W1D2_Tutorial1

w1d2_tutorial1.ipynb

{
  "cells": [
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      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/gist/xanderladd/3239c32b208e18e7af0b5f96a15285d0/w1d2_tutorial1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "fUYwAlgO1YuB"
      },
      "source": [
        "# Tutorial 1: Linear regression with MSE\n",
        "\n",
        "**Week 1, Day 2: Model Fitting**\n",
        "\n",
        "**By Neuromatch Academy**\n",
        "\n",
        "**Content creators**: Pierre-Étienne Fiquet, Anqi Wu, Alex Hyafil with help from Byron Galbraith\n",
        "\n",
        "**Content reviewers**: Lina Teichmann, Saeed Salehi, Patrick Mineault,  Ella Batty, Michael Waskom"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "uEDFqfY_1YuG"
      },
      "source": [
        "<p align='center'><img src='https://github.com/NeuromatchAcademy/widgets/blob/master/sponsors.png?raw=True'/></p>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "FKItwVfj1YuG"
      },
      "source": [
        "___\n",
        "# Tutorial Objectives\n",
        "\n",
        "*Estimated timing of tutorial: 30 minutes*\n",
        "\n",
        "This is Tutorial 1 of a series on fitting models to data. We start with simple linear regression, using least squares optimization (Tutorial 1) and Maximum Likelihood Estimation (Tutorial 2). We will use bootstrapping to build confidence intervals around the inferred linear model parameters (Tutorial 3). We'll finish our exploration of regression models by generalizing to multiple linear regression and polynomial regression (Tutorial 4). We end by learning how to choose between these various models. We discuss the bias-variance trade-off (Tutorial 5) and Cross Validation for model selection (Tutorial 6).\n",
        "\n",
        "In this tutorial, we will learn how to fit simple linear models to data.\n",
        "- Learn how to calculate the mean-squared error (MSE) \n",
        "- Explore how model parameters (slope) influence the MSE\n",
        "- Learn how to find the optimal model parameter using least-squares optimization\n",
        "\n",
        "---\n",
        "\n",
        "**Acknowledgements:** \n",
        "- We thank Eero Simoncelli. Much of today's tutorials are inspired by exercises assigned in his mathtools class."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "cellView": "form",
        "execution": {},
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 501
        },
        "id": "Gtsrw7QL1YuH",
        "outputId": "adac8f1c-167c-4cfd-ef80-c0b3f016d4e5"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.lib.display.IFrame at 0x7f8e4d6aeb50>"
            ],
            "text/html": [
              "\n",
              "        <iframe\n",
              "            width=\"854\"\n",
              "            height=\"480\"\n",
              "            src=\"https://mfr.ca-1.osf.io/render?url=https://osf.io/2mkq4/?direct%26mode=render%26action=download%26mode=render\"\n",
              "            frameborder=\"0\"\n",
              "            allowfullscreen\n",
              "        ></iframe>\n",
              "        "
            ]
          },
          "metadata": {},
          "execution_count": 1
        }
      ],
      "source": [
        "# @title Tutorial slides\n",
        "\n",
        "# @markdown These are the slides for the videos in all tutorials today\n",
        "from IPython.display import IFrame\n",
        "IFrame(src=f\"https://mfr.ca-1.osf.io/render?url=https://osf.io/2mkq4/?direct%26mode=render%26action=download%26mode=render\", width=854, height=480)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "-QxNBqPD1YuI"
      },
      "source": [
        "---\n",
        "# Setup"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "cellView": "both",
        "execution": {},
        "id": "dNaLSz_f1YuI"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "cellView": "form",
        "execution": {},
        "id": "PVaHJNEf1YuJ"
      },
      "outputs": [],
      "source": [
        "#@title Figure Settings\n",
        "import ipywidgets as widgets       # interactive display\n",
        "%config InlineBackend.figure_format = 'retina'\n",
        "plt.style.use(\"https://raw.githubusercontent.com/NeuromatchAcademy/course-content/main/nma.mplstyle\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "cellView": "form",
        "execution": {},
        "id": "GfJXfBwn1YuJ"
      },
      "outputs": [],
      "source": [
        "#@title Plotting Functions\n",
        "\n",
        "def plot_observed_vs_predicted(x, y, y_hat, theta_hat):\n",
        "  \"\"\" Plot observed vs predicted data\n",
        "\n",
        "  Args:\n",
        "    x (ndarray): observed x values\n",
        "    y (ndarray): observed y values\n",
        "    y_hat (ndarray): predicted y values\n",
        "    theta_hat (ndarray):\n",
        "  \"\"\"\n",
        "  fig, ax = plt.subplots()\n",
        "  ax.scatter(x, y, label='Observed')  # our data scatter plot\n",
        "  ax.plot(x, y_hat, color='r', label='Fit')  # our estimated model\n",
        "  # plot residuals\n",
        "  ymin = np.minimum(y, y_hat)\n",
        "  ymax = np.maximum(y, y_hat)\n",
        "  ax.vlines(x, ymin, ymax, 'g', alpha=0.5, label='Residuals')\n",
        "  ax.set(\n",
        "      title=fr\"$\\hat{{\\theta}}$ = {theta_hat:0.2f}, MSE = {np.mean((y - y_hat)**2):.2f}\",\n",
        "      xlabel='x',\n",
        "      ylabel='y'\n",
        "  )\n",
        "  ax.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "xZVCLliK1YuK"
      },
      "source": [
        "---\n",
        "# Section 1: Mean Squared Error (MSE)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "cellView": "form",
        "execution": {},
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 581,
          "referenced_widgets": [
            "ad07d56ee4694a0fa6a9ef86404899bc",
            "6d8b1eebba264c439a4680098e387286",
            "d4ee84db138b4de68c57b503fa0ddf23",
            "a4d4ce1abd554fba945a6bec91462048",
            "c03c6166e1f5469190234e00657be523",
            "31ffb065acae4c06917cf0c6e2a0d68f"
          ]
        },
        "id": "mPYaJsA51YuL",
        "outputId": "56b15d88-1a7a-414a-f4ed-faf6297a9138"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Tab(children=(Output(), Output()), _titles={'0': 'Youtube', '1': 'Bilibili'})"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "ad07d56ee4694a0fa6a9ef86404899bc"
            }
          },
          "metadata": {}
        }
      ],
      "source": [
        "# @title Video 1: Linear Regression & Mean Squared Error\n",
        "from ipywidgets import widgets\n",
        "\n",
        "out2 = widgets.Output()\n",
        "with out2:\n",
        "  from IPython.display import IFrame\n",
        "  class BiliVideo(IFrame):\n",
        "      def __init__(self, id, page=1, width=400, height=300, **kwargs):\n",
        "          self.id=id\n",
        "          src = 'https://player.bilibili.com/player.html?bvid={0}&page={1}'.format(id, page)\n",
        "          super(BiliVideo, self).__init__(src, width, height, **kwargs)\n",
        "\n",
        "  video = BiliVideo(id=\"BV1tA411e7NW\", width=854, height=480, fs=1)\n",
        "  print('Video available at https://www.bilibili.com/video/{0}'.format(video.id))\n",
        "  display(video)\n",
        "\n",
        "out1 = widgets.Output()\n",
        "with out1:\n",
        "  from IPython.display import YouTubeVideo\n",
        "  video = YouTubeVideo(id=\"HumajfjJ37E\", width=854, height=480, fs=1, rel=0)\n",
        "  print('Video available at https://youtube.com/watch?v=' + video.id)\n",
        "  display(video)\n",
        "\n",
        "out = widgets.Tab([out1, out2])\n",
        "out.set_title(0, 'Youtube')\n",
        "out.set_title(1, 'Bilibili')\n",
        "\n",
        "display(out)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "eIH_bCLv1YuL"
      },
      "source": [
        "This video covers a 1D linear regression and mean squared error.\n",
        "\n",
        "<details>\n",
        "<summary> <font color='blue'>Click here for text recap of video </font></summary>\n",
        "\n",
        "**Linear least squares regression** is an old but gold  optimization procedure that we are going to use for data fitting. Least squares (LS) optimization problems are those in which the objective function is a quadratic function of the\n",
        "parameter(s) being optimized.\n",
        "\n",
        "Suppose you have a set of measurements: for each data point or measurement, you have $y_{i}$ (the \"dependent\" variable) obtained for a different input value, $x_{i}$ (the \"independent\" or \"explanatory\" variable).  Suppose we believe the measurements are proportional to the input values, but are corrupted by some (random) measurement errors, $\\epsilon_{i}$, that is:\n",
        "\n",
        "\\begin{equation}\n",
        "y_{i}= \\theta x_{i}+\\epsilon_{i}\n",
        "\\end{equation}\n",
        "\n",
        "for some unknown slope parameter $\\theta.$ The least squares regression problem uses **mean squared error (MSE)** as its objective function, it aims to find the value of the parameter $\\theta$ by minimizing the average of squared errors:\n",
        "\n",
        "\\begin{equation}\n",
        "\\min _{\\theta} \\frac{1}{N}\\sum_{i=1}^{N}\\left(y_{i}-\\theta x_{i}\\right)^{2}\n",
        "\\end{equation}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "vZI9gFhg1YuM"
      },
      "source": [
        "We will now explore how MSE is used in fitting a linear regression model to data. For illustrative purposes, we will create a simple synthetic dataset where we know the true underlying model. This will allow us to see how our estimation efforts compare in uncovering the real model (though in practice we rarely have this luxury).\n",
        "\n",
        "First we will generate some noisy samples $x$ from [0, 10) along the line $y = 1.2x$ as our dataset we wish to fit a model to."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "cellView": "form",
        "execution": {},
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "YfY1E7hh1YuM",
        "outputId": "6d978c81-0458-4328-c76d-5baa0664bb8b"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ],
