{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WHPFGk_7OkHg",
        "tags": []
      },
      "source": [
        "```{index} single: application; regression\n",
        "```\n",
        "```{index} pandas dataframe\n",
        "```\n",
        "```{index} single: solver; highs\n",
        "```\n",
        "\n",
        "# Wine quality prediction with L1 regression"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1LZZDfmaOkHo",
        "outputId": "00288bfb-14c0-4c0c-99d5-e62c163bd369",
        "tags": []
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m5.6/5.6 MB\u001b[0m \u001b[31m14.7 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hUsing default Community Edition License for Colab. Get yours at: https://ampl.com/ce\n",
            "Licensed to AMPL Community Edition License for the AMPL Model Colaboratory (https://colab.ampl.com).\n"
          ]
        }
      ],
      "source": [
        "# install dependencies and select solver\n",
        "%pip install -q amplpy pandas matplotlib\n",
        "\n",
        "SOLVER = \"highs\"\n",
        "\n",
        "from amplpy import AMPL, ampl_notebook\n",
        "\n",
        "ampl = ampl_notebook(\n",
        "    modules=[\"highs\"],  # modules to install\n",
        "    license_uuid=\"default\",  # license to use\n",
        ")  # instantiate AMPL object and register magics"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7zCMJVsQOkHr",
        "tags": []
      },
      "source": [
        "## Problem description\n",
        "\n",
        "Regression is the task of fitting a model to data. If things go well, the model might provide useful predictions in response to new data. This notebook shows how linear programming and least absolute deviation (LAD) regression can be used to create a linear model for predicting wine quality based on physical and chemical properties. The example uses a well known data set from the machine learning community.\n",
        "\n",
        "Physical, chemical, and sensory quality properties were collected for a large number of red and white wines produced in the Portugal then donated to the UCI machine learning repository (Cortez, Paulo, Cerdeira, A., Almeida, F., Matos, T. & Reis, J.. (2009). Wine Quality. UCI Machine Learning Repository.) The following cell reads the data for red wines directly from the UCI machine learning repository.\n",
        "\n",
        "Cortez, P., Cerdeira, A., Almeida, F., Matos, T., & Reis, J. (2009). Modeling wine preferences by data mining from physicochemical properties. Decision support systems, 47(4), 547-553. https://doi.org/10.1016/j.dss.2009.05.016\n",
        "\n",
        "Let us first download the data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 441
        },
        "id": "IwrjDMunOkHs",
        "outputId": "da10886e-d2ed-4450-828e-80b37876f255",
        "tags": []
      },
      "outputs": [
        {
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              "      <th></th>\n",
              "      <th>fixed acidity</th>\n",
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            "text/plain": [
              "      fixed acidity  volatile acidity  citric acid  residual sugar  chlorides  \\\n",
              "0               7.4             0.700         0.00             1.9      0.076   \n",
              "1               7.8             0.880         0.00             2.6      0.098   \n",
              "2               7.8             0.760         0.04             2.3      0.092   \n",
              "3              11.2             0.280         0.56             1.9      0.075   \n",
              "4               7.4             0.700         0.00             1.9      0.076   \n",
              "...             ...               ...          ...             ...        ...   \n",
              "1594            6.2             0.600         0.08             2.0      0.090   \n",
              "1595            5.9             0.550         0.10             2.2      0.062   \n",
              "1596            6.3             0.510         0.13             2.3      0.076   \n",
              "1597            5.9             0.645         0.12             2.0      0.075   \n",
              "1598            6.0             0.310         0.47             3.6      0.067   \n",
              "\n",
              "      free sulfur dioxide  total sulfur dioxide  density    pH  sulphates  \\\n",
              "0                    11.0                  34.0  0.99780  3.51       0.56   \n",
              "1                    25.0                  67.0  0.99680  3.20       0.68   \n",
              "2                    15.0                  54.0  0.99700  3.26       0.65   \n",
              "3                    17.0                  60.0  0.99800  3.16       0.58   \n",
              "4                    11.0                  34.0  0.99780  3.51       0.56   \n",
              "...                   ...                   ...      ...   ...        ...   \n",
              "1594                 32.0                  44.0  0.99490  3.45       0.58   \n",
              "1595                 39.0                  51.0  0.99512  3.52       0.76   \n",
              "1596                 29.0                  40.0  0.99574  3.42       0.75   \n",
              "1597                 32.0                  44.0  0.99547  3.57       0.71   \n",
              "1598                 18.0                  42.0  0.99549  3.39       0.66   \n",
              "\n",
              "      alcohol  quality  \n",
              "0         9.4        5  \n",
              "1         9.8        5  \n",
              "2         9.8        5  \n",
              "3         9.8        6  \n",
              "4         9.4        5  \n",
              "...       ...      ...  \n",
              "1594     10.5        5  \n",
              "1595     11.2        6  \n",
              "1596     11.0        6  \n",
              "1597     10.2        5  \n",
              "1598     11.0        6  \n",
              "\n",
              "[1599 rows x 12 columns]"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "base_url = \"https://raw.githubusercontent.com/ampl/mo-book.ampl.com/dev/notebooks/02/\"\n",
        "\n",
        "\n",
        "wines = pd.read_csv(\n",
        "    base_url + \"data/winequality-red.csv\",\n",
        "    sep=\";\",\n",
        ")\n",
        "display(wines)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yBh-Zn7lOkHv"
      },
      "source": [
        "## Model objective: Mean Absolute Deviation (MAD)\n",
        "\n",
        "Given $n$ repeated observations of a response variable $y_i$ (in this wine quality), the **mean absolute deviation** (MAD) of $y_i$ from the mean value $\\bar{y}$ is\n",
        "\n",
        "$$\\text{MAD}\\,(y) = \\frac{1}{n} \\sum_{i=1}^n | y_i - \\bar{y}|$$\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 428
        },
        "id": "bkdVvp_yOkHw",
        "outputId": "3c0d41dc-8a49-45bd-a028-34d4ddb583ef",
        "tags": []
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "MAD =  0.6831779242889846\n"
          ]
        },
        {
          "data": {
            "image/png": 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BX4tn9SAjo19CgiDCQCpI1yc/+cmKFRkANm3ahFdeeQU33ngj3vWudzHvSaVSSKVS3ktKEHWIXlFU1eZQHIHgFwaapR79xtgeVaBJF3CaEeozhChNpTQ21cMSBCGKlAV5enoasZjxlng8jlLJXSAHgmhE7MbbEvm0NhT1+Dr1OlJUXAoJgmhM6kFG1oOVmyCI2iNlQb7ooovwpS99CStWrMCGDRvw5z//Gf/4j/+I97znPUGVjyDqGr1C0lTDMFmrIomi6F2sm6pFEjpUVTW0BYLQUw+KrV8007MSBCGOlIL8jW98A5/5zGdwzTXXYGBgAEuWLMH73/9+fPaznw2qfARRdxiCcenmoM1kQaapdzQxLNg0T3MkCIJgQnKQIAgWUgpyR0cHbr75Ztx8880BFYcgGgtDUKQmGojJOhVNzHviieakmeIhEAQPEoMEQbCQ2oNMEIR7mkkhCXruHUZ08EZ4ffp6ayaPBoIWrZoV6uV8muH4RYIg5CEFmSB8Rj/cGix2NFUhIgS1xubCGKCN3j5BACQHCYJgQwoyQdQIihpc3zSa/Y0sJwTR+DSa3PIbEoMEQbAgBZkgakQzKSQxcueMJHovBlqwaV7o1ROEBvUGgiCskIJMEAGi14lJISEiBbVHgiCanCZatyYIQgJSkAnCZ2wH3CYaiIM2IIdhoDa/vnr0CDAu2NRf+Ql/oFffPIT5qutBRka/hARBhAEpyAThO9UhVz9BIIWEiBLUGpsLChhIEFZoWCYIggUpyARRI5ppHG7EHciN8Ez6NkgLNs0LvfrmoRHkVpDQYhFBECxIQSaIAGlahYRmZZGnmZojQRAEQRCEKKQgE4TP2CkezaSQKE2gIdf7+6yH/YEEQXgj1D3IIeYtCgXPJDTo8A1CDynIBBEgeh2k0RWSRn++RkD/juhtNS/UVQmiDI1bhAbpx4QeUpAJIkD0+5safRjWzzOCj2JNQ5kbmtblnzB4ddC+y+aBJCVBEIQ8pCATRIA007E6+uejSVn0afDmSBAE4QjJQUKD1t0JPaQgE4TP2B6D3OADsf7xyMIbTZppwYawh149QRCEkWaInUKIQwoyQfiMYd8x2J8bkUZXuBrt6Rr8dREc6NU3D6EG6aqDhkbbDQiNRl7Xr4e+GDVIQSaIANEHACk1eLjMWu5BjgL1/jZpwCQIotkplcIuAREVmmDaQkhACjJBBEgzKSEGBTngvMIYyBph8DQGjWuixkkY330zCaYmpxHkVpBQT6gPaiGzGnlrWAM/WmCQgkwQNaLxXZB1QbpIGEcTwx7k8IpBhAu9eoIgCIKwhxRkgvAZu5XOBtePSeGqM8iK2FwYz2QPrxwEESUafeG6UajFa6KFfUIPKcgEESDNFDW40RWuRns6WtAgiMYn1CBdDSc1iUamkaNYN/j0LBBIQSaIADHu+WxsaqlwRWGltx4HHJXzF9FE0KsnakBdyMh6KCNRk9cUhXkFER1IQSYIn2nWc5DR4C6c5rGz3q0jZEFuLoxHztHLbxZozs+n0T27GoWaBOkKPIfwIOVfHlKQCSJAjPv+Gnsg1k80GvtJ6xfah9q86OUPvXuCIOoJsiATtYYUZILwGYMSAvbnRsTwrI3+sHUKHfNEEM0F9XI+VD+ERiMf80TIQwoyQdSIRnflanQLeaM9XakUdgmIsGi0tkwQbmnwYathoPfkDao/eUhBJogAaSa3xlIN3clpndc7ZEFuLpppuwcRDeqhlZEcrA9q8Z7IgEzoIQWZIHzGLnJ1o89JGz1ityVIVx0+JO1BJoDG7J8EG5rz8yE5WB/U5BzkBu4tpPzLQwoyQQRIc52DzP5MRBN6RwRBNDskBgkNUiIJPaQgEwThC42ucDXC4+mfodEXbAgjtIDVnNCrdoA6AzEP6ceEHlKQCcJvVPYfja6QGI95auxnbQToDRFEYxKVPeYRKQaXOigiAWNbIkuvPPXQF6MGKcgE4QN2E5JmstrU8vHoOAZ3GIPGNXiDJGyhd08QZagr1B9BvTOaVhB6SEEmCJ+xO/u40S3ItYzYHcZAZgnSVfsi+Eqp3h+AkIK8OpoHg7UtvGLUBbRYVB/UQn7FGlhDbuBHCwxSkAmiRjT6MEzzjOhjfEf0wpoVevONjd0iLWGF6qc+qE0Ua4KoQgoyQfiMnVt1o69UN7o7eaM9ElmQm4tG7JMEm0Yfa/yEqqo+oNdE1BpSkAnCB+wGWcPZwA0u4RvdhbzRoNfVvNC7J4gy1BWICg3sh0wyXx5SkAkiQIznIIdXjlpgdOtr8IcF6n7EoQWN5qLp+mcT49fbbWB9oQJZ2+uDWrynJmjuhASkIBNEjWj0gbiWQbrCoBEGz0Z3gyfEoHff2FCQLqLRMCzwBSTAmmFBiBCHFGSC8AE760wzWZD1zxf0o9I45h2yIjYXjb5AR1QxjEEe0mkGOUvdoj5QazC/oCjWhB5SkAnCZ0T2Izcmjf18jfB0zbQnnrCHXj0hQjNMqht/XG48aOwiagEpyAThA3bWmVKDux3rMViQG/1hGwB6Rc0L9c/Ghl5vfUL9kgMd8+QJalrykIJMEDWi0QVULVygokS9PyMF6WoujHv4QisGUUcoDa0ylInSwi71SzGCsvo3g8cEIQ4pyARRIxpdISk1uIbcCGNng78igkODix9Ch19BuppBYaB+UR/UYn6hNEODJ4QhBZkgfEC1+Wx3TSNS04lGCANZI7w//TM0+oINQRCNIbeCJEpxGehdiVGLegrbm8BvSPeXhxRkgggQvRLS6AqJYb81DfXRh15RkxEdRYAIFr/kbzPMqaPUFxpNKfOTWtSMXomkV0GQgkwQtaKJBG4zDC71+IxqEy3YEPbQAhYhQrO5nFKvqA+CGrr0e+5pfCSkFORVq1ZBURTLvw996ENBlY8g6gLbo50M22YaW+DWMmJ3GNO2Rpsq0vhPEI2JPvBUo8mtRoZEsj218FAzWJADySE8aLyXJyFz8WOPPYZisVj5+7nnnsPrX/96XHrppb4XjCDqFdsjn0o1LkiNaTYBXO8LHrRC3lwYFuvo1TcN9Kr5lEr6hV0VYS4pUL8UIzgLcvB5EPWDlILc399v+Pumm27C2rVrceaZZ/paqKhRKqnYOZxFRzqBhR1pAECuUMTARA7Lelod3ZAKxRL2j81iWU8rYjEx4auqKvaOzmBhZwqpRNzzM3hBK8virjQS8Wh45WtlKpRULOkuv5Mdg1ks6WrF+ExeqK5LpXIaS7qtz1UolrB9MItFnSl0Z1qY9w9MziKdjKMzncTEbL5aNn05dZ93DWexayiLpT2tKBRVHJyYRTKuYGm3cxsyMzmbx/DUHNLJOA7rSmOuUMKhidlKe1RVFTuGsuhIJdCRTmJ0eg5LulsBAIOTObQkYuhqTRrS3DMyDQBY1tOK4nzdKArQ3dqCXLGIhR1pzOaLODA+i0RMsbR94wovcGhiFm2pBNpTRjEzPVfA+Ewei7takS+WcHC8Wu7xmTwOjM9U2vzirjTiMcVwjZnn949jTV87WlvK95RKKiZmCpXfD4zPYHFXq1T9aoxP5zFXLGEqV8DB8VnDbyPZPJ7bNw4ASMZjOKyrXD9drUnsHMpiZW8GmRYxEau1xaU9rYgLyggZcoUidgxmcWB8pvIdb/wvllTsG52RkllmNLm3fEH5vU3O5jEzV8RcsYS+9hTSybhveTUDenk1VyxhfCaPYknF2HQeq/va0JaytrWZuWKl7w9M5irfa+8+mytg51AWmZY4WhIxW1k0M1fEwYlZzOaL3Ha9Z2Qa4zN5rOlvs1wzlSsgmytgUWe68t3gZA7ZXAGdrUmMZOcwmy+ivyNluYYlr2bzRQxn57CwI2WRD1O5AoYmc5jKFWDHos40+tpbsG9sxtAeh6ZySMZi6MokDXK2py2JwclcpY7s+uyB8RnM5ktoTyVwaGIWLYkYYgowmy+hLZVAKhHDku6y7Dug6x/amLaoM42SqmLHYPm9LOtpxY6hLFriMbSnE+hta2HODUayc+Vnny1gOKt716qKQxOzGJzMoSOdQFdrEl2tSewdncFhXWkMTOYwVyhhUWcKLfEY9oxWZURuflxZ1JnGgfEZdLe2GOSs1h4PjM/azlXGZ/KYK5TQ35ECAOwbm8Fodo7ZZlVVxb6xGXS2JjExk8fS7laUVGD74BR621qQzRVRVNX571UMTeUMbdZprsJ6Z3o5+Pz+CXRnkpgrlLCmv50ri3nzB7fYLboGkZeeg+Oz6EgnmDIkbLRnTyerz31wfBYHxmfQ1ZqsyBmROhrNzqGkquhtT1Xamr7v60XfwOQslvVkAAD7x2bQkym3/fLcaBqqWp4rJeKxyrzIaT6XKxQNMsQPzPpFNlfA5GwBJVVFj27uqije25GdLG5UXPeGubk5/OAHP8DHP/5x7ovO5XLI5arCemJiwm2WofHU3jH89PG9AIDPXng0Wlvi+O79O7F3dAZ/ceIynLiyh3v/T5/Yi2f2juN1R/TjvA2HCeX55z3lPJd2p/E3Zx/u+Rm8cO+WQdzx/CEctbgDV566KtSyaDy0Yxj/+/QBAGUl6rDONP68Z6zyu0hd3/niIdzz8iCOWdaFy05eYfjtrpcGsPnlQbQm4/jMhUdZ2vj4TB7/9MetAIAbL9mEr/9hCzMPvTV5+2AW2wd34MjDOrB3dBpTubI3xuWnrMDGpV1iDz7Pl3/7UuXzR885HD//817sGZnB205YipNWLcBTe8Zw+3yb1Xj/GWvQ15HCP/5xS6XcGvvHZvDNzdsBANectRYPbh/CU3vGDfd/6oIj8e17t2N0urwYcOlJy3DCimrb1w/tQ1M53HxntX703PS7l5AvqrjmrLW44/mD2D6YxUXHLsZr1vbhm5u3GZTbnkwS3Zkkdg5N483HLsGpa3stdfGDh3dj/aJ2XHXaagDAHc8fNPz+L3dtw4fPXldZIJDhpt+/xP39h4/stnzX196Coak5LOtpxYdet04on18/ewAPbR/GKasX4OLjl0qX04lfPLkPT+81vk9eQJhfPb0Pj+4cxWnrenHhMUtc5fnjR3fjhQOTOG/DIrzuiIWGNtvf3oKPn3cEAODnT+7Fk7vHcPrhfXjjpsWu8moG/vDCQdy7ZQjHr+jG03vGDG60K3sz+MCZay33fO0PL2N6rohLT1qGXz9zwPL7Dx5+BbuGpyt/28mir97xMmbyZXll1671MmRtfxvee/oaw++3PbgL+8Zm8H/PPxJdrWXlU5NFehSlLGs608ZrzHLkn+7cYpAVmgwBgC/95kVLumaScQVvPX4pbn98Lxa0JfHJNxyJmbliRZbfeMkmQ5vV0OrojucP4r6tQzhhRTcuPWk5gPIE/F/u2uaY9/vOWIN7Xx7Ay4emcP7Gw3Dm+n48unMEv3xqP1b3ZdCRTuKZ+f66sjeDV3Tv6K3HL8Uv/rwPh3Wm8dFzy3ODuUIJX73jZWZek7OFiizWuPCYxZb20BJXcOTizkq+GjffuRWXnrQMP318L1KJGG548wYAwB9fPITNLw9WrrNrFzf9rlyHn37TUZjOFfCvd5frZ8WCDD54lrHNvnBgAj94uCpT33nyCgxnc7jj+UOG61YsyGBmroDBqTlDm928ZRB/eP4Qjl7cgSsYc5XfPncAD2wbxkkre/C2E5dZfv/JY3sqn7X3Ysc9Lw/gzhcHsHFpJy4/ZaXtdX6g1fWxy7rwl6a5ilcOTczin+9ij9VRQBsb1/S1Vb77854x/HnPGJJxBX//lo0AynO2u18awKalXXjnKdY6KpVU/MN8H7nhzUdjYCKHb27ebnh/Md0879/u2Y7PXXQ0Dk3M4t/v3VFp+9rYCADHL+/G21+1HP/4xy2YnC3LostOXo5jlnUzn+Xf7tmOwckc3nnyCmxaJjfns+Pnf96HP+8ew5nr+3D+xsX4ok72daSNKp7WZjcs6cRfvVquzfJkcaPieinql7/8JcbGxvDud7+be92NN96Irq6uyr/ly5e7zTI0xmeq1kFtRXrv/Crrk6+MOt6vDTj3bx0SzvOJXeV0943NOlwZPA9uHwYAvHhgMuSSVHlkx0jl84HxWWwbnDL8ft/WQfMtFrT3YZ4QAMDARLneZ/JFpquN2ZpoB0sFeengZEU5BmBQ7N2wY2gKe0bK7fHx+faob7P6fIencpbvzdePz+QtyjEADE7OVpRjwNr29QrXruGsbXnzxfJ12wamsH2wfJ32PvUTXgAYnc5j51B5cvjYrhHYoS//fYx+tt3UPvxCUcpKvJ6hqbIlZ6/OEuPEQ/N97JGd9s/ohW0D1ufnuZBpE4AHtg27zvOFeXnx4Dbr+xicryMAeHL3GAA5+diM3LulXD9/3m1UjgFggtHfAWB6rixn7nzBqGBofdUsJ57dZ+33ACrKMWDfrs0yxMzETB6qWp5oATBYtI1lQ2WyeWiCfU05PaOs0I8Jeg7rTGNlb8bwT1HKcujh+XtGsuUyjU7PMdPQo8lrTc5o7ReAwZOIx4sHJvDyoXKf1Pr+o/N9f+fQtKH+9MoxUJ7kAsDBieoYND1nbylnlekBRp+cK6rMsRAA/jCvoOYK1X1C924xjrFO8m5oMufYRsz5P7V3rGIZ17N7ZLoiQ57eO1b5/oH5d/KCzVxFk2eP68YuOzk45tAWNHn13D7/jD52ZdHq2rzI6QdBjY1+ofWPHUPWOYU2lwCA++fnfHYyrKir3KnZQqX96duh2RAyM1fEywfLbUlr+9rYCFRlgSavAOBpznxucF7mPbXHWW8Q5c/z8kcbH/ToywVU2+zz++Xb7KCNvG5kXFuQ/+M//gMXXHABlizhWxeuu+46fPzjH6/8PTExUX9Ksk97EZosIGSgmK1f1r+d0xB9H1HfiqKPvKh9siuzYrO/Sl9fbvemBr3HUV9y87tzys/uuXmIHLmRjCk4dW0vfvvsQcdrwyRM2WNW5gj/ka1i1fR/LajkKZCpn8fdXHz8EqzsbTN8d8OvnkeuULLIOq+5irZ1p8fj/c76jSffWGXyQx7IviIV5u1HYgk4ldVrU7ErR7PsQXUzNtYjQoFUfZYHtmUJKF1unk3Snv3ElYL8yiuv4M4778TPf/5zx2tTqRRSqZSbbCKJl8A8zSGGaoPTW/BTFkgH7ggxGE4YEx+NMBWhIM6PFFtkUep2gkHjZeMgrayo7u7zUgatj0ZposZbaHUjU0TvcZpH8BYpZecgUTlb180itlC6us9uxj9bxSkECRmRV9WQmN+nqCGgkY468yILGqkeRHHlYv29730PCxcuxJve9Ca/yxNJDB3LgwBrxgZWK9z0e9G34U3xC37EYzYrm2wNxxjYHJvg3oLsbXLpBK/7BFHLIvWgKEA9xJViyZ5aTcZo0td8sN65JkdFFA8/2wxrAUvba+j3ol5oi4QcGRSVaPUq+NY6OxwXID0+X1QWEMKiWaal5tes/V3idFpVVeWXvwUqNIwmpyi0KC6LtIJcKpXwve99D+9617uQSEQv4l0QqP7ox4SPOLnGiVr/RJBesYdeUZS61RUG12NokTnlJqF+tPGgJ4e89+U0CXRlWRC4RoFSt64h9X5MVbPBXyBy52TtZxswyD1GupUJaQS8arTvLOOIZ+8fQQuyw2W8SbvsKytG5HhBVTUvxIZYGAHCUGLCkMl1OnxJY36fWt/n1bibtyFSn/W4KGM8Aqv+yu8GaQX5zjvvxO7du/Ge97wniPJEEr/aQrOs1DUaUZcFesVR+2hXZn0btFMq3Qq/Wi8MGPIOID8Ry0tMMUa+jCphFpEUcX/gvkKXLtZ+vhpHpa/iYu3OguznpEzz+uBaj1ykK7wH2cPvrN94XixRsSADqqsFCCf54fXp7O4PRUEOxbIY/fHLD8ztSPvLcDwlw8rcSNXjpX0ZvQ+9l6UekDYBn3feeU2zesDCUwNrmrW64LFzl6lFXtbf/Z1k1QrfJwY19LQw96UgrBGigd7qtVeTi3Xj4M5+HI58cttX/ZysKjYu1m5cgO3u51/Hv5C7B1myXKzrw5iL2Fnw/E7Xr/vD6BskKoPD2te1BTv+fUEoyKG0LZMHhyx6mVFSVcTqduYjjv8njjcgquGzhwbW+O2pZliEnYv3Ivo+ZAfyoKM5myc8LOuBvQXZKORY17tVnEsen9tp4ufFxdRN1xN5hpiiIFYHm5BZE2KajNUXXjwVav2u2XuQxdVylaHCu1WoZFysveImPe1ZDfMMWY8Abpmki2TBl+CPcDsuOP1evcCNNdRu7IiO5T1YmmVeaoy5Um1XdrFYtL+DWEyqx6ZlsCCHV4yaQgqyAKqNIiFLk8ihmmARZC7eC0/wqTafmddyLqh1dGVtgmB3iXEfie6zfiLqckYVtCst9305Ze1qD7KICZn6NRE+8lZFd/d5weseZLclZSlNmizhLbS6yc+v6uR6JTF+4uVbZFR4FCI0iyqgQTdR2/RD0AL0771Uo73jzTJ+mRfwq0EDObiZVwpUaFgKpl99qVkWj0hBFsCvptAsK3WNgIyrnfnXwAd0kWu8WL1trnFqv4YByEWvkSmy9Rzk2i5EVMoBpS76NauMtVKOmnlLTq1wdBN0eZ9bWMlW9yA731+VJWyPFxlYz16N1WCfphdrsON1uss0Zd2weMnNQ/RLLS/vL9mPdqJC5e73tL/P2+9u028WJaBpMM3ptH7BP1INDbOC4GcU62bpGqQgS+KlXTRLMISaELDbmF5oOlk8ar0H2SzQ9c/h5O0rEqTLn2OeXCXBhf++/M9PNEhXPfTrMEvYJGNp4Ph5zJlIBFdZnLaWaF+5ly+ubmNSCdJlStTr9pgoWmii0v+C2oPslSjtQTYuMteGOhi+fMGwOAOdBdmhzwdRPfW4aNyMQbpIQRbAa+AOjSaRQzXBarWVfy+892FIzoMwCGYPsvkb8f2lejdlW6txjV0gRe8Xfl8+IZJkvQTpYluQa5N3swymQVMP7cyOssVG+yx2vfU7d3kz9yDP16b5CCR9Fq4syMJWUQevJK5FWC49lot1FIJ0idauc0Azd+WplsPfheL6o54lizjmvq29d96ihKrKL4BHNRivqvq4BSQyy27BQgqyED41hmj2m7rEPGi6eUPiFmSHyYzD337DsyDLNDGju5uzxVwmWIobvATpCmIyowrsAYspSl0c80TUP7yJmmPftLnez27DmzTp85Hrq3qrj3+FtbcgV/9mKZZOuNlXywrSxT8GWW7xgJVWKHuQGXFDhI78ksjDT0kcin7skzFGhmYZvszu/RUZyJNbAfWTwLa2BNhm9ONPs6wdkYIsgFe3K42orizVI0G41NrhlBV/D0s4ksROUNoFoVFtrpHL0zl/7v2uchXDTd8TqQcF9THBYEexrk3bbJbV5jBx3WeDmgBaosEyrpFU6tzKfOYClhbMkLsHWT4vcauoUzpiiw0i+UbFEloOjOR/pRreoZtgjLYLwuHWWyj6eUTaShCYF+lEFglVVb5J1cN8wCtRkSlBQwpyDWmGjhMWbvqrqEXG0YJsdh2z9V32B3N++qdwcgcSWeyx+14uSJf/6JU8c1FCC9JVJxZkcrFubJzq2Pz6ZQJm+VEGdnwCucz97ONafVijWHvLz7ctWL6+l+h2wCgUzX4xufYYFkZqVIDoj17+YDAOqDrPjYBjpziVxdd0Ocl6naaYj8lqBkhBFsA4aLpPp1kEUS3wQ5Dx3oebaJssghAkVhdrneJYic7qnI7dwOBHkC539/N/j2KQrjrQjQGw23rtJgOEH0SprTn2ddPPJYZ84fdZ6zVu+zir2rRFLV6QLjf5id7jxSuJmZ7PlvCgMBdT5DmD9kCxK4Lb4w69EMaCgX7+EKW2ouGX3DMbB7Rn5W9n8Hb+fK2plWVXZPtZI0AKsgB+tbk66meRxzxouhIMglFhHY95qvGgYs5OsfnsdK+x3N5XB0UWkvgRv91XpNO9bvqeSGloD7IYUbZi1QtR2qIj+zpZWzvEFvEMifiG1mWtk+PqF+4mm2L36PsDc/uDoDVeJNeoBOli1adIbTnHvnBXHqcyhGNB1n+uTQkMx4vVoZwWLbN53792HysegGzaekR6VlALEbxkPfcTTj01KqQgS+KlYURpglPvBC3HzUcCiF5rvj6Icoqtutt8r7vXLh23g6TRBccubVdJOxKaBRl1svDFKGSthrg6nHMRDjgpO+ZfWR4q3NgNKizXuLaOMPqn03F4gDsLon8WZPf3Wq5nvqtwrKPmXP2weHl9FlsLcshyKwy5GfYzs3Bc9Bcss/noTpaMYaVVF+P7PDWzIEewnQQBKcgCmPcuuKWeOlq94ea18BYsZFyOuWdpBjARsexBVqx/iOwvtlPk3bZxof3Ngvez8BLF11XXE6iHWKw+LMhsF+vajXLNMqAGiZ9R3FmTQ6n7mWk6K7z6z1wrKes+4dIZYcl5O1ni1cXar3YuHaSLk29UlB4V1jYi5EUgkYefwRjDsKaGsc/TcL5tHVoGRUtsnO+oQs9qbgJ+tYmgmlaQTdaPbXj1BinIAvgxSAO0B9lPojS559lSgiim+dlZwatEhL+dldxtmUUmYn69N3bQKX8rW3RiWQf6Mbu+aph/cwynweLrETYSb4TVr5wDFxp/Zx0pJ6IE2h1FJwMniLU1X91nN5NA4XsYi6iiMph5zBOnLqMymS0rJebvRO7z9rvb9MOotrDfVESaigGnBWjxo9WM851SSex+owu6cz5hzgd45fOzXBFsJoFACrIAzdIY6gk3A60Znpud3r1ONop10PAsyFJC0Mbi696q5Lz6zXUddMjWyS3S7/cgokSU9yD7m28jUo9726IGr2/LVq+IFZeXNvM7XhqMz7Jl9tMSamdp9CoHxfVjuQUGPcx6kLQgy1paa3UcmJtrvJZM5EjEWuGHJ5csegW0HsW0cJ8z1K0qJIdUFQYN2a/qCWrRKsg2q087KotuQUMKsiSejnGoB1NTnRB0/5SyqFrccGx/8gWRNGVdrEXSd6qHksDg7pcAZ03weELbTd8TXy2u037dHGNcwxDW+OGHosiKmC9iJTV6ubi0ILO+s6lKwz5FF5FavcUo0afDycOHfitbTn/ytKbjx6KH17LZlSFsHSAUBT2Cg4KT2BMts3nxQcSTBTDONcTikoQ3H/BigJAies0kEEhBFiBIt1DCHX6sYInu6XNWDI0XGJVr/yUJVxGcF84iudq5L/oRpMvue1nXQT0yEbr9QKSNxRSxgD+iBCUjwp/sEUEivQdZ4j7WFbL5sY95sk+DpUS7bcOshQW7PlszC7LkmOKYntTV8vgxjpXTUBnfOd0nnoe70wrYGYSxd9uveDduicp+dRlE68kcpIt1zJNlj7ylvboqYs0I0lMraMNPFEmEXYB6ox4FCCGPURjwXzo/SJf/iOwzEXEbsyunXfqOK7kCD+vozuQBv91+hCzIUOrCM8QPJcdT/iQ3I4XMRIoZsZpxO1fuMRRdESupH+fRMy3INsttXqNmi7tY88vi1mU+KIKy9ArFrXD83VvhgvZ2kiLshcwICmq/olgb5jioLtY4zUnqKYhZkPqJPmlysSYq+NUW6iHabb3gxyvhR7E2rjYGXRYZ3EQCZV1rN/m0e17nerCzIDtfU/6Nj5MiKrJwIIOoi7WvFmT/kjIS8oAW9YlFPcDdgyyZlmr6n3stU7Fh3WmfGjNIl6T12s82JCIP3Ew2XSnVjCBdsnkH3b8CEx9uG6D4z45E18W6RvkIjP1h4jTuuwrSpbItx5atIZAP0iUyiAe2EOHzHMiQtA+LlfUGKcjSNEnLiDh+dFDRCaeTMLMK1WBNyOYk9fnJuCHLrpw7ugUK7NkzDEqSleOHBVsGkfIpiuLrnqNarqGRJCNEYFqLJe9RGZ/5Z/1alWi3k3d2FGtnC7KbSazoHWFbYGRllj/nFVvrJ+x64B9NVvuyGXKsUf5Bz1eCRrzP6T+rwts3lACCmAX1amvVn8Lut7WCFGQB/AssREQJ3vsw71fh4cWi6wZ+MCpeGezLaYxQKJ+vNXX297xVSKcJiTGIjfVaXj910/dEJuQxxV+lNqgAH2EPZ2yX3LBLVV+IntsuAmuPr+21rL7GWAzjpcV2XeYpJ9Y0XR/zxKg3sT3I8nmFNXGUfv9hBIBS+QsntvdJ5CErPfltVjIxHwhbJNaj4iNeZrMF2SqTLMYHU9p+1U8YDhleiy5iXGk0SEGWxEvDiNF5MHWD8T3LKYb6v4MYcKyKZfVzNUiXnRVYN0jYrBzbB9vil8vuWe2sQG4mS7yy+D2hEZmQK6iP4HtOe0bDIOz86w1nDwqpHiR8PatfeYmCXN1fLJe36/bCsiDb5lfNpOhGoAje4r+3S7D4F6TLiC+WaQ9piASKqyUiRyX6nmfEDch+eY6ZZYlB4bNL2+HvqBHkAoeoxb2RIAVZAL3raJO0i+aAI3llJma1XnXlRc12wqi8s7+3exzH57T52W6tgRfcjInjHmR/34PI/FhR/A3SFVgUa0mLu+/5M5UsQoaw1mFY/cpZFJj7tnXiL2S9Dmjfm91itdfFTS9jgZv3K7Of2wt+LD6WVHfeViWHzL08OtfiFrKEqtW0IugFfa84elW5WJRSTQuEFQsyx/igv46HSD8OqpqDfX02xpUGhhRkSSIoPwiX8ASZiMtx5VqLUA1mUieSHzgu1uUJis19+vRcCj+RwaPEmCiL4jTw8N6TO8XTuYS+H/PkX1KOhC3LojgZq2dkqpPl7moHq18xI1tzysKahItY71jHQ8nC3INsm6832S16D+syN09Xqy4UlGtp2NsseM8Vtot1reom6sGXnMZu0bZp3jYnahGVrR+RBfOgFMxatZkoBnMLAlKQBfCrLdSDK2YzwQ3SZVpt5FHriT4vO4VzjXU1lP2bXbAtJ5dDu1/tXLgswtyhGo3HLUgUwCVCg4DvQboC2oMc8oDGtGA3ySDrF342DamqF7T+8/dzWoUAd1KqBely4XJqlivMY55sKtMgB4O0IPuscMomJyuz/Cht2Wonn67TNV7Kxq23EARU2CIx7AULN4jLBf1n1ShbNJnk5FTtU/UEZkHm/OY9irX+c/21EzeQgiyJl5WfoALwEP5jcL9hKIy88zmD3tNjcV/UfeYpWOUyG1RUm/R599tjuwfZYI0PbrU6jHOQnSzIUR5Iwi4ZWZDlcBo/ZGrTvAePn671Stl3x1I8RcZSPyZlLJloJyZZlm4ZxOvUH2rVh8T1fu6qh+t0+XlWP8sqAfxFHXfl8QJrK0Lgedp8jgpOHlpuLMgqzFsn7dPwKhNqSZB76o314C2teoEUZAH8ckEhC3K04E04ZY4jEnXP8QuzcGLuEWSVhZMOO8qs+Xr39cC6xvwcTunr3xfTQu5wtyxi+42UughPzxzQajjYR3xeURf4G6RL/Hp225HKirkwxpeb1mv8nJTF7I55KjnLQTMGz5aQvIlksw3OxZOXpzVfkTp2usTLs/AVo3CFVq2aklevibBxtxVCZSp8LC+7IAweQdVy7V5f/bUTN5CCLIBhhc1Du6Ag1tFC2MXaYeXbatENdhXYevRA9bNic432nVDwMZvvHScqdhZkGyuQl3OQ2S67tbcgK4q/x+/UkloWjaef08KhP8hZkMV7n/ACnKD1wi4gDit9YynFSmxOl+li7ZAvKx03ectc5+4oumgJGEcLlnlxVyDNIJ+QexZ3KBZk3efa5crMv14QX+gzPqfomed2HnB2CPXjgCo6yNcX1GJllCEFWYQmaQzNhug5yE6yrNbCwmJ51X1ROQeZcZ91dZStyNtbkPnlkp3sWCzhDvfWOkiXyGDo6GItmaedZcsr4VtDrPlHbXIfdby0DHNNy9S8aJAuQ/qm31kTf74ypVryditnWV3K1oKsK5PoMU/6lETL6PtiXkQmKbxSqIxSOkWoBpzryktV8tJuFiVATxRlslNcDvGFvurnkmmxxu5d87bPRRGR/uQW1p7tRicRVsZD2SHk4rmwspdiIjeM6cI4AGB4JoPBbA7ThREAwOTcLAazHdz7tWun5mYxmO0UynNybhjThWkAwGB20G3RfSGbH8F0oRCJsmhodcrDqayT+RFMF2aZ12bzI5grljepDM+0YjA7Z/h9eGaiUoah6XZDeUZnShjMpsqfZ4ccyzoxl8dgNuP4PNW8pwxpDs+0VP6emCvnrW+zGmO5Eoan5yrXDk+3YTBb7oNjunKO5wqYLkxY8h2abjHka27747lhTBemLPcNZAfRmowDAAazM5U0xmZVTBdGAQBT+RSGptu4dTWRK2Aw2zr/nMOYLkwafh+cHgBiaWYao7NpDGYLtmlrVPt1GiMziuO7m8wVMTwTt71uYGoAibjzOqR2fwnxQPrYlK4Pa4zn5jCYbeOWB3Df5/VpDE0PWupoYHoQ7YUEpgsjlQE3KvIlikwVRjFdsB8zB6YG0ZIwtjWtzuNzSUwX8pXvR2ZaMDBVsLwTfR/TGJyetVw3lB1EImG8bmR2pHLdnKoY3uXQTLby2+isgsFsnCsbtf46OjOok1ftGMzOWp5NYyqfwmB2EMWSamy/04PI5I1TnbL8MMrHwewgRmeGq/nNtDDLp8lr7bdYrNpux3LGZ1IU9mRyYi6H6UK2fH8+gcHsoGE8EuVQdgCZZALDuvoVoSVvbA8yaM/Kyu/Q1ABSCbY8HJ1JIBYzytThmU6kdWNfuf6qcn1iLo+5fLEyF2IxOf/eAU3O5Q3l1GOWa5O5vG29ae/FDv0cwS+5NTQ9XR3Lc7MYzLZXyh2UjByZGdXNZTqRahGfi9SCLGPs0jOYHUAs3opsYQSFojr/nbWOhmfGKs85MtOCsdnpyjxnKDuIuVJyvg9WZezITDtGZ6rz/cHsgKW9DGaNY9t4rjr/M1OZX+RbfHuPM8Vq2xie6bRtz4mCsc/L5j88PalrJ21YkJWTVVFiMjvpfBEARa3xppmJiQl0dXUBnwKQrmXOBEEQBEEQBEEQRFMyC+AmYHx8HJ2d9kZLcrEmCIIgCIIgCIIgCJCCTBAEQRAEQRAEQRAASEEmCIIgCIIgCIIgCAAh7kHevn87Ojr5wa2iwn8/uRcvHihv5n/r8UuxYUkXvvibFwAAKxdkcMWpq7j3a9eu6W/DO09eKZTnfz20C6+MlANTXP+mo12W3B9uvnMLpnKFSJRFQ6tTHk5lvfWBHdg/Nsu8Vp/+hccsxnHLewy/P79/HL/48z4AwDtetRz/77E9ld82Le3CW45bCgD44wuH8MjOYW451h/WgbefuNzhaaq8dHACP3tib+XvM9f34d4tQwCAE1f24IKNi/HzJ/fihQPGQFsbFnfi6CVd+OkT5bK+5bil2LS0CwBw/9aBShrrFrZj++CUJbjMWev7sXlLNbDDigWtuPLU1ZW/9W1Wz7WvX4/2lnKQnD2jWdz24CsAyvX07L5yoJy+9hTeduJSfPveHbbPfczSLrx5vl5vf3w3thwyBgR7z2mrsKQ7w2wb+mflod27uCuNk1YtwP8+vZ97/QkrenDGEf24+Y9bmL9/8g1HIJWIC+fbnkrg2nPXO14vyz/+4WVM54uG71b3teHyU9jySF+Hbvu8Po0Pn70O37h7m+H3D71uHXoyLfjK719Efj64SlTkSxS55f4dODRhHxjl/5x3RCUYnoa+XWkyHABef/QiHLOsG1//w8uG649e3IlLTlhm+G7/2DRufWCX4bsrTl2JlQuMAd4e3TWMPzx/CEA5cNXfXVB9lzsGp/CjR3cDqMqoe14+hAe2sWWjJnP112hjr/nZNPraU/jAmWuRL5bwld+/VPme1Qd/99wBPPHKqOG76990NP60bRCbXy7LOL1c1aPJay3/lngMf3v+kQCAXz+zH0/tGatcm0nGLf0OKMvO3SMzAID2dALXnrPe8f2y+PDZ69DV2oKdw1P44cO7he/rziQxNu0uSNenzj8SiXiMKWevPfdwtKeSzN9OP7wPyXgMd780UPnunaeswJq+9srfP3r0FewYzFb+Xt3XhkKxhD2jM9xn+ZvXHQ4A+ObmbRiZD6jJkiVmuTaczeFbm7cz09W/Vxb/8PuXKkG6/JJbr4xk8V8PlcdH/fj6pd++UBmP/ZaRT7wygt89dxAAcPmrV2B1b7vDHbXlG3dvxfiMfVt912tWYnlPG276/YuVIF2sOtI/5zlHLsTu0WlsnZ9DvP/MNehvTxvaDwD8xYnLMJqdw13zbfaq01bheyZZeP2bjja0q+NXdONNm5Ywy6pd19WaxIfPPtzp0YXQP/c7T1mBHz3ClgOdrUlM6OpRth29eGAC//1ked558XFLsVFgPhVVJicmsXbJWsc9yKFFse5r60Nnm1hE57DpaJlGJlGuqgWtfehv60YmsWD+tzb0t/Vz79eu7Wppd7xWozM1iUyiHMVM9J6gaEsOoVQsRKIsGlqd8nAqa0fLODKJGcu1qqoa0u9K9aG/zZhfTzpZubcn3YdMojqod7Z0V9LrTOWRSfDXoLpaOqXq9VC6BZlEVRHtbOlDJlGaL+sC9Lf1o6NlptJmK8+b6kJPa1elrN3pXvS39czfV6qk0ZFsRybRYlGQO1p6kUlUJ3ttyYyh3G3JiUqb1dPX2oeOdBIAkJ3JIJOYnC93NzLzE9eOlhT6WvuRSYzZPndnSlevLVlkEi2G3xe09qO/LcNsG73z/daJar9uRXdqATIJ/oS1O70Ai9r6kUlYJ9IA0JfpRzrprCBr+bYlE4H0sUxyEFCNE/UOjjzS16Hb8ujT6G3tRyZhjK65oLUPfW0ptCcHkFNKnvJqBtqTY5jktMe+TB8yLdU+r5djmUQcpWL1/Xen+tCX6UYmYYxk2pnqsryD2dw0MgnjYtuCdB/624wT6Z6UgkyiPAGLKcZ3OTKZRiZRnox2tpRlVFeqaCsbe9JlmdvZUr2m/F135RpzP29PptDf1o+5QgmZRFUJW9i20BLduzudRyZhPD6mv60f3Sm1IuP0clWPJq+1/FOJWOVZO1pyyOjy6kglANUagbctmanI8Pb5Pu/0fln0tvajp60F49nWSv2K0J5MYi7hTkHub+tHIh5jytkFrf3oak0yf+tK9aElEUMmUa2PslyuGko6klPIJKoRgNuTbSjEVcN4x3oWrf7bkyOYTcxVymnGLNfU0iwyiVHLdYDxvbJoSw4g4bPcmpxurYyP+vG1LbGgchSR3zKyKxVDZr7Oyv06WoarjpZh5PP2bbUn3Y/+tja0JQ4hr5QriVVH3enqc3al+9CemKrMIXpb+9HflkZbotx+tOjzPek+qMW5SptdkO63yEK9LACArlSP47japmuzXtE/94J0n60caEskUdD1edn8D7VW5509gvOpqJIqsqOMmyEXa0lk7e16A32Md2Cqx3wIeRTdCZb692Q9+47/MryeHSh7N/c8Y1VLk33urOE8UpvPJZV95qr5OS31xCs0Iw1zuR3PQdadhyhyzrMslrNbBe5RFMXQjrwSzCnI7LqppfNQEO+r2fB0DrKns2Kt37GO23Q6A9f8mdf+WCe0i8pZs+xjHaNqV5d28oldNsZvqnPegPgZy05UyxhuXxb5sTz+qKbvrNcYkhN4LP010n3EobzNRj0+sug4Zu7b+rvM8yZ9OzJcJ9DPROYDftazXVmDpMaOx6FBCrIABkXCw71EtLCbvJgHRqfJoFVRDPZAdWv5BCeOgoq/XWpOkxm7cpRs+o/fVeP3hKYkMImNKfbtCHDx/oPSkCNIswyytcLav3WfTdeaF8u46bKXN2SKhlLJ+pmXv/abnezwSsym0xoXCsVy1CdlviVum481bTfdIYwexCsnr85Yi6BOz6xCvJ26gSfiwxBPvHlF9Xt/C6bv3z6t2/iKk8IpXGbT5KPE6et6+aCvb+Zc0MX7EFG0RdEbDoJc1Ck51EMjQgqyAEahJTkx0F3fRHPfukD/PngTMZYw41uc7dPyA94ko2qdYdzHsZCa2zhrAunU9sVW+8XqzQ1+17VIegoUroIsi5/WaD3sNhxIVuz8WQpB7bJvCJzamVVuyV1vB2sy5DRB4slQ7RNfObHKMbeKAavaRBZHRbMzeCKZntxOEWcvurqYaKvG/2sBr5y8YqgMDdlpkbWkOteLl8k6L+0wLMi2SrHANb7kH0Gp7Dy+ipXZrBAb5iJ2KavmunfOS2g+EFA1167JRq+dBAEpyCJ4aHWGO/2cSROeMa7861fHTIokczKj/2yveAaBuXxFYddD84RT/9l5YmjOx6JwC4zuPAuN0+DsVEbehEak6/Fc1+2IKfaTYCA6E46wjbWs7LX65dUfUUWRrCfuYpTLdOzSs/uO9Zv23kX6hp03Dtc92/QTq97salJ/q6hc1WNW1ux2VbFcrN0oepWFBOn75PMSS1dOeXZaJFXVYGUXd5EmuGw56JU2dgl8V9xtxud6wY0njLldad5i2neayDC/A7YFWbiourIEg9c5EA+jDPeWVr1ACrIksu3CrQWZ5oy1pcQZJBzdwAQsITxkX7VVkdN9rrgvMiZgJdXkTsVeQS2pKrP9WV2s+eViYWep14Ji8HBayfV9cBdIT1H89QypZb+3m4DVyvW5HidjUYavnLD6i7zlpfqd02IW52/VPl3TJSarDzdLW9gWZGfXZ7v8zHfyXKxF8rG9WQDtDtlbvXQ9vos17zeVoXDwFRARZdDLIqTTQkuY20BErMm+5KP7HMV9105DoqhcsFiQOTWpLdqqKkwVHsH64cgfPX6+2gg2k0AgBVkA48Rc8l7d9TKT32ZpgGFi5xonYknkWkIDn6yY8xNLwXyV7ABstRgL3mezKi5itRbKQPwCqbtFUlMUhW9BlixSFNbFgpA9PIs/LQb6A6/9WhVWGbVCbDGK73prlQEiVmCjjJCUFxzs2pyIlZqXtSsXa9XwnxRuFZqgFCFuG1BFFkEDerF2+UVsniW2yOxvoe28yiKDwzsVbTNml2rWczulJBucUKQsXglqW5YZJwNFI0IKsgDGtuC+YdSqIRPyGISlkMu0vaUh+CBd5r+Ngl//v/k+EbdqVRWLYi0apMtuAPbk9sksn0QCrDQFn0ePAocgXZJlCEpZZHoU1MhCUU5TTMki7HHcg2xRgjnXOvyux40FmZeGSD9lxVJw21xY9SaiuIo+o96NWtTFmiWz3Sg+1Yl94Kuyljylf2P87rS4XCpZI18zE3aJU9K1diW1y84QqTjAMkVRJjtakK0nsTExLxiy+rr2/BULMkx9laUgR6jSgvQAEPGuaTRIQRbASwcwuFiTfhwp7FxT5N28+IO831gnEaL3mY42MP5aTc/mAcz5mK8SsUjzjlFxDALmuEfZ3W9e7okpCndvqIjsqMUAK5OD7HtxW4DqZMR78s2A7AIrt79IvFLR18+yUrM/l/+XdZ+12xLiVA4W9nuQqzcXBeUqL3O7ox2N22KsiwGimCf2svf5DV8GOy+SsQJJBqgfC4wptdUEhDwYfC6SnYdXveDKgqyqpuc2UtmDLLBobr23xsc8CbpYe8U4d6y/duIGUpAlkXaf1V1Pe5Cji53r7/yP1utV9mdeunbIvmpekC7tN9YRRWUXN5sJp/Mjuw/SZSoD67PQHmTH1X5/hbaQBdmHfmqUEQFFsXZowyLf+02zDLJ+4djWZKtT8HpWP/BmQRZQ6jQlumT9rnyveP7MIF22ll39Z3Ye1j3I+mNWjL/ZHydlnZy7C9Jl/F/2Pje4jfysqtYm52hBllxglB9Lvf0eJPYLzv4WimcciAKynjMi15kXXnhnnovO9WTws5qNp7GIpexnwK5GhhRkAby0BbeT9mZpgFGB5wLotGpodbHWfRZ4j9LzWodVd/t8+JMRDbvzf13vQbZRxL3Uk4zCJ4r5dpHknCIwi6QRNS8T0XYil6YVrZnpFYwouavVG7z3ZrXM8YPU2KXD/Y57jZxCqJr+N1/P162dn8vuGDs7q7e5bPbWPeP3MsdJeTnmSZagFCFesuajdVjXswI/BikRvHot+Y2dVZM33/Cep+5zBOWv06KxaJG5xzyZ+qCdV5NfW4UCsyALXudmmhHEQkHUkVaQ9+3bh7/6q79Cb28vWltbsWnTJjz++ONBlC0yeFlha5J2VPcYBgbGIG29vvrZokBzLLN+wD16QDX8ZymW3aBr/swqN2+vdfl3+wkl6x4vgzFb4bLfr+YqJ5GbfFjdroWMYA3sInvGeddJ5c/sQyQdZXA0IAsonPprxSeW/AVCEQxJVCzI9qloPxndqv2cVbLzdDPWG/aHmn6L22jIevdtt27S5fxUw/+y97lB5Pxq9m+sdmhduDH+7VwvXsSI43neNRZRQuNFgIWqR4nszsXafgEPqC7aqqrAHmTzvUKlCQaZ4+9cpF75FMVo50GQkLl4dHQUp512Gl73utfhd7/7Hfr7+7F161b09PQEVb5I4KUpcPQuIkIYrRNiil/l+pAHUVFhZQ7SZSf47Y5AcDqSw9YlzGblkbOu4JiOl2tE7xU7B9lJQ3bO1+1RcDLI1IuoZ4BU/sz2VP7fHIAmClb0RsBLX3PCjyBdrBRiCnvBD/DXgmHr+iw4CTSUkROkS8SCXMnbxUNV6lLyVs/eNoKLa4bfBK5neUep3kWs67vD1AMqVk1VDdQNWsRrIkycxgPR+jCLFabXoDYmKTB+of3FXOgVy99YFv/qWe+BJRo3wc0Y24y6jJSC/JWvfAXLly/H9773vcp3q1ev9r1QUaFQLGH/2CxXgAxN5bBtYAqrejPYPzaLJd1p5IsqDk7MAgDGpucM10/M5pHLl9Dfkap8d2hiFpOzebTE41jW04rJXAFD2ZzhvnyxhO2DU1jS3YrOdBKqqmLv6AwO60ojGY8hVyhi/9gsEjEFy3paMTadhwogGVcwM1dERzqJnUNZlFQVq/va0JZKYDQ7BxVATyaJvaMzyBVKmM0XAQDtqQR621vQkU4ayjEzV8Su4SxW9bahtSUOABjJzmFiJo/2dAKtyTh2DmXRnUliWU+mct9ItlwPU7MFLOlOIxGPYf/YDNrTCewbnUEqEcOKBeU6XNrTinisXO7R6Tks6W4FAAxO5tCSiKGr1VgmO3YOZdGeSqC/I4XZfBFDUzkk4zHMzBWRL5awazhbuXbbwCRSifLzaHVQfWcFPLdvHPGYgiXdrZjKFYxtwiQuJmYL2DMyjUWdabx0cMKxnC8fnMD2wSms6WszlLsjncTBiVnMzBUrE6ql3a14ZXjacP+ekZnK5x1DWbx8cBJbDk1Z8pmeK+CF/eOVvw+Nz+Llg5M4rMtYzkMTOcu9APDCfuOzzBVKeG7fOFoSMSgAcgW2dN4+OIV4TMH+sRnsHKrW+b6xarlHsnOG98Fi13AWO4eyyBdL2DZgfb5DE7O2k9r9YzM4enEn9o3NYK5QQjwG9LalMDDfpha0teDQfJ8FgOGpOYxN57nlAZwV2l3DWXRNJ9HVmkRPWwtUVcXukWkUSypaEjEk4zHsHa3Ww2SugJ1DWczmi2hJlNuqxvIFGaiqirHpPGYLRaztb8fB8VnMFUuYK5RQnB/ll3S3YiQ7h67WJNpScYzPsJ9j7+gMCsUS5ool7BjMQlGAtpYEpnIFw3WHJmahqkChpKK3vQXj03ks62lFSQX2jc5gWU8rsnMFDE2V+3gqEav0WR5zhRL2jEwbKnHHUBaFUgmLu1qxf2wG6WQcizpTaJmvJ0UBlvVkMJsvYnK2gMO60pZ0SyUVO4ezmCuUkIzHMJsvoqs1iWU9rSiWVOwYyqK/PYWethZM5QrI5gpY1GlMhyWvAODA+AwyLQlMzOQrcnZgMod4DOhIJ7GoM419YzMYzc5hVV8b2ufl7PhMHrlCCYd1pTGSnUNLIoa4omAql0exBCzsSGFSl9dsvoidQ1mkk2WZpAC271Fj53z/mZjNI18sP7sde0ancezybsv3u4ay2D08jbZUHDFFQU9bCyZnC9b7R6Zx/PJuTMwUsGe0LI8Ojs8YrtkxNIXuTEu5b+v6vaqqODA+gx2D1v6uKADUcvme2zeOUd34uXMoiwVtLWhLJSzjKlB+ZyPZOewdnbb8ZsmH8d3EbB4vHpis5scoH1CuoxcPVGXh1GwBAxPlfmgeO+I2vpp6WZkrlLDl0CSmckXmtTy2D0xhNl9ENmd9RzzsZLUIz+0bR1sLe+q4bXDKtp3uGJxCS8LYJrccmkJHOol8sYREXMHApHHs0WQKj1yhiOf2lcc1/f07h7JIJWJQFGA2X8KCTIvlOQ6Mz4LHs/vGkZmf5+hJJ+OGsSZfLGFgMoe5QgkxBVixIIPR6TwmZvLoSCeQSsaxa779arJxYHIWAxM5LOtpRVdreX72im4MPDgxi4GJWYyZ6nPbwCTWLezAVK6Apd2tGJiYxfhMHi2JGDrTyXl5pGCuUMKa/raKDCmWVOwZma6MF0B5oUjfN/eOzqC3LYtcoYRUIoaethbMzBXRnUlix2B5/phKxNCSiGF5TwaKUr5nUWcaLYkYDozPVOp6dHoOigJ0t7bgwMQMFne1IpsrYEl3K/LzY06+WMLS7lb0tFXfjTZXW9rdiqGpOUzO8uXenpFprJ6fO2lMzxVwaCKHmbki2lJxrFiQwdBUtW0MTMwa5m0HxmeRjMcq32hu3c/vnzBsOXuRMZ/Tj9+AVflUVRWvDE8b2v5svjx3Wj4/Rz44MYt4DJgrqGhtiUNVVUzPFSt13ZlOoqiqaE3GMTCZw/RcAaoKpJMxg3wemLRvz/p+WSyVx1+tTIcmZpHNFdDVmsSB8Vm0p6rzgJiioLUljmndXOTg+Ax2DWUxlSsgHlPK735sdn7e34puU1+rVxRVYsno6KOPxhve8Abs3bsX9957L5YuXYprrrkGV199te09uVwOuVy1YU5MTGD58uUYHx9HZ2ent9IHzO2P7cGf94wZvrv4uCU4ZU0vrvv5s4bvu1qTGJ/JY+PSTmw9NMUcgDYt7cKz84L8ujceic50EhOzedz425cq15xz5ELc9dKA4b4bL9mEX/55Hx7ZOYKeTBJ/e/6RuH/rIH777EGsX9SOq05bjZvv3FJRbC48ZjF+/cwBQxqHdaYrSvvK3gyuPn0Nrv/lcwCANx+7BL96ej+zDm68ZBO+/NsXK51wbX8btg9msba/De89fQ0KxRI+8z/PV65f2JGqDFLXnns4FnWmkS+W8FndNUcv6cSpa3rxH3/aacirI53A5GwBr1rVg0tOWIYbfvU8coUSPnDmGixoa8GX5+vpxks2Weqfx3VvPBLfvGe74wRThg1LOvH8vMLIqm8AWN2Xwc4h58maxjtetRwKgJ88tsevYhIBc+Exi3Hauj6h9vjFizfileEsbrl/p+O1LPraWwwTxuULWg2LI244dlkXpnIFbLdRBuy47OTl2HpoCo+/MorT1vXigW3Dht/fe/pq/MefdlZWnT989jp84+5trsoYU4Bjl3fjz7vHAAAnrezB46+MAqjKGD1P7h7FTx/fa0nnmrPW4uWDk7jrpQGkEjF87qKj8Xe/KMvAj73+cCzsKKeTKxRxw69eqNy3aWkX3nnKCuwZmcY3N2+vfH/hMYvxxxcOGWT91aevrrzfZT2t+OCZa/HpeTkrwvHLu/H2Vy3Hf/xpJ3MRyC3xmNW6ICKfvvCWDfjCr1/AXNE6Tbhg42F4YPsQJmbklLPWZBwzebYymIgpKPhsIrvxkk2W7/60dQi/edYqs/3m6MUdeEGndBPNwRWvXon/eviVyt/6edHHX78eHekEvvDrF1BSy/OeNx+7BD98ZLd0PpedvBw/ftR+vnDMsi5cdvIKAMDPn9yLx3aNSucBGOePGmcc3ocFbS345VP7sbI3gzcfu0RIxr//jDV48cAE7ts6BABoT8Vx3QVHVSK+f/WOlzCSzeNtJyzFfz+5T6h8fe0tGJ/JIz8vp1riikFmvfs1q/D9B3cZ7ulMJzDBWPwDqvN5N5y2rhcXHrOk8vfLBycteevzKZZKrhbHvLK6L4P3nbEWk7P5ytzaDy49aRlOWBFtr+KJiQl0dXU56qFSe5B37NiBb33rWzj88MNxxx134IMf/CA+8pGP4LbbbrO958Ybb0RXV1fl3/Lly2WyDBWzcgzYuxZonem5fRO2q7P6FauBeWEzYeqE928dZN67Z6Q8kRmdt2o9tL08IdUshXqr3wPbhiz364Xb2HS+soJoztPJ9UKbSGv/myc6+hVcrU70K09A2RL5vM6SqaEp4ZoQ1+rxpYOTGJxkWzVFGJjICQm71mQcrUnrajGL53XWVPMSU2p+VU5v6e1vd15RG5/JW1aLNRa0iVnNeSwxWdt6Mu7TTCViWNmbQWdr1ZLQkU6gIy3llOKZZFypWN6B4I4MOn55NzYuNQrSdQvbsXFJF4DyIpMT+WLJ9v3akUrEsKynbHHQrJoaZuXYTRt5eu+4bd9IJeyHh6f3jFWUVLNyDAAvHpjwzV28pKKiHAOo5AvA4JGgMW5j+R+fyWNw3oqQK5QMithuXV+dMk2atEXNLYeMis6D24cssl5vTZiYySMvegbbPNqYI6ocH7usS+g61jK4yOJdvqii1cZa+OD24YpyLOOyZ6ccm9PRZAyvHbolaDf+9lQcRy3uwIalYu8nKDItcazszVhklxNHL+nEhccslrpnZW8GK3szTIurGU2maZjfRzLOf0F654iFHSms7M0Ie5ZptKfKdbO6L8O9bml3uvJsK3szQmOc2YvBPC+ayhUqbr2Ts4WKp0SmpWzttKPPNI94dOcItxx62a5XjjvSCYMXoxPa/FH/nu7bOoTHdpXzf2V4GtsHxWTWSwcnDeWayhUNJ2SMZMu/3W0yFOnJtMSRaYlj8fycxuztZV7QOzRhtayaPaX0+DmP4M09y23BnXLsVYZp8p/lIaThZk7RSDukpEaeUqmEE044AV/+8pdx/PHH433vex+uvvpq/Pu//7vtPddddx3Gx8cr//bsqW/rmF9bNKr7S/xJTypvzg6CICYjLETOiqs1q/oyWLGgOnCLKstmt96Fnan578t/v+2EpbjkhGVC6dg5dJx+eL9QWexYv6gd7zi5ujh11OIOvHpNr6u0VvZmcMObN+ADZ641rBRuWNKJtwk8p5+87YRlBjfG1mQc7z9jja95vHZdH97+quW4/JSVhondlaeuRNf8IsOpa3vxqlXOq6ay/f2wrjT+6pSVAJz3Wp3hso2w3NIzLXHc8OYNvsmDWgb18BKdWSofxv1Fw9aLYEklYvjLeeuQE17KotXnh89eh6MXd1i+18rihq7WpEHO6vcGL+5K4wNnrsWnLjjSVdo8gh5+3nLcUlx56ir0cFwN+ztSOG2dOxl8zLIuw8Kghv49vPX4pfjMhUfjA2euxeXzMsSOc45ciOOWV5X5s9b347R1fXj7SWLy/PgV3fjAmWvxgTPXYt3CdsfrV/e14eTVVXmZTlTbwIYlnXifgwzX9z0t3xNXylmtjlrciQ+cuRbvO2Mt97p3nrKykscHzlyLjZ4XPVSL7NBk++EL2/HBs9biiEXWOjxzfT/OPnKhMSWHjm33+zHLuvCGDYsM321Y4ryI4td4YC6WzPhw7LIufObCo/GZC4/Gu05dNZ8e/35NLitK9Rl446kX+WCOuh3Uvm59nzGzaWkX1vZb5QMLXulYcwr9GMDCMS5LHSHV2hcvXoyjjz7a8N1RRx2F3bvtXUNSqRQ6OzsN/+oZvzbXh7rJnZO5XdRNV9nU2U5+BUbFXXQV0fyYZgGpKIICV7V/NXZ72URRTOVS4F6Q6YtiPRPUVZKuMdetcF1LYFf17p5drlPEFEZGNrhtI6x+6nUFXYFiPH6ihrJAJFgc4F2WsyZYUQ944wbtMcp9S7F8D7gfN8ztzNyXzd/5RVDnjVfSF0jeLJOl0hfIQ7beDOPD/EfRMUKx+cy7Xp+f3iKsKHLH51XaiUC+hjII3mCR8wL38Hp+OZq38YqSToEDUHE3NuRr6n/lfPgyxv4sb8XS9kTetV/zQ6fzr3kYyqmI3a/JYtF5j59KXlBHqnFCTEj1fd44xZxTKAo3/QbSj+UU5NNOOw0vv/yy4bstW7Zg5Ur+6iRRhtUOg7CsOHVIuyjFgHdFTBQvuQQ18VQUxTBhE60L8zu03mYdjOzSsXs2rwI7FlO4k1EZ9M+iL1dMCXraycZaBn9LwZq0u6F8ZIRk3rC+NztYkyoRWGXSJmJ+raTX0oJsV8d+n+/MkqHG43uis0jothwqqjIpppgXPaqJuh03zO2LJVuCkCpBD3PVstvjZTHPbjzQfy+TtGKzECesRCrsMYGXn/4yvewytzMWfvQr0THVfJ3XsZglF7RAUFpbZ+VQVu6sabkhpgCxmPU7J/yaH3qKqq9vN/OfnepBk8uifc5P8RDUWdq88T7GWEyxg1f3zIUa8NtK01qQP/axj+Hhhx/Gl7/8ZWzbtg0/+tGP8J3vfAcf+tCHgipf9AjYxZqVvKxC6NQhVc7Eze0kmwVvUhzFPqSYluWF68L0mOZnE06G8158sSCbND3XCrKNwsha4Q4as6UyCA1dMUw6Feb35t9YqAzXOue8xevU7eo+S17IWpDs7tcIahWdhegRNIG4WOselNef/aAWXU2/qGO2vujfqdtxw6wMsZ4pCGU2aDklYv2OKeKLX9YM2H3Ty2MZlOv5z6J5xFzIYP07iBtkrDu5E9grdbGwzD2PluNijUq7YWdidd/ll6NkI3gVxZqWkGXVNwXZtFgpMbFmtdNymvb3aHLZU59zSVBjAG+8l1lY55WPlQer7TQqUgryq171KvziF7/Aj3/8Y2zcuBFf+MIXcPPNN+Pyyy8PqnyRQ4V7CybrLjeuJk75OwpN1ZivXobKTrKFJr4sC5WHDhbUZNssPEXrwmpBNilOgspoSVVtn82ra5PZOl42GLhVftjWApGV/yAwl8fvMhjmfpy0nfI19zuhvCUGdD9drHmWDBFMa00GxTFoRLPyatVmyWGjXFUDtZzXYpJS0p3Bqpg8RPxwsTbfpW/CFStsAEKlVhZkHl56mJ2cM8h4iaTN3j+8W228Lg1pOWPML262IAukYM5btpmIW5D5f8tSKlllj/lvVtFY8wgn+WL3K2tcEVF+/XKxNpdLZnjQl0BfZP655VUXaxF54kXmmG8NTEHmvK+yEisGr97s8nBa+GsUpEPOXnjhhbjwwguDKEtd4Fdj1xqlVVBYM5DN01GBNq3X6f+SXiHkZFWxkvvsYhLUZNusNIrWhdP7kTJE27lYe4yNYV71UxT3A72dtcDtyr8XzANBELnbuS3K5qWq8hbkmMRqrdu6Z8kL7R27tRhYB+ha+hrbWJCFrhKHJYbMsikiHtauUWHcH2m0IHsYN+axeGEoRhkFBGVB9j9NQ/qV/+0zYm17kUmfbd11L6Fipn3AsMkjpigomlq2rGu3uS2Z95XKKCjVxTy55xXNwloW5xt5cp61wU2/RxawebeQb7f2e5Ddebr5ZUE2W7ZljE6Gdqp7F7wUNLksaqzwIh/Mtwa1SMob7xVFEZ+/Subh1M8aSD+WV5AJD0oyU/mVn1A57zF2LoZaMv6tYV4hdBJcIp2fVR4vclZe4IhdXxYG1Wt9syCb3YBtUFUVqo3w8epiHVMUKCYl2+0qqXEFVz+hjcgeZJ8L4eQCKkp575mkBVkiT7eLKOw9yNX8WTg/hTLfvspXms/g9Qt2XAe7a40LFPp+a1wwFMvLKaZE4BbkGnQ2/TgR45glXFuQzQtc0pZIdwTvYj2vtDlk47YcsZidlZH92RGbhTi2ldo4TrLKJpCdIW2LBVmi7G5fZZAWZF6vV1WrgljdI6sp+1bMiwqAvQu1Pi8W5TpWLN85wevn4qLOukDADHhoczcrmJxT/vpFPpFZip+yJ6gRgDcnjNmLaguyFmSnqmkkC3JtzvRpIPy2hopMuuxWG0XTtP5uXMPUp2fuD45pcX9TLen7QWDumop50Ba7zVwas3wQlRflarKxIHt1sYbZ+uneeqFfmTRPbsNxsWZ/9gujdYQ9OJf/dshclR8sYzHxyaLbxQFW9/Tq3irrCugnIhMl3nWiRWU9U033IAeXdAUVqsE90daC7JOSwupfQSizQdedSJG9BDVUYFVwtO/dYjTilv9wE8hKtAzGhVbj967GO8lbRC+3nkrhfCdP3jktrJXzsCmLeX7mUA67uRdrrUuszTpfI4JlCifjYu1ivJfdg+ynfAjOgmz/W3kuJvYU3CBdrEU4h/QaSD8mBVkW1cUkt3KvKR3zd/Z5ylmZHYN0wdgp9J/NbhluBbA+Xb/Fg7zAER/keUGY7DAXhzXwiKRlfi/msnnBXAYvyqydxcf1xMYjiumz7xNqn5JzFaQL4nVqXgQRhRmkS/vfbqImmUdQkwRW+ezknwqTLNL9oU+GN6l0Qj/xK3kZLASoiQVZp+SbFTreuCGK2ZLIO0LOT4KWUyKpK4p7rw87Y77b+jPLzeriBCsPvlVJzIXVqOAboljH5Muu/1/4PsEbLAuhAvfwFvHZQbqMLtbMxQ/Fqqy734NszcNrkC7xLqUIBemyS042YjpgDDRY8ylKQGMA910Iei2W4XmDyFdWA+nHpCDLUlZivLd4TSCITByt7ijeLMhm1z9DkK6YnAAWMeay0vDkqhqQu6ZZeIq6NZvbg1moiB48xA3S5TWKtWnlVFW9WAfZA1RYrjVBu3nHGBNH9nX8dNwG6RK2dCiKq3fALBLH1U+oLCJ5BIS9i7Wxr9q9C9Gisu7XuzyqnDzqBcNYYVLotO9jXhbbzMqHQdEKTp4ELaqqHhi8a9xbfO32UrqtP1YQR62MQvdLLixbxlqTBVpGjlXd2eXqUvR682Uiixp8Lxb74KyVhQlWORheXyJzPRbMIF0iLtYBHfPkNkiXaGkqx2gJ9jkv8qFW3lPcKNaK/OKBaB5Oydb6JJMgIQXZBW6be8nkfqf/Xyp/ARdqp/sN1mzOvltnF2uBB2Be4r4TFYNyWYkZO7f4HmTj3+a7RK0E5fdi52ItloYdCowDg/1uZ4G0bKwUZYtIbYWjohgLEYRsNj6j3ERQT3lrg2TeEgOdW68AbpAunyq0llGs7eWf/R5kPaITGtZletmkulgQkaEWExG91d2s0Gnfi046WfCsWEE+XtDRElju4VZLpPt4CTEbueD6HGTY1YnYBNmN5VpfVr3iZZbpTvi1iGcHbxuAHXwXa9Ye3KoCx8qzkrdFQXZnLLF/33z8i2JtXiAQl5NuFuWLlcW8BjrmiWvNF3+7vPIx9yA7pNxA+jEpyLJ4sR6z7hSyIKv8v61pOv9utxfPrOB4sVZrv/GCALlBfrItdr15hVY8CqAxfdb5uGLumfYWZK+CnbU/1a3yY3cOoZc9dW4xWxuCCNIlOul0eno3FmSZ54m5tCDzupNdck5PYe4DQSmKzJgNXOsN23PGsGDIsUDbpaVhlk1BrgvUoq9ZjnnSZap3vXYdjVkxKZG634IN0hVY0gB0FmR9nowyuA+UKKrOisM6nUDYgiy5SFleVNHnbRxT3LQn2Vtktq4Y/hYay/m/WY95EsiD0V6cxAtvPsHz3rCDNycSF/HWeY5UkC4XC+JFSR9rP4erMKJY2y2gseCVj/m+HZJtpCBdFMVaEhXuO4/sZK6ap8r924ys0q2/Pi7ZtrkKshaky4dNGPoUgtzPqH980bqw7EG2KKLiq7W8BRhFgWv3BbN1sexi7TItc5l0P4QhG83zOr/VdDcDMgvVRZSu8njubiInCnv/1/wE3/UE3tiWa+lobLsHWbWXe3qELcgC9wbqYl2DvqYvvl1bFJxzMmGdGa9PNyiiMIfzsh3EbgLMs1jzy2L2DLLv/+xzkPXvzTljc7IGC7JNvqJp+X0fr43awY8uzdiDrLkAV+rdepcCa59w3oPM/p3lbSRSHbLzQzssRh9GOXnW78pnSSUwFAtyQOlyLchQhAUo14LsonNFQLT6BlmQXeBW4ROxUojgh1XCTrCaO50XF2ueG7lsJ9KnEdg5yCYLnPAeZNPf1gFVbDA2T+ANacbcWQf1ZdLfrzLKKZOW3ecwzkHWu7DLRH2WyaPyWfA6Ji4tyEJpw98o1hp2yTlloyimRa3A+qz1O7sYBXp3YcAoR/TJ2E7MTHkxXawtx7fUcmnAf/Tlt5tcut37DvCtc0HKkqDllGZ54S2uyVh5zCgsbYmRh3B6