2-Overview-of-Supervised-Learning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $\\S$ Supervised Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $\\S$ 2.3. Two Simple Approaches to Prediction: Least Squares and Nearest Neighbors\n",
    "\n",
    "In this section we develop two simple but powerful prediction methods: The linear model fit by least squares and the $k$-nearest-neighbor (kNN) prediction rule.\n",
    "\n",
    "The linear model makes huge assumptions about structure and yields stable but possibly inaccurate predictions. The method of kNN makes very mild structural assumptions: Its predictions are often accurate but can be unstable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\S$ 2.3.3 From Least Squares to Nearest Neighbors\n",
    "\n",
    "The linear decision boundary from least squares is very smooth, and apparently stable to fit. It does appear to rely heavily on the assumption that a linear decision boundary is appropriate. In language we will develop shortly, it has low variance and potentially high bias.\n",
    "\n",
    "On the other hand, the $k$-nearest-neighbor procedures do not appear to rely on any stringent assumptions about the underlying data, and can adapt to any situation. However, any particular subregion of the decision boundary depends on a handful of input points and their particular positions, and is thus wiggly and unstable—high variance and low bias.\n",
    "\n",
    "Let's expose the oracle first! The data is generated with following steps:\n",
    "1. Generate 10 means $m_k$ from a bivariate Gaussian for each class  \n",
    "\n",
    "  \\begin{equation}\n",
    "  m_k \\sim \\begin{cases}\n",
    "  N((1,0)^T, \\mathbf{I}) & \\text{ for BLUE}, \\\\\n",
    "  N((0,1)^T, \\mathbf{I}) & \\text{ for ORANGE}\n",
    "  \\end{cases}\n",
    "  \\end{equation}\n",
    "  \n",
    "2. For each class, we generate 100 observations as follows:\n",
    "  1. Pick an $m_k$ at random with probability 1/10\n",
    "  2. Generate $x_i \\sim N(m_k, \\mathbf{I}/5)$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0.],\n",
       "       [0., 1.]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.eye(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define a function generate_data(sample_size)\n",
    "def generate_data(sample_size:int)->tuple:\n",
    "    # Parameters for mean distributions\n",
    "    mean_blue = [1, 0]\n",
    "    mean_orange = [0, 1]\n",
    "    mean_cov = np.eye(2)\n",
    "    mean_size = 10\n",
    "    \n",
    "    # Additional parameters for blue and orange distributions\n",
    "    sample_cov = np.eye(2)/5\n",
    "    \n",
    "    # Generate mean components for blue and orange (10 means for each)\n",
    "    sample_blue_mean = np.random.multivariate_normal(mean_blue, mean_cov, mean_size)\n",
    "    sample_orange_mean = np.random.multivariate_normal(mean_orange, mean_cov, mean_size)\n",
    "    \n",
    "    # Generate (n=sample_size) blue points\n",
    "    sample_blue = np.array([\n",
    "        np.random.multivariate_normal(sample_blue_mean[random.randint(0, 9)],\n",
    "                                      sample_cov)\n",
    "        for _ in range(sample_size)\n",
    "    ])\n",
    "    # Generate (n=sample_size) 0\n",
    "    y_blue = [0 for _ in range(sample_size)]\n",
    "\n",
    "    # Generate (n=sample_size) orange points\n",
    "    sample_orange = np.array([\n",
    "        np.random.multivariate_normal(sample_orange_mean[random.randint(0, 9)],\n",
    "                                      sample_cov)\n",
    "        for _ in range(sample_size)\n",
    "    ])\n",
    "    # Generate (n=sample_size) 1\n",
    "    y_orange = [1 for _ in range(sample_size)]\n",
    "\n",
    "    data_x = np.concatenate((sample_blue, sample_orange), axis=0)\n",
    "    data_y = np.concatenate((y_blue, y_orange))\n",
    "    return data_x, data_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(sample_blue)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "200"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(data_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "200"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(data_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample_size = 100\n",
    "data_x, data_y = generate_data(sample_size)\n",
    "sample_blue = data_x[data_y == 0, :]\n",
    "sample_orange = data_x[data_y == 1, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot\n",
    "fig = plt.figure(figsize=(15, 15))\n",
    "ax1 = fig.add_subplot(2, 2, 1)\n",
    "\n",
    "ax1.plot(sample_blue[:, 0], sample_blue[:, 1], 'o')\n",
    "ax1.plot(sample_orange[:, 0], sample_orange[:, 1], 'o', color='orange')\n",
    "ax1.set_title('0/1 Response')\n",
    "plt.show()\n",
    "\n",
    "plot_x_min, plot_x_max = ax1.get_xlim()\n",
    "plot_y_min, plot_y_max = ax1.get_ylim()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\S$ 2.3.1. Linear Models and Least Squares\n",
    "\n",
    "> The linear model has been a mainstay of statistics for the past 30 years and remains one of our most important tools.\n",
    "\n",
    "### Linear Models\n",
    "\n",
    "Given a vector of inputs $X^T = (X_1, \\cdots, X_p)$, we predict the output $Y$ via the model\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{Y} = \\hat{\\beta}_0 + \\sum^p_{j=1}X_j\\hat{\\beta}_j = X^T\\hat{\\beta}=\n",
    "\\begin{bmatrix}\n",
    "1&X_1&X_2&\\cdots&X_p\n",
    "\\end{bmatrix}\\begin{bmatrix}\n",
    "\\hat{\\beta}_0\\\\\n",
    "\\hat{\\beta}_1\\\\\n",
    "\\vdots\\\\\n",
    "\\hat{\\beta}_p\\\\\n",
    "\\end{bmatrix}\n",
    "\\end{equation}\n",
    "\n",
    "where the constant variable 1 in $X^T = (1, X_1, \\cdots, X_p)$ and $\\hat{\\beta}^T = (\\beta_0, \\beta_1, \\cdots, \\beta_p)$. The term $\\hat\\beta_0$ is the intercept, a.k.a. the _bias_ in machine learning.\n",
    "\n",
    "Here we are modeling a single output, so $\\hat{Y}$ is a scalar; in general $\\hat{Y}$ can be a $K$-vector, in which case $\\beta$ would be a $p \\times K$ matrix of coefficients.\n",
    "\n",
    "In the $(p+1)$-dimensional input-output space, $(X, \\hat{Y})$ represents a hyperplane. If the constant is included in $X$, then the hyperplane includes the origin and is a subspace; if not, is is an affine set cutting the $Y$-axis at the point $(0, \\hat\\beta_0)$. From now on we assume that the intercept is included in $\\hat\\beta$.\n",
    "\n",
    "Viewed as a function over the $p$-dimensional input space,\n",
    "\n",
    "\\begin{equation}\n",
    "f(X) = X^T\\beta\n",
    "\\end{equation}\n",
    "\n",
    "is linear, and the gradient $f'(X) = \\beta$ is a vector in input space that points in the steepest uphill direction."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How to fit the model: Least squares\n",
    "\n",
    "Least squares pick the coefficients $\\beta$ to minimize the residual sum of squares\n",
    "\n",
    "\\begin{equation}\n",
    "RSS(\\beta) = \\sum^N_{i=1}(y_i - x_i^T\\beta)^2 = (\\mathbf{y} - \\mathbf{X}\\beta)^T(\\mathbf{y} - \\mathbf{X}\\beta)\\\\\n",
    "=(\\mathbf{y}^T - \\beta^T\\mathbf{X}^T)(\\mathbf{y} - \\mathbf{X}\\beta)\\\\\n",
    "=\\mathbf{y}^T\\mathbf{y}-\\mathbf{y}^T\\mathbf{X}\\beta-\\beta^T\\mathbf{X}^T\\mathbf{y}+\\beta^T\\mathbf{X}^T\\mathbf{X}\\beta,\n",
    "\\end{equation}\n",
    "\n",
    "since $\\mathbf{y}^T\\mathbf{X}\\beta$ is a scalar quantity, thus $\\mathbf{y}^T\\mathbf{X}\\beta = (\\mathbf{y}^T\\mathbf{X}\\beta)^T=\\beta^T\\mathbf{X}^T\\mathbf{y}$ Then \n",
    "\n",
    "\\begin{equation}\n",
    "RSS(\\beta) = \\mathbf{y}^T\\mathbf{y}-\\beta^T\\mathbf{X}^T\\mathbf{y}-\\beta^T\\mathbf{X}^T\\mathbf{y}+\\beta^T\\mathbf{X}^T\\mathbf{X}\\beta\\\\\n",
    "= \\mathbf{y}^T\\mathbf{y}-2\\beta^T\\mathbf{X}^T\\mathbf{y}+\\beta^T\\mathbf{X}^T\\mathbf{X}\\beta\n",
    "\\end{equation}\n",
    "\n",
    "where $\\mathbf{X}$ is an $N \\times p$ matrix with each row an input vector, and $\\mathbf{y}$ is an $N$-vector of outputs in the training set.\n",
    "\n",
    "$RSS(\\beta)$ is a quadratic function of the parameters, and hence its minimum always exists, but may not be unique.\n",
    "\n",
    "Differentiating w.r.t. $\\beta$ we get the *normal equations*\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\partial{RSS}}{\\partial{\\beta}}=-2\\mathbf{X}^T\\mathbf{y}+2\\mathbf{X}^T\\mathbf{X}\\beta\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{X}^T(\\mathbf{y} - \\mathbf{X}\\beta) = 0.\n",
    "\\end{equation}\n",
    "\n",
    "If $\\mathbf{X}^T \\mathbf{X}$ is nonsingular, then the unique solution is given by\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{\\beta} = (\\mathbf{X}^T\\mathbf{X})^{-1}\\mathbf{X}^T\\mathbf{y},\n",
    "\\end{equation}\n",
    "\n",
    "and the *fitted value* at the $i$th input $x_i$ is \n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{y}_i = \\hat{y}(x_i) = x_i^T\\hat{\\beta}.\n",
    "\\end{equation}\n",
    "\n",
    "At an arbitrary input $x_0$ the prediction is\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{y}(x_0) = x_0^T \\hat\\beta.\n",
    "\\end{equation}\n",
    "\n",
    "The entire fitted surface is characterized by the $p$ parameters. Intuitively, it seems that we do not need a very large data set to fit such a model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Estimated Coefficients for OLS ===\n",
      "beta0: 0.4409182185615338 (constant)\n",
      "beta1: -0.09141131859617739\n",
      "beta2: 0.20146884857094918\n"
     ]
    }
   ],
   "source": [
    "# Linear regression\n",
    "mat_x = np.hstack((np.ones((sample_size*2, 1)), data_x))\n",
    "mat_xt = np.transpose(mat_x)\n",
    "vec_y = data_y\n",
    "\n",
    "# Solve (X^T*X)b = X^T*y for b\n",
    "ols_beta = np.linalg.solve(np.matmul(mat_xt, mat_x), np.matmul(mat_xt, vec_y))\n",
    "\n",
    "print('=== Estimated Coefficients for OLS ===')\n",
    "print('beta0:', ols_beta[0], '(constant)')\n",
    "print('beta1:', ols_beta[1])\n",
    "print('beta2:', ols_beta[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "200"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(mat_x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear model in a classification context\n",
    "\n",
    "FIGURE 2.1 shows a scatterplot of training data on a pair of inputs $X_1$ and $X_2$.\n",
    "* The output class variable $G$ has the values $\\textsf{BLUE}$ or $\\textsf{ORANGE}$.\n",
    "* There are 100 points in each of the two classes.\n",
    "* The linear regression model was fit to these data, with the response $Y$ coded as $0$ for $\\textsf{BLUE}$ and $1$ for $\\textsf{ORANGE}$.\n",
    "\n",
    "The fitted value $\\hat{Y}$ are converted to a fitted class variable $\\hat{G}$ according to the rule\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{G} = \\begin{cases}\n",
    "1 & \\text{ (ORANGE) } & \\text{ if } \\hat{Y} \\gt 0.5,\\\\\n",
    "0 & \\text{ (BLUE) } & \\text{ if } \\hat{Y} \\le 0.5.\n",
    "\\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "And the two predicted classes are separated by the *decision boundary* $\\{x: x^T\\hat{\\beta} = 0.5\\}$, which in linear."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> The decision boundary is $\\hat{y}=0.5$ then\n",
    "$\\hat{y} = X^T\\hat{\\beta} =\n",
    "\\begin{bmatrix}\n",
    "1&x&y\\\\\n",
    "\\end{bmatrix}\\begin{bmatrix}\n",
    "\\hat{\\beta_0}\\\\\n",
    "\\hat{\\beta_1}\\\\\n",
    "\\hat{\\beta_2}\\\\\n",
    "\\end{bmatrix}= \\hat{\\beta_0} + \\hat{\\beta_1}x + \\hat{\\beta_2}y = 0.5$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 2 Axes>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"FIGURE 2.1. A classification example in 2D.\"\"\"\n",
    "# Plot for OLS\n",
    "ax2 = fig.add_subplot(2, 2, 2)\n",
    "\n",
    "ax2.plot(sample_blue[:, 0], sample_blue[:, 1], 'o', color='C0')\n",
    "ax2.plot(sample_orange[:, 0], sample_orange[:, 1], 'o', color='orange')\n",
    "\n",
    "# OLS line for y_hat = X^T\\beta_hat = 0.5\n",
    "ols_line_y_min = (.5 - ols_beta[0] - plot_x_min*ols_beta[1])/ols_beta[2]\n",
    "ols_line_y_max = (.5 - ols_beta[0] - plot_x_max*ols_beta[1])/ols_beta[2]\n",
    "ax2.plot([plot_x_min, plot_x_max], [ols_line_y_min, ols_line_y_max], color='black')\n",
    "\n",
    "# https://matplotlib.org/examples/pylab_examples/fill_between_demo.html\n",
    "ax2.fill_between([plot_x_min, plot_x_max], plot_y_min, [ols_line_y_min, ols_line_y_max],\n",
    "                facecolor='blue', alpha=.2)\n",
    "ax2.fill_between([plot_x_min, plot_x_max], [ols_line_y_min, ols_line_y_max], plot_y_max,\n",
    "                facecolor='orange', alpha=.2)\n",
    "ax2.set_title('Linear Regression of 0/1 Response')\n",
    "ax2.set_xlim((plot_x_min, plot_x_max))\n",
    "ax2.set_ylim((plot_y_min, plot_y_max))\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.6629370145399807"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ols_line_y_min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.321034034948018"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ols_line_y_max"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Where the data came from?\n",
    "\n",
    "We see that for these data there are several misclassifications on both sides of the decision boundary. Perhaps our linear model is too rigid -- or are such errors unavoidable? Remember that these are errors on the training data itself, and we have not said where the constructed came from (although this notebook already exposed the oracle). Consider the two possible scenarios:\n",
    "* $\\text{Scenario 1}$: The training data in each class were generated from bivariate Gaussian distributions with uncorrelated components and different means.\n",
    "* $\\text{Scenario 2}$: The training data in each class came from a mixture of 10 low-variance Gaussian distributions, with individual means themselves distributed as Gaussian.\n",
    "\n",
    "A mixture of Gaussians is best described in terms of the generative model.\n",
    "* One first generates a discrete variable that determines which of the component Gaussians to use,\n",
    "* and then generates an observation from the chosen density.\n",
    "\n",
    "In the case of one Gaussian per class, we will see in Chapter 4 that a linear decision boundary is the best one can do, and that our estimate is almost optimal. The region of overlap is inevitable, and future data to be predicted will be plagued by this overlap as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\S$ 2.3.2 Nearest-Neighbor Methods\n",
    "\n",
    "Now we look at another classification and regression procedure that is in some sense at the opposite end of the spectrum to the linear model, and far better suited to the second scenario.\n",
    "\n",
    "> Nearest-neighbor methods use those observations in the training set $\\mathcal{T}$ closest in input space to $x$ to form $\\hat{Y}$.\n",
    "\n",
    "The kNN fit for $\\hat{Y}$ is defined as follows:\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{Y}(x) = \\frac{1}{k}\\sum_{x_i\\in N_k(x)} y_i,\n",
    "\\end{equation}\n",
    "\n",
    "where $N_k(x)$ is the neighborhood of $x$ defined by the $k$ closest points $x_i$ in the training sample. Closeness implies a metric, which for the moment we assume is Euclidean distance.\n",
    "\n",
    "> So, in other words, we find the $k$ observations with $x_i$ closest to $x$ in input space, and average their responses.\n",
    "\n",
    "In FIGURE 2.2 we use the same training data, and use 15NN averaging of the binary coded response as the method of fitting. Thus $\\hat{Y}$ is the proportion of $\\textsf{ORANGE}$s in the neighborhood, and so assigning class $\\text{ORANGE}$ to $\\hat{G}$ if $\\hat{Y} > 0.5$ amounts to a majority vote in the neighborhood.\n",
    "\n",
    "We see that the decision boundaries that separate the $\\textsf{BLUE}$ from the $\\textsf{ORANGE}$ regions are far more irregular, and respond to local clusters where one class dominates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# K-nearest neighbors\n",
    "def knn(k: int, point, data_x, data_y) -> float:\n",
    "    if not isinstance(point, np.ndarray):\n",
    "        point = np.array(point)\n",
    "    distances = [(sum((x - point)**2), y) for x, y in zip(data_x, data_y)]\n",
    "    distances.sort()\n",
    "    return sum(y for _, y in distances[:k])/k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2kAAANeCAYAAACI90azAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nOzdeXgUVdYG8PdmgSRCQAmCiWzqwIggsuqIg7iMgKJGXFACjqOj4L4AjojfuCIMQccFFFFxgeCOUUBAHWQYVwQBQRRcIGAisoYASSDL/f6oqtDpVHV3ddfa/f6exyek0stNOqbq9Dn3HCGlBBEREREREXlDktsLICIiIiIiosMYpBEREREREXkIgzQiIiIiIiIPYZBGRERERETkIQzSiIiIiIiIPIRBGhERERERkYcwSCMiIqKEJoT4sxBig9vriAdCiO+EEP0dfk4hhHhJCLFHCLHcyecmsguDNIorQoijhBDvCiEOCCGKhBDDdG5zrxDiUSFEIyHE20KIzUIIGe6kIoRYKoSoFELsF0LsFELMFUIcY9s3Q0REllL/3p8bfFxK+T8pZSc31hRMCPGAEKJKPdeUCiE+F0L8ye11RUpKeZKUcqnDT3sGgL8AOFZK2UfvBkKIYep1wQEhRKEQ4qigrzdSz+1NhBBXqD/3ciHE0lBPLIToL4SoVV+vfUKIDUKIv1n2nVHCYpBG8WYagEMAWgHIA/CsEOKkoNucD+AD9d+fAhgOYFuEj3+LlLIJgBMANAEwJeYVExFRQhJCpBh86Q31XJMF4BMAb9nw3EIIES/Xge0AbJZSHtD7onod8ByAEVCuD8oBPBN0s34AVksp9wPYDeAJAJMifP4S9fXKBHAngOeFEJ4I+sm/4uV/TiIIIY4AcCmA/5NS7pdSfgrgfSh/lLXbHAmgI4AvpJSHpJRPqLerMfNcUspSAIUATgl47D8KIT4SQuxW30m7IuBr5wsh1qvvshULIcaox/sLIX5Vs3s71Xd58wLu10wI8aoQYof6DuB92klVCHGNEOJTIcQUtcRjkxBiUMB9rxFC/KI+56agx71WCPG9er/FQoh2Zr5/IqJ4ov0tDvh8sxBijBDiWyHEXiHEG0KItICvDxZCrA7IdJ0c8LV7hBA/q3971wshLgn42jVCiM+EEP8WQuwG8ECodUkpqwEUAMgRQrRUH6OZEOJFIcRv6vnkESFEsvq1ZCHEY+r5ZJMQ4ha1UiRF/fpSIcQEIcRnUAKV46I8d2UJIear3/9uIcT/As5NddlKIURjIcQTQogS9b8nhBCNA3/mQojRQojt6vdjmIESQmQLId5Xn+8nIcT16vHrALwA4E9CyWY9qHP3PADzpJTL1CDs/wAMEUI0DbhN3Ru4UsqPpZRvAigJ9frovF5SSvkBlCDvZHV9SQG/E7uEEG8KNYsnhEgTQsxWj5cKIb4WQrQKeK0mCiGWq7+D74mA7J8Q4iKhlJaWqrc9MeBrhr+/YV67bCHEO0K55tgkhLjNzPdP1mKQRvGkI4AaKeXGgGNrAARm0gYA+I+U0lRQFkwI0QLAEAA/qZ8fAeAjAHMAHA3gKgDPiMNZvBcBjJRSNgXQBcCSgIdrDeXd0hwAfwUwQxx+B+5pAM0AHAfgTABXAwg8iZ0KYIN6/8kAXhSKIwA8BWCQ+pynA1itrjUXwL3q+lsC+B+A12L5eRARxaErAAwE0AHKBfc1ACCE6AFgJoCRAFpAydC8rwUfAH4G8Gcof7sfBDBb1C+NPxXAL1DOFRNCLUAI0QjK3/1dAPaoh18BUA2loqM7gPMA/F392vUABkF5A7EHgFydhx0B4AYATQHsQHTnrtEAfoVyDmkF5ZwidZ5rPIDT1PV0A9AHwH0BX28N5eeUA+A6ANOE8maqntfU58wGcBmAR4UQ50gpXwQwCsqbr02klPfr3PckKNcDAAAp5c9Qqm46BtzmfAALDJ47ImpAdhGUc/JP6uHboLwOZ6pr3wOl6gdQzvnNALSB8rs0CkBFwENeDeBa9X7VUM7rEEJ0hPLzuAPKa/ABgHnq74tG9/cXBq+dGqjNg/JzygFwDoA7hBADYviRUAwYpFE8aQJgb9CxvVBORJoLcLjUMRpPCSH2AtgJ5Y/wrerxwVBKLV6SUlZLKb8B8A6UEwkAVAHoLITIlFLuUb8e6P+klAellP+FcpK4Qn1ndCiAcVLKfVLKzQAeQ0BmEECRlPJ5Neh8BcAxUP7oAkAtgC5CiHQp5W9Syu/U4yMBTJRSfq++S/sogFMEs2lERIGeklKWSCl3Q7l41SonrgfwnJTyKylljZTyFQAHoQQjkFK+pd6vVkr5BoAfoQQnmhIp5dPquSLwgjzQFUKIUigX7NcDuExKWa1mWQYBuENKeUBKuR3AvwFcqd0PwJNSyl+llHugX673spTyO/Xv/0BEd+6qgnK+aSelrFL39OkFaXkAHpJSbpdS7oAStAaew6rUr1epGaj9ABqUCQoh2kDZd/YPKWWllHI1lOzZiODbGgh5fSCEOA5AqpQy2uYx2QGv17sA7pJSrlK/NhLAePU1OQgle3qZmt2sghKcnaD+Lq2UUpYFPO4sKeU6tYzz/1D/2mCBlPIjKWUVlK0X6VDekNUY/f4avXa9AbSUUj6kVhr9AuB5HP7dIocxSKN4sh9KPXigTAD7AOUdLigbixfF8By3SSmbQXlX6kgAx6rH2wE4VS0fKFX/WOdBeZcQUMowzwdQJIT4r6i/CXxPUB19EZR3zbIANFI/D/xaTsDndXvppJTl6j+bqI83FMq7cr8JIRYIIf4YsNYnA9a5G4AIelwiokQXuFe5HMqFPqD8DR0d9Pe+DZS/2xBCXC0Ol0KWQslAZQU81tYInvtNKWVzKG+6rQPQM+C5U6H8Xdce/zkoWTCoawh8fL3nCjwW7bkrH0qm6EOhlNXfY/B9ZKPhOSw74PNdarCoCfw5Bz/ObinlvqDHivS8FfL6ALG/gVuivl6ZULJdZwd8rR2AdwN+vt9D2WLRCsAsAIsBvK6Wg04WQqQG3DfwtSqC8tpnIejnKqWsVW+re32A+j9Xo9euHdRgM2Ct9+LwG7/kMAZpFE82AkgRQvwh4Fg3AFoGqTeUdwx3xPpEUsq1AB6BUpohoPxx/K+UsnnAf02klDeqt/9aSnkxlBNpIYA3Ax7uSLU8UdMWSh38TijveLUL+lpxhGtcLKX8C5R3zH6A8o4Y1LWODFprupTyc3M/BSKihLQVwISgv6EZUsrX1IqE5wHcAqCFeuG+DsobYRq9jJMuKeVOKJmYB9SSya1QsnZZAc+dKaXUyhN/w+E3DwEleGzwsEHfi+lzl1rdMVpKeRyACwHcJYQ4R+e5StDwHGZqn1fA4xwVtIcs4vMhlOuAbtonauasMZTrBsCCUkcAUDNl/wDQVd1aACg/40FBP+M0KWWxmsl6UErZGUoWbDCUEkdN4OvXFso1wU4E/VzV65A2iODnEeK12wpgU9A6m0opz4/yx0ExYpBGcUPNHs0F8JAQ4gghRF8AF0N5pwrQeadMKJuatc3gjdRNvIEn01BegXLiugjAfAAdhRAjhBCp6n+9hRAnCqWtb54QoplallCGho1KHlRv92cof6TfUksY3wQwQQjRVD353wVgdriFCSFaCWVT8RFQTuj7A55zOoBx2p4DoWxCvzzC75mIyO9S1b/12n9GHRaNPA9glBDiVG0PsBDiAjWAOAJKELQDAITSCKNLLIuVUv4AJdtyt5TyNwAfAnhMCJGp7oE6XghxpnrzNwHcLoTIEUI0hxIwhBLVuUsojVNOUM+X2nG9vd6vAbhPCNFSCJEF4J+I4Bym8zPYCuBzABPV1+xkKHvYCiJ8iAIAFwplHt4RAB4CMFdKuU8IkQ6lHHWpdmOhNGBJA5ACIEl9zlS9B9ZZ6yEoWxP+qR6aDuU83k597JZCiIvVf58lhOiqljCWQQnCAn+Ow4UQnYUQGeqa3w64NrhACHGOuq7RUM71Yd9sDfHaLQdQJoT4hxAiXf0ZdBFC9I7k+ybrMUijeHMTlLrs7VBODjfKw3uxAlvvazZAqSHPgXISrED9d/0MqX+In4Kyn2wflM3bV0J5h2sbgH9BeacOUOrmNwshyqCUIA4PeKhtUDYSl0A5kYxST8qAsuftAJRN5p9C2dw9M4LlJUH5o10CpZzxTCg/G0gp31XX9rq6nnVQ9jgQESWCD6D8rdf+e8DMnaWUK6DsE5sK5W/3T1CbMkgp10O5QP8CwO8AugL4zII15wO4QQhxNJRMSyMA69XnfxtKxQSgBJAfAvgWwCoo32s1DDoYx3Du+gOAj6G8AfgFgGek/my0RwCsUNezFsA36rFoXAWgvbrOdwHcL6X8KJI7qtcBo6CcY7dD2Yt2k/rlc6A0HakMuMsIKL8bz0JpAlOBw9UokZgJoK0Q4kIAT0LpNP2hEGIfgC+hNI8BlLLSt6EES98D+C/qB7GzALwM5XVJg9KEBOreueFQmovthJIRu1C9LglH97VTg78Loexd26Q+7gtQGpuQC4T+Pk+i+CKUzdarAWQbbG52hVAGaM+WUh4b7rZERERmCGUsy3QpJRtDGRBCPANgnZQyeG6aq4QyRHu2lPIFt9dC7mAmjRJFMyjdljwToBEREVlJLVM7XwiRIoTIAXA/lKwTGVsN/ozIg8zWYRP5klRmp20Me0MiIiL/ElDa3L8BpURvAQ7vjSIdUsoZbq+BSA/LHYmIiIiIiDyE5Y5EREREREQe4kq5Y1ZWlmzfvr0bT01ERA5auXLlTillS7fX4RdZWS1k+7acK09ElAhWrlpreI50JUhr3749VqxY4cZTExGRg4QQRW6vwU/atz0WKz6OZMoGERH5WxJEix6G50iWOxIREREREXkIgzQiIiIiIiIPYZBGRERERETkIQzSiIiIiIiIPIRBGhERERERkYcwSCMiIiIiIvIQBmlEREREREQewiCNiIiIiIjIQxikEREREREReQiDNCIiIiIiIg9hkEZEREREROQhDNKIiIiIiIg8hEGa320qAArbA3OSlI+bCtxeERERkftKFgJLBwOLeisfSxa6vSIiooiluL0AisGmAmD5DUBNufJ5eZHyOQB0yHNvXURERG4qWQismwDUViqfV25TPgeA7EHurYuIKELMpPnZmvGHAzRNTblynIiIKFFtnHY4QNPUVirHiYh8gEGan5VvMXeciIgoEVT+bu44EZHHMEjzs4y25o4TERElgrRW5o4TEXkMgzQ/6zYBSM6ofyw5QzlORESUqDreDCSl1T+WlKYcJyLyATYO8TOtOcia8UqJY0ZbJUBj0xAiIkpkWnOQjdOUEse0VkqAxqYhROQTDNL8rkMegzIiIqJg2YMYlBGRb7HckYiIiIiIyEMYpBEREREREXkIgzQiIiIiIiIPYZBGRERERETkIQzSiIiIiIiIPIRBGhERERERkYcwSCMiIiIiIvIQBmlEREREREQewiCNiIiIiIjIQxikEREREREReQiDNCIiIiIiIg9hkEZEREREROQhMQdpQog0IcRyIcQaIcR3QogHrVgYERGR3/EcSURE0Uix4DEOAjhbSrlfCJEK4FMhxEIp5ZcWPDYREZGf8RxJRESmxRykSSklgP3qp6nqfzLWxyUiIvI7niOJiCgaluxJE0IkCyFWA9gO4CMp5Vc6t7lBCLFCCLFix44dVjwtERGR54U7R9Y7P+7c5c4iiYjIUywJ0qSUNVLKUwAcC6CPEKKLzm1mSCl7SSl7tWzZ0oqnJSIi8rxw58h658esFu4skoiIPMXS7o5SylIASwEMtPJxiYiI/I7nSCIiipQV3R1bCiGaq/9OB3AugB9ifVwiIiK/4zmSiIiiYUV3x2MAvCKESIYS9L0ppZxvweMSERH5Hc+RRERkmhXdHb8F0N2CtRAREcUVniOJiCgalu5JIyIiIiIiotgwSCMiIiIiIvIQBmlEREREREQewiCNiIiIiIjIQxikEREREREReQiDNCIiIiIiIg9hkEZEREREROQhDNKIiIiIiIg8hEEaERERERGRh6S4vQCKf4WripG/eANKSiuQ3TwdYwd0Qm73HLeXRURE5KrC9eXIX7YfJWW1yM5Mwth+TZDbOcPtZRGRBzBII1sVrirGuLlrUVFVAwAoLq3AuLlrAYCBGhERJazC9eUYt6gMFdXK58VltRi3qAwAGKgREcsdyV75izfUBWiaiqoa5C/e4NKKfGBTAVDYHpiTpHzcVOD2ioiIyGL5y/bXBWiaimrlOIVQshBYOhhY1Fv5WLLQ7RUR2YKZNLJVSWmFqeMJb1MBsPwGoKZc+by8SPkcADrkubcuIiKyVElZranjBCUgWzcBqK1UPq/cpnwOANmD3FsXkQ2YSSNbZTdPN3U84a0ZfzhA09SUK8eJiChuZGfqX4IZHScAG6cdDtA0tZXKcaI4w78EZKuxAzohPTW53rH01GSMHdDJpRV5XPkWc8eJiMiXxvZrgvSgeqb0FOU4Gaj83dxxIh9juSPZSmsOwu6OEcpoq5Q46h0nIqK4oTUHYXdHE9JaKSWOeseJ4gyDNLJdbvccBmWR6jah/p40AEjOUI4TEVFcye2cwaDMjI4319+TBgBJacpxojjDII3IS7TmIGvGKyWOGW2VAI1NQ4iIKNFpzUE2TlNKHNNaKQEam4ZQHGKQRuQ1HfIYlBEREenJHsSgjBICG4cQUWQ4v42IiEgf57eRxZhJI6LwOL+NiIhIH+e3kQ2YSSOi8Di/jYiISB/nt5ENGKRR/GFZnvU4v42IyP9YkmcPzm8jGzBIo/iileWVFwGQh8vyGKjFxmhOG+e3ERH5g1aSV7kNgDxcksdALXZGc9o4v41iwCCN4gvL8uzRbYIyry0Q57cREfkHS/Ls0/FmZV5bIM5voxixcQjFF5bl2YPz24iI/I0lefbh/DayAYM0cs6mAvsv8jPaqqWOOscpNpzfRkRkj5KF9l/gp7VSSx11jlPsOL+NLMZyR3KGU3vFWJZHRER+4tReMZbkEfkKgzRyhlN7xTrkAX1mABntAAjlY58Z3s0AsRMlEVFic2qvWPYgoMt4IK01AKF87DLeu9kfdqKkBMdyR3KGk3vF/FKWxwHRRETk5F4xv5TkcTg0ETNp5BC2cG+InSiJiIjt2xtiJ0oiBmnkEO4Va4idKImIiHvFGmInSiIGab7nlz1Nftsr5gRmF4mI7OWHfU1+2yvmBGYXKQHU1NSE/Dr3pPmZ3/Y0+WWvmFO6Taj/+gHMLhIRWcVP+5r8slfMKR1vrv/aAcwuUtw4cKACL815H48/Oyfk7ZhJ8zOn9zT5JWvnF8wuEhHZx8l9TX7I2PkJs4sUh37fvgv/9+izaNttMG69Jx9NM9uEvD0zaX7m5J4mv2Xt/ILZRec4MUydiLzDqX1NfsrY+Qmzi85xYph6Avth42Y8/mwBXn1jAQ4dqsKZZ16MESPGonv309GjhzC8H4M0P8toqw6H1jlutVBZO17oktfxTQaixJPWSh0QrXPcSqEydrzQJa/jmwy2kFLi0y9XY8rUWXh/0TI0bpyGCy74G/Ly7kK7dh0jegwGaX7m5J4mdiIMqXBVMfIXb0BJaQWym6dj7IBOyO2e4/aySMM3GYgSj1P7mtiJMKTC9eXIX7YfJWW1yM5Mwth+TZDbOSP8HckZfJPBUjU1NXh3wSeYMnU2vlq5Ds2bt8D11/8Tl19+M4466mhTj8Ugzc+0i0snSriczNr5TOGqYoybuxYVVUqXnuLSCoybuxYAGKh5Bd9kIEo82gWm3WVcTmXsfKhwfTnGLSpDRbXyeXFZLcYtKgMABmpewTcZLFFeXlnXDOSXzb+iTZvj8Y9/TMOFF16DtLToftcZpPmdU3ua2InQUP7iDXUBmqaiqgb5izcwSPMKvslAlJic2NfEToSG8pftrwvQNBXVynEGaR7BNxlisn3Hbkx94U08M/Nt7Npdiq5dT8PkyU/izDMvRnJyckyPzSCNIuNk1s5nSkorTB0nF/BNBiKyi1MZOx8qKas1dZxcwDcZorLhR6UZyCuvK81A+vW7CCNGjEW3bqdDCONmIGYwSKPIsROhruzm6SjWCciym6e7sBrSxTcZiMhO7ESoKzszCcU6AVl2JidAeQbfZIiYlBKffbWmrhlIamojXHDBNcjLuwvt23ey/PkYpBHFaOyATvX2pAFAemoyxg6w/n9YigHfZCAictTYfk3q7UkDgPQU5Th5CN9kCKmmpgaFC5ZiyrTZ+HLFWjRrdhSuu+4+XHHFLaabgZjBII0oEiFmbGn7zuKyuyNnixERUSghZmxp+87itrsj54vFtfLySrz82jw8/swc/Lx5K4499jjcffdUXHjhNUhPP8L252eQFq94cW2dCGZs5XbPiY+gLBBnixFRvOLFtTUimLGV2zkjfoKyQJwvFrd27NyDaS++iWkvvo2du/agy0l9MGnS4zjrrEtibgZiBoO0eMSLa2s5PWNLDbBl+Rb8Xt0SE0tGYAXOdz47x9liRBSPeHFtHadnbAUE1+XJR2Pytqvxym9nupOh43yxuLPxp6K6ZiCVlQfVZiBjcMopZ1jWDMQMBmleEm32K/h+Vft5cW0lJ2dsBQTYAkDrlO2YeOxU3PMrMG7uIQAOzl7jbDEi8opoM1969+PFtXWcnLEVFFxn1PyOu1s8hd0VtXi/9Czn569xvljc+Hz5GuQ/PQvvLfyv2gzkarUZyB9dXRfb63iFdnFeXgRAHs5+bSowf7+qXfq35cV1dIxmadkxY0sne5WRdBB3t361bvaaY5z8vomIjGgX55XbAMjDma+ShdHdT28mFMCL62gYzdKyY8aWTnCtnR+Bw/PXHOPk906Wq6mpwbvzP8HpA69F30HXYcmna3DtteMxb14Rxo+f4XqABjBI845QpWVm72fErYvrTQVAYXtgTpLyMVzg6TXdJigztQLZNWPLIJDOTt0JwOHZa05+30RERkJlvqK5n9GljxsX1yULgaWDgUW9lY/hAk+v6XizMlMrkF0ztgyCaO38CDg8f83J750sU1FRiekvvY0TT7scQ/46FltK9mHs2KexYMFW3Hjjw2jRwjtBdszljkKINgBeBdAaQC2AGVLKJ2N93IQTbWlZpNkxty6u42F/nJMztjLaqlnR+kqqsgA4PHuNs8WIYsZzpAWiLSsz/HqtcjHt9vDeeNgb5+SMrbRWullQ7fwIODx/jfPFfGXHzj14ZuZbmPrCW9i5aw9OOqk3Jk2agv79L0FKijd3f1mxqmoAo6WU3wghmgJYKYT4SEq53oLHThwGF+dhs19G90s+Amic5f7Fdbw0n3Bqxla3CfWDWgDltY0xedvV7sxe42wxoljxHBkrg4vzsJkvo/ulZAKdx7p/cR0ve+OcmrHV8eb6QS0Onx8Bl+avcb6Y5/348xb8+9k5eOm1eaisPIg//3kwRowYi+7d/+xKMxAzYg7SpJS/AfhN/fc+IcT3AHIA8ARkhs7FeUTZr24TgC//Bsiq+sdllTeyHmw+UV+45jAB2avA7o4rcT4mDomT2WtECYTnSAvoXJxHlPnqeDPw7YNQ4uQANWrZeP/5li7TNDaeqC9cc5igzFV58tGYvONqzCs9EznxNn+NYvbF199iytRZeHfBUqSkpOL880dg+PDR6NDhRLeXFjEhpbTuwYRoD2AZgC5SyrKgr90A4AYAaNu2bc+iIp3sT6KLtrvj21nAIZ1mIRntgNzNli/TkN7614w3yBA6vDYvCC79BJRAvM8M94NpIpsIIVZKKXu5vQ4vMDpH1js/tsnpWbT6PVfW52nRdnf8zzlA1d6Gx9NaOx+kBX8PNRXeWZvbgks/ASUQ7zKemSqKWG1tLd5fuAxTps3GZ1+tRmbmkbjssptwxRW3ICurtdvLayApCejRw/gcaVmQJoRoAuC/ACZIKeeGum2vXr3kihUrLHlegtKQA3qvowCG2byJti4wK1KeL3AdyRlAh78Cm15hYAIoTVMYsFKCYZCmiPQc2atHN7ni45nOLSzeLeoNw/PjwK/tfe7AoCw1E6g6gPpZvRRAiPqVMIkamCwdbFDSmoABK5lWUVGJV99YgMemFeDHX7YgO7s9hg27ExdddC0yMhwugTUhXJBmyU45IUQqgHcAFIQL0MgG0e5ni1WDzFDQibCmHCj5QAnI2HyCpZ9ECYrnSBdFu58tVsGZIb2MGaqB5EwgpQUbT7D0k6Kwc1ep0gzk+bewY9dunHhiTzz66GScffalnm0GYoYV3R0FgBcBfC+lfDz2JZFp0e5ni1Uk7f/Lt7D5hMatYNoq0ZbjEiUwniNdFu1+tljpNQXRU70POHeJvWvxA7eCaatEW45LUfnpl61KM5A581BRWYkzzrgADw8fg549z/R8MxAzrAgz+wIYAWCtEGK1euxeKeUHFjw2RcKtVumRZID8EoA4wa1g2grxMEqByB08R7rJrTbpkWaA/BKE2M2tYNoK8TBKwSe+WrEO+VNfxdz5nyAlJRWDBg1HXt5dOP74k9xemi2s6O74KZTNSOQmN7JVRpkhjV8CEKf4ee5YvIxSIHIYz5Ee4EabdKPMUCC/BCFO8PPMsXgZpeBRtbW1mL/4f8ifOguffrkamU2b45pr7sHQobciK+sYt5dnK/8XbJJ79DJDWvOQjHb+CUCc5NfST+6nIyKKnF5mSKQCyelKiaOfghCn+HXmGPfT2aKy8mBdM5CNPxch+5h2GD36CVx88XWebgZiJQZpFD0/Z4bIHL/vpyMicpKfM0Nkjt/303nMrt2leGbm25j6/JvYvnM3/vjHHpgwYRLOOeeyuGgGYkZifbdkPSczQ1Y2rvBbEwy31+vn/XRERG5wMjNkdeMKvzXCcHO9ft5P5yG/bP4Vjz9TgJkFSjOQvqcPwkOPjEXPnv3jqhmIGQzSvM7ti3OvsLJxhd+aYHhhvcyaEpEX+S2YsIPVjSv81gjD7fUyaxqT5SvXIX/qLMyd/wmSk5IxUG0GcsIJXdxemussG2ZtBodZR6jBHDJwEHSwaAZB+22otN/WSxSAw6zN4TBrE4IvzoHEHAZt9SBovw2W9tt6CbW1tVjw4aeYMnU2ln3xDZo2bYZLL70RQ4feipYts1Qb0PoAACAASURBVN1enmMcGWZNNmFHvcOsbFzhtyYYflsvEZET2FVPYXXjCr81wvDbehNYZeVBzH5rIR6bVoAfftyEY45pi7vu+jcuvvg6HHFEU7eX5zkM0rwsTi7OC1cVI3/xBpSUViC7eTrGDuiE3O455h7EysYVfmuC4bf1EhE5IQ4uzgvXlyN/2X6UlNUiOzMJY/s1QW7nDHMPYnXjCr81wvDbehPQ7j178ezMt/H082/i9x278MdO3fHII3Nw7rmXISUl1e3leVaS2wugEIwuwrXjmwqUUrg5ScrHTQVOrSxihauKMW7uWhSXVkACKC6twLi5a1G4qtjcA3WboJR6Boq2cYXOY1WLdDywZRg63LMAfSctMb8+O1n5vRMRxQuji3DteMlCpRRuUW/lY8lC59YWgcL15Ri3qAzFZbXK+bGsFuMWlaFwfXnY+9bT8WalzDNQLI0rdB6vorYxbt+Yh77Tt5tfn92s/v7JMpuKinHbPflo03Uw7nv0WZzwhz549tn/YNbslRg48CoGaGEwSPOyUBfn2n618iIAUvn4xQhg+U2uLNVI/uINqKiqqXesoqoG+Ys3mHugDnnKXryMdgCE8jHavXlBj1WekoN7fr0FL5f0jS2QtIuV3zsRUbwIdXFeshBY+5CaYZHKx7UPeSpQy1+2HxXV9Y9VVCvHTckepOzDS2sNQCgfY9mXF/B4EgLFh1riH7/egvdKz4o+kLST1d8/xezrb77D0OvG4YRel2D6S3Nx9jlX4PXX1+LJpz5A795nJ2y3RrPYOMTrjLo7GjWTAIBGLYCeT3riIr7DPQug9xsmAGyadIHTy9HVd9ISFJdWNDie0zwdn91ztgsrIoofbBxiDhuHmGTU3fE/5wBVe/Xvk9baE933OkzeZnx+vLu108vR1Xf6dhSX1TY4npOZhM9GHe3Cisiramtr8cFHn2HK1Nn47+cr0aRJJoYMGYUrr7wNRx9tcotLgmDjED8I1WbfaA5ZqH1ph3Z5pqV8dvN03QAou3m6C6vRV6KzvlDHiYjIQaHa7BvNIjMK0ADPtJTPzkzSDYCyM71T5FSis75QxynxVFYeRMHbSjOQ7zduQuvWbXDHHY8hN/fvaNIk0+3l+Zp3/hIkKr2yxeU3hN9fFq5phNYFMta1RbLnLcTtxg7ohPTU5Ho3T09NxtgBnWJbm4WMAkYvBZJERAlJa7MfWLa4bkLsZYtaF8hY1hXpfjeD247t1wTpQW+Vp6cox73CKGD0UiBJ7thTWoZHH5+J9qdchL/f/ghqRTM8/PBsFBb+jOHD72KAZgH+X+a2UG32Q+k2AUpRRAjlW6JvLhJp8BjmdrndczBxSFfkNE+HgFJCOHFIV/PdHW0UcSDpg0YtRERxJVSb/VBSIrhArNwWXWMRM4FjiNvmds7AxIGZyMlMUs6PmUmYODDTfHdHG5kKJD3eqIWssXlLCW4fNwVtul6A8ROewXEn9MIzz3yM2bO/waBBeWwGYiHuSXPbnCTAqCp9WJhyguU3AT9NN7g/gNQWQG1FdMOwIx2gHCeDlsOOCeBgcaKocE+aOdyTFmRRbxieIwd+bXy/koXAtw8CqDa+TbBIB2GbGZ4cB4OWIxoTwMHicW/l6u+RP/VVvPXef5CUlIQBA4Zh+PDR+MMfTnZ7ab7FPWleF8sMrD7PAC37AituB6p21f9acoaSaIt2GHakM9riZJZbbvec0Nk9DhYnInJetDOwtMBg4zT9++uJdBC2mflscTDLLbdzRvjsHgeLx6Xa2los+s/nyH96FpZ+pjQDycsbjSuvvA2tWh3r9vLiHssd3RZuBla4ErsOecDlO4E/zW7Yov3Qbv3njCSACjejzezt/C5OglEiIl8JNwMrVIld9iAlWzVwBXDyw/VbtBuJJHgKN58t2tv6WRwEo3TYwYOHMLPgPXQ940pccOUd+P6n33HHHVMwf/5W3H77ZAZoDmEmzQuS0g9naQLb5weX2Gn7vYCG2Ru9LpBrxkefpes2Qb+8L3iAcqS387tYMp5ERGSe1tWxthLKe8q19dvnB5fYheraGNwF0rAMMYLgqePN+qV9esOTzdzWz6LNeJKn7Cktw/SX3sFTM97Atu070bFjNzz00Cycd95Q7jVzATNpbtKCsMBSxZqAtu/RNhXRhMvShRLpAOVEGbQcy8+SiIjMqddwAwBqDwc3gaWM0TQVAcJn6EIxMzw5UQYtx/LzJNcVbf0Nd45/DG26XoB7H5mG9sf1wNSpH6KgYBXOP384AzSXMJPmpnD7nGItsdMCJaMZbJHcP5LbRno7P4v1Z0lERJGLZI9TLCV29fas6cxfi+T+dtzWr2L9eZIrvlnzQ10zECEEzjvvKgwfPhodO3Zze2kEBmnuCheEWVFiZxRAhRqgTfoSIRglIvKCSAKwWEvsjIKnUMOzyVgiBKNxQEpZ1wzkk09X4IgjmmLYsDsxdOhtaN26jdvLowAM0twULgiza7+Xmb1uVE/YVv1ERBS7SAIwO/Z7mdnnRg1E1K6fXHHw4CG89s5iTJk2G9/98DOOPjoHt9+ej0suuR5NmjRze3mkg3vS3BRun5Nd+71i3eumSbDhzoWrijFu7loUl1ZAAigurcC4uWtRuKrY7aUREcWXSPY42bHfK5Z9bsESbLhz4fpyjFtUhuKyWuUcWVaLcYvKULi+POx9yT6le/fhX0++jA7dL8bfbn0Qh6oz8OCDr+K9937BiBFjGKB5GDNpbopkn5MdJXaGZZZFwFtZyny1Q7tDl0EmYDYuf/EGVFTV1DtWUVWD/MUbmE0jIrJSpHucrC6xMyyz3AYs6gXdLpN6EjAjl79sPyqCZodXVCvHmU1zXtHW3/Dkc6/h+VcLsf9AOU7tcy7G/99YnHrqXyCEcHt5FAFm0tzWIU8JhDLaKsHTmvH2Z6RC7Wmr2gUc2gVAKoHXFyOA5Tc1vJ1V2TgfKSmtMHWciIhioM05O/kh5fNv/2l/RirsfrZa5UPlNuDb/wP+c47+eqzMyPlESVmtqeNkj1Xf/oC8kffh+J65eGrGG/hzv0tQULAK0575CKeddh4DNB9hkOY2LSNVXoS6wGj5DfYGanplloYk8NP0husJlY3Tbhtn5ZDZzdNNHSciohjVa8UvD2ek7ArU9MosQ6naq7+eUBm5koVxWQqZnal/SWl0nKyjNQM595Kb0OOs4Sj84FNceeXteO+9X/Dww7PRqdMpbi+RosD/c9zmRkaq3l63SMiG6wmVjVt+g5J9czr4tNnYAZ2Qnppc71h6ajLGDujk0oqIiOKc0xmp4H1ukdBbT6iM3NqHgG8fdC7wdMjYfk2QHrSJJj1FOU72OHSoCq+8Nh8n//kqDLriNnz7/a+47bbJWLBgK+688zG0bm2iGzh5DvekOS249b1ed0cg8llo0dL2uhW2N15DqPXodZ7U1JQDP88AZE3D49oMOB/S9p2xuyMRkQ30Wt/HMgstWoH73JYO1u8yGW49ep0nNbKq4bHgGXA+pO07Y3dH++0t24/nXn4HTz73Bkq2bccJJ3TBAw+8jAEDrkJqaiO3l0cWYZDmJL1mGxAAZMPbmpmFFotQwVao9WiB1hfD9W8fHKBp7A4+bZbbPYdBGRGR1YwabaQ0BarLGt4+0llosep4s7L3LJzg9WjBViT31dgZeDokt3MGgzIbbS3ehiemK81A9u0/gD59zsE9947Bn/40gHvN4hCDNCfplTZCokGgZsUstEiFC7YAIKmR/no65AErb1cbjQQRyfqBmlPBJxER+YdRWWNyY2WPmJWz0MzIHhQ+0BKpIdajdoOMhFOBJ/nO6rUbMGXqbLxR+BGklPjLX4Zi+PDR+OMfe7i9NLIR96Q5yTCLJK2fhWZGh7zQ+9Nqq5VgLLgByKYCoErnHc6kRsDxN4SeAUdERKQxyiJVlVk/C82stNahvy6rge+n1G8ComUG9QI0kYoG75E7GXiSL0gp8eEnX+IvQ25G9/55ePeD/+GKK25FYeHPeOSRAgZoCYCZNCcZ7UHLaAfkbnZ8OfWELHusPZwtC5yHtma8fm19clOgzzNAy76hZ8AREREBShZJb+9XWivrZ6GZFWp/GQBAKl0egcNlmkmNDG6fBHT9p/LPcDPgKCEdOlSFN979EFOmzca33/2Ili2PwS23TMKll45E06bN3V4eOYhBmpP0AiGvZJciKXvUaA1AjDKDVbsPPyaDMiIiCkcvEPJKdqneYO0ImojUVoYO6LTHY1BGAfaW7ceMV+biyedeR/Fv23H88Sfh/vtfwsCBw9gMJEExSHOSFrB4NbvUIU9dW4TdHg0zg9x3RkREJtQLhDyYXdKyeZF2ezTCfWcUZGvxNjw14w089/Jc7Nt/AL17n4277xmD008fyGYgCY5BmtO8nl0y0+3Ry5lBIiLyF7fLGiMRtvRRldoMqDnozcwgecKadRsxZeosvP6u0gzk3HOvwPDho3HiiT3dXhp5BIM0qi8425d6FFCzD6g9dPg2WiDm9cwg+UrhqmLOoCMibwvO+KU0BWoq6u/PTkoDThxT/3ZeywySK6SU+HjpV8ifOgsfLf0KGelH4PLLb8FVV92O7Oz2Ie+7rKgYBes2YFd5BVpkpCOvSyf0a8dzZDxjkEYNBWf7ggdwBwZiXs8Mki8UrirGuLlrUVGljG0oLq3AuLlrAYCBGhF5S3DGT28IN/edUYCqqmqlGcjU2Vjz3UZkZbXGLbdMxJAhI5GZeWTY+y8rKsb0lWtxsEY5R+4sr8D0lco5koFa/GKQRvUZBWQMxMhG+Ys31AVomoqqGuQv3sAgjYi8wSgY80OZJrmirGw/np9ViCemv4ZfS37Hccd1xj//ORMDBw5Do0aNI36cgnUb6gI0zcGaGhSs28AgLY4xSKPDNhXU32MW2G6fQRrZqKS0wtRxIiJHaXPPtD1mWqt9gAEaNfBr8e946vnX8dzL76Js33707NkfY+6eidNPH4ikJPMjineV658LjY5TfGCQ5jehSg9jtWZ8w4YhWrt9Bmlko+zm6SjWCciym6e7sBoi8qVQZYex2jitYbOQ2krlOIM0Un373Y94bNpszHlnMWpra+uagXTu3Cumx22RkY6dOgFZiwyeI+OZ+XCe3KNlusqLAMjDma5NBdY8vtHcM6Pj5G2bCoDC9sCcJOWjVb8nNhg7oBPSU5PrHUtPTcbYAZ1cWhER+YqW6arcBkAeznSVLLTm8St/N3ecvK9koTJSYVFv5WOUvytaM5CBl9+Kbv2uwtvvL8Vll92EwsKf8eijr8UcoAFAXpdOaJxc/xzZODkZeV14joxnzKT5id2ZLs49ix8+K13V9p2xuyMRRcXuTFdaK/35aJx75k8WlK9WVVXjzcKPMGXabKxeuwEtWrTCTTdNwKWXjkKzZkdZulxt3xm7OyYWBml+Ynemi3PP4ocPS1dzu+cwKCOi6Nid6dKbj8a5Z/4VQ1BfVrYfL8wuxBPTX8fW4m3o0P6PuO++F3D++cNNNQMxq1+7HAZlCYZBmp/Yneni3LP4wdJVIkokdme6guejce6Zv0UR1BeXbMdTM17Hc6+8i71l+9Czx5m4a8zz6Nv3/KiagRCFwyDNT5zIdMXabt/OxiYUOZauElEicSLTZUWrfTubm1DkTAT1677/CVOmKs1AampqcM45l2H48DE46aTeDiyUEhmDND/xeqbLzn1QDP7MYekqESUSP2S67Gzjz+DPnDBBvZQSn/xvBfKnzsKi/3yO9PQMDBkyCsOG3YmcnA4uLZoSDYM0v/HyYGm79kH5rAmGJ3g9oCcisprXh0rb1dyEM9zMMwjqq1r+BW+/swhTps7GN9/+gBYtWuHGGx/BpZeOQvPmLdxdMyUcBmlkWuGqYv0ufHbtg/JhEwxP8HJAT0QUpwrXlyN/2X6UlNUiOzMJY/s1QW7nDPuam3CGW3QCgvp9+w6ozUAuwZZff1ObgTyPQYOGo3HjNJcXSomKQRqZUriqGOPmrkVFVQ0AoLi0AuPmrgUA5Nq1DyrOmmAYBrlERORrhevLMW5RGSqqlc+Ly2oxblEZACDXruYmcTbDzTDItUHJbzvw1IzXMf3ludhbtg89evTDHXc9hzPOuIDNQMh1/A0kU/IXb6gL0DQVVTXIX7xBKadLDvpDasU+KKMgz4dNMLQgt7i0AhKHg9zCVcVuL42IiGKUv2x/XYCmqahWjqPjzcq+p0BWNDcxCvJ8OMNNC3KLy2qVc6Qa5BauLw97XzO+++FnXHvrg2jf/SLkT52F3n0G4uWXv8SMGf9Fv34XMkAjT7Dkt1AIMVMIsV0Isc6Kx/OkTQVAYXtgTpLycVOB2ytyRUlphfHxDnlAnxlARjsAQvnYZ0bsJXd2BX8uCBnkElHcSYjzI6Dsi1o6GFjUW/lYstDtFbmipKzW+Hj2IKDLeCCtNQChfOwyPvaSRLuCPxeEDHJjpDUDOX/o7ejSdyhem/sxLrlkJObO3YhJk95Ely6nxvwcRFayqtzxZQBTAbxq0eN5S4SNK0KWsbnZndDC585uno5inUAtu3m68g879kHFUROMkEEuEcWjlxHP50cgosYVYUvY3OpOaPHzZmcmoVgnUMvOVN8Tt6O5iR86W0YoZJAbperqarz9/n8wZepsrFzzPY466miMGvUwLrvsRjYDIU+zJJMmpVwGYLcVj+VJoRpXqEKWsWlBXnkRAHk4yHMiG2fxc48d0Anpqcn1jqWnJmPsgE4WLDaEDnlA7mZgWK3yEfBlZrMumI3wOBH5W9yfH4HQjSsQQQmbFuRVbgMgDwd5dmfjbHjesf2aID3o7e/0FOW4rbIHAf3nAwO/VgK0jdN8mdWsC2YjPB7K/v3lePK513BCryG46vrx2LW3FuPHz8C8eUX4+9/vY4BGnudY0a0Q4gYhxAohxIodO3Y49bTWiKBxRcgytgiCPNtY/Ny53XMwcUhX5DRPhwCQ0zwdE4d0dbbxhZtBb4xcC3KJyLPqnR937nJ7OeaFaVwRtoQtTJBnGxueN7dzBiYOzEROZpJyjsxMwsSBmbY1vmjArYDXIlYEub9t24l7H56GNicPxh33PoYjWxyHxx57D2++uR6XXHI9uzWSbzjW3VFKOQPADADo1auXdOp5LWHUtVAkKYFBh7zQZWxudie04blzu+c43o0wsJT0i853oXWKP1vyaz83dnckIk2982OPbv46PwJKeZ1e10IIoGQhSsq6696troTNre6ENj1vbucM54Iy1C8l/aLz02id4t92/NrPLZrujut/+AWPPTMbs99aiKqqapx11hCMGDEGXbueZveyiWzBFvyR6Dah/p40jayp25uW3fwY471adrWm1xO8/6zRUcAhnXdmfdQZMbjt/9HJBplYn7TkdyPIJSKyTceb6+9Jq1MLrJuAvx5zK17+7cwGd6srYbOrNb2ewD1oEAB0YmIfdUUMbvlveH70UTt+M0GulBL//WwlpkydjQUffYq0tHRcfPH1yMu7C8cee7zNKyWyF3uMRkLrWiiSG35NzeCELGNzqjuhXhlgVRmQ1Mj+57ZRcClpSVWW/g19FHgSEcUNrWuh3iVFbSXubv1q6BI2p7oTBpcCQqcZhc+6IgaXkhqeH30UeEaiuroab7z7Ifqc+1ecdfEofLFiA0aOfBDz52/BP/4xjQEaxQWrWvC/BuALAJ2EEL8KIa6z4nE9pUMeIA26C5VvqbdXCwCShajbk1ZY2t+e1vTB9PafySoguamp5y5cVYy+k5agwz0L0HfSEutmeEU5xiC4lHTytqtRXtu4/o18FngSUWJIiPMjoJbS6VdqZtRsr7dP68h0gcYpwJ3zy9B3+nYUlp5pT2v6YHp70AAol0KRPW/h+nL0nb4dHSZvU9Zu1fyuKEcYBHc91D0/+izwDGX//nI89dzr+EPvIbjy7/dix55q3Hvvc3h/XhGuv/6faN7cIEgl8iFLyh2llFdZ8TieF6ZsUSthCyzN07o8Ykh/5GpdCe1iVO5XtRu4fGdEDxFcWli3fiC2Er0IxxjoCW77/37pWQCAe7NnoXXKDn+15HdzFAMROS5hzo9AyLJFrYQtuDxP6/SIgWcit7/Ne6YMS/6k0hUxDMO1A7HtQYtghIGR4Jb/Dc6PfmrHH2Icwrbfd+Lp59/Asy+9gz2lZejWrS+m3DYN/fpdxMHTFLf4m21GBGWLrg4rNir3M1EGaNv6Y+gyqVdK+tGBc/Fl128Ot+T3Q6Dj466URERhRVC2aOew4rCMSv4iLAW0be0xdJnU64b40f6z8OVxbyuBZ//5/gnQdLpSfv/pK/j77Q+j3SkXYuITL+OU7udi5szP8eKLn6J//1wGaBTX2DjEjAiGKrs6rFivwYnJMkDb1h9Dl8m46YgYKlD1Q5BJRBRKBEOV7RhWHDG9BicmSgFtW3sMXSZj6YboKQGBqpTAsh+AKQsqMX/V02jcOA0XXfR35OXdhTZtTnB5oUTOYZBmVoe8kBfUwaV5gcdtFy6IjKDUzrb1x9jhMi46Iro5ioGIyAnZg0JmboLL8wKP2y5UEBmi1M72tcfY3dLplv+2qPwd1TXA3K+BKQuAr38BspoC9w8BzrhxC448sqXbKyRyHPPEFnN9WHGHPKX8L7gMMMJSO9vW71SHSy+zoByViMjPrBhWHJPsQUoJYGApYIQDoG1bu1PdLT3qwIEKTF3SBB1HA0OfBvYcAJ79G7DlKWDc0HYM0ChhMUizWGCXRwEgp3k6Jg7papwFirLjoWkR7gkzvf5IaWMM7O5w6WUMVIkoweV2zqjX6TEnMwkTB2bqZ4Ki7HhoWoR7wkyt3QxthIHd3S095vftu3DfhGfQ5uQLcOuL+9CqeRLm3gH8MAUYdS7QqHEGirN4fqTEJaTUb5lrp169eskVK1Y4/rz1eKHL3qYC4KtrgdpDh48lNQJOnWl6LYWrikPv2ZqTBP32yELJupEzovi9C/vaEnmYEGKllLKX2+vwi149uskVH890dxERlP45soa1DyljZDQiFej6z6jWUri+3Hjf1qLeMDw/RtD1kcz5YeNmPP5sAV59YwEOHapC//65GD58DPq334ScnePRqHoLDqW0RXHWBOxpFv5aaFlRMQrWbcCu8gq0yEhHXpdO6NeO50jyvqQkoEcP43NkYu5Ji6EdvJGoLqRX3l4/QAOUz1febmodEbXNj3FPGFkkzJ7GYLaNRCAi0hNDO3gjIQMkI99PqR+gAcrn308xvY6wrfNj3BNG4Ukp8emXq5E/9VXMW/Q/NG6chsGDr8WwYXeiXbuOAIA9OD2ioCzQsqJiTF+5FgdrlHPkzvIKTF+pnCMZqJHfJWa5Ywzt4PVoF9LFpRWQUC6k73hjNbo/9GHoQdCHdpk7biCitvkstfMlV0c6kC/YNnyeElMM7eD1aAFScVmtcn4sq8Ud88vQ/enfQw+Crtpr7ngIYVvnJ/ieMDvV1NTg7fc/xmnn/Q39Bl+P/325Htdffz/mzSvCuHHP1gVo0SpYt6EuQNMcrKlBwTqeI0mxrKgYIxcswWVvLcDIBUuwrMg/58jEzKRZ3GVP70IaAPaUVzmS9YiobX4E4wPIe1wd6UCGvFKCykwrWS6GdvB69AIkANhTIa0ZBB2BsK3zIxgdQOYcOFCBl1+bh8efnYNfNv+KNm2Oxz33PIPBg/+KtDTrXu9d5frnQqPjZD8vlZ/6PdOamEGaxaV/oS6YtayH7gVTagugSidrltrC1PNH3DbfZKkduc/VkQ6ky0uBUahMK4M0iorFpX+hZohp2SzdIC0lE6gu0z9uUkSt88OMDqDIbN+xG1NfeBPTXnwLu/fsRdeup2Hy5Cdx5pkXIzk5OfwDmNQiIx07dQKyFhk8R7rBa0FRqEyrH4K0xCx3tLj0L9wFs2EQ1+tJZSN0IJGqHDfB9bb/ZBu+tt7jpRJUZlrJchaX/oWbIWYYxHUei4bvI6eox81xve1/Atjw42aMvGsC2nYbjEceexFdT+6PF174FDNnfo6zzx5iS4AGAHldOqFx0GM3Tk5GXheeI93gtfJTv2daEzOTZkXpX0CXvo+Oy8Y/i4bh7V1n6t7UMIizqARRe8fcC+VXZC2+tt7jpcCImVaynFWlf2qHyE/b/46SQ1n417ar8X7pWQ2fziiIs7AEUcvUmW5eQiFJKfHZV2swZeosvL9oGVJTG2Hw4L9h2LA70b69M0GSlg3xSnldovNaUOT3TGtiBmlAbKV/Qd0hM6qLMenYqUhNSsJrO/5c76Zhsx4WlSDmds+J7MLdC6MHIuSVfT9ui/i1JUd4KTAaO6BTvdJLgJlWskCspX8BHSIFgJxGO/CvY6cCQL1ALWw2y8ISxNzOGeGDMi+MHjAhqq6ZFqipqUHhgqWYMm02vlyxFs2aHYXrrrsPV1xxC4466mjbnz9Yv3Y5DMo8wmtBUV6XTvXKLwF/ZVoTs9wxVjrdIVNkBSYe/zqeGHqK9YOgraIFl+VFAOTh0QN2DdCOgV7HzHFz17JzHbnOSyWotg2fJ4qFTofI9KSDmNRhtvWDoK2iBZaV2wDIw6MH7BqgHSO9rpnjFpWF7pgZo/LySjzz4lvo1OcyXPa3f+DXbQdw991TMX/+Fowa9ZArARp5i9fKT/u1y8Gonl2RlaGcI7My0jGqZ1ffBPWJm0mLRYjukJ7OeoQaPeCxbFr+4g34yxEf4+7WryI7dSdKqrIwedvVyF/cyLKfLzN1FA2vlaB6+m8OJSaDTpAZNdvx2SiPXsiHGj3gwWza6pXz8NEJL9c7P75fepZxI5YoaJm6rdv2QK5bgL0rF2Bf2V506XIq/vWvf6N//1zb9pqRP3mx/NTPmVYGadEw6g6ZepTzazHDgtEDTgU2vfABJh47FRlJBwEAxzbagUnHTsW4XwHg7Jgf3/YOfT4qKyXz4j0w4hsYFBM/Doe2aPSAIyWIJQtxd4unGpwfAWCezr6/aBSuL8fogu+x/ct371w+IgAAIABJREFUcWDdEsjqQzjiD6fhlrvvxl8H5EIIEfVjH7m3ADk7x6NR9RYcSmmL4qwJpodYk3f5OSiKlFNjBhikRaPbBODLvwGyqv7xmn3KxbnNF+PhLqAMvx7j6AEnW4+Py55VdwKqW2bSQYzLngVgSsyPb2vr8qA9i3VlpQADNfI8L40YIJ9qeQaw9W394w4IFyjpft2CwFIrQdTmwmkliIDFs+A2TtM9P97d+lWsrD0n5of/fPkaXHfXC9j9/ZdAcgqadDkbmb1zkdqiDb6oScc1MQZo7X6/AclSOT82ri5Cu9+V8yMDNfIDJ8cMcE9aoE0FQGF7YE6S8tFor1aHPCBVZ1ZL7SEle2Kj+wrX4s43Vhvu1Qq5lyvG0QNOth5vlbLD1HGzbO3QF6qslDyvcFUx+k5agg73LEDfSUsSbh+kl0YMkIeULASWDgYW9VY+htqrteNTc8ctdN+HpbhzvvFeLaO9XF9nXB/z6AG9wd3aLDhLGWT3slN3Rj1WoKamBu/O/wSnD7wWfQddh9JN69DsT1fg2BtnosXAW5Haog2A2Lv05ewcXxegaZJlOXJ28vzoB8uKijFywRJc9tYCjFywBMuKEuv8CDg7ZoBBmsZsU41Du/WPmygdNKtwVTEKvtwCGXQ88AIq5AVWhzygzwwgox0AoXzsMyPi7I6TrceFQXbP6LhZRp34LOnQZ0FZKbmDDWu8NWKAPMJsUw2LSgfNKlxfjoLVlQ3PkQGBklEgdcc3fwK6jAfSWgMQyscu403tRzOa+RZqoHdUDLJ7lSlHm87YVVRUYvpLb+PE0y7HkL+OxZaSfRg79mmcPPo1NO83AslHHFnv9rF26WtUrX8eNDpO3qFlkHaWK+dHLYOUaIGak2MGGKRpzGY/jIKFwOORZuYilL94Q4OTj0a7gAp7gdUhD8jdDAyrVT6aKL+zNbAJZvHA8WC2duiL5HeDPIlZJIf/Pyd/CNVUQ49RiWDgcTOZuQjlL9tvfI5UA6WQgVT2IKD/fGDg18pHkw1DjGa+hRvobZrBwPGMk26J+CF27NyDB/71HNp2uxA3jpmERumtMGnSm5g790cMHXoLru5xii1d+g6l6J8HjY6Td3htULVbjN6osGPMAIM0jdnsR7ggwoZ296HeydYuoKy+wAos/So/VI3UpPq16La1Ho8x6xeOra3LbQ4wPcniNyTcwiySt0YMkEeYzYwZBBF1pYM2tbsPlbHSAiWrA6nC9eXoO307OkzehvIqidSg7VphZ8FFI3tQ1Fm/H3/eghtHT0TbboPx4OTncWLnMzBjxn/x8stf4dxzL6/r1mhX6/LirAmoEfXPjzUiA8VZ8Xt+PHJvAbr83B49NiShy8/tceRef54fvTao2i1Ojhlg4xCN2aYaWrBg1MHPhnb3RkN0BVB3AWXlcNvgBgJ7yquQmizQPD0Veyuq7O/6ZtGgbyO2degL97sRb+KoUYqXBlW7xWsjBsgDzDbV0IIFo8HQNrW7z85MQrFOoCZwOFAa269JveYeQPSBVHCjkD0VEqnJQPNUYG8l7B0wbXLQ9xdff4spU2fh3QVLkZKSigsuuBp5eXehQ4cTDe9jR5c+rTlIonR3jKdGKV4bVO0WJ8cMCCmNigPs06tXL7lixQrHnzek4AtNQMl+RJu9mZME6BZeCKXUMArBQZP6aMg7rS16tTuq7qKqWXoqhABKy2MLpPpOWqJ7wZrTPB2f3RN7G3yKE4XtDd7gaKeU1Eb6MB5o+673/1h6ajIHRMdACLFSStnL7XX4Ra8e3eSKj2e6vYz6tMxXYGCVlGZ6z1adRb1heH4c+HW0q2wQNKmPiNPbpmBzaW1dN8ezjmuET345FHOb/L7Tt+sGhTmZSZ6YB1dbW4v3Fy5D/tRZ+Hz5GmRmHonLLrsJV1xxC7KyWru9vITQ5ef2aFzd8Px4MKUd1h2/2dRjOdX2PdTzB3Y1BJQMkp+GQ3tNUhLQo4fxOZKZNI3V2Y9IMnMmZ2kZvcMNoN6FZWlFFdJTk/HvoafEdGHJ0i+KiEXz97zQ9p1ZJCId4TJjZkWSmStZaPr5tEArsL3+Wcc1wjvrKuu1xX9nXSUmDsyMOcPlWKMQkyoqKvHqGwvw2LQC/PjLFmRnt8eYMU/hoov+howMi0svKSSrGqU42fbdiBcHVcc7BmmBrCyv6zZBPzMXvGctXIlYUCCX220Ccu+pv8a+k5bYMvPLqdIvL2RQKAYxzt8DbJ5bZ1K8D6omiorJ8rqQOt6sn5kL3rOmfV3bs6atQ6MTyOV2HlQv+Oo7fbthW/xYgzSj8kqrG4VEOiB7565SPDPzLUx9/i3s2LUbnTv3wsSJ+TjrrCFISeHlnhsOpbTVzaSZbZQSqmmHk0FSIgyq9hI2DrFLuMYX4bpJbioA3soCvhgetvmIXRkvJxoIsOV5HLCgUQqztkQJJFzji0i6SX43Cfj2/8I2H7Ez2zW2XxOkB8U+VjcKMZrrps19A4CfftmKm8f+C21PHoz7Jz2HTif+Cc89txSvvLIcf/nLFQzQXGRVoxQ27UhM/D/XTqEyc6FKxPT2x2l0mo/YlfFyovTLSxkUipIFpcJs2EGUYEJl5sJ1kyxZCGx9u+HXdZqP2Jnt0iuvtLpRSKgB2a0P/Iwp02Zh7vxPkJKSikGDhmP48NE47rjOlj0/xcaqRils2pGYGKS5JVSJmF6WLVBQgGdlR8dgdpd+OZ1BYWmlTWIsFbbzd5iIfCbcnjWj+WxAgwDPym6OenI7Z9jTvVEVnPGTshYVPy3HyuVz8adf1yOzaXNcc804DB16C7KyjonpudxuTBGv9jTLi7mTY16XTrpNO+xo+07ewSDNLaH2rH0xIvR9g/b6eLXZQSQBkZMZFK80p6CGvPo7TEQuCLdnzSjTBjQYC+BEtisake4z0zKBsvoQ9q9bgrKv30X17mI0at4KY8Y8iYsuutaSZiBeaExBxti0IzExSHNLqBKxNeP1s2wAKmobY13zMegddNxrzQ4iDYiczKCwtNLbvPY7TEQuCddN0iDTViuBlRnXNzw/2pztMit4VIC2zwxAg3WO7FaD0ZNfx+4VC1BbXopGrU/AMbn34K5ho3DWce0sW5NXGlOQMTbtSDwM0txkVCKmk2WTEthT0xQPlNyAjzacgInNij19QRtpQGRFBiXSEkY2p3CXn0tN/bx2Il8KtWdNJ9NWK4FZu87HpO9PxcQm5Z4KyoKF2memrfuXzb/i8WcKMLNgHioqK9HsD32Q1isXOZ36YHjXP5q6WI+kjJGNKdzn53JTP6/dyxikeVFAlq32wBaUVGVh8rar8X7pWeoNajD6zTW4843Vnr1gNBMQxZJBMVPCyOYU7vFzqamf104Ul9Tgbds3T+Po5B0NzpEPfFzmufLGQKE6Ti5fuQ75U5VmIMlJyRioNgM5/viTonquSMsY2ZjCXX4uN/Xz2r2OLfi9qkMekLsZx6+dhzN+eCkgQFPUSOnplvVGgY/VAVGojF0wJ0YKkD4zr5PX+HntRHErexD+tH4mjtM5R5ZWImTLercFd5aUshblP32F3W/8A6eedw0Wf7ICV199N96ftxn33z8z6gANCF3GGCivSyc0Tq5/fmRjCudE+jp5kZ/X7nX+C9I2FQCF7YE5ScrHoJlh8SaSoMaLF4xOBURmM3YTh3RFTvN0CAA5zdMxcUhXZkMc4OdSUz+vnRJQyUJg6WBgUW/lY9DcsHgSaRt9rZTQK7T5arL6EPatWYySF27CjnceRvKBUtx1178xf/5W3HLLRLRsmR3zc0VaxtivXQ5G9eyKrAzl/JiVkY5RPbsyE+IQP5eb+nntXuevcsfg+WHacGcgpvbfXqbXWEOP1y4YnerWZ7aEkc0p3OHnUtNI1s49a+QJJQvr79XSBjwDxvu7fEyvvb4RK4ZXW+XPrQ+hx/ZCvPXaO6javwcZx5yAK++YiluuHGn54GkzZYxsTOEeP5ebRrJ27lmLjr+CNL35YTrDnaO2qSCmgbx2CA52koRAjZQNbufGxW64C1MnAiLO1/IHP79O4dbOPWvkGRun1W9bD+gOeI5ayULjjosu0GuvX14lsadC5xxpwfBqs4Lb7F99QhnWfTQXMwvmobyiAn1PH4ThI8agV6+zIISwZQ2cr+UPfn6dwq2de9ai568gLWiIc9jjZng4SxcY7ARfEALuXOzGemFqVeaB87WsYXcmyG+vU/DP49KeOfjkhx26a+doB/IMo/lhoeaKRcqjWbrg9vrB7e0Ba4dXRypwHQd/24jV772Lzzd8huTkZJw/KA95eaNxwglddO9rZdaB87Vi50QWyE+vk97PY1TProZr53iH6PkrSMtoqz8/LGi4c1TsztKFYOYCOdqLXasvwmO5MLU682Blxi6Ryta077W4tAICgPbes12ZIL+Umur9fr6zsthw/yL3rJFnGMwPCx7wHBW7s3QhRDr4GYhueLWZx4/U5KVl2PXDcpQtn4uDW9dBND4CmX2GoN0Zl+H+q4Ya3s+OrIOVZYyJUramfZ/BZXx2ZoH8UG5q9Ps5qmdXPHfB2br34Z616PkrSNOZH4bkDOV4rOzM0oUQTcBi9mLXjnKsWC5MvZp5SKSyteDvNbg4yAuvh1vM/n76eb8dxRmd+WFISlOOx8rOLF0IZgY/a8wMr47m8UOprDyIgrcXYsUTr6Bq11YkN22JI8/+O5qcfB6SGmdgX5j7eznrkChla8HfZzCvvB5uiOb308/77dzmr+6OHfKAPjOAjHYAhPKxzwxrMl1G2TgrsnQhRNzeO4aulna0EI+lxb5XMw9utFovXFWMvpOWoMM9C9B30hLHRinofa/B3H493GL295OjHcgzsgcBXcYDaa0BCOVjl/HWZLqMsnFWZOlCCDX4uU4MHS0jevwI7N6zF48+PhPtT7kIf7/9EaSkNkLWhWOQM/J5ZPbORVJjJeALd2Hq5ayD063WlxUVY+SCJbjsrQUYuWAJlhU5c37U+z6DeeH1cEM0v58c7xA9f2XSACUgs6P80M4sXQgRXRDGuF8u3HNEU+IXSyMIr2YenA4e3czcRfI9uf16uCWajqGAf/bbUZzLHmRP+aGdWboQQg1+Vv4R2165cI8frhRyU1Exnpj+Gl6c/R4OlFfg9NMH4v4Hx6Di6E547pt1phtBeDnr4GQA6WbWLpLvxwuvhxui+f300347r/FfkGYXLdixorujiS6REV0QxrhfLtRzRBsoxHJh6tVOf04Hj26WfRp9rxovvB5uieb30y/77YiipgU8VnR3NNElMjszCcU6gVRdt8YY98qFevxQpZDHHtyMKdNm4a33/oOkpCQMGDAMI0aMwQkndK17DCGE6QtTL3f5czKAdLPs0+j71Hjl9XBDtL+ffthv50UM0gJZkaUzmfWK6IIwxv1yoZ4jlkAh2gtTr2YenA4e3Sz71PteteYhOR55PaIVa/MXr/5+ErnOiiydycyX3iy0et0aY9wrF+rxg0shpazFrg0r8dc576Js07do0iQTw4ePwdCht6JVq2MbPHY0F6Zezjo4GUC6Wfap931qsjz0ekQj1sYvXv79jEcM0qxmMusV0QVhjF0tQz3HnW+s1r2P3YGCFzMPTl+cu1n2Ga+BiFUlpF78/SSKCyYzX2G7NcbY0TLU4985X8mayeoqHFj/CcqWF6Jq1xYkN83CHXdMQW7u9WjSJDPCbzxyXs06OHmB7mbZZ7wGIlaVkHr19zMeCakzGNluvXr1kitWrHD8eR0xJwkNe+UBgACG6de+hxWcnQOU/XIWNE3pO2mJbqCQ0zwdn92j306VrGE0886o1TuFx99n7xFCrJRS9nJ7HX7Rq0c3ueLjmW4vwz6LesPwHDnwa/OPF5yZA5S9chY0TDn13z9j47IF2LdyHmoO7EHq0R2UNvo9zsOMi86L6bEpNL0Oi42TkzGqZ1cGCFEauWCJbuCblZFu2D6f7JWUBPToYXyOZCbNanbMcrNyv1wQr+4PSwTxms1yk1c7hxKRyupZblbulVMVbf0N/352Dta8UoiDlRVIa98dLQaPRlq7bkhLScHwbidF/dgUmXjNZrnJy51DSR+DNKvZ1SXSpq6WDBTcxbI6a3m1cygR/T97dx8fZ1Xn//99kkyaTG/TtJY2pS0WWm/K1kK5UVwQvCm43lRWd4WC67qK7Oqu+tOqbNXFVb743aIuK7jQr+t6QxUEod4gsCBKvVmQYqm0QEEsgaY3NKVp00yaTCbn98c1084kM5OZzFxznWuu1/Px0DQn87nmXMmQM5+ccz4nzY8qkVWqaPn7LU9q7XXf0a0/+rmMMXrTmy7SK15/qX5xuJFEIQAsq6sulyuHIj+StGrzcdbLL0EkCpUWdwDyqXRmmNcl4DMfZr4qYa3V3T//rdZ+7bv6xa83aeLEybr44o/p3e/+yNFiIO8OoF+VFngARqq08AuvydojSfODX2e51YkgzweDT8o4dsJPlcwM87oEasSvs9zKMDAwqO//8B5dc/1N2vbkM3rJSzr0kY+s1Tve8QFNmjQ10L4FeUYYqq/t4Hp1dK9R89BzGmyap64ZV+nA1NqPj5UsIeU1GYyqJGnGmPMlXSupUdI3rLVfqsZ1UZ+CPB8MPqjwsPVqG+/MMK9L+IUx0h09B3t147d+qGtvvEW79+7TSSf9mT7/+e/oTW/6a8VizUF3T1KwZ4ShutoOrtf8vZep0Xrj44ShTs3f642PQSVq43kN8ZoMRsVJmjGmUdL1kt4oaaekh40xP7bWPl7ptUPFkZmEMKC4Q52p8LB1V/C6hB8YI9PKOMDaD53P79a1N35f/+87G3S4L6Ezznij1nz2EzrjjDfKGFOzfpSCAg/1o6N7zdEELaPRJtTRvSaQJG28eE0GoxozaadL+qO19k+SZIy5WdLbJUVnAHJsJsF1FHeoMxUetu4KXpfwCWNkmQdYV9PmPzypa66/Sbfcca+MMXrjG9+tSy75uBYvfpWvz1sJCjzUj+ah/ONgoXZX8ZoMRkMVrtEh6fmsz3em23IYYy4zxmwyxmzat29fFZ7WIcVmEsZhw+YunfWl+3XCp+/UWV+6Xxs2d1Whk+5YvWKxWmONOW2U/Q+xQsdLVHLsRAB4XcInY46ROeNj9/6adq4mih1gXaYNjyd01g0v6IR/26OzbnhBGx5PjHpMphjIG97xDzrl3Ev0o7t+o4su+qg2bPiTvvCF7zqdoElegYcJjbm/i8op8AB3DDblHwcLtbuK12QwqjGTlm+dwKiTKq216yStk7zDrKvwvLVRyjLGKs4kRKF4QVBl/6nc5xO/jp2oMY6jgE/GHCNzxsdTloZnfJRKW8Z4ZG/+2ELtBWx4PKEr7j6k/iHv865Dw7ri7kOSpJWviGtwMHm0GMjWJ/6ol7ykQ//0T/+mCy+8LPBiIOUI4owwKvf5o2vGVTl70iQpZeLqmhGu8ZFz64JRjSRtp6Tjsz6fK2lXFa4bvFKXMVbxAOuoFC+oddn/KCS/gQnhsROFcG4dfFC/Y2SpyxirdID12o2HjyZoGf1D0tX37NFT9/1K1954i3bteUEnnXiyrrzy21qx4t3OFAMpVy3PCKNyn38y+85cqO5YKc6tq71qJGkPSzrJGHOCpC55R4pcXIXrBq/Ugghz3iz98T9Hx895c9lPSfECf9Rj8uvUzCDHTgCF1O8YWWwZY3aSNvO10vO3jY6f+dqynm7XoeGcz4cO7dOhTT/Sc1vu0e8G+3XG6W/QFWs+oTPPfJNzxUBcVo+V+1yaGTwwdVUokzIEr+IkzVo7ZIz5sKR75JUX/qa1dlvFPXNBqcsYd/0s/+MKtRdB8QJ/1Fvyy8wgEA51PUaWuoxx36/zP65QewFzpjSo69CwBvf+SYd+d7v6nvyVZK2mLzlX//GptXrZy5aVdT146q1yHzODqBdVOSfNWvszSeVnJK4rdRljFfekrV6xOOfNt0TxgnzKnUWqt+S3HmcGgXpVt2NkqcsYq7AnzVqrN0x4XNf84CYldjwq09yqyae8RTPOuFD/eN7r9TLefOcoZyap3ir31ePMIKKpGtUd69ecN2vUnu98BRGqWN1u5bIOXX3hyeqY1iojqWNaq66+8OTRb7x3rJc2LJC+1+B93LG+7OcKq8wsUldPv6yOzSIVq4JZduU+x7+/fs4M1nt1UQBVkm+5YkOLVzwkW6G9ZyXsSRscTOo7N/9US8++WP/6iU8odnC3Ot74Ac39+//Worf+k/7xvNePeuPddnC9ljyzQKdsb9CSZxao7aBbv7/9lplJ6k54Y2RmJmljZ/7f5eOp3Ofy99jvmcGNnV364J3365233qkP3nl/we8rUKmqzKTVpR3rpR3fVm4RLiOd8Dc5e282bO7So89drE9O/4riDQPHHlpBdbsxixcEfC5b0HuhxjOLVHLlvh3rpU0fkZJZZbAdPPfOr5lBF5ZRBv368lM93xsiZtddUtdPR7d3vCVnP9qGxxN69PlL9cn2/8gdI/Mlc1kOHjqsdd++XdfeeLO6dr+gE09coiuv/JZWrLioaDGQtoPrc6rpTRjq1Py93u/vWu0LCno/VLkzSaVW7ms7uD5dAKNTkpFJvz8K4ntcjJ8zg0EvpQz6teWner638SJJKyRf0RDZnH1mx97QnqUXE4P65HHf0ZxYt47E5ih+2v/17w19qQVNfFDLN/GF3tCOdxap7OQ3W42+v6Xya1ls0MsoXUgS/VLP94YIylc0RMrZZ3asZP45erF/+NgY2fQSxV/54bwHWT/ftUfX3niz1n37DvUe7tNpp52nT12xWq9+9YqSioF0dK/JKXcuSY02oY7uNTVJIGr1Jr7YG9rxzCSNVblvZPI78qSlWn6Px7JqyeKcn4FUvTO9glxKGXSC6Kd6vrdKkKQVUsI+s+w3tD/uOVc/7jlXkrdE8Td/dV6gffNLrd7EF3tD69v+sryJeZYafH9L5deZXkEXWAk6SfRTPd8bIqiEfWbZJfNzxsgpDfrNG1+SE7Zl61O65rrv6uY77vX2n73hr3TppZ/Qy152Slndah7K/3u6UHu11eJN/FhvaP2YScqX/I5Uq+/xWPw80yvIIiv1vNeunu+tEiRphZRQNCSwN7RVPJetXLW652JvaH0rrjJWElaD7285/DjTK+gCK0EniX6q53tDBJVQNGRkyfyR7dZa3ffLh7T2uu/q3l8+pHjrRL3rXR/WxRd/VLNnzx9Xtwab5mnC0OjxcbCpNr+/a/Emfqw3tH7MJJWSgNXqe1wKv870CrLISr1V4cxWz/dWCQqHFLL0Km9fWbYR+8wKvXH1/Q1tCX3zS63uudgb2pKLq5SrWBKW/v7We1GNkgqs+FhUJbD/pmqgnu8NEbToQ96+smwj9pnNmZL/LcZxE4d10w9+pmXnrNKb3vlhPbrtOX34w1frp3c+r49//KvjTtAkqWvGVUqZ3PExZeLqmuH/+CgVfrNezTfxY72hPXt+hy4/9WTNiHtj5Ix4qy4/9eSKkpaxErCUievn+kTdF9QYq8iKnwVVavHaCko931slmEkrJLP3aMsab4YlPs9LgrL2JAVWLr+EvvmlVvc81oyOH7NIWnpV/j1pze3SqddqQ8/rwrunaMf6kl4vYy6j9LlojYtHUFSr2IeL9waMW2Y/2VPXe0scW2Z5CVrWPrPVZ09K70nzPh8eSOjIY3fr6T/8VJfue0Evfekr9LnPfVPnn3+xmpsnVKVbmT1RXoGL5zTYNE9dM66q2V4pP/dDZZQym1PtmaSuGVeN2JMmWRlJVoNN8/VzfUIf23KiBlJev8K2p+hYUZTir5liSyn9LlpTi9fWeFSj4Ier9xY0Y60d+1FVtnz5crtp06aaP68folitrRb3PHJPmuS9oa3KjFkxRZKZs750f97EsWNaq37zaR/3IFYqX0GUxrh0+rryE6sNCwostZ0vrXy2kl4eewpH/pvasLlLn//JNh1IJHPaK3kdunJvtWSMecRauzzofoTF8lOW2k33fTPoblTNhscT+uJPntXTv9ygvi13KzWQ0PLl5+qSSz6h17zmfDU01N+CHr+r1I3ckyZ5b2grnS0bS7FE5oN33p83cZwRb9WNf+Hw+Kh8RVG8mcHOWevKSq6WPLMg71Lbgab52rrw2Wp01akKiBs7u/TNR7epdzB3jBzva9Gle6uVhgbplFMKj5EkaXBW0G9oRz5/vgRN8k7S2/Glv6hZv8pWzcTqew0aWdXLY6SL8+8/yavEmb2g5PsjQTbnE3OHkKSVp56StD9se1rXXPddff/2/5G1Vq9//bt0ySUf1ytewcuhUi68oc3uQ6F3kkbSbe9yeHxU9ZKrU7Y3HD2WIJuV0e8XlzE+qvSZvaDk+0NBtjAk5y4YK0ljuSPKUsvEyZcljSXKV13SW9gxmvN7iqpZDbQaRWsCPuevFPkK12Sj2AeQn7VWP3/gd7rm+pt0z/3/my4G8iFddNFHNWfOgqC756taJk5+FcYo1Vhv0jPCsKeoWhVBq1W0xoWz/saSr3hNtqgX/KgWkjSULErnPOV7k26lUYlaKPYUVbMaaL59e+UWrQnonL9y/sAwVhLmfGIO1FgyOaQfbLhX11x/kx59bLtmzDhOH/rQ/9GFF35QU6dOD7p7vovaOU9jvUmXwrOnqFrJVb59e+MpWhPEWX/l/oFhrCQsDMl5GNTfYnC/+VjZznXFyuLXm0Jv0q1U/aqSfqtmNdATVnl72eLzJRnvY7l72wI45y/zB4auHm9ZTuYPDIWqcxZLwkKRmAM1cujQYX3l6zdp4akrdcnln9XhQ7264fJ2PX/NHn357Bu1QHcF3cWaKFYWvx4Ve5NerYqStVKtiqAHpq5S56x1GmiaLyujgab5Ze9rk2p/1l/mDwzd6WWrmT8wFKvOWSwJC0tyHgbMpJUjBMu0slV7aaIr5zzVYslloT1o5e5FCnpfnaTqVwM9YVVlr/cAzvkr9yC/LnpQAAAgAElEQVTpfJUYJWlaa0xXvu2V7ifmgM+6dr2g/1h3s2789h06eKhXp55yjv7lH1bpPfO/rphJ/+50cJlWtmouT3TpnKdaLLssVGGy3L1ILuytq2ZF0ANTV1X8Wq/1WX/jOUg6XzVGSZoUi+nvlr0yFMl5GJCklSOgZVrj4cfSxKAPOpZqt+SyGuXSC/W14+AdOq3nmtoWzag0saqmaiyZLFO5f2AY8ygCIKIee/yP+vL1N+l7P7xHqVTqaDGQV77yNC15ZoFiQ7n/Tfm9TGu8qr08MchDjrPVatllNUqmF+rr4qE79HpdU9OiGdVIrqqlWssmSzWePzAUO4oA1UOSVo4AlmmNV7kzB6Vw4ZwnP+4rn2q8Sc/X1zdOvE9Ldl4nNQx4DY7PxvoigHP+xvMHhiAL1wAusdbq/o0P65rrb9LdP/+tWlvjuvDCy3XxxR9TR8cJRx9X62ValRjP7EExrpzzVO37KqQab9Lz9XXF5Pt07uB1mpAeI10smuG3Wp/1N94/MARdvCYKSNLKEcAyrfHyY2miC7MLtVxyWemb9Hx9+uRx31FrJkHLcHQ21lc1ntlz4Q8MQNgkk0O69Uf36ZrrbtLmx55Ue/ss/cM/XKW//MvL8xYDqfUyrUpUe3miKzMLtVx2Wemb9Hx9yjdGujob66dazuy58gcGjEaSVo4AlmmNl19LE4OeXRjPfQW1LyxfX+fEuvM/2MHZ2Hriwh8YgLDo7e3TN27aoH+/4WY9t3O3TljwMn3mM9/QBRes0oQJLQXjar1MqxJ+LE90YWah3PsKck9Yvr4WGiNdnI2tF678gQGjkaSVI4BlWuNVrzMH5d5XkMcG5Ovr7uRMdTS/MPrBDs7G1pug/8AAuG7X7n36j3U364Zv3a6Dh3p1yiln62MfX6ezznqzGhrGLgZd62ValajX2YNy7ivoYwPy9bXQGOnibGw9ceEPDBiNJK1cLhVgKKJeZw7Kva9a7WErta+7FnxWHXs/FYrZWADRsO3JZ3TNdTdp/W13K5VK6bzz/lKXXPIJLVlyetnXcqkAQzH1OntQzn3Vav9aOX3dEv+sjkt9KhSzsYDfSNLGY8f6UMym1evMQTn3FfSxAaP7ep60oy0Urx8A9ctaq1/++hGtve67uuu+36i1Na53vOODuvjij2nu3JdWdO22g+tDMZtWr7MHpd6XC8cGjO7reeo82BaK1w/gN5K0coXsrLSoc+HYgFFCMhsLoP4MDQ3pth//XGu/9l39/g9Pavr0l+jyy7+gd77z7zVtWnvF1287uD5nX1oUq/OFhSvHBowUltlYwG9jLzJHrmJnpcE5q1csVmusMaetHvbmAUA5Dh9O6Nobv68Tl1+oiz6wRi8eslqzZp1+8pNOvf/9n6lKgiZ5+9Gyl6pJx6rzwS2rlizWhMbc8bEe9uUB9YKZtHKF6Kw01O/evHoSVPVNIAp27+nW1/7fLfrP//6heg4e0rJlf65/+uh/6s///C0lFQMpV5jOSou6et2XV2+CrMCJYJGklStEZ6XBU6978+pBkNU3gXr2+JN/0jXXf1frb7tbQ0MpnXvuhbr00k9oyZIzfH3eMJ2Vhvrdl1cvgq7AiWCRpJUrRGelIRjMDJUuyOqbQL2x1uqB3zyia667SXfe+2u1tLTq7W+/TKtWfUxz5y6sSR/CdFYagsHMUOmCrsCJYJGklStEZ6Wh9vLNDH3slkf10VseVQcJ2yhBV98E6sHQ0JB++JP7dc11N2nTo49rettMXX75v6aLgcyoaV/CdFYaai/fzNC1v3tU33x0m973qleSeIzgQgVOBIckbTyozocC8s0M2fRHlvKN5mT1TSAkDh9O6Jvrf6yv3vA9PfvcLs2fv0j//M836s1vvlQtLcH9N0R1PhSSb2ZIknoHkyzjy8PVCpyoDao7AlU01gxQZimfs3aslzYskL7X4H3csd7Xp6P6JlC+PXu7teaL12ve0rfoI/98jaa2naBrrtmgW299QhdeeFmgCRpQTLEZoMwyPpe1HVyvJc8s0CnbG7TkmQVqO+jvGEkFzmhjJg2ookIzQ9mcXcoXwBmAVN8ESvfE9h368tdv0nd/8DMlk0M699wLdcklH9ef/dmrg+4aUJJCM0MZLi/jC+IMQCpwRhtJGlBFq1csztmTlo+zS/mKnQHo4/Jeqm8ChVlrtfG3v9c119+kn97zq3QxkA/o4os/puOPPzHo7gFlWbVkcc6etJFcXsZX7AxAP5f3UoEzukjSgCrKnhnq6umX0bE9aZKPS/l2rK+8mA1nAALOGBoa0u0//YWuue4mPbx5m9raZuiDH/y83vWuf6h5MRCgWjLJxn9t3qbDyWTO1/xcxtd2cH3FxWw4AxC1RpIGVFn2zFBNyvFXa5kiZwACgRseHtbX1t2sr97wfe3o7NK8eSfpiitu0F/8xXvYa4a6kJkZqlUp/motU+QMQNSasdaO/agqW758ud20aVPNnxeoSxsWFEiu5ksrny39OiOTPck7A/D0dVQzxbgZYx6x1i4Puh9h0dTUZFOplJYufY0uvXS1/vzP36rGEYUDAJRuyTML8iZXA03ztXXhsyVfZ2SyJ3lnAHbOWkc1U4xLQ4N0yimFx0hm0oAQKDojV61lipwBCARu0qQp+spXfqqlS18TdFeA0Cg2K1etZYqcAYhaI0kDHJfvgOyc89aquUyRMwCBQM2f/1ISNKAM+Q7Izj5zrZrLFDkDELXEOWmA4/IdkJ1z3trSq7xlidka4147AAB1LN8B2dlnrnXNuEopkztGpkxcXTMYI+E2kjTAcYXOVTvafsIqb99YfL4k431kHxkAIAIKna2WaT8wdZU6Z63TQNN8WRkNNM1nHxlCgeWOgOMKHZA9Z1pr1l61aZoz7ZscBA0AiJRCB2RPjMX0wTvvT+9Tm61VS36jsxcyPiI8mEkDHLd6xWK1xnKru7XGGnXuy2bqitsfU1dPv6yO7VXbsLkrmI5m27Heqzr5vQbv4471QfcIAFCHVi1ZrAkjKqA2GqMjqSF1J7zxMbNPbWNn8ONj28H1WvLMAp2yvUFLnlmgtoOMj8iPJA1w3MplHbr6wpPVMa1VRlLHtFZdfeHJ+sWT+4rvVQtKppR/olOSPXZuG4kaAKDKzp7foctPPVkz4t4YOSPeqnisSUPDuUdMZe9TC0qmjP+EoU4Z2aNntpGoIR+WOwI+q8aB1tkHZGd87JZH8z620B62mtmyJvesNcn7fMsa9skBAI6q1oHWmQOyM9556515H1do/1qtdHSvyTlnTZIabUId3WvYI4dRSNIwbtVIPurdmOXzK1Bsr1qgqnVuGwCEWLUSkHo1Vun8ShTap9YeD3Z8rNaZbYgGljtiXDLJh5P7oRwyZvn8ChTaq7Z6xeKKr12RQuezjefcNgAIoUwC4uKeKFeMVTq/Evn2qU1obNSqJcGOj4XOZhvPmW2ofyRpGBc/k496Mmb5/AoU2qsW+Gwm57YBiDg/E5B6MVbp/Erk26d2+aknBz6TyZltKAfLHTEufiYf9cTvJYn59qoFLrPvbMsab4ljfJ6XoLEfDUBE+JmA1Au/lySO3Kfmgsy+s47uNWoeek6DTfPUNeMq9qMhL5I0jIuz+6Ecs3rF4pw9aZIjSxL9dsIqkjIAkeXqniiXrFqyOGdPmuTGkkS/HZi6iqQMJSFJw7hENvkoU2aWiwIrtUVRGwBBimoCUo7MLBfFVWqLgjbhQZKGcSH5KJ2TSxLrmJ8VNQGgFCQgpXFxSWI987OiJqqPJA3jVrfJx4717KcKsWJFbery9QrASfWagLQdXM+eqpAqVtCmHl+rYVdRdUdjzLuMMduMMcPGmOXV6hQQmB3rpd9dJiU6JVnv4+8u89oRChS1gSsYI1Fv2g6u1/y9l2nCUKeMrCYMdWr+3svUdpAxMgwoaBMulc6kbZV0oaQbq9AXoKrGtS9pyxoplchtSyW8dmbTQoGiNnAIYyScNZ69SR3da9Roc8fIRptQR/caZtNCgII24VJRkmatfUKSjDHV6Q1QJePel5R4rrz2MvvEHj7/UdQGrmCMhKvGuzepeSj/WFiovdw+sYfPXxS0CZeaHWZtjLnMGLPJGLNp3759tXpaRNS4D9uOzyuvvUSZpLGrp19Wx5LGDZu7KrouRnP2kG+ggOzxcf9+xkf4b7yHbQ825R8LC7WXKpM0die8MTKTNG7sZIysJlcP+UZ+Y86kGWPuk3Rcni+tsdb+qNQnstauk7ROkpYvX25L7iEwDuPel7T0Km8PWvaSx8a4114BX4tZUOhklLotagPnVGOMzB4fly5lfIT/xrs3qWvGVZq/97KcJY8pE1fXjMrGSD8LWlDoJFe9FrSpR2MmadbaN9SiI0A1jXtfUia5KZL0bNjcpSt/vE09/UlJUls8pn956yuLJgW+FbPIFDrJJJWZQifZ9wLAN4yRCKPx7k3KJDfFkp6NnV36r83bdDjpjZGTm2N636teWTQx8KugRabQSSapzBQ6yb4XwFU1W+4I1NLqFYvVGmvMaSt5X9IJq6SVz0oXD3sfRyRoq2/dcjRBk6QDiaRW37al6NLFQslhxcUsihU6AQAgj1VLFmtCY+4YWerepANTV2nrwmf1+8XD2rrw2VEJ2nUPbzmaoElS72BS12/aUnTpYqHksNKCFsUKnQCuq6hwiDHmHZK+JmmmpDuNMY9aa1dUpWch5UdxCApOlM+vw7bX3rNdyeHRq5GSKVt06aJvxSx8LHQCoDKMkbn8KAxBsYnx8euw7fVbtytlR4+RQ8O26NJFvwpa+FnoBPBbpdUd75B0R5X6EnrjrihY42tGhR/7kootTyz2Nb+SRsXnpc90y9MOIFCMkceMt5pgra8ZJX7sTSq2PLHY1/xKGgeb5mnC0OgxstJCJ0AtVHpOGrL4URzC14ITETbe2clCe90yXyvGl2IWPhU6AYBq8qMwhJ/FJqJuvDOUhfa6Zb5WjB9Jo1+FToBaIEmrIj+KQ/hWcKIGXF2mWcns5OoVi7X61i2jljzGGk0w53CVUOgEAILmR2EIv4pN1ILLyzQrmaFctWSxrnt4y6glj00NJpCzuEopdAK4iiStisZdUbDG16wFl5dpVjI7mfl6udUdfXXCKpIyAE4bbzXBWl+zFlxfplnJDGXm6+VWd/TTgamrSMoQSiRpVeRHcQjfCk74zOVlmpXOTnIGFwCUx4/CEH4Vm/Cb68s0K52h5BwuoDpI0qrIj+IQvhWc8JnLyzTDOjsJAGHlR2EIv4pN+M31ZZphnaEE6g1JWpX5McsSxpkblxOhwGYnd6xn7xiAyPJjhiWMszauJ0FBzFC2HVzPvjFgBJK0OuNKsQ6Xl2kGMju5Y31uFcZEp/e5RKIGADXiQsEO15dp1nqGsu3g+pwKjBOGOjV/rzc+kqghykjS6ohLxTpcX6ZZ89nJLWtyy+RL3udb1pCkAUANuFKwIwzLNGs5Q9nRvSanRL4kNdqEOrrXkKQh0kjS6ohrxTrCuEzTN4nnymsHAFSVSwU7wrhM0y/NQ/nHwULtQFQ0BN0BVI/LxToiLz6vvHYAQFW5XrAjqgab8o+DhdqBqCBJqyOFinK4UKwj8pZeJTXGc9sa4147AMB3hQpzuFKwI6q6ZlyllMkdH1Mmrq4ZjI+INpK0OrJ6xWK1xhpz2lwp1hF5J6ySTl8nxedLMt7H09exHw0AamTVksWa0Jg7RrpUsCOqDkxdpc5Z6zTQNF9WRgNN89U5ax370RB57EmrI64X64i8E1aRlAFAQMJQsCOqDkxdRVIGjECSVmco1gEAQH4U7AAQFix3BAAAAACHMJOGo1w5CBsAANe4cBA2gOggSYMktw7CjhISYwBwnysHYUcNiTGijOWOkCR9/ifbCh6EDX9kEuOunn5ZHUuMN2zuCrprAIC0jZ1d+trDWwoehA1/ZBLj7oQ3RmYS442djJGIBmbSoA2bu3Qgkcz7NQ7C9s/ae7YXTIxdn01jBhBAFGQShWFr836dg7D9s37r9oKJscuzacz+oVpI0lB0toyDsP1TKAF2PTFmaSyAqMiXKGTjIGz/FEqAXU6MWRaLamK5I4omBRyE7Z9CCbDriXGxGUAAqCfFEgIOwvZXoQTY5cS42OwfUC6SNBRMCqa1xpgZ8dHqFYvVGmvMaWuNNTqfGId1BhAAylUoIWgwRpefejKzIz5atWSxJjTmjpGuJ8ZhnP2Du0jSUDBZuPJtrwyoR9GwclmHrr7wZHVMa5WR1DGtVVdfeLLziXFYZwABoFyFEoV/PG0pCZrPzp7foctPPVkz4t4YOSPe6nxiHMbZP7iLPWk4mhRQCKL2Vi7rCN33efWKxTl70qRwzAACQLkyCQGFIIJx9vyOUH2vVy1ZnLMnTXJ/9g/uIkmDpHAmCwgGST2AKAlbooDgkNSjmkjSAJSNpB4AgNFI6lEtJGmAgziHDACA0TiHDFFBkgY4hnPIAAAYjXPIECVUdwQcwzlkAACMxjlkiBKSNMAxnEMGAMBonEOGKCFJAxzDOWQAAIzGOWSIEpI0wDGFDhfnHDIAQJQVOlycc8hQjygcAjiGc8gAABiNc8gQJSRpgIM4hwwAgNE4hwxRwXJHAAAAAHAISRoAAAAAOIQkDQAAAAAcwp40oAY2bO6iEAgAAHls7OyiGAgwAkka4LMNm7t0xe2PqT+ZkiR19fTritsfkyQSNQBApG3s7NINjzymgZQ3RnYn+nXDI94YSaKGKGO5I+CztfdsP5qgZfQnU1p7z/aAegQAgBvWb91+NEHLGEiltH4rYySijSQN8Nmunv6y2gEAiIr9ifxjYaF2ICpI0gCfzZnWWlY7AABR0R7PPxYWageigj1pgE8yxUK6evplJNmsr7XGGrV6xeKgugYAQGCyC4VMao6p0Ril7LFRckJjo1YtYYxEtJGkAT4YWSzESkcTtQ6qOwIAImpkoZDewaSaGowmNcXUl0xS3RFII0kDfJCvWEgmQfvNp88LplMAAAQsX6GQoWGrlpYmfXvlmwLqFeAe9qQBPqBYCAAAo1EoBCgNSRrgA4qFAAAwGoVCgNKQpAE+WL1isVpjjTltFAsBAETdqiWLNaExd3ykUAgwGnvSAB9kioKsvWe7dvX0aw7FQgAAOFoQJFPdkUIhQH4VJWnGmLWS3ippUNIzkv7WWttTjY4BYbdyWQdJGRBhjJFAfmfP7yApA8ZQ6XLHeyUtsdb+maSnJF1ReZcAAKgLjJEAgHGpaCbNWvs/WZ8+KOmdlXUHQNAyh3CzTBOoDGMkUH+yD+JmqSb8VM09ae+TdEuhLxpjLpN0mSTNmzevik8LhJtLSdHIQ7i7evp1xe2PSRKJGlCZgmNk9vjY0cH4CGS4lhCNPIi7O9GvGx7xxkgSNVTbmMsdjTH3GWO25vnf27Mes0bSkKT1ha5jrV1nrV1urV0+c+bM6vQeCLlMUtTV0y+rY0nRhs1dgfQn3yHc/cmU1t6zPZD+AK6rxhiZPT62tzM+AtKxhKg74Y2PmYRoY2cw46OU/yDugVRK67cyRqL6xpxJs9a+odjXjTF/I+ktkl5vrbXV6hgQBcWSoiBmrjiEGygPYyTgj2IJUVCzVhzEjVqqqHCIMeZ8SZ+S9DZrbaI6XQKiw7WkiEO4gephjATGz8WEiIO4UUuVVne8TtJkSfcaYx41xtxQhT4BkeFaUsQh3EBVMUYC4+RiQsRB3KilSqs7nlitjgBRtHrF4pxCHVKwSRGHcAPVwxgJjN+qJYtzinRIwSdEHMSNWqpmdUcAZXIxKeIQbgBA0FxNiDiIG7VCkgYEjKQIAIDRSIgQZZXuSQMAAAAAVBFJGgAAAAA4hCQNAAAAABxCkgYAAAAADiFJAwAAAACHkKQBAAAAgEMowQ9ExIbNXU6dxwYAgCs2dnY5dyYboo0kDYiADZu7dMXtj6k/mZIkdfX064rbH5MkEjUAQKRt7OzSDY88poGUN0Z2J/p1wyPeGEmihqCw3BGIgLX3bD+aoGX0J1Nae8/2gHoEAIAb1m/dfjRByxhIpbR+K2MkgkOSBkTArp7+stoBAIiK/Yn8Y2GhdqAWSNKACJgzrbWsdgAAoqI9nn8sLNQO1AJJGhABq1csVmusMaetNdao1SsWB9QjAADcsGrJYk1ozB0jJzQ2atUSxkgEh8IhQARkioNQ3REAgFyZ4iBUd4RLSNKAiFi5rIOkDACAPM6e30FSBqew3BEAAAAAHEKSBgAAAAAOYbkjIm3D5i72aQEAkMfGzi72aQEBIUlDZG3Y3KUrbn/s6CHPXT39uuL2xySJRA0AEGkbO7t0wyOPHT3kuTvRrxse8cZIEjXAfyx3RGStvWf70QQtoz+Z0tp7tgfUIwAA3LB+6/ajCVrGQCql9VsZI4FaIElDZO3q6S+rHQCAqNifyD8WFmoHUF0kaYisOdNay2oHACAq2uP5x8JC7QCqiyQNkbV6xWK1xhpz2lpjjVq9YnFAPQIAwA2rlizWhMbcMXJCY6NWLWGMBGqBwiGIrExxEKo7AgCQK1MchOqOQDBI0hBpK5d1kJQBAJDH2fM7SMqAgLDcEQAAAAAcQpIGAAAAAA4hSQMAAAAAh5CkAQAAAIBDSNIAAAAAwCEkaQAAAADgEJI0AAAAAHAISRoAAAAAOIQkDQAAAAAcQpIGAAAAAA4hSQMAAAAAh5CkAQAAAIBDjLW29k9qzD5JnXm+NENSd427EwTus75wn/UjCvco1fY+51trZ9bouUKvyPgo8fqsJ1G4R4n7rDfcZ/UVHCMDSdIKMcZsstYuD7offuM+6wv3WT+icI9SdO6z3kTl5xaF+4zCPUrcZ73hPmuL5Y4AAAAA4BCSNAAAAABwiGtJ2rqgO1Aj3Gd94T7rRxTuUYrOfdabqPzconCfUbhHifusN9xnDTm1Jw0AAAAAos61mTQAAAAAiDSSNAAAAABwiHNJmjFmrTHmSWPMH4wxdxhjpgXdJz8YY95ljNlmjBk2xgRe5rOajDHnG2O2G2P+aIz5dND98Ysx5pvGmBeMMVuD7otfjDHHG2N+YYx5Iv16/UjQffKDMabFGPM7Y8yW9H1+Pug++ckY02iM2WyM+WnQfUHpGB/rQxTGyCiMjxJjZD1yaXx0LkmTdK+kJdbaP5P0lKQrAu6PX7ZKulDSxqA7Uk3GmEZJ10u6QNIrJF1kjHlFsL3yzbcknR90J3w2JOnj1tqXSzpT0ofq9Oc5IOk8a+1SSa+SdL4x5syA++Snj0h6IuhOoGyMjyEXoTHyW6r/8VFijKxHzoyPziVp1tr/sdYOpT99UNLcIPvjF2vtE9ba7UH3wwenS/qjtfZP1tpBSTdLenvAffKFtXajpBeD7oefrLW7rbW/T/+7V94vro5ge1V91nM4/Wks/b+6rKpkjJkr6S8kfSPovqA8jI91IRJjZBTGR4kxMsAu+cK18dG5JG2E90m6K+hOoCwdkp7P+nyn6vAXVhQZYxZIWibpoWB74o/0EodHJb0g6V5rbV3ep6R/l/RJScNBdwQVYXwMJ8bIOsUYWRecGh+bgnhSY8x9ko7L86U11tofpR+zRt408vpa9q2aSrnPOmTytNXdX1uixhgzSdIPJX3UWnso6P74wVqbkvSq9D6fO4wxS6y1dbWfwhjzFkkvWGsfMca8Luj+YDTGx7oeHyXGyLrEGBl+Lo6PgSRp1to3FPu6MeZvJL1F0uttiA9yG+s+69ROScdnfT5X0q6A+oIqMMbE5A0+6621twfdH79Za3uMMb+Ut5+ibgagtLMkvc0Y82ZJLZKmGGNustZeEnC/kMb4WPcYI+sMY2TdcG58dG65ozHmfEmfkvQ2a20i6P6gbA9LOskYc4IxplnSuyX9OOA+YZyMMUbSf0l6wlr7laD74xdjzMxMpTxjTKukN0h6MtheVZ+19gpr7Vxr7QJ5/23eT4IWHoyPdYExso4wRtYPF8dH55I0SddJmizpXmPMo8aYG4LukB+MMe8wxuyU9GpJdxpj7gm6T9WQ3tT+YUn3yNtA+wNr7bZge+UPY8z3Jf2vpMXGmJ3GmL8Luk8+OEvSpZLOS//3+Gj6r0z1ZrakXxhj/iDvTdS91trAy+8CIzA+hlxUxsiIjI8SYyR8ZEK8WgIAAAAA6o6LM2kAAAAAEFkkaQAAAADgEJI0AAAAAHAISRoAAAAAOIQkDQAAAAAcQpIGAAAAAA4hSQMAAAAAh5CkAQAAAIBDSNIAAAAAwCEkaQAAAADgEJI0AAAAAHAISRoAAAAAOIQkDQAAAAAcQpIGAAAAAA4hSQMAAAAAh5CkAQAAAIBDSNIAAAAAwCEkaQAAAADgEJI0AAAAAHAISRoAAAAAOIQkDQAAAAAcQpIGAAAAAA4hSQMAAAAAh5CkAQAAAIBDSNIAAAAAwCEkaQAAAADgEJI0AAAAAHAISRoAAAAAOIQkDQAAAAAcQpIGAAAAAA4hSQMAAAAAh5CkAQAAAIBDSNIAAAAAwCEkaQAAAADgEJI0AAAAAHAISRoAAAAAOIQkDQAAAAAcQpIGAAAAAA4hSQMAAAAAh5CkAQAAAIBDSNIAAAAAwCEkaQAAAADgEJI0wAfGmHnGmMPGmMYSHrvAGGONMU0Fvn6lMeam6veyNMaY9xpjfu3j9e8yxvxN1udfNMZ0G2P2lPN9BAAAqBckaRFnjPmwMWaTMWbAGPOtEV/LJA+Hs/732SLXel368dePaP+1Mea9/tzB+KT7eWKRr783/ZjVI9p3GmNeN9b1rbXPWWsnWWtTVeiu74wxK4wxG40xvcaYfcaYB4wxb6vFc1trL7DWfjvdj+MlfVzSK6y1x4Xt+wgAAFANJGnYJemLkr5Z5DHT0m+UJ1lrvzDG9fokvccYs6BK/Suo0MxTFb0o6VPGmCk+P0/N5JuRMsa8U9Ktkr4jaa6kWZI+J+mtte2dJGm+pP3W2hcqvVANXh8AAAC+IEmLOGvt7dbaDczHxZYAACAASURBVJL2V+mSPZK+JelfCj3AGPM+Y8wTxpgDxph7jDHzs752rTHmeWPMIWPMI8aYP8/62pXGmNuMMTcZYw5Jeq8xZqox5r+MMbuNMV3ppXKN6cefmJ4ROphePndLun1j+pJb0rODf12gq09I+l9JHytwHw3GmE8bY54xxuw3xvzAGDM9/bWcJYzGmBOyZqruM8Zcn2cJ4ypjzHPpvq4Z8bUWY8wt6fjfG2OWZvXj5caYXxpjeowx27JnwIwx3zLG/Kcx5mfGmD5J5464ByPpK5K+YK39hrX2oLV22Fr7gLX2AwXuu9jP6PT0zOwhY8xeY8xX0u0t6Z/b/nQ/HzbGzEp/7ZfGmPcbY94g6V5Jc9I/l2/l+T4W+3m/1xjzG2PMV40xL0q6Ml//AQAAXEeShlJ0ppf5/bcxZkYJj79K0l8aYxaP/IIxZqWkf5Z0oaSZkn4l6ftZD3lY0qskTZf0PUm3GmNasr7+dkm3SZomab2kb0saknSipGWS3iTp/enHfkHS/0hqkzdD9DVJstaenf760vTs4C1F7uWzkj6WSb5G+CdJKyWdI2mOpAOSrs/zOKXv5XeS2uUlD5fmecxrJS2W9HpJnzPGvHzEfd+qY9+XDcaYmDEmJukn6ft8iaR/lLR+xPf+Ynk/k8mSRu4tWyzpeHnf01IV+xldK+laa+0USQsl/SDd/jeSpqafq13S5ZL6sy9qrb1P0gWSdqV/Lu/N89zFft6SdIakP8n7XlxVxj0BAAA4gyQNxXRLOk3eErRT5b3JXz9WkLV2j6QbJP1rni9/UNLV1tonrLVDkv6PpFdlZtOstTdZa/dba4estV+WNEFeIpHxv9baDdbaYUlT5L2p/6i1ti+9RO6rkt6dfmwy3fc51toj1tqyi19Yax+VlwB9qsC9rLHW7rTWDshLvt45cpmdMWaevO/j56y1g+l+/DjP9T5vre231m6RtEXS0qyvPWKtvc1am5Q389Ui6cz0/yZJ+lL62vdL+qmki7Jif2St/U16huzIiOdsT3/cPca34qgxfkZJSScaY2ZYaw9bax/Mam+XdKK1NmWtfcRae6jU55Sk9MxbsZ+35CV4X0v3rT/vhQAAABxHkoaC0m+yN6Xf8O6V9GFJbzLGTDHHqu4dNsYczhP+fyWtyF6WlzZf0rXpJW898vZ9GUkdkmSM+Xh6KeTB9NenSsqevXt+xLViknZnXe9GebMokvTJ9LV/l14G+L5xfis+J+nvjTHH5bmXO7Ke+wlJKXl7urLNkfSitTZR4D4y9mT9OyEv+Rr1+HSCujN93TmSnk+3ZXQq/f0s8lwZmWWus4s8JscYP6O/k7RI0pPpJY1vSbd/V9I9km42xuwyxvxbehawHGP9vKXi9woAABAKbKxHOWz6o7HWPqfcJCL3gdbuN8b8u7wlh9mel3SVtXbUjFx6b9On5C3322atHTbGHJCXaI3sQ+ZaA5JmpGflRvZhj6QPpK/9Wkn3GWM2Wmv/OMZ9jrzOk8aY2+Ut0xx5L++z1v4mz70syPp0t6Tpxph4VqJ2fDl9yH68MaZB3vLNXZmvGWMashK1eZKeyr6FItfdLu8+/lLSNWN1YqyfkbX2aUkXpft4oaTbjDHt1to+SZ+X9Pn09+Zn6ef+r7GeM0vRn3dasXsFAAAIBWbSIs4Y05TeT9QoqTFd4CFTpOEMY8xi4xXIaJf0H5J+aa09WOLlvyLpNZKy91bdIOkKY8wr088x1RjzrvTXJsvbb7RPUpMx5nPyljTmZa3dLW8p4pfTs3sNxpiFxphz0td+lzFmbvrhB+S9gc+Uct8r6aUl3ofkJRh/K28vXPa9XJVZqmmMmWmMeXuefnZK2iTpSmNMszHm1Sq/cuKpxpgL0z+bj8pLVh6U9JC8ipqfTO9Re1362jeXclFrrZX0/0n6rDHmb7O+j681xqzLE1L0Z2SMucQYMzOdMPakm1PGmHONMSeni3wckrf8sayy+mP9vAEAAOoFSRo+I6+Aw6clXZL+92fSX3uppLsl9UraKi8xuCjPNfJK7zn6N3kFJjJtd8hbCnmz8So0bpW3z0jylsPdJW8WqFPSEY29fO09kpolPS4vEbtNx5bunSbpofRyzB9L+oi1dkf6a1dK+nZ62dxflXAvO+Qt2ZuY1Xxt+rr/Y4zplZc0nVHgEqskvVre8sIvSrpF3vezVD+S9Nfy7vFSSRdaa5PW2kFJb5P3PeyW9HVJ77HWPlnqha21t6Wv/T55s3N70338UZ6Hj/UzOl/StvT3/FpJ707vgztO3s/mkLxloQ9IGs8B3cV+3gAAAHXBeH9IB1BLxjsO4ElrbcGjCgAAABBNzKQBNWCMOS29NK/BGHO+vJL6G4LuFwAAANxD4RCgNo6TdLu8MvQ7Jf29tXZzsF0CAACAi1juCAAAAAAOYbkjAAAAADgkkOWOM2bMsAsWLAjiqQEANfTII490W2tnBt0PAADCJJAkbcGCBdq0aVMQTw0AqCFjTGfQfQAAIGxY7ggAAAAADiFJAwAAAACHkKQBAAAAgENI0gAAAADAISRpAAAAAOAQkjQAAAAAcAhJGgAAAAA4hCQNAAAAABxCkgYAAAAADiFJAwAAAACHkKQBAAAAgENI0gAAAADAIU1Bd6BsAy9KvU9Lgz1S8zRp8knShOn526XS2iqN9+OaxEc73sU+ER/u+EqvOWG6AABAbRhrbc2fdPny5XbTpk3lBw68KHU/JMUmSo1xKZWQkn3SlEXSoady2xN7JFkpPrt4W6XxflyT+GjHu9gn4sMdX+k1k33SjDPGlagZYx6x1i4vOxAAgAgL13LH3qe9NxNNEyVjvI+xidLeB0a3J1+UkgfGbqs03o9rEh/teBf7RHy44yu9Zmyi9/sXAADURLiStMEe7y+72RrjUv/u0e3DSSmVHLut0ng/rkl8tONd7BPx4Y6v9JqNce/3LwAAqIlw7UlrnuYtvWmaeKwtlZBaZ49ub4iNjs/XVmm8H9ckPtrxLvaJ+HDHV3rNVML7/QsAAGoifHvSdt/rLcVJJaXGmBRrk9qXS/s35bYrJhlJNlm8rdJ4P65JfLTjXewT8eGOr/SasTZp9hvZkwYAQI2Ea7mjJO/dw7EPx/6Rp92qtLZK4/24JvHRjnexT8SHO77SawIAgJoJ10xa90PS8EDu0pyhPunQH6UpJ+a273/Y+9h+WvG2SuP9uCbx0Y53sU/Ehzu+0msO9UkNE7wKj2ViJg0AgPKFayaNwiHERyHexT4RH+54CocAABAqFA4JekM+8cSHoU/EhzuewiEAAIRKuGbSJp/kHao61CdZ631M9kmzzhndHpvubXYfq63SeD+uSXy0413sE/Hhjq/0msk+7/cvAACoiXDNpE2YLk1Z5B3A2r/b+yvwrHOkyQu9r49sL7Wt0ng/rlnt+L5npd0/8/7dPF16ybnSnAvC0/+oxbvYJ+LDHV/GNQ+mJmr3zq0aTOxWc7xds+cu09RxVHYEAADjE67CIQMvesVDYhO9PRKphPcX3imLpENP5bYn9kiyUnx28bZK4/24ZrXj9z4gbbvKK7qS0dAivfwT0tST3e9/1OJd7BPx4Y4v45qH+3q0uW+RmuMz1RprVH8ypcTgkJbNa9O0eHPZv7YpHAIAQPnCtdyx92nvzUTTRMkY72MmCRnZnnzRO/tnrLZK4/24ZrXjn/56boImScNHpGe+EY7+Ry3exT4RH+74Mq6563Cj2lLPKd7cJGOM4s1Nijc3aUd3XzC/9wEAiKBwJWlUdxxf/JG9yuvI3nD0P2rxLvaJ+HDHl3HN3sGY4qY3p6011qhD/SPiAQCAb8KVpGWqO2bLrlCWrSEmNcbGbqs03o9rVju+ZZbyapkVjv5HLd7FPhEf7vgyrjm5OamEnZzT1p9MaUprnqqPAADAF+Hbk7b7Xm/ZTirpvemItUnty6X9m3LbFZOMJJss3lZpvB/XrHb8C7+Vnr9FGh489r00MWnBJdKMs9zvf9TiXewT8eGOL3LNw93btOtwo3oHY5rcnNTU2IAe7VukfYOTlEwNK9bYoGnxmF570kz2pAEAUCPhmkmT5L3TOPbh2D/ytFuV1lZpvB/XrGb8jNOk+auk5nbv8+bp0vx3SzNOD0f/oxjvYp+ID3d8nraDqYna3LdIg8MxtcV6NTgc0+a+RepJTZaMZLz/OxoKAABqI1wzad0PeQUwsg9eHeqTDv1RmnJibvv+h72P7acVb6s03o9rEh/teBf7RHy44wtc88kXBnUwvkzx5mOnsWzZeUCy0tLj2462JQaH1NzUoGXzjrWVipk0AADKF66ZNAqHEB+FeBf7RHy44wtcczCxX62xxpzmoSGrZGo4p43CIQAA1Fa4DrPOFA7J/kty9ub37PaGPJvc87VVGu/HNYmPdryLfSI+3PEFrtkcb9fBZCpnJq2pyUjW5DyUwiEAANRWuJY7UjiE+CjEu9gn4sMdX+CaB6edo191ptSTSB4tEhJrNJKMkqlhCocAABCQcC13lJR343yhdoo8EB/WeBf7RHy44wtc06b/mVskxOZpAwAAtRKumTQKhxAfhXgX+0R8uOMpHAIAQKiEayaNwiHERyHexT4RH+54CocAABAqFA6hyAPxrsW72Cfiwx1P4RAAAEIlXDNpk0+Skn3e0h9rvY/JPmnWOaPbY9O9zfZjtVUa78c1iY92vIt9Ij7c8QWuOXvuEiUGh5QYHJK1VonBIU1tjWlaPJbTlhgc0gkzJo79OxoAAFRFuGbSJkyXpiyS9j7gLf1pne29cZm80Pv6yPZS2yqN9+OaxEc73sU+ER/q+IOpidq9c6sGE7vVHG/X7LnLNHXacXppqk8PPrNf+3qPaObkFp25sF2SRrWNp7IjAAAYn3AVDhl40SseEpvo7c1IJby/LE9ZJB16Krc9sUeSleKzi7dVGu/HNYmPdryLfSI+1PGH+3q0uW+RmuMz1RprVH8ypcTgkF46c5L+tO+w4s1NR9tf6D0iI2nm5Jacxy6b10YJfgAAaqTi5Y7GmBZjzO+MMVuMMduMMZ+vRsfy6n3ae4PSNFEyxvsYm+j9xXhke/JF7zyhsdoqjffjmsRHO97FPhEf6vhdhxvVlnpO8eYmGWMUb25SvLlJDz6z/+i/M+0H+5PqSSRHPXZHd59vv9oBAECuauxJG5B0nrV2qaRXSTrfGHNmFa47GtUdiY9CvIt9Ij7U8b2DMcVNb05ba6xR+3qPUN0RAAAHVbwnzXrrJQ+nP42l/+fPGkqqOxIfhXgX+0R8qOMnNyeVGJ6c09afTGnm5Bb1U90RAADnVGVPmjGmUdIjkk6UdL219lN5HnOZpMskad68ead2dnaW/0QDL0q77/WW8qSSUmPMq1jWvlzavym3XTHJSLLJ4m2VxvtxTeKjHe9in4gPVXyfbVHXwDT1DsY0uTmpqbEBPdq3SPsGJymZGlassUHT4jGdPHeaHtvZo55E8mh7rNFIMkqmhnMe+9qTZrInDQCAGqlKCX5rbcpa+ypJcyWdboxZkucx66y1y621y2fOnFnBs5mcD8f+kafdqrS2SuP9uCbx0Y53sU/EhyL+sG3RHxILNTgcU1usV4PDMW3uW6Se1GTJSMb7v6NhNh2b227zPhYAANRG1as7GmP+RVKftfaaQo8Zd3XH7oek4YHc5T5DfdKhP0pTTsxt3/+w97H9tOJtlcb7cU3iox3vYp+ID038U117NDgck20/42jblp0HJCstPb7taFticEjPdvdpwYyJOcsdCz22ualBy+YdaysVM2kAAJSvGtUdZxpjpqX/3SrpDZKerPS6eVE4hPgoxLvYJ+JDE5+vSEihYiAUDgEAwE3VOMx6tqRvp/elNUj6gbX2p1W47mgUDiE+CvEu9on40MTnKxJSqBgIhUMAAHBT+A6zpnAI8fUe72KfiHc2vpQiIYWKgVA4BAAAN1WlcEht5dk4X6idIg/EhzXexT4R71x8eUVC8hcDoXAIAADuCddMGoVDiI9CvIt9It7J+FKLhFA4BACAcAnXTBqFQ4iPQryLfSLeyfhSi4RQOAQAgHCpRuGQ2qFwCPFRiHexT8Q7GV9qkRAKhwAAEC7hmkmbfJKU7POW/ljrfUz2SbPOGd0em+5tth+rrdJ4P65JfLTjXewT8U7Gz5mU0oHGeUoMDslaq8TgkKa2xjQtHhuzLTE4pDMXth/991iPPWHGxLF/RwMAgKoI10zahOnSlEXS3ge8pT+ts703LpMXel8f2V5qW6XxflyT+GjHu9gn4gOPP5iaqN07t2owsVvN8XbNnnu65k2ZrAef2a99vUc0c3KLzlzYLkkltc1vn1jyY8dT2REAAIxPuAqHDLzoFQ+JTfT2ZqQS3l+WpyySDj2V257YI8lK8dnF2yqN9+OaxEc73sU+ER94/MGJy/T7PUbx5ia1xhrVn0zphd4jMpJmTm4puy0xOKSXzpykP+07POY1E4NDWjavjRL8AADUSLiWO/Y+7b3BaZooGeN9jE30/uI8sj35onee0Fhtlcb7cc0IxW944ojO+m6LTvhKr866cZ82PGVC1X9eU8TXKn73zq2KNzcp3twkY7xk7WB/Uj2J5Lja4s1NevCZ/SVdM97cpB3dfUGPAAAAREa4kjSqO9ZV/IbHE7ri123q6muSldR1aFhX3H1IG7abUPTft3gX+0R84PGDif0lVWKkuiMAAOEXriQtU90xW3bVs2wNMakxNnZbpfF+XDMi8Ws3HlZ/Kvcl2D8krd3YG4r++xbvYp+IDzy+Od6u/mQqp7mpySjW2DCutuzqjqU8luqOAADUTvj2pO2+11sKlEp6b2RibVL7cmn/ptx2xSQjySaLt1Ua78c1IxJ/wrdOkJUZ9WM2stqx5uXO99/X19T+B6Wdt0uDL0rN06X5F0sv+2h474n4suL7bIu6BqapdzCmyc1JzZmUUqrtdP2qM6WeRFLJ1LBijQ2KNRpJRsnUcNlt0+IxnTx3mh7b2TPmNafFY3rtSTPZkwYAQI2EayZNkjJv6s2Iz/O1W5XWVmm8H9eMQPycibl/wc+YM2nEBR3tv2/x3Q9Kz37HS9Ak7+Mz66SdPw7vPRFfcvxh26I/JBZqcDimtlivBodj2ty3SD2pyd5DjWS8/0uH2graVMY1AQBArYRrJq37IWl4IPcw2KE+6dAfpSkn5rbvf9j72H5a8bZK4/24ZkTiNzye0BV39eQseWxtkq5+4wSt7HjO+f77Fn//m44laNma26Wzbw/nPRFfcvxTXXs0OByTbT/jaFticEjPdvdpwYyJOQdPb9l5QLLS0uPbym4r55qJwSE1NzVo2bxjbaViJg0AgPKFayaNwiF1Fb/yFXFdfdY+dUxMykjqmNKgq8+fopVLpoWi/77F50vQJGlwf3jvifiS43sHY4qb3py2cop8UDgEAIDwC9dh1pnCIdl/ic7ekJ/d3pBnk3u+tkrj/bhmhOJXnjSolSftGT3rEJL++xLfPL3wTFpY74n4kuMnNyeVGJ6c05Zd5CN71qupyUjW5Dy21LZyrknhEAAAaitcyx0pHEJ8FOK7H5E6vyMNDx577Tc0S0u/JLXOCec9EV8wfmSRkKmxAT3at0j7BieNq8gHhUMAAAi/cC13lJR3432hdgqHEB/G+Bmvlua/x5tRk7yPCy+T5r4tvPdEfN74YkVCZKTxF/mgcAgAAGEWrpk0CocQH4V41/q06y7pqeukI3ulllnSog9Lcy4IT/8djs9XJKTSIh8UDgEAIPzCNZNG4RDioxDvUp923SVtvcpL0CTv49arvPYw9N/x+HxFQiot8kHhEAAAwo/CIRQOiUb8rrukJ7/qFeRoOU5a9CFvNsjF/rvUp6eul4aP5H59+IjXXuj751L/HY/PVySk0iIfFA4BACD8wjWTNvkkKdnnLR2y1vuY7JNmnTO6PTbd26w/Vlul8X5ck/jqxnf9TNr6xWMVE4/s8WaDnt/gZv9d6lNmBm2kI3vD0X/H4+dMSulA4zwlBodkrVVicEhTW2OaFo/ltCUGh3Tmwvaj/y722FLbyrlmYnBIJ8yYmP+1AAAAqi5cM2kTpktTFkl7H/CWDrXO9t74TF7ofX1ke6ltlcb7cU3iqxf/5Je9vYzZho9IT/+ntOIhN/vvSp9iU6TkQY0Sm+LtsXK9/47FH0xN1O6dWzWY2K3meLtmzz1d86ZM1oPP7Ne+3iOaOblFZy5sl6RRbfPbJ+Ztr6StnGuOp7IjAAAYn3AVDhl40SseEpvo7e1IJby/TE9ZJB16Krc9sUeSleKzi7dVGu/HNYmvbvx9r1P++nRGes3N7vXfpe/p3gekbVflJrkNE6RXrvESD9f771D8wYnL9Ps9RvHmJrXGGtWfTOmF3iMykmZObinalhgc0ktnTtKf9h0eV3yl10wMDmnZvDZK8AMAUCPhWu7Y+7T3BqlpomSM9zE2Mf0X/xHtyRe984jGaqs03o9rRjH+hY3SA2/1EqqH/lba9qXqPX/LrPyvp5ZZ7ty/iz+TpolSx5ulJZ859j1smeV93vHmcPTfofjdO7cq3tykeHOTjPGStYP9SfUkkmO2xZub9OAz+8cdX+k1481N2tHdV7Nf9QAARF24kjSqO9Zn/Au/TVcQTM9AHNkr7fi296a4Gs+/6ENSQ0vuYxpavHYX7t/Fn0l225wLpHN+Kp38Re9jpvx+WPrvSPxgYv+4qzNS3REAgGgJV5KWqe6YLbtqWraGmNQYG7ut0ng/rhm1+N13jq4gaJPS09dX5/nnXCAtWXPscOiW47zPM9UJg77/A5ulX75Fuvs07+OLm4PvE/FVj2+Ot6s/mcppbmoyijU2jNmWXYlxPPGVXpPqjgAA1Fb49qTtvtdbSpRKem+EYm1S+3Jp/6bcdsUkI+/NfrG2SuP9uGbU4h9+f4EfuJFO+7r7/a8kvvsRqfM70vDgsdtuaJYWvEdqPzWc90S8+myLugamqXcwpsnNSc2ZlFKq7XT9qjOlnkRSydSwYo0NijUaSUbJ1HDRtmnxmE6eO02P7ewZV3yl15wWj+m1J81kTxoAADUSrpk0Sd47omMfjv0jT7tVaW2VxvtxzSjFZ2a4RprQHo7+VxLfdUdugiZ5n++8Pbz3FPH4w7ZFf0gs1OBwTG2xXg0Ox7S5b5F6UpO9hxrJeP+XDrUltqnC+EqvCQAAaiVcM2ndD3lV5rIPkx3q80qBTzkxt33/w97H9tOKt1Ua78c1oxbf/Tup8/u5Sx4bmqWXf1I6fqX7/a8k/u4iEwznZ/03EqZ7inj8U117NDgck20/42hbYnBIz3b3acGMiTkHR2/ZeUCy0tLj24q2VRpf6TUTg0NqbmrQsnnH2krFTBoAAOUL10wahUMqi9/3W+nRfz6292nXXW70v22Zt0es5ThJxvs4523S3LfX5vmDjG8u8KY3NqI9TPcU8fjewZjipjenrdLCHxQOAQAgWsJ1mHWmcEj2X7KzN/Rntzfk2eSer63SeD+u6Uf8rruk5245trTuyB6vouL8i6QZpwff/5dccKxqYGbWwqXvn1/xHSulzvWj96TNXZn7uDDdU8TjJzcnlRienNOWXaQje9aqqclI1uQ8Nl9bpfGVXpPCIQAA1Fa4krTJJ3lLHiXlHDI76xzvkNns9th0SdZ7w1+srdJ4P67pR/xT1+XZ+3RE2vUTafaK6jz/3ge8ioxHXvDe0M5fJc19ixv372r87PO9N/3P3+p931peIh3/Lmnma8N7T0HH92yTnrtZGtjvneu28P3SjNfU7PnnTEppc99CNQ8O5RwGfebCdv1p32FJOto+tTUmI285YbG2SuMrvWZicEiLjyt/qSMAABifcCVpE6ZLUxZ5yUD/bi8RmHWONHmh9/WR7aW2VRrvxzWrHX9kb/7v6cB+r2pdpc+/7Uve2WY2vSSqf5f09NekwQPSxAXB37/L8e2neks+XepTWOP7npU6b5JS6f2NR/ZIT/ybtPRLUscFvjz/wZR3UPVgYrea4+2aPfd0zZsyWQ8+s1/7eo9o5uQWnbmwXfPbvRm4ke2ltlUaX+k1x1PZEQAAjE+4CocMvOjNpMUm5v6Fe8oi7y/c2e2J9MHI8dnF2yqN9+OafsQ/8Jb8idqEGdKp11X+/L//SP7rt8zyDkAO+v5rFL9ha4/W/npAu3qlOZOl1a+doJVLptXna8rF+IKv85dIb/pt1Z//cF+PNvctUnN85tFZpxd6j8hImjm5JWcm6qUzJ+lP+w4r3txU9LF+xFd6zcTgkJbNa6MEPwAANRKuwiG9T3tvkJomSsZ4H2MTvb9sj2xPvuidZzRWW6XxflzTj/hFH/b2OmVraJHmvLU6z3/khfw/syMvuHH/NYjf8ES/rrh3QF29Xsnyrl7pinsHtOGJ/vp8TbkYX+h1OLDPl+ffdbhRbannFG9ukjFG8eYmHexPqieRzGmLNzfpwWf2H/13scf6EV/pNePNTdrR3VfVX+cAAKCwcCVpVHccf/ycC6R5f52uGmi8CopL1kjTl1Xn+VtmKa/s9jB//0qIX7vxsPqHcr/cP+S1l/X8Dt1T6OKLvQ59eP58lRz9qM5IdUcAAKIlXElaprpjtuyqa9ka/n/23j08ruq89//smdkz0kij+8W6WLKRLYMNGBMbzCXYhJDgQoJDm5JTEvJrDk2TQJK2idMQmpYmpcnBOef05IE0TdO0ISEJzVOOIeGYQAjmYjAYMMQX8A1bRhfrZl1nJM1t//5YmtFc9oxGmhlpNn4/z5Ns6Z31fddae7Z59tJa67t0sOuzx7LV5yNnvvS1l8NF/wjX7YXNv1YDt1zV3367mpmL+8yl4oXS/zzru0fjX2wjROPvxmeq0PTtt5vPGLfdlpf6Pc4APiPeydHh0NDt8f9pjXVSnK1sPvTZ5hR3R0EQBEFYWKy3J63nSbUUKRRQL1J6pTK+GHwlPo4OGsrIIl0sW30+clpV3/cC9DymzKoaFwAAIABJREFUzEKKG6D5JqhYY532Z6m/4hdL6PImv8g2lQTY/bHT8kwtlH7gVeh6GPxnlK55q3IwnUP9XqOIrqkKxvw6HmeAxtIQpTVrGB84SPe4PRov16d43dtOv7+UQCiMbreh2zVAIxAKR2MVbp0LmivY3znMsC+Qtmw+9NnmrHDrXLmyVvakCYIgCMICYS13R0C9Uc1cZn4wiUcGoLPFstXnI6cV9TUboO5yZUte/R4YfFXt77FK+7PUb3vPGe7cXctEaGYWotgeZtt7zsy9/gLpkyX1NZdBzUYgoJYu2vQ56ceNIvb72vBoo1TqY/jCHvZ522gpW8Ipb4DK8KmYeCsjIQ9oBhqaSgdoGKhfZ2IwfU2Im5XNhz7bnIIgCIIgLBzWmkkbeAnCU/GHyUYOPi5bER8f3Kuu1RvSx7LV5yOn6AtbPzUAR+5XLoLOSmi6EVapZZ07DvnY/swY3WNhGj02tm3ysHW1e271F8I9GXgZenaqPkbOGitZXrjfSQ71R7pO4w/rGNWXRmM+f5CTA16W1ZTEHfz8RucQGLB2aWXa2GLrs83p8wdxOmysa5n7WWkykyYIgiAIc8dae9LEOCT3+v4X4PWvweMbYNcN0L3TWu1faH3fC3DgHnX+FoZaUnfyp+q+AVtXu9n9mTpO3PIGuz9TNzNAm0v9MbEdh3xc8f0+lv+vMa74WSU7Dmtz0s/rnvS/oPoU6ePkaXjzOzPPRr7rX2S9mRnIYht/iHGIIAiCIJxdWGuQJsYhudV374RTD6k9OpGX8QP3QOcj1mj/Yuh7HoPwZHzcCKiZtVzVb9NhaB++J6/nwx2beKjxk3yo4mm6fE7u/M0oOw755p5zLm3qfozooeQRwpPQ93Rhfic51puZgSy28YcYhwiCIAjC2YW1ljuKcchM2ahJxxlwVqkld5Xr0usTDRXCfgiZnH3kqoEP7LGGScRC6/felvr5vPi7ual/4FXoeEB9P9P4wi6+2nkHjw5fTVNJkN0fPZW/e7L3syk6qMHlPy+87yTHeq/h4fmxtXFmIItt/CHGIYIgCIJwdmGtmTTAdON/qrhBZrFs9fnImU4/8DKc+oUabIG6djwIZ/am1g+8rF78I5rAkPkADWBqML/tt7LeWYUpzqrc1d/1f+MGaABu2xRfWfIAAN1ee37vibPatIsUN8y/T4X8nSaUNTA30yBl3MxkI3OTjoXTZ5tTEARBEISFwlozaWIcoq77/356v1ACRUvU+Wdm+l03mGvMKKqHC/9xYe7p4fuh6xFl219Ur865qruqcE0mBl6Gjp/HL3m0OeH8r6tz53JR/+Pmkw5hQ+Oc/b+iqczG7s/U5a5PiWUP368G/bEDRZsLln0CzvlE4X0nOdaLcYgYhwiCIAjCYpP1TJqmaUs1TXta07Q3NU07qGnaF3PRMFPEOESVnezFlEjcTJ9Kk4itCFbevjD3tHunMqjwnyFuT1zvM4VrMlG5Ds6/Sw2I0ZS749KbZwZouajfaf4i3B2oodgB264qzW2fEstWrVN9ivSxaAmsuQtKlhXmdyLGIXnPKcYhgiAIgrCw5OKctCDwJcMwXtM0zQO8qmnak4ZhHMpB7ngixiGxfwmPNQSIjdtMNrmbxbLV5yPnbPqi+hQzafWp9ak0APYSVTZxJivf9/TI/eYGFUfvVzN5i/Wdzqav2zIzKIvMxMy1/u6d0zb+p9VSyXP/ciZn09akmSxf2MUPhz7Bt651xTtG5uue1F0O58X8vSUyE1Wo30kO9R5nAF84tXFI7KyTw6GBocWVNYsttj7bnGIcIgiCIAgLS9YzaYZh9BiG8dr0z2PAm0BTtnlN8ayEgFe9MBqGuga8UL8pOa5XKbOA2WLZ6vORczZ9221qxisWmwtWfi61vi2N4YWjGN6/Czb9Sg3QFuqeppwR7Fvc7zTf+nd2xNj4o2YSD/wDdP0/Va7hOmj79PSgW4Oietyrv8Ddt32OrSsChdmnd5G+sTTEkL0Fnz+IYRj4/EF8/iAb26qjP0fi5cU6FW591thi67PN6fMHWV5TYv7vVRAEQRCEnJOLmbQomqYtA9YBL5l89mng0wAtLS3zq8BVBWXtM8vhihvUi5enTX2eGM80lq0+HznT6YNeaLxBWaL7z6jPGv4AsKnZDjN9yfLU93VqUOly3f7OR+HgPeAfVGYUDdepNk90g16uZjSC48ntKW5Y/O80n/pXbk+28Q9PwVv/E4qbVLnq96illVbpk4X1I6ESejoP4Pf14HRX09B8CS1lHvYcH6R/bJJaTxEb26pprVaDlMR4prHF1mebcz7OjoIgCIIgzI+cGYdomlYKPAPcYxjGw+nKZmXBP/AS6CVqb0nIp/4yXtYOo0fi477pg3jdDelj2erzkTNf+uf+EKYGku+rqwbe+1+5rX/0LXjjTjX4SIkdNA2M4EzI5oL2L8DKPy+8+5cr/Qv/DXO/PE3NaFqxTxbVj3uH2edtx+mupVi3MxEI0Tc2iQbUeoqiMZ8/yDm1pbzdP47b6UhbthD12eb0+YOsa6kUC35BEARBWCByYsGvaZoO/Bfw4GwDtKwYO6pesBwl6uXeUaJ+730mOR44o2zmZ4tlq89HznzpGz+knAhjsTlVPNf1H7xnlgEaQEgNypxVRA0qzv8baL6hMO9frvSRvYOJFNUXZp/6noWX/hR+tUJd+54tvHs6T333uJ3K0CncTgeapuF2OhiZCDDsC8TF3E4He44PRn9OV7YQ9dnmdDsdnBjw5uK/4oIgCIIgZEAu3B014N+ANw3D+F/ZNykN4u6Ynd7Mta/lZrWsLtf1+wfJiJAXzr8brturjg9o3FK49y9X+vbbTfYUFql4ofWpe+f0/rnp/YOTver37p0LU3+e9WZOjoXozijujoIgCIJwdpGLPWlXAJ8A9mua9vp07GuGYfy/HOSOR9wds9cnuvbN151wtvqd1ZkN1JxVYE/IUcj3Lxf6umkXx1TujoXUpyP3m+yfm1Txxi2Fc0/nqTdzcixEd0ZxdxQEQRCEswtrHWY9dQZ6nlRLmUIB9XKvV0L1ehh8JT6ODhrK4j1dLFt9PnK+G/QT3fDGV+MPRE7E5oTWW6F2Y+G1X54pFdv72dTf34Z/Lvz2J+jHBw7SPW5nzK/jcQYo16d43dtOv7+UQCiMbreh2zVAIxAKR2MVbp0LmivY3znMsC+Qtmwh6rPNWeHWuXJlrexJEwRBEIQFIid70hYWLe4y84NJ3CCzWLb6fOS0ur75w8pG3lmlQs4qqNkc83sltN4CNZcVZvsXW18obUpxsPZMvMDbHxMbCZWwz9uOP6xTqY/hD+vs87YzHPKABpr6v2mpYRKbvmZUthD12eYUBEEQBGGhsNZM2sBLyowidrlT5JDdshXx8cgyvuoN6WPZ6vORU/Rz0w+8DD071X6ponp1JlzJ8rnVPzUwvfywF4rqlJnKOZ8orGfq7Z9A96/UOXKRg8ddNfltU2RPWuySR1sRnH+XWu5YqM+Eif6tPj8j7nVxS/ve6BwCA9YurUwb8/mDnBzwsqymxJL6bHP6/EGcDhvrWlIM2tMgM2mCIAiCMHesNZMmxiGzmzzsugF+uxn2/ZVys7NS++ej738BTv50+mBoQ13f/I66F5nW3/dCzOHShhqonfjx4t0/s1jvM6pNk70z/Txwj+p/PtvUuEUNyIqWqN+LlswM0ObS/gJ4pvy+Qcsaf4hxiCAIgiCcXeT0MOu8I8YhqfWJMx6BEWWDr2npDSkKpf3z1Xc/pvYexRKeVIdmn/v5zOrveSzZHMMIwNH7oekP8tv+TGNH7zfvZ/djUHt5ftvUuAXqrjKfySrEZyKF3umuZsSixh9iHCIIgiAIZxfWWu4oxiGp9a9/Bfxnku+Zs0pZ3Bdo+3cc87D91VK6x+00lgTZtn6Uree5Mq8/pbGFBpf/PLP2770tdY4N3yuMZ2rv50i5M+iSHxbUd1oIeq9RRNdURdQgpLE0RKjyEp7rCFnS+EOMQwRBEATh7MJaM2mAqXFAqnhkADpbLFt9PnLOVW82QAMV11D7troeVbb4zipovH56Bmbx2r/jmJs7ny9jIqRW3XZ5de58vhIcfrZWZ1h/Kqv/4obM2++sMr1/pwM1XPZvzTODxxXBxXumXNVq31wizuoUxhkF8Ewukn7cKGK/rw2PNkqlPoYv7GGft42WMg8Gw6BBrCGGZmKSYRYDc5MNq+izzSkIgiAIwsJhrZk0MQ5Jrd//99N7qhIoWqIMJvZ/I365nKbDBX9rbjyxQO2/4vt9dI3G730BaPJo7L75dGb1H74fOh6Mt/q3uWDZJzI3/hh4GTp+HrfkcSLs4q877+DR4asBKHbAt64YZOsK3+I8U+/sgDfvTehnEbT+N6i5pDCfyUXSH+k6jT+sY1RfGo0ttnHHYuvFOEQQBEEQrIUYh7xbjEPab1cv7bHYilT8ze8k72cyAiq+iO3vNhmgAXSPGZnXX7UOlt48bWyhqeuau6BkWebtr1wXY46hcTpYFzdAA5gIwvZXyhbvmWq+ERo/HN/P8+9S/S/UZ3KR9GN+Hbc2FhdbbOOOxdaLcYggCIIgWAtrLXcU4xB17d45YxfvrISmG2HV7eqzaLwKVn5WmT78/uvJdYAyFzmzT83ELGT7p2kss5nOpDV6tLnVX3c5nPfFmVhk1mUu7a/bEjVYueze06bLu7q9juk9Tyb6WPL1TDVuSTZDicwk5btNFtJ7nAF8YU9cbLGNOxZbL8YhgiAIgmAtrDVI86xUSx5B/UU95IOAF+o3weiR+LheBRjqhT1dLFt9PnKm0/c/B8f/VS37BLWXquNBcDep2Za6q5S+rF3pg97097TjQfXSW7567u3vfASOfR+mBtXZYitvV7pEfe8zyp1wsk/trVrxGWi+kW1X6Nz55CQTwZkXwmIHbLvMWNTvtNEDXfETMQA0lhrKwOLd9ky9y/SNpSH2edtw+oMU63YmAiF8/iAb26p5u39cPWfT8fJiHQ21nC9dzOr6bHP6/EFWLZn7UkdBEARBEOaHtQZprio1+Oh9Ri19Km5QL26eNvV5YjzTWLb6fORMpd/3lzMDtAhhPxz9Z7W80UxvK4bwhPk9Dfuh82EITcI7v1Sza8WNcNG9ULMxdVu7d0L3ozN7pCZ74cA3wXsK1nx1pv6D31bne0WWW04NqL1VI2+xtWkLXH8R25/up3s0QKM7wLZLJti64dJF/U63ve8i7vx/fUwEQtHbVGwPs+2aJqgun+l/39NqkFzcAA1/oJZYWvGZsrh+JFRCT+cB/L4enO5qGpovoaXMw57jg/SPTVLrKWJjWzWt1WoGLjGeaczq+mxzzsfZURAEQRCE+WEt45CpM2omTS+J/wt7ZNYoNu6bPpjY3ZA+lq0+HznT6V/4GOZeaxp88GVzfe8zyliEkIluGpsrfvBnL4KVn4fmG8zb+vzNKYxK6uHSf5+p/6U/nT6AObHcErjyoYW/fxnqd5yqZ/vveugeU8syt12hs7X1jCo7cmB6P1/M2Wo2l9oLF5lJtNIzZWH9uHeYfd52nO7a6KxP39gkGlDrKYqbCTqntpS3+8dxOx1py74b9dnm9PmDrGupFAt+QRAEQVggrGUcMnZUvaA5SkDT1DUyCEmMB86o85Rmi2Wrz0fOdHpniiVHRfWp9U1/ABfeTeqv25Y8OxeahJMPpG6r2cAL1JLG2Pon+1KU612c+5ehfmvt6+z+Mw8nvrKE3Z+pY+sFlTNlj/8w+fDr8BQc/Z41nykL67vH7VSGTuF2OtA0DbfTwchEgGFfIC7mdjrYc3ww+nO6su9GfbY53U4HJwZmWTotCIIgCELOsNYg7Wx3d+x/AYIJgwNQdvrtt6sleLtugN9uhn1/pV5qIzRugWW3qLKJWsxdFpMGWLFtLao31xTVx7c/XbnEnBEW+zudTZ9ygNqbm/qteE8WSW/m5FiI7oqLrRd3R0EQBEGwFtYapEXcHWOJdX2LxaabO/ElxrLV5yOnmb57J5x6CMIJOe0lsOzj6ucD90wvQTTU3rKD9yhdhNrLVdlYG/dlH1dOkGYU1aVuazrL/9j2pys3l/6nKrsY+tkGnlZ5pt4Feo8zgM+Id3J0ODR0e/x/2mKdDGcr+27UZ5tT3B0FQRAEYWGx3p60nifVUqhQQL3I6ZVQvR4GX4mPo4OGMqxIF8tWn4+cZvoDdyuTikScVcrk4/WvpP78/LvT1z+4Ry1tjD0o2V4E59wGFWtSt3VoH3Q9oup1VkHD9coOP7H9fS9Az2Mz5ZpuVGeTLeT9y6W+fzec/Gn82XM2pzqvzaz/hfpMWVA/PnCQ7nE7Y34djzNAuT7F6952+v2lBEJhdLsN3a4BGoFQOBqrcOtc0FzB/s5hhn2BtGXfjfpsc1a4da5cWSt70gRBEARhgbCWuyOg3t5mLjM/mMQjA9DZYtnq85EzUW82AGM6bszy+Wx1VW8EIwRdO8A/BK4aWP01GH8b3rgrZnB1k3J8jOhrLoGaK1ENCKhlambtr9mgBi84zcsuxP3Lpb7mEjCC0J0w8Kxal7v6rXZPFkA/Eirh9952KsOnqNTH8IU97PO2MhLygGagoSkpoGGgfp2JwfQ1IW5W9t2ozzanIAiCIAgLh7Vm0gZeUgYNsYfZRg4uLlthfshv9Yb0sWz1+chppt91g7mborMK1t6j3BtN3RaXwOZfz73+t38CJ38Sbyhic0LrLTMHZy9k/wtQv+OQj+1Pn6Hba6exzM62q0rZutptnWfKYvq3+vyMuNfFHbz8RucQGLB2aWXamM8f5OSAl2U1JWelPtucPn8Qp8PGupa5n5UmM2mCIAiCMHestSftbDYOab+dJNMPWxE0Xq/0s+39mmv97/zS/Dy2zh2Zt7/3GTW4fHyDuva/YGmTitiyOw75uPPxUbq8Dgw0ukbD3Pn4KDsO+azzTFlM7/cNWta4Y7H1YhwiCIIgCNbCWssdI8YhsX+JjzUUiI3bTDa5m8Wy1ecjp5m+cQuMvT29B2xImVS0366WJgLUbVHXI/crl0FnFaz8rNLNp/7ASHIc1H6ix9ejxvfhmaV+dZfH670n42fiJk8r4xPNEV92oe5fjvXbnx1nIhgvmwiq+NZ2wxrPlMX0Tnc1I4FQ3KyPw6GBocUVNYvFmmScjfpsc4pxiCAIgiAsLNZa7ng2G4ckGld07lCfOaug+Saofk9u69/3VzDRnfl3U3MVtPzR7PrI8kwLmFSk0y//t2YMtKTuaRic+IzXes9Ugem9RhFdUxVRg5DG0hChykt4riNkSeOOxdaLcYggCIIgWAtrLXcETI0HUsUNMotlq89HzlT6/j3Q8aB60QVlXHHyARh4Obf1n/tltQctUwaehTN7Z/QTPebl/GdUW8/sVaYke29TzpS5bn+e9Y0lCdNoROKh3NS/CH0qFP24UcTvfW34wzqV+hj+sM4+bzvDIY+pyQWmJheZm2ScPfpscwqCIAiCsFBYaybtbDQO6Xs2ZgljJYSmIOQliViDkFzV7z0Bx384fUhzBs9JpA1BLzx7E/gHzctpOsq9L2agYyuC8+9SyzMX+zvNQB/Zkxa75LHYAd+6rkwtdyzkZ6rA9Ue6TuMP6xjVl0Zji228YXW9GIcIgiAIgrWw1kza2WYc0vtM/AHV/jPmAzSYHkjluP7mG9Wg67q90wdgz0KkDXY31F2dbGQSwQgQN0ADCE+qwWgu259H/dbVbr51XRlNJQE0DJrKbGqAttpd2M+UBfRjfh23NhYXW2zjDavrxThEEARBEKyFGIcUsnHI77+mBi+ZUFSf+/pj9e23w++/nlkbQj41I1Z+Lhz8h8zaDzODvMX+TjPUb13tZmv9QfVL7KxRIT9TFtB7nAF8YU9cbLGNN6yuF+MQQRAEQbAW1ppJ86yEgFctnTIMdQ14oX5TclyvUmYFs8Wy1ecjZ0Q/2ZfZfbE5oe22/N6Tuqtmb0fNFfH60NTsmliK6gvjO11sfSG2aQH1jaUhhuwt+PxBDMPA5w/i8wfZ2FYd/TkSLy/WqXDrs8bOdn22OX3+IMtrSmb/NywIgiAIQk6w1kyaqwrK2tUywIke9Zf5+k3gaVOfJ8YzjWWrz0dOT5v62cwh0VEKml3Z5Bc3KpMPvRy6f5Pfe1LcmN7xsfO/oG8XrLkLmrYog5OUTFv4R391Qs2Vat9SIXyni60vxDbNQT8SKqGn8wB+Xw9OdzUNzeso9ywxiavBf3zsElrKPOw5Pkj/2CS1niI2tlXTWq0GCYnxTGNnuz7bnPNxdhQEQRAEYX5Yyzhk6owyD9FL1N6WkE/9Zb6sHUaPxMd90/u43A3pY9nq85Ezoj/6L3Dku/GHStuccN5X1H6xfNefqO/4JRz/gTrUOh02F6z9Fuz7EikNRy74Bhy9X80WuqphxWdm+rTY3+li6wuxTXPQj3uH2edtx+mupVi3MxEI4fMHOae2lLf7x3E7HdF439gkGlDrKUobE312+mxz+vxB1rVUigW/IAiCICwQ1lruOHZUvSA6SkDT1FUvUX/FT4wHziib+tli2erzkTOib74Bzv+badMOTZ0x1noLLN26MPUn6ivWqPpne2zCU3DwHiiqM/+8aAk0/QFsfgw2fA8u/GZ8nxb7O11sfSG2aQ767nE7laFTuJ0ONE3D7XTgdjrYc3ww+nMkPjIRYNgXmDUm+uz02eZ0Ox2cGEhhWiQIgiAIQs6x1iDtbHN3tLuVAUfEYfGCu6Fy3cLWn1i2ch1c+PepnRsj+Adh5e3J5TRdmZAsVvutoC/ENok7o6X14u4oCIIgCNbCWnvSzjZ3x0LV121R1yP3Tx8PYIKzWu1X0rT4c96ablQDz8Vsf6HrC7FNeXBn3HW4jx8+f4KRiQC1Hhe3bmxl86q6gnRHtLpe3B0FQRAEwVpYb09az5NqeVUoAHZdOcNVr4fBV+Lj6KChzuRKF8tWn4+cVtIPvAodD8TvU7M5Ye23ldFIobe/EPUF0CavUUTXVAVjfh2PM0BjaYjSmjWMDxyke9w+E3cNo0Fc2XJ9ite97fT7SwmEwuh2GxVunQuaK9jfOcywL8BrHUP8an8PgdDMf390u8aNaxvZsKwS0AiEwin1kbhu15LKmsXOdn22OSvcOleurJU9aYIgCIKwQFhrJg1Qb5Qzl5kfTOKRAehssWz1+chZyPqBl6FrB/iH1IxZ1eUw+nt12LazClr/BJo/DIOvFmb7raBfxDaNG0Xs97Xh0Uap1MfwhT3s87bRUraEU94AleFT0fjzY2vRgCZHd0zZVkZCHtAMNDRVxXRtxnQ9Tx3uixugAQRCBk++2cf6ZZVoGCipuT42blZW9LnPKQiCIAjCwmGtmbSBl5QpRexyq6BX2baXrYiPD+5V19hDhs1i2erzkbOQ9QMvQ8fP4w/Ztjnh/K/PLGMs5PZbQb/IbTrSdRp/WMeovjQa8/mDnBzwsqymJG5p3BudQ2DA2qWVaWOJ+g/f97zpi78GfHPrmln12dZ/tumzzenzB3E6bKxrmYllisykCYIgCMLcEeOQd7PJQ+8zsOsGeHyDuva/kH39nTviB2igljoeub/w+m9V/Vlg/FHjcWFGjcdVkMYbVteLcYggCIIgWAtrDdIixiGxxBoaxGLTp/fXzBLLVp+PnLnQe08qG/zJ6XOsJk/DqYdgaF929QeGMGWyN7ftP5v1ucrZvXNmkP7MDeqZyEDvcQbwGamNP2JxODR0u23WWKL+1o2tuBzxZVwOG7dubM1In239Z5s+25xiHCIIgiAIC4u1ljuKcUjm+n1/BRPdyffQWQVr75l//W98Re09M8t7/t2F0/886ZMMNVzDlNomC++ZGtwDJxMMXexFTC7/HKeK35e18UcuTCoOdo/y2zf7GJ4IUF6sc82qWi5urSxI4w2r68U4RBAEQRCshRiH5EJfiMYTEz2YEhlgzbf+ppvM3Rybbiys/udBb2aosd/XxgXu45RqgcJ6pjofjv+OAEKT0PEL/O0fzNr4IxcmFRe1VEybhEAgbBAMGnPSZ1v/2aYX4xBBEARBsA7WmkkT45DM9c/epA6UTsRZBe97Irv6pwaSzz5bdXtm+oGXoWen0hbVQ8MWqLmk8O6fid7MUEMbfAmnLUB705Lc1Z+LPu39LGYYaBy4ambJqlWML0QvxiGCIAiCcDZhrT1pYhySub7uarAVxcc1HRquz77+xi2w+ddw3V644G6oXJeZvv8FOPnT+H1yJ38KfS/Mv//9L8DrX5sxR+nembf7b2ao4dbGGPMn7NUphGdKN3+ZDria4n63ivGF6MU4RBAEQRDOJqw1SBPjkMz1jVvgvC9D0RJAU9dlH4e6yxev/d2Pqb1TsRgB6HlsfvV371RmKIEhooO+A/dA5yN5ab+ZoYbP8OBxJvSpEJ6p5q1Jg/Sw5uJU89/ExaxifCF6MQ4RBEEQhLMJa+1J86xUSx5BzSiEfBDwQv0mGD0SH9erAEMtE0sXy1afj5w50zdAw7Uzcd/pBal/x4Extu9pont0jEbPONuu8rB1laEOvzbDPzS/+o/cl7zvKjwJx34AH3gh5/e/sTTEPm8bTn+QYt3ORCCE397CupIjhfdMNXwQ3E1w/Idqaamrlslz/4537Ftxx7S/vFhHQy1nSxfz+YNsbKvm7f5xANFbTJ9tTp8/yKolc1/qKAiCIAjC/LDWIM1VBWXt6vyviR41s1C/CTxt6vPEeKaxbPX5yGlR/Y6u5dz5fAUTwSAAXWMGdz4+DN4xthY3mDtOFjeo/VZzrT/W9j+Wqf6c9H8kVEJP5wH8vh6c7moami+hpczDnuOD9I9NUuspYmPbUkL2Ct6KK7eOcs8S07yxOZ/vLecn+ys5PeqnsXSYbRfuZ+vq4qRysTmT41cBmMfGq/E3nz8dO5/yiiWcM+hNaH81QFKswj5GT+c+/L5Byt3VnNt8PuUVJaZlM421Vot+MfXZ5pyPs6MgCIL3L3WgAAAgAElEQVQgCPPDWsYhU2fUTJpeEj/DUNauZhhi45FZI3dD+li2+nzktLD+iu/30TWW/Ew1eTR2f2AnHP9BsjNk26eh9aNzr/+ZG8wHaq66mZm0efZ/pGQdr53WcDsd0dmEvrFJNKDWU5Q25vMHuXiJQbl3X1z9495h9nnbcbpreenEIPc9fRx/cGbvT7EDvnWti/e3+KLlYnOeU1vK2/3j825Tpnq/r591JUcoLanI6T1ZqPaLPvc5ff4g61oqxYJfEARBEBaInOxJ0zTtR5qm9WmadiAX+VIydlS99DpKQNPUVS9RsxWJ8cAZtVdptli2+tly9j0Lz3wIfrsZXvks9Pwm/21aRH23yQANUPGKNdB6S/w+udZbVHw+9bffoQZ5sdiKYMWns+5/T+cB3E4HbqcDTVMDk5GJAMO+wKwxt9NBT+eBpPq7x+1Uhk7hdjr4yZ5TcQM0gIkgbN8diCsXm3PP8cGs2pSpvjJ0iu5xe87vyUK1X/S5z+l2Ojgx4M3Pf9cFQRAEQUgiV8Yh/wFcl6NcqbGau2PvM8rIIuJm6D+j3Ay7d0aL7jjq5IpfLGH5vae54vt97Djki9fvumHGubD/hfz1qXvnTF3P3zzjkjjH/jeWmT9SjWU2VbZy3Ywz5OZfQ9W6+be/cQu03DztZDg96Dv/Lmi+Metnwu8bzMqJz+8bTOsOOTA2hRndo2FTF8mFdAdM5ViZ7T2xsjui1fXi7igIgiAI1iIngzTDMJ4FzuQiV1qs5u549H5lZBGLEVBnjAE7Dvm4c3ctXV4dA+gaDXPn46PsODAM3pNw8J54u/pTD8HQvtz3aWhf/GBy8jR0P6pcEufY/21XlVKcsNOx2KHieflOai+Hi/5RDfrab1f39jeXwOH/Pa/2R+p3uquzcuJzuqvTukPWeFyY0VhmM3WRXEh3wFSOldneEyu7I1pdL+6OgiAIgmAtcrYnTdO0ZcCvDcM4P8XnnwY+DdDS0vKejo6OuVcydQZ6nlTL00IB9XKtV0L1ehh8JT6ODhpqUJQulq0+Xc5frQRS3N/WT3DF7/6QLm+yd0tTaZjdaz5jbrLhrIK19+S2T298Rc3yJeKqgQu/Oef+7zhZy/a9pXSPBmgsCbHt4kG2tvvz9p14jSJGT++jrus+7EbMDJXNqZZTVq6LK9s1VcGYX8fjDNDoGkaD+FhpiFDlJTzXEWLYFyAQCqPbbeh2DdAIhMJpYxVunfe22rEPvUz3uD2at1yf4nVvO/3+Ul7rGOJX+3sIhGaeD5cd/uJSuKl9plxszguaK9jfOTzvNmWqr3WOc1HJEUYCrpzek4Vqv+hzn7PCrXPlylrZkyYIgiAIC8SCnZNmGMYPDMNYbxjG+tra2iwyaXGXmR9M4gaZxbLVp8rpqk7djVO/YL3+nOlH3eOaWq5nRmQwlcs+mQ3QAKYGM9MnxLauDLH78ys48Rkfuz/Ww9YV3jnp59L+XxzzsOkXVYTefiB+gAbKoKTrkWjZcaOI3/va8Id1KvUx/GGd58fW8vzY2rjYPm87wyGPqkoDTf3fdNVGRrHhkId93nbTvGhwYXMFN17USMX07EStG750iZ/3tsaXi6+HrNqUqX4o5OH1FG1fiPpFny99tjkFQRAEQVgoFmwmLZZ5uzsOvAThKWVkECHoVfbtZSvi44N71bV6Q/pYtvp0Ob0n4M3vJC95nOZ0sI6Nh36UFG/yaOxedSv4B5NFzip43xPZ96l7p1oaOHkaNVaP34MCQFE9bH7MXJ9t/TnQ7zjk4693jjIVgrcv+BA2zexZ1tRSSOBI12n8YR2j+tLop290DoEBa5fOnAHl8wc5OeBlWU0Jbqcjbdl86AuxTaK3tj7bnD5/EKfDxrqWuZ+VJjNpgiAIgjB3FmwmLSdYzTik+UZlZJGCekc/xfaEDfoO2HaVB+quVk6FsWg6NFyffZ+6d8bsQQPTAZqmw8rbU9a145CPK77fx/J/a+aKXyxRhieZ1p+qTXM0Ltn+7DhT09tpugM1yX0ANdCcxsyQ491o8iB60YtxiCAIgiBYm1xZ8P8ceBFYpWlap6Zp/z0XeZOwmnFIyKccCIuWmHZHK6rnW1cO0VSiDn62a9M27M+OscP3ETjvy/F29cs+DnWXZ9+nIyaGJqrAdF31sPyTMwc9J+h3HPJx5+OjdI2GMdDo8urK8CQyUFsg45Lu0ZkXyXtP34ovnGDGYXMpM5FpzAw53o0mD6IXvRiHCIIgCIK1sd5h1lYyDonk7HsB3nko/hBnTVeDrpor2HG8iDufK2MiNPNiVOzQ+NamCbYu68/IOCPR+KK0Zk3qPr18m+ntNdA4esGvovrxgYNxxhcRk42rf1FBny9Z31QSYPfHTqe9p2bGHe7ffxGbydLOsLOWY6v+PaXJx2cfC8S148MVT/OVJQ/QqA9AcRP+5j/mVPH7TI07FtPkoWn4YS4a2k5JqAefo5HfV32F4yUfLmjjCdFbWy/GIYIgCIJgLay13BFQo4yZy8wPJvHFNg6JXGs2KJdB57SRiLMKWj8GNZcAGtv3lsYN0AAmggbbX3LOWpeZGcY+bzsjoZLUfXJWYUZQr47qO/xLkowvIiYb/SYDNIDuqFOl+T1NZdyhpTAu0fwDaU0+PrHWhtMe7RyPDl/N1Uf/g7tL3+CdTW+x1/1nKY07FsvkoWX0/7Jx8GuUhrrRMCgJdrGh/6ssG9+xaG0S/dmiF+MQQRAEQbAK1ppJs5pxSIY5l/9bMwYzg40IGnDiK0viyibqzcwwfP4g5b59nFvnNK9/akAtL4xZ8hi2FdO58rsA1J/4e5z+LvzOJnqX/x0j9R8FZgwF/s/vjtFvchhzU5mN3Z+pS9n/VMYdWzuupDTUlZRvytnMkY0H4somGhr8+MUTPHmoj9GJADUeF7dubOWS5VUFa/KQqq9+11IOX7p/Udok+ne/XoxDBEEQBMFaWGsmzWrGIRnmbJzek5ZIY5ktqWyi3swMo1i34/cNpq6/cYsyNClagoFGQK+JDtCaj34Bl78TDQOXv5Pmo1+gvPeXwIyhwK0bW3E54tsWPbA6Tf9TGXe8Uv4lwrbiuHiAInqX/21S2URDg/MbyvmLa1bw6B1X8qNPbmDzqrpFN2lIpy8JmZx9B+hTnYvWJtG/+/ViHCIIgiAI1iL5JOVCJmIcEjs7FGtSERu3mWxyN4tlq89Bzm3rR7lzdzUTMWO1YnuYbVckGGGc2afO/fIPKXOP9tvxONfhC8ebYUwEQpS7q9PX37gFGrdwNGZ2a9VLF2ALT8Q3LzzBkpPfYKT+ozgcGhgam1epZZsP7OlgYGyKWjd87X1lbF3tTtt/jzOQ1FaHQ6Oz/CN01npYcvIb6FOd+J1NvFaxDVvlTbgTymJoSfrEWKwhQuwMQSHovfZG05m0gKvZsn0SfeHrs80pxiGCIAiCsLBYa5DmWamWPIKapQn5IOBVLoSjR+LjehVgqKV36WJz1fc/B/vvhsk+KKqDpR+F2iuzyrn1PAPcLrbvDtA9GqbRA9ve18TWlt6Zsp2PwMmfgDE9kps8Dfu/QUvb59nr/jOc/iDFup2JQAifP8i5zeeDd19S/TuO2tn+n710jxk0ejQ+vyFMU2MLTn8wbjYnFn2qUy2hLNbRUEufNrXXcsnyKvy+ftaVHKG0xADDSNv/xtIQ+7xtcW2N5OzxfIThuj+Ktv+c2lLe7h8HSCrrM9H7Evq/sa26IPVHlnyVtT1fwR4zGA5qxZxqvgvDMFLmfOrNXh55o5ve0SlqSp3celkrly6vLog+ib7w9dnm9PmDrFoy96WOgiAIgiDMD2sN0lxVUNYOvc+o5XTFDWow4GlTnyfGM41lqg+MwNs/hND0Xq7JXvV76TlqMDXHnDu6lrP9tWq6R4M0lvrYduE7bF1dPKMfOz6jP/xPMwO0CEaAoo5/58Jrt9HTuQ+/b5BydzXnNp9PecUSsMffqx39F3HnM6eZCKp9iF1jBn//rJ0vfdCJx+flPFsDZeHk5XhjtgZODnjZ2KZm0PYcH6R/bJJaTxEb25YSslfwVucB/L4enO5qGprXUe5ZwkiohJ64+CW0lHkS9GY5q2mtLjGNZxorWH3zn/JyIMyagf+BJ9xDqKiZoZV38+rE++k/0mea852hCXa83s1UUC1BGxj3892njvGHF0/wuatXLH6fRG8JfbY55+PsKAiCIAjC/LCWccjUGTWTppfEz1qVtatZm9i4b/rMLXdD+thc9M/9oTLdSMRVA+/9rznl3HFY487fjMYtcdSAWy608w+bjGT9bzYk1xvh8l9k1KcrfjBC13jyNsTqEgffu2U9DUMP03T0i3GzPCFbMV0r/w89lTfRNzaJBtR6iqJ/YTeLxc6EuZ2OtGVFP3vsUz/ey8C4n0RqSp383YdWW6JPVtO/cvIMj+0/zeC4n+pSJzeta+KWja0L2v63To/x0N5OBsanqCpx8tnNbbTVluTkmZprm3z+IOtaKsWCXxAEQRAWCGsZh4wdVYMORwlomrrqJWq2KDEeOKPO6JotNhe92QANVHyOObc/Nx43QANlc/3g70PsOKYn69ORYZ+6x83znPEGcTsdjNT/MV0rv8uUU7lNTjmb6Vr5XUbq/1h9PhFg2BfA7XSgaVrKmNvpYM/xwejP6cqKfvbYoMkADWBw3G+ZPllJ/8yRfn728jsMjPsxUDOX//FiB997+tiCtX/X4X7+9bkT9I9PYQCDXj//4/G3eLVjKCfP1Fzb5HY6ODHgTf/fIUEQBEEQcoa1BmmL7e7oTLEnQ0+IZ5CzezTePS2CAWzfHUjWO8rM67a7M+5TKhfJWvdMW0bqP8rhS/dzf/1bHL50f9R+H6zjZGd1fWKsxpNgIBMTt0qfrKR/8lAvgVD8CgN/MMzOA6cXrP1PvtkbXd4aIRAyeGhvZ1JZcXcUBEEQhHcf1hqkRdwdY4l1EozFpoNdnz02F33TVrAlLPexOaF5a2Y5z+yDA3fD4xt4cfWn+HDF06bd7B4NJ+tXbwPsCSUd0HJzxn3atn6UYnv8y5fLDp9YG781Mdb1La42h4Zut80aE312+sTYrRtbcSYceeBy2Lh1Y6tl+mQl/UjiFPc0o5PBBWt/qjYMjE8llZ3PMzXXNom7oyAIgiAsLNbbk9bzpFreFwqowYleCdXrYfCV+Di62uRlBNLH5qof3AOdD4P/DDiroOkmqN04e86hfdDxIIRnlq75wi6+2nkHjw5fHdfNptIwu7+4OrlNA69C13TdeqUaHNZcgdcoomuqgjG/jscZoLE0RGnNGtM+7ThexPa9pXR77TSWhPjC+ikq6lbT7y8lEAqj222s9v+aCwfvxT7ZidfeyCvlX6Kz/CPodg3QCITC0bJmsQq3zgXNFezvHGbYF0hbdj76vSfP8OSbvYxMBKko1vngmnouaCpfsPrzrTeLHe0b4/GDvfSOTlFerHPNqloubq20TJ+spP/OE0cYNpk1qi9z8fXrz1uQ9n9r52HTNlS6db50bXtOnqm5tKnCrXPlylrZkyYIgiAIC4S13B0BNXKaucz8YBKPDEBni81FX70Rqt+jli7adMCZWc6uR+IGaABu2xRfWfJA3CCt2B5m26X+ZD1AzWVQsxEIROsfN4rY72vDo41SqY/hC3vY523jwsoSyk36tLVtkq1tYzF6D8+PqTIaGsvGd3DhwNdwGMo8pDTUxZVDd7HHrs4z0zCiZdHU8kyzGExfMyg7F/2+U0M88kZ3dDna8ESAh/d1ETIMzm8oz3v9C6VPjK1fVsWnrjyH33cOMzIRIBg0LNcnq+g/uKaeh/d1xS151O0af/becxas/WZtcDlsfGhtQ86eqbm2SRAEQRCEhcNaM2kDL0F4Kv6A5qAXRo9B2Yr4+OBeda3ekD6WrT7TnI9vwOxVxwCuPL6Dbq+DxjIb264qZWu7kXGbjsQcRh3B5w9S7tvHuXXOOetXvXQBzql3ktrpdy3lP5ueBQPWLp3Zg/dG51BSzOcPcnLAy7Ia5USXruxc9dt/c4RNrif4ypIHaNQH6A7UcO/pW3kxdB0/+uSGrOrfdbgvekB3ebHOxze28ME1DTltfyb6hb6nok/Wv35qmGeODjAwNkWNx8XN65tZWule0PYP+QLR57G61Mk159Zx08XNi/JM+fxBnA4b61rmflaazKQJgiAIwtyx1kyafxhc1fGxiElG5YXx8XAgeUxkFstWn2nOonp1AHUCmt3N7o+egrrLZ4KGkXGbxvw6lfoYsb5rxbodv28Q7G1z1qc70DoYNDASEiTGdh3u44EXO+gfn6K21MWtl7WyeVWdadlUsYihwXkNZUllN7me4NvN9+G2qb05zc5+vt18H3d2AmyYVZ+q/l2H+7jv6WNRs4bhiQD/+twJXA57Vu0v7/0lS05+A32qk+X2Bl4p/zIs/VRGbcr0nog+9/o1jWV88vLl0ZhhGDx7pG9B2795VV302YvUb2bykUn9r50c4qnDfYxOBKnxuLh1Yyub2mszblOxbmfIZ+4yKgiCIAhC7hHjkGz1meZsv51k4w/UzODQvnm3yeMM4DM8cbGJQAinuxpCPnYc8nHF9/tYfu9prvjPFnacKI+W23HIx2cfC3DNz4r41I/3sutwHwFXc3IbgYCreVZDgshAp3/a3KB/fIr7nj7GrsN9SWXN9LHtT2Vo8NWGn0QHaBHctim+2vCTjPSp6n9gT0eSm95UMMwDezoy0pu13939EM1Hv4Bz6h00DEpD3Vw5dBflvb+cd04rGG+IvrD0uw738av9PYxMBDGA/jH17/KJQ6fFOEQQBEEQChRrLXcsBOMQs1iimUjrn8C5f5Gc87VtEBpP7pezCtbeM682eQ0Pz4+tjTP+qHDrvLfVzvZHX+TBQzoGWrSqIrvBFy/VmAza+P6rYaZi3s90u8bd57/OzfxDdE8aQFArZk/1P9JV8REgtSHB9icOm7rSlRc72PaBVTkxNPjjY8vVfpkEDDT+o+XYvE0m/vrh/Skfu7+74bx5GTLU/m4V7kBXUr5xexO/bHq2YI0zzgb9ax1DPHW4n5GJABXFOu8/r441jWWWaf9c9P/01DFGUpiQ7Lj9CjEOEQRBEIQCxFozaQCRAYeW8LtZ3CCzWDb6gT1w8gE1QAN1Pf4D6Hw0OafZAC2imWebDMw3/j92cDBpgAYwGdL40evw8wPBuAEaqHOY7j2ynjca7yVYtBQDjXFHE7sr/5GTZVunqzYzFFCxVLbhIxPBpLJm+kwMDXyORtM6vI7GjPSp6i9PMUtQXqxnpDdrf3Gg2zRnSah73jnn0ifRm+tf7xyenllSA5fhiQCPvNHN/s4RS7R/rnqzARqoPW9zyykIgiAIwkJhrZm0QjQO+d0HZgZZsTir4aqH43OmLFsF73sCunfCkfthslfFVn4WlsacwTYH45DPP7iHvtiNajFEhm1m37wG/OLTG+dl0vCpH++lf2wqKWetx8WPPrkhJ4YGy0Z3cPmZr2ELx8/0dbd/N3rw9nxNGmL3pAE4HTY+f/WK6L6gubZ/66krcPmT9/j5XUs5fOn+eeUsJOON8t5fUnX8bkqC3QRczZxe9reM1H+04Nt/x8/3zfk5LaT2z1Wf6t9lTamTbR9YJcYhgiAIglCAWGsmzT+sTDliiZh0JMbD00sCZ4tlqzcbdAH4B5NzNl4PWsKMjaZDw/VqgHbgnmlzEUPp3/yOiqepf8yv49bG4mLFup1+b+rBd43HRY3HlfKziMmBmUlBIBROir3WMZTyRTBy6HI6fWIsXf1H3R+mc+V38bumZ/rsjTxfeU90gDabPlX9m1fVccfVK6j1uNCAsiIHd1zdFh2gzaf9vcv/lrCtOL68VszpZX8775xz6VM+9eW9v6T56BcoDXahYeCceofmo1+gvPeXBd/+AZPnFIjGC739c9XfurF1egnjDC6HjVsva804Z7FuZzTFjJwgCIIgCLnHWu6OEeOQ2NmpWJON2LjNZPmaWSxbvbMq9UxaYs7ay0FzQM9ONVtWVA8NW6DmEtj/9xCejM8RnlQza41bUtbvcQbwhZONQ2pLtJQzaZFBU+LMUWRAFWtSEPsXdodDAyP+Ze9Azwi/2t8Td55ThJpSJ5+8bFl0oGOmN4vNVv9I/Uejg7LIX/2r56BPVX/ETS921mK2tqZrf0/lTbBSi7o7eh2NvF7xZcpjBpS5uicLrV9y8htxs5kAtvAES05+A0fT+wu6/TUel/nM0vQfLqxw/+ei37yqjo4zXp481MfoRCDq7njJ8ipODngzyinGIYIgCIKwsFhrkOZZqZY8gpqlCvkg4IX6TTB6JD6uVwGGWs6YLpatvvVP1B602IOqbS5Yc5fKnZiz4YPQ9v/NxHzTM2eTveZ9nuwFw1Blhw/CqV/A1KAa4LXdRmPZBvZ523D6gxTrdiYCIXz+IH/xvmV8c+dJ4reJGayuL+LHL55kcNxPicuOw2bH6w9RU+rk1svUi5vPH2RjWzVv96s9dJG8an+WWvoUiT31Zp/pAK2+zMW3b7oAt9OBYRgp9WaxudRf6Pqeyo8wXPdHTARC9I1NogH6LPpC7xOkP6oh0/qfOHSaB186xZAvEH3+Ll1enff237y+mX997kTS0tZPbGxRZwxa4P7PVb+pvZbN7bXUeormldPnD7JqydyXOgqCIAiCMD+sNUhzVUFZO/Q+o5YoFjeoAZZn+jywxHimsWz05/4FlJ4DB+9RSxSd1WqAdt5fwtjxzHM6q5Q+EWcVdP8GvCeh46cQmp5tmzwNb95L6dpv09JwDXuOD9I/Nkmtp4iNbdVcfW49AP/0u5P0ew1qSzQ2tdfy6P4z0ZfT8akQLoeNv7n+PDwuB/1jk5wc8LKxrZrWajWLlJg3MTbsM18C1Tc6xTm1pbPqU8Ui9X/v6WPsPHCa0ckg9WUu/uy95+CdCmWsz7b+xdIXYpti9efZGigLJxuj+ByNXNhcMav+mSN9PBkzwB8Y9/Pdp47xhxdP8LmrV+S1/X2jU1xzbi0vHD/DyESAujIXm9trsUH0+S/0+78Yz9R8nB0FQRAEQZgf1jIOmTqjZtL0kviZsLJ2NRMWG4/MULkb0sey1ecq58gBtQctdsmjzQXnbYPmG+GZG0xn28LOWo7Ub2N573dx+jtRZ7GFCBUt5XD9VxlvuDn61/DP/PTVqKNbLJVune9//D1xfzU/p7aUt/vHcTsd0XhkJij2r/GpcsbOpKXTm8Ui9T+4p4P/eLEDf8yMh27X+POrzuEDq5fMqs+k/YWoL8Q2Jeobhh6m6egXsccseQzbinl7+f/mzaIbZtXf8bN90fP0YqkpdfJ3H1pd8P23mj7bnD5/kHUtlWLBLwiCIAgLhLWMQ8aOqkGPowQ0TV31EjUzlRgPnFFnjM0Wy1afq5xLt8L5d0HREkBTM3LnbVNxTYPJPtNbovn7ae/8Oi5/JxqgEUIDHJPvcO47X6Zh6P+iaRpup8N0MAXK2dDtdETLuZ0O9hwfjP4ciY9MBBhOKHvNeXVJpgROh43N7bUZ6c1ikfof3tcVN0ADdUzAQ690ZqTPtv7F0hdimxL1I/V/TNfK7zLuaMJAw+9aSufK7zLR9LGM9AMmAzSAwXG/JfpvNX22Od1OBycGUmxyFQRBEAQh51hruaN/GFzV8bGIO2PlhfHxcCDZY94slq0+lzkbt6j/GYZa4tj4wZlyRfXTzo+J2LAZ5i+89mkjh4jJRnmxI+Vh07FEnOTOayiLiweDBkZCB85vKCccMnju+CADY1PUeFx8YmMLtuk8s+nNYpH6B8f9mBHrzpdOn0n7Xzs5xFOH+xidCEYNFTa112asz7b+hcqZD/1I/Uf53cQ1GBisX1Y9J3068w6r9N9K+mxzFut2hnzm/x4FQRAEQcg91hqkFaK7Yz5ymunbb4cD30wwKClKdoRMINbg4drV9Tzyenec0Ydu17j2vPo4zVyd5C5ureRPrzwnGou4I6bT7zrcxwN7Ougfm6K8WOe2K0NRF8hI/dWlTgZMBmqxxwdk44S363BfnDNl/9jUtONliKWV7kVz8is0d8B86G/d2JrSXdQK7beaPtuc4u4oCIIgCAuL9fak9TyplgeGAmDXQa+E6vUw+Ep8HF2dzGwE0sey1ecjZyr9wKvQ9bCy/NcroXkr4a5HsZkZjkxzhgYeaXke3W5Dt2u8dmqYxw/2MjIRoLxY57o19VzcUkkgFCYQCqPbbVS4dS5ormB/5zDDvkA0rpY1anFlzWKz6feePMMjbyQPFj90QQMXt1ZG9T96/m1+9vI7SeVuXNvImsayedcfKftPTx1jxOTsp0q3zo7br8hb/2fT5yNnIeoPdo/y2zf7GJ5+Fq9ZVcvFrZWWab+V9NnmrHDrXLmyVvakCYIgCMICYa2ZNECNaGYuMz+YxCMD0Nli2erzkdNMX3MZ1GwEAmqZpE3HTxGOk/+Ow0ieUfOFXXyz6xY02wgXL6vEAC5uqeCC5nKCQQOHQ8Nh0wADNNDU/0UXOhnTdcfGNZOyZrF0+idNbPsDIYOnDvdF2wmwflkVXn+IJw/1MjIRpKJY54Nr6qPtT1f/k4d6uf/pYwz5ApQXO7h2dT3rWyvjypoN0IDo3r189X+xci6Gfn/nCE8d7mdkIkB9mYsPrqmnvd6DhsZFLRWsX1aJBgTCxqzfab7bH9vWimKd96+u4/yGckvf/1zmFARBEARh4bDWTNrASxCeil9CGPTC6DEoWxEfH9yrrtUb0sey1ecj5xz0R7pOU3zmOeoHfoZj8h3C2LATpitQy72nb+XR4auxTY8Dy4p1rj2vjk9evjyqjxwGvXbpzBlIsYc5xy6DMis7H/3XHzlo+tKnAY/ecWXW9f/mYA//8uzbcQNBl8PGh9Y2cFFzRbTsp36813xfVKmTbR9Ylbf+z6ZfjO8kH/ohXyBpSaPTYePzV6+ILm0tlPabtdXlsHHHdFuteP9zmdPnD+J02FjXMim/ANAAACAASURBVPez0mQmTRAEQRDmjrXcHf3DypQjlohJR2I8PL18cLZYtvp85JyDfsyvE6jcwOFL99O2/9es2P8oy/f/mivf+nceHb5ayQz1l/CRiQCPvNHNrsMzTpHBoEEgFO+gGDEUMDP+SCw7H33snrJYIvFs639ob2fSTN1UMMyTh3rjyt66sTXJmdLlsHHrZa157f9i5FwM/QN7OuIGPQD+oIoXWvvN2joV01Yr3v9c5izW7YymmHkWBEEQBCH3WGuQFjEOiSXWZCMWmz695yshNrQPdt0Aj29Q185H5qbPJDbXNmWh9zgD+AwPQMrBTyyBkBH3kuxwaOj2+Mcg1lAgFrOy89HfurEVlyNeEzGNyEX9qezdRyaCcWU3r6rjxosaKS/W0YBaj4s7rl7Bpcur89r/xci5GPoBk1lKiHfnLJT2z9ZWK97/XOYU4xBBEARBWFistSfNs1IteYT4g6PrN6mDo2PjehVgqKWDkdjwQeh4cMYhcfI0vLkd1n5L5ZlNn2lsLm3KUt9YGmKftw2nP8gnNrZw39PHk84WS2RgbArDMJgIhKIDFJ8/GHdw7ca2at7uHweIxs3Kzke/st7D7bTxwIsdDIz7qXTr3HJpC5vaa/H5g1nXX1XiZNCb7ApZ6dapcOtxZTe117K5vTbp4N589n82/WJ8J/nQp3LnrC51pn3+FqP9KZ1ES13RZ3JsKsjnHnyNM14/NaUubt7QzKolnoJof76fKZ8/yKolc1/qKAiCIAjC/LDWIM1VBWXt6qDoiR4121S/CTxt6vPEeGKs8+F4C3tQe9wO/x+45qnZ9alinY/CK7eDf1AdQr3mLmjakrneLJZhn0rrN9FStoQ9xwexAR+5qJFdR/rpG51C09RSx0TKi3WePdJHraeIjW3qfKs9xwfpH5uMxlqrS0zjmcZaq0t48lAv9/3uGMPTRgx3vG8F166uj7Z12wdWxelj25RN/Z/d3Mb/fOJI3AyBbte4/eoVXNBckXH7s+1/NvqFatPYVJB/fe5tekenKCtysOX8JXzu6hU5qf+ac+v4r9e6CMY8hC6HjWvOrZv1+Vvo78SsrbpdY8OyCk4OeBmbCsY9U/3jU/zLs2/z19edG32m3+3P1HycHQVBEARBmB/WMg6ZOqNm0vSS+FmnsnY16xQb950GDHA3zMR+uxlznzINNj02u94s1vFLOP6DhPPLXGp2ruzc+eWcpU87OqrZvjtA92iYJaUGN66t5+o158T91fuc2lIe3NPBf7zYETezpts1/vyqc/jA6iVMBEL0jU1OL/UrStK/3T+O2+mIxs3KptIf7/dy7+OH8Yfi6/6TS5byBxc0ptU/9WYvj7zRTe/oFDWlTm69rJVLl1fPuf5/3nXcdNYjE322/c9GvxBteunEID949m3Gp+KXujkdNj62oZlLllXlpP6XTgxGZ0zry1zcuLaRa86rX/T+F+t2njh0mgdfOsWQL0BNqZMNyyrZe3IobnY38u/kcw++lnJ29ps3rnnXP1M+f5B1LZViwS8IgiAIC4S1ZtLGjqpBS8TxMHLtfSbeCdFRAoEz0z+vmIk5K9UZY4k4q5LzmunNYh0/M5+dO3gPXPXw/HKm6dOOY27u3D3FRFCFe8Y1/n1PHyXuCjavqou6tO05Psg159XjKdJ5YE8HA2NTUXfHD65pAMDtdCgbegNaq0sBePnEGX784kkGxv3UlDr55GXLonkTy6aKAdz3u2NxAzRQ++F2vN7DH72nJW39sQPLgXE/9z99HA2NyhI94/o9Lgffu+ViU9e6TPR7jg+yrKaEl0+cSbp/EXfMTPSR3+dy//KRM7FP9z99PMkoA5SxxyOv99Be58lJ/VevqufqVfWmToKL1X+308Guw33863MnovdgYNzP797q546rV0Sfs4i7odvp4IzJAA2UK+SwL7Dg7V/oZwrgxICXdS0ymyYIgiAIC4G1jEOydXdsvB60ROOOIqi7ev5OjGaDPlBLH/Pg7rj9lbLoAC3CVIg4M5CGoYfZ8vZlXLKnlj8fvob/uu4kj95xJX95zUrWNJbFaWOd3HYd7uO+p49F9+YMjPu57+ljUTfIubjGDadwgks8myxR/8CejqQ9dRGXvYV20nvpxCD3PX2M/rGpvLpjvtYxxKd+vJcP3/c8n/rxXl47OZRXd0AzJ8NYRiYCBedOmGt9OjdHM31NqbkpT3mxwxL9F3dHQRAEQbAW1ppJi7g7xp4dFuuEGBu3mTiR1V4OmgN6dsJkLxTVQ9ttULI8M71ZzFmVYnauev450/Sp22v+lUVc6Mp7f0nT0S9iD0+oZky9Q/PRLwDgcLwfjHjLeYdDi8ZmsyH/4fMnGJkIUOtxcevGVjavqovTR5gIhKgo1k0HauUJDnGJ+nQue2Z1pao/4loXO5M2V/32Jw4n3Y+IO2bknK9s6z/QM8Kv9vdEjwzoH5viV/t7sNk01i+rznmfJgKhlPc4QnmxntYJMNv6C0E/1+fs5g3NpmfvXbu63tRJsdD6n21OcXcUBEEQhIXFenvSep6EwJCafbLroFdC9XoYfCU+jq5ORzYC6WPZ6gdehY4HEvakOWHtt6G4MfOc/buhc4cq76qB1V8z1V/xUA1d48kDtVo3PLR1kubDn8MZ6Ev6fNzexGPLdwMagVCYQCiMbrdNnxOmYn/zyMGUt163a3EvqLpd48a1jWxYVpmUs8Ktc3p0iv/x+FtJmpvWNXFBU7lp/YFQmH966ljSbBuogcPXtqxK2/7Y+i9ormB/5zDDvkDasun0m7bvSnk//u6G83JS/3eeOGI6mK0o1vnyB9pz3qf9ncPcteOg6T2O/Y4ubqnMyz0tFP32Jw4zkjglneY5izzT9z99jCFfgPJiB9eeV2/6/Bdi/7PNWeHWuXJlrexJEwRBEIQFwlozaYAa0cxcZn4wiUcGoLPFstHXXKauXQ+rGTVnFbT+CTR/GAZfzSxn/4vxRwNMDcDvvwbn3AYVa+LKbnvPOHc+X8ZEaOav90V2g09dpDEU8LA80I8ZJaFuDEDDAA009X9xsfJih+mLq6aRdDh0IGTw5Jt9rF9WaZrz2tX1nDrj5ZHXexiZCFBerHPdmnoubqkgEDZM69fQuHZ1HY+83p00uLt2dd2s7Y+NwfQ1g7Kp9JVunSGf+YAxV/WnWhY6PBHIS5/Ud5N8j0Etabv+wiWsa6lQJfNUf670r3cO89tDfQxPP1/XrKrl4mWVGemvWVUXN4OZyXN27ep66stcjEwECAYNHA5tUfs/V322OQVBEARBWDisNZM28JIy5YhdAhj0wuixeJMNgMG96lq9IX0sW30ucr5xl/mSyaJ62PxYkn5H7xq2PztO92iYxpIg29aPsPXSNarMrhvU+W8J+F1L+c+mZ+MMEWDGTGPt0sronrTYJX4uhy3l/iUN+ObWNUk5zUwiEutKF/vNwR5+uucUIxMBamKWVmaqz7b+iP6dIV+cuQSoF/kvvG9ldLljtvV//N9eSjlz+NP/fmnO+xRrnPHAng76x6YoL9a57crlOevTQuhTPatmxh+p6t91uM90Ca8V+j9XfbY5ff4gToeNdS1zPytNZtIEQRAEYe5YaybNPwyu6vhYxGSj8sL4eDiQ/Odfs1i2+lzkTGU+MtmXXNaAravdbF09bSrS/0J8zvbb4cA9EJ6ckdmKOb3sbwlOGBgJDQgGZ2KRl/QHXuygf3yK2lIXt17WGn2ZT6TG44rTR4gYEvz/7J17dBvXfee/A8wABEAQoPgSHyIlUSItS7JF25LlRInlKrKdNrGdND5O2q3dOIl226hps43jvOqVnaZN4/R0N1V6GnePW6tttm5ax7KT9dqKavmRhrYSUbIky6SepPgQXwJIEENiBsDsH8MHQAxBkAOAGPH7OccC+eN8f/c3M5c0Lu6939lQnWpSkq79Ke68fiWKRBs+2FQJQRAWrDfb/pT+zutXwinaE9wdRexqrpy+Ttlof1dzheGMzq7mipyc05R+5+R5/OrSVWjQkva/5fKaZkufbv/k529vzKj9nc2V8DpFS57/QvVmc7okOwKyscMlIYQQQrKPtQZpZo1DFmjSkZE+GznnMh8pqkw9dr72az4MxCJQO56CqA5CddbhyurHMFJ1P8TuwLyGAjubK7FtzYqUT9iNZi0e3N5QkCYJ2dTvTBiUTc0wZLP9m1aXwmYT8NrZIQyFIij3OnF7Uzm21PkL9poUgn6hxh+FVn++9TQOIYQQQqyFtZY7FqJxSDZyDrcCl2aZj9iLZvakLaL9Ef/teKMzljWTgtO9o/jZmVn7fxpKC9Ikwer6bOT020OoFXvhFkKQNS8C9nrUV69CV99llMa6puPd0RqMxEoK/ppkw/hjSn+kfRCHzvRjZDwKv0vCXRur0prZFOL50ziEEEIIubax1kwaAH1EMvMy84VBPB/GIdnIWbYd0GJAz/OAkujuWKs/7HqR7WfTpGBLvX/SJARQ4xqiUS1nJgdvX7qKb/70DPpHIxkZQhSiSYNZvZmcPnsIWzwdGFGdCCheeB0qWjwdKHZIKPN0oHfMnhRvCzdhKF684PZXjz2PlsB34Y72IizW4FclX8Jl/315uaaLMf4A9L518MSMaUpwXMVzbT2IaRo2VfsKuk8sZZ/K/0d5hBBCyPLGWjNp16pxSA707w0oGHG3WM7k4Ej7AP761XNJD7ROZwhRaPVnQ282pzD8Fhw2FU21K6djc/Wpjp4rUOIStLJb0+ac3b6v/0eoO/sF2Cafxwfoex+7138Pr6sfyss1XYzxx5OvtE8/rD2RCq8TTz+0NSvXvxD1NA4hhBBCrIVt/kPmRxCEuwVBaBcE4ZwgCF/JRk5DlKBuypHIlEnH7Hh8cvnffDGzejM5e18CTnwNOPp7uitj70tZOydFHoZLsieFo1ENaiw+b2zKUGAp9AdaO5MGaMCMIYQV6s+G3mxOtxBCSJm1f2iOPhVSJLiF0ILbX3npiaQBGgDY4uNYeemJvF3Tnc2V+OKu9fgfH9mApx/aOr13MJ1+2GCABiQ/RL0Q+8RS9ymXZMfoHI+LIIQQQkj2MT1IEwTBDuD7AD4M4HoAnxIE4XqzeQ2ZMg5JJNGkIxGbNLlna56YWf1ic/a+pLswKgH9+4kr+ve9L2XlnBzuMoyrsaSwKAqQ7LZ5Y4mGAvnWz2cIUej1Z0NvNqes6UsZk5ijT3kdKmTNu+D2pUg3jJAi3QV5Taf0ZcXGe6rKvc68tG/VPkXjEEIIISS/ZGMmbRuAc5qmXdA0TQHwLwDuzULeVLzrATWsL93SNP1VDQNVt6fGpRW6gcd8MbP6xebs+H6STT4A/fuO/Quq6flLFXj/s7VY850reP/fDuD5kwFADaO6bhNkJQpZiULTNMhKFD6XBL9bmjcmK1FsbyxbEv1cb6LLih2WqD8berM5A/Z61BTHMuqTNcUxBOz1C25fddYa3ifFUVuQ13RK//GWWjjE5D97kl3AA7fUFXSfWOo+JStRrCn3GN5zQgghhGSfbBiH1AK4nPB9N4BbZx8kCMIeAHsAoL6+fnEtOVcAJU1A/2v60i1Xtf7G09uo/3x2PNOYWf1icho8cBoAMNGvn2MGNT3fswZffdOP8ai+r7BnNI5HX4lAFlfjt96/EmtjYbSeH8ZgaAIV3iJsb9SfBZVJrKHMk/Gx2dTvuq4Szx/vTbL7F20Cdl1XiRsmbemz1f7lwDiOdAxiYNKg5H2NK3B7U+WSnn92cq5CsUPKqE8WV92O+pKVC24/6Pwj7FL+BKI2s+RRRRGO+R+Z8z4t9TVtKPPgt7c3YGRcxUunrmB0IoqqEic+94G18DpFvN4xUJC/E4XRp8oW5exICCGEkMVh2jhEEIT7AdyladpnJ7//HQDbNE37g7k0piz4h94CJI++tyYm6zMDJU3AaEdyXL4CQAPc1eljZvVz5Rx9D3j320BkECiqAho/C/g2zxz75gPGA7WiKuDWv8+opvf/7QB6Qqn3r8zjwHO//z5cGByD2yHCJdkxrsYwEJqAAKDCW5Q2JitRrK0oXjL94TP9OHiiF/2jEZQXO/DgbQ24dU1ZVtt/6+Iw9r96PsWg5HMfWIObG0qX9PzN5lTkQd3N0eOft5+PhYNoCzfB4a5YcPvu3mdR0/VNuNReKI5a9K95DH2lHy/IPrXc9WZzykoULfWltOAnhBBC8kQ2ZtK6AaxK+L4OQG8W8qYSOqu/wZxyp5t67X8t2bVO9OjW9QAgrksfM6s3ivUdAs58Z+a5ZxNXgDPfBRo+BZRv04+t2AFc/rfUc6z4gH6OGdTUazBAA4CrYQWt54eTXNvcDhEj4yqgAQ1lxWljAJZUv2tDFRorilNc57LZ/j+2dhkalDz7y258YH3Fkp5/pjnfvnjV0N3QE+pC75gdTb75f096x0IojXdBc1QvuP3x2k/iOe2uJCdA9xz3aan71HLXm80JABeHwmip52waIYQQkg+ysSftKID1giCsEQTBAeCTAF7IQt5UrOLueP5/Jz+YGtD3m/U8P3Ps4Jup5zcVz7CmmhLj21de7LS0E10+9OkMSpa6/kxyHmkfwP5Xz+lvqAEMhiLY/+o5HGkfyIu7Y76vCfV0dySEEEKWE6YHaZqmRQHsBfAygDMA/lXTtNNm8xpiFXfHiX7j+pXAzLFzHTPRn3FNj3ywGM7k91dwijY8sLXO0k50ZvRH2gfw8DNH8d1DZ/HwM0dxpH3A8NhEN79Eyr3OJT//THIeaO1M2rcHzDyqIB/ujmbrpz6/ero7EkIIIdbCWg+zjlzVlxKqAX1GyS7pbodltwDDv0yOQwIEAJqaPmZWbxRr+zIQDaXW71gBbPkOnj8rYfvAl7BSGjQ+5pa/ybimZ8+twJNHvRiW46hwx/E7N4rY0rgG9dWrcLI7iKCsom7kx7hl5C/hifVCFmvQ5v8SzrrvgWS3QbILAASosTjUWByS3Qa/W8LmOv+0fipudGwh6Y91BvDiyT6osZk+LdkFfHRzNW5qKM3o2HtvrMHO5oqU9tfLL6Al+F24o70I22vwS98fo9v3sZycfyY5v3Fw7s9BfnB/A7Z4OjCiOhFSJHgdKmqKYygu34ixodPoHbNPx31SBMfDTRhUiqHG4jjdO4qfnRlAcFxFhRv43I0K3rfag4C9HvXVq9DVdxmlsS64hRBkzYvuaA1GYiUF2yeoz05Ov1vCjvUV3JNGCCGE5Ils7EnLM0LSy8wXBvGpAeh8MbP6xNjQ20B01gwYAAh2oPbjeP5sEb76Zgl2ex/Et+v2w21LWHYnSEDtvQuq6YF1Y/hIo4qeiB8hxam/Ifd0IGb3QwOweux5bA98fdqFzxPtwfbhryEWBy7774MGQIAGCICg/4OpYYs22U5i3OjY2bG3L13FN396Bv2Trom7mitw0+rSjPWLbf9w+0DSoAsA1JiGw+0DKe3fUOeHzS7gZ+/qA5KpOrfU+6fbrw7+GDv7vw1PtAd6i/pPimM92BH4OlrtArp9H8v69cvkmvhcIkbGoyndzOeSEIh5cTzchFqxF6VSCHLci7ZwI+pLVqIrrKI03pUQb8BIzAsIGk52jyQNXAdl4C/fdiAmqPidzR0odkgo83Sgd8yOgKLP1rV4OtAWbsJQvHjR97StK4D/d7ofI5P34e6NVbip3p/1a5pr/cnuERxuH8TIuAq/S8KHrq/EpmpfwdRvNichhBBC8oe1ZtKG3gLikRnjA0B/5tPouWRDBAAYPqq/lm1NHzOrnx078hFj10axBGj5C7z/X6rRE9bHxvf4X8WXVx5AjTSEgVgFVt70B0DNh7NyTu8NKBhxt6ClrQWOSOITEnQU5yq033oSJ7oDScYPACArUVwaCqcYdxgdOzt2pH0Af/3quRTXxL13rEOpR5pXn0n7AVnFgdZODIUiKHFJ2L2hEg+9bw3u2f+m4ZtJAcALe3dkVP9U+/EL/4xtQ1+BPT5ukHHmGv5r7etZvX6ZXpOpPWmRDK9zJjU9/MxRDBrs1astseHnn/UY9smOnitQ4hK0slsNc87X/jO/uIiDx3sNZzQfet+arF3TXOsDsjrn/djZXLnk9ZvNKStROEQbWupnYpnCmTRCCCFk4WTDOCR/WME4ZK69ZtEQEFfRG57ZRPZC8A7seO/vsfbki7jt3af1AVqWzkmRh+GS7JAi3YblTMWzbVJwoLXT0DXxQGtnVgwNjnUGsP/VcxgMRaBBdxI8eKIXR9oH0u4zy7T+qfY3Dv1F2gEaoF/DpTJ52Nlcib13rIPPpb+5rvA6pwcE2TZT6R2N58x45NC7/Yazn4fOJP8eLbXxxnz6dHsEC6F+GocQQggh1sJayx2njEMSZ5cSDRES4zaDTe5GMbP62bGiqrmff2aTUOOJTc+kJZLk1JiFc3K4yzCixqA66wxn0lRnHQDdJACakPSzREOBxE/YjY6dHUvnmpiJfr72D7cPprwZVmMaDrR24sHtDYazGQ9ub8i4/qn2vfE+w/NIJGSrxl8dPptigW/m+i3kmuxsrjScNVvsPS33Og1n0mpKbHpfDF8CXvsIMDGg9+emz8PraIEcTzUeybR9oyWbRnGz1zTX+nT9vhDqN5uTxiGEEEJIfrHWckcrGIcE2oDOf0624BckYPV/Acrfj+fPF+Grb5RgPDYzKHPZ4/jzHQHct2Yka+c04r8db3TG4O//EbYPf216TxoARAUX3iz9Vk6ML/7n4Rlb+ER8Lglf+3DzvPr52n/0uVNzdo//8ZENON07isPvDSAoq/C7Jey6rhIba0oWbKhw9/nbIE6kDm6nUFCERy/vxY8DO6dj6YxH8mnysFi9kZmK0w780a3Ap1f+B4ou/g0Qm5j+WVxwIlT/39Ba9Nlp45GFtv/dVzoQNOgvfpeEL93ZlLfzP3rpKg6d6cfIeBR+l4S7NlZhc60vY/2fvfTeHP1exCN3NtM4hMsdCSGEkAVhreWOAPQRyczLzBcGcQ2ZxczqE2Pl24DGPYCrRg84VgANn9TjEHBf4wT+fEcAtR4VAjTUemL48x2juG+dnPVz0gBcKrkPPy/9M4yJtdAgICzWorX8z3Cp+L4EaeaGAsbHzsR2X185+SZvBsmuxzPRz9e+f45P830uCQIEbKn344l7N+LIIzvxxL0bsaXev6D6p2KB9fsQFVxJbWi6nQLGxFo81veFpAEaMLVMb8DU9cvFPYGgm6DUvrYBv3F6Fe67vANrx15IOfaGOj/u3VIzfY0r3MAfb1PwgQYJ6PyXpAEaANi0CBw9/4pgzLvo+u/aWGXYX+7aWJXV859Lf6wriMd/8i7+7VjP9OxdcFzFc209ON4dzLj9ufr9rubKnNaf3z5FCCGEkHxhrZk0KxiHFEJNCcYhS2FS8PLpPvxTaxdGxlWUJywDzEb7x7uCePGdvqQljZJdwBd+bT12Nldmpf4p/c3aS6jv/hakSDdUZx1+pP43fKf9FoyOq3O+aRUA/Mue7Utq8jA75uv/EWrPfiFpj13c5kL3+u/hdfVDGbW/6fVSCAZnrUHAP6+5kLEZy03BJ+FQeqA663Bl9WN4Xf0QjncF8drZIQyFIij3OnF7Uzm21PlzbvxxpH0A3/uPsyl74qao8Drx9ENbM27/SPsADrR2YjCku5p+dsearPdJGocQQgghywNr7UlTgoCzLDk2ZWhQekNyPK6mfvxrFDOrz0XOLOgVuQ8uX6ohgDbrYKPYlKHAhuqSBeuPtA/g2aPd+nO2imcGaNlqf2NNCRrKPAnujiJ2NVdOt2G2/kS93PQA2ms/OX1e+hv69OYJ5V6n6fazfU9WXnoixQTFFh/HyktPIFq1K6P2VWctHAYmNGF7taFJxWx9deA5VA88Cgn6bJwjchl1Z7+AVf4/g1pzT5KT468uXZ3T5MLsPU3UH2jtnHOABiTvr8yk/Z2T/fBXl65Cg4ZbVpctSL/Q+heiN5vTJdkRkBUQQgghJD9Ya5BmBeOQQqgpwTgknyYFs23hB8ci2P/qOQD6G9hstb+zuWx6UDb1qX826k+nn+8NPTBjUrLUJg+zY+kcPjNtv6vuG1h94YtJexvjNheOr3gEkt02r77q4hPTA7QpbPFx3Dz6XVz23ZfV8z/VN4JD7w5gdPzM9EzutjUrUvRzmX1MkegWutTGH0vdp2gcQgghhOQXa+1J864H1LC+HFDT9Fc1DFTdnhqXVugGHPPFzOozzXn5eeCdPwGO/j5w5DeAnv+bu5rUMKrrNkFWopCVKDRNg6xE4XNJ8LuleWOyEsX2xrIF6w/8Yg4b8l905qX9XOrnfUNf7MDn72jEtjUrTLef7XNSHLWGNSuO2ozbv+y7D4FN+zEu1UGDAMVZhwtr/gqByvsz0juUHsMaPNHerJ7/y6f7cPB4L0Yml6QOhiL461fP4fCZ/hR9WfHcJhiSXcADt9QVdJ/MZ5+SlSjWlHvmvF6EEEIIyS7WmklzrgBKmoD+1/TlgK5qfTDjbdR/Pjueacysfr6cvS8BvS/MOD5O9AOnvgmEu4CNX8lJTT7vSqyNhdF6fhiDoQlUeIuwvVFffjU7dujdfnzj+dMIjqvwuyTs/bV1uOO6KsNj08bGjAcyg2MRXBoKz69PiDWUeRbc/msdA/jP81cxMq6ixu/Cp9+/Gl6nmHn9adr3uSRDF8KqEif+9b/eNn3c1HnO1l8OjONIxyAGRvX9Su9rXIHbmypzfk0GQxMI+x/BrUNfgS1xT5rgwFDVf8EHG+wIxrwZ5awoexidNQ/MxIUibK/zZ1TTzUV1hm6ZsaI6bK7zZ+38/6m1K2XGU4nGcfBEL772G9cnHbvruko8f7w35YOFkiI7vrCrCV6niNc7Bkxf/0LRm825GGdHQgghhCwOaxmHRK7q5iGSR9+3FZP12aaSJmC0IzkuXwGgAe7q9DGz+kxyvvnA3M9Ou+l72a9JDWPE04JjVwS4HSJckh3jagwDoQkIACq8RdOxn57sxf95+3LSXid37QAAIABJREFUG1uH3YYv392MxgrPvPrE2N4fthkO1CqKndj/Wy3z6qdishLF2opiXBgcy7j9966E8HdvXEx6w+2w27Dng2tw5/UrM6o/XfuvvHsFP3j9QvJ1Em345NY6bFu9Iq3+rYvD2P/q+aSHfDtFG/5y6yn8mvK/4FJ7oThq0b/mMfSVfjxr1yQxVtz3LDb0/zlsEz1AUSWw/vNA1e0YCwfRFm6Cw12R9XuS0v7lLyUNFGM2F45Xfwd9/o9lrU/c+/2fz2nq8tojO1P0Pz3ZixdP9CEoqygvduKBrXVoXunN+vkvtd5sTlmJoqW+lBb8hBBCSJ6w1nLH0Fl90CJ6AEHQXyWPPos0O65e1Z8xNl/MrD6TnBP9xuczMZCbmiQP+rpPwe0Q4XaIEAR9sDYyriIoq0mxg8f7UmceYnHs/49zGekTYw/e1gCnmNylnKIND97WkJF+KuZ2iGg9P7yg9p/9ZXfKjIgSi+PZX3ZnXH+69u/aWI17t9RMWv3rzn9/cMc6NFV559X/Y2tX0gANAO4qPoxdoT+BW+2BAA1OpRt1Z/8Q1YEfZ+2aJMbGqh9AR9PfAx86Auz8KVD764DoQe+YHaWxrpzck9ntv1X+bUQcU8slV6Fn/fdwxvmRrPaJxH1kiZQXOwz1TVVe/PHuJrywdwee/t2tuGtjdU7Of6n1ZnO6HSIuDoUX9OeaEEIIIYvHWoM0JajPFiUy5YQ4Ox6ffLjzfDGz+kxyFlUZn09RVW5qsruhyMNwSanujrNd84wewAvoz4rKRJ8Y29lcib13rENFsf5GuaLYib13rEtyd0ynn2LKdW4h7c+1Zywxbrb9TdU+/NGudfob+oe2YmdzZUZ6o9q+vPIAXLbk+LTjYpauyWy9Ig+n9KmQIsEthBZ9TRbS/q+Eu9F+60mc+mAA7beexEjV/VnvEw9ub0h5XtnUBwVm67ey3mxOl2TH6Bx/KwghhBCSfay1J82q7o5NnwdOfQuIJ7jb2Yr0+BK7O/pckuFAze+SFuUkt7O5EtvWrDB8/lIunezKvU4MGgyGEmdWpo6dep6VbuEvYfeGyiS79Gw78RnVViMNpdQKzO24mI2afO6ylD7ldaiQ494Fn5PZa5Ir/c7mSnReDU+6O6pJ7o6XhsIFX3+u9HR3JIQQQqyF9fak9R3Sl/fFVMAu6c6GZbcAw79MjkPSnyysqeljZvWZ5gy0AT0HAeUq4FgBVP8GUPm+3NQklWLEfzve6IwhKKtQY3FIdtvkDIMANRafjp3sGcFzbT1JSx4lu4BH774OK0uc8+qNYn63hM11fpzsDuZNf/TSVRw80ZtyHvfeWIONNSXTxx7rChqeb+Jx2a7/WGcAL55MXlb68+s+jVrHYEoXH7PX4qdrfp6Ta/qBBjt8wdeS+lRY8+IduRFeYRRuIQRZ86I7WoORWMmS31Pqs6c3m9PvlrBjfQX3pBFCCCF5wlrLHQHoI5KZl5kvDOIaMouZ1WeSs3wbUPtxfYCmXAX6fgIMvZ27mjAZFgBB/2fyMC0p1lLvx8dbdCt2QJ9Z+9S2Vdh9fVVG+rljmbWfLf2Wej8+url6+jyqSpz41LZV2FLvTzr25dP9KXvw1JiGQ2cGclb/DXV+3LulBv6Ea/yq4w8RFVxJdUQFF46v+FJOr+nsPuURIrjBfR4Om4qA6oXDpqLF0wGffXTJ7yn12dabzUkIIYSQfGGtmbSht4B4JHkJYDQMjJ4DStYlx4eP6q9lW9PHzOozzdn7km67P2XDD+hLHhs+pQ/gsllTNIz3BhSMuFuSljFNPfj5xlWlaWOyEjVcrngt6L/x/GkYIQB4Ye+OvNbv6/8RVpzfB0+0F6qzDldWP4aRqvtzdk18chuuq3TM26c6eq5AiUvQym7NavvUL53ebE5ZicIh2tBSPxPLFM6kEUIIIQvHWjNpVjUOAYCO7ycP0AB9j1rP80tqHFKIJge51PtcxtswE/eu5av+kar78W81b+Af6s9NG2mYzZlOb2QcYtR/jMxECvmeUk/jEEIIIeRag8Yh+TAOAea24VcCk3vLsljTAoxDCtHkIJf63Ruq8OI7fUl2/ZJdwIPbGwqm/nwahxj1HyMzkWxek7cvXk1r3GK1PmUFPY1DCCGEEGthreWOVjYOObVP34s2G8cKYMt3slvTAoxDCtHkINf6o5eu4tCZfoyMR+F3SbhrYxU21/oKpv5cXRMj4xCj/mNkJhKw16O+ehW6+i7rz1VLMBkRANSKvRkZjzz95gX8cNbD040MXqzWpwpdT+MQQgghxFpYayYNwGzjg5kvDOJTA9D5Ymb1meSsvRfo/OdZe9IcupnIHMYfZs/JyBBAMDAEMIpdy/ot9X5sqvFBFAWINgECADWu5aT9491BHHp31oCwzrdk1ySTPjVlJtIT8SOgeOF16GYixQ4JZZ4O9I7Zp+M7vCcgACnHtoWbMBQvTmn/hROpD0+fMm7ZVOOzbJ+ygt5sTkIIIYTkD2vNpFnZOAQA2r8/acMf0B9k3fR5wFme/ZpoHFIQ+ssBGX/3xsWkpZUA4C0SsecDa7GzuTKvNWVqHGL29ySd8chXnjtp+IZfwIxxSyHfU6vqaRxCCCGEWAsah+TLOAQAVrQAm/YBdx8Fdv4EqPlwbmqicUhB6J892p0yQAOA0EQU+189hyPtA3mtaV7jkN6XgCMfAY7+HnD8a/r3UyygT6YzHikvdsKIROOWQr6nVtXTOIQQQgixFtYapE0ZhySSaLKRiE1KNeQwipnV5yJnFvQOdxnG1VhSWBQFSHbbvLFEQwHqF68fGotgLiLROA60dua1JseUcUgiU/2n9yXg1LeAiSt6XA3o308N1BbQJ70OFbJmbDzywNY6OMXk2mYbtxTyPbWq3mxOGocQQggh+cVagzTvekAN60uvNE1/VcNA1e2pcWmFbsAxX8ysPhc5s6CvrtsEWYlCVqLQNE1f7uaS4HdL88ZkJYrtjWXUm9Sv8KQ3WRgKRfJaU3Xdprn7VMd+/ZEQicQn9EdHLLBP1hTHELDXG9Z/c0MpPveBNagodkIAUOqW8FvbVmHbmhWWuKdW1ZvNKStRrCn3GPZjQgghhGQfaxmHOFcAJU1A/2v60itXtf7G0duo/3x2PNOYWX0uci5APxLzoK/7FBS5Dw53GarrWuDzr8TaWBit54cxGJpAhbcI2xt1m/NMYg1lnoyPpd5Y/3s7G/EX/++9FKOMKXwuCTfU+fNWk8/vwQhaZvWVD8JnD8/9iIiJK/petAX0yeKq23FDqQd93W1Q5GH43GW4rm4TfH69/oHRCB66rd6S99TKerM5F+PsSAghhJDFYS3jkMhV3TxE8uh7Y2Ky/sl+SRMw2pEcl68A0AB3dfqYWX0uci5APxYOoi3cBIe7Ai7JjnE1BlmJYm1FMS4MjsHtEKfjA6EJCAAqvEVpY9RnT/+rzgCe+c9LCEWSl5Q5RRs+94E1aF7pzUpN1038BPXdfwop0oNxqQbvVX4F6qpPzatX5EHdubFtj/FArWglsOPZrPTpEU8Ljl0RlvyeLEe92ZyyEkVLfSkt+AkhhJA8Ya3ljqGz+htE0QMIgv4qefRP8WfH1av6vpr5Ymb1uci5AH3vmF1/bpVDhCDob4DdDhGt54env56Kj4yrCMrqvDHqs6e/a2M1fvi52/DHu5vgm9zTU+F1Yu8d63DXxuqs1OTv/xHWXvwiHJFuCNDgVntwQ++XUR348bz60lgXesfsQNNewFaU/PtmK9IdSLPUp/u6TxXEPVmOerM53Q4RF4fCS/BHnxBCCFmeWGu5oxIEnGXJsSnXudIbkuNxNfXhPkYxs/pc5FyAPqRIKJVCSHz7NOXatqG6JOnYaFSDNiuBUYz67Ot3NlfC6xShQcMtq8vS6ufK+VrHAL77ShBDYxGUe514cHsDvE4RWwJPwhYfTzpe1Max8tITGKm6P+05uYUQAooXWPNhPdDxfX2Jo1QKbPjvugMpkJU+rch9cPlSnQStek+tpDeb0yXZEZAVEEIIISQ/WGuQNuXumPicpkTXucS4zcCJzChmVp+LnAvQex0q5Lixk964GoPbMXOLRVEANCHpWKMY9UurN4q98u4VHDozML2/bTAUwf5Xz+GjN1bjoVgfjJAi3fPWJGv6A6gB6AOymg8bPyctC33a4S7DiEXvidX1ZnPS3ZEQQgjJL9bbk9Z3SF9KFVN162+pFCi7BRj+ZXIckv6EXE1NHzOrz0XONPqwVoSeiB8hRYLXocInRXA83IRBpRhqLA7JboPfLWFznR8nu4MIyup0XLILAASosXjaGPVLqzeK/eWhDgTk1OdU+V0Sfr7hYXiiPSk/G7PX4ke1r6etqcIxhi2eDoyozuk+VeMMotg2kfU+PeK/HW90xix5T6yuN5vT75awY30F96QRQgghecJae9IA6O/+Zl5mvjCIa8gsZlafi5wG+jGtCO/IjVDi+hJHJS6hLdyEYMwLCICg/zOdTpvUJse1DGPUL60+OWY0QAOA4LiKd1Y8gqjgSopHBReOr/jSvDUFYl4cDzcl9amTciPG4pP707Lcp619T6yuN5uTEEIIIfnCWjNpQ28B8UjycqtoWLcIL1mXHDdasmUUM6vPRc459B09V6DEJWhlt07HTnQHAA24cVXpdExWorg0FMbqck/SMiajY6kvPL1R7NP/8DaGxlL3BLkkGxyiHTudr+Ar1f+IldIgwmINjvu/BN/1n15UTcLwW3DYVDTVrpxpKAt9+r0BBSPuFkveE6vrzeaUlSgcog0t9TOxTOFMGiGEELJwrDWTpgR1A4NEpgwNZsfjk0ut5ouZ1eci5xz6kCLBLYSSYtGoBjUWT4pNGQK4pFSThtnHUl94eqPYg7c1QLQJSTG7AChRDSPjKg4G78BtZ57Gde/+FI/FX8RZ9z2LrskthBBSZu0/yqRP974EHPkIcPT3gONf079P0CvysGXvidX1ZnO6JDtGx41ncwkhhBCSfaw1SJsyDkkk0dAgEZs0uT9mnphZfS5yzqH3OlTIWrJJiCgKkOzJtzHREGC+Y6kvPL1R7NY1ZfjNm2pRXuyAAN3G3+0UEZs1Ex6JxnG4fdBUTUlmIlPM16d7XwJOfUt3hgT0fWunvjUzUJs0DrHqPbG63mxOGocQQggh+cVayx2vUeOQ2WYgNcUxFJdvxNjQafSO2dOahBSiSQH1xvqTPSN4+XQ/guMqfC4RuzdUYevq0kXnfPwnZ+b8VfmLj2821Hf1XdafqyeEIGtedEdrMBIrSTrW0Exksk/OZWbjOPFFSOpg6q+sWInODU+jpjiGWOk2GofQOIQQQgghGWCtmTQAhsYFc8XzZfJhIudcZiCdykq0zTJ0mNskpBBNCoC3L13Fk6904PGfnMGTr3TgWFcwr+0Xkv54dxDPtfUgOLlkbGQ8ioMnek1dE98cMxt+l2So99tDaPF0wGFTEVC9cNhUtHg64LOPJh1rZCbSFm7CSMwz03Fn9V9RHTKsxREdTOq7hXRPlp+exiGEEEKIVbDWTNo1aBxiZAay1CYD2dA/d6wbPz7eCyU6s7dFsgu498YaPPS+NQVff7b1Dz9zFIOhCGbjc0l45M6mReU80j6A7/3HWUw9Ow0AnKINH72xGlvq/Cl6n9yG6yodizajSadvOvdZOCKXU85Pca5C+60nC/KeLCc9jUMIIYQQa2GtmbRr0DjEyAxkqU0GsqF/6dSVpAEaAKgxDYfO9Fui/mzrhwwGaAAwMq4uOufO5kp8dHM1fC4RAvR9anvvWIdN1T5DvSIPmzKjSae/svoxxG3JjwGI21y4svqxOeufqy2r3FMr6WkcQgghhFgLcf5DCogp45DE2alEQ4PEuM1gKZhRzKzeZE6vQ4UcTzYDSdzQn/gJtygKgCYkHWsUKwT96EQ05VwBfZmfFerPtr7c65xzJs3I5CHTmm5aXYqbGkoNZk1S9T53WUqfNOp/c7WfTq9VfQgAsPLSE5Ai3Qjba3B13T6MVN2ftn4r31Mr6c3mpHEIIYQQkl+sNUjzrteXPAL6J/oxGVDDQNXtwGhHclxaAUDTlx6mi5nVm8xZUxxDW7gRDiUKl2THuBqDrESxvbEMFwbHAGA67nNJEKAvPUoXKwR9VYkT/aOpg5JSt2SJ+rOtf+CWOvzg9QtJSxMdog33bqmGP0/X5Lq6TUC4LalPGvW/xeq1yk+gr/RjGAhNTM7sFcGlaTm9Jx39Ibx4og9BWUV5sRMPbK1D80qvJfpEPvVmc8pKFM0rF77UkRBCCCGLw1qDNOcKoKQJ6H9NX07oqtYHQ95G/eez45nGzOrnyDkS86Cv+xQUuQ8Odxmq6z4IALNi21Bf4kXr+WEMhiZQ4S3C9sYyNJTpsxWz45nGllr/1Q9vwKP//g4iCUsenaINn79jHS4NhQu+/mzrV5W68ejd1+Hv3riA/tEISopEfHjTSnxmx9q81eTzezCCloz6Xy702b6mlwPjeP5473QfGxyL4AevX8Cjd1+H3ddXFXyfyLfebM7FODsSQgghZHFYyzgkclWfSZM8ybNWJU36rFViXL4CQAPc1eljZvVz5BzxtODYFQFuhzj9aXTSDEOamKxEsbaiGBcGxyyt/+fWTjzX1oPhMQVlxQ78+uaV2LZ6hWXqn9JXB55D1cUn4FB6MC7VoLf+TyDXPJCz9q1wTQpB//AzRzE0pqT8mSh1S/jmvRsLvv586s3mlJUoWupLacFPCCGE5AlTM2mCINwPYB+ADQC2aZq2iJHXAgid1QdSU3tipl77X0t2UhQ9gHp18ut16WNm9XPk7Os+Bbe7ZXqvh9shYmRcBTSgoaw4bQzQP8VOdF2zon7Xhip89Mba6dt3ojuAoKwuaf3Hu4J47ewQhkIRlHuduL2pHFvq/HPqqwM/Rt3ZP4QtPq7/XO3B2otfRLdoh1B1f07qL+R7Wkj6YYMBGgAEZDWlnxVi/fnUm80JABeHwmip52waIYQQkg/MujueAvBxAK9noZb5sZC7oyIPW9YJ7lrVH7sUwMETvRgMRaABGAxFcPB4L451BubUr7z0xPQAbQpbfBwrLz2Rs/qtdE2XUl/udcIIn0u0RP351NPdkRBCCLEWpgZpmqad0TStPVvFzMuUu2MiiU6KidgkwC7NHzOrnyOnw12GcTWWFBZFwdDJb3Ys0XWN+uzpD7cPJhl3APpjAQ63D86plyLdMGIqvpj6j7QP4OFnjuKe/W/irw6fxene0UWf01Jf06XUP7i9AZI92YXQKdqw+/oqS9SfT73ZnOMq3R0JIYSQfJKVPWmCIBwB8KV0yx0FQdgDYA8A1NfX39zZ2bnwhiJXgb5DgBrQZ6/sEiCVAmW3AMO/TI5DAgQAmpo+tkB9WCtCT8SPkCLB61BR4wxCAJJjxTHESrfhjc4YgrL+HCzJbpt8QylAjcXTxvxuCZvr/DjZHaQ+i/pvHDw9Z9f603s3Gup3vncrimM9KceP2WvwfP3PF1z/sa4gnmvrSRosTj3ke2NNyaKuSf3oQWwe/g48sV6E7TU4WfYIuko+Zol7YlZ/smcEL5/uR3Bchc8lYveGKmxdXWqZ+vOlN5vT75awY30F96QRQggheWLePWmCIPwMwEqDH31d07SDmTakadpTAJ4CdOOQjCtMrSjpZeYLg/jUAHS+WIb6Ma0IJ+VGeIVRlEohyHEv3gzdCAFArdg7HWsLN6K+xAsNQUAABP0faAAEaBnFgMlX6rOm97skBA2WbPld0pz64yu+hO1DX4OozSx5jAou/Mr3CCAAx7qCeOFEL8ZVfXmY22HHJ26uxeY6v2H9L5/uN5zNO3RmAJtqfAs+p1Wjz2Pr4Fen6yuO9WDr4FcBAOeL7y34e2JW31Lvx031fqhxDdGoBlEULFV/PvVmcxJCCCEkf+RtJi2RRbs7Dr0FxCPJD4iOhoHRc8nGHwAwfFR/LduaPrYAfUfPFShxCVrZrdMx/cHBSHqYsKxEcWkonLQhf65jqc+f/plfXMTB472Gs1gPvW/NnHpf/48MH9J8pH0Af/WzDsRn/QqJNgG/eVMtPn5TXUr933jeeDZPAPDC3h0LPqc1/7kRxVGjmb5aXHz/6Xn1S31PqM+P3mxOWYnCIdrQUr/wZ6VxJo0QQghZOGaNQ/LLEhuHhBQJbiGUFCs0k4Aj7QPY+8M2PPrcSez9YRuOtA/ktf1C1m+q9uGjm6tR4XVCAFDhdeKjm6uxsaYkrX6k6n6033oSz9Sfx49qX8dI1f0AgAOtnSkDNACIxjW8dOqKYf0+l/HkdaIJxkLOyRPtNczniSXHC/WeUE/jEEIIIYSkYtaC/2MA/hpABYCfCoJwXNO0u7JSmRFTxiGJM16Jxh+JcZvBJnej2AL0XocKOe5NiomiAGhCUixxQ37iJ9RGx57qG8GhdwcwOn4G5V4nHtzegG1rVmSsT4wdaR/A/lfPJT3cd/+r5wAAO5sr59Uvpn6r6W9qKMWnJx8gDczMGiym/aFQBHMxOhE11O/eUIUX3+lLesi3ZBfw4PaGRZ1TWKwxnEkL22sWdU4LbZ96a+jN5qRxCCGEEJJfrPcw6zwah8w2CfFJERwPN2FQKc7KhvzTvaM4eCJ1+d1vbVuFh3esXbBJwJOvtGNkPJpy2XwuEY/c2WwZk4Ol0B+9dBWHzvRjZDyKUreEz9+xDitLnGn1//PwOf2ZUgZUlTjxJ7+xwVCf2JbfJeGujVXYXOtb1Dk1hg8m7UkD9D1zRyu+jfOeeyx9T6incQghhBCyXDE1k7Y0CEkvM18YxE0YhxiZhLSFGzAS8wKClpUN+YfODBiaSLxwog8P71i7YJMAowEaMBnPQJ9Pk4OT3SM43D6IkXEVfpeED11fiU3Vvry1nxhr6wokDZYDsoonX27HA1vr0FTlnVO/+/pKPHesJ2XJo90m4HMfmPv+ban3Y1OND6IoQLQJEACo8cX1qc6S+wAAm68+CU+0F2GxBu+seASXS+4FZuXM5zWlvvD0NA4hhBBCrIO1ZtLyaBySqUmImQ359+x/0/DNjwDg2x/fvGCTgIefOYpBgyV4FV4nnn5oa8GYHARkNWlZJqA/32rvHeuws7ky7yYLT77cYTgjVl7swN//7ra0+md+cRE/fadv2t3RWyTiodsasKrUvWQmD9RTn+2cNA4hhBBC8guNQ+bQZ2oSYmZDfqJZRCLlxc5FmQQ8uL0BTjH5ljpF2/R+p0IxOTjQ2pk0QAOASFSP56P92bG5liwOjynz6jdV+/Dlu5rx4t4deHHvDvzws9tx5/Url9TkgXrqaRxCCCGEWBtrDdKmjEMSSTT+SMQmTe4tmyc2h97rUCFrqSYhkt02byxxQ366Yx/c3jC5/2MGp2jDA1vrMtLPju1srsTeO9ahvFjfN1Je7JiencpF/YvVz2W4MRXPdfuzY745DBHKih0px+bj+i3FPaH+2tabzUnjEEIIISS/2Pft25f3Rp966ql9e/bsWbjQ7gbGLurrAQVJH1ipYaDsZmD8SnI8HgPsRYDdmT42h94pjONidC3iNhdEm4BxNYZYXINLssMh2tLGZCWKzXV+DIQmAGDOY6tKiuCUbOi6KiOixlFR7MSDtzXg5obSjPRz5byjuQL/fXcTtq4uxepyz5zHvvLuFfzg9Qv4v6eu4NC7V+BziagqKcq4/sWe/9uXrkJWYim3t6LYid3XV+W8/dn6kiIRZ66EEEvYXOYUbfjU1lVYtcKd9farA8+h8cwnUX3h61g/9iMIRZWIFG/M6jlRT302c8pKFBuqS1A0a9YtEx5//PG+ffv2PbVgISGEELKMsZZxiHMFUNIE9L+mL1F0VQNVtwPeRv3ns+OZxryNGIl50Nd9CorcB4e7DNV121Bf4kXr+WEMhiZQ4S3C9sYyAMgo1lDmyejYz+xYi8/sWJsUW1tRnLF+se2/1jGQZFwyNKbge4fP4TdvGsfv37Eup+3vuq4S/36sB9GEQZFkF7B1tR+XhsILun5mr//2xjLcUOfHhBrHS6euYHQiiqoSJ7764Q1oqfdnvX1377MovfDFaTdGt9qDLX1fxltqHK8Ld2ftnKinPts5F+PsSAghhJDFYS3jkMhV3TxE8uizalMzYSVNwGhHcly+AkAD3NXpY2oYI54WHLsiwO0Q4ZLsGFdjGAhNQABQ4S1acExWolhbUYwLg2OLypkP/d4ftmFwLHXZYXmxA09+4oact//WxWEc+EUnhsYUlLol/Pat9bjz+pWWuX6L1e/quBVuNfW5ZhFHHdpvPWnJc6K+8PVmc8pKFC31pbTgJ4QQQvKEtfakhc7qAzHRAwiC/ip59Jmx2XH1qv7cs/likj6D5naIcDtECII+WBsZVxGU1UXF3A4RreeHF50zH/ohgwEaoJtl5KP9O5qr8Pe/uw1/et9G/PHuJty1sdpS12+xepfaa3jdHUqPZc+J+sLXm83pdoi4OBTO5V93QgghhCRgrUFajtwdFXl42Tnxzeks6XVaon6r6sP2ahihOusse07UF76e7o6EEEKItbDWIC1H7o4Od9mSuaYtlT6dXb8V6req/njpI4jbXEnxqODCldWPWfacqC98Pd0dCSGEEGthvT1pfYf0JYsxVR9wSaVA2S3A8C+T45B0t0ZNTYqFtSL0RPwIKRK8DhU1xTHESrfhjc4YgrIKNRaHZLdNWuMLUGPxBcf8bgmb6/w42R1cVM586U/3juJnZwYQHFfhc0nY1VyBmxpKLVO/VfW1weewJfAkPLE+yGIN3lnxZZz33GPpc6K+sPVmc/rdEnasr+CeNEIIISRPWMvdEYA+8pp5mfnCID41AJ2MjWlFOCk3wiuMolQKQY570RZuRH2JFxqCgAAI+j/QAAjQFh0DJl8LWL+l3o9bVpdCAKDGNUSjmqXqt6r+Usl9OOe+F6IoQLQJEAAgrln6nKgvfL3ZnIQQQgjJH9aaSRt6C4hHdMOPKaJhYPQcULIuOT57TeF3AAAZ5ElEQVR8VH8t2zod6ui5AiUuQSu7dTomK1FcGgpjdbkHbsfMmPVEdwDQgBtXlS44ZjYn9ctbX4g1UW9tvdmcshKFQ7ShpX4mlimcSSOEEEIWjrX2pJk0DgkpEtxCKCm21BvyraY/1hnAw88cxT3738TDzxzFsUsBS9VvBX0h1kS9tfU0DiGEEEKshbWWO04ZhyTOmCUahyTGbamb3L0OFXLcmxRL3Dyf+GmyKAqAJiQdm2nMbM5C1Z/qG8GLJ/sw9QDswVAEL57sg80m4JbVZQVffyHrj7QP4EBrJ4ZCEZS4JOzeUMlrSn3W9GZz0jiEEEIIyS/WWu5o0jgkrHnxZuhGDCrFBbMh30r6P3vpPchKLOW2+F0SvnRnU8HXX6j6Y11BPNfWMz34BQDJLuDeG2uwsaakYM7pymgE33/1HAKyCp9LxO4NVdi6urQgryn1NA4hhBBCrIy1ljsC0EdeMy8zXxjEteQfaTDeJI8540ab5zONmc1ZWPrj3UHDARoABMfVgq+/kPUvn+5PGqABgBrTcOjMQMGc09uXruLJl9sRkPUlbyPjURw80YtjXcGCvKbU5yInIYQQQvKFtWbSaByyZPqHnzmKwVAERvhcEv7pM9m7pstN/43nTxteVwHAC3t3FMQ5ffof3sbQmJJSo88l4ZE7mwrumlJP4xBCCCHEylhrJo3GIUumH5pjgAYAu5orCr7+Qtb7XMZbQ8u9zoI5p2GDARoAjIyrBXlNqadxCCGEEGJlrDVImzIOSSTROCQRmzS5N20Gr0OFrM1tHJKIKAqQ7LZFxczmLER94oAhEZdkw00NyZ+uF2L9hazfvaEKTjE5LtkFPLi9oWDOqazYeC+SzyUV5DWlPrs5aRxCCCGE5Bf7vn378t7oU089tW/Pnj0LF9rdwNhFfR2YIOkDMzUMlN0MjF9JjsdjgL0IsDunY05hHBejaxG3uSDaBIyrMchKFJvr/BgITQDAdDwW1+CS7HCItgXHzOYsRL1LsqHtchDxhNWxDtGGB7bWobGiuODrL2T9mnIPGsrcuDgkY1yJodQt4RM312Jnc2XBnFORaMOp3lHEEjqAQ7ThEzfXptz/Qrim1Gc3p6xEsaG6BEWzZt0y4fHHH+/bt2/fUwsWEkIIIcsYa1nwO1cAJU1A/2v6EkdXNVB1O+Bt1H8+Kz4S86Cv+xQUuQ8Odxmq67ahvsSL1vPDGAxNoMJbhO2NZWgo0/eyzY6biZnNWWj6VaVuPHr3dfi7Ny6gfzSCkiIRH960Ep/ZsdYS9Re6PhyJ4aHb6guqpsTYb29vwPU1Pvz5S2cyuv+FVj/15nMuxtmREEIIIYvDWsYhkau6eYjk0WfVpmbSSpqA0Y6k+Fg4iLZwExzuCrgkO8bVGAZCExAAVHiLpmOyEsXaimJcGByD2yGmPTbTmNmc1C9vfSHWRL219WZzykoULfWltOAnhBBC8oS19qSFzuoDMdEDCIL+Knn0GbRZ8d4xO0pjXXA7RAiCALdDxMi4iqCsJsXcDhGt54env053bKYxszmpX976qdjbF6/iMwd+iU8+1YpH/u0d/M2r5yx7TtQXRp9abE63Q8TFofBS/x+AEEIIWTZYa5C2AHdHIyfHQnRNo556o9ixzgD2v3oOg6EINABDYwr+/VgP3ro4bMlzon7p+xTdHQkhhBDrYK1B2gLcHY2cHAvRNY166o1ih9sHEYnOeqMd13DgF52WPCfql75P0d2REEIIsQ7W25PWdwhQA/oz0OwSIJUCZbdgbOg0esfsCCkSvA4VPimC4+EmDCrFUGNxSHYbJLsAQIAai0/H/G4Jm+v8ONkdRFBW0x6bacxsTuqXt16yC3j0uVNz/hr86b0bLXdO1C99nzKT0++WsGN9BfekEUIIIXnCWjNpAHSf/ZkXQMBIzIO2cBOUuIRSKQQlLqEt3IRgzAsIgKD/A304qhnEJl8zOjbTmNmc1C9nvX+OWYtSt2TZc6J+qfVmcxJCCCEkX1hrJm3oLSAe0Q1CpoiG8d6AghF3C9yOmScKnOgOABpw46rStDFZieLSUBiryz2L0uciJ/XLW3+iO4DjXUG8+E5f0pJHyS7gv35wLe7aWG25c6J+6fuUmZyyEoVDtKGlPvnB9ZnAmTRCCCFk4VhrJm0O4xBFHrbshnzqqTeKbawpwd471qHC64QAoKLYid0bKnHn9SsteU7UL32fMpOTxiGEEEJIfrHWw6ynjEMSZ9JiMhzuMoyosaRPg0VRADQhSW4US9w8vxh9LnJSv7z1U7GdzWXY2VwJYGbWw6rnRH1h9KnF5qRxCCGEEJJfrLXccQ7jkBH/7XijM2bJDfnUU2+Fmqi3tp7GIYQQQoi1sNZyRwCAkPQy9YW1N+RTT70VaqLe2nqzOQkhhBCSL6w1k0bjEOotrj/eFcRrZ4cwFIqg3OvE7U3l2FLnt/Q5UV/4ehqHEEIIIdbCWjNpNA6h3sL6Y5cCOHiiF4OhCDQAg6EIDh7vxbHOgGXPiXpr6GkcQgghhFgLaw3SpoxDEpk0DhlXY0lhURQg2W3zxhI3zy9Gn4uc1F+b+sPtg1BjyTPXakzD4fZBy54T9dbQm81J4xBCCCEkv1hrkOZdD6hhIBoGNE1/VcOortsEWYlCVqLQNA2yEoXPJcHvluaNyUoU2xvLFq3PRU7qr039yBwzESPjqmXPiXpr6M3mlJUo1pR7DPsvIYQQQrKPtSz4nSsw4mlBX/cpKHIfHO4yVNe1wOdfibWxMFrPD2MwNIEKbxG2N5YBQEaxhjJPxsfmKyf1156+qsSJ/tFISreuKnHi0lDYkudEvXX0ZnMuxtmREEIIIYvDUsYhQVlBW1cAbocIl2THuBqDrESxtqIYFwbHkuIDoQkIACq8RWljZvW5yEn9taV/6+IwDvyiE0NjSkqfluwCfmvbKvz65hpLnRP11tKbzSkrUbTUl9KCnxBCCMkTllrueHEoDLdDhNshQhCE6a9bzw+nxEfGVQRldd6YWX0uclJ/7ejfvngV33/1vOEArcLrxL1barC+0mupc6LeenqzOd0OEReHwkvwV58QQghZnlhqkDY6rqY4kVndNY36a1t/oLUTkWjyzwF9gPb0Q1uxqdpnuXOi3np6ujsSQggh1sJSg7QSl5TiRGZ11zTqr239UCh1DxqA6bgVz4l66+np7kgIIYRYC8vtSXvz7CCCsgo1Fodkt8HvlrC5zo+T3cGkuGQXAAhQY/G0MbP6XOSk/trRf/3504aujj6XiEfubLbkOVFvPb3ZnH63hB3rK7gnjRBCCMkTlppJAwANAARA0P+BljauZRgzq89FTuqvBf3u6ysn3/TOINkF7GqutOw5UW9VvdmchBBCCMkXlppJa+sKQInG4XbMPDlAVqK4NBTG6nJPUvxEdwDQgBtXlaaNmdXnIif115b+SPsADrR2YjAUgc8l4bM71mBnc6Wlz4l6a+nN5pSVKByiDS31M7FM4UwaIYQQsnBMzaQJgvCkIAjvCYLwjiAIPxYEwZ+twoygcQj1VtTvbK7E0w9txb6PXI8/2rVueoBm5XOi3lp6GocQQggh1sLscsdDADZpmnYDgA4AXzVf0tzQOIT65aBfypqOtA/grw6fxeM/OYOHnzmKI+0DeW2f+sLsUzQOIYQQQvKLOP8hc6Np2isJ37YC+IS5ctKzptyDtq4AACQ9ZHV7YxkuDI4lxX0uCQL0ZTrpYmb1uchJ/fLTv3y6D88e7cbQWAR+t4R7bqzG+ipvXmt66+Iw9r96HsrkIwMGQxHsf/UcItEYbm4otdw1pT57OWUliuaVC1/qSAghhJDFYWqQNouHATw71w8FQdgDYA8A1NfXL6oBv9uBtRXFaD0/jMHQBCq8RdjeWIaGMg8ApMQzjZnV5yIn9ctHf+jdfvzg9QtQY/r+0ICs4l+OdmNCjWNVqStvNf3vNy5OD9CmiETj+KfWLtx/yypLXVPqs59zMc6OhBBCCFkc8xqHCILwMwArDX70dU3TDk4e83UAtwD4uJaBE4kZC/62rgDcDjHpE961FcW4MDiWFB8ITUAAUOEtShszq89FTuqXl/6xg6cRkFP3+5QXO/