Wasserman_Chapter_9.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Wasserman_Chapter_9.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyP6mSompZ91KbEvHTOXPvVC",
      "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/sajad13901/Statistics_Wasserman/blob/main/Wasserman_Chapter_9.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "id": "5EuHOEDDemoj",
        "outputId": "f47df893-a8b2-4735-8af8-e0e459c7fca7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Simulated MSE: 0.015\n"
          ]
        }
      ],
      "source": [
        "# Chapter 9, problem 2, part d\n",
        "import numpy as np\n",
        "\n",
        "a = 1.\n",
        "b = 3.\n",
        "n = 10\n",
        "n_sims = 10**6\n",
        "\n",
        "samples = np.random.uniform(low=a, high=b, size=[n_sims, n])\n",
        "a_mle = np.min(samples, axis=1)\n",
        "b_mle = np.max(samples, axis=1)\n",
        "\n",
        "tau_mle = (a_mle + b_mle)/2 \n",
        "tau = (a + b)/2\n",
        "mse = np.mean((tau_mle - tau)**2)\n",
        "print('Simulated MSE: %.3f' %mse)\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Chapter 9, problem 3, part c\n",
        "import numpy as np\n",
        "from scipy.stats import norm\n",
        "\n",
        "data = np.array([ 3.23, -2.50,  1.88, -0.68,  4.43,  0.17,\n",
        "                  1.03, -0.07, -0.01,  0.76,  1.76,  3.18,\n",
        "                  0.33, -0.31,  0.30, -0.61,  1.52,  5.43,\n",
        "                  1.54,  2.28,  0.42,  2.33, -1.03,  4.00,\n",
        "                  0.39])\n",
        "\n",
        "# calc se using delta method\n",
        "n = data.size\n",
        "c = norm.ppf(0.95)\n",
        "se_delta_method =  np.std(data) * np.sqrt((1 + 0.5*c**2)/n)\n",
        "print('se delta method: %.3f' %se_delta_method)\n",
        "\n",
        "# calc se using parametric bootstrap\n",
        "n_sim = 10**5\n",
        "samples = np.std(data) * np.random.randn(n_sims, n) + np.mean(data)\n",
        "tau_boot = c * np.std(samples, axis=1) + np.mean(samples, axis=1)\n",
        "print('se param bootstrap: %.3f' %np.std(tau_boot))"
      ],
      "metadata": {
        "id": "Y4vJWdJMZpQe",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d160ef96-9b06-4dff-d5ae-d3b958e44bf6"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "se delta method: 0.558\n",
            "se param bootstrap: 0.556\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Chapter 9, problem 7, part d\n",
        "import numpy as np\n",
        "from scipy.stats import norm\n",
        "\n",
        "n = 200\n",
        "x1, x2 = 160., 148.\n",
        "p1_hat = x1/n\n",
        "p2_hat = x2/n\n",
        "psi_hat = p1_hat - p2_hat\n",
        "\n",
        "# calc C.I. using delta method\n",
        "se_delta = np.sqrt(p1_hat*(1-p1_hat)/n + p2_hat*(1-p2_hat)/n)\n",
        "c = norm.ppf(0.95)\n",
        "print('90%% C.I. using delta method (%.3f, %.3f)' %(psi_hat-c*se_delta, psi_hat+c*se_delta))\n",
        "\n",
        "# calc C.I. using parametric bootstrap\n",
        "n_sim = 10**5\n",
        "x1_samples = np.random.binomial(n, p1_hat, size=n_sim)\n",
        "x2_samples = np.random.binomial(n, p2_hat, size=n_sim)\n",
