curve_fitting_12_11.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "collapsed_sections": [
        "TNCUZwu4YyOv",
        "idimWVgUPFbc"
      ],
      "authorship_tag": "ABX9TyPUYBKx04qNPxYNy3oY85WP",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/thinhtoohan/curvefitting/blob/main/curve_fitting_12_11.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Imports"
      ],
      "metadata": {
        "id": "G1IX-TOZXOiN"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {
        "id": "evkgS6FMHR07"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.preprocessing import PolynomialFeatures\n",
        "from scipy.optimize import minimize"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Data Initialization"
      ],
      "metadata": {
        "id": "OllSK7BLYXKJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X = np.array([0, 0.5, 1, 1.5, 1.9, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.6, 7, 7.6, 8.5, 9, 10])\n",
        "y = np.array([1, 0.9, 0.7, 1.5, 2, 2.4, 3.2, 2, 2.7, 3.5, 1, 4, 3.6, 2.7, 5.7, 4.6, 6.0, 6.8, 7.3])"
      ],
      "metadata": {
        "id": "YlZz-qi8HZcf"
      },
      "execution_count": 51,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Scatter Plot\n",
        "From the scatter plot, we can see the upward trend in y as x increases."
      ],
      "metadata": {
        "id": "p1kLjY5wYgVJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.scatter(X,y)\n",
        "ax.set_xlabel('X')\n",
        "ax.set_ylabel('Y')\n",
        "ax.set_title('X vs. Y')\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "-3Yr7ACNI2qQ",
        "outputId": "2089258b-50e2-4e8b-8ee3-90881e4adfa7"
      },
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Linear Regression"
      ],
      "metadata": {
        "id": "TNCUZwu4YyOv"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "lr = LinearRegression()\n",
        "lr.fit(X.reshape(-1,1),y.reshape(-1,1))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tDwze8WbI7fn",
        "outputId": "4f6c4fcb-e210-435d-bbd7-94c50c6dd44c"
      },
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression()"
            ],
            "text/html": [
              "<style>#sk-container-id-7 {\n",
              "  /* Definition of color scheme common for light and dark mode */\n",
              "  --sklearn-color-text: black;\n",
              "  --sklearn-color-line: gray;\n",
              "  /* Definition of color scheme for unfitted estimators */\n",
              "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
              "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
              "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
              "  --sklearn-color-unfitted-level-3: chocolate;\n",
              "  /* Definition of color scheme for fitted estimators */\n",
              "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
              "  --sklearn-color-fitted-level-1: #d4ebff;\n",
              "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
              "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
              "\n",
              "  /* Specific color for light theme */\n",
              "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
              "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-icon: #696969;\n",
              "\n",
              "  @media (prefers-color-scheme: dark) {\n",
              "    /* Redefinition of color scheme for dark theme */\n",
              "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
              "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-icon: #878787;\n",
              "  }\n",
              "}\n",
              "\n",
              "#sk-container-id-7 {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "#sk-container-id-7 pre {\n",
              "  padding: 0;\n",
              "}\n",
              "\n",
              "#sk-container-id-7 input.sk-hidden--visually {\n",
              "  border: 0;\n",
              "  clip: rect(1px 1px 1px 1px);\n",
              "  clip: rect(1px, 1px, 1px, 1px);\n",
              "  height: 1px;\n",
              "  margin: -1px;\n",
              "  overflow: hidden;\n",
              "  padding: 0;\n",
              "  position: absolute;\n",
              "  width: 1px;\n",
              "}\n",
              "\n",
              "#sk-container-id-7 div.sk-dashed-wrapped {\n",
              "  border: 1px dashed var(--sklearn-color-line);\n",
              "  margin: 0 0.4em 0.5em 0.4em;\n",
              "  box-sizing: border-box;\n",
              "  padding-bottom: 0.4em;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "#sk-container-id-7 div.sk-container {\n",
              "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
              "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
              "     so we also need the `!important` here to be able to override the\n",
              "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
              "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
              "  display: inline-block !important;\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-7 div.sk-text-repr-fallback {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              "div.sk-parallel-item,\n",
              "div.sk-serial,\n",
              "div.sk-item {\n",
              "  /* draw centered vertical line to link estimators */\n",
              "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
              "  background-size: 2px 100%;\n",
              "  background-repeat: no-repeat;\n",
              "  background-position: center center;\n",
              "}\n",
              "\n",
              "/* Parallel-specific style estimator block */\n",
              "\n",
              "#sk-container-id-7 div.sk-parallel-item::after {\n",
              "  content: \"\";\n",
              "  width: 100%;\n",
              "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
              "  flex-grow: 1;\n",
              "}\n",
              "\n",
              "#sk-container-id-7 div.sk-parallel {\n",
              "  display: flex;\n",
              "  align-items: stretch;\n",
              "  justify-content: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-7 div.sk-parallel-item {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "}\n",
              "\n",
              "#sk-container-id-7 div.sk-parallel-item:first-child::after {\n",
              "  align-self: flex-end;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-7 div.sk-parallel-item:last-child::after {\n",
              "  align-self: flex-start;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-7 div.sk-parallel-item:only-child::after {\n",
              "  width: 0;\n",
              "}\n",
              "\n",
              "/* Serial-specific style estimator block */\n",
              "\n",
              "#sk-container-id-7 div.sk-serial {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "  align-items: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  padding-right: 1em;\n",
              "  padding-left: 1em;\n",
              "}\n",
              "\n",
              "\n",
              "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
              "clickable and can be expanded/collapsed.\n",
              "- Pipeline and ColumnTransformer use this feature and define the default style\n",
              "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
              "*/\n",
              "\n",
              "/* Pipeline and ColumnTransformer style (default) */\n",
              "\n",
              "#sk-container-id-7 div.sk-toggleable {\n",
              "  /* Default theme specific background. It is overwritten whether we have a\n",
              "  specific estimator or a Pipeline/ColumnTransformer */\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "/* Toggleable label */\n",
              "#sk-container-id-7 label.sk-toggleable__label {\n",
              "  cursor: pointer;\n",
              "  display: block;\n",
              "  width: 100%;\n",
              "  margin-bottom: 0;\n",
              "  padding: 0.5em;\n",
              "  box-sizing: border-box;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "#sk-container-id-7 label.sk-toggleable__label-arrow:before {\n",
              "  /* Arrow on the left of the label */\n",
              "  content: \"▸\";\n",
              "  float: left;\n",
              "  margin-right: 0.25em;\n",
              "  color: var(--sklearn-color-icon);\n",
              "}\n",
              "\n",
              "#sk-container-id-7 label.sk-toggleable__label-arrow:hover:before {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "/* Toggleable content - dropdown */\n",
              "\n",
              "#sk-container-id-7 div.sk-toggleable__content {\n",
              "  max-height: 0;\n",
              "  max-width: 0;\n",
              "  overflow: hidden;\n",
              "  text-align: left;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-7 div.sk-toggleable__content.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-7 div.sk-toggleable__content pre {\n",
              "  margin: 0.2em;\n",
              "  border-radius: 0.25em;\n",
              "  color: var(--sklearn-color-text);\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-7 div.sk-toggleable__content.fitted pre {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-7 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
              "  /* Expand drop-down */\n",
              "  max-height: 200px;\n",
              "  max-width: 100%;\n",
              "  overflow: auto;\n",
              "}\n",
              "\n",
              "#sk-container-id-7 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
              "  content: \"▾\";\n",
              "}\n",
              "\n",
              "/* Pipeline/ColumnTransformer-specific style */\n",
              "\n",
              "#sk-container-id-7 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-7 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator-specific style */\n",
              "\n",
              "/* Colorize estimator box */\n",
              "#sk-container-id-7 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-7 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-7 div.sk-label label.sk-toggleable__label,\n",
              "#sk-container-id-7 div.sk-label label {\n",
              "  /* The background is the default theme color */\n",
              "  color: var(--sklearn-color-text-on-default-background);\n",
              "}\n",
              "\n",
              "/* On hover, darken the color of the background */\n",
              "#sk-container-id-7 div.sk-label:hover label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "/* Label box, darken color on hover, fitted */\n",
              "#sk-container-id-7 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator label */\n",
              "\n",
              "#sk-container-id-7 div.sk-label label {\n",
              "  font-family: monospace;\n",
              "  font-weight: bold;\n",
              "  display: inline-block;\n",
              "  line-height: 1.2em;\n",
              "}\n",
              "\n",
              "#sk-container-id-7 div.sk-label-container {\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "/* Estimator-specific */\n",
              "#sk-container-id-7 div.sk-estimator {\n",
              "  font-family: monospace;\n",
              "  border: 1px dotted var(--sklearn-color-border-box);\n",
              "  border-radius: 0.25em;\n",
              "  box-sizing: border-box;\n",
              "  margin-bottom: 0.5em;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-7 div.sk-estimator.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "/* on hover */\n",
              "#sk-container-id-7 div.sk-estimator:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-7 div.sk-estimator.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
              "\n",
              "/* Common style for \"i\" and \"?\" */\n",
              "\n",
              ".sk-estimator-doc-link,\n",
              "a:link.sk-estimator-doc-link,\n",
              "a:visited.sk-estimator-doc-link {\n",
              "  float: right;\n",
              "  font-size: smaller;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1em;\n",
