module3updated_LS_DS_133_High_Dimensional_Data_Assignment.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "module3updated_LS_DS_133_High_Dimensional_Data_Assignment.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/geraldm24/DS-Unit-1-Sprint-3-Linear-Algebra/blob/master/module3updated_LS_DS_133_High_Dimensional_Data_Assignment.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7wMWCkE1RZpM",
        "colab_type": "text"
      },
      "source": [
        "# Vertical Line Test"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W0-g7aprRv2j",
        "colab_type": "text"
      },
      "source": [
        "## 1.1 Create two graphs, one that passes the vertical line test and one that does not."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fIJhCtF6RW_U",
        "colab_type": "code",
        "outputId": "3f577bb0-5715-4856-d613-c6b1d99e4416",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 294
        }
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "nx  = [1, 3, 5, 7]\n",
        "ny = [1, 5, 1, 5]\n",
        "\n",
        "plt.plot(nx, ny, label=\"line N\")\n",
        "plt.plot()\n",
        "\n",
        "plt.xlabel(\"x axis\")\n",
        "plt.ylabel(\"y axis\")\n",
        "plt.title(\"Make N\")\n",
        "plt.legend()\n",
        "plt.show()\n"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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621ECnle+IxCRVOAKYPNpDyUBJafcLuXbxQIRmSMiW0Vka0VFhVMx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\nrkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tnpGRmIVdlt2",
        "colab_type": "code",
        "outputId": "8c58f89e-1cac-486f-9fe9-167d1b2fb7f2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 294
        }
      },
      "source": [
        "ox = [-2.2, -2, -2, -1.5, 1, 1, 0, 1, 1, 1.5, 2, 2, 2.2]\n",
        "oy = [0, 1, -1, 3, 5, -5, -3, 5, -5, -3, 1, -1, 0]\n",
        "plt.plot(ox, oy, label=\"line O\")\n",
        "plt.plot()\n",
        "\n",
        "plt.xlabel(\"x axis\")\n",
        "plt.ylabel(\"y axis\")\n",
        "plt.title(\"Make O\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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9Rg1AxEPK/PevaGf++5EagIhHtpccZJEy/30rmpn/fqUGIOIRZf77WzQz//1K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\nEZGAUgMQEQkoNQARkYBSAxARCaj/D2mB8kbdvdXSAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ckeTKqMgRy7g",
        "colab_type": "text"
      },
      "source": [
        "## 1.2 Why are graphs that don't pass the vertical line test not considered \"functions?\""
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Gtl20YeDR6x-",
        "colab_type": "text"
      },
      "source": [
        "Because when you pass an x into a function it cannot have multiple outputs"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g21uN62xSKSk",
        "colab_type": "text"
      },
      "source": [
        "# Functions as Relations"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gwkcV-EMSMNd",
        "colab_type": "text"
      },
      "source": [
        "## 2.1 Which of the following relations are functions? Why?\n",
        "\n",
        "\\begin{align}\n",
        "\\text{Relation 1: } \\{(1, 2), (3, 2), (1, 3)\\}\n",
        "\\\\\n",
        "\\text{Relation 2: } \\{(1, 3), (2, 3), (6, 7)\\}\n",
        "\\\\\n",
        "\\text{Relation 3: } \\{(9, 4), (2, 1), (9, 6)\\}\n",
        "\\\\\n",
        "\\text{Relation 4: } \\{(6, 2), (8, 3), (6, 4)\\}\n",
        "\\\\\n",
        "\\text{Relation 5: } \\{(2, 6), (2, 7), (2, 4)\\}\n",
        "\\end{align}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qaRs0BxBkqU_",
        "colab_type": "text"
      },
      "source": [
        "relation 2 because it's the only relation with unique x coordinates"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "y0U30PrlTAAa",
        "colab_type": "text"
      },
      "source": [
        "# Functions as a mapping between dimensions\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pw-OU9qmT5Ua",
        "colab_type": "text"
      },
      "source": [
        "## 3.1 for the following functions what is the dimensionality of the domain (input) and codomain (range/output)?\n",
        "\n",
        "\\begin{align}\n",
        "m(𝑥_1,𝑥_2,𝑥_3)=(x_1+x_2, x_1+x_3, x_2+x_3)\n",
        "\\\\\n",
        "n(𝑥_1,𝑥_2,𝑥_3,𝑥_4)=(x_2^2 + x_3, x_2x_4)\n",
        "\\end{align}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "STqNsDtrma31",
        "colab_type": "text"
      },
      "source": [
        "m is 1d and 3d\n",
        "n is 1d and 2d"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k4tKHjdHUevC",
        "colab_type": "text"
      },
      "source": [
        "## 3.2 Do you think it's possible to create a function that maps from a lower dimensional space to a higher dimensional space? If so, provide an example."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2nEWvwVyVWdW",
        "colab_type": "text"
      },
      "source": [
        "# Vector Transformations"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1n0-6FsYVcVk",
        "colab_type": "text"
      },
      "source": [
        "## 4.1 Plug the corresponding unit vectors into each function. Use the output vectors to create a transformation matrix.\n",
        "\n",
        "\\begin{align}\n",
        "p(\\begin{bmatrix}x_1 \\\\ x_2 \\end{bmatrix}) = \\begin{bmatrix} x_1 + 3x_2 \\\\2 x_2 - x_1 \\\\  \\end{bmatrix}\n",
        "\\\\\n",
        "\\\\\n",
        "q(\\begin{bmatrix}x_1 \\\\ x_2 \\\\ x_3\\end{bmatrix}) = \\begin{bmatrix} 4x_1 + x_2 + 2x_3 \\\\2 x_2 - x_1 + 3x_3 \\\\ 5x_1 - 2x_3 + x_2  \\end{bmatrix}\n",
        "\\end{align}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1wpv-gp6qMYj",
        "colab_type": "text"
      },
      "source": [
        "p = [1,3],[-1,2]\n",
        "q= [4,1,2],[-1,2,3],[5,1,-2]\n",
        "\n",
        "```\n",
        "# This is formatted as code\n",
        "```\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VROBGRfquGhB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "Q = [4,-1,5],[1,2,1],[2,3,-2]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n5HUOQIxZ2gp",
        "colab_type": "text"
      },
      "source": [
        "## 4.2 Verify that your transformation matrices are correct by choosing an input matrix and calculating the result both via the traditional functions above and also via vector-matrix multiplication."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0UANR1IEaVWE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "F=[1,0,0],[0,1,0],[0,0,1]\n",
        "np.dot(F,Q)\n",
        "U=[1,2,0]\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vEoiri3mak7j",
        "colab_type": "text"
      },
      "source": [
        "# Eigenvalues and Eigenvectors"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5HY0R4u7anIr",
        "colab_type": "text"
      },
      "source": [
        "## 5.1 In your own words, give an explanation for the intuition behind eigenvalues and eigenvectors."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VdehMwBtatKI",
        "colab_type": "text"
      },
      "source": [
        "# The Curse of Dimensionality"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4oVrJax-a3SK",
        "colab_type": "text"
      },
      "source": [
        "## 6.1 What are some of the challenges of working with high dimensional spaces?\n",
        "\n",
        "1. Overfitting \n",
        "2. our brains are use to spaces of 2d and 3d so visualizing data is challenging as distance between points begins to be less distinguishable. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZiBJxsZla88c",
        "colab_type": "text"
      },
      "source": [
        "## 6.2 What is the rule of thumb for how many observations you should have compared to parameters in your model?\n",
        "\n",
        "You want 5 times more data than you have of features/parameters."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NZmqdeygbHJx",
        "colab_type": "text"
      },
      "source": [
        "# Principal Component Analysis"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7iEheetpbJdN",
        "colab_type": "text"
      },
      "source": [
        "## 7.1 Code for loading and cleaning the 2013 national dataset from the [Housing Affordability Data System (HADS)](https://www.huduser.gov/portal/datasets/hads/hads.html) --housing data, can be found below. \n",
        "\n",
        "## Perform PCA on the processed dataset `national_processed` (Make sure you standardize your data!) and then make a scatterplot of PC1 against PC2. Some of our discussion and work around PCA with this dataset will continue during tomorrow's lecture and assignment.\n",
        "\n",
        "Not only does this dataset have decent amount columns to begin with (99), but in preparing the data for PCA we have also [one-hot-encoded](https://hackernoon.com/what-is-one-hot-encoding-why-and-when-do-you-have-to-use-it-e3c6186d008f#targetText=One%20hot%20encoding%20is%20a,the%20entry%20in%20the%20dataset.) all of the categorical variables. This has the effect of creating a new column for each individual category of each categorical variable. After processing this dataset has 64738 columns. --Das a lot of columns.\n",
        "\n",
        "Don't worry too much about the mechanics of one-hot encoding right now, you will learn and experiment with a whole bunch of categorical encoding approaches in unit 2. \n",
        "\n",
        "The code below will read in the dataset and perform the one-hot encoding of the categorical variables. Start adding your PCA code at the bottom of the provided code."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Us4nNFs02HlD",
        "colab_type": "code",
        "outputId": "669d032f-bdbd-4683-9205-957b01d22451",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 347
        }
      },
      "source": [
        "from urllib.request import urlopen\n",
        "from zipfile import ZipFile\n",
        "from io import BytesIO\n",
        "import os.path\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Read Natinal Data \n",
        "national_url = 'https://www.huduser.gov/portal/datasets/hads/hads2013n_ASCII.zip'\n",
        "national_file = 'thads2013n.txt'\n",
        "\n",
        "if os.path.exists(national_file):\n",
        "    national = pd.read_csv(national_file)\n",
        "else: \n",
        "    z_national = urlopen(national_url)\n",
        "    zip_national = ZipFile(BytesIO(z_national.read())).extract(national_file)\n",
        "    national = pd.read_csv(zip_national)\n",
        "\n",
        "print(national.shape)\n",
