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  "nbformat": 4,
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  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Lecture 7 - Search\n",
        "\n",
        "We will discuss:\n",
        "\n",
        "1. Idea to solve search on a list of integers\n",
        "2. Write the algorithm for basic search (code)\n",
        "3. Analysis - run time, correctness, space usage\n",
        "4. Structured vs Unstructured data\n",
        "5. Idea to search through structured data\n",
        "6. Implementation of searching through structured data\n",
        "\n",
        "Learning Objectives -\n",
        "\n",
        "1. Writing basic search algorithm\n",
        "2. Analysis - runtime, correctness, space usage\n",
        "3. Performance of algorithm on different input types\n",
        "4. Generating ideas to improve efficiency for searching through structured data\n",
        "\n",
        "Announcements -\n",
        "\n",
        "1. Homework 1 due TONIGHT\n",
        "2. Lab 3 due this Thursday\n",
        "3. Homework 2 (released on PL)\n",
        "4. Office hours today 5pm-8pm (HYBRID) https://edstem.org/us/courses/102969/discussion/8226240\n",
        "\n",
        "(My office hours today 7-8pm @ Siebel 2322 + Zoom)"
      ],
      "metadata": {
        "id": "uK4kIBwsN-4R"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Discovery clicker\n",
        "\n",
        "Scan and use join code 277\n",
        "\n",
        "OR Visit clicker.cs.illinois.edu and use join code 277\n",
        "\n",
        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ScB4bXbzwagSoEdghoH81LwwCGi+DgMiL/A0CGmvzES+8GgHqkwScx0YXL7waAWoEdgjoX80Lg4DGyyAg8iJ/g4DG2nzEC69GgPokAeex0cULr0aAGoEdAvpX88IgoPEyCIi8yN8goLE2H/HCqxGgPknAeWx08cKrEaBGYIeA/tW8MAhovAwCIi/yNwhorM1HvPBqBKhPEnAeG1288GoEqBHYIaB/NS8MAhovg4DIi/wNAhpr8xEvvBoB6pMEnMdGFy+8GgFqBHYI6F/NC4OAxssgIPIif4OAxtp8xAuvRoD6JAHnsdHFC69GgBqBHQL6V/PCIKDxMgiIvMjfIKCxNh/xwqsRoD5JwHlsdPHCqxGgRmCHgP7VvDAIaLwMAiIv8jcIaKzNR7zwagSoTxJwHhtdvPBqBKgR2CGgfzUvDAIaL4OAyIv8DQIaa/MRL7waAeqTBJzHRhcvvBoBagR2COhfzQuDgMbLICDyIn+DgMbafMQLr0aA+iQB57HRxQuvRoAagR0C+lfzwiCg8ZodBKwGP+L9vPx///vfJIPVfOE1GReb+igB57EZjxdejUBTy1fjRd0IyNcjvP436qQPjxawVV6tCurR4/if1Xzh5cwgsEPAeWxe4IVXI9DU8tV4UTcC8vUIL4OAR4z8739bIdSTBDTWZgtejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxejRc1AicJOI+NLl54NQJNLV+NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4NV4USNwkoDz2OjihVcj0NTy1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxeb/BqVdxT/3e0r8p9ywBejdeqmo/NGbwaL+pGQL4e4WUQ8IiRoy+sjS61xtoygNcbvFoV99QGAY01Xm/walXcU+v3jTVejRd1IyBfj/AyCHjESIOAZuSoWmNtxuD1Bq9WxT21D9vGGq83eLUq7qn1+8Yar8aLuhGQr0d4GQQ8YqRBQDNyVK2xNmPweoNXq+Ke2odtY43XG7xaFffU+n1jjVfjRd0IyNcjvAwCHjHSIKAZOarWWJsxeL3Bq1VxT+3DtrHG6w1erYp7av2+scar8aJuBOTrEV4GAY8YaRDQjBxVa6zNGLze4NWquKf2YdtY4/UGr1bFPbV+31jj1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxeb/BqVdxT+7BtrPF6g1er4p5av2+s8Wq8qBsB+XqEl0HAI0YaBDQjR9UaazMGrzd4tSruqX3YNtZ4vcGrVXFPrd831ng1XtSNgHw9wssg4BEjDQKakaNqjbUZg9cbvFoV99Q+bBtrvN7g1aq4p9bvG2u8Gi/qRkC+HuFlEPCIkQYBzchRtcbajMHrDV6tintqH7aNNV5v8GpV3FPr9401Xo0XdSMgX4/wMgh4xEiDgGbkqFpjbcbg9QavVsU9tQ/bxhqvN3i1Ku6p9fvGGq/Gi7oRkK9HeBkEPGKkQUAzclStsTZj8HqDV6vintqHbWON1xu8WhX31Pp9Y41X40XdCMjXI7wMAh4x0iCgGTmq1libMXi9watVcU/tw7axxusNXq2Ke2r9vrHGq/GibgTk6xFeBgGPGGkQ0IwcVWuszRi83uDVqrin9mHbWOP1Bq9WxT21ft9Y49V4UTcC8vUIL4OAR4w0CGhGjqo11mYMXm/walXcU/uwbazxeoNXq+KeWr9vrPFqvKgbAfl6hJdBwCNGGgQ0I0fVGmszBq83eLUq7ql92DbWeL3Bq1VxT63fN9Z4NV7UjYB8PcLLIOARIw0CmpGjao21GYPXG7xaFffUPmwba7ze4NWquKfW7xtrvBov6kZAvh7hZRDwiJEGAc3IUbXG2ozB6w1erYp7ah+2jTVeb/BqVdxT6/eNNV6NF3UjIF+P8DIIeMRIg4Bm5KhaY23G4PUGr1bFPbUP28Yarzd4tSruqfX7xhqvxou6EZCvR3gZBDxipEFAM3JUrbE2Y/B6g1er4p7ah21jjdcbvFoV99T6fWONV+NF3QjI1yO8DAIeMdIgoBk5qtZYmzF4vcGrVXFP7cO2scbrDV6tintq/b6xxqvxom4E5OsRXgYBjxhpENCMHFVrrM0YvN7g1aq4p/Zh21jj9QavVsU9tX7fWOPVeFE3AvL1CC+DgEeMNAhoRo6qNdZmDF5v8GpV3FP7sG2s8XqDV6vinlq/b6zxaryoGwH5eoSXQcAjRhoENCNH1RprMwavN3i1Ku6pfdg21ni9watVcU+t3zfWeDVe1I2AfD3CyyDgESMNApqRo2qNtRmD1xu8WhX31D5sG2u83uDVqrin1u8ba7waL+pGQL4e4WUQ8IiRBgHNyFG1xtqMwesNXq2Ke2ofto01Xm/walXcU+v3jTVejRd1IyBfj/AyCHjESIOAZuSoWmNtxuD1Bq9WxT21D9vGGq83eLUq7qn1+8Yar8aLuhGQr0d4GQQ8YqRBQDNyVK2xNmPweoNXq+Ke2odtY43XG7xaFffU+n1jjVfjRd0IyNcjvAwCHjHSIKAZOarWWJsxeL3Bq1VxT+3DtrHG6w1erYp7av2+scar8aJuBOTrEV4GAY8YaRDQjBxVa6zNGLze4NWquKf2YdtY4/UGr1bFPbV+31jj1XhRNwLy9Qgvg4BHjDQIaEaOqjXWZgxeb/BqVdxT+7BtrPF6g1er4p5av2+s8Wq8qBsB+XqEl0HAI0YaBDQjR9UaazMGrzd4tSruqX3YNtZ4vcGrVXFPrd831ng1XtSNgHw9wssg4BEjDQKakaNqjbUZg9cbvFoV99Q+bBtrvN7g1aq4p9bvG2u8Gi/qRkC+HuFlEPCIkQYBzchRtcbajMHrDV6tintqH7aNNV5v8GpV3FPr9401Xo0XdSMgX4/wMgh4xEiDgGbkqFpjbcbg9QavVsU9tQ/bxhqvN3i1Ku6p9fvGGq/Gi7oRkK9HeBkEPGKkQUAzclStsTZj8HqDV6vintqHbWON1xu8WhX31Pp9Y41X40XdCMjXI7wMAh4x0iCgGTmq1libMXi9watVcU/tw7axxusNXq2Ke2r9vrHGq/GibgTk6xFeBgGPGGkQ0IwcVWuszRi83uDVqrin9mHbWOP1Bq9WxT21ft9Y49V4UTcC8vUIL4OAR4w0CGhGjqo11mbMKq9WBfXqB+SqM3LfnJGvxmtVvZr71XzhtZrkN/YlX83HWV4GAY8YaRDQjBxVzzaK0Xyt8hqN1+y2Vl+kV4HJfXNGvhqvVfVq7lfzhddqkt/Yl3w1H2d5GQQ8YuToh1qjSz3bKEbztcpLkhuB1RfpVsU9tdw31vLVeK2qV3O/mi+8VpP8xr7kq/k4y8sg4BEjRz/UGl3q2UYxmq9VXpLcCKy+SLcq7qnlvrGWr8ZrVb2a+9V84bWa5Df2JV/Nx1leBgGPGDn6odboUs82itF8rfKS5EZg9UW6VXFPLfeNtXw1Xqvq1dyv5guv1SS/sS/5aj7O8jIIeMTI0Q+1Rpd6tlGM5muVlyQ3Aqsv0q2Ke2q5b6zlq/FaVa/mfjVfeK0m+Y19yVfzcZaXQcAjRo5+qDW61LONYjRfq7wkuRFYfZFuVdxTy31jLV+N16p6Nfer+cJrNclv7Eu+mo+zvAwCHjFy9EOt0aWebRSj+VrlJcmNwOqLdKvinlruG2v5arxW1au5X80XXqtJfmNf8tV8nOVlEPCIkaMfao0u9WyjGM3XKi9JbgRWX6RbFffUct9Yy1fjtapezf1qvvBaTfIb+5Kv5uMsL4OAR4wc/VBrdKlnG8VovlZ5SXIjsPoi3aq4p5b7xlq+Gq9V9WruV/OF12qS39iXfDUfZ3kZBDxi5OiHWqNLPdsoRvO1ykuSG4HVF+lWxT213DfW8tV4rapXc7+aL7xWk/zGvuSr+TjLyyDgESNHP9QaXerZRjGar1VektwIrL5ItyruqeW+sZavxmtVvZr71XzhtZrkN/YlX83HWV4GAY8YOfqh1uhSzzaK0Xyt8pLkRmD1RbpVcU8t9421fDVeq+rV3K/mC6/VJL+xL/lqPs7yMgh4xMjRD7VGl3q2UYzma5WXJDcCqy/SrYp7arlvrOWr8VpVr+Z+NV94rSb5jX3JV/NxlpdBwCNGjn6oNbrUs41iNF+rvCS5EVh9kW5V3FPLfWMtX43Xqno196v5wms1yW/sS76aj7O8DAIeMXL0Q63RpZ5tFKP5WuUlyY3A6ot0q+KeWu4ba/lqvFbVq7lfzRdeq0l+Y1/MKr+OAAAgAElEQVTy1Xyc5WUQ8IiRox9qjS71bKMYzdcqL0luBFZfpFsV99Ry31jLV+O1ql7N/Wq+8FpN8hv7kq/m4ywvg4BHjBz9UGt0qWcbxWi+VnlJciOw+iLdqrinlvvGWr4ar1X1au5X84XXapLf2Jd8NR9neRkEPGLk6Idao0s92yhG87XKS5IbgdUX6VbFPbXcN9by1Xitqldzv5ovvFaT/Ma+5Kv5OMvLIOARI0c/1Bpd6tlGMZqvVV6S3Aisvki3Ku6p5b6xlq/Ga1W9mvvVfOG1muQ39iVfzcdZXgYBjxg5+qHW6FLPNorRfK3ykuRGYPVFulVxTy33jbV8NV6r6tXcr+YLr9Ukv7Ev+Wo+zvIyCHjEyNEPtUaXerZRjOZrlZckNwKrL9KtintquW+s5avxWlWv5n41X3itJvmNfclX83GWl0HAI0aOfqg1utSzjWI0X6u8JLkRWH2RblXcU8t9Yy1fjdeqejX3q/nCazXJb+xLvpqPs7wMAh4xcvRDrdGlnm0Uo/la5SXJjcDqi3Sr4p5a7htr+Wq8VtWruV/NF16rSX5jX/LVfJzlZRDwiJGjH2qNLvVsoxjN1yovSW4EVl+kWxX31HLfWMtX47WqXs39ar7wWk3yG/uSr+bjLC+DgEeMHP1Qa3SpZxvFaL5WeUlyI7D6It2quKeW+8ZavhqvVfVq7lfzhddqkt/Yl3w1H2d5GQQ8YuToh1qjSz3bKEbztcpLkhuB1RfpVsU9tdw31vLVeK2qV3O/mi+8VpP8xr7kq/k4y8sg4BEjRz/UGl3q2UYxmq9VXpLcCKy+SLcq7qnlvrGWr8ZrVb2a+9V84bWa5Df2JV/Nx1leBgGPGDn6odboUs82itF8rfKS5EZg9UW6VXFPLfeNtXw1Xqvq1dyv5guv1SS/sS/5aj7O8jIIeMTI0Q+1Rpd6tlGM5muVlyQ3Aqsv0q2Ke2q5b6zlq/FaVa/mfjVfeK0m+Y19yVfzcZaXQcAjRo5+qDW61LONYjRfq7wkuRFYfZFuVdxTy31jLV+N16p6Nfer+cJrNclv7Eu+mo+zvAwCHjFy9EOt0aWebRSj+VrlJcmNwOqLdKvinlruG2v5arxW1au5X80XXqtJfmNf8tV8nOVlEPCIkaMfao0u9WyjGM3XKi9JbgRWX6RbFffUct9Yy1fjtapezf1qvvBaTfIb+5Kv5uMsL4OAR4wc/VBrdKlnG8VovlZ5SXIjsPoi3aq4p5b7xlq+Gq9V9WruV/OF12qS39iXfDUfZ3kZBDxi5OiHWqNLPdsoRvO1ykuSG4HVF+lWxT213DfW8tV4rapXc7+aL7xWk/zGvuSr+TjLyyDgESNHP9QaXerZRjGar1VektwIrL5ItyruqeW+sZavxmtVvZr71XzhtZrkN/YlX83HWV4GAY8YOfqh1uhSzzaK0Xyt8pLkRmD1RbpVcU8t9421fDVeq+rV3K/mC6/VJL+xL/lqPs7yMgh4xMjRD7VGl3q2UYzma5WXJDcCqy/SrYp7arlvrOWr8VpVr+Z+NV94rSb5jX3JV/NxlpdBwBtGtiqoEWgEvOjg1Qg0tXzh1QhQI7BDQP/a8cJOEHAeWwb+axDQgK1OdFoV1Ag0AhorXo1AU8sXXo0ANQI7BPSvHS/sBAHnsWXAIKDx+o9BQARG/gQBjbXZiBdejUBTy1fjRY3ASQLO40m6no1AI+A8Rl7+i4AGzCCg8aJ+g4DG2nzEC69GoKnlq/GiRuAkAefxJF3PRqARcB4jL4OABswgoPGifoOAxtp8xAuvRqCp5avxokbgJAHn8SRdz0agEXAeIy+DgAbMIKDxon6DgMbafMQLr0agqeWr8aJG4CQB5/EkXc9GoBFwHiMvg4AGzCCg8aJ+g4DG2nzEC69GoKnlq/GiRuAkAefxJF3PRqARcB4jL4OABswgoPGifoOAxtp8xAuvRqCp5avxokbgJAHn8SRdz0agEXAeIy+DgAbMIKDxon6DgMbafMQLr0agqeWr8aJG4CQB5/EkXc9GoBFwHiMvg4AGzCCg8aJ+g4DG2nzEC69GoKnlq/GiRuAkAefxJF3PRqARcB4jL4OABswgoPGifoOAxtp8xAuvRqCp5avxokbgJAHn8SRdz0agEXAeIy+DgAbMIKDxon6DgMbafMQLr0agqeWr8aJG4CQB5/EkXc9GoBFwHiMvg4AGzCCg8aJ+g4DG2nzEC69GoKnlq/GiRuAkAefxJF3PRqARcB4jL4OABswgoPGifoOAxtp8xAuvRqCp5avxokbgJAHn8SRdz0agEXAeIy+DgAbMIKDxon6DgMbafMQLr0agqeWr8aJG4CQB5/EkXc9GoBFwHiMvg4AGzCCg8aJ+g4DG2nzEC69GoKnlq/GiRuAkAefxJF3PRqARcB4jL4OABswgoPGifoOAxtp8xAuvRqCp5avxokbgJAHn8SRdz0agEXAeIy+DgAbMIKDxon6DgMbafMQLr0agqeWr8aJG4CQB5/EkXc9GoBFwHiMvg4AGzCCg8aJ+g4DG2nzEC69GoKnlq/GiRuAkAefxJF3PRqARcB4jL4OABswgoPGifoOAxtp8xAuvRqCp5avxokbgJAHn8SRdz0agEXAeIy+DgAbMIKDxon6DgMbafMQLr0agqeWr8aJG4CQB5/EkXc9GoBFwHiMvg4AGzCCg8aJ+g4DG2nzEC69GoKnlq/GiRuAkAefxJF3PRqARcB4jL4OABswgoPGifoOAxtp8xAuvRqCp5avxokbgJAHn8SRdz0agEXAeIy+DgAbMIKDxon6DgMbafMQLr0agqeWr8aJG4CQB5/EkXc9GoBFwHiMvg4AGzCCg8aJ+g4DG2nzEC69GoKnlq/GiRuAkAefxJF3PRqARcB4jL4OABswgoPGifoOAxtp8xAuvRqCp5avxokbgJAHn8SRdz0agEXAeIy+DgAbMIKDxon6DgMbafMQLr0agqeWr8aJG4CQB5/EkXc9GoBFwHiMvg4AGzCCg8aJ+g4DG2nzEC69GoKnlq/GiRuAkAefxJF3PRqARcB4jL4OABswgoPGifoOAxtp8xAuvRqCp5avxokbgJAHn8SRdz0agEXAeIy+DgAbMIKDxon6DgMbafMQLr0agqeWr8aJG4CQB5/EkXc9GoBFwHiMvg4AGzCCg8aJ+g4DG2nzEC69GoKnlq/GiRuAkAefxJF3PRqARcB4jL4OABswgoPGifoOAxtp8xAuvRqCp5avxokbgJAHn8SRdz0agEXAeIy+DgAbMIKDxon6DgMbafMQLr0agqeWr8aJG4CQB5/EkXc9GoBFwHiMvg4AGzCCg8aJ+g4DG2nzEC69GoKnlq/GiRuAkAefxJF3PRqARcB4jL4OABswgoPGifoOAxtp8xAuvRqCp5avxokbgJAHn8SRdz0agEXAeIy+DgAbMIKDxon6DgMbafMQLr0agqeWr8aJG4CQB5/EkXc9GoBFwHiMvg4AGzCCg8aJ+g4DG2nzEC69GoKnlq/GiRuAkAefxJF3PRqARcB4jL4OABswgoPGifoOAxtp8xAuvRqCp5avxokbgJAHn8SRdz0agEXAeIy+DgAaMGgEEdgisDuZcRC0jeOHVCDS1fOHVCDT1ar5aFdQIIHCSwOz7qkHASds9GwEEThKYbaz//e/Jsv/42Xg1dHjh1Qg0tXzh1QhQI4DAv0pgtt8bBPyrkbJvBBCYbawGASmcq7+oyVey8T944dUINLV8NV7UCCCwQ2C2fxkE7ITEThBAoBGYbawGAclIg4CE6z944dUINLV8vcGrVUGNAAInCcy+rxoEnLTdsxFA4CSB2cZqEJBs9+GRcBkENFx44RUJNPlq/2pVUCOAwEkCs++rBgEnbfdsBBA4SWC2sRoEJNtXX6TlK9no/xrQcOGFVyRAjgAC/yqB2fcJg4B/NVL2jQACs43VICCF0yAg4fILd8OFF16RQJOv9q9WBTUCCJwkMPu+ahBw0nbPRgCBkwRmG6tBQLJ99UVavpKNfuFuuPDCKxIgRwCBf5XA7PuEQcC/Gin7RgCB2cZqEJDCaRCQcPmFu+HCC69IoMlX+1erghoBBE4SmH1fNQg4abtnI4DASQKzjdUgINm++iItX8lGv3A3XHjhFQmQI4DAv0pg9n3CIOBfjZR9I4DAbGM1CEjhNAhIuPzC3XDhhVck0OSr/atVQY0AAicJzL6vGgSctN2zEUDgJIHZxmoQkGxffZGWr2SjX7gbLrzwigTIEUDgXyUw+z5hEPCvRsq+EUBgtrEaBKRwGgQkXH7hbrjwwisSaPLV/tWqoEYAgZMEZt9XDQJO2u7ZCCBwksBsYzUISLavvkjLV7LRL9wNF154RQLkCCDwrxKYfZ8wCPhXI2XfCCAw21gNAlI4DQISLr9wN1x44RUJNPlq/2pVUCOAwEkCs++rBgEnbfdsBBA4SWC2sRoEJNtXX6TlK9noF+6GCy+8IgFyBBD4VwnMvk8YBPyrkbJvBBCYbawGASmcBgEJl1+4Gy688IoEmny1f7UqqBFA4CSB2fdVg4CTtns2AgicJDDbWA0Cku2rL9LylWz0C3fDhRdekQA5Agj8qwRm3ycMAv7VSNk3AgjMNlaDgBROg4CEyy/cDRdeeEUCTb7av1oV1AggcJLA7PuqQcBJ2z0bAQROEphtrAYByfbVF2n5Sjb6hbvhwguvSIAcAQT+VQKz7xMGAf9qpOwbAQRmG6tBQAqnQUDC5RfuhgsvvCKBJl/tX60KagQQOElg9n3VIOCk7Z6NAAInCcw2VoOAZPvqi7R8JRv9wt1w4YVXJECOAAL/KoHZ9wmDgH81UvaNAAKzjdUgIIXTICDh8gt3w4UXXpFAk6/2r1YFNQIInCQw+75qEHDSds9GAIGTBGYbq0FAsn31RVq+ko1+4W648MIrEiBHAIF/lcDs+4RBwL8aKftGAIHZxmoQkMJpEJBw+YW74cILr0igyVf7V6uCGgEEThKYfV81CDhpu2cjgMBJArON1SAg2b76Ii1fyUa/cDdceOEVCZAjgMC/SmD2fcIg4F+NlH0jgMBsYzUISOE0CEi4/MLdcOGFVyTQ5Kv9q1VBjQACJwnMvq8aBJy03bMRQOAkgdnGahCQbF99kZavZKNfuBsuvPCKBMgRQOBfJTD7PmEQ8K9Gyr4RQGC2sRoEpHAaBCRcfuFuuPDCKxJo8tX+1aqgRgCBkwRm31cNAk7a7tkIIHCSwGxjNQhItq++SMtXstEv3A0XXnhFAuQIIPCvEph9nzAI+FcjZd8IIDDbWA0CUjgNAhIuv3A3XHjhFQk0+Wr/alVQI4DASQKz76sGASdt92wEEDhJYLaxGgQk21dfpOUr2egX7oYLL7wiAXIEEPhXCcy+TxgE/KuRsm8EEJhtrAYBKZwGAQmXX7gbLrzwigSafLV/tSqoEUDgJIHZ91WDgJO2ezYCCJwkMNtYDQKS7asv0vKVbPQLd8OFF16RADkCCPyrBGbfJwwC/tVI2TcCCMw2VoOAFE6DgITLL9wNF154RQJNvtq/WhXUCCBwksDs+6pBwEnbPRsBBE4SmG2sBgHJ9tUXaflKNvqFu+HCC69IgBwBBP5VArPvEwYB/2qk7BsBBGYbq0FACqdBQMLlF+6GCy+8IoEmX+1frQpqBBA4SWD2fdUg4KTtno0AAicJzDZWg4Bk++qLtHwlG/3C3XDhhVckQI4AAv8qgdn3idVBwL9qtH0jgAACqwR8cK860/bFx8aLGgEEEEAAAQT+3wT+axAgFggggMA3CPiAfMNnPr7hoyoQQAABBBD4mwQMAv4mfWsjgAACFwn4gLwI++BSfDwI16MRQAABBBD4CAGDgI8YrUwEEEDAB+QbGeDjGz6qAgEEEEAAgb9JwCDgb9K3NgIIIHCRgA/Ii7APLsXHg3A9GgEEEEAAgY8QMAj4iNHKRAABBHxAvpEBPr7hoyoQQAABBBD4mwQMAv4mfWsjgAACFwn4gLwI++BSfDwI16MRQAABBBD4CAGDgI8YrUwEEEDAB+QbGeDjGz6qAgEEEEAAgb9JwCDgb9K3NgIIIHCRgA/Ii7APLsXHg3A9GgEEEEAAgY8QMAj4iNHKRAABBHxAvpEBPr7hoyoQQAABBBD4mwQMAv4mfWsjgAACFwn4gLwI++BSfDwI16MRQAABBBD4CAGDgI8YrUwEEEDAB+QbGeDjGz6qAgEEEEAAgb9JwCDgb9K3NgIIIHCRgA/Ii7APLsXHg3A9GgEEEEAAgY8QMAj4iNHKRAABBHxAvpEBPr7hoyoQQAABBBD4mwQMAv4mfWsjgAACFwn4gLwI++BSfDwI16MRQAABBBD4CAGDgI8YrUwEEEDAB+QbGeDjGz6qAgEEEEAAgb9JwCDgb9K3NgIIIHCRgA/Ii7APLsXHg3A9GgEEEEAAgY8QMAj4iNHKRAABBHxAvpEBPr7hoyoQQAABBBD4mwQMAv4mfWsjgAACFwn4gLwI++BSfDwI16MRQAABBBD4CAGDgI8YrUwEEEDAB+QbGeDjGz6qAgEEEEAAgb9JwCDgb9K3NgIIIHCRgA/Ii7APLsXHg3A9GgEEEEAAgY8QMAj4iNHKRAABBHxAvpEBPr7hoyoQQAABBBD4mwQMAv4mfWsjgAACFwn4gLwI++BSfDwI16MRQAABBBD4CAGDgI8YrUwEEEDAB+QbGeDjGz6qAgEEEEAAgb9JwCDgb9K3NgIIIHCRgA/Ii7APLsXHg3A9GgEEEEAAgY8QMAj4iNHKRAABBHxAvpEBPr7hoyoQQAABBBD4mwQMAv4mfWsjgAACFwn4gLwI++BSfDwI16MRQAABBBD4CAGDgI8YrUwEEEDAB+QbGeDjGz6qAgEEEEAAgb9JwCDgb9K3NgIIIHCRgA/Ii7APLsXHg3A9GgEEEEAAgY8QMAj4iNHKRAABBHxAvpEBPr7hoyoQQAABBBD4mwQMAv4mfWsjgAACFwn4gLwI++BSfDwI16MRQAABBBD4CAGDgI8YrUwEEEDAB+QbGeDjGz6qAgEEEEAAgb9JwCDgb9K3NgIIIHCRgA/Ii7APLsXHg3A9GgEEEEAAgY8QMAj4iNHKRAABBHxAvpEBPr7hoyoQQAABBBD4mwQMAv4mfWsjgAACFwn4gLwI++BSfDwI16MRQAABBBD4CAGDgI8YrUwEEEDAB+QbGeDjGz6qAgEEEEAAgb9JwCDgb9K3NgIIIHCRgA/Ii7APLsXHg3A9GgEEEEAAgY8QMAj4iNHKRAABBHxAvpEBPr7hoyoQQAABBBD4mwRmBwGrLzp/06z/v7X/97//rW5tcl/yNWlL3pTcN2SruV/1cZVXc/2eetXHewTaSqv54mPzcVUtX82ZVV6tCupVAqt91SBgNTFxX6sBi2Vck2v411AfXUjuG97V3K/6uMqruX5PverjPQJtpdV88bH5uKqWr+bMKq9WBfUqgdW+ahCwmpi4r9WAxTKuyTX8a6iPLiT3De9q7ld9XOXVXL+nXvXxHoG20mq++Nh8XFXLV3NmlVergnqVwGpfNQhYTUzc12rAYhnX5Br+NdRHF5L7hnc196s+rvJqrt9Tr/p4j0BbaTVffGw+rqrlqzmzyqtVQb1KYLWvGgSsJibuazVgsYxrcg3/GuqjC8l9w7ua+1UfV3k11++pV328R6CttJovPjYfV9Xy1ZxZ5dWqoF4lsNpXDQJWExP3tRqwWMY1uYZ/DfXRheS+4V3N/aqPq7ya6/fUqz7eI9BWWs0XH5uPq2r5as6s8mpVUK8SWO2rBgGriYn7Wg1YLOOaXMO/hvroQnLf8K7mftXHVV7N9XvqVR/vEWgrreaLj83HVbV8NWdWebUqqFcJrPZVg4DVxMR9rQYslnFNruFfQ310IblveFdzv+rjKq/m+j31qo/3CLSVVvPFx+bjqlq+mjOrvFoV1KsEVvuqQcBqYuK+VgMWy7gm1/CvoT66kNw3vKu5X/VxlVdz/Z561cd7BNpKq/niY/NxVS1fzZlVXq0K6lUCq33VIGA1MXFfqwGLZVyTa/jXUB9dSO4b3tXcr/q4yqu5fk+96uM9Am2l1Xzxsfm4qpav5swqr1YF9SqB1b5qELCamLiv1YDFMq7JNfxrqI8uJPcN72ruV31c5dVcv6de9fEegbbSar742HxcVctXc2aVV6uCepXAal81CFhNTNzXasBiGdfkGv411EcXkvuGdzX3qz6u8mqu31Ov+niPQFtpNV98bD6uquWrObPKq1VBvUpgta8aBKwmJu5rNWCxjGtyDf8a6qMLyX3Du5r7VR9XeTXX76lXfbxHoK20mi8+Nh9X1fLVnFnl1aqgXiWw2lcNAlYTE/e1GrBYxjW5hn8N9dGF5L7hXc39qo+rvJrr99SrPt4j0FZazRcfm4+ravlqzqzyalVQrxJY7asGAauJiftaDVgs45pcw7+G+uhCct/wruZ+1cdVXs31e+pVH+8RaCut5ouPzcdVtXw1Z1Z5tSqoVwms9lWDgNXExH2tBiyWcU2u4V9DfXQhuW94V3O/6uMqr+b6PfWqj/cItJVW88XH5uOqWr6aM6u8WhXUqwRW+6pBwGpi4r5WAxbLuCbX8K+hPrqQ3De8q7lf9XGVV3P9nnrVx3sE2kqr+eJj83FVLV/NmVVerQrqVQKrfdUgYDUxcV+rAYtlXJNr+NdQH11I7hve1dyv+rjKq7l+T73q4z0CbaXVfPGx+biqlq/mzCqvVgX1KoHVvmoQsJqYuK/VgMUyrsk1/Guojy4k9w3vau5XfVzl1Vy/p1718R6BttJqvvjYfFxVy1dzZpVXq4J6lcBqXzUIWE1M3NdqwGIZ1+Qa/jXURxeS+4Z3NferPq7yaq7fU6/6eI9AW2k1X3xsPq6q5as5s8qrVUG9SmC1rxoErCYm7ms1YLGMa3IN/xrqowvJfcO7mvtVH1d5NdfvqVd9vEegrbSaLz42H1fV8tWcWeXVqqBeJbDaVw0CVhMT97UasFjGNbmGfw310YXkvuFdzf2qj6u8muv31Ks+3iPQVlrNFx+bj6tq+WrOrPJqVVCvEljtqwYBq4mJ+1oNWCzjmlzDv4b66EJy3/Cu5n7Vx1VezfV76lUf7xFoK63mi4/Nx1W1fDVnVnm1KqhXCaz2VYOA1cTEfa0GLJZxTa7hX0N9dCG5b3hXc7/q4yqv5vo99aqP9wi0lVbzxcfm46pavpozq7xaFdSrBFb7qkHAamLivlYDFsu4Jtfwr6E+upDcN7yruV/1cZVXc/2eetXHewTaSqv54mPzcVUtX82ZVV6tCupVAqt91SBgNTFxX6sBi2Vck2v411AfXUjuG97V3K/6uMqruX5PverjPQJtpdV88bH5uKqWr+bMKq9WBfUqgdW+ahCwmpi4r9WAxTKuyTX8a6iPLiT3De9q7ld9XOXVXL+nXvXxHoG20mq++Nh8XFXLV3NmlVergnqVwGpfNQhYTUzc12rAYhnX5Br+NdRHF5L7hnc196s+rvJqrt9Tr/p4j0BbaTVffGw+rqrlqzmzyqtVQb1KYLWvGgSsJibuazVgsYxrcg3/GuqjC8l9w7ua+1UfV3k11++pV328R6CttJovPjYfV9Xy1ZxZ5dWqoF4lsNpXDQJWExP3tRqwWMY1uYZ/DfXRheS+4V3N/aqPq7ya6/fUqz7eI9BWWs0XH5uPq2r5as6s8mpVUK8SWO2rBgGriYn7Wg1YLOOaXMO/hvroQnLf8K7mftXHVV7N9XvqVR/vEWgrreaLj83HVbV8NWdWebUqqFcJrPZVg4DVxMR9rQYslnFNruFfQ310IblveFdzv+rjKq/m+j31qo/3CLSVVvPFx+bjqlq+mjOrvFoV1KsEVvuqQcBqYuK+VgMWy7gm1/CvoT66kNw3vKu5X/VxlVdz/Z561cd7BNpKq/niY/NxVS1fzZlVXq0K6lUCq33VIGA1MXFfqwGLZVyTa/jXUB9dSO4b3tXcr/q4yqu5fk+96uM9Am2l1Xzxsfm4qpav5swqr1YF9SqB1b5qELCamLiv1YDFMq7JNfxrqI8uJPcN72ruV31c5dVcv6de9fEegbbSar742HxcVctXc2aVV6uCepXAal81CFhNTNzXasBiGdfkGv411EcXkvuGdzX3qz6u8mqu31Ov+niPQFtpNV98bD6uquWrObPKq1VBvUpgta8aBKwmJu5rNWCxjGtyDf8a6qMLyX3Du5r7VR9XeTXX76lXfbxHoK20mi8+Nh9X1fLVnFnl1aqgXiWw2lcNAlYTE/e1GrBYxjW5hn8N9dGF5L7hXc39qo+rvJrr99SrPt4j0FZazRcfm4+ravlqzqzyalVQrxJY7auzg4BVIzWK5sxs8P/731bIJfUqr0vlP7OMPtGsXM09H/nYCLyhXj2Pb9BVhb7aMrB6Hld9XOXVXL+nNgiIrFeDH8u4Jl89kKs+rvK6FphHFlrN1yre1dzzsSWGj43XqnrVx1Ve9tUI6KuN1+p5XPVxlVdz/Z7aICCyXg1+LOOafPVArvq4yutaYB5ZaDVfq3hXc8/Hlhg+Nl6r6lUfV3nZVyOgrzZeq+dx1cdVXs31e2qDgMh6NfixjGvy1QO56uMqr2uBeWSh1Xyt4l3NPR9bYvjYeK2qV31c5WVfjYC+2nitnsdVH1d5NdfvqQ0CIuvV4McyrslXD+Sqj6u8rgXmkYVW87WKdzX3fGyJ4WPjtape9XGVl301Avpq47V6Hld9XOXVXL+nNgiIrFeDH8u4Jl89kKs+rvK6FphHFlrN1yre1dzzsSWGj43XqnrVx1Ve9tUI6KuN1+p5XPVxlVdz/Z7aICCyXg1+LOOafPVArvq4yutaYB5ZaDVfq3hXc8/Hlhg+Nl6r6lUfV3nZVyOgrzZeq+dx1cdVXs31e2qDgMh6NfixjGvy1QO56uMqr2uBeWSh1Xyt4l3NPR9bYvjYeK2qV31c5WVfjYC+2nitnsdVH+cNRTkAACAASURBVFd5NdfvqQ0CIuvV4McyrslXD+Sqj6u8rgXmkYVW87WKdzX3fGyJ4WPjtape9XGVl301Avpq47V6Hld9XOXVXL+nNgiIrFeDH8u4Jl89kKs+rvK6FphHFlrN1yre1dzzsSWGj43XqnrVx1Ve9tUI6KuN1+p5XPVxlVdz/Z7aICCyXg1+LOOafPVArvq4yutaYB5ZaDVfq3hXc8/Hlhg+Nl6r6lUfV3nZVyOgrzZeq+dx1cdVXs31e2qDgMh6NfixjGvy1QO56uMqr2uBeWSh1Xyt4l3NPR9bYvjYeK2qV31c5WVfjYC+2nitnsdVH1d5NdfvqQ0CIuvV4McyrslXD+Sqj6u8rgXmkYVW87WKdzX3fGyJ4WPjtape9XGVl301Avpq47V6Hld9XOXVXL+nNgiIrFeDH8u4Jl89kKs+rvK6FphHFlrN1yre1dzzsSWGj43XqnrVx1Ve9tUI6KuN1+p5XPVxlVdz/Z7aICCyXg1+LOOafPVArvq4yutaYB5ZaDVfq3hXc8/Hlhg+Nl6r6lUfV3nZVyOgrzZeq+dx1cdVXs31e2qDgMh6NfixjGvy1QO56uMqr2uBeWSh1Xyt4l3NPR9bYvjYeK2qV31c5WVfjYC+2nitnsdVH1d5NdfvqQ0CIuvV4McyrslXD+Sqj6u8rgXmkYVW87WKdzX3fGyJ4WPjtape9XGVl301Avpq47V6Hld9XOXVXL+nNgiIrFeDH8u4Jl89kKs+rvK6FphHFlrN1yre1dzzsSWGj43XqnrVx1Ve9tUI6KuN1+p5XPVxlVdz/Z7aICCyXg1+LOOafPVArvq4yutaYB5ZaDVfq3hXc8/Hlhg+Nl6r6lUfV3nZVyOgrzZeq+dx1cdVXs31e2qDgMh6NfixjGvy1QO56uMqr2uBeWSh1Xyt4l3NPR9bYvjYeK2qV31c5WVfjYC+2nitnsdVH1d5NdfvqQ0CIuvV4McyrslXD+Sqj6u8rgXmkYVW87WKdzX3fGyJ4WPjtape9XGVl301Avpq47V6Hld9XOXVXL+nNgiIrFeDH8u4Jl89kKs+rvK6FphHFlrN1yre1dzzsSWGj43XqnrVx1Ve9tUI6KuN1+p5XPVxlVdz/Z7aICCyXg1+LOOafPVArvq4yutaYB5ZaDVfq3hXc8/Hlhg+Nl6r6lUfV3nZVyOgrzZeq+dx1cdVXs31e2qDgMh6NfixjGvy1QO56uMqr2uBeWSh1Xyt4l3NPR9bYvjYeK2qV31c5WVfjYC+2nitnsdVH1d5NdfvqQ0CIuvV4McyrslXD+Sqj6u8rgXmkYVW87WKdzX3fGyJ4WPjtape9XGVl301Avpq47V6Hld9XOXVXL+nNgiIrFeDH8u4Jl89kKs+rvK6FphHFlrN1yre1dzzsSWGj43XqnrVx1Ve9tUI6KuN1+p5XPVxlVdz/Z7aICCyXg1+LOOafPVArvq4yutaYB5ZaDVfq3hXc8/Hlhg+Nl6r6lUfV3nZVyOgrzZeq+dx1cdVXs31e2qDgMh6NfixjGvy1QO56uMqr2uBeWSh1Xyt4l3NPR9bYvjYeK2qV31c5WVfjYC+2nitnsdVH1d5NdfvqQ0CIuvV4McyrslXD+Sqj6u8rgXmkYVW87WKdzX3fGyJ4WPjtape9XGVl301Avpq47V6Hld9XOXVXL+nNgiIrFeDH8u4Jl89kKs+rvK6FphHFlrN1yre1dzzsSWGj43XqnrVx1Ve9tUI6KuN1+p5XPVxlVdz/Z7aICCyXg1+LOOafPVArvq4yutaYB5ZaDVfq3hXc8/Hlhg+Nl6r6lUfV3nZVyOgrzZeq+dx1cdVXs31e2qDgMh6NfixjGvy1QO56uMqr2uBeWSh1Xyt4l3NPR9bYvjYeK2qV31c5WVfjYC+2nitnsdVH1d5NdfvqQ0CIuvV4McyrslXD+Sqj6u8rgXmkYVW87WKdzX3fGyJ4WPjtape9XGVl301Avpq47V6Hld9XOXVXL+nNgiIrFeDH8u4Jl89kKs+rvK6FphHFlrN1yre1dzzsSWGj43XqnrVx1Ve9tUI6KuN1+p5XPVxlVdz/Z7aICCyXg1+LOOafPVArvq4yutaYB5ZaDVfq3hXc8/Hlhg+Nl6r6lUfV3nZVyOgrzZeq+dx1cdVXs31e2qDgMh6NfixjGvy1QO56uMqr2uBeWSh1Xyt4l3NPR9bYvjYeK2qV31c5WVfjYC+2nitnsdVH1d5NdfvqQ0CIuvV4McyrslXD+Sqj6u8rgXmkYVW87WKdzX3fGyJ4WPjtape9XGVl301Avpq47V6Hld9XOXVXL+nNgiIrFeDH8u4Jl89kKs+rvK6FphHFlrN1yre1dzzsSWGj43XqnrVx1Ve9tUI6KuN1+p5XPVxlVdz/Z56dhAgYPdCYCUEfiKweh5/2vff+ncX0d8i/7vryn3jKfeNl3w1Xqv54mPzkfoNAqvn8Q2696owCIisBT8CI3+CgBedZqM+0XitquW+OSP3jZd8NV6r+eJj85H6DQKr5/ENuveqMAiIrAU/AiN/goAXnWajPtF4rarlvjkj942XfDVeq/niY/OR+g0Cq+fxDbr3qjAIiKwFPwIjf4KAF51moz7ReK2q5b45I/eNl3w1Xqv54mPzkfoNAqvn8Q2696owCIisBT8CI3+CgBedZqM+0XitquW+OSP3jZd8NV6r+eJj85H6DQKr5/ENuveqMAiIrAU/AiN/goAXnWajPtF4rarlvjkj942XfDVeq/niY/OR+g0Cq+fxDbr3qjAIiKwFPwIjf4KAF51moz7ReK2q5b45I/eNl3w1Xqv54mPzkfoNAqvn8Q2696owCIisBT8CI3+CgBedZqM+0XitquW+OSP3jZd8NV6r+eJj85H6DQKr5/ENuveqMAiIrAU/AiN/goAXnWajPtF4rarlvjkj942XfDVeq/niY/OR+g0Cq+fxDbr3qjAIiKwFPwIjf4KAF51moz7ReK2q5b45I/eNl3w1Xqv54mPzkfoNAqvn8Q2696owCIisBT8CI3+CgBedZqM+0XitquW+OSP3jZd8NV6r+eJj85H6DQKr5/ENuveqMAiIrAU/AiN/goAXnWajPtF4rarlvjkj942XfDVeq/niY/OR+g0Cq+fxDbr3qjAIiKwFPwIjf4KAF51moz7ReK2q5b45I/eNl3w1Xqv54mPzkfoNAqvn8Q2696owCIisBT8CI3+CgBedZqM+0XitquW+OSP3jZd8NV6r+eJj85H6DQKr5/ENuveqMAiIrAU/AiN/goAXnWajPtF4rarlvjkj942XfDVeq/niY/OR+g0Cq+fxDbr3qjAIiKwFPwIjf4KAF51moz7ReK2q5b45I/eNl3w1Xqv54mPzkfoNAqvn8Q2696owCIisBT8CI3+CgBedZqM+0XitquW+OSP3jZd8NV6r+eJj85H6DQKr5/ENuveqMAiIrAU/AiN/goAXnWajPtF4rarlvjkj942XfDVeq/niY/OR+g0Cq+fxDbr3qjAIiKwFPwIjf4KAF51moz7ReK2q5b45I/eNl3w1Xqv54mPzkfoNAqvn8Q2696owCIisBT8CI3+CgBedZqM+0XitquW+OSP3jZd8NV6r+eJj85H6DQKr5/ENuveqMAiIrAU/AiN/goAXnWajPtF4rarlvjkj942XfDVeq/niY/OR+g0Cq+fxDbr3qjAIiKwFPwIjf4KAF51moz7ReK2q5b45I/eNl3w1Xqv54mPzkfoNAqvn8Q2696owCIisBT8CI3+CgBedZqM+0XitquW+OSP3jZd8NV6r+eJj85H6DQKr5/ENuveqMAiIrAU/AiN/goAXnWajPtF4rarlvjkj942XfDVeq/niY/OR+g0Cq+fxDbr3qjAIiKwFPwIjf4KAF51moz7ReK2q5b45I/eNl3w1Xqv54mPzkfoNAqvn8Q2696owCIisBT8CI3+CgBedZqM+0XitquW+OSP3jZd8NV6r+eJj85H6DQKr5/ENuveqMAiIrAU/AiN/goAXnWajPtF4rarlvjkj942XfDVeq/niY/OR+g0Cq+fxDbr3qjAIiKwFPwIjf4KAF51moz7ReK2q5b45I/eNl3w1Xqv54mPzkfoNAqvn8Q2696owCIisBT8CI3+CgBedZqM+0XitquW+OSP3jZd8NV6r+eJj85H6DQKr5/ENuveqMAiIrAU/AiN/goAXnWajPtF4rarlvjkj942XfDVeq/niY/OR+g0Cq+fxDbr3qjAIiKwFPwIjf4KAF51moz7ReK2q5b45I/eNl3w1Xqv54mPzkfoNAqvn8Q2696owCIisBT8CI3+CgBedZqM+0XitquW+OSP3jZd8NV6r+eJj85H6DQKr5/ENuveqMAiIrAU/AiN/goAXnWajPtF4rarlvjkj942XfDVeq/niY/OR+g0Cq+fxDbr3qjAIiKwFPwIjf4KAF51moz7ReK2q5b45I/eNl3w1Xqv54mPzkfoNAqvn8Q2696owCIisBT8CI3+CgBedZqM+0XitquW+OSP3jZd8NV6r+eJj85H6DQKr5/ENuveqMAiIrAU/AiN/goAXnWajPtF4rarlvjkj942XfDVeq/niY/OR+g0Cq+fxDbr3qjAIiKwFPwIjf4KAF51moz7ReK2q5b45I/eNl3w1Xqv54mPzkfoNAqvn8Q2696owCIisBT8CI3+CgBedZqM+0XitquW+OSP3jZd8NV6r+eJj85H6DQKr5/ENuveqmB0E3EPQVtLwGy+NovGibgScx8ZrVa1PrDrzxr5W+8Rq7ld5raZx1cdVXvbVCDiPjZfz2HgZBDRe/3EgGzAHsvGibgScx8ZrVa1PrDrzxr5W+8Rq7ld5raZx1cdVXvbVCDiPjZfz2HgZBDReBgGRlwMZgZEnAi7IhGtWrE/MWvPExlb7xGruV3mthnHVx1Ve9tUIOI+Nl/PYeBkENF4GAZGXAxmBkScCLsiEa1asT8xa88TGVvvEau5Xea2GcdXHVV721Qg4j42X89h4GQQ0XgYBkZcDGYGRJwIuyIRrVqxPzFrzxMZW+8Rq7ld5rYZx1cdVXvbVCDiPjZfz2HgZBDReBgGRlwMZgZEnAi7IhGtWrE/MWvPExlb7xGruV3mthnHVx1Ve9tUIOI+Nl/PYeBkENF4GAZGXAxmBkScCLsiEa1asT8xa88TGVvvEau5Xea2GcdXHVV721Qg4j42X89h4GQQ0XgYBkZcDGYGRJwIuyIRrVqxPzFrzxMZW+8Rq7ld5rYZx1cdVXvbVCDiPjZfz2HgZBDReBgGRlwMZgZEnAi7IhGtWrE/MWvPExlb7xGruV3mthnHVx1Ve9tUIOI+Nl/PYeBkENF4GAZGXAxmBkScCLsiEa1asT8xa88TGVvvEau5Xea2GcdXHVV721Qg4j42X89h4GQQ0XgYBkZcDGYGRJwIuyIRrVqxPzFrzxMZW+8Rq7ld5rYZx1cdVXvbVCDiPjZfz2HgZBDReBgGRlwMZgZEnAi7IhGtWrE/MWvPExlb7xGruV3mthnHVx1Ve9tUIOI+Nl/PYeBkENF4GAZGXAxmBkScCLsiEa1asT8xa88TGVvvEau5Xea2GcdXHVV721Qg4j42X89h4GQQ0XgYBkZcDGYGRJwIuyIRrVqxPzFrzxMZW+8Rq7ld5rYZx1cdVXvbVCDiPjZfz2HgZBDReBgGRlwMZgZEnAi7IhGtWrE/MWvPExlb7xGruV3mthnHVx1Ve9tUIOI+Nl/PYeBkENF4GAZGXAxmBkScCLsiEa1asT8xa88TGVvvEau5Xea2GcdXHVV721Qg4j42X89h4GQQ0XgYBkZcDGYGRJwIuyIRrVqxPzFrzxMZW+8Rq7ld5rYZx1cdVXvbVCDiPjZfz2HgZBDReBgGRlwMZgZEnAi7IhGtWrE/MWvPExlb7xGruV3mthnHVx1Ve9tUIOI+Nl/PYeBkENF4GAZGXAxmBkScCLsiEa1asT8xa88TGVvvEau5Xea2GcdXHVV721Qg4j42X89h4GQQ0XgYBkZcDGYGRJwIuyIRrVqxPzFrzxMZW+8Rq7ld5rYZx1cdVXvbVCDiPjZfz2HgZBDReBgGRlwMZgZEnAi7IhGtWrE/MWvPExlb7xGruV3mthnHVx1Ve9tUIOI+Nl/PYeBkENF4GAZGXAxmBkScCLsiEa1asT8xa88TGVvvEau5Xea2GcdXHVV721Qg4j42X89h4GQQ0XgYBkZcDGYGRJwIuyIRrVqxPzFrzxMZW+8Rq7ld5rYZx1cdVXvbVCDiPjZfz2HgZBDReBgGRlwMZgZEnAi7IhGtWrE/MWvPExlb7xGruV3mthnHVx1Ve9tUIOI+Nl/PYeBkENF4GAZGXAxmBkScCLsiEa1asT8xa88TGVvvEau5Xea2GcdXHVV721Qg4j42X89h4GQQ0XgYBkZcDGYGRJwIuyIRrVqxPzFrzxMZW+8Rq7ld5rYZx1cdVXvbVCDiPjZfz2HgZBDReBgGRlwMZgZEnAi7IhGtWrE/MWvPExlb7xGruV3mthnHVx1Ve9tUIOI+Nl/PYeBkENF4GAZGXAxmBkScCLsiEa1asT8xa88TGVvvEau5Xea2GcdXHVV721Qg4j42X89h4GQQ0XgYBkZcDGYGRJwIuyIRrVqxPzFrzxMZW+8Rq7ld5rYZx1cdVXvbVCDiPjZfz2HgZBDReBgGRlwMZgZEnAi7IhGtWrE/MWvPExlb7xGruV3mthnHVx1Ve9tUIOI+Nl/PYeBkENF4GAZGXAxmBkScCLsiEa1asT8xa88TGVvvEau5Xea2GcdXHVV721Qg4j42X89h4GQQ0XgYBkZcDGYGRJwIuyIRrVqxPzFrzxMZW+8Rq7ld5rYZx1cdVXvbVCDiPjZfz2HgZBDReBgGRlwMZgZEnAi7IhGtWrE/MWvPExlb7xGruV3mthnHVx1Ve9tUIOI+Nl/PYeBkENF4GAZGXAxmBkScCLsiEa1asT8xa88TGVvvEau5Xea2GcdXHVV721Qg4j42X89h4GQQ0XgYBkZcDGYGRJwIuyIRrVqxPzFrzxMZW+8Rq7ld5rYZx1cdVXvbVCDiPjZfz2HgZBDReBgGRlwMZgZEnAi7IhGtWrE/MWvPExlb7xGruV3mthnHVx1Ve9tUIOI+Nl/PYeBkENF4GAZGXAxmBkScCLsiEa1asT8xa88TGVvvEau5Xea2GcdXHVV721Qg4j42X89h4GQQ0XgYBkZcDGYGRJwIuyIRrVqxPzFrzxMZW+8Rq7ld5rYZx1cdVXvbVCDiPjZfz2HgZBDRe1AgcJaDhH8X7+Ye7ID8fAQAQ+JGAe+hHRAT/BwRW7yG5/z8w1Z/+SGA29/9b3dmPSAkQeI+Ai+g9T5cq0u6X3LAXBDYJuIc2fXllV6v3kNy/krDNOmZzbxCwGRi7+iYBF9E3fb9V9epFdKt+6yCAwM8E3EM/M6L4cwKr95Dc/7mn/vJnArO5Nwj42TwKBG4RcBHdIv3NdVYvom+6oWoENgm4hzZ9eWVXq/eQ3L+SsM06ZnNvELAZGLv6JgEX0Td9v1X16kV0q37rIIDAzwTcQz8zovhzAqv3kNz/uaf+8mcCs7k3CPjZPAoEbhFwEd0i/c11Vi+ib7qhagQ2CbiHNn15ZVer95Dcv5KwzTpmc28QsBkYu/omARfRN32/VfXqRXSrfusggMDPBNxDPzOi+HMCq/eQ3P+5p/7yZwKzuTcI+Nk8CgRuEXAR3SL9zXVWL6JvuqFqBDYJuIc2fXllV6v3kNy/krDNOmZzbxCwGRi7+iYBF9E3fb9V9epFdKt+6yCAwM8E3EM/M6L4cwKr95Dc/7mn/vJnArO5Nwj42TwKBG4RcBHdIv3NdVYvom+6oWoENgm4hzZ9eWVXq/eQ3L+SsM06ZnNvELAZGLv6JgEX0Td9v1X16kV0q37rIIDAzwTcQz8zovhzAqv3kNz/uaf+8mcCs7k3CPjZPAoEbhFwEd0i/c11Vi+ib7qhagQ2CbiHNn15ZVer95Dcv5KwzTpmc28QsBkYu/omARfRN32/VfXqRXSrfusggMDPBNxDPzOi+HMCq/eQ3P+5p/7yZwKzuTcI+Nk8CgRuEXAR3SL9zXVWL6JvuqFqBDYJuIc2fXllV6v3kNy/krDNOmZzbxCwGRi7+iYBF9E3fb9V9epFdKt+6yCAwM8E3EM/M6L4cwKr95Dc/7mn/vJnArO5Nwj42TwKBG4RcBHdIv3NdVYvom+6oWoENgm4hzZ9eWVXq/eQ3L+SsM06ZnNvELAZGLv6JgEX0Td9v1X16kV0q37rIIDAzwTcQz8zovhzAqv3kNz/uaf+8mcCs7k3CPjZPAoEbhFwEd0i/c11Vi+ib7qhagQ2CbiHNn15ZVer95Dcv5KwzTpmc28QsBkYu/omARfRN32/VfXqRXSrfusggMDPBNxDPzOi+HMCq/eQ3P+5p/7yZwKzuTcI+Nk8CgRuEXAR3SL9zXVWL6JvuqFqBDYJuIc2fXllV6v3kNy/krDNOmZzbxCwGRi7+iYBF9E3fb9V9epFdKt+6yCAwM8E3EM/M6L4cwKr95Dc/7mn/vJnArO5Nwj42TwKBG4RcBHdIv3NdVYvom+6oWoENgm4hzZ9eWVXq/eQ3L+SsM06ZnNvELAZGLv6JgEX0Td9v1X16kV0q37rIIDAzwTcQz8zovhzAqv3kNz/uaf+8mcCs7k3CPjZPAoEbhFwEd0i/c11Vi+ib7qhagQ2CbiHNn15ZVer95Dcv5KwzTpmc28QsBkYu/omARfRN32/VfXqRXSrfusggMDPBNxDPzOi+HMCq/eQ3P+5p/7yZwKzuTcI+Nk8CgRuEXAR3SL9zXVWL6JvuqFqBDYJuIc2fXllV6v3kNy/krDNOmZzbxCwGRi7+iYBF9E3fb9V9epFdKt+6yCAwM8E3EM/M6L4cwKr95Dc/7mn/vJnArO5Nwj42TwKBG4RcBHdIv3NdVYvom+6oWoENgm4hzZ9eWVXq/eQ3L+SsM06ZnNvELAZGLv6JgEX0Td9v1X16kV0q37rIIDAzwTcQz8zovhzAqv3kNz/uaf+8mcCs7k3CPjZPAoEbhFwEd0i/c11Vi+ib7qhagQ2CbiHNn15ZVer95Dcv5KwzTpmc28QsBkYu/omARfRN32/VfXqRXSrfusggMDPBNxDPzOi+HMCq/eQ3P+5p/7yZwKzuTcI+Nk8CgRuEXAR3SL9zXVWL6JvuqFqBDYJuIc2fXllV6v3kNy/krDNOmZzbxCwGRi7+iYBF9E3fb9V9epFdKt+6yCAwM8E3EM/M6L4cwKr95Dc/7mn/vJnArO5Nwj42TwKBG4RcBHdIv3NdVYvom+6oWoENgm4hzZ9eWVXq/eQ3L+SsM06ZnNvELAZGLv6JgEX0Td9v1X16kV0q37rIIDAzwTcQz8zovhzAqv3kNz/uaf+8mcCs7k3CPjZPAoEbhFwEd0i/c11Vi+ib7qhagQ2CbiHNn15ZVer95Dcv5KwzTpmc28QsBkYu/omARfRN32/VfXqRXSrfusggMDPBNxDPzOi+HMCq/eQ3P+5p/7yZwKzuTcI+Nk8CgRuEXAR3SL9zXVWL6JvuqFqBDYJuIc2fXllV6v3kNy/krDNOmZzvzoIcCBbkFcD1qqgXs39ar7wamcGL7wagTfUq7l/g+69KlbvoXsE3lhp9TzKV8sXHxuvVfV/DQJWrWn70sAar1W1xtqcwQuvRqCp5avxWlWv+rjKa3Vf3nNWnWn7Wj2P8sXHRuANtUHAGz7+RwN7w0gXZPMRL7wagaaWr8ZrVb3q4yqv1X15z1l1pu1r9TzKFx8bgTfUBgFv+GgQ8IiPLshmJF54NQJNLV+N16p61cdVXqv78qG26kzb1+p5lC8+NgJvqA0C3vDRIOARH12QzUi88GoEmlq+Gq9V9aqPq7xW9+VDbdWZtq/V8yhffGwE3lAbBLzho0HAIz66IJuReOHVCDS1fDVeq+pVH1d5re7Lh9qqM21fq+dRvvjYCLyhNgh4w0eDgEd8dEE2I/HCqxFoavlqvFbVqz6u8lrdlw+1VWfavlbPo3zxsRF4Q20Q8IaPBgGP+OiCbEbihVcj0NTy1Xitqld9XOW1ui8faqvOtH2tnkf54mMj8IbaIOANHw0CHvHRBdmMxAuvRqCp5avxWlWv+rjKa3VfPtRWnWn7Wj2P8sXHRuANtUHAGz4aBDziowuyGYkXXo1AU8tX47WqXvVxldfqvnyorTrT9rV6HuWLj43AG2qDgDd8NAh4xEcXZDMSL7wagaaWr8ZrVb3q4yqv1X35UFt1pu1r9TzKFx8bgTfUBgFv+GgQ8IiPLshmJF54NQJNLV+N16p61cdVXqv78qG26kzb1+p5lC8+NgJvqA0C3vDRIOARH12QzUi88GoEmlq+Gq9V9aqPq7xW9+VDbdWZtq/V8yhffGwE3lAbBLzho0HAIz66IJuReOHVCDS1fDVeq+pVH1d5re7Lh9qqM21fq+dRvvjYCLyhNgh4w0eDgEd8dEE2I/HCqxFoavlqvFbVqz6u8lrdlw+1VWfavlbPo3zxsRF4Q20Q8IaPBgGP+OiCbEbihVcj0NTy1Xitqld9XOW1ui8faqvOtH2tnkf54mMj8IbaIOANHw0CHvHRBdmMxAuvRqCp5avxWlWv+rjKa3VfPtRWnWn7Wj2P8sXHRuANtUHAGz4aBDziowuyGYkXXo1AU8tX47WqXvVxldfqvnyorTrT9rV6HuWLj43AG2qDgDd8NAh4xEcXZDMSL7wagaaWr8ZrVb3q4yqv1X35UFt1pu1r9TzKFx8bgTfUBgFv+GgQ8IiPLshmJF54NQJNLV+N16p61cdVXqv78qG26kzb1+p5lC8+NgJvqA0C3vDRIOARH12QzUi88GoEmlq+Gq9V9aqPq7xW9+VDbdWZtq/V8yhffGwE3lAbBLzho0HAIz66IJuReOHVCDS1fDVesOr43AAAIABJREFUq+pVH1d5re7Lh9qqM21fq+dRvvjYCLyhNgh4w0eDgEd8dEE2I/HCqxFoavlqvFbVqz6u8lrdlw+1VWfavlbPo3zxsRF4Q20Q8IaPBgGP+OiCbEbihVcj0NTy1Xitqld9XOW1ui8faqvOtH2tnkf54mMj8IbaIOANHw0CHvHRBdmMxAuvRqCp5avxWlWv+rjKa3VfPtRWnWn7Wj2P8sXHRuANtUHAGz4aBDziowuyGYkXXo1AU8tX47WqXvVxldfqvnyorTrT9rV6HuWLj43AG2qDgDd8NAh4xEcXZDMSL7wagaaWr8ZrVb3q4yqv1X35UFt1pu1r9TzKFx8bgTfUBgFv+GgQ8IiPLshmJF54NQJNLV+N16p61cdVXqv78qG26kzb1+p5lC8+NgJvqA0C3vDRIOARH12QzUi88GoEmlq+Gq9V9aqPq7xW9+VDbdWZtq/V8yhffGwE3lAbBLzho0HAIz66IJuReOHVCDS1fDVeq+pVH1d5re7Lh9qqM21fq+dRvvjYCLyhNgh4w0eDgEd8dEE2I/HCqxFoavlqvFbVqz6u8lrdlw+1VWfavlbPo3zxsRF4Q20Q8IaPBgGP+OiCbEbihVcj0NTy1Xitqld9XOW1ui8faqvOtH2tnkf54mMj8IbaIOANHw0CHvHRBdmMxAuvRqCp5avxWlWv+rjKa3VfPtRWnWn7Wj2P8sXHRuANtUHAGz4aBDziowuyGYkXXo1AU8tX47WqXvVxldfqvnyorTrT9rV6HuWLj43AG2qDgDd8NAh4xEcXZDMSL7wagaaWr8ZrVb3q4yqv1X35UFt1pu1r9TzKFx8bgTfUBgFv+GgQ8IiPLshmJF54NQJNLV+N16p61cdVXqv78qG26kzb1+p5lC8+NgJvqA0C3vDRIOARH12QzUi88GoEmlq+Gq9V9aqPq7xW9+VDbdWZtq/V8yhffGwE3lAbBLzho0HAIz66IJuReOHVCDS1fDVeq+pVH1d5re7Lh9qqM21fq+dRvvjYCLyhnh0EvIFXFasEXETNmVVerQrqVQKrL2By3xLDx8ZrVc3HVWfsC4EdAqt9YofQv7ETg4B/wye7/GUCqy/4q411ldcvx8Lj/hIBuf9L4H95WT7+MtC/9Dg+/iXwlkXgHyKw2if+IYQTWzUImLDBJm4TWP2wXW2sq7xu58Z6ZwjI/Rmut5/Kx9vEz6zHxzNcPRWBlwis9omXGN+oxSDgBmVrzBFY/bBdbayrvOaCZUN/REDu/wjb3B/xcc6SP9oQH/8Imz9C4FMEVvvEp0z4hWINAn4Bokf8ewRWP2xXG+sqr38veXb8/0VA7t/IBR/5eJKAe+gkXc9GoBFY7fetCmqDABn4JIHVF4rVxrrK65PhfbBouX/DVD7y8SQB99BJup6NQCOw2u9bFdQGATLwSQKrLxSrjXWV1yfD+2DRcv+GqXzk40kC7qGTdD0bgUZgtd+3KqgNAmTgkwRWXyhWG+sqr0+G98Gi5f4NU/nIx5ME3EMn6Xo2Ao3Aar9vVVAbBMjAJwmsvlCsNtZVXp8M74NFy/0bpvKRjycJuIdO0vVsBBqB1X7fqqA2CJCBTxJYfaFYbayrvD4Z3geLlvs3TOUjH08ScA+dpOvZCDQCq/2+VUFtECADnySw+kKx2lhXeX0yvA8WLfdvmMpHPp4k4B46SdezEWgEVvt9q4LaIEAGPklg9YVitbGu8vpkeB8sWu7fMJWPfDxJwD10kq5nI9AIrPb7VgW1QYAMfJLA6gvFamNd5fXJ8D5YtNy/YSof+XiSgHvoJF3PRqARWO33rQpqgwAZ+CSB1ReK1ca6yuuT4X2waLl/w1Q+8vEkAffQSbqejUAjsNrvWxXUBgEy8EkCqy8Uq411ldcnw/tg0XL/hql85ONJAu6hk3Q9G4FGYLXftyqoDQJk4JMEVl8oVhvrKq9PhvfBouX+DVP5yMeTBNxDJ+l6NgKNwGq/b1VQGwTIwCcJrL5QrDbWVV6fDO+DRcv9G6bykY8nCbiHTtL1bAQagdV+36qgNgiQgU8SWH2hWG2sq7w+Gd4Hi5b7N0zlIx9PEnAPnaTr2Qg0Aqv9vlVBbRAgA58ksPpCsdpYV3l9MrwPFi33b5jKRz6eJOAeOknXsxFoBFb7fauC2iBABj5JYPWFYrWxrvL6ZHgfLFru3zCVj3w8ScA9dJKuZyPQCKz2+1YFtUGADHySwOoLxWpjXeX1yfA+WLTcv2EqH/l4koB76CRdz0agEVjt960KaoMAGfgkgdUXitXGusrrk+F9sGi5f8NUPvLxJAH30Em6no1AI7Da71sV1AYBMvBJAqsvFKuNdZXXJ8P7YNFy/4apfOTjSQLuoZN0PRuBRmC137cqqA0CZOCTBFZfKFYb6yqvT4b3waLl/g1T+cjHkwTcQyfpejYCjcBqv29VUBsEyMAnCay+UKw21lVenwzvg0XL/Rum8pGPJwm4h07S9WwEGoHVft+qoDYIkIFPElh9oVhtrKu8PhneB4uW+zdM5SMfTxJwD52k69kINAKr/b5VQW0QIAOfJLD6QrHaWFd5fTK8DxYt92+Yykc+niTgHjpJ17MRaARW+32rgtogQAY+SWD1hWK1sa7y+mR4Hyxa7t8wlY98PEnAPXSSrmcj0Ais9vtWBbVBgAx8ksDqC8VqY13l9cnwPli03L9hKh/5eJKAe+gkXc9GoBFY7fetCmqDABn4JIHVF4rVxrrK65PhfbBouX/DVD7y8SQB99BJup6NQCOw2u9bFdQGATLwSQKrLxSrjXWV1yfD+2DRcv+GqXzk40kC7qGTdD0bgUZgtd+3KqgNAmTgkwRWXyhWG+sqr0+G98Gi5f4NU/nIx5ME3EMn6Xo2Ao3Aar9vVVAbBMjAJwmsvlCsNtZVXp8M74NFy/0bpvKRjycJuIdO0vVsBBqB1X7fqqA2CJCBTxJYfaFYbayrvD4Z3geLlvs3TOUjH08ScA+dpOvZCDQCq/2+VUFtECADnySw+kKx2lhXeX0yvA8WLfdvmMpHPp4k4B46SdezEWgEVvt9q4LaIEAGPklg9YVitbGu8vpkeB8sWu7fMJWPfDxJwD10kq5nI9AIrPb7VgW1QYAMfJLA6gvFamNd5fXJ8D5YtNy/YSof+XiSgHvoJF3PRqARWO33rQpqgwAZ+CSB1ReK1ca6yuuT4X2waLl/w1Q+8vEkAffQSbqejUAjsNrvWxXUBgEycJSAi7vh1VgbL/lqvFbVq7lfzdcqr9V8re5LvladeWNfq/lapbvaV/nYErPqY6vintog4B7rT66kgTXbNbDGS74ar1X1au5X87XKazVfq/uSr1Vn3tjXar5W6a72VT62xKz62Kq4pzYIuMf6kytpYM12Dazxkq/Ga1W9mvvVfK3yWs3X6r7ka9WZN/a1mq9Vuqt9lY8tMas+tiruqQ0C7rH+5EoaWLNdA2u85KvxWlWv5n41X6u8VvO1ui/5WnXmjX2t5muV7mpf5WNLzKqPrYp7aoOAe6w/uZIG1mzXwBov+Wq8VtWruV/N1yqv1Xyt7ku+Vp15Y1+r+Vqlu9pX+dgSs+pjq+Ke2iDgHutPrqSBNds1sMZLvhqvVfVq7lfztcprNV+r+5KvVWfe2NdqvlbprvZVPrbErPrYqrinNgi4x/qTK2lgzXYNrPGSr8ZrVb2a+9V8rfJazdfqvuRr1Zk39rWar1W6q32Vjy0xqz62Ku6pDQLusf7kShpYs10Da7zkq/FaVa/mfjVfq7xW87W6L/ladeaNfa3ma5Xual/lY0vMqo+tintqg4B7rD+5kgbWbNfAGi/5arxW1au5X83XKq/VfK3uS75WnXljX6v5WqW72lf52BKz6mOr4p7aIOAe60+upIE12zWwxku+Gq9V9WruV/O1yms1X6v7kq9VZ97Y12q+Vumu9lU+tsSs+tiquKc2CLjH+pMraWDNdg2s8ZKvxmtVvZr71Xyt8lrN1+q+5GvVmTf2tZqvVbqrfZWPLTGrPrYq7qkNAu6x/uRKGlizXQNrvOSr8VpVr+Z+NV+rvFbztbov+Vp15o19reZrle5qX+VjS8yqj62Ke2qDgHusP7mSBtZs18AaL/lqvFbVq7lfzdcqr9V8re5LvladeWNfq/lapbvaV/nYErPqY6vintog4B7rT66kgTXbNbDGS74ar1X1au5X87XKazVfq/uSr1Vn3tjXar5W6a72VT62xKz62Kq4pzYIuMf6kytpYM12Dazxkq/Ga1W9mvvVfK3yWs3X6r7ka9WZN/a1mq9Vuqt9lY8tMas+tiruqQ0C7rH+5EoaWLNdA2u85KvxWlWv5n41X6u8VvO1ui/5WnXmjX2t5muV7mpf5WNLzKqPrYp7aoOAe6w/uZIG1mzXwBov+Wq8VtWruV/N1yqv1Xyt7ku+Vp15Y1+r+Vqlu9pX+dgSs+pjq+Ke2iDgHutPrqSBNds1sMZLvhqvVfVq7lfztcprNV+r+5KvVWfe2NdqvlbprvZVPrbErPrYqrinNgi4x/qTK2lgzXYNrPGSr8ZrVb2a+9V8rfJazdfqvuRr1Zk39rWar1W6q32Vjy0xqz62Ku6pDQLusf7kShpYs10Da7zkq/FaVa/mfjVfq7xW87W6L/ladeaNfa3ma5Xual/lY0vMqo+tintqg4B7rD+5kgbWbNfAGi/5arxW1au5X83XKq/VfK3uS75WnXljX6v5WqW72lf52BKz6mOr4p7aIOAe60+upIE12zWwxku+Gq9V9WruV/O1yms1X6v7kq9VZ97Y12q+Vumu9lU+tsSs+tiquKc2CLjH+pMraWDNdg2s8ZKvxmtVvZr71Xyt8lrN1+q+5GvVmTf2tZqvVbqrfZWPLTGrPrYq7qkNAu6x/uRKGlizXQNrvOSr8VpVr+Z+NV+rvFbztbov+Vp15o19reZrle5qX+VjS8yqj62Ke2qDgHusP7mSBtZs18AaL/lqvFbVq7lfzdcqr9V8re5LvladeWNfq/lapbvaV/nYErPqY6vintog4B7rT66kgTXbNbDGS74ar1X1au5X87XKazVfq/uSr1Vn3tjXar5W6a72VT62xKz62Kq4pzYIuMf6kytpYM12Dazxkq/Ga1W9mvvVfK3yWs3X6r7ka9WZN/a1mq9Vuqt9lY8tMas+tiruqQ0C7rH+5EoaWLNdA2u85KvxWlWv5n41X6u8VvO1ui/5WnXmjX2t5muV7mpf5WNLzKqPrYp7aoOAe6w/uZIG1mzXwBov+Wq8VtWruV/N1yqv1Xyt7ku+Vp15Y1+r+Vqlu9pX+dgSs+pjq+Ke2iDgHutPrqSBNds1sMZLvhqvVfVq7lfztcprNV+r+5KvVWfe2NdqvlbprvZVPrbErPrYqrinNgi4x/qTK2