D0Q1vzVtMnn2o1dPETADz9u7dY6ppSn92cshJFS30pLfgJIYSQPDHvnjRN0z6kadomg/+mBmgPAfgIgN/OZIBmhotDYbgdItwOEYIgTH/den44JT4yriIoq/PGzOpzkZP65aU3GqABwPCYkteayr1OwzrKvU7LXVPqs5vT7RBxcSicyz/vhBBCCEnArLvj3QAeBXCPpmlydkqaG7o7Un8t6n0u41XHiYOmfNT04PYGOMXkPwlO0YYHtzdY7ppST3dHQgghxMqYdXfcD8AL4JAgCMcFQfjbLNQ0J3R3pP5a1O/eUJUyOJLsAh7c3pDXmnY2V2LvHevgm3Txq/A6sfcO/ZEBVrum1NPdkRBCCLEylnqYdVBW8ObZQQRlFWosDslug98tYXOdHye7g0lxyS4AEKDG4mljZvW5yEn98tMfvXQVh870Y2Q8Cr9Lwl0bq7C51mfpc6K+cPRmc/rdEnasr+CeNEIIISRPZNPdMS9oACAAgv7PtNGBUVyAllHMrD4XOalfXvot9X5sqvFBFAWINgECADWuWfqcqC8svdmchBBCCMkflppJa+sKQInG4XbMjC1lJYpLQ2GsLvckxU90BwANuHFVadqYWX0uclK/vPWFWBP11tabzSkrUThEG1rqF/6sNM6kEUIIIQvH7J60vELjEOqXg74Qa6Le2noahxBCCCHWwlKDNBqHUL8c9IVYE/XW1tM4hBBCCLEWllruSOMQ6peDvhBrot7aehqHEEIIIdbCUjNpgPEm97njRpvfM988n7k+FzmpX976QqyJemvrzeYkhBBCSL6w1EwajUOoXw76XOR8+XQf/qm1CyPjKsq9Tjy4vQE7mystc02op3EIIYQQspyw1EwajUOoXw76bOc80j6Av3vjIoLjKjQAg6EI9r96DkfaByxzTaincQghhBCynLDUII3GIdQvB322cx5o7UQkmvymOxKN40Brp2WuCfU0DiGEEEKWE5YapK0p90BWopCVKDRNm/56e2NZStznkuB3S/PGzOpzkZP65a3Pds6hUMTw92koFLHMNaF+afuUrESxptyT57/4hBBCyPJFnP+QwsHvdmBtRTFazw9jMDSBCm8RtjeWoaFMf/MwO55pzKw+FzmpX976bOb0uSQEDZaq+VwSbqjzW+aaUL+0fWoxzo6EEEIIWRyWMg4JygraugJwO0S4JDvG1RhkJYq1FcW4MDiWFB8ITUAAUOEtShszq89FTuqXtz7bOV959wqeev0ilIR9Rk7Rhs99YA2aV3otcU2oX9o+JStRtNSX0oKfEEIIyROWWu54cSgMt0OE2yFCEITpr1vPD6fER8ZVBGV13phZfS5yUr+89dnOedfGauz54Br4XdLkm28n9t6xDndtrLbMNaF+afuU2yHi4lB4qf8XQAghhCwbLDVIo7sj9ctBn4ucd16/Ep/dsRoHP/9+PP3QVuxsrsxr+9Rbu0/R3ZEQQgjJL5YapNHdkfrloC/Emqi3tp7ujoQQQoi1sNyetDfPDiIoq1BjcUh2G/xuCZvr/DjZHUyKS3YBgAA1Fk8bM6vPRU7ql05/uncUh98bQFBW4XdL2HVdJTbWlLBPUW9pvdmcfreEHesruCeNEEIIyROWmkkDAA0ABEDQ/4GWNq5lGDOrz0VO6vOtP9k9goMnehGQ9Yc+B2QVB0/04mT3CPsU9deA3mxOQgghhOQLS82ktXUFoETjcDtmnhwgK1FcGgpjdbknKX6iOwBowI2rStPGzOpzkZP6pdE//MxRDBo8U6zC68TTD21ln6LesnqzOWUlCodoQ0v9TCxTOJNGCCGELBxLzaTROIT6XOrTPfQ5n/UX0jWh/trQ0ziEEEIIsRaWGqTROIT6XOrLvU4YMRVnn6LeqnoahxBCCCHWwlLLHWkcQn0u9cc6A3jxZB/U2MzvhGQX8NHN1bipoZR9inrL6mkcQgghhFgLcf5DCgvjTe7GccFg87tRzKw+Fzmpz7/+hjo/bHYBh88kuDtuqMSmah/7FPWW15vNSQghhJD8YamZNBqHUL8c9IVYE/XW1tM4hBBCCLEWltqTRuMQ6peDvhBrot7aehqHEEIIIdbCUoM0GodQvxz0hVgT9dbW0ziEEEIIsRb2ffv25b3Rp556at+ePXsWrHNJdly+KgMARJuAcTUGWYlic50fA6GJpHgsrsEl2eEQbWljZvW5yEn98tYXYk3UW1tvNqesRLGhugRFs2bdMuHxxx/v27dv31MLFhJCCCHLGEsZh/jdDqytKEbr+WEMhiZQ4S3C9sYyNJR5ACAlnmnMrD4XOalf3vpCrIl6a+vN5lyMsyMhhBBCFoeljEOCsoK2rgDcDhEuyT79Ce/aimJcGBxLig+EJiAAqPAWpY2Z1eciJ/XLW1+INVFvbb3ZnLISRUt9KS34CSGEkDxhqT1pF4fCcDtEuB0iBEGY/rr1/HBKfGRcRVBW542Z1eciJ/XLW1+INVFvbb3ZnG6HiItD4aX+XwAhhBCybLDUII3ujtQvB30h1kS9tfV0dySEEEKshaUGaXR3pH456AuxJuqtrae7IyGEEGItLLcn7c2zgwjKKtRYHJLdBr9bwuY6P052B5Pikl0AIECNxdPGzOpzkZP65a0vxJqot7bebE6/W8KO9RXck0YIIYTkCUvNpAGABgACIOj/QEsb1zKMmdXnIif1y1tfiDVRb2292ZyEEEIIyReWmklr6wpAicbhdsw8OUBWorg0FMbqck9S/ER3ANCAG1eVpo2Z1eciJ/XLW1+INVFvbb3ZnLIShUO0oaV+JpYpnEkjhBBCFo6lZtJoHEL9ctAXYk3UW1tP4xBCCCHEWlhqkEbjEOqXg74Qa6Le2noahxBCCCHWwr5v3768N/rUU0/t27Nnz4J1LsmOy1dlAIBoE6Yfsrq5zo+B0ERSPBbX4JLscIi2tDGz+lzkpH556wuxJuqtrTebU1ai2FBdgqJZs26Z8Pjjj/ft27fvqQULCSGEkGWMpfakAbrD48WhMEbHVZS4JKwp98DvdhjGAWQUM6vPRU7ql7e+EGui3tp6szkX4+wIcE8aIYQQshgsN0gjhBBiHThII4QQQhaOpfakEUIIIYQQQsi1DgdphBBCCCGEEFJAcJBGCCGEEEIIIQUEB2mEEEIIIYQQUkBwkEYIIYQQQgghBYSpQZogCN8UBOEdQRCOC4LwiiAINdkqjBBCCCGEEEKWI2Zn0p7UNO0GTdO2APgJgMeyUBMhhBBCCCGELFtMDdI0TRtN+NYDIP8PXSOEEEIIIYT8//buL2TPOY7j+PvT0BRyYDWZ4UDLElNL5ITZwfxpohTlT1FLUVMKawdy4EjJASUhB4YUItJMpp34N8za2qal5EGN5F+KZl8Hz02j9Tyz+5rffV17v+qp5/dc133dn2/Pc9f9fX7X73drQI4a9wJJHgBuAn4ELpnhvFXAKoCFCxeO+7SSJEmSNEipmnnyK8lbwPwDHFpbVa/sd94aYG5V3Tfbky5durQ2b978X7NKknomyUdVtbR1DkmS+mTWmbSqWn6Q13oWeB2YtUmTJEmSJB3YuLs7nrnfcCWwc7w4kiRJknRkm/V2xxkfnLwILAL2AV8At1XVVwfxuG9H5x8OJwHfHaZrt2JN/THEuqypHya1ptOqal7rEJIk9clYTdokSrJ5aOsfrKk/hliXNfXDEGuSJOlINe7npEmSJEmSOmSTJkmSJEkTZIhN2uOtAxwG1tQfQ6zLmvphiDVJknREGtyaNEmSJEnqsyHOpEmSJElSb9mkSZIkSdIEGWSTluTBJDuTbE3ycpITW2caV5Jrk2xPsi9Jr7fZTrIiya4ku5Pc2zpPF5I8lWRPkm2ts3QhyalJNibZMfq7W906UxeSzE3yQZJPR3Xd3zpTF5LMSfJJktdaZ5EkSeMbZJMGbADOrqpzgM+ANY3zdGEbcA2wqXWQcSSZAzwKXAYsBq5Psrhtqk48DaxoHaJDe4G7quos4ALg9oH8nn4DllXVucASYEWSCxpn6sJqYEfrEJIkqRuDbNKq6s2q2jsavgcsaJmnC1W1o6p2tc7RgfOB3VX1eVX9DjwPXNU409iqahPwfescXamqb6rq49H3PzPdAJzSNtX4atovo+HRo69e756UZAFwBfBE6yySJKkbg2zS/uUW4I3WIfS3U4Av9xtPMYA3/0OW5HTgPOD9tkm6Mbo1cAuwB9hQVX2v62HgbmBf6yCSJKkbR7UOcKiSvAXMP8ChtVX1yuictUzftrXu/8x2qA6mpgHIAX7W65mMIUtyHPAicGdV/dQ6Txeq6g9gyWit6stJzq6qXq4lTHIlsKeqPkpyces8kiSpG71t0qpq+UzHk9wMXAlcWj35MLjZahqIKeDU/cYLgK8bZdEMkhzNdIO2rqpeap2na1X1Q5J3mF5L2MsmDbgIWJnkcmAucEKSZ6rqhsa5JEnSGAZ5u2OSFcA9wMqq+rV1Hv3Dh8CZSc5IcgxwHfBq40z6lyQBngR2VNVDrfN0Jcm8v3Z7TXIssBzY2TbVoauqNVW1oKpOZ/q19LYNmiRJ/TfIJg14BDge2JBkS5LHWgcaV5Krk0wBFwKvJ1nfOtOhGG3ocgewnunNKF6oqu1tU40vyXPAu8CiJFNJbm2daUwXATcCy0avoS2j2Zq+OxnYmGQr0/8w2FBVblsvSZImSnpyJ6AkSZIkHRGGOpMmSZIkSb1kkyZJkiRJE8QmTZIkSZImiE2aJEmSJE0QmzRJkiRJmiA2aZIkSZI0QWzSJEmSJGmC/AlwE/UcV2ed6gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1080x1080 with 3 Axes>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"FIGURE 2.2. 15-nearest-neighbor method\"\"\"\n",
    "# Compute KNN for k = 15\n",
    "knn_grid = np.array([(i, j)\n",
    "                     for i in np.arange(plot_x_min, plot_x_max, .1)\n",
    "                     for j in np.arange(plot_y_min, plot_y_max, .1)])\n",
    "\n",
    "# knn15_result contains the x coordinate，y coordinate of point(x,y) and knn value\n",
    "knn15_result = np.array([\n",
    "    (i, j, knn(15, (i, j), data_x, vec_y))\n",
    "    for i, j in knn_grid\n",
    "])\n",
    "\n",
    "# Plot for KNN with k = 15\n",
    "\n",
    "knn15_blue = np.array([\n",
    "    (i, j)\n",
    "    for i, j, knn15 in knn15_result\n",
    "    if knn15 < .5\n",
    "])\n",
    "knn15_orange = np.array([\n",
    "    (i, j)\n",
    "    for i, j, knn15 in knn15_result\n",
    "    if knn15 > .5\n",
    "])\n",
    "ax3 = fig.add_subplot(2, 2, 3)\n",
    "# KNN areas\n",
    "ax3.plot(knn15_blue[:, 0], knn15_blue[:, 1], 'o', alpha=.2)\n",
    "ax3.plot(knn15_orange[:, 0], knn15_orange[:, 1], 'o', color='orange', alpha=.2)\n",
    "# Original data\n",
    "ax3.plot(sample_blue[:, 0], sample_blue[:, 1], 'o', color='C0')\n",
    "ax3.plot(sample_orange[:, 0], sample_orange[:, 1], 'o', color='orange')\n",
    "ax3.set_title('15-Nearest Neighbor Classifier')\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.10742982, -2.75163406],\n",
       "       [-2.10742982, -2.65163406],\n",
       "       [-2.10742982, -2.55163406],\n",
       "       ...,\n",
       "       [ 4.39257018,  3.34836594],\n",
       "       [ 4.39257018,  3.44836594],\n",
       "       [ 4.39257018,  3.54836594]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.10742982, -2.75163406,  0.33333333],\n",
       "       [-2.10742982, -2.65163406,  0.4       ],\n",
       "       [-2.10742982, -2.55163406,  0.4       ],\n",
       "       ...,\n",
       "       [ 4.39257018,  3.34836594,  0.46666667],\n",
       "       [ 4.39257018,  3.44836594,  0.53333333],\n",
       "       [ 4.39257018,  3.54836594,  0.53333333]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn15_result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "FIGURE 2.3 shows the results for 1NN classification: $\\hat{Y} is assigned the value $y_l$ of the closest point $x_l$ to $x$ in the training data. In this case the regions of classification can be computed relatively easily, and correspond to a _Voronoi tessellation_ of the training data. \n",
    "\n",
    "The decision boundary is even more irregular than before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 4 Axes>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"FIGURE 2.3. 1-nearest-neighbor method\"\"\"\n",
    "# Compute KNN for k = 1\n",
    "knn1_result = np.array([\n",
    "    (i, j, knn(1, (i, j), data_x, vec_y))\n",
    "    for i, j in knn_grid\n",
    "])\n",
    "\n",
    "knn1_blue = np.array([\n",
    "    (i, j)\n",
    "    for i, j, knn1 in knn1_result\n",
    "    if knn1 < .5\n",
    "])\n",
    "knn1_orange = np.array([\n",
    "    (i, j)\n",
    "    for i, j, knn1 in knn1_result\n",
    "    if knn1 > .5\n",
    "])\n",
    "\n",
    "# Plot for KNN with k = 1\n",
    "ax4 = fig.add_subplot(2, 2, 4)\n",
    "# KNN areas\n",
    "ax4.plot(knn1_blue[:, 0], knn1_blue[:, 1], 'o', alpha=.2)\n",
    "ax4.plot(knn1_orange[:, 0], knn1_orange[:, 1], 'o', color='orange', alpha=.2)\n",
    "# Original data\n",
    "ax4.plot(sample_blue[:, 0], sample_blue[:, 1], 'o', color='C0')\n",
    "ax4.plot(sample_orange[:, 0], sample_orange[:, 1], 'o', color='orange')\n",
    "ax4.set_title('1-Nearest Neighbor Classifier')\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The method of kNN averaging is defined in exactly the same way for regression of a quantitative output $Y$, although $k=1$ would be an unlikely choice."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Do not satisfy with the training results\n",
    "\n",
    "With 15NN, We see that far fewer training observations are misclassfied than the linear model fit. This should not give us too much comfort, though, since using 1NN  _none_ of the training data are misclassified.\n",
    "\n",
    "A little thought suggests that for kNN fits, the error on the training data should be approximately an increasing function of $k$, and will always be 0 for $k=1$.\n",
    "\n",
    "An independent test set would give us a more satisfactory means for comparing the different methods."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Effective number of parameters\n",
    "\n",
    "It appears that kNN fits have a single parameter, the number of neighbors $k$, compared to the $p$ parameters in least-squares fit. Although this is the case, we will see that the _effective_ number of parameters of kNN is $N/k$ and is generally bigger than $p$, and decreases with increasing $k$.\n",
    "\n",
    "To get an idea of why, note that if the neighborhoods were nonoverlapping, there would be $N/k$ neighborhoods and we fit one parameter (a mean) in each neighborhood."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Do not appreciate the training errors\n",
    "\n",
    "It is also clear that we cannot use sum-of-squared errors on the training set as a criterion for picking $k$, since we would always pick $k=1$! It would seem that kNN methods would be more appropriate for the mixture Scenario 2, while for Scenario 1 the decision boundaries for kNN would be unnecessarily noisy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\S$ 2.3.3. From Least Squares to Nearest Neighbors\n",
    "\n",
    "A large subset of the most popular techniques in use today are variants of these two simple procedures. In facti 1NN, the simplest of all, captures a large percentage of the market for low-dimensional problems.\n",
    "\n",
    "The following list describes some ways in which these simple procedures have been enhanced:\n",
    "* Kernel methods use weights that decrease smoothly to zero with distance from the target point, rather than the effectve 0/1 weights used by kNN.\n",
    "* In high-dimensional spaces the distance kernels are modified to emphasize some variable more than others.\n",
    "* Local regression fits linear models by locally weighted least squares, rather than fitting constants locally.\n",
    "* Linear models fit to a basis expansion of the original inputs allow arbitrarilly complex models.\n",
    "* Projection pursuit and neural network models consist of sums of nonlinearly transfromed linear models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $\\S$ 2.4. Statistical Decision Theory\n",
    "\n",
    "In this section we develop a small amount of theory that provides a framework for developing models. We first consider the case of a quantitative output, and place outselves in the world of random variables nad probability spaces."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Definitions\n",
    "\n",
    "Let\n",
    "* $X\\in\\mathbb{R}^p$ denote a real valued random input vector, and\n",
    "* $Y\\in\\mathbb{R}$ a real valued random output variable,\n",
    "* with joint distribution $\\text{Pr}(X,Y)$.\n",
    "\n",
    "We seek a function $f(X)$ for predicting $Y$  given values of the input $X$.\n",
    "\n",
    "#### Loss\n",
    "This Theory requires a _loss function_ $L(Y, f(X))$ for penalizing errors in prediction, and by for the most common and convenient is _squared error loss_:\n",
    "\n",
    "\\begin{equation}\n",
    "L(Y, f(X)) = (Y-f(X))^2.\n",
    "\\end{equation}\n",
    "\n",
    "#### Expected prediction error\n",
    "This leads us to a criterion for choosing $f$ the expected (squared) prediction error:\n",
    "\n",
    "\\begin{align}\n",
    "\\text{EPE}(f) &= \\text{E}(Y-f(X))^2\\\\\n",
    "&= \\int\\left(y-f(x)\\right)^2\\text{Pr}(dx,dy)\\\\\n",
    "&= \\int\\left(y-f(x)\\right)^2p(x,y)dxdy\\\\\n",
    "&= \\int_x\\int_y\\left(y-f(x)\\right)^2p(x,y)dxdy\\\\\n",
    "&= \\int_x\\int_y\\left(y-f(x)\\right)^2p(y|x)p(x)dxdy\\\\\n",
    "&= \\int_x\\Biggl(\\int_y\\left(y-f(x)\\right)^2p(y|x)dy\\Biggr)p(x)dx\\\\\n",
    "&= \\int_x\\Biggl(E_{Y|X}([Y-f(X)]^2|X=x)\\Biggr)p(x)dx\\\\\n",
    "&= E_XE_{Y|X}([Y-f(X)]^2|X=x),\n",
    "\\end{align}\n",
    "\n",
    "By conditioning on $X$, we can write EPE as\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{EPE}(f) = \\text{E}_X\\text{E}_{Y|X}\\left(\\left[Y-f(X)\\right]^2|X=x\\right)\n",
    "\\end{equation}\n",
    "\n",
    "and we see that it suffices to minimize EPE pointwise:\n",
    "\n",
    "\\begin{equation}\n",
    "f(x) = \\arg\\min_c\\text{E}_{Y|X}\\left(\\left[Y-c\\right]^2|X=x\\right)\n",
    "\\end{equation}\n",
    "\n",
    "Where $argmin$ is argument of the minimum. The simplest example is $argmin_xf(x)$ is the value of $x$ for which $f(x)$ attains it's minimum. \n",
    "\n",
    "Since \n",
    "\\begin{align}\n",
    "E(E(X|Y))&=\\int E(X|Y=y)f_Y(y)dy\\\\\n",
    "&=\\iint xf_{X|Y}(x|y)dxf_Y(y)dy\\\\\n",
    "&=\\iint xf_{X|Y}(x|y)f_Y(y)dxdy\\\\\n",
    "&=\\iint xf_{XY}(x,y)dxdy\\\\\n",
    "&=\\int x\\Bigl(\\int f_{XY}(x,y)dy\\Bigr)dx\\\\\n",
    "&=\\int xf_X(x)dx\\\\\n",
    "&=E(X)\n",
    "\\end{align}\n",
    "and then \n",
    "\\begin{align}\n",
    "E\\Bigl((Y-f(X))^2|X\\Bigr)&=E\\Biggl(\\Bigl([Y-E(Y|X)]+[E(Y|X)-f(X)]\\Bigr)^2|X\\Biggr)\\\\\n",
    "&=E\\Biggl(\\Bigl([Y-E(Y|X)]\\Bigr)^2|X\\Biggr)+E\\Biggl(\\Bigl([E(Y|X)-f(X)]\\Bigr)^2|X\\Biggr)+2E\\Biggl(\\Bigl([Y-E(Y|X)][E(Y|X)-f(X)]\\Bigr)|X\\Biggr)\\\\\n",
    "&=E\\Biggl(\\Bigl([Y-E(Y|X)]\\Bigr)^2|X\\Biggr)+E\\Biggl(\\Bigl([E(Y|X)-f(X)]\\Bigr)^2|X\\Biggr)+2\\Biggl(\\Bigl([E(Y|X)-f(X)]\\Bigr)E\\Bigl([Y-E(Y|X)]\\Bigr)|X\\Biggr)\\\\\n",
    "&(\\text{since } [E(Y|X)-f(X)] \\text{ is constant given } X)\\\\\n",
    "&\\text{and since }E\\Bigl([Y-E(Y|X)]\\Bigr)=E(Y)-E(E(Y|X))=E(Y)-E(Y)=0\\\\\n",
    "&=E\\Biggl(\\Bigl([Y-E(Y|X)]\\Bigr)^2|X\\Biggr)+E\\Biggl(\\Bigl([E(Y|X)-f(X)]\\Bigr)^2|X\\Biggr)\\\\\n",
    "&\\ge E\\Biggl(\\Bigl([Y-E(Y|X)]\\Bigr)^2|X\\Biggr)\n",
    "\\end{align}\n",
    "\n",
    "When $E(Y|X)-f(X)=0\\\\\n",
    "E\\Bigl((Y-f(X))^2|X\\Bigr)=E\\Biggl(\\Bigl([Y-E(Y|X)]\\Bigr)^2|X\\Biggr)$\n",
    "#### Regression function\n",
    "The solution is the conditional expectation a.k.a. the _regression_ function:\n",
    "\n",
    "\\begin{equation}\n",
    "f(x) = \\text{E}\\left(Y|X=x\\right)\n",
    "\\end{equation}\n",
    "\n",
    "> Thus the best prediction of $Y$ at any point $X=x$ is the conditional mean, when best is measured by average squared error."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusions first\n",
    "\n",
    "Both KNN and least squares will end up approximating conditional expectations by averages. But they differ dramatically in terms of model assumptions:\n",
    "* Least squares assumes $f(x)$ is well approximated by a globally linear function.\n",
    "* $k$-nearest neighbors assumes $f(x)$ is well approximated by a locally constant function.\n",
    "Although the latter seems more palatable, we will see below that we may pay a price for this flexibility."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The light and shadows of kNN\n",
    "\n",
    "The kNN attempts to directly implement this recipe using the training data:\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{f}(x) = \\text{Ave}\\left(y_i|x_i\\in N_k(x)\\right),\n",
    "\\end{equation}\n",
    "\n",
    "where\n",
    "* \"$\\text{Ave}$\" denotes average, and\n",
    "* $N_k(x)$ is the neighborhood containing the $k$ points in $\\mathcal{T}$ closest to $x$.\n",
    "\n",
    "Two approximations are happening here:\n",
    "* Expectation is approximated by averaging over sample data;\n",
    "* conditioning at a point is relaxed to conditioning on some region \"close\" to the target point.\n",
    "\n",
    "For large training sample size $N$, the points in the neighborhood are likely to be close to $x$, and as $k$ gets large the average will get more stable. In fact, under mild regularity conditions on the joint probability distribution $\\text{Pr}(X,Y)$, one can show that\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{f}(x)\\rightarrow\\text{E}(Y|X=x)\\text{ as }N,k\\rightarrow\\infty\\text{ s.t. }k/N\\rightarrow0\n",
    "\\end{equation}\n",
    "\n",
    "#### Isn't it perfect?\n",
    "\n",
    "In light of this, why look further, since it seems we have a universal approximator?\n",
    "* We often do not have very large samples.  \n",
    "  Linear models can usually get a more stable estimate than kNN, provided the structured model is appropriate (although such knowledge has to be learned from the data as well).\n",
    "* Curse of dimensionality.  \n",
    "  As the dimension $p$ gets large, so does the metric size of the $k$-nearest neighborhood. So settling for kNN as a surrogate for conditioning will fail us miserably.  \n",
    "  The convergence above still holds, but the _rate_ of convergence decreases as the dimension increases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model-based approach for linear regression\n",
    "\n",
    "How does linear regression fit into this framework? The simplest explanation is that one assumes that the regression function $f(x)$ is approximately linear in its arguments:\n",
    "\n",
    "\\begin{equation}\n",
    "f(x)\\approx x^T\\beta.\n",
    "\\end{equation}\n",
    "\n",
    "This is a model-based approach -- we specify a model for the regression function. \n",
    "\n",
    "Plugging this linear model for $f(x)$ into EPE and differentiating, we can solve for $\\beta$ theoretically:\n",
    "\n",
    "\\begin{equation}\n",
    "EPE(\\beta)=\\int(y-x^T\\beta)^2P(dx,dy)\n",
    "\\end{equation}\n",
    "\n",
    "Then\n",
    "\\begin{equation}\n",
    "\\frac{\\partial{EPE}}{\\partial{\\beta}}=\\int2(y-x^T\\beta)(-1)xP(dx,dy)\\\\\n",
    "=-2\\int(y-x^T\\beta)xP(dx,dy)\\\\\n",
    "\\text{since } y-x^T\\beta \\text{ are scalars }\\\\\n",
    "=-2\\int(yx-xx^T\\beta)P(dx,dy)\\\\\n",
    "\\end{equation}\n",
    "\n",
    "Let\n",
    "\\begin{equation}\n",
    "\\frac{\\partial{EPE}}{\\partial{\\beta}}=0\n",
    "\\end{equation}\n",
    "Then \n",
    "\\begin{equation}\n",
    "\\int(yx-xx^T\\beta)P(dx,dy)=E(yx)-E(xx^T\\beta)=E(yx)- E(xx^T)\\beta=0\n",
    "\\end{equation}\n",
    "Then\n",
    "\\begin{equation}\n",
    "\\beta = E(xx^T)^{-1}E(yx)\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "\\beta = \\left[\\text{E}\\left(XX^T\\right)\\right]^{-1}\\text{E}(XY)\n",
    "\\end{equation}\n",
    "\n",
    "Note we have _not_ conditioned on $X$; rather we have used out knowledge of the functional relationship to _pool_ over values of $X$. The least squares solution\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat\\beta = \\left( \\mathbf{X}^T \\mathbf{X} \\right)^{-1} \\mathbf{X}^T \\mathbf{y}\n",
    "\\end{equation}\n",
    "\n",
    "amounts to replacing the expectation in the theoretical solution by averages over the training data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### kNN vs. least squares\n",
    "\n",
    "So both kNN and least squares end up approximating conditional expectations by averages. But they differ dramatically in terms of model assumptions:\n",
    "* Least squares assumes $f(x)$ is well approximated by a globally linear function.\n",
    "* kNN assumes $f(x)$ is well approximated by a locally constant function.\n",
    "\n",
    "Although the latter seems more palatable, we have already seen that we may pay a price for this flexibility."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Additive models (Brief on modern techniques)\n",
    "\n",
    "Many of the more modern techniques described in this book are model based, although far more flexible than the rigid linear model.\n",
    "\n",
    "For example, additive models assume that\n",
    "\n",
    "\\begin{equation}\n",
    "f(X) = \\sum_{j=1}^p f_j(X_j).\n",
    "\\end{equation}\n",
    "\n",
    "This retains the additivity of the linear model, but each coordinate function $f_j$ is arbitrary. It turns out that the optimal estimate for the additive model uses techniques such as kNN to approximate _univariate_ conditional expectations _simultaneously_ for each of the coordinate functions.\n",
    "\n",
    "Thus the problems of estimating a conditional expectation in high dimensions are swept away in this case by imposing some (often unrealistic) model assumptions, in this case additivity."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Are we happy with $L_2$ loss? Yes, so far.\n",
    "\n",
    "If we replace the $L_2$ loss function with the $L_1$:\n",
    "\n",
    "\\begin{equation}\n",
    "E\\left| Y - f(X) \\right|,\n",
    "\\end{equation}\n",
    "\n",
    "the solution in this case is the conditional median,\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{f}(x) = \\text{median}(Y|X=x),\n",
    "\\end{equation}\n",
    "\n",
    "which is a different measure of location, and its estimates are more robust than those for the conditional mean.\n",
    "\n",
    "$L_1$ criteria have discontinuities in their derivatives, which have hindered their widespread use. Other more resistant loss functions will be mentioned in later chapters, but squared error is analytically convenient and the most popular."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayes classifier: For a categorical output with 0-1 loss function\n",
    "\n",
    "The same paradigm works when the output is a categorical variale $G$, except we need a different loss function for penalizing prediction errors. An estimate $\\hat{G}$ will assume values in $\\mathcal{G}$, the set of possible classes.\n",
    "\n",
    "Our loss function can be represented by $K\\times K$ matrix $\\mathbf{L}$, where $K=\\text{card}(\\mathcal{G})$. $\\mathbf{L}$ will be zero on the diagonal and nonnegative elsewhere, representing the price paid for misclassifying $\\mathcal{G}_k$ as $\\mathcal{G}_l$;\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{L} = \\begin{bmatrix}\n",
    "0 & L(\\mathcal{G}_1, \\mathcal{G}_2) & \\cdots & L(\\mathcal{G}_1, \\mathcal{G}_K) \\\\\n",
    "L(\\mathcal{G}_2, \\mathcal{G}_1) & 0 & \\cdots & L(\\mathcal{G}_2, \\mathcal{G}_K) \\\\\n",
    "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
    "L(\\mathcal{G}_K, \\mathcal{G}_1) & L(\\mathcal{G}_K, \\mathcal{G}_2) & \\cdots & 0\n",
    "\\end{bmatrix}\n",
    "\\end{equation}\n",
    "\n",
    "The expected prediction error is\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{EPE} = \\text{E}\\left[L(G, \\hat{G}(X)\\right],\n",
    "\\end{equation}\n",
    "\n",
    "where the expectation is taken w.r.t. the joint distribution $\\text{Pr}(G, X)$.\n",
    "\n",
    "Again we condition, and can write EPE as\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{EPE} = \\text{E}_X\\sum^K_{k=1}L\\left(\\mathcal{G}_k, \\hat{G}(X)\\right)\\text{Pr}\\left(\\mathcal{G}_k|X\\right)\n",
    "\\end{equation}\n",
    "\n",
    "and again it suffices to minimize EPE pointwise:\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{G}(x) = \\arg\\min_{g\\in\\mathcal{G}}\\sum^K_{k=1} L\\left(\\mathcal{G}_k,g\\right)\\text{Pr}\\left(\\mathcal{G}_k|X=x\\right)\n",
    "\\end{equation}\n",
    "\n",
    "#### 0-1 loss for Bayes classifier\n",
    "\n",
    "Most often we use the _zero-one_ loss function, where all misclassifications are charged a single unit, i.e.,\n",
    "\n",
    "\\begin{equation}\n",
    "L(k,l) = \\begin{cases}\n",
    "0\\text{ if }k = l,\\\\\n",
    "1\\text{ otherwise}.\n",
    "\\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "With the 0-1 loss function this simplifies to\n",
    "\n",
    "\\begin{align}\n",
    "\\hat{G}(x) &= \\arg\\min_{g\\in\\mathcal{G}} \\left[1 - \\text{Pr}(g|X=x)\\right]\\\\\n",
    "&= \\mathcal{G}_k \\text{ if Pr}\\left(\\mathcal{G}_k|X=x\\right) = \\max_{g\\in\\mathcal{G}}\\text{Pr}(g|X=x)\n",
    "\\end{align}\n",
    "\n",
    "This reasonable solution is known as the _Bayes classifier_, and says that we classify to the most probable class, using the conditional (discrete) distribution $\\text{Pr}(G|X)$. FIGURE 2.5 shows the Bayes-optimal decision boundary for our simulation example. The error rate of the Bayes classifier is called the _Bayes rate_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import random\n",
    "import numpy as np\n",
    "import scipy\n",
    "import scipy.stats\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"FIGURE 2.5. The optimal Bayes decision boundary for the simulation example.\n",
    "Since the generating density is known for each class, this decision boundary can be\n",
    "calculated exactly.\"\"\"\n",
    "sample_size = 100\n",
    "# Parameters for mean distributions\n",
    "mean_blue = [1, 0]\n",
    "mean_orange = [0, 1]\n",
    "mean_cov = np.eye(2)\n",
    "mean_size = 10\n",
    "\n",
    "# Additional parameters for blue and orange distributions\n",
    "sample_cov = np.eye(2)/5\n",
    "\n",
    "# Generate mean components for blue and orange (10 means for each)\n",
    "sample_blue_mean = np.random.multivariate_normal(mean_blue, mean_cov, mean_size)\n",
    "sample_orange_mean = np.random.multivariate_normal(mean_orange, mean_cov, mean_size)\n",
    "\n",
    "# Generate blue points\n",
    "sample_blue = np.array([\n",
    "    np.random.multivariate_normal(sample_blue_mean[random.randint(0, 9)], sample_cov)\n",
    "    for _ in range(sample_size)\n",
    "])\n",
    "y_blue = np.zeros(sample_size)\n",
    "\n",
    "# Generate orange points\n",
    "sample_orange = np.array([\n",
    "    np.random.multivariate_normal(sample_orange_mean[random.randint(0, 9)], sample_cov)\n",
    "    for _ in range(sample_size)\n",
    "])\n",
    "y_orange = np.ones(sample_size)\n",
    "\n",
    "data_x = np.concatenate((sample_blue, sample_orange), axis=0)\n",
    "data_y = np.concatenate((y_blue, y_orange)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def density_blue(arr:np.ndarray)->np.ndarray:\n",
    "    densities = np.array([\n",
    "        scipy.stats.multivariate_normal.pdf(arr, mean=m, cov=mean_cov)\n",
    "        for m in sample_blue_mean\n",
    "    ])\n",
    "    return densities.mean(axis=0)\n",
    "\n",
    "\n",
    "def density_orange(arr:np.ndarray)->np.ndarray:\n",
    "    densities = np.array([\n",
    "        scipy.stats.multivariate_normal.pdf(arr, mean=m, cov=mean_cov)\n",
    "        for m in sample_orange_mean\n",
    "    ])\n",
    "    return densities.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2.53219024 -2.30121419] [2.50789865 2.91277445]\n"
     ]
    }
   ],
   "source": [
    "min_x = data_x.min(axis=0)\n",
    "max_x = data_x.max(axis=0)\n",
    "print(min_x, max_x)\n",
    "arr = np.array([(i, j)\n",
    "                   for i in np.linspace(min_x[0]-.1, max_x[0]+.1, 100)\n",
    "                   for j in np.linspace(min_x[1]-.1, max_x[1]+.1, 100)])\n",
    "proba_blue = density_blue(arr)\n",
    "proba_orange = density_orange(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.63219024, -2.40121419],\n",
       "       [-2.63219024, -2.34652744],\n",
       "       [-2.63219024, -2.29184069],\n",
       "       ...,\n",
       "       [ 2.60789865,  2.90340094],\n",
       "       [ 2.60789865,  2.9580877 ],\n",
       "       [ 2.60789865,  3.01277445]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot\n",
    "fig = plt.figure(1)\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "# Original data\n",
    "ax.plot(sample_blue[:, 0], sample_blue[:, 1], 'o', color='C0')\n",
    "ax.plot(sample_orange[:, 0], sample_orange[:, 1], 'o', color='C1')\n",
    "# Bayes classifier\n",
    "mask_blue = proba_blue > proba_orange\n",
    "mask_orange = ~mask_blue\n",
    "ax.plot(arr[mask_blue, 0], arr[mask_blue, 1], 'o',\n",
    "        markersize=2, color='C0', alpha=.2)\n",
    "ax.plot(arr[mask_orange, 0], arr[mask_orange, 1], 'o',\n",
    "        markersize=2, color='C1', alpha=.2)\n",
    "ax.set_title('Bayes Optimal Classifier')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### KNN and Bayes classifier\n",
    "\n",
    "Again we see that the kNN classifier directly approximates this solution -- a majority vote in a nearest neighborhood amounts to exactly this, except that\n",
    "* conditional probability at a point is relaxed to conditional probability within a neighborhood of a point,\n",
    "* and probabilities are estimated by training-sample proportions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### From two-class to $K$-class\n",
    "Suppose for a two-class problem we had taken the dummy-variable approach and coded $G$ via a binary $Y$, followed by squared error loss estimation. Then\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{f}(X) = \\text{E}(Y|X) = \\text{Pr}(G=\\mathcal{G}_1|X)\n",
