PCA.ipynb

pca.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/firmai/77dcd6bf6e326b69de2eef06d8cddf32/pca.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WcNKR4REML6K"
      },
      "source": [
        "**NOTE:** This Jupyter notebook is derived from the Jupyter notebook located at https://github.com/ageron/handson-ml as of 01/06/2019, as discussed in Hands-On Machine Learning. It is used here for educational purposes only."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "om2pCOMPML6O"
      },
      "source": [
        "# Setup"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "7ztvPw8QML6O"
      },
      "outputs": [],
      "source": [
        "from __future__ import division, print_function, unicode_literals\n",
        "\n",
        "# Common imports\n",
        "import numpy as np\n",
        "import os\n",
        "\n",
        "# to make this notebook's output stable across runs\n",
        "np.random.seed(42)\n",
        "\n",
        "# To plot pretty figures\n",
        "%matplotlib inline\n",
        "import matplotlib as mpl\n",
        "import matplotlib.pyplot as plt\n",
        "mpl.rc('axes', labelsize=14)\n",
        "mpl.rc('xtick', labelsize=12)\n",
        "mpl.rc('ytick', labelsize=12)\n",
        "\n",
        "# Where to save the figures\n",
        "PROJECT_ROOT_DIR = \"../..\"\n",
        "CHAPTER_ID = \"unsupervised_learning\"\n",
        "\n",
        "\n",
        "def save_fig(fig_id, tight_layout=True):\n",
        "    path = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID, fig_id + \".png\")\n",
        "    print(\"Saving figure\", fig_id)\n",
        "    if tight_layout:\n",
        "        plt.tight_layout()\n",
        "    try:\n",
        "        plt.savefig(path, format='png', dpi=300)\n",
        "    except:\n",
        "        plt.savefig(fig_id + \".png\", format='png', dpi=300)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hFKx0kmnML6Q"
      },
      "source": [
        "# Projection methods\n",
        "Build 3D dataset:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "pWnQphzXML6Q"
      },
      "outputs": [],
      "source": [
        "np.random.seed(4)\n",
        "m = 60\n",
        "w1, w2 = 0.1, 0.3\n",
        "noise = 0.1\n",
        "\n",
        "angles = np.random.rand(m) * 3 * np.pi / 2 - 0.5\n",
        "X = np.empty((m, 3))\n",
        "X[:, 0] = np.cos(angles) + np.sin(angles)/2 + noise * np.random.randn(m) / 2\n",
        "X[:, 1] = np.sin(angles) * 0.7 + noise * np.random.randn(m) / 2\n",
        "X[:, 2] = X[:, 0] * w1 + X[:, 1] * w2 + noise * np.random.randn(m)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wR55JNJjML6R"
      },
      "source": [
        "## PCA using SVD decomposition"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MDTTjkjGML6S"
      },
      "source": [
        "Note: the `svd()` function returns `U`, `s` and `Vt`, where `Vt` is equal to $\\mathbf{V}^T$, the transpose of the matrix $\\mathbf{V}$. Earlier versions of the book mistakenly said that it returned `V` instead of `Vt`. Also, Equation 8-1 should actually contain $\\mathbf{V}$ instead of $\\mathbf{V}^T$, like this:\n",
        "\n",
        "$\n",
        "\\mathbf{V} =\n",
        "\\begin{pmatrix}\n",
        "  \\mid & \\mid & & \\mid \\\\\n",
        "  \\mathbf{c_1} & \\mathbf{c_2} & \\cdots & \\mathbf{c_n} \\\\\n",
        "  \\mid & \\mid & & \\mid\n",
        "\\end{pmatrix}\n",
        "$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "7uMlUUsiML6S"
      },
      "outputs": [],
      "source": [
        "X_centered = X - X.mean(axis=0)\n",
        "U, s, Vt = np.linalg.svd(X_centered)\n",
        "c1 = Vt.T[:, 0]\n",
        "c2 = Vt.T[:, 1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "_ZYu1GBGML6T"
      },
      "outputs": [],
      "source": [
        "m, n = X.shape\n",
        "\n",
        "S = np.zeros(X_centered.shape)\n",
        "S[:n, :n] = np.diag(s)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "OWfvRRy_ML6T",
        "outputId": "435e2ff8-8d1b-40fe-b6df-8a98ab527685",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "np.allclose(X_centered, U.dot(S).dot(Vt))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "hanhCOjlML6U"
      },
      "outputs": [],
      "source": [
        "W2 = Vt.T[:, :2]\n",
        "X2D = X_centered.dot(W2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "u57a6UbpML6U"
      },
      "outputs": [],
      "source": [
        "X2D_using_svd = X2D"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MJdTtfAzML6V"
      },
      "source": [
        "## PCA using Scikit-Learn"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gRESUr-5ML6V"
      },
      "source": [
        "With Scikit-Learn, PCA is really trivial. It even takes care of mean centering for you:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "SiQ6H5koML6V"
      },
      "outputs": [],
      "source": [
        "from sklearn.decomposition import PCA\n",
        "\n",
        "pca = PCA(n_components = 2)\n",
        "X2D = pca.fit_transform(X)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "eXlEkCupML6W",
        "outputId": "ea586aeb-8fb2-41c5-822d-3795266154d2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1.26203346,  0.42067648],\n",
              "       [-0.08001485, -0.35272239],\n",
              "       [ 1.17545763,  0.36085729],\n",
              "       [ 0.89305601, -0.30862856],\n",
              "       [ 0.73016287, -0.25404049]])"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "X2D[:5]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "9isxyE-MML6W",
        "outputId": "ca4b3ce0-acef-4ac9-a512-60fe0669ae34",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-1.26203346, -0.42067648],\n",
              "       [ 0.08001485,  0.35272239],\n",
              "       [-1.17545763, -0.36085729],\n",
              "       [-0.89305601,  0.30862856],\n",
              "       [-0.73016287,  0.25404049]])"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ],
      "source": [
        "X2D_using_svd[:5]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eWvrxo_MML6W"
      },
      "source": [
        "Notice that running PCA multiple times on slightly different datasets may result in different results. In general the only difference is that some axes may be flipped. In this example, PCA using Scikit-Learn gives the same projection as the one given by the SVD approach, except both axes are flipped:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "z_k50SmZML6X",
        "outputId": "d445d3fe-6127-4caa-9436-d2d39d12075b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ],
      "source": [
        "np.allclose(X2D, -X2D_using_svd)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mPMfTq-qML6X"
      },
      "source": [
        "Recover the 3D points projected on the plane (PCA 2D subspace)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "iIbLrGe1ML6X"
      },
      "outputs": [],
      "source": [
        "X3D_inv = pca.inverse_transform(X2D)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GMeCec-zML6X"
      },
      "source": [
        "Of course, there was some loss of information during the projection step, so the recovered 3D points are not exactly equal to the original 3D points:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "4jouR2VLML6X",
        "outputId": "fdbd3953-33cb-48f3-d5b1-1fa3ccfdbfc5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ],
      "source": [
        "np.allclose(X3D_inv, X)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Jq2ofBX1ML6Y"
      },
      "source": [
        "We can compute the reconstruction error:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "id": "BvV16GaOML6Y",
        "outputId": "5666d00d-df9d-4ce4-92a2-7933a9afff6e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.010170337792848549"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ],
      "source": [
        "np.mean(np.sum(np.square(X3D_inv - X), axis=1))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jAmrHThoML6Y"
      },
      "source": [
        "The inverse transform in the SVD approach looks like this:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "id": "FRu62JgUML6Y"
      },
      "outputs": [],
      "source": [
        "X3D_inv_using_svd = X2D_using_svd.dot(Vt[:2, :])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5VQntmpqML6Y"
      },
      "source": [
        "The reconstructions from both methods are not identical because Scikit-Learn's `PCA` class automatically takes care of reversing the mean centering, but if we subtract the mean, we get the same reconstruction:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "id": "Ez5Ur5e_ML6Y",
        "outputId": "9eb0770a-b43e-4f49-c1df-8c433b4230ba",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ],
      "source": [
        "np.allclose(X3D_inv_using_svd, X3D_inv - pca.mean_)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "faC3Js2lML6Y"
      },
      "source": [
        "The `PCA` object gives access to the principal components that it computed:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "id": "cGqX9f35ML6Y",
        "outputId": "a1d7dc04-6532-48bc-c984-4f8a3abdabc6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-0.93636116, -0.29854881, -0.18465208],\n",
              "       [ 0.34027485, -0.90119108, -0.2684542 ]])"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ],
      "source": [
        "pca.components_"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "USboZ-6UML6Z"
      },
      "source": [
        "Compare to the first two principal components computed using the SVD method:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "id": "WdM9xTytML6Z",
        "outputId": "8ebcf7fe-a404-43c3-eb95-b2647913aa91",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.93636116,  0.29854881,  0.18465208],\n",
              "       [-0.34027485,  0.90119108,  0.2684542 ]])"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ],
      "source": [
        "Vt[:2]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8RCCB9EzML6Z"
      },
      "source": [
        "Notice how the axes are flipped."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ryd62PyNML6Z"
      },
      "source": [
        "Now let's look at the explained variance ratio:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "id": "YAdN-BLFML6Z",
        "outputId": "a6fcba31-417b-4eb0-c57d-a6eed77a4ea0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.84248607, 0.14631839])"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ],
      "source": [
        "pca.explained_variance_ratio_"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GVsgvKseML6Z"
      },
      "source": [
        "The first dimension explains 84.2% of the variance, while the second explains 14.6%."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N-o-cw2YML6Z"
      },
      "source": [
        "By projecting down to 2D, we lost about 1.1% of the variance:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "id": "hLO5sM3dML6Z",
        "outputId": "3d894cc0-d1f4-4736-82ed-f14e5a098246",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.011195535570688975"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ],
      "source": [
        "1 - pca.explained_variance_ratio_.sum()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UikbW0HXML6a"
      },
      "source": [
        "Here is how to compute the explained variance ratio using the SVD approach (recall that `s` is the diagonal of the matrix `S`):"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "id": "H3YVxv1FML6a",
        "outputId": "5df1b3dd-d807-48ff-efe7-be11c42c30c0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.84248607, 0.14631839, 0.01119554])"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ],
