tutorials/W1D5_DimensionalityReduction/W1D5_Tutorial3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/NeuromatchAcademy/course-content/blob/master/tutorials/W1D5_DimensionalityReduction/W1D5_Tutorial3.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "a1pq-AcBBJ5L"
   },
   "source": [
    "# Neuromatch Academy: Week 1, Day 5, Tutorial 3\n",
    "# Dimensionality Reduction and reconstruction\n",
    "\n",
    "__Content creators:__ Alex Cayco Gajic, John Murray\n",
    "\n",
    "__Content reviewers:__ Roozbeh Farhoudi, Matt Krause, Spiros Chavlis, Richard Gao, Michael Waskom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "_coTqnWnBo7V"
   },
   "source": [
    "---\n",
    "# Tutorial Objectives\n",
    "\n",
    "In this notebook we'll learn to apply PCA for dimensionality reduction, using a classic dataset that is often used to benchmark machine learning algorithms: MNIST. We'll also learn how to use PCA for reconstruction and denoising.\n",
    "\n",
    "Overview:\n",
    "- Perform PCA on MNIST\n",
    "- Calculate the variance explained\n",
    "- Reconstruct data with different numbers of PCs\n",
    "- (Bonus) Examine denoising using PCA\n",
    "\n",
    "You can learn more about MNIST dataset [here](https://en.wikipedia.org/wiki/MNIST_database)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 518
    },
    "colab_type": "code",
    "id": "o3An8t_BXkpj",
    "outputId": "917065c1-9a21-462b-b1f6-0c13a6b9e0fa"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Video available at https://youtube.com/watch?v=oO0bbInoO_0\n"
     ]
    },
    {
     "data": {
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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"854\"\n",
       "            height=\"480\"\n",
       "            src=\"https://www.youtube.com/embed/oO0bbInoO_0?fs=1\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7fada3ff24d0>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# @title Video 1: PCA for dimensionality reduction\n",
    "from IPython.display import YouTubeVideo\n",
    "video = YouTubeVideo(id=\"oO0bbInoO_0\", width=854, height=480, fs=1)\n",
    "print(\"Video available at https://youtube.com/watch?v=\" + video.id)\n",
    "video"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Lvd-FYmlXyiH"
   },
   "source": [
    "---\n",
    "# Setup\n",
    "Run these cells to get the tutorial started."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ExhYAoZHv-8_"
   },
   "outputs": [],
   "source": [
    "# Imports\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "cellView": "form",
    "colab": {},
    "colab_type": "code",
    "id": "4GcQOmtlBb8V"
   },
   "outputs": [],
   "source": [
    "# @title Figure Settings\n",
    "import ipywidgets as widgets   # interactive display\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "plt.style.use(\"https://raw.githubusercontent.com/NeuromatchAcademy/course-content/master/nma.mplstyle\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "cellView": "form",
    "colab": {},
    "colab_type": "code",
    "id": "LFts1a8oflAC"
   },
   "outputs": [],
   "source": [
    "# @title Helper Functions\n",
    "\n",
    "\n",
    "def plot_variance_explained(variance_explained):\n",
    "  \"\"\"\n",
    "  Plots eigenvalues.\n",
    "\n",
    "  Args:\n",
    "    variance_explained (numpy array of floats) : Vector of variance explained\n",
    "                                                 for each PC\n",
    "\n",
    "  Returns:\n",
    "    Nothing.\n",
    "\n",
    "  \"\"\"\n",
    "\n",
    "  plt.figure()\n",
    "  plt.plot(np.arange(1, len(variance_explained) + 1), variance_explained,\n",
    "           '--k')\n",
    "  plt.xlabel('Number of components')\n",
    "  plt.ylabel('Variance explained')\n",
    "  plt.show()\n",
    "\n",
    "\n",
    "def plot_MNIST_reconstruction(X, X_reconstructed):\n",
    "  \"\"\"\n",
    "  Plots 9 images in the MNIST dataset side-by-side with the reconstructed\n",
    "  images.\n",
    "\n",
    "  Args:\n",
    "    X (numpy array of floats)               : Data matrix each column\n",
    "                                              corresponds to a different\n",
    "                                              random variable\n",
    "    X_reconstructed (numpy array of floats) : Data matrix each column\n",
    "                                              corresponds to a different\n",
    "                                              random variable\n",
    "\n",
    "  Returns:\n",
    "    Nothing.\n",
    "  \"\"\"\n",
    "\n",
    "  plt.figure()\n",
    "  ax = plt.subplot(121)\n",
    "  k = 0\n",
    "  for k1 in range(3):\n",
    "    for k2 in range(3):\n",
    "      k = k + 1\n",
    "      plt.imshow(np.reshape(X[k, :], (28, 28)),\n",
    "                 extent=[(k1 + 1) * 28, k1 * 28, (k2 + 1) * 28, k2 * 28],\n",
    "                 vmin=0, vmax=255)\n",
    "  plt.xlim((3 * 28, 0))\n",
    "  plt.ylim((3 * 28, 0))\n",
    "  plt.tick_params(axis='both', which='both', bottom=False, top=False,\n",
    "                  labelbottom=False)\n",
    "  ax.set_xticks([])\n",
    "  ax.set_yticks([])\n",
    "  plt.title('Data')\n",
    "  plt.clim([0, 250])\n",
    "  ax = plt.subplot(122)\n",
    "  k = 0\n",
    "  for k1 in range(3):\n",
    "    for k2 in range(3):\n",
    "      k = k + 1\n",
    "      plt.imshow(np.reshape(np.real(X_reconstructed[k, :]), (28, 28)),\n",
    "                 extent=[(k1 + 1) * 28, k1 * 28, (k2 + 1) * 28, k2 * 28],\n",
    "                 vmin=0, vmax=255)\n",
    "  plt.xlim((3 * 28, 0))\n",
    "  plt.ylim((3 * 28, 0))\n",
    "  plt.tick_params(axis='both', which='both', bottom=False, top=False,\n",
    "                  labelbottom=False)\n",
    "  ax.set_xticks([])\n",
    "  ax.set_yticks([])\n",
    "  plt.clim([0, 250])\n",
    "  plt.title('Reconstructed')\n",
    "  plt.tight_layout()\n",
    "\n",
    "\n",
    "def plot_MNIST_sample(X):\n",
    "  \"\"\"\n",
    "  Plots 9 images in the MNIST dataset.\n",
    "\n",
    "  Args:\n",
    "     X (numpy array of floats) : Data matrix each column corresponds to a\n",
    "                                 different random variable\n",
    "\n",
    "  Returns:\n",
    "    Nothing.\n",
    "\n",
    "  \"\"\"\n",
    "\n",
    "  fig, ax = plt.subplots()\n",
    "  k = 0\n",
    "  for k1 in range(3):\n",
    "    for k2 in range(3):\n",
    "      k = k + 1\n",
    "      plt.imshow(np.reshape(X[k, :], (28, 28)),\n",
    "                 extent=[(k1 + 1) * 28, k1 * 28, (k2+1) * 28, k2 * 28],\n",
    "                 vmin=0, vmax=255)\n",
    "  plt.xlim((3 * 28, 0))\n",
    "  plt.ylim((3 * 28, 0))\n",
    "  plt.tick_params(axis='both', which='both', bottom=False, top=False,\n",
    "                  labelbottom=False)\n",
    "  plt.clim([0, 250])\n",
    "  ax.set_xticks([])\n",
    "  ax.set_yticks([])\n",
    "  plt.show()\n",
    "\n",
    "\n",
    "def plot_MNIST_weights(weights):\n",
    "  \"\"\"\n",
    "  Visualize PCA basis vector weights for MNIST. Red = positive weights,\n",
    "  blue = negative weights, white = zero weight.\n",
    "\n",
    "  Args:\n",
    "     weights (numpy array of floats) : PCA basis vector\n",
    "\n",
    "  Returns:\n",
    "     Nothing.\n",
    "  \"\"\"\n",
    "\n",
    "  fig, ax = plt.subplots()\n",
    "  cmap = plt.cm.get_cmap('seismic')\n",
    "  plt.imshow(np.real(np.reshape(weights, (28, 28))), cmap=cmap)\n",
    "  plt.tick_params(axis='both', which='both', bottom=False, top=False,\n",
    "                  labelbottom=False)\n",
    "  plt.clim(-.15, .15)\n",
    "  plt.colorbar(ticks=[-.15, -.1, -.05, 0, .05, .1, .15])\n",
    "  ax.set_xticks([])\n",
    "  ax.set_yticks([])\n",
    "  plt.show()\n",
    "\n",
    "\n",
    "def add_noise(X, frac_noisy_pixels):\n",
    "  \"\"\"\n",
    "  Randomly corrupts a fraction of the pixels by setting them to random values.\n",
    "\n",
    "  Args:\n",
    "     X (numpy array of floats)  : Data matrix\n",
    "     frac_noisy_pixels (scalar) : Fraction of noisy pixels\n",
    "\n",
    "  Returns:\n",
    "     (numpy array of floats)    : Data matrix + noise\n",
    "\n",
    "  \"\"\"\n",
    "\n",
    "  X_noisy = np.reshape(X, (X.shape[0] * X.shape[1]))\n",
    "  N_noise_ixs = int(X_noisy.shape[0] * frac_noisy_pixels)\n",
    "  noise_ixs = np.random.choice(X_noisy.shape[0], size=N_noise_ixs,\n",
    "                               replace=False)\n",
    "  X_noisy[noise_ixs] = np.random.uniform(0, 255, noise_ixs.shape)\n",
    "  X_noisy = np.reshape(X_noisy, (X.shape[0], X.shape[1]))\n",
    "\n",
    "  return X_noisy\n",
    "\n",
    "\n",
    "def change_of_basis(X, W):\n",
    "  \"\"\"\n",
    "  Projects data onto a new basis.\n",
    "\n",
    "  Args:\n",
    "    X (numpy array of floats) : Data matrix each column corresponding to a\n",
    "                                different random variable\n",
    "    W (numpy array of floats) : new orthonormal basis columns correspond to\n",
    "                                basis vectors\n",
    "\n",
    "  Returns:\n",
    "    (numpy array of floats)   : Data matrix expressed in new basis\n",
    "  \"\"\"\n",
    "\n",
    "  Y = np.matmul(X, W)\n",
    "\n",
    "  return Y\n",
    "\n",
    "\n",
    "def get_sample_cov_matrix(X):\n",
    "  \"\"\"\n",
    "  Returns the sample covariance matrix of data X.\n",
    "\n",
    "  Args:\n",
    "    X (numpy array of floats) : Data matrix each column corresponds to a\n",
    "                                different random variable\n",
    "\n",
    "  Returns:\n",
    "    (numpy array of floats)   : Covariance matrix\n",
    "\"\"\"\n",
    "\n",
    "  X = X - np.mean(X, 0)\n",
    "  cov_matrix = 1 / X.shape[0] * np.matmul(X.T, X)\n",
    "  return cov_matrix\n",
    "\n",
    "\n",
    "def sort_evals_descending(evals, evectors):\n",
    "  \"\"\"\n",
    "  Sorts eigenvalues and eigenvectors in decreasing order. Also aligns first two\n",
    "  eigenvectors to be in first two quadrants (if 2D).\n",
    "\n",
    "  Args:\n",
    "    evals (numpy array of floats)    :   Vector of eigenvalues\n",
    "    evectors (numpy array of floats) :   Corresponding matrix of eigenvectors\n",
    "                                         each column corresponds to a different\n",
    "                                         eigenvalue\n",
    "\n",
    "  Returns:\n",
    "    (numpy array of floats)          : Vector of eigenvalues after sorting\n",
    "    (numpy array of floats)          : Matrix of eigenvectors after sorting\n",
    "  \"\"\"\n",
    "\n",
    "  index = np.flip(np.argsort(evals))\n",
    "  evals = evals[index]\n",
    "  evectors = evectors[:, index]\n",
    "  if evals.shape[0] == 2:\n",
    "    if np.arccos(np.matmul(evectors[:, 0],\n",
    "                           1 / np.sqrt(2) * np.array([1, 1]))) > np.pi / 2:\n",
    "      evectors[:, 0] = -evectors[:, 0]\n",
    "    if np.arccos(np.matmul(evectors[:, 1],\n",
    "                           1 / np.sqrt(2)*np.array([-1, 1]))) > np.pi / 2:\n",
    "      evectors[:, 1] = -evectors[:, 1]\n",
    "\n",
    "  return evals, evectors\n",
    "\n",
    "\n",
    "def pca(X):\n",
    "  \"\"\"\n",
    "  Performs PCA on multivariate data. Eigenvalues are sorted in decreasing order\n",
    "\n",
    "  Args:\n",
    "     X (numpy array of floats) :   Data matrix each column corresponds to a\n",
    "                                   different random variable\n",
    "\n",
    "  Returns:\n",
    "    (numpy array of floats)    : Data projected onto the new basis\n",
    "    (numpy array of floats)    : Vector of eigenvalues\n",
    "    (numpy array of floats)    : Corresponding matrix of eigenvectors\n",
    "\n",
    "  \"\"\"\n",
    "\n",
    "  X = X - np.mean(X, 0)\n",
    "  cov_matrix = get_sample_cov_matrix(X)\n",
    "  evals, evectors = np.linalg.eigh(cov_matrix)\n",
    "  evals, evectors = sort_evals_descending(evals, evectors)\n",
    "  score = change_of_basis(X, evectors)\n",
    "\n",
    "  return score, evectors, evals\n",
    "\n",
    "\n",
    "def plot_eigenvalues(evals, limit=True):\n",
    "  \"\"\"\n",
    "  Plots eigenvalues.\n",
    "\n",
    "  Args:\n",
    "     (numpy array of floats) : Vector of eigenvalues\n",
    "\n",
    "  Returns:\n",
    "    Nothing.\n",
    "\n",
    "  \"\"\"\n",
    "\n",
    "  plt.figure()\n",
    "  plt.plot(np.arange(1, len(evals) + 1), evals, 'o-k')\n",
    "  plt.xlabel('Component')\n",
    "  plt.ylabel('Eigenvalue')\n",
    "  plt.title('Scree plot')\n",
    "  if limit:\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "7jFNyCJ5ChXQ"
   },
   "source": [
    "---\n",
    "# Section 1: Perform PCA on MNIST\n",
    "\n",
    "The MNIST dataset consists of a 70,000 images of individual handwritten digits. Each image is a 28x28 pixel grayscale image. For convenience, each 28x28 pixel image is often unravelled into a single 784 (=28*28) element vector, so that the whole dataset is represented as a 70,000 x 784 matrix. Each row represents a different image, and each column represents a different pixel.\n",
    " \n",
    "Enter the following cell to load the MNIST dataset and plot the first nine images."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 430
    },
    "colab_type": "code",
    "id": "f4TNMebrBDSQ",
    "outputId": "a943a6ad-6fc1-46d9-a51d-e69eca6c7297"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 413,
       "width": 418
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import fetch_openml\n",
    "mnist = fetch_openml(name='mnist_784')\n",
    "X = mnist.data\n",
    "plot_MNIST_sample(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "L590FVgkXrTV"
   },
   "source": [
    "The MNIST dataset has an extrinsic dimensionality of 784, much higher than the 2-dimensional examples used in the previous tutorials! To make sense of this data, we'll use dimensionality reduction. But first, we need to determine the intrinsic dimensionality $K$ of the data. One way to do this is to look for an \"elbow\" in the scree plot, to determine which eigenvalues are signficant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "OxtBZtgXHIAT"
   },
   "source": [
    "## Exercise 1: Scree plot of MNIST\n",
    "\n",
    "In this exercise you will examine the scree plot in the MNIST dataset.\n",
    "\n",
    "**Steps:**\n",
    "- Perform PCA on the dataset and examine the scree plot. \n",
    "- When do the eigenvalues appear (by eye) to reach zero? (**Hint:** use `plt.xlim` to zoom into a section of the plot).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 461
    },
    "colab_type": "code",
    "id": "3kiAFD9KOG8F",
    "outputId": "62d1745f-ec6b-47a4-b015-42cfb7735660"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function pca in module __main__:\n",
      "\n",
      "pca(X)\n",
      "    Performs PCA on multivariate data. Eigenvalues are sorted in decreasing order\n",
      "    \n",
      "    Args:\n",
      "       X (numpy array of floats) :   Data matrix each column corresponds to a\n",
      "                                     different random variable\n",
      "    \n",
      "    Returns:\n",
      "      (numpy array of floats)    : Data projected onto the new basis\n",
      "      (numpy array of floats)    : Vector of eigenvalues\n",
      "      (numpy array of floats)    : Corresponding matrix of eigenvectors\n",
      "\n",
      "Help on function plot_eigenvalues in module __main__:\n",
      "\n",
      "plot_eigenvalues(evals, limit=True)\n",
      "    Plots eigenvalues.\n",
      "    \n",
      "    Args:\n",
      "       (numpy array of floats) : Vector of eigenvalues\n",
      "    \n",
      "    Returns:\n",
      "      Nothing.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(pca)\n",
    "help(plot_eigenvalues)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "7zgeszJSHVr9"
   },
   "outputs": [],
   "source": [
    "#################################################\n",
    "## TO DO for students: perform PCA and plot the eigenvalues\n",
    "#################################################\n",
    "\n",
    "# perform PCA\n",
    "# score, evectors, evals = ...\n",
    "# plot the eigenvalues\n",
    "# plot_eigenvalues(evals, limit=False)\n",
    "# plt.xlim(...)  # limit x-axis up to 100 for zooming"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 430
    },
    "colab_type": "code",
    "id": "HAM5vUWJBpiJ",