        "national.head()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(64535, 99)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
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              "      <td>-9</td>\n",
              "      <td>55846</td>\n",
              "      <td>13750</td>\n",
              "      <td>22897</td>\n",
              "      <td>36614</td>\n",
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              "      <td>4</td>\n",
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              "      <td>4</td>\n",
              "      <td>97.093197</td>\n",
              "      <td>2</td>\n",
              "      <td>'1 Adequate'</td>\n",
              "      <td>'-5'</td>\n",
              "      <td>'1980-1989'</td>\n",
              "      <td>'1 Single Family'</td>\n",
              "      <td>'4 4BR+'</td>\n",
              "      <td>'1 Owner'</td>\n",
              "      <td>'4 200%+ Poverty'</td>\n",
              "      <td>'4 200%+ Poverty'</td>\n",
              "      <td>'4 200%+ Poverty'</td>\n",
              "      <td>'4 200%+ Poverty'</td>\n",
              "      <td>'3 150-200% Poverty'</td>\n",
              "      <td>'3 GT FMR'</td>\n",
              "      <td>'3 GT FMR'</td>\n",
              "      <td>'3 GT FMR'</td>\n",
              "      <td>'2 50.1 - 100% FMR'</td>\n",
              "      <td>'2 50.1 - 100% FMR'</td>\n",
              "      <td>'4 60 - 80% AMI'</td>\n",
              "      <td>'5 80 - 100% AMI'</td>\n",
              "      <td>'6 100 - 120% AMI'</td>\n",
              "      <td>'4 60 - 80% AMI'</td>\n",
              "      <td>'4 60 - 80% AMI'</td>\n",
              "      <td>'.'</td>\n",
              "      <td>'3 50% or More'</td>\n",
              "      <td>'-5'</td>\n",
              "      <td>'-5'</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>'100006520140'</td>\n",
              "      <td>67</td>\n",
              "      <td>'5'</td>\n",
              "      <td>'3'</td>\n",
              "      <td>55846</td>\n",
              "      <td>949</td>\n",
              "      <td>13750</td>\n",
              "      <td>22897</td>\n",
              "      <td>36614</td>\n",
              "      <td>13964</td>\n",
              "      <td>3</td>\n",
              "      <td>1985</td>\n",
              "      <td>'1'</td>\n",
              "      <td>1</td>\n",
              "      <td>200000</td>\n",
              "      <td>-6</td>\n",
              "      <td>'1'</td>\n",
              "      <td>1</td>\n",
              "      <td>6</td>\n",
              "      <td>2364.585097</td>\n",
              "      <td>2</td>\n",
              "      <td>32220</td>\n",
              "      <td>'1'</td>\n",
              "      <td>279</td>\n",
              "      <td>1</td>\n",
              "      <td>'1'</td>\n",
              "      <td>179.000000</td>\n",
              "      <td>70.666667</td>\n",
              "      <td>1578.857612</td>\n",
              "      <td>2351.169341</td>\n",
              "      <td>1820.442900</td>\n",
              "      <td>1411.700224</td>\n",
              "      <td>0</td>\n",
              "      <td>-9</td>\n",
              "      <td>55846</td>\n",
              "      <td>13750</td>\n",
              "      <td>22897</td>\n",
              "      <td>36614</td>\n",
              "      <td>44676.8</td>\n",
              "      <td>17875.000000</td>\n",
              "      <td>...</td>\n",
              "      <td>4</td>\n",
              "      <td>191.827492</td>\n",
              "      <td>3</td>\n",
              "      <td>161.926709</td>\n",
              "      <td>7</td>\n",
              "      <td>673.494512</td>\n",
              "      <td>4</td>\n",
              "      <td>247.752301</td>\n",
              "      <td>3</td>\n",
              "      <td>97.224801</td>\n",
              "      <td>5</td>\n",
              "      <td>404.382763</td>\n",
              "      <td>4</td>\n",
              "      <td>148.756610</td>\n",
              "      <td>3</td>\n",
              "      <td>'1 Adequate'</td>\n",
              "      <td>'-5'</td>\n",
              "      <td>'1980-1989'</td>\n",
              "      <td>'1 Single Family'</td>\n",
              "      <td>'3 3BR'</td>\n",
              "      <td>'1 Owner'</td>\n",
              "      <td>'4 200%+ Poverty'</td>\n",
              "      <td>'4 200%+ Poverty'</td>\n",
              "      <td>'4 200%+ Poverty'</td>\n",
              "      <td>'4 200%+ Poverty'</td>\n",
              "      <td>'4 200%+ Poverty'</td>\n",
              "      <td>'3 GT FMR'</td>\n",
              "      <td>'3 GT FMR'</td>\n",
              "      <td>'3 GT FMR'</td>\n",
              "      <td>'3 GT FMR'</td>\n",
              "      <td>'2 50.1 - 100% FMR'</td>\n",
              "      <td>'6 100 - 120% AMI'</td>\n",
              "      <td>'7 120% AMI +'</td>\n",
              "      <td>'7 120% AMI +'</td>\n",
              "      <td>'5 80 - 100% AMI'</td>\n",
              "      <td>'4 60 - 80% AMI'</td>\n",
              "      <td>'.'</td>\n",
              "      <td>'1 Less than 30%'</td>\n",
              "      <td>'-5'</td>\n",
              "      <td>'-5'</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>'100007130148'</td>\n",
              "      <td>26</td>\n",
              "      <td>'1'</td>\n",
              "      <td>'3'</td>\n",
              "      <td>60991</td>\n",
              "      <td>737</td>\n",
              "      <td>14801</td>\n",
              "      <td>24628</td>\n",
              "      <td>39421</td>\n",
              "      <td>15492</td>\n",
              "      <td>2</td>\n",
              "      <td>1980</td>\n",
              "      <td>'1'</td>\n",
              "      <td>1</td>\n",
              "      <td>-6</td>\n",
              "      <td>-6</td>\n",
              "      <td>'2'</td>\n",
              "      <td>100</td>\n",
              "      <td>4</td>\n",
              "      <td>2314.524902</td>\n",
              "      <td>2</td>\n",
              "      <td>96874</td>\n",
              "      <td>'1'</td>\n",
              "      <td>759</td>\n",
              "      <td>5</td>\n",
              "      <td>'2'</td>\n",
              "      <td>146.000000</td>\n",
              "      <td>12.500000</td>\n",
              "      <td>759.000000</td>\n",
              "      <td>759.000000</td>\n",
              "      <td>759.000000</td>\n",
              "      <td>759.000000</td>\n",
              "      <td>96900</td>\n",
              "      <td>0</td>\n",
              "      <td>60991</td>\n",
              "      <td>14801</td>\n",
              "      <td>24628</td>\n",
              "      <td>39421</td>\n",
              "      <td>48792.8</td>\n",
              "      <td>16651.125000</td>\n",
              "      <td>...</td>\n",
              "      <td>3</td>\n",
              "      <td>102.985075</td>\n",
              "      <td>3</td>\n",
              "      <td>55.308707</td>\n",
              "      <td>3</td>\n",
              "      <td>195.972115</td>\n",
              "      <td>3</td>\n",
              "      <td>102.985075</td>\n",
              "      <td>3</td>\n",
              "      <td>55.308707</td>\n",
              "      <td>3</td>\n",
              "      <td>195.972115</td>\n",
              "      <td>3</td>\n",
              "      <td>102.985075</td>\n",
              "      <td>3</td>\n",
              "      <td>'1 Adequate'</td>\n",
              "      <td>'Central City'</td>\n",
              "      <td>'1980-1989'</td>\n",
              "      <td>'5 50+ units'</td>\n",
              "      <td>'2 2BR'</td>\n",
              "      <td>'2 Renter'</td>\n",
              "      <td>'3 150-200% Poverty'</td>\n",
              "      <td>'3 150-200% Poverty'</td>\n",
              "      <td>'3 150-200% Poverty'</td>\n",
              "      <td>'3 150-200% Poverty'</td>\n",
              "      <td>'4 200%+ Poverty'</td>\n",
              "      <td>'3 GT FMR'</td>\n",
              "      <td>'3 GT FMR'</td>\n",
              "      <td>'3 GT FMR'</td>\n",
              "      <td>'3 GT FMR'</td>\n",
              "      <td>'3 GT FMR'</td>\n",
              "      <td>'3 50 - 60% AMI'</td>\n",
              "      <td>'3 50 - 60% AMI'</td>\n",
              "      <td>'3 50 - 60% AMI'</td>\n",
              "      <td>'3 50 - 60% AMI'</td>\n",
              "      <td>'7 120% AMI +'</td>\n",
              "      <td>'0 Not Assisted'</td>\n",
              "      <td>'1 Less than 30%'</td>\n",
              "      <td>'-5'</td>\n",
              "      <td>'-5'</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>5 rows × 99 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "          CONTROL  AGE1 METRO3  ...          FMTBURDEN  FMTREGION  FMTSTATUS\n",
              "0  '100003130103'    82    '3'  ...     '2 30% to 50%'       '-5'       '-5'\n",
              "1  '100006110249'    50    '5'  ...  '1 Less than 30%'       '-5'       '-5'\n",
              "2  '100006370140'    53    '5'  ...    '3 50% or More'       '-5'       '-5'\n",
              "3  '100006520140'    67    '5'  ...  '1 Less than 30%'       '-5'       '-5'\n",
              "4  '100007130148'    26    '1'  ...  '1 Less than 30%'       '-5'       '-5'\n",
              "\n",
              "[5 rows x 99 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O5zrMTud2qFU",
        "colab_type": "code",
        "outputId": "c41f9724-c1f9-4b14-b678-14f4e4d0d3cb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        }
      },
      "source": [
        "# Look at datatypes\n",
        "# a lot of object datatypes even though they seem to be strings of numbers.\n",
        "national.dtypes"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "CONTROL            object\n",
              "AGE1                int64\n",
              "METRO3             object\n",
              "REGION             object\n",
              "LMED                int64\n",
              "                    ...  \n",
              "FMTINCRELAMICAT    object\n",
              "FMTASSISTED        object\n",
              "FMTBURDEN          object\n",
              "FMTREGION          object\n",
              "FMTSTATUS          object\n",
              "Length: 99, dtype: object"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yIrOjVmd2yLz",
        "colab_type": "code",
        "outputId": "6924e9d5-b87f-44b7-a9b4-6913593c4879",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "# check for null values\n",
