Gradient_Decent.ipynb

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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Gradient Decent",
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/reddyprasade/Machine-Learning-with-Scikit-Learn-Python-3.x/blob/master/Gradient_Decent.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a5qbsjatjQes"
      },
      "source": [
        "### Gradient Descent \n",
        "\n",
        "* Gradient Descent is a popular optimization technique in Machine Learning and Deep Learning, and it can be used with most, if not all, of the learning algorithms.\n",
        "* A gradient is the slope of a function. It measures the degree of change of a variable in response to the changes of another variable.\n",
        "* Mathematically, Gradient Descent is a convex function whose output is the partial derivative of a set of parameters of its inputs. The greater the gradient, the steeper the slope.\n",
        "* Starting from an initial value, Gradient Descent is run iteratively to find the optimal values of the parameters to find the minimum possible value of the given cost function.\n",
        "\n",
        "#### Types of Gradient Descent:\n",
        "\n",
        "\n",
        "Typically, there are three types of Gradient Descent:\n",
        "\n",
        "- Batch Gradient Descent\n",
        "- Stochastic Gradient Descent\n",
        "- Mini-batch Gradient Descent"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_XuWmiBbY9Z2"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kAb7ntY7Y9aB"
      },
      "source": [
        "plt.style.use(['ggplot'])"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YjrBt3VLY9aD"
      },
      "source": [
        "# Create Data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3YaEIonqY9aF"
      },
      "source": [
        "<h5> Generate some data with:\n",
        "\\begin{equation} \\theta_0= 4 \\end{equation} \n",
        "\\begin{equation} \\theta_1= 3 \\end{equation} \n",
        "\n",
        "Add some Gaussian noise to the data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6uZUKbTJY9aG"
      },
      "source": [
        "X = 2 * np.random.rand(100,1)\n",
        "y = 4 +3 * X+np.random.randn(100,1)"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ySi6YTFiY9aL"
      },
      "source": [
        "Let's plot our data to check the relation between X and Y"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hGwW_tP3Y9aM",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "outputId": "0068053b-0525-43c7-e491-b7227bea23b4"
      },
      "source": [
        "\n",
        "plt.plot(X,y,'b.')\n",
        "plt.xlabel(\"$x$\", fontsize=18)\n",
        "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
        "_ =plt.axis([0,2,0,15])"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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GrrMjw0D7kfvaP6ONdbHEGh7ej4HiHjt5eYzWEbPEGh4mBopJwZQz4mG5hjYy/9auPstoHXG8jxWEi4mBYk4w5YxA28RS0pBZ3gn0WUbsiHlGGDomBoo5wZQzutrGaHXy7pJZ3gnms2KtI247SJg4UfFdxBbruF42xZxg7qrV1TbB3A3MCHctC5bMu4zF6h3LOtP+Dnp5eZao+L5l4BkDxZxgyhldbdNZnbztyHHgQBMee8z/GYURS1AyyztGLBVFUvuDBLdb6D6YrhUmBopJwZQzOtvGX+fXvrykKIDXC3i96nKKkUtQMss7sVYq6kr7gwSrFTF/htSGiYHIj4s7v/ZHjiaTgMkkoCjqMwqjTdWk7mt/kDBxYiIyM+Pj+2RiIArCxUeOixadQV2dWVVOkTlV04glqXjVdpBgt/fUdeVULTExEAWh45FjY5fbhNKhX5wE2pekzOZkTJ16DlOmnNM0QTAxxTcmBgpZdzuNaOp0Lo410JFjqPV3f+MS7UtSLS0C69cn4a23EjUbszDyWAlpg4mBQtLdTiOaOh0tYvU3LtFWkvJ6ASEAIRR4PNqNWfiLqX1sRv2+SJ64u44hmuafG1Ewc/zDeX95eQL+/GeTob6X7v6twfB3XUBbSWratLOwWsO/ZqC0VAnrt35xTKmpLb65/FOnphvqO6LIiKszhmg6WjWq7g6w+nu/+ntJN8z3osW6P12t7pqT48GUKY1h30L07rstcLuTQ/6tXxwTZ1vFn7hKDPyBd193L3Dy9/5Vq2yG/F60upirq3GJcK8Z2LmzB9xuhL1PL27XSAvjUeTFVWIw2sqP0aq7Fzi1f395eQL++18TzObg74im5eB1tF7MNXJkE6zWZLjd3V+6It6udqY4Swz8gRuLelomMH16C+64o67L76U75cBomg3VXTk5Hmzd2owtWxp5C1EKWVwlBqDjDzyeOgutBLtP1aU9gUGDAt85LdwZM/E4vpSbK5CZ2aB3GBSF4i4xtBePnUWkhbJPLy7tjR3b6e3HO31P24yZQO2FM77UPsG1vWfkyCbk5QUM0xBKSxVs2WLjQQ+FTLPEcPbsWaxZswbHjx+HoiiYOXMmhg0bplXzfnEwWr5Q9unFpb3c3JSASw6EMmOmfcce6viSusxlA6CgpaV1EPbDD1sMvy5/d2YlEWmWGNauXYtrr70Wjz32GJqbm9HUpP/ALwej5Qt1n4ZTuw5mxoy/M5dQxpfaJxyvt/U5IVqTT0mJ8W/Y0t1ZSRTfNEkM586dw8GDBzF79uzWRi0WWCz6V7E4GC2f1vu0s/b8nUnMmdMQdDztE1zrjKnW5SmCLXnpTeasJIo/ihAi4r/yr776Ci+99BIGDBiAr7/+GkOGDMGDDz6Inj17qrZzOp1wOp0AgIKCArjd7kiH1i0WiwXNzc16hxFQPMZZWqogL88Ct7t1NdStW5uRmxvaT720VEFJieJLBG3/P3q0OSr2Z1mZBdu2eTF2rAj5b9dSPP4+I8VqtUr5HE0Sw9GjR/H0009j8eLFyMrKwtq1a5GYmIi77767y/dVV1dHOrRusdvtcEXBOrzhxqn1jC3Z+zNS8cf69641xilPRkaGlM/RpJ6Tnp6O9PR0ZGVlAQByc3OxadMmLZqOeZHq/GJhxhbn3hOFR5PE0Lt3b6Snp6O6uhoZGRnYu3cvBgwYoEXTmtHjeojy8gTcdZcdHg+QkJCMt95ySWubM7aI4pdmI8DTp0/HypUr0dzcjD59+mDWrFlaNR1xeh1dv/12IlqHYVpvVP7224nS2uWMLaL4pVliGDx4MAoKCiLy2Xpfvazf0bUS4HH4OGOLKH7pP2e0m4xQC9fr6HrKlHPYsCHxQilJYMqUc1I/nzV6ovgU9YnBCLVwvY6uc3I8eOstbdvV++yMiCIv6hODUWrheh1da9luJM/OyssTUFVlQnZ2AhMOkc6iPjHEYy1cr6P27p6ddRa3Ue/gRhSvoj4xAPodreuxeqWeYyrhLETXfnXSzuI2QjmQiH4QE4lBD3qtXqlnJxrK2VlbAnO7FZhMNjgc5zuN2yjlQCJqxcQQJr1Wr9S7Ew327Kx1/yjweltXJ/33vxM7vX1nW8KpqkpFdnbHO7gZfcDb6PERhSquE8P69YnYvDkRkyY1Ytq0xpDeK3v1ymA7l3DGVPQoeY0c2QSTyXZhyWoFQghMnXoO/ft7/caRk+NBXp4XLlfHpKD3dOSuGD0+onDEbWJYvz4RCxb0BgB8/HHr7SFDSQ4y76kbaucSypiKXiWvnBwPliw5g6ef7g2vV8BqFZgypTHkto0+/mD0+IjCEbeJYfPmxAv/13q/4c2bE0M+a5B1T91gO5dwShZ63rBl2rRG/OhHzd0qs+hdOgvE6PERhSNuE8OkSY0XzhSE77Fegulcwi1ZaHXDls6SVndnjBl9OrLR4yMKR9wmhrazg3DHGGQKpnMJt2Qhs+TVmUjX2Y2+NIfR4yMKVdwmBqA1OeiZENoL1Ll0p2Qhq+TVmWCSFmfuEEWPuE4MXTFaR2bkkkWgpMWZO0TRhYnBD6N2ZEYtWQRKWpy5QxRdmBj8YEcWuq6SFmfuEEUXJgY/2JF1LdQym5HLYETUUUwlBlnjAuzIOhdumc2oZTAi6ihmEoPscQF2ZP6xzEYU+0x6ByBL+w7L41Gwc2cPvUOKSa1lNgGzObIXzBGRfjQ9Y/B6vVi4cCHS0tKwcOFCqZ/NcQFtsMxGFPs0TQybN29G//790dgo/6IydljaYZmNKLZpVko6deoUKioqMGHChIi1kZPjwZw5Dey0iIi6QbMzhtdeew3Tpk3r8mzB6XTC6XQCAAoKCmC327UKLywWi8XwMQLGibO0VEFJiYKxYwVyc0WH140SZyCMUy7GaTyaJIZdu3YhJSUFQ4YMwf79+zvdzuFwwOFw+B67XC4twgub3W43fIyAMeJUzxoTfmeNGSHOYDBOuRinPBkZGVI+R5PEcPjwYZSXl2P37t1wu91obGzEypUrMXfuXC2aJwPgNFei6KFJYrj33ntx7733AgD279+P999/n0khznDWGFH0iJkL3MjYOGuMKHponhiuvPJKXHnllVo3GxSjLbUdazjNlSg68IzhAqMutU1EpLWYWRKju7ikBhFRKyaGC7gGEBFRK5aSLuDgKBFRKyaGdjg4SkTEUhIREV2EiYGIiFSYGIiISIWJgYiIVJgYiIhIhYmBiIhUmBiIiEiFiYGIiFSYGIiISIWJgYiIVGI2MZSXJ2DVKhvKyxP0DoWIKKrE5FpJvLcCEVH4YvKMgfdWICIKX0wmBt5bgYgofDFZSuK9FYiIwqdJYnC5XCgqKsLp06ehKAocDgcmTZoU0TZ5bwUiovBokhjMZjPuv/9+DBkyBI2NjVi4cCGys7MxYMAALZonIqIQaDLGkJqaiiFDhgAAEhMT0b9/f9TW1mrRNBERhUjzMYaamhocO3YMmZmZHV5zOp1wOp0AgIKCAtjtdq3DC4nFYjF8jADjlI1xysU4jUcRQgitGjt//jyeeeYZTJ48GSNGjAi4fXV1tQZRhc9ut8PlcukdRkCMUy7GKRfjlCcjI0PK52g2XbW5uRmFhYUYM2ZMUEkhWLzCmYhILk1KSUIIrFmzBv3798cdd9wh7XN5hTMRkXyaJIbDhw+jpKQEgwYNwvz58wEA99xzD6677rpufW77K5zbHjMxEBF1jyaJ4Uc/+hHefPNN6Z/beoWzDQB4hTMRkSRRfeUzr3AmIpIvqhMDwCuciYhki8lF9IiIKHxMDEREpMLEQEREKkwMRESkwsRAREQqTAxERKTCxEBERCpMDEREpMLEQEREKkwMRESkwsRAREQqTAxERKTCxEBERCpMDEREpMLEQEREKkwMRESkwsRAREQqTAxERKSi2a09KysrsXbtWni9XkyYMAF33nmnVk0TEVEINDlj8Hq9ePXVV/HUU09h+fLl2L59O06cOKFF00REFCJNEsORI0fQr18/9O3bFxaLBaNGjUJZWZkWTRMRUYg0KSXV1tYiPT3d9zg9PR1ffPFFh+2cTiecTicAoKCgABkZGVqE1y3RECPAOGVjnHIxTmMx1OCzw+FAQUEBCgoKsHDhQr3DCSgaYgQYp2yMUy7GKY+sGDVJDGlpaTh16pTv8alTp5CWlqZF00REFCJNEsPQoUPx7bffoqamBs3NzdixYwdycnK0aJqIiEJkXrRo0aJIN2IymdCvXz+sWrUKW7duxZgxY5CbmxvwfUOGDIl0aN0WDTECjFM2xikX45RHRoyKEEJIiIWIiGKEoQafiYhIf0wMRESkotmSGG0CLY3h8Xjw4osv4ssvv0RycjLmzZuHPn36AAA2btyI4uJimEwmPPTQQ7j22mt1i/ODDz7Af/7zH5jNZvTq1QszZ87EpZdeCgCYOnUqBg0aBACw2+1YsGCBbnF+9NFHeP31132zwPLy8jBhwgTfa++88w4AYPLkyRg3bpxucb722mvYv38/AMDtduPMmTN47bXXAGi3P1evXo2KigqkpKSgsLCww+tCCKxduxa7d+9Gjx49MGvWLF89V8t9GSjOTz75BO+++y6EEEhMTMQjjzyCwYMHAwBmz56Nnj17wmQywWw2o6CgQLc49+/fjz//+c++f98jRozAlClTAGi3hE6gGN977z188sknAFpXcDhx4gReffVV2Gw2Tfely+VCUVERTp8+DUVR4HA4MGnSJNU2Un+fQkMtLS3i0UcfFf/73/+Ex+MRjz/+uDh+/Lhqm61bt4qXXnpJCCHEp59+KpYtWyaEEOL48ePi8ccfF263W5w8eVI8+uijoqWlRbc49+7dK86fPy+EEOLDDz/0xSmEENOmTYtIXOHEuW3bNvHKK690eG99fb2YPXu2qK+vV/2/XnG2t3nzZlFUVOR7rNX+3L9/vzh69Kj47W9/6/f1Xbt2iSVLlgiv1ysOHz4snnzySSGEtvsymDgPHTrka7+iosIXpxBCzJo1S5w5cyZisYUS5759+8Rzzz3X4flQfy+RjLG9srIysWjRIt9jLfdlbW2tOHr0qBBCiHPnzom5c+d22Ccyf5+alpKCWRqjvLzcl81yc3Oxb98+CCFQVlaGUaNGISEhAX369EG/fv1w5MgR3eK86qqr0KNHDwBAVlYWamtrIxJLd+PsTGVlJbKzs2Gz2WCz2ZCdnY3KykpDxLl9+3aMHj06IrF0Zfjw4bDZbJ2+Xl5ejrFjx0JRFAwbNgxnz55FXV2dpvsymDivuOIK3+tZWVmqa4i0FCjOzmi5hE4oMW7fvh033XRTROIIJDU11Xf0n5iYiP79+3foc2T+PjUtJQWzNEb7bcxmM5KSklBfX4/a2lpkZWX5tktLS4tYZxzsEh5tiouLVWUtj8eDhQsXwmw24+c//zluvPFGXeP87LPPcPDgQVx22WX45S9/Cbvd3uG9Rtmf3333HWpqanDVVVf5ntNqfwZSW1sLu93ue5yeno7a2lpN92WoiouL8eMf/1j13JIlSwAAt956KxwOhx5h+Xz++eeYP38+UlNTcf/992PgwIEh//vTQlNTEyorK/Hwww+rntdjX9bU1ODYsWPIzMxUPS/z96n5GEOsKSkpwZdffon2l4OsXr0aaWlpOHnyJJ599lkMGjQI/fr10yW+66+/HjfddBMSEhLw73//G0VFRXjmmWd0iSUY27dvR25uLkymH05mjbQ/o8m+ffuwbds2PPvss77nFi9ejLS0NJw5cwZ//OMfkZGRgeHDh+sS3+WXX47Vq1ejZ8+eqKiowPPPP4+VK1fqEksgu3btUp2JAfrsy/Pnz6OwsBAPPvggkpKSItaOpqWkYJbGaL9NS0sLzp07h+Tk5A7vra2tjdiyGsEu4VFVVYWNGzfiiSeeQEJCgur9ANC3b18MHz4cX331lW5xJicn+2KbMGECvvzyS7/vNcL+BIAdO3Z0OF3Xan8GkpaWBpfL5Xvc9ndouS+D9fXXX+Oll17C/PnzkZyc7Hu+La6UlBTccMMNESvHBiMpKQk9e/YEAFx33XVoaWnB999/b8gldPyVN7Xel83NzSgsLMSYMWMwYsSIDq/L/H1qmhiCWRrj+uuvx0cffQQAKC0txZVXXglFUZCTk4MdO3bA4xx6NowAAAPtSURBVPGgpqYG3377bYdTKS3jPHbsGP7yl7/giSeeQEpKiu/5hoYGeDweAMD333+Pw4cPY8CAAbrFWVdX5/v/8vJyXyzXXnst9uzZg4aGBjQ0NGDPnj0Rm+UV7JIo//3vf3H27FkMGzbM95yW+zOQnJwclJSUQAiBzz//HElJSUhNTdV0XwbD5XJh6dKlePTRR1WrgZ4/fx6NjY2+/6+qqvLN9tLD6dOnIS5cX3vkyBF4vV4kJycbbgmdc+fO4cCBA6oYtN6XQgisWbMG/fv3xx133OF3G5m/T82vfK6oqMC6devg9Xpxyy23YPLkydiwYQOGDh2KnJwcuN1uvPjiizh27BhsNhvmzZuHvn37AgDeeecdbNu2DSaTCQ8++GCH2qmWcS5evBjffPMNevfuDeCHaZSHDx/Gyy+/DJPJBK/Xi9tvvx3jx4/XLc433ngD5eXlMJvNsNlseOSRR9C/f38ArfXnjRs3AmidwnbLLbfoFicAvPnmm/B4PLjvvvt879Nyf65YsQIHDhxAfX09UlJSkJ+fj+bmZgDAT37yEwgh8Oqrr2LPnj2wWq2YNWsWhg4dCkDbfRkozjVr1uCzzz7z1ZvbplKePHkSS5cuBdB6Nj569GhMnjxZtzi3bt2Kf/3rXzCbzbBarXjggQdwxRVXAPD/e9EjRqB1qmdlZSXmzZvne5/W+/LQoUP4wx/+gEGDBkFRFADAPffc4ztDkP375JIYRESkwiufiYhIhYmBiIhUmBiIiEiFiYGIiFSYGIiISIWJgYiIVJgYiIhIhYmBiIhUmBiIiEiFiYGoC263GzNmzMDMmTN9aza1WbNmDaZOnYrt27frFB1RZDAxEHXBarUiPz8fp06dwocffuh7/o033kBxcTGmT5+u281biCKFiYEogHHjxmHgwIHYtGkTzp8/j3/+85/YtGkT8vPzcdttt+kdHpF0XESPKAi7du3Cn/70J1x11VXYv38/brvtNkyfPl3vsIgigmcMREG4/vrrcfnll2Pfvn0YOXIkHnroIb1DIooYJgaiIOzYscN357jExETfmvhEsYiJgSiAPXv24MUXX8SNN96IUaNGYdu2bThx4oTeYRFFDBMDURe++OILLF26FFdccQXmzp2Lu+++G4qi4I033tA7NKKIYWIg6sSJEyfw3HPPISMjA/Pnz0dCQgL69euH8ePHo7y8HIcOHdI7RKKIYGIg8sPlcmHJkiW45JJL8OSTTyIpKcn32i9+8QtYrVb87W9/0zFCosjhdFUiIlLhGQMREakwMRARkQoTAxERqTAxEBGRChMDERGpMDEQEZEKEwMREakwMRARkQoTAxERqfw/YFdbwLm60CsAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Iu-naihzY9aR"
      },
      "source": [
        "#  Analytical way of Linear Regression"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "myA1zAnBY9aS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "12c903a0-5eed-49c2-957f-6b9f42034964"
      },
      "source": [
        "X_b = np.c_[np.ones((100,1)),X]\n",
        "theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)\n",
        "print(theta_best)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[3.9073148 ]\n",
            " [3.01648259]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cwFeVycaY9aa"
      },
      "source": [
        "<h5>This is close to our real thetas 4 and 3. It cannot be accurate due to the noise I have introduced in data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mLJ9auYUY9aa",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3c0fe3b9-6562-4458-bc84-35251238c532"
      },
      "source": [
        "X_new = np.array([[0],[2]])\n",
        "X_new_b = np.c_[np.ones((2,1)),X_new]\n",
        "y_predict = X_new_b.dot(theta_best)\n",
        "y_predict"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[3.9073148 ],\n",
              "       [9.94027997]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kDwGIe-8Y9af"
      },
      "source": [
        "<h5>Let's plot prediction line with calculated:theta"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GnIBx5ndY9ag",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 304
        },
        "outputId": "2a14c700-56ce-4719-a96d-e861b6c6c75e"
      },
      "source": [
        "plt.plot(X_new,y_predict,'r-')\n",
        "plt.plot(X,y,'b.')\n",
        "plt.xlabel(\"$x_1$\", fontsize=18)\n",
        "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
        "plt.axis([0,2,0,15])\n"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.0, 2.0, 0.0, 15.0)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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pbofny1GAqt0sLheM+/Z5rl98w/btyJFHYgumwjLwJEZcOxLllkWQx46FiIpqeI+l8H2PO8I4kK+8DobG4wwHDhyAw+HA7bff7tVzKyoqsGnTJjz77LMwmUx45plnkJ+fjylTpvhVNHV8zf0xTZsW7Ko6Dl+OAtrVzSIE9F9/rRgwrp859GWfm5Dz8/9F+rURuHPeQIhu3VDZ6KnhuMNsTjjOTPI6GJKTkyFJEnJycnDw4EH88pe/RM+ePb1uyOVyQZZl6PV6yLKM+Ph4vwqm8NDcHxODwXv1RwFCAJIkEB/vbPXxvnSz6H74oSEI8vKg/+EHAIAjKQm111wDm8WCvNhrcNO9g2D/QYJxv8C69KY7/XDcYTYnHGcmSUK4VyrxxtKlS3HixAl069YNzz//PKKaOcmkJRs3bsT//d//wWQyYeTIkVi8eHGTx1itVlitVgBAdnY2ZFn2+vWDwWAwwOFwBLuMNoVinYWFEqZNM0CWAZMJ2LzZAYtFH3J1Nqe927OwUEJuroRJkwTS073+82vilVd0+N3v9HC53NeY37zZoXg9r+usqICUmwtdTg50W7ZAOnwYACASEyEmT4Zr6lS4pk4FkpM9M4f+8hcdHn9cD6dTgl4v8PjjTjz0kKvJ73npe9zc7xuKn0+g6fvUWp1qvaftpVb3vE9nPicnJ+PEiRO45ZZbfAqFqqoqFBUVYdWqVYiOjsYzzzyD3NxcTJo0SfG4rKwsZGVleW6XtXOmQqCZzeaQqrGlPvtQqxNw72Pefruh3uRkOxyO0KizrbEPs9mMzZvP+9U1o+xead+qnidOxECIWLhcEmRZYNOmGiQnN1wkvqX3Xbp4EaavvnKfYZyXB+OePe6ZQ9HRsKWnwzZnjnvmUEqKZ+YQAKC83PPf1FQjjEb39Y2NRoHU1LMoK1P+Hs29x829vaH4+WzufZo2La7FOpOT3f+Adk+wapekpCRVXsfrYHA4HNi/fz8GDhyIyZMn+9TInj170KNHD3Tt2hUAMH78eBw+fLhJMJD/OmJ/bqhM82scBADa3I6FhZLf21rN7hWvuzDsdphKSz0DxqaSEkh2O4TRCHn0aFQ+8ABkiwXyqFHur/Ze8HbcIlTeY1919q5Or4Pho48+wpkzZ3D//fdD8vFEFLPZjCNHjsBms8FkMmHPnj0YOHCgz8VSyzpLf67aLg3Um26qaXM75uZKfm9rNfujW9w5u1ww7N8P3c6dSPjsM5i2b4euuhpCkmAfPhzVd9/tXnNo3DiI6Oh2tR+un7Hm3yffr+zWUbUaDFVVVSgtLcXx48fx4Ycf4vrrr/fMTvLFoEGDkJ6ejmXLlkGv16N///6KLiNqv3AcANPCpYEKuJd/BlrejpMmtf2Ylqh9IlZamh1pY2Tov/0WEW/WHRHk50NfUeH+bQYORM2NN8JmscA2YQLEJWuddQb+TIsO1zOavdXq4PO2bdvwwgsvIC4uDpMmTcKtt96q6clsp06d0qwtf4Ra32hHGmNoTjDqbK4vGUDAxhjUojt9uuH6xdu2wfD99wAAZ69e7hCwWNDlF79AmR/XL24vX3fEgXzf1RzT6Qh/R5qMMVgsFlgsFlUaosAL50P7QGnpm2Fb21HrbS2dP4+IggLPOIHxyBEAgKtbN9gyMlC1cCFsFgucAwd6Zg51UWGpCV+F2lgXu1j9w+sxUKcXkoFaU4OIoiLPpSuNu3dDcrngioqCPH48Ls6ZA9ligT0lxX2lmxARajtidrH6h8FAYcmb7oyQWpLD4YCxtNRzYpmppASSLEMYDJCvuAJVv/ude8B49GivZw41pubv2tprhdqOuLOPFfiLwUBhx5vujLYeE/DQcLlgOHgQEXVHBKbCQuiq3Ocg2IcNQ/Wdd7qDYPx4iC5d2tWUmt07bb1WKO6IQ/KIMMQxGCjseNOd0dpjAtVPrv/uu4Yjgrw86OtOGHNcfjlqZsxwB0FmJlwqzxxSs3vHm9cKtx1x/ZeE666TPCexhTsGA4Udb7ozWnuMNzs/b44odGfOICI/3zNgbDhxAgDg7NkTtsmT3UFgscDZu3f7f+lWqNm9E2pdRYHW+EvC88+7z+QOp9BrCYOBwo433RmtPaalnV99GPTtq8PSpU2PKKQLF7Br7TEUflqLq868i4nH1wEAXHFx7plDv/0tZIsFjkZrDmlBze6dUOwqCqTGXxJkWQR9MF0rPi2ipzWex6AO1um7S48IGn9zlCTA5QJcLgl6nQt/GP8JHql9DMWlUcgSn0OGCSadAx/Oex0j5/4M9uHDgzJzKJS2Z2tCuc7G77vJBLz9dllIB4PmayURdSaX9pM3/uaok1zQwQkJgMllxzXb/wyM1uOzCQ9DLoyE06WDLOnxr6RbkDKyquVGKOQ1PkK67rooJCeHbiioicFA1BIhYDh0CBHbtuHanAo87/wvyDDCJOxY2Ssbp/uOQvq0SFw+739QFhOD0cVGGOcAsIt297+H1FTaTq7+S4LZHBnUlVO1xGAgakR/4oR71lD9RWp++gkAYOnfHx9f0w1bIqfh6vkDkDx2gec59X2x/va/t9ZtpdfHYs6ci5g166KmAcFg6twYDOSz9u40Qmmnoysr85xdHJGXB8N33wEAnN27w2ax4Ms+NyHXYcH4aZFIS7NjKACzuVuLfeK+TtVsbmps424rp1Ng7dpovPtulGbLS4TashakPQYD+aS9O41g73SkykqYCgs9QWA8cAAA4IqNhW3CBFTfdZf7IjWDB6O4xNRQ62vtW4CtJc1Nja2fFeVyAUIAQkiw27VbXqK5mhrXxpAIf50uGELp22pH1N6TpVp6fnGxEbt365CaqvI88dpamEpKGoKgtBSS0wkRGQk5LQ0Xli+HzWKBfcQIwKD8c9Bi3Z/mpsbWd0m9914U1q2LhtPp3zkDhYUSNm2K8fmzfmlN8fFOHkF0Mp0qGIL9bTUctPcEp+aer3xfEtv3vjidMO7Z03CGcVERpNpaCJ0O9pEjPauQymlpQBtLUmtxMldrq7umpdkxa1aN35cQnTvXAFmO9fmzfmlNobYwHgVepwoGfsDbr70nODX3/BdfjPH/fREChiNHPMtMRBQUQHf+PADAPnQoqm+91R0E6ekQdZeW1ep39aUdtS+NWVAQAVmG35/1S9vtTGc7UycLhs52On+gtHctnMbPLy424vvvddDrvb8i2s5N57D9/QpMrf4Ekw6+Bv3p0wAAR9++qJk+HbLFAltmJlzdu/tdY3O1diQTJthgMsVClts/dbazne1MnSwY+AEPLcppmcD8+U7ccMPZJu+LrqLCM310h7UaN/24FjIGYwVG45OJLlzxe/cMIme/fm2211ne+7Q0OzZvdmDTphr1LiEa5tuMGnSqYACafsA7085CK95uU2XXnkC/fu73R6qubpg5tG0bjPv3AwBcMTHY2vM5yFIknEIHWa/HZ5mPonKwDQUftH3thc42vpSeLpCczDOvyXedLhga64w7i0DzZZsquvb0Tkw5+ioSZ7wK086dkBwOCJPJPXPooYfcM4dGjsTI0ijF2cXezpjxZ3ypccDVP2fCBBumTWvHBtKQv7OSiDQLhurqaqxZswYnTpyAJEm49957MXjwYK2abxYHo9Xn1TZ1OmHctw9TvtqGTUMrkL83EVNlK9Lf/Ar21FRULVgAW2Ym5LFjgagoxVN9mTHTeMfu6/iSspsrBoBUN200Bp9+6gz5dfnbMyuJSLNgeO211zBq1CgsXboUDocDNlvwB345GK2+ZrepEDAcO+YZJ4jIz4fu3DkAQObgwUi73QLZcg/s13+AMoejzTa8mTHT3JGLL+NLjQPH5XLfJ4Q7fHJzQ/+CLe2dlUSdmybBcPHiRRw4cACLFi1yN2owwGAIfi8WB6PVV79NCz+1YbIxDxP/911E/DYP+h9/BAA4evdG7bXXwlY/c6hnT89zY7p1g6+rlLX0HjZ3JHH//VVev8eNA849Y8q9PIXRKDBpUsiuVO+h5qwk6nw0uR7Dt99+i5dffhl9+vTBd999hwEDBuCOO+5A5CUnGFmtVlitVgBAdnY2ZFkOdGntYjAY4PDiG26waVJneTmk3FzocnKg27IF0pEjAABhNsM1ZQrE1KlwTZ0KDBjQ4kVq1KyzsFDCtGkGyDJgMgGbNzuQnu7bR72wUEJuruQJgvr/