    "outputId": "ce24d578-f189-48a8-b9eb-e9efd2d95e6b"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XX3xRbJ9Wr16tAwcOSJJat26tpk2blvAJCFwAANULgQsAAKgyhQvd7t69W3fffbdlLY/iZGZmaty4cdqwYYN5bsqUKZapLP7+/rr33nvN4+eff77EERopKSmaNWuWTpw4Uew9ZQ1cJOlvf/ub2f773//udkFZZwUFBRo/frzuv/9+DR482Jw+NGLECHOdlMWLF+vLL78s9d1r165Vnz599Nhjj+npp58uc9+LhkLu/m7y8/M1adIky05LQ4YMcbmvpBEukjRy5EizPX/+fP32228u92RkZOiRRx4xj2+88cZSPoF1ehKBCwDA2whcAABAlXHekWbJkiW6/vrrtXHjRuXl5Vnuczgc2rVrl6ZMmaKWLVtq9uzZ5rUePXpo+PDhLs++//77zfaXX36pYcOGKTEx0XLPmTNn9I9//ENNmjRRfHy8Bg4cWGxfLyZwGTFihGrWrClJ2rVrl9q0aaNp06ZZpkJJ0rFjx/T++++ra9eumjlzpnm+cKpNaGio4uPjzX4MHz5cd911lzZu3GjpV1ZWllasWKF7771Xffv2NUe2VMQaNi1bttSYMWM0ffp0ffrpp5o6dapatWqlt99+27xn8ODBatCggUttadtC33rrreaIpIyMDPXu3Vvz5s2T3W5XXl6evvjiC1111VXatm2b+Yy//OUvpfbZ+b12u93zDwsAQCWwGRfz0wQAAMBFSE5OVufOnS0jJKQL65+0a9dO4eHhysrK0p49e9xuAdy5c2d9+eWXbn/Jl6T4+HjNmjXLcq5t27Zq1qyZTp8+rQ0bNlh+EW/UqJEOHjxoju749NNPdeedd0qSBgwYoO+++67Mn/Gzzz7TiBEjXEbY1KpVSzExMUpLS1NKSopL3VtvvWXZ+jo1NVU9e/bU3r17LfeFhISobt26Kigo0LFjx1xGonTt2lUJCQmWbZ49sX37dl1xxRUe31+3bl1t2bJF9evXd7nWuXNnc+2Vf/7zn3r44Ydd7pk2bZomTpxoOefr6yvDMFy+uylTpujRRx8ttU+ffPKJ7rnnHkkXvu/CXaMAAPAGRrgAAIAqExsbq0WLFlnWKJEujNTYtGmTEhIS9N///tclbAkODtYTTzyhdevWFRu2SNKMGTN03333Wc7t3LlTX375pdasWWMJW5o0aaKEhIRi11e52P8nNXToUC1YsEC1atWynE9JSdHevXtdwpbY2Fh98MEHlrBFkmrWrKmVK1eqf//+lvNZWVnav3+/Dh06ZAlbbDab7rrrLn333XdlDlvKqnPnzlq7dq3bsEWSZXHg6Ohot/dMmDBBEyZMsJwrKChwCVsmTJhgmVpUEucRLvXq1fOoBgCAykLgAgAAqlT79u21detWffbZZxo0aJA5Baeo8PBw3XzzzZo5c6b279+vl19+2WWL4aL8/Pw0Z84cff311xo8eLDLQrCS1LFjR7311lvauXOn4uLiLNecj9u0aXMRn+6Cm2++WYmJifr444916623umydXK9ePd1+++2aO3euDh48qFGjRrl9Tt26dfX9999r7dq1mjRpkkt/g4KC1LNnTz3zzDNKTEzUJ598UmzAUVYTJ05Uz5491aBBA4WGhqpBgwa66aabtGbNGm3evNmlL87Gjh0r6cK0pEGDBrm9x2azadq0afrqq6/Uq1cvl+vXXXedfvzxR02bNq3ERYedtWrVymwPHTrUoxoAACoLU4oAAIBXGYahQ4cOad++fcrMzFRYWJhq1qyp9u3bl3stktTUVK1evVqpqanmM5s3b15izTfffKMjR45ozJgxFbIWiiTl5eUpLS1NGRkZioiIUK1atTwOEZwZhqH09HSdOXNGfn5+qlOnjstW1Bfr559/VseOHc3jgoICj7exdufcuXMKCQlxG3q5s2fPHu3Zs0e+vr6Ki4u76MBr7dq1OnjwoEaMGFFhf38AAFwMAhcAAABo27ZtuvLKK81jh8NxUaEQAAC4gClFAAAAcFk7hbAFAIDyIXABAACAS+ACAADKx7NJtZeItLQ05eTkqHbt2iXOJ87Pz9cvv/yi4OBg+fn5yW63Kzc3V3a7XTabTYGBgUpOTlZMTIxl6G1Rv/zyizZt2qTMzEw1a9ZMAwYM8Ggu9IkTJ7RixQqlpqaqbt26GjRokMLCwkqty8rK0uLFi3Xs2DHVqFFDffv2LXEnh0IOh0MJCQlKTEyUv7+/unXrVqZtIQEAwO9fQUGB2WZ0CwAA5XfJBy45OTmaNWuWZs6cqT179kiSIiMj1adPH02cOFFXX321S82zzz6rl19+udRn+/r66tixY6pTp47l/IkTJ/TUU09p7ty5lvNXXHGFpkyZon79+rl9XnZ2tt544w29+uqrysrKMs/XqVNHzz33nEaNGuU2KDIMQ/PmzdPkyZN17Ngx83xQUJAeeughPf7444qMjHT7zg0bNuihhx7S5s2bLeeHDh2ql156SU2bNi3xOwAAAJcG5xEuBC4AAJTfJb1o7rlz59S/f39t2rTJ7XWbzab58+frjjvusJz/6quvdMstt7jc7+vra/7fn6ioKI0ePVqvvPKKZQX8HTt26Oqrr9b58+clXdhSMjIyUtu2bVN2drYkac6cObrvvvsszz579qyuuuoq7d69W5LUsGFDNWrUSPv27VNKSookafTo0Zo1a5blhyDDMHTnnXdq3rx5kqQaNWqodevWSkpK0v79+yVd2P5y3bp1LltSvvPOOxo/frwkKTAwUFdccYVyc3P1888/m59x06ZNpe7mAAAAfv9++OEH9ezZU9KFn3ny8/O93CMAAH7fLuk1XDZv3qxNmzbJz89Pjz76qPbu3aukpCStXLlSvXv3lmEYmjx5sssPFLGxsWb72LFjys7OVkFBgfLz81VQUKC8vDydOXNGb7zxhiVsycnJ0ZAhQ3T+/Hk1bNhQixYt0s6dO7V+/Xrt379fQ4cOlSSNHTtWR48etbxz7Nix2r17t0JCQvTmm2/q4MGDWrdunQ4fPqwXX3xRkvTBBx/oq6++stTNmDHDDFvGjh2rgwcP6ocfflBiYqI+++wzRUREaNu2bfr73/9uqfvpp580YcIESVLv3r21c+dObdy4Udu2bdOmTZvUunVrpaen6+6779YlnMkBAID/LyQkxGx7MpUZAACUwriEFRQUGHPmzDF27tzpci0rK8uoXbu2IclYs2aN5dqSJUsMSUZISIjhcDg8ft+0adMMSUZYWJjx22+/uVy32+1GmzZtDEnGI488Yp7fsmWLIcmQZCxYsMDts0ePHm1IMrp162aey8jIMGJiYgxJxsSJE93WzZ0715BkBAYGGufPnzfP9+vXz5BkdO/e3cjLy3Op27t3r+Hj42NIMlatWuXpVwAAAH6nCgoKjHvuucdo0KCB8fbbb3u7OwAA/O5d0mu4+Pj4uEzdKRQcHKzGjRvr1KlTysjIsFwrnMLTqFEj2Ww25ebmav369Tpx4oTCwsLUq1cv1ahRw+WZn3/+uSRpwoQJbtc+8ff318iRI/XII49o6dKlev311yVJ//nPfyRJvXr10pAhQ9z2969//as++OADbd68WWfOnFGNGjW0cuVKpaWlKTIyUv/4xz/c1o0YMULjxo1Tdna21qxZoxtuuEFpaWlKSEiQJE2dOtXtujAtWrRQr169tGrVKi1dulR//vOf3T5furDI3ptvvimHw6H8/HxzxJC/v7+CgoIUEhKi8PBwBQcHy9/fXw0aNHBZlNfhcKigoMAyYggAAFQdHx8fffTRR97uBgAAl4xLOnApyZo1a/Tjjz/Kx8dHLVu2tFw7efKkpAtDa++55x4tXLhQmZmZ5vWIiAhNmjRJTz75pBlWpKenm2vF3H777cW+t2vXrpIu7GCUlJSkOnXqaNmyZaXWXXHFFfL391deXp5WrlypW2+91awbMGCAIiIi3Nb5+/urY8eO+u9//6vly5frhhtu0IoVK2QYhurXr6/u3buX2NdVq1Zp+fLleuWVV4q9z+Fw6NFHHy32elG9evXS6tWrJUmrVq1S37595XA49Oc//1mrVq3y+DkAAAAAAFRXf5jApaCgQD/++KPWrFmjFStWaPny5TIMQxMmTFCTJk0s9xYGLj/99JN++uknSVJ4eLgaNGiglJQUpaam6tlnn1V6erqmTp0qSVq3bp0KCgpUo0YNtWvXrth+dOjQwWz/+uuvCgwMNBep7dWrV7F1gYGBatmypX755RclJiZKkhlOlFRX+M7//ve/butK2oWgsK+FdcXxZKtrZ3l5eWbbz8/P3BXB+TwAAAAAAL9nl/SiuYUMw1CvXr3UvXt3TZ48WcuWLZOfn5/Gjh2rF154weX+wsBFujCaZf78+Tp9+rR2796to0ePatKkSZKk6dOn6+DBg5KkpKQkSVLjxo1LDCCcF6HLyMjQqVOnzOOiwU9RhaNYCndAKnxnaVs3F24JXTh1qvDzefq+jIyMEhfOLWvgYrfbzbbzFCICFwAAAADApeIPEbhIF3Yecg4G8vPzde7cOeXm5rrcW7iGS2hoqJYtW6ahQ4eaU4eCgoI0ZcoUNW7cWA6HQ99//70kmc8pLXxwDhWCgoIs7y+ttjCoCAoKKtM7K6KupJEwJV1zp3B7bEkKCAgw2zk5OWV6DgAAAAAA1dUfInCx2WxauHChzp49a65/YhiGPv30U/Xv398ldLn55pvVunVrffvtt+rWrZvL83x8fDRw4EBJF9aCkf63lWJWVlaJfTlz5ozZDg0NtWzBWFrt6dOnzTrndzqvL1OWurK+ryRlGeWSnp5utqOiotyeBwAAAADg9+wPs4aLdGE6T+/evdW7d2+9++67GjdunLZt26ZPP/1UI0eONO978MEH9eCDD5b4rLp160qSOSWoYcOGkqSDBw+qoKBAvr6+buuSk5PNdrNmzeTv7y+bzSbDMLR//35FR0e7rTMMQ6mpqZIu7CAkSQ0aNFBycrL2799fYl8L31lYV9jX0uoKR/oU1pXk4YcfliT5+vrK399fhmEoLy9POTk5yszM1Pnz55Wbmyu73W7uYiRdWBunUOFUKQAAAAAAfu/+UIGLs/j4eE2bNk379u3T2rVrLYGLJwpHxQQHB0uSuc1xTk6Ofv31V5edjwpt2LBBktS8eXNza+lmzZopMTFR27dvV5cuXdzW7dmzR2fPnpUk856OHTtq69at2rFjR7H9dDgc2rhxo6T/7ZBU2Nft27eX+BkL+1pYV5LCLa7LqnB9GUk6d+6cDMMo8xQlAAAAAACqmz/ElCJ3fHx81KdPH0nWUSeeKtySuVmzZpKkWrVqqX79+pKkH3/8sdi6lStXSrKGGB07dvS4rlGjRqpdu7bHdTt27DCnBhW+s7DuwIEDSktLc1uXl5entWvXuvS1ogUEBJjr4xQUFFgW1AUAAAAA4Pfqkg5cpk+frvvuu8+ySKuzI0eOSLoQYjjLzc01p9O4s3XrVm3ZskWSNGzYMPN87969JUnvv/++2119Dh8+rC+//FKS1KNHD/P8tddeK0n67LPP3K5jkp+fr7feesulrvB9u3bt0vr16932ddq0aZIuTD8qDIRat26t2NhYSdLs2bPd1n388cdmX7p37+72nopSONJHUrEBEAAAAAAAvyeXdOAydepUffTRR3rooYdcApAlS5Zo0aJFkqRRo0ZZrvXr108NGzbU0qVLXZ557NgxM2Rp2rSpJYwYP368JGndunV66qmnLKM1du/erX79+ikvL09RUVG68847zWvDhw9XTEyM0tPTddddd5lrtUgXFtkdPHiwEhMTJcmytkzr1q3NUTojR47Url27zGv5+fmaPHmyPvroI0nSAw88YE7V8ff317hx4yRJzz33nBYvXmz5jJ9++qkeeOABSdLgwYPVuHFjl++hIhUGQZJ09OjRSn0XAAAAAABVwWa4G4pxiZg+fboeeughSRfWPbn++usVFBSkjRs36uuvv5YkXX/99S6Bw8CBA/X9998rKChIDz30kHr27ClfX18tWbJEs2fPVlZWlnx8fLR8+XJzdEqh8ePH65133pEktWrVStdff73S09P12WefKSMjQ5I0Z84c3XfffZa6+fPna/jw4ZKkmJgYDRs2TD4+Pvr222916NAhSReCoQ8++MBS9+uvv6pDhw7Kzs6Wn168HB8AACAASURBVJ+fhg8frtjYWK1bt06bN2+WdGHNlvXr11t2RMrJyVHHjh21d+9eSdKAAQPUvn177d27V998842kC+urbN68Wc2bNy/7l18Ghd+3JH3zzTcaPHhwpb4PAAAAAIBKZ1zCHA6HMXnyZEOS2z8DBw400tPTXeqSk5ONrl27FlsXERFhLFy40O078/PzjXfeeceIiIhwqWvQoIExd+7cYvu7bNkyo2nTpi51oaGhxtNPP23k5OS4rdu3b5/Ru3dvlzqbzWbcddddxvHjx93WnT592oiPj3f7Ga+++mpjy5YtHnzL5TdixAjzvR9//HGVvBMAAAAAgMp0SY9wKbR37179+9//1u7du5Wenq64uDiNGjVKXbt2LXZHHMMwtGTJEr3++uvat2+f8vPz1aRJE40aNUp33nmnwsLCSnzniRMnNHPmTB08eFCBgYG68sorNXr0aAUFBZVYl52drZkzZ2rXrl2y2+2Ki4vT2LFjzYVyi2MYhubPn69169bpzJkzqlevnu677z61a9eu5C9H0vr16/XFF1/o5MmTiomJ0Q033KCBAwdW2W5B8fHxmjVrliRpxowZ5nQnAAAAAAB+r/4QgQuqt8mTJ2vKlCmSpJdffllPPPGEl3sEAAAAAED5XNKL5uL3ISIiwmyfO3fOiz0BAAAAAKBiELjA6yIjI8322bNnvdgTAAAAAAAqBoELvC4mJsZsnz592os9AQAAAACgYhC4wOucFyAu3DobAAAAAIDfMwIXeJ3zzk3Z2dle7AkAAAAAABWDwAVex6K5AAAAAIBLDYELvC4kJMRsZ2VlebEnAAAAAABUDAIXeF14eLjZZg0XAAAAAMClgMAFXufv72+27Xa7F3sCAAAAAEDFIHCB1wUEBJjtvLw8L/YEAAAAAICK4eftDgDOI1zcBS47duzQ7t27lZ+fr9q1a+uaa65RYGBgVXYRAAAAAIAyIXCB1zkHLvn5+WZ706ZNeumll/Ttt99a7o+JidHIkSM1ceJE1atXr8r6CQAAAACAp2yGYRje7gT+2HJychQcHCzpwvSi3NxcFRQUyM+v5DwwNjZWixcvVufOnauimwAAAAAAeIzABV6Xl5dnruPi4+OjgoICSZLNZiu1tlatWtqyZYsaNWpUqX0EAAAAAKAsWDQXXuc8ksXhcJSpNiUlRU899VRFdwkAAAAAgHJhhAuqBefRLIX/JD0Z4SJJgYGBSkpKUlRUVKX0DQAAAACAsmKEC7yuvJlfbm6uy8K6AAAAAAB4E4ELvK4iBlklJSVVQE8AAAAAAKgYBC7wOud1WwqnERUunOupoKCgCu0TAAAAAADlQeACr3MOXHx8fFzOeSIuLq5C+wQAAAAAQHkQuMDrnEez+Pr6SpLy8/M9rq9bt6769u1b4f0CAAAAAOBiEbjA6+x2u9kOCAiQJOXk5HhcP378ePn7+1d4vwAAAAAAuFgELvC67Oxssx0aGlqm2m7dumnChAkV3SUAAAAAAMqFwAVel5uba7YDAwMlSVFRUXrqqafk5+dXbN2AAQO0bNmyMoc0AAAAAABUNgIXeN358+fNdmF4YrPZ9OKLLyoxMdEygiUqKkrx8fFasmSJFi1apIiIiCrvLwAAAAAApbEZhmF4uxP4Y9u8ebO6desmSerUqZN+/PFHt/fZ7XZzjRcAAAAAAKozRrjA686ePWu2IyMji72PsAUAAAAA8HtB4AKvy8zMNNthYWGl3uu8yC4AAAAAANURgQu8znkNF3eBS9OmTWWz2eTv76+wsDAdP368KrsHAAAAAECZEbjA67Kyssx2SEiIy/X8/HzLf0vauQgAAAAAgOqAwAVed+bMGbMdFRXlcr0waClE4AIAAAAAqO4IXOB1zmu4hIeHu1z39fW1HBcUFFR6nwAAAAAAKA8CF3hdaWu4+Pv7W47z8vIqvU8AAAAAAJQHgQu8rrQ1XAIDAy3HOTk5ld4nAAAAAADKg8AFXpeammq2Y2JiXK4HBwdbjglcAAAAAADVHYELvO7kyZNmu3bt2i7XmVIEAAAAAPi9IXCB1yUlJZntevXquVwvuitR0V2LAAAAAACobghc4HXOi+ZGRka6XC+6hktubm6l9wkAAAAAgPIgcIFXGYZhCVxCQ0Nd7iFwAQAAAAD83hC4wKuSk5Nlt9slSVFRUW53KSp6LjMzs0r6BgAAAADAxSJwgVclJyeb7Tp16ri9JywszHJM4AIAAAAAqO4IXOBVKSkpZjs2NtbtPUUDF+cpSAAAAAAAVEcELvAq5/AkPDzc7T1FF9JNT0+v1D4BAAAAAFBeBC7wqtOnT5vtmJgYt/fUqFHDcnzmzJlK7RMAAAAAAOVF4AKvcl6Pxd0ORZJrEOM8DQkAAAAAgOqIwAVede7cObNd3JSiWrVqWY7T0tIqtU8AAAAAAJQXgQu8ynm0StFgpRAjXAAAAAAAvzcELvAq59EqNWvWdHtP0e2iT5w4Ual9AgAAAACgvAhc4FXZ2dlmOyQkxO099evXtxwnJSUpPz+/UvsFAAAAAEB5ELjAq5y3hQ4LC3N7T0BAgKKjo81jwzCYVgQAAAAAqNYIXOBVWVlZZru4ES6SVLduXcvxyZMnK61PAAAAAACUF4ELvConJ8dsBwYGFntf0XVckpKSKq1PAAAAAACUF4ELvMp5SlFERESx99WrV89yfOzYsUrrEwAAAAAA5UXgAq/KzMw026GhocXe17BhQ8vx8ePHK61PAAAAAACUF4ELvMp5SlFwcHCx9xVdw4WtoQEAAAAA1RmBC7zK00VzGzRoYDk+cuRIpfUJAAAAAIDyInCBV+Xm5prtkhbNveyyyyzHTCkCAAAAAFRnBC7wqoKCArPt41P8P0d3i+YahlFp/QIAAAAAoDwIXOBVzqFJSYFLbGysZY2Xs2fPKjk5uVL7BgAAAADAxSJwQbVhs9mKvebj46PmzZtbzu3fv7+yuwQAAAAAwEUhcEG1UdoUobi4OMvxnj17KrM7AAAAAABcNAIXeJXzNCKHw1HivS1atLAcHz58uFL6BAAAAABAeRG4wKsCAgLMtt1uL/HeoltDHz16tFL6BAAAAABAeRG4wKuct4J23iLanYYNG1qOjx07Vil9AgAAAACgvAhc4FX+/v5mOy8vr8R7L7vsMsvxgQMHKqVPAAAAAACUF4ELvCosLMxsZ2RklHhvXFycZSejgwcPKisrq9L6BgAAAADAxSJwgVcFBQWZ7dKmFIWEhKhRo0bmsWEYOnjwYKX1DQAAAACAi0XgAq9yXsMlJyen1Psvv/xyyzHTigAAAAAA1RGBC7zKeUrR+fPnS72/cePGluPjx49XdJcAAAAAACg3Ahd4VVnWcJGkunXrWo5PnDhR4X0CAAAAAKC8CFzgVSEhIWY7Ozu71PuLbg19+PDhCu8TAAAAAADlReACryrrCJeiU4oOHTpUwT0CAAAAAKD8/Lzdgaqye/du/fDDD8rOzlbLli11zTXXKDg4uNS6w4cPa8qUKdqzZ498fHzUqVMnPfroo6pZs2aJdefPn9fUqVO1ceNGZWZmqlmzZnrkkUfUqlWrEusKCgr00Ucf6ZtvvlFqaqrq1Kmj+Ph49e/fv9S+rl69Wu+++66OHTumqKgoDR48WKNHj5afX8l/zb/99ptef/11JSYmyt/fX926ddOkSZMUFRVV6jvLKzw83GyfPXu21PuLBi7sUgQAAAAAqJaMS9zWrVuNa665xpBk+RMUFGQ8/PDDht1ud1uXnZ1tPP3000ZQUJBLbUREhDF16tRi3zl37lyjTp06LnU+Pj5GfHy8kZWV5bbuhx9+MDp27OhSJ8no16+fcejQIbd1hw4dMm655Ra3dS1atDBWr17ttu78+fPGpEmTDH9/f5e66Oho47333ivl2y2/5557znznE088Uer9mZmZln76+/sbDoej0vsJAAAAAEBZXNIjXBITE9WrVy9z95u2bdsqKipKiYmJSk5O1tSpU2UYhqZOnWqpMwxD8fHx+uSTTyRJV155pYYOHSqHw6G5c+dq3759evjhhxUaGqr4+HhL7fvvv68xY8ZIkurUqaMxY8YoMjJSS5YsUUJCgt5//31lZ2fr448/ttRt3bpVffv2VU5OjgIDAzVmzBg1adJE27Zt0//93/9p+fLluuGGG7Rp0yaFhoaadWfOnFGfPn20f/9+SdIdd9yhHj166MSJE3rvvfe0b98+DRo0SJs3b7aMrnE4HLr77rv11VdfSZK6d++uIUOGyG6368MPP9SBAwc0ZswYRUREaNiwYRXx1+FWZGSk2fZkl6KQkBCFhIQoKytLkpSXl6ezZ89WyWgcAAAAAAA85u3EpzLt2LHD8Pf3Nzp06GBs3LjRPJ+Xl2e88cYbhiQjODjYSElJsdQtWLDAHEHx0ksvGXl5eZbaCRMmGJKM8PBwS+3hw4eNwMBAQ5Jx++23G6dPn7Y8d968eeZzV6xYYXlmq1atDElG+/btjX379rl8jho1ahiSjOeee85ybdSoUYYko0aNGsayZcss11JTU43OnTubI2SczZkzx+zLtGnTjIKCAvNabm6uMXr0aEOSUatWLePcuXMlfs/l8f7775v9GD16tEc1jRo1soxy+fXXXyutfwAAAAAAXIxLetHcdu3a6eTJk/rpp5/UrVs387yfn58mTZqktm3bKjs7W1u2bLHUvfDCC5Kku+66S08++aRlDRQ/Pz+99tprql+/vs6fP68vvvjCvPbGG28oNzdXLVq00Mcff6waNWpYnjts2DANGTJEkvThhx+a5xcuXKg9e/YoICBACxYsUPPmzV0+xzPPPCNJ+uCDD2QYhiTp6NGjmjt3riRpxowZ6tevn6UuJiZGM2bMkCQtX75cR48elXRhBM+LL74oSbr//vs1YcIE+fj8759CQECApk2bpujoaKWkpGjRokXFf8nlFBQUZLY92aVIksv6OampqRXaJwAAAAAAyuuSnlIkXQgd3DEMQ3l5eZKkwMBA8/yJEyf0888/S5L+/ve/u60NDAxU//79NWfOHCUkJGjs2LGSpCVLlkiSHnvsMUuQ4GzQoEFauHChEhISZBiGbDabWXfnnXcqLi6u2LqHH35YR44c0W+//aZmzZpp6dKlcjgcatasme644w63dZ07d1ZsbKySk5OVkJCgkSNHKjExUfv375fNZtPTTz/tti4sLEy9e/fWggULlJCQoOHDh7u9T7qw0O+bb74ph8Oh/Px85efnS5L8/f0VFBSkkJAQhYeHKzg4WP7+/mrYsKE6dOggSYqIiDCf48miuZJUq1Yty3FKSopHdQAAAAAAVJVLPnBxJz09Xc8995z27dun2NhYderUybyWkJAgSWrSpImaNWtW7DO6dOmiOXPmaNWqVZKk/fv3m+uoDBgwoMQ6STp16pT27t2rli1bavny5aXWxcXFKSoqSunp6Vq1apWaNWtm1l133XWWESrObDabunTposWLF2vVqlUaOXKkWdehQwfVrVu3xL4uWLDA/IzFcTgcevTRR0u8x1nPnj21du1aSdZtoTMzMz2qr127tuX4xIkTHr8bAAAAAICq8IcJXPbs2aM5c+Zo9erV2rp1qwoKCiRJ//znPy0Lt27atEmSdNVVV5X4vMIw5vTp07Lb7dq8ebOkC9sW16tXr9Q6STp58qTCw8PNwKCkd9psNsXFxenHH3/UyZMnLX3905/+5FFfy1tXnOLCnuI4j2RxDlzOnTvnUX3R7zcpKalM7wcAAAAAoLL9IQIXh8OhHj16WH7RDwoK0qeffqpbbrnFcu+ZM2ckuU5bKSo4ONhs2+12s67o+iJFBQQEuK3z5J2F05TsdvtF9bWw7vTp0x711fl9hdOf3Clr4FK4lowk1a9f3+35khQd4ULgAgAAAACobi7pRXML+fj46O2339b1119vrumSk5Oj+Ph4l+kyhaFC4TokxXHewjgkJMTjOudpM6GhoZYQw9N3Fm4LXda+lqeuuLDF+XmeOnPmjHJzcyVd2Dq7sD4lJaXUPkmuAROL5gIAAAAAqps/ROAiXdhxaPHixUpOTta8efNUp04dpaamatCgQZY1QAqnuKSnp5f4vMJRIuHh4fLx8VF4eLik0hd+LayTpMjISMuUmtJqC0e0FE6BKmtfC+s87WvR95WkrKNcCp/t5+enqKgo83xpn0VyXQjZ+TsFAAAAAKA6+ENMKXLm4+OjYcOGqVWrVrriiiuUlZWl2bNnmzsStWjRQpK0e/fuEp9z5MgRSVLHjh0tdYcOHVJmZqY5mqS4usDAQLVs2VK+vr4KDg5Wdna2du/eXez6L7m5uebUGed3Hj9+/KL7Wta6kjz88MOSJF9fX/n7+5u7QOXk5CgzM1Pnz59Xbm6u7Ha7zp07p6ysLLM2KirKDGDS09NLnepUdLttT0IaAAAAAACq0h8ucCnUoUMHXXfddVq6dKl27dplni8MF3bt2qX8/Hz5+bn/ilavXi1J6tq1qySpbdu28vX1VUFBgXbu3Klu3bqVWNexY0dzPZd27dpp8+bN2r59u/r27eu2buPGjbLb7fL19TX72LFjR61cuVI7duwo9nNmZWWZi+QW9vWKK66QJG3fvr3EtVmKfsaSvP7666XeU5zo6GgdPHhQkpSWllbs1tiFnEfESJ5vJw0AAAAAQFW5pKcUGYZhLhTrTuEuPNnZ2ea5wjAiJyfH3HmoqLNnz+qHH36Q9L8wIjg4WC1btpT0v6DCXX8WL15sqZP+F/IUVyfJrGvfvr25CG5h3fr164v9nAkJCcrLy5PNZjO3vy6sS0tLs4RNzk6dOqUtW7a49LUyREREmG3ntXGKU3SKE4ELAAAAAKC6uaQDl+uuu0516tTRr7/+6nLN4XCYC+Y6j0apUaOGevfuLUl66aWXZBiGpc4wDD3//PPKzMyUv7+/evbsaV4bMmSIJOmtt95yGwJ8/fXX2rhxoySpT58+5vlbb71VkrRkyRJt27bNpe7gwYOaOXOmJFlGwAwcOFCBgYFKSUnRrFmzXOoyMzP13HPPmZ+xcO2WRo0a6corrzQ/Y1GGYeiZZ55Rfn6+QkNDix2tU1Gio6PNdlpaWqn3Owc0kufbSQMAAAAAUFUu6cAlLS1NZ86c0W233WZOWZEujIgYM2aMdu3aJX9/f40ePdpS9/TTT0u6EIAMGzZMJ0+elHRhJMx9992nqVOnSpJGjx6tOnXqmHV/+9vfVKNGDR0/flx9+vTR1q1bJV0IMKZNm6bbbrtN0oUpRIMGDTLr+vTpo+7du8vhcOiGG27QggULzKAnISFBnTt3VkZGhoKDgzVx4kSzLjo6WuPHj5ckTZo0Sa+88oo50mX//v3q0aOH2YennnrK8hmfeeYZSdL8+fM1cuRIc6efjIwM3XHHHWaAM378eI8WzS0P5zVbPNlxKCgoyLJIr91uV15eXqX0DQAAAACAi2Ezig7huIRs3LhR1157rbKzs2Wz2dSmTRsFBQVp9+7d5qKtr732mh577DGX2ieffFKvvPKKJCkgIEANGjTQyZMnzelHbdq00YYNG8xRI4UWLFigu+++23znZZddprNnz5oLu4aHh2vDhg1q06aNpW7Pnj3q16+fjh8/Lul/2yUXhj2S9O9//1sjRoyw1GVlZalv377asGGDpAvTbaKionT06FE5HA5J0rhx4zRjxgyXzzh+/Hi98847ki6EGPXq1dPx48fNLZu7du2q1atXm1OYKssTTzyhV199VZL04osvuoRD7kRGRlpGtpw+fdplMV0AAAAAALzlkh7h0r17d3333Xdq27atDMPQzp079eOPPyorK0uXXXaZZs+e7TZskaSXX35Za9asUcuWLWW323XgwAFlZ2erRo0aevXVV7Vp0yaXsEW6MD1o165dGjBggAzD0OHDh5Weni4/Pz+NHTtWe/fudQlbJKlVq1bavXu3HnzwQdlsNiUlJZlhy4ABA/TTTz+5hC2SFBISonXr1untt99WeHi4zp49q8OHD8vhcKhNmzb68ssvzVClqLfffltLly5VkyZNlJOTowMHDig3N1c1a9bUm2++qTVr1lR62FL4GQo5r6fjaU1Z6gAAAAAAqAqX9AiXQoZhaMeOHdq9e7fS09MVFxena6+9Vr6+vqXW5ubmauvWrTp27Jiio6PVqVMnl11ySnrngQMHFBgYqHbt2qlhw4Ye9ffgwYPas2eP7Ha74uLi1LZtW4/qUlNTtWPHDp0+fVr16tVTt27dPPqM2dnZ2rp1q06cOKGYmBh16dLFbZhUWaZMmaLJkydLkh555BGPdjxq0qSJZZrYb7/9pqZNm1ZaHwEAAAAAKIs/xLbQNptNHTp0UIcOHcpcGxgYqB49elTpOy+//HJdfvnlZa6rWbOmrr322jLXBQcH609/+lOZ6ypKaGio2c7MzPSopujIm8IpYgAAAAAAVAeX9JQi/D44j6bxdMchphQBAAAAAKozAhd4XUxMjNn2ZJciiREuAAAAAIDqjcAFXue8u1Dhbk6lKTrChcAFAAAAAFCdELjA68LCwsx2RkaGRzVFFwMu3AIbAAAAAIDqgMAFXhcREWG2z58/71FNQUGB5diT3ZgAAAAAAKgqBC7wOuddijydGuTjY/2nywgXAAAAAEB1QuACrwsMDDTbOTk5XuwJAAAAAAAVg8AFXufv72+28/LyvNgTAAAAAAAqBoELvM55elDRtVmKU3TNlvz8/ArtEwAAAAAA5UHgAq9zDk88XYuFRXMBAAAAANUZgQu87mICF5vNZjk2DKNC+wQAAAAAQHkQuOB3yXmhXUmy2+1e6gkAAAAAAK4IXOB1FzM6JSAgwHKcm5tbUd0BAAAAAKDcCFzgdc6BS9GpQsUpumaLp1ORAAAAAACoCgQu8DrnsMR5x6KSFB0V42lQAwAAAABAVSBwgdfl5eWZbX9/f49qigYzjHABAAAAAFQnBC7wupycHLMdFBTkUU1+fr7lmG2hAQAAAADVCYELvC4rK8tsh4SEeFRTdEQLgQsAAAAAoDohcIHXOW/pXHT3oeIwpQgAAAAAUJ0RuMDrLmYNFz8/P8tx0SlGAAAAAAB4E4ELvC4zM9NsezqlKDc313Ls6cgYAAAAAACqAoELvI41XAAAAAAAlxoCF3hddna22Q4ODvZiTwAAAAAAqBgELvC606dPm+3o6GiPagoKCizHjHABAAAAAFQnBC7wuvT0dLMdFRXlUY3zqBhJCgoKqtA+AQAAAABQHgQu8DrnRXPDwsI8qim6hkvRbaIBAAAAAPAmfkuF12VkZJhtTxfNLbotdNEpRgAAAAAAeBOBC7wuNTXVbNesWdOjGsMwLMc2m61C+wQAAAAAQHkQuMDrzp8/b7YjIiI8qikasBQNYAAAAAAA8CYCF3id8xouoaGhHtWwSxEAAAAAoDojcIHXnTt3zmyHh4d7VFN0hEvRRXQBAAAAAPAmAhd4XU5OjtkODg72qIY1WwAAAAAA1RmBC7wuOzvbbF/sLkX5+fkV2icAAAAAAMqDwAVed/r0abMdGRnpUU1gYKDlODc3t0L7BAAAAABAeRC4wOuOHz9utuvVq+dRTUBAgOXYbrdXaJ8AAAAAACgPAhd4VX5+vjmlyGazebwtdNHAhREuAAAAAIDqhMAFXlV0hyJPF8MtutZLVlZWhfYLAAAAAIDyIHCBVyUnJ5vt2NhYj+uKBi7OC+8CAAAAAOBtBC7wqvT0dLNdo0YNj+uKbh/NCBcAAAAAQHVC4AKvysjIMNthYWEe14WGhhb7HAAAAAAAvI3ABV7lHJQUDVFKUjScIXABAAAAAFQnBC7wqtOnT5vtskwpInABAAAAAFRnBC7wqpSUFLNdq1Ytj+vCw8Mtx+fPn6+wPgEAAAAAUF4ELvCq1NRUs12WwCUyMtJyfPbs2QrrEwAAAAAA5UXgAq9y3s65LGu4FJ1+dObMmQrrEwAAAAAA5UXgAq/Kyckx24GBgR7XEbgAAAAAAKozAhd41blz58x2RESEx3XR0dGWY+epSQAAAAAAeBuBC7zKeWRKWXYpioqKkp+fn3mcmZlpmZ4EAAAAAIA3EbjAq5x3Fyq681BJbDabyyK7p06dqrB+AQAAAABQHgQu8KrMzEyzHRYWVqba2NhYy7HzFtMAAAAAAHgTgQu8ym63m+2AgIAy1RYd4ULgAgAAAACoLghc4FXlCVzq1q1rOT5y5EiF9AkAAAAAgPIicIFXXey20JJ0+eWXW44PHjxYIX0CAAAAAKC8CFzgVc4jXIKCgspU27RpU8txYmJihfQJAAAAAIDyInCBV5VnhEvRwOXo0aMV0icAAAAAAMqLwAVeVVBQYLZ9fX3LVNugQQPL8bFjxyqkTwAAAAAAlJfNMAzD253AH5e/v7/y8/MlSbm5uWVaONdut1tGxdhsNuXm5srf37/C+wkAAAAAQFkwwgVeVRi2SJKfn1+ZagMCAiw7FRmGoQMHDlRY3wAAAAAAuFgELqg2fHzK/s+xWbNmluPDhw9XVHcAAAAAALhoBC6oNi5mdlu9evUsx0lJSRXVHQAAAAAALhqBC7zKZrOZbYfDUeb62rVrW45PnTpV7j4BAAAAAFBeBC7wKuediZx3LPJU0REubA0NAAAAAKgOCFzgVc7rtlxM4NKoUSPLMWu4AAAAAACqAwIXeJXzzkTOOxZ56rLLLrMcM8IFAAAAAFAdELjAqwIDA8223W4vc32DBg0sxwQuAAAAAIDqgMAFXuXv72+28/Lyylxfr149y7Sk1NTUiwpuAAAAAACoSAQu8CrnES65ubllrvf19VWtWrUs59gaGgAAAADgbQQu8Krw8HCzfe7cuYt6RtGdik6cOFGuPgEAAAAAUF4ELvCq4OBgs52Tk3NRz6hfv77l+MiRI+XqEwAAAAAA5UXgAq+KjIw022fOnLmoZzRt2tRyvHfv3nL1CQAAAACA8iJwgVfFxMSY7dOnT1/UM5o1a2Y5Pnz4cLn6Bk9bhAAAIABJREFUBAAAAABAeRG4VLLMzEwlJyfLMIwy1dntdiUlJSk/P79MdQUFBUpKSirz9BzDMJSWlnbR66hcrJCQELOdlZV1Uc8oOqXo5MmT5eoTAAAAAADl9YcIXBwOhxYuXKgbb7xRzZo1U1xcnEaOHKmEhAS393/66adq2bKlOnbsqC5duqhDhw5q2bKlmjRpoqZNm6p169aKiYlRmzZtlJGR4fYZy5YtU/v27RUWFqbatWsrOjpar7zySqmhwp49e3T99dcrKChIdevWVXBwsMaMGVNqiJCWlqYHHnhAISEhZl2/fv20bdu2EuvsdrvefPNN1axZUzVr1lRkZKRat26tr776qswh0cUICwsz28V9l6Upumju8ePHy9UnAAAAAADKy2ZUxW/VXnT8+HGNGDFCa9eudXs9Pj5e7777rmw2m3nunXfe0fjx40t99mWXXaZt27YpOjraPJeZmanhw4fr22+/dVtTv359rVixQi1atLCcNwxDTz/9tF577TUVFBS41IWEhOiTTz7RkCFDXK795z//UXx8vNLT092+88knn9RLL73kcn7Hjh267f+xd59hUV3r+/jvGRgYOgKCCFYUrKjYI5pEf2qMRo01GixRY0lMMUePfhP1aPQYNcVzUo5GTSxRbNHERBNrLFiwByUGFAw2iiC9DczM/r/gPzuzpUiZmU25P9fl5d6z97PWw+gbnmutZ40ahdu3b5cYN2DAAPz000+So5tNbf78+Vi9ejUA4KOPPsKCBQsqPEZ8fLxklYu7uztSUlJMliMRERERERFRRdXqFS43b95E9+7dcfr0adjY2GD69OnYuXMn1q1bh/bt2wMA1q9fj59++kkSFxQUJF5/9tln2LRpE7Zv347du3cjNDQUW7duxa+//oqYmBhJsQUApk2bJhZbQkJCcP36ddy9exfr1q2Dt7c3Hj58iGHDhkGj0Uji1q5dixUrVkCn04k5379/Hz///DM6deqE3NxchISEFCuOXLp0CSEhIUhPT4evry92796Ne/fu4cKFC3j55ZcBACtWrMCuXbskcampqRg6dChu374NOzs7rF69Gnfu3EFUVBTmzJkDGxsbHDlyBHPnzq3Cv8DTmeKUIk9PT0nB7PHjxygsLKxybkRERERERESVJtRio0ePFgAIjRs3Fi5duiR5lpubK3Ts2FEAILz44ouSZ8eOHRMACFZWVoJOpyv3fEePHhUACACEzZs3F3seFxcnODs7CwCE//3vf+Lnjx49EhwdHQUAwowZMwStViuJy8/PFzp37iwAEMaNGyd+rtfrha5duwoAhG7dugkZGRnF5pw1a5YAQGjSpInkZ5kzZ44AQKhXr54QHR1dLG779u3idxATE1Pu76CiVq9eLX5nc+bMqfQ49evXF8cBINy/f9+EWRIRERERERFVTK1e4bJw4UIsW7YMV69eRZcuXSTP7OzsxJUsBQUFkmePHz8GAPj6+kKp/Psr0mq1ZfY1Wbt2LQBg2LBhmDRpUrHnTZo0wbRp0wAAP/zwg/j5tm3bkJ2dDR8fH/znP/+BlZWVJM7W1hYffPABAODAgQPi6o3Lly/j0qVLUCgU2LRpE5ydnYvN+a9//QtA0ck9hn4uhYWF2LBhAwBg1apV8Pf3LxY3btw4tGrVCjqdDgcOHCj1Z64q41OKqrINqEGDBpL7pKSkSo9FREREREREVFXWcidgToGBgQgMDCzxmU6nw+HDhwEAfn5+kmeGBrVNmjTBL7/8gp07d+LQoUNITk6GWq3G0KFDsWTJErRu3VqM0Wq1OH78OABg1qxZpebUu3dvfPbZZwgLC0N+fj7UajWOHj0KAHjttdegVqtLjQOArKwsXLx4Eb169RLj+vTpgzZt2pQY5+XlhYCAAERHR+Po0aPo3LkzwsPDkZ2dDXt7e0ycOLHEOIVCgeDgYERFReHo0aN45513Sv2ZdDod1qxZA71eD61WK56spFKpoFarYW9vDycnJ9jZ2UGlUsHHxwedOnUCAHh7e4vjxMfHlzrH03h5eeHGjRviPQsuREREREREJKdaXXApy5o1a8TTbJ5sRJuYmAgAuHDhAgYPHix5lp+fj927d+P777/Hjz/+iJdeeglAUS+VjIwMqFQqBAcHlzpv165dxXGuX7+ODh064OTJkwCA559/vtQ4Dw8PNG3aFHFxcQgPD0evXr1w5MgRAEDfvn3L/Fm7du2K6OhoXLhwAQDEuF69epXZELdr167YuHGjGFcavV6PefPmlfmOMT8/P8TExAAoWkVkUJXThQYMGAB/f3+o1WpkZGSwhwsRERERERHJqs4VXLRaLZYsWSKe2jNw4ED0799f8o5hhYuhse2wYcMwZcoUNG3aFPfv38eCBQsQGRmJqVOnIjY2Fk5OToiOjgYA+Pv7w8HBodT5vby8xOu0tDQ8ePAAeXl5ACCu+ihNgwYNEBcXh7S0NAAQ5yxPnGG+ysYJgiBpTGvMeNtVeRi2bAFA/fr1xeuqbCmqSMGHiIiIiIiIyNzqVMHl3r17CAkJQVhYGAAgODgYu3btKlZIMKxwAYDFixdjyZIl4juBgYHo3r07mjZtiuTkZBw9ehQjRoxAdnY2gKLjm8tiPJdSqRTjAJRZqDG8b/y3IfZpcYaeMIa4rKyscuVqPF9pxRbj98orMzMTer0eSqUSrq6u4ucZGRllFnaIiIiIiIiIaopa3TTX2J49e9ChQweEhYVBoVBg7ty5OHr0KFxcXIq9aygCvPvuu5Jii4GHh4e41cjQt8WwNedpRxtnZGSI1w4ODrCxsRHvnxZrWKFiKLAYYisaV95cn4wrTUULJHq9XvweDD1egKJmvsYFqIqIiIjA2rVr8emnn2LTpk24e/dupcYhIiIiIiIiMoVav8JFp9Phn//8Jz777DMAQPPmzbFp0yb06dOn1Jhvv/0W77//Ptq3b19qMaFly5YAgNu3bwMA6tWrB0C6OqYkhiIGULRlx7iYkZiYWOJJQ0/GGrb6uLm5ITU1VdwCVd64iub65AlAJVEqldDr9U99zyArK0vMw8nJCbm5uQCKVr84OTmVe5xr165h+fLl2Ldvn+RzhUKBQYMGYf78+WX+WxMRERERERGZQ60vuMybNw9r1qwBUHQK0BdffPHUFRv29valnm5kYDhNSKfTAYD4fnJyMpKSkiS9WowZTtJxd3dHs2bNABT1MUlOTsaNGzdKPKLZMK6hQNKtWzdxzpiYGMnpPGXNaRxn/HlpIiMjJXFlee+99wAUbV9SqVQQBAGFhYXIz89HTk4OsrKyoNFoUFBQgMzMTLFvDVC0oshwqlBaWhp8fHyeOh8A7N27F2PHjhX/DYwJgoBffvkFhw4dwpdfflnmyVFEREREREREplarCy7x8fH4z3/+AwCYO3cuVq9ebbL+IBEREQD+Xv3RokULODo6Ijs7GxERERgwYECJcSdOnABQVMQw5NKpUyccOXIEERERGDlyZIlxp06dAlC0GiQgIECM27dvn5hLSRISEhAVFSXOaYgDigoqWq0W1tYl/zcwzvVpPv7446e+Uxpvb2+xkW9CQgLatWv31JibN2/i1VdfLbHYYkyv1+ONN96Aj48Phg4dWukciYiIiIiIiCqiVvdw2bt3LwRBQL169bBs2TKTFVvS09Px888/A4B4LLRSqUSXLl0AoNj2FoP8/Hzs3bsXgLSIYbjet28fBEEoMXb79u0Aio5qNjSpNcSdPXtWXCHypNDQUACAnZ0d2rZtC6Co4GJtbQ2NRoNff/21xLiLFy+KRzeXp+BSFR4eHuJ1eU8qWrBggXiKVHm8++67FdryRERERERERFQVtbrgcvr0aQDAyJEjxS1A5bFy5Uq89NJLePToUbFner0eb731FjQaDRwcHCSrJiZNmgSgqAfMpUuXJHGFhYV499138fDhQwDA6NGjxWcTJ04EAPzxxx9Yu3ZtsTk3bdqEH3/8EQAwduxY8fO+ffvC19cXhYWFeO+994qt9ggPD8eKFSsAAKNGjRJXsri4uGD48OEAgPnz5yMzM1MSFx8fj5kzZwIoWrnztOOjq8rb21u8flo/GqCo8XBphaLS/PXXXzh58mRFUyMiIiIiIiKqlFpdcDEcf3zlyhWMGjUKwcHBaNeuHZo0aQJPT094eXnhueeew7FjxyRx3377LQ4cOICBAwfi+vXr4ufh4eEYMmQItm3bBgD4xz/+ITlaOSQkBJ07d0ZhYSGCg4OxaNEiXL58GcePH0f//v3x9ddfAygqzBhWmwBFDXhnz54NAHjzzTcxbtw4nDlzBufOncOsWbMwZcoUAECrVq0wefJkMc7a2hqffvopgKKVLD169MAvv/yCy5cv49NPP8Wzzz6L1NRUODg4YNGiRZKf8aOPPoKdnR3+/PNPtG7dGlu2bMG1a9ewc+dOdO7cGdeuXQMArFixotQtR6bi7u4uXhs3FS7NiRMnoNVqKzzP999/X+EYIiIiIiIiokoRarGJEycKAJ76p3HjxpK448ePC9bW1uJzJycnoV69epKY8ePHC4WFhcXmjI2NFXr37l3qXAMHDhRycnKKxWVnZwtTpkwpNc7f31+Ijo4uFqfX64WPP/5YsLOzKzHOzc1N2L9/f4nfz8GDBwUfH58S46ytrYUPP/ywkt98xfz3v/8V533zzTef+v727dvL9e/65J/Ro0db4KchIiIiIiIiEoRa3TT3ww8/hI+PD1JSUuDt7Q0vLy/Y29vD0dERjo6OKCwsRFhYGLp37y6J69u3L27cuIHly5djx44d4koZAHj22Wfx5ptvYuTIkWIvFWPNmzfHyZMnsXnzZnz00UeIi4uDSqVCUFAQli5din79+pWYq4ODA7755htMnDgR8+bNQ2RkJAoLC+Hn54d58+Zh0qRJJa40USgUmDt3LkaMGIE5c+YgLCwM6enpaNCgAaZOnYq5c+fCxcWlxDlffPFF3Lx5E4sWLcLu3buRmJiIevXqYfDgwVi6dCmaN29eka+70hwdHcXrnJycp75fnmOqnzYPERERERERkTkpBKGULq0EAHjw4AFiYmKg1WrRrFkz+Pn5VSher9dDoVBUuGGvIAgQBKHEos7T6HQ6WFlZWSyuqnbv3i32phk5cuRTt/4kJyfDx8cHhYWFFZrno48+woIFCyqdJxEREREREVF51eoVLqbg6+sLX1/fSsdXpmACoFJFGoPKFk3kKLYARUddGxivJipN/fr1MX78eGzZsqXcc1hbW2PChAmVyo+IiIiIiIioomp101yqGVxdXcXr8jTNBYD33nuvQgWisWPHwsfHp8K5EREREREREVUGCy4ku3r16onX5S24BAYGYvPmzeVaQdSiRQt8/PHHlc6PiIiIiIiIqKJYcCHZVbRprkFISAj279+Phg0blvpOt27dcPr0aXh7e1cpRyIiIiIiIqKKYNNckl1aWhrc3NwAAM7OzsjIyKhQfF5eHrZu3Yr33nsPAODm5oYhQ4ZgxIgReP7550s83YmIiIiIiIjInFhwIdnl5+fDzs4OAGBjYwONRiNzRkRERERERERVwy1FJDuVSiVeV/SoZyIiIiIiIqLqiHstSHbGx19XdcFVfn4+0tLScOPGDezfvx/29vZsmEtEREREREQWx4ILyc644FJVhw8fxvDhw8X7gQMHmmxsIiIiIiIiovLiliKqVXx8fCT3Dx8+lCkTIiIiIiIiqstYcCHZmbJvc+PGjSX3d+/eNen4REREREREROXBggvJzrhRrnED3cqoX7++eOIRAGRlZSE9Pb1KYxIRERERERFVFAsuJDtTFlwUCgUaNGgg+ezRo0dVGpOIiIiIiIioolhwIdnl5+eL17a2tlUez9PTU3KflJRU5TGJiIiIiIiIKoIFF5KdVqsVr6u6wgUo2lZkLCUlpcpjEhEREREREVUECy4ku4KCAvHaFCtcvL29Jffx8fFVHpOIiIiIiIioIlhwIdnl5eWJ12q1usrjPbmliCtciIiIiIiIyNJYcCHZZWVlideOjo5VHs/Ly0tyn5CQUOUxiYiIiIiIiCqCBReSXU5Ojnjt4OBQ5fGeXOHy+PHjKo9JREREREREVBEsuJDsNBqNeG2KLUVOTk6S++zs7CqPSURERERERFQRLLiQ7IyPhTZFwcXV1VVyn5aWVuUxiYiIiIiIiCqCBReSnfGWInt7+yqP9+QKF+MeMURERERERESWwIILyc64IOLs7Fzl8dzc3CT3PKWIiIiIiIiILI0FF5KdqbcUPXnSkfGx00RERERERESWwIILyS43N1e8NlXBRaFQiPfZ2dnQarVVHpeIiIiIiIiovFhwIdmlpqaK109uB6oMKysr2NnZST4zLuoQERERERERmRsLLiQ744KLu7u7ScZ8snCTnJxsknGJiIiIiIiIyoMFF5Kd8SlFT/ZfqSwfHx/JfXx8vEnGJSIiIiIiIioPFlxIdsbbfZ7cClRZT66USUtLM8m4REREREREROXBggvJzrjg4uDgYJIxnyy4cEsRERERERERWRILLiS7jIwM8dpUW4qe7OGSnp5uknGJiIiIiIiIyoMFF5Ldw4cPxeuGDRuaZMwnCy6PHz82ybhERERERERE5cGCC8lKr9cjKSlJvPf29jbJuF5eXpL7xMREk4xLREREREREVB4suJCsMjMzodPpABRtJ7K1tTXJuPXr15fcp6SkmGRcIiIiIiIiovJgwYVkZbzVx8PDw2Tjenp6Su4TEhJMNjYRERERERHR07DgQrLKzMwUr03VMBcAGjVqJLm/e/euycYmIiIiIiIiehoWXEhWxg1zTdW/BQB8fHxgZWUl3icnJ0uOnyYiIiIiIiIyJxZcSFbGzWxNdUIRAFhbW8PX11fyGVe5EBERERERkaWw4EKyys7OFq+dnJxMOnbTpk0l9yy4EBERERERkaWw4EKyMj49yJRNc4HifVzu379v0vGJiIiIiIiISsOCC8nKuGmus7OzScdu0qSJ5P6vv/4y6fhEREREREREpWHBhWRl3MjW3t7epGM3b95cch8bG2vS8YmIiIiIiIhKw4ILySorK0u8NnUPFz8/P8l9TEyMSccnIiIiIiIiKg0LLiSr1NRU8drNzc2kY7do0UJyHxMTA0EQTDoHERERERERUUlYcCFZGZ9SZOoeLg0bNpRsU8rMzMSjR49MOgcRERERERFRSVhwIVmZc0uRQqGAv7+/5LPo6GiTzkFERERERERUEhZcSFYZGRnitYuLi8nHb9WqleT+5s2bJp+DiIiIiIiI6EksuJCs8vPzxWu1Wm3y8du1aye5j4iIMPkcRERERERERE9iwYVkVVhYKF5bW1ubfPzAwEDJPQsuREREREREZAksuJCsNBqNeG1ra2vy8Tt06CC5v379OnQ6ncnnISIiIiIiIjLGggvJSqvVitcqlcrk4zdq1AgeHh4AilbQNGjQAPfu3TP5PERERERERETGTL+Hg6gCjAsu5thSpFAoMHz4cPTt2xcvvviiWRrzEhERERERET1JIQiCIHcSVHcpFArxmv8ViYiIiIiIqLbgCheqNvR6PZRK8+1yEwQBcXFxSE9Ph5OTE5o0aWKWbUxERERERERE7OFCsjIusJirma1er8cPP/yADh06oHnz5ggKCkLLli3h6+uLBQsW4O7du2aZl4iIiIiIiOoubikiWanVavGkotzcXNjZ2Zl0/PT0dAwePBjnzp0r9R1bW1ts3rwZr7zyiknnJiIiIiIiorqLK1xIVsaNco0b6JqCXq/HyJEjyyy2AEVHU48fPx4HDhww6fxERERERERUd7HgQrIyXtGSm5tr0rG3bNmC3377rVzvCoKASZMmmTwHIiIiIiIiqptYcCFZOTk5iddZWVkmHXvz5s0Vej81NRV79+41aQ5ERERERERUN7HgQrJydnYWrzMzM002blpaGs6cOVPhuO3bt5ssByIiIiIiIqq7WHAhWdWrV0+8fvz4scnGTUhIgF6vr3BcTEyMyXIgIiIiIiKiuosFF5KVp6eneJ2cnGyycT08PCoVZ9zEl4iIiIiIiKiyWHAhWRkXRlJSUkw2bv369SWrZ8qrcePGJsuBiIiIiIiI6i4WXEhWxitcEhMTTTauQqHAtGnTKhw3atQok+VAREREREREdRcLLiSrhg0bitcJCQkmHXv27NkV2iLk7u6OkJAQk+ZAREREREREdRMLLiQr41OKsrOzTTp248aN8dVXX5X7/VWrVsHe3t6kORAREREREVHdxIILycrBwUG8zsnJMfn406dPx6ZNm2BnZ1fqO1ZWVvj6668xdepUk89PREREREREdRMLLiQr4xUl5ii4AMDkyZMRHR2Nt956S/K5l5cXZs2ahXPnzmH69OlmmZuIiIiIiIjqJoUgCILcSVDd9fvvv6NTp04AgHbt2uHGjRtmnU8QBERFRUGv18Pf3x8qlcqs8xEREREREVHdVP6OokRm4OjoKF7n5uaafT6FQoHWrVubfR4iIiIiIiKq27iliGRlvKUoKyvLonPrdDqcOnUKH374oUXnJSIiIiIiotqPW4pIVoWFhbCxsRHvtVotrKyszDpnbm4uevXqhVu3bomrahITE+Hl5WXWeYmIiIiIiKjuqFNbirKzsxEbGwsAaNu2Laytn/7jC4KAs2fP4ubNm1AqlejcubPYc+Rp/vzzT1y8eBE5OTlo2bIl+vXrB6Xy6YuKkpKScPLkSSQnJ8Pb2xuDBg0q13HF+fn5OHz4MB48eABXV1f07dsX3t7e5foZT506hejoaKhUKnTr1g3t2rUr189YVSqVCnZ2dsjLywMA5OXlSbYZmYO9vT1UKpVkC9OZM2cwcuRIs85LREREREREdYhQB8TExAjjxo0TVCqVAEAAINSrV0+YOXOmkJKSUmpcRESE0K9fPzHG8GfUqFHCrVu3So1LTEwUXn/9dUGhUEjiunTpIpw4caLUuLy8PGHlypWCk5OTJM7Hx0f49ttvBa1WW2KcXq8Xdu/eLTRt2lQSZ29vLyxatEjIzMwsdc6LFy8KvXr1KvYzhoSECHFxcaXGmZKnp6c4b3x8vEXmfO+99yQ/7xtvvGGReYmIiIiIiKhuqBZbisLDw7Fq1SpMmjQJw4cPN+nY33//PSZPniweOaxUKqHX68Xn/v7+uHbtWrEVJKGhoZgwYQL0ej2srKzQvn176PV6XL9+HUBRs9fz588XWwnyxx9/oFevXsjIyBDHd3FxwfXr16HRaAAA3333HUJCQiRxWVlZCA4OFsf39vZG48aNcevWLaSlpQEAZs6cibVr10riBEHA5MmTsXXrVgCAs7MzWrVqhcTERNy7dw8A0KVLF5w+fRp2dnaS2K+//hozZ84EULTSpH379tBoNPjjjz8AAG5ubrh48SL8/PzK92VXUkBAAG7dugWg6Ptr06aNWecDgIMHD2LIkCHivSVOSCIiIiIiIqI6xBJVndTUVOHQoUNCdHR0ic/HjRsnABCUSqWwfft2k827detWcQVDhw4dhCNHjggajUZITk4WFixYID5btmyZJC46OlpQq9UCAKFr165CRESE+OzixYtCYGCgAEBo3769ZNVJfn6+0LJlSwGA0LBhQ+GHH34Qn92/f18YMWKEAECws7MT7t+/L5kzJCREACCo1Wph1apVQmFhoSAIgpCVlSUsXrxYzHX//v2SuHXr1onPpk6dKqSmpgqCIAg6nU7Ytm2buFpm3rx5krhr164J1tbWAgAhODhY+PPPP8VnYWFhQkBAgABA6Nmzp6DX6yvz9ZdbUFCQ+DNcunTJrHMZpKWlFVuBlJycbJG5iYiIiIiIqPYze8Fl9+7dgoeHh1hQmTdvXrFf4O/cuSM0btxYACC4ubkJGRkZJpn7tddeEwAIkyZNEnJycoo9NxRA+vbtK/l8zJgxAgChTZs2Qm5ubrG4uLg4wcbGplgB5PPPPxe38pRUXCooKBBat25drABy5coV8Zf+Xbt2lfizTJ48WSyAGGRnZwv169cXAAhvvfVWiXHffPONAECwtbUVsrKyxM9feOEFsaBUUFBQLO7mzZuCUqkUAAgnT54scWxTMd7SdOrUKbPOZaxTp06SgsvevXstNjcRERERERHVbmY9Fjo2NhavvvoqUlJSxK08H3/8Mf73v/9J3mvWrBm2bdsGAEhNTcX+/ftNMv/atWtx8+ZNbN68ucyms8ZbbfLy8sT5P/nkk2LbcACgSZMmeOGFFwAAR44cET/ftWsXAOCdd96Bv79/sTiVSoUpU6YUi9uzZw8AoHfv3hgzZkyJOc6YMQMAcOHCBXGLkaGxrrOzM5YtW1ZiXEhICNRqNTQaDcLCwgAUfceG+desWQOVSlUsrnXr1ujTp0+xXEui0+nwySefYPXq1VixYgU+/PBDfPjhh/joo4+wZs0afP311wgNDcUPP/yAAwcO4MSJE0hPTxfjnZycxOvMzMwy5zKl5557TnJ/8uRJi81NREREREREtZtZTynatm0bCgsLAQAHDhzAO++8g9u3b2PhwoUICQmBi4uL+G5wcDD8/f1x69Yt7N69GxMmTKjy/La2tmjdunWJz1JTU/HLL78AAIKCgsTPw8LCoNFo4OzsjP79+5c6drdu3fDTTz/h6NGjAICMjAyEh4cDAEaPHl1mHABEREQgKSkJXl5eYkGjrLiOHTvC2toaWq0WJ06cwIgRI8S4gQMHSr5LYzY2NujUqRPOnz+Po0ePYtCgQfjtt9+g1+vh7e2NZ555psxcT548iaNHj+Lf//53qe/p9XrMmzev1Ocl2bBhA6ZNmwYAqF+/vvh5cnJyhcapimeffRZr1qwR7w0FKSIiIiIiIqKqMusKl9OnTwMA/Pz88MILL2DDhg0AgPT0dHzxxReSdxUKBZ599lkAEBvHmktubi7Gjx+P/Px8WFlZYeLEieKz3377DUDRapOyjo3u0KEDAODWrVvQ6XQICwuDTqeDq6ur+KysOEPdWJR6AAAgAElEQVRsWloarl69CqD4igtjarUarVq1AgBER0dLci0rznjOqKioYnEKhaLccaUpz1HXTzIcAw1Acgy08VHN5hYcHCy5v3HjhthcmYiIiIiIiKgqzFpwSUxMBFD0i62hoGLYivPZZ58hOztb8n7Tpk0BAA8fPoROpzNLTrdv30bv3r1x+PBhAMDy5cvRokUL8XlCQgIAoHnz5mWOY7yiJDc3V4xr1qxZmQUI4+0z2dnZSEpKEu/LO2dWVpYk16edImSIM3zflYkTyjjMqjIFF+N/e+NtW5YsuLi7u0v+7XU6Ha5cuWKx+YmIiIiIiKj2MmvBpaCgAABgZWUlfrZ8+XIAQFpaGtavXy9533h1QWV+iS+LIAjYvHkzgoKCcPXqVSiVSqxcuRILFiyQvGc4utk455IYtkoBEHukVCUOQJkraoC/v0+1Wl2pXA1x+fn55Yoznq+slTBlPSuNoQ8NIC1eGfd2sYSePXtK7s+cOWPR+YmIiIiIiKh2MmvBxbCC4vDhw+Iv7507dxZXuXz66aeSgoNhK1Hz5s0r9Ut8aTIzMzFu3Di89tpryM7ORvPmzXH69GnMnz+/2LuG5rpP21qSmpoKoKgRrkqlKneccaHBwcFB0sy3vLEODg6VyrWicU/OV5aKFsiMe7UY93B59OhRhcapqid72Fy4cMGi8xMREREREVHtZNamuXPmzMHhw4fx8OFDrF69GgsXLgQAvP/++zh06BDi4+Px3XffYdq0abh37564zWfo0KEmy+HBgwcYNGgQIiMjAQCzZ8/GypUrSy0i+Pj4AADu3LlT5riGgoHhNCJfX18AQFxcHHQ6XamrR4wLDS1atICNjQ0UCgUEQcCdO3fg5uZWYpwgCMXm9PHxwaNHjyqda0XjyvLee+8BKFo1o1KpIAgCCgsLkZ+fj5ycHGRlZUGj0aCgoACZmZmSn9Pd3V28Ni5IWUL37t0l9+Hh4RAEwaQFPyIiIiIiIqp7zFpwGTBgAPr06YPTp09j0aJF+PPPP/F///d/6N27N4KDg3HmzBmsWrUKo0ePRkhIiLj15eWXXzbJ/IIgYMyYMYiMjISTkxNCQ0MxZMiQMmM6deoEoOgUobJ+8TacSGQ4dahjx44AiprBxsbGllqkMMS1bNlSLDq0aNECt2/fxvXr19GlS5cS46Kjo5GRkQEA6Nq1q5jrtWvXymwyrNfrxVUbT+b6tObET/6MZfn444+f+k5pDFudgL+3O1lK+/btYW9vL/aOefToEe7du4cmTZpYNA8iIiIiIiKqXcy6pUihUOCbb75Bs2bNAAChoaFo3749evfuLZ5MExMTg1atWolH8o4aNQq9evUyyfxXr17F+fPnxbmfVmwB/i64pKSk4P79+yW+o9frceLECQB/FyM8PT3RsGFDAMDly5dLHf/48eOSOOM5yxPXuHFjNGjQoNxxN27cQEpKimROQ1xsbGypK0q0Wi1OnTpVLFdzqMi2KlOztraWHAsOlP19EhEREREREZWHWQsuQNHqjYsXL2Lq1Klin48zZ87g0KFD4juG04xGjRqFrVu3mmzuPXv2AADatm2LwYMHlyumadOm4uoGwzHWT/rxxx/FYkyPHj3Ez59//nkAwPr160s81ef+/fv44YcfSo3buXMnMjMzi8XpdDp8+eWXpcZFRkaKq1Ge9PnnnwMAGjZsKG4latu2LTw8PCAIAjZu3Fhi3LZt28RijPGc5mC8vcjSW4qAor5CxgzHdBMRERERERFVltkLLgDg4eGBjRs3IiUlBTt37sSECRPQqVMn+Pn5oWPHjpgxYwYiIyOxZ88eyRHBVfXnn38CAAYNGgS9Xo+kpCRERUXh0qVLOH36NMLCwoo1aVUoFJg9ezYAYPXq1fjxxx8lzw8ePIgpU6YAAHr16oUOHTqIz958800AwKlTp7BkyRLJiUTR0dEYMGAACgoK4OzsjJCQEPHZ+PHj4ebmhrS0NEycOFFSdMjIyMDw4cMRFRUFAHjrrbfEZ23btsVzzz0HAHjttdcQHR0tPtPpdFi4cCG+/fZbAEW9awzbo1QqFWbOnAkAWLp0KY4cOSL5Gffs2SN+By+++KK4QslcjP/N8/LyzDpXSZ5c4fL7779bPAciIiIiIiKqXRRCSUsxaolBgwbh0KFDUKvVKCgogF6vL/aOQqHAvHnzsGrVKvGzwsJCdOvWTfzFe+DAgejSpQvu3LmDnTt3QhAEqNVqnD17ttgv6zNnzsTXX38NoKg/yODBg5GRkYHt27eLq1fWr1+P119/XRK3bds2TJgwAUDRqT2vvvoqlEol9u/fj9jYWADAxIkTsWXLFklcVFQUOnXqhPz8fNjY2CAkJASenp4ICwvD2bNnAQDt2rVDeHi4pFFwbm4uOnbsiNu3bwMAXnrpJQQGBiI6Ohrff/89AMDJyQkXL15Eq1atKvK1V9hff/2F5s2bAyjaMnX37l2zzvekGzduIDAwULz38fHBgwcPLJoDERERERER1S61uuCyaNEiLF++vMRnDg4O0Ol0yM/PR6tWrcTVMAYZGRl4//33sXbt2mLbgzp27Ig1a9aIq0uMabVafPXVV1i4cCGys7Mlz7y9vbF06dJixRaDX375BW+88UaxgoNarcbbb7+NpUuXShrMGty8eRMzZszAmTNnij0bM2YMPvnkEzRq1KjYs5SUFPzzn//Epk2bij3r1q0b/vvf/5p9OxFQtKXM29sbQFEvnKSkJLPPaaygoACOjo6SFUlpaWlwdXW1aB5ERERERERUe5i14LJ+/Xr89ttvcHBwgKOjo/jH3t5ePApZr9dDr9dDEATodDpkZGTA1dUVb7/9donFhYrQ6XSIiIhASkoKGjRogAYNGsDe3h729vZQKpXQarW4evWqpBHtk8LDwxEaGooHDx7Azc0N/fv3x+jRo8V+NKW5f/8+vvrqK9y5cwe2trYICgrCjBkzJA1iS5KTk4Mvv/wSkZGRKCgoQIsWLfDmm2+KDXlLo9frsW3bNoSFhSE1NRUNGzbElClTxAa5ZTl58iS+//57xMfHw93dHYMHD8awYcMsdjRyamqqeDS0q6urLH1c2rVrhz/++EO8DwsLQ3BwsMXzICIiIiIiotrBbAWXrKwsODs7Vzr+q6++whtvvGHCjKi6yszMhIuLC4CilUdPrgyyhHHjxmHnzp3i/bp16zBjxgyL50FERERERES1g9ma5jo4OGDo0KGVilWr1cV6o1DtZWNjI14bb+uxpICAAMl9TEyMLHkQERERERFR7WBtroENDV/z8vKQnJyMlJQUaDQaFBQUQKvVQqlUin8UCgVu3bqFqVOnAig6jtkSvUOoerC2/vu/oVarlSWHli1bSu4NzYSJiIiIiIiIKqPaNM3VaDRwdnZGQUEBXn75Zezbt0/ulMhCdDqdWHRRKBQlniZlbhcuXJAU+dq0aSPp6UJERERERERUEWbbUlRRtra28Pf3B4AST9uh2su4Oa9c9T/D/z2D2NhYWQo/REREREREVDtUm4ILANSvXx8AkJycDI1GI3M2ZCmWOg2pLPXq1ZMcA63RaJCQkCBjRkRERERERFSTVauCizGuLiBLa9GiBWxsbBAUFIR+/fohOTlZ7pSIiIiIiIiohqo2PVzi4uLQunVr5Ofnw9vbG/Hx8XKnRBZi3MMFkG9b0ZkzZ9CxY0c4OjrKMj8RERERERHVHmY7pUir1WLYsGEIDw+Hl5cXmjRpAl9fXzg4OECr1aKgoAAZGRl49OgR7ty5g3v37omxISEh5kqLqiHjAotSKd+iq+DgYNnmJiIiIiIiotrFbCtc7ty5Az8/vwrHderUCceOHYObm5sZsqLqSKPRQK1WAwBUKhUKCgpky0UQBERGRuLRo0dQq9Vo2bIlPD09ZcuHiIiIiIiIaiazrXBp1qwZli9fjh9++AGxsbFIT08v9o5KpUKjRo3QuHFjNG7cGM8++ywmTpwo2V5CtZ9xg2QbGxtZctDr9Th48CA+/PBDXL58WfzcysoKQ4YMwezZs9GvX79q0eCXiIiIiIiIqj+L9XDJzs5GZmYmNBoNHBwc4OjoCDs7O/4CS3j8+DE8PDwAAK6urkhLS7Po/BqNBmPGjMFPP/1U5nszZ87El19+CSsrKwtlRkRERERERDWVxZaSODo6shkplSgnJ0e8luP/yFtvvfXUYgsArFu3DnZ2dvjss88skBURERERERHVZNX2WGiqO4wLLg4ODhadOzw8HBs2bCj3+2vWrJFsOSIiIiIiIiIqSZVXuERFRSE7OxsKhQJWVlawsbGBSqWCSqWCtbU1rK2tYWVlBaVSCVtbW9ja2sLa2ppbiUiUn58vXlu6h8v27dsrHLNx40Z06dLFDNkQERERERFRbVGlgsvmzZvx2muvVThOqVRCrVbD1tZW/NvGxgZ2dnZwcXHBG2+8gbFjx1YlNapBsrKyxGsnJyeLzn3w4MEKx+zatQtffvklmzsTERERERFRqar0G2NsbGyl4vR6PXJzc5Gbm1vi82vXrrHgUodkZmaK1y4uLhadOzExscIx6enpyM7OhqurqxkyIiIiIiIiotqgSgWXDz74APXr10dGRgb0ej10Oh0KCwtRUFAArVaLwsJCaLVa6PV66PV68bO8vDzk5uYiJydHvM7Ly0NBQQH0ej2mTJliqp+PaoCMjAzx2tIFF09PT9y9e7fCcXIdX01EREREREQ1Q5UKLmq1Gm+//bapcqE6ynilk729vUXnbtOmTYULLp6enhbPk4iIiIiIiGoWnlJEssvOzhavLd3DZdasWRWOeeWVV8yQCREREREREdUm1a7gkpmZiQcPHsidBlmQcQ8XR0dHi849ePBg+Pv7l/t9hUKBt956y4wZERERERERUW1g9oKLXq/HqVOnJEf/lvTO2bNnMX36dPj4+MDPzw+3b982d2pUTaSkpIjXHh4eFp1bqVRi165d5e4d83//939o0aKFmbMiIiIiIiKims7s59rOnDkTGzZsgI2NDRo1agRXV1fY29vD2toaer0e2dnZiImJkTROdXJyglqtNndqVE0Y93Cx9AoXAOjYsSNOnz6NkSNHIiYmptT3lixZgsWLF1swMyIiIiIiIqqpzFpwCQ8Px4YNGwAABQUF5TpG2tnZGT/99BMaNWpkztSoGsnKyhKvHRwcZMkhMDAQkZGR2LJlCxYvXoykpCQARQ1yx4wZg7FjxyI4OFiW3IiIiIiIiKjmMWvBZfv27UWTWFtj6NChiI2NRWpqKmxsbODo6Ag3Nzf4+PjAx8cHZ8+exZkzZ6BQKBAYGGjOtKiaefTokXhdv3592fKwtbXF9OnTMX36dKSnpyM7OxsNGjSAtbXZF4IRERERERFRLWP2FS4A8NJLL2Hv3r1lvpuamoq2bdsiMTERa9euxfvvv2/O1KgaMW6a6+rqKmMmf3N1da02uRAREREREVHNY9amuYatIuVZteDm5obp06cDAL799lsIgmDO1KgaSU1NFa+rW5FDo9HgxIkTWL16tdypEBERERERUQ1i1oJLw4YNAQAnTpyATqd76vudOnUCAMTGxkq2mVDtlpiYKF43aNBAxkz+Fh8fD19fXzg5OaFv375YsmQJtFqt3GkRERERERFRDWHWgsvYsWMBALdv337qliKg6IheA65wqRu0Wi00Gg0AQKFQyNY090ne3t7Q6XQoLCwEAOTl5eH69esyZ0VEREREREQ1hVkLLiEhIeIWkVmzZiEiIqLM93fu3Amg6KQid3d3c6ZG1YTxceDOzs5QKBQyZvM3hUKBHj16SD47f/68TNkQERERERFRTWPWgouDgwPmzZsHoKhPR8+ePbF48WLExcVJ3ktMTMSiRYuwY8cOAMD48eOhUqnMmRpVE48fPxav3dzcZMykuGeeeUZy/9tvv8mUCREREREREdU0CsHMe3f0ej0mTZqEbdu2ST5v3bo1nJ2d8ejRI/z111/i50qlEpcvXxb7uVDtduXKFXTp0gUA0LFjR1y7dk3mjP5mnBtQ1NA3JSUFVlZWMmZFRERERERENYFZV7gARQWULVu2YOXKlZITaP78809cuHBBUmyxt7fHli1bWGypQ3JycsTr6tK/xaBjx46oV6+eeJ+env7UbXFEREREREREgAUKLkBR0WX+/Pl4+PAhNm/ejOeeew5NmjRB/fr14efnh1deeQUbN25ETEwMQkJCLJESVRPJycnidXXr22NlZYVnn31W8hm3FREREREREVF5WJt7AkEQxEao9vb2mDRpEiZNmmTuaamGMD4S2tvbW8ZMSta3b1/8+OOP4v2xY8cwd+5cGTMiIiIiIiKimsCsK1z+8Y9/wNXVFePGjcPBgweh0+nMOR3VQJmZmeK1s7OzjJmUrH///pL7sLAw8RhrIiIiIiIiotKYteCyZ88eZGZmYufOnRgyZAj8/PywYsUKJCUlmXNaqkGMCy4uLi4yZlKygIAANGzYULzPzc3FuXPnZMyIiIiIiIiIagKzFlw2btyI9u3bi/d3797FBx98gEaNGmH8+PG4cOGCOaenGsC44OLk5CRjJiVTKBTFVrn8+uuvMmVDRERERERENYVZCy4DBgxAREQELl68iNmzZ8PNzQ0AUFhYiB07dqBHjx7o2bMndu7cicLCQnOmQtXU48ePxevq1jTXYNCgQZL7gwcPypQJERERERER1RRmP6VIoVCga9eu+OKLLxAfH49du3ZJVgyEh4dj3LhxaNasGVasWIGUlBRzp0TVSG5urnjt6OgoYyalGzhwIKysrAAAnTt3xowZM9jHhYiIiIiIiMpkkWOhDWxtbTFmzBgcOXIEd+7cwdy5c+Hq6goAePjwIT744AM0bNgQ77zzjiXTIhkZFy5sbW1lzKR0rq6umDRpEvbv34/Lly/j7bffrra5EhERERERUfWgEARBkGvy3NxcbN++HXPmzEFOTo74eaNGjXDv3j250iILCg4OxtmzZwEAp06dQp8+fWTOqGQ6nU5c5UJERERERET0NBZd4QIU/eJ6/PhxTJ48GV5eXpg+fbqk2NK6dWts3brV0mmRTIz/7R0cHGTMpGyGYotOp8OuXbvQo0cPeHt7w8fHB8888wy++uorSQNgIiIiIiIiqtsstsIlMjIS3333HbZv346HDx9Knrm4uGDcuHGYPHkyunXrBoVCYYmUqBrw9/fH7du3AQBRUVEICAiQOaPShYeHY/LkyYiOji7xuaOjIz7++GPMnDnTwpkRERERERFRdWNtzsFTU1OxZcsWfPfdd7h27ZrkmeG43ddeew3Dhg2DnZ2dOVOhaqqgoEC8VqlUMmZStuvXr2PAgAHIysoq9Z3s7GzMmjULWVlZmDdvngWzIyIiIiIiourGbCtcBEFAQECAuHrBoEmTJpgyZQomT56Mxo0bm2NqqkF8fHwQHx8PALh37x4aNWokc0bF6XQ6BAUF4fr16+V6X6FQ4PTp0wgODjZzZkRERERERFRdmXWFS15eHgDAxsYGL7/8MqZOnYp+/fpBqbR46xiqpoxPKVKr1TJmUrpTp06Vu9gCFBUbv/jiCxZciIiIiIiI6jCzFVwUCgXCwsJw/vx5DBgwAO7u7uaaimowrVYrXltbm7X+V2k//vhjhWP279+PtLQ01KtXzwwZERERERERUXVn1t9wmzZtiqZNm5pzCqrhakIPl6tXr1Y4RqPRICIiAs8995zpEyIiIiIiIqJqzyJLCgRBQEJCAhITE5GSkgK9Xg+lUgmdToe0tDTExcUhNjYWd+7cQUpKCnx8fBAaGgo3NzdLpEcyMi642NjYyJhJ6VxcXCoVp9PpTJwJERERERER1RRmLbhoNBqsXLkSW7duxZ07d8odFxkZiePHj2P06NFmzI6qA+OihJWVlYyZlK6yq7S8vLxMmwgRERERERHVGGbtXrtkyRIsWbKkQsUWDw8PDB06FAMHDjRjZlQdVddmyiNGjKhwjLe3NwICAsyQDREREREREdUEZjsWOikpCT4+PtDpdLC1tcWIESPQv39/ODk5QaPRICcnB4IgwN7eHp6envDx8UHTpk3h6OhojnSomlIoFOK1Xq+X3FcXgiCgY8eOFTqpaNmyZVi4cKEZsyIiIiIiIqLqzGwFl4iICHTs2BEAMG3aNGzYsMEc01ANZ1xg0Wq11XZb0YkTJzBw4EAUFhY+9V0PDw9ERUXxZC4iIiIiIqI6zGx7OJo3bw61Wg0AOH36NDQajbmmohrM+GQi4yOiq5vnn38e+/btg52dXZnveXp64vjx4yy2EBERERER1XFmK7g4OTlh2bJlAIBbt25h6dKl5pqKajBr67/7NlfnggsADBkyBBERERgzZkyxZ/b29hgxYgQuXbqEwMBAGbIjIiIiIiKi6sRsW4qAol+ge/bsicuXLwMAXn/9daxatQr16tUz15RUwzg7OyMrKwsAkJaWBldXV5kzKp+EhARs27YNWq0Wfn5+eOmll566+oWIiIiIiIjqDrMWXAAgMTERL730klh08fDwwPz58xESEoIGDRqYc2qqAdzd3ZGamgoASE5OhoeHh8wZEREREREREVWd2Qoujx8/xrvvvourV68iPT0d8fHxkudWVlbo06cPmjVrBi8vL6hUKjx+/BgZGRkYPHgwXnnlFXOkRdWMt7c3EhMTAQAPHjyAj4+PzBlV3vXr1+Hg4AA/Pz+5UyEiIiIiIiKZma3gsmzZMixevLhSsVZWVsjLy5M0VKXaqUWLFoiNjQUAREdHw9/fX+aMKmb37t04fPgwzp07h6ioKMyaNQv/+9//5E6LiIiIiIiIZGa2prnDhw9H27Zt4evri4CAALRv3x4BAQHw9fWFg4NDmbEDBgxgsaWOMO57UhNPsrKzs8O3336LqKgoAMCuXbtQUFAgc1ZEREREREQkN+unv1I57du3R2RkZKnPCwoKkJ6ejrS0NOTn50Ov18PDwwMeHh5sPlqHGI4OB4C8vDwZM6mcAQMGwM3NTexDk5qaioMHD+Lll1+WOTMiIiIiIiKSk9lWuDyNjY0NPD09ERAQgA4dOqBTp05o1KgRiy11jKOjo3idnZ0tYyaVY2trW6zfUGhoqEzZEBERERERUXUhW8HFWFxcHBYtWoTff/9d7lTIwmxtbcXrmrilCABCQkIk94cPH66Rq3WIiIiIiIjIdCxScNHr9Xj48CFyc3NLfP7BBx9g+fLl6NOnD8LCwiyRElUT9vb24nVp/z+qu+7du8PLy0u8z8rKwsGDB2XMiIiIiIiIiORm9oLL5cuX0aVLF/j6+sLX1xdbtmwp9s6bb74JJycnZGVlYeLEiWw6WocYF1xq4pYiAFAqlcW2Fe3bt0+mbIiIiIiIiKg6MGvB5dGjR+jfvz+uXbsGAEhLS8PkyZOxf/9+yXvPPPMMvvnmGwBF24sOHTpkzrSoGnFzcxOvU1JSZMykakaNGiW5P3ToELRarUzZEBERERERkdzMWnDZsWMH0tPTAQD/+c9/4OHhAQB45513ivXrGDFiBBo2bAig6GhdqhsaNGggXiclJcmYSdX07NlTUjxKS0vDhQsXZMyIiIiIiIiI5GTWgothpYqXlxdmz56Nzz//HABw9+5dbN68WfKulZUV+vbtCwD8RbUOcXZ2Fq+zsrJkzKRqrKysMHDgQMlnv/76q0zZEBERERERkdzMWnCJj48HAPTr1w9WVlYYO3YsgoKCAAAfffQRCgsLJe/7+/sDAO7fvw+9Xm/O1KiaMF7hYvj/UlMNGjRIcn/gwAGZMiEiIiIiIiK5mbXgYmiC6uDgUDSZUol///vfAIpWuezcuVPyvqHnxZOFGKq9fHx8xOuHDx/KmEnVvfjii1AoFOJ9REQEEhISZMyIiIiIiIiI5GLWgouvry8A4OzZs+KKlYEDB6Jz584AgJUrV0pWsty6dQsA0LBhQyiVFjmxmmRmXHCp6cUJd3d3dOvWTfLZL7/8IlM2REREREREJCezVjWmTp0KALh58yZ27NgBAFAoFHj//ffFz3/66ScAQEZGhrgF48UXXzRnWlSNGDeaffz4MQRBkDGbqnvy/+7BgwdlyoSIiIiIiIjkpBDM+BuuTqdDYGAgbt68CZVKhaVLl2L27NlwcHBA27ZtERUVhW7duuH8+fOYMGECQkNDART1vhg8eLC50oIgCFi/fj22b9+OL7/8EoGBgZLnt2/fRmhoKNRqNVQqFQoKCpCfn4+CggIolUrY2tri0aNHqF+/PhYuXFjiapzc3Fx8/vnnOHfuHHJyctCiRQv84x//EPvUlEav12PHjh3Yv38/kpOT4e3tjWnTpokNhcty7tw5rFu3Dg8ePICLiwuGDBmCyZMnw8rKqsy4u3fv4pNPPkF0dDSsra3RvXt3zJkzR9LQ1pycnZ3FhrmPHz+WFGFqmitXrqBLly7ivYuLC1JSUmBtbS1jVkRERERERGRxgpmdOXNGcHZ2FgAIAAQnJydh5syZwquvvip+1qNHD8m1Vqs1Wz55eXlCSEiIOF9oaGixd/71r3+Jz5/256+//ioWv2PHDqFRo0bF3rWyshJmzZol5ObmlpjbhQsXhO7du5c4zwsvvCDExcWVGPfgwQPhlVdeKTGuTZs2wunTp0uMy83NFT744APB1ta2WJyHh4ewYcOG8n+xVdC8eXNx3lu3bllkTnPR6XSCu7u75Ls8f/683GkRERERERGRhZl1hYtBZGQkXn/9dYSHh5f5Xtu2bXH06FF4e3ubJY8HDx5g+PDhuHLlivjZsWPH0K9fP8l7Z86cQe/evQEAPXv2hJOTE2xsbKBSqaDVaqHVauHh4YGpU6eiT58+kkapW7duxaRJkwAAHh4eeP311+Hq6opDhw7hxIkTAIAJEyZg69atkjlv3LiBHj16IDc3FyqVClOmTEGLFi0QERGB0NBQ6PV6tG3bFuHh4XB0dBTjMjMz0b17d0RFRQEAhg0bhl69eiEhIQEbN25EVlYWnEu+uZoAACAASURBVJyccOHCBbRu3VqMEwQBr7zyCnbv3g0ACAoKwsiRI1FYWIjNmzcjLi4OABAaGopx48ZV6Xt/mqCgIFy7dg0AcOnSJckKkZpo7Nix2L17Nzw8PODj44PZs2dj2rRpcqdFRERERERElmSpyo5OpxPOnj0rLFy4UOjUqZOgUqkEAIJKpRJ69eol7NmzRygsLDTb/Hq9XmjTpo0AQFAqlYJCoRAACIcPHy727tmzZ8XVCdnZ2eWe4+HDh4KdnZ0AQBg6dKiQnJwsmX/79u3iuMeOHROf6XQ6ITAwUAAgtG7dWrhx44Zk3N9//12oV6+eAEBYsmSJ5NmsWbMEAIKzs7Pw888/S54lJycLnTt3FgAI/+///T/JM+NcVq5cKfnu8/PzhSlTpogrXTIyMsr9HVTGc889V+L3UlOdOnVKuHLlitxpEBERERERkYwsdhSQUqnEM888g2XLluHq1avQaDTIy8uDRqPBmTNnMGrUKLP2uVAoFPD19UXr1q1x6tQp2NraAgBycnKKvZueng4AcHV1FY+0Lo/PPvsMeXl5aN68OXbs2AEPDw/J/OPHj8eIESMAAN9884347Oeff8b169dhbW2NvXv3ol27dpJxO3TogMWLF4txwv+/KCkxMRHr168HAHz++ecYMmSIJM7DwwPr1q0DULSSx7BqBQCWLVsGoKix8fz58yXfva2tLT7//HO4u7sjJSUFP//8c7m/g8pwcnISrzMzM806lyX06dMHQUFBcqdBREREREREMpKtk6dCoYBarbbonIcPHxaLFRqNBgCgUqmKvZeYmAgAaNq0KfLz83Hy5EkcOnQIDx8+hKOjI4YOHYrhw4dLthIBf59IM2/ePNjb25eYw9ChQ7Fv3z4cO3YMer0eSqVSjBszZoxk28+TcXPmzMH9+/dx69YtBAQE4MiRI9DpdGjWrBlCQkJKjOvSpQu8vb2RkJCAY8eOYdq0aYiNjRW3IC1atKjEOAcHB/Tr1w+7d+/G0aNH8eqrr5b4HlDUHHnNmjXQ6/Xiliug6LtVq9Wwt7eHk5MT7OzsoFKp4ODggPbt24sFKRcXF3EsQ/Pc2iAzMxNxcXEoLCyEl5eXeEw6ERERERER1X5mL7gIgoD//ve/OHXqFFxdXeHn54eAgAAEBASgSZMmcHZ2Lla4MCeFQoGMjAyx8FLSCpaEhAQAQFpaGpo2bYqkpCTJ882bNyMoKAj79+8Xf4m+d++eWMR44YUXSp2/a9euAIDk5GTcvHkTbdu2xZEjRwAAgwYNKjWuWbP/j707j4/xXP8H/plkJplksq9iCVFKLBWKqqVIqaK1nKO+WkVtLbVUqaObWqtoHVXaOj3d1FLl1FqcWoLYammDkFhiCxEi+55MZp7fH/nNfWbMTPbJI5nP+/Xyet3Pcj3PNRF/zOW+rzsEvr6+SElJwcGDB0XBBQCee+65Enci6tChA3bs2IGDBw9i3Lhx2LdvHwCgRYsWaNiwYYlxmzZtEr1nrNHr9Zg5c2aJ9zxsxYoVmDp1KgCY9KSpDQWXpKQkLF++HF988QVyc3PF+Q4dOmDChAl45ZVXqr3YSERERERERNXL5gWXiIgIvP3229YTUCrh7e0Nb29v+Pj4iD/+/v5o1aoVOnTogFatWlVpUSY1NVWMAwICzK4bCi63bt0CUFwQ6N+/P0JCQpCQkID169fjr7/+wtChQ3Hs2DEoFAqcOnUKAFCvXj00atTI6ruNt4W+e/cu/P39xXu6du1qNU6hUKBJkyZISUnB3bt3AQAnT54EAHTp0qXEz2t458NxJb0PAJo2bSriJEmy+ndgaVvs0mRkZIhxbVpStGfPHgwZMsSk0GJw+vRpnD59GsuXL8euXbsQHBwsQ4ZERERERERUHWxacMnMzBQ79lhTVFSEBw8e4MGDB1bvCQ0NxbJly0qcAVIeKSkpYhwYGGh23bCkCChekrNjxw6TnZPGjh2Lnj174sSJE2JHI0MRx1IBx5hSqYRSqURRUREKCwtNij/+/v4lxrq4uAAACgsLAaDM77QWV9b3FRUVVXnBJSkpSYyN8yjp9+BRd+7cOQwePFgsV7PmwoUL6N27N06ePAkvL69qyo6IiIiIiIiqk02b5m7evBkJCQlQqVS4cuUK4uPjcezYMaxduxYffPABwsPDTXqodO3aFX379sXTTz8NX19fcT42Nhb9+vXDO++8UyV5JScnAygufvj4+JhdNyxradmyJX7//Xezbaq7d++OZ555BkBxM1oAohhh6F9iTX5+vrjn4eVMOp2uxFhDXoY4wzttHefi4lJiUaUis4+MZ7h4e3uLsaFhcU30xhtvlFpsMbhy5YrV/jlERERERERU89m04HLx4kUAQO/evdG0aVM0aNAAnTt3xquvvoqFCxfiwIEDuHnzJgYOHAgAOH/+PKZOnYrjx4+LHicffPCB6HexbNkyREREVDovQ8ElICDAYiFhwYIFePfddxEREWGxIAMAnTp1AgCxlMhQzDAuJFiSlpYmxh4eHib9S8oa6+HhUaF3VjauJOWd5ZKdnS3GxkuKjM/XJJcuXRJLtcpq7dq1yMvLs1FGREREREREJCebLikyLGGpU6eO1Xvq1q2LrVu3Yvr06fj888/x97//HdHR0WjcuDFCQ0OxcOFCNG/eHCNGjAAAbNiwAeHh4ZXKy/Cl3nhmhbGOHTuiY8eOJT7DUIgxzAJp1qwZgOLmuVlZWSZFBGOGfi1KpRItW7YUu/bk5OQgJiYGDRo0sBin1WpFb5m2bduKd8bHxyMmJqbEXA3vNI4DUO64kkyfPh0A4OjoCJVKBUmSoNVqkZ+fj5ycHGRlZaGgoACFhYXIzMw0+Z0wLjrV1IKLYaep8sjIyMBvv/2Gl156yQYZERERERERkZxsWnAx9Oa4fft2ifcpFAp88skn2L59O27cuIGvv/4an376qbg+fPhwbNmyBVu3bsW+fftK7CdSFvn5+QBgdevmsjAUPwxbGrds2VL0Zrlw4QKefvppi3GRkZEAgDZt2oiZO0888QROnDiBc+fOoU+fPhbjzpw5g7y8PDg4OKBdu3YAigsh+/btw7lz56zmWVBQgD/++AMARBHJUEA5f/58iT9LQ66lFZ8AmPx9lZehVwyAGjvj486dOxWKu379ehVnQkRERERERI8Cmy4p6tatGwDgwIEDuHHjRon3qtVq9OvXD4D5zAuFQiGuxcfHV3onG8MX/LL223iYXq/Hli1bAEAUVtRqNVq0aAEAOHz4sNVYw0wI4yKGoQBSlriWLVuKGSGGuBMnTlj9LAcPHhQFpvbt25vEpaWl4cKFCxbjkpOTzQo1tmK8RXJNLbiU1oDYGqXS5huFERERERERkQxsWnDp0aMHGjduDL1ej48//hiSJJV4/82bNwGYzngwMF52kpOTU6m8DA15Db1cHnbu3DmsW7fOar4bNmxAfHw8AOCVV14R5wcPHgwAWLVqlcX+KHv27BGzRp599lmzuD179iAqKsos7vbt21i1apVZXJ8+faBWq5GcnIxvv/3WLC4vLw9z584FADz55JNiCVX9+vVF8WXRokVmcZIkYd68eSgsLIRarbY6W6eqGGYJAaX3lXlUNW/evEJxDRs2rOJMiIiIiIiI6FFg04KLg4MDxowZAwD47rvvMGnSJNHz5GFHjx7F7t27AQD9+/c3u278RdzJyalC+RQVFSE2NlbshJOamoqjR4/i8uXLJve99NJLGDFiBGbMmGFSdNHpdFi3bh3Gjx8PAOjVqxcaN24srk+cOBHe3t5ISEhA7969cfbsWQDFBYyvv/4aAwYMAFD85XzQoEEiLjw8HJ06dYIkSXjhhRewdetW8d7IyEi0b98eGRkZcHJyEr1SgOIeNJMmTQIAvPPOO1i6dCm0Wi2A4plAXbt2FY1c33//fZPP+OGHHwIANm7ciHHjxomtsnNzc/Hqq6+KAs+ECROsNg6uKsZNeSs7e0ku/fv3N9vNqjTu7u547rnnbJQRERERERERyUkhlTbtpJKys7PxzDPPiJkbarUavXv3Rvfu3eHu7o6kpCScPHkSu3btgiRJ8PHxwZ07d8xmubzzzjtYtmwZHBwckJeXV+6ii16vR4cOHfDXX3+ZXVMoFIiOjkbLli0BAHPmzMH8+fMBAKGhoejWrRuUSiX27t2LuLg4AMXNfv/44w+zJre//vorXn31VeTn58PBwQGNGzdGRkYGHjx4AKC4b8yxY8cQFhZmEhcbG4tnn31W9IapX78+HBwcxEwaAPj+++8xevRok7jc3FyEh4eLwoqPjw98fX1x48YNsf30mDFj8O2335r1apk0aRK++uorkVeDBg1w584dMYMoLCwMR48eNdu+uqo9ePAAAQEBAIpnH1mbefSoW7hwYbm2ep42bRqWL19uw4yIiIiIiIhINlI1uHfvntSjRw8JQIl/1Gq19N///tfiM/r27SsBkBo3blyhHPR6vRQeHi55e3tLnp6ekru7u/jz+OOPS4mJieJenU4nLVq0SPL29jbL0cHBQRo0aJB069Ytq++Ki4uTnnvuObO40aNHSzdv3rQal56eLk2ePFlSKBQmsT179pROnDhhNa6oqEhasWKF5ObmZhLXtGlTaePGjZJOp7Mau3v3bqlRo0Ymcd7e3tKSJUuknJycUn6qVSMjI0O8W6PRVMs7bSEvL0/q2bNnqb/nAKTg4GDp7t27cqdMRERERERENmLzGS4GOp0Ov//+O9avX49t27YhNzdXXNNoNBg8eDD+8Y9/oHXr1hbjhw4dis2bN2P+/PnlmkVQGZmZmfjuu+9w6dIlFBUVISQkBCNHjkRwcHCpsZIk4a+//sK1a9fg7OyM1q1bmyw/KklcXBxiYmKQn5+PJk2aoG3btmXalSkpKQlRUVFITU1FUFAQunTpApVKVWpcbm4uTp8+jYSEBPj6+uKpp56Cl5dXmXKtCnl5eWLHKCcnpwo3M34U5ObmYuTIkfj111+t3tO8eXPs3r0bISEh1ZgZERERERERVadqK7gYy87OxtWrV5GamgqNRoPWrVuXumwlMzMTp06dQnh4OBwcbNp6hqqZVqsVS8QcHR3FUqiabP/+/fj000+xd+9eca5r164YOHAgxo8fb9IomIiIiIiIiGofWQouRMb0ej0cHR3FcW36lSwoKMClS5cQEBBQ7qa6REREREREVHNVScGlqKgIZ8+eRVhYGJRKZVXkRXZEkiSTWUu1qeBCRERERERE9qlKqiP16tVDUlISmjdvjpiYGNFvJC8vDxs2bEB2djZcXFzg4eEBT09PeHh4wMXFBY6OjtDpdCgoKEBBQQG0Wi0CAwPxxBNPVEVaVEPYS4ElOTkZ27dvx9ixY+VOhYiIiIiIiGys0jNc0tLS4OPjI46zsrLg5uYGAJg7dy7mzZtX7mfu2LEDL774YmXSohqkNvZwMTBsR56cnCy2+M7NzTXb9pyIiIiIiIhql0p3n/X29kZYWBgAoE+fPqLYAqDCPSsyMzMrmxbVIIWFhWJcll2VahIHBwfcuXNHFFsAICMjQ8aMiIiIiIiIqDpUWdPcoqIii/1bLl68iOTkZOTm5iIjIwOZmZnIyMhAfn4+dDodHB0d4ezsDGdnZyiVStSrVw8DBgzgTkR2JCMjQ2xD7e7uXusKbo0bN8aNGzfE8ZUrV9C0aVMZMyIiIiIiIiJbq7IOt9aa5bZs2bKqXkG1VEFBgRg7OzvLmIlt+Pn5mRRc7t27x4ILERERERFRLcdpJCS7/Px8Ma6NBZeHl9bdu3dPpkyIiIiIiIioulS64CJJEu7cuQOdTlcV+ZAdMm6SW9t6uACAv7+/yXFqaqpMmRAREREREVF1qXTB5d1330WDBg0wYMAAq/cUFBSYNA0lMmY8w8WwW1Ft4uvra3KcnJwsUyZERERERERUXSpVcNHpdPjmm28AAEePHrV4j2Fb3IYNG2LlypUlPi89PR1du3ZF06ZNERsbW5nUqAYxbpLr6ekpYya2ERgYaHKcmJgoUyZERERERERUXSpVcDl79izS09MBAO3bt7d4T1paGqKjowEA27ZtK/F5x48fx7FjxxAXF4f169dXJjWqQQy/QwDEbkW1iZ+fn8mx8eclIiIiIiKi2qlSBZfz58+L8VNPPWXxHg8PDzG+f/9+ic+rU6eOGN+9e7cyqVENkpKSIsYPL7+pDdzd3U2OMzIyZMqEiIiIiIiIqkulCi5paWli3LhxY4v3qFQq8SW6tIKL8ewG4y/hVLsZFyCMC3S1xcNNc5OSkmTKhIiIiIiIiKpLlRVcSpqZYJi5kpKSYrIjzcOMd6gp6T6qXWr7DBcfHx+TYy4pIiIiIiIiqv0qVXDRarViXNLuMkFBQQCKt5B+8OCB1fuMn2H8bKrdcnNzxVij0ciYiW14e3ubHHOXIiIiIiIiotqvUgUX4+UfxrNdHmbcm6WkZUXOzs5izIKL/cjKyhLjh/ud1AYBAQFwdHQUx6mpqcjLy5MxIyIiIiIiIrK1ShVc6tevL8Y3b960ep9hhgtQcsFFqVSKcUkzZqh2MS641MYZLo6OjmY7FZVUoCQiIiIiIqKar1IFl9DQUDE23rHoYWWd4aLT6cTY1dW1MqlRDZKYmCjGxsW52oTLioiIiIiIiOxLpQourVq1Eo1uT5w4AUmSLN5n/CX63r17Vp9nXIxp0aJFZVKjGiQzM1OMjXeqqk0eLiQZF5mIiIiIiIio9lGWfot1Li4uePLJJ/HHH3/gzp07GDRoEHJycqBUKuHk5AR3d3d4enqa/G/+8ePHsXv3bmg0Gjg5OaGoqAjZ2dlISkrCunXrxH0dOnSoTGpUg+Tk5IhxbZ3ZZDzLCwDu3r0rUyZERERERERUHSpVcNFqtYiJiRHHO3bsKDVm+/bt2L59e4n3aDQadOnSpTKpUQ2SlJQkxv7+/jJmYjsPz3Ax/sxERERERERU+1RqSZGjoyMaNGhQVbkAAJo2bYpNmzbV2i/eZEqSJJMGsj4+PjJmYzsP/z6z4EJERERERFS7VWqGi4ODA06cOIGzZ89Co9EgODgYPj4+0Ol0KCgoQHZ2NjIyMpCRkYFr164hPj4eXl5eyMrKQm5uLgoLC6FUKqHRaBASEoKuXbuaLb2g2i01NVVsAe7p6QkXFxeZM7KNwMBAk+OSmkcTERERERFRzVepggsAuLu7o1u3bibnHBwcoFKp4ObmJgooHTt2rOyrqBayh9ktgHkPl4SEBJkyISIiIiIioupQqSVFRJVl3DBXo9HImIltPbz0jgUXIiIiIiKi2o0FF5JVRkaGGHt4eMiYiW093DS3pO3RiYiIiIiIqOZjwYVkZVxw8fLykjET2/Lx8YGzs7M4zsrKQnp6uowZERERERERkS2x4EKySk1NFePa3MNFoVAgODjY5Fx8fLxM2RAREREREZGtseBCssrMzBTj2rykCAAaNmxocnzjxg2ZMiEiIiIiIiJbY8GFZGW8rMbT01PGTGyvcePGJsfXr1+XKRMiIiIiIiKyNRZcSFbGBRdvb28ZM7G9xx57zOQ4Li5OpkyIiIiIiIjI1lhwIVnZ05KiJk2amByz4EJERERERFR7seBCsrLngsvVq1dlyoSIiIiIiIhsjQUXkpXxkqLavC00YF5wuXXrFgoKCmTKhoiIiIiIiGyJBReSVVZWlhi7u7vLmIntubq6on79+uJYr9fj2rVrMmZEREREREREtsKCC8nKngouANCsWTOT48uXL8uUCREREREREdkSCy4kK3sruDRv3tzkOCYmRqZMiIiIiIiIyJZYcCFZZWdni7Gbm5uMmVSPFi1amBzHxsbKlAkRERERERHZEgsuJKvCwkIxdnJykjGT6hEaGmpyzBkuREREREREtZNCkiRJ7iTIfjk7O4uiS25uLlxcXGTOyLYePHiAgIAAcezs7Izs7GwolUoZsyIiIiIiIqKqxhkuJKuioiIxtoeig7+/PwIDA8VxQUEBrl69KmNGREREREREZAssuJCs9Hq9GDs6OsqYSfVp3bq1yfH58+dlyoSIiIiIiIhshQUXemQ4ONjHr2Pbtm1Njk+ePClTJkRERERERGQr9vENl2oEe2kn1KFDB5NjznAhIiIiIiKqfVhwIVkpFAoxNl5eVJs9vKQoOjrabopNRERERERE9oIFF5KVcaNcrVYrYybVp0mTJnB1dRXHSUlJuHnzpnwJERERERERUZWr/dvC0CPNyclJFFq0Wi3UarXMGdmeUqlEx44dkZiYiH79+qFp06Z2M7uHiIiIiIjIXigkrmUgGXl7eyM9PR0AkJKSAh8fH5kzqh6xsbEIDQ2VOw0iIiIiIiKyES4pIlm5uLiIcW5uroyZVC8WW4iIiIiIiGo3LikiWalUKjG2lx4uBjqdDps3b8aRI0eQk5MDHx8f9OrVC3369IGjo6Pc6REREREREVElsOBCsnJychJjeyq4bNy4EfPnz0dsbKzJ+eXLl6Nhw4Z499138cYbb5js4kREREREREQ1B5cUkaw0Go0Y5+TkyJhJ9Vm6dClefvlls2KLwa1btzBx4kRMnjyZ20UTERERERHVUCy4kKzc3NzEOCsrS8ZMqsfhw4cxa9asMt371VdfYcWKFTbOiIiIiIiIiGyBBReSlbu7uxjbQ8Fl9uzZ5bp/wYIFKCgosFE2REREREREZCssuJCs7KngkpSUhKNHj5YrJjU1FTt27LBRRkRERERERGQrLLiQrOyph8uhQ4cq1JPlt99+s0E2REREREREZEssuJCsPD09xTgjI0PGTGyvojsOZWdnV3EmREREREREZGssuJCs7GmGS/369SsU5+PjU8WZEBERERERka2x4EKycnV1FePc3FwZM7G9J554Ah4eHhWKIyIiIiIiopqFBReSlT01zdVoNJgwYUK5YlxdXfHqq6/aKCMiIiIiIiKyFRZcSFYuLi5inJeXJ2Mm1WPKlCkmfWtKM378eHh7e9swIyIiIiIiIrIFFlxIVsYzXDIzM2XMpHrUr18fu3fvLlPRpXv37vj444+rISsiIiIiIiKqaiy4kKwCAwPF+N69ezJmUn06d+6M48ePo0ePHlbvGTFiBPbs2WPSVJiIiIiIiIhqDqXcCZB9q1OnjhjbS8EFAFq0aIGDBw/i+PHjmDNnDrKysuDt7Y0XXngBgwYNQr169eROkYiIiIiIiCpBIUmSJHcSZL8SEhLEdsn+/v5ISkqSOaNHi06ng6Ojo9xpEBERERERUTmx4EKy0mq1cHZ2huHXUKvVQqnkxKvk5GR8/vnn8PHxwfTp0+VOh4iIiIiIiMqJBReSnb+/P5KTkwEAd+/eRVBQkMwZyefEiRN47733cOTIEej1egQGBuLmzZtQq9Vyp0ZERERERETlwKa5JLu6deuKcUJCgoyZyK9Zs2b4888/odfrAQD379/Hhg0bZM6KiIiIiIiIyosFF5JdQECAGNt7DxcfHx+MHz/e5Nznn38OTkQjIiIiIiKqWVhwIdkZ78hj7zNcAGDKlClwcPjfP83o6GgcOXJExoyIiIiIiIiovOy64JKUlFTmmQNZWVnIyckp9zsKCgqQlpZW7hkKOp0OKSkpYmlJWUmShNTUVGi12nLFAUBmZiZyc3PLHVdZfn5+YpySklLt73/UhISEYODAgeJYqVRi27ZtMmZERERERERE5WWXBZekpCT07t0bgYGB+O2336zep9fr8f3336NBgwbw8PCAm5sbmjdvjv/85z+lFlAOHTqE9u3bQ61Ww8fHB/7+/vj000+Rn59fYlxcXBwGDx4MZ2dn+Pn5wcXFBW+++Sbu379fYlx6ejpmzJgBNzc3+Pr6wtnZGX379sX58+dLjCsqKsJXX32FoKAgeHp6QqPRoHXr1vjtt9+qbRmLr6+vGKemplbLOx91b775Jlq0aIG1a9fiwYMH+Oc//yl3SkRERERERFQOdrdLUVRUFAYOHIjbt28DALZs2YLBgweb3Xfjxg38/e9/R1RUlMXndO/eHbt27YJGozE5n5+fjxEjRuA///mPxbjg4GDs3bsXzZo1M7u2YMECLFiwwOLsFDc3N/z0008Wc92+fTvGjRsndvoxplAo8OGHH2L+/Plm12JjY/HSSy/h4sWLFnPt27cvtm7dCmdnZ4vXq8oXX3yBt956CwAwadIkrFq1yqbvqwkkSYJCoZA7DSIiIiIiIqogu5rhsmXLFjz99NOi2AIAXl5eZvfl5uZi4MCBiIqKglKpxPvvv4+YmBjExMTgH//4B9RqNQ4fPoyJEyeaxU6cOFEUW4YMGYIzZ84gLi4OX375JQIDAxEfH4+BAweioKDAJO7777/HRx99BK1Wi7Zt22Lfvn24fv06tm3bhjZt2iA7Oxuvvvoqrly5YhJ39uxZDBs2DMnJyQgMDMTatWtx7do1HD16FAMGDIAkSViwYAF++eUXk7iMjAwMGDAAFy9ehJOTExYsWIBLly7hwoULmDp1KlQqFfbs2YMZM2ZU+OddVm5ubmJckWVbtZFxsUWSJNy6dQvnzp3D9evXUVRUJGNmREREREREVCaSndDr9ZKXl5cEQGratKmkUqkkANKuXbvM7l20aJEEQFKr1dKpU6fMru/cuVMCIAGQoqKixPnIyEhxfvXq1WZxN2/elDw8PCQA0qpVq8T51NRUkduoUaMkrVZrEpefny89+eSTEgBp2LBhJp+pS5cuEgApLCxMSk1NNXvnhAkTJABScHCwVFRUJM7PmjVLAiC5u7tL0dHRZnHr16+XAEgODg7S1atXza5XpQ0bNoif29ChQ236rppEp9NJ27Ztk8LCwsTPB4AUEBAgvfvuu9LNmzflTpGIiIiIiIissJsZLgqFAosWLcLs2bMRFRUlZhA83FNFkiR8+eWXAIDZs2ejQ4cOZs964YUX8NRTTwGASTNTQ1zfvn3xxhtvmMU1bNhQbPm7ZcsWcX7Dhg1IT09HYGAgvvzySyiV+PaYnwAAIABJREFUSpM4Z2dnzJ49GwCwc+dOFBYWAgDOnz+PY8eOAQB++OEHeHt7m71z3rx5UCgUiI+Px59//gmguG/L6tWrAQCLFi1Cq1atzOJefvllhIaGQq/XY8eOHWbXq5K7u7sYZ2Vl2fRdNUVmZiZ69OiBQYMG4ezZsybXkpKSsHjxYjRr1gw///yzTBkSERERERFRSZSl31J7GJYAFRUViaKFi4uLyT2xsbFISEiAQqHAhAkTrD7rmWeewcmTJ7F//37MnTsXOp0O+/btA1Dc8LSkuGXLluHo0aPIzc2Fq6sr9u7dCwB47bXXzHrCGHTr1g1A8ZKbkydPolu3biKuc+fOCAsLsxgXEBCA0NBQxMTEYP/+/ejYsSNOnz6NjIwMODs7Y8yYMRbjFAoFnnnmGcTGxmL//v2YPn261c+k0+mwfPly6PV6FBUViSUvKpUKarUarq6ucHd3h4uLC1QqFTQaDerWrSv62Bj/HZTWVNge6PV6DBkypNStoAsKCjB8+HC4ubnhxRdfrKbsiIiIiIiIqCzsquBikJaWJsaenp4m1wxFjLCwMPj4+Fh9hmHmy8mTJ6HX6xEVFYXU1FQ4ODjgmWeeKTWusLAQZ8+eRYcOHXDw4EEAQHh4uNU4Hx8fPPbYY7h27RpOnDhhUnApKc7wzpiYGJw4ccLkMz799NNwdXUtMe5f//qXiLNGr9dj5syZJd7zsPbt2+P06dMAYJIDe7gA69atE8W70kiShJEjRyIhIaHEv0siIiIiIiKqXnazpMiY8dbDgYGBJtcuX74MAGjbtm2Jz6hTpw6A4tky2dnZIq5Jkybw8PCwGmf8vrS0NNy9e1csoynrOw0Fo7LmGhQUVKE4w/syMjKg1+ut3ufgUP5fo7y8PDFWq9Vi/HAzYXv0448/luv+9PR0q7tiERERERERkTzssuCSkpIixg8XXAzFD+OdcyxxdHQUY4VCUeY4hUIhYh0cHEx6llhbTvTwOw0FjvLm+nBcWd9nyNuaihRcMjMzxdi4h4vxeXuUkZGByMjIcsW88MILqFu3ro0yIiIiIiIiooqwyyVFycnJAIoLDg8XK5ycnACUPtMiPT1djF1dXUVcaT1IsrOzodPpxPsNcYZ3lrQsxPBOQ6GkvLlWJq6kgktJ16wxnuFiXPjJzc0t97Nqk8TERPH7UZq+ffti/vz5aN++vY2zIiIiIiIiovKy6xkuAQEBZtcMO/3cu3evxGcYluf4+fnB0dHRJE6SJKtxDy9nMu4TU9Z3GmbllDVXwzsrG1eS8s5yMS64GBeZjM/bI39//1LvUSgUWLFiBXbv3s1iCxERERER0SPKLme4GGZRWOq18sQTTwAAoqOjS3zGhQsXAAAdO3Y0iUtNTUViYqLVJR6GOE9PTzRt2hQODg4ICgpCYmIioqOjERoaajEuLS0Nd+7cMXvn5cuXK5xreeNKYtjFyNHRESqVCpIkQavVIj8/Hzk5OcjKykJBQQEKCwuRmZlpMrvG2dlZjO294OLj4wNfX1+TZW8PW758OaZOnSqOc3Nz8dVXX+H777/H/fv3oVar0bx5c4wZMwZDhgwx+fkSERERERFR9bDLgotWqwUAk+U8Bobtla9fv47MzEyrDXAPHToE4H/FiJCQEHh4eCAzMxPnzp2zWnAxxHXo0EHMCgkLC0NiYiLOnTuHoUOHWow7cuQIJEmCRqNBixYtABQ3vd28eTPOnTtn9bMmJyeLwoohV0Oz3JiYGGi1WqhUqjJ9xpJ8+umnpd5jjfH7DVtK2yuFQoFx48ZhyZIlFq8PHDgQb731ljhev349pk2bJpbJGdy9excRERGYMWMG1qxZgz59+tg0byIiIiIiIjJll0uKDFtBGzesNWjRooXoKbJ9+3aL8VevXsWpU6cA/K8Y4eDgIJZ3bN261WJcYWEhNm/ebBJnPN66davV5Ujr168HADz55JOima1hi+njx48jMTHRYtzPP/8MoLi4ZJjZ0qZNG6hUKhQWFmL37t0W46KiohAbG2uWqy0Y94ApaTmWvZg0aRKUSvNaqFKpxPLly8Xxpk2bMGLECLNii7H79++jf//+2LVrl01yJSIiIiIiIsvssuDi6+sLABa/qKpUKrz88ssAgI8++sik5wpQvLTn9ddfh16vR0BAALp37y6ujRo1CkDxtr5nzpwxidPpdJg5cyZu3boFAHjppZfEtVdffRUAEBsbi6+//tosp40bN4pCjXFcz5490aBBAxQVFWHmzJlmWzdHRUVhwYIFAIDBgweLGT0eHh4YPHgwAOC9994zKzwlJSVhwoQJAICGDRuKwo6tVKTpbm3WoEEDfPXVV2bne/XqhZCQEADF/Xdef/31MhWodDodXn755VJ79hAREREREVEVkuxIdHS0NH/+fGnUqFESAMnR0VGaNm2a9Mknn0harVbcd/v2bcnDw0MCIAUGBkrff/+9FB0dLe3cuVN67LHHJAASAOnLL780eb5Wq5Xat28vAZCcnJykOXPmSOfOnZMiIyOl5557TsQNGzbMLLfJkyeL68OHD5dOnjwpnT59Wpo2bZo436RJEykvL88k7pdffhHXn3rqKWnv3r3S+fPnpVWrVklqtVoCIKnVaikmJsYk7urVq5KLi4sEQKpfv760bt066cKFC9KWLVuk+vXri2euXbu2Cv8GLCsqKhLvs7NfyRL98MMP4u8QgLR69WpxbenSpSY/s7L8WbRokYyfhoiIiIiIyL4oJMk+1nDodDpoNBqrWyEfO3YMnTt3FscREREYM2aMmJFiTKFQYMqUKfj888/NZmdcv34dI0eOxLFjxyy+p0ePHtixYwfc3d1Nzufk5GDy5Mn48ccfLcaFhIRg586daNmypcl5SZKwdOlSzJ071+KW1B4eHvjuu+8wZMgQs2u7du3C+PHjLS5HcnR0xKxZs/Dxxx9bzKcqFRUViT4uDg4OZd4W2R7Ex8fjs88+w8qVKxETEyOaKnft2tXq75g1zZo1Q2xsLGcUERERERERVQO7KbgAwFdffYWzZ89Cp9OZLMWoU6cO5s6da9ZENycnB3PmzMGaNWuQnJwMV1dX9OrVCwsXLkTr1q2tvkev1+O7777Dxx9/jPj4eCiVSoSFhWHu3Lno27dviV94Dx48iBkzZuDChQsoKipCo0aN8M4772DcuHEWm/waxMXF4a233sLhw4eRk5MDX19fjBkzBrNmzRJLqCzJyMjA+++/j19++QUpKSlwc3NDv379MH/+fDRr1sxqXFUqLCwUO+kolUrR1Jj+R5Ik6PV60b9Ho9GI3bbKIy0tDV5eXlWdHhERERERET3ErgoulVFYWAiVSlXu2QFarRaOjo5iR6Ky0uv10Ol0VncQskb6/9sxl1ScsaawsLBCcZWVk5MDNzc3AIBarbb7raHLIigoqEI9WVJSUuDj42ODjIiIiIiIiMiYXTbNrQgnJ6cKLcVQqVTlLrYAxUtryltsAYqXO1W0aCJHsQWAyVIoFxcXWXKoaQzNc8vDycmJs1uIiIiIiIiqCQsuJLvCwkIxlqvoU9P8/e9/L3dMz549K1T8IyIiIiIiovLjty+SnXHPlorM6rFH48aNE8uwymrq1Kk2yoaIiIiIiIgexoILyc545yjOcCkbT09PLFmypMz3d+zYEc8//7wNMyIiIiIiIiJjLLiQ7IxnuLDgUnZvvvkmli1bVup97dq1w65du7iciIiIiIiIqBrxGxjJLisrS4zLu0zG3k2fPh3Hjx/Hs88+a3YtMDAQkydPRmRkJPz8/GTIjoiIiIiIyH4p5U6AKC0tTYy9vb1lzKRmevrpp7F//37cuHED69atg6urK9q2bYsePXpwVgsREREREZFMWHAh2WVmZoqxu7u7jJnUbCEhIZg9e7bcaRARERERERFYcKFHQGpqqhhzhkvV0el0iIyMhIODA7p37y53OkRERERERHaF6w1Idg8ePBBjf39/GTOpHfbt24ehQ4eifv36CA8PxyeffCJ3SkRERERERHaHM1xIdunp6WLs5eUlYya1Q7169bB582ZxfOjQIeTk5ECj0ciYFRERERERkX3hDBeSXUpKihhzN53KCw0NRUhIiDguKCjA3r17ZcyIiIiIiIjI/rDgQrLLzs4WY24LXXkKhQIvvviiybktW7bIlA0REREREZF9YsGFZGe8pMjDw0PGTGqPwYMHmxz/9ttv0Gq1MmVDRERERERkf1hwIdndvXtXjOvWrStjJrVH165dTZZnpaen49ixYzJmREREREREZF9YcCHZcZeiqqdUKtGvXz9x7OfnZ/JzJiIiIiIiIttiwYVkVVBQgOTkZACAo6MjAgMDZc6o9njxxRfh6+uLRYsW4caNG3jppZfkTomIiIiIiMhuKCRJkuROguzXvXv3EBQUBADw9fUVxReqvLy8PGRmZrKIRUREREREJAOl3AmQfbt3754Y16lTR8ZMah8XFxe4uLiI4/Pnz+Pzzz/HrVu3oFAoEBwcjOHDhyM8PBwKhULGTImIiIiIiGofFlxIVsZ9RYybvFLVuXXrFqZNm4Zt27aZXfvhhx/QrFkzrFy5Er1795YhOyIiIiIiotqJPVxIVpzhYlt3795Fjx49LBZbDC5fvoy+ffti06ZN1ZgZERERERFR7caCC8kqNTVVjDnDpWpJkoQxY8bg5s2bpd6r0+kwatQoXLx40faJERERERER2QEWXEhW2dnZYuzu7i5jJrVPVFQUfv/99zLfn5+fj88//9yGGREREREREdkPFlxIVmlpaWLs7e0tYya1z9atW8sds3HjRuTm5togGyIiIiIiIvvCggvJKicnR4w1Go2MmdQ+x44dK3dMdnY2Tp06ZYNsiIiIiIiI7AsLLiSr9PR0Mfby8pIxk9rH2dm5QnEFBQVVnAkREREREZH9YcGFZJWZmSnGHh4eMmZS+wQHB1cojs2LiYiIiIiIKo8FF5JVRkaGGHOGS9Xq06dPuWPc3d3RvHlzG2RDRERERERkX1hwIVkZL1+p6BIYsmzgwIEICQkpV8xrr73GXjpERERERERVgAUXklVhYaEYOzk5yZhJ7ePo6IiFCxeW+X4nJydMmzbNhhkRERERERHZDxZcSFbGWxC7uLjImEnt9Morr2DFihWl3ufk5IQ9e/agcePG1ZAVERERERFR7ceCC8kqLy9PjF1dXWXMpPaaOnUq9u3bhzZt2li83qNHD9y+fRvh4eHVnBkREREREVHtpZAkSZI7CbJf/v7+SE5OBgDcv38fAQEBMmdUe0mShCNHjuCf//wnPDw80LhxY4wdOxYNGjSQOzUiIiIiIqJahwUXkpVGoxHLirKysuDm5iZzRvZLkiQcOHAAH3/8MS5cuACtVovAwEAMGjQIb7zxBpcbERERERERlQMLLiQrpVIJnU4HoLiBrkqlkjkj+3Tr1i28/PLLOHHihMXrCoUC48aNw6pVq9jcmIiIiIiIqAzYw4VkZSi2AMW76lD1S0lJQXh4uNViC1A8++XUqVM4c+ZMNWZGRERERERUc7HgQo8MhUIhdwp2adq0abh+/brV60qlEp999hnOnj2Lzp07V2NmRERERERENReXFJGsjIss/FWsfsnJyahTp47JTCNjCoUCP//8M/7v//5PnNPr9di+fTuOHDmCnJwc+Pj4IDw8HM8++ywcHFjDJSIiIiIiAgCl3AkQGej1en5hr2Z79uyxWmwBgPfee8+k2LJt2zbMnTsX586dM7lv8eLFaNKkCWbNmoWxY8dythIREREREdk9frslWRl/Mdfr9TJmYp+ioqKsXgsJCcGcOXPE8RdffIHBgwebFVsM4uLiMH78eLz11lucrURERERERHaPBReSlfGMFhZcqp+Xl5fVa2+99ZbYkej48eOYNm1amZ65cuVKrFy5skryIyIiIiIiqqlYcCFZGe9MVNLSFrKNRo0aWb02ZMgQMf7oo4/KNWtl3rx5KCgoqExqRERERERENRoLLiQrpfJ/bYSKiopkzMQ+9evXD66urmbnW7ZsiXr16gEo3jb64MGD5XpuamoqduzYUSU5EhERERER1UQsuJCsVCqVGLPgUv38/PwwcuRIs/NNmjQR48OHD1doudfOnTsrlRsREREREVFNxoILyYozXOT34YcfitksBsaFsIrKysqq9DOIiIiIiIhqKhZcSFaGpqwAUFhYKGMm9qtevXo4ePAgQkJCxLn79++bXK+IkhryEhERERER1XYsuJCsXFxcxDg/P1/GTOxb06ZNERUVhffeew+enp64fPmyuNayZUt4eHiU+5mtW7euyhSJiIiIiIhqFBZcSFbGS1e4q428PD09sWjRIiQkJGD58uViloubmxveeOONcj1LrVZb7A1DRERERERkL1hwIVk5OzuLMQsujwaNRoNXXnkFgYGB4tyUKVPKNctl9OjR8PPzs0V6RERERERENQILLiQrNzc3Mc7JyZExEypJgwYNsGvXLri7u5d6b6dOnbB48eJqyIqIiIiIiOjRxYILycq4h0teXp6MmVBpunbtimPHjqFLly5W73nppZewf//+CvV8ISIiIiIiqk2Upd9CZDsajUaMs7OzZcyEyqJ169Y4cuQIIiMjMXv2bGRlZcHb2xv9+/fH3/72N5OdjoiIiIiIiOwZCy4kK+OZEFlZWTJmQmWlUCjQvXt3REZGWr0nLi4OderUMVkyRkREREREZE+4pIhkZbykKDc3V8ZMqCpkZGRg4cKFePLJJ/HNN9/InQ4REREREZFsWHAhWRkXXPLz82XMhCpr3bp18PPzw+zZs5GZmYkVK1agqKhI7rSIiIiIiIhkwSVFJCs2za09nn/+eSiVShQVFaFXr14YOHAg0tPTuT00ERERERHZJRZcSFZqtVqMuaSoZvPz88OSJUvQsWNHdOrUSe50iIiIiIiIZMWCC8mKTXNrl6lTp8qdAhERERER0SOBBReSlfEuNtwWuvbIz8/H6tWrsW3bNqSlpcHNzQ2dOnXC7Nmz4eXlZXa/JElQKBQyZEpERERERGQbbJpLstJoNGLMJUW1w7fffouQkBC8/fbbOHz4MM6fP4/jx4+jRYsWJsWWtLQ0zJ49G3Xr1oVSqYSrqyvatWuHVatWITMzU8ZPQEREREREVHksuJCsjJcUpaWlyZgJVYVVq1Zh/PjxuHfvnsn5YcOGYezYseL466+/RnBwMBYuXIjExETo9Xrk5eUhKioKU6ZMQf369fHLL79Ud/pERERERERVhkuKSFZ16tQR48TERBkzocqKjo7G9OnTzc6rVCosXbpUHP/444948803S3xWVlYWhg0bBp1Oh1deeaXKcyUiIiIiIrI1znAhWfn4+Ihxenq6jJlQZa1YsQJardbs/HPPPYcGDRoAABISEjB58uQyP3Ps2LG4detWleVIRERERERUXVhwIVkZN83NycmRMROqDL1ej+3bt1u8NnDgQDFeu3Ztuf6e+/Tpw94+RERERERUI3FJEcnK1dVVjPnFuua6fv06kpOTLV7r2rWrGO/YsaNMz+vVqxeWLl2Ktm3bVkl+RERERERE1Y0zXEhWxgWXvLw86PV6GbOhijL+e3xYUFCQGEdHR5f6rI8++gj79u0zK7YUFhZaXLJERERERET0KGLBhWTl6OgolhVJksTtgGuowMBAODk5WbxmPHPJ29u7xOdMnz4d8+bNE8c5OTn47LPPULduXTg7O8PJyQl169bFO++8g7i4uKpJnoiIiIiIyAZYcCHZGW8NnZWVJWMmVFGOjo54/vnnLV67ffu2GDdu3NjqM8LCwrB48WJxvGvXLjRs2BAzZ8402cEqMTERy5YtQ9OmTTFz5kzOiiIiIiIiokcSCy4kOy8vLzFOS0uTMROqjBkzZlg8/+eff4rxsGHDrMYvXrwYKpUKAHDs2DH87W9/Q0pKSonv/OyzzzBlypQKZEtERERERGRbLLiQ7IwLLlxSVHN169YNAwYMMDv/yy+/iPHIkSNNtgI3qF+/Pvr06QMA0Gq1GDVqFAoLC8v03j179uDKlSsVzJqIiIiIiMg2WHAh2bm4uIhxXl6ejJlQZSgUCvz8889mS4siIyPFLBdXV1d88cUXZrHGhZoDBw7g2rVrpb4vKCgI//73v3Hp0iU8/vjjlcyeiIiIiIioarHgQrIzLrhwa