      "source": [
        "np.square(s) / np.square(s).sum()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c4d3D8bMML6a"
      },
      "source": [
        "Next, let's generate some nice figures! :)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "id": "MCsdJc0UML6a"
      },
      "outputs": [],
      "source": [
        "from matplotlib.patches import FancyArrowPatch\n",
        "from mpl_toolkits.mplot3d import proj3d\n",
        "\n",
        "class Arrow3D(FancyArrowPatch):\n",
        "    def __init__(self, xs, ys, zs, *args, **kwargs):\n",
        "        FancyArrowPatch.__init__(self, (0,0), (0,0), *args, **kwargs)\n",
        "        self._verts3d = xs, ys, zs\n",
        "\n",
        "    def draw(self, renderer):\n",
        "        xs3d, ys3d, zs3d = self._verts3d\n",
        "        xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
        "        self.set_positions((xs[0],ys[0]),(xs[1],ys[1]))\n",
        "        FancyArrowPatch.draw(self, renderer)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T2L0nBpWML6a"
      },
      "source": [
        "Express the plane as a function of x and y."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "id": "AhLqvnF1ML6a"
      },
      "outputs": [],
      "source": [
        "axes = [-1.8, 1.8, -1.3, 1.3, -1.0, 1.0]\n",
        "\n",
        "x1s = np.linspace(axes[0], axes[1], 10)\n",
        "x2s = np.linspace(axes[2], axes[3], 10)\n",
        "x1, x2 = np.meshgrid(x1s, x2s)\n",
        "\n",
        "C = pca.components_\n",
        "R = C.T.dot(C)\n",
        "z = (R[0, 2] * x1 + R[1, 2] * x2) / (1 - R[2, 2])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LK-qR95jML6a"
      },
      "source": [
        "Plot the 3D dataset, the plane and the projections on that plane."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "uIaLY64NML6a",
        "outputId": "d59233be-3717-4c26-9acc-cddf10dc6340",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Saving figure dataset_3d_plot\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x273.6 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "\n",
        "fig = plt.figure(figsize=(6, 3.8))\n",
        "ax = fig.add_subplot(111, projection='3d')\n",
        "\n",
        "X3D_above = X[X[:, 2] > X3D_inv[:, 2]]\n",
        "X3D_below = X[X[:, 2] <= X3D_inv[:, 2]]\n",
        "\n",
        "ax.plot(X3D_below[:, 0], X3D_below[:, 1], X3D_below[:, 2], \"bo\", alpha=0.5)\n",
        "\n",
        "ax.plot_surface(x1, x2, z, alpha=0.2, color=\"k\")\n",
        "np.linalg.norm(C, axis=0)\n",
        "ax.add_artist(Arrow3D([0, C[0, 0]],[0, C[0, 1]],[0, C[0, 2]], mutation_scale=15, lw=1, arrowstyle=\"-|>\", color=\"k\"))\n",
        "ax.add_artist(Arrow3D([0, C[1, 0]],[0, C[1, 1]],[0, C[1, 2]], mutation_scale=15, lw=1, arrowstyle=\"-|>\", color=\"k\"))\n",
        "ax.plot([0], [0], [0], \"k.\")\n",
        "\n",
        "for i in range(m):\n",
        "    if X[i, 2] > X3D_inv[i, 2]:\n",
        "        ax.plot([X[i][0], X3D_inv[i][0]], [X[i][1], X3D_inv[i][1]], [X[i][2], X3D_inv[i][2]], \"k-\")\n",
        "    else:\n",
        "        ax.plot([X[i][0], X3D_inv[i][0]], [X[i][1], X3D_inv[i][1]], [X[i][2], X3D_inv[i][2]], \"k-\", color=\"#505050\")\n",
        "    \n",
        "ax.plot(X3D_inv[:, 0], X3D_inv[:, 1], X3D_inv[:, 2], \"k+\")\n",
        "ax.plot(X3D_inv[:, 0], X3D_inv[:, 1], X3D_inv[:, 2], \"k.\")\n",
        "ax.plot(X3D_above[:, 0], X3D_above[:, 1], X3D_above[:, 2], \"bo\")\n",
        "ax.set_xlabel(\"$x_1$\", fontsize=18)\n",
        "ax.set_ylabel(\"$x_2$\", fontsize=18)\n",
        "ax.set_zlabel(\"$x_3$\", fontsize=18)\n",
        "ax.set_xlim(axes[0:2])\n",
        "ax.set_ylim(axes[2:4])\n",
        "ax.set_zlim(axes[4:6])\n",
        "\n",
        "# Note: If you are using Matplotlib 3.0.0, it has a bug and does not\n",
        "# display 3D graphs properly.\n",
        "# See https://github.com/matplotlib/matplotlib/issues/12239\n",
        "# You should upgrade to a later version. If you cannot, then you can\n",
        "# use the following workaround before displaying each 3D graph:\n",
        "# for spine in ax.spines.values():\n",
        "#     spine.set_visible(False)\n",
        "\n",
        "save_fig(\"dataset_3d_plot\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "id": "QyG5mNGuML6a",
        "outputId": "4722a880-19e9-4b07-9f94-5cbd08533c39",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 314
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Saving figure dataset_2d_plot\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "fig = plt.figure()\n",
        "ax = fig.add_subplot(111, aspect='equal')\n",
        "\n",
        "ax.plot(X2D[:, 0], X2D[:, 1], \"k+\")\n",
        "ax.plot(X2D[:, 0], X2D[:, 1], \"k.\")\n",
        "ax.plot([0], [0], \"ko\")\n",
        "ax.arrow(0, 0, 0, 1, head_width=0.05, length_includes_head=True, head_length=0.1, fc='k', ec='k')\n",
        "ax.arrow(0, 0, 1, 0, head_width=0.05, length_includes_head=True, head_length=0.1, fc='k', ec='k')\n",
        "ax.set_xlabel(\"$z_1$\", fontsize=18)\n",
        "ax.set_ylabel(\"$z_2$\", fontsize=18, rotation=0)\n",
        "ax.axis([-1.5, 1.3, -1.2, 1.2])\n",
        "ax.grid(True)\n",
        "save_fig(\"dataset_2d_plot\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bbqGsCjHML6a"
      },
      "source": [
        "# PCA"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "id": "tXfETIrhML6b",
        "outputId": "529f406d-c503-421b-d486-386eeccc46ce",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 314
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Saving figure pca_best_projection\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x288 with 4 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "angle = np.pi / 5\n",
        "stretch = 5\n",
        "m = 200\n",
        "\n",
        "np.random.seed(3)\n",
        "X = np.random.randn(m, 2) / 10\n",
        "X = X.dot(np.array([[stretch, 0],[0, 1]])) # stretch\n",
        "X = X.dot([[np.cos(angle), np.sin(angle)], [-np.sin(angle), np.cos(angle)]]) # rotate\n",
        "\n",
        "u1 = np.array([np.cos(angle), np.sin(angle)])\n",
        "u2 = np.array([np.cos(angle - 2 * np.pi/6), np.sin(angle - 2 * np.pi/6)])\n",
        "u3 = np.array([np.cos(angle - np.pi/2), np.sin(angle - np.pi/2)])\n",
        "\n",
        "X_proj1 = X.dot(u1.reshape(-1, 1))\n",
        "X_proj2 = X.dot(u2.reshape(-1, 1))\n",
        "X_proj3 = X.dot(u3.reshape(-1, 1))\n",
        "\n",
        "plt.figure(figsize=(8,4))\n",
        "plt.subplot2grid((3,2), (0, 0), rowspan=3)\n",
        "plt.plot([-1.4, 1.4], [-1.4*u1[1]/u1[0], 1.4*u1[1]/u1[0]], \"k-\", linewidth=1)\n",
        "plt.plot([-1.4, 1.4], [-1.4*u2[1]/u2[0], 1.4*u2[1]/u2[0]], \"k--\", linewidth=1)\n",
        "plt.plot([-1.4, 1.4], [-1.4*u3[1]/u3[0], 1.4*u3[1]/u3[0]], \"k:\", linewidth=2)\n",
        "plt.plot(X[:, 0], X[:, 1], \"bo\", alpha=0.5)\n",
        "plt.axis([-1.4, 1.4, -1.4, 1.4])\n",
        "plt.arrow(0, 0, u1[0], u1[1], head_width=0.1, linewidth=5, length_includes_head=True, head_length=0.1, fc='k', ec='k')\n",
        "plt.arrow(0, 0, u3[0], u3[1], head_width=0.1, linewidth=5, length_includes_head=True, head_length=0.1, fc='k', ec='k')\n",
        "plt.text(u1[0] + 0.1, u1[1] - 0.05, r\"$\\mathbf{c_1}$\", fontsize=22)\n",
        "plt.text(u3[0] + 0.1, u3[1], r\"$\\mathbf{c_2}$\", fontsize=22)\n",
        "plt.xlabel(\"$x_1$\", fontsize=18)\n",
        "plt.ylabel(\"$x_2$\", fontsize=18, rotation=0)\n",
        "plt.grid(True)\n",
        "\n",
        "plt.subplot2grid((3,2), (0, 1))\n",
        "plt.plot([-2, 2], [0, 0], \"k-\", linewidth=1)\n",
        "plt.plot(X_proj1[:, 0], np.zeros(m), \"bo\", alpha=0.3)\n",
        "plt.gca().get_yaxis().set_ticks([])\n",
        "plt.gca().get_xaxis().set_ticklabels([])\n",
        "plt.axis([-2, 2, -1, 1])\n",
        "plt.grid(True)\n",
        "\n",
        "plt.subplot2grid((3,2), (1, 1))\n",
        "plt.plot([-2, 2], [0, 0], \"k--\", linewidth=1)\n",
        "plt.plot(X_proj2[:, 0], np.zeros(m), \"bo\", alpha=0.3)\n",
        "plt.gca().get_yaxis().set_ticks([])\n",
        "plt.gca().get_xaxis().set_ticklabels([])\n",
        "plt.axis([-2, 2, -1, 1])\n",
        "plt.grid(True)\n",
        "\n",
        "plt.subplot2grid((3,2), (2, 1))\n",
        "plt.plot([-2, 2], [0, 0], \"k:\", linewidth=2)\n",
        "plt.plot(X_proj3[:, 0], np.zeros(m), \"bo\", alpha=0.3)\n",
        "plt.gca().get_yaxis().set_ticks([])\n",
        "plt.axis([-2, 2, -1, 1])\n",
        "plt.xlabel(\"$z_1$\", fontsize=18)\n",
        "plt.grid(True)\n",
        "\n",
        "save_fig(\"pca_best_projection\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pvPCVGoVML6b"
      },
      "source": [
        "# PCA for Portfolio Optimisation"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "id": "_eK7M6zZML6b"
      },
      "outputs": [],
      "source": [
        "from matplotlib import style\n",
        "import seaborn as sns\n",
        "from scipy.stats import randint as sp_randint\n",
        "from sklearn.decomposition import PCA\n",
        "from pathlib import Path\n",
        "import pandas as pd\n",
        "style.use(\"ggplot\")\n",
        "\n",
        "df = pd.read_csv('https://open-data.s3.filebase.com/Dow_adjcloses.csv', parse_dates=True, index_col=0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "id": "aMgElWFyML6b"
      },
      "outputs": [],
      "source": [
        "# Dropping 'Not a Number' columns for Dow Chemicals (DWDP) and Visa (V)\n",
        "df.drop(['DWDP', 'V'], axis=1, inplace=True)\n",
        "# Copying the dataframe to add features\n",
        "data = pd.DataFrame(df.copy())\n",
        "# Daily Returns\n",
        "# Daily Log Returns (%)\n",
        "# datareturns = np.log(data / data.shift(1)) \n",
        "\n",
        "# Daily Linear Returns (%)\n",
        "datareturns = data.pct_change(1)\n",
        "\n",
        "# Dow Jones Equal Weighted rETURN\n",
        "datareturns[\"DJIA\"] = datareturns.mean(axis=1)\n",
        "\n",
        "# Data Raw\n",
        "data_raw = datareturns\n",
        "data_raw.dropna(how='all', inplace=True)\n",
        "\n",
        "# Normalizing the returns\n",
        "data = (data_raw - data_raw.mean()) / data_raw.std()\n",
        "\n",
        "# Getting rid of the NaN values.\n",
        "data.dropna(how='any', inplace=True)\n",
        "data_raw.dropna(how='any', inplace=True)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "id": "dxRQKQHNML6b",
        "outputId": "41d28a24-1865-44b8-da67-d6c4c77e200a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 417
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                 MMM       AXP      AAPL        BA       CAT       CVX  \\\n",
              "Date                                                                     \n",
              "2000-01-04 -2.783305 -1.714531 -3.315064 -0.118649 -0.672149 -0.030177   \n",
              "2000-01-05  3.491453 -0.250475  0.522450  3.667073  1.828679  1.321853   \n",
              "2000-01-06  3.995818 -0.021248 -3.400666  0.108313  1.770951  2.389941   \n",
              "2000-01-07  1.337698  0.604016  1.791770  1.497066  1.573522  1.067883   \n",
              "2000-01-10 -0.371257  0.624764 -0.727008 -0.780316 -1.653060 -1.711071   \n",
              "\n",
              "                CSCO        KO       DIS       XOM  ...       NKE       PFE  \\\n",
              "Date                                                ...                       \n",
              "2000-01-04 -2.304726  0.236964  3.089027 -1.283097  ... -2.927985 -2.410473   \n",