        "tau_boot = x1_samples/n - x2_samples/n\n",
        "se_boot = np.std(tau_boot)\n",
        "print('90%% C.I. using param bootstrap (%.3f, %.3f)' %(psi_hat - c*se_boot, psi_hat + c*se_boot))\n"
      ],
      "metadata": {
        "id": "nwpGL5lVV5L5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7b901921-dd27-4405-e90e-e99991535858"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "90% C.I. using delta method (-0.009, 0.129)\n",
            "90% C.I. using param bootstrap (-0.009, 0.129)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Chapter 9, problem 9, part a & b\n",
        "import numpy as np\n",
        "from scipy.stats import norm\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "n = 100\n",
        "mu = 5.\n",
        "data = mu + np.random.randn(n)\n",
        "x_bar = np.mean(data)\n",
        "theta_hat = np.exp(x_bar)\n",
        "c = norm.ppf(0.975)\n",
        "\n",
        "# delta method\n",
        "se_delta = theta_hat/np.sqrt(n) \n",
        "print('95%% C.I. using delta method (%.3f, %.3f)' %(theta_hat - c*se_delta, theta_hat + c*se_delta))\n",
        "\n",
        "# param bootstrap\n",
        "n_sim = 10**5\n",
        "samples_param = x_bar + np.random.randn(n_sim, n)\n",
        "theta_boot = np.exp(np.mean(samples_param, axis=1))\n",
        "se_boot = np.std(theta_boot)\n",
        "print('95%% C.I. using param bootstrap (%.3f, %.3f)' %(theta_hat - c*se_boot, theta_hat + c*se_boot))\n",
        "\n",
        "# non-param bootstrap\n",
        "theta_boot_nonparam = []\n",
        "for _ in range(n_sim):\n",
        "    tmp_data = np.random.choice(data, size=n, replace=True)\n",
        "    theta_boot_nonparam.append(np.exp(np.mean(tmp_data)))\n",
        "se_boot_nonparam = np.std(theta_boot_nonparam)\n",
        "print('95%% C.I. using param bootstrap (%.3f, %.3f)' %(theta_hat - c*se_boot_nonparam, theta_hat + c*se_boot_nonparam))\n",
        "\n",
        "\n",
        "# true dist. of theta_hat, simulation \n",
        "samples = mu + np.random.randn(n_sim, n)\n",
        "x_bar_samples = np.mean(samples, axis=1)\n",
        "x_cdf_org = np.sort(np.exp(x_bar_samples))\n",
        "y_cdf_org = np.linspace(1/n_sim, 1, n_sim)\n",
        "\n",
        "# dist. of theta_hat, delta method \n",
        "x_cdf_delta = np.linspace(100, 220, n)\n",
        "y_cdf_delta = norm.cdf((x_cdf_delta-theta_hat)/se_delta)\n",
        "\n",
        "# dist. of theta_hat, param. bootstratp \n",
        "x_cdf_param = np.sort(theta_boot)\n",
        "y_cdf_param = np.linspace(1/n_sim, 1, n_sim)\n",
        "\n",
        "# dist. of theta_hat, non-param. bootstratp \n",
        "x_cdf_nonparam = np.sort(theta_boot_nonparam)\n",
        "y_cdf_nonparam = np.linspace(1/n_sim, 1, n_sim)\n",
        "\n",
        "print('theta_hat true: %.3f' %np.exp(mu))\n",
        "print('theta_hat MLE : %.3f' %theta_hat)\n",
        "\n",
        "plt.figure(figsize=(12,8))\n",
        "plt.plot(x_cdf_org, y_cdf_org,           'k-', lw=4,  label='true data ECDF')\n",
        "plt.plot(x_cdf_param, y_cdf_param,       'g-', lw=4, label='param boot CDF')\n",
        "plt.plot(x_cdf_nonparam, y_cdf_nonparam, 'b-', lw=4, label='nonparam boot CDF')\n",
