{
  "cells": [
    {
      "cell_type": "markdown",
      "id": "4b823a0b",
      "metadata": {},
      "source": [
        "# 4. Linear Models for Classification\n",
        "\n",
        "### *Table of Contents*\n",
        "* 4.1 [Discriminant Functions](#4.1-Discriminant-Functions)\n",
        "    * 4.1.3 [Least squares for classification](#4.1.3-Least-squares-for-classification)\n",
        "    * 4.1.4 [Fisher's linear discriminant](#4.1.4-Fisher's-linear-discriminant)\n",
        "    * 4.1.7 [The perceptron algorithm](#4.1.7-The-perceptron-algorithm)\n",
        "* 4.2 [Probabilistic Generative Models](#4.2-Probabilistic-Generative-Models)\n",
        "* 4.3 [Probabilistic Discriminative Models](#4.3-Probabilistic-Discriminative-Models)\n",
        "* 4.4 [Laplace Approximation](#4.4-Laplace-Approximation)\n",
        "* 4.5 [Bayesian Logistic Regression](#4.5-Bayesian-Logistic-Regression)\n",
        "    * 4.5.1 [Laplace approximation](#4.5.1-Laplace-approximation)\n",
        "    * 4.5.2 [Predictive distribution](#4.5.2-Predictive-distribution)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "id": "9f58992a",
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "The autoreload extension is already loaded. To reload it, use:\n",
            "  %reload_ext autoreload\n"
          ]
        }
      ],
      "source": [
        "# Dependencies\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from sklearn.datasets import make_classification\n",
        "\n",
        "# Project\n",
        "from prml.distribution import Gaussian\n",
        "from prml.linear import (\n",
        "    BayesianLogisticRegression,\n",
        "    FisherLinearDiscriminant,\n",
        "    GenerativeClassifier,\n",
        "    LeastSquaresClassifier,\n",
        "    LogisticRegression,\n",
        "    Perceptron,\n",
        "    SoftmaxRegression,\n",
        ")\n",
        "from prml.preprocessing import LinearFeature\n",
        "\n",
        "# Set random seed to make deterministic\n",
        "np.random.seed(0)\n",
        "\n",
        "# Ignore zero divisions and computation involving NaN values.\n",
        "np.seterr(divide=\"ignore\", invalid=\"ignore\")\n",
        "\n",
        "# Enable higher resolution plots\n",
        "%config InlineBackend.figure_format = 'retina'\n",
        "\n",
        "# Enable autoreload all modules before executing code\n",
        "%load_ext autoreload\n",
        "%autoreload 2"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "db4ef7ea",
      "metadata": {},
      "source": [
        "The goal in classification is to take an input vector $\\mathbf{x}$ and assign it to one of $K$ discrete classes $\\mathcal{C}_k$, where $k=1\\dots,K$. The input space is thereby divided into *decision regions* whose boundaries are called *decision boundaries* or *decision surfaces*. Linear models define decision surfaces as linear functions of the input vector $\\mathbf{x}$ and hence are defined by $(D-1)$-dimensional hyperplanes inside the $D$-dimensional space. Datasets whose classes can be separated exactly by linear decision surfaces are called *linearly separable*.\n",
        "\n",
        "There are three distinct approaches to the classification problem:\n",
        "\n",
        "1. Discriminant functions that directly assign each input vector $\\mathbf{x}$ to a class.\n",
        "2. Models that directly learn the conditional probability $p(\\mathcal{C}_k|\\mathbf{x})$ using parametric modelling.\n",
        "3. Generative approaches that model the class conditional density $p(\\mathbf{x}|\\mathcal{C}_k)$, and the prior probabilities $p(\\mathcal{C}_k)$ for the classes. Then they derive the posterior using the Bayes theorem.\n",
        "\n",
        "In the linear regression models, the model prediction $y(\\mathbf{x}, \\mathbf{w})$ was given by a linear function of the parameters $\\mathbf{w}$. For classification problems, however, we wish to predict discrete class labels. To that end, we consider a generalization of the above model in which we transform the linear function using a nonlinear function $f(\\cdot)$ so that\n",
        "\n",
        "$$\n",
        "y(\\mathbf{x}) = f(\\mathbf{w}^T\\mathbf{x} + w_0)\n",
        "$$\n",
        "\n",
        "In machine learning, the function $f$ is known as an *activation function*."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "aebbe509",
      "metadata": {},
      "source": [
        "## 4.1 Discriminant Functions\n",
        "\n",
        "A discriminant is a function that assigns one of $K$ classes to an input vector $\\mathbf{x}$. *Linear discriminants* define decision surfaces that are hyperplanes.\n",
        "\n",
        "\n",
        "### 4.1.1 Two Classes\n",
        "\n",
        "The simplest linear discriminant function is obtained by taking a linear function of the input vector so that,\n",
        "\n",
        "$$\n",
        "y(\\mathbf{x}) = \\mathbf{w}^T\\mathbf{x} + w_0\n",
        "$$\n",
        "\n",
        "where $\\mathbf{w}$ is a *weight vector* and $w_0$ is a *bias* (the negative of the bias is also called *threshold*). Then, an input $\\mathbf{x}$ is assigned to a class $\\mathcal{C}_1$ if $y(\\mathbf{x})\\geq0$ and to class $\\mathcal{C}_2$ otherwise. Thus, the decision boundary is defined by $y(\\mathbf{x})=0$.\n",
        "\n",
        "Consider two points $\\mathbf{x}_A$ and $\\mathbf{x}_B$ onto the decision surface. Then, $y(\\mathbf{x}_A)=y(\\mathbf{x}_B)=0 \\Leftrightarrow \\mathbf{w}^T(\\mathbf{x}_A-\\mathbf{x}_B)=0$, which implies that the vector $\\mathbf{w}$ is orthogonal to every vector lying in the decision surface as depicted below:\n",
        "\n",
        "<img src=\"../images/fg4_1.png\" width=\"400\"/>\n",
        "\n",
        "Note that for more than two classes ($K>2$), a *one-vs-the-rest* classifier can be used in order to avoid regions of input space that are ambiguously classified. The linear function of each class takes the form $y_k(\\mathbf{x}) = \\mathbf{w}_k^T\\mathbf{x} + w_{k0}$, and assigns a point $\\mathbf{x}$ to class $\\mathcal{C}_k$ if $y_k(\\mathbf{x}) > y_j(\\mathbf{x}) \\; \\forall j\\neq k$.\n",
        "\n",
        "In the following sections we explore three approaches to learning the parameters of linear discriminant functions:\n",
        "\n",
        "1. Least squares\n",
        "2. Fisher's linear discriminant\n",
        "3. Perceptron algorithm"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "010ca3f2",
      "metadata": {},
      "source": [
        "### 4.1.3 Least squares for classification\n",
        "\n",
        "In [Chapter 3](ch3_linear_models_for_regression.ipynb), we minimized the sum-of-squared error function led to a closed-form solution for the parameter values. Can we apply the same principle to classification problems?\n",
        "\n",
        "Consider a general classification problem having $K$ classes, using a $1$-of-$K$ binary coding scheme or *one-hot* encoding for the target vector. Each class $\\mathcal{C}_k$ is described by its own linear model $y_k$. We can group these models together using vector notation so that\n",
        "\n",
        "$$\n",
        "\\mathbf{y}(\\mathbf{x}) = \\mathbf{\\tilde{W}}^T\\mathbf{\\tilde{x}}\n",
        "$$\n",
        "\n",
        "where $\\mathbf{\\tilde{W}}$ is a matrix whose $k^{th}$ column comprises the $D+1$-dimensional vector $\\mathbf{\\tilde{w}}_k=(w_{k0},\\mathbf{w}_k^T)^T$ and $\\mathbf{\\tilde{x}}$ is the augmented vector $(1, \\mathbf{\\tilde{x}}^T)^T$. The parameter matrix $\\mathbf{\\tilde{W}}$ is determined by minimizing the sum-of-squares error function, as presented in [Chapter 3](ch3_linear_models_for_regression.ipynb). Thus, the solution for $\\mathbf{\\tilde{W}}$ is obtained from\n",
        "\n",
        "$$\n",
        "\\mathbf{\\tilde{W}} = (\\mathbf{\\tilde{X}}^T\\mathbf{\\tilde{X}})^{-1}\\mathbf{\\tilde{X}}^T\\mathbf{T}\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "id": "60bb27c6",
      "metadata": {},
      "outputs": [
        {
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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 435,
              "width": 568
            }
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# number of training points\n",
        "N = 100\n",
        "\n",
        "x_train, t = make_classification(\n",
        "    n_features=2, n_informative=2, n_redundant=0, n_classes=2, n_clusters_per_class=1, n_samples=N\n",
        ")\n",
        "\n",
        "x1, x2 = np.meshgrid(np.linspace(-5, 5, 100), np.linspace(-5, 5, 100))\n",
        "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
        "\n",
        "feature = LinearFeature()\n",
        "x_train_linear = feature.transform(x_train)\n",
        "x_test_linear = feature.transform(x_test)\n",
        "\n",
        "model = LeastSquaresClassifier()\n",
        "model.fit(x_train_linear, t)\n",
        "predicted = model.predict(x_test_linear)\n",
        "\n",
        "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
        "plt.contourf(x1, x2, predicted.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)\n",
        "plt.xlabel(\"$x_1$\", fontsize=12)\n",
        "plt.ylabel(\"$x_2$\", fontsize=12)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "3f3019b8",
      "metadata": {},
      "source": [
        "The least-squares approach gives an exact closed-form solution for the discriminant function parameters. However, even as a discriminant function (making decisions directly) it suffers from some problems. We already know that least-squares solutions lack robustness to outliers, and this applies equally to classification, as depicted in the following figure. Note that the additional outlier data points produce a change in the location of the decision boundary, even though these point would be correctly classified by the original decision boundary. The sum-of-squares error function penalizes predictions that are *too correct* in that they lie a long way on the correct side of the decision boundary."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "id": "0c8d1352",
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1500x500 with 2 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 472,
              "width": 1234
            }
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# number of training points\n",
        "N = 100\n",
        "\n",
        "# number of outlier points\n",
        "n_outliers = 5\n",
        "\n",
        "x_train, t = make_classification(\n",
        "    n_features=2, n_informative=2, n_redundant=0, n_classes=2, n_clusters_per_class=1, n_samples=N, random_state=12\n",
        ")\n",
        "\n",
        "x1, x2 = np.meshgrid(np.linspace(-5, 5, 100), np.linspace(-5, 5, 100))\n",
        "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
        "\n",
        "outliers = np.random.random_sample((n_outliers, 2)) + 3\n",
        "x_train_outliers = np.vstack((x_train, outliers))\n",
        "t_outliers = np.hstack((t, np.ones(n_outliers, dtype=int)))\n",
        "\n",
        "feature = LinearFeature()\n",
        "x_train_linear = feature.transform(x_train)\n",
        "x_train_linear_outliers = feature.transform(x_train_outliers)\n",
        "x_test_linear = feature.transform(x_test)\n",
        "\n",
        "model = LeastSquaresClassifier()\n",
        "model.fit(x_train_linear, t)\n",
        "predicted = model.predict(x_test_linear)\n",
        "\n",
        "plt.figure(figsize=(15, 5))\n",
        "\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
        "plt.contourf(x1, x2, predicted.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)\n",
        "plt.xlabel(\"$x_1$\", fontsize=12)\n",
        "plt.ylabel(\"$x_2$\", fontsize=12)\n",
        "plt.title(\"Original decision boundary\")\n",
        "\n",
        "model.fit(x_train_linear_outliers, t_outliers)\n",
        "predicted_outliers = model.predict(x_test_linear)\n",
        "\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.scatter(x_train_outliers[:, 0], x_train_outliers[:, 1], c=t_outliers)\n",
        "plt.contourf(x1, x2, predicted_outliers.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)\n",
        "plt.xlabel(\"$x_1$\", fontsize=12)\n",
        "plt.ylabel(\"$x_2$\", fontsize=12)\n",
        "plt.title(\"Outliers decision boundary\")\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "3dd6c46f",
      "metadata": {},
      "source": [
        "The failure of least squares should not surprise us since it corresponds to maximum likelihood under the assumption of a Gaussian conditional distribution, whereas binary target vectors clearly do not have a Gaussian distribution."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "c1648744",
      "metadata": {},
      "source": [
        "### 4.1.4 Fisher's linear discriminant\n",
        "\n",
        "Consider a two-class problem in which there are $N_1$ points of class $\\mathcal{C}_1$ and $N_2$ points from class $\\mathcal{C}_2$, so that the mean vectors of the two classes are given by\n",
        "\n",
        "$$\n",
        "\\mathbf{m}_1 = \\frac{1}{N_1}\\sum_{n\\in\\mathcal{C}_1}\\mathbf{x}_n, \\qquad\\qquad \\mathbf{m}_2 = \\frac{1}{N_2}\\sum_{n\\in\\mathcal{C}_2}\\mathbf{x}_n\n",
        "$$\n",
        "\n",
        "Then, the simplest measure of separation of the classes, when projected onto $\\mathbf{w}$, is the separation of the projected class means. This suggests that we might choose $\\mathbf{w}$ so as to maximize \n",
        "\n",
        "$$\n",
        "m_2 - m_1 = \\mathbf{w}^T(\\mathbf{m}_2 - \\mathbf{m}_1)\n",
        "$$\n",
        "\n",
        "where\n",
        "\n",
        "$$\n",
        "m_k = \\mathbf{w}^T\\mathbf{m}_k\n",
        "$$\n",
        "\n",
        "is the mean of the projected data from class $\\mathcal{C}_k$.\n",
        "\n",
        "The idea proposed by Fisher is to maximize the function that gives a large separation between the projected class means while also giving a small variance within each class, thereby minimizing the class overlap. The within-class variance of the projected data from class $\\mathcal{C}_k$ is given by,\n",
        "\n",
        "$$\n",
        "s_k^2 = \\sum_{n\\in\\mathcal{C}_k} (y_n - m_k)^2\n",
        "$$\n",
        "\n",
        "where $y_n = \\mathbf{w}^T\\mathbf{x}_n$ is the projected data point in the one-dimentional space. We can further define the total within-class variance for the whole data set to be simply $s_1^2 + s_2^2$. Then, the Fisher criterion is defined as the ratio of the *between-class* variance to the *within-class* variance as follows,\n",
        "\n",
        "$$\n",
        "J(\\mathbf{w}) = \\frac{(m_2-m_1)^2}{s_1^2+s_2^2}\n",
        "$$\n",
        "\n",
        "In order to explicitly show the dependence on $\\mathbf{w}$, we may rewrite $J(\\mathbf{w})$, using $(4.20)$, $(4.23)$, and $(4.24)$, as follows,\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "J(\\mathbf{w}) &= \\frac{(m_2-m_1)^2}{s_1^2+s_2^2}\\\\\n",
        "&= \\frac{(\\mathbf{w}^T\\mathbf{m}_2-\\mathbf{w}^T\\mathbf{m}_1)^2}{\\sum_{n\\in\\mathcal{C}_k} (y_n - m_1)^2 + \\sum_{n\\in\\mathcal{C}_k} (y_n - m_2)^2}\\\\\n",
        "&= \\frac{(\\mathbf{w}^T(\\mathbf{m}_2-\\mathbf{m}_1))^2}{\\sum_{n\\in\\mathcal{C}_k} (\\mathbf{w}^T(\\mathbf{x}_n - \\mathbf{m}_1))^2 + \\sum_{n\\in\\mathcal{C}_k} (\\mathbf{w}^T(\\mathbf{x}_n - \\mathbf{m}_2))^2}\\\\\n",
        "&= \\frac{\\mathbf{w}^T(\\mathbf{m}_2-\\mathbf{m}_1)^2\\mathbf{w}}{\\mathbf{w}^T\\big(\\sum_{n\\in\\mathcal{C}_k} (\\mathbf{x}_n - \\mathbf{m}_1)^2 + \\sum_{n\\in\\mathcal{C}_k} (\\mathbf{x}_n - \\mathbf{m}_2)^2\\big)\\mathbf{w}}\\\\\n",
        "&=\\frac{\\mathbf{w}^T\\mathbf{S}_B\\mathbf{w}}{\\mathbf{w}^T\\mathbf{S}_W\\mathbf{w}}\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "Then, by computing the derivative with respect to $\\mathbf{w}$, we find that $J(\\mathbf{w})$ is maximized when,\n",
        "\n",
        "$$\n",
        "(\\mathbf{w}^T\\mathbf{S}_B\\mathbf{w})\\mathbf{S}_W\\mathbf{w} = (\\mathbf{w}^T\\mathbf{S}_W\\mathbf{w})\\mathbf{S}_B\\mathbf{w} \\Leftrightarrow \\mathbf{w} \\propto \\mathbf{S}_W^{-1}(\\mathbf{m}_2-\\mathbf{m}_1)\n",
        "$$\n",
        "\n",
        "This result is known as the *Fisher's linear discriminant*. To that end, the projected data are compared against a threshold $y_0$ and classified as belonging to class $\\mathcal{C}_1$ if $y(\\mathbf{x}) \\geq y_0$, and to class $\\mathcal{C}_2$ otherwise."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "id": "eccc8b3a",
      "metadata": {},
      "outputs": [
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 434,
              "width": 546
            }
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# number of training points\n",
        "N = 100\n",
        "\n",
        "x_train, t = make_classification(\n",
        "    n_features=2, n_informative=2, n_redundant=0, n_classes=2, n_clusters_per_class=1, n_samples=N, random_state=15\n",
        ")\n",
        "\n",
        "x1, x2 = np.meshgrid(np.linspace(-5, 5, N), np.linspace(-5, 5, N))\n",
        "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
        "\n",
        "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)\n",
        "plt.title(\"Training data (2 classes)\")\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "778439cc",
      "metadata": {},
      "source": [
        "One way of choosing the threshold $y_0$ is to model the class-conditional densities (one per class) $p(y|\\mathcal{C}_k)$ as Gaussian distributions, then estimate their parameters using maximum likelihood, and finally, estimate the optimal threshold using decision theory. In the case of binary classification, we can equate the Gaussian functions and solve for $\\mathbf{x}$. The result is a quadratic equation having coefficients relating to the gaussian means and variances."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "id": "4b512547",
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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GxhXa9mtf+5onwZFM7E+ZCI787Gc/C9+mvYf1NNUvmyKnFdjUhWwER+xAO/T73Xffvc9jnzx5cvh2Pvjggz7fTrr/33bQGxlwSCR2CuMf/vCHhNvac2bvbaH3uMWLF/drjOn8rMh0cMQWCwL39vlo0/sig02JTiCE7LzzzuHtZ86c2e3369evd1MWQ8HinoIZxl4/oam+9t7Z2NgY9ftzzz03fH8WZAGQORRkBZBVV1xxhSvYlsiJJ54Yvmzp2+liqa2hFOuf/vSnrthlT2zqiaVdG0vPtvTXnljK7q9+9atexxFK0bbU7Z6eh96KR1pxTmNTcaygYG+dMWyKUKiQ7V/+8pduv7fpHKEUc0s7ttTuXGLxsMjpTVYwNdG0EmPTGWy6RMjvfve7Xu/jm9/8pkvBTuQb3/iGS4c2lpZt+0U6WWr2brvtlvD3VrzXijmG/PGPf4xbJDA0LcIKaYamtsRj+05oPzI21SY0ta2/LrroIjetJJnXeWgKVqHtT+li00Qip/DEFqSO54wzzuhx+fOf/9zvcUUWWLUpadkQOcUlmalymb6ddLOpppMmTQoXZk6GTZWx6aqJ2NQLm+4S2u+TLf6ZSK5/VsSy8fX2+WiFa0PvvTal6b777ku4rU0ts+m3oc99myYby6bIhIqwn3baae7/2hP7nx933HHhqUD//Oc/82J/BQoRNUcAZI19kbCK9j2xrhohPXWbSVVk/RKr9J4Mq+3w2GOPuctWZ6CnLg9WBd86cfTGDsA+/vhjN7f57rvv7lP9APtya/PUjdUcsXnmvbEDVavvYgf0NsfZaqNYR4aQyC9j3/3ud92Bcy6xcduc6tDcdqs/0RvrkmI1VkwynRAOP/zwHn9vB6XWwSY0Dts/7cAkXZJ5TPYF+oEHHggHM2JZjYEQ63hjtWd6YvPt7TFYjZvQbVoXhP7q7bm0fdHGZvUQ7GDADrZSaUubD/tTuoQORI3V/khGZE2meCyAdvTRR/e4jdUYsboMtm9YjQUbR2QND6tpEWK1JbIhMoBl+6rVibB6EX25nQ8++MBdtuCy1fvJFhuzvYdbLRt7H7aD8c+TIT8X6kpkrwurjdJT0C6Z11roczV0sqG/n6u5/lkRyWo3hYJNvbHXw3PPPRc+gWBdfuKJPLlgAfXIz9H+ft/4wx/+EP6+ERkIj9wHLChu92vvWwDSj+AIgKyxg67e2k9aIbmQdBTCC33JDLXmtRZ+kcX8ehLZVtG+pPbEWkcmw4p5WvZM6OA1FCCxTJVkghzGinGGWNtZOxOcjNCZLPsibn8X+aUudCbM9FSw1SuRmTu2H0XuJ4lY8cwQOxC2Ync9ZTMkE+jIxP4ZCrz0dnbRWDG/kGXLlrnie1aIMt7z1FMWSuzzFAqOhIql9oftV70d0NnjtWBiqMW0PZfZDI5kY39Kl8jnJVH743Rnqlh2XWQx3N5Ya/JssP3KCopa0MaCCPa+e8wxx7jMHvv/WEZesu/DoUDihRde6IprWuaWFa22ArSZYIU2LUOptyzE2Oe1t9dStt+3cv2zoi+fy6F9wopSW2amteG2z8h4+0JkcMT2vd4+oy3TxorQ98buL9H3DctOsbbEVmzb9iPLBrLsO8tms6LJyWSTAUgOwREAWRPvDEusyOBJqKNLf0VWb7cOFL2dVY3HMj16kmyq6//7f//PnXW2L/cWpPj73//uFmNV/q3TgGWDWIZNooNFOygLeeONN9zSn8djX5ZDB6mhFONcY2euQyyVOxk2rcSylUJdEuxAo6eD2VT3T/sSnS4WKEgmOGD7WeRjsuclMjjSl+fJOiWl8yA3mecxk89lruxP6WIdhiJfq/a+0dvBUGQmQuQ0mN4O0qwrjnXaCnVXSVayQZR0uOWWW9xZdgsOWgaMTXGyxTrBWGckG79NibT30URn1y0LyDIgQp2FbApLaBqLdaqy92E78D/ooINch5H+sgPbZIPyqT6v2XzfyofPikipTEGxAJIFG6zLlwUh/va3v+m8886L2sayb0IZR6HtY9k+Gfl/mzlzZr+/b1j2i03btfHYa9u6MZ1//vlusc8OC4Rb5yjbX/uSSQXgS9QcAZA1Xp3dCKUp90dvgZrepi9EpsXbWamrrroq6qDU2Jcum6tsZzCttoV98Yn8IpqpxxP7BbyvtVAyKVRHI5WpBbHb9nag4eXZt2TPePf2mPryPKXyHCUjH85iZmN/SpfI4I1Na0lXXZh4bApAKDBiwbpzzjnHBRFsKqA9Z3b/XxTzj5rWZQeT2WKtcK1l6ZlnnhkVGLD3NJuucs0117jgiD1viQ5MLWhi09Ps93Z7kezxW3aABVAs+GU/I+u+pMqyUiIDI5b9ZdkElkFiATYLtoWeU1vsIDeV5zWbr7d8+Kzoy+dyvEyQeHV5ItdZxme8TNhMfd8499xz3WvOgn6R/3MLpFg2iX1fsCw4q00VygQEkDqCIwAKXuQBjRU0jPwimuxy++23p208NrXnRz/6kTvgsLn6v/nNb/Ttb39bG220UdR8fwug2NnL2ABJ5OP5wQ9+0KfHM3369PBtxGYsRB445orIL+GpTC2I3Dab0zZSZf/vdDymvjxP+fIc+XV/siyGSOksVB3J6i2Eai7Y82PZbaFAw/jx4937TmRhy0wEh5INslgWj71vWvaIZeL97Gc/c2fx7f09siaK1cSw98h47ADT6kq8/fbbLuBkAQur6ROZDWFZFpapYrV5IrONUmHv4yE2FeLZZ59147IsF8s+iK3Zkc0snFR5/VmR6SCcZWyGAm6WkWn1uUIsMGjTYEMS1eyJDbZaYC3Vz+dENY0scGbFjy0b1sZi+7bVQot8XVoGlE3RtP0MQOoIjgAoePZFOjItOJUD0UwKFfi0M6CWwmtzjq3mwwknnBA1vzt2GlDk4wkVlewPO6CIPMM2f/585XJ6dLIp/1a0NjQFwqQjPT5T7OxfMgcaoTPNiR5TX56nyAKNufwc+XV/sgyzyCyzu+66KyP3E9kdxYIEsRkV8abgpHuaZKpn3S2wYAeMNl3RimDa68OK5u6xxx7hbX7729/22hHJpiJYwMKC4FYo1YIlP/zhD8PTcmxdX6bF2AG1ZQoaO4C9/PLLe830SHVKUzal+7Mi0/tHqmx/iuw+E5kp8vjjj4cLoW+22WZR9Z8i1dbWRgW80vEZHcu+A1iNFOvC98orr7j7sK48odoydkLllFNOSfv9An5AcARAwbOaDJFF7UJnR3ORdRWwqTWWyh1ic6AjRRbutMcSr75AqiJvM7LjSV9kIs07souRzbdOJs098syZTVPKRn2IvrL/YWShw0QiC/3ZF+TYxxT5PCW7n0du11NHJi9kaspAvu1PkQc61kEr3W2kY2sZJVPk8z//+U+v20Rmclhh7N70dzqAHWxbO247u25FK0MeeuihlG7HgiVXX311VEAk9n04GRassTpXxgpu91Z024qAZ6u4bS58VmR7/0hGZEaInbQIfb5GFmK1qa89sUyjkGxkcFiw14rJ/t///V94nWVEWXYqgNQQHAGQl6wwYioF5qz1XchNN92kXHfggQeGL1vqeCTrymBnp4xlm6T6xT+eyMJy1irQ2ktm63+TDCtIZwekobOx8eaDx7J0+HzpqmD+9Kc/9bqNdRDp6TFZocrIDIPITId4rEZDZEHfXHueMrEv5eP+9P3vfz+c7m9TCyyzI91FbCNT83vLrrNASuSBWCKRGS9WJ6S3QO4999yjdLAz99ZePdF7aDreh1N9TuPVj4plhWVzXTo/KyL3j97aQds+Zy1uM80ykUInUyyLx4KANp0uVLzX9NYGO/L7hv1P03ECIxn23SCygHNf93vAzwiOAMhLka0JbW55b6yYWShF2rrDpFJDJF1psfYlMtk52pGt/GLPNtoX/7PPPjt8/bTTTkvqOejpC5OllIfqMFi6fOTtZ/p/k2wGwfe+973w9csuu6zH27azvFakLuTUU09VrrMD9J6yR6wY3/333x++HpldFFlQM/R/tHnpPU0FsDPaNqUr8oDfCvrlkkzsS/m4P1lg5Pe//334uk0TsQP3dNaniKy10VOWhAWT7LkLZUT0FoQK1amw/dGmJiRiz2/kc5xo+lmydSd6eg9NNjujp9tIdv8NBbVsSkhoik08lmGQD8GRdH5WRGahWJZGT4EWKw6cja5W9t4QmRliGSMWGAnVG7JW0jatprdMr9AJDJsqm8qULNs37TUWuy4Za9eujfqO0Zd9FvA7giMA8lJkyvS9997b6/abbrqpm5ceWRjPiqIm+tJh85/ti7xVr49Mwe8POziwM1J2v3bGvqfuBhdffHH4erx2gRbs2WqrrdxlO6jbaaed3POQ6MDBHqcVHLRpE5EFAkOsHeCVV14Zvm4HYlaN3zJT4rGUXUvjjXewE/m/sd+na564fQkPFa21FGyr2h/vbKNlTBx11FFRRfasvWcus+kA9oXYzjjalIBYdtB4yCGHhM9A7rvvvu7xx0tT/8lPfhK+fsUVV7jrsQeyFiCzto9WdNNYG1Srh5Dvr/NC3p+saLO9d4RYFxl7D7DXak+vMftf22u7t2kh+++/f3gakxWEtPuKzXawQPGhhx7q9sdkuvzYfmW1ESIPrG3qSCTbpy1ryraLLU4ay7JVbMrLr3/966haOZHsAPuGG27Qfffdl/A91Nr12gGsBSsSvWfae3Rk8DDe+3AymSPf+MY3otopxyuoaxkztp29B6TSPckL6fyssPe7UPDMAi0W8I3d52zK27HHHuueo972j3SJzAyx/cimusb7XSIWELv22mvD1y04YtleierJ2GvAgmN2osP2zdjnwF4b9lzZWBJlddn3AAuOh97r7XVi33sApKYkxe0BICfYF3Sbe28uuOACV4TPDhQivzz97//+r/siF2IBB/tCfccdd7gvIzan3Ir1WWDBvkRYO1Ur2Grb2FSD0JmiyLPX/WVndux+bbH0Vwu82AGaTR+wYm92v5HzhO0Ljn2xjGVn7uxgx9r2WVE8O2ixL1BWJNLObNmUAXuM9sXSDkasTXDoICBy6kUk+2Jm1flDZy/ty6hlKkyZMsWNw8ZoHRusBWXowCTe9AKbb21BIDvragGhLbbYwqW429hCB192m/aFOhX2v/zrX//qDlLsC6IVTbRgj519tOKR9qXQDvY//PDD8N9MmDAhajpErrL6FRb8sKJ6FviwQr3WzcL+h1Zwzw4wImvoWDp7InZQa+nnoelWP//5z93/1P5X9hza/8WyUCLP0lrALPIsbi69zv/whz+Ep8PZc2H/88jWxzblpC8HAfm4P9n/yV7b9p5nB9L2v7THf8YZZ7j3Emtfa+8r9lq39xp7TPb6jwwAWAAtcspJiL1OLRgcmrpl71H2/Nhr1c5A22vephjY82IHtDaWZDJoLChtASZ7P7Xx2n5tUxcsU8Xeb63mjR00WiDFDrTjZURFsuKo5513nlvsQHLbbbcNnyG390H7n0XWkLEsgN122y3qNuzg04LFtthjsTHZc2eBCQskWx2ayNec1XS45JJLen2siR6/ZR7YfdpzaO/PVszT3lPtubQ6QqHCphY8ev/993vMMMkF6fqssNexBW+tDW0oe86CKLat7ae2v9g+Z69PC5Ra5yTbLzPNvkvYPmHBUstWCtVWsSB2sp9bFgizz3LrpGTsdWVZKHa79lqzz3DL8rCgkt1PTwFOe/2GMqus252Nz55nC8JY9pi9fmw/Cr3OLUvWirUC6IMgAPTRtGnT7DS2Wy6++OK428yePTu8jW2fjND2Pb1FtbW1Bb/yla9EbRu7zJ8/P+7f/uY3vwnW1dX1+LehJRAIBA888MC4t3PccceFt7vtttt6fVwLFy4MlpeXJ3W/tkyfPj24ZMmSHm9z1apVwcMPP9yNM5nbrK2tDd5+++093uZ1110XHDhwYFLPzWOPPRb3Nh566KFgWVlZwr+15y6S7T+97Ushzz//fHCTTTbpdXz77LNPcPny5T3e1rhx43rdX/rzP++J3V/otmwctk+fdNJJPT6miRMnBufNm9frbbe3twfPOOOMYHFxcY+3N2jQoF4fRzKv4djHkoxkn/ujjjqqx8dg4+uPdO5PfXm/64v//ve/wa997WtJv5fYMmTIkODZZ5/d42NobGwM7rfffj3ezujRo4PPPPNMSo/10UcfDVZVVSW8TXu/uf/++3vdj+69996k3+uKioqCp512mntdxRowYEDSz9t2222X8DWX7HMwa9asHh+/Ld/73veCLS0tUZ+rifbtZLbp6/trKtLxWdHZ2Rk8+eSTe/z7XXbZxX1+JvM40vVYf/3rX3cbxwEHHJDy7dx9993BUaNGJb2/TZ061e0Hkb75zW8m/ffDhg1z+xuAviFzBEBesjM4Nv3AzuLaGSs7i2VnC5OZB2+p0nZWx1K5bQqLFQq0s1xWvNLOIo4ePdqdmZk+fbpLdY7sdNMfliFi6ft2Furpp592Z8HtrLTdd+hsrJ29DGVVWFZIb+wssZ21s8dvc7YtHd7OQtr9WEq3zXu2+dF2Rtxuz7ISIotcxmOZKpY6bHVZLDsnsoOCZX9YHQE782tjtDPp8VgKsKWlWxtiy2KwM1t2liwdhenszKt167CzjHZG1s66WdaN7RN2Vt3aeNo0iHhnx3OZjX/mzJk6/PDD3X5tdSUs88bOZttzbs+31XpIJrXczsJbVpSd2beUcGvTamdh7Syj7TN21tH2bTtTnc7MqEyws622P9n+bf/r2HbGftyfLDvLsuXsdW/Ta+w9xTIq7LmxbAzbZywzZvz48e79xB6DdXGJbJ0aj53Jt9u1jBHLsLMz/3Z79rq3TA/L5LH3Trtte69Jlt23ZWPYdBh7T7F90c5uW+aHTVOy7Be7nGiqTIi1WQ3VLrFpCPbebWfnLUvG2Jl027ft8dpUjETtiO390TISLEPDXmeWWWfTj2y/sufAPgMmT57sHq/VdoksrNoXNoXN/lfXXHONG3soU8YyxqyIpj2nuT71L1OfFfbcWiacZc5ZJo/VXbL/j70v2d/b7VtGU2/7brrZFJVQhlYqU2piWUan/f8te8qeI9vf7DPfPg/tdWrfC+xx7rnnnu492fbfWJYlaq9Fex+358feryzjxLKx7PPAMpssg8r+3sYd2QUIQGoCFiFJ8W8AAEA/2YGgHbwaC4r1dmAIAACAzKEgKwAAAAAA8DWCIwAAAAAAwNcIjgAAAAAAAF8jOAIAAAAAAHyN4AgAAAAAAPA1giMAAAAAAMDXaOULAAAAAAB8jcwRAAAAAADgawRHAAAAAACArxEcAQAAAAAAvkZwBAAAAAAA+BrBEQAAAAAA4GsERwAAAAAAgK+VeD2AQtHS0qI333zTXa6vr1dJCU8tAAAAAADp1tHRoRUrVrjL22yzjSoqKvp9mxzBp4kFRqZOner1MAAAAAAA8I0XX3xRU6ZM6fftMK0GAAAAAAD4GpkjaWJTaSIjVyNHjvR0PAAAAAAAFKIlS5aEZ25EHov3B8GRNImsMWKBkdGjR3s6HgAAAAAACl1Jmup9Mq0GAAAAAAD4GsERAAAAAADgawRHAAAAAACArxEcAQAAAAAAvkZwBAAAAAAA+BrBEQAAAAAA4GsERwAAAAAAgK8RHAEAAAAAAL5GcAQAAAAAAPgawREAAAAAAOBrBEcAAAAAAICvERwBAAAAAAC+RnAEAAAAAAD4GsERAAAAAADgawRHAAAAAACArxEcAQAAAAAAvkZwBAAAAAAA+BrBEQAAAAAA4GsERwAAAAAAgK8RHAEAAAAAAL5GcAQAAAAAAPhaRoMjy5cv1z/+8Q/99Kc/1de//nUNHTpUgUDALccff3xG7vNvf/ub9ttvP40YMUIVFRUaN26cjj76aD3//PMZuT8AAAAAAJDfSjJ548OHD1e2NDc367DDDtMjjzwStf6zzz7TX/7yFxc0sSDNxRdfnLUxAQAAAACA3Je1aTVjx451GR2ZcuKJJ4YDIzNmzNCsWbP04osv6pZbbtGmm26qrq4uXXLJJbr55pszNgYAAAAAAJB/Mpo5YpkaU6ZMcYtlkXzyyScaP3582u/n3//+t+666y53+YADDtDf//53FRcXu+t23wceeKAmT57sskguuOACHX744aqrq0v7OAAAAAAAQP7JaObIpZdeqm9+85sZn17z61//2v0sKSnRTTfdFA6MhFitkyuvvNJdXrt2rWbOnJnR8QAAAAAAgPyR991qNmzYoCeffNJd3meffTR69Oi4233rW9/SwIED3WXLLAEAAAAAACiI4MhLL72ktrY2d3natGkJtysrK9Muu+wS/pv29vasjREAAAAAAOSuvA+OvPPOO+HLW2yxRY/bhn7f0dGhDz74IONjAwAAAAAAPi/Img0LFy4MX040pSZkzJgx4csLFizQlltu2af7iWfJkiVJ3xYAAAAAAMgdJYVQcyRkwIABPW5bXV0dvtzQ0JDS/UQGVgAAAAAAQOHI+2k1LS0tUXVFelJeXh6+3NzcnNFxAQAAALluxYoVCgQCUYutAwC/yfvMkYqKivDlUGHWRFpbW8OXKysrU7ofm4bT27SaqVOnpnSbAAAAAADAe3kfHKmpqUl6qkxjY2PSU3Bi9VbPBAAAAAAA5Ke8n1YTGbTorWhqZPYHNUQAAAAAAEBBBEciO868++67PW4b+n1JSYkmTJiQ8bEBAAAAAIDcl/fBkSlTpoQLsc6ZMyfhdlaP5IUXXgj/TWlpadbGCAAAAAAAcldRIdQc2Xvvvd3lf/3rXwmn1jzwwANav369u3zIIYdkdYwAAAAAACB35Xxw5Pbbbw+3FbvkkkvibvOjH/3I/ezo6NDpp5+uzs7OqN+vXLlSF1xwgbtcW1urk08+OQsjBwAAAAAA8nu3mmeeeUYffvhhVJAixNZb4CPS8ccf36f72WuvvfTtb39bd911lx588EHtu+++OvvsszVq1Ci9+eab+sUvfqHPPvvMbXvllVeqrq6uz48JAAAAAAAUlowGR2bOnKk77rgj7u+effZZt6QjOGJuvfVWN23mkUce0ezZs90SqaioSD/5yU/0ve99r8/3AQAAABSSqqoqXXzxxd3WAYDfZDQ4kk2VlZV6+OGH9de//tVlpLz++utau3athg8frj333FNnnHGGdt11V6+HCQAAAOSM6urqhFPXAcBPAsFgMOj1IAqBFYIdM2aMu7xgwQKNHj3a6yEBAAAAAFBwFmbg+DvnC7ICAAAAAABkEsERAAAAAADgawRHAAAAAACArxEcAQAAAAAAvlYw3WoAAAAApGb16tWus2Okp59+WoMHD/ZsTADgBYIjAAAAgE91dnbqnXfe6bYOAPyGaTUAAAAAAMDXCI4AAAAAAABfIzgCAAAAAAB8jeAIAAAAAADwNYIjAAAAAADA1wiOAAAAAAAAXyM4AgAAAAAAfI3gCAAAAAAA8DWCIwAAAAAAwNcIjgAAAAAAAF8jOAIAAAAAAHyN4AgAAAAAAPA1giMAAAAAAMDXSrweAAAAAABvVFRU6LTTTuu2DgD8huAIAAAA4FM1NTW68cYbvR4GAHiOaTUAAAAAAMDXCI4AAAAAAABfIzgCAAAAAAB8jeAIAAAAAADwNYIjAAAAAADA1+hWAwAAAPjU2rVrdfDBB0etmzVrlmpraz0bEwB4geAIAAAA4FPt7e2aM2dOt3XIrPXvvafP7r1X1ePGadxRR6mohMMywGu8CgEAAAAgSxY9+KDmnn++gl8EoVqWLtWk887zeliA71FzBAAAAACy4OPbb9er55wTDoyY+XfeqY7mZk/HBYDgCAAAAABkVDAY1Lxf/1pv/+xn3X7X2dSk5U895cm4AHyJ4AgAAAAAZEhXR4feuOgiffi73yXcZvHDD2d1TAC6o+YIAAAAAGRAZ0uLXj37bC194oket1s2e7Y6GhtVUl2dtbEBiEbmCAAAAACkWfv69XrhhBO6B0aKijTp/PMVKC4Or+pqadGyJ5/M/iABhBEcAQAAAIA0alm+XM8ddZRWv/hi1PqisjLtdOON2uyUUzR0t92ifreIqTWApwiOAAAAAECaNMyfr2cOP1zr3303an1JTY12ueMOjdxvP3d91De/GfX7Ff/5j9o3bMjqWAF8ieAIAAAAAKSB1Q15/uij1bxwYdT68vp67X7XXRoydWp43Yh991WgtDR8vautrdfaJAAyh+AIAAAAAKTBgvvvV8vSpVHrqseN0x733quBW2wRtb5s0CAN23PPqHV0rQG8Q3AEAAAAANJg9SuvRF23gMju99yjqjFj4m4/av/9o66veOYZta1dm9ExAoiP4AgAAAAApMHa11+Pur7xMceofOjQhNsP33tvV6Q1JNjRoaWPP57RMQKIj+AIAAAAAPRT68qValqwIGpd3fbb9/g3pTU1GjZ9etQ6utYA3ijx6H4BAAAAeKysrEyHHXZYt3VI3ZqYrJHiqirVTJjQ69/Z1JrIbJFVzz+v1lWrVD5kSEbGCSA+giMAAACATw0aNEj33nuv18MoCGvmzo26XrvNNgoUF/f6d8P32kvFlZXqbG5214OdnVry2GPa+H/+J2NjBdAd02oAAAAAIM31Rup22CGpvyupqtLwGTOi1i3+xz/SOjYAvSM4AgAAAAD9YNkea994I2pd7XbbJf33o775zajrq158US3Ll6dtfAB6R3AEAAAAAPqh4aOP1NHQkFIx1kjDpk1TcXX1lyuCQS159NF0DhFALwiOAAAAAEA/rHnttajrlaNGqWLYsKT/vriiQiP23TdqHV1rgOwiOAIAAAAAaSzGmkrWSMhG++8ffZuvvKLmxYv7PTYAyaFbDQAAAOBT69at08knnxy1bubMma6LDfrexre2D8GR+j32UOnAgWpfvz68bvGjj2rTk05KyxgB9IzgCAAAAOBTbW1tuu+++6LW3XTTTZ6NJx9ZrZEN77/f78yRorIyjdhvPy2I+H8sfvhhgiNAljCtBgAAAAD6aO2bb7oCqiGBkhIN2mqrPt3WqJipNdYeuGnBgn6PEUDvCI4AAAAAQJqKsQ6cNMkVWO2LobvuqtK6uqh1ix95pF/jA5AcgiMAAAAAkKbgSF+m1IQUlZZq5Fe/GrWOrjVAdhAcAQAAAIA+CAaDWpvG4Ei8rjXr335bDfPn9+s2AfSO4AgAAAAA9IG12m1duTJqXe122/XrNofsvLPKhw6NWrf4H//o120C6B3BEQAAAADogzVz50ZdL62tVfXGG/frNgPFxRr59a9HrbOWvgAyi+AIAAAAAPSBdZOJVLfddgoEAv2+3djgiLUK7mxp6fftAkiM4AgAAAAApCFzpG6HHdJyu7Vbbx29Ihik7giQYQRHAAAAACBFXW1tWvf222mtNxJSUl2tipEjo9Y1fPRRWm4bQHwERwAAAAAgRevffdcFSDIRHDE1m20WdZ3gCJBZBEcAAAAAIEVrYlr4Vm+yicoGDUrb7Q/YZJOo6wRHgMwiOAIAAAAA/QyO1G2/fVpvfwCZI0BWERwBAAAAgBStzXRwJDZz5OOPFezsTOt9APhSScRlAAAAAD5SWlqqadOmdVuHnrWuXq3GTz/NaHAktuaI1TdpWrRI1WPHpvV+AHyO4AgAAADgU7W1tXrqqae8HkbeWfv661HXiyoqVDNxYlrvo2zIEJUOGqT2deuiptYQHAEyg2k1AAAAANCPeiO122yjopL0nncOBAIUZQWyiOAIAAAAAPQjc6QujS18I1GUFcgegiMAAAAAkKRgV1f3zJEddsjIfcVmjmwgOAJkDMERAAAAAEhSw/z56tiwISuZIzVxMkeCwWBG7gvwO4IjAAAAAJCktXPnRl2vGDFClSNHZiVzpH3tWrWtXp2R+wL8jm41AAAAgE9t2LBBF154YdS6K664QjU1NZ6NKdetiak3UpuhrBFTNWaMisrKXBvfyOyR8iFDMnafgF8RHAEAAAB8qqWlRTfddFPUuksuuYTgSA9i643Ubb99xu4rUFys6o031ob3348KjgyZOjVj9wn4FdNqAAAAACAJHU1N2vDee1kLjsTrWENRViAzCI4AAAAAQBLWvfWWgp2dUZkdg7beOqP3WbPpplHXaecLZAbBEQAAAABIwpqYYqw1EyeqpKoqo/cZW5SV4AiQGQRHAAAAAKAPxVgzPaUm3rSa5kWL3PQeAOlFcAQAAAAAkrA2thhrBjvVhFSPHy8FAlHrGufPz/j9An5DcAQAAAAAetG8ZIlali2LWle7ww4Zv9+SykpVbrRR1DqKsgLpR3AEAAAAAFJs4VtSU6MBltWRBdQdATKP4AgAAAAAJNGpJrbeSKAoO4dTNTF1RwiOAOlHcAQAAAAAetH42WdR12s23zxr903mCJB5BEcAAAAAoBdNMcGR6nHjsnbfsR1rGj/5RF0dHVm7f8APCI4AAAAAQC+aFiyIul41ZoxnmSNdbW1qXrgwa/cP+AHBEQAAAADoQfv69Wpft86z4Ej5kCEqrauLWkfHGiC9CI4AAAAAQApZIwoEVBXTXjfTajbdNOo6dUeA9CpJ8+0BAAAAyBPFxcXacsstu61DtMaY4EjFiBEqKivL6hhsas3ql18OXyc4AqQXwREAAADApwYPHqy3337b62HkXzHWsWOzPobYoqwER4D0YloNAAAAAORoMdae2vkGg8GsjwMoVARHAAAAACDHgyM1MZkjViS2deXKrI8DKFQERwAAAAAgleCIB9NqKkeNUlF5edQ6ptYA6UNwBAAAAAASCHZ2qmnRoqh1VaNHZ30cgeLiuFNrAKQHwREAAAAASKB52TIF29s9L8hqCI4AmUO3GgAAAMCnGhsbddVVV0WtO++881RdXe3ZmHK9U01xZaXKhgzxZCyxHWs2EBwB0obgCAAAAOBTTU1NuvTSS6PWnX766QRHIjQtXNitGGsgEPBkLDWbbhp1ncwRIH2YVgMAAAAASWaOeFGMNWRATHCkZckSdTQ2ejYeoJAQHAEAAACAZDvVeFCMNaR6/HgpJmul4eOPPRsPUEgIjgAAAABAssGRMWM8G0txeXm3+2dqDZAeBEcAAAAAIIHGmGk1XnWqSTS1huAIkB4ERwAAAAAgjo6mJrWtWpUzmSPx2vnSsQZID4IjAAAAAJDElBpT6WHNEVMT086XmiNAehAcAQAAAIAkgiPl9fUqqaxULmWONH7yibo6OjwbD1AoCI4AAAAAQI4XY01UcyTY3t6t3TCA1BEcAQAAAIA4YoMOVR4XYzVldXUqGzw4ah1FWYH+IzgCAAAAAHE0xmSOVOdA5ogZEFN3hKKsQP8RHAEAAACAOJoWLsy5aTWmhna+QNoRHAEAAACAGMFgsPu0mhwJjsTWHSE4AvQfwREAAAAAiNG6YoW6WlvzJjhiwRwAfVfSj78FAAAAkMcCgYCGDh3abR26F2MtKitTxfDhysXgSEdDg1qXL8+Z8QH5iOAIAAAA4FMWGFmxYoXXw8iLYqyVo0crUJQbifeVI0equLJSnc3NUdkjBEeAvsuNVzcAAAAA5JDmmGKsudKpxliQpnqTTaLW0bEG6B+CIwAAAAAQozFHi7GG0LEGSC+CIwAAAAAQoylmWk2uBUcGxGSOEBwB+ofgCAAAAADkW3Bks82irjd8/LFnYwEKQdaCI59++qnOPfdcbbHFFqqurtbgwYM1ZcoUXXXVVWpqakrLfXzyySe64IILNHnyZNXW1qq0tNTdz2677abLLrtMy5cvT8v9AAAAAChcna2talm6NGpd1dixyuXMERtvR2OjZ+MB8l1WutU89NBDOvroo7V+/frwOguIvPzyy26ZOXOmHn74YW0WE/1MxZ/+9Cedcsopao6o2GzWrFmj559/3i3XX3+97rrrLu277779ejwAAABAIbDvzrfeemvUuhNPPFGVlZXys+ZFi7qtqxo9Wrmkety4buuaFy9WzYQJnowHyHcZD47MnTtXRx55pHvjHTBggH784x9rxowZ7roFKv74xz/q/fff1/777+8CJTU1NSnfx7PPPqvjjz9eXV1dKioq0nHHHaeDDjpIo0aN0meffaY77rjDBWhWr17t1r/11lvaJCbSCgAAAPhNQ0ODzjjjjKh1RxxxhO+DI7HFWEvr6lTah+OUTCquqFDZ4MFqW706vK55yRKCI0CuTqs566yzXCCkpKREjz/+uC666CLtuuuu2muvvXTzzTfrV7/6ldvOAiRXX311n+7j8ssvd4ER89vf/tZFvy0IYtN2Dj30UD344IP64Q9/6H5vY7nmmmvS+AgBAAAAFHK9kVxq4xupYuTIbpkjAHIwOPLiiy/q6aefdpdPOukkFxSJZXVIJk2a5C7btJf29vaU7+e5555zP4cMGaLTTjst7jY//elPw5dtig0AAAAA5GMx1pDK2ODIkiWejQXIdxkNjsyaNSt8+YQTTog/gKIiHXvsse7y2rVrNXv27JTvp62tzf0cP358wm0GDRqkoUOHRm0PAAAAALGaYqbV5Fox1oTBETJHgNwMjjzzzDPup3WnsQ4yiUybNi2qfkiqJk6c6H7Onz8/4TZWDHblypVR2wMAAABArKaFC/Mjc2TUqKjrLWSOALkZHJk3b577aV1orOZIItbeN/ZvUnHqqae6n6tWrdLvf//7uNv87Gc/67Z9KhYuXNjjsoQ3IgAAACDvBYPB7tNqcqxTTQjTaoA86FbT0tISztQY3cubSV1dncsuaWxs1IKYN6JkWLsxy1K58847dfrpp+uVV17RgQceqJEjR7puNdbmNzTF53//93+1zz77pHwfY3I0WgwAAAAgfdrWrFFHQ0PUuupcnVYTkzliwREL7gQCAc/GBOSrjAVHNmzYEL5sLXx7EwqOWDuxVBUXF7t2vQcccIB++ctfaubMmW6JZO2DrVNOXwIjAAAAAPwhNmskUFzcrStMrmaOdLW2uta+5UOGeDYmIF9lNHMkpKysrNfty8vLw612+8Km41jmyJtvvhn399ah5pZbbnGdcTbaaKOUb7+3jBabVjN16tSUbxcAAABA7hZjrdxoIxX1UCLAS+XDhlmHC6mrK6ooK8ERIIdqjlRUVIQvJ9MdprW11f2srKxM+b6sXbC1CX7ooYdc4MOm0SxdutTdrwU1brzxRlVVVemuu+5yAYy333475fuwqUE9LTaFBwAAAEB+y5dirMaCNhXDh0eto+4IkGPBkZqamvDlZKbK2JSaZKfgxAZVjjrqKK1bt04jRozQCy+8oKOPPlrDhw9XaWmpC1ycdtpp+s9//uMCNosXL9Zxxx3Xh0cEAAAAwHdtfHO0GGsI7XyBPMgcGfJFOpd1c+nJmjVrwsGRVAuf/vOf/9SiRYvc5TPPPNMFSOLZaqutXNDEWMHW119/PaX7AQAAAFD4unWqydFirCG08wXyoJXvlltu6X5++OGH6ujoSLjdu+++G75sNUFSEdn6d8cdd+xx28mTJ8e9TwAAAAAwjTHBkeocnlZjaOcL5EFwZI899nA/LSvEsjUSmTNnTvjy7rvvntJ9lEQUR+opAGPa29vj/h0AAAAAdLW3d5uWkss1R+K282VaDZB7wZGDDz44fPm2226Lu01XV5frMmNqa2tdy91UjB8/Pqowa08igzCRfwcAAAAALrAQ0fklL6bVkDkC5H5wxDrD7Lnnnu6ytdG1drqxrr766vDUmLPOOssVUY301FNPKRAIuOX444/v9vd7772360Rjfve73yVs5fvoo4/q73//u7tsHW223377NDxCAAAAIH/V19crGAxGLbbOr2I71ZTU1Kh00CDlVc2R5cvV1UtGPYAsB0fM9ddf79rz2pSX/fbbT5dffrnrKDN79mydcsopOv/88912m2++uc4999yUb9+yTS688EJ3ecOGDdptt9100UUXudt/7bXX9Nhjj7luNQceeKDLUjFXXHGFiqwfOAAAAAAk6lQzZow7SZvLKmIyRyzzxQIkAFKT8cIbO+ywg+6++27XKWb9+vUucBHLAiMPP/xwVPvfVPy///f/tHr1aheIsbbBFoCxJZZlpfzyl78Md60BAAAAgISdanK83ogpq6tTUXm5ulpbo6YHVcVklADoWVbSJw444AC98cYbOuecc1wgxKbBWMbHTjvtpCuvvFJz587VZptt1ufbt2jutddeq5deekmnnnqqtt56axdoKS4u1qBBg1yXmh/+8Id666239KMf/Sitjw0AAABAYci3TjWhY6FuU2soygqkLGstW8aNG6drrrnGLamYPn26m/uYDAuCRLbrBQAAAIA+T6vJ8WKskUVZG+fPD1+nKCuQOgpvAAAAAECcgqz5MK0mbjtfgiNA7maOAAAAAMgtra2tevDBB6PWWSOD8vJy+U37+vVqX7s2P4MjtPMF+o3gCAAAAOBT1jDhiCOOiFq3fPlyX7bzjS3Gqji1PPImc4SaI0DKmFYDAAAAwPdii7FWjBih4jzJoIlt50vmCJA6giMAAAAAfC+2GGt1nhRjjTetpn3NGnU0N3s2HiAfERwBAAAA4Hv5Wow1XnDEtJA9AqSE4AgAAAAA3+vWxnf0aOWLkupqlQ4aFLWOqTVAagiOAAAAAPC92IKsVXk0rcZQlBXoH4IjAAAAAHwt2NmppkWL8nZajaGdL9A/BEcAAAAA+FrzsmUKtrfnbUFWQ+YI0D8ERwAAAAD4WuyUmuLKSpUNGaJ8QjtfoH8IjgAAAADwtW71RkaPViAQUF5PqyFzBEgJwREAAAAAvtatU02eTamJN63GWvkGg0HPxgPkG4IjAAAAAHytaeHCvG3jmyhzpLO5We3r1nk2HiDfEBwBAAAA4GstS5dGXa/caCPlm4rhw6WYqUBMrQGSR3AEAAAAgK/FBkdcoCHPFJWWqmLYsKh1FGUFkkdwBAAAAIBvWV2O5tjgyIgRyke08wX6rqQffwsAAAAgjw0ZMkTLly/vts5PrC5HV2tr1LrKPA2OuHa+c+dGFWUFkByCIwAAAIBPFRUVqb6+3utheKpl2bJu62Knp+QL2vkCfce0GgAAAAC+FVtvpGzwYBWVlakggiNkjgBJIzgCAAAAwLcKpd5I3JojBEeApBEcAQAAAOBbsdNq8rXeSLzMEcuKCXZ2ejYeIJ8QHAEAAADgW4XQxjdR5ogFRlpWrPBsPEA+oSArAAAA4FNtbW167rnnotbttttuKsvTmhvpyBzJ5+BIqF5KV1tbVFHWfM6GAbKF4AgAAADgU+vWrdOMGTOi1llrXz91sOmWOZLHgYRAUZEbf9Nnn4XX0c4XSA7TagAAAAD4VnNs5kgeB0fiFmWlnS+QFIIjAAAAAHyps7VV7WvWRK2rzONpNYZ2vkDfEBwBAAAA4Eux9UYKInOE4AjQJwRHAAAAAPhSbHCkuLJSJTU1ymdMqwH6huAIAAAAAF+KLVZqWSOBQED5rILMEaBPCI4AAAAA8KVCauMbUhWTOdK2apWrrQKgZwRHAAAAAPhSoXWqiZc5YmjnC/SO4AgAAAAAX4rNHMn3TjWmtKamW90U6o4AvSM4AgAAAMCX4tUcKQR0rAFSR3AEAAAAgC8VYs0RQ3AESB3BEQAAAAC+E+zqUsvy5YWZOUI7XyBlBEcAAAAA+E7b6tUKdnQUZOYI7XyB1BEcAQAAAOA73QIGRUUqHzpUBZk5QnAE6BXBEQAAAAC+063eyLBhKiopUSHWHKGVL9C7wnj1AwAAAEhZXV2d3nrrrW7r/KBQi7HGyxzpaGhQ+4YNrs0vgPgIjgAAAAA+VVJSoq222kp+1LJ0acEGR+I9FivKWjpxoifjAfIB02oAAAAA+E4hZ44Ul5d3q59CxxqgZwRHAAAAAPhOc0zmSGydjnxHUVYgNQRHAAAAAPhOIWeOxG3nS+YI0COCIwAAAAB8p5BrjhgyR4DUUJAVAAAA8KmOjg699957UesmTpzoCrUWMuveYkukihEjVEho5wukprDf9QAAAAAktGbNGm299dZR65YvX676+noVsuaYKTWGzBHA35hWAwAAAMDXU2pKBw5USVWVCjlzxIIjwa4uz8YD5DqCIwAAAAB8pdCLscbLHAm2t6t11SrPxgPkOoIjAAAAAPwdHCmweiOmfOhQBUpLo9bRsQZIjOAIAAAAAH93qinA4EigqKhbRgx1R4DECI4AAAAA8JXmAm/jm7AoK5kjQEIERwAAAAD4ih9qjhja+QLJIzgCAAAAwNfBkcoCnFZjaOcLJI/gCAAAAADf6LKuLStWFHzNkbjtfJlWAyREcAQAAACAb7jASDDoj2k1ZI4ASSM4AgAAAMC3U2qKyspUNniw/JA5YoGhrrY2z8YD5DKCIwAAAAB8ozkmOFI+bJgCgYAKUUVMcMQyZmI79QD4HMERAAAAAL7REhMcKNRirKZ04EAVV1VFrWtZvtyz8QC5jOAIAAAAAN8GRwq13oixjJiKYcOi1rXGZM4A+BzBEQAAAAC+rTlSqJ1qEgV/yBwB4itJsB4AAABAgRs0aJBmz57dbZ2vgiMFnDliYjNHYh8/gM8RHAEAAAB8qqysTNOnT5ef+KnmSKjgbCQyR4D4mFYDAAAAwBeCcbq1FHzmSOy0GjJHgLgIjgAAAADwhfZ169TV2uqvmiNkjgBJITgCAAAAwBfiZU3EBg8KPXOkleAIEBfBEQAAAAC+rDdSNniwisrKVMhigz8dDQ1uARCNgqwAAACAT3V1dWnVqlVR64YMGaKiosI8h9qt3sjIkSp0sQVZTcuKFRowYIAn4wFyFcERAAAAwKcsMDIs5uB5+fLlqq+vlx+m1VQWeDFWU1JVpZKaGnVs2BD1PAwYP97TcQG5pjBDwgAAAADQy7SaQu9Uk7BjDXVHgG4IjgAAAADwhdjMEd8ER2Kyg1pp5wt0Q3AEAAAAgD+DIz6oOWJo5wv0juAIAAAAAF/oVpDVr9NqyBwBuiE4AgAAAKDgdba2qn3NGt8VZI3Xsca61QCIRnAEAAAAQMGLly1RMWKE/Jg5Qs0RoDuCIwAAAAB8Fxwp/qLFrV9rjgSDQc/GA+QigiMAAAAACl7LkiXdsikCgYD8mDnS2dysjoYGz8YD5CKCIwAAAAAKnl/b+Jry+vpu6yjKCkQjOAIAAACg4DXHBkd8Um/EFJeXq7SuLmodwREgGsERAAAAAAUvNhhQ6aPgSKK6IwC+RHAEAAAAgC9rjvg5ONJKcASIQnAEAAAAQMHzc82ReI+XaTVANIIjAAAAAApasKur2zQSP9UcMUyrAXpW0svvAQAAABSogQMH6p577um2rtC0rV6tYEeHv2uOkDkC9IjgCAAAAOBT5eXlOvzww1XompcujboeKC5W+dCh8pPYdr5kjgDRmFYDAAAAoKC1xARHLFBgARI/Z45YQdZgMOjZeIBcQ3AEAAAAQEHzezHWeDVHutra1L52rWfjAXINwREAAAAAvsoc8Vsx1njTagxTa4AvERwBAAAA4KvMkUofZo4UlZaqbMiQqHUUZQW+RHAEAAAAgK8KsvoxcyRuxxoyR4AwgiMAAACAT61YsUKBQCBqsXWFhpoj8euOkDkCfIngCAAAAICCRs2R+MER61gD4HMERwAAAAAUrI6GBrdE8m3mSOy0GjJHgDCCIwAAAAAKVnOcAIBfM0fKY6fVkDkChBEcAQAAAOCbKTWlAweqpLJSfkTmCJAYwREAAAAABatbMVafZo3ErTmyYoWCXV2ejQfIJQRHAAAAABQsOtUkfuzBzk61rV7t2XiAXEJwBAAAAEDBInPkS+VDhkhF0YeATK0BPkdwBAAAAEDBal6yJOq6nzNHAsXFqqivj1pHUVbgcwRHAAAAABSs1piDfz8HR+J2rCFzBHAIjgAAAAAoWLGZEX4PjnTrWEPmCOAQHAEAAABQkKwTi3Vk6alji9/EPn4yR4DPERwBAAAAUJCsE4t1ZInk+8yR2Ha+ZI4ADsERAAAAAAWpW1ZEUdHnHVt8rNu0GjJHAIfgCAAAAICCFFtPo3zoUNexxc+6FWQlcwRwSj7/AQAAAMBvBgwYoBtuuKHbuoItxurzeiPxMkdaV65UV0eHiko4NIS/8QoAAAAAfKqyslKnn366ChVtfLvrFiAKBl2ApHLECK+GBOQEptUAAAAAKEix9TTK6+vld2V1dQqUlkatoygrQHAEAAAAQIFqiW3jS+aIAkVFqogJElGUFSA4AgAAAKBAxR70U3MkQccaMkcAgiMAAAAAfFJzhOBI/I41ZI4ABEcAAAAAFJ5gZ6crNNpTUMCvYoNEZI4AWQyOfPrppzr33HO1xRZbqLq6WoMHD9aUKVN01VVXqampKa339a9//UvHH3+8NttsM3dfgwYN0uabb67DDjtMv/vd79TQ0JDW+wMAAADy0cqVK1VfXx+12LpC0Lp6tQuQRKLmSIJpNWSOANlp5fvQQw/p6KOP1vr168PrLCDy8ssvu2XmzJl6+OGHXTCjP9asWaMTTjhB//d//9ftd3bfH3zwge6//37tuuuu2n777ft1XwAAAEC+CwaD3YIhtq4QdDvgLypS+eDBXg0npzNH6FYDZCE4MnfuXB155JFqbm7WgAED9OMf/1gzZsxw1++66y798Y9/1Pvvv6/999/fBUpqamr6dD/r1q3Tvvvuq1deecVdP+SQQ1ymyKabbqri4mItWLBAc+bMccERAAAAAIWtNbZTTX29AsXFno0nl1CQFfAgOHLWWWe5QEhJSYkef/xxl7URstdee2nChAk6//zzXYDk6quv1iWXXNKn+znzzDNdYKS8vFz33HOPDjzwwKjf77TTTi5gcu2116ozJr0OAAAAQGGJzRyh3kjizJG21avV2dqq4vJyz8YEFHTNkRdffFFPP/20u3zSSSdFBUZCrA7JpEmT3OXrr79e7e3tKd/PM888oz/96U/u8s9//vNugZFIgUDABWoAAAAAFK7YbAg61XypPE7tldjitYDfZDQ4MmvWrPBlqwUSdwBFRTr22GPd5bVr12r27Nkp388NN9zgflrh1TPOOKPP4wUAAABQGGjjm1jpwIEqiskSoSgr/C6jwRHL6DDWMWby5MkJt5s2bVr48rPPPpvSfbS1tYULsFrNkYqKCnfZps5YnZFPPvlELS0tfXwEAAAAAAoic4RONVHZ9NQdAbIYHJk3b577aV1oeprKYu19Y/8mWa+//no4+LHNNtu4rjRnn322hg4dqrFjx2r8+PEuo8QCJ0899VSfHwsAAACAPK45Ul/v2VjyomMNmSPwuYwV37CARagt2OjRo3vctq6uzmWXNDY2umyPVLzzzjvhy11dXa7wqrXsjc0u+de//qUnn3xSl19+uS644AKlauHChT3+fsmSJSnfJgAAAIAsdashc6TH4AiZI/C7jAVHNmzYEL5sLXx7EwqONDQ0pHQ/q1evDl++8sorXVDma1/7mi677DJtu+22LpPE2vdeeOGFrt2v/bRMlYMOOiil+xkzZkxK2wMAAADwRrCzUy2xwRFqjvRYlJWaI/C7jE2riazzUVZW1uv21oLXWNvfVFhAJfI+bfrMP/7xD02ZMsXdZn19vU499VS3zoq/mh//+McKBoMp3Q8AAACA/NC6apWllUetI3MkGpkjQJYyR0KFUUPTWnrT2trqflZWVvb5fkLZI8XFxd2222OPPfStb31L9913n6tr8uabb7rMkmT1Nt3HptVMnTo1hZEDAAAAyITYLIhAcbHKBg/2bDy5KDZYFNvdB/CbjAVHampqwpeTmSoTygBJZgpOovuxLJEddtgh4bZf/epXXXDEvPTSSykFR3qrmwIAAAAgN+uNWDHWwBdZ5PgcmSNAtIy9Q1hGx5AhQ5IqZrpmzZpwcCTV2h6R2/cWwIjcdkXMGyYAAACAwswcod5I75kj7evWqTOiNALgNxkNn2655Zbu54cffqiOjo6E27377rvhy5MmTUrpPrbaaqvw5c7Ozh63jfx9T62FAQAAAOSv2CyIcoIj3cQLGJE9Aj/LaITA6nw8/fTTLivklVde0c477xx3uzlz5oQv77777indx7hx4zR27Fh99tln+uSTT1yh1UAgEHfbjz76KHx5o402Sul+AAAAgEJTVVWliy++uNu6fBd7kE/mSHclAwaouKpKnU1NUc9b9dixno4LKMjgyMEHH6zLL7/cXb7tttviBke6urp05513usu1tbWaMWNGyvdz6KGH6tprr3Vte5988knts88+cbd74IEHogI3AAAAgJ9VV1frkksuUaGJLS5KcCQ+e14aP/kkfL2Vdr7wsYxOq7HuLXvuuae7fMstt+j555/vts3VV1/tuseYs846S6WlpVG/f+qpp1wmiC3HH3983Ps5++yzw11rfvjDH7ogSaw///nP7rbM/vvvn3JtEwAAAAD5WXOEaTXJ1R1hWg38LOMlm6+//nrXntdqjuy3334uk+SFF17Q7Nmzdcopp+j88893222++eY699xz+3QfNq3msssuc5etRa8FZSxTxaby2P2ceeaZ4cDKwIEDXZYJAAAAgMLUEtN8gcyRJDvWkDkCH8t4VVJrrXv33Xfr6KOPdhkdF110UbdtLDDy8MMPR7XlTdV5552n1atX68orr9R7772nE088sds2w4YN06xZszRhwoQ+3w8AAACA3NXV0aHWlSt7zJBA/IwaMkfgZ1lp9n3AAQfojTfe0DnnnOMCIVbkyeqL7LTTTi6YMXfuXG222Wb9vh/LSnn22Wd1zDHHaOONN1Z5ebkGDRqkKVOm6Gc/+5nef/997brrrml5TAAAAAByT9uqVVbYMGodmSNJTqshcwQ+lrV+ttZV5pprrnFLKqZPn+460CTLgh8EQAAAAAB/is1+CBQXq2zwYM/Gk1fTasgcgY9lLTgCAAAAILfYtPRQA4WQp59+WoPzOJgQe4BfXl+vQFFWEubzPnMktssP4CcERwAAAACf6uzs1DvvvNNtXT6LnRrClJrEYp+bjoYGt5QMGODZmACvEEIFAAAAUDBaYzrV0MY3sXjPTWynH8AvCI4AAAAAKBjdMkfoVJNQSVWVSmI6hlKUFX5FcAQAAABAwYitOVJRX+/ZWPKyYw11R+BTBEcAAAAAFG5whMyRlOqOtJI5Ap8iOAIAAACgYMR2XKHmSM9o5wt8juAIAAAAgILQ1dGh1pUro9aROZLitBoyR+BTBEcAAAAAFAQXGAkGo9ZRc6RnsZk1ZI7ArwiOAAAAACjIKTWBkhKVDR7s2XjyAZkjwOcIjgAAAAAoCLFZD+X19QoUcciTas2RYEz2DeAHvFMAAAAAKMxONRRjTTlzpKulRR0bNng2HsArBEcAAAAAFOS0GoIjvbPsmlhMrYEfERwBAAAAUBBiD+rpVNO74vJyldbVRa0jOAI/IjgCAAAAoGBrjqBvdUcAvynxegAAAAAAvFFRUaHTTjut27p81bJiRdR1MkeSD45seO+98HWCI/AjgiMAAACAT9XU1OjGG29UoWiNnVZDzZGkxAaRYp9HwA+YVgMAAAAg73V1dKh11aqodeUER5ISG0RqJjgCHyI4AgAAACDvta5cKQWDUevIHElOxYgRPXb9AfyA4AgAAACAvBd7QB8oLVVZTBcWJFmQlcwR+BDBEQAAAAB5L/aAvnzoUAWKONzpS80RK2wb7OrybDyAF3i3AAAAAJD3Yjus0KkmebG1WYLt7Wpbs8az8QBeoFsNAAAA4FNr167VwQcfHLVu1qxZqq2tVd4HR6g3kjTLslEgEFWzxZ7P8iFDPB0XkE0ERwAAAACfam9v15w5c7qtK4SaI2SOJK+opMQFSFpXrIiapjRo0iRPxwVkE9NqAAAAABRezZH6es/Gko9iM23oWAO/ITgCAAAAIO9ZEdFIZI70sygrHWvgMwRHAAAAAOS92IN5ao6khuAI/I7gCAAAAIC81mXdVVatilpHcKSfwRGm1cBnCI4AAAAAyGutK1f22p4WPYt9vsgcgd8QHAEAAACQ12KzHAKlpSqrq/NsPPkoNtOGzBH4DcERAAAAAIVVb6S+XoFAwLPxFMK0GsvG6ero8Gw8QLYRHAEAAACQ11rpVNNv3Wq0dHV1q+MCFDKCIwAAAAAKKnOEeiOpKxs8WIGSkqh11B2BnxAcAQAAAJDXYutj0KkmdYGiIpXX10eto+4I/ITgCAAAAIC81kpwJC0qR4yIuk7mCPyE4AgAAACAvEbmSHrQzhd+RnAEAAAAQF6j5kh60M4XfhZdcQcAAACAb5SVlemwww7rti6fdLW3q2316qh1dKvpm9jnjcwR+AnBEQAAAMCnBg0apHvvvVeF1MbXMK2mb2Kft9haLkAhY1oNAAAAgLwVO/WjqKxMpbW1no2noDJHCI7ARwiOAAAAACiceiP19QoEAp6Np5AyR2y6Umdrq2fjAbKJ4AgAAACAgplWw5SaviuPU6uldeVKT8YCZBvBEQAAAAAFkzlCMda+Kx04UEUVFVHrWpYu9Ww8QDYRHAEAAACQt2LrYti0GvSNTUeinS/8im41AAAAgE+tW7dOJ598ctS6mTNnui42+SL24J3Mkf6x56/ps8/C12nnC78gOAIAAAD4VFtbm+67776odTfddJPySWy7WWqO9A/tfOFXTKsBAAAAUDjTagiOpLedL5kj8AmCIwAAAADyUldbm2s3G4nMkf6h5gj8iuAIAAAAgLzUEqfNLDVH0tvOl+AI/ILgCAAAAIC81Boz5aOorEyleVRMNi8yR5hWA58gOAIAAACgYOqNWDta9F1s5k3Hhg3qaGrybDxAthAcAQAAAJCXurXxpd5Iv8V7DskegR8QHAEAAACQl2IP2gmO9F9JdbVKBgyIWkfdEfgBwREAAAAAeal1xYqo6wRHMjO1Jra2C1CICI4AAAAAKIjMkdhOK+gb2vnCjwiOAAAAACiMmiP19Z6NpZDQzhd+RHAEAAAAQGHUHCFzJC1o5ws/IjgCAAAAIO90trSofe3aqHUER9KDaTXwI4IjAAAAAPJOvGyGihEjPBlLoYl9HinICj8o8XoAAAAAALxRWlqqadOmdVuXj8GR4jgtaJGezJHmZcsUDAYVCAQ8GxOQaQRHAAAAAJ+qra3VU089pXzUsnRptyk1HLynR+z0pK6WFnVs2KDSgQM9GxOQaUyrAQAAAJB3YjNHKqk3kjblcbr+UJQVhY7gCAAAAIC80xwncwTpUVxertK6uqh1FGVFoSM4AgAAACD/2/hSjDWtaOcLvyE4AgAAAKAgao4gfWjnC78hOAIAAAAg/zNHCI6kVezzSTtfFDq61QAAAAA+tWHDBl144YVR66644grV1NQolwW7urplMlSOHOnZePwQHCFzBIWO4AgAAADgUy0tLbrpppui1l1yySU5HxxpW71awY6OqHVkjmQ4OELmCAoc02oAAAAA5HWnmkBxscqHDvVsPIWIgqzwG4IjAAAAAPK6GGt5fb0LkCCDmSMrVrjpTEChIjgCAAAAIK9QjDXzymMyR4Lt7Wpbs8az8QCZRnAEAAAAQF6hjW/muWlKgUDUOoqyopARHAEAAACQV8gcybyikpJudVyoO4JCRnAEAAAAQF5pjjlIp41vdoqytpI5ggJGcAQAAABAXiFzJDsqRoyIuk7mCAoZwREAAAAAeYWaI9lBO1/4CcERAAAAAHmjo7FRHRs29JjhgAy182VaDQoYwREAAAAAeSNe9gKZI9lp50vmCAoZwREAAAAAeTulpqSmRiVVVZ6Nx1fTasgcQQEjOAIAAAAgbzvVMKUmc2IzclpXrlRXR4dn4wEyieAIAAAAgLwRO7WjkuBI1jJH1NWltlWrvBoOkFElmb15AAAAALmquLhYW265Zbd1uYxONdlTNniwAqWlCra3RwWneM5RiAiOAAAAAD41ePBgvf3228rnzBEO1DMnUFSkivp6NS9eHF5H3REUKqbVAAAAAMgb3TJHmFaT3Xa+dKxBgSI4AgAAACBvkDmSXbTzhV8QHAEAAACQF6xTSsuKFVHrCI5kFu184RcERwAAAADkBWslax1TItGtJrOYVgO/IDgCAAAAIC/EHphbJxXrqILsZY60kjmCAkW3GgAAAMCnGhsbddVVV0WtO++881RdXa28KMY6bJjrqIIsZo4QHEGBIjgCAAAA+FRTU5MuvfTSqHWnn3567gZHKMbqeeZI2+rV6mxtVXF5uWdjAjKBMCsAAACAvEAb3+yL9xy72i9AgSE4AgAAACAvNJM5knUlNTUqqqiIWkdRVhQigiMAAAAA8jJzpJLgSMYFAoHu7XwJjqAAERwBAAAAkBeoOeIN2vnCDwiOAAAAAMh5wWCwe3CEmiNZQTtf+AHBEQAAAAA5r6OhQZ1NTVHrCI5kB5kj8AOCIwAAAADyrt6IYVpNdnSrOULmCAoQwREAAAAAOa85JjhSWlen4vJyz8bjJ+WxmSMER1CACI4AAAAAyHmxUznoVJM9TKuBHxAcAQAAAJB302qYUuPdtJqODRvUEVP/Bch3BEcAAAAA5Dza+OZOcMSQPYJCQ3AEAAAAQM6jja93SqqrVTJgQNQ66o6g0BAcAQAAAJB/02oIjmQVdUdQ6Eq8HgAAAAAAbwQCAQ0dOrTbulzEtBpv2fPd8NFHPbZWBvIZwREAAADApywwsmLFCuW6rrY2ta5cGbWuksyRrKocOTLqesuSJZ6NBcgEptUAAAAAyGktcQI4ZI5kV0VMcKRp8WLPxgJkAsERAAAAADktdgpHUVmZSmtrPRuPH5E5gkJHcAQAAABA3nWqydXaKH4JjjQTHEGBITgCAAAAIKdRjDX3giNtq1ers7XVs/EA6UZwBAAAAEBeTauhGKv3NUcMU2tQSOhWAwAAAPhUc3Ozbr311qh1J554oiorK5VLyBzxXmlNjUoGDFBHQ0PU1JrqjTf2dFxAuhAcAQAAAHyqoaFBZ5xxRtS6I444IueCI80xmSNWcwTeTK3Z8MEH4evUHUEhydq0mk8//VTnnnuutthiC1VXV2vw4MGaMmWKrrrqKjU1NWXkPu12N9lkE1esyZaNiWoCAAAAeYfMkdycWkNwBIUkK5kjDz30kI4++mitX78+KnDx8ssvu2XmzJl6+OGHtdlmm6X1fn/6059q/vz5ab1NAAAAANkTDAa71RwhOOIN2vmikGU8c2Tu3Lk68sgjXWBkwIAB+sUvfqHnnntOTz75pL773e+6bd5//33tv//+2rBhQ1rv97rrrlNFRYVqamrSdrsAAAAAsqd97Vp1tbVFrWNajTdo54tClvHgyFlnneUKPZWUlOjxxx/XRRddpF133VV77bWXbr75Zv3qV78KB0iuvvrqtNxnZ2enC7zYT7s/m8IDAAAAIP+n1JiK+npPxuJ3BEdQyDIaHHnxxRf19NNPu8snnXSSC4rEsjokkyZNcpevv/56tbe39/t+7XZeeeUVTZw4URdccEG/bw8AAABAbhRjLR86VEVlZZ6Nx89ia44wrQaFJKPBkVmzZoUvn3DCCfEHUFSkY4891l1eu3atZs+e3e/Cr1ZrxPz+979XGW+cAAAAQN6iGGvuqBw1Kup6+/r16mhs9Gw8QN4ER5555hn307rTTJ48OeF206ZNC19+9tln+3Wfp512mhobG3XMMcdo+vTp/botAAAAAN7qVoyVeiOeiffcM7UGhSKjwZF58+a5n9aFxmqOJGLtfWP/pi/uuusuPfLII6qrq0tb/RIAAAAA3qFTTe4oqaxUaV1d1DqCIygUGWvl29LSopUrV7rLo0eP7nFbC2ZYdollfCxYsKBP97dmzRqdffbZ7vIVV1yh+jQXaVq4cGGPv1/CmwIAAACQdkyryb2irO1r1oSvU3cEhSJjwZHItrzWwrc3oeBIQ0NDn+7vvPPO07Jly1zR11CL4HQaM2ZM2m8TAAAAQIrBEabVeF53ZP0774SvkzmCQlGUycyRkGSKopaXl7uf1vY3Vf/5z3906623uqk7VoQ1EAikfBsAAAAAck8zmSM5hXa+KFQZyxypqKgIX25ra+t1+9bWVvezsrIypfuxv/ve976nYDCos846S9tuu60yobfpPjatZurUqRm5bwAAAMCPOltbo6ZwmEoyR3IrOLJ4sWdjAfIiOFJTUxO+nMxUGZtSk+wUnEi/+MUv9N5777lpL5deeqkypbe6KQAAAAAyO6XGMK3GWxVkjqBAZTRzZMiQIVq1alWvxUytmGooOJJqbY8rr7zS/dxnn3300EMPxd0mdNv20zramGHDhmmvvfZK6b4AAAAAeNeppriqSiUpnkxFZjNHrCCrZfFT2gD5LmPBEbPlllvq6aef1ocffqiOjo6E7Xzffffd8OVJkyaldB+hKTu33XabW3pi3XOOOuood3natGkERwAAAOBr1uHRDmzzqY0vB+G5FRzpbG5W+7p1Kqut9WxMQE4XZDV77LFHOGPjlVdeSbjdnDlzwpd33333TA4JAAAAQJ6gjW/ucf+DmAAVU2tQCDIaHDn44IPDlxNldXR1denOO+90l2trazVjxoyU7sMi3b0t48aNc9vaz9C6p556ql+PDQAAAECWO9VQb8RzRaWlKq+v7za1Bsh3GQ2OWPeWPffc012+5ZZb9Pzzz3fb5uqrr9a8efPcZes2U1paGvV7C2JY6pwtxx9/fCaHCwAAACCHM0cqyRzJCbTzRSHKaHDEXH/99a49r9Uc2W+//XT55ZfrhRde0OzZs3XKKafo/PPPd9ttvvnmOvfcczM9HAAAAAB5olvNETJHcgLBERSijBZkNTvssIPuvvtuHX300Vq/fr0uuuiibttYYOThhx+Oav8LAAAAwN+oOZKbaOeLQpTx4Ig54IAD9MYbb7gsEguCWGvfsrIybbbZZjr88MN1xhlnqKqqKhtDAQAAAPCF1tZWPfjgg1HrDjzwQJWXl8trwa6u7sERMkdytp0vkO+yEhwJFUO95ppr3JKK6dOn97u92CeffNKvvwcAAAAKkWV2H3HEEVHrli9f7lr8eq1t9WoFOzqi1pE5khuYVoNClPGaIwAAAACQquaYeiMqKlL50KFeDQc9ZY4sXeoyfYB8RnAEAAAAQM7pNqWmvl5FJVlLfEcKNUe62tpcpg+QzwiOAAAAAMg5FGPNXRaoCsQEqpoXL/ZsPEA6EBwBAAAAkHNo45u7AsXFqhg2LGoddUeQ7wiOAAAAAMg5ZI7kNtr5otAQHAEAAACQ8wVZyRzJLbTzRaEhOAIAAAAg55A5ktsqR42Kuk7mCPIdwREAAAAAOV9zpJLgSE5njlCQFfmO4AgAAACAnNK+YYM6NmzoscYFciw4QuYI8hzBEQAAAAA5JV4WQuw0DngrNljVsny5ujo6PBsP0F8ERwAAAADklKaFC6Oul9fXq7i83LPxoPfMEXV1qXX5cq+GA/QbwREAAAAAOaV50aKo61WjR3s2FsRXNniwimICVkytQT4jOAIAAAAgpzNHmFKTewKBgCpj2isTHEE+IzgCAAAAIKdrjpA5kid1RwiOII+VeD0AAAAAAN4YMmSIlsfUibB1OZc5stFGno0FidGxBoWE4AgAAADgU0VFRaqvr1eu1xwhOJKbCI6gkDCtBgAAAEDO6GhqUtvq1VHrqgiO5MW0GoIjyGcERwAAAADkbL0RQ+ZIfmSOUHME+YzgCAAAAICcEVtvxFrGllRVeTYeJBbbRah15Up1trZ6Nh6gPwiOAAAAAMjZzBGyRvInc8S0LFvmyViA/qIgKwAAAOBTbW1teu6556LW7bbbbiorK/NsTM0xmSPUG8ldJTU1Kq6uVmdjY1TdkeqxYz0dF9AXBEcAAAAAn1q3bp1mzJgRtc5a+3rZwaaJTjV5IxAIuOyRhg8/DK+j7gjyFdNqAAAAAORsG18yR3Ib7XxRKAiOAAAAAMgZ3TJHRo/2bCzoHcERFAqCIwAAAABygnU6aV2+PGodmSP51bEmXitmIB8QHAEAAACQE+IdWFNzJLdVxGSOUHME+YrgCAAAAICcDI6UDhyo0poaz8aD3jGtBoWC4AgAAACAnNAU08aXeiP5FxxpX7dOHU1Nno0H6CuCIwAAAAByslNNbD0L5P60GkP2CPIRwREAAAAAOdmpporMkZxXUlmp0traqHXUHUE+IjgCAAAAIDczRyjGmheoO4JCQHAEAAAAQE7WHKGNb34gOIJCQHAEAAAAgOe62tvVsmxZ1DoyR/ID7XxRCAiOAAAAAPBcy9KlUldX1DpqjuQHMkdQCAiOAAAAAMi5YqzF1dUqHTTIs/EgeQRHUAgIjgAAAADwXHOceiOBQMCz8aDv02osOBIMBj0bD9AXJX36KwAAAAB5r66uTm+99Va3dV5oWrw46jr1RvI3c6SzsVEdGzaodOBAz8YEpIrgCAAAAOBTJSUl2mqrrZSTmSPUG8kbFcOHd1tn2SMER5BPmFYDAAAAIOdqjlSOGuXZWJCa4vJylQ8dGrWuOSYTCMh1BEcAAAAAeK45JjhiNUeQ33VHgHxCcAQAAACAp4Kdnd0OpiuZVpPXdUdaCI4gzxAcAQAAAOCplmXLFOzoiFpH5kh+oZ0v8h0FWQEAAACf6ujo0HvvvRe1buLEia5Qq5edaorKy1U2ZEhWx4D+ia0RQ80R5BuCIwAAAIBPrVmzRltvvXXUuuXLl6u+vt7TTjXWxjcQCGR1DOgfMkeQ75hWAwAAACCnOtUwpSb/C7K2LF2qYDDo2XiAVBEcAQAAAJBTnWoscwT5nTnS1damtlWrPBsPkCqCIwAAAAByK3OETjV5p2LYMAWKi6PWMbUG+YTgCAAAAABPkTmS/ywwUj5sWNQ6giPIJwRHAAAAAHgm2NXVLThCzZHCmFrTQnAEeYTgCAAAAADPtK5a5epTRCJzpDDa+cZOlwJyGcERAAAAAJ6JbeMbKC119SuQf6rGjIm63vjpp56NBUgVwREAAAAAnonNLrCpGYEiDlPyUfW4cVHXmz77zLOxAKniXQcAAACAZ7rVG6FTTcEERxo/+0zBYNCz8QCpIDgCAAAAIHcyR6g3kreqxo6Nut7V0qLW5cs9Gw+QCoIjAAAAAHKm5gidavKX1YopKi/vlj0C5AOCIwAAAAA807R4cdR1Mkfyl9WKic0eaaIoK/IEwREAAAAAnrB6FN0yR6g5Ulh1RwiOIE8QHAEAAADgibY1a9TZ3By1jsyR/FYdkznCtBrkixKvBwAAAADAG4MGDdLs2bO7rcuW2KyRQHGxKoYPz9r9I/26TashOII8QXAEAAAA8KmysjJNnz49Z+qNVIwYoaISDlHyGZkjyFdMqwEAAADgCeqNFH7Nkfa1a9W2bp1n4wGSRXAEAAAAgCeaFy2Kul45apRnY0F6WM0Ymx4ViY41yAcERwAAAAB4oikmOELmSP4rKi3tFuRiag3yAcERAAAAALmROUKnmoJAUVbkI4IjAAAAgE91dXVpxYoVUYut8yxzhOBIQdYdaWRaDfIApaABAAAAn1q1apWGDRsWtW758uWqr6/P+H23r1+vjg0botaROVIY6FiDfETmCAAAAICsi80aUSCgypEjvRoO0ohpNchHBEcAAAAAeN7Gt2L4cBWVlXk2HmRuWk3L0qXqbGnxbDxAMgiOAAAAAPA8c4QpNYWbOWLIHkGuIzgCAAAAwPNONRRjLRwlVVUqj6lbQ90R5DqCIwAAAACyjswRf2WPEBxBriM4AgAAAMDzmiNkjhR2x5om2vkixxEcAQAAAJB1TYsXR12vHD3as7Eg80VZGwmOIMcRHAEAAACQVR2NjWpfsyZqHZkjhaUqJjhCQVbkOoIjAAAAADwtxmoqR43yZCzI0rSaRYvU1dHh2XiA3hAcAQAAAOBpMdbyoUNVXFHh2XiQ+YKswY4ONcdMpQJyCcERAAAAAJ5mjlBvpPCU1dWppKYmah1Ta5DLCI4AAAAAyKqm2E41TKkpOIFAoNvUGtr5IpcRHAEAAADgbeYIxVj9UZSVjjXIYQRHAAAAAHhac6SKaTUFqVvmCMER5LASrwcAAAAAwBsDBw7UPffc021dppE54g/VMZkjTKtBLiM4AgAAAPhUeXm5Dj/88KzeZ2dLi1pXroxaV0VwxBcda6wgazAYdPVIgFzDtBoAAAAAWRNvagWZI/6YVtPZ3KzWFSs8Gw/QE4IjAAAAALKm4eOPo65XjBihkupqz8aDzLH/bVFZWdQ6ptYgVxEcAQAAAJA1DR99FHV9wKabejYWZFagqKj71BqKsiJHERwBAAAAkDUN8+dHXR+wySaejQUedKwhcwQ5iuAIAAAAAO8yRwiOFDQyR5AvCI4AAAAAPrVixQrXOSRysXWZYp1KYmuOMK2msJE5gnxBcAQAAABAVrQuX67OxsaodQPGj/dsPMi8qnHjoq4THEGuIjgCAAAAwJMpNcVVVa6jCQpXdUxwpH3NGrWvX+/ZeIBECI4AAAAAyIpuU2rGj3cdTVC4qjbaSIr5HzdSdwQ5iHciAAAAAN4ERyjGWvCKyspUOXJk1LomptYgBxEcAQAAAJAVFGP1p9ipNdQdQS4iOAIAAAAgK2jj60/d2vkSHEEOIjgCAAAAIOM6mprUvHhx1LpqgiP+bOdLzRHkIIIjAAAAADKu8ZNPolcEAqreeGOvhgMv2/kSHEEOIjgCAAAAIOtTaipHjVJJZaVn44F3NUdali1TZ2urZ+MB4iE4AgAAACDj6FTjX9VjxkSvCAbVtGCBV8MB4iI4AgAAACDj6FTjXyUDBqhsyJCodUytQa4hOAIAAAAg48gc8bfYoqx0rEGuITgCAAAAIKOCXV0ER3wutu4ImSPINQRHAAAAAGRU89Kl6mppiVrHtBp/oWMNcl2J1wMAAAAA4I0BAwbohhtu6LYu051qrAZFeX192u8HuYtpNch1BEcAAAAAn6qsrNTpp5+e8fuJDY7YlJpAIJDx+0XuqIoNjixapGBnpwLFxZ6NCYjEtBoAAAAAGdU4f37UdeqN+E9szZFge7ualyzxbDxALIIjAAAAALKaOVJNcMR3ygYPdtOpIlF3BLmE4AgAAACAjOrWqYZirL5j06hip9YQHEEuITgCAAAAIGM6GhrUsmxZ1LoaMkd8iaKsyGUERwAAAABkLWtERUXd2rrCn3VHGgmOIIfQrQYAAADwqZUrV2rSpElR6+bNm6ehQ4dmLDhSNXq0isvL03b7yOOONUyrQQ4hOAIAAAD4VDAYdAGS2HXpRL0RJJpWY5kjtr/R1hm5gGk1AAAAADKmW3CEeiO+FTudqrOpSW2rVnk2HiASwREAAAAAWWvjS3DEvypHjFBRWVnUOjrWwHfBkU8//VTnnnuutthiC1VXV2vw4MGaMmWKrrrqKjU1NfXrtu3vH3jgAX3/+993t1lXV6fS0lINGTJEu+66qy655BItXbo0bY8FAAAAQO+CnZ1q/OSTqHVMq/GvQHGxKkePjlpHcAS+qjny0EMP6eijj9b69eujAhovv/yyW2bOnKmHH35Ym222Wcq3/cYbb2j33XdXQ0NDt9+tXr1aL7zwgluuvfZa3XzzzTryyCP7/XgAAAAA9K5p0SJ1tbVFrRswfrxn40Fu1B1pjJhqRTtf+CZzZO7cuS4gYYGRAQMG6Be/+IWee+45Pfnkk/rud7/rtnn//fe1//77a8OGDSnfvt1uKDBiQZLLL79cTzzxhF599VU99thjOuWUU1RUVOS2+853vqNHH3007Y8RAAAAQO9TakoHDVLZkCGejQe51843dh8BCjZz5KyzzlJzc7NKSkr0+OOPu2kuIXvttZcmTJig888/3wVIrr76ajcFJhUW+DjiiCN08cUXa8stt+z2+/32209f//rXdcghh6izs1NnnnmmPvjgAyoiAwAAABnWMH9+t3ojfA/3t5oJE6Kur3/vPc/GAmQtc+TFF1/U008/7S6fdNJJUYGREKtDEuqtfv3116u9vT2l+9htt9109913xw2MhBx00EH61re+5S5/9NFHLpsFAAAAQGZRjBWxBm6xRbcAWmdLi2fjAbKSOTJr1qzw5RNOOCFh5sexxx6rH//4x1q7dq1mz57tsj3SbcaMGbr//vvDAZIdd9wx7fcBAEAiLWrXerVqnVtawj9D6xrVpnZ1qUNdalenuxz6GVrXpaBKVaxSFanM/Sz+4mdR+HK5ijVQ5RqkCtWqQoNU/sXPzy+XZafcGADEb+NLMVbfq9l8c8myh4LBz1d0dWnDBx+odpttvB4afC6j35CeeeYZ99O600yePDnhdtOmTQtffvbZZzMSHGltbQ1fLi4uTvvtAwD8p1UdWqoGLdEGLYn4GbtulZrVpk7lgkqVuGDJCA3QSNVolGo0UgPcz88vf/5zuKpVIj4vAfRPZOFNU00xVt8rqa7+vChrRJcam1pDcAQFHRyZN2+e+2ldaKzmSCLW3jf2b9Jtzpw54cuhaTwAAPRmtZr0kdboY63RR1oddXmh1uuL8155o1kdanZBmwbNVeI291YRYLQGalMN1qaq02bu5+eX7adlogBAT9rWrVPrypVR68gcganZYovo4EiGjgGBnAiOtLS0aOUXb4ajY3pZx6qrq3PZJY2NjVqwYEHax/L666+7VsFmm2226VNwZOHChT3+fsmSJX0eHwDAW0EFtUjr9ZaWh5e3tUIfarXWyp/zoC3os0Dr3fKUPun2+6GqcoGSLTRUW2uYttFwbaNhLvMk4EIrAPwuNmskUFLiMgYAqzuy9LHHwtfXv/uup+MBMhociWzLay18exMKjoTa8qZzOs3JJ5/sOtUYayXcF2PGjEnruAAA3livFpcx8aaWRQVDrO5HtliNkFANkNDPASoL1xOxnyXu5+eX7addL1LA1R9p+6IWyec/O8PX7bJlhlgdEwvqWE0T+2m/S7eVanLLf7Uoav1gVX4RLBkWFTQZSKYJIL/XG6kaM0ZFpaWejQe5W5TVptUEg0E6GaFwM0dCysrKet2+vLzc/bS2v+l0xhln6OWXX3aXjzvuOB1wwAFpvX0AQG7XBHldS/WiFuklLdZLWqR3tTLtU2GsCGqohsfIiJ+hdcNUHRUIqVBpVrNiWtQRFSxZreaoGimL3c8N7qfVS+lPMMVu+z/61C0h9lXXMkymaqPwsq2GUxwWKHAUY0WywZH2NWvUsmyZKkeM8GxMQMa+lVRUfHmGqK2tLemCqZWVlWkbw+WXX66ZM2e6y1OmTNGNN97Y59vqbbqPTauZOnVqn28fAND/IIBNg3lWn4WDIRYYSUfWRLECGqtBrtbGJq7mRt0XPwdrnAapTpU5O5XExlWpUrdYoKY3XepyBWStnkqotsqHX9RascufaV3KwSXbfp5WuuUOve7WWWedHTQiHCzZWaNdXZNcfR6BQlVVVaWLL76427p0oI0vEqkaPVrF1dXqbGyMmlpDcAQFGRypqfnyC1gyU2VsSk2yU3CS8Yc//EEXXXRRuODrI4884qbu9FVvdVMAANllB/FWFySUpWCLZT30h01tsakgoWWShroAiAVGbHqLH9jknXpVu2UHjYybjfOJ1rpAyQda7aYkhaYoNao96fuxqUA2JSdyWo5l23xF4zRNG7ufW6qeYAmQYfb9+JJLLsnIbTfMnx91neAIQgJFRRo4caLWvPpqeN2G997T8OnTPR0X/C2jmSNDhgzRqlWrei1mumbNmnBwJB21Pf72t7/ptNNOc5fHjRunJ554QkOHDu337QIAvNOhTlcrJBQIeVqfak0fi6VaDQ878LZ6GJHBEAuCcDDes3KVaKKGuiU2WPWp1rlAyZtf1HGxy+9plauTkgyb4nO33nZLqOjr58GSce6nTcWx4A2A3NfV3h7VjcQQHEHs1JrI4AhFWeG1jE723XLLLfX000/rww8/VEdHR8J2vu9GvBD622b3wQcf1LHHHquuri6NHDlSTz75JFkfAJCnPtEaPa6P9Jg+0pP6uE9FU0P1LqZoI03RqHC9i2zW/fADC1qMV51bDtSXc8mtHOzrWuamOoWW97Uqqdu0gq8PaJ5bTJ0qtLc20Ve1qb6qzTRGgzL2eAD0T9PChQq2R2eTERxBj0VZaeeLQg6O7LHHHi44Ylkhr7zyinbeeee4282ZMyd8effdd+/z/Vkg5IgjjnCBGMtasYyRTSn8BAB5o0Gtmq1PXEDElmQPoiPZ1IzdNMYFQSwgMlkj6ZTiIQtCWT0RW0LWqlkva3E4WPKCFmqZvpx3nohlCt2nd9xibNqTBUksWGKZJVXqvQA8AG+KsZYNHqyyujrPxoPcY9NqYveZztZWFX/RqAMoqODIwQcf7Iqimttuuy1ucMQyPO688053uba2VjNmzOjTfT333HM66KCDXGHXQYMG6bHHHtNWW23Vz0cAAMh0EVXrHvOg3tOj+kDPaUHKBVTHq9YdGIcWqxHC1JjcVqtK7aNN3RJZTHeOPtEcfep+LtD6Xm8nVOT1Or3gOgbtqXH6mjbTN7V5t2k/ALKLYqzoTU1McCTY2en2m0FbbunZmOBvGQ2OWPeWPffc02WP3HLLLa6V7q677hq1zdVXX615X6RQnXXWWSqN6X3+1FNPhQMm9ve33357t/t57bXXtP/++7sMFSsq9fDDD2vy5MmZfGgAgH7UDrEgyP/pPRcUsYPiVEzUkHDBTluYWpH/LJg1QUPccrImh6dUzfmivowFS6xbTk9a1al/6WO3/EiPu/3kQE3UQdpCu2i0iqlVAnjbxpfgCGKU1tSoaswYNUV0BbW6IwRHUJDBEXP99de7qTLNzc3ab7/9XAcZC3bY9bvuuks333yz227zzTfXueeem/Ltf/TRR/rqV7+qtWvXuus///nPXebIW2+9lfBvhg0b5hYAQHZsUKse04cuGPKw63HSnPTfWlHOfbWJ9tOm2lebaiMNzOhYkRs2Vp1bjtP27vpCrQvXn3nChUp6LsZrhWCv0nNuqVeVyyaxQIntS0y/Ab60evVqdzIzkp3YHDx4cL9ul+AIks0eiQ2OAAUbHNlhhx1099136+ijj9b69evD7XUjWWDEsj0i2/8my968ly9fHr5+zjnn9Po31ss9Uy3LAACfW60mzdK7rj7Ek5rvWrcmo0RF2l1jXDDE6knsoBF0KIFGa5BO1I5u6VSXq1nyebDkQ1ezpFPBhH+7Qk26Ta+5pUIlLkByqLbUQZropvgAftbZ2al33nmn27r+6hYcoQ4gEhRlXfavf4WvExxBQQdHzAEHHKA33njDZZFYEMRa+5aVlWmzzTbT4YcfrjPOOENVVVXZGAoAIAsBkXv1jpvekGwL141UowM0Ud/QBE3XxqoRxdiQmE2RCRV5/YmmuQKv/9Z8/VMf6h9637UETqRFHXpI77vFWjpbAO4IbeWm4AyicC+QFq2rV6t9TfRUODJHEM/AmE6lBEfgpUAwGEx8qgVJs4DPmDFj3OUFCxbQPhiAb/Q1ILK9RrgDUlt21EiKqCItur7IKrEpXFbX5i19mV3akzIVu643oUAJHY7gFytWrOg23dyysuvr6/t8m6tfflnPHnlk+HqgtFTfeOstFZVk5bws8kjD/Pmavc8+Uev2feEFVfRj/4M/LMzA8TfvUACAlDWqzQVE/qI39ESSARE7Sz9D492B5wHaXGNVm5Wxwl9sCtZUjXbLz7W3PtbqcKDkaX2acPqNTfsKZZRY5xvLKDlKW7v9lRolQP+m1FRvvDGBEcRVPXasiisr1dncHJU9QnAEXuBdCgCQdJcZywz5i97U3zVPjWrv9W+svsPXtZkO11baXxM4G4+s20SDdbZ2dYtlOVlB4Pv1jh7Vhwnr4FjnGwuo2FKjMlef5Ght66Z80fUG6B1tfJGsQHGxK8q69rXXwus2vPuuhsUUCQaygeAIACChoIJ6RYv1Z72hv7kJCo0pBUSsQwj1Q5ArBqtKx2g7t6xTix7Se7pHb7sOOIkCJRvUptv1mltGqUb/o210jLbVthqR9fED+TRVIhLBEfRkYExwhLoj8ArBEQBAN59pre7U6y4oYi1Re0NABPnGiq8ere3cYoGSB8OBkg/VnmCa2GJt0K/1nFu20TCXTfIdbUt7aSAGmSNItWNNJIIj8ArBEQCA06J2V0fkVs1102d6q9ZdrIBrt2sHh1aXgYAI8jlQEsoosc43Vp/kr3rTvQ66ErwS3tRyXaB/6cd60hVyPVE7uNdBGV+t4HNdbW1qWrAgah1tfJFKcGTDRx+5/aiojHpPyC4+wQHA59Nm5mqJC4hYLZG1aun1b6ZolDtjfqS21nANyMo4gWypVaWO0/ZuWaz1uktv6U96Q69padztLXhi9UtsGaoq99qwQMk2Gp71sQO5oPGTTxTsjJ6mRuYIUgmOBNvb3dQsm24DZBPBEQDwoZVqdMEQC4q8oWW9bj9eteEpBBM1NCtjBLw2SgP1Q+3mlre0zL1mrEPTAq2Pu/1KNek6veCWnTTKBUms440FXAC/WPvmm1HXK0aMUGlNjWfjQe4rHThQlaNGqXnx4qipNQRHkG0ERwDAR1kiT+kT/UEv6wHNS1hXIWSgyt2B3bHaTrtqjAIKZG2sQK6xPKnLNVy/0F76jz512ST36m1XsDWel7XYLT/UYzpMW+p7mqw9NJbXEXwXHKnddlvPxoL8yh6JCo7MmycddJCnY4L/EBwBAB9kidyh13WzXtH7SRRX3Uvj3RnvQ7SFqsR8XyBSkYo0XePd8ht9XffpHZeBZQGTeFrU4Qob27Kl6nWKJrvaJnVkk6BArX399ajrtdtt59lYkD+sne+yf/87fJ2irPACwREAKNAskaf1qf6gV9zBW6I2pSFjNUgnfFFnYbzqsjZOIJ9Vqyxcn+QDrQq3/LWuNvG8oxU6S//UhfqXq9ljgZKdNZpsEhSMztZWrbMz/hHqyBxBEgZNmhR1ff1773k2FvgXwREAKCBr1Kw79JoLiryrlT1uW65iHaotXVDEskXsjDiAvpmgIfqF9tZlmqHH9ZFu0auuPXC86WvN6ggHUrbVcBcksZo+A1XhydiBdLGz/VZMMywQ0KBttvFySMgTNTFFWVuXL1frqlUqHzLEszHBfwiOAEABeE1LdKNecsUi7cCrJ1toqE7VTjpG22qwqrI2RsAPilWkr2uCW1aoUXfqdVfn5wOtjru9FUQ+XY/ofD3h6vucrqnaSsOyPm74V0VFhU477bRu69IxpcZa+FKMFcmoHjdOReXl6mptjQq21e++u6fjgr8QHAGAPNWmDt2vebpRL+pZLehx2zIVu6KQdoZ6T40jjR/IgnpV61zX7WZXzdZ8l9FlxZA74mSTNKpdv9PLbpmujXWGpuogTVSJij0ZO/yjpqZGN954Y2bqjZA1giQVlZSoZvPNtS6ioK9NrSE4gmwiOAIAeWaR1rsz0VZgdZkae9x2cw1xARE7Iz1U1VkbI4AvWTByL23ilmVq0G2a616/87U27vbWVcqW0RroXr/f1WQN14CsjxtI1Zo33oi6TjFWpNqxJjI4soGirMgygiMAkEcFVn+rF/V3zVOnggm3LVGRvqVJ+r520jRtTJYIkEMsyHGh9tT52l1P6GMX6LTaJPFe0wu1Xj/RbF2mOTpcW7lskl0o4Ioc1b5+vRo//jhqXR3BEaRg4MSJUdfXERxBlhEcAYAc1qoO3aW3dL1e0Fwt7XHbkRqgU7STvqfJGinmeAO5zAogf1WbuWWh1rkpN5ZNsjxONpgVdf2r3nTLFI3S2drFTZMr42sccsjaiDP+pqiszLVnBVLJHInU8MEH6urocFNugGxgTwOAHLRUG1ztgd/r5bgHS5G+onE6XVN0iCaplPoEQN4ZrUH6mfbS/9NXXOvtG/SiXtDCuNu+pMX6jh7Qj/S4K95qwVCrbQJ4bW3MlJqBkyapuLzcs/Eg/4MjXW1tapw/XzUTJng2JvgLwREAyCGvaLGu0wu6W2/FbQEaUqVS123GDo620fCsjhFAZpSrRN/Rtm6x9wIrtmzZIq3q7LbtEjXo/+nf+pnmuDbAZ2kX3gvgqW7FWLfd1rOxID+V1dWpYsQItSxdGtWxhuAIsoXgCAB4rFNdmqV3da2e77XrzCaq05maquO1vWpVmbUxAsiuyRqlW3WwfqV9davm6ia9pE+1rtt2Fji5RXPdspfG6yztrG9qczdtB0jG2rVrdfDBB0etmzVrlmpra1O7HYqxIk11R2KDIxsdcICnY4J/EBwBAI9sUKs76LF6Iom6VoSEDnr21+Yq5qAH8A3rMnW+9nDtgP9P77nMsmf0Wdxt/635bpmgwTpHu+o4bacqlWV9zMgv7e3tmjNnTrd1qWheulQty5ZFraMYK/o6tWZ5xP5owREgWwiOAECWWfHF3+i/rvjiOrUm3K5CJS5d/gfamXR5wOdKVKxDtaVbbMqNBVXvSjD97gOt1ml62E27sa5V1uVmBEWakcUpNSU1NareeGPPxoPCqTtCcATZRHAEALLEDmiu0fO6R2+ro4d6IqNU4wqsWqFFO2sMALFTbu7Ut9yUm54KN69Ws36hp3WVntP/aBuXfUKgFZnQbUrNttsqUESWI/ofHLEpNm1r16osxWleQF8QHAGADOpSlx7WB7paz2mOPu1x2500yh28WItOus4A6I1lg1yqGfqx9nBZJNfqBb2h6KkNpk2dul2vuWVfbaJztZv206YKKODJuFF4KMaKdKkeP961gbZONZHZI0N32cXTccEfCI4AQAa0qF1/1hu6Ws/rXa1MuJ0dmhyoie5gZQ+N5WAFQMoqVKrjtYOO0/au5ohlqD2iD+Ju+4Q+dss2GqYfaTd9W1urjK+D6IdgV5fWvvlm1DqCI+irotJSDZgwQevffju8juAIsoVPQwBIo9VqcinuVlNkWZw098hWvCdoe9d+c4KGZHWMAAqTBVf31iZueUfLXSbJn/R63FbAb2q5jtMsXaQndbZ20Xc1WYNU4cm4kd8aPv5YHQ0NUesoxor+dqyJDI5seO89T8cD/yA4AgBp8InWuAORW/SqGpW4yv9IDdCZ2lmnaLIGqyqrYwTgH1tqmP6oA/UL7eXaAN+ol7RSTd22W6QNOk9P6Gf6j6tzZF2xRmuQJ2NGYUypqRgxQhXDqW2DvqMoK7xCcAQA+llk9dd6TvfqbXUqmHA7S2G3qTNHkcIOIIuGaYAu0QxdoD3cVL9rEkz1W69W915mrYKteKtNuaF4K5LBlBpkPDjy/vsKdnYqUEw9NmQW39ABIEVBBfWEPtKv9Kye1Pwet91b43Wedqf4IQBPVarUTZ05STu4ItFX6Vk9rc+6bWedtO7U6275ujbT+dpd07Qx719IvhgrU2qQ5uBIV0uLGj/9VAM22cSzMcEfCI4AQJI61Kl79Y4LirympQm3K1ZAR2grd+Z1R43K6hgBoCdFKtIBmuiW/2qhC5I8oHlx894e1YdumaqNXJDkYG2hYtGeFV/qbG3VunnzotbVkTmCfiofMkTl9fVqXbEiamoNwRFkGsERAOhFo9p0m+a6zjOfaG3C7aq/ODNrxQ3HqTarYwSAVFl1kft0pD7UKjfd5ja9phZ1dNvuRS3SYbpHEzTYBX2P1XauQw5gB6zB9og6W4GABm2zjZdDQgFlj6yIDI7Mm6dR3/iGp2NC4SP8DwAJrFSjLtFsjdO1OlOPJgyMDFe1fqm9tUA/1LX6GoERAHllMw3RTfqmPtM5ukTTNTRBsegPtFqn6B/aWNfpcj2ttWrO+liR21NqBmy6qUprajwbDwqrY02kdRHda4BMIXMEAGJ8qrW6Ws9ppl5Vc5yzqCF2FtXqiRyjbTmLCiDv1ataF2u6ztNuLovE3gfnxwkKW5tyawH8Sz3tOm+do121kQZ6MmbkWL0RptQgTWIzkFa/8oq6OjpUVMLhKzKHzBEA+MKbWqajdb821fX6rV5MGBjZWRvpAR2peTrDTaMhMAKgkFSpTKdrqt7XmfqbDtUOGhF3uwa1uemG43WdTtL/6V19mQIPf1jzxhtR1wmOIF2G7rJL1PWOhgate+stz8YDfyD0BkB+7zzzjD7TFXpGj+iDHrfdXxNcUcI9NY7ODQAKXomK9W1toyO1tf6lj10xavsZq11dulVzXW2mg7SFLtDu2kVjPBkzUldWVqbDDjus27retK9fr8aPo/eHOjrVIE3Khw7VgAkT1PDBl9/NVj7/vOq2397TcaGwERwB4Etd6tI/9L4LijyvhQm3K1GRjtLWbvrMNhqe1TECQC6wYPC+2tQtr2qxC5JY566umB43dm2W3nXLNI3TBdpDX9NmBJNz3KBBg3Tvvfem/Hdr33wz6npRWZlqYupEAP3NHokKjrzwgiZ8//uejgmFjWk1AHylTR26Q69pG/1OB+muhIGRKpW6rjMf6Qe6U98iMAIAkmtPfpcO1wc6U9/XTqpIcJ5tjj7VN/QXba/f6696w7VCR2FZGzOlZuCkSSouL/dsPCg8Q3fdNer66pdfVldbm2fjQeEjOALAFxrUquv0vDbVb3S8ZumdBHPjh6hSl2q669pgnWfG0nkGALrZRINdh5tPdLYu0p6qVUXc7d7QMn1HD2iCfqsb9aKaxIFNoaAYKzJtyNSprj10SFdLi9bE7HdAOhEcAVDw7Xgv1myN1bU6R49podbH3W6cBuk3+ro+1Tn6qaZrSIJWlgCALw3XAP1Ce7uA8q+1n0YpfhtXa4V+hh5xbYB/rjlaQxvggsscqaXeCNKsrK5OA7fYImrdqhde8Gw8KHwERwAUbDveH+gRFxS5zH0Rb4m73dYapj/pEH2gH+hM7axq9V6EDgAQrUblOle76WOdpVt0oCZqSNztVqhJP/kiYP0jPaZFCQLWyG3NS5eqZdmyqHUUY0U2ptZYUVYgUwiOACi4drzH6IFe2/HuqbH6h/5Hb+j7OlrbqVTFWR8rABSacpXoRO2od3S6a3k+VRvF3Y42wIU1paakpkbVG2/s2XhQuIbEtPRdM3euOlvin/AC+otuNQAKph3vlXpGD/fSjtfOZ1qbyd00NmvjAwC/KVKRDtEkHawtNEefuM5gj+mjHtsA27bW4WZnjfZkzH61bt06nXzyyVHrZs6c6brYJD2lZtttFSjinCsyVHfE9q2uLnfdCrKuefVVDd1tN6+HhgJEcASAL9rx/o+20fnaXVtpWFbHCAB+Zm18p2u8W+ZqiWsDfI/ejtsG+O961y20Ac6utrY23XfffVHrbrrpph7/hmKsyJbSmhrVbr11VEDOptYQHEEmEBwBkJfteP+mt9yX7ERdZ0LteL+rHfVD7UrXGQDw2A4aqb/pMP1ce+lqPecyRlrjtPi1NsC2bKfhLqh9hLZSCVMfc0awq0tr33wzah3BEWR6ak1UcISirMgQ8t8AFFw73sGq1MWapk91tq7T1wmMAEAO2fSLNsDWHezH2kODVB53u9dpA5yTGj7+WB0NDVHrKMaKbBZltUBJR2OjZ+NB4SI4AiDnLVeDfqJ/99qOd6wG6Xp9zbWUvEQzNFTVWR8rACD5NsC/1D7uPfsq7auRGtBjG+Bxuk6X6SmtUlPWx4rEU2oqRoxQxfDhno0HhW/w5MkKlHw54SHY0aHVL7/s6ZhQmAiOAMhZH2m1TtM/3Bfin+s/PbbjvVOH6EP9QD/QLrTjBYA8MlAV+pF213ydrZk9tAFeqSZdrKdcoPwsPepatiP7mFKDbCupru62nzG1BplAcARAznlFi3WE7tHm+q1+p5fVkkQ73mNoxwsAed8G+KQk2gA3qV2/0X9dy/ajdb9e19Ksj9XPuhVjZUoNPJhas4rgCDKA4AiAnGnH+7g+1N66QzvpZt2rd7p1Mwix84rP6kT9Rydqf21ONwMAKMA2wC/oZM3Wca5rTTydCuovelPb6/f6mv6k2ZrvPkuQOZ2trVo3b17UujoyR5AFQ3fZJer62rfeUvuGDZ6NB4WJbjUAPNWuTt2tt/RrPeeK7yVSqiIdrW11nnbXJNVndYwAAG/bAFt2yFV6VnfpLRcUifWYPnLLThql87SbvqVJdLjJgPXvvKNge/uXKwIBDdpmGy+HBJ+o23FHFZWVqavti8LMXV1a9eKLGrH33l4PDQWEzBEAntigVl2j51xa9DH6e8LASI3K3Bddm4t+qw4mMAIAPrSdRujPOlQf6Sz9QDu7Vu3xvKzFOlL3uWmZv9V/1UiHm7RaPmdO1PUBm26q0poaz8YD/yiuqFDdDjtErWNqDdKN4AiArFqs9bpQT2iMrtG5elwLEnSeGaEBuuKLLga/0n7aSAOzPlYAQG4Zp1pdr6+7z4bLXFeyqrjbzdda/UCPuuKt1u1smaJbz6Jvlv7rX1HXh02b5tlY4D+xdUdWPv+8Z2NBYWJaDYCseEfL3dSZP+sNtasr4Xaba4jLFLEpNBUJzgwCAPxtiKr0E03TudpVt+s19/liAZFYq9Xsup3ZlJzjtL1+qF01UUM9GXO+a1q0SOtj6o2M2Gcfz8YD/xkSU3fE9se2NWtUVlfn2ZhQWMgcAZAxVhjv3/pY++sv2ko36Ta9ljAwsrvGaJa+rXk6XSdrMoERAECvqlSm0zRV7+tM3a3DXM2ReFrVqZv1iibpBh2sv+lpfUrx1hQti8kaKa2tdXUggGyp2247FVVURK1b+d//ejYeFB6CIwDSrk0d+rNe1476g/bWnXpEH8TdznrMHKIt9JxO0jM6SQdpC9elAACAVFjx1SO0tV7Ud/WUjtf+mhB3OwuH/J/e01d0m3bWH11B8A51Zn28hTClZviMGSoqIQkd2WMFWQfvtFPUOuqOIJ14RwOQNmvU7M7MWRG8RUrcXq1cxTr+i/TmzUlvBgCkscPNNG3slre1XFf3MJ3zJS3Wt3WfxmmQztIuOkk7aKCiz0rjc+3r17vOIJFG7LuvZ+OBv1v6rnzmmfD1lQRHkEYERwD023yt0XV6QbfoVTUqosVfjMGq1OmaojM0VcM0IKtjBAD4y1Ya5rqc/Vx76bd6Ub/TS1qn1m7bfap1+qEe0yV6St/Vjq4bzljVyi9KS0s1Laawqq2LtPyppxTs6Ig6g1+/xx5ZGyOQqChrwwcfqGXFClXU080Q/UdwBECf2Fzt57RA1+p5/V3vqquHudubabDO0S6uGF61yrI6TgCAv43SQF2ufXSR9tStmuuC+Z/EKd66Xq26Ws+73x+hrXSOdtUUbaRCV1tbq6eeeiqlKTVDd9tNJdXVGR4Z0N2grbdWyYAB6mhoiJpas9EBB3g6LhQGJvcDSLmeyF/1hqbqj9pDt+p+zUsYGNlTY12R1Xd1hiuYR2AEAOCVGpW76TMf6Ezdo8O1c4LAR6eC+pvecp9zu+sW3au3fV2XpKutTcvnzIlaR5caeMXq3AyeMiVqHVNrkC5kjgBIyio1uXoiN+hFLe6hnkixAjpMW7p6IlM1OqtjBAAgmeKth2sr91llGZBWl2SW3o0b5rff2zJWg3Smpupk7ahaVcpPrNZI5Fl6M3yvvTwbD2B1R5bPnh2+vur55z0dDwoHwREAPZqnFbpeL+hOva5mfTnfONYAlYXnam8s+s0DAHK/eOvuGuuWD7VK1+u/btpNU5zaWZ9pnc7TE64uyQnawX3WTdAQ+UHslJra7bZTxfDhno0HGLLLLlHXGz/9VM1Llqhy5EjPxoTCwLQaAN10qUuP6H19TX/SlrpRf9ArCQMjG6tW1+irWqgf6hp9jcAIACDvbKYh+q2+oQU6R5drb22kmrjbWdFxy6CcqN/qAP1V/9JHrgZXoQoGg92CI0ypgdcGTZqk0kGDotYxtQbpQHAEQNg6tbgskYm6Qfvrr3pMHyXcdg+N1f06ws3dtqJ1g2h/CADIc4NVpQu1p+brbP1Nh2pqgrokFg75h97XvvqTttKNukkvqiFOJ5x8t/6dd9SyZEnUuuF77+3ZeAATKC7WkKlTo9YxtQbpwLQaAHpXK9yZsDv0uhrUlnC7EhXp29paZ2ln7eSDCv4AAH8qVbG+rW3c8rwWuA429+sdV6w11jyt1Ol6RD/WkzpRO7iW9ZaJki82bNigCy+8MGrdFVdcoZqamm5ZI1Vjx6pm882zPEIg/tSapU88Eb6+8vnnXaZTIBDwdFzIbwRHAB9PnXlUH+o3+q8e7yFDxAxRpU7VTjpNU1xLRAAA/GJXjXHLZ1rrTiT8Ua9qrVritgK2IIplYH5DE3Smdta+2kRFOZ6o3dLSoptuuilq3SWXXPJ5cOTJJ7tNqeHgE7lg6K67Rl1vXrxYTQsWqHrsWM/GhPxHcATwYdeZ2zRXv9PL+lhretx2Ww13Ref+R9uoUqVZGyMAALlmrGr1K+2nn2qaK1L+W72od7Wy23aWW/KwPnDLRA1xJxaO1XZ51+WmafFirX/77ah1TKlBrrAMprLBg9W2enV43aoXXiA4gn7J7VA2gLR5SYt0gmZptK5xFfcTBUaKFNChmqQ5Ol6v6VSdpB0JjAAA8IUBKtdpmqp3dLoe1zE6QJsrUS7Fe1qls/RPbaRrdIoe0muKrt+Ry5bFTKkpra3V4J128mw8QCTLYIrtWmNTa4D+IHMEKGDNatfdeks36iW9rMU9bjtYlfqeJuv72smdHQMAAD23At5Xm7rlY612n7W36FWti1OY1doD36xX3LKbxrhsksO0pcpz+Kt47JSa4dOnq6gkd8cLf06tWfLII+Hry/79b3U0N6ukMr+ytJA7eIcDCtBHWq3f6SXdqrlaE2dedKTtvpg6cxRTZwAA6JNNNFhX66u6VNP1Z73hpty8oxVxt31OC9xyjv7psjOtpte4HDsp0d7QoFX//W/UuuG08EWOsYDdm1YDJ/h5oeSOhgYtefRRjfnWt7weGvIU02qAAtGuTt2nt7Wv7tRm+o2u1vMJAyOlKtJR2lrP6ETN1ak6kakzAACkZcrNqZqit3SantSxLjukOMGkmxVq0hV6RuN1nfbXX/Sg3lWHOpULVj73nILt7eHrRWVlGrbnnp6OCYhVOWqU6vfYI2rdZ/fe69l4kP/IHAHynKXyztSrLktkmRp73HaMBrozVHamargGZG2MAAD4bcrNXtrELYu0Xn/8YkrNEjV029bOeT+iD9yykWrcZ/TJ2lFjNEheWTFnTrfpCyUD+N6A3DP2iCO04umnw9dXv/iiGubP14Dx4z0dF/ITmSNAnmaJPKB39FX9SZvqN7pcz/QYGNlPm2qWvq2PdZYu0lcIjAAAkCUbaaAu0Qx9qnN0rw7XDG2ccNtF2qDLNEcb6zp9U3/RQ3rPk2ySFc89F3WdKTXIVdZBqbSuLmrdgvvu82w8yG9kjgB5liViGSK3aK6Wxjn7FKlOFTpO27sCq5traNbGCAAAuitVsQ7TVm6ZpxWuNtgdel3r4xRw7VIw3A54tAbqJO2gE7VD1gqmW+0GFReHr4+ghS9yVHF5uUYffLDm33ZbeN2CBx7QxHPOoYAwUkbmCJAHHWf+rNc1Q7e7LJFf6OkeAyN7aKzu1CFapHN1rb5GYAQAgBwzSfX6jb6hxTpXt+hATdVGCbddqPW69ItsEssYvUdvqVUdWRtr7bbbqmL48KzdH5CqsYcfHnW9dflyLY+ZGgYkg3AakIOCCupVLXEtAf+qN+O2BYxUqwodq+1cK96tNCxr4wQAAH1XrTJXFN2W17TE1SWxbjcb1Ba3Nsnj+sgtg1Wpo7WtyyjZViPSPq7mri4N+iJzxKYtALls4MSJqt1uO619/fXwus/uuYeMJ6SM4AiQQ1arSX/Rmy4o8rqW9br9bhqjUzRZh2srus0AAJDHttdI3aRv6lfaV3frbf1BL+slLY677Wo16zf6r1sma6Qr4mpd6GpVmfT9BYNBPfXUU7rmmmu6/e6UBQu0a3W1vjFwoL5CvRHkSfZIZHBk+ezZalmxQhX19Z6OC/klELR3RvTbwoULNWbMGHd5wYIFGj16tNdDQh4VV31MH7p5xw/qPbX1Unjt/7d3J/BRVXf/x7/Z9xAEguwBQgBZFGRRUZYKuP1tgbq1Upei8ldqXSt96NNH26oFl9aldUGFiv23oCz6t6jVIpuKsiqyL7KFLewJ2bfndU4yY/ZMkpnMJPfzfr3u6965uTP3YKfJvd97zu+4nhbdqYHqK7q5AgDQXG0o7U1iepFWVZukrEiFaoJ6256ko9VNITWMnl+/fr1uueUWbd68udY29OnTR3PmzNHAgQPr9W8AGkN+RoY+ufhiFWZnu/f1fuQRJU+e7Nd2oWndfxOOeAnhCOrKdJ81gYi54EmrZQreIMle6JgnQ+PUSxF0+gIAwDGylKcF2mqLsi/T3lqPb684+yDFBCUVh9t+8sknGj9+vDIza772KCsmJkaLFi3SmDFj6tV+oDFs+NWvlLpwoft1TLduGvXxxwoKMlfSaG5SCUcCF+EIPHFUZ/X/tNGGIhs9GDbTWS10uy7Q7RqgLo1UoR4AAASuXTqhv+lru5ipf2tjht2YkOQn6qcD67dr+PDhdQpGygYkK1asoAcJAtaJNWv0xU03lds3bN48nTNokN/aBN8hHAlghCOoTqby7HAZU2DNDJ8ptCXVqheuENs7xBRZu7yWbrEAAMCZClVkrytMbxJznZGvohqPDykOUnS/15WxObXe5+zbt682btzIk3gEJHNbu3T0aGXu/b53VafrrtMFM2b4tV1oOvff3HUBPqoj8oF2aKIWqK2e1k+1QB9oZ43ByFB10Eu6Rof1kObpeo1VMsEIAACokrlGuFopmq8bdVAP6XldqYFqV+3xhcu+a1AwYmzatEnLmSIVAcqEdp0qTOt76IMPVHD2rN/ahKaFOy/Ai9PvfqH9+oUWq72e1TX6h515JlP51b6nk+I1TZdpm36hL3Wn7tZgnaPoRm03AABo2tooRr/URVqnyfpWd+tXukTtFFv+oJfWeuVcL730klc+B/CFThMmKKh0GmqjMCtLBxcv9mub0HRQ1RFoYCCySWmaq022sOpena71PTEK0491nm7V+RqpJAWTUQIAAC8xM9k9pbF6UpdrifboTX2thelfK3fRVq98/sKFC5Wenq74+HivfB7gTZGJiUocOVJHlyxx7zvwzjvqcuONfm0XmgbCEaAetihN87RZb2uztul4rccHK0hj1E0/VT87zV6sIhqlnQAAwJlCFaIrlGyX1andNbTwCa98bmFhoQ4ePEg4goDV+frry4UjpzZsUMbOnYrr0cOv7ULgIxwBPLRNx2wYYpbNOubRe0wdEROI3Gif41To3goAANAYzlY/xLc+MjJqnyUH8BfTcySidWvlHv/+Aeb+d95Rn2nT/NouBD7CEaCWQGSBttpAxJOpd40UtdLN6mdDkWS18nkbAQAAahIb690HNHPjtquVktVd53j1cwFvCA4LU8cJE7R75kz3vtRFi9T74YcVHB7u17YhsBGOABVqiGzQYS3UVrts9WDIjNFR8bpBfWwgYirFB4kp7gAAQGAwU1yGhITYITENFhqsP3fYoj9rt/qrrcarlx0y3E9tuf5BQA2tKRuO5J08qSOffqr2V17p13YhsBGOwPEKVaQvdMCGIYu0Vft0xqP3dVCcrlcfG4qY4TMUVgUAAIHI1AcZP3685s+f3/APG99Lii+pnWZ61Zrld1qubmppQxITllykjlwXwa9iu3XTOYMG6eTa72dpOvD224QjqBHhCBwpW/n6VHv0nrbpPW1XmjI9ep+ZFs8ViFzMH34AANBE3HPPPd4JR+4ZXOXu73RKz+gLu5yrWI1TLxuUjFCSIrjlgJ96j5QNR9JWrlT24cOKatfOr+1C4AoqLi4u9ncjmoPU1FR16tTJbh84cMB2X0RgOaIM/Us79L526D/6TlnyrDhZe8XZP+4mELlUnQlEAABAk2Mu+fv166fNmzfX+zO69k3R2I3PaGHQVh1TlkfviVW4rlB3Xaueulo91EYx9T4/UBcFWVn65OKLVXD2rHtfzwcfVMqUKX5tFwL3/ptwxEsIRwKzfojp6vm+tuv/a7vW6JDH703WOe6uoUMYMgMAAJqB9evXa/jw4crM9KzHbFkxMTFasWKFBg4cWO8hyaYiycXqpP+jFF2rFPVRInVK4FPfTJum/fPmuV9HtGmjUZ98orC4OL+2Cw1HOBLACEcCw1nl2uEyH2qXFmuHDijd4/eer7algUhv9eWPNQAAaIbmv/CCfnb//cqpwy2ACUYWLVqkMWPGVPkw6msdcQclm3XM48/tqgQblFylHhqpJEUpzOP3Ap449c03+mzChHL7kiZOVL/f/c5vbYJ3EI4EMMIR/zB/kLfomD7UThuIrNQ+5avIo/cGK0jD1Ek/VE8biDAdHQAAaO5W3XqrvlqyRH9OS9P+/NqHGPft21dvvvmm7THiiR06rkXapne1TV8pVZ7eaEQqVCPURVcq2YYlKWrFgyp4xVeTJilt2bLvdwQF6dJ33lHLAQP82Sw0EOFIACMcaTxnlFPaO2SnPtKuOvUOiVO4/aNrAhHzh7eVon3aVgAAgEBxeuNGrRw/3m6bW4BNOTla0ratPv3663LHmWl/J0yYYIu4jhgxQkFB9QspjuqsPtBOO8T5Y+1Wpof13owkJZQGJcn6gboqViUz5AB1lZWaqqVXXKGinBz3vvhevXTZu+8qOIzeSk1VKuFI4CIc8Z08FehLpdoiqmZZrYMq9Pg5RMkfVxOGmLGtw9VF4VRMBwAADrR68mQd/c9/3K8jWrdW//nz1a5z53LH7d69W926dfPquXOUr2Xaawvjm7CkLg+3whRsa5WMVjddrq4arA4KU4hX24fmbdfMmdo6Y0a5fb2nTlXyXXf5rU1oGMKRAEY44t2hMpuU5g5DlmtvnZ40hCrYzipjnjSYqugU+wIAAE6Xvn27ll99daWbwxbjxysxMbHc/rS0NLVp08bnRfPNLIKmF/AqHajTgy/TE9jUKDFhiVl6qw3XeqhRUX6+Vo4bp/Rt29z7giMjNerf/1Y0921NUqoP7r95hA6/M38gd+qEfZpgFjNk5qjqVkW9k+LtMBlX18t4RfqsvQAAAE3NrpdfLvc6rEULJf30pzqVnd3obTFBxvk61y6/0XCdUraW6DtbP86EJYeUUeP7M5RX2gNlh33dTrG6XN00Skk2NOmqloQlKMcMn+n/xBP67LrrzJgyu88Ms/n20Uc15PXX6z10DM0L4Qj8EobsKBOGmJ4hh/X9/OOeCFeILrO9Q3rY8ajn8cQAAACgShm7d+vg4sXl9nW97TaFxsZKfghHKmqpKF2nPnYx14nf6qgNSczymfbXWmzfXEf+XRvtYnRUvC3uaoKSEUpSss7hOhFqecEFdqaavW+95d5nCrUe/vBDta/QqwrOxLAaL2FYTfUKVaTNStPnOqAV2mcDkSN1DEOMC3SuxpR2nzTDZqIV7pP2AgAANBcFmZn2aXnGjpJeFkZITIxGr1ih8IQEHTt2rNGH1dRFhnLt9aMZam16l3yrtDp/RnvFucMScw3ZS60VrGCftBeBLT8jQ0vHjlVu2vffo4g2bTTq448VFh/v17ahbhhWgyYhS3m2aKoJQ0zab8aRnlFunT+ni1pojLrbMMQMlWmjGJ+0FwAAoDkyz0C/njq1XDBidJ040QYjTUGcInSNUuxiHFGGHYLtqk3nSWFXM0znn9pkF6OlInWJOmmYOmuYOtkCr1Fi1hInCIuLU9//+R+t+8Uv3Ptyjx3T1meeUf/f/96vbYP/EY6gwVJ1Rl/ZMGS/DUTW67AKaun+WBUzXtTV/dEEIt0YLwoAAFBvu1591Q4ZKCuuRw/1mDLF/drUWmjdunW5YwK5/sK5itNP1d8uZgjOLp3UJ9pdOlR7n9I8qFt3SjlarJ12cc2GM1Dt3GGJmRmnneIa4V8Df2h35ZVKHDVKaUuXuvft+8c/1HHcOJ0zcKBf2wb/YliNlzhlWM1Z5WqtDtkw5Cul2nVtRbNq6uJowhDXwnhQAAAA70hbvlxfTZrkLj5pmGEDly1apJikJDVHJizZpuO2np0rLKnPUG5Xsf+h6qgh6qCh6qAL1V4xDOluNrJSU7XsyitVWKbmTlzPnhr+3nu2eCsCH8Nq0KjyVKDNOqZ1ZcIQ87qoDlOtlZWkBJvGu8KQ7oQhAAAAXpe5d6/W339/uWBEQUEa+NxzzTYYMcx1pZnW1yz/V4MrzYhohnt7MgzHMMcd0BbN1xb7OkRB6qtEG5iYsGSQ2tsJAUIV4uN/FXzBTN/b8777tGX6dPe+jO3b9d2sWUqePNmvbYP/0HPES5p6zxFXEGJ6hZgwZJ0O2/nn81RYr88zf0BMAVXTPdEUvjKhSHtR5AgAAMDnBVh//GNl7CwZMuLS6+GH1ePuu+V0phKeGQr+WelwcHO9W98Hf5EK1flqa3uVXKh2dmhOHyUqjMCkSSjKz9fK8eOVvnWre19wZKRGffSRokvv6+Cs+2/CEYeGI3t0yhax8kYQYrRQhO12WBKEdLaJeqwivNpmAAAAVM9c1q+7995KdUbaXXWVLnzxxYCuJeIv6cpx184zgYnZPqu8en9ehELUvzQwMQ8KTXjST20ZkhOgTn3zjQ0Ty/ayajlggIbOnm2LtyJwMawGXvNv7dLdKj/fvadCFWx/6ZsAxNW1MEWtmBINAADAj3a98krlAqwpKbpgxgyCkWrEK9LOjmgWo1BFtm6Jq7aeWZvpgz3tXZKrQq3RIbu4mP/yprbe+aVhiWvdSS0YYu5nLc8/X0kTJ2rvW2+5953asEFf3HyzLpo1SxEVihWjeaPniEN7jqzRQQ3Rax4da2aNMV0FTRBykTraLoNMdwYAABA4ji5bptV33FG+AGuLFiUFWLt08WvbmrpM5dnZGF2BibmO3qczDf5cM6WwqWNihuL0URv3OlGxXmk3PJOfkWGLs+YcOVJuv6nPc9GcOYru0MFvbUP1GFYTwJpaOJKjfMXpj5Wm3O1ug5CScZNmbYKQloryWzsBAABQewFWUzshP71MsdHgYA194w0lDh9e43uzs7M1a9ascvt+/vOfKyqK67+aHFemDUzMYoaom6Hqe3TaK5/dWtHlwhJT+LWXWqutYulp4iPp27bpy1tvVe7x4+X2R557ri7629/sFNgILIQjAayphSPGeM214yLLFpFKIAgBAABoMszN3KqJEysVYO39yCMezbpx7NgxJSYmltuXlpamNm3aeL2tzd1JZWmDjtigxIQm3+ioduhEvQu+VhSvCBuS9FSr0nVruzZDdiKoluCVkHHVrbcqOzW13P6whAQNnTXLDsFB4CAcCWBNMRwBAABA03VkyRJ98+tfK+/kyXL72199tQa+8IJHdUYIR3wrS3l2Rkgz+cE3OmIDE7M+o1yvnSNYQUpSgg1JKi5dlaBIhsN7LOfoUduDpGLYGBIdrcGvvKI2w4b5rW0oj4KsAAAAgMMVZGVp8xNPaP/cuZV+Ftezp86nAGvAiFa4BquDXVyKVaz9OmMDk81Ks+HJJqXZQrA5KqjzOUzPlO90yi4fa3e5n5lvgSn8aoISM3y+q10S3Os2imGoThmRbdvqkrlzbf0eU5jVpTAry+4b+NxzanfFFXX+3PT0dHszf/bsWcXGxtob+fj4eC+3Hg1FOAIAAAA0oalHNzz4oB0CUJGpj2CebodGR/ulbfCMCSO6KMEu16qne7+ZKccEHK7AxLU2Q3PqE5oYZoiACWLM8qn2VPp5tMJsrxNXYGK2u6iFDVQ6q4WdhNhpM1KGJyTYQqxr77lHx1audO8vysvT2l/8Qv0ff1xdbryx1s8xAzSWLVumv/71r3r33XdVWFjo/llISIjGjx+ve+65RyNHjiTMDBAMq/EShtUAAADAV4oKCrTr5Ze148UXVVzmJsul7ejROv/JJxXRqlWdPpdhNYGvSEU23DA9S7brhLbruHv7kDJ8eu4wBbuDErN0Urxdd1C8OijOrlspqlkGKIW5udrw8MM6/MEHlX6W9LOfqceUKYqs5v8n69ev1y233KLNmzfXep4+ffpozpw5GjhwoFfa7RSpTbnmyL59+/TCCy9o8eLFtvERERHq3r27brjhBk2ZMkXRXkq4P/zwQ82cOVNr1qyxv+zNL/bBgwfrrrvu0lVXXSVfIRwBAACAL5heIuYmrWw3/7K1EPr+9rfqdP319Xr6TDjStKUrx/Ys2aWTlZajymyUNoQrRO0UWy4wMet2itO5irWL+bmZAbOpDeExQeS3jz6qff/8Z6WfBUdGKunmm5V8112KaN3avf+TTz6xvUIyMz3/7x8TE6NFixZpzJgxXmt7c5faVMOR999/XxMnTrRjraqSkpJiQ5Pk5OR6n6OoqMgGIG+88Ua1x9xxxx169dVXFRzs/WSTcAQAAADeVJiTowMLFmjL9Om25kFFLQcM0IBnnlFMUlK9z0E40nxlKFe7S4OSnTpph+zs1Wnt0Snt0xkVqKhR22N6oZQEJd+HJmbYTqJibO2TxDLLOYpSSID0RjG3y9uefdb23KpK2ZBk8/79Gj58eJ2CkbIByYoVK+hB0pzDkQ0bNmjYsGF2DnVTfOa//uu/NGrUKPt67ty5eu2119wBydq1axUXF1ev85jPnT59ut0eMGCAHnnkEdszZffu3XrqqadsO1zHPfnkk/I2whEAAAA0lLk0P7lunVIXLNChDz5QwdmzlY4JCglRyr33KvnuuxUc2rASgoQjzmTqmxxUuvaUhiUloclp7dNpO4TngNIbPTypOANPa0XboMSszdAdsy7Zjq60z4QpZqpjXw7v+W72bBtUFhcUVBuS3H/ihHYdPVrvc/Tt21cbN26kBklzDUdMcrZy5UqFhobaJOziiy8u9/Onn37aBhnGo48+qscee6zO59ixY4cdq1VQUKBBgwbZ80RFRbl/npWVpREjRtjwxbRj69atDeqlUhXCEQAAANRX1oEDOrBokVIXLVLW/v3VHhfTpYsG/OlPannBBV45L+EIqgtPjuqsDUlcBV1LQpOS4MQEK0d01hZ8DRQmUDETF7dUpA1LzDCeknXJa/Mz19LCvY5wv47wYK4S8//TnS+9ZHt0Vaz9szE7W/99+HCD/x1Lly61RVrRzMKR1atXa+jQoXZ78uTJeuWVV6ocDmMSMhNYJCQk2F/GYWF1m4vbVPl9ubSb06pVq3TRRRdVOubLL790BzPmeFM12JsIRwAAAFAX+enpOvzRRzqwcKFOrllT6/Gdb7pJfaZNU2hMjNfaQDiC+ipQoQ1IDirDhiVl16ZQrPmZWU4q299N9UikQm1YEl9hiav0Olwt9p9S3EvvKmThEqmwpIfN9KNH9UU9htNUdP311+vtt9/2wr+oeUv1wf23T6fyNVMWudx+++1VHmPqf5hKvma4y+nTp21SNnbsWI/PYbKd9957z2736tWrymDEMPt79uyp7du32+P/8pe/0F0JAAAAPmeuV80T5/StW5W+bZt7bfbVKihIrYcNU/dJk5Q4fHhjNBfwSKhC1FEt7FKTXBXYXigmKDlcui7ZztAxZSlNmXY5pkydUo78xUyXbBaPCtl2NmnIuTr37h/qhr9+q6ELdulLLwQjxoKFC/V6+hdqHW/6voQpSqE2uDHbJevyrwOlNktz4NNw5LPPPnMXl7nwwgurPc4MeXH5/PPP6xSO7NmzR4cOHar0OdWdx4QjBw8e1N69e9W1a1ePzwMAAABUN81u/unTyj1xQnknTth17vHjdpaZM1u3KmP79iprh9QkNjlZnSZMUIcf/lBR7dr5rO2Ar5nhKp2VYJfa5KlAx0sDExOcmFDlhLLtvhPKKl2XvHYteao8tXVjOdIlTi88dYlaj2mnorF7vPKZRYWFmv7RCzpzaSedbBulopDgWgvdmv/GEQqx68gy22Zd8rpkO7x0Ma9L1pVfJypGP5czi8L6NBwxQ2UMU9/D1PqojunxUfE9ntqyZUuVn+PJeZwcjhTl5SmnAcWCAAAAauPR6O06HFPp84qLv99n1uZ1UUkXd7suKir5uWttfl5YWLIUFNibELOuuK8oN9fOFFOYnV2ynZ1dsph9pUv+mTPKPXnShiF5p0559u+oRVhCgjpce60NRVr060cvZzhOuELVXvF28USxipWpPDt0x/Q6KVlnV/n6tHJ0Rrl27Vq8FawcbxEub7r7gZVKiYxUYUiQsmLDlBUXpqzY8JLt2DBlx4YpM65knR0TpryIEBWEBasgPNiu88NKX4cFKzM8WGfCglUUHKTCkGAVB8tuFwcH2bV7OyRIRUFSx8g2+nkXwhGvysnJ0fHjx+12beN/WrZsaXuXmCmPzHihuo41cqntPK4xSUZDzlOVw14ovtOYzu7Zo+VXX+3vZgAAADhaUFiYEkeMsIFI4siRComI8HeTgCYjSEGKVYRdzEiXuspRfrnAJF25dgrk9CqWDOXpjHJ0Vnl2Ma/d27HhXi1OGxVc0lskpLBYcWfy7CJPhvt4wdGU1tKH/y0n8lk4kpGR4d42U/jWxhWOnK1jl8O6nMecw6Wu5ykbrAAAAAB1FdaypVr06qW4Xr3sOr53bzt8hkAE8I9IW7cjTG1V+/1qTc50PKNWIa+qsMIMNvURIqlVA6fobpBg5/ZY82nPEZfw8Nq7GUWU/lHIzs722Xlc56jPeQAAAABPApCIVq3sEpmYqLiePRVfGoREtm0bcENlzKw0Ppy8EnCEFvEtNH78eM2fP7/Bn3Vp27aKjYqyQ/r8ITokUk7ls3AkMvL7/6h5eaYbUM1yS//Hj4qK8tl5XOeoz3lqG4ZjhtUMGTKkTp8JAAAAHwgOLgkhXOvSxWwHhYQoKDTUroNL10Fl18HBCg4PV0hUlEIiI0sWsx0RUbIu3R8aG6vw0hDELGY7vGVL+5kAnOeee+7xSjjy2Ny5diIRU8/I1IjMP3vWFnS2S0ZGla+L8/NVVGEpzssr/9r0anHVXTJ1mFx1mcpuFxaqY1DNsw81Zz777R0XF1enISxmSI2nQ3Dqex7XOepzHm/MmxxI4nr00FWbNvm7GQAAoJnzqKeEB8e4P6fC2h1+lO4LtJ4ZAJxh5MiR6tOnjzZv3lzvz+jbt68NRszvsYjWre3S2Iod3JPMpz1HWrVqpRMnTtRazPTUqVPu4KKutT3Khha1nads7w+n1xAxT0VC69h7BgAAAABQmQk05syZo+HDh5d7KO8pUx/zzTff9HvAG+TggLnmSZMb6LzzzrPrXbt2qaCgoNrjtm3b5t7u3bt3vc5R8XO8fR4AAAAAAKozcOBALVq0qNxEIJ4wx5v3mfejmYYjl156qV2b5GzdunXVHrd8+XL39rBhw+p0jq5du6p9+/aVPqcqK1assOsOHTooKSmpTucBAAAAAKAmY8aMsfedZoiNp0NpzPHmfWjG4ci4cePc27Nnz67ymKKiItv9yEhISNCoUaPq3O3nRz/6kbtnyJdfflnlcWa/q+eIOd7J3YUAAAAAAL5heoB8++23Wrp0qa677jqFhJgJer8XGhqq66+/3v5848aN9BhxQjhiZm+57LLL7PYbb7yhVatWVTrm2Wef1datW+32fffdp7CwsHI/X7ZsWUll8aAg3XbbbVWe5/7773d/4e69995K0/Sa12a/64tojgcAAAAAwBfM/asp0vrOO+/o5MmT2rJli7766iu7NnU53377bftzHtoHDp/PNfb888/boTImoBg7dqymTZtme4eY13PnztXMmTPtcSkpKXrooYfqdQ7z3l/96leaPn261q5da883depUde/eXbt379aMGTO0YcMGe6w5rkePHl79NwIAAAAAUJX4+Hi7wOHhyIABAzRv3jxNnDhR6enpNhypKtxYvHhxuWl56+qJJ55QWlqaZs2aZYOQm266qdIxkyZN0uOPP17vcwAAAAAAgObHp8NqXK699lo7luqBBx6wQUh0dLStLzJo0CB3r47k5OQGnSM4ONgO3TEhi6kpYoq0hoeH27V5/cEHH+j111+3xwEAAAAAALgEFRcXF7tfod5SU1PVqVMnu33gwAF17NjR300CAAAAAKDZSfXB/TfdKAAAAAAAgKMRjgAAAAAAAEcjHAEAAAAAAI5GOAIAAAAAAByNcAQAAAAAADga4QgAAAAAAHA0whEAAAAAAOBohCMAAAAAAMDRCEcAAAAAAICjEY4AAAAAAABHIxwBAAAAAACORjgCAAAAAAAcjXAEAAAAAAA4GuEIAAAAAABwNMIRAAAAAADgaIQjAAAAAADA0QhHAAAAAACAoxGOAAAAAAAARyMcAQAAAAAAjkY4AgAAAAAAHC3U3w1oLgoKCtzbhw8f9mtbAAAAAABorg6Xuecuey/eEIQjXnLs2DH39pAhQ/zaFgAAAAAAnHIvnpSU1ODPYVgNAAAAAABwtKDi4uJifzeiOcjJydG3335rt9u0aaPQUDrl4PsuX67eRKtXr1a7du383SSg3vg+o7nhO43mhO8zmhu+06iOGUrjGr3Rr18/RUZGqqG4g/cS8z/G4MGD/d0MBDjzC71jx47+bgbgFXyf0dzwnUZzwvcZzQ3faVTkjaE0ZTGsBgAAAAAAOBrhCAAAAAAAcDTCEQAAAAAA4GiEIwAAAAAAwNEIRwAAAAAAgKMRjgAAAAAAAEcjHAEAAAAAAI4WVFxcXOzvRgAAAAAAAPgLPUcAAAAAAICjEY4AAAAAAABHIxwBAAAAAACORjgCAAAAAAAcjXAEAAAAAAA4GuEIAAAAAABwNMIRAAAAAADgaIQjAAAAAADA0QhHAAAAAACAoxGOAAHqww8/VFBQkHt57LHH/N0koFZ79+7Viy++qB//+Mfq0aOHoqOjFRkZqY4dO2rcuHGaO3euCgoK/N1MwNq3b58eeugh9erVSzExMTrnnHM0ePBgPf3008rKyvJ384BarV27Vr///e81duxY+3s2IiJCsbGxSklJ0e23367PPvvM300EvGLq1KnlrouXLVvm7yahGQoqLi4u9ncjAJSXmZmpPn362At3l0cffZSABAHtt7/9rZ544gnV9mfF3HzOnz9fnTt3brS2ARW9//77mjhxotLT06v8ubm5XLx4sZKTkxu9bYAnhg8frpUrV9Z63C233KLXXntN4eHhjdIuwNu+/vpre+1Q9uHK0qVLNXLkSL+2C80PPUeAAL3JNMFIYmKiv5sCeOzw4cM2GDFP4M1N5+zZs+1TS/Nk86233rIXNsaaNWs0evRonT171t9NhkNt2LBBN954ow1GzFN2E+p98cUXWrJkie688057zI4dO3TNNdcoIyPD380FqnTo0CG7bt++ve677z4bOq9evVqrVq3Sn/70J3Xo0MH+fM6cObrtttv83FqgfoqKinTXXXfZYITrYvga4QgQYNatW6cXXnjBdo01F+xAU9GqVSvNmDHDhiQmDDEX48OGDdOFF15owxJzwX7DDTfYY3fu3Gkv3gF/MDeS2dnZCg0N1ccff6xp06bp4osv1g9+8APNnDlTTz31lDsgefbZZ/3dXKBKZjjYvHnztH//fj333HN2OKMJoS+66CI98MAD9mm76QFl/POf/9SKFSv83WSgzsw1sXmoYr7vkyZN8ndz0MwRjgABpLCw0D61NGtzsU53bjQlJhh55JFHFBcXV+XPQ0JC9NJLL7m7dpunnEBjM0/WXUMRzIW2CUUqMnVIevfubbeff/555efnN3o7gdr861//soGz+d1aldatW5cL9/idi6bGBH+mN7XxyiuvMDQMPkc4AgSQP//5z7a7t3nSYwpPAc2xd0n//v3t9u7du/3dHDjQu+++6942BSurEhwcbOs0GKdPn7Zj24GmaNSoUe5tfueiqZkyZYodgnvrrbdqxIgR/m4OHIBwBAigWT5M0VXj5ZdftsNqgOYoNzfXrqt72gn4kmv2DlMbxwz5qk7ZC/HPP/+8UdoG+Or3rcHvXDQlb7/9tu0dZWYRe+aZZ/zdHDgE4QgQIO6++247deTNN99sx70DzVFaWpq2bt1qt13DFoDG5Pr+mWGLpuZIdcz49orvAZqa5cuXu7f5nYumwvTYM7WhXEN2zRAxoDEQjgAB4B//+Ic++ugjJSQkUKQSzdrTTz/tnorPVZwVaCw5OTk6fvy43e7YsWONx7Zs2dL2LjEOHDjQKO0DvD3Lx/Tp092v+Z2LpsLULzty5Igt6k4RVjQmwhHAz06ePGmryht//OMfmaYMzdZXX31lZ1Rw3Zia3lJAYyo7La+Zwrc2rnCEaafRVOuYmQLExoQJE2ocRgYEClMw+/XXX7c9+0wR1qCgIH83CQ5COAL42cMPP2yHGgwdOtTO4w40R0ePHtV1111ne42YC50333xT0dHR/m4WHNhzxMWTWQ9ctZ/MtL9AUxtO8+tf/9pum4cuppYZEOjy8vLstXBxcbF9cNi3b19/NwkOQzgCeMDczDV0+dvf/lbpc5ctW6bZs2fbImkmHTczJABN9ftc09P6a665Rqmpqfa16eZNXR34Q2RkZLmLcE+LWUZFRfm0XYA3bd68WePHj7dhtPnOv/POO/RKRZPw5JNPatu2bercubN7kgKgMXEnBviJueiePHmy3f7lL3+pCy64wN9NAnzypP5HP/qR1q1b5+4pZcYSA/4QFxfn3vZkqExmZqbHQ3CAQLBnzx6NHTtWp06dsg9e5s6dq+HDh/u7WUCtTChihpcbL774ontYI9CYqi/TDsCrMxW0a9eu3OuFCxdqx44dCgsL03nnnWcvYCrasmWLe3vTpk3uY8wQnK5duza4TXAmX3yfq2KeWpoCgEuXLrWv77jjDluQFfAX8xS9VatWOnHihLsnU3XMzaUrHOnUqVMjtRCov0OHDmn06NF2bXr4zZo1y4bTQFOpkWN69HXr1s3O3ljVdbG5Fnb59NNPbdFW49prryVMgVcQjgAeKDulo7e4umvn5+frzjvvrPX4BQsW2MUwQ3EIRxBI3+eqZkn42c9+pvfff9++vvHGG/Xqq6/6/LxAbUwYbQr+7dq1ywZ41U3na55iujAFKgKdmYVpzJgx+u6779xP3m+55RZ/Nwuo83Wx+Q7/5Cc/qfX4P/zhD+V6TBGOwBsYVgMA8DozZMz11Mc80fn73/9OTR0EhEsvvdSuTa8Q13Cv6gpaupjpJIFAdebMGV1xxRXu3qamrtOUKVP83SwAaHK4UgX85LbbbrPVuGtaXMMRDFOYyrXfvBcIVA8++KCdhs+4/PLLbTHA6p7OA41t3Lhx7m3TC6+6nk9z5syx2wkJCRo1alSjtQ+oCzP8wBS8Xr9+vX39m9/8RlOnTvV3s4A6M4Xea7suLluk1Vwju/YnJSX5te1oPghHAABe89hjj9lxw8Yll1yi9957zz0dKhAIhgwZossuu8xuv/HGG1q1alWlY5599ll3bZ777rvP1oYCAo2pz2Bmpfn888/d39XHH3/c380CgCaLR3kAAK8wY9x/97vf2e0OHTroqaeesuOAa9KzZ09uPNHonn/+eTtUJjs7287sMW3aNNs7xLw2w8Fmzpxpj0tJSdFDDz3k7+YCVTJ1GT7++GO7baZHnzRpUrmClRWFh4fb7zQAoGqEIwAAr3AVDDYOHjzoru1QExOe0B0WjW3AgAGaN2+eJk6cqPT0dBuOVGRuIhcvXlxu+l8gkJhZ78rO3NG/f/8aj+/SpYv27t3bCC0DgKaJYTUAAMBxTKHgjRs36oEHHrBBSHR0tK0vMmjQIM2YMUMbNmxQcnKyv5sJAAAaSVCxqWIDAAAAAADgUPQcAQAAAAAAjkY4AgAAAAAAHI1wBAAAAAAAOBrhCAAAAAAAcDTCEQAAAAAA4GiEIwAAAAAAwNEIRwAAAAAAgKMRjgAAAAAAAEcjHAEAAAAAAI5GOAIAAAAAAByNcAQAAAAAADga4QgAAAAAAHA0whEAAAAAAOBohCMAAAAAAMDRCEcAAAAAAICjEY4AAAAAAABHIxwBAAAAAACORjgCAAAAAAAcjXAEAAAAAAA4GuEIAAAAAABwNMIRAAAAAADgaIQjAAAAAADA0QhHAAAAAACAoxGOAAAAAAAARyMcAQAAAAAAcrL/BeYq/tSen8m4AAAAAElFTkSuQmCC",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 434,
              "width": 547
            }
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# split data points according to the classes\n",
        "x_0 = x_train[t == 0]\n",
        "x_1 = x_train[t == 1]\n",
        "\n",
        "model = FisherLinearDiscriminant()\n",
        "model.fit(x_train, t)\n",
        "\n",
        "# create a Gaussian distribution per class\n",
        "g0 = Gaussian()\n",
        "g0.ml(x_0 @ model._w)\n",
        "g1 = Gaussian()\n",
        "g1.ml(x_1 @ model._w)\n",
        "\n",
        "root = np.roots(\n",
        "    [\n",
        "        g1.var - g0.var,\n",
        "        2 * (g0.var * g1.mu - g1.var * g0.mu),\n",
        "        g1.var * g0.mu**2 - g0.var * g1.mu**2 - g1.var * g0.var * np.log(g1.var / g0.var),\n",
        "    ]\n",
        ")\n",
        "\n",
        "x = np.linspace(-5, 5, N)\n",
        "plt.plot(x, g0.pdf(x), \"springgreen\")\n",
        "plt.plot(x, g1.pdf(x), \"firebrick\")\n",
        "plt.plot(root[0], g0.pdf(root[0]), \"ko\")\n",
        "plt.plot(root[1], g0.pdf(root[1]), \"ko\")\n",
        "plt.plot(np.zeros(x.size) + root[1], np.linspace(0, 1, N), \"k--\")\n",
        "plt.title(\"Intersection point of Gaussian curves\")\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "0959caba",
      "metadata": {},
      "source": [
        "The figures below compares the optimal threshold against the naive zero threshold. Note that the selection of the decision threshold is crucial for an effective model."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "id": "da186854",
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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pMYLBoMa/MEldqUuWbwz+lLqx3V/l1j8md9FJcmvvlZq/8m1oJ/iNnIo/yam6rLWrl3UJa1epVDJCTvcbpLJ9JSdFy0gCAICsQycvAHnDKpaeufGlpCqfTKAooKF7b9Fuy/fP3v1Sk16frEW/LFZjQ5NKu5VqpdVW0NB9ttRamwywldKQYnT1at+Ypyf4NM77GjRsfeUMbxnFrtAg1d/v75BujeQUSCVD5ZQM9RLK1DhRrrvY2opZ/0I5gQFS8WDJKfL32AAAAAAAdIFVB66i1Tforx+/nJn0WNsdOGT5v3Slbz/5QRNemqR5MxaoobZBJaXF6tG3hwaP3EyDhg3MrY7myCrjnnnfl3HGPjtBI47eXgUFBWlI9Jrl/el7nNYKN1OuRWp4xd9fpVo8zxRtIKdoA6nlV2/5Rje0wNqTSU6ZnMK+UvG2UoF/nQwBAEDuIMkLQN4oLi3SkL230ujHxiY1zha7baJu3X+/wWqsb9Lbj4zVuGc/0KJ5llyxtB8+na4JL03Uymv31Y6HDtPQvbeUU0C2VyqR6LW06gXV+mbS976M9cV7X6u+uj6HljjI5uSnZQJzhatK5auSSwoAAAAAyCnbHzRUD/3rqaTG6L/uylojost/KBTS+Ocn6p3H39OcaT8vv8OUn/TJW5+p50o9NOyAIdrp8GFebBHoSh+9+akv4yycu0jTPv+ptQg5V+K0TrHk1qtr+LFWY0fxvF5S2V7E8wAAQMwoQQGQV3Y4dBsVlxYnvH8gENAuf9y+7evF86t140l36uW73mg3wSvS7O/m6pHLntb9FzymYJOfN4ZoD8s3aqnr1DeuqyW//lZxlgsKKqK0Rc9wBZXpngEAAAAAAF3Snb/PKsklh+x27E5tHfabGpp1z7mP6LErn20/wSvCwp8X6aU7RunfJ9+l6lyKhyDjWSLikgX+xfQWz/MxPpgJyzcW9FD2xiIBAAASR5IXgLzSZ+VeOuHqI+Qk2Jr6yH/+wevIZWqX1HkBnhlTW1tOx1OBde95j3o36sjSIEKWaW5s9ne8Bn/HSytbxrBosLJPhRRYK92TAAAAAAAg5YpKinTKjceoPMGu4rses6M232Uj73moJaS7z3lYn46eEtcY07+YoX//+W411DQkNAcgXs2N/hYJNzU0KZcKcp3iocpKRRunewYAACDLkeQFIO9suM16+tO1R8XV0cs6eB176WHactdN2v7u/vMf088/zktoDp+9+4Ve/c9bCe2L5BK98jHZq7Rbqb/jVfg7Xro5pbsp65Tu2NqWHgAAAACAPNB3jRV1+p1/Uo8Vuse13+4n7KJ9/zyy7esXb3tdX46fmtAc5nw/Vw9c/ERC+wLxKiktTrhQuT1lGRLP860gt2SX7OvOH9hYKmz9+QEAABJFkheAvLTR9uvr7w/+RVvtvpmXwNURu5HebOeN9Lf7TtGWIzdt+/ufvpqpr97/Jqk5jH78PTXWNSY1BuKvFjP5lujVq18PBYo7vs7jUVxWrB59cmyZwKKNpIKVlU2c0t8D1AAAAAAA5IP+6/bTOQ+dph0O2bbThJV1t1xLp9x0rPb604i2ZRrrqxv07lPjk5rD52O+1Ozv5yY1BhATR+q7+gq+DbeSj2NlREFuYS+peGtlE+J5AADAD/78xhcAslC/NVfSMf86VAeesZcmvDhJX0/6TrWL6yXXVXlVmdbedA1ts/9g9Viharl9xzz9ftLHb6ht0MRRkzXsgOy6Gc12FkSYE5zlBRAG9O+tfFBSXqItdt1EH7z8UdJjbb3H5gqUFCmnOI6cbifJrb5UUosyXsnOUmG/dM8CAAAAAIAuV9W7UgeftY/2OXWkJr3+qT57d4pqFtaquSnoLefYf71VNGz/wV7nr2V98MpHvixZZ3HBQ8/ZL+lxgM5ss99gPXPjS0mPs8bGA9p9T2RColcycVqn/Ai5TZ9JqlHGC6wrFW+V7lkAAIAcQJIXgLxX2atCux6zg/eIRUNNgya9PtmXY4995n2SvNKY6JVPtj94qC9JXtsdNEQ5qXhjORV/lltzqyRXGSswyEtIAwAAAAAgn5WUFWvb/bbyHvHE4fzw4Ssfa/+/7uHNAUilrffaXC/e9pqXxJiM4QcNVU7GaQv7yqk6T+6Sf1nUXhmroK+cin9ITpYtLwkAADISyzUCQJxmfjtXzY3N/oz1zWwFk7xJB2IxYIP+WmPj1ZMaw5Y6WGWdHO4gVbKjnIpzJZV1zfECvy8BG5OioXKqLpCcHOukBgAAAABAillH/bnTf/FlrMb6Rs354WdfxgKi6VZVrq333DKpMbr3qdJmOw9SzioaKKf75ZLTp2uOFxhoB419+8K15FRdLhV2T+WsAABAHiHJCwDiVFdd5/N49b6OB7TLcXTMpYeqoldFQrv3WLG7jvrnH5TzSraS0/M/csqPkwpWTumhnNId5XS/WirePnpz1cBGcir+LqfyLMmhShgAAAAAgHjVLfG3y0/dEuJ56Br7n7GH+q+bWIyqqDigE68+QoHiHF/UJ7CGnJ63yak4XQqsl+JjbSCnx7+l0r0llXe8XeEAOd1OltP9CqmwZ2rnBAAA8kqO/8sOAPxXUOBvfmxBIfm26Bp9Vuml0249Qbf99V4tmV8d8349Vuqhv9x8nHqu1EN5oaCbVLaXnNI9peBUKTRXCtVZVpbcljlSw7M+HKSbVDxYckrkVJ4hhY6TGt9tHd+1Y5XIKegllWwrFfb34XgAAAAAAOSvgkLH5/GI56FrlJaX6NSbj9Ntf73PWxUiVsWlxV6CV7Kd/bOGdb4vGS6nZLgU/FFqmS6Far2/d91mqe4efw5TumPrMpHdjpXKDpOaxstt+UEK1bTOwamSYzG/wLpe0S0AAIDfSPICgDhV9Ojm21iO46i8souWhgMk9V+3n86+/1Q9ee0L+nzsVMl1O9zWKXC08fAN9Yez9/E6eeUdC8QUrS9p/d//ym2W2/i25C5KbuzSnbxErjYFVVLZ3iL0AwAAAACA/8qronTcSUBFD3/HA6Kp6l2pM+8+Wc/e+LI+eOVjBZuDUbdfa9MB+sNZ+6r/eqntUp+xAqu3Pn5j8Ta36X0pOCXJcQdJhav8/nVBqRfjc7RTcuMCAADEgSQvAIhT//X6qbJnhaoX1iQ91nqD16byD12uV7+eOvmGYzR/1q8a9+wHXnBoyfwlbd+3hK4he22hYQcMVs++tBNfvipwV6nhySQGKZBTOtLHSQEAAAAAgGiKS4u09mZr6LtPpiU9Vvc+VVp5rb6+zAuIp6PX4ecfqH1OHan3X5yk9174UL/8NL/t+2UVZdpixCba7qAhXpEnluaU7i63JrkkL6/rPwAAQJqR5AUAcQoUBbTNflvp9ftHJz3W8IO38WVOQKLLN+532u7ewyoAm+qbVVJerMJAYbqnltGc8gPkBj9rXcoxof2PkQoJtgEAAAAA0JW2P2ioL0leww7YmqJNpHWViV2OGu49Qi0hNdQ2ekmMgWJ+3RdV8RCpZEepMcGYfsnOki3DCAAAkGbciQBAAobtP8RbajEZPVfqoUHDBvo2J8Rv+swF6Z5CRiUvlleVkeAVC6dYTuW5UuGa8e9berBUtlcqZgUAAAAAAKLYZMcNVdmrIqkxCgoLte3+W/s2JyAZlmxo8TwSvGLgOHK6nSwVDY1/36Khcrr9yRsDAAAg3UjyAoAE9OrXQ8P/kFwXrn1P3Z2qvzTqF1jF+5NELySkoEpO1aVS8fAY/zlVKafbX+R0O6wLJgcAAAAAANorcLN4XDJ2PnyYuvep9G1OANQWo015nNYpklP5t9YiTJXEsEOJt61TeZbkkEgHAAAyA9kFAJCgA8/cSxttt35C++5x4ghttfumvs8J8SHRC0kpKJNTebqcHne1BoecHstvExgop+JMOb3ukUp3SscsAQAAAADAb4bus6V2PXrHhPbdbKeNtM9fRvo+JyDfWYy2y+K0ToFXhOn0vEdO+fFSwcrLb1Owivc9p+e9rQWbdPACAAAZhNRzAEiQdeE64eoj9OgVz+qDlz+KaR9Hjg44cy/tdPiwlM8Psfk9gDDL+3NA/95pnhGyTmHv1oBP+aFS6FfJrfEqA+VUSQXJLQORFm6z/VBe0AsAAAAAgFyz76kjVVZZqhdufS3mfbbdb7AOPXd/FRRwrwykMk47JzjLS/RKeYy2oJtUtqec0j2k0GJJ1b99o1Iq6J59iV1ePK9AcgrTPRMAAJBiJHkBQJJt3o+66A8avPvmGvPUeH327pdyXXe57YpLizV49828JR5XXrtvWuaKDAoiIDdZ8KfQrp0su35CDVLTWLmNb0rBHyU1//bzdJeKh8gp3U0KDEj3LAEAAAAA8Icj7Xr0Dtpg6Lp654nxmvT6ZDU3Ni+/WUGBNt1hQ21/8FCtu+VaaZkqkG+6vCDXi+dZd/52OvRnMrdFapokt+F1KThVUsNv3+gmFW0sp3SkVDQo+5LVAABAp0jyAoBkOdLAwWt7j4U/L9JHb36uxb8sVlNDk0q7lWiFVftoy103UWlFabpnik6Q6IW84jbLrXtcsmCQ6tr5/mKp8XW5ja+3LjtZfqxUtE46ZgoAAAAAgO/6r7uyjrjwIB1w+p766M1PNX/mAjXUNnrFmj1W6q4tRmysHit2T/c0gbxEnLYDVmBu8bq6ZyS3vaUta6XmCXKbJ0gF/eWUHy6VDEnDRAEAQKqQ5AUAPuq5Ug/tcsR26Z4GksDyjcgLoXq51VdJwc9j2z44Ve6SC+RU/J9UsnWqZwcAAAAAQJcpryrTdgeSBAFkGhK9luGG5Nb+R2p8I7btQzPl1lwjp+VIqXz/VM8OAAB0ERaQBwAgarJXexVRQBZzg3Krr4k9watNs9ya66WmePcDAAAAAAAAEovR2sNitPkep3XrHog9wStyv/qHpPrXUjInAADQ9UjyAgAghkSvfA8iIIfUPysFP01wZ0sQu1YKtbO8IwAAAAAAAJACeV+Q2/iB1PBywru7dfdIwem+TgkAAKQHSV4AAMRQLZbXQQTkDrdZbkOylXs1UuM7Pk0IAAAAAAAA6Fw+F+S6DS8lO4Lchld9mg0AAEgnkrwAAIgBiV7ICU3vS+7ipIdxG0ZJruvLlAAAAAAAAIBY5GVBbvAnKfhl8uM0jpFCtX7MCAAApFEgnQcHAMSnqaFZk16frI/e/FSL51WrubFZpd1K1HeNFTV0n600cKu1JSfds8xdvwcQZnl/DujfO80zAuLjNrzpz0ChmVJwqlS0fozbL5GaP239U0HJqZQCa0mB1f2ZDwAAAAAAGSrUEtKUcVP1/suTNH/mr2qoa1RJebF69+2pwXtsro132ECBIn5VA8Qbp50TnOUleuV6jNZt/J9PIzVJTWOk0t1j2zzU0BrPc3+V3CbJKZcKV5EC60sOv4QAACBdsvbOYdKkSXr11Vc1btw4ffnll5o3b56Kioq08sora9ttt9Xxxx+vYcOGpXuaAOCL2sV1GnXv25rw0iTV19Qv9/2Z38z2kr9WWn0F7XjoMA07YGs5BdxopUo+BRHwe0B2wexfVbekXgWFBaroUa6eK/XIvoBGy0x/x4qW5GWdvoJft3b9ahrfmty1rMB6ckpHSsXbSE6Rf3MDAABARiKeByCfBJuCevvRcRrz9AQt/HnRct+f/d1cfT7uK1X1rtSwA4ZoxFHDVVzKvTHgW0Gu6+rXuYtUs6hWbshVt+7l6tWvpxfby7pOXj5xW2Z2XiPeMlNuwxtSw9uS6pb/fsHKrfG8kh2lgm6+zQ0AAMTGcd3sW2tn++2319ixYzvd7qijjtLdd9+t4uJi3+cwc+ZMrbrqqt7z0WM/Ut9+K/t+DAAw82bM121/vV/zZs6PeZ/NdtlYx/zzEAWKszaXNytYopch0St3WRD2vWc/1LjnP1D1gpqlvrfSgBW1/UFDNWSvzVRaUaZs4C44RFKzL2M55UdLZft2cKBGudU3S80TYhusYCU5VedJha3/tgIAAEubM2uOtl1vG+/5jBkz1L9//3RPCcjKeJ4hpgegK1iR2H/O/q++/fiHmPdZfYP+OuXGY1XZqyKlcwNyPU5r778PXv5IY56ZoF9+XDqmXtWnStvuN1jDDhisHit2VzZwF/9dCn7nz2DFw+VUnt7BgVy5dY9IDc/GOFg3OZV/k4o39WduAADkmDkpiudl5W//Z8+e7f1pVX4HH3ywtttuO6222mpqaWnRhAkTdP3112vWrFn673//q+bmZj366KPpnjIAJGTRL4v175Pv1sJflq/2i+aTtz5TKNiiE64+QgUFWVaZlEVYvjF32VKoT1z9vN5/+SOv0q89P0//RU9d94JeuPU17XbcThp57A5Z0NmrxLckL6mDX7qFGuRW/6t1OcdYhX6Wu+g8Od3/KQXW9Gl+AAAAyCTE8wDki6aGZt1++n2aNiW+7js/fjlTN596t/529ykqrShN2fyAnF15oWmmHrnlNU184j01N7Qf/1oyf4leu+ctjbr/bQ3de0sdcvY+CpQUZUE8zydOcccJXrW3So2j4xisVm71ZXIq/iaVDPVrhgAAoBNZ+Zv/gQMH6oknntBPP/2km266SQceeKC22morDRkyRGeeeaYmT56sdddd19v2scce05gxY9I9ZQCInyvd/feH4k7wCvv0nS+8JR7RlcleC9I9FfigoaZe//7zPZrw4qQOE7wiNTU06aXbR+nhfz0d0/ZpVdjDv7EKerQfEKq5Kb4Erza1cpdcJrXwPgIAAMhFxPMA5Isnr30h7gSvyCUcH/rX077PCch1oVBIr182TqOveV+NRYUKVUZPlHRbQhr//Ie65S/3qqG2URmtoJd/Yzk92/1rt+7xOBO8wkJya26Umr9OemoAACCHO3m9/PLLUb/fp08fr/pv77339r5++umnvZbwAJBNvp70naZ/MSOpMUY//p5GHDVcRRlfjZQj1WK/tQVHYqp/rfESq376aoZqlzSoMFCgip7dNGjb9bXpThsqUJT6f7YEm4P6z98f1rRPp8e974SXJqmsqkwHnrmXMpVTvK3c+id8GKlMKmqnFXvzZKn5w8SHdRfJrX9STsUpSc0OAAAAmYd4HoB8sGjeEn3wysdJjTF59Of65af5WnG1Pr7NC0iVxrpGTXr9U3098TvVLqnzCgDLu5dr7U3X1NZ7bqbSbl3Tle6Z61/WxNc+8Z43fycVrR3bft99Mk33nPuwTrnxGBUGCpWJnOJt5DaN9Weskm2X/8uW+VLDM0mMGpRbd5+c7lcnMzUAAJDLSV6x2HHHHduef//992mdCwAkYsxT7yc9Rt2SOn30xqcasveWvswJSIUZU2fpfw+P0cdvfa6WYMty35/46ieq6FWhYfsN1o6HbauKnhUpm8vYp97X1x9+l/D+bz8yVpvuOEhrbTpAGalkhFT/lFdll5TSHaWCsuX+2m0YpaQ1jpHKj5YKypMfCwAAAFmFeB6AbGedgUIty8c24jX26fd14P9lbhEZsGD2Qi8O9v4rH6mhtmG573/85md6/pZXNXj3zbXzEdulNGnxm0nf650n30t4/68mfKP3nvtQ2x+coUsOFm8pOb0lN8nu94ENpcCqy/212/Bm8rHC4LdS8HspsFZy4wAAgNxcrjEWjY2/t1ctLMzM7HsA6Mji+dX69N0vfBlr7LMf+DIOkAoTXpioq4++VRNHTW43wSus5tcajbrvbV155C2a8/3PKZmLLbX47lMTkh7HjzFSprCXVDwk6WGc0t2W/8uWeVLzpKTHlhoTbA8PAACAbEc8D0A2s7iCJYr4wbqFB5uCvowF+O3bj37QlX+8yUusai/BK6ypoUnjnntfV/7x3/pifOqW83v3SR/ieU+O97qQZSSnUE7prqmJ57nNUqMleSXPl+JPAACQv0le7777btvz9ddfP61zAYB4zfxmttxQktUzv/nxy5lSht6fIr9Z4PPhS5+W2xL7tb5o7iLdcOIdmjt9nu/zmfrhd5o3Y37S40z+3+dasqBamcopP0JSZRIjdJOaPpZCy/yMTRbI9ufDxm1KvpMhAAAAsg/xPADZbPH8JVo0b7EvY9XX1GvezCS79gAp8N0n03Xrafeqvqbj5K72kr3uOPMBfZmCRK9Fvyz2pVh67rRf9O1H05SxSveSCldPYoCA3OC01iLNSMFvJHeRfNFIsTkAAF0hJ5O8QqGQrrrqqrav//CHP8Q9xsyZM6M+5syZ4/OsAeB39UvqfRvLksUa6mK/6Qa6wveTp+mxq55LaN+6JfW644z71Vjf5OucPnjlI1/GsY5kH73+qTJWYV85VRdIWn65xdjUyq17UO7CE+TW3tda8ed91vgTyPaEfAouAQAAIK/ieYaYHoB0qauu93c8H+ODgF8JVXf97QEFm4MJxajvOfcRXwosI00aNdm3YmlbejJjFZTJqbxAKlgpwQGCUsNzchedLHfJtVJoSQpicDWSSwdCAABSLaAcdOONN+rDD1vbIh9wwAHaYost4h5j1VWXX5caALpKQcDfZSkCRTn5cY8sNuq+0XF18FrW/JkLNPHVTzTswK19m9OCOQszcqyUKFpHTvcr5VZfKYUSXf6yWWp4WW5wupzKf1hdpo8TbE0cAwAAQP7wI55niOkBSJdCn+N5hUUsW4vM8s7j45NKZmysb9T/HhmnQ8/dz7c5zfcxBvdrpsfzCnvLqbpKbs3VUnBqgoO4UvMEuYuny6m62P8YnBWDOvwuAgCAVCrIxbbu5557rvd8xRVX1B133JHuKQFA3Cp7dvNtrOLSYgWKubFC5