Wyz6DvG+FxUZsGWLC5MmCZ9/dy3x70g9JpNJldfRJBiOHTuGRx99FE8++SQGDRqE1157DVFRUZg7d26rz+OFetThb52tzS6SLl6Eaft2z0qkxn37IAkBV5cukMePdx8RWCxw/PzngE4X0Dr9qb89wv191xrrVE+HulBPYmIiEhMTMWjQIABAeno6NmzYoEXTYS9QO78mffT/OI0M3XbP9YtNO3ZAstvdM4fGjEHl0qXumUOjRgFGo2p1tAfn3hP5R5Ng6NatGxITE3Hq1CkkJSVhz5496NOnjxZNayYY50MUFxtx001m2O2A0RiLd99V77KDBfkm2GXA6ZIApxN7567BL+1PQEgS7CNGoOo3v4FssUAeNw7ikplDRNSxaTYCPH/+fLzwwgtwOBzo0aMHFi5cqFXTARes8yHeey8K7mEY94XK33svyv92hYD+66/ds4a2bcP1uXY871rvvmKZ5ED61UZUzHwFtvR0iPh4NX8NIgoxmgVD//79kZ2dHZDXDvbZy8E7H+LSQdzmB3Vbovvxx4ZVSPPyYKgb03FedhlGT7Ngfe+P8YU9E+nXmDA0bT5qVaqaiEJb8OeMtlMonL0crPMhZs26iHXrouq6kgRmzbrY6uOlc+cQUVDQMGB89CgAwNWtG2yZmai6/37YMjPhrJs5NALACAAA++mJOpMOHwyhcPZysM6HSEuz4913W25XqqmB6auvoC8pgfnzz2Hcs8c9cygqCnJ6Oi7efLN75lBKitczh4J9dEZEgdfhgyFUzl4O1gwYRbt2O4ylpZ6rlZlKSiDJMoTRCMfo0ah84AHImZmQr7jCPbnfR4E8OgvYFdyIyGcdPhg649nLnm/t6bVIj97VME6wfTt01dXumUPDhqF6/nzYLBbETp+O8pqadrfb3qOzlo42VL2CGxG1W4cPBiB439Y1X71SCOz8pBxz7/s5ZLsOJhjwL/wJE1AIx4ABqLnxRtgyM2HLyIBISPA8LbZLF0CFYPBnIbrGq5O2dLQRCt2BRNQgLIIhGLRavVJ3+rRnCqlp2zbs/v42yHgSTughw4RN16/A5Y+Z4OrdW/W2L+XL0Vn9UYAsS9DpYpCVVdvizj9UugOJyI3B4KdArV4pnT+PiMJCzxnGxsOHAdTNHMrIwJgbhsL4ugQ4BIxGHdLuGQxXb+2+XXt7dObePhJcLvfqpJ9/HtXi5TvrA2f37nikpja9gluoD3iHen1EvurUwbB2bRQ2bozC9Ok1mDfPt64W1VavrKmBqagIpe99j8J8E6788W1kiHy4IiMhjx+Pmptuci81MWwYoNdjOIB10yt82hEF44ItEybYoNPF1C1ZLUEIgTlzLqJ3b1ezdaSl2TFtmgtlZU1DIdjTkVsT6vUR+aPTBsPatVFYtqwbAOCLLyIAwKdw8Puaug4HjLsaDRiXlKDQdgV+iX9Bhgn/Zfgt/vlEPkbO/RkQEdFi2962F6wLtqSl2fHUU+fx6KPd4HIJmEwCs2bV+Nx2qI8/hHp9RP7otMGwcWP9+j7u6w1v3Bjl81GDV9fUFQKGgwcbgqCwELoq93PsKSmo/vWvsfHsAsj/jILTJUEWArkXRmNkRNPX9afLIpgXbJk3rwZDhzra1c0S6uMPoV4fkT86bTBMn15Td6QgPLfVoj9+3DNYHJGXB33dUr2O/v1RM2MGbBYL5MxMuOpmDo0tNsL4kQDsLe9c/O2y0OqCLS2FVntnjIX6dORQr4/IH502GOqPDvwdY2hM99NP7hPK6oLAcPw4AMDZowdskya5g8BigbOFmUPe7Fz87bLwu8vLB4HuZw/15bNDvT4iX3XaYADc4eBPIEgXLsBUWAh9SQm6W60wHjwIAHB17QpbRgaq7rkHssUCR3Jyi1cru1RbO5f2dFl41eXVDt6EFmfuEHUcnToYWqPYkQ2vhKm42DNOYNy9G5LTCREZCcfYsbjwq1+5Zw6NGOU1tFsAABBbSURBVAHo9QGpJ5S7LNoKLc7cIepYGAzNKN6uw5y5CbDbAZNkgtVwEzLkLyD0ethHjULVfffBZrGg6zXXoLwqcN/ELxWqXRZthRZn7hB1LAwGwD1z6PBhz4Dx3i8yYJcfhRMGyELgs9TFGHLfnZDT0yFiYxueFxkJaBgMoay10OLMHaKOpdMGg/7kSc/ZxRF5edCfOQMAcPzsZ0ifPAGmLQKyy3128eg/ToSN33A9fB0vCOVuMCJqKqyCobUdlq683DNrKGLbNhi++w4A4OzeHbbMTMgWC2wWC5x9+2IogLeLz3FH1gx/xwtCtRuMiJoKm2C4dIf1zusnkWHb2jBgfOAAAMAVGwvbhAmovusu2DIz4RgypNmZQ9yRNY/jBUThL2yCoeBLPewy4HRJgNOJPTe/jF+I/4KIiICcloYLy5a5Zw6lpgKGsPm1NcfxAqLwp+ke0uVyYfny5UhISMDy5cvb92JOJ4x793oGjG8olPC8ayNkGGGSnBh3YyLKZr0NOS0NiIpq+/XIKxwvIAp/mgbDxo0b0bt3b9T4c9EYIWA4erRhwLigALrz5wEA9iFDMPI2C97vtQW5F8cifYqElLS5kFWun9zYzUYU3jQLhvLycuzYsQMzZ87Exx9/7NVzdN9/7xkjiMjPh/7HHwEAjr59UTN9OuTMTNgyM+Hq0QMAkAogFY5A/QpERJ2CZsHw+uuvY968ea0eLVitVlitVgBAdnY2eo0bBwAQ3bvDNWUKHFOnwjV1KjBgAIwAjAC6aFB7SwwGA8xmcxAr8E6o1FlYKCE3V8KkSQLp6aLJz0OlzrawTnWxztCjSTCUlJQgLi4OAwYMwL59+1p8XFZWFrKysjy3zz/2GGwWCxxDhwI6XcMD61YrDTaz2YyyEKmlNaFQp3LWmGh2mmso1OkN1qku1qmepKQkVV5Hk2A4dOgQiouLsXPnTsiyjJqaGrzwwgtYvHhxq8+rvuceLcojDXCaK1HHoUkw3HLLLbjlllsAAPv27cNHH33UZihQeOE0V6KOgxP6SROc5krUcWgeDMOGDcOwYcO0btYrvGZAYHGaK1HHwCOGOrxmABGRm67th3QOjQdH7XYJBQURwS6JiCgoGAx13IOjAnq94OAoEXVq7Eqqw8FRIiI3BkMjHBwlImJXEhERXYLBQERECgwGIiJSYDAQEZECg4GIiBQYDEREpMBgICIiBQYDEREpMBiIiEiBwUBERAphGwzFxUa8+GIMiouNwS6FiKhDCcu1knhtBSIi/4XlEQOvrUBE5L+wDAZeW4GIyH9h2ZXEaysQEflPk2AoKyvDqlWrcO7cOUiShKysLEyfPj2gbfLaCkRE/tEkGPR6PW677TYMGDAANTU1WL58OVJTU9GnTx8tmiciIh9oMsYQHx+PAQMGAACioqLQu3dvVFRUaNE0ERH5SPMxhjNnzuCbb75BcnJyk59ZrVZYrVYAQHZ2Nsxms9bl+cRgMIR8jQDrVBvrVBfrDD2SEEJo1VhtbS0ee+wxzJw5E+PHj2/z8adOndKgKv+ZzWaUlZUFu4w2sU51sU51sU71JCUlqfI6mk1XdTgcWLlyJSZOnOhVKHiLZzgTEalLk64kIQTWrFmD3r1744YbblDtdXmGMxGR+jQJhkOHDiE3Nxf9+vXDgw8+CAC4+eabMXr06Ha9buMznOtvMxiIiNpHk2AYOnQo3nnnHdVf132GcwwA8AxnIiKVdOgzn3mGMxGR+jp0MAA8w5mISG1huYgeERH5j8FAREQKDAYiIlJgMBARkQKDgYiIFBgMRESkwGAgIiIFBgMRESkwGIiISIHBQERECgwGIiJSYDAQEZECg4GIiBQYDEREpMBgICIiBQYDEREpMBiIiEiBwUBERAqaXdqztLQUr732GlwuF6666irMmDFDq6aJiMgHmhwxuFwuvPrqq3jkkUfw7LPPIi8vDydPntSiaSIi8pEmwXD06FH06tULPXv2hMFgQEZGBoqKirRomoiIfKRJV1JFRQUSExM9txMTE3HkyJEmj7NarbBarQCA7OxsJCUlaVFeu3SEGgHWqTbWqS7WGVpCavA5KysL2dnZyM7OxvLly4NdTps6Qo0A61Qb61QX61SPWjVqEgwJCQkoLy/33C4vL0dCQoIWTRMRkY80CYaBAwfihx9+wJkzZ+BwOJCfn4+0tDQtmiYiIh/pH3/88ccD3YhOp0OvXr3w4osvYvPmzZg4cSLS09PbfN6AAQMCXVq7dYQaAdapNtapLtapHjVqlIQQQoVaiIgoTITU4DMREQUfg4GIiBQ0WxKjXltLY9jtdrz00kv4+uuvERsbiyVLlqBHjx4AgPXr1yMnJwc6nQ533nknRo0aFbQ6P/74Y/zrX/+CXq9H165dce+996J79+4AgDlz5qBfv34AALPZjGXLlgWtzq1bt+LNN9/0zAKbNm0arrrqKs/P3n//fQDAzJkzMWXKlKDV+frrr2Pfvn0AAFmWcf78ebz++usAtNueq1evxo4dOxAXF4eVK1c2+bkQAq+99hp27tyJiIgILFy40NOfq+W2bKvOL7/8Eh988AGEEIiKisLdd9+N/v37AwAWLVqEyMhI6HQ66PV6ZGdnB63Offv24S9/+Yvn73v8+PGYNWsWAO2W0Gmrxg8//BBffvklAPcKDidPnsSrr76KmJgYTbdlWVkZVq1ahXPnzkGSJGRlZWH69OmKx6j6+RQacjqd4r777hM//vijsNvt4ve//704ceKE4jGbN28WL7/8shBCiG3btolnnnlGCCHEiRMnxO9//3shy7I4ffq0uO+++4TT6QxanXv27BG1tbVCCCE+/fRTT51CCDFv3ryA1OVPnVu2bBGvvPJKk+dWVlaKRYsWicrKSsX/g1VnYxs3bhSrVq3y3NZqe+7bt08cO3ZMPPDAA83+vKSkRDz11FPC5XKJQ4cOiYcfflgIoe229KbOgwcPetrfsWOHp04hhFi4cKE4f/58wGrzpc69e/eKp59+usn9vn5eAlljY0VFReLxxx/33NZyW1ZUVIhjx44JIYS4ePGiWLx4cZNtoubnU9OuJG+WxiguLvakWXp6Ovbu3QshBIqKipCRkQGj0YgePXqgV69eOHr0aNDqHD58OCIiIgAAgwYNQkVFRUBqaW+dLSktLUVqaipiYmIQExOD1NRUlJaWhkSdeXl5sFgsAamlNSkpKYiJiWnx58XFxZg0aRIkScLgwYNRXV2Ns2fParotvalzyJAhnp8PGjRIcQ6RltqqsyVaLqHjS415eXnIzMwMSB1tiY+P93z7j4qKQu/evZvsc9T8fGraleTN0hiNH6PX6xEdHY3KykpUVFRg0KBBnsclJCQEbGfs7RIe9XJychTdWna7HcuXL4der8e//du/Ydy4cUGtc/v27Thw4AAuu+wy/PrXv4bZbG7y3FDZnj/99BPOnDmD4cOHe+7Tanu2paKiAmaz2XM7MTERFRUVmm5LX+Xk5OCKK65Q3PfUU08BAK6++mpkZWUFoyyPw4cP48EHH0R8fDxuu+029O3b1+e/Py3YbDaUlpbirrvuUtwfjG155swZfPPNN0hOTlbcr+bnU/MxhnCTm5uLr7/+Go1PB1m9ejUSEhJw+vRpPPHEE+jXrx969eoVlPrGjBmDzMxMGI1GfP7551i1ahUee+yxoNTijby8PKSnp0OnaziYDaXt2ZHs3bsXW7ZswRNPPOG578knn0RCQgLOnz+P//zP/0RSUhJSUlKCUt/ll1+O1atXIzIyEjt27MBf//pXvPDCC0GppS0lJSWKIzEgONuytrYWK1euxB133IHo6OiAtaNpV5I3S2M0fozT6cTFixcRGxvb5LkVFRUBW1bD2yU8du/ejfXr1+Ohhx6C0WhUPB8AevbsiZSUFHz77bdBqzM2NtZT21VXXYWvv/662eeGwvYEgPz8/CaH61ptz7YkJCSgrKzMc7v+99ByW3rru+++w8svv4wHH3wQsbGxnvvr64qLi8PYsWMD1h3rjejoaERGRgIARo8eDafTiQsXLoTkEjrNdW9qvS0dDgdWrlyJiRMnYvz48U1+rubnU9Ng8GZpjDFjxmDr1q0AgMLCQgwbNgySJCEtLQ35+fmw2+04c+YMfvjhhyaHUlrW+c033+C///u/8dBDDyEuLs5zf1VVFex2OwDgwoULOHToEPr06RO0Os+ePev5f3FxsaeWUaNGYdeuXaiqqkJVVRV27doVsFle3i6J8v3336O6uhqDBw/23Kfl9mxLWloacnNzIYTA4cOHER0djfj4eE23pTfKysqwYsUK3HfffYrVQGtra1FTU+P5/+7duz2zvYLh3LlzEHXn1x49ehQulwuxsbEht4TOxYsXsX//fkUNWm9LIQTWrFmD3r1744Ybbmj2MWp+PjU/83nHjh1444034HK5MHXqVMycORPr1q3DwIEDkZaWBlmW8dJLL+Gbb75BTEwMlixZgp49ewIA3n//fWzZsgU6nQ533HFHk75TLet88skncfz4cXTr1g1AwzTKQ4cO4e9//zt0Oh1cLheuv/56XHnllUGr86233kJxcTH0ej1iYmJw9913o3fv3gDc/c/r168H4J7CNnXq1KDVCQDvvPMO7HY7br31Vs/ztNyezz33HPbv34/KykrExcVh9uzZcDgcAIBrrrkGQgi8+uqr2LVrF0wmExYuXIiBAwcC0HZbtlXnmjVrsH37dk9/c/1UytOnT2PFihUA3EfjFosFM2fODFqdmzdvxmeffQa9Xg+TyYTbb78dQ4YMAdD85yUYNQLuqZ6lpaVYsmSJ53lab8uDBw/iT3/6E/r16wdJkgAAN998s+cIQe3PJ5fEICIiBZ75TERECgwGIiJSYDAQEZECg4GIiBQYDEREpMBgICIiBQYDEREpMBiIiEiBwUB0CVmWsWDBAtx7772e5TjqrVmzBnPmzEFeXl6QqiMKPAYD0SVMJhNmz56N8vJyfPrpp57733rrLeTk5GD+/PlBW5efSAsMBqJmTJkyBX379sWGDRtQW1uLTz75BBs2bMDs2bNx7bXXBrs8ooDiWklELSgpKcGf//xnDB8+HPv27cO1116L+fPnB7ssooDjhXqIWjBmzBhcfvnl2Lt3LzIyMnDnnXc2eUx+fj42bdqEb7/9Fl27dsWqVauCUCmRutiVRNSC/Px8z0WBoqKiPMsdNxYTE4Np06bh5ptv1rg6osDhEQNRM3bt2oWXXnoJ48aNg16vx5YtW3D99dc3uUhQamoqAOCrr74KRplEAcEjBqJLHDlyBCtWrMCQIUOwePFizJ07F5Ik4a233gp2aUSaYDAQNXLy5Ek8/fTTSEpKwoMPPgij0YhevXrhyiuvRHFxMQ4ePBjsEokCjsFAVKesrAxPPfUUunTpgocffhjR0dGen914440wmUz4xz/+EcQKibTBMQaiOmazGX/729+a/VlCQgLWrl2rcUVEwcFgIGoHl8sFh8MBp9MJIQRkWYYkSTAajcEujchvPMGNqB22bt2K1atXK+7r3r07z2egDo3BQEREChx8JiIiBQYDEREpMBiIiEiBwUBERAoMBiIiUmAwEBGRAoOBiIgU/h8A3TkwJx8hvAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ORr_MxoXY9al"
      },
      "source": [
        "# Gradient Descent"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yOs3ormtY9al"
      },
      "source": [
        "## Cost Function & Gradients\n",
        "\n",
        "<h4> The equation for calculating cost function and gradients are as shown below. Please note the cost function is for Linear regression. For other algorithms the cost function will be different and the gradients would have  to be derived from the cost functions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0F0hkmH2Y9am"
      },
      "source": [
        "\n",
        "\n",
        "<b>Cost</b>\n",
        "\\begin{equation}\n",
        "J(\\theta) = 1/2m \\sum_{i=1}^{m} (h(\\theta)^{(i)} - y^{(i)})^2 \n",
        "\\end{equation}\n",
        "\n",
        "<b>Gradient</b>\n",
        "\n",
        "\\begin{equation}\n",
        "\\frac{\\partial J(\\theta)}{\\partial \\theta_j} = 1/m\\sum_{i=1}^{m}(h(\\theta^{(i)} - y^{(i)}).X_j^{(i)}\n",
        "\\end{equation}\n",
        "\n",
        "<b>Gradients</b>\n",
        "\\begin{equation}\n",
        "\\theta_0: = \\theta_0 -\\alpha . (1/m .\\sum_{i=1}^{m}(h(\\theta^{(i)} - y^{(i)}).X_0^{(i)})\n",
        "\\end{equation}\n",
        "\\begin{equation}\n",
        "\\theta_1: = \\theta_1 -\\alpha . (1/m .\\sum_{i=1}^{m}(h(\\theta^{(i)} - y^{(i)}).X_1^{(i)})\n",
        "\\end{equation}\n",
        "\\begin{equation}\n",
        "\\theta_2: = \\theta_2 -\\alpha . (1/m .\\sum_{i=1}^{m}(h(\\theta^{(i)} - y^{(i)}).X_2^{(i)})\n",
        "\\end{equation}\n",
        "\n",
        "\\begin{equation}\n",
        "\\theta_j: = \\theta_j -\\alpha . (1/m .\\sum_{i=1}^{m}(h(\\theta^{(i)} - y^{(i)}).X_0^{(i)})\n",
        "\\end{equation}"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KdAHnLQKY9ao"
      },
      "source": [
        "\n",
        "def  cal_cost(theta,X,y):\n",
        "    '''\n",
        "    \n",
        "    Calculates the cost for given X and Y. The following shows and example of a single dimensional X\n",
        "    theta = Vector of thetas \n",
        "    X     = Row of X's np.zeros((2,j))\n",
        "    y     = Actual y's np.zeros((2,1))\n",
        "    \n",
        "    where:\n",
        "        j is the no of features\n",
        "    '''\n",
        "    \n",
        "    m = len(y)\n",
        "    \n",
        "    predictions = X.dot(theta)\n",
        "    cost = (1/2*m) * np.sum(np.square(predictions-y))\n",
        "    return cost\n"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ea8UaAOCY9as"
      },
      "source": [
        "def gradient_descent(X,y,theta,learning_rate=0.01,iterations=100):\n",
        "    '''\n",
        "    X    = Matrix of X with added bias units\n",
        "    y    = Vector of Y\n",
        "    theta=Vector of thetas np.random.randn(j,1)\n",
        "    learning_rate \n",
        "    iterations = no of iterations\n",
        "    \n",
        "    Returns the final theta vector and array of cost history over no of iterations\n",
        "    '''\n",
        "    m = len(y)\n",
        "    cost_history = np.zeros(iterations)\n",
        "    theta_history = np.zeros((iterations,2))\n",
        "    for it in range(iterations):\n",
        "        \n",
        "        prediction = np.dot(X,theta)\n",
        "        \n",
        "        theta = theta -(1/m)*learning_rate*( X.T.dot((prediction - y)))\n",
        "        theta_history[it,:] =theta.T\n",
        "        cost_history[it]  = cal_cost(theta,X,y)\n",
        "        \n",
        "    return theta, cost_history, theta_history\n",
        "        \n",
        "    \n",
        "    "
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2hZ9kXyUY9ax"
      },
      "source": [
        "<h3> Let's start with 1000 iterations and a learning rate of 0.01. Start with theta from a Gaussian distribution"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Rh60XqBnY9ax",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "77accd27-4c03-4d08-dd0f-36f494e713d3"
      },
      "source": [
        "lr =0.01\n",
        "n_iter = 1000\n",
        "\n",
        "theta = np.random.randn(2,1)\n",
        "\n",
        "X_b = np.c_[np.ones((len(X),1)),X]\n",
        "theta,cost_history,theta_history = gradient_descent(X_b,y,theta,lr,n_iter)\n",
        "\n",
        "\n",
        "print('Theta0:          {:0.3f},\\nTheta1:          {:0.3f}'.format(theta[0][0],theta[1][0]))\n",
        "print('Final cost/MSE:  {:0.3f}'.format(cost_history[-1]))"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Theta0:          3.718,\n",
            "Theta1:          3.173\n",
            "Final cost/MSE:  5052.950\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NV5EvxK2Y9a6"
      },
      "source": [
        "<h3> Let's plot the cost history over iterations"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BPUTrv47Y9a7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 500
        },
        "outputId": "37bce727-c07c-47a9-d6f4-85858559fe94"
      },
      "source": [
        "fig,ax = plt.subplots(figsize=(12,8))\n",
        "\n",
        "ax.set_ylabel('J(Theta)')\n",
        "ax.set_xlabel('Iterations')\n",
        "_=ax.plot(range(n_iter),cost_history,'b.')"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TAxDvDXuY9bD"
      },
      "source": [
        "<h3> After around 150 iterations the cost is flat so the remaining iterations  are not needed or will not result in any further optimization. Let us zoom in till iteration 200 and see the curve"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ae_Zh6wrY9bG",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 500
        },
        "outputId": "c26036a3-9142-46d0-dacd-9dcb14ac2876"
      },
      "source": [
        "\n",
        "fig,ax = plt.subplots(figsize=(10,8))\n",
        "ax.set_ylabel('J(Theta)')\n",
        "ax.set_xlabel('Iterations')\n",
        "_=ax.plot(range(200),cost_history[:200],'b.')"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WcoAfP7UY9bT"
      },
      "source": [
        "<b>It is worth while to note that the cost drops faster initially and then the gain in cost reduction is not as much"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LcqnZSymY9bU"
      },
      "source": [
        "### It would be great to see the effect of different learning rates and iterations together"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j0CVFwvtY9bW"
      },
      "source": [
        "### Let us  build a function which can show the effects together and also show how gradient decent actually is working"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u71DHEAeY9bZ"
      },
      "source": [
        "\n",
        "def plot_GD(n_iter,lr,ax,ax1=None):\n",
        "     \"\"\"\n",
        "     n_iter = no of iterations\n",
        "     lr = Learning Rate\n",
        "     ax = Axis to plot the Gradient Descent\n",
        "     ax1 = Axis to plot cost_history vs Iterations plot\n",
        "\n",
        "     \"\"\"\n",
        "     _ = ax.plot(X,y,'b.')\n",
        "     theta = np.random.randn(2,1)\n",
        "\n",
        "     tr =0.1\n",
        "     cost_history = np.zeros(n_iter)\n",
        "     for i in range(n_iter):\n",
        "        pred_prev = X_b.dot(theta)\n",
        "        theta,h,_ = gradient_descent(X_b,y,theta,lr,1)\n",
        "        pred = X_b.dot(theta)\n",
        "\n",
        "        cost_history[i] = h[0]\n",
        "\n",
        "        if ((i % 25 == 0) ):\n",
        "            _ = ax.plot(X,pred,'r-',alpha=tr)\n",
        "            if tr < 0.8:\n",
        "                tr = tr+0.2\n",
        "     if not ax1== None:\n",
        "        _ = ax1.plot(range(n_iter),cost_history,'b.')  "
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tuI2x9deY9br"
      },
      "source": [
        "### Plot the graphs for different iterations and learning rates combination"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uJNi998qY9bv",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 928
        },
        "outputId": "cc9a39a0-e7e9-4f70-c7bb-217b1f23475b"
      },
      "source": [
        "fig = plt.figure(figsize=(30,25))\n",
        "fig.subplots_adjust(hspace=0.4, wspace=0.4)\n",
        "\n",
        "it_lr =[(2000,0.001),(500,0.01),(200,0.05),(100,0.1)]\n",
        "count =0\n",
        "for n_iter, lr in it_lr:\n",
        "    count += 1\n",
        "    \n",
        "    ax = fig.add_subplot(4, 2, count)\n",
        "    count += 1\n",
        "   \n",
        "    ax1 = fig.add_subplot(4,2,count)\n",
        "    \n",
        "    ax.set_title(\"lr:{}\".format(lr))\n",
        "    ax1.set_title(\"Iterations:{}\".format(n_iter))\n",
        "    plot_GD(n_iter,lr,ax,ax1)\n",
        "    "