        "plt.plot(x_cdf_delta, y_cdf_delta,       'r-', lw=4, label='delta method CDF')\n",
        "plt.legend(loc='best')\n",
        "plt.show()\n"
      ],
      "metadata": {
        "id": "cMx65jwfV5pe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 570
        },
        "outputId": "4f4c72e1-437d-4629-f540-315923b2e1e0"
      },
      "execution_count": 83,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "95% C.I. using delta method (137.373, 204.350)\n",
            "95% C.I. using param bootstrap (136.969, 204.754)\n",
            "95% C.I. using param bootstrap (139.591, 202.132)\n",
            "theta_hat true: 148.413\n",
            "theta_hat MLE : 170.862\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Chapter 9, problem 10, part a\n",
        "import numpy as np\n",
        "from scipy.stats import norm\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "n = 50\n",
        "data = np.random.uniform(0, 1, n)\n",
        "theta_hat = np.max(data)\n",
        "\n",
        "# dist. of theta_hat, formula\n",
        "x_cdf_exact = np.linspace(.9, 1, n)\n",
        "y_cdf_exact = x_cdf_delta**n\n",
        "\n",
        "# dist. of theta_hat, param. bootstratp \n",
        "n_sim = 10**5\n",
        "samples_param = np.random.uniform(0, theta_hat, [n_sim, n])\n",
        "theta_boot = np.max(samples_param, axis=1)\n",
        "x_cdf_param = np.sort(theta_boot)\n",
        "y_cdf_param = np.linspace(1/n_sim, 1, n_sim)\n",
        "\n",
        "# dist. of theta_hat, non-param. bootstratp \n",
        "theta_boot_nonparam = []\n",
        "for _ in range(n_sim):\n",
        "    tmp_data = np.random.choice(data, size=n, replace=True)\n",
        "    theta_boot_nonparam.append(np.max(tmp_data))\n",
        "x_cdf_nonparam = np.sort(theta_boot_nonparam)\n",
        "y_cdf_nonparam = np.linspace(1/n_sim, 1, n_sim)\n",
        "\n",
        "plt.figure(figsize=(8,6))\n",
        "plt.plot(x_cdf_param, y_cdf_param,       'g-', lw=4, label='param boot CDF')\n",
        "plt.plot(x_cdf_nonparam, y_cdf_nonparam, 'r-', lw=4, label='nonparam boot CDF')\n",
        "plt.plot(x_cdf_exact, y_cdf_exact,       'b-', lw=4, label='exact CDF')\n",
        "plt.legend(loc='best')\n",
        "plt.show()\n"
      ],
      "metadata": {
        "id": "t3SyDD4aYFzP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 374
        },
        "outputId": "c3f20909-0fc7-4924-890e-63e01c7626ca"
      },
      "execution_count": 89,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ],
            "image/png": 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Zu3YtSUlJ5Ofnc/LkSQYOHMjmzZvJycnh4osvZvjw4QwePNhxR6nXXnuNpKQkhgwZwk033cSqVatYtGgR9913H0OHDmX37t2O93366ad57rnnOKt0Ln3Dhg2ZOXNmBcfGcPfdd9OhQwc+/PDD4A+2iEgdEO0TuPQ9Yx/btm1jwYIFfPHFF8THx3P77bczf/58pk2bxoQJE/j1r39NXl4eU6dOZdCgQRQVFfHee+/RvHlzjh49yujRo5kwYQJbt27lySefZNWqVSQmJpKZmUnr1q2ZMGECV155JZMnTy733ps3b2bEiBGu+zp8+HC2b9/OxIkTAbjwwguJjY2lYcOGfPnllyE7JiIika6wuJBDOYeq37EK4T4zVhj7+OSTT1i3bp33PtB5eXm0a9cOgEceeYSRI0eSkJDA7NmzAc8SgL/61a/4/PPPiYmJYf/+/Rw+fJjly5dz7bXXkpiYCEDr1q1D3lf/25iuWLHC+34iIvXJwZyDWMr+JnpWpXN/q+fi4vLXjHVmHEbWWqZPn87TTz9dbltGRgY5OTkUFhaSn59PkyZNmD9/Punp6axbt474+Hi6d+/uWOYwEAMHDmTdunVcdNFFrvb/5ptvuPjii8/ovURE6hL/IeoYEwMUu25/8CD4rjzbujU0bRqizrkUkdeMw7WC4sUXX8zChQs5cuQIAJmZmXz//fcA/OQnP+E3v/kNN954I7/85S8ByM7Opl27dsTHx7NixQrvvhdddBHvvPMOGRkZ3teB6pcfvO+++zhUej+2goIC/vKXv1RwbCyzZ8/m4MGDjB8//gyOrohI3VI+jANbr730T7dXt27B9ihwOjP2MWDAAJ588kkuu+wySkpKiI+PZ86cOXz22WfEx8dzww03UFxczLnnnsvy5cu58cYbueqqqxg8eDDJycn069cP8JzlPvTQQ1xwwQXExsYybNgwXn31Va6//npmzpzJ7NmzWbhwIWeffbb3va+44goOHz7MJZdcgrUWYwwzZszwbr/vvvv4zW9+Q25uLqNHj2bFihU0aNCg1o+RiEik8b8vtTGBnWfu3esshyOMtYSiRA39fohIRe5Zeg+/X/N7bznvuQQScnwuGVazhOJvfwsPPlhW/tnP4MUXQ99PLaEoIiJ1VtoJv2HqAKPNf5i6a9dgexQ4hbGIiEQ1/2vGJsBrxpEwTK0wFhGRqFbxbGr3ImECV8SFcbiuYUtk0++FiFSkuKSYAycOOOoCCWNrNUxdTkJCAhkZGfrDKw7WWjIyMkhISAh3V0Qkwhw5eYSikrIvCbdu1JpABqmzsiAnp6zcqBG0bRu6/rkVUV9t6ty5M2lpaaSnp4e7KxJhEhIS6Fzb96cTkYi3N9t5wbdz887A9xXvXFF7v+vFXbtWv4ZBTYioMI6Pj6dHjx7h7oaIiEQJ/zDu0rwLgYRxJFwvhggbphYREQmEfxh3axFYmkbC9WJQGIuISBT7PtuZpt1aBhbGkfC1JlAYi4hIFPM/M+7aIrBTWw1Ti4iIBCnUYaxhahERkQD5D1MHGsYaphYREQlCTkEOmXmZ3nJcTBwdm3Z03T4/Hw4fLivHxECnTqHsoXsKYxERiUrfHyt/VhwbE+u6vf9ZcadOEB8fip4FTmEsIiJRKfVYqqMcrV9rAoWxiIhEqbrytSZQGIuISJTyH6bu3qJ7YO0j5GtNoDAWEZEolZqd6igHemasMBYREQmS/5lxoNeMK1okIlwUxiIiEpX8rxl3b9k9sPY6MxYRETlz+UX5HMo55C3HmJjS5RPdKS6GffucdTozFhERCYD/EPVZzc4iPtb9l4QPHICiorJy69bQtGmoehc4V2FsjBlvjNlhjNlljHmggu1djTErjDHfGGM2GmOuCH1XRUREPL479p2j3LNVz4Da79njLJ99drA9Ck61YWyMiQXmAJcDA4ApxpgBfrv9GnjbWjsMuB74Y6g7KiIictqeLGea9mjZI7D2fmHcM7AsDzk3Z8ajgF3W2j3W2gLgLWCi3z4WaF76vAVwIHRdFBERcfIfpo72MI5zsU8nwPcydxpwjt8+jwEfG2PuApoAl4SkdyIiIhXwH6YO9DvG3zmb0yOwLA+5UE3gmgK8aq3tDFwBvG6MKffaxpjbjDEpxpiU9PT0EL21iIjUN/5hHO1nxm7CeD/QxafcubTO1y3A2wDW2tVAApDo/0LW2pettcnW2uS2bdueWY9FRKTe+y4rtBO4oiGM1wK9jTE9jDEN8EzQWuS3z17gYgBjTH88YaxTXxERCbkTp06QkZfhLcfHxHNWs7Nctz950rmOcWwsdOlS+f61odowttYWAXcCS4FteGZNbzHGPGGMmVC62z3ATGPMBuDvwM3WWltTnRYRkfqr3NKJLbsFtI6x//Xibt0gzs0Mqhrk6u2ttUuAJX51j/g83wqMCW3XREREytudtdtRjvbrxaA7cImISJTZnekM42i/XgwKYxERiTI7M3c6yr1a9wqovcJYREQkSP7D1ApjERGRWuZ/K8yzWwV2Y2mFsYiISBCKSorYm73XURfINeOSkvKzqRXGIiIiAdibvZeikrK1D9s1aUeTBk1ctz90CPLzy8otW0KrVqHs4ZlRGIuISNTwn0ldF4aoQWEsIiJRpNz14tYKYxERkVrlH8Y9W0b/d4xBYSwiIlFkzzGdGYuIiISV/zXjunArTFAYi4hIlLDW1skbfoDCWEREokRGXgbHTx33lhvHN6ZD0w6u2+fmwsGDZeWYGOjaNZQ9PHMKYxERiQq7Mnc5yme3OhtjjOv2qanOcteuEB8fgo6FgMJYRESiQrnvGAc4eWunc32JiBmiBoWxiIhECf/rxYHe8OPbb53lPn2C7VHoKIxFRCQq+IdxoOsY+58ZK4xFREQC5H/NuHfr3gG19z8z7h1Y8xqlMBYRkahQLozbBJamOjMWEREJwvFTxzly8oi3HB8TT5fmXVy3z8mBAwfKyrGx0COw+4XUKIWxiIhEPP+z4p6tehIbE+u+vbM5PXpEzteaQGEsIiJRwD+MA73zViTPpAaFsYiIRIGdGc4LvsGGcSRN3gKFsYiIRIFvM51pGuhM6kievAUKYxERiQLbj253lPsl9guovc6MRUREgmCtLRfGfRP7BvQaOjMWEREJwpGTRxyrNTWJb0KnZp1ct8/MMmRklJUbNoQu7r8VVSsUxiIiEtEqmkkdyGpNO3c7o65XL8/yiZEkwrojIiLiVG7pxABXa/p2lzPqIu16MSiMRUQkwu3I2OEo920T4PXiPc6bg0Ta9WJQGIuISIT7NsM5FbpPm8DS1P/MWGEsIiISoKDDeLeGqUVERM5YiS1hZ6bze0mBhLFFw9QiIiJBSTueRn5RvrfcKqEVbRq1cd3+EB3IySmbed20KbRvH9IuhoTCWEREIlZFQ9QBfa0J55h0nz4QQPNaozAWEZGItS19m6Mc6G0wt+PcPxKvF4PCWEREIti2o84w7p/YP6D2WxngKA8YUMmOYaYwFhGRiBXsAhHbcIZ3/8CyvNYojEVEJGKVOzNuqzNjERGRWnMs/xiHcg55yw1iG9CzVU/X7Y/TjDTKVoSIjdU1YxERkYD4T97q3bo3cTFxrtv7T97q1QsaNAhJ10JOYSwiIhHJf4g60OvF0TJEDQpjERGJUP5nxoHOpI6WyVugMBYRkQi1PcM5k7quTt4ChbGIiESoYG/4oTNjERGRIOQX5bMna4+jLpB1jPNIYA9lM6+NgX6BZXmtUhiLiEjE2XF0BxbrLXdv2Z0mDZq4bv8tfbA+EdetGzRuHNIuhpTCWEREIk59uQ3maQpjERGJOJuPbHaU6/JMalAYi4hIBPIP48HtBwfUXmfGIiIiQSoXxu2CC+M6cWZsjBlvjNlhjNlljHmgkn3+nzFmqzFmizHmzdB2U0RE6ouTBScdM6kNJqCvNRXaOHbivAl1pIdxtTf5NMbEAnOAS4E0YK0xZpG1dqvPPr2BB4Ex1tosY0y7muqwiIjUbVvTtzpmUvds1TOgmdS7SnpSRLy33LFDCS1bRvZAsJvejQJ2WWv3WGsLgLeAiX77zATmWGuzAKy1R0LbTRERqS+CvV68rcT5feQBfYuD7lNNcxPGnYB9PuW00jpffYA+xpgvjDFrjDHjK3ohY8xtxpgUY0xKenr6mfVYRETqNP8wHtR2UEDttxQ7h7T79ykJuk81LVTn7XFAb2AcMAX4P2NMS/+drLUvW2uTrbXJbdu2DdFbi4hIXbI5Pbgz443FA53tB9SNM+P94LM6M3QurfOVBiyy1hZaa78DvgUidAlnERGJZJsOb3KUB7YdWMmeFdtY4tw/aWDdCOO1QG9jTA9jTAPgemCR3z7v4zkrxhiTiGfYeg8iIiIBSD+ZzsGcg95yg9gG9GnTx3X73FzYWXK2o25Q/zoQxtbaIuBOYCmwDXjbWrvFGPOEMWZC6W5LgQxjzFZgBXCftTajpjotIiJ108bDGx3lgW0HEh8bX8ne5W3ZguOe1Gezi6ZNQ9a9GlPtV5sArLVLgCV+dY/4PLfAL0ofIiIiZ2TD4Q2O8pAOQwJqv9GZ5SSxEbgoyF7VvMj+4pWIiNQr/mGc1C4poPYVh3HkUxiLiEjE8B+mDs2ZceRTGIuISEQoLC5ka/pWR11Se/dnxtYqjEVERIKy/eh2CooLvOWzmp1FYuNE1+0PHIDMzLJyY07SM0q+2KMwFhGRiFBuiLp9cEPUg9lEjM89riOZwlhERCJCuZnUQYZxtAxRg8JYREQiRLmZ1AFcLwaFsYiISNCCnUm9yXkXTYWxiIhIII6cPMKhnEPecsPYhgHdBrOgALZtc9YNZlPFO0cghbGIiITdhkPOIeqB7QYSF+PqJpEAbN8ORUVl5S7spRXHQtW9GqcwFhGRsAv1TOpoGqIGhbGIiESAYGdSb3A2VxiLiIgEKtiZ1OvWOctD2FDxjhFKYSwiImFVUFzAtnTn7KtAZlJbC19/7awbwbqKd45QCmMREQmr7Ue3U1hS6C13bt6Z1o1au26/Zw9kZ5eVW5DN2ewOZRdrnMJYRETCyn8mdbBD1MNjN2CC7VQtUxiLiEhYBTt5q6IwjjYKYxERCatgv9bkH8YjYtcH26VapzAWEZGwCmYmdYWTt6IwjN3f3kRERCTEDuUc4sjJI95yQlwCvdv0dt0+NRWyssrKzZpBLxMdaxj70pmxiIiEjf/krUHtBgV0G8xy14uHQ4yJjjWMfSmMRUQkbL4+6BxjDvp68YhgexQeCmMREQmbdQedaTqiY2BpqjAWEREJUrkwPst9mlpb8TB1NFIYi4hIWBzLP0bqsVRvOdbEBjST+vvvITOzrNy0KfRxvwRyRFEYi4hIWHxz8BtHuV9iPxLiEly39z8rHjYMYqI01aK02yIiEu38J28FMkQNFXy/OEqvF4PCWEREwuTrQ840Hd4hsAu+a9c6ywpjERGRAK074BxnHt7RfRiXlMCXXzrrRo0KRa/CQ2EsIiK1Lisvix0ZO7zlGBPD0A5DXbffvh2OHy8rt2oFvd3fuCviKIxFRKTWfbX/K0d5ULtBNGvYzHX71aud5dGjwUTbuok+FMYiIlLr1qStcZRHdxodWHtnc37wg2B7FF4KYxERqXVr9vuFcefgwnh0YM0jjsJYRERqVYkt4cs05+yrQMI4Oxu2bCkrGxPdk7dAYSwiIrXs24xvycovW/ewRcMW9E3s67r92rWeW2Ge1r8/tGgRyh7WPoWxiIjUqtX7nLOvzul8DjHGfRzVtevFoDAWEZFatvaA824dgU7eqmgmdbRTGIuISK3yn0k9stNI122trXuTt0BhLCIitejEqRNsOLzBURfI5K1du5wrNTVr5rlmHO0UxiIiUmu+3P8lJbbEW+7bpi+JjRNdt/c/Kz7nHIiNDVXvwkdhLCIiteaLvV84ymO6jAmofV28XgwKYxERqUVf7PML466BhfGqVc6ywlhERCQARSVFrE5zntqe2+Vc1+2PHYONG511CmMREZEArD+0npyCHG+5beO29G3j/mYfK1c6b/YxaBC0aRPKHoaPwlhERGrFZ6mfOcpju43FBLDU0uefO8sXXBCKXkUGhbGIiNSKz/c603Rst7GBtfcL47GBNY9oCmMREalxJbaE/3z/H8MZJzwAAB7NSURBVEfdBd3cn9rm5EBKirPu/PND0bPIoDAWEZEat+XIFsfiEC0TWjKo3SDX7VevhuLisnLv3tCxYyh7GF4KYxERqXGff+8cYz6v63nExri/W0ddvl4MCmMREakFn33vN3mrq64X+3IVxsaY8caYHcaYXcaYB6rYb5IxxhpjkkPXRRERiWbW2nJnxoFM3srPhy+/dNbVuzA2xsQCc4DLgQHAFGPMgAr2awb8DPjSf5uIiNRfOzN3cvjkYW+5SXwThncc7rr9V1/BqVNl5W7dPI+6xM2Z8Shgl7V2j7W2AHgLmFjBfr8Bfgfkh7B/IiIS5fzPis/tci7xsfHu29fxIWpwF8adgH0+5bTSOi9jzHCgi7X2g6peyBhzmzEmxRiTkp6eHnBnRUQk+gQzRA0KY1eMMTHA74F7qtvXWvuytTbZWpvctm3bYN9aRESiQLnJWwGE8alT8IVzbYk6N5Ma3IXxfqCLT7lzad1pzYBBwKfGmFRgNLBIk7hEROT7Y9+zN3uvt9wwtiGjOo1y3X7VKsjNLSufdRb06hXKHkYGN2G8FuhtjOlhjGkAXA8sOr3RWpttrU201na31nYH1gATrLUpFb+ciIjUF8u/W+4oj+o0ioS4BNftly1zli+9FAK4nXXUqDaMrbVFwJ3AUmAb8La1dosx5gljzISa7qCIiESvpbuXOsoX97g4oPYVhXFdFOdmJ2vtEmCJX90jlew7LvhuiYhItLPWsiJ1haPusrMvc90+IwPWrXPWXXJJKHoWeXQHLhERqRE7MnZw5OQRb7lpg6aM7DTSdfvly53rFyclQfv2oexh5FAYi4hIjVjxnfOseEyXMcTFuBqQBerPEDW4HKYWEREJ1NLdS+lwAm7YBO1OwrgdebDhPs/pbjUPW2JZ9tbjQKL39S7d