+iazdXVFTt27MDy5csRGBgozs+ZM0eMhw8fjh9++AFK5f92pe/cubMY79y5s9T3dO/eHdHR0Rg3bpzVZr1ERERERERyUpZ+i/3R6/WIi4uDWq2GSqVCYWEh8vPzUVhYCAcHBzg7OyMpKQleXl5o0aKF1efExcXh9OnTyMnJQZMmTdC9e3coFIpS35+SkoLIyEg8ePAAQUFB6N27N9RqdalxhYWFOHDgAO7cuQNPT090797d5EuvNZIk4cSJE7h8+TKUSiU6dOiA5s2blxpXVYyb5qanp1fbe8k2VCoVpk2bhgkTJuDXX3/F3r174e/vjxs3biAkJAQA8Nprr6Fjx46YO3cuNm/ejDp16oj4mJiYEp//5JNPYteuXdBoNOLc4cOHsXDhQkRHR0Or1SIgIACDBg3C66+/Lt5JRERERERUrSQyM3fuXAlAqX+USqWUkJBgFp+cnCxNnjxZcnR0NLn/qaeekg4fPmz1vQUFBdLy5cslLy8vk7jg4GBpzZo1UlFRkcU4vV4vbd++XWrSpIlJnJubmzR37lwpKyvL6jvPnTsnhYeHm8QpFApp1KhRUnx8fPl/eBXw9ttvi3cvWbKkWt5Jj47U1FTpxo0b4vhvf/ub1X9zrq6u0tWrV8W9t2/flrp162b1foVCIb3++utSQUGBDJ+MiIiIiIjsGZcUWRAWFlbqPc7Ozhg7dix8fX1Nzl+5cgXNmjXDqlWroNPp0KhRI4SFhcHJyQknT55E9+7dsW7dOrPn5ebmokuXLnj77beRnp4OPz8/tGvXDp6enoiPj8eoUaMwefJkszhJkjBhwgQMHDgQcXFx0Gg0aNu2LerWrYvs7GzMnTsXPXv2tNgb5ccff0Tbtm0REREBR0dHtGrVCs2aNYMkSVizZg3CwsLK1Eujstzd3cU4JyfH5u+jR4u3tzcaNWokjkvaOnrq1Klo0qQJgOIdrcLDw3HkyBGr90uShG+++QZDhw6FTqerspyJiIiIiIhKw4KLBUFBQWIcGxuLlJQUZGVlIT8/Hzk5OcjIyEBubi5Wr14NZ2dnca9WqxVb2QYEBGDjxo24fv06oqKicOXKFQwePBgA8Prrr+POnTsm75wyZQrOnDkDlUqFefPmISEhAX/++Sdu376NDz74AACwevVqbN++3SRuzZo1+OabbwAU98a4ceMG/vrrL8THx2PNmjVwc3PDmTNn8NFHH5nEXbhwAW+88Qb0ej06duyIqKgoREdH49KlSzh06BAef/xxpKamYsSIEZAkqep+uBYYF1yysrJs+i569A0fPtzqtddff12MZ8yYgatXr5bpmdu3b8fy5csrnRsREREREVGZyTvB5tG0b98+CYDk7Ows6fX6MsetXr1aAiCp1Wrp4sWLZtcLCgqk0NBQCYA0Y8YMcT46OlpSKBQSAGnNmjUWnz169GixLMkgLy9PqlOnjgRAGj9+vMW47777TnyWzMxMcf7FF1+UAEhhYWFSfn6+WVxsbKzk4OAgAZAiIiLK/DOoiH/9619iCcjo0aNt+i6qGXr06GG2POiJJ54Q11NTUyWVSlWmpX+GP8HBwVaX5REREREREVU1Ns214MGDBwCA4OBgKBQK6HQ6nDlzBgkJCXBzc8PTTz9tMivDYOPGjQCASZMmWWym6+TkhHHjxmHGjBn4/fff8dlnnwEANm3aBEmS0LFjR4wYMcJiThMnTsQPP/yAU6dOITU1FT4+PoiMjMS9e/fg5uaGxYsXW4wbMWIEpkyZgtzcXERGRqJ///7IyMjA7t27AQD//Oc/TWbpGDRv3hw9evRAREQEfv/9d/Ts2dPqz0un02H58uXQ6/UoKipCUVERgOLmqWq1Gq6urnB3d4eLiwtUKhU0Gg3q16+Ppk2bAgACAgLEs5KSkqy+h+zHypUr0bVrV2RkZIhzzzzzjBjv2bMHWq22XM+Mj4/HoUOH8Oyzz1ZZnkRERERERNaw4GJBYmIigOLdcyZOnIhNmzYhNTVVXPf19cWsWbMwffp0ODo6AgCys7Nx7NgxAMD//d//WX12x44dARQv6UlMTERQUBD27t0r4qztYtSmTRs4OTmhsLAQERERGDJkiIjr3bs3fHx8LMapVCq0a9cOR48exb59+9C/f38cPHgQOp0O/v7+6NGjR4m5RkREYN++fVYLOkDxrk4zZ860et2S9u3b4/Tp0wAAPz8/cT4lJaVcz6HaqVWrVoiIiEC/fv1w//59AEC9evXE9aioqAo99+TJkyy4EBERERFRtWAPFwsMBZc///wTq1evRmpqKpycnNCwYUO4u7sjJSUF//jHP/Dee++JmOPHj0Or1cLd3R1t27a1+uw2bdqI8aVLl5CZmSkKDyUVP5ycnBAaGgqguK8MABw8eBAA0L179xI/j+GdluJK2qb64ThrHBzK/2uUmZkpxt7e3mLMbaHJoF27doiNjcW7774LV1dX5Ofni2vGW4mXlUqlQoMGDaoyRSIiIiIiIqtYcLHAUHABABcXF/z73/9Geno6bt68iXv37ondgpYtW4YbN24AAO7evQsAaNSoEZRK6xOH3NzcRIEiOzsbSUlJ0Ov1ACB2X7HGy8tLxBm/s6xxhoa05Y3Ly8sTOVpSkYJLYWGhGBsvaSooKCj3s6j28vb2xieffIL09HQMHTpUnA8JCSnzM7y8vDBnzhwkJSVZXbJHRERERERU1VhwscDQR8TZ2Rm7d+/GuHHj4OLiAgBwdXXFihUrEBISAr1ejz179gCA+N93wxIja/R6vSheqNVqk/+1Ly3WUKRQq9Um7yypwFNSXGnvM/TIUKktD+KHAAAgAElEQVRUJRZVSpolY43x5zYuuBgXYogMVCqVSV+k559/Hq6urqXGvfbaa7h16xbmzp0rCohERERERETVgQUXC/r06YOGDRvi119/tbjMx8HBAf369QMAHDp0CADEl7/c3NwSn228ZEaj0Zh8aSwtNi0tTcSV551VFVeS8s5yMS64GIpZQPFsGqLS+Pn5YdSoUSXeM2fOHPzwww8my48uXbqEb7/9FitWrMBPP/2E+Ph4W6dKRERERER2ik1zLZgxYwZmzJhR4j2GBp6G5Ud169YFANy6dQtFRUVWZ50YdkACipf0GJYY6fV6XL9+Hf7+/hbjJEkSsYbdferWrYu7d+/i+vXrJeaanJxsFgeg1LiH31eS6dOnAyieNaNSqSBJErRaLfLz85GTk4OsrCwUFBSgsLAQmZmZ0Ol0ItbJyUmMuaSIyuqDDz7Ajh07kJCQYHbt5Zdfxty5c8XxxYsXsWjRIvz888+QJEmcVygU6NevH5YtW4ZmzZpVR9pERERERGQnWHCpoIeX6Rga5RYUFODq1auiwe3D/vjjDwDFvV4M2yE//vjjuHTpEs6dO4ennnrKYty1a9fEDj6GnY7CwsJw5swZnDt3zmqekiSJdxriDLmeP3++xM/4cFxJPv3001LvsUalUolxebf6JftVr149REREoE+fPrh586Y47+vriy+//FIc79mzB4MGDbK4XE2tVmPcuHEsthARERERUZXjkqIKOnDgAADgscceA1D8Jc+wA8qff/5pNS4iIgKAaRHDUAApS1zdunXF7JqyxF26dAn37t0zeach7saNG1a3YdbpdDh8+LBZrrZg3EvGeOYLUWkef/xxnD17FrNmzRJLh958802x89W1a9cwZMgQi8UWR0dHbN68GYMGDRLn0tPT8eGHH6JVq1aoV68emjVrhuHDh+Pw4cMmM2OIiIiIiIhKw4KLBUVFRWJHH0tiY2Nx5MgRAMCwYcPEeUO/l2+//dbil7PExERs3rwZANCpUyezuE2bNplsl2yg1+vF/9hbiouJicGJEycs5rpy5UoAgL+/v9jZJTQ0VMyu+e677yzG/fLLL2JJkfE7bcF4+RULLlRenp6eWLx4MRISEvDTTz9h6tSp4tr7779vtVfRzJkz0b9/fwDFM8GWLFmC4OBgfPzxx7h48SLu3r2LK1euYMOGDejRowfatWuHq1evVstnIiIiIiKiWkAiM88//7zk4uIiHThwwOxaUlKS1Lp1awmAVL9+fUmn04lrJ06ckABIAKS5c+dKWq1WXIuLixNxGo1GSk5OFtcyMzMlHx8fCYA0aNAgKS0tTVzLysqShgwZIp77cE7h4eESACk0NFS6cuWKOK/T6aQFCxZICoVC5GPso48+Erns37/f5Nr27dslDw8PCYDUq1evcv70yk+v14vPx19Jqio5OTmSWq02+d0y/AkICJBycnLEvQsWLLB438N/fH19Tf6dERERERERWaOQJM6Tf1ifPn2wd+9euLq6YtasWXjmmWegVCrx3//+F19++aXYaWjHjh148cUXTWInTJiAf/3rXwCANm3aYMCAAcjIyMDatWvFrj9ffPEFpkyZYhK3bt06jBgxAgAQGBiIkSNHwsHBAdu3b8elS5cAAEOHDsXGjRtNtmG+dOkSwsLCUFBQAGdnZ4waNQp16tTBkSNHcPDgQQBAs2bNcOrUKZPdWvLy8tCmTRvxP/aDBg1CWFiY+B99oHg3oz/++AOtW7eumh+sFXq93mRZEX8lqSr897//Rd++fS1emzFjBj777DMAwOnTp9GpUyexXXtJ3N3dsWjRIkyaNKlC26ETEREREZEdkbng80i6d++e1KZNG6v/y61Wq6WffvrJYqxWq5WWLVsmubq6msX5+flJK1eulPR6vcXYHTt2SMHBwWZxTk5O0ltvvSVlZ2dbjIuOjpY6d+5sMdeBAwdK169ftxiXlJQkjRo1ymJcWFiYdPjw4Yr9AMtJq9WK9zo4OFTLO6n227x5s9V/w0ePHhX3jRw5stSZLY6OjtJ7771nMvuMiIiIiIioJJzhYoVer8eWLVuwdOlSXLp0CUVFRQgJCcGYMWMwevRo+Pj4lBh/69YtrFy5EteuXYOzszPatm2LN998E+7u7iXGZWdn44svvkB0dDTy8/PRpEkTTJ48GQ0bNiw13x9//BGRkZFITU1FUFAQRo8eXab+KxEREdi0aRMSEhLg6+uLfv36YciQIXBwqJ4WP4WFhXB2dgZQvGORpQanROV1/PhxdOnSxey8s7MzcnJy4OjoCJ1Oh4CAAKSmplp9jqurK3bu3Inw8HCT8zk5OUhOToZarYafn5/JLC0iIiIiIiIWXEh2ubm50Gg0AIq/DOfn58ucEdUG6enpqFOnDgoKCkzON2zYUGwjfe3aNTRp0sTqMxQKBXbu3Cma6wLFy/gWLlyIn3/+WSxD8vb2xqhRozBt2rRSi6NERERERGQfuEsRyc54ZyLOEqCq4uXlhZEjR5qdNy7AlDbjbOLEiSY7Gb377rto0aIF1q9fb9LzJS0tDVqtVmzZTkRERERExIILyU6r1Yqxk5OTjJlQbTNt2jSTbccBICkpSfzO+fv7w8XFxWKsi4sL5s2bJ46XLl2KJUuWWGzqPHr0aKz6f+ydd1RUx//+H1h6UREV7AWx9xYL9t6wRgV7ib13E2uMxhKVKCqxi6KosWIvqNixY0FQRBAVC1IUabs7vz84O7873FmTfL5J1iTv1zl7zuzeZ+fOLsuFefZdfH35ubKysrBlyxZUrlwZDg4OcHR0RIUKFbBgwQLEx8f/WS+PIAiCIAiCIIgvGDJcCJOj1Wr52NLS0oQrIf5tVKhQAVu3bhXqEen1ety7dw9AdspQly5dpM9t37498uXLBwB48uQJZs2aJdWVKVMGq1ev5vcvXrwId3d3DBw4EPfv30dqaio+fvyI8PBwzJw5E8WKFcOCBQuoGxdBEARBEARB/Mshw4UwOcoUDzJciD8bb29vBAUFCek+e/fu5eOJEydKn+fp6cnH27dvFyKxlCxatIhHydy9exdt2rRBTEyM0fVkZWVh5syZmDFjxh96HQRBEARBEARB/LMgw4UwOWlpaXxsZ2dnwpUQ/1batWuHx48fY+3atbCxscHGjRv5565mzZoYMGCA6jl16tTh46CgIOm8BQoU4MaMTqdD3759kZqa+pvrqVy5MmrWrPk/vBKCIAiCIAiCIP4pkOFCmBxlVyIbGxsTroT4N2Nra4vhw4cjLS0N8fHxQu2WdevWoU+fPoI+f/78fBwVFSWds0OHDrzQ88WLF3mqkjFsbGzg6+uLsLAwfP311//rSyEIgiAIgiAI4h+AxW9LCOKvRWm4WFtbm3AlxH8VS0tL+Pv7o02bNpg/fz4iIiKQkpKCvHnzAgDy5cuH5ORk1fM8PDz4+ODBg589h5WVFQ4dOoSWLVvyx/R6PY4dO4awsDBkZmaiQIEC6NixI4oUKfInvTKCIAiCIAiCIEwFGS6EyVFuZHPnzm3ClRD/ZczMzNC7d294eXnhwoULQttnd3d3aZRLoUKF+DgsLOyz8//888/cbGGMYf/+/fjhhx9w+/ZtQTd69Gh07NgRs2bNorQjgiAIgiAIgvgHQylFhMlR1rygGi6EqTE3N0fjxo1RqlQp/pisxgsg1h/6nFnYsGFDDB8+nN+fNWsWunXrpjJbgOyol9OnT+PcuXNGC/USBEEQBEEQBPHlQxEuhMlJTEzkYycnJxOuhCDkdOvWDUWLFsXz58+Fx+Pi4vhYadDkZPr06Xy8Z88eLFiwwKjWzc0Nx44dg7u7+/9hxQRBEARBEARBmBqKcCFMTkpKCh9TShHxJWJhYYGtW7fCyspKePzmzZt83KNHD+lz8+TJg1atWgHIjl6ZPHmy0fO4uLggODhYMFvu3buHbt26IV++fLC1tUWhQoXQp08fXLhwAYyx/8vLIgiCIAiCIAjiL4QMF8LkJCUl8XGePHlMuBKCME7Tpk1x7NgxIQorKCiIpxXVrl1bKKJroEWLFrCwyA4mvH79OmJjY42eY9OmTShWrBiA7FS7Hj16oEqVKti3bx8SEhKQnp6OV69eISAgAI0aNcLo0aORkZHxZ75MgiAIgiAIgiD+JMhwIUzOx48f+djR0dGEKyGIz9OsWTNERkZi2rRpAICEhAT4+/vz4ytWrFDVISpbtiwfnzp1yujcLVu2RLt27QAAOp0OXbt2xZ49e6Rac3Nz+Pj4YPXq1dTZiyAIgiAIgiC+UMhwIUzOhw8f+Nje3t6EKyGI3yZfvnxYtGgRGGO4ffs2qlSpwlN7atWqhePHjwuRWra2tnz8uWiUoUOH8vHatWtx8uRJo9pffvkF48aN4/ezsrKwfv16tG3bFnXr1kWLFi0wffp0PHny5H96jQRBEARBEARB/N8hw4UwOfHx8Xzs4uJiwpUQxB+jWrVqqFevHszMzPhjDRs2xIMHDzB8+HBoNBq8efOGH1O2kVZibW2NNm3a8Pu+vr5Gzzlw4EAMGTKE3w8MDESZMmUwdOhQHD9+HNeuXcOZM2ewePFiuLu7o0+fPkIUGUEQBEEQBEEQfw9kuBAm5/3793zs7OxswpUQxJ9DoUKFsHbtWrx//x4dO3bkj9epU0eqr1atGhwcHAAAkZGRiIiIkOocHR3x008/8ftbtmyBl5cXnj17JtV36NABP//8M5+bIAiCIAiCIIi/D2oLTZic5ORkPqaiucS/iVy5cqFFixb8fs2aNeHh4YGLFy8KOmXky927d43O5+3tjbx58wLINmZGjBhhVNulSxfs3r2bF+w1zL1x40bEx8fD2toaZcuWRb9+/XihXoIgCIIgCIIg/jzIcCFMjrItNBXNJf7tTJs2TWW4GDodAZ83Hbt27crHK1euRHp6ulTn7u6O7du3c7MlMjIS06dPx4EDB1StpJOSkrB48WJoNBrhcb1eDzMzMyFdiiAIgiAIgiCI3w+lFBEmh2q4EP8lOnTogMWLFwuPxcXF8XHJkiWlz9NoNGjcuDEAgDGGAwcOGD2Hr68v75b06NEjeHh4YP/+/SqzZejQofjpp5+42ZKeno41a9bAzc0NlpaWsLS0RPHixTFjxgyjaUsEQRAEQRAEQcgxYzn/AyeIvxGdTiekPBi+VSeIfzsBAQGYMGEC3r59CysrKyQkJMDBwQGMMdSqVQu3bt0S9IUKFcKLFy8AADExMShRooR03vLly+Phw4cAgMzMTNSpU0eaplS+fHncvn2bt5UODg5Gnz598OrVK+m87dq1g7+/P9VZIgiCIAiCIIjfCUW4ECYlNTWVj+3t7clsIf4z9O7dG9HR0fD19YWlpSVvA21mZobx48er9Dqdjo+VraZz0q1bNz4+cOCA0ZowP/74Izdbbty4gQ4dOhg1W6ZOnYojR44IZsuHDx8QFhaG69evIyYmRhU9QxAEQRAEQRD/dSjChTApz58/5wU7XV1djW74COK/RFZWFtq0aYPg4GD+mEajQXp6OiwsLKDX62Fvby+t4RISEoKGDRsCAHr16oVdu3apNC4uLnjx4gU0Gg10Oh2qVKnCo2Jy0rdvX/j7+/P77969g4+PD3x8fATDtGrVqliyZAlatmxJxilBEARBEARBgCJcCBPz9u1bPs6fP78JV0IQXw6WlpY4ePAgWrVqxR/T6XQIDw8HAJibm6NNmzbS55YqVYqPz507J9V06NCB1225cOGCUbOlSJEiWL16Nb9/5swZlCxZEgsWLBDMFgBo0qQJWrVqJZgtsbGx2LlzJzZs2IC9e/fi9evXn3nVBEEQBEEQBPHvggwXwqR8/PiRj3PlymXClRDEl4WDgwOOHj2K9evXw83NDQCEQrkTJ06UPs/c/P9f1nN2HjLQoEEDPj506JDRNUyfPp13DgsPD4enp6fwO2ugY8eO8PHx4fejo6MxYsQIlC5dGt7e3vjmm2/QvXt3lCpVStWhiSAIgiAIgiD+rZDhQpiU5ORkPs6dO7cJV0IQXx4ajQZDhgxBREQEQkJC4OLiwmu5eHh4oEOHDqrnKNPyihYtKp3X1dWVj+/fvy/VWFhYwMvLi98fOXIkPn36pNI5Ojpi/fr1/H5ISAgqVaoEPz8/ZGVl8cfNzMzg7+8PDw8P/tjHjx+xYMEC1KhRAyVKlEClSpXQv39/XLx4kWrCEARBEARBEP94yHAhTEpKSgofG75JJwhCRKPRoGHDhhg6dCiPWjEzM0NgYCBatGghaB89esTHTZo0kc6nTAdycnKSaurXr4+8efMCyE4NMpaeNHToUN7OPS4uDp06dZIaM2PHjhUK+vr6+qJYsWKYOXMmbt++jZiYGDx48AD+/v5o2LAhZs2ahczMTOk5CYIgCIIgCOKfABkuhElRFv38XOcVgiDU2Nvb48iRI1i8eDHvIHTkyBF+fMyYMULbdQNxcXF8rKz5oqRmzZp8rJwzJ8oomJkzZyIpKUmlyZs3L+bPn8/vr1ixAmPGjEFiYqJKq9FosHnzZvzwww+wsrISjmm1Wop8IQiCIAiCIP4xkOFCmBSl4WJjY2PClRDEPxMrKytMnToVMTExWL9+PfR6PTc9ChcujKFDh6qec+PGDT7u1auXdF5DdAsgGjRKXF1duTGTmZmJffv2SXW9e/fmEWxhYWGYOnWq0dezZs0aDBgwgN9PSEjAzJkzkT9/flhaWsLKygoVKlTA0qVL8e7dO6PzEARBEARBEISpIcOFMCnK1AOKcCGI/x17e3sMGTIEO3fuRJ48efjjPj4+6N69u6A9cuQIL35btWpVNGvWTDWfMlKlQIEC0nOWL1+ejy9fvowPHz5IdV26dOFjX19faLVaqa5bt26CQfTLL7+gePHiWLBgATdXtFotwsPDMXXqVDRo0ACRkZHSuQiCIAiCIAjC1JDhQpiUhIQEPjakRBAE8edhaWmJwMBALF68mBsxSUlJ2LRpE9f4+PioilbHxMTwcdmyZaVzK+suKQtgK9FoNLxQrl6vN9oVSaPRYOnSpfz+9u3bMXz4cFX7aQOenp4IDQ1FmTJlpMcJgiAIgiAIwtSQ4UKYFOVmysHBwYQrIYh/LxqNBlOnTkVsbCz8/PxQoUIF3LhxAxkZGQCAypUr4/Tp00Iky6VLl/i4RYsWKFGihGpepWFasGBB6bldXFxgaWkJIDs16fXr11Jds2bNULJkSQBAfHw8Ro4cafT1tG7dGr/++qtgEp09exbt27dH+fLlUb58ebRq1QqbN2+WFvAlCIIgCIIgiL8DMlwIk0Jdigji78PR0RHDhg3j3YCsra35sVq1auHhw4eYPHky7Ozs8OrVK5w4cQJAdovosWPHquaLiori47Jly6qK3ALgpo7h/Mbo1KkTH+/YscNoepKrqyt27NjBTZyIiAh4eHigWbNmOHr0KB49eoRHjx7h1KlTmDVrFh48eGD0nARBEARBEATxV0KGC2FSlGkIyroTBEH8/Tg7O2Pp0qVISEjAwYMHhWOjR49G27Zthcfi4+MRHh4OAMidOzf69++vmvP9+/e8OHaePHmQK1cu6bkbNGjAx0FBQUbX+P333/OCvjExMWjSpIkQjWMgf/78OHfuHGrXrs0fS0hIwOzZs+Hp6YnWrVujb9++OHXqlLTzkVarRUpKCvR6vdG1EARBEARBEMTnIMOFMCnKlCJ7e3sTroQgCAM2NjbclDBgaWmJ/fv3o0+fPoJ23bp1fDx+/HhoNBrhOGMM9+7dAwCYmZkJkSxKXF1d+fj+/ftSjaOjI/r27cvnHTRoEOLj46Xa7du3o3Tp0gCyo2ymTZuGEiVKYP78+QgKCsLJkydx/vx5VKlSBWZmZnzOc+fOoXHjxrCyskLu3LlhZWWF5s2bY/fu3cjKypKeiyAIgiAIgiBkkOFCmJT379/zsbINLUEQXx7W1tbYtm0bzp8/jw4dOgAANm7cyCPVKlSogE2bNnEDw8DevXv5eMKECdK5lbVWnJycpJo2bdrw9vF3795FcHCwVNejRw+0atUKAKDT6fD1119jyZIlvDOTgS1btsDFxQVAdiHhFi1aoGnTpggJCeFRLzqdDsHBwZgwYQIuXLggPR9BEARBEARByCDDhTApypSinF1SCIL4MmnUqBGCgoKQmZmJixcvCsf69euHffv2CQV4f/nlFx7NVr16dQwYMEA15/Pnz/m4VKlS0vM2adKEjw8cOGB0fePGjePj5cuXS1OU2rdvz9tha7VadOjQwaiBU7FiRdy+fVton63T6RAWFobz58/j5s2bKjOHIAiCIAiCIMhwIUyKMkRfVnCTIIgvF0tLS1SpUkVllnbu3BlRUVFYvnw5gOzoEWXq0bp169C7d2/hOTdu3OBjb29v6fmKFCnCx6GhoVKNq6sr6tevDyD7+rJ48WKpbtCgQXzs4+MjrQMDZNeCOXHiBDeQtFotAgMDUblyZVStWhVNmjRBrVq1ULlyZbx69Up4LmMMd+7cwbFjxxAcHIzY2FjpOQiCIAiCIIh/J2S4ECZFabgYuo4QBPHPx8HBARMmTABjDDqdTkglsrS0xLZt2+Dv78/rrAQGBvLjvXr1Emq6GFBeL4y1kW/evDkfh4SECK2rDVhbW/P6NIwxwQzKia+vLwoXLgwgOyKvUaNG8PLy4sWCDa9n165dvDU2YwxHjx5FvXr1UL16dbRr1w7NmzdH8eLFsXPnTtU5tFot3rx5gzdv3kCr1RpdC0EQBEEQBPHPggwXwqQoN1AWFhYmXAlBEH8V5ubqPzVmZmbo27cvb+HcoEEDHgFiZWWFtWvXqp734sULPi5evLj0XCVKlOBjYzVXqlSpwot0R0ZG4vHjx0Z1PXr0AJBtovTo0QNXrlxR6aZPn446deoAyDZPevbsifbt2+PatWuCbsqUKfDy8uL3ExMTMW/ePDg7O8PFxQUuLi5wdHTEyJEjkZiYKF0TQRAEQRAE8c+BdriESVF+m0sRLgTx30Oj0aBFixZo0aKF8Hjnzp0RGBiIvn37IiMjAwAQFhbGj3t6euKnn35Szads8WwsTVEZPaOMVMmJsiNTYGAgTp48qdI4ODhgypQp/P7UqVOxZ88ela569epYuHAhv79//37069dPVfvF0tISgwcPFgoHp6WlYePGjbhz5w4yMjJQoEABeHp6olGjRqoCxQRBEARBEMSXA0W4ECYlMzOTj8lwIQhCyddff40HDx6gX79+AIDDhw/za4aHhwdq1aqleo6yTXSxYsWk83748IGPP9cdrWPHjny8bds2oxpHR0cA2e2sV6xYIdUtWLCAR/FduHABPXr0kBbaXb9+PWrWrAkguzDvihUr4ObmhjFjxmDjxo3Yvn07li9fjiZNmqBjx454+/at0fUTBEEQBEEQpoUMF8KkKA0XKppLEERO3NzcsHXrVnz48AHLli3j3YzMzMywdOlSlVH78OFDPm7cuLE0VVHZEcnNzU16XhsbG5QrVw5AdstqYx2MlKbMjh07pJqCBQvymjFarRYDBw6U1mpp06YNevbsCSA7Uuebb77BxIkTVcV4AaBFixbYvXs38ufPzx/LyspCREQEbty4gSdPnkCn00nXQxAEQRAEQfw9kOFCmBS9Xs/HGo3GhCshCOJLxsHBAb179xYMkiZNmmDPnj2wtrbmj12/fh2vX78GABQtWpTXYFESHR2Nd+/eAQAKFy6Mpk2bqjTKlJ6kpCSe1pSTqlWr8vHRo0elmg4dOvB6NOfPn0dUVJRUN3HiRD7esGEDNm/eLNVVrlwZBw4cgJ2dHQAgIyMD69evR+nSpVGuXDnUrl0b7u7uqF27Nn8vlKSnpyM+Ph4fP34UUrAIgiAIgiCIPxcyXAiTojRcZIU1CYIgPkenTp1w69YtHmmi0+mwatUqfnzGjBncmDCg1+uxa9cufn/8+PGqeZOSkvjY2dnZaK2UPHny8PGbN2+kmq+++oqPg4KCpBonJyc0a9aMv4a5c+dKdRqNBtu2beNFf2NiYlCpUiUMHTpUaDtta2uLjRs3wsXFhT92584ddOrUCXZ2dihYsCAcHR3h7e0tFC8HgLi4OCxYsACjR4/GpEmT4OfnJ01/IgiCIAiCID4P7XCJLwYyXAiC+F+oUKECDh06hCdPnmD69OmwsrLiESmVKlXCoUOHuEFh4Oeff+bjjh078lQeA2lpadxAsba2RqlSpaTnVnYTKlCggFSjfNxYR6TmzZvzKL/Q0FC8fPlSquvZsyePqklNTUWrVq3w5MkTlW7hwoWoXr06gOw0pv79+6N69eo4dOgQj2pxcXHBqlWreFpWfHw8Ro8eDXd3d8ycOROrV6/G8uXLsX//fiGKiDGGs2fPom3btihTpgzKlCmDZs2a4dixY9KIGZ1Oh/T0dOnrIQiCIAiC+DdDO1yCIAjiX4Gbmxt+/PFHzJ49WzAImjdvjmvXrqFVq1b8scePH/OUHTMzM2zbto0X5zUQEhLCx8OHD5eeMzo6mo8rVqwo1aSkpPBxvnz5jK7dwNmzZ6UaAOjbty8f//jjj4iMjFRpihcvjlGjRvH7I0eOhL+/v0q3fPlyvp6XL1/Cw8MDq1evFsyRAgUKICAggJsyERER8PDwQLNmzXD8+HE8fvwYjx8/Rnp6Opo2bcojgfR6Pfbt24dq1arB0tIStra2cHR0lNa5iYyMxPr167FixQps3rzZaMoVQRAEQRDEPw0yXIgvBqolQBDEX0XFihVx4sQJ3L59G7169UL37t1x//59nipjaWmJLVu24MiRI6hXrx4ACDVUBg8eDAcHB9W858+f5+ORI0dKz61M9SldurRUo6xhZSx9yd7enqcdMcawdetWqa53797cIDlz5gzWr1+v0hQpUgS9evUCkG2O9O7dW2p0zJs3j5sysbGxaNq0KS5fvixoHBwcsGPHDtjY2AAAoqKiULVqVXTr1g13797l1/bmzZvD29ubPy8iIgIDBgxA+fLlMXToUAX68REAACAASURBVEycOBGDBg1C6dKlERAQQH8TCIIgCIL4x0OGC/HFoKznQhAE8VdQrVo17Ny5E3v27MGyZcsEE8XMzAzt2rXD5cuX8fz5c/Tt25cbMk5OTggICFB1PQoICODpS/Xr10edOnVU57x27Rof9+nTR5o+qWxnXaRIEenaK1WqxLu5hYWFIS4uTqrz9PTk4w0bNkg1Xbt25es4deoUzp07p9LY29sLUT+DBw+WdkwaPXo0SpQoAQBISEhA8+bNcf/+fUHj6OiIdevW8fvBwcGoVq0atm7dqrr2L1u2DL179+bGk06nw/bt29GpUyc0bNgQbdq0wYwZM4ToIoIgCIIgiC8RMlwIk6LcvFALU4IgvhQMESBKQ8bT0xOHDh2Cs7Mzf+zVq1cIDAwEkG3Y7NixA66ursJcJ0+exNu3bwEAJUuWRJcuXVTne/ToER83aNBAasooz6tsba1Eo9GgVq1aALLbRB87dkyqa9OmDR/v3btXqmnZsiUvOHz//n2cPn1aqhs8eDAfT548GTExMVKNoZbN8+fP0aVLF2ldl+7duwvdmoKCglCxYkX07dsXhw4dwsWLF3HixAkEBASoIoG0Wi1OnTqFrVu3IjAwEDdu3KAoGYIgCIIgTAoZLoRJMYS9A9n/LBMEQXzJtG3bFo8fP8b333/PH5s1axaPhHFzc8OlS5eEdtFpaWnw8/Pj95ctW4ZChQoJ84aGhvJW1aVKlZKaMsnJyXycP39+6fqcnZ15etLbt2+F5yhxd3fn4zNnzkg1TZo04eMDBw5INeXLl+dpUsnJydIaLQB4+hIAzJkzR6hrY8DGxgYrV67k93/99Vd07twZERERKt3hw4d5VI1Wq4W/vz8qVqyIVq1aYcCAAfDy8kLXrl1VETkpKSn4+eefMWbMGIwePRqLFi2Sts5mjCEpKQmvX79WdXEiCIIgCIL4vZDhQpgUQ84/kL0pIQiC+NJxcnLCrFmzwBjDy5cvcfHiRaH1dKlSpXDjxg0EBATwQro+Pj7cUClevDhCQkJQpkwZ/hytVou1a9fy+9OnTxcMaQBC5Ii7u7u01suHDx/4OG/evEZfg3JuY+mcytSm69evSzX169fn45MnTyIzM1OlyZ8/P2+NnZWVhX379knn6tatGwoWLAggu17MoEGDpGubOXMmqlSpAgBIT09Hhw4d0L9/f6GAsIWFBfbu3cuNrbS0NHz//fcoVaoUxo8fD19fX6xevRonTpwQ3qesrCxs2bIFpUuXhpOTE1xdXWFjY4Np06apvhTQ6XR4/Pgxbt++jejoaEqLJQiCIAhCBRkuhEmxtbXl40+fPplwJQRBEH+cggULolixYqoUIAsLC3h7e/PCvA8fPoSTkxM/7ubmhrt372LFihUoVqwYAGDNmjVITU0FANSqVQu7du3iNVsAIC4ujpsuefPmRffu3VXrSUtLQ0JCAoBsQ7to0aLSdSujOgoXLizVKCM7HB0dpRpl+lR4eLhUU7ZsWT4ODQ01GnXTtWtXPl6zZo1gHhnIlSsXxo8fz++PGzcOJ06cUOlGjx6N2rVrA8g2ZTw9PTFnzhz+3hjm2rZtGzefwsPDUbZsWQwcOBBPnz7lujJlymDmzJk8BTYrKwtbt26Fu7s7ypQpgxo1aqBUqVLw9vZWRcMkJiZi165dWLt2Lfz9/REWFiZ97QRBEARB/Dshw4UwKcr6CIaNBkEQxL8Je3t7uLi4CJ2IgGxDZPz48YiJiUF4eDg2btwopNp06dIF586dQ40aNfhjys5EEyZMkJ5PWaS3f//+Uo0yGkQZpaLkxYsXfGwwhXJiSKUCIBhKSuzt7fn4c9f55s2b8/H+/fulmo4dO/L57t69KxTiNWBmZoZJkybx+7NmzZLWnxkzZgyP4nn9+jWaN2+uKsRrbm6Obdu2ccPpxYsXqFKlCgYMGCBoS5YsiV9++YWbN4mJiZg3bx5KlSqFXr16YeTIkejfvz9+/PFHVSTM+fPn0atXLzRq1AgtWrTAsGHDcPPmTao/QxAEQRD/AshwIUyKtbU1Hxs6fRAEQfzXKFeuHNq1a8dTagzUq1cPN27cwMmTJ9GgQQPcunWLR1HUq1cP3333nWqugIAAPh45cqQqNQmAUEx37NixKjMIyDY0DHTq1Em6bmXxXjc3N6nGUDAYgOr1GciTJw9y584NAHj37p1gCCnp0KEDHxuKFeekbt263Eh58+YNVqxYIdUNHDiQjydOnCjtwNSlSxdehDgtLQ2tW7cWChwbWLduHV9/XFwcatasiblz5yIpKYlrypUrh02bNvFoqLt376Jx48Zo0qQJdu3ahQsXLuDMmTMICgpCnjx5hJSx1NRU+Pn5YfLkyZg0aRKWL18ujQB6+PAhAgICsGnTJgQFBUk1BEEQBEH8jTCCMCE1atRgABgAFhoaaurlEARB/KPQ6/Vs4cKFTKPR8GuphYUFi4uL4xpfX19+zHCzsrJiL1++5JrBgwerNM7OziwtLY1r6tevr9IUK1aMH09LS2Ourq4qTZ48ebjm06dPzMHBQaXJlSsX13z48EF13HALCwvjuqpVq0o1c+fO5Zp169ZJNRUrVuSaxMREZmlpKdUdPHiQ6+bNmyfVfPXVV1yTmZnJatasKdUdP36c68LCwliePHlUGnNzc3bx4kWuS09PZ0uWLGEuLi6CbuLEicLn4Pbt2+zrr79Wve8RERGC7tGjR8zLy4vly5eP2djYMFdXVzZo0CCWkpKi+mylpqayuLg4lpiYyPR6veo4QRAEQRC/DUW4ECZFWZ9AVmyRIAiCMI6ZmRlmzJiB+/fvY8CAAQCyC/DOmjWLa0aNGoU1a9bwGiRA9vXW19eX3/f19RVaRQNAQkIC/P39+f0lS5YI12wgu7jt5cuXAWSnSI0YMUK1xqSkJNy4cQNAdt2uYcOGqTQpKSk83cjBwcFoepKylowyekSJoWsSAAQHB0s1devW5eOTJ09KOxHZ2tqiZcuWALK7FinTuZR4eXnx8datW3Hz5k2VpkyZMmjdujWA7Pfey8tLuv5hw4ahQYMGXNetWzdMnTpVqLnj5uaGhQsX8vvbt29HzZo1sWfPHmGuNWvW8MLMGRkZ6N+/P8qXL4+dO3fi3bt3SE9PR2JiIkaMGCG8r7dv30anTp1gb2+PIkWKwMnJCW3atFHVWUtMTISfnx9mz56N+fPnY8eOHdL38e3bt7h+/TpCQ0ONtjMnCIIgiH8tpnZ8iP82jRs35t/GBQcHm3o5BEEQ/2j0ej27f/8+i4yMVEUlhIeHsz59+vBrrrW1Nbt//z4/npGRwWbMmMGsra25xt3dnaWnp3PN0aNHmZ2dnRBJ0a1bN348JSWFVa9eXRW5MWjQIK6Jjo5mNjY2Ks21a9e4plevXtIokRs3bnDNV199JdXs2rWLa3r06CHVzJgxg2vmz58v1dSoUYNrHjx4YDTqJjIykuuaN28u1UybNo1r9u7da3Sup0+fct23334r1axbt45rrl27JkQ3GW7KqBu9Xs+6desmnWvx4sVcl5WVxQYMGCCNPnr27BnXJScns9mzZ6sidH744Qfh8xYVFcW++eYb1fr27dvHchIWFsa2bNnC/Pz82K+//so+fPig0iQkJLAjR46wwMBAduzYMZaQkKDSEARBEMSXBhkuhElp3bo1/yfsyJEjpl4OQRDEv56MjAx2/PhxduLECfb+/XvV8fj4ePbDDz8wJycnVrNmTbZ9+3bheEREhLCB12g0ghHy9u1bVq9ePWGTbWNjw16/fs01Bw8eVKXxfPvtt/x4aGio1CDYvXs31wwdOlSqWblyJddMnDhRqhk1ahTXrFmzRqpp2bIl1xw/flyqsbKy4prU1FSjqUmnTp3iOqXppbzVqlWLaxISEqRzWVhYCD+znO+z4bZhwwau8ff3l2oKFSrEMjIyuG7kyJFSna+vL9e8f/9eaqjVrVuX6XQ6rtuwYYPUCMqZCnXz5k3WtWtX1VyZmZnC52nmzJnM0dFR0A0ZMoTl5O7du+y7775jw4YNYxMnTmR79uwR1sVYtrF08uRJtnnzZrZ9+3Z25coVSpkiCIIg/jLIcCFMivJbzG3btpl6OQRBEMTv5NmzZ2z27NlsxowZLDAwUNjYZmVlMT8/P1aqVCl+je/Vq5fw/LNnz7KSJUvy487OzuzTp0/8eM6NOAA2fPhwfjwsLExqEIwePZprjEWTeHp6cs3Jkyelmjp16nDNzZs3pRplfZrExESpBhCjYJSvWXmbOXMm12zevFmqadiwofD+yzRmZmbszZs3XFenTh2pbvLkyVxz/vx5qcbZ2ZmbMnq9XvozAcBOnjzJ5zp+/DgzMzNTaUqXLi1ES/n7+6t0lpaWQt2Ze/fusfz586vmqlmzpmDKPHz4kHXv3l2Yz8rKit28eVP4TPr7+7Ny5coJc9WvX1+oVcQYY1evXmWdO3dmFStWZBUqVGCtW7dm0dHRgkav17OgoCA2Z84cNm3aNLZ06VL26tUrlpNHjx6x1atXs0WLFrG1a9eye/fuqTQEQRDEvxcyXAiTovxG7eeffzb1cgiCIIg/EZ1Ox27evMm2bdvGjh07xrKysoTjGRkZbPPmzczJyYlZWVkJkRmfPn1ibdu2FTbHuXPnFgq8tmrVSrqxN6DVaqUGh6urK9dkZmayYsWKqTQuLi5ck5SUxMzNzaXmhmHjr9frpalSAFh4eDifq3z58lLN1q1bucZYFIzScPLz85NqypUrxzUvX740agKFhIRwXf/+/aUaZSrYlStXpJqCBQtysy0rK0v6XgJgv/zyC5/r6tWr0giYfv36cU1iYiIrUqSI9D2/desW1928eZPlzp1bpZs9ezbXpKens/bt26s0efLkEQpMP3v2jLVo0UKlW7RokfJjyw4cOCAU/QfA2rVrJ2jCw8NZ3759VZ8b5WecsezP+U8//