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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uvdWJTZuS472kuMrPt8Dnk+D3S/D5JOTnW+K9JCKihLJlixVerwQhJHi9El54wRbvJRERERFRgmBwRURERNQF5Odb4PVKUBQJ9fXA736XhsJCU7yXFTd5eR6YTAIGg4DJJJCX54n3koiIEozQPXr//aSE/nuJiIiIiDoPgysiIiKiLiAvzwNZBtRvFKoBViJXGblcPmzeXIpHHnGzTSARURxMnVob9veSWoVFRERERNTRGFwRERERdQEulw9Ll1bAaBSQZQGzmVVGLpcP8+dXMbQiIooDl8uHESO8urETJwxxWg0RERERJRJjvBdARERERKpZs2px/vn1yM+3IC/Pw8CGiIjiasgQHw4eNGuPCwosKCw08e8nIiIiIupQrLgiIiIi6kJYZURERF0F2wUSERERUTwwuCIiIiIiIiKiCC6XD6NHK7oxtgskIiIioo7GVoFERERERESUUNavX48jR44gLS0Nzz//vDa+Y8cO7Nq1C7Is47LLLsOsWbMAANu2bcOePXsgyzLuuusuDBs2DABw9OhRbNy4EYqiYMKECZgyZQoAoLi4GCtXroTb7ca5556L+fPnw2g0wufzYe3atfj2229ht9uxcOFCZGdnd/4GtMAFFwD/+EfDY7YLJCIiIqKOxoorIiIiIiIiSijjxo3DkiVLdGPHjh1DYWEhnnvuOSxfvhyTJ08GAPz444/Yv38/li9fjt/97nfYsGEDFEWBoijYsGEDlixZghUrVmDfvn348ccfAQCbNm3CDTfcgDVr1iAlJQV79uwBAOzZswcpKSlYs2YNbrjhBrz++uud+8ZbYdYshe0CiYiIiKhTMbgiIiIiIiKihDJ06FDYbDbd2Pvvv4+bbroJJpMJAJCWlgYAKCgowOjRo2EymZCdnY2cnBx8/fXX+Prrr5GTk4NevXrBaDRi9OjRKCgogBACX375JUaNGgVADckKCgoAAIWFhRg3bhwAYNSoUTh27BiEEJ30rltn1CiBESO8ujG2CyQiIiKijsTgioiIiIiIiBJeUVERvvrqKyxZsgRPPPEEvv76awBAWVkZMjMztXkOhwNlZWUR45mZmSgrK4Pb7YbVaoXBYNDND7+XwWCA1WqF2+3urLfYakOG6NsCBtsFEhERERF1BJ5xRURERERERAlPURRUVVVh6dKl+Oabb7BixQqsXbs2LmvZvXs3du/eDQB45pln4HQ647IOADAajZgzR8LrrwOKEmwXKPDuuxm47jolbuvqDoxGY1x/7bo77l/rce9aj3vXNty/1uPetR73rm266v4xuCIiIiIiIqKE53A4MHLkSEiShNzcXMiyDLfbDYfDgdLSUm1eWVkZHA4HAOjGS0tL4XA4YLfbUVNTA7/fD4PBoJsfvFdmZib8fj9qampgt9sj1jJx4kRMnDhRe1xSUtJRb7tJTqcTubklGDEiEwcPmrXxzz+vR0lJWdzW1R04nc64/tp1d9y/1uPetR73rm24f63HvWs97l3bxHP/+vTpE/M5tgokIiIiIiKihDdixAh8+eWXAICffvoJ9fX1sNvtcLlc2L9/P3w+H4qLi1FUVITc3FwMGjQIRUVFKC4uRn19Pfbv3w+XywVJknDhhRfiwIEDAIC9e/fC5XIBAIYPH469e/cCAA4cOIALL7wQkiTF5f22FNsFEhEREVFnYcUVERERERERJZSVK1fi+PHjcLvdmDt3LqZNm4bx48dj/fr1+Ld/+zcYjUbMmzcPkiShf//+yMvLw0MPPQRZljF79mzIsvoZ0LvvvhtLly6Foii46qqr0L9/fwDAzJkzsXLlSrz55psYOHAgxo8fDwAYP3481q5di/nz58Nms2HhwoVx24OWmjq1Fq+/nqJrF7hlixUuV2W8l0ZEREREPQyDKyIiIqIeorDQhPx8C/LyPHC5fE1f0BPU18O+dClsGzYAfj/OPvIIqrvRN4KJKD5iBUYLFiyIOn7LLbfglltuiRi/7LLLcNlll0WM9+rVC3/4wx8ixs1mMx566KEWrrZrcLl8GDHCq2sXeOKEIY4rIiIiIqKeisEVERERUQ9QWGjC9OmZ8PkkmEw2bN5c2iPDK6mmBmm//S2Sd+0C/P6I522rVjG4IiLqIEOG+HTBVbBdYE/8+4aIiIiI4odnXBERERH1APn5Fvh8Evx+CT6fhPx8S7yX1C6k2lr0HjAAvfv2Re++fZEzeDCS33svamgFAEpycievkIgocUydWgu1S2KwXSCwZYs1zqsiIiIiop6GFVdEREREPUBengcmkw0AYDIJ5OV54ryi1pHOnkXO0KGAEK26XmRmtvOKiIgoKFq7wDNnpDiuiIiIiIh6IgZXRERERD2Ay+XD5s2l3e6MK6mqCjnnn9/qoCqcv2/fdrkPERFFl5Ghr3gtL2cjFyIiIiJqX80OrtavX48jR44gLS0Nzz//PACgqqoKK1aswJkzZ5CVlYUHH3wQNputwxZLRERERLG5XL4uH1i1d1AVTklP75D7EhGRKitL0T3mOVdERERE1N6a/dGocePGYcmSJbqx7du34+KLL8bq1atx8cUXY/v27e2+QCIiIqKerrDQhDVrbCgsNMV7Ke1OqqpC7379Gs6oOu+8DgutAEDY7R12byIi4jlXRERERNTxmh1cDR06NKKaqqCgAGPHjgUAjB07FgUFBe27OiIiIqIerrDQhOnTM/Hcc3ZMn57Z7cMrqbq6U4OqcILV/0REHSp4zlWoEycMcVoNEREREfVEbWpGXVlZiYyMDABAeno6Kisr22VRRERERIkiP98Cn0+C3y/B55OQn29pdH6wOuvAAamTVtg4qbZWH1QNGdKpQVXEetzuuL02EVGiGDJE3xYw2C6QiIiIiKg9NPuMq6ZIkgRJiv0NlN27d2P37t0AgGeeeQZOp7PxhRmNTc6h5uN+ti/uZ/vhXrYv7mf74n62L+5ndJMmSVi1CvB6BcxmYNKkZDidSVHnHjgg4fbbjfB6gVWrgJ07szBqVCeHRLW1MGVkxDWcakyyxQJzC3+f8fcmEVHLTJ1ai9dfT4GiBNsFCmzZYoXLxQ+zEhEREVHbtSm4SktLQ3l5OTIyMlBeXo7U1NSYcydOnIiJEydqj0tKShq9t9PpbHIONR/3s31xP9sP97J9cT/bF/ezfXE/o8vNBd5804T8fAvy8jyoqACeeEL9efhB9zt22OD12uH3S/B6BXbsqEVublXHLrCuDr1zc7tsUBXOPWAAalr4+6y9fm/26dOnzfcgIuoOgu0CDx40a2NsF0hERERE7aVNrQJdLhc+/vhjAMDHH3+MESNGtMuiiIiIiBKJy+XD/PlqANXYeVd5eR6YTAIGg1qdlZfnaf/FeDy61n+9Bw3qNqEVJAnC0nirRSIiah9sF0hEREREHaXZwdXKlSvx+9//Hj/99BPmzp2LPXv2YMqUKfj888+xYMECfPHFF5gyZUpHrpWIiIh6qOC5TYn+Da+mzrtyuXx46qlKXHGFB//xH/6IiqxW8Xr1QdW553afoCqUJAFCIGnv3nivhIgoIUydWgtZBoBgu0BgyxZrnFdFRERERD1Bs1sFLly4MOr4448/3m6LISIiosRTWGjC9OmZ8PkkmEw2bN5c2j6BTDekVlTZAAAmk4ioqCosNOGJJ9Lg80k4dAjo18/U8r3yertvOBUqeLaqEA0/l2XUXXVV/NZERJRA2C6QiIiIiDpKm864IiIiImqr0Cqj4ONEDa5cLh82by7VzrsK34fQvfJ6RfP2qqcEVaGCQVXYz4XBAKSkxGFBRESJacgQny64CrYLTNS/x4mIiIiofTC4IiIiorhqqsoo0bhcvpjf8Avdq5hnXNXXo/eAAT0vqIr2foLjkgTIMiDLUEyJ3W6SiKgzTZ1ai9dfT4GiBNsFCmzZYoXLVRnvpRERERFRN8bgioiIiOKqqSqjjlRYaIrL67ZW6F5NmpSM3FxfzwyqGiNJDT8A7X0LWYYCA97blYK03vy0PxFRZ2C7QCIiIiLqCAyuiIiIKO4aqzLqKN31bC3XsFpMntILeKYnB1USAPX9KZAg655SAythMEASoiG4EhKqvCZs256CHTsyu82vJxFRd8d2gURERETU3uSmpxARERH1PKHnRfl8EvLzLfFeUnR+P3r37dvw42c/69nVVaFnVqkDEJAinoMkQYS2BfT71ZBL1HftX08ioh5m6tRayDKg/qktQVGAF16wxXlVRERERNSdMbgiIiKihKSeFyVgMIiudbZWeFB1zjnxXlH7Cg2fwh9rbQDVh8HASopynaQoEEYjRFISAEAWCizwwislda1fTyKiHi7YLjDUrl1JKCzkmYNERERE1DpsFUhEREQJKdrZWnE580pR0Lt//855rXiQJH2FWOjjKGdVhc6RAj8NJFf6a/1+SH4/RHIyYDBAqqmBVanDpBlmzJnGNoFERJ1J3y5QghACW7ZY4XJVxnVdRERERNQ9MbgiIiKihBV6tlannXklBHr369f+9+0qmgqqmnMNAMgyJEXRXyMEhNUKqbpGbUhVU6u2DLRaIcxmSF4vpk7zwMfQioioU02dWotNm1IghNouEABOnDDEd1FERERE1G0xuCIiIiKC/syr4ON2Ca6EUCuqevK5VLHECqpkGVCUyLEo4ZUwmSD5Gn4dpOoanBZZMMEHG6pgrq4BFEUNr1JSIJeXt/ObIKKeaP369Thy5AjS0tLw/PPP655755138Nprr+GVV15BamoqhBDYuHEjPv30U1gsFjzwwAM499xzAQB79+7F1q1bAQC33HILxo0bBwD49ttvsW7dOni9Xlx66aW46667IEkSqqqqsGLFCpw5cwZZWVl48MEHYbN1//OgXC4frr22Djt3JmljBQUWFBaaWAFLRERERC3GM66IiIiI0I5nXgUqqrQzqvr167mhVWirv1iPQ/8bfm20sbC9knw+KOnp2mMBIAtn4IEZpchEndkOyeuFXFkJqbYWwmptwxsiokQxbtw4LFmyJGK8pKQEn3/+OZxOpzb26aef4tSpU1i9ejXuvfdevPLKKwCAqqoqbNmyBcuWLcOyZcuwZcsWVFVVAQBefvll3HfffVi9ejVOnTqFo0ePAgC2b9+Oiy++GKtXr8bFF1+M7du3d8K77Rz3318FWQbUP6klKAqwZQv/TCYiIiKilmNwRURERISGM68eecTd4jaBCRVUteRxY+ONzTWZdENyRQUUpxMiNRXBqxwohxlewJoEJTMTis0G+P3wZ2c3/T6IKOENHTo0aqXTq6++ipkzZ0IK+TOqsLAQV155JSRJwpAhQ1BdXY3y8nIcPXoUl1xyCWw2G2w2Gy655BIcPXoU5eXlqK2txZAhQyBJEq688koUFBQAAAoKCjB27FgAwNixY7XxnsDl8mHECK9u7MyZGH/WExERERE1gq0CiYiIiAJCz7xqTI8Op0JFO68KiH2GVVCwFaAQDdfIcmSLQEmCSEqCVFenv97ng5KVBbm0VJsvl5RA2GxQemXD5xEQNXVw1FcCdSYI2QpYLBAWC4z/9//CP3hwO20AESWSgoICOBwODBgwQDdeVlamq8DKzMxEWVkZysrKkJmZqY07HI6o48H5AFBZWYmMjAwAQHp6OiorK6OuZffu3di9ezcA4JlnntG9fmczGo3Nfv1evfTnWlVVWeK69nhryd5RJO5f63HvWo971zbcv9bj3rUe965tuur+MbgiIiIiakJCB1XBx6Ft/0IDKaD5Z1YpChS7HbLb3fASdXWAyQQlLQ1ySUnD5WfOqC0CzWZINTWQqqq0H6b0dCAjGQLJgN+vPu92Q7Fa4c/JaY+dIKIE4/F4sG3bNvz+97/vtNeUJElX2RVq4sSJmDhxova4JOTPx87mdDqb/fppaakAUrTH+/fL2LmzLGHPuWrJ3lEk7l/rce9aj3vXNty/1uPetR73rm3iuX99+vSJ+RxbBRIRJbjCQhPWrLGhsNDU9GSiHqKp3/e61n99+/bc0Kot51NFq7IKHwtUVOmmud1QUlMh7PaGQZ8PckkJFKcTSlZWw9yKCsjFxRBJSVCys9XnDAbIFRWQKiuB+nrAYICw26E4HIDFov4gImqh06dPo7i4GI888gjmzZuH0tJSLFq0CBUVFXA4HLov5ktLS4NBTcIAACAASURBVOFwOOBwOFBaWqqNl5WVRR0PzgeAtLQ0lJeXAwDKy8uRmpraSe+wc0ydWhtxztULL0S2ZCQiIiIiagwrroiIElhhoQnTp2fC55NgMtlafK4PUXcU7ff95Cm9em44FSqigkqC+s3FGHOiPdauRWTlVZRqLKmuDorDAbmioqHt39mzAAAlO1sNrQLfxA1WXClZWeo9As9p4xkZUILtt4QAfD5IVVVqQJacDMgyDN9/j3q2CiSiFjrnnHPwyiuvaI/nzZuHP/zhD0hNTYXL5cLOnTsxZswYnDx5ElarFRkZGRg2bBjeeOMNVFVVAQA+++wzzJgxAzabDcnJyThx4gQGDx6MTz75BNdddx0AwOVy4eOPP8aUKVPw8ccfY8SIEXF5vx0leM7VwYNmbWzXriQUFpr4b0wiIiIiajYGV0RECSw/3wKfT4LfL2mP+U0F6uny8y2orjNCggD8AG6K94o6SXjllAAUhJTfqx+Ob/zMqmgVWlFCLcXp1Lf9KyuDsFgg0tIgnT2rnWklFxdDWCxqgBWYh/p6yGfOAIBagRV4Dn6/euYVABiNUDIyALMZwhz45qgQgBDwulwt3hoiSjwrV67E8ePH4Xa7MXfuXEybNg3jx4+POvfSSy/FkSNHsGDBApjNZjzwwAMAAJvNhltvvRWLFy8GAEydOhU2m1pdNGfOHKxfvx5erxfDhg3DpZdeCgCYMmUKVqxYgT179iArKwsPPvhgJ7zbzjVkiC8kuJIghMCWLVa4XNHP8yIiIiIiCsfgiogogeXleWAyqd9gMZkE8vI8cV4RUccIPaNqWZzX0mlCq6KiPBaSFAivZMhQtNwKQPSgSpYhkpK00Em7lyRBSU2FXNnwDUm5pEQ9n8pk0kIoyeOBVFwMJT0dIjUVEALymTPaOCRJ1yZQqqzUwi+RkgKRktIQYgFqm0CTCVJNjdqOMLBWy759qLvxxjZtHRH1fAsXLmz0+XXr1mk/lyQJc+bMiTpv/PjxUQOvQYMG4fnnn48Yt9vtePzxx1u42u5l6tRabNqUAiEa/mY5ccIQ30URERERUbfC4IqIKIG5XD5s3lyK/HwL8vI8rLaiHiM0qEoY0Vr8AdHb/AmhaxKohleRVVbCZILka/hzQaqrg0hJgeTxqMFR4P5yZaUaOtXXN7T9q6hQ7x1o+yfV1UE6e1YbF3Z7QxAVCLHk4mL1mrQ0iLS0hhUpivacSEpSgy+jERBCbREIAH4/6nNz4Rk1qqU7R0RE7cjl8uHaa+uwc2fDGYcFBRa2CyQiIiKiZmNwRUSU4FwuH7+JQN1eQgZVwaqooFhBVTitikpAlqSGSqto51P5fFAyMrQwCgCk6moA6vlUUkUFJK9XXU6wvV+w7V8gaNLGMzMhAs9JtbWQ3G5Ibrf6XFaWrppKqqqCFKjgUtLSgJB2gsH3KHm9qO/dG4aSEnUvDAYYv/sOaf/rf6Fi9erG94CIiDrU/fdX4f33k6Ao6t8yisJ2gURERETUfAyuiIiIqNMUFprapcIvIYKq8Aqq0KAq/Lyq4OPGzqcKDaVCw6mw+4QHVXJ5OYTVCpGSooVQQOB8KptNbQmoKFpbP61qKiRokouLtfOphNkMkZ7eUCkVqLYKUrKyIGw2iMA5MQAAj0dtRRg820qSICwWGMrK1PcHQBgM8Fx5JSqXLo3YSiIi6lwulw8jRnhDzroCDh/mtx+IiIiIqHn4L0ciIiLqMKFBVXq6hOnTM+HzSTCZbNi8ubTZ4VVCBFWNCQ+qgsKrrhobi7F/IjkZUm1tw9TycigOh/rzsjL15WtqINXUQMnMBAwGSNXV6o+qKkhVVRBWa0NQVV8PuaysIcBKT9dXU3k8DW3/AiFWeDWV9nzgbKtoFVf+7GwomZkw/fOfaitCvx9JH30Ez+7dqLvhhuj7RUREnWbIEJ8uuDp+3IxNm5Ixa1ZtI1cRERERETG4IiIiog5SWGjSBVW//rWAzyfB71dDmPx8S8zgikGVFL16qrGKqtBwKxhUhY5JEoTZrLX204Zra6FkZUE6e1Y9uwoNgVVE279A1ZSSmakGSlDPsgoGW0Bk27/gtQCgOBwQFovWMhCAdvYVAChOJyDL+pAK0MIwYberlVqSBMOZMzCcOaN7jzW//CXqrrsOREQUf1On1uK111IArSmtwCuvpDC4IiIiIqImMbgiIiKiDpGfb9EFVYACk0kNXUwmgbw8jzY34YKqaG0AgditAEOvAyJDqRhBlZKaCjkQCgHQQislK0vf9u/MGYikJDUw8vu1gCqi7V+grV/weZhMauu+IJ8vou1frGoqGI1qkJWUBJGUpJ8TPBcrEGTBaIwMs4RA7S9/CeOJEzD9618AAOtf/wpvXh4811wTff+IiKjTuFw+XH65BwcPWrSxr782obDQxPNViYiIiKhRDK6IiIioQ+TleWAyqecUmUwCs2YJ3HhjKfLzLVj2vzOAm5Qm7tBzCEiQEBJURauciiZa279Y4VWUiir57Fk1GEpO1p9bdeaMejaV2axWWtXVaT9EcrIWEgWrobQAKyNDX01VWtrQ1s9qVc+8CmsLKFVWqtcGXi8igAqeXxUMwSQpcg7UdoVQlIazryQJye+8o5ujZGTAO3p0rN0kIqJOtmSJG1OmWCCEWnUlhMCWLVa4XJXxXhoRERERdWEMroiIiKhDuFw+bN4cElSNVQOYyXFeV6cIC6YkWQKUGC3+oo2FhlLRWgHGqMiSvF4oDgfkigrt3sFASsnKUm8XqGaSKyoABNr3paaqY8XFkGprtTOvlKyshrZ+igK5pER7LcXpVM+8Cl1+aFvArKyItoC6aiqHAzAaI8+vArTWgNocqMFYOM+oUfBccQVMx48j+b33IJeXw/D996i/6KKo+0NERJ3L5fJh5Eiv7qyrw4f5bQgiIiIiahz/xUhERETtrnf//oCiYDISJKgKD6FCg6vwAKqx60LHwlsBxqBkZ+sCI935VMFqJjQEVlpIFGgJGJyvtQoMvoWqKn3bv+xsfcDk82lBlkhJgUhJiQigdOdXZWfHrKYK3kdxOtWBaK0BA68JIQCz+g1Qy4EDsBw4oJ9jNkdeR0REcTNkiE8XXB0/bsamTck864qIiIiIYmJwRURERG0WDKoSRrRgKvS58DmNiXY+lSxDGI2Q6usjpivp6Vq1FKBWOYnkZAi7XR9gFRfrgiK5pATwK5BOF0MCoDgyIs6ukurq1NdIS4Ow2Rra8iGymgomU+T5VcFwLC0NsFgiz68C1MCrvFxtC2gyqfODgVWowP2UrKyGvQnMD+Xv3Rs1v/oVfBdcAOOJE/D36xd5LyIiipupU2vx2mspANR2gYDAK6+kMLgiIiIiopgYXBEREVGLJVxQFSpGm76o84SIbPsXPhY6N2RMqq+HsFggeTy628oVFVAyMyEbjcDp0+rcQHu/YGCkhUhCaIFTXXo2ystkCABW1CC9rFz9/iHUIEoXQvn9DUFV4OypVldTBc/HCj4XHngF7+d2Q5jN6voDexK16gpA1Z13QtjtsL7xBgxFRbAvX649JzIyUHfttVGvIyKizudy+XD55R4cPGjRxr7+2oTCQhNcLl8cV0ZEREREXRWDKyIi6nYKC03Iz7cgL8/Db3h0koQPqkIrp4LhUmtbAcYKviRJDaRKSxuGAqGVkp0Nye3Wzp4KzglWI0k1NWprv0BbwPBwSC4uhqW8GL0A+CHjDLIhpyTDZlPfg1xWBgSqu4LnSsWqphJ2u1rhFaWaSqqtheR266upooVPgTaFoc8Juz36vggBxWaDXF2tDdn+9KfIW+bkoGbGDNRdc030+xARUdwsWeLGlCkWCKFWXQkhsGWLFS5XZbyXRkRERERdEIMrIiLqVgoLTZg+PRM+nwSTyYbNm0sZXnWARAqqgo2LNNHOq5Kk2KFUeEVVtPOpwiusAiLa/gUDqfBzq8KqloKPtdZ8DgdEMAQKtOLTrglUS3m9QHmZDAkKcnAKcjWAmsDZVQ6Hbl26aqpAOBYRQIW2Bgw8J5KTIZKTI96nXFwMJT294fwpgyFmNZUwmSD5Qv6fliRdaBVUd911qL7zTgiDAdbNm2HdsgX25cvhvewy1F9wQdR7ExFRfLhcPowc6dWddXXihCGOKyIiIiKirozBFRERdSv5+Rb4fBL8fkl7zOCqZaJVrCVSUBVeQSVJMiCiVEU193yq5gRVMaqs5IoKKKmpgNmsnkEVHC8uhkhJgUhJ0aqTguNAINiSZSiKArm4WK2YClCys/XVVoGWgUkAnNYU1Mo2eM3ZWoakq6ayWtWzraJVU1VVQaqpaaimitHKT/J4IFVW6p6LFVLB69XupV3vi/H/sySh7IUX4Jg7FwCQtHMnknbujD6XiIi6nIwMv+7xoUMWtgskIiIioqgYXBERUbeSl+eByWQDAJhMAnl5niauaH/duVVhsGLNXWeGAf6mL+iJQkMpSQqeE9/wOHxOULQKq+B4lKBKWK2QamoiXl7JylKDqEBQKIdVNgXDKam6GlKg0kgLfhQFcklJwxyLRR8KBYKs0NdSsrK0xwYA9ppqSBVV6vNOJyDLzaumstkgbLao84LtBQFAWCwN1V9hc+HxAKGBmNkcOS/APW8e7OvW6a4PhlahlMxM1Eyfjtqbb46oHCMioq4jKyv0QyJsF0hEREREsTG4IiKibsXl8mHz5tK4BUfdtVVh73POAfx+TAYQGaX0cOFBVTSNtf0LnxfjNcLb/gVDq4i2f2GBULS2f8EQSHsuWGnldDZcJ8uQSkogBe8tSWpQFX42VWiQlZ2tVlVZrfrlV1ZC8niarqZyuyF5vVAyMxteM0Y1lVxWpg+SJEkfWjVBF1qFqZo3D9V33gnzwYOw/vnPsK1fD9v69QCAiuefh2fcuGa/DhERdY6pU2uxaVOKds4VwHaBRERERBQdgysiIup2XC5f3MKi7tKqsPfPfgbU18d7GZ0vvFIqeD5VeHAVK5SKNRYrsAqdWlGhVhulpOha98nFxWrrvdRUXRVV+LlVwbHwtn+akCooAEBWVuTZVG43pNpa9drMzOhnSYW0HtSqqdLSENEYMTAveB8AEHZ75DxAbfknSWroFVx7I9VP1dOnI2Xz5pjPhzu9bx9sL7+MlD/9CQBgW7cOthjBlveSS5p9XyIi6jwulw/XXluHnTsbPsTAdoFEREREFA2DKyIi6vHas7VfV2hVGA2DqpDHktQQQIVXWIVWVAWvDW/7Fx5UNRJaKU6n7mwqyeNRK5fC2/7V1UGqq9O15ZPOnoVUV6fNEcnJ+hCrtDSiWkr3vCxDPnVK97yw2yHsdt0atYAsNVWteIoWZkGt+BJmM0RamjoQYx6EgFxerg+mGmn55xkzBpZ9+3RjjYVW5StWwHTypFZBBQC9xoyJOtd3wQWomTYNdddcAyQlQaquVs8FIyKiLun++6uwa1eSVnUlhMCyZanYurU03ksjIiIioi6kXYKrd999F3v27IEkSejfvz8eeOABmBv5BgYREVFnae/WfvFuVRiUsEFVeFVUtLOomnNd8NoY4ZWSkgI5UBkVKqLtXyC0UrKztfOngJC2f4EzpIBAgBRyBpWSnQ2Rmtpwr+JirVpKpKQ0tOMLLreiApLXq16blgaEBV0AAK9Xa1cYfC5qy7+6OkiVZ3HWmgWzRYLZDN1ZWLq5lZVqGBYM8CQpdjVVlJaM4aGVbrkjR8I9bx4yf/MbbSzjwQdjzgeAshdfhG/ECMilpUjevh22deuQ9tRT2vOVy5ah7tprG70HERHFh8vlQ25uPU6ebPhWxMGDZlZdEREREZFOm4OrsrIy7NixAytWrIDZbMby5cuxf/9+jOPZAkQU0J7VLkQt1RGt/eLRqrD3wIFqO7ZEEy1was6cWGdWRQu5ooRXwdAq/NwqubgYMJmgZGSo4VTgfhFt/wIBUmg1VmiAJFVWNlpNFfVsqvT0iDZ9WrWW3Q6RnAyYzZFBVbDFoNGoBU4eOQnlwgpRDUjVQIZDUYum6usheTy6qiWtAiuK+v79Yfzv/24YiHWGWEDxRx8h+6qrtMfmQ4eQeehQzPl1Eyag8tlnYfj+ezhvvRUA4Jg7N+Z8f+/e8PziF42ugYiI4mvOnCosWpQOIHjWlcALL9iwYUN5nFdGRERERF1Fu1RcKYoCr9cLg8EAr9eLjIyM9rgtEfUA7V3tQtRSXbW1X1MSNqiKdh5V6HNAy8+nCr1PrGBFkiJCKkA9typYNaUFST6fem6V2QyRnq7OCzynBVgZGZFnV4UHUaGvU1KirT94HlZ4ACVVVUGqqdGuD/2vbs3l5YDPp7UrhCRFzPN6JQgAOTiFU+gFr1eC2SwAoxHCGP2fh/XnnAPjDz/oxnShVZiyDRvgmD1bNxYaWkVz+tAhyCUlyLr+egBA0ocfImn48Jjza6ZORe1tt6E+N1cdCK+eIyKKYf369Thy5AjS0tLw/PPPAwBee+01HD58GEajEb169cIDDzyAlECQv23bNuzZsweyLOOuu+7CsGHDAABHjx7Fxo0boSgKJkyYgClTpgAAiouLsXLlSrjdbpx77rmYP38+jEYjfD4f1q5di2+//RZ2ux0LFy5EdrS2rD3YrFm1ePVVK44fb+jSsmtXEquuiIiIiEjT5uDK4XBg8uTJuP/++2E2m/Hzn/8cP//5z9tjbUTUA3REtQtRS7hcPjz1VCXeey8Z119f22V///U+91zA0z1CtQ4T2rovfLw5Y7HOp4rRTjCi7V9Iiz3J44FUWamOB9sBBoOgQAWT5PVCCq+0AiDV1KjhUfB1nM6I4Cii2srpjFifVk1ltULYbNoPHb8fcmkphMWiVUYpMT5AJJeVQbFagaQkmM0CEiScQg4kAGZzWOgXJTwMD61C1U2YAEANmoLCQ6twZ955B4rTiV55edpYr5EjG73GM3o0KlavVtfl9SLpww9hf+YZmD/9VJtT8dxz8Iwf3+h9iIjGjRuH6667DuvWrdPGLrnkEsyYMQMGgwGbNm3Ctm3bMGvWLPz444/Yv38/li9fjvLycjz99NNYtWoVAGDDhg34/e9/j8zMTCxevBgulwv9+vXDpk2bcMMNN2DMmDH44x//iD179uCaa67Bnj17kJKSgjVr1mDfvn14/fXX8WATLVJ7ouHDfSHBlXrW1ZYtVrhclXFdFxERERF1DW0OrqqqqlBQUIB169bBarVi+fLl+OSTT3DllVfq5u3evRu7d+8GADzzzDNwRvkGjW5hRmOTc6j5uJ/ti/vZfJMmSVi1CvB6BcxmYNKkZDidSdrz3Mv21RX288ABCZ98IuHKKwVGjWrG2UOdsJ4nnzTC6wUOHbJg1Chbs9fVkftpSk8HAucZJaxgKNJUhVUweAqtpgm9Nux8qoix4P1TU4GzZxumFhcDBgOQlQWcOqUfB4CcHPW/geeC51bBZGp4LvB8aBCFnBwgJGCSz5wB/P6G9WVn666XAeD06YZ1Bp/LyYHXq+aZlnqorfyC6wzMkQNrkaA2W9L4fEBpqX6dTieCkV5SEpDpDNzbApiFD5AtaK76F1+EMaRln/WjjxreXxT+J5+E8pvfwDRwoDbW66abGr0GAHyffw7Y7UBNDUyXX47kAweQHC3cCrmHfeJE2GOdwRVDV/izk4g619ChQ1Ec+mc3oPsA5pAhQ3DgwAEAQEFBAUaPHg2TyYTs7Gzk5OTg66+/BgDk5OSgV69eAIDRo0ejoKAAffv2xZdffonf/va3ANSQ7K233sI111yDwsJC3HbbbQCAUaNG4T//8z8hhICUYNWiU6fWYtOmFAgRbBcIHD7cLg1hiIiIiKgHaPO/DL/44gtkZ2cjNXC4+OWXX44TJ05EBFcTJ07ExIkTtcclIWc+RON0OpucQ83H/Wxf3M/my80F3nyz4Yyr3FwfQreOe9m+4r2f+taQoku0htyxwwav1w6/X4LXK7BjRy1yc6uadW177mfO4MFam7eEEV7pFN7OLzy4Cp8Xfj5VeCvARtr+iZQUSIFzqjRnz0LJzFTb/gVDKL8fOHVKa88HhARXgZBIq7QCtLOrtOfS0tQgKnT5ISGYkpUFZGbq1+H3a6+vvW5WVsPzgfepVFbDWFsNH5JQ6k5Xz6EKvpaiQJZlKIG5cnGx+t4MBvV5g0FdV5TzwSS3G8Juh9EIBLsCKjDFPEus9NVXkfmb3+jf4733ItbJY/UDB6J0yxZk3norjN9/r77m44/D8PjjMa8BgNI330T94MGAx4Neo0erb+Oiixq2Jco1ntGjUXvbbfCMGdPw3hUFaOH/t+31/3qfPn3afA8i6hr27NmD0YE/i8rKyjB48GDtOYfDgbKyMgBAZsif8ZmZmTh58iTcbjesVisMgT+XQueXlZVp1xgMBlitVrjdbu3r6UThcvlw7bV12Lmz4QNtx4+bsWlTMmbNSvAP9hARERFR24Mrp9OJkydPwuPxwGw244svvsCgQYPaY21EnaKwsCFUifc32Hsql8vHvW2h7vr7siu2hozXGVc5Q4ZEBic9XXhQ1Vg7v+aOhVdTxaA4nVpLPwDa3ivZ2dqZTwAgl5aq44EwSqquVn/U1UGqq9Ou0V6yuLgh5Ao8p3u+tBSorIz5fPAeoc9HO3MqdF7wuRqDDVWwa88Hz6HSzsMKqaaKdj8AQH29um8heyfs9uhzAVTNnQvbiy/qxsJDq3CnCwthW7MGKa++CgAwfvcdejVyLhUAVD79NOquvx5QFPQaMUJ9ndtvb/SaoOIPP9TOFoMQMB0+jLTHHkPSrl0AgNLXXkP90KHNuhcRUTRbt26FwWDAL37xi7itoaUdSzpSR1WlLl4sYedOAAhWXQls3JiKhQtT2v214oUVvW3D/Ws97l3rce/ahvvXety71uPetU1X3b82B1eDBw/GqFGjsGjRIhgMBgwYMEBXWUXUlemrQ2xdojqEqD1/X3Z2ABavkKgxLpcPmzeXdvg+MKgKe9zSlkexzqcKb/sXIJKTIYW0WtTOoQo/tyosDAo+DoZRSmoqRDD0CZwXpV1vMjUeQjmdapVTKEXR1hKspmospBIpKRApKbo1BpnNAkb44UQJTqMXzGahvS4ARIvxpLNntcoxAA0lVTEoDgfkQBUAgIjQKtyZnTth/OorZCxcqI31crkavcbzi1+gYuVKAED25ZdDqq9H2mOPIe2xxxq9DgBKNm+GPzc3sFgFGfPmITtwnlZMCdZui4ja1969e3H48GE8/vjjWvs+h8OB0sAHHwC1asoRaEkaOl5aWgqHwwG73Y6amhr4/X4YDAbd/OC9MjMz4ff7UVNTA3uUDxS0tGNJR+qoiv7cXODyyx04eLChVe1XX8nYubOsx3xNFu9uCN0d96/1uHetx71rG+5f63HvWo971zbx3L/Gupa0SxPpadOmYdq0ae1xK6JO1RWrQ6jnaypMaq/fl/EIZjsrJGqpjqj6yznvPEhVzWs52CPFOo8qXGPVVM05n0qS1BZwwTOigsO1tWpoJIQueJGLiyHsdojkZKC+XnsuPMAKjslnz2rnXilZWfrnS0oiqqWarKaS5cigKhCIhb5+rAopubgYwmyGSE+H2QykOmRUeXshw6yeE6hz6lREm0LRSKup2smTkfzOO/rXC9m7cJXLlsF70UXI+uUvtbGs666LOT/o9OHDAIDsMWMg1dXB8ve/N1mBBQDlq1bBe8UV6gO/H71GjoRz+vQmr/MNGYLaW25B3aRJECFnixERtdTRo0fx9ttv46mnnoLF0hCmuFwurF69GjfeeCPKy8tRVFSE3NxcCCFQVFSE4uJiOBwO7N+/HwsWLIAkSbjwwgtx4MABjBkzBnv37oUrEPIPHz4ce/fu1c7QuvDCCxPufKtQS5a4cdNNFoRWXb3wgg0bNpTHeWVEREREFE88/ZQSWlesDqGerTlhUnv9voxXMNtTW0PmnH8+JLc73suIn2jVVUBkhVVLWgHGeJ3wKqBgaBVRTRUWBgWfk9xu7ddKC4iEgHzmTGTQFLqk0OccDq2ySePzqW0H0bxqKiUtDbBYAIMh+rwzZwAhdM9FVl2plVdSTQ2EbNZXUOXkxDyXqvaXv0TyX/+qGwsPrUJ5Ro1CxfLl2tlSAJC2ZEnM+UGnDx0CDAZkzJ4N89GjANCskOrskiWovfVW9UGgXWDGb3/b5HVBJX/+M/xhrakNP/wA00cfoe6aa9R9JyJqxMqVK3H8+HG43W7MnTsX06ZNw7Zt21BfX4+nn34agNpd5N5770X//v2Rl5eHhx56CLIsY/bs2ZADf4/dfffdWLp0KRRFwVVXXYX+/fsDAGbOnImVK1fizTffxMCBAzF+/HgAwPjx47F27VrMnz8fNpsNC0MqWBORy+VDv35+/PijQRs7dozfpiAiIiJKdJIQ4YdPdI6ffvqp0edZ4te+uJ+xtaaVGvez/STaXq5ZY8Nzz9nh90swGAQeecSN+fMjq3Za2+IvdD/1IZlgK8wWSvigKjxsCgZNwbHgYyEaqqRCPzEe3vYv1highjH19RHD4UFV6HgwiNKNO53a/cOvUzIz1cqt4NsJnhMVes8wjYVcQcEzshqbA0CrulLS0xFZOhUm8N4avR8AWZahRKtca4bThw83K2AKVfzBBxAOB+xLl8K6dWuzr6u9/nqcDXwTOPRMq+Yq++Mf4Qtbq/HYMSTv2IHkbdsgefThvnZ+Vgu0199FjbU5ICJqi6a+fu5IHf3v9dmzM7BzZxKCFVcA8PbbJT3i362J9rVOe+P+tR73rvW4d23D/Ws97l3rce/apke3CiTqznpqdQh1Tc2tpmqP35ddtW1fV5VzwQWQAi3jEkJ4BVW0qqjwObHuAzSv7V+sKqv6eigOB6S6Okg1NQ3Ti4u1oEcuK9PCrYi2f8FqqpB/aDVaTZWaGlFNJdXUaK0fhcUCkZYWPcw6XQwBwJvqgCnZqDujKtrrafeIUXWlvc/Q5ySp8dAqWjvFRpzZuTOixV9ToVXZUEuOkQAAIABJREFUxo3wXXIJrJs2wb5iBQAg++qrG70GAOoHD0bpm29q6+zlciH5vfeQ/N57TV4LABXPPQdPoCoheI/Uxx+H4957m7xWSU9HzW23oa4Z7QyJiKjruP/+qkBw1dAucNmyVGzdWtrElURERETUUzG4IiLqRJ0dJjGYjS1n6FBIlZXxXkb8NDeUCp8T7XyqYLVVlEBFsdkgRzkLLKLtX6A1YHjbP7miAgAgrFaIwMH2cmmpWsEUmCNstjafTSWsVgirtdE5Xi9QLnLUb6tVAhkGBWYzIFVUQPJ6oWRlae8/ZkhVWgolJQVIStLdOxapujoyGGskqHIvWICkjz6C6YsvtLGmzqWquuceVM+dC8uHHyL90UcBAI677mr0mqDgeVbBkMp48mSzK7kqnnkGntAwLHCuVXNV3303am69FUpOTrOvISKirsfl8mHw4HqcPNnw7YmDB80oLDTx37FERERECYrBFRFRJ2OYFB85F14IKRCCJKTQECo8+IhyPpUQ6meeGz2zKtZ9QqcGQivF6dRVRIVWJEl1dVq1W0SlUmBMqqnRqrGihVBatZTVGllNdfYspLo69flY1VSKoq0v2HIwfI7Xq34KPAen4YcBtV4nzGYBkZ6OqBFgsD1g6BlWmZnRZqrrrKmJCM+iVXOFcv+P/wH72rXaY/vq1Y3OB9SwybxvHzIWLAAA2F5+GbaXX27Wdeqi1JAKaN55VgBw9tFHUTt9esOAx6Oep/U//2ezrgeA8rVr4c3LixiXysvVtoHbt0M+dQpl/+f/wD9gQLPvS0RE8TdnThUWLUpHaNXVCy/YsGFDeZxXRkRERETxwOCKiIh6pIQOqsIrpUIrooKPo80LGRNC/daRDDQEVaGt/mK1/YPask0O23u5pATIzIRiMOgrrcKCKsnthlRb2zAnrG1eq6qpUlMhUlMbnRMtqApfn9ksUA0Zp5ADCUCGWYmYG1p11Vh7QC34Cwn7wkOrcGUvvgjH3Lm6sdDQKprThw/D+NVXyJw5UxtrTth0+tAh9UywVoRU7ocfRs2vfqU9lioqkD1hAlKffbZZ1wNA5dKlUVv+Jb3zDtKefLLRa+XSUgZXRETdzKxZtXj1VSuOH284B3LXriRWXRERERElKAZXRETUI+RcdBGk8gT9VG60oAqIXWEVfl1Iiz8BCUI7HF3SPvcMWYYwmSD5Ir95FNH2LxBaKdnZukomlJZCBqBkZAAmkzo32BIwGBBlZUHY7Q33Ki5uuLfRGFFNJZ85o73PWNVUUm0tJLdbu3+sM6SCoZmw2yGSkxveQ4DZDGQ4FHi9ElKrT0N4rRBmm24fYvJ4AIslZOGxgz8AKNm2Dc6bb9aNhYdW4U4fPAi5rAxZkyZpY80Jm4o/+USt7AoNqZrZss/929+i5o47tMfy//t/yPrlL2H/j/9o1vUAUL5+PbyXXx4x7pw8GYaffmrWPWpvvBG1U6bAN2xYk2d+ERFR1zR8uC8kuJIgBKuuiIiIiBIVgysiIuqWel18sXYuUsIJb9/XSOVU1OtCz6IKu1cwsgr+TEJDCBAMrYTdrgVBgL4qqbFqKrmuDjh7FnJIwBhRTfX/2Tvz+Cjqu49/ZvZMsskmewWveoFttZ5EMWgRFAFFRS0VtbQerS3QxwNtrYhiS4VSrYCiYKuItl4RikK1gqAVFBBJPB4LfVqtaItKNtnNtUn2nHn+2J3JzOzM7szs5v6+Xy9fuL97f7n3s5/Pt6lJ1icTg3g+223l90OJOMZiAef1gi8pEYUo2VqZvYQ9+PJymWgmPu9MlGHadQXY7Tw4l7ZIxQaD2SKWVLRS0HXllSh9/nlZm1K0UhKqq0PlySfD8o1viG3VKuKPkub165E68sj0+IyoFRg3Lu88IB1L2CWpfSU4ucoffFDXfAAIPfMMkpIzAwASCd1uLvEst92GrquvNjSHIAiCGNhMn96Np58uA8+Lb5sh1xVBEARBEMQwhYQrgiAIDerrbdi1y4Ha2ljBfywXc63hyrAWqtREKCVSASoT88cwLMDrqE8ldf8w6XjA9EtGDLhKN9i2NvlxOjrEOlBZQlVGLBIfS/6Fx5NVuyorsk96VEmflptK6rgS+nJG/mXOreW6EgQtaeQf73SCdzqzx2buQil25XReqaAUrZR0XnstIv/zP6IbCgC8M2aAZVlwOea1rFqFeMY5JQhDvssv13WmyKxZ6LzhBvGxfdcuVCnqaeWjed06pI4+WtbGNjYWV6RKJOB4+22UbNwIx/btAIDQ008j+c1vGtqDIAiC6H9qahKYPDmKTZuEn7lp19W6daWoqWnLOZcgCIIgCIIYWpBwRRAEoUJ9vQ0zZniRSDCw2VyoqwuZFpyKudZwovqkk8CGQv19jP5Hqz6VtF8BlxnKA2AZjfpUUteVdK7fD7apSfRZCaIVFwiAaW0FE4+n2zPxf6LAk0iknVSpVJbTCsgIR+EwWMk+MoGH4/LWrpK6pPiSEvDl5aqOK1k0YA4xSzyXzZaOLwS0BS0ASKXS92bt+fVJzaFVKI0NDTJxp+zJJ1H25JM550gj+4S5VbNn69qva/p0dMybJz52vvwy3PfcA9ejj+o+c9PmzVkxjo7t2+GbPl33GgDQet99iJ13nmqf9e9/h/eaawytRxAEQQwuZs+OYPNmp8x11dBAL1sQBEEQBEEMN+g3QIIgCBV27XIgkWCQSjHiY7Nik5m1hqNDi4SqDHrrU2nG/vFAT2Wq9P+pCVUaUYFsU1O6lpTHkzv2T3BTCUKSw5HXTcWyLLjMXjI3ld0OvrIyp+OKCwQ0RSXl2VSjAQEw7e1golHZGrncUWxzs1yMsVg0xwJArKYGjvr6nGOUKEUqIH9dquSRRyK0fj18Ph8smdi/8gcf1BXZlzjhBIT/+EfxcfkDD6D02WdRum6d7jOLNbEkuJYtQ9nTT+teA1B3ZAlU3XAD7O+9p2ud+GmnoXvaNMTOPRd8aamhMxAEQRADi2zXFbBvnx1PP12CmTO7+/FkBEEQBEEQRF9CwhVBEIQKtbUx2GwuAIDNxqO2NtZnaw0Xh1b1ySeLrp1hhTL2T61eFaBdnypfG8MIRarSDyXtvMsFJhKRj+e4tGspkQDb2ppuSybBBoPpmk8lJWk3VOZjpeWmYmIxMEKf1ysXhBKJHqELGm6qWKzH3VVRATidOUUqvqxMFE9yRv55vaLgxFdUgK+oyB4L9bpUSgeRlK5LLkHpxo2ytnyilRmRSpgnHct9/DnKvl4D3snk/E0uOWoUQpIYQt/kybDt3Wsoqq9x926ZwwwAfJdcAssXX+heAwCCb76p7k6LxVA9dqyhteInnYSWxx7LOhdBEAQxNJg9O5IRroQ34vBYscJFwhVBEARBEMQwgv7iJwiCUKGmJoG6ulBRXE9G1yqm22sgQUKVxmMjbVr1qaRuKkmNqkR5FeyRlp4lM6IVFwjI3VQZ15TSTcV0dGRF7gn9emtTCTF8uRxXXCAAKBxbAHriB6Ez8k/anyPyjw2H09GAknvMWZdKGbUIZIlWShrffhvVZ58tazMjUin/Px4HWsIseACdEaDKA9jtAFdWhqZMjSdhjvXjj42JVPX18s8tnpfV1TK9Tgbrvn3wfv/7htbqvuACtN97b84x7JdfouTVV+H8y19gaWpC6JlnkDrqKEP7EARBEAOHmpoExoyJYfduh9h24ICVXFcEQRAEQRDDCBKuCIIgNKipSRRNMDKyVrHcXv0dN1h9yimiIDKsyVWfSm2MtA3QV58qq+5V+v3J9kgLeIcDfEWF7GMhE3kkdaPEdp9P3FN0Sgl9brdM5GG6u/PWpmKbm3ucYVVVaTErV+Sf4JLSGtfUBPC8vsi/RAJMNCpz+3Aej/pYLRSilZLw738Pz09+ImtTilZq5BOp1IjHGfAADscXsFh4/PzHHbj3ya+D7ew0JlJl9hZgIhHDIlVqxAg0v/KKal/F3Xej5K9/NbRe269/jeiFF2oPSCTguf562Pbty7kOGw6TcEUQBDHIufPODkyb5gC5rgiCIAiCIIYnJFwRBEEMMIw6tKQC1ZQpPW1m4gYLEbtIqMqgR6jKFfsnc08xPesphCq+tBRMV1fW0pzfL/s4MLEYmKYmUYzKVbdKaJM64/S4qWT1pCRCmDBfiNxjJc9bzbGlKj4lkz0OKZtNfI6qCPGA0nVsNvCZeVpzND9OKkTHjwcbicAuiQVUilZqmBGplHMBoOrE0WDA4AAOA5MCqv7AAXb98wHA9t57hkQuAOi6+mp03HZbdodJV1bTq6/mdLk5N22Ce/58XWtxZWWITp2K7osuQvL44w19PAmCIIiBCbmuCIIgCIIghjckXBEEQQxA9Dq0lALV5s0pjBxpLm7QqNhVfeqpchFjOKJWrwrIFq701qdSiwLMrMPb7WDi8Z6mjGilN/ZPEKPEulXocS5J60bJ3FTt7fndVNL+jDiWJUikUmBDofT/G438s1pzjpX15YgHBADEYoDDIW/LI3JEbrgBrsceEx8733wz53gAaNyzB2DZwkQqiSAkm2sHqjwc4nEGTieTVeZJKVKV/+53hkWq1t/9DrEJE7La2a++gv+iiwytBWhHBwIAeB6B2lowCWNCeeipp5D81rcMn4UgCIIYPKi5rh5/vIyEK4IgCIIgiGEACVcEQRCDGKVAtX07g5EjzcUN5hO7SKhCttgkvBivjPlTQ805JaynjAJUmx6Pgy8rAzgOTHfPCzZsMAje6UzHAYZCQColtgPZbiqtulVif2dn+oHVCs7jAV9R0TMgHgfb2io+VBOypHvzDgd4txuwWMQaV9L7UztjTpHK7ZYJT7lEKralJe3SkqIUrRS0Ll2KyltvlbVJRSs1gtu2gXe55CLV6afnnCMgikyxGKrHjk3P1SEy2e2A3c4j9flnaJS446pHjzYsUoWeew7J447Lai+pq0PFffcZWis6ZQraFi3S7Ld88gl8M2YYWhNI1wuD1NWntf7nn8O2dy+iEyemL4kgCIIY1NTUJHD88XHs29fzPf2TT2yor7cNifqvBEEQBEEQhDYkXBEEQQxilALVuHFpAcVo3KDaWvf8/jg4ljT23uEHA2quKCVq9amMxP6xbJabSkDpphJEJaWbiolGwUSjqn3ifIVziW1qMuam8vsBuz1n/apckX9MVxcQiQAVFYDTqTkOyMQbtrXpq2EFqDqpskQrBc0bN8J3ySWyNqVopSRUV4fkyJEycShwzjk55wgIIhXb1AR/JtOzkJpU1aNHw3b00ajO9/kpIbh9e1r8VOA//3yw4bDudYB0Xa9EjojAquuug/1//9fQmt1Tp6J94cK849jGRpT96U+w/Oc/cOzYkT2A5xGdOtXQ3gRBEMTAZPTohES4YsDzPFatcmH16pZ+PRdBEARBEATRu5BwRRAEMYhRClRnnumGYMDQGzcoMPXHJ6IrmhGqUgCixT/vgCdXfaoixv4pxStBtOI8HpmAIHUkMR0dotNKbPf7xXWUQpVM6MnUfhKFKIslq04U29ICSOLaVN1UHCdGDgo1p4T6VTIkda6ENfjSUjAuV/Y9qdSl4h0O8FpClXCn0nvN46QKbtmCwPnny9qUopWStnvvRfSCC2TiklenW0gQmax798L7gx8AKECkisdRXVtr2EmlFLoAgIlEDK8D5HY8Me3tCKjECuajee1apI45Ju+4yhtvhGPnTl1rcl4vui+9FNELLjB8HoIgCGJgMn16N55+ugw8L8QFAps3O8l1RRAEQRAEMcQh4YogCGKQY1SgEqg+7TSwjcPcUSVF6ojSM1bLZaUj9g8MA66iAmx7u3yJcFgUhGR1qxRilChSZcQhaZ/Qn9NNJalrJfarOJSUY1TrV0FFSMtRa4oNBsF5PBCLM+WrS5VIADabZAGNO83Q8uCDqLr5ZlmbUrRS0jV9OjrmzZOJOu677oL7rrtyzgN6BCLnq6+K4/WKQ4njjkP4uefEx7b334fnRz8qikjlfPlluO+5x9A6XFUVmrZu1ewvXbMG5Q8/bGhNrfMpse3ZA8+sWYbWbVu4ENFzz9UVI0gQBEEMTmpqEpg8OYpNm5yZFnJdEQRBEARBDAdIuCIIghgmDHuhSik2adWrUj42GPunJX5xfr9MaBJEKy4QSEf9ZR6zLekXYWKuKsQ4O+x2Hs5WhZtK4rQSXFCiyKQiLslqk9ls4KqqssYwbW1gYjHZ+qqRf62t6XpbJSXgy8vF56AGGwym15G4u3LWpQqH06KWFKlopSA2dmyWG0cpWilJVVej+a9/lYlDpevWoXTdupzzgB4BxvXggyj74x8B6BepBHFMoGLBApS88kpBIpXP50Nzc7MpF1XXVVeh42c/U+/keVTniAHUov3OO9H9ne/kHsRxumuASem46SZ0XXON4XkEQRDE4Gf27Ag2b3aS64ogCIIgCGIYQcIVQRC9Qn29zVB9JaL4kFClEJByuaTU2qSilFatKzXxSsOxxTY1iSJOXjcVD9jaWyBINlFPAHZ7z3il00omBiWTeWtXSaP8YLWC83jAu93IOrk0GlCI/KuszB6HdP0tprNTd10qNhjM6s8SrfKgJ0KusaFBJuxYGht1CT2CQOS5+mrY/vlPAPpFqva77kL3ZZeJj6tHj9Ytjgl0XXklOn7+c3kjz8vOwLKsrhpXoeefR3LUKNU++86dqLrxRt3nEgi+/Tb4PE6nkrVrUbFkieG1mzduROqww/QN5nnYPvoIzldfhXPTJrDt7Wh+4QWkjj3W8L4EQRDEwIRcVwRBEARBEMMPEq4IYojSn8JRfb0NM2Z4kUgwsNlcqKsLkXhVBPJ9TANjx8Ly+ec4pB/ONiDQI1TpbVOrT5Ur9q+qSnRKSeH8fiCV6qlblYno451O8BUV6WWVtal8PkS6LIhEGFiRhA/NcLQE00dRcUFJRSq+rAx8WVnOMVwgoOmmynJ0aUQDCoKW1Pkl7K2GmpMqZzygSZQiFaBPbBJEKulYvSJV+LHHkDjtNNm8invvRcW99+qaDwDh3/8eCYXDyf7OO+bqUdXXZ7sHJWczSnT8eLQ98EDuQZk6XEbpnjoV7QsX6h7v/Otf4b777rzj2EgEKcOnIQiCIAYy5LoiCIIgCIIYXpBwRRBDkP4WjnbtciCRYJBKMeJj+oOyMNQ+plMWXgCbjtoxwwKtmD/lYy3hClCvT6Vsy8C7XGAikZ6hGdGKCwTkbqqMq0lZm4qJRsFEo7I+oZ9tbkYFD7gAHMQINGIEqqo42O3pmL58biomEgHT1ZXud7sBhyOnSCVEByrPohwrjQbUFLQAMLEYeIulp4YVjDup9NAfIlXzhg1IHX64bJ7nhht0zRX337EDcDplbWYEJQBI7N+P5owjTorliy/gu+QSw+s1r12L1DHH5BzjWrECZU8+aXjtps2bwfl8usba3nvP0L0mjz0W0SlTEJ08Wb9TiyCIYc/KlSvx3nvvwe1244GMQB+JRLBs2TI0NTXB7/dj7ty5cLlc4Hkea9aswfvvvw+Hw4E5c+bgmMz3yzfffBPr168HAFx++eUYP348AODTTz/FI488gng8jlNPPRXXXXcdGIbR3IPIDbmuCIIgCIIghhckXBHEEKS/haPa2hhstvQf4DYbj9raWJ/tPVTZtcuBl6OTcC5eB1IApvX3ifoZNXcV0NOWqz6V0ZpVPCC+t1cYHomAd7nAl5TI61apxf5J2ysrIWT+Md3dYDo6egQkhQsqHgcOaTmY3rI1LUIpY/ricaTdWJmzcYFA+lzKF8ASCZm4Jv1XifI55BoLjgPT3g6+slJs4h0O9bGSOZruNQ36Q6QKbt8uOsiYcBiB88+Hb5qxL7xGFWHZVD2qq69Gx223ZbX7APguvhiWL780vKba2aQw7e0ITJhgeN3uadPQvmCBzsHdqD77bMN7RCdMQNuSJTJxlCAIwijjx4/HlClT8Mgjj4htL730Ek488URceumleOmll/DSSy9h5syZeP/993Hw4EE89NBD+Pjjj/H4449j8eLFiEQiWLduHZZkYlHvuOMO1NTUwOVy4bHHHsNPfvITjBo1Cr/5zW/wwQcf4NRTT9Xcg8iPmutq0yZyXREEQRAEQQxF6C/+IkN1fYiBQH8LRzU1CdTVhXJ+LQhfKxdcwGDkyD493qCh6rrr4HztNQDA4n4+S7/DsAAvqeUjCE3K+j6C+JSvPhXLqteiYhhwHk9PtB8ALjPsIEbgEByUiVdMJCLG5eWqWyW0sa2tPesGArIaQWwwKFvDHgiArw7IhCppf9TtR0uLBTxGgAHSrizl/j5f+rnabKriE9PWBiYWM1+XimVlopWS5KGHwqoUVfKIVv0hUjXu2SOey/nyy3Dfcw8C48bpmqvcX4BtbjYlUmk6kxIJVJ95pnwPlgWXp8ZV5zXXIHLTTTnHuG+/Hc7XXzd81uBbb4EvLdU11nfJJbB88YXhPZr//GekjjrK8DyCIIh8HH/88QhKfq4CwJ49e/DLX/4SAHDOOefgl7/8JWbOnIn6+nqMGzcODMPguOOOQ2dnJ1paWrB3716cdNJJomPqpJNOwgcffIATTjgB3d3dOO644wAA48aNw549e3Dqqadq7kHkR811BfBYvLgC69eH+vNoBEEQBEEQRJEh4aqI9Hc8G0EI6BGO+uIMWvtKv1YefBB4/nl6lyQAVM6di5IXXujvYwwMlGJT+nWJ/EidV0rnlNLpo1EHSBCtOL8fTLDHTVWNg+AB8Eo3VcZxxbtc4ov4giCk5aZCKiWP/PN6syP/olEw7e09YxSxgPEIAx7ACBxMj28B+OocbqpUCmwoBK6iQoyq491uzWvNEqm01hX6SkrAdnfL2rJEKwWNu3ejeswYWVuvi1QSgck3bRosBw6g+vTTdc1VWwMA3PPmmatHpeF6cs+bJ4rWRsgnJFk/+QTeGTMMrxuZPRudP/qRrrHODRvgNlC3SqDzhz9EZM4cw/MsBw7AuXkznJs3w/rvfwMAQk89heS3vmV4LYIgiLa2NlRl4nMrKyvR1tYGAAiHw/BJ3lTg9XoRDocRDofh9XrFdo/Ho9oujM+1h5KtW7di69atAIAlS5bI9u9rrFZrv+4vZd48Bps3Q+a62r3bjk8+8ePMM/X8sti3DKS7G4zQ/ZmH7s48dHeFQfdnHro789DdFcZAvT8SropIf8ezEYSUXMJRfyP9WonH+WH7teK+806UPvVUfx9jYCCN/tOqT6XlnDIS+6cB5/OBVdQKYpuakCyvRFO7E9WCOASA0XBTCQ4soU/plMpXm0rZzzud4BW1kKT1q+yVATBgcFDFcSVdT9zHYskZDyi6syRn0CQeFyMPxTUUopWSpk2bUH3hhbI2pWilRrFEKmGOEYGp87rrEPmf/5G1VY8eXVSRymx9q8aGBvh8PtUaVwWtu3u3rgg+NhSCf9Ikc3tIHG56sW/fjqq5c3UOtucfQxAEkQeGYcBovMmlL/aYOHEiJk6cKD7W+n7fF+T6edPXjBwJzJ7twsqV5egJc+Zx++3cgHRdDaS7G4zQ/ZmH7s48dHeFQfdnHro789DdFUZ/3t+hhx6q2UfCVRHp73g2ghgsSL9W7HYMm6+V8t/8Bq6HH+7vY/Q/yvpUwgvYyug+5ThhrJZ4pSZ4WSxAKpV1BC4QkEf7ZX5AK2tTWSOtOIQBkqwNSXcV7PbsulVKN5WsbhXSzq1cIpXg1MoSinhedHNxVVWAzSarX2UHUOXhEI8zqOhsTNfB0hH5x4bD4G028OXleccCSN+fxSJvyyMMhB99FJ5Zs2Rt/ilTdMUEgudRXVMjtvWVSBV67jkkM5FOAACOQ/Xpp6NszRrdawBA6wMPIDZ+fFa7/a23UHXLLYbWAoDWpUsRO+cczX7Htm2ovPVWw+tGZs1C5w036BprVgRrXrcOqaOPNjTHsWULKu+4Q/d4zuNBdNIkRCdNQuLEEw0LYgRBEFLcbjdaWlpQVVWFlpYWVFRUAEg7qaR/zIdCIXg8Hng8Huzbt09sD4fDOP744+HxeBAKhbLG59qD0M/8+RGsXVuKpqae309277ZTrSuCIAiCIIghBAlXRWQgxLMRxGBA+rVywQUlGDmyuF8rA6XWnOuRR1C+eNhXp8oWoKRxfvnmCePyxf5pvVidSoF3OMBwHJDo+Vxgg8G0A8nrzVmbimVZ4OBBWPkErK3ZTithTpZbSiIKIZEA29Ii61cTipRrZMULKs/o8cBut8Ju58G51IUnJhYD09YmF7QyL5yporxrIFu0UhCZMweulStlbUrRSo3GhgYw3d0InH222GZYpMqIS0bmAtmOH+fGjfBedZXu+eI69fWqkZOFuKhyoVyXZVlU5qlxBWifU0nZ44/DtWpV3nFKIjfcgE4dH3Mp1r174f3BDwzvlRw1CuEnntBdW4sgCMIINTU12LZtGy699FJs27YNp2d+xtTU1GDTpk0466yz8PHHH6O0tBRVVVU45ZRT8NxzzyGScVx/+OGHuPrqq+FyuVBSUoJ//etfGDVqFLZv344pU6bk3IMwxujRCWzaJPyOknZdrVrlwurVLbmmEQRBEARBEIMEhufzvXLYO3yZp+4FWfyKC91ncaH7NI9SVCr2XcprzfF9WmuubPVqVCxY0Cd7DWiUrii1x0BPm1R0EpxTyhfZ1QQVNfcVst1U0nYApvvU+vMKUIr4PXFMc7N49pxuJ4nolXMcIDq08o6TohQA8xA/+WTYP/xQ//oZGhsaYDlwAIHLLgOnQ2hRzgUAy/798E2fbmpvKcUUlZjOTgTGjTO8VvKYYxBau1azv2LBApS88kredViWld1nx9y56Jo5M+8867598H7/+/oOqyCfuKbE8sUX8F1yiam9ml94AaljjzU11yjF+lmUK+aAIIiBxfLly7Fv3z50dHTA7XbjiiuuwOmnn45ly5ahubkZfr8fc+fOhcvlAs/zWL16NT788EPY7XbMmTMHx2a+P73xxht48cUXAQA2oe8tAAAgAElEQVSXX345JkyYAAD497//jZUrVyIej+OUU07B9ddfD4Zh0NHRobpHPvL9/dybDMS/ferrbZg2TajFkBauGAZ46aXmAfUG0oF4d4MJuj/z0N2Zh+6uMOj+zEN3Zx66u8IYqFGBJFwNE+g+iwvdpznURKUpU9xFvcsVK1y4//5ypFIMLBYeP/95B268MVK09aWUPfEEKu6+u1fWHtRIBSWpCKUlVCmFEy0xRU28AsCXlYHp7Mxq1xSw/H7RBSZE8UnnSM8hq3vFMOm5EvQIWUilwGbigriKCkBRt0ptPT3iExsM9jwXHTDd3eBLSnSNLYTGhgbY330XVbNnZ/UphRa1uQDgWrkSZatXm9pbihmRKjZmDFoVDjIA8E+cKHPO6SX41lva7iCJY8wo+WpcFbp+0+bNaeFVJ2ZFPABoefBBxCXOO6NYPvsMzq1b4dy6FdaPP0bLww8jXltraA0SrgiCGOiQcJXND39YhU2bnEgLVwDAY8qU6IByXQ3Uuxss0P2Zh+7OPHR3hUH3Zx66O/PQ3RXGQBWuKCqwjxkoEWYE0R/s2uVAIsEglWLEx5nUlKKhp9ac2a/D0mefhfvnPy/aWYcEytg/o0XMjcT+MQy4qqos8YDp7ATn9QIWS+7YP6E2lUSsUrqpsuL6RozoEVpSqax+XZF/FkvuyD+J+KRZlyoYBF9WBr6sTPXsWeObmrJEtt4QrRobGlD6zDMoX7pUbNMjFnFeL5peey1rvF6hKXXIIWh++WXxMRsMwn/BBYaFqqZNm7Luycg5lORyIwXOOAOMSr21fLTffju6Z8zIO87smTuvvx6Rn/5U/4QCxDDDe0nhebhWrdIlaNrff9+wcEUQBEEMPmbPjmDzZifS78VN/y61aZOTal0RBEEQBEEMAUi46kPkbhNXn0aYEYRRekNkVReVtN0nZshXa87I12HJn/+MyptuKur5Bh3K+lTKeD4t4UoYJ3VJsWz6sZ6aVRm4ykqwra09QyWxeTKRSnA0CdF8ySTYcDjdp+JiYrq6wEQiYh/vdKrWrgIAFmnRhy8v1xwjXT+XSMU7neAzRdhziVTK/pwiVTCY1a8mxhRKY0MD3LffDufrr4ttesSS6Hnnoe2++wAAh2QEDzYU0i20tC1YgOi0aeLjyptugmPHDsNCjZqoVLJ+PSoWLTK0DpDbIcR0dSHw7W8bXhPQF8NXumYNyh9+GEDawVZtIHrRaMyff9Ik8WvLCPHRo9Hyhz8YngcA4HkExo0D09Wle0rK70fs/PMRnTgRiRNPNBR/SRAEQQxeamoSmDw5mnFdAUJk4Lx5bmzZQu+6JgiCIAiCGMyQcNWHqLlNSLgiBiK9JbLmE5WKRU1NQnPtXF+Hzr/8BVWzZvXKmQYtSuEKUK8tpSVUKcdpObI0XmhmW1vBl5aCd7n0uakk1uZ8bippfBvb3AxGxU3FsiyiUQ7xOANnZwz2zrSIpiVkAQATjYJpb5edQVOkCoWAVKowkcpITSudNDY0wD9+PNiODrFNj1DUceut6Pre92Tjna+/DqcwN4+g0PTaa2n3nGRP98KFcC9caPj8SnrDRWV2zZZlyxDPE6vHRCIInHOOqfWbtmwB5/HoHu+eNw/OjAPOKEbFMJFkEtVjxpia2n3xxWi/+27AYjG3N0EQBDFkUHNd7dtnw9NPl2DmzO7+PRxBEARBEARhmqIIV52dnXj00Ufx3//+FwzDYPbs2TjuuOOKsfSQQk+EGUEMBHpTZM0lKvUF0q/DS9kNWLzkMmBJvx1n4KGsT2VmrtJNpVGbivN4RFeUrF3hpmK6usB0daVfiLdawXR3g8kIKmruJFHEEvoqKuTiDs/LRSyvV7WWjzDGzgFhjEAnnKjyBGC3SwZJ6mQJe/BOJ3iVOlZMLAamrU0eDSgRadT27yuRSinA6BFkWlauRHzMGKC7G9UZ91H50qWy2MB8+4pk4uf8kybpPziA1t/+FrGJE2VtbDhsSlBKHnkkQuvXq/ZZDhyAT+L6MoIeYcesAJa69VYEr7pK93ilY84Ijbt3A1YTvzbGYqgeO9bUnnxpKYLbtpGDiiAIgtCkpiaB2bM7sHJlOQBBvOKxYoWLhCuCIAiCIIhBTFGEqzVr1uCUU07BbbfdhmQyiViMBBk1+sptQhCFMlRFVsebb+Li730PYgCV8XIzQwulmyqXG0qPw0poV7ZprCuIVlmxf1puKonIJQo4GeFILbJPtl7GASX054z8ywhLXCCAzk4WgumIB+BoCYJh0mIYnE5xXBaZc4njAPAOB3gt51VLS3qsxEGSV6TSEARzYVakat6wAanDD4d9xw5UZeIzq+bMMbQvkC74GXnqKbgXLDAe9Vdfn/V8Tbuo3nkHsNlU+8yu2VxXh9TIkTnHeL7/fdj27TO1vpoA5vP5AJUCqiV1dajIxDMaJfjGG+DdbsPzCnGIpQ47DM0bNhgXy5XwPNhwOKcgTBAEQQw95s+PYNs2J/bu7fnZfuCAFYsWuTB/fqQfT0YQBEEQBEGYpWDhqqurC//4xz/w00yxbavVCquZd+QOE/rbbUIQehgqIqt9xw54r7iiv48xcFCrT8Uw2Q6rXEKVsk0NhgHvcoGJZL9QwPn9okNJXCYYBF9eDr6kBExbG5jMmx90uak8Hnntqra2LBFLKQAxHR1gujPvwLVY0o4rjbpU5QDKABzECDAAYlUKx5XiXOI6WoIWINbukUYVclVVqmN7BqjUAMvzIr9ZkSr41lvgS0tR9cMfwv7BBwBgyG0kFViE/YR/WZaFW0dNpr6I+rPv3m1IfNOzpoDlv/+F79JLTa0d3LYNvMulayyzaxeqr7zS1D7hJ59M14MyCBMOI3D++ab25FwuNG3bZmqu7AxdXXC+9hqs//gHnH/7W1YdrrZFixCdMqXgfQiCIIjBw+LFbZg2zQep62rlynJMnjx4/5YhCIIgCIIYzhSsMAWDQVRUVGDlypX4/PPPccwxx+Daa6+FUyUmiSCIwcNgFFnte/bAa/LF4iGJmtikF8GNpXRTqQkoatMzolWWm0oRqyf0MR0dYvyf0CdEAmq6qSQxfQAAmw1cVRVkFbkUY7hAIC2SlZdnnVcQlKR1qViWRTzKwRXnYbfzsNvVBTVNd1QikXZTSfqlgpUqyWR2JFueOzcrUgkuJunYwLe/nXceAMRPOQUtq1dn7WdEYIrV1qL14YdlbWWrV5sSqcJPPIHEySer9pkVvYKvvw6+sjLnGLNrd111FTp+9jNdY7WiClmWRb6vcGndMSOwX30F/0UXGZ4HAMmjj0Zo3TpTc6XYGhrg+fGPDc1JfOMbiJl0fhEEQRCDl5qaBMaMiWH3bkemJS1eLV5cgfXrQ7mmEgRBEARBEAMQhud5Pv8wbf79739j/vz5+PWvf41Ro0ZhzZo1KCkpwZWKdwBv3boVW7duBQAsWbIE8Xg857pWqxXJZLKQoxES6D6LC91n8SjkLpmGBlhN1k4Zkkij/5RuKqBH/BDapGKIUJtK6eIxEkfn8QAqNavgdAKVlcDBg9l9I0b0/L+yPxCQn1HZL52rNkY5X4DngcbG9P/7/bJ4Ps311PZSwnFAMKhvrEB3N1BSon88gMSnn8J2zDGG5gBAYv9+AIDt6KMNz00+8QT4CRPSDw4cgE2nuCXbf+dOWI84Qvb1buYsQM9zUcKuXg3LvfcWdU0Bs2fVs7ZINArbN79pag/+lFOQfPFF4xP/8Q/YLrzQ1J5cbS1Szz5raq4Uy4IFYP/0J8PzUj/7GbipU4Gjjir4DMX6uW5Xs2QSBEEUgS+//LLf9vb5fGhWiaYdaNTX2zKuK0AQrgBgw4bmfntD3mC5u4EK3Z956O7MQ3dXGHR/5qG7Mw/dXWH05/0deuihmn0FO668Xi+8Xi9GjRoFADjzzDPx0ksvZY2bOHEiJkoKqOe7DPqEKy50n8WF7rN4GLlL69//Dv/kyb18okGKIDop34ug1pYrClApUqk5rzIo3VSQ1KwCJHWjolFRAMrqkwhNssi/ri4wUqdVVVVaiJIeWSFkcYFA1hhwnLpjSzoucxdsOAwkk+m9MvWP2BEjwHFc9n0JNayU+wUCmi43pq0tu3aQw5HTFddYX4/qmhpZm+Woo/K6bIQoO6kbyHLkkQCQd27w7bfBZ8Q0oSYTe+21sjF69xf3/vxz+M48EwzLwiJ5vvnWiU6ejLbFi7M7mps1nU55z7Z7d7ajLbMmAFkdLyPrAkDju++qC6Eq3+PMnh+Q1wyTff/M8b3Uvn07qubONbVndNIktP3mN+qden8WJpOoHjNGszvfGUJPPYXkt75V2BlyUKyf67l+6SYIgiB6l5qaBObM6cDKleWQRgaS64ogCIIgCGLwUbBwVVlZCa/Xiy+//BKHHnooPvroIxx++OHFOBtBEBnq622Dvt6UGaz/+hf8gstjuKMUoNTqVemZp5wvdSTlqFkFmw1IyD/3pJF5sjhAZZSeJK5PLWZPaFcKTLJIvVQqb+0q6frSPVRj/GIxsG1t6VpUfn96nMej8uR71pWtk6OGlep4IFu0UtC4e3fWC/tK0Up1XkMD2GAQ/gsu6JmnM75OrR5V4Oyzdc1VW0NYx0x8XuOePaqfg+5f/ALOjGPbCMmvfQ2hXA4kntd1v2q033UXui+7TNdYs1GCQP5aWmqUrF2LiiVLTO3XdcUV6PjFL0zNFbD85z/w6bwbNZo3bkTqsMMKOgNBEAQxfJk/P4K1a0vR1NTzRpLdu+2or7cNq7+jCIIgCIIgBjsFC1cAcP311+Ohhx5CMplEIBDAHJPFzgmCyKa+3oYZM7xIJBjYbC7U1YWG7B9dlk8/1V1fZ8ijJkwZcU4p23hevWaVBlluqoxoxQUCWXWjlGKU8FirNlWWSOX3qwpZYn/GAZU1pqWl51x+v7aYJDmv2O9waApPbDAIzuuVOWeMilS5xgPp2kmB886TteVyowg0NjSg7PHH4Vq1qmeeUZGK41B9+umG5gJA28KFiE6d2tOQEX5MiVRqggzPmxZ58gk8fSEeFbTHO++ILj+9lD36KGyrV6PaRB07TSebAUrq6lBx332m52s638ySTML2wQewfvYZui++OO1mJAiCIIYlo0cnsGmT8Htc2nU1b54bW7ZQYgZBEARBEMRgoSivGBx11FFYYvLdvQTRVwxW19KuXQ4kEgxSKUZ8PJjOnwvLf/8L22GH4ZD+PshAQy2uT/jXbOyf3jpVwhJ63VTxONjWVvU+Sb+4hoq4JBPIoOGmSqXAhtIRL7zDAd7tTgtaec6utad0LF9WBr6sTLa/FmZEquZnn4Xv6qtlbUrRSo3GhoYsMcSoSFWybh0qMhFvRoSVxvp62edMxYIFcGf+M0LomWeQ/MY3xMdCHFvgjDPApFKG1gKArssvR8f8+Zr9pc88g/KlSw2vC+gXqPwTJ6ZFUxM0v/QSUkccYWiOd/p0WLVqZOUQnwGge+pUtC9caGi/rP2/+11YP/3U1NzY2LFoXbGioP2VOP72N1T+7Gc5x/ClpYiarNtFEARBDH5mz45g0yYneuICgX37bHj66RLMnNndr2cjCIIgCIIg9FHEt7oSxMClvt6G737Xh0QCsNnKsXZt/xXoNUptbQw2mwsAYLPxqK2N9fOJzMMePFiQK2HIohSkihX7p1WbyucDq1LLhfP70zWhQj01APK6qRROKLXIP1ntqmjUXOSfxZJznNQhlUukUvbnE6kwYoSsLZ9I1bpoESoVwopStFLDrEgVPe88tGVcL9LxhkQqtag/ExF6qsJPLCY7C8uyuh1COYWkPPWSchH+/e+R0PH8XCtWoOzJJ03tkeVO00Eh3xu7vvMddNx5p+n5THe34YhIKa1LliB2/vmm5ythQyH4J00yPC9x/PGITpqEqCQ2kyAIghh+aNW6WrHCRcIVQRAEQRDEIIGEq2HMYHUgmWHduhLE4wDAIB7nsW5dyaB5zjU1CdTVhQblx4ptbkb1ySf39zH6Hz31qRhGf+wfx6nH/inbNAQwQbTKclMp4vTY5mZxfzXRhw0GgUSip8/tzh35V1EB3ukE73Rqj8lRl0ocZ7WK9aiKKVKpOaly+Vk6r74aZc8+K2tTilZqmBWpQk89heS3viUb73z9dTh1Ch6J449H+E9/Eh9b9+6F9wc/MCyYdF96Kdrvvjur3azw0n7HHej+7nc1+3s75s/W0ADPj39sav3o+PFoe+ABQ3MKeT7dF1yA9nvvFR8LDja9OLZsQeUdd5jev2nzZnA+n+n5Ssp/9zuUPvecqbnx005D6/LlMrckQRAEQQjMnx/Btm1O7N3bE8V74IAVixa5MH9+pB9PRhAEQRAEQeiBhKthynCqm5RG+QK+sdi0/qamJjEoPj5MOIwRJ57Y38fof9QcVEqnlN42tdg/rXgwhgEqKoD29qwuzusFk0iAkfTlc1PxLhf40tL04ExUn1bdKuk8aX8+IQtOp7pIFQoBmSi5XGKW2vPINVYYbzTuL/m1r8H6n//I2pSilZL46NFoefRRsZ6UgB7hovHddwGLBZb//Ae+yy4DAHivuSbvPIGmv/wF3KGHyva07dtnWDRRRgYC6fszK74k9u/XFFrc8+fDuWmTqXX1CFRMezsCEyaYWl/vHlIKEqguuwztd91ler7nqqtg+9e/TM9X+7ibxXLgAHzTppmeHz3vPLT99rdFOw9BEAQxfFi8uA3TpvkgdV2tXFmOyZMH15sBCYIgCIIghiPDWrgaTo4jJUO5bpIa06d3oa6uJBMVyGP69K7+PtKQgGlvx4jjj1ePrxuuaNWnUj7OJVypxf4p27TICFNZbqpM/J9SpJL+v9JNxUQiYCLpd6Ryfr888k9atwoakX+JhKwWkFYsIGIxsG1tsjNwXq/q02NbW4F43JhI5ffLPg75RCq1u1aKVkois2YhVlsrE5fsDQ1ZopUagiDiP/dc8R6qzzgj7zzlfABihJ7/4ot1z1ddJ4NZ8UUrjs8HgGlpQWDiRFPrNm/ciNRhh+UexPOmog4F+lKgivzoR+icPdvcZJ6H7eijdUcvKomfdBJa1qwxt7cKVbNmwb5nj+n5oT/+EckTTijaeQiCIAiipiaBMWNi2L3bkWlJi1fz5rmxZYt+xzJBEARBEATR9wxb4Wr4OY7kDKW6SXqoqUlg7drBGbc3kGA6OzHi618noUqKVn0qoU14rBbxp9UmzNfjskI6oo+JxcBEoz3DpWKUREAS26uqAJtN1qbppuJ5MUYQAPiSEvCVlVB+FmTNV9S/Uq7F+Xzp5+VwqIpJTHc3mI4Oef2qykrNe2CDwZ411Z6HGmqCYB6BsHXpUpSsXw/H22+Lba5HH4Xr0Udz74UeUaQY9ah8l1wCyxdfGBZOml96CakjjpC12d5/37QAk0voUa7JsiwCOoQWZayh3vWN0JcCVfv8+ei+/HJTc63//Ce8WnXSdIjZbb/6FaIXXWRqbyWW/fvhmz7d9HzO60XTa68V5SyqJJOwfPEFUkce2Xt7EARBEIOKO+/swLRpDvS4roB9+2wUGUgQBEEQBDHAGbbC1XBzHCkZzHWTzDJY4vYGFN3dOGTUKBKqpKjVp8p1P1IBSm8UoDBWgyw3lcStxLIscPBgT5/STZURjpROKNmRgsG8bipZf0ZYylWXii8pAV9eDjCMupiUTIINh3vGCXNKSlTvgA0G0yKW3a75PLIwIVIltm6F5dxzZW2Vt96ae58MjQ0NAMfJXFd6xQ9l3SdhnuGovyK6qJTxg8VYE9AnIBW0/p49+tyKRdirZflyxL/9bVNzPd/7Hmz/93+m92567TVNp2Jfn0Vaj63ocBzKly6F/d13wZeUwPb3v2cNafv1rxG98MLe2Z8gCIIYVNTUJDBnTgdWriwHRQYSBEEQBEEMHoatcDXcHEdqkJBDZBGL4ZBjjyWhSko+YQrIFrO02himZz2dbiq+rAxMV5fsDFIxSojOk7VLXEdqdauUkYAyEUoRCSidK47RiPxTc2ypiklS15XQb7XmrGHFl5aCd7my1tcklRJdWj0L5RYvgtu3IzBunKzNNnEi8vmDIrNno/NHP0Lpn/6E8uXLxXa9Aoi0npBj2zZU3norKpYsQcWSJbrmA0DXVVeh42c/k7WVPvts0V1U1v/7P3i/9z1Tawa3bYP3qKM0a1wBhYlGTZs2pWMhdVLIXoUIM4XsCyhcdz5fzvvMha2+Hp6f/MT0OZJf+xpCL75oen4+3PPmwWnCnRU/4wxEFWIzQRAEMbyZPz+Cbduc2LvXlmlJi1eLF1dg/fpQfx6NIAiCIAiC0GDYClfD0XFEDA8M1W5LJHDI0UeTUKWFVGgSHgv/ajmn1NrU3FRK8SqD0k3FdHaK7UDu2lRsS0s6FlDyQrZM4Mm4moS6VWDZLAGIiUbBZOpkCfOLLlJpua6EdS0WmXPElEilfKygsb4+qw6SUrRSo+nll8EdcohMfHCtWgXXqlV55wJy0UF0URmsx6Tloip97jlD6wBA49tvAxquNrMCS/dFF6H9V7/KOcZ9xx1wbtliav3WZcsQ0/GxAlBwvavmF19E6mtfMz4xHkd1ba3pfQHjUYZaFCqUhZ5/HslRo4pyFiUla9caEmiVtKxahfipp4qxpwRBEAShxeLFbZg2zQdpZODu3XbU19votQCCIAiCIIgByLAVrgByHBFDj7y125JJHHLUUSRUCSgFKLUYQD3zlPOlzh4tlw/DAFYrkEzKl5C6qdREKr9f3F8QhKROK9ZqBZd5Dnkj/3g+y23FO53gnU75mcJh8ZzC/jmFJxgQqSAXpvKKVMlk+t6k5BGpgm+9hYAivk2PmNHY0ACfzweLpF6OX2etoNShh6L5L39JP4hGUX3WWel9C4z6q5o1q+guqt6M+XO89hoq580TH7Msi2odNa4AoPuSS9B+zz36DpJIoPrMM/WNVSG4ZQt4j8fwPOerr8J9112m9+246SZ0XXON6fniOV55Be4FC0zPT1VXo/mvfy34HGrY33kHVT/9aUFrhJ5+GslvfrNIJyIIgsjPyy+/jDfeeAMMw+CII47AnDlz0NraiuXLl6OjowPHHHMMbrzxRlitViQSCTz88MP49NNPUV5ejltuuQWBzO8zL774It544w2wLIvrrrsOp5xyCgDggw8+wJo1a8BxHM477zxceuml/fl0hwU1NQmMGRPD7t2OTEvadTVvnhtbtphzLxMEQRAEQRC9x7AWroihiyHX0RBCWbvtnR1WXHxpNQlVAkrByahzSq1NLfZPy03l94tiE4AeMSgQAFIpsKGeqJIsN5UQ+SeZnxX5l3FasUiLWLki/3inE3xFRbZQFIuJNbN4lwt8aSk4jRf0jQhPbFMTwPOFi1TKxwraFi7MegFfKVqp0djQAMtnn8H3ne+IbdWjR4Nl2bxRgdLaT4IIZPnyS0OCkFrMXfXo0aZEJWn0oJRCxI18daLYr77SLeqprq/TXcREIgicc475fXI4zHJRqGsp+OabYu0206i4x4wIgQAQXr0aicyLpsWEPXgQ/qlTC1qj47bb0HX11UU6EUEQhHnC4TBeffVVLFu2DHa7HUuXLsXOnTvx3nvvYerUqTjrrLPwhz/8AW+88QYmTZqEN954A2VlZVixYgV27NiBZ555BnPnzsWBAwewc+dOLF26FC0tLfj1r3+NBx98EACwevVq3HXXXfB6vZg3bx5qampw+OGH9/MzH/rceWcHpk1zQOq62rfPhkWLXJg/P9KvZyMIgiAIgiDkkHBFDDnyuo6GMLVjuhFLVYIFD6QA3NffJxpAaMX+aY3VErT01KbSWFsamZcr8o/p7BQjAtXEIaa7G0xHh2pcH8uy4DhOX10qiWtLXMPhyBkNyHk8onikKVI1NwMcJxepctUe4vm0SKWM+8ojUvEOB5iYvD6hHmGmsaEBgTPPBJPo+b6gux6VStSf/+KLdc1VW0NYxz9liqE1AIDzetGkVgOI500LLe2/+AW6r7hCe0AqheozzjC1NgAk9u/XVZOJbWyE/8ILTe/T+O67eZ14ahSz/pRZ3PPnw7lpU7+fI4sCXW0AkBw1CqHnny/SgQiCIHoPjuMQj8dhsVgQj8dRWVmJvXv34uabbwYAjB8/HmvXrsWkSZNQX1+P7373uwCAM888E0888QR4nseePXswduxY2Gw2BAIBjBgxAp988gkAYMSIEaiurgYAjB07Fnv27CHhqg+oqUlgzpwOrFxZjh7xisfKleWYPHl4veGRIAiCIAhioEPC1TDhnXcYvPqqa1g4kJSuo127HEP3OfM8DjniCFFkMfby+RBHb+yfmptKGKsW+6dsy8B5vTLHlNgeCMiEKCAjAlmtopNJdFNl/uVLS7PdVAqRipe4RphIRC5U6a1LpRHjJ54j48oSx6vAhkJAKiUXqXw+1bHpTi5dk0oqUjGMqRo1StFKCe90IrhjR5YYYUSk8vl86Fy5EhW//a2huQAQmTMHnT/8YU9DMonqMWPMuaj6IeavN9ZWfmZY//lPeAtw2ZgRaNjmZvgnTza9p9l9ZXAcqk8/vaAlwr//PdxTpugSAo3gveIKWP/974LWaHznnT6rO8U2N8O+cyccO3fCvnMnmFgMoRdeQEoS8UkQBGEEj8eDiy++GLNnz4bdbsfJJ5+MY445BqWlpbBk3hTh8XgQDocBpB1a3kxtTovFgtLSUnR0dCAcDmOUpEagdI5XUsvT6/Xi448/7qunN+yZPz+Cbduc2LtX+DlFkYEEQRAEQRADERKuhgH19TZceaUV8Xj5sHAg1dbGYLO5AAA2G4/a2twvbg8qFEIVIcFoxF++NqlDS4fLShCt8rmpxL5kUtVNxQaDYLq6wHR1pfs8ntx1qdzudKSfy5U5Xvq5qLmxdIlZGuOAnlpXMpFK8sJLFolE+v7sdskibM7IObO0LVyI6JQpMjcQE43qEl/af/5zdF95JQC5WCNEBVboiGJTc1G5Vq6Ea8nxsawAACAASURBVOVKvU8BANA9bRraVVxjFQsXomTDBkNraZ1NSUEClUYsoRL722+j6uabDUfbifuYEIrK778fpQW4e1p/9zvEJkwwPR8Aqq6/HvYPPyxojd5wT1Xeeisc27YVtEbTK6+AGzGiSCfKTcn69ahYtEj3eLa5mYQrgiBME4lEsGfPHjzyyCMoLS3F0qVL8cEHH/T5ObZu3YqtW7cCAJYsWQJfrjcG9TJWq7Vf9y82K1cySCcPyyMDly4NYPFi47+n5GKo3V1fQ/dnHro789DdFQbdn3no7sxDd1cYA/X+SLgaBuza5UA8juHhQEI6AqKuLjQ0alyRUKWN3ti/XHOVgpSam4phwLndYt0nKUqRCkgLQUJtKMTjYFtbxXYgI/Rk3q3LtLaCicdVxSPpeso9c46pqgJstsJFqpYWIJGQi1Qata6AdHwhz7KAw9HT2EuOi+C2bSh76imUPfGE2OZesEBfTGBGaGHa2hA491wAQMX996Pi/vt17y8VEphwGIHzzy+eiyoWMy0ktaxYgfjYsZr9hQhUwTfeAO925x1X8uc/o2LxYtP7mBFpCo732707byxlTjJOukJoefhhxGtrC1pDSelzz6H8d78raI3eOJcqHJd2eu3fb3yqy4V4bS1iY8ciXlubO5aUIAhCBx999BECgQAqMq7zMWPG4J///Ce6urqQSqVgsVgQDofhyfxe5PF4EAqF4PV6kUql0NXVhfLycrFdQDpH2h4KhcR2KRMnTsTEiRPFx8V22BrB5/P16/7FZuRIYM4cV1Zk4AMPWDBuXEtR/34canfX19D9mYfuzjx0d4VB92ceujvz0N0VRn/e36GZmvFqkHA1DKitjcFuL0c8zg89B5IGNTWJQStYHXLEEdnun+FOVs0pBjwYMNCoQ6XWJhWqjLqpMqIV5/Ol6zcJ7RpuKiYSAROJyPqEelLSOEEuEJA9A7VIwCyRKiMoaY0RHFdMezuYaFR2Bk2RqrUViMfTL/hm7oOrqlIdCwBMezt4h0MmUkmjC1VJpUzVHGpsaMgSJgLpt8jqmgsoXFQ1Nbr3Dr75JrxHHy3+8BbWMSqUtN1zD6KXXJLV3lsxf/5Jk1RjK/XQsmoV4jpqWLmWL0fZn/5kag+gnwSqAp1L/nPOARsprHB7sd1TzP/+L6oN1lhTEp04EW2ZKMzehOnuRuDsswteJ/zkk0iceGIRTkQQBKGOz+fDxx9/jFgsBrvdjo8++gjHHnssTjjhBLzzzjs466yz8Oabb6Im8zvF6NGj8eabb+K4447DO++8gxNOOAEMw6CmpgYPPfQQLrroIrS0tOCrr77CyJEjwfM8vvrqKwSDQXg8HuzcuRM33XRTPz/r4QdFBhIEQRAEQQxsGJ7vHyvHl19+mbN/KCql9fW2fnMBffKJH6++2j34HUgDhGJ+fpJQpYJSgGLZtMiU+XbFIS0wsciMEYQoATXnlEZtKr6kBEx3d1a7mpsKyAg6Npt6nyLyT9ZXWSmLzGPa2mQ1mjifL/t8EseWcn0pTDQKpr09/aC6GlyOb+uCyytW7kEsZYPdzsuS/JSwTU3gyssBp1N7kALeZgOTMP59Rk2k0gNXVoam7dsBmBc3pIKC9e9/h/eaawCkhUDOwNenmjDhu+ACWFQ+X8yuJ1D26KNwPfaYqXW7L7sM7XfdlXec+7bb4HzzTVN7ANnnz/e90/qPf8A7c6bp/eKnnoqWxx83PR/d3aguUFwJPfUUkt/6VkFrSGE6OhAYP161z8jnZ29EDiphGxvhv/DCgtcJP/44EqeeWoQT6adYP9dzvVuMIIjBwwsvvICdO3fCYrHgqKOOwqxZsxAOh7F8+XJEIhEcffTRuPHGG2Gz2RCPx/Hwww9j//79cLlcuOWWW1BdXQ0AWL9+Pf72t7+BZVlce+21ODXzve29997DU089BY7jMGHCBFx++eV5z5Tv7+feZCj+bQ6k/z6fNk2IxUkLVwAwZ04H5s8v7M0qAkP17voKuj/z0N2Zh+6uMOj+zEN3Zx66u8IYqI4rEq76gPp6G9atK0VdXSlSqXTdpb6uMzVQ77M/xbxCKEQIJKFKBaWjSk24AsQ2QbgCJOKVTqFKC768HExHR1Y7Fwik61FlimmL451O8JkImXwiFjhO5tQCy6aFKtmCaUeW6nwpqVRPPS2PJyviTPpCtuC64ioqZMJTPA60hFkxGKXKw8Fuz8Qclpfnd09JYCIRsb6WEUJ1dfDOmGF4XvOGDUgdfjjK77sPpXV1hue3z5+PbsmLQ/mELi1hIPTHPyJ5wgnysV99Bf9FFxk+EwA0v/QSUkccodpXqJijR7Dwfuc7sH72Wa/uAfT8LPJOn24qFk4g9PzzSEoK3hulUPcWUHwhyMyZlJ+fjTt3yuM6ewGpsFsIwtfyQIGEK4IgBjokXPUOixYJkYGAVLzasKG5KH+fDuW76wvo/sxDd2ceurvCoPszD92deejuCmOgClcUFdjL1NfbMGOGF7EYk3ldfnjUmdKDcDeJBAObzdXnYp5Z6uttuPJKK+Lxcl3nJqEqD9LYPuGx8K9SVxcFrZ5CymBYgFe5X5ZVjw6EupuK6egQXU/SPmUcoCBiMdFoVhSfdE7eyD9pf0aAyhKrJGKWKJRZLKqiFtPRkXaOlZQA5ek/vvmKClFckxKPM6jGQbSjAl0oRTzOwG7ntcUygVgs60XxfKJVfPRo2FVe4NcjWqlF/fmmTcs7Tzkf6Km9VLFoESoWLdK9hnIdAbPCB+9wILhzp3pnLIbqHDWq8qFHSOnruD3lfizLorpAB5temEhEd6ykFqG6OiRHjixoDSnFEMykUXm99culY8sWVN5xR8HrBLdsAZ+jNh5BEARB9DdakYE331yJHTuack0lCIIgCIIgehESrnqZXbscSCQY8Hz6F2CGGT51pvIh3E0qVRwxr6/cW7t2ORCPQ/PcJFQpyOemkkb85Zonmc9yHHiGSUtXDNLilRoaHwepGCUTqTIvAEudTEK/8C9fVpYVCSgTofz+nCIVrFZwHo+qSKQUu8Aw6iJVJAKmq6tnHNKOMb68XKxxpVyXd7nAl5YCAOx2Ho0YIcp/drvKPSeTWW6ufE6O8B/+AM+PfyxrUxOt1GhsaAD7xRfwS2pBGXmRXypwmK1FFdy6Fbyittchp59elPhBJb1V36oY6+vdQySZRPWYMX23n4KB5p7yXHUVbP/6V0FrdE+divaFC4t0InXcd9wB55YtBa/TuGsXcuaN9iJsOAz7nj2w794N+7vvwvLVVwCA0LPPIvn1r/fLmQiCIIjBx+LFbZnIwJ43x332mRWLFrmKFhlIEARBEARBGIOEq16mtjYGmy3tSLBYeMyY0YXp07sHhbOot5HeTaFiXl+6t2prY7DbyxGPp0XIxb+tApaQUCWiFJxyOqd0tvG8XOBiWTAaUYCc3y+L3JO2g+dlkX1KN5UoUkliAWUiVSgEprMTTGcnAIAvLc0tUkHdbaUcJ/SrilSS/USRyuXSdjodPAimrAx8WZnqcwDSrzFXeTjRaWW3cgAUd6kUrRQ07tqF6tpaWZtStFKjY+5cdM2cmSU26BUfGnfsEGMPpfWXjIoXSqHCvmcPAhMnZg/UETcZ3L5ddt9ShpJA5dy4Ee5f/cr0Xt2XXQb78uWmHEJsczP8kyeb3hsAmjduROqwwwpaQ8D5yitwL1hQ8Dq9XXeqGKJeyu9H86uvar/JoBdhOjvhveoqWL74wtjEZLJ3DkQQBEEMSWpqErj88i6sX1+KHvGKx8qV5Zg8eXBF2hMEQRAEQQwVSLjqZWpqEqirCw3KOk69TTHvptjurVxcfNkIdAoCS6pXthi8KF/YNPpCpyBUKUQqzbFqzRnRKstNJWkHAKa7W6xpJQpYfn/P3plIQDWBSYBpa8sbCShdX7qGqkjV1QUmEpH18woRSrluVv+IEeC1HH/xOGCzAQwDu13qtMotznT+4Aco++MfZW1K0UqNxvp6gGFkL56XL1uG8mXL8s4FNFxUZ52la664xrvvAhaLrK169GhTL+jHxo5F64oVqn2FCATBt9/OW1eskPW5qio0bd2qe3yhYkfT5s3ZNdwyqLcWb2+geGJQMcQyoJfFKZ4vyp0lTjwR4SefLPw8Jih96imUP/SQ6fnRCRMQP+MMxMeMQeprX+sXgY0gCIIY/KxY0Yb337dj/37hJZK0eDVvnhtbtlDNDIIgCIIgiL6GhKs+oKYmQYKVBsW6m2K6t5RQ9J8EvbF/RhxWKm4qaLmp3G6wbW3Z7YEA2JYWINHzucQGg2Isn/hY8i/vcGRH/kmcWlkiVCIhF6B8PvBuN5Qhe8rYQM24P4lwJopUpaVinJ8SNhhM90ucVrlqUrEtLeAUsXdm47yUopUajQ0NqLz5Zjjefltsq66p0bV+629+g9ikSek5khfhC3VRVY8ejeozzjC0hnItZQ2hQkSC8BNPIHHyyTnHFLJ+/KST0LJmje7xfV3vSsDy3//Cd+mlBe3d9Npr4LzegtYQKIpYJnECFptctbpYloXen07x005Dy2OPFe9gOmGbmuCfMqXgdZLHHouW5cvB5SjcShAEQRCFsHx5a1Zk4L59Ntx4oxsrVmT/DUIQBEEQBEH0HiRcEUOCYrq3SKjKgVrsn942LfFKDS03VVsbYLGA83hkIpNW5B+Syaw+oZ+JxcAIfZWVchGI52UCFO90gq+oyBkLKNTFUhWpolEw7e2yc/AlJZouGzYYTPeXl/esn0ukCgaz+rNEqyLBsyyCe/aYj/oTxA6eF4WtynnzgHnzdJ9BKZiUPvkkylesMCVACK4wJe758+HctAksy6La4PeDzpkzEZk7N+eYQsQSI/WP2HAY/vPPN70XYF6gUnuOLMvCZ+A+i+VWKoY41fLoo4iffnoRTpONde9eeH/wg4LX6ZoxAx23316EExmjYuFClGzYUPA60QkT0Hb//eSaIgiCIPqFmpoE5szpwMqV5ZBGBq5fX4oRI1JU74ogCIIgCKIPIeGKGDKYdW8dctRRMqcOkUGtVlVWP8CDAaP0HQlzDbipYLEAqezsRWXkH1IpsE1N4CorAbsdTGsrmHg8vbxK5J/SaSWsKUVPXSo9QhaAtCCWcYWJIpXTCV7NjcHzYJuaChepcowHgOikSXC+9lrOMWo0b9gApqMD3pkzxTaG43SJALzFguC77wIw76JKjhyJUF2dZNG02GVGhIjMmoXOG27Iarfv2IGqm24yvJ5APmGlEMEkMmcOOn/4Q11jKxYsQMkrr5jeq33+fHRffrnhedZ9++D9/vdN7wsAwW3btGu2GcA/cWLaeVkAsbPOQmsBsXW5KHn+eVTcf3/B63TceCO6rr0WQLYjsLewfPEFfJdcUpS1QnV1SI4cWZS1CIIgCKLYzJ8fwbZtTuzda8u0UL0rgiAIgiCI/oCEqwFOfb2N6mMVGRKqNFATqhimxyUlCFCiKAUxoooHCxaK2D9BnFITr9RIpcSYPKarq2e41DGVEXoAgG1tFc8jCjfxONjW1qzIPylsMJi3LpUydlCrdhViMTG6UBDLeIcDvNpYjgPb3CyKXllnV8GMSIVkMuuO9YhWjQ0NWSKLb9q0vPOAnjpS0kgzJpUyJNqoxfxZP/nEnItKRUxi2tsLEpF6U6BqW7QIUZ1RagXH++3aZSoysli1pwoVWkrq6lBx331FOUtvUDlnDhy7dxe8TsuDDyJ+9tlFOJF+3LffDufrrxe8TvyUU9CyenURTkQQBEEQ/cPixW249FIfeF5wXaXFq5tvrsSOHU15ZhMEQRAEQRDFgISrAUx9vQ0zZniRSDCw2VyoqwuReGWCESNHgunu7u9jDDzU6lMp4/3UEMf1ZL8DAM+wYHhO3ZmlgdJNJQhWgggk7cuK/BNELEmsH+fzZdetUtScUgo/TFcXmEhP7AcXCKjH7GVEMWEfsCygqJMlkkiAbWmRi1Qsqy06ZUQtwyKVGlZr3qjLxvr6rPpTRqP+ZC4qA3WkOq+/HpGf/lR8XHXDDbC/917RBCrl2QpdUya0SOINzRB+7DEkTjtN19j+qD9lf/ddVM2eXdi+Raj1xB48CP/UqQWtAfSeOFUMEQ8AmjZuBHfYYUVZSw+2996DR8V1aIbmF15A6thji7JWMWAiEdg++AD2+nqwbW3ouOUW8G53fx+LIAiCGKTU1CSwZEkrfvGLSkj/5vnsMyvVuyIIgiAIgugjSLgawOza5UAiwSCVYsTHJFzlZ8Rxx4Hp7OzvYwxstMQlrTpUnIqbSogCzPwhxwjtGnCVlT0uKWHpYDDtOvL75SJVxjHFeb3pCEGoRP4p6kkx7e1gJU4O3uXKFn4ygpJ4pkAAfGmp6PQSkYpUmdpVsNvVowG7u8F0dKSdVsILpTabpugk1LuS9ecStYBs15pOOm6+GSUbN8K6f7+sXY/40rJqFeJnnAHrJ5/AO2NGz1yTLiqmsxOBceNQ9sQTKHviCd1rAEDLsmWIjxuX1d5rDqpkEtVjxgCAqRpXzevXI3XkkXnHWf/+d3ivucbQ2krMiDPFck8VRIEioHiOnTsBh6PgdZQUS5xqfOcdwGbLP7BIFOvcsXHj0LpsWVHWKgaW//wHlbfcAuvnn+saHzv7bMTOO6+XT0UQBEEMZWbO7Mbnn1tU611dc00X/V1OEARBEATRy5BwNYCprY3BZkvX/bDZeNTWxvr5RAMTEqpUULqn1NxVRhDmS+cxDFhI3oOoWJJ3u8VaT0BPtB8XCADJJNhwODOQz3JTiSJVKCTOlwk7mfnKyD/R3QSkXUwKt5WqoCQRs/jycvAlJdoiVXs7mGgUvN0OvrIyPaekJD1HBTYUAjguvbdwL1r1roQ9OjvBl5UpGvN/vNRcVOUPPph3HqDuojLivGldtgwxibAkrFMsF1VBAlUO4UAQ08wS3LIFvMeTd5x/wgSw7e2m92l5+GHEa2sNzXH+9a9w33236T0BoHH37rRoWwDKj50ZITD8xBNInHxyQedQo2jiVC85u9RQRiWauU+B0HPPIXncccU6WkHYPvwQnuuvL2iN+OjRiJ9+OuJjxiBx0klFOhlBEAQxnJk/P4JXXy3B/v3C70MUGUgQBEEQBNFXkHA1gKmpSaCuLkQ1rhSM+PrXZdFuBNTrUylj/3K5qZRtgpsqX20qJv3nG+f1ykQmAGDa2sC53YDDkTPyj41GgcyL+mJfJioQgBgJmLMulUT8ApCO+ssnUgkOKQ13FNvcnL4bm02MDuQrKuTimHR8MCh3XWXuJRdsU5NM1AKQLVqpEH70UXhmzZK16XGvpA4/HM0bNsD58stw33NPz1yTLiphXuXcubrnq60jXc+smBCqq0Ny5EjVPraxEf4LLzS1LqA//q7geL/6esOicqF7cl4vmnTUQOvNMwBAdPJktC1eXPA6MuJxVBsU/LToM3GqSE40AOBLSxF8662irFUo9j17UKX4nmWW2JgxaL/33rQbliAIgiB6meXLWzFtmg/KyMCrr67Cs8+25JxLEARBEARBmIeEqwFOTU1i2AtWI77xDTAdHf19jIGLgZpSqvw/e2ce30Sd///XTO40TdskTVnPn4iuX2+X6qKIiiLeinisYj3w+PoVRUTXBYVddRVEXYUV7eKuCN7nAt4XqxRvC8Kq6Lqs4rVK0za90qS5Zn5/JJPOTGaSyWSStPB+Ph77WPuZz7w/n3wobZhn3u+3SjZVQSHS0kres4pNZ1wJIinTlwqikn+ykn5sIJCZAyj3pRKvIfSRypJP4qyu9N5UJZW4/GD6YSjn86m/3kAAvMslKTGYtx9VNJpV0kwureQoCUEAWdJKCUGCiKWC6ccfNUuGjuefR3KnnVL3bdkC35lnAihcUnSsXInkLrtIxrxnnqlbdoQuvRT9Ktlg5i+/hLepSVdcAGhrbc0StD6fDxCVoBSXEdS9ToESpGrpUriam4tbU4cUk+zhL3+B68EHi9oDAMS3bBnsGWYAph9/hO+00wyJVS455b7lFjheeMGQWPFXXkFHnp8j5cDI/lmA9nKbBEEQBFFqGhvjmDatL6tkYEuLnfpdEQRBEARBlBASV8SQg0SVDK1l/8RzeIADCxZc5mswonuVsqk4TjGrivN4JAIoM15fDyYaBSMqgaZa8k/WV0oyPxQCm86g42pqckoq4X5NkkrWAysrnsmUyYjKJZ3YQABcbS1gtSq+hiwSiVRfLrkkyNOHp33VKtRPmiRdW0FaKdG2fj3ct94Kx6pVmbFCsjaUsqj0yAD5g3/HqlXwnX56wXEAgGdZBFpbFa/Z3n4btb/9ra64gDZB4VixAu5583SXYosdcAC6CuzlVWzmUnLHHdFRhBAxffstfGecUdQegNznq66D1bG98QZqb7hB/4bSxA46CF0GyLe8cBwaDj7YsHA5z1MuVkuEZeNGeC65xLB4Hc8+i+TIkYbFIwiCIIhSMmdOCJs2WdDSYoe839WIEUnMmUPVQAiCIAiCIIyGxJWIdessVJavAoz4n/+RyA9ChlLZvzwIswV5NVjYAsol/3KMs8EgwLKp7B9RJpTw33JJJf7vLEklm8f5/WBZFlxaDGiSVMlkdu+rfJKKZTMZVKrSKR2X83pT4kkcXwU2EMi+rqEnEFdbm+n5JSCXVkoI5fDkgkOr8BCXvBPfU6gwkT9IZ3/6CfWnnKJbvKg9mHc+/jiq77lHV8xcccUUK4vEmWlaqL7zTjiffrqoNYvKDDKoFF2u3mF6qLnxRthff73oOH3XXovweecZsKPc1F51FWwffGBIrFL18CoE8+efw3vhhYbF63zkEST22ceweARBEARRaZ54oguHH16f1e+qubkau+6aRFNTpJLbIwiCIAiC2OYgcZVm3ToLfvMbL+JxBhaLC08/3UnyqkSM2HtvMD1UUkERpV5V8utA7n5VPA+GYaTyiucARkFMmUxAMpk1LC/5B45L9WNK96xi+vvB9PenlhUklVAOEAATCoEJh7MklWS7gcCgzEIBkspkyi2pRGupSSdh/5JeWipxxfHl1/OWB1SLJZNWSrStXw/f8cfDJJKF3t/8RvMagtywvfUWaq+/HgDQMHZsQfsMvPOOpByikElitKCSZ4sZFVdM0f2nCpRFxa4X33tvBB99VPf9RvSdMlqoNIwerTuDTUznww8jse++Bu1KBQP7YwFl7JGlgm3tWl296NQILl+O+H77GRaPIAiCIIYDixZ1Y9IkH3he+FhgSl7NmlWLvfZK0PMDgiAIgiAIAyFxleaDD2yIxxkkk0zma3rjaQwj9tkHjIYH9dsl+cr+CV8rZV2pySueB5iUDMpkWjEseIsFTFz2PZ1MgnO7wcTjYCKDnxKUZEyJ+1KJhGNG2qTL9MnLAfIulySeRCyJ+lZlMq5KJKmUsr/4qirwVVWK84XXW6ikCk+eDOeKFTnnKBE56ST0/vGP+rOoFMr8FXI/AMT23x9dy5Zlre8fN05zDLU9ifFcdBEsn32mK2auuAJMVxf8Eybojq+0hs/nU+3JVHPddbCvWWPoeoVghJwaOP549MybV3QcASP2BACBNWvAV1cbEkuN+okTNZfjzEfHM88gufvuhsTSg23NGtRed51h8YIPPoj4QQcZFq8k8DxM//0vLBs3wrpxIywbN8K8ZQuAyv95EARBENsmjY1xLFjQjVmzajH4L62UvJoxoxbvvdeeOwBBEARBEAShGRJXaQ49NAqLJfWg3WLhceih0QrvaPhCoioHWsr+Kc0RxrT0psrILlF5QCAjrbj6emnJv3SZRk0l/8QSS7jm8UhLAnZ0SMVSXV229ElncGUooaTKJZyY/n4gkQBfUyMaZPJnUsn/HABN0qpt/fqsB/uOl1+G4+WX897LuVxob2kBYGyZv4bRo2H99FNdwqFt3brsrEAde8qKm0fm1Pzud7D/4x+64/effz5C11yjeX6xr2dgwgT03HGHrnvdc+fC8eqrRa0PGJvxY5ScUvv+MQomFIL/yCMNi1fJrCn788+j5o9/zBrXm8HWfccdiBYpeUuNedMmeC+4QNe9bCiE7FxigiAIgiiepqYIvvvOhObmaog+JohvvzVjypQ6PPFEV877CYIgCIIgCG0YJq44jsPs2bPh8Xgwe/Zso8KWjcbGOJ5+upN6XOlgxL77gumiN+hZaC37J8xTElLicaUMq/Q4bzaDSSSyLnE+H1hZtgjb3p7JOFKUVKLyefK+VLzNJpE6TF9fqgdWGt5uz/SSGtwEl5VtBZaVZFxBoceV0ZKKDQQk5QwBqGddZSZkCyoAmh62t334IRrGjJGMFZpF5br/flQ99BCA1IPYQoSBXAoI9+qRDu0vvghuhx2yxkstqIqNH1i7Nv+fcRrvWWfB/M03WeMsy0KrFtArNsxffAHv+efruteI9bNIl4Q0gkIy2PRglEQDgI5Vq5DceWfD4hWC88knUf2nPxkWr/d3v0OkgNKiZSeZRN0VV8Ba5Pcsb7cjOm4cYgcdhPiBByIxapSkRyFBEARBlII5c0LYutWEFSucGJRXPFpa7Jg3z4U5c0IV3iFBEARBEMTwxzBx9corr2DHHXdEJDJ8m5I2NsZJWGmgYd99JWXhiDRKokpJXKmVAVSTV/IxpaUFaSWTW4K04vx+MH19mXKAQo8n3m4H73an5gqSSpQJJRFB0SjYnh4wMrkkKecll1Q+n0RSZRBlbgFIZVzJ11OYW5CkEvevyjMfANjOTnBer3RQg6Bqf/VV1J9wQta4XFopEZ48GX1z5mSJgkIexvddfTXCF16Y+foX6TgNjY2aYwj03ngjImeckTU+1AWVZmHD87rORUz4jDPQd+ONhd+YTKLhkEOKWhsA2j76CDAX/6ub7exE/cSJRccBSpuJZOQ+gcplTTn+/ne45883LJ7wfWi0CDQKo0sXAmXqbUYQBEEQGlm8uAcbNlixZYvwviwlr5qbq7Hrrkk0NQ3f5yIEQRAEQRBDAUPEVWdnD1Bg3wAAIABJREFUJz755BNMnjwZL730khEhiSEEiSoNMIxUVOXqTaUkqnJkU6ll/XAejyTbKTXIpYQNx0l6t8izk9j2doDnwQwMgBkYkFwDkOk3Jc+Akszh+aySgLBYlMsCih6scn6/pByfOOMK8Xjmey0TJ1fpvnR/rUL7USGZzPpUfpa0UkBJUilJKyWEB+ZiSeNcsaKgvljih+5VS5bA9be/ofree1F9772Dk1TkppjkiBHoUChP2DB6dFEP13NJAfOXX8Lb1KQ7dr74YozIwhHWKlQMGLF2cOlSxA88sOg41vffR9306UXHAUorfIzMmgq8+SZ4j8eweFqxv/giam6+2bB4sYMPRteSJYbFM5RYDP6xY8HoKFGoRnLHHdHxzDOA3W5YTIIgiGLo7+/HkiVL8MMPP4BhGFxxxRXYYYcdsHDhQrS3t6O+vh4zZ86Ey+UCz/NYtmwZNmzYAJvNhmnTpmHkyJEAgDVr1mBF+r3e5MmTcdRRRwEAvvnmG9x///2IxWI46KCDMHXqVDAlLJ9LlIZFi7oxaZIPPC/td5XqgQWSVwRBEARBEEVgiLhavnw5mpqacmZbrV69GqtXrwYALFiwAD55OTH5xszmvHMI7RRynpYddwSG4Ce4K4pcQMlFk9o/NNXEFaCcYaUkqRgGcLuBdC+qzPRgEHA4gJoaYOvWwXEhk2nEiNT/9/cDfX2pa4Jo8vsHBQfPA21tEgmFESMG70/PYdvaBr92uwGnUzKHBYB4HBAJM4wYkVpHPg8AuruBtDRjhes2W2Zuln4RXqN4X1YrMGJE9lyBcDi1Tzl55E5yxgyY/vznrPGGk07Ke2/i/vvBn3giTFdcAfa11zLjQiaUFrEU37Jl8Isvv4TlxBOlMQRUYrGicUmsNJbddsuOpXFvajEBwAfAsvvuyhJWY/zE3XeDnzxZNX4GjkutpXMdAEhedx24q67KuZbSz07LbrupB9W4NnfssUj+9a+K12oUR5Ux3Xgj2CefLH4/p5+O5D33qF4v6rfxli2wHH105stfyK9r3KOA2vcfAOTXz/pgVqyAOV8GUQGvg99zTyRef131ugnazrwU75XYZ5+F6Xe/0zBR++tN/PnP4E89NeecSr/jo/edBEGIWbZsGQ488EBcd911SCQSiEajWLlyJfbbbz9MmjQJq1atwqpVq9DU1IQNGzZg69atuPfee7F582Y8+OCDmD9/PkKhEJ577jksWLAAADB79mw0NjbC5XLhb3/7Gy6//HLsscceuP3227Fx40YcdNBBFX7VRKE0NsaxYEF3WlQpy6sC2qoSBEEQBEEQIooWV+vXr0dNTQ1GjhyJTZs2qc6bMGECJogagef7BPtQLX8zXMl1ng377ZeduUNIyZU5lW9MKZtKnKElFlVqAiwtrTi/XyqYIhEgEgFXU5OSPulMKQAZ0cM7neBFGUhsIADIe07JM6lEIixTTlCWxcSEw2BEMo3z+1NZTOJ5OXpXwe0G3O5UDyHZ+Sj1r8rEVZEibCCQnWllt6tLlDTBBx6A5/LLpa9t4UJNfY3a1q8HEwrBf+SRg/u44orMf+eLEVyyBHFBICUSaPj1rwEApl13lczTuhdA+ne9YfTorFha44ljZtHRoZolozm2rAeXPL5ArmwcQ3pPqfxcrJ02DbaPPgLDsjDJvocKyTPRs7acfBlJWvfTc9ttGMiVIVjE71yte1T6+y4nb2+yErw3sL/0EmpuuinnnEL+3JO/+AU68mWgG/A6Cn2vxHR1wS96L6ZGIa+Vq6lB+xtv5C9hOcTf0xn1vnMHhX6ABEEML8LhML788ktceeWVAFJi22w2o7W1FTens2uPPPJI3HzzzWhqasK6detwxBFHgGEY7Lnnnujv70dXVxc2bdqE/fffHy6XCwCw//77Y+PGjdhnn30QiUSw5557AgCOOOIItLa2krgapjQ1RfDddyY0N1dDSV6NGZPAqFGV3SNBEARBEMRwpGhx9dVXX2HdunXYsGEDYrEYIpEI7r33Xlx99dVG7I8oAQ377y8pI0fIUOtNJf9aaxlAYFBeyT+hzjDgq6vBpDOixHA+X6ovVTQ6GEYsdES9n9iensH7ZJKKCYfBhMOpa3V12eX+xL2mGAZcfX2WABJ6YonX4O128OmyTrEYEAsxsFp52LvTkspkypTfUy3dx/PA1q1gqqokD6pzlvrjODDRKHiHQzqcrzygCnJppUTnU08hscceWQ/nCylxJhYYwn2e//s/zfcrxRHHE2KyLIuGAkp45XzALuu9pQdNJebicU09wXLRO2sWImefXdA9lg0b4Ln00qLWBYwpo2dUubyOlSuR3GUXQ2KJMX/+ObyiXmrFwJtMCHz8sSGxtGJbuxa1M2caFo+rrkb7mjWGxTOKuqlTYf30U0Njdt13H2KHHmpoTIIgiKFMIBCA2+1Gc3MzvvvuO4wcORIXXXQRenp6UFdXBwCora1FT/r9dzAYlGRser1eBINBBINBeEWlqD0ej+K4MJ8YvsyZE8LWrSasWOGEXF5dfDGDtWsruz+CIAiCIIjhSNHiasqUKZgyZQoAYNOmTXjxxRdJWg0xGg44AGxHR3Z5JiKFWtk/Lf2qlLKphJJ/SvJKAaavDzCbwbndksw3oS9UpheUKGtJKSNJGBP+n3c4cksqKPStAsB0d4OJxSRzeJlYkqzJAwneiRDcYMCgzuOH1arwOsNhMKFQSmYJ/aUYBhgxAnyuLKr6+qxzlEsrOX1XXIHqv/wl5xw12tavz5II3nPOKeh+AXGcQsVEPkFVKAPjx6PnT39SvGZ//nnU/PGPuuIC2kWEkb2nNCPKZCtq3Y8/zuqLVihGyam2Dz8ELBZDYokxstdU2wcfQOkHQamyqa3vvYc6g997lLKvlx7M//43vOeeKxkrVFQr0dbaWnC5xiFFJALzli0wf/01zF9/DSYeR+h//xd8TSFFNwmCIAZJJpPYsmULLr74Yuyxxx5YtmwZVq1aJZnDMEzJe1IVWmq/lFA51fw8+SRw0UVJPPmkCYPyCvj6axMmTfLj3XeN6w25PUHfe/qhs9MPnV1x0Pnph85OP3R2xTFUz8+QHlfE0EIQVYQGCu1NpTWbKs8/ZLNK/iUSYIPBjNRRlFQigSOXVELMDGlJxYj6zilJKske0nP42lrIXrlEenFud6oEX3p+KMQgFErtiwcQizGwd7dl7Yl3OsEr9ZsS7UW+P71ZVFqkVaClBWxHB3xnnCEZ1/rwvv2VV8A1NGTdU+jD/8Dbb6dKMcr2oFciJK+9FgHZw229e5PT+eijSOy9d845TH8//EccUdQ63QsWIHrssQXdY4R06Xz4YST23VcyVqhoMUxOlUCaWN95B3UGNVpI7LYbOp97zpBYWrC0turKUMzFUBNTRopDge4770T0mGMMj1subG+/jarlywu+z/zNN4hTyS2CIHTi9Xrh9Xqxxx57AADGjBmDVatWoaamBl1dXairq0NXVxfc6fdvHo9H8l6hs7MTHo8HHo8HX3zxRWY8GAxi7733hsfjQaeo+oUwX06hpfZLCZXx18af/gREozWyzCsera0mTJwYxxNPdFV4h8MP+t7TD52dfujsioPOTz90dvqhsyuOSp5frnL7hoqrffbZB/vss4+RIQkNNBx0UJaAINLIBZQ4G0ptvtq9wv1Kn25nWfBmM5hEIusS5/VmlWZkA4FUlpXHk8qySt8nzBPLoYykEmVLKUkqucTSIqkUxVAsBra7OzWnri6V2cEwqhLJ3d8GF4CtGAEGgNXKg3OpCyemvx9MNApO9g/0fJIqscsuMH//fc45aihlUYn7UuUi6fej49VXAUgfLNefeGJBe+hasgQxWdm9htGj4R8/vqA4At23347oxIlZ4z6fDw0Kfa0KQcsD/UpkTxmx5sAxx6Dnzjt132+EmBMohTgxNGuqjJk4lnXrNJXtLIShJKZsb7yB2htuMDxufMuW4fnmnOfham6G1YCSkTzLIrn77oiPGoXkyJFI7L57pkwtQRCEHmpra+H1evHTTz9hhx12wGeffYaddtoJO+20E1paWjBp0iS0tLTg4PT7usbGRrz22msYO3YsNm/eDKfTibq6Ohx44IF48sknEQqFAAD//Oc/MWXKFLhcLjgcDvz73//GHnvsgbVr1+L444+v5EsmDGTx4h50drJoabFDLK9aWuyYPr0Gixf35IlAEARBEARBAADD82pP8EvLTz/9lPM6mVJ1/GPGwPTDD5XextBESVSJRZPwEFYYEz+UVRoTxgt5eGsyAclk1jDn94MZGADT26t4DUiXB5SJMS3l/uQoSSolxGUBOZ8v9+tMJgfFmixeLJbKtLJaeUl1MDYQkJYGVIBlWXBFlroSaGttLaonk/Cgu/quu+B86ildMcKTJ6NvzpzBAZ5HQ2Oj7j0Fly9HfL/9ssaZUEhRvhVynvke7LOdnahXkGOFEFyyBPEC/ky8kyfD/N13Ra0JFCctxP2civ3+NFqeOJ55Bu477jAkVvTQQ9F9332GxMqHZeNGeC65xNi/70NITJUiW6rn5psxcMopOecMxfdKTDiMuiuuMDxucsQIhC67DMkSdbg36ixzfVqMIIjhw7fffoslS5YgkUjA7/dj2rRp4HkeCxcuREdHB+rr6zFz5ky4XC7wPI+lS5fin//8J6xWK6ZNm4bdd98dAPDWW29h5cqVAIDJkydjfPoDS19//TWam5sRi8Vw4IEH4uKLL85bejDfv59LyVD8fTPUaWz04+efTRBKBiJd02Ly5DDJqwKg7z390Nnph86uOOj89ENnpx86u+IYqhlXJK6GAf5x42D65ptKb2Poo9SbimEGRZDwtTCH57VLKnl5QGF6bW0mO0kyXl8PcFxWphUwKH2Yvj5JKb/MfaJ1tAgorZJKkpEl7xsln9vVBcTj4G02bX1C0lKr0NJ+bHs70NBQ8INsnmXRc9ddqL3uuoLuE2h7/33AZoNlwwZ4Lr1UVwxA9uA8HkfDmDG6Y7W/+CI4hR/W1fPnw/n3v2uOIxcDA0cfjZ677sp5T7mzp6xr16Ju5syyrimn6oEH4PrrX/POyydauJoatL/1lu59KGFo1tS6dXlLlxqBWPblwkixWi6q/vY3uJYsMTyuEa+v3O+VTD/8gJq5c0sSu+eWW5D8f/+vJLG1QOKKIIihDomr4cW6dRZMmuRL/9OU5JVe6HtPP3R2+qGzKw46P/3Q2emHzq44hqq4oh5XQ5D6Y46B+V//qvQ2hj7ybColcSWeJ5ZPhfSrSs9XklRsdzf4qirwTqckEyrTDyotiJhIBExfX+qa0LPK4wFfXT14TyAgLQdYX6+73J9S76t8QourrYWQLsXV1SnOlcwXxzOZcksr+Z+JsLf6euTLZVMq88dwnCZpFTn1VPTedBOYcBj+ceMy4w2HHZb3XvkeMmv39MB/9NGpODoEQ6ClBbzLlTVerKwIrF4Nvq5O9ZeN6fvv4Tv99KLW6HzsMST+53+0TY7F0HDooUWtBxQnXuqPPBJsujxPMfSfdx5C115bdBwB1333oWrZMkNiRY84At0LFxoSKxfmzZvhPeccQ2MOCTFVZEakGl0LFyJmUEnJcmF9/324HnigJLG7Fi0Cn+P3CkEQBEFsazQ2xrFgQTdmzarFYMnAVNnAVA8skLwiCIIgCILIAYmrIYCnqQm2t9+u9DaGNmpSSitKvakEOaUkr5RCCH2f/H6JGGL6+8H09w/2g4rHUxlLGBRYvNMpETtsIJDqbZWG8/lKL6lEZQbFGVe5hBMbCICrqQFstqw1ct4jn6Phz2tg/HjYFf4eaBU6wkNw8XzHCy/A8cILmu4XxwAA048/wnfaaQXtQRLro48Ac/aP2GIFVb6H/ZbddkNDkaXYChEKRmQHdT7+OBJ77aXrXqOyk4IPPIC4gsDw+XwI6fjUiaFZU2UQPKavv4bv7LMNjam073J/isf9+9/D8corhscdEtKtAGquuw6mEpx7sqEBPfPnK/6sIwiCIIjtnaamCFyualx5pQkkrwiCIAiCIAqDnjRUgLpLLoH9tdcqvY2hhbw3ldLXgHQMUBdS8gwrYVyp5F8OqSKXVEBaFFmtqQwljkv1pQIyskq4TzyfCYfBhMOpa3V1+iSVaC3xGkoiSZzhlbnOMOq9rgT5JishmFNScRyQSEDS1CrfPWlC06bB1dwsGVOSVkooCSqlr7XEAADLp5/CM3VqwTEysRQygkw//oiGX/+64Fhqe5Rj/te/4D3vPOWLGvuxdaxaheTOO2uaa4SEGZgwAT06ezMZJYECb72lrfSlBmpmzYJ99WpDYoXPPht9s2YZEksN03ffwTd5sqExKy5viizPqUZw2TLE99/f8LglIRaDR0OJRj0MjB+P8EUXlSQ2QRAEQWwvXHoph1CoTzXzasSIJObMKb5CAEEQBEEQxLYGiasyUPWXv8B9222V3sbwQi6ulK7nmivIKwVJxTudGYkkhqutBdvfD8Tjg2HEZfFEGUuIxRRL5gljwv/z1dVSkSOOIayrIKmYgQEwvb2SOWBZzRlXvMMB3uHImpv1moRtVVWBr6pSnC/ck7U2y2ZJKzm9c+bAPW9e1rhcWqndG5k8uThBle5lBQC21atRm5YDugSVwkN6z/nnF1VmTHiNapSz91T9UUeBTcvOcqwnxyg5ZaRMaRg9GizLFp3BBpRe8ogzBI2i0mLKe/bZMH/9teFxK/26tGL6z39Qc+utOeeYrVbEdMQOn3EGBk49Vd/GCIIgCIIoiKamVF9jJXnV3FyNXXdNZuYQBEEQBEEQKUhclYCqBx+E+6abKr2NoYtaNpX861xCSt6vCtBc8k+QVnxNDZiewdIM4lKAgFQIyWUPy7LA1q2Sa7zdLpU76QwpRiQDlCQVGwymMpdEc3i7HbzdnrX3QnpXIZkE29kJ3maTZJnkzIhKJsGEQllZKVqyqJRQklZKKPWxcs+bp/n+zkcfRWLvvQEAzocfRvW99wIovJeVsBc5DaNHFyVW2j7+GDCZFK9Z1q2D5/LLdccGgPY33wTn8QDIXYrN/vLLqPnDH4paC9D54D+RKDoLraj1FfCcey4s//63IbH6ZsxA+IILDImlBPvTT6g/5RRDY1ZS4Ih7xRlJ+wsvgNtxR8PjGk3VQw/B1tJSkth9M2Yg/qtflST2kIDjYNmwIfW702oFu3UrTIEAmNigwuufMgXcL35RwU0SBEEQhJRc8mrWrFp8952JMq8IgiAIgiBEkLgyAPvzz6PuyitzZwhtzxRaBjCXuAKUs6nU5FUazueTlNkDUg9OOa8XMJmUJZWobJ48kwomk1TmJBJgg0EwAwODaypJKqWSgGnhICEtnQCAd7nAO52Z+Upk9uzzDQo7+R4V7pGXBoTJlLeU2sDhh8P+7rs556jRtn49am64AfY33pCMa5VC/ZdcgtC0aQAA9x//CMfzzwMAvOefr2svEngeDY2NxQmqHCKgbNlT4bAxaymUQMyH6fvv4Tv99KLXBgySKuk/U6Mopehh29tRf/zxhsaspJhS+x4sNoNtOGRLlap0HwB033knuIaGzNc+nw/BMvYMKymxGJzPPANTW1vxsajnFkEQBDEEaWqK4LvvTGhuroZS5tXWrSbqeUUQBEEQBJGG/mWvA9vLL6cyJEhU5SdfPymlkn9i+ZSrX5WS2GIYRUnFdnRkyuFJJFVaDnEeT+ZBV0ZSiUr6SQRQLAa2uzsr+ymnpDKZwHm9yv2oenrARKPSfahJJ1GpQfH1nBlR0SjYnp6sOXmzqDhOMWtNi7TqfPRRsMEg6mbMkIxrFSq8xYLAhx8CADwXXADLpk0AgKqlS1G1dKmmGALyB93Wd95B3TXX6JY7vMOBgMoZWNeuRd3MmbriCgTeeScjKnORSwxo1QKdTz+NxKhRBewOcPz973DPn1/QPWoYISEaGhsN+1nc84c/YEBWbi9XBlshsMEg6o89tug4YiolcYwUlGKM7EFWEngenhL2fAouXbpNChcmEtFUHlYP0bFjkWxoANfQoOnnJkEQBEFUmjlzQti61YQVK5xQ6nkFgOQVQRAEQRAESFxpwvb66/BccgmJKi0IoklALZsqV8k/pZhKZ8/ziv2qBGnF+f0SecT094Pp75f0c8pIqmAwM08sdJhwGEwolF2ib8QIcMLr5HnJdd5uB+925+9Hlc524mtqoPSdJexXsieGyZ9FJZJwAACbTZ+kUim1KIZ3OND+0kvwH3OMZLyQDKj4li3o6OiA/9e/BpMumcjE4wWLJflDfOF+vYKq8+GHkdh3X8Vr5cqeMmKdyMkno/eWWwq6x3P++bB88UXRa8cOOABdDz1UXJB4HA1jxhS9F4FSyZ5SlL6rlJgyqt+YGK62Fu3/+IdhItBo2GAQtUVK51wEH364ZLErBdPXB9df/1rSNSInn4zEL39Z0jUIgiAIotwIYkpNXnV2snjiia4K7pAgCIIgCKLykLhSwNLamvo0OYmq3KhJKfl1MUrZVGoxlUoByrKsBGnF+f1gu7qAeDxzjQ0EALM5U4pPkEaKQggA09sLZmAgS1JJPsWdSAzKLgyW8csSQ6LMKPE6eUv91dYCVmsqhEiwyRGEWqFZVGwwqFyaUIOkalu3LqvsGhOJZEkr1fvTD+HlD8Utu+1WUOkwowWVmhxwrFwJb5Elv9o++ihvBkX9hAmp790iEV6HVjFglJzonT0bkbPOKiqGkaKka+FCxI44wrB4AkwoBP+RRxoasxJiyoieakq0ffBB5mfXUMP6zjtwPfhgSWIndt8dvQb0jRtKMF1dcBUrnPMQPv10JEeOLOkaBEEQBDGUWby4ByNGJBXLBra02HHSSV68/HJnZTdJEARBEARRQUhcATB9/TXqjz02U66NUEEpmypXD6p8Y8K4Ul8qhgHvcICJRKTjPA/O50uJG1GmVUb8pMVNRj6JRJNY6giSK0tSud2DWwiHpdfTUonz+1Pl2NKvhxkYANPbK4mjmhmV7oUFSHto5cuikkss3unMXRYpmRwspyhCUVrJCPzjH4oySmuvIDVBVVQG1cAAGsaO1RVHMV4R+yoktoDtH/9A7e9+V/J15BglhDpWrEBy111138/098NvoEwqhfBhIhH4Dz88a7yYnkyVEFOlyJaKjhmD7vvvNzyuEbjnzoX5hx9KEjt0ySUlkaCVwvT993A++2xJ1yAhRRAEQRDamTMnhF13TWLWrFrI5dXGjVaSVwRBEARBbNdsl+KK6epCzaxZcLz8cqW3MnxQy6YSyyulflXyvlQcpxiLq6oCm86CygxHIuDc7tTbd5EYEpcCBKTl9zKSSiSF2M5OIJnMLvcngm1vl173eBTlkKT0oNUKvrY2VRrQboccxfXMZlVJJWR8ifeutNesdZSyqEymnPcAwMDEibC/8UbWuOYMqo8/BkymogWVUCoQSPWwEnqh6HkAP3DMMei5886s8aoHHyz6gX5ba2vOzDQmHIZ/3Lii1gCKl1N6RYuW7LBC9lEMwYceQvyAAwyLB0AiP42i3GLK8eyzcC9YYHjctnXr1Eu1VhBPkRmPueheuFCTyB8OmL/4Ao5XXy3pGuHf/AbJnXYq6RoEQRAEsT3S1JT6oOagvAJIXhEEQRAEQWxv4ioaxS/ok8DKyLOnhEwoLeUSc/WrUpJXCplabH8/YDKBc7slZdPYtLASZE5eSSWU8VMo0ye+TyKVfL5UDPnLEs+pqZH0imJZFry4x1V6Pd7hAF9drbhuBtF88Rze7ZZkfCntRymm3oevStJKifZXXwXn92cLqkMO0bwWb7cj8N57g/eKYhVaKhAA2l9/HZzPlzXeMHo07EUIFM7tRvvbb+ecY4SgaX/hBXA77qhtMs9rznbLRzGihe3oQP1xxxmyj2L3oojBvbCA1B7L2ZOpFNlS4bPPRt+sWYbHLYpEItU3skQEly8fkiKuUGxvvAHrZ5/lnGNyOuGQ9XkshPBZZyG5yy667ycIgiAIoniamiLYa68EzjvPg1BI+KDcoLxqbPRjyZIuNDbGc4UhCIIgCILYpti+xJVIRBAiGEY5c0ppLFfJP3k2ldqDw3RMzutNZUMJJJNgu7pSIsZslkoqQfT4fJmsF12Sqr4+W/7Is7HSayhJIqavb7B8obAXtbKAGMz24rzewSyoHPMBAPE4mGgUvMslGc6XeQUAkVNPheOFF/LOU6L7rrsQPfrorIfn9SecoDlGfL/9Ug+N0wixmIEBXQ/lleRG9YIFRQuUfNLECIEQmjYN/RofzjO9vfCPH1/0moA0g61QjBQnHc89h+RuuxkWD4kEGn79a+PiobwZU9W33w7nc88ZHrcS5QhzYdqyBTU336x63Wy1whOL6Y4ffPhh3fcOFZzLl8PUWdpPTpOQIgiCIIjhRWNjHI8/HsSkST7wvDTz6uefTTjtNB+mTevDnDmhSm6TIAiCIAiibGxf4spiqfQOKoM8w0mtN5VW1Er+qfWrQkoGsbKH6WxnJzi3G7DbpZJK6AFVV5f5M8tIKlEMichJZzHJy/PJZY9EPAkxTCZFKaRU6o+vrgZfXQ1WLvBUsqg4rzcrrnyNrLUtFvB5vlfVBJUWaRU54QT03nZblqSovf76vPcKhKdMQd911wFIicP6448HAFg++8wwQdUwenRRIiX+y18i+MQTqtfrx4/PZPQVg1ZxYPnkE3guu6zo9fKtmZ2HNojp66/hO/tsQ/aQbx8Fk0wWlMWnhbJJHQOz4sT0XXMNwuefb3hcvTgfewz2N98sSezYgQciNHNmSWKXC9eiRWCSyZKuIRdSNp8PfWXKCBxyRKNg+vvBhkJg+voy/w+TCbExY8A7HJXeIUEQBEEURGNjHKtWdeDyy+uwdasJg32vAIBHc3M1tm41YfHingrukiAIgiAIojxsX+LKaq30DiqPkF0F5M6wElAqAyiMq8TnamvBdndLw3R0gLfZwNfUSCVVby/Q25sRWIBIUon3RLHFAAAgAElEQVRKBkrkTiIBNhjMK6lYWYYd5/dnxJOEdLzM/tNlA1WzqNJxmerqwQdjebKo2EBA8hoVX5cSyaRivyqtWVVt69dnyR/Hq69q7ofSO2cOIpMnAwCq77wTzqefBgA4n3gCzhxSSDHWjTcicsYZkrHamTPhePfdogRVLjlhf+EF1Nxyi+7YWtYQ42puRtXSpUWvx1VXo33NGl336im9qIZaSUZdcBwaDj7YmFhpytWbyXvOOTBv3mx43KGULVXKflJ911yD+EEHAQB8Ph+Cw0y0VN99d8nXoB5SKUxffw3z118XF4TjwEQiJK4IgiCIYUljYxzr1wdw0klebNxoxaC8SmVfrViR6sFM8oogCIIgiG2d7UtcFZNlNFTJl00lLwOoNk8YA5QllcrZ8TYbmGhUMiZIK87vl8gjJhoFEwiAd7nAO52SLCVBYAn3Ze4Jh8GEQrklFc9LJZXZDM7jyZ9FJWR0mc3KAonjMhlekiwqv1/a40oEE4mA6evLipdXUKlkqilJKyWUBBWgvfRb16JFiI0bl3WPe948uOfN0xQjs5ePPgLM0h8tDaNHwz1/Ptzz52ffoCZBRQwcfTR67rpL8RrT1wf/UUcVtEcltEoE/+GHS7L29NJ/8cUIXXllwfdZPvsMnosuUp+g4TzFGCZPSpB1VBYxlac3Fsuy4HSIwO577kH0yCOL2ZlhlFJKdf3lL6mf58OQcgip/gsvNE7+Dkc4DpYNG6RlgQ2Ed7vB1dSAr64G53KlSuyat6+3tgRBEMS2ycsvd2LKlDq0tNihJK86O1k88URX7iAEQRAEQRDDmO3rX/fbesaVkqTK9dBXqV+VmrxSiSNIK7mkAlKSiLfbwbvdEknFhEJgQqHMfZn5wWAq+0kmqSQPRWMxyXU+nfWUJYZE6wGp3lY5e1EJMU2mwfJ+Kn2uMvEDAUk5QwDgHY78n/KOxbK/FzU+nC9WUHU++igSe++ddU/dNddoul++FzF1V1wB68cfF9WHKJdEMaL/Uvurr2rqFWZUr6fORx5BYp99Cr7PyF5TgZaWrH5puiiFmGptLVi0FYqRZylmKGRLMaEQ6nTIT60M135S5RBSocsuS/1u2x6Jx2F7/31A9qGVUhE7/PBhK0cJgiAIohieeKIL8+a50NxcDbm8ammxo7HRjyVLutDYGK/sRgmCIAiCIErA9iWuhnvGlVYplavknxylvlRq8ioNV18vkUJAWvwI0keUqcQMDIAZGEjdJ5ZUQjlAQRiJSvRl5sjLAXo8gNWa3beqvx9Mf//gPL9fXVKJygJyPl/moXm+Mn9Zc/KUBhTuU5yjQaC2ffyxYr8frQ/h2198EdwOO8D8r3/Be955mXFvgf1y4nvuieCTTw4OiOSFXiHQP3UqQlddlfna5/OhI/39YoRk6Js+HeFcGUlpjBIagbVrwVdVFXSP9d13UTdjhiHrA1KJIj7PQjFa8ihl3xkJ090N/zHHGB5XLHiLOc9isH7wAVxLlpQs/rCTUjyP6nvuKfkyoWnTts8Sc5EIbO+8U5aleIcDsYMPziqdSxAEQRBENnPmpD7wqSSvfv7ZhNNO82HatL7MPIIgCIIgiG2F7UtcaSy7NiTJlU2lpVcVMCiv5DKKYVJnI28qzzDgvN6sEj+CtOL8fiCZHLyeTCpKHrmk4m02xX5UEklVX58SVfKXoJBtxVdVKYoDeeYWAPWygEhngoXDKfkm+l7RK6i0ZPYE3nwT/mOPzRpXklaK97/9Nni3G3WXXQbrJ59kxutPOUXT/QLiB/UAUHvllbB9+CEs//63bpmhlpHiHzcOVcuWZb5mWVZXTyYtGS9GiRg92TVGSqC2Dz+UZPbpxXAxZdC+1NhWs6Vqfvc7mNraShI7Om4c+i+9tCSxS0IyiepFi0q+TN+MGdtdCTk2EIBl48ayrMU7HIiNGVPSnwcEQRAEsb2SLa+AlLwCAB7NzdXYtMlCpQMJgiAIgtim2M6e4pS2JFVR5OtVpTRfPlecISVIKoV+VbzJBEYuqZJJcG53qteUCEFKcX4/EI+D7Rp8M5wlqUSZVhlJ5XRKBU56DpOrZxWQtZaQHaUog0RzudraTEaTqjhS6V3FC/0xVGB6e1OCTCZAtQiqYHMzPNOmZY0rSSsl2j74ALBasx7k+8eP13R/Jo74gb0oe6rQTCyB3t//HpFJk7LG7S+8YIh0yCsY8vQnMnQtGfaXXkLNTTcZsjZvMiHw8cdFx2kYPVq3CFSi7b33SpYVYdqyBb4zzzQ8bvvLL4MbMcLwuFopZT+p3rlzkdhjj5LFN5RYDNWLF2cNm5xOVIfDhi3TN3Pm0P7dbjCWjRulvSPdbthkv7eNgvP5ED/wwO3qfAmCIAhiqDJnTgjHHRfF5ZfXYetWE5RKBx51lA9r1pS/UgBBEARBEEQp2L7E1VBFKQNKLZtKrS+VWoaVwjiTTIK3WsHEYtLp6YdfnN8PRKNge3oGr8kllUgWZSRVdbVE4jDhcCaLSUBJUsl7Y3F+P2CxKAohxSwqlbmSfad7XKUGc/SuQqq8IQYGwNfWSsa19DPpP/98VD36aNa4krRSoq21FeC4rD5RDYcequn+TByRhPGeeSbMW7ak4hiYPcX09sI/fjzct96qK6ZAfMuWnKXYTN9+C98ZZxS1hkChcsrQrKl16zT3MlPD6AykwDvvlKx3zDaXLcXz8GgoQamX4NKlwyIjiOnvL2kJQ4G+664r+RpDBdsbb5RtLb6qCrGxY8u2HkEQBEEQxtHYGMf69QFMmVKHlhY75PJq82YL9t/fj4ceor5XBEEQBEEMf4b+UzIjGSqlAvOV/FObJx+XZVKpzlXaQlpacfX1YCIRMKHBmthySSXuIZW5VlubVQ6Q6esD09eXeikOR6qUn/ihOM9LS/3Z7eDdbkWJxAwMgEmLNCGWeE9Z89OCTIgpkDMbKl3mUD6Ht9vzZpnwe+wBfPVV1riStFKibf16WNeuRd3MmZLxhoMP1nQ/APRfcAFCQp+kREIiu/RIg+6FCxE94ois8YbRo4uWEIE33wSvUPoRAHwAHCtWwD1vXlFrCBQiNpzLlqH6vvsMWTe+zz4IPvJIUTEMF1MtLTmzCPVidI8ugcC771akvxD788+onT1b8ZrZaoVHJvkLZTj0k2KCQbhEJTxLRfL3v0dfBXqGlRWeh+3NN8u2HOf3pzKjCIIgCEPhOA6zZ8+Gx+PB7NmzEQgEsGjRIvT19WHkyJGYPn06zGYz4vE47rvvPnzzzTeorq7GNddcA3/63xcrV67EW2+9BZZlMXXqVByY/nm9ceNGLFu2DBzH4ZhjjsEkhQoGBKHGE090Yd48l0LpQB6dnam+V5Mnh7F4cU+OKARBEARBEEOb7UtcGVQ+qyCUMqfylQEUo5ZhpSSvhP9W6leFtKQKhcBEIoPhxf2qgFQJvfR6GUnl8Qz2kOJ5sO3tYLu7B+PW1GTJH6a/X5od5fGo9peS97YCw6QElJI8EvXUEmdR5Szzl96zJOsKAEym/GX+YrFM6UHJ69u8GVr+BNvWr0f9EUeATYs/gUIEhVj6+I4/Hqb0n1nVI4+gSocoURI7DaNHo1Ym0Qql5w9/wMBpp6ler732WthaWrLGWZaFu4C/mwPHHYee+fM1zzc0a6rIbB/DxdRbb4GvqZGM+Xy+nBlsWihFtpRR5RALxfnkk7C/9lrJ4g91KWX68Uc4n3665OtozZCylXgfJSMeh+3tt8u2HOf1Iq7h7yHv8yG+rYtAgiCICvHKK69gxx13RCT9b6fHHnsMJ510EsaOHYu//vWveOuttzBx4kS89dZbqKqqwuLFi/Hee+/h8ccfx8yZM/Hjjz/i/fffxz333IOuri7ceuut+POf/wwAWLp0KebOnQuv14sbbrgBjY2N2GmnnSr5colhhlA6cOrUOgSD4tKBAMBjxQonPvjAhiVLKPuKIAiCIIjhyfYlrsrRpyFfrypBnKhlTSk9wBeyqZRKCirdk0yC83pTkioaHQwjl1QiYZSRVOleUgAy5QDZYDAzj/P58pf6q68HX1U1KLuE7aZLBwqvifP5JPvJetlCCUKXazBzK49sYgOBVKaXOGuDYfIKKmZgQFmUKUgrJdrWr1d82F+IAMhIkWgUDYcdlhnX2gdLTHDZMsT3318yJpQMLEZKxPfeG8EcWWVGCY/uu+5C9OijNc2tvuMOOJ95xpB1ByZORM/tt+u+33AxlSNTTS/O5csVew8VS1tra9l74ZSyn1Tk9NMRmTQJPp8PwSEoBsxffAHHq6+WfJ1tuWQf09sL64cflm29xKhRSI4cWbb1tjmi0VQGuDgDUuV9E+fxaP79TRAEoURnZyc++eQTTJ48GS+99BJ4nsemTZswI51xftRRR+HZZ5/FxIkTsW7dOpx11lkAgDFjxuChhx4Cz/NobW3FYYcdBovFAr/fjxEjRuA///kPAGDEiBFoaGgAABx22GFobW0lcUUUTGNjHJ99FsBRR/mwebMF8tKBP/9M2VcEQRAEQQxfti9xJcgfrdlO+VCSUuIxuaTKda+A8BBGSVIpZVJxHLi6ulR/KtG1TFaS35/JOMpcU+j7xHR3g4nFUhlXQuj6eqnwiccl18Ew2XOArJKAQrYV73Qq9tMR1s7sV7gvj6BSmpNXUEUiiqXIFKWVAoGWFviPPDJrXI+g8o8bJ+n/pUd6yDOAbG++idrZs+GZOrXgWLniijFKzrS/9hq4+npNGUJDJWvKaDElnIGRWHbbDQ0GZ5fG99237JlFpZRS3XfdlT/bskJYP/oItnffLfk626qQMv34I8xffFG29eKjR4Pzesu23jZDIpHqk6mQHV4Qaj/ryizRCYLY9li+fDmampoy2VZ9fX1wOp0wpUvPezweBNMf7gsGg/CmfxeYTCY4nU709fUhGAxijz32yMQU3+MV/e7wer3YvHlz1h5Wr16N1atXAwAWLFgAX/pDf5XAbDZXdP3hTDnO7vPPgZNPTuLNN4XMK0CeffXDDza8+24FKtAUCX3v6YfOTj90dsVB56cfOjv90NkVx1A9v+1LXKn0e9IdSy2bSitqkopl1TOpamrA9kg/LcV2dQFISxuOk8iljEBqaACX3qswJpZZnN8vKX3HBgLS6243YLdnlwTs7QUzMCCJo5rhlEhksre42trMp6H52lrVsntsMAgkElll/vIKqnA4JahkZ6u1f07v9dfDfdddWeNK0kqJ7ttvR3TiRDChUNY9hcqPjmeflXxKn+nqgn/CBF2xxJRDTmnNwqmdMcOwh/WS3l8FYriYeuUVcOlP0xqB+7bb4Fi5MvckHQ9siy2BWBCxGDyXXVay8MHly439WW8Q9tdeg2XTppKvsy0KKcunn4