              "  height: 1em;\n",
              "  width: 1em;\n",
              "  text-decoration: none !important;\n",
              "  margin-left: 1ex;\n",
              "  /* unfitted */\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted,\n",
              "a:link.sk-estimator-doc-link.fitted,\n",
              "a:visited.sk-estimator-doc-link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "/* Span, style for the box shown on hovering the info icon */\n",
              ".sk-estimator-doc-link span {\n",
              "  display: none;\n",
              "  z-index: 9999;\n",
              "  position: relative;\n",
              "  font-weight: normal;\n",
              "  right: .2ex;\n",
              "  padding: .5ex;\n",
              "  margin: .5ex;\n",
              "  width: min-content;\n",
              "  min-width: 20ex;\n",
              "  max-width: 50ex;\n",
              "  color: var(--sklearn-color-text);\n",
              "  box-shadow: 2pt 2pt 4pt #999;\n",
              "  /* unfitted */\n",
              "  background: var(--sklearn-color-unfitted-level-0);\n",
              "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted span {\n",
              "  /* fitted */\n",
              "  background: var(--sklearn-color-fitted-level-0);\n",
              "  border: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link:hover span {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
              "\n",
              "#sk-container-id-7 a.estimator_doc_link {\n",
              "  float: right;\n",
              "  font-size: 1rem;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1rem;\n",
              "  height: 1rem;\n",
              "  width: 1rem;\n",
              "  text-decoration: none;\n",
              "  /* unfitted */\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "}\n",
              "\n",
              "#sk-container-id-7 a.estimator_doc_link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "#sk-container-id-7 a.estimator_doc_link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "#sk-container-id-7 a.estimator_doc_link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "</style><div id=\"sk-container-id-7\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-7\" type=\"checkbox\" checked><label for=\"sk-estimator-id-7\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LinearRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Intercept and slope of the regression line are as follows."
      ],
      "metadata": {
        "id": "NK3gB9ztZt-y"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Slope: \", lr.coef_)\n",
        "print(\"Intercept: \", lr.intercept_)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0Ff5GhdxKpbY",
        "outputId": "c7112571-dcbf-45ff-e744-112f9ce4cec6"
      },
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Slope:  [[0.61077172]]\n",
            "Intercept:  [0.42612616]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Polynomial Regression\n",
        "We can fit a degree-2 polynomial to the data as well to see if it is more suited."
      ],
      "metadata": {
        "id": "idimWVgUPFbc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "poly = PolynomialFeatures(degree=2, include_bias=False)\n",
        "poly_features = poly.fit_transform(X.reshape(-1, 1))\n",
        "poly_reg_model = LinearRegression()\n",
        "poly_reg_model.fit(poly_features,y)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "BksIl8_bPIxn",
        "outputId": "678eb97e-0cdc-4552-8829-7eeb65533a47"
      },
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression()"
            ],
            "text/html": [
              "<style>#sk-container-id-8 {\n",
              "  /* Definition of color scheme common for light and dark mode */\n",
              "  --sklearn-color-text: black;\n",
              "  --sklearn-color-line: gray;\n",
              "  /* Definition of color scheme for unfitted estimators */\n",
              "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
              "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
              "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
              "  --sklearn-color-unfitted-level-3: chocolate;\n",
              "  /* Definition of color scheme for fitted estimators */\n",
              "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
              "  --sklearn-color-fitted-level-1: #d4ebff;\n",
              "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
              "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
              "\n",
              "  /* Specific color for light theme */\n",
              "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
              "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
              "  --sklearn-color-icon: #696969;\n",
              "\n",
              "  @media (prefers-color-scheme: dark) {\n",
              "    /* Redefinition of color scheme for dark theme */\n",
              "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
              "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
              "    --sklearn-color-icon: #878787;\n",
              "  }\n",
              "}\n",
              "\n",
              "#sk-container-id-8 {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "#sk-container-id-8 pre {\n",
              "  padding: 0;\n",
              "}\n",
              "\n",
              "#sk-container-id-8 input.sk-hidden--visually {\n",
              "  border: 0;\n",
              "  clip: rect(1px 1px 1px 1px);\n",
              "  clip: rect(1px, 1px, 1px, 1px);\n",
              "  height: 1px;\n",
              "  margin: -1px;\n",
              "  overflow: hidden;\n",
              "  padding: 0;\n",
              "  position: absolute;\n",
              "  width: 1px;\n",
              "}\n",
              "\n",
              "#sk-container-id-8 div.sk-dashed-wrapped {\n",
              "  border: 1px dashed var(--sklearn-color-line);\n",
              "  margin: 0 0.4em 0.5em 0.4em;\n",
              "  box-sizing: border-box;\n",
              "  padding-bottom: 0.4em;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "#sk-container-id-8 div.sk-container {\n",
              "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
              "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
              "     so we also need the `!important` here to be able to override the\n",
              "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
              "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
              "  display: inline-block !important;\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-8 div.sk-text-repr-fallback {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              "div.sk-parallel-item,\n",
              "div.sk-serial,\n",
              "div.sk-item {\n",
              "  /* draw centered vertical line to link estimators */\n",
              "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
              "  background-size: 2px 100%;\n",
              "  background-repeat: no-repeat;\n",
              "  background-position: center center;\n",
              "}\n",
              "\n",
              "/* Parallel-specific style estimator block */\n",
              "\n",
              "#sk-container-id-8 div.sk-parallel-item::after {\n",
              "  content: \"\";\n",
              "  width: 100%;\n",
              "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
              "  flex-grow: 1;\n",
              "}\n",
              "\n",
              "#sk-container-id-8 div.sk-parallel {\n",
              "  display: flex;\n",
              "  align-items: stretch;\n",
              "  justify-content: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  position: relative;\n",
              "}\n",
              "\n",
              "#sk-container-id-8 div.sk-parallel-item {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "}\n",
              "\n",
              "#sk-container-id-8 div.sk-parallel-item:first-child::after {\n",
              "  align-self: flex-end;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-8 div.sk-parallel-item:last-child::after {\n",
              "  align-self: flex-start;\n",
              "  width: 50%;\n",
              "}\n",
              "\n",
              "#sk-container-id-8 div.sk-parallel-item:only-child::after {\n",
              "  width: 0;\n",
              "}\n",
              "\n",
              "/* Serial-specific style estimator block */\n",
              "\n",
              "#sk-container-id-8 div.sk-serial {\n",
              "  display: flex;\n",
              "  flex-direction: column;\n",
              "  align-items: center;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  padding-right: 1em;\n",
              "  padding-left: 1em;\n",
              "}\n",
              "\n",
              "\n",
              "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
              "clickable and can be expanded/collapsed.\n",
              "- Pipeline and ColumnTransformer use this feature and define the default style\n",
              "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
              "*/\n",
              "\n",
              "/* Pipeline and ColumnTransformer style (default) */\n",
              "\n",
              "#sk-container-id-8 div.sk-toggleable {\n",
              "  /* Default theme specific background. It is overwritten whether we have a\n",
              "  specific estimator or a Pipeline/ColumnTransformer */\n",
              "  background-color: var(--sklearn-color-background);\n",
              "}\n",
              "\n",
              "/* Toggleable label */\n",
              "#sk-container-id-8 label.sk-toggleable__label {\n",
              "  cursor: pointer;\n",
              "  display: block;\n",
              "  width: 100%;\n",
              "  margin-bottom: 0;\n",
              "  padding: 0.5em;\n",
              "  box-sizing: border-box;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "#sk-container-id-8 label.sk-toggleable__label-arrow:before {\n",
              "  /* Arrow on the left of the label */\n",
              "  content: \"▸\";\n",
              "  float: left;\n",
              "  margin-right: 0.25em;\n",
              "  color: var(--sklearn-color-icon);\n",
              "}\n",
              "\n",
              "#sk-container-id-8 label.sk-toggleable__label-arrow:hover:before {\n",
              "  color: var(--sklearn-color-text);\n",
              "}\n",
              "\n",
              "/* Toggleable content - dropdown */\n",
              "\n",
              "#sk-container-id-8 div.sk-toggleable__content {\n",
              "  max-height: 0;\n",
              "  max-width: 0;\n",
              "  overflow: hidden;\n",
              "  text-align: left;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-8 div.sk-toggleable__content.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-8 div.sk-toggleable__content pre {\n",
              "  margin: 0.2em;\n",
              "  border-radius: 0.25em;\n",
              "  color: var(--sklearn-color-text);\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-8 div.sk-toggleable__content.fitted pre {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-8 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
              "  /* Expand drop-down */\n",
              "  max-height: 200px;\n",
              "  max-width: 100%;\n",
              "  overflow: auto;\n",
              "}\n",
              "\n",
              "#sk-container-id-8 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
              "  content: \"▾\";\n",
              "}\n",
              "\n",
              "/* Pipeline/ColumnTransformer-specific style */\n",
              "\n",
              "#sk-container-id-8 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-8 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator-specific style */\n",
              "\n",
              "/* Colorize estimator box */\n",
              "#sk-container-id-8 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-8 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-8 div.sk-label label.sk-toggleable__label,\n",
              "#sk-container-id-8 div.sk-label label {\n",
