{
  "cells": [
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      "cell_type": "markdown",
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      "source": [
        "# 3.5.2 - Advanced - Geospatial Analysis\n",
        "\n",
        "## Outline\n",
        "\n",
        "### Prerequisites\n",
        "\n",
        "-   Geospatial Analysis 1\n",
        "-   Intermediate R skills\n",
        "-   Theoretical understanding of multiple regression\n",
        "-   Basic geometry\n",
        "\n",
        "### Outcomes\n",
        "\n",
        "After completing this notebook, you will be able to:\n",
        "\n",
        "-   Manipulate geospatial objects in R using the `sf` package.\n",
        "-   Perform geospatial operations on real world data.\n",
        "-   Use the `sf` package to read in shapefile data from online sources.\n",
        "-   Calculate distances using geospatial operations.\n",
        "-   Understand applications of geospatial analysis in the context of\n",
        "    economic research.\n",
        "\n",
        "### References\n",
        "\n",
        "-   [Geocomputation with R](https://r.geocompx.org/intro)\n",
        "-   Disdier, Anne-Célia, and Keith Head. “The Puzzling Persistence of\n",
        "    the Distance Effect on Bilateral Trade.” The Review of Economics and\n",
        "    Statistics, 2008.\n",
        "-   Pebesma, E., & Bivand, R. (2023). [Spatial Data Science: With\n",
        "    Applications in R.](https://r-spatial.org/book/)\n",
        "-   Tinbergen, J. (1962) Shaping the World Economy: Suggestions for an\n",
        "    International Economic Policy. The Twentieth Century Fund, New York.\n",
        "-   \n",
        "\n",
        "## Introduction\n",
        "\n",
        "In this notebook, we’ll continue our discussion of geospatial analysis\n",
        "with vector data. We’ll use trade data and shapefiles from Statistics\n",
        "Canada for our examples."
      ],
      "id": "0f01d3da-4659-44c7-bcf9-57ab8ae271d9"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# load packages\n",
        "library(tidyverse)\n",
        "library(ggplot2)\n",
        "library(sandwich)\n",
        "library(lmtest)\n",
        "library(sf)\n",
        "library(spData)\n",
        "library(rmapshaper)\n",
        "library(crsuggest)"
      ],
      "id": "7e950947-c70b-4910-bff4-ccd5a959a21e"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Part 1: Understanding Geospatial Data\n",
        "\n",
        "> **Note**: geospatial files tend to be quite large and we use `for`\n",
        "> loops in this notebook. It is possible that the code takes a while to\n",
        "> run successfully.\n",
        "\n",
        "### File types and sizes\n",
        "\n",
        "In the previous notebook, we only worked with user-generated data and\n",
        "with datasets embedded in the package `spData`. It’s likely that for\n",
        "your applications, you’ll have to work with external geospatial files.\n",
        "\n",
        "The most common of geospatial file type is the **ESRI Shapefile** for\n",
        "vector data. This file has the extension `.shp` and typically comes in a\n",
        "zipped folder with at least three associated files. The `sf` function to\n",
        "read shapefiles is `read_sf(\"filename.shp\")`. There are many places to\n",
        "find shapefiles online. Some good places to look include\n",
        "[Geocommons](http://geocommons.com/), [Natural\n",
        "Earth](https://www.naturalearthdata.com/), and [Living\n",
        "Atlas](https://livingatlas.arcgis.com/en/browse/#d=2).\n",
        "\n",
        "Other common file types for vector data include:\n",
        "\n",
        "-   GeoJSON (`.geojson`): extension of JSON file, mostly used for\n",
        "    storing latitude and longitude coordinates.\n",
        "-   ESRI FileGDB (`.gdb`): stores objects created by ArcGIS (a popular\n",
        "    software for geospatial analysis.\n",
        "-   GeoPackage (`.gpkg`): lightweight, platform-independent, and compact\n",
        "    format.\n",
        "\n",
        "It’s important to keep in mind that these files come in varying forms\n",
        "and sizes. It’s very common for shapefiles to be extremely detailed and\n",
        "highly-defined, which can exponentially increase the file size and\n",
        "runtime of your analysis. The function `ms_simplify()` from the package\n",
        "`rmapshaper` simplifies shapefiles by reducing the number of vertices of\n",
        "the spatial objects while maintaining the integrity of the shapes.\n",
        "\n",
        "Let’s read a shapefile of Canadian provinces and plot them on a map with\n",
        "the attribute `province`."
      ],
      "id": "907c9607-bc19-4aba-860f-74e17ad84a3c"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "shape <- read_sf(\"advanced_geospatial_datasets/advanced_geospatial_datasets.shp\")\n",
        "\n",
        "shape_plot <- plot(shape[\"province\"])"
      ],
      "id": "40efdacb-94b2-47eb-9dfb-28ec1efe86e0"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Zoom in on the province boundaries and look at how detailed they are.\n",
        "We’re likely not going to need this level of detail for our analysis, so\n",
        "let’s simplify the file to avoid large runtimes. We’ll do so by using\n",
        "the function `ms_simplify()` to reduce the number of vertices to 1% of\n",
        "our current number."
      ],
      "id": "d0b059eb-6b81-4d50-9bc0-606a05951a19"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# run the code below to learn more about the function ms_simplify()\n",
        "# ?ms_simplify"
      ],
      "id": "bbd062f7-3273-4d02-a025-262f8eb89ec8"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# keep parameter indicates % of vertices to keep\n",
        "canada_shape <- ms_simplify(shape, keep = 0.01, keep_shapes = TRUE)"
      ],
      "id": "bdd0afdf-9e76-4839-be3e-ad4606646957"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "plot(canada_shape[\"province\"])"
      ],
      "id": "d1c6e5ae-a4ea-4e41-b96b-d74d40d0aaba"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Note how now we have simplified the boundaries of the provinces. We can\n",
        "use the function `object.size()` to compare how much memory we’re saving\n",
        "by using our `canada_shape` instead of the large `shape` object."
      ],
      "id": "69bf615b-a598-4259-9d5c-2441a4e9ea83"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "object.size(canada_shape)\n",
        "object.size(shape)"
      ],
      "id": "a21d0783-0ec8-4e74-a867-f7ff7ab3734c"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "> **Note**: the object `shape` was already a simplified version of the\n",
        "> high-definition shapefiles on the Statistics Canada website.\n",
        "> Performing basic geospatial operations on those files could take\n",
        "> multiple *minutes*!\n",
        "\n",
        "### Choosing an appropriate CRS\n",
        "\n",
        "As explained in our previous notebook, a CRS is the grid of reference\n",
        "for our geographic objects. These grids can be either **geographic**,\n",
        "coded in spherical longitude and latitude coordinates, or **projected**,\n",
        "coded in planar (x,y) coordinates.\n",
        "\n",
        "The manner in which we identify the CRS is through a parameter of the\n",
        "form `AUTHORITY:CODE`. In the previous notebook, we used the identifier\n",
        "`EPSG:4326` to refer our geometric objects to the CRS WGS84, which is\n",
        "the most popular geographic CRS worldwide. When choosing a geographic\n",
        "CRS, you typically cannot go wrong with WGS84.\n",
        "\n",
        "Choosing a projected CRS is often a tricky task - it depends on how you\n",
        "plan on using it. When projecting a geographic CRS, there will\n",
        "unavoidably be distortions to either the distances or the areas of the\n",
        "projected objects. The most common types of projections include:\n",
        "\n",
        "-   **Lambert azimuthal equal-area (LAEA) projections**: preserve\n",
        "    equal-area at all locations but distorts shapes beyond thousands of\n",
        "    kilometers.\n",
        "-   **Azimuthal equidistant (AEQD) projections**: maintain accurate\n",
        "    straight-line distance between a point and the center point of the\n",
        "    projection.\n",
        "-   **Lambert conformal conic (LCC) projections**: the cone is set to\n",
        "    keep distance and area properties reasonable, which is useful for\n",
        "    regions covering thousands of kilometers.\n",
        "-   **Stereographic (STERE) projections**: projections for polar\n",
        "    regions, but with distortions on areas and distances thousands of\n",
        "    kilometers from the center.\n",
        "\n",
        "The package `crsuggest` has a function `suggest_crs()`, which takes a\n",
        "spatial object with a geographic CRS and returns a list of possible\n",
        "projected CRS’s that could be used for the given object.\n",
        "\n",
        "We can use the function `st_crs()` to find out the CRS of our objects\n",
        "and `st_transform()` to change the CRS of the object."
      ],
      "id": "8f3ab4ff-90f7-459a-9bf5-705d776d0735"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# run the cell to get information from the CRS\n",
        "print(st_crs(canada_shape))\n",
        "st_crs(canada_shape)$IsGeographic\n",
        "st_crs(canada_shape)$units_gdal"
      ],
      "id": "4da7bf31-258e-4288-9478-3e9bade5c7ac"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "From the output above we can see that `canada_shape` is in a geographic\n",
        "CRS called NAD83. This geographic CRS is customized to North America and\n",
        "has an `AUTHORITY:CODE` of `EPSG:4269`.\n",
        "\n",
        "### Using S2 for operations in spherical coordinates\n",
        "\n",
        "Now that we’ve looking in more detail at CRS’s, it’s time to introduce\n",
        "`S2`. `S2` is a dependency of the `sf` package and is used for geometric\n",
        "operations on spherical coordinates (i.e., when the CRS is in longitude\n",
        "and latitude coordinates). `S2` setups are especially important when\n",
        "calculating distances or setting buffers around objects.\n",
        "\n",
        "This is better illustrated with an example. Let’s suppose we want to\n",
        "draw a buffer of distance 10 meters around the province of Alberta.\n",
        "Let’s perform this operation on our `canada_shape` dataset, first with\n",
        "`S2` turned on and then with `S2` turned off."
      ],
      "id": "84e6b8a5-4558-4d71-9fd4-3a7315cecf0e"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# turn on `S2`\n",
        "sf_use_s2(TRUE)\n",
        "\n",
        "# define Alberta\n",
        "alberta <- canada_shape[canada_shape$province == \"Alberta\", ]\n",
        "\n",
        "plot(st_buffer(alberta, dist = 10))"
      ],
      "id": "563bf78f-d2d8-4c44-9e6e-14960eaa81c2"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# turn off `S2`\n",
        "sf_use_s2(FALSE)\n",
        "\n",
        "# define Alberta\n",
        "alberta <- canada_shape[canada_shape$province == \"Alberta\", ]\n",
        "\n",
        "plot(st_buffer(alberta, dist = 10))"
      ],
      "id": "3b0bf570-d852-40e5-a1ac-da41ebe21e8f"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Notice the difference? That happens because when `S2` is turned off, the\n",
        "operation is performed in *degrees* and not in meters. Since the length\n",
        "of degrees change according to the longitude and latitude of the object,\n",
        "the buffers won’t be equidistant to the borders.\n",
        "\n",
        "Now, let’s try to calculate the distance between Alberta and Ontario\n",
        "with `S2` turned on and off."
      ],
      "id": "96b23eca-01ae-49cd-8a51-a5aec92a5367"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# turn on `S2`\n",
        "sf_use_s2(TRUE)\n",
        "\n",
        "# calculate distance\n",
        "alberta <- canada_shape[canada_shape$province == \"Alberta\", ]\n",
        "ontario <- canada_shape[canada_shape$province == \"Ontario\", ]\n",
        "\n",
        "st_distance(alberta, ontario)"
      ],
      "id": "903830c2-ccf4-4a0f-ae1c-0a898362daee"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# turn off `S2`\n",
        "sf_use_s2(FALSE)\n",
        "\n",
        "# calculate distance\n",
        "alberta <- canada_shape[canada_shape$province == \"Alberta\", ]\n",
        "ontario <- canada_shape[canada_shape$province == \"Ontario\", ]\n",
        "\n",
        "st_distance(alberta, ontario)"
      ],
      "id": "d4bd2efe-08e5-479f-872d-fe363b794e8f"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Notice that when `S2` is turned off, we get a very different number. The\n",
        "main takeaway is that we should use `S2` when applying geospatial\n",
        "operations to objects with geographic coordinates.\n",
        "\n",
        "The diagram below shows how R uses `S2` for geometric operations.\n",
        "\n",
        "<figure>\n",
        "<img src=\"attachment:media/s2_operations_diagram.png\"\n",
        "alt=\"Lovelace, Robin and Nowosad, Jakub and Muenchow, Jannes, (2019). Geocomputation with R.\" />\n",
        "<figcaption aria-hidden=\"true\">Lovelace, Robin and Nowosad, Jakub and\n",
        "Muenchow, Jannes, (2019). Geocomputation with R.</figcaption>\n",
        "</figure>\n",
        "\n",
        "Let’t turn `S2` back on for the remainder of our analysis."
