUELFy40bU+ePNnCiOoHT+Rt3LhxSk1NlVRxd/7gwYO1aq+heOmll/Taa69JkqZNm6bXX39dUsXdYef5LQ4dOsQcIE7qOm/0X9fMnj1b69evlyT5+vrqwoUL8vHxsTgqoAJ30AGLNW3aVFFRUcb2uXPnLIzGnkpKSjR16lRToenj46N169ZRnN9FXeSMvuu6uLg49ejRw9jesGGDhdHUH57Im/OjHufPn691ew3BwYMH9de//lWSFBwcrGXLllkcUf1gRd7ov65xzltxcTFLXcJWKNCBOpSbm2uaEbvSzZs3jddcwTUrLy9XXFycaYk7f39/JSUlafz48RZGZl+eyBl91zVFRUU6efKkrly5UuWY890zLm6YeSJveXl5ys/Pr7LfuQ9XDntt7LZs2aJbt25JqnjEoEOHDnI4HHI4HFVWh+jevbscDocSExOtCNVWPJk3+q9rrl27dsf/j9y+zCjfX7ATCnTAwwoLC9WjRw8FBwerY8eOxnC3SiUlJaZJYCIjI+s6RFt75ZVX9P777xvb/v7++ve//82d8x/hrpzRd2unZ8+eCg0NVa9evfS3v/3NdKy8vFzffPONsc066P/j7rwNGTJErVq10oMPPlhlJQOpYvnBSt26datF5A0HcyK4xhN5o/+6ZurUqWrbtq3atWun6dOnVznuvPJIaGioQkJC6jI84EdRoAMe5u/vr+DgYOMq9+rVq7V//35JFV/mS5cu1YULF4zzeQ71f/bt26c//elPpn1///vfNXjwYIsisj935oy+WzvOw//ffPNN0w/plStXKisry9geNWpUncZmZ+7OW4cOHVRYWChJSkpKUkpKinHsrbfe0ldffWVs/+IXv6hV7A1FWFiYYmNj7/jv9tUfYmJiFBsby0UmeSZv9F/X/PSnP9X169clVSyx5rycWnJysv7zn/8Y23x3wW6YJK4RYpI411SXt5SUFGNiGEmm45988okmTpxobHt5eSkyMlLff/+9srOzjf2PPfaYNm3a5KmPUO9MmDDBtLarn5+fYmJi7nju0KFDtWjRoroKzbZcyRl91zMOHDigoUOHGkNevby81K1bN+Xl5ZmGZnfq1Enp6ekKCAiwKlRbcSVvBw8e1PPPP28cW7t2rVq1aiWpYjKuIUOGmIa0RkREqLCw0LQsVffu3bVz506GulaDSeJc82N5o/+6X3Z2tvr27Wta/rNTp05q1qyZjh8/buxr27atPv/8c7Vo0cKKMIE7YvFVwE0uXbpkWmfa2ciRI/XKK69oyZIlKisrU2lpaZWZVh955BGtW7euDiKtH3Jyckx3CqSK51LvluO2bdvWRVi25mrO6Lue8fDDD+utt97SnDlzVFRUpNLS0ipr84aHh+u9996jOHfiSt6uXr1q6sNFRUXG6+7du+uNN97QnDlzVFxcLEk6evSoqb2uXbtq48aNFDewBP3X/dq0aaPExEQ99dRTRpF+6tSpKuds3ryZ4hy2wxB3oI7Mnz9f27dv18SJE9WuXTt5e3srKChI/fv316pVq7R161Y1b97c6jBtY+/evTwHeY88lTP6rusmTpyotLQ0zZgxQx06dJCPj48CAwPVq1cvLVu2TKmpqcb63vgfd+dt0qRJSktL0/Tp0432HA6H0d6ePXvUpk0bD34iwHX0X9cMGjRIX3zxhebMmaMuXbrIz89PgYGBioyM1HPPPad9+/YpIiLC6jCBKhjiDgAAAACADXAHHQAAAAAAG6BABwAAAADABijQAQAAAACwAQp0AAAAAABsgAIdAAAAAAAboEAHAAAAAMAGKNABAAAAALABCnQAAAAAAGyAAh0AAAAAABugQAcAAAAAwAYo0AEAAAAAsAEKdAAAAAAAbIACHQAAAAAAG6BABwAAAADABijQAQAAAACwAQp0AAAauKioKDkcDjkcDv3ud79zW7tjxowx2p05c6bL7Xz11VduiwkAgPqMAh0AAFji7NmzmjFjhh599FGrQwEAwBaaWR0AAADwrJiYGD344IOSpLCwMIujqbBx40bNmjVLxcXFVocCAIBtUKADANDArVu3zuoQqsjMzKQ4BwDgNgxxBwAAAADABijQAQDwkMcff9yYRG3hwoWmYwUFBWrZsqVxfPHixabj2dnZxjGHw6FPP/1UklRWVqb169dr9OjRat++vUJCQtS9e3fNnDlTBw8evGMc1U0Sl5+fr2XLlik6OlohISHq0qWL5s2bp+zsbG3cuNH426ioqB/9vMXFxVq5cqV69+5ttDNz5kydOnXKdJ7D4dCrr75aZZ/D4VBiYuKPvgcAAA0ZQ9wBAPCQcePGadeuXZKklJQU07G0tDSVlJQY25999pnp+LZt24zXQUFBGjRokAoKCvTUU09px44dpnPPnDmjM2fOaMOGDfr973+vWbNm1TjGCxcuaPz48Tpx4oSxLycnR//85z+1ZcsWxcXF1aid/Px8jRw5UhkZGaZ2kpKSlJycrB07dqhz5841jgsAgMaIO+gAAHjIuHHj1KRJE0nS6dOnlZWVZRzbvXu36dwDBw4oLy/P2HYu0EeNGiVvb2/9+te/NhXnrVu3VnR0tJo3by6p4u76888/r+3bt9c4xmeeecZUnAcEBKhnz54KCgrS5cuXtWLFihq18/HHHysjI0PBwcHq06ePgoKCjGN5eXmmdmJjY9W+fXvT38fGxio2NlahoaE1jh0AgIaGAh0AAA9p27atoqOjjW3novv2Ar2srEzp6emSpJKSEuPOu1QxVP7IkSN69913jX1LlizRN998o127dikzM1PDhg2TJJWXl2v58uU1ii8tLc14T0kaMGCAMjMzlZqaqpMnT2rGjBkqKyur8eedO3eujh8/rk8//VRHjhxRjx49jGOff/658To5OVmTJ082/W1ycrKSk5P12GOP1fj9AABoaCjQAQDwoPHjxxuvK4e55+bm6tChQ5IkPz8/43hqaqokKT09XdeuXZMkBQYG6tFHH9WHH35onNemTRvFx8eradOKr/H7779fL7zwgnH866+/1qVLl6qNzXnYfdOmTbV69Wo98MADkiRvb2/98Y9/NJZnq05oaKiWLl2qZs0qnp5r3ry5fvaznxnHaxIPAACNHQU6AAAe5Fygp6Wl6caNG9q9e7fKy8slSU8//bS8vb0lSXv27JEkffLJJ8bfDB8+XP7+/srMzDT23T6BnMPh0PDhw03ve7cJ45w5D7lv166dwsPDTcd9fHw0YMCAGn3OXr16GcV5pcpiXxJLqgEAUAMU6AAAeFB4eLi6du0qqaJITU1NNQ1vHzt2rPr06SNJOnz4sK5cuWIaCv/4449LqpiE7V5cuXKl2nMq79JLuuuz361bt67R+zk/c16p8sKDJOOCBAAAuDtmcQcAwMPGjx+vY8eOSap4Dr3y+XJ/f3/169dPQ4YMUXp6usrLy5WUlKTjx49Lknx9fTVy5Ejj3Erh4eHGsmt3ExAQUG1czufc7QJATk5Ote1IkpeXV43OAwAAd8cddAAAPGzcuHHG602bNunbb7+VJPXr10++vr4aOnSocXzlypXG68GDB8vhcEiSHnroIWP/2bNndevWLQUFBRn/srKy9Pbbb2vfvn26evWq6e713XTp0sV4ffLkSV28eNF0vKioqMryb57CHXYAACjQAQDwuOjoaP3kJz+RJP3www/G/iFDhkiSevfubRTizscrh7dL0pgxY4zXxcXFmjNnjjFEPT8/XwsXLtTixYs1YcIEjRw5Ujdv3qw2rtGjRxuvy8rKNHPmTOP9i4qKtGDBAp07d+5eP26N+Pj4mLZzc3ONOAAAaKwo0AEAqANjx46tsm/w4MGSpGbNmlWZjM3Ly8v0N3379tWIESOM7a1bt+qhhx7SkCFDFBUVpf379xvH4uPj5evrW21MjzzyiAYOHGhs79q1S926ddOgQYMUHh6uxMTEmn/AexQcHGzajo2NVZ8+fZSQkOCx9wQAwO4o0AEAqAPOs7lLFZOq9ezZ09iuvJteqX///mrZsqVp3z/+8Q/FxMQY29euXVNGRoby8vKMfbNmzdIvf/nLGse1Zs0adejQwdguKCjQ/v37dfXqVXXt2tW0XnmTJk1q3G51hg0bZnpu/eLFizp27JjOnz/vtvcAAKC+oUAHAKAODBgwwLTs2KBBg4x1zCWZnkOXqhb0UkVRn5KSotWrV2vw4MEKDg5Ws2bN1KJFCw0bNkzr16/XihUr7imu1q1bKzU1VfPmzVNYWJh8fHzUvn17zZ8/Xzt27DDFfPuw9Nro1KmT3n33XcXExMjPz0/33XefIiMjTc/aAwDQ2DTJz89nVhYAABqh3NxcZWdnq02bNlXu1leaPXu21q9fL6liUjvnJeAAAIB7cQcdAIBG6sCBA+rfv786duyokJAQTZ482TRJ26lTp0wFebdu3awIEwCARoM76AAANFJ5eXmKiIhQQUGBsa9169YKCwtTfn6+jh07ZirYt2/frr59+1oRKgAAjQJ30AEAaKSCgoL02muvmSZry8nJ0d69e3X06FFTcb5o0SKKcwAAPIw76AAANHKHDh3SmjVr9MUXX+j8+fMqKCiQr6+vQkNDFRMTo+nTp5uWYwMAAJ5BgQ4AAAAAgA0wxB0AAAAAABugQAcAAAAAwAYo0AEAAAAAsAEKdAAAAAAAbIACHQAAAAAAG6BABwAAAADABijQAQAAAACwAQp0AAAAAABsgAIdAAAAAAAboEAHAAAAAMAGKNABAAAAALABCnQAAAAAAGyAAh0AAAAAABugQAcAAAAAwAYo0AEAAAAAsAEKdAAAAAAAbIACHQAAAAAAG6BABwAAAADABijQAQAAAACwAQp0AAAAAABsgAIdAAAAAAAboEAHAAAAAMAGKNABAAAAALABCnQAAAAAAGyAAh0AAAAAABugQAcAAAAAwAYo0AEAAAAAsAEKdAAAAAAAbIACHQAAAAAAG6BABwAAAADABijQAQAAAACwAQp0AAAAAABsgAIdAAAAAAAboEAHAAAAAMAGKNABAAAAALCB/wPLgelB/UgbqAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "height": 500,
              "width": 500
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kS9jJgg8LbYl",
        "colab_type": "text"
      },
      "source": [
        "The plot shows that there is no clear trend in relation between y (number of satellites) and weight."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wek89zWbLbYm",
        "colab_type": "text"
      },
      "source": [
        "### Fit a LM vs GLM (Gaussian)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3vPOe936LbYn",
        "colab_type": "code",
        "colab": {},
        "outputId": "ea46656d-1c1f-4149-e0c3-bf74ea3635f7"
      },
      "source": [
        "formula = \"\"\"y ~ weight\"\"\"\n",
        "fit_weight = smf.ols(formula=formula, data=crabs_df).fit()\n",
        "print(fit_weight.summary())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   R-squared:                       0.136\n",
            "Model:                            OLS   Adj. R-squared:                  0.131\n",
            "Method:                 Least Squares   F-statistic:                     27.00\n",
            "Date:                Mon, 22 Jun 2020   Prob (F-statistic):           5.75e-07\n",
            "Time:                        23:43:22   Log-Likelihood:                -430.70\n",
            "No. Observations:                 173   AIC:                             865.4\n",
            "Df Residuals:                     171   BIC:                             871.7\n",
            "Df Model:                           1                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "Intercept     -1.9911      0.971     -2.050      0.042      -3.908      -0.074\n",
            "weight         2.0147      0.388      5.196      0.000       1.249       2.780\n",
            "==============================================================================\n",
            "Omnibus:                       38.273   Durbin-Watson:                   1.750\n",
            "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               58.768\n",
            "Skew:                           1.188   Prob(JB):                     1.73e-13\n",
            "Kurtosis:                       4.584   Cond. No.                         12.6\n",
            "==============================================================================\n",
            "\n",
            "Warnings:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NNUcO4QBLbYv",
        "colab_type": "code",
        "colab": {},
        "outputId": "c36bc35a-37e7-4320-ae63-5ff5a278380d"
      },
      "source": [
        "response, predictors = dmatrices(formula, crabs_df, return_type=\"dataframe\")\n",
        "fit_weight2 = sm.GLM(response, predictors, family=sm.families.Gaussian()).fit()\n",