rAELT/as495eoLk+rcWaWNdo39j+dxlLCUCq8npcYucirOlwKDExwlOkVt9naRy/+bm+PcZCAAAgMxHPA9ALqjwMZ7njdeDe2NkjmBTUONfnJj0OB+++rEaav1bdaLJxxicJaFlvMLucqoul1P5L6l4m8R/zRuaI3fJv+TKz2TSAskp9XE8AADQnpz6rf8XX3yh/fffX8FgUKWlpXrqqae8wFAiZsyYEfX71tp98ODBCc4UAKIbMGhVlVeW+dLmfcNhA32ZE2IzfeYCDejfO93TyGjjnvnAl3FmfTtH33/6o9badIAv45WWl/gyTutYxcoKVllXMlROoL/cRacnPk7wE6mwl3/zKvTnNQUAAEB+xfMMMT0A6dKtqlxrDFpN06b8lPRYKw1YUX1W9vE+G0jSx299rtrFtb4kUn346mRtf/AQX+ZV4mMMrqQ8SxKUHEcqHiQnsLbcpk8lJfi6hGZLDRP8m1fhaq1zAwAAKZUzSV7Tpk3TrrvuqoULF6qwsFCPP/64tt9++4TH69+/v6/zA4B4FJUUaeg+W+l/j4xJeqzhBw/1ZU7oXL/AKpoTnEWiVye+mzzNv7E+meZbklfvVXrp+8nTfRmrV7+eyiZuw6jkB2n6XHJ6Sm7yre2d0hHJzwcAAAB5F88zxPQApNN2Bw/1Jclr+4OGSuRKIIN872c8b/I035K8evfrOBkyVFmqgurYu4b17ttDWaVpbOIJXmHBSa0d/oNTkp6OU7pb0mMAAIA8Wa5x9uzZ2mWXXbw/HcfRfffdp3333Tfd0wKApGx34NZJj9Fvzb5aZ7M1fZkPYk/0MpbohfbVLK7zbaw6H8faes8tfBmnMFCoLXfbVFkjVC81jE5+HPcXqWgjf7p4BdZLfhwAAABkNOJ5AHLRFrtsrG7dk1tmsbi0WEP23Ny3OQF+qF3iYzzPx7G2HLmpnILlf9XZ/F3rwxK97BGLIXtvqazhunIbXvNhoKBU4EexcqlUnFyiPgAAyJMkr/nz52vEiBH64YcfvK9vueUWHXXUUemeFoA0am5s1pRxU/Xe8xP1zpPj9cGrH+unr2ZKrrLKCqv20fCDt0l4fwuS73/6HlT9pTnRi2Sv5fnZtbu9IE6iBm61llZcvU/S42y+y0aq7FWhrNH8vqTYqxqjcm2J2eRa2ztl+9DaHQAAIMcRzwOwrFAopG8mfa8JL07SO0+M1/svTdK3H/3g/X02CRQHtO+pI5MaY48Td1FpRZYsG4f84WOsxuLWfumxQpU23XHDDr9viV6ms0Svfmv11dqb+bNaQJdomd768EPzN1LBysmNYV28Csr8mQ8AAMjd5RoXL16s3XbbTV9++aX39VVXXaVTTz013dMCkCbzZszXmKff94JAddWWaLC0VddbRdsdNFRb7raJSsqKlQ0O+tve+nXuQn0+9qu49/3D2ftpw23ohpPuRC+Wb1xea0XrfF/GKq/yMXjgOBp+8LZ66roXkhpmm/0GK5u4wbn+DRZaIKfyLLnVV9gX8e9fsptUPNy/+QAAACDjEM8DEKn61xqNf2GSxj47QQvnLlru+7379dSwA4dom322VEXP7Cio2nb/wZo/61e98WD8XbO3O2CIRhzJfTEyT0VVuW9jdevu31hmhz9sq0/+93nURK+itX9P9GpvCcche2+RXUWHLT7G89yfpaobpcXn2xoM8e8fGCSn/HD/5gMAAHKzk1ddXZ323HNPffzxx97X559/vs4555x0TwtAGrghVy/cNkr/POA6vf3o2HYTvMyMr2fp0cuf1sX7Xq3vP/WpyiXFCgoLdOI1R2ro3lvFvE8gENDR/zxU2x88JKVzQ2xYvnF56225ln9jDV5bftruoK21/tB1kxrj7nMe1nM3vaL5WfOat/+ZmRC3TireXE7F3+KvJSjZRU63E7IroAYAAIC4EM8DEMkKNS/c+0q9ePtr7SZ4mQVzFuqFW1/TBXtfpYmvTVa2sG5e+5+2h5w4WuyPPHYnHXru/nTlR0Za18d4np9jmbU3X0M7HbZd1G3Cyzd21NXrpdtH6aF/PqUfv5ihrOB10/dLSE7hinK6Xyg53eNP8Ko8V3KKfJwPAADIuSSvpqYm7b///nrvvfe8r08//XRddtll6Z4WgDQleD106VN644HRcmNcj7F6YY1uPuVufTn+a2WDwkChjrjoIJ1518naYsQmKigs7LA70oijdtBFz5ylwXts1uXzRPREL3uwfGOrYQcMllOQfMRy9Q37a/UN+svv99sJV/1Ra2+2RsJj1C2u01sPj9ElB16nd5+coMxX4t9Qzm9BspKhcqoulwIbdb5PwUpyup0sFe8gt+E1ubVPyK1/Ta61inezbJ1dAAAAdIh4HoBIbz08Vg/96yk1NwVj2r65sVkPXPSYRj82TlnBkXY5argueOJMb2WBkrL2772LSoq0zb6D9Y+HT9fef96NBC9krI132EBVvSuTHqesokxb7rap/HbAGXtqyN5bdrpdR4lewaYWL/H0mqNv1ZPXvKBQS4YvFev4GM/zFEuBdeR0v1oq3saipJ1sXymVHiyVHyO3cYzc2ifl1r0kt3Gy5Lb4PDcAAJD1yzUedthheuONN7znO+20k44//nhNmTKlw+2Li4u17rrJdeUAkJlevvMNffDyR3HvF2wOet12/nbvn9V/3X7KBlaRZI8lC6o1+e0vtGT+EjU2NKmsolQrrb6CNtlhQwWKs/JjvU1TQ7O++eh7VS+o8V6jssoy9V+nn/qusaJygSV6sXyj1LNvT220/Qb67J0vkhpn+4OGKhVKu5XqtFuP11PXvaTxL01SKJhYYMJtCenJa55X3ZI67X7CzspUTmGfGFNkY1AQcV0XWWDon1LLLLkNr0tNk6TQEvsElpxuUmBtqWQHqfkzubUPSFq+Vb6rblLpbnLKDpQKfFyaEwAAAF2OeB6AsI/e+FTP/fvlhPZ9+oaX1HOlHtp0p0HKBn3XXEmHnrOf9jttd01+e4oWzF6ohtoGlZSXqFffHtp0x0Eqr8ru+11Lhvnuk2la+PNiNdU3eXGVFVbtrQEbrkrSWg4JFAW07f5b67V73kpqnKF7b6niUv+7PllB6ZEXHqwVV11Br9//thrrGztN9Cpau/3lG999cryW/Fqj4y4/zFtpIyMV9PFvLKf37531raNX5VlSy0Kp8S25TeNan6uxNZ5XuIpUvJMU+llqfENqeGq54VwVScXDpPIj5BT29G+eAADA47hu9rVIcOJcxmf11VfX9On+Ls02c+ZMrbrqqt7z0WM/Ut9+K/s6PoDOzZ/1qy7Z75qYO3i1Z72t1tZfbz/R13khfr/8NF9jnn5f7780UfU1yyd6rLXpAC+hxwJ4FlDIdpboZfI50evHL2fqhuNvV7A5sQSqfmuupHMfOk2BktS2Al88v1rjn//Q68zV0M61Gauj/nmItt5zc2Wk0BK5C09oTb5KklNxplQSvT1+mHXsUsMTsY4slZ8op2xkUvMDACBbzZk1R9uuZxX10owZM9S/v7/dTIF8iecZYnpAegWbgrpgzytVvagm4TGsm9BlL//D68aN9LFC1PHPT9S4Zz/Qwl+WX26z74AVtd3BQzVkz829xC9kv+pfa3T5YTd6fyaivKpc5z1yunr27aFUskTKD1+drDcfeke/zrEEpY4Vra12E73MiCOHa7/T91BGcl25i/7cmmyVrNL95XQ7MrbDNk6Qam6MPY5YMlJOtxN/TyIDACCPpCqel6Ep6ADQuXHPfJBUgpf5euJ3mjt9nm9zQnxCoZCevuFl/fPAazX6sbHtJniZ7ydP1/0XPKZ/HXidZn07V9mO5RvlLbNoiU+J3OBX9anSKTcdm/IEL9O9T6V2PGxY0i3an/33K153uoxUUPVbG/YkOd2l4iExberW3B5Hgpe3h1T3H7m1jyY8PQAAAABA+n3yvylJJXiFk4s+fedL3+aE+I19+n1duNdVeunO19tN8DJzp/+ip659QRfsdaWmjJva5XOE/yp7VejPNx3b4fKj0Vjh7snXH53yBC9jSYXbHzREpd1KEl6+0bz58Biv+15Gchw5pf4UQzqlu8W0nVv/mlRzbXyFoo2j5FZf7iWlAQAA5W+SlzUfi+eRiqo/AOmv+hv/4kRfxhr3zPu+jIP4E7zuO+9RL7krVgvmLNQNJ9yhaZ//pFxgiV4mXxO9tth1E514zREKlMTenW2lASvqb/eeot4rd12r74mvfewtN5CMml9rvGVWM5VT6kNVYsmuklMUWwevxgRb+zc8LbfhzcT2BQAAQFoRzwNgxjwzwZdxxvo0DuL36n/e0uNXP6dgMLZEDyvqvPP/HtCHr36S8rkh9VZbv7/OuOskr6NePB28/nrHid5qDV3l+8+ma/Z3sRULW6KXPSzRa6lkL9f1OtVlrJKdbIHr5MYo2spborEzbuNHUt3diR2j+WO5tXcmti8AAMiNJC8A+PbjaapdXOvLWJ/873NfxkF8nrn+5YTOfUNdg+448wFvuc5cS/TKx2SvTXccpPMfO1M7HLKtSis6rq5bYdU+OvDMvfT3B/+iPqv06roJuq7efdqfRNCxT2dwALpoXal0r8T3Lxwgp2y/TjdzW2rj7ODVjtq7Jbc5uTEAAAAAAF3Olnj74VN/Eji/mfS9ahfX+TIWYjf+hYl65e74i68sefehfz3lraqA3Ej0Ov+xM7TniSO8jvsdqexRod2O3VHnP36m1tqk6xK8wt3m4tVeVy+75q3gPCMVVMrpdlLi+zvd5XQ7rvPtrAuXt0RjEhrflBuck9wYAADAE3vrDADIINaW3bexfq3xVgITy8J3GVty8Z0n30t4f0vwe+G213T8FX9ULiV6zQnO8hK9BvTvrXyy4mp9dPDZ+2ifU3fTpNc/1Y9fzFBdTb0CgUJ169FNG247UOtvvY6cgq5/k86fvVBzYqz668x3n0xT3ZJ6lVeVKRM55cfI/X/27gK8qXv9A/j3JGmT1AsFiltx9xYoNlw2GMwFmDHGXP/b7nbncufKnCljQzdgMNiwAi3u7lqkUG+TNsn5P79T2IBa5MS/n+fJ3UbPec8PKL3k7Su2HKBohWM3ampBivwPoLHj51WoxrpFC2TTIkjGYSrEIiIiIiIiIk/JzlAvnyfknstFeHSYqjGpfKYCM2a+O8/p+21WK355cw6en/4487ABICI2AkPv6Y9Bd/TFthW7sHvdfhRkF0CGjPDIMCR0bKg0d+pCvfNtyK3LnVvpKgq9QhL+LfTKy8xTtko06dQIPsnQD5ItC3Lhjw7eGAEp6llAW6PSK+UiUTCnQlFtwY9A1BOuxyEiIgpyLPIiIr9UbFZviotIMIjVgRothxt6yorprk80EqvvRHIwOs7+0eD+UOwVrIVegj5Mjx6juiovX5GXma9yvDyfLfKCpIEU8RDkghqAabZSTFUpXQdIkQ8rnYN2df2Zl6pyVBTOAVjkRURERERE5FfUnoZTpGJ+kCq37o9NyoR9V5w+chZ71u9Hsy4Jqp2LvEur06J9v9bKy5e+d2AuNDt//4WJXheLvdTOD6ou7FpI2iqQ876yrxhLWx9S5BOAtpZ98QunQRXFa0um80sh6sQjIiIKUqxoICK/ZIz4d2Syq0INoSzw8iBTnglrF2xUpThv9Zy1CDSi0Eu8gnV9o6+xWtRNQFssVvg0SYIUfhOkmC8hGW8FpGplXGQA9AMhRb8DKfo5+wq8RI2XZZf4CqDOOeVzgDVDnVhERERERETkEQYV83lCWKSPNlEFIhlYPsP1pk1n1+gROcKqUv7tYrHXKbEJxNfp+0CK/QpS+ERAW9ZqTA0QkgQp8kVI0e/aX+BlKwSsx1Q6pBWymX/+iYiIXMVJXkTkl2olxPtkLKrcztS9KDIVqRJr499bMeSuqxCIgn2ql68wqpww9psEtDa6pAvQOLIkkSPWOIrJXlIEoK1j32rGK1mOqHpE2XoOkjZO1ZhERERERETkPlVrxkBv1Ls0YefSBtCY6tGqnIsqd/roWaQfOKVKrC3LdypT3by1xo8Cn/g6I0kSZDFVXoVCrxq6Wv804/p0nlZjAAwDIOn7A7Z0wJYFyGZACgO0NQFNlOMx5Sx1z2g9rm48IiKiIMTRNUTkl2o2qoGGbcvqSHFcz1HdVIlD9snOEMUi6sjN8IMuKhcLvQRO9PKeanWqwhCuVyVWVFwkouOcSKZ4k6QBdPWB0DZAaAcgpIlzBV6CrPJoezmw//wTEREREREFmhB9CLoO6aBKrG7DOrFIyINyMnJViyWm8+fnFKoWj+hKkkZC3ea11YklSaidEP9PntYvSFLJpK6Qlhfyec2cK/ASZJWm8v/DjnWSREREVCEWeRGR3+o9JsnlGMYIIzoNbKfKecg+xUXqrb8rMhcj0PlVAiFAE9AicayGHiO7KUmmoOVsMqnceOzYJiIiIiIi8jfJKuTz1IxD9ilWOQendjyiK/W8NlGVOG16tQzuqYGSumt2AT9rgCUiIvJBLPIiIr/V4arWiK0R41KM5DGJCDWEqHYmsm+cftCtviO/1muM60khSatBz1FdEdS0DVUNJ2lrqBqPiIiIiIiI3K92k3g075rgUoxWPZojvkE11c5Ens3nKfEi1S4cIbpc50HtVPm87RXsBaWaKurG0zVWNx4REVEQYpEXEfktMZJ9wtu3I9QQ6tT9TTsnYNg9/VU/F1WsZqN41WLFN6quWiyi8sQ3qoE2yS1citFlcHvE1Ajirj9RlKUTSfwIdYJp6wCaSHViERERERERkUeNfelGVImPdereuNpVcdvz16l+JqpY9frVoNFqVYkVFReFsAg2bpJ76Y2h6HWdawVadZrWcrko1e9JekDXRKVgBkhifSQRERG5hEVeROTX6javjfs+GO9wV07Tzo0x4a3boAvRue1sVLaE9g1Qo7463ZY9R3VTJQ5RZW574XrUcLJLWHyduvGpkaqfye9IEmAYok4s403qxCEiIiIiIiKPi6oaiQc/vQvV6lR16L7q9eLwwKd3IbKKSg1EZLfw6DC079dKlVg9rukCSSOpEouoIsPuGYCWSc2c/jo14e2x/FwVjLeqE0fftyQ/SERERC5hkRcR+b0mHRvh8Sn3o03PFpBQ8ZuEsKgwDB7fD5M+vAMGlceMU/lkm4ycc7k4dfgsMk6cQ9LVnV2OGR0XhTa9XJuuRORIMvPBT+9G7SY1HbqvYZt6uP/jO6EP07vtbP5EMopiN1c7f8Mghbq+QpOIiIiIiIi8p1rdODz+zX1IGtGl0ibMkFAdkq7ugse/mYS4WiqvDqPyyUBeVj7OHM1QXl0Guz6BR9Jo0PNaNm2SZ2h1Wtz15q3K9w0cISYNPvTp3ahSM8ZtZ/MnUkhrQHL110ICjDerdCIiIqLgxhE2RBQQ4htUw73vjUPGyfNYNWstNv61VSkqKjYVwxhpUNatialPHfu3QYg+xNvHDRpZZ7Kxas46rJq9BtkZOZd9TIx4t1mtTsfuc0MP5Y06kSNM+WasW7AR6//cgqyzOSgyFSmTAEU3sEgYi7WMGm3ZNfAx1aPx6Ff3YuFXS7Dq93UoyC4o9zkRVSKQfG03DBrfl19zLqUxAuETgfyPnY8R9Sy7/oiIiIiIiAJARGwEbn1+DEY9NBSpv6/Hmj824PzJLJgLzNCH61G1ZiwSR3RGt+EdER4V5u3jBg1Tnglpf2zEyhlpSD90ulTBXXGRxenYHfu3VfIrRI6wFFuwddlOpM7bgIzjGUp+T6xjjI2PUYoPOw9qj1BD2fk3cd09b9+OJT+vwvJfVuH8qcxynxNqCEXXIR0x/N4BnBh4KZGHE/m47KcA2JyLEXYXJG242icjIiIKSpIsy7K3D+GPjh8/jrp16yr/vjRlA+Jr1vL2kYioLOIrHGsBPM5cWIRf3/oNa+ZvhGxz8o1fBUT3lXhzXl4xTqBJt5xAAwdXGNDlROfp/M8XK5+TIllcnpj4GPS5rjv63dKzwiLCYnMxNizagjV/bELmqSyYC83KtC7RUZw4vBPaX9Wa62ArIBfMBAp/cvzGiMcg6Xu440hEREQ+Lf1EOno06678+7Fjx1CnTh1vH4nIbzGnR+QHmM/z2iT++V/+hb9/XKE0xamtZsMaePSriQiLMqoemwKTpciCRd8tQ8rMNKWhuzzGCKOyOWLoXf2Vhu/y2Gw27Fy1FyvnrMGZI2dRmGdSCrui4iLRaWA7JA7tWOH2j2DP0crmdUDeGxe+SDvAMBpS+C3uOhYREVHQ5fP43UciCmxMCHmlmObjB77Bsd3H3RK/VY/mGP/azUFT4HXR4ePngjqJ4AqxUuCTB79BxvFzlV6bdSoLcz76A3s3HMCdr98CQ3jZaxbFdC7RTSxe5DgpbDRkTVUg/1ORsrPjjggg8mlIoVzRSkREREREFPCYz/PKpKRvn5uGTX9vc0v8WgnxmPTBHSzwIrvl5xTgi8e+x/7Nhyq9tjCvEEumpmBX6l5M+vAOZcJXWTQaDVonN1dezgrmHK2k7wJZ8waQ85L4HbLjjhAg/B5Ihqs8cDoiIqLgEVzfISciIrcS040+e/Q7txR4RcSEY9jdA3DvO2OVMdvBpKau9j9JBHJM1ulsfHDvF3YVeF1q5+o9+OKJ75UkJ6nMlgsUzAYKp1Ve4KVpAEQ8A6nq9yzwIiIiIiIiInIHGZj62iy3FHiJJrnkaxPx2JcTuaaR7FZkKsanD02xq8DrUmK96AcTv0BeZp7bcrTiJXK0QZenlYsA099A/heVF3hJcUDYvUDsNBZ4ERERuQEneRERkWr+nLIUh7Ydcfp+SZIQERuOgpxCWC1WGMINqN0kHj1HJaJj/zbQhQbv/22JBIIYCX4xgRCsHWMOkWV8+dQPyDqT7dTte9bux9xP/sSoh4epfrSgVbwDcs6bYuaffddrq0AKaeXuUxEREREREREFrU1LtmHNvA0uxYiKi0JhTgGKiyzK+rtqdaoq6/MSh3eucH0eUVlmvPM7Dm8/6tS9Z4+fw5TnpuGBj++CJ/K0QZGjtaZDznkFsKXbd70mDFJoB0DDsYxERETuELzfLSciUosMZJw4h+yMXGWSlShMqla3KsKjwxBMTAVmLPtllUsxZFlWkj8j7x8Cm2xTRmhT6YleQZVEcMG+jYdwePsxl2KkzFqDIXdfpfy5JhcVbYKc+7qd6xkvKN4IOfe/kCJfBDRc6UBERERERETqyTqbg8z0TJgKiqAPC0WV+JjgmzYlAwu++tvlMHWa1FTW5NlszOeRa3LP5yHNxaLD3Wv24fjek6jTtBbcJWgKvazHIWc9K35nHLjnKOTs/4MU/Tqgre7O0xEREQUlFnkREbkwNnr9n5uxYkYqju0+cdnHNFot2vVthd5jktCkYyNACuw33itmpGHpzytRmGdyOd7q39Zh+IQBQT21y9EkQubpLKyavVaZopafXQhJIynrLVt0a4LEEZ0RFhWcxTHiz6arzAVmrJm/Cb2vT1LlTEHLchRy7luOFXj9c+9+yLn/A0K7ANbDgC0fkEIATQyk0G6ArrkYA+iOUxMREREREVGAsVlt2L5yt5Iz2JW2t9THm3ZOQO/rktCmVwtodVoEKnNhEVJ/X48lU1Nw7uR5l+PtTN2DjOPnEBfIxS4qE5sMxAS1nWv2IT8rDzabjLBIIxq1qY8eo7oiNj4GwWjVnLXKhgdXrZieipufHQ1PNOQePl7yvYGAK/ay5ZZM8HKkwOsiORNy9otA2EjAchCQRQwNoImEpGsPhHYCJBaEEhEROYPfQScicoIo7vrlzTkoyC0s8+M2qxWb/tqqvETH0J2v34Lq9eIQaA5sOYzPH/se+dn5qsUUsUSyrX2/1qrFDEQiibBh9wbMfn8+9m08CCmn9OfiztV78PvkP9F5YDsMGt8X1eoG3udgRcWHm5fuUCXWyllpLPJykVwwVcz7cz6AZUvJ68q4pt8BbX1IhiGAvm9J8RcRERERERFRGQ5tPYIp//kZ59Izy71m7/r9yiu2egzGvnQDmnRqhECTcfI8Pn3wG5w+clbVuGL60vB7B6oaMxCJYriFU5Yq+WWxFeJKe9btx8IpS9CmV0sMvL03Gratj6AhAytnr1El1LqFm3HtI8NhCNPD3QJ1qpdcOB+wnXEhQDqQP7n0D2MBIMVBMgwEDIOUwi8iIiKyH8ukiYgc9NePKUpCqLwCryuJ0dBv3/Epjuw8jkCyf+MhfDjxS1ULvC5NdlDlE8+mjJ2BHb8cUNZc2iLLXidYbCpWOjPfuO1DJUkULE7sPwWbCl1/wsn9p1TpIAxa1gygeJ0b4x+BnP8Z5JxnAWu2+55DREREREREfmvbil34YOIXFRZ4XSrzTBY+uv8rbPp7GwKtwOudOz5VvcDrYmyq2N71B5QcXerv68os8LpI5Pq2Lt+Bd+7+TJneHyzysvOReSpLlVhFpiKcccPneeVTvc4pL78nWwDzYjfGz4BcOBVy1mOA5Zj7nkNERBSAWORFROSANX9sxOwP5jl8nyiEmvzwlIBJdoifx2ePfQdLsROr1+xgKjC7JW4gFXj99MoMyDab8t/FF2q3yiv0Ekx5ZqVLUxTnBQOTnUWY9ipUOV4wkU0iISS7/0FiraMo9LI5MUKeiIiIiIiIAtahbUfx9dM/orjIsTyWaPgSjZ77NhxEICgyFePTh6Yg55x73jeb8pnPq8iBzYfxyYPfoDDP/knnIvc39bWZQVPopXb+rSDXhanyThZ6XVrs5deK1ikrF91OFHtlP8NCLyIiIgewyIuIyE4FOYWY9vpsp+/PzczDjLd+RyD467vlKMxzX9GLNkTLyUnlOLzjGKa+NqvUj4tCL/EShV7lFXtZiq34/PHv3JbM8yUanVbVeLoQdeMFFXdO8bqS7STk3P+JllfPPZOIiIiIiIh8lwz8+NJ0hwu8LhL5qR9emg7bhUY7f7Zm/gacPuzC6rVKhOhDYHHy1znQ5Z7Pc6lh9uc3ZivrRgOdVqdTNZ5O5fygvQKh0EsWRV4ekw8552XApv7GECIiokDEIi8iIjulzdugjHl2xfaVu/1+mpcp36RMNHOneZ8twoNJz+Dxvi/g+xd/VQqbPDEIyB8s/m75PxO8ylLZVC9RrJgyIw2BLrJKhKoFXvqw8qekUSVsOZ59nmUHULzFs88kIiIiIiIin7Rn/X6ccrGw6dzJ89i5ai/8mgwsn57q1kdsXLwFD/V4Fg/3/A8+e+Rb7Fi9B7KNCT0hZWYaCnIKnL5f5AIX/7AcgS48JkzVeBGx4fCWi1O9/HZ9oy3bs8+TMwDzX559JhERkZ9ikRcRkR1EQmLFDNcTITJkrJy5Bv5szfxNLhe72UtMC1szbwPeGvcx3rj9I+zbGBjj8Z2VdSYbW5bvqPS6ygq9Vs5eG/CT0uq1qI2ouChVYrXp1QKSRlIlVnDy/OeabFpQxg8WA+YUyLkfQs55BXL2y5Bz3wMKFwA25xOtRERERERE5LvUanRbrkJe0Jv2bz6M9AOnPPKsYnMxtq3chU8f+gb/HfU/rP1jE4KZyMGtnOV6Pnjr8p1KbjCQ6Y2haNYlQZVY1erGoUb9avA2/53q5Y183sLS0/nFfxdtgpw3GXLO65CzX4Kc+zZQMB2w+tuvKRERkTrUnX1KRBSgjuw6jrPHMlSJtW7BJox8YAj81e61+7zy3GO7j+PD+77Cbc9fh65DOyAYrZ6zrsIpXmUVeoUklBR6aXJN/3wsJyMH25bvRPur2tg1uW3D4m04deg0CnMLldH70XFR6Ni/Dar7QKKkPFqdFj1HdcUfX7reAZY8JkmVMwUtKRyQPZyELF4PWM8C2mqANQuyaV5JN6BceqqYXJQCFPwA6JMhGa8GtCXJNyIiIiIiIvJvpgIzNi+rvFnOHrtW70FeVj4iYrw3GcgVu9d4ZxKZmIL23X+n4dTh07h64mAgCHvoxGaH7AzXp5zLsqw0bg6fMKDSa8VayG0rduHIjmMoyC2ERqNRplq16t4MDdvU9+nfh15jkrBn3X5V4vhK06Yo9Eq3nFAKvRrUqQq/yed5mu00ULwZCO0A2EyA+U/Ipj8BW+kCVRmrgcJfgJBukIzDgZAWnj8vERGRl7DIi4jIDpmnslSLlXU2GzabTXlz7Y9EQstbbFYrvn/hFxgi9GjbqyWCzcFtRxy+RxR7hSSUTPW6tNDr4LajFRZ5nTp0Bst+WY21f2yEucBc6uNzJ/+J5t0SlAKodr1b+UzS5FI9RnXFgm+WQLbaVxhXlhoNqqNZ58aqnivo6BoDRSc9/FC5ZG2jXBdyzquAXNnXcJE4WgzZvBxSxKOAvquHzklERERERETukpORa3eznD3T+bPO5PhtkVdelncnWP85ZSn0RgMGje+DYHNo61EVYx2u8OPZGblImZGKVXPWIudcbqmPL/j6b9RtVlvJ53Ub2gG6UN/7FmHb3i0RUy1ayaE7SzSpJg7vBF/y70SvE8o/fb3YS9IlQC72/ARDuXgrJG09yLmvANbKcuE2oDhVOadkvA0wjgQk38tRExERqc0/KwyIiDzMXKjuesIiUzH8eXWlV58vy5jy7M/IPZ+HYCMmaTnj0vWNF1c4FuSUn9xbNXstXrnxPSUpVFaB10W71+zHl0/8gM8f/071PyNqiKkejYG393b6flG4du3Dw5gccJFkGOSV58qWI5Czn7OjwOtSRZDz3gTM6qzzICIiIiIiIu8pUjlXYS4sP0fi67ydzxN+/3QBDm11vIHR3xXkqldgl5/zbwPnlcT0q5eve1sp5CqrwOuiY3tOYOqrM/C/cR/75PpHjVZTko9zwfB7BiAsyghf5DfrG/X9vDMnxHYOcs5/7Cjwupxc+ANQOMNtxyIiIvIlLPIiIrKDIVyvWixJkqA3hMJfhUd7/w1ykakIq39bj2AjuTD9TRR6XVrspdVqy7xuyU8pmPrqTIemX4nx76/e8J5PJoZGTByELkOcW+95w5PXoHXP5qqfKejoWgDaep5/rmlRyYQuh8mQ894DLMGXeCYiIiIiIgokaubzBGNESeOcPwrzgXyesPSX1Qg2am5z0OrKjrVz9R588uA3KMyzPw9yYl86Xr7+XRzecQy+ptPAdrjm/iFO3Zs8Ogn9b3O+6dPThV4+W+yljQZCkzz/3KKtJWsbnSAX/gyYPT99jIiIyNNY5EVEZIdqdeJUixVXu4pPrrazV8M29eELUmalKmsvg0lETJjLMS4WehUZQ8os1pr53jyn4p47eR7/Gf46fnxxurLq0VeIP2u3v3A9+t2SbPc9YlT9+FduVEbXkwokCZJxlBce7NzkuxLFkAtnq3gWIiIiIiIi8rToalEIUWkdnUarRWz1GPirRj6Sz9u8ZFuFU6YCkZorPsOjS+cGTx08jS+f+hFWi9XheKZ8E94a9zEmPzIF+zcegi8ZOLYPbnr6WuXPnr2G3NUfNz4lVvbB54lCL1+f6iUZr/bCt5FzXLpbLvxVrAJR7TRERES+iEVeRER2qJ0Qj7rNSt50uSpxRGf4s+7XdHHozbW7ZJ7Kwu60fQgmzRObqhJHFHo1antFck+W8dsnC10e/Z86dz3euO1DbF22E7405n30I8Pxfz8+iO4juyLEULrATYiKi8SQu67Ci7OfROfBzk3/onKE9gIMro3a97ii1YDNtcQSEREREREReU+IPgSdBrVXJVb7fq1gjPTfSV6tejZDbLz3i9REIdKa+RsRTNTK5wktk5qV+rEF3yxRth64YvvK3Xhvwmf464cVYsC5z+h5bTf8d9bjGHB7H4RHl10spzfqlUbNZ6c9guETBvhFgdelLhZ6+SRdY0jh98KviDWPlt3ePgUREZFbeWGhMhGRH5KgvFmc+qpre921Oi16jOwKfxZVNRId+rXGhsVbvH0UnD58Fi27l05uBKrEoR3x20cLXE7c1GxUumhx/6bDSD9wCmooNhXjiye/xz3/ux1t+7SEr6jbvDZu+c9ojHpwKLau2ImsMzkoNhUp6xaq16uGlj2aQhfCvxq5bZpX2B2QxRdTk3PT4jzPApj+BsK8MYWMiIiIiIiI1NBrTBLS5q5XJY6/rwxMvjYJv3+6wNtHwanDvjMB3hMS2jdAzcbxLufdQg2hSBzW8bIfyz2fh01/b4NaZn84H5ZiKwbf0Re+Iq5WFYx8YIhSwLUtZRcyTpxHYV4h9EYDYmtEK7lHQ5i6q1npEob+kGCDnP+5aPGFP5BNCyGFtPD2MYiIiNyG38kkIrJTl8Ht8dvHC5Cfne90jI4D2iKySgT83YDbe2Pz0u1OjQFXU2GeCcHEEGFAt6EdkTIrzfXE5BVdbStmpEJNYqrXN/+Ziv/78SHEN6gGXxIWZUTi8E7ePkZwFnqF3wHomkAunANYfWsNQFnk4u2QwCIvIiIiIiIif1W/ZR00aF0Ph7cfdTpG7YSaaNKhEfxdj1FdsHRqCnKz8rx6jmDL54kcXO/rkjDtjdkuhek6pIOSG7zU6t/Wq56fnTt5IWol1EDbXr7TuCnoQnXocFUbbx8jOBkGQtLWgVwwHbB4v/G7UsU7vH0CIiIit+K6RiIiO4UaQjD+lZsgaZz70lmtThzGPDoCgUBMRLr1uet84vck2AwY2wdhkUan76/RoDq6Db+860/YlbYXahMTvf7+cYXqccnP6ZMhRb8NKepNQN8X0DYApGqApiagaw6E9nbxAWoW0no38U1ERERERESuG/viDQiLCnPqXkO4AeNevtHvVsCVJSImHPe+P05ZY+lNwZjP6zasE+IbVHf6fmOEUckJXmlX2h64w8Kv/3ZLXPJjIS0hRf8XUszHgGEEoG0MaKoDmhqALgHQ93NxroiK63Bl5vOIiCiwsciLiMgBLRKbYPzLNyprFx1RrU5V3P/xnUoyJVB0HdoB4166yeFfCzVFxUUh2FStFYsJ74xDSKjOqVWb930wHnpj6GU/brPaUJBTCHdYt3ATCnPdE5v8mCQBIU0gRTwAKeZdSFU+hxT7CaTo1yBFPgTJeIOTceOA0PZqn5aIiIiIiIj8WPV6cZj04R0Ij3YsL2eMMGDie+NRKyEegaJBq7p48NO7Hf61UFN01UgEG1HYNunDOxHtRC5T5AAnvHM74mpXKfWxvKwCuMORnceVF1Ep2lqQwsdDinkLUuxnkGInQ4r+H6SI+yFFPOJk0FDAMEDlgxIREQUuFnkRETmo08B2ePCTu5WJSJWRIKFdn1Z4/Jv7ynwj7u+6DGmPJ6ZMQqeB7ZWfqyeJrsM2yS0QjBI6NMBDn01wqGhQdAs+/s0kxNUq/Xlos9ngLmKaV9q8DW6LTwHKeD0k462O3aOpAyn6FUByftJdKVLwFZISEREREREFIlHcJPJzCR0a2nV9wzb18fjX4voGCDSN2tbH//3wIHpdlwSdzpXJO87pOKAdglGVmjFKbq5mwxp23yNyfw9NvgdNOpa9LtSdOb2UGWlui00BSp8EKeIJkbl34KZISFEvAdr66p1DCr5CUiIiCi6e/xs8EVEASOjYEM//+hj2bjiAFdNTsWX5Ttis1svegCeN6IKeo7sFZHHXlasb73j1JgyfMADv3fMZcs7leuS5XQZ3gDFSxTHOfqZhm3p47tdHsXL2OqyclYbM01llXie6TXuNSVLGwpc3Dl8XokOoMRRFhUVuOeuBLYfR96aebolNATzpS58MWI8BRasAWCq4Ng6SYSBgGAZojIAtR71z6JqqF4uIiIiIiIi8PtHrkS/uxfG96UoBy9oFG1FkKrqsobDzwPbodV0i6rWog0AvOLrhyZEYMXEwPpjwGY7vS/fIc+u3rKO8gpX4dX/y+wew9o+NWD59NU7uP1XmdbE1YtDz2m7oOaorImIjyo3n7BpSe+zffMhtsSmAhbQBDMMB00IAFW13CAcM/SAZrga0VQGLiqtHtYFXnEtERHQpFnkRETlLApp2bqy8LEUW5GXlo8hUrIxyD48Jg0ajCbpE2TNTH8bkR6Z4ZJx3rzGJCAamAjO2LNuB8yczYS4ogiFcjyo1Y9G2T0slyTP4jr4YOLY3tq/ajUNbj6IgpwCSRoOImDA079YUCe0bKJ+rZTl8/Bwa1Kmq/HujtvWwe81+t/wc8rO5rpEcIBdDzv8CMC8R/1HJxRogNAkwjgKkC6tjLQfVO4ummnqxiIiIiIiIyCfUaVoTNz0zCtc/eTXyswtgyjdDH6ZXcila3YX3lkEiLNKAJ769H9+98As2Lt7q9ueJRsRgYLVYsX3lbqQfPANTngkhhhBEx0UqGx8iq0RcKODqpjRG7krbi7zsAshWG4yRRjRqVx+tezSHRlt5brlRm3o4tPWwW34OBTnM55EDZBkonAm5cAYAOxqJda0hGW8sadgUineodxZtrHqxiIiIfBCLvIiIVKAL1SGmejSCnUhSPPz5vVg0ZSlWzlqD3Ky8cq+VJAmyePPnhD439FAmiAWy9IOnsXx6KtbO3whzobnUxw1hBnQd1gG9xyQhvlENtO3VUnnZq6auNtItJ/4p9EoeneS2Iq8gq3ckV9gKIee+Alh22XsDYJ4L2XYKUuTjgBQCyOpN8pLsSUoRERERERGRXxIFXVFVI5VXsOc173jlZiS0b4SlP6/E2eMZbsnnNeuSgK5DOyKQZZ3JxsrZa7Fq9poytx38+tZvaN+vDXpfl4TG7Rv883KWKBb7+6cVcAeNmLJOHiNytMLFhly/IsuQ8z8FzH/bf49lDeScZyFFvQBoogA5W8UDBVexLhERBR8WeRERkarESsDhEwdi8J39sHnpdqTN24Dzp7KUrrWLU6gSh3VCtXpx+PShb5QJaI7o0L8tRj86HAFLBhZOWYp5k/+EXMEUI1OBSVkVmjI9DVffPxgDb+9T7sQuewq92vZuiehqUcg+q+KquwvCo8NVj0kBSLZCznvHgQKvSxSvg3z+dkB/lX3dgnafqVi9WEREREREREQ+StJI6H19kjI5f/fa/Vg1Zw1OHTqLwtxCZY1lVFwEOvZvh1Y9muLzR79H+qHTDsWv27wO7vnfbXZNp/JXm5dsx7fPT0OxubjCCV8bFm1WXkkjuuDGp0dCF6JzabNC825NsHvNPqgtLMZ9qyCpdI5WuLQh15/IBT84VuB1kfUw5Mw7gdBEwFa6KNJ5FhVjERER+R4WeRERBZmju44jbe4GnD1xHuYCE/RGPWJrRKPrkI5I6NDQ4UKhiroAOw9qr7zK8/g39+Hzx39A+sFTlcaTIKHfLckY+eCQgF6FOeuD+Q514IlCsN8+XoCC7AKMfHCo00mEo+kn0Om67ljy6UKoTXRqElVKrGcs3uhKAMD8h8ptqyxQJCIiIiIiIu/LOHEeq39bi5P7TqEwzwRdqBaRVSPRvm9rZbK7WsVTotirRWIT5VWeR7+aiG+enaqsGbRHu76tMfaF65WVmIEqbe56/PjSjAobNq+UOncdcjNzcc9bt7u0JnTQuL7Ys2a/Q8+2R3Pm8zzuys0LfqF4H2Ca40IAK1C0SsUDiS9kzOcREVFgY5EXEVEQkG0y1v+5Bct+WYnDO46Vec2qOWtRs1G80rXX/ZouLiUX7FWtbhye+fkh7Fy9FytmpGLnqj2lEhIRMeFIuroLeo7uhrhaVRDIVkxPc3rE+uIflqNq7SpIHp3odBKh0wDgzJGz2D5/A9RiiNCj8+DyC/2I/hnrblK5QEsN2vrePgEREREREREFMTFVa8nUlDJzZsK6BZsQUy1aWdvX96YeMIQb3H6msCgj7v/wThzaflTJ521ctBUWy+WTc8T0ry6DOyiTweo2L2kwDFR71x/Aj6/MdKrIavvK3Zj+1u+48elRTj+/aefGytaDGe/OhZrE7x153sWG3MPHTyj/9PViL1/M50k65vOIiCiwsciLiCjAWYos+OGl6Vj/5+ZKrxUTtaa9MVtZs3j3m7d6JDEkpnK17tlceWWeysLxvekoyC2ELkSLyCoRaNS2vjIVLNCZC4vw+6cLXIrx28cL0W1YJ2VlpjNqhtTG4Dv6Qhuixaa/t0KTa4KrEod3ht4Y6nIcCnCWPYD1CHyKLgHQNfT2KYiIiIiIiCgYycAfX/2F+V8srvTSrLPZmPf5IiX3d98Hd6BqrVj3n08CGrapp7zGPDpCaSotyC5UPhQeE4aGrevBGOn+vKLXySVT+WWbzekQKbPS0OemnohvUM3pGH1v6glJo8GMt39XZaJXk46NEN+ohstxKMCnetly1J/C5bIIILS7tw9BRETkVoG774qIiGCz2fD1M1PtKvC61O41+/DxA9+g2FwMT4qNj0GbXi3QbVhHdBrYTulEC4YCL2H9ws3KuH1XFOYVYsOiLS7FqKWvi7F33oJrJg1BjXb1Xe7svOqWZJdiUHCQzcvhayTDEG8fgYiIiIiIiILU3Ml/2lXgdalTh8/gvbs/Q9aZbHhSeHQYWnVvhi5D2iuvlklNg6PAS0xb2nkMx3aXTFxyxcqZaS7H6HNDdzz8xb1KI60rRLHYsAkDXD4PqTnV6xx8UlGq6NyETzH0BaTAXQ1LREQksMiLiCiAzftsEbYu3+HUvYe2HcHPr89W/UxUBhnKeHs1LJ++WonnEgno27MPbn/xBoz4v1HKZC9H6fQ6THhnLKrU9ED3KPkX2QZYzwGWY4A1HbAVAraz8ClSFSC0h7dPQUREREREREFo/aItWDhliVP3Zp7JwmePfac0fpL7qZXPS5u3Xpny76qEDg0w8b3xeOr7B2CMNDoV46anr1UmeZHvFHqJlyj08mqxlywD1izAKvJ5JwBbLmTrGfgWHZs2iYgoKATHeBQioiBkyjNh6c+ujUteO38jht7TH3G1qqh2Lip7rP7xvSdViSW6B3PO5yKqaqQ63WKJQNy74zD75Rl2d4KGx4Tj3nfGopGLk8AowFjPQjYtBMx/A3LOFR8Mh+8wQIp6GpC4ZpSIiIiIiIg8TAYWfvW3y7mhHSv3KNPyyb22rdilShwx3f/gliNokdhElXj1WtTBf2c8jk8fnoKju47bdY9Wp8Vtz1+vTGMj3+O19Y22XMC8BLLpT8B26ooPup5/VpMU8SCgjff2MYiIiNyORV5ERAEqbf5GFJlc6wCTIWPlzDUY+QA7YNwpLytf3XiZ+aoUef1T6FUXeObnh5Eycw1SZqUh61RWmddGVo1Az5HdkHxdEqLjfOtNPnmRLR9y/mdAUUVFp+r+GXBeeEmBl66xtw9CREREREREQWjfpoNIP3RalQlTLPJyLzEtrSCnQNV8npoiq0Tgsa8mIm3eBqyYnooT+9PLvE5v1KPr0I7oc2MPxDeopuoZyH2FXoJbi71kK+SCHwHTHwCKy7koF75BCyn8PkDf09sHISIi8ggWeRERBSIZSFFpXPjq39Zh+IQB0IXy/zLKk3kqC2vmb8SZ4xkw5ZsRaghBbPUYdBncHrUSKu8eslrUHaFvKbZAbeHRYRh8R18MHNsb21fuxt51B5CXkw/YZIRFhaFx+wZo17cVdCH8PKFLWM9Dzn2xZJS7T5OAkC6Qwm8DtLW9fRgiIiIiIiIKUikz0lSJszN1DzJOnEdcbU7nL09BTiHW/rERx/emK5O0dKFaRFaJRLs+LdGkQyMlVVARmx/k80Q+t+e13dBzVDcc2HoY25bvRE5mHixFVoRFGFCnWS10HtQOhnCD6s8m91AacgH3TvWSiyDnvAlYNsHn6VpACrsFCGnp7ZMQERF5DL8TS0QUgPJzCnDq8Bl1YmXn4/SRDNRuwlHHV9qzbj+W/bIa21bshCzLpT6+6LulSGjfEL2uS0LH/m0hacrODhkj1E2kiKIrd9FoNWjbu6XyIqqQrRBy7iu+U+AV2l2ZKgbrUUAW3bGhgCYGCE2CZBgAaOM8ex7ZCsiFgKQHpBDPPpuIiIiIiIh80v5Nh1SLJdb/scirtBP7TmHpzyux/s9NKC4qXVi19OcU1GxYA8ljktD9ms4I0YeUW0AVEqorM4YzjJFuLLSSgMbtGigvCgxuW98oy5BzP/CdAi9dC0ATCxTvBeQ8kZ0GNJFASHtIhsGArr5nzyO+B6Dk83SAFOrZZxMREV3AIi8iogCk5qhwd8Tzd7JNxpyP/sBfP66o9Nr9mw8prw1/bcX4l28sMzFUtVYswqPDlYI6V0XEhKNKfIzLcYhcJRdOA6yH4SskXQJgHOndQ1gzAfNfkM1LANsl6zekaECfDMkwiJPEiIiIiIiIglhBbqFqsdTIMwUasbFg6muzINsqnsIlVmb++tYcpM5dh/veH4+oqpFlXle/ZV0l7+cqCRLqNa/jchwKzqleh4+fUP6pSrGXeSlQrM6GEFVoqkGKfNi7Z7AVAkUrIJsWXch1Xmz2NgChXSEZhgC6poBUyfg/IiIilbDIi4goAEkqv6FQO55fk4Fpb8zBytmOjc/fsnQ7Jj/yLe77YHyplYZanRbdr+6MxT8sd/l43a/pqkzbItdkncnGjlV7kHsuDxaLBWGRRtRtXhtNOjbkG3Z7kx+mv+BTNNHee7YtF3L+10DRKlHpVfrjcjZgmgfZNA/QtYUUcTeLvYiIiIiIiIKQmjk4ScP80KVWTE/DL/+b7dA9x3afwLt3TcZjX9+HyCoRpT7e89pEVYq8WvZohio12bTpKlOeCVtW7ET2mRwUFRbBEK5H9QbV0Kp7MyX/GqhUm+olpniZ5sOneDOfJxdDLvgZMC0Un11lXGAqKf4qWgFoG0AKuwMIbe2FgxIRUbBhkRcRUQASU6FUjRfjvvV//kaMc3e0wOvS9Y7T3/odNz1zbamP9RydiL9+WAH5n04g57r+kkcnOn1/0JNl7F53ACkzUrFl+U7I1tJdnTUaVFN+jROHd4Ix0uiVY/qFohQA6nUfu04HhHTyzqOtZyDnvATYTtp3vWUr5KynIUU9DYS0cPfpiIiIiIiIyIeER4ehyFSkSqyIaObzLtq9dr8ymcsZZ4+fw+ePf49Hv7oXmisK5zpc1Roz3g1HXpZrU9N6jUly6f5gd3xvupLPW7tgU5l/fsQkth4ju6Lntd0QU92LRUO+Xuhl2Q9Y1VsZqwYp1Et/NmyFkHNfByzb7bveehhy7ouQIiYB+j7uPh0REQU5tnIQEQUgY6RBmTqkhui4KNSoX02VWP7OUmTBgm+WuBRj1ey1OHcys9SPx9Wugo4D2roUu9Ogduz6c5K5sAifP/EDPrrvS2xesr3MAi/h9OGzmPHOXLxw7ds4uOWIx8/pL2Qx2t2XhPYENFGef64tB3LOi/YXeP0jD3LOK4DlqJsORkRERERERL6oedcmqk3xShDTyEkx7/PFkGXnGysPbTuCnav2lvpxXagOfW9KdulsNRvHo2X3pi7FCFayTcbsD+bj9Vvex8rZa8otkMw5l4sFX/+N/478H9Yv3IxAJQq9xEsUeomXo2Sza3lv1WkbALpmnn+ubIGc+5b9BV7/sELO+wgwr3PTwYiIiEpwkhcRUYASHWA/vTLD5Tiiw4nr/0ps+Gsr8rNd68wTk7pWzlqDa+4fXOpjNz97LU4dPoMT+9Idjlunaa0yJ4SpxeVx3z5e4PXRpK9waKv9RVt5mXn4YOIXmPj+eDTvmoCCnEKsmbcBe9bvR35OoRgKhogoIxq3b4ikazojIkbd6Xo+z3oavkQyDPHKc+X8LwCb43+eS4iOwf9BivmIK0KJiIiIiIiCRPKYRKTOdb1AoH2fVgE7schRx/eexKGth12Os3xGKlonNy/14wPH9VbWOm5eus3hmJGxEbj3nbGlJoSRHWTgh5enK/k4e1mKLZjy3M8ozDMpf9ZEQ6/I925bsRO55/NgKbbCGGFA3Wa10WNUV6Up15+nejnMegq+RDIM9k5OrHAOYHG2GFCGnPcepJDPvNNwSkREQYFFXkREAarzoPaY9f485U2rszRaLbqP7KrqufxZyvRUVeKs/m0tht3TX+n2u5Qh3IAHPr4Lkx+ZgiM7j9sdr0Hrepj47lgYwvTw2XHfvkqW8d3zvzhU4HWRSAR98fj3aJHYBDtW70GxqbjUNdtSdmHe54uUKW0Dbu+NWo3jERRkNVc1igI5F4or9VcBIep0QjvEmgEUufg1Q0wAK94EhHZU61RERERERETkw+q3rIN6Lerg6C7780Jl6Tk6UbUz+buUGWmqxNm1eg8yTpwvVfgjCrTGv3IjvntBwsbFW+2OFxsfg/s/uMNvC4m8bf6XfzlU4HWpX/43B3vW7cfeDQfLbOjdlbYXi79bhhbdm2HAbb3QtHNjBAc183kRyqR6p4kJXvq+8MoUL9MCF4OYANNfQJj7GrKJiCi4sciLiALKyQOnlDd3Z4+fgynfDH2YHlVqxKDL0A5o0LIuEETDUEINIRh8Z3/M/mCe0zF6X98dMdXYcSIUmYpxaLs6q9PysvKVz1WRtLtSZJUIPPz5vVj03TKsnJWmdJGVR1ybPDpJKR4Sv9/uJAq9hMPHS7rAAqXYa8/6A9iy1NHR2/8yF5iV9Y6VFYOtnb8RG//aivEv34T2/Voj4EkGMeNdnVgh7QFtI8D0q/gVd/DejpDCJ8AbZNPikrZSl+MshMQiLyIiIiIiCmBZZ7KR+vt6ZbJ5YV6h0hQXWSUSHa5qg5aJTSFpgiihB2DEvQPx6UNTlGnwzmjaOQHNuySofi5/tWfdAVXiiN+PfRsOllmUJT5n73jlZjTp0BhLfk7B2WMZ5cbRG/XoOrSj0gAqcnvkuOyMXCz8xvnVgmJ156Yl2yr9/d65erfyumbSEAwc2ycIvrdgUC+Urg4Q2hMomAXgvGP3autAinwakNyb7y5T0VpAznQ5jGz6E5JxpNidq8qxiIiILsUiLyLyfzKUN2XLflmF/ZsOlXnJsl9XoW7zOuh9XRK6De8YNCOw+9+SjNOHzyiToxzVpmcLXPvQULecyx8V5BSoGi8/u/zOKFGwNXzCAAy+oy+2LN2BtPkbcf7keZgLimAI16NKrVgkDuuEtn1aQhfi2f8rD7SpXikz1JnOZg+L2YIvn/oRd//vVrTve3mhV7G5GBsWb8Wa+Rtx7sLvtT4sFFVrxqLb8E7oNKAtQvReSGw4SxMHWLPViVW8quQlxSqT14Ai++7TD4AUfjcgeeGvu+Kc5r/UiVW8HrCeB7Ts7CUiIiIiosByYPNh/D01BVuX74Rss5X6eOrv61C1VhUkj05ErzGJSjNnMGjZvRnGPH41pr/9m8P31mxYA3e/eWsQFKPYL1/FnF5+VvmTxkUxYq/rEpE8upvSVLhqzhqkHzwDU54JIXodouOi0GlAO6UZ2V3T+IPF6jlrYbNaPfa83z5ZAKvFiiF3XXXZj9tsNuxctRerfluL9IOnld9r3YXf6w5XtUXS1Z0QHhUGv6GtBlhUimXZXfJSJvQ7MKVf1wZS5BOAxjsFkLLpb5UCnQWKtwKh7dWJR0REdAkWeRGRX7MUW/Dz67ORNnd9pdce230cP748XZnaM/61m6E3hiLgScDNz1wLY4QBf/+0wu7bugzpgFufGwONNjiK4ezt8FLT0d0nlGTP8T0nUZBrglanQWRsBNr2aoke13ZFbI0YpYCr08B2ysuXqFHopRQ1LdqCzUu3I+dcLorMFoRFGJR1hj1GdUXd5iWTw9zdKbx52U54lCxjyn9+xtM/PoT4htWVSWALvl6CVXPWoiD78qRjXiZw7sR57F1/ADPfm4ce13TFkLv6+UVSW9L3hlygTqfsP+zqojMA+j6QDIMAXX14dV2lCl1//7CdYpEXEREREREFDhlY9P0y/PZx5SuxRCPUnI/+wLoFm3DfB+MRUz0awaDPDd2VJsCpr80qswCuLA3bNsDEd8ciLMro9vP5FRVzellnc/Dza7Owb+NBFFxo4AyLCUPTTo2VQsRaCfFKsVfzrgnKK9BcLGpas2ADMtOzYLrQkBpXp4rSkNqsS4LbJ+/ZrDasnLUGnjbv80Wo3aQm2vZuqfw6LJu2Gkt/Xonzp0rnfzJPZeHw9qOYN3khOg/qgOH3DvCLr11SaG/IZpWKnP5hT3GXFgjtBskwBNC1BCQvVqlaj6sYS2zEYJEXERGpj0VeROS3ZJuMb5//BZv+2urQfdtW7sKnD32DBz6+SxmlHejEG+trHx6GNsktsPSXVdi6bEe5BUstEpui13VJaJss3kx5/Kg+LSxS3QTZ75+UTmSKYqcT+9OxcMoSJWEwYuIg1GxUA77I2fWNYlXlom+XKd24BTmFZXbxpsxMQ4PW9XDVLcno2L+N297Y71i9F7LVvkSp2hO9/v4pBcPvHYjJD0/Bsd0lv4YVEQVgi79fht1r92Hi++MRHRcJn6bvCxT85Ph6RZdEAZHPQAptCq+T1Z38B5ud3Y5ERERERER+4I+v/sL8L8SKe/uJfMm7d03GE9/eHzQr7rpf0wUNWtfFsmmrsG7hZhSZyp5sLRrlel/XHV2GtPf4xHd/EB4dhoLc8ifqO2LptJWlfiw3K0/ZpJAyMxUJ7Rti6D39lWKnQGIpsmDptFVYMT21zKKmQ9uOKIWY1erGoc/13ZE8JhFandYtZzm25ySyzqo0Pd5BC7/5Gy0SmygNnFuW7aj0+uIiC1LnrsPO1D2474M7UKdpTfi0kFaApg5gO+7JhwIR9ykNoz5BNG76an6QiIjoAklWezRJkDh+/Djq1q2r/PvSlA2Ir1nL20ciCjrzPl+MBV85vw4r6eouyrSqYJN5Ogtr/9iMjBPnYCowQW/Uo0qNGHQe3B7V68V5+3g+7Y3bPrSrIEcthjCDstqvebcm8GViqpc9hV6nj5zFJw9+o0ynslfv67tjzGMj3DJVbuE3SzH304XwBp0hBFXjY5UkoKNqJsTjsS/vhVHlwkO1yXmfAeZFHn6qEVL0S4CuMbzKlgM5c5xq4aTIF4DQtqrFIyIi/5N+Ih09mnVX/v3YsWOoU6eOt49E5LeY0yPyrs1LtuPLp35w+n7RFPb41/e5fVqQrynMNWHtgk04uf8UCvMKlZVwUbGRaH9VazRoWZfNmhX44aXpdm2BUIskSbjhyZFKoVOgrLv8/LHvlMZMe7VMaoY737jFLWspt6/cjcmPTIG3JHRoiP2bDjl8X3h0OB7/5j6P5d9FvtapDQymBZDzv4RnaSBFPALoe8Db5PN3qjadXwobBxivViUWERH5p3Q35fPY1kFEfsmUb8KSn1JciiHe3A+9qz+q1IxBMBFrAAeN7+PtY/il5NFJmPrqDI89TxThTX7kWzw4+W40btcAvurS9Y1CWQmEcycz8f6Ez5GTketQ7OW/robVYsNNT49UfaKXzWKFt1hMxU4VeAnp+0/hp1dm4K43b4Mvk8JugVy8DbCle/CphZBzXoUU/RagdW6VqCqk8JJORBSrE08bq04cIiIiIiIib5KB+V86NsHrSmIF2s60vWjVvRmCiTHSgN7XJ3n7GH4peXSiR4u8xFyFaW/OVjZIJF3dGf7MXGDGR5O+crjpVUyu+uyRb3H/R3eqvknD6sV8nuBMgZeQn52Pzx77Dv+Z9ohbmllVox8AmNcCli0efKgNct4HkDRxQIiXv7ZrqgBWdYq8oGE+j4iI3MOH/yZBRFQ+MYnKXGh2+Q33ytlpqp2JAl/nQe1gjDB49JmWYgu+ePx7pWPTl4lCr39XOJYUe11ks9rw2aPfOlzgddHKWWlYOXst3JEg9Veb/t6OjCt+nX2OJhJS1HOAprpnnytnQS6cCa+StEBoSXeGy7T1S0blExERERER+bkDWw4rk6hclTI9VZXzUHAQk87qNvf8++qfXp2J43s92fimvp9eneX0VoN9Gw9ixnvzVD9TmI9Ptq+IaPjclrLLY88TOdor87SVknSQIp8EdM3hWRbIBd/B2yR9T5UiGYAQ/y7yJCIi38UiLyLySytmqJPMWT17nVJEQ2QPvTEU/W/r7fHn5mXlI22e5zoOXVFWodf2lN0uJ3EXfbdMKRZTU91mJWf1Vykz/KBIVRsPKep1QNfGs881LwNshfAmyTBEpTiDVZ9iR0RERERE5M/5PLGuTUwMJ7KLBAy7u7/HHyvbbFg2bRX8lWgu3LBos0sxVs9Zi9zzeVBTzUbVodFqEexfB11pyK2Uxggp6gVA3xceZdkNWJyblKYafb8L0/ldjdNb+XUkIiJyBxZ5EZHfyc8pQPpB17v+hNysPJw5kqFKLAoOg8b1RedB7b2SAJBtMvzBxSTCxW4xNZIX506cx87UvVBTQocGiG/o4SlTKlo9d73XR9TbRRsLKfpFSNHvlIx8h94DDzUBRcvgVbomgLahi0EMQGgvlQ5ERERERETkXfs3qvPNexkyDm45okosCg5terXANZPUacZyxPo/Nym5bH+UMtP15kKRt1r9m7qNqxGxEejQrzX81e41+zw6nd/pQi8pFFLEA5BiPgMM1wJSFDxBNi2EV2kiARWmeSlNm0RERG6i7jJsIiIPKMhW942xv77RJu+QNBLGvngDQg2hWP2b+isEy3PmaIYy5rxp58bwFyKJsOvETuzYcVSVqvKVM9PQuqeTo8JlGXs3HMSKGWnYv+kgCrILleFIulCdX38tPJ+eiWp14+AXdA0hRUwEwsZBNv0FFE5x6+Nk8zrVpmk5/nArUCS+PrjWWSpF3M2uPyIiIiIiChhq5uCYzyNHDRzbB9oQLWa9r/4KwfIUF1mwdv5G9L1JrRVwnmEpsmD17+oUZ6XMSsWgcX2UiWrOOLHvFFJmpGL7qt3Iy8yDxWKDISwU/kys8YyrU9WjOdp0y4l/Cr0aOPJsbXVI4bcCYTdALtoO5L0MtypaB2AivEKWActOwObi9DnDNYCuvlqnIiIiKsV/v7NJRETkJRqtBrc8OxqtejTDsl9WY9+GA+VeqwvRqbYSVCQA/KnIS8jfXqT80xZpgCbX5FKsQ9uOOnXfhkVbMP+Lv3D68JlSH7MU+8EkrAoUuPhr6hVi5Ls2Bm6fSydnu/sJZTxTBkx/QC6cBciurQ6RjLd5fiw+ERERERERUaCSgKtuSUaD1nWxdOpKbF62Q1mpWJYQfQiKzcWqPPb4vnT4m7PHz6FApULKzFNZyD6Xi+i4SIfuO7D5MOZ8vAAHtxwu9bHCPD/Mh12iILfQ48+8ONHrYrGXQ4VeghQCSRfngXxeTkl+TXTnepJ5DeTCnwDrcdfihPaCFHa7WqciIiIqE4u8iMjvhEeHqxwvTNV4FCQkoH3f1sor/eBppM1dryRACvPM0BtDEFM9Bl2GtMeXT/6A3PMudv94MQHgqoIcE4r3l/x7SIJB+aezxV754ufvyJt8WcbcyYuw8JslCFS6ENcmRXmNFOGBh6iTjLWbbIWcPxkwu/r5pocUfg9gYIEXEREREREFlojocGSeyVIpFvN55JzG7Roor6wz2Uj9fT1O7EtXcm5i2ntklQi069MKy39Zhd1rLyS0XFSQ44/5PHXPLArGHCnyWrdgM3546Vdl3WMgEhPlvOXSqV4OF3rBE/k8UXhp9ey3rwvnQC743sUgkrLWUgq72fMFakREFHRY5EVEficsyojaTWoqb8BdFRUXhRr1q6lyLgpeNRvVwKiHhpX5MTXXAYqpYJcyF5hxcv8ppfhJI0kIjwlH7Sbxpa7zJo323ze1otgrJMH5qV5arcahN8kLv1ka0AVeQkSsJ5IrbqCtFyCFZBfIMuT8L1wr8NLUgmQYVDK9S+Onv69EREREREQVaNK5Edb+sdHlOJIkoXGHBqqciYJXTPVoDLnrqjI/tnr2WtWeowu9vKBHTPwX+by8rALYbDaERxpRKyEe+jA9fIVGo26RilZnf1HTlmU78N3z0yC7f2aU10TGqNvE7uxUr8PHTyj/tLvYSxMNSDGArE6xbtkMgOTB3LZpgWsFXuLXQz8AkmEAoI1T82RERETl8p3vAhMROaDXmCT8/Posl+P0HNXNoTeZRI6KjI1QxpKrE6skASASQSump2LNHxtRZCoq9bweI7ui57XdEBsfA2+LuCJp4Uqh15WxKrJvw0HMnfwnfJFGp4HNUvY6AEfUb1XH4VH3PkNbFQjpAhSvc98zdA3hMUUrAfNiFwJogchnAF0tFQ9FRERERETke/k8NYq82vZuidga3s95UOBSs6kuMqYklsgPrpy1BqvmrEVu5uVT/0MNoeg2tCN6XZekFHx5m2gkVTeefZP3xHS1b5/zzQIvUVwqiw0DLjJGGJDQsRF8gcNTvSQNoO8PmGa471A6DxbwWg5Dzv/KtRjhd0PSJ6l1IiIiIrto7LuMiMi3dBncHobwktVvzpI0GvQY2UW1MxGVpV3vVqrEEZ+vjTs0xGePfYdXb3oPKbPSShV4CSJJtHDKEjx39RuY/vbvsFldLyZyRULHhqUmi11c3+ioFolN7L7276kp8EUiaTdobF/VkuP+TJla5c74+gHwFNk018UIVsDsm0WJREREREREamnYuh7qNiuZIBPM74fJ94mVjWpp3aslZrwzV8nViZzdlQVegsjxiVyfyPmJ3J8pz/EJ+GqqVqcqqtVRZypRvRZ1EB5lX5GXKIIrK9/pbRIkDJugTp4pcUQXhBpC4Cv+nep1TnlVRplYJVYT+mm+8FKy6Q/xv64FMS1Q6zhERER2Y5EXEfklMb56oIuFEsmjuyljuYncqfvILtBoXZ8W16pHM3z99I/YtmKnXdeLzrJlv6zCF49/r4yB9xYxfavTwHaqxOp9fXe7rjufnontKbvgayKrRuDhLyZg0B19lbWzrhD3q/Xr6jUhHdy3tlHX3HOdf5Z9gMXJysVLmf4GbN5N4hIREREREbmVBAyfMNClEAkdGqJZlwTVjkRUllY9m6kyIb9a3Tgs/2Ullk5bafcUKJH7e+fuycg9X7oYzFMkjYTkMYmqxOp9nX1FmSJ/Kaac+ZqQUB3uevNWDLnzKjRo7XoeS3xPwteIQq9Li70qpK0GhPZ000kigVD78r8us+UB5hWux7FsB6zH1DgRERGR3VjkRUR+a9C4Pug2rJNT97ZIbIoxj45Q/UxEV4qqGokO/Vq7HCfj2DllTaOjtq3chamvznK5KcnbHbYiiVK3uX3dvqm/r4ds8+xPOCy6/I7EmPgYjJg4CP/55VHUb1kHIfoQjHxwmEvPG/XgMCWOX5MkSJFPlSRw1A5tGAVPkUVxlioKgOJUlWIRERERERH5ptbJzTHqoeFO3VujfjXc89btSgEKkTtpNBr0HOV6kZMx3IDtK3c7fJ/IAYqJXsXmYnhL4ohOSoGTK8Ii7W9SFL9OOedy4UlhFUwYM0YY0e+mZCWf1/5Cbvfah4dBq3O+mbfP9T2Ur2O+yt5CLyl8AqCtr/rzJeNwQPJQvrNIbIFQZ2qcbPpLlThERET2cu1vaERE3iQBtz4/BoYwPZZPX233bR0HtMXYF25w6Q0ZkSOG3zsQO1P3ojCv0Kn7azaKR/pBxwu8LlozfwM6D2yHlt2bwRsatKqLDv3aYNOSbU7dL2k1uHqS/aO6Tx5w/tfKWVfd3At1m9fC3nX7kZ9doNTUiWlbTTo0UhLYGu3ldfViVez5k+ex8JslDj9r8B39lAlxAUFbE1L0C5BzXgHkTHViGkYDeg/++liPqhZKthyHpFctHBERERERkU/qf2uyUjwy/e3f7J5uJJqmJr43HuEVNFkRqanPDUlY+8cGnD5y1qn7q9SMxdHdx51+/uHtR7F02ioMHNsH3iBWLA4c1xfzv1jsdIxh9w60u0nx5D7P5/Oad0vAVbf0wtblO5CXmQ9LsRXGCAPqNquFjgPalVqr2LhdA9z+wvX49rlpdn/tunQF6OhHnStw9XShV7rlxD+FXg3qVC19kSYMUuTzkHNfAayH1HlwSBfAOBqeIlud/7NZikXFWERERHZgkRcR+X1X1fVPXIPWyS2U1XQ7V+2BXM7IoiadGivjodv3bR0wHX9ZZ7KRdSYH5kIzDOEGxNWuwmSXD6peLw4T3rkdnz40BUUmxzqEGratr/w+u2rF9FSvFXmJgszbX7xB+Xkc2u54QczNT1/r0CqGwjzPr7wLjzYoKzXFy14j7hukrLOc+cF8yFabXcVu1z44FP1uSUZA0TWEFP0/yAU/AEWiYNeF9aKGUZDCboZHyYUqxspXLxYREREREZEP6319Ehq1racUsWxYtEVZ1VaWmo3j0XtMEpKu7gydi1OFfEVeVj7OncyEKd8EvVGPmOpRiKke7e1j0RVErvW+D+/Ae3d9hqyzjuXmqsTHolqdqjif7lpD28qZaeh/Wy8lB+4NQ+/qj4wT55UGUkf