            "image/png": 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Ws2FGC8eCsKU9f/Kezz94wLq7z/54KWV097TLvkopL7bxs9/UxhoAAIChMz0xJlzhWNJG1J57/9P7kQPW3fvMf+IBAABgCDnZ0kdVVb35sDW7p1+e6EE5AAAAQA2ELe3ZuOfzh5L8wT7rHtpnDwAAcEyY8wF0m7ClPf/uns8fyf5hyyO7H//gsHktAABAb80vr+XK3FJurKzf9+zc5Hguz065KhiohZkt7bn3BqIv3HfVK89+pYu1AAAAR/T8zVu5eG1hz6AlSW6srOfitYW8cPN2jysDTiJhS3sWk9za/fwv7bWglPJpSb5498v39aIoAADgcPPLa3n6+svZqQ5et1MlT11/KfPLa70pDDixhC1tqKqqSvLDu19+ZSnljXss+5tJRpN8IsmP9KYyAADgMFfmlg4NWu7aqZKrc0vdLQg48YYubCmlPFxKadx95ZV/Bg/d+/1Syuhrtv6jJB/KnSG4P11KefPu+31qKeWbkvyD3XXfX1XVYi/+LAAAwMEWVzf2bR3az8LKehZX3XcBdG7owpYkv5jkd+55vWH3+3/7Nd//7ns3VVX1+0nemuR3k3x+kg+UUv4gyWaS/y3Jp+ZO+9A7uv9HAAAA2tFpS5BWIuBBDGPY0rGqql5M8gVJvjPJUpJPSfKHSf51krcneUtVVR/rX4UAAMC9Nre2e7oPIBnCq5+rqnrjA+5fTfLf774AAIBjbPR0Z7/ydLoPIBnCsAUAABgerWajo33/fuNjedfcUkZPn0qr2cj0xFjNlQEnmbAFAAA4saYnxnJucvzIQ3K/9+d+41Vfn5scz+XZqY7DG2C4mNkCAACcaJdnpzJSHuw9bqys5+K1hbxw83Y9RQEnmrAFAAA40VrNRp45/9gDBy47VfLU9ZfcVAQcStgCAACceBfOnslzT85kZnL8gd5np0quzi3VVBVwUpnZAgAADIVWs5FWs5HF1Y3ML69lc2s7H/n4dr73537zSO+zsLKexdUNQ3OBfQlbAACAoTI9MfbJoOTd8ysdvcf88pqwBdiXNiIAAGBobW5t93QfMByELQAAwNAaPd3ZYf9O9wHDQdgCAAAMrVaz0dN9wHAQtgAAAENremIs5454Q9HM5Lh5LcCBhC0AAMBQuzw7lZHS3tqRklyanepuQcDAE7YAAABDrdVs5Mv+1CNtrf0rTzyqhQg4lLAFAAAYavPLa/k/fvGDba39Z7/w25lfXutyRcCgE7YAAABD7crcUnaq9tbuVMnVuaXuFgQMPGELAAAwtBZXN3JjZf1IexZW1rO4utGlioCTQNgCAAAMrU5bgrQSAQcRtgAAAENrc2u7p/uA4SBsAQAAhtbo6VM93QcMB2ELAAAwtDq9xtn1z8BBhC0AAMDQmp4Yy7nJ8SPtmZkcz/TEWJcqAk4CYQsAADDULs9OZaS0t3akJJdmp7pbEDDwhC0AAMBQazUbeeb8Y4cGLiMlefb841qIgEOZ6gQAAAy9C2fP5NGHH8rVuaUsrKzf93xmcjyXZqcELUBbhC0AAAC5c8Kl1WxkcXUj88tr2dzazujpU2k1G2a0HIF/fiBsAQAAeJXpiTHhQAfml9dyZW4pN/Y4GXRucjyXnQxiiJjZAgAAwAN5/uatXLy2sGfQkiQ3VtZz8dpCXrh5u8eVQX8IWwAAAOjY/PJanr7+cnaqg9ftVMlT11/K/PJabwqDPhK2AAAA0LErc0uHBi137VTJ1bml7hYEx4CwBQAAgI4srm7s2zq0n4WV9SyubnSpIjgehC0AAAB0pNOWIK1EnHTCFgAAADqyubXd030wKIQtAAAAdGT09Kme7oNB4W84AAAMucXVjcwvr2Vzazujp0+l1WxkemKs32UxAFrNRk/3waAQtgAAwJCaX17LlbmlPQecnpscz+XZKb8Uc6DpibGcmxw/0pDcmclxYR4nnjYiAAAYQs/fvJWL1xb2/SX5xsp6Ll5byAs3b/e4MgbN5dmpjJT21o6U5NLsVHcLgmNA2AIAAENmfnktT19/OTvVwet2quSp6y+5OYYDtZqNPHP+sUMDl5GSPHv+caelGArCFgAAGDJX5pYODVru2qmSq3NL3S2IgXfh7Jk89+RMPu9P7N8eNDUxlkcefn0Pq4L+EbYAAMAQWVzdONJ8jSRZWFnP4upGlyripPjtD38kv37A35Nf/9CG1jSGhrAFAACGSKctQVqJOIjWNHg1YQsAAAyRza3tnu5jOGhNg1cTtgAAwBAZPX2qp/s4+bSmwf2ELQAAMEQ6vQnGDTLsR2sa3E/YAgAAQ2R6YiznJsePtGdmcjzTE/vfMsNw05oG9xO2AADAkLk8O5WR0t7akZJcmp3qbkEMNK1pcD9hCwAADJlWs5Fnzj92aOAyUpJnzz+uhYgDaU2D+wlbAABgCF04eybPPTmTmX1aimYmx/PckzN529k39LgyBo3WNLifc1sAADCkWs1GWs1GFlc3Mr+8ls2t7YyePpVWs+EXYY7k8uxULl5baOv6Z61pDANhCwAADLnpiTHhCg/kbmva09dfPjBw0ZrGsBC2AAAA8MAunD2TRx9+KFfnlrKwsn7f85nJ8VyanRK0MBSELQAAANRCaxrcIWwBAADok5MaSmhNY9gJWwAAAHpsfnktV+aWcmOPdptzk+O5rN0GBpqrnwEAAHro+Zu3cvHawp5BS5LcWFnPxWsLeeHm7R5XBtRF2AIAANAj88trh97YkyQ7VfLU9Zcyv7zWm8KAWglbAAAAeuTK3NKhQctdO1VydW6puwUBXSFsAQAA6IHF1Y19W4f2s7CynsXVjS5VBHSLsAUAAKAHOm0J0koEg0fYAgAA0AObW9s93Qf0j7AFAACgB0ZPn+rpPqB/hC0AAAA90Go2eroP6B9hCwAAQA9MT4zl3OT4kfbMTI5nemKsSxUB3SJsAQAA6JHLs1MZKe2tHSnJpdmp7hYEdIWwBQAAoEdazUaeOf/YoYHLSEmePf+4FiIYUCYtAQAA9NCFs2fy6MMP5ercUhZW1u97PjM5nkuzU4IWGGDCFgAAgB5rNRtpNRtZXN3I/PJaNre2M3r6VFrNhhktcAIIWzpQSvnzSd6eZCbJRJIqyf+X5N8k+f6qqv6fPpYHAAAMiOmJMeEKnEBmthxBueP7krwvyVckOZNkJ3fClskkX53k50op39G/KgEAAIB+ErYczdcn+eu7n/9Ekumqqh6qquqhJG9K8t7dZ+8opXxZH+oDAAAA+kzYcjRft/txOclXVVW1dPdBVVW/njunXX5z91tv63FtAAAAwDEgbDmaz9r9+G+rqtp+7cOqqj6e5Jd2vxztWVUAAADAsSFsOZq7p1b+o1LKfcOFSymfkuQ/3v3yAz2rCgAAADg2hC1H8727H5tJ3lNKad59UEr53CQvJPmcJL+R5Dt7Xx4AAADQb65+PoKqqn6qlPKOJP9zki9P8uWllI/uPn59kt/LnUDmnVVV/cFh71dKebGNH/umTusFAAAAes/JliOqquq7kpxP8u93v/X63VeSfGruzGr59D6UBgAAABwDTrYcQSnloSTvzp2bhj6Q5GuT/OLu4z+V5B8muZjkLaWU2aqqXjro/aqqenMbP/PFJE88SN0AAABA7whbjubbcydo+fUkX1xV1dY9z/7PUsq/zp3biKaTfE+SL+59iQAAAEA/aSNqUyllLMk37n75Pa8JWpIkVVV9NMl37375RaWUz+xVfQAAAMDxIGxp33ReOQn0GwesW7rn88nulQMAAAAcR8KW9u3c8/lnH7Bu4p7PN7pUCwAAAHBMCVva92tJ7l7z/A2llPvm3ZRSXpdXWo0+nDuzXQAAAIAhImxp0+48lh/c/fKJJD9VSnmslDKy+3o8yc8k+dO7a76rqqpP9KNWAAAAoH/cRnQ035JkKslfuuf1sd1nf+yede9J8m29LQ0AAAA4DpxsOYLd0y1/OclXJHlvkt9OUnYf307yz5K8taqqr3aqBQAAAIaTky1HVFVVleQndl8AAAAAr+JkCwAAAECNhC0AAAAANRK2AAAAANRI2AIAAABQI2ELAAAAQI2ELQAAAAA1ErYAAAAA1EjYAgAAAFAjYQsAAABAjYQtAAAAADUStgAAAADUSNgCAAAAUCNhCwAAAECNTvW7AAAAOMzi6kbml9eyubWd0dOn0mo2Mj0x1u+yAGBPwhYAAI6t+eW1XJlbyo2V9fuenZscz+XZqbSajT5UBgD700YEAMCx9PzNW7l4bWHPoCVJbqys5+K1hbxw83aPKwOAgwlbAAA4duaX1/L09ZezUx28bqdKnrr+UuaX13pTGAC0QdgCAMCxc2Vu6dCg5a6dKrk6t9TdggDgCMxsAQDggdU5wHZxdWPf1qH9LKysZ3F1w9BcAI4FYQsAAB3rxgDbTluC5pfXhC0AHAvaiAAA6Ei3Bthubm13VE+n+wCgbsIWAACOrJsDbEdPd3b4utN9AFA3YQsAAEfWzQG2R207etB9AFA3YQsAAEfyIANs2zE9MZZzk+NHev+ZyXHzWgA4NoQtAAAcyYMMsG3X5dmpjJT21o6U5NLsVEc1AUA3CFsAADiSXgywbTUbeeb8Y4cGLiMlefb841qIADhWTBEDAOBIejXA9sLZM3n04YdydW4pC3u0Lc1MjudSB1dLA0C3CVsAADiSXg6wbTUbaTUbWVzdyPzyWja3tjN6+lRazYYZLQAcW8IWAICaDEsgcHeA7VGG5D7oANvpibET+c8SgJNJ2AIA8IDml9dyZW5pz/Dh3OR4Lp/AVpfLs1O5eG2hreufDbAFYNgYkAsA8ACev3krF68t7HvK48bKei5eW8gLN2/3uLLuMsAWAPbnZAsAQIfml9fy9PWXDz3dsVMlT11/KY88/PoTFToYYAsAexO2AAB06MrcUlttNMmdwOXq3NKJCx46GWA7LLNtABhewhYAgA4srm4caUBskiysrGdxdeNEBgvtDLAdxtk2AAwnM1sAADowv7zW032Dblhn2wAwnIQtAAAd2Nza7um+QXbU2TbDGkgBcHIIWwAAOjB6urNu7E73DbJOZtsAwCATtgAAdKDT2SLDNpPkQWbbAMCgErYAAHRgemIs5ybHj7RnZnL8RA7HPYjZNgAMI2ELAECHLs9OZaS0t3akJJdmp7pb0DFktg0Aw0jYAgDQoVazkWfOP3Zo4DJSkmfPPz50LUSJ2TYADCf/KwYA8AAunD2TRx9+KFfnlrKwx2ySmcnxXJqdGsqgJTHbBoDhJGwBAHhArWYjrWYji6sbmV9ey+bWdkZPn0qr2Ri6GS2vdXe2zVGG5A7jbBsAThZhCwBATaYnxoQEe7g8O5WL1xbauv55WGfbAHCymNkCAEBXmW0DwLBxsgUAgK4z2waAYSJsAQCgJ8y2AWBYCFsAAOgps20AOOnMbAEAAACokbAFAAAAoEbCFgAAAIAaCVsAAAAAaiRsAQAAAKiRsAUAAACgRsIWAAAAgBoJWwAAAABqJGwBAAAAqJGwBQAAAKBGwhYAAACAGglbAAAAAGokbAEAAACokbAFAAAAoEbCFgAAAIAaCVsAAAAAaiRsAQAAAKiRsAUAAACgRsIWAAAAgBoJWzpUSvnjpZRvKaX8fCnld0opHyul/HYp5V+VUr61lPIf9LtGAAAAoPdO9buAQVRK+bNJ3pNkYvdbf5TkI0ke2X19SZKfTPJL/agPAAAA6B8nW46olNJK8tO5E7RcT3I2yemqqh5O8mlJziX5tiS/37ciAQAAgL5xsuUISikPJfnhJK9P8q6qqi7d+7yqqo8kubn7AgAAAIaQky1HczHJ5yT5UJJv7nMtAAAAwDEkbDmar9v9+ONVVW31tRIAAADgWNJG1KZSyh9L8p/sfvliKeVMkncmeUvuzG/5cJIbSb6vqqqfbvM9X2xj2Zs6KBcAAADoEydb2vfGJJ+6+/nnJPnlJG9P8plJ/nD341uT/PNSyg+UUko/igQAAAD6y8mW9j18z+fvTPJ7Sb4iyXurqvr47kmXf7T7vW9I8qtJvuOgN6yq6s2H/dDd0y9PdFo0AAAA0FtOtrRv5DWfP1lV1U9UVfXxJKmq6laSr0zyb3fX/J1SijALAAAAhoywpX0b93y+VFXVT752QVVVO7lzuiVJPiPJoSdXAAAAgCMs7OEAACAASURBVJNF2NK+D97z+a8dsO5X7vn8s7tUCwAAAHBMCVvaVFXVel4duOzn3sG4VZfKAQAAAI4pYcvRvG/34+cdsObz7/l8pYu1AAAAAMeQsOVo3r37sVlK+dLXPiyljCT5W7tffjDJL/SqMAAAAOB4ELYcQVVV70/yE7tf/mAp5a/cvXFo9+rn9yR5fPf5390dmAsAAAAMEVcTH93XJ/nMJH8md4KXj5VSPpLk4XvW/P2qqv5JH2oDAAAA+kzYckRVVf1hKeXPJvlrSS4m+cIkY7nTNvT+JO+qqurn+1giAHRscXUj88tr2dzazujpU2k1G5meGOt3WQAAA0XY0oHd9qAf3H0BwMCbX17Llbml3FhZv+/ZucnxXJ6dSqvZ6ENlAACDx8wWABhyz9+8lYvXFvYMWpLkxsp6Ll5byAs3b/e4MgCAwSRsAYAhNr+8lqevv5yd6uB1O1Xy1PWXMr+81pvCAAAGmLAFAIbYlbmlQ4OWu3aq5OrcUncLAgA4AYQtADCkFlc39m0d2s/CynoWVze6VBEAwMkgbAGAIdVpS5BWIgCAg9UetpRS3lNK+ZK63xcAqNfm1nZP9wEADItunGy5kGSulLJUSvnmUspnduFnAAAPaPT0qZ7uAwAYFt1qIypJPifJM0lul1J+vJTyF7v0swCADrSajZ7uAwAYFt0IW96c5B8n2cid0OVTkpxP8jOllJVSyjtLKY904ecCAEcwPTGWc5PjR9ozMzme6YmxLlUEAHAy1B62VFX1i1VVfVOSz0ryZJKfz53QpST57CR/P8lKKeW9pZS3llIM6QWAPrk8O5WR0t7akZJcmp3qbkEAACdA14KOqqo+WlXVu6uq+qIkX5DkSpLfzZ3Q5VSStyZ5b5JbpZT/qZTy2d2qBQDYW6vZyDPnHzs0cBkpybPnH9dCBADQhp6cKqmq6lerqnpHkkeSfHWS/3v3UUnyJ5P83SS/UUr52VLK+VKKyXsA0CMXzp7Jc0/OZGaflqKZyfE89+RM3nb2DT2uDABgMJWqqvrzg0uZTPINSb4+d1qOkuRuMb+T5IeSfG9VVbd7X93xUUp58YknnnjixRdf7HcpAAyBxdWNzC+vZXNrO6OnT6XVbJjRAgAMszYbrl+tbydIqqpaKaX8qyRvSvJluRO03P1DfGaSb0nyP5RS3p3kqaqqfq8/lQLA8JieGBOuAAA8oJ4Ppy2lfFYp5e+UUpaT/MskX3r3UZJfTfKuJLfzyk1Gb0/ygVLKf9jrWgEAAACOqidhS7njraWUn0zyW0n+QZLPyZ1A5Y+S/GiS/7Sqqi+oqupykjcm+S+TfGB3zWSS/7EXtQIAAAA8iK62Ee3eMPRkkr+aO4Nwk1dahZaTfH+Sd1dV9bv37qvuDJL5qVLKTyf5F0n+fJK3dLNWAAAAgDrUHrbs3iT0pbnT/jObO+HK3YBlO3eue/6+qqrmDnuvqqp2Sin/e+6ELWfqrhUAAACgbt042fLBJI3dz++GLL+V5AeSXKuqavWI77e++/F1NdQGAAAA0FXdCFvuDrL9RJKfSfJ9SX626vyO6Q8m+Sd1FAYAAADQbd062XItyQ9UVfXBB32zqqp+OXdmvgAAAAAce90IWz67qqqdLrwvAAAAwLFX+9XPghYAAABgmNUetgAAAAAMs260EQEAwNBYXN3I/PJaNre2M3r6VFrNRqYnxvpdFgB9JGwBAIAOzC+v5crcUm6srN/37NzkeC7PTqXVbPShMgD6TRsRAAAc0fM3b+XitYU9g5YkubGynovXFvLCzds9rgyA40DYAgAARzC/vJanr7+cnergdTtV8tT1lzK/vNabwgA4NoQtAABwBFfmlg4NWu7aqZKrc0vdLQiAY0fYAgAAbVpc3di3dWg/CyvrWVzd6FJFABxHwhYAAGhTpy1BWokAhouwBQAA2rS5td3TfQAMJmELAAC0afT0qZ7uA2AwCVsAAKBNrWajp/sAGEzCFgAAaNP0xFjOTY4fac/M5HimJ8a6VBEAx5GwBQAAjuDy7FRGSntrR0pyaXaquwUBcOwIWwAA4AhazUaeOf/YoYHLSEmePf+4FiKAIWRSFwAAHNGFs2fy6MMP5ercUhZW1u97PjM5nkuzU4IWgCElbAEAgA60mo20mo0srm5kfnktm1vbGT19Kq1mw4wWgCEnbAEAgAcwPTEmXAHgVcxsAQAAAKiRky0A9Iyj9gAADANhCwBdN7+8litzS7mxxxDJc5PjuWyIJAAAJ4g2IgC66vmbt3Lx2sKeQUuS3FhZz8VrC3nh5u0eVwYAAN0hbAGga+aX1/L09ZezUx28bqdKnrr+UuaX13pTGAAAdJGwBYCuuTK3dGjQctdOlVydW+puQQAA0APCFgC6YnF1Y9/Wof0srKxncXWjSxUBAEBvCFsA6IpOW4K0EgEAMOiELQB0xebWdk/3AQDAcSFsAaArRk+f6uk+AAA4LoQtAHRFq9no6T4AADguhC0AdMX0xFjOTY4fac/M5HimJ8a6VBEAAPSGsAWArrk8O5WR0t7akZJcmp3qbkEAANADwhYAuqbVbOSZ848dGriMlOTZ849rIQIA4EQwhRCArrpw9kweffihXJ1bysLK+n3PZybHc2l2StACAMCJIWwBoOtazUZazUYWVzcyv7yWza3tjJ4+lVazYUYLAAAnjrAFgJ6ZnhgTrgAAcOKZ2QIAAABQI2ELAAAAQI2ELQAAAAA1ErYAAAAA1EjYAgAAAFAjYQsAAABAjYQtAAAAADUStgAAAADUSNgCAAAAUCNhSw1KKU+VUqq7r37XAwAAAPSPsOUBlVI+N8nf63cdAAAAwPEgbHkApZSRJD+U5HSSf9PncgAAAIBjQNjyYP7bJH86yY8keV+fawEAAACOgVP9LmBQlVImk3xbkt9N8o4kf7O/FQHAg1lc3cj88lo2t7YzevpUWs1GpifG+l0WAMDAEbZ07geSfFqSv1FV1e+UUvpdDwB0ZH55LVfmlnJjZf2+Z+cmx3N5diqtZqMPlQEADCZhSwdKKW9PMpvk/6qq6ocf4H1ebGPZmzp9f+D4c5KAfnv+5q08ff3l7Oxzl96NlfVcvLaQZ88/nredfUNviwMAGFDCliMqpTyS5NuTfDTJX+9zOcCAcpKA42B+ee3AoOWunSp56vpLeeTh1/t7CQDQBmHL0f3jJJ+e5FuqqvrNB3mjqqrefNia3dMvTzzIzwGOFycJOC6uzC0dGrTctVMlV+eWhC0AAG1wG9ERlFK+Nsl/nuSXknxHn8sBBtBRTxLML6/1pjCGzuLqxp4nqw6ysLKexdWNLlUEAHByCFvaVEqZSPJdST6R5O1VVW33uSRgAHVykgC6odMgTwAIAHA4YUv7nk3yGUm+P8mvlVJG730l+dS7C+/5/qfu92bA8HGSgONkc6uzf2fQ6T4AgGEibGnf5O7Hb0qyscfr6XvW3v3e/9LLAoHjzUkCjpPR052Nbet0HwDAMPH/mADa9KDXNDtJwHHS6aBbA3IBAA4nbGlTVVVfctDzUsq3Jvl7u2tLD0oCeqSua5qdJOA4mZ4Yy7nJ8SO1ts1Mjh8pYAQAGFbaiAAO8PzNW7l4bWHfX0jvXtP8ws3bh76XkwQcN5dnpzLS5r8eGCnJpdmp7hYEAHBCCFsA9lH3Nc13TxIchZMEdFOr2cgz5x87NHAZKcmz5x8X/AEAtEnYArCPblzT7CQBx82Fs2fy3JMzmdknCJyZHM9zT87kbWff0OPKAAAGV6mqNn+ToC9KKS8+8cQTT7z44ov9LgWGyuLqRv7Cd/6/R973vnf8mUNPojx/89ahJ2buniTwCy699KBDoAEATqCOZrKaugiwhwe5pvmwX04vnD2TRx9+KFfnlrKwxyyYmcnxXGpz6C7UaXpiTLgCAFADYQvAHrp9TXOr2Uir2XCSAAAATiBhC8AeenVNs5MEAABw8hiQC7AH1zQDAACdErYA7ME1zQAAQKeELQD7cE0zAADQCWELwD5azUaeOf/YoYHL3WuatRABAACJAbkAB3JNMwAAcFTCFoBDuKYZAAA4CmELQJtc0wwAALTDzBYAAACAGglbAAAAAGokbAEAAACokbAFAAAAoEbCFgAAAIAauY0IoMtcGQ0AAMNF2ALQJfPLa7kyt5QbK+v3PTs3OZ7Ls1NpNRt9qAwAAOgmbUQAXfD8zVu5eG1hz6AlSW6srOfitYW8cPN2jysDAAC6TdgCULP55bU8ff3l7FQHr9upkqeuv5T55bXeFAYAAPSEsAWgZlfmlg4NWu7aqZKrc0vdLQgAAOgpYQtAjRZXN/ZtHdrPwsp6Flc3ulQRAADQa8IWgBp12hKklQgAAE4OYQtAjTa3tnu6DwAAOH5c/QxQo9HTnf3Xaqf7oFsWVzcyv7yWza3tjJ4+lVazkemJsX6XBQAwEPy/e4AatZqNnu6Dus0vr+XK3NKes4fOTY7n8uyUv68AAIfQRgRQo+mJsZybHD/SnpnJcScGOBaev3krF68t7Dvk+cbKei5eW8gLN2/3uDIAgMEibAGo2eXZqYyU9taOlOTS7FR3C4I2zC+v5enrLx96bflOlTx1/SVDnQEADiBsAahZq9nIM+cfOzRwGSnJs+cf15LBsXBlbunQoOWunSq5OrfU3YIAAAaYsAWgCy6cPZPnnpzJzD4tRTOT43nuyZm87ewbelwZ3G9xdWPf1qH9LKysZ3F1o0sVAQAMNgNyAbqk1Wyk1Wy41YVjr9OWoPnlNX+XAQD2IGwB6LLpiTG/kHKsbW5t93QfAMBJp40IAIbc6OnO/t1Lp/sAAE46YQsADLlOhzQb7gwAsDdhCwAMuemJsZzbZ5jzfmYmx7XHAQDsw/lfgAFl8C51ujw7lYvXFtq6/nmkJJdmp7pfFADAgBK2AAyY+eW1XJlb2vOq3nOT47k8O6W9gyNrNRt55vxjefr6ywcGLiMlefb84/6OAQAcQBsRwAB5/uatXLy2sGfQkiQ3VtZz8dpCXrh5u8eVcRJcOHsmzz05k5l9WopmJsfz3JMzedvZN/S4MgCAweJkC8CAmF9eO/TUQZLsVMlT11/KIw+/3ukDjqzVbKTVbGhTAwB4AMIWgAFxZW6prXkayZ3A5erckrCFjk1PjAlXAAA6pI0IYAAsrm7s2zq0n4WV9SyubnSpIgAAYD/CFoABML+81tN9AABA54QtAANgc2u7p/sAAIDOCVsABsDo6c5GbHW6DwAA6JywBWAAdDro1oBcAADoPWELwACYnhjLucnxI+2ZmRx3mwwAAPSBsAVgQFyencpIaW/tSEkuzU51tyAAAGBPwhaAAdFqNvLM+ccODVxGSvLs+ce1EAEAQJ+YnAgwQC6cPZNHH34oV+eWsrCyft/zmcnxXJqdErQAAEAfCVsABkyr2Uir2cji6kbml9eyubWd0dOn0mo2zGgBAIBjQNgCMKCmJ8aEKwAAcAyZ2QIAAABQI2ELAAAAQI2ELQAAAAA1ErYAAAAA1MiAXKA2bscBAAAQtgA1mF9ey5W5pdxYWb/v2bnJ8VyenUqr2ehDZQAAAL2njQh4IM/fvJWL1xb2DFqS5MbKei5eW8gLN2/3uDIAAID+ELYAHZtfXsvT11/OTnXwup0qeer6S5lfXutNYQAAAH0kbAE6dmVu6dCg5a6dKrk6t9TdggAAAI4BYQvQkcXVjX1bh/azsLKexdWNLlUEAABwPAhbgI502hKklQgAADjphC1ARza3tnu6DwAAYFAIW4COjJ7u7Ob4TvcBAAAMCmEL0JFWs9HTfQAAAINC2AJ0ZHpiLOcmx4+0Z2ZyPNMTY12qCAAA4HgQtgAduzw7lZHS3tqRklyanepuQQAAAMeAsOUISimfUUr5q6WUf1pK+ZVSyh+WUj5WSvntUspPllK+rN81Qi+1mo08c/6xQwOXkfL/t3f/wXafdZ3A3580QBoSoOGuUcDS4E2kKnWhtGW8i4JZQZTRtYqAUNEVllGYVqAidZmh6rh0KSy0ruPyo+wiv1E6OqiIkqkrZt20W1DqICSRVArYLDEMJJQUQp7943zv5nCb3Nzkfs+P3Pt6zZw5z/P9Pt97Ps2cJue87/M83+S6yy+yhAgAAFgV7FR5eu7ON/+ZHUny9SQP7x4/XlUfTPJTrbV7JlAfjN0zLzk/jzhvfW7csSe79h28z/nLtmzKldu3CloAAIBVQ9hyetYmuTXJ/0jyodbap5Okqi5I8sokv5DkaUnemOSKiVQIEzA3O5O52Zns3n8oO/ceyOEjR7Nh3drMzc7YowUAAFh1hC2n5wdba7csPNhauzPJ86vqaJIXJnluVf1aa+2ucRcIk7Rt80bhCgAAsOrZs+U0nChoWeCmofbjR1kLAAAAMJ2ELf06MtQ+Z2JVAAAAABMjbOnXk4bad0yqCAAAAGBy7NnSk6p6SJJruu5HWmufWsI1ty/hRz96WYUBAAAAY2VmSw+qak2Styf5tgyWEr14shUBAAAAk2JmSz9uSPL0rv2i1trHl3JRa+3iU43pZr88bhm1AQAAAGNkZssyVdVrc3wmy0taa2+dZD0AAADAZAlblqGqXpPkZV336tbaGyZZDwAAADB5lhGdoaq6PsnVXfflrbXXTbIeAAAAYDoIW85At3RofkbLy1tr10+yHgAAAGB6CFtO04Kg5WozWgAAAIBhwpbTsGCPlpe21l4/yXoAAACA6WOD3CWqqvOT/ErXPZbkV6vq7kUeVy/y4wAAAIAVysyWpVuzoL35FOM3jLAWAAAAYEoJW5aotXZnkpp0HQAAAMB0E7YAnEV27z+UnXsP5PCRo9mwbm3mZmeybfPGSZcFAAAMEbYAnAV27j2QG3bsya37Dt7n3KVbNuWq7VszNzszgcoAAICFbJALMOXee9tncsVNu04YtCTJrfsO5oqbduV9t9015soAAIATEbYATLGdew/kmpvvyLG2+LhjLXnFzR/Pzr0HxlMYAABwUsIWgCl2w449pwxa5h1ryY079oy2IAAA4JSELQBTavf+QyddOnQyu/YdzO79h0ZUEQAAsBTCFoApdaZLgiwlAgCAyRK2AEypw0eOjvU6AACgH8IWgCm1Yd3asV4HAAD0Q9gCMKXmZmfGeh0AANAPYQvAlNq2eWMu3bLptK65bMumbNu8cUQVAQAASyFsAZhiV23fmjW1tLFrKrly+9bRFgQAAJySsAVgis3NzuTVlz/mlIHLmkquu/wiS4gAAGAK2EURYMo985Lz84jz1ufGHXuya9/B+5y/bMumXLl9q6AFAACmhLAF4CwwNzuTudmZ7N5/KDv3HsjhI0ezYd3azM3O2KMFAACmjLAF4CyybfNG4QoAAEw5e7YAAAAA9EjYAgAAANAjYQsAAABAj4QtAAAAAD0StgAAAAD0SNgCAAAA0CNhCwAAAECPhC0AAAAAPRK2AAAAAPRI2AIAAADQI2ELAAAAQI+ELQAAAAA9ErYAAAAA9EjYAgAAANAjYQsAAABAj4QtAAAAAD0StgAAAAD0SNgCAAAA0KO1ky4AFrN7/6Hs3Hsgh48czYZ1azM3O5NtmzdOuiwAAAA4KWELU2nn3gO5Ycee3Lrv4H3OXbplU67avjVzszMTqAwAAAAWZxkRU+e9t30mV9y064RBS5Lcuu9grrhpV953211jrgwAAABOTdjCVNm590CuufmOHGuLjzvWklfc/PHs3HtgPIUBAADAEglbmCo37NhzyqBl3rGW3Lhjz2gLAgAAgNMkbGFq7N5/6KRLh05m176D2b3/0IgqAgAAgNMnbGFqnOmSIEuJAAAAmCbCFqbG4SNHx3odAAAAjIKwhamxYd2Z3Yn8TK8DAACAURC2MDXmZmfGeh0AAACMgrCFqbFt88ZcumXTaV1z2ZZN2bZ544gqAgAAgNMnbGGqXLV9a9bU0sauqeTK7VtHWxAAAACcJmELU2Vudiavvvwxpwxc1lRy3eUXWUIEAADA1LGzKFPnmZecn0ectz437tiTXfsO3uf8ZVs25crtWwUtAAAATCVhC1NpbnYmc7Mz2b3/UHbuPZDDR45mw7q1mZudsUcLAAAAU03YwlTbtnmjcAUAAICzij1bAAAAAHokbAEAAADokbAFAAAAoEfCFgAAAIAeCVsAAAAAeiRsAQAAAOiRsAUAAACgR8IWAAAAgB4JWwAAAAB6JGwBAAAA6JGwBQAAAKBHwhYAAACAHglbAAAAAHokbAEAAADokbAFAAAAoEfCFgAAAIAeCVvOQFVtrKprq+qOqjpcVV+qqtuq6mVVdf9J1wcAAABMztpJF3C2qapHJvnLJBd0h+5J8oAkj+8ez6mq7a21L06kQAAAAGCizGw5DVW1NskHMgha/jnJD7XWHphkfZJnJTmU5LFJ3jGpGgEAAIDJEracnucleUzX/snW2oeTpLV2rLX23iQv7M79SFVtn0SBAAAAwGQJW07P87rnW1prf3OC8+9Jsq9r/+x4SgIAAACmibBliapqfZK5rvvBE41prbUkf9Z1nzKOugAAAIDpImxZugtz/M/r7xcZN3/uW6tq02hLAgAAAKaNuxEt3cOG2p9bZNzwuYclOXiygVV1+xJe99FLGAMAAABMCTNblm7jUPueRcYNn9t40lEAAADAimRmywS11i4+1Zhu9svjxlAOAAAA0AMzW5bu0FB7/SLjhs8dOukoAAAAYEUStizd54faD19k3PC5z590FAAAALAiCVuW7h+SHOva37PIuPlzd7fWTro5LgAAALAyCVuWqLV2T5KdXfeHTzSmqirJU7vun4+jLgAAAGC6CFtOz9u65ydX1WUnOP+MJI/q2r83npIAAACAaSJsOT1vS3JHkkry/qraniRVtaaqnpHkzd24D7bWdkyoRgAAAGCC3Pr5NLTWjlbVjyW5JckFST5cVfdkEFqt64Z9LMlzJlMhAAAAMGlmtpym1tqdSS5K8htJ/j5JS/L1JLcnuTrJE1prX5xYgQAAAMBEmdlyBlprh5K8qnsAAAAA/H9mtgAAAAD0SNgCAAAA0CNhCwAAAECPhC0AAAAAPRK2AAAAAPRI2AIAAADQI2ELAAAAQI+ELQAAAAA9ErYAAAAA9EjYAgAAANAjYQsAAABAj4QtAAAAAD0StgAAAAD0SNgCAAAA0CNhCwAAAECPhC0AAAAAPRK2AAAAAPRI2AIAAADQI2ELAAAAQI+ELQAAAAA9ErYAAAAA9EjYAgAAANAjYQsAAABAj4QtAAAAAD0StgAAAAD0SNgCAAAA0CNhCwAAAECPhC0AAAAAPRK2AAAAAPRI2AIAAADQI2ELAAAAQI+ELQAAAAA9ErYAAAAA9EjYAgAAANAjYQsAAABAj4QtAAAAAD0StgAAAAD0SNgCAAAA0CNhCwAAAECPhC0AAAAAPRK2AAAAAPRI2AIAAADQI2ELAAAAQI+ELQAAAAA9ErYAAAAA9EjYAgAAANAjYQsAAABAj4QtAAAAAD0StgAAAAD0SNgCAAAA0CNhCwAAAECPhC0AAAAAPRK2AAAAAPRI2AIAAADQI2ELAAAAQI+ELQAAAAA9ErYAAAAA9GjtpAsATs/u/Yeyc++BHD5yNBvWrc3c7Ey2bd446bIAAADoCFvgLLFz74HcsGNPbt138D7nLt2yKVdt35q52ZkJVAYAAMAwy4jgLPDe2z6TK27adcKgJUlu3XcwV9y0K++77a4xVwYAAMBCwhaYcjv3Hsg1N9+RY23xccda8oqbP56dew+MpzAAAABOSNgCU+6GHXtOGbTMO9aSG3fsGW1BAAAALErYAlNs9/5DJ106dDK79h3M7v2HRlQRAAAApyJsgSl2pkuCLCUCAACYHGELTLHDR46O9ToAAACWT9gCU2zDujO7O/uZXgcAAMDyCVtgis3Nzoz1OgAAAJZP2LJEVfXQqvr5qnpHVX2iqr5SVfdW1Wer6g+r6icmXSMrz7bNG3Pplk2ndc1lWzZl2+aNI6oIAACAUxG2LN3dSd6a5DlJLszgz+7rSR6e5MeT3FxVf1pV6ydXIivRVdu3Zk0tbeyaSq7cvnW0BQEAALAoYcvSrU1ya5JfSvIdrbVzW2sbkmxJclM35mlJ3jih+lih5mZn8urLH3PKwGVNJdddfpElRAAAABNmF82l+8HW2i0LD7bW7kzy/Ko6muSFSZ5bVb/WWrtr3AWycj3zkvPziPPW58Yde7Jr38H7nL9sy6ZcuX2roAUAAGAKCFuW6ERBywI3ZRC2JMnjkwhb6NXc7EzmZmeye/+h7Nx7IIePHM2GdWszNztjjxYAAIApImzpz5Gh9jkTq4IVb9vmjcIVAACAKSZs6c+Thtp3LOWCqrp9CcMefUbVAAAAABNhg9weVNVDklzTdT/SWvvUJOsBAAAAJsfMlmWqqjVJ3p7k2zJYSvTipV7bWrt4CT//9iSPO+MCAQAAgLFasTNbqurnqqot4/HDS3ypG5I8vWu/qLX28RH9JwEAAABnATNblqGqXpvjM1le0lp76yTrmRbulgMAAMBqtpLDlncn+eNlXP+lxU5W1WuSvKzrXt1ae8MyXmtF2Ln3QG7YsSe37jt4n3OXbtmUq7ZvzdzszAQqAwAAgPFZsWFLa+3eJPeO4mdX1fVJru66L2+tvW4Ur3M2ee9tn8k1N9+RY+3E52/ddzBX3LQr111+UX76km8fb3EAAAAwRit2z5ZR6ZYODQct10+ynmmwc++BRYOWecda8oqbP56dew+MpzAAAACYAGHLaeiCluGlQ6s+aEmSG3bsOWXQMu9YS27csWe0BQEAAMAECVuWaMEeLS+1dGhg9/5DJ9yjZTG79h3M7v2HRlQRAAAATJawZQmq6vwkv9J1jyX51aq6e5HH1Yv8uBXlTJcEWUoEAADASrViN8jt2ZoF7c2nGL9hhLVMlcNHjo71OgAAAJh2wpYlaK3dmaQmXcc02rDuzN5CZ3odAAAATDvLiFiWudmZsV4HAAAA007Yiv1c+wAADrBJREFUwrJs27wxl27ZdFrXXLZlU7Zt3jiiigAAAGCyhC0s21Xbt2bNEhdZrankyu1bR1sQAAAATJCwhWWbm53Jqy9/zCkDlzWVXHf5RZYQAQAAsKLZpZRePPOS8/OI89bnxh17smvfwfucv2zLply5faugBQAAgBVP2EJv5mZnMjc7k937D2Xn3gM5fORoNqxbm7nZGXu0AAAAsGoIW+jdts0bhSsAAACsWvZsAQAAAOiRsAUAAACgR8IWAAAAgB4JWwAAAAB6JGwBAAAA6JGwBQAAAKBHwhYAAACAHglbAAAAAHokbAEAAADokbAFAAAAoEfCFgAAAIAeCVsAAAAAeiRsAQAAAOiRsAUAAACgR8IWAAAAgB4JWwAAAAB6JGwBAAAA6JGwBQAAAKBHwhYAAACAHglbAAAAAHokbAEAAADokbAFAAAAoEfCFgAAAIAeVWtt0jWwiKr6l3PPPXfThRdeOOlSAAAAYFX56Ec/+q7W2nNO9zphy5Srqn1JHpTkzjG95KO750+O6fVgWnjvsxp537Naee+zGnnfs1ot973/SWELy1ZVtydJa+3iSdcC4+S9z2rkfc9q5b3PauR9z2o1qfe+PVsAAAAAeiRsAQAAAOiRsAUAAACgR8IWAAAAgB4JWwAAAAB6JGwBAAAA6JGwBQAAAKBHwhYAAACAHlVrbdI1AAAAAKwYZrYAAAAA9EjYAgAAANAjYQsAAABAj4QtAAAAAD0StgAAAAD0SNgCAAAA0CNhCwAAAECPhC0AAAAAPRK2kCSpqo1VdW1V3VFVh6vqS1V1W1W9rKruP+n6oG9V9dCq+vmqekdVfaKqvlJV91bVZ6vqD6vqJyZdI4xDVb2iqtr8Y9L1wChV1YOq6ler6n9V1ReG/t6/pfsc9JBJ1wh9q6ofqqr3VdU/VdWRqvpqVX26qt5ZVT8w6frgdFXV+qp6WlW9sqpu7t7b859lrl3iz9hcVa+rqk91/08crKqPVNXzq6p6qbM1n6tWu6p6ZJK/THJBd+ieJOckeUDX/1iS7a21L469OBiRqvp6krVDh44k+UaSBw4d+2CSn2qt3TPO2mBcquo7k/xtknXzx1prvXzAgGlTVU9O8u4km7tDX8vgM89wwPLY1trfjrs2GIXuC+PvJnnh0OGvds/nDh17fWvtpWMrDJapqp6U5JaTnP711tq1p7j+4iQfSvLQ7tDhDD4LzX83+FCSH2utfW05dZrZsspV1dokH8ggaPnnJD/UWntgkvVJnpXkUJLHJnnHpGqEEVmb5NYkv5TkO1pr57bWNiTZkuSmbszTkrxxQvXBSFXVmiRvzeDDxd9MuBwYqaqaS/InGQQtNye5JMm61tp5GYTslyb5rSRfmliR0L+fy/Gg5Q+SbGutrW+trU/y6CR/1J17iRm9nIW+mGRHkuuTPDvJ3Uu5qKoenOSPMwhaPpnkktbaxgz+LXhxkq8neWqSNyy3QDNbVrmq+oUkb+m639da+5sF55+d5F1d99+21naMsz4Ylap6cmvtZIl4quq/5fgHlPNba3eNpzIYj6q6KoMPEu9MsjfJqxIzW1h5qmp9kjuSPCrJb7fWrpxwSTAWVXVLkidl8Hf8ha21owvO3y+DL5uPSvKe1tqzx14knIGqOqe19o0Fx+5M8sicYmZLVf1mkldmMMvru1tr+xacvybJf8pgxvt3tdZ2n2mdZrbwvO75loVBS+c9SebfgD87npJg9BYLWjo3DbUfP8paYNyqaksGv8X/lyQvmXA5MGpXZPBl8u4kL59wLTBO39Y9/93CoCVJWmtfz2ApaZJsGFtVsEwLg5bTNP+d9j0Lg5bOb2ewrOicJM9ZxusIW1az7jc9c133gyca0wZTn/6s6z5lHHXBlDgy1D5nYlXAaLw5g+myL22tfWHSxcCIzX+w/v3W2pFFR8LK8unu+Xu7rQO+STez5V933f8ztqpgQrq96s7vuif7/ns4yUe67rK+/wpbVrcLc/w98PeLjJs/961VtWm0JcHUeNJQ+45JFQF9q6oXJNme5MOttd+bdD0wSlX1gByfnXh7VZ1fVW+qqruq6mtVtb+qPlBVPzrJOmFEfrd7nk3y7qqanT/Rfel8Xwazvv4xyevHXx6M3fcMtZfy/fe7lvNiwpbV7WFD7c8tMm743MNOOgpWiO7Wn9d03Y+01j41yXqgL1X18Aw2kvtqvvnuFLBSXZDk/l37URl8gH5Bkm9J8pXu+elJ/riq3tzX7T5hGrTWPpDBUtGvJfmpJHuq6p6quieDvVqelEEgc2lr7csTKxTG53S//z6oqs54iZ2wZXXbONRe7Na2w+c2nnQUrADdHVrensE65yMZ7EoOK8Ubkzw4ybWttU+fajCsAOcNtV+ZwV0mnpFkQ3cnokcm+f3u/PNjDyNWmNbaG5JcnuT/dofOzfHbPt8/g71aHjyB0mASxvr9V9gC8M1uyOC3nEnyotbaxydZDPSlqp6b5Ecz2Azxv0y4HBiXNQvav9Ba+4NuY9C01j6T5FlJ/q4b82sn2tsCzkZVtb6q3pvBbW4/k8H+E/+qezwlyScy2ED61qq6aGKFwgolbFndDg211y8ybvjcoZOOgrNcVb02x2eyvKS19tZJ1gN9qarNGdzm+RtJXnCiu1LACjX8uWVPa+0PFw5orR1L8tqu+9AkF4+jMBiD65P8dJJPJXlia+0vWmsHusdfJPn+JLuTzCT5nQnWCeMy1u+/wpbV7fND7YcvMm743OdPOgrOYlX1miQv67pXd9NuYaW4LoMvkW9K8smq2jD8yPE9LTJ0/P4n+2FwFhlek//JRcZ9Yqj9yBHVAmNTVRuT/Ieu+zsnuhNXa+2rSf5r1/03VfUt46oPJuR0v/9+ubs70RkRtqxu/5DkWNf+nkXGzZ+7u7V2cLQlwfhV1fVJfqXrvry19rpJ1gMjsKV7/sUMfkOz8HHN0Nj5Y68ZZ4EwCt3nlsU2QZw3vDFuG1E5ME7bkswvifvHRcbtGWpvOekoWBmG70C0lO+/n1hkzCkJW1ax1to9SXZ23R8+0ZhuV/6ndt0/H0ddME7d0qGru+7LW2vXT7IeAHo3//nlwkXGDN/ec98Ia4FxOTbUXmy21uahtu0CWOl2Z7B/UXLy778PTPLErrus77/CFt7WPT+5qi47wflnZHCrxCT5vfGUBOPRBS3DS4cELaxIrbUntdbqZI8kvz40dv74L0+wZOjTf++eZ6vq3y082d2Fbj50/1ySj46rMBihTyb5atd+/ok2fq6qc3J8qdEXM9jbBVas1lrL8e+0z6qqC04w7EUZ3KXrG0neuZzXE7bwtiR3ZDB99v1VtT0ZfPCoqmckeXM37oOttR0TqhF6t2CPlpdaOgSwMrXWPpLkD7ruW6rqJ+e/eFbV+UnenWT+Tiz/sdswF85q3X4sb+m6j0vygap6TPcZf01396E/TfJ93Zg3tNa+MYla4UxU1XlVNTP/yPFsY/3w8W5vumGvTXJ3Bpvg/klVXdz9vPtX1S8m+c1u3Jtaa7uXVeMg3GE16xK9W5Jc0B26J4M367qu/7Ek21trXxx3bTAK3Yfrf+q6x5J84RSXvLa19tpTjIGzVlVdm+RVyWBmy2Srgf5108L/NIO7ryTJvRl83jlvaNivt9auHXNpMDJVdW6Sm/PNyyXu7Z4fMHTs3UmuELZwNqmqO7O0Dc3f1lr7uQXXXpzkQxncPCAZLKFbl+R+Xf/Pk/xYa+3eLIOZLaS1dmcGv9H5jQw2DWpJvp7k9gym1T5B0MIKs2ZBe/MpHgsTcQDOIq21ryR5cpIXJPmrJF/J4O/2zyV5T5I5QQsrTTe75Ucy2Bbgj5J8Nsc3g74ryfuTPL219jOCFlaT1trtSb47yesz2CT6fhn8u/DXGfw78bTlBi2JmS0AAAAAvTKzBQAAAKBHwhYAAACAHglbAAAAAHokbAEAAADokbAFAAAAoEfCFgAAAIAeCVsAAAAAeiRsAQAAAOiRsAUAAACgR8IWAAAAgB4JWwAAAAB6JGwBAAAA6JGwBQAAAKBHwhYAAACAHglbAAAAAHokbAEAAADokbAFAAAAoEfCFgAAAIAeCVsAAJapqn6gqr5RVa2qPlNVD1lk7Jaq+lI39nBVfec4awUARk/YAgCwTK21/5nkuq777UnedKJxVbU2ybuSPKg79MuttU+NvkIAYJyELQAA/XhVkl1d+xlV9e9PMuYJXfv9rbW3jKUyAGCsqrU26RoAAFaEqnpUkr9NsjHJV5I8trW2pzv3xCS3JDknyV1Jvre19sVJ1QoAjI6ZLQAAPWmtfTrJi7ruA5O8q6ru1+3h8o4MgpZjSZ4raAGAlcvMFgCAnlXVO5P8TNf9z0m2JPnprv9brbVXTqQwAGAshC0AAD2rqgdlsJxoy4JT/zvJE1trR8dfFQAwLpYRAQD0rLX25STPSTIcqnw5yXMELQCw8glbAABG47MZbJI77/ZuTxcAYIUTtgAA9Kyq1mSwIe6Dhw4/uap+cUIlAQBjJGwBAOjfNUm+v2vvSPKlrv26qrpwMiUBAONig1wAgB5V1WVJ/jrJ2iSfT3JRkqckeVc35O+SXNZau3cyFQIAo2ZmCwBAT6pqY5J3ZhC0tCTPa639S2vt3Une3g373iTXTahEAGAMhC0AAP35nSTf0bVf11r78NC5FyWZ3yD3qqp66lgrAwDGxjIiAIAeVNWzc3yp0MeSPKG19rUFY4aXGN2d5KLW2hfGWigAMHJmtgAALFNVXZDkd7vuPUl+ZmHQkiSttV1Jru2635rkrWMoDwAYM2ELAMAyVNU5+ebbPL+0tfbJRS55dZK/6tpPr6oXj7I+AGD8LCMCAAAA6JGZLQAAAAA9ErYAAAAA9EjYAgAAANAjYQsAAABAj4QtAAAAAD0StgAAAAD0SNgCAAAA0CNhCwAAAECPhC0AAAAAPRK2AAAAAPRI2AIAAADQI2ELAAAAQI+ELQAAAAA9ErYAAAAA9EjYAgAAANAjYQsAAABAj4QtAAAAAD0StgAAAAD06P8BEy04dIiXE4gAAAAASUVORK5CYII=\n"
          },
          "metadata": {
            "image/png": {
              "width": 557,
              "height": 413
            },
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# @title\n",
        "\n",
        "# @markdown Execute this cell to generate some simulated data\n",
        "\n",
        "# setting a fixed seed to our random number generator ensures we will always\n",
        "# get the same psuedorandom number sequence\n",
        "np.random.seed(121)\n",
        "\n",
        "# Let's set some parameters\n",
        "theta = 1.2\n",
        "n_samples = 30\n",
        "\n",
        "# Draw x and then calculate y\n",