        "print(fit_weight2.summary())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                 Generalized Linear Model Regression Results                  \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   No. Observations:                  173\n",
            "Model:                            GLM   Df Residuals:                      171\n",
            "Model Family:                Gaussian   Df Model:                            1\n",
            "Link Function:               identity   Scale:                          8.6106\n",
            "Method:                          IRLS   Log-Likelihood:                -430.70\n",
            "Date:                Mon, 22 Jun 2020   Deviance:                       1472.4\n",
            "Time:                        23:43:22   Pearson chi2:                 1.47e+03\n",
            "No. Iterations:                     3                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "Intercept     -1.9911      0.971     -2.050      0.040      -3.894      -0.088\n",
            "weight         2.0147      0.388      5.196      0.000       1.255       2.775\n",
            "==============================================================================\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OwrvKro9LbY2",
        "colab_type": "text"
      },
      "source": [
        "Thus OLS and a GLM using Gaussian family and identity link are one and the same."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3qM9rWyiLbY3",
        "colab_type": "text"
      },
      "source": [
        "### Plotting the linear fit"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2i_Tku63LbY5",
        "colab_type": "code",
        "colab": {},
        "outputId": "76437f9a-c9f2-4214-e04c-cd9a341c4e1d"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.scatter(crabs_df[\"weight\"], crabs_df[\"y\"])\n",
        "line = fit_weight2.params[0] + fit_weight2.params[1] * crabs_df[\"weight\"]\n",
        "\n",
        "ax.plot(crabs_df[\"weight\"], line, color=\"#f03b20\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x2ad2f7712668>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "height": 480,
              "width": 640
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EgfV-nTjLbZD",
        "colab_type": "text"
      },
      "source": [
        "###  Comparing Mean Numbers of Satellites by Crab Color"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z1TZZreELbZE",
        "colab_type": "code",
        "colab": {},
        "outputId": "1bb2bc3c-5d7e-4602-ddb0-0bd5da16f9bb"
      },
      "source": [
        "crabs_df[\"color\"].value_counts()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2    95\n",
              "3    44\n",
              "4    22\n",
              "1    12\n",
              "Name: color, dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dgEuWCgtLbZL",
        "colab_type": "raw"
      },
      "source": [
        "color:\n",
        "    1 = medium light, \n",
        "    2 = medium, \n",
        "    3 = medium dark, \n",
        "    4 = dark\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e2jth2g6LbZM",
        "colab_type": "code",
        "colab": {},
        "outputId": "838e06aa-ff46-4041-edbc-f1667a00ddf4"
      },
      "source": [
        "crabs_df.groupby(\"color\").agg([\"mean\", \"var\"])[[\"y\"]]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead tr th {\n",
              "        text-align: left;\n",
              "    }\n",
              "\n",
              "    .dataframe thead tr:last-of-type th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr>\n",
              "      <th></th>\n",
              "      <th colspan=\"2\" halign=\"left\">y</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th></th>\n",
              "      <th>mean</th>\n",
              "      <th>var</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>color</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4.083333</td>\n",