        "national.isnull().sum().any()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2u9tdmwX3KL_",
        "colab_type": "code",
        "outputId": "7ee3b324-64e9-4660-e570-723173b18b34",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "# check for number of categorical vs numeric columns\n",
        "cat_cols = national.columns[national.dtypes=='object']\n",
        "num_cols = national.columns[national.dtypes!='object']\n",
        "\n",
        "print(f'{len(cat_cols)} categorical columns')\n",
        "print(f'{len(num_cols)} numerical columns')"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "32 categorical columns\n",
            "67 numerical columns\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UMHOtOs_3gcL",
        "colab_type": "code",
        "outputId": "ef242c46-a3c9-4317-f8ed-ebb624a447c6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        }
      },
      "source": [
        "# We're making a copy of our data in case we mess something up.\n",
        "national_processed = national.copy()\n",
        "\n",
        "# Categorically Encode our Variables:\n",
        "# They need to all be numeric before we do PCA.\n",
        "# https://pbpython.com/categorical-encoding.html\n",
        "\n",
        "# Cast categorical columns to \"category\" data type\n",
        "national_processed[cat_cols] = national_processed[cat_cols].astype('category')\n",
        "\n",
        "national_processed.dtypes"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "CONTROL            category\n",
              "AGE1                  int64\n",
              "METRO3             category\n",
              "REGION             category\n",
              "LMED                  int64\n",
              "                     ...   \n",
              "FMTINCRELAMICAT    category\n",
              "FMTASSISTED        category\n",
              "FMTBURDEN          category\n",
              "FMTREGION          category\n",
              "FMTSTATUS          category\n",
              "Length: 99, dtype: object"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ymxU-aPtQ1eq",
        "colab_type": "code",
        "outputId": "ab914601-0b06-4415-f831-c3d93b567eb1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 264
        }
      },
      "source": [
        "# Replace all category cell values with their numeric category codes\n",
        "for col in cat_cols:\n",
        "  national_processed[col] = national_processed[col].cat.codes\n",
        "\n",
        "print(national_processed.shape)\n",
        "national_processed.head()"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(64535, 99)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
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              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>CONTROL</th>\n",
              "      <th>AGE1</th>\n",
              "      <th>METRO3</th>\n",
              "      <th>REGION</th>\n",
              "      <th>LMED</th>\n",
              "      <th>FMR</th>\n",
              "      <th>L30</th>\n",
              "      <th>L50</th>\n",
              "      <th>L80</th>\n",
              "      <th>IPOV</th>\n",
              "      <th>BEDRMS</th>\n",
              "      <th>BUILT</th>\n",
              "      <th>STATUS</th>\n",
              "      <th>TYPE</th>\n",
              "      <th>VALUE</th>\n",
              "      <th>VACANCY</th>\n",
              "      <th>TENURE</th>\n",
              "      <th>NUNITS</th>\n",
              "      <th>ROOMS</th>\n",
              "      <th>WEIGHT</th>\n",
              "      <th>PER</th>\n",
              "      <th>ZINC2</th>\n",
              "      <th>ZADEQ</th>\n",
              "      <th>ZSMHC</th>\n",
              "      <th>STRUCTURETYPE</th>\n",
              "      <th>OWNRENT</th>\n",
              "      <th>UTILITY</th>\n",
              "      <th>OTHERCOST</th>\n",
              "      <th>COST06</th>\n",
              "      <th>COST12</th>\n",
              "      <th>COST08</th>\n",
              "      <th>COSTMED</th>\n",
              "      <th>TOTSAL</th>\n",
              "      <th>ASSISTED</th>\n",
              "      <th>GLMED</th>\n",
              "      <th>GL30</th>\n",
              "      <th>GL50</th>\n",
              "      <th>GL80</th>\n",
              "      <th>APLMED</th>\n",
              "      <th>ABL30</th>\n",
              "      <th>...</th>\n",
              "      <th>COST08RELPOVCAT</th>\n",
              "      <th>COST08RELFMRPCT</th>\n",
              "      <th>COST08RELFMRCAT</th>\n",
              "      <th>COST12RELAMIPCT</th>\n",
              "      <th>COST12RELAMICAT</th>\n",
              "      <th>COST12RELPOVPCT</th>\n",
              "      <th>COST12RELPOVCAT</th>\n",
              "      <th>COST12RELFMRPCT</th>\n",
              "      <th>COST12RELFMRCAT</th>\n",
              "      <th>COSTMedRELAMIPCT</th>\n",
              "      <th>COSTMedRELAMICAT</th>\n",
              "      <th>COSTMedRELPOVPCT</th>\n",
              "      <th>COSTMedRELPOVCAT</th>\n",
              "      <th>COSTMedRELFMRPCT</th>\n",
              "      <th>COSTMedRELFMRCAT</th>\n",
              "      <th>FMTZADEQ</th>\n",
              "      <th>FMTMETRO3</th>\n",
              "      <th>FMTBUILT</th>\n",
              "      <th>FMTSTRUCTURETYPE</th>\n",
              "      <th>FMTBEDRMS</th>\n",
              "      <th>FMTOWNRENT</th>\n",
              "      <th>FMTCOST06RELPOVCAT</th>\n",
              "      <th>FMTCOST08RELPOVCAT</th>\n",
              "      <th>FMTCOST12RELPOVCAT</th>\n",
              "      <th>FMTCOSTMEDRELPOVCAT</th>\n",
              "      <th>FMTINCRELPOVCAT</th>\n",
              "      <th>FMTCOST06RELFMRCAT</th>\n",
              "      <th>FMTCOST08RELFMRCAT</th>\n",
              "      <th>FMTCOST12RELFMRCAT</th>\n",
              "      <th>FMTCOSTMEDRELFMRCAT</th>\n",
              "      <th>FMTINCRELFMRCAT</th>\n",
              "      <th>FMTCOST06RELAMICAT</th>\n",
              "      <th>FMTCOST08RELAMICAT</th>\n",
              "      <th>FMTCOST12RELAMICAT</th>\n",
              "      <th>FMTCOSTMEDRELAMICAT</th>\n",
              "      <th>FMTINCRELAMICAT</th>\n",
              "      <th>FMTASSISTED</th>\n",
              "      <th>FMTBURDEN</th>\n",
              "      <th>FMTREGION</th>\n",
              "      <th>FMTSTATUS</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>82</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>73738</td>\n",
              "      <td>956</td>\n",
              "      <td>15738</td>\n",
              "      <td>26213</td>\n",
              "      <td>40322</td>\n",
              "      <td>11067</td>\n",
              "      <td>2</td>\n",
              "      <td>2006</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>40000</td>\n",
              "      <td>-6</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>6</td>\n",
              "      <td>3117.394239</td>\n",
              "      <td>1</td>\n",
              "      <td>18021</td>\n",
              "      <td>1</td>\n",
              "      <td>533</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>169.000000</td>\n",
              "      <td>213.750000</td>\n",
              "      <td>648.588189</td>\n",
              "      <td>803.050535</td>\n",
              "      <td>696.905247</td>\n",
              "      <td>615.156712</td>\n",
              "      <td>0</td>\n",
              "      <td>-9</td>\n",
              "      <td>73738</td>\n",
              "      <td>15738</td>\n",
              "      <td>26213</td>\n",
              "      <td>40322</td>\n",
              "      <td>51616.6</td>\n",
              "      <td>20234.571429</td>\n",
              "      <td>...</td>\n",
              "      <td>4</td>\n",
              "      <td>72.898038</td>\n",
              "      <td>2</td>\n",
              "      <td>48.402635</td>\n",
              "      <td>2</td>\n",
              "      <td>290.250487</td>\n",
              "      <td>4</td>\n",
              "      <td>84.001102</td>\n",
              "      <td>2</td>\n",
              "      <td>37.077624</td>\n",
              "      <td>2</td>\n",
              "      <td>222.339102</td>\n",
              "      <td>4</td>\n",
              "      <td>64.346936</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>5</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>50</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>55846</td>\n",
              "      <td>1100</td>\n",
              "      <td>17165</td>\n",
              "      <td>28604</td>\n",
              "      <td>45744</td>\n",
              "      <td>24218</td>\n",
              "      <td>4</td>\n",
              "      <td>1980</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>130000</td>\n",
              "      <td>-6</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>6</td>\n",
              "      <td>2150.725544</td>\n",
              "      <td>4</td>\n",
              "      <td>122961</td>\n",
              "      <td>1</td>\n",
              "      <td>487</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>245.333333</td>\n",
              "      <td>58.333333</td>\n",
              "      <td>1167.640781</td>\n",
              "      <td>1669.643405</td>\n",
              "      <td>1324.671218</td>\n",
              "      <td>1058.988479</td>\n",
              "      <td>123000</td>\n",
              "      <td>-9</td>\n",
              "      <td>55846</td>\n",
              "      <td>17165</td>\n",
              "      <td>28604</td>\n",
              "      <td>45744</td>\n",
              "      <td>55846.0</td>\n",
              "      <td>19911.400000</td>\n",
              "      <td>...</td>\n",
              "      <td>4</td>\n",
              "      <td>120.424656</td>\n",
              "      <td>3</td>\n",
              "      <td>103.094063</td>\n",
              "      <td>6</td>\n",
              "      <td>275.768999</td>\n",
              "      <td>4</td>\n",
              "      <td>151.785764</td>\n",
              "      <td>3</td>\n",
              "      <td>65.388468</td>\n",
              "      <td>4</td>\n",
              "      <td>174.909320</td>\n",
              "      <td>3</td>\n",
              "      <td>96.271680</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>5</td>\n",
              "      <td>3</td>\n",
              "      <td>7</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>53</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>55846</td>\n",