lgzXYNrPGSr8ZrVb2a+9V8rfJazdfqvuRr1Zk39rWar1W6q32Vjy0xqz62Ku6pDQLusf7kShpYs10Da7zkq/FaVa/mfjVfq7xW87W6L/ladeaNfa3ma5Xual/lY0vMqo+tintqg4B7rD+5kgbWbNfAGi/5arxW1au5X83XKq/VfK3uS75WnXljX6v5WqW72lf52BKz6mOr4p7aIOAe60+upIE12zWwxku+Gq9V9WruV/O1yms1X6v7kq9VZ97Y12q+Vumu9lU+tsSs+tiquKc2CLjH+pMraWDNdg2s8ZKvxmtVvZr71Xyt8lrN1+q+5GvVmTf2tZqvVbqrfZWPLTGrPrYq7qkNAu6x/uRKGlizXQNrvOSr8VpVr+Z+NV+rvFbztbov+Vp15o19reZrle5qX+VjS8yqj62Ke2qDgHusP7mSBtZs18AaL/lqvFbVq7lfzdcqr9V8re5LvladeWNfq/lapbvaV/nYErPqY6vintog4B7rT66kgTXbNbDGS74ar1X1au5X87XKazVfq/uSr1Vn3tjXar5W6a72VT62xKz62Kq4p54dBAj+vRBYaYfAagNbPY+rvHYSZSf/JwRWc/9/UtPJv3UeT9K992y5v8faSgj8qwT0+3/Vuf/nvg0C3vBRFY8QWG2sqy+Gq7weiePny1jN/aoxzuOqM21fct94USPwRQL6/RuuGwS84aMqHiGw2lhXXwxXeT0Sx8+XsZr7VWOcx1Vn2r7kvvGiRuCLBPT7N1w3CHjDR1U8QmC1sa6+GK7yeiSOny9jNferxjiPq860fcl940WNwBcJ6PdvuG4Q8IaPqniEwGpjXX0xXOX1SBw/X8Zq7leNcR5XnWn7kvvGixqBLxLQ799w3SDgDR9V8QiB1ca6+mK4yuuROH6+jNXcrxrjPK460/Yl940XNQJfJKDfv+G6QcAbPqriEQKrjXX1xXCV1yNx/HwZq7lfNcZ5XHWm7UvuGy9qBL5IQL9/w3WDgDd8VMUjBFYb6+qL4SqvR+L4+TJWc79qjPO46kzbl9w3XtQIfJGAfv+G6wYBb/ioikcIrDbW1RfDVV6PxPHzZazmftUY53HVmbYvuW+8qBH4IgH9/g3XDQLe8FEVjxBYbayrL4arvB6J4+fLWM39qjHO46ozbV9y33hRI/BFAvr9G64bBLzhoyoeIbDaWFdfDFd5PRLHz5exmvtVY5zHVWfavuS+8aJG4IsE9Ps3XDcIeMNHVTxCYLWxrr4YrvJ6JI6fL2M196vGOI+rzrR9yX3jRY3AFwno92+4bhDwho+qeITAamNdfTFc5fVIHD9fxmruV41xHledafuS+8aLGoEvEtDv33DdIOANH1XxCIHVxrr6YrjK65E4fr6M1dyvGuM8rjrT9iX3jRc1Al8koN+/4bpBwBs+quIRAquNdfXFcJXXI3H8fBmruV81xnlcdabtS+4bL2oEvkhAv3/DdYOAN3xUxSMEVhvr6ovhKq9H4vj5MlZzv2qM87jqTNuX3Dde1Ah8kYB+/4brBgFv+KiKRwisNtbVF8NVXo/E8fNlrOZ+1RjncdWZti+5b7yoEfgiAf3+DdcNAt7wURWPEFhtrKsvhqu8Honj58tYzf2qMc7jqjNtX3LfeFEj8EUC+v0brhsEvOGjKh4hsNpYV18MV3k9EsfPl7Ga+1VjnMdVZ9q+5L7xokbgiwT0+zdcNwh4w0dVPEJgtbGuvhiu8nokjp8vYzX3q8Y4j6vOtH3JfeNFjcAXCej3b7huEPCGj6p4hMBqY119MVzl9UgcP1/Gau5XjXEeV51p+5L7xosagS8S0O/fcN0g4A0fVfEIgdXGuvpiuMrrkTh+vozV3K8a4zyuOtP2JfeNFzUCXySg37/hukHAGz6q4hECq4119cVwldcjcfx8Gau5XzXGeVx1pu1L7hsvagS+SEC/f8N1g4A3fFTFIwRWG+vqi+Eqr0fi+PkyVnO/aozzuOpM25fcN17UCHyRgH7/husGAW/4qIpHCKw21tUXw1Vej8Tx82Ws5n7VGOdx1Zm2L7lvvKgR+CIB/f4N1w0C3vBRFY8QWG2sqy+Gq7weiePny1jN/aoxzuOqM21fct94USPwRQL6/RuuGwS84aMqHiGw2lhXXwxXeT0Sx8+XsZr7VWOcx1Vn2r7kvvGiRuCLBPT7N1w3CHjDR1U8QmC1sa6+GK7yeiSOny9jNferxjiPq860fcl940WNwBcJ6PdvuG4Q8IaPqniEwGpjXX0xXOX1SBw/X8Zq7leNcR5XnWn7kvvGixqBLxLQ799w3SDgDR9V8QiB1ca6+mK4yuuROH6+jNXcrxrjPK460/Yl940XNQJfJKDfv+G6QcAbPqriEQKrjXX1xXCV1yNx/HwZq7lfNcZ5XHWm7UvuGy9qBL5IQL9/w3WDgDd8VMUjBFYb6+qL4SqvR+L4+TJWc79qjPO46kzbl9w3XtQIfJGAfv+G6wYBb/ioikcIrDbW1RfDVV6PxPHzZazmftUY53HVmbYvuW+8qBH4IgH9/g3XDQLe8FEVjxBYbayrL4arvB6J4+fLWM39qjHO46ozbV9y33hRI/BFAvr9G64bBLzhoyoeIbDaWFdfDFd5PRLHz5exmvtVY5zHVWfavuS+8aJG4IsE9Ps3XDcIeMNHVTxCYLWxrr4YrvJ6JI6fL2M196vGOI+rzrR9yX3jRY3AFwno92+4bhDwho+qeITAamNdfTFc5fVIHD9fxmruV41xHledafuS+8aLGoEvEtDv33DdIOANH1XxCIHVxrr6YrjK65E4fr6M1dyvGuM8rjrT9iX3jRc1Al8koN+/4frsIOANvKpAAIEvElh9kXZxtzTysfFaVfOxOYNX40XdCMhX40WNwEkCBgEn6Xo2Agh8koAXnTds5yMfTxJYHczJ/UnXPVu+ZACBHQIGATte2AkCCDxCwIvOG0bykY8nCRgENLqrvFoV1PqqDCCwQ8AgYMcLO0EAgUcIeNF5w0g+8vEkgdUPW7k/6bpny5cMILBDwCBgxws7QQCBRwh40XnDSD7y8SQBg4BGd5VXq4JaX5UBBHYIGATseGEnCCDwCAEvOm8YyUc+niSw+mEr9ydd92z5kgEEdggYBOx4YScIIPAIAS86bxjJRz6eJGAQ0Oiu8mpVUOurMoDADgGDgB0v7OT/atcOchzbkSSK/r//RVePa9AIGFSkLqgzTs+nx+NGinIEAQKPCLjovNFIfdTHkwLVH7Zyf7Lrni1fMkCgI2AQ0OmFNyFA4BEBF503GqmP+nhSwCBg0616batQ7VyVAQIdAYOATi+8CQECjwi46LzRSH3Ux5MC1R+2cn+y654tXzJAoCNgENDphTchQOARARedNxqpj/p4UsAgYNOtem2rUO1clQECHQGDgE4vvAkBAo8IuOi80Uh91MeTAtUftnJ/suueLV8yQKAjYBDQ6YU3IUDgEQEXnTcaqY/6eFLAIGDTrXptq1DtXJUBAh0Bg4BOL7wJAQKPCLjovNFIfdTHkwLVH7Zyf7Lrni1fMkCgI2AQ0OmFNyFA4BEBF503GqmP+nhSwCBg0616batQ7VyVAQIdAYOATi+8CQECjwi46LzRSH3Ux5MC1R+2cn+y654tXzJAoCNgENDphTchQOARARedNxqpj/p4UsAgYNOtem2rUO1clQECHQGDgE4vvAkBAo8IuOi80Uh91MeTAtUftnJ/suueLV8yQKAjYBDQ6YU3IUDgEQEXnTcaqY/6eFLAIGDTrXptq1DtXJUBAh0Bg4BOL7wJAQKPCLjovNFIfdTHkwLVH7Zyf7Lrni1fMkCgI2AQ0OmFNyFA4BEBF503GqmP+nhSwCBg0616batQ7VyVAQIdAYOATi+8CQECjwi46LzRSH3Ux5MC1R+2cn+y654tXzJAoCNgENDphTchQOARARedNxqpj/p4UsAgYNOtem2rUO1clQECHQGDgE4vvAkBAo8IuOi80Uh91MeTAtUftnJ/suueLV8yQKAjYBDQ6YU3IUDgEQEXnTcaqY/6eFLAIGDTrXptq1DtXJUBAh0Bg4BOL7wJAQKPCLjovNFIfdTHkwLVH7Zyf7Lrni1fMkCgI2AQ0OmFNyFA4BEBF503GqmP+nhSwCBg0616batQ7VyVAQIdAYOATi+8CQECjwi46LzRSH3Ux5MC1R+2cn+y654tXzJAoCNgENDphTchQOARARedNxqpj/p4UsAgYNOtem2rUO1clQECHQGDgE4vvAkBAo8IuOi80Uh91MeTAtUftnJ/suueLV8yQKAjYBDQ6YU3IUDgEQEXnTcaqY/6eFLAIGDTrXptq1DtXJUBAh0Bg4BOL7wJAQKPCLjovNFIfdTHkwLVH7Zyf7Lrni1fMkCgI2AQ0OmFNyFA4BEBF503GqmP+nhSwCBg0616batQ7VyVAQIdAYOATi+8CQECjwi46LzRSH3Ux5MC1R+2cn+y654tXzJAoCNgENDphTchQOARARedNxqpj/p4UsAgYNOtem2rUO1clQECHQGDgE4vvAkBAo8IuOi80Uh91MeTAtUftnJ/suueLV8yQKAjYBDQ6YU3IUDgEQEXnTcaqY/6eFLAIGDTrXptq1DtXJUBAh0Bg4BOL7wJAQKPCLjovNFIfdTHkwLVH7Zyf7Lrni1fMkCgI5AdBFQPik7rvAkBAtWLdLUzztVqZ954r+p+rOae15Z7Xrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSeawbNNSAAAgAElEQVTFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCweakmQCAk4It7a0b1B9G2CtVVgep+rOae15ZkXrw2ga26mq9tFaoJbAIGAZuXagIEQgK+uLdmVH8QbatQXRWo7sdq7nltSebFaxPYqqv52lahmsAmYBCwef3joBjBlD8h4CK9tZEXr01gq5avzUv1JiBfm5fqTaCar20VqqsCfqdtnTEI2LwMAkYv5W8IVL+4qwc+ry33vHhtAqpPCtiPJ3U9u5ovnXlDoHovrOoaBIydEbARTPkTAtUv7up+5LXFnhevTUD1SQH78aSuZ1fzpTNvCFTvhVVdg4CxMwI2gil/QqD6xV3dj7y22PPitQmoPilgP57U9exqvnTmDYHqvbCqaxAwdkbARjDlTwhUv7ir+5HXFntevDYB1ScF7MeTup5dzZfOvCFQvRdWdQ0Cxs4I2Aim/AmB6hd3dT/y2mLPi9cmoPqkgP14Utezq/nSmTcEqvfCqq5BwNgZARvBlD8hUP3iru5HXlvsefHaBFSfFLAfT+p6djVfOvOGQPVeWNU1CBg7I2AjmPInBKpf3NX9yGuLPS9em4DqkwL240ldz67mS2feEKjeC6u6BgFjZwRsBFP+hED1i7u6H3ltsefFaxNQfVLAfjyp69nVfOnMGwLVe2FV1yBg7IyAjWDKnxCofnFX9yOvLfa8eG0Cqk8K2I8ndT27mi+deUOgei+s6hoEjJ0RsBFM+RMC1S/u6n7ktcWeF69NQPVJAfvxpK5nV/OlM28IVO+FVV2DgLEzAjaCKX9CoPrFXd2PvLbY8+K1Cag+KWA/ntT17Gq+dOYNgeq9sKprEDB2RsBGMOVPCFS/uKv7kdcWe168NgHVJwXsx5O6nl3Nl868IVC9F1Z1DQLGzgjYCKb8CYHqF3d1P/LaYs+L1yag+qSA/XhS17Or+dKZNwSq98KqrkHA2BkBG8GUPyFQ/eKu7kdeW+x58doEVJ8UsB9P6np2NV8684ZA9V5Y1TUIGDsjYCOY8icEql/c1f3Ia4s9L16bgOqTAvbjSV3PruZLZ94QqN4Lq7oGAWNnBGwEU/6EQPWLu7ofeW2x58VrE1B9UsB+PKnr2dV86cwbAtV7YVXXIGDsjICNYMqfEKh+cVf3I68t9rx4bQKqTwrYjyd1PbuaL515Q6B6L6zqGgSMnRGwEUz5EwLVL+7qfuS1xZ4Xr01A9UkB+/GkrmdX86UzbwhU74VVXYOAsTMCNoIpf0Kg+sVd3Y+8ttjz4rUJqD4pYD+e1PXsar505g2B6r2wqmsQMHZGwEYw5U8IVL+4q/uR1xZ7Xrw2AdUnBezHk7qeXc2XzrwhUL0XVnUNAsbOCNgIpvwJgeoXd3U/8tpiz4vXJqD6pID9eFLXs6v50pk3BKr3wqquQcDYGQEbwZQ/IVD94q7uR15b7Hnx2gRUnxSwH0/qenY1XzrzhkD1XljVNQgYOyNgI5jyJwSqX9zV/chriz0vXpuA6pMC9uNJXc+u5ktn3hCo3gurugYBY2cEbART/oRA9Yu7uh95bbHnxWsTUH1SwH48qevZ1XzpzBsC1XthVdcgYOyMgI1gyp8QqH5xV/cjry32vHhtAqpPCtiPJ3U9u5ovnXlDoHovrOoaBIydEbARTPkTAtUv7up+5LXFnhevTUD1SQH78aSuZ1fzpTNvCFTvhVVdg4CxMwI2gil/QqD6xV3dj7y22PPitQmoPilgP57U9exqvnTmDYHqvbCqaxAwdkbARjDlTwhUv7ir+5HXFntevDYB1ScF7MeTup5dzZfOvCFQvRdWdQ0Cxs4I2Aim/AmB6hd3dT/y2mLPi9cmoPqkgP14Utezq/nSmTcEqvfCqq5BwNgZARvBlD8hUP3iru5HXlvsefHaBFSfFLAfT+p6djVfOvOGQPVeWNU1CBg7I2AjmPInBKpf3NX9yGuLPS9em4DqkwL240ldz67mS2feEKjeC6u6BgFjZwRsBFP+hED1i7u6H3ltsefFaxNQfVLAfjyp69nVfOnMGwLVe2FV1yBg7IyAjWDKnxCofnFX9yOvLfa8eG0Cqk8K2I8ndT27mi+deUOgei+s6hoEjJ0RsBFM+RMC1S/u6n7ktcWeF69NQPVJAfvxpK5nV/OlM28IVO+FVV2DgLEzAjaCKX9CoPrFXd2PvLbY8+K1Cag+KWA/ntT17Gq+dOYNgeq9sKprEDB2RsBGMOVPCFS/uKv7kdcWe168NgHVJwXsx5O6nl3Nl868IVC9F1Z1DQLGzgjYCKb8CYHqF3d1P/LaYs+L1yag+qSA/XhS17Or+dKZNwSq98KqrkHA2JlqwBysYyOj5fK1NYbXG17bKu5VO1c36+p+3FahWu5lgACBvwSq5331/Mp6/Sf6Zhr51xb873+vem2rUB3djv9U88Vr2zNVr20V96qrub8nsH2SfG1e1Wq5r3bGexHoCFTP++r5lfUyCNg2VbaR//67LUR1UkC+trbwesNrW8W96uqF4p7A9knV/bitQrXcywABAn8JVM/76vmV9TII+Cvq//3v2UYaBGyNjFbL19YYXm94bau4V129UNwT2D6puh+3VaiWexkgQOAvgep5Xz2/sl4GAX9F3SBgE1L9iUD2oIgOmnhtaat6bau4V129UNwT2D5JvjavarXcVzvjvQh0BKrnffX8ynoZBGybKtvI6A+1TVe1fG0Z4PWG17aKe9XVC8U9ge2TqvtxW4VquZcBAgT+Eqie99XzK+tlEPBX1P1FwCak+hOB7EERHTTx2tJW9dpWca+6eqG4J7B9knxtXtVqua92xnsR6AhUz/vq+ZX1MgjYNlW2kdEfapuuavnaMsDrDa9tFfeqqxeKewLbJ1X347YK1XIvAwQI/CVQPe+r51fWyyDgr6j7i4BNSPUnAtmDIjpo4rWlreq1reJedfVCcU9g+yT52ryq1XJf7Yz3ItARqJ731fMr62UQsG2qbCOjP9Q2XdXytWWA1xte2yruVVcvFPcEtk+q7sdtFarlXgYIEPhLoHreV8+vrJdBwF9R9xcBm5DqTwSyB0V00MRrS1vVa1vFverqheKewPZJ8rV5VavlvtoZ70WgI1A976vnV9bLIGDbVNlGRn+obbqq5WvLAK83vLZV3KuuXijuCWyfVN2P2ypUy70MECDwl0D1vK+eX1kvg4C/ou4vAjYh1Z8IZA+K6KCJ15a2qte2invV1QvFPYHtk+Rr86pWy321M96LQEeget5Xz6+sl0HAtqmyjYz+UNt0VcvXlgFeb3htq7hXXb1Q3BPYPqm6H7dVqJZ7GSBA4C+B6nlfPb+yXgYBf0XdXwRsQqo/EcgeFNFBE68tbVWvbRX3qqsXinsC2yfJ1+ZVrZb7ame8F4GOQPW8r55fWS+DgG1TZRsZ/aG26aqWry0DvN7w2lZxr7p6obgnsH1SdT9uq1At9zJAgMBfAtXzvnp+Zb0MAv6Kur8I2IRUfyKQPSiigyZeW9qqXtsq7lVXLxT3BLZPkq/Nq1ot99XOeC8CHYHqeV89v7JeBgHbpso