Lecture_4_~_Stochastic_Gradient_Descent.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyNTSNkHGMZhMBEYvaxzz0fD",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/LunaEyad/Deep-Learning-Foundations/blob/main/Lecture_4_~_Stochastic_Gradient_Descent.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Lecture 4 ~ Stochastic Gradient Descent"
      ],
      "metadata": {
        "id": "r3DY_GarIwsy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "\n",
        "from random import Random\n",
        "from math import sqrt, ceil\n",
        "SEED =8\n",
        "def generate_points(n = 1000):\n",
        "\n",
        "    random_gen = Random(x = SEED)\n",
        "\n",
        "    lst_x , lst_y =[],[]\n",
        "    for _ in range(n):\n",
        "        lst_x.append(random_gen.uniform(a = 0, b = 1))\n",
        "   \n",
        "    for _ in range(n):\n",
        "        lst_y.append(random_gen.uniform(a = 0, b = 1))\n",
        "\n",
        "    return lst_x, lst_y\n",
        "\n",
        "\n",
        "data_x , data_y = generate_points()\n",
        "\n",
        "def calc_grad(x_p,y_p, batch_x, batch_y):\n",
        "  sum_x, sum_y= 0, 0\n",
        "  for x_i ,y_i in zip( batch_x, batch_y):\n",
        "    inv_sqr= ((x_i - x_p)**2 + (y_i - y_p)**2 )**(-0.5)\n",
        "    sum_x+= inv_sqr * (x_i - x_p)\n",
        "    sum_y+= inv_sqr * (y_i - y_p)\n",
        "  return( -sum_x / len(batch_x), -sum_y / len(batch_y) )\n",
        "\n",
        "def loss (x_p , y_p, batch_x, batch_y ):\n",
        "  \n",
        "  return(\n",
        "      (1/len(batch_x)) * sum([\n",
        "          sqrt((x_i-x_p)**2+(y_i-y_p)**2)\n",
        "          for x_i,y_i in zip(data_x,data_y)\n",
        "      ])\n",
        "  ) \n",
        "  \n",
        "losses_sgd , losses_gd =[],[] \n",
        "x_p_sgd=0.3\n",
        "y_p_sgd=0.3\n",
        "x_p=0.3\n",
        "y_p=0.3\n",
        "sampler=Random(x=SEED)\n",
        "EPOCHS=100\n",
        "BATCH_SZ=4\n",
        "N=len(data_x)\n",
        "NUM_BATCH=ceil(N/BATCH_SZ)\n",
        "DELTA=1e-2\n",
        "indices=[i for i in range(len(data_x))]\n",
        "\n",
        "for _ in range (EPOCHS):\n",
        "  sampler.shuffle(indices)\n",
        "  #SGD\n",
        "  for batch_ind in range(NUM_BATCH):\n",
        "    batch_indices=indices[batch_ind*BATCH_SZ: (batch_ind+1)*BATCH_SZ]\n",
        "    batch_x=[data_x[i] for i in batch_indices]\n",
        "    batch_y=[data_y[i] for i in batch_indices]\n",
        "    grad_x_sgd,grad_y_sgd= calc_grad(x_p_sgd,y_p_sgd,batch_x,batch_y)\n",
        "    x_p_sgd-=grad_x_sgd* DELTA\n",
        "    y_p_sgd-=grad_y_sgd* DELTA\n",
        "    losses_sgd.append(loss(x_p_sgd,y_p_sgd,data_x,data_y))\n",
        "\n",
        "  #GD\n",
        "  grad_x, grad_y= calc_grad(x_p,y_p,data_x,data_y)\n",
        "  x_p-=grad_x* DELTA\n",
        "  y_p-=grad_y* DELTA\n",
        "  losses_gd.append(loss(x_p,y_p,data_x,data_y))\n"
      ],
      "metadata": {
        "id": "DaL3A0QZI5M1"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from matplotlib.pyplot import figure\n",
        "fig=figure(figsize=[10,10])\n",
        "ax=fig.add_subplot(1,1,1)\n",
        "ax.plot(losses_sgd ,\"r\")\n",
        "ax.plot([i*NUM_BATCH for i in range(len(losses_gd)) ], losses_gd, \"b\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 609
        },
        "id": "UaNm6GsoMZjZ",
        "outputId": "e782e2d1-8934-46a2-92bd-3df0e7d24b7a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fe9887d2cd0>]"
            ]
          },
          "metadata": {},