      ],
      "attachments": {
        "media/s2_operations_diagram.png": {
          "image/png": 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v3z68+uqrcsei51C/fn0EBQVh2bJlyMvLw+DBg7FgwQJwQAIRUcXhMDAioudQ\nUFCAOXPmYOnSpQCAH374AZMmTZI5FZW32NhYODo64vLlyxg0aBC2bt0KfX19uWMREVV5LCtERM8o\nPT0dX3zxBUJDQ9GhQwds3LgRVlZWcseiFyQ7OxsODg5ITExEq1atEBoaCnNzc7ljERFVaRwGRkT0\nDMLCwjBy5EiEhobC3t4eSUlJLCpVnJGREWJjYzF58mRkZmaiZ8+e2LRpk9yxiIiqNJYVIqIyWrFi\nhbRS1BdffIGQkBDUr19f7lhUAfT09LBmzRr4+/sDAMaOHYspU6agoKBA5mRERFUTh4EREZXStWvX\nMGfOHPz0009o3LgxfvzxR4wePVruWCSTlJQU2NvbIzMzE2+99RaCg4NhZGQkdywioiqFZ1aIiErh\njz/+gIODA3766Sf07NkTCQkJLCrVnLm5OQ4dOoRBgwYhMTER5ubmiI2NlTsWEVGVwrJCRPQfVCoV\n7O3tsW/fPrz//vtITEyEqamp3LGoEtDX10dUVBTmzZuHK1euQKlUYsWKFXLHIiKqMjgMjIjoKebP\nn49FixYBAL7++mvMnj1b5kRUWe3atQujR4+GRqOBg4MD/P39OZeJiOg5sawQEZUgMzMTn332GbZt\n24bWrVvjxx9/xKBBg+SORZVcZmYmhgwZgtTUVHTs2BGRkZFo27at3LGIiHQWh4ERET3m999/h729\nPbZt24Z33nkH8fHxLCpUKq1atcJff/2FUaNG4fjx4+jWrRsiIiLkjkVEpLNYVoiIHvHDDz9g6NCh\nSElJwbRp0xAVFcUVnqhM6tWrh61bt+K7777D7du3MXz4cHzxxRe4f/++3NGIiHQOh4EREQHQarX4\n7LPP8O2336JevXrw9fXFxIkT5Y5FOi4xMREODg7Izs6GUqlEQEAADAwM5I5FRKQzWFaIqNo7cuQI\nZs2ahd27d8PS0hI//PADevbsKXcsqiIuX74MR0dHxMbGwtjYGCEhIejevbvcsYiIdAKHgRFRtRYc\nHIxhw4Zh9+7dGDNmDOLj41lUqFw1a9YMMTExmDZtGrKystCrVy+sX79e7lhERDqBZYWIqq0lS5bA\n0dERmZmZWLhwITZv3gyFQiF3LKqCatWqhZUrV2Lr1q2oWbMmJkyYgLFjxyI/P1/uaERElRqHgRFR\ntXPp0iV8+umn8Pf3R4sWLeDr6wsnJye5Y1E1kZqaCnt7e5w+fRrdu3dHSEgIjI2N5Y5FRFQp8cwK\nEVUr8fHxGDZsGPz9/aFUKqFWq1lUqEKZmZkhKSkJQ4cOxcGDB2FhYQG1Wi13LCKiSollhYiqjQ0b\nNsDOzg5//vknJk+ejD179qBj/JgulwAAIABJREFUx45yx6JqqFGjRggPD4ePjw9yc3Nha2uLJUuW\nyB2LiKjS4TAwIqoWPvvsM3zzzTfS3AEPDw+5IxEBANRqNZydnXH16lUMHToUKpUKjRo1kjsWEVGl\nwLJCRFXa6dOnMWPGDISFhcHMzAwrV66Era2t3LGIisjKypIuRtq2bVuEhobCzMxM7lhERLLjMDAi\nqrKioqJgZ2eHsLAwODo6Qq1Ws6hQpWRsbIw//vgDbm5uOH36NHr06IHg4GC5YxERyY5lhYiqpJUr\nV8LOzg4nTpyAl5cXtm/fjubNm8sdi+iJ6tatC39/f6xduxb379+Ho6MjZsyYgXv37skdjYhINhwG\nRkRVSl5eHmbOnIm1a9eiadOmWLlyJd577z25YxGVycGDBzFixAhkZWXBxsYGQUFBaNasmdyxiIgq\nHM+sEFGVkZycjCFDhmDt2rXo3bs3oqKiWFRIJ3Xv3h2HDh2CUqlEbGwszM3NkZiYKHcsIqIKx7JC\nRFXCli1b8M4772D//v348MMPsWfPHrzxxhtyxyJ6ZgYGBoiOjsZnn32G7Oxs9OnTB2vWrJE7FhFR\nheIwMCLSefPnz8eiRYsAAMuWLcPMmTNlTkRUviIiIjB69GjcvHkTo0aNwoYNG1CvXj25YxERvXAs\nK0Sksy5cuIDp06cjICAA7dq1g6+vL4YMGSJ3LKIX4vjx47C3t8fx48dhZmaGyMhItGrVSu5YREQv\nFIeBEZFOUqvVGDx4MAICAjB06FD89ttvLCpUpXXs2BEHDx6Eg4MDUlNTYWFhgV27dskdi4johWJZ\nISKd88MPP2Dw4ME4fPgwZs2ahfDwcLRt21buWEQvXP369REUFIRly5bhxo0bGDx4MBYsWAAOkiCi\nqorDwIhIZ9y/fx/Tp0/Ht99+i4YNG2LlypUYP3683LGIZBEbGwtHR0dcvnwZgwYNwtatW6Gvry93\nLCKicsWyQkQ6IS0tDdOnT8fu3bvRo0cP+Pr6wtraWu5YRLLKzs6Gg4MDEhMT0apVK4SGhsLc3Fzu\nWERE5YbDwIio0gsODsbgwYOxe/duuLm54bfffmNRIQJgZGSEhIQETJ48GZmZmbCwsIC/v7/csYiI\nyg3LChFVakuWLIGjoyPOnTsHHx8f+Pv74+WXX5Y7FlGlsmbNGvj7+6Nu3bp4//33MWXKFBQUFMgd\ni4jouXEYGBFVSv/73/8wbdo0bNy4Ea+99hpWrlwJBwcHuWMRVWopKSkYPnw4zp07B2tra4SEhKBZ\ns2ZyxyIiemY8s0JElc6ff/6JwYMHY+PGjRg4cCCioqJYVIhKwdzcHCkpKRg0aBDi4+Nhbm6OxMRE\nuWMRET0zlhUiqlQ2bdqEwYMHIyEhAZ6enoiKikKnTp3kjkWkM/T19REVFYWFCxfi4sWL6NOnD77/\n/nu5YxERPRMOAyOiSmPu3Lnw8fFB3bp1sXLlSnz88cdyRyLSabt27cLo0aOh0Wjg5uaGdevWoW7d\nunLHIiIqNZYVIpLdP//8g2nTpmH79u3o2rUrfH190a9fP7ljEVUJmZmZsLe3R0pKCszNzREREQFj\nY2O5YxERlQqHgRGRrNRqNQYPHozt27fD2dkZv/32G4sKUTlq1aoV/vjjD7i5uSElJQUWFhZQq9Vy\nxyIiKhWWFSKSzY8//oj+/fvjyJEjmDdvHrZt2wYjIyO5YxFVOXXr1oW/vz9+/PFH3LhxAwMHDsTS\npUvljkVE9J84DIyIZDF9+nT4+vrC0NAQK1aswJgxY+SORFQtHDx4ECNGjEBWVhYcHBzw66+/ol69\nenLHIiIqEc+sEFGFOnHiBOzs7ODr64u+ffti586dLCpEFah79+44dOgQlEolgoOD0aNHD5w+fVru\nWFVaWlqa3BGIdBbLChFVmPDwcAwYMABRUVGYOHEioqKiYGlpKXcsomrHwMAA0dHR+Oyzz5Camopu\n3bph165dcseqUvLz8xEUFIRx48ahT58+qFGjBkaPHo34+Hi5oxHpFA4DI6IKsWzZMnz66afQ09PD\nN998g+nTp8sdiYgAREREYPTo0bh16xbmzZuH+fPno0aNGnLH0lm7d+9GREQEwsPDcfbsWTRq1Aiu\nrq44fPgwDhw4IO03ZcoUeHh4oGPHjjKmJar8WFaI6IW6efMmpk2bhvXr18PU1BTLly/H4MGD5Y5F\nRI84fvw47O3tcfz4cQwaNAgBAQFo1KiR3LF0RkJCglRQjhw5AgAYNWoUXF1dMWzYMGm/s2fPQqVS\nQaVSIT09HcCDi3h6enrC09MTBgYGsuQnqsxYVojohUlOToaHhwcOHDgAe3t7rFy5EiYmJnLHIqIS\n3Lx5E2PHjkVwcDDatm2L0NBQmJmZyR2r0jp69KhUUAqHdtna2sLV1RWurq7Q09N76uOTkpKk4nLx\n4kUAQLt27eDh4QFPT88Xnp9IV7CsENELsXXrVkyYMAF5eXn47LPP8NVXX8kdiYhKYeXKlZg9ezZq\n166NX3/9FQ4ODnJHqjQyMzMRHh6OiIgIaY7PG2+8IRWUZs2aPdNxf//9d6hUKmzevBn5+fkAgJ49\ne8LT0xMuLi7llp9IF7GsEFG5W7hwIRYsWICmTZti6dKlcHd3lzsSEZVBbGwsHB0dcfnyZcyaNQtf\nf/01atZ8+po8ISEhGDFiRAUlrDjXrl2TCkp4eDju3LmDNm3aSAWlvOecBAQEQKVSISwsTNpmZ2cH\nT09PDBo0qFyfi0gXsKwQUbm5dOkSPvnkE2zduhXW1tZYvnw53nrrLbljEdEzyM7OhoODAxITE6FU\nKhEQEPDEORUbN27EuHHjkJycDAsLiwpOWv7u3buH0NBQqaBcuXIFTZo0gYuLC1xdXWFlZfXCM9y4\ncUMaJhYXFydtHzt2LDw9PdG9e/cXnoGoMmBZIaJyERsbi48++gjp6el4//334evrC319fbljEdFz\nKCgowIwZM/Ddd9/B2NgYERERMDc3L7LPoUOH0KdPH9y4cQMWFhZITk6WKe3zi46OlgpKRkYGatSo\ngTFjxsDV1RV2dnay5crMzJSKS+E1W+rVq4dJkybB09MTrVu3li0b0YvGskJEz239+vWYMGECAGDJ\nkiX4/PPPZU5EROVp27ZtGDduHO7fv49169bBzc0NAKDRaGBhYYGsrCzcu3cPADB//nwsWLBAxrRl\nk5iYKBWUw4cPAwDeeecdaZhXZVvGOTk5WSouOTk5AABDQ0N4eHjAw8MDDRs2lDkhUfliWSGi5zJ7\n9mwsXboU7du3xzfffFMlx6wTEZCamgp7e3ucPn0akydPxqpVqzBgwADs27ev2L4ZGRmV+qf9qamp\nUkEpvPZJz549pWFeurKE8J49e6BSqbBlyxZotVoAQKdOneDp6YmPPvpI5nRE5YNlhYieSUZGBiZN\nmoTdu3djyJAhWLZsGV5//XW5YxHRC/S///0PLi4u2LlzJ4yNjZGVlVXifm+//TZiYmIqON3TnT9/\nHuHh4QgPD8dvv/0GAGjfvr10BqVdu3YyJ3w+gYGBUKlUCA0Nlbb16dMHHh4eePfdd2VMRvR8WFaI\nqMx+++03uLu74+LFi5g2bRpWrlwpdyQiqkDvvfceVCrVU/dZuXIlpk2bVkGJSnb9+nWEhoZKJUWr\n1aJp06bSGZQ333xT1nwvQl5enjRMLDY2Vto+cuRIeHp64u2335YvHNEzYFkhojJZtWoVpk2bhiZN\nmmDx4sWYNGmS3JGIqAIdOnQIffv2xY0bN/CkjxA1atRAw4YNkZmZKctCGzt27JCGeV2+fBl6enoY\nPXo0XF1d8c4771R4HrmcO3dOKi6pqakAgFq1amHcuHHw9PREly5dZE5I9N9YVoioVPLz8zFlyhSs\nX78eb775Jr7++mv+hI6omtFoNOjXrx8OHTpUqv1HjBiBHTt2vOBUD/z+++9SQTlz5gwAYMiQIXB1\ndcWYMWMqJENldujQIWl+yz///AMAMDAwwIQJE+Dp6QkjIyOZExKVjGWFiP7TkSNHMH78ePz1119w\ndXXFsmXLYGhoKHcsIqpg7u7u+OWXX8r0mB07drywhTf++OMPqaCkpKQAAKysrKR5KFw+vWRqtRoq\nlQpbt27FrVu3AABt27aVlkKuU6eOzAmJ/sWyQkRPFRQUBBcXF+Tn52PhwoWYN2+e3JGISAa+vr6Y\nPn16mR5Ts2ZNNGzYEGfPni234nDs2DGEhYUhPDxculji66+/Ls1DadOmTbk8T3Wxfft2qFQqhISE\nSNu6desGDw8PuLu7yxeM6CGWFSJ6okWLFmH+/PkwMTHBkiVLMGrUKLkjEZFM3N3dERwcjBs3bpT5\nsZ988gl8fX2f+bmzs7MREhKC8PBwREVFAXhwbZHCCzbyau7P7+bNm9L8lv3790vbBwwYAE9PTwwb\nNkzGdFSdsawQUTG5ubn48MMPERwcjEGDBuHrr78udtVqIqqeQkJCEBISUubiEhMTU6Z5brdu3UJw\ncDDCw8MRERGBW7duQaFQYNSoUXB1dYWtre0zpKfSOH/+PFQqFTZv3owjR45I20ePHg0PDw9YW1vL\nmI6qG5YVIioiMTER7733Hk6fPo2pU6di6dKlUCgUcsciokpGo9FIxeXRa3uUpFatWmjZsiUyMjL+\n87iPLjV86dIlAMCwYcPg6urKs7sySElJkea3nD9/HgDQsGFDjB07Fp6enujQoYPMCamqY1khIsmG\nDRvwwQcfoGHDhvD29oanp6fckYhIB5S2uMyfPx8LFiwotl2tVksF5fTp0wCA3r17SxPlGzZs+KKi\nUxnExMRApVJh27ZtyMvLAwC0bNlSWgrZwMBA5oRUFbGsEBEAYNq0aVi1ahW6deuGxYsXY9CgQXJH\nIiId9F/FJTk5GRYWFjh48KB0FqVwKeTOnTtL81BatWpV0dGpDIKCgqBSqYosTd2lSxdMmDABHh4e\nMiajqoZlhaiay8rKgpubG/bu3YtRo0bh66+/5ocEIioXJRWXFi1aoG3bttLV1Y2NjaV5KJaWlnLG\npWdw69YtaX7L3r17pe29e/fGxx9/DBcXF/nCUZXAskJUje3ZswfOzs64du0avvzySyxatEjuSERU\nxVy6dAnBwcEICAhATEwMAKBu3brSEC+lUilzQiovWVlZ0oUnC697AwBDhw6Fh4cHBg4cKGM60lUs\nK0TV1IoVKzBz5ky89tpr8Pb2hpubm9yRiKiKuHPnDrZv3y6t5HXz5k0AD65o7+rqigEDBvCCjVXc\n4cOHpfktmZmZAB6U1FGjRsHT05PLTVOpsawQVTNCCLi7u8Pf3x/9+/eHj48PevbsKXcsIqoCwsPD\nERYWhoiICOTk5AAA3n77bWkeSv369WVOSHLYu3cvVCoVAgICcP36dQDAK6+8AldXV3h4eKB169by\nBqRKjWWFqBo5duwYRo8ejZSUFEyaNAlfffUVGjduLHcsItJh+/fvly7YeOrUKQCAhYUFRo8eDVdX\nVxgbG8uckCqT4OBgbN68GUFBQdK2jh07SkshN2jQQMZ0VBmxrBBVE4GBgXB2dka9evXg4+OD6dOn\nyx2JiHRUSkqKdMHG5ORkAEDr1q3h7OwMV1dXdO3aVeaEVNndvn1bmt+iVqul7T179sS4cePw0Ucf\nyZiOKhOWFaJqYO7cufDx8UHXrl3h4+ODoUOHyh2JiHRMRkYGgoKCEB4ejv379wMAGjduDCcnJ7i6\nupbp6vREj/rnn3+k+S1JSUnS9oEDB2LixIlwdHSUMR3JjWWFSEdpNJr/nKCal5eHMWPGICIiAu++\n+y58fHx4tWEiKrVr164hMDAQ4eHhiIyMlLa/++67cHFxwciRI2VMR1XRkSNHpPktGRkZAIAaNWrA\nyckJH3/8MUtxNcSyQqSDFixYgH379knLgJYkMTERzs7OOH/+PL744gssXry4AhMSka66d+8eAgMD\nERoaioiICOlK5QMGDJDmoSgUCplTUnWwb98+bN68GQEBAdBoNACAJk2awMnJCVOnTkWXLl1kTkgV\ngWWFSMccOnRIunDaJ598Al9f32L7/PTTT5g0aRJatGgBb29vjBs3rqJjEpGOiYqKwo4dOxAREYHs\n7GwAQPfu3aULNrZo0ULmhFSd7dixA1u2bEFgYKC0zcTERFoK2cjISMZ09CKxrBDpmLfffhv79u2T\nfr9jxw6MGDFC+v2UKVPw/fffo2/fvvDx8UGvXr3kiElEOuDAgQMIDg5GREQETpw4AQBo27atNFHe\nzMxM5oRERWm1WqhUKmzduhW///67tN3S0lJaCrlOnToyJqTyxrJCpEN8fX2LrOJVo0YNNGzYEPv2\n7UPz5s3h7OyMAwcO4MMPP4SPjw+aN28uY1oiqoyOHj2K7du3IyIiAgcPHgQAGBgYwMnJCS4uLrCx\nsZE5IVHpXLhwQZrf8vfff0vb+/Xrh7Fjx8Ld3V2+cFRuWFaIdMTZs2dhbm4uXVDrUW3atMHFixeR\nn58PHx8ffPrppzIkJKLK6vz58wgMDERYWJh0ZrZWrVpwcnLC6NGjYW9vL3NCoudz9OhRqFQqBAYG\n4vTp09L2kSNHYty4cRg2bJiM6eh5sKwQ6YjHh389Tl9fHxs2bCgyJIyIqq/r168jMDAQISEhiIiI\nkLYPGjRImihfu3ZtGRMSvRj79++X5rdcvXoVAFC/fn04OTlh4sSJsLKykjkhlQXLCpEOCAkJKdUS\noStXrsS0adMqIBERVVaBgYHSRPkbN24AeHChvcJ5KK+88orMCYkqTkhICLZu3YrAwEDcv38fAPDq\nq69KSyFzOf/Kj2WFqJLTaDRo3bo1rl+/jtL8dY2JieE69ETVzO7duxEUFISIiAhcuHABANCxY0dp\nHoqpqanMCYnkdefOHWl+y65du6TtZmZm0lLIBgYGMiakJ2FZIark3N3d8csvv5Rq35o1a6Jhw4Y4\ne/bsf14wkoh02x9//IHAwEBERETg+PHjAIBXXnkFTk5OGDNmDKytrWVOSFQ5ZWdnS/Nb/vzzT2l7\nr169MGrUKHh4eMiYjh7HskJUie3duxf9+vUr8+MsLCyQnJz8AhIRkZyOHTsmTZQvXP2oTp060kT5\noUOHypyQSLekpqZi8+bNCAwMxMmTJ6XtQ4YMgaurK8aMGSNjOgJYVoiQkZGBtLQ0pKWlITU1FZmZ\nmejUqRPMzMykr82aNavwXBqNBpaWljh37pw0zrYsNmzYwGUbiaqA7OxsaaJ8TEyMtH3IkCHSPJRa\ntWrJmJCoaoiNjZXmt1y+fBnAvz8MGDt2LAYOHChzwuqJZYWqjdOnT0ulpLCYpKWl4fbt2//52GbN\nmhUrMJ06dXqh1zGZNm0aVq1aVabH2NvbY8SIERgxYgSHgRHpsJs3b0oT5cPDw6X5ar169YKTkxNc\nXV3RtGlTmVMSVV2hoaHYtm0bAgMDUVBQAODBZwEnJyd88MEH6N69u8wJqw+WFapyTp06JRWRwlt6\nenqJpaSwdBQWkMLfFz7+8a+PKywxjxeZ5y0xhw4dgqWl5RPvr1mzpnS2pW/fvnB3d2dBIaoCduzY\nIV2wsfCaSoUTgMeMGcOVi4gqWH5+vjS/JSoqStrevn17aSnkVq1ayZiw6mNZIZ114sSJIkUiLS0N\nx44dg1arLbbvk0pJWT1aXh593sc1bdq02FkYU1NTGBoalup5LCwskJKSUmTbowXF3NxcKiitW7cu\n8+sgospDrVYjMDAQ4eHh+OeffwAALVq0kOahvPXWWzInJCIAyMnJkea3JCYmStt79OghLYXcoEED\nGRNWTSwrVOkdO3as2NCtEydOvNBSUhZCiGJnYVJTU5Genl5s36ZNmxY7C/P666/DyMhI2mfBggVY\nuHAhAKBGjRrS8A8WFKKq4+DBgwgMDERoaCiOHTsGAHjppZfg5OSEUaNGYfDgwTInJKKnSUtLk+a3\nFP4dBgBbW1s4OTlhwoQJMqarWlhWqNJ4dNhW4Yf+U6dOVZpSUlZCiBKHkz2txLRs2RJBQUHSa2ZB\nIao6Tp48KU2U/+uvv6Tt9vb20jwUItI9cXFx0vyWixcvStsLf/jg6OgoYzrdx7JCFerRD/CPzic5\nefIk7ty5U2x/XSglZVX4HjxeZEoqMQYGBsWGk3Xo0AHGxsYyJCeisrp06RICAwMRHBwMtVotbe/b\nt680D+Xll1+WMSERlaewsDAEBAQgMDAQ+fn5AAB9fX3pAq28aHPZsazQC3Hv3r1iQ7eOHTuGU6dO\nVZtSUlZnzpxBUlKS9N4VFppHTy8XMjAwKDacrF27dnjttddkSE5Ej7pz5w4CAwOxfft2hIeHS3PN\nunbtKhWUtm3bypyyetBEz4JyrApNPHci8gtLKOQO9Ay0Z9Xw+3Y51uwwwrKT62GnJ3ciKo27d+9K\n81siIyOl7a1atYKTkxPef/99dO7cWcaEuoNlhZ7L3bt3iw3dOnHiBEtJObp//36Jw8lKKjEvv/xy\nkQJjamqK9u3bc6USogoQHh4uXbDxf//7HwDgtddek4aC9OjRQ+aEFUWDhE1+UMcGYfWGBOQUPNys\np4BCoYCiqRFMLZUY4jYFM0eavtACkb7UGt1mJ0AxUoWMYBfo2nqJGeE+8PnOD6roDGibjkdkdhnL\nSk4C/L73Q3B0PJKytGjS1BD6DerBxMYBrmNdYadQ4cOfu2H9IivkxPhBFa2Gat1mJF95+HiFPgwN\nmwDa26jX1ASmPZRwnTwLLm885Z3UZmDnSh8s3xyJpBwtFA2M0MnKDg5jXKFUBGHNqfFY/bHJ87wt\nOufixYvYsmULAgMDER8fL203NzeXlkJ+dO4qPUYQlYJWqxVJSUni119/FXPmzBEjRowQZmZmok6d\nOgJAsZuZmZlwcnIS8+fPFwEBASI1NVXul1DlFBQUiMOHD4stW7aIL7/8Ujg4OIjXX3+9xO/Hyy+/\nLGxsbMRHH30kVq1aJXbv3i3OnDkj90sg0nl79+4VU6ZMEcbGxtLft0aNGonx48eL3377Te54Mjsj\nVvdTCADC1GOPyL0rhLibK9KCvYSdMQSgEKYTgkT2i4xwN1vEB0eKpMsv8kn+lftXvDhzt5wPeiNI\nuOhDoOl4EVnqY+eKpG9dhGkDhTAd6SVUCY+8y3dzRdrOZcLFQl8oFBD64yKLPDJpkaUAIBRveYu0\nwue7cUZEfqkUhnoQUJgKl81P+K7dThPLBhsKRWcXsb7wOW+cEfE/zxTK1goBKITy2+r9f09aWpqY\nP3++6NSpU5H/p/v27StWr14t8vPz5Y5Y6fDMChWh1WqLzClJT0/HqVOncPLkSWns5aN4pqTyeXwY\nWeGvjx8/Xmzfl19+uchwso4dO6J9+/Zo06aNDMmJdMOhQ4ekCzY+OtfMwcFBWm6YAECLYJcmcNyi\nhekXSUhb/O+1o7TRU9HJbg0yCvRhtzYdkRNKt6x75ZaBNXY+MApbD4fyHKpVoMbU9v2xJq+0Z1a0\nSJinhN2SZBhNCEL893Yln1HSJGDuYCWWt/RDboCLdIZLs24IjCbuBPotQ5p6Jv49B6LBzondMGRd\nBtDUAaojQXB57NuW8V1/dJqRjZmxafB+fMXtU35wtJkKzZw07PGoXmdWnuTAgQPS/Jbs7GxpOxfd\nKIojH6upW7duFRlWdPz4cZw8eRKnTp1iKdFxtWrVQpcuXdClS5ci2+/du1ficLK4uDjExcUV2bdJ\nkyZFhpN16NAB7dq1Q7t27SrypRBVGhkZGQgMDERQUBD+/PNPabtSqZTmoTRu3FjGhJWR4omfMhT9\nxsPl9TXwOaqBeksQMiZMga5/fM3ZMhfescCacj9yPSjK8GlNEzUVrksSoGk9BUHfPKGoAIC+Fbx/\nmAn1nFxoAEi944nPpQ+7sQ4w2bAcGVd2IihGC5cxjw7iy4E6Kh5aPSVMSvqvot14eE/2w9TSv5Qq\nr1evXujVqxdWrVqFiIgIBAYGSkuah4aGYuLEiXBycoKTkxOGDBkid1zZsKxUcXl5eUXmlBw/fhyn\nTp1iKamGatWqha5du6Jr165FthcUFBQrMGlpaf9ZYjp16oT27dujffv2aNeuHWrUqFGRL4fohbt2\n7Zr04WHPnj3S9m7duknzUExMdP0jtkz0TGBiogCOaqG9nA1NAXT6E4kmZi4cJm9GDlzkDVKQjDXz\nVMgoUMDygylQ/tf1CS2mYqqFCrl4pKw8TdMmMNQDMgoAbV6RigMA0BYA0Krhty4ZriUsaGA6bAhM\nE0r7YqqXoUOHYujQofDz85Pmt4SHh+OXX37BL7/8Il0odtSoUbCyspI7boXS4X8a6FHXr18vUkoK\nz5KcPHkSd+/eLbY/SwkV0tPTe2KJKcuZmEeHkxWehWnXrh1q1apVkS+H6Lncu3evyE837927BwBo\n06YNnJyc4OzsjG7dusmcsirIhSb3wa8URkYw0gNQkIPkQD+sWeeHpLeCEP9BBmZNnAVVuj5c1+7E\n6mEPPhhrz6qxZsUa7DymBXIzkKE1gtJlJrym28Hk0U/HBRok7/CD3zo/qF9fjbRvlUUSaI5uxrLF\nfkjIyEbaqWzUa6eEywxvzHV6fNK/BsnrvOG9IxmaG9nIOAuY2I6H1+KZUBoCmui5GD8vGBlaAAU7\nMcuqG7yhQLcZwVg/5uGH+SsJ8Fu8DJv/ykD2qQzk6neDcuxMeH9qB5Min8S0yNixHHN/iEQO6uF2\n7m0Y9bMGil9urGSJKvgd0gJ6plD2My3FAwzhMHt8KQ8OaDMykFEAQM8IJu0erzeGUNpaQhGdgIR5\nSijPr4HfNy4wfbQwdXbAeHAi+dPo6enBzc0Nbm5uuHTpknThybi4OKxatQqrVq1Cp06dpKWQO3To\nIHfkF0/uSTNUNhqNRhw4cECsW7dOzJgxQwwfPlyYmpqK2rVrc6I7VYi7d++KQ4cOic2bNwsvLy8x\nYsQI0aFDhxL//Onr64tevXqJCRMmiBUrVoiwsDCRnp4u7t4t7xmoRM8nMjJSuLu7C319fenPb5Mm\nTcTEiRNFdHS03PF0VpDQVKoVAAAgAElEQVTbwwn2XyQVvSN9mbBqgH8nXN9OEus/HS+U7Qon5C8T\nXiPthN0bhgKAMPHYI4QQ4nbyMqE0NBEOP6eJ2w+2iDObxwtTBYR+P28Rf6PwCc6IoMUzhYPFg++n\n4cPHF8rdPVMoh3mJPecfbsjeI7x66wvoGQq779P+3fHuGaFyMxUmTutF2u2Hj905XpjoQSg6zxR7\nCp/vbrzweh0CDVxE0OP/vGWoxPh+DmJZQu6D398+I4I8LIUCECZjVI8sMHBbJH2jFIbtHMT6Iw+f\n7HaaWD/ywXtQmgn2aYuthAIQUNiJ9blP3/dJcn+2EwpAKPotE0Wmwt89I1bbPng/9fst+3fy/aNu\nJwnvfv/+HVK0VoqZPyc9WFyBnkt6erpYuHCh6Ny5c5H/Z62srMSKFSvE1atX5Y74wrCsVFLXrl0T\ncXFx4qeffhIzZswQw4YNYymhSi0/P18cOnRIqFSqUpUYa2trMWHCBLF8+XIRGhoqUlNTxZ07d+R+\nGVSNxMXFiU8++US0bNlS+rNZo0YN4ezsLAIDA+WOVyVIZeXT+IflQojcI+vFeIsH2w2HrS7yoTd7\n7cMPyu1cxPoMIcTdbJEU9nA1r7tJwusNhVAMXv3YCmK3xR4P0wfPM32P9DxCCHF7s4NQPF5WciPF\n+HZWwvtI0ay3w8Y/WO3KcLyIfHiQtBVKod/UQax/9AlvR4rxhhDQMxEzYx9ue2JZyRaqkYbCbu1j\nq2ddXi/sGkBAz1TMTHh4WPVMYarQFw6bH2sZJ5cJK0XpysqeCaUvNk9SUlnJTQ4S3sNMhAIKYdjP\nS0Q+bQm3G2li/ceWQl/vkX/zLVzEst1ninxv6NkdOHBATJs2Tbz66qtF/m8dPHiw+Pnnn+WOV+44\nDExmV69eLXE+ycmTJ1FQUFBsfw7fosqqdu3aMDc3h7m5eZHtd+/eLXE4WXx8fJH15v+fvbOPbqpK\n2/7lQ8GDUzBg0aCADRRoCmLDl6SCSrAqgaBNbaHJgGKEWRBgXiaAQouzphZcg4FRTMEHW3XQhI/a\nopQUBRsRfFK02CpoioANX5pqgUSLJkD1fv9Ic2iatJSvnrbs31pd6MnOOfc+Sc7Z19n7vm7AX+W3\nYVJ/ICfm5ptvbsnuMNop33zzDV+w0eFw8NsfeeQR3skrMvJSC/0Zl4vrkyzoUjl4TjnhrAZEEi3S\n5+kwZ6oc4nojEVGkfwFWT9Uc6KIBQAyZSgkA8G0xIvcrQJqpaJApwUExUwvZ2gyUv5WNgiUKaKLq\nXhF1C8mb8GzPRf7RKgxdroWj/ijobBUkg2XoGeGFqwpArxLkrrHBNyIHE+ofkFMia4sZ8sMSTGjo\neNWQo/nI3e6B66wB2j31ttd64IuVQVYL+FweAD6YX85GRYQSGeMbpMRHyzBUDJScvcSx4Hf0BHBN\nFvn7DuTiWWURvIfLUHLEA8SoYbQVQz9W0nRtnEgpdGvKMCElGxmLMpC7zwPPVxYseKQI5qlG5K7R\nQcZ+YldFQkICEhIS8J///AdFRUX80tXt27dj+/btQYn5SUlJQod71TCx0kJUV1eHzSc5cuQIEyWM\ndk3Hjh0RHx+P+Pj4oO3nz58Pm9gfTsTceuut/G+gvjNZTEwMOnfu3JLdYbRBTpw4wd/M9+7dy28f\nOXIkn4fSp08fASNs//RMzIK5nnVxo0T4h8EcFzoctu+0oaoWiIvqFvq+WDkSxEB5lR32ckCTGNgf\nQpy0KkrL4eFk0K0zQ9PUoPmIHfaTAOTdQpLPxaM00F1KqADwHbCjrFYE7UIzTIlNNDyVi4I9PkAs\ngSQkpua7gXWL6gbAA5x1w+cDcBWigLtHh5wiAyTfrMS4MQtgO1qOslOdm13EUzxWj5wSLfTvZGDB\nC7mwnfSg/J1nofR1RvlmTfMS+hmXRKlUQqlUIicnh89v+eCDD7BhwwZs2LABUVFRvHAZO3as0OFe\nEUysXGN+/vlnfPvtt0H1SQKzJUyUMBgX6dSpU7NFTGMzMbfeeiv/2wmIl8BMzC233NKS3WG0Mn75\n5RdeoOzYsYPf3r9/f/7G3fC7x2jNeFBV5QEAeM96Q1+O6ImevTjgpAfusz6giSG12+MGal1wngQQ\n28Qhz7r9LmUev7VvEzXbG8Xn8cFX64Hz5CX2cNTpT9C/ylGZVCYDByd8PifKjgDqa/EVH2xAzgob\nEmYXwTJPD8WI/LpZr1CqvqoAFy+92NMIEWTTTShO0iF7ZjIW5DlRtSULxr0aGJsh9hjNp0OHDtBq\ntdBqtaiurubrt3z66adYu3Yt1q5di5iYGP76J5M14+FBK4GJlSukqqoKDocDBw8eDBIlhw8f5t1j\n6sNECYPRPJoSMeGWk5WUlKCkJNgLMyBipFIpL14Cf2yJT/smIFC2bNnCPyDq0aMHf4N+6KGHhA2Q\ncYWIIBJxADyocjqBkKosnH/2IUICSe+mn/13E3UDfOWw7XQiPTaM9fSRcpRHySCL7AZRBOArL4H9\nrA7KkEuHB84jgCSmcRHCRXLg4IN9exE80zWhcsVXgfKjEsgi6mYsqlxwXcWMiGh8MpRRBSg4VQHb\n9gogvhmOYD4ffBzX5IyJZEYusvckIPmdAiyYmY2EIj2kYUaQZW9mw7fcBHXD+EUy6Neb4axIwMpv\nnCgvrwJGsbmV60WPHj2g1+uh1+vx3Xff8dfF/fv346WXXsJLL72E4cOH81bId999t9AhNwkTK5fg\nxx9/hMPhwKFDh0KWbzFRwmC0HJ06dYJMJgt5GnTu3Lmwy8nCiZiuXbti0KBBiI2NDZmJ6dKlS0t2\nh3EN2bFjB1+w0e32++F27NgRGo0GKSkpeOKJJwSOkHEtGDomAdxbRXB+YkN5rQKy+iOY2iq4T/mA\naAUUg5vej/QeKTg4YVuVgYIUM9RBY2YPClaZwa2QQRYtw9AooORkPrI3pEM5I1jY+D4xIrtqAYxN\n1Mrl7hkKKWdBSWEWsj5Rwjg2WK4431qJ/HtyIBvsX/5VftaGoj0+qMeHkQ61YWaUGhKlxoIZMhS9\nVI6SdStRNCMHyqim3lCFgsxciBalQ9Hk1JEY6tU50JdOQPbOBdC9nABbmDoqOGtD0U4P1ElhdsbJ\noRwjxspvPHxuEuP6M3DgQGRkZCAjIwN79+7lhcu+ffuwb98+PPfccxg3bhxSUlKg1Wpb5wM9oTP8\nWwsnTpygjz76iEwmE/2///f/aOLEiTRw4EDq0KEDc9+6UamppOI1BlLGSki/ozlv8FLZcgWJo2Rk\n2HGFnpGMa4bP56Mvv/yS3nnnHXr++edp0qRJ1K9fv7C/565du9KoUaPoqaeeoqysLNq4cSPt27eP\nPB6P0N1gNMLevXvJYDBQnz59gj5LpVJJb731Fv32229Ch8ggL+WnNWJd3Ng7Nvvdu8K2rykmfYzf\nhUu3tcE11mkiBceRfJUjePsOv8NXkBtYdT5pxHUuVcN1lFNat6+aSrIuVpC8nnOZfbHUbwUcJaf0\nIhe/3WUzknq0nqy8dXEZpcfXWQZX+/te6XQR0UW7X4jlZNjsqLPxdZPDoid5YsAC2E350/1OXtxw\nA9nrd89rJV0vECLVZG7OrcVbRlmj6yybxxuprKaxhi6yLtZRui14p7wj2+gG1sVE5C1JJ1kkCJyU\n9EWhwVini4gbnl7PQro+lWQcyxGi1GRuyk2M0SJs376dnnnmGerSpUvQNTQ5OZk2btwodHhB3HBi\n5fjx4/Thhx/yomTChAk3jCjxVljJNF9DiuFSkg6WkWy4jGTD5aSYaiDT1jJyufLJsLT40ju6ETic\nT+nTFSSNBCFCTLpmiRU3mVNE/roBqxpe4q8hXr+I0iTKSNJLTJLBMpKPkpNyehbl2CrJ6y2jrBlG\nchARHbaSabmB1IO5i9/rCI5EvSQkFotJHCMjRZKesgocTVtKeivJulxHisFiEkWJSBwtJUWa/3vj\n2JFO+jXXsb/XmCsRMdOmTaPMzEyyWCxUWlpKbjcTo0LgcDiarDNw8uRJoUNkBFFJxtH+a49oan6z\nbGsDtrmNtXfb0kkmAiFaTabygMhwkClJQpKknNDaH+HEChG5Cvy1WQLfIU4kIi7CLxSK6/+8a+yU\nPipQN4QjUbSUpNEi4iIbDtbdZE7iCOBINsNIpqU6MmyuG5EfziF1dL1rS6SIRJEgRCnIWF6vl658\n0tXVmRHFayjrzXyyWoykT5GTVAQCRCRLMZBxazOut247GVWSOhtoJRnWWMl+2EVer5e81ZVUttVE\nhiQ1GbaGqoaypTJ/nDEGsofYH3vJsUJBIvjjbyh0rNNFF62Ktzou1lepLiPzLBmJIqWk28yUSmvi\njz/+IIvFQklJSSH3P51ORx9++KHQIbZfsXL06FFelPz973/nRcn//M//tHtREoqLijOVJOFEJJth\nomJn8C3AXWqm9MS6i1pa824oNwZeMqdwlyFWiKi6jKxb7eS6TgWwXLYsUsZw/htZgSOo0Ja7PJ+y\nkqQkiuQIsQ1uMjY9SSLqnvoF7hMX3OTYbCB5lP8mLJtfTGGH4F4HGceLiRusoZySujfXVJL9TQMp\normLRd3aOF6vl7788ktav349Pf/886RSqRoVMV26dKFRo0bRX//6V/rXv/5FZrOZPv/883ZdlEso\nfvjhB3rllVfo/vvvD/oMpFIpvfDCC3TgwIFL74TRwrjJvt5I6dPl/rolACFSSsr5WWRq9MFIJVlX\nGUhZN1gHJyHlfCNZD4e29B4wU3qKnCRiMUni5aRIVJNhXSPX3TqxIpkb+iDOtcdE+kQpiSM54qKk\npJhuJHt1uO6UUc58Jcl6ccRFikmaqCdTSejV0ltuIvVgEYnEMlKvsAdfT51WypquIKm4bh/j9ZRT\nHuaKe6KYjNPlJIniiBNJSD41i4qdxWQYLCHFjCzKD/eeRvGSY6uRDCkKkkXXibFIEUniFaRZnEP2\nBprBZcsh42KNXwyiThylpZNxtTWkOGSOqq6eS4SYZCodpa8vIy8RWRfryXygjIrX+48rjRaTuJeY\nRL2kJE9LJ/Nlxc9oaaqrq2nNmjU0duzYoOttnz59yGAw0N69ewWJ6yYioqtbSCYsTqczKJ+kfk7J\nn3/+GdL+xsspqULRTAWS33IhYbkN1oVh1pgCQK0TlmnjoDtlgHOHnlkK1mGb3RPj3gB0RS7kNGU7\n2QJUFc6BQpMN5+B02HZmQR52WWnd512YAOuJHCgCa7oPLkOCLAMlEWqYXflBdp1V7yRD+kwBPJBA\nX+SAKTH4G+J8bRzi/uGCYY8DWQ3dW47kInnMHHiWOFA8N0yiajvA5/OFTeyvrKwMadulSxfExcUF\nJfQHcmJuu+02AaJvm/z222/8uuqioiJ+e8+ePflE+dGjRwsYIaPNsPNZ9FTmott8Oxwr5EJHw2C0\nGQ4fPsxfh7/66it++5AhQ/jr8MCBA1skljaTYP/999+HuG4FxAkTJY3jfEMH7VsV4MaakNOYUAGA\nCAk0q7JgneaEuxZBRboYrYCTudDPzEZFrQzpaxsTKgAghnKVCbqSXL/lJv85Np7MKE7SQvmPAlhO\nOZG/xQ5ToqLeq1WwbbfDF6GAJFwSaYwOWbNzMedK+tRG4DgOw4YNw7Bhw4K2NyZiPv/8c3z++edB\nbSMjIyGVSoPES+CvR48eLdmdVs2WLVv4go0XLlwAAHTu3Jm/MU6cOFHgCBltjloA4CDp3z4fpjAY\n14v+/ftjyZIlWLJkCUpLS4Mcxfbv34+lS5figQce4K/Pd9xxx3WLpdUNSb///vuwguTw4cMINwnE\nREkTnCpAxgtF8EAM3XxdiNFjCGI15iSZ4WuJ2NoKreIX4oNtxTIUVAHceD3mXMo3P1IB/TM22D1A\ns6bIuJ7oKQJwCvB4PGhYocBXC8BnQ+4b5dCGcX+RqiZAWoIbjsZEjNfrDetOVlpaitLS0qC2kZGR\nQc5k9cXM7bff3pLdEQybzcbfBE+fPs1vV6lUfMHGm2++WcAIGW0LHzynAFGU/0rl83nhiZBBMZat\nF2AwrpQRI0ZgxIgRWLFiBe++mJeXh927d2P37t2YO3cuf82eMmUKOnbseG0DEGTxGREdPnyYtm/f\nTq+99hrNmzePlEol9e/fn2666aYbMKfk+lC5WuF3MRHryHo1iSgXXFS8Sk/qsXKSxfjXnipmmULW\nuxIReZ3FZJyrJkWikhTDpSQZrCDdcitVhj2+m+yr9aRWaUg/S0OKGC74c+dklFXuP36ZJYt0YyUk\nW1xG3sP5pB8rIZFYRvpAcmC1nUyzlKQYqyRloowk0VJSTM2i4voxeiup+M100gyXkHq9m+iElbJS\nZCQWcSSKkZNutT0kZ6N4rvhizsqJYspKk5NExJFosJLSixqcALeDrKv1pBwsJk1BmHNz2EpZ05Wk\nSFSQLEZMkuFqMqy/RGI7EVGNtc65hiP5imbmhtS4g/JZqMJIcq7OTaahS0u1mdSR/nMuy2zgpENE\njhVy//coQkTyWWZyNHz/BQeVlbNMp0vx+++/U2lpKf33v/+lRYsW0cSJE0kikYS93kVGRtLQoUMp\nNTWV0tPT6a233qI9e/aQy9U+ElNLS0tp0aJFIf0fM2YMrV69ut30k9HyuNYpSRQhItkMMzlq3FQ8\nV0ay+cUsF5PBuMb8+eeftHHjRkpOTg66jnMcR1OnTqWtW7des2Ndd7ESECWrV6+mefPm0fjx45ko\naRFclDPeP/jnxppC7AebjddBphQF6d4sqxvIe8nxpoYkESBusD7INcVbbiSFWELqNwMDcC9VWvyO\nK6KxWQ2sDN1knSUlLlpH+YGERlc+6WL8SX3qNyvJ6yUibxnlLNTxQkY610jpSUpSDvcn90nmFhN5\n7ZQ+nCNutJF3gnEX6UgSARKpcshFRFRtp5ylOpLXDfqVq8ykHysn9Qw9aRKlJIrwH1e+vCzopsaL\nlTU5pBuvJv1yI2XNVfiT1cWai7GfsJJxvoZkdcnqDcWKe08WKaLlZNhRNwi7UGfhGCEm5bpLfDp7\nDP7jQUS6ouZ8aGFoVKx4qWxpnRgRqynnRJj3essoa6zo4oUoWkGGN8uCxRDjivntt9+otLSU3n77\nbVq0aBFNmDChURHzl7/8hWQyGaWkpNDixYspNzeXdu/eTT/++KPQ3bgkhw4domXLllF8fHxQn+65\n5x7KzMykiooKoUNktAO8pUZSDxYRx3EkHqwg3apiYtKXwbi+nD59ml5//XUaN25c0PVdLBbT3Llz\naffu3Ve1/2smVg4fPkxFRUUhoiTcDZeJkhbggp0MsXWDyyRzeJcnIiJXMeUsN5AmSUlKlf9PPdVA\nWZv9gsOxSkGSqfkN3h+wo6z3pP9CmV8wjDc1uDF4qXiu1C806j/dKk0naQRIPCvYocWxXBbWtpL3\nfY/RUI6T/LMtW61UVk38YF403Vqv/8WkE4MQpSNrvUG1fb5/ECgea6B8fmDur48iAgiRSjLVG7AX\nzxUTwJEkJafejIKX8qeKCRCRZmv9KL1knSoKFStuK+liOJLW8+4nIqqsm7Hgxuc0eTP1WtR1MxtS\nMpQ00bApwogV7wk7mRcqSBzht7Y07mnCpaXGQTmzZHWiDhetKXdUsieW14nLFTH33nsvJScn0/PP\nP085OTm0a9cuwa18f/rpJzKZTPTggw8GxdurVy+aP38+2e12QeNjMBgMxrXlyJEj9NJLL9HQoUOD\nrvuxsbG0dOlS2r9//2Xv86rFyj//+U+KiYlhoqS1caGY9HW+7pwqp3GxUkflGkW9AXHd8PNCGaUP\n5kgUryTNVE3Qn3K0jGTxMpIv9osNb4GGxBEcyZaHLiOiA1kkiwBBpCZz3UyEq26JmnRpg8JfRToS\nhRnABwbskvlhBjduOxmnaiirfiFGbzEZYvyD8/x6o2m/fzxHyjcbnJELdkofXDfrsu7ikYOWgdXD\nvzSKI8WaYJlRPF8SIlZcbyqJi5CQwdYg7hoHWd/MIeuBpof7gboDiJBSemmTTRsnIFYixCQbryTF\ncL9VNTgZ6d60k6uZisNlM5FuuKjeb1xEsqk5TRQdY1xrfvvtN/riiy/o7bffpoULF9KECRMoOjo6\n7PW3c+fONGTIEPrkk09aLD6fz0fvvPMOTZo0KWRp2/Tp06mo6EqnBxkMBoPRlti3bx8999xz1Ldv\n36D7wahRo2jlypV0/PjxZu3nmqQPHzlyJOj/6ye81//3pptuuhaHYzSHiJ7oGQXgKOA74YSzFpA1\n8WlLZDL0jLDBGSHF0Ni6FGpPGcqP+CBZmAVzpqzJw9l32lBVC8RFdQt9MVaOBDFQXmWHvRzQJAJc\npP8Ybo87uC3HoVsE4I7qBlFQf7i6l8O4WonkMKz3W1L6TpbAvC4XRQddcHoaj5dreC4i5FCMlWDZ\nN05UVDhxqcx0juvs/49ab9