cRq1KjBihUrxsqXL8+GDh3KPn78KOh0Oh07f/4827FjB9uzZw+7efMmReYQBEH8AyDDhTAp3333Hf8nZN68eaZeDkEQBPEFkZmZyRYvXsycnZ2l5nx8fDwrU6aMaoN89OhRrlm/fr3UADh9+jTXLFmyRKp58uQJ1xirK6OMyKhbt65Uo6xRpkylVd527tzJNV5eXlLNlClTuGbx4sVSTbNmzbjmxIkTUo2ZmRmPNtFqtSxfvnxSnTKFy1h61uDBg7nm9OnTUo1GoxFqrhhLhTpx4gTXTJ48Wapp0aIF16SkpLASJUqoNHZ2diw5OZnrRo8eLZ1ryZIlwmdJZs5VrVpViN5auHCh9HwvXrzgmvPnzzNbW9vPGkqMMbZp0yZVBI+FhQW7cuUK1+h0OrZ7925WpUoVQdegQQNVZM7ly5eZp6cnK1euHCtTpgxr0qSJUKfJwM2bN5mfnx/z8fFh27dvl9bDycrKYg8fPmRXr15l4eHhQkQRQRAE8fshw4UwKYsWLeL/PCjDmwmCIAjCwMePH9mGDRuYp6cnGz9+vJB69Pr1a9ayZUujpoNer5cWoFVGJHz69Ik1aNBApZk1axbXXLt2TbppX7t2LdcEBARINatWreKaFStWSDVKI8mY2aCMODFWm6Vu3bq/uebcuXNzTUJCglQDgN29e5frKlWqJNWsXr2aayZMmCDVeHh4cE1MTIxUY29vL6QvFS5cWKpTRsosX75cqunevTvXGCt4bGlpKdTDMZYupaxhdOzYMalmxIgRXPPy5Uvm5OQkNWWUdYw2bdoknUtZYDkzM1Na8DhnZE50dDRr1qyZSjdp0iSm5OrVq6xDhw6CpnTp0iwpKYlrDFFnOc2nnEWR9Xo9O3z4MPPy8mItW7ZknTp1Yj4+Pkyr1Qq6lJQUtmHDBjZ37ly2YMECFhgYqIp0Yyy7NlRQUBA7cOAACw0NVdXeYSz7OnDnzh129epV9vjxY4rwIQjiHwEZLoRJWblypfQfFoIgCIL4vej1enbmzBkhBengwYOCZvPmzaxAgQL8uJmZmZBWk5KSooo+yZcvnxBFMGvWLNWmtlq1avx4RkYGK168uEqTMyojZwFYAGzkyJFcY6z2TOPGjbnm7t27Uk2RIkW45s2bN1KNRqPhG1qtVitN7wHE6J2yZctKNcrIHGNdoYYNG8Y169atk2qqV6/+m68NgNAxSWaSAWCbN2/mmjlz5kg1yqLIT58+lWqsrKyEjklVq1aV6s6dO8c1xooP9+7dm2uioqKkETA2NjZCtMmkSZOkcym7S8XHx0ujfNzc3ISaOVu2bJHW1rl06RLXvHz5klWoUEGlad68OVNy7tw5Vrt2bUFjb28v1Cr6+PEjW7hwoSqCZ/ny5cJcssLJbdu2FQyXxMRE9sMPPwidsTQaDTt79qwwlyE9q3nz5qx27dqsRYsWbNeuXdKObXPmzGGjRo1iU6ZMYbt371YZPDqdjp07d45t376dBQYGstDQUDJ4CIL4nyDDhTApym8Dv/76a1MvhyAIgviHo9PpVN+yG/j06RPbuHEjK1q0KKtRowYbNmyYEC2j1+tZYGCg0Iln7ty5wvEff/xRZVAoU4bCwsKEFCjDTVksVZYO5Obmxo9rtVqh4LByQ56amsp1jRo1UmnMzMyESIqmTZtKN+3Pnz/nGnd3d6nmwoULvzmPMsJn1KhRUo0y0uKnn36Sapo0acI1Z8+eNWqAGEhNTZXW1QHAQkNDuc5Y0eCFCxdyjbGoI2WkVGRkpFSTK1cuHrGh0+mkRX4BsF9//ZXPNW3aNKmmc+fOwvlkBomlpaVgyhiLzFH+XIy1D2/fvj3XpKenSw0ljUYjGG+nTp1iVlZWKp0yPSslJUWaNqYs+syYPEIpT548LD4+nmtCQ0NZ3rx5VTpl9Jler2erVq0SDFUArFKlSoJh+vjxY9a7d2/hc6PRaATTyVgKV40aNVR1dW7fvs169uzJqlevzqpUqcK6dOnC3r59K2iSk5PZggULmKenJ2vVqhXz8vJSpXnp9Xp28uRJNn78eDZo0CA2fvx4dvDgQWmUz5s3b9iDBw9YdHS00GWMIIgvFzJcCJOizC9v2rSpqZdDEARBEIwxxuLi4tihQ4ekbYPDw8OFQrOVK1cWalw8evRIVVRVGeGg1+ulm25l7RljkSDKjfShQ4ekGmUrZ2MapQGwYMECqWbTpk1cY8wkUKbA+Pr6SjX9+/fnGmNpV5UrV+aahw8fSjW2trZck5aWJtUAYI8ePeI6WY0fAMzf359rjNXnUUbmrF69WqpRRuYY62YFgL17947rcnZKMtyUBXXnz58v1SijTaKjo6Uac3NzYeNvLBIoMDCQa5Qp3spbhw4duObt27dSQ8nR0VEwAvv27SudS1k36cCBA1KN0kh5/vy51GwpWrSoYDb88MMP0rkuX77MNffu3ZMaoUozMCsrSxqlZW9vz6KiorjuxYsXrGPHjiqdMv1Mq9Wy+fPnq9LLlNcBxhgLDg5mHh4egsba2ppdv35d0F2+fFlVJNzT01OVnnX//n02YsQI1rFjR9a5c2c2efJkoZ4RY9nXn0uXLrFNmzax9evXs6CgIGmNnhcvXrAjR46wPXv2sODgYFXNIMayTewrV66w48ePs8uXL6tMKcP5wsPDWUhICLt+/TpLTExUaQji3wwZLoRJuX//Pv/D4e7uburlEARBEMTvRq/Xs7CwMBYeHi5NSTh48CBP0bC1tRW+SWeMsT179gjRJcrNtF6vZ1OnTlVt6sqVKyeca+bMmSqNslOTTqdjnp6eKo0ymuLdu3fSDkvKVt7Pnz+XRkk0aNCAa96/f8/s7e1VGmUNF2M1VRwdHbkmLS2N2dnZSXXKLlWyzTgAdvHiRa5p3LixVLNx40auGTJkiFQzbtw4rvn555+lGuVru3jxolRjY2PDNR8+fJBqAAjFcuvXry/VzJ8/n2t8fHykGmUdn+fPn0s1lpaWwkZclkoEiKbbjz/+KNV4eXlxze3bt6UaV1dXoZtVoUKFpLrHjx/zuYylqH3//fdcc+nSJWkkkPJz+enTJ6nxZmVlJRhTxkxFZZRbQkKC1DBTRmjp9Xo2cOBAlSZ37txCdNKePXukUVrK6KusrCxp1zJXV1fBxIuOjla1RgfEmkeMZUco5fydUP6eM5bdrWvUqFHM0tKSa8qWLSv87qWmprJVq1axggULco2dnR17+PCh8D4cPnxYlX6Ws7ZQRkYGW7duHatYsSLLlSsXc3JyYt26dVMZPJGRkWzIkCHMw8OD1atXj3l7e6sKPicmJrK5c+ey1q1bs4YNG7LOnTuzGzdusJyEhISwadOmsREjRrBp06axU6dOqYz1jIwMdvbsWbZ79252+PBhwXRTkpSUxMLDw1lkZKSQgpiTrKwsikr6j0KGC2FSlPnlTk5Opl4OQRAEQfzpfK72g1arZSdPnmTt27dngwYNYg8ePBCOr1+/XvXNvLLALmOMrVq1SmVQKCM40tLSVKkn5ubmwgZi8+bN0g3py5cvuUa2iTQ3NxdSTmQdgaytrYWNSPPmzaUbW+W3+uPGjftNjcxIAsC2bdvGNWPHjv3NTbuxaBKlkbBnzx6ppmzZslwTFRUl1Wg0GuHnbSwVSrlZNdY+XFmfpnfv3lKNsrjyxo0bpZry5ctzjbEaNgBYbGws1xlLz1K2NJcVqM65JmPdrJQtzZOTk6WpS4CYnte5c2epxsfHh2vWrl0r1ShTqqKioqQ/F41GI6Q4GWvZvm/fPq7ZunWrVKM08J48eSI1FQsUKCAYDcbS9JTveWxsLCtatKhKo6wdxRhjs2fPVmny588vRJycOnVKWl9IaQbGxsYyNzc3lWbFihVck56erirQDGSnZimjck6cOKFq/25tbS1cB9+9e8e8vb1VPx/l77lWq2Vz5sxRtYjv2rWr8B5cvnxZ1fo9d+7c7OnTp1yTkZHBNm7cqErrzGleRUVFsSFDhghGdNeuXQVDPDMzk23ZskUw/IoVKyb8XjGWbeR99913rGnTpuyrr75i7dq1Yzdv3hQ0er2eBQUFsWHDhrFevXqxb775hh0/flz19yU2NpYtXbqUTZkyhc2ePZvt27dP+oXA+fPn2bZt29iOHTvY5cuXpX+nXrx4wc6ePctOnTrF7t27J9Wkp6ezhw8fsuvXr7OnT59SrSMJZLgQJiU9PZ1fgCwsLOiXlCAIgiBy8PHjR+bn58dcXFxYpUqVmKenp9CGmLHs4qnKor4lSpQQNoo6nY5t375d+HY+5zfbmzdvVm1yv/32W37806dP0louyoK/ycnJqnQqQOzUZKzbz9ChQ7nmyZMnzMLCQqVRGiXGar0MHDiQa4zVXlF2Mrpz545UU7NmTa559uyZdENubW3NN5BZWVlGW2wrjStZkVvg99XMWbduHdcMGzZMqhk7dizXGIvMUUaAhISESDUWFhZc87kUrqtXr3JdzmgGw01pgBgrBuzt7c01v/76q1RToEABrklNTZVGZgFg4eHhXGfM4FOm5xlLqVJGML148UIaTWNra8tNEr1e/7tqIg0aNEiqGT16NNdcvnxZqsmfPz//zOn1etakSROpTlnMeceOHVKNsvvU48ePpRFqOWv9yDqWFSpUSIjeGDBggPR8ynpXFy9eZNbW1irNlClTuCYlJUWoqWW4NWrUiGv0er30fPb29sI18PDhw0LUjuG2fv164Xyy6LKOHTsyJcuWLVNdD1xcXISIm1u3bkl/1wMCArgmKyuLffvtt8zBwcHo7wJjjJ08eVL1u1WyZEkhSu3Fixds1KhRwntqbm7Ozpw5wzU6nY7t27dPdY2eMWOGcL7Hjx+zwYMHC2aSh4eHkHr28eNH5uPjI9ROsrW1FQxRxrKNqQEDBjBnZ2em0WhYnjx52IkTJwRNYmIimz17NitWrBiztbVlTk5ObNKkSSqj6MqVK6xnz56sbt26rEGDBmzcuHGqSKi4uDg2YcIE1rp1a/alQIYLYXKUFwZlDjBBEARBEH8cY0WDGcv+h/vatWts2bJlbMOGDaoQ+CdPnggpNjY2NkJNlLS0NDZmzBjhH3ErKyvhG+nExERVvQl3d3dhXbKoEltbWyFNYtu2bapNTaFChfg//Xq9njVs2FA1j4ODg9DyuVOnTipNrly5hHoTsk25ubm5UIC4e/fu0k2kslvO3LlzpZpjx45xjbHoHWXUgjHNnDlzuGbhwoVSze+JzKlYsSLXPHr0SKrJGZkjMxsAsX14zmKzhtuWLVu4pl+/flKN0mwwZhTVqlWLa4wZEmZmZvwzkpmZKd1kA6IBYiz1TFlTxs/PT6pRRpLcu3dPqsmVKxf//Gu1WqPpcCdPnuRzGTPUhgwZwjXnz5+XagoVKsQ1mZmZqoLChpsyssNYxJiyE5ms4DcANn78eK45d+6cVKNMdUxPT1e1Hjf87GJiYrhu+PDh0rn27NnDNcYiioYPH841MTEx0u5wxYoV4z8XvV5vNGJKWeh427ZtUs3KlSu5Jjo6WlozKKdRJKt35OjoKFwHd+/eLTV7ldeUp0+fqiKFANEM12q10vPlrEG2bds2Vfqora2t8Fl58OCBNC1Q+R5otVo2cuRI1dpz1jFau3Yty5Url+rzq7yGR0REqCKTNBqNUCA9JSWFjRgxQthXfil8OSsh/rMoC7Dl/MaOIAiCIIi/H61Wy86ePctOnz4t/ONrIDo6mteYKVWqFBsxYoTQhthQv6FZs2b8b/xPP/0kzPHLL7+oNkHK1BPGGNu/f78qakRpTLx9+1a6yVe2Tn737h2rWLGiSqNMzbp27Zo0WmLevHmCRlbHpkePHlwTHx8v3dgpN8nR0dHSDdSAAQO4JiIiQrqpU9beMba5r1OnDtc8efJEqnFwcOCatLQ0aaQBAMFwkm3oALEYbps2baSaZcuWcY2sNhEA1qdPH67ZuXOnVKMsUmysXsyfaRQpI4qMRW0of7Zr1qyRaqpUqcI1t27dkmoA8N81vV5vtM6Nstjx+PHjpRrl79GpU6ek3+l3JQAAIABJREFUmgoVKnBNYmKiNKJMo9EIKUeVK1f+zc/A4MGDpRpl7ZZ9+/ZJNcqosnfv3knXpOzWptfrjbasV0Z2GGvXPnnyZK45fvz4b64pMTFRlbYEZNdEUr5POQ1nw2337t1cI0vjBETj0VjqmbLIeGZmJqtZs6b0Z6fcVxkzg5VrCgkJkV6blOlw7969k342c5rqMsPQ2tqaxcXFcY2xlEdlSuzTp0+FWkGG24gRI7gmLS1Nar5/KXw5KyH+syj/yMkKWxEEQRAE8c/l06dP7MGDB1Lj5t27dzzaxczMjOXLl0+IGGEsuyilMuXDxcVF2NwkJSWxwYMHCxuF3LlzC//YJyQkqDrLlChRQmgLfvLkSVVKhaurqxB9K4u6sbCwYNHR0Vxz5swZ1SbJxsZGKNAqS6vJGZkj64Tj4OAgFC9t3bq1SmNhYSHMI6ulAYDduXOHa4YOHSrVKFNAjBkOytQcWZ2QnJtIf39/qUbZNvpzxXeVP1OZBoDwXhszLpSvzdgGec2aNVxjrJ7K4MGDucbYBrJGjRpcY8xwMTc355rMzEyjr+3atWtcJ0vfA0SDy1gKlzKl0FgkVKlSpbgmJibG6JoMqTR6vZ65urpKNQcPHvzNz9LUqVO5ZsuWLVKNskCxsY5mdnZ2PGpDp9MZXZMy7cpY5JXSdDVmkigLnhur5WRjY8Oj6j5nFCmvf8ainJTFs411flN2f42Li5OaV46Ojtwo1+v1RmtHKfdnxq4VymLPxtJGu3TpInyeZGaSs7OzkDInM1IAseaVMRP3S8EcBGFi8uXLx8dv37414UoIgiAIgvizsbW1RYUKFeDk5KQ65uzsjJkzZ4IxBp1Oh7dv36JJkyaCJnfu3Jg2bRoYY0hNTcXz58+RJ08e4fiGDRvw+PFjjBgxAkWLFkX58uURGBgIrVYLAMibNy8OHTqECxcuoHPnzgCAZ8+eYcmSJXyeli1b4vbt2+jWrRvMzMwAAPHx8Zg5cybX9OnTB8eOHUPJkiX5Y1qtFqNHj+b3mzVrhrNnz6J8+fL8sfT0dCxdupTfX7JkCUaNGiW8zo8fP2L9+vX8/saNG4U5ZJoFCxbAzs5O0Gi1WmzYsIHfnzx5MmRs2bKFj8eOHctfs5JDhw7x8cSJE6XznDp1io9HjBgBS0tLleb8+fN83L17d+TPn1+luXHjBtLS0gAAVatWRe3atVWa+Ph4vHv3DkD2z7ROnTrSNUVGRvJx/fr1pZqoqCg+rlKlilTz4sULPi5evLhUEx8fz8dFixaVal6/fs3HhQsXlmr0ej0+fvwIALC0tETu3LmlOiWy9xoAHB0d+TglJUWqUc5veE9zovydffPmjVRjZmaGvHnzAsh+Dcr3Q0mhQoX4+M6dO1JNsWLF+Pjy5ctSjfLncOnSJaPzGN6b8PBwo2sy/NwZYzh27JhUU6tWLT4+fPiwVKP8jAUFBUk1X331Fezt7QEAERERiIiIUGns7Ozg4eEBIPu93L9/v3SuNm3a8PGePXukmg4dOvDxvn37+LVQScuWLWFtbQ0AuH37NsLDw1WaQoUKoWbNmgCAjIwM7Ny5U3q+Tp068fHq1aulGsO1F8i+/nz69Em6bgsLCwDZn4ELFy6oNOXKlePXxg8fPmDlypUqjex6ZirIcCHw+vVrTJ06FR06dICnpyfmzZuH5OTkv+38ygvwq1ev/rbzEgRBEATx5fB7/kG2s7MzusksVaoU1qxZg9jYWFy5cgWTJk3i/7gb8PDwwP79+6HT6aDT6TBnzhzhuLu7O3799Vc8ffoUM2bMwOTJk1G8eHGkpqZyTatWrRAREYGAgAAULVoUbm5uePPmDYKDg7mmTp06uHfvHnbv3o3ixYvDzs4Ou3fv5kaAubk5Vq1ahb1796JSpUr8eT/++CP/Xyh//vwICQlB69athTX6+Pjw9dSsWROHDx8WNtgA4Ovri6ysLABA48aNsWLFCtX7tXHjRr4Zr1ixIn766SeVZtOmTfjw4QMAoHLlyvDy8lJpgoKC8Pz5cwCAq6srBg4cqNLcu3cPoaGhALINuJEjR6o0aWlp2L17N4Dsz8KECRNUGgA4ePAgH0+aNEmqUW6ejRlFZ8+e5eORI0fC3Fy9Lbp37x4ft2vXTjrPgwcP+LhOnTqqnwUAvHz5kr+P+fPnR5kyZaRzxcbG8rExjfJ/ZWMGj9JAKViwoFSTkJDAx66urlJNYmIiHxcoUECqYYwhKSkJAKDRaIQvUpUoN9dKw1SJTqfj45xGovJ8BgxmQU6srKz4WK/XSzUAkCtXLj5Wvh9KlK/n2bNnUo3y/Xv48KFUozSKjJlJRYsW5des8PBwoyaXu7s7gOz34vTp01KN8rpizEyqVq0aHx89elSqqVGjBh9fuHCBf46VODk5oUKFCgCyf85KE1aJwUwCRDNXSfPmzfn4wIEDUk2LFi34+MSJE0hPT1dplK/N1JDh8h8mKysLixcvhru7O5YuXYojR44gKCgIc+fOhZubG9auXfu3rEPpnv+dRg9BEARBEP9NzM3NpRtsAyVKlMDChQuxdOlSjBs3jn8zbcDS0hLe3t6IjY3FkydPEBoaimbNmgkajUaDr7/+Gs+ePUNqaiqio6OFTbSZmRm6du2KsLAwXLp0CePHj8eECRMQExPDN5X58uXDsWPHEBwcjPbt2wMAnj9/jvnz5/N5mjZtijt37qBnz578NcXGxmLhwoVcM378eAQEBMDZ2Zk/9uHDB8ybN4/fnzhxItasWSNsYlNSUuDn58fvb9q0ia/DQFZWlvANs4+Pj7AhMqA0fb799luVkWR4roGePXuiX79+n9V06dIFdevWVWnWr1+PjIwMAEDdunXRtGlTlebAgQPcmChZsiS6du2q0pw5c0YwpZSRBQaePXuG+/fvA8iOGhkyZIhKwxjD8ePHAWT/3I0ZRcqIjcGDB0s1yg29cnOqRBm9Y2zjGR0dzcfKzbmS58+fcxOkcOHCgkGhRGlE5IzKMqCMFipRooRUozSTlNEuf1SjjGgpUqSIVAMA79+/B5D9M3FxcZFqlHsTWWQWAMGQNUT75ERpJtna2ko1Go1GOs6JjY0NgOx1yyJXADHKSWmcKVHuwYxFASmvGQZjNSdKU+/x48f8dy8nyi/Z7969K9X80SinixcvSjWlS5eWPm4STJfNRJiaESNG8By3cuXKsVmzZrFZs2YJfec3btz4l69j+vTp0pxEgiAIgiAI4v+j1WqF4sQ5iY2NZbNnz2bTpk1jvr6+qpapycnJbNmyZQzI7jxSrFgxduvWLUETHR0tFBm1t7dnUVFR/HhmZiZbtGgRc3Jy4horKyuhHWx6ejobN26cUGTYzMxM6AyUnp4uLbCqLJip1WqlHZsOHTrENe/evZO2o96wYQPXJCQkSNsLK9siJyQkSIvCLl26lGtu3LjBbG1tVRpl4dzY2FhphxpljZrU1FRpy+CcGlk3o3r16nHNp0+fpJqSJUtyTVZWFitevLhKY2FhIdRCktUDAsRuTpMnT5ZqlN1ptm/fLtUoC9QePXpUqlG2oH7w4IFUo+zA9PHjR+FzqLwpX5ux2iTKejjG6vgoP0djx46VapQ1itavXy/VKGuqXLhwQarJmzcv16SkpEg1AFhsbCzXKfdtyltQUBDXdOnSRar5/vvvuWbevHlSjbJQd1BQkFSj/Lz9nlo/jDFVMXTDTVnsOGdnIsNtyZIlXGOsfouyW5upIcPlP4ryQjdt2jThj3dGRgb/Q5srVy6h8NhfgbIQnrKCOUEQBEEQBGEa9Ho9i4iIYI8fP2Y6nU51/MOHD8zPz481bdqUeXt7s40bN6pakkdHR7Np06YxILsFr5eXl6oV+c2bN1mfPn34/4Kurq7s2bNnKk2PHj24pmjRokJh4NTUVDZz5kyhQ1S+fPlYfHw81yQnJ7MhQ4YIRY8dHR2Fzev79+9VRYaLFi0qtBA/deoUc3BwEDS2trbs+fPnXHPjxg3phvLq1atcExERIe38dP36da45cuSItNipsh3u8uXLpRtOZYtpHx8fqWbFihVcc+LECalm4MCBXPPs2TNpm21lUeCMjAxWuHBh6aZc2YK5XLlyKo2dnR1LTk7mcxnreqV8j2bMmCHVKNtZGzNBlN3MDh48+Juv/+7du1JN3bp1uebt27fSYrAuLi5c8+nTJ6FLq/Km7AwmMwkBsSuUt7e3VKPswmasQ5HytRkrnKzsDBYZGSnVWFtb82tEVlYWs7KykuqUncFkJikAtn37dq4ZNGiQVDNhwgSu8fX1lWqaNWvGvhTIcPmPUrduXQaAde3alen1etXx9PR0frFUVp//K1D+ogwfPvwvPRdBEARBEATx5aHT6di7d+94hxIZWq2W3b9/XzA3lCQmJrIVK1aw3r17s7Fjx7Lz58+r/s+Niopio0aNYi4uLqxWrVpswYIFqnOGhIQIUQEzZswQjkdGRrKuXbsKLafbtGkjGFPR0dGsa9euwiawatWqQtTR8+fPVdEHOTeKR48eVbUi7t69Oz+u1+u5qaW8tW3bVnhv+/bt+1kThDHGZs2aJd1MK02ArVu3SlttKzv+XLx4URoJtHfvXq45deqU1ExSRhSFhoZK27V7e3tzzatXr6RdiBo0aMA1xiKKypQpw39mWq2WlSlTRqVxcnISOoM1b95cpTE3NxeiwIx1F7p8+TLXGOvotXnzZq4xFi00ZcoUrrl+/bpUo4xMefnypdQoc3Nz45qMjAxpRy9LS0uWlJTEdY0bN5aeLywsjGuMmUDK17Z06VKpZtq0aVyze/duqaZVq1Zc8+jRI+nnsXDhwuxLgQyX/yBv3rzhH0zlL0dODGGeXbt2/ex8Wq2WLV26lC1evJgtWLCAzZs3j82bN48tXLiQLV++nPn5+bGAgAC2b98+FhQUxIKDg4WLkrLFWt++ff+010kQBEEQBEEQ/ytarZa3F5YRFRXFpkyZwsaNG8eWLFkijQp/9OgRGzhwIOvWrRv75ptv2PXr11Um0N27d1m3bt1YlSpVWNOmTVlISIhw/M2bN0IKPiC2WWaMsR07dqhSh5SpVzqdjs2cOVO18VamZzCWHQ2T0+QYMGCAoNm9e7fKBKpdu7Zg3ly+fFkV6VK9enVBExQUpDJmckYUHTt2TKWxtLQU9hL37t1jBQsWVG26r1y5IvwcZJE3ytSb+/fvS9PBlClTT548YS4uLirNmDFjuObVq1dSg6dHjx7Cz1QW4aSMKMnIyGAVKlRQaZydnYWW9i1btlRprKysWFxcHNcYa8V9/vx5rlm4cKFUo2yPfuDAAanmu+++4xpjJpDSBExKSmL29vYqTbly5bhGq9VK0+FsbGwEEyhnVJrh9qXw5ayE+NvYuXMnd/5k0S0G/Pz8GACWJ0+ez+oyMzOlH/LP3dq1a8efv2/fPv64p6fnn/paCYIgCIIgCOLfQnh4OLt27ZoQdWEgMzOTHThwgDVo0IB17dqVzZ07V9iYM5ZdY8NQi8Xc3JyVLFmSPXr0SNDExcWxKVOmCP+7Hz16VNC8fftWFaWxcOFCQfPx40e2bNkyIcVEWTeHsWwDo3fv3sI8OSPe79+/z9q2bStoGjduLJhhcXFxrG/fvkLKWNWqVYWyCbGxsaxjx46qDb5SEx4ezipVqiRoChYsKNSEiYiIUEXD2NnZsejoaOF9zlk7xsLCgkVERHDNo0ePWNGiRVX7pFOnTglrLl269GdNkISEBFatWjWVRhmZlZycLE3jUUbCZGRkqN5nIDsSyIBer2dDhw5VafLmzSt81oxF+YSHh3PN2rVrpZpjx45xzY4dO6SaRYsWcU1oaCiztrYmw4X4cjAUH1O6rDKCg4P5BzbnxVqJVqv9w4aLsnDU8ePH+eMtWrT4014nQRAEQRAEQRByPveFqoGkpKTPRvkwxlh8fDx78+bNZ+d7/fo1i4qKMjrX27dv2erVq9nPP//Mjh49qqoHxFh2Id1hw4axIUOGsFmzZrGYmBjVOaOjo9mYMWOYt7c3Gz16NLt9+7ZKc+vWLebp6cnKlCnD6tevzwIDAwVNVlYW27FjB3Nzc+N7lGHDhgkpY+np6WzVqlWsWLFiXOPh4SGYN2lpaWzJkiVC9E39+vUFTXx8PBsyZIgQeeTu7i4Yam/evGH9+vUTzKS8efOyV69ecU1ycjLr37+/kF5ja2vLIiMjuSYlJYV9/fXXwp7MzMyMBQcHC69r4MCBqr2bn58f1+h0OjZlyhRVKo/SBNFqtWz48OGqeXr27Cn8LFauXKmap3HjxoLG19dXpSlSpIgQCXXkyBFVJNSXwpezEuJvw5DDqQx9k3HlyhX+gVW6ujnR6/V/2HCpU6cOf35ISAh/XFl5nSAIgiAIgiAIwlSkpaUJG3sZL168YFevXhVq3SjRarXs0qVLbPv27ezMmTNSMykuLo5NmzaNDRgwgE2cOFFqFD158oR98803rHbt2qxdu3Zs69atqrkiIiLY0KFDma2tLStfvjybOnUqy8jIEDRXr15lXl5efP9Vu3ZtoYMQY4xdu3ZNMGfs7e2F6BzGGLt9+zbr2bOnYPDkLFdx5MgRVqdOHWEfqOxExlh2ClK7du0Eja+vr6A5e/Ysq1WrlqDJGQl19+5docbOl4IZY4yB+E/Rv39/+Pv7Y+TIkVi9erVR3enTp9GyZUsAQGZmJiwtLY1qzczM/tAaKleujLCwMADArVu3ULNmTQBA1apVcefOnT80F0EQBEEQBEEQBPH70ev10Ov1sLCwMKrR6XR48eIFnJ2dYW9vb1Tz4MEDODg4oGTJkqp9IWMMkZGROHHiBHLlyoVGjRqhVKlSqnlevnyJ3bt3w9raGjVq1ECdOnWEuRhjCA0NxcqVK+Hg4IDSpUtj6NChyJ07tzDPnTt3sHTpUgQEBPyRt+Mvw/i7S/xrMfyyJCcnf1aXmJgIALCxsfms2QIA5ubm0Ov1v3sNHz9+5GO7/9fenUc3Va39A/+mbZqkTYd0LkXmWQRBBRRFFHFkuv7E6YqCFxEEZVJRUHyvsyhwERf3Va++4KyoiCIiILNXQQQLyIyg0JaOaZu2mbN/f3Tt7UmblAKhaev3s1YXIWfIzunTffZ5zt77xMSo11VVVfXeBxEREREREZ2+iIgIRERE1LlOZGQkWrVqdcp1evToEXS5TqdD586d0blz5zr306JFC0yZMqXO/fTt2/eUiZQLL7yw0SRbACZc/pI6deoEANi3b1+d6x0/fhxAddCeyrRp0wBU/8Hp9XoIIeB2u+FwOFBZWQmbzQan0wmXy4Xy8nJER0erbePj49Vrm8122t+HiIiIiIiIqLFhwuUvSCZQfv31V3g8nqDdyDZu3AgA6NOnzyn3+fLLL59xeYxGo3rtcDjOeD9EREREREREjUXdfYioWZIJF6fTia1btwZcp7Ky8rQSLmdDm/DxeDzn9LOIiIiIiIiIGgITLn9BiYmJGDhwIADgxRdfRKB5k+fMmYOysjJERkZiwIAB57Q82uFFTqfznH4WERERERERUUNgwuUvaubMmQCAFStWYPTo0SgsLARQ/TSiSZMm4emnnwYA3HXXXTjvvPPOaVm0PVy8Xu85/SwiIiIiIiKihsDHQv+FPfzww5g7dy6A6icFtW3bFjk5OSgtLQUAtG/fHj/99BMsFss5LYcQwm+GbIYkERERERERNXVMuPzFrVmzBhMmTMCRI0fUe7GxsZg6dSqmT5+OxMTEc14GJlyIiIiIiIiouWHChWC32/H9998jJycHFosF/fr1Q1paWoN9vsfjgV6vB1D9PHgOKyIiIiIiIqKmjgkXCjun06keDa3X6+FyucJcIiIiIiIiIqKzw0lzKey0CRbtE4uIiIiIiIiImiomXCjsHA6Hem0wGMJYEiIiIiIiIqLQYMKFwk6bcJFDi4iIiIiIiIiaMiZcKOwqKirUa7PZHMaSEBEREREREYUGEy4Udto5XDikiIiIiIiIiJoDJlwo7JxOp3rNhAsRERERERE1B0y4UNhxDhciIiIiIiJqbphwobCrrKxUr2NiYsJYEiIiIiIiIqLQYMKFwq68vFy9jouLC2NJiIiIiIiIiEKDCRcKu6KiIvU6JSUljCUhIiIiIiIiCg0mXCjsSktL1evExMQwloSIiIiIiIgoNJhwobDTDimKj48PY0mIiIiIiIiIQoMJFwo7q9WqXlssljCWhIiIiIiIiCg0mHChsNP2cElISAhjSYiIiIiIiIhCgwkXCju73a5e87HQRERERERE1Bww4UJhp024xMbGhrEkRERERERERKGhE0KIcBeCyOv1wuFwQK/XIzo6OtzFISIiIiIiIjorTLgQEREREREREYVYVLgLQGS322EwGBAR0bRGuDmdTpSXl6OgoAA5OTkoKipCcXExqqqqYLPZYLVaUVJSAqvVCofDAafTCZfLBbfbDafTiYqKCtjtdjgcDrjdbng8nlqfERERgYiICERHRyM6OhpRUVHQ6/XqJyEhAUlJSYiNjUVCQgLi4+MRGxuL5ORkxMTEwGg0wmg0Ij4+HgkJCTCbzUhNTUVCQgJiY2MRGRkZhiN3drxeL6qqqlBVVYWKigqUlJTg5MmTKC8vR2VlJSoqKlBeXg6HwwG73a5+5HK73Y6Kigo4nU643W7Y7Xa4XC54PB71e/B6vfD5fKiZj46MjITBYEBMTAwMBgNMJhNiYmIQHR0Ng8GgfgeJiYmIjY2FxWKB2WxGUlISMjIykJqaioyMDFgsFhgMhjAdwfpxu90oKChAeXk5Tp48ifz8fNhsNtjtdthsNlRVVaGyshJlZWWorKyEzWaDzWZDRUUFKisrVazb7Xa43W51jLXHNCIiAlFRUTAYDIiOjobZbEZcXJz6SUxMRHx8vDqm8v9JSUlISEhQcWyxWJCUlASdThfGI1Z/Mm5zcnKQk5Oj4vfkyZMoKSlR8S3rCRnL2uPq8XhUzGpFRkb61RcGg0H1HIyNjVU/Mo6Tk5PVMY6Pj1dxGhsbi7i4OCQnJyMhIQFRUU23ueB2u1FYWOhXZ8j4LS8vR25uLgoKClBUVISCggJYrVaUl5ereJfH2efzqX1GRUX5HV+j0YiEhATExcWpv/m4uDjExMQgPj4eKSkpMJvNyMjIQFZWFuLj49WxbSpx63A4UFpaisLCQpw4cQJ5eXkoLi5W9aqsf6uqqlBcXIyysjJVX8j61ul0wuPxwOfzwev1+tUHUVFRiIyMRGRkJIxGI6Kjo9W/Mn7j4uJgsVgQHx8Po9EIk8mElJQUpKamIikpCWazGWazGYmJiUhLS0N8fHyTjF2Px4OTJ08iJycHFRUVfue1qqoqlJWVqTpZHnO5ntPphMPhQEVFhTrmLpfLL351Op3f+cxoNKrjazQaERMTg7i4OJhMJiQnJyM1NVW1L2Rsp6amIi0tDWlpaU0mhrVcLhfKyspgs9lQWlqq6oP8/HyUlpaipKRExbask+Wx17bd5PGW5zm3263aEFo6nc4vxqOiolRdbDQaYTab1e/BbDarujkuLk614WJjY9V5UNuma+ztibpUVFSo38HJkydVPVJUVASr1YrS0lLYbDaUl5er9oWM9aqqKrhcLtXGlu03IUTA9ptsc+j1ehgMBhgMBpjNZphMJlV/x8bGIj4+HqmpqcjMzERiYiJMJpNaVvP30NSuXVwuFwoKCtTxkz82mw35+fkoKSlBXl4e8vPz4XQ64XQ6YbfbYbVaUVVVBYfDAZfL5VeXB6rPdTodIiIioNfrVbtEr9cjKioKJpPJr20nz5Py/CnPmSkpKYiLi0OLFi2QlpaG2NjYJlnXAOzhQmEihFB/NAaDAS6XSzWoUlNTVYNJVoTx8fGqkZWYmIiUlBR18jcajX4XbDLJEB0drU5sQPWFusfjURd+DocD5eXlquGtPZnKCl2ehK1WK3Jzc1FUVIS8vDyUl5fD6XSG8xCGhNFoREZGhjp5y8SArPTkCcVisagTjTy+JpMJBoNBnbxkA0ImiXQ6HYQQ6gQoGyN2u11V4larVV3kyAscWemXl5erZElpaSlKS0vVCbc5kBcJLVq0ULGenJyMxMREdfEgj31cXJxqIMiLZ6PRCL1er451RESEamTIRqCMbZvNphrq8gJIJp4qKytRXFyMoqIi5OTkoKCgALm5uSguLq7VYGnM9Ho9LBaLOinHx8cjMzNTJW9kciEhIUEdZ3nRFhUVpeqRqKgoVXfIGJZ1h7ZxXV5ejrKyMpUMkY1Gq9WKwsJCdSEkG/RlZWUoKytTy5oag8GAjIwMFZdpaWnquMr62Gw2IyYmRiUe5cWbTPLIGJbHVjZUZdzK+kLW0bK+kMdYJkocDgeKi4tRWFioLn4qKirUsZX/lw117TxhjU1kZCTS09ORlZWFhIQExMTEICYmRl3YJiUlqQti2eCXsSovkE0mk0qwyXpBr9erc6y2XtAmRrQXM/ICxmq1ori4GHl5eep8J+vexnwc62IymZCVlYWkpCSYTCZ1E0IeP5kMkxdRcj35e5B1rvw9aOtdeYy9Xq+6yJb1hLyA1x5Xm82GyspKVT/Lc2BJSQnKy8tRUlKizndNpf6Njo5W9WxGRgYyMzORkpKikjYyKa79v4z1uLg4dfNC1rvaNkTNdoRsS2iTG/IGgExIVVRUqIRfeXk5rFYrKisr1c2ZnJwcWK3WgDe5miqZEJPtZ3mOs1gsSE9Ph8ViQUpKiroJpL1pJOsL7bHXtuGA6jpExrbX61VtOHm8a9a58phrb37Jm16yTSL/JsrKysJ89M5OTEwMTCaTSpTJOkUmFGJiYlQyWP5eZF0j/wZq3lTVxr9Op4PP51PnRG07RNYzpaWlfm28kpISlJWVqZu+J06cUDfOSkpKwn3IzlhUVBTi4uKQmZmpEl/ynCnb0Wlpaeo4yzrbZDLh4osvDutNZiZcKKx8Pl+T7GVBREREREREjZvT6QzrHKFNr58lNStOpxMGg6ElNPJIAAAgAElEQVRJ9haJjIxU3d5atmypur/Ju2byTpm8WyYz2HL4iczMmkwm1c1UZrUB+HXTk1ltOZRA3t2RGWyZ4ZZ3KouLi/3uDMs77OXl5eoucGVlZZiP4JnR6XR+dx8TExORmZmp7qDJOwzy2Gq7R8seU7Ibr+zKK+8syJ+ad3rkHWJ5Z0cO95B3E2T3SnknWNszymazoaioCCdPnlT/lpaWwuv1hvtQnpIcfpaRkaF6QsmutfL4y7sM2qFA8q6wXq9HTEyM3zA4GeMytj0ej+ryLnuJyB95POVdShnD8i6wvGMm7+Y0FQaDAcnJycjMzERWVhZatGiBuLg4pKenq7vt8g6kjFlZZ2h7lcl4lT1FatYXsiefrDtkjybtcCV5110eW+0wEVm/lJeXN5m77cGkpqaquJXDMOUdyczMTGRkZKheZ9qu/DExMbXqBXm3UTtExuFwqN5MMka1d96Liopgs9mQm5uLvLw81WW+KfXYk8NYU1JSVNzKO7mynpWxm5SUBIvFonqTaHvnaYdVaOsDbS8G7R1cl8vlVz/IIV/y7m5hYSEKCwvVXXXZo6SgoAA2m63Jxm5aWhpatmypeuMkJCTAZDKpOjgjI0MNKzGZTOrcJ3tAmc1m1assOjrar9eCbF9oz2OyR4J8Tw45KCoq8ms3yDqjoKBAnc+aItmGk8PU5HksPT0diYmJSE5OVsdW9tSTQ09kXSzbc7Lnkza+a/YUqRnjbrdbDRN1OByqJ6rsbSaPs6xTZO/rsrIyv3NjYWFhreFLTYl2OLZsZ8TGxiIlJUX10pHDqmSdrG3PadtyNXtZ1zw3anuryuMue+iUlpaqmJdD9vLy8lQ9Ln8vZWVlqjdPU6q/pYiICNVDVXsdYjabVW+ozMxMpKenq3aI0WhUPXO01zPyeAeLd23Ma69j5PlStpfleVLW8bI3sGzbyWkbHA7HGX1nnU4HvV4f4iN5mmVgDxdqDOSJX9sIlRetsvKTjazS0lLVeJXdy2X3RjnfgWykacfRykpBXrDILtraLtyyO7xsjMsuagkJCcjMzKw1prOpjiUEqruIVlRUqHHgpaWlKC4uRn5+vuryWVpaqo69/D3IhnBVVZVf1155rGuOXZYNa9nwk5W1wWBQjZq0tDQkJiaqE4Bs8MgTgXZoTVMcM1uT1+tFfn4+CgsLkZubq040RUVFao4EmayxWq2oqKhQFx3aoVna8bOSHCcuG+ZybKy8YNfGvYz5pKQkJCcnIysrC2lpacjKykJqamqTmvtAdqOVc3WUlpYiLy9PxbK8UCgvL0dxcbGKbW0XXTnPhOw2LWljWF7MyGF48jhr546Q3btlAkquK4czWSyWJlV3CCFQWVmpLq5kjGrH2suGkqwnZPLB5XKp9WrWFVqy67R2nio5dE52CZYXRUajUQ0fk/VETEyMOu7y/7LOMJlMjbYnpdPpRF5eHnJzc1VCTHbPLy4uRklJCRwOh98QWPl/eVzlOU/GsYxhLdng1A7xslgs6hhph37IBndKSopKZsshY00pboHq2JXz9JSVlfkNq5QJhqKiInVBJefu0M7bIeNWHns5n0/N+ahkG0MeZ+2FYc2h0PJcKN9PTk5WcybJ+aqaSv2rnc8rNzcX+fn5aj477fwcNS9a5XYycaatG2pemsi5N+SPto6QST55Q0DOoaSdU007r895552H5ORkREdHN7l4DsTj8aCwsFAlX