8iLM3FJ2ulxZ+5Mnw/OBg6AwFhGRkCssLuSzXZ+wdh70Or1y4hefA59X1cxrN2eTyhxvuQGnOP+jXwF5Ie9rJNAwtYiIhFzKgRS67s8pC+IALcM5Jn0eK2l8JkEcFwcJ7r9KFS4KYxERCbmPd39Mw6Izb+8fxpeyrJI9qzF9elSEsYapRUQk5D7YWcFSBZ07w113ee7aUcWjqCSG5b/6kWNE+tIHkqH73IrbQMX13brBmDG184GDpDAWEZGQysjNIOVACuXuidyxI9x/f7XtV30O2T5B3KYNDPufyXV6LLcOfzQREQmHj3d/jMVWv2Ml/vUvZ/nyyyGmjqdVHf94IiJS25bsWlL9TlXwD+Orrgrq5aKCwlhEREKmxJbw0a6Pzrj97t2wbVtZOS4OLnN/B82opTAWEZGQSTmQwtHco2fc3v+s+PzzoWXLIDsVBRTGIiISMh/u/DCo9osXO8v1YYgaFMYiIhJCwVwvPn4cPvvMWXfllUF2KEoojEVEJCTST6azdv/aM26/dCkU+dwopG9f6N07BB2LAgpjEREJCf+vNPVpE1iS+l8vri9nxaAwFhGREPG/69aYLu7vflVcDEv8RrgVxiIiIgEoKC4oF8ajO4923X7VKjjqMwm7ZcuouZNlSCiMRUQkaB/u/JDjp457y+2atCOpfZLr9u+84yxffjnEx4eqd5FPYSwiIkF7e+vbjvKk/pOIjYl11bakBN5911l37bWh6ll0UBiLiEhQcgtzWbRjkaNuyqAprtuvXg0HDpSVmzaF8eND1bvooDAWEZGgLN21lJyCHG+5Y9OOnNvlXNft/Yeor7wSGjUKVe+ig8JYRESC8u425xjztQOuDWqIevLkUPUseiiMRUTkjOUX5bP4W+c9LCcNmOS6/ZdfQlpaWblxY8/krfpGYSwiImfskz2fOGZRt2/SPqAh6oULneUf/cgTyPWNwlhERM7Ym5vfdJR/3O/HxMXEuWprbfkwrm+zqE9TGIuIyBk5ceoE7217z1F3/aDrXbf/8kvYu7es3KgRXHFFqHoXXRTGIiJyRt7d9i55RXnectcWXRnbbazr9m+84SxfcQU0aRKq3kUXhbGIiJyR1za85ihPHTyVGOMuVgoK4O9/d9bdeGOoehZ9FMYiIhKwvdl7+TT1U0fdTUNuct1+yRLIzCwrt25df4eoQWEsIiJnYP7G+Y7lEkeeNZJ+if1ct3/9dWf5+uuhYcNQ9S76KIxFRCQg1lpe3+hM05uS3J8VZ2bCYudXk7nJffM6SWEsIiIBWXdwHduObvOW42LiAppFvWABFBaWlXv3hnPOCWUPo4/CWEREAvL6BudZ8RW9r6Btk7au27/mnPfFtGlgTCh6Fr0UxiIi4lphcSF/3+ycBh3IEPXOnbBmjbNu6tRQ9Cy6KYxFRMS1pbuXkp6b7i23TGjJlX2udN3+r391lseOhe7dQ9S5KKYwFhER1/y/W/z/Bvw/EuISXLUtKIlj3jxn3fTpoepZdFMYi4iIK8fyj7FoxyJH3bQh01y3fy9rHOllJ9W0aAHXXReq3kU3hbGIiLiyYPMCThWf8pZ7tuoZ0ApNc9OvcZRvuqn+3v7Sn8JYRESqZa3lpbUvOepuSroJ43Ia9Hb68umJZEfdT34Ssu5FPYWxiIhU67PvP2Pzkc3ecqyJ5ZZht7hu/2ecyXveeTBoUMi6F/UUxiIiUq0/rv2jo/zjfj+mS4surtrmkcCr3OyomzUrVD2rGxTGIiJSpb3Ze/nHtn846u4YeYfr9gu4jmO08pbbtIFJk0LWvTpBYSwiIlX669d/pdgWe8v9Evsxrvs4V20t8AJ3O+r+678gwd23oeoNhbGIiFSqsLiQv37jvFPHz875meuJW59wMRsZ4i0boyHqiiiMRUSkUv/Y9g/2n9jvLTeKa8SUQVNct3+Oex3lq6+Gs88OWffqDIWxiIhUyFrLi1++6KibNmQaLRJauGq/eXcjljLeUXfvvZXsXM8pjEVEpEIr965kTZpzVYf/Pue/Xbf//ZsdHOUfNNnID34Qkq7VOQpjERGp0LOrnnWUx/caz4C2A1y1PXQI5i9t46i7p8P8kPWtrlEYi4hIOdvSt7H428WOugfGPOC6/ezZUFBYFjE92c2PW30Wsv7VNa7C2Bgz3hizwxizyxhT7l/DGPMLY8xWY8xGY8wnxphuoe+qiIjUlsc+e8xRHtFxBGO7jXXVNiMDXnLeOZOf8yKxpiREvat7qg1jY0wsMAe4HBgATDHG+I9TfAMkW2uTgIXAM6HuqIiI1I6vD37N21vedtQ9cN4Drr/O9MILcOJEWTmRdGYwr/IG4urMeBSwy1q7x1pbALwFTPTdwVq7wlqbW1pcA3QObTdFRKS2PLT8IUd5WIdhXNP/mkr2dsrM9AxR+7qfZ2hCbsUNBHAXxp2AfT7ltNK6ytwCfBhMp0REJDw+//5zPtr1kaPufy76H2KMuylGFZ0V384fK28gAMSF8sWMMVOBZOCCSrbfBtwG0LVr11C+tYiIBMlay4OfPOioO7/r+YzvNb6SFk6ZmfC//+usu49ndVbsgpv/1dkP+C7N0bm0zsEYcwnwEDDBWnvKfzuAtfZla22ytTa5bdu2Z9JfERGpIUt2LmHVvlWOuqcvftr1teLf/97vrLhloc6KXXITxmuB3saYHsaYBsD1wCLfHYwxw4A/4wniI6HvpoiI1KQSW1LuWvGPev+IMV3HuGp/4IBniNrXfVMP0pSToepinVZtGFtri4A7gaXANuBta+0WY8wTxpgJpbs9CzQF3jHGrDfGLKrk5UREJAIt2LyADYc3OOr+56L/cd3+kUcg12c0um1buH2Szs3ccnXN2Fq7BFjiV/eIz/NLQtwvERGpJYXFhTy84mFH3ZRBUxjSYUglLZw2bYJXXnHWPf44NG2s7xW7pTtwiYjUc/O+mcfurN3eclxMHE9c+ITr9vffDyU+udu3L9x6ayh7WPcpjEVE6rG8wjye+NwZvLcMu4VerXu5ar9sGXzk/CYUzzwD8fGh6mH9oDAWEanHXvrqJQ6cOOAtJ8Ql8PDYh6toUaawEO65x1k3dixcdVUoe1g/KIxFROqp7PxsfvvFbx11d426i07Nq7qvU5nZsz3Xi3099xy4/CaU+FAYi4jUU0+vfJrMvExvuXnD5vxyzC9dtd23Dx591Fl3000wcmQoe1h/KIxFROqhL9O+5JkvnGv63PuDe2nTuE