              "      <td>1100</td>\n",
              "      <td>13750</td>\n",
              "      <td>22897</td>\n",
              "      <td>36614</td>\n",
              "      <td>15470</td>\n",
              "      <td>4</td>\n",
              "      <td>1985</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>150000</td>\n",
              "      <td>-6</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>7</td>\n",
              "      <td>2213.789404</td>\n",
              "      <td>2</td>\n",
              "      <td>27974</td>\n",
              "      <td>1</td>\n",
              "      <td>1405</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>159.000000</td>\n",
              "      <td>37.500000</td>\n",
              "      <td>1193.393209</td>\n",
              "      <td>1772.627006</td>\n",
              "      <td>1374.582175</td>\n",
              "      <td>1068.025168</td>\n",
              "      <td>28000</td>\n",
              "      <td>-9</td>\n",
              "      <td>55846</td>\n",
              "      <td>13750</td>\n",
              "      <td>22897</td>\n",
              "      <td>36614</td>\n",
              "      <td>44676.8</td>\n",
              "      <td>19937.500000</td>\n",
              "      <td>...</td>\n",
              "      <td>4</td>\n",
              "      <td>124.962016</td>\n",
              "      <td>3</td>\n",
              "      <td>109.452905</td>\n",
              "      <td>6</td>\n",
              "      <td>458.339239</td>\n",
              "      <td>4</td>\n",
              "      <td>161.147910</td>\n",
              "      <td>3</td>\n",
              "      <td>65.946449</td>\n",
              "      <td>4</td>\n",
              "      <td>276.153890</td>\n",
              "      <td>4</td>\n",
              "      <td>97.093197</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>67</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>55846</td>\n",
              "      <td>949</td>\n",
              "      <td>13750</td>\n",
              "      <td>22897</td>\n",
              "      <td>36614</td>\n",
              "      <td>13964</td>\n",
              "      <td>3</td>\n",
              "      <td>1985</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>200000</td>\n",
              "      <td>-6</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>6</td>\n",
              "      <td>2364.585097</td>\n",
              "      <td>2</td>\n",
              "      <td>32220</td>\n",
              "      <td>1</td>\n",
              "      <td>279</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>179.000000</td>\n",
              "      <td>70.666667</td>\n",
              "      <td>1578.857612</td>\n",
              "      <td>2351.169341</td>\n",
              "      <td>1820.442900</td>\n",
              "      <td>1411.700224</td>\n",
              "      <td>0</td>\n",
              "      <td>-9</td>\n",
              "      <td>55846</td>\n",
              "      <td>13750</td>\n",
              "      <td>22897</td>\n",
              "      <td>36614</td>\n",
              "      <td>44676.8</td>\n",
              "      <td>17875.000000</td>\n",
              "      <td>...</td>\n",
              "      <td>4</td>\n",
              "      <td>191.827492</td>\n",
              "      <td>3</td>\n",
              "      <td>161.926709</td>\n",
              "      <td>7</td>\n",
              "      <td>673.494512</td>\n",
              "      <td>4</td>\n",
              "      <td>247.752301</td>\n",
              "      <td>3</td>\n",
              "      <td>97.224801</td>\n",
              "      <td>5</td>\n",
              "      <td>404.382763</td>\n",
              "      <td>4</td>\n",
              "      <td>148.756610</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>5</td>\n",
              "      <td>6</td>\n",
              "      <td>6</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>26</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>60991</td>\n",
              "      <td>737</td>\n",
              "      <td>14801</td>\n",
              "      <td>24628</td>\n",
              "      <td>39421</td>\n",
              "      <td>15492</td>\n",
              "      <td>2</td>\n",
              "      <td>1980</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>-6</td>\n",
              "      <td>-6</td>\n",
              "      <td>2</td>\n",
              "      <td>100</td>\n",
              "      <td>4</td>\n",
              "      <td>2314.524902</td>\n",
              "      <td>2</td>\n",
              "      <td>96874</td>\n",
              "      <td>1</td>\n",
              "      <td>759</td>\n",
              "      <td>5</td>\n",
              "      <td>1</td>\n",
              "      <td>146.000000</td>\n",
              "      <td>12.500000</td>\n",
              "      <td>759.000000</td>\n",
              "      <td>759.000000</td>\n",
              "      <td>759.000000</td>\n",
              "      <td>759.000000</td>\n",
              "      <td>96900</td>\n",
              "      <td>0</td>\n",
              "      <td>60991</td>\n",
              "      <td>14801</td>\n",
              "      <td>24628</td>\n",
              "      <td>39421</td>\n",
              "      <td>48792.8</td>\n",
              "      <td>16651.125000</td>\n",
              "      <td>...</td>\n",
              "      <td>3</td>\n",
              "      <td>102.985075</td>\n",
              "      <td>3</td>\n",
              "      <td>55.308707</td>\n",
              "      <td>3</td>\n",
              "      <td>195.972115</td>\n",
              "      <td>3</td>\n",
              "      <td>102.985075</td>\n",
              "      <td>3</td>\n",
              "      <td>55.308707</td>\n",
              "      <td>3</td>\n",
              "      <td>195.972115</td>\n",
              "      <td>3</td>\n",
              "      <td>102.985075</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>5</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>7</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>5 rows × 99 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "   CONTROL  AGE1  METRO3  REGION  ...  FMTASSISTED  FMTBURDEN  FMTREGION  FMTSTATUS\n",
              "0        0    82       2       0  ...            0          2          0          0\n",
              "1        1    50       4       2  ...            0          1          0          0\n",
              "2        2    53       4       2  ...            0          3          0          0\n",
              "3        3    67       4       2  ...            0          1          0          0\n",
              "4        4    26       0       2  ...            1          1          0          0\n",
              "\n",
              "[5 rows x 99 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6NS5AQpcQ8Je",
        "colab_type": "code",
        "outputId": "4d47d86e-eb27-40f4-95f0-d9aa39d0cbfd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        }
      },
      "source": [
        "# Now we only ahve numeric columns (ints and floats)\n",
        "national_processed.dtypes"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "CONTROL            int32\n",
              "AGE1               int64\n",
              "METRO3              int8\n",
              "REGION              int8\n",
              "LMED               int64\n",
              "                   ...  \n",
              "FMTINCRELAMICAT     int8\n",
              "FMTASSISTED         int8\n",
              "FMTBURDEN           int8\n",
              "FMTREGION           int8\n",
              "FMTSTATUS           int8\n",
              "Length: 99, dtype: object"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WAJ8bjVcEwhA",
        "colab_type": "code",
        "outputId": "bd65f4e5-fd67-4efa-b88e-2767cb1a19ec",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "from numpy import array\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.decomposition import PCA\n",
        "from sklearn.cluster import KMeans\n",
        "features = ['LMED','VACANCY', 'NUNITS', 'ROOMS']\n",
        "# Separating out the features\n",
        "x = national_processed.loc[:, features].values\n",
        "# Separating out the target\n",
        "y = national_processed.loc[:, 'OWNRENT']\n",
        "# Standardizing the features\n",
        "z = StandardScaler().fit_transform(x)\n",
        "print(z)\n",
        "pca = PCA(n_components=2)\n",
        "principalComponents = pca.fit_transform(z)\n",
        "principalDf = pd.DataFrame(data = principalComponents\n",
        "             , columns = ['principal component 1', 'principal component 2'])\n",
        "\n",
        "print(\"\\n Eigenvectors: \\n\", pca.components_)\n",
        "print(\"\\n Eigenvalues: \\n\",pca.explained_variance_)\n"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ 0.45495261 -0.26814014 -0.25370079  0.19364061]\n",
            " [-0.99132355 -0.26814014 -0.25370079  0.19364061]\n",
            " [-0.99132355 -0.26814014 -0.25370079  0.71870772]\n",
            " ...\n",
            " [ 1.47038526 -0.26814014 -0.25370079 -0.33142649]\n",
            " [ 0.93356881 -0.26814014 -0.25370079 -1.3815607 ]\n",
            " [-1.40543448 -0.26814014 -0.25370079 -1.3815607 ]]\n",
            "\n",
            " Eigenvectors: \n",
            " [[-0.00272964  0.33963844  0.6470288  -0.68263607]\n",
            " [ 0.84529745 -0.44635829  0.28954658  0.04898244]]\n",
            "\n",
            " Eigenvalues: \n",
            " [1.32302901 1.03741637]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YrdqzS58T3Rr",
        "colab_type": "code",
        "outputId": "ad952290-7079-4e2c-a198-5e63fbaf2654",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 406
        }
      },
      "source": [
        "principalDf"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>principal component 1</th>\n",
              "      <th>principal component 2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-0.388650</td>\n",
              "      <td>0.440284</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-0.384703</td>\n",
              "      <td>-0.782250</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-0.743132</td>\n",
              "      <td>-0.756531</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-0.384703</td>\n",
              "      <td>-0.782250</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1.501081</td>\n",
              "      <td>0.041466</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>64530</th>\n",