2TdIc91+fn5aqirtl0t2xE16+VgyRvt70AmOWRir2adK4+5/J1oh/HVvCmZnJzcZH8PXq9XDX2X9XFZWRmKiorUMHk5p5U8V8obRdq/CW37zu12+w2zBf5s18l5ULQ3C+Vxl20Rea6UxzchIQEtWrRAixYt1E2dxno+PBWn04mysjI1tYM87rL+0c5Dox3yLYTApk2bwlp2JlwoLGRFIivZplrZEgVy/PhxvP3226pRIS9eWrVqhfT09HAXj4iIiIiIGgATLhQW69evx9VXX63+bzAYYLFYcOONN+Ktt94KY8mIzl7N+Jb69++PLVu2hKFERKGze/duzJ07V/WOkk93aNOmDa6//vpwF4/orJSWluLQoUOqJ4per1dDUWNiYsJdPKKzUlVVhcLCQtVbUw5PlQ8+IGrKcnJy8P3336vesNoesm3btg1bufiXRWFRc/4Qp9OJkydPIi8vL0wlIgqdYPPjxMfHN3BJiELv999/x5IlS2q9f8MNNzDhQk3eli1bMHTo0Frv33DDDVi5cmUYSkQUOuvWrWN8U7O1c+dO3HbbbbXeD3d8N+2JEKjJqjm+XArnDNJEocL4puaM8U3NGeObmjPGNzVnjTW+mXChsLDb7QHfNxgMDVwSotBjfFNzxvim5ozxTc0Z45uas8Ya30y4UFjYbLaA78fFxTVwSYhCj/FNzRnjm5ozxjc1Z4xvas4aa3wz4UJhUVVVFfD92NjYBi4JUegxvqk5Y3xTc8b4puaM8U3NWWONbyZcKCwcDkfA941GYwOXhCj0GN/UnDG+qTljfFNzxvim5qyxxjcTLhQWwSY10uv1DVwSotBjfFNzxvim5ozxTc0Z45uas8Ya30y4UKOi0+nCXQSic4bxTc0Z45uaM8Y3NWeMb2rOwh3fTLhQWERFRQV8P1hmkqgpYXxTc8b4puaM8U3NGeObmrPGGt9MuFBYBPuD8Hq9DVwSotBjfFNzxvim5ozxTc0Z45uas8Ya34FLRXSORUT45/p0Oh0iIiLC3uWLKBQY39ScMb6pOWN8U3PG+KbmrLHGt04IIcJaAvpL8nq9EEKoP4Jw/yEQhRLjm5ozxjc1Z4xvas4Y39ScNdb4ZsKFiIiIiIiIiCjEOIcLEREREREREVGIMeFCRERERERERBRiTLgQEREREREREYUYEy5ERERERERERCHGhAuFXWVlJaxWKzh/M/3VOBwOFBcXM/apSXA6nTh8+DB8Pl+91y8qKmJ8U6Nnt9vhcrlOaxuXy4XCwsJ6/z0QNSWMb2pMqqqqUFZWVq913W43CgsL4fV6T+szfD4fCgsLT/tcUB9MuFBYCCHw+eefo3PnzjCbzUhKSkJWVhZef/11eDyecBePqF6ys7Nx//33o1evXmjbti2GDRuGxYsXw+1217ndli1b0LdvX5hMJqSkpCAxMRHPPPMMKisrG6jkRKfnp59+QqdOndCxY0fMnDmzznW3bt2K/v37w2g0IjU1FfHx8Zg9ezZsNlsDlZao/rZs2YJWrVqhX79+9UoO7tixAwMHDoTRaERaWhri4uLw2GOPobS0tAFKS1Q/Bw8exOOPP46rr74aAwcOxIMPPoiNGzeecrtdu3Zh8ODBKr5jY2Mxbdo0FBcXN0CpifwJIfDvf/8bycnJGDZsWJ3r7t+/H0OGDFGxGxMTg4kTJyI/P7/O7UpKSvDQQw8hNjYWaWlpMBqNuPHGG7F79+6QfhGiBlVUVCQGDhwoAAT86datm8jLywt3MYmCcrvdYvr06UKn0wWM4YsuukgUFhbW2s7pdIo77rgjaOxnZmaK7OzsMHwjouBKS0tFq1atVJzecMMNAddzu91izJgxQeM7NTVVbNu2rYFLTxTcpk2bRGxsrAAgrr322jrX9Xq9Yvz48UHr/aSkJLF58+YGKjlRYD6fT8yaNStoPfzUU08F3W7KlCkiIiIi4HYJCQlizZo1Dftl6C/N4XCI++67T8Vg//79A67n8/nEE088IaKiogLGrtlsFsuXLw+47SeffCIsFkvA7XQ6XdC/l9PFhAs1KK/XK6655hoVzBMmTBB79uwRhw8fFi+++KJITEwUAMQVV1whfD5fuItLVEtVVZW4/vrrVQxfddVV4s033xTvvfeeGD58uHp//PjxtbadMGGCWj58+HCxfft2cfToUfHmm2+Kli1bCgCidevWoqKiIgzfjCiwmkmUYAmX6dOn+62zbds2cfToUbF48WLRunVrAUC0aNFClJaWNvA3IKpNm2y54IILRElJSZ3rz549W8X3oEGDxA8//CCOHj0q3n//fdGhQweVVAyUbCdqKG+88YYAIKKiosTEiRPFl19+KZYuXSruuusuFb8//fRTre1efPFFtXzAgAFiy5Yt4tixY+Ljjz8WXbp0EQBEYmKiyMnJCcO3or+akpIS0a9fP7+2x4033hhw3UWLFql1+vTpI9avXy+OHTsmli1bJnr06CEAiNjYWHH48GG/7bZt2yaio6NV2+TDDz8UR48eFVu2bBFDhgxR+1y6dOlZfx8mXKhBvf/++ypruGLFilrLd+7cqTKUy5YtC0MJieq2ePFiAUDo9XqxaNGiWonBKVOmqMaO2+1W72/btk1V3vPnz6+1XW5urkhJSREAxEsvvdQg34XoVJYvXy4AiMjISDFs2LCgCZfdu3erO//PPfdcrfguLCwUmZmZdd5hJWoox48fV/Vtr169RFFRUZ3rHzp0SLVNnnjiiVrxbbVaVVLx4YcfPpdFJwrK6/Wq5N+//vUvv2U+n0/07dtXABCPPvqo37Lff/9dGAwGAUBMmzZNeL1ev+U2m0107NhRABAPPPDAOf8eRM8884xqe3Tt2lUAEFdffXWt9QoKCoTZbBYAxLhx44TH4/FbbrfbRc+ePQUAcdddd6n3fT6fuOSSSwQAcckllwS8ETR27FgBQLRt27bW38TpYsKFGtRll10mAIj7778/6Dq33367ACDuvvvuBiwZUf2UlJSI2bNnB7xDJIQQn332mUqsOJ1O9f7o0aMFADFw4MCgvbfkHdR+/fqdk7ITnY6CggKRlpamGuhPPfVU0ITLxIkTBQDRt2/foPH90ksvCQCiR48e57roREG5XC7VFrn44otP2bNFCCEeeeQRFbs1G/TSwoULBQDRvn37UBeZqF527dql2h+BkoiTJ08WAMSwYcP83pd1e6dOnYTL5Qq477feeksNfWYPdDrXDh8+LMaNGyd+/PFH8fjjjwsA4rLLLqu13ty5cwUA0bJlS2G32wPua+nSpQKAiI+PVzdCt27dqjoA7NmzJ+B2ubm56u9p586dZ/V9OGkuNZiysjJs3boVADBhwoSg6w0YMAAAsHbtWj7dghodi8WCf/7zn7j44osDLl+1ahUA4LzzzkN0dDQAQAiBNWvWAKiOfZ1OF3BbGfvbtm3jBIwUVkIIjB8/HgUFBWjXrh2eeuqpOteX8T1+/PhTxveuXbtOOYkd0bnyn//8B//973+RnJyML774AhaL5ZTbyPi+//77ERkZGXAdGd9HjhzB0aNHQ1dgonpyOp3qdURE7Uu8kpISAIDRaPR7X8b3fffdB71eH3DfMr7z8vKwd+/ekJSXKJj27dvj9ddfR9++fVFVVQUAMJlMtdaTsTtmzJhacS3J2C0vL8dPP/3kt92VV16J888/P+B2mZmZ6Nixo9/6Z4oJF2ow69evh9frRXJyMi644IKg68kL2dzcXJw4caKhikd01nbu3Il3330XAPC3v/1Nvb9v3z7k5OQAAK666qqg28vY9/l82L59+zksKVHd3n//fXz++ecAgDfeeAMxMTFB1/39999x8OBBAMDVV18ddL0LL7xQXazK5DtRQ/J4PHjllVcAALNmzUJKSgp++umnOpPc+fn5+OWXXwDUHd/dunVTFwSMbwqHLl26ICUlBQBw8803w2q1AqhOoH/wwQf44IMPAACXX3652kZ7M7Su+G7fvj0SExMBAD/++OM5KT9RIDJRGB8f7/e+w+FQT96qK3bT0tJw3nnnAfgzdlevXn3K7QDgkksu8dvuTDHhQg1m//79AKob3YEy71JmZqZ6LU8WRI3dqlWrcNVVV8HhcCApKQmPPfaYWiZjv2XLlkhNTQ26j4SEBHVhy9incDlx4gQmTZoEAPjHP/6BQYMG1bm+jO+kpCS0atUq6HpGo1H1JmB8Uzh8/fXX+O233wBUP+o8LS0Nffr0Qd++fZGWloZhw4bhhx9+8NtGJhONRiM6d+4cdN9RUVGqfpcXCEQNyWw247nnngMAbNiwAZ06dcKoUaPQqVMn/P3vf4fX68Xtt9+OcePGqW0OHz4Mr9cLnU6HHj16BN23TqdDRkYGANbf1LDkI8ll/EnHjx+H3W4HAPTq1avOfchrSxm7st1yutudKSZcqMFUVFQAAGJjY+tcT5uMqSsxQ9QYuFwuPPLII7jhhhtQVlaG5ORkrF692i9xWN/YB/6MecY+hYMQAvfeey/KysrQqlUrzJs375Tb2Gw2AIxvavw2bdqkXn/44YcoLy9X/3e73fjqq68wYMAArFu3Tr2vrb+DDZeTGN8UbmPHjlXD9ouKivDee+/h8OHDAIDu3btj7ty5MBgMan0Z30ajEVFRUXXuW/ZQZHxTQ5IJl/T0dL/3ZewCp25/1Izd070mPduY518MNRg5n4V2jGkg2m699WnAE4XLgQMH0K9fP9VF/corr8T27dtx0UUX+a0nGzenin23231ayRmiUHvuuefUWOW33367VhfeQOob30IIVb8zvikcZLfwiIgI3H///di6dStOnjyJvXv3Yv78+UhOTobH48GMGTPUNvVtuwBgfFPYrVy5EosXLwYA6PV63HvvvbjssssAAHv27EHXrl2xefNmtb6Mb4fDccp5E+VdfsY3NaRgCRcZu8Cp6+easVvfdkuoYr7uVCZRCMmu5Hl5eXWuJ4Nbp9OpsahEjc1XX32FO+64A5WVlTAajXj++ecxefLkgFlwGfsFBQXw+XxBM+XaZGPNrpNE59q3336LJ598EkD15HQvvvgi5s2bB4PBgOjoaDVR4p49e/Dggw/immuuwbBhw1R8l5SUwOl0+t091bLb7XC5XAAY3xQecnjQ22+/jXvuuUe9n56ejq5du6Jbt2647rrrsH37dhw8eBCdOnVS8V1RUQGbzYa4uLiA+/Z6vSgrKwPA+KbwcLvdeOihh2C323HFFVfgnXfeQZs2bQAAGzduxKhRo3D8+HEMHz4cf/zxB8xms4pvIQQKCwuRlpYWcN9CCNU+Z3xTQwqWcNFOeJ6Xl4cOHToE3UfN2LVYLLBarfW+Jj3bmGcPF2owcmzovn374Ha7g663Z88eANUT0AVr2BCF05o1azBixAhUVlaiR48eyM7OxtSpU4MmUmTsV1VVqfkDApGxbzKZgs6aTnSuvPPOO+q13W7H2rVrsXLlSixbtgwff/wxdu/eDaB63PRrr72GESNGYOvWrWoSdI/Ho8ZFByLjOzIy8pTjponOBTnev0WLFgGXX3PNNapRLycu79q1q+qOLmM4kH379qkeAsGeYkd0Lv3f//0fjh49ijZt2uDbb79VyRagugfu0qVLAVRfRH7yyScAgA4dOqinu8g6PpCjR4+qv58+ffqco29AVJt8SlHNHreZmZlITk4GUHfsFhQUqCcjytiV7fK6tgP+rPPPNubZw4UaTM+ePQFUZ+D3798f9ElF69evB8AKnRqvxx9/HD6fDxdddBE2bNgAs9lc5/oZGRlIT09Hfn4+srOzg2bhZez37t076KMZic6V1157DUOGDEFxcTFcLhfcbjecTidcLhdcLhc2bdqErVu3IisrC4MGDUL79u1xySWXIDIyEm3btsXRo0eRnZ2t6vqaZHz36NEj4OMdic41k8mEyspKFBUVBVweERGBxMRE5Ofnq67mJpMJXbp0wa+//ors7GxceumlAbeV8a3tFUPUkL766isAwG233Rawju3bty+6d++OPXv24MCBAwCqJ3vu0aMHtm3bhuzs7KCTpMv4btmypd8cdUTnmsfjAeA/hAioHgnRq1cvrF27FtnZ2X5PB9WSTzJKSEhQj3m+8MIL8cUXXyA7Ozvo5+bm5qq/k7O9JmUPF2owiYmJ6NSpEwBg2bJlAdcpKSnBypUrATDhQo3TkSNH8PPPPwMAXnnllVMmWyQZz/JRuzV5PB58/PHHfusSNSSLxYI77rgDkyZNwrRp0zBjxgzMnj0bzz77LObMmYPrr78eQHXCZMmSJZg9e7a68y9jNljd7vP51CNJGd8ULrLnoGxE12S32/H7778DqL6wlE4V30IIvP/++37rEjU0mUis62lxcuJn7ZO0TtU+AcD4prCRPVvkBP1a2ro52BxEMnYvueQS1RNdbrdlyxYUFhYG3O7DDz8EUD1/S7du3c7iGzDhQg1MjpmeN28ejhw54rfMbrdjwoQJsNlsMBgMGDZsWDiKSFQnOdlcVlYWrrzyynpvJ2P/o48+8puwDqi+GJ01a5aaX2DkyJEhKi1R6NT1hBYZ38uXL8fq1av9lgkh8PTTT2PXrl0AGN8UPrLO/vjjj+Hz+WotX7VqFRwOBywWi1/9LuN79erV+PLLL/22EUJgzpw52Lp1KwDg1ltvPVfFJ6qTHF4h7+jXZLVa1ROL2rdvr96X8f3999+ri0xJCIGFCxeqHi6sv6mhyfk8AyVGRo0aBQDYtWsX3nzzzVrLFy9ejOXLlwPwr5uvueYaZGZmwuVy4eGHH651Pti2bRuef/55AMDNN9+sbi6dMUHUgGw2m2jTpo0AIMxms5g7d6745ZdfxOrVq8VFF10kAAgA4tFHHw13UYkCWrBggQAgUlNTxV133SUGDx4sevfuLTp27ChatGgh0tLSxIUXXijmzZsnfD6f2s7r9YorrrhCABBRUVFixowZYseOHWLTpk3ipptuUrE/fPjwMH47ouCefPJJAUDccMMNtZb5fD5x7bXXCgAiIiJCTJ06Vfz8889i8+bN4uabb1bxPXjwYL+/C6KGtGPHDhWLM2fOFC6XSy3bv3+/aNWqlQAgxo8f77edz+cTI0aMEACETqcTEydOFNu3bxfff/+9uOOOO9Q++/fvz/imsPnss89ULM6ZM0dUVlaqZcePHxe33nqrACBMJpMoLCz02/bOO+9U244dO1Zs27ZN/PDDD2L06NHq/d69ewuPx9PQX4v+ghwOh1i0aJF44oknREZGhgAgrrrqKjF58mSxc+dOv3XHjx+vYvSuu+4SP/74o9i6dat44IEH1PtdunQRTqfTb7v33ntPLe/Xr59YvXq12Llzp5g/f76Ijo4WAERMTIw4ePDgWX8fJlyowf3yyy+iR48eKshr/txyyy1+jSCixuTDDz8MGrs1f/bs2eO37R9//CGuvvrqoOtfdtllwmq1humbEdWtroSLEELk5uaK66+/Pmh8X3zxxbUa+UQNTdsI79atmxg3bpy46aabhE6nEwBE+/btRXFxca3tCgoKxPDhw4PGd48ePUROTk4YvhFRNa/XK6666ioVk7GxseKCCy4QXbt29YvVV199tda2JSUlKiET6Kdbt27i2LFjYfhW9Fc0Y8aMoLF48803+61bXl4u7r777qDrd+jQQezfv7/WZ/h8PvH8888Lg8EQcLvExETxxRdfhOT76IQ4xUPXic4Bt9uN+fPn49VXX0Vubi4MBgMuvfRSPPPMM+jfv3+4i0cUlMvlwrx583Dw4EFYLBZkZWXBbDYjNjYWcXFx0Ov12LFjB9xuN5588sla3RCFEHjvvffwz3/+E8eOHUNERAQuuOACPPXUUxg6dGidwzaIwum3337D0KFD8eCDD2L8+PEB1xFC4JNPPsHs2bPVE7m6deuGJ598Ev/v//0/xjeFndvtxsKFC/HSSy+hoKBAvW80GnH77bfjhRdeqPMRoMuWLcOsWbNw6NAhAEDnzp0xa9Ys3HbbbUGfVEfUUOx2O15++WV89NFH2Ldvn3rfZDJh0KBBmDx5Mq655pqg269cuRIzZszAgQMH4PP50LFjRzz22GO46667zn5YBVE97d27F6+//jrsdjtEdQcRANVPOfzHP/4RcC6h7777Dg8//DD27t0Lj8eDdu3a4ZFHHsGYMWPqfBDF4cOH8dBDD2HLli2w2WxITU3F2LFj8cgjj4RsAnQmXCjsPB4PIiMj2RCnvxyPx4OIiAg20qlZ8nq90Ol0jG9qlKqqqrBmzRrk5+cjMTERgwYNUnNg1Afjmxq7vLw85OXlITo6Gu3btz+tp8P5fD4IIZhkoSbnTGNXCAGPx3NOnhLKhAsRERERERERUYgxLU9EREREREREFGJMuBARERERERERhRgTLkREREREREREIcaECxERERERERFRiDHhQkREREREREQUYky4EBERERERERGFGBMuREREREREREQhxoQLEREREREREVGIMeFCRERERERERBRiTLgQEREREREREYUYEy5ERERERERERCHGhAsRERERERERUYgx4UJEREREREREFGJMuBAREVGz4HQ6sW/fvnAXg4iIiAgAEBXuAhARERGdruLiYsybNw/Z2dmwWq3IyMjA0aNHsXPnTixevBj33HNPuItIREREf3E6IYQIdyGIiIiI6kMIgXfffRfTp09HUVFRwHVuueUWLF26tIFLRudSdnY2vvvuOzzwwAMwGo3hLg4REVG9sIcLERERNQlWqxW33HIL1q1bV+d6OTk5DVQiaig33ngjcnNzUVhYiBdeeCHcxSEiIqoXzuFCREREjV5VVRWGDBmiki06nQ7Tpk3D77//jsrKSr8eLXa7PVzFpHOkpKQEALBq1aowl4SIiKj+mHAhIiKiRk0IgdGjR+O///0vACAzMxPr1q3D3Llz0apVK8TExOCWW27ByJEjAQB9+vQJZ3HpHIiJiQEA2Gy2MJeEiIio/phwISIiokZtyZIlqgdLfHw8vv32WwwcOLDWeh988AF+/PFHvPbaayH53BUrVuDVV1+F1+sNyf6klStX4scffwzpPk/F5/Phu+++CzjcSgiBczWln8/nw9q1a5Gbm3tWnxsbGwsA0Ov1IS0fERHRucRJc4mIiKjR+uOPP9C9e3fVs2H58uUYNmzYGe3L5/NhxYoV2LFjByoqKtCtWzeMGjUq4EW83W5Hq1atUFRUhHfeeQejRo2CEAJLlizBW2+9hcjISDz77LO4/PLLAQB79+7F+++/j/379yMmJuYV7mIAAA8ESURBVAZTp05F7969a+13+fLlGDFiBPR6PXJzc5GSkoK9e/diw4YNsFqtaNOmDUaOHIno6OhTfp/ff/8dn376KXJzc2GxWHDrrbeiU6dOAdedP38+pk2bhi5dumD37t2IiopCTk4OJk+ejFWrViEiIgITJ07E7NmzYTKZgn6m1WrF//7v/2Lv3r0QQiA9PR19+vTB0KFDVS8UrXnz5mH69Ono2rUrdu3ahaioKJw4cQKTJ0/Gt99+G/Rzn3jiCSxfvhxJSUlITU3Ft99+i4qKCsTHx+PSSy/FiRMnIIRA69atsXjxYqSlpZ3yeBERETU4QURERNRIPfzwwwKAACAmTJhwRvvw+Xxi5cqVonfv3mpf8qdbt25i06ZNtbZZs2aNWudf//qXcLlc4tZbb/XbNiIiQixdulS8+OKLIjIy0m+Z0WgUS5curbXfcePGqXVWrFghrrzyylpl6tKli1i3bl3Q75OXlycmTZok9Hq933Z6vV7MnDlTOByOWttMmjRJrXf48GGxZMkSER8fX+uzb7rppoCf6XK5xHPPPScSEhJqbQNAJCQkiC+//LLWdhMnTlTrHDlyRCxevDjg5w4ZMkRt43a7hU6nC/g5gX4WLlwY9FgRERGFExMuRERE1CjZ7XaRnJwsAAiz2SzKysrOaD9z5syp84I9JiZG7Nu3z2+bzz77TC1/9913xZ133umXaJGv4+Ligu43LS2tVvJjzJgxanldSQW9Xi+ys7NrfZc//vhDZGZm1vl9pk6dWmu7GTNmqOUzZ870W/+CCy7w+x5Hjx7129bn84l77rmnVqKqZ8+ewmg0qvcsFosoKCjw2/bRRx+t83PNZrP6/7Fjx9R2jzzyiEhKSgr6HZOSkkRSUpLo1KmTOHjw4OmGBBERUYPgHC5ERETUKH366acoLi4GAIwePRrx8fGnvY/Nmzfj0UcfVf+/8cYbsWrVKqxduxZDhgwBUP0EpJkzZ/ptpx3Ss3TpUnzwwQcAgMsuuwz79u1DYmIigD8ncT3vvPPwzjvv4MSJE2jXrh0AoKCgAHv27PHbb3JysnothEBERARGjRqFTz75BGvXrsXNN98MAHC73Zg1a5bftj6fDyNHjkReXh4AIDU1FYsWLcKWLVvwyiuvqOOzYMECHDlyxG9bo9GoXj///PMAgNatW2P16tXYtWsX5syZo5Z/9913ftt+9NFHWLJkCQCgf//+yM7Oxq+//opffvkFBQUFWLx4MeLi4mC1WvH555/X63PXrFlT5+fOmTMHxcXFcLlcKCgoQK9evQAAFosFVVVVKC4uRnFxMQ4cOICOHTuCiIioMWLChYiIiBqlf//73+r1pEmTzmgfM2bMUK/nzZuHFStW4LrrrsOgQYPw5Zdfom/fvgCAr776yu9x0trEyJdffgkAuPbaa/Hdd9+hU6dOfnOljB07Fnv37sWoUaOQlZWFqVOnqmUHDhzwK492v2lpadi8eTPeeecdjBw5EoMGDcLSpUtx4YUXAgC++eYbVFVVqfWXLVuGrVu3AgC6d++O/fv3Y8KECejfvz+mT5+ON998E0B1Yuazzz7z+1y32+33/4SEBKxbtw6DBw8GAPztb39Ty06cOOG37v/8z/8AANq1a4dvvvkGPXr08Fv+ww8/qMRTXFxcnZ+bmJiI9evX45prrjnl5wLVk+SmpqYiISFB7a+uOWaIiIgaEyZciIiIqNH57bff1GOgBw8ejM6dO5/2Pk6ePIkffvgBANCrVy9MmTIFOp1OLdfpdJgyZQoAwOPxYPv27WpZSkqK37569+6NTz/9VPXYsFgsAIAWLVrgjTfegNlsVuvKJAYAHDt2zG8/2l46ixYtwmWXXea3PCIiArfccgsAwOv1Yvfu3WrZF198oV4vWLAASUlJftuOHDkSLVq0AAD1vSVt4gYAnnvuOdUTB/BPBBUUFKjXhw4dwsGDBwEAjz32mEqoOJ1OLFiwAO3atcPrr78OAOjZsyduvfXWU35u27ZtT/m5Nckki8PhCLoOERFRY8OECxERETU6v/32m3od6BHQ9fHtt9+q1/fdd59fskXq3r27er1z5071WpsYyczMxFdffeXXe0M+kUcIUWu/HTp0QFRUFADg6NGjfsu0+xBBHhTZs2dP9fqXX34BUN1rZdWqVWr/V111Va3tdDodzj//fADAjh07/JZZrVb1ulOnThg/frzfcu2jr7W9Ur755hsA1T1i7rzzTlRUVGDevHlo164dpkyZgqKiIgDADTfcgFWrVqnvHehzO3fujPvvv79en1uTTLh4PB54PJ6g6xERETUmTLgQERFRoyPnKQGgem2crp9//lm9vvjiiwOuc95556nXclgM4J8IGDFiRK0yyCEuFRUVtfYZGRmp1q85l4o24VJZWRmwTNpeH3IOm+PHj6vkxkUXXRQweaT9PtrvAvgnPsaMGYPIyEi/5dqyaPcthzD16tULr7zyClq3bo3p06cjNzcXAHD55ZdjzZo1WLlyJTIyMmqV50w/tybtMCL2ciEioqYi6tSrEBERETUsg8GgXgdKatSHdjhLsKSNtpdJbGysel1aWqpeywlytdLS0gBUJzaqqqpUjxepZcuW+OOPP3D48GG/97Xfq+ZwGyki4s/7YbJ89fku2vW13wXwT3z8/e9/r7VdsN4lcrsNGzZgw4YN6v3rr78ejz/+OK644oo6EyVn+rk11Uy4aIdwERERNVbs4UJERESNjnZYzbJly065/s8//4xhw4Zh3rx56j1tT5Hy8vKA2x06dEi97tChg3ote5PU3I8kEy5A4MleW7ZsCaC6Z4q2R4b26UfaXjRa2mFI8nPq812AP7+P9rsAfyaQYmNj/Xr1SNqEhnb/2gSRTqfDrbfeih07duCbb77BgAED6ky2aD/XbDarY1Kfz61rPfZwISKipoIJFyIiImp0OnfujEsvvRQAsG7dulqPKpbcbjeeffZZ9OvXD1999RWmT5+uesRccsklaj35pKGa5OOOTSYTrr76avW+NuGSmppaa7v09HT1+vjx47WWZ2VlBVyu1+vV62Bzkbz33nvq9XXXXafK0Lp1awDA119/HTBZc+TIEWzZsgUAMHToUL9lsodMZmZmwM+Mi4tTZdOWt2vXrgCqH++8c+dOfPzxx+oRzTV5PB4sXLjQ71HYZ/q5NTHhQkRETRETLkRERNQoaSdYHT58OBYuXKgu4G02G5YsWYLevXvjySefVMmLa6+9Vg2nGTp0qHqSz4IFC2pd0G/YsEE9Snnw4MF+w4K0w5gCDV85VQ8X7bCfP/74Q73W9gjJzc31S7p4PB68+uqr+PrrrwEAffr0QatWrdR2o0ePBlD99KX58+f7fV5VVRXGjRun/j9s2DC/5fJzag590pZLJkW0887cf//9iIiIgMPhwMyZM/2GCGnZ7XaMGjUKDz30EO6+++56f25ERISa+6XmfDda2rlfmHAhIqKmggkXIiIiapTuvvtujBgxAkD15KoPPfQQkpOTkZqaivj4eIwePdqvN8WUKVOwYsUKldQwGAwYM2YMgOpJeHv27IlZs2bhP//5D+644w4MHjwYLpcLOp0OTz75pN9na3tUlJWV1SqbtoeLdoJfSZtwCdZz4+WXX0ZaWhquuOIKDB06FB06dMDkyZPV8pplGj16tOoN8sgjj2DEiBFYtGgRnnnmGXTr1g3r1q0DUD1XSs0hRXIeGu3cNDW1adMGQHVCR05m27p1a/Wo55UrV6JLly54+OGH8cknn2D16tVYvHgxxo0bhxYtWuCjjz4CAPTr1++MPjcvLy/ovDbaJEuwoVhERESNDSfNJSIiokZJp9Pho48+wrhx4/DOO+8AqL7w1l5863Q6DB8+HFOnTsWAAQNq7ePpp5/Ghg0b8PPPP8NqteL555+vtc7cuXNrPcWoU6dO6nXNiW+BP59SBAD5+fm1lrdt21a91vZwqclqtaphQFovvvgihgwZ4vdemzZtsGjRItx3330AgOXLl2P58uV+63Tv3h2vvfZarf3JYVHyqUeBtG3bFps2bQIAFBQUqO/wxhtvIC8vDxs3bkRBQQHmzp0bdB8jR47EggULTvtzN2/erD5XJmC0tL9z7SO7iYiIGjP2cCEiIqJGy2AwYMmSJdi3bx/Gjh2Ljh07IjMzExdffDGmTJmCw4cPY9myZQGTLUD1UJb169fjgQceqDWspXfv3vjmm28wderUWtv17NkTl19+OQCgffv2tZZrnwIU6PHO2oRNsGTD+eefj3bt2qn/G41GjBkzBrt378aMGTMCbjN27Fh8/vnn6N69e63yPPHEE9i8eXPApyrJhNL5558fcL81l2nnmomLi8N3332HxYsX46abbvKbSBeo7sVy7733YsOGDfjkk0/8tj2bz9WSQ8P69u0bMCFDRETUGOmE9nmIRERERM1UaWkp1q5di4qKCrRt2/aUT9kpLCzEsWPH/CbflXw+H1q3bo0TJ05g7ty5mDZtWq11XnvtNWzcuBEvvPCCGuKzadMmXHnllQCAhQsXYtKkSfB4PKisrER8fPwpn/ojCSHwww8/4MCBA0hISMDll1/uN69MoPJu374dXbt2RVxcXMB1nE4n5syZg86dO6thRIFUVFTg2LFjcDgcyMrKQnp6ut+jrLW8Xi9+/vnns/7cyspKvPvuuxgwYAC6desWtGxERESNCRMuRERERGcgPz8fhw4dQv/+/eudKNm4cSMGDhwIoDohM3HixHNYQiIiIgonzuFCREREdAbS09P9Js+tD5/Pp17XN0lDRERETRPncCEiIiJqIEy4EBER/XUw4UJERETUQJhwISIi+utgwoWIiIiogTDhQkRE9NfBhAsRERFRA5GPNwaAlJSUMJaEiIiIzjU+pYiIiIiogQghsGTJEthsNkyYMAFRUXx+ARERUXPFhAsRERERERERUYhxSBERERERERERUYgx4UJEREREREREFGJMuBARERERERERhRgTLkREREREREREIcaECxERERERERFRiDHhQkREREREREQUYky4EBERERERERGFGBMuREREREREREQhxoQLEREREREREVGIMeFCRERERERERBRiTLgQEREREREREYUYEy5ERERERERERCHGhAsRERERERERUYj9fxhtslU8KGYPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 414,
       "width": 558
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# to_remove solution\n",
    "# perform PCA\n",
    "score, evectors, evals = pca(X)\n",
    "\n",
    "# plot the eigenvalues\n",
    "with plt.xkcd():\n",
    "  plot_eigenvalues(evals, limit=False)\n",
    "  plt.xlim([0, 100])  # limit x-axis up to 100 for zooming"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ccOz9ePZPGMz"
   },
   "source": [
    "---\n",
    "# Section 2: Calculate the variance explained\n",
    "\n",
    "The scree plot suggests that most of the eigenvalues are near zero, with fewer than 100 having large values. Another common way to determine the intrinsic dimensionality is by considering the variance explained. This can be examined with a cumulative plot of the fraction of the total variance explained by the top $K$ components, i.e.,\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{var explained} = \\frac{\\sum_{i=1}^K \\lambda_i}{\\sum_{i=1}^N \\lambda_i}\n",
    "\\end{equation}\n",
    "\n",
    "The intrinsic dimensionality is often quantified by the $K$ necessary to explain a large proportion of the total variance of the data (often a defined threshold, e.g., 90%)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "1W30pzQPIwZ0"
   },
   "source": [
    "## Exercise 2: Plot the explained variance\n",
    "\n",
    "In this exercise you will plot the explained variance.\n",
    "\n",
    "**Steps:**\n",
    "- Fill in the function below to calculate the fraction variance explained as a function of the number of principal componenets. **Hint:** use `np.cumsum`.\n",
    "- Plot the variance explained using `plot_variance_explained`.\n",
    "\n",
    "**Questions:**\n",
    "- How many principal components are required to explain 90% of the variance?\n",
    "- How does the intrinsic dimensionality of this dataset compare to its extrinsic dimensionality?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 230
    },
    "colab_type": "code",
    "id": "XnQt-y4_WwVp",
    "outputId": "86fb7b14-4973-422c-f61f-15703a856bc1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function plot_variance_explained in module __main__:\n",
      "\n",
      "plot_variance_explained(variance_explained)\n",
      "    Plots eigenvalues.\n",
      "    \n",
      "    Args:\n",
      "      variance_explained (numpy array of floats) : Vector of variance explained\n",
      "                                                   for each PC\n",
      "    \n",
      "    Returns:\n",
      "      Nothing.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(plot_variance_explained)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "FEVRB7fCVcOR"
   },
   "outputs": [],
   "source": [
    "def get_variance_explained(evals):\n",
    "  \"\"\"\n",
    "  Calculates variance explained from the eigenvalues.\n",
    "\n",
    "  Args:\n",
    "    evals (numpy array of floats) : Vector of eigenvalues\n",
    "\n",
    "  Returns:\n",
    "    (numpy array of floats)       : Vector of variance explained\n",
    "\n",
    "  \"\"\"\n",
    "\n",
    "  #################################################\n",
    "  ## TO DO for students: calculate the explained variance using the equation\n",
    "  ## from Section 2.\n",
    "  # Comment once you've filled in the function\n",
    "  raise NotImplementedError(\"Student excercise: calculate explaine variance!\")\n",
    "  #################################################\n",
    "\n",
    "  # cumulatively sum the eigenvalues\n",
    "  csum = ...\n",
    "  # normalize by the sum of eigenvalues\n",
    "  variance_explained = ...\n",
    "\n",
    "  return variance_explained\n",
    "\n",
    "\n",
    "#################################################\n",
    "## TO DO for students: call the function and plot the variance explained\n",
    "#################################################\n",
    "\n",
    "# calculate the variance explained\n",
    "variance_explained = ...\n",
    "\n",
    "# Uncomment to plot the variance explained\n",
    "# plot_variance_explained(variance_explained)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 433
    },
    "colab_type": "code",
    "id": "7HhFNTajH55u",
