ProbabilityEtc.ipynb

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      "name": "ProbabilityEtc.ipynb",
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      "include_colab_link": true
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
    }
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/ZuckermanLab/T32_Nanocourse/blob/main/ProbabilityEtc.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ooim-BFkrwRZ"
      },
      "source": [
        "a = 4\n",
        "b = 5\n",
        "c = 6\n",
        "print(a,b,c)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F6nqwry7P77i"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UUxGydAKtoxc"
      },
      "source": [
        "# do some math\n",
        "f = b * c\n",
        "print(f)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O0imlMQLsLDJ"
      },
      "source": [
        "print(f\"a = {a}    b = {b}    c = {c}\")  # The f enables printing values within a (quoted) string\n",
        "print(a, \"\\n\", b, \"\\n\", c)  # lots of ways to print things - \"\\n\" is new line 'character'"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OInfWCdAtEc9"
      },
      "source": [
        "a = 7"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D1aguln2tOLZ"
      },
      "source": [
        "# ORDER MATTERS IN PYTHON NOTEBOOKS - BE CAREFUL!\n",
        "print(a)\n",
        "# re-run first definition of a above and print again"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kaYpRO3wvKHH"
      },
      "source": [
        "# LISTS AND LOOPS ARE KEY ELEMENTS OF PYTHON COMPUTING AND DATA ANALYSIS\n",
        "instructors = [\"Olga\", \"Nick\", \"Luke\", \"John\", \"Dan\", \"Jeremy\"]  # a list of strings\n",
        "quant = len(instructors)  # number of elements in the list\n",
        "print(f\"There are {quant} instructors:\")\n",
        "for teacher in instructors:  # The colon \":\" here indicates the following line(s) depend on this line\n",
        "  print(teacher)  # ALL INDENTED LINES DEPEND ON ALL PREVIOUS NON-INDENTED LINES"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QFdR2Sfx67VL"
      },
      "source": [
        "from random import *  # we often want to use a library of functions that is not part of basic python\n",
        "max = 20\n",
        "rand_list = []  # blank list to start\n",
        "count = 0\n",
        "while (count < max):\n",
        "  count = count + 1\n",
        "  rand_list.append( random() )  # random with empty argument \"()\" gives a number between 0 and 1\n",
        "print(f\"We obtained {len(rand_list)} elements\")\n",
        "print(rand_list)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UfwO94kW-5_z"
      },
      "source": [
        "# Make a new list by doing some math on every element of a list\n",
        "squaredvals = []  # empty list\n",
        "for number in rand_list:\n",
        "  squared = number**2\n",
        "  squaredvals.append( squared )\n",
        "  print(number, squared)   # good to print things to check program is performing correctly"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_X9_FOwuvSUF"
      },
      "source": [
        "# NUMERICAL PYTHON - NUMPY\n",
        "# Every mathematical operation has a better implementation in numpy - faster, less memory\n",
        "import numpy as np  # we can make our own abbreviation - np is typical\n",
        "count = 20\n",
        "array_rand = np.random.rand(count)  # a single command accomplishes same as our loop above\n",
        "# Note this is an ARRAY, not a list.  Arrays can be very complex objects - e.g., like matrices.\n",
        "print( array_rand )\n",
        "sq_array = array_rand**2.0  # a single command does the same operation on ALL elements\n",
        "print ( sq_array )"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lCKhwJqEBTVF"
      },
      "source": [
        "# turn it into a function\n",
        "def square_this_array( input_array ):\n",
        "  return input_array**2.0\n",
        "print( array_rand )\n",
        "array2 = square_this_array( array_rand )\n",
        "print( array2 )\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qClfrDJn9hj5"
      },
      "source": [
        "NUMBER ONE THING TO KNOW ABOUT PYTHON - \n",
        "WHATEVER YOU WANT TO DO, IT'S SAFE TO ASSUME SOMEONE HAS DONE IT BEFORE ...\n",
        "SO GOOGLE IT.  Finding the precise thing you want may take some rephrasing of your search, or tweaking exisiting code.  But\n",
        "DON'T BE AFRAID TO EXPERIMENT - IT'S JUST CODE!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hugdhJcPN1N1"
      },
      "source": [
        "# Probability distributions in one dimension (1D)\n",
        "# Bin size matters!!\n",
        "import matplotlib.pyplot as plt\n",
        "u5 = plt.hist(array_rand, bins = 5)\n",
        "u10 = plt.hist(array_rand, bins = 10)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zvaW0VqJks8n"
      },
      "source": [
        "# Make plots a little easier to understand\n",
        "u5 = plt.hist(array_rand, bins = 5)\n",
        "u10 = plt.hist(array_rand, bins = 10, alpha=0.5)  # alpha is transparency parameter"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YlDcvrqaQFXy"
      },
      "source": [
        "# Better use a density!\n",
        "# DEFINE\n",
        "nbin = 5\n",
        "u5_norm = plt.hist(array_rand, bins = nbin, density=True)\n",
        "nbin = 10\n",
        "u10_norm = plt.hist(array_rand, bins = nbin, density=True)\n",
        "plt.show(u5_norm, u10_norm)\n",
        "# How to 'reality check' a density?  Guesstimate the area"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "moH0oFklRJ1G"
      },
      "source": [
        "# Noise and sampling - Less data, less idea what's going on\n",
        "# Noisy data could support different hypotheses!\n",
        "# Let's examine effects of having more data\n",
        "def make_array_rand_plot( count ):  # function to make histogram\n",
        "  tmp_array = np.random.rand(count)  # compare to code above\n",
        "  return plt.hist(tmp_array, density=True)\n",
        "unorm_20 = make_array_rand_plot( 20 )\n",
        "unorm_200 = make_array_rand_plot( 200 )\n",
        "unorm_2000 = make_array_rand_plot( 2000 )\n",
        "plt.show()\n",
        "# Run cell multiple times to see range of outcomes (due to random noise)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2AkbZGBRVuUu"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t0h1g9fKUYZu"
      },
      "source": [
        "# The difference between variance and uncertainty\n",
        "# Variance - often measured by standard deviation - tells us the \n",
        "# amount of variability expected among samples from a distribution\n",
        "# (e.g., from repeated runs of an experiment)\n",
        "# Uncertainty, on the other hand, tells us the precision with\n",
        "# which we know a certain value.  If we have made many measurements,\n",
        "# the uncertainty can be *much* smaller than the standard deviation.\n",
        "# How many replicates is enough?  That depends on the question you\n",
        "# want to answer.  For example, it's easy to distinguish the average\n",
        "# height of adults from those of pre-school children, but distinguishing\n",
        "# the average heights of 13 vs. 14-year-olds would require many measurements.\n",
        "mu1 = 10.0\n",
        "sigma1 = 1.0\n",
        "data1 = np.random.randn(1000) * sigma1 + mu1\n",
        "plt.hist(data1, density=True)\n",
        "mu2 = 0.25\n",
        "sigma2 = 0.25\n",
        "data2 = np.random.randn(10) * sigma2 + mu2\n",
        "plt.hist(data2, density=True)\n",
        "plt.show()\n",
        "# We can have a very precise estimate of the mean of a data set with large variance\n",
        "# We might have a poor estimate of the mean of a low-variance data set - 'poor'\n",
        "# in the sense that we cannot be confident the mean is positive in this case."
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3LoRHY6qBzLg"
      },
      "source": [
        "# Visualizing distributions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u0mbdaH1J-m0"
      },
      "source": [
        "# 2D distributions and visualizations (John)\n",
        "# contour plots, heat maps\n",
        "# comparing 2D densities via heat map"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PCPSG9hUKOot"
      },
      "source": [
        "# Marginalizing/projecting: 2D -> 1D (John)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IXVCedncKY12"
      },
      "source": [
        "# Dimensionality reduction (John)\n",
        "# PCA"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ezvPp_Kr1dUV",
        "outputId": "961c0913-6353-47f3-e354-87383a367f60",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "import this"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The Zen of Python, by Tim Peters\n",
            "\n",
            "Beautiful is better than ugly.\n",
            "Explicit is better than implicit.\n",
            "Simple is better than complex.\n",
            "Complex is better than complicated.\n",
            "Flat is better than nested.\n",
            "Sparse is better than dense.\n",
            "Readability counts.\n",
            "Special cases aren't special enough to break the rules.\n",
            "Although practicality beats purity.\n",
            "Errors should never pass silently.\n",
            "Unless explicitly silenced.\n",
            "In the face of ambiguity, refuse the temptation to guess.\n",
            "There should be one-- and preferably only one --obvious way to do it.\n",
            "Although that way may not be obvious at first unless you're Dutch.\n",
            "Now is better than never.\n",
            "Although never is often better than *right* now.\n",
            "If the implementation is hard to explain, it's a bad idea.\n",
            "If the implementation is easy to explain, it may be a good idea.\n",
            "Namespaces are one honking great idea -- let's do more of those!\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7DVmvV8jznWM"
      },
      "source": [
        "import numpy as np\n",
        "from  matplotlib import pyplot as plt\n",
        "from sklearn.decomposition import PCA"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eP-hp1XAzpOk"
      },
      "source": [
        "## Make some sample data\n",
        "\n",
        "Let's make some sample data, and plot it in a few  different ways."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SJKQg9pGzqm5"
      },
      "source": [
        "# No magic numbers!\n",
        "sample_size  = 100000\n",
        "\n",
        "x_data = np.random.normal(loc=5, scale=1, size=sample_size)\n",
        "y_data = np.random.normal(loc=5, scale=.5, size=sample_size)"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "id": "OraWzEa3z2TT",
        "outputId": "dc496df4-286d-4886-af4a-d8d597fddd25"
      },
      "source": [
        "# First, the scatter plot of course. I set the aspect ratio equal so you can see\n",
        "#   this is an ellipsoidal distribution of data\n",
        "\n",
        "plt.scatter(x_data, y_data)\n",
        "\n",
        "plt.gca().set_aspect('equal')\n",
        "plt.xlim(0, 10)\n",
        "plt.ylim(0, 10)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
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          "metadata": {},
          "execution_count": 7
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          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "H7RuMW2kDRfa",
        "outputId": "546618f2-4cca-46dc-a19a-e7b67714141f"
      },
      "source": [
        "# Because if I don't, the auto-scaling might make you think it's circular!\n",
        "\n",
        "plt.scatter(x_data, y_data)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f0321112710>"
            ]
          },
          "metadata": {},