              "      <td>0.690568</td>\n",
              "      <td>-0.853736</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>64531</th>\n",
              "      <td>-0.030190</td>\n",
              "      <td>0.405135</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>64532</th>\n",
              "      <td>-0.032992</td>\n",
              "      <td>1.272907</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>64533</th>\n",
              "      <td>0.685332</td>\n",
              "      <td>0.767699</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>64534</th>\n",
              "      <td>0.691717</td>\n",
              "      <td>-1.209454</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>64535 rows × 2 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "       principal component 1  principal component 2\n",
              "0                  -0.388650               0.440284\n",
              "1                  -0.384703              -0.782250\n",
              "2                  -0.743132              -0.756531\n",
              "3                  -0.384703              -0.782250\n",
              "4                   1.501081               0.041466\n",
              "...                      ...                    ...\n",
              "64530               0.690568              -0.853736\n",
              "64531              -0.030190               0.405135\n",
              "64532              -0.032992               1.272907\n",
              "64533               0.685332               0.767699\n",
              "64534               0.691717              -1.209454\n",
              "\n",
              "[64535 rows x 2 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k7j31MoaXfaC",
        "colab_type": "code",
        "outputId": "3344867f-4a79-42b7-ba78-21e879edbfbd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 406
        }
      },
      "source": [
        "PCAdf = pd.concat([principalDf, y], axis=1)\n",
        "PCAdf"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>principal component 1</th>\n",
              "      <th>principal component 2</th>\n",
              "      <th>OWNRENT</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-0.388650</td>\n",
              "      <td>0.440284</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-0.384703</td>\n",
              "      <td>-0.782250</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-0.743132</td>\n",
              "      <td>-0.756531</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-0.384703</td>\n",
              "      <td>-0.782250</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1.501081</td>\n",
              "      <td>0.041466</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>64530</th>\n",
              "      <td>0.690568</td>\n",
              "      <td>-0.853736</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>64531</th>\n",
              "      <td>-0.030190</td>\n",
              "      <td>0.405135</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>64532</th>\n",
              "      <td>-0.032992</td>\n",
              "      <td>1.272907</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>64533</th>\n",
              "      <td>0.685332</td>\n",
              "      <td>0.767699</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>64534</th>\n",
              "      <td>0.691717</td>\n",
              "      <td>-1.209454</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>64535 rows × 3 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "       principal component 1  principal component 2  OWNRENT\n",
              "0                  -0.388650               0.440284        0\n",
              "1                  -0.384703              -0.782250        0\n",
              "2                  -0.743132              -0.756531        0\n",
              "3                  -0.384703              -0.782250        0\n",
              "4                   1.501081               0.041466        1\n",
              "...                      ...                    ...      ...\n",
              "64530               0.690568              -0.853736        1\n",
              "64531              -0.030190               0.405135        1\n",
              "64532              -0.032992               1.272907        1\n",
              "64533               0.685332               0.767699        1\n",
              "64534               0.691717              -1.209454        1\n",
              "\n",
              "[64535 rows x 3 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T79KkiKfE9OM",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 294
        },
        "outputId": "908cab48-04d2-456d-e6a4-17c7b27cff1d"
      },
      "source": [
        "mapping = {}\n",
        "elbow = []\n",
        "for k in range(1,20) :\n",
        "  pkm = KMeans(n_clusters = k, init = 'k-means++', n_init = 10)\n",
        "  pkm = pkm.fit(PCAdf)\n",
        "  elbow.append(pkm.inertia_)\n",
        "  mapping[k] = pkm.inertia_\n",
        "plt.plot(range(1,20), elbow, 'bx-')\n",
        "plt.xlabel('K vals')\n",
        "plt.ylabel('Distortion')\n",
        "plt.title('Elbow Clusters')\n",
        "plt.show()"
      ],
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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DIz58kvxcYFBZtYG5rLXyV4A+kno2K1/ivfL5dXP9Dmn4cBg1ChYuhF13dWIxs66hpslF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\nZmYV5+RiZmYV9/8BSmILOhE6LL8AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "G7YTG9OTPkmI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 354
        },
        "outputId": "db4b8344-fe0e-4a2c-db66-802d16a3f56a"
      },
      "source": [
        "for key, val in mapping.items():\n",
        "    print(str(key)+':'+str(val))"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1:168093.94352371988\n",
            "2:118554.916831395\n",
            "3:91330.82526544644\n",
            "4:69879.68744558976\n",
            "5:57009.56646441372\n",
            "6:49079.18380523987\n",
            "7:42203.34823350757\n",
            "8:37675.48378078768\n",
            "9:33890.800922684226\n",
            "10:30997.183783326756\n",
            "11:28755.88375539621\n",
            "12:26733.627202919037\n",
            "13:25406.540986829106\n",
            "14:24051.841522567767\n",
            "15:22475.48278021261\n",
            "16:21114.00472240411\n",
            "17:20064.49579973604\n",
            "18:19258.09051703342\n",
            "19:18208.275030770004\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c_5xjmMqYb8Y",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 294
        },
        "outputId": "9c1349bd-7c34-46ff-8daa-c778d7cadf45"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.colors as colors\n",
        "import matplotlib.cm as cmx\n",
        "uniq = list(set(PCAdf['OWNRENT']))\n",
        "xp = PCAdf['principal component 1']\n",
        "yp = PCAdf['principal component 2']\n",
        "ore = PCAdf['OWNRENT']\n",
        "hot = plt.get_cmap('hot')\n",
        "cNorm = colors.Normalize(vmin=0, vmax=len(uniq))\n",
        "scalarMap = cmx.ScalarMappable(norm=cNorm, cmap=hot)\n",
        "for i in range(len(uniq)):\n",
        "  ore = PCAdf['OWNRENT'] == uniq[~i]\n",
        "  plt.scatter(xp[ore],yp[ore], label=uniq[i], color=scalarMap.to_rgba(i))\n",
        "plt.title(\"Data After PCA\")\n",
        "plt.xlabel('PC1')\n",
        "plt.show()\n"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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iy51QdbG/71Cq7xhAip9bhsrarKmttbVEveLmCcTpuqiOS6b5ggcXp/rejXkE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\nCznDMEyBw0LOMAxT4LCQMwzDFDj/P1h99qRxsB1hAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Emu3ON3_QcqT",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 141
        },
        "outputId": "b997ac04-132b-44bb-f1be-4f26f85ddae6"
      },
      "source": [
        "kmeans = KMeans(6)\n",
        "kmeans.fit(PCAdf)\n",
        "# to add a column use pd.series\n",
        "PCAdf['plabels'] =  pd.Series(kmeans.labels_)\n",
        "print(kmeans.labels_)\n",
        "print(PCAdf.head())"
      ],
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[2 3 3 ... 0 1 4]\n",
            "   principal component 1  principal component 2  OWNRENT  plabels\n",
            "0              -0.388650               0.440284        0        0\n",
            "1              -0.384703              -0.782250        0        4\n",
            "2              -0.743132              -0.756531        0        4\n",
            "3              -0.384703              -0.782250        0        4\n",
            "4               1.501081               0.041466        1        5\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tBWqa_fbQ2VZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 264
        },
        "outputId": "d4999b60-8fa0-40e1-d8b3-88a89d645a0a"
      },
      "source": [
        "plt.scatter(xp,yp, c=PCAdf['plabels'])\n",
        "plt.show()"
      ],