              "      <td>9.719697</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3.294737</td>\n",
              "      <td>10.273908</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>2.227273</td>\n",
              "      <td>6.737844</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>2.045455</td>\n",
              "      <td>13.093074</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "              y           \n",
              "           mean        var\n",
              "color                     \n",
              "1      4.083333   9.719697\n",
              "2      3.294737  10.273908\n",
              "3      2.227273   6.737844\n",
              "4      2.045455  13.093074"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hsXqg-AELbZS",
        "colab_type": "text"
      },
      "source": [
        "Majority of the crabs are of medoum color and the mean response also decreases as the color gets darker."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cQmcbPLtLbZT",
        "colab_type": "text"
      },
      "source": [
        "If we fit a linear model between $y$ and $color$ using `sm.ols`, color is treated as a quantitative variable:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CwQO-8CaLbZU",
        "colab_type": "code",
        "colab": {},
        "outputId": "42ce6d0e-37fa-439d-fb5f-8b641fb73b0a"
      },
      "source": [
        "mod = smf.ols(formula=\"y ~ color\", data=crabs_df)\n",
        "res = mod.fit()\n",
        "print(res.summary())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   R-squared:                       0.036\n",
            "Model:                            OLS   Adj. R-squared:                  0.031\n",
            "Method:                 Least Squares   F-statistic:                     6.459\n",
            "Date:                Mon, 22 Jun 2020   Prob (F-statistic):             0.0119\n",
            "Time:                        23:43:23   Log-Likelihood:                -440.18\n",
            "No. Observations:                 173   AIC:                             884.4\n",
            "Df Residuals:                     171   BIC:                             890.7\n",
            "Df Model:                           1                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "Intercept      4.7461      0.757      6.274      0.000       3.253       6.239\n",
            "color         -0.7490      0.295     -2.542      0.012      -1.331      -0.167\n",
            "==============================================================================\n",
            "Omnibus:                       38.876   Durbin-Watson:                   1.780\n",
            "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               59.793\n",
            "Skew:                           1.207   Prob(JB):                     1.04e-13\n",
            "Kurtosis:                       4.570   Cond. No.                         9.39\n",
            "==============================================================================\n",
            "\n",
            "Warnings:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "po8CnUd2LbZb",
        "colab_type": "text"
      },
      "source": [
        "**Let's treat color as a qualitative variable:**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n3XedkRHLbZc",
        "colab_type": "code",
        "colab": {},
        "outputId": "73594869-2e36-41e6-9c01-c78a2692422d"
      },
      "source": [
        "mod = smf.ols(formula=\"y ~ C(color)\", data=crabs_df)\n",
        "res = mod.fit()\n",
        "print(res.summary())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   R-squared:                       0.040\n",
            "Model:                            OLS   Adj. R-squared:                  0.023\n",
            "Method:                 Least Squares   F-statistic:                     2.323\n",