        "x = 10 * np.random.rand(n_samples)  # sample from a uniform distribution over [0,10)\n",
        "noise = np.random.randn(n_samples)  # sample from a standard normal distribution\n",
        "y = theta * x + noise\n",
        "\n",
        "# Plot the results\n",
        "fig, ax = plt.subplots()\n",
        "ax.scatter(x, y)  # produces a scatter plot\n",
        "ax.set(xlabel='x', ylabel='y');"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "VftDC02O1YuN"
      },
      "source": [
        "Now that we have our suitably noisy dataset, we can start trying to estimate the underlying model that produced it. We use MSE to evaluate how successful a particular slope estimate $\\hat{\\theta}$ is for explaining the data, with the closer to 0 the MSE is, the better our estimate fits the data."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "XN9fbWdk1YuN"
      },
      "source": [
        "## Coding Exercise 1: Compute MSE\n",
        "\n",
        "In this exercise you will implement a method to compute the mean squared error for a set of inputs $\\mathbf{x}$, measurements $\\mathbf{y}$, and slope estimate $\\hat{\\theta}$. Here, $\\mathbf{x}$ and $\\mathbf{y}$ are vectors of data points. We will then compute and print the mean squared error for 3 different choices of theta.\n",
        "\n",
        "As a reminder, the equation for computing the estimated y for a single data point is:\n",
        "\n",
        "\\begin{equation}\n",
        "\\hat{y}_{i}= \\theta x_{i}\n",
        "\\end{equation}\n",
        "\n",
        "and for mean squared error is:\n",
        "\n",
        "\\begin{equation}\n",
        "\\min _{\\theta} \\frac{1}{N}\\sum_{i=1}^{N}\\left(y_{i}-\\hat{y}_i\\right)^{2}\n",
        "\\end{equation}"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "execution": {},
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "PwIzC4vS1YuN",
        "outputId": "9c9c13ef-7251-44e2-cde9-4f97f3921a78"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "theta_hat of 0.75 has an MSE of 9.08\n",
            "theta_hat of 1.0 has an MSE of 3.01\n",
            "theta_hat of 1.5 has an MSE of 4.52\n"
          ]
        }
      ],
      "source": [
        "def mse(x, y, theta_hat):\n",
        "  \"\"\"Compute the mean squared error\n",
        "\n",
        "  Args:\n",
        "    x (ndarray): An array of shape (samples,) that contains the input values.\n",
        "    y (ndarray): An array of shape (samples,) that contains the corresponding\n",
        "      measurement values to the inputs.\n",
        "    theta_hat (float): An estimate of the slope parameter\n",
        "\n",
        "  Returns:\n",
        "    float: The mean squared error of the data with the estimated parameter.\n",
        "  \"\"\"\n",
        "  ####################################################\n",
        "  ## TODO for students: compute the mean squared error\n",
        "  # Fill out function and remove\n",
        "  ####################################################\n",
        "\n",
        "  # Compute the estimated y\n",
        "  y_hat = theta_hat*x\n",
        "\n",
        "  # Compute mean squared error\n",
        "  mse = np.mean((y-y_hat)**2)\n",
        "\n",
        "  return mse\n",
        "\n",
        "\n",
        "theta_hats = [0.75, 1.0, 1.5]\n",
        "for theta_hat in theta_hats:\n",
        "  print(f\"theta_hat of {theta_hat} has an MSE of {mse(x, y, theta_hat):.2f}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "cellView": "both",
        "execution": {},
        "id": "vOAOgSks1YuO"
      },
      "source": [
        "[*Click for solution*](https://github.com/NeuromatchAcademy/course-content/tree/main//tutorials/W1D2_ModelFitting/solutions/W1D2_Tutorial1_Solution_12a57de0.py)\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "wm0ztcpd1YuO"
      },
      "source": [
        "The result should be:\n",
        "\n",
        "theta_hat of 0.75 has an MSE of 9.08\\\n",
        "theta_hat of 1.0 has an MSE of 3.0\\\n",
        "theta_hat of 1.5 has an MSE of 4.52\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "g7eiRgPq1YuO"
      },
      "source": [
        "We see that $\\hat{\\theta} = 1.0$ is our best estimate from the three we tried. Looking just at the raw numbers, however, isn't always satisfying, so let's visualize what our estimated model looks like over the data. \n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "cellView": "form",
        "execution": {},
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 304
        },
        "id": "7F1HsjWU1YuO",
        "outputId": "1fc5346f-16e0-43b2-cbdf-0650d44c09e6"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f8e4e9a84d0>"
            ]
          },
          "metadata": {},
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1296x288 with 3 Axes>"
            ],
            "image/png": 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K/QpEe3evq2N1Jamtq0ft3b1p33PuzKlaOb9JTcHAiM83BQNaOb/Jl13lS62zX6Ok36U72RhzsqSHJE0c/FKfpCpJpw4+zjPGfMJauyfN658l6S5J8b+VtksKSPqYpI8ZY26TNN9y9jIAAEBOZZKE0IkYRYacCgAAAK6RUwEAAADIyPe/L33rW6nH8dJvQQp3RtKel0lOGKqrUaiuRu3dvQp3RtTXP6DKinKF6mp8nWuWVGe/QVsltUq6TtIFkt5wMskYM0HSbxXblHpB0kxrbZWkQyV9RdJeSWdIuj6doIwxQUmrFduUCkt6t7V2gqQJkq4dHHaxpH9N5/oAAABIXyZJCFCEyKkAAADgCjkVAAAAgLQcfXSsk1+qQj9rKfQrYH39Azmdd7CG2ipdHArqn5vrdXEo6OtCP6n0iv0es9YGrLWnW2uvsNbeKWm3w7mXSzpS0i5JZ1lrn5Ika+0ea+1/SrpqcNylxpiGNGK7VrFNrjcknW2tbR+8fp+19ipJtwyO+6YxpjqN6wMAACBN+U5CgAJCTgUAAADXyKkAAAAAuGJM7PH664nHnHceRX4+UVmR3sGz6c4rdiVV7Get3ZfB9IsG/7zTWts1wvM3KHYE1ShJn3VzYWPMoZLOHfz0RmvtthGGLR78c7ykT7q5PgAAADJDEgLEkFMBAAAgHeRUAAAAAByJF/kl09ISK/C7667cxISMhepqcjqv2JVUsV+6jDHvljR18NMHRhpjre2T9Njgpx9zeYtTJY1Ncf0Nkv6W5vUBAAD2a+/u1W3hLt3Q2qHbwl1q7+7Nd0gFjyQEyAw5FQAAKDbkVe6QUwEAAABIqK/PWZHf5s2xIr9PfSo3cSFrGmqr1BgMuJrTFAz4/rhdr/C2OGdOHPbxX5OM+6ukMyW9x8PrHy/pBJfXB1BALG2EAeRJuDOipa0dWtPV847nGoMBLWyuZyMlgXgSMtLPLhGSEOAA5FQAAKAokFelh5wKAAAAwDs88ojU3Jx6XDSauhAQBW9hc73mrWhT1EG5RJmRFjTXex+UT9HZz5mjh338WpJx8efGG2Mq07j+VmvtLgfXPzrJmP2MMU+nekg6zkWc8etKkqLRqNupADRU7GdYkADIoVVrN2reiraEGytruno0b0WbVq99NceR+cfC5nqVOfyrmyQEeAdyKgAA4HvkVZkhpwIAAAAgSfr852PFe6kK/ayNPdhXLwqhuhotnj09ZV5YZqQls2fwRrokKPZzZvjbB3cmGTf8OTdvOYyPTXbt4c/n9e2Mo0ePliT19/fnMwzAt+K/O/HfJQDwWrgzokUt61O+UyZqpStb1incGclNYD5DEgJkhJwKAAD4GnlV5sipAAAAgBIXP6r35z9PPi5e5IeiM3fmVK2c36SmBEf6NgUDWjm/SXNmTslxZP7CMb5FzFp7cqoxg50oTnJz3aqqKr311lvaunWrxo4dS3cywAVrrbZu3Sop9rsEALmwtLXDUUtsKbYxtay1g02VBObOnKrJ1eO0rLVDbSN082gKBrSAY7uAouFVTgUAAPyHvCo7yKkAAACAEuSkpmTaNOmll7yPBXkXqqtRqK5G7d29CndG1Nc/oMqKcoXqatRQSw2FExT7OdM77ONxkrYnGDcuwRyn1x+XdNTQ826unXXjx49XT0+Ptm+P/Riqq6tVUVEhYwyFf8AIrLWy1qq/v19bt27V9u3bZYzRhAkT8h0agBLQ3t2b8IipRNq6evTvD76gT71vEovqEZCEAGkhpwIAAL5FXpVd5FQAAABAiXBSP/Kzn0lf/rL3saDgNNRWkQOmiWI/ZzYP+3iSEm9MTRr8c7u1ti+N61cbY8Zaa3eluP7mBM/nREVFhSZPnqxNmzZp+/bt+4v+ADhjjNHkyZN1yCGH5DsUACUg3aOjbvzDS7rxDy+pMRjQQroqjIgkBHCFnAoAAPgWeZU3yKkAAACAItTXJzk54W7DBumYYzwPByhGZfkOwCf+OuzjE5OMiz/3vMfXf87l9bOusrJSwWBQEydO1JgxY+joB6RgjNGYMWM0ceJEBYNBVVZW5jskACWir38go/lruno0b0WbVq99NUsRAShR5FQAAMC3yKsAAAAAIIVHHol18ktV6BeNStZS6AdkgM5+zrRL2ihpqqRZku46eIAx5lBJHxj89GGX139c0i5JYwevv3aE6x8j6fg0r++JQw45REcccYSOOOKIfIcCAAASqKzIfLkXtdKVLes0qXosnSgApIucCgAA+BZ5FfLmjTdiR5r9z/9IEydK118vXXhhvqMCAAAAhnzuc9J//3fqcdZ6HwtQIujs54C11kqK/+10vjHm2BGGXSapUtI+Sb9wef0dku4e/PTLxpgJIwz7xuCfvZL+x831AQBA6crWJlLUSstaO7JyLQClh5wKAAD4GXkVcurNN6Xzzot1RTnqqFihnyS99ZZ09dV5DQ0AAADYz5jYI1Whn7UU+gFZVnLFfsaYamNMTfyhoZ/BuOFfN8YcfMbmf0h6Q9I4SfcbY04evN4YY8yXJX13cNwt1tr2Ee57uzHGGmMS/S32HUk7JB0l6T5jTP3gvEONMd+R9KXBcd+z1m5N77sHAAClpqG2So3BQFau1dbVo/bu3qxcC4B/kVMBAIBSQ14Fz23ZIs2ZE9ssra2V7r575HEXXZTbuAAAAICDxYv8kqmro8gP8FDJFftJelbSlmGPKYNf/9eDvv7T4ZOstW9LOlvSW5LeI+kpY8x2SX2SfiZpjGJHQX0tnaCstV2S5kjaqdjRVe3GmG2S3pZ0jSQj6TZJ16VzfQAAULoWNterLEXe5VS4M5KdCwHwM3IqAABQcsirkHVvvSV95jOxjdIjjpDuuivx2DFjYh3+vvOd3MUHAAAADOekyO/GG2MFfh10NAe8VIrFfmmz1j4t6QRJP5HUIWm0Yp0jHpf0RUlnWmt3Z3D930maIelWSRskVUjaKul/JZ1nrb1k8PgrAAAAx0J1NVo8e3pWNqb6+gcyvwiAkkVOBQAA/Iq8ClnR0yNdeGFsk7SmRvrVrxKPHTVKammJbZbu3i2dc07u4gQAAAAkqbfXWZHfhg2xdeuXvpR8HICsKM93ALlmrT02w/ndkv5l8OFm3uclfd7BuJckXZpObAAAAInMnTlVk6vHaVlrh9q6etK+TmVFyS0fARyEnAoAAJQq8iqkpatLmjbN2VhjpNWrpfPO8zYmAAAAIJnWVun001OPi0ZTFwICyDpeVQAAACgRoboahepq1N7dq988u0k3/uFl19cYN2aUB5EBAAAAgD9kI68K1dV4EBkKysaN0jHHOB+/apU0Z4538QAAAABOzJsn3XFH6nEcnlIQ2rt7Fe6MqK9/QJUV5QrV1aihtirfYSEHKPYDAAAoMQ21VfrGrOP19CvbtMZlN4qWZ17T3JlTPYoMAAAAAPwhnlfd8eRG9bo4lreqopzNl2K1aZM0ZYrz8b/8pXT++XRCAQAAQP45XZNS5FcQwp0RLW3tGHGPrzEY0MLmet5kVuTK8h0AAAAA8uPckya5ntPW1aP27l4PogEAAAAAf2nv7nVV6CdJvf0D5FTF5JVXYhujxjgr9DvjjNhRZ9ZKF1xAoR8AAADyK76WTaa+PrZ+pdCvIKxau1HzVrQlbOaxpqtH81a0afXaV3McGXKJYj8AAIAStXPPvrTmhTsjWY4EAAAAAPwn3dyInMrnOjuHNkWPPTb1+ObmoQK/Bx+kwA8AAAD556TI76abYmvY9vbcxISUwp0RLWpZr2iKusuola5sWUfuWcQ4xhcAAKBE9bnsQJHpvELQ3t2rcGdEff0DqqwoV6iuhiO0AAAAAKSFnKqEcqoNG6Rg0Pn4UEh67DEK+5AXxphxkk6TdLKkkwb/nDr49DXW2qsdXKNW0hWSzh6cu0vSc5J+LmmFtbT2AQDAd3p7pfHjU4/bsEE65hjPw4F7S1s7Uhb6xUWttKy1g+N8ixTFfgAAACWqsiK9pWC68/Ip3BnR0taOEduaNwYDWthcT8IDAAAAwBVyqpiizalefVWaOjX1uLimJumJJ6QyDlRC3jVK+l26k40xJ0t6SNLEwS/1SaqSdOrg4zxjzCestXsyDRQAAORAa6t0+umpx0WjvFmlgLV39yY8ujeRtq4etXf3lsYbtEoMWScAAECJSncjxm8bOKvWbtS8FW0Jk6A1XT2at6JNq9e+muPIAAAAAPgZOVVMUeVUmzcPHWnmtNBvYCB2vNmTT1Loh0KyVVKrpOskXSDpDSeTjDETJP1WsUK/FyTNtNZWSTpU0lck7ZV0hqTrPYgZAABk02c/G1vXpir0szb2oNCvoKV7JC9H+RYnMk8AAIAS1VBbpcZgwNWcpmDAV+8ACndGtKhlfcq25lErXdmyjqQHAAAAgGPkVEN8nVO98cZQgd+kSc7m7N07tCk6apS38QHuPWatDVhrT7fWXmGtvVPSbodzL5d0pGLH9p5lrX1Kkqy1e6y1/ynpqsFxlxpjGrIeOQAAyFx8bfvLXyYfF1/Pwhf6+gdyOg+FjWI/AACAErawuV5lDt+sVWakBc313gaUZUtbO1JuSsVFrbSstcPbgAAAAAAUFXKqIb7KqbZsGdoEPeooZ3P27BnaEC3331HMKB3W2n0ZTL9o8M87rbVdIzx/g2LH+o6S9NkM7gMAALItvr5N5t3vpsjPpyor0stB0p2HwkaxHwAAQJa0d/fqtnCXbmjt0G3hLrV39+Y7pJRCdTVaPHt6ys2pMiMtmT3DV8dNtXf3JjxmKpG2rh5f/HcDAAAAihE5VWEpupzqrbeGNkCPOMLZnP7+oc3Q0aO9jQ/IM2PMuyXFz69+YKQx1to+SY8NfvqxXMQFAABScFLkd8stsTXtCy/kJiYH/Jj/5VO6uaSfclA4RwknAABAhsKdES1t7RhxE6QxGNDC5vqCXkzPnTlVk6vHaVlrh9pG+B6aggEtKPDvYSTpHh8V7oz46lgtAAAAwO/IqQpTUeRUW7dKAXdHLWvXLqmiwpt4gMJ24rCP/5pk3F8lnSnpPU4uaox52sGw45xcCwAADNqxQ6qsTD3ulVekqVNTj8shv+d/+dJQW6XGYMDVG7KagoHCyc2QVRT7AQAAZGDV2o1a1LI+4bFGa7p6NG9Fm5bMnqE5M6fkNjgXQnU1CtXVqL27V+HOiPr6B1RZUa5QXY1vE4G+/oGczgMAAADgHjlV4fJtTrV9uzRhgrs5O3ZI48Z5Ew/gH0cP+/i1JOPiz403xlQOdvsDAAC58MQTUiiUelw0mrrbXx4US/6XLwub6zVvRVvCn99wZUZa0FzvfVDIC4r9AAAA0hTujCRNSuKiVrqyZZ0mVY8t+HcjNdRW+XYj6mCVFektddOdBwAAAMAdcqrC5qucqrdXGj/e3Zy+PunQQ72JB/Cn4X957UwybvhzVZKSFvtZa09OdePB7n8npRoHAEDJuvxy6Uc/Sj3OOqgCy5NizP9yLVRXo8Wzp6f8OZYZacnsGfz8ilhZvgMAAADwq6WtHY7ePSPFkpNlrR3eBoQDpJvEkPwAAAAAuUFOVdjSzY3GjRmV5UgS2LEj1q3EGOeFftu3xzZAraXQDwAAAIUvvt5NVegXX+MWMLf53zd+vU63hbvU3t3rbWA+M3fmVK2c36SmYGDE55uCAa2c30RnxCJH2xIAAIA0tHf3ak1Xj6s5bV09au/uLZouD4WuobZKVRXl6nVxhFRVRTn/fQAAAIAcIKcqfA21VWoMBlz/d2p55jXNnTnVm6B27XJ/3O62be6P9QVK0/Cd9HGSticYN/yXkN13AAC84OQI3lmzpAce8D6WLEgn/9u0bZeuue95SVJjMKCFzfU0axgUqqtRqK5G7d29CndG1Nc/oMqKcoXqasiXSwSd/QAAANIQ7ozkdB7ca+/udVXoJ0m9/QO8SwwAAADIAXIqfzj3pEmu58SLMrOmv3+oo4nTQr+enqHuJhT6AU5tHvZxsl/++HPbrbVJj/AFAAAuxde9yaxeHVvn+qTQT8o8j1vT1aN5K9q0eu2rWYqoODTUVuniUFD/3Fyvi0NBCv1KCMV+AAAAaehzWUSW6Ty4x+YhAAAAULjIqfxh5559ac3LOK/as2doo3PsWGdzIpGhAr/q6szuD5Smvw77+MQk4+LPPe9hLAAAlI6+PmdFfps3x9a6n/50buLKomzkcVErXdmyjj0cQBT