              "  /* The background is the default theme color */\n",
              "  color: var(--sklearn-color-text-on-default-background);\n",
              "}\n",
              "\n",
              "/* On hover, darken the color of the background */\n",
              "#sk-container-id-8 div.sk-label:hover label.sk-toggleable__label {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "/* Label box, darken color on hover, fitted */\n",
              "#sk-container-id-8 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
              "  color: var(--sklearn-color-text);\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Estimator label */\n",
              "\n",
              "#sk-container-id-8 div.sk-label label {\n",
              "  font-family: monospace;\n",
              "  font-weight: bold;\n",
              "  display: inline-block;\n",
              "  line-height: 1.2em;\n",
              "}\n",
              "\n",
              "#sk-container-id-8 div.sk-label-container {\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              "/* Estimator-specific */\n",
              "#sk-container-id-8 div.sk-estimator {\n",
              "  font-family: monospace;\n",
              "  border: 1px dotted var(--sklearn-color-border-box);\n",
              "  border-radius: 0.25em;\n",
              "  box-sizing: border-box;\n",
              "  margin-bottom: 0.5em;\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-0);\n",
              "}\n",
              "\n",
              "#sk-container-id-8 div.sk-estimator.fitted {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-0);\n",
              "}\n",
              "\n",
              "/* on hover */\n",
              "#sk-container-id-8 div.sk-estimator:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-2);\n",
              "}\n",
              "\n",
              "#sk-container-id-8 div.sk-estimator.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-2);\n",
              "}\n",
              "\n",
              "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
              "\n",
              "/* Common style for \"i\" and \"?\" */\n",
              "\n",
              ".sk-estimator-doc-link,\n",
              "a:link.sk-estimator-doc-link,\n",
              "a:visited.sk-estimator-doc-link {\n",
              "  float: right;\n",
              "  font-size: smaller;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1em;\n",
              "  height: 1em;\n",
              "  width: 1em;\n",
              "  text-decoration: none !important;\n",
              "  margin-left: 1ex;\n",
              "  /* unfitted */\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted,\n",
              "a:link.sk-estimator-doc-link.fitted,\n",
              "a:visited.sk-estimator-doc-link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
              ".sk-estimator-doc-link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover,\n",
              "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
              ".sk-estimator-doc-link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "/* Span, style for the box shown on hovering the info icon */\n",
              ".sk-estimator-doc-link span {\n",
              "  display: none;\n",
              "  z-index: 9999;\n",
              "  position: relative;\n",
              "  font-weight: normal;\n",
              "  right: .2ex;\n",
              "  padding: .5ex;\n",
              "  margin: .5ex;\n",
              "  width: min-content;\n",
              "  min-width: 20ex;\n",
              "  max-width: 50ex;\n",
              "  color: var(--sklearn-color-text);\n",
              "  box-shadow: 2pt 2pt 4pt #999;\n",
              "  /* unfitted */\n",
              "  background: var(--sklearn-color-unfitted-level-0);\n",
              "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link.fitted span {\n",
              "  /* fitted */\n",
              "  background: var(--sklearn-color-fitted-level-0);\n",
              "  border: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "\n",
              ".sk-estimator-doc-link:hover span {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
              "\n",
              "#sk-container-id-8 a.estimator_doc_link {\n",
              "  float: right;\n",
              "  font-size: 1rem;\n",
              "  line-height: 1em;\n",
              "  font-family: monospace;\n",
              "  background-color: var(--sklearn-color-background);\n",
              "  border-radius: 1rem;\n",
              "  height: 1rem;\n",
              "  width: 1rem;\n",
              "  text-decoration: none;\n",
              "  /* unfitted */\n",
              "  color: var(--sklearn-color-unfitted-level-1);\n",
              "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
              "}\n",
              "\n",
              "#sk-container-id-8 a.estimator_doc_link.fitted {\n",
              "  /* fitted */\n",
              "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
              "  color: var(--sklearn-color-fitted-level-1);\n",
              "}\n",
              "\n",
              "/* On hover */\n",
              "#sk-container-id-8 a.estimator_doc_link:hover {\n",
              "  /* unfitted */\n",
              "  background-color: var(--sklearn-color-unfitted-level-3);\n",
              "  color: var(--sklearn-color-background);\n",
              "  text-decoration: none;\n",
              "}\n",
              "\n",
              "#sk-container-id-8 a.estimator_doc_link.fitted:hover {\n",
              "  /* fitted */\n",
              "  background-color: var(--sklearn-color-fitted-level-3);\n",
              "}\n",
              "</style><div id=\"sk-container-id-8\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-8\" type=\"checkbox\" checked><label for=\"sk-estimator-id-8\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LinearRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Regression Coefficients: \", poly_reg_model.coef_)\n",
        "print(\"Intercept: \", poly_reg_model.intercept_)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-NUqWSe6PosT",
        "outputId": "1ed66080-4076-440f-9937-3b46955b5482"
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Regression Coefficients:  [0.16803115 0.04580581]\n",
            "Intercept:  1.1036336950108052\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Plot with both fitted models"
      ],
      "metadata": {
        "id": "i61MPW9_bCsC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots()\n",
        "\n",
        "ax.scatter(X,y)\n",
        "\n",
        "X_ = np.arange(0,11,0.5).reshape(-1,1)\n",
        "ax.plot(X,((lr.coef_*X)+lr.intercept_).reshape(-1,1),\"g-\",label=\"Linear Regression\")\n",
        "y_predicted = poly_reg_model.predict(poly_features)\n",
        "ax.plot(X,y_predicted,\"r--\",label=\"Polynomial Regression\")\n",
        "\n",
        "ax.set_xlabel('X')\n",
        "ax.set_ylabel('Y')\n",
        "ax.set_title('X vs. Y')\n",
        "ax.legend()\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "ugEEUl9nQfTq",
        "outputId": "c504a200-85f0-46f9-ca76-b65f0f69fe2f"
      },
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Linear Fit Minimizing Sum of Absolute Deviations"
      ],
      "metadata": {
        "id": "RCw9Ce5GNFWs"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def lad(params, x, y):\n",
        "    m, b = params\n",
        "    y_pred = (m * x) + b\n",
        "    return np.sum(np.absolute(y - y_pred))\n",
        "\n",
        "def linear_regression_minimization(x, y):\n",
        "    initial_guess = [0, 0]\n",
        "\n",
        "    # Minimize the MSE function\n",
        "    result = minimize(lad, initial_guess, args=(x, y),tol=1e-5,method='Nelder-Mead')\n",
        "\n",
        "    if result.success:\n",
        "        return result.x  # Returns [m, b]\n",
        "    else:\n",
        "        raise RuntimeError(\"Minimization did not converge\")\n",
        "\n",
        "m, b = linear_regression_minimization(X, y)\n",
        "print(f\"Slope (m): {m:.4f}\")\n",
        "print(f\"Intercept (b): {b:.4f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YtT9a0eHfXYi",
        "outputId": "3fcd2b96-446f-4449-d837-63ae29ddb398"
      },
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Slope (m): 0.6375\n",
            "Intercept (b): 0.5812\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Linear Fit Minimizing Maximum Absolute Deviation"
      ],
      "metadata": {
        "id": "Tc9A_bvrNUlU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def max_deviation(params, x, y):\n",
        "    m, b = params\n",
        "    y_pred = (m * x) + b\n",
        "    return np.max(np.absolute(y - y_pred))  # Max absolute deviation\n",
        "\n",
        "def linear_regression_minimization_max_deviation(x, y):\n",
        "    initial_guess = [0, 0]\n",
        "\n",
        "    # Minimize the maximum deviation function\n",
        "    result = minimize(\n",
        "        max_deviation,\n",
        "        initial_guess,\n",
        "        args=(x,y),\n",
        "        tol=1e-5,\n",
        "        method='Nelder-Mead'\n",
        "    )\n",
        "\n",
        "    if result.success:\n",
        "        return result.x  # Returns [m, b]\n",
        "    else:\n",
        "        raise RuntimeError(f\"Minimization did not converge: {result.message}\")\n",
        "\n",
        "\n",
        "m, b = linear_regression_minimization_max_deviation(X, y)\n",
        "print(f\"Slope (m): {m:.4f}\")\n",
        "print(f\"Intercept (b): {b:.4f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ri6d9yiCGO-N",
        "outputId": "82a69fb6-5b75-403b-a9d2-e53bf90aaa6e"
      },
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Slope (m): 0.6250\n",
            "Intercept (b): -0.4000\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Polynomial Fit Minimizing Sum of Absolute Deviations"
      ],
      "metadata": {
        "id": "S-hUox4rNtXn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def poly_lad(params, x, y):\n",
        "    b_1, b_2, b_3 = params\n",
        "    y_pred = b_1 * x**2 + b_2 * x + b_3\n",
        "    return np.sum(np.absolute(y - y_pred))\n",
        "\n",
        "def polynomial_regression_minimization(x, y):\n",
        "    initial_guess = [0, 0, 0]\n",
        "\n",
        "    # Minimize the MSE function\n",
        "    result = minimize(poly_lad, initial_guess, args=(x, y),method='SLSQP')\n",
        "\n",
        "    if result.success:\n",
        "        return result.x  # Returns [m, b]\n",
        "    else:\n",
        "        raise RuntimeError(\"Minimization did not converge\")\n",
        "\n",
        "b_1,b_2,b_3 = polynomial_regression_minimization(X, y)\n",
        "print(f\"Coefficient (a): {b_1:.4f}\")\n",
        "print(f\"Coefficient (b): {b_2:.4f}\")\n",
        "print(f\"Intercept (c): {b_3:.4f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rkWUB0HFZKp5",
        "outputId": "808b287f-bfef-4ee4-cabd-d5cd6ab12c11"
      },
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Coefficient (a): 0.0348\n",
            "Coefficient (b): 0.2887\n",
            "Intercept (c): 0.9885\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Polynomial Fit Minimizing Maximum Absolute Deviation"
      ],
      "metadata": {
        "id": "2F_-J8CzNzAP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def poly_max_deviation(params, x, y):\n",
        "    b_1, b_2, b_3 = params\n",
        "    y_pred = b_1 * x**2 + b_2 * x + b_3\n",
        "    return np.max(np.absolute(y - y_pred))  # Max absolute deviation\n",
        "\n",
        "def polynomial_regression_minimization_max_deviation(x, y):\n",
        "\n",
        "    initial_guess = [0, 0, 0]\n",
        "\n",
        "    # Minimize the maximum deviation function\n",
        "    result = minimize(\n",
        "        poly_max_deviation,\n",
        "        initial_guess,\n",
        "        args=(x,y),\n",
        "        method='SLSQP'\n",
        "    )\n",
        "\n",
        "    if result.success:\n",
        "        return result.x\n",
        "    else:\n",
        "        raise RuntimeError(f\"Minimization did not converge: {result.message}\")\n",
        "\n",
        "\n",
        "b_1, b_2, b_3 = polynomial_regression_minimization_max_deviation(X, y)\n",