              "2000-01-05  0.305449  0.823741  1.857074  3.247575  ...  3.023666  1.148279   \n",
              "2000-01-06 -1.119210 -0.104682 -1.845881  3.696220  ... -0.316511  2.151911   \n",
              "2000-01-07  2.382987  5.050971 -0.867545 -0.216324  ... -0.041103  4.320217   \n",
              "2000-01-10  1.482524 -2.486755  8.090552 -0.944732  ...  0.855881 -0.131547   \n",
              "\n",
              "                  PG       TRV       UTX       UNH        VZ       WMT  \\\n",
              "Date                                                                     \n",
              "2000-01-04 -1.504783 -0.763609 -2.479568 -0.698935 -2.097284 -2.506437   \n",
              "2000-01-05 -0.671468  0.510782 -0.588825 -0.164440  2.128033 -1.568817   \n",
              "2000-01-06  2.659281  0.070428  2.165327  1.801922 -0.346058  0.914757   \n",
              "2000-01-07  5.999317  2.158221  2.340150  5.871398 -0.496143  5.006585   \n",
              "2000-01-10 -0.413525 -1.026003  0.558540 -0.923939 -0.357794 -1.231132   \n",
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              "                 WBA      DJIA  \n",
              "Date                            \n",
              "2000-01-04 -2.167895 -2.739489  \n",
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              "2000-01-07  1.453883  3.054606  \n",
              "2000-01-10  1.667529  0.250687  \n",
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            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ],
      "source": [
        "data.head()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "id": "0rhDFCPAML6b",
        "outputId": "6d3d8ba9-25f8-4bbe-cc05-d1d9a4e4a51b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 343
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1152x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Visualizing Log Returns for the DJIA a\n",
        "\n",
        "plt.figure(figsize=(16, 5))\n",
        "plt.title(\"Dow Jones Industrial Average Linear Returns (%)\")\n",
        "data.DJIA.plot()\n",
        "plt.grid(True);\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "id": "eiExf2D6ML6c",
        "outputId": "2a5ab777-586c-4b22-8448-556e3ea99b93",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "PCA()"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ],
      "source": [
        "# Taking away the market benchmark DJIA\n",
        "stock_tickers = data.columns.values[:-1]\n",
        "n_tickers = len(stock_tickers)\n",
        "\n",
        "# Dividing the dataset into training and testing sets\n",
        "percentage = int(len(data) * 0.8)\n",
        "X_train = data[:percentage]\n",
        "X_test = data[percentage:]\n",
        "\n",
        "X_train_raw = data_raw[:percentage]\n",
        "X_test_raw = data_raw[percentage:]\n",
        "\n",
        "# Applying Principle Component Analysis\n",
        "# Creating covariance matrix and training data on PCA.\n",
        "cov_matrix = X_train.loc[:,X_train.columns != 'DJIA'].cov()\n",
        "pca = PCA()\n",
        "pca.fit(cov_matrix)\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "id": "lmCKEgPHML6c",
        "outputId": "564ad16a-848d-4aa2-eea1-1838317be675",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 326
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "21 principal components explain 95.00% of variance\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "def plotPCA(plot=False):\n",
        "\n",
        "    # Visualizing Variance against number of principal components.\n",
        "    cov_matrix_raw = X_train_raw.loc[:,X_train_raw.columns != 'DJIA'].cov()\n",
        "\n",
        "    var_threshold = 0.95\n",
        "    var_explained = np.cumsum(pca.explained_variance_ratio_)\n",
        "    num_comp = np.where(np.logical_not(var_explained < var_threshold))[0][0] + 1  \n",
        "\n",
        "    if plot:\n",
        "        print('%d principal components explain %.2f%% of variance' %(num_comp, 100* var_threshold))\n",
        "\n",
        "        # PCA percent variance explained.\n",
        "        bar_width = 0.9\n",
        "        n_asset = stock_tickers.shape[0]\n",
        "        x_indx = np.arange(n_asset)\n",
        "        fig, ax = plt.subplots()\n",
        "\n",
        "        # Eigenvalues measured as percentage of explained variance.\n",
        "        rects = ax.bar(x_indx, pca.explained_variance_ratio_[:n_asset], bar_width)\n",
        "        ax.set_xticks(x_indx + bar_width / 2)\n",
        "        ax.set_xticklabels(list(range(n_asset)), rotation=45)\n",
        "        ax.set_title('Percent variance explained')\n",
        "        ax.set_ylabel('Explained Variance')\n",
        "        ax.set_xlabel('Principal Components')\n",
        "        plt.show()\n",
        "\n",
        "plotPCA(plot=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "id": "8yNG5h7qML6c"
      },
      "outputs": [],
      "source": [
        "projected = pca.fit_transform(cov_matrix)\n",
        "pcs = pca.components_"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "e7wYTMpjML6c"
      },
      "outputs": [],
      "source": [
        "# Sharpe Ratio\n",
        "def sharpe_ratio(ts_returns, periods_per_year=252):\n",
        "    '''\n",
        "    Sharpe ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk.\n",
        "    It calculares the annualized return, annualized volatility, and annualized sharpe ratio.\n",
        "    \n",
        "    ts_returns are  returns of a signle eigen portfolio.\n",
        "    '''\n",
        "    n_years = ts_returns.shape[0]/periods_per_year\n",
        "    annualized_return = np.power(np.prod(1+ts_returns),(1/n_years))-1\n",
        "    annualized_vol = ts_returns.std() * np.sqrt(periods_per_year)\n",
        "    annualized_sharpe = annualized_return / annualized_vol\n",
        "\n",
        "    return annualized_return, annualized_vol, annualized_sharpe"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "id": "v7QoTMY8ML6c",
        "outputId": "af0db788-83da-4f2f-d922-14be543e28b1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 510
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Eigen portfolio #18 with the highest Sharpe. Return 73.22%, vol = 52.77%, Sharpe = 1.39\n",
            "      Return       Vol    Sharpe\n",
            "18  0.732203  0.527742  1.387424\n",
            "4   0.591001  0.655269  0.901922\n",
            "22  0.496591  0.591244  0.839909\n",
            "15  0.564721  0.812595  0.694961\n",
            "0   0.380484  0.632765  0.601304\n",
            "9   0.314115  0.542399  0.579123\n",
            "26  0.298652  0.617072  0.483983\n",
            "7   0.429301  0.930989  0.461124\n",
            "13  0.162942  0.685799  0.237595\n",
            "20  0.230046  1.636941  0.140534\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ],
            "image/png": 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3b0ZcXBzGjh3b5b6jR4/G9u3bsW/fPowZMwYLFy7EnDlz8P7771v9Pno6hlqtRm1tLR588EGkp6fjpptuwsCBAzuVjCSEuAbGpcmbhBDSjyUmJmLp0qV4/vnnnT2UfqmwsBCJiYnYvn07/vd//9fur5eRkYEhQ4Zgw4YNdn8tQgixBeWgE0IIcYpNmzYhNjYWSUlJKCwsxKpVq5CQkIAbb7zR2UMjhBCnogCdEEKIU1RXV+N3v/sdSktLER4ejilTpmDLli2yMpqEENIfUYoLIYQQQgghLoQWiRJCCCGEEOJCKEAnhBBCCCHEhVAOugW21ExWikajQVVVlcNflyiHzqF7o/Pn/ugcuj86h+6PzqH1YmJiunyMZtAJIYQQQghxIRSgE0IIIYQQ4kIoQCeEEEIIIcSFUIBOCCGEEEKIC6EAnRBCCCGEEBdCATohhBBCCCEuhAJ0QgghxMPwyivg2mZnD4MQ0ksUoBNCCCEexHB4DwyrH4LhmQfBG646eziEkF6gAJ0QQgjxIPzIHuFGcxP4mWNOHQshpHcoQCeEEEI8SVWFeLviivPGQQjpNQrQCSGEEA/BOQdqJAF6ZZnzBkMI6TUK0AkhhBBP0VgP6HTmTV5JM+iEuCMK0AkhhBBPIU1vAQAK0AlxSxSgE0IIIZ6ipkOA3tQA3tzonLEQQnqNAnRCCCHEQ/Dqis530iw6IW6HAnRCCCHEU3RMcQHAqZILIW6HAnRCCCHEQ/Cays53UiUXQtwOBeiEEEKIp6AUF0I8AgXohBBCiKewEKBTqUVC3I/a2QOQ2rlzJ/bs2YOioiJMmTIFjz/+uMX99uzZg++++w5XrlyBv78/pk6dirvvvhteXl4AgDVr1iA3NxcqlfD9Izw8HOvWrXPY+yCEEEIcjTc3Ai3NnR+gFBdC3I5LBegDBgzAvHnzcPr0aegkjRY60ul0WLRoEYYOHYr6+nq89tprCAoKwu23327eZ8mSJZg1a5Yjhk0IIYQ4X7Uk/zxyEFBVDnAO1FaDt7WBeXs7b2yEEJu4VIA+ceJEAEBeXh6qq6u73O/GG2803w4PD8cNN9yAs2fP2n18hBBCiMuqLhdvR0UDej1QUykE6VXlQHSc88ZGCLGJSwXovZWVlYX4+HjZfZ9//jk+//xzxMTE4K677sKIESO6fH5mZiYyMzMBAGvXroVGo7HreC1Rq9VOeV2iHDqH7o3On/vr7+ewWduMBuNt/9gEtDOGNmNVl5DWJvi6wc+mv59DT0DnUBluH6Dv2rULeXl5eOSRR8z33XvvvYiLi4NarcaBAwfw2muv4Y9//CMGDRpk8RizZ8/G7NmzzdtVVVV2H3dHGo3GKa9LlEPn0L3R+XN//f0cGoryzbe1gcHAADFIunrpAlSJqc4Ylk36+zn0BHQOrRcTE9PlY25dxeXo0aP44osvsHr1aoSEhJjvHzp0KPz9/eHt7Y2MjAykpqbi5MmTThwpIYQQYl9cmoMeESXkoZtQJRdC3IrbzqCfOnUKH3zwAZ577jkMHjy4230ZY+CcO2hkhBBCiBNISiyyiCjAywumTz5eQZVcCHEnLjWDrtfrodPpYDAYYDAYoNPpoNfrO+139uxZvPXWW1ixYgWGDBkie6ypqQmnTp0yP3f//v3Izs7GNddc46i3QQghhDietAZ6RBQQGS1u0ww6IW7FpWbQt27din/84x/m7f3792P+/PmYOXMmnn76afzlL3+BRqPB1q1b0dzcjFdffdW8b3p6OlavXg29Xo+vvvoKpaWlUKlUiI2NxcqVK7vN8yGEEELcGW/VAo31woaXGggdAPj6iTtUlYMbDGAql5qXI4R0waUC9AULFmDBggUWH9u4caP59u9+97sujxESEiIL3AkhhBCPJ509D9cIgXhAIBAUDDQ2AO1tQF01EB7pvDESQqxGX6UJIYQQd9dxgagJpbkQ4pYoQCeEEELcHJctEBVnyZmkkgstFCXEfVCATgghhLg7WYqLdAadSi0S4o4oQCeEEELcnTRA11CKCyHujgJ0QgghxM3xGjEHnUly0GUpLhSgE+I2KEAnhBBC3J0sxUVSqSVKmuJCOeiEuAsK0AkhhBA3xtvagLoaYYOpgAEa8cHQcMDHR7jd3ATe1OD4ARJCbEYBOiGEEOLOaiUlFgeEg6nFFieMMUAjmUWvoDQXQtwBBeiEEEKIO5PWQJdWcDGR5aFTmgsh7oACdEIIIcSN8apy822m6RygM6rkQojboQCdEEIIcWc1Pcyg00JRQtwOBeiEEEKIO5NWcJF0ETWhUouEuB8K0AkhhBA3xiUBurQGupk0xYUWiRLiFihAJ4QQQtyZdJGopQA9IlIovwgAddXgulbHjIsQ0msUoBNCCCFuiuv1QG2VeIelFBe1NxAuqY0uWVRKCHFNFKATQggh7qquGjAYhNshYWDePpb3i6JKLoS4E3XPuzjWzp07sWfPHhQVFWHKlCl4/PHHu9z3X//6F7Zt2wadToeJEydi2bJl8Pb2BgBUVFRg/fr1yM3NhUajwZIlSzB69GhHvQ1CCCHE/mQLRC2ktxixyEHg2acBCLXQmb3HRQjpE5ebQR8wYADmzZuHGTNmdLvfqVOnsG3bNrz44ot49913UVFRgc2bN5sfX7duHRITE/G3v/0Nd911F/785z+jvr7e3sMnhBBCHIZL8s8tLhA1iaRuooS4E5cL0CdOnIgJEyYgODi42/327t2LGTNmID4+HkFBQbjjjjuwZ88eAMDly5eRn5+PBQsWwMfHB5MmTcLgwYNx+PBhB7wDQgghxEF6KLFoIm1WRKUWCXF9LpfiYq2SkhKMHz/evJ2QkICrV6+ioaEBJSUlGDhwIPz9/WWPl5SUWDxWZmYmMjMzAQBr166FRqOxuJ89qdVqp7wuUQ6dQ/dG58/99cdzeLWpHlrj7aCEZAR08f7bhqWhxnjbq6bSZX9O/fEceho6h8pw2wBdq9UiICDAvG263dLS0ukx0+M1NTWwZPbs2Zg9e7Z5u6qqyuJ+9qTRaJzyukQ5dA7dG50/99cfz6G+tMh8u8k3AM1dvH/u7Sc+p+IyKivKwVRedh+frfrjOfQ0dA6tFxMT0+VjLpfiYi0/Pz80Nzebt1taWgAA/v7+nR4zPS6dUSeEEELcXk810I2YXwAQHCpstLcDtZYnrAghrsFtA/S4uDgUFhaatwsLCxEaGorg4GDExcWhoqLCHLSbHo+Li3PGUAkhhBDFcYMBqLEuBx2AfKFoZZl9BkUIUYTLBeh6vR46nQ4GgwEGgwE6nQ56vb7TftOnT8euXbtQUlKCpqYmbN26FRkZGQCESwaJiYnYsmULdDodjh49isLCQkyaNMnB74YQQgixk/o6YTYcAAKDhVnybjBJgE4LRQlxbS6Xg75161b84x//MG/v378f8+fPx8yZM/H000/jL3/5CzQaDa655hrcdttteOmll8x10BcsWGB+3pNPPon33nsPixcvhkajwW9+8xuEhIQ44y0RQgghyrOygotZpLRZEc2gE+LKXC5AX7BggSzQltq4caNse+7cuZg7d67FfaOiorBmzRqlh0cIIYS4BC4N0MO7qYFuQrXQCXEbLpfiQgghhBArSJsUaXoO0FkUpbgQ4i4oQCf9Aucchm1/h/79tfTBRAjxDLYsEAU6pLhcAedc+TERQhThcikuhNjF+Z/B//UVAICrvcGWrnDygAghpG+4dAbdmhSXkDDA1w9o1QItTUBTAxBEa7MIcUU0g076BZ6fK97OO+/EkRBCiEKqysXb1qS4MAZoBop30NVEQlwWBeikf7gsdttD5RVwbUvX+xJCiIvjnAM11jUpkpGkufAKquRCiKuiAJ30C1waoANAaaHlHQkhxB00NQipKgDg6w8EBFn1NOlCUZpBJ8R1UYBOPB43GIArxfL7SgucMxhCCFFChxrojDHrnhdJAToh7oAWiRLPV1UO6HTy+4oLnDIUQghRhCxAtzK9BQCLjIapdgunZkV9wjkHfv4J4BwYPd76L0mEWIECdOL5Oqa3AOAlBY4fByGEKERWwcWGAJ1m0BV08jAM618FAKgeXgWMm+rkARFPQikuxOPxsuLOd5YWUA1gQoj7qraxBrpJeCSgMn7019WA61qVHVc/wk8clNw+5MSREE9EATrxfBZm0NHSLK+AQAghboTLAvSBXe/YAVOr5SkxleVd70y6xS/liLepfC9RGAXoxOPJKrj4+ou3i/MdPxhCCFGCJEBntsygAx3SXCgPvTd4XY28Dn11BfjVWucNiHgcCtCJR+MGPVBWYt5mYyeKj1EeOiHEXfVykSgAMEmAzikPvXcks+dm+TSLTpRDATrxbFXlQJuxgkvoAGDYSPExCtAJIW6ItzQDzU3ChrcPEBJm2wEkzYpoBr13+KVsC/dRgE6UQwE68WzS9JaYwWDxSeZNqoVOCHFL0tnzcBtqoBvRDHrfcQsz6JSHTpTkcmUWGxsbsX79epw5cwbBwcG45557MHVq59JFr7zyCrKzxW+w7e3tiImJwRtvvAEAePzxx1FXVweVcbV6amoqnn/+ece8CeIyeKkYoLOYwUD0YICpAG4AysvAW1vBfH2dOEJCCLGRpMSiTRVcTKTdRCsoQLcVb9MBhZc6P1CQC67Xg3l5OX5QxOO4XIC+YcMGqNVqfPTRRygoKMCrr76KhIQExMfHy/ZbvXq1bHvNmjUYOXKk7L5nnnkGo0ePtvuYiQu7LCmxGBMvBOMDo4ErpUKQfrkISBrqvPERQoiNeLW4ONGmGugmGkmAXl0BbtCDqSiotFrBRUDfLtweFAu0tgK1VYCuFSgtAAanOHV4xDNYneJy7tw5vPfee3j55Zfx3nvv4ezZs4oPRqvV4siRI7jzzjvh5+eHtLQ0jBs3Dvv27ev2eRUVFcjOzsa0adMUHxNxb9IKLixmsPD/2ETx8RKq5EIIcTOyGXTbA3Tm5y/mrevbgZoqhQbWP0jzz1lKGlhyqvgYpbkQhVg1g/7DDz/giy++wMyZMzF06FBUVVVh3bp1uPPOOzF79mzFBlNWVgYvLy/ExMSY70tISEBWVla3z9u3bx/S09MRFSX/Q/X222/DYDAgKSkJ9913HxITEy0+PzMzE5mZmQCAtWvXQqPR9O2N9IJarXbK63oyrtejorzUvB0xaixUgcFoTB2BpuMHAAB+1eUIUejnTufQvdH5c3/95RzWNV6Fqb1QcEIy/Hvxnmti4tFWXwcACNG1wNdFfm7ucA7rivPMP/+gMePBm5vQaPxM8S0tRKiLj9/e3OEcugOrAvTt27fj+eeflwW4kydPxhtvvKFogK7VauHv7y+7LyAgAFqtttvn7d27F3fccYfsvieeeALJycngnGPHjh14+eWX8eabbyIwMLDT82fPni17H1VVjp9N0Gg0TnldT8avlIoVXMLCUdPSCrS0goeLX+RacrOhU+jnTufQvdH5c3/95RzqJal7jT7+aOrFezaEiQHU1Ys5UMUkKjG0PnP1c8g5hyH7jHm7aWCcWFEHgDbrNNpcePyO4Orn0JVIJ6Q7sirFpaGhAXFxcZ0O2tjY2LeRdeDn54eWlhbZfS0tLfDz8+vyOTk5Oairq8OkSZNk96elpcHHxwe+vr745S9/icDAQNmiUtIPdKjgYhaXKN4uKQDn3GFDIoSQPpNWcdH0IgcdkDcrooWi1qsoAxquCrcDgoBBcUBCCuBlnO+suAzeWO+88RGPYVWAnpaWhs8++wytrcJFHa1Wi40bN2LYsGGKDiY6Ohp6vR5lZWJd1sLCwk4LRKX27NmDiRMndhvEA7C5DBVxf5byzwEA4ZGAv/FKSnMjUFvt4JERQkjvcF2rGCB6eQFh4b07UBSVWuwNWf3zlDQwlQrM2wcYnCzen3/B8QMjHseqAH3ZsmUoLCzEokWLsGzZMixevBiFhYV46KGHFB2Mn58fJk6ciK+++gparRY5OTk4duxYl4s/dTodDh06hIyMDNn9VVVVyMnJQXt7O3Q6HbZv3476+nqkpqZaPA7xUF3MoDPGgLgE8TGqh06I2zP88C/Uf/AnoQW7J5MuEA2L6HX1FUbNinpHUv+cpaSJt2mhKFGYVTnoAwYMwEsvvYSqqirU1dVhwIABiIiIsM9E2TQAACAASURBVMuAli5divfeew/Lli1DUFAQli1bhvj4eGRnZ+OVV17Bxo0bzfsePXoUgYGBGDFihOwYLS0t2LBhA8rLy+Ht7Y3ExESsXr0awcHBdhkzcU1dzqADYHGJ4LnC4mNenA82apxDx0YIUQ6/mAX+5YdoAcAaGsAWLXf2kOxHlt4ysPfHkaa4VF4B55yuNFuBX5RUcBmSLj6QnAr88K2wj4UmRoTYqssAXfrLajAYAADh4eEIDw+X3WdqBKSUoKAgrFq1qtP96enpsuAcAKZOnWqxiVF8fDxef/11RcdF3AvX6wFJBRdEd0iT6pCHTghxX/y8WPaX555z4kjsj9eIAToL70WTIpPgUMDXH2htAbQtQGO9cB/pEm9uFK/MqlRAothDgyWnwryaKf8C1ZYnfdZlgL5o0SJ8+umnAIC77767ywN89dVXyo+KkL6qKAPajY0kBmjAAuTVe1hckvmPKacAnRC3xoskXR0rysCbmzr9znuMKskMem+aFBkxxoRZdFMviIoyCtB7Ik1diU8G85WsfYuIEmrL19cJX3jKSoHYwZ2PQYiVugzQ33jjDfPtd955xyGDIUQxsvxzC4uMYwYDjAGcA+Wl4G06YaEPIcT9dGy7XpwPpI60vK+7k+ag97aCi0mUGKDzyiuynGrSGe8i/xwwfuFJTgNOHRb2zcsBowCd9EGX+SnSIvOHDh1CZGRkp/+OHDnikEESYqvu8s8BYyc9Uw6mwQBI6goTQtwHb6yX52Wjw4y6h1EsxQUA08jz0En3pPnnkOafG0kXioIWipI+siqBfOvWrTbdT4jTdVUDXUqSh05pLoS4KUvBuAcH6LIZ9D6kuADosFCUKrl0h+v1svKJlq42UCUXoqRuq7icPSssvDEYDObbJuXl5Z26fhLiKnqaQQeMeegnDgkbFKAT4pZ4YZ6F+zwzQOftbUCdsW8DY0B439qps6hB4locmkHvXmkB0Grsaj5AY/nqReIQYfGowQCUFXv2Wghid90G6OvXrwcg1Bs33QaEXKuwsDAsWbLEvqMjpBd4eztQflm8w1IOOoylFk3PoVrohLinwoud77tSCt6qlS/i8wS11cK6GQAIDQdTe/fteLJa6BSgd6e7/HPz/b5+wpXZojzhPBVcAIaPddAIiafpNkB/9913AQiLRH/96187ZED9Eb9ai+bDu8DHTQNTW1WannSn4jKgN1ZwCY8E8wuwvJ+01GJxPtUBJsQNyfLNfXwAnQ7gBmGhqIU8YbcmzbWP6Fv+OQChq7KXF6DXA1drPfNLjVJ6yD83Ycmp4EXCVR2edx6MAnTSS1bloFNwbj+Gz96BYdViNPz1TeDcSWcPxzNYk38OCPmbvsY0rcZ64GqtfcdFCFEUb2oUZ3691PAdJ/bF8MSFolwSoLO+5p8DYF5eQpBuQrPoXbJmBh0AkCTNQ7/Q9X6E9MCq6drm5mZs2bIFWVlZaGhoAOfmcvyy1BfSC4HBQr4aAMPBH+A1ZryTB+T+rMk/BwCmUgFxCWLr5pICICzczqMjhChGGoTHJsA7dSRaD+7q/JinqFamBrpMZLQYmFdekV9ZJAAAXlst/ux9fIC4pC73ZSlpYsOivPN0ZZb0mlUz6Bs2bEB+fj7mz5+PxsZGLFmyBBqNBnPmzLH3+DwemzxT3Dh9VCgZRvqEWzuDDiEP3fw8ykN3abymEvo/Pgv9O38ANy3WIv2aKZUAAFhCCrylVTQsLB51e0pWcDFiUWIlF06VXCzLE2fPkTis+1TUqGhh4g0Amhrk66EIsYFVAfqZM2ewYsUKjB8/HiqVCuPHj8fTTz+N/fv323t8Ho9FxwNJw4QNfTv40X3OHZAnkNQ0724GHUCnPHTiuvj2L4DcLOGLrGmWlPRv0gWig1OgThJbr6OsCLxN5/gx2ZE8xUWBHHSgQ6lFSnGxRFr/nPWwrkFoWETlFknfWRWgc84RECAstPPz80NzczPCwsJw5Qr9MitBOotOgUff8PY2YZGoSXRct/szqoXuFrhBD37mmHhHPuV2Enk5RZYwBKrAIGEGExAWPpYWOmlkdiJLcRmoyCGZpJILr6DPdEuszj837SNrWJTT9Y6EdMOqAD0hIQFZWVkAgLS0NGzYsAEbNmxAdHR0D88k1mDjpwGmclmFF8E97UPFkcovCx/MABARJXQM7U5sonj7SokQ4BPXk58LNFw1b3riAkBiG97SLH4Z9/IS1pMAYINTxH086N8JN+iB2irxjj52ETWjZkXd4rpW+XoGafDdBWpYRJRgVYD+8MMPIzJS+GOwePFi+Pj4oKmpiaq7KIQFBsF34jTzNs2i954t+ecAwPwDAI1xJkqvB66U2GlkpC9ks+eA0ARE1+qcwRDXIMk/R/RgMG8f4bYkQIcn5aHX1YqTD8GhYL6+yhxXGqDXVAodM4moIFf8uQ+KAwsK6fk5ScOERlIAUFJIa2ZIr/QYoBsMBuzZswcREREAgNDQUDzyyCN4+umnERfXffoAsZ7/jFvMt/nh3fRHsrdkFVwsNyjqRJrmUlyg7HiIIvjpo/I7DAbPS18gNpHOjrOEZIu3PWkGXZbeotTsOYzNdUIHCBt6PVBT2f0T+hlZeouVdfWZf4A4QcQNQpBPiI16LLOoUqnw/fff41e/+pUjxoPGxkasX78eZ86cQXBwMO655x5MnTq1036bN2/G119/DbVkNfXrr7+OgQOF2dCCggKsX78epaWliI2NxaOPPorExESHvIfe8LlmvPBH8motUF8HZJ0ERo1z9rDcjq0z6ICxo+ipI8IG5aG7HF5dYTEY54WXwEwLrEn/I10gmjBEvB0vmUEvKQBvb/eIBnDSBaLQKFRi0SRykNgHorJMPqvez0kDdFiRf27CklPN6ao87zxY6iilh0Y8nFUpLtOmTcN///tfe48FgFDSUa1W46OPPsLy5cvx0Ucfobi42OK+119/PTZu3Gj+zxSct7e3449//CNuuOEGfPzxx5g+fTr++Mc/or293SHvoTeYlxpsUoZ5mx/4wXmDcWdW1kCXYpKatrRQ1PV0mj038aTZUWIz2QJRSVoLCw4RZ5jb24Arlj8/3I7CTYqkmCQgp4WiIs45cElSwSXFhs60kskDykMnvWHVtMLFixexc+dObN++HREREbKi+y+99JJig9FqtThy5AjeeOMN+Pn5IS0tDePGjcO+fftw7733Wn2cc+fOQa/XY86cOWCM4ZZbbsG3336Ls2fP4pprrlFsvEpj188C/8/XAAB++gh4UwOYqZ4q6RFvawMqJIucom1PcUEJlVp0NbL882snAycOCvcXeVB+MbEJ17YA5aXCBlN1bhwzOMWcqsEL82Rfwt2WLMVF6Rl0ScEHKrUoKi8FGhuE24HBwKBYq59KDYtIX1kVoM+aNQuzZs2y91hQVlYGLy8vxMTEmO+TVpDp6Pjx41i8eDEGDBiAm2++GTfeeCMAoLi4GAkJCbJfhoSEBBQXF7t2gB47GEgcKuSrtbeDH9sPlnFLz08kgvISc1dWaAYKuZXWiBwI+PgCulagvg68vhYsZID9xkmsxrXNwPmfzduquXfCYAzQUVoA3t4GZqqARPqP4nzA1NE6Jr7TgkmWkAJ+6rCwUXQJmGL/zy9745ImRcweKS6m16FKLmYd01tsCrAHxQH+AUBLs5C2WlVOqUN9wNt0QFMDWFiEs4fiMFYF6BkZGXYehkCr1cLfX14WLyAgAFpt5xXQkydPxuzZsxEWFobc3Fy88cYbCAgIwNSpU6HVas1126XHaWlpsfi6mZmZyMzMBACsXbsWGo1GoXdkPbVaDY1Gg+b/uRUNH70BAPA6ug8R8+93+FjcVUv2CZj6sPokDsEAG85jdUIK2nOFL4IhDXXwTR7awzM6M51DohztoT24akxNUycOQcTY8agaGAN9+WWgvR1hLQ3wVigPnc6f+2g+VAbjvCb8hg5HqPG8mc5h66ixqNv2d+G+y0UI94DzWnW1GqbSAWEpw+Ct4HvSDU2DMQMd6toqRDjx5+VKv4f1JfkwRQ1Bo69DoI3jqh02ArrTwhXAoKrL8E8fqfAIXZPS59BQfxXVqxbDUFuNkCdfgH/GLxQ7titzqZUzfn5+nYLolpYW+Pl1ngmVVpBJTU3FLbfcgsOHD2Pq1KkWj9Pc3Nwp+DeZPXs2Zs+ebd6uqqqyuJ89aTQaVFVVgQ8fC6jVQHs72nOzUHnmhNW51P2dIUe80tKmGWTTeTQMihO6VAK4eu40VLG2XxI3nUOiHMOP4loM/fBrUVVVBX1sorl9du2pn6AKDlfktej8uQ9D9hnz7dZBcebzZv47GiZWOWnLv4DKinIwlZfDx6kUzjkMktzwOpU3mIL/VrmP+NnYXlaCyspKp6VjuNLvof7cKfPt5kGD0WLjuAzxyYAxQG84fRxN6dcqOj5XpfQ5NOz7D3htNQCgfvtXaBo5XrFjO5s0Y6QjqxaJOkp0dDT0ej3KysRLbIWFhYiPtzKX2Cg+Ph6FhYXCAg+joqIim4/jDCwoBBgzwbxNNdGtx8tsr+Bi1s/y0PnlIuhfewaGj9e5bElPbtCD//yTeZuNEf4os8FiGT1QHnq/JO8gmtLpcRY6AAg1fnFr1QLlbp620VAHtOmE2wGBYAGByh4/KAQwNXVr1Qqv18/xpgagzLjA2MtLSD+1EUsWq77I0mWIbaQ/u8KLQupjP+BSAbqfnx8mTpyIr776ClqtFjk5OTh27BimTZvWad9jx46hsbERnHNcvHgR3333HcaNE8oSjhgxAiqVCt999x3a2tqwc+dOAMDIke5xeUk1WcyX5Ef2CB3kSM8ui9UabL3qwKS10PtBJRfD1xuBi9ngB38AP7zb2cOxTNo9NCTM/AEpDcg8qs41sQpvbQXKjA3FGOu8QNRksAfVQ5fknyu+QBQQZsul+dFUyQWQVl6JT+5dY6gkSVBfnEfN1XpJ9uXGYAAu9o8vOy4VoAPA0qVLodPpsGzZMqxbtw7Lli1DfHw8srOzsXDhQvN+Bw4cwPLly3H//ffjnXfewW233WbOlVer1Vi5ciX27t2LRYsWYffu3Vi5cqWsZrpLG3GtEJAAQF0NkHWq+/2JsIDEVMGFMWGBji1iE8XbZcXgLlySs694exsgSRHgh/c4bzDdkFZvYaPGgamMf66kM+gl+S57BYDYSUm+0PwFEDo7+llOXZTNrLt5gM6rJBVcIpRrUiQjqeTCqZILuCQIZDbUP5diQSHAQGPlF72ervj1Am+oFys2me7LPeek0TiWVRFrW1sb/vGPf+DAgQNoaGjAp59+itOnT6OsrAw333yzogMKCgrCqlWrOt2fnp6OjRs3mrefeuqpbo+TlJSE1157TdGxOQrz8gKblAH+/TcAhDQXNvI6J4/KxV0pFT+0NQNtnu1ggUFC7eSaSqC9XchxjvXQ3P9L54FWyRqN8z+D11aDDXCt1fHS+udstJhzyEIGAGERQF01oNMJ595TzxXphEsaFMnSnTpgg1PMZe6kKTFuqcZ+NdDNx40cJJYFpEou4JL657Cl/nkHLDkV3Bhg8rwcq7uREiMLNeT5hbNOGIjjWTWD/umnn6K4uBjLly83LxyJj4/H999/b9fB9Wfs+pnm2/zkYfCmRieOxvX1poNoJ7I0F8/NQ+dZJzvcwcGP7XPOYLog6x6qVgPDO5RHpTSX/kt6vqUdRDsaLJ1Bz5OtSXI70hrodgrQESVJcennM+i8vR3Iv2De7u0MOgAgOVU8LjUsspnsi5JJfq6Q6ubhrArQjx49iuXLl2PYsGHmAD08PBw1NTV2HVx/xuISxQ+f9jbwn3506nhcXi86iHbEZAtFC/o2HhfGz53sfJ+LpbnIuoemje6UxiBfKEoBen/S0wJRs3ANEGRs9NbS5NZBp6wGut1m0CnFxay0QOiLAQDhkWDhvS8ZyCQBOvIudL0jscji4lp9O5Dv+V92rArQ1Wo1DKYGMEb19fUIDqYul/Ykm0U/+EM3exLlZ9AL+jQeV8Ub6sWAVqUCTE1+ivPBS4u6fqKDyfLPR0/o9Li0tTvNoPcfvE0n+zKO+G5SXBjrMIvuxv9Oqh2Rgy5dJNq/U1yUyD83i00ATE3zaqvAa1yjhKQ74O3tQIHkS801E8XH+kGai1UB+qRJk/DOO++gokL4I1FbW4u//vWvmDx5sl0H19+xCdMAL+Mygbzz4KbKBaQzRWbQJdUgPDVAzz4ldmBMTgXGiLnd/Mge5wyqg47dQ6X552Yd0xc6TCAQD1VSIHYLHhgL5h/Q7e6e8EWOc94hQB9onxcK14ifNw1X+00pO4sUyj8HhDVlshKN/WDmVzEl+cI6IwCIiAIbf4P5IX7B8xeKWhWg33PPPYiKisKKFSvQ3NyM5cuXY8CAAfjVr35l7/H1ayw4RB5AHaJZdEu4rlW8fM1UQLSNFVxMoqIBbx/hdl01eGN99/u7I0n+ORs+FqpJGeZtfnSfawS6WaeEhboAEJcIZmnGcEAEEBwq3Na2uHX6ArGebIFod+ktJtIAvdBNK2g0Nwn/xgHAx1dM21EYU3nJ89sry+3yOu5AmvesxKJOlix2O6Y8dOvxS+LPiiWngg2TlMrOOw/e1uaEUTmO1SkuixYtwsaNG/HRRx/hs88+w6JFi9ynbKEbk9VEP0Q10S26UiLOCkcOAjMF2TZiXl7y9BgPm0XnnMvyz9nwa4CR1wEBQcId1RXARQsLchyMn+4+vQUwpS94UJ1rYh1pmbrBPQfoLEG+VsEtF4pWSwLliCj7dviULRTtn2kuvKYSMKWh+PjKm9j1kqxhEQXo1utwJYOFhQNRxs6bbTqgINc543IQq+ugl5WV4Z///Cc2b96Mr7/+Wtbtk9jRiGvFmcK6aln9aiJQJP/cyKMbFl0uFurqA0BAIJA4FEztDTZuqnkXfmSvkwZnfP0uuodaIk1fgLuX0SNWsXkGXTMIMKXBNNYDtW6Y/yttUmSvCi5GTJKH3l8XikpnbZE0TJi46SvJDDoKLgq9KEiPpAtE2RDhSw4bNkJ83MPz0K0K0H/88UesWrUKhYWF8PPzQ1FREZ555hn8+CNVFrE3plaDTcwwb9NiUQsUyD838+BKLrLyiuljzB88bOJ0cZ+ffnTuh0cX3UMtoY6i/QtvawOkC5m7qYFuwlQq+UJSN/x3wqulNdDttEDURFLJpd92E1U4vQUw9m7QGNcOtLcBxQWKHNeT8ZoqoS8JIFzJMDUTlKS5eHoeulU5Kl9++SWee+45DB8+3HxfdnY23nnnHUydOrWbZxIlsCkzwTO3ATDWRG9uAgsIdPKoXAe/XCxuxMT36VgsLlFsbuLBATobPlZ8YEi62KSpuRE4exy4ZpITRthN91BLLNS5tuvlf+JclwuF8mqAkMpmSs3qARucYp5p44V5YE76t91rjqiBbiRtVsT7a4qLJM2P9XGBqBRLTgOvEtKVeN55sKSuJx8IgDxJecWkYWDGlGo2bKTYUOtSNnh7u/kxT2PVDHpLSwuGDRsmu2/o0KHQarV2GRSRY3FJQLyxwkibjmqidySdQe9rR0npDPrlIo9pI8/bdIDkciAbIQboTKWSz6Ifdl6aS1fdQy3SDAT8jV9UmxrE2RbikeTpLd00KOoowb3XKkhn0BHuwBn0fpjiwlu1QLFknYO0hnlfyeqhW6jtTWRkC0QlpS5ZRKT4RbVV65ZXxaxlVYA+d+5cfPHFF9AZy93odDp8+eWXmDt3rl0HR0RMuliU0lzMeGsrYJyVgEoFDOxlBRcjFhQitJEHhEUonlIPODdLLFc1KLZTsxNZGtXpo+DNTQ4cnPF1e+oe2kHHhaKUh+7hCm1bIGrC3L0WurRJkcZOJRZNIiXHr6kU6lD3JwUXxTKe0fFggdZdpbEGo46iNpFV0kmW16KX5aHnem6ai1XXBb7//nvU1dVhx44dCAoKQmOj0HY+LCwM33//vXm/9evX22eUBGzidPB/fAzo9cClHPArpWCDYp09LOe7UixWcImKBvP27vsx4xKFBbkQ0lxYb8s2upAu01tM98UOFq7SFOcLnWtPHgKbMtuRQ+yxe6glLCEF3FgznRddArv2ensNjziZzQtETQbFAj4+whfUuhrwq7VgoQPsMEI7qXFAkyIj5uMLhIULi8kNBuGqVFR0z0/0EPxilvm2UvnnZvGJQhnfNh1QVQ5eXyvkppNOuK5VXrGp45WMYSOBQ7uFfc+fBW6a58DROY5VAfoTTzxh73GQHrDgUGDUeODUYQAAP7QL7JcLnTwq55N1v+zrAlEjFpcIfva4sFGSD4x3/3UW8vKKnQN0QJhF58X5wv6H9wAOD9B7Lq/YiawRjZvWuSY94u1tQvt1EysWiJowlZewUNRUEaIoDxh1nbIDtBOubQEaG4QNtRpwREAXOUis9lR5pX8F6NK28grmnwMAU3sDCSliKdu8805b6+PyCi+J600GxQo9YSTYsBFiHvrFLHCDXvg99zA9prgYDAbs2rULQ4cOxfDhw7v9j9iXavJM821+aDfVRAeUreBi4mGlFnldjViRxksNpI60uB+bMA0wLbI8/zN4bbVjBghj99ALPXQPtcDt0xeIdS4Xi82rIqKEVDQbuG1HUWmJxfDI7hdNK4RJ8tD700JRbjAIQbORNO9ZKZTmYh1Zeoul8xAZLVzpAYCWZo+ruGbS42+7SqXCmTNnqDqCKxh1HWD6YKqtAnJ+7n7/fkDJGugmLC5J3PCAX3yefVrcGJLeZeoIGxABpI4yPomDH9vngNEZWdM91JKB0YCvn3D7aq3wZYR4HGl6C2xZIGp+jpsG6DWOq+BiFiltVtSPFoqWXxYWmwPC5+zAGMVfQh6gX1D8+J6ipysZjDFZV1FPrYdu1dfxOXPmYPPmzWjvbwtGXAxTe8urbdBiUfvMoA+MES4nA8JCqeZGZY7rLOdOmG+ynhZeyqq57LHXiDrpVXoLJOkLJu4UfBHrSdKXmA3pLeJz3LOpFa+S1EC3dwUXE2mzon5UC12af46UNPtMSkoXOxbkekyVMCVxzsV0NHRzJWOoZKHoec9cKGpVDvrOnTtRV1eHf//73wgJkV9aVHphaGNjI9avX48zZ84gODgY99xzj8Va69u3b8fevXtRWVmJ4OBg3HTTTbj11lvNjz/++OOoq6uDynhJMDU1Fc8//7yiY3UGNnkW+A/fAgD4yUPgLc1gpk55/QzXtog1gr28FJvxYGo1EB0vLJgEhFn0YZbTQlwdNxjAs06Zt6XlFS1h104G//v7xmYa+eClRX0vXdnjGK3vHmoJS0gxf7jyoktWp8cQ99HrEosm0fHCl+72dqC6ArypASwwWMER2om0xKLGMTPoLCpazO/tRyku8qBQ4QWipuMOiAAGaIQr4K1aoWpVL75werTKK2KzuoBAYJDlIg0sVVIPPfccuMHgkBQwR3K5RaIbNmyAWq3GRx99hIKCArz66qtISEhAfLy8AQ3nHI8//jgSEhJQXl6OP/zhD4iIiMCUKVPM+zzzzDMYPXq0w8buCGxwspAjXVIA6ISa6OyGG509LOcoKxFvR8UIi3AUwuISxQWTJQWyy2lupaRA/GMXFCKfbbaABQQCY8YDxw8CAPiRPWDz7rfvGG3oHmqR5AOOu9HsKLEO1+vlqWa2VHAxYmq10InQFOgX5QHpYxQZn11Ja/uHOyHFpaq83zQA49bM2ioheRhwvEp4zbzzvboi5Mlk6S3JqV0H3YPigOBQ4bOjqQEoKwZiExwzSAex6uuGoxaGarVaHDlyBHfeeSf8/PyQlpaGcePGYd++zrmwt912G5KTk+Hl5YWYmBiMGzcO58/3j0UX8prou5w4EueS55/3rYNoJx6Shy4vr3iNVTMMqkkZ4vOP7hMWT9mRTd1DLaCFosrjBr1wqdkVlBULpekAIFwjVLTqBeaGeeimzpMAOvUusJvAYLEBWKsWqK9zzOs6EW+sB64YJ3y81EBiL67SWElW05sWinbW0wJR02OMydNcPDAP3er+qAUFBcjOzkZDQ4PsD/edd96p2GDKysrMAbdJQkICsrKyunmWMJuek5OD2bPlZeHefvttGAwGJCUl4b777kNiYqLF52dmZiIzMxMAsHbtWmg0mr69kV5Qq9VWv67hF79E5dZPhJroF7MQ1qaF2gNqdduqobYSzcbbgSlpCFLwvLWOGIO6LcJtdXkpwq04ti3n0FFqL5yFMbRB8MQb4G/F+Pj0m1D56dvgjQ1AdQVCq8rgM9x+s43V507AtLolZOos+Nn4M+QDwlBhqnNdU4Vwby+oelHn2hXPnzPoK8pQu+YpGOqqEfbSW/Ae6twKXS1njqDeeNt36HCEdXOOujuHzcPHoGHffwAAPldKuj2Oq6isq4bp63H40FR4OWjM1dFxaDcGj6G6FvhoHNeW3hm/h63552H6GuKdkorwGPv1GNFdOxG1W/4GAFAVXvTIvzl9OYfVhRfNnweh106CbzfHab52IhpOCFd7fQpy3eJ32hZWBeiZmZn49NNPMXr0aJw6dQrXXHMNzpw5g3Hjxik6GK1WC39/eYWJgIAAaLXabp+3ZcsWcM4xY8YM831PPPEEkpOTwTnHjh078PLLL+PNN99EYGBgp+fPnj1bFtxXVVX18Z3YTqPR2Pa6I68DjI1danZsheq2e+00Mtell7QCbg7TQKvgeePBYoDXVnARlRXlPdZZtfkc2hlv1cIgqeDSGD8ETdaO79opwL6dAIC6/2yDKso+H1i8ugIGU1qKWo2GuGQ09uZnGJsI5AtVEapP/dRjrr0lrnb+nEX//p+EWWsANZ++C6+nXnLqeAxnxTUUukFx3Z6j7s4hDxe7ZLbmZrv8ueZtOhhMpU5VKtRwFZiDxmwYoAEg/H2ty82BKlL5iiZdccbvoeHkEfPt9sFD7Pr6PDRCmKXXt0N/uQiVBXk2lw11db09h7ylWfw8YCrUh0d1+2+exyaab7eeeny1cAAAIABJREFUPYHKykq3S8eSTkh3ZNW15G3btmH16tVYuXIlfHx8sHLlSvzmN7+Bl5eyheH9/PzQ0tIiu6+lpQV+fn5dPmfnzp3Yu3cvnn32WXhLukimpaXBx8cHvr6++OUvf4nAwEBkZ2d3eRx3I6uJfnCX3dMQXJI9KriYjhcSJuRDA4CuFags7/4JrujCObF0YWyCsEDJSrJqLj/9KDSKsYPedA+1RJrH6S7pC66Inz8LnDws3pFzRrj870TS89mrBaImcQmAKX2qvBS8pbn7/Z1NWgM9LAJM4c/bbkX1r1KLsvzzIXbMPwfAvH3kC0Pzc+36em4l/4LYGTwuAcyvhwIYMQlAQJBwu74OKC+17/gczKoAvb6+HunpwqpmxhgMBgPGjh2L48ePKzqY6Oho6PV6lJWJK8cLCws7LRA12bVrF7755hu8+OKLiIjoPvhwt29VPRo9HggyViGoqQTO96+a6FzbLC6g8vIS6mErzc3z0LkN5RU7GZIOmMq6NTcCZ5X9XTfpbXnFTty0jJ4r4QYDDMZL72Z6Pbg0YHcwbtCL1ZQA+Xm2EfP2kfdKKHbxzrOyGugOKrFoImlW5OmVXHh7O1AgqUluzwWiRvJ66Dnd7Nm/2LpQl6lUgCQFz9Py0K0K0MPDw1FRIfyxiI6Oxk8//YTs7Gyo1VansFvFz88PEydOxFdffQWtVoucnBwcO3YM06ZN67Tv/v378cUXX+D555/HwIEDZY9VVVUhJycH7e3t0Ol02L59O+rr65GamtrpOO6Kqb3BJkhrovezxaKXi8XbCldwMWFu3lFUVl5xuG0pH0yl6lATfa9i4zIfs5fdQy1xxwWAroYf2StWOZHef/yAE0ZjdKVUuIIFAGHhYL1YWyDlTh1FuWQGnUUM7GZP5TFpLXRPn0EvzhfWrwBCl9ow66809lrSMPNN6igqknYQtfaLkqzC2gXPqoduVYB+2223obRUuHQwf/58vP322/j973+PX/3qV4oPaOnSpdDpdFi2bBnWrVuHZcuWIT4+HtnZ2Vi4cKF5vy+//BKNjY147rnnsHDhQixcuBAffvghACEtZsOGDVi8eDEeeeQRnDp1CqtXr0ZwsBvUvbWBrJrLiYNCwNNPcDumt5jJAvT8rvdzQbym0pxHDLU3MGxE90+wgE3MEI93+ih4c5NCozPqbfdQS2IShCspAFB5xf2bSzkYb20F/3qjeZtdL67nQfZpp6W5yMpm9iW9xUR2pcXFZ9CrXWUG3bMDdHlbefvUP+9INjucf6F/pqh2wA0GWVUba88FGyat5HLOdapPKcCqKfCMjAzz7bFjx+Ljjz9Ge3t7t7nhvRUUFIRVq1Z1uj89PR0bN4ofIO+++26Xx4iPj8frr7+u+NhczuBkoe5naSGgawU/fhBsyuyen+cJZCUW7ROgs7hEsRGCm82g83NieUUMGwHm42vzMVjsYCA+SZhham8DP3lI0X9fiqW3AGDe3sK/A1M6RHE+kDqqT8fsT/h/vxGapwBAcCjYPQ+DV5QJzVsMBvCTh53Tb0HaoEiBetEsIdn8O+3qM+jyAN1BJRZNBoSLjZ0aroJrm3vOB3ZX0rrbds4/N4uIEtY41dcBLc1CiUd7TTS5i7Ji4WcBCD8bjZVXjeKTAT9/QNsi/A2rKpfX8ndjNhUcvnr1KsrLy1FdXW2+TZyHMQYmWyz6gxNH41iyGXR7dbqMjhNnZavKXX9RmVQf0lukZLPoR5RLc+lr91BLZOkLlIduNX61FnznVvM2u/1eML8AsOvEpm/8J+ekuSi2QNQkLgkwrUcqKwFvbe37Me2ESwJ0h9VAN72eykseIFV45iw65xz8ohNm0BkDpHnolygPXfYzSEmzet0g8/IChkjz0D0nzcWqAP3UqVN4+OGH8dBDD2H58uWy/4hzsYkZYmWCC+c8P1/QRJqDbq8ZdLW3vM1waaFdXkdp3KAHl5RX7E3JQfNzJ0wTA5qcM+Cmsm991dfuoZYkUMOi3uDb/i40pAGEaj9T/gcAwK6bLO6Ucxq8wbFpLtxgAIqUWSBqwvz8gYGxphcAXDl1TVrFxdEz6ED/SHOpqQLqjH/TfP0d2olSulDUVCK2X5MtELXti5I0zQUetFDUqhSXv/71r7jjjjuQkZEBHx8fe4+J2ICFDhBqohu7MfJDu8BuvcfJo7Iv3twkXo73Uss/SBTG4hLBjYE5L8kHG+KYGZY+KcwTWh8DQOiAPn3osAERQqpIzhmAc/Bj+8Bu/GWfh9jX7qGWsMEpkvQFF88vdhG8JB/8x0zztmr+YnM5PxYeKSzUMqW5nHJwmkvFZaDVWHY3JAwIC1fksGxwCrixayQvyrNvW/de4u3tgPTLcLjjG7CwyEHi71NlGRxRB41frYXB13ExhmxRYvIwh5ayZMlp4s+XFop2qOBiW0EPNmyk+LP0oADdqk/FxsZG/M///A8F5y6q39VEL5PMng+KBVO4mpCMZKGou+Shdyyv2NcSo/JqLnv6dCzzcST1z/tSvUUmLhFgxj9pV0rAW7tvcNbfcc5h2PKxMJMMACOvBRt5rWwfNk6a5vKjI4fXaYGoYqVyEyS57K56paWuWjwvoQOEEpGOFunYWuj81GEYnlmCqkfucFyawkXr2srbReIQ8e/V5SLlF+G7Ed5QL9Yw91LbviA8IQUwrbOqKheKJHgAqwL0mTNnYvfu3fYeC+mt0RPEYv3VFUCu5+RgWeKQCi6m40tqobtLqUWeJVkg2of8cxN27WShEgwAFOeDlxZ1/4Qe8OoKMV1IrQZsrdHeBebrBwwypS9wef1s0tnZE+JaBaaCav6STruwa8UAHTlnHJvmovACUfFYblBq0dnpLQCY5MqkvVMneUszDJvWC3X3m5tgeH+trMyk3V63D2kVfcV8/YTmWYDw96qgHzcsktaCT0ix+QspU3vLyjJ6Sh56l1OPL774onnGgnOOHTt2YNu2bQgLC5Pt99JLzm0DTYQKFmziNPDdOwAA/MAPYJ5cwUJWwcVyEyvFSGfQSwvBDQZF0jHshbc0y0tVKRD8soBAYMx44PhB4TWO7AGbd3/vx6hQ91BLWEIKuPEKCy+65B4pSU7A9XpZUyJ2w40WF1uzcI08zeXkIbBpNzlmjJI0JUUWiJpIg/3SIvC2NqEKkAvh1WIBBkcvEDWTdhOtsG+zIv6vL4GrteIdDVdheO9lqFa9BuZrewUqq15T2yKuQWAMSB7W/RPsgKWkgRsnEnjeeUX+XrsjeanL3l3JYMNGiGuvLpwFJmUoMDLn6jJAnzlzZrfbxLWwybPEAP3EQfB7HlY08HEljpxBR+gAICgEaKwXyjhVV7h2CafzZwC9Xrg9OBksJKz7/a2kmpQBgylAP7oP/Pb7ev1FRcnyip0MTgFMaTiuOjvqAvj+78VUMV9/sNvu7nJfNm6qeaaRHz8AOCBAFxaISs6fAgtETVhAkPA7XHkF0LcLX/gTlDu+IqSzx+EOroFuohkoBK6cAzVV4O1tdmkIxy8Xgf/wbecHivLAP30LWPZb+3QCL8gFTOmgMYOFfxeOlpQK7PkOQP/OQ+eXbK9/3pEsD91Dsgi6DNCltc+JG0gYAkTHCx+6rVrwEwdljYw8igMquJgwxoRZ9Jwzwh0lBS4doPNzypRX7GTkdUIaVXOj8CXlUo6sxbLV41Owe6glsoWirt6Ixkl4SzP49s/N2+yW+WAhXXfoZNdOBv9qg7CRcwa84SpYcKh9B1l5RayJHBSi/CLJwcnmvGpedEnWidYlSGuga5yU4uLtA4RFCAvyuUH40jAwRtHX4JzD8MWH4qTCsJEInvELNHzwJ+HxY/uFiYab71D0dQF0KK/onIXCLDlV7LWRdx6cc/t8GXFhvL0dKJBUsbFxgahZ0jAhFbO9DbhSCn61ts+dh52t2ymwvLw8FBWJs5X19fV46623sHLlSnz44YfQamkRlqtgjIFNkXQWPbjLiaOxH97cKJbFUtu3gouJO+WhS/PP+1JesSOm9gYbN1V8nd4uFlWye6gl8eK5QlkReJtO2eN7AP7dFrHEZXgk2Oxbu92fhWsAU6qQMc3F3mS54QkpigctspQZF7zS4swa6DKyhaJ2SHM5fkCc/FCpoLr7IQTc/EuwaTebd+H//EzWM0Ep8rrbTkqFGxgDBBo7nDc12D2VyCWV5AM649/piCiwsIheHYZ5+8jSlDwhD73bAP2TTz5BXV2defv9999HWVkZZs2aheLiYmzatMnuAyTWYxMzxFXh53/2zJro0tnzQXGOKYslyUN35QCdV14R/8D7+Cr+oSOr5vLTj+DtbTYfw67pLTDmy0cZv7Tp9W5Tu95ReFU5+H+3m7fZvPut6jLr8KZFsgWiys9uu3xTK+kMerjzAnQmCdCV/jzhrVoYNkvWQcyYA2b8W8vuXiY2n+Echo/eMJfGVOS1DQbZwkTmqA6iHXRqWNQP01zkC3X7dh7YsJHiRq77l1vsNkAvLS1FerrwId/U1ISTJ0/iiSeewM0334wnn3wSx48fd8ggiXVYWDggmTVVqiSeK3Fo/rnpdWSlFl23Mgg/J6nekjpK+YVvQ9LFfNjmRuCsbb//9ugeaolbVOlwEv71RuESMAAkDgUbf4NVz5MG6Mj5Gdw0A28ndlsgaiJdKFpSAG5KsXAB3GAQ+zwAgNJXmWwhnUFXuJso37FFfJ/BoWC3iusgmNobqkefEVObWppgePdl5UoRXikBTMcKDnXIldiuMOni1Lx+2FG0QwfRvmBDxYZFHj+Drtfr/3975x0fRZ3+8c93skk2m0LK0lIhtCCINEGRIooNRLDBSTkVwYZyp/wQz3KH3nnSPOVQ4C4RvUNRPMudpycqFkCQIiA9FCEFCJBCSN0km/n+/pjdnZlkE7LJ7s53k+f9evFiZ3bKN5md7DPP9/N8HpgcHtPHjh1DdHQ04uMVDZrVakV5edv17RQVre6cb/2m9Xmi6xxc/BOgIz5J7daaf1ap/hcQnbzFB24ATJLqeKJv9OwAvuge6g6tnph06C74iSPgOza5lqVJDzS50JfFxGkymr6VuXDOAW1W24sWi05YZDs1+KupVgI2USi5oMrAIiKNLfbvoLVa9J78gp87A/7VJ65ldud99Yo0WVQMpEefAZyWe2dPQ854BVxu+cOUVn/uSVt5X8BSNfaAbTKDrq0FaOGsb7c0wDmrfjrb792PvU2jf52TkpLw44/KH+ItW7bg8stV676ioiJYLBbfjo7wGNZ/CGAJVxYKzgHHDxk7IC9jSAY9OETTHpzrHxIEgdfWqlpOAKzPwEa2bj5s6LXqOffu8CijpWtO5KXuoe6gDHp9OOeQP3hTXTFwGJiHRb76pkU+lLkUnFNmaAClMNna0TfnEVXmUiCGvAXQS1y81ayIcw75/XT1ISS1F9jVo92fP6U72L2Pqyv2/wT+n7Vut/UIrazCaCvWLj0UtxxAmc1pQw3WeFEBUOSYRQkJ1dsaNwMWatYnfgI8/mn0G3Lq1KlIT0/H/fffj927d2PixImu97Zu3YpevZpZbUv4DBYcAjZkpGuZb/3GwNH4AD86uGhhouvQTx5RXS9irWrDHi/DEpLVQkx7jUeZVL5Pqz/3jbwFQH35gjMQaMvs3qoGJUEmSHfe6/Eh2MBhaiCRuR+8pLjxHZqLjwtEnei07QI9yHEBHFxcaKUfBWeV2Y2Wsm+nKo9jDNKUhxt9WJeGjgK76Q7XMv/fvyDvbFlXW2/qnlsKs4QrDmyAYvuYdbzxHVoTWklP155eqSnTy1wCW4feaICelpaGFStW4Pnnn8frr7/ukrcAwMCBA3HvvZ7/kSd8D7ta9aznP21tNU/kvLwMuFikLASHAO19lFlzh+A69Lr2ir6cstVl0bc3Tebiq+6h7mARUWr3RXuN6vfdRuE1NZA/fNu1zK4bB9bBc80ti4lTC4+5DL5nm5dGqIf7uEDU3bGFmmnRtClnRmfQwyPULtXV1erf32bCa6qV7Lnz+CNvapLFJbtjOtBXnRXkby/T1Sl4NAZtW3lTM9rK+wDtQ0Jbkrn44kFJWyjaqgN0AAgLC0NqairCwvQ6uPj4eMTGxnp9QGVlZViyZAmmT5+ORx99FD/84P5JmXOOd955BzNmzMCMGTPwzjvv6J7us7KyMH/+fEybNg3z589HVlaW18cqLF17Ap0SlddVleC7fW+L5he00pJOCWCSHxxcHLAksa0WfWWv6A42ZKQmk7oP/ELhJffxZfdQt2iy6EIFXwbAv/tMkY0AQHgk2LjJzT6Wzmrzp5ZlMRtC51/vy+ApRTPTknNSnHodrcTFyAJRJ14sFOXrP9Z/FidOa9J+TAqCNOv/gA6OJGF1FeQVf25esbJG84yU7h63lfcJXTX2gBSgt4zuvVU3u9yT3issNgDhepZnZGTAZDIhPT0dc+bMQXp6OnJz62fANmzYgJ07d2LJkiVYunQpdu3aha+//hoAYLfbsXjxYowYMQJvvfUWRo0ahcWLF8PeRqa6GWP6YtEvPwY/sl+cL6BmYoT+3EVCF/X1qWzvTPV6CV5ephRgAkrg3PsKn56PxcQBvRz1KJyD79zU+A7wvb1iXXSZV5H0xX6Gl5aAf/aBa5mN/5WSFW0mbNDV6sPZkQNel7lwzoEcTQY9xfsFoi7axSrFygBQVQmcP+O7c3kALxLEA905Bl2haPMDdF5wDvyLD9Xj3j5dme1q6jgsEZAeexZwPtwXnoe8apHHEjaR5C1OtIWiOJEp1PeLr+DVVXppWap3JNMszKImaDgPaB26UAG6zWbD9u3bMXnyZJjNZqSlpWHw4MHYtKl+ALBx40aMHz8ecXFxiI2Nxfjx47FxozLdfvDgQdTW1mLcuHEIDg7G2LFjwTnHgQOBPd3hCeyqa9WnyNPZkJc+C/m5hyF/tg5cM4UaUBjh4OIkJk6d6q0sVwtbRCBzr9LpD1Cs85yNL3yI3s3l+0a39XX3UHdop83bcgadf/a+8nkFgA7xYKNubnyHS8Ci49SmRVz2/uxcUT5QVqq8Dgv3qf0dY0zMQtFCzd9nAQJ0bzUrkj94U3HMAYDkbmAjbvD4GKxzEqSZc9WHxKMHwLXFz01A7xoiRoCOzolAmMN0o6RY74PfWsn+Re0g2ynRo4e1S8F6tg4dulABel5eHoKCgnRa95SUFLcZ9NzcXKSkpLjdzvmeVofb0HFaKywmDmz0WP3K/LPg/3kX8tMzUfvqHyDv3BxQnRaNzKAzxoTVoWv9z31hr+gONnCY0lYZUKYRTzfibOPr7qHu0GbQc096xZot0OBnT4Fv/MK1LN19H5ip5d74OpnLLi+7udSxV/S1/Z2+UNR4S07OOVB4Tl0hXIDevAw6P7Ab0NQsSFMearZEkV0xBGzCVPXY330OefNXTRuHvUZfhGlUB9E6MElqczIXXz4o6XXogeuHbjJ6AFpsNls9rbvFYoHNVr/I0Waz6Wwendtxzuu953y/stK9f/WGDRuwYcMGAMDChQthtVpb+qN4jMlk8vp5+WO/g/2W21H5zeewbf4avNyRmeIcOLRH0S1HRCJ0xI0Iu/5WmFJ7GuoHeynyz56CU6QT0+cKmPx8nUp69Eal42k8rOg8Iuqc3xfX8FJwzlGQuRfOCdHoYaMR4pcxWFF85XBU/fgdAMC8fwcir3Bv7XjxyD447+Dwq0bV+735ZnhW5MdYIV8oAKqrEFNVCVNSl0Z3MeL6+ZLivy9GlSNDFdxnAGKuH+eV+7t2zK0oeD9d+Tty9ABiTBKCor1Tj1SWfwZOxaglrS8iPbwenl5DW9/+uPg/RQIUnJeDGIOvv3zxAvIdbc9ZmAXW5BTD/yZXd0/DBcfroAsFiPPwd8RralD4L7VjqPm6sWg3dHiD2zflGvJfP4KL58+gauu3yvLaVYjqfTlC0i5vdL+aowdR5EhKBXWMh7Wbj3oxNIOyPgNQfkgp9g/Ly/H4sy8STbmGxbknUOV4HXHFYFi8+PPKQ0cgfwVT/kZl/4LYcAuksMCzBRcqQDebzfWC6MrKSpjN5ktu69yOMeb2OBUVFfWCfydjxozBmDFjXMsFBf6XL1itVt+cN7o9cOd9YOPvAfZsU2wXD+9VPrgAeFkpKr/4CJVffKRkN68ZAzb0WrBI7003eQNeVgK52OEgEBKCC0EhYH6+TnKc6hpTcfQQbHXO77Nr2Aj87CnI+Y6MmzkMF2M7+u33wgdeDTgC9Irv18N24x317NK4XAt5p5plrezRt97vzVfIiV1cnQqL9v4EKaxx7bUR189X8Mx9qhUdY6i9/dcoLLx0MW+T6XEZcPQgIMso3PAZpGvHXnKXplCbqUqhKtvHo8rD6+HpNeQx6mxO9S+ZyM/PNzQg5lnH1Nex7b17zZoJD1G/N+15uR7fI/L6j9TZzzALqsdNbvQYTb2GfMrDyqzHqSzAbseFl+dDevYvYLENB3ryLjWLL3ftKdT9zp1WiwAqDv7s8WdfJC51DTnnkA+rfTvKOyaiwts/b0KK8tmQa1G4Y4vPzROai1YxUhehJC6dO3dGbW0t8vJUnVt2djaSkpLqbZuUlKRzZsnKynJtl5SUhOxsfSFfTk6O2+O0FVhIKKShoxD0xIuQXs4AmzClfgOQU1ng6zIgz7sPtSsXgu//SZwW2DoHlySfNblpDJaodXIRQ+KitVdEWj8wkx+fufsOUnX5hef1LZud+Kt7qBt09m1tSIfO5VpdUyJ21bVNsrLzBDbI+02L6nYQ9faY3RLXQf0MV5SrDiNGIZr+HACiY1U5W1mpZ83JLhSCf7bOtcxumwIWFeOVYbFQM6TZzwIRjpqbkmLF2aW6qsF9tLKKlraV9zoaiQtyTgSU/NRj8vPU7wVLuOo650Vag8xFqADdbDZj6NChWLduHWw2GzIzM7Fz506MHDmy3rYjR47E559/jqKiIhQVFeGzzz7DqFFK4VqfPn0gSRK++OIL1NTUYP369QCAvn371jtOW4TFtYd0668gvfQ3SHP/BHbVaCBEYzVVawd2b4X81xchP/0A5I//AX72tHEDhsEOLk7ik9XC23N54FUNfxH4C3/aK9aFmYL1emQ3xaL+6h7qDr3PtfH6Yn/Bf/weyHU8QIaEgE2c7vVz6JoWHT0IXnKh8R2awoVC9UvbHKZa6vkQxhiQIo4OnWv0536p1WgCTJKarUPnH74FOPtwJKSAjR7n3bFZO0J6+GnA+Xcl+zj4mhVuXVA458BxrYOLGPpzJywiSu1YXWs3/LPoS7jmOiA1zSffC62hUFSoAB0AZs6cierqasyaNQvLli3DrFmzkJSUhMOHD2P6dPWL5oYbbsCgQYMwd+5czJ07FwMHDsQNNyhV4SaTCfPmzcPGjRtx33334bvvvsO8efNg8md2MQBgkgSW1g/SA09AWvIPsOmP1rc6Ki4C/+IjyM8/gtpF8yH/8LXiyuFvdA4uxsyEsNBQoKPDVYLLQF4jhZF+gNtrgCMad5TL/D+Fp3Nz+ekHZUwa/NY91B11OkUGus1oU+BVNvB/r3Etsxtvb3TKv7mw6FjA2bHPW24uOXUKRP30MMdE8szXZdD92IjtUjTDyYUf2Q++Q3Vgk+55yCudIuvCel0ONnmmet5t34Fv+LT+hoXn1UZL5jAgwaBETyOwVE2hqLsZydbCCT9YXWo6iiLraKMzK6IiXMQaERGBp556qt763r17Y80azRcPY5g2bRqmTXPf6KBr165YtGiRz8bZ2mCWcLCRNwMjbwY/kwO+5Rvwbd8plk9Ojh8GP34Y/P10sEHXKF3g/DRNyM+oDjyGZdABsIQurtkEfioLzI+SjXr8kqlmp9p3alZ3yBbTvTcQ216xx6soU1p4978KgH+7h7ol1qpMf5eVApUVinzBiN+RH+FffgI4azXaxehapHsbNvgaV2aK/7QFaKEOXWtz6MsOovUQqKMoL9R6oIuRQQcA1r6TqxCd55/FpVT63G6H/N7f1f2HjATr5bsZbDZ6nOLW9IPSC4X/6y3whGRd0kIX8Kb28mujuyaTmuaq60ErdnLxhxc9i4oGOicpnaTtduDkUbV/R4AgXAadMB4Wnwzp7vshLVqtaPz6DwW0mY8qG/jWbyAvfKrJ9lYtxkgPdC06q8Uso0YBoI69okEFMEyS6niib1Rf+7t7aB3q+ly3dh06Ly4E//Jj1zKbMNWnv3O9zOUA+MWWyVx4tsb+zh/6cwd1m1oZ2iRG638tigYd0PvRN0Hiwr//n/pwHmoGu+t+Hw1MgTEGNuVhVVfOZch/WwJ+XpPtF9H/vA5MM4PNT7bOAJ1XVqifDaa3l/Q2TJNF50cCT+ZCATrRIMxkAus/FEGzn4W0eDXY3fcrT6Qa+LoMXdbHF/DSi6o2NSTU0C8upgnQuUgBugHyFte5h17res337nAVkfm7e6g7mEDZUV/D//0O4JzGTewCds31je/QQli7GI3Mhbdc5qLR3Po1g96hMxDqeJApvajOQBiBTuIiUAa9gypx0QW9buAlF8A/Xavue+tkpfuwj2HBwYoePdpxrooyyG+85JJk8uPaAF0s/bmLhBQg1OFaV1QAfsF4Fx+vc/KIy0UOiSm+TdwEuA6dAnSiSbCoGEg33g7phdchPbNUrbquskFe84Zvs07a7HlnYxxcXCSpTi44lWVYto2XXlQzwpJk6NQdS0hWfy/2GvA9PxrSPdQtuk6RrbjoKucEuMMTGgCku2f4ZQpfVyT80w/NPg4vLlL1waFmoFNCS4fWZJgkAcma+9qgBzleUaZ2fQ0OASKjDRmHWzwoEuUf/VORlAFAxwSwMbf5cGB6WHQspEefUV1nzuRAfvM1JWt7ypm1ZV5rK+9tWFCQ3umqFcpcuB8LdbVOLjhxpF6NlOhQgE54BGMMrGtPSPfNUae3D+65ZLv3lqB3cDHYKjO2vdqSubzUsGwbP6SxV0ztBWYJN2QcTnRZ9O0bjeke6m5cKWoBIHLL8olaAAAgAElEQVQMli/4CM455H+tVrNSlw/2Y0fZq1Vno2MHmy9z0QbFSV39rg/WzbRkGzTTUid7bnSDIh1xHdW/9xcKwGvcBzr8l0yl14YD6Z4HvdK91hNY1x5g02erK37eBnnVQqWwH1DcZARuWqMrFG2NAbqmQNTXVpcsJk59uKypBjR9BgIBCtCJZsG6pYFdd6trma/L8I7VmjtE0Z/DoWtO6KKuMMoPXQD9uRY2ZKT6BZ65D/LGL9X3DJK3AACsndQHqrISV+OiVsW+n4BMR9MPSYJ0t2/1vlpYuxh1Gplz8N1bm3UcwwpEnaR0V8dilBRKKxWMFUh/DkU+ghiHGxDnQGF9v3gu10Je+zd1xYCrDPvbJA27DuyGCeoKTUJDVP25E50OvZUF6FyWdbMC/rgWOj/0ANOhU4BONBs2cZqqBy8vBX8v3SfnEcIDXYPROnTOuS6DbqT+3DWGmDhVZsM5oPVnv8IgeQsc8oUkfRa9NcHtdsgfqm3U2cibwTr7d5aJDW550yKjCkSd6B4KDPKf5poMOrOKFaADuKTMhW/+Wr2/gkMgTXrATwNzD7vzPvfOUd0F1Z870cpvso8HnCyjUfJyVflTu5j6zRJ9gTZAPxZYDYsoQCeaDTOHQfq1OpXIf/oBfM+2RvbwHM65UBl0AEBSF/W1EYWiZ3JUva4lAujSvfHt/YTWzcWFn7uHuoO1Yh063/wl4GwiFmYBu+0ev4+hnsylObIvowpEnXRKUJu1XSgA19rL+gttVjpWnAJRJ1obV35eH6DzshLwTzQ2yLfcBeaP4KsRWFAQpAfn6R8sIHCBqAMWpQlca6oNdwvzJrpOrqm9/CLj0jYswvFMcbqjNwEK0IkWwS4boHOLkN9dpRQ7eYvSYsXHGlCKxwT44mIaiYshGXStvKX3FcL4+bKBw9TiLOc6P3cPdUuKQI1ovAivKNO7ZYy9Gyyynd/HwaJaJnPhJcWq9CgkpJ5TlD9gQUFAorZQ1P8PclynQRc9g653cuGfvKPU5Di2Yzf7zn/fE1h4JKTZz6kuPfHJ/snatpBWK3MxoJMrs3ZU44aqyoCaRaUAnWgx7O4HlOkqALhYBP7h2947+GmBHFycJKSor8+eAq+p9uvptQE6BNCfO2GWcKCOnMUw9xbtGFqhFzrnXAmKnA+vcR3Arh9v2Hh0MpddHspctEWZiV190m2yKRhuyaltUiSgxIVpAnSukbjw7OPKTI4DafJMsOAQv46tMVhCMqTn/gJ2+3RIs58Rq/i2IbQyl19aT4DujwZF7tDp0APIblGAaIcIdFh4BKQpD7mW+eavwA/v9cqxRekgqoWZw9Rskiwrujo/waurAI2Ozl9uHU1FuupadcGI7qHu6JSg+OcDQHFRixvqGA2vqQZf/ZrSDMYBu/NeQ4MivczlkEcyF20wbIi8xUmywTMtRZoMumBFogDcNivisqwUhmochCDAQ3ldWKcESGPvBusQb/RQmgRLVYNXfiKzVbhP8dIS4PwZZcFk8m+tic4PPXB06BSgE16BDRwGDBzmWpbXvAFeVdXyA4umP3ei8UP3q8zl+CFFlwgAnRLARJsK7zvIJRVgI270e/dQdzApSO9fb1ARoDfgFy9AXvos+Lbv1JV9B+n8yI2ARcUAzlbuHspcjC4QdcJSjCsU5VU2tRlbUBAQHePX8zeJOkWiXJbBf/xOdeUwmZTseSBkqEUnqYvihQ8ABefAf/ja0OF4Ba29Ykp3vyYUdH7oxw6By4GhQ6cAnfAa0pSHAKcfd/5Z8E/fbfExRXNwccJ0VotZfjuvTn/eZ6DfzttUmCkY0jNLIb24Auyehy69g58wXL7gBXjOL5Bfmqu3KRtxozDT9myQ1s3Fg6ZFRheIOolPBoJMyuv8s+DlXqyluRTa7HmMVZi6Ei3MEg5ERCoL9hog7xT4R2+r7994O1jHwMhQiw4zBYMNv8G1zN//O7hW7hmAaAtEmb8bRXXoDLSLVV5XlgdM4S0F6ITXYO1iwDTWWvzrT8FPHm328YR0cHFglNWiLkAXQT7iBhYcDNY5UYig0UWK1snleCMbignftRXyoqfVYkomgU2eCTZ9tt8bwTSETuZy/DB48aXblPOyElV7bQo29B5npmB9fYk/H+S0HuiizYpp0chc5LeXqVn/GCvY2LsNGlTrhN15n3o/VFdD/vtiReIYoOj15/510mGM6dxcAkXmQgE64VXYsOuB3lcoC1yG/I/lzfdxvXgBcDrCmMOAWKt3BukNNAE6ck/6RSPIi4uA04521UEmnb8r0Tgi+Fw3B8455P++r3RCdH45h4VDmvN7SGNuE+ohiEVF62Uuu3689E66AtEuYCaTbwbXRLQyF+7Hzwkv0BSIChygawtFtV0ZpUkzwELNBoyo9cJCQyE9+JRq/3kmB3xdhrGDaibcbgdOarp4dvNzBh2oo0MPjEJRCtAJr8IYgzR9tlqUdzob/IuPmnewM3UcXAQKRmDtqFp3lZUAfvBN1jYnQvfeQui7A4bOSUphEgAUnlcyt4LDq6rA/75EZ6WIDp0h/W4JWF/x5E0AdFr4pshchCkQdZJsUFOrIm0G3Xgr2Qap4ykOAEjrB2jkTYT3YAnJYJNnuZb5pi8h7/RAPiYKuSfV2qm4DmDRcX4fgl6HflDpaio4FKATXoe17wR2+3TXMv/8g2bp50TVnwOODpWJmulwf8hcdPpzcewVAwFmMgHaugHBs+i8qADy4qf1QW7vKyA9sxSsc6JxA7sEOpnLL4fBLzQucxGlQNSJYbUKOg90gX26tU4uABAUBOmeB8VKnrQy2Igb9Q++a17X2VwGAvyEcfIWF52TgIgo5XVZKZB3yphxeICx84kaysrKsHLlSuzbtw+RkZGYMmUKhg9370zw6aefYuPGjcjPz0dkZCRuuukm3Hbbba73Z8+ejeLiYkgOz+xevXrhueee88vPQSiw68aB79ysFLTV2iH/46+Qnl7kWfGToPpzJyyhi0tXx0+d9Om5uCyDH1Yz6OwyCtA9haV0cwWEPOcXYTX8/MQRyCv+rEi8HLDR48AmPWC4BORSsMh2QNrlwOG9LjeXRv3ZtQWiKQJ0xE3sAkiSYp967gy4rQLMbPH5abnWA13gDDpr3wlaMR+77lbhkietDcYYMH02eNYxoOAcUFkBOX0ppKcWCv/3wIVGf47u/vM/18IYU2QuuxXpHT96ACxB7M+uMBn0jIwMmEwmpKenY86cOUhPT0durnt/ac45Zs+ejbfeegvPPvss1q9fjy1b9M0x5s+fjzVr1mDNmjUUnBsAk4Ig3fu4Kis4eRT82888OobIGXQAeh26rzPop06qBVmR7fS2gUTTCAAdurzte8hLnlGD86AgsKmPQJryUMB8GeuaFv3UcNMiXl7m8tNGkEmIh3AWEqp2MuUcyM3yz4kDpUg0XiMVaxcDNv4eY8fTRmCWcEgPzlMsOAHl+/Tf7xg7KA/QO7gYE6ADdWQuAaBDFyJAt9ls2L59OyZPngyz2Yy0tDQMHjwYmzZtcrv9hAkTkJqaiqCgIMTHx2Pw4ME4cqT1dNtqLbD4ZLBxk1zL/JN3mjw1pzi4aB7QBPjyrgtL6uJ67WsnF517S+/+YnRUDTB08oVssawWuSxD/vif4G/+RbGwA4DwSEi/fQHStbcYOjZPYQOuVrLQAHD8UMMyF62EJCEFLFgQNxo/NyziNTXqAxmTgBj/63ObCouIApvxBNiQkZDm/B4szPezC4QC69oT7PZfu5b5lx+DH9hl4IiaBi/KB4oc7lMhofrElp9hPTSFoscOCt8ASoiUTF5enivYdpKSkoJDhw5dcl/OOTIzMzFmzBjd+uXLl0OWZXTt2hXTpk1Dly5dGjzGhg0bsGHDBgDAwoULYbX63y3EZDIZcl5fw6c+hKI922DPOQFUV8G0Lh3Rf3jtkprF2sJ8FFSWA1CyB9YevYTTOcphA+FSjp49hSDOfXYNi44egNMLJ3LoCIS1ws+Kr+FRkTgvBQFyLXD+DGItYZCcvv0w7h6UK8tR8tqLqNqx2bUuKLELop9ZDJPAevMGsVpx4fJBqN67EwAQnvkzLOMn19usvOAsnE7jYT0vQ5QXfvfeuIYVvfuh9EelEVToudNo5+PPhD3vFAodgYIUa0X7Tp0vsYfB3HK78s9HtNbvQm/A73kAxb8cRvWebcryW8sQ++o/ESSSwxn019B2ZC8cc78I7tkHsR2Nq7HgMTHID48ELy8FLl5ATHUlTALLXIQI0G02G8LC9I4UFosFNpvtkvv+61//Aucco0ePdq17/PHHkZqaCs45/ve//+Gll17Ca6+9hvDwcLfHGDNmjC7ALygoaOZP0nysVqsh5/UHfNqjwMtPAVxG9d6dyP90HaRrxjS+j8axhHdOQmHhpT2VDSGugzI9bbfDlv0LLkZEe/0UvMoG+fA+13JZcjeUt9LPis+JT3LJkQp/3qmb8jTiHuQF5yC//ifVPhMALh8MPnMuioPNQIBeZ7nflYAjQC/d9BUqrr6+/jaaz7StYyKqvfCzeuMa8jjVqcR29CBqfHwN+HF19leOiWu13wNNpTV/F3oDPu1Rpbbr4gXwkmIULHkO0hMvCNXcSnsN5Z93utbbk7sbfm15997A3h0AgKLtmyGNvMnQ8WgT03Xxyzz5ggULMGnSJLf/nn/+eZjNZlRWVur2qayshNncuK/q+vXrsXHjRjz99NMI1kyPpqWlISQkBKGhobj99tsRHh6Ow4cPN3Ikwpewrj3BblCLePkHbyqe3o0gvP7ciUYLbs/yUQOcI/uBWrvyOiHFEIuq1oJIHUX50YNKZ1BNcM5unAjpsWeVro0BjF7mchi8qP6XstbBRYgCUSfJmvqOvFyfN4fRFYjGCqw/J4SARUVDeuBJwDmjnLmv+VbGfkDXoMigAlEtWpkLjondsMgvGfQFCxY0+r7NZkNtbS3y8vLQubMyvZednY2kpKQG9/n222/x73//Gy+88ALi4hoPWESTRrRF2G1TwfdsU4rCKsohv/c3BD3yu4Z30OnPG/4cGA1L7AL+83YAgD37F6DvYK+fQzubQPaKLSS5G7D1G+V1tnGFovLmr8DfXaU+eJlMYNNmQ7qmfqY5EFHcXPoBjs8u370VbIzmIb2iHDifpywEBektSw2GmS1AxwTg3GnFzeV0NtC1p+9OqLVYtFKATlwa1vsKsLF3g3/+AQCAf7oWvFdfsO6XGTwyPby6Sl9rkmpAg6I6sJ59XU5E/OgBcM6FjRGFqDQzm80YOnQo1q1bB5vNhszMTOzcuRMjR450u/3mzZvx3nvv4bnnnkPHOnqmgoICZGZmwm63o7q6Gp9++ilKSkrQq5fxH4y2DAsNhfTrx9QVu38E37W1we0DJYPONAUvdh+1kNcViJK9YotgKf4tAKwLr62FvO5N8H++rgbnke0gzf1TqwnOnbBBWjeXOs1VcjUPR52TwYJD/DSqpqErFPV1QXHhOfW1wBaLhFiw8fcA3R2e4rIMOX2poq0WiazjQG2t8rpTIlh4pLHjAZRmZM4mg0UFinWloAgRoAPAzJkzUV1djVmzZmHZsmWYNWuWK4N++PBhTJ+uNr55//33UVZWht/97neYPn06pk+fjr///e8AFGlMRkYG7r//fjz88MP4+eef8cwzzyAyUoAPRhuHpfUDG3Gja1leu8rtHxTFwUVsD3QXmuY3vpC48MJ84KyjoUJwCNBDrAxJwJHYVZ0azjsFXuVb+YIWXlEO+fU/gm/4j2480rOvCJf58gY6mcsvmTqZizbo1T40CYO2aZKPH+S4JoNOEheiqbCgIEgz/w+wRCgrigogv71cKGcSnbylm/HyFkD5vWm92LnAMhchikQBICIiAk899ZTb93r37o01a9a4lt94440Gj5OUlISlS5d6fXyEd2B33Qe+/yeguAgoKQb/YDXY/b/Rb3ShEKisUF5bwoF2sf4faFPp0EmxjqqugnyhEHjuEcUfuF0MEB2rjD06Vll2vIY5rMlTavyQmj1Hjz6KTzPRbJg5TJEvnD0FcFnxl/fDFwc/d0YpBj2r6V434CpIM55QxtQKYZFRdWQuW8DGTFDe1GalRdKfO2DJ3dRpcF975ms90EniQngAi2sP6b45SmMzAPh5G/j3/wMbPc7YgTnQ+p/74+9sU2E9+6oz00cPAMPEnL0UJkAn2gbMEgFp6iOQ33gJAMC3fgM+ZKReW10ney6qPgxQGjIhqavaKe3caeDcadTNYeiWQ0IdwXsMmDNodwT0rJ36GmHhgFbe0kfMzpeBBkvuBu4IlHnOCZ9ndvihnyH/bTFQUeZax8ZNArttSqv3s2eDh7tqKPhPWwBHgM5zNAWi2gZSoqAd0+kscHsNmMn7Pu28tha4oCmgjSWJC+EZbMBVYNfd6moEyD94E7xbb51Mywg454rbjAPmlOMIgF6HThl0gnDB+g9VvrgdulR5zRuQFix3ZRIDRX/uRLr1V5Dfeg0oKW7aDtVVSoHc+bzGA/ngEFWnDNKfe42UVGDHRuW1j+UL8rbvwN9aphQbAkBwCNi9j0MaOsqn5xUFNuAq8HdWKD//L5lK0xJLOHDujGMDSZEdCQYLjwCsHRV9qt2uFK37IuApLlI/G5HtaIaMaBbsrvsUqUbuScBuh5y+BNKzfzF2di4/T+1+bYlQZi5FoUt3ICQEqK4G8s+CFxWACeYlDwikQSfaFuyeWYCzYKTwvL5tcaDozx2wvgMhLf0H2q9ZD+mF1yE98aLSbe+Oe8GuH68Uy3W/DGjfSfmj0FRqqtUv73axQII4TheBjL+sFuVNX4Kvfk13DaV5L7eZ4BxQOk8i7QrXMt+1Fcg5CTh1svFJYKGCBqX++Jzo5C3GNXAhAhsWHALpwXlAqMOa+uxp8LV/M3RM/LiqP0e3NKFmC5kpGEgVX4dOGXTCEFhUDNjkmeCrXwUA8G8/A79yBFi3NH0GvbO4FotaGGOQIqKUjH98MhoS5XDOgcpypbV3cRH4xSLXa1y8AF5cqC5r/JfZDbcJLfUJKLSZ0NM54DU1Xm8zL2/4FHxdhroiIQXSbxaACdzG3Vewwde4ain4ri1qkS5g+DR8Y7DkVPDdDqepnF8A3OD1c+g90EneQjQf1ikRbMrD4G+9BgDgP34LufcVkK4efYk9fYS2QFQAe8W6sJ59wTMdzdKOHgAETJxQgE4YBrvqWvAdG4EDuwHOIf9jOaTnXwXytB7o4mfQPYExpkz3WSKAzkmNB/K2SiVQDw4Go+ya12CWCGU2I/+sIiE6k6N37Wgh8v/+Bf6JWtSOlO6QfrtAySa3QerJXLRabgELRJ2wFD8Uimoz6HFUIEq0DGnYdZAP7wXf9h0AgL+7ErxrT7BO/peXaAtERXFw0cJ69hFehy7OnAPR5mCMQZr2qOpJmpcLvmaFEpgCShDbLsa4ARoIYwwszALWOZGCc1+Q7H0/dM455H+/ow/Ou6VBevKPbTY4Bxwyl96qzAVH9qvvefHByOtos/u5J5SCTm9TpGlSRB7ohBdgUx8GOjjax1fZIKcvAa+p8esY5IpyVarKJN82+mouXXsCJkeO+uwp8JILxo7HDRSgE4bC4jqA3flr1zL/8Vv1TcEdXIjARdda3gsBOucc/IPVrs5+AIBel0P67QtglvAWHz/Q0TYtUlcyIQtEnbCoGCDaIUmqrgbOnvb6OXQSlzh6ECdaDjOHQXponhp85pwA/+htv46h5uhBtc4kqYuQVrIsJFT/4CBgFp0CdMJw2Khb1I5o2vWtTN5CiIOuULSFnSK5LCtTydoGRH0HQZrzeyG/mIyADbgKCArSr+yUKP7vJ8XHhaIFWokLZdAJ78CSu4HdNcO1zL/5L/jP2/12/hrtLJmA8hYnrEdf12sRZS4UoBOGwyQJ0r2PA3V9hilAJ3yFVr5wKqvZ8gVeWwv+9jLwjevVlQOugvToM2SZp6GezAViF4g60Y3RywE6l+U6EhfSoBPeg103DrhiiGtZfvuvis2pH6jJVAN0dBPH/7wurFcf12t+9ICBI3EPFYkSQsA6JYLdOllnt8jiA8PBhQg8WGQ7INYKFBUodpZ5uUBHzyQG3G4Hf/MvLj9/AGBDRoHN+K3STprQwQZdA35gt7pC4AJRJ/qOoo0H6JxzxXmpvExpSuX4x8vLgfJSdV15OXhFmbLO7tAGWyLAwiy+/WGINgVjTOky+uJvlWZY5aWQM16BNPcln/594nKtInFxjkNABxcX3XorM3u1tcDpbPCyEqHqhShAJ4SB3XQH+O4flUxVmCUgvsCJACa5mxKgwxF89R/c5F15TbXSHXTvDtc6NuJGsGmPKN1liXq43FwcsxVCF4g60XYUzT4B+T9rHUF2KXhFueO1JiC32xs+VmNQITjhA1hEFKRZ/wd5yTMAl4Fjh8A/Wwc2YYrvTnomV7k3AMXkQeDPNgs1K/f4yaPKiuOHgP5XGTsoDRSgE8LATCZIT74IvvVbsF6XU3Ed4VNYcjdVl+mBjR6vqoK84iXA0cIeANh1t4JNnilUMw7RYOGRYFeNBt+yQZFziOjsUJeYOCCyndIRsaoS/LP3vX8Okwns+vHePy5BAGA9LgO77R7w/7wLAOCfrwPv1RcsrZ9PzsdP1GlQJLjRA+vZF/x0lpJNDxZLlkgBOiEULDwS7IYJRg+DaAPo5AtNLBTllRWQl78IHDukHufmO8Hu+LXwX0QiwKY9Anb1dYqzQ7AHXXUNgjEG1ru/0q+hKZiCgXBHnwNLOBAeqfjuhzuWHT0QWHgkEO5Yjo6jZAThU9jYu5SmPEf2Kz1HMv4C6Q/LFKmft9F0EBW5QNQJG3s32MSpSndRwaAAnSCItklKHZ9rWW50c15eBnnZAnU6FACbMAVs3GQKzpsIMwUDvfpeekOBYJNnAO07AhXlgCawZs6GY+ERrqCcCoMJEWFSEKSZT0J+4TdAWQlwsQjy6tcgTXkIiLGCmbwXCnJtB1GBC0SdiPxwTAE6QRBtk3axQFQ0UFIMVNlQm5cLhLr/Y81LL0J+9fdA7knXOnb3/ZBuvN1foyUMgkXFgE2cZvQwCKJFsOg4SDOegPzXF5QVB3ZBfuZBQJKAGCtg7Qhm7aBoxq0dlQZ51o5AVEyTpXu89CJw/oyyYDLpazgIjxEqQC8rK8PKlSuxb98+REZGYsqUKRg+fLjbbT/44AN88sknMGme/JYuXYqODieGrKwsrFy5EqdPn0ZCQgIeeeQRdOnSxR8/BkEQAQBjTPkCObALAFBz4gjQe2C97XhxIeS//F5xenHuO+VhSKPH+m2sBEEQLYVdPgjsxtvBv/pEXSnLQOF5oPA8+BF1tVP+h+AQxaNfE7S7gndrJ7DwCHUnTfYcKd3BgsWTjQQSQgXoGRkZMJlMSE9PR1ZWFl5++WWkpKQgKcm93d7VV1+NOXPm1Ftvt9uxePFijB07FjfddBO+/vprLF68GH/96191AT1BEG0bltwN3BGg2385Wi9A54XnIb/yHJB/1rGDBHbv45Cuud7fQyUIgmgx7PbpgMmk+H7nnwMuFjW+Q42ji+7Z02rNjvb9sHDAmXm/eEE9TwDoz0VHmGjVZrNh+/bteOWVV2A2m5GWlobBgwdj06ZNmDp1qkfHOnjwIGprazFu3DgwxjB27Fj897//xYEDB9C/f38f/QQEQQQaLCXV9WVjP3FE9x4/f0YJzh1WjAgKAnvgSUhXjvDvIAmCILwEM5mUIN0Br64CCvOBgnPgBed0/6PgnGIf2hiV5Yr0TyP/AyhA9wbCBOh5eXkICgpCfHy8a11KSgoOHTrU4D67du3C/fffj5iYGNx888248cYbAQC5ublISUnRFW6lpKQgNzeXAnSCIFQ0GsmaE0fBOAdjDPxMjiJrcWaXTCZIDz0FJpBHLkEQREthIaFA50SgcyLclbrzinJXsM4Lz9cP4Kur6h/TbAF69HFzNMIThAnQbTYbwsLCdOssFgtsNpvb7YcNG4YxY8YgOjoax44dwyuvvAKLxYLhw4fDZrPBYrHUO1ZlZaXbY23YsAEbNmwAACxcuBBWq9ULP5FnmEwmQ85LeA+6hoEHj4tDfkQkeFkpeHkp4uQayBVluPDKc0rxKACEhCD66YUIHUDBuejQPRj40DUUDSuQnOL2Hc45+MULqD2fh9pzZ1B7Pg9y6UVYrhqFoK5UINpS/BagL1iwoMFseK9evTBjxox6AXRlZSXMZrPbfRITE3X7jx07Ftu2bcPw4cNhNpvrHauioqLeA4CTMWPGYMyYMa7lgoKCJv1M3sRqtRpyXsJ70DUMTHhSKnB4LwCg8JO14Ju/VCz1ACA0DNLjz6M0qTtK6doKD92DgQ9dwwAktqPyr/cAAEAkXcMmo1WN1MWvAXpj2Gw21NbWIi8vD507dwYAZGdnN1gg2hhJSUn47LPPwB3T1QCQk5ODm2++2eNjEQTRumHJqeCOAJ1/+bH6hiUc0pw/kJaSIAiC8DvC9KU2m80YOnQo1q1bB5vNhszMTOzcuRMjR450u/3OnTtRVlYGzjmOHz+OL774AoMHDwYA9OnTB5Ik4YsvvkBNTQ3Wr18PAOjbN7AaZBAE4QfcefVGREGa+ycKzgmCIAhDEEaDDgAzZ87EihUrMGvWLERERGDWrFmuDPrhw4fx5z//GWvWrAEAbNmyBStXrkRNTQ3i4uIwYcIEXHvttQAUDdu8efOwatUqvPvuu0hMTMS8efPIYpEgiHqw5G5627B2MZCe/CNYfLJRQyIIgiDaOIxzzi+9WdvizJkzfj8n6e4CH7qGgQmXZch/fAI4dRKItUJ68k9gHRvWBRLiQvdg4EPXMPCha9h0hNCgEwRBiAiTJEhPvojIszkoTewGFma59E4EQRAE4UOE0aATBEEYBYtsB/PVoyk4JwiCIISAAnSCIAiCIAiCEAgK0AmCIAiCIAhCIChAJwiCIAiCIAiBoACdIAiCILJOCA4AAAnDSURBVAiCIASCAnSCIAiCIAiCEAgK0AmCIAiCIAhCIChAJwiCIAiCIAiBoE6iBEEQBEEQBCEQlEEXhKefftroIRAthK5hYEPXL/Chaxj40DUMfOgaegcK0AmCIAiCIAhCIChAJwiCIAiCIAiBCFqwYMECowdBKKSmpho9BKKF0DUMbOj6BT50DQMfuoaBD13DlkNFogRBEARBEAQhECRxIQiCIAiCIAiBoACdIAiCIAiCIASCAnSCIAiCIAiCEAiT0QNo65SVlWHlypXYt28fIiMjMWXKFAwfPtzoYREesGDBAhw7dgySpDzvxsbGYtmyZQaPimiI9evX4/vvv0dOTg6uueYazJ492/Xe/v378eabb6KgoAA9evTAo48+ivbt2xs4WsIdDV3D8+fP47HHHkNoaKhr2wkTJuCuu+4yaqiEG2pqapCRkYH9+/ejrKwMHTt2xJQpUzBgwAAAdB8GAo1dQ7oPvQMF6AaTkZEBk8mE9PR0ZGVl4eWXX0ZKSgqSkpKMHhrhATNmzMD1119v9DCIJhATE4M77rgDe/fuRXV1tWt9SUkJli5diocffhiDBg3CunXr8Nprr+Gll14ycLSEOxq6hk7efvttBAUFGTAyoinU1tYiLi4OCxYsgNVqxZ49e/Dqq69i6dKlMJvNdB8GAI1dQyd0H7YMkrgYiM1mw/bt2zF58mSYzWakpaVh8ODB2LRpk9FDI4hWy9ChQzFkyBBERkbq1u/YsQNJSUm4+uqrERISgrvvvhtZWVk4ffq0QSMlGqKha0gEBmazGZMmTUKHDh0gSRIGDRqEDh064MSJE3QfBgiNXUPCO1AG3UDy8vIQFBSE+Ph417qUlBQcOnTIwFERzWHt2rVYu3Yt4uPj8atf/Qp9+vQxekiEh+Tm5iIlJcW1bDab0alTJ+Tm5iIhIcHAkRGe8uijj4Ixhn79+mHatGmIiooyekhEIxQXFyMvLw9JSUn46quv6D4MQLTX0Andhy2DAnQDsdlsCAsL062zWCyw2WwGjYhoDlOnTkViYiJMJhO2bNmCRYsWYfHixejUqZPRQyM8wGaz1fsCofsxsIiKisLLL7+MLl26oLS0FG+++SaWL1+OZ5991uihEQ1gt9uxfPlyjBo1CgkJCXQfBiDuriHdhy2HJC4GYjabUVlZqVtXWVkJs9ls0IiI5tCjRw+EhYUhODgY1157LXr