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "id": "zgDaGAkVz3lP",
        "outputId": "9d2b5067-0f46-474d-a5b0-61246c033558"
      },
      "source": [
        "# But this looks like a big blob -- can we get better insight into this?\n",
        "# Do a 2-D histogram. Here, try adjusting the number of bins and see how\n",
        "# that affects the resolution of the histogram.\n",
        "\n",
        "#  This returns \n",
        "counts,  x_bins, y_bins, _ = plt.hist2d(x_data, y_data, bins=50)\n",
        "\n",
        "plt.colorbar()\n",
        "plt.gca().set_aspect('equal')\n",
        "plt.xlim(0, 10)\n",
        "plt.ylim(0, 10)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.0, 10.0)"
            ]
          },
          "metadata": {},
          "execution_count": 11
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "id": "e5THLqw_0QPL",
        "outputId": "2d1858ed-b2f3-43f1-8a6b-6c2c040b3e24"
      },
      "source": [
        "# And a contour plot. Here, try playing with the levels the contours are plotted\n",
        "# at, or try omitting that argument entirely.\n",
        "\n",
        "plt.contour(x_bins[:-1], y_bins[:-1], \n",
        "            counts/counts.max(), \n",
        "            levels=[0.05, 0.1, 0.25, 0.68, 0.95, 0.99])\n",
        "\n",
        "plt.colorbar()\n",
        "plt.gca().set_aspect('equal')\n",
        "plt.xlim(0, 10)\n",
        "plt.ylim(0, 10)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.0, 10.0)"
            ]
          },
          "metadata": {},
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GjVBaFy9Fbjr"
      },
      "source": [
        "#  Projecting a distribution into  lower-dimensional space"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I2LjJfT4FgUg"
      },
      "source": [
        "A common early step in data analysis is dimensionality reduction from whatever high-dimensional space your data might live in.\n",
        "\n",
        "For an example from the simulation world, say you're watching two molecules bind. From your simulation you have the full XYZ coordinates of every  atom in each molecule. But, maybe all you really  care about is the distance  between them. The first step of your analysis would involve a dimensionality reduction  from that full space of coordinates (3 * N_ATOMS coordinates), to a center of mass distance (3 coordinates)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "58mL-VcEGP0z"
      },
      "source": [
        "## Simple projection"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VKFqxeCIFgtg"
      },
      "source": [
        "sample_size  = 1000\n",
        "\n",
        "x_data_1 = np.random.normal(loc=3, scale=0.5, size=sample_size//2)\n",
        "x_data_2 = np.random.normal(loc=7, scale=0.5, size=sample_size//2)\n",
        "\n",
        "x_data = np.hstack([x_data_1, x_data_2])\n",
        "y_data = np.random.normal(loc=5, scale=1.5, size=sample_size)"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "id": "jaIMOH49Feud",
        "outputId": "04aef2d7-6113-4956-8b47-37dadeb5231b"
      },
      "source": [
        "plt.scatter(x_data, y_data)\n",
        "\n",
        "plt.gca().set_aspect('equal')\n",
        "plt.xlim(0, 10)\n",
        "plt.ylim(0, 10)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.0, 10.0)"
            ]
          },
          "metadata": {},
          "execution_count": 14
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p5ZwPXGhFhDu"
      },
      "source": [
        "To project this to 1-dimension,  we can try projecting along either  the X coordinate or the Y coordinate.\n",
        "\n",
        "Let's do this by making a histogram, where we're taking our coordinate of interest, breaking it  up into bins, and then adding up counts in each bin."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "id": "0waTlawsFjZy",
        "outputId": "8fed50e1-cd52-4aaa-d2b3-fbc5c5ea4ef2"
      },
      "source": [
        "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(12,4))\n",
        "\n",
        "ax[0].hist(x_data, bins=20)\n",
        "ax[0].set_title('Projection along  X')\n",
        "\n",
        "ax[1].hist(y_data, bins=20)\n",
        "ax[1].set_title('Projection along  Y')"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Projection along  Y')"
            ]
          },
          "metadata": {},
          "execution_count": 15
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y9x5_o1fFjop"
      },
      "source": [
        "Clearly, these resolve different features of the distribution."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SMDrM-3EFj9X",
        "outputId": "e1b54f56-68a4-4898-e1ac-0874106762d0"
      },
      "source": [
        "# Come back to this\n",
        "\n",
        "pca = PCA()\n",
        "pca.fit(np.array([x_data, y_data]).T)"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "PCA(copy=True, iterated_power='auto', n_components=None, random_state=None,\n",
              "    svd_solver='auto', tol=0.0, whiten=False)"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZdoD9eTQFkMm",
        "outputId": "821bb9f5-f29d-4789-89e2-085e7defad4e"
      },
      "source": [
        "pca.components_"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.99999937,  0.00112492],\n",
              "       [-0.00112492,  0.99999937]])"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wGJ19CuGGKO3"
      },
      "source": [
        "## PCA"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QQ5Mjn6u2ntH"
      },
      "source": [
        "### Preparing some sample data\n",
        "\n",
        "First, let's generate some data and rotate it.\n",
        "\n",
        "Pay attention to the shape of the data! There are some  subtleties with this that will become important. Right now, it's organized as `[dimension, sample]` -- in other words,  as `[[x_coord_1, x_coord_2, ...], [y_coord_1, y_coord_2, ...]]`, and NOT `[[x_coord_1, y_coord_1], [x_coord_2, y_coord_2], ...]`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "reCfg5km3Cib",
        "outputId": "28952c7b-b3d4-4b63-c960-610d79c1f12b"
      },
      "source": [
        "sample_size = 500\n",
        "\n",
        "x_data = np.random.normal(loc=0, scale=1, size=sample_size)\n",
        "y_data = np.random.normal(loc=0, scale=.5, size=sample_size)\n",
        "\n",
        "data = np.array([x_data, y_data])\n",
        "data.shape"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2, 500)"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xBaaLVCbHPwf"
      },
      "source": [
        "Quick note:\n",
        "\n",
        "The `*` operator \"unpacks\" an array-like into arguments.\n",
        "\n",
        "So,\n",
        "`plt.scatter(*[[x_coord_1, y_coord_1], [x_coord_2, y_coord_2], ...])` \n",
        " is just like doing \n",
        " `plt.scatter([x_coord_1, y_coord_1], [x_coord_2, y_coord_2], ...)`.\n",
        "You'll see this a lot in the context of matplotlib."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "xAS6w7TZ3x__",
        "outputId": "8e71cc3f-6296-4648-ab99-174b6e18c02e"
      },
      "source": [
        "plt.scatter(*data)\n",
        "\n",
        "plt.gca().set_aspect('equal')\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-5.0, 5.0)"
            ]
          },
          "metadata": {},
          "execution_count": 17
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4KwDpIo7HYLj"
      },
      "source": [
        "Now let's rotate that data a little,  and plot that."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Llf4jTRE3Ei1"
      },
      "source": [
        "# Rotate by Pi/3 radians\n",
        "rotation_radians = np.pi/3\n",
        "\n",
        "# Build a rotation matrix, and use it to rotate our coords about the origin\n",
        "rotation_matrix = np.array([[\n",
        "                            np.cos(rotation_radians), -np.sin(rotation_radians)],\n",
        "                            [np.sin(rotation_radians), np.cos(rotation_radians)]\n",
        "])\n",
        "rotated_data = rotation_matrix @ data"
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "iPraEXn93cVt",
        "outputId": "8ee1067b-c7db-4777-fe4a-851eabcb86ed"
      },
      "source": [
        "plt.scatter(*rotated_data)\n",
        "\n",
        "plt.gca().set_aspect('equal')\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-5.0, 5.0)"
            ]
          },
          "metadata": {},
          "execution_count": 19
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP0AAAD4CAYAAAAn+OBPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAUOklEQVR4nO3df4wc5X0G8Oe59QB7kLAQu028tnP0h4ygjjlxom7vjxYnikmhcDKhhNaRokillRoJV66pDZUCUVRcnRqolEiVlf7RKlYxDeQaEioDMvmjVo1y9tmhDrgiBEyWRLkUX0h6B967+/aPvVnv7s3szu7O7szs+3wkZN/e3sxr7Gffd96fNDOIiDuGki6AiPSXQi/iGIVexDEKvYhjFHoRx6xJ4qZr1661kZGRJG4t4oQTJ078zMzWBX0vkdCPjIxgeno6iVuLOIHkG2HfU/NexDEKvYhjFHoRxyj0Io5R6EUco9CLOEahF3GMQi/iGIVexDEKvYhjFHoRxyj0Io5R6EUco9CLOEahF3GMQi/iGIVexDGxhZ5kjuQMyW/FdU0RiV+cNf19AF6O8Xoi0gOxhJ7kBgC3AvhqHNcTkd6Jq6Z/DMD9AJbD3kDyXpLTJKdnZ2djuq2ItKvr0JO8DcBPzexEs/eZ2UEzGzOzsXXrAnfmFZE+iKOmHwdwO8nXATwOYDvJr8VwXRHpga5Db2b7zWyDmY0A+BSAo2a2q+uSiUhPaJxexDGxnnBjZt8B8J04ryki8VJNL+IYhV7EMQq9iGMUehHHKPQijlHoRRyj0Is4RqEXcYxCL+IYhV7EMQq9iGMUehHHKPQijlHoRRyj0Is4RqEXcYxCL+IYhV7EMQq9iGMUehHHKPQijlHoRRyj0Is4RqEXcUysh12I9MLUTAmTR87irbkFrC/ksXfHZkyMFpMuVmYp9JJqUzMl7H/qJSyUlwAApbkF7H/qJQBQ8Duk5r2k2uSRs9XA+xbKS5g8cjahEmWfQi+p9tbcQluvS2tq3ssqaXqGXl/IoxQQ8PWFfAKlGQyq6aWO/wxdmluA4eIz9NRMKZHy7N2xGXkvV/da3sth747NiZRnECj0Uidtz9ATo0U8snMLioU8CKBYyOORnVvUidcFNe+lThqfoSdGiwp5jFTTS52wZ2U9Qw8O1fRSZ++OzXXj4kD4M3SnHX5p6ih0UdehJ7kRwL8A+FUABuCgmf1Dt9eVZPjhaxXKdibN1Ia8MOzhl+8uorxsgT+nD4Teo5l1dwHyQwA+ZGYnSb4PwAkAE2b2/bCfGRsbs+np6a7uK8kaP3A0cCitWMjj2L7t1a8bPxzCFFcCHtTKUMdd+0ieMLOxoO91/UxvZj82s5Mrv/8FgJcB6G9oAEzNlDB+4Ciu2fdtjB84WjdsF7XDL2g0IOzn0jZyMKhi7cgjOQJgFMCLcV5X+q/VeH3UDr+ovf7rC/lUjhwMothCT/IKAE8C2G1m7wR8/16S0ySnZ2dn47qt9EirWjds0szN166rax0Uhr2W9/I7CjVy0B+x9N6T9FAJ/CEzeyroPWZ2EMBBoPJMH8d9pXda1bpBHX43X7sOT54o1XXueUOElyPKS/V/5USl17fY0FkXdeRAOhdH7z0B/BOAl83sS90XSZLk956HfSo31rrzFxarzf9Dx8+t+rnysqGQ90AC5+fL1df99418IF8NfNSRA+lOHDX9OIBPA3iJ5KmV1x4ws2diuLb0Uaue9tpad2qmhL1fP11Xg4d9UPx8oYz1hXxd6H3HfvA2/mbqJXxxYguA1rPvNKTXva5Db2b/iUprTTKuWU97YzN88sjZVU32MM066QDgX198sxr6ZrShRjw0DVeqwoJJAMf2ba8LVtQe9VaddACwFHGuiIb04qHQS1U7vefNQpwjV62Ia9YZl2O0hqKG9OKh0EtVO2vX9+7YjNxQcFiXzFY9b0+MFjH+61cHvv+e394Y+Hrj5KAr88HDfxrSa49CL1Xtrl1v9o8naPONQ3/6O9i1bVO1Zs+R2LVtU+DzfNDkoLmF1R2BGtJrX9dz7zuhuffpVttDfuXKcNvcfLmu9g6be9/oqmEPw5esaau3fWqmhD1PnG75rN/YuSgXNZt7r6W1Uqexh7y2dq3tLY/6HH1+vlwdqqv9eSB4PN6/f6vAE1DgO6SaXupEqcGLK8/QUWr6IIW8h/cWl+t64v0Zejkycm9+44o+uainq+xksESpwUtzC4GdflHNLZRXDb35MY8aeEC99p1S814AtJ5+W4sApt94G5d5Q5GWzfaKeu07o9BL5I0ufAYEzrPvlSECyw03U69959S8l8gbXdTqZ09QY+AJ4M4btUNupxR6aTr9tpjCJrQBeOEV7cnQKTXvHTM1U8LDT5+pDqMV8h6uzHuBE1/Wh+xblwaluQWMHziq1XYdUE3vEH85bO0S17mFMt55twyvYUqt/8w8MVrEnTcWI8+P7xcCqTl6K2s0Tu+QZmPwJOD/Uxj2hnCpl8PcfHnVltVp4I/pN9K4/UWakScAmo9r1372z5eXMV9eBoDAjS/6ISzYaPK6xu2jUfN+QDTbrtqXxnFtb4i4atirdhru2rYJeS/X0ehAGv98aaSafgBE3VFm747N2H34VOA1kjJ519a6Mo4fONpRp6HG7aNTTT8Aou4ok7be7ULeW1WmTpvoOgUnOoV+AETdUWZqppSqzQznFsqrHkc6aaIXC3kFvg1q3g+A9YV8YK+8HyB/Xn2nq+J6qXbIDQg+NdcbIkAEbsSpZn37VNMPgGbbXNXuQJNm/uNI0O49k3dtxeQnt1ZnB/pzBlrt7CPBVNNnVOP+73feWMQLr8yumqEWpWOMqIzTJz0UX5pbwNRMKXTve4U7Hgp9BgX11j95ohRY60XpGDPUj9MnSfvY956a9xnUzv7vWRu71j72vaeaPoPa6a2fv7DYjyLF6q2VZn7Y8VU62qo7Cn0GteqtB9rfGCNNCsNe6GQjADraqktq3mdQlEMpOtkYIw3yXg5mCH180dFW3VNNn0GNRzoXhj28V17C7sOnsPvwKQx7Q9UFM1mSI/HIzi34y5Cpws06JbXYJjrV9Bk1MVrEsX3b8ejdN+CX7y3WhTyLgQeAZTNMjBabnqnXznl7Ekyhz7h2joyudfklORRCzoZLih/cZo8v7Zy3J8HUvM+4Tpu1/3dhCUB6nvlrg9v4+BLUQ6/e+85p55yMG/3Cs4ltdBGXIQLvv6yyT59/wo3OqeuOds7JgE7HntMyk64rdvHMPP+EGw3F9Y6e6VMg6FjmqBs9Bu1i6yMqp8amXVi3o4bieiOW0JO8heRZkq+S3BfHNV3Szdhzs01qC8Me5jLe9NdQXPy6Dj3JHICvAPgEgOsA3EPyum6v65Ko02qDNGven58v9/Ukml7QUFz84qjpbwLwqpm9ZmYXADwO4I4YruuMTsae/Y0wB5l/Br3EK47QFwG8WfP1j1Zeq0PyXpLTJKdnZ3UkUa12x56zsjFGFFcNe9i1bdOqbbwI4E+2bVInXg/0rffezA4COAhUhuz6dd8siDIuXSur8+obEcDn//B6TIwWMfbhqzX23idxhL4EYGPN1xtWXpM2hO0WE2RQOrcMFz/w2vnzS3fiaN5/F8BvkryG5CUAPgXgmzFcV0IMSudWGk/EdUHXoTezRQCfA3AEwMsAnjCzM91eV8LdfO26pIsQWWNfRe3r6qRLRizP9Gb2DIBn4riWNDc1U8Kh4+civ9+f1pqUoL4HfwmtmvPJ0Iy8jHn46TORx96JyrTWtM3KW1pZQivJUOgzpp3FNf6HQ9oW5KTtrHvXKPTSd0tmoSfrSu9plV3KtFptV8h7TRfZZIVW0SVHNX2KBK222334FEa/8Gy1Vnzo9usrZ7sNAK2iS4Zq+hQJm2l3fr68qlZ86JtnBqLGH5SJRlmimj5FmgWgsVZ8bzGbm182GpSJRlmi0KdIqwD4J7/seeL0QMy9B7SKLgkKfYoErbardWW+cvJLkpNt4nTVsKdOvAQo9Cnin80etDV13suhvLQ8MDU8UNkARMN2/afQp8zEaBGnPv9xPHb3DSgW8jX73NnKttXZNMTKXvu15hbKkfcClPgo9H3g73Jzzb5vR56UUnuCzbvlZSyk/NSaVrPslgPOpwM0bJcEDdn1WOPpse1OSsnKhhlR+hmWQ96iYbv+Uk3fY92esupCIDRs118KfY91s9MtMFiByHtDOocuBRT6HuvmlNWpmRLmLyxGvleaJ+d6Q8QjOz+CR3ZuqXZQFgt5ratPgJ7pe2zvjs11z/RAtNqtsS/AR1SWzPq/+rwc4Q0xlcdUN55Lp5AnS6HvsXZ3uvWFdeBZza9+8IcIlJesoyOr+0E726aLQt8H7e70OjVTirSnvR/xsF7xtJg8clahTxE906eM36zPklZ9CS6MQGSJQp8yWRmXr2VofpDmII1ADAKFPmWa1Ypp3jzDrNK30FhGDcmlj0KfMmG1YrGQx+RdW6vDXWncXHLZgCsuW6MhuZRTR17KNBviq+0QnJopYe+/nUa5g148L0fcNHIVjr92PvZluufnyxi+ZA0evfsGhT2lVNOnjL+8NkptecVl0T6zc0OsLtfNkSgvGV7/3wX8/R9tbbt8UdoX/voCrZ5LJ1oCGzKMjY3Z9PR03+87KMIm7oQhgd/9tatx8tzPV7Ugol7DyxGTn9yKidFipZXx9dMt5wUUC3kc27c90vUlXiRPmNlY4PcU+vRr3BZ7/sJi4AEWORLLZsh7Qz2Zmedff30hj5EP5PFfr73ddI4AAfzwwK2xl0NaaxZ6Ne9TLmhb7LATa5bN8MMDt+LdHm2auWRWLcOxHzQPPKChurRS6FOunXF7AzB+4GgqZuhpqC691Hufcu3OZosyfbeXCEReXyDJUOhTbn0hHxjkQt7D5ZeuSTzktdRxlw1q3qdY2Hr6vJfDQ7dfj2P7tqdmDb2a89mh0KeU34HX2GlXyHt14/ZhnWXD3lDsHwj+LMBiIY9d2zZp5l1GqXmfUmEdeJdfuqYuXGEz+P525xYAwMNPn4ntfPols7rZgZJNXdX0JCdJvkLyeyS/QbIQV8FcF3VvvWYz+KbfeBtzEQMfdS6/tqzOvm5r+ucA7DezRZJ/B2A/gL/uvlgS1oE3RGJqplRX0wZt0jE1U8Kh4+cQZfQu7+Vw541FPHmiFGl4UOvjs62rmt7MnjUzv6fpOIAN3RdJgPBz7ZbMIs1rnzxytmngc2Rdy+CLE1tWtRgqJ+uspkk32RbnM/1nARyO8XpO82vuPU+cXrUSzm9iN3uublUb+7P3Gu9Ze82gOf7qpc++ljU9yedJ/nfAf3fUvOdBAIsADjW5zr0kp0lOz87OxlP6ATcxWsRyyNoI/9jqsOOyWtXGUWrrdlb8SXZ0veCG5GcA/BmAj5rZfJSf0YKb6MYPHA2dnPPe4vKqWtgPZbOVeLXvk8HUswU3JG8BcD+A26MGXtoT9Gyf93IgVx8IWduzXltLA/Vj7Aq827p9pv8ygEsBPMfKP6rjZvbnXZdKqsL2zd99+FTg+2tbBe1uvS1u6Cr0ZvYbcRVEwgWFN6iDD0jn3nmSLpqRl1Fhe9vFveedr3EjD83Kyy7Nvc+oYkjve9jr3QjayEN74GWXQp9RYR18vRhDD1oHoOm42aXmfUZ1ejBmJ6KuA5BsUOgzrF+982HrADQdN5vUvJeW+vkoIb2nml5a6uejhPSeQi+RaKLP4FDzXsQxCr2IYxR6Ecco9CKOUehFHKPQizhGoRdxjEIv4hiFXsQxCr2IYxR6Ecco9CKOUehFHKPQizhGoRdxjEIv4hiFXsQxCr2IYxR6Ecco9CKOUehFHKPQizhGoRdxjEIv4hiFXsQxCr2IYxR6EcfEEnqSe0gaybVxXE9Eeqfr0JPcCODjAM51XxwR6bU4avpHAdwPwGK4loj0WFehJ3kHgJKZnY7w3ntJTpOcnp2d7ea2ItKFlufTk3wewAcDvvUggAdQadq3ZGYHARwEgLGxMbUKRBLSMvRm9rGg10luAXANgNMkAWADgJMkbzKzn8RaShGJTcvQhzGzlwD8iv81ydcBjJnZz2Iol4j0iMbpRRzTcU3fyMxG4rqWiPSOanoRxyj0Io5R6EUco9CLOEahF3GMQi/iGIVexDEKvYhjFHoRxyj0Io5R6EUco9CLOEahF3GMQi/iGIVexDEKvYhjaNb/PSpJzgJ4oweXXgsgK9t1ZamsQLbKm6WyAr0p74fNbF3QNxIJfa+QnDazsaTLEUWWygpkq7xZKivQ//KqeS/iGIVexDGDFvqDSRegDVkqK5Ct8maprECfyztQz/Qi0tqg1fQi0oJCL+KYgQw9yT0kjeTapMvSDMlJkq+Q/B7Jb5AsJF2mRiRvIXmW5Ksk9yVdnmZIbiT5AsnvkzxD8r6ky9QKyRzJGZLf6tc9By70JDeicpLuuaTLEsFzAH7LzD4C4H8A7E+4PHVI5gB8BcAnAFwH4B6S1yVbqqYWAewxs+sAbAPwFykvLwDcB+Dlft5w4EIP4FEA9wNIfQ+lmT1rZosrXx5H5eTfNLkJwKtm9pqZXQDwOIA7Ei5TKDP7sZmdXPn9L1AJUzHZUoUjuQHArQC+2s/7DlToSd4BoGRmp5MuSwc+C+A/ki5EgyKAN2u+/hFSHKJaJEcAjAJ4MdmSNPUYKhXUcj9vGtsBlv1C8nkAHwz41oMAHkClaZ8azcprZv++8p4HUWmaHupn2QYVySsAPAlgt5m9k3R5gpC8DcBPzewEyd/v570zF3oz+1jQ6yS3ALgGwGmSQKWpfJLkTWb2kz4WsU5YeX0kPwPgNgAftfRNmigB2Fjz9YaV11KLpIdK4A+Z2VNJl6eJcQC3k/wDAJcBeD/Jr5nZrl7feGAn55B8HcCYmaV2tRXJWwB8CcDvmdls0uVpRHINKh2MH0Ul7N8F8MdmdibRgoVg5dP+nwG8bWa7ky5PVCs1/V+Z2W39uN9APdNn0JcBvA/AcyRPkfzHpAtUa6WT8XMAjqDSKfZEWgO/YhzApwFsX/n/eWqlJpUaA1vTi0gw1fQijlHoRRyj0Is4RqEXcYxCL+IYhV7EMQq9iGP+H4hYuVy6IJK8AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s43_aS4ZHhPd"
      },
      "source": [
        "### 2-D component analysis\n",
        "\n",
        "Now, let's estimate  the principal  axes of this data. Imagine we're starting with the rotated data -- how can we separate out the original x and y axes?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r9qer6AT3tMz"
      },
      "source": [
        "from sklearn.decomposition import PCA"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XBI-OVZa7u45"
      },
      "source": [
        "Here, we'll do the PCA decomposition.\n",
        "\n",
        "Remember  that our data was originally in the  shape `[dimension, sample]`. For PCA, we  need it in `[sample, dimension]`.\n",
        "\n",
        "Think of it like a list of observations. Each observation has 2 numbers associated with it (the coordinates).\n",
        "\n",
        "Here, you can explicitly specify `PCA(n_components=2)`, but it should automatically detect that 2 components works best."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PEAFcEKT_CGG",
        "outputId": "a6e74bd0-d5cd-4b7d-dbca-9986eceea169",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "rotated_data.T.shape"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(500, 2)"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1ZMlHumh4G6V",
        "outputId": "ffe9a757-c53e-439e-e106-3b6bcafc2ab6"
      },
      "source": [
        "pca = PCA()\n",
        "pca.fit(rotated_data.T)"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "PCA(copy=True, iterated_power='auto', n_components=None, random_state=None,\n",
              "    svd_solver='auto', tol=0.0, whiten=False)"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FxoNtzzk6m9a"
      },
      "source": [
        "That was easy!\n",
        "\n",
        "Now let's look at the components in their vector form, and  the amount of total variance each component  explains"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mt7dPvmB4fdf",
        "outputId": "52d2b0e7-7f82-4b73-bfd5-36ee9cef7a45"
      },
      "source": [
        "pca.components_"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.49902547,  0.86658732],\n",
              "       [-0.86658732,  0.49902547]])"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kcqc_Jpk8KRy",
        "outputId": "d9026b48-a2c9-4c6d-e056-df0729e22ab1"
      },
      "source": [
        "pca.explained_variance_ratio_"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.78894168, 0.21105832])"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mJ5gcyvmIKY3"
      },
      "source": [
        "The PCA rotation matrix should be pretty similar to the inverse of the rotation  matrix (and should get closer with more samples!)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d8g8HCcLH_CZ"
      },
      "source": [
        "np.linalg.inv(rotation_matrix)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vBlQpAwv7aIH"
      },
      "source": [
        "Slight detour for a cell:\n",
        "\n",
        "Implicitly, we know that when you write down the component vectors as  in `pca.components_`, they start at the origin.\n",
        "\n",
        "To plot them, however, we're using the function `plt.scatter(x_data, y_data, ...)`,  so  we need to have the origin explicitly in the data. Let's make both component vectors start  at [0,0]."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "h3ZJh_3T7Yzj",
        "outputId": "6bd4e71f-1589-4b56-b6ce-2dea06cfa8fe"
      },
      "source": [
        "pc1_vectors = np.array([\n",
        "                         [0,0], \n",
        "                         pca.components_[0]\n",
        "                        ])\n",
        "\n",
        "pc2_vectors = np.array([\n",
        "                         [0,0], \n",
        "                         pca.components_[1]\n",
        "                        ])\n",
        "\n",
        "# Now, you can see we have an array of [[x0, y0], [x1, y1]]\n",
        "pc1_vectors"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.        , 0.        ],\n",
              "       [0.49902547, 0.86658732]])"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "133DvMDi8QDl"
      },
      "source": [
        "Let's visualize these components over our data. With enough samples, these should describe it pretty well.\n",
        "\n",
        "I've also shown in the legend the percentage of  total  variance each PC describes. Note which one is higher."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "eiAypC2q4kT8",
        "outputId": "5bd68abb-cfd9-4f29-8ee3-b14a6d89764f"
      },
      "source": [
        "# To make the component lines longer, try multiplying by some scalar\n",
        "\n",
        "plt.plot(*pc1_vectors.T, color='orange', linewidth=3, \n",
        "         label=f'PC1 ({pca.explained_variance_ratio_[0]*100:.0f}% of var)')\n",
        "\n",
        "plt.plot(*pc2_vectors.T, color='red', linewidth=3, \n",
        "         label=f'PC2 ({pca.explained_variance_ratio_[1]*100:.0f}% of var)')\n",
        "\n",
        "plt.scatter(*rotated_data)\n",
        "plt.legend(loc='lower right')\n",
        "\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "\n",
        "plt.gca().set_aspect('equal')\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-5.0, 5.0)"
            ]
          },
          "metadata": {},
          "execution_count": 27
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fym1Fq_y5svP"
      },
      "source": [
        "Now, let's re-plot our data in PCA space. This should remove the rotation we added in.\n",
        "\n",
        "(Note that this might be reflected over one or  both axes from the initial data)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "id": "TawshSeE5sJR",
        "outputId": "97cd54bc-96c9-4759-ffbd-2cccf3ed847d"
      },
      "source": [
        "pca_data = pca.transform(rotated_data.T)\n",
        "\n",
        "plt.scatter(*pca_data.T)\n",
        "\n",
        "plt.xlabel('PC1')\n",
        "plt.ylabel('PC2')\n",
        "\n",
        "plt.gca().set_aspect('equal')\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-5.0, 5.0)"
            ]
          },
          "metadata": {},
          "execution_count": 42
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vuh0yRXKGk_B"
      },
      "source": [
        "# Aside: Prettier plotting with Matplotlib"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kUUDMHahGqJG"
      },
      "source": [
        "I've used a few of matplotlib's different plotting/formatting options in the notebook up to here, but let me explicitly show a few more examples."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9E0mncaDHnB5"
      },
      "source": [
        "## Scatter plots and colormaps\n",
        "\n",
        "In addition to plotting points with a list of x values and a list of y values, you can also color them according to a \"z\" value, which goes in the `c` argument of `plt.scatter()`.\n",
        "\n",
        "Below, I plot the PCA-transformed data, colored by the x-coordinate in the original basis.**bold text**\n",
        "\n",
        "**NOTE:** Colormaps are not a unique concept to scatter plots. You can use them in line plots or contour plots as well, in the same way. I'm just demonstrating here with our same dataset."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "id": "QPhgLp1nH8kh",
        "outputId": "8feb4237-a33c-489e-a0e6-dede846ac010"
      },
      "source": [
        "# pca_data = pca.transform(rotated_data.T)\n",
        "\n",
        "x_positions = rotated_data[1]\n",
        "plt.scatter(*pca_data.T, c=x_positions)\n",
        "\n",
        "plt.xlabel('PC1')\n",
        "plt.ylabel('PC2')\n",
        "\n",
        "plt.gca().set_aspect('equal')\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-5.0, 5.0)"
            ]
          },
          "metadata": {},
          "execution_count": 43
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ThUDBQPBIGQI"
      },
      "source": [
        "Matplotlib specifies different 'colormaps' for this coloring. (It automatically normalizes your data, but you can set limits for the colormap range with `vmin` and `vmax`.\n",
        "\n",
        "The main thing to know about colormaps is there are a few types, which you can read about [in the matplotlib documentation](https://matplotlib.org/stable/tutorials/colors/colormaps.html#classes-of-colormaps).\n",