7AQAApKWyojyn8+Aem4cAAABA4SKn8oec5lV79w5tch5yiLM53d1DBX4TJ7q/J4Dh2iVtHPx41kgDjDGHSvrA4KcP5yIoAACKVjgcW/tWpejGFo3G1rtHHZWbuDyQrTwuaqVlrR1ZuRbgZ7wyAgAAkIZQXU1O5/lNe3evwp0R9fUPqLKiXKG6mpy3D2fzEAAAAChc5FTJFUJOJeUgrxoYkEaPdnfxzZt9vdEJFCprrTXG/Lekb0k63xjzXWvthoOGXSapUtI+Sb/IcYgAABSHyy+XfvSj1OOs9T6WHMlmHtfW1aP27l6OrEVJYycTAAAgDQ21VWoMBrSmq8fxnKZgoOiTj3BnREtbO0b8uTQGA1rYXJ+zzTk2DwEAAIDCRU41skLKqSSP8qp0Cvw2bZImTUorFqAUGWOqJY0a9qX4SV/jjDHDf0H7rbV9wz7/D0lfkHSkpPuNMRdZa582xoyRNF/SdwfH3WKtbfcofAAAilOqY3rjiqjILy6d/C+ZcGek6HNDIBmO8QUAAEjTwuZ6lTnMzcqMtKC53tuA8mzV2o2at6ItYbK2pqtH81a0afXaV3MSTzx5dKMUNg8BAACAQkFOdaBCy6mkLOZV+/YNHdHrtNDvlVeGjuil0A9w61lJW4Y9pgx+/V8P+vpPh0+y1r4t6WxJb0l6j6SnjDHbJfVJ+pmkMYod3/s1778FAACKRHwdnMyZZw6tfYuUm/wvlb7+gexcCPApiv0AAADSFKqr0eLZ01MmJ2VGWjJ7RlF3jAt3RrSoZb2iKfLQqJWubFmncGckJ3GxeQgAAAAULnKqIYWaU0kZ5FXR6NDGZrnDQ4Zefnlok3Pq1PQCBpARa+3Tkk6Q9BNJHZJGS9oh6XFJX5R0prV2d/4iBADAJ5wU+a1eHVv7/u53uYkpj5zmf05UVnCIKUobxX4AAAAZmDtzqlbOb1JTgk4HTcGAVs5v0pyZU0Z8vlgsbe1IuSkVF7XSstYObwMaxOYhAAAAUNjIqWIKNaeSXOZVn5quUP3hsU3NUaOST4h75pmhAr9gMPOAAchae6y11jh4fD7B/G5r7b9YaxustWOttdXW2g9Ya5dba6M5/nYAAPCPvj5nRX6bN8fWv5/+dG7iKhCp8j+n2MtBqaPcFQAAIEOhuhqF6mrU3t2rcGdEff0DqqwoV6iupiSOhG3v7k14zFQibV09au/uzcnPZ+7MqZpcPU7LWjvUNkKcTcGAFjTXkxwCAAAAeUJOVdg5lZQir7JWG3748djHSxxecO1a6ZRTshojAAAAkDcPPyydcUbqcfHu1yVseP73m2df041/eCnfIQG+Q7EfAABAljTUVpXERtTB0j0+KtwZydnPq9Q3DwEAAAA/IKdyPy+XP68D8qqOLbr4A+9yd4EnnpDe/35vggMAAADy4TOfkX71q9TjrMM23iWkobZKR1QdktbcXOdC2cQ+FbKBYj8AAABkpK9/IKfzMlGqm4cAAAAACpefcioZowZJDU7H//GP0gc/6GFAAAAAQB447c5HkV9SvsqFMhTujGhpa8eIXd0bgwEt5AQquFCW7wAAAADgb5UV6b1/JN15AAAAAFBMCj6nMmbo4URra2xT01oK/QAAAFBcnKyLm5qG1sNIquBzoSxZtXaj5q1oG7HQT5LWdPVo3oo2rV77ao4jg19R7AcAAICMpPtOI96hBAAAAAAFmlO5LfB74IGhDc2PfMS7uAAAAIB8cLI2Xr48th5+8sncxFQECjIXyrJwZ0SLWtYrmqL2M2qlK1vWKdwZyU1g8DWK/QAAAJCRhtoqNQYDruY0BQMcpwtL7ro8AAAgAElEQVQAAAAAKqCcym2B36pVQwV+s2ZlNxYAAAAg37Zvd7Y+3rgxtiaePz83cRWRgsmFPLS0tSNloV9c1ErLWju8DQhFgWI/AAAAZGxhc73KHO4HlRlpQXO9twEBAAAAgI/kLadyW+B37bVDBX5z5mQnBgAAAKCQPPxwbH08YULycdFobF08ZUpu4nKovbtXt4W7dENrh24Ld6m9uzffISVVzPtL7d29CY/uTaStq6fg/5sh//x1kDUAAAAKUqiuRotnT0/ZirzMSEtmz/BVi3UAAAAA8FpOcyqnhX1xixZJP/hB+vcDAAAA/OD882Pdq1OxDtu05Vi4M6KlrR0jFpc1BgNa2FxfkHszxby/lO6RvOHOiK+6FyL3KPYDAABAVsydOVWTq8dpWWuH2kZIJpuCAS0o0GQSAAAAAPLN05zKbYHfV78q/eQn7u8DAAAA+I3TtXKBFvlJ0qq1G5MWy63p6tG8FW1aMnuG5swsrE6EUvHuL/X1D+R0HkoHxX4AAADImlBdjUJ1NWrv7lW4M6K+/gFVVpQrVFfDu5AAAAAAIIWs5lRuC/z+8R+lm25yNwcAAADwKyfr5RNPlNav9z6WDIQ7Iym74klS1EpXtqzTpOqxBVk0V4z7S5UV6ZVkpTsPpYP/QwAAAJB1DbVVvk2+AAAAACDf0s6p3Bb4XXSR9POfu78PAAAA4FdO1szLl0vz53sfSxYsbe1IWegXF7XSstaOgiz2iyum/aV0f87jxozKciQoNmX5DgAAAAAAAAAAAKTJmKGHE+eeGzuCzFoK/QAAAFAa3n7b2Zp548bYOtknhX7t3b1aM8Kxt8m0dfWovbvXo4gwXENtlRqDAdfzWp55zYNoUEwo9gMAAAAAAAAAwE/cFvidddZQgd+vf+1tbAAAAECheOih2Jr5sMOSj4tGY2vlKVNyE1eWhDsjOZ0H9849aZLrORRkIhWK/QAAAAAAAAAAKHRuC/xOO22owO/++72NDQAAACgkc+fG1s2zZiUfF18vO11jF5i+/oGczoN7O/fsS2seBZlIhmI/F4wx1sXj0TSuf7XDa9d58f0BAAAAgJfIqQAAAFxyW+B3yilDG5Z/+IOnoQEAAAAFJ752Xr06+bj4mtnnKivKczoP7lGQCS/wG+xOd4rnR0uKH7i9NoP77JWU7GB1fqsBAAAA+BE5FQAAQCpuu4ocf7z0/PPexAIAAAD4gZM19PTp0rp13seSQ6G6mpzO85v27l6FOyPq6x9QZUW5QnU1aqitymkMFGTCC/zf4YK19shkzxtjvi7pPwY/XZHBrZ6w1n4og/kAAAAAUHDIqQAAABIYM0bau9f5+KlTpVde8S4eAAAAwA+cFPmtWCFdcon3seRBQ22VGoMBrelK9r7nAzUFAzkveMu1cGdES1s7Rvy5NAYDWthcn7OCRwoy4QWO8c2u+YN/Pm6tfTGvkQAAAACA/5BTAQCA0hEIDB0z5qTQr7p66LgxCv0AAABQqrZuHVpHJ/Pqq7G1c5EW+sUtbK5XmcPm4GVGWtBc721AebZq7UbNW9GWsAByTVeP5q1o0+q1r+YknnhBphulUJCJzFDslyXGmP8n6fjBT5fnMxYAAAAA8BtyKgAAUBImTRramNy6NfX49753qMCvx3m3DgAAAKDotLTE1tGBFIVT0Whs/Tx5cm7iyrNQXY0Wz56esuCvzEhLZs8o6o5x4c6IFrWsV9QmHxe10pUt6xTujOQkLgoykW0U+2VPvAPF25LuymcgAAAAAOBD5FQAAKA4vfvdQwV+mzenHt/QMFTg9+yz3scHAAAAFLJTT42tpc89N/m4+BraydG+RWbuzKlaOb9JTQk6yDUFA1o5v0lzZk7JcWS5tbS1I2WhX1zUSstaO7wNaBAFmci28nwHUAyMMZWS5gx++itr7c4ML3mCMeavkqZJikp6TdL/SfqZtZZXdwAABa+9u1fhzoj6+gdUWVGuUF0N7aYBAAmRUwEA8E7kVT43Y4a0fr3z8ZMmSZs2eRcPAAAA4DdOi/asw+quIheqq1GorqZkc8n27t6ER/cm0tbVo/bu3pz8fObOnKrJ1eO0rLVDbSPE2RQMaEFzPYV+cIRiv+w4X1Ll4MfZOG6qRlJA0jZJ4yU1DD7mG2N+YK39lpOLGGOedjDsuLSjBADgIOHOiJa2doy4mG4MBrSQRSoAYGTkVAAADCKv8jG3HUQmTJC2bfMmFgAAAMCvnKyrq6qk7du9j8WHGmqrSqK472DpHskb7ozk7OdV6gWZyB6K/bLjC4N//sVa62QzKJEOSVdIukdSl7V2rzFmjKQPSfqBpJMlfdMYs9Va+6NMAgYAIJF0F5ir1m7Uopb1Cdtjr+nq0bwVbVoye0bRtwkHALhGTgUAKCrkVSWkslLascP5+NGjpT17vIsHAAAA8CsnRX4/+Yn01a96Hwt8p69/IKfzMlGqBZnIHor9MmSMOUFS0+CnGXWgsNb+YoSv7ZH0sDHm/xQ7dmqmpKuNMcuttW+nuN7Jqe452KnipDRDBgAUkUy6R4Q7I0k3pOKiVrqyZZ0mVY+lEwUAQBI5FQCguJBXlYijj5Zef93dHI4WAwAAAN6pp0eaODH1uK4u6dhjPQ8H/lVZkV75U7rzgHwqy3cARSDegaJf0h1e3cRa2y/p3wY/rZTU7NW9AAClZ9XajZq3om3EDSlpqHvE6rWvjvj80taOlBtScVErLWvtSDdUAEDxIacCABQF8qoiV18f6zRijPNCP2uHHgAAAACGtLTE1tapCv2i0dh6mkI/pJDum+F4Ex38iGK/DAweB3Xh4Kd3W2u3eXzLPw37eJrH9wIAlAi33SPCnZEDvt7e3ZtwMyuRtq4etXf3ug0VgB/9+c/S3LnSHXdIO3fmOxoUGHIqAECxIK8qUu9731CBX2enszkU+AEAAACJhUKx9fW55yYfF19TOznaF1DsaNzGYMDVnKZggON04UsU+2XmHEnxMt+MjpsCACBfMu0ecfAmlVPpzgNQ4Navl847b2hT9H3vk1avlubNk775zXxHh8JDTgUAKArkVUXk1FOH1rJ//rOzORT4AQAAAMnF19hPPJF8HOtqZGBhc73KHNaHlhlpQXO9twEBHqHYLzPx46Y6Jf0xB/f7+2Efd+XgfgCAIpeN7hF9/QNp3TvdeQAKzHPPSXPmDL1YM2OGdPfdI4/dty+3scEPyKkAAL5HXlUEzjhjaD0bDjubQ4EfAAAAkFp8nZ3M+PGsrZEVoboaLZ49PWXBX5mRlsyewRG+8K3yfAfgV8aYqZJOH/z0v6zN7F8eY4xJdg1jzCGSvj/46Q5JrZncDwCQO+3dvQp3RtTXP6DKinKF6moKpiV0Jt0j4t9DZUV6y4l05wHIsxdekK65RrrzTnfzGhul667zJib4EjkVAMCpQs6pJPIq35o9W/rNb9zNYfMRAAAAcMbJ8bvXXy8tXOh9LCgpc2dO1eTqcVrW2qG2Ed6Y1xQMaEFzPYV+8DVeDUrfJYp1RhyQdLuTCcaYqyVdNfhp0Fq7YdjTHzTGfFvSzyU9aq3dNDhntKQPSlosaebg2GuttdsyjB8A4LFwZ0RLWztG7PDQGAxoYQEsJLPRPSLd7yHf3zsAh+6/Xzr77PTmfvvb0le/KgUC2Y0JxYKcCgCQlB9yKom8ylcuvFD6xS/czaHADwAAAHCmp0eaODH1uK4u6dhjPQ8HpStUV6NQXU3Bv3kQSBfFfmkwxpRJunjw099Za1/PxmUlNQ8+ZIzZpVi3iQmSRg+OiUpaYq39YRbuBwDw0Kq1G7WoZb2iCfYE1nT1aN6KNi2ZPUNzZk7JbXDDpNsF4rnNb+uG1o79C+PGYMDVsVVNwQCLaaBQPfSQNGtWenMXLZK+/nVnL+igpJFTAQBS8UtOJaWfVz2zcatuC3ft32wgr/LIpZdKt97qbg4FfgAAAIBzd98tnXde6nHRqLOOf0CWNNRWkTejKFHsl57TJU0d/Hh5lq65XtLlkt4vabqkGkmHSdop6XlJj0m6xVq7Pkv3AwB4JNwZSbopFRe10pUt6zSpemzeujGke98Hn+vWg8917//83UdWyRhn+yFlRlrQXJ/WfQF44JFHpObm9OZecYV0+eXS4YdnNyaUAnIqAEBCfsqppPTzqkdf3KJHX9wiKdapsPm4I/TUhp6U37dEXpXSV78qLV3qbg4FfgAAAIA7/+//SX/6U+pxrLUBIKso9kuDtfZhxbpGuJ13taSrEzz3lqQfZRQYAKAgLG3tcLQ5I8U2p5a1duRtYyqd7hEjefGNXhnF/nFM9q2XGWnJ7BkcNQXk08qV0kUXpT//pZekadOyFw9KEjkVACAZP+VUUnbyqjVdPXpqQ49mv2+yWp7dlPT7J69K4N/+TVq82N0cNh0BAAAA95x252O9DQCeKMt3AAAAFJP27l7XGzxtXT1q7+71KKLUFjbXqywLXdPjKdvxR47cDrspGNDK+U15P2ILKDmrVsVefIk/3Bb6Pfts7EWZ+INCPwAA4CE/5lRSdvKqqJVant2kb8w6Tk3BwIhjyKsOcu21Q+tcp4V+w9e2AAAAAJyLr72TOeww1tsA4DE6+wEAkEXhzkja8xpqRy6S81qorkaLZ093dExWKlbS+LGj9fDXPqhwZ0R9/QOqrChXqK4mb98fUHJaWqRzz01//tq10imnZC8eAAAAF/yYU0nZy6uiVnrkhTe16h/fr/buXvKqkVx3nXTFFe7msNEIAAAApM9JJ7+lS6UFC7yPBQBAsR8AANnU1z+Q03nZMnfmVE2uHqdlrR1qy/BI3/j8i0PBbIQGIJX775fOPjv9+S0t0qc+lb14AAAAMuDXnErKXl4V71TYUFtFcV/cDTe43zikwA8AAABIX0+PNHFi6nEbNkjHHON5OACAIRT7AQCQRZUV6f3Tmu68bArV1ShUV3NA94jnNr+tB5/rdn2tfHfVAIraQw9Js2alP/+Xv5QuuCB78QAAAGSRn3Mq6Z151f+1b9GjL25xfR1yKknLl0tf/KK7ORT4AQAAAJm56y5pzpzU46JRZx3/AABZVxivggEAUCRCdTU5neeF4d0jbmjtSKvYrxC6agBF49FHpY98JP35t98ufe5zWQsHAADAS8WQU0lDeVVf/0BaxX4lm1Pde690zjnu5rDJCAAAAGTu/e+Xnnwy9TjeYAMAeUexHwAAWdRQW6XGYEBrXBzZ1BQMFGzHBr931QB86bHHpA9+MP35t9zivgMKAABAgSCnymyeLz34oHTmme7mUOAHAAAAZIfTdbUPi/yGn2RVWVGuUF1NweaOAOBGCb1qBABAbixsrte8FW2KOsh7yoy0oLne+6DSVCxdNYCC9uSTsXdNpuunP5Uuuyx78QAAAOQZOVUJ5FSPPCI1N7ubs2+fVFbmTTwAAABAqXFS5DdxohSJeB9LloU7I1ra2jHim8gagwEtbK4v/pwLQFHj1REAALIsVFejxbOnqyxFnlRmpCWzZxR0QhHvquFGIXfVAArC00/HXkiJP9wW+v3oR7F3UcYfFPoBAIAiQ05VpDnVY48NrYGdFvoNDAyteyn0AwAAADIXX5Mns2xZbA2ex0K/9u5e3Rbu0g2tHbot3KX27l5H81at3ah5K9oSdotf09WjeSvatHrtq9kMFwByis5+AAB4YO7MqZpcPU7LWjvUNkJC0RQMaIFP3jlUTF01gLz4y1+k9743/fk/+IG0aFH24gEAAPABcqoisWaN1NTkbs7evVI5L1sDAAAAWfPWW1KNg9zplVekqVO9jyeJTLryhTsjWtSyPmXuFbXSlS3rNKl6rC9ySgA4GK+aAADgkVBdjUJ1NWrv7lW4M6K+/gFVVpQrVFfjqy4N8a4aqRIkP3TVAHLiueekE09Mf/5VV0lXX521cAAAAPyKnMqnnn1WOukkd3P27JFGj/YmHgAAAKBU3XWXNGdO6nHRqLNjfT22au3GpHlTvCvfktkzNGfmlHc8v7S1w9GbrKRYwd+y1g7/518AShLFfgAAeKyhtspXG1EjKaauGkDWvfiidNxx6c+/8kpp8eLsxQMAAFBkyKl8YP16acYMd3P6+6VDDvEmHgAAAKCUNTZKa9emHmcdVsblQKZd+dq7exMe3ZtIW1eP2rt7fZ9vAig9FPsBAABHiqWrBpCxTI/l/drXpB//OHvxAAAAwBeKLqd64QXp+OPdzdm5Uxo71pt4AAAAgFLntDtfARX5xWXalS/cGUnrvuHOiD/zMQAljWI/AADgSjF01QBcef556YQT0p//5S9LP/tZ9uIBAACAr/k6p3rpJamuzt2cvj7p0EO9iQcAAACAoyK/fYGA/vvep2JvOgp3FdSbjrLRla+vfyCte6c7DwDyiWI/AAAAYLiODqmhIf35l1wirViRvXgAAACAfHrlFenYY93Nefttafx4T8IBAAAAMMhBkd9L31msRUefFiumu+/5A55rDAa0sLn+gA55+ZCNrnyVFemVvqQ7DwDyib+5AAAAUNq6uqRp09Kf39ws/f732YsHAAAAyLfXXpMmT3Y3p6dHqq72Jh4AAAAAMW+9JdU4KM575RWt6pYWtaxXNEHXvDVdPZq3ok1LZs/QnJlTshyoc+l21/u/9i2xToUV5Zp02Ni0rpHvQkcASAfFfgAAACgtnZ1SfX368488Unr99ezFAwAAABSC11+Xjj7a3ZwtW5xtNAIAAADIzOrV0ty5qcdFo5IxCndGtKilTVGbYriVrmxZp0nVY/NW+JZud71HX9yiR1/csv/zqopy9booHGwKBgrmKGMAcKMs3wEAAAAAnmpvjx1nEH+4LfSrqpKsHXpQ6AcAAIBi8cYbQ+tkp4V+b7wxtDam0A8AAADw1syZsfV6qkK/+Bp98Gjfpa0dKQv94qJWWtbakWGg6ctWkaGbQr8yIy1ozqApAADkEcV+AAAAKC5dXQcW97373e7mG3Ngcd/27d7ECQAAAORDJDK0Vj7qKGdzNm0aWh/X1nobHwAAAIChNftTTyUfF1+nD9Pe3as1CY7uTaStq0ft3b1uo8yKhtoqNQYDObtfmZGWzJ7BEb4AfItiPwAAAPjbpk0HFvdNm+b+GtHo0Isi0Wj2YwQAAADyaevWofXy4Yc7m/PKK0Nr5EmTvI0PAAAAQEx83Z5MTc2IRX5x4c5IWrdOd142LGyuV1mKb9uNqgRHAzcFA1o5v0lzZk7J3s0AIMfSO/wcAAAAyJc33nDegSSRaDT1CyYAAACAn23fLk2Y4G7O889Lxx/vTTwAAAAAEnPyevUNN0hf+UrKYX0ujrPNxrxsCNXVaPHs6VrUst7x8cPJ9PYP6JZ5J+u1bbvU1z+gyopyhepq1FBblfnFASDPKPYDAABAYXvrrdg7FTOxb59URlNrAAAAFLkdO6TKSndz/vIXacYMb+IBAAAAkFgk4qzz9saN0hTnnegqE3S182petsydOVWTq8dpWWuH2lweQzyS17bt0sWhYBYiA4DCQrEfAAAACsu2bVJ1dWbXGBiQRo3KTjwAAABAIdu1Sxo3zt2ctWulU07xJh4AAAAAya1aJZ1/fupxaZ5QE6pL783z6c7LplBdjUJ1NWrv7lW4M6K+/gE9s3GrHn1xi+tr5bNTIQB4iWI/AAAA5FdvrzR+fGbX2LNHGj06O/EAAAAAhW73bqmiwt2cJ56Q3v9+b+IBAAAAkNrJJ0vPPJN6nM3sHNuG2io1BgNa46I7XlMwUFBH3DbUVu2P57ZwV1rFfvnuVAgAXuEsMwAAAOTWzp2xdyPGH+kU+vX3x17wiD8o9AMAAECx27t3aA3ttNDvD38YWjNT6AcAAADkR3wdn6rQL752z4KFzfUqc9gUsMxIC5rrs3JfL/i5UyEAeIFiPwAAAHhr9+4Di/sOPdT9NXbuPLC475BDsh8nAAAAUGj27RtaR48Z42zOQw8NrZtPO83b+AAAAAAkFl/LJ3PEEVkt8osL1dVo8ezpKQv+yoy0ZPaMgi6Mi3cqdKPQOhUCQDbRtxQAkHft3b0Kd0bU1z+gyopyhepqWIADfjYwkHmnvd5eqbIyO/EAAAAUOXKqIhONSqNGuZtz773Sxz/uTTwAAAAA3ElV4CdJP/2pdNllnoYxd+ZUTa4ep2WtHWob4UjfpmBAC5rrC7rQL25hc73mrWhT1EFNZKF3KgSATFHsBwDIm3BnREtbO7RmhASjMRjQQp8kGEDJ27dPKs9wWbltmzRhQnbiAQAAKBHkVEXEWqnM5SEsd90lnXeeN/EAAAAAcCcSkQ4/PPW4jRulKVO8j2dQqK5Goboa379JLN6pcFHL+qQFf37oVAgAmaLYDwCQF6vWbky6IF/T1aN5K9q0ZPYMzZmZu6QHgAPpdBo5WCQiTZyYnXgAAABKEDlVEUinwO+OO6TPftabeAAAAAC4d+ed0gUXpB4XjTrr+OeRhtoqXxX3jaSYOhUCQCayXuxnjPmVpJuttX/I9rUBAMUh3BlJ+c4bSYpa6cqWdZpUPZaFOZBP6WxCHuyNN6Ta2uzEAxQ5cioAQCrkVD6Wztp6+XJp/nxv4gEAZA25HACUmJNPlp55JvU46+DcWThWLJ0KASATXnT2mytpjjHmZUm3SrrdWvumB/cBAPjU0taOlJtScVErLWvtYGMKyCWK+4B8I6cCACRFTuVDbjt4/PSn0mWXeRMLAMAr5HIAUAqcru0p8vNUMXQqBIB0ZbiLm5CRNE3SYkmvGmPuMsac4dG9AAA+0t7dqzUjtNZOpq2rR+3dvR5FBEBS7AWK+COdQr/XXou9eBF/UOgHZIqcCgAwInIqHxm+xnbiuuuG1tMU+gGAX5HLAUCxcrK2P/LIoTU9AAAe8aLY72RJN0vqVSypGS1ptqTfGWO6jDHfMsZM8uC+AAAfCHdGcjoPQALDNx7ddhmRpA0bDizuO/rorIcIlDByKgBAQuRUBc7tGvu73x1aU19+ubexAQC8Ri4HAMXIyfr+P/8ztqZ//fXcxAQAKGlZL/az1j5rrf2ypKMkzZf0hGJJjZF0jKRrJHUZY+4xxpxtjPGquyAAoAD19Q/kdB6AQZkW93V2Hljcd8wx2Y8RgCRyKgBAcuRUBcjtOvvSS4fW1d/6lrexAQByhlwOAIpIJOJsjf/qq7F1/T/9U27iAgBA3h3jK2vtLmvtbdbaUyWdIGmppLcUS2rKJZ0t6R5JG40x1xpj2DEGgBJQWVGe03lAycq0uO/Pfz6wuO9d78p+jACSIqcCAIyEnKpAuF1rX3jh0Nr65pu9jQ0AkFfkcgDgY/fcE1vjH3548nHRaGxtP3lybuICAGCYnLxryFr7N2vt1yRNkvQZSY8MPmUkHS3pm5JeMsY8aIyZbYzh1UcAKFKhupqczgNKRqbFfY8/fmBx39/9XfZjBJA2cioAQBw5VR65XW9/8pND6+uVK72NDQBQkMjlAMAnrr46ts7/5CeTj4uv79N5DR4AgCzJaYtwa+0ea+2d1trTJdVJWizpdcWSmjJJH5V0l6RNxpgfGGOm5DI+AID3Gmqr1BgMuJrTFAyoobbKo4gAn8q0uK+19cDivlAo+zECyDpyKgAAOVWOuV1zf/SjQ2vs3/zG29gAAL5BLgcABeqYY2Jr/WuuST4uvsYHAKAA5LTYbzhrbZekRyU9Gf+SYkmNkXSEpG9I6jTG3GSMOSw/UQIAvLCwuV5lDvdJyoy0oLne24AAP8i0uO/++w8s7vvIR7IfI4CcIqcCgNJFTuUxt+vu979/aJ398MPexgYA8D1yOQAoAPH1/saNiccceSRFfgCAgpTzYj9jzFHGmH8zxnRKekhSvBeukfQ3STdIenXw89GSvijpKWPM4bmO9WDGmM8bY6yDx+kZ3ONdxpibjTFdxph+Y8wWY8xDxphzs/m9AEA+hepqtHj29JSbU2VGWjJ7BsdNoTRlWtx3990HFveddVb2YwSQF37OqSTyKgDIBnIqD7hde0+fPrTWfuIJb2MDABQFv+dyAFAUnKz577gjts5//fXcxAQAgEvlubiJMcZI+gdJX5B0lqRRiiUrkrRb0t2SbrbWPjY4/quSzpb0bUmnSApK+o6kf85FvA5EJW1J8vzudC5qjDlLsTbt4wa/tF1SQNLHJH3MGHObpPnW8vYBAP43d+ZUTa4ep2WtHWrr6nnH803BgBY017MpBUfau3sV7oyor39AlRXlCtXV+O+YsnQK+ob7xS+kz3wmO7EAKDhFmFNJ5FUAkBFyqixwuwYPBqWXX/YmljwripwKAApQkeZyAOAvvb3S+PGpx/X0SNXV3scDAECGPC32M8YcI2m+pIslHR3/8uCfnZJukXSbtfat4fMGN13uM8bcL+kBSR+VdKaXsbr0qrX22Gxe0BgTlLRasQ2psKRLrLXtxphKSf+qWDJ3saQXJP0wm/cGgHwJ1dUoVFfDpgLSFu6MaGlrh9aMsLnZGAxoYSFvbmZa3Ld8uTR/fnZiAVCwijinksirACBj5FRpcLsOnzhRikS8iaUA+DqnAoACVuS5HAD4w5o1UlNT6nHRqNrf7FP4+Yj6+iPkVACAgpf1Yj9jTLlirce/KKlZseQlnsAMSLpH0k3W2tZU17LWRo0xtyuWzEzNdqwF5lpJh0p6Q9LZ1tptkmSt7ZN0lTHmSEmXSvqmMeZWa+3W/IUKANnVUFtF0gTXVq3dqEUt6xVN0JdpTVeP5q1o05LZMzRn5pTcBjeSMWOkvXvTn3/DDdJXvpK9eAAULHKqjJBXAShJ5FQpuC3wGzNG2p1Wg1lf8V1OBQAFjlwOAArEtddKV12Vepy1sTe/3PIkb34BAPiKF539XpMU/xcvnsS8IulWSSustd0urxf/l3VUFmIrSMaYQyWdO/jpjfENqYMsVmxTarxiyeJtOQoPAICCE+6MJN2Uiota6cqWdZpUPTb3CXlNzf9n7+7Do6ruvf9/VkAMkKik0aggEk2iVsEWIdETq55fatGK9apwiwIAACAASURBVDat4Dk2bVFbW6tQj7bAbVux574hfbKCPfWpQav2VKiltqVaralVT8TATR/A+pCkhoKi0TSoEyBgyPr9MROTwDzsvWfPzJ6Z9+u65iLJrLXmGyM6n6zvXlv65z8Tj4ulsVFauNC/egBkEzKVB+QqAMAIXk7SzqM7vGdFpgKA7EOWA4BMmjxZ2rYt/pjiYunddyVx8QsAIHsVpGDNwxUOMQOSfiPpAknHWWuXeggyUjgc/UTSff6VGDhnShob+fjRaAOstVskvRj59GNpqAkAgMBa3tyecFNq0ICVVjS3p7YgSTr33PCG4uDDbaPfTTeFNxcHHzT6AfmMTOUNuQoA8t3w9+NODX8PnkcCmakAIPuR5QAgEwYzQLxGv4ULw+/5I41+bi9+aeno9rFgAACSk6qT/Zok3W2tfS3Zxay1z0ual3RV/jrcGLNR0gkKX1H1uqRnJf3YWvtHD+udMuzj5+OMe17SSZJO9vAaAADkhLauUNQj9eNp7exRW1fI31ubXXyx9PDD3udff730ve/5Vw+AXJIPmUoiVwEA/MAJfq4FJlMBQO7JlywHAMHgJAs89ZR01lkHfNnLxS+cdA0ACIpUNPsda60dSMG6QTJO0nRJOySNl1QeeVxmjLlH0hestf0u1js68ucOa+3uOOMGw+HRcca8L7JxlsiJTtYCACAovF5B19LRndzG1Kc/Lf30p97nf+lL0o9+5H0+gHySD5lKyoJcRaYCgICiwS8pGctUAJD78iXLAUDmhELSIYckHrdjh3TYYVGf4uIXAEC28/02vjkeZLZLulnSqZIKrbUlCm9Q1Up6IjJmnqQfuFx38F3BrgTjBp/nXQQAIG/19rnp+0hi3lVXjbwNmNtGv09/euQtwWj0A+BQjmcqiVwFAPCCW/T6Jm2ZCgDyTB5kOQDInNbWcBZI1Og3MBB+/x+j0U9K7uIXAACCIBUn++Usa+3jkh7f72v7JD1rjJklaY2kiyRdbYxZYa1tz0CZw2s7LdGYyEkV09NQDgAAvigq9Pb2JeG8666Tbr3V09qSpGuvlVas8D4fAPJENuUqMhUAZBgn+KVEyjIVAAAA4Lebb5aWLEk8zkUO4OIXAEC24zc0PrHWDhhjblB4U6pA0oWSbnE4PRT5c1yCcYPPh+KOAhAYbV0htXR0q7evX0WFo1VbUcoR30CSaitK/Zl3443S0qXeC5k3T1q50vt8AMAByFUA9kemykM0+KWcb5kKAAAASJWJE6Xt2+OPOeQQ6Z13XC/NxS8AgGzH/5F8ZK3tMMZ0SyqVdJyLqYPvVCYYY8Zaa3fHGDdxv/EAAqqlo1vLm9u1vrPngOeqy0u0oK6SX5IDHlWVFau6vCTq369YaspLVPXjFdLXv+79hefOlR580Pt8AIAj5CoAEpkq79Dgl1aeMxWNtgAAAEg1J9lg4UKpsdHzS3DxCwAg2xVkugBIkp4f9vEpccYNPve3FNYCIEmrNmxVQ1NrzF+ar+/sUUNTq1Zv2JbmyoDcsaCuUgUJMv+V69doy7dna8u3Z2vVF//FfaPfBReENxAHHzT6AUDQkauAHEGmyhPGDD2cGv7+HElxkqkGFRhpfl1lagsCAABAfnOSDZ56KpwFkmj0k4YufnGDi18AAEFCs5+PjDHHK3z6hCR1upj6P5IGT504L8bax0o6KfLp454KBJByLR3dWrxmswYS7DsMWGnRmk1q6ehOT2FAjqmtKNWy+qkjNqeGN/dt+fZsff1Jl7fYPeeckZuHa9f6WjMAwBlyFZDfyFQ5jga/wIiWqaIpMFJj/TROMQEAAID/QiFn+WDHjnAeOOss316ai18AANmMZj+HjIn/LiPy/Hcjnw5IctwhYK3dKekXkU+/ZIw5NMqwhZE/Q5Iedro2gPRa3tyecFNq0ICVVjS3p7YgIIfNffrneqUxiea+GTNGbhw++WRqCgUAvI9cBSARMlUOKi6mwS+g5s6crPuvqFFNjFNNaspLdP8VNZoz85g0VwYAyCRjzOeMMdbB46OZrhVAlmptDeeDQw6JP25gIJwJDjvM9xK4+AWp0NYV0j0tnbqtuV33tHSqrSuU6ZIA5KjRmS4gixxrjFktqUnS7yV1WmutMaZAUrWkJZJmRcbeaa19efhkY8y9kj4rSdbaaG8bvinpYklHSfqNMeYKa227MWa8pOslfTEy7v9Ya3f4+p0B8EVbVyjmbaZiae3sUVtXiKO/ASfuuEP60pe8zz/hBOmll/yrBwDgBbkKQExkqhwycaK0fbu7OTT2ZURtRalqK0rV1hVSS0e3evv6VVQ4WrUVpfy9AgAMSHorzvN70lUIgBxx883SkiWJx6UpG8ydOVmTJozTiuZ2tUbJojXlJZpfV0mjHxJq6ejW8ub2qL/TqC4v0QL+PQLgM5r93JkZeUjSHmNMSFKxpIOHjblH0ny3C1trO40xcyT9XNJHJLUZY96RVCRp1LC1vxtjCQAZ5vX2US0d3fwCHYjm3nulefO8z580Sdq2zbdyAAC+IVcBiIpMleVOOEFqa3M3hwa/wKgqK+bvEQBgf9ustVMyXQSAHODkYqBDD5Xefjs99QzDxS9I1qoNW7V4zeaYdylY39mjhqZWNdZP49R0AL6h2c+5LknXSjpD0ockHS5pgqQ+SZ2SnpW00lrb4vUFrLWPGGOmKXxrqXMVPo1ih6Q/K3yqxS/izQeQWb19/WmdB+Sc1auluXOTW4PNQgAIOnIVgJjIVFloxgxp40Z3c3jPDgAAAOQHk+AeuZK0aJG0bFnqa0mAi1/gRUtHd9xGv0EDVlq0ZpMmThjLCX8AfEGzn0PW2t2Sfhh5eJn/OUmfczDu75K+4OU1AGRWUaG3/6R6nQdkvV//WrroouTWYKMQALIKuQpAPGSqLHHOOdJTT7mbw/t2AAAAIH84afJ7+mnpIx9JfS1ACi1vbk/Y6DdowEormttp9gPgC34bCgA+8frmjDd1yBuPPSadd15ya7BJCAAAkLPIVAF2wQXSI4+4m8N7dwAAACB/hELSIYckHrdjh3TYYamvB0ixtq6Q1nf2uJrT2tmjtq4Qp0gCSBrNfgDgk6qyYlWXl7h6Y1dTXsIbOuSup54Kn/qRDDYIAQAA8gaZKmDmzpVWr3Y3h/fvAADkksONMRslnSBplKTXJT0r6cfW2j86XSSyRiIneqoQQOa1tkqnn554HFkBOaalo9vzPH6PASBZBZkuAAByyYK6ShU4OJ1ckgqMNL+uMrUFAem0bl34eP7Bh5dGP2tHPgAAAJBXyFQZNm/e0Pt5p41+vH8HACBXjZM0XdJehfcTyyVdJulJY8xKYwwHigD5bMmScG5I1OhHVkCO6u3rT+s8ABiON+IA4KPailItq5+qxWs2ayBOdikwUmP9NG43hez25z9L06cntwYhHwAAAMOQqTLg2mulH/7Q3RzexwMAkMu2S7pZ0hpJL1tr9xhjRkmqiXz9o5LmSdop6dpEi1lrT0s0JnL6X5K/aAQQTVtXSC0d3ert61dR4WjVVpQmd6rY0UdLr78ef8xhh4Vv1wvksKJCb602XucBwHD8lwQAfDZ35mRNmjBOK5rb1Rrl9lM15SWaX1fJphSyz5/+JJ2W8Hdz8bEpCAAAgATIVGnwta9J3/2uuzm8lwcAIC9Yax+X9Ph+X9sn6VljzCyFmwAvknS1MWaFtbY9A2UCSKClo1vLm9u1Pkqmqi4v0QK3mco4OIJ90SJp2TIXVQLZy+vvJPhdBgA/0OwHAClQW1Gq2opS/6+YAtLphRekk09Obg02BAEAAOABmSoFbr45fKstN3g/DwAAhrHWDhhjblC42a9A0oWSbslsVQD2t2rD1rinpa/v7FFDU6sa66dpzsxj4i/mpMnvmWekM890XyiQxarKilVdXhK1oTaWmvISfqcBwBc0+wFAClWVFfOmLQE27wKkvV2qqkpujYEBZ+EfAAAAcIBMlVjcTPWd70gLF7pbkAY/AAAQh7W2wxjTLalU0nGZrgfASC0d3XEb/QYNWGnRmk2aOGHsgSeNvfuudOihiV9sx47wLXuBPLWgrlINTa0J/75JUoGR5tdVpr4oAHmBZj8AWYkGsezn+xHycO8f/5CmTEluDZr7AAAAshKZKvvFylSf3fgb3fzEne4W4309AAAAkBOWN7c7ajySwg1/K5rbh/ZinntOOuOMxBO5QAiQFL4rwbL6qQkbbAuM1Fg/jX1PAL6h2Q9AVqFBLDf4eoQ8nNu+XZo4Mbk19u2TCgr8qQcAAABpR6bKDftnqpqtm7XqZ4vdLUKDHwAA8MAYc7zCp/pJUmcmawEwUltXyNUtRSWptbNH/7xhsT7w/cbEg2nyAw4wd+ZkTZowTiua29Ua5e9fTXmJ5vO7FgA+o9kPQNagQSw3+HKEPJx56y3piCOSW6O/Xxo1yp96AAAAkFFkqtwwmKlOffUl/fKBG9xN5uIdAAAQhzHGWBu7m8cYYyR9N/LpgKS1aSkMgCMtHd2uxq//YYOO2Lkj/qCSEumf/0yiKiD31VaUqrailLsoAEgbmv0AZAUaxHJHUkfII74dO8LBOxl790oHHeRPPQAAAAgMMlWO+NOfVHvaaXrFxZRLf/SMHvzSmSkrCQAA5JRjjTGrJTVJ+r2kTmutNcYUSKqWtETSrMjYO621L2emTADR9Pb1Oxq35duzEw9avFhaujTJioD8UlVWTHMfgLSg2Q9Axri5uoEGsdzg9Qj5tq4Qb46jefdd6dBDk1ujr086+GB/6gEAAEBakanyxKZN0qmnuppy/Fd/pX0FkRO6//EOmQoAALgxM/KQpD3GmJCkYknDf4l4j6T56S4MQHxFhfG3/h01+T3zjHQmFwsBABBkNPsBSLuWjm4tb26P2vRVXV6iBXWVIzaVaBDLHW6PkB8+j5+lpF27pPHjk1tj505p3Dh/6gEAAEBGkKnywAsvSCef7GrKiAa//ZCpAACAQ12SrpV0hqQPSTpc0gRJfZI6JT0raaW1tiVjFQKIKdoFW2P39unFH3wq8eS3307+cAEAAJAWNPsBSKtVG7bGvXXU+s4eNTS1qrF+mubMPEYSDWK5xOkR8n7Ny3p79kiFhcmt8e67UjF/DwAAAHIFmSqHtbVJJ5zgakrFDQ+rf1TiX+/lbaYCAACuWGt3S/ph5AEgy1SVFau6vETrO3t0wltb9NjKaxLOmXvHs1p11RlpqA4AAPiFZj8AadPS0R13U2rQgJUWrdmkiRPGqrailAaxHJLoCHm/52Wd996TxoxJbo2eHmnCBH/qAQAAQKCQqXJQZ6d03HGuplRd/0vtHX2Qqzl5k6kAAACAPLf0rXWq+Pb1CcdNWbhWBUa6v64yDVUBAAA/FWS6AAD5Y3lze8JNqUEDVlrR3C6JBrFcEu0I+VTOC7x9+yRjhh5eGv3efFOyduhBox8AAEDOIlPliK1bhzKA00a/3bsla9X2xruuG/2kHM5UAAAAAMJmz5aMUcU3Yjf67Sgs1pSFa99v9Gusn0ZWAAAgC/FbWwBp0dYV0vrOHldzWjt71NYVokEshww/Qt6pmvKS3Ll12MCANGpUcmu89pp09NH+1AMAAICsQabKctu3SxMnupvT2yuNHz/iS3mfqQAAAACMZEzCITd+7Gr99MMff//zmvISza+rJPMBAJClONkPQFq0dHR7nje4meEGmxnBtaCuUgWJs6ckqcBI87P5CHlrR57c56XRb8uWkSf30egHAACQl8hUWairaygLOG30e/fdoff++zX6DcqrTAUAAAAgusGsEc9f/6q2N95VxTdv0PXnVummCz+ox687S6uuOoNGPwAAshgn+wFIi96+/qTmLairVENTq6NbVrGZEWy1FaVaVj9Vi9dsjvvzzMoj5K2VCpLso29rkyr59xcAAAAjkamyxFtvSUcc4W7Ojh3SYYc5Hp7TmQoAAADIEm1dIbV0dKu3r19FhaNVW1Ga+gumdu6UiooSjwuF3h9XJXEhlwMZ+XkCAOARzX4A0qKo0Nt/bgbnsZmRW+bOnKxJE8ZpRXO7WqPcfiqrjpB3cER+XM8/L518sj+1AAAAIGeRqQJsxw6pxN3JifrnP93PGSanMhUAAACQRVo6urW8uV3ro7wPry4v0YJUvA/fvFmaNi3xOOvg6i6MkJGfJwAASaLZD0BaeH0jPHwemxm5pbaiVLUVpdl3tVSyzX0bN0rTp/tTCwAAAPIGmSpg3nnH1Wl8kqQ335QOP9y3ErI2UwEAAABZatWGrXEvoFrf2aOGplY11k/TnJnHJP+Cd90lXXVV4nE0+XmS9p8nAAA+odkPQFpUlRWrurwk6pUxsdSUlxywQcFmRu6pKisO9s8u2ea+Z5+VzjjDn1oAAACQt8hUAdDbKxW7/Gf0+uvSkUempp6IwGcqAAAAIAe0dHQnPCldkgastGjNJk2cMNb7hVQXXCA98kj8MeedJz36qLf1kd6fJwAAPqPZD0DaLKirVENTa8I3zlL41lHz6yolKeYmFJsZSIlkm/uefFI65xxfSgEAAACGI1NlwK5d0vjx7ua8+qo0cWJq6gEAAADgGzcXQS1vbneUxaRwg9iK5nb3zWFO9iduv1364hfdrYsDpOXnCQBAitDsByBtaitKtax+asIrZQqM1Fg/TZI05851UU+uqC4v0QJuLwU/JNvc98gj0vnn+1MLAAAAEAeZKk36+qSxY93N2bJFOvbYlJQDAAAAwF8tHd1a3tzuOCu1dYVcnbIuSa2dPWrrCjm7yMrJPsVf/ypNm+aqBkSX8p8nAAApVpDpAgDkl7kzJ+v+K2pUU14S9fma8hLdf0WNrKwamlpjvtle39mjhqZWrd6wLZXlIhcZM/Lh1po1krVDDxr9AAAAkEZkqhTZs2coIzht9Pv734dyAY1+AAAAQFZYtWGr66zU0tHt6bXiztu509k+RSgUzhw0+vkmJT9PAADSiJP9AKRdbUWpaitKYx6P3tLRnfCkCil8bPaiNZs0ccJYTqNAbMme3PfAA9Jll/lTCwAAAOADMpVP3ntPGjPG3ZyXXpJOOCE19QAAAABIKa9Zqbev39PrRZ23ebOzxj3r8B6zcM3XnycAABlAsx+AjKkqK4563PXy5vaEQWvQgJVWNLfn58ZUjom1Uelass19d98tXXllcmsAAAAAaUCm8qC/XzroIHdz/vY36YMfTE09PvItUwEAAAA5ymtWKir0tqU+Yt5dd0lXXZV4Ek1+KefLzxMAgAzi/0gAAqWtKxTz6PRYWjt71NYVYhMjS7V0dGt5c3vUn3t1eYkW1FXG33hMtrlv+XJp/vzk1gAAAAACgkwVxb590miXvwL7y1+kU09NTT0+SzpTAQAAAHkgmazk9f10bUWp9M1vSv/5n/EHnnee9Oijnl4D7iX18wQAIAAKMl0AAAzX0tGd1nnIrFUbtqqhqTVmwF7f2aOGplat3rBt6IvGjHy4tXRp+Mq4wQeNfgAAAMghZKqIgYGhzOC00W/DhqGckCWNfp4yFQAAAJCHkslKVWXFqi4vcTWv+cEbVHXkIfEb/e68M5w/aPRLKy8/z5rykty9QA4AkHVo9gMQKL19/Wmdh8xp6ejW4jWbEx6Z/0rjbM2pnuy9ue/rXx/Z3Ld4sbeCAQAAgCyQ15nK2qHcMGqUsznr1g1lhRkzUlufz5xmqgErLVqzKfcaOgEAAAAXks1KC+oqVeBgi2LLt2dry7dn6/h/vBR70KZN4QzyhS94qgnJc/rzlKQCI82vq0xtQQAAuMBtfAEESlGht/8seZ2HzFne3B51U2rLt2cnt/BXviL94AfJrQEAAABkqbzLVNZKBS6vZX3qKemss1JTTxrFylTRDFhpRXM7t50CAABA3ko2K9VWlGpZ/dSoF9wc3L9XL3+/PvFiu3dLhYWe6oC/4v08hyswUmP9NLIUACBQsvQ3uQByldc3y7zJzi5tXaH3bzO15Pd36HN/Wut9sSuvlO6+26fKAAAAgOyWF5nKS4PfE09IdXWpqScDhmcqp1o7e9TWFeLWUwAAAMhLfmSluTMna9KEcVrR3K7Wzh5N3vG6nr7r84kXsQ6v0kFa7f/z3F9NeYnm11VmV14GAOQFmv0ABEpVWbGqy0tcbVrUlJfE3Kxo6wqppaNbvX39KiocrdqKUjY2Mu2rX1XV976nLV7nz50rPfigjwUBAAAAucPvTCUFKFcZh/dYGvTII9L556emlgzzekvelo5uMjEAAADyUrJZaXguWtDxB/3L974ef/KMGdKGDcmUjDSorShVbUVpcHIvAAAO0OwHIHAW1FWqoanV0e2ICow0v67ygK+3dHRreXN71NBWXV6iBVyJkz5Llkg33+x5+h+Om6HLL1kiSbr+3CpdG+XnDQAAAGCIH5lKCkiuctvg96tfSZ/4RGpqCZDevv60zgMAAABygZesNDwX3bv6Jp3TuTH+xG98Q/rWt/wpGGlTVVZMcx8AIGvQ7AcgcGorSrWsfqoWr9kcN3AVGKmxftoBm0urNmyNO3d9Z48amlrVWD9Nc2Ye42PlkCQ1NkqLF3uevvbEj+iaixZGfa6okP9tAQAAAIkkm6mkDOcqtw1+q1dLl1zibw0B5zUbkakAAACQz9xmpVd37NLiNZv1SuPsxIvn8MniAAAgWPgNH4BAmjtzsiZNGKcVze1qjXKKRE15ieZHOUWipaM7YUiTpAErLVqzSRMnjOWEv2Tdeqt03XWep99y5mVaUftvjsbyswIAAACc8ZqppAzlKrcNfj/9qfTv/57ca2Yxr/+8yVQAAADId06zkiTVVh6uuQnWm3X5D9V+xBTdXzlTtSmoFwAAYH80+wEIrNqKUtVWlKqtK6SWjm719vWrqHC0aitKYx6lvby53dHx61J4Y2pFczubHW7dfrt09dXe5y9eLC1dqjl3rot6O7BYaspLOEIdAAAAcMFLppLSmKvcNvitXCnNm+f+dXJQVVmxqstLyFQAAACAB3Gz0ngjFSd+33zSdQ9p95jC8CfsN+UMt/kZAIBMoNkPQOBVlRU7eiPd1hVytdEhSa2dPWrrCvFGPZ57701uQ+0rX5F+8IMDvrygrlINTa2ONhELjN6/kg4AAACAO04zlZSGXDV2rNTX53zxNWukiy92VU++IFMBAAAAyRmRlTZtko48LuGcKQvXRv06+03ZraWjW8ub26Pm4eryEi2IcTI+AACZUJDpArKJMeYDxph5xpgHjDEvGGN2GmP2GGNeNcY8bIzx/NtnY8znjDHWweOjfn5PQC5p6ehO67yc9bOfhU/YGHy4bfT7whcka4ceURr9pPCVc8vqp6ogwWEeBUZqrJ9GiAIAIAeQqYDgS0muKi0dyhdOGv1Wrx7KEzT6xUSmAgAAAHxw553hrHLqqXGHTVm4Nmaj3yD2m7LTqg1b1dDUGvPCt/WdPWpoatXqDdvSXBkAANFxsp87b2jkP7M+