16oU9e/YYPSzCQ9zdjxUVFXQ/BhBmsxndunVDUFAQoqOj8cADD2Dv3r31rishBrIs4/XXX4fJZMKMGTMA0H0YaDR0Dek+bDkUoBtI586dUVtbi7y8PNe67OxsKhANcBhjoAa9gUdSUhKys7NdyzabDefOnaP7sRVA96N4cM6xatUqXLx4EXPnzoXJpEzo030YODR0DRvbnmg6FKAbiNlsxtChQ7Fu3TrYbDZkZmZi586dGDlypNFDI5pIeXk5fv75Z1RXV6O2thabN2/G4cOH0b9/f6OHRjRAbW0tqqurIcsyZFl2XbshQ4YgJycH27ZtQ3V1NT788EOkpKSQ7lVAGrqGx44dw5kzZyDLMkpLS/HWW2+hT58+sFgsRg+ZqEN6ejpOnz6N+fPnIyQkxLWe7sPAoaFrSPehd2CcHmkMpaysDCtWrMD+/fsRERGBqVOnkg96AFFSUoKXX34Zp0+fhiRJSEhIwOTJk9GvXz+jh0Y0wAcffIAPP/xQt+6uu+7CpEmTsG/fPqxevRr5+fku/+UOHToYNFKiIRq6hvHx8XjvvfdQUlKCsLAwV3FadHS0QSMl3JGfn4/Zs2cjODjY1T8CAB588EGMGDGC7sMAoLFryBij+9ALUIBOEARBEARBEAJBEheCIAiCIAiCEAgK0AmCIAiCIAhCIChAJwiCIAiCIAiBoACdIAiCIAiCIASCAnSCIAiCIAiCEAgK0AmCIAiCIAhCIChAJwiCIDxmx44deOSRRzB9+nScPHmy0W3feOMNvP/++wCAw4cP4ze/+Y0/hkgQBBGwNN6XlSAIgghYZs+ejeLiYkiSBLPZjP79++OBBx6A2Wz2+DgPPfSQrgHXmjVrMGPGDFx55ZUeHat3795YtmyZR/sQBEG0NSiDThAE0YqZP38+1qxZg0WLFuHEiRP46KOPmrxvbW1tg+/l5+cjKSnJG0MkCIIg6kAZdIIgiDZAbGws+vfvj9zcXPz0009Yu3YtioqK0KVLF8ycOROJiYkAlGz5DTfcgB9++AFnzpzBkCFDUFBQgEWLFkGSJNx555346KOPIMsy5s2bh+joaCxfvhynTp1CRkYGsrKyEBsbiylTpmDw4MH1xnHw4EEsX74cq1atAoBG99u9ezfWrFmDwsJChIWFYdy4cbjtttv890sjCIIwCArQCYIg2gAFBQXYs2cPkpOTsWzZMsybNw+XXXYZPv/8cyxatAivvvoqTCblK2HLli14+umnERUVhZCQEBw7dkwncZk4cSImTZqEJUuWoFOnTrDb7Vi0aBFGjx6N5557DpmZmVi8eDEWLlyI+Pj4Bsd0qf1WrVqFJ554Ar1790ZZWRnOnz/vl98VQRCE0ZDEhSAIohWzZMkS3Hffffj973+Pyy67DImJiRgwYAD69esHk8mE8ePHo7q6GkeOHHHtc8stt8BqtSIkJKRJ5zh27BhsNhsmTpwIk8mEvn37YuDAgfjhhx9atF9QUBBOnTqFiooKREREIDU1tfm/CIIgiACCMugEQRCtmHnz5umKO9PT09G+fXvXsiRJsFqtKCoqcq2zWq0enePChQuwWq2QJDXn0759e90xm7Pf3Llz8fHHH2Pt2rVITk7G1KlT0bNnT4/GRhAEEYhQBp0gCKINERMTg/z8fNcy5xwFBQWIjY1t0TELCgogy7JrXVOOean9unfvjqeeegrp6em48sor8eqrrzZ7jARBEIEEBegEQRBtiGHDhmHPnj3Yv38/7HY7/vvf/yI4OBi9evVqcJ/o6OhG9d89evRAaGgoPv30U9jtdhw8eBC7du3CNddc0+hYGtvPbrdj8+bNqKiogMlkgsViAWOs2T83QRBEIEESF4IgiDZEfHw8Hn/8caxevdrl4jJ//nxXgag7Jk6ciNWrV+Odd97BHXfcUc9JxWQyYf78+cjIyMAnn3yC2NhYPPbYY0hISGh0LI3tZ7fbsWnTJqxevRqyLCM+Ph5z5szxyu+AIAhCdBjnnBs9CIIgCIIgCIIgFEjiQhAEQRAEQRACQQE6QRAEQRAEQQgEBegEQRAEQRAEIRAUoBMEQRAEQRCEQFCAThAEQRAEQRACQQE6QRAEQRAEQQgEBegEQRAEQRAEIRAUoBMEQRAEQRCEQPw/WVMjEatU+0EAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "def optimizedPortfolio():\n",
        "    n_portfolios = len(pcs)\n",
        "    annualized_ret = np.array([0.] * n_portfolios)\n",
        "    sharpe_metric = np.array([0.] * n_portfolios)\n",
        "    annualized_vol = np.array([0.] * n_portfolios)\n",
        "    highest_sharpe = 0 \n",
        "\n",
        "    for i in range(n_portfolios):\n",
        "        \n",
        "        pc_w = pcs[:, i] / sum(pcs[:, i])\n",
        "        eigen_prtfi = pd.DataFrame(data ={'weights': pc_w.squeeze()*100}, index = stock_tickers)\n",
        "        eigen_prtfi.sort_values(by=['weights'], ascending=False, inplace=True)\n",
        "        \n",
        "        eigen_prti_returns = np.dot(X_test_raw.loc[:, eigen_prtfi.index], eigen_prtfi / n_portfolios)\n",
        "        eigen_prti_returns = pd.Series(eigen_prti_returns.squeeze(), index=X_test.index)\n",
        "        er, vol, sharpe = sharpe_ratio(eigen_prti_returns)\n",
        "        annualized_ret[i] = er\n",
        "        annualized_vol[i] = vol\n",
        "        sharpe_metric[i] = sharpe\n",
        "\n",
        "    # find portfolio with the highest Sharpe ratio\n",
        "    highest_sharpe = np.argmax(sharpe_metric)\n",
        "\n",
        "    print('Eigen portfolio #%d with the highest Sharpe. Return %.2f%%, vol = %.2f%%, Sharpe = %.2f' % \n",
        "          (highest_sharpe,\n",
        "           annualized_ret[highest_sharpe]*100, \n",
        "           annualized_vol[highest_sharpe]*100, \n",
        "           sharpe_metric[highest_sharpe]))\n",
        "\n",
        "\n",
        "    fig, ax = plt.subplots()\n",
        "    fig.set_size_inches(12, 4)\n",
        "    ax.plot(sharpe_metric, linewidth=3)\n",
        "    ax.set_title('Sharpe ratio of eigen-portfolios')\n",
        "    ax.set_ylabel('Sharpe ratio')\n",
        "    ax.set_xlabel('Portfolios')\n",
        "\n",
        "    results = pd.DataFrame(data={'Return': annualized_ret, 'Vol': annualized_vol, 'Sharpe': sharpe_metric})\n",
        "    results.dropna(inplace=True)\n",
        "    results.sort_values(by=['Sharpe'], ascending=False, inplace=True)\n",
        "    print(results.head(10))\n",
        "\n",
        "    plt.show()\n",
        "\n",
        "optimizedPortfolio()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "id": "z2WAWJ_iML6c",
        "outputId": "3fea3b59-1585-47d1-ce81-3eab8736542c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Sum of weights of current eigen-portfolio: 100.00\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "        weights\n",
              "NKE   21.756781\n",
              "MCD   17.083256\n",
              "JPM   16.051491\n",
              "AXP   13.932022\n",
              "BA    12.613809\n",
              "PFE   12.433935\n",
              "XOM   11.696040\n",
              "GS     8.975823\n",
              "MSFT   8.091432\n",
              "MMM    7.695248\n",
              "UTX    7.646166\n",
              "UNH    7.542567\n",
              "CVX    7.201652\n",
              "WMT    4.345706\n",
              "IBM    3.288317\n",
              "INTC   2.845518\n",
              "KO     1.549044\n",
              "HD     1.326262\n",
              "CAT    1.034091\n",
              "AAPL   0.352664\n",
              "CSCO  -1.274397\n",
              "VZ    -2.599362\n",
              "DIS   -3.594352\n",
              "WBA   -4.074086\n",
              "MRK   -6.104985\n",
              "TRV   -8.858042\n",
              "JNJ  -12.990403\n",
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          },
          "metadata": {},
          "execution_count": 37
        }
      ],
      "source": [
        "def PCWeights():\n",
        "    '''\n",
        "    Principal Components (PC) weights for each 28 PCs\n",
        "    '''\n",
        "    weights = pd.DataFrame()\n",
        "\n",
        "    for i in range(len(pcs)):\n",
        "        weights[\"weights_{}\".format(i)] = pcs[:, i] / sum(pcs[:, i])\n",
        "\n",
        "    weights = weights.values.T\n",
        "    return weights\n",
        "\n",
        "weights = PCWeights()\n",
        "portfolio = portfolio = pd.DataFrame()\n",
        "\n",
        "def plotEigen(weights, plot=False, portfolio=portfolio):\n",
        "    portfolio = pd.DataFrame(data ={'weights': weights.squeeze()*100}, index = stock_tickers) \n",
        "    portfolio.sort_values(by=['weights'], ascending=False, inplace=True)\n",
        "    \n",
        "    if plot:\n",
        "        print('Sum of weights of current eigen-portfolio: %.2f' % np.sum(portfolio))\n",
        "        portfolio.plot(title='Current Eigen-Portfolio Weights', \n",
        "            figsize=(12,6), \n",
        "            xticks=range(0, len(stock_tickers),1), \n",
        "            rot=45, \n",
        "            linewidth=3\n",
        "            )\n",
        "        plt.show()\n",
        "\n",
        "    return portfolio\n",
        "\n",
        "# Weights are stored in arrays, where 0 is the first PC's weights.\n",
        "plotEigen(weights=weights[4], plot=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {
        "id": "livSWkMuML6d",
        "outputId": "42bfbae1-1664-4a3c-843a-3d3d1bcee2f3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Current Eigen-Portfolio:\n",
            "Return = 59.10%\n",
            "Volatility = 65.53%\n",
            "Sharpe = 0.90\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "def plotSharpe(eigen):\n",
        "\n",
        "    '''\n",
        "\n",
        "    Plots Principle components returns against real returns.\n",
        "    \n",
        "    '''\n",
        "\n",
        "    eigen_portfolio_returns = np.dot(X_test_raw.loc[:, eigen.index], eigen / len(pcs))\n",
        "    eigen_portfolio_returns = pd.Series(eigen_portfolio_returns.squeeze(), index=X_test.index)\n",
        "    returns, vol, sharpe = sharpe_ratio(eigen_portfolio_returns)\n",
        "    print('Current Eigen-Portfolio:\\nReturn = %.2f%%\\nVolatility = %.2f%%\\nSharpe = %.2f' % (returns*100, vol*100, sharpe))\n",
        "    year_frac = (eigen_portfolio_returns.index[-1] - eigen_portfolio_returns.index[0]).days / 252\n",
        "\n",
        "    df_plot = pd.DataFrame({'PC': eigen_portfolio_returns, 'DJIA': X_test_raw.loc[:, 'DJIA']}, index=X_test.index)\n",
        "    np.cumprod(df_plot + 1).plot(title='Returns of the market-cap weighted index vs. First eigen-portfolio', \n",
        "                             figsize=(12,6), linewidth=3)\n",
        "    plt.show()\n",
        "\n",
        "plotSharpe(eigen=plotEigen(weights=weights[4]))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XN8F03KHML6d"
      },
      "source": [
        "## Investigating Hierarchical Clustering"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
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        "id": "tXZ8qFz9ML6d",
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        {
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              "                 MMM       AXP      AAPL        BA       CAT       CVX  \\\n",
              "Date                                                                     \n",
              "2000-01-04 -2.783305 -1.714531 -3.315064 -0.118649 -0.672149 -0.030177   \n",
              "2000-01-05  3.491453 -0.250475  0.522450  3.667073  1.828679  1.321853   \n",
              "2000-01-06  3.995818 -0.021248 -3.400666  0.108313  1.770951  2.389941   \n",
              "2000-01-07  1.337698  0.604016  1.791770  1.497066  1.573522  1.067883   \n",
              "2000-01-10 -0.371257  0.624764 -0.727008 -0.780316 -1.653060 -1.711071   \n",
              "\n",
              "                CSCO        KO       DIS       XOM  ...       NKE       PFE  \\\n",
              "Date                                                ...                       \n",
              "2000-01-04 -2.304726  0.236964  3.089027 -1.283097  ... -2.927985 -2.410473   \n",
              "2000-01-05  0.305449  0.823741  1.857074  3.247575  ...  3.023666  1.148279   \n",
              "2000-01-06 -1.119210 -0.104682 -1.845881  3.696220  ... -0.316511  2.151911   \n",
              "2000-01-07  2.382987  5.050971 -0.867545 -0.216324  ... -0.041103  4.320217   \n",
              "2000-01-10  1.482524 -2.486755  8.090552 -0.944732  ...  0.855881 -0.131547   \n",
              "\n",
              "                  PG       TRV       UTX       UNH        VZ       WMT  \\\n",
              "Date                                                                     \n",
              "2000-01-04 -1.504783 -0.763609 -2.479568 -0.698935 -2.097284 -2.506437   \n",
              "2000-01-05 -0.671468  0.510782 -0.588825 -0.164440  2.128033 -1.568817   \n",
              "2000-01-06  2.659281  0.070428  2.165327  1.801922 -0.346058  0.914757   \n",
              "2000-01-07  5.999317  2.158221  2.340150  5.871398 -0.496143  5.006585   \n",
              "2000-01-10 -0.413525 -1.026003  0.558540 -0.923939 -0.357794 -1.231132   \n",
              "\n",
              "                 WBA      DJIA  \n",
              "Date                            \n",
              "2000-01-04 -2.167895 -2.739489  \n",
              "2000-01-05  0.502376  1.631646  \n",
              "2000-01-06 -1.584911  0.181378  \n",
              "2000-01-07  1.453883  3.054606  \n",
              "2000-01-10  1.667529  0.250687  \n",
              "\n",
              "[5 rows x 29 columns]"