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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X0qzfJe/i0a1Lqh2j1O2sIuKVqSzip/kpZT8DItrw8t7VlLnLfdQlLgfPbl9B\npq2YrTmpPuuAnKZfizYkFmR5LBBXd/PSNPjqyHYua9+Lr45sr9HNUwNirCEUOm1csfITsmzFlLld\nWGUD/9v7O28Mv9znucLHSu6c7sN4YstPZ32P/uCqzv3r/Br+JMYaTLjJ6rHWYxAS4/2YYasnBF2A\naJrGuoPHWbIzEVXT+D3pKKWOqoJhlARmo5GSStstRgO92kQz97YrMBnK610cL8ln8tJ3vT5amyWZ\nl4ZexmXte1Vsm7z03VrHewMcueYpcmwlvJe4kYXH95xV0MNMVjbPeKDK4qZTcdNzwUt+eVI4E6OQ\ncGueTiCrbGRQy3bVulU6BUWwaMptTFz6Dlk2z+491WGVjVhkA+HmAJLP8rmelmHtlL0qmsdTQs+w\naByK2+NvZJEN3NdrNHf2GO4xrqZpvLp3DR8kbcKpuuvk8wX437DpTO/ge6HZG5qmkVpagFU2+r22\ne01Zl5nMXesW4FTdKJqGWTIQZDTx45Q5tY5e0asf6lTwzPcrWbr7ADan7xmUS9VwnSHudpebXSnp\n3PzBt1w1JJ6pfeLYmpPis1SRQ1VYn3mUKW26893RXbyTuIH0c3wEX3RsL5IkuL/3RTw9YBI3//4V\nm7KOeS1cVW6/wp68DPpH/hE7/d2x3XUmMr7ssCsuOge3IMHLrNwoyXw7/kbiW7QGoF1geK2F3Ka4\ncCjus4YXnjlb92XvoaIc5o25njvWfYtLVbArbiwGA73DY7i522DvYwvBg/FjuC1uKKszDvP8zlWU\nuZ0IBC5V4YqOfcgsK+JXLzkBgyPbcaK0kAybpztnRMsOWAxG2gWF8XjfibUuw7sp+zgPb1pEgdOG\nqmn0Cm/F6yMu90jjr2tGterEwsm38unBrRwrzmNoVAeu7zKA8HOoyeMLfUZ+AeBWVPanZyNLAlXR\nuHnut9hdvmO8a4LVZCQ6JIg/Xz6UR7Yt9hkzLgH+WAYTlAuGAcGrw2cxJKo9t66Zz968TK+LoUZJ\n5tsJNxEfEcPR4lxybKXszE3jpd2/+sGa2jMquiMJJ1NRNQ2DJCMB9/YaxdLUJEpdDkZGd2TBsd2U\n1UEtFMOpp4WaYJQkts54EFmSWJaaRJatmP4t2jAsqgNCCGxuFz+l7GdfQSZdgiOZHtubYKO54vwS\nlwOH4uZocR6FThsDIttWCFZqST6PbP6RXXnpmGUD13UewKN9x5NjK+GSn9+v8pTVJyKG7ybcfM4J\nQmmlhUxZ9l6Vm6csBG0Cw1g19e5zbv7R0Ogz8ibKsZx81h48isVoZFKvLoQF1i70atORFP765VKc\nihtNAyHAcZ4iDmBzukgvKDCwfZAAACAASURBVGJ/Uk61nXb8FcugUf6Y7ETj3g3fsXH6/UxqE0dS\nQbbXWGSXqnCkMIdntv3MgcJsjJLcoCVcEwuy+GHSrWzIOkaYycLajCO8uOuPm8q5uJtqilJDEZeF\noH+LthWNpK/o2KfK/mxbMbN++Zgil/2UX93I//b+zneTbiHQYOKRzT+yMfsoIOgQFM5/hlxaZdbZ\nLiic+V4KWElCMH/CjeTZSzlYmMOYmM4VCVLnyldHtnvcvBRNI9deypacFIZF+a/XaGNAF/IGYk9K\nBnd+8gOFtvKV63YRIcy/5zrCAq2oqsq8DTv4dsteUnILkCSBLAQvLlnNy9dO46K4WFyKisVY/Z/v\nZHEp9366CJsfhNsbTrfCom37iR8Rw8ZaxntXx8VtuvF4v0k8tfUn1mcf89ivAtOWf0Ch04FL8y3O\nz+5YQZnbhVtTK54YajM79Se5jjK6hbakW2hL0ksLeXiz93jy6rDKRuJCW7K/IKvKzcsgJCQhvN7Q\noHyRsrrCBWZJxiDJhBgtvFyp9veZPL9zJTn2kgq/+mm3zhNblpDnKONocV7FZ3u46CQ3rP6SX6be\n5dMPXOxy8PCmRazNTMYgychC8FS/iect4gCppQVeo3g0NLLKapZkdqAgmw8PbuZYcR6DI9txS9wQ\nv/Zn9Se6kDcAWYUlzH5nfpVtqXlFjH3hfX586GZm/O9THO5KX8JKunPfvB8xSAKXotIuIpSnZ4xn\nRNfy2cV/l/7OvPU7casqkhDEt432Wi/EG0ZZomfraMqcLpKzc2tcSTC/1EaUzb9F+xNOpiEE7M7P\n8HnMSS8tvc6kyEt4l1tT6RUWTYjJyt78DL+GgFXH6dK0p7NFa4sAHus7nlmx8Vz/2zySi3NxqypG\nSaaFOYCbug7iuZ2eDZIBZnToxZrMZK9t0KIsQdzVYwRtA0MZE9PFa+ar3e1m2YlElp844PG9UNHY\nkpOC1WD0uEG6VYX5R3Zwf2/vcd/3b/iBjdnHcKpKxU3o2e0raBMYxojo2Bp8Kr4Z1rIDq9IOeaxL\nKJpGn1NrEtWxNjOZu06tEyiaxp68DOYn72Tx5NtoExh6XrbVBbqQNwB//eonr9tdispVb3xRVcTP\nQFFVlFO/l+O5Bfzl88V8dufVfPDbFn7Z98dikqpp7ErN9DqGJECWJEyyjEtRUTSVq4bEc+vowTw2\nf2mtysG6Q93sKkrza2X7XEcply2fi1k2nLPQGoXsc7aeYStm8ZQ5TFn2ns/xZSGQNHD5aXl0fExX\ncu2lXLr8Q/IcpWc/4QxMkoGeYdEEGc0snHQrm07VSI8NCmd0q87IksS+giy+P7anynm3dB3MU/0n\nUeC0c9GPr2OrtJYRfKpwmNVg8nndd/av5+U9q6v9FDTA4cVt5VAVn5E02bZiNp0S8crYFBfvJW44\nbyGfGRvP+wc2kVlWVHGN8szWODr6SIY6jaZpPLGlahKWU1VwO+28smd1tU8tDYUu5A3Agcwcn/uK\n7bUTLofbzdurNrE6seYdY0wGA/+YOYF/LFyFhoaiany/dS/zN+2mNovfGhruaBeanwvWaZTXL+8Z\nFO5RPbEmCCDMZCHHh2AWOMo4UJBN5+AWHC466fWY06VfXX6IjY4LbcmbI6/gpV2rKHSWndOtwaG6\nufX3rxnQsg39ItowuW03MkqL+CBxExaDgVu7DeW/Q6fzVL+JLElJJNoaxPiYLqSUFXCgMJuuIS3Z\ne+VjbMg8yku7fyUpP4sSt5NxP73NvwZNZaKXnqA7ctP4vz2ra2SfNz+8VTYyKLKd1+NP2kvL8xG8\nuD8yvCQk1RarwcjCSbfwzv4N/HwiCavByA1dBnJNp7PHoZ+0l3q92apo1YaRNiR61EoDMPX/PuZ4\nboHfxosKCSS7yLfgmeQ/FvqsRgPjenYmNa+QvamZ5zXf1NBAAmcnB1qQ//3OwQYTZsnISWftxFwW\ngn4RrdlWTenY0wu03vzlshBc1bEvPxzf67XRb20wC5kws5U8h61af74/GBkdy2djrwfgSNFJ7lq3\ngIyyIoQQ5Qk/w2by6aGtrEr37PX50UWzGdO6c5Vt1/82j0017IN6JgYh0cISyIpL7iSoUlTLaWwu\nJ/Hf/9fr929Mq858NKbhimOVupwMXPiKVx97p+AIfpl6dwNYVY6vqBW9+G8D8M8rJvncF2Lx/Zjr\nDUkIusdU3x38orhYAk1Ggi1mZg3qxTMzJrA/Leu8nQYCgVAFxlSTf/Lxz6DE7Tqn4luKplUr4lAu\n4L5EfGaHeB7vN5EbOnu2WKstDk0hy15S5yIOsD7rGPvzM3GpCtf9No+jxbnYFBdlbie5jjLuWPeN\nVxEHeMhLtcGcWsa0nybCHMDlsfEsnnyrVxEHSCkt8NoqD6iTEMzaEGg0Mb51F0xS1bh1q2zklm5D\nG8iq6tGFvAEY1LEt906smiEnCcE7N83kjRtmeE2wuWZoPFcM6uURqWIxGnhk6hhCLN5/MBaDgQ2H\njlPqdFFsd/BDwn6eX/wriuo/5RVOAXWgUxoazvMQwNp+uY1C4qOLZnOwMIcBP7zM3IObz/naDcWX\nh7ezJuMINrend7+6he8Cp91j/7jWXWt9/RCjha0zH+SFIZdWG+FR6nZi8VFJ0lf0TX3y0uBLGRDZ\nFotsINhoxiTJXNWxL9c20hIBzdpHfuN737Dt2B8zsxn9e/L81VMAWHfgKE8uWI6mwTOzJjCxV+2/\ntOfD3ROGcfeEYSQcPUGwxURcTFTFvpWPz+G/P/3OwcxcusdE8si0MUSFBKGqGl2iI/l03TYKyuz0\nadeKR6eNoVNUBAvuu55Zr31OqeOMVXpVxVXpB2pzuVi0M8n/b6gR5leolCe4uGoYuePSVG5a81Xd\nGlXHhJqtnLSXevVZny3s8nhJHp1DIiteP9h7DF8e3kZZDdcJLLKhxs0feoW38jnGtHY9ajRGXRJs\nsvDFuD9xtDiP9NJC4sKiiGzEvU6brY/84v98SGq+56LJxF5d2HH0BLllVR/Zw6xm1v/9Hq59+yt2\nV4r2aBFkZc1TdwEw+43P2ZP+x+LYvhcerCPrPdl7IoP9aTnEhIUwomv7KoWrXIrC3NVb+WLjDvJL\nz68OeG3R0FBDFFydGmd3dn9lljYVdsx6mGx7CTNWfOiRbRsgG3GcqvdxJhKCjTPu9xCrIqedgT+8\n4rOUsACCjGacipsZHeJ5btAlNW7e8VPKfh7d8mNFiF+AXJ6Ov2DizQRUE0lzIVPnzZdrQ10Lucvl\not/f36z1edEhAWQVecbaWgwydh8hgSvvm83E1+d7bJ8zqh8PThtHryf+V2X7JT078H83/FFhbtTf\nXyXQYmHZ43ciSVWntaU2B5e/MY8TlW5IgvLFzXl3z+bODxaQnFc/5UMrc3qRE0CzqDg7ORrts52/\nyuk2Bf416BKu7Vxe3/rhTYtYfuJARRy1RTbQObgFN3YZxGMJVcNfBTAiKpYH4sfgUNz0b9GmSgPs\nG1d/yXovVR8BXh8+kzaBYbQLDKNFNTNWVSuP+FibmUwLcwAzY+OJCQjhYGEOXx7eRqatiKEtOzC7\n8wCsla7dkOTYSngvaSNrM5NpaQni9u7DGBPT+ewn1iEXlJBvPpLCrXO/q7Px65J9LzzoIf6NEVeo\nCzXKjRZw6vvTCF0rBgStA8NIKc1vaFPqFIOQ2DbrYYKM5bPYtZnJ3Lf+e4rc5aGsJknm9u7DuLvH\nSKwGI2/uW8db+9chCwlVU+kS0pIsWzE2xYVAoKLy0uBLmdq+JwBHi/O4eNm7uM/Qio7BEfxyyV1n\nLdjlUhVuWzOfHblplLldmE5lcb458gpGRnfkhZ0r+Tp5J6qmEWw081T/Sczo0LsOPqmac9JewtSf\nP6DIZa9wzVllIw/Hj+WWOO89W+uDCypqpXNU5NkPaqQ0BRHX0JAdEsItnapm1dAWeUdB40SZ/8I8\nGyu3xA2pEPHkolxu/v2rChGH8sXD9xM3VtQ2v7fXKLbMeIBPxlzL4slzSCsr4KSjlFK3kxK3gzK3\ni0e2/MjR4jygXLA/uOgaIs0BWCQDRiHRv0Ub5o29vkZNnRce28P2k2kVtdqdqoJNcfPAxoX8Y9vP\nfJ28E7vixqkq5DrKeGrrTw0erz03aTNFLkfV9SXFxct7VmNz133d9drSLIU8MjgA2cf3q5FqTpNC\nIJDsMsajJuTMRupTodyl4q3rTlPAVxOHMxkX05nH+06oeP3PHSu8HufSVCYtfZciZ/kaSrDJwqCW\n7Thakus1msWtqixI3lnxenRMZzbOeIAlF8/h98vuZcHEm2lVw3KwC4/t9dp0QtU0vju628OXb1Pc\nvLlvbY3GrivWZCZ7jSOXhcTBwuwGsKh6mqWQA6x87DaPn4JJlnh8WtPp99fYEQgMWcY6CT280Hlh\n8LRqq0qe5nhJPmklfzx1HCr0nTVc6nbwdSVxBih02r3e7Nya6lGbRRKCjsEtat0MwSh5ryOuaprP\ncrKppQ37JNXKR0s5l6o0ysJZzVbIo0JD2PvCg3w05wpuHNGPhffdwI5/3c+0/j29vulm+0HUMUqI\n0iwecwwIvhp3A53OUoejrhkZFcuqqXdzVae+vDni8opiW75ILs5j4rJ3K2bVXUJ8uxUVTWPjGYuW\nw6I6eA1VDJCNjPNTK7JrOvcjQPZcwAw0mLwmBQkgPjzGL9c+V26PG4b1DJuNkky/Fq0bZdGsZq9f\nQzu357HLxtE1pvwLHh5o5a7xntlZ1wzrQ5uwptXYtaFRLSru9s5m8S3qEhrJkKj2/DL1bj4ePZvp\n7XsRbvJd1VEAIQbvSVjngkFIjGnVmc/GXV/R4X5S2zheHjr9rOc6VYX3TvUYfWbAFJ/HyULQ/owS\nsW0Dw/hT10FVRMsqG+kV0YoJrT3rr5wLF7ftzrT2PbHIBsySgUCDiWCjmQ8uupqH4sd6CKZFNvJg\n/Bi/XPtcGR4dy1P9JxFoMBFkMGGWDAyKbMvbI69sULt80SyjVqqjxG5n6LPveN237OFbuPfThRw5\n+UeUg9VoIOGff2HAU6/i8GM2ZHPA2daBGqE0CyEPMph4c+QVXHSqYfOBgixm/vKxzyzDc41Pl4VA\nIHBrKgKQTtUSHxvThRcGTWXh8b0sONXI+sqOfQkwmHhu+3JsavU1X8bHdOGD0dcAsCbjMLet+cYj\n9tsqG1k8+TY6hbSosl3TNFZnHGH+ke2UKS6mt+/FjA7xtW6tdjYOFeawKfs4YWYrE1t3qwgzXJKy\nnzf3rSPbVkyfFq15tM84evpIGKpvHIqbw0UniTAHEFPPLeK8cUGFH1bHTe9/TcLRdK/7OkaGs+Th\nm73uawrRJPWJhoazix0tqPnc3IySzOQ23Vh+4kCdNJ+QhKB/RBt256VX9MyUEYSarfx88R3ct/EH\nduamVSz+WWQDbQJCSS8tPKuQD23Znvt6j2Zoy/YIIThpL+WBjQvZdjIVSQhCTVZeGnJpxY2quZNr\nL2V77gnCTFYGRrZrsq3dzkQX8lOM/te75JZ678B+evZ9Jk99s4yFO+ogrb2JoqHh7GRHC9aahX+8\nvjAICQlwerlJRJoDyXWUeiQvGYRA1bSzzv4F5aVb+7Vow4cXza6YTec5yihzO2kTEFqjUMGmRFJB\nFqszjmCVjUxt14OW1vJFyNf3ruXdxPUYJQMaGqEmC5+Nvf6sdcibAnrPzlN0jm5BbvIJr/tah3t/\ndNp23PsM/kLF1cqpi/g54mvadNJH7fTTSTgGgGra1GlAmdtFQk4qz+1YwdP9J2GWDUSYA4jwY7f2\nxoCmafxz+wq+OboTl6pikCRe2v0r/xs6A6vByPtJG3GoCo5TbrEyt5M5a+azcurdze5mdppm4N2s\nHW/ccJnPfW/f5L3zx/T+PevKnCaJMdOEIc144eS++wm3pla4VGp9LnBP9xH8uedIFk26lR8nzcEi\nec7DnKrC/CPbGbLwf6zP9J5W39TZlH2cb4/uwq64UTQVh+LGobh5aPMiPj641SNmXQOy7SUkFmQ1\njMH1QLMX8vWLtvLB4/PY8vN2AIIsFj667YoqYV1CwEtXT6FtRJjXMe45o+TshY5AIHIlRF6z//o0\nKo4U53J/r9H0jojBbJB9zi5VoMTt5M5131Lg8O5GbMosOr4Xu5cEI4OQOOGjHIMkBCWuxlnYzR80\nW9dKfnYBt/Z4gJL88kfWb/6ziNCWIXx66A0GxrZmxM9pHNl5DIBWnaIZ9dAfDVln/e9TDmbnYTbI\nrHnqDoIsFtY+dTvjXpiLu1Lkyuxh8dw9bgRjXnivXt9bQ+MOceOOdTaoayXCFECZ4vTICmzOLD2R\nyIZFx/j7gMlc1r4XEeYA0sqqL5r284kkZjfSGtrng6+Hwf4t2pJeVuTxvVBVjfiIho1Nr0ua7ZTq\n4bH/qBDx0xTmFPHoxGe5NPBPFSIOkJmcxVVRt3P0RBq9nvgfB7PLa0w43ApDn32HOz5aQH5BQRUR\nB1iUsJ/IkAC2/u1Oj+vve+FBNj91u1fb6rP8rb/R0FCiXQ1eY6XIZb+gRBzKxSvfaeOJrT+xJSeF\nt0ZeQZDR7DMD1K0plJxj8+rGzIwOvT1iz6HcdfVIn3F0CAqv2C8JgUU28OzAixtNVcW64LyjVoQQ\n7YDPgGjKv2vva5r2WnXn1HXUiqqqTDFcU+vz0v86DOTa3dtCTAaKnN4FZcW9VzP5zW88tp8W8jND\nGpc/cgttI8IadaijdnouJIGjrQ3CaXaLnoGyCZfq9hpd0lgY3aoTH4+5lmKXg3cTNzA3aZPHQqhF\nNvD9xFuIC4vyMUrTRNM0nt2+nG+P7sKlKhiEjBDw8tDpXNyuB3a3i4XH97Iq7SAtLUFc33Wgz0YW\nTY06Cz8UQsQAMZqmbRdCBAPbgJmapu33dU5dC7nT6WKa5bpan5f+6PByh3kD8t1913PF6180qA01\nwd7OBhGNt4RtcydANvL1hBvpEtISWQhuWP0F23NPVCm5OjO2N/8aNLWBLa07EvOzWJ1xGIvByLR2\nPYiqZQ2YpkidhR9qmpYBZJz6f7EQIhFoA/gU8rrGZDJiDbJgK/HsliPJAlVpvOEWTUHENTRM2Wbc\nwoUarlfMqiveG3kVd69f4LU7T5ni4rIVH2KVjQQbzRSfqpstIRACprbtziPx4xrA6vqjR3g0PcKj\nG9qMRoFffeRCiFigP+DRtVYIcYcQIkEIkZCT47tCm7/460f3eG4UcN/b3v3WOjVHIJAcEsZUE3JG\ns10vb1AkIXjOR0naytgUF9n2Emyn1gtUNBRN4/vjexix+HV+TT9U16bqNAL8JuRCiCDgO+ABTdM8\nmmVqmva+pmmDNE0b1LJly1qPby+z89HTX/L8da/y21frznr86CuH89aWF+g5vBshkcHEj+7B+7te\nZtrtk2jXvY3H8QEhlnK3iqaV/ys3+o//n36tU4HQBIYcY3mQs45fUTWNE2WFPntlng0NsKtu7lz7\nDc9u+5nduXpSW3PGLyn6QggjsARYrmnaK2c7vrY+8h2/7uGxyc+hVYoaCW8VxrzktzBZfDdpfeCi\np9m3/kDF614j43j003u5qYtnGj5Ax+sGsXtfCsUTO4EsQANz0klkISiLCYBQa9UTylwQeGE3idUk\nDWcnB1pQ410Y1Cn3md/QdSCPVWpCodP0qMvFTgF8CuRpmvZATc6prZBPC7wep80zmH/U5UN5ZsFf\nvZ7z0Ni/s2dNosd2k8WI0+67VZOG59qdJoE71IyhwEFpl3DUFgEEbs9EaBqZ9w0Gg3+rxDUlNKHh\n7G5HM+kp+40dsyTzyrCZTGkb12xT1Zs7dVlrZSRwA7BHCHG6/ciTmqYt9cPYJG097FXEATb/tM3n\ned5EHKhWxMGHFqkgFzkRGgQdyodDlbLHpAv3B6GhoQaquojXEQKQECin3CsC74kwp0P6z/ZM5FAV\nHtj4Ay0sgbw54gr6R3q6GOsbVdN4Z/965ifvwOZ2MTqmMw/Hj22UzRsaM/6IWllHHf6MHaW+ExrU\n+qwP7usdXkAzG+0MGVEDVFwdHbqInydGIeHSVGQhVenWY5GNPNxnLEtTEsl3ljG+dVfmdBvK0ZJ8\nXtv7OwcLc+gQHM79vcaQUVbIUwlLz+pRd2kqmbZibvr9S9Zedi+hJutZzqg70suKmLniwyot5RYf\n38vvGUdYfskdjbKlWmOl0YccxI/ugWSQUN2e840ew/zTweRsCAC3509E89XhuZnijnAhVIFm1FCi\n3NB8E+XqhRCjhU/GzMahKHQICuP9A5uYf2QHDsVNK2sILw6exqiYTtzSbUiV86ICgvly/A0e423J\nSWFpaqLPZhiVUTWVn1L2c12XgX57P7VB1TRmr/rMoy+oBpS6HHx6MIGH+4xtENuaIo0+RV+SJO57\na47HdqPZyFNf1cgl7zc0/ni01QAqx6OXOAlafZyAhDRQmmdstalYxhBrQ2vjrBBx6Zz65OhAeZmB\nO9Z+S6jJQnRACKFGK6qqYpEMFLns/HnDdyTkpAKwNDWRSUvfpfeC/zDzl4/YmHXMY7xH+4yvcQMF\nm+LmpN176dz6YEnKPrJtxV73uTSVrTkp9WxR06bRz8gBpt0+iZ7D4/jgsc/JTsllwITe3PyvawkI\nqr/HwjN/Hqf9lXJaESEbTmA5+kfxotBVx8m/uDP2vs0nWSHA6GTBdd8gmVXeON6X9QWtCTfYiTGX\nsjqvLWrjnxPUOQGykTIvVfmq46SjlCtXfsL/DZ3O+0kby8sCaGqFw3vOmq95tO94nt+5sqI86568\nDOas/ZoPR89mWFSHirHmHd6GWsPghQCDkUEt21d7jENx89reNXyTvBOH6mZMq8482W8irc/Df61p\nGn9LWMa3R3dV24WpOTSBqE+abYegSdJVdTr+aRQJJLWq0J/+RDMeGgLGJnGvPCsPjNzILQN3Vlnb\nzXZYmLJ1JiWK/5oQN2VkIVDq4Pd0pu/8NH0iYvhh0q0Vr//02zw2Zh/3apcspAqXi1U20r9FGz4b\ne1210Ss3r/6SLTmpOE61mZMQhJutrJx6NyHVNKaujsXH9/Lk1qUeNcMrYxQyi6fcRrfQ2uebNHd8\nRa0022mUbKiftyZ5mVSc/mmYj3opMdpEk4qmxR30CNAJNzr4KH4lsu5eAfAQcaOQMErnH5rqTcQB\nDhedrPK6a2hLr5UQDULiru4jiA+PoXd4Kx7rO54PR8/2KuKKqrIkZT/X/zqP9VnHKkQcyrNGS1wO\n3ti39pzrnM87vK1aEZeFxFsjL6+xiO/OTeee9Qu45Of3+VvCMk6UFpyTXU2dZivkL636m9ftrbv6\n393hM6DFW02X09mjjRYNUUmYwyxlDGuXQouAMo8jjZJG96B8Lm91uD4NbFDMkkyn4AjMsgGjkE71\n4fT+DXBpKtPadq8zW9oEVHVx3NBlEGc+YcsIBka24/740SycfCuLJt/GDV0HVfT0rIyqacxZ+zVP\nbFnCppzjXrNKHarCZ4cSGL74Nf6WsAxFrd1NvMztXcQFMK1dT7bOeIAJbWoWxLAq7SDX/vY5K04c\n4GBhDt8k72Taz3M5WpxbK5uaA83jud8Lb//lE6/bXXbf+eSBYVZKC2o309BkAYrm9afsbOUjfErR\nwFCfES9npjmd/oF62mCUFN6Y/hM702MY2eEEfWPK22P5egK3ygrPdd3IxMhUHkocTanSvENZLm3f\ni38MnEKWrZh/71jJmsxk5FMNks8kwGBCE8Jn/Pf5YJGNPBg/psq2eYcTkCUJpXLUioA5ccNqNObv\nGYdJOJl6Vj+/W1NBgx+O7SbKGsRfel1UY7svbd+T5KLcKjN9gFCTlVeGzcAg1WxuqWkaf9v2c5Wa\n9G5NpdTt4L+7fuPtUVfW2KbmQLOdkSfv9vQVAuSk5nLHyzd6bB88tT+d+sTW+jriVCx75R+qBmhG\nCUtyHriqRrAIp4Ilqeojcd1TrsJCqMRF5jC2o69ejhqjYlMY2SGde4Zto29MFkKcPVRelmBkWDr/\n7b7Wv2Y3MiySgecGXcKy1CT+sW05azKOoPjowykJgVU20jUkssaRJNVhEBIBBiMGIRFpCeSfA6cw\npdJsv9TlZH7yTo/QQ0XTeP/ARp/jOk5Fr6iaxooTB33OmL1hU9x8cnBrrd7HjV0H0TE4goBTTR6M\nQsIqG3h52PQaizhArqOMfIfnU6IGbL4AI16a7Yy8OrKPZ3ts27p0xzmNJTRQZMAoI9kVEKAEGpFK\nXIT8dhzNYsQW1wLhVtEMEgE7Mwlcn4q9d/0X+5eFxoLrF7D1RGs2p7bD5jYSZrHRNTKPjOIgckoC\neWBkeeHK2mqPWVYZHZFGuMFOvttMc8wScqhuRi1+nUKXvdpFTQnBoMh2vDTkUtyqyhv71qJoniGp\nvmbqspDQNK3CtWGWDLQKCMapuFENGjM79Obitj2qnJNjL6nSh7Yyx4rzPN+L4ua57Sv4/tgeNDQM\nkoStFiJ+miLXH6Wiy9xObvjtC3bmlRfoCjSY+NegS5jeoXfFMQEGE99PuoVlqYmsyUymdUAIV3fq\nR/ug8FpdN8jgu8ZRhDmglu+i6XNBCvnC13/263iSAuJ07LgGhhJXRZx5+JJDhPx6DCXEhCHfjuRQ\n0ATlfvIzf3jetvmRUEt5luygNumM6HCcwW0zuLJ3Ik5FxigpZBQH0TGi+h6Q1eFWJSJMp4W8+aEB\nec7qXW9GSeLu7iO5P340DsXNUwlLPcLszELmlrgh9AiP5oktP+FQ3SiahlU2YpJk3hx5Bd8k72B1\nxhEssgFJSGSUFuE8dTP4+NBW1mYdZeGkWzlSnMuPKfuwu9xe3TsCvHbHeTphKUtTEytcHNUlEQUZ\nzbQJCOFAoWf56d6Vxp6y7D3Sy/4ofFrqdvLgpkVEWoIYER37x/uXDcyMjWdmbLzPa54Ni8HItPY9\nWZqSWMVNY5WN3F5DV1Jz4oIUcn9zNumVy1zIZZVmO9U5TM9JzBX+8JJ5P9dicHHzgPJSOELAK9N+\nQdXAIIHZUP4jjg0/5t2NuwAAIABJREFUdxEvt0KQYgvyacOFgEtVeTtxPTvy0ggymPgt43CV2btB\nSNzVcwT39R4NwKQ2cSw/cYDdeenEBoUzo0Nvgk2WCuFbn3mUu9Z/WyHiUC66x0ryeCphKT+m7MOl\nKqia5nPRdU7c0Cqvi5x2lqTsr1EGaKjJwocXzUbRVG7+/SscihsVDUkIzJKBv/efAsCe3PQqIl6Z\nf25fzs+XePa1PV+eG3gJpS4nv2ccwShJuFSVm7oO5qpOff1+rcaOLuQNSMTHOzFnl/v5nNGB5F7X\nA0w1K4trNboIMTvIKQ0gOqiEB0du4qkVE3CpMpUf2gOMLtyqxOw+e7hpwK6K8yXhWe/rfB4GbIrM\nh6k9cWn6V8qtqazNTPa5b0lqYoWQm2UD0zv0YnqHXl6P35OfgcNLk+kyt4vvj+2ucpNQvMwQZCGx\nMv0QQyolDmXbSzBK8lmFXBYSyy++k5bW8kX77ybezNuJ60kqyKZHWDT39BxZESa4pRq/dFrp+U0Q\nfGE1GHln1JVk24rJLCumY3AEwecY397U0X91dcTZIhVa/WdjlfmTKauUmP8lkPHYiGrH7R6ZyVXx\nSUQE2NidGcW1fXZjlAUBJhfvzFjC17t7k1USRGJOC6xGhXdn/EiniAICzXXb/cEqKzwQu4vF2Z04\nYQ+p02vVBy3MAZS4HDhqMGutLSftJTU+tnVACBbZSKm7agVQ46l4cW/iXRm3prI0NZEn+02s2NY2\nILRGGaCRlkAiLYEVr+PConht+Cyvx1aXJVrXlQyjrMEXRL/O6tCFvIE4XXq0Mhpg3p2Fo4/3WPdL\n4w7w9wlrMEoKBlljdOxxDJKGJMHKwx15ZuVY3KqEW5XoFJFPdmkgdy+6lA8u/5G4yNwaRaCcK5oG\nTgUuCjvBV5k96+YidYwAoq3BXN95AHf2GMFPqft5cNMiv1+jU3ALZv3yEUkF2bSwBHJ3jxFc13kA\nQggKHDaWpu4n32ljRFRHJrXuxr/kX7C5XRWLnwJORXgIXMrZ47jNp5KSXKrCr+mHSCkp4NL2PVmS\nst9nco5Rkni678Qa1y3v26I1MdYQMmye7pW/D5hSozF0zp1mIeQv3/Y2yz9ZDQIu+/MU/vLabQ1t\nElBNohC+Z+umk2V4L9yr8efhW7Aa/5hZmwzloxzIacETyydgd/8Rw33gZCQAn1y5kO4tc+u82q4Q\nYJJhdIuMJivkg1u253hxPh8c2MSWk6k83X8Sg1u2IyEn1S9x4JIQmCSZffmZFW6NjLIiXti5isL/\nb++8w+Oozv3/OTNb1ZvVLNtyt+XeC6YYTHHBdgyhgyEEQkJu+g3J5Sb3Jje/ECA33CSQHkJI6BCM\nQwDTsSnGNsa4F7nIcpFl9b5l5vz+2JUsaWdVLFm7K53P8+jxemZ25t2Z3e+cec9bPI3MGDSEL254\nBlNKvIbBI9oH5MYlMSMjj31VpZxoqEEIwaikDP57xuXc8u6TnR5TR3D9yOmcbKjhmrf+SrW3Ca/h\nx6HbSHO6cepJVHgayI1LYm/VqZZUMF1o/GbvB1w0eBRxHUSItOa1xV/i5nf/zvaKk0Cg9syPZy5u\nM9GpODfEvJC3qakiYe2vX2PtI70bldKXaB0kLNV7rJNtntg2Ca/RPlNP4LZ7mZZb0qcl0xv9GuPj\nysl01rO+Mg8ZQ6kKrf28G0oOsfS1P/LA7CvZX3Uaj+mnyfDj1GwhySydkWx3keRwMS19MMcbqvmk\n7Fib9Y2Gj9/u/RD7Pr1NHLfH9HO4roLDdRXE2exMSMvmkflXkR0XcF09OPtKvrPpn2iIlknI9khg\nZf4kvr3xJUoaalu28fm9+EyD60dO4wfTLuP8fz7cptBCk+HnUE05f977Mf82sWsJPwl2R0vtF9M0\n0boRF67oGTEt5Pdc+mPrFbFc+sOUlpErTs3PmEGVlm85WZuAKUN/NHF2X6AaQB8JuRBwZfZRrsw+\niscQzPvoOmqN2O1p6pcmD+/ewFtLv8zzh7ezr/oUFU0NrC85FCKZutCYkpbDjsoSpJT4pYlTs+HQ\ndZ5btJqRSYEnpHkv/dLyWIYpQYT3xzf4feytLOV/t7/L9sqT1HibuCBnBC8supWdFSd5cPs7IbW9\nIVDl8HhdFR+Vhqbce02DtUW7uHn0LKoswio9psE/j+7qspC3Rol43xLTZ3vrWzsibUKvYy8N1ohu\nPRklJVPNg2FLtMwfWozTFurrrGhwY1084Nxj1yT57ip6Pzm9bzlUW0GczcEd4+by8zkrmJc13LIQ\nll3TWZk/ifeW3s2yoQUUpGRx7chpvLnkrhYRh/DlWWUXrlST6WdN0U4Ka8oobarjxSM7uOXdJ1mY\nO5q5mcMs3+8xDXITwk82mlLi0HTL0Xzz51JEPzEt5LGM1Y9OALaKRlLX7EOr9wXE3GcQv+k4jnXH\n8ZnWl+uqiXtIdTdh18488rtsPm6YsgMhZURqdJlS8D9jNpKke2O6OqKANhUFlw4ZH2YCUDIpNYer\n33qMN47vp6iukmcOfsrPt7/bJkLk6xMvwKW3fRB263ZuHjUTu975A3JrwTWkpMbTyKo3HuWdE4WW\nUixNE0EgHtyKOZnDGByfTH5Cash30qXbuH7ktE5tUkSemBbyoQV5kTahV5GATTPJbyjhZ/kv8ury\nR3l8zpNcZOyicJuLOlOnfZtSrwnlQuO565/j5mnbyU+tZHJ2Cf9z6Tvcc+GH6HrAW2OafVd0UUqw\naZIJiZW8Ouslbhm8m0Q9fO/VaMah2dBbuQly45P52ayluHQb8TYHCTYHLt3GdyZdxG3rn+ZEQw31\nfi/1fi8e08/LR3fzjyPbW94/J3MYv56/iqHxKQgCWZNfGjeP7029hEfOuwq3bsfVjVGwH8nxhpqw\nha40ofFk4VZqvU2W6/3B6oV3jpsXciMwTJPzs0d22RZF5Ij5xhJ91UCir8ge2sQj6w7gijMJ1hWi\nqUHwyL2DWXlfBSOcDS3u8+ZL98fyYdyRXhR2UvMcZ/53yv76FFZ9shRPDCYLDYlP4d1ld4csr/E2\nsaHkEJoQVHub+PHW18NOgrZvANGM1zCwa1qbEX5z+OG+6tO8VLSzpeaKzzAwCV+bvCNWDJvA2ycK\nqfWF3kxHJWXw2hV3cskrv6Woru0cjIZg2dACHpq3stvHVJwbwjWWiL1fVjveMJ/j5pF3U3I4UAhr\naEEef975UMwK/E3fKsUdb9L6KdsVJ7nzv4+R4GwryM2lza9MPtmhUEdSxAFeKBmJ32IyNtpx6zZW\njw75zQCQ5HCxdGgBTX4fs9Y81GEkS/tknmasaoKnON0tDZHvnXopG0oOUuVtYl7mML658SU+qziB\nrxtJSnE2O4tyx/Ja8b6QdboQTEnLpcrbaJlebyJZX3Kwy8dSRI6YF3KAvx18JNIm9BqT59Vh5Sp1\nhmlPKgRk2bwRH3V3RI3PgRFDXrx43YFfGiwZUsAto2d1uO32ipNoFl15mnFqOkuHnF1c/faKE6wp\n2klZUz0VngYemruC/966jg0lhxBCWKbut8at25mUmsMVQ8axreI4TxZubZMA5NRtfLlgPi49fA35\nBHv/LIDW3+gXQt5dLr/tItb95d02y0ZNz6dw65GI2NOaqjKdrCGh/s6O3CaS0Lopkab5xuI1BVOT\nSnn+1GhioZiWU7Pxf/NXMi4li9y4zksNxNsdmGEmczUEOXHJzMkcRr3PS7y966GYTxVu5Sfb3sRj\nBCppbq84wVMHt/LEwpv4+fZ3ePnorg7fPzIhnVvGzOSaEdPQhOD7Uy4hNy6JP+37mCpPI9MyBnPv\n1EUMT0wHYFHuaN48caDNaD/wRNLxjUwRHQxIIW8v4kBUiDhAsS+O4dKDQ5yZu/CZguOGixy9CQcy\nRNRP+Rzk2L19XRW3Q5qPK4BTnvh2a/swuL2bTEzNDnZ6f4UGv4/lQyewavhknGEiSgpSsshwJlDs\nr2wzWagBefHJnGyo5ksbnqXJ8JPhiiPHncS1I6exKn9ym0nURr+PNUd28EHpEbJcCTx18NM27pom\nw8/JhhoW/usRfJ20V3Nrdn4w4zLOzx7RskwIwa1jZnPrmNmW77lv1lJOb3iWnZUnsQsdj+ln6ZAC\nJeQxQsxPdoYjVn3ky7fWkR9fz6L4UiSBZhAHPAmsqR1MtqjjhrTjOFuJ/CdNyRR54liSVIJLyDYT\noaf9DjJs3oiP1hsNnbkfXkuDGd1t4Fy6jUW5o3nrRGGLC8Kt2xmfksVTF98ctoPNoZpybn73CWp9\nHqSUeEw/8TYH9X6vZQMKt25nQfZwfnteoB3Z2ycK+e6mf9Lg9+I1DXQhOmxc0ZXPsWnFN7v1BNBM\nYU0Zx+qrGJucSU4XnkgUfUu/nezsb9RJGxsbM9jSmEaa7qXOtNEgbTgwKJHx/L+yCQyx1ZOi+9jv\nScCDjcG2BnTRdqQuAbdmUuSLY7gjNOOvL/FLjfy4GnbXpUfUDiumpuVyrL6a8SmZ3DR6Jl/78MU2\nI+FGw8e28uNc8PLDLB0ynrsLFpDSbsJiRFI665d9lfdPHeaHn7xGWWMdNRYRIq33+X7JYTafLuah\nne+xtawYv2wbH342CAJ+7/+advlZiTgEolhGtUpgUsQGvSLkQogrgF8COvAnKeXPemO/AxHfaQnZ\nEj8apcaZJA4/Gt7ghGGxP57iVvNc012VIRdSE+DsIOW7L7ELg1Oe6Gu/lepwsbvqFG6bnQlpOZQ1\n1Vu2SzORnGqs5dH9m3iicCuvXn4Hjx7YxPOHP8Nj+BmbkslDc1awu/IUp5vqulSLxWv6+cWOd9lR\nebKNiJ8tAliZP5Hbxsyx7Aik6N/0WMiFEDrwCHApcAzYLIRYK6Xc3dN9Dzwk9ZpueVE68oqm6x5L\n94ldSLJtHbcmO9dICR9V5VDuaz2KjbyPXAOqvE1IwOs1eGz/JsanZHXaKNlj+lm87g+BrjzBZXur\nSlmy7o/kxad0GknSjCElm8uKO9xGAHaht+kOZIVNaHyl4Dy+HmxWoRh49EZM2GygUEp5SErpBZ4G\nVvTCfvs51qMwkdTc4adz8mwNrE45zDBHQ9isTbcW+Vonb54eglPzYxcG0SDiELgxtj4zTYaf3ZWn\nutTx3tNKxJuRELbV2dmgCcGktBy+NqHjglUpDjcPz1+lRHyA0xtCPhhoPbQ4FlzWBiHEnUKILUKI\nLadPhzZxHViEE1dBU/iOWUDAXTLbXc7nE49yddJRRtjrsYVpGCHpu7T8cAgB/2/cRl6btYaFacew\nRXHdFYeuc8fYuaQ53Gd1qzGDFQ97igDy4lN45Lyr+dzw8A2KB7ni2bLym1yaN7bHx1TENn2WpSGl\n/IOUcqaUcuagQYP66rAxhqRsbUBCHMJgsrOKma4KkrVAZmCK5uWb6fu5LL6Eye4aEnUDj9RC6q80\nE02Smeeq576xHzDEXYdovrv4QfggdYPAbl2ht0+p9Xn4v53rqfd7z6pmoy60HjVRcGo23LqN+2Yu\n5a0lXyY3LonsuCQmpFh3jLph1Iwud/BR9G96Y7LzODCk1f/zgssU3Ubgr5IMt9dxY/LR4BLJEgEb\n6jMYbG/EJQz04G/XISQGkgrDRoatrW9WSij1O8mxRUexKlPCwYYkPPucpB7S8ORIbLWChP0CvQES\nDgqOXWsiw2Sw9hUGEuMs+3SmOeP44/nXcMeGZ1hfcqjL0SdOTefyvHHMzRzGkqEFJLbKpmzy+7hq\n+BQOb38npDDW7/d8yIKs4UzP6F/F4xTdpzeEfDMwWggxnICAXwfc0Av77dcIB8h2JTg0tyRnpcEN\nyUdxam3H0wviy9CRLSLejC4gTQ+dYBMCsqNAxP0GfPe+K9h/OIPiSzTS39ZJ9AsSC9tu15RuImO0\nB0Vz2N8v530OIQQPzV3JreufZl9VaUtcuQQS7U7SnHGUNNS0NHV26TbGpWTy8znL2yQIAVR7G1n5\nxl8oa6yzrG7YZPj5+fZ3ePLim/vgUyqimR4LuZTSL4T4KrCOQPjho1LKjvOHBzi2VEn6Ujj9ApiN\nAWXWXBL3GJg2z7rDug3Z7cd9QeTrr5wuT2DngWxMUyN9nURYfAiJpOICGfj2xCD5CWk8duH15CWk\nAJDocLV07jlSV8nY5EGMSspACEFZUz0vHP6Ml4p2YUiTz+VP4tbRs0JEHODhXe9zsqGmwyJZe6pK\nz9nnUsQOvRJHLqV8BXilN/Y1EBj6fUnaIkieJ2k8AgKBLU2Sdkkgk9MKTUC5306y7sfWahu/FPgk\nuCxS96Fv0/QPHEnj72umcqg4jeF5lVx/5Wd89OkQzGBDDM20NsSIA3/7LP4Y4lhDNT/Z9ia/W3B1\nm+UT03KYmJYDwP7q03xn41r2Vwcydmdk5PHzuSs6rOfy6rG9nVY6THPG8ZX3n2dPdSljkwbx1QkL\nWo6pGDiozM5zinWonTMzIK4p5wX+mqNYpIRDvgRLMfeYgjfqM7kgrpx03YMAJIIywwFSMtgRWTfK\njn1ZfO+By/D6dKTUKClNYPOOwfj9XbiL+CXOEtA9Ak+2xIgxUfeZButPHuR4fTWD40PbqtV4m7j2\nrb8GUviDy7aUFXPNm3/l3WV3h0397ywCxqHpnGiopqiuAgkU11Wy4dQhHr3gOuZkDuvhp1LEErFT\nW7QfcepF6+VCQJPUWFubi08K/DIwSegxNfZ7E6nz6hz2udGExCYkTabgzfpMnMLEJ0MF00DQGGYU\n3Ns88rc5eLx2ZLDuuETD57MhZef+Et0ryHxTI/19weBnNVI2isC9zQ+OEmKi7adD1zlSV2G57qWi\nnfjMtl0xDSmp9DTw9okDYfd5w8hpIW3hIDA0SHPGkeGKx2saLfuVBPzmP9r6+ll/jt6gzufhP7e8\nwsTnH2Dcc/dx+/qnKa6riqhN/Z1+OyJ3xDvw1lsX9O9rbMkSVz54joOvTODM7GhrwbamVIp9cUx1\nVeIUJns8SRz2xbEy8QSTXNXYg9qcbDO4PrmYV6ozWZRUhg2jpdkEwEFvPMU+N4sSzm3cvpRw8Kh1\nU+GuorUauSfuBW+GROqQ/p6gejrUTo5uNfcaBiMTz9SSqfV5+NuBLbx+bB/lnvo2dcCbaTL93LPp\nZcanZDEk6F9vzeoxs9lSdoz1JQcRCDQhSHG4+eP51zA6eRDjnrvP0pZ91YFJ1kiEJkopWf3eU+yu\nLMEbdAutLznEqjf/wttLvkximN6hip7Rb4V8TcVjLHHdENnRnJAM/a5J5iowvaA5oPI90LtQdqTc\ncPJW/ZmaGW7hY7KrGns7t4sNyfS4auxBEYczPvERjnoydOtejWeD3xA8vXYyhUfTWXTeQeZPL2LT\nZ4P5ZGcu0uKJoKuIdu4nzS9If19rEfekHTKqhdwhNHLjkrj01d/hNQzGJQ+i3NtAhaex05T9Wl8T\nd33wHP+6/I6QdTZN47cLrmZfVSk7Kk6SE5fEvKz8luzTJIeLSk9oCYYkuyti8eXbyk+wv6q0RcQB\nTClp9Ht54cj2sGV0FT2j3wq53W7nDeM53l/zMWt++QpTFk7g5h9e06flbYd8RzJoJWjOwB9AygXQ\ndKT7+0rW/RhShAi5JiDT5sVp4SQzJdSZdtIJiElPJz7r6h08vmYapqmxeXsehgF+49yEmrQeoUdb\n32aBIDcuiVONtSTYnTg1ncOt3Co7q051eV8SOFJbwd6qUxTVVaIJwYKsEbhtZ0r+jk3JZGxK6GPc\nF8bM4Te7P2gz2nfrdr4QQbEsrDltOXZqNPzsrCzpc3sGCv1WyJtZsHIOC1bOicixs68D0U7ndBfE\njem+oFYYDmwiNFdTSqgzNezCDIkxl61GulKCEYzw686xpQS/X6O2wcH3H7i8JQLF47XRV3VTvGkE\n0lS1Pjtkh+hCUOVtJNnh5oHZS7l9w7M92p8pJZ974y84tMCXxQQenr+KC3M67mB/1/j5VHoaeKJw\nK3ZNw2eaXDNiCl8pOK9H9vSEEUkZlt8vl26jIEyGqqLn9Hshb8+CVXN4/x8f983Bwk0ln4UQ+aSG\nKQVWgdinfE5S9OaCVGfQW1U/FAJsZ3Hcxiadn/7mIjZ9NgQzpIFy3yiqoxwSd4A3A7yZICPcn8Iv\nTfx+L/V+L3dseK7H+2t2Q7R2R9z9wQt8sPzfSHaET3XVhODeaZfytYkXcKK+mtz45DZZoZFgevpg\nRiZmsK/6jHtFQ+DS7Vw1fHJEbevPDLiolf96/jth181aOhWHK1QlLrxx7lkcKbxP92zcG+m6x3KP\nQkCuw8PbdYPwSYHHFHhMDY+p8VTVEBoN7awKZ3l9Gtt2ZXHTt65h47ZhFiLedwgpSNusk/l69H1d\nzbOYhNGDN0C7pmMTmmUNdCFg3bF9Xdpfot3J2JTMiIs4BFrK/W3hjVw5bAIOTUcTgnlZ+byw6NYO\nb0qKnjHgRuSni8vCrivacYx/NTzJa4+9wwu/+CdJGYl8589fIWd4Fu890ZFvPfC878iRDFpl4syD\n2i3gKwdHLzVb8UkRtmWbX2psaBzEp55URjvq8EmN/d4EkBCnWycKtbE+qEVCgGmC12fjry9M4x+v\nF2AY0SOemiFI2yCouEAiBaCD8IPWCPYKaBpKxN0uneHW7Xx+xBSqPI0Mjk+mxtvEkwe3hmxnmJIG\nf2ikS2c0+n08ffBT/lW8m0S7k5tHz2Rhzqg+nfxMtDt5YPaV3D9rGYAq7NUHDDgh/8M9fwu7rvRo\nQOSvuHUhV9y6sGV5Y11HzRkCjufEKZIxD5sIWyA6JfVC6KQfQLeoNh2U+p1k25ra+MK9pmBXUxKC\nwMTmp02pLesc+EMmR60wgT8/M52JY05T1+DgX2+PY9eB6PRnJhzScFRJaseZGG5wHxXEHwJhCIx4\ngTFVo3SIDzOOiD1vCuD2MbPJjkvige3v4A/WL4+z2ZkzaBj/OfXSlpT8LaeL+ceRHZbhiRfmjAhZ\n1hEew881b/2VQ7XlNAWjZTafLuaW0TP57pSLe/qxuo0S8L5jwAn55jc+7fZ73nrm/bDrXCMkTUUw\n4ieyTVihHte7Qg6CF6pzuSm1mLhgCzddSLZ7kjnqcWBD4ms3HDXR8ElwhPk9SQk+4PHjI3n+9Uk8\n+6/YKHbiqBCkfxhqq14v0T8wyBMa0gZV0yS1k2SfjdJHJKbxnUkLuTBnFC5b4Kc1NzOf5w5/Rp3f\nwxV547goZ1Sb5hUzMvK4Im8s647vo8EfuIIu3c5No2YwPLF7PU5fPrqbw7UVLSIOgf6gj+3fxOox\ns8hyJ/bK51REHwNOyOsru9/6rPyYdcYeQNoySflagS01dF37iJWectp083/loxlmbyBR83PMF0el\naUdgkqU3UWK09UEOt9W0JA81hx6aMpDxuacpgQbDxntNmdRojlhInuyUlnh0GahznrhXElek0TBc\nUjdW9uokqYZo4x9363a+M3khl+eNa7Pd+NQsfph6WXibheDBOcu5suQQLxXtxK5prMqffFYp9m+f\nOGA5srdpOltOF7N0aEG396mIDQackAdqlHSPja9uCbsuZTboDtnrom2NQCI44ktos1Siccpw03ro\nKZAc9ifhl3DgaDqPr51KybFksvKqSVl4moZMAwcmXnQ0myR+cD11RxKJeidzN7DXaNhrwFEGCfsE\nJStMZC984/PikpmWkce6Y3uxB0MGvznxwhAR7ypCCC7MGdlpuGFnZLoT0IWwrIOe6oy+5teK3mPA\nCfmIqcM5uPVwt97jdISPBrClQfaNYDYFXCl9I+ihaEiM1nHjCDRM1u0Zyq9/sRDDJ0BqHDuZhPZp\nHgVf2kfi8FoADJ9Ad/aqHyiq0AyBrVYSf0BQN77z27hNaPhl+P5Kd42fz/WjplPtbaSsqZ68+BSc\nFjVR+prrR07n2UPbMFq5VgSQYHcyZ9DQyBmmOOdET0hCH7Hiy+Efc8Nx5/3hC/d7SwIuC90dOREH\ngWFxKU0Ejz85C8OrQ3P4oNQwfTqHXww8untrdLbdN5nqfSn0p9F4ezS/wN1JP