          "execution_count": 13
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ],
            "image/png": 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/f3j/fbj//qwrkSRJbZHPkFVDtt46TengnFmSJNWW/IasGuguhHTQ6L32gn/+Ez75JOtqJElSa+UzZNVQdyGkLsMZM9LkpJIkqTbkM2TVmMGDYY010pxZNdIAJ0lS7uU3ZNVYWjngAHjjDXjyyawrkSRJrZHPkFVj3YUAO+8M888Pf/5z1pVIkqTWyGfIqkHzzAN77AG33Qaffpp1NZIkqSX5DVk11l0IcPDBMG2aA+AlSaoF+QxZNdhdCPCjH8Hqq6cuwxrMiJIk5Uo+Q1YNO+igNAD+8cezrkSSJDUnvyGrRpuCdt4ZFljAAfCSJFW7fIasGu0uBJh7bthzT7j9dpg8OetqJElSU/IZsmrcQQfB9Olw/fVZVyJJkpqS35BVo92FACuumGaAv+KKmn4akiR1afkMWTXcXVhw8MEwdiw8+mjWlUiSpFLyGbK6gJ12ggUXdAC8JEnVqlUhK4SwaQhhbAhhXAjhhGa22z6EEEMIQ+subxRCGB1CeKXudP1yFd5hNd7PNtdcsNde8Pe/w6RJWVcjSZIaazFkhRC6A5cCmwGDgV1DCINLbDcfcBTwbNHqycBWMcYVgb2B6pirvAt0F0LqMvzuO7j66qwrkSRJjbWmJWtVYFyMcXyMcTpwMzCsxHZnAucBUwsrYowvxBg/qLs4BpgrhNCrgzWrzuDBsO668Kc/wcyZWVcjSZKKtSZk9QXeK7r8ft26/wkhrAL0jzHe3cz9bA/8O8Y4rc1VVkKNdxcWHHYYTJgA992XdSWSJKlYhwe+hxC6ARcCxzSzzfKkVq6Dm7j+oBDCqBDCqEmdMcCoi3QXAmyzDSy+OFx6adaVSJKkYq0JWROB/kWX+9WtK5gPWAF4JIQwAVgdGF40+L0fcAewV4zx7VIPEGO8IsY4NMY4tE+fPm1/Fu3RRVqy5pgjTU56333wdslXV5IkZaE1Iet5YFAIYWAIoSewCzC8cGWM8csYY+8Y44AY4wDgGWDrGOOoEMKCwN3ACTHGJ8tffjt1oZYsgAMPhG7dnM5BkqRq0mLIijHOAI4ARgCvA7fGGMeEEM4IIWzdws2PAJYGTg0hvFi3LNLhqtVA376p2/Cqq+Dbb7OuRpIkAfRozUYxxnuAexqtO7WJbdctOn8WcFYH6qucLtJdWHDYYWnOrNtuS/NnSZKkbOVzxvcu1l0IsN56sOyyDoCXJKla5DNkQZdryQohtWY99xyMGpV1NZIkKZ8hqwu2ZEHqJpx7brj88qwrkSRJ+QxZ0OVasgAWWAD22ANuugk++yzraiRJyrd8hqwu2pIFqctw6lSPZyhJUtbyGbK6sJVWgrXXTgPgPZ6hJEnZyW/I6oLdhQVHHpmOZ3jXXVlXIklSfuUzZHXh7kKAYcOgf3/4wx+yrkSSpPzKZ8iCLt2S1aNHGpv10EMwZkzW1UiSlE/5DFldvCUL4IADYM454Y9/zLoSSZLyKZ8hKwd694bddoMbboDPP8+6GkmS8ie/IasLdxcW/N//wTffOJ2DJElZyGfIykF3IcDKK6fpHC65xOkcJEnqbPkMWZCLlixIrVlO5yBJUufLZ8jKSUsWwDbbQL9+DoCXJKmz5TNk5UiPHnD44fDgg07nIElSZ8pvyMpJdyHUT+dw8cVZVyJJUn7kM2TlqLsQ0nQOe+2VpnOYNCnraiRJyod8hizIVUsWwM9/DtOmwZ/+lHUlkiTlQz5DVs5asgCWWw422wwuvTSFLUmSVFn5DFmQu5YsgKOPho8/hr/9LetKJEnq+vIZsnLYkgWwwQaw4opw4YW5zJiSJHWqfIasnAohjc165RV46KGsq5EkqWvLb8jKaVPObrvBIovARRdlXYkkSV1bPkNWTrsLIc2XddhhcPfd8MYbWVcjSVLXlc+QBbltyQI49FDo1Qt+//usK5EkqevKZ8jKcUsWpO7CPfaA666DTz/NuhpJkrqmfIYs8YtfwLffwuWXZ12JJEldU35DVo67CwGWXz5NTvrHP8LUqVlXI0lS15PPkJXz7sKCX/4SPvkErr8+60okSep68hmyIPctWQDrrgtDhsAFF8DMmVlXI0lS15LPkGVLFpBehuOOg7feguHDs65GkqSuJZ8hC2zJqrPddjBwIPz2t74kkiSVUz5Dli1Z/9OjRzpw9DPPwJNPZl2NJEldRz5DlhrYd1/43vfg/POzrkSSpK4jvyHLvrH/mWceOPzwNC7LQ+1IklQe+QxZdhfO5ogj0nENL7gg60okSeoa8hmywJasRvr0Sd2GN9wAH36YdTWSJNW+fIYsW7JKOvpomDHDA0dLklQO+QxZKmnppWGHHeCyy+CLL7KuRpKk2pbfkGV3YUm/+hV89RVcemnWlUiSVNvyGbLsLmzSyivD5pvDxRfDN99kXY0kSbUrnyELbMlqxoknwuTJcOWVWVciSVLtymfIsiWrWT/7Gay9dpqcdPr0rKuRJKk25TNkqUUnngjvvw833ph1JZIk1ab8hiy7C5u18cawyipw7rkwc2bW1UiSVHvyGbLsLmxRCGlPw7fegn/8I+tqJEmqPfkMWWBLVitsuy388Idwzjm+XJIktVU+Q5YtWa3SvTuccAK8+CLce2/W1UiSVFvyGbLApplW2n13WGIJOOssXzJJktoinyHLlqxWm2OONDbr6afhwQezrkaSpNqRz5ClNtl3X+jbF04/3dYsSZJaK78hy7TQar16pbFZTzwBjz6adTWSJNWGfIYsuwvb7IADYPHFU2uWJElqWT5DFtiS1UZzzgnHHw+PPAKPPZZ1NZIkVb98hixbstrlwANh0UXhzDOzrkSSpOqXz5Cldpl7bvjlL2HkSHjqqayrkSSpuuU3ZNld2C6HHAK9e8MZZ2RdiSRJ1S2fIcvuwnabZx449lgYMQKefTbraiRJql75DFlgS1YHHHYYfO97cNppWVciSVL1ymfIsiWrQ+abL7Vm3XdfmglekiTNLp8hSx12xBHQpw+cemrWlUiSVJ3yG7LsLuyQeedNs8CPHOm8WZIklZLPkGV3YVkccggsthiccoqZVZKkxvIZssBUUAZzzw0nnphash56KOtqJEmqLvkMWbZklc2BB0K/fmlslrlVkqR6+QxZYCIokznnhJNOSjPAjxiRdTWSJFWPfIYsW7LKar/94Ac/sDVLkqRi+QxZKquePdPg9+efh7vuyroaSZKqQ35Dlk0uZbXXXrDUUilszZqVdTWSJGUvnyHL7sKym2MOOP10eOkluOWWrKuRJCl7+QxZYEtWBey6K6y4YmrN+u67rKuRJClbrQpZIYRNQwhjQwjjQggnNLPd9iGEGEIYWnf5eyGEh0MIU0IIl5Sr6A6zJasiunWDs8+Gt9+Gq6/OuhpJkrLVYsgKIXQHLgU2AwYDu4YQBpfYbj7gKODZotVTgVOAY8tSrarellvCGmvAGWfAt99mXY0kSdlpTUvWqsC4GOP4GON