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              "      <th>MMM</th>\n",
              "      <th>AXP</th>\n",
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              "      <th></th>\n",
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              "      <th>2000-01-04</th>\n",
              "      <td>-2.783305</td>\n",
              "      <td>-1.714531</td>\n",
              "      <td>-3.315064</td>\n",
              "      <td>-0.118649</td>\n",
              "      <td>-0.672149</td>\n",
              "      <td>-0.030177</td>\n",
              "      <td>-2.304726</td>\n",
              "      <td>0.236964</td>\n",
              "      <td>3.089027</td>\n",
              "      <td>-1.283097</td>\n",
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              "      <td>-2.927985</td>\n",
              "      <td>-2.410473</td>\n",
              "      <td>-1.504783</td>\n",
              "      <td>-0.763609</td>\n",
              "      <td>-2.479568</td>\n",
              "      <td>-0.698935</td>\n",
              "      <td>-2.097284</td>\n",
              "      <td>-2.506437</td>\n",
              "      <td>-2.167895</td>\n",
              "      <td>-2.739489</td>\n",
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              "      <th>2000-01-05</th>\n",
              "      <td>3.491453</td>\n",
              "      <td>-0.250475</td>\n",
              "      <td>0.522450</td>\n",
              "      <td>3.667073</td>\n",
              "      <td>1.828679</td>\n",
              "      <td>1.321853</td>\n",
              "      <td>0.305449</td>\n",
              "      <td>0.823741</td>\n",
              "      <td>1.857074</td>\n",
              "      <td>3.247575</td>\n",
              "      <td>...</td>\n",
              "      <td>3.023666</td>\n",
              "      <td>1.148279</td>\n",
              "      <td>-0.671468</td>\n",
              "      <td>0.510782</td>\n",
              "      <td>-0.588825</td>\n",
              "      <td>-0.164440</td>\n",
              "      <td>2.128033</td>\n",
              "      <td>-1.568817</td>\n",
              "      <td>0.502376</td>\n",
              "      <td>1.631646</td>\n",
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              "    <tr>\n",
              "      <th>2000-01-06</th>\n",
              "      <td>3.995818</td>\n",
              "      <td>-0.021248</td>\n",
              "      <td>-3.400666</td>\n",
              "      <td>0.108313</td>\n",
              "      <td>1.770951</td>\n",
              "      <td>2.389941</td>\n",
              "      <td>-1.119210</td>\n",
              "      <td>-0.104682</td>\n",
              "      <td>-1.845881</td>\n",
              "      <td>3.696220</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.316511</td>\n",
              "      <td>2.151911</td>\n",
              "      <td>2.659281</td>\n",
              "      <td>0.070428</td>\n",
              "      <td>2.165327</td>\n",
              "      <td>1.801922</td>\n",
              "      <td>-0.346058</td>\n",
              "      <td>0.914757</td>\n",
              "      <td>-1.584911</td>\n",
              "      <td>0.181378</td>\n",
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              "    <tr>\n",
              "      <th>2000-01-07</th>\n",
              "      <td>1.337698</td>\n",
              "      <td>0.604016</td>\n",
              "      <td>1.791770</td>\n",
              "      <td>1.497066</td>\n",
              "      <td>1.573522</td>\n",
              "      <td>1.067883</td>\n",
              "      <td>2.382987</td>\n",
              "      <td>5.050971</td>\n",
              "      <td>-0.867545</td>\n",
              "      <td>-0.216324</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.041103</td>\n",
              "      <td>4.320217</td>\n",
              "      <td>5.999317</td>\n",
              "      <td>2.158221</td>\n",
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              "      <th>2000-01-10</th>\n",
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            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ],
      "source": [
        "data.head()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {
        "id": "zKe7_aKCML6d",
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        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import matplotlib.cm as cm\n",
        "\n",
        "#A messy plot of all the processed adjusted closing prices\n",
        "%matplotlib inline\n",
        "plt.plot(data);\n",
        "plt.xticks(rotation='vertical');\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "id": "yD9xUDZeML6d",
        "outputId": "10446545-2b83-4551-a25a-7ad60f18f51e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 445
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 504x504 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "#find correlation matrix, i.e. the \"distances\" between each stock\n",
        "corr = data.corr()\n",
        "size = 7\n",
        "fig, ax = plt.subplots(figsize=(size, size))\n",
        "ax.matshow(corr,cmap=cm.get_cmap('coolwarm'), vmin=0,vmax=1)\n",
        "plt.xticks(range(len(corr.columns)), corr.columns, rotation='vertical', fontsize=8);\n",
        "plt.yticks(range(len(corr.columns)), corr.columns, fontsize=8);\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LaJ7qrnjML6d"
      },
      "source": [
        "### Clusters of Correlation - Agglomerate"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VmbRB319ML6d"
      },
      "source": [
        "\n",
        "\n",
        "The next step is to look for clusters of correlations using the agglomerate hierarchical clustering technique. Its primary advantage over other clustering methods is that you don't need to guess in advance how many clusters there might be. Agglomerate Clustering first assigns each data point into its own cluster, and gradually merges clusters until only one remains. It's then up to the user to choose a cutoff threshold and decide how many clusters are present.\n",
        "\n",
        "Linkage does the actual clustering in one line of code, and returns a list of the clusters joined in the format: Z=[stock_1, stock_2, distance, sample_count]\n",
        "\n",
        "There are also different options for the measurement of the distance. The option we will choose is the average distance measurement, but others are possible (ward, single, centroid, etc.).\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "id": "jyfWLWiFML6d",
        "outputId": "089c2463-f31c-4da0-8b52-6a47cd06d053",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([5.        , 9.        , 0.27207065, 2.        ])"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ],
      "source": [
        "from scipy.cluster.hierarchy import dendrogram, linkage\n",
        "Z = linkage(corr, 'average')\n",
        "Z[0]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qg2NW6OKML6d"
      },
      "source": [
        "### Cophenetic Correlation coefficient"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2VGuAOAzML6e"
      },
      "source": [
        "It's important to get a sense of how well the clustering performs. One measure is the Cophenetic Correlation Coefficient, c. This compares (correlates) the actual pairwise distances of all your samples to those implied by the hierarchical clustering. The closer c is to 1, the better the clustering preserves the original distances. Generally c > 0.7 is consistered a good cluster fit. Of course, other accuracy checks are possible."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {
        "id": "1UyfxhKmML6e",
        "outputId": "25466204-182c-45a3-c5b9-0cd6f1853fa0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.7996812457331596"
            ]
          },
          "metadata": {},
          "execution_count": 43
        }
      ],
      "source": [
        "from scipy.cluster.hierarchy import cophenet\n",
        "from scipy.spatial.distance import pdist\n",
        "import pylab\n",
        "c, coph_dists = cophenet(Z, pdist(corr))\n",
        "c"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o6IIdf2rML6e"
      },
      "source": [
        "### Dendogram"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vjN6LF9sML6e"
      },
      "source": [
        "The best way to visualize an agglomerate clustering algorithm is through a dendogram, which displays a cluster tree, the leaves being the individual stocks and the root being the final single cluster. The \"distance\" between each cluster is shown on the y-axis, and thus the longer the branches are, the less correlated two clusters are."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {
        "id": "XpKyvZuqML6e",
        "outputId": "27640816-16fc-4bba-f4fe-acfc4e214e57",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 509
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1800x720 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.figure(figsize=(25, 10))\n",
        "labelsize=20\n",
        "ticksize=15\n",
        "plt.title('Hierarchical Clustering Dendrogram for '+\"DJIA\", fontsize=labelsize)\n",
        "plt.xlabel('stock', fontsize=labelsize)\n",
        "plt.ylabel('distance', fontsize=labelsize)\n",
        "dendrogram(\n",
        "    Z,\n",
        "    leaf_rotation=90.,  # rotates the x axis labels\n",
        "    leaf_font_size=8.,  # font size for the x axis labels\n",
        "    labels = corr.columns\n",
        ")\n",
        "pylab.yticks(fontsize=ticksize)\n",
        "pylab.xticks(rotation=-90, fontsize=ticksize)\n",
        "plt.savefig('dendogram_'+'DJIA'+'.png')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vMf7FmrpML6e"
      },
      "source": [
        "According to the dendogram above, the two most correlated stocks are CVX and XOM. That is Chevron Corporation and ExxonMobil. Both businesses are oil corporations, so it makes sense that they would be strongly correlated. Let's plot them below to visually see how well they correlate. In addition, let's pick two stocks that are not well correlated at all to compare to, say, MCD and JPM."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {
        "id": "sKW-4UISML6e",
        "outputId": "16cd9a88-149b-4a07-d47c-d02eea033f1e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 305
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x288 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "#plot sample correlations\n",
        "f, (ax1, ax2) = plt.subplots(1, 2, figsize=(10,4), sharey=True)\n",
        "plt.subplots_adjust(wspace=0.05)\n",
        "\n",
        "#high correlation\n",
        "sA = \"CVX\"\n",
        "sB = \"XOM\"\n",
        "ax1.plot(data[sA],label=sA)\n",
        "ax1.plot(data[sB],label=sB)\n",
        "ax1.set_title('Stock Correlation = %.3f'%corr[sA][sB])\n",
        "ax1.set_ylabel('Normalized Adj Close prices')\n",
        "ax1.legend(loc='upper left',prop={'size':8})\n",
        "plt.setp(ax1.get_xticklabels(), rotation=70);\n",
        "\n",
        "#low correlation\n",
        "sA = \"MCD\"\n",
        "sB = \"JPM\"\n",
        "ax2.plot(data[sA],label=sA)\n",
        "ax2.plot(data[sB],label=sB)\n",
        "ax2.set_title('Stock Correlation = %.3f'%corr[sA][sB])\n",
        "ax2.legend(loc='upper left',prop={'size':8})\n",
        "plt.setp(ax2.get_xticklabels(), rotation=70);"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZwMj7pmlML6e"
      },
      "outputs": [],
      "source": [
        ""
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.6.3"
    },
    "colab": {
      "name": "PCA.ipynb",
      "provenance": [],
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}