        "print(f\"Coefficient (a): {b_1:.4f}\")\n",
        "print(f\"Coefficient (b): {b_2:.4f}\")\n",
        "print(f\"Intercept (c): {b_3:.4f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1j3DRdM7d8Nx",
        "outputId": "45c4eb0a-5816-4c9c-8f73-84b4636afe29"
      },
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Coefficient (a): 0.1260\n",
            "Coefficient (b): -0.6301\n",
            "Intercept (c): 2.4781\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots()\n",
        "\n",
        "ax.scatter(X,y)\n",
        "\n",
        "X_ = np.arange(0,11,0.5).reshape(-1,1)\n",
        "\n",
        "ax.plot(X,((0.6375*X)+0.5812).reshape(-1,1),\"g-\",label=\"Linear Fit(Min SAD)\")\n",
        "ax.plot(X,((0.625*X)-0.4).reshape(-1,1),\"m-\",label=\"Linear Fit(Min MAD)\")\n",
        "ax.plot(X,((0.0348*(X**2))+(0.2887*X)+0.9885).reshape(-1,1),\"b--\",label=\"Polynomial Fit(Min SAD)\")\n",
        "ax.plot(X,((0.126*(X**2))-(0.6301*X)+2.4781).reshape(-1,1),\"r--\",label=\"Polynomial Fit(Min MAD)\")\n",
        "ax.set_xlabel('X')\n",
        "ax.set_ylabel('Y')\n",
        "ax.set_title('X vs. Y')\n",
        "ax.legend()\n",
        "plt.title(\"Comparison of Linear Fit and Polynomial Fit Curves\")\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "rBtLct7pjA_h",
        "outputId": "3d53c08e-3404-443f-afdb-0adca6022cc4"
      },
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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SpUoVGjRowPr16xk8eDAA69evp1GjRhnuC4Z85kNDQ3F3d8/w5ZtVWV70nvKsnLx/hipbtmy+fOZyer/Ojcz+vrp168a4cePYtGkTU6ZMQQjB5s2badeuna5M//zzDwD9+/fPMu+oqCicnJyyvbcWZTJQyQf29va4u7tz8eLFHO1n6B9xViMqstounuk8Z4jDhw/z1ltv8frrr7N06VLc3NwwMzMjKCiIDRs2ZEj/vBEi6XXv3p1mzZqxbds2du/ezZdffsmcOXPYunUr7dq1y3E5X6bRJYa8f1qtlpo1azJv3rxM06Z9sdy8eZM33niDKlWqMG/ePDw8PDA3N2fHjh3Mnz8/w3BSQ9+/gpDTz15efu6fJ7+Ds379+jF69Gju3r1LUlISf/75J0uWLMm0HHktL+8pOX3/jC2n9+us7tPP68Cf2d+Xu7s7zZo148cff2TKlCn8+eef3L59mzlz5ujSpP2dfvnll1kOs7a1tQXy/t5amMhAJZ907NiRb7/9luPHj+s102TGy8sLrVbLP//8o/vFA3D//n2ePn2Kl5dXnpZNq9Vy69YtXS0KwPXr1wF01b8//fQTlpaW/P7773rzYQQFBb3w8d3c3BgxYgQjRowgMjKSunXrMmvWLNq1a6c712vXrumaM9Jcu3Ytz65F+uOk/8WRnJxMcHBwvn4hvYjy5ctz7tw53njjjecGttu3bycpKYlff/1V79dy+qahgpSTX9J5/dlzdnbGyspK9+s0vWvXruUqz8x4eXlx/vx5tFqtXq3K1atXda8/T48ePRg3bhwbN24kISEBMzMz3nvvvVyXZe/evcTExOjVqhhalheRn/cOQ+W05iYn92snJycAvdGB8Pwas6y89957jBgxgmvXrrFp0yasra3p1KmT7vW0Jk17e3uD7knPu7cWZbKPSj755JNPsLGxYciQIdy/fz/D6zdv3mThwoUAtG/fHoAFCxbopUn71dyhQ4c8L1/6X2pCCJYsWYKZmRlvvPEGoPySUqlUer8SQkJC+Pnnn3N9TI1Gk6FvhIuLC+7u7rrq4fr16+Pi4sI333yjV2W8c+dOrly5kmfXolWrVpibm7No0SK9X4crV64kKioqX655XujevTthYWGsWLEiw2sJCQnExcUB//0STn9uUVFRBfplkZ6NjU2GG3tW8vqzp1aradOmDT///DO3b9/Wbb9y5Qq///57rvLMTPv27YmIiGDTpk26bampqSxevBhbW1uaN2/+3P1LlSpFu3btWLduHevXr6dt27aUKlUq12XRaDQZamTmz5+PSqXK1y+u/Lh35FTaPCWGfuZycr+2t7enVKlSHDp0SC/N0qVLc1zOd955B7VazcaNG9m8eTMdO3bUm2OlXr16lC9fnrlz5xIbG5th/wcPHgCG3VuLMlmjkk/Kly/Phg0beO+996hatareTIfHjh1j8+bNulk6a9euTf/+/fn22295+vQpzZs35+TJk6xZs4YuXbrg6+ubp2WztLRk165d9O/fn1dffZWdO3fy22+/MWXKFF3bd4cOHZg3bx5t27alV69eREZG8vXXX1OhQgW9PhM5ERMTQ9myZXn33XepXbs2tra27N27l1OnTuk6YpqZmTFnzhwGDhxI8+bN6dmzJ/fv32fhwoV4e3szduzYPLkGzs7OTJ48mYCAANq2bctbb73FtWvXWLp0KQ0aNHjuZGaGmDdvHtbW1nrbTExMmDJlygvl27dvX3788Uc++OAD9u/fT9OmTdFoNFy9epUff/xRNxfKm2++ibm5OZ06dWLYsGHExsayYsUKXFxcCA8Pf6Ey5Ea9evVYtmwZM2fOpEKFCri4uGSoMUuTH5+9gIAAdu3aRbNmzRgxYoQugKhevXqu83zW+++/z/LlyxkwYAB//fUX3t7ebNmyhaNHj7JgwQKDOmv269ePd999F4AZM2bkuiydOnXC19eXTz/9lJCQEGrXrs3u3bv55ZdfGDNmjF7n47yWH+9fTpUvXx5HR0e++eYb7OzssLGx4dVXX82yL1ZO7tcAQ4YMYfbs2QwZMoT69etz6NAhXa10Tri4uODr68u8efOIiYnJUINmYmLCd999R7t27ahevToDBw6kTJkyhIWFsX//fuzt7dm+fbtB99YizWjjjYqJ69evi6FDhwpvb29hbm4u7OzsRNOmTcXixYt1cwAIIURKSooICAgQPj4+wszMTHh4eIjJkyfrpRFCGc6Xfox9GiDD0LS0YXRffvmlblvaMMubN2/q5uMoXbq08PPz0xumK4QQK1euFBUrVhQWFhaiSpUqIigoSDfcLrtjp38tbbheUlKS+Pjjj0Xt2rWFnZ2dsLGxEbVr1850zpNNmzaJOnXqCAsLC1GiRAnRu3dvcffuXb00Wc1tkVkZs7JkyRJRpUoVYWZmJkqXLi2GDx+uN1dL+vxyMjw5s4darRZCZD08uXr16hnyy2zoZ3JyspgzZ46oXr26sLCwEE5OTqJevXoiICBAREVF6dL9+uuvolatWsLS0lJ4e3uLOXPmiFWrVmUYXprVZyorWV33NJkNT46IiBAdOnQQdnZ2ekOZs/Kin73Mhr0ePHhQ1KtXT5ibm4ty5cqJb775xuDPSnbnnOb+/fti4MCBolSpUsLc3FzUrFnToGGsaZKSkoSTk5NwcHDQG56fXTkyO4+YmBgxduxY4e7uLszMzETFihXFl19+qTfMNa0shtw7hPjvs7t582a9Mj37GTX0/cvJ8OTnDb19dniyEEL88ssvolq1asLU1NTgocqG3q/j4+PF4MGDhYODg7CzsxPdu3cXkZGRWQ5Pft69Y8WKFQIQdnZ2mb7nQgjx999/i65du4qSJUsKCwsL4eXlJbp37y7++OMPIUTO7q1FkUqIPO5xJhVqAwYMYMuWLZlWI0qSZFypqam4u7vTqVMnVq5caeziSFKhIPuoSJIkFRI///wzDx48yLD4niQVZ7KPiiRJkpGdOHGC8+fPM2PGDOrUqZNtx1tJKk5kjYokSZKRLVu2jOHDh+Pi4sL3339v7OJIUqEi+6hIkiRJklRoyRoVSZIkSZIKLRmoSJIkSZJUaBXpzrRarZZ79+5hZ2f3QotdSZIkSZJUcIQQxMTE4O7unmEhz2cV6UDl3r17GVb3lCRJkiSpaLhz547eKuSZKdKBStqU1Hfu3NEti51XUlJS2L17N2+++SZmZmZ5mrf0H3mdC4a8zgVDXueCIa9zwcmvax0dHY2Hh4dBS0sU6UAlrbnH3t4+XwIVa2tr7O3t5R9CPpLXuWDI61ww5HUuGPI6F5z8vtaGdNuQnWklSZIkSSq0ZKAiSZIkSVKhJQMVSZIkSZIKrSLdR8VQGo2GlJSUHO2TkpKCqakpiYmJaDSafCqZJK9zwciv62xmZoZarc6z/CRJkp71UgcqQggiIiJ4+vRprvZ1dXXlzp07co6WfCSvc8HIz+vs6OiIq6urfP8kScoXL3WgkhakuLi4YG1tnaMbqVarJTY2Fltb22wno5FyT17ngpEf11kIQXx8PJGRkQC4ubnlSb6SJEnpvbSBikaj0QUpJUuWzPH+Wq2W5ORkLC0t5RdoPpLXuWDk13W2srICIDIyEhcXF9kMJElSnntpvxnS+qRYW1sbuSSS9HJL+xvLaT8wSZIkQ7y0gUoa2W4uSflL/o1JkpSfXvpARZIkSZKkoksGKkWQSqXi559/NnYxciwkJASVSsXZs2ezTfvo0SNcXFwICQnJ1bEOHDiASqXK1YgvY0pOTsbb25vTp08buyiSJEmFggxUCqEBAwbQpUuXLF8PDw+nXbt2BVegHFKpVBker732Gh4eHoSHh1OjRg1ACSbUajVRUVEZ8pg1axadO3fG29sb+C/IUavVhIWF6aUNDw/H1NQUlUqlC2yaNGlCeHg4Dg4OL3Qu27Zto1GjRjg4OGBnZ0f16tUZM2ZMpmnbtGmDWq3m1KlTGV4bMGCA7lqYmZlRunRpWrduzapVq9Bqtbp05ubmTJgwgYkTJ75QuSVJkl4WMlApglxdXbGwsDBqGYQQpKamZvl6UFAQ4eHhusevv/6KWq3G1dUVU9PnDzaLj49n5cqVDB48OMNrZcqU4fvvv9fbtmbNGsqUKaO3zdzc/IXn9vjjjz947733eOeddzh58iR//fUXs2bNyrTT6O3btzl27BgjR45k1apVmebXtm1bwsPDCQkJYefOnfj6+jJ69Gg6duyody179+7NkSNHuHTpUq7LLkmS9LKQgUoRlL7pJ62mYevWrfj6+mJtbU3t2rU5fvy43j5HjhyhWbNmWFlZ4eHhwahRo4iLi9O9vnbtWurXr4+dnR2urq706tVLNz8G/NeUsnPnTurVq4eFhQVHjhzJsoxpk4ClPUqUKKHX9BMSEoKvry8A3t7eqNVqBgwYAMCOHTuwsLCgUaNGGfLt378/QUFBetuCgoLo37+/3rZnm35Wr16No6Mjv//+O1WrVsXW1lYXOGRl+/btNG3alI8//pjKlStTqVIlunTpwtdff50hbVBQEB07dmT48OFs3LiRhISEDGksLCxwdXWlTJky1K1blylTpvDLL7+wc+dOVq9erUvn5ORE06ZN+eGHH7IsmyRJUnFRrAIVIQRxyXGGP1JykPY5DyFEvp/bp59+yoQJEzh79iyVKlWiZ8+eul/pN2/epG3btrzzzjucP3+eTZs2ceTIEUaOHKnbPyUlhRkzZnDu3Dl+/vlnQkJCdIFDepMmTWL27NlcuXKFWrVq5bq8Hh4e/PTTTwCcOnWKsLAwFi5cCMDhw4epV69epvu99dZbPHnyRBckHTlyhCdPntCpU6dsjxkfH8/cuXNZu3Ythw4d4vbt20yYMCHL9K6urly6dImLFy8+N18hBEFBQfTp04cqVapQoUIFtmzZkm15AFq2bEnt2rXZunWr3vaGDRty+PBhg/KQJEnKcyEhMGAAPH5s7JK8vBO+ZSY+JR7bz20L/Lixk2OxMbfJ12NMmDCBDh06ABAQEED16tW5ceMGVapU4fPPP6d37966vhUVK1Zk0aJFNG/enGXLlmFpacmgQYN0eZUrV45FixbRoEED3WymaQIDA2ndunW25enZs6fe5F/r1q3jlVde0T1Xq9WUKFECAGdnZ1xdXXUTkYWGhuLu7p5pvmZmZvTp04dVq1bx2muvsWrVKvr06YOZmVm2ZUpJSeGbb76hfPnyAIwcOZLAwMAs03/00UccPnyYmjVr4uXlRaNGjXjzzTfp3bu3XtPb3r17iY+Pp02bNgD06dOHlStX0rdv32zLBFClShXOnz+vt83d3Z3Q0FCD9pckScpTGg307QtHjqCOiYF+/YxanGJVo/IyS1+7kTaVeVrTzblz51i9ejW2tra6R5s2bdBqtQQHBwPw119/0alTJzw9PbGzs6N58+aA0vcivfr16xtUnvnz53P27Fndw5DgJk1CQgKWlpZZvj5o0CA2b95MREQEmzdv1guynsfa2loXpIByndI3bz3LxsaG3377jRs3bjB16lRsbW0ZP348DRs2JD4+Xpdu1apVvPfee7q+Nz179uTo0aPcvHnToHIJITL0pbGystI7hiRJUoH58ks4cgRsbdF8/rmxS1O8alSszayJnRxrUFqtVkt0TDT2dvYvPOW4tVn+z46bvkYh7UsvbTRJbGwsw4YNY9SoURn28/T0JC4ujjZt2tCmTRvWr1+Ps7Mzt2/fpk2bNiQnJ+ult7ExrGbI1dWVChUq6G178OCBQfuWKlWKJ0+eZPl6zZo1qVKlCj179qRq1arUqFHDoCHPz9a6qFQqg5rlypcvT/ny5RkyZAiffvoplSpVYtOmTQwcOJDHjx+zbds2UlJSWLZsmW4fjUbDqlWrmDVrVrb5X7lyBR8fH71tjx8/xtnZOdt9JUmS8tTff8P06cr/Fy0CHx+4csWoRSpWgYpKpTK4CUar1aIx02BjblPk16CpW7culy9fzhA4pLlw4QKPHj1i9uzZeHh4ABTIPB7m5uaA8qWeXp06dVi3bt1z9x00aBAjRozQCw4Kgre3N9bW1rqOyOvXr6ds2bIZ5rXZvXs3X331FYGBgc9d/2bfvn1cuHCBsWPH6m2/ePEiderUyfPyS5IkZSkhAfr0gZQUePttpY/Kc0Z3FpRiFagUJVFRURlqCUqWLKkLJHJi4sSJNGrUiJEjRzJkyBBsbGy4fPkye/bsYcmSJXh6emJubs7ixYv54IMPuHjxIjNmzMijM8mal5cXKpWK33//na5du2JjY6Nrlpo8eTJPnjzByckp032HDh1Kt27dcHR0zLfy+fv7Ex8fT/v27fHy8uLp06csWrSIlJQUXVPWypUreffdd3Vzw6Tx8PBg8uTJ7Nq1S9d3KCkpiYiICDQaDffv32fXrl18/vnndOzYkX7PtAEfPny4QN4DSZIkncmT4fJlKF0ali+HQrI8RtGuKniJHThwgDp16ug9AgICcpVXrVq1OHjwINevX6dZs2bUqVOH6dOn6zqsOjs7s3r1ajZv3ky1atWYPXs2c+fOzcvTyVSZMmXw9/cnICAANzc33SikmjVrUrduXX788ccs9zU1NaVUqVLZzsnyIpo3b86tW7fo168fVapUoV27dkRERLB7924qV67MX3/9xblz53jnnXcy7Ovg4MAbb7zBypUrddt27dqFm5sb3t7etG3blv3797No0SJ++eUXvVqX48ePExUVxbvvvptv5yZJkqQnOhrSRh+uWgWFqOlZJQpi7Gw+iY6OxsHBgaioKOzt7fVeS0xMJDg4GB8fn+d2zMyKVqslOjoae/sX76MiZS2r6/zbb7/x8ccfc/HixWJ3/d977z1q167NlClT8izP/Pw8v+jf2sskJSWFHTt20L59e4NGokm5I69zPnnyBH75RWny+Vd+XevnfX8/Szb9SIVShw4d+OeffwgLC8tVc1dRlZycTM2aNTP0WZEkScp3Tk56QUphIQMVqdDKak2dl5m5uTlTp041djEkSSoufvwRYmJg0KBC0yflWTJQkSRJkqTi6PZteP99iIoCa2vo2dPYJcpU8Wr8lyRJkiQJtFqlmScqCho1gm7djF2iLMlARZIkSZKKm/nzYf9+sLGBtWshH0dQvigZqEiSJElScXLhAqSNKpw/H7KYDLSwkIGKJEmSJBUXSUnQuzckJ0PHjjBkiLFLlC0ZqEiSJElScbFvH1y8qEzo9t13hXakT3qFt1FKkiRJkqS81a4dHDyorOtTurSxS2MQWaNSBKlUqgyL4BUFISEhqFQqg1Y6fvToES4uLoSEhOTqWAcOHEClUvH06dNc7V8YJCcn4+3tXSALREqSVIw0awZvvmnsUhhMBiqF0IABA+jSpUuWr4eHh9OuXbuCK1AOqVSqDI/XXnsNDw8PwsPDdQv4HThwALVaTVRUVIY8Zs2aRefOnfH29gb+C3LUajVhYWF6acPDwzE1NUWlUukCmyZNmhAeHo6Dg0OuzyOnx0yvTZs2qNVqTp06leG1AQMG6K6LmZkZpUuXpnXr1qxatQqtVqtLZ25uzoQJE5g4cWKuz0GSJAmAWbPg+nVjlyJXZKBSBLm6umJhYWHUMgghSH3O8t9BQUGEh4frHr/++itqtRpXV9dsFxKMj49n5cqVDB48OMNrZcqU4fvvv9fbtmbNGsqUKaO3zdzcHFdXV1R50P5q6DHT3L59m2PHjjFy5EhWrVqVaZq2bdsSHh5OSEgIO3fuxNfXl9GjR9OxY0e969q7d2+OHDnCpUuXXvg8JEkqpn78EaZOhfr14dEjY5cmx2SgUgSlb/pJ+9W/detWfH19sba2pnbt2hw/flxvnyNHjtCsWTOsrKzw8PBg1KhRxMXF6V5fu3Yt9evXx87ODldXV3r16kVkZKTu9bSmlJ07d1KvXj0sLCw4cuRIlmV0dHTE1dVV9yhRooRe009ISAi+vr4AeHt7o1arGfDvGhM7duzAwsKCRo0aZci3f//+BAUF6W0LCgqif//+etuebfpZvXo1jo6O/P7771StWhVbW1tdsJAdQ4+Z/rWOHTsyfPhwNm7cSEJCQoY0FhYWuLq6UqZMGerWrcuUKVP45Zdf2LlzJ6tXr9alc3JyomnTpvzwww/ZllOSJCmDsDD44APl/6NHQ8mSxi1PLhSrQEUIgSZOU+CPglig+tNPP2XChAmcPXuWSpUq0bNnT90v85s3b9K2bVveeecdzp8/z6ZNmzhy5AgjR47U7Z+SksKMGTM4d+4cP//8MyEhIbrAIb1JkyYxe/Zsrly5Qq1atXJdXg8PD3766ScATp06RVhYGAsXLgTg8OHD1KtXL9P93nrrLZ48eaILko4cOcKTJ0/o1KlTtseMj49n7ty5rF27lkOHDnH79m0mTJiQ7X45OaYQgqCgIPr06UOVKlWoUKECW7ZsyfYYAC1btqR27dpsTVtq/V8NGzbk8OHDBuUhSZKko9XCwIHKqsj168P06cYuUa4Uq1E/2ngth20L/obfLLYZaht1vh5jwoQJdOjQAYCAgACqV6/OjRs3qFKlCp9//jm9e/fWLfJXsWJFFi1aRPPmzVm2bBmWlpYMGjRIl1e5cuVYtGgRDRo0IDY2FltbW91rgYGBtG7dOtvy9OzZE7X6v3Net24dr7zyiu65Wq2mRIkSADg7O+Pq6oqJiRI3h4aG4u7unmm+ZmZm9OnTh1WrVvHaa6+xatUq+vTpY9Dy4ykpKXzzzTeUL18egJEjRxIYGJjtfjk55t69e4mPj6dNmzYA9OnTh5UrV9K3b99sjwNQpUoVzp8/r7fN3d2d0NBQg/aXJEnSWbIE9uwBKytYtw4MuE8WRsWqRuVllr52w83NDUDXdHPu3DlWr16Nra2t7tGmTRu0Wi3BwcEA/PXXX3Tq1AlPT0/s7Oxo3rw5oPS3SK9+/foGlWf+/PmcPXtW9zAkuEmTkJCApaVllq8PGjSIzZs3ExERwebNm/WCrOextrbWBSmgXKf0zVvPY+gxV61axXvvvafrh9OzZ0+OHj3KzZs3DTqOECJDvxorKyvi4+MN2l+SJAmAy5chrSP+3LlQubJxy/MCjFqjotFo8Pf3Z926dURERODu7s6AAQOYOnVqnnSCfJaJtQnNYpsZlFar1RIdHY29vb3ul/6LHDe/pf91n3bt0kaQxMbGMmzYMEaNGpVhP09PT+Li4mjTpg1t2rRh/fr1ODs7c/v2bdq0aUNycrJeehsbG4PK4+rqSoVnpmV+8OCBQfuWKlWKJ0+eZPl6zZo1qVKlCj179qRq1arUqFHDoCHPz9aAqFQqg5vlDDnm48eP2bZtGykpKSxbtky3XaPRsGrVKmbNmpXtca5cuYKPj0+GfJ2dnQ0qpyRJEgBffQWJidC2LQwfbuzSvBCjBipz5sxh2bJlrFmzhurVq3P69GkGDhyIg4NDpl+qL0qlUhncBKPSqlBr1Kht1C8cqBhb3bp1uXz5cobAIc2FCxd49OgRs2fPxsPDA6BA5u4wNzcHlC/y9OrUqcO6deueu++gQYMYMWKEXkCQ37I75vr16ylbtmyGOW52797NV199RWBgoF5z2LP27dvHhQsXGDt2rN72ixcvUqdOnRcuvyRJxcg330C5cjBoUJGYffZ5jBqoHDt2jM6dO+v6Vnh7e7Nx40ZOnjxpzGIVClFRURl+sZcsWVIXSOTExIkTadSoESNHjmTIkCHY2Nhw+fJl9uzZw5IlS/D09MTc3JzFixfzwQcfcPHiRWbMmJFHZ5I1Ly8vVCoVv//+O127dsXGxkbXLDV58mSePHmCk5NTpvsOHTqUbt264ejomO/lNPSYK1eu5N1339XNE5PGw8ODyZMns2vXLt1nPSkpiYiICDQaDffv32fXrl18/vnndOzYkX79+untf/jw4QJ5PyRJeomYmcGnnxq7FHnCqIFKkyZN+Pbbb7l+/TqVKlXi3LlzHDlyhHnz5mWaPikpiaSkJN3z6OhoQOkkmZKSopc2JSUFIQRarVZvEi1DpTUJpOVRkIQQHDhwIMOv6EGDBrFixQoA3Xmlle3Z/6ffVqNGDfbv38/UqVNp1qwZQgjKly9P9+7d0Wq1lCxZklWrVjF16lQWLVpE3bp1+eKLL+jSpctzj/M8maV7Ng83Nzf8/PwICAjgww8/pG/fvgQFBVG9enXq1q3LDz/8wLBhwzLd18TERNcZN7PyPe95ZuXJ6hwMPeapU6c4d+4cy5cvz5CfnZ0dLVu25LvvvqNdu3YIIdi1axdubm6Ympri5ORErVq1WLBgAf3790elUunyOH78OFFRUXTt2vWFPof5+XnWarUIIUhJSXlujVFxkHYfevZ+JOUteZ2zEB2NybJlaMeOhX9rrF9Ufl3rnOSnEgUxdjYLWq2WKVOm8MUXX6BWq9FoNMyaNYvJkydnmt7f35+AgIAM2zds2IC1tbXeNlNTU1xdXfHw8NA1MUhFx++//46fnx/Hjh0r8k1vL2LQoEFUr16d8ePHG7soWUpOTubOnTtEREQ8dxJASZLyV51Fi/Dct497jRpxatIkYxfnueLj4+nVqxdRUVHY29s/N61Ra1R+/PFH1q9fz4YNG6hevTpnz55lzJgxuLu7ZzqZ1uTJkxk3bpzueXR0NB4eHrz55psZTjQxMZE7d+5ga2v73BEkWRFCEBMTg52dXb507JUUWV3nbt26ce/ePWJiYnLV3PUySE5Opk6dOowbNw4rK6sXyis/P8+JiYlYWVnx+uuv5+pv7WWSkpLCnj17aN26tUFD5qXckdc5I9W2bZju24dQqXD57DPav/ZanuSbX9c6rUXEEEYNVD7++GMmTZpEjx49AGVkRWhoKJ9//nmmgYqFhUWmU8ebmZlluIAajQaVSoWJiUmufpGnVY+n5SHlj+dd52c7lRY3lpaWTJs2LU/yys/Ps4mJiW7dIvmloZDXomDI6/yv8HAYMQIA1cSJmP4763deyutrnZO8jPoNHB8fn+GmqVarC7xPiCRJkiQVSULA4MHKGj6vvAKZdI8o6oxao9KpUydmzZqFp6cn1atX5++//2bevHkGT+AlSZIkScXaN9/Azp1gYaHMPvsS9sk0aqCyePFipk2bxogRI4iMjMTd3Z1hw4YxvYiuRyBJkiRJBSYhAfz9lf/PmQPVqxu1OPnFqIGKnZ0dCxYsYMGCBcYshiRJkiQVPVZWcPw4LFsGH31k7NLkm2K1KKEkSZIkvVTKlYMvvzR2KfKVHM4iSZIkSUXJyZOwb5+xS1FgZKAiSZIkSUVFbCz06gVvvAEbNxq7NAVCBiovodWrVxfoGjgvIiAggGbNDFvROo1Kpcqw8J+hWrRowZgxYwxK27dvXz777LNcHQeUtauKYv+rSZMm8dFL3N4tSUXauHFw8yZ4eEC7dsYuTYGQgUohNGDAAFQqFSqVCnNzcypUqEBgYOBLOT35+PHj+eWXX/I0z/TXL/3jxo0bbN26VW+Bv6yCiXPnzrFjxw69VbxbtGiBSqVi9uzZGdJ36NABlUqFf1oPfODUqVO8//77L3QuwcHB9OrVC3d3dywtLSlbtiydO3fm6tWrGdJu3LgRtVrNhx9+mOG1AwcO4OTkhFqtrAbu4OBAnTp1+OSTTwgPD9dLO2HCBNasWcOtW7deqOySJOWxX3+FFSuU1ZC//x6KyA/SFyUDlUKqbdu2hIeH888//zB+/Hj8/f358iXsMGVra6tb6C8vpV2/9A8fHx9KlCiBnZ1dtvsvXryYbt26YWtrq7fdw8OD1atX620LCwvjjz/+wM3NTW+7s7NzhjWociIlJYXWrVsTFRXF1q1buXbtGps2baJmzZo8ffo0Q/qVK1fyySefsHHjRhITEzPN88qVK9y7d49Tp04xceJE9u7dS40aNbhw4YIuTalSpWjTpg3Lli3LddklScpj9+/DkCHK/8eNgxYtjFqcgiQDlULKwsICV1dXvLy8GD58OK1ateLXX38F4MmTJ/Tr1w8nJyesra1p164d//zzT6b5hISEYGJiwunTp/W2L1iwAC8vL7RaLQcOHEClUvHHH39Qv359rK2tadKkCdeuXdPbZ9myZZQvXx5zc3MqV67M2rVr9V5XqVQsX76cjh07Ym1tTdWqVTl+/Dg3btygRYsW2NjY0KRJE27evKnb59mmn1OnTtG6dWtKlSqFg4MDzZs358yZM7m+fukfarVar+mnRYsWhIaGMnbsWF2tCyjLL2zZsoVOnTplyLdjx448fPiQo0eP6ratWbOGN998ExcXF720z9bWqFQqvvvuO95++22sra2pWLGi7j3NzKVLl7h58yZLly6lUaNGeHl50bRpU2bOnEmjRo300gYHB3Ps2DEmTZpEpUqV2Lp1a6Z5uri44OrqSqVKlejRowdHjx7F2dmZ4cOH66Xr1KkTP/zwQ5ZlkySpAAkBQ4fCgwdQsybMmmXsEhWoYhmoxMVl/Xj2h+jz0iYkZJ82r1hZWZGcnAwoTRunT5/m119/5fjx4wghaN++fabLZnt7e9OqVSuCgoL0tgcFBTFgwAC9JQw+/fRTvvrqK06fPo2pqaneDMHbtm1j9OjRjB8/nosXLzJs2DAGDhzI/v379fKdMWMG/fr14+zZs1SpUoVevXoxbNgwJk+ezOnTpxFCMHLkyCzPMyYmhv79+3PkyBH+/PNPKlasSPv27YmJicnVdXuerVu3UrZsWQIDA3W1LgDnz58nKiqK+vXrZ9jH3Nyc3r17613P1atXGzybckBAAN27d+f8+fO0b9+e3r178/jx40zTOjs7Y2JiwpYtW9BoNM/NNygoiA4dOuDg4ECfPn1YuXKlQeWxsrLigw8+4OjRo0RGRuq2N2zYkLt37xISEmJQPpIk5aO9e2H7dmXW2XXrlFloixNRhEVFRQlAREVFZXgtISFBXL58WSQkJGR4TQlPM3+0b6+k0Wg04smTJ8LaWptl2ubN9fMtVSpjmtzo37+/6Ny5sxBCCK1WK/bs2SMsLCzEhAkTxPXr1wUgjh49qkv/8OFDYWVlJX788UchhBBBQUHCwcFB9/qmTZuEk5OTSExMFEII8ddffwmVSiWCg4OFEELs379fAGLv3r26fX777TcB6K5fkyZNxNChQ/XK2a1bN9E+7YIJIQAxdepU3fPjx48LQKxcuVK3bePGjcLS0lL3fPr06aJGjRpCo9Fkei00Go2ws7MT27dv1zvOtm3bnnv91Gq1sLGx0T3effddIYQQzZs3F6NHj9al9fLyEvPnz9fbf9u2bUKtVgutVqu3PW3fs2fPCjs7OxEbGysOHjwoXFxcREpKiqhdu7bw8/PLMu9nr09sbKwAxM6dO7M8lyVLlghra2thZ2cnfH19RWBgoLh582aGa+Th4SF+/vlnIYQQDx48EObm5uLWrVu6NH/88YcAxKNHjzIcY+fOnQIQJ06c0G1L+9s6cOBAlmVL87y/teImOTlZ/PzzzyI5OdnYRXmpFbvrrNUKsXatEEuWFPih8+taP+/7+1nFskalKPjf//6Hra0tlpaWtGvXjvfeew9/f3+uXLmCqakpr776qi5tyZIlqVy5MleuXMk0ry5duqBWq9m2bRug1AD4+vri7e2tl65WrVq6/6f1t0j7lX3lyhWaNm2ql75p06YZjpk+j9KlSwPKqtjptyUmJma5xPf9+/cZOnQoFStWxMHBAXt7e2JjY7l9+3am6bPi6+vL2bNndY9FixYZvG9CQgIWFha6pqBn1a5dm4oVK7JlyxZWrVpF3759MTU1bO7E9NfHxsYGe3t7vZqMZ3344YdERESwfv16GjduzObNm6levTp79uzRpdmzZw9xcXG0b98eUPqYtG7dmlWrVhlUJiEEgN75WllZAcrCoZIkGZlKBX36QCYd5YuDYjkzbWxs1q+p1frPIyIEJiaZf2E9s/AzeVlL7uvry7JlyzA3N8fd3d3gL8LMmJub069fP4KCgujatSsbNmxg4cKFGdKlX3Y77UsrpytZZ5ZHTvLt378/jx49YuHChXh5eWFhYUHjxo11zV6GsrGxoUKFCjnaJ02pUqWIj48nOTkZ8ywW+Bo0aBBff/01ly9f5uTJkwbn/ezS5iqVKttrbGdnR6dOnejUqRMzZ86kTZs2zJw5k9atWwNKJ9rHjx/rggtQru/58+cJCAjIsEL5s9KCzfSBa1pzlLOzs8HnJklSHtu6FZo3h5IljV0SoyqWNSo2Nlk/LC0NT5vueyHLtLkvo/JF6+npqRekVK1aldTUVE6cOKHb9ujRI65du0a1atWyzG/IkCHs3buXpUuXkpqaSteuXXNUnqpVq+p1IAU4evToc4+ZG0ePHmXUqFG0b9+e6tWrY2FhwcOHD/P0GOmZm5tn6P/xyiuvAHD58uUs9+vVqxcXLlygRo0aeX4NnkelUlGlShXi/u0A9ejRI3755Rd++OEHvRqkv//+mydPnrB79+7n5peQkMC3337L66+/rheUXLx4ETMzM6q/pIucSVKhd+oUdO+udJ6NiDB2aYyqWNaoFGUVK1akc+fODB06lOXLl2NnZ8ekSZMoU6YMnTt3znK/qlWr0qhRIyZOnMigQYP0fn0b4uOPP6Z79+7UqVOHVq1asX37drZu3crevXtf9JT0VKxYkbVr11K/fn2io6P5+OOPc1zWnPD29ubQoUP06NEDCwsLSpUqhbOzM3Xr1uXIkSO6oOVZTk5OhIeHZ6ghyUtnz57Fz8+Pvn37Uq1aNczNzTl48CCrVq1i4sSJAKxdu5aSJUvSvXv3DE1V7du3Z+XKlbRt21a3LTIykuTkZGJiYvjrr7/44osvePjwYYZRQocPH6ZZs2b5eu0lScpCfLzS1KPRwOuvw7/N6MVVsaxRKeqCgoKoV68eHTt2pHHjxggh2LFjR7ZfmoMHDyY5OdngESrpdenShYULFzJ37lyqV6/O8uXLCQoKokUej+VfuXIlT548oW7duvTt25dRo0ZlGPablwIDAwkJCaF8+fJ6NQpDhgxh/fr1z93X0dERmxepNstG2bJl8fb2JiAggFdffZW6deuycOFCAgIC+PTTTwFYtWoVb7/9dqb9ad555x1+/fVXvRqpqlWr4u7uTr169Zg9ezatWrXi4sWLGWqFfvjhB4YOHZpv5yZJ0nN8/DFcvw5lysDSpUoflWJMJdJ60hVB0dHRODg4EBUVhb29vd5riYmJBAcH4+Pjg+Wz7TkG0Gq1REdHY29vn20bf1ExY8YMNm/ezPnz541dFJ3Cep0TEhKoXLkymzZtonHjxsYuzgvLyXXeuXMn48eP5/z58wb1jXrRv7WXSUpKCjt27KB9+/b5WttW3L3U13nnTvi3Yzx79kCrVkYrikYr+PNGJA+v/Empqo1oVMEFdRZ9NnPqed/fzyo83wxSvomNjeXixYssWbJEruFiICsrK77//vt87R9TWMXFxREUFPRCHbglScqFhw8hrcZ79GijBim7Lobz2px9DFpzCoBBa07x2px97LoYns2eeU8GKsXAyJEjqVevHi1atMhVs09x1aJFi0xnp33Zvfvuu3rD3yVJKiDTpikdZ6tVg88/N1oxdl0M54O1Z7iyoyzxwf+NOIqISmT4ujMFHqzIn0zFwOrVqzOsTyNJkiQVMp9/rkx5Pnp0xmGlBUSjFUzddJ37mxuQGOxCrHUSsR32AgIBqICA7ZdpXc01z5qBsiMDFUmSJEkqDBwdwcg/Ko/feMz5ZXVJeWSHylSD8xuXsbVNBZRJxgQQHpXIyeDHNC5fMPO7yKYfSZIkSTIWjUaZ2K2QjGt5FJ+IQ5MbmDrF4dr3KPY1wzJNFxmT+Qrt+UEGKpIkSZJkLF9+Ce+8A337Gq0IcXFw8aLyfxc7S2yq3cN90CHMXbJeDNbFruBG+MlARZIkSZKM4e+/Yfp05f9GGuFz7Rq8+iq0bq30423oUwI3B0tMTDNf2kMFuDlY0tCnRIGVUQYqkiRJklTQEhKgd29ISYGuXaF//wIvwpYt0KABXLqkPA8LA7WJCr9OygSQz3aVTXvu16lagXWkBRmoSJIkSVLBmzQJrlwBV1dYvrxAZ59NSYFx46BbN4iJUWbp//tvqFdPeb1tDTeW9amLq4N+846rgyXL+tSlbQ23AisryEDlpbR69WocHR2NXQyDBAQE0KxZsxzto1Kp+Pnnn3N1vBYtWjBmzBiD0vbt25fPPvssV8cBZR2hBQsW5Hr/wmDSpElykkBJymt79sCiRcr/V62CUqUK7NBhYeDrC/PnK88/+QT++EOJl9JrW8ONIxNbsqp/A6WY/RtwZGLLAg9SQAYqhdKAAQNQqVSoVCrMzc2pUKECgYGBpKamGrtoeW78+PH88ssveZpn+uuX/nHjxg22bt3KjBkzdGmzCibOnTvHjh07GDVqlG5bixYtUKlUzJ49O0P6Dh06oFKp8Pf31207deoU77///gudS06PmWbjxo2o1Wo+/PDDDK8dOHBAd01MTExwcHCgTp06fPLJJ4SH60/kNGHCBNasWcOtW7de6DwkSfpXcjIMHqz8f8QIaNeuQA8/cyYcPQr29spgozlzIKtJqNUmKl1flIY+JQq0uSc9GagUUm3btiU8PJx//vmH8ePH4+/vz5dffmnsYuU5W1tbSpTI+05Zadcv/cPHx4cSJUpgZ2eX7f6LFy+mW7du2Nra6m338PDIMHleWFgYf/zxB25u+r80nJ2dsba2fuFzyckx06xcuZJPPvmEjRs3kpiY+TDCa9euce/ePU6dOsXEiRPZu3cvNWrU4MKFC7o0pUqVok2bNixbtuyFz0OSJMDcHDZuhLZtlRE/BeyLL5Qmn9On4e23C/zwuSIDlULKwsICV1dXvLy8GD58OK1ateLXX38F4MmTJ/Tr1w8nJyesra1p164d//zzT6b5hISEYGJiwunTp/W2L1iwAC8vL7Rare4X9h9//EH9+vWxtramSZMmXLt2TW+fZcuWUb58eczNzalcuTJr167Ve12lUrF8+XI6duyItbU1VatW5fjx49y4cYMWLVpgY2NDkyZNuHnzpm6fZ5t+Tp06RevWrSlVqhQODg40b96cM2fO5Pr6pX+o1Wq9pp8WLVoQGhrK2LFjdTUMABqNhi1btmQ6fX7Hjh15+PAhR48e1W1bs2YNb775ZoZVnp+trVGpVHz33Xe8/fbbWFtbU7FiRd17+jw5OSZAcHAwx44dY9KkSVSqVImtW7dmmq+Liwuurq5UqlSJHj16cPToUZydnRk+fLheuk6dOvHDDz9kW05JkgzUtKmy+GAe/JDJzpMnMHfuf9O02NnBjz9CxYr5fug8UzwDlbi4rB/P/vp8XtqEhOzT5hErKyuSk5MBpWnj9OnT/Prrrxw/fhwhBO3btyclJSXDft7e3rRq1YqgoCC97UFBQQwYMEBvJd1PP/2Ur776itOnT2Nqaqq3LtC2bdsYPXo048eP5+LFiwwbNoyBAweyf/9+vXxnzJhBv379OHv2LFWqVKFXr14MGzaMyZMnc/r0aYQQjBw5MsvzjImJoX///hw5coQ///yTihUr0r59e2Jish7Pn1tbt26lbNmyBAYG6mpdAM6fP09UVBT169fPsI+5uTm9e/fWu56rV682eA2lgIAAunfvzvnz52nfvj29e/fm8ePHz90np8cMCgqiQ4cOODg40KdPH1auXGlQ2aysrPjggw84evQokZGRuu0NGzbk7t27hISEGJSPJEmZuH0brl4t0EOePQv168PHH//XJ6UoKp6Biq1t1o933tFLqnJ1zTrts22L3t4Z07wgIQR79+7l999/p2XLlvzzzz/8+uuvfPfddzRr1ozatWuzfv16wsLCsuxgOmTIEDZu3EhSUhIAZ86c4cKFCwwcOFAv3axZs2jevDnVqlVj0qRJHDt2TNdsMHfuXAYMGMCIESOoVKkS48aNo2vXrsydO1cvj4EDB9K9e3cqVarExIkTCQkJoXfv3rRp04aqVasyevRoDhw4kOX5tmzZkj59+lClShWqVq3Kt99+S3x8PAcPHszRdfvf//6Hra2t7tGtW7cMaUqUKIFarcbOzk5X6wIQGhqKWq3OtLYCYNCgQfz444/ExcVx6NAhoqKi6Nixo0HlGjBgAD179qRChQp89tlnxMbGcvLkyWz3M/SYWq2W1atX06dPHwB69OjBkSNHCA4ONqh8VapUAdALStzd3QHlukiSlAtJSdC9O9Stq3QMKQCrVkHjxnDrlvLV1Lx5gRw2XxTPQKUISPuitbS0pF27drz33nv4+/tz5coVTE1N9Va3LVmyJJUrV+bKlSuZ5tWlSxfUajXbtm0DlF/jvr6+eHt766WrVauW7v9pfR/SfllfuXKFpk2b6qVv2rRphmOmz6N06dIA1KxZU29bYmIi0dHRmZb1/v37DB06lIoVK+Lg4IC9vT2xsbHcvn070/RZ8fX15ezZs7rHorQe9gZISEjAwsJC1xT0rNq1a1OxYkW2bNnCqlWr6Nu3L6ZZ9UZ7RvrrY2Njg729vV7tRVYMPeaePXuIi4ujffv2gNLHpHXr1hlq1LIi/q0fTn/uVv8ujhYfH29QHpIkPWPsWDhxAiwt4ZVX8vVQCQlKX93Bg5UGgvbt4a+//ht6nBOPEx7z6f5PuR53Pe8LmgPFc1HC2NisX1Or9Z6KiAhUJlnEc89uz8OqcV9fX5YtW4a5uTnu7u4GfxFmxtzcnH79+hEUFETXrl3ZsGEDCxcuzJDOzMxM9/+0LyqtNvPZCbOSWR45ybd///48evSIhQsX4uXlhYWFBY0bN9Y1exnKxsaGChUq5GifNKVKlSI+Pp7k5GTMzc0zTTNo0CC+/vprLl++bFCNSJr01wKU62HoNTbkmCtXruTx48e64AKUa33+/HnGjRuX7THSAs/0QWxa05Szs7NB5ZQkKZ01a2DZMmWelPXroVy5fDvUrVtKo8DZs8rhZsyAyZMzflVlJzopmgV/LuCr418RnRRNLdtajGFMfhTZIMWzRsXGJuuHpaXhaZ9dhjuzNLkuovJF6+npqRekVK1aldTUVE6cOKHb9ujRI65du0a1atWyzG/IkCHs3buXpUuXkpqaSteuXXNUnqpVq+p15gQ4evToc4+ZG0ePHmXUqFG0b9+e6tWrY2FhwcOHD/P0GOmZm5uj0Wj0tr3y7y+ey5cvZ7lfr169uHDhAjVq1Mjza5DbYz569IhffvmFH374Qa826e+//+bJkyfs27fvufknJCTw7bff8vrrr+sFJRcvXsTMzIzq1avn+TlJ0kvt77/hgw8A0E6fzvFKDfnlbBjHbz5Co837RQgjIpQ1e0qVgt274dNPcxakxKfE8+XRLym3sBx+B/yUIMWlFp2cO+lqW42heNaoFGEVK1akc+fODB06lOXLl2NnZ8ekSZMoU6YMnTt3znK/qlWr0qhRIyZOnMigQYP0fnEb4uOPP6Z79+7UqVOHVq1asX37drZu3crevXtf9JT0VKxYkbVr11K/fn2io6P5+OOPc1zWnPD29ubQoUP06NEDCwsLSpUqhbOzM3Xr1uXIkSO6oOVZTk5OhIeHZ6ghyU/ZHXPt2rWULFmS7t27Z2i2ateuHevWrdMLUCMjI0lMTCQmJoa//vqLL774gocPH2YYJXT48GGaNWuWr++DJL10Hj9WqjcSE4ls9gZdzJpyb8WfupfdHCzx61QtTydQa9IENmxQ+qaULWv4fkmpSaw4s4JZh2cRERsBQJVSVQhsEchbFd9i185dWTaFF4TiWaNSxAUFBVGvXj06duxI48aNEUKwY8eObL80Bw8eTHJyssEjVNLr0qULCxcuZO7cuVSvXp3ly5cTFBREixYtcnkWmVu5ciVPnjyhbt269O3bl1GjRmXZqTUvBAYGEhISQvny5fVqEYYMGcL69eufu6+joyM2L1BrlhvPO+aqVat4++23M72hdO3alZ07d+rVTlWuXBl3d3fq1avH7NmzadWqFRcvXsxQW/PDDz8wdOjQvD0RSXrZLVoEwcHEl/Widd2h3IvRb76OiEpk+Loz7LoYnkUG2bt/Hzp1gnRTH9Gtm+FBSqo2lZVnVlJpSSU+2vkREbER+Dj6sKbLGi4Mv0C36t0wURk/TFAJY9bnvKDo6GgcHByIiorC3t5e77XExESCg4Px8fHB8tnmHANotVqio6Oxt7fXG8JblM2YMYPNmzdz/vx5YxdFp7Be54SEBCpXrsymTZto3LixsYvzwnJ7nXfu3Mn48eM5f/58lv2kXvRv7WWSkpLCjh07aN++fYHWthU3ReI6azRo/f0Z8LQsh2wyjxxUKOvnHJnYMsezvh49qgwkundPGUx0+rThywVptBo2XdqE3wE/bjy+AUAZuzJMe30aA+sMxFz9X9+8/LrWz/v+fpZs+ikGYmNjCQkJYcmSJcycOdPYxSkSrKys+P777/O1f0xREBcXR1BQ0At15pakYkmt5sSAMRxK19zzLAGERyVyMvgxjcuXNChbIWDBAmWNntRUqFoV1q0zLEgRQvDz1Z+Ztn8alx4oSyY7WzszpdkUhtUbhpVZ4WzelXefYmDkyJFs3LiRLl265KrZp7jK62atoujdd981dhEkqei4dQsWL4bZs8HCgsiYzJeveJah6aKjlWHHW7Yoz3v2hG+/zX7KLiEEv9/8nan7pvJX+F8AOFo68nGTjxn16ihszV98zq/8JAOVYmD16tUZ1oqRJEmS8lB8PHTtCufOKZOZfPMNLnaGNYUaku7ePWjZEq5dAzMzmDcPPvww+5qUgyEHmbp/KkduHwHA1tyWMa+OYXyT8ThaOhpUPmOTgYokSZIkvQghYPhwJUhxdoapUwFlxWE3B0siohLJrDNoWh+VtBWKn6d0aShTRlmZZfNmaNTo+elP3D3B1P1T2XtLGZlpaWrJhw0+ZGLTiTjbFK05kV76QKUI9xWWpCJB/o1Jxd7y5fD998qkJZs26YbdqE1U+HWqxvB1Z1CBXrCSVhHi16lalh1p/131BAsLZS7StLVBnzf34rmIc0zbP43t17cDYGZixtC6Q/n09U9xt3PP/TkaUeEZZpHH0nony2m/JSl/pf2NFdrRF5KUn06cgFGjlP/Png2+vnovt63hxrI+dXF10G/ecXWwZFmfulnOoxIaCs2aKbPvp3F2zjpIufrwKu9teY9Xlr/C9uvbMVGZMPCVgVz/6Dpfd/i6yAYp8BLXqKjVahwdHXXrqFhbW+dowhqtVktycjKJiYmFatjsy0Ze54KRH9dZCEF8fDyRkZE4Ojqifmb5CUl66UVGwrvvQkqKMrnbhAmZJmtbw43W1Vw5GfyYyJhEXOyU5p6salJ27YLevZU5427ehGnTwC2LeeGCnwQTeCiQ7899j1Yoy3H0qNED/+b+VC5VOU9O09he2kAF0K2Ga8iib88SQpCQkICVlZVRZ+R72cnrXDDy8zo7Ojrq/tYkqVi5cUNZO65KFQgKem7PVrWJKtshyBqNsj5PYKDS7aVePWWET2ZBSlh0GDMPzeS7v78jVZsKQOfKnQn0DaRW6VoZdyjCXupARaVS4ebmhouLCykpKTnaNyUlhUOHDvH666/LKu18JK9zwciv62xmZiZrUqTiq0kTZWnilBSws3uhrB4+VGpRdu9Wng8bpsyX8uwcipFxkcw5Moelp5eSmKoMa36z/JvM9J1JgzINXqgMhdVLHaikUavVOb6ZqtVqUlNTsbS0lF+g+Uhe54Ihr7Mk5aGUFGWMMOTJashaLbzxBpw/r6x1+8030K+ffponCU/46vhXLPhzAXEpcQA082zGzJYzed3r9RcuQ2EmOwVIkiRJkqGuXoWKFWHnzjzL0sREafKpVEnpm5s+SIlJimHWoVmUW1SOWYdnEZcSR333+vze53cODjj40gcpUExqVCRJkiTphcXEKJO6hYbC3LnQtq3hC+w8Iy4Orl+HOnWU52+9pWRn/u8yOwkpCSw7vYzPj3zOw3hlKY+aLjWZ4TuDtyq/Vaz69MlARZIkSZKyI4Qyf/2VK+DuDhs25DpIuXZNGSQUHg5//w2ensp2c3NI1iSz8sxKZh6eyb2YewBULFGRQN9AulfvXihWMy5oMlCRJEmSpOzMn69MCWtmpgzFKV06V9ls2QIDByqDhVxd4f59JVBJ1aay7vw6Ag4GEPI0BAAvBy/8mvvRt3ZfTE2K79d18T1zSZIkSTLEgQPKcsWgBCyNG+c4i5QUmDhR2R2geXNlplmX0lo2XdyM3wE/rj26BoCrrStTm01lSN0hWJha5NFJFF0yUJEkSZKkrNy7B++9p0xy0qcPjBiR4yxu3VJWOj55Unk+cSLMmCHYeWs7036exvn75wEoaVWSSa9NYkSDEVibWeflWRRpMlCRJEmSpKyUKAGdOyvDcZYvz1W/lMWLlSDF0RGCggQ2Nffy2pqpnAxTIhd7C3smNJ7AmEZjsLN4sflYXkYyUJEkSZKkrFhawrffQnQ0WOeuluOzz5Td2w85xfxrEzi07hAA1mbWjH51NBOaTKCEVfYrKBdXxa/7sCRJkiRl5++/leaeNPb2Bu969qwys2za7peenOZey3a8u7shh0IPYaG2YMyrYwgeHcxnb3wmg5RsyBoVSZIkSUrv/Hlo2lRZvnjLFoOnxxdCaeb5+GNITgbHsuH8U+lDtl3dBoCpiSmD6wxm6utTKWtfNj/P4KUiAxVJkiRJSvP0qTKpW0KC0h/FwOaehw+VYcf/+5/yvEz903wR2xauPsJEZUKfWn3wa+5HOacXn3K/uJGBiiRJkiSB0lbTty/cvAleXrB+PRiwTtyBA8qCgvfugdosBW3r8YQ1WAwq6FatGwEtAqjqXDX/y/+SkoGKJEmSJAkBY8cqVSIWFvDTT1CyZLa7LV0KI0cKhFBBqato3n0PXM/TsVJHZvjO4BXXV/K/7C85GahIkiRJ0rx5SgcTgDVroF69bHd5GP+QE6rvEeoRUGsttB3DG5UbM7PlcRqVbZTPBS4+ZKAiSZIkFW8PHkBgoPL/uXOVCd6e4+9LMWyL/JL5f84nNjkWRiyhSW03Zvr+D18f3wIocPEiAxVJkiSpeHN2Vjqa/PILjBuXZbIHT+Po0O86p3ZUh0E7oUwsdd3qMrPXTNpWaFusVjQuSEafRyUsLIw+ffpQsmRJrKysqFmzJqdPnzZ2sSRJkqSXnRD//b9OHTTT/Th+6zG/nA3j+M1HaLTK64mpiXyybi1uVe5wansd0JhS+vE7/NT9J04PPU27iu1kkJKPjFqj8uTJE5o2bYqvry87d+7E2dmZf/75BycnJ2MWS5IkSXrZhYfDW2/BokXQuDG7LoYTsP0y4VGJuiSl7dU0rH6etWufEPXLdEi1Qm0fycdzzzNz8MeoTbIfESS9OKMGKnPmzMHDw4OgoCDdNh8fHyOWSJIkSXrpxcRAx45w5gx88AG71u5g+IazpNWvCDTEqQ9w9+kOTk76DK52BaBG09v8vsUNd9dWRit6cWTUpp9ff/2V+vXr061bN1xcXKhTpw4rVqwwZpEkSZKkl1lKCnTvrgQpzs5otvxEwG9XEYBAS5zJEe5ZfMgj8/loLvsqQYo6ldlfJHPukCfurmbGPoNix6g1Krdu3WLZsmWMGzeOKVOmcOrUKUaNGoW5uTn9+/fPkD4pKYmkpCTd8+joaABSUlJISUnJ07Kl5ZfX+Ur65HUuGPI6Fwx5nQtGrq+zEKg/+ACTXbsQVlZofv6ZE8KOR7HxpJie4pF6PUkmtwAwEbY4vZJIavgNHGqH81rnSmg0JfSW/ykO8usznZP8VEKk701UsMzNzalfvz7Hjh3TbRs1ahSnTp3i+PHjGdL7+/sTEBCQYfuGDRuwzuWqlpIkSVLxUGnTJqpu3IgwMeHEpEncb9iQczHn2BC+gWvx1+CJN+qDM+jcfw/veLbBRm1j7CK/tOLj4+nVqxdRUVHYZ7Pgo1FrVNzc3KhWrZretqpVq/LTTz9lmn7y5MmMSzd0LDo6Gg8PD958881sTzSnUlJS2LNnD61bt8bMTFb15Rd5nQuGvM4FQ17ngpGb66zavh3TjRsB0C5aRHL7miw46MeB0AMggL+Hwq6FaJKt+EPVjIvtLujtv6p/Axr6FL9VjvPrM53WImIIowYqTZs25dq1a3rbrl+/jpeXV6bpLSwssLCwyLDdzMws324K+Zm39B95nQuGvM4FQ17ngpGj69yuHbz9NhFlHRnstIMd349U8kgoi8nPP5F0rSEAFmUfY9PwJkkaZbixCnB1sKRRBRfUJsV3CHJef6ZzkpdRA5WxY8fSpEkTPvvsM7p3787Jkyf59ttv+fbbb41ZLEmSJOklcynmFgHdVWy+GgT/gFqlxjdhEWe+G8bjR2pQa3Bqdh27BrdQ/TvMJC0s8etUrdgGKSkPUyAx+3T5yaiBSoMGDdi2bRuTJ08mMDAQHx8fFixYQO/evY1ZLEmSJOllcPs2D1cuZmztcNZf2IBAoFKp6FWzF+X/mU+gnzMAtWrBB9Mf8/31e4RH/be7q4Mlfp2q0baGm5FOwHhSHqdwZ94d7i68i0UXC+hqvLIYfQr9jh070rFjR2MXQ5IkSXqJ3Am9gLrZ67jfeUr55iB8oWvVrgS0CKCGSw3u34fl82HgQPD3BwsLZ97XtuRk8GMiYxJxsbOkoU+JYleTkvI0hbvz73J3wV000coQJ9Pzphhx3I3xAxVJkiTJODRa8dJ9MUfERvDFvhl0Hr2M5ncEd+3gVtcWHOnwFSF/1qWGi5KudGm4fh3Sj8NQm6hoXL6kcQpuZKnRqdxddJe7X90l9WkqADa1bPCY5sEJ0xNGXSJABiqSJEnFUGZTxrsV4aaOR/GP+PLYlyz5cxErNiXQPATiLNVEbv6O0aUG0LcTXLkCFhbw7rvKPnk8WLRISo1NJWxxGHfm3iH1sRKgWFezxjvAG+euzqRqUmGHccsoAxVJkqRiZtfFcIavO8OzlfkRUYkMX3eGZX3qFplgJTopmvnH5zPvz3lEJ0Uzew/0vAhaUzUWP+/it5OtCAyE1FRwdQU7O2OXuHDQxGkIWxrGnS/uKB1mAavKVnj7e+PSzQWV+t8alEIwwZ0MVCRJkooRjVYQsP1yhiAFlOlEVEDA9su0ruZaqJuBEjWJzD0+l7l/zuVxwmMAPrtSholHwwC4PyuILtNbcfKkkr5bN1i2DEoWz5YdHU2Chnvf3OP27NukRP4boFS0wtvPG5ce6QKUQkQGKpIkScXIyeDHes09zxJAeFQiJ4MfF8r+GkmpSSw7tYyAKwE8TX0KQOWSlQn0DeTdM4mwdQhn3vLnNf++JCSAoyN8/TX07AlG7GZhdJpEDeErwrn92W2SI5IBsCxnifd0b1x6u2BiatSl/55LBiqSJEnFSGSMYZNiGJquoKRoUlhzbg2BBwO5E30HAG8Hb/xb+NO7Vm9MTUyhOlC/AZEhVUj4CVq1gqAgKFvWuGU3Jm2SlvCV4YR+FkpymBKgWHhZ4D3Nm9L9SmNiVngDlDQyUJEkSSpGXOws8zRdftNoNfxw8Qf8D/pz4/ENANxt3XnL8S3m9p6LTVgEIuIBoSlueHkBVavStirs2wfNm4NJ4f8ezhfaZC0RqyMInRlK0h1lMV+LshZ4TfXCdaArJuZF58LIQEWSJKkYaehTAjcHSyKiEjPtp5I2Zbyx17URQrDt6jam75/OpQeXAHC2dmbya5MZXHsw+/fsx/zRUzSt2/DofipdTXbz8+VKeHgo+/v6GrHwRqRN1XL/+/uEzgglMUSpFTN3N8drihduQ9wwsSg6AUoaGahIkiQVI2oTFX6dqjF83RlUoBesFIYp44UQ7Lqxi6n7p3Im/AwAjpaOfNzkY0a9Ogpbc1tSUlJQJyUR2/JtnIJvEosPEWoHDh+GXr2MUmyj06ZqidwQSUhgCIk3lQDFrLQZXpO9cHvfDbWV2sglzD0ZqEiSJBUzbWu4saxP3QzzqBh7yvgDIQeYum8qR+8cBcDW3JYxr45hfJPxOFo66tLFRmkoOXIFTg9O8YgSfOizk19+LE39+kYptlEJjSByUyQhASEkXE8AwMzZDM9Jnrh/4I7auugGKGlkoCJJklQMta3hRutqroViZtoTd08wdf9U9t7aC4ClqSUfNviQiU0n4mzjrJf22FFBcPux9I7eSyIWrO/+K1tXV8bKqsCLbVRCK3iw5QEh/iHEX4kHwLSkKZ6feFLmwzKobYp+gJJGBiqSJEnFlLGnjD8bcZbp+6ez/fp2AMxMzBhadyifvv4p7nbume7zeNIX9I7+Bi0qrk37nlGBTQuyyEYntIKHPz8kxC+EuItxAJg6meIxwYMyH5XB1O7l+1p/+c5IkiRJKtSuPryK3wE/frz0IwAmKhP61+7P9ObT8Xb0zpBeq/139E5iIu0ffQ/A332HUGva2wVYauMSQvBo+yNC/EKIPRsLgNpBjcc4D8qOLoupw8v7df7ynpkkSZJUqAQ/CSbgYABrz69FK7QA9KjRA//m/lQuVTlDeo0GvvoKfv8ddu8GtaUlJkcOo9mwgbseHtQq6BMwAiEEj3c8JtgvmNi//g1Q7NSUHVOWsmPLYuZkZuQS5j8ZqEiSJEn56m70XWYdmsV3f39HqlZZ+K5z5c4E+gZSq3Tm4catW9C/Pxw5AlbE89NP1nTvDpQogXbYMNhh5JXy8pkQgie7nxA8PZiYkzEAmNiYUHZ0WTzGeWBW8uUPUNLIQEWSJEnKF5Fxkcw+Mpulp5aSpFEmHWtdrjUzW86kYZmGme4jBKxcCWPHQmwsVLC+xxnrpthGTgA+LMDSG4cQgqf7nhI8PZjoY9EAmFibUGZkGTwmeGDubG7kEhY8GahIkiRJeepJwhPmHpvLwhMLiUtROny+5vkas1rO4nWv17PcLyIChg6F//1Ped62STQ/P2mPxZUQWLIYBg/iZR7e8/SgEqBEHYoCwMTSBPcR7nh+4ol56eIXoKSRgYokSZKUJ2KSYlh4YiFzj80lKkn5sq3vXp+ZvjN5s/ybqLJZFbBvX9i7F8zN4fPAFMbufRfVsXNQujTs2vXSBilPjzwlxC+Ep/ueAqCyUOE+zB3PSZ5YuFkYt3CFgAxUJEmSpBeSkJLA0lNLmX10Ng/jHwJQw6UGM3xn0Lly52wDlDTz58OQIfDdCkGNr4bC3j1gYwO//Qbe3vl4BsYR9WcUIX4hPNn9BACVmQq3oW54TvbEsmzhWGupMJCBiiRJkpQryZpkvjvzHTMPzSQ8NhyAiiUqEtAigPdqvIeJ6vnryvzxB1y6BKNGKc9r1IDjx0Hl7w9r1oBaDT/+CPXq5fOZFKzo09GE+IXweMdjAFSmKlwHu+I1xQtLTxmgPEsGKpIkSVKOpGpTWXtuLQEHAwiNCgXA08ETv+Z+9KvdD1OT53+1JCTApEmwaJESizRpgm76e9XxYxAYqDz55hto3z4/T6VAxfwdQ4hfCI+2P1I2qMF1gCten3ph5fNyNmvlBRmoSJIkSQbRCi0/XvoRvwN+XH90HQBXW1emNpvKkLpDsDDNvj/FqVPQrx9cvao8f/99qFo1XYLGjWHuXIiOVtqBXgKx52MJ8Q/h4TalWQwTKN23NN7TvLEqLwOU7MhARZIkSXouIQS/XvuVafuncSHyAgAlrUoy6bVJjGgwAmsz62zzSEqCmTPh88+Vidzc3CAoCNq0eSahSgXjx+fDWRS8uEtxhASE8GDzA2WDClx6ueA93RvrStlfM0khAxVJkiQpU0II9tzaw9R9Uzl17xQA9hb2TGg8gTGNxmBnYWdQPlotvP46nDypPH/vPVi6FEqU+DdBSAh8+iksWwb29nl/IgUs7mocoYGhRP4QCQJQgXN3Z7z9vLGpamPs4hU5MlCRJEmSMjgcephP933K4duHAbA2s2b0q6OZ0GQCJaxKZLO3PhMTZehxaCgsWQLvvpvuxcePoW1buHZNqU1Zty4Pz6Jgxf8TT+iMUO6vvw/KCgE4v+uMl58XtjVsjVu4IkwGKpIkSZLOqbBTTNs/jd9v/g6AhdqC4fWHM7nZZFxsXAzO5/fflWlPXv93frcRI6B3b3BySpcoMRE6d1aClLJlYc6cPDyTgpNwK4HQmaFEfB8BGmVbqS6l8Pb3xra2DFBelAxUJEmSJC7cv8D0A9P5+erPAJiamDK4zmCmvj6VsvZlDc7n0SMYNw6+/x58fODCBWUqFBOTZ4IUrVbpVXvkCDg4wM6dUKZM3p5UPksMTVQClNURiFQBQMmOJfH298aunmHNYlL2ZKAiSZJUjF1/dB3/A/78cPEHBAITlQl9avXBr7kf5ZzKGZyPELB5M3z0EURGKq04nTsr/2bq44+VHczMYNs2ZRKVIiLxTiK3P7tN+MpwRIoSoJRoWwLvAG/sGxb9PjaFjQxUJEmSiqGQpyHMODiDNefWoBFKe0W3at0IaBFAVeeq2eytLyxMadr59VflebVqysKCjRplscPXX8O8ecr/V68GX9/cnUQBS7qXxO3Pb3Pv23uIZCVAcWrlhHeANw5NHIxcupeXDFQkSZKKkXsx95h1aBYrzqwgRZsCQIeKHZjhO4M6bnVynF9ICNSurUx7YmYGU6bA5Mlg8bwpVZo1U5p5PvoIevXK3YkUoKSIJO7MuUPYsjBEkhKgOLZwxDvQG8dmjsYtXDEgAxVJkqRi4GH8Q+YcmcOSU0tITE0E4A2fN5jhO4PGHo1zna+Xl1IhEh6u1KIY1IJTqxacP/9Mp5XCJzkymdtf3Obe0ntoE5RhPA6vOeAd6I2Tb+Eu+8tEBiqSJEkvsaeJT5l3fB7z/5xPbHIsAE08mjDTdya+PjlvcklNVVpueveGUqWUPihr1oCtrTIdfpYOH4b4+P9meCuRsyHOBSn5YTJ35t4hbHEY2nglQLFvZI/3DG+c3nAyeJFFKW/IQEWSJOklFJscy+ITi/ny2Jc8SVRW563rVpeZvjNpW6Ftrr5sz5+HwYPh9Gn46y9lZA8og3ae68AB6NBBGelz8CA0bJjjYxeElMcp3Jl3h7CFYWhilX47dg3s8A70pkSbEjJAMRIZqEiSJL1EElMT+eb0N3x+5HMi4yIBqOZcjRm+M3i7ytu5+rJNm/5+9mylRsXBAZo3N3DnvXvhrbeUlQjffBNq1szx8fNbytMU7i64y935d9FEKwGKbR1bvAO9KdmhpAxQjEwGKpIkSS+BZE0yQX8HMePQDMJiwgAo71Qe/xb+9KzRE7XJ89plsnbsmLI24JUryvO331Zml3V3N2Dn33+HLl2Uid3at4effgJLy1yVIz+kRqdyd9Fd7n51l9SnqQDY1LLB29+bUl1KyQClkJCBiiRJUhGm0WpYf2E9/gf8CX4aDEBZ+7JMf306A14ZgJnaLNd5b9oEPXsqc6SULq30TXnnHQN33rFDiWqSk6FTJ2XOlOcOBSo4qbGphC0J486Xd0h9rAQo1tWt8fb3xrmrMyoTGaAUJjJQkSRJKoK0QstPl39i+oHpXH14FYDSNqWZ0mwK79d7H0vTF6+5aNNGWeW4TRuYOzcH/V9PnVJqUlJSlGDlhx/A3PyFy/OiNHEawpaGceeLO6Q8VIZmW1f5N0DpJgOUwkoGKpIkSUWIEILf/vmNafuncTbiLABOlk5MbDqRkQ1HYmOe+9V5Hz2CoCAYP14ZzePoqEyBn+MBOnXqQNeuSufZ9euVCVaMSJOg4d4397g9+zYpkUqAYlXRCm8/b1x6uKBSywClMJOBiiRJUhHxx60/mLp/Kn/e/RMAO3M7xjUex9hGY3GwzP3MqGnT348cCQ8egIuLsgwP5HIUsakprF2rRDumxvua0SRqCF8Rzu3Pb5McngyAZTlLvKd749LbBRNTE6OVTTKcDFQkSZIKuWN3jjF131T2h+wHwMrUio8afsQnTT+hpHXJF8o7LAw+/BB++UV5Xq0aVK6ci4w2boR9+2D5cmUFQiPWomiTtISvCid0VijJYUqAYuFlgfc0b0r3K42JmQxQihIZqEiSJBVSZ8LPMHXfVHbe2AmAudqcYfWGMaXZFFxtXV8ob41GGb0zdSrExuZg+vvMrF0LAwYoTT3Nmv1XHZP+eFrByeDHRMYk4mJnSUOfEqjzuE+INkVLxOoIQmeGknQ7CQCLshZ4TfXCdaArJuYyQCmKZKAiSZJUyFyKvITfAT9+uvITAGqVmoGvDGRa82l4OnjmyTH691e6j4CyeOCKFblcwDgoSJkFTggYOhT69MmQZNfFcAK2XyY8KlG3zc3BEr9O1Whbwy2XZ/AfbaqW+2vvEzojlMRg5Rjm7uZ4TfHCbYgbJhYyQCnKZKAiSZJUSNx4fAP/A/5suLABgUCFil41e+Hfwp8KJSrk6bGGDVNGEH/+uRJfmOTmu3zFCnj/feX/w4crVTTPZLTrYjjD151BPLNrRFQiw9edYVmfurkOVkSqIOKHCEICQki8qQQoZqXN8Jrshdv7bqitcjd3jFS4yEBFkiTJyG5H3WbmoZms+nsVGqHMjNq1alcCWwRS3aX6C+ef1ln28WP44ANlW7NmcPu2skZPrixbBiNGKP8fNQoWLFA6z6aj0QoCtl/OEKQACEAFBGy/TOtqrjlqBhIagdlBM858fIbEf/4NUJzN8JzkifsH7qitZYDyMpGBiiRJkpFExEbw2eHPWP7XcpI1SqfPdhXaMcN3BvXc6+XJMW7eVEbz7NoFVlbKnCg+PspruQ5Sbt+GMWOU/48bp0yyksksrieDH+s19zxLAOFRiZwMfkzj8tl3ChZawYMtDwj2C8b6qjWJJGJa0hTPTzwp82EZ1DYyQHkZyUBFkiSpgD2Kf8QXR79g8cnFJKQmANDCuwUzfWfS1LNpnhwjKUmJH2bOVGawt7CASZOUCdxemKcn/PgjnDypHCCLqeYjY7IOUnKSTmgFD39+SIhfCHEX4wDQ2mrx/sQbzzGemNrJr7KXmXx3JUmSCkh0UjTzj89n3p/ziE6KBuDVMq8yq+UsWvq0zLO1ZQ4eVJp4rioT1tKqFSxdChUrvmDGUVH/LZXcubPyeA4XO8Nmx80qnRCCR9sfEeIXQuzZWADUDmrcR7tzsfJFPLp5YGomv8ZedvIdliRJymdxyXF8fepr5hydw+OExwDULl2bmS1n0qFihzxd/O7+faV5JylJWZ9n/nzo0SPLSg/DffYZfPONEgWltR1lo6FPCdwcLImISsy0n4oKcHVQhiqnJ4Tg8Y7HBPsFE/vXvwGKnZqyY8pSdmxZsIWLOy6+4AlJRYUMVCRJkvJJUmoS3/71LbMOz+J+3H0AqpSqQmCLQN6p9g4mqrwZNivEf4FI6dLKXCj37yuxhaNjHhwgMBD8/JT///ab0unFAGoTFX6dqjF83RlUoBespMVNfp2q6TrSCiF4svsJwdODiTkZA4CJjQllR5XFY7wHZiWVSeRSUlLy4KSkokIGKpIkSXksRZPCmgtrCDwYyJ3oOwD4OPrg38KfXjV7YWqSd7feixeVmWXnzoUGDZRt06fnQQ0KKBHQ9OlKPxSAOXMMDlLStK3hxrI+dTPMo+Kabh4VIQRP9z0leHow0ceUJjETKxPKjCyDx8cemDsbf0FDyXhkoCJJkpRHNFoNBx8fZMK3E7jx5AYAZezKMO31aQysMxBzdd594cbFwYwZ8NVXkJoKEyYorTKQh0HK5MlKcALKgcaNy1VWbWu40bqaa6Yz0z49qAQoUYeiADCxNMF9uDueEz0xLy0DFEkGKpIkSS9MCMG2q9uYtm8alx9eBsDZ2pkpzaYwrN4wrMys8vBYsGWLssLxHaWyhrffhoUL8+wQykEmTIB585TnCxcqc6W8ALWJSm8I8tMjTwnxC+HpvqcAqMxVuH/gjuckTyzccjqHv/Qyk4GKJElSLgkh2HVjF1P3T+VM+BkAbNQ2THxtImObjMXWPLcTlWTu0iX46CPYr6xNiJcXLF4MnTrl6WGU6pq9e5X/f/31fxO75YGoP6MI8Qvhye4nAKjMVLgNdcNzsieWZQ0bJSQVLzJQkSRJyoUDIQeYum8qR+8cBcDW3JaPGnxE9ajqdG/aHbN8WD34xAklSLG0hIkTlYdV3lXW/MfWVglU9u2D997LkyyjT0cT4hfC4x3KqCeVqQrXQa54TfHC0ksGKFLWZKAiSZKUA3/e/ZOp+6byR/AfAFiaWvJhgw+Z2HQijuaO7NixI8+OpdUqk8B6eyvPBwyA69eVOVLStuXpwQ4dghYtlOfOznkSpMT8HUOIXwiPtj9SNqjBtb8rXlO9sPLJjyhLetkYHKjcu3cPd3f3/CyLJElSoXU24izT9k/jf9f/B4CZiRlD6w7l09c/xd1OuTfm5bDZU6eUZp6wMGXiNhsbZb2/2bPz7BD/0WiUlQmDguDbb5X/v6DY87GE+IfwcNtDZYMJlO5TGq9pXlhXsH7h/KXiw+BApXr16nz99df06tUrP8sjSZJUqFx9eJXp+6ez+fJmAExUJvSv3Z/pzafj7eid58d78EAZbLNqldKn1dYWzpxRFhHMFxoNDBwIa9cqkZCNzQtlF3cpjpCAEB5sfqBsUIFLTxe8p3tjXVkGKFLOGRyozJo1i2HDhrFt2zaWL19OiRIlst9JkiSpiLr15BYBBwNYd34dWqEFoEeNHvg396dyqcp5frzUVGWa++nTlZnqAfr2VUYH58n6PJlJTFQOsmULqNWwcSN065arrOKuxhEaGErkD5G6md2c33PGe7o3NtVeLPiRijeDA5URI0bQrl07Bg8eTLVq1VixYgWd8ryruSRJknHdjb7LzEMzWfn3SlK1qQB0rtyZQN9AapWulS/HjImBpk3hwgXl+SuvwJIlyrZ88/ixslbPkSNgZgY//ABdu+Y4m/h/4gmdEcr99fdBieco9U4pvP28sa2Zt6OepOIpR51pfXx82LdvH0uWLKFr165UrVoVU1P9LM6cOZOnBZQkSSoIkXGRzD4ym6WnlpKkSQLgzfJvMtN3Jg3KNMjXY9vZQdWqSn+UWbOULiJqdT4eMD5eiYKuXlUWGdy2DXx9c5RFwq0EQmeGEvF9BGiUbSU7l8Tb3xu7V+zyodBScZXjUT+hoaFs3boVJycnOnfunCFQkSRJKkqeJDxh7rG5LDyxkLiUOACaeTZjZsuZvO71er4cMykJFiyA3r2hbFll26JFYGoKJUs+d9e8YW2tjOhZtQp27IAaNQzeNTE0UQlQVkcgUpU2nhIdSuAT4INdPRmgSHkvR1HGihUrGD9+PK1ateLSpUs4OzvnV7kkSZLyVUxSDAtPLGTusblEJSmdQuq712dWy1m0Ltc6T1c0Tu+332DMGLhxA86eVbqFgLKYYL7TaP6rqvHzU4YVGRgZJd5J5PZntwlfGY5IUQIUpzZO+AT4YP+qfX6VWJIMD1Tatm3LyZMnWbJkCf369cvPMkmSJOWb2KR4Ju+ey/cXFxKdrEw+VtOlJjN8Z/BW5bfyLUC5cUMJUH77TXnu5gYdOuTLoTK3YgWsWQO7dys1KiqVQUFK0r0kbn9+m3vf3kMk/xugtHLCO8AbhyYO+V1qScLgNcY1Gg3nz5/PtyBl9uzZqFQqxowZky/5S5JUvCVrkhn5y+eUmO3JkjN+RCc/xlTrTgX1p8x+bSedq3TOlyAlNhamTIHq1ZUgxcwMPv4Yrl2DPn3y/HAZCQHTpsH778PRo0pzjwGSIpK4MfYGJ8qfIGxJGCJZ4NDcgVcOvkLtPbVlkCIVGINrVPbs2ZNvhTh16hTLly+nVq386VEvSVLxlapNZe25tUzaO53I+LsAqLXOOKb2xEbzBqlJaj5cf5ZlfUxoWyPvxwHPmweff678/803lb4olfN+dHPmkpOVnrnff688nz4dPvzw+bs8SObOF3cI+zoMbYIyjMfhNQe8A71x8nXK7xJLUgZG7wkbGxtL7969WbFiBTNnzjR2cSRJeklohZYfL/2I3wE/rj+6DoBaOOGQ8h62mjaoUNbiEYAKCNh+mdbVXFGbvHitSmqqUnMCMHas0toyYYIyGjifWpYyioqCd99V1uxRq2H5chg8OMvkKY9SuDP3DncX30UbpwQo9o3slQCllVO+NYlJUnaMHqh8+OGHdOjQgVatWmUbqCQlJZGUlKR7Hh0dDSjTVufl1NVpeab/V8of8joXjOJ0nYUQbP9nO/4H/bn44CIADuYlMIvvjKO2PSZYghp0s5L963FsAn/eiKShT+4ns4yMTGHFipp88YUJ+/alYGKiLCCYttpxamqus86ZsDBM33oL1YULCBsbNBs3Itq2hUze/9QnqYQtCOPe4ntoY5UAxba+LZ7TPXFs44hKpSK1wApumOL0eTa2/LrWOclPJYQQ2SfLHz/88AOzZs3i1KlTWFpa0qJFC1555RUWLFiQaXp/f38CAgIybN+wYQPW1nJqZkkqzoQQnI05y4aIDfwT/w8A1ibWdHbpzFvOb2Glzr8F8FJTVeza5c2mTZWJibEAICDgKLVrP8y3Yz6PdXg4r0+ahDAx4c+pU4kqXz5joliw2G6BxXYLVPFKbYmmnIbEnomk1k9VqpkkKZ/Ex8fTq1cvoqKisLd//qgxowUqd+7coX79+uzZs0fXNyW7QCWzGhUPDw8ePnyY7YnmVEpKCnv27KF169b5sly7pJDXuWC87Nf5yO0jTD84nSN3jgBgbWbNyAYjGffqOEpYleBk8GMGrTmVbT6r+jfIUY2KELB9u4rJk9X884/yze7hEc3Spea0aZOfM7YZ4MwZKFEiwzLLqdGphC8JJ2xBGJqnykxt1jWt8ZzuSYm3ShSJJp6X/fNcmOTXtY6OjqZUqVIGBSpGa/r566+/iIyMpG7durptGo2GQ4cOsWTJEpKSklA/MzWjhYUFFhYWGfIyMzPLtw9rfuYt/Ude54Lxsl3nU2GnmLp/Krtv7gbAQm3BiAYjmPTaJFxsXHTpGlVwoYStFRFRiWT2y0wFuDpY0qiCi8F9VB4+VJbFOXBAee7iAn5+GlxdD9CmTbuCv87r14OTE7Rvrzx/9VW9l1NjUwlbEsadL++Q+lhpyrGuZo13gDfOXZ1R5UHfnIL2sn2eC7O8vtY5yctogcobb7zBhbSFLf41cOBAqlSpwsSJEzMEKZIkSWku3L/AtP3T+OXaLwCYmpgyuM5gpr4+lbL2ZTOkV5uo8OtUjeHrzqBCv3dK2tezX6dqOepIW6IEREcrfVDGjoVJk8DKSsuOHQVcSS0EzJ6tjIG2tlZmkatYUfeyJl5D2NIw7sy5Q8pDpV+AVWUrvP29cenmgkpd9AIUqXgxWqBiZ2dHjWembbaxsaFkyZIZtkuSJAFcf3QdvwN+bLq4CYHARGVCn1p98GvuRzmncs/dt20NN5b1qUvA9suERyXqtrs6WOLXqVq2Q5NjYmDxYhg9GmxswMQEgoLA0RE8PZU0Bd63MzUVRo5URvQAjBgB//ZH0SRouLf8Hrdn3ybl/r8BSgUrvPy8KN2ztAxQpCLD6KN+JEmSshPyNITAg4GsObcGrVBGpnSr1o2AFgFUda5qcD5ta7jRuporJ4MfExmTiIudJQ19Sjy3JkWjUeZImzYN7t9XYoPp05XXjDr1U2ws9OihzCKnUikTtIwciSZRQ/iKu9z+/DbJ4ckAWPpY4jXdi9J9SmNiavA8n5JUKBSqQOVAWmOvJEkScC/mHrMOzWLFmRWkaJVagY6VOjLDdwavuL6SqzzVJioalzdsfZu0+U/SWqnLl4dXcnfYvHXzJrzzDpw7p7Q9bdiAtn1nwpeFETorlOQwJUCx8LTAa5oXrv1dMTGTAYpUNBWqQEWSJAngYfxDZh+ZzdenviYxVWmmaVWuFTN8Z9CobKN8P/6lS0qAsmuX8tzJSalFGTECzM3z/fDZCwpSghRnZ7Q/bSPiqg+hlU6QdFsZFWlR1gLPTz1xG+SGibkMUKSiTQYqkiQVGk8Tn/LVsa9YcGIBscmxADTxaMKslrNo4d2iwMoxY4YSpJiZKV1Apk5VOs8WGv7+iOgYIr36Edw/hcRgZeZdczdzPKd44jbEDbWlHJAgvRxkoCJJktHFJsey6MQivjz2JU8TnwJQ160uM3xn0K5Cu3yf2yMhAeLj/1tM+LPPlME0s2ZBhQqG5aHRCk4GK6sxnwx+nKOhztl6+BDmzIFZs9CamBK58SGhO3uRcCMGALPSZnhN9sLtfTfUVjJAkV4uMlCRJMloElMT+eb0N3x+5HMi4yIBqOZcjRm+M3i7ytv5HqBotbBhgzKyt3lzWLtW2V6uHGzaZHg+uy6GE7D9Mo9jE/iiIQxac4oStlYGjSbK1qlTypo9t28TdzmGizcHknAtAQCzUmZ4TPSgzIgyqK1lgCK9nGSgIklSgUvWJLPq71XMPDSTsJgwAMo7lSegRQA9avRAbZL/X7qHDsH48XD6tPL88GFlCLKdXc7y2XUxnOHrziAAi3TFjohKZPi6MyzrUzd3wYoQ8O23iFGjUCUnk2juweUdr5JAAqYlTPH8xBP3D90xtZW3cenlJj/hkiQVGI1Ww7rz6wg4GEDw02AAPOw9mN58Ov1r98dMnf+zjF69qtSgbNumPLezg8mTYcwYsMrhckAarSBg++VMZ7t9oVWZ4+MRw0eg+n4NKuABzbia/AkqR0d8JnhQ5qMymNrL27dUPMhPuiRJuZbWLyO7OUm0QsuWy1vwO+DH1YdXAShtU5pPm33K0HpDsTS1LJDybt8OXbooTT4mJvD++xAQoEx/nxsngx/rTR73LAGERyVyMvixwUOixc2baFp3xjT4EgITbjGUe3a98BjvSdkxZTF1kLdtqXiRn3hJknIlrV9G+i9qt2dmeRVC8Ns/vzF131TO3T8HgJOlExObTmRkw5HYmNvkezmFUOZDA2jRQukw26SJ0mG2WrUXyzsyJusgJafphBA83vmY8InnqBIcQjJOXLX0w27CWzQaVxYzJ7mmjVQ8yUBFkqQcS98vI720fhlLe9fB3OYKU/dP5c+7fwJgZ27H+MbjGdNoDA6WDvlexthYWLAA9u+HvXuVYMXODi5fhlKl8uYYLnaG1QQ9L50Qgie7HxPsF0LMiRigBJctZ+IwuCFVAxpgVlIGKFLxJgMVSZJyJLt+GUkmV+ix7VOihVKDYmVqxUcNP+KTpp9Q0tqw5o8XkZwM336rzIUSqQwkYufO/xYVzqsgBaChTwncHCyzXZW5oU/GSViEEDzd95Q7U85Q9uRk1LyHiVUDynxYBo+Pm2DuUhhmlpMk45OBiiRJOZJVv4wk1Q2emq0lUf0XCDAzMeeD+sOY0mwKrrau+V4ujQY2blTW5AkJUbaVLw8zZ0LbtvlzzGdXZU7veasyPz34lODpwWgPHac6AVgSiZ19ONqLV7DwsM2fwkpSESUDFUmScuTZ/hbJqlCizNYTrz6mbBAm2GpaM79dIEOaNCyQMoWHQ5s2/63J4+oKfn4weLAyu2x+Sr8q8+PYBN32zFZljjoaRbBfME//eII7v1KBJZiQirZcRcx+2QoySJGkDGSgIklSjqT1t0hR3SPKdCNx6gOgEiBU2Gia45DaCzPhTvXS5QusTKVLg6kpODrCxIkwahRYWxfY4XWrMv95I5KHV/5kVf8GejPTRv0ZRYhfCE92P8GERKqo5uMqdis7d+2KSVAQ2NsXXIElqQiRgYokSTniWiKWBJuvidT8DiotANaaJjik9MZceD23X0ZeOXcOvvwSvvkGbG2Vocbr1ys1KU5O+XbY51KbqGjoU4IdV9AN044+HU2IXwiPdyhT65uq46jvMB7Lx9eUQs+erax+mM8z8EpSUSYDFUmSDBIRG8Fnhz9j+V/LSdYmgwqsNPVwSOmLhVAWxHlev4y8cOuW0gdl40Zl2HGVKsqCgQBVq+b54XIt9u9Y7s66y6NfHykb1ODazxWvTz2xDGgIvz9R5uhv0cKo5ZSkokAGKpIkPdej+Ed8cfQLFp9cTEKq0gejhXcLOnqNYctxW8KT/+uzklm/jLwQEaF0il2+HFJTlW3vvac8CpO4C3FYz7bm3J/KiCdMoHTPUnhNcMH6lX9nlfvmG3j6FNzdjVZOSSpKZKAiSVKmopOimX98PvP+nEd0UjQAr5Z5lVktZ9HSpyUqlYoxrxs2M21uCQHTp8O8ecrqxqB0mv3sM6hbN88O88LiLscREhDCgx8fYIYZqMClpwveH1pjPW0wTLOGX35RmnusrQu2A40kFXEyUJGkHDB0yviiLC45jq9Pfc2co3N4nKD0rahdujYzW86kQ8UOeisaq01UBk8NnxsqFfzzjxKkvPoqfP45+Prm2+FyLP5aPCEBIUT+EEnaRCrJTZJ5demrOCRehXfbwN27SmBy+TLUqGHcAktSESQDFUkykCFTxhdlSalJfPvXt8w6PIv7cfcBqFKqCoEtAnmn2juYqEzyvQxxcbBsmbIeTwWl2wszZ0KPHtC5c+Hpcxp/I57QwFDur78PSn9iSnUtRdkpZTl45wC2h9fCuHGQkgKVKsHWrVC9ulHLLElFlQxUJMkA2U0Zv6xP3SIbrKRoUlhzbg2BBwO5E30HAB9HH/xb+NO7Zm/UJup8L0N8vBKgfPGFMpvsxYuwerXyWoUK/wUtxpZwK4HQmaFEfB8BGmVbybdK4u3vjV0dO1Kioqg7YSHqAweUF7t2BTn0WJJeiAxUJCkb2U0ZrwICtl+mdTXXItUMpNFq+OHiD/gf9OfG4xsAlLErw7TXpzGoziDM1Pm/xkx8vNK3dM6c/6a79/GBli3z/dA5khiaSOisUCKCIhCpyiehRPsSeAd4Y1//vyBE3b8/HgcOINRqVLNnw/jxhacaSJKKKBmoSFI2spoyPo0AwqMSORn8OF/7a+QVIQTbrm5j+v7pXHpwCQBna2emNJvCB/U/wNLUsIX2XtSKFUpH2YgI5bmPjzLUuG/f/J9N1lCJdxO5/dltwr8LR6QoAYpTGyd8AnywfzVjLYn2k09IOnIEs02bMH3jjYIuriS9lGSgIknZeHbK+BdNZyxCCHbd3IX/IX/OhJ8BwNHSkU+afMJHr36ErXnBTt8eFqYEKd7eSoDSr1/hCVCS7iVx+/Pb3Pv2HiJZCVAc33DEJ8AHh6bpVn4+fhyuXoWBAwEQDRqw55tvaPf668YotiS9lGSgIknZSJsyPq/SGcPB0INMuTGFK+euAGBrbsvYRmMZ13gcjpaO+X78xESlBqVmzf/mOBszBsqWVQIU80KyUHBSRBJ35tzh3jf30CYqvWQdXnfAJ9AHx+aO/yVMSFBmnps3T4muXn0VqlUDQBSWaEuSXhIyUJGkbDT0KYGbgyURUYmZ9lMpiCnjc+vPu38ybf809t7aC4ClqSUjG4xk4msTKWVdKt+Pn5gI332nDCu+d0/5Pj9+XOm24egIQ4bkexEMkvwgmTtf3CHs6zC0CUqAYt/UXglQfB31hmRz9CgMGgTXryvPe/QAt6LZkVqSigIZqEhSNtQmKvw6VWP4ujOoQC9Yye8p43PrbMRZpu2fxv+u/w8AMxMzWpdozbJey/B08sz34yclwcqVysRsYWHKNg8PGDAAtFpQ5/9AIoOkPErhztw73F18F22cEqDYvWqHT6APTq2d9AOU+HiljWrBAmUmOnd3Zarcjh2NU3hJKiZkoCJJBmhbw41lfepmmEclv6aMz62rD68yff90Nl/eDIBapaZ/7f5MbjqZS0cv4Wab/+XcsgXGjlXmOQOleWfKFKUSwsIi3w9vkJQnKdydd5e7C+6iiVXGGdvVt8M7wJsS7UroByigzNvfqBFcuKA8HzBAafYx1gqIklSMyEBFkgzUtoYbrau5FsqZaW89uUXAwQDWnV+HVmhRoaJHjR74t/CnUslKpKSkcIlLBVIWjUYJUtzdlQBlyJDCE6CkRqVyd8Fd7sy7gyZaCVBsX7HFO9Cbkh1LZgxQ0piaQq9esHix0tmmffsCLLUkFW8yUJGkHMjvKeNz6m70XWYemsnKv1eSqlVW6+tSpQuBLQKpWbpmvh8/OVmZmM3KShlWDNCtm9LXtEcPsCwk/YtTY1IJWxTGnbl3SH2qXCebmjZ4B3hTqnMpVJkFm4cPK1Pf16unPJ8wAT74QOlcI0lSgZGBiiQVQZFxkcw+Mpulp5aSpEkCoE35NszwnUGDMg3y/fhxcUrFwty5Sh8UV1d4910lYDExUVpGCoPU2FTCloRx58s7pD5WAhTratZ4+3vj/I5z5gFKfLxSFbRoEVSpAmfOKBGXqakMUiTJCGSgIklFyJOEJ3x57EsWnVhEXEocAM08mzGz5Uxe98r/uTuePIElS2DhQnj0SNnm5gaffKIEKIWFJl5D2NIw7sy5Q8rDFACsKlnh7e+NS3cXVOosmngOH1bmRLl5U3neuLGyXk9hqRqSpGJIBiqSVATEJMWw4M8FfHX8K6KSogBo4N6AmS1n0rpc66z7VuShjRvh/fchNlZ5Xr68EqD07194+qBoEjTcW36P27Nvk3JfCVAsy1vi7eeNS08XTEyziKbi4pRalMWLlRE9ZcsqVUZt2xZg6SVJyowMVCSpEEtISeDrU18z+8hsHiUoVRg1XWoyw3cGb1V+K98DFCH+W6qmShUlSKlVCyZPVpp6TAvJHUSTqCH8u3Buf3ab5PBkACy9LfGa7kXpvqWzDlBAmeDl9df/q0UZMkRp03JwyHofSZIKTCG5zUiSlF6yJpkVf61g1uFZhMeGA1CpZCUCWgTQvXp3TFT5285y8SLMnq0s+rt0qbKtTh1lsrZXXy086+xpk7SEr1IClKS7Sl8dC08LvKZ64TrAFRMzA66Tmxt4eSk9g1esgDZt8rnUkiTlhAxUJKkQSdWmsvbcWgIOBhAaFQqAl4MXfs396Fu7L6Ym+fsn++efyiyyv/6qPDc3h8BAKPXvJLaNGuXr4Q2mTdESsTqC0JmhJN1WAhTzMuZ4feqF2yA3TCyyCVAOH4batZVITKWCdeuUET6yFkWSCh0ZqEhSIaAVWn689CN+B/y4/kiZmt3N1o2pr09lSN0hmKtzvxiORis4GfwYUFaCblTBRW/uFyFg714lQNm/X9mmUsE778CkSf8FKYWBNlXL/bX3CZ0RSmKwMvGeuZs5nlM8cRvihtoymylvb99W2q02bFCGGi9bpmwvYlPgp72nhW0+H0nKDzJQkSQjEkLwy7VfmLZ/GhcjLwJQyroUk5pOYniD4VibWb9Q/rsuhhOw/TKPYxP4oiEMWnOKErZWerPpLl0KI0cq6U1NlflQPvlE6ZNSWAiN4P6G+4QGhpJwIwEAMxczPCd74j7MHbVVNgFKTIzSljVvnrIAUVrblVZbuIYrGSDtPU0/Q7JbIZshWZLykgxUJMkIhBDsvrmbqfuncvreaQAcLBwY33g8YxqNwc7C7oWPsetiOMPXnUEAFum+x8MfJzF02SVWDFdm233vPfD3VyZeHT8ePPN/KSCDCY0g8sdIQgJCSLj2b4BSygyPiR6UGV4GtU02AYpGA6tWKSsd37+vbGveXAlY6tbN59LnvfTvaXoRUYkMX3eGZX3qymBFeunIQEWSCtjh0MN8uu9TDt8+DICNmQ2jXx3N+CbjKWGVNyswa7SCgO2X9b7QkpJMeHLam8d/lsPUIYGAsmdpXc2VUqVU3LlTuKYKEVrBg58eEOIfQvzleABMS5ji8bEHZUaWwdTWwFvX558rQQpAhQrKaJ633io8vYFzILP3NI1AWSAzYPtlWldzlc1A0ktFBiqSVEBOhZ1i6v6p7L65GwALtQUjGoxg0muTcLFxydNjnQx+rGsa0CSY8eicJ+9/7U1UlBKNiFQ1d8OUfg6Ny5csNEGK0Aoe/vyQEP8Q4i4oE9qZOppSdnxZyo4qi6m9Abcsjea/5ZmHDVOWcR49GkaMUHoHF1Hp39PMCCA8KlH3nkrSy0IGKtL/27vv8KjK9P/j75lJD6mE9DIBQQgISAkCCog09QuiroqCIrq6shQBKwIpFBFcG8qCuuL6W8TVtRdAkSpSBVGQLqmkEVJJncyc3x8PIQk1QDIzmdyv65ormTOTM/ecyWQ+ec5TRCPbm72XWetn8dWhrwBw0jvx1+v/yox+Mwj3Dm+Ux8wpLseU70HRzmhK9oWjmdRb3cmnFO/YY3hel4be2UJO8YU/+KxJ0zROfnOS5PhkTu1RM8oZvA2ETwknfGo4zr7Ol97JiRPqHFZyMnz7rWo1adUKjhyxnwlfrkJ9Xyt7eU2FaChN/90rhJ06fPIw8Rvi+Xjfx2ho6HV6Huz8IHH942jt17pRHzvQy43KTF9O/WoEwDWokPH3H+U71ywqz7qfLWmaRt6qPJLjkyn+pRgAQ4taAcW/HgGlokLNKDt3LhSqWXv55RfoeXrNIwcIKVD/18rWr6kQDc0x3sFC2JHkgmRmb5zNB799gEWzAHBvx3tJ6J9Ah1YdGuUxTSb49FP1/f33Q2y0P61jf6M8KQ3PTsfxjs5lQC8zK3cYwKxDBwT7qGGttqBpGvlr8kmKS6J4uwooeg894ZPDCX8qHJeAepyi0TT47DM1RCkpSW3r2lV1lO3Z+AszWltstD8hPm5kFZaft5+KrV9TIRqLBBUhGkhGcQbzNs3j3d3vYrKodWb+r93/MefmOXQN7tooj1lQoCZTXbQI0tMhIgLuuQecnHQkjuzA+FO7gbp9R6u/jR8eY/VOl5qmUbC+gKS4JIp+LgJA764nbEIYEc9E4BJYzz4kGRlw773w88/qekgIvPiiGlttuMRIoCbKoNcRPzyG8ct3o4M6YcWWr6kQjU2CihBXKbc0l5c2v8TinYspr1L9Awa1HsScm+dwQ3jjTOV67Jhawfi999R6egBBQWrRwMpKdbZjWKcQlozpdmYelWrBNppzo2BjAUnxSRRuVKdndK46wsaHEfFcBK7Bl7mqYUCAGm7s7q5aVJ55Bjw9G6Fq+1L7Na3dsdZWr6kQ1iBBRYgrVFBewCtbXuH17a9zqlJ1AO0T0Yd5A+cxwDig0R73jTdg2jQ1VxlAp07q+v33nzvEeFinEAbHBLPtaA65B7axbGzPc2ambWyFPxeSFJ9EwdoCAHQuOkIfDyVyeiSuofUMKMXFsHQpTJkCzs5q9M6KFRAaCmFhjVa7Pap+TWVmWtFcSFARDqexpxc/VXmKRdsX8fKWlykoLwCgW0g35t48l2HXDGvwFY2rqlSrSfUyNL17q5AybJgKKIMGXXxaEINeR2y0PysPYNUPtKLtRSTFJ5H/fT4AOmcdIX8NIXJ6JG4R9ezwaTbD++/DzJmqBcXNDSZNUrc5YD+U+jLodTIEWTQbElQuRNPwPXLE1lWIy9SY04uXV5Wz9JelzN88n5ySHABiWsUw5+Y53Nn+zgYPKEVF6tTOG2/ArbfWLEsTGwtHj0KbNg36cA2m6JcikuOTyVup1hfSOekIHhdM1Iwo3KLqGVA0DVatUosN7d2rtl1zjf0+aSFEo5GgcgG6H36g/zPPYPn8c3UOfMSIJrcmSHPTWNOLV5oref/X95mzaQ7Hi48D0MavDYkDEhnVaRQGfcN23kxNVZ1j331XhRWAlSvVyB7n06N17fHzunhPMcnxyZz8+qTaYIDgh4KJmhmFe2v3+u9o+XJYuLAmoPj5QXw8jB/fpCdsE0JcGQkqF6A7fBizkxOGrVvhzjvh2mvh6adhzBj7mmtcAI0zvbjZYubDvR+SsCGBpAI1/DXCO4K4/nGM7TIWZ0M95vi4DDt3qpG1//ufOuMBamHAadPUr51zwz5cgzm19xTJCcnkfp6rNughaHQQUbOi8Gh7BYsqfvqpCiktWqgVjqdPB38ZcitEcyVB5QIskyax1t+fwQcOYHj7bTh0CB57TK0bMnmyWr1N/ruzGw05vbhFs/DZ/s+I2xDHwdyDAAR5BjHjphk81v0x3JwaJ6h++y3897/q+1tuUQFl2DD7bcgr2V9CcmIyJz45oTboIHBUIFFxUXi2r+cInKws1Xz0+ONgNKptL7wAvXqpFhRf38YoXQjRhEhQuYgKPz8sc+dimDlTtcO/9pqarGLFCnXuXNiNhpheXNM0vjvyHbPWz2JP1h4A/N39ea7vc0zoOQFPl4Yb/nr0KPzznzB0qLqA+qxOS1PL0nTp0mAP1eBKD5WSPDuZnI9yzkzm0eovrTAmGPHsWM9jdOgQvPIKfPCBGk9dUqI644DqhBMb2zjFCyGaHAkq9eHlpf69nTgRPv5YNUNXd5wsKVGtKxMnqnGiwiauZnpxTdNYl7SOmetnsi19GwBeLl481fspptwwBR83nwap0WxWfU0WL4bvv1fb/vijJqiEhcGyZQ3yUI2i9GgpKbNTyP4wG04PjQ64KwBjvJEWnVvUbydbt8LLL8OXX6oOs6CGMQ0Z0ig1CyGaPgkql8PFRc18Wdt778Hbb6vLbbepjrf9+jXJZeSbsiudXnxL2hZmrJvBhuQNALg7uTO512Se6fMMLT0aZvhnbq76NVm6VK2XB+rX49ZbVb61d2VJZaTMTSHrgyw43Xem5YiWGBOMeF3vVb+daBoMHw7ffVezbcQI9X7p27fhixZCOAwJKlfrppvUnOWffab+XV65UjVbP/ssjBzpsNN525vLnV58d+ZuZq6byaqjqwBwMbjwRPcnmH7TdIJbBDdobXfcAVu2qO/9/ODRR1UfUXscuVNbeUo5KfNSyHo/C61KHVH/2/wxJhjx7ul96R1UVqoewDqdusTEwA8/qLD/9NPQoXHWPRJCOBY77abXhFx/PXzyiTrnPn68GhG0Ywf85S/qD3Npqa0rbDaqpxcP9ql7eifYx+3M0OQ/cv7g7k/upvs73Vl1dBUGnYHHuj3GkUlHeOPWN646pJSVqW4X1Yv4ggom3bur0zrHj6szH/YcUsrTyzn898Nsb7udzHcz0ao0/Ib4cf3W6+n8XedLh5TCQjW8ODoaNm6s2V69eOB770lIEULUm7SoNJRrrlG9IxMS4K231KVTJ/CoNTyztLTuddHgLjS9eFLBn4z5fAwr9q5AQ0OHjtGdRxPfP55r/K+56sdNSlITsr33HuTlqX6hkyer2x5+GMaNs/+zgRUZFaS+lErG2xlolaoFxXegL8ZEI743+l56B8ePqye+dKma8h7UARkwQH0fENAodQshHJsElYYWGAizZ6v/Hmv/W33smGp9GTcOpk6FqCjb1ejgak8vnlqYyhPfPs/7e97HrKkOFnd3uJvEAYl0DOx4VY9jsagzGW+9pc74VfcNjYxU/a+r2evw4mqV2ZWkLkglY0kGlnLVS9annw/Rs6Px7e976R3s3w//+IeaqM2kVo0mJka9B+6/v/EKF0I0CxJUGkuLFupS7aOP1DSjb7wBb76pJsoYPRruuqvup5poEFmnspj/03yW7lpKpbkSgNva3sbsAbPpHtr9qvdfUQFdu8LBgzXbhgyBCRPg9tubRtekyhOVpL2cxvG3jmMpUwHFu4+3CigDfeu/JMBDD8GuXer7fv3USsa33Wb/CU0I0SRIULGWF15Qi6gtXAhr18KaNeoyfrwa/fD66xDcsJ04m6OTpSdZ+PNC3tzxJmVVZQAMMA5g7s1z6Rt55aNLNA1+/RW6dVPXXV1Vo0FmpmokGz8e2rVriGfQ+EwnTaT9I430N9OxlKiA4tXLi+jEaPyG+F04oJSVwddfqyH6//43eJ/uq/Lgg6oZ6dln4YYbrPMkhBDNhgQVa9Hp1L/cQ4ao00ArVqim8kOH1KQafn41983IgJAQ++/UYEeKKop4betrvLrtVYoq1AI5vcJ6MW/gPAZGD7ziBQMzM1Xn2PfeU5O0HTmiuiOBahzz8wPPhpsHrnGdgpT4FDLfysRcrE6DtejegujZ0fjf6n/+Y2Q2w/r18OGHamRbdd+TESNU5xtQnXGefNI6z0EI0exIULGF1q3VsvUzZqgm82PH1L/ooP5179dPfR09Wl2uvda29TYAs0U7p4NrfdfcuZiSyhIW71zMgp8XkFemVuvtEtSFuQPncnvb268ooFRVqYV7//UvNe1H9bo7Xl5qCZrqoBIeftXl19FYx6iqsIrUV1LxfsWb9NJ0ADy7eBI9O5qWw1ue/xhlZKiFh1asUGmtWlSU+p288caabRKohRCNyKZBZf78+Xz++eccPHgQd3d3+vTpw4IFC7jWAT6Y60Wngx491KVaUpJa/6SkBObMUZeePdWqdPfdB0FBtqv3Cq3el0niN/vrrMUT4uNG/PAYbrn2ykaCVFRV8M6ud5j30zyyS7IBaB/QntkDZnN3zN3odVfWP+K339REbLU/m/v2hb/+VU2X01itJxc7Rley4jNAVXEVxxcdJ+0faVQVVKFDh0dHD6JnRxMwMgDd2SGosrJm/SqLRQUVTVPNRvfdpwJKnz7S90QIYVU2/YuzceNGJkyYwLZt21izZg0mk4khQ4ZQUlJiy7Jsq3VryM5WTe233aZ6Ze7cqZrWw8LUekNNyOp9mYxfvvucBQOzCssZv3w3Px7Ivqz9mcwm3t31Lm3fbMvk1ZPJLskm2jeaD0Z+wL7x+7in4z2XFVLKyup2iG3XTo0ib9VKrYywfz9s3qzOcjRmSLnYMVq9L/MCP3l+VaeqSF2QyrbobSTNTKKqoAr39u6UPFNC111daXVXq5qQkpcH77yjWvFGjKjZSXi4Gmr/1VcqOC9ZolpRJKQIIazMpi0qq1evrnP93//+N4GBgezatYt+/frZqCo74OkJDzygLjk5qvPihx/C9u11V6s7fFidNho0CJzs7yye2aKR+M3+805pr6FmjH1p1UGmta/Pvsx8tO8jEjYk8Gf+nwCEeYUxq98sHrn+EZwNzpdV22+/qVM7y5erRqoDB1QDl7s7bNigOspaY3Hs+hyjxG/2Mzgm+JKngcylZjKWZJC6IBXTCTVM2L2dO8YEI353+rHq+1UqoJSXq3Nay5err9VDip2cVHDxP73MQFxcgz1PIYS4Unb16VZ4et4Rf3//895eUVFBRUXFmetFRarTpMlkwlT9x7aBVO+vofd72fz81HzrTzyhenK2bn3mg0X/1lsY3nwTLTAQy733oj3wAFr37nbTZ2BHUh55p8pwvchQ3fxTamTOhY6zpml8eehLEjclsj93PwCtPFrxXJ/neLzb47g5uYEFTJZLv05FRfDxx3qWLdOxa1dNy4C3t0ZKShVhYep6x9PTq1jjpa/PMco7Vca2oznnrFNUzVxmJvvdbNJfTseUrYp2a+NGxIwIWo1qhc5Jd+b4aq+8gvbSS+hqzfGjXXcdlgcewHLffaojjq1/55swu/m74eDkOFtPYx3ry9mfTtO08/0zZ3UWi4URI0ZQUFDA5s2bz3ufhIQEEhMTz9m+YsUKPJrhjK/XfvQR0atX41rrQ6esZUtyO3Uit3NnUm++uck21Wuaxu7i3XyY+SHHyo4B4Gnw5M7AO7k94HbcDe6Xtb/vv49i2bJOVFSobO7kZCE2NpPBg1Po3PlEk5j35BwmcPnBBddPXdHnq9fZEmih/L5yTP0raZGdQcDvv5PTrRulp/s2Ra5Zw/WLF1MaEMDxfv1I69ePYqPRhk9CCNEclZaW8sADD1BYWIi398WX5bCboDJ+/HhWrVrF5s2bCb/AcIrztahERESQm5t7ySd6uUwmE2vWrGHw4ME4O1/eaQWrMpnQ/fgj+hUr0H39Nboy1UKhRUdTdejQmbvpNmxAa9uWM80GVrAjKY9HPth50fu46jXm9LDUOc4bUzYSvzGeLelqJb8WLi2Y3HMyU3pNwdfNt16PnZWlvlZPTbNunY5hw5zo0EHjkUcsPPCAhVatruhpNaj6HCOAZWN7nmlRsVRayP53NukvpVOZriazc410JeoxC63892LYvAndhg3oTvcINr/6KhV/+5v6fY6NxWX/fjTpb9IomszfjSZOjrP1NNaxLioqIiAgoF5BxS5O/UycOJFvv/2WTZs2XTCkALi6uuJaPYy3Fmdn50b7ZW3MfTcIZ2fVCXLECNUzdOtWWLcOnZdXTd1VVWqRxKIi1Vt04EC4+Wa1BktgYKOVdsM1gfi3cCersPy8fTB0QLC3G1CCs7Mzu7J3MXPdTNYmrQXAzcmNiT0n8tyNzxHgcenRQadOwRdfqK4XP/6o+h+/+qq6bfBg2LYNYmN16HQGwD6aUOp1jHzcuOGaQHRmjawPskiZk0JFqgrsLmEutBlXTuD/ux/drJS6P+zqCn36YAgPP/O74BwQgNMttzTukxL2/3fDQchxtp6GPtaXsy+bBhVN05g0aRJffPEFGzZsIDo62pblNH3u7iqEDBxYd3tODrRtC7t3qw64hw+rheNALZz4t7/BxIkNXo5BryN+eAzjl+9GB3U+iKt70Tx/a3sO/vE/Rn4ykpVHVwLgrHfm8e6PM+OmGYR4XXxorsmkJvhdvlwNUKm9WPXRozXf6/XQq1eDPK0GVZ9jFH9rB3L+XxYZ8b/inrqNKH6l0suI07znCHksBIO5HBZkqM6wvXqpEDpwIPTurVbzBul3IoRosmwaVCZMmMCKFSv46quv8PLyIut0e72Pjw/u7pfXB0FcRGgo/PIL5OfDpk1qptF169TsZfv2wcmTNffNy4P589UH3Y03XvU6RMM6hbBkTLdz5ggJ9nFjXH9n3jswhc8OfwaAQWdgbJexzOo/C6Ov8ZL71jQ1Bc3vv9dsa9tWTTkzejS0aXNVpVvNhY7RtYYKXkpOJ3jAv/Eq3EkINS0m2jXd0U2qbn30VK9rp05115cSQggHYNOgsmTJEgAGVC8Df9r777/Pw9XTc4uG4+cHd9yhLgAnTqixuJ0719xnwwa1Eu4//qHmcOnZU4WW/v3V/YKCLntU0bBOIQyOCT4z66qJLL5OWsT4H5dj0Szo0HFvzL3MHjibdi0vvGDO0aNqFvenn1al6XSqtMxMtUjvmDEquNjJoKfLMiwmiMH+sKPMhZyCMlpuKif22T64VJ2ocz/tui7oBg1Ed/bpG1ljRwjhoGx+6kfYUKtWarrV2iIi4NFHVavLsWOqY8e2bfDii+r2L76AkSPV93/+qS4xMaqT7kUSgkGvI6JVGR8cmMt7v75HlaUKgBHtRjBQN5C/j/z7ec9ZnjgBn3yiTu1s26a29eihFp8GNSfZwoWqq06TUFys1neqfTl4EI4cQW8w0Oa9oxgSMyjdX0o+19HCcAxzz354Tvw/DMMGomvZ0tbPQAghrMouOtMKO9Kzp7oApKTUnCbaulUFl/a1Zmf73/9g+nT1vZcXdOigQkv15aabwNubnJIc5v80nyW/LKHCrDqBDm0zlDk3z6FrYFdWrlxZp4TqRXqXL4fVq1VfYFD9TAYPVl1xqvn4NNaBuApmM6SmqhBy9ChMmFAT4kaPhm++Oe+PaTonjtz3Myb8cfJ1omzKUlpOjcbJW96mQojmS/4CiguLilJzx1efhisvrztdq6enCidHjqiWgh071OW0om2beOnUKhZtX8SN+0uYlgmG9u2558Yn6Ny+H1T6YsrLq1n177S9e2HUqJrr3bur0zqjRtUMN7Yr1WHu4EEVTg4fhlrD6Ln33prRVddeq47RtdeitWtHqTmCjI3e5B1rRbkWjN7bhaip4YRPCcfZt6k0EwkhROORoCLqr3oESbVJk9SlslK1HOzfD/v3Y9r3Oyd3/0zXH/6PbIuaPfiJlABGbs6FdQfhn1PO7MIZuAOYP/4Y0/+pRn31/GUJWwNW4hbsS2RnX/xb+0KVD3zrC76+MGxYTafRsjLVYeVy57s3mVS4qn3p1q1mFeuNG9UiP2ffp/qyalXNVPNffw2vv153/y4uapnl9u1VjdVeeglt4ULyVueRHJdM8S/FABhaGIh4MoyIaRE4+0tAEUKIahJUxNVzcYGYGMraRrM4NJmX3DZwsuNJsMB1gdcx5+Y5jGhdBMYf4M8/MZ0ooDy7AKdTBbhr6kP8nx/6M/VVlYV0v+7mhtxvIRfYd57HS06uCSpxcarjr7u7CjE+Puqrr69q8fnXv9T31fddskQFjdotHtWOHFHhAtQ5p5deuvBzPnRIDf8F1aO3tFS1lrRvr74ajZw93a2maeSvLSQ5PpmibSrA6T30hE8OJ/ypcFwCrLC4kBBCNDESVMRVqzRX8u6ud5n30zwyT6nZUNu1bEfigETu7XivWs24PXzq/iBvvgmbas1v0sKlgn5dDvH6sx41n+uPPqrmAykshIKCmkv1dT+/mh0UFKivZWXqknnWSsMLF9YElcpKyM2te7ubm+pf4+VV0xkG1OM/+mjNbWdfao99Hj5cXS4if10+SXFJFP18OqC46wmbEEbEMxG4BEpAEUKIC5GgIq5YlaWK//z2HxI3JpJSqOb4MPoaie8fz5jOYziR7URlRc0Zo7171XQfOp2aFHf0aBgxQs+WLUncdluHmpE7N9xQ/+G2S5eqMHK+QHPqVE1IAXWaasyYuoHjQsOFRo6sGd10FQo2FZAUl0ThRrUek85VR9j4MCKei8A1+NxZloUQQtQlQUVclNminZn/JNDLjdhof3Q6jY/3fUz8hniO5B0BIKRFCDP7zeTWoL/y7VcuDJysunh89hnceafa1+jR6ozNqFFqFDQ0wISpBoNqYandynIhYWFWW+uocEshSXFJFKwtAEDnoiP08VAip0fiGioBRQgh6kuCirig1fsy68yWqqHh5rWbSo+PSC46CECARwBPtJ2Lz7FxrJjqwoSf6+5j9+6aoNKuHTzzjDWfgfUVbS8iKT6J/O/zAdA56wh5NITIFyJxi3C7xE8LIYQ4mwQVcV6r92UyfvluNFRAKdfvpsB5OZVVR6AIPJ29mX7js9wV+iQxbetO296nj5pH7u67a1pOHF3xrmKS4pPI+y5PbTBAyLgQImdE4m6U5SCEEOJKSVAR5zBbNBK/2Y8GlOv3UeD0HyoMf0B+FOx/DteSXnS4XcfzN96BQa/j+uvVKZ2//EWFEyudXbELxXuKSU5I5uRXp9dL0kPwQ8FEzYrCvbUEFCGEuFoSVMQ5diTlkVz0O/nO/6EirwIOjYAD/4aMHgBUOpnJ7rWGHUl59G7Tkq1ba6YfaS5O7T1FcmIyuZ+dHkWkh6DRQUTNisKjrYdtixNCCAciQUXUsTd7L1N+fIasvdGw5X+QX2sYrk7DNeIknteqVa5zilXfleYUUkr2l5CcmMyJT04vFqiDwFGBRMVF4dne07bFCSGEA5KgIigshPc/zWCTIZ4vU95DQwPTNBVSDFW4G0/ifk02Hm2zMXhWnvm5QK/m0zm09FApybOTyfkoB06vpdnqnlYY4414dpSAIoQQjUWCSjOVkqLWxvv48zK2/OSMpSoU7jDB9Rr3xNzLvtJYcj1/wc2Yi96l7lo8OiDYRw1VdnSlR0tJmZNC9vJssKhtAXcGYEww0qJzi4v/sBBCiKsmQaUZycmBt95SS9P89lv11tMdPgMO0DW0M//+2x66BHdhdQc16gfONCAAKqQAxA+PwaDX4ajKkspImZtC1gdZcDqntRzeEmOCEa9uXrYtTgghmhEJKg6svByys9UiyNXmztXQNB3ozBDxM1z7Nb0H5fLaA+PpFT7tzP2GdQphyZhudeZRAdWSEj88hmGdQqz5VKymPLWclHkpZC3LQqtSEc3/Nn+MCUa8e3rbuDohhGh+JKg4mNxc+O47+Oor+OEH6NkT1q+HgvIC3tz3Ck79vTH57oW2K+nbvj1zB85lgHHAefc1rFMIg2OCz5mZ1hFbUsrTy0l9MZXMf2WimVRA8RvihzHRiM8NPjauTgghmi8JKg5g925YuVIt+Lt1K1gsNbcdS7Iwe91CXtu5gILyAhgA3UO6M3fgcoa2GYpOd/HQYdDr6N2mZaPWb0sVmRWkzk8l4+0MtEoVUHwH+mJMNOJ7o69tixNCCCFBpSnKyoLg4JrrCQmqY2y1rl3h1ttNlLf5hP+cmEr8T2oobcdWHZlz8xxGth95yYDi6CqzK0ldkErGkgws5SrZ+fTzIXp2NL79fW1bnBBCiDMkqDQBZWXw00/w/ffq8scfcOwYREer2++6C5ycYOhQuGVIJT+eXMbcTXM5nnocgDZ+bUgckMioTqMw6A02fCa2V3mikrSX0zj+1nEsZSqgePfxVgFloG+zD3BCCGFvJKjYqbQ0+PRTFUw2blQdY6vpdLBrV01QefhhePAhM8t/X86QrxNJKkgCIMI7grj+cYztMhZng7P1n4QdMZ00kfZKGumL0rGUqIDi1cuL6MRo/Ib4SUARQgg7JUHFTuTlqb4lAQHq+s6dMK1mEA6hoarFZOhQGDQIWp7uNmLRLHy6/1PiN8RzMFetaBzkGcSMm2bwePfHcXVqRtPGnocp30T6q+mkv5GOuViNM27RvQXRs6Pxv9VfAooQQtg5CSo2UlUFO3bUnM7ZuRNmzoTERHX7LbeoUDJkiPoaE6NaUqppmsa3h79l1vpZ/JatJkXxd/fnub7PMTF2Ih7OzXu9marCKtJfTyfttTTMhSqgeHbxJHp2NC2Ht5SAIoQQTYQEFSuqqIBly+DHH2HtWjV1fW1Hj9Z87+OjRvGcTdM01iatZea6mWw/vh0ALxcvnur9FFN7T8XbtXnP9VFVXMXxRcdJ+0caVQVVAHh28sSYaCRgZAA6BxxaLYQQjkyCSiPRNNi/HzIz1akaAGdnmDED8vPVdT8/GDy4puUkPPzi+/w59WdmrJvBxpSNALg7uTO512Se6fMMLT0cdwhxfVSdqiJjcQapL6dSdVIFFI8OHhgTjLT6SysJKEII0URJUDkPs0VjR1IeADuS8rjhmsBLTnJmsahgsmGDumzaBCdOQGSkWlcHQK+HSZPUCJ0hQ6BHDzDUYxDOroxdzFo/i1VHVwHgYnDhie5PMP2m6QS3CL7ETzs2c6mZjCUZpC5IxXTCBIB7O3eM8UYC7wtEZ5CA0hRVvwcdfaJBIcSlSVA5y+p9mSR+s5+8U2UsjIVHPtiJfwv3i04b/+yz6pTOyZN1t7u7Q9u2cOoUtDi9fl11H5T6+CPnD+I2xPH5gc8BMOgMPHL9I8zqN4sIn4greXoOw1xmJuPtDFJfSsWUrQKKWxs3FVDuD0TvpLdxheJKVb8Hay/dEOLgSzcIIS5Mgkotq/ephfg0wLVWS0dWYTlP/Gc3z8bGYkpvxU8/wfLl4Oambi8vVyHFwwP69oUBA6B/fzV9vYvL5ddxNO8oCRsSWLF3BRoaOnSM7jya+P7xXON/TUM81SbLUmEh490MUl9MpTKzEgA3oxtRcVEEjQlC7ywBpSmr/R6sLauwnPHLd7NkTDcJK0I0MxJUTjNbNBK/2X/mD6RmgWPHfMjf0YpTKS2pSPNnQnlN6pg0SYURgL//He6/H7p3v3gwuVRzdmphKnM2zuH9Pe9j1tRIlbs73E3igEQ6BnZs6KfcpFgqLWQuyyR1XioV6RUAuEa4EjUriuCxwehdJKA0dWe/B2vTUCt3J36zn8ExwXIaSIhmRILKaTuS8uo0NRf8Es20H+uGA51LFb1usHDHrS4YjTXb27e/9P4v1pzd1ajjxZ9e5O1db1NpVq0Et7W9jTk3z6FbSLerel5NncVkIeuDLFLmpFCRqgKKS5gLUTOiCHkkBL2rBBRHcfZ78GwakFlYzo6kPIdef0oIUZcEldNyiuv+gXSPyMPd3YQuNB+XiJO4ReThElTI86O7cEfXsMva94Was48X5nDff5dQ4fYdFWb1+AOMA5h781z6Rva9mqfT5FmqLGQvzyZldgrlSerYuAS7EPlCJCGPhWBwa95LATiis9+DV3s/IYRjkKByWqCXW53rrsGFLF++ium79FSYdRe836WcrznbQglFTl9S5PQlmq4MzBAb1osXB85jYPTAZj0ZmWbWyP4om5TEFMqOlgHgHOhM5PORhD4RisFdAoqjqu9763Lfg0KIpk2Cymmx0f6E+LiRVViuzofrwGCoiRc6INhH9Su5HLWbsy2UU+z0LUVOn2HRFQPgbInG1/Qgrw2YRJ/WAQ31dJoczayR/Wk2yYnJlB1SAcWppRORz0US9vcwDJ4SUBzd2e/Bs13pe1AI0bRJUDnNoNcRPzyG8ct3c3Z7RvX1+OExl92JL6e4HA0TxYZVFDp/gkVXAICTJRxf0xg8LH3QoefEqYqrfg5NkWbRcPrZiV+n/0rZgdMBxc+JiGciCJsYhpOX/Io2F2e/B2uHlat5Dwohmjb5FKhlWKcQlozpdmYelWrBVziHg8lsYmvWJxx3nY9ZfwIAJ0sQPlUP4GkegI6aVoLm1pytaRq5X+aSFJeE5z5PyijDydeJ8KfCCZ8cjpO3/Go2R7Xfg7U71l7pe1AI0fTJp8FZhnUKYXBMMNuO5pB7YBvLxvas18y0tZktZj7a9xEJGxL4M/9P0INBa4mPaRQtzIPQ4Xzmvs2tOVvTNE5+e5Lk+GRO/XpKbfPQiJwWSeRTkTj7Ol9iD8LRVb8HZWZaIQRIUDkvg15HbLQ/Kw9wWX8gLZqFLw58QdyGOPaf2A9AK49W3HnNRFZvvw49Lo3WnG3vU45rmkbe6jyS45Ip/kX1zzG0MBAyMYT9HfcTeV8kzs4SUoRi0OtkCLIQApCg0iA0TWPV0VXMXDeTX7N+BcDXzZdn+zzLpF6TaOHSgtVtz51HpaGas+15ynFN08j/MZ/kuGSKthUBoPfQEzYpjIinI9D56Phj5R82rVEIIYT9kqByldYnrWfm+plsSdsCQAuXFky9YSrTek/D1833zP0aqznbnqccz1+vAkrh5kIA9G56Qv8eSuRzkbgEqil8TSaTTWoTQgjRNEhQuULb0rcxc91M1iatBcDNyY2JPSfybN9naeXZ6rw/09DN2fY65XjBpgKS45Mp2FAAgM5VR+gTKqC4hrharQ4hhBBNnwSVy7Qnaw8z183kuyPfAeCsd+bx7o/zwk0vEOoVatVa7G3K8cIthSTHJ5P/Yz4AOhcdIY+FEDU9CtcwCShCCCEunwSVejpw4gDxG+L53/7/AaDX6Xm4y8PM6j8Lo6/RJjXZy5TjRduLSIpPIv/70wHFWUfIoyFEvhCJW0TzGnYthBCiYUlQuYRj+cd4ccuLLP99ORbNgg4dozqNImFAAu1atrNpbbaecrx4VzFJ8UnkfZenNhggZFwIkTMicTe6N8pjCiGEaF4kqFxAelE6S9KWsPb3tVRZqgC449o7mHPzHK4Lus7G1Sm2mnK8eE8xyQnJnPzqpNqgh+CHgomaGYV7GwkoQgghGo4ElfN4Z9c7TF41mQqzmtZ+aJuhzLl5Dj3Detq4srqsPeX4qX2nSE5IJvezXLVBD0EPBBE1KwqPdh4N8hhCCCFEbRJUzqNzUGcqzBXEeMbw5p1vMrDNQFuXdEHWmHK85EAJyYnJnPjkxJnhRIGjAomKi8KzvedV718IIYS4EAkq53FD+A1sG7eNzN2Z3BR5k63LuaTGmqOl9FApybOTyfko50xzTat7WmGMN+LZUQKKEEKIxidB5QK6hXRjpW6lrcuot4aco6XszzKSZyeTvTwbLGpbwJ0BGBOMtOjcokEeQwghhKgPCSrijLKkMlLmppD1QRaY1baWw1tiTDDi1c3LtsUJIYRoliSoCMpTy0mZl0LWsiy0KnWOx/9Wf4yJRrx7etu4OiGEEM2ZBJVmrDy9nNT5qWS+m4lmUgHFb7AfxkQjPr19bFydEEIIIUGlWarIrCB1fioZ72SgVaiA4jvQF2OiEd8bfW1bnBBCCFGLBJVmpDK7ktQFqWQsycBSrnrJ+tzkg3G2Eb8BfjauTgghhDiXBJVmoPJEJWkvp3H8reNYylRA8e7tTfScaHwH+qLTWW9lZSGEEOJySFBxYKaTJtJeSSN9UTqWEhVQvGK9iJ4djd8QPwkoQggh7J4EFQdkyjeR/lo66a+nYy5W44xbdGtB9Oxo/G/zl4AihBCiyZCg4kCqCqtIfyOdtFfTMBeqgOLZxZPoxGhajmgpAUUIIUSTI0HFAVQVV3F80XHSXkmjKl+t9OzR0YPoxGgC7gxA10CLEgohhBDWJkGlCas6VUXG4gxSX06l6uTpgNLeA2OikVZ/aSUBRQghRJMnQaUJMpeayViSQeqCVEwnTAC4t3PHGG8k8L5AdAYJKEIIIRyDBJUmxFxmJvOdTFLmp2DKVgHFrbWbCigPBKJ30tu4QiGEEKJhSVBpAiwVFjL/lUnKiylUZlQC4GZ0I2pWFEEPBqF3loAihBDCMdnFJ9zixYsxGo24ubnRq1cvduzYYeuS7IKl0sLxpcfZfs12jkw8QmVGJa4RrrR7ux2xh2IJeSREQooQQgiHZvMWlY8//php06axdOlSevXqxeuvv87QoUM5dOgQgYGBti7PJiwmC1kfZJEyN4WKlAoAXMJciHohipBHQ9C7SjgRQgjRPNj8E+/VV1/lscceY9y4ccTExLB06VI8PDxYtmyZrUuzOkuVCig72u/g8GOHqUipwCXYhWsWXUOvo70I+3uYhBQhhBDNik1bVCorK9m1axfTp08/s02v1zNo0CC2bt16zv0rKiqoqKg4c72oqAgAk8mEyWRq0Nqq99fQ+z0fzaxx4r8nSJuXRvnRcgCcA50JeyaM4MeDMbgbsGDBYrI0ei3WZs3j3JzJcbYOOc7WIcfZehrrWF/O/nSapmkN+uiXISMjg7CwMLZs2ULv3r3PbH/22WfZuHEj27dvr3P/hIQEEhMTz9nPihUr8PDwaPR6G5wFnH92xvVjVwzpBrXJy0LFXRVU3loJbjauTwghhGgEpaWlPPDAAxQWFuLt7X3R+9q8j8rlmD59OtOmTTtzvaioiIiICIYMGXLJJ3q5TCYTa9asYfDgwTg7OzfovjWLxskvTpI2J43S/aUAOPk5ETYtjOC/B+Pk1aRelqvSmMdZ1JDjbB1ynK1DjrP1NNaxrj4jUh82/UQMCAjAYDCQnZ1dZ3t2djbBwcHn3N/V1RVXV9dztjs7OzfaL2tD7lvTNHK/yiU5PpmS30sAcPJ1IvypcMInh+Pk3XwCytka8zUUNeQ4W4ccZ+uQ42w9DX2sL2dfNu2Z6eLiQvfu3Vm7du2ZbRaLhbVr19Y5FdTUaZpG7je57Oq+iz/u/IOS30sweBuIio+iV1IvjDONzTqkCCGEEBdi80/HadOmMXbsWHr06EFsbCyvv/46JSUljBs3ztalXTVN08hbnUdyXDLFvxQDYGhhIGxyGBFPReDsL/8JCCGEEBdj86By3333ceLECeLi4sjKyqJr166sXr2aoKAgW5d2xTRNI//HfJLjkinaps7D6T30hE0KI+LpCFwCXGxcoRBCCNE02DyoAEycOJGJEyfauowGkb9eBZTCzYUA6N30hE4IJfLZSFwCJaAIIYQQl8MugoojKPipgOS4ZAo2FACgc9UR+kQokc9F4hpybgdgIYQQQlyaBJWrVLilkOT4ZPJ/zAdA56Ij5LEQoqZH4RomAUUIIYS4GhJUrlDRjiKS45PJW50HgM5ZR/AjwUS9EIVbpMzUJoQQQjQECSqXqXhXMUnxSeR9pwIKBggZF0LkjEjcje62LU4IIYRwMBJU6ql4TzHJCcmc/Oqk2qCH4IeCiZoZhXsbCShCCCFEY5Cgcgkl+0pIn5dO7me5aoMOgkYHETUrCo92TXB9ISGEEKIJkaByAaUHSnH/hzt7ft4DGqCDwPsCiYqLwrODp63LE0IIIZoFCSrnkf5GOkenHsVFU/OetPpLK6Lio2jRqYWNKxNCCCGaFwkq5+HT3wcAUy8TPd/qiW8PX9sWJIQQQjRTNl2U0F55dfWi+4HulE4vxbOLnOYRQgghbEWCygW4tZa5UIQQQghbk6AihBBCCLslQUUIIYQQdkuCihBCCCHslgQVIYQQQtgtCSpCCCGEsFsSVIQQQghhtySoCCGEEMJuSVARQgghhN2SoCKEEEIIuyVBRQghhBB2S4KKEEIIIeyWBBUhhBBC2C0JKkIIIYSwW062LuBqaJoGQFFRUYPv22QyUVpaSlFREc7Ozg2+f6HIcbYOOc7WIcfZOuQ4W09jHevqz+3qz/GLadJBpbi4GICIiAgbVyKEEEKIy1VcXIyPj89F76PT6hNn7JTFYiEjIwMvLy90Ol2D7ruoqIiIiAjS0tLw9vZu0H2LGnKcrUOOs3XIcbYOOc7W01jHWtM0iouLCQ0NRa+/eC+UJt2iotfrCQ8Pb9TH8Pb2ljeCFchxtg45ztYhx9k65DhbT2Mc60u1pFSTzrRCCCGEsFsSVIQQQghhtySoXICrqyvx8fG4urrauhSHJsfZOuQ4W4ccZ+uQ42w99nCsm3RnWiGEEEI4NmlREUIIIYTdkqAihBBCCLslQUUIIYQQdkuCihBCCCHslgSV81i8eDFGoxE3Nzd69erFjh07bF2Sw5k/fz49e/bEy8uLwMBARo4cyaFDh2xdlkN76aWX0Ol0TJkyxdalOKTjx48zZswYWrZsibu7O9dddx2//PKLrctyKGazmVmzZhEdHY27uztt2rRhzpw59VovRlzYpk2bGD58OKGhoeh0Or788ss6t2uaRlxcHCEhIbi7uzNo0CCOHDlitfokqJzl448/Ztq0acTHx7N79266dOnC0KFDycnJsXVpDmXjxo1MmDCBbdu2sWbNGkwmE0OGDKGkpMTWpTmknTt38vbbb9O5c2dbl+KQ8vPz6du3L87OzqxatYr9+/fzyiuv4OfnZ+vSHMqCBQtYsmQJb731FgcOHGDBggUsXLiQN99809alNWklJSV06dKFxYsXn/f2hQsXsmjRIpYuXcr27dvx9PRk6NChlJeXW6dATdQRGxurTZgw4cx1s9mshYaGavPnz7dhVY4vJydHA7SNGzfauhSHU1xcrLVt21Zbs2aN1r9/f+3JJ5+0dUkO57nnntNuvPFGW5fh8G6//XbtkUceqbPtrrvu0kaPHm2jihwPoH3xxRdnrlssFi04OFh7+eWXz2wrKCjQXF1dtY8++sgqNUmLSi2VlZXs2rWLQYMGndmm1+sZNGgQW7dutWFljq+wsBAAf39/G1fieCZMmMDtt99e5/daNKyvv/6aHj16cM899xAYGMj111/Pu+++a+uyHE6fPn1Yu3Ythw8fBuC3335j8+bN3HrrrTauzHElJSWRlZVV5++Hj48PvXr1strnYpNelLCh5ebmYjabCQoKqrM9KCiIgwcP2qgqx2exWJgyZQp9+/alU6dOti7Hofz3v/9l9+7d7Ny509alOLRjx46xZMkSpk2bxgsvvMDOnTuZPHkyLi4ujB071tblOYznn3+eoqIi2rdvj8FgwGw2M2/ePEaPHm3r0hxWVlYWwHk/F6tva2wSVITNTZgwgX379rF582Zbl+JQ0tLSePLJJ1mzZg1ubm62LsehWSwWevTowYsvvgjA9ddfz759+1i6dKkElQb0ySef8OGHH7JixQo6duzInj17mDJlCqGhoXKcHZic+qklICAAg8FAdnZ2ne3Z2dkEBwfbqCrHNnHiRL799lvWr19PeHi4rctxKLt27SInJ4du3brh5OSEk5MTGzduZNGiRTg5OWE2m21dosMICQkhJiamzrYOHTqQmppqo4oc0zPPPMPzzz/PqFGjuO6663jwwQeZOnUq8+fPt3VpDqv6s8+Wn4sSVGpxcXGhe/furF279sw2i8XC2rVr6d27tw0rczyapjFx4kS++OIL1q1bR3R0tK1Lcji33HILe/fuZc+ePWcuPXr0YPTo0ezZsweDwWDrEh1G3759zxlef/jwYaKiomxUkWMqLS1Fr6/7sWUwGLBYLDaqyPFFR0cTHBxc53OxqKiI7du3W+1zUU79nGXatGmMHTuWHj16EBsby+uvv05JSQnjxo2zdWkOZcKECaxYsYKvvvoKLy+vM+c6fXx8cHd3t3F1jsHLy+ucPj+enp60bNlS+gI1sKlTp9KnTx9efPFF7r33Xnbs2ME777zDO++8Y+vSHMrw4cOZN28ekZGRdOzYkV9//ZVXX32VRx55xNalNWmnTp3i6NGjZ64nJSWxZ88e/P39iYyMZMqUKcydO5e2bdsSHR3NrFmzCA0NZeTIkdYp0Cpji5qYN998U4uMjNRcXFy02NhYbdu2bbYuyeEA5728//77ti7Nocnw5MbzzTffaJ06ddJcXV219u3ba++8846tS3I4RUVF2pNPPqlFRkZqbm5uWuvWrbUZM2ZoFRUVti6tSVu/fv15/x6PHTtW0zQ1RHnWrFlaUFCQ5urqqt1yyy3aoUOHrFafTtNkSj8hhBBC2CfpoyKEEEIIuyVBRQghhBB2S4KKEEIIIeyWBBUhhBBC2C0JKkIIIYSwWxJUhBBCCGG3JKgIIYQQwm5JUBFCCCGE3ZKgIoSwG2azmT59+nDXXXfV2V5YWEhERAQzZsywUWVCCFuRmWmFEHbl8OHDdO3alXfffZfRo0cD8NBDD/Hbb7+xc+dOXFxcbFyhEMKaJKgIIezOokWLSEhI4I8//mDHjh3cc8897Ny5ky5duti6NCGElUlQEULYHU3TGDhwIAaDgb179zJp0iRmzpxp67KEEDYgQUUIYZcOHjxIhw4duO6669i9ezdOTk62LkkIYQPSmVYIYZeWLVuGh4cHSUlJpKen27ocIYSNSIuKEMLubNmyhf79+/PDDz8wd+5cAH788Ud0Op2NKxNCWJu0qAgh7EppaSkPP/ww48eP5+abb+a9995jx44dLF261NalCSFsQFpUhBB25cknn2TlypX89ttveHh4APD222/z9NNPs3fvXoxGo20LFEJYlQQVIYTd2LhxI7fccgsbNmzgxhtvrHPb0KFDqaqqklNAQjQzElSEEEIIYbekj4oQQggh7JYEFSGEEELYLQkqQgghhLBbElSEEEIIYbckqAghhBDCbklQEUIIIYTdkqAihBBCCLslQUUIIYQQdkuCihBCCCHslgQVIYQQQtgtCSpCCCGEsFsSVIQQQghht/4/ABERPvl6M+IAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}