Se9Jmhh5XGSMeVTSp6y1uzy+xoCkt+I8v8fjukDO6+3rT+u8nPHLX0r19d7nNzRI993naercmZM1acI4rWhuV2uUEFVTXqL5XC0FAEAuIVMBAedbrpo0SXrtNecLPPCAdNllnl47n5GpAAAAAI/OO0967LG4Q/5w3AxdfskSx0vm/X5TFmrp6NbiNZsTnpg+YKVFazZp4oSx5CsAQMbR7OfOaEnrJd0r6TFr7SuSZIyZIunrkq6QdL6kOyU1eHyNbdbaKUnWCeSlokJv/0nzOi9r/fa30uzZ3ud/8pPSQw/5Vk5tRalqK0rV1hVSS0e3evv6VVQ4WrUVpRx3DwBA7iFTAQGXVK6qqJD+/nfnk1audH+SOA5ApgIAAABcMAmOxpbU8rWlusxMc7103u035YDlze0JG/0GDVhpRXM7zX4AgIzjHYc7/5+19sn9v2it3SLpSmNMv6SrJH3aGPO/rbWc5Qukkdc31zn/pvyJJ6Rzz/U+/+MfDzcIplhVWTEbUQAA5D4yFRBwbvPRoyuv0UlvbZG+7XDCHXdIV13lui4kRqYCAAAA4nDQ5KdNm6SpU3V4V0j6wdOuXyLn95tyTFtXKOate2Np7exRW1eI7AUAyCia/VyItim1nyaFN6YkaYYkNqaQcfl0ZX9VWbGqy0tcvTGvKS/JvX8eTz8tnX229/lnnSU99ZR/9QAAAESQqZCN8ilTSc5y1a9/8hVNe6PD+aK33SZdc40P1QEAAACAC729UrGD/NbbK40f//6nfu835VuuzBYtHd2e5/HzAwBkEs1+/uob9vGojFUBKPxGc3lze9QgUl1eogV1lTl5hdGCuko1NLU6OnK7wEjz6ypTX1SqrVsn/cu/eJ8/Y4a0YYN/9QAAAHhHpkJg5GumkqLnqlU/XaiaV//mfJHvfle64Qb/iwMAAACARP76V+lDH0o8zsbeTPJjvymfc2U26O3rT+s8AAD8QrOfv84Z9vFmj2scbozZKOkEhTe3Xpf0rKQfW2v/6GahyDqJnOi6QgTeqg1btXjN5pgBZH1njxqaWtVYP01zZh6T3uJSrLaiVMvqp8b9/qVw8Gqsn5adIWrjxnCDnlcnnii9+KJ/9QAAAPjnnGEfk6mQMfmcqaShXNW94Kv68rrVzicuXSotXpy6wgAAAAAgnttvl66+OvG4OE1+g5Ldb8r3XJkNigq9tUp4nQcAgF8KMl1ArjDGHCZp8Dfaz1hrX/a41DhJ0yXtVfjnUy7pMklPGmNWGmN494C4Wjq6EwYPSRqw0qI1mzwfUR1kc2dO1v1X1KimvCTq8zXlJbr/iprsCU+bNknGDD3cNvpNnhwOroMPGv0AAEAAkakQFHmfqW6+WTJGc6uPddbod9NNQ1mDRj8AAAAAmXDeeeH9k3iNfrNnD2UXh7zuN+V9rswSXg8EycqDRAAAOYVNDh8YYwok3S/pKIVvO3WNh2W2S7pZ0hpJL1tr9xhjRkmqiXz9o5LmSdop6VonC1prT3NQ+0aFN8KQYG3/uwAAIABJREFUI5Y3tzs6UlwKh4gVze05+aa0tqJUtRWlausKqaWjW719/SoqHK3ailJVlRVnurz4XnpJOukk7/MnTJB6DjwSHgAAIKjIVAiSvMxUS5dKN97oeHjPtf+hkhXfT2FBAAAAAOCAMYnH3HWX9PnPe34JL/tNeZkrs1BVWbGqy0ui3mY5lprykuDvMwIAch7Nfv5YLml25OMvW2s3uV3AWvu4pMf3+9o+Sc8aY2YpvGF1kaSrjTErrLXtSdaMHNTWFXL1hlSSWjt71NYVytk3plVlxcH/3jo6pMpK7/PHjJH27PGvHgAAgPQjUyEQ8ipTNTRIDzzgfPywDbLoZ1oAAAAAQJo4afLbvFk65RTfXtLpflNe5cocsKCuUg1NrY6aMwuMNL8uif08AAB8wm18k2SM+Z6GTp24zlq70u/XsNYOSLoh8mmBpAv9fg3kBq/HfHM8eJr94x8jb8vrpdFv+G15afQDAABZjEyFIMn5THXllUM5xEmj33/911DuSOIkDAAAAABIWm/vUJ5JNM5aXxv93Mj5XJljaitKtax+qgoS/GtVYKTG+mmcwAgACASa/ZJgjPmOpOsjn95grb01Va9lre2QNPgu77hUvQ6yW29ff1rnwaFXXx3Z3Ddlivs1hjf3WYdnvwMAAAQcmQpBk5OZ6stfHsoiTU2Jx99661DuuPrq1NcHAAAAAPH89a/hPFOc4NS7wRwzfnx66oohJ3Nljps7c7Luv6JGNeXRz7GvKS/R/VfUaM7MY9JcGQAA0XEbX4+MMd/V0MkQX7PWfj+T9QCSVFTo7a+013mIoadH+sAHkluDhj4AAJDjyFQIopzJVNdfL91yi/Px3/mO9NWvpq4eAAAAAHDr9tudXYAUsP2UnMmVeaa2olS1FaVq6wqppaNbvX39KiocrdqKUm6vDAAIHN41eBC5zdTg6RNfs9Z+Nw2vebykwXOBO1P9eshOXo+O5sjpJL39tjRhQnJrDAwkPnoeAAAgR5CpEFRZnakWL5YaG52P/9SnpJ//PHX1AAAAAIDkvnlq1izp8cfjLzp7tvSb3/hbqE+yOldCVWXFNPcBAAKPZj+X9tuUusGP0yeMMcba2JedGGOMpMHNrwFJa5N9TeSmqrJiVZeXaH1nj+M5NeUlvGl1KxSSDjkkuTVo7gMAAHmKTIUgy7pMtWSJdPPNzscHeEMMAAAAQG5p6ejW8ub2qPmqurxEC+oqRza4Odkzuesu6fOf97FK/2VdrgQAAFmnINMFZBNjzHc0tCn1H242pYwxnzPG2MjjnP2ePtYYs94Yc5Ux5rjIRpSMMQXGmNMlPSrp4sjYO621Lyf5rSCHLairVIHDHrICI82vq0xtQblg585wyBx8uG30GzUq3Nxn7dCDRj8AAJCHyFTIBoHPVEuXDmUTJ41+5547lENo9AMAAACQBqs2bFVDU2vMhrf1nT1qaGrV6g3bhvJNPJs3hzNNwBv9BgU+VwIAgKxGs59DxpjJkr4a+XRA0kJjzBtxHje4fImZku6Q9HdJu40xb0naJWmdpFmRMfdImp/8d4NcVltRqmX1UxOGiAIjNdZP41jwaHbvHtncV1Tkfo19+4Y21Pr7ae4DAAB5j0yFbBHITPX97w/lkxtvTDz+zDOH8kii218BAAAAgI9aOrq1eM1mDcQ8f18at3e3XmmcrTnVk+MvtnNnONeccoq/RaZYIHMlAADIGdzG17mC/T4uSzDeTXdQl6RrJZ0h6UOSDpc0QVKfpE5Jz0paaa1tcbEm8tjcmZM1acI4rWhuV2uUq6Zqyks0f//j0fPZnj1SYWFya/T3h0/wAwAAQCxkKmSNQGSqFSukBQucj58xQ9qwIXX1AAAAAIADy5vbYzb6fbDrFT1yr4Nr8GycTsEsEYhcCQAAcpKxOfBmCd4ZYzZOnz59+saNGzNdClKkrSuklo5u9fb1q6hwtGorSlVVVpzpsjJr717p4IOTW+O996TR9EsDAJBFOGYXKUGmyn1pzVR33SVddZXz8SefLD3/fGpqAQAAGIlMhZQhV+WOtq6QPvaDpw/4+qf/9Fv9n9/fnniBHN23Zq8OAABE+JKr6FQBclxVWTGBYd++5Bvz9uyRxozxpx4AAAAAWSPlmeqee6TLL3c+/vjjpY6O1NUDAAAAAB61dHSP+PyGp+/TNetWx53z+4pqvXrvg5pXW57K0jKKvToAAOAnmv0A5J6BAemss6SWJO7S1teX/Ol/AAAAABDNAw9IDQ3Ox0+cKL36aurqAQAAAAAf9Pb1S5J+e898nfzmK3HHfu28+Vp96sckSddH5gEAACAxmv0AZL+BAencc6U//MH7Grt2SWPH+lcTAAAAAAy3erU0d67z8RMmSD09qavHAW41BQAAAMAxa3XtR6t0bYJh517+X2o//NgRXysqZMsaAADAKd45Acg+1kqjRoX/9Kq3Vxo/3r+aAAAAAGB/Dz8sXXyx8/GFhdLu3amrx6GWjm4tb27X+s4Dmw2ry0u0oK5StRWlGagMAAAAQODs3i2NG5dw2AnXr9Ge0WOiPke+AAAAcI5mPwDBZ61UVBQ+fc+DHYXFOuPqe9R3UKEkqcBIjS/0aM5Mmv0AAAAA+Oy3v5Vmz3Y3J5kLmXy2asNWLV6zWQMxSlrf2aOGplY11k/TnJnHpLc4AAAAAMHxyivS8ccnHDZl4dq4z9eUl3CCOAAAgAs0+wEIHmulsjLprbc8Td910MGacc0D2jUm+m15B6y0aM0mTZwwlqvFAAAAACTv8celWbPczQlQg9+glo7uuI1+g8hUAAAAQB5bu1a68MK4Q/589Am6uOH7CZcqMNL8ukq/KgMAAMgLBZkuAAAkSccdJxkTfhQUuGv0GzVKeucdzbnjWU1ZuFYf/I9fxGz0GzRgpRXN7UkWDQAAACBvPfnkUIZx2uhn7dAjgJY3tyds9BtEpgIAAADyzOLF4fwTr9FvyRLJWrU9/LgKTPzlCozUWD+NC4gAAABc4mQ/AJlx8snSCy94n9/VJR1xxPuftnWFtL6zx9USrZ09ausKcTw8AAAAAGeeflo6+2x3cwLa2Lc/MhUAAACAqD78Yekvf4k/5ne/G3ER1NyZkzVpwjitaG5Xa5ScUVNeovl1lTT6AQAAeECzH4D0qK6WNmzwPn/7dumoo2I+3dLR7WnZlo5uNqYAAAAAxPbSS9JJJ7mbkyUNfsORqQAAAAC8z9rwXZgS2bJFOvbYqE/VVpSqtqJUbV0htXR0q7evX0WFo1VbUUqGAAAASALNfgBS4+yzw6deeLV1q3TMMY6H9/b1e3oZr/MAAAAA5LD2dqmqyt2cgYHwLa2yFJkKAAAAgHbtksaPTzxu926psNDRklVlxXnb3EejIwAASAWa/QD447zzpMce8z7/lVek8nLP04sKvf3nzOs8AAAAADnmlVek4493NyfLG/yGI1MBAAAAecxpHsrCU8wzoaWjW8ub27U+yi2Mq8tLtIBbGAMAgCQ4OH8ZAKK4+OLwptbgw22jX1tbOBQOPpJo9JPkORQRpgAAAIA8tmXLUKZx2ug3MDCUY3Kk0U8iUwEAAAB5ae3axHno9NOHMhASWrVhqxqaWqM2+knS+s4eNTS1avWGbWmuDAAA5Aqa/QA48+//PrK57+GH3c1/4YWRzX2Vlb6WV1VWrOryEldzaspLOC4dAAAAyDfbtg3lGicXHR12WM42+A1HpgIAAADyyOLF4Wxz4YWxxyxZEs5A69alraxs19LRrcVrNmsgQV/kgJUWrdmklo7u9BQGAAByCs1+AKK7/PKRzX0/+5m7+Zs2jWzuO+mk1NQ5zIK6ShU43HcrMNL8On8bDgEAAAAE1PbtQ9lm8uTE48eOlfbtC2eZHTtytsFvf2QqAAAAIMddemk43zQ2xh7zu9+Fs9BNN6WvrhyxvLk9YaPfoAErrWhuT21BAAAgJ9HsByDsy18e2dx3zz3u5m/cOLK5b+rU1NQZR21FqZbVT024OVVgpMb6adxuCgAAAMhlb7wxlG8mTkw83pihBr9du6SC/PuVCZkKAAAAyEHWhk8sN0ZatSr2uC1bwmNnzUpbabmkrSsU89a9sbR29qitK5SiigAAQK4anekCAGTI9ddLt9ziff5zz0k1Nf7V45O5Mydr0oRxWtHcrtYooaqmvETz6yrZlAIAAABy0ZtvSmVl7ub090ujRqWmnixEpgIAAAByRF9f+NRyJ+MOPjj19eQ4r7fkbenoVlVZsc/VAACAXEazH5AvbrxRWrrU+/xnnpHOPNO/elKotqJUtRWlausKqaWjW719/SoqHK3ailICEwAAAJBrurulww93N+e996TR/EokFjIVAAAAkMVefVU65pj4Y446Stq+PT315Inevv60zgMAAPmL32wDueq//1u67DLv8//wB+lf/9W/ejKgqqyYjSgAAAAgF+3YIZWUuJuzd6900EGpqSdHkakAAACALPLMM9JZZ8Uf87nPSffck5Zy8k1Robdtd6/zAABA/irIdAEAfPLQQ5IxQw+3jX6PPSZZO/TI8kY/AAAAADmmt3co7zht9NuzZyjj0OgHAAAAIBf98IfhnBSv0e+uu8K5iEa/lKmtKE3rPAAAkL+4VADIVg8/LF18sff5v/61dOGF/tUDAAAAAH7buVMqKnI3p69POvjg1NQDAAAAAEFx6aXSqlXxx6xbJ51+enrqyXNVZcWqLi/R+s4ex3Nqyks4TR0AALhGsx+ySltXSC0d3ert61dR4WjVVpTmz5vg3/5Wmj3b+/xf/EKqr/evHgAAAABZKfC5avduqbhY2rfP+Zxdu6SxY1NXEwAAAAAEgbXSoYdKoVD8ca+/Lh15ZHpqwvsW1FWqoalVAzbx2AIjza+rTH1RAAAg59Dsh6zQ0tGt5c3tUa+GqS4v0YK6ytw75vrxx6VZs7zP/+MfpbPP9q0cAAAAANkt0Lmqr0/6wAfCTXtO7dwpjRuXupoAAAAAICj6+pxd4LRnjzRmTOrrQVS1FaVaVj9Vi9dsjtvwV2Ckxvppube3CQAA0qIg0wUAiazasFUNTa0xj71e39mjhqZWrd6wLc2V+eyPf5SMGXq4bfR74onwFV2DDxr9AAAAAEQEMlft2SMddlg4/4wdm7jRb8y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          },
          "metadata": {
            "image/png": {
              "width": 1277,
              "height": 269
            },
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "#@title\n",
        "\n",
        "#@markdown Execute this cell to visualize estimated models\n",
        "\n",
        "fig, axes = plt.subplots(ncols=3, figsize=(18, 4))\n",
        "for theta_hat, ax in zip(theta_hats, axes):\n",
        "\n",
        "  # True data\n",
        "  ax.scatter(x, y, label='Observed')  # our data scatter plot\n",
        "\n",
        "  # Compute and plot predictions\n",
        "  y_hat = theta_hat * x\n",
        "  ax.plot(x, y_hat, color='r', label='Fit')  # our estimated model\n",
        "\n",
        "  ax.set(\n",
        "      title= fr'$\\hat{{\\theta}}$= {theta_hat}, MSE = {np.mean((y - y_hat)**2):.2f}',\n",
        "      xlabel='x',\n",
        "      ylabel='y'\n",
        "  );\n",
        "\n",
        "axes[0].legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "7KaMk0le1YuO"
      },
      "source": [
        "## Interactive Demo 1: MSE Explorer\n",
        "\n",
        "Using an interactive widget, we can easily see how changing our slope estimate changes our model fit. We display the **residuals**, the differences between observed and predicted data, as line segments between the data point (observed response) and the corresponding predicted response on the model fit line.\n",
        "\n",
        "- What value of $\\hat{\\theta}$ results in the lowest MSE?\n",
        "- Is this a good way of estimating $\\theta$?\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "cellView": "form",
        "execution": {},
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 462,
          "referenced_widgets": [
            "a87f2827e8134d518e6a6c2968258a4c",
            "9c1d5b5dbcd64e32a5456f4350f7905d",
            "924ecc6425cf475ba4c14a63bb4f50b8",
            "1f1710dc5a814c41a56d85fe0f4624ab",
            "3814fa88c5bb47aa80cde03b38a85674",
            "9faf4d4b2e9c446c9cdea66217658505",
            "ed5adfe7cf5140cf8df7f01a135ac30e"
          ]
        },
        "id": "Xk1Z-iiv1YuP",
        "outputId": "fbfb18d5-ebeb-4300-f645-9f8a21846054"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "interactive(children=(FloatSlider(value=1.0, description='theta_hat', max=2.0), Output()), _dom_classes=('widg…"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "a87f2827e8134d518e6a6c2968258a4c"
            }
          },
          "metadata": {}
        }
      ],
      "source": [
        "#@title\n",
        "\n",
        "#@markdown Make sure you execute this cell to enable the widget!\n",
        "\n",
        "@widgets.interact(theta_hat=widgets.FloatSlider(1.0, min=0.0, max=2.0))\n",
        "def plot_data_estimate(theta_hat):\n",
        "  y_hat = theta_hat * x\n",
        "  plot_observed_vs_predicted(x, y, y_hat, theta_hat)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "lrNMNDEr1YuP"
      },
      "source": [
        "[*Click for solution*](https://github.com/NeuromatchAcademy/course-content/tree/main//tutorials/W1D2_ModelFitting/solutions/W1D2_Tutorial1_Solution_b528a7bb.py)\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "EePdN9Kl1YuP"
      },
      "source": [
        "While visually exploring several estimates can be instructive, it's not the most efficient for finding the best estimate to fit our data. Another technique we can use is to choose a reasonable range of parameter values and compute the MSE at several values in that interval. This allows us to plot the error against the parameter value (this is also called an **error landscape**, especially when we deal with more than one parameter). We can select the final $\\hat{\\theta}$  ($\\hat{\\theta}_\\textrm{MSE}$) as the one which results in the lowest error."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "cellView": "form",
        "execution": {},
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "ejzGdW6H1YuP",
        "outputId": "2ed927a9-6563-4d8d-8ef0-66ec9f3b21dc"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "image/png": {
              "width": 558,
              "height": 413
            },
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# @title\n",
        "\n",
        "# @markdown Execute this cell to loop over theta_hats, compute MSE, and plot results\n",