    "\\end{equation}\n",
    "\n",
    "if $\\mathcal{G}_1$ corresponded to $Y=1$.\n",
    "\n",
    "Likewise for a $K$-class problem,\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{E}(Y_k|X) = \\text{Pr}(G=\\mathcal{G}_k|X).\n",
    "\\end{equation}\n",
    "\n",
    "> This shows that our dummy-variable regression procedure, followed by classification to the largest fitted value, is another way of representing the Bayes classifier.\n",
    "\n",
    "Although this theory is exact, in practice problems can occur, depending on the regression model used. For example, when linear regression is used, $\\hat{f}(X)$ need not be positive, and we might be suspicious about using it as an estimate of a probability. We will discuss a variety of approaches to modeling $\\text{Pr}(G|X)$ in Chapter 4."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $\\S$ 2.5. Local Methods in High Dimensions\n",
    "\n",
    "We have examined two learning techniques for prediction so far;\n",
    "* the stable but biased linear model and\n",
    "* the less stable but apparently less biased class of kNN estimates.\n",
    "\n",
    "It would seem that with a reasonably large set of training data, we could always approximate the theoretically optimal conditional expectation by kNN averaging, since we should be able to find a fairly large neighborhood of observations close to any $x$ and average them.\n",
    "\n",
    "### The curse of dimensionality (Bellman, 1961)\n",
    "\n",
    "This approach and our intuition breaks down in high dimensions, and the phenomenon is commonly referred to as the _curse of dimensionality_ (Bellman, 1961). There are many manifestations of this problem, and we will examine a few here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The first example: Unit hypercube\n",
    "\n",
    "Consider the nearest-neighbor procedure for inputs uniformly distributed in a p-dimensional unit hypercube. Suppose we send out a hypercubical neighborhood about a target point to capture a fraction $r$ of the observations. Since this corresponds to a fraction $r$ of the unit volume, the expected edge length will be \n",
    "\n",
    "\\begin{equation}\n",
    "e_p(r) = r^{1/p}.\n",
    "\\end{equation}\n",
    "\n",
    "Note that $e_{10}(.01) = 0.63$ and $e_{10}(.1) = .80$, while the entire range for each input is only 1.0. Soto capture 1% or 10% of the data to form a local average, we must cover 63% or 80% of the range of each input variable. Such neighborhoods are no longer \"local\".\n",
    "\n",
    "Reducing $r$ dramatically does not help much either, since the fewer observations we average, the higher is the variance of our fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import math\n",
    "import random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"FIGURE 2.6. (right panel) The unit hypercube example\"\"\"\n",
    "fraction_of_volume = np.arange(0, 1, 0.001)\n",
    "edge_length_p1 = fraction_of_volume\n",
    "edge_length_p2 = fraction_of_volume**.5\n",
    "edge_length_p3 = fraction_of_volume**(1/3)\n",
    "edge_length_p10 = fraction_of_volume**.1\n",
    "\n",
    "fig1 = plt.figure(1)\n",
    "ax11 = fig1.add_subplot(1, 1, 1)\n",
    "ax11.plot(fraction_of_volume, edge_length_p10, label='p=10')\n",
    "ax11.plot(fraction_of_volume, edge_length_p3, label='p=3')\n",
    "ax11.plot(fraction_of_volume, edge_length_p2, label='p=2')\n",
    "ax11.plot(fraction_of_volume, edge_length_p1, label='p=1')\n",
    "ax11.set_xlabel('Fraction of Volume')\n",
    "ax11.set_ylabel('Distance')\n",
    "ax11.legend()\n",
    "ax11.plot([.1, .1], [0, 1], '--', color='C0', alpha=.5)\n",
    "ax11.plot([.3, .3], [0, 1], '--', color='C0', alpha=.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The second example: Unit ball\n",
    "\n",
    "In high dimensions all sample points are close to an edge of the sample.\n",
    "\n",
    "Consider $N$ data points uniformly distributed in a $p$-dimensional unit ball centered at the origin. And consider a nearest-neighbor estimate at the origin. The median distance from the orign to the closest data point is given by the expression (Exercise 2.3)\n",
    "\n",
    "\\begin{equation}\n",
    "d(p,N) = \\left(1-\\frac{1}{2}^{1/N}\\right)^{1/p}.\n",
    "\\end{equation}\n",
    "\n",
    "A more complicated expression exists for the mean distance to the closest point.\n",
    "\n",
    "For $N=500, p=10$, $d(p,N)\\approx0.52$, more than half way to the boundary. Hence most data points are close to the boundary of the sample space than to any other data point.\n",
    "\n",
    "Why is this a problem? Prediction is much more difficult near the edges of the training sample. One must extrapolate from neighboring sample points rather than interpolate between them."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The third example: Sampling density\n",
    "\n",
    "Another manifestiation of the curse is that the sampling density is proportional to $N^{1/p}$.\n",
    "\n",
    "If $N_1=100$ represents a dense sample for a single input problem, then $N_{10}=100^{10}$ is the sample size required for the same sampling density with 10 inputs. Thus in high dimensions all feasible training samples sparsely populate the input space."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The fourth example: Bias-variance decomposition\n",
    "\n",
    "Let us construct another uniform example. Suppose\n",
    "* we have 1000 training examples $x_i$ generated uniformly on $[-1,1]^p$, and\n",
    "* the true relationship between $X$ and $Y$ is  \n",
    "\n",
    "  \\begin{equation}\n",
    "  Y = f(X) = e^{-8\\|X\\|^2},\n",
    "  \\end{equation}\n",
    "  \n",
    "  without any measurement error.\n",
    "* We use the 1NN rule to predict $y_0$ at the test-point $x_0=0$.\n",
    "\n",
    "Denote the training set by $\\mathcal{T}$. We can compute the expected prediction error at $x_0$ for our procedure, averaging over all such samples of size 1000. Since the problem is deterministic, this is the mean squared error (MSE) for estimating $f(0)$.\n",
    "\n",
    "\\begin{align}\n",
    "\\text{MSE}(x_0) &= \\text{E}_\\mathcal{T}\\left[f(x_0)-\\hat{y}_0\\right]^2 \\\\\n",
    "&= \\text{E}_\\mathcal{T}\\left[f(x_0) -\\text{E}_\\mathcal{T}(\\hat{y}_0) + \\text{E}_\\mathcal{T}(\\hat{y}_0)-\\hat{y}_0\\right]^2 \\\\\n",
    "&= \\text{E}_\\mathcal{T}\\left[\\hat{y}_0 - \\text{E}_\\mathcal{T}(\\hat{y}_0)\\right]^2 + \\left[\\text{E}_\\mathcal{T}(\\hat{y}_0)-f(x_0)\\right]^2 + 2\\left[\\text{E}_\\mathcal{T}(\\hat{y}_0)-f(x_0)\\right]\\text{E}_\\mathcal{T}\\left[\\hat{y}_0 - \\text{E}_\\mathcal{T}(\\hat{y}_0)\\right]\\\\\n",
    "&= \\text{E}_\\mathcal{T}\\left[\\hat{y}_0 - \\text{E}_\\mathcal{T}(\\hat{y}_0)\\right]^2 + \\left[\\text{E}_\\mathcal{T}(\\hat{y}_0)-f(x_0)\\right]^2 \\\\\n",
    "&= \\text{Var}_\\mathcal{T}(\\hat{y}_0) + \\text{Bias}^2(\\hat{y}_0)\n",
    "\\end{align}\n",
    "\n",
    "We have broken down the MSE into two components that will become familiar as we proceed: Variance and squared bias. Such a decomposition is always possible and often useful, and is known as the _bias-variance decomposition_.\n",
    "\n",
    "FIGURE 2.7 illustrates the setup. Unless the nearest neighbor is at 0, $\\hat{y}$ will be biased downward. The variance  is due to the sampling variance of the 1NN."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.52362402, -0.94160915,  0.76358392, -0.92365576, -0.30958527,\n",
       "        0.41281719, -0.7303279 , -0.91000641,  0.45042398,  0.65164906,\n",
       "        0.6156556 ,  0.43792673,  0.60248841, -0.83713385, -0.26846477,\n",
       "        0.35379219, -0.5860781 , -0.84750126,  0.15911063,  0.63183339,\n",
       "        0.47572948,  0.23940263, -0.13400333, -0.6860668 ,  0.22164816,\n",
       "        0.64684125, -0.47198284, -0.92006244, -0.24139513, -0.85121428,\n",
       "       -0.98214255,  0.87564502, -0.96080989, -0.88877688,  0.94252343,\n",
       "       -0.03999984, -0.17849397,  0.90958777,  0.06223157, -0.47722939,\n",
       "        0.80215919, -0.43945665, -0.59054645,  0.69098503,  0.8374996 ,\n",
       "       -0.01377477, -0.7367969 , -0.08373888,  0.97429187,  0.66285725,\n",
       "       -0.10196032,  0.52860923,  0.00819558, -0.28304599,  0.73095748,\n",
       "        0.26700299, -0.53518844, -0.43642706, -0.47041087, -0.41063947,\n",
       "       -0.63719431,  0.59294264, -0.61269841,  0.22890798,  0.90696006,\n",
       "       -0.11469428,  0.54643137,  0.09056606,  0.62173869, -0.63675044,\n",
       "       -0.9171507 ,  0.71368708, -0.53387976, -0.98530483,  0.44847328,\n",
       "        0.39126753, -0.42727058, -0.26641845, -0.36734638, -0.81923262,\n",
       "        0.60957656,  0.34521713,  0.4844742 , -0.95246551,  0.48442516,\n",
       "        0.30898226, -0.69295518,  0.75276877, -0.88029808,  0.97490338,\n",
       "        0.51909274, -0.89696155,  0.07237896,  0.30061967,  0.77811674,\n",
       "        0.32136716, -0.96534051, -0.98091785,  0.71521181,  0.0677101 ])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([random.uniform(-1, 1) for _ in range(100)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.48601796, -0.44968368],\n",
       "       [-0.77970785,  0.89003972],\n",
       "       [-0.79092711,  0.61238668],\n",
       "       [ 0.67055626,  0.44152098],\n",
       "       [ 0.66777796, -0.89992495],\n",
       "       [-0.5107149 ,  0.13814159],\n",
       "       [-0.48246821, -0.55975761],\n",
       "       [ 0.51114079,  0.9236153 ],\n",
       "       [-0.43424228,  0.7123616 ],\n",
       "       [-0.57744428,  0.47452944]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " np.array([\n",
    "     [random.uniform(-1, 1) for _ in range(2)] for _ in range(10)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"FIGURE 2.7. (bottom panels) Bias-variance decomposition example.\n",
    "Given the dimension p, 100 simulations are done and the following steps are\n",
    "taken for each simulation.\n",
    "1. Generate data of size 1000 from [-1, 1]^p\n",
    "2. Grap the nearest neighbor x of 0 and calculate the distance, i.e., norm\n",
    "3. Calculate y=f(x) and the variance and the squared bias for simulation\n",
    "of size 100.\n",
    "\"\"\"\n",
    "import math\n",
    "def generate_data(p: int, n: int) ->np.ndarray:\n",
    "    if p == 1:\n",
    "        return np.array([random.uniform(-1, 1) for _ in range(n)])\n",
    "    return np.array([\n",
    "        [random.uniform(-1, 1) for _ in range(p)]\n",
    "        for _ in range(n)\n",
    "    ])\n",
    "\n",
    "\n",
    "def f(p: int, x: np.ndarray) ->float:\n",
    "    if p == 1:\n",
    "        return math.exp(-8*(x**2))\n",
    "    return math.exp(-8*sum(xi*xi for xi in x))\n",
    "\n",
    "# np.linalg.norm to return one of eight different matrix norms, or one of an infinite number of vector norms\n",
    "# ord=2 is the Order of the norm\n",
    "# axis=1 it specifies the axis of x along which to compute the vector norms, 0 for columns; 1 for rows.\n",
    "def simulate(p: int, nsample:int, nsim: int) ->dict:\n",
    "    res = {'average_distance': 0}\n",
    "    sum_y = 0\n",
    "    sum_y_square = 0\n",
    "    for _ in range(nsim):\n",
    "        data = generate_data(p, nsample)\n",
    "        if p == 1:\n",
    "            data_norm = np.abs(data)\n",
    "        else:\n",
    "            data_norm = np.linalg.norm(data, ord=2, axis=1)\n",
    "        nearest_index = data_norm.argmin()\n",
    "        nearest_x, nearest_distance = data[nearest_index], data_norm[nearest_index]\n",
    "        nearest_y = f(p, nearest_x)\n",
    "        sum_y += nearest_y\n",
    "        sum_y_square += nearest_y*nearest_y\n",
    "        res['average_distance'] += nearest_distance\n",
    "    average_y = sum_y/nsim\n",
    "    res['average_distance'] /= nsim\n",
    "    res['variance'] = sum_y_square/nsim - average_y*average_y\n",
    "    res['squared_bias'] = (1-average_y)*(1-average_y)\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "nsim = 100\n",
    "data = {p: simulate(p, 1000, nsim) for p in range(1, 11)}\n",
    "dimension = list(data.keys())\n",
    "average_distance = [d['average_distance'] for p, d in data.items()]\n",
    "variance = np.array([d['variance'] for p, d in data.items()])\n",
    "squared_bias = np.array([d['squared_bias'] for p, d in data.items()])\n",
    "mse = variance + squared_bias\n",
    "\n",
    "fig2 = plt.figure(2, figsize=(10, 5))\n",
    "ax21 = fig2.add_subplot(1, 2, 1)\n",
    "ax21.set_title('Distance to 1-NN vs. Dimension')\n",
    "ax21.plot(dimension, average_distance, 'ro--')\n",
    "ax21.set_xlabel('Dimension')\n",
    "ax21.set_ylabel('Average Distance to Nearest Neighbor')\n",
    "\n",
    "ax22 = fig2.add_subplot(1, 2, 2)\n",
    "ax22.set_title('MSE vs. Dimension')\n",
    "ax22.plot(dimension, mse, 'o-', label='MSE')\n",
    "ax22.plot(dimension, variance, 'o-', label='Variance')\n",
    "ax22.plot(dimension, squared_bias, 'o-', label='Squared Bias')\n",
    "ax22.set_xlabel('Dimension')\n",
    "ax22.set_ylabel('MSE')\n",
    "ax22.legend()\n",
    "plt.savefig(\"savefig.pdf\", dpi=300, facecolor='w', edgecolor='w',\n",
    "        orientation='portrait', papertype='letter', format='pdf',\n",
    "        transparent=False, bbox_inches=None, pad_inches=0.1,\n",
    "        metadata=None)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Frobenius norm is given by:\n",
    "\n",
    "$||A||_F = [\\sum_{i,j} abs(a_{i,j})^2]^{1/2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the target function (no noise)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import random\n",
    "import numpy as np\n",
    "\n",
    "def f(p: int, x: np.ndarray) ->float:\n",
    "    if p == 1:\n",
    "        return math.exp(-8*(x**2))\n",
    "    return math.exp(-8*sum(xi*xi for xi in x))\n",
    "x_cords = np.linspace(-1.0, 1.0, 201)\n",
    "y_cords = [f(1, x) for x in x_cords]\n",
    "\n",
    "#The training point (10% of total) is indicated by the blue tick mark.\n",
    "fig9 = plt.figure(1, figsize=(6, 6))\n",
    "ax91 = fig9.add_subplot(1, 1, 1)\n",
    "ax91.plot(x_cords, y_cords, 'g')\n",
    "ax91.plot([0,0],[-0.05,1.05], color=\"0\", linewidth=1)\n",
    "ax91.plot([0.2,0.2],[f(1,0.2),1], \"b--\", linewidth=0.5)\n",
    "ax91.plot([0.0,0.2],[1,1], \"b--\", linewidth=0.5)\n",
    "ax91.set_title('1-NN in One Dimension')\n",
    "ax91.set_xlabel('X')\n",
    "ax91.set_ylabel('f(X)')\n",
    "ax91.margins(0,0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In low dimensions and with $N = 1000$, the nearest neighbor is very close to $0$, and so both the bias and variance are small. As the dimension increases, the nearest neighbor tends to stray further from the target point, and both bias and variance are incurred. By $p = 10$, for more than $99\\%$ of the samples the nearest neighbor is a distance greater than $0.5$ from the origin.\n",
    "\n",
    "Thus as $p$ increases, the estimate tends to be 0 more often than not, and hence the MSE levels off at 1.0, as does the bias, and the variance starts dropping (an artifact of this example).\n",
    "\n",
    "Although this is a highly contrived example, similar phenomena occur more generally. The complexity of functions of many variables can grow exponentially with the dimension, and if we wish to be able to estimate such functions with the same accuracy as functions in low dimension, then we need the size of our training set to grow exponentially as well. In this example, the function is a complex interaction of all $p$ variables involved.\n",
    "\n",
    "The dependence of the bias term on distance depends on the truch, and it need not always dominate with 1NN. For example, if the function always involves only a few dimensions as in FIGURE 2.8, then the variance can dominate instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"FIGURE 2.8. The variance-dominating example.\"\"\"\n",
    "\n",
    "#plot the target function (no noise)\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "\n",
    "def f2(p: int, x: np.ndarray) ->float:\n",
    "    if p == 1:\n",
    "        return (x+1)**3/2\n",
    "    return (x[0]+1)**3/2\n",
    "\n",
    "x_cords = np.linspace(-1.0, 1.0, 201)\n",
    "y_cords = [f2(1, x) for x in x_cords]\n",
    "\n",
    "\n",
    "#The training point (10% of total) is indicated by the blue tick mark.\n",
    "fig8 = plt.figure(2, figsize=(12, 6))\n",
    "ax81 = fig8.add_subplot(1, 2, 1)\n",
    "ax81.plot(x_cords, y_cords, 'skyblue')\n",
    "ax81.plot([0,0],[-0.05,4.05], color=\"0\", linewidth=1)\n",
    "ax81.plot([0,0.2],[f2(1,0),f2(1,0)], \"b--\", linewidth=0.5)\n",
    "ax81.plot([0.2,0.2],[f2(1, 0), f2(1, 0.2)], \"b--\", linewidth=0.5)\n",
    "ax81.set_title('1-NN in One Dimension')\n",
    "ax81.set_xlabel('X')\n",
    "ax81.set_ylabel('f(X)')\n",
    "ax81.margins(0,0)\n",
    "\n",
    "def generate_data(p: int, n: int) ->np.ndarray:\n",
    "    if p == 1:\n",
    "        return np.array([random.uniform(-1, 1) for _ in range(n)])\n",
    "    return np.array([\n",
    "        [random.uniform(-1, 1) for _ in range(p)]\n",
    "        for _ in range(n)\n",
    "    ])\n",
    "\n",
    "def simulate(p: int, nsample:int, nsim: int) ->dict:\n",
    "    res = {'average_distance': 0}\n",
    "    sum_y = 0\n",
    "    sum_y_square = 0\n",
    "    for _ in range(nsim):\n",
    "        data = generate_data(p, nsample)\n",
    "        if p == 1:\n",
    "            data_norm = np.abs(data)\n",
    "        else:\n",
    "            data_norm = np.linalg.norm(data, ord=2, axis=1)\n",
    "        nearest_index = data_norm.argmin()\n",
    "        nearest_x, nearest_distance = data[nearest_index], data_norm[nearest_index]\n",
    "        nearest_y = f2(p, nearest_x)\n",
    "        sum_y += nearest_y\n",
    "        sum_y_square += nearest_y*nearest_y\n",
    "        res['average_distance'] += nearest_distance\n",
    "    average_y = sum_y/nsim\n",
    "    res['average_distance'] /= nsim\n",
    "    res['variance'] = sum_y_square/nsim - average_y*average_y\n",
    "    res['squared_bias'] = (f2(1,0)-average_y)*(f2(1,0)-average_y)\n",
    "    return res\n",
    "\n",
    "nsim = 100\n",
    "data = {p: simulate(p, 1000, nsim) for p in range(1, 11)}\n",
    "dimension = list(data.keys())\n",
    "average_distance = [d['average_distance'] for p, d in data.items()]\n",
    "variance = np.array([d['variance'] for p, d in data.items()])\n",
    "squared_bias = np.array([d['squared_bias'] for p, d in data.items()])\n",
    "mse = variance + squared_bias\n",
    "\n",
    "ax82 = fig8.add_subplot(1, 2, 2)\n",
    "ax82.set_title('MSE vs. Dimension')\n",
    "ax82.plot(dimension, mse, 'o-', label='MSE')\n",
    "ax82.plot(dimension, variance, 'o-', label='Variance')\n",
    "ax82.plot(dimension, squared_bias, 'o-', label='Squared Bias')\n",
    "ax82.set_xlabel('Dimension')\n",
    "ax82.set_ylabel('MSE')\n",
    "ax82.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What good about the linear model?\n",
    "\n",
    "> By imposing some heavy restrictions on the class of models being fitted, we can avoid the curse of dimensionality.\n",
    "\n",
    "Suppose the relationship between $Y$ and $X$ is linear,\n",
    "\n",
    "\\begin{equation}\n",
    "Y=X^T\\beta+\\epsilon,\n",
    "\\end{equation}\n",
    "\n",
    "where $\\epsilon\\sim N(0,\\sigma^2)$.\n",
    "\n",
    "We fit the model by least squares to the training data. \n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{\\beta}=(X^TX)^{-1}X^Ty=(X^TX)^{-1}X^T(X\\beta+\\epsilon)\\\\\n",
    "=\\beta+(X^TX)^{-1}X^T\\epsilon\n",
    "\\end{equation}\n",
    "\n",
    "For an arbitrary test point $x_0$, we have $\\hat{y_0} = x_0^T \\hat\\beta$,\n",
    "\\begin{equation}\n",
    "\\hat{y}_0=x_0^T\\hat{\\beta}=x_0^T\\beta+x_0^T(X^TX)^{-1}X^T\\epsilon\\\\\n",
    "=x_0^T\\beta+(X(X^TX)^{-1}x_0)^T\\epsilon\\\\\n",
    "=x_0^T \\beta + \\sum_{i=1}^N l_i(x_0) \\epsilon_i,\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "where $l_i(x_0)$ is the $i$th element of $\\mathbf{X}\\left( \\mathbf{X}^T \\mathbf{X} \\right)^{-1} x_0$.\n",
    "\n",
    "Since under this model the least squares estimates are unbiased, we find that the expected (squared) prediction error at $x_0$:\n",
    "Since\n",
    "\\begin{equation}\n",
    "\\text{E}_{y_0|x_0}\\text{E}_\\mathcal{T}[y_0-x_0^T\\beta]=\\text{E}_{y_0|x_0}[y_0-x_0^T\\beta]\\text{E}_\\mathcal{T}=0\\text{E}_\\mathcal{T}=0\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{E}_{y_0|x_0}\\text{E}_\\mathcal{T}[y_0-x_0^T\\beta]^2=\\text{Var}(y_0|x_0)=\\sigma^2\n",
    "\\end{equation}\n",
    "And\n",
    "\\begin{equation}\n",
    "\\text{E}_{y_0|x_0}\\text{E}_\\mathcal{T}[\\text{E}_\\mathcal{T}(\\hat{y}_0)-\\hat{y}_0]=\\text{E}_{y_0|x_0}0=0\n",
    "\\end{equation}\n",
    "\n",
    "And since the expectation of the length $N$ vector $\\epsilon$ is zero.\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{E}_\\mathcal{T}(\\hat{y}_0)-x_0^T\\beta=\\text{E}_\\mathcal{T}(x_0^T\\beta+(X(X^TX)^{-1}x_0)^T\\epsilon)-x_0^T\\beta\\\\\n",
    "=\\text{E}_\\mathcal{T}(X(X^TX)^{-1}x_0)^T\\epsilon=0\n",
    "\\end{equation}\n",
    "\n",
    "And \n",
    "\\begin{equation}\n",
    "\\text{E}_{y_0|x_0}\\Biggl([y_0-x_0^T\\beta][\\text{E}_\\mathcal{T}(\\hat{y}_0)-\\hat{y}_0]\\Biggr)=[\\text{E}_\\mathcal{T}(\\hat{y}_0)-\\hat{y}_0]\\text{E}_{y_0|x_0}[y_0-x_0^T\\beta]=0\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "\\begin{align}\n",
    "\\text{EPE}(x_0) &= \\text{E}_{y_0|x_0}\\text{E}_\\mathcal{T}\\left(y_0-\\hat{y}_0\\right)^2 \\\\\n",
    "&= \\text{E}_{y_0|x_0}\\text{E}_\\mathcal{T}\\Biggl([y_0-x_0^T\\beta]+[\\text{E}_\\mathcal{T}(\\hat{y}_0)-\\hat{y}_0]+[x_0^T\\beta-\\text{E}_\\mathcal{T}(\\hat{y}_0)]\\Biggr)^2 \\\\\n",
    "&= \\text{Var}(y_0|x_0) + \\text{E}_\\mathcal{T} \\left(\\hat{y}_0 - \\text{E}_\\mathcal{T}\\hat{y}_0\\right)^2 + \\left(\\text{E}_\\mathcal{T}\\hat{y}_0 - x_0^T\\beta\\right)^2 \\\\\n",
    "&= \\text{Var}(y_0|x_0) + \\text{Var}_\\mathcal{T}(\\hat{y}_0) + \\text{Bias}^2(\\hat{y}_0) \\\\\n",
    "&= \\text{Var}(y_0|x_0) + \\text{Var}_\\mathcal{T}(\\hat{y}_0) + 0 \\\\\n",
    "&= \\sigma^2 + \\text{E}_\\mathcal{T}x_0^T\\left(\\mathbf{X}^T\\mathbf{X}\\right)^{-1}x_0\\sigma^2.\n",
    "\\end{align}\n",
    "\n",
    "Note that\n",
    "1. An additional variance $\\sigma^2$ is incurred, since our target is not deterministic.\n",
    "2. There is no bias, and the variance depends on $x_0$.\n",
    "\n",
    "If\n",
    "* $N$ is large,\n",
    "* $\\mathcal{T}$ were selected at random, and\n",
    "* $\\text{E}(X)=0$,\n",
    "\n",
    "then $\\mathbf{X}^T\\mathbf{X}\\rightarrow N\\text{Cov}(X)$ and\n",
    "\n",
    "\\begin{align}\n",
    "\\text{E}_{x_0}\\text{EPE}(x_0) &\\sim \\text{E}_{x_0}x_0^T\\text{Cov}(X)^{-1}x_0\\sigma^2/N + \\sigma^2 \\\\\n",
    "&= \\text{E}_{x_0}\\Bigl[\\text{trace}(x_0^T\\text{Cov}(X)^{-1}x_0)\\Bigr]\\sigma^2/N + \\sigma^2 \\\\\n",
    "&= \\text{E}_{x_0}\\Bigl[\\text{trace}(\\text{Cov}(X)^{-1}x_0x_0^T)\\Bigr]\\sigma^2/N + \\sigma^2 \\\\\n",
    "&= \\Bigl[\\text{trace}(\\text{Cov}(X)^{-1}\\text{Cov}(x_0))\\Bigr]\\sigma^2/N + \\sigma^2 \\\\\n",
    "&= \\text{trace}\\left(\\text{Cov}(X)^{-1}\\text{Cov}(x_0)\\right)\\sigma^2/N + \\sigma^2 \\\\\n",
    "&= \\text{trace}(I_p)\\sigma^2/N + \\sigma^2 \\\\\n",
    "&= \\sigma^2(p/N)+\\sigma^2.\n",
    "\\end{align}\n",
    "\n",
    "The expected EPE increases linearly as a function of $p$, with slope $\\sigma^2/N$. If $N$ is large and/or $\\sigma^2$ is small, this growth is variance is negligible (0 in the deterministic case).\n",
    "\n",
    "By imposing some heavy restrictions on the class of models being fitted, we have avoided the curse of dimensionality. Some of the technical details are derived in Exercise 2.5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### EPE comparison: 1NN vs. least squares\n",
    "\n",
    "FIGURE 2.9 compares 1NN vs. least squares in two situations, both of which have the form\n",
    "\n",
    "\\begin{equation}\n",
    "Y = f(X) + \\epsilon,\n",
    "\\end{equation}\n",
    "\n",
    "* $X$ uniform as before,\n",
    "* $\\epsilon \\sim N(0,1)$,\n",
    "* $N=500$.\n",
    "\n",
    "For the orange curve, $f(x) = x_1$ is linear in the first coordinate, for the blue curve, $f(x) = \\frac{1}{2}(x_1+1)^3$ is cubic as in the figure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.61759521,  0.59642885,  0.52856294, -0.51102936,  0.7582173 ,\n",
       "        0.37392417,  0.04149905,  0.38397366,  0.85792946, -0.58157994])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.uniform(-1, 1, size=(10, 3))[:, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.01719569,  0.8104598 ],\n",
       "       [-0.7992207 , -0.1717739 ],\n",
       "       [ 0.45592493, -0.80862509],\n",
       "       [ 0.94327868, -0.63571168],\n",
       "       [-0.61028311,  0.4234042 ],\n",
       "       [-0.33729951, -0.40925221],\n",
       "       [ 0.31626791, -0.45314239],\n",
       "       [-0.02476081, -0.01779324],\n",
       "       [ 0.75235307, -0.3562242 ],\n",
       "       [-0.07984536, -0.76341629]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cut the dimension using [:, :dim]\n",
    "np.random.uniform(-1, 1, size=(10, 3))[:, :2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.00848305, -0.14429979],\n",
       "       [ 0.08565318, -0.71950832],\n",
       "       [ 0.1717854 , -0.34590402],\n",
       "       [ 0.03021633, -0.48307884],\n",
       "       [ 0.77018078,  0.02259718],\n",
       "       [ 0.10105322, -0.42038542],\n",
       "       [ 0.18740025, -0.1727471 ],\n",
       "       [-0.06960062,  0.02860003],\n",
       "       [-0.35619697, -0.0278165 ],\n",
       "       [-0.33956579,  0.00973043]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.random.uniform(-1, 1, size=(10, 3))[:, :2])*(np.random.uniform(-1, 1, size=(10, 3))[:, :2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.10496641,  0.26744231],\n",
       "       [ 1.        , -0.21702965,  0.50820341],\n",
       "       [ 1.        ,  0.42527179,  0.75056226],\n",
       "       [ 1.        ,  0.61792228,  0.9076206 ],\n",
       "       [ 1.        , -0.52970636, -0.66967477],\n",
       "       [ 1.        ,  0.46928742,  0.52278373],\n",
       "       [ 1.        ,  0.49645549,  0.42786775],\n",
       "       [ 1.        , -0.97161169,  0.62793184],\n",
       "       [ 1.        , -0.62037455, -0.75072864],\n",
       "       [ 1.        ,  0.93673585, -0.89934708]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use np.hstack to combine the columns\n",
    "np.hstack((np.ones((10, 1)), np.random.uniform(-1, 1, size=(10, 3))[:, :2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.08955780990662486"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# generate random errors with default (mean=0,std=1) distribution\n",
    "np.random.randn(100).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0511418057538773"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randn(100).std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 0])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([1] + [0]*3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"FIGURE 2.9. Relative EPE (at x_0 = 0) ratio for 1NN vs. least squares\"\"\"\n",
    "size_simulation = 10000\n",
    "size_train = 500\n",
    "p = 10\n",
    "\n",
    "list_epe_ols_linear = []\n",
    "list_epe_1nn_linear = []\n",
    "list_epe_ols_cubic = []\n",
    "list_epe_1nn_cubic = []\n",
    "\n",
    "for _ in range(size_simulation):\n",
    "    epe_linear = []\n",
    "    # Generate data\n",
    "    train_x = np.random.uniform(-1, 1, size=(size_train, p))\n",
    "    # train_y_linear is the first column of train_x (X_1)\n",
    "    train_y_linear = train_x[:, 0]\n",
    "    train_y_cubic = ((train_x[:, 0]+1)**3)/2\n",
    "    train_error = np.random.randn(size_train)\n",
    "    train_ye_linear = train_y_linear + train_error\n",
    "    train_ye_cubic = train_y_cubic + train_error\n",
    "    \n",
    "    epe_ols_linear = []\n",
    "    epe_1nn_linear = []\n",
    "    epe_ols_cubic = []\n",
    "    epe_1nn_cubic = []\n",
    "    for dim in range(1, p+1):\n",
    "        # Cut the dimension\n",
    "        partial_x = train_x[:, :dim]\n",
    "        partial_1x = np.hstack((np.ones((size_train, 1)), partial_x))\n",
    "        \n",
    "        obs_y_linear = np.random.randn(1)\n",
    "        obs_y_cubic = .5 + np.random.randn(1)\n",
    "\n",
    "        # Least squares for linear f\n",
    "        xx = partial_1x.T @ partial_1x\n",
    "        xy_linear = partial_1x.T @ train_ye_linear\n",
    "        xxxy_linear = np.linalg.solve(xx, xy_linear)\n",
    "        hat_ols = np.array([1] + [0]*dim) @ xxxy_linear\n",
    "        epe_ols_linear.append((hat_ols-obs_y_linear)**2)\n",
    "\n",
    "        # 1NN for linear f\n",
    "        mat_norm = (partial_x*partial_x).sum(axis=1)\n",
    "        nn = mat_norm.argmin()\n",
    "        hat_1nn = train_ye_linear[nn]\n",
    "        epe_1nn_linear.append((hat_1nn-obs_y_linear)**2)\n",
    "        \n",
    "        # Least squares for cubic f\n",
    "        xy_cubic = partial_1x.T @ train_ye_cubic\n",
    "        xxxy_cubic = np.linalg.solve(xx, xy_cubic)\n",
    "        hat_ols = np.array([1] + [0]*dim) @ xxxy_cubic\n",
    "        epe_ols_cubic.append((hat_ols-obs_y_cubic)**2)\n",
    "        \n",
    "        # 1NN for cubic f\n",
    "        hat_1nn = train_ye_cubic[nn]\n",