04GZgWIntzgTOIwUrAGKMX8cYnyheVzXsLqyIEOA3v4EPPoBLqqftUpKkTteakNUXeK/o8vt16/4nhLAK0D/GeHcZa6scuwsrap11YJNN4Nxz4csvs65GkqRsdHjgewihG3AhcEwH7uOgEMKoEMKoSZMmdbSk1rElq6LOOQc++wwuuCDrSiRJykZrQtZEoH/R5X516wrmA1YAHgkhTABWB4YXBr+3Rozxihjj0Bjj0D59+rT2Zu1nS1bFrbIK7LgjXHQRfPxx1tVIktT5WhOyngcGhRAGhhB6ArsAwwtXxhi/jDH2jjEOiDEOAJ4Bto4xjqpIxeViS1bFnXkmTJ2aWrUkScqbFkNWjHEGcAQwAngduDXGOCaEcEYIYeuWbl/XunUhsE8I4f1SeyZ2OluyOsUPfwj77guXXw7jx2ddjSRJnSvEKmvRGTp0aBw1qsKNYBtsANOnw+OPV/ZxxAcfwNJLw7Bh8Le/ZV2NJEnlFUIYHWMsOUTKGd9VUd//Phx9NNx8M1Q6O0uSVE3yGbLsLuxUxx0HvXunU7OtJCkv8hmywL/2nWj++eHUU+Hhh+G++7KuRpKkzpHPkGVLVqc7+GBYaqnUmjVzZtbVSJJUefkMWep0PXumqRxefRWuvz7raiRJqrz8hiy7CzvdjjvCT34Cp5ziwaMlSV1fPkOW3YWZCAHOPx8mToTf/z7raiRJqqx8hiywJSsj66wDW24Jv/kNfPJJ1tVIklQ5+QxZtmRl6re/ha+/htNOy7oSSZIqJ58hS5labjk49FD4859hzJisq5EkqTLyG7LsLszUr38N880Hxx6bdSWSJFVGPkOW3YWZ6907TVB6331OUCpJ6pryGbLAlqwqcPjhaYLSY4+FGTOyrkaSpPLKZ8iyJasq9OqVBsGPGQNXXpl1NZIklVc+QxbYklUltt0W1l47dR1++WXW1UiSVD75DFm2ZFWNEODCC2Hy5HTYHUmSuop8hixVlSFDYK+94OKLYdy4rKuRJKk88huy7C6sKr/5TTqI9DHHZF2JJEnlkc+QZXdh1Vl88XTg6OHDYcSIrKuRJKnj8hmywJasKnTUUbD00ul0+vSsq5EkqWPyGbJsyapKvXqlcVljx8Ill2RdjSRJHZPPkKWqtcUWsNlmcPrp8PHHWVcjSVL75Tdk2V1YtS66CL79Fk48MetKJElqv3yGLLsLq9oPf5jGZV1zDTz/fNbVSJLUPvkMWWBLVpU75RRYZBE48kiYNSvraiRJart8hixbsqre/PPDeefBM8/AtddmXY0kSW2Xz5ClmrDXXrDmmnD88fDZZ1lXI0lS2+Q3ZNldWPVCgMsug88/dxC8JKn25DNk2V1YM1ZcMY3LuuIKB8FLkmpLPkMW2JJVQ047DRZbDA49FGbOzLoaSZJaJ58hy5asmjL//HDhhTB6dGrRkiSpFuQzZIEtWTVm551h/fXT2KxPPsm6GkmSWpbPkGVLVs0JAS69FL7+Ou1tKElStctnyFJNWnZZOOaYNG/Wo49mXY0kSc3Lb8iyu7AmnXIKDBwIBx8M06ZlXY0kSU3LZ8iyu7BmzT03XH45jB0L556bdTWSJDUtnyELbMmqYZtsArvuCuecA2+8kXU1kiSVls+QZUtWzbvootSqdcgh5mVJUnXKZ8hSzVt0UTj//DQA3gNIS5KqUX5Dls0fNW+//dIBpI89FiZNyroaSZIaymfIsruwS+jWLc0A/9VXcPTRWVcjSVJD+QxZYEtWF7HccnDCCXDjjXDffVlXI0lSvXyGLFuyupSTTkph6+CDU6uWJEnVIJ8hC2zJ6kJ69YKrroL33kutWpIkVYN8hixbsrqcNdaAo46Cyy6Dxx7LuhpJkvIastQlnXUWLLkkHHAAfPtt1tVIkvIuvyHL7sIuZ5554C9/gbfegl//OutqJEl5l8+QZXdhl7X++nDggfC738Hzz2ddjSQpz/IZssCWrC7s/PNh8cXTZKXTp2ddjSQpr/IZsmzJ6tIWWAD+9Cd49VU488ysq5Ek5VU+Q5a6vC23hL33ht/8xm5DSVI28huy7C7s8i6+OHUb7r03TJ2adTWSpLzJZ8iyuzAXFlwwTVL6+utwyilZVyNJypt8hiywJSsnNt4YDjkk7W34xBNZVyNJypN8hixbsnLl/PNhwADYZx/4+uusq5Ek5UU+Q5ZyZd554ZprYPx4OP74rKuRJOVFfkOW3YW5ss466diGl14KDzyQdTWSpDzIZ8iyuzCXzjkHllsudRt+9lnW1UiSurp8hiywJSuH5poLbrwRJk2Cgw/2IyBJqqx8hixbsnJrlVXSLPC33w433JB1NZKkriyfIQtsxsixY4+FtdaCI46ACROyrkaS1FXlM2R16wazZmVdhTLSvTtcf31q0NxzT5g5M+uKJEldUT5DVo8e/mXNuQED0p6GTzwBv/1t1tVIkrqifIas7t1hxoysq1DGdt8ddt4ZTj0VRo3KuhpJUleTz5Bld6FI3YWXXw6LLQa77gpffZV1RZKkriSfISsEB74LgIUWgptuSrPBH3FE1tVIkroSQ5Zyb621Upfh9denebQkSSqH/IYsqchJJ6WwdeihMG5c1tVIkrqCfIYssCVLDfTokVqx5pgjjc+aPj3riiRJtS6fIcvuQpWwxBJw5ZVpT8OTTsq6GklSrTNkSUW22w4OOQQuuADuuy/raiRJtSy/IUtqwoUXwgorpNng338/62okSbWqVSErhLBpCGFsCGFcCOGEZrbbPoQQQwhDi9b9qu52Y0MIm5Sj6LKwJUtNmGsuuO02+PbbND7LeWslSe3RYsgKIXQHLgU2AwYDu4YQBpfYbj7gKODZonWDgV2A5YFNgcvq7i9bdheqBcsuC3/+czrszimnZF2NJKkWtaYla1VgXIxxfIxxOnAzMKzEdmcC5wFTi9YNA26OMU6LMb4DjKu7v2wZstQKu+8OBx4I554L99yTdTWSpFrTmpDVF3iv6PL7dev+J4SwCtA/xnh3W2+bCcdkqZV+/3tYaSXYay94772Wt5ckqaDDA99DCN2AC4FjOnAfB4UQRoUQRk2aNKmjJbWOLVlqhbnmgltvhWnTYJdd4Lvvsq5IklQrWhOyJgL9iy73q1tXMB+wAvBICGECsDowvG7we0u3BSDGeEWMcWiMcWifPn3a9gzaw+5CtcEyy6T5s556Cn71q6yrkSTVitaErOeBQSGEgSGEnqSB7MMLV8YYv4wx9o4xDogxDgCeAbaOMY6q226XEEKvEMJAYBDwXNmfRVsZstRGO+8Mhx8Ov/sd3H571tVIkmpBiyErxjgDOAIYAbwO3BpjHBNCOCOEsHULtx0D3Aq8BtwHHB5jnNnxsjvIkKV2uPBCWH112HdfeP31rKuRJFW7Hq3ZKMZ4D3BPo3WnNrHtuo0unw2c3c76pKrRs2eaP2vIkDQz/HPPwXzzZV2VJKla5XfGd1uy1A79+sHNN8Obb8L++/sxkiQ1zZAltdF666W5s267DS66KOtqJEnVypAltcOxx6Yuw+OOg0cfzboaSVI1ym/IkjogBLjmGlh6adhxR3j33awrkiRVm3yGLLAlSx02//zwz3+miUq33Ra++SbriiRJ1SSfIcvuQpXJD38IN90EL7yQjnPox0qSVGDIkjpoiy3gzDNT2Prd77KuRpJULfIbsqQyOvFE2GEHOP54GDEi62okSdUgnyELbMlSWRUGwi+/fDqQ9LhxWVckScpaPkOW3YWqgHnnhTvvhG7dYOut4csvs65IkpQlQ5ZURksumQ4g/dZb6aDSM2ZkXZEkKSv5DVlShay3Hlx2WRqbdeyxWVcjScpKqw4Q3SXZkqUKOvBAeO01uPhiGDwYDjoo64okSZ0tvy1ZhixV2Pnnw2abweGHw8MPZ12NJKmz5TdkSRXWowf87W+wzDKw/fZpnJYkKT8MWVIFLbAA/OtfaY/DLbeETz/NuiJJUmfJZ8gqsMtQnWDJJdMxDv/zH9hmG5g6NeuKJEmdIZ8hq9CSZchSJ/nZz+C66+CJJ2DffWHWrKwrkiRVWj73LjRkKQM77wwTJsAJJ6TWrbPPzroiSVIl5TtkSZ3suOPg7bfhnHNg4EA44ICsK5IkVUo+Q1aBLVnqZCHApZfCu+/CIYfAEkvAxhtnXZUkqRIckyV1sjnmgFtvTQeT3n57eOGFrCuSJFWCIUvKwPzzwz33wMILpwlLx4/PuiJJUrnlO2RJGerbF+67D777DjbZBD75JOuKJEnllM+QVWBLljK23HJw110wcWKarHTKlKwrkiSVSz5Dlt2FqiJrrAG33AKjR8NOO6WWLUlS7TNkSVVgq63gz3+Ge+9N0zo4Wakk1b58TuHgmCxVoQMOgA8/hFNPTQPiL7zQj6ok1bJ8hqwCW7JUZU4+OR1E+uKL4XvfS5clSbUpnyHL7kJVqRBSC9bnn8Mpp8BCC8Hhh2ddlSSpPQxZUpXp1g2uugq++AKOOAIWXBB23z3rqiRJbZXvge9SlerRI+1xuN56sPfeaZoHSVJtyWfIKrAlS1Vszjnhn/+EH/8YdtwRHnoo64okSW2Rz5Bld6FqxHzzpVnhl146TfPw5JNZVyRJai1DllTlvvc9GDkS+vVLxzl8/vmsK5IktUa+Q5ZUIxZdFB58EHr3Tsc5fOmlrCuSJLUknyGrwJYs1ZB+/dK4rHnmgY02gtdey7oiSVJz8hmy7C5UjRowIAWt7t1hww1h7NisK5IkNcWQJdWYQYNS1+GMGWmKhzffzLoiSVIp+Q5ZUo0aPBgefrg+aL31VtYVSZIay2fIKrAlSzVs+eVT1+F338G66xq0JKna5DNk2V2oLmKFFVLQmj49tWiNG5d1RZKkAkOWVONWWCF1HU6bllq0HKMlSdXBkCV1AcUtWuus4/QOklQN8hmypC5oxRXh0UfT/xDrrOOEpZKUtXyGLFuy1EUttxw89hjMNVcaozVqVNYVSVJ+GbKkLmbppVPQWnBB2GADePrprCuSpHwyZEld0IABqetw0UXTIXgefjjriiQpf/IdsqQurH//FLQGDoTNNoPhw7OuSJLyJZ8hq8CWLHVxiy+egtZKK8F228GNN2ZdkSTlRz5Dlt2FypGFF4aRI9Meh3vuCZdcknVFkpQPhiwpB+abD+6+G4YNg//7PzjrLD/+klRp+Q5ZUo7MOSfcdhvssQeccgr8/Ocwa1bWVUlS19Uj6wIy5b/yypk55oDrroPeveHii+GTT+Daa6FXr6wrk6SuJ58hy+5C5Vi3bnDhhWlQ/PHHw+TJ8I9/pC5FSVL55Lu70JClnAoBjjsutWI9/HA6sPTHH2ddlSR1LfkOWVLO7b13mj/rjTfgZz+DceOyrkiSuo58hqwCW7IkNt8cHnoIvvgC1ljDw/BIUrnkM2TZXSg1sNpqKVwtsACsv34aoyVJ6hhDliQABg1KQWvllWGHHdLeh5Kk9st3yJLUQJ8+qetw223hF7+Ao46CmTOzrkqSalM+Q1aBLVnSbOaaC269NYWsP/whBa4pU7KuSpJqTz5Dlt2FUrO6d09zaV1yCdxzD6y5Jrz7btZVSVJtMWRJatLhh6djHr7zDqy6Kjz3XNYVSVLtyHfIktSiTTZJA+LnnhvWWSd1JUqSWpbPkFVgS5bUKoMHw7PPwtChsPPOcNppHlxaklqSz5Bld6HUZn36wMiRsM8+cPrpaZqHr77KuipJql6GLEmt1qsXXH11mkNr+HD46U9h/Pisq5Kk6pTvkCWpzUJI82fddx9MnAg/+Qk8+GDWVUlS9clnyCqwJUtqtw03hOefh8UXT4PjL7rIr5QkFctnyLK7UCqLpZZKex4OGwZHHw277urEpZJU0KqQFULYNIQwNoQwLoRwQonrDwkhvBJCeDGE8EQIYXDd+p4hhGvqrnsphLBuectvJ0OWVDbzzQe33w7nngu33Qarrw5vvZV1VZKUvRZDVgihO3ApsBkwGNi1EKKK3BRjXDHGuDLwW+DCuvUHAsQYVwQ2An4XQsi+9cwxWVJZhQDHHw8jRsBHH6WpHv71r6yrkqRstSbwrAqMizGOjzFOB24GhhVvEGP8b9HFeYBCE9Fg4KG6bT4BvgCGdrDm8rElSyqrDTeE0aNh0CDYems46SSYMSPrqiQpG60JWX2B94ouv1+3roEQwuEhhLdJLVlH1q1+Cdg6hNAjhDAQGAL071jJZWB3oVQxP/gBPPEEHHAAnHMObLQRfPhh1lVJUucrW9ddjPHSGONSwPHAyXWrryaFslHAxcBTwMzGtw0hHBRCGBVCGDVp0qRyldQ0Q5ZUUXPOCX/5C1x3XTre4Y9/DA89lHVVktS5WhOyJtKw9alf3bqm3AxsAxBjnBFj/EWMceUY4zBgQeDNxjeIMV4RYxwaYxzap0+f1tbefp99lk7vvbfyjyXl2F57pZC18MKpRevMMz0cj6T8aE3Ieh4YFEIYGELoCewCDC/eIIQwqOjiFsBbdevnDiHMU3d+I2BGjPG1slTeEY88kk7PPjvTMqQ8WH75FLR23RVOPTXNqfXRR1lXJUmV12LIijHOAI4ARgCvA7fGGMeEEM4IIWxdt9kRIYQxIYQXgaOBvevWLwL8O4TwOqkbcc9yP4F2efrpdOqB16ROMe+8cMMNcMUVabzWSiulPRElqSsLscrGJQ0dOjSOGjWqsg9y9NFpeup55zVoSZ1szBjYeed0+stfwllnQc+eWVclSe0TQhgdYyw5c0L2c1ZlwXmypMwsv3w6HM8hh8D558Oaa8Lbb2ddlSSVXz5DlqRMzTUXXH55min+rbdg5ZXh2mvd4VdS15LvkOUvupSp7beHl16CIUNg331hp53qd/6VpFqXz5A1s26qru7ds61DEkssAQ8+COedB//8J6y4IowcmXVVktRx+QxZhRYsx2ZJVaF7dzjuOHjmGZh//jSn1tFHw7ffZl2ZJLVfPkNWgSFLqiqrrJKOfXj44WkH4FVWSYPkJakW5TtkSao6c88Nl1wC998PU6bAGmvAKafA9OlZVyZJbZPPkOWAd6nqbbQRvPoq7LlnmktrtdXg5ZezrkqSWi+fIavA7kKpqi2wAFxzTRoQ/+GHMHQonH66rVqSakO+Q5akmrD11qlVa6ed4LTT4Cc/SWO3JKma5TNk2V0o1ZzeveHGG2H4cJg8OXUf/upXMHVq1pVJUmn5DFmSatZWW6XjHu6zD5x7bpot/rHHsq5KkmaXz5DlWCyppi24IFx5ZdoDcfp0WGcdOPBA+PzzrCuTpHr5DFm77ppO99kn0zIkdUxhD8TjjksD5JdbDm65xREBkqpDPkPWkkum00GDsq1DUofNPXc6JM+oUdC/P+yyC2yxBYwfn3VlkvIunyGrW93TnjUr2zoklc3KK6fD8lx8MTz+OCy/PJx5pgPjJWUn3yGrcKBoSV1C9+5w1FHwxhswbBicemo64PT992ddmaQ8ynfIsiVL6pL69oWbb07hKgTYZBPYcUd4992sK5OUJ/kMWd27p1NDltSlbbQRvPJK6ja86y5Ydtl0/ttvs65MUh7kM2TZkiXlRq9ecPLJqQtxyy1TF+LgwXDHHe6FKKmyDFmScuEHP4Bbb4WHHoJ554Xttqtv6ZKkSjBkScqV9daDF16AP/4R/v3vtFfiwQfDxx9nXZmkrsaQJSl3evSAI46AcePgyCPh6qvTtHnnnuuUD5LKJ98h6/XXs61DUqYWXhguuigdC3H99dMBp5ddNh2I2v/BJHVUPkNWYe/CG2/Mtg5JVWGZZeDOO+HBB1Pw2nNPGDLE+bUkdUw+Q5YHiJZUwvrrp8Pz/PWv8MUXaX6tjTZKY7ckqa3yGbIkqQndusFuu6UpHy66KA2SHzIkHRNx7Nisq5NUSwxZklRCr17w85/D22/DSSelyUwHD4b994f//Cfr6iTVAkOWJDVjgQXgrLNg/Pi0J+KNN6YxXEceCR9+mHV1kqqZIUuSWmGRRVL34bhxsPfecNllsOSS8ItfwEcfZV2dpGqU75DVt2/WFUiqMf37wxVXpDFbu+ySJjVdckk45hgnNJXUUH5D1qKLwhZbZF2FpBq19NJwzTUpbO24I1x8MQwcCEcfDR98kHV1kqpBfkNWCB4dVlKHLb00XHddfdj6wx9S2DrsMJgwIevqJGUp3yFLkspk0KAUtt58E/bZB668Mq3bb7+0TlL+5DdkgS1ZkspuySXhz39OUz8cdhj87W/pUD3bbw/PPZd1dZI6U35Dlt2Fkiqof3/4/e/TnFonnggPPQSrrZZmlR8xwp8fKQ8MWZJUQYsskubZevdduOCC1HW46aaw8spw/fUwfXrWFUqqFEOWJHWC+eZL0zyMHw9XXw0zZ6b5tgYMgN/8Bj77LOsKJZWbIUuSOlHPnrDvvvDKK3DffbDCCqk7sX9/OOIIj48odSX5DlmSlJEQYJNN4P774aWX0vQPf/lLGiS/+eYpgM2alXWVkjoivyELbMmSVBV+9CO49to0buu00+Df/4bNNoPll4dLL4X//jfrCiW1R35Dlt2FkqrMoovCr3+dwtYNN8C886YuxL594fDDYcyYrCuU1BaGLEmqMj17wh57pHm1nn0WttsOrroqjd9abz247Tb3SpRqgSFLkqpUCLDqqmkm+fffh/POS4fq2WmnNFD+V79KeytKqk6GLEmqAb17w3HHwbhxcM89sMYacP75sNRSsPHG8Pe/27olVRtDliTVkO7d06D4O+9Ms8mffno6OPUOO0C/fmkurtdey7pKSWDIyroKSWq3vn3h1FPhnXdS69baa8Mf/5j2SlxjjXSQavdMlLJjyJKkGldo3br99jR264IL4Msv4cADYbHF0iD6Bx5Is8xL6jyGLEnqQhZZJHUZjhkDzzwD++wDd9+dxm0NGJBml3/99ayrlPLBkCVJXVAIsNpqcNll8OGHcMstadLT886DwYNhyBC46KJ0naTKMGRJUhc355xp2oe774YPPoCLL4Zu3eDoo9Ng+Y03TjPOf/FFxoVKXYwhS5JyZNFF4aij4PnnU7fhiSemaSH23Tddt+22qdXrm2+yrlSqfYYsScqpZZeFM8+Et99OM8sfdlg63WWXNLZrl13S/FsGLql9DFmSlHOFmeUvugjeew8efjjtkfjQQ2n+LQOX1D6GLEnS/3TvDuuuC3/6Uxq/NXJkw8DVuzdsvz389a9pmghJTTNkSZJK6tEDNtigPnA9+CDstx88/XQKXn36wOabwxVXuJeiVIohS5LUoh49YP314ZJL0oSnTz0FRx6ZDulz8MHw/e/D6qvDueemAfX+vEqGrKyrkKSa061bOmzPBRekQfMvv5wG0M+cCb/6VZqHa5ll4Be/SN2MHrhaeWXIkiS1Wwiw4opw8slpWoj33ksToC6zDFx+eepu7NMnzdN13XXw8cdZVyx1nh5ZF5AZQ5YklV2/fnDooWn5+us0juuuu9Jy221pmyFD0rEWN9887dXYvXu2NUuVYkuWJKki5pkHtt46DYyfOBH+/W84++w0A/0558BPf1rfynXVVakVTOpKQqyyoDF06NA4atSoyj/QggumX4CJEyv/WJKkBj77DB54AEaMSMsHH6T1yy2XDvOz0Uaw9tow33zZ1im1JIQwOsY4tOR1uQ1ZIaTTKnv+kpQ3McKYMfWB6/HHYerUtEfj6qvDhhum5Sc/gZ49s65WasiQVYohS5Kq0tSpaYqIkSNTa9fo0emneu65Ya21YL310nQSP/5xCmJSlgxZpRiyJKkmfPYZPPpomg7i4YdTqxekrsS11oJ11knLKqvAHHNkW6vyp7mQ5f8AkqSqtvDCsO22aYE0DcTDD6fg9cgjcM89af0888DPfgZrrpnC12qrwVxzZVa2ZEuWLVmSVINiTP2Kc83Fxx/DY4+l0PXYY/Dqq+nqOeaAoUNT6PrZz9IEqossknXh6mrsLizFkCVJteuqq+CAA2DcOFhqqQZXff45PPkkPPFEGkT//PPw3XfpukGD0tQRP/1pCl2DBztPlzrG7kJJUtdy++3p9M03ZwtZCy0EW26ZFkgNXqNHp+D11FNw991p9nmAeedNE6KuvnpaVl0VFl20E5+HujRDliSp9sycmU67tTyn9pxzpu7Cn/0sXY4xNYA9+yw880xazjuv/i5/8IMUtgrLj3/sfF1qH0OWJKn2zJqVTlsRshoLIXUbDhoEe+yR1n3zTWrtev55eO65tBQOAxQCLLtsGt81dGg6LNDKK6eB9lJzDFmSpNrTgZBVSmEOrrXWql83aVIKXaNGpeWBB+CGG9J1heD14x+nqSNWWSUFr4UWKks56iJaFbJCCJsCvwe6A1fGGM9tdP0hwOHATGAKcFCM8bUQwhzAlcAqdY91fYzxN2Wsv+NirB8EL0mqDWUOWaX06ZMOYr355vXrPvggBa4XXkjHYnzsMbjppvrrl1giha2VV4aVVkrLwIEVLVNVrMWQFULoDlwKbAS8DzwfQhgeY3ytaLObYox/qtt+a+BCYFNgR6BXjHHFEMLcwGshhL/FGCeU+Xm033/+AwMGZF2FJKktCiHrjTfSFPCd5PvfTwe93nrr+nWTJqXA9dJL8OKLabnrrvoS55kHVlwRfvSjdLriirDCCvC973Va2V3bk0/CMsukVFxlWtOStSowLsY4HiCEcDMwDPhfyIox/rdo+3mAwrwIEZgnhNADmAuYDhRvm72vv866AknqumJMTT077VTe6dgLCeaww+DQQ8t3v+3Qpw9ssklaCr75Js3X9cor8PLLabn9drjiivptFl88ha0VVoDll0/TSQweDAss0PnPIRMxpr1Df/jDjt3PmmumAXZvvlmeusqoNSGrL/Be0eX3gdUabxRCOBw4GugJrF+3+nZSIPsQmBv4RYzxs44UXHbOkyVJlXPrrWl0+TvvwMknl+9+CyGrEp57Lk0X//zzaaR7O8w9d/3eiQUxpu7GV19tuPzpT/Dtt/Xb9e2bwtZyy6Vl2WXT6SKLdLHRLRddBMcck17vn/ykY/f11lvlqanMyjbwPcZ4KXBpCGE34GRgb1Ir2Ezg+8BCwOMhhJGFVrGCEMJBwEEASyyxRLlKkqrDm2/C9Onp39Wu5oc/TEfqvfzyrCtRtZo8OZ1++GF577eSrRaFz/NPflLWf8RDSAGqb9+GrV4zZ6aRK6+9lo7LWDi96qqGnS0LLZS+cssum04Ly1JLQa9eZSuz8zz5ZDr9z3/aH7IqGbbLoDUhayLQv+hyv7p1TbkZKPzi7gbcF2P8DvgkhPAkMBRoELJijFcAV0Ca8b11pXfQqafCGWfU6CdTNaXQFN4VW03ffDMthqyOe/11uOUWOO20rCupjHJ//j/9tP23jREuvhh23RUWW2z26zt5GEn37rDkkmkpTKAKKT9MnJg+Gm+8kU7HjoX774drr63frlu3NLfXoEFpaFJheoqll05DjtvVS/vKKzBlSpoWv63uuw9OOQWefhp6NBMzZsxIp81t05J//7v9t+0ErXlmzwODQggDSeFqF1J4+p8QwqAYY6GtbgugcP5dUtfhDSGEeYDVgYvLUHfHDR6cTgvHWpDKbfLkdGTbWrPttmlK7Pff90Bvnanwm3TMMe2f+XLmzPSXuZxjnzqqGvu3Xn0Vjj46LaXC3yefdH5NJXTrBv37p2XjjRte99V/I28+MIGx0wb+73+dt96C66+H/xaNfO7ePQWwpZdOLV5LLZXCXOF03nmbePAf/Sidticc77VX2hvg00+bnz6/cN8d+Yycc077b9sJWgxZMcYZIYQjgBGkKRyujjGOCSGcAYyKMQ4HjgghbAh8B3xO6iqEtFfiNSGEMUAArokxvlyJJ9JmL7yQTv/4x/Rf+KxZ8I9/wHbbVX5f2/vvhw028IBZnWHixPRfUmcfJ+O999K+3Gef3bmPWw533plOF120a7a+VbuOtK6vuWaavrwa3rfp01PTSzWaMmX2dXvuCTfeWD9wqsrNd/s1DNl/f4Y8+CDstv7/1seYMuK4cbMvzz+fjutYbJFF0hQTAwem0FU4P4Al6c979OxIkS2Fp3KErHJ3Q5dZq9roYoz3APc0Wndq0fmjmrjdFNI0DtXn7bfT6aOPptPLL4cjjoArr4T996/c444cmTrjTzsNfv3rtK7oaPJqhcmTYcKE1g1I7dcvnTb+o7PxxrD77rD33rPfphzefTed/utflbn/anPiiek9KZ4wqFrFCKefDgcemAbHVJuOBKRnnilfHR31i1/AZZfBL3+ZLpc7+H3/++UNQzfeWH++WoeR/PGPcOSRqVHg+efTurFj07jIOiGk/48WXbT+MELFPv8cxo9PfwLfPv4Kxk/7Pu/Mu+X/ZrgvHFoI3iYwi779U5fjgAHp/8Yf/KDhaclZ7ydNSqfvvNN8a3g5QlZ9wVUpvzO+F1qRCm/Q8OHptNKpuPDhe/bZ+nWnn56WTz4pPc/H11+n/YGrbQ6Qr75Ku9BUskVu5sy0201xm/bqq6dfiI78aD/wQFraGrJihM8+a3mCm0KALt5lqLOMHJlC3n77tf22f/97+x7zN3VzDNdCyPrtb9P37bzzsnl/WvLaa2ka8c4ycmSaMbPcvy9PP51OGzedlEthPE9rTZ+e/hk4+eSWfzuqqbu12NFHp9Pvvmt3QFlooXRYoCFDgJ0PTis/SPc1Ywa8f/9rvDPHMvxn4wOYwAAmbHAaEybA44+nEQSNM83CC6ewtcQS9V2b/dmV/rxHv4fe4fsrr9Z0Zp0woV3PoYEqH/ie3zloCwPtCl/U++9Pp198Ub/N+PFw9dXw5Zfle9z36mbDuPfe+nWnn55OC1+gxn7847aPjZk1K31wC3/smzNuXJqYZfz4lrctiBHmnx8OPrhtdbXVwQen8SnFP4qFVsjOECP84Q/1gxyuugp69067/jTnwQfT6Usvtf+xr7gCzjqr7bfbaKP2tcaOGQM77ND8NjNnpj9WtWjjjWG33dKwAEitx9Xo/PPT6cyZacbLQlhpj5Z+A2bNSp+XopaQJo0cWXo3+RdeSK3KjQeLNw4B5W7JKg5Zn3+ewmlz/vpX+N3vUshq6Q9za/YEvuWW9FtQ6vtwzz1pqEIp331Xv8dlWxWe89Sp5WkFaqTH+xMYsMXyrPfPn7MP13Eap3PttfDIIykPTZ2adgR8/PHU8Hf22Wn6s759U6PVjTfCCSfA7tzE2jzOkifuwpxzpn0LhgyBYcPStGZnnw3XXQcPjFmc11iOL6b0aP/Ho8pbsogxVtUyZMiQ2Cn+8IcYIcYttkiX00c2xl/+sn6bXr3q17/+esce76WXYpwyJcY//an+PgsKl4vXFWvuumIHHBDjPvuk899+m24zxxwt3+7kk9O2Z5zR8rYFhfvv2bN+3bvvxvjRR/WXr7wyxrFjW3+fpRSe+8yZs69ry+2LzZzZ8H6//LLp2z/4YNpuvvnS6dCh6fTWW1v3uKXe22nT0v08+GDba2+N9t7uiitmr/mVVxpus9ZaTX922/OYjT32WIxvvNHx+ymlUOOQIeWrtz0mTYpx9OjZ1xdq2mabdHnChHS5f//W33fx85oxo+Xn+dRTrX8tmtpu/fXT+pEjG65fZZW0/oAD0ulee7X+ebTGggvW17Tcci0/hz//OW1z4IExPvpo07/DMcZ41VX1l0NIfy8am3fedP3EiTGeckrD9xRi7NevdB177jn7b1prFWp6//30PCA9r/Zq/Bq8/HK6vMIK7f6OfPlljK+xbBzBRvGqvR6Jp5+ePgKbrfBuXHHwd3HhhUv/PM41V4xLLZV+YnbaKcajjorx3HNjvP76GB94IP0UTZoU46xZdQ/04Yfp9+KnP832+xxjJI1PL5lp8ttduM02qW97m22a3mbatPrzTz+dJidpj2+/Tc3xW2zR/H9zpTrQ2+LKK9PpNdfUp/vW7D1ZaMGaNi3tonLHHXD88c3f5pFH0mnxf3GFOc4KH/kDDkgtZMWtg+01dWrqmiw2c2b7uiqL/wM++eTU1fXVV6lL8uWX03v1yivpv9lCa8dXX6XTUaPSaUe6E7bfPt3PBhtUxwDlglKvZeG9e+AB+Oij9C9sJa29djqt5OvS1m6mchsyJHXnNvUcC60shc9Ye/eAbs3tfvrT+vMxpuaIJZds2+MUXs/Gn59Cb0Hht+ipp9p2vy0pbo1qzQD7QotPCDDnnM1vW6h5zTXhiSdSL8P//V/DbQqD56dPhzPPTEuM9XW9/37p+y4cYXratPaPw+3Xr761ur0tWaVaSAv9esV/+4rNmJGe7wcfpN+DwuenaGex+eeH+XmD5XgDdjsGNiG16F+5cvp7O+YOvv0WJh7xGz64+l4+4Pt8sP+pfLDgYCZOTCN2Xngh7eBcaiaNOeZI480We/89FuVLFht6GYtyF4vxET96FNZZp30vR6Xkt7uw8ZisgvPPL737bnPNyzNmpC6/4v1mC3bdNf3RhvQH6p6i/Qfuuit1CS2+eLpcaLL/+uuOTy1RfPvCj/lxx6WBqI0VxtE8/HD6