0lLZx+/nM46fMV4pYtPWfFcmYUxiIi9UxBcQG3Lr4Vi/XWdWzakZ+P/rmr9kuWwD/+4ax7+mlo1y6UvaxfFMYiIvXMk58/yeYjmx118ybOo1nDZtW2PXEC7rjDWTdqFNx2Wyh7WP8ojEVE6pEtR7bw9MqnHXXThkxzvRjEvfdCampZOSYG5s71/JQzp8MnIlJP5Bflc93C6ygqKfLWtW/Snhd++EIVrcp89BG8/LKz7r//G4YNC2Uv6yeFsYhIPfHoikfZkr7FUffSFS/RulHrattmZcEttzjr+vaFp54KZQ/rL4WxiEg9sGrfKp5d9ayj7sbBNzKp/yRX7e+6y7My02kxMfC3v0GjRqHsZf2lMBYRqeOOnzrOTe/d5Jg93bl5Z+ZcMcfVWsWvvgrz5zvrHngAzjknxB2tx1yt2iQiItHJWstti29jT9YeR/28CfNokdCi2vab1+Zx+8xYoIG3LilhB4+8PwXeP+VZIcL/Ya3nZ35+qD9OnaUwFhGpw/7y9V9YsGWBo+6OkXdw6dmXVts2JweuHX+cvKL23rpG5DI/fxINt26poqUESsPUIiJ11KbDm/jZRz9z1A1pP4RnL322khZlrIVZs2B7ZntH/Z/4KYM4wyDu5O6e1/WRwlhEpA7Kzs9m0tuTyCvK89Y1iW/CgskLaBRf/ayr558vf534v5jHdF47sw516lT+ZtbipWFqEZE6psSWcNN7N7Ezc6ej/qUrXqJvYt9q2y9eDPff76wbxCZe4k7PHT5Gj/ZMpzbG89P/UVF9hw5azqkKCmMRkTrEWsv9y+5n8beLHfW3DruVm4feXG37jRvhhhs8w9SnteAYC5lMY/Kgd28YMiTEvRYNU4uI1CHPrnqW51c/76gb3nE4f7jiD9W2PXAArrrKM3HrtFhTzDtcS1++DXVXxYfCWESkjnjlm1f45b+d6xG3b9Kef17/TxLiEqpsm5EBl14Ke/c662f3/gOX8u9Qd1X8KIxFROqAJTuXMHPxTEddswbNWHLjEjo371xl2xMn4IorYOtWZ/0dd8DtnRaFuqtSAYWxiEiU+2LvF0x6exLFtthb1zC2IYumLGJ4x+FVts3Ph6uvhq++ctZPmAAvvlgTvZWKKIxFRKLYhkMb+NGbPyK/yHm3q/nXzGdc93FVtj150nON+JNPnPUXXggLFkCcpvjWGoWxiEiU+mr/V1z6+qVkn8p21L90+UtMGlD1AhAnTsDll8O//S4HjxwJ//wnJFR9iVlCTGEsIhKF/r7p74x9ZSzpuemO+sfHPc4do+6osm1WFlx2GfznP876QYNgyRJo1izUvZXqKIxFRKJIiS3h/mX3c8M/buBU8SnHtrtH383DYx+usn1qKowZA2vWOOuHDYMVKyAxMcQdFld0RUBEJEoUFhcyY9EM3tj4RrltD4x5gKcufqrKJRFTUuDKK+HwYWf9qFHw0UfQqlWoeyxuKYxFRKLAiVMnmPzOZD7e/bGjvkFsA/585Z+rvbvWu+/CtGmQm+usP/98+Ne/oHnzEHdYAqIwFhGJcFvTt3LdwuvYfGSzo75t47Z8cMMHjOw0stK2RUXwq1/BsxUs1HTddfDqq5qsFQkUxiIiEcpay7xv5nHXh3c5Vl8COLvV2Xw09SN6te5VafvDh2HKFM+1YH/33w9PP+1Zw0HCT2EsIhKBjp86zk/+9RPe2vxWuW0jOo7ggxs+oH3T9hW09PjgA5gxA44ccdbHx8NLL8Ftt4W6xxIMhbGISIRJOZDCdQuvY0/WnnLbbhh8A3N/NJdmDSv+/lFuLtx7L/zpT+W3deoECxd6VkCUyKIwFhGJEIXFhTy/+nkeWfEIhSWFjm2N4xsz54o5TB8yvdIZ08uWwaxZsKd8hnPBBZ67arWv/GRawkhhLCISATYc2sDU96aWm6QFkNQ+iQWTF9AvsV+FbY8ehXvugddeK78tNhYefRQefFC3t4xk+qcREQmjzLxMHl3xKH9K+ZNjoYfT7hh5B89d9lyFSyAWFMCcOfD445CdXW4zvXrBG2/AOefURM8llBTGIiJhUFxSzF++/gsPLX+IjLyMcttbJbTirxP+ytX9ry63zVp4/3345S9h587yr20M3HknPPUUNG1aE72XUFMYi4jUouKSYhZuXchTK59i4+GNFe5z4+Ab+f0Pf0+7Ju0c9dZ67pT18MOwbl3Frz9oEPzf/2mSVrRRGIuI1IKikiIWbF7Ak/95ku1Ht1e4T4+WPXjhhy8wsd9ER31JiWclpd/9Dr78suLXbx53kl/3XcjPey4m/rdFnkbWVvwIZNvm8tewJfQUxiIiNSinIIe3Nr/FM188w87MCsaU8cyUfuj8h/jFD37huDackwPz58Pvfw/fflvx68dQzK38hd8UPUy7LemwpSY+hdQ0hbGISA3YcGgDc1Pm8vrG1zlZeLLCfQyGKYOn8LtLfkfn5p299du2wdy5nltVHj9e+Xtcw7s8zqMMqs0E1rJONUJhLCISIll5Wby56U3+7+v/Y8PhDZXuF2tiuTHpRn513q/om9jX0zbL8z3gV1+tfCj6tCuvhMcv/JTh90wOYe9dmDjRc1FaQk5hLCIShOz8bP6x7R+8t/09Pt79cbk1hn3FxcQxfch0HjzvQc5ufTbZ2fD66/D227B0KRQWVtqUuDi44QbP3bUGDwb+6fddpuRkeOABz1Tq04+YGGc5mG2JidC7t+e5hJzCWEQkANZadmftZtnuZXy0+yM+2vURBcUFVbY5q9lZTB8yndtG3IbJ7s7iN2HRIvj006oDGKBtW5g503NnrS5dqnqTs2DSpIA/j0QGhbGISDWOnDzCZ6mfsWzPMpbtWUbqsdRq28SYGC7teSnX9ZxFiyNXsuL9OH54e+UTsfxdeCHceqsnXxs2DK7/EvkUxiIiPopKilh/aD2r961mzf41rN63mu+OfeeusYUudizn2J/R9PBlfP1uU27Z5PmGkBu9e8NNN3ke3buf8UeQKKQwFpF6KyM3g63pW1l/aD3rD61nw+ENbD6yucrrvl4lBo51h8NJtMq6hDbZl5K5uyf7jsazL4A+9OoF114L110HSUm6JFtfKYxFpE6z1pKem87W9K2Ox5b0LRw5eaT6FyiO84Tu0b5wtB+ND/ajw55BHMobSK71LGOYVfpwI44izm26gauaf8ZVzT6jb8NU+JeFf1H5jTioYFtOTsDHQiKXwlhEol5+UT6px1L5Lus7vjv2nfdn6rFU9mTtISu/iqgsjoMTZ0F2FzjexRO8px+ZZ3t+2rI/lblABSsUVimJDVzAZ1zGx1zAZzTLyQFlqfhQGItIRCkuKeZY/jHvIys/y/MzL8tbPnLyCAdzDnLgxAEOnjjI4ZOHnS9SmAB5rSE3EU4OL/3ZDk62h5wOkNPeE8AnzvLUExOy/jfmJCNZy2jWcC6rOI+VtHZ93hyEjh1r/j2kxiiMRSRo1lpOFZ8irzCPvKI8x8/cwlyyT2WXhatPqPr+PL3tRMGJyt+oKB7W3A35PeHUMMhvCfkt4FQLyGsF+a08P4sa18rnbkkWg9nEML5hOF8zjG8YwFbiKL8UYo3q0gXuvrt231NCylUYG2PGA/8LxAJ/sdb+1m97Q+A1YASQAVxnrU0NbVcrVlhcSIktcdRZKp66aCuZ0ljR/tG2b2X7R9u+le0f8n2LiqC4GGstxnf30rYWn2t1vvW2fL33dX3qTem+JbaEkpJiLJ7ntqTE89NaSkqKPdttCVC27+ntp/d1bK/gNYqtp01xSRElJSWl5eKy58WefYptsef1S+utLaGopIjikmKKSoooKi6ksLiQohLPz4LiAk9dief5qaJ88gvzOVV8ilOF+eQXe8r5hXmcKj6FBcexPD0PaeR+6JsBhTFl9U2BZha6nd7Xlu1/+jVMBc9LbDEPf/G7Cv99a9JZ7KcXu+jPNvqxnX5sZxCb6cR+zL//DQ2GgxnhvEkGVHxDjUDq3ewbFwddu3pu1CFRq9owNsbEAnOAS4E0YK0xZpG1dqvPbrcAWdbaXsaY64HfAdfVRIf9zVg0gzc2vlEbbyV1yPMfwS/WhLsXErgSfscJcmgW0ldtzyG6sM/76MF39OA7upNKL3bRhNyKGzZrBuPGQWxsSPsj9Y+bM+NRwC5r7R4AY8xbwETAN4wnAo+VPl8IvGSMMbayUxQRkTPUguxqwziOQtqQQWsyaUu699Gew3TgEO05zFkc4CwO0J7DNKCa22BV5r77FMQSEm7CuBM4vjaXBpxT2T7W2iJjTDbQBjjqu5Mx5jbgNoCuXbueYZdFpD77OS+STwItyHY8WpHlfTQlh5B+XfcXv4Dzz4f4eM+wcHw89OjheYiEQK1O4LLWvgy8DJCcnBySs+a4mDgaxDYoV28q+U/RVPKN+or2j7Z9K9s/EvatbP9w7du4URanYo/7bvCyPm0dl5N996mkHke9qWQf430/x38Epfuf3tf4vYZ/O1NaZ09X+15L9Nv/dN3p1/SWTj83p5+XbjExpc2N51iWbjMxMd66GBODMQZDTGk9fu/v83z3bmjZEm6/3Vlf0TXQarbf693eBEyngNsHtL1BAxg7Fvr0QaQmuQnj/YDv7ck7l9ZVtE+aMSYOaIFnIleNe2XiK7wy8ZXaeCupS34e7g6IiJRxM/1uLdDbGNPDGNMAuB5Y5LfPImB66fPJwHJdLxYREXGn2jPj0mvAdwJL8Xy1aZ61dosx5gkgxVq7CPgr8LoxZheQiSewRURExAVX14yttUuAJX51j/g8zweuDW3XRERE6gd9S1xERCTMFMYiIiJhpjAWEREJM4WxiIhImCmMRUREwkxhLCIiEmYKYxERkTBTGIuIiISZwlhERCTMTLhuIW2MSQe+D8ubBy4Rv+UgpVo6ZoHR8QqcjlngdMwCE+rj1c1a27aiDWEL42hijEmx1iaHux/RRMcsMDpegdMxC5yOWWBq83hpmFpERCTMFMYiIiJhpjB25+VwdyAK6ZgFRscrcDpmgdMxC0ytHS9dMxYREQkznRmLiIiEWb0PY2PMeGPMDmPMLmPMAxVsf8EYs7708a0x5pjPtmKfbYtqt+fh4+KYdTXGrDDGfGOM2WiMucJn24Ol7XYYY35Yuz0PjzM9XsaY7saYPJ/fsbm13/vwcHHMuhljPik9Xp8aYzr7bJtujNlZ+pheuz0PjyCPV737O2aMmWeMOWKM2VzJdmOMmV16PDcaY4b7bKuZ3y9rbb19ALHAbqAn0ADYAAyoYv+7gHk+5Zxwf4ZIPGZ4rrP8tPT5ACDV5/kGoCHQo/R1YsP9mSL4eHUHNof7M0ToMXsHmF76/CLg9dLnrYE9pT9blT5vFe7PFKnHq7RcH/+OjQWGV/bfF3AF8CFggNHAlzX9+1Xfz4xHAbustXustQXAW8DEKvafAvy9VnoWudwcMws0L33eAjhQ+nwi8Ja19pS19jtgV+nr1WXBHK/6ys0xGwAsL32+wmf7D4Fl1tpMa20WsAwYXwt9Dqdgjle9ZK39HMisYpeJwGvWYw3Q0hjTkRr8/arvYdwJ2OdTTiutK8cY0w3P2dxyn+oEY0yKMWaNMebHNdfNiOLmmD0GTDXGpAFL8IwouG1b1wRzvAB6lA5ff2aMOb9Gexo53ByzDcA1pc+vBpoZY9q4bFvXBHO8oH7+HatOZce0xn6/6nsYB+J6YKG1ttinrpv13J3lBuBFY8zZ4elaxJkCvGqt7YxnuOd1Y4x+1ypX2fE6CHS11g4DfgG8aYxpXsXr1Cf3AhcYY74BLgD2A8VVN6nXqjpe+jsWAer7H8j9QBefcufSuopcj98QtbV2f+nPPcCnwLDQdzHiuDlmtwBvA1hrVwMJeO7xGsjxrivO+HiVDudnlNavw3NdsE+N9zj8qj1m1toD1tprSv9H5aHSumNu2tZBwRyv+vp3rDqVHdMa+/2q72G8FuhtjOlhjGmAJ3DLzSY0xvTDc7F+tU9dK2NMw9LnicAYYGut9Dq83ByzvcDFAMaY/njCJb10v+uNMQ2NMT2A3sBXtdbz8Djj42WMaWuMiS2t74nneO2ptZ6HT7XHzBiT6DPa8iAwr/T5UuCy0v8+WwGXldbVZWd8vOrx37HqLAKmlc6qHg1kW2sPUpO/X+Ge1RbuB55hwW/xnHU8VFr3BDDBZ5/HgN/6tTsX2ITnWswm4JZwf5ZIOWZ4Jot8UXps1gOX+bR9qLTdDuDycH+WSD5ewCRgS2nd18BV4f4sEXTMJgM7S/f5C9DQp+0MPJMDdwH/Fe7PEsnHq77+HcMzynkQKMRz3fcWYBYwq3S7AeaUHs9NQHJN/37pDlwiIiJhVt+HqUVERMJOYSwiIhJmCmMREZEwUxiLiIiEmcJYREQkzBTGIiIiYaYwFhERCTOFsYiISJj9fzpqlw4lUtftAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}