YEfFFt+DLFcGi+eP6ZgnN0qMbF3KbF0x3ud8j3MUa/ZCmpaX3eKH+XvH4YTrkSZfyXy3XvF0LPXDtCDbKffGjETeR+UcZPi/gG5F8h25hGfN982CbLNQwy1XFFYffYIUZFk4SozjrQaLSvmzqLXXqFw7WZCdy6Kf+BiO66hZkC65TqR/ZtlJp+jllqAVLoN0WSd94oLKdlBgpCuD2TruSWrbTPq8ltEtge8nFEzf6aqSG9lRmTAJXOpyws3rH14GO6O11nUy8vnafa+KyREvXaOWCnItNjQYFhEUdp5e5kPc/Z0BPl7Qczil8r+9ZVXxUA67RQl9HnKBrthKLvt9sxRp/XOKZqq/31wWmbK7XhVwlb5I2Xi9vuxiLX69sSxy99kG6WKk5dXF2gtMF2vBhUqRcsse8+QF60JqUC7W/DL48ZjsaOr8lBtIPyYFWRYv7sL6fiIbpMtu75xb9FYWfRksQboc0uEe88RIX0O2D3lxsRa93LyKLh6ky5iBddIn9ryqam/9KluhvUkelmXbDYrN57IFs/bS0Wx18rsEhvQ9rKDrz5QVzrvyvz9Kuix+uS/W0pIqegapfRRr92WtqYt1DdCX384Txs76KIpRhug/BydLAj/mSTH+b/4MOHu7cH8Du697jVOhT9+pDIbycJ6TfYMpSJfBEynAfHV4st47wD3mSbW6WJuvZy9+WMcB1zFimIupzg/mT5AusWOe7OaWXoKmiXrz+UlgLtacB1EURTg4LK8NNZKy64bw9iAPDQG5nPx97e1Aa6t9mm4nJJkM0NbG/Kl1chyxUhEAkBiOAZ0q2sZHhJLNt6Qw11pO1yIExsYQGxp0TEsdGER6dARtU+X6UgYG0ZKdBJQ08/pUdhKJQp6f5mAHM99Uj70AbpnJIjmne2eDg1BGp23LHx9KA+k8lJFptE6OY6aji3ldcnYaLblZ45eD1XpJjiiIqTOVv9WB9upnRcF0Zw8z3URuFqnZaShDbULvKz2qoKhW321sRTf7ufJzSE9PVcs/UkLb+Fjl71RHEW3j49XrhzugpOKVdKc7uqEypJc6l0NLdsqQVjWNIbRNjCCRr2rQilJt7ooCTLd1ohS3dulYsYD06AiUoWSlDC3pOSQ7SkL1MpvpQDGZrKanSc1SCcmRYd17SiKWmBXuG7OZdhSTLczfRNNIDLchNZqtXN8anwFmF9hen5kYhSIpI1pGUkBHCchk7IfikRFDXTAZHERiZMJyjV5GmElNTZT7wsQICkV+uRMjXWifHAVmCwCAQiKJXFsHO10HGdFaSgODg2gdG0HbhLFvFhMJAOx0NRnRMhJH6/hwZcEnPpx0fKelWFxORgBIDLeU342O1Miwof9pMkJVjQsUxZJakRGJ4RTQVpbxGM5ayzo4iOTIkOX7bJexrRW1552XEXpZJczgIJRSiSkj4vk80tOTAIC2uaRBToow024vI1qnJizf68uvDA4hNWpt45mWOBId/cz8lFIJmckx2/K0JmfRmp1DcabcZjNKGm3j5fecGi0BuX4glWLeK/zcg4OWr2Iz9n3JjYzQmEulkU9nmApO6+Q4WvKFyt/p9ByS8Zztc+jlu1lG6CfA6ewE4oVyuq2o1l98OAO0zFXuYeWjyQizRVFRFGB8HPHhMev7ziVQmi0YvkuNxoHBcoGSI8NIZycw29bJfK6WmSxaRoYQU5Sq3NaNmckRBcqQwiwvT0bEphn9lkPLSAKYbxqZiVHbeQRmZoAp/XjvIOdRHl/bxsv3mGWEFqRLP4/Qrk+NAhhsYfazltEE4pg2ziMYzVQvI9LJeKX969NrGWlBTJkxfjdarnOujBgfMcjWtK69JUcS3HrRzyP06wFKqVQu41yroZzpljjUuaIlnZaRWKWtAUCyMIdCLGm5Tp9WMjaDtvEZZAotaEnGKmW2I62mkZiLoZBiz7F5MiI5ogCD8crfiWHjuKHJCBZ6XcOJVtM8s5hKYTZdlhHmxRS9jDAwOIjY0DhnDj+EVHbSMI/QSzbWPCIx0gUUbXQ0Pckk0N3N/m1yEpjlvyNb4nFggc0cMJsFpqfL6QsQnoK8dq27+/71X4EPfYj921FHlZVkN3zuc8ANNzB/ev/178aivdsN310vmOxD578Dv7r60wBMFmQAuPhibLr3XmwSSOcDpr/Pf+0bcNvHvsq89m3fugGbHvqjY5qsZxg84dV49NPfqZZTV+bzf3AzTv39/zNcv9QmHT3LALx/2Vrc/M+/qHynH4zP+J/v49zb/92xfNczPk919uBL37uXme9Jd/8Sb/nul5lp8Thv/v//fnwP8/ejHtuMy7/+CcN3F5queQvjPq0MX7x1s2XQBIDeZ57A6z7wDrzZplyftCvwPP/0Tz/HwIp1lu/79u3CG95+iaEM5jLx+M7n/wM7N76q8nfl3Q0P49gT1+NYF2kCwA//z9fw3GvOY/52/XvOEkwFOBzA+bq/J792M7D6bOa1H/voxWifGBVO28DnPge84d3s304/Hee88ALOcUhiMQBzyfQywsypn3gv8MTD+JRgEa/VfX721NfjR5/4OvM6URlxNeO7HRtOwgO3/JR5vV5GvNb028kOeR0yyQg9djKCxVtg7H+ajFBh9UTRywiNlWC34TPm/+m57r+fMfytKeB6GSEjezQyNjJixctP4X2f+2vDdzLp82TExz52CfMeffrnzP8z8/t/+RFeWrrR8n1mckyqL1u4/Xbg0kvZ5fKQbteNXwPWs2WPFxlx59s/gLvecY3O86PKX//du7Bwz3bLPa+yfGPFLCP0gR+v+Mq1WPP8445psNpJRUawLIrvfS+W/Oxn0u33HACrN5yEW/7+Vubvehlxqu5785jJytcsI/QlXvbdf8P132DPiZz4GGcegVtvBf7mbyp/ngxnWabHLCPU+SBdrHmExnmozkPM6OcRaqt1YYolI/T38b47G3wZ8Za3X8Kc22i8mvObfh6hn1dmJsew+PDjuOXkceTffh1/PuX1zN+8yIj/ee/f4eEL/pL5m4yMML9LTUawYOkaPPTv4pHz34FfzssIczwSnozYOP/PjreZ5hH6dEXnEUzOPBPYvJn926c+BXzzm+7SPfpo4Pnn2b999avA5z8vnBS5WNcQmX3EYVGr/RP14LohGqTLL6LaJsw0UhAGWWrtQh7Vmq6PlmrEHARPs/b6Sb0H5XKLUuvQsJ4J2sU6eBdu37NQmB8Jn1FV/7Ze1Ke4kd9qxIPaahlzBPugZFAzTf9IQa4hdaL/GAiqzLU/MVeeoAJS2FIn7SPqAjLq5SPCw+xi7TdNqyCHXQBJgi5vdQ9yUJNUf+M9mKNK14sMrcfFWj/nVPU4pwT8nurUXxsIgqBjsTQjpCDXEP3kLKpyTfYg+kbGn4AU4jRzXdcLdTgfq+Bn2euxGswxIIIIoFUvXiB+U2/9IujyBh4EDN4CclnSU8zBF+vshdYRJdU/C6qXgIJh4qecrDfZUxOYQdj8Srp5KlxRazyiT0xMoKurC+Pbt6Ozgx3ohUsNg3Rd9/NnARg3zp+2rhevWt2Lm/+4RShZfXCNZT2t2Ds6AwC49KRlOKFTwRNbD+F3zx3kpnHt69fjP/60E5Mz5c3w7z9zDX7454M4NB+k68ZLNlXKCogF6XrrCUvxiyf3Wb4/Zf0i3H2oeu//OW89vnPfDkzOFixBuj51wZHYPTKNHz2ym5nHRccuxrHLe7BjcAo/eGyfIbjGeRsW4Q/PHwLADsDzyfOPwFd//zIA4DXrerGoM10pr77sIkG6Lj5+KX75Z+uzmjljfR+KJRUPbBsGAJz0qvW4d4t1T7s5SNeGJZ14fn81wM2JK3vwxCvV/SnvPX01Uok4/u2ebQDsg3QdszCN5NQkXjpgDSDwN69bh+8/vAtTM9VAC22pOLK5crtsTycwmMjYBtc457Akzj5yEb746xcAAGv62nDqul788GH2u9NjDtL1mrW9uOjYJUCphBef24n/fmIvAODCYxZj3cJ23HznVsc0y+l6D9J12ckr8MpIFg/Ov7M1/W04/9WH46v3sZ/LTQCetxy/FJuWdgGZDH78/DCe2VsOjHHjJbroASMjuOvZ/Xhox7BtOlecuhIvHpjE47vEg3Sd0Z/ABUf24Z/++HLlXdvxgbPW4v89ugej0+XAPOYgXfqgP04yYmFHGu87cw3+86Gd2D08Y/itmEhgzbqleIHRTjUZcc5RC3HXiwPV51jfh/sYfUmPmyBd521YhJNX9xq+u/2x3dhyqNo/NRlx0bGL8cSuUeyfD9By2cnL8dP7tyI1O43zNx6Gk1aV9/xuOzSFnzxmbD/XX3g07tsyYHkG8z7hBW1JjGTzFRlhJ2d5/N0bj8L19x9wDNK1oK0F17xuXaVPiyAbpEsrv6IAn37T0bh/6wDufdlYB12tSfQt68czA9b34xSka1VfBsPZfGVsW9mbwSvD0wCAk1cvwHmnrgdSKcP4piEqI66/8GjLd7tzCr716AHm9X4E6frbNxyBnrYWDE3l8PU/lOcK3bOTyOeqfe7oJZ1Yt7Adv3pqPzMtvXw3y4gLNh6GydkC/rRtyBCAR19/b3/VcqxfVO3/rHaiyYiLj1uCfFHFb54t18mnzj8SXflpDI5M4Nubdxju6WpNYnzGKDtef/QinLKm3A/v2zKAe3aMcYN0XbCuG8mYUpn7nLq2Fw9tL8vOs47ox2nr+vCl37xoudcsI5JxBX//lvIOykef240/PLaTmSeLCzYehhPn+/wXfvOi7TzixgvWGYJ0Pb1nFP/7NLvtaCxf0Io9I2W5aZYR5288DN2tSfz0we2VeYR2/Smre/H6DYtwz0uHKvMQjfM2LMLqvjZ8+97y+5ju6EZLSwK5gnGviF5GxGLA372x3P717//Nxy3BqgVt+Je7q2O19g54MuLshUnDGHdYVxoH5+XpuUcvxJ0vDFju09DmEWeu78Nz+yYwnC2PU0qphPdv7MLK3jZDOeMxhemRc85RC3Hq2r7K3zc9sA/jpbjlOqAqI7ozSYxN57G4O41UIoZdQ9O25QTK49+evLsgXaeu7cU5Ry2q/P3rZ/bjqd1jlb/9CtKl7zMAkGrPYCReLu/5Gw9DNlfA/VvLstouSNf1Fx6NJ18ZxW+fZbfna1+/Hl+7Z6dhHvHqNQvwxCujyBdV5jziA2etRV87O7CigRCDdE1MTqJr7VqMj4+js5Mtp4Awg3T19QGcgrlOMwD0AnluQR/Q34dsl3wwMMM5yKoKdPdgbkER2a45zl2A2teH6a4xZFvKDbzU14+5tiwwzZ7g5to64BQffK6nF9muGcv3xa4u4FD12fQyYK61zTBIq/39KMWyyHZNgUV+QR/QvwCFUhozHexrACCfzlgEhtrXj2zXYCWdQme6Ul67spsppNIopNLILxC8vrcPpRKQHdSOBGCvlBWTLYZBb7anC9lstSvle3uRHaveq/b3Q03Eke3iT+iKiRYUu3uRnbZGZFQWLsRs1ySyLdV3Hm9NIDuvMMdbEyjNWAUgAJTiCRQW9AH9/ZVyz/S0z9ex/Xuxo1ItsRiKvX3IdpUHm2JfH7CwE9kueyVRFFaAIhalvj4U0IpsV/mdzfVwFtAA+0ilvDx6+4D+7vm/bJ5twQLkFuSQHbafWBd7+5CbTSIrEf+n2NUF9PdjpnsI2Vn2+63Q34/ZniyySbY8UVD1UnCSETOdaaC/H7nuSWQLWeHyajIiv6AP2a5qeWe7e5Htcr/plyUjAMy3a6Pcn+3JIjtrXXgxnydfLKk6GdEH9Jcn+IViytov+vuRHyo5PoO2r1mTEaKyylDO/n6osUPs9JPJSt/ItLcY+rQXSvEEMx2t/DEFQH8/CsOqpQ5SbUmgJQXAOqFRYzFu+Wa72zCTmKvItVxPG7KF8iQvv6DPNoI1IC4j0M+IsD1sP0F2IyPMsKw3uY5uzKSrk99cTxeKvR3IdrEngnr5bkZRqhZkvSKqr79SXx/QX/3Nqb4UowkZ6OoCYmlku8YM16XakoZxCJiX/fP9sDBcwuwh+34y19qGwoI+xBKxytyn2NuH7FC5dxZ6+6AsXIhsF7sP2KFm2qT6QrGvH+gvXz/dyTFStLYaxpTiTALZLv4Ma7org2yR3cY0C7J+HqFdX+jtBfr7URwsVeYhGoXePqC/w/A+WPYtvYzQ+i1gfP/F3j6o/e2GsTq/oLfyDpjljidQ6OszjHGz3Wlk5/v9XI9R5tujGCzf6vw8Av3thnLGFPYe62Jvv0Hml1qGKic3mNHSSrQmkU3mMdvdCjURQzbPVnw1ZjrTKEzYK2g8GZFf0GuQObnuHLLjYs66dgvELPR9BgDi6USlHsweJnaLVejvR34yZtuelf5+5NrsdR3mPKK/HxBRkHl0dJT/+U1bW/kfZ1zRE56CXMe4NbqzbhN1kRE5v1MG2wPkzS7WnLzKgt4+D+0nVhJO7h/me4znQMs9v+j15X1dOoHj+hxkmP4Wc0rhtivFmq4+VaccWPXt1gVHf59x35riq9ufCIrJlSgW898BiHU+KAunZlZS5R1ctLxFXlUQ51DbJScrgYLamstKt8TJzE6O6Pue3VnkIu/Oj3OQo3R2slYWXjv0ut/Nro0FKUsCd8tUDP/ZwpPBvFotnz3tVATxh1QUBQqjV4u+A5mxqJyfMW19QEwZGWbQ6SVfqtv2JXIbtw+rVvlpvt7+vHHzfU7lYH8fczlW8+ZE4lLLOm/U/jYYkWzuNhdB5LXr5ZhIO/Hius6bu/qJOYisYpmXic5f7X9zM0esx7gAdtAeZElU1X3XMUaxNv7Pozyx1k/mXBZAh10EV3PT5mVljgrL+h1wJyDMtWy0/MilJXp9edWtWgOiUazNj2eeIIiKCxX29R1jRC2Nx9ifWbCik7uVY8ZJifH7MPanmMsQaPqeMlClB16l8r/ApBP853czcPmlcAe1k4dVn3Y58aJYG2Szh8mR2SXQTaRs4aqqwUREKz8v6JRZbnqhVoGigt+DrOXDfx5eOXgyvTweMN6Fy/ozR71llb9yLUPKGIZKUaVad50+IKbMq/Ein9zeKtLWnQwL5t+1RT0tabs8zN+LyCpWWVhRjkXkDm9OJCPjrZeqlu/tkrMoyAItpqir30aJvWoOIquXFzJR7nltiC2z+Ak3jnpMCrIr3M71WIqiaFr6eZeXFSmtbdtFWzULYF5eoscVsC5x6kTm4umFr2ykWNHrY6ZIJYZBm1Ng88BgsfQqitCgWiqpttYvVhp2llwWflqQrSuV1c9hLB5ardjBWVF5g7HTZKWk2lsn7fMu5ycyqAdR/35NJmpqQeYu2rHlSMmnBUirghycBbkWXU0rf4zTDhVzhCdJ9Lfq0w/yqKTAg2hpFnf9d5Ll4JbRpsq9WEXZ3gGMax0mzaJF0N8TlxjL7NOTvT64fPgyiGVlNGdivS/GeOci4sXOg89NW+Gd7CEjNzU5rNVlxYIscK95DBZ5jqocq70CF9TisNmab15cFO1HXMdFVl93SI8syE2Ml7ZudJPW/heRcGIrayJoncrexdqUNddTSHWwIKvcvHiYhYoXF3NxF2uTBdnmsxnL2GZRkIWyd7YgW/KRmFRIvFcn7CyqMquW/mGsmCDyNwzI3IUSfjrmPbBCeSvG//kXO7hsuqgbv6ozKDcz1uTDbkJitt/bKcV2RRV5Bj9crEWpRV+zuH4yWoTMZMwJN4qWu3wCTBziiiUPngIXs1kI9PIezAuNgLhHkOzChqqaF0bEFqN5yN7mtqZE6pi3MMbamlbtZ9pCFDsPiwVZyAPRZq5nqgERZZs/D5KwIJvSq3pUOqdhNUA456fVgQIl8OM7zU8Q1BBgbgtG2Snuy8ff2ceW91waRz8mBdkVLhu8wY1vvlWKJmUIasCxrjqhucjYCU0/Lci8Ujl1MnNd6YV3UBZks1DRB5HlyVSr1Zexsie46mzrVgTr3hnjpISfNmvA9WMiYigD/LfeypZHsTOteElflx7v+ZxaGcu1zjFvgXxRucb/scluMiGbT2AKssy1JnmllwsGeWOTqkhefliQI7QF2WJBZlsZ/dtYYVxwC06WBH8Mk319iZaDd6tik7ZrmW63uCloQTJ62TijQjXFjmCn5YTdYq3YvcG1AZ6cVxm/my2q7Dp2J+BZJXHrbcQIrF/NR1BuqWp1zqQNL5pcFhGX1nmQ+IKFaBX6KYODEufmd2GeD/LelR5ZF2vHcpGC3Lx4auyGADHa/84pmi21lv25EoXShIntxE3C0uhUdt4eZKcplarfH6iaXCMlpZfo9TGTJcTg9sVzLWKko0d8Jc/+fETWBEbGxdr8q3mCIoNxgDKu/NdaNpqtV0EIZ3FXJef+IDvwslw1edfy2qmbqrG7R1YO1tKCbJdXeWJa/btokMdW2SySlzVv49+ysspcFh612O9fNE/cbRQm0ckYCzvlKtAgXcElXU6/ouhYrbKs63hpsIjF2IuRXp6LJdWZ74D5HHI5q6oxGf1YKxVczMMTu21fQtulHDzr7IJUOS2Iuikzc/7FmE+IWIB5FmTRtUC9p5w2XlUsyAJlcDO/qtSv4n8gSzNW9/lgxj6rq7lxPijaN2SDdDmlG3T91hJSkCUR3XfLvNfwWbV+ycmTF6RLpjzmFTvr78bGzXex9rAH2aEP6QVlSTXtwZa0yghfbxo09AEpZAYG1gqniMxw2gtifjeG8jmMnH5akI3pGtOrtXA0W1KCcPOWtY7YUVLlg3RVy+Ccs9Pkyc27cfs+zU8pu/daOB9GdfIX9XSf9X/oP9op2C5enaysMhWFS01crDXLi5YnK0BTTMahj4/bIFNe8gkmfe2D7jvedbLp2+brx6KnfkFEXgkXCmIFY1vSj18ySqAxK7lnd9tmZVx6WZS32hh/F4pi7XJ8tduD7Ob5/QjSpV8oNm/5E0nCXAUydcIKdho0wblYG/82RoKHcHfgvTc3VdVIFmQ65kkSLxFODUJQyoLMD9IlM6HSVuzEo1hzBH3JeY8y4C44mXHualQsggzSVdLlExNUQJ2CdIl6/fL2dLPcGGXcyyyrxaqHYCiGdI2rlmEIR/PeOb+LIOPK7oSsvlSZZwvkG4SLu9vkarUXVyZIl6rayxERC7KbQGMNE6RrvhPY9W+/mh1rH2wQBD1JZvZDxldug3TZTYC9PJdxIZD/vi33uiiD/jpjQMzgFFcv12t4tSCztlJVPTUU27IpcKd82BkozGmJiB2eh5KoqNPOgQas8yoxBZm9mCNCuQ5rO0kJKkgXrx7M3pA8nAwzZhwX4htoEzJZkF3gtrnrG2L13DfRPHUWZNNvMhMqrenaTdzMHYJ/zrG9S7DxOnlU84SVs0DghFz96JRiURdriwXZ+LfdkRzWcvL2IFvLIOVibR4M4c8E20/l0S2K6bP/E2sxq5bzog8/qB0zzfn/RQa7IKznricTpucMahWdGaSLs4dYtZEjxmTs7nej7ErfEqk9yNXgNmVYfcvr+duKTf8KUpwEvwd5/n/HyaTL9G1dcL0vehq/t/7Ctm7K52vnYi1lQZbOlZ2/3/fxY7NYxwHt70q7sal3N8oHS26x5iQiYoffvgQtyPr0TDFxRGSsuQQybb7s7RIsvCNK/cTcT4z1IBGki7sH2Vu/rndIQZbEy+RFNXxWLd/Z52nag2wJ8CCWvz5YlLg7jJOrEO9e+/I57l82lcFoQefeyshL7DrF5Aot6vZlFjCWc5AlVvLsisqemLI/M+83lam8B8y7JDNMbqFY6jBozHuKgrA6mQORuYXlWieKSK4sq4D5d7/ydUqqVhZkVqq2WamMhbfKZztlWSBdDq6eW1heyScti37vHmAfndkvzxGjJTK4Bwy66ipBzQx5spQe+5Lwyui2X/JgubezLZmM5zCk45xXSTXGwLC4hwriZUHFtYu1wDW8rRVMF2vLOcg2ebsoMlsEWZ9eZE7oyx5knQVZe04ta5E0LNGbxbKtXCu6BcAv3GyzAUS2TNlf75cFWSRf2d/rCVKQJVHhYQ8yQ8lz42Jtt/rohKLrNKLBY/iuQmJRed24mJgnrLVxsba3ysrtQbamKzSoqvYWeZbAkzsH2fqdH8ZBs1sPUBvXTz3mMvidv+i+SOdzkK3BWcTL4HyN074yNxNCtxYpOxdCv5E55gkw9lW7KNb2LtbyzxCoi3UNZiJF08TdzuXOy8KRsf+6syTKEvw5yP5eZ0b0GCCv6bGtxWLfOWH33mXatZfFUbeB5US9wex/sw/Sxc/D3eIzS5643YvLqzNRWcffgyxgQTbPryQEhdcz293gduRzVkTt54OihgpWwDiv0DnITYyX/QTGQFuaQBC5z/i3uUGLWqX0+1jFJ248VyGHPchq9TrxVK0XlF25q38HeQ6yHoMFWcrF2rzCKT6wyewHkTkH2epO5T6KtV2ZqqvftROQCqzWC//djP1JRwVcu6CITMoU8J/d1W8un91qQXaXjhOs6rS1AJtcG0sMeWz+7BVXZ8D7lrt3zJYedtAmH71GDBbBAOVIjUSU0+Iadw8yLyK9z/3VfKsXWS703lTTArTegiydo7v7wgrSBVhlTGUrA8eC7N7FmpWWu20RvPYgKuv0hoBKFOvKb97K4ITeSBQUTvN1UWRPJjEoyBBrp6oqP945tZvGUY9JQXaF2/mTyvjsxgJrjYAoXgatE4kLM95vYqtPblxMjNFmjXUQ2DnIpo4f1/UOvgXZmD7rIHuRga1UsrfIK4o1AFacYb21gxWQw4+JCGvlv7Yu1saJpNvonNw8YH1GFk6Rmt2s1mq5CVuQXVuQTPk6TJCdHsP8e1CBSuSCdNl7orC8e6zpRsuCXAsqFuT5lsi0ayn+LSLVzoIcXNqAThbqv2Nd5zJ9vy3IdreJllkvI90E9tKPtTLP4OU1+m2918Prw6xYFNW9/vZjqAKXQboY4xIrHSex46RcSlmQ5z9r86rK+OBC9EntQVYEZwc+ymC3Y5+zV6DZgmz8TWjOSRZkLqQg1xCmBVngPrN7otXFWsKCPN927aJYm+Em7bD6xNtn7XhmrCkomf7qoBRkMwYLrYwbj2UPsth9ThZ5y7l3ghZuuzL4bkH2MV2pMgSdPuMZ3eBmtVZDNEgXdw+yRPrmoDFmnB7DYiEJyITM8p6xxATQPYS+WMYo1vw0zfeKEmSQrlp0M7OLNfu4OAVeeoatEhng89XqODpnN0mf8/Nyr8ECVf4sejyg0ZPIuRQqVI6LtUBhKxfzy8XD7SKJyG1OnnVOxzzZ5eLqmCeGPGMpT06eiE5WSZko1trjms9BFlkctHrSieULzC8yBKz1WBeHg8mH52ouumgproXo8pUsVz1DCrIkXgLt6DuKjECw7lcxTz7F8i+7n85bkAWlGX8l1CHKNecZnXI3u1Qbg+vI1b9bi4zeauzlmCdRF0Sn1Tyei7Wz0LJZkvaIzD7oIFBVq6u575NOwUmYSJt2vQdZ5BqH1XFe2WX2IAIiLoTm67mXu0bEgqw9gnmBwuBirV+Qs7Uguyifm3OQI2RBrrp+2jeemJ8WZJeWROl8IjKJ83vPsOt9tSaVSUuerQx7rzyz3Da6WLu0gtfIuVPknfFiLpRU65ytIiYqC1HW+1heZCKwRJCbV+h0jKOorNNXjfbeK6e6CJbD+LdQtgDcu6l7wa2+4OxibTbEGBVksb3y/luQa7X4WAtIQZZEhSq74KK7t4rMMU9mweM2AI4+gJHoPTyrl/l8Yuvv5g+sH+3yNZh0TJYf/r1mZK/X0A/aUtEbzSt7ohZkh8UXa1AGw4/ctM2/qqrqepKoLyGrCLVUlFWIK7BuMe7tcZ9B+RxeyXu0fAWz5e9b5Ck5NhNuOxdrhwdxWtTzC6ZsspVX5iBd1c+8IIjcvBxwE5xM9I5a6NFaHXEXXuDfpMgYFT84ajVJ9iovbNO1SdbLvlqWp0xQx7yYt/i4P57KpeV5/m5XeQo+n/1v1nHA7LHD3uvvDlY7Yj2DiIs1rxSisk5/ndnF2pUFWaJman3KBhBg/A1TKzKftiFkQVblx5FGUoCdIAXZBW7bOysojEhaVpdq498ye2yrLtaCCjJPAVYh9ABs/VjcAuUmSJe+D7udnJtdVuwwp89a2RMaVOHkYm0qnwcLsnkF3zUmoVzOy3uyoqiqanLRDNGC7LhtIFgXa8D9JEr2WBGnp3B2IfQHpn5s+lt7hvLE1MaCLOCh4uYJ6n0PcjVIF3/hxZNF1sa9NtBjnmoko5zykQn+aLhP0uMjaNxsQzF4H7lsQPU4V+eNA07HqblzsbbPx3Cdg9hxsiCLyjr9deYgXSKiz3LMk4wFGcEreG6PYTUj2yXiJjkq+piyy/Z12OVckwi7APWGl7mLySg6/51zguYJk9vJZ3lfgubSImNBti8X38XaflXQOaCRPh+xCawdfrhY84SqOXnrAe5i+Tm1BWuQLvHVc0uQLolymbFb+a9akN2l65agA/uILkQ4tTJWcBYnZB/H7bmq5glq1cXSzoIsvsAF1G4VvZwXa8FKtZTL7uxj5oKeaZuHKK6iWEdHP7ZE12Xh9sgYFkrAfbmaT3Bpy+B3MbxM/kWDETrf63y92fOH56HFz9c9bqvKrTKvIRKs0U8PB7tjnsyIiB1ukEpBwaW/Tgs0KnXMk0SZzDgp+Rp+imA/DDQsLDFpLFvNnB/UjYt1VGRnLSAFWRI3LgnsdKwTNjucjkwRtiDrupSbiIPs3zgWZt11Zhz3MJr2BOqvFil7dUrsPkiXcT+c/XVWixXLPcpZqqgquCO+5fgoqZVTd2VyTtdanlq64JRUq4XX/yjWxvRtcTarBrYfSYN7Gbdtyd3i7GJdGwsya6HNnFXFggzeOcgCFmQXj1DvFuRqFGsOirfI8cYFN0OygVHrfYh2cD1SXKTnetHTdB93MY01vkla/sueP3oLsuMtjsi2F7ctwGvLKXdvGwuy9j/Lguw2Z0ZWbtJiKZeqjTzlob+uso1NNfzHRaatsu6NSt93Qn5x3PhZ5H7eFkqCXKxtEYnO7CVN7aNYkC6zy4bxb1HBFFOqq1Ki9/DKp6oOliHOMzo9Ny9IV62iWAu7MJuexTzJE3Wx1p8PyC4Pr3wOq42mn0uq6ssElBWkq7YrjKrJih2Ei7VBReaUxLlNuw7SJfhMbvfy2Vlw7NKTDdIV1BjMStb+mCd7uWlQtJkLeu7enRvZI1pXQUUG16OVn2fN8NWC7MGKKUOtvFycPXs48sTF6416gCsN3yzI+rFW8hncH4nnra54sqS6yGz/m5v8zLDav5NMZymXsoYL83WaXNG+Ets+Z7acCmU7f63H7SAucCunZdun2ZNO9Dgy+T3IctfXM6Qg22DXaFTOb45p6j5LBekyTzYtvwtakHUNW9jFGry6EHM7lJnEVu7RLyaYyiBSdr1wcO3iIrhHyhI11zBoi+PYtswDQ8z2J6dbhe4RwbxqCYS7QhtEzqxndEO5v7gsgw/X8d6L7TFPNrc4G8vdLeLJwo6Qb16wKj+E1e3bKGO4aar8gIQy5QvinqAQmrDC/fnblrRcyk75fGojoxwXLv3Ozy8LsqS3iZv3ZlCQ3e5B9slzQeo+jy+NNw5Uzxv3r2Uw5ZaL5FkLYXr54M7FWjGUUSQJc9Fl+rLM3ly/cCvNZctp9MKQiHsjvQe5eTRkcrG2wa7JeHFHYB0rIpKafxZkRbcHWegW7sSwpPLLX7mPaZERtyDDtE+iVlGsY4KDvmXPI8uqKpAfz53dXB592iLps1YT/TkH2fqstVyhLamMvTc+5yG8B9lx0Se4/UgashPbSvo2v9ndIvKsegJT+hjJ2mVljrKqlwss7x5zNu5crOXvEZbN8klLo5WfJyu8HvOkTzpm+Nz4FmRubAsXb9jLY8m6SRvzlbP8q2a57UOQLmkXa58WE2Rx2poG+ONyrs/Pkr6Lh3AK7CUq6/TXuTkH2csxT2WC7fx+eU/JltKNBVlVneMBeS5YHUMWZBt4kUzdTkyMVlB+PoaymBqwWZEStiCjKtzFXaw5FmSHwDU8oeecvX5lUmyPoB431nJLGoKDvjl1/ZUy+3KdrFSeVstNt6qqezmnLyHLclDLFVpVZey98bkAxvcp3g7MuArYxCgDD7dBuuzus/s+Ki7WdtZe9rX29zp5qJi3eXgpnxNBWdvdIBKky899feazPBsd3jO6crH2oPSJvkOnq8RSMW7x0U/m3W5hqxVe2zovSBfPC8u9i7VVdjGTcqh2Vv5ugqfqrzMHjRWyIFtNyEL5avmJHn/kF27nn7JeWkbZKdgL1aj3tnAhBdkGXpt2a0U2GkXtratmWEG6WMq2IzrhIL4vwv46nvJsSIFp5eHfaLbu2AXXEcH1hFNwddr8KMx9uQLZOVmprG5w4pNJ1t4hPxRJlvJYSxcc1bQHOQgLsl9unyqC34/ktnyyx8Y49alaBelipepmD7IhKCDzXncLo27et5uJZlBU9iDzFGT4t69Pn0yQFuTauVjz4e5B9rcoXGSOx3N0sXahgPh9ooLYvd6t1m4oj/Pst8tbZHZbXpUxT2Nagx1aHCt/g6FGcg+yovM8kWnrlmM0Ze4VXED3U22sVT+OG+ZB4v1QdhxpgnXLCqQg22DbQTy0dn07lHEpYblY68snE6RLEy6ih7rzk3Y65klLg22R4WEIoKMaB5TaBenSfxZ3hXO90lviW6mcJqk8LPeqakMc82S2IAchvUUXIpytqvLDrqxVnn9eLe8+9rV26Tn1qVq5WLMtyMa/tUcwX2uWMdX72Wm6UXZF5axducKmGsXaoV35pSA3g9lYB/dpXfWZ4OuPfSIC/3cnZAJOho3nIF0lTiyKAMZQlhLEPObJobk5BfYSlXX6yPhaVfKOBDVjrn6Z9xFGkC63BjVnTw3jFcYtgYpQvZRcrPw2k4ymPcg22LoVewi0Y06n/L8zVtdA894PsQLpV4lFJ3uqat/BzYqr5V7T/3qc9quYA+g4uUCKpiWDuJuK8W+3kZ0dLcgcgegkTS0u1s7FEYL5XDUWoOaFDL+z97LPTY+nPciiFmSXiyh2ewDt7pA5pg1wHwfACVYx2OcgW7eq2J6DzPJ4cWlTcKVUS8jmoBFzsfZ6zJNeOaoSpAW5Vjg9g9/P6M3F2p98Rcc6P/Diku+6rtzdVkGFiIWSsQjhMmOW7HKyBjNL5KBUi8o6TabEdHKj4lApkITVk04o2/K1kte7wVzbtZDTgLUviPZDsiDbQxZkG+z33fqTvjZZc2VBNkWPFm3gMZ17ibgF2V6Ulyf89vdWz3r2ZkF2azF3e72GcJAuTvoye5CdQu57EezMs5l9GCnYwb88JytMub6ME2y/VzhFrRtOXUp0SwIL0Sdy2itqh91E3S5YjKwFOaidTjKr89YgXWwZyno018c81WjfclBU3SE5iyuKj0G6JCLzNwScZ6yl/bjsBOB9EU4U3qJy1PHlmCebBUPtHbD6k/s9yAyZ4iIt1nMbtr7JWpB1SpxMTB4vQbrKx0DWtq3VSp6bjxcVPuYpwDLVO2RBtsHp/F+vVKyrAmmZJ4FmxVTYgqybyIhadHjlK9eRc96u9iCbrDv6AUV20ulmkgqITxjMqZujCYpS9nYRL6ud5YV9rTUvt/AWTMp51W4AKplcxYOYaPmVolNQO+Y98/+LPpfb57d4GDi8S6c+ZfF6CchtmJWqNar8/LVmBdnkpVL9bE3VzbsD3FnOhS3I8klLo9URd3uH4t+iFCsqfj1TL4+gKPDYoLw9qBfLtz8lkMnU2+0iW22YC9qu9yCLeT06XcPK3Wi4ECuPJt5iOmW1YkwRuN9iQZaoF6+eEm5w262c7rM7zlD7LPScLrza6kWm+YGUBfmGG26orMBo/4488sigyhYqtkqAT+lXo/aJWJBNZTBZosTPQa52GvFzkO2Fq7kc1nu1vKy/yZ2DbBQFsvNU11Y7QUFgt+ex/Lk20sQpH/Pvfq0bsrKt9R6foCPfiu5xdh7QPMgPH56Ll0TcruJsvnbqU+b2FdS2Wvbim/HvqszjXGfjbq3h1vof6DnINbBMVBdK7AkqSFczTcRYuGk7XsYb0VvZ3kjVz0LHy5jjdohlzaVWLtZe2zpvq42Wtp9jqHAwVRdhrN3MQ41RrLW8renZYWlf0i7WAu3TiwGBN84EiHmbg1gwMvnyRT1GgJ9IW5A3bNiAO++8s5pAojGN0Py9tf6ZkEVSMltfSqpqDI4guHKnKNW9hn7scyuXw/leVn05u1jrrzUFg6iRi7XoAGoNgOFOYXOqE7PAk0nbPOB6Edr6pFjPWuuJrdm1yP/0Ba1aTvtyTf1WBC23WluQlcpEzcaC7BjF2vx3MLMEkQCAVTc+kwXZJkgXs6yS3h2sPMTvEbuuJhZkLYo1Z8Yuut9NBKMF2Z80w6TW7pwe1GMoHlqU7MKGXy7Wxsm6XBpu343Xd6qWhQk/Dx/3ILN2ITvtJ2bB6o96+SYq66qR8fV7kMUNRuZiUJCuMhYLssBzuj2+sFmQ1m4TiQQOO+ywIMoSGWbzRTy7b5z529h0HjsGs57z2D40hef3j2NiJu947b6xGcPfu4azyBWqs6gdg1NCeepDqeQFZ2H7x2ZsJ7d7RqYxNJWzvffFAxNY1tOKoUnrNVsP8cu8d3S68jmbKxiEmmjZ3V6vISp49e8CMLt9iUtj2cm0zNQgqFU/Vqq1nBSqqtnVPNi8eak7vb3ByRzmCu7aouhT8fcg2/8YlwzS5dSntg8Y+3ehGMwgPDlbwHPzsjqdjKFYsn8PB8dnDX/rn2FiJl9JhyXfXzo4galcUbhcilJum25kz76xaeeLaoRWfq4F2cd9fQrnr2bDzbzVD1dlx2t9SMv8aLUot+Vel/e5Pv1hXiZMzRaqnhmK8T1Xjkpk5OG2vLuGpjGb9x4lkTW26uWbqKybnivLUf2Wv8HJHJ7bN479prkusxxmQ4FQrtq9pvmC4r+Fd9dQFjuHymNIvljCXFARKs0oxo8i9bL10BQmZgty2TSRWJZWkLdu3YolS5YgnU7j1FNPxY033ogVK1bYXp/L5ZDLVRWkiYkJAMBQdgi5uL1yFSYDk7P4f0/sYP720sAIXhrwnsf0JPCdP4kldO+2EcPfT+wx/v3QLuPfdswUZqHEE5guTAA2fSJXSmO6UE3vTzvs0/79i/x8d40CtzxwgPnbtEOf1D/z7jHTjwL9eVEmjfGJWeHrAWCm0IZiSa08//D0UOVztlDCdMFcEDZjufbKfS3FJAazgwBgqFdZBrODyOZHMF0YrXw3W4pX0sxD4aY/lutCa7a1cs3CZAaD2UFXZZpTWzCYLe/OKOnqa3x2GKqSxHRhBNMF54HOD7KFdqi5aj1MzKUwmC15qmszIzNDSM6Vn3dOHaukrb3XCrEJw/sx8/ge93WdLYxw09bKM5EbsX32mWIa04VZ5m/ZwhymC1WlNp5ox2B2EJP5YXZ6Dn3KqX/7xfZhYPsD+7nXZNIpTBdyXDmybRjYxknnR4/LvbuWeKw8MXJRD5u3iuWVV9Ou+7Aw8+WfKuQxmG3DTHHKkl82r2BsNuWqHEq8hKn8bKVdTuaTlXTGch0YzM7LEWUc03nxBQo9ln46j115K+/OJS3xmCFPLZ/DWtowPVFdfFEVBaOzSdtyHJaqXt+eTmBKN5HNFjqQV+cs907MVWXhVL4Dg9lqf+eOD7MdiMcUpmwz36fESyhhErOF6vuYyndV3tV0IevYFoqIYzxXldNDurF2utCOwaz12VhMF9KVso7MWtsmj/HcMJLZ1Hw69veZ289svuiqrWvt6pWx6neJuGJYPBydTWEwW8R4bsaSx8hsOwazs9J5/+9z1utHZoaQKyYMaakxIK+OIm+zmDlTTGNyzjg/NMg3SVlXRAyT+XIbeHzPCB7f84rQfaOzQ0CspfK3yNioMTkXR043b2L1dUUBFpn6qgyvjAE3333Q1b169P2fxXSx3fAupuaq73Nkdggzc87t9L+f4v/OGl/Gcy1Ip7LV+TXjnqgzmZ0Uuk5RJezrv/vd7zA1NYUjjjgCBw4cwOc//3ns27cPzz33HDo6Opj33HDDDfj85z9v/eFTANKiORMEQRAEQRAEQRCES2YB3ASMj4+js7PT9jIpBdnM2NgYVq5ciX/8x3/EX//1XzOvYVmQly9fTgoyQRAEQRAEQRAEURsEFWRPEba6u7uxfv16bNu2zfaaVCqFVCrlJRuCIAiCIAiCIAiCCBypY57MTE1NYfv27Vi8eLFf5SEIgiAIgiAIgiCIUJCyIH/iE5/ARRddhJUrV2L//v343Oc+h3g8jssuu0w64+0f2Y6OTva+5XpgdHoO/3ZP2XJ+xGEduPTE5bbX7hnN4rYH2QEI3nPaKizpzgjlmS+W8JXfv1T5u7M1WYmC/d7XrsZhXa2G67/4mxcqn69/09FCefjBXS8dwkPbhwEAf/mqFVi3sB1/2jqIzVvKm/c3LenCs/uNUcI/eu7h6EglhfOYzRfxtT+8DAB40zGLcfzyHqH7tDrpbU/hg2euFc6Pxe+fP4jHGQHSalnX9UihWMJN8+34+BXdeNOmJYHl9bvnDuCJV8oBPK4993C0S7Qxr2htras1iQ+ffXhN8rx3ywDu3zpk+O6as9ZiQZuzF49W3rX9bbjs5JWu8r/n5UN4YFu577/9pOVYv6gq45/bN45fPrUPAHDRsYtx7LJqn/Uqq3719H48s3cMAHDWEf147br+ym962dOTacGHXrfONp3/fXo/np5P59yjFuHVa3qlyxIWd798CA9uM8pdM9sGpvCTx3YbvvvI2Yejs9Vbv3j54CR++sQew3d97Sl8QEDGfvu+7RicP+ngE+cdgXQyLpyv1m4ScQWfOv8oAMA//P6lSuAdksXhUss5iH6e9c5TVmBNX7X9//bZA3hyd3kcePdrVmFZj9icS4SXDk7gZ0/stXzf1hLHx15/BPdes7y+6NglOHZZd+XvFw9M4L+fLKf9V69egVW91j6tv+bM9X24d0s5vdPW9WLjki58+75ywNn2dALXnrNe7uFcsnVgEv/vsbI8eOOmxfjts9ZgrW85bgk2Le0OJH+9HL/ugqNsT2kQ5eEdw7jzxUMAgL84cZnhfR+zrBtvPnYJHtw+hLsZEXxPXduLc45cZJv2jqEp/OiRskw+/fA+nLl+oeWanzy2G9vmT4bwQ143O5MTk1h7k/PYJKUg7927F5dddhmGh4fR39+P1772tXj44YfR39/vfLOJvrY+dLbZ+35HnQTmkEmUlaOuVCf62+zrYHo2g0yCHTWtv20h+ttamb+ZKRRLyCSqHbCrpQWF/BwAoK+t35JOJrFAl4/8O3JLT7qITKK8tb0v04f+tg70tKrIJMpRL7tbe5BJGCdB/Zl+dKTFO32uUEQmMT/pTfehv22Bwx1ltDppT7R4rpOedB4ZRg+qZV3XI/p23JXqCbS+ulJzyCTKg2OfZBvzSqWtJZM1axM96RIyCWNUzv62hVjQ1mJzRxWtvJ0t7a7L253S9/1+9LdVFeTeTBKZxMx8OY191qus6krlkEmUHaK6032GNLp1sqejhd/ve1qr6fS29qG/rU+6LGHRo6v73nm5a2akNY1MwngEV19bP7o8TriGMilkEsaIq+3JlNC7bEuMIpsoK8gL2/uRSogryFq7aYkrlbzakgNIKOU+QLI4XGo5B9HPs3pb+9HfVlUmu9PGcaC/zT8FebA1hUzCejRbe0vC8ZnN8npBax/626oLh4daWypp92UWor+tzZKG/pqedH8lvZ50P/rbupFJjAEAOmo4DpXlTFke9Lb2IZOwnlhTHgPEDBuy6MeDhW393HPcRehJK8gkysao3tZ+w/vW5jDdaSCTsIby7jGNR2bGs60VmWx3bVcqi0yiPIb7Ia+bnVRRbNuvlIL8k5/8xFVhGhG3B9ubkUnGnKe+z/tVHr/RiqUYDjFnXRfN8vMI+szdRiWsdx1WvsGcAMyGJQdk5wZe6kl/rzmZIGUU70xww28OZVDMh0nWESL1y7rE49zRNu9adrd6HD8IfzGfb2v4LcD2EbPZqCiSpbnfWGSXbLHNZ+Ea5oiSafmEXd3XU5/VF9XStkz/W+6VSNv2Gt3nsN5jM+JpD3JTI6Gc8hQpmUkjT+hHqc+wJqRBKvNhPTsJKndQtQUIa/FJssY9HGwgMZAHqCybJ50SclIJUE4FjWESZ3cN8z7vz+lXVdGiI+EWXvvXyyK/u7VdmxVqyw6X6NOwk6c8maX/u7YLVuzPhmtqUxRfnts4p5W71/f5bp2NS/UMKcgu8W9C4E8ZotRpWBNS3uqu/jrhPLyK1whNCpuNsOqtGV4XczAOaWJkzlhk0uRHvryknfKN6qKjCEKT0sAsyN7TAEimEsEQ5MKLXZsV6RMWC7KLDmCYW1l+s88rSHgePZXva1QcX+bGvEUIBy3KccwRuFa/ZE2GmdpBCrJLYhITKW4HkWjs5o4e1uqgEywLspNlRrb8+utr6cJqLEOEKp2ILLVsJay8whpQzfkG6mLNSVpmksiSXfWC2/L6ozy4T0Mvv92mUmeviggYqxeJ/W9eEbHs2sFTaM1piPRT8yKZ6MKh39SzJ44Tsgq/zOMLveO6W7qtX0hBdolfTdSL8AhrdVAGbfBwVJBr3ek9uJFqRLPGo094e5BDybamsBefamg54ExEgyyGk4dK9To++vqrt5V6hfMX73s/3ounuvJFFtfZyyJ8h9eODS7W/udsk6dzTo4LdiJKNkeJNsaEiNa4W099lru/3eE5HONeCLwXvYhshnlMVCAF2SV6weZlePfS1vWR+aLUZ1gCWy9E4j60uig8b1QXJYhoUUsPBz9caD0F6eLsmZPxuvGCecJiUHodKiNIN/CgEfEoYnrg++GB6NOiZ5T2QxP1Bb/tBOdtZ2tBFrjXGlfGnIZcubkW5Jr2C/04wM64fvupzfPYfu85aUNckPqtt/qDFGSXGFx8PcyA/VKyoqSssYSyMUiGv1aMsJ48QlVOCFBPK9ZuYW9BlntuL0G6jFFUxWyafuBXX3SSU1FGxJ2S9b0fY4dfNeU2nTp7VUQAKDafgWC9QbxEaZa1RrLgLYwZPWLC8SRqBHhB3pye1e96j9Jcv9EhBdkHVAcbEdflz0Nbj4nMiEKAteqphCSobSFLBdGAsCZYYbVT3kQiSOWTl6+z7ImmV44IbheA/HjOMI49NNznS+5Eo2CVAfp+7bfCIlYG5jWcQIbmv2XTU0JcEtbnG4n5no/IPo/T5SKp+RGngZCHFGSX+Dch8ODOaJj4+VCYANDqKeZzWaNg3YlCGYjoU8tWwj5jvHb5G6w43Emqz/kKpu282q//XF/9W8T6zfreFwuyhyT82IJQZ6+KCADhPcg+txU7NVRsD7IP+XOeLQoyTGa7Rz1gLjYrEK0emX3mdlfqnbqi8E6bBVKQXSLjYs1TpPxyLY6UssYQ2E5WHNni6y93NcGiIF1NQbMFtwhKAXKTv+UIk5oVwvSnxOKcMaiNj2WqBS4divzZg+xPuq4jcQdoISTqA7P11PBbgM52tgqg0L38q2S3fCimP8LzHnL2GKzXfuplruqcNvtqgwW5PqutLiEF2SVRCNIVUQ9rA1o9GQQmY5Zaj8KSVvIIEWoZpItpQZZMw6/FtlpaM0RTdow4qvtcb/1bJEgX28PADwuy+zR8WKskCIfo9QHKHru+JmAeNl/Cfwbn7yNlKJkngkXyhHRsDadFWcm2GcV33KiQguwSQxN1GOF5zbkRg3SxotUahDjjHr8s6bUkQlVO2NBs74j1vLKywUuQLp6CKbufTipfw2KheQIjbhWO1fGI6KZK/XoPYW/xabJuTkiiOE1APODpqE6zgmx14LW9lvV9Lc+e5yGypa5ex2bePnEWfrwDT4EzCdfU8XQgXPzq3FFLx2+01S69kIj7MJvy/Lw+VFiUFiUINs3mYs2a/dV0DzLHqyVYC7KYEux4JqXA8SRRxXjsn5hbo1+KbegeQPX1qogAMFpSTb8F6ILvdu9p+V4/ysKWfQqiMubZyKJIlE0eu0UNEQu/Y9quSkQEBSnILtELNqe1HX7wiGDcGcOENVA5WY8iVHxh6rHMRO2pZTsJyoVWFKOiap9voC6P5r8FrBmsa6MkU0VwZUH26T14C9LlRzyIOntZRE0J0sPByzm/PFll/lusjRvlb1iLfCILlvXaZ23HNbuFEofGJ/KKyIAcDqQgNwhRFTbVKNZ8y4zsJF5mgYKJHxInmlVONDFR2p/EnewF6GJt+c3mMzud+rUgi9SvdV+4/3lXvvMnaWnq7LURPiG6IOe77JH83nANZxuKOQ2RPs27PyzqTY464bSo4XQ999rGqqq6hxRkH/CiazWiizVrD7Ld77zrok6jCf5GJ6xFpLCDdNWS8Fys9WUwTzp1Sq/Tar7hPh8KVkPcLI74FpDNQ9/yZa2yzt4VUVuCDGhq14fcHPNkjb7Nn0uZvzd/DqtfiHjt1GuflV2EkHlOOznqh5cNIQ8pyD7gtIGeN3loxCBdetgWZH/zcJWcD/UVzRon7IhoF/GVsD1J9LnzgnQFWgZBazKLIOVU0Mham/wk7Lqqs1dFBADXkmr4zd/W4qWv+SGvuUfrRWDQs4+HUJ/Ijmt+vANysQ4HUpB9wMseZL+ERJSEjeF5Fet3zGOeovQAgogc40AQtST0fsSZpAZqQeZYiGQmx8afw65MOdzUr38xMOqrrojmIsiFQ/s9yM558hR5wCSBRBTuiHRDN9s96gV7S767hQChPcjOlxABQApyyDRikC49mg7p5HZdjzTKcxDBUst2EiU5YHF1DjY3oV+cV/urn+tt/UtkIcBpz6Nbwq6rKLV7Ihx42yz07dN3F2vJ7w3XSMgjEQUsyL3WxDyWeuVXtMwcn95ZtCAF2Qec3B94bd6/PcjR6VmsgUpfPNYxT17KH1aQrghVOWGDfu9OM7yu8F2s7Sdohv10fm+zEHWvdKgf0SjcUURkEdL8fZDHPIlWnx/WEcN78yE9ov7g7detlewR+d5wjamkTnuSnfKRkXVBIhb3oT57qnWfuMP1Prhgk4t1OJCC7ANe2m69TcJkqVqQ9d81xjM3+rsj/KGmQbpClugKp59Hobs4KYRGORVsWYJEdNLumwxjJCOatt9BuqLQzojaw3vtsQAVR09BuiTktW2fjqCiqS9RPctRFrILIk7tQLH5TIQPKciE7+jnO1XhHeAKrqubvBeChFn0qWeLoBuiNFmyWiv1Fh6fJ6n6z5b3LC57lADLGDRuFh4bxcWaIHgEKfr9DdJlv6go8ghRMT6IWLLrVWZYFn5rkGeJTMihQAqyDzhFsa6zeZZn9NWhyRKeZaleaZTnaGSazcU67EkHq+9X/g4wX+4ZqIrYdYDJ0lRnDUZsv6J5cufPQ4a9+FRnr4oIAP42C0lNUwIvQbpk5LV9XAHnz2ESlXL4hZ37vt1jSs0TG6yu6h1SkGtAvVki/ESTDcbjUxqjPhrkMYgGIuw2qV+QMPdzgwU5QC8SXtJO2UZxgimKSP2av/drQSXshZm6e1mE7/DmWYEuznnI0ymKtXRZItINRGIChL2o5hbZhV+ve5SJ8CAF2QfI+8GI3h1EE5R6GRD3udWFFaSrURR9Ilhq20pC15DtCalofPdr07UGJbO++reIkcxq/fApbw8vV6VDTAg/4HhQBHm+uRcXa4tLNScNIYU7IsHqZLx26g1ZWScVxTrs8ZswQAoyESjMY54aTGAS9UFYza6mQboi1LWsFuTg8uIHBxOfHOt/jlJdiuCmvI1yzKDMIgjRfATZJOz6kFCQLp4rOMwLduw0bL1eQuwGYsp8nWJj9RdxgWcn51wTjts4iUAgBdkHnFbAwxqvozBPYB3z5Lfl1VVqPpSBLMhE1AhbOTAE6ONM/mpZTKPyxL82yEBiwSNvQvbrCcMWhWHnT4QPb3tEGAv0Yi7WDh4ths92Clhw1nE/8GZhjz7OY4r3PEg/DgdSkH0gqo03LPljjGI9/79BQa5laYKjUQR8sxC28lgLwu5bhiBdpt/0ZfNbZorub3Y8cqOO5ZTIUTbWMzz9eciwFwvrbzGD8JuwWoCvFmQX+fOdtENCoBiN0medn0N8zLFrMhFVMRoeUpB9wKnxNoYYEEfvDsJyPwl7MgWA9iATDUmUJh3W4zDCKZtMNzWUOTpVKYQbC71/e5A94PM5yATBaw612oPsRknkBu0SSU9gkawW6PNutHmSrEVcKlK5fHGIACEFuQaEZbmKwp5LVgj8WL2ZZmxoMLlPBEQtm0nYbdJwrBZnsue71w1nYuh2shalxQYRRMQqz/XUW97u0yHrCOEHoke9+Y0XC7I1IrK97BJRzKKijIoUIyJFlcZSbIfnkHGjtyOqXqqNDinIPhDVxhulCV6QUSRd4cseZB/KQTQ8tRQPYU86jOcg21tHgoxczFPMZfYg11v/FjpaxeFv13mHXFd19qqIAOC1AWPf8Le1eDAgSx0BZJ+PzXYKH9y3/aBZ+qbdc/px1jVF+g8HUpAJ/2H05bAnUMHQkA9F1DFRsSCw0E/k/F5UFH1qp8lxPR9PIlJ28/d+efOw8gstOGU42RIhw2tvQbZFW9dagdm1NeK+t/x53bmmC7Ui1zRIR3WMa+GDRIqqEa7RIQXZB0oOrTe0lbvQXKyt9RGVvTF+Um8Wpmak2QaWsCcdvOoO9pgnscSdylDXFuQ6K6+GH0eYNMq2HSJ4/O4ntotRAvMc5yOAnPOxyzPMHhHWiQW1QHbh1PHyBqufRoIU5AYmrH7Hmu+I7KWpKT5MyurNwkQ0PmFbkHnKjr6/BGlB9uJiXc8LeYZJqd01pr/Dbi8E4RcGDxXzbyE0c5E8/bAg+3l/EIgcT1XPaE/h9jgrkblxk63zRwZSkGtAaK5mERJAdRwc1hYyWhAi1LKZhN0kRS3Ige5B5ga6kQiYEnZlSmI45klwshao62lYFVhn743wB66LdQgL9GIWX3Fkg/CFOf8TkaP12k1lyy3zHmyvbDZXuIhACnINqDdLhFdYfTlylgofytNs75VwR22DdNVHm/TdgixoJXb0dqtnF2uBQETWxYPwobkf0YiIKbRmC3JwPbKmC7VRECwBIbvI6NQOROqKRGQ4kILsA37soWp06tkyY0cjDwJEfRJ6m+SIQoOLtc/Z8har3B6DUi+LDRpuihu5hUuXNMpzEMEQxtYJP/Ygy6YXlX4gezxVPeMY+LFRJrxNCCnIPhBV/TgsAcQKWqYX3I0iMBpFwDcyUe2bQRH2BEnUddrvRUVhC7LEan7dWZANG7HtLuLcExJN1kWJgBD1HKlVmxeRH2Z57VUuysRbqBX2oigiBfRItZ7ZzyN3zBP7e6dAwEQwkILsA45NN7StWBESQFET3D4H6YrEMxFNT9jNULRbBTncm+WeMTK1zH6wsGtTDjdWm3qzktvRII9BeIB3jFwYMVBE2qRMWcTS0xsijNRUxRLYC12vfVb03GndDQ7pEVGFFGTCd1iCuN6sMSLEQhh0ifqjlm0jbAuyKLWMYm17oVOa9VGVFUTkkfn7IB8xvHOQ6+zFEb4Qtf4qsvjkt7xuxHlW1HGqcsdzkoVcf4gwIAXZB5wme+FFsQ4nXxaRs1T4PjBF7PmIyBDWyn0YiCu+AWrI5p9c70H2UJ4QcCNjo/CMfiyWROAxiAhh3eqh966o1R5k+Yt4fUG22GH2bRGLfb32WUu9+mghtj3miTysQ4EUZB8I8sgSL4QlgFj7aBpxZTNyZzsTTU/Y7VBUEvpvQbZ3LTReJ069LXoZrehiZa+3Z7SjQR6D8AC334fiYu2ck9/tNnKGCHD2RUevqK5wDNLlwzuJpobR+JCC7AOOFuTaFMOab4QEEG9/UCPQKBNNor4Jux2KBpkJdA+yeZ+t7rPcHuT6ws2rbxSxRW7VBI8wWoe7IF3213qNih2FHmLUj6NQIv+wexrHY54E0m7EOXM9QApyDWi2ts3qzHrBHVWLO0HUO/Uy5QjyHGTebzIKYdiLDbLoJ5yiHjtRsDjReED4gWh/rVWTdxOki9cX5NMLv28DZrkUjTL5iePJCBLvwe5KkpHhQAqyDzg13bBWf6Iw+dEwFKUB+3ojCn6i/gi7HYq7WPt8zBPnL+P+Q4k0m6BLBxqkK8C0LXm5XAQhmgPjiRM12oPsc5AukSsNx2lGsB80Yj91fAwnBbpB6qERSYRdgIbAabLXgAohD3YU6+CkQBSql4RcNIlE26hlXnXSDmvpYm34zeFt6EV5lBYYhXBR3LAXVAjCLwxeahEQ/CI9y9z9vJab150jUCXz8qZckkaRPNo44Wa8KBaLyOfm0JGYfzvFPGZnZy3XZWIlqPPXsH4njCSTScTjcc/peFKQb7rpJlx33XX46Ec/iptvvtlzYeoVJ8ET1iHfYc19mC7W+t9rVpLa0YhByAh/aMT2bofwHmTfXaztg3QZo1j7m2+UcKMgBDlGiKbtSxRrzvsniDD6vcjik0VB5l4rkJ5gsMIoUHcLkA7IPI2qqjh48CDGxsZQKqk4a2n5zcemBrFz57Dl+lP6ixU9YufOnX4Ut+Hp7u7GYYcd5qmduVaQH3vsMXz729/GMccc4zpzojFh7ZfQDxZBnoEaFo0m7In6pF6aod97qkSD0zj103qpPxZuFiHr+HEJwkDUxmCxPcPmIF2cPchCmbr6qWY0oseK4x5kxu+acrxw4UK0pNIYzs4BALpak2htsaplAxOzFQX5sK5Wz2VuZFRVxfT0NAYGBgAAixcvdp2WKwV5amoKl19+OW655RZ88YtfdJ15oxBVD+soRQls9CBdDSj3CUKa0OIt6D+bOqNx/2GNClQnNMqEtTGeggiKMOZCXqNOu7k26t05jOO2gkb2OYrFYkU57u3tRaFUQiJfTiWVbkGaoSAnZ1UU5wfXdDrttcgNT2treRFhYGAACxcudO1u7SpI14c+9CG86U1vwrnnnut4bS6Xw8TEhOFfo9HT1sL9Pe6jf09rsvyiO9IJdGf4+fa1838PivaUtYPrJ6nJuL+x4dJJ+ca/IJP0nG8yXn2m/vaU5/SakY6U9/dAVIn7MENykis82tNia66tpj7bM98f9X3KLeYU9HXiJItTifqNW5mIVctu95j6awAEOkvtbq3d+NOtk+cLHMZjonb0d5THxVorbuY5RipZ+34tMu8zX9Fikj8icyX9NbyFQqd5qp8kYuxFybYW7/tCRegQHIdEyeiUVtm2bB6T8/l8Oc1MRjwNH8bFZkOrX62+3SDdin7yk5/gySefxGOPPSZ0/Y033ojPf/7z0gWrBz5w5ho8uH0Yb9zIN+F3tSbxuiP6MTlbQK5Qwsmre/D4rlGctKpHOs/3n7kGd704gHOPWoi2VAKlkoqTVi1gXnvpicvx2+cO4DVre6Xz8cJp6/owMJHD0Us6Dd+fv/EwzMwV0NeewmUnL8cL+yegKMD6RR2u8nnbCUuxZ3QaG0z58Hj/GWvw0I5hvHGTe7cLjd72FM5c34fWlgSOW9YdSl3XK3/16hV4ft8ETl/fF3ZRAqeWQ1siHsN5GxZheGoO+WIJp64Rb49XnbYKT74yijdsOMx1/q9e04sD47M46jB2n7z0pGXYOZjFscu6TXmvxp0vHsJZR/S7ypcXHXVpTyuOX9GNuUIJRzjImqXdrThtXS96PCwShEVrSxznHrUQqmqc0JmvOWZZF57ZOw7AXwvyZScvx0sHJ3Hssm78efco3nSMdxnrxHtOW4UnXhnF+RurbTascY+wcuWpK/HHFw7hzPXu+rUsF2w8DNlcoaKYayzqTOP0w/t8V5w0/vJVy/E/T+3H2oVtSMQUzBVKlvkPC01e3/vyIE5a1YOl3Ub32Z62Fpx1RD9SiZitC/mCthacub4frS1x5l78q09fjUd2juDCGvRHjUxLAuccuRCxWNmA8RcnLsWuoWl0tSZx10tl19cgvVfOPKIfY9N5bFza5Ut6G5Z04lWrerCyN4NUIo5Xr1mAh3eMAKiON+bHSSVieO26PrQxDEbl6+eDewnkvyDTgvHZPDps0iKs+LHlQlElztvYs2cPTjrpJPzxj3+s7D0+66yzcNxxx9kG6crlcsjlcpW/JyYmsHz5coyPj6OzU1yxIQiCkOVnT+zFE6+MAgBuvGRTTfO+7ufPAihbt/7v+UfWNO9m44lXRvGzJ/YCKC9cruxtC7lE0WVgYhb/dOdWAMBJK3vwthOXhVqeG371PHKFEoDa91GCaCSmcgV86TcvAigr7ccu7w63QCbufukQ/vhCWUH+1PlHossHT74wmJjN48bfvgQA+IsTl+HElT14Zu8YfvzoHgDAJ99whK0ny+zsLHbu3InVq1cjnU6jWCrhwHg5MvWCthbbxU1CDnM965mYmEBXV5ejHir1Jp544gkMDAzghBNOqHxXLBZx33334V//9V+Ry+Usvt6pVAqpFLmfEgRBEMFg3NtG7mhc9FG9I+BR7veZ2ARBRBODbG4QMR31fd+Ee6QU5HPOOQfPPvus4burrroKRx55JP7v//2/vpw7RRAEQRBuoQkLH+NRMOFXFqnHBOEP4ffm5oBVz34csUXvL1pIKcgdHR3YuHGj4bu2tjb09vZavicIgiCIWkATC3fQYgJBNA6R78+cWBH1iv9hJYmoEAEHK4IgiGCIgvsmDX9EVIna2bEEQTQuis3neqYSbEu/dUVSrqqqirlCCXOFEnKFYk3/ic6R/vM//xO9vb2GmFIAcPHFF+OKK66Qet56wfNu8M2bN/tQDIIgiMYkfBW98dFPSEjn42OcyIVXDoIg/CUKWyZ4GM+kj3ZZebCihXshX1Rx851bkU7GEK9xYIgb3nw0Ugnn7bGXXnopPvKRj+BXv/oVLr30UgDlc4Z/85vf4A9/+EPQxQwFsiATBNGw1PMgTBBBE4UJdQScPAiCIPwjfLHqO62trXjnO9+J733ve5XvfvCDH2DFihU466yzwitYgFA8cYIgGpYouFgTwePFva3Z0NcOWZAJgggDEj1VknEF1557OHrbWpBuqW2w45a4uJ306quvxqte9Srs27cPS5cuxfe//328+93vblhDBCnIBEEQBNEkKOSOThANST3153oqKw/Wc8g+m6IoaEkoaEnEhNydw+L444/Hsccei//8z//Eeeedh+effx6/+c1vwi5WYJCCTBBEwxIF+3GDzAMijeGIDapwYRp15Z8giGgThe0dbnEqucyT1VstvPe978XNN9+Mffv24dxzz8Xy5cvDLlJg0B5kgiCIAImCkt7okJ7njihUm0o9hCCIOkI/3miKvuG7Bh6Q3vnOd2Lv3r245ZZb8J73vCfs4gQKKcgEQTQsjTtMEXbQHmQ+xj3I4dcVhQkgiOYjAqLHV5pFjnV1deFtb3sb2tvbcfHFF4ddnEAhBZkgiIalScYsgnBFo01SCaKZof4cDRr9Nezbtw+XX345UqlU2EUJFNqDTBAEQdQ1Rpc3ggdF/CYIgvAHP4J01Qujo6PYvHkzNm/ejG9+85thFydwSEEmCIIg6pp6DvhSawx1RdVGEA1DPcnBelYineq5nt6DDMcffzxGR0fxla98BUcccUTYxQkcUpAJgiCIusYw2WrMuUkgRKGqaBsEQfhDPSmdjapESlNH1bBr166wi1BTaA8yQRAE0TDQxEsccrEmCCIMGln0NPKzNROkIBMEQRB1jfGIjfDKURdErK6aJforQRCNAUtukhxrPEhBJgiCIOoashq7gyzIBNE41FNvrqeyEs0JKcgEQTQutKrbFFAUa3GorgiCCBulQRbnmimKdbNBCjJBEATRMDTKxKsmUFURRMNQT7KvfkrKR/NeUnWr8eTR1BiQgkwQRONC41RTQEGsxdHXD7lYEwRB+AuJ1caAFGSCIBoXcrFuCmhC4g6qNoJoHOqpP9ezzPYzSFcdV0PDQwoyQRAE0TDU88SrFujdMGMxqiyCIAg/IanaGCTCLgBBEARBeEPRfaLpiShUUwTRONTT4mA97ZfmwQ7S5fLZBgeBFpdqWXs70NrK/m1oiG3i7u93l1eTQBZkgiAIoq5RaBOyKxpkjkoQBFEznBZh3YrV1mVLgIUL3f279Vb7hI86in2PJGeddRY+/OEP49prr0VPTw8WLVqEW265BdlsFldddRU6Ojqwbt06/O53v6vc89xzz+GCCy5Ae3s7Fi1ahCuuuAJDQ0OV33//+9/jta99Lbq7u9Hb24sLL7wQ27dvr/y+a9cuKIqCn//853jd616HTCaDY489Fg899JB0+WUhBZkgCIKoa0jPE0fh/EUQBEHI0yzhTm677Tb09fXh0UcfxYc//GF88IMfxKWXXorXvOY1ePLJJ3HeeefhiiuuwPT0NMbGxnD22Wfj+OOPx+OPP47f//73OHToEN7+9rdX0stms/j4xz+Oxx9/HHfddRdisRje+ta3olQqGfL99Kc/jU984hN46qmnsH79elx22WUoFAqBPiu5WBMEQRANA1lF+RjOQaa6IoiGoVHclqMOO0iXyv29UTj22GNx/fXXAwCuu+463HTTTejr68PVV18NAPjsZz+Lb33rW3jmmWdw55134vjjj8eXv/zlyv233norli9fji1btmD9+vV429veZkj/1ltvRX9/P1544QVs3Lix8v0nPvEJvOlNbwIAfP7zn8eGDRuwbds2HHnkkYE9K1mQCYIgiLpGPzFs4LmJ71BdEQRBuKeRlWEWxxxzTOVzPB5Hb28vNm3aVPlu0aJFAICBgQE8/fTTuOeee9De3l75pym0mhv11q1bcdlll2HNmjXo7OzEqlWrAAC7d++2zXfx4sWVPIKELMgEQTQsatM4PjU3TTZH8YR+/xxZnAiCINzD2o/sVq7O7N2PVi9Buux48UX351CZSCaThr8VRTF8pz17qVTC1NQULrroInzlK1+xpKMpuRdddBFWrlyJW265BUuWLEGpVMLGjRsxNzdnm68+jyAhBZkgCIKoa4xuw6T0iUI1RRAEIYefctMwXvX3u49izaOvz/80BTjhhBPw3//931i1ahUSCetzDQ8P4+WXX8Ytt9yC008/HQDwpz/9qdbFtIVcrAmCaFjoyJ/mg964OLSWQBAE4R3yVbPyoQ99CCMjI7jsssvw2GOPYfv27bjjjjtw1VVXoVgsoqenB729vfjOd76Dbdu24e6778bHP/7xsItdgRRkgiAaFnKxbj5I6eNjsLbTcgJBEAQRAEuWLMEDDzyAYrGI8847D5s2bcK1116L7u5uxGIxxGIx/OQnP8ETTzyBjRs34mMf+xi++tWvhl3sCuRiTRAEQdQ1Pm2vajpoMYEgCMI9zSRDN2/ebPlu165dlu/0Eb0PP/xw/PznP7dN89xzz8ULL7xge/+qVasMfwNAd3e35bsgIAsyQRAE0TCQVZQgCIIIClacC1qkbTxIQSYIgiDqGjrbVxyqK4IgCPewxSZpyI0GKcgEQRAE0YSQtZ0gCMI9JEEbF1KQCYJoWMjtiSDsIQsyQRAEQVghBZkgCIJoGEjp40NWY4IgCH+g8aZxIQWZIAiCaBhIAeSjn9DFaHZHEAQhBUtskrda40EKMkEQBNEwkM4nDtUVQRAEQVghBZkgCIIgmhDSjwmCILxAUrRRIQWZIAiCaBhousJHXz9kQSYIgpCDeQ5yCOUggoUUZIIgCIJoSkhDJgiCIKLDu9/9blx88cVhF4MUZIIgCKJxoMBTfFjWD4IgCEIeTZxSkK7GIxF2AQiCIAiCqA169ThGujJBEERolNQShqcHy5+VFrTma6+W9WZ6EVPIXmqGFGSCIAiiYSADqThkTSYIgnCPVwk6PD2M4767yo+iuGbgEwPob+t3vO6ss87Cpk2bEI/Hcdttt6GlpQVf/OIX8c53vhN/8zd/g5/97GdYtGgRvvGNb+CCCy5AsVjE+973Ptx99904ePAgVqxYgWuuuQYf/ehHK2kWi0V88pOfxK233op4PI6//uu/hhoRczwtGRAE0bBEQ8wSBEEQBNGoREWpC5rbbrsNfX19ePTRR/HhD38YH/zgB3HppZfiNa95DZ588kmcd955uOKKKzA9PY1SqYRly5bhpz/9KV544QV89rOfxd/93d/h9ttvr6T39a9/Hd///vdx66234k9/+hNGRkbwi1/8IsQnrEIKMkEQBNEwkFWUj756yMWaIAiCEOXYY4/F9ddfj8MPPxzXXXcd0uk0+vr6cPXVV+Pwww/HZz/7WQwPD+OZZ55BMpnE5z//eZx00klYvXo1Lr/8clx11VUGBfnmm2/Gddddh0suuQRHHXUU/v3f/x1dXV0hPmEVcrEmCIIgCIIgCIKQoNkWZI855pjK53g8jt7eXmzatKny3aJFiwAAAwMDAIB/+7d/w6233ordu3djZmYGc3NzOO644wAA4+PjOHDgAE455ZTK/YlEAieddFIkLPKkIBMEQRBEk6Cf0Cl0zBNBEIRn3KpzvZlePPXeXQCAnrYWtCbDCdIlSjKZNPytKIrhO218KZVK+MlPfoJPfOIT+PrXv45TTz0VHR0d+OpXv4pHHnnEn4IHjNSb+Na3voVvfetb2LVrFwBgw4YN+OxnP4sLLrggiLIRBEEQBBEQTWb8IAiCiBQxJYbeTDlAVm+mBa0tjWO3fOCBB/Ca17wG11xzTeW77du3Vz53dXVh8eLFeOSRR3DGGWcAAAqFAp544gmccMIJNS+vGak9yMuWLcNNN92EJ554Ao8//jjOPvtsvOUtb8Hzzz8fVPkIgiAIgiAIgiAiSQQ8giPH4Ycfjscffxx33HEHtmzZgs985jN47LHHDNd89KMfxU033YRf/vKXeOmll3DNNddgbGwsnAKbkFKQL7roIrzxjW/E4YcfjvXr1+NLX/oS2tvb8fDDDwdVPoIgCIIgAoAsyARBEO4hEWrP+9//flxyySV4xzvegVNOOQXDw8MGazIA/J//839wxRVX4F3velfFDfutb31rSCU24tqWXywW8dOf/hTZbBannnqq7XW5XA65XK7y98TEhNssCYIgpOhMJ50vCpjetpawi9DwtCToQAY3RKHe2lNxTOWKyLTEwy4KQTQM6WT0+lNbA/ZxTYb6Ib+iHvBr8+bNlu+0Lbd69AG2vve97+F73/ue4fcbb7yx8jmRSODmm2/GzTff7FcxfUNaQX722Wdx6qmnYnZ2Fu3t7fjFL36Bo48+2vb6G2+8EZ///Oc9FZIgCMIN5xy1EFO5PI5d3l3zvD945lo8sH0Ib9y4uOZ5NxuLu1rx2nV96GoNf0GkHrhg42HI5gpY2JEOuyi4+vQ1uPPFAZxz1MKwi0IQdc9bj1+K/WMzWL+oPeyiWDh+RQ92DU9jbX9b2EXxzJs2Lcb4TB5LulsBAJuWdmH74BRW9mak0+rOtKBQLCEVgQVLooqiSsbSnpubw+7duzE+Po6f/exn+O53v4t7773XVklmWZCXL1+O8fFxdHZ2eis9QRAEQRAEQRBExJmdncXOnTuxevVqpNPhL1A2Krx6npiYQFdXl6MeKm1Bbmlpwbp16wAAJ554Ih577DH88z//M7797W8zr0+lUkilUrLZEARBEARBEARBEERN8WzPL5VKBgsxQRAEQRAEQRAEQdQjUhbk6667DhdccAFWrFiByclJ/OhHP8LmzZtxxx13BFU+giAIgiAIgiCIhkBydyshiR/1K6UgDwwM4Morr8SBAwfQ1dWFY445BnfccQde//rXey7I/2/v3oOiLPc4gH8XdoEFggU2LqsglNcUFUEN9aSTjGiGZk0abWRlndFwFI+DdsbT6UyXI9l0Mac07WYThTWRZpmkSN5CEAQE9SCkiZW4JxGBg8nK/s4fHd7Dq3jJYHdZvp+ZnVmf5+Hd59nv7O778919XyIiIiIiIlek0/12Isnm5mbo9XoHz8Z1NTc3A/j/830jfleB/M4779zwAxEREREREfVE7u7uMBgMsFgsAABvb2+nv7xTdyIiaG5uhsVigcFggLv7jV9+64avg0xERERERETXJzQ0FACUIpk6n8FgUJ7nG8UCmYiIiIiIqItpNBqEhYUhODgYVqvV0dNxOTqd7g8dOW7DApmIiIiIiMhO3N3dO6WQo67xhy/zREREREREROQKWCATERERERERgQUyEREREREREQAH/Aa57eLNDQ0N9n5oIiIiIiIi6oHa6s+2evRK7F4gNzY2AgDCw8Pt/dBERERERETUgzU2NsLf3/+K/Rq5VgndyWw2G37++WfcdNNNTn1x7IaGBoSHh+PkyZPw8/Nz9HToCpiT82NG3QNz6h6YU/fAnLoH5tQ9MCfn110yEhE0NjbCZDLBze3KvzS2+xFkNzc39O7d294Pe8P8/PycOmj6DXNyfsyoe2BO3QNz6h6YU/fAnLoH5uT8ukNGVzty3IYn6SIiIiIiIiICC2QiIiIiIiIiACyQr8jT0xPPPPMMPD09HT0Vugrm5PyYUffAnLoH5tQ9MKfugTl1D8zJ+blaRnY/SRcRERERERGRM+IRZCIiIiIiIiKwQCYiIiIiIiICwAKZiIiIiIiICAALZCIiIiIiIiIALJA79MYbbyAyMhJeXl4YPXo0CgsLHT2lHmX58uUYOXIkbrrpJgQHB+Oee+5BZWWlasyvv/6K1NRUBAUFwdfXF/fddx9Onz6tGlNTU4OpU6fC29sbwcHBSE9Px8WLF+25lB4jIyMDGo0GaWlpShszcg4//fQTHnroIQQFBUGv1yM6OhpFRUVKv4jg73//O8LCwqDX65GQkICqqirVNurq6mA2m+Hn5weDwYA5c+agqanJ3ktxWa2trXj66acRFRUFvV6PW2+9Fc899xzan0OTOdnfrl27kJSUBJPJBI1Gg40bN6r6OyuTgwcP4k9/+hO8vLwQHh6OFStWdPXSXMrVcrJarVi6dCmio6Ph4+MDk8mEhx9+GD///LNqG8yp613r9dTe3LlzodFo8Nprr6namVPXup6Mjhw5gmnTpsHf3x8+Pj4YOXIkampqlH6X2fcTUsnKyhIPDw9599135dChQ/LEE0+IwWCQ06dPO3pqPUZiYqK89957UlFRIaWlpXLXXXdJRESENDU1KWPmzp0r4eHhkpubK0VFRXL77bfLmDFjlP6LFy/KkCFDJCEhQUpKSmTLli1iNBrlr3/9qyOW5NIKCwslMjJShg4dKgsXLlTamZHj1dXVSZ8+feSRRx6RgoICOXbsmOTk5Eh1dbUyJiMjQ/z9/WXjxo1SVlYm06ZNk6ioKDl//rwyZvLkyTJs2DDZt2+f7N69W/r27SvJycmOWJJLeuGFFyQoKEi+/PJLOX78uHz66afi6+srK1euVMYwJ/vbsmWLLFu2TLKzswWAfP7556r+zsjk3LlzEhISImazWSoqKuTjjz8WvV4vb731lr2W2e1dLaf6+npJSEiQDRs2yL/+9S/Jz8+XUaNGSWxsrGobzKnrXev11CY7O1uGDRsmJpNJXn31VVUfc+pa18qourpaAgMDJT09XQ4cOCDV1dWyadMmVY3kKvt+LJAvMWrUKElNTVX+3draKiaTSZYvX+7AWfVsFotFAMjOnTtF5LcPPJ1OJ59++qky5siRIwJA8vPzReS3F7mbm5vU1tYqY1avXi1+fn5y4cIF+y7AhTU2Nkq/fv1k27ZtMn78eKVAZkbOYenSpTJu3Lgr9ttsNgkNDZWXXnpJaauvrxdPT0/5+OOPRUTk8OHDAkD279+vjPn6669Fo9HITz/91HWT70GmTp0qjz32mKrt3nvvFbPZLCLMyRlcurPYWZm8+eabEhAQoHrPW7p0qQwYMKCLV+SarlZ4tSksLBQAcuLECRFhTo5wpZx+/PFH6dWrl1RUVEifPn1UBTJzsq+OMpo1a5Y89NBDV/wbV9r341es22lpaUFxcTESEhKUNjc3NyQkJCA/P9+BM+vZzp07BwAIDAwEABQXF8NqtapyGjhwICIiIpSc8vPzER0djZCQEGVMYmIiGhoacOjQITvO3rWlpqZi6tSpqiwAZuQsvvjiC8TFxeH+++9HcHAwYmJisG7dOqX/+PHjqK2tVeXk7++P0aNHq3IyGAyIi4tTxiQkJMDNzQ0FBQX2W4wLGzNmDHJzc3H06FEAQFlZGfbs2YMpU6YAYE7OqLMyyc/Pxx133AEPDw9lTGJiIiorK3H27Fk7raZnOXfuHDQaDQwGAwDm5CxsNhtSUlKQnp6OwYMHX9bPnBzLZrPhq6++Qv/+/ZGYmIjg4GCMHj1a9TVsV9r3Y4Hczi+//ILW1lZVaAAQEhKC2tpaB82qZ7PZbEhLS8PYsWMxZMgQAEBtbS08PDyUD7c27XOqra3tMMe2PvrjsrKycODAASxfvvyyPmbkHI4dO4bVq1ejX79+yMnJwbx587BgwQKsX78ewP+f56u959XW1iI4OFjVr9VqERgYyJw6yVNPPYUHHngAAwcOhE6nQ0xMDNLS0mA2mwEwJ2fUWZnwfdC+fv31VyxduhTJycnw8/MDwJycxYsvvgitVosFCxZ02M+cHMtisaCpqQkZGRmYPHkyvvnmG8yYMQP33nsvdu7cCcC19v20jp4A0dWkpqaioqICe/bscfRUqJ2TJ09i4cKF2LZtG7y8vBw9HboCm82GuLg4/POf/wQAxMTEoKKiAmvWrMHs2bMdPDtq88knnyAzMxMfffQRBg8ejNLSUqSlpcFkMjEnok5itVoxc+ZMiAhWr17t6OlQO8XFxVi5ciUOHDgAjUbj6OlQB2w2GwBg+vTpWLRoEQBg+PDh+O6777BmzRqMHz/ekdPrdDyC3I7RaIS7u/tlZ1s7ffo0QkNDHTSrnmv+/Pn48ssvkZeXh969eyvtoaGhaGlpQX19vWp8+5xCQ0M7zLGtj/6Y4uJiWCwWjBgxAlqtFlqtFjt37sTrr78OrVaLkJAQZuQEwsLCcNttt6naBg0apJxxsu15vtp7XmhoKCwWi6r/4sWLqKurY06dJD09XTmKHB0djZSUFCxatEj5dgZzcj6dlQnfB+2jrTg+ceIEtm3bphw9BpiTM9i9ezcsFgsiIiKUfYoTJ05g8eLFiIyMBMCcHM1oNEKr1V5zn8JV9v1YILfj4eGB2NhY5ObmKm02mw25ubmIj4934Mx6FhHB/Pnz8fnnn2PHjh2IiopS9cfGxkKn06lyqqysRE1NjZJTfHw8ysvLVW+mbR+Kl7646febOHEiysvLUVpaqtzi4uJgNpuV+8zI8caOHXvZJdKOHj2KPn36AACioqIQGhqqyqmhoQEFBQWqnOrr61FcXKyM2bFjB2w2G0aPHm2HVbi+5uZmuLmpP47d3d2V/7FnTs6nszKJj4/Hrl27YLValTHbtm3DgAEDEBAQYKfVuLa24riqqgrbt29HUFCQqp85OV5KSgoOHjyo2qcwmUxIT09HTk4OAObkaB4eHhg5cuRV9ylcav/c0WcJczZZWVni6ekp77//vhw+fFj+/Oc/i8FgUJ1tjbrWvHnzxN/fX7799ls5deqUcmtublbGzJ07VyIiImTHjh1SVFQk8fHxEh8fr/S3nUZ+0qRJUlpaKlu3bpWbb77Z6U4j70ran8VahBk5g8LCQtFqtfLCCy9IVVWVZGZmire3t3z44YfKmIyMDDEYDLJp0yY5ePCgTJ8+vcNL1cTExEhBQYHs2bNH+vXrx8sHdaLZs2dLr169lMs8ZWdni9FolCVLlihjmJP9NTY2SklJiZSUlAgAeeWVV6SkpEQ5+3FnZFJfXy8hISGSkpIiFRUVkpWVJd7e3rwsze9wtZxaWlpk2rRp0rt3byktLVXtU7Q/Yy5z6nrXej1d6tKzWIswp652rYyys7NFp9PJ2rVrpaqqSlatWiXu7u6ye/duZRuusu/HArkDq1atkoiICPHw8JBRo0bJvn37HD2lHgVAh7f33ntPGXP+/Hl58sknJSAgQLy9vWXGjBly6tQp1XZ++OEHmTJliuj1ejEajbJ48WKxWq12Xk3PcWmBzIycw+bNm2XIkCHi6ekpAwcOlLVr16r6bTabPP300xISEiKenp4yceJEqaysVI05c+aMJCcni6+vr/j5+cmjjz4qjY2N9lyGS2toaJCFCxdKRESEeHl5yS233CLLli1T7cAzJ/vLy8vr8LNo9uzZItJ5mZSVlcm4cePE09NTevXqJRkZGfZaoku4Wk7Hjx+/4j5FXl6esg3m1PWu9Xq6VEcFMnPqWteT0TvvvCN9+/YVLy8vGTZsmGzcuFG1DVfZ99OIiHTtMWoiIiIiIiIi58ffIBMRERERERGBBTIRERERERERABbIRERERERERABYIBMREREREREBYIFMREREREREBIAFMhEREREREREAFshEREREREREAFggExEREREREQFggUxERHTdvv32W2g0GtTX1zt6Kp3mkUcewT333OPoaRARETkFraMnQERERF3vhx9+QFRUFEpKSjB8+HClfeXKlRARx02MiIjIibBAJiIicmItLS3w8PDosu37+/t32baJiIi6G37FmoiIqJ0LFy5gwYIFCA4OhpeXF8aNG4f9+/erxuzduxdDhw6Fl5cXbr/9dlRUVCh9J06cQFJSEgICAuDj44PBgwdjy5YtSn9FRQWmTJkCX19fhISEICUlBb/88ovSP2HCBMyfPx9paWkwGo1ITEzEgw8+iFmzZqnmYLVaYTQa8cEHHwAAtm7dinHjxsFgMCAoKAh33303vv/+e2V8VFQUACAmJgYajQYTJkwAcPlXrK+1/ravmefm5iIuLg7e3t4YM2YMKisrb/AZJyIich4skImIiNpZsmQJPvvsM6xfvx4HDhxA3759kZiYiLq6OmVMeno6Xn75Zezfvx8333wzkpKSYLVaAQCpqam4cOECdu3ahfLycrz44ovw9fUFANTX1+POO+9ETEwMioqKsHXrVpw+fRozZ85UzWH9+vXw8PDA3r17sWbNGpjNZmzevBlNTU3KmJycHDQ3N2PGjBkAgP/85z/4y1/+gqKiIuTm5sLNzQ0zZsyAzWYDABQWFgIAtm/fjlOnTiE7O/uG1w8Ay5Ytw8svv4yioiJotVo89thjf+RpJyIicg5CREREIiLS1NQkOp1OMjMzlbaWlhYxmUyyYsUKycvLEwCSlZWl9J85c0b0er1s2LBBRESio6PlH//4R4fbf+6552TSpEmqtpMnTwoAqaysFBGR8ePHS0xMjGqM1WoVo9EoH3zwgdKWnJwss2bNuuJa/v3vfwsAKS8vFxGR48ePCwApKSlRjZs9e7ZMnz79utYvIspzsH37dmXMV199JQDk/PnzV5wPERFRd8AjyERERP/z/fffw2q1YuzYsUqbTqfDqFGjcOTIEaUtPj5euR8YGIgBAwYo/QsWLMDzzz+PsWPH4plnnsHBgweVsWVlZcjLy4Ovr69yGzhwoPLYbWJjY1Xz0mq1mDlzJjIzMwH8drR406ZNMJvNypiqqiokJyfjlltugZ+fHyIjIwEANTU1nb5+ABg6dKhyPywsDABgsViu+7GIiIicEQtkIiKiTvT444/j2LFjSElJQXl5OeLi4rBq1SoAQFNTE5KSklBaWqq6VVVV4Y477lC24ePjc9l2zWYzcnNzYbFYsHHjRuj1ekyePFnpT0pKQl1dHdatW4eCggIUFBQA+O0kX11Bp9Mp9zUaDQAoX+cmIiLqrlggExER/c+tt96q/Pa3jdVqxf79+3Hbbbcpbfv27VPunz17FkePHsWgQYOUtvDwcMydOxfZ2dlYvHgx1q1bBwAYMWIEDh06hMjISPTt21d166gobm/MmDEIDw/Hhg0bkJmZifvvv18pUs+cOYPKykr87W9/w8SJEzFo0CCcPXtW9fdtZ8JubW39w+snIiJyVbzMExER0f/4+Phg3rx5SE9PR2BgICIiIrBixQo0Nzdjzpw5KCsrAwA8++yzCAoKQkhICJYtWwaj0aicCTotLQ1TpkxB//79cfbsWeTl5SnFc2pqKtatW4fk5GQsWbIEgYGBqK6uRlZWFt5++224u7tfdX4PPvgg1qxZg6NHjyIvL09pDwgIQFBQENauXYuwsDDU1NTgqaeeUv1tcHAw9Ho9tm7dit69e8PLy+uySzxda/1ERESujkeQiYiI2snIyMB9992HlJQUjBgxAtXV1cjJyUFAQIBqzMKFCxEbG4va2lps3rxZdYQ2NTUVgwYNwuTJk9G/f3+8+eabAACTyYS9e/eitbUVkyZNQnR0NNLS0mAwGODmdu2PZLPZjMOHD6NXr16q3wm7ubkhKysLxcXFGDJkCBYtWoSXXnpJ9bdarRavv/463nrrLZhMJkyfPv2G109EROSqNCIijp4EERERERERkaPxCDIRERERERERWCATERERERERAWCBTERERERERASABTIRERERERERABbIRERERERERABYIBMREREREREBYIFMREREREREBIAFMhEREREREREAFshEREREREREAFggExEREREREQFggUxEREREREQEAPgvAzOUuDqfOrYAAAAASUVORK5CYII=",
            "text/plain": [
              "<Figure size 1200x400 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def MAD(df):\n",
        "    return (df - df.mean()).abs().mean()\n",
        "\n",
        "\n",
        "print(\"MAD = \", MAD(wines[\"quality\"]))\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(12, 4))\n",
        "ax = wines[\"quality\"].plot(alpha=0.6, title=\"wine quality\")\n",
        "ax.axhline(wines[\"quality\"].mean(), color=\"r\", ls=\"--\", lw=3)\n",
        "\n",
        "mad = MAD(wines[\"quality\"])\n",
        "ax.axhline(wines[\"quality\"].mean() + mad, color=\"g\", lw=3)\n",
        "ax.axhline(wines[\"quality\"].mean() - mad, color=\"g\", lw=3)\n",
        "ax.legend([\"y\", \"mean\", \"mad\"])\n",
        "ax.set_xlabel(\"observation\")\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "18q5veuGOkHx"
      },
      "source": [
        "## A preliminary look at the data\n",
        "\n",
        "The data consists of 1,599 measurements of eleven physical and chemical characteristics plus an integer measure of sensory quality recorded on a scale from 3 to 8. Histograms provides insight into the values and variability of the data set."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 806
        },
        "id": "QDE7TMklOkHy",
        "outputId": "52750b23-46e0-4517-bafb-6fccce162bdb",
        "tags": []
      },
      "outputs": [
        {
          "data": {
            "image/png": 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aNUVHR6tWrVqOn8WefS+FstixY4eMMWrQoEGBPLdt2zZHjivK6dOnNW7cONWpU0ehoaGqWbOmatWqpYyMDKcYd+7c6bHcJbmeW4ty++23a+/evY5763311Vc6cOAAuQtQ6Y83XJF/bFOc/Hs6lWb9drtdzz//vBo0aOCUk3766acCOeniiy926yE4hw4d0unTp8slJwEV2bn7vavHHklJSRo9erReffVV1axZUykpKZo1a1aJx0BlPS8rjKu5xVWTJk1SRkaGLrroIjVr1kxjxozRTz/9VKrY9uzZo9q1aztumZDvwgsvLDCtK+ecZ3MlZ6Nk3FMKxTpy5IjWr18vSdq6davsdrujCp5/M7wHH3ywyG/ACtvZS6NPnz5avXq1xowZo+bNmysqKkp2u13XXXedyzdL94W+fftq1KhRevvtt/XPf/5Tb731llq2bMnBGSq80NBQ9ezZUx9//LFeeuklHThwQKtWrdLUqVM9svyMjAx16NBB0dHRmjRpkpKTkxUWFqaNGzfq4Ycf9lhesNvtslgs+vLLLxUcHFxgfEn3p7r33ns1b948jRw5Um3atFG1atVksVjUt29fv85dKSkpio+P11tvvaWrr75ab731lhISEtS5c2dfhwZUaGW5p4srpk6dqrFjx2rIkCGaPHmyYmNjFRQUpJEjR/p1TgIqsnP3e3eOPZ599lkNGjRIn3zyiZYuXar77rtP06ZN03fffVfi/SXL4uyHykiezy1XX321du7c6WjXq6++queff16zZ8/WnXfeKUmOh0uVFJs73D3nLO+cXVlQlEKxhg8frr/++kvTpk3To48+qhkzZmj06NGS5LiKyGq1lniiUrdu3UIvv9y+fXuJMRw7dkzLli3TxIkTNW7cOMfwc5dXq1YtRUdHOz3VyxV169Z1LK9Tp06O4bm5uUpLSyvyKVT5irtUPjY2Vt26ddPbb7+t/v37a9WqVZoxY4Zb8QGB6tZbb9Ubb7yhZcuWadu2bTLGOH66J/1v3yssD/zyyy+qWbNmkT8VW7lypY4cOaKPPvpIV199tWN4WlpagWnL8lOa5ORkGWOUlJTkuMLLHQsXLtTAgQP17LPPOoZlZWUpIyOjwHrKkrvO5UpuLa5fgoODddttt2n+/Pl66qmntGjRIt11112FHhwDlU1pjzeksuWjfPk3Gf/555/dLhQvXLhQ11xzjV577TWn4RkZGU4PVEhOTtbatWuVm5srq9Xq0rJr1aql8PDwUuckAGe4e+zRrFkzNWvWTI8//rhWr16tdu3aafbs2ZoyZUqh07tzXla9evUCxyw5OTnav3+/0zBXc4s7YmNjNXjwYA0ePFgnTpzQ1VdfrQkTJjiKUtWrV9euXbsKzJd/JXm+unXrasWKFTp16pTT1VK//fab03SunnPC8/j5Hoq0cOFCvf/++3ryySf1yCOPqG/fvnr88cf166+/SpLi4uLUsWNHvfLKKwUSk3TmMu58N9xwg7777jt9//33TuPPvt9SUfJPgs6thJ9b3AkKClLPnj312WefOa7uOlthlXRJatmypWrVqqXZs2c7HuMsnXmy17lJuDD5J81FTTtgwABt3bpVY8aMUXBwsPr27VviMoGKoHPnzoqNjdX777+v999/X61atXK6zLl27dpq3ry53njjDaf95+eff9bSpUsdT/ksTGF5IScnRy+99FKBaSMjI0v9c75bbrlFwcHBmjhxYoEcYowp8IjgwuI8d76ZM2cW+BavV69e+vHHH/Xxxx8XWEZRuevs/ju7fampqdq6dWuxcUmu5a5jx47p7rvv1okTJ3hiKPBfpT3ekMqWj/JdfvnlSkpK0owZMwrsv8WtWyo8Jy1YsMBxD9B8vXr10uHDh/Xiiy8WWEZR6wgODlZKSooWLVqkvXv3OoZv27ZNS5YsKTYuAP/j6rFHZmam8vLynMY3a9ZMQUFBys7OLnL57pyXJScn65tvvnEaNmfOnALHMa7mFlede3wVFRWlCy+80KldycnJ+uWXX5zOOX/88UetWrXKad6UlBTl5uZq7ty5jmF2u12zZs0q0Aap5HNOeB5XSqFQBw8e1LBhw3TNNddoxIgRkqQXX3xRK1as0KBBg/Ttt98qKChIs2bNUvv27dWsWTPdddddql+/vg4cOKA1a9bojz/+0I8//ihJeuihh/Tmm2/quuuu0/333+949GjdunVL/H1wdHS0rr76ak2fPl25ubk677zztHTp0kKviJg6daqWLl2qDh06aOjQoWrUqJH279+vBQsW6Ntvvy300e1Wq1VTpkzR3XffrU6dOunWW29VWlqa5s2b59I9pVq0aCFJuu+++5SSklKg8NStWzfVqFFDCxYs0PXXX6+4uLgSlwlUBFarVbfccovee+89nTx5Us8880yBaZ5++mldf/31atOmje644w6dPn1aM2fOVLVq1TRhwoQil922bVtVr15dAwcO1H333SeLxaI333yz0JOlFi1a6P3339fo0aN1xRVXKCoqSj169HCpDcnJyZoyZYoeffRR7d69Wz179lTVqlWVlpamjz/+WEOHDtWDDz5Y5Pzdu3fXm2++qWrVqqlx48Zas2aNvvrqK9WoUcNpujFjxmjhwoXq3bu3hgwZohYtWujo0aP69NNPNXv27CKv2Jw2bZq6deum9u3ba8iQITp69KhmzpypJk2a6MSJE8W2LT93PfbYY+rbt6+sVqt69OjhKFZddtllatq0qRYsWKBGjRrp8ssvd6nPgMqgNMcbUtnyUb6goCC9/PLL6tGjh5o3b67Bgwerdu3a+uWXX7Rly5ZiC0Ddu3fXpEmTNHjwYLVt21abN2/W22+/XeB45/bbb9e///1vjR49Wt9//72uuuoqnTx5Ul999ZXuuece3XTTTYUuf+LEiVq8eLGuuuoq3XPPPcrLy3PkpNLeDwaobFw99li+fLlGjBih3r1766KLLlJeXp7efPNNBQcHq1evXkUu353zsjvvvFP/+Mc/1KtXL3Xp0kU//vijlixZUuDqJ1dzi6saN26sjh07qkWLFoqNjdX69eu1cOFCx3mpJA0ZMkTPPfecUlJSdMcdd+jgwYOaPXu2mjRposzMTMd0PXv2VKtWrfTAAw/ot99+U8OGDfXpp5/q6NGjkv53Bas755zwMO896A/+IP+xwuc+OvTcx6DfcsstpmrVqmb37t1O033yySdGknnqqaccw3bu3Gluv/12k5CQYKxWqznvvPNM9+7dzcKFC53m/emnn0yHDh1MWFiYOe+888zkyZPNa6+9Vugjyc/1xx9/mJtvvtnExMSYatWqmd69e5t9+/YV+pjSPXv2mNtvv93UqlXLhIaGmvr165vhw4eb7Oxspz44+xHNxhjz0ksvmaSkJBMaGmpatmxpvvnmmwKPGi3sMaZ5eXnm3nvvNbVq1TIWi6XQRx7fc889RpJ55513im0nUNGkpqYaScZisZjff/+90Gm++uor065dOxMeHm6io6NNjx49zNatW52mmTdvXoFcsWrVKnPllVea8PBwk5iYaB566CGzZMmSAvv3iRMnzG233WZiYmKMJMdjggvbn8/Nhfk+/PBD0759exMZGWkiIyNNw4YNzfDhw8327duLbf+xY8fM4MGDTc2aNU1UVJRJSUkxv/zyS4FHKRtjzJEjR8yIESPMeeedZ0JCQsz5559vBg4caA4fPlxkvPmxNWrUyISGhprGjRubjz76qMDjkI0p/LHOkydPNuedd54JCgoqNBdPnz7dSDJTp04ttp1AZVSa442i8lFRx2dFLccYY7799lvTpUsXU7VqVRMZGWkuueQSM3PmzGJjzsrKMg888ICpXbu2CQ8PN+3atTNr1qwp9NHqp06dMo899phJSkoyVqvVJCQkmL/97W9m586djmkKyytff/21adGihQkJCTH169c3s2fPLjK3ApVZ/n5x6NChQseXdOyxa9cuM2TIEJOcnGzCwsJMbGysueaaa8xXX33ltJzCjjlcPS+z2Wzm4YcfNjVr1jQREREmJSXF/PbbbwWW6WpuKepY5lxTpkwxrVq1MjExMSY8PNw0bNjQPPHEEyYnJ8dpurfeesvUr1/fhISEmObNm5slS5YUegx06NAhc9ttt5mqVauaatWqmUGDBplVq1YZSea9995zTOfqOWdJ7x3cYzGmhOt8AZTZqFGj9Nprryk9Pb3Akx8AwF/961//0qhRo7R7926nR7wDAAAEskWLFunmm2/Wt99+q3bt2vk6nEqNohRQzrKyslSnTh11795d8+bN83U4AOASY4wuvfRS1ahRQytWrPB1OAAAAKVy+vRppyfl2Ww2de3aVevXr1d6ejpP0fMx7ikFlJODBw/qq6++0sKFC3XkyBHdf//9vg4JAEp08uRJffrpp1qxYoU2b96sTz75xNchAQAAlNq9996r06dPq02bNsrOztZHH32k1atXa+rUqRSk/ABFKaCcbN26Vf3791dcXJxeeOEFNW/e3NchAUCJDh06pNtuu00xMTH65z//qRtvvNHXIQEAAJRap06d9Oyzz+rzzz9XVlaWLrzwQs2cOdPpxunwHX6+BwAAAAAAAK8Lcmdim82msWPHKikpSeHh4UpOTtbkyZOdHsFtjNG4ceNUu3ZthYeHq3PnztqxY4fTco4ePar+/fsrOjpaMTExuuOOO0p8dDUAAAAAAAAqDreKUk899ZRefvllvfjii9q2bZueeuopTZ8+XTNnznRMM336dL3wwguaPXu21q5dq8jISKWkpCgrK8sxTf/+/bVlyxalpqbq888/1zfffKOhQ4d6rlUAAAAAAADwa279fK979+6Kj4/Xa6+95hjWq1cvhYeH66233pIxRomJiXrggQf04IMPSpKOHz+u+Ph4zZ8/X3379tW2bdvUuHFjrVu3Ti1btpQkLV68WDfccIP++OMPJSYmlhiH3W7Xvn37VLVqVVksFnfbDCBAGWP0119/KTExUUFBbtXUyxU5CaicyEkA/Ak5CYA/cTU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            "text/plain": [
              "<Figure size 1200x800 with 12 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig, axes = plt.subplots(3, 4, figsize=(12, 8), sharey=True)\n",
        "\n",
        "for ax, column in zip(axes.flatten(), wines.columns):\n",
        "    wines[column].hist(ax=ax, bins=30)\n",
        "    ax.axvline(wines[column].mean(), color=\"r\", label=\"mean\")\n",
        "    ax.set_title(column)\n",
        "    ax.legend()\n",
        "\n",
        "plt.tight_layout()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0CigwX_ROkH0"
      },
      "source": [
        "## Which features influence reported wine quality?\n",
        "\n",
        "The art of regression is to identify the features that have explanatory value for a response of interest. This is where a person with deep knowledge of an application area, in this case an experienced onenologist will have a head start compared to the naive data scientist. In the absence of the experience, we proceed by examining the correlation among the variables in the data set."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 545
        },
        "id": "Arp6oxe4OkH1",
        "outputId": "56f945f8-38d0-4634-cac8-248957ec6a9f",
        "tags": []
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "_ = wines.corr()[\"quality\"].plot(kind=\"bar\", grid=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 174
        },
        "id": "PpNJXwj6OkH2",
        "outputId": "4ea11a0f-7b46-424e-ebf6-c69ead7014a6",
        "tags": []
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-d9b386c1-69ed-4df0-b774-7a48665f9b72\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>volatile acidity</th>\n",
              "      <th>density</th>\n",
              "      <th>alcohol</th>\n",
              "      <th>quality</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>volatile acidity</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.022026</td>\n",
              "      <td>-0.202288</td>\n",
              "      <td>-0.390558</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>density</th>\n",
              "      <td>0.022026</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.496180</td>\n",
              "      <td>-0.174919</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>alcohol</th>\n",
              "      <td>-0.202288</td>\n",
              "      <td>-0.496180</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.476166</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>quality</th>\n",
              "      <td>-0.390558</td>\n",
              "      <td>-0.174919</td>\n",
              "      <td>0.476166</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
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              "      border-bottom-color: var(--fill-color);\n",