LdurVs68XGjatIr7XhDNPdLXkvUA54hyNVInio9C8lCGKbYf369aipqcHIkSOxqQy/u9WYMGECJqTf8wMouhR0MRhRinp7pVxnt3w58NhjDtx6azVCIXHpwFT2VWurCT4fg7lze9HUFMkZayhB33v6obPTD51dcdD56YfOTj90dsVRyfPbYYcdVK9tX+KKZQGzGYgr1HjOU+KPA5N+26eiWOS9puTZVIKIUioPqCSpOA68yzVYWk+YnpZWnN8PxGKSXlNZWUhiidXWBhbILrUn9KyS9ZnKl0UllO/j3W7wbnfWcUjiCbFUelwBSJU1DIclQgtIZ2vlgOnvT2VLyR5cKWV2FYKStFKi7YMPAKs1S3jU3nADcMMNBa0plwdCTF+69IgeAi0tyr2/eN44OaVFevA8GhobFS+xLAtTgRlCekWL0WKq4/nnkTSwrEspekuFzz4bfbNmGR5XCcunn6L67rtLFn8o9pNyPP00zD/+WNI1OJcL/ZdfXtI1yo3tjTfKul50wgTKwtFKNJr5QEy5oRJ/BEEMBb766iusW7cOGzZsQCwWQyQSwfLlyxEOh5FMJmEymRAMBuFJ/zvF4/Ggs7MTXq8XyWQS4XAY1dXVmXEB8T3i8c7Ozsw4QRRDU1METU0RTJlSh5YWO+Tyqq+PxaxZtViyxIVFi7qp9xVBEARBEEOa7UtcAeAZBoyWPlSiMU70Zk8yB1CWTrnKACqNcxx4hwNMRPrJJ0FacX4/mL4+yXW5pGIiETB9fZJrvMs12M+KZcH39ICJRLKkUlbPqnSWU2ZOOttJSTqJ5wolAcX7ykKQbRYLuLq6zDDvcikLFuEs+vrA22xZD7TkfbSUSO64I0z//W/eebloW79ekukk0HDooQXFaX/xRXAikywWFXqlRdfixYiJemIJML29mjPE8qFFFNVdcgmsGzcasl7v9dcjcs45Bd9nuJh67jkkd9vNkFi106fD9v77hsQSI/+zKdWnJNy33ALzN98YHhcAuKoqdDc3lyS2XlwLF4LhOJicTlSLSnoaSWLXXRE588ySxK4EWmQU43bD1ttryHrRiRMNibNNw3FZfSjLBe9wgK+pqcjaBEEQxTBlyhRMmTIFALBp0ya8+OKLuPrqq3HPPffgww8/xNixY7FmzRo0pj+UNXr0aKxZswZ77rknPvzwQ+yzzz5gGAaNjY249957cfLJJ6Orqws///wzRo0aBZ7n8fPPPyMQCMDj8eD999/H1VdfXcmXTGxjPPFEF+bNc6G5uRpKpQO3bDFT7yuCIAiCIIY825e44nkwQj+FfPJK6XYwqYwrpf5TctQ+2c0wgMWSlfUlSCnO70+V6BPtRS6pxNcz1zwe8CJZxAYCqSwmIWOrqgp8dTX46urBReUPtMxmcB6PcpaTLLtL2ItqRlQyKe2zJWC15izzx6SlllxISfatQnTsWNjeey9rXKu0ih52GLoXL1aUH4UKEbFM8Fx4ISyffw4AqD/llILiCAwcdxx65s/PGjd//jm8BvUCyiunOA4NBx9syFri9QoRLUaLqc4nn0Rizz2LD5RMouGQQ4qPI6PnllswcPLJhseVU8p+UqHLLkPs8MNLFr9QSpkRJhA74IBUhs9wh+NgS/fWKBcko3LDBgLSD8vEYpkSvKWG8/kyH04hCILYHjnvvPOwaNEiPPXUU9htt91w9NFHAwCOPvpo3HfffZg+fTpcLheuueYaAMDOO++MQw89FNdeey1YlsUll1wCNv1vxIsvvhjz5s0Dx3EYP348dt5554q9LmLbZM6cEI47LorLL6/D1q3y0oGA0PuqpcWGhx7qouwrgiAIgiCGHAzP57E1JeKnn37Keb0kWQOJBH4xatRgM3Chv5QgrYQyfoKIyjwcYlKZWgCA9Dy5mBKOUd5TyWYDE40qbofz+5U/Cc0wqSyndBm/rPvE/Z7i8aySPuLMJwH5OpzXq9wXQrYm5/PlLq8kmq+0rhpsVxd4hgFfW6tpvpjYfvvB+tlnBd8n0Pn00+DcbtSfcILuGCzLYusbb4BPZ43ZX38dNTfeqDuegJI8cjz7LNwLFhQdO3Liiei99dacc+qmToX100+LXgsAuhcuRPSII/LOE/9dN1xMPfwwEvvuW3Qc/9ixJenfUoreUvKfnaWUUl3NzZqyHstBqYSU0+lEOJ1xFR03DrESCMqyEonA9s47ZVuOd7sRGzMm8zXVnRYRiWT1rCwUj8eDoA5xRdlQ2Rj1vZmrPjdBEEQx5Pv3cymh39/6GQpnN316DVasEJfSH5RXAkM1+2oonN9whc5OP3R2xUHnpx86O/3Q2RUH9bgaCjAMeJMJTCKRkjbyflNyhDKAjHha+j/k9zKMoqQSvubq67MkFBsIgLfZUg+PEonBT02L+klxsiwqAFKxJO9HJY4jzPH7gREjwMlKGiplW6mVBBTP5x2OwQyoHPMBpHpscVzWHHGZQDWYcFixV5VWadW2bh38hx4KRpbd5v3NbzTdn4mTlgtMMAj/scdmxuVlAwuNJ6Z2xgzY3n23aHHTfccduTM94nE0iB4iF0uh4kXp9bEsi4YCe1wJBB98EPGDDtJ1rwDT3w+/BsFWKEZJMzWY3l7UTZ+eNW62WuGJxYqOP1T6SZUjQypywglI7L234jWbz4e+If7mhw0EYDGoTKcWErvvjuTuu5dtvWEBz4Nta6vY8pQNRRAEQRCEGosX9+DCC8OYMaMW335rhlL5wBUrnHjzTTvmzu1FU1NEJRJBEARBEET52L6ecnBcSkaxLHiWHSwbCKiXClQSWwyTekAk6gMFpCWV2QyupiZTJk+AbW9P9XFyOiX9qphoFEwgALDsoNzhuJTwgUgumUzZvagCAanEcrsBuz1rHhONAj09EPKmcvWskqwJqTjLKagURBuQfpiWC54HolHAbs++pCCt5HBuNzqfegr1J56Yda0hXXdeC4F33smsJ5cremRS23vvZb0mIU6xcqrj+eeR3Gkn1eveSZNg/uGHotYQ6Hz8cST22kvzfKMzprqWLEGsyPKERu9JoBTZUgK2NWtQtWxZyeIPBSlVDiEVPussJHfZpeTrlALzpk1F9+YrhHhjo3rp1+0QpqtLNVu65JjN+X93Cvh84GS9HwmCIAiCIOQ0Nsbx3nvteOwxB26+uRqRiLx8II++PhazZtViwQI3Zs8mgUUQBEEQRGXZvsQVy4KJxVLiyWTK6jOlJql4i2XwPoFEIvVwqbpaWqovkQDb2QmuthawWlPZT2nBJfSc4h2OjOBh+vvB9PdL+k1xNTVSAZTuLyURSvJMK0CSqQWkxA/vcqUywZQyrjo7M2UTxSUBNQkqcbnCPPcI5wKOA+QP2BhGUVrJ6bnpJrhvvRWM/DX09ipKKyWiY8ei+957AWTLDP+4cZpiiAkuX474fvtJxjJyauzYguOJafvgg+yzSsOEw4bKmEIEjOFiavFiuE89VXc6Kvvf/6L+1FMN3RMAtL/0Erhf/MLwuABQe/XVRZcHUyO+zz5g77wTwQpmCJVDSPVfcEHqZ9Aww/aPfwyWqi0D0SOO0PTzdZsnmVQsu1suOL8/d8ldgiAIgiCIMtHUFEFTUwQnneTFxo1WKGVfdXWlBNYrr9jxxBNdKpEIgiAIgiBKS9HiqqOjA/fffz+6u7vBMAwmTJiAEzWKhErAW62pT1GzLGCxSLOmBKGVSEikDBOPA2Yz+KoqML29g/MTCbBdXalPqZtMkgdjbHc3gHRJPItF0guKiUQyGVdcfb2kRwwbCEgeagulBJWyrcTkyqJi+vuB/n6wQCbrC0j3uVIhI6hkPa7yCSomFAJvs6VesxiNJYw6H3kE3gsuyBqvueUWTfcDQNtHHwFmM9w33wzHiy9mxm3vvVeweAmfey76fvtbyZgQw3PRRQXFytpnDmFUf8wxme+hYsmXoSXGcDG1aBFiOqSgwHDLliplP6neOXOQ2HPPvPNspVic51F9zz2liCwh9L//O1iGdJhge+ONsq4XnTBhu5cg7NatFVubr6oadt+jBEEQBEEQcl5+uROPPebArbdWIxSSZ18BAI+WFjt2220ELr00hDlzQpXbLEEQBEEQ2yVFiyuTyYTzzz8fI0eORCQSwezZs7H//vtjJ40PyssNb7eDGRgAkslUJhIglVfJJHiHAzCbwYRCknGmtzcle3he0kdK+O+M5BH1mcpkY1ksEunDRKNgenqkpf58vuwyf+GwNIuqulqSsSUhGpVIL2EOX1UFpro6K+MKEAkqQbDJ7lWDDQRSwk4mpHiXK+d9mXlmc6rXmAwlaaVE+Jxz0Hf99bC0tsLzf/8nudbw619riiFGIjJEfaCcTz4J55NPFhxPMa4Ipru7IllThoupP/8ZscMP13Wv+fPP4b3wwqJ6XCkRaGnR/H2oGZ4vWlTmIrh0aWX60ySTqF60qOTL9F11FWAriVIrCWIZxbjdsIk/sFACohMnljT+kCYSKVkGoha4ESMqtjZBEARBEEQlEbKvpk+vwYoVTkizr1LlA2MxBs3N1XjwQRcJLIIgCIIgykrRT0rr6upQV1cHAHA4HNhxxx0RDAaHprgS9bViYrFBSQVIJBUzMJDqOeXzgYnFJFlWbGdn6lo6wylT6g/I9KXiamsHxQ/Pp8bj8UEBxTCpTCuxHBL1tcoM+f2pcn/yXk/JpKSHVqZsn82mLJx4Hti6NZVxlRZf4jVUSWeJcV5vKhNNtrd8RA8+GLbWVsVrStJKibaPPwYTCsF/9NGScedTT8H51FOaYmRiieQO29YmKTFYjNBRk0YNo0cbJooCb74JXkP/Gf/YsanvX4PoXrgwVW5MB6XIluKtVgQ++MDQmOxPP6H2hhsMjSmmIv2kBgZQff/9JV+m75prsn42DEkSCdjeequsS26vMipvNlQsJvngh5FwdXXDSpASBEEQBEEMBRYv7sGFF4YxY0Ytvv3WDKXygSSwCIIgCIIoNwzP83z+adoIBAK46aabcPfdd8Mpky2rV6/G6tWrAQALFixALBbLGctsNiOhUW5oJpmEZdddgf5+QPxw3+kEqquBvj4gHJbe43Kl/sfzQFtbdkxx74pYDJA/kPP5sjMp5A/2PB7lfkbyNfM9lBPPdzoBt1t9rhhh33r7cMRiqv2YtJD87W/BTZsGy8iRumMIxDdvzpw3s349zGeeWXRM7sQTkZRJALPZjMT338NSZC+rDC4X4p99lneaefRoMAY+9E3cdx/4k04q+D7m7bdhvvhiw/YhEP/PfwwVIewjj4BdudKweHISJYytSG8vTH/+c84pLMsqZlcWQnLuXOWef0OJnh4w77xT8mVMJhOSySTgdIKXCfRtnq4uIGJsU+6CfrfvsIOha2+LlOS90naKUWdpLeL9EEEQRC5++umniq3t8/l096Td3hluZyctHygwKLAEqqs5zJ3bi6YmY98ryhlu5zeUoLPTD51dcdD56YfOTj90dsVRyfPbIcezH8PE1cDAAG666SZMnjwZv9ZQqi3fG++SHFgigYZDDgF4PiuTCgwDrrY2VS4vHh8s8SdgsaQ+zQ2kMpE6OwHxw2GLJXW/uDfWwIB0DZNJua+UqP8VAMBsTpXhU1bRPm8AACAASURBVEM8P9/cNCzLgu/qAhONDmZoFUK6z1cxD7Pb1q1D/VFHgQ0V9+msjlWrkNx5ZwCA/YUXCup/pUbPrbdiQKE3m1rWkB45EFi7VtLPTAnvOefAvHlzQXFz0XPzzRg45ZSC7ytFttTAMceg5847s8b1/l0vZT+p8FlnYeDkk0sWXw7b3o6qRx4xJJbT6URYLuDT9F13nSFrlArTd9/B/NVXZVsvOXIkEqNG5Zyzzbz5SSalv2fKDFdfD5hM2855DhHoPI3DqLPM9aabIAiiGEhcDU+G69nNm+fC3/7mRDyeW2DV1XGYPbt0Amu4nt9QgM5OP3R2xUHnpx86O/3Q2RXHNi2uEokE7rjjDhxwwAE4WePD3oqIq2QSI/bdF2AY8DZbqtTfwACYvj7JNK6mZjCzSUFiSa4DymX+FMrrAZD0qwKQWyLJhJaW8nziNcSxtYoWNhDQvI4SvXPmwPTdd6h67DHdMQCg5w9/wMBppwEA3LfdBocBmS0dK1ciucsukjHT99/Dd/rpBcdSOs/EqFHofPrpnPfVTZ0K66efFryeGj233FKwYHGsXAn3bbcZtgcBrX225Cj9XS+llOq+++5UP7oyYPrhBzifeabk64iF1FD7ZW39+GMw3d1lWy8+erTyBwR0MtTOUyBvSb4SwlutmkqXKjFUz3O4QudpHCSuCIIY6pC4Gp4M97PLFljiZxeDj5Lsdh4XX2x8CcHhfn6VhM5OP3R2xUHnpx86O/3Q2RXHNiuueJ7H/fffD5fLhYsuukjzfRURVwB8EyfC8uWX4K1WwGoFb7enyuPxPJjeXjDR6OBkeRYVz4Pp6Un1x0rDV1UpZtGIe18B6iIrdVEqvjRlRInu0TJfIlpiMTDxeN7sn1wEH3gAnssv130/AAyMH4+eP/0JAOA78USYlEoxFkjg3XclPbwAwH/IIZneZsXS9uGHgMWi+v1Zd8UVsH78sSFrAUDPTTdh4NRTC7qnFNlSvddfj8g55xQfKBaD57LLJENWqzVv6VCtlKuflPnLL+F45ZWSr6MnQ6ocv2xsb7xR0vhyokceWbHeRWX55T0wALaMck8O19BQttKQ9GbSWOg8jYPEFUEQQx0SV8OTbeXspk+vwYoV4nYQygLLYuFx2WXGCaxt5fwqAZ2dfujsioPOTz90dvqhsyuOoSquzKpXNPLVV19h7dq12GWXXXD99dcDAM4991z86le/Kja08SSTMHV2gvN6wUSjYEIhMKFQqkxgTQ34mprBt1yxGNjubmnGk88HvrYWEtMXi0myqIRsLEWhlUymSgwKcwXhxLKqWU7icoOSOTnuyUwJBJSFmdWaEnd56JkzBzXz5ileK0RaCZk4cqFif/tt2HVIlrZ16yQPWU3ffQff5MkAAP/hhxccT4xaOTsB99y5cLz6KliWRUORfYQAoPfGGxE54wzN813NzahaurTodeXozZYSY/7Xv+C+/XYDdqNMOaSU9aOPYHv33ZKvMxRL9pVdRh177NDvo6WTimZDud3gZT0mCYIgCIIgCKIYFi/uwYUXhnHDDTX44gsLBmUVA3EJwXicQXNzNf76VxdGj47hxhv70NgYr8ymCYIgCIIY1hQtrvbaay88U4ZSWEYRi3KIxUyw2pyw+p0Ax4EJhSSfdhfkk0QMJRKSrCjeZgNfUwNYrdkCSS6ofL5UVpfJpC6oenoy2V7iObzdnsoKU31BKcGmlHWlqeQfz6s+PFaTVkq0ffwxwLJoaGzMuqYnA0guUsQxlNYoKHZra+rPQwH3H/9oaMZS37XXInzeedomcxwaDj7YsLUFuhYuROyII4qK4Xz8cdhLJDb4XXdFcO7cksQWsL/+Oiyff17SNYChJ6TKLqMmTizremUhGKyoiOJGjKjY2gRBEARBEAQh0NgYx5tvdmDdOouCwALEAiuRYPDRRzacdpoNfn8S113XV7I+WARBEARBbJsULa6GE+s22GHt+RXGc/9AvN+KRLUVZqc19Ql1tzs1ieNSPa16elJfm83g6upS/59PUAnZTWqCStyzimUlfXYk2V4KsIFAag/yviJK4qwQCsh4aH/5ZfBuN/zjxmVdazjkkIKWje+3H4LLl2e+Nn/5JbxNTYPxipBHvTfcgMiZZypec917r6FyqG/6dIQ1lsh0/+EPcLz8smFrCxSbLVXKflJ9M2cifuCBOef4fD5AZzqq46mnYP7vf3XdqxXebkfoyitLuoZmYjHY1qzJOYVxu2FLZ2kawTYlozguq89gXnT2clJc3usFLBbD4hEEQRAEQRBEuRELrPnz3WhtNYHjTJBmYQnwCARMmDWrFgsWuDF7di8JLIIgCIIgNLFdiasP3zPjSu5TdKAeAOCJ9YPtT4skiwWc252STl6v9Ea5oKqrSz18VBNUov5TvNMJ3uVKjTNMTsnERKNgenpS+5BlWWmRU0woNLiWTrrvuAOJvfaC77TTsq7Vn3RSQbH6p05F6KqrMl+LZZTls8+KklPycoECjhUr4J43z7CSdX1XXYXw1KlZ41m1P6NRNBx2mCFriul8+mkkRo3SfX8ppVTwgQeyvk+NwrV4saSXXClI7rADwueeW9I1tMB0dcHa2lq29XiHAzEF+TwcqWQmFEDZUARBEARBEMT2S2NjHCtWpJ6TTJ9eg1Wr7OA4FmplBLu6WMyaVYvf/74GBx1EZQQJgiAIgsjNdiWuxhwaw3+YUfgl/y9wMANVDnBWx+CEZFLar6q2FrBa1QVVPJ7KzgLAV1eDd6Rj5eo/Jcq6ypQQFC7ZbODzCapYLCVsFD61r1VaRU44AQOnnIK6adOyrtXOmqUphkD3HXcgOmECAMD8+efwikRJ1bJlqFq2rKB4Aj3z52PguOOyxu0vvYSam24qulyggJqYklN32WWwfvJJ5mujelzpzZZiwmHUXXFF0eurUap+UtV33501ZnI6UR0OG7ZGbL/9Kp4lZPr2W5j//e+yrZcYNQrJkSMBALzPh+hwbEgZjWZ+nv5/9u48vsky3/v4906alpa0paXsyihQfFRA0LKKLIKO4zgjh5eKIjqouIEiOA4gHhXHQXkGkRkRxKOIDhx9UA/KHMcNZFNApUCRZZTVlaV0AdrSNmlyP3+UhqZN2jRNm5R83q/XvMbc65Vfb3In+ea6rnBwt2njuwdqWprcAcwJCAAAAESrefNOaN68E5o5065FixJUWlq1B9aZAMvhODOMYPPmbv3hD0V67LHC8DQcAABELMM0zZpGqGswhw4dqnF9tR4toWCaSrmkj5wlLjUzSmU7dbI8ZEpKKg+o/DCKi2UUFEiSz95QPp0OtczYWJktWtStnad7bNVnCECzWTMVTJ7s6XlksVjkDjJoqdzrJ5TzP/kKbZp9/LGSH3ssZOc4OWWKikeNqnEbo6BArYcMqdNxA6nnsY8+CupvGLNzp5Jmz67zfoEwrVblv/ZayI/rK5AKVEJCgk4FEFyVDhwoR9++QZ+nvmK//FJGCIfgq42jb9/yefTqqEFeO4MQzt5QZnx8ULXzJVLqebagnqFFPUMnVLVs3759CFoDANXV9vm5IXG/CV601m7p0ng9+2yijh+3Vlpa9UdiZ76Kiokxddll1XthRWv9QoHaBY/a1Q/1Cx61Cx61q59w1q+mz9BR1eNKbrdibW7F2gxJzeS2VwqgTFNGUZGM01+ge4YD1OkvQePjqx/PNGWcPCmjtFTu5GQpLu7MOput5tDidM8rd2qqFFPlz1BTj60qin//e8X/85/VlhslJXUaLi97zRqZSUmK/fJLpVSZz6dlLcGPP/kLF8pRZT6p2M8/V8qkSZJCE4KdnDZNxTfeWOM2LcaPV9xXX9X7XJWZ6ek6+uabdd6v+cKFitu0KaRtqXBq1CiVXHttSI9Zn0AqUO4RI1TQrl2Dn8eXuE8/bdTzlV55ZfV/702AceKEjOLwjUXPkHwAAABA0zFmTLHGjCnW0qXxeu65RB07VrkHllS1F1ZZGb2wAACAt6b3DWp9WK0qGTpUzT7+WO7WrWU9dEhms2aS1SoZhky73fdwe2VlsuTlSVL5/FfW078aMgyZycmqqcuaUVgomabMxMQqK2qe76oyV+vWslYawrAyX6GVP0e//lqyWn0GRq2HDg34OF7HrNJrKnbjRqU8+KAkKeW++4I6ZmUFf/yjTo0e7Xe9JTc3pL3AKmR//rnMhAS/69PS0qQqSXRDzid1/P/+35B+ed8YgdSpm2+Wq0OHWreL81HL+mj0MCrMwxLWmWnKcvRo2E7vbtGiweZGAwAAABA5KgKszEybnnkmSVu3WuV0+htGUJJMFRVZtGBBohYutOvcc6Xx4+M1Zkz4fkQHAADCI7qCK5dLzdaskeLiZDlxQmbz5mfWmaaMU6dkFBXJbNasPGiqmO8kJqbmkMnhkOX48WpzVkmBzzslh8PvcIX+Qitfjm7ZotgvvlDKQw9VW9emT5+Aj1Mh9403VNatm+exbfNmpVYKpOobGtU2lF/qLbeEPGQp/t3vdHLGjMB3ME2ljh3rtSgmNlapDkdI2pO3eHG16yZYjRFIFd55p8yUlAY/j4dpKm7lysY7n5pWGFVtSD6HwxO0NwZ6QwEAAACoSUaGU8uX50pSwL2w3G5DP/wgTZ3aQtOnJ6t5c1NjxtATCwCAaBFdwZXVqqKxY8u/BLfZFLN/v3fvqebNvcOsylwuWXJzZSYmVh82MDa29t5TpimjpMT3kIOnjxEI5wUXKO+//1ttMjJ8rg8mSKrca8q2datS777b87hlPXsRFTz8sE7deqvPddaff1ba9dcr6a9/rdc5qqroWRYIIz/fM3RhQ8h74436H8Q0lfj88/U/Ti0Kx4/3f32GWkmJ4tavlyQZSUmKa4S5o5pEGOV0ypKbG7bTu1u3DlmICgAAAABV1d4LS6raC8vlMnTypKEFCxL10kt2tWrl1h//WEBPLAAAzmLRFVy53Wr++utnHlcNN07PWSXTlJmcfKbH1eltAwmn3PHxspSUVF9nGAGHAqduuUXO7t2VPH16tXW2777zG1r5k7N8uVIuu0w5OTmy7dhRrfdQfXpNFTzwgE7dcYfPdWnXXafE558PaehyYsYMlfzudwFta/vmmwbrgeS+/HLlValj3Q/iVuLcuSFpT00KHnww4GC0Pix5ebJlZjb4eSq427WTs3v3RjtfMKr1hmpMNlv50KYAAAAIWE5OjubPn6/jx4/LMAwNHz5c1157rQoLCzV37lwdO3ZMrVq10uTJk2W322WaphYvXqxt27YpLi5O48ePV6dOnSRJa9eu1fLlyyVJI0eO1JAhQyRJBw4c0Pz58+VwONSrVy/dcccdMip/9gSiQNVeWPPm2fXLLxaZpkU1DSVomoays62enlhxcaa6d3dq+vQCZWQ4G/lZAACAhhJdwZXFooKJExW3bp3cSUlqtnatd3h1es6qGrndMgoLvYcSrLS/z9DKh+OzZqnFtGk+1yW89Zb01lsBHUeSnBddpLwlSyRJMXv3quXNN3utTxs5UhaLRW3c7oCPWaHwvvtUVKkHVoWY3bvV8rbblPjii0p88cU6H9efqnNm+RP///6f4j/6KGTnraxg8mQ5e/ascRtfc1x5OJ1KfOGFBmiZt4LJkxu8d4z1xx8V8+23DXqOypzdu8vdrl2jna8ujKIiGQUFYTt/wEPypaXJ3QhBJQAAwNnIarXqtttuU6dOnVRcXKxp06apR48eWrt2rbp3764RI0bo/fff1/vvv68xY8Zo27ZtOnLkiF544QXt3btXr776qp555hkVFhbq3Xff1axZsyRJ06ZNU0ZGhux2u1555RXde++9Sk9P17PPPqusrCz16tUrzM8cCJ+KXliS9OCDyfrf/20mp7NygFWhek+sU6cMffVVnK6/Pk6xsaZ69XIQYgEAcBaIruDK7fYOFPwNJ+dySaZZvr5qOGWxyExKCuh0x595Ri189JqS5De08ufYBx/I3a6drPv2Ka3KnFC23buD7jVVdOedKpwwodryiuPZFy6UfeHCoI5dVd7ChXL27l3rdin33y/j1KmQnLOq/JdekpmQENzOJSVKnD9fkmRNSFBiA7Wx4OGHq193IWTbulUWf6FbA3AMHFhjzc20NJU2YnsqhLM3lDs5WWqsYRkBAAAQsJSUFKWcns81Pj5eHTp0UF5enjZv3qwZp+fJHTx4sGbMmKExY8YoMzNTgwYNkmEY6tq1q4qKipSfn69du3apR48esp+e87hHjx7KysrSxRdfrOLiYnXt2lWSNGjQIG3evJngCjht3rwTmjfvhDIzbZo9O0Vbt0rFxUYtPbEkyZTDcSbEiolxKyFBzIsFAEATFV3BlcWiU7fcorh161Tat6+sP/+suK++qt5rJcD5kVzt2sl5wQXlPbd88Bda+VL829/q5J//LOsPPyht5Mhq61tdd13Ax6qs8P77VTRunNLS0pRzOhyI3bRJKQ88IElq/tprav7aa0Ed24th6Ghtw8SVlSm1nnNm1STY+aSMwkLZX345xK2pruCPf2ywY8d9+mmDHduX0uHDI2ouJEtOjlRWFrbzB9wbCgAAAE1Gdna2Dh48qC5duujEiROeQKtFixY6ceKEJCkvL698NIbTWrZsqby8POXl5allpWGbU1NTfS6v2B6At4wMpz77zO35HmPmTLsWLUpQaWnV+bAkX0MKlpVZdPKktGBBohYssCs21lTr1m49+GAhc2MBANAERFdwVVZWPgyfpIT33itfVsuX78XXXqv4f/3LZw8Y6+HDsh4+HPDps9eulVFQoFY+5miK/9e/ys9TR0V33aXC8ePPLDBNrzmw7C+9JPtLLwU9VGCF3LfeUtnpXwX6YsnJabBQytGzpwonT67zfsaJE7K/+moDtMhbQwVSjR5GXX11o57Pr7KyRu0RVpW7VauAw2sAAACcnUpKSjRnzhyNHTtWCVVGDzAMo8HnpFq1apVWrVolSZo1a5ZXONbYYmJiwnr+poza1U/l+s2dK82d69aXX5p67DFD27ZZVFIiuVyGvIOs6iGWZMjhMPTzzxbP3FixsVLr1tKUKW6NGxf8dyWRimsveNSufqhf8Khd8Khd/URq/aIruKoyn5VMU2UdO6p04EA1W7lS1mPHqu0S/+GHAQ/bdnzuXDl69VLr05PuVuVveU2Kbr9dhQ895Hkc99lnajFliudx80WL1HzRojoft7Ky885T7v/8j9/1tsxMJc2cWa9z+FM4YYIcffrUaR9Lbq6av/56g7SnspoCqbi0NBXUNVxxuxV3+sNnY4mEMKrWIfkcDlka6lemNpvclX7RCgAAANSmrKxMc+bM0RVXXKG+fftKkpKTk5Wfn6+UlBTl5+cr6fTw8ampqZ4eIZKUm5ur1NRUpaamavfu3Z7leXl5uuiii5Samqrc3Nxq21c1fPhwDR8+3PM4J4w/7Ko8egfqhtrVj6/6dekiLVt25vHSpfF67rlE5eRYZJpVQyzJ15CCLpeh4mLphx+kCROsmjjRIovFVHz82TO0INde8Khd/VC/4FG74FG7+gln/dq3b+93XXQFVyqf06n5a6+Vz2ElKebHHxXz5psB7evo0UPH58xR6j33KObgwWrrWwTRK6jwnntUdO+95Q9cLrWpEuI0/8c/1Pwf/6jzcSs79q9/KbVbN58XYPNFixS3fn2D9JY6Pnu23K1bB7y95dAhNT/dI66hlJ17ropvuil0BywpUdz69aE7Xi3cbdrIeckljXa+akpLZcnPD9vpGZIPAAAADck0TS1cuFAdOnTQdZWGa8/IyNC6des0YsQIrVu3Tr1Pz92bkZGhjz/+WJdffrn27t2rhIQEpaSkqGfPnnrrrbdUWFj+Bfj27ds1evRo2e12xcfHa8+ePUpPT9f69et1zTXXhOW5AmeDMWOKPUP/LV0ar3nz7Dp2zCKHQ1XmxZL8zY3lchlyuQw5neVDC770kl2GIcXGmrrkEqemTy9QRoazkZ4RAACQJMM0zao/R2kUhw4dqnF9gyR9brfanP6A4UvpgAEqvPNOJaxYofj//d+QnPLEzJkqOf1BJG7VKrWYOjUkx61QMTeWLy0mTfKEDLGxsXI4HCE7b96iRVJMYLmn9ccflfDOOyE7ty+lvXvLMWhQSI5l5OcrdvPmGrdJSkrSyZMnQ3K+sosvlqtDh5Acq65q7Q3VgMykJJkJCfwqIsSoZ2hRz9CinqFFPUMnVLWs6ddiAJqGb7/9Vk888YQ6duzoGQ7wlltuUXp6uubOnaucnBy1atVKkyd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            "text/plain": [
              "<Figure size 2160x1800 with 8 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HpO8RUv9Y9cB"
      },
      "source": [
        "<b> See how useful it is to visualize the effect of learning rates and iterations on gradient descent. The red lines show how the gradient descent starts and then slowly gets closer to the final value"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LAVyPFtTY9cC"
      },
      "source": [
        "## You can always plot Indiviual graphs to zoom in"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PR0UBSaoY9cG",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 592
        },
        "outputId": "09329a90-3a9f-4b29-bf6a-824ebb08d494"
      },
      "source": [
        "_,ax = plt.subplots(figsize=(14,10))\n",
        "plot_GD(100,0.1,ax)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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CCwAARVCUp/2mqZmf+YxtWIkvW6a+z35W8YMOkiRZT3f1lvb2gCKRoCQpEgmq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\nI7QAAAAACDRCCwAAAIBA+x9OmyTyZYl2rQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f618af92f98>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UBx-2txOY9cM"
      },
      "source": [
        "# Stochastic Gradient Descent"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "s6VcRoNfY9ck"
      },
      "source": [
        "def stocashtic_gradient_descent(X,y,theta,learning_rate=0.01,iterations=10):\n",
        "    '''\n",
        "    X    = Matrix of X with added bias units\n",
        "    y    = Vector of Y\n",
        "    theta=Vector of thetas np.random.randn(j,1)\n",
        "    learning_rate \n",
        "    iterations = no of iterations\n",
        "    \n",
        "    Returns the final theta vector and array of cost history over no of iterations\n",
        "    '''\n",
        "    m = len(y)\n",
        "    cost_history = np.zeros(iterations)\n",
        "    \n",
        "    \n",
        "    for it in range(iterations):\n",
        "        cost =0.0\n",
        "        for i in range(m):\n",
        "            rand_ind = np.random.randint(0,m)\n",
        "            X_i = X[rand_ind,:].reshape(1,X.shape[1])\n",
        "            y_i = y[rand_ind].reshape(1,1)\n",
        "            prediction = np.dot(X_i,theta)\n",
        "\n",
        "            theta = theta -(1/m)*learning_rate*( X_i.T.dot((prediction - y_i)))\n",
        "            cost += cal_cost(theta,X_i,y_i)\n",
        "        cost_history[it]  = cost\n",
        "        \n",
        "    return theta, cost_history"