1uaEH+lzX3afzeWERYUpzqnjZq/Og9jCEGfDNs1OVnLw9xFS4G566plQTqK9P9LpY7FVmoZc2FlLUK5ALpwHKlPsC5x8Y0hVS5CNiTyg8xqZmDo75PCIi8qzAeFdERMFNAlomNVVeJW86NyLjxDmYC8wINYYitkYMug7pgJqNaiAQiKTX5qU7kDI9Ffs3X94pI2k0aN+nFZLHJKJZ5wTl14Z8Q5OOjfDw5xPw2aPf2j16XEy/EomDL5/6weXni5HnIoFYtVYsvEF0vj3wyV1KAsTeMfW6EC1u++/16Dy4vUPPcnWUvDPqNq/j1H19b+6pTPpKmbkGqb+vQ0FO6YIhMREs6eouSB7dDdXqxiEgaatCinwYsN2hJIZkMTLddl7MOxdZl8oLv7QNIBmvBfQ94XFqjpHnGC8iIiIiIgoidZvXVqbiiBVoIp8nJnMX5hZCFxqCqCoRaN+vDRLaNwiI/JZsk7Fn3X6smJGKrct3lpoCJJpTe41JQrs+Lbl9wIfE1aqCx6fch8mPfIsT+9Ltuqdeizq44amReHvcJy4//1x6Jnau3ovWPZvDm5s0xFrDpT+L9Xb2GXr3AAy7u79Df3Z1em/k82o5dZ/I5b0450ms/m09UmalIvNUVqlrdCE6JaeZPDrRoSIyX53qVfZELyOk8PGA8SZl/aFsXgpYT11oiBT5vErWjUpxkIzDAMMIzxZ4Kc8OVTGYmrGIiIgqxyIvIgooYpLVsHv6I1CJ4pifXplRbpGQbLMpK/HES3Q63vHqTajVON7j56TyVwv8d9YTWPfHJiyfkYr0MtYKarRadOjXWinUE6v+pjz3syrPFhPuRGfswHHeGfEu6MP0uPedcdi6YieWrlqGo6l7y7zuYlFTr+uSlD/TjoqsGglPqt20Jhq0cq7ISxCFWyKhPWLiQGxL2a2scTQVmJVVtFVqVUGb5OZ2j7b3e5ooIExM4xp1+Y9bT0M2LQKKNwK2HPEDgBQB6JpAMgwGdE0ByUtZf0m9wklJilEtFhERERERkb8QU66vCrSp1Zc4vjcd3/7nZ6QfOl3uNfs2HFBe0XFRuPW5Md6bxk6liAbip75/AFuW7VSK9MTvU1mad01A8pgktO3VEn/9uKLcbROOWrdwk/eKvC5s0hjz6HB0uKq1silg09/bYLVYy2y67DSovVKsKHKgjor2cD5PTNFztLH0UpFVIjBofB8MGNsLu9P24dThsyjILUSoPgRRVSPQplfLgNi4cXGq1+HjJ5R/ll3sZQAMAyAZBlz+4yKHZ14CWUzut2aVNHNqIgBtXUj6AUBoR88Xd7khnweNd5qqiYgoeLHIi4jIT6T+vl4p8Lqy0688ooDo3bsmY+L749G4XQO3n4/sIwp3RAGX6OI6uO0Iju0+qXSpakO0SlJTrPuLuiSpkXXa9VWN/8RSYe2jq8Sq1HZ9WqF6zxily+3s9qPIOZeHYrMFxkgDaifEo32/1i4VNYmVrKm/rYOniOSVGgVG4ufcsX8bVc4UcLQ1IIXfBkC8fIuk7wG5WKXPN32SOnGIiIiIiIjIJ+zbeBCfPfIdTAX2raLLzsjBp498i9uevw7dhnV0+/nIPmK6msjZiNepg6exf/Nh5GeXTGMPjzaiSadGqFG/mnvyeSrGcoXIL4vXmEdHKI2k509lwVxQBEN4KKrWqopOA9u6VNTUtncrzHh3rt25b1d1HdZRydOqUQQnijIDvTDz4lQvh5s5jSMhGUfC10j6JMim6erECrV/LSkREZEaWORFROQHtq3Y5VCB10WFeSZ89si3eOybSYhv8G+igXyABDRqW195VcRsKlLtkUWmSkZkq0EG9qzfryR7RGKyyGSBMUKPGvWrI+nqzqheL+7fLrB4IDY+puwOMBeI1a1Va1fBuRPn4W5RcVHo4kLXHwWAUFGY9TUA+9awlkvXAdBy8iIREREREVGgSD94Gp8/Zn+B16WT+n94aToiYsPRKsALR/xRfKMaystTOTg1c4MVOb73JNLmbUTGiXMwF5ihN4YqebtuQzuVrBuU/p1g1efGHqo/v0rNGLROboFtK3bC3XQ6Hfq64edAfkTXANA1Byy7XYsjVQVCO6t1KiIiIruwyIuIyMcVm4uVxI6zXUxiTPS012fh4c8nqH42cj9DuEHFWK53p5XHUmTBytlrsWL6apw+craMK3Zg0XdL0bxbE/S9qSda92j+TwfY4ePnlCvUKvbSaDXoNToRsz/8A+4UagjFve+OVdZQUhCTQgBDf8A027UwYu0kERERERERBYyfXp2lNGA6Qyn0evFXvDL3aehC+W0cf6NmDk7N3GApMrB+8RYs+2U1Dm09XOYlYkVj3ea10fu67ug2vKMyucqd0/I9UeR124vXXzZ5jYKTZBgCOc+1Ii/JMBCQtKqdiYiIyB5eWnZMRET2EhOR8rPzXR4Nf/LAKdXORJ5Tva56U67iVIx1qbysfLw/8UtMf/u3cgq8/rV7zT5MfngKZr43D7JNVgq9lKlewD/FXmpIvi4JtZvWhLuERRkx6cM7UL9lHbc9g/yHZBwFaGo5HyCkq+e6/mQbULwDMC8HTH8C5hVA8V7AQ+sQiIiIiIiIgsGx3SfKLZqxV+75PGxesl21M5HnVKtbMsne13KDVzZsfvv8NEx5dmqln6vi8/nHl6fji8e/h7nQfZPFWiY2Rfu+bdwWX6PVKqtQOw9s57ZnkB8J7VEyWd9Z2vqAYTg8QuTtLAcBc8qFfN5SoGgrIFs883wiIvIpLPIiIvJxK2akqhQnTZU45FlJI9Qp/NCF6NBlkPprBU15Jnww8QuHE5dLpqbglzfnKB2DgtqFXmKk/H3vj0ecyqsgNTotOg1shye+vR8JHRuqGpv8mCYCUtR/Ska0O0rXAlLkI4B0Ye+Bu1izgYKZkDMnQs55DnLeB5DzP4ec9z7knP+DnPUgUDgfsLlWVExERERERETq5eGWq5QXJM/qPKidkotTQ9LVXaA2m82Gr5+ZinULNzl037aUXZj8yLdKgZhbSMC4l29AQgf1c27Nuybg4c/uQaJKuVYKAJIGUuTjgC7B8Xs11SFFPgtojHArmwkwLYac/Rjk7Mch5713IZ/3EeTcFyBnToCc/zNgVa95moiIfB+LvIiIfNiZoxk4svO4KrHWLdikTE4i/9KwTX3UaerChKALOg1qh/DoMKjtm//8jJP7nZsSlzIr7bKk58WpXqLQS41ir5jq0Xj864lo2La+3fc06dwYE96+HR0HtEX1+nGIqBKBmPgY1G1RByMmDsKr85/GHa/djOr11OvIpAChjYcU/QagbWz/PaHJkKJeACQ3r/w0/QU56x7IhT8BcjnT9mwnIBd8DTnzHsC81r3nISIiIiIiCmA2qw3r/9ysSqyDWw4j4+R5VWKR54gcnMjFuapus9po2Loe1DZ38iJsXb7DqXv3bTiA6W//DncJ0YfggY/vQpfB9k9YEqsXJ7wzFj1HJaJmwxqIqhqJ6Lgo1EqIR7+bkvHfmU/ggU/uRuP2Ddx2bvJTGiOkyJeAkET779E1hxQlcoBuzg8XbbtQxDUZsJbTYC1nAqbpkLPuBQp/46R+IqIgwWXuREQ+7PypLNVimfJNMBeYYYgwqBaTPEAC+t7YAz+8NN2lMH2u7w61iQLEHat2uxRjwTd/o8eoLtDqtP/8mCj0SrecUAq9Grg4iSuyaiQe+2oidq/dr0zF27ZiZ6liRzGdq12fVug9JglNOjVUJiq17dPKpedSkNJWhRT9P6B4M2TTQqB4vci2XHGRAdAnQzIMBnQemAZXMAty4Y8O3FAIOe8NSPIDgKGvGw9GREREREQUmApyClBkUm+lXdapbMTVqqJaPPIMkYtbM2+DSzF6i3yeyoO/C3IKsfTnlS7FWDVnLYbcdZXSYOkOulAdxr18I/rd3BMrpqdh/Z+bUFzG9LCmnRPQ+7oktOnVQskttu3V0i3noQCnMUCKehKw7IOsrEJMAVB85UVASLeSfF5Ia/dP5DevhZz3tlisaucNVsgF3wG2TEhhY91/PiIi8ioWeRER+TBRlKUmE4u8/FK3YZ2wM20fNixyrgv06vuGoF6LOj65SjQnIwdbl+9Eh6vaXPbjahZ6SRoJLRKbKK/MU5k4sOWoknAV73XDo8PRuENDRMdFuvgzIb9hywFsZwBbISAZAE1VQKtislx8YoV2gBTaAbL1LGBOBWynANkCaCIBXTtIoW08k2wxL3OwwOtfcv4nkDSxQKj6a16JiIiIiIgCmamwSOV46uYHyTNELm7ExMGYO3mhU/d3GtgeicM7qX4uUXhWbL6ygMUxsixj5aw1GH7vQLj71/DW58dg1MNDsW/9QeRl5cNisSI8Mgz1WtZWJnhRkBB5PJFfs+UBUgigiQE0NdTNr+maQIpoAoSNhWxOA6xHxFdgQAovmd4V2rnk2e5WvA9y3jsOFHhdwvR7Sa7TOMIdJyMiIh/BIi8iIh+mD1N3hZch3M0rwcgtRJHS7f+9TknAODpKfcDtfTBoXB/VzyS6/jaotHpAFItdWeR1sdBLOHz8hPJPV4u9hNj4WHSOj3U5DvkZMaq8eAtk04Kyp2vpWkMyDAFCuwCSCn89tpmAohRATPOyHrrig7Mha2qWdP7p+wKaCLiFbIac97ULAWyQ87+AFPIJu/+IiIiIiIgcYFA7nxfGhk1/NXh8X2W7wuLvlzl0X9verZRcoMgJqkoGVsx0vWlTWDl7jTLN69Lp/O4SHhWG9v1au/05VDk1GnIdYjlYks9TpmtdUUCrrV+SXwvtpaxddJlsBYrWlUzzsmy54oNzIUvRgL4/JMNAQOu+AkO54MsyJok5cv8PkPS9AU2UquciIiLfwSIvIiIfVk3FN0wRMeEBkxQS6/bMpiKEGkKg0WgQDMSY8rv/dyv++PwvLJ22CqYCU4XXR8VFYcS9A9H9mi5uOc/RXcfLHJPujAObD5fU3JSTt1JzqhcFIcshyLnvAbbjFVyzHXLedkCqAiniftemVxVthpz7LoC88q+xpUMumAIUTIUUcU9JsZfalORXvmsxRIdk8WZlMhkRERERERHZJyzKCGOEEYV5harEi6sdIM1qMmAuNCs5Lk8UBvkECRj5wBBl4tTvk/9UJtpXRORu+97UA0Pv6e+WnGduZh7OHM1QJ9b5PJw9moH4RjVUiUe+zx0NueWyZkLOe0/J2ZV/zRHI+Z8D+d9BCh8HiOIrp593DHLOG0rOrlxyNmCaCdk0CzCMgRR2o/qNkZZ9gGW/q0EA099A2CiVDkVERL6GRV5ERD6saq1YNOnUGPs2HHA5ljLe24+HsYjEQerv67H693XIOH5OGQt+sZip6+D2SB6diLgALwASyZ3hEwei/9jeWLdgE1JmpOHE/n/feEqQkNCxIXpd1x3t+rQslTDLzy5AbmY+bFYrwiKNiI6LcrojUMRSi9ViVVYPVNTpemmhl8BiL7JL0TbIua+XjFa3h3wecu4rkCIeBPS9HH+eeSXkvPeVKVh23gA57yNIYoWk8RqoRpZLuhzVCGVaqKyeJCIiIiIiIvvzN92GdcSyX1a5HKt5tyaIqR4Nf2UuLML6hZuVqU/H96YrOSlB5KXa9WmN5DGJqN+yDgJd0tWd0XVoB2xZtlOZaL9/w0HIl0wZr51QU/m16DKkQ6n8mJgElnMuD8VmC4wRBkRXi3S6SC4/R53CQ3fFI//g9oZcazrk7P8Csr0FiSbI+Z8B1rOQwm9x/HmWfZCzX3KgWVIGTNMh2zJKmkVVLPRSpoipEcf8JySRa5SCo0GeiCjYsMiLiMjH9RqTpEqRlyiC8kdiLeCM9+Ziw8ItsFhKT44SHXB//bhCebXs3hzXPz4C1erGIZCJZI/4/RQvkSwrzC2EpNEgPMqodENeSqx43LB4K1JmpOLwjmOXfSy2egx6jOqK7iO7Ijou0qEzSCp3KUkOdItxqhfZxXIEcu4b9hd4/cMGOe9DSFKUYxO9incq99lf4PUvueA7SJoqgD4ZqrCdKWNNpJPEekvZDEhc90tERERERGSv5DFJqhR5ibygPxINffM+X4wV01OVIqUrFeQWInXuOuVVr0UdjH5kBBI6NEAgE4VZHfu3UV6WIovya2Cz2mCMNEJvDL3sWpvNhp2r9mL5jFTsWr3nsoIwUeiVOLyzUhQmJoQ5Qu2hQ/7cUEyucVtDri0Hcs7LDhR4XcI0s2RFoXGE/fdYz0DOec25afhFSyEXxEIKvxWqEE3t5tXq5QYtB4CQJurEIyIin8ISXiIiHycmMoliHFe07tncL6dcnU/Pwtt3foo18zaUWeB1pZ2rd+Ot8Z/i0LajCBYiCSQ6OkWR1pUFXikz0/DM0Nfww4u/lirwEjLPZGHe54vwn+GvY+qrM5WCMHuFRYdBLTqdDnqj3onR4CVJBKKyyPmfAnC2o1QUen0EyMX2T87K+6xkHLqT5LwvSoqp1GDLhHpkJcFGRERERERE9otvUA0tEpu6FKNqzVi0SW4Bf2MuMOPTh77Bom+XllngdaWju47jw/u+wPo/NyNYiBxeVNVIJad3ZYHXztS9eGHk/zD50SlKrvPSAi+hMM+EpdNW4qUxb+PTh6co2w/sJRpE1RQeHa5qPPIvIkerdp5WLvgJsJ1y4f7vlMIt+6//vmQNo7PE6kbrcefvv+wwZieaVStgy1IvFhER+RQWeRER+UGX1/hXb4IuxLnhizHVonHT09fC34h1gB8/8BVOHz7j4H35+OTBb3DqkGP3BRQZmP3BfEx7YzYKcipfqyhG5a+asxYf3PcVTHn2vZFs0KoOQg2XJ6Gc1bRLY4c7/y4mEUQCgcVeVIplX8nLFXImULTGvmuLtwM2VxM6+cq6x0tlZ+Riz7r92Lx0O3as2oPje05Ctl2e3C2TvcVpdlOp+IyIiIiIiCiI3PzMaKWQxxkhoTqMf/VmaLQav5vg9eVTP2L32v0O3/ftc9OwfdVuBLPU39crhVvn0u1r3tqxajfeGvcxzh6zb+pRREwEajaOhxpia8Sgej3/ayom9alW6GXLA8zLXTyNDbJpkX2XWh3I/VXgyueJrRv7Nx7C1mU7sT1ll9KQLqb3VY75PCIisg/XNRIR+YHG7RvgzjduwTdP/4Riu94QlIiOi8Kkj+5QusL8zS9vzsHpI2edurcwrxBfPfUjnp32CCRN8M0NXzhlqbK+0lGHth7GF0/+gPs+GF9pUaEh3ICuQzpi5ew0eHP1wKWjwbm+kS6STX+qFGchJH1Pu65T53kLIIf0VZLhK2akKomgK4u6qtWpip6jE5F0dWeElzdRT6PepL0S7MwlIiIiIiJyVJWaMZj04Z1KE6Mj05ZC9CG4641b0bBNPfibv35Iwa60vU7dK8sypjzzM1787UlExATf+9CtK3bip1dmKL8OjhAFYaLh9fFv7kNEbETFF0tA7zFJmPbmbNcOC6Dntd2g0fhXESL5+PpG81KxA9H1w5j/AsJuAKSQyq+D1fXnmZYAxptxdE+GsqJ23Z+bYTFf/j0c8TWt+8gu6HltIqrWii07jqTupD1Iwfd1lIgoWPBvYEREfqJtr5Z46LMJqNnIvm6r5l0T8MS3k1BLpe4sT8o6k42Nf211KUb6odMOdw0GghP7TmHuZOcLTsTUoGXTVtt1bfKYRLgqNj4GrXo2cykG1zfSZWRLqYlYTrPsBKxnK5+aVbxWlcedPnwUr938Dj554GtsW76zzKldZ4+fUyb1PTP0VSydulJZFVmKJl7FXo4IQON/hcJERERERES+oE7Tmnhiyv1o2rmxXdfXSojHI1/ci9Y9m8PfiGlcy35d5VIMU4EJab+vR7ARay2//+8vDhd4XZormPHePLuu7TK0A/RGPVyh0WrR/ZouLsWgwOPq+kbZ7HjTctmBcoCiyte/ykWufb26KD/HhI8f+BRv3vaRMo3vygIvIS8rH4u+XYbnr3kTv/7vN9isttKBJB2gqQXVaOuoF4uIiHwKJ3kREfkR0cH3n2mPYP+mQ8qUF7HCSyRQLp2u1G1oR/Qak4j4RjXgr1bOWuN0UuNSv32yAC0Sm8CXiNHMGxZvVboaxZs78YYuLMqIBq3rI2lEp/In89hpxXT7CrQqi9Hvlp6VduOJRGWH/m2xyYWCvOETBqrS9fdvAuEEJ3oFO1uuOl1//8TLALTVKvh4jipdf0f36fHxM7VRkGPfigWRMJrx7lylKHbUQ0MB6ZKphZpwILQ7UKRCcswwAJDYF0JEREREROQsMbXlocn34OSBU1gxIw3r/tikFDNdpNVp0eGqNsqk88btGijTlvzR1uU7kZMh3iO7ZuGUJeh3a7JPTYmy2WzYuXovNi/ZjuxzubAUFcMYYVCaa5Ou7lL+ZB47rZm/CYV5/35OOGPj4q0Y/fBwRFapeJqXIUyPgeP6YO5k56eg97m+u9OrSCnwOb15webcVo8yyXbk16znXX5M9jktPnyqDk4fO23nuWQs/3U1zp08j7vfuq3UNg3J0B9ywfcunwu6DhXnM4mIyK+xyIuIyN9IQELHhsqr2FyMvMx8mAuLYAjXK2/iRWLIr8nAqt/WqRLq2O4T+PPbZRg0rg+8LTsjF0unpig/t4KcglIf3/T3Nsz9dCE6DWqH/rf0Ujo3HWXKM2Htgk0un1WMeReJK3u6Rm//7/XIPJWFw9uPOvycAbf3QeLwTk6ekqg8riVFS5Eri+d6Qdm50zpMfq4WCnIc//otVrNGVo1E/9t6XfbjkmEwZBWKvCTDQJdjEBEREREREZSCoBufGonrHhuhrG805ZuhN4Yq+TxdqP9/q2bVHHWmXItip88f/Q4T3xvv9YI3c4EZy6enYuXMNCVfdqUty3Zg4ddLlBxav1uS7Z7YdhkZSJmR6vJZRSPwqjnrMPiOvpVeO3h8P5w+chZr/9jo8HPa9GxR0mxGZGdDrmBXsVelOTgH2OyJ5VpOz2yS8NnztXD6WKjD925fuRs/vTITY1+4/vLGTX0/oGCqaO906WwiL0hERIHLd1ohiIjIYSH6EGXdXXzD6oipHu3/BV4XEjlqdP1dNPeTBdi+aje86cjO43j9lvex+IflZRZ4XWQptmDNvA3KaOcNi7Y4/JyNf29DkUmdCUZp8+wbjR9qCMEDH9+JFolNHYo/4t5BGHn/ECdPR1QRo7rhpMriuTZ9T5jzZRxyM51P6M/5eAEyT2dd/oO6ZoDOxUmGId0Arf9OhSQiIiIiIvJFIn8n8nginyfyeoFQ4CWcOnxGtVgilyfyaN4kJme/c+dk/PbxgjILvC6SIWPbyl34YOIXWPDV30rRliOO7DqO9EN2TgFSKZ8niudu++91SB6T5FD8LkM64K43b4VGy28tkn0cWt8ouZ5j+4fG6PbnLZ0Vg2P7DU7fv3b+RuxM23f5D2qiAH3lhZoV0tQEQtlYTUQUyPg3MSIi8immfHWn8Ii8yqz35jmcYFHL8T0n8cG9XygdmvayWCz45tmpWO9goVfGCTveLNsdq/zk1ZXEmtD73h+P21+8AQ1a1yv3Oo1Wi44D2uKxr+/D4Dv7eb0bkwKUJlLdQi9N9Uo+HgXA+RUFWRlabF5d8SqFyshWG1bNuqJjWpIgRTwGSDHOBdXUhBRxn0vnIiIiIiIiouBhyjOrGm/+54tQkFMIbxB5vHfv/gwn9qc7dN+8zxfht08XOnTPuROur4z7J9bJTLtzoGId5o1PjsSkD+9UJpFJFSTqmnVJwD1v3Y5xL94YMEWJ5J1CrwqLvbSOb7Yol8aOWNo6Toe3WoCV86PhqhVlTPGTwsYB2kZORgyDFPl/gMRv/xMRBTL+bYyIiHxKiF79/2sS48f3rN+vJCQ8SSSiPnl4CsyFziW5fvjvr6hRLw51m5e8Ea6MOV+dKV5KrALHiu1EB1+3oR2Vl1iTuWHRVmRlZKPYZIExwoDq9ePQbVgnRMc5XwxDZBdJCxj6AKYFrsfSdQC0VSp5ngQY+gOm2U49YtWCaMhW1yseV85Zg8F39YMu5JKvodrqkKJegJzzMiA7UASqqQ0p6vkLBXNERERERERElQsxhKAwT72irOIiC9LmbUC/m3vCk2SbjM8f+w7nTjpXfLXo26WonRCPzoPa23W9qUC94jib1apsCrC7EEsCWiY1VV4ZJ89j7byNyEg/r+QY9WGhiK0ejS5DOyK+QTXVzkjBXeiVbjmhFHqVtb5R0veBbFFhI4dUFQhpU/llhgGQ87Y79Yjta8KRlRHi1L2XxUnZhfPpmahSM/bfH9QYIUU+Bzn3FcB6wIFoEZCi/gPo6rp8LiIi8m0s8iIiIp8SFhWmFCmIhISaUmakebzIa9WctS6tnhQTvRZ9vwx3vnaLXdeHhoVCLfowvdP3iqI0ewvTqDSb1Yaty3di64qdyM3Mh81igTHSiLrNaiPp6s6IqsrCm8pI+sGQVSjykgyD7bxuAGQni7w2LFPn9zP3XB72rj+oJGYvo6sHKfoNyAXfAkVpotewgighgL4XpLDbWeBFREREREREDhGNfa7kwcqbctP3xh6QNJ4bB79rzT4c2n7UpRh/fPkXOg9sb9cUe71RvXyepNFc3vzlgLhaVTD0nv6qnSXoyMC+TQex4c8tyqpPs6kYxgg9qtethqRrOqNGfRbKXSz2KrfQKzQZyP8OgGvFopJhYEkTaGVCEwEpCpAd/7q1fmmkakWlGxdvRf/be1/+AW00pKiXIRf+BJj+FuWgFQcK6QIpXEwAq6nKuYiIyLexyIuIiHyKmAjV4ao2WLdwk6pxt6XsKhlX7qGckM1mQ8pMUVDhms1LdiA7I9euCVhVL+34cVGVeCdXvJHTCnMLsXTaKqyavVZJBl1p01/bMO/zxejQrzX63ZKMBq3YlVUu0bGmaw1YnOvG+2dNY2gn+64V4+RDugHFaxx+TFaGen8dzz5bTlJKWxVS5GOA9Txg/guyeTlgyxB90SKjBWhrQNL3A8SLxV1ERERERETkhE4D2inT3dV09lgGTh/N8OgkqbLWp7lzq4CaOTgllufq4Ug06RZbkPrbeiyfnor0g6fKvGbxD8uUz4W+N/ZEm+QWQf97dGmhl/BPsZfGeGFa/lwXoosGRjuLFSVx7WDA9KtX83lZ5eXzNAZI4XcCxpuBomWQTX8B1vQLBV86QFMFCO1ZUtSmra7aeYiIyPdxKS8REfmc5DGJbnnDbXJwBaErdqXtc3qs+5Vj1lfPWWvXtaI4ztluvSt1HdJRlThkf9Lyzds/xvzPF5dZ4HWRzWLFhkVb8Pb4T5CiQtIxkEkRkwAp2sm7QyFFPCZaYB143kRAE+/QU2QZKDKrl9kzF1ayslWsngy7HlLsJ5Cq/gKpynRIVadBivkAMF7DAi8iIiIiIiJympg+rlZe6lJ5mfnwlMxTWcr6NDXY2/zZoHU9VKsTp8ozuw5lPs+TCnIK8fH9X2Pam7PLLfC6aM+6/fjssW8x/e3flebgYCcKvS6ucLxY7CVIxhsBbQOn4yr5Oa39jdBS2OiSRlEHmc3qfXu9qLJ8nlL8NgRSzDuQqk4tyedV+QVS7GeQwm9lgRcRURBikRcREfmcxm0boHYT9UcLW4orWlOmrv2bDqkXa7N9scKjw9BpUDtVVjWeOZaB7Sm7ldWB/ubSxIA/OHcyE+/e/ZlS6OXIKO9pb8zBsmmr3Ho2vyamU0U970Shlx5S5JNASBPHbtNElTxPY//XLkkCDGEOHq8CxnCDYzfYM7qeiIiIiIiIyA4RMeHoOKCtWxo3PeXg1iOQRUeWCvZvtC+fJ1ZRqtXwarVYsf7PzTAXmFWJR+UTv8YfTvoS+zYedOi+Zb+uwtRXZ5VsnKB/Cr3+oTFCinwO0NZ3OJYUdieg7+PgTSGQIv/P4UIvQ5h6v4GGCCfyeSKpSEREQYvrGomIvCDjxHmsnJmG3esOoCA7X5nmEhZlREL7hkge3Q3xjWogqEnATf83Cu9N+FxJTqglLNIITynILlQtVr4DsXpf1x1r5m1wOUnx28cLlH+PjotCz1Hd0H1UV8RUi4I/jfv+Z9S3D7MUWTD54SnIych16v7p78xFfIPqaJ7oYEFSsNA1hBT9BuS8jwHLjsqv1zaAFHEfoKt8nULZ98dDin4dcv43QNFq8Ttc8fUhXVC9ngFHd1Xc7Wmv6vXV6fwlIiIiIiKi0vIy87D69/XYunyn8u+WIisMkQbUaVoTydcmonG7BkG/hu2aSYOxK20vcs/nqRYzPMqD+bwcFfN5IpaoA7HjcyJpRGfM+2wRikyVTPSpxKJvlyr/NIQbkDisk1I8Ft+QU37c4fsXpju9njT193Wo1Tge/W7uqfq5AoI2FlLUq5DzPweKVop214qvl+JK1hrquzn3PE0YpKjnIBf8DJgWXliHWAFdE9Ro2BQHt++FGqrXZT6PiIgcwyIvIiIPOrz9GP746i/sXLUH8hVvTs6fysTxvSeVbp4mnRpj8B390Lyrk4UGAaBh2/q46elr8ePL01WJJyaDabSeG2CpZjONxoFj129ZBwNu64PFPyxT5dnZGTmY/+ViLPp+Gca+eIOyEtLX/TvquyTR4svFXhv/2ob0g6edDyDLWPD13yzyqmyiV/TLgOUwZNOfgHn5FckaHRCaBMkwGNA1d/0Pr5joFfkwYB0HmP+CbF4C2MTv8YWv+VJVQN8LkmGgcrbu16Th6K7Zrn/eN6qBhq3ruhyHiIiIiIiISjdrzv9iMTYu2gqL5YpmnjNA+oFTWLdgE2olxKP/rb3RTazMC9Jir5jq0bj/wzvxxm0fqjIRK9QQiur1PFgAoWY+z4H8gmj+veXZ0Zjy3M+qPNuUb1JyzMt/XY3hEwdh8Pi+Qfs56Q4n9p3C5qXbXIqxaMpS9BqTCF0ov01bbuFV5COA9VbIpsVKjg1y1uXX6NqX5PNCO7k+rV5M9Aq/HTBeBxSllDzTeljMx7twQQSgT7yQP2yE7iOPIHXuXlW+xnUaqP4ERCIiCmz82wMRkYesW7AZP7z0q12TqfZtOID9Gw5izONXo88N3RGskq7ujDV/bMC+DY6NvS5L8mh1xp7bS6xOVEtYlGOxrrl/MPJzCrD6t7WqnaHYXIyv/+8n3PLcGOX3xR/4w1SvFTNSVVkNenJ/OmolqL/iNKDoxJSuCUD4HYAtR/Tnit5WQBOjJHJUp40BwsZAChujFONBNgGSXuxhuOyyLkM6YM5Hf8CU79oqheQxSZcXqNlyAVlMiBMrVyOV4jOOciciIiIiInJ8fd/kR75FQY54D1mxk/tP4fsXfsGhbUdx/ZNXQ+NI114AqdOsFvrc2BNLf05xOZYomNOH6eEp4dHhqsUKizY6VFjVeXB75GbmYca7c1U7g2gynjt5IfKz8zH6keGqxQ12KSrk83Kz8rB5yXbl950qoK0GKfxmIOwmwCaKvPLFaHxAilJWO6pOxDQMLGnOVPJ5ZkDSlbwu0ahtPdRuWhMn9qa79Lgug9vDeOn2EZuYAJgtsvHiK9KFvGVw/n8JERGVj//PQETkoWk93z7/s0OrB8Wb8Olv/4aUGWkIZsPuGeByDEOYQSmk8KSmXRqrFqtZF8cmukkaSen+u2bSEKUbSC3ic/KnV2di99r98Bf/TvU6p7x8yfG96Ti09YgqsVbMWKNKnKAgCrq0VQFtXSVR5JYCr1LPlEqSRGUkZQzheiRd3cWl8CIZ1G1Yh5LEk+kvyFmPQ84cCznrfshZD0LOGg85axJQ+FtJ8RcRERERERFV6viek/j4/q/tKvC6VMrMVPzyxqTBj74AAIl1SURBVG+VbhgLZIPG9VFlor7S0ORBCR0aQKN1cSLQBc2c2NDQ96aeuPP1WxEZEwE1LZmagmW/rFY1ZrAyFZix5o+NqsRarkKxWNAQuTVtLKCto0zGd0uBV1nP1BhKFXhd/FjfG11ctylJ6C0a/GUrYF4DOftFyJm3QM66D3LWQ5Cz7oKceQfk/B8A61nXnkVERAGFRV5ERG525mgGvnt+mtP3//K/Ocqax2DVpEMjNGhdz6UYyWMSYfBg15/QrHMCatSv5nIcXYjOuclZEjBwXB+89sezuO6xq1U5iyDbbJj13jy/SlSKQq9Li718hZjA5YuxgoblKOT8LyFnPwk58z7ImQ9Azn4WKJgJWEXH3BVEcZR5HWBeCpiWlvy79Yox8U4acd8g1GtZx6l7Ja0Gd7x2EwyaxZDP3wU5/1PAWsb0Q9spyAXfQc4U10wB5CtWjBAREREREdE/zIVFygQvc6FzU5dXzk5D6tz1CFaRVSLQ3cWGppZJzVC7STw8KapqJNr3a6VKrF5OFqh17N8Gr8x/GuNeugkN29SHWuZ++qdSoESuOb77JIpMRarEOrTlCGxWMYGd7GY9Bzn/Z8jZz0DOvB9y5iTI2U9Bzv8WsJYxVUs0RBZtBszLlcZImFMB6ylVjpI4vJNLk9hGPzwMtesdg5w5EXLem4BlS+mL5BzANBty1gTIuW8DNjHJjIiIgh3XNRIRudnSaSthKXb+m+myLOPvqStw52u3IChJwN1v3oq3x3+KzDOOF1S0SGyKERMHwuOkkmTO9Hd+dylMp4HtEBHj/Kh4Y6QBfW7sgT439EDGiXOY/+XfWPvHBpfOdGJ/Og5uO4JGbdVLNAXj+kZHO4Erkp+tXix/kJ2Ri12pe5B7Pl+ZkCgmWdVrURsNW9etfCVh0UbIhTMBy67SH7OdgCx+vPAXIDQJMI6BJJsgmxYARStFZdgVN+iA0ERIhsGAroXT6xD1xlDc9/54fPLgNzi2+4Td9+lCtLj9xevQos1SyAWL7LyrGDDNhWw5DinqKUBSb9ofERERERFRoFi/cDOyzpbRAOSAxd8vQ9KIzg6t7AskYx4bgRP7T+HQNsenmFerG4dxL98IbxD5vI2Lt7oUo3aTmmjkQoGWLlSHLkPaK6+sM9lIm7cBcyf/6dKZTAUmrFuwCcmjE12KE+zyVcznia0JBbmFLuV+/Ykp34Ttq/Yg60wOik1FMEYYUL1+NcR0smMql+UQ5IJfgeJ1IoF3+cfEf1r2QTb9DujaQwobA2hiIZsWljRqIq90PF3bknxeaBfRQenUz0ds07jt+etQbLZgy9LtDt079O7+6HdtDuS8r+2/qWg1ZOsxSJHPl2wpICKioMUiLyIiNxLdUWvnb3I5zuYlO5Sihui4SASjmOrReOizu5UCiLMOTGJq3bM57nj1Zmh16oxZd1Ti1Z2xdNoqpbjKGWLV4sCxfdQ5jFTy67hz9W5Vwq2Ykep3RV7CvxO9SgppvFnsJTlZEFR2LAQ+Wca+jYeUz73NS3fAVsb629pNayrJ2C6D20N/5fQ+WQYKZ0IunGrHwyxAUQpQtArylYmjUtethCwKwHStIUU+AWgine5yfuSLCZj+zlys+2MDLMUVd3LWamTG9ZMKkNB+DmDe5vgDLZsg575XcuYy1kgSEREREREFLbkk7+Gq00fOYs/6/WjWxfG1fYEgRB+iNDR9/vh3Dk0gr5UQj0kf3IHw6DB4a6tA864J2L12v9Mxht87ULXiPiWfl7pHlVji8zr52sSgLTz0tXyeO+L5opP7T2HFjDSs/WNjmdMRq3aLRL9hndD9mi5KfqwUcyrkvPfKaL4sg2Uz5JzNdly3FXLeVkBTC1LU04C2JGfsTEHmXW/cggVf/Y0lP6+AKa/iKW+x1Ytx9fgcdBmYBrnAie8bWY9Bzn0FUtRrnllZSUREPonf0SEicqMNf25RuqRcZbNakfq76FIJXqKD7/Epk9Dn+h4whBsqvLZKfCxGPTQcE94eW7rQw4PEisj7PhiP8GjHu7EkjQZ3vn4L4htWV+08h7YfRV6WOiOdty7bCX/mC+sbw6LUS1Z6K/HpKUWmYnzx5I94f8LnSjdtWQVewom96fj5tVl4cfTbpSdiFc6ys8DrUg6MzLdsh5z9NGDNhLPERK9bH7Ph5R/34eo7ziKuZvFlH9fpZXTpl4tH3j2Gpz89ioTWGYDFiQKvi4rXAOYlzt9PREREREQUgA7vOIbje0+qEitl1hoEs7AoIx74+C6MuHcQouOiKrk2DANu643HvpyoFDZ5jQTc9cZtqNnIuVWRox4Yira9Wqp2nIKcQhzYfFi1YpuM9POqxApWaubzRIGX2MIQqGSbjDkf/oFXb3oPKTNTy11/e25NLuZ8vwzP3vw+Nl85Ecu8DnLe2/YVeDnDdhJy1tPKpDBnabQaDBsXhld/2oObHj6Nuk0u/36QpJXRonM+JrxwEi98exhd+p1Xmi+dZj0CufAn5+8nIiK/x0leRERudHTXcfViObDCK1CJ0dXXPXE1rp40COsWbsb6RVuQfTYbRYXFyrq26vWqovs1XdGye1NoNL5Rx1yjfjU8+tVEfPrg1ziXbl/xh96ox11v3oqWSU1VPYtYbacW8abcUmRRupX8lbfXNzbr3EjFWIHbFWwuLMJHk77Coa32r3fIPpuDd+/+DPd/dCcat28AFG32TPJDJIZyX4MU/QogOVFgKtYoFk5DZAww8IYs5VVkAgrztQjR22AIk6H2lzbZNB+S/qogGQdHRERERERUuaO71MvBHVMxlr8SuaPBd/bDgLG9sW3FLqTNXa9M6jflm6EPC0VsjWh0HdoJHfu3UaZ/+QJRePPw5/fg88e/x8Eth+0u2Lnu8WvQ+/okVc+Sm1nGqjkX5GXmI65WFVVjBpO6zWspDchi9aCrEjo28pkctjsKvH54aTrWzN9g1/XFYnBeQjG+eGkGbs8zIVGsurWegpz3Tsl4RbfKg5zzMqTo/wHaOMdvL9qkTBrTG2zoMSRHeVmKgYI8LbQaGYZwG7Rqp9BNSwDjLZzmRUQUpPz3O7NERH6gIK9QvVg56sXyd2I6V89ruykvfxDfoBqe/ulhpMxKQ8qMNJw/VXaxV1ikUXkD2+eGHqhaK1b1c5Q3/chZlmL/LvLy9vrG+EY10KRTI+zbcNDlWMnXJSIgyTK+fW6aQwVeFxUVFuGzx77DU98/gKoRs+Ax1gOA6U/AeLVj91kOQS74ttQPhxrES90/u5exHgEse4CQ5u57BhERERERkR8pyFUzn1egWix/p9Vp0b5fa+XlL82mD02+G2vmb8KK6avLne6mC9Gh06B26HdjT9RpVkv1c1hVzudZi92YYwgCYgp74vBOWPbLKpdj9b5O3YJAXzL/i8V2F3hdWugVkiDj+/fnI6ZGDJq1ShEZPniEnAW54GdIkQ84dp8tD3LuO6W2AehCgKhYd/5ZMwFFKwDDIDc+g4iIfJV/f2eWiMgPkhdq0YWoF4u80wE4cGwf9L+tF3au2oudqXuQn1MAq9WG8EgjGraph44D2iHU4L6ORYOK479Fd6IhLHDGiXtrqlevMUkuF3k165qgTIwLRLvX7MfWZTucvr8guwDzJs/B2EeuGPXuZrJpISTDCIemY8mmeW49U4XPNi+BxCIvIiIiIiIihU6n3mQdLfN5fk0UcPUY2QU9rumCQ9uPYtPf25BzPhcWswWGCANqN45H12EdER6t3gq/sppCVY0Xxck/rkoek+RykVdUXBTa9lZvracvyTqTjYVTljp1rzLRCzZM/fgPjH9qNxo4tzXVOUUpgG0coIm0/x6z+Hl6p5hXNv8NiUVeRERBiUVeRERuFBkToVqsiNhw1WKR94gR3K2TmysvT6vTpKZSnCXLro+4rtOsNhBg290uLfQSPFHs1a5vK9RtXhvHnFzHKmk1GHpXfwSqFTNSXY6x6e+9GD1eg4iYyzvq3Mp2CijeAoS2t/P6XMC8El5jPe29ZxMREREREfkYNXNwEbHq5QbJiyQoDZri5WlRcZGIqhqJnHO5LscSawbjanNVoxpbG7oM6YB1CzY5HWPY3f1VbRD3JavmrINscy0Pd3LpOZwYY4OEGNSPz4JnWADz34BxpH2Xy7LS6Ok1FubziIiCVWAueyYi8hFterVQL1ZP9WJRcIqpHo3Wyep8HiWPDsz1gKLQ698VjiXFXu4kkjn3vjcOsfExTt1/89PXIqFjQwSizNNZ2Lpip8txLMUyVv8ZBU+Tixzo6DSL8fPF8B6uAyYiIiIiIrqoRVIzaLTqFF+0USkPQ8HdMNpjZFdVYiUO64QQvfu2CASTW54djUbtGjh1b98be6Lntd0QiMR60ZWz16gSa9v0kgl5R07FKC9PkM0O5PMsuwBbOryH+TwiomDFIi8iIjdq2qkxajSo7nKcyCoRysQfIjXWA7rKGGFA50HtEMg8WegVUy0Kj309EbUS4h0qDhv70o3oPrILAtX2lF2Qba5PnRO2pXqhc9qWafelsu04vCtwVq8SERERERG5KjouEu37uZ6HkyAh+drAbJIjz+oxqqsynd9VyWP4+agWUSx3/4d3oFUPx7Y1DLnjKox5dAQC1ZGdx5GTkaNKrK2p4aghmxAPU0lsTxR62RyYGmZlPo+IiLyDRV5ERO4kqVNU03NkN+hCuGGXXNeiWxPUaVrLpRi9r+sOvTEUge7iVC9PFHrF1ojB41MmYcxjI1C9fly514UaQtFzVDc8M/UhdB3aAYEs93y+erGyvfD1Uy6y/1pbAbxKU82x6y2HAXMqYPqrZApZ8U5AtrrrdERERERERB6nRj6vdXJzVKnpmekzFNhE3qjz4PYub4mIb+h6MzL9Sx+mx73vjsW4l25Cwzb1y71O0mjQvm8bPPz5BAyfOFD5nkGgyj2fp1qsYrMGReaSX6yLhV5uJ5sduNbLk7S0DubzrKcBcxpgWgKYlwNFmx37+RIRkc9gxQARkZt1v6aLMqI4/cApp+6vEh+LPjf1UP1cFJwkjYR73rodb43/2Kk33S2TmmHYhAFuOVuwE4VzfW/qib439sDudQewbflO5Gblw1psgTHSiLrNaqPb0PYwRBgRDIqLLKrFsjhQb6UaKdyBa/XuPIkdj+9d+UUi6WNeBdm0ALAeKCNIHCTDQEDfH9DymxhEREREROTfmnRopBRlbF66zan7RZPWiImDVT8XBa+b/m8UTh06g2O7Tzh8r9g0cduL17vlXMFOrNPsMqS98jq+5yTW/7kFWRnZKDIVwxCuR/W61ZA4vCNiqkcjGFhUzOeVxJOgN6gz6d8uGke2AXi3CVrS96n8ItkGFG2AbFoIWDaVcUE4YOgHyTAI0LrWGE5ERJ7DIi8iIjcLNYRg0gfj8c6dk5F52oFxv+Kv2NHhmPThHYiIcaBYgKgSVWvF4uHJ9+Djh75B5qkshzr+xr92MzRaDgJ1K0lC864JyiuYhUWqV8xmjLDB47R17b9WioXXaGoBIW0qvqZ4B+TctwE5u/xr5AzIhVOBwl8hhY0DjENVPyoREREREZHHSMDYl25A9n05OLTtiEO3anVa3PnGLajdJN5tx6PgnBol1gNOfvQ7HN5+1O77aifUxH0fjEd4VJhbz0dAnWa1lFcwE42qajKEezinp61j/7UaL+bzRIGZvm/Fl1jTIee+XslayXzANBeyaS5gGFaS05O0ah+WiIhUxu/SEhF5gLKK7Zv7lEk89qpWJ065h2O0yR3iG9XAk9/er6z+E92lFYmNj8GoB4fhnrdvD4o1jeQb6qqYFKvTuBieJhn6OXCt96Y1SoYhSmFhuczrIOe8WHGB12UskAu+gpz/k1pHJCIiIiIi8lrj5gOf3IW2vVs51LB0/0d3onWP5m49GwWniNgIPDT5Hgy54ypExkRU+rnY/9ZeePSre4NmihR5X62EeEgV5ZkcidXABq2H640kvQMbLELEClUvFU/qkyueOmY5DDnr/yop8LqCaT7k3LcAWd1pbEREpD5O8iIi8hDxZvrxKfdh89IdSJmeiv2bD5V5Xd3mddD7uiR0HtQOIfoQj5+TgkdU1Ujc9My1GPXgUKTN34gNi7cgJyMX5kKzkgiqXr8aelzTFa16NlNGjxN5UrOuCYirUxUZx8+5HKvnNY0BpMNjdB0AbbxjU790rQHLdniUeKZYsVie4n2Q895WCrccZpoJaKsAooiMiIiIiIjIT4lmtwlv3Y5da/YhZWYqti7fCVkuvTosrnZVJF/bDUnXdEF4NCcmkXuLD4dPHIjBd/bD5qXbkTZvAzJOnIcp3wRDmEFp1uw2tAM6DWRumTwvploU2vRqia3Ld7gcq+eopgAOwGOkOCC0k/3XawzKqkOY5rnzVGU8twaksNvK/7j1POScVwDkOh67eC3k/C8hRUx06YhEROReLPIiIvIgXYgOnQe2U14n95/CnnX7kZ9dANkmIyw6DAkdGqJ+SwdGAgeYjJPncerAGRTmmRCi1yGyagQatq7H9YBuZogwoM8N3ZUXka+QNJKSIJ/94R8udxA27noTkL0ZQB48QTKOcPwewxDIeR4s8tI1gRT5FCCVn/CVC74U2R2nHyHnfwcptCegiXQ6BhERERERkddJQIvEJsor83QWtqfsRu75PBQXW5QmOTGJulmXBOV9bDASvxbHdp9AQW6h0iQYHhOGBq3rcRq8m+lCdeg8qL3yIvIlvcYkuVzkJTZPdB1xPWDdDliPwRMk4zCRkHTsHsMgyJ4s8pLiIEU9D2iiyr1ELpwGyOedf4Z5MaDvD4Q0cT4GERG5FYu8iIi8RBQeiFews1lt2LpiJ1JmpGL32v2lPh5TLRo9RnVFj1HdEB3HQgGiYCI6oP/8dikKcgqdjtH/1t6QdPFA1NMlawdRBLcyjAZCnUiwhiYCIV2A4nXuONUVz+oNKeJeMYO+/Gss+wBL6a/JjikCzEsB49UuxiEiIiIiIvINsTVikDwm0dvH8D4Z2L/5MFbMSMXmJdtgtVgv+7Ah3IDE4Z2QPCYJ8Q2qee2YROR5zbsmoHaTmjixz/mp+j2v7QZjZDRg+w/krKddK1qyh8jJGRxv2oS2dkkuUEy0dzdda0gRjwDa2PKvseUB5hUuP0o2LYTEIi8iIp/F0ShEROQ1Jw+cwktj3sGXT/5QZoGXkHU2G/O/WIz/DH8df05ZpiSRiCg4iBUX97x1O3QhWqfuF8nkbsM6lPxHSAtIUS8DUjTcxjACUtjNzt0rSSWJGl0LuEcEYBgFKWYypMiHKi7wupDMUYMSp4xVJkREREREROS/k7vem/AZ3rtnMjYs2lyqwEsQqwOX/bIKL1/3Nn58aQYsxRavnJWIPE9MNbzn7dsRGRvh1P1NOzfGNfcPLvkPTTVIMW8A2vpwm5BOkCIfdXiK10VKLlB/FdwjVIktRb8NKfqligu8BNFsqUaDa1EKYHNi3SMREXkEJ3kREZFXHNp2FB8/8LWS9LGHzWrF758uQOaZLNz45EhlVL6vEys59248iIKsAuW/w2LC0LRTI9RqzAlu/ubw8XNoUKeqt48RlJp0aoQJ74zFl0/9iKJC+5MUPa9NxPVPXK0UT/0jpAmkmI8A85KS4iPbqbJv1rWCZBgMWbYBhb8AtpMVP0xTHZLxesDQz+7zlR3HAISNBXL+D6oImwRJVxOQIgBtzQpXM15GFGWZU9U5g/g1th4CdI3UiUdEREREREReI9ZVvj/hC2ScOGf3Palz1+H8qUzc9/54ZcWgr8s8lYUdq/cgLzMfFotVWclZr0UdJLRv4Bf5SCJfEFerCh6cfDc+fXCKks93ZArY3f+7DbqQS75WaOIgRb+FmkUrceTsAmV9Y/34MmJq65Xk8zQ1gcKfAcveSp4WUbKi0TgGkJxrMFWI3KNxHGBeLkbjw2X6oZD0SaJ6DNDEAxqj3bfKRauhDgtQtM71XCcREbmF7/+NmoiIAk7G8XOY/Mi3dhd4XUqsdYyJi8LgO33zDYboTNz893Ysn5GKg1sOl3lNQvuGSL4uCe37trr8DSv5pJq62ki3nGChlxe17N4MT0y5D79PXoTtKbsg28qfDFWjQXUMuK0Xkq7ufHmB10WaCGV9oCRGsBdvVdYSynKeyARB0kQBIR0BXV3lUuVufU/lOqUorHgbgJKiTcAAhLSEpB8MhHZ0utuvlKJl6sRRckySckaHyeJrs+Nfn8tlPc8iLyIiIiIiIj8n8nifPDTFoQKvi/as249v//sL7nrtFt8slJKBXWv2Yfn01SV5hzImUsc3qK7k8xKHdVTWURJRxUSj8xPf3Y+5n/6J9X9uQnFR+QVQUXFR6D0mCQPG9oZWV0bBlaQD9H1QU98H6eY1OJK5H/VrihydDZJobgxpUTIdX0zKF9eHtgMsh0ryeUVrADnnQqBQJUclGQYAoT0AKVSVn6tUvAqyGgVeF4W0cu4+W6Z6Z7C5eUUmERE5jd9ZJiIij5v1wXzkZ+c7ff+8zxehy5AOqFqrkvHEXuj0+/SRKcoEr4rs33xIedVOqImJ749DbI0Yj52RnC/0Eg4fP6H8k8VenlcroSbufWcszqdnYuWsNdiWsgt5WfmwFFsRHmlEnea1kTy6G5p1blx2cdeVxDUi4RParuL88oXrJHGtIIs1FHJJcskdLMdUCyVbjzmXO5fNUFexyvGIiIiIiIjI0/76MQXpByrOeVVk019bsX1YJ7Tu2Ry+xFRgxjfPTMWOVbsrvO7U4TOY/tZv+PObJbj33XGo37KOx85I5K+i4yJx6/NjMOrhoUibu0FZ8Zp9NhdFpiIYIwyoXr8aul/TFe36tCy7uKsMNfXdkK6tgyOZleRodQ0hRUwEMLFkar0owrJ3yr0TOTjVWE+4cBAVVjVeDCUX+2RNLhERsciLiIi8UAi1dflOl2KIbjpR5HHN/YPhKzJOnMe7d01GdsbFrqDKndifjrfHf4pHv5rocwVrVDZO9fK+KjVjcfWkwcrLK1wZ324POV/FWGJCmRM04VCVGC9PREREREREfstqsWLV7DUux1kxI9WnirxEgdcH936Bo7uO231PzrlcvD/hc0z68E4kdGjg1vMRBYrwqDBcdUuy8vJKQ67SEOqeAi+F7eLkfzXku5aDk+1fj1lhKA3zeUREvkqlvTJERET2EcVZZY08d9Tq39bCUsGIZ4+Pq3/wa4cKvC7KOpuNTx76RkkqkX/4N4ng+HoCokqpNCa+JJbeyftCAE119c6hLfkzQ0RERERERP5py7KdSnGTq3au2qM0SvoC2Sbj66enOlTgdZGYQvT5Y9/i7LEMt5yNiPwsT6vqhDAXcoNaFScMqhmLiIhUxSIvIiLyqA2Lt6oSR6xp27P+AHzBiulpOHPU+aTO6cNnkDIjTdUzkfsTCOIlEgheTyJQYJHUm+onSc6vgpX0A9Q5hK4DoI1TJxYRERERERF5xYZFW1SJI0PGxr/UyQ26akfqHuxcXfGKxooU5BZi/pd/qXomIvLPQi9Jo+KWDo0L+TyDSvk8KQ4Iaa9OLCIiUh2LvIiIyKOcmXZVnpwM1zsIXWWz2ZAy0/UCLRFDdBCSf/GFJAIFFknfXb1g5cWSbYD1FFC8r+Ql/v3KCYv6/qpsdpcMQ1yOQURERERERN6VfTY7oPJ5QsqMVJdjbFq8DXmZeaqch4j8uCE3VL18nhTao+wPiNydNQOwHACK9wLW44BcfPk1IR1Umc4vGQYCktblOERE5B6uf+eGiIjIXjJQbLrijYcLzKYieNvOVXtx/lSmy3HOnTyPnWl70ap7M1XORZ4jEgjplhP/JBAa1Knq7SORPwtNBKRoQHYxga5rC2hrXf5j1izA/Bdk0yJAvmL6oFStJIEjiru00SUvfTJgXur8GTQ1gdCOzt9PREREREREPqHIrGI+r9D7+byMk+exY+Uel+NYLBas/n09Bo7to8q5iEi9PK1Hc7S6uoCuFWDZ4fqE/9Aul/+YrRAoSoFsWgBYj1xxQwRg6AfJMAjQ1hQjxSAZhkEumOLCIQwXmj+JiMhXsciLiIg8RwIMEXoU5plUCWeMMMDbtq5w8Y3bJbYt3+n1Ii9LsQWbl+5A6m9rcerQWZjyzQjR6xAVF4lOA9qj+zWdEVklwqtn9OWJXl5JIlBgkUJKEimmma6FMQz+9z9kK+SC7wGRDIKl7Bvks5ALfwIKfwEMQyCF3Q4p7C7IloNlJJDsYYQU+ZSSXCIiIiIiIiL/ZgxXLwcXFun9fN72lbuV1ZFq2Lp8p9eLvMR2gD3rD2DlzDQc2XlcWSWp1WkRERuu5Bp7jUlEtbpxXj0jUaA35IpcnJy3Q4UJWrp/J3eZ/oBc8BOA8r6fkgeYfods+h0ISYIUMQkwDAOKdwLFa5w5AaSIRwCt8ysjiYjI/VjkRUREHlWjQXUc3n5UnVj1q8HbcjPzfTKWo6wWKxZ9uwzLp69G7vnLx8ybCsTZ8nBiXzrmf7EIHfu3xTWTBiM23nff7OVl5WPN/I0lia2cAuiUxFYEWvVohra9WyqJroDqFqOAIhlHQi5KBWwnnQsQ0hkI7Vby73Ix5Jw3AMsmO2+2AKa5kK3pkCKfgBT5POTclwHrYQcOEAEp6hlAV8+Z0xMREREREZGPiW9YHfs3H1IlVvX6rq8Sc1XeFbkvl2J5MZ8n6tRS567Hou+W4szRKyZ2A8jPzsfpw2ewZGoKWiQ2xdX3DUK9FnXgq4pMxdiwaAv2rN+PgpxCpcYlPNqIhPYN0WVwe+jD9N4+IvkJrzTkhiYBug4O5OCuoK0LGK4u+XdZhlzwrZKjs1txKuSck5Ai/wsp8hHIue8AxescOIAOUsT9gP6KSWJERORzAqLI68iRI/jwww8xf/58HDt2DHq9Ho0bN8b111+PSZMmISwszNtHJCKiC7pf3UWVIq9aCfFo0LIuvE0UR6kWq7icCTtuZso34cunfsTuNfvs+vmuW7gJe9btx33vj0fd5iVvmH3F8b3pSuJKJITEVLIrpc5dh6i4KPQc1Q19buyO8KgwtyURDh8/ofyTxV7kME04pKjnIGc/V3qtYmV0zSFFPApIUklCKO8D55JLxesh530MKeJhSFGvQi74DjAvEynXSp7fAVLEXSUj4omIiIgqwHweEZH/SLqmC1bOdmYqzOX0Rj06DWgDb7NabKrFEisbvcFms+HX//2OlJmpdl2/K20v9m88iHGv3IT2fVvDl2SezsKSn1YqBWuFeYWlPr5uwSbM/uAPdBvWEf1uTUZcrSpeOSf5H4825IpViZGPQ859AbDsc/DeapAi/wNojCX/XTjTsQKvi6xHIOe+Cinq5ZIJ+4UzIReKOJUUtuoSIIWNA0JaOv5MIiLyOL/fnzJ37ly0bdsW7777Lvbs2YOCggJkZmZi/fr1ePLJJ9GhQwfs37/f28ckIqILOg9ur8qaxV5jkpT1j94WFnnhjZcKjFHqxbKXKIT6/PEf7CrwulTOuVx8OOkrnD5yFr5CTO568/aPsGb+hjILvC7KycjBH18uxpu3fohTh8647Tz/FnuVjAYncoi2BqToN5Qki91Ce0CKegHQXPgaW7QSKFrt/BmKUoCiNCXBJEXcCyn2K0hh40s6C//pFZEAqSpgGAkp5lNI0c+xwIuIiIgqxXweEZF/EY2WdZu7PgGq69COMKi4+tFZRhVXRqqZG7SbDPz6lv0FXhcVF1nw1f/9hJ2pe+ErDmw+jNdu/gBLfk4ps8DrIlOBSdlA8PrNH2D3Wv4dgRzL0YqXyNG6PU8rcmiRLyqrE+2ma1qSA9Re2FpiOQa5cKrzZ7AegFw4Wyk6Q9h1kKp8/f/t3QeYnFW9P/Dfuz2bCgEuIQEDhN6lE0IHEUSqiA3hKiJylYugKPevoF5URMF2r1hR4SooKIpeEAsl1FAFNFxqkIRQBdK2ZLPzf94JCSVtZ+fdead8Ps8z7mx23jMHZLM73/mecyIZ8bHiwtCIttc8cERE+76RjP5K8abgBVA7arrkdc8998Q73/nOmDNnTowYMSLOOeecuOWWW+LPf/5znHDCCcXHPPTQQ3HwwQfH3Llz854uAMUVe23FXZTKMXz08NjprdtFNZiwSXY7Wa2X4VgD9bsL/xgP3Tm4YCQ9BvG7p/+0uHIwb7f+9s746dmXRf+ige+s9sLsF+P8Ey5c7nb2WVH0oizNq0cy6tzikYnRmm6Vvrxma3tE+/6RjP5aJCNPi0heDWsK3VeXPYVC9/+++knTiIhhh0Qy5huRrH7ZK7fLI1n9+5EMPzaiee2ynw8AqH/yPIAalETs867dyxsiSWLPo0soPgyh9TLcmT6PXe7v/MO9MfXy0gpeSxT6++OHn/qfmJvhkZWD9ehfZ8S3Tv5+MWMs5USC//rYj0pesAoVy2mbOiIZ9YlIRp9XLFFFtC7nQUlE686RjDw7klFfimheLdM8L3qujSgsfOWpWiPa94pk9BcjGXvpq3ne2J9GMuLk0haYAlAVavq4xlNOOSW6urqipaUlrr322th111dfIOyzzz6x0UYbFVf/pcHQ1772tTj77LNznS8Aix184v7xyF+fiMfvm1Hytc0tzfHBL78n2jvboxrs8rY3x1X/fc1Kd44aiNa2ltjpbW+OSupZ0BNTr7itrDGemfFs/O2m/4ut9tgs8vLYfU/E/5xzxaCunf/y/PjvUy6KM3/+79HWsbwX3OVzfCNlSY9dbNs2krZtIxa9ENH3UERhfkTSHBEjI1o3Kx7vuIy+xyP6Hiz/+fv+VlxBGC3rLjuv5YZUAAArJ88DqE3pgsv/u/ORuO2qOwd1/dGfOCzGbfAvUQ022XFSrDF+bDw/q/yyx5QjdomKKkT88eIbyhoi3RXr5l9PiwM/sE/k5aVnX44LP/6T4u5ipUoXeX7/k5fEp392Sqwx3tGNVOnxjS0bLi5Rdb4/YuGDEYV08UJ/RDI8omWjiOblPH9/V0TP9eU/d+Hlxbvzt09Z9mtp6QuAmlazO3lNmzYtpk6dWrz/gQ984HWB0BKnnXZabLbZ4jedv/GNb8TCha+0lgHIVWt7a5x0/vtj/S3XK+26tpb4wJfeExvvsGFUixFjhseb99+67HG2f8u2MXxUZ1TSHdfcW1z9Vq50q/Q8Xf3DvxRXIQ7WczOfjzuuvieGml29KFsa/rTvGtGxX0T73hHtOyy/4JVmOT03Zva0hSzCJQAAeR5AbUsi3n3mEbHjgaXvrn/YRw+KPd5R4TLUSiRNSUw5cpdMdvGauMUbFkUNsccf+EfMfOipsse56Ve3R/+i/Hbnv/6yW0rawWt5RbU//0922QeNo6LHNy7ZGT/N8Dr2jujYN6J9l+UXvFILb0//687kaQvd8jyAelWzJa8rr7xy6f3jjz9+uY9pamqKY489tnj/pZdeiuuuu65i8wNg5YaP7oxTLvxQ7HX05GjreO1Z8MuXFsL+/Xsfjm322iKqzb7vnhJJ0+B/pDY1N8fex5S35f1g3PTr9EVj+abf9lC88NSLkYfnZ74Q02/5v7LHuTHd4r4QQ07Ri4pZ9Gx2Y/VnOBYA0NDkeQC1Ld1h//2fe2cc/tGDYuSYEat8/JrrrhEnnPu+2P/YPaPa7HroDjF89PIXTg3Ufu/bs1h+q6R0B64svPjsS/H3Wx6KPPT19sWtv72j7HGm/f6e4kkFUDc57aLnshurP8OxAKgqNVvyuummm4ofhw8fHttvv/0KH7fnnq++eLj55psrMjcABr6j1zs+8fb44v/+R7zjtLfHuA3WjuQ1yciwEcNit0N3ik9d/LE4/aKTK74ybqAmbLJOvOvTRwz6+nQV5ISNx0VFFSJmPfx0ZsM99Uh2Y5Xipl9Ni0IG7ax0BeTj9z8RlQwQYEgVuqtzLACgocnzAGpfugvWfsfuGf/5+0/H8V94V2y47cTiAsbX5n3pIs2P/tcJcdblp8e2+2wZ1SjdUf9D5x1bPD54MPZ515TY4YBtotKy2MVr6VgPZzdWKe79ywMx76X5ZY+T7uaVnlQA9ZLTFuR5AAzA4H57rQLTp08vfpw0adJKfwnfdNNNl7kGgOoybGRH7HXM5OKt0F8orsBqaWsp3mrF5MN2jP6+RXHZV66MQmFgpaMkSeKYTx0eu759h6i0nq6e6F+0KLPxFszrijw8fM9jGY71eKy/9ZsyGw9y1TQsu7GSMsYq9Eb0zYjon7P486ZRES1vikjaM5seAFA75HkA9SPN7XY4cNviLV1/193VE83NTcWSV62YtN3EOOnrx8X3P3lJsTA0UOmO/Ef8+8GRhwVzs8vgujIcqxQP351hnnf3Y7H7ETtnNh7kKUk6sjtsoqlj8NcW+iMWpXneyxGFvoim4RHN6y0+ehKA3NXOu+ev0d3dHc8//3zx/oQJE1b62NVWW624OnD+/Pnx5JNPDvg5Zs6cudKvz549e8BjAVDaasCOEWW8AMnRlKN2iX+ZuGb87w/+HA/f9ehKH7vxDpPioA/uGxttv0HkIesCXWtrPr9SzH95QWZjLXg5n2ALhkTTWhmOtWbp1yx6Kgrdf4jo/kv6nfqGLw6P6Ngnko4DIpqra8UkAFDbeV5KpgeQgySio7M2F/NsuvNG8YmLPhK/+94f497r/haF/v4VPnb8pHFxwPv3Wlxsy0mWmV5LHeR5WY4FuWvOMs8bxFiLXoro+VMUuq+NKCz+vf1VLRFtkyPpeGtEy0ZpIy2rmQLQCCWvuXPnLr0/YsSqW8NLQqF58+YN+DnWXbc6jwQDoLptvMOGxdvTjz0TN15+W3GnqSXloc7Rw2LjN29YLIOtvX6GL9gGobmlOTpHDsts9d/I1a3igWqStO8Vhe4rsxmrY++BP7jQG4V534novWElD5of0X1VFLqvimibEsmIkyOStiymCgA0eJ6XkukBUKq1N/iX+OCX3xsvPfty3HzlHXH/1Okx76V5sWjhomJ+tu5m42PKkbvEhltPLBba8jRq9RHxzIxnazvP0w2B5WvdKSLSBfDlH7WYtJeS5xUiun4Rha4rIqJvBQ/qK+Z9hTTza9kskhGnRzSvVvY8AWiQkle68m+JtrZVvyHU3r54BUlXlx06AKhcOHT0Jw+NarbNXlvGrVfdUfY4I1cbEetvtV7kYcTozniutIX9KzR8TGc2A0E1aFkvomXziL6/lznOlhHNK99pY6n+rijM/UJE34MDH793ahTmPBvJyM9me8QkAFB15HkAVLsxa42Ogz+0X/FWrbbZa4tMjjtMIomt9tg88jB81PDMxhoxJruxIHdpNpYutuy+urxxkjERbWlhbAAKhSjM+3ZE73UDH79vehRe/lQkoz8X0bz2oKcJwOA0RQ3q6Hj1GK/e3t5VPr6np6f4cdiwgb9xlG4Fv7LbtGnTBjl7AKgO6Y5iWdjtsB0zP/5xoDbaYcPMxkp3YIN6knQcVLkxCv1RmPe10gpeS/T9XxTmfjWisKj0awGAmlGJPC8l0wOgnu3yth2itb217HG23H3TGLtOPrvwbLzDBpmNtdH28jzqS/E4xLLHeEtEMrC/JwoLLi6t4LX0wueiMOc/I/pf3a0XgMqoyZ28Ro4cufT+QLZsT7d2H+hW8EtMmDDAHQsAoEa9afMJMXGLdWPG3wa/FVaSJDHliGzKYoORPvcff3x9FKJQ1jjrbTah+O8D6krbrhFte0T03jjI6/eOaNt5YI9Nt2pfeHcMWt89ET03RHTsM/gxAIBo9DwvJdMDoJ4NG9kROx64Xdzym/JKy7tntPhzMLbZe4viyQBzXyztSOY3GjaiI3Z4yzaZzQuqQvOESDqPjcKCnw7u+pZNIoYdPrDH9j0e0X1lDFr/U1HoujyS4ccPfgwAGmcnr7Fjxxbvz5w5c6WPffHFF5eGQuuuu25F5gcAteKIU98WLS2D73wfcNxesdraYyIvq48bE1tO2bTscfY4ateotBkzX6j4c9JgkiSSESdHtO5Y+rWtu0Qy4sPFMQaiUO428sUx/re4RTwAUJ/keQCQjYNO2LdYkhqsrXbfLLbcrfw8bbBaWlti8mEDPEpuFbuatQ9b9RHQUHM6Do3oGGBR67WaN4hk5KcjkraK5XnR/eeI/lePZQdg6NVkySu1+eaLzwp/5JFHoq+vb4WPe/DBV4+M2WyzzSoyNxpT38K+uPe6B+IPF10fv/n2NfG/3/9T3HzlHTGvzNUoAENpw20mxrGfOzqSptJ/JdjpoDfHIR9+S+TtwA/sG80tzYO+/l8mrlXxVX/jWsYXPyp6MeSS1khGnvFKMDSQbdrbIjqOjGTk6QPe1j36Hll8K9eix7IZBwCoWvI8qk4h4qE7H40//fSG+M1/XRO/++4f4/pf3BLPe60GVLHV/mVMnPT144s7WZVq/S3Xi+O/+O6Iga3pGjJ7vnO3GDlm8EW1YSOGxT7vnpLpnGhMaU6bZrRVldOmCzeHvy+S4R9O97UdyAXF3fyTUV+IaBo1sOfonx/RM8jd/19nQUTv1AzGAaCuj2tM7b777jF16tTiqr677rordt55+UfJ3HDDDUvvT548uYIzpFG89OzLcdMVt8dNV94ec/+5bKHrF+e2xHb7bxV7HrVrrL/1m3KZI8DKbH/ANtExoiN+dObPonv+wFbd7P++PePQf3trJE05J0IRxSMn3/fZo+PHn/15ydeOXH1EfOQbx0dr+6rLLH29fXHfDX+Ppx55OrrmdUdre0uMHDsytt17yxi7zmqDChBm981aGiBMnLB4VwPIXNJUDIZi2GERPddFofuaiP6nX/+YpnGRdBwY0b53RFNpIWuhJ7sgp9B7YyStG2U2HgBQXeR5VIuuud1x2+/ujBsvvzWe/cfzy3z9l2kpcddNirs+b7n7plXx2hfgtd60+YQ47Ycfie/8+0XxwuwXB3TNNnttEe///DFVsfvVqLEj48NfPy6+8eHvRW93b0nXpqcSnPi1Y4s7/K9Kob8QD057JB6/74lYMLer+Pf5iDEjYovdNo4Jm6xTxj8B9eS1OW1VZbQdB0TSvldE782Ld9164+LIZHRE+/6RdOwf0bxmaWMvTI98Le17b2XZYHEOAFREUijU5pko06ZNWxoEnXjiiXHhhRcu85j+/v7YcsstY/r06TFmzJh49tlno7V1gDsSrEK6rfyS7eKvm3pXrD3OL4ON6K5r/xoXf+4XsbB3xatPX2v3w3eJd55xaDQ11+wmekAdmz9nQdx21V0x9fJb47nlrFzq6OyInQ7erhhyj9vgX6Ia/07+6Vm/WOmOAK+15rprxMnfOL74cWX+OfulYvB/62/viHkvLT4y5rWSSGKL3TeJKWn4n251P4jsPw0RUlUVIlC/0l//+/8ZUXilnJ6MiGhafcBHMy4z3NyvRvTeks3cWneNZNQnshkLoI7MnjU7Jm+yW/H+k08+GRMmTMh7SlCTeV5KpseMB56MCz/+45g7wN33N9lxUpxw7vti2MjSd8wBGGoLexbGXX+8r5jnzfjbk8t8vam5Obbbd6tinjdp24m57+D1RumcL/z3H8fclwb2d3LnyGFx4lffH5PevP4qc85br7wjpv7q9nh+1gsr3NVsyjt2je3337p4hCQsyWirNqftnxNReDmi0PdKnje2uLhzUBZcHoWun2Uzr3Tx6Gr/lc1YAHVk9hDleTVb8krtsccexdV/aWv/xhtvjF133fV1Xz/vvPPik5/8ZPH+WWedFWeffXZmzy0QIj2K8WfnXF7ydelqmQ+e+95oGsTRaED9SN+46O3qjbZhbVX390G6wu3hux+LZ2Y8V9yxqq2jNUatMSo2323j6Ohsj2r29Izn4rqf3RTTrr57hasAx45brVjImnLEzsUdzFbm7j/eFz8567LikbwDsc3eW8Zxnz+m+O+sVIpe1KrCnHMiFt6VzWAt20Uy+jORmzQkS7erTwtvyfCIZPBHwQJkScmLepJnnpeS6TW29LXuf33sR8VSRCnGTxoXp37vw4pe0OgKEd1dPdHa1hLNLdX3enHm/z1VLE2lO1alpaXhYzpjs503Ku6aVc3mvDA3brjslrj5ymkrLOAOHz08dnv7jrHXMbvFmLVGr7o4durAy7zrbjo+Trrg+Bi9RnX/e6JyGiGnLcy/JKL7V9kMlqwWyeo/jNwU+tN/oMUfmzojkuwWiACUQ8lrOe65557ilu1dXV0xYsSIOPPMM2Pvvfcufn7ppZfG9773veLjNt5447jzzjtj5MjsfkETCDW2B29/OL790R/GYL999j5m9zjqtEMynxdQ3V56bk7c8utpxSMh0t2hCmkyFBFj1hwdO751u5hy5C6DOvaPZXXP645pV98bT0x/MhbM6Yrm1uYYMXp4bDl509h88sYDKtbd+ts745IvpId0lGbSduvHR7/9wWhpG9wKwEYIEagvhbkXRPRmdGRj226RjDw9KqrQE9FzcxR6rnnDtvdJRMtWi4+xbNtx1YWvdDVl38Ov7JDWFJGMjGjZJKJp2FD/EwANQMmLepJnnpeS6TWu5558Ps499tvRNa9rUNenO3r927c/UHULtYChz5hu+9+7i5neU48+vfQ9gXRHqW332Sr2fMeujv3LSF9vX9x73QPx0J2PxvyXu4rZafrveaM3b7B4t60BZG2P/nVGfOvkH5Rc5k0XhZ72o5MVvWicjHbBr6LQdUk2YzWNj2S1b0VFpYWu3rui0J3meX9Ng7lXv9a8QSQdb4lomxLRtIqCfn9XRN9D6SrWV8YYHtGyYUSz92mA8il5rcBVV10V733ve2POnPQv32WlgdDvf//7mDRpUqbPKxBqYIWIc959QTz1yNODHiI92uvsX38i1qjXXw6B15n7z3nxy6/+Nu7+8/1R6H/Ni43l/N2w5R6bxdGnHxqrjxtT0Tnyeg/f9Vh84yPfX+n/Xyuz44HbxXFfOGbQz1/3IQJ1pTD/5xHdpRcil6vjyEiGvycqIn0Z1HVFFLp+GxGrWN2brB5J53siOvZedoy+6VHo/kNE761pJP2GCzsi2vdcXBRreVPm/whA41Dyot7kleelZHqN68efvTTuuPqessY48Wvvj6332DyzOQHVKy0J/ebb1xR3l1rRbvGvPfbvqNPeHhO3XPzzhXy88NSL8eX3fTMWzFkwqOvTHb1O/+FHBr1wk/pUtzltz61RmHdeNmO17hDJqDOjYnpuXLwTWeH5VTywM6LjbZF0Hr3ssZaLnlxcEOu+Lq3zvuG65oi2nSNpPzCidYvFO/4DVFGeV/PLjg455JC477774tRTTy0GQJ2dnTFmzJjYYYcd4txzzy2uDhyKQIjGla4EKafglUpXoNz0q9szmxNQvZ79x/Nx3vH/FXf98a+rLAylfzfcf+Pf47zjv13cXp38XPntqwdd8Erdcc098eSDiwOAwRjXMr74ccbMFwY9BlRK8sbiUzlaNo3omRqRlqbSkKX3nohCaatvB6TQF4V550eh62erLngVH//PKMz/1isB0itrZPrnRGHOWVGY8/9e2clsece6dkf0/CEKL5+6eMezwsrfGACARiHPo9LmvTgv7vnj/WWPc+Mv02I/UO/SXeG/8ZEfxHWX3rTKglfq8Qf+EV8/8cL46/V/q8j8WL5rf3zdoAteqTTLu/MP92Y6J2pf3ea0bTtEJKOyG6vnlojuayO6/xTRMy2if2DHpZYkzeQWXBaFeV8fQMErtSCi+xdRmHveq/liYWEU5n0rCi+dEtF99XIKXqlFEb23RGHuZ6Mw5z8iFr2Y9T8JQGPv5JUXq/4a148/c2nxzftypWfIf/F/z7QqBOrYy8/PLRa2Xnz6pZKvHTFmeHziopPt+JeDf0yfGeceW/720rsdulO85/8dWfY4dbtajLpSmPOfEQvvLnOUzsXhyzJGRHTsF0nHARHNa2cSCBXmfTuiN12pV7pk2Hsj2vdaXO7qL7H437JpJCM/4whHoGR28oLsyPQa07U/uT5+8+30jbzynf2rT8Sa666RyVhAdR4Z+M2Tvx+P3juj5GubW5rj5G/+a/F4Vyp/rOan33rOgEp5K/OmzSfEJ3/y0czmRf2ox4y2MP/iiO5flzlKa7r34XL+vC2ifcoru9tvGJnouioKCy4a3LXp0Y3DT4qY+8WIvgdKu7ZprUhGfSGiec3BPTfQsGbbyQuqw/03Ts9knPkvz4/H7nsik7GA6nTJFy4fVMErNe+l+fHDM39WPCKWyrrx8tsyGSctBKcrP8tVt6vFqCtJx9syGGVFq23nRXRfGYWXPhKF+f/z6k5ag9V706ALXqlC1yVRmPPZ0gteqb4HozAv3dHLX+4AAJV0/9Rs8rzUAzc9mNlYQPX5/ff+NKiCV2pR36L44ad/Ft0LejKfFyt32+/uKrvglXri7zOLN1heRpve0oy2XnLaYgEryt2IYkU78PdG9Pw5Ci9/IgpzvxpRKPPvxb4Zgy94FaczNWLOZ0oveKX6n43C3C9E9A9+p0CALCl5QYmreLoXLG/rzsGZ9+L8zMYCqsvTM56Lv9/yYNk7Sj12vzJopf3tlv/LZJyFPQvj4bsfy2Ss1xa96iVEoM60bRvRccjQP0/3FYt34SqjJFXo/l358+gv40jdhXdG9GZTJgUAYODHNWY3ljwP6lVv98KYesVtZS/uvuN/yz8JhHzyvOJYyrw0yoLc5jUjGf7hoX+e9OjDOZ+L6B/8+6uF4tGKZVr0aBnXzoxC12/KnwNABpS8oAR9fYuyHW9htuMB1eOmMgOhJW68/NZMxmGACtkG9vNeWpD5arG6CRGoO0nncRHt+w39E/VeF4UF/zO4a/sejeh7OPKWSTAFAMCALerrz3AseR7Uq7uu/Wt0zSt/V/Yb0jzPBs4VNTfTPE+ZlwZakNuxTySdxw/985Szu33//IieGyN3PX+MKKxo5zKAylHyghJ0DGuPpubmzMbrHDUss7GA6tG/qD9u+92dmYx1zx/vj6652e0gyKoVFmUX/vcvyj78V/SiaiVJJMNPeiUYGjG0z9X9q4hFs0u+rNDz56gK6dbwi57MexYAAA2jc2R2GdywkZ2ZjQVUl5uvnJbJOLMffTpm/M1rvkoq9GeZ52U3FvWrrhbkDjskkhFnRDStNbTPs/COiN5B/D3be3PasIrcFV6K6L0971kAKHlBSZKI9TZdJ5uhkiQmbDwuk7GA6jLnhbnRNS+bYlZfX1+88NQ/MxmLAUjSwL6jKt9IWF6IUBerxagvSfpNdEgkq/8wkhGnRLRssuxjmidm8lSF7mtLv6ivjGMWM1boTgMqAAAqYd1NF78Jm4X1NstuLKC6PDPj2czGejrDsVi1YVmWeS3OpwR1U/Rq3zmSMd+JZOT/i2jdYdkKQZK+n9le9tMUuq8p/ZpFs6JaFHrkeUD+lLygRLsfsUsm42y1x+YxZq3RmYwFVJesCl5DNR4rN3HL9TIb602bT4ihVDchAvUnaY1o3zOS0V+KZPXLIhnzw8W31S+LaF43m+fo/nNEobfEi7I7QrVshRfzngEAQMOYcuTOmYyzxvixselOkzIZC6g+XfOz2ymmW55XURM3Xze7sbbIbiwaQ90syE0Xb7a9OZJRZ0ay+qWRrPbjSMZ8P5LVfhbRsV82u2n1/TViUYmLMAvlH6ObGXkeUAVa8p4A1JrtD9gmrrjgd9E1r7xfKvY4atfM5gRUl9aO1qoej5WbcuQu8fdb/6/scTbbZeNYY8LYAT12wZyuuP13d8W91z0Qc/45Nxb29sWwER0xfqNxMfmwnWKj7TYo7jK2PGmAMLtvVjFAmDjA54OKF76aV4soFKKw4KcRvVMzGnhexML7I9q2L+Ga7HbqK1uhCraZBwBoEOttNqH4pn25x6elrxeTphW8OANqXlt7a/R0ZfNarbWjLZNxGJjdj9gp/njx9WWPM3qNUbHVlM0G9Ni+3r64+0/3x7Sr744Xn34perp6o6OzPdaYsHrs8rYdYus9N4+mZnttNJK6ymmTlohk1KsLLbsuzm7snlsjOo8sYS7yPIDXUvKCErV1tMZex0yOq3/wp0GPMWHjdaz6gzo2crURxSNZC4VCJuONXmNkJuMwMFvuvmms9i9j4sVnXhryMu9Lz74cv/vuH+POP9wbC3sWvu5r6Zqgpx55Ou64+p4Yt8Hase97psSuh+yw3LLXqzt6zar9AIH6lBa85l8Y0fPHbMftL/H7tGn1qBpNw/OeAQBAQ9n/2L3i+2cM/g3K4aOHx66HpscXAfVq9Joj49l/ZPMGvjyvstKFlpvvuknZCzd3P2LnVRazuhf0xB8uui5uuXJazHtp/jJfn/34M3H/1OkxZs3RMeWoXWO/906JljZvxzZa0atudP1vFBb8INMhC4WXVrSeebmSptUjm3daMpB05j0DAMc1wmAc9MF9Y6vdB7aa441GjR0ZJ371/Vb9QR1rH9YWWw5wxdeqrL/1xGLhiMpJg5z9jt2zrDHGbbh2sSy2Mk8+OCvOPfZbcetv71im4PVGsx97Oi75wi/jki9cHov6FpU1N8hF91XZF7xSJR7XmLRPiWqRNA3tca4AALzetvtsWSx6DUZLa0uc+NVjY/gob+xBPdt+v20yGScthVrkXXkHvH+vSEqqjrxe58hhxR0bV+al5+bE+R/8Tlz74+uWW/B6/WNfjqu+c018+6M/LO7iDzWn957MC16DyfOibXJUjWZ5HpA/JS8YZAHgA19+T2yz95YlXTd2ndXjlAtPjNXHKWxAvcvqSNY9He2ai73esVvsku6aNQgjVx8RHz7//Std9ff048/GN076fsx5YW5JY9961R3xP+dcEdWzdAkGoNAThQW/rI7dsFq3i2haK/LXFlFFhTMAgEZx2L+9teSiV8fwjjjp68fHhttOHLJ5AdVh9yN3jqSp/LfNdnv7jnZuysFG228QR576tkFd29LSEh/66rHFXG9F5s9ZEN/8yPdj1sOzSxr74bsfi//+94tWucgTqk2h6+dDM3BSYp7XvGZE645RDZKO/fKeAoCSFwxWa3trfPDL74l3nPb2WGP8yo/G6ujsiD3esWt84qKTY+2Ja1ZsjkB+Ntt5o1hzwhpljTFyzIjYbt/SyqRkJIl4z38cGZMP26mky1Zfe7X49wtPjDXWWfGRcH29fXHhx38cXfMGt4Lv9t/dFdf/8pZBXQu56LkpjUKHZuzmdUt7fNIUSceBkbu04NW04uAYAIAhkkQc9tG3xge//N5Yb7OV78TQ1Nwc2++/TXzix/9mRx5oEGPWGh1b77l5WWOkO0mlZTHysfe7d48j/r20olf6/s1JXz8uNnrzBit93E/PuiyemfHsoOb1+P1PxC+/+ttBXQu56Htk8W0IJKXmecVyVRXkec0bRrRslPcsAMJSAihDU1NT7HXM5Njz6N1i+m0PxS2/uSOenvFcdM/rjtaOlhi9xqhiGLTjQdtFR2d73tMFKig9kvVdZx4e3/7oj6J/0aJBBULHfPpwq/5ylO7E9e4zj4wNt1s//vI/U2PmQ0+t8LHDRnTELm/bId5y/N4rXfGXuve6B+K5mS+UNbc/X3xj7HHULsWfQ1DtCt3XDGGwsn7p13UcFNF7a0Tfw4N73pZNIvr+L8qRpHMAACA32+27VfH2xN9nxtTLb4t/TJ8ZC+Z2RUtrcwwfMzy2nLxpTD58pxg1dmTeUwUq7IhTDo5H73l8lUfxrchBJ+wXa4xf8eI/ht6+75kS4zcaF3/8yXXx4LRHVrp713b7bxUH/uu+q1yc/9SjT8cDNz1Y1rxu+91dcchJb1lldgjVoND9hyEauTOibRCnl7RuG9G2Z0TvDYN72qYJEf1pvt8/+Dxv2OB2CgTImneOIaMyx+a7bVK8ASyxyY6T4tizjo6fnH1ZFPpLe/Fw1CfeHtvuYxev3CUROx/05tj5rW+Oxx/4R9z862kx+/FnYsGcBdHW0VYMZbbbd+vY4S3bRPuwtgENeePlt5Y9rX8+/WL8/eaHYsspm5Y9Fgyp/vkRix4dkqGTjrcO8sK2SEb+RxTmfCZi0ZOlXduyTcTIT0d0/SSi++rBPX3nvw6unAYAQObetPmEeNNnj8p7GkAVSQtaHz7/uPj2R38Y3fO7S7p298N3Lpa8yF+6A2N6e/Yfz8fUK26Lxx94spjnpYs6R4wZHpvvunHs9vYdYsRqAytc3Xj5bWXPaVHforj5yjviwH/du+yxYMj1/nVoxu3YJ6Kpo/TrkiSSER+Jwtx5EQvvKu3apnUiGfW5iIV3RGH+hTEo7ftGtO0xuGsBMqbkBQBDaMe3bhudo4fFTz57Wcx/ef6Atgd/938cEdsfsE1F5scAJRHrb7Ve8VaO2Y89E4/eOyOTKU391a1KXlS/wtwhGnh0RPvkwV/eNCqSUV+MwryvDzwYat8/kuEfjEhaIzo/EIVCb0TPn0t62mTYuyOs+gMAAKhqaf5z2g9Piu+dfnE8N/P5VT4+aWqKt31o/zjwX/cpZkhUj7XWWyOOPLW81+G93Qtj2u/vzmQ+N/36tjjw+L39d0KDZnpNg1+0mUpaIxn5qSgs+NHAF1+2bBvJyFMjmkZGNB8QSaErCgt+Utrztk2JZPiJxaIZQDVQ8gKAIbbFbpvEF676VNz5h7/G1MtvjSf/b9Yyj1l74lox5R27xi4HvTk6RgxiJQs1IT0KpBrHgqFTGJphh78/IinzKOym4ZGM+o+IvscXHynZc2NE9LzhQSMiOvaPpGP/iOa1X/3jpCmS4R+JaJ4Yha5fRRReXMVzjYuk8z0R7buVN2cAAAAqYp0N147PXn5a3Hfj34s7QT14+8PLPGb0GqOKu3ftdtiOMWat0bnMk6H37BPPRU/XG/OCwXnx6Zdi7ovzHNlIDRj8sYYr3Q2reVx5YyTNkQw/IaLj0Ch0XxvR86eIwpw3PKg1on2PSDreEtEy6fVfGnZoJE1rR2HBJRH9s1bxXKMjGXZo8bkUvIBqouQFABWQHuU3+bAdY/KhO8asR56O52e9EN0Leop/vvraY2K9TSdYwdUAuuZ2ZTfWnOUfGTBj5gsxccLYpZ/3L+qP/v7+aGn1ax85SIYmtEzKDYReq2X9SEacFNF5XMSixyP65y3evi9d4dey4eKdu5Y7iSRi2MGLA6PeO6KQriDsezAi+l55QEdE69aLVyi2bi0MAgAAqDHp0X7b7r1l8fb8U/+M2Y88EwvmdUVbe2uMXH1krL/VutHc0pz3NBliCzLM85aMt6qSV6G/UDzesZjniRNqzriW8TFj5uIC0Wtz2prL9Fa1qLHUIVs2yG6w5rUiGf7eiM53FhdwRn9a9FoU0TSiuCgzXdy5Qu07R9K2U8TCBxYv/Fx4T0QsydpbIlo2Xpz3te2y4lwQIEfe7QOASkoixm+0dvFG42luye5Xr+bW5uUGCLMXzoqb/nR/3P2n++Iftz+8tFjW1tEWE7daL/Y4cpfYeq/NhZBULhBqGr/qlXGlaurMdrzimMMimjYv/bqkJaJ910jad40opDuX9Ra3nxcCAQAA1I811lm9eKPxZJ2hLS/TSz316NNx4+W3xb1/uT/m/XN+FKIQLS0tMW7Sv8Tkw3aKnd66XbR3lrmrORVTzGn7Zi2zILdmtG4W0XtLtmMmQ5Dnpflb68aDuC6JaNsqkratFn9eWBhRWLT45AALNYEqp+QFAFAhI1YbPqRj3X/j9PjNf10Tsx97Olpf2Ym66ZWv9Xb3xkN3PFK8jVpjVBzw/j1j72Mme9HK0EqSSDoOjMKCH2Y4aHtE01pRlYrfTwJXAAAAqBdZ5nnF8ca8frwnH5wVl59/VTxyz+PLPLavr6/49Uu//Ou48ptXx+5H7BSHnPSWaGnz9m6tFb1StVT2StoPjELWJa/mdaNqpWUxCzaBGrHkfT8AAIbYJjttGK0ZhTBb7b7Z6z6/7mc3xXdP+0mx4JVa+MjiP+8f2bHMtXOenxOXf+2quPjzlxePc4Qh1b5XtsWn9j0Wr6oDAAAAGGJrrbtGrLnuGpmMNWm79aPjNbtxPXDTg3H+CRcut+D1Rt0LuuNPl9wY3/q3H0TX3CVHy1ELRa/0llpS9qoJrVtENE3IbryWSREtE7MbD6CBKXkBAFTI8FGdsf1bts1krClH7bL0/s2/nhaXX3BVcRv313pt0Wt5Za/brrozLvvyla8cMQdDpGl4RMdBmQ2X7gwGAAAAUAlJUxJ7HLVrJmPt+Y7dlt5/5J4Z8f1PXFzcfb8UaSHsu6f/JPp6+zKZE5VRc0WvdHf+zndkN1zHWzMbC6DRKXkBAFRQFqHQxjtsGGuvv/i4uqdnPBc///KvV/jYtOi1sl29bvr17XHntfeVPSdYmaTz3RGtO5Y/UMuWES3rZzElAAAAgAHZ5W3bR2t7eUe5jRo7Mrbea/Pi/Z6u3vjBJy8uHsc4GA/f/Vj8/vt/Kms+5Fv0qomyV/uUiI7Dyx8nWS2ibXIWMwJAyQsAoLLetPmE2KGM3bxaWlvi0JNfXfl0wy9ujkL/qo9cXFnR67qf3zTo+cCAJM2RjDw9onWnMsYYG8mIU7KcFQAAAMAqdY4aFgedsF9ZYxz2sYOKuV7qjqvvibkvzStrvJuuuC16uxeWNQaVV2vHNyad743oKGdHr7ZIRn4qImnLcFYAjU3JCwCgwt732XfERm/eoOTrkqameP/nj4mJW65b/Lx7QU9M+/09A75+ya5ebzy+ccYD/4h/TJ9Z8nygJElrJCPPiBj2/rSuWOK1a0Yy+qyI5rFDNTsAAACAFTrg2L1i98N3GdS1B5+wf+x80JsXf1KIuPGXt5Y9nwVzu+Kua/9a9jjko2aKXumxjcPfFTHijIgYUeLFHZGM/HRE60ZDNDmAxqTkBQBQYS1tLXHyN/81tttv6wFf09HZESddcFy8eb+tlv7ZPX+6P7oXdJf8/Mvb1euWK+8oeRwYVDDUeWgkq/0goiUNN5NVXNAS0TYlktFfjmieUKFJAgAAALxBEvGuTx8eBx6/z8AvaWqKd5z29jjoQ6/uAvbE9Jkx65HZmUzp5iunZTIO+e7qVQvHNybtO0ey+g8j2vcf2OLNlm0iGf2liLZtKjE9gIZS4hJ6AKiQQkRPd280NzcVCzFQb1rbW+ODX3xPPHj4zjH18tvirzf8bbnHLq621pjY/cidY/JhO8XI1V+/Wmr2Y88M+vnTolfrpFeLXrMfH/xYULKmUZGM/n8R/XMiuv8chZ6/RPQ/m/6XufglStNakbTvFdG+X0TzmLxnCwAAwAD19fbFokX90d7Rtup1PVBrkohDPvKW4sLNqZffGtOuvid6u3uXediwER2xyyE7xh5H7RJrrbfG67729ONp/pGNLMciP2nRa3bfrGLRa+KEsdW9S/+IkyI6j4/onRqFnj9G9KWnQ6SLkJsjkjER7btF0nFgRPO4vGcLULe8aw5AVYVA9173QLHw8vgD/4hFfYuKf97W0Rab77pJTDlql9h0x0kCIupHErHpTpOKt5eefTnuu2F6zH1xXizsXhjDRg6L8ZPWjs132ziampe/+WrXvNJ38Vrejl5p2eulnrRcAxXWNCqi8/BIOg9f/HmhLyLxEgUAAKBWFPoL8eC0R+LGy2+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            "text/plain": [
              "<Figure size 1500x500 with 2 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 450,
              "width": 1212
            }
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "model = FisherLinearDiscriminant()\n",
        "model.fit(x_train, t)\n",
        "optimal_threshold = model._threshold\n",
        "\n",
        "plt.figure(figsize=(15, 5))\n",
        "\n",
        "# predict classes using the optimal threshold\n",
        "predicted = model.predict(x_test)\n",
        "\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
        "plt.contourf(x1, x2, predicted.reshape(N, N), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)\n",
        "plt.title(f\"Optimal threshold ({round(optimal_threshold, 2)})\")\n",
        "\n",
        "# set threshold to zero and make predictions\n",
        "model._threshold = 0\n",
        "predicted = model.predict(x_test)\n",
        "\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
        "plt.contourf(x1, x2, predicted.reshape(N, N), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)\n",
        "plt.title(\"Zero threshold (suboptimal)\")\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "25e96427",
      "metadata": {},
      "source": [
        "### 4.1.7 The perceptron algorithm"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "6530549f",
      "metadata": {},
      "source": [
        "Another linear discriminant model is the perceptron. It corresponds to a two-class model in which the input vector $\\mathbf{x}$ is first transformed using a nonlinear transformation to give a feature vector $\\boldsymbol\\phi(\\mathbf{x})$, and then use it to construct a generalized linear model of the form\n",
        "\n",
        "$$\n",
        "y(\\mathbf{x}) = f\\big(\\mathbf{w}^T\\boldsymbol\\phi(\\mathbf{x})\\big)\n",
        "$$\n",
        "\n",
        "We assume that the vector $\\boldsymbol\\phi(\\mathbf{x})$ typically includes the bias component $\\phi_0$. The nonlinear activation function $f(\\cdot)$ is given by a step function of the form\n",
        "\n",
        "$$\n",
        "f(\\alpha)=\n",
        "\\begin{cases}\n",
        "    +1, & \\quad \\alpha \\geq 0\\\\\n",
        "    -1, & \\quad \\alpha < 0\n",
        "\\end{cases}\n",
        "$$\n",
        "\n",
        "That is because for the perceptron it is more convenient to use target values $t=+1$ for class $\\mathcal{C}_1$ and $t=-1$ for class $\\mathcal{C}_2$, instead of $t \\in \\{0,1\\}$. We consider an error function called the *perceptron criterion*. Note that we are seeking a weight vector $\\mathbf{w}$, such that the inputs $\\mathbf{x}_n$, belonging in class $\\mathcal{C}_1$, have $\\mathbf{w}^T\\boldsymbol\\phi(\\mathbf{x}_n) > 0$, whereas the ones belonging in class $\\mathcal{C}_2$, have $\\mathbf{w}^T\\boldsymbol\\phi(\\mathbf{x}_n) < 0$. Given the coding scheme $t \\in \\{-1, +1\\}$, it follows that all inputs must satisfy $\\mathbf{w}^T\\boldsymbol\\phi(\\mathbf{x}_n)t_n > 0$. Thus, the perceptron criterion tries to minimize the quantity $-\\mathbf{w}^T\\boldsymbol\\phi(\\mathbf{x}_n)t_n$, for all misclassified inputs. More formally,\n",
        "\n",
        "$$\n",
        "E_P(\\mathbf{w}) = -\\sum_{n\\in\\mathcal{M}} \\mathbf{w}^T\\boldsymbol\\phi(\\mathbf{x}_n)t_n\n",
        "$$\n",
        "\n",
        "where $\\mathcal{M}$ denotes the set of misclassified patterns.\n",
        "\n",
        "We apply the stochastic gradient descent algorithm to the error function. Thus, the change in the weight vector, according to gradient descent, is given by,\n",
        "\n",
        "$$\n",
        "\\mathbf{w}^{(\\tau+1)} = \\mathbf{w}^{(\\tau)} - \\eta\\nabla E_P(\\mathbf{w}) = \\mathbf{w}^{(\\tau)} + \\eta\\boldsymbol\\phi_nt_n\n",
        "$$\n",
        "\n",
        "The *perceptron convergence theorem* states that if there exists an exact solution (the data are linearly separable), the the perceptron algorithm is guaranteed to find the solution in a finite number of steps. On the other hand, if the data are not linearly separable the perceptron never converges. Moreover, note that the perceptron **does not provide probabilistic outputs, nor does it generalize to $K>2$ classes**.\n",
        "\n",
        "Another important limitation arises from the fact that it is based on linear combinations of fixed basis functions."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "id": "603d828a",
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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9NMe2l19+eTaDL7/9AQcc0KhOXm+//XY2mzZ/PKaZamPGjJlju08++WSWLmfpGGms9HlSOCtu5513nuMYTsdXmhFX+NzU9PmWOhOmmc7pOa3uOEqv5V//+tfK1zzNIBw3blxROqLlpfHT8VVTB8TUDW+xxRarHLsus0MBAACYs5NX3uqrr175+0MPPbRRnbwK6x+pK0+qkc3eVevDDz/MrbzyypXbzTXXXNWeNxbeb74ulM5tU52oUOoIs/vuu1dumzq5pLpNOXfySo8n3/Vo9lpgqjsU1n3SOXt1mqJGkV7HVBObOHFilX9P3fXT+Xva/zRWqrnU1Bm+8HGnukKqVaSOSbM/7sI6Ul2e08LjY6+99srVZpdddqncPtVkG7NCQGGdL9W8anp9jj766NwLL7zQLLXhwk5e+ZrQHnvskdUnC6Va0o477jhL16Znnnmm2epGha9tuk16bIUrAhSO21zHZnq+0vNw9tlnz/G59c477+SWWWaZWV6r6mrKdenklcbfcMMNK7dbbbXVquwqlerTJ510UmUtMD2u2lZhqE16PQtr2gsssECVK0X8+9//zj6nCmuLNX2+FbuuV5+OaE1VfwZo7YS8AGgzIa98G/CaTlRT8CK/7UEHHVTlNqmAlW9D3adPn1qDSykIlR8znYjV1Jq7LlIxJz/eu+++W6fHnU5g67IEZV2e09NOO61ym1RsqMkFF1xQuW06AW6Mvn37VhbTanoNa3PKKadU7lNawrK2pQAKiyxnnnlmldsUPtfpcuONN9ZYJCpsH37FFVfkGiMVaZZffvlsrBQuq65QUfja5gNm1RVWmvPYTEWOmt5D//znPyu3rSkoWJdw0kYbbVS5zTnnnFPjY0lF5aWXXrpy+5oKf3VRuCxFKkJUt2xpOh4322yzWZ6j6t6L9ZGO3fx4F198cVFDXnWVxssvYZCKYAAAADQ85JWWkSsMOQwdOrRBIa90np0CEvntLrroomr3JdUc0lJZtYWYCu83XVKQqzopDJHCCnWpqZRDyCvVJu6///5qt03LNBaG1qZNm1Z2NYr0HOfHOuqoo+r0uNOlqgmNDXlOv/jii8pjrlu3bnMEmQp9++23lWGV9Nw3plbx+9//vnK/0sTChmqK2nBh/TFdttpqq2prlumY2mCDDSq3XXfddXPNVTcq3Mf0GtY0Sbo5j83qarbJyJEjc/369as1KFiXcNLVV189yxKqtdVWC8es7ruGukoBy/xYqb42+yT2Qum9Onu9urnqeg0JeRW7/gzQ2rUrdScxAGhOZ555ZtY2uTq/+tWvKq8XtqgvdP7552ftrpMTTjgha0ddk7TEX74NdGrjnFocN0Za3q6wRXxdpP3s169fFMM+++yTLfGXpJbkqe10XZZq3G+//Rp1v6kVdJLaftf0GtYktfxOyxjk24NfeumlWfv7mqR26vn209ddd12t95GWHaiprXlqN51fGi+5/PLLozFS6+x8u+/UVj4tn1AXf/nLX7JlAIqpIcdmaj9f03to3333jZVXXjm7nmpJ//znPxu0b6nVfloOMfnJT35S63KIqR348ccfX/lzXV776qT3fVp+snBJz+qWLU3H44UXXlj0pQzT+7a+r02xpeUm8kueprbt+fc0AAAA9bfJJpvEBhtskF1Py3RVt2RbbVJdIi1nlqy44opxyCGHVLttWv4r1RPyrr/++hg7dmyN43fq1CnOOeecav/epUuX2H333Wutx5WLbbbZpsblArfaaqvo379/dj0tP1a4pFs51CiStGxdvrZW1xpBWnKtGMvNJWm5xvxzmJZiS0t/Victc5eO7/wxn2oLDVVYh0hLKjZUU9eGU00o1Y6qq1mmumz6e15aGvCDDz6I5q4bpeOotqU2m+PYTEui/v73v6/27+n9mF6nwnr1j3m1+iv8LEt15dpqq3/84x+zpUCTdJznP2sborAmethhh8WQIUOq3Ta9V9daa61ojXW9htSfAVqbH7+hBYA2IBWNtt122xq3SYWVvLS+e1Xuu+++yus///nP63TfG220UTzwwAPZ9RTCWWmllardNhU3nn/++Xjrrbfim2++iXHjxlUWDpIRI0ZUXn/99dfrdP81hY7qa8CAAVlB64477shCRamgV1UB8JVXXsmKVvki4I477tjoAtCnn34aY8aMif/85z8Nekwvv/xyfP3119n1jTfeOOadd95abzP//PNnJ82pCPP2229nxcu555672u332muvWsfce++9K4sC6aR4woQJWcGuOilIl46Jd955J0aPHp0VCQuLAu+///4sx0Rtx3l6PTbbbLOor6Y4NuvyfKVt0vGUPPbYY9EQhe/bVDyuS4gqvW/z6hqeq0rhPqfA2tJLL13j9ksssUSsscYa8dxzz9X5PtLxkJ6j9LwPHz48K7SkUGNV6vraNMQXX3yRFeQ//PDD7LidNGnSLIWzzz77LPtv+l36fEihSAAAABrm1FNPjXXWWSe7/u9//zsLFCy++OL1GiMfNsp/eV7b+fIOO+wQffr0ie+++y6mTJmSnbvWFHpK+5cPPTWmHlcudtlllxr/np6/FVZYIUaNGlX5eJZbbrlmr1G8+eabWZgo3X+qEaTXavb9TFKNJ9UUapsEudtuu0UxHXDAAZXPQwrdHHjggU0+gTTVFgvDjam+Wd0kvJo0dW04hXNqC46lYyq9b/KBsVR7WnLJJZu1btTQY6LYx2Z6DfITkqvzi1/8Io444oisjvnll19mobiaQlJVGTlyZOVzk2p76X1el+8j1lxzzbj//vuzmnKqLS+//PJRX6kGm+ra9a0/F046bSl1vaaoPwO0NkJeALQZ6UQ3dT2qSd++fSuvVzUbJQVs0klOfibiySefXKf7fvfddyuvDxs2rMptUnEszSq6+uqrs5OXuvj222/rNJspFd+KXYhJIa98saWqkFdhESadSKeT2sbYdddds05s+QJYPuiVZhDVJayVFIZmUkHj17/+dZ1ul+9Wlk5g0+1qCnmlE/fapEJMmpWWwlrpJDUVN6q6XbqvVKC95ZZb5ih4NOaYSDNz61PEaqpjM3WXW2yxxWrdrvC5SSfv6XWob6erwtc+Fb4+//zzWm9TWMSo7n1bF4UzNOtyfOS3q0vIa/r06dnszXPPPTc7Xor12tRX2td0rKbZo3WdDdkU+wEAANCWrL322rHllltmAYJUXzjxxBOzyXh1lc7fCr8kr0vnl1RbS12d/vvf/2Y/v/rqqzWGvGYPODWkHldOivF4mrJGkcJ+qSt9vn5ZmxT0SeGTNCGwJvku68WSAlZpYmUK3KQJkCnQMftzm8ImKRSTryH99Kc/bXSXqJNOOikLDt17772x7LLLZqs6pPdQ6rxfl1pTU9aGG1I7ytecqusO1pR1o/oeE011bNbl+UpjpO8G8q9Der7qG/IqfN+m8FNd68qffPLJLK99Q0JeqXacn/Dbs2fP7HitTV2Po3Kp6zVV/RmgNRLyAqDNqCmYk1cYAksnwVXN2MlLrcL//ve/13s/Uieq2aViTmpvnWbL1EddTnga0368OqnF+EILLZTtdyrmpYJgCg4VnugWFhUbO9Mu+dOf/hSPP/54NpMnnWzefvvt2SVJs1TTzKHUnSt1sUonu1VJhaPCk+N0KcbrV2jBBResdYxUNBo0aFBlB640K2l2qdiQHk9t99fUx0RTHpt1ea5m3y6F3dLYc801V732p/C1T8Xv+qrv61Co8PVtyGOuTnoutttuu3jwwQfrtT91LZTU1b/+9a/sPV7fVvfF3g8AAIC22s0rBa7SOVmaEHfMMcfUKYiUpABFYTefVOupi8Il82r7kr2+9biqugul5fE++uijGse46KKLojkU4/E0RY0ivf777rtvXHnllfUeL52f1xakKXZ9MU0+TAGrdPzmJ4ued9551U4g3XPPPbNQVWMstdRS8de//jWOPPLI7PlKdbmjjjoqu6THn0KO66+/fmy//fZZl/WqNFVtuFBDakdV1Rabum5U12OiqY/N+jxf+ZBXVc9XbQrft6mjVVO89tUp3N/Uka4ugcS6Pi/lUNdryvozQGtUc49LAGhF6tv5p7riV2NVFR5LbaXzJzEpoJTaR6cCXVqeMN/tKZ1opUvh0m+FS/ZVp2vXrlFsqU12OjmvquiS3HrrrZXP1aqrrtqgGUqzS8sZPvHEE3HWWWfNUkxMUqEvnZDuscce2RIAqTiTgmbN9foV6tatW53GKVyecfYT0lSE2WmnnSpP/FPRJIXc0mufZnyl5R3Ta58/JgqLJMU+Jpry2GzIc9XQE/jGvvaFbcHrKz1PjX3MVUmzRfOFuvT5ljrb3XTTTdnSounxpmJj/rUpLNTUt2hTk1QcS0sq5MdMMwlT8T3Ntv3qq68q27rnL6lVfH2OEQAAAGqWln1LSyjmz7OOP/74Bp2v1vVcdPbtajtHL0Y9Lk3yS4GKmi5tqb5YVY0iLT9YWB9K3dVS56TUISvVl1KtqfD8vDDQV6r6YgqW5Jfiu/baa7M6RuGSbTfeeOMs2xbD73//+6x+lSZWFr6W6TlK3b1STTF1fNpkk02y566l1habo25U12OiqY/NYj1ftWmO1765a4vlUtdryvozQGukkxcA1EPhyVHqJFSMk7tnn302uyRpCb/UqWrppZcu+xkqabZdKhakk6zrrrsuC1/ll2QsDH0VqwiTpBl7f/jDH7KCTOrC9eSTT2bPXWolPWLEiMoiUNqX9Ld00ldYcCh8/X7zm99kJ63Flu6/uk5ihVJQK2/27VNILs0ISwYOHJi1rR8wYECzHxNNfWym56ouCp+rpC7P7+wKX/vbbrutsgDeHNJz19jHPLtUALvwwgsrf77qqqtir732avZjJM2yzReoUoe/u+66q8aZteXy+QUAANCanHLKKXHHHXdkX3jfeeedWR0hTbqrz/lq/ly0LsGAmmoalKZG8be//a3yeqrXpWXPalIO5+cpzLPpppvGAw88kC2DmI7hXXfdNfvbzTffXLnUZVp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            "text/plain": [
              "<Figure size 1500x500 with 2 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 450,
              "width": 1212
            }
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# number of training points\n",
        "N = 100\n",
        "\n",
        "x1, x2 = np.meshgrid(np.linspace(-5, 5, N), np.linspace(-5, 5, N))\n",
        "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
        "\n",
        "model = Perceptron()\n",
        "\n",
        "plt.figure(figsize=(15, 5))\n",
        "\n",
        "x_train, t = make_classification(\n",
        "    n_features=2,\n",
        "    n_informative=2,\n",
        "    n_redundant=0,\n",
        "    n_classes=2,\n",
        "    n_clusters_per_class=1,\n",
        "    n_samples=N,\n",
        "    random_state=10,\n",
        "    class_sep=2,\n",
        ")\n",
        "\n",
        "model.fit(x_train, np.where(t == 0, -1, 1))\n",
        "predicted = model.predict(x_test)\n",
        "\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
        "plt.contourf(x1, x2, predicted.reshape(N, N), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)\n",
        "plt.title(\"Linearly separable data\")\n",
        "\n",
        "x_train, t = make_classification(\n",
        "    n_features=2,\n",
        "    n_informative=2,\n",
        "    n_redundant=0,\n",
        "    n_classes=2,\n",
        "    n_clusters_per_class=1,\n",
        "    n_samples=N,\n",
        "    random_state=14,\n",
        ")\n",
        "\n",
        "model.fit(x_train, np.where(t == 0, -1, 1))\n",
        "predicted = model.predict(x_test)\n",
        "\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
        "plt.contourf(x1, x2, predicted.reshape(N, N), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)\n",
        "plt.title(\"Non-linearly separable data\")\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "d4e27e7c",
      "metadata": {},
      "source": [
        "## 4.2 Probabilistic Generative Models\n",
        "\n",
        "Models having linear decision boundaries arise from simple assumptions about the distribution of the data. A generative approach models the class-conditional densities $p(\\mathbf{x}|\\mathcal{C}_k)$, as well as the class priors $p(\\mathcal{C}_k)$, and use them to compute the posterior probability $p(\\mathcal{C}_k|\\mathbf{x})$ throught *Bayes theorem*. To that end, the posterior probability for class $\\mathcal{C}_1$, in a binary classification problem, is as follows,\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "p(\\mathcal{C}_1|\\mathbf{x}) &= \\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x})} \\\\\n",
        "&= \\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1) + p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)} \\\\\n",
        "&= \\frac{1}{1 + \\exp(-\\alpha)} = \\sigma(\\alpha)\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "where,\n",
        "\n",
        "$$\n",
        "\\alpha = \\ln\\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}\n",
        "$$\n",
        "\n",
        "*Proof*\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "\\sigma(\\alpha) &= \\frac{1}{1 + \\exp(-\\alpha)} \\\\\n",
        "&= \\frac{1}{1 + \\frac{1}{\\exp(\\alpha)}} = \\frac{\\exp(\\alpha)}{1 + \\exp(\\alpha)} \\\\\n",
        "&= \\frac{\\exp\\big(\\ln\\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}\\big)}{1 + \\exp\\big(\\ln\\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}\\big)} \\\\\n",
        "&= \\frac{\\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}}{1 + \\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}}\n",
        "= \\frac{\\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}}{\\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1) + p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}} \\\\\n",
        "&= \\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)\\big(p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1) + p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)\\big)} \\\\\n",
        "&= \\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1) + p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "The function $\\sigma(\\alpha)$ is the **logistic sigmoid** briefly presented in [Chapter 3](ch3_linear_models_for_regression.ipynb).\n",
        "\n",
        "For $K>2$ classes, the posterior for class $\\mathcal{C}_k$ is as follows,\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "p(\\mathcal{C}_k|\\mathbf{x}) &= \\frac{p(\\mathbf{x}|\\mathcal{C}_k)p(\\mathcal{C}_k)}{p(\\mathbf{x})} \\\\\n",
        "&= \\frac{p(\\mathbf{x}|\\mathcal{C}_k)p(\\mathcal{C}_k)}{\\sum_i p(\\mathbf{x}|\\mathcal{C}_i)} \\\\\n",
        "&= \\frac{\\exp(\\alpha_k)}{\\sum_i \\exp(\\alpha_i)}\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "which is known as the *normalized exponential* and can be regarded as a multiclass generalization of the logistic sigmoid function. The quantities $\\alpha_k$ are defined as follows,\n",
        "\n",
        "$$\n",
        "\\alpha_k = \\ln(p(\\mathbf{x}|\\mathcal{C}_k)p(\\mathcal{C}_k))\n",
        "$$\n",
        "\n",
        "The normalized exponential is also known as the *softmax function*, since it represents a smoothed version of the max function, because if $\\alpha_k \\gg \\alpha_i\\; \\forall i \\neq k$, then $p(\\mathcal{C}_k|\\mathbf{x}) \\approx 1$ and $p(\\mathcal{C}_i|\\mathbf{x}) \\approx 0$.\n",
        "\n",
        "### 4.2.1 Continuous inputs\n",
        "\n",
        "Given the formulation above, the next step is to assume the form of the class-conditional densities. The Gaussian distributions may be used for modelling continuous variables. Assuming that all classes share the same covariance matrix, the density for class $\\mathcal{C}_k$ is given by\n",
        "\n",
        "$$\n",
        "p(\\mathbf{x}|\\mathcal{C}_k) = \\mathcal{N}(\\mathbf{x}|\\boldsymbol\\mu_k, \\Sigma)\n",
        "$$\n",
        "\n",
        "Thus, from $(4.58)$, we have,\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "\\alpha &= \\ln\\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}\n",
        "= \\ln\\frac{\\mathcal{N}(\\mathbf{x}|\\boldsymbol\\mu_1, \\Sigma)p(\\mathcal{C}_1)}{\\mathcal{N}(\\mathbf{x}|\\boldsymbol\\mu_2, \\Sigma)p(\\mathcal{C}_2)} \\\\\n",
        "&= \\ln\\frac{\\mathcal{N}(\\mathbf{x}|\\boldsymbol\\mu_1, \\Sigma)}{\\mathcal{N}(\\mathbf{x}|\\boldsymbol\\mu_2, \\Sigma)}\n",
        "+ \\ln\\frac{p(\\mathcal{C}_1)}{p(\\mathcal{C}_2)} \\\\\n",
        "&= \\ln\\frac{\\exp\\big\\{-\\frac{1}{2}(\\mathbf{x}-\\boldsymbol\\mu_1)^T\\Sigma^{-1}(\\mathbf{x}-\\boldsymbol\\mu_1)\\big\\}}{\\exp\\big\\{-\\frac{1}{2}(\\mathbf{x}-\\boldsymbol\\mu_2)^T\\Sigma^{-1}(\\mathbf{x}-\\boldsymbol\\mu_2)\\big\\}}\n",
        "+ \\ln\\frac{p(\\mathcal{C}_1)}{p(\\mathcal{C}_2)} \\\\\n",
        "&= -\\frac{1}{2}(\\mathbf{x}-\\boldsymbol\\mu_1)^T\\Sigma^{-1}(\\mathbf{x}-\\boldsymbol\\mu_1) + \\frac{1}{2}(\\mathbf{x}-\\boldsymbol\\mu_2)^T\\Sigma^{-1}(\\mathbf{x}-\\boldsymbol\\mu_2) + \\ln\\frac{p(\\mathcal{C}_1)}{p(\\mathcal{C}_2)} \\\\\n",
        "&= - \\frac{1}{2}\\mathbf{x}^T\\Sigma^{-1}\\mathbf{x} + \\boldsymbol\\mu_1^T\\Sigma^{-1}\\mathbf{x} - \\frac{1}{2}\\boldsymbol\\mu_1^T\\Sigma^{-1}\\boldsymbol\\mu_1\n",
        "+ \\frac{1}{2}\\mathbf{x}^T\\Sigma^{-1}\\mathbf{x} - \\boldsymbol\\mu_2^T\\Sigma^{-1}\\mathbf{x} + \\frac{1}{2}\\boldsymbol\\mu_2^T\\Sigma^{-1}\\boldsymbol\\mu_2 + \\ln\\frac{p(\\mathcal{C}_1)}{p(\\mathcal{C}_2)} \\\\\n",
        "&= \\boldsymbol\\mu_1^T\\Sigma^{-1}\\mathbf{x} - \\boldsymbol\\mu_2^T\\Sigma^{-1}\\mathbf{x} - \\frac{1}{2}\\boldsymbol\\mu_1^T\\Sigma^{-1}\\boldsymbol\\mu_1 + \\frac{1}{2}\\boldsymbol\\mu_2^T\\Sigma^{-1}\\boldsymbol\\mu_2 + \\ln\\frac{p(\\mathcal{C}_1)}{p(\\mathcal{C}_2)} \\\\\n",
        "&= (\\boldsymbol\\mu_1 - \\boldsymbol\\mu_2)^T\\Sigma^{-1}\\mathbf{x} - \\frac{1}{2}\\boldsymbol\\mu_1^T\\Sigma^{-1}\\boldsymbol\\mu_1 + \\frac{1}{2}\\boldsymbol\\mu_2^T\\Sigma^{-1}\\boldsymbol\\mu_2 + \\ln\\frac{p(\\mathcal{C}_1)}{p(\\mathcal{C}_2)}\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "To that end, using $(4.57)$, we derive that,\n",
        "\n",
        "$$\n",
        "p(\\mathcal{C}_1|\\mathbf{x}) = \\sigma(\\mathbf{w}^T\\mathbf{x} + w_0)\n",
        "$$\n",
        "\n",
        "where,\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "\\mathbf{w} &= \\Sigma^{-1}(\\boldsymbol\\mu_1-\\boldsymbol\\mu_2) \\\\\n",
        "w_0 &= -\\frac{1}{2}\\boldsymbol\\mu_1^T\\Sigma^{-1}\\boldsymbol\\mu_1 + \\frac{1}{2}\\boldsymbol\\mu_2^T\\Sigma^{-1}\\boldsymbol\\mu_2 + \\ln\\frac{p(\\mathcal{C}_1)}{p(\\mathcal{C}_2)}\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "Note that the prior probabilities $p(\\mathcal{C}_k)$ enter through the bias parameter $w_0$, thus making parallel shifts of the decision boundary.\n",
        "\n",
        "For the general case of $K$ classes, from $(4.63)$, we have, \n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "\\alpha_k &= \\ln\\Big(\\frac{1}{(2\\pi)^{D/2}}\\Big) + \\ln\\Big(\\frac{1}{|\\Sigma|^{1/2}}\\Big) -\\frac{1}{2}(\\mathbf{x}-\\boldsymbol\\mu_k)^T\\Sigma^{-1}(\\mathbf{x}-\\boldsymbol\\mu_k) + \\ln p(\\mathcal{C}_k) \\\\\n",