            "Date:                Mon, 22 Jun 2020   Prob (F-statistic):             0.0769\n",
            "Time:                        23:43:23   Log-Likelihood:                -439.89\n",
            "No. Observations:                 173   AIC:                             887.8\n",
            "Df Residuals:                     169   BIC:                             900.4\n",
            "Df Model:                           3                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "=================================================================================\n",
            "                    coef    std err          t      P>|t|      [0.025      0.975]\n",
            "---------------------------------------------------------------------------------\n",
            "Intercept         4.0833      0.899      4.544      0.000       2.310       5.857\n",
            "C(color)[T.2]    -0.7886      0.954     -0.827      0.409      -2.671       1.094\n",
            "C(color)[T.3]    -1.8561      1.014     -1.831      0.069      -3.857       0.145\n",
            "C(color)[T.4]    -2.0379      1.117     -1.824      0.070      -4.243       0.167\n",
            "==============================================================================\n",
            "Omnibus:                       37.294   Durbin-Watson:                   1.779\n",
            "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               55.871\n",
            "Skew:                           1.179   Prob(JB):                     7.38e-13\n",
            "Kurtosis:                       4.479   Cond. No.                         9.31\n",
            "==============================================================================\n",
            "\n",
            "Warnings:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I9S3ZSccLbZq",
        "colab_type": "text"
      },
      "source": [
        "This is equivalent to doing a GLM fit with a gaussian family and identity link:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vBGpU-BNLbZ2",
        "colab_type": "code",
        "colab": {},
        "outputId": "6cf065c6-aa0f-468d-a7e6-9be9126af5dd"
      },
      "source": [
        "formula = \"\"\"y ~ C(color)\"\"\"\n",
        "response, predictors = dmatrices(formula, crabs_df, return_type=\"dataframe\")\n",
        "fit_color = sm.GLM(response, predictors, family=sm.families.Gaussian()).fit()\n",
        "print(fit_color.summary())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                 Generalized Linear Model Regression Results                  \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   No. Observations:                  173\n",
            "Model:                            GLM   Df Residuals:                      169\n",
            "Model Family:                Gaussian   Df Model:                            3\n",
            "Link Function:               identity   Scale:                          9.6884\n",
            "Method:                          IRLS   Log-Likelihood:                -439.89\n",
            "Date:                Mon, 22 Jun 2020   Deviance:                       1637.3\n",
            "Time:                        23:43:23   Pearson chi2:                 1.64e+03\n",
            "No. Iterations:                     3                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "=================================================================================\n",
            "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
            "---------------------------------------------------------------------------------\n",
            "Intercept         4.0833      0.899      4.544      0.000       2.322       5.844\n",
            "C(color)[T.2]    -0.7886      0.954     -0.827      0.408      -2.658       1.080\n",
            "C(color)[T.3]    -1.8561      1.014     -1.831      0.067      -3.843       0.131\n",