        "\n",
        "# Loop over different thetas, compute MSE for each\n",
        "theta_hat_grid = np.linspace(-2.0, 4.0)\n",
        "errors = np.zeros(len(theta_hat_grid))\n",
        "for i, theta_hat in enumerate(theta_hat_grid):\n",
        "  errors[i] = mse(x, y, theta_hat)\n",
        "\n",
        "# Find theta that results in lowest error\n",
        "best_error = np.min(errors)\n",
        "theta_hat = theta_hat_grid[np.argmin(errors)]\n",
        "\n",
        "\n",
        "# Plot results\n",
        "fig, ax = plt.subplots()\n",
        "ax.plot(theta_hat_grid, errors, '-o', label='MSE', c='C1')\n",
        "ax.axvline(theta, color='g', ls='--', label=r\"$\\theta_{True}$\")\n",
        "ax.axvline(theta_hat, color='r', ls='-', label=r\"$\\hat{{\\theta}}_{MSE}$\")\n",
        "ax.set(\n",
        "  title=fr\"Best fit: $\\hat{{\\theta}}$ = {theta_hat:.2f}, MSE = {best_error:.2f}\",\n",
        "  xlabel=r\"$\\hat{{\\theta}}$\",\n",
        "  ylabel='MSE')\n",
        "ax.legend();"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "2BVkXEL31YuP"
      },
      "source": [
        "We can see that our best fit is $\\hat{\\theta}=1.18$ with an MSE of 1.45. This is quite close to the original true value $\\theta=1.2$!\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "rMAE_Tzj1YuP"
      },
      "source": [
        "---\n",
        "# Section 2: Least-squares optimization\n",
        "\n",
        "*Estimated timing to here from start of tutorial: 20 min*\n",
        "\n",
        "While the approach detailed above (computing MSE at various values of $\\hat\\theta$) quickly got us to a good estimate, it still relied on evaluating the MSE value across a grid of hand-specified values. If we didn't pick a good range to begin with, or with enough granularity, we might miss the best possible estimator. Let's go one step further, and instead of finding the minimum MSE from a set of candidate estimates, let's solve for it analytically.\n",
        "\n",
        "We can do this by minimizing the cost function. Mean squared error is a convex objective function, therefore we can compute its minimum using calculus. Please see video or Bonus Section 1 for this derivation! After computing the minimum, we find that:\n",
        "\n",
        "\\begin{equation}\n",
        "\\hat\\theta = \\frac{\\mathbf{x}^\\top \\mathbf{y}}{\\mathbf{x}^\\top \\mathbf{x}}\n",
        "\\end{equation}\n",
        "\n",
        "where $\\mathbf{x}$ and $\\mathbf{y}$ are vectors of data points.\n",
        "\n",
        "This is known as solving the normal equations. For different ways of obtaining the solution, see the notes on [Least Squares Optimization](https://www.cns.nyu.edu/~eero/NOTES/leastSquares.pdf) by Eero Simoncelli."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "caFB1Nid1YuQ"
      },
      "source": [
        "## Coding Exercise 2: Solve for the Optimal Estimator\n",
        "\n",
        "In this exercise, you will write a function that finds the optimal $\\hat{\\theta}$ value using the least squares optimization approach (the equation above) to solve MSE minimization. It should take arguments $x$ and $y$ and return the solution $\\hat{\\theta}$.\n",
        "\n",
        "We will then use your function to compute $\\hat{\\theta}$ and plot the resulting prediction on top of the data. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "execution": {},
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "sOFyNs331YuQ",
        "outputId": "2951b71e-0295-433e-9484-04723e8ed84d"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "image/png": {
              "width": 557,
              "height": 413
            },
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "def solve_normal_eqn(x, y):\n",
        "  \"\"\"Solve the normal equations to produce the value of theta_hat that minimizes\n",
        "    MSE.\n",
        "\n",
        "    Args:\n",
        "    x (ndarray): An array of shape (samples,) that contains the input values.\n",
        "    y (ndarray): An array of shape (samples,) that contains the corresponding\n",
        "      measurement values to the inputs.\n",
        "\n",
        "  Returns:\n",
        "    float: the value for theta_hat arrived from minimizing MSE\n",
        "  \"\"\"\n",
        "\n",
        "  ################################################################################\n",
        "  ## TODO for students: solve for the best parameter using least squares\n",
        "  # Fill out function and remove\n",
        "  ################################################################################\n",
        "\n",
        "  # Compute theta_hat analytically\n",
        "  theta_hat = np.dot(x, y) / np.dot(x,x)\n",
        "\n",
        "  return theta_hat\n",
        "\n",
        "\n",
        "theta_hat = solve_normal_eqn(x, y)\n",
        "y_hat = theta_hat * x\n",
        "plot_observed_vs_predicted(x, y, y_hat, theta_hat)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "cellView": "both",
        "execution": {},
        "id": "w0I2-v1P1YuQ"
      },
      "source": [
        "[*Click for solution*](https://github.com/NeuromatchAcademy/course-content/tree/main//tutorials/W1D2_ModelFitting/solutions/W1D2_Tutorial1_Solution_7a89ba24.py)\n",
        "\n",
        "*Example output:*\n",
        "\n",
        "<img alt='Solution hint' align='left' width=848.0 height=561.0 src=https://raw.githubusercontent.com/NeuromatchAcademy/course-content/main/tutorials/W1D2_ModelFitting/static/W1D2_Tutorial1_Solution_7a89ba24_0.png>\n",
        "\n"
      ]
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      "source": [
        "We see that the analytic solution produces an even better result than our grid search from before, producing $\\hat{\\theta} = 1.21$ with $\\text{MSE} = 1.43$!"
      ]
    },
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      "source": [
        "---\n",
        "# Summary\n",
        "\n",
        "*Estimated timing of tutorial: 30 minutes*\n",
        "\n",
        "Linear least squares regression is an optimization procedure that can be used for data fitting:\n",
        "\n",
        "  - Task: predict a value for $y_i$ given $x_i$\n",
        "  - Performance measure: $\\textrm{MSE}$\n",
        "  - Procedure: minimize $\\textrm{MSE}$ by solving the normal equations\n",
        "\n",
        "**Key point**: We fit the model by defining an *objective function* and minimizing it. \n",
        "\n",
        "**Note**: In this case, there is an *analytical* solution to the minimization problem and in practice, this solution can be computed using *linear algebra*. This is *extremely* powerful and forms the basis for much of numerical computation throughout the sciences."
      ]
    },
    {
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      "metadata": {
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      },
      "source": [
        "# Notation\n",
        "\\begin{align}\n",
        "x_{i} &\\quad \\text{input, independent variable}\\\\\n",
        "y_{i} &\\quad \\text{measurement, dependent variable}\\\\\n",
        "\\mathbf{x} &\\quad \\text{vector of input values}\\\\\n",
        "\\mathbf{y} &\\quad \\text{vector of measurements}\\\\\n",
        "\\hat{y}_{i} &\\quad \\text{estimate of dependent variable}\\\\\n",
        "\\epsilon_{i} &\\quad \\text{measurement error}\\\\\n",
        "\\theta &\\quad \\text{slope parameter}\\\\\n",
        "\\hat{\\theta} &\\quad \\text{estimated slope parameter}\\\\\n",
        "\\hat{\\theta}_\\text{MSE} &\\quad \\text{slope parameter estimated via the mean squared error}\\\\\n",
        "\\textrm{MSE} &\\quad \\text{mean squared error}\\\\\n",
        "\\end{align}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "0llH50W21YuR"
      },
      "source": [
        "---\n",
        "# Bonus"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {},
        "id": "pgnzerrj1YuR"
      },
      "source": [
        "---\n",
        "## Bonus Section 1: Least Squares Optimization Derivation\n",
        "\n",
        "We will outline here the derivation of the least squares solution.\n",
        "\n",
        "We first set the derivative of the error expression with respect to $\\theta$ equal to zero, \n",
        "\n",
        "\\begin{align}\n",
        "\\frac{d}{d\\theta}\\frac{1}{N}\\sum_{i=1}^N(y_i - \\theta x_i)^2 &= 0 \\\\\n",
        "\\frac{1}{N}\\sum_{i=1}^N-2x_i(y_i - \\theta x_i) &= 0\n",
        "\\end{align}\n",
        "\n",
        "where we used the chain rule. Now solving for $\\theta$, we obtain an optimal value of:\n",
        "\n",
        "\\begin{equation}\n",
        "\\hat\\theta = \\frac{\\sum_{i=1}^N x_i y_i}{\\sum_{i=1}^N x_i^2}\n",
        "\\end{equation}\n",
        "\n",
        "Which we can write in vector notation as:\n",
        "\n",
        "\\begin{equation}\n",
        "\\hat\\theta = \\frac{\\mathbf{x}^\\top \\mathbf{y}}{\\mathbf{x}^\\top \\mathbf{x}}\n",
        "\\end{equation}\n",
        "\n",
        "<br>\n",
        "\n",
        "This is known as solving the *normal equations*. For different ways of obtaining the solution, see the notes on [Least Squares Optimization](https://www.cns.nyu.edu/~eero/NOTES/leastSquares.pdf) by Eero Simoncelli."
      ]
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            "children": [
              "IPY_MODEL_9c1d5b5dbcd64e32a5456f4350f7905d",
              "IPY_MODEL_924ecc6425cf475ba4c14a63bb4f50b8"
            ],
            "layout": "IPY_MODEL_1f1710dc5a814c41a56d85fe0f4624ab"
          }
        },
        "9c1d5b5dbcd64e32a5456f4350f7905d": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "FloatSliderModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "FloatSliderModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "FloatSliderView",
            "continuous_update": true,
            "description": "theta_hat",
            "description_tooltip": null,
            "disabled": false,
            "layout": "IPY_MODEL_3814fa88c5bb47aa80cde03b38a85674",
            "max": 2,
            "min": 0,
            "orientation": "horizontal",
            "readout": true,
            "readout_format": ".2f",
            "step": 0.1,
            "style": "IPY_MODEL_9faf4d4b2e9c446c9cdea66217658505",
            "value": 1.2
          }
        },
        "924ecc6425cf475ba4c14a63bb4f50b8": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "model_module_version": "1.0.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_model_name": "OutputModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/output",
            "_view_module_version": "1.0.0",
            "_view_name": "OutputView",
            "layout": "IPY_MODEL_ed5adfe7cf5140cf8df7f01a135ac30e",
            "msg_id": "",
            "outputs": [
              {
                "output_type": "display_data",
                "data": {
                  "text/plain": "<Figure size 576x432 with 1 Axes>",
                  "image/png": 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