hJ5wQvriFvYyK+WOO5p//MLrWq6u1r/9bfZ1jV+jb79t3Q958R/ZwvN48slUa+G1KAxYb7ynaeFzs9BC6X0aO7blx2vsrrvafpv2KD5+R2sUJgYsVvix3XjjtFt2W3z+eX04bclHH9V3pUOabbtSY3myDLaPPVa/U0RTCuNDC4PyW/Nb8M03s19u65i83/0u7df/cht3AH/ssXTa+LtQ6FrsWbd/2mqzHSgkiTEdFqcwkLu1Sv0mF2pp6nEKp2eckc737p2+83ff3fB+C78RTzyRTpsL5g891PBya3/zPvqo+eunTUvjPwsah6nC82lPyJo8uWHAfuWVhvfV+Dvy8MOpkWCOOdJI90GDYK210me01DxjSy+dTgtTkRT+Wb3zTpgyhbnmgqVf/xdr8zi7cAtHbz2OCy5IP/OPPDiTN8dGpkxJf1LHjk37p91yC1y89wscs8tENtgAejOZD/g+94zqw3kcz5H8kT//ue0vRcU11cSV1dJp3YUff5zaWy69NF0ubrd87LHZ111xRdP38+tfp2023TSd3n9//fXF99FUO+lOO6XTa6+N8T//SefXWWf2+2hJYbtvvkntqoXLhx4a49NPN30/hfU/+9nstTVl992bb24vdCe2pQn3pZdSV1qp2v7+99nX/ehHpWt6993SNRV8+WXD+yicn2eeGI88Mp2/6KIYV189xiOOKP2eXXVVjBttlM5Pnz77cyl1mxkzZr8uxhhffbX+M1fqPgpmzYpxxIjUPD5jRoxvvx3jZ581/9izZsV4771FbezNKFXzTTeVvq6p2zRV/9SppWu4//4Yzzmn9GNfd12MN95Y/5lurVGjSj9W4X5///vmP5u33576J9pqxowYv/sunf/iixifeKLh9f/85+zvTan6CnUVzvfokT5jX3xR+nELXV8jR9bfZo89Sr8vb79duusd0tAJiPFf/yr9OC39fhR+A998s75bHWI86KD68x980PC2X30V4377pesWWCDGxRaLcZNNZn+MCRPStsXmnnv2z8xZZ6Xv0sCBs29f3F1Y6vNWWKZPj/H000t/tu+9N3VNTptWv/7aa+vPX3ZZy7+fc85Z+rVorPD7Uup1hvpu7yuvbP5+Yoxx111j3HHH+svF34HCMnZsjC++mM4vtVTD57DAAs2/Zo0Vbr/aajE++WSMzz5bv+2vfjX781loofS9Law/9NDSz6PU9wPiTEKcxPfihxPb0QVbBjTTXVhyZZZLp4WsyZPj/35wY2z4hj/+ePqxLF53+eWl72eRReq3CSGdbrRR/fXNfTAbLz//eekPbnNf2Bhj/PTTGIcPr99u2LD0BW7tF6Kwfs01W962YLPN6rcp/AEsXB41Ksb//rf+8sSJ9X98Gps1K1338MP1X8pStd1+e+nXtNS2r7ySajrrrPp166yTxlWMHFkfsCHGlVdueH+FH+CLL279+9anT4x//Wv9mLYPP2x62+LHbvxj8cgjpZ9PjDHec0/D2xUeo9S4j+Ltrruu/jO51VbpD8+UKaXfi1L1FsaelfpcFN6zlt6PwncNGv4Bvffe5l/XQsCCGMeNK13ztGkp0BcUgkbxGJpp01K4KNxX8diz5l6Htho0KAWiGGNcb710H19/XX/95Zc3fH6vvpoCTyE8NfW5gPr7K/joo/qwdMYZ6boTTyz9OoaQtnvttXT5rLNmf65Q/0/i3Xe3/nW5887ZH2+bbUrXXuq+jzmm/rqFFmr6tYf0T2qpeoqXlVeO8fvfT+dPPrnh9q0NWVtuWXr9X/8a4xJLpPPvvFO//h//SKfzz9/896GgMJZswoTS18eYAnrhPgr/oDRV79VXN30/jV+rwmdmgw1K31fh79mSS9avmz69fvxZU0tjxbeHGH/4w/rzv/xlw/GChWXRRRs+z+aeR/H5Uu9TJzNklfL55+npX3hhulz8Jj31VIxHH91w3SWXpMGGjbX0oWvug9nS0vg+Ci0hL7xQ33pS6svSo0eMN9/c9P2efXbp59C37+zbbrpp6ddvww3rtykMaC2+3SuvNLx85JGl76dw/W67lf5yFdbddlvp13TWrPTDXfylPfLIGE87rennXzzwufFSaAH44x/b954V/4fb1u3nmqv+OR51VP368eNnv12hxbPx6/Xmmw23O/PM0o+7xRb1LSmfftr8j3hxSCp+zNtum33955/P/j7demvDbT7+OAWjUgPtm1qeeCLVucwyaXBuwbLLNnwN/vKXdHn//evX7bNP0/fb3Gcyxhifey7Gt95qeP0XX6QQP2JEwz+Uxbcr/CH99NP66xv/EzV6dH0wuu++2etqqt7iwHj22fUh66STSt+mW7d0uxEj0uUNN5y9ZohxxRXT6XHHxXjHHTH+9rfpt2batLQzQmG7556L8YYbmq5xhx2afr2HD0+tw88+O/vtS4WsmTPTP72F9cWButT9/+AHDS8fcUR6LnPMEeOAAWldv35t+46WWooHzt9yS/s+XxdcUPr6xs/tqKPS356mHuOaa+pv179/WjdpUun7K25Rau0y//z1rW+tfZ6F17rU8otfpN/sUtcde2zDy2edlf5Rafx5aer9hxSSO5khq5SvvkpP//zz0+XiN6m4a62wLL10/fniLpqWPnSN1y++eOs/3DGmH7nC5X79YnzooXS+uDm+8dK9e/3ecE0tTzyRAtqECaWb3YuXU06Z/fUr/m91wIDZn+tjjzW83Ldv6fehcP3OO8/+2hVfv+aazb/mZ5/d+te1NUupVr3WLIU/ZK1Z5pqrYZiC1Mxe3NUKDVvkCstbb5V+vUaPbrjd2ms3/fgPPxzjv/+dzjcXeAYOLP3Z3Hbb2dcvtli6rrCXUlPL4MH13VNtXXbaKf3x/eST2V+DwuXCXrYxpv+Qm7qvqVPrt5s6NYWnwnVN/VcNDf9TnzGjYbAoruOcc+pv19RwgVJLU6F31qzUxVq8bu+902lTIavQunbllenyBhs0/11qvOy33+wtqTD7Z601y29/W/p1KvX5inH2FpGtt26+9uJursJS2POwUssNNzR9XeGf4fffr9+Lufj6008vvQd28Tbbbtt86/i1185+uyWXTJfffTcF/cL64j3my7kUK/6b1dRS6h+0ppZSob2lz24nM2SVUvxj+s03DZt6W/rxL/wX1717829yqR/K4ubx1nxwzz+/4brC7r8tLfPM07rt9tuvYXN+az60pVqCGj/XQhgsLEss0fA+Zs4s3UIC9S12MTb8kf3mm6a7Qfffv/WvayWXwtQgrVmWW67pZvuWluKQVXi/X321PjRVeomx6c/YlCmzjz8q57LLLqXribH+8hpr1K9r7h+O559PfwBvuil1+zb3fBs/RmFZaaWGlwtTLxSWwue5pdaA4qWpFtEZM+qnTGi8FKZiabwUpnEpXF5vvaafS6mlf/80JrIzPldNvZ+Nl+Zaqjt7ae4fvOJg1fh9aOrzVWqbl15q+jHmmy+NLS5uXSteytFy19IyfHh97c19jwpLS//Yt7Q01/Je6vWssOZClnsXQjpUwYYb1l8u3tOklD33TG9lS5OglToGYlt2Hz/kkPpDUhQ0tWttYwsu2LrtunVr3XQEM2ako52HAKNHN7xuzjkbTq4Ks0/02