    "        epe_1nn_cubic.append((hat_1nn-obs_y_cubic)**2)\n",
    "\n",
    "    list_epe_ols_linear.append(epe_ols_linear)\n",
    "    list_epe_1nn_linear.append(epe_1nn_linear)\n",
    "    list_epe_ols_cubic.append(epe_ols_cubic)\n",
    "    list_epe_1nn_cubic.append(epe_1nn_cubic)\n",
    "\n",
    "arr_epe_ols_linear = np.array(list_epe_ols_linear)\n",
    "arr_epe_1nn_linear = np.array(list_epe_1nn_linear)\n",
    "arr_epe_ols_cubic = np.array(list_epe_ols_cubic)\n",
    "arr_epe_1nn_cubic = np.array(list_epe_1nn_cubic)\n",
    "\n",
    "# Compute EPE, finally\n",
    "epe_ols_linear = arr_epe_ols_linear.mean(axis=0)\n",
    "epe_1nn_linear = arr_epe_1nn_linear.mean(axis=0)\n",
    "epe_ols_cubic = arr_epe_ols_cubic.mean(axis=0)\n",
    "epe_1nn_cubic = arr_epe_1nn_cubic.mean(axis=0)\n",
    "\n",
    "# Plot\n",
    "plot_x = list(range(1, p+1))\n",
    "fig4 = plt.figure(4)\n",
    "ax41 = fig4.add_subplot(1, 1, 1)\n",
    "ax41.plot(plot_x, epe_1nn_linear/epe_ols_linear, '-o',\n",
    "          color='C1', label='Linear')\n",
    "ax41.plot(plot_x, epe_1nn_cubic/epe_ols_cubic, '-o',\n",
    "          color='C0', label='Cubic')\n",
    "ax41.legend()\n",
    "ax41.set_xlabel('Dimension')\n",
    "ax41.set_ylabel('EPE Ratio')\n",
    "ax41.set_title('Expected Prediction Error of 1NN vs. OLS')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10000"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# list_epe_ols_linear is 10000 X 10 list\n",
    "len(list_epe_ols_linear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10000"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# arr_epe_ols_linear is 10000 X 10 array\n",
    "len(arr_epe_ols_linear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.98240917],\n",
       "       [0.97851524],\n",
       "       [1.01285594],\n",
       "       [1.00377149],\n",
       "       [0.99835949],\n",
       "       [1.00265193],\n",
       "       [1.00174265],\n",
       "       [0.99765609],\n",
       "       [1.02053042],\n",
       "       [1.00488109]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "epe_ols_linear"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Linear case\n",
    "\n",
    "Shown is the relative EPE of 1NN to least squares, which appears to start at around 2 for the linear case.\n",
    "\n",
    "Least squares is unbiased in this case, and as discussed above the EPE is slightly above $\\sigma^2 = 1$.\n",
    "\n",
    "The EPE for 1NN is always above 2, since the variance of $\\hat{f}(x_0)$ in this case is at least $\\sigma^2$, and the ratio increases with dimension as the nearest neighbor strays from the target point.\n",
    "\n",
    "#### Cubic case\n",
    "\n",
    "For the cubic case, least squares is biased, which moderates the ratio.\n",
    "\n",
    "Clearly we could manufacture examples where the bias of least squares would dominate the variance, and the 1NN would come out the winner."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> By relying on rigid assumptions, the linear model has no bias at all and negligible variance, while the error in 1-nearest neighbor is substantially larger. However, if the assumptions are wrong, all bets are off and the 1-nearest neighbor may dominate. We will see that there is a whole spectrum of models between the rigid linear models and the extremely flexible 1-nearest-neighbor models, each with their own assumptions and biases, which have been proposed specifically to avoid the exponential growth in complexity of functions in high dimensions by drawing heavily on these assumptions.\n",
    "\n",
    "Before we delve more deeply, let us elaborate a bit on the concept of _statistical models_ and see how they fit into the prediction framework."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $\\S$ 2.6. Statistical Models, Supervised Learning and Function Approximation\n",
    "\n",
    "### Review\n",
    "\n",
    "Our goal is to find a useful approximation $\\hat{f}(x)$ to $f(x)$ that underlies the predictive relationship between the inputs and outputs.\n",
    "\n",
    "In the theoretical setting of $\\S$ 2.4, we saw that\n",
    "1. for a quantitative response, squared error loss lead us to the regression function  \n",
    "\n",
    "  \\begin{equation}\n",
    "  f(x) = \\text{E}(Y|X=x).\n",
    "  \\end{equation}\n",
    "\n",
    "2. The kNNs can be viewed as direct estimates of this conditional expectation,\n",
    "3. but kNNs can fail at least two ways:\n",
    "  * If the dimension of the input space is high, the nearest neighbors need not be close to the target point, and can result in large errors,\n",
    "  * if special structure is known to exist, this can be used to reduce both the bias and the variance of the estimates.\n",
    "  \n",
    "> We anticipate using other classes of models for $f(x)$, in many cases specifically designed to overcome the dimensionality problems, and here we discuss a framework for incorporating them into the prediction problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\S$ 2.6.1. A Statistical Model for the Joint Distribution $\\text{Pr}(X,Y)$\n",
    "\n",
    "### The additive error model\n",
    "Suppose in fact that our data arose from a statistical model\n",
    "\n",
    "\\begin{equation}\n",
    "Y = f(X) + \\epsilon,\n",
    "\\end{equation}\n",
    "\n",
    "where the random error $\\epsilon$ has $\\text{E}(\\epsilon)=0$ and is independent of $X$.\n",
    "\n",
    "Note that for this model,\n",
    "\n",
    "\\begin{equation}\n",
    "f(x)=\\text{E}(Y|X=x),\n",
    "\\end{equation}\n",
    "\n",
    "and in fact the conditional distribution $\\text{Pr}(Y|X)$ depends on $X$ only through the conditional mean $f(x)$.\n",
    "\n",
    "The additive error model is a useful approximation to the truth. For most systems the input-output pairs $(X,Y)$ will not have a deterministic relationship $Y=f(X)$. Generally there will be other unmeasured variables that also contribute to $Y$, including measurement error.\n",
    "\n",
    "The additive model assumes that we can capture all these departures from a deterministic relationship via the error $\\epsilon$.\n",
    "\n",
    "#### Where the deterministic rules\n",
    "\n",
    "For some problems a deterministic relationship does hold. Many of the classification problems studied in machine learning are of this form, where the response surface can be thought of as a colored map defined in $\\mathbb{R}^p$.\n",
    "\n",
    "The training data consist of colored examples from the map $\\{x_i,g_i\\}$, and the goal is to be able to color any point. Here the function is deterministic, and the randomness enters through the $x$ location of the training points.\n",
    "\n",
    "For the moment we will not pursue such problems, but will see that they can be handled by techniques appropriate for the error-based models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The i.i.d. assumption\n",
    "\n",
    "The assumption in the above additive error model that the errors are i.i.d. is not strictly necessary, but seems to be the back of our mind when we average squared errors uniformly in our EPE criterion.\n",
    "\n",
    "With such a model it becomes natural to use least squares as a data criterion for model estimation as in the linear model\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{Y} = \\hat\\beta_0 + \\sum_{j=1}^p X_j \\hat\\beta_j.\n",
    "\\end{equation}\n",
    "\n",
    "Simple modifications can be made to avoid the independence assumption; e.g., we can have\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{Var}(Y|X=x)=\\sigma(x),\n",
    "\\end{equation}\n",
    "\n",
    "and now both the mean and variance depend on $X$.\n",
    "\n",
    "In general $\\text{Pr}(Y|X)$ can depend on X in complicated ways, but the additive error model precludes these."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For qualitative outputs\n",
    "\n",
    "So far we have concentrated on the quantitative response.\n",
    "\n",
    "Additive error models are typically not used for qualitative outputs $G$; in this case the target function $p(X)$ _is_ the conditional density $\\text{Pr}(G|X)$, and this is modeled directly.\n",
    "\n",
    "For example, for two-class data, it is often reasonable to assume that the data arise from independent binary trials, with the probability of one particular outcome being $p(X)$, and the other $1 − p(X)$. Thus if $Y$ is the 0–1 coded version of $G$, then\n",
    "\\begin{equation}\n",
    "\\text{E}(Y |X = x) = p(x),\n",
    "\\end{equation}\n",
    "\n",
    "but the variance depends on $x$ as well: $\\text{Var}(Y |X = x) = p(x)\\left(1 − p(x)\\right)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\S$ 2.6.2. Supervised Learning\n",
    "\n",
    "Before we launch into more statistically oriented jargon, we present the function-fitting paradigm from a machine learning point of view.\n",
    "\n",
    "Suppose for simplicity the additive error model\n",
    "\n",
    "\\begin{equation}\n",
    "Y = f(X) + \\epsilon\n",
    "\\end{equation}\n",
    "\n",
    "is a reasonable assumption.\n",
    "\n",
    "Supervised learning attempts to learn $f$ by example through a _teacher_. One observes the system under study, both the inputs and outputs, and assembles a _training_ set of observations\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{T} = \\left\\{ (x_i, y_i) : i = 1, \\cdots, N \\right\\}.\n",
    "\\end{equation}\n",
    "\n",
    "The observed input values to the system $x_i$ are also fed into an artificial system, known as a learning algorithm (usually a computer program), which also produces outputs $\\hat{f}(x_i)$ in response to the inputs.\n",
    "\n",
    "The learning algorithm has the property that it can modify its input/output relationship $\\hat{f}$ in response to differences $y_i − \\hat{f}(x_i)$ between the original and generated outputs. This process is known as _learning by example_. Upon completion of the learning process the hope is that the artificial and real outputs will be close enough to be useful for all sets of inputs likely to be encountered in practice.\n",
    "\n",
    "This learning paradigm has been the motivation for research into the supervised learning problem in the fields of machine learning (with analogies to human reasoning) and neural networks (with biological analogies to the brain). The approach taken in applied mathematics and statistics has been from the perspective of function approximation and estimation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\S$ 2.6.3. Function Approximation\n",
    "\n",
    "Here\n",
    "* the data pairs $\\{x_i, y_i\\}$ are viewed as points in a $(p+1)$-dimensional Euclidean space.\n",
    "* The function $f(x)$ has domain eqaul to the $p$-dimensional input subspace (or $\\mathbb{R}^p$ for convenience), and\n",
    "* $f$ is related to the data via a model such as $y_i=f(x_i)+\\epsilon$.\n",
    "\n",
    "The goal is to obtain a useful approximation to $f(x)$ for all $x$ in some region of $\\mathbb{R}^p$, given the representations in $\\mathcal{T}$.\n",
    "\n",
    "> Although somewhat less glamorous than the learning paradigm, treating supervised learning as a problem in function approximation encourages the geometrical concepts of Euclidean spaces and mathematical concepts of probabilsitic inference to be applied to the problem. This is the approach taken in this book."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Associated parameters and basis expansions\n",
    "\n",
    "Many of the approximations we will encounter have associated a set of parameters $\\theta$ that can be modified to suit the data at hand. For example, the linear model\n",
    "\n",
    "\\begin{equation}\n",
    "f(x) = x^T\\beta\n",
    "\\end{equation}\n",
    "\n",
    "has $\\theta=\\beta$.\n",
    "\n",
    "Another class of useful approximators can be expressed as _linear basis expansions_\n",
    "\\begin{equation}\n",
    "f_\\theta(x) = \\sum_{k=1}^K h_k(x)\\theta_k,\n",
    "\\end{equation}\n",
    "where the $h_k$ are a suitable set of functions or transformations of the input vector $x$. Traditional examples are polynomial and trigonometric expansions, where for example $h_k$ might be $x_1^2$, $x_1x_2^2$, $\\text{cos}(x_1)$ and so on.\n",
    "\n",
    "We also encounter nonlinear expansions, such as the sigmoid transformation common to neural network models,\n",
    "\\begin{equation}\n",
    "h_k(x) = \\frac{1}{1+\\text{exp}(-x^T\\beta_k)}.\n",
    "\\end{equation}\n",
    "\n",
    "### Least squares again\n",
    "We can use least squares to estimate the parameters $\\theta$ in $f_\\theta$ as we did for the linear model, by minimizing the residual sum-of-squares\n",
    "\\begin{equation}\n",
    "\\text{RSS}(\\theta) = \\sum_{i=1}^N\\left(y_i-f_\\theta(x_i)\\right)^2\n",
    "\\end{equation}\n",
    "as a function of $\\theta$. This seems a reasonable criterion for an additive error model.\n",
    "\n",
    "In terms of function approximation, we imagine our parametrized function as a surface in $p+1$ space, and what we observe are noisy realizations from it. This is easy to visualize when $p=2$ and the vertical coordinate in the output $y$, as in FIGURE 2.10. The noise is in the output coordinate, so we find the set of parameters such that the fitted surface gets as close to the observed points as possible, where close is measured by the sum of squared vertical errors in $\\text{RSS}(\\theta)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the linear model we get a simple closed form solution to the minimization problem. This is also true for the basis function methods, if the basis functions themselves do not have any hidden parameters. Otherwise the solution requires either iterative methods or numerical optimization.\n",
    "\n",
    "While least squares is generally very convenient, it is not the only criterion used and in some cases would not make much sense. A more general principle for estimation is _maximum likelihood estimation_."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Maximum likelihood estimation\n",
    "\n",
    "Suppose we have a random sample $y_i, i=1,\\cdots,N$ from a density $\\text{Pr}_\\theta(y)$ indexed by some parameters $\\theta$. The log-probability of the observed sample is\n",
    "\n",
    "\\begin{equation}\n",
    "L(\\theta) = \\sum_{i=1}^N\\log\\text{Pr}_\\theta(y_i).\n",
    "\\end{equation}\n",
    "\n",
    "> The principle of maximum likelihood assumes that the most reasonable values for $\\theta$ are those for which the probability of the observed sample is largest.\n",
    "\n",
    "#### Least squares = ML with Gaussian errors\n",
    "Least squares for the additive error model $Y = f_\\theta(X) + \\epsilon$, with $\\epsilon \\sim N(0, \\sigma^2)$, is equivalent to maximum likelihood using the conditional likelihood\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{Pr}(Y|X,\\theta) = N(f_\\theta(X), \\sigma^2).\n",
    "\\end{equation}\n",
    "\n",
    "So although the additional assumption of normality seems more restrictive, the results are the same. The log-likelihood of the data is\n",
    "\n",
    "\\begin{equation}\n",
    "L(\\theta) = -\\frac{N}{2}\\log(2\\pi) - N\\log\\sigma - \\frac{1}{2\\sigma^2} \\sum_{i=1}^N \\left( y_i - f_\\theta(x_i) \\right)^2,\n",
    "\\end{equation}\n",
    "\n",
    "and the only term involving $\\theta$ is the last, which is $\\text{RSS}(\\theta)$ up to a scalar negative multiplier.\n",
    "\n",
    "#### Multinomial likelihood for a qualitative output $G$\n",
    "\n",
    "A more interesting example is the multinomial likelihood for the regression function $\\text{Pr}(G|X)$ for a qualitative output $G$.\n",
    "\n",
    "Suppose we have a model\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{Pr}(G=\\mathcal{G}_k|X=x) = p_{k,\\theta}(x), k=1,\\cdots,K\n",
    "\\end{equation}\n",
    "\n",
    "for the conditional density of each class given $X$, indexed by the parameter vector $\\theta$. Then the log-likelihood (also referred to as the cross-entropy) is\n",
    "\n",
    "\\begin{equation}\n",
    "L(\\theta) = \\sum_{i=1}^N\\log p_{g_i,\\theta}(x_i),\n",
    "\\end{equation}\n",
    "\n",
    "and when maximized it delivers values of $\\theta$ that best conform with the data in the likelihood sense."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $\\S$ 2.7. Structured Regression Models\n",
    "\n",
    "### Review & motivation\n",
    "\n",
    "We have seen that although nearest-neighbor and other local methods focus directly on estimating the function at a point, they face problems in high dimensions. They may also be inappropriate even in low dimensions in cases where more structured approaches can make more efficient use of the data.\n",
    "\n",
    "This section introduces classes of such structured approaches. Before we proceed, though, we discuss further the need for such classes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\S$ 2.7.1. Difficulty of the Problem\n",
    "\n",
    "Consider the RSS criterion for an arbitrary function $f$,\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{RSS}(f) = \\sum_{i=1}^N \\left( y_i - f(x_i) \\right)^2.\n",
    "\\end{equation}\n",
    "\n",
    "Minimizing the RSS leads to infinitely many solutions: Any function $\\hat{f}$ passing through the training points $(x_i,y_i)$ is a solution. Any particular solution chosen might be a poor predictor at test points different from the training points.\n",
    "\n",
    "If there are multiple observation pairs $(x_i,y_{il})$, $l=1,\\cdots,N_i$, at each value of $x_i$, the risk is limited. In this case, the solution pass through the average values of the $y_{il}$ at each $x_i$ (Exercise 2.6). The situation is similar to the one we have already visited in $\\S$ 2.4; indeed, the above RSS is the finite sample version of the expected prediction error\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{EPE}(f) = \\text{E}\\left( Y - f(X) \\right)^2 = \\int \\left( y - f(x) \\right)^2 \\text{Pr}(dx, dy).\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Necessity & limit of the restriction\n",
    "\n",
    "If the sample size $N$ were sufficiently large such that repeats were guaranteed and densely arranged, it would seem that these solutions might all tend to the limiting conditional expectation.\n",
    "\n",
    "In order to obtain useful results for finite $N$, we must restrict the eligible solution to the RSS to a smaller set of functions.\n",
    "\n",
    "> How to decide on the nature of the restrictions is based on considerations outside of the data.\n",
    "\n",
    "These restrictions are somtimes\n",
    "* encoded via the parametric representation of $f_\\theta$, or\n",
    "* may be built into the learning method itself, either implicitly or explicitly.\n",
    "\n",
    "> These restricted classes of solutions are the major topic of this book.\n",
    "\n",
    "One thing should be clear, though.\n",
    "\n",
    "> Any restrictions imposed on $f$ that lead to a unique solution to RSS do not really remove the ambiguity caused by the multiplicity of solutions. There are infinitely many possible restrictions, each leading to a unique solution, so the abmiguity has simply been transferred to the choice of constraint."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Complexity\n",
    "\n",
    "In general the constraints imposed by most learning methods can be described as _complexity_ restrictions of one kind or another.\n",
    "\n",
    "> This usually means some kind of regular behavior in small neighborhoods of the input space.\n",
    "\n",
    "That is, for all input points $x$ sufficiently close to each other in some metric, $\\hat{f}$ exhibits some special structure such as\n",
    "* nearly constant,\n",
    "* linear or\n",
    "* low-order polynomial behavior.\n",
    "\n",
    "The estimator is then obtained by averaging or polynomial fitting in that neighborhood.\n",
    "\n",
    "The strength of the constraint is dictated by the neighborhood size.\n",
    "\n",
    "> The larger the size, the stronger the constraint, and the more sensitive the solution is to the particular choice of constraint.\n",
    "\n",
    "For example,\n",
    "* local constant fits in infinitesimally small neighborhoods is no constraints at all;\n",
    "* local linear fits in very large neighborhoods is almost a globally llinear model, and is very restrictive."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Metric\n",
    "\n",
    "The nature of the constraint depends on the metric used.\n",
    "\n",
    "Some methods, such as kernel and local regression and tree-based methods, directly specify the metric and size of the neighborhood. The kNN methods discussed so far are based on the assumption that locally the function is constant; close to a target input $x_0$, the function does not change much, and so close outputs can be averagedd to produce $\\hat{f}(x_0)$.\n",
    "\n",
    "Other methods such as splines, neural networks and basis-function methods implicitly define neighborhoods of local behavior. In $\\S$ 5.4.1 we discuss the concept of an _equivalent kernel_, which describes this local dependence for any method linear in the outputs. These equivalent kernels in many cases look just like the explicitly defined weighting kernels discussed above -- peaked at the target point and falling smoothly away from it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Curse of dimensionality\n",
    "\n",
    "One fact should be clear by now. Any method that attempts to produce locally varying functions in small isotopic neighborhoods will run into problems in high dimensions -- again the curse of dimensionality.\n",
    "\n",
    "And conversely, all methods that overcome the dimensionality problems have an associated -- and often implicit or adaptive -- metric for measuring neighborhoods, which basically does not allow the neighborhood to be simultaneously small in all directions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $\\S$ 2.8. Classes of Restricted Estimators\n",
    "\n",
    "The variety of nonparametric regression techniques or learning methods fall into a number of different classes depending on the nature of the restrictions imposed. These classes are not distinct, and indeed some methods fall in several classes.\n",
    "\n",
    "Each of the classes has associated with it one or more parameters, sometimes appropriately called _smoonthing_ parameters, that control the effective size of the local neighborhood.\n",
    "\n",
    "Here we describe three broad classes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\S$ 2.8.1. Roughness Penalty and Bayesian Methods\n",
    "\n",
    "Here the class of functions is controlled by explicitly penalizing $\\text{RSS}(f)$ with a roughness penalty $J$\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{PRSS}(f;\\lambda) = \\text{RSS}(f) + \\lambda J(f),\n",
    "\\end{equation}\n",
    "\n",
    "where the user-selected functional $J(f)$ will be large for functions $f$ that vary too rapidly over small regions of input space.\n",
    "\n",
    "#### Cubic smoothing spline\n",
    "\n",
    "For example, the popular *cubic smoothing spline* for one-dimensional inputs is the solution to the penalized least-squares criterion\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{PRSS}(f;\\lambda) = \\sum_{i=1}^N \\left(y_i-f(x_i)\\right)^2 + \\lambda\\int\\left[f''(x)\\right]^2 dx.\n",
    "\\end{equation}\n",
    "\n",
    "This roughness penalty controls large values of the second derivative of $f$, and the amount penalty is dictated by $\\lambda \\ge 0$. For $\\lambda =0$ no penalty is imposed, and any interpolating will do, while for $\\lambda = \\infty$ only functions linear in $x$ are permitted.\n",
    "\n",
    "### Various penalties\n",
    "\n",
    "Penalty functionals $J$ can be constructed for functions in any dimension, and special versions can be created to impose special structure. For example, additive penalties\n",
    "\n",
    "\\begin{equation}\n",
    "J(f) = \\sum_{j=1}^p J(f_j)\n",
    "\\end{equation}\n",
    "\n",
    "are used in conjunction with additive functions $f(X) = \\sum_{j=1}^p f_j(X_j)$ to create additive models with smooth coordinate functions.\n",
    "\n",
    "Similarly, _projection pursuit regression_ models have\n",
    "\n",
    "\\begin{equation}\n",
    "f(X) = \\sum_{m=1}^M g_m(\\alpha_m^T X)\n",
    "\\end{equation}\n",
    "\n",
    "for adaptively chosen direction $\\alpha_m$, and the functions $g_m$ can each have an associated roughness penalty.\n",
    "\n",
    "### Connection with Bayesian framework\n",
    "\n",
    "Penalty function, or _regularization_ methods, express our prior belief that the type of functions we seek exhibits a certain type of smooth behavior, and indeed can usually be cast in a Bayesian framework.\n",
    "* The penalty $J$ corresponds to a log-prior, and\n",
    "* $\\text{PRSS}(f;\\lambda)$ the log-posterior distribution, and\n",
    "* minimizing $\\text{PRSS}$ amounts to finding the posterior mode.\n",
    "\n",
    "We discuss roughness-penalty approaches in Chapter 5 and the Bayesian paradigm in Chapter 8."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\S$ 2.8.2. Kernel Methods and Local Regression\n",
    "\n",
    "These methods can be thought of as explicitly providing estimates of the regression function or conditional expectation by specifying the nature of the local neighborhood, and of the class of regular functions fitted locally.\n",
    "\n",
    "The local neighborhood is specified by a _kernel function_ $K_\\lambda(x_0, x)$ which assigns weights to points $x$ in a region around $x_0$ (FIGURE 6.1). For example, the Gaussian kernel has a weight function based on the Gaussian density function\n",
    "\n",
    "\\begin{equation}\n",
    "K_\\lambda(x_0, x) = \\frac{1}{\\lambda}\\exp\\left(-\\frac{\\|x-x_0\\|^2}{2\\lambda}\\right),\n",
    "\\end{equation}\n",
    "\n",
    "and assigns weights to points that die exponentially with their squared Euclidean distance from $x_0$. The parameter $\\lambda$ corresponds to the variance of the Gaussian density, and controls the width of the neighborhood.\n",
    "\n",
    "The simplest form of kernel estimate is the Nadaraya-Watson weighted average\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{f}(x_0) = \\frac{\\sum_{i=1}^N K_\\lambda(x_0, x_i)y_i}{\\sum_{i=1}^N K_\\lambda(x_0, x_i)}.\n",
    "\\end{equation}\n",
    "\n",
    "### Formulation\n",
    "\n",
    "In general, we can define a local regression estimate of $f(x_0)$ as $f_{\\hat{\\theta}}(x_0)$, where $\\hat{\\theta}$ minimizes\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{RSS}(f_\\theta,x_0) = \\sum_{i=1}^N K_\\lambda(x_0, x_i)\\left(y_i -f_\\theta(x_i)\\right)^2,\n",
    "\\end{equation}\n",
    "\n",
    "where $f_\\theta$ is some parameterized function, such as a low-order polynomial. Some examples are:\n",
    "* $f_\\theta(x) = \\theta_0$, the constant function; this results in the Nadaraya-Watson estimate.\n",
    "* $f_\\theta(x) = \\theta_0+\\theta_1 x$ gives the popular local linear regression model.\n",
    "\n",
    "### Association between kernel methods and kNN\n",
    "\n",
    "Nearest-neighbor methods can be thought of as kernel methods having a more data-dependent metric. Indeed, the metric for kNN is\n",
    "\n",
    "\\begin{equation}\n",
    "K_k(x,x_0) = I\\left(\\|x-x_0\\| \\le \\|x_{(k)}-x_0\\|\\right),\n",
    "\\end{equation}\n",
    "\n",
    "where\n",
    "* $x_{(k)}$ is the training observation ranked $k$th in distance from $x_0$, and\n",
    "* $I(S)$ is the indicator of the set $S$.\n",
    "\n",
    "These methods of course need to be modified in high dimensions, to avoid the curse of dimensionality.\n",
    "\n",
    "Various adaptations are discussed in Chapter 6."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\S$ 2.8.3. Basis functions and Dictionary Methods\n",
    "\n",
    "This class of methods includes the familiar linear and polynomial expansions, but more importantly a wide variety of more flexible models.\n",
    "\n",
    "### Linear expansion\n",
    "\n",
    "The model for $f$ is a linear expansion of basis functions\n",
    "\n",
    "\\begin{equation}\n",
    "f_\\theta(x) = \\sum_{m=1}^M\\theta_m h_m(x),\n",
    "\\end{equation}\n",
    "\n",
    "where each of the $h_m$ is a function of the input $x$, and the term linear here refers to the action of the parameter $\\theta$.\n",
    "\n",
    "This class covers a wide variety of methods.\n",
    "\n",
    "In some cases the sequence of basis functions is prescribed, such as a basis for polynomials in $x$ of total degree $M$.\n",
    "\n",
    "#### Splines\n",
    "\n",
    "For 1D $x$, polynomial splines of degree $K$ can be represented by an appropriate sequence of $M$ spline basis functions, determined in turn by $M-K-1$ _knots_. These produce functions that are piecewise polynomials of degree $K$ between the knots, and joined up with continuity of degree $K-1$ at the knots.\n",
    "\n",
    "#### Linear splines\n",
    "\n",
    "As an example consider linear splines, or piecewise linear functions. One intuitively satisfying basis consist of the functions\n",
    "\n",
    "\\begin{align}\n",
    "b_1(x) &= 1, \\\\\n",
    "b_2(x) &= x, \\\\\n",
    "b_{m+2}(x) &= (x - t_m)_+, m=1,\\cdots,M-2,\n",
    "\\end{align}\n",
    "\n",
    "where\n",
    "* $t_m$ is the $m$th knot, and\n",
    "* $z_+$ denotes positive part.\n",
    "\n",
    "Tensor products of spline bases can be used for inputs with dimensions larger than one ($\\S$ 5.2, and the CART/MARS model in Chapter 9).\n",