9TWODu4mL/atQG/\naZLscDMyKeOsRbzB7+U3uz9g8Wt/YOXrj/LcoW2YPWiyOiZ5EPfPXka8zUGCzUmcbmdIfCp/v+hG\ny3rniv5D5IcRfYw8ix/K8Kn5YddVfgxJ03tgUK8RmvIogIpi63rX9cfjME3Bzocn4K2OfPzxuUYi\nMboYxmxKidlBtE+938uHpw5zQQ9cIV7DCESY1FTgMQMj6B9tfZ2PSo/wi7krz3q/y4ZO4NLBY9lR\ncZJ4m4NxKZkqemQAMOBu0+89u7Hb72lsDF9F0Qw/D9rnaK3aLdsxGWqvx+a2LtqkuwykDzzl/V/E\nAaQN6gq6dhM3kehCkGy3rtQnkZQ11ffInnXH91JUV9ki4hCIMFl3bB8HqntWrdKp25g5aAjjU7OU\niA8QBpyQX7b6orDrwn3n96zfHfY99uTo+KFoSKY6K0nSfKRqHs6PK2WCs5qRFxxHs7f1f2t2g+zz\nTrHjVxPoz+6UZiSSpmyJtxvRfD7TxKnbiNNDQ10MUzKrhz7nj0qOWCb8CARby471aN+KgceAE/JL\nbjw/rGCv+tYyy+WzlkwLuz8tSrrZ+L0Cm4Brk46yMuk4pw0XpX4nU7JLSZ9WjrCZ6C4/wmaSPrWC\nmiOJNJZEifHnGIHAfVzgPAmEn8MMIS8+mfzEtDbNHdzBmiFW9cO7Q058UkuRrNZoQjDInWDxDoUi\nPAPORw7wXMVjXJ99Bz7PmRHRhdfM464HV3Pi4En+Y/FPOXHwFEITzLxsCj9eew/xKW7qq0Jj0O1u\nHei45nRfcOL9LH6/aQLnf3E3+dlVLHKdwgmsenwx7txGRl57CN1hYHo1TqzPob54YImFkIKsVzUa\nhkrKLu680bNbt/PFcXO5IHskfy/8hH8e3UWczc6No2awbEjP47GvHj6F3+/5CDjztCQIZH+en929\njE6FQpzN5F9PmTlzptyyJXxsdqSoKKnk2sF3hgSaJ6Un8sLpR7lh2F2cLi5vWT5+7mh+9eFPuXf7\nqj62NJSdvx10MujSAAATxUlEQVRDbWEyILDbDJISPFTVuqKqVkq0UDfKpOI8GYgpF4ABmi6waxoO\nzYbXNLhr/Hy+NvH8c2rHR6eO8I2Na2jwezGlJC8+hd8tuLrbGZ2KgYMQ4hMp5cz2ywfkiDwc/3PN\nLyyzhWrKa3n/xY95suh3IeuklAyPn8jh+p1tlue4hnOyqXvx6meLlFB3JIlmf7fPr1Ne1ZwAEgUF\nvKOMhEINW52kerKJkQCuk3DP/EuYNX8kR8sq2P3mUT5+cDd3uPazYvl0liyeihauYlkYDNNk0+mj\nVHkbmZGRR6ZFevy8rHw+Wv51CmvKcOo2hiVYpAcrFF1ACXkr9n9yMOy6f/7udRZ8LrRBRVHDHo43\nFoYsL/ee7FXbOsL0WdcpD6CE3ApXicBVEvCvaEJAgWSIM5kf//gFTpXW4PMFXB6/+d3b7Nx5nO/d\nYz1/YsXh2nJueucJan0eBIE6418cO4dvT14Ysq0mBGOSB/XKZ1IMXNRzdyvcCeEDjXNGWHdMPtZw\nAMMMjT7wmr3XK7MjpARvtR3ps7qUEuHovxmbvYXDaaOgIJe33t5NWXldi4gDNDX5eHf9Xo51UG+n\nNVJKbl//DKcaa6n3e6nze/GaBn/Zv5l3Thw4Vx9BMcBRQt6K2396Q9h1X/nlbZbLk+zp6JojZLld\nnJv4bCnP1A9v/rfw2fzgoDt0VC6Vj7xTRo7IZPKkIWz9tIimptCbsq4L9uw90aV97a0q5XRjXciV\naDR8PH7gk16wVqEIRf3KW7H49ks4/+rQbkD3PP5VHI5QsQYYnzQbKwE1OTcj4YaTLvz1OqZf0HjK\nxa6Hx1N3KAUkaHYzaEvwT5Nwjpoj9yfsdh0hBDnZydhsVudLkJHRtRKw9X4vmrD+WdX6+uYpTTHw\nUD7ydvzw2W9TV13Hml+9SmpOCku/eGmH29f7qzHM0PBDKSUpeiZVRmmv2lexM41j6wYT6vcWAV+5\nboKhBdabyjfeFbbvKMbr9bN0yRReeHELfv+Zm7CmCZKT3UyZ3LUEoElpOUiLG7tLt7G0F8IWFQor\nejQiF0I8KITYK4TYLoR4UQjRsyyJKCEhOYGbfvD5TkUcYG/NFoTFCMzE6HURlya4Mjoa1YngCFwJ\neHcQBErJZmen8JMfX0VGegIulx2HQ2f06Cwe+t8buhy14tRt/GTmYly6DS14Hdy6neGJaVw3Mnxi\nmULRE3o6In8D+L6U0i+EuB/4PnBPz82KHTShn2locI4x/ZA4ohahS6TR/pgDOzpFCCybTGuaQAgw\nDGm5jaYJpk3Px24PuFSmT8vn6Sfv5sSJSpwuO4O66FJpzfJhExmbnMmThVspbarjktzRXDlsQlSU\nulX0T3r0zZJSvt7qvxuBq3tmTuxRkDybl4//uU+OpelQunEQ+SuKOLJ2GNIvAAGaCVJ0v2NGDJGY\n6KKx0Yvfb51j/+1vLebZ5zZx7FgFuq4xaeIQvvn1y0lJieOVVz9j05ZDpKXGs2vXcSqr6vF4/Lic\nduLjnfz7txa32ZemCfLy0npk79iUTH4084oe7UOh6Cq9ltkphPgn8IyU8u9h1t8J3AkwdOjQGUVF\nRb1y3GhgS/mbvHj8N+f8ONKEopfzSC2oRnMYlG1Lx19vw2jSqNyZRn8ekQfq44iwZYhvvWUBt9y8\noNP9GIbJ5i2HOXSolMGDU5k/b3TLaFyhiHbCZXZ2KuRCiDeBbItV90opXwpucy8wE1glu3BniNYU\n/Z5w/+47qPGXd75hEIGwnBTLd0/gSOOulh6brWmOGd/+fwXoThPTpyF0ia/WhvQN7Md2u13nuae/\nSlJSF4uOKxQxSDgh73SyU0q5SEo50eKvWcRvBZYBN3ZFxPsrTUa4+tQCt56A1upUCzQS7Wksz/5K\nyNZHGneRKMLX2hCaiaYF6oj7qp14K1xInxpRArz9TvhywwpFf6anUStXAN8FlkspG3rHpNijyajH\nKz1h1kouyPgcLv1MyVi3Hs8NQ/+dt8uesnxHnaxAGsJy8m7HryfgrbWfad0G9GeXSlfx+QxOl9Va\nris+VsHjf3ufPz/6Hnv39V3pBIWir+jp8/jDgBN4I9iJZKOU8q4eWxVj2IQDQfi5xo/K/0VjqxF7\no1HPE0X3U+evtNxeItGEDUTb+HRpBkuqmCqPqz1ut50JBYNDlr+0diu//f3bGIaJaZo8/48tLFk8\nmX+7u/PQUoUiVuhp1Mqo3jIklgmEIAb62LfHJhw0mQ3IVh0NJCYeszGsnxxA1wnZm6aDPdGHp9K6\nBdlARdMEw4ZmMGd22x6aFRV1/Pb3b+H1njmTHo+PV1/bzsULCyyFX6GIRdTQrhfwmo1hBdmUBj4z\ntOen12wiw2EtJElaGoZFswopIXFETc+M7Ye4nHYe+t8b0PW2X+ePNx1Es+ge7/H4ePe9PX1lnkJx\nzlFC3gs4NDdu3bptWoojA7tFUS2H5uKSrOvIduW3WR6vJzMx9TzLfQkByaOs/cADmeRkN05naG9N\nXdcs2/oJIcLUVFEoYhMl5L2AJjQuybo2pOKhXTi4MvcOku0Z6OKMF0vDRqItlYKU2fzbmF/wzTEP\nc2XuHXxp5H38x4S/0GBYj7qlCbVHBlaLts5wOm0sWzrVct3cOaMwjNAnJbtdZ9HFqu6Jov8wsIOP\ne5G5GUuway7ePvUMNb4KMpy5XJGzmjFJ0xkSN4bXTj7OjuoPAJiQPI/FOatbxD3DlUuGK7dlX9NT\nL2bzsQ84/k4OVbtTsCX4yL2whOTRNZx8Pysiny/acDoD527a1GF8/urZltskJbn5/j3LuO/+l9E0\ngWkGqkLedON8Ro5U51HRf1A9O6OQ6ppGrrvt53jr9ZZ64prdIH5oLbUH+0Vdsh7hdNq49po5nH/e\nmC4JclVVA+9/uB+f12De3JFkZ6tzqIhNVM/OGGLNmk8wG11I40y0henTqT+SSr8uqNJFTFOyauXM\nLmdxpqTEsWyJtftFoegPKB95FLL5k8Nt2o0143JaN7cYSDidNi5eWKBS8RWKVighj0IyByVaRlsY\nxsDuv+l02li6ZArf+oaqKqhQtEa5VqKQq1fN4qONhXg8Z2LJdV0jNyeFw0fKImhZZMjMTOJ3j9xK\nYqIrJFZcoVCoEXlUUlAwmG99YzHx8U7cbgcOh07B+Fxuvsk6vrw/43LZueP2C0lJiVMirlCEQY3I\no5RLF03gogvHcfRoGYmJbjIzkzh5sirs9uE65MQymiZYfuU0Ll6oYr4Vio5QQh7F2O16m/C6nJwU\n4uMd1NeHpvzruoZhmP1KzG+6cT633nJ+pM1QKKIe9awaY0yfNsxyuWn2LxEXApaqkEGFoksoIY8x\nrEbjAHZ7/3q4mj9/9Fk1PlYoBiJKyGOMObNH4nSEirbXG1otMRYRItBo+ZtfuzzSpigUMYMS8hhj\nyeIppKbFt2kY7HLZuXTRxAha1TsIAZMnDeFPf7idtDRVHEyh6Cr963l8ABAf7+T3v7mN5/+xmfc/\n2E9SoourVs1i5ox8Xn9jZ6TN6xFSgsNhUy4VhaKbKCGPQRITXdy2+nxuW902omPG9GF8srUoZPsL\nzx/Dexv295V5PSIu3tn5RgqFog3KtdKP+NlPr20Tc63rgju/eBHD8gdF0Kqu43TaWb5sWqTNUChi\nDjUi70fousZ//sdy7vn3pTQ0eEhMdKNpgnfe3YPbbaex0ddm+zM1uiOL02lHmiY3XD+XaVOtwysV\nCkV4lJD3M0pOVfPS2q0UFZUxoWAwy5ZNY8F5Y/j9H9/B6/W3dMzRdY24OAe1tU0RtVcIwaWLJnDr\n6vNJS7Vul6dQKDpGuVb6EXv2nuD2L/6JF/6xhY0fH+RvT3zIrbf9gfKKOh751S3Mnzcam03DZtNY\ncN4Yli6eEmmTkVIyaFCiEnGFogeoEXk/4sH/fYXGpjPuE6/Xj99v8Mc/vcsP7l3Bj/5rFc0doYQQ\nFBaW8PSzH0fK3BZOHK+MtAkKRUyjRuT9hIYGD8XFFSHLTVOyafOhlv8LIRDBYuejRmXjckX+Xu73\nm5E2QaGIaSL/K1Z0m5qaRp56eiMb3t+H221n5YoZXHLxBMtmFBBIGAqHzaYDkcsKdbnsXHTRuIgd\nX6HoDyghjzEaG73cdfdjlJfXtbSDe+Q3b7Fn70nOmz+GDz7c32aE63TaWHHl9LD7S0xwUVfnsVxn\nVRrX6dAxTNntUfTw4elcftkU/vLYevx+A8OQuFx2ZkzPZ97c0d3al0KhaIsS8hhj3es7qaysb9PT\ns8nj4823dvLIr27h9OkaDh06jaYL/H6TObNHct21c8Lu7+qrZvPHP79LUyvfuk3XiIt3UFNjEdEi\nBH5/91vO3XXnJcyaOYI5s0aw7vUd1Dd4WDB/DDNmDEfTwjxKKBSKLtErQi6E+Dbwc2CQlHLg9SLr\nQ7Z+eqRNC7hmbDad4mMVPPyrWygsPMWJk1WMHJHJ4MGpHe5vxfLpFB+r4JVXt2G32/D5DKZOGYrH\n6+Ozz4pDtu8s7nzmjOFs+eRwm2UXXjCWWTNHADBsWAZ33rGws4+pUCi6QY+FXAgxBLgMONpzcxSd\nkZOd3NJEojVSSjLSAzVKRo3KYtSoLKu3h6Bpgq999VJW33weR4rKyMpKJjsrmXff28u+fSVtRuoA\nycluysrqLPfldNp44GfXcvhIKc8+uxlTSj5/1UxGjco+i0+qUCi6Sm9ErTwEfBeIfIrgAGD58unY\nbG0vm6YJ0tMTmTBh8FnvNzk5jimTh5KdlQwERtGXLpqIw2HD5bITF+cgOcnNz356DSOGW6f83/3l\nRQAMz8/knu8u5fv3LFMirlD0AUL2oK2MEGIFcLGU8utCiCPAzHCuFSHEncCdAEOHDp1RVBRa3EnR\nNbZ8cpj7H/wX9fUeDMNkzOhsfviDleekauDx45Vs33GUpKQ4Zs8a0VI+9z9/+DwfbSxEykBLuru/\nskjVSVEozjFCiE+klDNDlncm5EKINwGrYdW9wH8Al0kpqzsT8tbMnDlTbtmypUuGK6wxTcnJk1W4\nXHbS01XtboViIBBOyDv1kUspF4XZ4SRgOPBZMMEkD9gqhJgtpSzpob2KTtA00elEpkKhGBic9WSn\nlHIHkNn8/+6MyBUKhULRe6gUfYVCoYhxei0hSEqZ31v7UigUCkXXUSNyhUKhiHGUkCsUCkWM06M4\n8rM+qBCngWgKJM8AYnGSVtndtyi7+5ZYtPtc2zxMShmSkRcRIY82hBBbrGIzox1ld9+i7O5bYtHu\nSNmsXCsKhUIR4yghVygUihhHCXmAP0TagLNE2d23KLv7lli0OyI2Kx+5QqFQxDhqRK5QKBQxjhJy\nhUKhiHEGpJALIR4UQuwVQmwXQrwohEgJs90RIcQOIcQ2IUTE6u4KIa4QQuwTQhQKIb5nsd4phHgm\nuP5jIUR+31vZxp4hQoh3hBC7hRC7hBBft9jmIiFEdfDcbhNC/DAStlrR2XUXAX4VPN/bhRDhu1v3\nAUKIsa3O4zYhRI0Q4hvttoma8y2EeFQIUSqE2NlqWZoQ4g0hxIHgv5alPYUQq4PbHBBCrI6wzdGj\nI1LKAfdHoDWdLfj6fuD+MNsdATIibKsOHARGAA7gM6Cg3TZfAX4XfH0d8EyEbc4BpgdfJwL7LWy+\nCHg50t+Fs7nuwBLgVUAAc4GPI21zu+9LCYHEkag838AFwHRgZ6tlDwDfC77+ntVvEkgDDgX/TQ2+\nTo2gzVGjIwNyRC6lfF1K2dzBeCOBWurRymygUEp5SErpBZ4GVrTbZgXw1+Dr54FLRLBIfCSQUp6U\nUm4Nvq4F9gBn34cu+lgBPC4DbARShBA5kTYqyCXAQSllNGVOt0FKuR6oaLe49Xf4r8BKi7deDrwh\npayQUlYCbwBXnDNDW2FlczTpyIAU8nZ8gcDoygoJvC6E+CTYqi4SDAZat7M/RqgotmwT/GJVA+l9\nYl0nBN0804CPLVbPE0J8JoR4VQgxoU8N65jOrntXrkmkuA54Ksy6aD3fAFlSypPB1yWAVffwaD7v\nEdWRXitjG2101KJOSvlScJt7AT/wRJjdLJBSHhdCZAJvCCH2Bu/Mii4ghEgAXgC+IaWsabd6K4HH\n/zohxBJgDTC6r20MQ0xedyGEA1gOfN9idTSf7zZIKaUQImbioqNBR/rtiFxKuUhKOdHir1nEbwWW\nATfKoCPLYh/Hg/+WAi8ScHP0NceBIa3+nxdcZrmNEMIGJAPlfWJdGIQQdgIi/oSU8h/t10spa6SU\ndcHXrwB2IURGH5tpSReue1euSSRYDGyVUp5qvyKaz3eQU83uqeC/pRbbRN15jxYd6bdC3hFCiCuA\n7wLLpZQNYbaJF0IkNr8mMLGx02rbc8xmYLQQYnhwxHUdsLbdNmuB5hn8q4G3w32p+oKgf/7PwB4p\n5S/CbJPd7McXQswm8F2M6M0naEtXrvta4JZg9MpcoLqVWyCSXE8Yt0q0nu9WtP4OrwZesthmHXCZ\nECI1GNVyWXBZRIgqHemLGd9o+wMKCfjatgX/miM+coFXgq9HEIgQ+QzYRcAlEyl7lxCI/DjYbAfw\n4+AXCMAFPBf8XJuAERE+vwsI+AW3tzrHS4C7gLuC23w1eF4/IzBRND/S34uOrns72wXwSPB67CDQ\nqzbSdscTEObkVsui8nwTuNmcBHwE/Ny3E5jTeQs4ALwJpAW3nQn8qdV7vxD8nhcCt0XY5qjREZWi\nr1AoFDHOgHStKBQKRX9CCblCoVDEOErIFQqFIsZRQq5QKBQxjhJyhUKhiHGUkCsUCkWMo4RcoVAo\nYpz/D07ag4WzqvvuAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BY8EYfGu8lMf",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        },
        "outputId": "5ebb3819-d6fc-4ffb-d8fe-fd4841c84406"
      },
      "source": [
        "print(xp)"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0       -0.388650\n",
            "1       -0.384703\n",
            "2       -0.743132\n",
            "3       -0.384703\n",
            "4        1.501081\n",
            "           ...   \n",
            "64530    0.690568\n",
            "64531   -0.030190\n",
            "64532   -0.032992\n",
            "64533    0.685332\n",
            "64534    0.691717\n",
            "Name: principal component 1, Length: 64535, dtype: float64\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XVk9f-o79c2o",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "national_processed[cat_cols].columns"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tP0OcgF_A_fy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "national_processed[cat_cols]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RQx7UvsucIrL",
        "colab_type": "text"
      },
      "source": [
        "# Stretch Goals\n",
        "\n",
        "## 1) Perform further data exploration on the HADS national dataset (the version before we one-hot encoded it) Make scatterplots and see if you can see any resemblance between the original scatterplots and the plot of the principal components that you made in 7.1. \n",
        "\n",
        "(You may or may not not see very much resemblance depending on the variables you choose, and that's ok!)\n",
        "\n",
        "## 2) Study \"Scree Plots\" and then try and make one for your PCA dataset. How many principal conponents do you need to retain in order for your PCs to contain 90% of the explained variance? \n",
        "\n",
        "We will present this topic formally at the beginning of tomorrow's lecture, so if you figure this stretch goal out, you're ahead of the game. \n",
        "\n",
        "## 3) Explore further the intuition behind eigenvalues and eigenvectors by creating your very own eigenfaces:\n",
        "\n",
        "Prioritize self-study over this stretch goal if you are not semi-comfortable with the topics of PCA, Eigenvalues, and Eigenvectors.\n",
        "\n",
        "![Eigenfaces](https://i.pinimg.com/236x/1c/f1/01/1cf101a9859437a5d096a04b05be06b4--faces-tattoo.jpg)\n",
        "\n",
        "You don't necessarily have to use this resource, but this will get you started: \n",
        "[Eigenface Tutorial](https://sandipanweb.wordpress.com/2018/01/06/eigenfaces-and-a-simple-face-detector-with-pca-svd-in-python/)"
      ]
    }
  ]
}