HiPqnPOSXv2lNKjR3qcd95pOEHqYovBqquWvk21TJDZlj2zJk9u/1QQjadS+PrrNOVERyaubIvXXy+9fzWkKSoqOU3CiBGzrxs9uuFn8Omn01QmMTa/h+M//wnLLJMmKS0cjaE5pbZpPOFs44k999svHa+kLZOfNrWX7H//m6bULiXG0uuLZweHtKdYWxTv9dmZmvsMnXZap5XRopNOavq6vfaCVVZJ55vbS/SBB9Jv3siRTV/flK++gsMPb3rugqamkiin4kmpW/M9arw3bFu19Hfw9tub/j50tqbSV1ZLp7VkFU9I2Z6lVFdJ8fKb35Ref8ghlf2Poq3LSivFuO66LW/XXDdYqZatUi00F16YmsdXW2326xqPpXCp7eWSS7KvAcrXjXzXXQ0H4me5FO9sU7wcf3zr76Mt3TVZLO1tOfvlL7OvvbmleOLMppZSrTRN7dRQTcujj8a4776d81hN9YIUL8Vd9RVGMy1ZIV1fPYYOHRpHFSZ8rLQyHo5AHXTEEXDJJVlXIdWufv06p9Wimm27bctz+FW7Dz5IB79Wx/3xj+lvS4WFEEbHGIeWvM6QJZEmMSzMNi5J6ho6IeM0F7LyOyZLtW3YsPLe36KLlvf+JEnZy3j8niGrJRttlHUF5VU43lWllBrsXwkDB5bvvh54AL73vZa3u+yydMiM1u58UMuaO6RSpRSOm7bBBpV7jHXXrdx9q2nLL9/x+yh1nL9Kflba6vTTW79t8Y5WbfHppy0fjqdaXXVVNo/blvelEpoarJXV0mkD32NMM8MWD5S74IKGh1m58so0QP7+++vnEWpuzp1SS2HX21LTJEyZ0vCx1lkn7ZpfmJkZ0m7fM2fOPu9Q8aRtc85Zvzt98Tw0r7yS7uuMM9Js34VDhVxwwey1rLhi/eEtCruIzzNP6TnDmltiTIMSBw2K8bzzOja4caON6idIPOCA+l33V1opzRJ/991pd+Hi+YH+8peG87Q0NWC/+H0sTMpZartNNkm7+O+0U8PDmlx+eYx/+lN6by67rPRr+sknaeLIv/41zWXzr3+l9XfcUT+7NqTJ8776Ks1nVHz7n/ykfp6rG26Yff6s4qVPn9lnr2+8nHBCy6/5V1/VTznQ3Pw/heXii+snwzzmmPR5W3XV+uvHjm36tS+efHLgwPptP/oofb4LE8Oeemr9DPyvvz7757zxziTFh3wqLLvumk6//DJNNHvJJaW3g9kPSdN4aWlQ/+67p89H4wHqv/hFmtUfGk6wWbx89lmMK6ww+/peveonXoW0A0lTM+ZPnlz/en7xRVpXOCzKoYfWb1fYAaUw590KK8w+G3rPnqW/E8WX/+//0lEdCu/PAQek+5o8uf59K8xL2LPn7HM+3X777JMXFy+Fw/KUmr7is8/STO6rr55+4wrrG88lttde6fTgg+vXFQaT3357mv5iu+3SZL6/+11aX5gmormJnZdaKk2RMGFC+j3fb790yK3mJjx+++2mf2+Kl/XWi/G99xquK1h99dK3KbzPq63WcBLe+eev/31fYom0I0fhKArffZcm/PzrX9Nz+e9/03u3664Nn/s776TfyuKjfRTPTF+87LBDfa2zZtVP5F2Ydb/wmW48UTGkncruvTdNC1GYfmLYsNKPc9JJ6fvf1PQVMPvM/xWAA98lSZLKzzFZkiRJncyQJUmSVAGGLEmSpAowZEmSJFWAIUuSJKkCDFmSJEkVYMiSJEmqAEOWJElSBRiyJEmSKsCQJUmSVAGGLEmSpAowZEmSJFWAIUuSJKkCDFmSJEkVYMiSJEmqAEOWJElSBRiyJEmSKsCQJUmSVAGGLEmSpAowZEmSJFWAIUuSJKkCDFmSJEkVYMiSJEmqgBBjzLqGBkIIk4D/dMJD9QYmd8LjqPV8T6qT70v18T2pTr4v1acz3pMfxBj7lLqi6kJWZwkhjIoxDs26DtXzPalOvi/Vx/ekOvm+VJ+s3xO7CyVJkirAkCVJklQBeQ5ZV2RdgGbje1KdfF+qj+9JdfJ9qT6Zvie5HZMlSZJUSXluyZIkSaqY3IWsEMKmIYSxIYRxIYQTsq6nqwshTAghvBJCeDGEMKpu3cIhhAdCCG/VnS5Utz6EEP5Q9968HEJYpeh+9q7b/q0Qwt5ZPZ9aFUK4OoTwSQjh1aJ1ZXsfQghD6t7ncXW3DZ37DGtPE+/JaSGEiXXflxdDCJsXXferutd3bAhhk6L1JX/TQggDQwjP1q2/JYTQs/OeXe0KIfQPITwcQngthDAmhHBU3Xq/Lxlp5j2p/u9LjDE3C9AdeBtYEugJvAQMzrqurrwAE4Dejdb9Fjih7vwJwHl15zcH7gUCsDrwbN36hYHxdacL1Z1fKOvnVksLsDawCvBqJd4H4Lm6bUPdbTfL+jlX+9LEe3IacGyJbQfX/V71AgbW/Y51b+43DbgV2KXu/J+AQ7N+zrWwAIsDq9Sdnw94s+719/tSfe9J1X9f8taStSowLsY4PsY4HbgZGJZxTXk0DLiu7vx1wDZF66+PyTPAgiGExYFNgAdijJ/FGD8HHgA27eSaa1qM8THgs0ary/I+1F03f4zxmZh+oa4vui81oYn3pCnDgJtjjNNijO8A40i/ZyV/0+paRtYHbq+7ffH7q2bEGD+MMf677vxXwOtAX/y+ZKaZ96QpVfN9yVvI6gu8V3T5fZp/o9RxEbg/hDA6hHBQ3bpFY4wf1p3/CFi07nxT74/vW2WU633oW3e+8Xq1zxF13U5XF7qkaPt78j3gixjjjEbr1QYhhAHAj4Fn8ftSFRq9J1Dl35e8hSx1vjVjjKsAmwGHhxDWLr6y7j85d3HNmO9D1bgcWApYGfgQ+F2m1eRYCGFe4O/Az2OM/y2+zu9LNkq8J1X/fclbyJoI9C+63K9unSokxjix7vQT4A5Sc+3HdU3m1J1+Urd5U++P71tllOt9mFh3vvF6tVGM8eMY48wY4yzgL6TvC7T9PfmU1G3Vo9F6tUIIYQ7SH/O/xhj/Ubfa70uGSr0ntfB9yVvIeh4YVLcXQU9gF2B4xjV1WSGEeUII8xXOAxsDr5Je88KeNnsD/6w7PxzYq25vndWBL+ua50cAG4cQFqprDt64bp06pizvQ911/w0hrF43tmGvovtSGxT+iNfZlvR9gfSe7BJC6BVCGAgMIg2eLvmbVtfS8jCwQ93ti99fNaPuM3wV8HqM8cKiq/y+ZKSp96Qmvi+V3iug2hbSniBvkvYwOCnrerryQtqD46W6ZUzh9Sb1fz8IvAWMBBauWx+AS+vem1eAoUX3tR9p8OI4YN+sn1utLcDfSM3p35HGG+xfzvcBGEr6gXsbuIS6iY5d2vye3FD3mr9M+kOxeNH2J9W9vmMp2hutqd+0uu/fc3Xv1W1Ar6yfcy0swJqkrsCXgRfrls39vlTle1L13xdnfJckSaqAvHUXSpIkdQpDliRJUgUYsiRJkirAkCVJklQBhixJkqQKMGRJkiRVgCFLkiSpAgxZkiRJFfD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          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}