2MvpDbdNVLV9bBni94bWt4l519UJxT2D7pOp+3FahWu5lgACBvwSq5331/Mp6GQT8FXV/EbAJqf5EIHtQRAdNvLa0Vb22Vdyrrl4o7glsnyRfm1e1Wu6rnfFeBDoC1fO+en5lvQwCtk2VbWT0h9qmq1q+tgzwesNrW8W96uqF4p7A9knV/bitQrXcywABAn8JVM/76vmV9TII+Cvq/iJgE1L9iUD2oIgOmnhtaat6bau4V129UNwT2D5JvjavarXcVzvjvQh0BKrnffX8ynoZBGybKtvI6A+1TVe1fG0Z4PWG17aKe9XVC8U9ge2TqvtxW4VquZcBAgT+Eqie99XzK+tlEPBX1P1FwCak+hOB7EERHTTx2tJW9dpWca+6eqG4J7B9knxtXtVqua92xnsR6AhUz/vq+ZX1MgjYNlW2kdEfapuuavnaMsDrDa9tFfeqqxeKewLbJ1X347YK1XIvAwQI/CVQPe+r51fWyyDgr6j7i4BNSPUnAtmDIjpo4rWlreq1reJedfVCcU9g+yT52ryq1XJf7Yz3ItARqJ731fMr62UQsG2qbCOjP9Q2XdXytWWA1xte2yruVVcvFPcEtk+q7sdtFarlXgYIEPhLoHreV8+vrJdBwF9R9xcBm5DqTwSyB0V00MRrS1vVa1vFverqheKewPZJ8rV5VavlvtoZ70WgI1A976vnV9bLIGDbVNlGRn+obbqq5WvLAK83vLZV3KuuXijuCWyfVN2P2ypUy70MECDwl0D1vK+eX1kvg4C/ou4vAjYh1Z8IZA+K6KCJ15a2qte2invV1QvFPYHtk+Rr86pWy321M96LQEeget5Xz6+sl0HAtqmyjYz+UNt0VcvXlgFeb3htq7hXXb1Q3BPYPqm6H7dVqJZ7GSBA4C+B6nlfPb+yXgYBf0XdXwRsQqo/EcgeFNFBE68tbVWvbRX3qqsXinsC2yfJ1+ZVrZb7ame8F4GOQPW8r55fWS+DgG1TZRsZ/aG26aqWry0DvN7w2lZxr7p6obgnsH1SdT9uq1At9zJAgMBfAtXzvnp+Zb0MAv6Kur8I2IRUfyKQPSiigyZeW9qqXtsq7lVXLxT3BLZPkq/Nq1ot99XOeC8CHYHqeV89v7JeBgHbpso2MvpDbdNVLV9bBni94bWt4l519UJxT2D7pOp+3FahWu5lgACBvwSq5331/Mp6GQT8FXV/EbAJqf5EIHtQRAdNvLa0Vb22Vdyrrl4o7glsnyRfm1e1Wu6rnfFeBDoC1fO+en5lvQwCtk2VbWT0h9qmq1q+tgzwesNrW8W96uqF4p7A9knV/bitQrXcywABAn8JVM/76vmV9TII+Cvq/iJgE1L9iUD2oIgOmnhtaat6bau4V129UNwT2D5JvjavarXcVzvjvQh0BKrnffX8ynoZBGybKtvI6A+1TVe1fG0Z4PWG17aKe9XVC8U9ge2TqvtxW4VquZcBAgT+Eqie99XzK+tlEPBX1P1FwCak+hOB7EERHTRVvT7JwMn/6wty0+W1eVWrq32senkvAicFfG9vutXzSx+3Plar/zUI2FpTDX71oNh0VcvXloGq17aKe9XVc6LaR173snnyk6p9PLlmzyZQFaie91Wv6vmlj9XEbO9lELB5/VMNfvWgGHl/vly+tghUvbZV3KuunhPVPvK6l82Tn1Tt48k1ezaBqkD1vK96Vc8vfawmZnsvg4DNyyBg9FK+CVQPVl9EWx+r1fq4dYbX5lWtrvax6uW9CJwUqN5zTq75k2dXzy99/KSrnf9rEDD2ohr86kEx8v58uXxtEah6bau4V109J6p95HUvmyc/qdrHk2v2bAJVgep5X/Wqnl/6WE3M9l4GAZuXvwgYvZRvAtWD1RfR1sdqtT5uneG1eVWrq32senkvAicFqveck2v+5NnV80sfP+lq5/8aBIy9qAa/elCMvD9fLl9bBKpe2yruVVfPiWofed3L5slPqvbx5Jo9m0BVoHreV72q55c+VhOzvZdBwOblLwJGL+WbQPVg9UW09bFarY9bZ3htXtXqah+rXt6LwEmB6j3n5Jo/eXb1/NLHT7ra+b8GAWMvqsGvHhQj78+Xy9cWgarXtop71dVzotpHXveyefKTqn08uWbPJlAVqJ73Va/q+aWP1cRs72UQsHn5i4DRS/kmUD1YfRFtfaxW6+PWGV6bV7W62seql/cicFKges85ueZPnl09v/Txk652/q9BwNiLavCrB8XI+/Pl8rVFoOq1reJedfWcqPaR171snvykah9PrtmzCVQFqud91at6fuljNTHbexkEbF7+ImD0Ur4JVA9WX0RbH6vV+rh1htfmVa2u9rHq5b0InBSo3nNOrvmTZ1fPL338pKud/2sQMPaiGvzqQTHy/ny5fG0RqHptq7hXXT0nqn3kdS+bJz+p2seTa/ZsAlWB6nlf9aqeX/pYTcz2XgYBm5e/CBi9lG8C1YPVF9HWx2q1Pm6d4bV5Vaurfax6eS8CJwWq95yTa/7k2dXzSx8/6Wrn/xoEjL2oBr96UIy8P18uX1sEql7bKu5VV8+Jah953cvmyU+q9vHkmj2bQFWget5Xvarnlz5WE7O9l0HA5uUvAkYv5ZtA9WD1RbT1sVqtj1tneG1e1epqH6te3ovASYHqPefkmj95dvX80sdPutr5vwYBYy+qwa8eFCPvz5fL1xaBqte2invV1XOi2kde97J58pOqfTy5Zs8mUBWonvdVr+r5pY/VxGzvZRCwefmLgNFL+SZQPVh9EW19rFbr49YZXptXtbrax6qX9yJwUqB6zzm55k+eXT2/9PGTrnb+r0HA2Itq8KsHxcj78+XytUWg6rWt4l519Zyo9pHXvWye/KRqH0+u2bMJVAWq533Vq3p+6WM1Mdt7GQRsXv4iYPRSvglUD1ZfRFsfq9X6uHWG1+ZVra72serlvQicFKjec06u+ZNnV88vffykq53/axAw9qIa/OpBMfL+fLl8bRGoem2ruFddPSeqfeR1L5snP6nax5Nr9mwCVYHqeV/1qp5f+lhNzPZeBgGbl78IGL2UbwLVg9UX0dbHarU+bp3htXlVq6t9rHp5LwInBar3nJNr/uTZ1fNLHz/pauf/GgSMvagGv3pQjLw/Xy5fWwSqXtsq7lVXz4lqH3ndy+bJT6r28eSaPZtAVaB63le9queXPlYTs72XQcDm5S8CRi/lm0D1YPVFtPWxWq2PW2d4bV7V6mofq17ei8BJgeo95+SaP3l29fzSx0+62vm/BgFjL6rBrx4UI+/Pl8vXFoGq17aKe9XVc6LaR173snnyk6p9PLlmzyZQFaie91Wv6vmlj9XEbO9lELB5+YuA0Uv5JlA9WH0RbX2sVuvj1hlem1e1utrHqpf3InBSoHrPObnmT55dPb/08ZOudv6vQcDYi2rwqwfFyPvz5fK1RaDqta3iXnX1nKj2kde9bJ78pGofT67ZswlUBarnfdWren7pYzUx23sZBGxe/iJg9FK+CVQPVl9EWx+r1fq4dYbX5lWtrvax6uW9CJwUqN5zTq75k2dXzy99/KSrnf9rEDD2ohr86kEx8v58uXxtEah6bau4V109J6p95HUvmyc/qdrHk2v2bAJVgep5X/Wqnl/6WE3M9l4GAZuXvwgYvZRvAtWD1RfR1sdqtT5uneG1eVWrq32senkvAicFqveck2v+5NnV80sfP+lq5/8aBIy9qAa/elCMvD9fLl9bBKpe2yruVVfPiWofed3L5slPqvbx5Jo9m0BVoHreV72q55c+VhOzvZdBwOblLwJGL+WbQPVg9UW09bFarY9bZ3htXtXqah+rXt6LwEmB6j3n5Jo/eXb1/NLHT7ra+b8GAWMvqsGvHhQj78+Xy9cWgarXtop71dVzotpHXveyefKTqn08uWbPJlAVqJ73Va/q+aWP1cRs72UQsHn5i4DRS/kmUD1YfRFtfaxW6+PWGV6bV7W62seql/cicFKges85ueZPnl09v/Txk652/q9BwNiLavCrB8XI+/Pl8rVFoOq1reJedfWcqPaR171snvykah9PrtmzCVQFqud91at6fuljNTHbexkEbF7+ImD0Ur4JVA9WX0RbH6vV+rh1htfmVa2u9rHq5b0InBSo3nNOrvmTZ1fPL338pKud/2sQMPaiGvzqQTHy/ny5fG0RqHptq7hXXT0nqn3kdS+bJz+p2seTa/ZsAlWB6nlf9aqeX/pYTcz2XgYBm5e/CBi9lG8C1YPVF9HWx2q1Pm6d4bV5Vaurfax6eS8CJwWq95yTa/7k2dXzSx8/6Wrn/xoEjL2oBr96UIy8P18uX1sEql7bKu5VOyfuWZ/8JLk/qXvv2dX9WM1X1eteYrZPqvZxW8W96mq+qn3kdS+bJz/JIGDUtSFHMOWTgHxNXNm/0NlWca+6+sV9T+CNT6qeE2/o3ltFdT9W81X1upeY7ZOqfdxWca+6mq9qH3ndy+bJTzIIGHVtyBFM+SQgXxOXQcDG9U/1i3tcxs+XV8+Jn2/MCFDdj9V8Vb3Gtl8rr/bxGsD4QdV8VfvIawxYtNwgYGyMDTmCKZ8E5GviMgjYuAwCRq9qefWcqHpV38tFeutM1Wtbxb1q58RmXc1XtY+8tnxVqw0Cxs7YkCOY8klAviYug4CNyyBg9KqWV8+Jqlf1vVykt85UvbZV3Kt2TmzW1XxV+8hry1e12iBg7IwNOYIpnwTka+IyCNi4DAJGr2p59ZyoelXfy0V660zVa1vFvWrnxGZdzVe1j7y2fFWrDQLGztiQI5jySUC+Ji6DgI3LIGD0qpZXz4mqV/W9XKS3zlS9tlXcq3ZObNbVfFX7yGvLV7XaIGDsjA05gimfBORr4jII2LgMAkavann1nKh6Vd/LRXrrTNVrW8W9aufEZl3NV7WPvLZ8VasNAsbO2JAjmPJJQL4mLoOAjcsgYPSqllfPiapX9b1cpLfOVL22Vdyrdk5s1tV8VfvIa8tXtdogYOyMDTmCKZ8E5GviMgjYuAwCRq9qefWcqHpV38tFeutM1Wtbxb1q58RmXc1XtY+8tnxVqw0Cxs7YkCOY8klAviYug4CNyyBg9KqWV8+Jqlf1vVykt85UvbZV3Kt2TmzW1XxV+8hry1e12iBg7IwNOYIpnwTka+IyCNi4DAJGr2p59ZyoelXfy0V660zVa1vFvWrnxGZdzVe1j7y2fFWrDQLGztiQI5jySUC+Ji6DgI3LIGD0qpZXz4mqV/W9XKS3zlS9tlXcq3ZObNbVfFX7yGvLV7XaIGDsjA05gimfBORr4jII2LgMAkavann1nKh6Vd/LRXrrTNVrW8W9aufEZl3NV7WPvLZ8VasNAsbO2JAjmPJJQL4mLoOAjcsgYPSqllfPiapX9b1cpLfOVL22Vdyrdk5s1tV8VfvIa8tXtdogYOyMDTmCKZ8E5GviMgjYuAwCRq9qefWcqHpV38tFeutM1Wtbxb1q58RmXc1XtY+8tnxVqw0Cxs7YkCOY8klAviYug4CNyyBg9KqWV8+Jqlf1vVykt85UvbZV3Kt2TmzW1XxV+8hry1e12iBg7IwNOYIpnwTka+IyCNi4DAJGr2p59ZyoelXfy0V660zVa1vFvWrnxGZdzVe1j7y2fFWrDQLGztiQI5jySUC+Ji6DgI3LIGD0qpZXz4mqV/W9XKS3zlS9tlXcq3ZObNbVfFX7yGvLV7XaIGDsjA05gimfBORr4jII2LgMAkavann1nKh6Vd/LRXrrTNVrW8W9aufEZl3NV7WPvLZ8VasNAsbO2JAjmPJJQL4mLoOAjcsgYPSqllfPiapX9b1cpLfOVL22Vdyrdk5s1tV8VfvIa8tXtdogYOyMDTmCKZ8E5GviMgjYuAwCRq9qefWcqHpV38tFeutM1Wtbxb1q58RmXc1XtY+8tnxVqw0Cxs7YkCOY8klAviYug4CNyyBg9KqWV8+Jqlf1vVykt85UvbZV3Kt2TmzW1XxV+8hry1e12iBg7IwNOYIpnwTka+IyCNi4DAJGr2p59ZyoelXfy0V660zVa1vFvWrnxGZdzVe1j7y2fFWrDQLGztiQI5jySUC+Ji6DgI3LIGD0qpZXz4mqV/W9XKS3zlS9tlXcq3ZObNbVfFX7yGvLV7XaIGDsjA05gimfBORr4jII2LgMAkavann1nKh6Vd/LRXrrTNVrW8W9aufEZl3NV7WPvLZ8VasNAsbO2JAjmPJJQL4mLoOAjcsgYPSqllfPiapX9b1cpLfOVL22Vdyrdk5s1tV8VfvIa8tXtdogYLMYggkAABR+SURBVOyMDTmCKZ8E5GviMgjYuAwCRq9qefWcqHpV38tFeutM1Wtbxb1q58RmXc1XtY+8tnxVqw0Cxs7YkCOY8klAviYug4CNyyBg9KqWV8+Jqlf1vVykt85UvbZV3Kt2TmzW1XxV+8hry1e12iBg7IwNOYIpnwTka+IyCNi4DAJGr2p59ZyoelXfy0V660zVa1vFvWrnxGZdzVe1j7y2fFWrDQLGztiQI5jySUC+Ji6DgI3LIGD0qpZXz4mqV/W9XKS3zlS9tlXcq3ZObNbVfFX7yGvLV7XaIGDsjA05gimfBORr4jII2LgMAkavann1nKh6Vd/LRXrrTNVrW8W9aufEZl3NV7WPvLZ8VasNAsbO2JAjmPJJQL4mLoOAjcsgYPSqllfPiapX9b1cpLfOVL22Vdyrdk5s1tV8VfvIa8tXtdogYOyMDTmCKZ8E5GviMgjYuAwCRq9qefWcqHpV38tFeutM1Wtbxb1q58RmXc1XtY+8tnxVqw0Cxs7YkCOY8klAviYug4CNyyBg9KqWV8+Jqlf1vVykt85UvbZV3Kt2TmzW1XxV+8hry1e12iBg7IwNOYIpnwTka+IyCNi4DAJGr2p59ZyoelXfy0V660zVa1vFvWrnxGZdzVe1j7y2fFWrDQLGztiQI5jySUC+Ji6DgI3LIGD0qpZXz4mqV/W9XKS3zlS9tlXcq3ZObNbVfFX7yGvLV7XaIGDsjA05gimfBORr4jII2LgMAkavann1nKh6Vd/LRXrrTNVrW8W9aufEZl3NV7WPvLZ8VasNAsbOVDfkuAzlBCYBB/7E5Qf3xmWgM3rZjxtY1Wtbxb3q6j2n2kde97Lpkwj8JVDdj3+997f+3SBglBewEUz5EwIuYFsbq17bKu5VO1c362q+qn2sem1dv1etj5s1r81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIGDUE7ARTPkTAtWLdHU/Vr2qYaz2sepVzVe1j1Wvar70cesMr81LNYGTAtX9eHLNnzzbIOATPf+XAIGvClQPfD88tljo4+ZVra72sepVPSeqfeRVTbL3OilQzf3JNb/47Oy5+p/omwn+i9vAmgj8bwWix9c/zq+tz/q4eVWrq32selXPiWofeVWT7L1OClRzf3LNLz47e64aBLwYN2si8BsC2YP1339/owH/o1Xq4/8I8suPqfbxyyz/78dXL/jVPvKqJtl7nRSo5v7kml98dvZcNQh4MW7WROA3BLIHq0HAFEB9nLiyxdU+VsGqF/xqH3lVk+y9TgpUc39yzS8+O3uuGgS8GDdrIvAbAtmD1SBgCqA+TlzZ4mofq2DVC361j7yqSfZeJwWquT+55hefnT1XDQJejJs1EfgNgezBahAwBVAfJ65scbWPVbDqBb/aR17VJHuvkwLV3J9c84vPzp6rBgEvxs2aCPyGQPZgNQiYAqiPE1e2uNrHKlj1gl/tI69qkr3XSYFq7k+u+cVnZ89Vg4AX42ZNBH5DIHuwGgRMAdTHiStbXO1jFax6wa/2kVc1yd7rpEA19yfX/OKzs+eqQcCLcbMmAr8hkD1YDQKmAOrjxJUtrvaxCla94Ff7yKuaZO91UqCa+5NrfvHZ2XPVIODFuFkTgd8QyB6sBgFTAPVx4soWV/tYBate8Kt95FVNsvc6KVDN/ck1v/js7LlqEPBi3KyJwG8IZA9Wg4ApgPo4cWWLq32sglUv+NU+8qom2XudFKjm/uSaX3x29lw1CHgxbtZE4DcEsgerQcAUQH2cuLLF1T5WwaoX/GofeVWT7L1OClRzf3LNLz47e64aBLwYN2si8BsC2YPVIGAKoD5OXNniah+rYNULfrWPvKpJ9l4nBaq5P7nmF5+dPVcNAl6MmzUR+A2B7MFqEDAFUB8nrmxxtY9VsOoFv9pHXtUke6+TAtXcn1zzi8/OnqsGAS/GzZoI/IZA9mA1CJgCqI8TV7a42scqWPWCX+0jr2qSvddJgWruT675xWdnz1WDgBfjZk0EfkMge7AaBEwB1MeJK1tc7