        "\n",
        "The type I probably use the most are \"diverging\", which have a visually distinct center point, and different colors in each direction out. I like 'seismic' in particular, which is white in the middle, red at one end, and blue at the other.\n",
        "\n",
        "We'll plot this same data with the colorbar shown. Note I assign the scatter plot object to a variable, and then pass that to the colorbar so the colorbar knows what colormap and range of values is being used."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pfU9kutzIT3X"
      },
      "source": [
        "from matplotlib import cm"
      ],
      "execution_count": 32,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "id": "Ud-mtLsCIS-k",
        "outputId": "990d7f9c-4701-486c-eac5-4eac7f9f09a9"
      },
      "source": [
        "cmap = cm.get_cmap('seismic')\n",
        "\n",
        "pca_data = pca.transform(rotated_data.T)\n",
        "\n",
        "x_positions = rotated_data[1]\n",
        "sc = plt.scatter(*pca_data.T, c=x_positions, cmap=cmap)\n",
        "plt.colorbar(sc)\n",
        "\n",
        "plt.xlabel('PC1')\n",
        "plt.ylabel('PC2')\n",
        "\n",
        "plt.gca().set_aspect('equal')\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-5.0, 5.0)"
            ]
          },
          "metadata": {},
          "execution_count": 44
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8sH9ba7OJjLs"
      },
      "source": [
        "You can see the colormap isn't centered -- our data isn't perfectly centered in x. By specifying vmin and vmax to be evenly spaced around 0, we can fix that."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VbvnAaJaBtbd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "outputId": "3607808c-e39c-4799-e695-bc43c5945a84"
      },
      "source": [
        "cmap = cm.get_cmap('seismic')\n",
        "\n",
        "pca_data = pca.transform(rotated_data.T)\n",
        "\n",
        "x_positions = rotated_data[0]\n",
        "sc = plt.scatter(*pca_data.T, c=x_positions, cmap=cmap, vmin=-5, vmax=5)\n",
        "plt.colorbar(sc)\n",
        "\n",
        "plt.xlabel('PC1')\n",
        "plt.ylabel('PC2')\n",
        "\n",
        "plt.gca().set_aspect('equal')\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-5.0, 5.0)"
            ]
          },
          "metadata": {},
          "execution_count": 45
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2Hnx-7nMKRPc"
      },
      "source": [
        "## Subplots, tick formatting, and shared axes\n",
        "\n",
        "Up to now, I've been using `plt.plot` to plot everything. This is sort of using a global instance of matplotlib.\n",
        "\n",
        "You can get a lot finer control over your plots by using `Figure` and `Axis` objects. A figure is like the whole plot you see, and can contain multiple sets of axes.\n",
        "\n",
        "Note that when we're working with axes objects, instead of the global `plt` instance, we have to use `axis.set_xlabel()` instead of `plt.xlabel()`. Most formatting commands follow that pattern."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        },
        "id": "jy8f5fM7KFsK",
        "outputId": "a79ce099-7085-4d93-f2da-8f42a4f7081e"
      },
      "source": [
        "# Create a figure\n",
        "fig, axes = plt.subplots(ncols=2, nrows=1, figsize=(8,6))\n",
        "\n",
        "axes[0].scatter(*pca_data.T, c=x_positions, cmap=cmap, vmin=-5, vmax=5)\n",
        "axes[0].set_xlabel('PC 0')\n",
        "axes[0].set_ylabel('PC 1')\n",
        "axes[0].set_title(\"Data in PCA basis\", fontsize=24)\n",
        "\n",
        "\n",
        "sc = axes[1].scatter(*rotated_data, c=x_positions, cmap=cmap, vmin=-5, vmax=5, label='test')\n",
        "axes[1].set_xlabel('x', fontsize=18)\n",
        "axes[1].set_ylabel('y', fontsize=18)\n",
        "axes[1].set_xlim([-5, 5])\n",
        "axes[1].set_ylim([-5, 5])\n",
        "axes[1].set_title(\"Data in x/y basis\", fontsize=24, color='green')\n",
        "\n",
        "# Explicitly set some parameters for the ticks\n",
        "axes[1].set_xticks([-3, 0, 3])\n",
        "axes[1].set_yticks([-4, 0, 4])\n",
        "axes[1].tick_params(labelsize=18)\n",
        "\n",
        "\n",
        "# Colorbar must be created at the figure level\n",
        "fig.colorbar(sc)\n",
        "\n",
        "# This just condenses some of the padding around plots.\n",
        "# I throw this in often to help manage whitespace.\n",
        "fig.tight_layout()"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x432 with 3 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VikSZMNkP65G"
      },
      "source": [
        "(That plot isn't meant to look pretty! Just an example of some of the things you can do.)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qe4QYnFrPNZv"
      },
      "source": [
        "Two final things about axes.\n",
        "\n",
        "Changing scales (i.e., from linear, to log, or matplotlib's \"symlog\" which is like log, but linear in a small range around 0)\n",
        "\n",
        "Matplotlib also makes it easy to use dual axes on one plot.\n",
        "\n",
        "Below, I demonstrate both of those, along with line styling (width and dashing)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "77X-Nto7QNPj",
        "outputId": "814674f4-baa8-4f17-a9a6-6297cc8de583"
      },
      "source": [
        "# Two plots on top of each other, which share their x axes\n",
        "# (Note the x-tick labels aren't duplicated)\n",
        "fig, ax = plt.subplots(nrows=2, ncols=1, sharex=True)\n",
        "\n",
        "x_values = np.arange(0,100)\n",
        "\n",
        "# Plot x^2 on the top plot\n",
        "ax[0].plot(x_values, x_values**2, linestyle='--', label=\"x^2\")\n",
        "\n",
        "\n",
        "# On the bottom, plot x^2 and x^3 on a shared x-axis.\n",
        "\n",
        "# You can use TeX in labels too!\n",
        "ax[1].plot(x_values, x_values**2, label=\"$x^2$\")\n",
        "# Make a new axis on the bottom plot that shares the x-axis\n",
        "ax1_twin = ax[1].twinx()\n",
        "ax1_twin.plot(x_values, x_values**3, linewidth=3, color='orange', label=\"x^3\")\n",
        "\n",
        "# By default, the legend will be weirdly sticking in the plot. \n",
        "# Let's put the upper-left corner of the legend at (100%, 95%)\n",
        "#   relative to the x-axis and y-axis respectively.\n",
        "fig.legend(loc='upper left', bbox_to_anchor=(1.0,0.95))\n",
        "\n",
        "# Make sure the legend isn't cut off by doing tight_layout\n",
        "fig.tight_layout()"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 3 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ODgBZhimTKSe"
      },
      "source": [
        "## Wrap-up\n",
        "\n",
        "Let's combine this all to make a pretty plot of our rotated data.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZNotR-1PT4os"
      },
      "source": [
        "import matplotlib as mpl"
      ],
      "execution_count": 40,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "ymx6ngoxTOr4",
        "outputId": "0b1df5e6-dfc2-4d78-c61d-0190991cb44c"
      },
      "source": [
        "# Create a figure\n",
        "fig, axes = plt.subplots(ncols=3, nrows=1, figsize=(10,4.5),\n",
        "                         # Make a small column for the colorbar\n",
        "                         gridspec_kw={'width_ratios':[1,1,0.1]})\n",
        "\n",
        "# Globally set font used to 18 -- 'rc' sets global plot formatting options\n",
        "plt.rc('font', size=18)\n",
        "\n",
        "axis = axes[0]\n",
        "sc = axis.scatter(*rotated_data, c=x_positions, cmap=cmap, vmin=-5, vmax=5, label='test')\n",
        "axis.set_ylabel('y')\n",
        "axis.set_xlabel('x')\n",
        "axis.set_title(\"Data in x/y basis\")\n",
        "axis.set_aspect('equal')\n",
        "\n",
        "axis = axes[1]\n",
        "axis.scatter(*pca_data.T, c=x_positions, cmap=cmap, vmin=-5, vmax=5)\n",
        "axis.set_xlabel('PC 0')\n",
        "axis.set_ylabel('PC 1')\n",
        "axis.set_title(\"Data in PCA basis\")\n",
        "axis.set_aspect('equal')\n",
        "\n",
        "for axis in axes:\n",
        "  axis.set_xlim([-5, 5])\n",
        "  axis.set_ylim([-5, 5])\n",
        "\n",
        "  # Explicitly set some parameters for the ticks\n",
        "  axis.set_xticks([-3, 0, 3])\n",
        "  axis.set_yticks([-4, 0, 4])\n",
        "\n",
        "\n",
        "# Colorbar must be created at the figure level\n",
        "fig.colorbar(sc, cax=axes[2])\n",
        "\n",
        "# This just condenses some of the padding around plots.\n",
        "# I throw this in often to help manage whitespace.\n",
        "fig.tight_layout()\n",
        "\n",
        "# Change the resolution of the figure -- this interplays with figsize\n",
        "fig.set_dpi(100)"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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b35EIe+J3QtcK+T6FsKHyQedc7DRZEUnr8RyLKxBWIn8P4G+TRhFFZKKm7k53X4P2LptDoAHe5WlPqiclsenPsdOlI74ODYgL0N72v6vfb9OlqwC+la/IuaSNBBn/87Uj8tj/RhgM/xc0g3Zsgh4R+X9ZF3LO/QjAj0RkL2j26pMAnA7dakOgW56cJCInOueeyFH26PnvAnCXiCysn/9EAKdBp9sF9evdIyLnOOeWjvb8RNMM65j292uEW9mdWP97IvijvX8lIn81iud9bAKuP966acI+Y/XnfRPAN0XkQOg2VCcBOBMaFBeg23SdIiLH55jqHXeNSa37iFoZp0y3P3+9zb1+ICEindAvRQD4bVJDpW6ip9OcXf+5HsAnUyqR2RiZ1KPtiMilCLNPPoQw+dXHReTMjKefiLD3Pk9AfAfCaWB/IupA6IgmAPzcOfd8vpLncpCIJE1tNn4WzHWRx+yzUoH2Xidmq8UoPqfOuXXOueuccx91zh0N7YC4vf7wXACfzXuuhPNvcs7d6Jy73Dl3AnS/ZZsWVwTwL+M5P9E0wTqm/d3q/X7ZRJywvgzmuMwD410qmv16vBZnH5KrbprQz5hzbpVz7hrn3J855w6Bvk8P1x/eB0DejoOk809q3UfUijhC3MZEt1LwkyR9M3LIQoSfgZUZp8uz9cPL051ERDLWje5e//lsxtTcs9HmHTcicgB0dBjQEZa3Q9+fpdBe4WtE5OiUbXosu/QWaEbOVM45JyL/DuBzAA6AvsdnIFyPO9GjJXMBHIv06d9neL8/GHnMPiub0rZeEpFXImbLl7zq0/L+GMAm6Pt+yljPlXD+F0Tk3dAe/z0AHCci3WlbdhBNZ6xjZozvQEdA5wM4WkQurI82joc/OvxjAI/keM550Jk2u0LX6463DIeLyO4Zo6156qZJ/Yw555aJyDuh+yIDE183TWrdR9QKGBC3qXqP5PUIE2A8AeCGyGH++pmDMs6VZ3qSP52oByOnF0Wv3QngwKSGTX1t2t/kuG7Lqr/G7yJMtPER59wKACtE5B+ga1H3BvCf0DW+cSwgviVj9NT3bWgvcAnAhxBmZ34RuiZqov0lEvb4FJFdEY469EO3h/LZ53Q3EZld35IkzifHW0jn3DYR2QJgF0zC96NzriIiaxFmHOV3MLUk1jEzh3Nuh4j8I7QTFQD+XUSeyJuNup546lDn3FX1v4sIv/MdgA/nmZUkIg8DuLH+53sx/oC4AOAjAGKX2ohuQ2gdNc9jZEA8lZ+x1d7vk1E3TWrdRzTdsVe0zdSnv54L3cPQevm2A7g42oPpnNsGTf4AAH8kIiMCLhHphTZy9slx+We934/NONYqll2h2z5Er1uEjlT+UY7rtrIroVOeAeAHzjl/7e5nANxX//0CEflg9MkishjAofU/80yXBgA45zYC+J/6nxcC2LP++7dHEVSPxjtE5M+id9bXDX4fOooMaDKv6CiwfVYE4Xpn/xwiIp9FuMYtloh8RETekjbVTkQuhjYIAOB3aeeLee6lIvJeEelOOeYEAK+s/7kqJbgnmpZYx8xY/wJNGAXod+SvReTtacthRGSRiFwF3VZod++h8xHO5rlrFEt0boaOYgLAuSKye9rBOf2ViLwheme9o/ZahMHhl5xz1chhE/IZE5FPishr6/lAkvjbL462bprUuo+oHbAXqAWJiN/wF2hW4gUAjgFwKnQarFkL4O0pmYe/AuDL9d9/ICLfhe6n2gfgCADvgW41cA2Ad2UU7Q5obyugiSG+CF0La5XIM845W7v6Fej2GwDwBRE5HbrNzyZoAol31X/+sv5zKveHnBIicgrCnuO1ABoC3vpo4qXQqWRzAHxRRO5yzj3lHWbZpYcRNlby+gYa1/856Ej0RHsEOop0Vf2z+yMAW6Hrlt6HcO3gs4jvqf8adK/KAoCPiMgxAH4I4CVoI/od0CBzOXQbkaR1accC+BKALSJyK3QK9wvQaZh7QLeustEAB+AfR/k6D4Z2cHxFRG6DNpaeh2bR3Q26lvIChFlG/2GU5yeaEqxjKKq+1Oat0DwIb4B+Hr4H4LMicgs0mdomaCbmRdClISdD8yVE+dOlvzOKMgyLyHXQ4LADuk3geHIxLIV+pn8iIjdAPx/90CRT70cYtD8ArTuiJuozdiaATwN4SUR+Aa0zX4IOWu0FnQVma/GHoNsyjcZk131Erc85x1sL3KBfUqO5bYF+Ac7LOK9AN71PO9eN0EyK9vfShHMVoGtYk87zqcjx/5Bx3XugFdLq+t+rJ+g9TCr/1d4x+2ecK/exCc+f572uKoDTU4691LvWMgCd3mN31e+/bYzvyXLv3LdO0md2KbTRsTbl3/oZAAemnOtD9fcp6fnLoclPltp9Mef4ds7/OzsAvDOhHGnnvzLn+csALp/I95o33sZ7y/nZZR2T7z1MKv/V3jH7Z5wr97EZ51k9EefxzhdAl8BsyPk56QfweQDz68/fHdqB66AdmHNGef0TvHM/Poby7+89/2poQLs1pfwPAFiYcr5xf8agAXOe93IDgHMy/p3jzj/uuo833tr9xhHi1jcMna62HfqFuAzAbwDc5HIk63HOOQCXicjPoMlRXgndimA9tJfyO8656wEgK1Gwc64qIq8F8FHoyOWh0JHN2H33nO6L9yvotjqvhk6b3Qhdi/Z9AFc7HSXNehmt6OsIR0Y/51K233HOfbc+RfFS6L/PP0CzTy+A9sADo5guHXE7gMPqv0/a1iPOuUfqSa8+Ah0l3Q/aUF4BnS75Jedc4p6Qzrmr6uvH/hLaU74Q2iB/BsAPAHzDOdef8Vn5EIDroElSjoeOUO8C/Xxuhe5rfBuA/3TORbOJ5vH30ID5LACvArAE2vgrQkfDVkAbPv/pwlEsoumOdQy9zOm0+C+IyDeg2/e9FjorZzfo+7sTuk/xMuiI/g1Op86byxDOTvypc277KK9/v4isgI64vkJEXu2c+804Xs9t9VlHH4Um7VoE/cwvh3bk/LtLWUY0QZ+xN0ETb50GfS8XQ+s4B93P+HHoDLBvupTEkikmu+4janmidRURtZp61slr6n/u75x7Lu34mOcH0AbuPtCe50XOufKEFpKIiIiIaBpjUi2i1mXZpX8/2mC47nyEiWy+zWCYiIiIiGYaBsRELUhEOhEmwRj1dOn6VhC2TVEF4T7IREREREQzBtcQE7Wg+mjunMwDPSJyJHRP4wXQzK62FcTVYxxhJiIiIiJqaVxDTDRDiMjVAN4duXs1gOOcc5unvEBERERERE3GKdNEM08VuufvVQBOYDBMRERERDMVR4iJiIiIiIhoRppRa4hFN4LbC7onKBERjc5sAOsce1JHjfUPEdG4sP4ZAxHpAtDZ7HIAKDvnBptdiCQzKiCGNkbWNrsQREQtbBGAF5pdiBbE+oeIaHxY/4yCiHT1AgM7ml0Q9ZKIHDBdg+KZFhD3AcDzzz+POXNGlaCXiGhG2759O/bZZx+AI5xjxfqHiGgMWP+MWecOAB8DUGpiIYYAfBHYAzpSzYB4upgzZw4bJERENOVY/xAR0VTqBtDVxOu3QgbnGRkQExERERERtbsAzQ1KWyEgboUyEhEREREREU04jhATERERERG1IY4QZ2NATERERERE1IYYEGdjQExERERERNSGGBBna4UyEhEREREREU04jhATERERERG1IY4QZ2NATERERERE1IYYEGdjQExERERERNSGGBBna4UyEhEREREREU04jhATERERERG1IUFzR0ClidfOiwExERERERFRGxI0NyhlQExERERERERNUajfmnn96Y4BMRERERERURtiUq1srVBGIiIiIiIiognHEWIiIiIiIqI2xBHibAyIiYiIiIiI2hAD4mwMiImIiIiIiNoQA+JsrVBGIiIiIiIiognHEWIiIiIiIqI2xBHibAyIiYiIiIiI2hAD4mwMiImIiIiIiNqQ1G/NvP501wpBOxEREREREdGE4wgxERERERFRGwoAFJp8/emOATEREREREVEb4hribAyIiYiIiIiI2hAD4mytUMZYIvJ/RcSJyL82uyxERDRzsP4hIiKaGlNR57bkCLGIHA/gTwH8vtllISKimYP1DxERtZJWHiGeqjq35UaIRaQXwHcBfADAliYXh4iIZgjWP0RE1GqCaXAbi6msc1suIAbwVQA/c87d3uyCEBHRjML6h4iIWkqzg+FxBJtTVue21JRpEXkbgGMBHJ/z+BKAknfX7MkoFxERtTfWP0REROMyW0T8v4ecc0NxB462zh2vlhkhFpF9AHwJwKXOucGcT7sCwDbvtnaSikdERG2K9Q8REbWqZo8Oe8HmWjTWi1fElXeMde64iHNuKq4zbiJyAYAfAah6dxcAOAA1ACXnXDXynLge+rXbtm3DnDlzJrnERETtY/v27Zg7dy4AzHXObW92eaYS6x8iouaZyfXPeIjIHADbrgMwq4nl6AfwVv11EYA+76HYEeKx1Lnj1UpTpu8AcGTkvm8DeBLAP8W9MfU3+eU3OjJMT0RElAfrHyIiakmF+q2Z16/ry9mhMeo6d7xaJiB2zvUBeMy/T0R2AtjknHss/llERETjw/qHiIhoajSjzm2ZgJiIiIiIiIjyEzQ3aVQrzI9q6YDYOXd6s8tAREQzD+sfIiJqBePc+mhCrj9ek13ntnRATERERERERPHaISCebAyIiYiIiIiI2hAD4mytUEYiIiIiIiKiCccRYiIiIiIiojbEEeJsDIiJiIiIiIjaEAPibAyIiYiIiIiI2pCguVsftcK2S60QtBMRERERERFNOI4QExERERERtaFC/dbM6093DIiJiIiIiIjaENcQZ2NATERERERE1IYEzQ1KuYaYiIiIiIiIaJriCDEREREREVEb4pTpbAyIiYiIiIiI2hAD4mwMiImIiIiIiNoQA+JsrVBGIiIiIiIiognHEWIiIiIiIqI2xBHibAyIiYiIiIiI2pCguVsftcK2SwyIiYiIiIiI2lChfmvm9ae7VhjFJiIiIiIiIppwHCEmIiIiIiJqQ1xDnI0BMRERERERURtiQJyNATEREREREVEbEjQ3KGVSLSIiIiIiImoKjhBna4UyEhEREREREU04jhATERERERG1IY4QZ2NATERERERE1IYYEGdjQExERERERNSGBM1NbNUKSbVaIWgnIiIiIiIimnAcISYiIiIiImpDhfqtmdef7hgQExERERERtSGuIc7GgJiIiIiIiKgNMSDO1gplJCIiIiIiIppwHCEmIiIiIiJqQxwhzsaAmIiIiIiIqA0JmhuUtsK2SwyIiYiIiIiI2hBHiLO1QhmJiIiIiIiIJhxHiImIiIiIiNoQR4izMSAmIiIiIiJqQwyIszEgJiIiIiIiakMMiLMxICYiIiKi9lCtAo88AvzqV8CmTcDcucAppwB/9EdAsdjs0hHRNMSAmIgmVqWijZHly4FaDTjoIOBVrwJKpWaXjIiI2lm5DHz5y1r/BIHWQS++CDzxBPCLXwB/9VdAT0+zS0k0pThCnI0BMRFNnHXrgC98Adi8WRsjgPbSX3cd8JGPAIcc0tzyERFR+7r+eg1+AQ2GAcA5/bl2LfCtbwEf/nBzykbUJAyIs7VCGYmoFQwMAP/8z8DWrfp3rRY2SAYGNFBev7555SMiovbV368dsBYAR9VqwMMPAxs3Tm25iJosmAa36a4VykhEreDee4Ft28Ig2OecTqW+446pLxcREbW/Vau0nsny5JOTXxYiaikMiIloYvz2t+mP12rZxxAR0aRzDhgeBgYH9TY8nDyw2jLyvoCWf6FEo9Ps0eFWCDa5hpioCZzTRJjOASJAoaA/W9rQUPYx5fLkl4OIiBJVqyO/rms1DYpLJa2PWtL++4eJtNIcfPCUFIdouhAA0sRGprRAJxQDYqIpNjyst6hiEejoaOHAeN99gTVrkhsjQQAsWjS1ZSIiopfVaul9l0NDQFdXmBOxpcyeDZx4InDfffH1UBAAhx4K7LHH1JeNqJma3bi0ZXPTGANioilUqcQHw0B4f8tuk3jGGZrQJEmtBpx55tSVh4iIGuRpk1YqQGfn5JdlUrzjHcALLwCrV2sA4I9M7bIL8IEPNK1oRE3DgDgTA2KiKUz+iyMAACAASURBVOJc9ozh4eHmf2+N2X77AW96E/CTnzQ2ROz3E04AjjuuuWUkIprBqtWJOWba6u4GrrhCR4nvugvYtAmYOxc45RS9dXc3u4RENA0xICaaIlnLmky1qkFxS7rgAmCvvYBbbgGee07v23VX4JxzgNNPb9F5eERE1DKKReDUU/VGRM0faeEaYiIyLfB9MDFe9Sq9DQxoL8CsWS065E1E1F6CIHsEmP2WRG2GAXEmBsREUyRvI6NtYkdOTSMimlY6OrID4lwzlGxNoEgLT2kimiEKheb2dOWdItlE/BYjmiJBMDLHR5QIe+eJiGhyFAo6ozgpuWOxmLHtUq0GbNkCbN8eVmadncD8+UBPz4SXl4hoKjAgJppCnZ3pW150dmaMEFcq2hDZsUMbJp2dwJw52hBpm6FlIiKaLMWidrwOD4cDN0GQMxhet25kdshyGfjDHzSL85w5Yy/YSy8Bjz2m1xAB9t4bOPJIzUNBRGPX0cER4gwMiImmUKGgezyWy43fD7kaI0NDwIsvNj5xcFBvs2YBu+8+9qDYOWD9euDpp4H+fj3fwQeP75xERDQtFQoZ9U2crVvTt0rYuFE7Z7NO7BywbZvWNaUSsGAB8OijwP33N06jWrkSeOYZTY516KEjz1OraQexiAbirKuI4jEgzsSAmGiKBYEGxbWa1vu5pkk7pz3wSV8q/f3aWJk/P18hbGigs1PPfeedwKpVYWNEBHjiCeCAA3Tv4FG3nIiIqG04p8Fnlr4+YN685Mc3bgR+9zsNiE2pBGzYEF7Hvyag+9vvvntYv1WrwD33AL/+tc6WAoCFC4HTTtOt/RgYEzViQJyJATFRk4zqu6m/P3tT823btCGS1hhYtw546ildAwZo4quODuDZZ/Vva4DYz2efBX7zG+Ckk8JzDAzofb/9LbBzp/bMH3+83kqlUbwoIiJqCbVavkZt2gjypk3A3XePTKQxNKT1SF9f/JoiEWD5cuDkk7UM3/uedthGz/3DH+pMp/POyy4nEZGHATFRK0hbeGxqNQ2ai8X4x59+Wtdn+QYGtHEye7Y2RuIsX6697qWSBt3f+Ib+tEbNhg3AzTdrgPzBD+p0ayIimvacGzlbKbZPNe+oa1pP7+9/n5xV0jmdbh1X1zmnnbmAji5Hg2HfPffouuN99slXXqKZYExrJCZQVmr7CBG5AsBFAA4FMADgXgCXO+eemvjCKeazJWoia4xYg2TS9PWNDIaNiE6dThrdtUQqAHDDDY3ZRX0bNwI33jgx5SUioklVrerqmWpVv+bt7+HhmK/4IMjX2dnbG39/X184MymOReOdncmPA+E64yRBADzwQHY5iWaSjo7m30bnNABfBXACgNcCKAK4VUQmLZU9R4iJmsAC4WinmW3pOKK+7+7WNcJpCoXkL51nn83e86m7O3kkulrVqWirViU/v1YDHn9cA+bxZBolIqJJFVf/GNtieMRko3nzdPlOkq6u5I7VgYHsQjkXP8IsEo74btiQXo/Vappvg4hCHR3NHSEe5bp+59zrG58u7wGwHsBxAH41YeXycISYqAmq1fjGiHMJvfNdXclToU3a+uGkUV0jkv5lucsuwNq16dcH9BovvJB9HBERNYUFvFnHxNZDSTsP+I/VasDmzTqzaP16vVie/BL23Lj7X/EK/T1pBNk/lrksiKar2SIyx7vl/c86t/5z82QVjCPERFMsT26SajUy2CsC7LGHbrsU15KZPTsclXVOe+NrNR31zbt2JC5gFgH23DM7WZevmZkMiYhoQtRqMVVHTw+w336aULFc1nqhpycMQjdt0plEw8Phc2xP4bRcFcDISF1Eb+eco88FgKOP1nXCaWuRjzpq1K+VqK1NnxHi6MjKpwF8Kv2pEgD4VwC/ds4lrP0bPwbERFMsT6JOP8nJy4pFYNEi3WZixw49qFjUQLirS4956SUdybVMn0EA7LprGEwncW5kdlARDahPO03/PvDA7GnXHR3Avvtmv0AiIppyNgupWs255V+cIAgDVN/WrbqLQdxF167VztW0gLha1XXKhYLWbfvsAxx2WOO65BNP1DXC5fLIuigItD48+ugxvCiiNjZ9AuJFAPwvgRwZY/FVAEcAOGWCS9WAATFRK7EKP26N7nPPjZyubOupurq0oWFZpX32t0h4TGcncOihmq3TEqnMnat/P/po8mjy8cdrEE1ERNPK0FA4ecgUCjq4O6rAuFzWZThWn3R16Syi1avTn9fXp3XEo48Cg4Ph/Ral2+iwcxoIx430zpsHvO99wDXXaMewFbxW072I3/3u7GnVRDNNWo6ZqdXnnMuxobkSkX8D8AYApzrncqzbG7tp8e4QtTsbgB0cDNcOFwpab4+6065S0YZFtapP7u3VxkTa2t3BQWDxYp3KtmNHWChjC5cLBV0Hdu658WuWL7xQG0KrV4ejxUGgjZFDDtHnERHRtDI4GJ8Pq1rVuLa7e2RQHBsk9/VpYqvofX192ZWZc1rpvfa1uiOBTYUql0cuBVq2DNh///jO30WLgMsv1y0B16zRgi5eDBx0EJfsELUBEREAXwFwIYDTnXPPTvY1GRATTTLnwuVWPmuIlEojY8/YvSCd00Ql27Y13rdlS749m7Zu1YbIo48CTz6p99VqOmzgZ/gaHNT9Io87buQ5SiXg/e/X5y9bpo2gefP02MWL2RghIppmarX05NAWk9rKGyBht4NyeWQwDISdo7Nm6cV27ky+2PCwJtqyNcY2fzuu0D/+MXDxxY0FM4WCzlg68sjka5mtW4Gbbwbuuks7hHfdFTj7bL3FnZuo3Yxt66Nm+iqAdwB4M4A+Edmjfv8251yOlPWj11LvDlErGhoaGQxHHy8UGmPJ2I72bdsag2GgscWyyy6a0CQpOLZCbN6svfHWCoqbQv273wELFgAHHDDyPEGgGT8t62eWjRuB224DnnhCy3vUUcBZZ2kgTUREkyqt/jFWJQTByProZdH6x2dBcU9P41SoqFIp3IIpbe8nQIPl++4Dzjgj+wUkWbcO+OQnw7wbdt93vqMB8qc/nW9/ZaJW1noB8YfqP5dG7n8vgKsn44It9e4QtaKkrX19lYrOJLPdj0b0zNdqOhKcxJ7Y0xNOiY6yYWdrjMTu7+T55S81M+h41mPddx/w5S+HGy8DOrr8ox8Bf/3XzAZKRDTJ0mJOX+Yyw6y9hK3i6uqKHyUuFLSj1RJrZe39BOjynFptbLOPnAO++MXGYNh/7PnndS3yn/3Z6M9N1EpaLCB2zo1u4+IJwPmNRJPIuXyNkVot/L6KrfcHB7OnRYtoQyRpe6Rdd9Wfs2Y1BqhpHhtHhvs1a4AvfUnfAP9alkDlc5/T0WoiIpo0eWPJzOPyLM0BktcSH3CAPjZvns5oylMHOZevVznOihWabDLpOrUa8KtfJXciE7UL6+1q1q2ZGa5zYkBMNA0EQcK6YZOn4QDoCeJ6AYMA2Gsv/f3AA/Of7/nn8x0X5+c/T37M9pu8/faxn5+IiDLlmeRTLOYIiLu704Ni58LkjL6uLmDJEmC33cL7Xv3q/Hvbj3Vk65lnsq9RqWjnLRHNaK0zfk7UgkS0oWH5Q5LEJXRukHfaclxjpbNTGyO2HdLee+v2FC+9lO+cY7VsWXrgXasBDz8MXHLJ5JaDiGgGsx0N0tYS59otb+7c5NFUq3tqNc0CfcABOrOpo0OX8kQD07lzNYv0sxnJY7u6clSQCQqFfKPaLTB6RTQuzZ4ynXd2SRMxICaaZF1d6QGxSI54t7NTb0ND8T3e/l7Chx2myU9qNW2IzJ/f+JwgAE47DbjuuuzC77ln9jFJ8oxC513cRkREY2YxaXT2sYju3JerrVwqaX1iS12sXrH6p1rV3196SaPvzk6dGp3k+OOzA+JjjslRME9/vwbtvb35clT09MQnjyRqJwyIMzEgJppkxaLWuXE5RkR0m8VcM8d22w1Yu1a/WPwn2BdNpaLrg7du1ft6e3WtVtzJe3qAPfbIHiV+5StzFCzBkiXAgw8mB8ZBABx66NjPT0REuYjo1353d7i5QKGg9VPemcsAtF7Zvr2xl9eSZQwMNA5D79ypySBnz9Z96qMjsb29wKmn6jreOAcdlH83g3XrgJtu0h0SrI48+mjdlunxx5ProfPPH1/iSKJWwIA4EwNioilQKul3kb/lrw365m6MWG/7hg1hhW9rtioVbYzYthj2WGcncPDB2hKKOv104Ic/TJ5Hd/LJ+aeqrVoF3Hmnbq1Uq2lD5ogjgN/8Jvk5zgHnnJPv/ERENG5BEL/1brS9GlsvVSoaeFarjfWPiE6PTqpL+vo0udV++4UZpm1YevFiXcLz8MPACy/o+ebNA449Vqde57FmDfCFL4R7R9kLeuQRDcL32UevHwRhxupaTYPxiy7Kdw0iamsMiImmSKEwzu0OBwZ0T19gZPrq6LYS1igol3WboyOP1ODYH12eNUsbAw88oNPW7Dnz5wMnnJB/uvQ99wDf+17YyAA0MF6+XBs1y5Y1Pma/f/CD+Rs8REQ0IWyTgVpNq4O4ZFpWVTQExtu2hfWO/2Ctlp0JeuNG7Ti1oNkC1SVLtM4588yxvZhKBfj2t5NHgCsVDcItj8bQELD77nq9JUtGOTxO1KI4QpyJATFRE/id2NbR7hvREHEOWL++8UFrxQwOpq/XrVY1KN6wQRsDhYIm1jrgAB05Pv104JRT9DzFog5n5/XCC8C112p54gLyNWu00TN7tvbQi+i6rvPP15FrIiKaMjaz2b6u7Ss/uhIHaExNASAc3Y3KyhoZVz9Vq7rH8LZtwKteNfrEVs5pZ+ytt2q9ZsPe1ar+bde0+vL55/W+N70JeMtbGAjTzJK5yfgky7uzSRMxICaaQpVK47TpUil+VvKIhsjAQHICqqyeeed0LZcdV61q4+CFF3QkeO5c/aLs7c3/QoaHgV/+Eli6NBz2rlb1/kql8dp9fRqML1kCfPjDumiaiIimVLU6MpeFLZ9Nig9fDpTT9q7PGv0JgjAhpD9bCNA1xi+8AOy7r/69dSvw2GNhvoxFi3T5zfz5jee84w4NhuOu1d3dGPXb/bUa8JOfALvuqokliWaKZo8Qt0BAzH2IiaZIuawJMC2u7ehIX6Jry7NefnKStC8aa8QMDjb2wNuU62XLGhsz27frFOo77wTuuw/YtGnkOSsV4Fvf0gaJH/za4jT/Rfkj2StWAP/0T43PISKiKTE42Ph33hQRziF5bjWQPdrqXHixzs6R57F9gFesAL7/feDRRzWT9ZYtGhxfey3w+99rx+rAgC4RStrD3soSTZTl13M//WlLTOEkoqnDEWKiKWAxqa9YjJ+mFiupIQKkV+wiGggHgUbgQdA4vc3WJe+yiybAWrassUAPP6zZQc84IwyoH3gAWLky/lqADnv7yU1MraYj08uW6RQ5IiKaErXayElGo541PGeOjuBGRTs5k9YA2Shtsdg4s6m/X4Pf228f+Vz7++679ThAl/rkqff8c/gvfv16ve2+e/I5iNoJR4gzMSAmmgJxS6zyLJl6OWDu6QkTasUdlHWSYlEbBEGgF/YTo2zfrplDly2LP9/TT2uCrEpFp7WtWJHvera3h98QEQHuv58BMRHRFKrVYpbi5OE/ae5cXQKTtHzHZiRF65AgCC9qSTP8qdOdnToSnMXqlT/8IbvesyDcufgZVlnrnonaCQPiTAyIiaZA3HdB5uiwc4AAQL23e84cDV7jjrOf0cZI3DQ3PyC2Yx96KP0FFArao//ss9qTn8auaeeO7lcZtyEzERFNuHJZY1h/QLZY1Bi0UsnYgre+bkdqVUA69Lt9/nyth2wWkHWA+uuBoqwC9OsmS34VBMBee2mna9aob0eHvqC0GVN+2Ws1rX+iwW9XF7DbbtnnIGoXDIgzMSAmmkTlcmM+K/tOCgJtDxQKKUGxCKRaARDoExYsCPcb9hsOhYLeH9cYsRHaaMbNcrkxcI3O544py8vXiUuLHb2mPR7NgB0EwB57pF+LiIjGbWAgvv9yeFirhe5u/b2jI6Yeqn+HS60KoD7KumFD4/Z59rO3N34qdZRfd9jPWk23Y/JHkbPql6yA2Dl9Yf398aPVp5+e0RNARDMNA2KiSdLXN3KXinJZb35DJNbLjYYaUKn3cm/Zoo0Hm2stoj3d1ao2VEbDGjXVqo765gly7adNW0sioj0AcY2RWk3XIxMR0aSp1dJj1Fot7BcVuMa6qB6YSq0CgfcdHldHVKuaACvPCFBHRzhaaz9tSvPwsC4NsnOWy42dvNZxazOM/JlOPguqd+zQY/xlOyLA/vsDF12UXVaidtLsbZeSZo9MIwyIiSbB4GDylo2A9twHgR5XKrn6zOjGoFSqFb3fucZ9FY1zGnTm7Zm35/gJUGo1XZtsSUpsilk0SYqIFjZrJBnQ5/b3xwfZ55yjDRIiIpo00YlEcYaHdaC0WqmhA1XIyyOv9anS0SfY1CZfdA/6NFYnWH1m2SbjRnG7u/Uxq4uq1cYlQzasHa2rSiWt0wqFMCDu6NDO43PPBc46S48hmkmaPWWaATHRzLRjR/Yxw8Nan5eCYaCjALh6r7yrAa4WNkZE0qd35WmM+Bk+h4bC4HdgYOQxpZJ+cVrw65weZ38HgZYnbpS4VNKeACuv9c7Png284Q3A2Wdnl5WIiMYl7+52pRJQ6gCkBp2RFMc57XhNatRm7YJgCTNslNdmDw0Px0ft/o4FFtkPD49MCNnRofdZcD00BLz0Uvz5hoZ03TCDYZqJGBBn4j7ERBMsKall3HGlkrYlgloVQa2CoFaB+MEwoBX9tm3xJ7E1wXkLZguaK5X40V47X6GgU6NttNgPnIEwcC4Ww4XQlYpm/4xmlS4WgX32Ac48cwz7fBARUZqGPevr8n7VFouAFDKaggMDjVm5orq6Rl7QAtShIa0Qh4bCWUZW4DyN5M5OPVcQaMfqrFmNj1ugvW1bdk/0jTdy/2EiisURYqImKRTqndXDGet303rmAW2MRBsCtZoGqH4ClL6+MAiO2xrDZ4FstarH9fTo7zt3NiboskRb27Ylj1Q7p1s3PfIIcNxxydckIqLcduwAXnxRqwjntCrYfXcdCI2rFqKsPxOQ+CUuJm5nAJtlZGbNCo+rVuO3NQoC3bopq07z+TkzrNBdXY0dujt25JsptX498MILwKJFYf6M4WH9e/bsfOUhakUcIc7EgJhojAYGtH7t7w+TQC9Y0Di4mublWdAWVMapVOKHm/2GS2+vNkTsvkpl5Pmq1XCdsE2ZzhLds9iyifb1hc+vVvXvrMaICPDrX4cBsZUjbJEREVFOmzcDzzzTeN/gIPDcc5pj8bDDkle2mIYYsKMj3ErJ2Eiuv2+w5aGINnC7u8OZR0mVnwW1PT3xWwjGiRv6LpXCgDiuvkuzcyfw4x8D118fpuDu6NDM0+9/v25vSNRump1UazT/R5uEATHRGLz4IvD88433bdum9x12mMaNadv1ingzv4IgbGz4LGiM3hdtjIhoA8N6yeO+eKwh0ts7+gZE9BydnWG58iTZsnJv2qTPu/FG4Kc/1RZdEACvehVwySXAoYeOvkxERDPM8DCwcmXy4/39wJNP6lfqli3xQfHcuTrQ+jJbk1urhTODbHmNVVaWTyJp+nRvbzhVOonlxCgU4uu96LFxhbeyJm03mOaOO4Cbbmq8r1IB7rxT37QvfEFfB1E7afYIcTOvnRPXEBON0pYtI4NhU6kAjz0WDqYmmT8/kock+mVljQob2Z01Kxx2jjYAbK7cnDn5po11dWXv42hliMso6if4yhtYi+hwxBVXANdco8GwXeOBB4CPfxy477585yIimsE2bsye5LNzp/ZBLlgAzJunA7jd3VpN7L57uMPRy2xNrwXDfoZnI6InGe/0YkvgmNZItkRaWaPNVpdlLZoWAQ46aGQwbGo1YN067bAlohmHATHRKK1bl/64c8ATT2ibYeHCMP4sFLQRYuu7RjzJglm/MRIEYeOhs1NbNknBrK35TWNrg7OScdlIQNI5orICbMsy+vTT8XsT12rA5z6nQxtERJQo79fkunV627hRV7bs3BlWEbY14PbtOrmoPOTgqt7+9El1iU1Zjtv5wOqqPGwadrEY//jwcPq0aqsv99tPy5N17a4u7VhOW6JTqwG33JJddqJWY4MuzbxNc9O/hETTiOWVylIu6/piG2QNAg2Ge3v1dxv8BfR7oogKBPVAMW7PYSAMRGfPTs86nWd9sI30lssj14zZFhVxAXE0kcouu+j88aze+X33BR58MH0Ee2gIWLoUOO+87PITEc1QeWPOclkDX+uQrdU0CAYav7JrNYfBsmBYOjCrswLJSoBhs5Ki05njZjDFPdeffWRTp21k2vJSJE27FtFdCw4/XOuLVavCOszemLh6ZudOrYOyyrdli3ZGt0ADnii3ZgelLfD/afqXkGgaGc2ODevXhwGw7Zw0MDBy14hKxWEI2hApSMIaYGMjvLZ+ylcuh62etBdgjRgLiv1pcrWaDhekTVM74wx9IcuX69CDvUA/AZevs1PPnZVEpVDQrJ9ERJRo3jxNnJVHtRqmliiVYqZKA0B9o7+qA4YqBXTlSZIYHWktl8Oh67j6yX9uNPeEje5avTNr1sjOWjuup0fngX/7242Zp22KtY062wuvVsMZV1lptwF9k5jokdoNA+JM07+ERNNIoZCdudP4O0/Ytr3d3eEgbEjg4LCz3IHZhQFkjLXqCaINDkt00tGRHMxa4yLaGOno0AJZYyJptFcE2HtvYMUK3ULJAuFSSa9viU78zKS2JdPGjVmvSsVNwyMiamPbtml26EpFY719900fBZ43Lz3mBMKvcuf0a7W7W5+THusJytUAJRFIWu9vdOPj6BKbUkl/JhXQT/5oHbH++QoFTbQxf75ukzQ4qC/giCOAAw4AvvKV8LlAOI27WNTz7r038NRTWqdZPg5bgpQ2QhwEwFln5d/EmahVNDvLdAt0MjEgphmvXNbBy0JBGxppdaEIsMcewJo16ef040rbNtHaCPHnFwAOZVdECTkzN5tKJZxeZpsbp2X5BMIR4ejvlvxqaEgbE3aeYhE46ig97uab9T4bRbDF0cPDYdKV9evDxsjAgP7Mms5drQInnDC6105E1KKGh4G77tJZv1YvOKdfoWedBey1V/zzRHQ3g0cfjX/cNi6w85VKYTw4skN2xNlRK3SiUMuoh/w6Jrpdk4hWehb42kWrVY3+bd2RFdICVX9k+tWv1hdpL8IKffPNyXWJ9Ty/9FJ4XX9XBb+XIOm5b3lL+usmorbEgJhmrMFBTXC8YkXYadzbCxx7LLBkSXKjYffdNd5L2nHIGiPVqvbMl0paz6cNvpqKK6CUVfDoVhTR4Nf29vXXcwWBNgo2bQpHkK1hEG0gdHQAr3+9rg/etEkLv3ChnvMf/zG5TDY1evPmsHyDg2EjJ230OgiAgw/WEQAiojbnHHD77cDateHfZnBQ474LL9Sv3jjd3Zo0+dlnG/sz/XyJ1lfpD8bm0tEBVBICRxsd9ivApCnWlgzSlMta8P7+MDq3gttyH6uz9tsvfJ5fcb74YvayoK1bw2P8OsfqKeus9e22m+6CsOeeyecmalWcMp1p+peQaBIMDQE/+Yl2Vvt1/o4dwK9+pR3Yxx0X/1wRzefxu981zgizZVBWd1t26az8JN4Z4ODC7ZXi2Bpgf9pX3BQw6+32n2fHRiNzm+ZsPep77qlRP6CNBLNlS3IyL1OrhevIots2FQrhdaIOPBC48kpOVSOiGWHDhuTt++zr+uGHgbPPTj9P0tRqEd1r2Fep5NidCE6P6e5u7ND0R2ltirN1fObdfs/mb9t+x9HCWGA8Z45eP47tkpAW3TdmDBv5WGdnuLsBACxeDPzLv+TPVkbUahgQZ5r+JSSaBL///chg2PfQQzpgOWdO/OOFgub9SNr+oqNjZPKSajVrtyOHgjig2DkymIzOc/NbNnn2HrYXOneuzg+PK0RHh17TguHxigvUbRGbTY8TAS67DLj4YjZGiGjGWLkyPa5zTkd/q9Xk5XdpK2NsJyKf5bWwtBExV0UhcIAADgGkqytcPhNdN1wqhaPEWQGxn1cC0N7iuMrTKsieHuDJJ7W+2nPPxsIefjjw2GPJ1woCYP/9depXWtBsU7lEgF13Zf1D7Y0BcSZ+A9CMY/sEZ3UwP/VU+nnScnNEM0kD2q7IWrvVUaiF66+6usIWk21HYSO8NtKaZ/jZ3ypp1qz4Qvhz7BYu1NHgaKA9d64usk6Ttq+kf62ODu2lLxa1d56NESKaQbLSPABh4uQ4fX2abyqpHkvKT9jf3zjo6xMROAkwWO1EDRLmp4gmvQLCKVBxj0XZ+mGT9n3vHLB6NXD33cBNNwHXXqvTpM1RR2myrbRzXHKJvgFx2bDjrpc0HYyIZgy2QmnGqVSS1//60nYJ2rBBc0XFtQNsRlY07vRzXyXl9Bh2BQxW6hV4f3+4DthvdFgPOpBvz0e7uD03bY4doHPJb7gB+N73tCfe3+Px1FOTrxUEuu7YsnTmySoYBLoQjohoBkmafeTr7GwMbPv7NV/U+vWa2DE68BoV1/fpnAbTO3eGE42sH9NuL1cRDX/EmDcv38Lk6DFZ9ZZf8L4+4Gc/0xdtZfrgBzUoBhoziBWLwLveBRxyCPDxjzdms4wTBPoP8ZrXZL8GolZmWaabdWOWaaLpp1AIO7bTROtRm8VsHdjOhcti/fo7rf0wMBDuB2kzSGzAVM8VoFathdtI+FtZ+Gx9V9b+T9E5eWmtJzventPfD9x7ryYoOeUUffykk3RY4qGHGt9EER19fu97tZG0ahXw9NPJexMD+vzXvCZ71JmIqM0ccoh+jSYRAQ49VL8mBwfDbd+BMI4DGhM2+l/tlUq43DaOjTz39sYt5XWoooBAHKS3V6Pn6Pd4raYFsyRVaaKFS+uRti0A/brFOeDBHUJjtQAAIABJREFUB4Hzz9f7Fi7UgPeJJ/RWrQL77KMZMW3t8ZIlwOc/ryPNv/ylzlEHGhNJzp6tuSuS1isTtQtOmc40/UtINMGCQHM4rVyZvn7LBi77+3UtlyW3tNnMQNgY8YNiC5rTGiLDw1oXd3dHA2iHQkFQgyDo7NSTxQW9Fo3niez95wwNpQfE/vRqQF/E8uXaetttN73eJZcAxxwD3Hcf8Ic/6JtxzDHA8ceHc8Uvv1wbIr/4hb7R0XM6p1lE3//+fGUnImojvb36lfnAAyMfs93vjjlG64oHHmicYh2tWyw/lL/V0s6djXGedbr6qSfiZjLp+QX19FqQINAZSeWy3ioVrRRt1pEtSM5br/T1pVe8O3Y0TqWy561Zox3E9qIKBd2VIG1ngt5e4Nxz9bZ5M3Dbbbq2uFjU4Pk1rwkrc6J2xoA40/QvIdEkOOaYMGFJlIjm8dhjD62bH3igcatePwC2pb1+UGs7UviNkUIhbIzYSHOpNHI0Weontd55zJqlrRZb+GXzrq1HvlhMT2gSDXBt/8c4tZq+YHtT7AUXCtoLbxmnRbT3fcmS5HMVi8CZZ+qtvx+44w7dY2TbNu3dP+cc4PTT06ezERG1icFBTea4fLnGdQsWaD102mnAsmUaJwJaJyxerNvwdnVpf2J0QDUpnvS/6qvVcJTYAt/oTCZbPhQfEzrUECCAl7ciCMJpTsb2nk/KMOnvYDA4mLx42uZyl8thxepfZ3gY+J//0VFimy49GgsWAG996+ifR0QzAgNimhGqVeCZZ3S2r4gmoTzvPI3T+vvDhoJzwL77Amecofc9+ujIeDNuSnR0kHbHDo1lbZcJO7+t1yoUtF0RN10Noj3zDoAA4UiwndjX2amNjLRFZBbgbt+ePH25VtNg1SL/aGPk978HFi0a23rfWbOAN75Rb0REM8zWrZqSwf/63rEDeO45/Uq9+GKNBSsVnQrt9xPaPsVjUSyGA7hJM5Zs1nNcveYgcM5BLKEjEF/X2B70/hIfO254OJzlZIkU7fFoBO9v4xRXV61fD3z/+8Cll47cU4qIknGEONP0LyHROL30knYs79wZVvoPPqgdxhddpHHi5s0ad+63X7ikdfv2sNfeV6tl/9+uVrXX3ZKW+I0Rf2r1wEB8RmpAGyMCb6/HuKnRIhpV79gxcq0woL3xFtiWSuHIcvRcAwNhMOyv3zLDw8CPf6yjuscem/7iiYgIgH6l/uhHIyfn2Ff0ypXA/feHaRqi4lbMWI7FrD2F8+ayGRqKX0ardVcQFj4I9KRxs5JKJQ14y2WtLyxrV7Re6unRijW63siuYR2yaYW9/37gda/LfmFEpBgQZ2KWaWprfX26a4PN5rK1VoDuLHTddcBee2mMd/TRjfmd4oJhO0dWYs2ODm0T+Gu24tjssFhBEC44BpJbNoWCDit0d4fHDA83rvOyQtlWGTaH20afbU6eZbROsnSpjiQTEVGmtWt1V4K0OmPZsuSVL0nbJ6XWHQgD3LTRYRP/lS8oSH0Ut1TSn9u3p9cPlgzSgmKbZm1Zv+wY2yXB/vYLkWfnhCeeyLflIBEpZpnOxICY2tqyZWG9HGVLlh5/PP65Sf9/y+XsBsbChdl5RszI+t8BcBDnwjlv1WrjEHeUNUR6ezUQttZStDXU1dU4h87f5zi+MCOv8+ij2S+KiIiwdm12fTE4qLOU4uy2m9ZhQ0NhTitbjpu2aYANyGTXQS5SPn1CoVqG9O/UC1erGpnPnq11UlzlaIUZHNQ6yEaTrZ6xjljbks8/R62+s0JaWmyfZbgmIpog038Mm2gcnngiu0Hw5JPAK1858v6FC/WnnzXakjoPDSVn6ATy1enxtLAd1TJk2Es+0tGhjYVaLX2rpR07wqlo0UxfNhWtVIpfGJ0ngncO2LRplK+JiIhGa+1azX1hX8u27LZS0fqnr0/7OP26yPJW+M8B0uokQbH4csYKAEChOoTCcEzyqyDQTtdaTaN0P9ukbdW3ffvIEWFjI8aDg2GFOjwcLq6O1luJRZbGTGBr1mjvd3+/roV61av0Z9SGDcDNNwO/+Y1e95BDNEnXK16RfU2iVsYp05mmfwmJxiHPrKqk+PL55+N3Kero0CW3zmlsaXGk1fudneHU7OxZIrrNEsIUWugYHkRQjRTctr6wxkJ02NsyRPf1xV/UCmcRvRW6XNZGhCU6yWKbJvvWrdN9h0U0Q8wee8Q/d+NG3fZizRptzJx4InDccS0xlYaIaCz22Se7n7G7O+yANVu2aIyXpFzWr1GbnezvZw+EealscDdpzXEhcOjqdAiCcJaQxAXDQFhvdHWFwW39Odi6NZxh5NcR/jC2Pb9Y1MrVZjbZdksiWtikTNR2joMP1nOUy8B//zfw2GONgfStt+pOBq97XfiiH30U+PSn9Y2x6dkbN+r2gG97G/COdyRfk6jVMSDONP1LSDQOCxdqZum0JMy77DLy/tWrtY6NY4myLF+VzQrr6Ag7uIeGwpnOfmd5I4fuLqCjoJWzwEEqZUg0GLaCAmELCAgbGv39Op3aWkX+aK//wm2qmjVk7JyDg2EDoVhM70VwThsjgK4l/s53NBj2LV4MXHaZrms2N98MfOMbYbmCQFN877cf8JnPjG0bDSKiaW7vvXXac9o64rh+wZUr823v648MW0xYqWiQ7Sd6LhZHVgc20Npw7WrKNn72xM5O7RW2C4roiOzGjWHnarSn2M8EZpWmKZXCLJOAFihpT8RCATjhBP37hhvCNU/Rtc233qp10EknabD92c+O7Ei2a1x7rXbmvvrV6a+dqFUxIM7ENcTU1o45JrtBccwxjfdVqzrVOk2l0tj48HcrsjrfZpVZXBotRxAAs7odAgEKlnckz5C2bWBs67B6e8Pfi8Uw2LVjolOn/XVahYJuX+H33CcR0cD1oIM0iP7qV7XnIGrVKuBrXwsD9wcfBL7+9XC+n59F9PnnNSDOs9iaiKjFiAAXXqjLb6P3AzqhZsGCkUti//CH7K9Ff+WLn8DRtgY2tszHr6usuqjWgKGyYLiit1rNIfPb2A9mazXtlPU7Vv2C+LOT0s7X3a0FHB5OTsIzbx5wySXai715sw6hp71Jt92mZbrzzvjpXiYIdBcFIpqxpn/ITjQOhx4KPPUUsGJF/ONHHTVyhu/GjdlTrS22szrbr7stmbMpl8N41erjzk6gUBAMlYHOTk1qIs4hyBMYWsPCtkiqVvWiadm+/KnSfsPE/i6VwgyiSaPEtk9VoQDce6++UXFqNd0v8qGHdFr09deH1487duVK3ef46KOzXzsRUYuZOxd473t11tHy5TpgWS7r19+WLTqYGQTaOXvSSTr5xo8vrf5I+3r3B2DitlAC9HzWfxoO3mo9pEloHQIEiL2Mv29wdB/B7u6wPogrpD8zyDpFo3WdLY624y2hpB0fBLo22CrsPAlCtm3TJT1JmTP9az/+eL69rIhakWWZbub1pzkGxNTWggB485t1kPKhh8LcHTZ97KmndEDz8MOB44/XPYH7+sJMnjZDK66OtLo42plty6v851ivfE9PY2OkUhVUB+tJUSAoAsmNEfvpNwJs6ppNNYsTTWqSFJj6ra8gaEyY0tOj06DthT74YPL1zIMPAkceqW9ymkJBj2VATERtqlTSqdEHHKDb/UWX0tRqOuC5alWYm8JUKmEiLb8/s6Nj5H1A8kQfPw1FtE6rVgERgRQ6EVS9xBpJe9PbfsR2oqR9o4w/tztujXB0o2Z7jl+5PvaYVtZA2AGcFRTbUiKimYxTpjNN/xISjVMQ6NKg44/X2Oy22xofr1SA3/1OHzvqKM35FH087rvEppz59bW/04RPRHvm4xNvCsrlejKuoANBrRIGxc6F89yMjfTa43kaBf7UtbgsYtHGSDR5Vrms06MPOkj/tp6FNDt25N8rMi1zNhFRm3jwwbDDNc7WrdoxO3v2yHqkXG4MlmfNGhkMW46qqDwDRNUqUAgETgKITZxO2pveeopHsx+wdcjGbZmUpw7w96bac8/sei8IgF13BY44ArjvvvTjDj+cgTO1LwbEmbiGmGYM54B77kl+fHAQ+O1v43N5WA+9KRRikpFAGyNxrBGTVN9aO6EWFBvvtD0gfZbUxN9HOIuNLJfLI89nqUjTBIFOPTMLFqQ3HizJypw5Ol8wTbUKHHhg+jFEKUSkQ0T2bXY5iNJUKrp8J+sr2/YcjmNf1d3djcFwZ6feZyteol/P0aRacZwDxFUhBS//RGenDi13djYebKO3NtQdfTzu5JWKTsGKeyxPPeZXuIccojkt0uaRH3209kSfcYZW2EnH1mrABRdkX5+I2hYDYpoxnn02fWYxEO5eFFc3+736PT2Nj/nZOqOJLIH0PYtNteIggYQ9ecUiXE/PyPlz9rvNi8uzNsN68vv74x8brRNPzM5WduKJWrbzz0/fsLmrCzj11NGXgSh0OIBnm10IojRDQ/GDrUnHxvH3Gd65U7/Sg0CT/y9apAOnBx7YmMcir4JUUXReJG6drramNxr0WnYu55IXLvv6+0fWGxYMZ+0/LKLzzU0QAO98Z7i9gy8ItCP2zW/Wv3t6gL/925Hzy63ufPvbdQoZUbuydmUzb9Pc9C8h0QTZvDk5t5OvWtXYMa7D2/YetoQoItr42H13zUll9Xo08M4Tc3ZIBR214YYMn+JvLukHs35DpbMzXM8Vx4af49ZoWcbnrJHmWg3Ya6/w72OOAe6/Xxe8RZ9n+0QecYT+fdFFOid9+fLGY61h8vGP69w/IqI2Viol7yjks10K4nI82eYBxnJPrVzZ+LgN4GoCR60esoLkUqDTn2OrKwuK/R5fvx4KAr1AdDq0HWtprqM5LapVvb+nJ6xYk0S3hNh/f+BjHwNuvx145BF9bleXbst05pk6OmyOOAK46irg5z/Xumt4WEeZzz9fs28StbNmB6UMiImmj46O/Lv7WAKTKNvVyI4plYBNm/Rm1+jqCpM123riajU9S6jAoSQJjRF7UmfnyHl01nLq7k6eigbEDzdYY6RW04A0LmC2a8yapY0PUygAH/gAcNNN2riwYLxY1DSp550Xtto6O4FPfxr42c/0tn59uJfkRReF+xoTJRCRZRmH5BieImqujg5gyRLtG0yTNljq10E2m9lPAAmEg6629Z9Nl541K3npjqCGDskxfN3REa4btgvZbgc2TWpoqPGYtMSPfg/BnDnhbgfRY845R9cDA3r8YD0b5R57aMLHt71N68euruQ3cJdd9NjLLst+nUTthFmmMzEgphnjwAPT1xAD6et8gTDIBbTetYzSfq+9dZDbdkvd3do+SBsELUoloVveK1ixGL+wbGhILzR7tjY6/JFim1cXDYijQw9dXfq8uMC5s1N70aNfaJ2dGtCedx6wdq2eb++944chOjt1M84LL9SGUnR/ZKJ0rwBwLZKnRe8J4JCpKw7NBENDWmc8/rh+vR15JHDyyenbtWc58MD0gNi+GuOSMwKNK2iCIAx409qb1ap+BQ8Oan0UO/Kcd+VMdPnO4GBjvWE9z1YRRqdc+TkrbGaSbRvonL4Yf9eDI47Q5992m9Zvtu/x0FCYDOu004DddmuJUSiipuAIcabpX0KasZzTGbkbNmjH8ZIl4+tkmjdPO4iTts8FwkZI3HX87ZWCIOx1j05h89kArN2iW22YQpBj6DqaRMt63i0ALhR0uGDHjrCBYtPUrJHiN0TsRdk0ts5OLaQVuljUxki1qq3CoSG9bdyo9+21l+4LuXix3vIaT2uSZqrHAPzGOXdV3IMicgyAD0xtkaidPfUU8NnP6oClfb/fdhvwrW8BV14ZJtwfrTVr9Hw2Jdrn1zFx/YqzZzfWNfaVPGdO+ha6NlIsorGkvxzY6rtCIHC19H7Zl08GhKPD0Q5YO6ZU0otZB6gf/PoBsE23tmD35QLVO3l/+9uwHjOWe6JS0d6KJ5/UjZ4XLcoqPRFRLAbENC0tX67LfZ57Lrxv4ULgPe/RzuCxqNW0Xk1aLus3RuKmS/vbJtVqOkM5CDTRZRobHR4Y0PMWi40Nl5dHArJiYj8Tp2WM9re8sDly1sCwDC5+z1xHR7hmy54TBPpiLEGKvQmHHgrce2/Yo++/abUa8Mwz2mo84QTg3HO5ZQVNpl8DWJLyeB+AX01RWajNbdoEfPKTYb+iv+Z3+3bgE58Avv717AT6cbZsCb+iLR8V0Dg7SQTYd98w78WsWeGymzjROiWObe1nVYdzGkgLLJIWuFoAoBYfFFtBLbuk1TezZoXJsmq1cGq0TaW2F+T/tMxgO3eGexwXiyO3GOzr08eS8mNYoF2pAD/4AfDRj7IeIorDEeJM07+ENOM88YQ2OKKJRzZtAj7/ea0/zz579OfduVPr6ug6q+gI77x5jc8rFnXgNe7/c9K0Np/Fn9YpXi5rQ6RQcAgCqQfoHZBqQqVvhbWg1CL6QkEbI9ZqGx4Oe+PtwnGFs9Fi63Wv1cKsK77HHhvZQDE21F2r6RriRYt0E2eiSeCc+2jG4ysBnDFFxaE2d8styRmhbcburbcCF188+nP7A6PWf+l3tFpseMop4XO2bAEefjj5nHliwGgn8PCwTibq7dWgWODgih2Q4TIcEnJZWH0QPVmppFOkRXROdn9//F7D/rn+//buPEqSs7zz/e/NzNq6qkvqfaElSwgtaLHQwiKN0WA2sRuDhe8YY44Zb3jGBvvAveAdL4Pn+gzXx2NjPBgMthjbgGzDgAxYRqwCtIEkEJIQaG+009Vd3bVl5nv/eOpRREZGRmRVV3Uu9f2ck6gqMzIispvO933e5Xn8DyHdvmRnj8vKMflscqNhowd3392aiRqAISAu1f93iA3nfe/Lb3PTr19ySXnZw6xKpXU0vlJp3cbqMefu3bYSeGHBVmXdequ1tUXnLOuQZDtWs7M2uxCCdT1iCIqhIsWc0fnsyHy6AzE6mnRSfMlzp/JKadVqa4fFZ4bTAXCtVp6S27OOXnMNATGAoXDNNcVffTFKX/7y6gLibG4pj/nSK5SkJFfho4/a61NTnbfcNBr5r6UX/PhsdPoYH0s9/ri4vIc4KIyO5tcO9DfkVRXIjgx3yneRNTKS/IGkZ4/9/SGUn8cHh5tNS9hIQAy0I6lWKQJi9JUHHpDuuKP4mMOHpWuvbR1B70a2M5COLb3jUKlIMzN2jQcesBVbPvCdx0f483jQnRcwN5vSgQNBW7ZE1apNVSuSKjUFn7HNk1eSIp2ExGtCdcoWneaboLNL2nxjtAfWZaPz/r79+5NpcAAYYEWTm65TneBu3pfNS5XezyvZ7/v3t7cdndqa+fnWpI0+UZsdBF5cbM1SLS0PDAdJilbmLwRrR9J1nxqNZHlzJ5VK62BqmaKG0xtPz2dRdp50+wUAqzBwaV5DCP8lhHB3CGE+hPC1EMIzen1PWDtevqhICN0dl3XgQP65xsas/fal04cOSZ//vG2Rfeghm83txFd2pVUq1hmZnLT/+v6v7MrjGO1/asvboEKlYj0hryvsI3ohWGckr2OQzgCWrgnZjbzjfKpCKi+WmT0Pe7cw5Gh/NoYnP7k4CX61urqJSK9GlG4zPIZLZ46emGh9TspPwuU8t6K/PjHR+rWcnnzNtlmTm/y41EH1evLw6ed0li8/0dxckvHZ2ye/YFlwmt5jnPeaT3mXtSvpvU+nkWgeyOVLpnv5WIVj2eYO1HROCOEnJb1L0i9J+pqkN0v6dAjh9Bjjwz29OayJ7P7dPDF2d1zWQw+1P5c3Mp/N7llWu/jwYVvOJrV2ZrK8I+TfCyFIoyOZWYD0nikfJc9mTPGpbd8jnF333e1a8ryANx1Ud1u0OQTphBMGYkkMsFq0PxvHS15iq5A6aTTsmG7deaf0ta9J991nX5ebN9vz2a9vyQZo8/jsbiczM9YuejBcFEc2GtYOTUxkKhw0m+1LlL2t8RFjD4RddhuPn2diojjglcqn2dM5MzrxzdgXXJA0xABaDeAe4mPd5q54hjiE8MEQwiVrfSNd+nVJ740x/k2M8VbZH9IRSW/o0f1gjZ1wgnTSScWN+diY9Mxndn/Ohx+2chk33tg6ip6eWE2fO9v2eiWiTm3y/LzNKkvtAXZW+vqTk7F135enwV5aSkbnFxftvx5l1+sWgc/P23GLi63r+3w/V1Fw6iPzZTPARcvj0udqNKw4JzDcaH82iPPOSwLevCXLr3ylVaTrxpe+JH34w1ZuydsS/8rOLcFXzX/ev+47tUNeBaGb8dBGwxI7jo15cYNUCaVONeK9YoHfvG+t8YA5XY3A6w53Gh2WkgzSeUKwjsCP/3gyepDH258zz7RKBwDy9Xp2eHXB+DFtc1ezZPo4SVeFEL4TQviNEMKT1vqm8oQQRiVdIOkqfy7G2Fz+/aIO7xkLIUz7Q1LBNyv6QQjSG96Q/Jznda/Lr9GYFaMFwn/919INN1g943RFiGzM6APgeddNvy+P78vq9P7sfU1PZ74ffGS+0zJm30+V7Yykl7Z5itJ6vXMnwj9A0TrwGG20/YwzitcNSnat5zzHOiTAOgkhTIQQXhFCaPs/9vL3+ytCCB3m1tbk+rQ/G0gI0i/+olXxOfHE5PmTTpJ+/det5G037r9f+sJyMbB02zE/33kXTFFiZU/enF6dLFn740mzuknymJ5BbjSt5JKkpC7g6KhFy9lGMn0Rb2+y0ok1fD9S9uJHjhQny9q0SXr2s6WtW6Wf+znpR380v9HfscM6DJddRv4KYDBsTreLndrt1bS5R2vF3yAxxleGEHZIep2k10t6RwjhKknvk/SxGGMX00qrsl1SVVJ24etDks7o8J63S/rddbofrJOnPU367d+W3v1uy7DpJiel175WetnLujvPddfZQ0ra7UbDYsFNT+yb6u5c9bq14b4cLd1h8X5DpypHWekV0M3oJS+UNPg+6p0tg5SuQZw3u5tOglKrWVCc7XWFYDU8imaHTz3VMkafc46VU7r66mQKPG3rVumlL7VpfWB9/YKkV8QYP559IcZ4MITwq5JOkPQX63R92p8NJgTpec+zx5EjSaKqlbjhBhtTzIsbl5aspvHYWGu7UZabcGEhqU2c3vY7N2dtZDdBcXrgNsYn5ohbKxyk9wF7e+G/l5VD8goFeUm2/GaL+HS3ZH9AF11kjx/8wLKNVSo2UjE5WXweAKZ/lkzfn3nlHZJ+L+cdq2lzj8qq/nRijI/I1nW/K4RwvqSflfR3kmZDCJdLeneM8Ttrd5ur9k7ZfbrNav/LQB+68EKb2b3lFpvZ3bzZlrF1uz222ZS+8pX81xoNi+88T0i6BmRRR8LL/E5OWhudnjxtNDrv/cpKlkkHNRtRtVrmgp4oq1JJRtFjtJtNTw904qUsvOeU/kCLi+VLpT3ADcHWBZ59tvXcvvUtG02YnLTnpqe7+8DA0XutpD8oeP1PJf2O1i8gXg3anyGRzuC8Eg88UPx13WzaV3q6HVpcTNqSvLZo06b8+2k2rV0bGSm/3/TrI0/ktOjQ8NVqSZuRbiyLeLIMH0FIB8DdpPB++GF7T3YEYssWewBYkaYqavYwj3Lq2vskpWdYVpmvf+0d1XBBCGGPpBcsPxqSrpR0jqRbQwj/d4zx/zv6W3zCo8vX2JV5fpekB/PeEGNcUOoPu+MXPvpSpSKde+7q3vvQQ+XVhw4fbm9vFxbaR+zTpqbaA1/v1ISQdGyK/q+WXDMmK9Kyb/Dfa7VkptinprspheQfYna2tfNSVp9Yku66S9qzp/W56WkboQd641RJNxW8fvPyMeuF9gcr1k2ewcOHk6/r9I4Wzw+V/r9NUdJGNztrA8d5OTIkC5h9MVII0Ur+lfEtO9lVS52kU2aPjVkD6R+u2+oFeQ00gFXxnXW9vP6yQzHGg128ZcVt7tFaTVKtkRDCq0MIn5B0j6TLZKPze