D2zmHalpXY4YuQoFtD06dIKZTTpU0eBwC4KBE4AD640fB0XTZcAhZs\nzocGJcgYo8CyrypgP+AFN715bxeP1SOnRAv9OxlY8EIubCc9KH/nWSh9nVG+WcMsr1uAW265hU92\n/O2338I6kh07dgyAP9l///79LRrfuXPncO7cOd7NCxDG6pLBYDAYwjJs2DD07dsXffv2RV5eHj7+\n+GMAABHh/PnzOH/+fLP2c9ViZd68eRg/fnxIjZNPPvkE7733XlDb2NjYsCKmQ4cOVxsGIwQJ5CPE\nwL4q4EgJyk4BsqZGkhGc3+UpAuD1gMcDNwDnUSd8aML2GB5UVfmVgfesN/TliJ7o2YsDTnrgPuv3\nmhKN10ItLkJBSQkqoEBgyO6pcsEFMdRJiiaOFy6EcuS+kIHckzLMecGI/MEVyLinCOUnm78LiUQM\nDk54a8P0oRG8tZdq4YPH4wNqPXCfbX4s9eHuGQopZ0GJz4OKg1VA4jWQBJFyZLyVAdvYDJS89iwW\njC1DjkoUtmnVVxXg4qUXxWOECLLpJhQn6ZA9MxkL8pyo2pIF414NjA3rsDCuCTU1NWEdxo4fPx7U\nrnfv3oiJicEjjzwSYpPcUnTt2hU6nQ46nQ6HDh1CYWEhCgsLsXTp0ha1umQwGAyGMBARNm/ejLy8\nPOTn5wPwu/c+//zzUKlUSEhIuKz9XbVY6d69O+677z7cd999QdvPnDkTImCOHDmCTz/9FAUFBUFt\nBwwYEFbEXHPrsxsKDgkaLaRvrETFWTssG5zQzb9Mn/lIEboB8Oyxwe5TQxGiHjwo3+eGbLgEIhEH\nwIMqpxMIMUnm/DMZERJIetftRKxBdp4Tnqm5WLBWjfxZUnBny5H9hg2SqblYmRR+4ByWU0WYk6hF\n0T25sBeo/U/3LykiwhDRGQAHSc+eV/DmxuAgiuSAWhfsJU5gVJjP4KgTzl4SSBr7NUarkSzPQMkn\nPti3W1E1V9eMGQwffD4O4Sai+Mji02FebsfQeUXIna2DQpYPTa/QdmVvZsO33AR1w9ouIhn0681w\nViRg5TdOlJdXAaPY3MrV8Msvv4QVJSdPBqvuPn36ICYmBuPHjw+yPY6JiQk/+ygQAwYMgMFggMFg\nQGlpKbZt24bCwkLMnTs3yOoyJSWlVcXNYDAYjMvno48+4m2Nf/31V/Tu3RuzZ8+GSqXCY489dsX7\nvW5VJLp3746RI0di5MiRQdvdbnfYGiqfffYZ3n///aC2/fr1CxEwgwYNYp77zYQbvQBZaQVIfscJ\n2+plKJqaA2XUZewgKg7SaKDoYC4y/qODrUGNDd9X2cjeo0bOcGDomARwbxXB+YkN5bWK4CVntVVw\nn/IB0QooBteLL1IETiwBV74Sc2Zz4GqBntNtsE+V4TKkCspXLUD2Nxz0K9RhB/Hh6sb4woiZqhMu\n+CJ6ImHMpZdmXQ5DRwwF95YNJeuyUTLDGFzQsdaJ3FUFGLrK0MQeJNAt1CJ7Ty6cO1fC+JkWxtFN\nD+wq3shAkSwLhuFNt5PMykX2Hhm0Gwqgn5kN+VZ9qGg6a0PRTg/U4QQkJ4dyjBgrv/H4RRmjWbjd\n7rCi5McffwxqFx0djdjYWEycODFkpqRTp04CRX9lBJau/etf/0JxcTEKCwuxbds2TJs2DTNnzuRF\ni0qlEjpUBoPBYDSTzz//nBcox48fx6233opJkyZh4sSJUKlUuOWWW67+INc1s+Yy8Hg89MUXX5DF\nYqHMzEyaOnUqyeVy6tGjR0jSqEQioYkTJ9KiRYvov//9L5WWltLvv/8udBdaJ247pY/yJ0SLk3LI\n0VgidZ07V0hCeqasLrlbQspMK1XWJVK7S3NIM6qe1W1NMelj/O10WxskrztNpOA4kq+ql3xfnU+6\naDFpNjcvs9u72Z9gL11cFvJawIFLsfqiBbD3cA6pxXXuV24ir9tNXrqYYB9Sr+RCGWXFB9sfExEV\nz6pLsG+QE+yvYcORfFXwfux8gn29frnMpK6zNJak5VBZ4PTUOMg8S07KVc0xlnZT8XzZRUe0isbP\nW6VFT7pVwRbMdCCLZNzF8xFEtbXOMpoj+VJ7iLuXdbqIuOHpDayn+aP5LZij1GRm/qAhnDp1inbv\n3k1r166luXPnkkKhILFYHPaalpiYSLNnz6ZVq1bR1q1byeFw0Pnz54XuwnXlwoULVFBQQNOnT6eo\nqCgCQHfccQfNmTOHPv30U6HDYzAuC/cOA8mixKRoYIHfOqikHJWERLG6ek6Y15bW3X/GteTgwYP0\n4osv0pAhQ/j7mEqlonXr1l2XOlmtRqw0xq+//kqlpaW0YcMGyszMpGnTplFCQkJYEXP33XeTUqmk\nBQsW0FtvvUWff/451dQwmyJyl5FpqpREAIlG6ci4NbgQofeEnXLmykkUARLFp1Nx/foZ3jIy1qux\ngQiORCJ/fRD1m8GDbLctnWQiEKLVZCqvGxHXOMiUJCFJUk6QCCCb3l87JFJMksF+ZzHZcBnJRslJ\nnqgmXWZw8cGAI1ZDS2Oiek5mkVJSzk0nwwwlKZJ0pIzxu18pputIt9xeT6yAEKujfCffSSpboSBR\nLyWZDtTfs5fy0/xwLVAAACAASURBVOqsiBuIqkChRFmQm5mXrNNFYd3GKtdr6mql+PssHSwhcSRI\nPN7UuIAMwUXWxX6rYYikpF6aQ9bySnLXeMnrdpFjTz4ZZ6hJszy0uKV3h97/Pk5OxjDlLLx7DH4x\nEyEmZQOh4+9TnVXxVsfF+irVZWSeJSNRpJR0m29spVJdXU27du2iNWvWkF6vp7Fjx9Ltt98eco3q\n27cvPfroo6TX6+k///kPbdu2jQ4ePEi1tbVCd0FwTp8+TW+//TYlJydTREQEAaABAwZQeno6ffXV\nV0KHx2gpXP6aWMpRUhL3kpA0Xk7y0QrSLDaRtcJN5DSRbqnfFdJlyyHj4kB9q0AxYRGJoyUkFotJ\nMlhOyunpZC69hB+mq5hMs5QkixaTKEpM4lg5qecbKb/EQfYVen9x4mYQKMQsSmmiXIBQeOvs/K/G\nVfIStOr+M64al8tFq1evpjFjxvC/twcffJCMRiN999131/XYrV6sNMbZs2dp3759tGHDBnrxxRd5\nERNugNC7d2967LHH6B//+Afl5ORQSUkJ/fLLL0J3ocVxl+aTcb7GX1k+WkLSeBnJYv03A+X0dDJt\ndYS/wNQ4KH+phuQxdYW24tWUvjl85XXvATOlp8hJIhaTJF5OikQ1GdbZyRVSQNA/UyCOkZKkl4hE\nkRwhIvhzE6lyqJIqybrKQMpAdXtOQsr5RrIerrerC5VkniUnSSRHXLScNCuKyXXBS/ZMOYlFElIs\ntFJl3fEDMyuK+UbSqxSkUClJmSgnxdQssh6u16NqO+UsVpO0rrI7F6+h9DXFVOkuo/xVBlLW2UKj\nl4IMq6xU6S4j83KdX6wBxMWqKX2dPch+2bUjizSjJSTiOBJFy0i9NJ8qr+Dxk7s8n7JmqUk+WEwi\nDgSOI3GMnJQzsshc3uATPGwl03IDqWO5i0WaRukofVUOFQc9XfNS2fK64pDgSDxKTfrMfKokIuti\nPZkPlFHxeiMZUhQkjRaTuJeYRL2kJE9LDz1mO+ann34im81GJpOJZs2aRQ8++CA/I9BQlDz22GM0\nd+5cevXVV8lqtdJ3331Hf/zxh9BdaBM4nU5avXo1JSYm8ud05MiR9PLLL9PRo0eFDo9xXXBT2WoN\nSSM5kialk7mk3tXzgpscRUbSxIuI4xrU1CL/CgAAxI3KuvhQrKaSrEvrHu5wUtJYGnmg4jSTJpoj\nSZKRik/UlTN2lVF+Zt31P0JG6c0UK0H1v1oh3opisu65jrWxWnn/GZePz+ej9evXk0ql4q/F8fHx\ntHTpUvriiy9aLI6biIiufjFZ68Hn8+Hbb78Nmxfz888/B7W96667wib2i0SXkzHBuCJOFuDZeWXQ\nrc8KzuEAgLMeOEtzsWCmDcoSK3SXk2dzCcpfGIqhL1ZAvd6F/Knsc2aEp6qqKiSfxOFw4PTp00Ht\n+vbti9jYWD6PRAj3rfbO/v37eUexzz//HACQmJiIlJQUpKam4tZbbxU4QsbV40PJCwooXypHzxn5\nsK9Rhs9b9JQgY7wCK3vnwr1Zw+dQet6YgJ4zi4CxRjhshnoWLx4UzRyKCW84gSg1zAfyoQlKbPTA\nkiqBtjQZ1gM5UDa4F1VteRYJmjJoSsqQFX9te8xgtGYKCwv5PBSfz4e+fftCpVJBpVJh3LhxLR7P\ndUuwFwqO4zBs2DAMGzYsaPv58+fhcDjw3XffBQmY/fv3Y+fOnUFte/bsGVbEdO/evSW70n6prcDK\naXq40spDhQoARIogGatEgtSJnuFeZzCuET/++GOQGAn8t9sdXNCmX79+GDVqVJAYiYmJQb9+/QSK\n/MZhyJAhGDJkCNLT0/HZZ5/xwmXmzJlBifkpKSlCh8q4Qjzb50D7Ugk80Xrkr2hEqACASI6stQbY\nlrjhQb1qWI2OZERQTlND8tZKOE8VIf8THzRp9YxAfDZYd3rAxUohCXOvESdlwTBWDdcV9ovBaEvs\n3r2bFyg//fQTunfvjilTpvAiRUiH3nYnVhqjU6dOiI+PR3x88OOR2tpaOBwOHDx4MGg25ttvv0Vx\ncXFQ2zvuuCNIvAT+evRoWO2P0SR7spG9pwpcjB1V09UQh3wLfah4Iwt2+QLomcEU4xpw8uTJsO5b\nv/zyS1C7fv36YfTo0SEzJRLJZdp+M64Lo0ePxujRo/Hvf/8bRUVFKCwsxNatW5GXl4dbb72VFy2P\nPPKI0KEymkttObJfMMNZy0H2jB6KSz2gip+DOfFmuHGp0r11RHWDOAJw1gK+s0ESp+74gO+rXOR+\nooNxbEOZJEayaihym9sXBqONsX//fl6gfPfddwAAtVrNC5TbbrtN4AjraLEFZ22MP/74gw4cOECb\nN2+mZcuW0fTp02nMmDFhnXyioqLowQcfpFmzZpHJZCKbzUZVVVVCd6H1Um0l/WB/DoUoRkGauelk\nXG0i0xoTGTMNpEmUkWK+NUyey9VTPFcS4hzGaD8cO3aMtm/fTkajkZ555hkaNWoUdenSJeQ3269f\nP5o0aRIZDAZau3Yt7dy5k5xOp9DhM66AmpoaslgspNFoiOP815U+ffqQwWCgvXv3Ch1eu8C1J4cM\nKUpSjFeQPFZC0tEaSrc0zFv0UuWeHEpPk5Mk0USVNQ7KmS4jsUhMijAugzx7DH7zkQgpGUqaF0/A\n3TFAwICFG2ukhld2b5HOn7cSISG9LaRnlKOqM5CJlJJmdag5CTnLmpeDccFNZZuzSJcoIen84uDX\n3GVkmqEkhUpNykQZiblm9rfhPi+4qHiVjhSDxSSKkpBiVsDh00sOi4HUw8UkihSRNNFQz0Cm7jw4\niylnoZpkvZSU0yB9p3JrOqnHK0mZpCR5jP98cKqcoHNxyTaN9f+Ci+yWLNKNlZB8aRnRhUqyZqpJ\n1ktEnFhG6hVhzjkReSvyKT1NSerpetIlyfyfYf2c1rRQsx1G8zh27BgZjUa67777+PP58MMP06uv\nvkqVla1zbMTEyhXw7bffUl5eHi1fvpyeeeYZGjNmDPXs2TNkQNS9e3caM2YM/e1vf6PVq1fTxx9/\nTD/++KPQ4bcOairJukJP6lFSEos4Ql3SuWJqOuXsuQ7OUoetfteYQAJ8tJIMy80XbYQZbQqn00lW\nq5VWrFhBTz/9NI0cOZIiIyNDfoMxMTE0adIkWrBgAb3++utUXFxMx44dEzp8xnXihx9+oNdff50m\nTpzIfweGDBlCL774Ih08eFDo8NoklW+qSSJWkLG0bmh4wUXW+TLiIjiSzS+uG2i6yb7GQJqx/od5\n3Oh0Ms1VknK8lEQRIMRnBbtB1sMRMPbglJRzhdfjRsXKhUoyJda5GY41ho/hcA6pe128ZohH6ch0\nufegCw7Kz9STuu4hnCRIrLjInCIJttYvzSJF1CXESsN9zsoh81w1aeZnkWlFwHSGI+niYrKvUJMi\nxUBZq42UniL1O3Ilmvhz4d5jIsP0gNlAsFjxlqaTbLCerIFzf8FF+dOlQULkkm0a6/8FB+WvyiLd\ncP9nIFuYQ8Y0BannZpExU08KcUBENpAdB0ykEHMkXx4QxF4qW17n+jnYQHa3l7zX4WFme+bXX3+l\nN954gx555BH+uz5ixAjKzMyk8vLmOkgIBxMr15CKigrKz8/nRcwDDzwQVsSIRCK6//77acaMGfTK\nK6/Qjh076OTJk0KHz2C0OiorK6mwsJD+/e9/07Rp02j48OF0yy23hBUljz/+OC1atIjWrVtHNpuN\njh8/LnT4DAGpqKigFStWBNlsjhkzhlavXk0//fST0OG1DQ6bSCHiSJbpCN5+oYyyhvst7DUF9RRG\noJ6TSEb6rW7yz7bkU3ETdaGKZ9StVojSkfUKB6DhxIq7PJ+yVBLiwJF4bDpZm9Af3sP5ZBhbf9WE\niKRJ6ZTfRNxNxREkVqpzSBkpCq69RURlS5WU3oyZJN62f5SBrPUcHL0lBn9tNLGc9JvrOXxdsJMh\nFgROQab6fb5gJ0NMqFixL5T6XdTqH9RlJs3Ui2KlOW0a7T8RuerKC4iG6ym/nuuma1249i4yJ4n8\n8Tvrba7JJ00UCJyMsoJKDDCaIi8vj1JTU+mmm27i7eAXLFjQ5upY3TA5Ky1BbGwsYmNjQ7YfOnQo\nbF7M//3f/wW169q1a0hOzKBBg9C7d++W6gKDIQjff/99WPctn88X1C4mJgaJiYm8A1cgp+Suu+4S\nKHJGayVwPV64cCG++OILPjF/3rx5mDdvHlQqFVJSUjB58mR06tRJ6HBbJSVrVsJ2ticMY6XBL0TI\noHsmAVmzbSh4LRfOpDoHLpEI3QBwMcnQq/z5H5LRajSV8cX/xq/BaMR3IBfPKovgPVyGkiMeIEYN\no60Y+rESNJX+yMWoYbQpoH0rAwteyIXtpAcVW5YheacF6hfMyF0obzzpvx6NO4l6ULBEh1xJNnTx\n/jYyjR7uZvQ5sM9uciWUverFHJ8AKbcSFaIEaJPq9S9CCml/DjjihqcKF1N0IkToJuKAk6HH8O0z\nYc4LMpiXKCHmAIiVmJNWEXTOmtOmsf5zkXXfhfE6qGMuvkN8jwySiCI4qzzwAf591TpgL/X4463v\nBBopw9BYDpa9Hriqmz5nNzoff/wxn4fidrsRFRWFZ599ls9DaYswsdICDBgwAAMGDAjZfuTIETgc\nDlRUVATZLO/duzeoXWRkZNjE/ujo6BbqAYNxbTh8+HBY963z588Htevfvz8effRRxMXFBblv3Xnn\nnQJFzmjLjBw5EiNHjsSLL76Ijz/+GIWFhXj//fdRWFiIGTNm8In5kyZNEjrU1kNtOayfOAHI0C3M\nGFQsV0AaYUN5qR0lZw3BblpduCbFQX26RXUD4AHOuuHzAbgKB0juHh1yigyQfLMS48YsgO1oOcpO\ndW5mLCLIpptQnKJHwfIFWPBaEZxnnShYooQnwo7i+dJL7yICoceKmgBdkgRF71jw7AgbstPmIGOR\nHurBSiiaE1a4fQa2RwCobfgCh84cAPjgbfhamBGfXKOF/I0M2F6cAMkGBXT/SEfGdAXk4+WX1aap\nWLnGRpqRdZ+Nz3dRrKAzuEgApzxwe1Dv+9AZoi4AIsTo2bOR/d3A7Nu3jxcoTqcTHTp0wJNPPskL\nlK5duwod4lXBxIqABAZgDW+QlZWV/GAuIGIOHz6ML774IqjdLbfcElbE9O3btyW7wWCE8N133wWJ\nkoAwqa0Nvnv2798fSqWSFyWBmRKxuFk+PwzGZfPwww/j4YcfhtFo5Gdb8vPz8e677+L222/nhcuD\nDz4odKgC40JVFQD44PWFeVksRs8IoLzWB+9ZXLHIkMpk4OCEz+dE2RFAfS3qmQw2IGeFDQmzi2CZ\np4diRD500eEaVqHiK0AaX+96EymFerkVymkWzEnTIfcrD2wrVqJoRmgdluYhhvrNYlj7L8CCFQUo\nfycDyRuMkM/IRu4qDaRCO17Gp6NopxgZczOQvdeG7Nk25K5SImOdGekBd7TmtLlWRMih1ciQnVkG\ne6kH+l51+691wXnCBy5+AtSsjBUA/4qETZs2IS8vD1999RUAYPz48Vi4cCFUKhV69ep1iT20HZhY\naYX07dsXffv2xcSJE4O2Hz16lB/4HTp0iBcy+/btC2p38803h9SICQwGGYxrSUVFRcjSLYfDgT/+\n+COoXf/+/TFx4kTExcVhwIABvFC/4447BIqccaPTsWNHqNVqqNXqIOGSnZ2N7OxsDBgwgC88OWTI\nEKHDFYBuEIkAVLngdPqA4Q1G1Vxn/7+inuh5FeNV0fhkKKMKUHCqArbtFUB8M2YwfD74uKZnbyQz\ncpG9JwHJ7xRgwcxsJBTpIW044ql1wrzOgTlrdCE2yFysBjkbXHCMWICSU2UoPwIor1RIRUigXJoP\n5YwSZGcakPVGCUrWapEcIUbZakWzZ6GuF6LhOphKtNBvWYmMF4wo+KYIGepkiEqLoY9pfptrhWxx\nPnJPJMOwPAu2MUYoogDnFiMspxTIeMsQ+jneQJw5cwYbN25EXl4edu3aBQBISEjASy+9BJVKhUGD\nBgkb4HXiBv7I2x7R0dGIjo6GUqkM2n78+HF+kFg/L6asrCyoXceOHUPyYQKDRwajKcLlkzgcDhBR\nULsBAwbwF8wBAwbwMyWsFhGjNXPbbbfh6aefxtNPPw2n08kLl2XLlmHZsmUYMWIEn9/Sp08focNt\nGSJkUMjFWHmwCrZP7PClNBhUn3LBDUA0VomEqxltR6mxYIYMRS+Vo2Rd3QxGVFNvqEJBZi5Ei9Kh\naFIkiaFenQN96QRk71wA3csJsC2WhQgDX0kBrFU66MJN5sYoMCEGKDnI+ZcmXQmeIuR+kgBdkggQ\ny6FfY0dy0gIo1StRnmeBbZUCSgFHYhXvWOBL00AWwUGalI788WrkahR4dosd5kIn9PMlzWpzTYno\nDBHXDZLeHlgWPYsCDvBFJsBUooMyWmhp1/IQETZs2IC8vDy8//77AACpVIrFixdDpVJBLpdfYg9t\nHyZW2gF9+vRBnz598NhjjwVt/+GHH/jBZf28GIvFEtSuQ4cOIUvJBg0aFNYsgNF++fPPP8Pmk1RU\nVIS0HTBgAJ544gnExcXxye4xMTGIimpylMFgtHokEgmfhP/VV19h27Zt+OCDD7Bo0SIsWrQIiYmJ\nSElJwZQpU9ClSxehw72OcFDM1kG2YRnK81bCvEQBXb1VJZ5SOyoghX5emIrzFy7vOPIXcpGxR4GM\nz3KhmyZF0WYDZGHFQRWKlmSgLNGIrHoH9QVWlzY8rkgB41sG2BOXoSRTiwXxdpjGN4jWZ8PKzCIk\nrwnTj1MVKDsJcPLk5i09qm3wLwDUulD0hhmKJD1vNCBOzIB+TDaePew3JGgWIbkpjWy7TDwHcmEW\nq2FKrBMBnBS6f2ixrDAb3SI7N7tNUDwN47rMOCteUkNbMgH2kvQbehbFarXyeSi///477rjjDsye\nPRsqlSpkvNfeuYG/Bu2fu+66C3fddVdINWeXyxU0GA2ImI0bNwa1u+mmm8LmxMTFxeGmm25qya4w\nriG1tbVh80kC1WvrM3DgQCQlJSEuLg5SqZSfKenevbsAkTMYLUt8fDzi4+ORkZGB3bt3o7CwEAUF\nBZg5cyZmzpyJJ598kl8q1h7hhmcgN7MEiiVFyHhmGeIs6ZBHAb4jFizItGPoC0XIGFXvSfdZH7wA\nfFUuOGsBSXNHGJwM6YVF4KZpkVG4AAkyG/T/0CM5cShkvUTAWRcqSopgfssGTM8OqTTvOuGCDwCq\nXKhqcFxuVAbML5QgYZEN2dOSIdqcj6z676/1oWJtMhKqMpC1RAflcDE4AJ6DBTDONqAoUg3TGkOT\njmYBPB6/q5XbUz9hHPDtyYB2iQQFmUqIIwB47Ch3cpA/o4X8EueI3+fZ4H0GktID5/widTlEcMPj\nrre51gO3x+ff7sFFl7BaJ3Jn6yDLu+hU5iwvh7uXFrokcfPbNNF/1ymX//WzDZKfzrr9ffC4/bN0\nAIAq2PeUw7OvBAn9zegpqlvuFwFwXDd06y2DcsYC6Me2z7xGu92OzZs3Iy8vDz/++CM6duyIyZMn\n84nynTt3vvRO2iNCeyczWg9VVVVks9nIZDLRrFmzaNy4cdSnT5+QmhYASCqV0pNPPkkvvPACbdy4\nkfbv30+1tbVCd4FRj3PnzlF5eTm9++67tGTJEnriiSdowIABYT/PgQMHUlJSEmVkZJDFYqEvvviC\nzpw5I3QXGIxWSWFhIc2cOZO6detGAKhr166k0+noo48+Ejq064CXKrdmkWaslMRiCUlHKUih0pNx\nR73aHuQlR4GR9ImBWiUcSVMMZLJdboFfLzm2GsmQoiBZtIi4CBAXKSJJvII0i3PI3mB3LltOULFf\nQESytHQyrraGFIfMUdXFFiEmmUpH6evLyHvBTllzc6jsgJ3yVxtIkygjSbSYxGIRiWPkpJ5vCjlm\neFxkX5fOF0WESEaaQNHh6hxScoFixDJ/FfvxajKsLwtbuT1on28G71OXmUPFJ4gqiy4Wf0SEiGRT\nsyjH5iJvhZWMC5UkqTueaJSOsjY7yH0gn4xzFXwVeMl4AxmL/GfIPl/i3z8nIuloJamTlKScbqTi\nejVdLt2msf67qHhNel0By7qaMMvNZHe5yL7eSPpAbRtOQurFJip21n0LKkykjBGTNFZC4iiOuAbV\n68FJybCn/dSvdzgc9M9//pPi4uL4Pk6aNIneeOMNqqqqEjq8VsFNRA0WnTMYDaiurg56Ah/Iizl2\n7FhI24EDB4adjenYsaMAkd8Y+Hy+sPkkR44cCWk7cODAIPOFwEzJrbfeKkDkDEbbpqamhs9vCcxM\n9+nTh59tGTlypMARMhhtDR9KXtIit1c2cqY2mD2p9cFTVQHbCh0yuGw4VrTdXI2qqio+Ud5utwMA\nxowZg8cffxwqlYrlEjeAiRXGFXP69OmgwXFggHz06NGQtv379w9J7I+Li8PNN9/c8oG3UX7//feQ\nfBKHw4HKysqQtrGxsUHnO+DA1da91hmM1soPP/yAwsJCbN26Fdu3bwcA3HPPPXx+S//+/QWOkMFo\n/Xi2P4uEf4iQe8DY6BI5X+GzSD6SDuu1Tuy/zpw7dw4WiwV5eXn8NWLQoEFITk6GSqXC8OHDBY6w\n9cLECuOa43a7Q0TMoUOHwoqYfv36heTDDBo06MZdlwngt99+C5voHu78BURJQAAGkt0jI6+ishqD\nwbgqKioqUFhYiC1btvBFfseMGYOUlBSkpaUxIwoGIyxVyH5EgjmlCTB+YoUhPozz1ykbMmZaMHRN\nDtRtJG1ly5YtfKJ8bW0t7rzzTqSkpEClUmHcuHFCh9cmYGKF0WL88ssvISLmu+++g9PpDGkrkUhC\nRExcXFy7GoTX1NQEiZJvvvkGFRUVOH78eEjb2NjYoOVbAVHyl7/8RYDIGQxGc/n8889RWFiI9957\njzexmDhxIlJSUqDRaBARwXxuGIwAFa9NgOIfRaiKEEM2fgIUI6SQiDjA54HrcBlspYB2rRn6hnV/\nWhm7du3iE+VPnToFjuOQlpbGJ8qz3/3lwcQKQ3BqampCRExFRUVYEdOnT5+w7mSteXlTQKQ1zCk5\nceJESNuYmBjce++9IcU8b+SZJgajvbBz504+v6W6uhqdOnXi81smTZokdHgMRqugam8uTGssKNpT\nhooqH8CJIBmcAMUkLfQz1JBeRRHS68nXX3/N56F8//33AICkpCQ+D4W5aF45TKwwWi2//fZbiIhp\nLEejV69eYRP7RaKWu6rVX/5WX5j88MMPIW2lUmlQvCUlJXj11Vchl8thMpkwdOjQFoubwWC0LOfO\nnUNhYSG2bdsGs9mM2tpa3H777XzhyTFjxggdIoPBaAbHjx/nCzZ++eWXAICHHnoISUlJUKlUkEja\nVl5Na4WJFUabw+fzhcxSNOZ+deedd4bkw8TFxV3VE46GxgKBWFwuV0hbqVQatHwrLi4OAwYMQKdO\nnULavv3225g+fTr69esHk8l0wxV9YjBuRKqrq1FYWIj3338fhYWFAPyGJIH8lsGDBwscIYPBqE9N\nTQ2fKF9cXAwAGDJkCJ+Hcu+99wocYfuDiRVGu+H8+fNhl1sdOnQopK1YLA6bE9OjRw++TX3L5vrC\n5KeffgrZXzins4EDB162ZfOOHTuQmpqKP//8EyaTCdOmTbv8E8FgMNok33//PQoLC5Gfn4/PPvsM\nADBixAheuPTq1esSe2AwGNeLzZs3Y9OmTSgoKADgX9ExZcoUqFQqPPDAAwJH175hYoXR7qmtrYXD\n4UBaWhp++OEHjBs3Dg6HAwcPHgxpe/vttyMuLg4OhwM///xzyOsNBUkg2b1Dhw7XLN4DBw4gNTUV\nBw8exMsvv4wFCxZcs30zGIy2QXl5OQoLC7F582Z8++23AICHH34YKSkp0Gq1zFyDwWgBdu7cyeeh\n1NTU4C9/+Qu0Wi1UKhUmTpwodHg3DEysMG4ITp8+jR49ekCtVuO9994DAPz5559hc0wcDkeQKAn8\nK5VK8T//8z8tFm9qaipsNhsWLlyIFStWtMhxGQxG6+PTTz9FYWEhLBYLv9w0OTkZkydPRkpKisDR\nMRjti3379vF5KAEjnCeffJLPQ+nSpYvAEd54MLHCuCHIycnBjBkzYDabodFohA6n2UydOhXvvvsu\nnnrqKZhMpnZl3cxgMC6fwsJCfPDBBzCbzfD5fOjatStfePLhhx8WOjwGo03y/fff83koBw4cAAAo\nFAo8+eSTUKlUbAmmwDCxwrghUCqV2LFjB86cOdOqbY7DsWjRIrz88st47LHHYDKZ0K9fP6FDYjAY\nAvPrr7+isLAQBQUF/Br63r178/ktrBo2g9E0Z86cgdlsxubNm/kcMZlMhsmTJ0OlUiEuLk7gCBkB\nmFhhtHt+/fVX9OjRAwqFAtu3bxc6nCvilVdewfz58zF06FCYTCbI5XKhQ2IwGK2EkydP8vktu3bt\nAgDcc889fOFJ9oCDwfBDRDCbzdi0aRO2bdsGALj77ruh0WigUqnYvbWVwsQKo91jsVig1Wrxv//7\nv5g5c6bQ4VwxmzZtwpQpU9CrVy+YTCY8/vjjQofEYDBaGd9++y22bduGDRs24OuvvwYAjB49Gqmp\nqdBqtawwHeOGxGq18ony586dQ5cuXaDVavHEE0/g0UcfFTo8xiVgYoXR7klJSUF+fj6qq6tx2223\nCR3OVbFnzx6kpqbizJkzMJlMmDFjhtAhMRiMVkpJSQm2bt0Ki8WC48ePAwAmTJiAKVOmQKPRtJhh\nCIMhBHa7nc9DCbh7pqam8nkoHMcJHCGjuTCxwmjXnD9/HiKRCMOGDcOePXuEDueacOTIEaSmpqK8\nvBxZWVlIT08XOiQGg9HK+eijj7BlyxaYzWacPXsWnTp14hPzmQUro71QUVEBs9mMvLw8vsZ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cZYneOywljNcFlhWuXSpUtIS0uDjY0NmjVrJjoOe4q5c+di27ZtOHnyJOzs7LBv3z7RkRhjrE6V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\n5Es1AAAAAElFTkSuQmCC\n"
        }
      },
      "id": "73f1d7f0-a309-4fc6-a120-d149f85d0614"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "sf_use_s2(TRUE)"
      ],
      "id": "9f9605c1-754e-4f90-ba83-89d0bd9af644"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Part 2: Gravity Equation of Trade\n",