WMVrHrBr/aRVzXJ3uukQDX3J9f84rOz56pBwItxsyYCvyGQPVgNAqYA6uPElS2u9rEKVr3gV/vIq5pk73VSoJr7k2t+8dnZc9Ug4MW4WROB3xDIHqwGAVMA9XHiyhZX+1gFq17wq33kVU2y9zopUM39yTW/+OzsuWoQ8GLcrInAbwhkD1aDgCmA+jhxZYurfayCVS/41T7yqibZe50UqOb+5JpffHb2XDUIeDFu1kTgNwSyB6tBwBRAfZy4ssXVPlbBqhf8ah95VZPsvU4KVHN/cs0vPjt7rhoEvBg3ayLwGwLZg9UgYAqgPk5c2eJqH6tg1Qt+tY+8qkn2XicFqrk/ueYXn509Vw0CXoybNRH4DYHswWoQMAVQHyeubHG1j1Ww6gW/2kde1SR7r5MC1dyfXPOLz86eqwYBL8bNmgj8hkD2YDUImAKojxNXtrjaxypY9YJf7SOvapK910mBau5PrvnFZ2fPVYOAF+NmTQR+QyB7sBoETAHUx4krW1ztYxWsesGv9pFXNcne66RANfcn1/zis7PnqkHAi3GzJgK/IZA9WA0CpgDq48SVLa72sQpWveBX+8irmmTvdVKgmvuTa37x2dlz1SDgxbhZE4HfEMgerAYBUwD1ceLKFlf7WAWrXvCrfeRVTbL3OilQzf3JNb/47Oy5ahDwYtysicBvCGQPVoOAKYD6OHFli6t9rIJVL/jVPvKqJtl7nRSo5v7kml98dvZcNQh4MW7WROA3BLIHq0HAFEB9nLiyxdU+VsGqF/xqH3lVk+y9TgpUc39yzS8+O3uuGgS8GDdrIvAbAtmD1SBgCqA+TlzZ4mofq2DVC361j7yqSfZeJwWquT+55hefnT1XDQJejJs1EfgNgezBahAwBVAfJ65scbWPVbDqBb/aR17VJHuvkwLV3J9c84vPzp6rBgEvxs2aCPyGQPZgNQiYAqiPE1e2uNrHKlj1gl/tI69qkr3XSYFq7k+u+cVnZ89Vg4AX42ZNBH5DIHuwGgRMAdTHiStbXO1jFax6wa/2kVc1yd7rpEA19yfX/OKzs+eqQcCLcbMmAr8hkD1YDQKmAOrjxJUtrvaxCla94Ff7yKuaZO91UqCa+5NrfvHZ2XPVIODFuFkTgd8QyB6sBgFTAPVx4soWV/tYBate8Kt95FVNsvc6KVDN/ck1v/js7LlqEPBi3KyJwG8IZA9Wg4ApgPo4cWWLq32sglUv+NU+8qom2XudFKjm/uSaX3x29lw1CHgxbtZE4DcEsgerQcAUQH2cuLLF1T5WwaoX/GofeVWT7L1OClRzf3LNLz47e64aBLwYN2si8BsC2YPVIGAKoD5OXNniah+rYNULfrWPvKpJ9l4nBaq5P7nmF5+dPVcNAl6MmzUR+A2B7MFqEDAFUB8nrmxxtY9VsOoFv9pHXtUke6+TAtXcn1zzi8/OnqvVQcCLIbAmAgQIECBAgAABAgQIECDwbYF/DQK+3QKfT4AAAQIECBAgQIAAAQIE7gkYBNyz9kkECBAgQIAAAQIECBAgQODrAgYBX2+BFyBAgAABAgQIECBAgAABAvcEDALuWfskAgQIECBAgAABAgQIECDwdQGDgK+3wAsQIECAAAECBAgQIECAAIF7AgYB96x9EgECBAgQIECAAAECBAgQ+LqAQcDXW+AFCBAgQIAAAQIECBAgQIDAPQGDgHvWPokAAQIECBAgQIAAAQIECHxdwCDg6y3wAgQIECBAgAABAgQIECBA4J6AQcA9a59EgAABAgQIECBAgAABAgS+LmAQ8PUWeAECBAgQIECAAAECBAgQIHBPwCDgnrVPIkCAAAECBAgQIECAAAECXxcwCPh6C7wAAQIECBAgQIAAAQIECBC4J2AQcM/aJxEgQIAAAQIECBAgQIAAga8LGAR8vQVegAABAgQIECBAgAABAgQI3BMwCLhn7ZMIECBAgAABAgQIECBAgMDXBQwCvt4CL0CAAAECBAgQIECAAAECBO4JGATcs/ZJBAgQIECAAAECBAgQIEDg6wIGAV9vgRcgQIAAAQIECBAgQIAAAQL3BAwC7ln7JAIECBAgQIAAAQIECBAg8HUBg4Cvt8ALECBAgAABAgQIECBAgACBewIGAfesfRIBAgQIECBAgAABAgQIEPi6gEHA11vgBQgQIECAAAECBAgQIECAwD0Bg4B71j6JAAECBAgQIECAAAECBAh8XcAg4Ost8AIECBAgQIAAAQIECBAgQOCegEHAPWufRIAAAQIECBAgQIAAAQIEvi5gEPD1FngBAgQIECBAgAABAgQIECBwT8Ag4J61TyJAgAABAgQIECBAgAABAl8XMAj4egu8AAECBAgQIECAAAECBAgQuCdgEHDP2icRIECAAAECBAgQIECAAIGvCxgEfL0FXoAAAQIECBAgQIAAAQIECNwTMAi4Z+2TCBAgQIAAAQIECBAgQIDA1wUMAr7eAi9AgAABAgQIECBAgAABAgTuCRgE3LP2SQQIECBAgAABAgQIECBA4OsCBgFfb4EXIECAAAECBAgQIECAAAEC9wQMAu5Z+yQCBAgQIECAAAECBAgQIPB1AYOAr7fACxAgQIAAAQIECBAgQIAAgXsC/wchx0EUvqrP9AAAAABJRU5ErkJggg==)"
      ],
      "metadata": {
        "id": "LktxlwG4nuPs"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Designing algorithms\n",
        "\n",
        "1. **Clear Expectations** - Understand what the input and expected output is.\n",
        "\n",
        "You can start by writing down a few example inputs and in each case writing/noting down what the expected output must be.\n",
        "\n",
        "2. **Boundary cases** - Beware of boundary cases.\n",
        "\n",
        "Make sure to know what behavior is expected on boundary cases such as empty input, inappropriate input, inputs with positive/negative numbers etc.\n",
        "\n",
        "3. **Idea** - Come up with an idea to solve the problem.\n",
        "\n",
        "It may not always be perfect, but there has to be a starting point. Once you have one, write down code that implements this idea.\n",
        "\n",
        "4. **Testing** - Design a few test cases to check whether your idea works correctly.\n",
        "\n",
        "The idea here is to make sure that your algorithm works correctly on ALL inputs. All inputs is an exhaustive set - so it may be difficult to test on ALL. Instead, try out different input types. Boundary cases, simple cases, large inputs, inputs with negative numbers etc. (depending on context).\n",
        "\n",
        "Best test cases are those that reveal any flaws in your algorithm - so put your code to the sword!\n",
        "\n",
        "5. **Fixing** - If your algorithm isn't working correctly, identify what caused the problem. Was it the idea? Was it the implementation? If you identify the issue, attempt a fix. Then, repeat steps 3 and 4 repeatedly until your algorithm works correctly.\n",
        "\n"
      ],
      "metadata": {
        "id": "T2fydqDhPOUP"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Analysis of algorithms (run time)\n",
        "\n",
        "Typically, we will analyze the run time of algorithms on inputs of size $n$. For a list type input, that would imply the running time on $n$ sized lists.\n",
        "\n",
        "What exactly is the running time of an algorithm on $n$ sized inputs?\n",
        "\n",
        "Note that **different inputs can lead to different run times**.\n",
        "\n",
        "For example, the code for ``` find_min(L)``` requires time $2n + 5$ when the minimum element occurs in position 0 and all subsequent elements are larger than it.\n",
        "\n",
        "If the list was a decreasing sequence of elements, the code inside the if statement executes each time leading to a run time of $4n + 3$.\n",
        "\n",
        "There are other variants of the input list that can lead to a runtime between these two quantities.\n",
        "\n",
        ">We will always consider the **worst-case running time of the algorithm** to represent its running time.\n",
        "\n",
        "For ``` find_min(L)```, the time taken is at most $4n+3$.\n",
        "\n",
        "Better still, since we only care about asymptotics, we will consider the running time of ``` find_min(L)``` to be $O(n)$.\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "A4gOYJYKUDN_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Search\n",
        "\n",
        "Consider the following situations :\n",
        "\n",
        "1.   A social media network portal verifying login details\n",
        "2.   Grainger library textbook look up\n",
        "3.   Sifting through a pile of clothes looking for a specific piece of clothing\n",
        "4.   Looking for your favorite music video on youtube\n",
        "\n",
        "\n",
        "Common denominator : **Search**\n",
        "\n"
      ],
      "metadata": {
        "id": "EqS8xAhNsM5N"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Search for 77 in the following lists :"
      ],
      "metadata": {
        "id": "i-t5k1LsyuvN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import random\n",
        "\n",
        "x = 10\n",
        "li = random.sample(range(1,100),x)\n",
        "print(li)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "67tWoxZjAW0U",
        "outputId": "e4161e1d-fee8-46fd-bdc1-fb63f9b1c83e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[858, 287, 672, 788, 677, 39, 940, 486, 623, 700]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import random\n",
        "\n",
        "x = 30\n",
        "li = random.sample(range(1,100),x)\n",
        "print(li)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SMoudiQBGgY5",
        "outputId": "781a7b41-1205-41b9-a2b4-be0599d374d6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[764, 91, 366, 762, 809, 922, 718, 383, 945, 144, 164, 137, 456, 34, 846, 19, 108, 290, 461, 110, 474, 292, 812, 783, 133, 415, 301, 488, 600, 895]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import random\n",
        "\n",
        "x = random.randint(10,30)\n",
        "li = random.sample(range(1,100),x)\n",
        "print(li)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KC-5GEjVGjF5",
        "outputId": "edeba187-c4cf-4b80-a15a-d575fc60fb1e"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[422, 284, 303, 468, 248, 292, 335, 912, 263, 194, 961, 443, 883, 419, 825, 866, 166]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Basic search algorithm\n",
        "\n",
        "Input - List li containing $n$ numbers, target element $t$\n",
        "\n",
        "Output - Yes if li contains $t$ and No otherwise\n",
        "\n",
        "Main idea - Iteratively check if each element of the list equals the target. Return yes if there is a match at any point and no if you reach end of the list without a match."