    "outputId": "9544f86d-bb24-40e8-dc44-a86d78a029c6"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 416,
       "width": 560
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# to_remove solution\n",
    "def get_variance_explained(evals):\n",
    "  \"\"\"\n",
    "  Plots eigenvalues.\n",
    "\n",
    "  Args:\n",
    "    (numpy array of floats) : Vector of eigenvalues\n",
    "\n",
    "  Returns:\n",
    "    Nothing.\n",
    "\n",
    "  \"\"\"\n",
    "\n",
    "  # cumulatively sum the eigenvalues\n",
    "  csum = np.cumsum(evals)\n",
    "  # normalize by the sum of eigenvalues\n",
    "  variance_explained = csum / np.sum(evals)\n",
    "\n",
    "  return variance_explained\n",
    "\n",
    "\n",
    "# calculate the variance explained\n",
    "variance_explained = get_variance_explained(evals)\n",
    "with plt.xkcd():\n",
    "  plot_variance_explained(variance_explained)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "8lVO2rHv0kDi"
   },
   "source": [
    "---\n",
    "# Section 3: Reconstruct data with different numbers of PCs\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 518
    },
    "colab_type": "code",
    "id": "FZX7wNXAFsj-",
    "outputId": "9917bcf5-45b5-4dd2-dd2e-50a7ab40020f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Video available at https://youtube.com/watch?v=ZCUhW26AdBQ\n"
     ]
    },
    {
     "data": {
      "image/jpeg": 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      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"854\"\n",
       "            height=\"480\"\n",
       "            src=\"https://www.youtube.com/embed/ZCUhW26AdBQ?fs=1\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7fad7beebb90>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# @title Video 2: Data Reconstruction\n",
    "from IPython.display import YouTubeVideo\n",
    "video = YouTubeVideo(id=\"ZCUhW26AdBQ\", width=854, height=480, fs=1)\n",
    "print(\"Video available at https://youtube.com/watch?v=\" + video.id)\n",
    "video"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "dhA1ioJJlrtw"
   },
   "source": [
    "Now we have seen that the top 100 or so principal components of the data can explain most of the variance. We can use this fact to perform *dimensionality reduction*, i.e., by storing the data using only 100 components rather than the samples of all 784 pixels. Remarkably, we will be able to reconstruct much of the structure of the data using only the top 100 components. To see this, recall that to perform PCA we projected the data $\\bf X$ onto the eigenvectors of the covariance matrix:\n",
    "\\begin{equation}\n",
    "\\bf S = X W\n",
    "\\end{equation}\n",
    "Since $\\bf W$ is an orthogonal matrix, ${\\bf W}^{-1} = {\\bf W}^T$. So by multiplying by ${\\bf W}^T$ on each side we can rewrite this equation as  \n",
    "\\begin{equation}\n",
    "{\\bf X = S W}^T.\n",
    "\\end{equation}\n",
    "This now gives us a way to reconstruct the data matrix from the scores and loadings. To reconstruct the data from a low-dimensional approximation, we just have to truncate these matrices.  Let's call ${\\bf S}_{1:K}$ and ${\\bf W}_{1:K}$ as keeping only the first $K$ columns of this matrix. Then our reconstruction is:\n",
    "\\begin{equation}\n",
    "{\\bf \\hat X = S}_{1:K} ({\\bf W}_{1:K})^T.\n",
    "\\end{equation}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Ls8Lm1wM6laH"
   },
   "source": [
    "## Exercise 3: Data reconstruction\n",
    "\n",
    "Fill in the function below to reconstruct the data using different numbers of principal components. \n",
    "\n",
    "**Steps:**\n",
    "\n",
    "* Fill in the following function to reconstruct the data based on the weights and scores. Don't forget to add the mean!\n",
    "* Make sure your function works by reconstructing the data with all $K=784$ components. The two images should look identical."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 318
    },
    "colab_type": "code",
    "id": "mozpTVpMniYw",
    "outputId": "cfee5dba-4277-4ce5-9910-f36c48faba70"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function plot_MNIST_reconstruction in module __main__:\n",
      "\n",
      "plot_MNIST_reconstruction(X, X_reconstructed)\n",
      "    Plots 9 images in the MNIST dataset side-by-side with the reconstructed\n",
      "    images.\n",
      "    \n",
      "    Args:\n",
      "      X (numpy array of floats)               : Data matrix each column\n",
      "                                                corresponds to a different\n",
      "                                                random variable\n",
      "      X_reconstructed (numpy array of floats) : Data matrix each column\n",
      "                                                corresponds to a different\n",
      "                                                random variable\n",
      "    \n",
      "    Returns:\n",
      "      Nothing.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(plot_MNIST_reconstruction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "YS1c_mSLIdMu"
   },
   "outputs": [],
   "source": [
    "def reconstruct_data(score, evectors, X_mean, K):\n",
    "  \"\"\"\n",
    "  Reconstruct the data based on the top K components.\n",
    "\n",
    "  Args:\n",
    "    score (numpy array of floats)    : Score matrix\n",
    "    evectors (numpy array of floats) : Matrix of eigenvectors\n",
    "    X_mean (numpy array of floats)   : Vector corresponding to data mean\n",
    "    K (scalar)                       : Number of components to include\n",
    "\n",
    "  Returns:\n",
    "    (numpy array of floats)          : Matrix of reconstructed data\n",
    "\n",
    "  \"\"\"\n",
    "\n",
    "  #################################################\n",
    "  ## TO DO for students: Reconstruct the original data in X_reconstructed\n",
    "  # Comment once you've filled in the function\n",
    "  raise NotImplementedError(\"Student excercise: reconstructing data function!\")\n",
    "  #################################################\n",
    "\n",
    "  # Reconstruct the data from the score and eigenvectors\n",
    "  # Don't forget to add the mean!!\n",
    "  X_reconstructed =  ...\n",
    "\n",
    "  return X_reconstructed\n",
    "\n",
    "\n",
    "K = 784\n",
    "\n",
    "#################################################\n",
    "## TO DO for students: Calculate the mean and call the function, then plot\n",
    "## the original and the recostructed data\n",
    "#################################################\n",
    "\n",
    "# Reconstruct the data based on all components\n",
    "X_mean = ...\n",
    "X_reconstructed = ...\n",
    "\n",
    "# Plot the data and reconstruction\n",
    "# plot_MNIST_reconstruction(X, X_reconstructed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 303
    },
    "colab_type": "code",
    "id": "P5q8yvs6TJAA",
    "outputId": "9f03d749-751b-4f4a-a60a-ff367c90c4d8"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 289,
       "width": 557
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# to_remove solution\n",
    "def reconstruct_data(score, evectors, X_mean, K):\n",
    "  \"\"\"\n",
    "  Reconstruct the data based on the top K components.\n",
    "\n",
    "  Args:\n",
    "    score (numpy array of floats)    : Score matrix\n",
    "    evectors (numpy array of floats) : Matrix of eigenvectors\n",
    "    X_mean (numpy array of floats)   : Vector corresponding to data mean\n",
    "    K (scalar)                       : Number of components to include\n",
    "\n",
    "  Returns:\n",
    "    (numpy array of floats)          : Matrix of reconstructed data\n",
    "\n",
    "  \"\"\"\n",
    "\n",
    "  # Reconstruct the data from the score and eigenvectors\n",
    "  # Don't forget to add the mean!!\n",
    "  X_reconstructed =  np.matmul(score[:, :K], evectors[:, :K].T) + X_mean\n",
    "\n",
    "  return X_reconstructed\n",
    "\n",
    "\n",
    "K = 784\n",
    "\n",
    "# Reconstruct the data based on all components\n",
    "X_mean = np.mean(X, 0)\n",
    "X_reconstructed = reconstruct_data(score, evectors, X_mean, K)\n",
    "\n",
    "# Plot the data and reconstruction\n",
    "with plt.xkcd():\n",
    "  plot_MNIST_reconstruction(X, X_reconstructed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "aHxJHV4BrRHi"
   },
   "source": [
    "## Interactive Demo: Reconstruct the data matrix using different numbers of PCs\n",
    "\n",
    "Now run the code below and experiment with the slider to reconstruct the data matrix using different numbers of principal components.\n",
    "\n",
    "**Steps**\n",
    "* How many principal components are necessary to reconstruct the numbers (by eye)? How does this relate to the intrinsic dimensionality of the data?\n",
    "* Do you see any information in the data with only a single principal component?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 341,
     "referenced_widgets": [
      "636acfcc47b6445c922c27f70a5a2b5f",
      "f47d8736a9c74694ab603b3e0685efc2",
      "dc9a44ad8a0f4ab6963ee5512ff799f8",
      "cbd07129a6ea4d8ca2f7cfb2a5a90cf3",
      "d91dff9707894e9fa33319470eb15734",
      "01c81f8f234849b79550cfc04f0e4480",
      "41278561305f4bd7afbbebb6b6454b2a"
     ]
    },
    "colab_type": "code",
    "id": "_ZGFzhXqlvmM",
    "outputId": "21e9882c-69bb-494b-aa86-4965bd887445"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 292,
       "width": 558
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# @title\n",
    "\n",
    "# @markdown Make sure you execute this cell to enable the widget!\n",
    "\n",
    "\n",
    "def refresh(K=100):\n",
    "  X_reconstructed = reconstruct_data(score, evectors, X_mean, K)\n",
    "  plot_MNIST_reconstruction(X, X_reconstructed)\n",
    "  plt.title('Reconstructed, K={}'.format(K))\n",
    "\n",
    "\n",
    "_ = widgets.interact(refresh, K=(1, 784, 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "bnmqJqd3nue7"
   },
   "source": [
    "## Exercise 4: Visualization of the weights\n",
    "\n",
    "Next, let's take a closer look at the first principal component by visualizing its corresponding weights. \n",
    "\n",
    "**Steps:**\n",
    "\n",
    "* Enter `plot_MNIST_weights` to visualize the weights of the first basis vector.\n",
    "* What structure do you see? Which pixels have a strong positive weighting? Which have a strong negative weighting? What kinds of images would this basis vector differentiate?\n",
    "* Try visualizing the second and third basis vectors. Do you see any structure? What about the 100th basis vector? 500th? 700th?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 230
    },
    "colab_type": "code",
    "id": "ZghlYuowoaAn",
    "outputId": "78d1de90-177b-40ad-8508-2f1973a24ebf"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function plot_MNIST_weights in module __main__:\n",
      "\n",
      "plot_MNIST_weights(weights)\n",
      "    Visualize PCA basis vector weights for MNIST. Red = positive weights,\n",
      "    blue = negative weights, white = zero weight.\n",
      "    \n",
      "    Args:\n",
      "       weights (numpy array of floats) : PCA basis vector\n",
      "    \n",
      "    Returns:\n",
      "       Nothing.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(plot_MNIST_weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "W7BkraA4IDR9"
   },
   "outputs": [],
   "source": [
    "#################################################\n",
    "## TO DO for students: plot the weights calling the plot_MNIST_weights function\n",
    "#################################################\n",
    "\n",
    "# Plot the weights of the first principal component\n",
    "# plot_MNIST_weights(...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 433
    },
    "colab_type": "code",
    "id": "OPYX_kK9nvBn",
    "outputId": "2add869c-8c2d-422c-827e-1324b59f8854"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 416,
       "width": 499
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# to_remove solution\n",
    "# Plot the weights of the first principal component\n",
    "with plt.xkcd():\n",
    "  plot_MNIST_weights(evectors[:, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xTHjnpZV43mU"
   },
   "source": [
    "---\n",
    "# Summary\n",
    "* In this tutorial, we learned how to use PCA for dimensionality reduction by selecting the top principal components. This can be useful as the intrinsic dimensionality ($K$) is often less than the extrinsic dimensionality ($N$) in neural data. $K$ can be inferred by choosing the number of eigenvalues necessary to capture some fraction of the variance.\n",
    "* We also learned how to reconstruct an approximation of the original data using the top $K$ principal components. In fact, an alternate formulation of PCA is to find the $K$ dimensional space that minimizes the reconstruction error.\n",
    "* Noise tends to inflate the apparent intrinsic dimensionality, however the higher components reflect noise rather than new structure in the data. PCA can be used for denoising data by removing noisy higher components.\n",
    "* In MNIST, the weights corresponding to the first principal component appear to discriminate between a 0 and 1. We will discuss the implications of this for data visualization in the following tutorial."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "4o207yNk0c-I"
   },
   "source": [
    "---\n",
    "# Bonus: Examine denoising using PCA\n",
    "\n",
    "In this lecture, we saw that PCA finds an optimal low-dimensional basis to minimize the reconstruction error. Because of this property, PCA can be useful for denoising corrupted samples of the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "X4dD9tPdgDW5"
   },
   "source": [
    "## Exercise 5: Add noise to the data\n",
    "In this exercise you will add salt-and-pepper noise to the original data and see how that affects the eigenvalues. \n",
    "\n",
    "**Steps:**\n",
    "- Use the function `add_noise` to add noise to 20% of the pixels.\n",
    "- Then, perform PCA and plot the variance explained. How many principal components are required to explain 90% of the variance? How does this compare to the original data? \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 230
    },
    "colab_type": "code",
    "id": "2E16UTYWemHT",
    "outputId": "76446c72-6a81-4216-fc97-741aacbcd0b6"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function add_noise in module __main__:\n",
      "\n",
      "add_noise(X, frac_noisy_pixels)\n",
      "    Randomly corrupts a fraction of the pixels by setting them to random values.\n",
      "    \n",
      "    Args:\n",
      "       X (numpy array of floats)  : Data matrix\n",
      "       frac_noisy_pixels (scalar) : Fraction of noisy pixels\n",
      "    \n",
      "    Returns:\n",
      "       (numpy array of floats)    : Data matrix + noise\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(add_noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "dFEaRM-giCRl"
   },
   "outputs": [],
   "source": [
    "###################################################################\n",
    "# Insert your code here to:\n",
    "# Add noise to the data\n",
    "# Plot noise-corrupted data\n",
    "# Perform PCA on the noisy data\n",
    "# Calculate and plot the variance explained\n",
    "###################################################################\n",
    "np.random.seed(2020)  # set random seed\n",
    "X_noisy = ...\n",
    "# score_noisy, evectors_noisy, evals_noisy = ...\n",
    "# variance_explained_noisy = ...\n",
    "# plot_MNIST_sample(X_noisy)\n",
    "# plot_variance_explained(variance_explained_noisy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 848
    },
    "colab_type": "code",
    "id": "wVWrn-mn5m4w",
    "outputId": "cc43d07c-f15a-4652-a697-03cdd7387450"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 416,
       "width": 424
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 416,
       "width": 560
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# to_remove solution\n",
    "\n",
    "np.random.seed(2020)  # set random seed\n",
    "X_noisy = add_noise(X, .2)\n",
    "score_noisy, evectors_noisy, evals_noisy = pca(X_noisy)\n",
    "variance_explained_noisy = get_variance_explained(evals_noisy)\n",
    "\n",
    "with plt.xkcd():\n",
    "  plot_MNIST_sample(X_noisy)\n",
    "  plot_variance_explained(variance_explained_noisy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "wWojBrz2xbjC"
   },
   "source": [
    "## Exercise 6: Denoising\n",
    "\n",
    "Next, use PCA to perform denoising by projecting the noise-corrupted data onto the basis vectors found from the original dataset. By taking the top K components of this projection, we can reduce noise in dimensions orthogonal to the K-dimensional latent space. \n",
    "\n",
    "**Steps:**\n",
    "- Subtract the mean of the noise-corrupted data.\n",
    "- Project the data onto the basis found with the original dataset (`evectors`, not `evectors_noisy`) and take the top $K$ components. \n",
    "- Reconstruct the data as normal, using the top 50 components. \n",
    "- Play around with the amount of noise and K to build intuition.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "j7ZORGDJihuH"
   },
   "outputs": [],
   "source": [
    "###################################################################\n",
    "# Insert your code here to:\n",
    "# Subtract the mean of the noise-corrupted data\n",
    "# Project onto the original basis vectors evectors\n",
    "# Reconstruct the data using the top 50 components\n",
    "# Plot the result\n",
    "###################################################################\n",
    "\n",
    "X_noisy_mean = ...\n",
    "projX_noisy = ...\n",
    "X_reconstructed = ...\n",
    "# plot_MNIST_reconstruction(X_noisy, X_reconstructed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 303
    },
    "colab_type": "code",
    "id": "KB5QiPn-3Pag",
    "outputId": "f3a06a58-20d6-4fde-a0e7-a4873dd8b0de"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 289,
       "width": 557
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# to_remove solution\n",
    "\n",
    "X_noisy_mean = np.mean(X_noisy, 0)\n",
    "projX_noisy = np.matmul(X_noisy - X_noisy_mean, evectors)\n",
    "X_reconstructed = reconstruct_data(projX_noisy, evectors, X_noisy_mean, 50)\n",
    "\n",
    "with plt.xkcd():\n",
    "  plot_MNIST_reconstruction(X_noisy, X_reconstructed)"
   ]
  }
 ],
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