            "C(color)[T.4]    -2.0379      1.117     -1.824      0.068      -4.227       0.151\n",
            "=================================================================================\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hj5wO5pMLbaf",
        "colab_type": "text"
      },
      "source": [
        "If we instead do a poisson fit:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yuL8VhblLbag",
        "colab_type": "code",
        "colab": {},
        "outputId": "9f9373b0-b8ca-403a-dbd2-60241363f885"
      },
      "source": [
        "formula = \"\"\"y ~ C(color)\"\"\"\n",
        "response, predictors = dmatrices(formula, crabs_df, return_type=\"dataframe\")\n",
        "fit_color2 = sm.GLM(\n",
        "    response, predictors, family=sm.families.Poisson(link=sm.families.links.identity)\n",
        ").fit()\n",
        "print(fit_color2.summary())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                 Generalized Linear Model Regression Results                  \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   No. Observations:                  173\n",
            "Model:                            GLM   Df Residuals:                      169\n",
            "Model Family:                 Poisson   Df Model:                            3\n",
            "Link Function:               identity   Scale:                          1.0000\n",
            "Method:                          IRLS   Log-Likelihood:                -482.22\n",
            "Date:                Mon, 22 Jun 2020   Deviance:                       609.14\n",
            "Time:                        23:43:23   Pearson chi2:                     584.\n",
            "No. Iterations:                     3                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "=================================================================================\n",
            "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
            "---------------------------------------------------------------------------------\n",
            "Intercept         4.0833      0.583      7.000      0.000       2.940       5.227\n",
            "C(color)[T.2]    -0.7886      0.612     -1.288      0.198      -1.989       0.412\n",
            "C(color)[T.3]    -1.8561      0.625     -2.969      0.003      -3.081      -0.631\n",
            "C(color)[T.4]    -2.0379      0.658     -3.096      0.002      -3.328      -0.748\n",
            "=================================================================================\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "at8MdOtYLbao",
        "colab_type": "text"
      },
      "source": [
        "And we get the same estimates as when using Gaussian family with identity link! Because the ML estimates for the poisson distirbution is also the sample mean if there is a single predictor. But the standard values are much smaller. Because the errors here are heteroskedastic while the gaussian version assume homoskesdasticity."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rUgahthJLbap",
        "colab_type": "text"
      },
      "source": [
        "### Using both qualitative and quantitative variables"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tLi0BDYJLbar",
        "colab_type": "code",
        "colab": {},
        "outputId": "0784afd3-45e1-4cc4-b02d-44b95104c909"
      },
      "source": [
        "formula = \"\"\"y ~ weight + C(color)\"\"\"\n",
        "response, predictors = dmatrices(formula, crabs_df, return_type=\"dataframe\")\n",
        "fit_weight_color = sm.GLM(response, predictors, family=sm.families.Gaussian()).fit()\n",
        "print(fit_weight_color.summary())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                 Generalized Linear Model Regression Results                  \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   No. Observations:                  173\n",