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Kq2aMN3FY9co",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "143a361d-a54e-458e-9d1d-8de2851af090"
      },
      "source": [
        "lr =0.1\n",
        "n_iter = 200\n",
        "\n",
        "theta = np.random.randn(2,1)\n",
        "\n",
        "X_b = np.c_[np.ones((len(X),1)),X]\n",
        "theta,cost_history = stocashtic_gradient_descent(X_b,y,theta,lr,n_iter)\n",
        "\n",
        "\n",
        "print('Theta0:          {:0.3f},\\nTheta1:          {:0.3f}'.format(theta[0][0],theta[1][0]))\n",
        "print('Final cost/MSE:  {:0.3f}'.format(cost_history[-1]))"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Theta0:          3.827,\n",
            "Theta1:          3.086\n",
            "Final cost/MSE:  46.802\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VXrjLr00Y9cs",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 500
        },
        "outputId": "c17a73a9-dc09-4a9d-8fa8-2239b11fca96"
      },
      "source": [
        "fig,ax = plt.subplots(figsize=(10,8))\n",
        "\n",
        "ax.set_ylabel('{J(Theta)}',rotation=0)\n",
        "ax.set_xlabel('{Iterations}')\n",
        "theta = np.random.randn(2,1)\n",
        "\n",
        "_=ax.plot(range(n_iter),cost_history,'b.')"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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mzJihzZs3x3ytyZMnq6ioSA6HQxMmTNDEiRP1ySefdHvM4MGDdeLEiW7Lpk2bpqFDh+qOO+7Q22+/3av6AQAAUk1CU8Df//73VVpaql/+8pfy+Xz69re/HfVx2dnZOnnyZK8KyMnJCf170KBBCgQCCgaDOnbsmJqbm7vdmNHR0aGLL7445mtt27ZNr7/+ug4dOiTLsnT69GmNHj2622NOnTql8847r9uyLVu2qKmpSS+99JLy8vJ6VT8AAECqSfgawNzcXI0fP14HDhyI+ZjRo0dr48aNfVJYQUGBRowYEfPPxEReixgIBLR8+XLdfffd8nq9crlc+s1vftPtMX6/X+3t7SouLu62/ODBgxo/fjzhDwAAGKFXfwfQ7Xarvb095u8nTpyozz//XG1tbedc2Lhx4zRkyBCtX79ebW1t6ujo0L59+7R7925JnSOHx44dU0dHh6TOm0kCgYCGDRumjIwMbdu2TTt27Oj2mh999JEuueSSbjeAdD3X5erV/TAAAAApq1epx+FwhAJXNLm5ubrkkkvk8/k0derUcyrM6XTqwQcf1KuvvqqFCxeGRu7mzp0rSSotLdX777+vO+64QyNGjNAzzzyj2267TRUVFQoEAvrXf/3Xbn/uRZLef//9bncFd+no6Ij5p20AAADSTa8CYG5urvbu3RsaMfv6668lSUOHDg09Zs6cOVq1apVKS0u7TdOuWrXqjNebM2dOt59HjBjR7W8Dejwe3XvvvVFrGTp0qJ588sluy66//npdf/31UR//xRdfqLW19YxQGAwG9cUXX2jkyJFRnwcAAJBuejXsNWPGDLW1tenOO+9UfX29Nm/erMLCwm43VYwaNUq//vWv4/69QDtceOGFWrJkSbdl9fX1WrBggb7++muVlZXZVBkAAED/6tUIYGFhoZ544glJ0qOPPqoTJ07orrvuSkZd/aKkpEQvv/yy3WUAAAD0q7O+8+Gpp57qyzoAAADQT7jzAQAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAzjsruA3nrhhRe0detW5eTkaPny5ZKk1tZWVVRU6NixYxo+fLgWL16s7OxsWZalyspKbdu2TZmZmSovL9eYMWMkSe+9957eeOMNSdKNN96oq6++2q6WAAAA+lXKjQBeffXVeuSRR7otW79+vS699FKtWLFCl156qdavXy9J2rZtm44cOaIVK1ZowYIFWr16taTOwPj666/r6aef1tNPP63XX39dra2t/d4LAACAHVIuAE6YMEHZ2dndltXW1mr69OmSpOnTp6u2tlaS5PP5dNVVV8nhcKikpEQnTpxQc3Oz6urqNHHiRGVnZys7O1sTJ05UXV1dv/cCAABgh5SbAo6mpaVFeXl5kqTc3Fy1tLRIkvx+vwoKCkKPy8/Pl9/vl9/vV35+fmi5x+OR3++P+trV1dWqrq6WJC1durTb6yWDy+VK+nsMZPRvbv8m9y7RP/2b27/JvUv29Z8WATCcw+GQw+Hos9crKytTWVlZ6OfGxsY+e+1oCgoKkv4eAxn9m9u/yb1L9E//5vZvcu9ScvsvLi6O+buUmwKOJicnR83NzZKk5uZmDRs2TFLnyF74h9rU1CSPxyOPx6OmpqbQcr/fL4/H079FAwAA2CQtAqDX69XGjRslSRs3btSUKVNCyzdt2iTLslRfX6+srCzl5eVp0qRJ2r59u1pbW9Xa2qrt27dr0qRJdrYAAADQb1JuCvi5557TRx99pOPHj+uuu+7SnDlzNGvWLFVUVGjDhg2hPwMjSZdddpm2bt2qRYsWadCgQSovL5ckZWdn60c/+pEefvhhSdLs2bPPuLEEAAAgXTksy7LsLiKVHDp0KKmvz7UQ9G9q/yb3LtE//Zvbv8m9S1wDCAAAgH5CAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAAHOJ/PrZUrs+Xzue0uBQAApAmX3QUgNp/Prblz8xUIOOR2Z6uqqkleb8DusgAAQIpjBHAAq6nJVCDgUDDoUCDgUE1Npt0lAQCANEAAHMBKS0/L7baUkWHJ7bZUWnra7pIAAEAaYAp4APN6A6qqalJNTaZKS08z/QsAAPoEAXCA83oDBD8AANCnmAIGAAAwDAEQAADAMARAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADEMABAAAMAwBMIX4fG6tXJktn89tdykAACCFuewuAInx+dyaOzdfgYBDbne2qqqa5PUG7C4LAACkIEYAU0RNTaYCAYeCQYcCAYdqajLtLgkAAKQoAmCKKC09LbfbUkaGJbfbUmnpabtLAgAAKYop4BTh9QZUVdWkmppMlZaeZvoXAACcNQJgCvF6AwQ/AABwzpgCBgAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAuuwvoSwsXLtTgwYPldDqVkZGhpUuXqrW1VRUVFTp27JiGDx+uxYsXKzs7W5ZlqbKyUtu2bVNmZqbKy8s1ZswYu1sAAABIurQKgJL0+OOPa9iwYaGf169fr0svvVSzZs3S+vXrtX79et18883atm2bjhw5ohUrVmjXrl1avXq1nn76aRsrBwAA6B9pPwVcW1ur6dOnS5KmT5+u2tpaSZLP59NVV10lh8OhkpISnThxQs3NzXaWCgAA0C/SbgRwyZIlkqRrr71WZWVlamlpUV5eniQpNzdXLS0tkiS/36+CgoLQ8/Lz8+X3+0OP7VJdXa3q6mpJ0tKlS7s9JxlcLlfS32Mgo39z+ze5d4n+6d/c/k3uXbKv/7QKgE8++aQ8Ho9aWlr01FNPqbi4uNvvHQ6HHA5Hr16zrKxMZWVloZ8bGxv7pNZYCgoKkv4eAxn9m9u/yb1L9E//5vZvcu9ScvuPzEHh0moK2OPxSJJycnI0ZcoU7d69Wzk5OaGp3ebm5tD1gR6Pp9sH3tTUFHo+AABAOkubAHjq1CmdPHky9O8dO3Zo9OjR8nq92rhxoyRp48aNmjJliiTJ6/Vq06ZNsixL9fX1ysrKOmP6FwAAIB2lzRRwS0uLnn32WUlSMBjUlVdeqUmTJmns2LGqqKjQhg0bQn8GRpIuu+wybd26VYsWLdKgQYNUXl5uZ/kAAAD9Jm0CYGFhoZYtW3bG8qFDh+qxxx47Y7nD4dDPfvaz/igNAABgQEmbKWAAAAAkhgAIAABgGAIgAACAYQiAAAAAhiEApiifz62VK7Pl87ntLgUAAKSYtLkL2CQ+n1tz5+YrEHDI7c5WVVWTvN6A3WUBAIAUwQhgCqqpyVQg4FAw6FAg4FBNTabdJQEAgBRCAExBpaWn5XZbysiw5HZbKi09bXdJAAAghTAFnIK83oCqqppUU5Op0tLTTP8CAIBeIQCmKK83QPADAABnhSlgAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwBMcT6fWytXZsvnc9tdCgAASBEuuwvA2fP53Jo7N1+BgENud7aqqprk9QbsLgsAAAxwjACmsJqaTAUCDgWDDgUCDtXUZNpdEgAASAEEwBRWWnpabreljAxLbrel0tLTdpcEAABSAFPAKczrDaiqqkk1NZkqLT3N9C8AAEgIATDFeb0Bgh8AAOgVpoABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQANOIz+fWypXZ8vncdpcCAAAGMP4nkDTh87k1d26+AgGH3O5sVVU18T+EAACAqBgBTBM1NZkKBBwKBh0KBByqqcm0uyQAADBAEQDTRGnpabndljIyLLndlkpLT9tdEgAAGKCYAk4TXm9AVVVNqqnJVGnpaaZ/AQBATIwAphGvN6Cf/7xVkrgZBAAAxMQIYJrhZhAAANATRgDTDDeDAACAnhAA0ww3gwAAgJ4wBZxmuBkEAAD0hACYhrzeAMEPAADExBQwAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgGnO53Pz38IBAIBu+DMwaYz/Fg4AAETDCGAa47+FAwAA0RAA0xj/LRwAAIiGKeA0xn8LBwAAomEEMM15vQH9/OetksTNIAAAQBIjgEbgZhAAABCOEUADcDMIAAAIRwA0ADeD8PcQAQAIxxSwASJvBpE6rwfMywuquTmj2w0iPp+7z28aOZvX7Ms6mAIH0F+SsQ8FkoEAaAivNyCvNxAKQ21tDnV0SE6nNGhQZyiS1C0o/epXLWcExJ5E7vzOJnyd7XNi7XTDp8C7fu6qza4dNQeJ5OBzTU+psl5T5WRzIH2ePp9bO3Y4NXGi2/ZaTEMANExXGOrocEiy1NHhUCAgvf56lvbty/i/YOiQZUm//GWuLEsJh8HwnV9GRrbmzv1akuKGr/BRSEnascOp+vohUZ8TS0873c4p8GxJCk2BRz7nbMLu2UqVg8RA0tMBy+dz6/XXs1RVlaVgMPFt1o5aE31+tBF6E/X0fenvMHM2J5sDyUDa/3SvJT+t9oUDKWTHQgA0TFcYsiz93whg57WBVVVZam//5zKnszMcRobBrmA3e/ZJSep2oDp40Bna+QWD0u9/f97/XXsoSZ3vc/CgU7///RA9/nhOt1FIlytbUufzMjKyQs/p6ZpFn8+t3/52aCi4Sp1htqYmGPriRZsCD39OZNjt2glF+wL3xXR2vBHJ3p4Jx6unv3ZAib5PvM8zLy+otrYze48X7Lq2u7y8oB5/PEenT3euSyn2Oj2XunsKZNFq7e0BLd4IfbLWYaLb+blsT+fy3Hjfl2SH/t7OaEQ72exLffGdDv88LatzX3jffceTehlQIrVI3ffdXb/v6+2tr/rr6T0GSsiOx2FZnbtMJObQoUNJff2CggI1NjYm9T0iD2gHDzr1hz+cp2DQIafT0rRppzVz5kk9/niOAgGHHI5/hkHJksPRuXOTHGGhUXK5OpcFAgodiDMyLP30p50jgV076sjXkzrfQ5Is65/PGTkyGPc6xa4Df/cg2fl6nUHSCoXV8OdGHmDDw260/rte55JLAmcsCw/C8Wrs3BFYUabaYy+LN9Ia+dqRvXbfAVlxQ+25bDvR+os2OhOt1q7Ps3vYsboFvMhg13ly0rnNRVt/XdtnRsY/l2VkWLr//uP6+c9b466XeHVH1hjt8XPn5nerNXw7Dj+gxdqmd+zIU339qdB3seu7Efk6fXmgjradSAobyT9z24+1PUXrT1JESIv93B078jRxYnPodaKHru41Rts2Ok9U438/Y30WPb1vTU2mli0bqmAw9n4q1ufQUw2R+/549UTbt8XrJXxZvG06fN273VaPgfpcg1ZkT+H77q5/97T/6s0+KdZ+8VzqjlZftGPqffcdlxR9O0jmcb+4uDjm7wiAvZQOATBSTxtztANxeGCLPFBJOmOHH77jjHYQDw9usULRr37Von/8Y1DUINn1JRs9ur3bAdThkDIz/9nTypXZ3eoID3uxQmG0UBEZhGPVHX2EZZcAABN9SURBVK3G8B1BvBAe7XHhO7dowTwzs/Nz+tOfhuj99zNDASjaeokcSUskpCQSnrtGE8K3q2i1Rn6ekQfxs3lOvMCS6HoJDyzRTlaiHfjD11+0baPrgBZ+wtQVdsO36WiPi3ZSk0ggixYU4213XUFZUug7EitQR25P8eru6YQw1oE/XogL/x739vsZ7XOK3Acm8h2KtU6jhejwGmJ977oCcKywJynqvi08pEVuv/H2pZH9Ra77ngJ1b4JWT/uatrah3U5+wo8viZyUJ7JPkjpHOyN77vqPEs4cUY4egLtmnXq7bUQe48Jf+/rrcwiAqSAdA6DU+2us4u38Et3B9rQTjAxrTqcUDCrqGX+8kYHIEaBYYTf8Sx3v/cKXRY5cxtqJhofdeAeJaDuM8GWRO7dYNUYL1+EH4niPixZSooWcWK/T9ZzwA0yitUbrL1qwizVqGG9kIDJk9+XnFC2kSYp6QIv87MI/k0TDZU+BLNoJUyIHpURH1yI/p2j9RS4LD2SxnhvtOeEncImMKMc6UY0WJKKFoZ5OUGMFsvB9Tfg+ILKGRE5+w0+Y4312Pa2Xrm1j376MM4JPaenphE+wowXqWCdRsfbd8Xp+552gvvzyy7j7w0ROys923xZvtqGn/U+8E53wzz3adtB17HrnnaDGjTumZCAA9qF0DYCJ6mnKp7fXgEUK77+nEaTIs9/wA3+saad4dUQLqeE7xHgH1XijM4mcbXftMA4fHqwNG5xn7DCijXady6hotB1nT+8XbxSrpwNotNGuyBOBtrahGjTo+BmfXU/B7mymmKKtl1jhI/JkJVoQjjZNG+29ezqghYedyB56E8h6OlmJN5oZayQp1olAT5eExAtNsUZKIw+msQJLT9/9nj73RE5CIr9DkfX0NJUavt31dPlLZEiNdkmBFP1ymniBu6cT9bMN1Il8zxO55OeJJ4K6/faGM44viZ6U93QC2tOJQCKzDZHLEpl1SmQ7CO8/GQiAfcj0AJhssa6DiXe9Wyx99fcHE5lW62nqoKdrrbqW5ebm6nvfy4gZGhIZ7Yo39ZnImWysg2W8azNjhfXIkYF466Vr3fflRejhIxGJhrRY14+GbyOxDvzxrieSYk/nZ2RYmjfP0g9+4E/wBpP4gSzedGhPU5aJTClHuxYtsr9o177Fe274NYDRTuAir78Ln76L9nn1FCQiLzOINUKYyOfT099UDf9sEvnexTph6im4xQvc0b6Lsb4n4TMm0QJ1rJOo3o6ahY8ARhsBS/SkPHI2Kd53O95lSdHqjnXiFW//GnndeaztoKsvRgBTBAEwueL1P5Bvq4+1Aw2XSLgsKCjQ//t/LWc9ypro+4Qvi3cNYE83S0R73948J1wytv3eXvQt9e6GgXP9Uy3h753IdUCJBrKebliKrDuR7benOs6m53gXwidyU0ZvTuxiXYJyNtdS9sXdo5Hfu5UrPaHR/2g3LiVyI4bU8w00sV4j3uMSfY/Ika1oN19FOzmIt+2fy7rozWeT6GxSvBPwsx1s4BrAFEEATK5U7f9cDk7hBmL/fTWS2pNk9T6QTxzCnUv/5xpY+mr7PReJ9J+M4DlQto/du4eHRv/7ch2cTVg62892IJ38JaI/PptEcBdwiiAAJlcq998XO4lU7v9cmdy7ZH//dgchu/u3W+To/0A+WYlnIJ38pQq7AqDRfwi6rq5OlZWV6ujo0IwZMzRr1iy7S0IK83oDKbvTBth+7ZcO6yAdejCF0+4C7NLR0aGXX35ZjzzyiCoqKvTBBx/owIEDdpcFAACQdMYGwN27d6uoqEiFhYVyuVyaOnWqamtr7S4LAAAg6YydAvb7/crPzw/9nJ+fr127dp3xuOrqalVXV0uSli5dqoKCgqTW5XK5kv4eAxn9m9u/yb1L9E//5vZvcu+Sff0bGwATVVZWprKystDPyb5QlYth6d/U/k3uXaJ/+je3f5N7l+y7CcTYKWCPx6OmpqbQz01NTfJ4PDZWBAAA0D+MDYBjx47V4cOH1dDQoPb2dm3evFler9fusgAAAJLO2CngjIwM3X777VqyZIk6Ojp0zTXX6IILLrC7LAAAgKQzNgBK0uTJkzV58mS7ywAAAOhXxk4BAwAAmIoACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGcViWZdldBAAAAPoPI4ADzEMPPWR3Cbaif3P7N7l3if7p39z+Te5dsq9/AiAAAIBhCIAAAACGyXjiiSeesLsIdDdmzBi7S7AV/Zvbv8m9S/RP/+b2b3Lvkj39cxMIAACAYZgCBgAAMIzL7gLwT3V1daqsrFRHR4dmzJihWbNm2V1S0jQ2NmrVqlX68ssv5XA4VFZWppkzZ2rt2rX6y1/+omHDhkmSbrrpJk2ePNnmapNj4cKFGjx4sJxOpzIyMrR06VK1traqoqJCx44d0/Dhw7V48WJlZ2fbXWqfO3TokCoqKkI/NzQ0aM6cOTpx4kTarv8XXnhBW7duVU5OjpYvXy5JMde3ZVmqrKzUtm3blJmZqfLy8pSfIovW/2uvvaYtW7bI5XKpsLBQ5eXlOu+889TQ0KDFixeruLhYkjR+/HgtWLDAzvLPSbTe4+3r1q1bpw0bNsjpdOq2227TpEmTbKu9L0Trv6KiQocOHZIkff3118rKytKyZcvSbt3HOtYNiO++hQEhGAxad999t3XkyBErEAhYv/jFL6z9+/fbXVbS+P1+a8+ePZZlWdbXX39tLVq0yNq/f79VVVVlvfnmmzZX1z/Ky8utlpaWbstee+01a926dZZlWda6deus1157zY7S+lUwGLR+9rOfWQ0NDWm9/nfu3Gnt2bPHuu+++0LLYq3vLVu2WEuWLLE6OjqsTz/91Hr44YdtqbkvReu/rq7Oam9vtyyr87Po6v/o0aPdHpfqovUea1vfv3+/9Ytf/MJqa2uzjh49at19991WMBjsz3L7XLT+w61Zs8b6n//5H8uy0m/dxzrWDYTvPlPAA8Tu3btVVFSkwsJCuVwuTZ06VbW1tXaXlTR5eXmhs5ohQ4Zo5MiR8vv9Nldlv9raWk2fPl2SNH369LTeBrr8/e9/V1FRkYYPH253KUk1YcKEM0ZzY61vn8+nq666Sg6HQyUlJTpx4oSam5v7vea+FK3/b33rW8rIyJAklZSUpO0+IFrvsdTW1mrq1Klyu90aMWKEioqKtHv37iRXmFzx+rcsSzU1NfrOd77Tz1X1j1jHuoHw3WcKeIDw+/3Kz88P/Zyfn69du3bZWFH/aWho0Oeff65x48bpk08+0TvvvKNNmzZpzJgxuvXWW9NyCrTLkiVLJEnXXnutysrK1NLSory8PElSbm6uWlpa7CyvX3zwwQfddv4mrf9Y69vv96ugoCD0uPz8fPn9/tBj09GGDRs0derU0M8NDQ164IEHNGTIEP3kJz/RxRdfbGN1yRFtW/f7/Ro/fnzoMR6PJ22DsSR9/PHHysnJ0fnnnx9alq7rPvxYNxC++wRA2OrUqVNavny55s+fr6ysLF133XWaPXu2JKmqqkqvvvqqysvLba4yOZ588kl5PB61tLToqaeeCl3z0sXhcMjhcNhUXf9ob2/Xli1b9NOf/lSSjFr/kUxY37G88cYbysjI0LRp0yR1jpq88MILGjp0qD777DMtW7ZMy5cvV1ZWls2V9h2Tt/VwkSeA6bruI4914ez67jMFPEB4PB41NTWFfm5qapLH47GxouRrb2/X8uXLNW3aNF1xxRWSOs+EnE6nnE6nZsyYoT179thcZfJ0rd+cnBxNmTJFu3fvVk5OTmi4v7m5OXSBeLratm2bLrroIuXm5koya/1Lirm+PR6PGhsbQ49L5/3Be++9py1btmjRokWhg6Db7dbQoUMldf59tMLCQh0+fNjOMvtcrG098ljg9/vTdt0Hg0F9+OGH3UZ+03HdRzvWDYTvPgFwgBg7dqwOHz6shoYGtbe3a/PmzfJ6vXaXlTSWZenFF1/UyJEj9YMf/CC0PPxahw8//FAXXHCBHeUl3alTp3Ty5MnQv3fs2KHRo0fL6/Vq48aNkqSNGzdqypQpdpaZdJFn/6as/y6x1rfX69WmTZtkWZbq6+uVlZWVltO/dXV1evPNN/Xggw8qMzMztPyrr75SR0eHJOno0aM6fPiwCgsL7SozKWJt616vV5s3b1YgEFBDQ4MOHz6scePG2VVmUv39739XcXFxt8uf0m3dxzrWDYTvPn8IegDZunWr1qxZo46ODl1zzTW68cYb7S4paT755BM99thjGj16dOis/6abbtIHH3ygvXv3yuFwaPjw4VqwYEFaHviOHj2qZ599VlLnWfCVV16pG2+8UcePH1dFRYUaGxvT+s/ASJ3Bt7y8XL/73e9CUyIrV65M2/X/3HPP6aOPPtLx48eVk5OjOXPmaMqUKVHXt2VZevnll7V9+3YNGjRI5eXlGjt2rN0tnJNo/a9bt07t7e2hbbzrT3787W9/09q1a5WRkSGn06kf//jHKX1CHK33nTt3xtzW33jjDb377rtyOp2aP3++LrvsMps7ODfR+v/ud7+rVatWafz48bruuutCj023dR/rWDd+/Hjbv/sEQAAAAMMwBQwAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAIy2f/9+PfDAA5o3b57q6+vtLkdS5/+Pes899yT1Perr6zVv3jzdf//92rdvX1LfC8DAQwAEYLR3331XI0aMUGVlpUpKStTQ0KA5c+YoGAxKklatWqU//vGPSa1hzpw5OnLkSOjniy++WM8//3xS37OkpESVlZU6//zztWHDhqS+F4CBhwAIwGitra0aNWqUnM7k7A67guRA5HQ6NWrUKB0/ftzuUgD0M5fdBQCAnYLBYOi/aIpUXV2tv/71r5Kkt99+W9/85jf10EMPye/365VXXtHHH3+swYMH64YbbtDMmTMlSWvXrtX+/fvldru1ZcsW3XrrrbrwwgtVWVmpgwcPatCgQbriiis0b948uVwuPf7445Kk+++/X5L0n//5n8rJydHKlSv14osvSpIOHDig1atXa+/evfJ4PPrpT38a+u+xVq1apczMTB07dkwff/yxRo0apUWLFqmoqEiWZWnNmjX661//qkAgoIKCAt1zzz0aPXp0qEen0zmgQyqA5CAAAjBWa2urPvvsM02YMCHq78vKyvTpp58qPz9fP/nJTyRJHR0deuaZZzRlyhTde++9ampq0pNPPqni4mJNmjRJkuTz+bR48WLdfffdam9v14EDBzRv3jyNHTtWTU1N+vWvf6133nlHN9xwg371q19pzpw5WrZsmYqKiiRJO3fuDNXQ3t6uZ555Rtdcc40effRRffLJJ/rNb36jpUuXqri4WJK0efNmPfLII7roootCU9b33nuvtm/fro8//ljPP/+8srKydPDgQZ133nndeszPz9f777+v48ePa+jQoX3+GQMYmJgCBmCkP//5z7r99tuVlZWl6dOnJ/y8PXv26KuvvtLs2bPlcrlUWFioGTNmaPPmzaHHlJSU6PLLL5fT6dSgQYM0ZswYlZSUKCMjQyNGjFBZWZk++uijhN5v165dOnXqlGbNmiWXy6VLLrlEkydPDo1MStLll1+ucePGKSMjQ1deeaX27t0rSXK5XDp16pQOHjwoy7I0atQo5eXldXv9adOmaejQobrjjjv09ttvJ/w5AEhtjAACMNL3v/99lZaW6pe//KV8Pp++/e1vJ/S8Y8eOqbm5WfPnzw8t6+jo0MUXXxz6OT8/v9tzDh06pFdffVV79uxRW1ubgsGgxowZk9D7NTc3q6CgoNs1isOHD5ff7w/9nJubG/p3ZmamTp06JUm65JJL9L3vfU8vv/yyGhsbdfnll+uWW25RVlZW6PFbtmxRU1OTXnrppTPCIYD0RQAEYKzc3FyNHz9eBw4ciPmYyOsDCwoKNGLECK1YsSLh91m9erW+8Y1v6J577tGQIUP09ttv629/+1tCz83Ly1NjY6M6OjpCIbCxsVHnn39+Qs+fOXOmZs6cqZaWFlVUVOitt94KTWdL0sGDBzV+/HjCH2AYpoABGM3tdqu9vT3m73NycnT06NHQz+PGjdOQIUO0fv16tbW1qaOjQ/v27dPu3btjvsbJkyeVlZWlwYMH6+DBg/rf//3fuO8Rbvz48crMzNRbb72l9vZ27dy5U1u2bNF3vvOdHnvbvXu3du3apfb2dmVmZsrtdp9xt3N7e7tcLsYCANPwrQdgNIfDoY6Ojpi//+53v6vf/va3mj9/viZMmKAHHnhADz74oF599VUtXLhQ7e3tKi4u1ty5c2O+xi233KL/+q//0ptvvqmLLrpIU6dO1T/+8Y/Q73/84x9r1apVamtr04IFC5STkxP6ncvl0oMPPqjVq1dr3bp18ng8uvvuuzVy5Mgeezt58qTWrFmjo0ePatCgQfrWt76lH/7wh90eEz6yCMAcDsuyLLuLAAC7/OEPf9DevXv1wAMPGDcSFgwG9eyzz2rkyJG6+eab7S4HQD/itA+A0WbMmKG2tjbdeeedA+a/gusP9fX1WrBggb7++muVlZXZXQ6AfsYIIAAAgGEYAQQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMP8fBtpsECOhFRQAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x6pQsDGvY9cv"
      },
      "source": [
        "# Mini Batch Gradient Descent"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XQd6KV8oY9cw"
      },
      "source": [
        "def minibatch_gradient_descent(X,y,theta,learning_rate=0.01,iterations=10,batch_size =20):\n",
        "    '''\n",
        "    X    = Matrix of X without added bias units\n",
        "    y    = Vector of Y\n",
        "    theta=Vector of thetas np.random.randn(j,1)\n",
        "    learning_rate \n",
        "    iterations = no of iterations\n",
        "    \n",
        "    Returns the final theta vector and array of cost history over no of iterations\n",
        "    '''\n",
        "    m = len(y)\n",
        "    cost_history = np.zeros(iterations)\n",
        "    n_batches = int(m/batch_size)\n",
        "    \n",
        "    for it in range(iterations):\n",
        "        cost =0.0\n",
        "        indices = np.random.permutation(m)\n",
        "        X = X[indices]\n",
        "        y = y[indices]\n",
        "        for i in range(0,m,batch_size):\n",
        "            X_i = X[i:i+batch_size]\n",
        "            y_i = y[i:i+batch_size]\n",
        "            \n",
        "            X_i = np.c_[np.ones(len(X_i)),X_i]\n",
        "           \n",
        "            prediction = np.dot(X_i,theta)\n",
        "\n",
        "            theta = theta -(1/m)*learning_rate*( X_i.T.dot((prediction - y_i)))\n",
        "            cost += cal_cost(theta,X_i,y_i)\n",
        "        cost_history[it]  = cost\n",
        "        \n",
        "    return theta, cost_history"
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "erQifW90Y9cy",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f15d9660-1d98-4450-b2e4-738c06744259"
      },
      "source": [
        "lr =0.1\n",
        "n_iter = 200\n",
        "\n",
        "theta = np.random.randn(2,1)\n",
        "\n",
        "\n",
        "theta,cost_history = minibatch_gradient_descent(X,y,theta,lr,n_iter)\n",
        "\n",
        "\n",
        "print('Theta0:          {:0.3f},\\nTheta1:          {:0.3f}'.format(theta[0][0],theta[1][0]))\n",
        "print('Final cost/MSE:  {:0.3f}'.format(cost_history[-1]))"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Theta0:          3.835,\n",
            "Theta1:          3.077\n",
            "Final cost/MSE:  999.096\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dfhKOX-8Y9c1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 500
        },
        "outputId": "c8a1836f-ac09-4d3d-e967-66f80394c284"
      },
      "source": [
        "fig,ax = plt.subplots(figsize=(10,8))\n",
        "\n",
        "ax.set_ylabel('{J(Theta)}',rotation=0)\n",
        "ax.set_xlabel('{Iterations}')\n",
        "theta = np.random.randn(2,1)\n",
        "\n",
        "_=ax.plot(range(n_iter),cost_history,'b.')"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}