      ],
      "metadata": {
        "id": "n0USN2C8Gq5U"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import random\n",
        "\n",
        "# Creating an input list of random numbers\n",
        "# generating a random list of size 30 in the range 1 to 100 (100 excluded)\n",
        "x = 30\n",
        "li = random.sample(range(1,100),x)\n",
        "print(li)\n",
        "\n",
        "#basic search algorithm\n",
        "def basic_search(l,t):\n",
        "    for i in range(len(l)):\n",
        "      if(l[i] == t):\n",
        "        return (\"Yes\")\n",
        "    return (\"No\")\n",
        "\n",
        "basic_search(li,77)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "collapsed": true,
        "id": "jcwr_WXHG_Vo",
        "outputId": "6a3a51ae-0db0-42f3-8f28-3bcf9f6081c1"
      },
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[99, 50, 90, 18, 57, 1, 76, 31, 2, 36, 94, 63, 17, 52, 79, 77, 44, 91, 55, 15, 58, 33, 85, 61, 38, 92, 97, 69, 49, 47]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'Yes'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Checkpoints\n",
        "\n",
        "1. Input-Output expectation\n",
        "2. Boundary Cases\n",
        "3. Idea\n",
        "4. Testing\n",
        "5. Fixing"
      ],
      "metadata": {
        "id": "fHOQni4AUPEr"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Analysis\n",
        "\n",
        "Okay, so we gave some algorithm that apparently performs search on the random list generated above. Does it work correctly for all possible inputs?\n",
        "1.   Correctness - Does this algorithm work correctly on all inputs? How do we make such a claim?\n",
        "\n",
        "2.   Efficiency - What is the running time of this algorithm?\n",
        "\n",
        "3.   Space usage - How much additional space/memory does this algorithm need?\n",
        "\n"
      ],
      "metadata": {
        "id": "SleW432fJ6Os"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Time complexity analysis\n",
        "\n",
        "Since the running time depends on the size of the input, we indicate run time as a function of the *size* of the input.\n",
        "\n",
        "$n$ : Size of input list *li*\n",
        "\n",
        "In this case, the input has two arguments, a list of $n$ integers and a target number $t$.\n",
        "\n",
        "What is the running time of *basic_search*?\n",
        "\n",
        "(Let loc(t) indicate the first location of $t$ if it exists)\n",
        "\n",
        "*   Computations performed :  \n",
        "\n",
        "1.   iterating over elements of the input list *li* until $t$ is found -   $loc(t)$ iterations\n",
        "2.   in each step, checking if current list element equals target $t$  - $ loc(t)$ steps\n",
        "3.   at an appropriate moment, the return statement indicating presence/absence - $O(1)$ steps\n",
        "\n",
        "\n",
        "#Exact run time :\n",
        "\n",
        ">  Depends on whether $t$ is in the list.\n",
        "\n",
        "1. if $t$ is absent : exactly $n$ comparisons - total $(2n+1)$ operations.\n",
        "\n",
        "2. if $t$ is present : depends on the first location $k$ where $t$ occurs in the list - total $(2(k+1)+1) = (2k + 3)$ operations\n",
        "\n",
        "#Worst case running time\n",
        "In any case, since $k \\leq (n-1)$, the total number of operations is at most $(2n+1)$.\n",
        "\n",
        "# Asymptotic run time\n",
        "\n",
        "Gives a clean asymptotic upper bound on the run time of the algorithm. Since the total number of operations is at most $(2n+1)$, we have:\n",
        "\n",
        "> The asymptotic run time of *basic_search* is $O(n)$.\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "O0r2xHTUR6cG"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Correctness\n",
        "\n",
        "We need to prove that the *basic_search* we wrote above works correctly on all possible inputs. How can we do that?\n",
        "\n",
        "There are two cases - either the list contains $t$ or it does not. We need to show that :\n",
        "\n",
        "\n",
        "\n",
        "*   if $t$ is in the list, *basic_search*  returns \"element present in list\".\n",
        "*   if $t$ is not in the list, *basic_search*  returns \"element not present in list\"."
      ],
      "metadata": {
        "id": "PXojNfmPMQyx"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "> Claim : If the first occurence of $t$ in the list is at position $k$, then the for loop runs exactly $(k+1)$ times and returns \"element present in list\".\n",
        "\n",
        "*Proof* - If the first occurence of $t$ is at position $k$, then the if condition fails for all $0 \\leq i \\leq (k-1)$. At the next iteration, with $i=k$, the if condition is successful as $li[k] = t$. So, the return statement is executed.  \n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "VIEJ4p2ckXwM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Is the proof of correctness complete?"
      ],
      "metadata": {
        "id": "j15va93GlY_-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\n",
        "> Claim 2 : If $t$ does not occur in the list at all, the for loop runs for exactly $n$ steps and returns \"element not in list\".\n",
        "\n",
        "*Proof* - If $t$ is not in the list, then the for loop in *basic_search* runs exactly $n$ times and since none of the elements of $li$ are equal to $t$, the loop ends and then returns \"element not in list\".\n",
        "\n"
      ],
      "metadata": {
        "id": "XDNzH3VJld0y"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "**Case - Doctor & Patient**\n",
        "\n",
        "Doctor X wants to look up the medical history of patient Y. How should X go about this task? Would it suffice to know whether Y's medical records exist?\n",
        "\n",
        "Often, it is helpful to not just know if the target element is in the list, but to get access to the element.\n",
        "\n",
        "\n",
        "\n",
        "> Modify the search algorithm to help access an element if it is found. What change would you make?\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "OssVSIwbxRpY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import random\n",
        "\n",
        "# Creating an input list of random numbers\n",
        "# generating a random list of size 30 in the range 1 to 1000 (1000 excluded)\n",
        "x = 30\n",
        "li = random.sample(range(1,100),x)\n",
        "print(li)\n",
        "\n",
        "#EDIT this basic search algorithm to return access to the element\n",
        "def basic_search(l,t):\n",
        "    for i in range(len(l)):\n",
        "      if(l[i] == t):\n",
        "        return (\"Element \" + str(t) + \" is present in the list at position \" + str(i))\n",
        "    return (\"Element \" + str(t) + \" is not present in the list\")\n",
        "\n",
        "basic_search(li,77)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "NuzZfFAkyPPs",
        "outputId": "accad48a-36bd-47e6-c662-906254a10a7d"
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[66, 23, 52, 20, 90, 48, 78, 5, 87, 1, 96, 74, 28, 97, 84, 2, 56, 89, 16, 27, 79, 77, 57, 46, 41, 17, 47, 11, 76, 69]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'Element 77 is present in the list at position 21'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Structured vs Unstructured data\n",
        "\n",
        "Let us try to search for a target in 2 different contexts -\n",
        "\n",
        "1. Unstructured data\n",
        "2. Structured data"
      ],
      "metadata": {
        "id": "pxDvce2xX-WL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Looking for element 77 in lists li, li2\n",
        "import random\n",
        "\n",
        "x = 30\n",
        "li = random.sample(range(1,100),x)\n",
        "print(\"Unstructured list : \")\n",
        "print(li)\n",
        "print(\"\")\n",
        "\n",
        "\n",
        "li.sort()\n",
        "# The above line sorts the list li - we will see more about sorting next week\n",
        "print(\"Structured list : \")\n",
        "print(li)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KasTpvWlwoMc",
        "outputId": "dd258149-22f6-46a6-918e-ae38dfaf9f40"
      },
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Unstructured list : \n",
            "[56, 60, 45, 72, 87, 25, 20, 30, 50, 94, 89, 14, 64, 51, 1, 55, 63, 47, 36, 17, 65, 27, 61, 33, 18, 41, 76, 71, 43, 40]\n",
            "\n",
            "Structured list : \n",
            "[1, 14, 17, 18, 20, 25, 27, 30, 33, 36, 40, 41, 43, 45, 47, 50, 51, 55, 56, 60, 61, 63, 64, 65, 71, 72, 76, 87, 89, 94]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\n",
        "> Are both lists *li* and *li2* equally difficult to search through? Why?\n",
        "\n"
      ],
      "metadata": {
        "id": "PPWAK9UKlOiF"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Structured vs Unstructured Data\n",
        "\n",
        "\n",
        "\n",
        "*   If data is structured (in this case sorted), then there are more efficient ways to search for an element.\n",
        "\n",
        "*   Main Idea - Pick some location and check for target. If the check fails, you can exclude one chunk of the list entirely. Now, search for the element in the remaining chunk.\n",
        "\n",
        "\n",
        "\n",
        "> **Which location should we pick to search within the list?**"
      ],
      "metadata": {
        "id": "NgPcxKcy0n8o"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Candidate position : 5\n",
        "\n",
        "\n",
        "*   Case 1 -\n",
        "```\n",
        "if(L[5] == t): Search successful - nothing more to do!\n",
        "```\n",
        "\n",
        "*  Case 2 -\n",
        "```\n",
        "if(L[5] > t): we need to check L[0:5]  - total 5 elements left to check\n",
        "```\n",
        "\n",
        "*  Case 3 -\n",
        "```\n",
        "if(L[5] < t): we need to check L[5:] - total (n-6) elements left to check\n",
        "```\n",
        "\n",
        "Either we find the element or we eliminate the left/right section of the list.\n",
        "\n",
        "Best case - we find the element!\n",
        "\n",
        "Worst case - we have to search through $n-6$ more elements."
      ],
      "metadata": {
        "id": "316KfSuU3oCE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Idea to search through sorted data - skip to position 5!\n",
        "\n",
        "# ALL print statements are only to visualize running of algorithm - IGNORE them for time complexity calculations\n",
        "\n",
        "import random\n",
        "\n",
        "x = 30\n",
        "li = random.sample(range(1,100),x)\n",
        "li.sort()\n",
        "\n",
        "def pos5_search_sorted(L,t):\n",
        "\n",
        "  print(\"Search space : \")\n",
        "  print(L)\n",
        "\n",
        "  if(len(L) <= 5):\n",
        "    for i in range(0,5):\n",
        "      if(L[i] == t):\n",
        "        return \"Yes\"\n",
        "    return \"No\"\n",
        "\n",
        "  print(\"element to compare against target : \", L[5])\n",
        "  print(\"\")\n",
        "\n",
        "  if(L[5] == t):\n",
        "    return(\"Yes\")\n",
        "\n",
        "  elif(L[5] > t):\n",
        "    #search through first 5 elements - L[0:5]\n",
        "    return pos5_search_sorted(L[0:5],t)\n",
        "\n",
        "  elif(L[5] < t):\n",
        "    # search through last n-6 elements\n",
        "    return pos5_search_sorted(L[6:],t)\n",
        "\n",
        "pos5_search_sorted(li,77)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 428
        },
        "id": "uMwK6l6_a6Ob",
        "outputId": "48c165ae-eff8-48c7-da4b-5baa196fa419"
      },
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Search space : \n",
            "[3, 7, 9, 14, 17, 19, 21, 27, 33, 35, 37, 38, 42, 44, 45, 46, 51, 52, 53, 59, 64, 68, 70, 73, 79, 80, 81, 87, 92, 99]\n",
            "element to compare against target :  19\n",
            "\n",
            "Search space : \n",
            "[21, 27, 33, 35, 37, 38, 42, 44, 45, 46, 51, 52, 53, 59, 64, 68, 70, 73, 79, 80, 81, 87, 92, 99]\n",
            "element to compare against target :  38\n",
            "\n",
            "Search space : \n",
            "[42, 44, 45, 46, 51, 52, 53, 59, 64, 68, 70, 73, 79, 80, 81, 87, 92, 99]\n",
            "element to compare against target :  52\n",
            "\n",
            "Search space : \n",
            "[53, 59, 64, 68, 70, 73, 79, 80, 81, 87, 92, 99]\n",
            "element to compare against target :  73\n",
            "\n",
            "Search space : \n",
            "[79, 80, 81, 87, 92, 99]\n",
            "element to compare against target :  99\n",
            "\n",
            "Search space : \n",
            "[79, 80, 81, 87, 92]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'No'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 70
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Analysis of pos5_search_sorted\n",
        "\n",
        "Let $T(n)$ denote the time taken by ```pos5_search_sorted ``` on lists of length $n$.\n",
        "\n",
        "The total time taken depends on -\n",
        "\n",
        "1. Length of list $L$\n",
        "2. The outcome of the comparison $L[5]$ vs $t$\n",
        "\n",
        "If the length of $L$ is less than 6, it runs a simple for loop and within 5 iterations returns the answer. Total time - $O(1)$. We will consider larger list sizes - $n \\to \\infty$ as we care about asymptotic behavior.\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "**Case 1 - L[5] == t**\n",
        "\n",
        "If $L[5] == t$, then the function returns \"Yes\" and terminates.\n",
        "\n",
        "Time taken :\n",
        "1. Checking if condition for length of $L$ - $O(1)$\n",
        "2. Checking if condition for $L[5] == t$ - $O(1)$\n",
        "3. Return \"Yes\" - $O(1)$\n",
        "\n",
        "> Total time - $O(1) + O(1) + O(1) = O(1)$.\n",
        "---\n",
        "\n",
        "**Case 2 - L[5] > t**\n",
        "\n",
        "If $L[5] > t$, then $L$ is sliced to $L[0:5]$ and the function is called on a 5 sized list.\n",
        "\n",
        "Time taken -\n",
        "\n",
        "1. Checking if condition for length of $L$ - $O(1)$\n",
        "2. Checking if condition for $L[5] == t$ - $O(1)$\n",
        "3. Checking elif condition for $L[5] > t$ - $O(1)$\n",
        "4. Slicing list down to 5 elements - $O(1)$ time\n",
        "5. Implementing function call ```pos5_search_sorted(L[0:5],t)```\n",
        "\n",
        "At this stage, the list has size less than 6, so the function call ```pos5_search_sorted(L[0:5],t)``` resolves in time $O(1)$.\n",
        "\n",
        ">Total time - $O(1) + O(1) + O(1) + O(1) + O(1) = O(1)$\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "> Python time complexity documentation - https://wiki.python.org/moin/TimeComplexity\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "tHzCmV-reUeU"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Case 3 - L[5] < t\n",
        "\n",
        "If $L[5] < t$, then $L$ is sliced to $L[6:]$ in the function call to ```pos5_search_sorted(L[6:],t)```.\n",
        "\n",
        "Time taken -\n",
        "\n",
        "1. Checking if condition for length of $L$ - $O(1)$\n",
        "2. Checking if condition for $L[5] == t$ - $O(1)$\n",
        "3. Checking elif condition for $L[5] > t$ - $O(1)$\n",
        "4. Checking elif condition for $L[5] < t$ - $O(1)$\n",
        "4. Slicing list down to $n-6$ elements - $ (n-6) $ time\n",
        "5. Implementing function call ```pos5_search_sorted(L[6:],t)```\n",
        "\n",
        "The function call ```pos5_search_sorted(L[6:],t)``` runs the same algorithm on a list of size $n-6$. The time complexity of this is $T(n-6)$ in accordance with the definition of $T$.\n",
        "\n",
        ">Total time - $O(1) + O(1) + O(1) + O(1) + n-6 + T(n-6) = T(n-6) + O(n)$ time."
      ],
      "metadata": {
        "id": "QWxNg_gakwYZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Final time complexity analysis\n",
        "\n",
        "Since we are concerned with the worst-case time complexity of algorithms, we have to consider the worst of all 3 cases for time complexity considerations.\n",
        "\n",
        "That is,\n",
        "\n",
        "$T(n) = max(O(1), O(1), T(n-6) + O(n))$\n",
        "\n",
        "Since the last term is clearly the dominant one,  we have -\n",
        "\n",
        "$T(n) \\leq T(n-6) + O(n)$\n",
        "\n",
        "This is a recurrence relation that characterizes the running time of ```pos5_search_sorted(L,t)```\n",
        "\n",
        ">We will see later that in such cases $T(n) = O(n^2)$"
      ],
      "metadata": {
        "id": "sVpD8QWll-pN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Slice-and-Dice!\n",
        "\n",
        "Main idea : To search through structured data, we can first check the middle position (median) of the sorted list. Depending on the result of the check:\n",
        "\n",
        " focus search on either left half or right half of the list!\n",
        "\n",
        " *   Case 1 -\n",
        "```\n",
        "if(li[(n/2)] == t): Search successful - nothing more to do!\n",
        "```\n",
        "\n",
        "*  Case 2 -\n",
        "```\n",
        "if(li[n/2] > t): we need to check li[0:(n/2)]  - total {n/2} elements left to check\n",
        "```\n",
        "\n",
        "*  Case 3 -\n",
        "```\n",
        "if(li[n/2] < t): we need to check li[(n/2)+1:] - total {(n/2)-1} elements left to check\n",
        "```\n",
        "\n",
        ">The advantage here is that in all 3 cases atleast half of the list is truncated!\n"
      ],
      "metadata": {
        "id": "my55o4g-6Hdd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import random\n",
        "\n",
        "#Generating an input list and sorting it\n",
        "x = 16\n",
        "li = random.sample(range(1,100),x)\n",
        "li.sort()\n",
        "print(li)\n",
        "\n",
        "#function slice_dice that slices search space in half at each step until target is found\n",
        "def slice_dice(l,t):\n",
        "  k = len(l)\n",
        "  print(l[k//2])\n",
        "  #important base case\n",
        "  if(k == 1):\n",
        "    if(l[k//2] == t):\n",
        "      return \"Element is present in the list\"\n",
        "    else:\n",
        "      return \"Element is not in the list\"\n",
        "  if(l[k//2] == t):\n",
        "     return \"Element is present in the list\"\n",
        "\n",
        "  elif(l[k//2] > t):\n",
        "    return (slice_dice(l[0:k//2],t))\n",
        "\n",
        "  else:\n",
        "    return (slice_dice(l[(k//2)+1:],t))\n",
        "\n",
        "print(slice_dice(li,77))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EuQuZDC55_j3",
        "outputId": "39ee1aac-c1ef-4db9-ea4e-6e5e507967e4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[2, 13, 16, 19, 20, 21, 30, 40, 65, 70, 72, 80, 84, 86, 88, 99]\n",
            "65\n",
            "84\n",
            "72\n",
            "80\n",
            "Element is not in the list\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Slice and Dice analysis\n",
        "\n",
        "\n",
        "1.   Run time analysis - How much time does *slice_dice* take on lists of size $n$?\n",
        "\n",
        "2.   Correctness - Does *slice_dice* return the correct answer on all input lists (and targets)?\n",
        "\n"
      ],
      "metadata": {
        "id": "6zArei2HjmLg"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Run time analysis\n",
        "\n",
        "*   Is slice_dice as efficient as linear_search?\n",
        "\n",
        "\n",
        "*   Computations performed -\n",
        "\n",
        "Each call of *slice_dice* entails :\n",
        "\n",
        "1.   Computing the length of the list - $O(1)$ time in python\n",
        "2.   Accessing the middle element - $O(1)$ time\n",
        "3.   Comparing middle element with target - $O(1) * 3 = O(1)$ time\n",
        "\n",
        "Within each call of *slice_dice*, total time = $O(1) + O(1) + O(1)$ = $O(1)$ time.\n",
        "\n",
        "\n",
        "> **How many total calls does *slice_dice* make?**\n"
      ],
      "metadata": {
        "id": "2kZoMYlTnIZh"
      }
    }
  ]
}