    "\n",
    "The parameter $M$ controls the degree of the polynomial or the number of knots in the case of splines.\n",
    "\n",
    "### Radial basis functions\n",
    "\n",
    "_Radial basis functions_ are symmetric $p$-dimensional kernels located at particular centroids,\n",
    "\n",
    "\\begin{equation}\n",
    "f_\\theta(x) = \\sum_{m=1}^M K_{\\lambda_m}(\\mu_m,x) \\theta_m,\n",
    "\\end{equation}\n",
    "\n",
    "e.g., the Gaussian kernel $K_\\lambda(\\mu,x)=e^{-\\|x-\\mu\\|^2/2\\lambda}$ is popular.\n",
    "\n",
    "Radial basis functions have centroids $\\mu_m$ and scales $\\lambda_m$ that have to be determined. The spline basis functions have knots. In general we would like the data to dictate them as well.\n",
    "\n",
    "> Including these as parameters changes the regression problem from a straightforward linear problem to a combinatorially hard nonlinear problem.\n",
    "\n",
    "In practice, shortcuts such as greedy algorithms or two stage processes are used ($\\S$ 6.7).\n",
    "\n",
    "### Neural networks\n",
    "\n",
    "A single-layer feed-forward neural network model with linear output weights can be thought of as an adaptive basis function method.\n",
    "\n",
    "The model has the form\n",
    "\n",
    "\\begin{equation}\n",
    "f_\\theta(x) = \\sum_{m=1}^M \\beta_m \\sigma(\\alpha_m^T x + b_m),\n",
    "\\end{equation}\n",
    "\n",
    "where\n",
    "\n",
    "\\begin{equation}\n",
    "\\sigma(x) = \\frac{1}{1+e^{-x}}\n",
    "\\end{equation}\n",
    "\n",
    "is known as the _activation_ function.\n",
    "\n",
    "Here, as in the projection pursuit model, the directions $\\alpha_m$ and the _bias_ term $b_m$ have to be determined, and their estimation is the meat of the computation (Chapter 11).\n",
    "\n",
    "### Dictionary\n",
    "\n",
    "These adaptively chosen basis function methods are a.k.a. _dictionary_ methods, where one has available a possibly infinite set or dictionary $\\mathcal{D}$ of candidate basis functions from which to choose, and models are built up by employing some kind of search mechanism."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $\\S$ 2.9. Model Selection and the Bias-Variance Tradeoff\n",
    "\n",
    "### Review\n",
    "\n",
    "All the Models described so far have a *smoothing* or *complexity* parameter that has to be determined:\n",
    "* The multiplier of the penalty term;\n",
    "* the width of the kernel;\n",
    "* or the number of basis functions.\n",
    "\n",
    "In the case of the smoothing spline, the parameter $\\lambda$ indexes models ranging from a straight line fit to the interpolating model.\n",
    "\n",
    "Similarly a local degree-$m$ polynomial model ranges between a degree-$m$ global polynomial when the window size is infinitely large, to an interpolating fit when the window size shrinks to zero.\n",
    "\n",
    "This means that we cannot use residual sum-of-squares on the training data to determine these parameters as well, since we would always pick those that gave interpolating fits and hence zero residuals. Such a model is unlikely to predict future data well at all."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The bias-variance tradeoff for the kNN\n",
    "\n",
    "The kNN regression fit $\\hat{f}_k(x_0)$ usefully illustrates the competing forces that affect the predictive ability of such approximations.\n",
    "\n",
    "Suppose\n",
    "* the data arise from a model $Y=f(X)+\\epsilon$, with $\\text{E}(\\epsilon)=0$ and $\\text{Var}(\\epsilon)=\\sigma^2$;\n",
    "* for simplicity here the values of $x_i$ in the sample are fixed in advance (nonrandom).\n",
    "\n",
    "The expected prediction error at $x_0$, a.k.a. _test_ or _generalization_ error, can be decomposed:\n",
    "\n",
    "\\begin{align}\n",
    "\\text{EPE}_k(x_0) &= \\text{E}\\left[(Y-\\hat{f}_k(x_0))^2|X=x_0\\right] \\\\\n",
    "&= \\text{E}\\left[(Y -f(x_0) + f(x_0) -\\hat{f}_k(x_0))^2|X=x_0\\right] \\\\\n",
    "&= \\text{E}(\\epsilon^2) + 2\\text{E}\\left[\\epsilon(f(x_0) -\\hat{f}_k(x_0))|X=x_0\\right] + \\text{E}\\left[\\left(f(x_0)-\\hat{f}_k(x_0)\\right)^2|X=x_0\\right] \\\\\n",
    "&= \\sigma^2 + 0+ \\left[\\text{Bias}^2(\\hat{f}_k(x_0))+\\text{Var}_\\mathcal{T}(\\hat{f}_k(x_0))\\right] \\\\\n",
    "&= \\sigma^2 + \\left(f(x_0) - \\frac{1}{k}\\sum_{l=1}^k f(x_{(l)})\\right)^2 + \\frac{\\sigma^2}{k}\n",
    "\\end{align},\n",
    "\n",
    "where subscripts in parentheses $(l)$ indicate the sequence of nearest neighbors to $x_0$.\n",
    "\n",
    "There are three terms in this expression.\n",
    "\n",
    "#### Irreducible error\n",
    "The first term $\\sigma^2$ is the *irreducible* error -- the variance of the new test target -- and is beyond our control, even if we know the true $f(x_0)$.\n",
    "\n",
    "The second and third terms are under our control, and make up the _mean squared error_ of $\\hat{f}_k(x_0)$ in estimateing $f(x_0)$, which is broken down into a bias component and a variance component.\n",
    "\n",
    "#### Bias\n",
    "The bias term is the squared difference between the true mean $f(x_0)$ and the expected value of the estimate, i.e.,\n",
    "\n",
    "\\begin{equation}\n",
    "\\left[ \\text{E}_\\mathcal{T} \\left( \\hat{f}_k(x_0) \\right) - f(x_0) \\right]^2,\n",
    "\\end{equation}\n",
    "\n",
    "where the expectation averages the randomness in the training data.\n",
    "\n",
    "This term will most likely increase with $k$, if the true function is reasonably smooth. For small $k$ the few closest neighbors will have values $f(x_{(l)})$ close to $f(x_0)$, so their average should be close to $f(x_0)$. As $k$ grows, the neighbors are further away, and then anything can happen.\n",
    "\n",
    "#### Variance\n",
    "The variance term is simply the variance of an average here, and decreases as the inverse of $k$.\n",
    "\n",
    "#### Finally, the tradeoff\n",
    "So as $k$ varies, there is a *bias-variance tradeoff*.\n",
    "\n",
    "More generally, as the _model complexity_ of our procedure is increased, the variance tends to increase and the squared bias tends to decrease, vice versa. For kNN, the model complexity is controlled by $k$.\n",
    "\n",
    "Typically we would like to choose our model complexity to trade bias off with variance in such a way as to minimize the test error. An obvious estimate of test error is _training error_\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{1}{N} \\sum_i (y_i \\hat{y}_i)^2.\n",
    "\\end{equation}\n",
    "\n",
    "Unfortunately training error is not a good estimate of test error, as it does not properly account for model complexity."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpretation & implication\n",
    "FIGURE 2.11 shows the typical behavior of the test and training error, as model complexity is varied.\n",
    "\n",
    "> The training error tends to decrease whenever we increase the model complexity, i.e., whenever we fit the data harder.\n",
    "\n",
    "However with too much fitting, the model adapts itself too closely to the training data, and will not generalize well (i.e., have large test error). In that case the predictions $\\hat{f}(x_0)$ will have large variance, as reflected in the above EPE expression.\n",
    "\n",
    "In contrast, if the model is not complex enough, it will _underfit_ and may have large mias, again resulting in poor generalization. In Chapter 7 we discuss methods for estimating the test error of a prediction method, and hence estimating the optimal amount of model complexity fir a given prediction method and training set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $\\S$ Exercises\n",
    "## Ex. 2.1 (target coding)\n",
    "\n",
    "Suppose each of $K$-classes has an associated target $t_k$, which is a vector of all zeros, except a one in the $k$th position. Show that classifying to\n",
    "the largest element of $\\hat{y}$ amounts to choosing the closest target, $\\text{min}_k||t_k − \\hat{y}||$, if the elements of $\\hat{y}$ sum to one."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have some input data $x$. Some algorithm assigns to $x$ the probability $y_k$ that $x$ is a member of the $k$-th class. This would explain why the sum of the $y_k$ is equal to one.\n",
    "For each $k$ with $1 \\leq k \\leq K$, let $t_k$ be the $K$-dimensional vector that has $1$ in the $k$-th position and $0$ elsewhere. \n",
    "\\begin{align}\n",
    "\\text{argmin}_k||y-t_k||&=\\text{argmin}_k||y-t_k||^2\\\\\n",
    "&=\\text{argmin}_k\\sum_{i=1}^{K}(y_i-(t_k)_i)^2\\\\\n",
    "&=\\text{argmin}_k\\sum_{i=1}^{K}\\Bigl(y_i^2-2y_i(t_k)_i+(t_k)_i^2\\bigr)\\\\\n",
    "&=\\text{argmin}_k\\sum_{i=1}^{K}\\Bigl(-2y_i(t_k)_i+(t_k)_i^2\\bigr)\\\\\n",
    "\\end{align}\n",
    "Since $\\sum_{i=1}^{K}y_i^2$ is the same for all classes $k$. For each $k$, the sum $\\sum_{i=1}^{K}(t_k)_i^2=1$. Also $\\sum_{i=1}^{K}y_i(t_k)_i=y_k$. This means that  \n",
    "\\begin{align}\n",
    "\\text{argmin}_k||y-t_k||&=\\text{argmin}_k(-2y_k+1)\\\\\n",
    "&=\\text{argmin}_k(-2y_k)\\\\\n",
    "&=\\text{argmax}_k(y_k)\\\\\n",
    "\\end{align}\n",
    "Then, for any $K$-dimensional vector $y$, the $k$ for which $y_k$ is largest coincides with the $k$ for which $t_k$ is nearest to $y$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex. 2.2 (the oracle revealed)\n",
    "\n",
    "Show how to compute the Bayes decision boundary for the simulation example \n",
    "in Figure 2.5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simulation draws $10$ “blue” centering points $p_1, \\cdots, p_{10} \\in \\mathbb{R}^2$ from $N\\Biggl(\\begin{bmatrix}\n",
    "1\\\\\n",
    "0\\\\\n",
    "\\end{bmatrix}, I_2\\Biggr)$ and $10$ “orange” centering points $q_1, \\cdots, q_{10} \\in \\mathbb{R}^2$ from $N\\Biggl(\\begin{bmatrix}\n",
    "0\\\\\n",
    "1\\\\\n",
    "\\end{bmatrix}, I_2\\Biggr)$.  The multivariate Gaussian densities:\n",
    "\n",
    "$$f_X(\\mathbf x)=\\frac{1}{(2\\pi)^{p/2}|\\mathbf\\Sigma|^{1/2}}e^{-\\frac{1}{2}(\\mathbf x-\\boldsymbol \\mu)^T(\\mathbf\\Sigma)^{-1}(\\mathbf x-\\boldsymbol \\mu)}$$\n",
    "\n",
    "The $p\\times p$ matrix $\\mathbf \\Sigma$ is the variance–covariance matrix of $\\mathbf X$.  \n",
    "\n",
    "The covariance matrix $$\\mathbf \\Sigma=\\begin{bmatrix}\n",
    "\\sigma_{11}&\\sigma_{12}\\\\\n",
    "\\sigma_{12}&\\sigma_{22}\n",
    "\\end{bmatrix}\n",
    "$$  $$\\mathbf \\Sigma^{-1}=\\frac{1}{\\sigma_{11}\\sigma_{22}-\\sigma_{12}^2}\\begin{bmatrix}\n",
    "\\sigma_{22}&-\\sigma_{12}\\\\\n",
    "-\\sigma_{12}&\\sigma_{11}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "The formula for the Bayes decision boundary is given by equating posterior probabilities. We get an equation in the unknown $z \\in \\mathbb R^2$, giving a curve in the plane:  \n",
    "\\begin{equation}\n",
    "P(\\text{blue})\\exp(-\\sum_{i=1}^{10}\\lVert p_i-z\\lVert ^2/2)=P(\\text{orange)})\\exp(-\\sum_{j=1}^{10}\\lVert q_j-z\\lVert ^2/2)\n",
    "\\end{equation}  \n",
    "\n",
    "In this solution, the boundary is given as the equation of equality between the two probabilities, with the $p_i$ and $q_j$ constant and fixed by previously performed sampling. Each time one re-samples the $p_i$ and $q_j$ , one obtains a different Bayes decision boundary. Note that if the prior probabilities are equal (as they seem to be in this example) we have \n",
    "$$P(\\text{blue})=P(\\text{orange)})=\\frac{1}{2}$$\n",
    "and they also cancel."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex. 2.3 (the median distance to the origin)\n",
    "Consider $N$ data points uniformly distributed in a $p$-dimensional unit ball centered at the origin. Suppose we consider a nearest-neighbor estimate at the origin. The median distance from the origin to the closest data point is given by the expression  \n",
    "$$d(p,N)=\\Bigl(1-\\frac{1}{2}^{1/N}\\Bigr)^{1/p}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We derive the distribution function (CDF) for the Euclidean distance (denoted by $y$) from the origin to the closest point of $n$ points $x_i$ where each point $x_i$ is drawn uniformly from a $p$-dimensional unit ball centered at the origin. The distribution function of $y=\\lVert x_i\\rVert$ is the ratio of the volume of a ball of radius $y$ and the volume of a ball of radius one. This ratio is $y^p$ and so $F(y)=y^p$. The distribution function for $y$ is then $f(y)=F'(y)=py^{p-1}$. \n",
    "\n",
    "Given $N$ such vectors $\\{x_i\\}_{i=1}^N$ the distribution function for the smallest radius $Y_1$ (from all of them) is given by $$F_{Y_1}(y)=1-(1-F(y))^N=1-(1-y^p)^N$$\n",
    "The median distance for $Y_1$ is found by solving for $y$ in $$\\frac{1}{2}=F_{Y_1}(y)$$ This gives $$y=\\Bigl(1-\\frac{1}{2}^{1/N}\\Bigr)^{1/p}=d_{median}(p,N)$$.\n",
    "\n",
    "The density function for $Y_1$ is given by the derivative of the distribution function $F_{Y_1}(y)$:\n",
    "\n",
    "$$f_{Y_1}(y)=N(1-y^p)^{N-1}(py^{p-1})=pN(1-y^p)^{N-1}y^{p-1}$$\n",
    "\n",
    "Then the mean distance to the closest of these $N$ points is given by\n",
    "\n",
    "$$d_{\\text{mean}}(p,N)\\equiv \\int_{0}^{1}yf_{Y_1}(y)dy=pN\\int_{0}^{1}(1-y^p)^{N-1}y^pdy\\\\\n",
    "=N\\int_{0}^{1}(1-t)^{N-1}ydt\\quad(t=y^p)\\\\\n",
    "=N\\int_{0}^{1}(1-t)^{N-1}t^{1/p}dt\\\\\n",
    "=NB(N,\\frac{1}{p}+1)$$ \n",
    "\n",
    "The Beta function is:\n",
    "\n",
    "$$B(x,y)=\\int_{t=0}^{t=1}t^{(x-1)}(1-t)^{(y-1)}dt,\\quad (x>0 ;\\quad y>0)$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex. 2.4 (projections a^T x are distributed as normal N(0, 1)) \n",
    "\n",
    "The edge effect problem discussed on page 23 is not peculiar to\n",
    "uniform sampling from bounded domains. Consider inputs drawn from a\n",
    "spherical multinormal distribution $X \\sim N(0, I_p)$. The squared distance\n",
    "from any sample point to the origin has a $\\chi^2_p$ distribution with mean $p$. Consider a prediction point $x_0$ drawn from this distribution, and let $$a = x_0/\\lVert x_0\\rVert$$ be an associated unit vector. Let $z_i = a^Tx_i$ be the projection of each of the training points on this direction. \n",
    "\n",
    "\n",
    "Show that the $z_i$ are distributed $N(0, 1)$ with expected squared distance\n",
    "from the origin $1$, while the target point has expected squared distance $p$\n",
    "from the origin.\n",
    "\n",
    "Hence for $p = 10$, a randomly drawn test point is about $3.1$ standard deviations from the origin, while all the training points are on average\n",
    "one standard deviation along direction $a$. So most prediction points see\n",
    "themselves as lying on the edge of the training set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The main point is that $\\sum\\lVert x_i\\rVert^2$ is invariant under the orthogonal group. As a consequence the standard normal distribution exists on any finite dimensional inner product space (by fixing an orthonormal basis). Further, if $\\mathbb R^p$ is written as the orthogonal sum of two vector\n",
    "subspaces, then the product of standard normal distributions on each of the subspaces gives the standard normal distribution on $\\mathbb R^p$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex. 2.5 (the expected prediction error under least squares)\n",
    "(a) Derive equation (2.27). The last line makes use of (3.8) through a\n",
    "conditioning argument.\n",
    "\n",
    "(b) Derive equation (2.28), making use of the cyclic property of the trace\n",
    "operator $[\\text{trace}(AB) = \\text{trace}(BA)]$, and its linearity (which allows us to interchange the order of trace and expectation)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(a): \n",
    "equation (2.27)\n",
    "\\begin{align}\n",
    "\\text{EPE}(x_0) &= \\text{E}_{y_0|x_0}\\text{E}_\\mathcal{T}\\left(y_0-\\hat{y}_0\\right)^2 \\\\\n",
    "&= \\text{E}_{y_0|x_0}\\text{E}_\\mathcal{T}\\Biggl([y_0-x_0^T\\beta]+[\\text{E}_\\mathcal{T}(\\hat{y}_0)-\\hat{y}_0]+[x_0^T\\beta-\\text{E}_\\mathcal{T}(\\hat{y}_0)]\\Biggr)^2 \\\\\n",
    "\\end{align}\n",
    "\n",
    "Since\n",
    "\\begin{equation}\n",
    "\\text{E}_{y_0|x_0}\\text{E}_\\mathcal{T}[y_0-x_0^T\\beta]=\\text{E}_{y_0|x_0}[y_0-x_0^T\\beta]\\text{E}_\\mathcal{T}=0\\text{E}_\\mathcal{T}=0\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{E}_{y_0|x_0}\\text{E}_\\mathcal{T}[y_0-x_0^T\\beta]^2=\\text{Var}(y_0|x_0)=\\sigma^2\n",
    "\\end{equation}\n",
    "And\n",
    "\\begin{equation}\n",
    "\\text{E}_{y_0|x_0}\\text{E}_\\mathcal{T}[\\text{E}_\\mathcal{T}(\\hat{y}_0)-\\hat{y}_0]=\\text{E}_{y_0|x_0}0=0\n",
    "\\end{equation}\n",
    "\n",
    "And since the expectation of the length $N$ vector $\\epsilon$ is zero.\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{E}_\\mathcal{T}(\\hat{y}_0)-x_0^T\\beta=\\text{E}_\\mathcal{T}(x_0^T\\beta+(X(X^TX)^{-1}x_0)^T\\epsilon)-x_0^T\\beta\\\\\n",
    "=\\text{E}_\\mathcal{T}(X(X^TX)^{-1}x_0)^T\\epsilon=0\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{E}_{y_0|x_0}\\Biggl([y_0-x_0^T\\beta][\\text{E}_\\mathcal{T}(\\hat{y}_0)-\\hat{y}_0]\\Biggr)=[\\text{E}_\\mathcal{T}(\\hat{y}_0)-\\hat{y}_0]\\text{E}_{y_0|x_0}[y_0-x_0^T\\beta]=0\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "\\begin{align}\n",
    "\\text{EPE}(x_0) &= \\text{E}_{y_0|x_0}\\text{E}_\\mathcal{T}\\left(y_0-\\hat{y}_0\\right)^2 \\\\\n",
    "&= \\text{E}_{y_0|x_0}\\text{E}_\\mathcal{T}\\Biggl([y_0-x_0^T\\beta]+[\\text{E}_\\mathcal{T}(\\hat{y}_0)-\\hat{y}_0]+[x_0^T\\beta-\\text{E}_\\mathcal{T}(\\hat{y}_0)]\\Biggr)^2 \\\\\n",
    "&= \\text{Var}(y_0|x_0) + \\text{E}_{y_0|x_0}\\text{E}_\\mathcal{T} \\left(\\hat{y}_0 - \\text{E}_\\mathcal{T}\\hat{y}_0\\right)^2 \\\\\n",
    "&= \\text{Var}(y_0|x_0) + \\text{Var}_\\mathcal{T}(\\hat{y}_0) \\\\\n",
    "&= \\sigma^2 + \\text{E}_\\mathcal{T}x_0^T\\left(\\mathbf{X}^T\\mathbf{X}\\right)^{-1}x_0\\sigma^2.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(b): \n",
    "\n",
    "equation (2.28)Note that\n",
    "1. An additional variance $\\sigma^2$ is incurred, since our target is not deterministic.\n",
    "2. There is no bias, and the variance depends on $x_0$.\n",
    "\n",
    "If\n",
    "* $N$ is large,\n",
    "* $\\mathcal{T}$ were selected at random, and\n",
    "* $\\text{E}(X)=0$,\n",
    "If\n",
    "* $N$ is large,\n",
    "* $\\mathcal{T}$ were selected at random, and\n",
    "* $\\text{E}(X)=0$,\n",
    "then $\\mathbf{X}^T\\mathbf{X}\\rightarrow N\\text{Cov}(X)$ and\n",
    "\n",
    "\\begin{align}\n",
    "\\text{E}_{x_0}\\text{EPE}(x_0) &\\sim \\text{E}_{x_0}x_0^T\\text{Cov}(X)^{-1}x_0\\sigma^2/N + \\sigma^2 \\\\\n",
    "&= \\text{E}_{x_0}\\Bigl[\\text{trace}(x_0^T\\text{Cov}(X)^{-1}x_0)\\Bigr]\\sigma^2/N + \\sigma^2 \\\\\n",
    "&= \\text{E}_{x_0}\\Bigl[\\text{trace}(\\text{Cov}(X)^{-1}x_0x_0^T)\\Bigr]\\sigma^2/N + \\sigma^2 \\\\\n",
    "&= \\Bigl[\\text{trace}(\\text{Cov}(X)^{-1}\\text{Cov}(x_0))\\Bigr]\\sigma^2/N + \\sigma^2 \\\\\n",
    "&= \\text{trace}\\left(\\text{Cov}(X)^{-1}\\text{Cov}(x_0)\\right)\\sigma^2/N + \\sigma^2 \\\\\n",
    "&= \\text{trace}(I_p)\\sigma^2/N + \\sigma^2 \\\\\n",
    "&= \\sigma^2(p/N)+\\sigma^2.\n",
    "\\end{align}\n",
    "\n",
    "The expected EPE increases linearly as a function of $p$, with slope $\\sigma^2/N$. If $N$ is large and/or $\\sigma^2$ is small, this growth is variance is negligible (0 in the deterministic case).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex. 2.6 (repeated measurements)\n",
    "\n",
    "Consider a regression problem with inputs $x_i$ and outputs $y_i$, and a\n",
    "parameterized model $f_\\theta(x)$ to be fit by least squares. Show that if there are observations with tied or identical values of $x$, then the fit can be obtained from a reduced weighted least squares problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To search for parameter $\\theta$ using least squares one seeks to minimize:\n",
    "$$\\text{RSS}(\\theta)=\\sum_{k=1}^{N}(y_k-f_{\\theta}(x_k))^2$$\n",
    "If there are repeated independent variables $x_i$ then this prescription is\n",
    "equivalent to a weighted least squares problem. \n",
    "\n",
    "Let $N_u$ be the number of unique inputs $x$, that is, the number of distinct inputs after discarding duplicates. Assume that if the $i^{th}$ unique $x$ value gives rise to $n_i$ potentially different $y$ values. With this notation we can write the RSS(θ) above as:\n",
    "$$\\begin{align}\n",
    "\\text{RSS}(\\theta)&=\\sum_{i=1}^{N_u}\\sum_{j=1}^{n_i}(y_{ij}-f_{\\theta}(x_i))^2\\\\\n",
    "&=\\sum_{i=1}^{N_u}\\sum_{j=1}^{n_i}(y_{ij}^2-2y_{ij}f_{\\theta}(x_i)+f_{\\theta}(x_i)^2)\\\\\n",
    "&=\\sum_{i=1}^{N_u}n_i\\Biggl(\\frac{1}{n_i}\\sum_{j=1}^{n_i}y_{ij}^2-2\\frac{1}{n_i}f_{\\theta}(x_i)\\sum_{j=1}^{n_i}y_{ij}+f_{\\theta}(x_i)^2\\Biggr)\n",
    "\\end{align}$$\n",
    "Let's define $\\bar{y}_i=\\frac{1}{n_i}\\sum_{j=1}^{n_i}y_{ij}$ which is the average of all responses $y$ resulting from the same input $x_i$.\n",
    "$$\\text{RSS}(\\theta)=\\sum_{i=1}^{N_u}n_i\\Biggl(\\frac{1}{n_i}\\sum_{j=1}^{n_i}y_{ij}^2-2\\frac{1}{n_i}f_{\\theta}(x_i)\\sum_{j=1}^{n_i}y_{ij}+f_{\\theta}(x_i)^2\\Biggr)\\\\\n",
    "=\\sum_{i=1}^{N_u}n_i\\Biggl(\\frac{1}{n_i}\\sum_{j=1}^{n_i}y_{ij}^2+\\bar{y}_i^2-\\bar{y}_i^2-2\\frac{1}{n_i}f_{\\theta}(x_i)\\sum_{j=1}^{n_i}y_{ij}+f_{\\theta}(x_i)^2\\Biggr)\\\\\n",
    "=\\sum_{i=1}^{N_u}n_i\\Biggl(\\frac{1}{n_i}\\sum_{j=1}^{n_i}y_{ij}^2+\\bar{y}_i^2-\\bar{y}_i^2-2f_{\\theta}(x_i)\\bar{y}_i+f_{\\theta}(x_i)^2\\Biggr)\\\\\n",
    "=\\sum_{i=1}^{N_u}n_i\\Biggl(\\frac{1}{n_i}\\sum_{j=1}^{n_i}y_{ij}^2-\\bar{y}_i^2+\\Bigl(\\bar{y}_i-f_{\\theta}(x_i)\\Bigr)^2\\Biggr)\\\\\n",
    "=\\sum_{i=1}^{N_u}n_i\\Bigl(\\bar{y}_i-f_{\\theta}(x_i)\\Bigr)^2+\\sum_{i=1}^{N_u}\\sum_{j=1}^{n_i}y_{ij}^2-\\sum_{i=1}^{N_u}n_i\\bar{y}_i^2$$\n",
    "\n",
    "Once the measurements are received the sample points $y$ are fixed and do not change. Thus the minimization of $\\text{RSS}(\\theta)$ is minimization of $$\\sum_{i=1}^{N_u}n_i\\Bigl(\\bar{y}_i-f_{\\theta}(x_i)\\Bigr)^2$$ which is a weighted least squares since each repeated input vector $x_i$ is\n",
    "to fit the value of $\\bar{y}_i$ (the average of output values) and each residual error is weighted by how many times the measurement of $x_i$ was taken. It is a reduced problem since the number of points we are working with is now $N_u < N$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex. 2.7 (forms for linear regression and k-nearest neighbor regression)\n",
    "\n",
    "Suppose we have a sample of $N$ pairs $x_i$, $y_i$ drawn i.i.d. (\n",
    "Independent and identically distributed) from the\n",
    "distribution characterized as follows:\n",
    "\n",
    "\n",
    "$$\\begin{align}\n",
    "&x_i\\sim h(x), \\text{ the design density}\\\\\n",
    "&y_i=f(x_i)+\\epsilon_i,  f \\text{ is the regression function}\\\\\n",
    "&\\epsilon_i\\sim(0,\\sigma^2) (\\text{mean zero, variance} \\sigma^2)\n",
    "\\end{align}$$\n",
    "\n",
    "We construct an estimator for $f$ linear in the $y_i$, \n",
    "$$\\hat{f}(x_0)=\\sum_{i=1}^{N}\\ell_i(x_0;X)y_i$$\n",
    "where the weights $\\ell_i(x_0;X)$ do not depend on the $y_i$, but do depend on the entire training sequence of $x_i$, denoted here by $X$.\n",
    "\n",
    "(a) Show that linear regression and $k$-nearest-neighbor regression are members\n",
    "of this class of estimators. Describe explicitly the weights $\\ell_i(x_0;X)$\n",
    "in each of these cases.\n",
    "\n",
    "(b) Decompose the conditional mean-squared error $$\\text{E}_{Y|X}(f(x_0)-\\hat{f}(x_0))^2$$ into a conditional squared bias and a conditional variance component. Like $X, Y$ represents the entire training sequence of $y_i$.\n",
    "\n",
    "(c) Decompose the (unconditional) mean-squared error $$\\text{E}_{Y,X}(f(x_0)-\\hat{f}(x_0))^2$$ into a squared bias and a variance component.\n",
    "\n",
    "(d) Establish a relationship between the squared biases and variances in\n",
    "the above two cases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(a) In the case of simple linear regression where there is only\n",
    "one response $y$ and one predictor $x$. Then the standard definitions of $y$ and $X$ state that $$y^T=(y_1,\\cdots,y_n)$$ and $$X^T=\\begin{bmatrix}\n",
    "1&\\cdots&1\\\\\n",
    "x_1&\\cdots&x_n\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "For linear regression we have $$\\hat{\\beta}=(X^TX)^{-1}X^Ty$$ and set $$\\hat{f}(x_0)=\\begin{bmatrix}\n",
    "1 & x_0\n",
    "\\end{bmatrix}\\hat{\\beta}=\\begin{bmatrix}\n",
    "1 & x_0\n",
    "\\end{bmatrix}(X^TX)^{-1}X^Ty$$ Then for $$\\hat{f}(x_0)=\\sum_{i=1}^{N}\\ell_i(x_0;X)y_i$$ the weight\n",
    "$$\\ell_i(x_0;X)=\\begin{bmatrix}\n",
    "1 & x_0\n",
    "\\end{bmatrix}(X^TX)^{-1}\\begin{bmatrix}\n",
    "1 \\\\\n",
    "x_i\n",
    "\\end{bmatrix}$$ for each $i$ with $1 \\leq i \\leq n$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(b) Decompose the conditional mean-squared error $$\\text{E}_{Y|X}(f(x_0)-\\hat{f}(x_0))^2$$ into a conditional squared bias and a conditional variance component. Like $X, Y$ represents the entire training sequence of $y_i$.\n",
    "\n",
    "Here $X$ is fixed, and $Y$ varies. Also $x_0$ and $f(x_0)$ are fixed. So the conditional mean-squared error \n",
    "$$\\begin{align}\n",
    "\\text{E}_{Y|X}\\Bigl(f(x_0)-\\hat{f}(x_0)\\Bigr)^2&=(f(x_0))^2-2f(x_0)\\text{E}_{Y|X}\\Bigl(\\hat{f}(x_0)\\Bigr)+\\text{E}_{Y|X}\\Bigl((\\hat{f}(x_0))^2\\Bigr)\\\\\n",
    "&=\\Bigl(f(x_0)-\\text{E}_{Y|X}\\Bigl(\\hat{f}(x_0)\\Bigr)\\Bigr)^2-\\Bigl[\\text{E}_{Y|X}\\Bigl(\\hat{f}(x_0)\\Bigr)\\Bigr]^2+\\text{E}_{Y|X}\\Bigl((\\hat{f}(x_0))^2\\Bigr)\\\\\n",
    "&=(\\text{bias})^2+\\text{Var}(\\hat{f}(x_0))\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(c) Decompose the (unconditional) mean-squared error $$\\text{E}_{Y,X}(f(x_0)-\\hat{f}(x_0))^2$$ into a squared bias and a variance component.\n",
    "\n",
    "$x_0$ and $f(x_0)$ are constant.\n",
    "$$\\begin{align}\n",
    "\\text{E}_{Y,X}(f(x_0)-\\hat{f}(x_0))^2&=f(x_0)^2-2f(x_0)\\text{E}_{Y,X}\\hat{f}(x_0)+\\text{E}_{Y,X}\\Bigl((\\hat{f}(x_0))^2\\Bigr)\\\\\n",
    "&=\\Bigl(f(x_0)-\\text{E}_{Y,X}\\hat{f}(x_0)\\Bigr)^2+\\text{E}_{Y,X}\\Bigl((\\hat{f}(x_0))^2\\Bigr)-\\Bigl(\\text{E}_{Y,X}\\hat{f}(x_0)\\Bigr)^2\\\\\n",
    "&=(\\text{bias})^2+\\text{Var}(\\hat{f}(x_0))\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex. 2.8 (classifying 2’s and 3’s)\n",
    "\n",
    "Compare the classification performance of linear regression and $k$–\n",
    "nearest neighbor classification on the *zipcode data*. In particular, consider\n",
    "only the 2’s and 3’s, and $k = 1, 3, 5, 7$ and $15$. Show both the training and\n",
    "test error for each choice. The zipcode data are available from the book\n",
    "website www-stat.stanford.edu/ElemStatLearn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The rpy2.ipython extension is already loaded. To reload it, use:\n",
      "  %reload_ext rpy2.ipython\n"
     ]
    }
   ],
   "source": [
    "%load_ext rpy2.ipython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%R\n",
    "#Reading the train and test files for independent and dependent variables\n",
    "#Train file as input\n",
    "X <- as.matrix(read.table(gzfile(\"./zipcode/zip.train.gz\")))\n",
    "y2or3 <- which(X[, 1] == 2 | X[, 1] == 3)\n",
    "X.train <- X[y2or3, -1]\n",
    "y.train <- X[y2or3, 1] == 3\n",
    "\n",
    "#Test file as input\n",
    "X <- as.matrix(read.table(gzfile(\"./zipcode/zip.test.gz\")))\n",
    "y2or3 <- which(X[, 1] == 2 | X[, 1] == 3)\n",
    "X.test <- X[y2or3, -1]\n",
    "y.test <- X[y2or3, 1] == 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex. 2.9 (the average training error is smaller than the testing error)\n",
    "\n",
    "Consider a linear regression model with $p$ parameters, fit by least\n",
    "squares to a set of training data $(x_1, y_1), \\cdots , (x_N, y_N)$ drawn at random from a population. Let $\\hat{\\beta}$ be the least squares estimate. Suppose we have some test data $(\\tilde{x}_1, \\tilde{y}_1), \\cdots , (\\tilde{x}_M, \\tilde{y}_M)$ drawn at random from the same population as the training data. If $$R_{tr}(\\beta) = \\frac{1}{N}\\sum_{1}^{N}(y_i-\\beta^Tx_i)^2$$ and $$R_{te}(\\beta) = \\frac{1}{M}\\sum_{1}^{M}(\\tilde{y}_i-\\beta^T\\tilde{x}_i)^2$$\n",
    "prove that $$E[R_{tr}(\\hat{\\beta})]\\leq E[R_{te}(\\hat{\\beta})]$$\n",
    "where the expectations are over all that is random in each expression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The expectation of the test term $$\\frac{1}{M}\\sum(\\tilde{y}_i-\\hat{\\beta}^Tx_i)^2$$ is equal to the expectation of $$(\\tilde{y}_1-\\hat{\\beta}^Tx_1)^2$$, and is therefore independent of $M$. We take $M = N$, and then decrease the test expression on replacing $\\hat{\\beta}$ with a value of $\\beta$ that minimizes the expression. Now the expectations of the two terms are equal. This proves the result. Note that we may have to use the Moore-Penrose pseudo-inverse of $X^TX$, if the rank of $X$ is less than $p$. This is not a continuous function of $X$, but it is measurable, which is all we need."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# References\n",
    "@book{friedman2001elements,\n",
    "  title={The elements of statistical learning},\n",
    "  author={Friedman, Jerome and Hastie, Trevor and Tibshirani, Robert and others},\n",
    "  volume={1},\n",
    "  number={10},\n",
    "  year={2001},\n",
    "  publisher={Springer series in statistics New York}\n",
    "}\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}