        "\n",
        "### Theory\n",
        "\n",
        "In the 1660’s, Isaac Newton formalized the law of gravity: particles\n",
        "attract each other with a force that is proportional to the product of\n",
        "their masses and inversely proportional to the square of their distance.\n",
        "In 1962, Dutch economist Jan Tinberg adapted the law of gravity to\n",
        "international trade. Tinberg (1962) proposed that the aggregate trade\n",
        "flows between any two countries is “proportional to the gross national\n",
        "products of those countries and inversely proportional to the distance\n",
        "between them.” Mathematically, that means\n",
        "\n",
        "$$\n",
        "Trade = G \\frac{Mass_{1}^\\alpha Mass_{2}^\\beta}{Distance^\\theta}\n",
        "$$\n",
        "\n",
        "Since then, there have been numerous attempts to estimate the effects of\n",
        "both economic mass and distance on trade flows empirically. By taking\n",
        "logs of both sides of the equation, we can show that the gravity\n",
        "equation translates to\n",
        "\n",
        "$$\n",
        "log(Trade) = log(G) + \\alpha log(Mass_{1}) + \\beta log(Mass_{2}) - \\theta log(Distance)\n",
        "$$\n",
        "\n",
        "In this section, we’ll try to estimate the effect of distance on trade\n",
        "flows using data from Canadian provinces and US states.\n",
        "\n",
        "### Empirical Methods\n",
        "\n",
        "Empirically, we can estimate the effect of distance on trade with an\n",
        "adaptation of the model above. For a Canadian province $i$ and a US\n",
        "state $j$:\n",
        "\n",
        "$$\n",
        "log(T_{ij}) = \\beta_{0} + \\beta_{1} log(Y_{j}) - \\beta_{2} log(X_{ij}) + \\sum_{i=2}^{13} \\gamma_{i} D_{i} + \\epsilon\n",
        "$$\n",
        "\n",
        "where\n",
        "\n",
        "-   $T_{ij}$ is total merchandise volume between province $i$ and state\n",
        "    $j$\n",
        "-   $Y_{j}$ is the GDP of state $j$\n",
        "-   $X_{ij}$ is the distance between province $i$ and state $j$\n",
        "-   $D_{i}$ is a dummy for province $i$\n",
        "\n",
        "This specification is similar to the traditional gravity equation; by\n",
        "controlling for provinces with dummy variables, we implicitly control\n",
        "for the economic masses of those provinces.\n",
        "\n",
        "The effect of interest is the coefficient on distance, $\\beta_{2}$,\n",
        "which can be interpreted as trade elasticity: the percentage change in\n",
        "total merchandise volume from a 1% change in distance.\n",
        "\n",
        "### Data Cleaning and Wrangling\n",
        "\n",
        "We have three datasets for this analysis: `canada_shape`, `us_states`,\n",
        "and `trade_data`. The first 2 datasets contain the shapefiles of\n",
        "Canadian provinces and US states, and the last file contains trade data\n",
        "from Statistics Canada. Let’s load our datasets."
      ],
      "id": "d7a1fec0-cdb4-4d2b-8be2-2223ee06c5ac"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# load trade data\n",
        "trade_data <- read_csv(\"advanced_geospatial_datasets/trade_data.csv\")\n",
        "head(trade_data)\n",
        "\n",
        "# view canada_shape (we've loaded it in the previous section)\n",
        "head(canada_shape)\n",
        "\n",
        "# view us_states (comes with spData package)\n",
        "head(us_states)"
      ],
      "id": "5bad75c1-9079-4c40-b789-cab89cb94dd0"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "By looking at the “trade_data” dataset, we see that:\n",
        "\n",
        "-   We already have data on total merchandise volume\n",
        "    (`tmerch_value_usd`) between provinces and states\n",
        "-   We already have data on the GDP of US states (`gdp`)\n",
        "-   We can easily create dummies for each Canadian province with the\n",
        "    column `province`\n",
        "\n",
        "Therefore, the only variable missing for our specification is the\n",
        "distance between each province-state pair. We can use our shapefiles to\n",
        "calculate the distance between provinces and states with the function\n",
        "`st_distance` from the `sf` package.\n",
        "\n",
        "We want a dataset with the following structure:\n",
        "\n",
        "| Province | State | Total Merchandise Volume (USD) | State GDP (USD) | Distance (Km) |\n",
        "|---------------|:-------------|------------------:|:------------:|:----------:|\n",
        "| Alberta | Alabama | USD | USD | Km |\n",
        "| Alberta | Arkansas | USD | USD | Km |\n",
        "| Alberta | Arizona | USD | USD | Km |\n",
        "\n",
        "The easiest way to do this is by creating an `sf` object with the\n",
        "distance values, and then merging it with `trade_data` using the fields\n",
        "`province` and `state`.\n",
        "\n",
        "Before we do that, let’s take a look at the CRS of our shapefiles."
      ],
      "id": "6ccb0e6d-d8e5-4feb-a20a-5eaa7bb2b876"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# look at CRS details\n",
        "st_crs(canada_shape)$WktPretty #WktPretty makes it easier to see the CRS parameters\n",
        "st_crs(us_states)$WktPretty"
      ],
      "id": "f4ae8c59-eff3-4957-afd4-dc41f14a1731"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Our objects reference the same CRS - the geographic NAD83 CRS. We could\n",
        "just go ahead and calculate the distance between our objects (as long as\n",
        "our `S2` is turned on!); however, for learning purposes, let’s take a\n",
        "look at the projected suggestions from the function `suggest_crs()`."
      ],
      "id": "f39aa56e-d474-4880-be2d-bcd7db68655d"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# find list of suggested CRS\n",
        "suggest_crs(canada_shape, type = \"projected\", units = \"m\") #note that the units must be in metres instead of km\n",
        "suggest_crs(us_states, type = \"projected\", units = \"m\")"
      ],
      "id": "eef515f1-38d2-4eaf-887e-deb23b5f6df8"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "This is quite an extensive list of candidates for our projected CRS. As\n",
        "you can see, the suggested CRS are very specific to the center of the\n",
        "geographic CRS - most of the suggested CRSs for Canada are artic/polar,\n",
        "while for the US they are based in Minnesota. Since our datasets are\n",
        "already in the same CRS, let’s stick with that."
      ],
      "id": "d23b47fb-6e76-477a-9ae9-578042afd3e3"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# selecting the columns we'll need from `us_states`\n",
        "us_shape <- us_states %>%\n",
        "            select(state = NAME, geometry) "
      ],
      "id": "5a83a044-e9bf-4bf1-bed2-288e6d90d2b0"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let’s plot our shape files on a map and then turn to merging our\n",
        "datasets."