2OMr48xPl/Sa2Sj9Wsmxrgo6QZJz0vdS2X59w5zgdioumlz6/XWLbmS/e55QbJxp2eg7hTwzs2V7zWenExmlmtlnaV0SSWp+45Eetl0NnrvJlHW4493dx3g2KlJ2lHw+g6tY9UE2h+sxumnl2+j8TLy3u54Goh05SGpvfJRJ4uLSS7GNM+b0akMYCFv9MqWOqcv5v/1SgmStUdbt3Z3jm6XXAEYOr1oc1fTgfi+LJD+e0nPiDF+I+eYqyXlVH09au+S9MEQwvWSrpWl4J6U9DfrcC0MsO3bk329Rbwjkg5yZ2dtiXY6FvX9Y2V7s+bmrO1Pb7XykX9fyuY5Ryqhi7JG6Yt1s9QszUfnvRPjyVLKzkP5JPSfb0l6vqyBzPPC5WPWE+0PVuS886x8U1GVgnTqiLya9tkZ4m5kK/NJNj46OWm/e7DcaEgTZXGnN2Dz8xZp+17A7GBtNgJPJ9c65RRrlK+7zvZAldm6tTi7NIAV6aMZ4pU4pm3uagLiX5P0kRhjx151jPGApFWUrS8WY/zH5YRevy9pt6RvSHpRjDGnwiw2svFx2+Z6882dOyI+cJ1OmunPj44m/YB0h6JstN+TPae373pp4GxZxmqli9jTb96zuqT3F/vr2d5Weml1CNJZZ9nN3357d9MC+/aVHwMcW++X5az4VozxE+kXQggvl/SbshIN64b2Byt13HHSq18tfeQjrdtw/Wv8rLMsR1Sa1yY+dMh2qqSTMK6kNLzz7bx5E7PNZtBSParWqTqCX/DAgdaaT7Vaa+NYrSY1ir0hTUf4Y2M2MvD440nDW7RaabV7pQDkGsSA+Fi3uavJMv1363EjK7j+n0v6817eAwbDc59rSU0efTRpl9NlKjZvzt+6G4JtX/I9XK7bchbO+wVjY9YxylpcDBofK+jheLB76JBF2FLSEfGL+Tq4er3zWu/paemLX7RzlHVERkakpzyl+EMCx1iM8X+FEC6R9PEQwm2Sbl9+6QxJp0n6cIzxfx2D+6D9Qdduv136+MctTqxU7Os7PZZ5113t1Y1yiXcfAAAgAElEQVTSbcjBg9YObd9ubVI3AbEH0On2Km8/sjsyFzQ9Fdvatxij7Xs/fDhJ7pitWJD+2ZdBLSy0Rv++DOuxx5LjPTtmti0aG5Oe8Yz2HBYAjsogBsTSsW1zKdyGoXXffcl+LK8R7J2RkRFp1y4bsE7Hl97Gew6Q6enk9aWlZOa4k7ws2B4MZ99Xb9g582aeY1wuxTQzYx2MdKmlbEfEP5CnyU53WjZvlu6+OzmHZ2XJ2ws2Omo1hUlkgj4UY/zpEMLHZRmnT5NVibld0u/GGD/c05sDMu66S/rwh5MxS1+N5Lwc7/y8JU7utBz69NOTCdN6XbrmmuLrjo8nTUWlkuyc6dRuNRpBh2alTZtia16LGG3/0NJSstenqH69N6DpDxmjBdPf/rat115YsA/hiR9HR1s3TL/0pewdBtATBMQYSt/4ho3MS0n5tfQI+MKC9J3vdC5h4cdccIG140tLNlB+zz2dr+l5rDwA933Hnfd9Bc0ekaY2xbbOkqSk9u/YmN1A0XJnXxeXDXQPHLBphlotGY2vVpMP5cHzjh3Ss5/d2zp1QInlwJfgF33v6quTn2tPlDZqPcYnUH2wtVJpzTtx+un2mJmxZmBmpvP1vDZxera52cwvCZxtk+qNoEOzQSMjUZUgVSpRYwuzyT7gELrbbuPRv7cr6cSQtVprSUB/3RNuAFg3K0kSv17X73f0fjF05uelK6+0n32ZmpS/wuvIEeto5K1EPvdcae/e5D0PFexaCMGWpWXLNI6MtE7sZjsiMQYdOhw0OhI1MhKTPceHDyRvSNcjLrqB7IbkEKyn5QFwvZ6suwuhdTp7YoJgGH1rObvkWyW9QtKopH+X9I4YY5dpb4Fj5+BB6f7litNleSJCsLHPqSlbTXTccdK2bbZq+IEHkrZMsq/p0dHWGLJateerOfuAs3kVJWtKqtXW2sd+H81mUFNRU2FBIR3Upv9bJjtDnL6Af4j0YKyr1fKXWAE4aoO6ZPpYogeMofPNbyb/+KrVznt//bnFRes0+EquXbtsG+2RI9K//qu128cfb4F2dnmzt+HpxCeuUrH3pjsj3kHJdpIazaDmopViGm/MrrwTUiSd+GRiIr8WcTf1PIDe+U1JvyfpKklzkt4kaaekN/TwnoBc6e/8br/Cm00LpI8ckU491VY5ZVcNeWm/445rrWSUDYZ9UtcHZLPZqhsNO8/ERLapsbrElcUFRdmehCd0W30gOxWU3SccY3uULlnDS61uYF0QEJcjIMbQeeyxZJY32xHIMzeXLFV71rNsVvirX23NT+Wzw+PjSekKyZaoZWd9fWJ3fLw9GPcAeXw8f0K2GhoK9SW13XJ6yXOevGRaUmvnxHtIHqmnnXBC53MDvfczkn45xvhXkhRCeL6kT4YQfi7G2Cx+K3BsTU8nP3ebGdqPXVqSPvc5myXutN1mdtYGaX1hUDqo9ff4KudGwwZ9fRbZeX4NbxLsHEEjtYa02Gxvg0KwhqtT2b4Yk/3A/rt/oOx5sjfSbCb7iVmpBKw5AuJyfPNg6HgguhJ+/Fe/aglOOuX1mJ+3DsTYWLKa2XlnJL1PWcqfQV5YSDoy6feMKCcY9pPkJcJKSy+r9s5JNvCVrMPhx/oHz0uDDfSPEyU9sXg0xnhVCCFK2ivp/p7dFTaU2VlL2H/PPfY1et559sgGrhMTlhn60Ufzv4Kzsm2J7/frtILYX0+XDcwGw1lzc+0DuPV6NuFWLG47x8bs4ukg1y/eaCTJG/35vNTY/rvXJ/RB21tukW67TXrqU60eFbPFAI4hAmIMjGbTEmHNzFhNxVNOyW8zzzxT+vzn7edGI39vVVp2QHp2tjjR5dxc++t5+4Odx57pzo0njfZEKk+cp9NFQ7Cp6cOHW5/3zkh6+M97SHlLo51PG3hn5IorpCc/2ToinbKMAb1Tk5SdmlqSREYeHBPXXiv9xV8kW2sk6bOftRVFb3ubBcBpz3629M//nHzXF7VDee1NNiD25JC+mqnRSBYOpSsoFLV12XP6Kqq0ZlwuyZCXBScEax8aDWso/Rhvf3wgdmmpc94LD57n5tqD5aUl6eabbeT5wgs7fxAAK0JSrXIExBgI114rXX65jbi73bul178+KUnhduywNvvIkaQjUlRDOBsQLy21H+/JuTwrqI/6N5uto/udrrG42D5L3B5EBzVCtfM/Si+ePD/fWhfSOyAeCC8uto7Ut1xiOdFWdra50ZDuvNNqVV16qQXfQP8Ikj4QQlhIPTcu6T0hhCdGiWKMrzrmd4ahd+ed0p/9WfIV61+t1ar0yCPS7/6u9Ad/YAO17uyzbWD28cdbc1pIrUuc83JKSK1tg2+xSWegluxr3tuldNnATrIBccdtwWNjxQOqlUr70ulqNSnHUMTLOaWXRnm5QP9gd9whnXZa69pzAKvGkulyHQvCAP3iq1+V/vRPW4NhSXr4YelP/kS67rr291x6qf03vYUpLz4sLotkxsctwB4ZSZJo+eRqo5F0UrrpjKTlHl+pFt+QF1Sen7fekAfCtZp1YA4eTIoo52k2rcNSrSaPdKdkYUG6/vriDwIcex+U9LCkmdTjckn7M88Ba+4Tn7D/pgNhr05QqdhX71vfKv3Lv7RWK3jta5OYrl5PyvCOjCTtSqctsx64jo7mB9Ku6Os+K3tc+5LsoFot2gvZaev0SECnAdd0hJ2XwCNG6Qc/sHYr+1p2mvuuu7r5SAC64AFxLx/9jhli9LVGQ/rgB1ufq1Zbsz3/5V9Kt94qXXZZstr37LOl22+3532rUnrJmZdEzAtK08+Pj7d3RpyXBu62jGK2/9D+vqhKbXlJ2uxs/gmKlkKXReTNZpJxzI9Pr5nz6P6BB+waLJ1Gn4gx/myv7wEbU4zSDTckq4Kq1fzv/Bilj3/cXnvpS+25LVukX/olyxh94402FulxYlHuqPRAbad2yvmW3k7tVFo6XvUB3tQnsPvyYyYm7CCP4r2YcaORJMbyn12l0r4PyFcxeUbJvKXUfo50wseiGWoAWGPMEKOvffObtmfYeSCb9YUvSO98Z7ISOATpVa+Snv98W2UsJeUnfLa3U8dh06YkTsyWWcoqWx2Wll0C13reqFpVqoTlD7l5c+sH9U1ji4vW4ci7Kc/eNTZmF8iuxTt4MOnApIPidGfEHTrU/QcDgCHlcaArS4L8iU8kCRUl+wq++27pwIFklvjIkWRmN7sMe3TUHj6J2k1uKY8xy471JmV8vLXkkgfDm8Zjy4Ih1Wq2fabZbM05ISXlFtJJsrxkQ5rXvPep9CLpAVpKAQJrptezw4MwQ0xAjL72gx8kP6dH1fNWYu3fL/3bvyXPVSrSBRdYRaFazTomi4vJ5Gt6xtZ/Tmfc9D1bRXyWuFPVozSPTcfGsqvR4nJFi+QEsVK1Dsf0dLIn2L9R0qMCflH/xskuU/M13o1G53IZUvuG5m5rTgLAEKtWLV9FtiJAJwsLNpDrPvOZZPVvuo2Yn7dxx3T6h3o9CVSzyZw78bwWZfdVq0lTU9aseDvq17WJ3SgFfy4qKJWTIq+WcLVqo8ceFKdHAbI3GGNSFLnsw/jxJ59c/uEBdKXXwfAgBMQsmUZfS1cDKkuOFaN09dXSK15hvzeb0j/8gwXKafW6dUTGxpI9VN5eT0zY7wsLnUtedFLUIZmYSBKjZGPNalUaG40tGaatMyKbgs7W7YgxWVbtmT092M1m7UpfpNsPMTbWmh0GADawSy+1rTvdVgI6csRyXnzpS7ZUWkrSP2RzSS0stCbFqteTgNVXGuellfCxTn9tZsZ+Hx/PPz47XurNim0jCpaAUk0pNKwtSie62rzZAuPFxdZEjp7qOjuNnuVB7tRU8eojj9BPOskKLQNYE2SZLkdAjL52zjnWFh861F1nZGYmGY266ipbqiYlmaDTnYG5OTvOZ2sXFlrrNC4tdQ6KfR+Z57dqNDpnC5Xsuj6pm45vq1Wp2Qyq16Mq1YZUCdYZ8Q5GrWY3NT/fmtp6cTGZMu9U3iJ98ZVE92efXZ5pDAA2iOc9T/r611tnfovU61aiKf1d79UJqtUkcE23F9WqDQBn27n5+fZ0Dr6sOrsqaXHRrr15c3576deX7Cs+u3XHB2KjlgdovdFsNpPsXvPz9ly63Ul/UN/ek+bn6Sbhxq5d0rOeVX4cAKwhAmL0tVrNMnW+5z3dZdIcGbFkWv/0T62rvHzrrLfp2YQivm3XazxKFiBPTbVfY2zM3p8ugeGD55OT+W1+dmTOOyPJ9YJiDAqNZlKM2DNAe0fCL+Ij81LSWXHZ8hXeEfEN0UVDhDFKp58unXpq52MAYIOp1aS3vEX69KettnA2l5QLwcr+felLnWdEvBSgJ3hMp3DIlkWSbLbZs1r7NfyYTkHvwkL+Fty8PBZPXF9NmyG2M7d/MClZiVSpWIO5tGQ3mN5HnF3R5M+31xlsNzlpBZwZkAXWVK+XLQ/Ckmm+ddD3LrnEMnWm9/fmqVSkpz1N+vCH8/deeQmm8XHrUHjW6Wq1NcFIehtTdnVXevtu3r3krXDOHlupZK8XVQt1VUKz/ZyezXNpKcmyMjFhHQdfQ+4fLl0HyvlMs+/5KrJnj3T++d2vCwSADaJWs+zRv/Vb1hZlYzZfEv3MZxbv/bV8Ee37kZtNiy3ztuKmV0j5YGyRvHOk0054Usl0Uq2qSpY852UTq9WSJVL+ITrxzcpbtrQ2on4TngzyS1+yOsSD0IMGBkSv9w8Pwj9nAmIMhEsusSVoe/fmx2uVirWx3awM9pF5KWmP5+ZaB7rdwkJrJuluOiN5naGxsdYson5tyZapVRWzY/KtB2V7Xx6Zez3IsqxejYZNd/u0QbagpSfwuuOOzslRAGCDO+kkC4rPPrv1+TPOkN72NunBB4u/in0ss9O449xcflzp5ea7SQeRbg7SdZFnZ1uXTbvQqf1pOSiz5DmE7rJ+pW+qWrXHli3ShRdKp50mPelJtvLpsceke++1DGRf+pL0j/9oG7EBHLVeB8ODEBCzZBoDY3RU+o3fkN77Xummm5Jgttm0/Bu/8AvS5ZcXn8P3aOV1Rup1G+z2xFrOt/J2M8nq50lnkfbtVr53LNsZqqipqLZFaq0nGB1tzxKdjtSLRuafuFDFemP79tm5fDr70Uelhx6SHn7YPuQ110jnnmvT7cwWAxgC+/dL119vX3EXXGBfg6u1b5/05jdbJbsDB2wscWHB4rhsEscsT8xcZHGxfcnz3JyNaXazdSgtXfXI2x9//qhNTNiH//73y0sqpZdM+9Lqk09O1qA7/4CLi9KnPiX9xE9QggnAuiMgxjERozXoRYmnurFpk/SmN1mn4+abbYD6xBNt2+sXvlD83lotW+6one+9SncWFhdb9wt305FIH5deHZZXtiOoix5OXm3HPXssiC3riPgN+RLrAwekiy+29151VesxknVUvv51+/m888rPDQB9amZG+s3ftJJ86dnS5z5X+qM/OrqE+tPT9vja12yrjgednbbAdrONVsof35ybs/FMH6Atkl4e7RO5xx+frE5qK1xQPj+c/8aREftAZQ1rnu9/32aFOw3menKOO+6QfviHV35+AE8gy3Q5AmKsq9lZ6X3vk/7+76XHH7f288Uvttnc005b/Xn37rWHZBOa73iHtZ/pxCNZ6URYRfI6HHNzNhjuJTCKzlGrJcGzH7t5cxKPZu8hKpQHxdnEWb6XeN8+W6PXTVCc9uCD0g03FB9z883SmWeurrMDAD22sCD9zM9YTJWtO/+5z9lrH/lI+6qglbjvPguGsztX0t/zvgW3rHRgEW+/PG9ip5VOUvugrpd3Sg/s+j7i5TtUY7kdyo3X0zkqXLNpK4t85VJZxYNs9umlJQuKy6a877mHgBg4Sr1etjwIS6bZQ4x1MzMjveY10l/+pQXDkrWBn/yk9KpXSdddd/TXuPFG6aMfTfJNdUpo5Qm0upHXPi8tJe15UWcmmwE0nYHak0NnR8qaqhSPz/tJ0hdpNm2/1Z13Ftd1zL7HPfKI/QUVaTTsGgAwgD75Senb386fnWg0LFD+2MeO7hpf+EJrXWE/t/+eXrIsJaXji2RzYXhJJj+HlwPO06md89QQHhxnt/82NKK6RlRXtXV41m82O+g6P9+6jaeogc3+wbhuesmDMLUE9Lle7x8mIMaG9q53WX6MbMPtSzfe9KaV5eTIajalK69sf05qrTrk+6bKglmXbdfHxmxZnMeUfs95nZrsyLwf58Hw0pLtO2uZrVDQYl5HxN/sPZi0Q4ds2loqr++YnlZw6f3HnYTQvm8ZAAbERz9aPoB5xRVHd4077mhtd7zqXaNhP2erEvhXaqeg2PNO+XtGRmypdHZG2HfB+DJsL800NmbXzQbefj/O7jN7E0FNVVRXzdoib7wOHWpvyLMBspdPyPJr+Khy2vHHl/8Fbd/e+XUAWCMsmca6OHzYagF3Gtz1XE5XXy298IWru8b+/cnMs5TUd2w0kpH0dGfEg1lf0pxndLT1tVrNOiN+jvR10lWPvMyv9x88qPb3LC627t9qXZZtBzVVUVMV1VRXxUPjet0C32wpJQ+G0zee7fFIrQlK8p4vEqOt9QaAAeR5AjuJ0Y45Gtnz1+vJ8uZqtX3PcKNh7ePkZOueZsnahOnp9hnivPFOL0Po18gG3h6UVyrJPfj1RkY8T1VeQ2g5p5uLdVWPzOZveo4xf8qnWrUPtrSUvN5odK5c8NSn2vadTmK09N0AjkqvZ2mZIcaGde+95dV7ajXptttWf41sTOiJK32UPi+b5pEjyTHZjszIiMV/Xr5pbCypbpStI+yzzp6oa2LCjvNrZksCp+PUTZs6JRazi9RjTfHwYZtKzitsnPcH63uKs8Wam80kK1ja1JS0e3fx6PzYmHTCCZ1fB4A+tmdPcRIrz014NJ7ylNZr+MBr0V7het12rMzNJV/no6PW/vhWm+x9Zgdq069lg+H0z97eScl9jo+XjInGqGZtuREcHU0axHS2rk58jbi3R52yWW7bZjWsnvrU/HNI0vnnM0MMrIFeL5cehICYGWKsi26qJDSbR5evadu29ud8JrZTRucYbfWXt/G+1MyDYf/d5Z0jnZwrPTKfx2eC0+fIW1adCFKQYm1UoVJvnZb2NXCdNo95z8hvaGHBPkzeN9Hu3dIpp0if+ERr5J528cVHlxIcAHrossssA3QnMdoxq9FoWBmnu+9O0jj416+PQ4ZQ3Bb6wp3JSWtLlpZag9XsqqS8svTdlFFqNpN2x/NpFG4fCsvptbIRto8Gz8/bSYp6uSEk+5Q84ZZ/sGrVRhJCkJ71LGnnTumb37Ss05L9fs45VkICwFEjy3Q5AmKsi5NOsrbsvvs6DyY3m1b6YrV82dnjjyexoNf89UoQnUbpPdFVCNKuXfacx5rpINhH19PnSHdMfJl0UecixmQJnFepKBSjmtWaKjH1DeIdkfR67JJzPPEHPzbWuhd4fNymRWo16WUvk7761dZla8cfLz396cwOAxhoL3qR9KEPWd367DhipSKddZb08pev/Lz1uvTud1sMl57R9eSJExPWTngbUzShummTLZOem7Pz+ld8um1ZXGwdPE6fr6zqgR8/MZEMFudVO2h7Q95NpyPyiYnOCR2zS6M8KF5asjpXp57auhfplFPs4cd3U5sKANYQATHWRQjSL/+y9La35b9eqUiXXGLt4kotLEjvfa9VBapUkjbUOw0+g7u4WDx7G0JrDUqvQZwdnV9aal82nf4cZbwcVFF9ylLpWhk+89tpyC09i+ybzNz0tHT22UlQvXWr9JKXWH2s2Vm70bJEJwAwAEZHpfe/X/rDP7Rs0j5DUq3aWODv/m77ft1ufPKT0re+ZT9n48YYbfxxasq+Zufni1dCnXmm/ffAgdbSSD4rLNl9+2Ct/76S+/ZVzL70ul4vX/xTbRRkvPRl0AsLycxvNvLP5q3YtctGyYumzAmEgXXR62XLLJnGhvaqV1mZwj/9U2vnvC5vvW4TkO961+rO+773SbfcYj/nba8NIcm0WTQKHqOtCn7wQSuHuLSUdF7StYQXFloDa0+a0m3b7cuz07PORTUkFYIqjZxvj/S09ObN1oNqK2qcyuiZft+Tn2zB7/R0/jWnpuwBAENkclJ65zult75V+sY37Cvy3HNXvzV1acmSQRbN+qYnOr0koA+q+iButWpjj3fdlbSP3uaMjiZLr/PaME/e6McUtidK8lv4MemAuu19MUqKqmQD4uy0tOe3SC+NlvJrC0oWCHezlwrAmiMgLkdAjHX1xjfaSPwVV1iirc2bpZe+1ALi1UxC7t9vnZoiS0tJbDc/n7TB6dVezaZto/3KV1rfu2NHkkDT2/pshyTdESlbLi21B8+LiwX9ghgVYkMhFsz+Vip2kmo1CXz9RjttFNm3r/tCzAAwZLZuPbotOu7hh9srDuVJB52+lLpWszxRlUpr4klfUezLnw8csDYs3U54zJmuXODv9YoHndqibK5FyZZoj4+3VksIIaoSmqo2lxRGaq0ZcbIBsbc9vja8aMWSJN1/vxVTPu648j88AGuKgLgcPWSsuxNOkN785rU519e/3rpMOo8PUPuq4iNHkjIT27ZJW7bYzLV3arxsRQg2W+wj951mgH1J3Ph4e7KTPNnSjPV6kvwrPSsQQlRQU7XGgoLXifIaTR6dVyrJMjXvRZX1zppNK5b51KeyFBoAjsJqv0J9W+499+S/trSUJGkMwQLW9MqivC1Anguj0bC9yJ2C4rzOaIx2DUskGTU6Io3ULHgN1eULjY7aQUuZ2eJm0wLbmRn7fWysvTxgmgfLHhQDOKZIqlWODRsYKL4kuky6Xfb9xLOz1qHYvz+JMb1ERjoBZrZsosek6XN6LUlfNdapH1Cp5H8RLC5aHGujdlFBUSPVqJGRoDAxYb2bsbFkqto/SKNhnRSf7S1Lc+37iQ8csAcAYFUOHZI+/OHuyrhnv5ZHRiwWLFtq7dUXJieTtqfRsEFYL+eUVZZpem6uc4e02ZQqQRobjcsz0CGZig7B2qLsqK5/IJ/C9iRb2Q/tH8DNzAzGVBGADYcZYgyMw4cta3U3I03ZhCHeGTl4MP94D5q93KInHpGS0fqpqfzl00WaTQvE8/oTzaYF3psmbHS+hW86O/74ZK9w2vS0pdeWkmmEbBITD6Ddww/b9DgAYEUWFmwv8v79yeKcTgGo16hP/z411X0SxrzSfDFaPDk11b4EOm9JdNbBg52+/qMmxksi/E2brBHMe94rGHhpB89q6aPFWUXLuwCsC5ZMlyMgxkA4dEj6/d+XHnkkGYTu1AHIdiY8B1U6cUkeT2biS8/Sz8/PJ4Pl6ddGR8uzdS4stGYITatWosY7ZSD1JdITE+3Lor3z4VPmnoXFp7KPHGkPorMBMwCgK1/8oq34dV6zvnXbiz0/Pd1ee9635ZQFrvV68TFHjlh74vuTS2sKL/Ol1dn2yvcuF/I2JtuGhGBT2b6syvcDpZdcpVWrxSuaAKwLAuJyBMQYCP/wDxYM+xJnH4TOdgQqFQta0zZtSjoqZdKzwllzc9bOT00lHaGichpps7P5CZ5HR2NxYq4QrDeVDYhjTD5Yusawr63L64yspr4IAECf/3zr70tL7Tkktm+37/n05KjPJruyRIzd1BROx5TdTriGYAPLU1PJPmWvntT1CTo9H4J9+DvvLF4Tvns3eSyAHiAgLsceYvS9w4ctG7Q3/M2mBabpjkCM0p497cmwPMPzWrXBfm7fN9xtooB63WLa9H1Uq2pfKl100awYk7V4k5O2nq4oscnOnd3dLACgRV4KhnQOCm+T3vhGq3Ln0rPC3ew9LgtQswF1s9ldZ9OD6HSSyU2bylc4PSHb2KUbwGrVou0TT+z8/k2bpCc9qcuLAcCxxQwx+t6DD7Y3+J6V0/fwVirSBRdY+3zddcny6HRJiaS0ROdrla3myi55m5+3WLSb93iHadu2pC5kpZtAPa8X5VmopSQDtS+hznPccTZaAABYsS1bkqTKeUKw7/bjj5fe8AbpscekBx6w1z7zmdbaxEWzxNkVTnnXyZqdLf56HxlJVlV5AOxZr0MIilrOLp335qJyfh4QeznAZlM64wz74IcO2WvVqrRrF6X/gB5ihrgc307oe91sOfL9vy96kXTxxdKNN1oSkcVF6fvfT5ItFy2b9tXJRbKdEc/6WRRkj41ZPyDGpD7yE/etoIoKpg18A3P2OSkJhD0D2Mkn2+hBeiojBJsZPukklqoBwCr9x/8o3X1359djlC65JPl92zZ7SFZz+Nvftp/r9c5x4fh4+c6WvBnkPXtsxfL997ePn46MJEG2j6MePGhjpPX6cqCsIA+LW1oJP9nsbPuHTae8TteG2rVLOucce73ZTJZpAegZyi6VIyBG39u3T9q6NUmqnCdG6bzz7Oddu6QXv9h+PnhQes97ktixaJY4mwglT15HZudOi0HzMk6PjCQZQEOwfoXvOfPZ67h8zbZL+xB+XnbPdHITj8jn56Uzz7T/zs7ac9PTJDEBgKP0Iz8iffazNvmZ3bdbqUinnCJdeGH+e5/9bOmuu5LkjPV6a41hT9AlWcex0zYfz22V/n1yUtq71/47PW0DwLOzSUW+vCXR9bq1V36NatV+qIQoKdqscYwKniwr3WBJ7TktFheTesUzM3aTO3bYg2AY6Ll6fQXbI9bp+v2Obyr0vUpFesUrOr8egvT0p1sgnDU9Lf3wD9vPXs8xrzMzOpoEzUX3kQ2It261PCGnn27bozxjZ61mHRTPe5V26FBS5kkKasZgse/y6zE9A+wdj/Ra7YWF1mkA36D86KPSbbdJP/iBDf/72mwAwFEZG5Pe/nbbmpP+Tq9UbFXSW9/aeeb3uOOsDZueTkrz+uSpl5X3c87OJp3H9Nf81JRt0a1UkuIDvl3nppukW26xfBu7d9tr4+PFHWAPziWvfxy0VK9osR60tNBQOEAYzOcAAB8fSURBVHIkSdCYbvyywfDCgo08p0eEFxdt5ODOOymzBGAgMEOMgfCjP2px3sc+1roHq9mUzjpL+vmf7/zeF7zAOhi33pp0RPI6C0tL1v6Pj7cvg67VrJPhcenoqD0aDemb37Qla9u2JRWPingSlNFRH6UPCiFIiqooqtJcUqjXk46EpwT1Ufi0uTnrBTkPjh96yKYsNm8u/bMFAJSbmpJ+5VdstdKdd9rX8mmnWcBb5N57pSuuaF02uLSUv0XHS/h6xYRTTkmC4c2bbUD1W99qjzP9+ac+tbvdMd4GpoNuW0VVUaxWFMdHFJqNZCT5scfsv9mMXr5XOM/srPTwwxalA+gZZojLERBjIIQgvfrVtmztC1+wEkyTk9KznmUdkqIOwH33WefFzyN1/nKYn7eOyuiozQjs3Cn90A9JJ5xgzz/4oD18NXOjYf2BQ4dsD9eePeUBsWQBdrqGpSTFGNSQFGrLUwYeFC8s2EmzmzCWllqD4bRmU/rud6WzzyaRCQCsoa1bpWc8o7tjFxelf/7npES882oJ6aXTadWqBa2emOv2221QdteuzpOuMdrX/o4d5bktOm0fSs8aV6vVpKHcts0a3vSHyOa3yPPII3bT5LAAeoaAuBw9ZQyUXbukyy7r/vhHH20dmfe2fGEh2YuVbacbDYs1t2yxmYDHH7eVyKeeaoPknUpnPPpoe9KsTnxbVfra9nNQoxlUGakoeCA7Pm4dD+9R+Zu6mYp+7LH8teQAgDXliWvSQe6tt3ZO/u8LftJ5JnwFU171gsXF8hh0YSFJ+Fzk8OH8LT2u2Yiq+qa6ECwa37vXlmrNzye1B8t4wWYGZoGeIalWOb6hMNSuuy6/Y+Dbc7MlLrx60dRUa96quTnpO98pXxr34IM2U1ymrFyTjc4v/1KpWFA7O2sJS/wD5WXxyjp4kIAYANbR974n/du/WfAbo5VAuuQSy0z9wAOtCR2z5uYsiH3Oc6zTODGRrGhKC8GagqWl1j3Hq+XxbKfzxKgkYvcLPvpo0u54Rq+xMWtniiJwEmsB6HMExBh4jz8uXXONZfGsVm0P1TOfacHu7bd37ogsLVmMuXNnspfr+OM7b4mqVstLN3WzgkyyDlDngDgqLjWkxSW7aK1mPaW5udYezJYtFtV3mn4AAKyrG2+UPvjB1qD3wAHp//wfC5BPOaU4IJasXXna0+yr/stfbn3Nk2j5Np2ZGWsWNm/uPOnabbBcfFzqhhcX7UPlBb3Vqo0UHziQ/yE3byYgBnqsXu/tP0OWTAPr7LrrpA99KOksSLa8+VOfkn75l8v/ETYaNsDty7CvvLL1dS9/4VWNlpYs0M6rBblm4vL/xGgfYGEhv7NRqVhnw28uT7druAEAK3L4sHT55a3tj/P9vDt3li9fnpqS9u+3EoMPP5yMe6b3/KWD10bDAuMtW9o7uZ6MqyjXldR577LffCWm1jguLHT+ED51PTaW3w6xQgnoOQLicgTEGFj33JN0RrLm56V3v9sSbj32WOdzhGCdhxjtPen23Dsj2Y7IoUPWN5iYaD/f1FSSD6tIupZk3k1V0p2Pw4fzP6Tf2ORkeykmf33btuIbAQCsyrXXFu+Ni9EyP+/ebYt5Os0S1+vSJz5h45vj460DsUXnnptrX2m0a1d3u2kmJjosmV6+yWoz1Yh1s/QpLyA+8USrNQWgpwiIy7GOBQPrc58r3v80P19edShG6e67LbC+9tqkw5KX9Crt8OH8AfO9e7sru5gXTD9xQ7Gp4KPznoq0TF6EffLJJZE3AGC19u8vX548MyO9/OX5JZakpA6xlKSJ8GC4LGeVj4Omqx40GuVNxsiIHeNtVYxKXSyq1lhQSC+ZLrsRr0W4bZtNW+/ZI51zTncJNQCgDzBDjIGVV4sxLUZbfnbKKbZ0Lc/oqAW/XsNx+3abGS4bnZcs4PbZ5RCS5ddlyZ9HRmwEv6XsUqrDMdJY0BOX7ia69uQmXiPyuOOs7kbHqBsAcLRGRro7bvdu6ed/XrrlFtvmc+SItTsjI63LomO0QLXRSNqhIs2mHTsykpSrn5mx8/iS6FotCZir1WT2OUZr92o1a7dGqk1Vm3VVYkNtl/UEGkW8TiGAvsMMcTkCYgysbmLFGKVXvlK64QZ7+L6qSqV1ZN4dPGg1JrtJSuJlgr2TUa1aRlFf8ubX8fv0ko6VSrIfeWzM7qESmqo2G6rEemtnpNvsKFu3Sied1N2xAICjdvbZ0he/2FrTN1tK79RTk4U6T3+69I1vtFc3yJqZSSZXi5qAkZGkdFJSz97auWrVkkSWVTuq15ffPxo0Gjqs/x4fL1+HTb4KoG9RdqkcATEG1kknWXmKolwfJ51kHYNnPMN+/shHktfyLC7ao5vR+WrV+gnp444cscf0tE3QFpXHaDTs2IkJabxSVyV0GJnvZlNyWQ8LALBm6nVbebS01NoG1WpJ+xGj9MIXtr+vTIzJgGkRH7xtr2dv7cvhw90tFIpRqjcqqlcrqoZmezs0OmqPTmuxJyZYkQT0MR/46uX1+x0BMQZSs2n7dW+5pTUjZzqQDUG6+OLkPUeOdPeFsLhoHRFfWpYnBNsq1Wlp9cGDNnpfNjovLXd+4ohqoaEotXdGJidtyqCTovobAIA11WxKf/VX0s03t2+v9ZVDY2PSf/pPltgxbcsWKxXYSQg22ep7gju1Q+Pj5Uu25+eLz5H+PI2GtDQyqkqoK6jZGuWHYNH33FySVVJKKh1MT/e2tw2gEAFxOXrRGDj1uvSe91hnxHmFono9mbX9qZ9qTbLc7QC27wf22o95XyJe7ajoC8Znf8ssLkpxpKJqZVSjWmwPikdGrDMyM9O+7mR62vYMAwCOiRtvlG66qfPrzab00z9tS6SzzjlH+vznO783RunSSy1h1j332OBqtohArdaav6JIvV4+0xxC1PTmqGpFeqJbmM7W5UudRketzfHl075xGQAGHAExBs6VV9rMcCchSL/2a+1banfutLb84MHO7x0bk577XFuK/cgj+SPw1Wr3gW43qpWoyU1R1UpFIYxbB6TZtJ6ML5muVGymeH4+GeqbmGjNyAIAWHdf+EJxFuhKxZJn5QXEZ5whfe970n33tT7v57voIhv/lCwZ13e/K33nO+1bg7rJoeHnLVKpRG05LrYn3EmP+GbXZFO9ABgozBCXIyDGQKnXpauvLq4CMTeXXzYxBOk//AfpX/+183svukh60pPs4SWZbrstlXgkJIPlZV8uZZUqJKlWjTr+uNh6ruz673SnhH1aANBTDz5Y/P3ebNoxeapV6SUvsRnmm29OqhJs3y6df75VRXB33SXdfnt+0q65ufI8Vp7noih4ntwUyzvK3UxFA+hbBMTlCIgxUB56yBKFFKlUbIb3jDPaXzv5ZFuO9sUvtpZHGhuzYPjMM5PnbrvNOiQxtu7B8jqPZYm3yvNc2TK14kPoiABAP5mYkA4cKD6m6Pu/WrXg97zzLLCtVNrrFC8tSd/+dn521mrVnp+ft7arUxOxc6fdx+xspzuJGi94f3IY7RAwyLwqZy+v3+8IiDFQ1uIf9CmnWGB8//3WUdi0STrhhNbVxzMztlQtO7JeqdjjyJHygHfnziTBSp5arctcWHRGAKBvPPOZ0sc+VjxLvH277f0t2r8bQud25LrrOncivU7xzIzlychrR7ZutSXXUrLTJu/6NC0AQECMAbNzpy0T6zzibQFoetlZnkpFOvHE/NdilK6/Pj+Q9efqdUu2uXlz/jm2b7dcVwsLnfcs19j+CwAD59nPlj77WWuHOg143nSTtH+/9KY3rTzv4YED0qOPFh/TbFowOzNjs8s7dtjvY2PW/kxOJsHu8cfbvaa3EnkwnlvZAMBQ6fWS5fW8fgjhJEm/Lem5knZL2i/pckl/FGPsMpuPlE2jAPS1Wk16/vOLjwlBev/7pa9/fXXXuO++4mXZzaYFzYcPWycjPUuwaZMl8zrhBLuP8fHOQfMIeUkAYOBs3iy95S0WhGZ5zqkQrLzS+9+/8vNnE27lSe8rrtdt1vj00639mZpqnfmtVCyh5PbtVvZpyxYPmkN3wTDTyMBA8yosvXysozNk8ewvSjpL0q9J+iVJ/20lJ2GGGAPn0kttufP11+e/PjpqM7Mf+IAFqKefvrLzf+975cc0m7ZkrV63Efrzz7dZgLx+w8SEjdovLNj7KpXlOsdBNjwPABgou3dLv/Vb0tvfbvuApfY8iM2m5aG47z4bJO1WXlLITrw8YNmeZj82N5t0WQZIAmJgoA3zDHGM8VOSPpV66nshhNMlvVHSW7o9DzPEGDjVqvRzPye97nVJsivP/pxNMHLllSs//6FD5cfEmOw5DkF67LHiPkOlYoHx5KT9t1JRd50MNnkBQF966CHr6I2M2COdfNGFIN1xR/J7jBbwFpXlK0qUlZauftQW6HarqI2h/QEwmI6T9PhK3sAMMQZSpZJk2Ow0uB2jjc7PzKxsD1e3A+bpJFzd1oRc1cUAAH1nJV/djYatarrxxmTQdd8+6VnPkp785NZj9+2zkn9FvDy927at+3tp44Fv9gMRDANDoddZnlPX3xxav1cWYowLa3mtEMJTJP2KVjA7LBEQY4B5uYqyf+hzc7Z/6rvflW65xZJcTU1JZ58tnXpq+8j67t3S979f3Nnx2QDJjuu0T7hUtiOSzihNZwQA+taePcl2mE5itH29V1zRHuQ+8ID00Y9aXozzz0+e37LF2qFOtYyl1tnhECyIPmq0OcBQqtd7O/eS6qffn3npHZJ+L+89IYQ/lvT/lJz6qTHG21LveZJs+fRHYozvXck9EhBjYG3fXh4MV6u2TPmjH7XZYo89H37YAuS9e6XLLmstjfGUp1hA3EkIFhC7Wi0/ucqKEAQDwEAZHZV+5Ecs43ReZ7NSsTbmwIH8GV9/z7//u7U709P2ewjSBRdI3/ymdO+9ref2msU+IBuCdM453dS9B7BR9VFAvE9SemNi0ezw/5D0gZJTP5H1J4SwV9LVkq6R9AsrvUcCYgys88+X/umfOu/FqlTsmK9+NemMpCdiJQt8P/1p6RWvSN53/PHWGbnxxval0CHYHuD01qqzz25dPg0A2Bhe8hJLmnXHHa2LfUKwlUP/+T9bO1XmppusnJOrVqVzz5XOOEN65BFrizZtssoGjy/vjNuyxQLuolrHANBHDsUYOxQjbRVjfETSI90cuzwzfLWkGyT9bIxxxRsZCYgxsMbHpde8Rrr88vbtT5WKLYt+wQukD32oeJ/x7be31xTeu9f2ZN13n43u+57h2VkLwEOwmsgnnngUy6UBAANtZER64xttAPXLX7b6wZOT0tOfLl10kQWxP/hB8Tli7Fx3eGysdTn09u22BBsAutVHM8RrbjkY/pyke2T7hnf4PuUYY8HGk1YExBhoz3iGdT4++UkrxSQlM8Mvf7mNpJf9Q4zRlqWddVbr82Njtowtq9kk+SYAwFSrFgA//entr3laiLLOaHobDgCspWEOiCW9QNJTlh/ZPcpd99QJiDHwzjrLHo89Zpmnt2xJ9lN1GnXPWskXxarLWwAANpTZ2e7al6POQ7HW0jfN6C8w0BqN3gbEq67E0oUY4wdUvte4FAExhkZe2Ylui4Hv3bu29wIAwCNd7YDroxniZtMaznTjWavZDRIYAxhSBMQYavv3d3fcxMT63kfXYrSOiK8vqVTaC04CAAZCtwkX+yIgbjZtmVWWB8jp9NYABka93tt/uus5Q7xWCIgx1Hy/b9lSkV4XLZeU3xnx0fqRkT7pMQEAurV3r5Vn6lQNQbI2qi8SZRXdpL8+Pn5s7gXAmiEgLkdAjKG2a1d5MDw52Qc1HGPMH5l3S0v2bUZ9JwAYGCMj0oUXStdck/96CNKZZ/ZBtYJms7zX6scwSwwMFALicnyrYaidcYaNzncSgmWk7nn73s0U9dLS+t8HAGBNXXyx1auXkrbG//tDPyS98IW9ua8W3fZYB6FnCwArxAwxhtroqPRjPyZdcYVNwmZni088Mb9UxjHXTUDcbCY1PAAAA6FSkV7yEum886RbbpEOHrSVSWeeaW3QQH2lD9TNApCsi9nLsaxeZrjuFgExht7JJ0uvf7107bXS7bfb0pEtW6QLLpDOPZdVyACA9bdnjz36UrcNYc+XUwFYqXq9t2NZBMRAn9ixQ3rpS+3Rl5OslUr5LHEIfXjjAICBF4IFxUXtUK1GGwQMIALicgTE2HD6sj2v1cr3CJNlGgCwXjwddl5QXK3SBgEDioC4HAEx0A9CkMbGpIWF/NerVdZ2AwDWj7dDjYY9fDlVrcZSaQBDjYAY6BfVqtV4rNftIVknpFaz1/pyahsAMFQYgAWGCjPE5QiIgX5SqdiytaJaUQAAAEBXmoqxlyXT+r9cGwExAAAAAAylxvKjl9fvb2wKAQAAAABsSMwQAwAAAMBQYoa4DAExAAAAAAwlAuIyBMQAAAAAMJSa6m1iq/5PqsUeYgAAAADAhsQMMQAAAAAMJZZMlyEgBgAAAICh1FRvg9L+XzJNQAwAAAAAQ4kZ4jLsIQYAAAAAbEjMEAMAAADAUGKGuAwBMQAAAAAMJcoulSEgBgAAAIChxAxxGfYQAwAAAAA2JGaIAQAAAGAoMUNchoAYAAAAAIYSAXEZAmIAAAAAGEpN9TYoJakWAAAAAKAnyDJdhqRaAAAAAIANiRliAAAAABhK7CEuQ0AMAAAAAEOJgLgMATEAAAAADCUC4jLsIQYAAAAAbEjMEAMAAADAUGKGuAwBMQAAAAAMpajelj6KPbx2dwiIAQAAAGAoMUNchj3EAAAAAIANiRliAAAAABhKzBCXISAGAAAAgKFEQFyGgBgAAAAAhhIBcRn2EAMAAAAANiRmiAEAAABgKDXV27JLvbx2dwiIAQAAAGAosWS6DAExAAAAAAylpnoblPb/DDF7iAEAAAAAGxIzxAAAAAAwlFgyXYaAGAAAAACGEkm1yhAQAwAAAMBQYoa4DHuIAQAAAAAbEjPEAAAAADCUmCEuQ0AMAAAAAEOJgLgMATEAAAAADCXqEJchIAYAAACAoUSW6TIk1QIAAAAAbEjMEAMAAADAUGIPcZmBmyEOIYyFEL4RQoghhKf1+n4AABsD7Q8AYPA0+uCx/o6mjR64gFjS/ytpf69vAgCw4dD+AAAGTK+D4WM2Q7zqNnqgAuIQwoslvVDSW3p9LwCAjYP2BwCA/nS0bfTA7CEOIeyS9F5Jr5R0pMv3jEkaSz21eR1uDQAwxGh/AACDq2/2EG8OIaRfWIgxLhzt2VfTRmcNxAxxsD+9D0h6T4zx+hW89e2SZlKP+9f+7gAAw4r2BwAw2Jp98JBk7WC6XXz70X6yo2ijW/Q0IA4h/PHyxueixxmSfkU2uv7OFV7inZKOSz32re0nAAAMItofAMDG0FRv9w8/ERDvU2u72LFdPQZtdIteL5n+H7Kovsj3JD1X0kWSFjJT7deHED4UY3x93huXp+GfmIrPvBcAsHHR/gAAcOwcijEe7PLYdW2js3oaEMcYH5H0SNlxIYRflfRbqaf2Svq0pJ+U9LX1uTsAwLCi/QEAbAx9s4e4a8e6je71DHFXYoz3pn8PIcwu//jdGCP7sgAA64L2BwAw2AYvIO7WWrXRAxEQAwAAAABWangD4rUykAFxjPFuSWzIAgAcU7Q/AAD0p9W20QMZEAMAAAAAyjBDXIaAGAAAAACGUkst4B5dv78REAMAAADAUPI6xL28fn+r9PoGAAAAAADoBWaIAQAAAGAosYe4DAExAAAAAAwlAuIyBMQAAAAAMJRIqlWGPcQAAAAAgA2JGWIAAAAAGEosmS5DQAwAAAAAQ4mAuAwBMQAAAAAMJQLiMgTEAAAAADCUmuptUEpSLQAAAAAA+hIzxAAAAAAwlCi7VIaAGAAAAACGEnuIyxAQAwAAAMBQIiAuwx5iAAAAAMCGxAwxAAAAAAwlZojLEBADAAAAwFAiIC5DQAwAAAAAQ4k6xGXYQwwAAAAA2JCYIQYAAACAoUQd4jIExAAAAAAwlBrq7aJg9hADAAAAAHqCgLgMe4gBAAAAABsSM8QAAAAAMJSYIS6zIQPigwcP9voWAGCg8L25NvhzBICV4XvzaC2qt4mt6j28dndCjLHX93DMhBCeJOn+Xt8HAAywfTHGB3p9E4OG9gcAjhrtzwqEEMYl3SVpd6/vRdKDkk6OMc73+kbybLSAOEjaK+lQr++lD2yWdc72iT+PfsHfSf/h76TVZkn740ZqONYI7U8L/l31H/5O+g9/J61of1ZhOSge7fV9SFrs12BY2mBLppf/ETGyJMn6ZpKkQzFG1qL0Af5O+g9/J234M1gl2p8E/676D38n/Ye/kzb8GazCchDat4FovyDLNAAAAABgQyIgBgAAAABsSATEG9eCpHcs/xf9gb+T/sPfCbD2+HfVf/g76T/8nQDHyIZKqgUAAAAAgGOGGAAAAACwIREQAwAAAAA2JAJiAAAAAMCGREAMAAAAANiQCIihEMLHQwj3hhDmQwjfDyH8XQhhb6/vayMJIfyXEMLdy38HXwshPKPX97SRhRDeGEK4OYRwcPnxlRDCi3t9X8Cwof3pD7RB/YP2Bzj2CIghSVdLeo2k0yW9WtIpkj7a0zvaQEIIPynpXbLyCudLuknSp0MIO3t6Yxvb/ZLeJukCSRdK+qykj4UQzurpXQHDh/anx2iD+g7tD3CMUXYJbUIIr5D0L5LGYoxLvb6fYRdC+Jqk62KM/3X594qk+yT9zxjjH/f05vCEEMLjkt4aY3xfr+8FGFa0P8cebVD/o/0B1hczxGgRQtgq6bWSrqEzsv5CCKOyUeCr/LkYY3P594t6dV9IhBCqIYT/S9KkpK/0+n6AYUX7c+zRBvU32h/g2CAghiQphPDfQwiHJT0m6URJP9bjW9ootkuqSnoo8/xDknYf+9uBCyGcE0KYlbQg6T2SfjzGeGuPbwsYOrQ/PUUb1Idof4Bji4B4SIUQ/jiEEEseZ6Te8ieSzpP0QkkNSX8bQgg9uXmgP9wu6WmSninpLyV9MIRwZm9vCeh/tD/AUaP9AY4h9hAPqRDCDknbSg77XoxxMee9+2T7hy6OMbJEZx0tL1c7IuknYoz/knr+g5KOjzEyU9InQghXSfpujPEXe30vQD+j/RkctEGDgfYHWF+1Xt8A1keM8RFJj6zy7b5yYGyNbgcdxBgXQwg3SHqeLJGMJzR5nqQ/7+W9oU1F/JsAStH+DA7aoIFB+wOsIwLiDS6E8ExJT5f0JUk/kJW8+ANJ3xUJHI6Vd8mWQ10v6VpJb5Yl0Pibnt7VBhZCeKekf5V0r6TNkn5K0nMkXdrD2wKGCu1P36AN6iO0P8CxR0CMI5JeJas/OCnp+5I+JekPY4wLvbyxjSLG+I/LSwx/X5bE5BuSXhRjzCY5wbGzU9LfStojaUbSzZIujTH+W0/vChgutD99gDao79D+AMcYe4gBAAAAABsSWaYBAAAAABsSATEAAAAAYEMiIAYAAAAAbEgExAAAAACADYmAGAAAAACwIREQAwAAAAA2JAJiAAAAAMCGREAMAAAAANiQCIgBAACGQAjhAyGEuPxYDCHcGUL4nRBCLXVMCCH8QgjhayGE2RDCgRDC9SGEN4cQNhWc+8QQwidDCEdCCA+HEP4kfV4AGFR8kQEAAAyPT0n6WUljkl4i6S8kLUl65/LrfyfpVZL+UNJ/lfSIpHMlvVnS3ZL+JXvCEEJV0iclPSjpYkl7JP3t8nl/Y90+CQAcAyHG2Ot7ADasEMIOSbdI+rMY439bfu5iSZ+T9OIY47/38PYAAAMkhPABScfHGF+Zeu4zkjbHGC8KIbxG0j9KemWM8WOZ9wZJ0zHGmZzzvljSJyTtjTE+tPzcL0n675J2xBgX1+szAcB6Y8k00EMxxkckvUHS74UQLgwhbJaN3v85wTAAYA3MSRpd/vm1km7PBsOSFE1bMLzsIkm3eDC87NOSpiWdtZY3CwDHGkumgR6LMV4ZQnivpA9Jul7SYUlv7+1dAQAG2fKM7/MkXSrpfy4/faqk21dxut2SHso891DqNQAYWATEQH94i6RvSrpM0gUxxoUe3w8AYDC9LIQwK2lEthLwf0v6veXXQq9uCgD6FUumgf5wiqS9sn+TJ/X2VgAAA+xqSU+TzQZPxBhfH2M8vPzaHZLOWMU5H5S0K/PcrtRrADCwCIiBHgshjEq6XJbo5Lcl/XUIYWdv7woAMKAOxxjvjDHeG2OsZ17735JOCyH8WPZNy+WYjutwzq9IOifTNr1A0kFJt67JXQNAjxAQA733R5KOk/Srsoydd0h6f0/vCAAwjD4sG3z9+xDCbywnc/yhEMLLJF0l6Uc7vO8zssD370II54YQLpWVbfoLtvgAGHQExEAPhRCeI6v9+LoY48EYY1PS6yQ9O4Twxp7eHABgqESrtflTkn5d0islfV7SzbI9xh+TZY7Oe19D0sskNWSzxZfL6hD/zrrfNACsM+oQAwAAAAA2JGaIAQAAAAAbEgExAAAAAGBDIiAGAAAAAGxIBMQAAAAAgA2JgBgAAAAAsCEREAMAAAAANiQCYgAAAADAhkRADAAAAADYkAiIAQAAAAAbEgExAAAAAGBDIiAGAAAAAGxIBMQAAAAAgA3p/weZM2gOZGkKjwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 1000x450 with 3 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TyJDIAGESUXq"
      },
      "source": [
        "## Further reference\n",
        "\n",
        "This really just scratches the surface of what you can do with Matplotlib -- the main idea is, you can basically do anything!\n",
        "\n",
        "For further reference, the Matplotlib documentation is a really good reference and also has lots of good examples and demo scripts.\n",
        "\n",
        "[Scatter plot documentation](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.scatter.html)\n",
        "\n",
        "[Line plot documentation](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html)\n",
        "\n",
        "[Various examples](https://matplotlib.org/stable/gallery/index.html)\n",
        "\n",
        "[Tutorials](https://matplotlib.org/stable/tutorials/index.html)\n",
        "\n",
        "(And that's just from their official website!)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xREShy1TKgsW"
      },
      "source": [
        "# Non-linear dimensionality reduction ... and on to ML (Jeremy)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a1-HCO5XNg09"
      },
      "source": [
        "# where to fit into exacloud?  First class or not?  Nick?"
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}