            "Model:                            GLM   Df Residuals:                      168\n",
            "Model Family:                Gaussian   Df Model:                            4\n",
            "Link Function:               identity   Scale:                          8.6370\n",
            "Method:                          IRLS   Log-Likelihood:                -429.44\n",
            "Date:                Mon, 22 Jun 2020   Deviance:                       1451.0\n",
            "Time:                        23:43:23   Pearson chi2:                 1.45e+03\n",
            "No. Iterations:                     3                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "=================================================================================\n",
            "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
            "---------------------------------------------------------------------------------\n",
            "Intercept        -0.8232      1.355     -0.608      0.543      -3.479       1.832\n",
            "C(color)[T.2]    -0.6181      0.901     -0.686      0.493      -2.384       1.148\n",
            "C(color)[T.3]    -1.2404      0.966     -1.284      0.199      -3.134       0.653\n",
            "C(color)[T.4]    -1.1882      1.070     -1.110      0.267      -3.286       0.910\n",
            "weight            1.8662      0.402      4.645      0.000       1.079       2.654\n",
            "=================================================================================\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yvM93NaULbay",
        "colab_type": "code",
        "colab": {},
        "outputId": "0964c68e-c118-43a4-c55d-ac0f48f3b1f5"
      },
      "source": [
        "formula = \"\"\"y ~ weight + C(color)\"\"\"\n",
        "response, predictors = dmatrices(formula, crabs_df, return_type=\"dataframe\")\n",
        "fit_weight_color2 = sm.GLM(\n",
        "    response, predictors, family=sm.families.Poisson(link=sm.families.links.identity())\n",
        ").fit()\n",
        "print(fit_weight_color2.summary())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                 Generalized Linear Model Regression Results                  \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   No. Observations:                  173\n",
            "Model:                            GLM   Df Residuals:                      168\n",
            "Model Family:                 Poisson   Df Model:                            4\n",
            "Link Function:               identity   Scale:                          1.0000\n",
            "Method:                          IRLS   Log-Likelihood:                    nan\n",
            "Date:                Mon, 22 Jun 2020   Deviance:                       534.33\n",
            "Time:                        23:43:23   Pearson chi2:                     529.\n",
            "No. Iterations:                   100                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "=================================================================================\n",
            "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
            "---------------------------------------------------------------------------------\n",
            "Intercept        -0.9930      0.736     -1.349      0.177      -2.436       0.450\n",
            "C(color)[T.2]    -0.8442      0.615     -1.374      0.170      -2.049       0.360\n",
            "C(color)[T.3]    -1.4320      0.629     -2.278      0.023      -2.664      -0.200\n",
            "C(color)[T.4]    -1.2248      0.658     -1.861      0.063      -2.515       0.065\n",
            "weight            2.0086      0.173     11.641      0.000       1.670       2.347\n",
            "=================================================================================\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}