      ],
      "id": "0fac2574-beb8-449f-b4a4-528d5bd38089"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "plot(canada_shape[\"province\"], reset = FALSE)\n",
        "plot(us_shape[\"state\"], add = TRUE)"
      ],
      "id": "e2544d2d-5a99-4902-a88c-3412fc77195a"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Creating our `sf` Object for the Distances\n",
        "\n",
        "Since our shapefiles are in two separate files, the approach we’re going\n",
        "to take is:\n",
        "\n",
        "1.  Create a vector with the labels `province` and `state`\n",
        "2.  Create a vector with the `distance` between each province-state pair\n",
        "3.  Merge those vectors together in a dataframe\n",
        "4.  Inner join the dataframe with the `trade_data` file\n",
        "\n",
        "By approaching the data wrangling step-by-step, we can see exactly what\n",
        "is going on and can check our work each step of the way. This is often\n",
        "preferred when working with multiple datasets and merging through\n",
        "variables that are not factors (we have to merge datasets through\n",
        "province-state names!).\n",
        "\n",
        "Let’s start with Step (1). We’ll create nested `for` loops, indexing\n",
        "provinces with `i` and states with `j`. Follow the comments of the code."
      ],
      "id": "c1d128d0-35e1-4bf2-835c-7b605d55ab0c"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "province_num <- nrow(canada_shape)    # each entry of `canada_shape` is a province\n",
        "states_num <- nrow(us_shape)    # each entry of `us_shape` is a state\n",
        "\n",
        "prov_state_vec <- c()    # create a placeholder vector that will contain the `province - state` pairs\n",
        "for (i in 1:province_num){    # start the loop with a province i, from a set of 1 to `province_num` provinces\n",
        "    prov_i <- canada_shape$province[i]    # select province name indexed by i\n",
        "\n",
        "    for (j in 1:states_num){    # for the selected province i, loop through the states, indexed by j\n",
        "        state_j <- us_shape$state[j]    # select state name indexed by j\n",
        "        prov_state_pair <- paste(prov_i, \"-\", state_j)    # paste prov i and state j as a string separated by a dash\n",
        "        prov_state_vec <- append(prov_state_vec, prov_state_pair)    # append the `province-state` pair \"i - j\" to the placeholder vector\n",
        "    }    # close state loop for state j and repeat process for state j + 1 \n",
        "}    # close province loop for province i and repeat process for province i + 1\n",
        "head(prov_state_vec)"
      ],
      "id": "9a4d05cb-569f-4268-86f9-1cc09889aecf"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let’s check if our loop worked as intended. We have 13 provinces and 49\n",
        "states, so we should have a total of $(13)(49) = 637$ province-state\n",
        "pairs.\n",
        "\n",
        "> **Note**: you can check the number of provinces and states by running\n",
        "> `nrow(canada_shape)` and `nrow(us_shape)`. We’re missing Hawaii and\n",
        "> Alaska, and we’re counting the District of Columbia as a state."
      ],
      "id": "77135a6d-0fbf-4ad4-9592-59a80cc293ca"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "length(prov_state_vec)"
      ],
      "id": "85bdede2-5a84-4b58-b434-a6718f7d9833"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "It looks like it worked! Now to Step 2. We repeat the same process, but\n",
        "instead of pasting strings, we calculate the distance between province\n",
        "`i` and state `j`. As noted earlier, our projected CRS is in meters, so\n",
        "those are the units of our distances.\n",
        "\n",
        "> **Note**: this operation might take a while to run."
      ],
      "id": "7391b22a-9064-4e39-bf98-c683da1b9e98"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "province_num <- nrow(canada_shape)\n",
        "states_num <- nrow(us_shape)\n",
        "\n",
        "distance_vec <- c()\n",
        "for (i in 1:province_num){\n",
        "    geo_prov_i <- st_make_valid(canada_shape$geometry[i])    # retrieve province geometry and adjust polygons with multiple vertices\n",
        "\n",
        "    for (j in 1:states_num) {\n",
        "        geo_state_j <- st_make_valid(us_shape$geometry[j])    # retrieve state geometry and adjust polygons with multiple vertices\n",
        "        distance <- as.double(st_distance(geo_prov_i, geo_state_j))    # calculate distance in meters\n",
        "        distance_vec <- append(distance_vec, distance)\n",
        "   }\n",
        "   \n",
        "}\n",
        "head(distance_vec)"
      ],
      "id": "af92e5cd-8b12-4832-af4a-ea0a78be786e"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Do you see the distances? For Step 3, let’s merge both vectors into a\n",
        "dataframe with `cbind`, and then separate the state and province match\n",
        "into 2 columns with `separate_wider_delim`."
      ],
      "id": "53ba78f2-418f-48e4-a0f8-6eca4c1b64f7"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# merging distance files\n",
        "distance_data <- as.data.frame(cbind(prov_state_vec, distance_vec)) %>%\n",
        "                separate_wider_delim(prov_state_vec, names = c(\"province\", \"state\"), delim = \"-\") %>%\n",
        "                mutate(province = trimws(province), state = trimws(state), distance_m = as.numeric(distance_vec)) %>%    # trimming white-space\n",
        "                select(-distance_vec)\n",
        "head(distance_data)"
      ],
      "id": "bb37de77-cfcf-4e1d-9a38-ca40fd621cd6"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "> **Note**: The reason we are able to use `cbind()` to merge the two\n",
        "> dataframes without a unique identifier is because they are ordered\n",
        "> exactly the same. Our two `for` loops create pairs in an identical\n",
        "> manner, so the distance pairs will ordered the same as our\n",
        "> province-state pairs. We would not be able to do this is if they were\n",
        "> ordered differently!\n",
        "\n",
        "As a sanity check, let’s calculate the number of pairs per province\n",
        "(each province should be paired with exactly 49 states) and confirm that\n",
        "provinces and states that border each other have distance equal zero."
      ],
      "id": "da9787e2-7892-4e24-a141-7fbe1abe8a09"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# group observations by `province` and calculate number of observations per province\n",
        "number_pairs <- distance_data %>%\n",
        "                group_by(province) %>%\n",
        "                summarize(n = n())\n",
        "number_pairs"
      ],
      "id": "ce710f97-7af4-4bf5-bec0-0fed0dd396cd"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# find border countries for distance in meters equal zero\n",
        "border_pairs <- distance_data %>%\n",
        "                filter(distance_m == 0)\n",
        "print(border_pairs)"
      ],
      "id": "d1b9e9d2-6f95-4cdb-8e95-d7ef6cfc2a58"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We only get 8 borders! That’s clearly not accurate.\n",
        "\n",
        "What’s going on here is that whenever dealing with geospatial data,\n",
        "we’re always working with approximations of actual physical objects, so\n",
        "the data is bound to have minor errors - it’s very hard to code physical\n",
        "elements into just a few data points! Let’s add a tolerance of 100m to\n",
        "our definition of border.\n",
        "\n",
        "> **Think Deeper**: how would you choose a reasonable tolerance for\n",
        "> distance calculations?"
      ],
      "id": "f88fa443-784f-4e7a-9b63-b80b938db055"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# find border countries for distance in meters equal zero\n",
        "border_pairs <- distance_data %>%\n",
        "                filter(distance_m < 100)\n",
        "print(border_pairs)"
      ],
      "id": "a3bc6789-87bd-48d1-88a2-3121210835a4"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Much better, but we’re still missing 2 border pairs - Ontario and\n",
        "Michigan and British Columbia and Idaho. Let’s check their distances."
      ],
      "id": "293d9dcc-96d6-4230-bc44-9061575d77da"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "missing_pairs <- distance_data %>%\n",
        "                        filter(province %in% c(\"Ontario\", \"British Columbia\"), state %in% c(\"Michigan\", \"Idaho\"))\n",
        "missing_pairs"
      ],
      "id": "070791cc-5d0d-4ca3-8bc8-84e676fb2789"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Our data says that those border pairs are a few kilometers apart. What\n",
        "happened here is that when we calculated the distance, we adjusted the\n",
        "borders of the `multipolygon` shapes to avoid duplicate edges with the\n",
        "function `st_make_valid()`. This affected the Ontario and British\n",
        "Columbia borders with some US states. Since this affects the distances\n",
        "in a similar manner, it likely doesn’t pose major issues to our\n",
        "analysis. Let’s proceed to Step 4."
      ],
      "id": "384550b9-fe8f-480a-970d-92454830e5a5"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# merge our `trade_data` with our `distance_data`\n",
        "geo_data <- merge(trade_data, distance_data, by = c(\"province\", \"state\"))%>%    # inner-join based on `province` and `state`\n",
        "                mutate(dist_km = if_else(distance_m < 1000, 1, distance_m/1000),   # setting borders to 1 km distance to avoid log zeros\n",
        "                       tmerch_mi = tmerch_value_usd/1000000,\n",
        "                       state_gdp_mi = gdp)%>%\n",
        "                select(province, state, dist_km, state_gdp_mi, tmerch_mi)%>%\n",
        "                filter(!is.na(dist_km), !is.na(tmerch_mi), !is.na(state_gdp_mi))    # remove pairs with no trade flows\n",
        "head(geo_data)"
      ],
      "id": "d7eccf14-aa83-4a32-a703-9203319a1bda"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Great! We finally compiled our data. Let’s look at how many pairs we\n",
        "have."
      ],
      "id": "7b3e8c91-d3aa-49e2-a69a-c0d2618880fa"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# group observations by `province` and calculate number of observations per province\n",
        "number_pairs_final <- geo_data %>%\n",
        "                group_by(province) %>%\n",
        "                summarize(n = n())\n",
        "number_pairs_final"
      ],
      "id": "5900ec48-4d62-462d-ba34-21ad2f970940"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "It looks like there are a few province-country pairs with few trade\n",
        "flows. Let’s filter out provinces that don’t trade with all 49 US\n",
        "states."
      ],
      "id": "a762b3ad-ae37-4928-9cdb-c83cca3fda5b"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# filter data\n",
        "model_data <- geo_data %>%\n",
        "              group_by(province) %>%\n",
        "              mutate(n = n()) %>%\n",
        "              filter(n == 49) %>%\n",
        "              select(-n)%>%\n",
        "              ungroup()\n",
        "\n",
        "nrow(model_data)"
      ],
      "id": "c0c878ff-e8d5-434e-a3c9-858357f69ca5"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "> **Think Deeper**: how would *not* removing those pairs affect the\n",
        "> results of our regression? Instead of filtering our dataset, what else\n",
        "> could we do to solve this issue?\n",
        "\n",
        "### Exploring our Data\n",
        "\n",
        "Now that we have our data, let’s plot a scatterplot to visualize our\n",
        "relationships. Let’s filter the data to only British Columbia pairs and\n",
        "plot the `distance` between the BC-state pairs against the `tmerch_mi`\n",
        "trade between BC-state pairs. Let’s also set the size of each data point\n",
        "to be the GDP of the US states."
      ],
      "id": "2ff32368-61af-4776-9f68-806fb47aa6a9"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# filter data to BC-state pairs\n",
        "BC_data <- model_data %>%\n",
        "            filter(province == \"British Columbia\")\n",
        "\n",
        "# plot dist_km against log(tmerch_mi) and add a line of best fit\n",
        "ggplot(BC_data, aes(x = dist_km, y = log(tmerch_mi), size = state_gdp_mi)) +\n",
        "            geom_point() +\n",
        "            geom_smooth(method = lm, se = FALSE, linewidth = 1)"
      ],
      "id": "7230a3a5-5f3f-4984-9dc5-4f20ffb54cb2"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The line of best fit shows a negative relationship between distance and\n",
        "trade. Also note that the largest data points are above the line: all\n",
        "else equal, higher GDP is associated with higher trade levels.\n",
        "\n",
        "### Running our Model\n",
        "\n",
        "Now, let’s run our model using `lm()`."
      ],
      "id": "1590b9fd-7b7a-48e5-a4e5-21e6363aa083"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "model1 <- lm(log(tmerch_mi) ~ log(dist_km) + province + log(state_gdp_mi), data = model_data)\n",
        "coeftest(model1, vcov = vcovHC)"
      ],
      "id": "9966a8f6-72ff-401d-84c1-334d7eb5c24d"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Our regression indicates that a 1% increase in distance is associated\n",
        "with a 0.5% decrease in trade flows. Our parameter is statistically\n",
        "significant at the 1% level. As expected, the state GDP control is also\n",
        "positive and significant.\n",
        "\n",
        "### Discussion\n",
        "\n",
        "Our geospatial analysis suggests that the relationships drawn by Tilberg\n",
        "hold for Canada and the US: distance is inversely proportional to trade\n",
        "flows. The negative relationship between distance and trade flows has\n",
        "been consistently found in the literature, but the magnitude of the\n",
        "effects vary with time and geography.\n",
        "\n",
        "In a comprehensive study about the effects of distance on bilateral\n",
        "trade, Disdier and Head (2008) compiled 1467 different distance effect\n",
        "estimates from 103 papers. They found that the mean distance effect is\n",
        "0.9 - that is, a 10% increase in distance lowers bilateral trade by\n",
        "about 9%. Furthermore, 90% of the estimates compiled fall within the\n",
        "range of 0.28 to 1.55, dependent on the time period and geography of the\n",
        "study. It seems that our results are in line with what the researchers\n",
        "found, which adds to the credibility of our estimates from a simple\n",
        "model.\n",
        "\n",
        "This example concludes our modules on geospatial analysis. If you’re\n",
        "curious to learn more about the topics explored in these modules, refer\n",
        "to:\n",
        "\n",
        "-   [Geocomputation with R](https://r.geocompx.org/intro): for more\n",
        "    context around Geospatial analysis in general\n",
        "-   [This blog\n",
        "    post](https://cran.r-project.org/web/packages/gravity/vignettes/crash-course-on-gravity-models.html):\n",
        "    for more ways to model gravity\n",
        "-   [This user\n",
        "    guide](https://www.unescap.org/sites/default/files/Gravity-model-in-R_1.pdf):\n",
        "    for more context aroung the Gravity Equation of International Trade\n",
        "    in R"
      ],
      "id": "9b2baa34-a788-4594-b046-ca71b24fdd83"
    }
  ],
  "nbformat": 4,
  "nbformat_minor": 5,
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    "kernelspec": {
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      "display_name": "R",
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