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              "\n",
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              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
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              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
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              "  </div>\n"
            ],
            "text/plain": [
              "                  volatile acidity   density   alcohol   quality\n",
              "volatile acidity          1.000000  0.022026 -0.202288 -0.390558\n",
              "density                   0.022026  1.000000 -0.496180 -0.174919\n",
              "alcohol                  -0.202288 -0.496180  1.000000  0.476166\n",
              "quality                  -0.390558 -0.174919  0.476166  1.000000"
            ]
          },
          "execution_count": 6,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "wines[[\"volatile acidity\", \"density\", \"alcohol\", \"quality\"]].corr()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0DYDAUmWOkH2"
      },
      "source": [
        "Collectively, these figures suggest `alcohol` is a strong correlate of `quality`, and several additional factors as  candidates for explanatory variables.."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z6iUTUznOkH3"
      },
      "source": [
        "## LAD line fitting to identify features\n",
        "\n",
        "An alternative approach is perform a series of single feature LAD regressions to determine which features have the largest impact on reducing the mean absolute deviations in the residuals.\n",
        "\n",
        "$$\n",
        "\\begin{align*}\n",
        "\\min \\frac{1}{I} \\sum_{i\\in I} \\left| y_i - a x_i - b \\right|\n",
        "\\end{align*}\n",
        "$$\n",
        "\n",
        "This computation has been presented in a prior notebook."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yhNZyRQAOkH4",
        "outputId": "2c1af878-4913-45d9-c1f5-0a07665f36d2"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Writing lad_fit_1.mod\n"
          ]
        }
      ],
      "source": [
        "%%writefile lad_fit_1.mod\n",
        "\n",
        "set I;\n",
        "\n",
        "param y{I};\n",
        "param X{I};\n",
        "\n",
        "var a;\n",
        "var b;\n",
        "\n",
        "var e_pos{I} >= 0;\n",
        "var e_neg{I} >= 0;\n",
        "\n",
        "var prediction{i in I} = a * X[i] + b;\n",
        "s.t. prediction_error{i in I}: e_pos[i] - e_neg[i] == prediction[i] - y[i];\n",
        "\n",
        "minimize mean_absolute_deviation: sum{i in I}(e_pos[i] + e_neg[i]) / card(I);"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LqIaS1NSOkH5",
        "outputId": "03f29f31-2d2d-4f19-faf3-11fddc767dae",
        "tags": []
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0.5411666021\n",
            "1578 simplex iterations\n",
            "0 barrier iterations\n",
            " \n",
            "The mean absolute deviation for a single-feature regression is 0.54117\n"
          ]
        }
      ],
      "source": [
        "def lad_fit_1(df, y_col, x_col):\n",
        "    m = AMPL()\n",
        "    m.read(\"lad_fit_1.mod\")\n",
        "\n",
        "    m.set[\"I\"] = df.index.values\n",
        "\n",
        "    m.param[\"y\"] = df[y_col]\n",
        "    m.param[\"X\"] = df[x_col]\n",
        "\n",
        "    m.solve(solver=SOLVER)\n",
        "    assert m.solve_result == \"solved\", m.solve_result\n",
        "\n",
        "    return m\n",
        "\n",
        "\n",
        "m = lad_fit_1(wines, \"quality\", \"alcohol\")\n",
        "\n",
        "print(\n",
        "    f'The mean absolute deviation for a single-feature regression is {m.obj[\"mean_absolute_deviation\"].value():0.5f}'\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bN7G8LR2OkH6"
      },
      "source": [
        "This calculation is performed for all variables to determine which variables are the best candidates to explain deviations in wine quality."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "KtwpP6g6OkH6",
        "outputId": "d1dec062-7807-45ec-b741-57320d238e1b",
        "tags": []
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0.6579111945\n",
            "1494 simplex iterations\n",
            "0 barrier iterations\n",
            " \n",
            "HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0.5980365332\n",
            "1642 simplex iterations\n",
            "0 barrier iterations\n",
            " \n",
            "HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0.6457762063\n",
            "1584 simplex iterations\n",
            "0 barrier iterations\n",
            " \n",
            "HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0.6579111945\n",
            "1508 simplex iterations\n",
            "0 barrier iterations\n",
            " \n",
            "HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0.6517416082\n",
            "1628 simplex iterations\n",
            "0 barrier iterations\n",
            " \n",
            "HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0.6579111945\n",
            "1543 simplex iterations\n",
            "0 barrier iterations\n",
            " \n",
            "HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0.6172771025\n",
            "1706 simplex iterations\n",
            "0 barrier iterations\n",
            " \n",
            "HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0.6544712022\n",
            "1648 simplex iterations\n",
            "0 barrier iterations\n",
            " \n",
            "HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0.6579111945\n",
            "1489 simplex iterations\n",
            "0 barrier iterations\n",
            " \n",
            "HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0.6320777409\n",
            "1636 simplex iterations\n",
            "0 barrier iterations\n",
            " \n",
            "HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0.5411666021\n",
            "1578 simplex iterations\n",
            "0 barrier iterations\n",
            " \n",
            "HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0\n",
            "2 simplex iterations\n",
            "0 barrier iterations\n",
            " \n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "mad = (wines[\"alcohol\"] - wines[\"alcohol\"].mean()).abs().mean()\n",
        "vars = {}\n",
        "for i in wines.columns:\n",
        "    m = lad_fit_1(wines, \"quality\", i)\n",
        "    vars[i] = m.obj[\"mean_absolute_deviation\"].value()\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "pd.Series(vars).plot(kind=\"bar\", ax=ax, grid=True)\n",
        "ax.axhline(mad, color=\"r\", lw=3)\n",
        "ax.set_title(\"MADs for single-feature regressions\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 862
        },
        "id": "Cmv7Xs_XOkH7",
        "outputId": "8ad4ee71-a483-4e6d-a1d0-12ab8fd19a11",
        "tags": []
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "wines[\"prediction\"] = [i[1] for i in m.var[\"prediction\"].get_values()]\n",
        "wines[\"quality\"].hist(label=\"data\")\n",
        "\n",
        "wines.plot(x=\"quality\", y=\"prediction\", kind=\"scatter\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HOR2h1RPOkH8"
      },
      "source": [
        "## Multivariate $L_1$-regression"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RxhlpUQXOkH8"
      },
      "source": [
        "Let us now perform a full multivariate $L_1$-regression on the wine dataset to predict the wine quality $y$ using the provided wine features. We aim to find the coefficients $m_j$'s and $b$ that minimize the mean absolute deviation (MAD) by solving the following problem:\n",
        "\n",
        "$$\n",
        "\\begin{align*}\n",
        "\\text{MAD}\\,(\\hat{y}) = \\min_{m, \\, b} \\quad & \\frac{1}{n} \\sum_{i=1}^n | y_i - \\hat{y}_i| \\\\\n",
        "\\\\\n",
        "\\text{s. t.}\\quad & \\hat{y}_i = \\sum_{j=1}^J x_{i, j} m_j + b & \\forall i = 1, \\dots, n,\n",
        "\\end{align*}\n",
        "$$\n",
        "\n",
        "where $x_{i, j}$ are values of 'explanatory' variables, i.e., the 11 physical and chemical characteristics of the wines. By taking care of the absolute value appearing in the objective function, this can be implemented in AMPL as an LP as follows:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3D4y_-wUOkH9",
        "outputId": "cfda81b9-ecf0-4ba4-d55b-5bd154241e26"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Writing l1_fit.mod\n"
          ]
        }
      ],
      "source": [
        "%%writefile l1_fit.mod\n",
        "\n",
        "set I;\n",
        "set J;\n",
        "\n",
        "param y{I};\n",
        "param X{I, J};\n",
        "\n",
        "var a{J};\n",
        "var b;\n",
        "\n",
        "var e_pos{I} >= 0;\n",
        "var e_neg{I} >= 0;\n",
        "\n",
        "var prediction{i in I} = sum{j in J}(a[j] * X[i, j]) + b;\n",
        "\n",
        "s.t. prediction_error{i in I}: e_pos[i] - e_neg[i] == prediction[i] - y[i];\n",
        "\n",
        "minimize mean_absolute_deviation: sum{i in I}(e_pos[i] + e_neg[i]) / card(I);"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "6gdby1EjOkH9",
        "outputId": "206a9a17-1e96-4e27-b5c7-a1eaa54e9e85",
        "tags": []
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0.4997972064\n",
            "1631 simplex iterations\n",
            "0 barrier iterations\n",
            " \n",
            "MAD = 0.49980\n",
            "\n",
            "alcohol 0.3424249748641086\n",
            "citric acid -0.2892764146613565\n",
            "density -18.50082905729104\n",
            "fixed acidity 0.06381837845852499\n",
            "sulphates 0.9060911918549712\n",
            "total sulfur dioxide -0.002187357846776872\n",
            "volatile acidity -0.9806174627416928\n",
            "\n",
            "\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def l1_fit(df, y_col, x_cols):\n",
        "    m = AMPL()\n",
        "    m.read(\"l1_fit.mod\")\n",
        "\n",
        "    m.set[\"I\"] = df.index.values\n",
        "    m.set[\"J\"] = x_cols\n",
        "\n",
        "    m.param[\"y\"] = df[y_col]\n",
        "    m.param[\"X\"] = df[x_cols]\n",
        "\n",
        "    m.solve(solver=SOLVER)\n",
        "    assert m.solve_result == \"solved\", m.solve_result\n",
        "\n",
        "    return m\n",
        "\n",
        "\n",
        "m = l1_fit(\n",
        "    wines,\n",
        "    \"quality\",\n",
        "    [\n",
        "        \"alcohol\",\n",
        "        \"volatile acidity\",\n",
        "        \"citric acid\",\n",
        "        \"sulphates\",\n",
        "        \"total sulfur dioxide\",\n",
        "        \"density\",\n",
        "        \"fixed acidity\",\n",
        "    ],\n",
        ")\n",
        "print(f\"MAD = {m.obj['mean_absolute_deviation'].value():0.5f}\\n\")\n",
        "\n",
        "for k, v in m.var[\"a\"].get_values():\n",
        "    print(f\"{k} {v}\")\n",
        "print(\"\\n\")\n",
        "\n",
        "wines[\"prediction\"] = [i[1] for i in m.var[\"prediction\"].get_values()]\n",
        "wines[\"quality\"].hist(label=\"data\")\n",
        "\n",
        "wines.plot(x=\"quality\", y=\"prediction\", kind=\"scatter\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n6dANSS4OkH-"
      },
      "source": [
        "## How do these models perform?\n",
        "\n",
        "A successful regression model would demonstrate a substantial reduction from $\\text{MAD}\\,(y)$ to $\\text{MAD}\\,(\\hat{y})$. The value of $\\text{MAD}\\,(y)$ sets a benchmark for the regression. The linear regression model clearly has some capability to explain the observed deviations in wine quality. Tabulating the results of the regression using the MAD statistic we find\n",
        "\n",
        "| Regressors | MAD |\n",
        "| :--- | ---: |\n",
        "| none | 0.683 |\n",
        "| alcohol only | 0.541 |\n",
        "| all | 0.500 |\n",
        "\n",
        "Are these models good enough to replace human judgment of wine quality? The reader can be the judge."
      ]
    }
  ],
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