        "&= \\ln\\Big(\\frac{1}{(2\\pi)^{D/2}}\\Big) + \\ln\\Big(\\frac{1}{|\\Sigma|^{1/2}}\\Big) - \\frac{1}{2}\\mathbf{x}^T\\Sigma^{-1}\\mathbf{x} + \\boldsymbol\\mu_k^T\\Sigma^{-1}\\mathbf{x} - \\frac{1}{2}\\boldsymbol\\mu_k^T\\Sigma^{-1}\\boldsymbol\\mu_k + \\ln p(\\mathcal{C}_k) \\\\\n",
        "&= \\ln A + \\ln B + Q + \\mathbf{w}_k^T\\mathbf{x} + w_{k0}\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "where,\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "A &= \\ln\\Big(\\frac{1}{(2\\pi)^{D/2}}\\Big) \\\\\n",
        "B &= \\ln\\Big(\\frac{1}{|\\Sigma|^{1/2}}\\Big) \\\\\n",
        "Q &= - \\frac{1}{2}\\mathbf{x}^T\\Sigma^{-1}\\mathbf{x} \\\\\n",
        "\\mathbf{w}_k &= \\Sigma^{-1}\\mu_k \\\\\n",
        "\\mathbf{w}_{k0} &= - \\frac{1}{2}\\boldsymbol\\mu_k^T\\Sigma^{-1}\\boldsymbol\\mu_k + \\ln p(\\mathcal{C}_k)\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "Then using $(4.62)$, we derive,\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "p(\\mathcal{C}_k|\\mathbf{x}) &= \\frac{\\exp(\\alpha_k)}{\\sum_j \\exp(\\alpha_j)} \\\\\n",
        "&= \\frac{\\exp(A + B + Q)\\exp(\\mathbf{w}_k^T\\mathbf{x} + w_{k0})}{\\exp(A + B + Q) \\sum_j \\exp(\\mathbf{w}_j^T\\mathbf{x} + w_{j0})}\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "and re-define $\\alpha_k$ as follows,\n",
        "\n",
        "$$\n",
        "a_k(\\mathbf{x}) = \\mathbf{w}_k^T\\mathbf{x} + w_{k0}\n",
        "$$\n",
        "\n",
        "Therefore, we see that for $K>2$ classes, $\\alpha_k$ are linear functions of $\\mathbf{x}$ since quadratic terms cancel each other due to the shared covariances. By relaxing the assumption of the shared covariance matrix among the classes, allowing each class to have each won covariance matrix $\\Sigma_k$, then we obtain quadratic functions of $\\mathbf{x}$, giving rise to *quadratic discriminant*.\n",
        "\n",
        "### 4.2.2 Maximum likelihood solution\n",
        "\n",
        "Given a set of data, comprising observations $\\mathbf{x}$ and corresponding class labels, we can determine the parameters of the class-conditional densities and class prior probabilities, using maximum likelihood. Suppose that we are given a dataset $\\{\\mathbf{x},t_n\\}$, where $t_n=1$ denotes class $\\mathcal{C}_1$ and $t_n=0$ denotes $\\mathcal{C}_2$. Then, for a data point $\\mathbf{x}_n$ belonging to class $\\mathcal{C}_1$ ($t_n=1$), we have,\n",
        "\n",
        "$$\n",
        "p(\\mathbf{x}_n,\\mathcal{C}_1) = p(\\mathcal{C}_1)p(\\mathbf{x}_n|\\mathcal{C}_1) = \\pi\\mathcal{N}(\\mathbf{x}_n|\\boldsymbol\\mu_1, \\Sigma)\n",
        "$$\n",
        "\n",
        "Similarly, for class $\\mathcal{C}_2$ ($t_n=0$),\n",
        "\n",
        "$$\n",
        "p(\\mathbf{x}_n,\\mathcal{C}_2) = p(\\mathcal{C}_2)p(\\mathbf{x}_n|\\mathcal{C}_2) =(1-\\pi)\\mathcal{N}(\\mathbf{x}_n|\\boldsymbol\\mu_2, \\Sigma)\n",
        "$$\n",
        "\n",
        "where $p(\\mathcal{C}_1)=\\pi$ and complementary $p(\\mathcal{C}_2)=1-\\pi$.\n",
        "\n",
        "Thus, the likelihood function is given by,\n",
        "\n",
        "$$\n",
        "p(\\mathbf{t},\\mathbf{X}|\\pi,\\boldsymbol\\mu_1,\\boldsymbol\\mu_2,\\Sigma) = \\prod_{n=1}^N \\big[\\pi\\mathcal{N}(\\mathbf{x}_n|\\boldsymbol\\mu_1, \\Sigma)\\big]^{t_n} \\big[(1-\\pi)\\mathcal{N}(\\mathbf{x}_n|\\boldsymbol\\mu_2, \\Sigma)\\big]^{1-t_n}\n",
        "$$\n",
        "\n",
        "and the log-likelihood is as follows,\n",
        "\n",
        "$$\n",
        "\\ln p(\\mathbf{t},\\mathbf{X}|\\pi,\\boldsymbol\\mu_1,\\boldsymbol\\mu_2,\\Sigma) = \\sum_{n=1}^N t_n\\big(\\ln\\pi +\\ln\\mathcal{N}(\\mathbf{x}_n|\\boldsymbol\\mu_1, \\Sigma)\\big) + (1-t_n)\\big(\\ln(1-\\pi) + \\ln\\mathcal{N}(\\mathbf{x}_n|\\boldsymbol\\mu_2, \\Sigma)\\big)\n",
        "$$\n",
        "\n",
        "1. Setting the derivative for $\\pi$ equal to zero, we obtain,\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "&\\frac{d}{d\\pi} \\ln p(\\mathbf{t},\\mathbf{X}|\\pi,\\boldsymbol\\mu_1,\\boldsymbol\\mu_2,\\Sigma) = 0 \\Leftrightarrow \\\\ \n",
        "&\\frac{d}{d\\pi} \\sum_{n=1}^N\\{t_n\\ln\\pi + (1-t_n)\\ln(1-\\pi)\\} = 0 \\Leftrightarrow \\\\\n",
        "&\\frac{1}{\\pi}\\sum_{n=1}^N t_n - \\frac{1}{1-\\pi}\\sum_{n=1}^N(1-t_n) = 0 \\Leftrightarrow \\\\\n",
        "&\\frac{1}{\\pi}\\sum_{n=1}^N t_n - \\frac{1}{1-\\pi}(N-\\sum_{n=1}^N t_n) = 0 \\Leftrightarrow \\\\\n",
        "&\\frac{1}{\\pi}\\sum_{n=1}^N t_n = \\frac{1}{1-\\pi}(N-\\sum_{n=1}^N t_n) \\Leftrightarrow \\\\\n",
        "&\\frac{1-\\pi}{\\pi}\\sum_{n=1}^N t_n = N-\\sum_{n=1}^N t_n \\Leftrightarrow \\\\\n",
        "&\\frac{1}{\\pi}\\sum_{n=1}^N t_n - \\sum_{n=1}^N t_n = N-\\sum_{n=1}^N t_n \\Leftrightarrow \\\\\n",
        "&\\pi = \\frac{1}{N}\\sum_{n=1}^N t_n\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "As expected, the maximum likelihood estimate for $\\pi$, is simply the fraction of points in class $\\mathcal{C}_1$.\n",
        "\n",
        "2. Setting the derivative for $\\boldsymbol\\mu_1$ equal to zero, we obtain,\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "&\\frac{d}{d\\boldsymbol\\mu_1} \\ln p(\\mathbf{t},\\mathbf{X}|\\pi,\\boldsymbol\\mu_1,\\boldsymbol\\mu_2,\\Sigma) = 0 \n",
        "\\Leftrightarrow \\\\ \n",
        "&\\frac{d}{d\\boldsymbol\\mu_1} \\sum_{n=1}^N t_n\\ln\\mathcal{N}(\\mathbf{x}_n|\\boldsymbol\\mu_1, \\Sigma) = 0 \n",
        "\\Leftrightarrow \\\\\n",
        "&\\frac{d}{d\\boldsymbol\\mu_1} \\bigg[ -\\frac{1}{2}\\sum_{n=1}^N t_n(\\mathbf{x}_n-\\boldsymbol\\mu_1)^T\\Sigma^{-1}(\\mathbf{x}_n-\\boldsymbol\\mu_1) \\bigg] = 0 \\Leftrightarrow \\\\\n",
        "&-\\frac{1}{2}\\sum_{n=1}^N -2t_n\\Sigma^{-1}(\\mathbf{x}_n-\\boldsymbol\\mu_1) = 0 \\Leftrightarrow \\\\\n",
        "&\\sum_{n=1}^N t_n(\\mathbf{x}_n-\\boldsymbol\\mu_1) = 0 \\overset{\\sum_{n=1}^N t_n = N_1}{\\Leftrightarrow} \\\\\n",
        "&\\sum_{n=1}^N t_n\\mathbf{x}_n = N_1\\boldsymbol\\mu_1 \\Leftrightarrow \\\\\n",
        "&\\boldsymbol\\mu_1 = \\frac{1}{N_1}\\sum_{n=1}^N t_n\\mathbf{x}_n\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "3. Similarly, the corresponding result for $\\boldsymbol\\mu_2$ is given by,\n",
        "\n",
        "$$\n",
        "\\boldsymbol\\mu_2 = \\frac{1}{N_2}\\sum_{n=1}^N (t_n-1)\\mathbf{x}_n\n",
        "$$\n",
        "\n",
        "4. Finally, the solution for the shared covariance matrix $\\Sigma$ is similar to the one derived for the multivariate Gaussian distribution is [Chapter 2](ch2_probability_distributions.ipynb), where the matrix $\\Sigma$ is defined in $(4.78)$, $(4.79)$, and $(4.80)$.\n",
        "\n",
        "**Note**: Fitting Gaussian distributions to the classes is not robust to outliers, because the maximum likelihood estimation of a Gaussian is not robust itself.\n",
        "\n",
        "\n",
        "### 4.2.3 Discrete features\n",
        "\n",
        "Consider the case of discrete binary feature values $x_i \\in \\{0, 1\\}$. When there are $D$ inputs, then a general distribution would correspond to $2^D-1$ independent variables. Assuming a *naive Bayes* approach, we have the following class-conditional mass functions,\n",
        "\n",
        "$$\n",
        "p(\\mathbf{x}|\\mathcal{C}_k) = \\prod_{i=1}^D \\mu_{ki}^{x_i}(1-\\mu_{ki})^{1-x_i}\n",
        "$$\n",
        "\n",
        "For $K$ classes, substituting into $(4.63)$, gives,\n",
        "\n",
        "$$\n",
        "\\alpha_k(\\mathbf{x}) = \\sum_{i=1}^D \\big(x_i\\ln\\mu_{ki} + (1-x_i)\\ln(1-\\mu_{ki})\\big) + \\ln p(\\mathcal{C}_k)\n",
        "$$\n",
        "\n",
        "In the more general case, where discrete variables can take $M > 2$ states, the class-conditional mass functions are defined as follows,\n",
        "\n",
        "$$\n",
        "p(\\mathbf{x}|\\mathcal{C}_k) = \\prod_{i=1}^D\\prod_{m=1}^M \\mu_{kim}^{\\phi(x_i)_m}\n",
        "$$\n",
        "\n",
        "where $\\phi(x_i)$ produces a $1$-of-$M$ binary coding scheme, where only one of the value among $\\phi(x_i)_1,\\dots,\\phi(x_i)_M$ is $1$, and the others are all $0$. Thus, by substituting the expression above into $(4.63)$, gives,\n",
        "\n",
        "$$\n",
        "\\alpha_k(\\mathbf{x}) = \\sum_{i=1}^D\\sum_{m=1}^M \\big(\\phi(x_i)_m\\ln\\mu_{kim}\\big) + \\ln p(\\mathcal{C}_k)\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "id": "33772469",
      "metadata": {},
      "outputs": [
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 413,
              "width": 546
            }
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# number of training points\n",
        "N = 100\n",
        "\n",
        "x_train, t = make_classification(\n",
        "    n_features=2, n_informative=2, n_redundant=0, n_classes=2, n_clusters_per_class=1, n_samples=N, random_state=21\n",
        ")\n",
        "\n",
        "x1, x2 = np.meshgrid(np.linspace(-5, 5, N), np.linspace(-5, 5, N))\n",
        "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
        "\n",
        "model = GenerativeClassifier()\n",
        "model.fit(x_train, t)\n",
        "predicted = model.predict(np.array([np.ravel(x1), np.ravel(x2)]))\n",
        "\n",
        "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
        "plt.contourf(x1, x2, predicted.reshape(N, N), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "a8694285",
      "metadata": {},
      "source": [
        "## 4.3 Probabilistic Discriminative Models\n",
        "\n",
        "An alternative approach, called *discriminative training*, is to directly maximize the likelihood function defined through the conditional distribution $p(\\mathcal{C}_k|\\mathbf{x})$.\n",
        "\n",
        "### 4.3.2 Logistic Regression\n",
        "\n",
        "Consider the binary classification problem. In the analysis of generative approaches we saw that under rather general assumptions, the posterior probability of class $\\mathcal{C}_1$ can be expressed as a logistic sigmoid acting on a linear function of the input vectors $\\mathbf{x}$ or the feature vector $\\boldsymbol\\phi$ (see $4.65$) so that,\n",
        "\n",
        "$$\n",
        "p(\\mathcal{C}_1|\\boldsymbol\\phi) = y(\\boldsymbol\\phi) = \\sigma(\\mathbf{w}^T\\boldsymbol\\phi)\n",
        "$$\n",
        "\n",
        "In the terminology of statistics, this model is known as *logistic regression*, although its a classification model.\n",
        "\n",
        "> One advantage of the discriminative approach is that there are typically fewer adaptive parameters to be determined. For an $M$-dimensional feature space, this model has $M$ adjustable parameters. By contrast, the generative model using Gaussian class conditional densities, would have used $2M$ parameters for the means and $M(M+1)/2$ parameters for the (shared) covariance matrix.\n",
        "\n",
        "We can use maximum likelihood to determine the parameters of the logistic regression model. Given a data set $\\{\\boldsymbol\\phi_n, t_n\\}$, where $t_n\\in\\{0,1\\}$, the likelihood function is given by,\n",
        "\n",
        "$$\n",
        "p(\\mathbf{t}|\\boldsymbol{\\Phi},\\mathbf{w}) = \\prod_{n=1}^N p(\\mathcal{C}_1|\\boldsymbol\\phi_n)^{t_n}\\big(1-p(\\mathcal{C}_1|\\boldsymbol\\phi_n)\\big)^{1-t_n} = \\prod_{n=1}^N y_n^{t_n}\\{1-y_n\\}^{1-t_n}\n",
        "$$\n",
        "\n",
        "The maximum likelihood is equivalent to the minimum of the negative of the logarithm of the likelihood, which gives the *cross-entropy error function*,\n",
        "\n",
        "$$\n",
        "E(\\mathbf{w}) = -\\ln p(\\mathbf{t}|\\boldsymbol{\\Phi},\\mathbf{w}) = - \\sum_{n=1}^N t_n \\ln y_n + (1-t_n)\\ln(1-y_n)\n",
        "$$\n",
        "\n",
        "> **Why is the error function called cross-entropy?**\n",
        "> \n",
        "> The cross-entropy for discrete probability distributions $p$ and $q$ is defined as $H(p,q)=\\sum_{x} p(x)\\log q(x)$. Since we assume that the target variables $t_n$ are probabilities taking only extreme values $0$ or $1$, and $y_n$ is a probability distribution, then $E(\\mathbf{w})$ can be interpreted as the cross entropy of the target variables and the posterior probability distribution.\n",
        "\n",
        "Then, taking the gradient of the error function over $\\mathbf{w}$, we obtain,\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "\\nabla E(\\mathbf{w}) &= -\\nabla\\ln p(\\mathbf{t}|\\boldsymbol{\\Phi},\\mathbf{w}) \\\\\n",
        "&= -\\nabla \\sum_{n=1}^N t_n \\ln y_n + (1-t_n)\\ln(1-y_n) \\\\\n",
        "&= -\\sum_{n=1}^N \\frac{d}{dy_n}t_n \\ln y_n + \\frac{d}{dy_n}(1-t_n)\\ln(1-y_n) \\\\\n",
        "&\\overset{\\frac{d}{dx}\\ln f(x)=\\frac{f'(x)}{f(x)}}{=} -\\sum_{n=1}^N \\frac{d}{dy_n}t_n \\ln y_n + \\frac{d}{dy_n}(1-t_n)\\ln(1-y_n) \\\\\n",
        "&= -\\sum_{n=1}^N \\frac{t_n}{y_n}\\frac{d}{da_n}y_n\\frac{d}{d\\mathbf{w}}a_n - \\frac{1-t_n}{1-y_n}\\frac{d}{da_n}y_n\\frac{d}{d\\mathbf{w}}a_n \\\\\n",
        "&= -\\sum_{n=1}^N \\big(\\frac{t_n}{y_n} - \\frac{1-t_n}{1-y_n}\\big)\\frac{d}{da_n}y_n\\frac{d}{d\\mathbf{w}}a_n \\\\\n",
        "&= -\\sum_{n=1}^N \\big(\\frac{t_n}{y_n} - \\frac{1-t_n}{1-y_n}\\big)y_n(1-y_n)\\boldsymbol{\\phi}_n \\\\\n",
        "&\\overset{(4.88)}{=} -\\sum_{n=1}^N \\frac{t_n-y_n}{y_n(1-t_n)}y_n(1-y_n)\\boldsymbol{\\phi}_n \\\\\n",
        "&= \\sum_{n=1}^N (y_n - t_n)\\boldsymbol{\\phi}_n\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "Note that the gradient takes the same form as the gradient of the sum-of-squares error function, however, $y_n$ involves a non-linear function. At this point we can make use of $(4.91)$ and $(3.22)$ to obtain a sequential algorithm (gradient descent) for optimizing the parameters."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "id": "482a2a0f",
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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MitJoOgrTAAAAAKA45HkAAABQPIrSaEqCLAAAAAAoDnkeAAAAFIuiNJqWIAsAAAAAikOeBwAAAMWhKI2mJsgCAAAAgOKQ5wEAAEAxKEqj6QmyAAAAAKA45HkAAABQ/xSlgSALAAAAAApFngcAAAD1TVEaPEqQBQAAAADFIc8DAACA+qUoDYYRZAEAAABAccjzAAAAoD4pSoN1CLIAAAAAoDjkeQAAAFB/FKXBCARZAAAAAFAc8jwAAACoL4rSYBSCLAAAAAAoDnkeAAAA1A9FaTAGQRYAAAAAFIc8DwAAAOqDojTYAEEWAAAAABSHPA8AAABqT1EajIMgCwAAAACKQ54HAAAAtaUoDcZJkAUAAAAAxSHPAwAAgNpRlAYTIMgCAAAAgOKQ5wEAAEBtKEqDCRJkAQAAAEBxyPMAAACg+hSlwSQIsgAAAACgOOR5AAAAUF2K0mAKQVa6CbIAAAAAoP4pTAMAAIDqUZQGU6QwDQAAAACKwURTAAAAqA5FaVAGgiwAAAAAKA55HgAAAFSWojQoc5AlzAIAAACA+qcwDQAAACpHURqUOchKhFkAAAAAUP9MNAUAAIDKUJQGZaYwDQAAAACKQ54HAAAA5acoDSpAkAUAAAAAxSHPAwAAgPJSlAYVIsgCAAAAgOKQ5wEAAED5KEqDChJkAQAAAEBxyPMAAACgPBSlQYUJsgAAAACgOOR5AAAAMHWK0qAKBFkAAAAAUBzyPAAAAJgaRWlQJYIsAAAAACgOeR4AAABMnqI0qCJBFgAAAAAUhzwPAAAAJkdRGlSZIAsAAAAAikOeBwAAABOnKA1qQJAFAAAAAMUhzwMAAICJUZQGNSLIAgAAAIDikOcBAADA+ClKgxoSZAEAAABAccjzAAAAYHwUpUGNCbIAAAAAoDjkeQAAALBhitKgDgiyAAAAAKA45HkAAAAwNkVpUCcEWQAAAABQHPI8AAAAGJ2iNKgjgiwAAAAAKA55HgAAAIxMURrUGUEWAAAAABSHPA8AAADWpygN6pAgCwAAAACKQ54HAAAAa1OUBnUcZKWbIAsAAAAA6p/CNAAAAPg3RWlQ5xSmAQAAAEAxKEwDAACANRSlQQEoTAMAAACAYrADAgAAAChKqwsnn3xyZFk2dPvDH/5Q6yFRhwRZAAAAAPVBnsd4yPMAAICm139vRM/1Ed2XRfRcF9F3d0Se13pUVElbtTpiZH/+85/jU5/6VK2HQaGCrIWl+9ss2LjWwwEAAABoOvI8JpPnyfIAAICmkfdG9FwWedd5EX23rf/31m0j6zwkon3viJbOWoyQKrFSWg0NDAzECSecEH19fbHpppvWejgUKMhKzLIEAAAAqC55HlNZMU2eBwAAFM7A6oieP0d0XxLRfXFE9zUR/UtGP77nL5EvfkPkKz47ckFa0n9H5Cu/EPniEyK6r6rY0Kk9RWk19NnPfjauvvrq2GGHHeL444+v9XAoEIVpAAAAANUnz2Oy5HkAAECh9N0V+YovR774+MiXnx75irMiX/GZyFd8OPIlr498+Scjem9eeyvO7ssjX35GRD5G0dpaVkS+4syIrgsq9SyoMUVpNXLXXXfF+9///tL9L37xi9He3l7rIVEwgiwAAACA6pHnMVXyPAAAoO7lvZEv/3TkS98e0X1eRHSNcFD/mu05l72vdIv+paUCtXzFp9f8baJdrvzimhXYaDiK0mrkzW9+c6xYsSJe85rXxL777lvr4VBQgiwAAACA6pDnUQ7yPAAAoG4NdEW+7LSInj+O/zF9t0S+9OTIV5ydfphkx3nkKz9fKoijsShKq4Ef/vCH8ctf/jI22mij+MQnPlHr4VBwgiwAAACAypLnUU7yPAAAoO7keWmLzlRkNvHHPhAxcP8U+18S0fOnqbVB3Wmr9QCazZIlS+LEE08s3f/oRz8am2yySVnaveeee8b8+6JFi8rSD/UbZC3qW1gKsrZZsHGthwMAAADQMCqV5yUyveYlzwMAAOpKz5URvVfXdAh513mRdexV0zFQXorSquyd73xn3HfffbHnnnvG8ccfX7Z2t9pqq7K1RTEJsgAAAACKk+clMr3mJs8DAADqRSoIq7m+myP6H4lo3ajWI6FMbN9ZRZdcckl89atfjba2tvjiF78YWZbVekg0GEv/AwAAAJSPPI9Kk+cBAAA1178wou/GqAv5I7UeAWVkpbQq6enpiRNOOCHyPI//9//+Xzz1qU8ta/t33333Bpf632233craJ/XJDEsAAACA+s/zEpkeiTwPAACoqe7Lo27k3bUeAWWkKK1KPvzhD8ett94aj3vc4+LUU08te/sLFiwoe5sUlyALAAAAoL7zvESmxyB5HgAAUCv5wOKoG9mMWo+AMrJ9ZxWk8OojH/lI6f7ZZ58dM2fOrPWQaAKW/gcAAACYHHketSDPAwAAaqNeVidri2jZtNaDoIyslFYFZ511Vmm5/8c//vGxatWq+MEPfrDeMTfddNPQ/QsvvDDuu+++0v0jjjhC6MWkmWEJAAAAMHHyPGpFngcAADTt6mTtu0e0uJ5uJIrSqqC7e01V6T//+c849thjN3j8GWecMXT/jjvuEGIxJYIsAAAAgImR51FL8jwAAKCastYFkdfDODqfV+shUGa274QmYOl/AAAAACgOeR4AAFA17XtFREdtx9C6bUTbjrUdA2WnKK0KzjnnnMjzfMzbqaeeOnT8RRddNPT7bbbZpqZjp3EIsgAAAADGR55HPZDnAQAAVZG2zOzYp4abNc6KbPZJEVlWhjFQTxSlQRMRZAEAAABAccjzAACAasg6D0v/O7VGpr88Itt4gg+aHdnc90e0bjm1vqlLitKgyQiyAAAAAKA45HkAAEDFtW0d2YzjJ//4joMjm/7CyOaeGTFt13H2uXNk8z4a0bbd5PulrilKgyYkyAIAAACA4pDnAQAAFTf9sMimv2rij+vYP7KZr1+z/WbrxpHNeXdk874Y0XlkRDZvnYNnRXQeEdm8z0U295SI1s3LNXrq0GQ3dAUaJshaGNssmOgSmgAAAABAtfO8RX0LS4Vp8jwAAKAiZhwZWevmka/6bsTAvWMfm82LbPqREZ2HrylIG65108hmvioi3fKeiIHVES2dEdG+/rE0LCul1YnTTjst8jwv3fbbb79aD4cmC7PMsAQAAACYGHketWDFNAAAoOI6do9s3tmRzT4tYtqzIyIVkw1qi2h7amSz3hHZ/C9HTD9iw0VmWXtE69yIrENBWpOxUhrwaGGaFdMAAAAAoN7ZAQEAAKi4VDzW/rTI2p+25ue8NyIGrHTGhFgpDSixYhoAAAAAFIc8DwAAqJpsmpXOmDBFacB6QZYwCwAAAADqn8I0AAAA6pWiNGCU5f+FWQAAAABQ70w0BQAAoB4pSgPWozANAAAAAIpDngcAAEC9UZQGjEiQBQAAAADFIc8DAACgnrTVegBAfQdZi/oWloKsbRZsXOvhAAAAAABjkOcBAMAI+v4Zedf5Ef3/ihhYGZG1RWTzI+t4dkT73hEt02s9QmhIitKAMQmyAAAAAKA45HkAAPCo7isi7zo3ou/2Ef54Z+R910es/GZE5/6Rdb4konV+DQYJjcv2ncAGWfofAAAAAIpDngcAQFPLByJf+Y3IV3x8lIK04VZHdP068qXvjOj7V5UGCM1BURowLoIsAAAAACgOeR4AAE0pzyNf9bWIrl9M8HEPR770/RH9iyo1Mmg6itKAcRNkAQAAAEBxyPMAAGg63RdFdP1mkg9eEfmyD0XkvWUeFDQnRWnAhAiyAAAAAKA45HkAADTVKmmrfzy1Ngbujei5slwjgqamKA2YMEEWAAAAABSHPA8AgKbQ+5eIgalvv5l3nVeW4UCzU5QGTIogCwAAAACKQ54HAECjy7vOL09DfbdE9N1dnragiSlKAyZNkAUAAAAAxSHPAwCgofXdVsa2bi9fW9CkFKUBUyLIAgAAAIDikOcBANCw8pVlbGtF+dqCJqUoDZgyQRYAAAAAFIc8DwCAxpSVsa3WMrYFzUlRGlAWgiwAAAAAKA55HgAADadlbhnbmlO+tqBJKUoDykaQBQAAAADFIc8DAKChtD+jTA21RbTtVKa2oHkpSgPKSpAFAAAAAMUhzwMAoFFknYeUp6H23SNa55WnLWhiitKAshNkAQAAAEBxyPMAAGgIrVtFtD21forboMkpSgMqQpAFAAAAAMUhzwMAoBFkM16+ZvvNyZq2a0TbDuUcEjQtRWlARYOsdBNkAQAAAED9U5gGAEDhTdshsllvndxj254Y2az/F5Fl5R4VNCVFaUDFKUwDAAAAgGIw0RQAgMLr2DuyWe9Kd8b/mLZnRDb7AxEtnZUcGTQVRWlAVQiyAAAAAKA45HkAABRax26RzTs7ovMlEdmc0Y9r2zmyWSdHNud9ES3TqzlCaHhT2EgXYDJB1sLS/W0WbFzr4QAAAAAA48jzZHkAABRS6yaRzXxFxIyjI3qujrzvXxGxIu3xGVnLvIj23SJat6z1KKFhKUoDqh5kLepbWJplKcwCAAAAgPpmoikAAIWXTYvo2COyjj1qPRJoKrbvBGoSZCWW/wcAAACA+ifPAwAAYKIUpQE1IcgCAAAAgOKQ5wEAADARitKAmhFkAQAAAEBxyPMAAAAYL0VpQE0JsgAAAACgOOR5AAAAjIeiNKDmBFkAAAAAUBzyPAAAADZEURpQFwRZAAAAAFAc8jwAAADGoigNqBuCLAAAAAAoDnkeAAAAo1GUBtQVQRYAAAAAFIc8DwAAgJEoSgPqjiALAAAAAIpDngcAAMC6FKUBdUmQBQAAAADFIc8DAABgOEVpQN0SZAEAAABAccjzAAAAGKQoDahrgiwAAAAAKA55HgAAAImiNKDuCbIAAAAAoDjkeQAAAChKAwpBkAUAAAAAxSHPAwAAaG6K0oDCEGQBAAAAQHHI8wAAAJqXojSgUARZAAAAAFAc8jwAAIDmpCgNKBxBFgAAAAAUhzwPAACg+ShKAwpJkAUAAAAAxSHPAwCAMsrziIHVEf0PRvQvjsh7az0iWE/b+r8CKE6QtahvYSnI2mbBxrUeDgAAAAAwBnkeAABM0cDyiO6LIu86P2Lg3mF/yCLado6s85CI9mdGZNaoovYUpQENMsNyoSALAAAAAOqcwjQAAJiEvDfyVd+KSMVoMdKqaHlE3/WRr7g+ItskspnHRXTsUYOBwr8pjQQaJsyy9D8AAAAAFCPLk+cBAMA4DayOfNnpEV2/GqUgbR35Q5Gv+ETE6nOrMToYlaI0oGEIsgAAAACgOOR5AACwAXlf5Ms/FtH314k/dGhlNagNRWlAQxFkAQAAAEBxyPMAAGAMXb+M6Lth0g/PV34lov++sg4JxktRGtCwQZYwCwAAAADqnzwPAABGkA9EvvrXU2ykP3KrpVEjitKAhg2yEkEWAAAAANQ/eR4AAKyj59qI/KGpt9P1u4i8pxwjgglRlAY0LEEWAAAAABSHPA8AAP4t7/5dmVpaEdFzVZnagvFTlAY0NEEWAAAAABSHPA8AAB41cF/52uovY1swTorSgIYnyAIAAACA4pDnAQBAKkpbXbam8rx8bcF4KUoDmoIgCwAAAACKQ54HAEDTyzrK11QZ24LxUpQGNA1BFgAAAAAUhzwPAICm1rJxfbYF46QoDWgqgiwAAAAAKA55HgAATatt6zI11B7R/uwytQXjpygNaDqCLAAAAAAoDnkeAABNp+/OiK4LytNWx94RLbPK0xZMgKI0oCkJsgAAAACgOOR5AAA0k3zlORHRVZa2ss5DytIOTJSiNKBpCbIAAAAAoDjkeQAANIX+hRF9fylPW50viGh7QnnagglSlAY0NUEWAAAAABSHPA8AgEaXd51fppbaIqYfU6a2YOIUpQFNT5AFAAAAAMUhzwMAoKF1X1Gmhvoi67ulTG3BxClKAxBkAQAAAEChyPMAAGhIeR6RLylje2VsCyZIURrAowRZAAAAAFAc8jwAABpPXlrhrHzN9ZSvLZggRWkAwwiyAAAAAKA45HkAADSULJXxdJaxvRnlawsmSFEawDoEWQAAAABQHPI8AAAaStvjytdWaxnbgglSlAYwAkEWAAAAABSHPA8AgEaRdTy3PA21bR/RtnV52oJJUJQGMApBFgAAAAAUhzwPAICG0LFXRMyacjNZ56FlGQ5MlqI0gDEIsgAAAACgOOR5AAAUXtYR0fm8KbaxcUT7HuUaEUyKojSAcQRZ6SbIAgAAAID6J88DAKDoshlHR7Q9dZKP7ohszrsismllHhVMjKI0gHESZAEAAABAccjzAAAorGxaZLPfHdG20wQfOCOy2e+NaHtChQYG46coDWACBFkAAAAAUBzyPAAACqtlemRz3hfR+dKImLXh46c9M7J5H4lon+wKa1BebWVuD6BJgqyFsc2CjWs9FAAAAABgA+R5AAAUesW0mcdGzHhJRM9lkXddENF3T0SsKG3TGS3zItr3iKzz4IjWzWo9WliLojSAKQRZiTALAAAAAOqbPA8AgELL2iM69o+sY/81P+d5RJbVelQwJtt3AkwhyEos/w8AAAAA9U+eBwBAw1CQRgEoSgOYAkEWAAAAABSHPA8AAKA6FKUBTJEgCwAAAACKQ54HAABQeYrSAMpAkAUAAAAAxSHPAwAAqCxFaQBlIsgCAAAAgOKQ5wEAAFSOojSAMhJkFUSeRwysjhhYHpH313o0AAAAANSIPK9A8p6IgWUReW+tRwIAAIxD23gOAmBiQdaivoWlIGubBRvXejgML0Tr+1vkXedF9PwpIrr//bfWrSLrODiiY7+Ilpm1HCUAAAAAVSbPq2P990Te9duIrosjYsW/f59tEtGxf2SdB0e0es0AAKAeKUoDqABBVp3puSnyVV+P6L9z5L/33x35qq9FrPpOROdzI5vxqohsWrVHCQAAAECNyPPqTP/CyFd8OaLvxpH/nj8U0fWjyLt+HNH+nMhmvD6idW61RwkAAIzB9p0AFWLp/zrRfXHkyz8wekHa2gdHdP0y8mWnRgysrMLgAAAAAKgX8rw60Xtr5EvePXpB2loGInouj3zZuyL6F1VhcAAAwHgpSgOoIEFWjXVfHfmKz6aplRN7XN+tkS//aETeW6mRAQAAAFCH5Hk11ndX5MvOWHurzvEYuD/yZWli6pJKjQwAAJggRWkAFSbIqpGBZZGvOCut5T+5x/elLT//r9yjAgAAAKDOyfNqJM8jX/6JiFg9uccPPBD5yi+Ue1QAAMAkKUoDqAJBVg10XxgRXVNs47dWSwMAAABoQvK8Guj9c8TAPVNs4+qI/vvLNSIAAGAKFKUBVIkgq8qzKrvOK0M7yyJ6rizHiAAAAAAoGHledZUlzyu1c35Z2gEAAKZGURpAFQmyqqT3ptJy/eWQd11QlnYAAAAAKB55XpX0L4novaY8bXX/vjRpFQAAqC1FaQBVJsiqgoGF5Wur/97ytQUAAABA4cjzqmDgvjQ9tDxtpd0P8hXlaQsAAJg0RWkANSDIqrCBVeVrKy9jWwAAAAAUkjyvwvKV9d0eAAAwYYrSAGpEkFVBWUd9tgUAAABAYcnzKijrLHODMj0AAKg1RWkANSTIqpCWjcrY1vzytQUAAABAocnzCpDnRVtEy6wytgcAAEyGojSAOgiy0k2QVUbTdo6I6WVpKmvfuyztAAAAANAY5HkV0LJ5ROvjy9NW++4R2bTytAUAAEyaojSAOiHIKqOW6RGdB5ShobaIzgPL0A4AAAAAjUaeV0ZZFlnnIeVpqkztAAAAU6MoDaCOCLLKJ+t83tQbad8zomVOOYYDAAAAQAOS55VRR9qxYIrbbrZuHdG2Q7lGBAAATIGiNIA6I8gqk9YFEZ1HTf7x2UaRzXhlOUcEAAAAQAPneTK9Kco6Ipt1whQamBbZzP8srboGAADUnqI0gDokyCqPbMaxER2T2X5zdmRz3hvRunEFRgUAAABAI+Z5iTxvijr2imzGayfxwLbIZp0UMW37CgwKAACYDEVpAHVKkFUGWRbZzDdFNv2YtHTa+B7TunVk8z4a0bZtpUcHAAAAQAOR55XJ9CMim/X/IqJzfMdn8yObc1pEx26VHhkAADABbRM5GIDqB1mL+haWgqxtFli1a1LScv0zjo6s47kR3b+LvOu3Efkj6x4UMe1ZkXUeEjFtZ0v8AwAAADAp8rwy6dg7smnPiuj5Q+Rdv4nov2f9Y9p2iKzz0Ij250Rk02oxSgAAYAyK0gDqnCCrTFrnR8x4aWTTXxzR9/eIgaUR0RuRzYxo3cpWnQAAAACUhTyvTFqmR3QeGlnHIRH9d0b0pxXouiKyGRGtm0e0blnrEQIAAGNQlAZQAIKsMspaI6Y9qdajAAAAAKCByfPKKO1q0LbtmhsAAFAYLbUeAADjD7KSFGQBAAAAAPVNngcAADQzRWkABSLIAgAAAIDikOcBAADNSlEaQMEIsgAAAACgOOR5AABAM1KUBlBAgiwAAAAAKA55HgAA0GwUpQEUlCALAAAAAIpDngcAADQTRWkABSbIAgAAAIDikOcBAADNQlEaQMEJsgAAAACgOOR5AABAM1CUBtAABFkAAAAAUBzyPAAAoNEpSgNoEIIsAAAAACgOeR4AANDIFKUBNBBBFgAAAAAUhzwPAABoVIrSABqMIAsAAAAAikOeBwAANCJFaQANSJAFAAAAAMUhzwMAABqNojSABiXIAgAAAIDikOcBAACNRFEaQAMTZAEAAABAccjzAACARqEoDaDBCbIAAAAAoFh5XrrJ8wAAgCJTlAbQBARZAAAAAFAs8jwAAKDIFKUBNBFBFgAAAAAUhzwPAAAoKkVpAE1GkAUAAAAAxcvzZHoAAECRKEoDaEKCLAAAAAAoVp6XyPMAAICiUJQG0KQEWQAAAABQHPI8AACgSBSlATQxQRYAAAAAFIc8DwAAKApFaQBNTpBVA/0PRPTcENF9RUTP9RF9d0fkea1HBQAAAEAByPNqYGBZRM+NEd1XRvRcG9H394i8v9ajAgCAutZW6wEAUB9B1qK+haUga5sFG9d6OI0p74vouTryrt9E9N20/t9bt46s85CI9n0iWqbXYoQAAAAAFIQ8rwrSJNK+m9fkeT1/SjNN1/57tklknQdHdBwU0TqvVqMEAIC6ZaU0AErMsKyg3tsjX/zmyFd8fOSCtKT/X5Gv/FLki4+PfPVvrZwGAAAAwJjkeRXU/1Dky06OfNn7I3ouX78gLckfinz19yJf8vrIV34z8oGBWowUAADqlqI0AIYIsiqg589rwqv8wXE+oCtiVSpOe23E6l9GDKys8AABAAAAKCp5XgX03xP50pPXbNE5vgdEdP0sYvHLI1/5/Yh+rwUAACSK0gBYiyCrjPruiHz5x1Jl2sQfmy+LfNXXI1/8H5Gv/F5EbqYlAAAAAOuT55VR/5LIl30wIl88iQf3RHT9KPIlb4h8+WciBlZXYIAAAFAcitIAWI8gqzzylV9cs/LZlHRHdP1f5Ms/HpH3lmlkAAAAADQSeV555Ku/HzHwwBRbGYjouTjyZe+LGFhWppEBAEDxKEoDYESCrClKy/v33V6+9nr/FPmKz0fkefnaBAAAAKBhyPOmaGBlRPcfy9def9pF4UMReXf52gQAgAJRlAbAqARZk5d3/bb8jfZcHNFzRfnbBQAAAKAhyPOmoPsPa3YtKKe+2yNf9ePytgkAAAWhKA2AMQmyJiGtZtZ9WWWa7vpVRdoFAAAAoDHI8yYn7ynjKmnDpcmreW9l2gYAgDqmKK1Krrnmmjj99NPj4IMPjgULFkRHR0fMmjUrtt9++3jta18bl156aa2HCDAqQdYE5StT2lSZtvtuiej7V2XaBgAAYC0yPaCo5HmT0P9IhRpebvcDAACaUlutB9AM9tlnn7jkkkvW+31PT0/cfvvtpds555wTr371q+MrX/lKtLe312ScABsKshb1LSwFWdss2LjWw6lveXdlm1/1k8jm/L+K9gEAANDsZHpA0cnz6ifTy1efG1n73hFZVrE+AACg3ihKq4J777239M8tt9wyXvrSl8bee+8dj3vc46K/vz+uuOKK+OQnPxkLFy6Mb33rW9Hb2xvf+973aj1kgBEJssYpm1HZ9nsviXzposg6j4ho30uYBQAAUAEyPaARyPMmIJseka+oTNv9d0a+5M2RdR4a0XlIRDatMv0AAEAdyfI8z2s9iEZ3+OGHl2ZMvuQlL4nW1tb1/v7QQw/FnnvuGbfddlvp54svvrg0E7Oc7rnnnthqq61K9y+65NrYfIsty9o+0FxSkJUIskaR55EvPj4iX1L5vjqeG9nMEyKy9f/9AgAAtbBo4aLY80l7lO7ffffdpS0PoYhkekAjkedtWL709Ii+P1e+o7adIpt9ckRLhSe2AgBAjfO8lrK0wph++ctfxtFHHz1ieJVssskmpZmVg/7v//6viqMDmNwMyyTNsGQEaeWyjgOr01f3BZGv/HypEA4AAIDykekBjUSet2FZ5wHV6ajvxsiXfzAi76lOfwAAUCOK0urE/vvvP3T/H//4R03HAjAegqyxZZ0Hp/+tTmfdF0V0/bo6fQEAADBEpgcUiTxvA9qfHZHNq05ffbdGvvKr1ekLAABqRFFaneju7h66P9rsS4B6I8gaQ+tjIqY9p2rd5avPjcj7q9YfAAAAMj2geOR5Y8imRdZ5SPX6SxNN+x+pXn8AAFBlbdXukJFdfPHFQ/d33HHHCT/+nnvuGfPvixYtmtS4AMYTZC3qW1gKsrZZsHGth1NXspknRL7snxED91e+s/zhiJ5rIjqeXfm+AAAAKJHpAUUkzxvD9CMjem+K6LupCp31R951fmQzj6lCXwAAUH2K0urAwMBAnHnmmUM/H3300RNuY6uttirzqADGT5A1ita5kc05JfJlp1elMC1f+ZXI2p8ZkfnXOwAAQKXJ9IDGWDFtoTxv3dXSZp8c+fIPlbbYrLiun0TeeVhkrXMq3xcAAFSZ7TvrwFlnnRVXXXVV6f6LX/zieOYzn1nrIQFMKshKN0v/r6N1i8jmnBmRza98X/kjkS8/MyLvq3xfAAAATU6mBzQCed4IWmZGNucDEa1PrEJnfRHL3hUxsLwKfQEAQHVZSqUOlvh/17veVbq/6aabxhe+8IVJtXP33XdvcKn/3XbbbVJtA0w8yDLDci2tcyPad4no/n3l++q9bs2KabP+s/J9AQAANCmZHtBI5HmjrJjWsU/kq/5e+b4G7ot8+Ucim3O6HRAAAGgo/t9tDf31r3+NI488Mvr6+qKzszN+9KMflUKsyViwYEHZxwcwWYKs9WVt20dejaK0pPuCiM7DItq2rk5/AAAATUSmBzRynpfI9B7V9qTq9ZW2Cu25LKJj3+r1CQAAFWb7zhq544474uCDD47FixdHa2tr/OAHP4h99tmn1sMCKBtL/6+jfe+ImF617vKu86rWFwAAQLOQ6QGNnuclMr1HtT0xovXxVesu7/pt1foCAIBqUJRWA/fee28cdNBBpX9mWRZf//rX44UvfGGthwVQscI0QVb6N25nROcB1euv++KIgdXV6w8AAKDByfSAZqAwbZgsi6zzkOqultZ3R/X6AwCAClOUVmUPPfRQPPe5z41//vOfpZ/PPvvsePWrX13rYQFUjCDr37LO50dEZ5V664ro/UuV+gIAAGhsMj2gmcjzhunYO6Jls+r113NV9foCAIAKU5RWRUuXLo3nPe95cfPNN5d+PvPMM+PNb35zrYcFUHGCrEe1bh7Z7HdU71+/+bLq9AMAANDAZHpAM5LnPSrriGzOeyNiVlW6y+V5AAA0EEVpVbJq1ap4/vOfH9ddd13p5/e+971x8skn13pYAFUjyHpU+y6RzXpXdVZMy3sr3wcAAEADk+kBzUye96jWBZHNPSMi27jyfcnzAABoIIrSqqCnpyeOPPLIuOyyy0o/n3jiifHBD36w1sMCqDpB1qM6nhXZvI9FdOwfEdMq10/LzMq1DQAA0OBkegDyvCFtW0c29+MRnS+o7KppmTwPAIDG0VbrATSDY489Ns4///zS/QMOOCCOP/74uOmmm0Y9vr29PbbffvsqjhCgukHWor6FpSBrmwVVmF1YzzMsZ701YsZxEd0XRt7714iBpRH9/4iIgTL18fjytAMAANCEZHoAa8jzHtU6L7KZx0XMeHlE92WR91z1aJ53R0R0l6WLrE2eBwBA41CUVgU/+clPhu5feOGF8bSnPW3M47feeuu48847qzAygNoQZA3TMjti+gsjm/7C0o9592URKz459Xbbdoho22rq7QAAADQpmR7Av8nzhsnaIzr3j6wz7YIQEf0LI1/y1jI0PDui/TllaAcAAOqD7TsBqAlL/48sa392RDZ/6u10HlqW8QAAAABAIs8bRetjI9p2mno7nQdFZNPKMSIAAKgLitKqIM/zCd3MqASahSBrBFlbZNOPmFobLZuaVQkAADBFMj2A9cnzRpZNf9EUW2iPrPOQMo0GAADqg6I0AGpKkDWCzhdGTNt9kg+eHjHzTRF9t0d0XxPRc1NE/31lHiAAAAAAzUqeN4L2Z0Q2/WWTfHAWMetNEQMPR/RcG9Hzl4i+u1J1dJkHCQAA1dVW5f4AYMQga1HfwlKQtc2CjWs9nNrLsshmvz3yFVlEz+UTeOD0iNYFEctPi/Uiq5YtI9p3iZi2a2RtT4homVHeMQMAAADQNOR5I5h+dEQ+ENH1owk8qDWibbuIFZ+LPPrW/lM2v1TsFtOeHVnbEyNa55d7xAAAUFGK0gCoC4KsdWTTIpt1UkTXjpF3/SJi4IExDm6NiGkRsTqi//aRDxm4N6Ir3X4ZefrXf8c+a7YESIEWAAAAAEyQPG+EiaYzj41o2yby1T+O6P/nBh6QJo2uiui7deQ/54sjui8s3UoTUNNk05TnTdu51BcAANQ7RWkA1A1B1jpSuDT9+ZF1HhrRe33kXedH9N8dMbAiIuuIaJkX0bp1RM+lEdE1gYb71oRZKdRqe1pks/8romVOBZ8IAAAAAI1InjeCjt0ja39ORN/fI+86L6LvbxH5ijUTS1tmr5kk2n1tRCydWLu9V0fee3Vpp4Rs9n9HtG5VqWcAAABloSgNgLoiyBpB1hLR/szI2p+59u/77oh86Xsjomfybff9JfKl74pszhkRrc43AAAAABMjzxtlsum07SKbtt3av+9fGvmykydekLZWG/dEvuQ9kc05pdQHAADUq5ZaDwAARgqykhRkMbp85RcmuELaKAbui3z5ByMGVpdjWAAAAAA0GXne+OSrvxsx8EAZWloZ+bIzIvoXlaEtAACoDEVpANQlQdYG9N1e2gKgbPr/Ffnqn5SvPQAAAACaijxvAwZWRHT/sYwNroh85dfL2B4AAJSXojQA6pYga3R513nlb7T7goi8t/ztAgAAANAU5Hlj6L4oInrK22bvtRH995W3TQAAKBNFaQDUNUHWCPL+iO7LKtDusoieK8vfLgAAAABNQ543srysq6QNa7frgoq0CwAAU6UoDYC6J8gaYan/cs+qfFTefXFF2gUAAACgufK8dJPnDTNQoXMhzwMAoE4pSgOgEBSmDddVuab77q9c2wAAAAA0FYVpw+QVyvTyRyLyvDJtAwDAFChKA6AwzLB8VDajcm3nCyPv/Wfl2gcAAACgqcjzHpVNr1jTedeFFWsbAAAmS1EaAIXT9EFWNisi0q1Clr078v5HKtc+AAAAAE2l6fO8pHXLyrW96n8i772lcu0DAMAkKEoDoJCaOsjKsojO/SvYQW/E8g9HDKyM6L8vov/+iIHVFewPAAAAgGbJ85o108s6D6hsB8s+FHn/soj+B9dkegPLbesJAEBNtdW2ewCYapC1sHR/mwUbRzPJOg+JvOsXleug/5+RL37V2r9re2JkHYdGdOwZkbVXrm8AAAAAGjbPW9S3sFSY1mx5XrTvGRHfiIgVFepgVcSS42KtMrSWzSPrfF5ExwERLbMr1C8AAIzMSmkAFD7ISppuhmXrFhHTdqlun31/j3zl2ZE/8h8Rq39hpiUAAAAAE9a0eV6a5Nn53Or2OXBf5Ku+Gfni4yNf+bWIvLe6/QMA0NQUpQFQeM0aZGUz/zMiq8WM0hWRr/pG5Cu/qDANAAAAgAlr2jxvxtERbdvXoOe+iK5fRb7sjIiB1TXoHwCAZqQoDYCG0JRBVuvGkc09pUaFaRHRfUHkq75dm74BAAAAKLSmzPOyjshmvyei9Qm16b/vpshXfDIi769N/wAANBVFaQA0jKYMslq3imzumdXfynNQ17kRPTfVpm8AAAAACq0p87yWOZHNOSOi46CIaKt+/73XRXSdV/1+AQBoOorSAGgoTbti2pz3RTbvf2oSZOVdv656nwAAAAA0hqbM81o6I5v1psjmfTki27Q2eV6eV71fAACai6I0ABpOUwZZSesWEW07Vaz5UXOq3qsi+pvsXAMAAABQNs2b582L6Ni3+nnewKKI3r9UrF8AAEgUpQHQkJo2yOrYu2JNZ1lEX29Ed9e6fxmI6L64Yv0CAAAA0PiaNs/r3K+ieV6yctn6/zkw7/59xfoFAIBEURoADaspg6z+RRVtvm1axOoVrbF8ydr/FyIfuK+i/QIAAADQ+Joxz8v67qx4H+0dA3H/XdPW/qU8DwCAClOUBkBDa6ogK63HX4UZjvM26Y8LfrRRdHdlw/peVfF+AQAAAGh8TZXnpVit63cV72NaR8Rf/jQzHrm/7d+/HFhd8X4BAGhuitIAaHhNE2SlwrD8kap0tcPOq+IX39j437/IOqvSLwAAAACNr2nyvKT/7qp086z9VsR3PrXZv38hzwMAoMIUpQHQFJoiyKriamVP3nVV3HzNzOhaNbhaWmvV+gYAAACg8TVFnpfkK6vSzfzH9EVrWx73/KN9zS8y/4kQAIDK8v84AWgajR9kTatqb7Pn9cdVv5+z5ofuKyP6H6xq/wAAAAA0tsbP81Jx2KNFYlXwmC1745JfzV3zQ98/I3pvqVrfAAA0H0VpADSVhg6yWmZFRFvVups+cyCuOO/RorRYHvnKr1StbwAAAACaQ0PneUnLvKp11TljIK7+/Zzo7U4/9Ue+4jMR+UDV+gcAoLkoSgOg6TRskJW1RUzbtWrddXe1xAMLh83k7L0mov/+qvUPAAAAQHNo2DyvtFDaHlXrq6cri56ulli2+NGJrQMPRPRcW7X+AQBoLorSAGhKjRpkZZ2HVq2vJQ+2Rffqlujv//fv8q7zq9Y/AAAAAM2jUfO86DgoIlqr0tWSh9YUo61a/u/+8q7zqtI3AADNR1EaAE2rIYOsaU+JaF1Q8W7uvKUzHrx3WrS159E6PDPrvqjifQMAAADQnBoyz2udH9H+nIp3s3JZS/z1mlml++2dw2aZ9l0f0b+k4v0DANB8FKUB0NQaLsjKsshmvL7isyv/+Mu5pX/O3ahv7T/kSyLy3or2DQAAAEDzarg8L0V6M14ZEbMr2seV58+J3q4sIstjzvxhRWlJ/lBF+wYAoDkpSgOg6TVckNW+U2Sz3laxf82vWNoS112yJiR75n7L1z8g76pIvwAAAAAwmOelW8Pkea2bRTbnfRExvSLN9/dHXPrreaX7T91tZUyfla99wIA8DwCA8lOUBgCNWJjWsXdks98TETPL2uzAQMR3z9os+rqzyFry2POwpesflFUmPAMAAACA4RqqMG3adpHN/UhEy6Zlb/pX39o4Hlw4rXR/78NHyPNa5HkAAJSfojQAaNQZlu27RDb/y5HNfH1EtmYm5FRnVP7gM5vGjVfMGppVufFm62zfmc2PyNqm3BcAAAAAjEdD5Xltj4ts3tmRzfqviJbHlaXJi346L87/wfzS/U226I0dnrlq/YOyTcrSFwAADOe/GgPAiEHWwthmwcZReGmWY+ehkXUcEnnPjRFdP4zou3nCzSxf0hrfO2vTuPHKNQVps+b2x4vf8OD6B3YcUI5RAwAAAMCE87yk8JleNi2iY6/IOvaKvO+OiNU/i+j544Sb6e6K+OU5m5SK0iKyaGnL49gT74/W1nUOnPbMiNa5ZRs+AAAMUpQGAI1emJZkWWQdT4vo/1vkjxal5XnEFefPjvvvao8dn7kqtt95dbSss4bqP2/ujEt+MS+uv3RW9PVkpd91zhqIN37g3njMluuskhZZZJ0HV+sZAQAAAMBaed6ivoWlVdMaJdPL2raNaN8z8mFFabde1xk3XDYrnvSM1fGUXVfGtI61H3P/3W1x6S/nxZW/mxOrV6ypQMta83jVSfeVHrNeH52HVP6JAADQlBSlAUAzzLB8VJ6vHLqfZRG7H7w8LvzJvPjiKY+NGbP7Y+PNe6NzxkD0dLXEkofa4uH7pq31+E0X9MR/vP/e2HKb3vUbb31cROtjqvE0AAAAAKApCtMi/p3nJTvs0hU93a3x7U9uFnmexWYLumPGzIHo620p7XZw393TIvI1k0sHdzx41X/fF0/ZdYRtO2N6xLRdqvAcAABoRorSAKCpgqy1p06mwrQDX7IkdjtwWVzx2zlx6a/nxR03r12IFlkeT37Wqtj78CXx5F1Xrb/E/xD/twIAAACA2mr0PC952u4r44PfuSOuuWh2XPrLuXHLtTPXO2brHVbH3s9fGrvsszzaO0dre92dEAAAoHz812MAaKIgK2vdOPIRfj973kAc/LIlceBRS+Lu2zti2eK26O3OYvqsgdh8q57YaLNxBFT991diyAAAAADQtHletIw8/o7OPPY8dFnscciyWHRnezzyQFt0r24p7YKw0Wa9scXWI+x0sJ7eyAdWR9Y6o+zDBgAARWkA0ExB1rTdIuKro86CTKugbbNDd0Sk20StiHzldyPrPCSitcDnCAAAAIDCa5g8r+2JES2bRgw8MOKf004IW27bU7pNysqzI2a+KqJ1y6mNEwAA1tGy7i8AgNGDrCQFWYXVOi+ifffKtd/148iXvD7yZR+J6Lk+Ih9pXTYAAAAAqLyGyPOylsg6nle59nv/FPmSt0S+9D0R3ZdE5ONZYQ0AADZMURoANFmQlXUeWvlOeq+OfPkZkS/9r4j++yrfHwAAAAA0aJ4XnQdWfvOjvlsjX3FW5IvfGNF7S2X7AgCgKShKA4BmC7Km7RDRcXB1+ur/V+RL3x3Rd9e/f5dmW/Y/FNF/T0T/IxF5f3XGAgAAAEBTKnye1zInspmvrU5f+eLIl50a0X3NsN/1rcnxSnneQ1ZTAwBgXCo8rQIAGjfIWtS3sBRkbbNg4yiabObrIx9YFtF7ZeU7y5dGvvT0iFn/EdFzeURP6rNv2AEzIjr3i6zzeRGtW1V+PAAAAAA0naLneZF2P+hfEtH1oyp01hf5io9HxFsj+m6J6PpDRKwe9ve2iPbdI+s8JKJth4gsq8KYAAAoGiulAUAzzrDMWiOb/Y6IziOq1OEjESs+FtFz6ToFacmqiK5fR77kxMiXfmDNbEsAAAAAKLNC53mliabHRjbzhLQVQhV6641Y8amIrt+sU5CW9EX0XBL5svdGvvSkiL6/V2E8AAAUjaI0AGjWICtrKS37n837YkTbk6Mu9N0Q+dKTI/rurvVIAAAAAGhAhc7zks5DIpv/1YiOQ6Mu9N8Z+dL3R/RcV+uRAABQZxSlAUCzB1mtm0Y2681RN/LFkS9LK6YV9HwCAAAAUNcKn+e1zI5s1uvXbKNZF7ojX/6xiN7baz0QAADqiKI0ACiD4gdZm6RpllE38kciX/mlWo8CAAAAgAZV+Dwvad066kdP5Cs+GZH313ogAADUCUVpAFAmhQ6ysmkRnftFXem9JqL/vlqPAgAAAIAGVeg8L0V6nc+NujLwQETPtbUeBQAAdUJRGgCUUZGDrKzj0Kg3edf5tR4CAAAAAA2syHletO8dEdOjnuRdv6n1EAAAqBOK0gCgzAobZLVtFdG2c9SVFGLlea1HAQAAAEADK2ye1zI9ovPgqCt9N0Te/2CtRwEAQB1QlAYAFVDUICub9daI7DFRP7oj7/5drQcBAAAAQIMrbJ434+URbTtGXVn17VqPAACAOqAoDQAqpJBBVuv8yOaeFtGyedSNlV+LGFhe61EAAAAA0OAKmedl0yKb/Z6ItidH3ei5NKL39lqPAgCAGlOUBgAVVMggq3WLyOaeGdG+f9rTsx5SrIjui2o9CAAAAACaQCHzvJaZkc05NaLzyIiYEfUg7/pNrYcAAECNKUoDgAorZpA1J7LZb41s/lcjm/6qiJYtazqcvOu8iDyv6RgAAAAAaA6FXTFt5qvW5Hkz3xTR9sTar5Zm9wMAgKamKA0AqqCQQVbSMidixpGRzf9cZLPeWbtxDNwX0Xdb7foHAAAAoOnyvHQrXp7XGdF5UGRzPxbZ3E9FRGeNBtIX0XN5jfoGAKAeKEoDgCopbGHaoI7nRDbrrbX7vw8DD9amXwAAAACaViEL0wa1bRPZnPfVbEvPvF+eBwDQzBSlAUAVFXaG5aCO/SObfWptgqy8q/p9AgAAAND0Cp3nTXtyZPM+EtGyWQ06l+cBADQzRWkAUAOFDrLad4qY+6GUaFW332x6dfsDAAAAgHXyvEJmeq1bRTb34xHZvCp3LM8DAGhmitIAoEaKXJiWtW0d2az/TolW9Tpt3bR6fQEAAADACHleUshMr2VWZHM/EBGzqtZl1lqL1dkAAKgXitIAoIYKPcOy41mRzX5fRHRWobNpkbdsVYV+AAAAAKBBC9PSimnzPhTRUp3Jn3nbdlXpBwCA+qQoDQBqrNBBVvvTI5t3dkTnSyKyORXsqDdixWcj8oEK9gEAAAAADZ7nlbby/FRkM46LaNm8sn2t+HTEwOrK9gEAQN1SlAYAdaDYQdbGkc18RcS8L1R2+f/eKyNf9tGIga7K9QEAAAAAjZ7ntcyImP6CyOb9T0TrtpXrp/9fkS99V0T/I5XrAwCAuqUoDQDqRKGDrIjIev+cpj9WtpO+qyNf/rGIvK+y/QAAAABAg+d5MXBvRP8dFe7j7siXnRIxsLyy/QAAUHcUpQFAHSlykJV3/aY6HfX9OfJV36lOXwAAAADQsHne+dXpaODeyJd/sjp9AQBQNxSlAUCdKWSQ1b8kou+m6vWXCuAGVlavPwAAAABopDwv6b6ken31/SWi7/bq9QcAQM0pSgOAOlS4ICt/pMod9kZ0X1TlPgEAAACgUfK8voh8SXW7XF2lnRYAAKgLitIAoE4VKsjKu6vf5epfROR51fsFAAAAgOLneb3V77PnErsfAAA0EUVpAFDHChNkZdOr32f+YES+qvr9AgAAAEDh87zOGnTaH9F/Zw36BQCgFhSlAUCdK0SQ1bJZRLRVvdt8oNrbhgIAAABAA+R5WRbRsmXVu837FKUBADQLRWkAUAB1H2S1TI9o3736/Q4sr36fAAAAAFD0PC/VpXUcWP1OTTIFAGgaitIAoCDqPcjKOg+tfqd5b/X7BAAAAIAGyPOi88Dq736Q91W3PwAAaqb6+2wBAFMKshb1LSwFWdss2DjqStuTIlqfENH/j+r1ueKDka+cHdEyNyLbKLL2p0V0HBDRMrt6YwAAAACAIuZ5LXMiOvaN6P599frs/kXk3Revye9aNopo2y6yzudGtG5WvTEAAFAVVkoDgIKp2xmWWRbZ7P+KiFlV7LQ/Il8S0f+viL7rI1/1zcgXHx/58rMj+hdWcRwAAAAAULA8L0V6M14b0fq4Kve6LGJgYUTfjRFdP4l8yX9GvuzDEb23VHkcAABUkqI0ACigug2yWreIbO4pEdmcGg6iL6LnosiX/HdEz/U1HAcAAAAA1Hme1zIjstnvj2jdqrbj6L0m8mXvi1j969qOAwCAslGUBgAFVbdBVtsTI5t7ZkTbzjUeSFfkyz8c0XNDjccBAAAAAHWc57VuHNmcD0e075vCvRoOJI981VcVpgEANAhFaQBQYPUbZG1eWjEtm/e5iM4jqryl53D9kS8/I/Kl74985dcj77klIs9rNBYAAAAAml3d5nktMyObfWJk874U2fSXR7RsWrOhpMK0fMk7I1/x+ci7r4nI+2o2FgAAJq+W0x0AgDIFWYv6FpaCrG0WbBx1pXXLyGa+NmLGcRHREzGwOvKsM2L1TyO6flSlQQxE9P11za3rl5GnArnOwyObfnhpewIAAAAAqKb6zvPmR8w4KrIZR0XkvREDKyOPjojeqyNWnl2aBFoV/X9fc+v+3Zr+O/aNbPpLS6u6AQBQDFZKA4AGULczLAdlWUTWEdE6L7KWzshmHhvZzNfXaDArIrp+EPni10Z0X1GjMQAAAADQ7HleutVtnpdk09bkea3TI+vcJ7LZ74uI9hoMpDui+/zIl5wQseqndkIAACgIRWkA0CDqvjBtXZ2HRjbrv9KdGg2gN/IVH4/ouqBG/QMAAADQ7Oq+MG249qdHNueMiGx+jQaQR77625Gv+rrCNACAAlCUBgANpHCFaR17Rcz7eJp2WbMh5Cu/ENF9Tc36BwAAAKC5Faowbdp2EfP+JyJm124MXb+KWH1u7foHAGBcFKUBQIMpxNL/w2SlLTRrO7MxX/nliLy/pmMAAAAAoHkVKs/rvSkiltd0DPnq70b0P1LTMQAAMDZFaQDQoIoSZOXdv6v1ECLyhyJ6rq31KAAAAABoYoN5Xr1nenn3BbUeQkQMRNRDrggAwKgUpQFAA6v7wrS8J2LggagHedd5tR4CAAAAAE0u5XlJXWd6/fdEPci7fhuR99V6GAAAjEJRGgA0uLqeYTmwMupG358jBlbUehQAAAAANLm6L0zLV0VdyBdH9N1W61EAADCKttH+AAA0VpC1qG9hKcjaZsHGUTeyjqp009sTcd3Fs2L1iraY1jEQc+b3x/bPWBkdnSMEWTGrKmMCAAAAgMLleSXtFe8hH4i47tKZsWJxW2QtEbPn9cf2T1sVM+cOrH3gwCMVHwsAAJOjKA0AmkRdBlnZ9IhIlWFdFe3m59/YJC76yfy1fjd9dn885+BlsfdhS2LTBY8u85/3VnQcAAAAAFDoPC9pnR/R92BFu/jT72bHdz65+Vq/a2vPY5d9lsc+hy+NrXfoiiyT5wEA1DPbdwJAE6m7pf9TctSxe0W7eHBhW1xx3tz1fr96eWtc9OP5cfrx28bPvrFxDKRJltmMio4FAAAAAAqd56UIrX3PirbftSqL3/7v+kV4fT1ZXPW7OfGJt28VX//w5tGd5rnK8wAA6paiNABoMvUWZGWdh1Ss7VRo9vn3L4iuVWP/X54LfrBRfPdTW8ZAbFSxsQAAAABAI+R50bF/Rbfw/N6nN4sH75k25jHX/3F2fO7dC6Krd9OKjQMAgKlRlAYATaiugqy27SJan1CRph++ry0eXDh2gDXoTxfMjF996aKKjAMAAAAAGibPa5kV0bF3xZr/y5WzxnXcHTdPj3NOuTjygbxiYwEAYPIUpQFAk6qnICubeUJEjK94bCJu+tP4AqxB533jonho4SNlHwcAAAAANFSeN/3YiKz8uw7c9ufO6OvOxn38jX+8JW669NayjwMAgKlTlAYATaxugqxp20U266S0bFpZm73kl3Mn9oA8j0t/8qeyjgEAAAAAGi7Pa90osjnvi4iJTQrdkD/+Yt7EH/PjK8s6BgAAykNRGgA0uboJsjp2i2zOqRHZnLI097frp8cD97RP+HFX/Ozq6OvuLcsYAAAAAKBh87y2bSKb99GIlgVlaW7pQ63j3rpzuJsv/1s8VOtzAQDAehSlAQD1E2RNe0pk878UMePNETF90s309kT88psbT+qxK5asjL9ff+ek+wYAAACApsnzWreIbN5Zkc16d0S26ZSa+vk5m8RA3/i37hyS5/HnP9w8pb4BACg/RWkAQH0FWVlHZNMPjGz+VyNa1oxpIvr7I779yc3jjlsmX9S27JEVk34sAAAAADRXntca0bFrZPO/ENG2y6SaOO978+NPF0x+B4XlDy2b9GMBAKgMRWkAQP0FWUnL9MjmfjSibcdxP6S7K4uvnrFFXPeH2VPqutf2nQAAAAAUQF3leVkW2Zx3R3Q8d9wPGRiI+OlXNpn0rgeDenv6pvR4AADKT1EaAFC/QVbLjMjmnBHR9owNHnrBD+fFGf+xddx4xawpdzt99uRXWQMAAACAps3zstbIZv1nROcLN3joDZfNjDPf9Lj4/f/NTw+cUrcz5HkAAHVHURoAUOdBVsuaGZZtO4952J8vmxVLHpxWli63fMJmZWkHAAAAAKqhrvK8FOnNfE1E5xFjHvPXq2fGvXd0lKW/LeR5AAB1R1EaAFD/QVbWFtmcd0VM233UQ/Y4ZFlZunr80+bF5ttuWpa2AAAAAKAp87wU6c04LqLzqFH/vuehS8vSz6x5rfH0/Z5SlrYAACgfRWkAQDGCrKw9stnviGzWf0W07bDen5+1//LonDUw5W72OewfEV2/i8jzKbcFAAAAAM2b52WRzXx5ZLM/EDFt1/W26Nz6Sd3xuO27ptzN7s97KNr6fhqR9065LQAAykdRGgBQqCArOvaKbO6HI5t7VkTLv5fl7+jMY+/nL5lS8/M37Y2d93ok8pWfL90i7yvDoAEAAACgSfO8pH2nyOa8O7J5X4xoe+pafzrgxYun1HRbRx57PX9J5Ku/H/myMyIGVkxxsAAAlIuiNACgeEFWSR4xcP9av3n+qx6O7XZeNanWOqYPxAmnLIq2aY/+ovv3ka/8ghXTAAAAAChknpdudZXnZbMi+v6+1q+eud+K2PvwSU40zfJ4zX/fFxtv9ujE0r6bIl/+oYi8pwyDBQBgqhSlAQCFLEzLu3673u9SQdkJ7783tp9gYdr02f3xn2csjK226177D90XRXSv3w8AAAAAFEFdFab1XBwRXettjHDUfz4Yexy6dEJNtbTl8aqT7o9n7L3Oymh9f4t85dfLMVoAAKZIURoAULzCtIHVEd0pxFrf9Fl5vOmDC+OQlz8SM+f0j9lM1pLHTs9ZEe8466544k5rB2KD8tU/s1oaAAAAAIVVL4VpI00yTVrbIo498YE45m33x0ab926wncc/ZXW87cx74tnPXT7yAd0XRgwsm+pwAQCYorapNgAANGth2sLYZsHGtRlE/x3rzapcd8W0w1/zcDzvmIfjuj/OjsvOmxv339Ueq1a2RHt7HnM26o9n7L089jxs6b+X9x9N2iK0988R7c8o//MAAAAAgKoVptUwzxtYFdH/r1H/nFZM2+v5y2L3Q5bFrdfOiEt+OTfu/FtnrF7RGi2tETPn9MVTdl1V2upzwRM2tD1nX0TX7yNmHFn2pwEAwPgpSgMAihdkDayzLP8opnVEacbkqLMmxynvOi8yRWkAAAAANECel1Q908vHl+e1tkY8ZbdVpduUuuv+bWTTX7Sm2g0AgJqwfScAUMCl/6scJvWlldkAAAAAoFF2QXi4sfO8gQci8pXV7RMAgLUoSgMAileY1jKrLmdyAgAAAEC9q0lhWlblPC+R6QEA1JSiNACgbIVpVQuy2p4QETOr09eaDqvYFwAAAAA0WGFay/SItidGdU2rcn8AAAynKA0AKF6QlbVHdB4QVdMyp3p9AQAAAEADFqZlHYdGVbXMrm5/AACsRVEaAFDIICvrfF5UTftu1esLAAAAABqxMK1jz4io0jaebc9YM7EVAICasRcVABWzenlXXPnLa+L6C2+MZQ8tj97uvpg+qzM2f/ymseeLnh077PbEyFqyWg+TCgRZi/oWloKsbRZsXLmOWreMaN8/oueiqLSs8+CK9wEAAABQa309fXHd726Mq35zXTx87yPRvaonOmd2xEZbzI/nHP7M2Hn/p0Zbu/+01Giqludl7ZHNeGnkq75RuT5qMaEVAIARuXIAoOyWPLgsfvWlC+Lq866P3u7edf62NBbdcX9c//sb4zELNon9j90r9jnqOYrTGky1gqxs1hsjX3Z/RN/NlZ1V2bp55doHAAAAqLHu1T1x3tcvjMvPvSpWLFm51t+WPhRx/78ejFuuvC1mz5sVe7342XHwa/eP9s5pNRsvBS5M6zw8ov+eiO4LKtdHtklE+zMr1z4AAONi+04Aymrh7ffFx1/zubj8Z1etV5C2rgfveSh++PFz4xvv+35pFiaNpSpL/2fTIpv9vohpu1aog47IZr6yQm0DAAAA1N6yh5fHWSd8Kc4/56L1CtLWtXzJivjN138fn3njl2L5IyuqNkYaKc/LIpv5xojOF1aui5nHRWStFWsfAIDxUZQGQNk8cNdD8Zn//HJpNbSJuPaCG+Kc9/8g8oG8YmOjgYOsls7IZr8rsln/FdH25DI23BbZrJMi2rYtY5sAAAAA9WP18q747Ju/Gnffes+EHnfnX++Oz731a9G1qrtiY6PRC9NeE9nsD0RMe3b6RfmanvHqiI49ytYeAACTZ/tOAMpioH8gvnTSN2Pl0rFnU47m+gtvjAu+dXEcfNx+ZR8bTbD0f5ZFdOwVWcdeEX13Rd59ScTAIxF5V0TLjIhs04j+2yN6rxlngzMjm/3OiPadKjNeAAAAgDrw3Q/+Xyz6x32Teuw9t90b3//wT+K1Hzy27OOiSbbybN8pspS/9T8U0f2HyAfujxhYFZF1RrRsHJEvi+g+f5yNtUU28/URnc+t3HgBAJgQRWkAlMVf/nhz3HfnA1Nq48LvXxIHvGKvaJvmX0+NpmpBVtL2uMjaXrH+7/M8ovemyLt/G9Hzp4joX/+Yls0i6zwkouOAiJbZlR0nAAAAQA09ePdDpYmiU3Ht+TfEC998aGy0xbyyjYsmzPNaN4mYcdTI66V1Hhp513kR3RdHRNcIB8yO6Dwoss7nRbRuWtlxAgAwIf6rPwBlccn/XTHlNpY/siJuuOiv8cyDn16WMdHEQdZoq6kNzb58ZM2qaQNLI8/7IkurqbVuEzHtaWuOAwAAAGhwl/w4TdqbmjzP45KfXBkvfPMhZRkT9aXmeV7StnVks94Qkbbl7P1TRP/DkefdkWXTI1o3j2h/VkQ2rTZjAwBgTIrSAJiyh+55OG696u9laeuSn/xJUVoDq4sgK2ndKKL14NJdJWgAAABAs+nr7Ysrfn51Wdq64tyr44g3HhwtrS1laY/6Ujd5Xsv0iI79SnfleQAAxeAKAYApu+vWe8vW1t23LCxbW9RvkJWkIAsAAACA6nv43sWxavnqsrS1fMmKWHz/0rK0RX2S5wEAMBmK0gCYstVlCrCSrlVdMdA/ULb2qE+CLAAAAIDaWb28q27zQeqTPA8AgIlSlAbAlLW2le9fJ1lLS7S0+NdTMxBkAQAAABQ/zyu1N621rO1Rn+R5AABMhP/qD8CUzdpoVvnamjcjIitbc9Q5QRYAAABA9c0uY56XzJo3s6ztUb/keQAAjJeiNACm7InP2DY6Z3SWpa2n7fPksrRDcQiyAAAAAKpr3mPmxoLttyxLW9s8ZauyF7lR3+R5AACMh6I0AKasc0ZHPPv5u5SlrX1euntZ2qFYBFkAAAAAVZRF7HNUeXK4fV66R1naoVjkeQAAFKoo7cYbb4wf/ehH8atf/SoeeeSRDR5/zjnnxOmnn16VsQEwtn2Oes6U29j2qY8r2wxNikeQBQAAxSPPAyiuZx2yc0yfNbXdD2bMmRHPfO7TyjYmipfnpZs8DwCAui1Ku+eee2LPPfeMnXfeOY455ph4wQteEFtssUW89a1vjRUrVoz6uK997WvxgQ98oKpjBWBkmz9+s9jryMkXprW2tcaRJz6/rGOieBSmAQBAMcjzAIqvY3p7vOBNh06pjRe99bBoa28r25goJoVpAADUZVHa6tWr46CDDoorr7wy8jyPOXPmxPTp06O3tzc+//nPxy677BK33357rYcJwDgc/c4XxFP23GHCj8uyLF596tHxhJ23qci4KBaFaQAAUN/keQCNY5+XPicOeuU+k3rs8167f+z5ol3LPiaKSWEaAAB1V5SWgqrbbrsttt5667j00ktj8eLFsXTp0vjhD38YW221Vfz973+PffbZJ2666aZaDxWAcax2dsLHXxXPOeJZ435Me2d7nPCJV5e2C4BBlv4HAID6Jc8DaCxHvu358cI3HxpZZOOeYHrkiYfHC/7zkIqPjWIZzPNkegAA1EVR2o9//OPSBcx3v/vd2GOPPUq/a21tjaOOOir+/Oc/x4EHHhj3339/HHDAAXH99dfXergAbEDbtLZ41Skvjf/66n/Groc8o1SoNpL5m86LI974vPjAue+Mp+3z5KqPk2JQmAYAAPVHngfQYLKIg4/bL973w/+K/Y7eMzpndo542PRZnbH/MXvF+390Uhz0yv/P3p2AWVnW/QP/nZmBGYZdFkEHxR1xyQ0VcU/NJVNz6y01zdzSNNOsbLHeN7My07Sy3JdSc18yTVNQUVTcN3BJUcBRREHWAYY5/+sc/pIL4sCcc57znPP5XNd5OcOc89w/03mZ+fJ97nub/Pvg45yCAADABzLZ3B77Cerdu3d079493njjjSV+vrW1NQ4++OD4+9//Hr169Yo77rgjtthii/znttlmm3jooYdi4cKFJZ46fSZNmpS/UzVn5AOPx4CBKyU9ElAlZr43K56574WY8e7MmD9vQTR27xIDV18xhg5fO2pqE+9GkxLNrZNjcFOfpMcAAKAdmic3x4h1FhWVJk6cGE1NTUmPRIHJ80pHpgckYd6cefHs/eNi6pvTYt7cedHQ2BB9VuoVG2w7NOq7dE56PFKU5+XI9AAAqjfPq4uEzZ49O9Zee+1P/XxdXV1cddVV0dDQEJdffnnssssucfvtt8fWW28dafX666/Hueeem//nyP3LrK+vjzXWWCMOOOCAOPbYY6OxsTHpEQEKpvsK3WLEPpsnPQYVsWNaSoOs7LyIBS9GZN/P/fVc7qsiom61iNqU/XMAAMD/J8+T5wGVrb6xPjbbdaOkx6AC8rxcMS23Y1r68ryFEa0vRbRNy9U0I6Ixoq4ponbRLnAAAKSklNanT5948803l/qa3HEAl156aT7Quvjii2P33XePW265JdLotttui4MOOihmzJix+PfmzJkTjz32WP5x0UUX5cOtNddcM9E5AaDcpC7IWvhmZFv+FdFyb+6v7T72yUxEp80i07BrRKeNct/sJDQkAAAsO3mePA8AKjPPmxYx79+Rbbk7Ijv1k5+vGxKZht0iOm8ZkemUxIQAAKmS+Llp66+/fj7EmjBhwme+9sILL4yjjz46Zs2aFV/84hfj5ZdfjjR58skn48ADD8wHWN26dYvTTz89f1zBPffcE0cccUT+NS+99FLsscceMXPmzKTHBYCyDLJyckFW2cmdiN76n8i2jIrs+z+K7PTjIlpuW0IhLf/iiAVjIzvz/yL7/skRC99JYGAAAFg+8jx5HgBURJ6Xs7A5si0PRHbGmZGdfkRk51695EJaTuv4yM46O7LTjolYkK7vaQAAqrKUtu222+Z//etf/9qu1//pT3+K4447LubOnRvvvJOuv8A94YQT8nPn7hC966674tRTT43hw4fHjjvuGBdccEH85je/WRxknXXWWUmPCwBlqdyCrOzCmZGd9cfIvvf1yL7/vYjZ50a0jmv/BRa+Ftn3f5DfWQ0AANJAnifPA4BU53ltCyI7+2+Rfe+bkZ1+bMTssyMWjImItnZe4L3IzvhJxPyniz0qAECqJV5K23vvvSObzcYf/vCHfMDTHueee26cfPLJ+felxaOPPhoPPPBA/vnhhx+eD68+7qSTTop11103//z3v/99LFiwoORzAkAalEWQtfDdyM48K2L61yPm3RMRs5b/WtlpkZ3xfxFt/z0OCAAAypU877/keQCQojyvbW5kZ18eMe2rES035Mtly29+ZGf+OqL1s3eOBQCoVomX0jbYYIN45ZVX4sEHH4za2tp2vy93F2Juq/x777030uDmm29e/Pywww5b4mtqamrikEMOyT+fPn16jBw5smTzAUDaJBpkLRgX2enfjpj/YOGu2fZ2ZOdeX7jrAQBAkcjz/kueBwApyfMWvhXZ6SdEtNyS+6BAF22J7OxLCnQtAIDKk3gpLWf11VePNdZYIzp37rxM79tyyy1ju+22izQYPXp0/teuXbvGpptu+qmv+/A/Ty7YAwDKLMjKFdJmnJYPnQqu5d6ItiJcFwAACkye91/yPAAo8zxv4TuRnf7DiOzUwl+79bmIhRMLf10AgApQV4pFjj/++PwW/dVs3Lhx+V/XXHPNqKv79P/ZhwwZ8on3tMekSZOW+vnm5uZ2XwsA0hZkNbdOzgdZg5v6FP/Izhln5NKmIi0wJ2L+AxENOxfp+gAA0D7yvOLneTkyPQCqUUnzvOyCyM48PSLeL94SLXdGpusRRbs+AEBalaSU9oc//CGmTJkSV155ZXTq1CmqTUtLS0yduujui6ampqW+tnfv3vm7L2fPnh0TJ7b/zopBgwZ1eE4ASKtSBVnZllsjYlbRrp9fY96DkVFKAwAgYfK84ud5OTI9AKpVyYpp80dHLHwjimregxFKaQAAyR3fed1118Wuu+4aM2fOjGrz4X/mbt26febrcyFWzqxZxf1LbwCoJEXf+j87L6JlZHGu/ZF1phV/DQAAaAd53iLyPABI71GeuV3Mii47IyK7sPjrAACkTElKaf369cv/OmrUqNh2223j7bffXq4g6Kc//Wmk9c7KD3Tu3PkzX19fX5//de7cue1eI3cX5tIejz766HJODwDpUdQgK3fHY5F3SVtcfgMAgITJ84qf5+XI9ACodkXN81pfjWh9OUoiO7806wAApEhJSmkPPfRQrL766pHNZuPpp5+O4cOHx8svt++bwPnz58dZZ52Vf//pp+fOfE+fhoaGj/zzfJZ58xb9ZXSXLl3avUbuGIGlPQYOHLic0wNAuhQryMoueDZKItNYmnUAAGAp5HnFz/NyZHoAUMRiWqnyvMhEZP77vQMAACUspa2xxhoxZsyYGDZsWP7jCRMmxIgRI5Z6p19bW1tcdNFFseaaa8Ypp5wS775bvK17i6179+6Ln7dnC//Zs2e3+2gAAKBEQVa2REcW1TaVZh0AAFgKeZ48DwDSnudl20qU59WsHJHJlGYtAIAUKUkpLadv37757f533333/MdTp06NHXfcMf75z39+4rXXXXddDB06NI466qiYPHly/o7MnEGDBkVa76zs06dP/vmkSZOW+tpp06YtDrHS+s8LABW/9X8RZep3TnoEAADIk+fJ8wCglFKb5zXI8wAAEi2lfbB9/a233hqHH354/uM5c+bE3nvvHZdddln+47vuuis222yz+MpXvpI/DiAXXuUeAwYMiHPPPTdeeumlSKtcKJfzyiuvRGtr66e+bvz48Yufr7vuuiWZDQAqVUGDrEwJdjyoWSmi0/rFXwcAANpJnifPA4C05nmZmv/ufFo8nSPqdyjBOgAA6VNT8gVrauLCCy+M0047Lf9xLtDJhVobbbRR7LbbbvHkk08uDq/69esXv/3tb+PVV1+N4447Ljp37hxptfXWW+d/zd01+fjjj3/q6+67777Fz3NHIgAA5RFkZTqtV6CJlrJGlz1t9Q8AQNmR58nzACCVxbS6RQXzosoV0moc3w0AUBaltA/kQqyf//zn+ee5wOqZZ55ZHF717t07Tj/99Hx49d3vfje/XX7a5e4g/cCll166xNe0tbXFFVdckX/eq1ev2GEHd1YAQNkEWZ23ye0TUbihPnH9ERH1uxTv+gAA0EHyvE+S5wFAGed5dWtG1K4RRVO7emQaDyne9QEAUi6RUtpbb70Vxx9/fJxxxhmRyWQ+8th0001jwoQJ8cMf/jC6du0alWLzzTePbbbJ/WV2xMUXXxxjxoz5xGvOOuusGDduXP75CSecEJ06dSr5nAAsXbYtG60LPv3YFio4yKppiGjYMYqi0xaR6Xa8XdIAAChb8jx5HkBqZSNa57fmfyV9eV7usdx5Xu57lYZdo2iFtO4/jqgp4k2sAAApl8nmbmUskXfeeSd+9atfxZ///OdoaWnJ/15u+dra2vxdhR/4zne+kw90Kk3uKIPcFv5z586Nbt26xamnnpq/ezL38TXXXBMXXHBB/nVrr712PPbYY9G9e+HOup80aVIMGjQo/3zkA4/HgIErFezaAJXuzVfeivuvfzieHvVczHxvVv7Prs4NnWPlNQfEiH22iE13+Vx0bvAXD2nR3Do5/+vgpj7L/uaFUyI7/cSImFugabotOrKzy74RmcQ2sAUAKKjmyc0xYp2t8s8nTpwYTU1NSY9EB8jzksvzcmR6AMtn2tvT48EbH41H73wypr39frQtXBh1dXXRb1Cf2HLPzWL4lzaLrj0bkx6TZcz0livPy86P7PTvRrS9WaBJOueP7MzvkKaQBgBUiOYi5XklKaW999578etf/zr+9Kc/xZw5c/LB1Qf22Wef/Nb+jz/+eHzjG9+I1tZFu88ceOCBcfnll1fc3YW33XZbHHTQQTFjxowlfj4XYN1+++2x5pprFnRdARbAsnv9hUlx49n/iFeeem2pr2vs3iW23W947H7kTlFbV1uy+UiomDb/mcjO/EVELO+OeTURdWtHpmGXRUd2Zirrex0AAKW0yiDPSz7Py5HpASyb95qnx/Vn3xbPjHr+I392fVxdp7oYtuvG8eXv7BGNPRSLKr6YtrA5su//MCK75D/LP1smorYpMvU75QtpUdNtOa8DAFCeUl1K69GjR8yePfsjPwDk7ijM3WU5bNiwxb939913x3777RezZs1a/Jqbbrqp4HcYJu3111+P3//+9/mwKhcsde7cOR9a7b///nHcccdFY2Ph784RYAEsm6dHPR+X/uiqWJDb2r+dhmyxVhzxm4OjobG+qLNRLsW0Xy/bjmm160R0Ozoytas4phMAqGhKaZVBnpd8npcj0wNov0kvvhl/POGSmPHuzHa/Z8Dg/nHceYdH7wG9ijob5VBMmxzZGf8X0Tal/e/JDFiU53XaQJ4HAFS05jSX0mpqaiKTyeRDrM022yx++ctfxk477bTE1z7xxBOxxx57xNtvv51/zwYbbBB33HFHDBw4sNhjVjQBFkD7vTj2lfjDty/Jb+u/rIYOXyeO/t3X7ZhWFUHW25Ft+UdEy71LL6fVrhnR9RuR6TSkQ3MCAKSFUlplkOeVB5keQPu8M3Fq/PYbf4pZ02cv83tXXLVfnHTJt6JrD8d5VvzNpm0zI1ruiGzLvyKy0z79dTUDIxq/Gpn6ER2cFACguvO8miiRtdZaK6699tp49NFHPzXAytlkk03ioYceyt9pmAu9nnnmmdhqq61i/PjxpRoVgCrWMqslLvrB35arkJbzwpgX4+7L7yv4XBTPwLqVY8Kkd5f9jbUrRqbr4ZHpfVFkuh4T0XnbiLqNFz06bROZrt+KTO+rItPrNwppAACkkjwPgFTIRlx86lXLVUjLefv1d+LqX95Y8LEobp6Xs8yZXk33iMYDItP7L5Hp9r2I+h0jOm0WUbdRRKetIrocEpnel0Wm9x8V0gAA0lJKu/DCC+P555/Pb+XfHquttlqMGTNm8VEAue3xR4wYEQ8++GCRJwWg2j18+xMxZ8acDl3jvuseitYF7T/2kxQX03JqukQ07ByZ7t+JTM+fLHr0ODGiYaeImoZCjwoAACUhzwMgLV5+8tWYOH7RzlnL66l7n4v3mqcXbCbKuJiWk6mLqB8emW7HRabHqZHp+dPI9Dg5Mo17R9T0KPywAABVqiSltMMPPzxqa5ftGLM+ffrEyJEjY7fddst/PG3atNhll12KNCEALLqr8v7rx3T4MjPenRlPj3y+ICNR+mLacpfTAACggsjzAEiLQuR5uZ0+R9/0cEHmISXFNAAAiq5kx3cuj8bGxrj11lvj0EMPzX/c0tKS9EgAVLD/PD0h3p4wpSDXevDmR5f4+1PffC9GXfNg3PqnO+PGc26POy++N54bPT7a2toKsi4dI8gCAICOkecBUEqz358TT91bmJtDH7p5bGTbsp/4/dyxoA/e9Gj84893xQ1n/yP+ecG/47E7n4r5LQsKsi4dI88DAChfdVHmcndkXnLJJbHSSivFGWeckfQ4AFSw5lffLti13nrtv+W2XJj1/JgX44Hrx8Tzo1+MbG5Lto/pvWKv2PrLW8SIvTeP7it0K9gcLF+Q1dw6OR9kDW7qk/Q4AACQOvI8AEplyhtTo23hwoJca+a0WTFn5tzo2rMx//GE5yfG/deNicfvejpaF7R+4vVdunWJ4XtuFtvst2X0X6VvQWZg+cjzAADKU9mX0j7wi1/8IpqampIeA4AK1jKrcHfwz/3/15o3Z15c8qOr8ruhLc20t6fHbef/K+6+4r444tcHxZAt1irYLCw7QRYAAHScPA+AYvsggyuUOTPmRJfuDXHjOf+MkVc/8Blrz417r34gRv79wTjwlL1im323LOgsLBt5HgBA+Snr4zs/7uijj056BAAqWF19p4Jdq1N9p5g3d36cc/QFn1lI+7CW2S3xxxMujWfuf6Fgs7B8bP0PAAAdJ88DoJg61dcV/HpX/PTazyykfVi2rS2u+dVNcdflowo6C8tOngcAUF5SVUoDgGLq2bd7wa7V2KNLnPHV38cb4yYt83tzRw5ccupVMenFNws2D8tHkAUAAABQvnr27VGwa2VqauKyn/w9xv7ryeV6/y1/uCOeuPuZgs3D8pHnAQCUD6U0APj/1h2+dtR3qS/Itd6ZODXemTR1ud+/YN6CuPX8fxVkFjpGkAUAAABQnvoP6hsrrzWwMBfLZuPlJ17t0CVuPPf2aGtrK8w8LDd5HgBAeVBKA4D/r6GxPjbfY5MoFy88+GJMffO9pMegHIOshW9FdvaVkZ1+cmTfOyqy7x0Z2enfjezsCyNaJyY9HQAAAEBpZCK23W94QS6VzWY7fI1pb02P50e/WJB5qLA8r21GxJybIvv+DyM77ZjIvvfNyE4/IbIzz4lY8EK+FAkAUGmU0gDgQ7bbvzAhViFkIxujr38k6TEopyBrwcuRff//Ijv9WxEtN0UsfDUi+05EdmrEwgkRLXdE9v0TIvv+TyLmP53cnAAAAAAlMmzXjaKha0OUi/uueyjpESinPG/h25Gd+fvITvtmZOdeGdH6YkTb2xHZ9yIWToyYf39kZ/w4su+fGDFvpHIaAFBRlNIA4EMGrr5i7PjVbaJcPPfg+KRHoFyCrHkPRHbGjyJan/zs17Y+H9mZP4+Y+49STAYAAACQmPrG+tj/5C9FuRj/yMvRuqA16TEohzxvwYuRnf69iPn35QK7pb924RuRnXVeZGf/JSK7sFQTAgAUlVIaAHzMPifsHpvuslGUg+lT3k96BMohyJo3JrKzzv7s8OpjsnMuiZh7R9HGAgAAACgHW35x09jzmC9EOcgdAzp3ZkvSY5B0ntf6WmRn/DwiZi3b++bdFdnZF9gxDQCoCEppAPAxNTU1cdj/fSV2Pni7yEQm0Vnmzpobk156M9EZSDjIWtgc2VnnLPfbs3MuiljwUkFHAgAAACg3u35jx/jqj/aLTp3r2vX6YqZ+T496vohXp+zzvLaWyM74ZUQsZzlx3t0R8/5d6KkAAEqufd+ZA0CVydRkYu/jd4+tv7xFPHDDw/HQrY/FnBlzPvG6tTZdI3r16xFj72zHkYrL6aLv/zV+ev3JUVO7qEs+492Z8dDNY2P8oy/HrOlzItvWFo09G2ONDVfNz9u3qU/RZuGjQVZz6+R8kDW4iP+bZ1tuz+3135ErRHbuLZHp9L0CTgUAAABQfkbsPSw+t926+Sxv9A0Px7vN0z7xmpXWHBBrbrx63H/dQ0Wb4/qzb4sNtxsaPfp0z3/cMmdejP3nk/HUqOdi5ruz8sd7duneJVZec0CM2GeLWHVoU9FmofR5Xsx/ICLbsfJbdu7NkanfKSKT7E3TAAAdoZQGAEuRK3jtc8Ie8cWjd4lXnpwQM96bGa3zF0Zj94ZYea2B0X+VvnHtb24p6gzvTHo3nntwfPRdeYW485KR8dS9z8bC1oWfeN2rT0+If195f6y71TrxhUN3iDU3HlzUuShBkNU2N6JlZMevs+CRiIXvRdSuUIipAAAAAMpWt97dYpevbx87HbxtvPr0GzH97ekxb+78aOhan8/6Vl23KR68ZWxRZ1jQsiB/U+nwvYbFnZfcE4/e/mS0zPnkrlkTnnsjHrz50Ri83qD4/Ne2jU123rCoc1GCPC+bjWzLHR2/TltzxIJnIjp/rhBTAQAkQikNANqhU32nWHfLtZb4ufktHdnFqn3+ecG/4+3X34n5LfOX+rpsZOOFh8bHuDEvxoHf3zu22XfLos9W7YoaZM0fnTvEtQAXaouYd09E4/4FuBYAAABA+aupqfnUmzYXfEbGVgijrn0w7r9+TLw/dcZnvnbC8xPj4lP/Fv95ekLs+90v5mcnpXnewlciFk4oyKWyLXdFRikNAEgx39UCQAc1dGso+hoTX5z8mYW0D8tms3HNr26K0Tc+UtS5+G+QlZMLsgop2/pqAa/1SsGuBQAAAJBmuV3Tim3me7PaVUj7sFF/fzCuPfPW3J2npDTPi9b/FO5aCwt4LQCABCilAUAHrbhq3yhX1/z65pjw3MSkx6gKRQmysrPL81oAAAAAKbbiqv2iXD1w/ZgYc9tjSY9RNXle7lHQPK+tgBlc26zCXQsAIAFKaQDQQZvtslF06lyeJ2Jn29ri31fel/QYVaPwxbTaKJzy/G8UAAAAoNRW22DVGDC4f5Srf102MrJttksrlYIW0zIFzOAKeS0AgAQopQFAB3Xp3hAbf37DKFdPjXo+pk95P+kxqkZBi2k1PTt+jWJcCwAAACDNMhHb7D88ytU7E6fGi485ujGVxbSaHoUYp/DXAgBIgFIaABTA5w/aJspVbre0h24Zm/QYVaVQxbRMp80KNFFEpnPhrgUAAACQdlvuvklkasr3r8lG3/Bw0iNUnYIU0+o2KtyJBZ2GFeY6AAAJKd/vtgEgRZrWXilWGdIU5er1FyYmPULVKUgxrdN6ETUF+O8q0zOi85Ydvw4AAABAhWjo1hDDv1S+N/FNeE6el2QxbbkzvdreBcvhMg1fKMh1AACSopQGAAVywPe+FOVq9oyWpEeo2hCrQ3dYZjKRadi144PU75Tbdq3j1wEAAACoIHsft1vU1tVGOZo9Y07SI1Stjt5sWpA8r9OmEbX9O34dAIAEKaUBQIGstsGqMWjIosCi3Mx8d2bMfG9W0mNUrQ4V0xo+H1G76vIvnukXmS57Lv/7AQAAACpU156NMWy3jaMctS1siylvTE16jKrVoWJa3boRnYZ3YPX6yDR+tQPvBwAoD0ppAFAomYgDT9k76jrVRbmZOvnd+NEev4xLf3x1vPbsG0mPU5WWu5iWqY9M9x9HZPoux6rdItPzxxE1PZbjvQAAAACVb8+jd4kefcsvO2ld0Bo/3/fM+MO3L45n7x8XkU16ouqz3MW03OkH3Y+PqBuyHKvWRabbSRF1qy3HewEAyotSGgAU0GobrBKH/eJ/ynLb/4WtC+Oxfz0Vv/3GH+POS+4VZCVYTFvmIKu2T2R6/iqidvX2v6dmQGR65d4zaJnnBAAAAKgWvfr3jGPPOSwaezRGORr38Evx55Mui8tOuyZfVCMtxbT6yPQ4LaLTFsvwpm6R6f7TiPrNlm0tAIAypZQGAAW20Y7rx7HnfiO69eoa5eq28/8VN//hjqTHqErLHWTVrpAvpmW6fTeibuhSXrdGZLoeF5le50TUrtTBaQEAAAAqX9M6K8X3Lj02VhzcP8rV2DuejItO+Wv+WE9SVEzrfkpkun9QTsss+XU1/SPTeEhkev8xovP6BZgYAKA8lN/5YgBQAdYZtmb8760/iMf+9XTcf91DMemlN6Pc3H3FqBgwuF9suac775IIsppbJ+eDrMFNfdr/xkxdRP3WkanfOqL1jYgFz0a2bcaiT9V0i+g0JKJureINDgAAAFCh+q/SN358zYnx7APj4v7rx8T4R16OcvPs6HFx4+//Gft994tJj1J1lj/Py0R0/lxkOn8uYuHUiAWPR7S9H9nsgsjUdI2oHRzR6XOLXgcAUGGU0gCgSOq7dI4Rew+LEXsNy5fSprwxNebOnhf1XTpFz349omvPxnh38rRomT0vrjrjxpg/d17JZ7zurNti010+F53qO5V87Wq33EHWB+pWyT/EVQAAAACFUVNbE5/bfr38Y+qkd2PSS80xZ+bcqO1UG917d4t+TSvElInvxtwZc+POS+6N5tfeLvmMo64enc8cB66+YsnXrnYdzvNq+0bUfiH/VKYHAFQDpTQAKLbMoiMAco+PW2mNAflfX312Qtx/3ZiSj9YyuyV+e9if4sSLjo6GxvqSr1/tOhxkAQAAAFAUfZv65B8f129Q3/yvLXPmxdVn3FjyubKRjXOOuiC+f8W3Y4WBvUq+frWT5wEAtF9N0gMAABHb7jc8sbUnvfxmXHDyFdG6oDWxGao9yMrJBVkAAAAApMOwXTeKhq4Niaw9a/qsOPdbF8as6bMTWb/ayfMAANpHKQ0AykBuu/21Nl0jsfVfHPtKnPeti+L9qTMTm6GaCbIAAAAA0qW+sT62/OKmia3/zqSp8Zuv/yHefv2dxGaoZvI8AIDPppQGAGXigO99KbG7K3Neeeq1+NEev4yLT/1bTHrpzcTmqFaCLAAAAIB02f2InaJf06LjPJPw7pvvxf/u99v8rmkvjHkpsTmqlTwPAGDplNIAoEystMaAOOq3h0Tnhs6JzZBta4sn7n4mzjz0j/lfKS1BFgAAAEB6dO3ZGMeee1j0XrFXonPkTkH44/EXxx0X3RORTXSUqiPPAwD4dEppAFBG1t5sjfjuhUdHn5VWSHSO1gWtccmpV8WT9zyb6BzVSJAFAAAAkB79BvWNky/5Vqy2/ipJjxL/+MtdcfuF/056jKojzwMAWDKlNAAoM4OGrBw/u/F7ccRvDo4hm6+5xNd06dYQmZri/jGejWxc9pNr4q3XphR1HT5JkAUAAACQHr3694yTLzk2TrzgmNh0l42WmNt1augU9Y31RZ/lnxfeHU+Per7o6/BR8jwAgE+qW8LvAQAJq6mtiY12WD//ePfNafHOxKkxd1ZLPrzq1a9HNK21Uvz1F9fHmFvHFn3HtHuveiC++qN9i7oOSw6ymlsn54OswU19kh4HAAAAgKXJRKy58eD844CT94zJr7wVc2e2RG1dbXTr3TUGDVkpRt/wSFx31q1FH+Wuy0bG57Zfr+jr8FHyPACAj7JTGgCUuT4r9Y4hW6wVG39+g1h/xJBoWnulfMi13f7DS7L+2DufygdolJ47LAEAAADSp1vvbrHOsDVjox3Xjw22XTdW22CVqOtUF1vssWl0buhc9PUnPD8xXn9hUtHX4ZPkeQAA/6WUBgApPuZz/a2HFH2d+S3z4+bz7ohsW7boa/FJgiwAAACAytCle0Ns/5URJVnrpnP+Ea3zW0uyFh8lzwMAWEQpDQBS7LD/+58YsNqKRV9n9E0Px8++fGY8c98LRV+LTxJkAQAAAFSGPY/ZJTbcrvhHa7785Gvxoz1+GSOvGh3hXtOSk+cBAETUJT0AALD8Gro1xIl/OTJ++dXfx/tTZxR1ramT342/nHx5DF5vlZg7uyXmzJgTNTU10bVXYwzdcu3YZt8to29Tn6LOUO1BVnPr5HyQNdj/zgAAAACplMvTDv/lV+OcYy6M156ZUNS1Zk2fHdeffVs8dNvY/Mezp8+Jtra2aOzRGKtvsGpss9+WserQpqLOUM3+W0ybLM8DAKpSJpvNuj+iCkyaNCkGDRqUfz7ygcdjwMCVkh4JgAJ6a8KU+L/9z0p6jBg6fJ3Y46idY/B6i/7MofByxbScRIKs3LeN2ZkR2VmLPs50j6jpXvo5AICy1jy5OUass1X++cSJE6OpyV90wvKS6QFUrvnzFsQPv/CLaJndkugcq6zbFLsd/vnYcLuhic5RDZleYsW0tjkR2dwNzbnjXLtF1PSMyGSSmQUAqKo8z/GdAFABBgzuH7t8fYekx4gXxrwYZ3/zz/H4XU8nPUrFSmTr/1xwNff2yE4/IbLTDo3s9OMWPaZ9PbLTT4xo+VdE29zSzQMAAACQcp3rO8X//HCfpMeIN8ZNyp+O8M8L/+2YzyJneiXN87ILIuY9ENn3T43stIMiO/1bkZ1+fGSnfyOy046KmHN9xMLppZsHAKhKSmkAUCG+9K0vxLDdNk56jGhtbY1Lf3R1PHPfC0mPUrFKVkzLtkV29tWRnfbNyM65OKJt0idfs/D1yM7+S2SnHb4ozLIJLwAAAEC7bPaFjWKv43aLcnD7BXfHnZfem/QYFa1kxbSWeyM77cjIzjo7onX8Jz+fnRrZuVdFdnruNedHZOcXfyYAoCoppQFAhcjUZOLrPzswdj54u6RHiWxk45IfXRXvvjlt8e8tbF0YLXPmueMyLcW07ILIzjwrouW6XJLVjje0LAqzZv0+IruwODMBAAAAVJhdvr59fPVH+0VdXV3So8Rt5/8rxj/y8uKP29ra8seL5n6lsMW0omR62WxkZ18V2dl/iMi+3443tEbMuzuyM34W0Ta78PMAAFUv+e9wAYCCFtP2Pn732PKLm8YDNzwSo296JFoXtCYyy4J5C+LXXz8vBgzuF82vTok5M+YsmjGTiYFrrBgj9t4ittxjk2jo1pDIfJVVTJscg5v6FDbAyt0luWDMsr93/v2Rnd0Yma5H5P5lF24mAAAAgAo1Yu9hsd5Wa8dDN4+NkX9/cHGOloQ/n3xFrLruyvHOxHfj/akzFv/+CgN6x5Z7bpaftVf/nonNVymZXnPr5HwxraCZXsttES3XL/v7WsdHduavI9PjJxGZToWbBwCoepls1hlL1WDSpEkxaNCg/PORDzweAwaulPRIAJTAe29Nj18dfG7Mnl6ed7p1bugcW31pWOx9/G7RqV7g0RG5IKtgIda8hyI767cdukSm+48jOm9SmHkAgFRpntwcI9bZKv984sSJ0dTUlPRIkFoyPYDqs2D+gvj1IX+I5v+8FeUoU1MTG+24fux/0peiZ9/uSY+T+jwvpyCZ3sKJkZ3+nfwZFssr0+XgiMZ9Oj4LAJA6zUXK8xzfCQAVbIUBveK7fzkqGrt3iXI0v2V+jLr2wfj90RfE7PeTuwO0krb+L4Rsy+0dv8bcjl8DAAAAoNp06twpTrzgqBgwuH+Uo2xbWzz572fit4f9Md6a8E7S41TIKQgdz/SyLXd2qJC26Bp35P4Fd3gWAIAPKKUBQIUbsPqKcdIlx0afgb2jXL323Btx/ncvzx/5SceLaR0Kslpfj2gd1/FhWp+MWFied/QCAAAAlLOuPRrjxAuPjtU2HBzl6r23psUfjr0opk95P+lRUq0gxbS2uREtIzs+THZqxPzHOn4dAID/TykNAKrAgMH94tSrv5PfVr9cj8l87ZkJcdv5dyU9RlR7kJWdV4AA64NrtYwq2LUAAAAAqkm3Xl3jxL8cGV//+Veie5/yPCZz2pTpceXPr016jNTrcDFtwcMR0VKQWbLz7i3IdQAAcpTSAKBKNHRtiO2/MiL2PfGLUa4evPnRmDd3ftJjVHeQVcjdzdreLty1AAAAAKpMbV1tbL77xnHUbw6OcjX+0Vei+VUZUJJ5Xra1gP/7y/MAgAJSSgOAKrP5bhtHQ2NDlKOW2S3x2J1PJT1GdQdZ2bmFGyI7p3DXAgAAAKhSq22wajStvVKUq/uvH5P0CFVeTCtknlfAawEAVU8pDQCqTH1jfWz5xU2jXD148yNJj1DdQVamgIXFTJfCXQsAAACgWmUitt1/qyhXj97+ZLTOb016jCoupsnzAIDypJQGAFVo9yN3in6D+kY5envC1KRHqO4gq7Zf4RavKc//xgAAAADSZviem8a6W64d5ahlTktMnzoj6TGqNs/LFDTP61O4awEAVU8pDQCqUNeejXHcud+Ibr26RjmGWNm2bNJjVG2QlanfrmDrZhoKdy0AAACAalZTWxPf/NXXomntgVGOWma1JD1C9RbTOm+Z+z8FWbeQ2SAAgFIaAFSpvk194gd/PT7q6uqi3Fz4g7/G+EdfidBNK32QVbdWRO0aHV+wbv2I2kEdvw4AAAAAeQ1dG+Kki4+NHn27R7n52y9uiCfufiYWti5MepTqy/NqukXUb9PxBTM9/3/BDQCgMJTSAKCK9V6xV+z6zR2j3Dw98rk479gL42dfPjOee2B80uNUXZCVadi9w2tlGnbr8DUAAAAA+KjODZ3if3745Sg3b4ybFBef+rc4dbdfxn3XjnGzacnzvAJkcfW7RGQ6dfw6AAD/n1IaAFS5HQ4cESuu2i/K0TuTpsb53700Rv39oaRHqa4gK7dNf6dhy79I5xHuqgQAAAAokg22XjeGbjUkytGs6bPi2jNvjmt+fVNk2zTTSpbn1a0e0dCBsmLtGpHpss/yvx8AYAmU0gCgyjV0a4hvnfuN6NWvZ5Sr6357Szx0y9ikx6ieICtTE5luJy46gnNZ1W0cmW7HR2QyHZwSAAAAgCXJ1GTi8DO+GqsObYpy9cAND8e1v70l6TGqqpiWafxaRP3Oy37x2qbIdD81oqahIyMCAHyCUhoAEH1XWiFOvvRbsfJaA6Nc/e0X18eUN6YmPUb1BFk1DZHp8ZP/H2S1p2BWG9Gwe2R6/NA2/wAAAABF1tBYHyecf2RssM26Ua7uv25MPHbX00mPUUU3mmYi0/XoyHQ5KHeUQfsu2mlYZHqcEVHbu4CTAgAskslms/bOrQKTJk2KQYMG5Z+PfODxGDBwpaRHAqAMLWxdGM/ePy5GXj06XnnqtSg3mUwmautqo0v3hnyBbut9togNtxua/z2WT3Pr5Pyvg5v6fPqLFk6NbMvdEfPujshO/+jnMr0j0/CFiPqdImpXKPK0AEAaNE9ujhHrbJV/PnHixGhqKt8dPKDcyfQA+EzZiJeffDVGXfNQPD3quSjHv/arrauLhq710W9Qnxi+52YxbNeNor6xPumxKjvPa5sVMW9kZFv+FdH25sc+2SWiYYdFmV7tou8zAIDq1lykPE8prUoIsABYVm+//k68/MSr8dozb8R7b02LbFs2evXvGX1XXiHW3XLtGPfwS3HHxfckPWb06NsjdvjKiNjp4G2jpsYmsEULsnKyrRELmyOyMxd9XNM9omaliIxSIADwX0ppUDgyPQCWxftTZ8b4R16O15+fGM2vTYlsW1t069k1+q3SN1bbcJWYP2d+XHba3/O/n6SGxoYY/qXN4ovH7JLf8Y1i5nnZiLa3ItreX5Tt1XSNqF05ItPOndQAgKrQXKQ8r64gVwEAKs6Kq/bLP3K7kS3JGhsNjm69u8UNZ/8j2hYujKTMmDojbvnDHfHSY6/G4Wd8Nbp0a0hsljRv/Z8LsnJb/y81yMrURdS5exIAAACgHPXs2z222GOT/OPTNPboEpf86KqYO6slktIypyVGXjM6xj/6chz9u0PzN8FSrDwvE1E7cNEDAKDEbCcCACy37Q/cKv7v1u/Hbod/Prqv0C3RWcY9/GKcvMNpcc7RF8ST9zybP4qUZQuycnJBFgAAAACVaehW68T/3frD2P+kL+VvSE1S86tvx2l7/zp+8ZWzY/SNj8S8OfMSnSdt5HkAQLlzfGeVsNU/AMXWuqA1Xhz7n5j21vS4+bx/Jnq3ZU7Pvj1iz2O+kD8KgCJs/Q8A8Ckc3wmFI9MDoKiyEa88NSGmvPFO/Puv98fbE6YkfqznDl/dOnY/4vNRU2NfjWXN9OR5AEC55Xm+owMACqKuU12st9U6sfWXt4gF81qTHifenzoj/vp/18Utf7gzH7DRPu6wBAAAAKgSmYg1Nx4cW+01LBoaOyc9Tf5Yzzsu+ndc9P2/Ruv85PPFtGV68jwAoNwopQEAhZWNsjo6867LR8a/LhuV9BipopgGAAAAUF0WtrZFuXh61PNxxc+vi2ybO02XhWIaAFBulNIAgMLKRDT2aIxycuuf7og3xk1KeoxUUUwDAAAAqB6NPbpEOXn8rqfikdsfT3qM1BbTZHoAQDlQSgMACm6VdRcVmsrJqGsfSnqE1FFMAwAAAKgOq647KMrNvVePzp/KwLKR6QEA5UIpDQAouG323TLKzWN3PhWz35+T9BipDLFs/Q8AAABQ2UbsMyzKzeSXm+O1Z19PeoxUUkwDAMqBUhoAUHAbbLNu9O7fK8rJwtaFceZhf4xn7n8h6VFSSTENAAAAoHL1G9Q31t1y7Sg3fzrxsnjwpkejbWFb0qOkjmIaAJA0pTQAoOBqamtip4O3jXLzzsSp8ZeTLo/rz7ot2toEWctKMQ0AAACgcu18yHZRbubMmBNX/fKG+PNJl8e8OfOSHid1FNMAgCQppQEARbH9gSNi8903iXI08prRcc0ZN0Vkk54kvcU0QRYAAABAZVln2Jqxz/F7RDl6/sHx8afvXBqt81uTHiV1FNMAgKQopQEAxZGJOOgn+8XwPYdFOXrw5kdj1HUPJT1GKgmyAAAAACrTTgdtG3t/e/coR688+Vr8/Te3JD1GKsnzAIAkKKUBAEVTW1ebL6Yd9JP9Y+DqA6Lc3HnRPTF3VkvSY6SSIAsAAACgAmUWHeN57LmHx1qbrB7lZsytY6P51beSHiOV5HkAQKnVlXxFAKC6ZCKGf2mzGL7nZvHKUxNi9E0PR/N/3o4Z782MGVNnJjrazGmz4ns7/jw22WmD2Ha/4bHmxqvl56X9QVZz6+R8kDW4qU/S4wAAAABQIEOHr51/NL/6djxw/cPx6rNvxOzps+O9t6YlOlc2m41fHHh2/qjRXJ634XZDo6bWHhztJc8DAEpJKQ0AKI1MxJobD84/8rIRvzrk3Jg4fnKiY2WzbfH43U/nHwNXWzEO+fkBscq6TYnOlCaCLAAAAIDKNXD1FeOAU/Za/PFf//f6GHPb2Ejai2NfyT969OkeX/nBPvG57ddLeqTUkOcBAKXi1gEAIBmZiO323yrKSfNrb8eZh/0xfwwA7WfrfwAAAIDqsM1+W0Y5mfHuzLjge1fEjefcnvQoqSLPAwBKQSkNAEjMsF03ipXXGhjlpG1hW/z1/66Pm8+7I+lRUkWQBQAAAFD5Vh3aFJvsvGGUm3v+dn/84dsX509noH3keQBAsSmlAQCJqetcF98657DoPaBXlJu7rxgVv/jK2TH+kZeTHiU1BFkAAAAAle+Q0w6I1T83OOkxPmHcwy/FD77wf/HwbY8pp7WTPA8AKCalNAAgUb3694yTL/5WNK29UpSb5v+8Fecdd1H8+68PJD1KagiyAAAAACpbp/pOcdx5h8cG2w6NcjNz2qy48n+vi7/+4vpY2Low6XFSQZ4HABSLUhoAUBbFtO9demwc/NP9Y5V1m6Lc3PT7f8TIq0YnPUZqCLIAAAAAKlt9l85x1JmHxNFnHRpDh68T5WbMrWPjql/eaMe0dpLnAQDFUFeUqwIALMdRnlvuuVn+8foLk2LcmJdi6pvvxSP/fCLayuCuxuvPvi36NPWODbddL+lRUhNkNbdOzgdZg5v6JD0OAAAAAAWWqcnEBtuum3+8M3FqPDXy+Zg+5f14+B+PR8vslqTHyx/j2XvFXvHFo3ZOepRUkOcBAIVmpzQAoOysOrQpdj18xzjoJ/vFaTecHF26d4lycMmProkpb0xNeozUcIclAAAAQHXoN6hv7HzIdrH/yV+KM/714+i/St8oB3defE+8+NgrSY+RGvI8AKCQlNIAgLLWd6UV4kdXfScGrrZi0qPEgpb5cfaRf87f8Un7CLIAAAAAqkvn+k7xgyuPj6HDhyQ9SmSz2fjTty+N1559I+lRUkOeBwAUilIaAFD2eg/oFSdf+q34wmE7RGOPxkRnmfHuzLjwlCsjsomOkSqCLAAAAIDqUt9YH8ec/fXY77t7Rp+VVkh0ltbW1vjLSZdHy6zkjxRNC3keAFAIdQW5CgBAkTV0bYgvfWvX2P2bO8Woax6Mf1xwdyyYtyCRWSY8PzFefvLVWGuT1ePNV96Kp0Y+FzPenRWt81ujS7eGWHmtAbHxThtGfZfOicxXrkFWc+vkfJA1uKlP0uMAAAAAUGQ1tTWxw/9sHdsfOCKevPfZuOZXN8fs92cnMsvMabPi4X88Htt/ZURMe3t6PP6vp+O9t6bHvJb50dBYH/2a+sRmX/hcdOvdLZH5ypE8DwDoqEw2t28tFW/SpEkxaNCg/PORDzweAwaulPRIANAhuTsbR988NkbfMCbeSeCOvVWGNkWnznXxn6cmLPHzuXLaFntsGtsdsFX0X6VvyecrV7kgK0eQBQCVq3lyc4xYZ6v884kTJ0ZTU1PSI0FqyfQAqCQLWxfG2DuejAdueDh/02ep9ezbI1ZdrymevX9c/ljPj6urq4uNd94gtj9gRAxef9Gfv8jzAKAaNBcpz1NKqxICLAAqVbYtG+MeeTleGvtKzJo+J2ZNnx1TJ70bza+9HeWgtq42Dv7pATFst42SHqVsCLIAoLIppUHhyPQAqFSvvzApnhn1fH4Hs9nvz4n3mqfHG+MnRbnY7fDPxxeP2iUik/Qk5ZXpyfMAoDI1FynPc3wnAJBqmZpMDB2+dv6xWDbiV4ecFxPLIMjK3QF62U+vjvnzFsSIvYclPU5ZsPU/AAAAQHVbdWhT/vFhf/3f62PMbWOjHNxx8T0xd2ZL7H/ylxTTPpTpTZikmAYAtF/NMrwWACAdMhEH/3T//Jb75eLqM26Mlx77T9JjlFWIlZMrpgEAAADA3t/eNbr36R7lYtS1D8ao6x5KeowyLKbJ8wCA9lFKAwAq0sprDYjDf/W1KBfZtra49fy7kh6jrCimAQAAAPCBbr27xXf+clTUltGNprf/5e5YMG9B0mOUZTFNpgcAfBalNACgYm243dD4xi+/GplMeeyx/9ozE2LSS28mPUZZUUwDAAAA4AMDVu0X37/y29Gpc3kU0+bMmBNP/PvZpMcoOzI9AKA9lNIAgIq26c6fi1MuPy66dO8S5eD+68YkPUJZhli2/gcAAAAgZ+U1B8TPbv5+9F+1X5SD+6+X5y2JYhoA8FmU0gCAirfKuk1x2vUnxw5fGZH0KDHu4ZeTHqFsKaYBAAAAkNOrX4/44V9PiL2/vXvUdUp217QJz70Rc2e2JDpDuVJMAwCWRikNAKgK3VfoFvud9KX431t/EDV1tYnNMWv67MTWTgPFNAAAAAByOjd0ip0P2S5+c89p0a1X10Rnmf2+TO/TKKYBAJ9GKQ0AqCp9BvaOI359UGLrZ9vaEls7bcU0QRYAAAAA9V06x4kXHB2dGjonNkNbWzaxtdNAMQ0AWBKlNACg6my47dA48JR9Elm7rnOyxw2khSALAAAAgA8MWK1/HH3W1xM7yrOxR5dE1k0TeR4A8HFKaQBAVdp2/y3jkJ8fWPJ1kwrO0kiQBQAAAMAHhmy+Zhx//hFRW1db0nUzNTXRrWeyx4emhTwPAPgwpTQAoGptsfsmsc1+w0u6ZkPXhpKul3aCLAAAAAA+sMbnBseB39+7tIs6unOZyPMAgA/YqgMAqGo7H7xdjL7+4chGacKlmdNmxa8OPi9aZrVEXX1d9OzbPTb5/Iax2a4bRX2XziWZIY1BVnPr5HyQNbipT9LjAAAAAJDwjaa3/elf+ZytFHK54W8OPS/mzmqJmtyuab27xnpbDYmt9tosuvXuVpIZ0kaeBwDk2CkNAKhqfVbqHRtsN7Rk67XMbomJ4yfFO5OmRvN/3orxj7wcV/3yhvjR7qfH9WfdFrNKFKaljTssAQAAAMip61wXW++7ZUnXfP2FSTHljanx1oQp8cqTr8Utf7wjfrT7GXHZT6/J/z6fJM8DAJTSAICql9vyv/eKvRKdIXen5chrRsdvDv1jvP36O4nOUq4EWQAAAADk7HrYDrH65wYnOkNra2uMvePJ+PUh58WLY19JdJZyJc8DgOqmlAYAVL1e/XrEcecdHr37J1tMy3n3zffinKP+Eu81T096lLIkyAIAAAAgt1va0Wd9PVYd2pT0KPmTEf50wqXxn6cmJD1KWZLnAUD1UkoDAIiIAav1j5MvOzaGbjUk6VFixrsz4y8nXx7ZtmzSo5QlQRYAAAAAXXs2xgl/PiqG7zksamprE52ldUFr/OXkK2LW9NmJzlGu5HkAUJ2U0gAAPrRj2rG/Pyx+ev3JscP/bBNdunVJbJZJL70ZLzz8UmLrlztBFgAAAAD1XTrHQT/dL06//Yex5zFfiN4rJncSwuz3Z8dDN49NbP1yJ88DgOpTl/QAAADlZsVV+8V+3/1ifPmE3fN3N7bMnhedGzrFpJea83c8ti1cWJI5HrhuTKy31TolWSutQVZz6+R8kDW4qU/S4wAAAACQkB59useu39gxdj1sx5g1fVbMmdkSdZ3qYs7MuXHuty7MF8ZKYfSND8dOh2wbNTX2BVkSeR4AVBffEQEAfIqa2pp8oNV/lb7Rq3/PWH/rIXHkbw6Ozg2dS7L+c6PHx7S3ppdkrbRyhyUAAAAAi2UiuvXuls/zVhjYK5rWHhgnnH9k9OrXsyTLv9s8LcY9/HJJ1koreR4AVA+lNACAZbDBtuvGyZccG5/bYf3IZDJFXSsb2Xh93KSirlEJBFkAAAAAfJqV1xoQ37v8uNhqr82jU32noq834bmJRV8j7eR5AFAdHN8JALAcQVZux7Rpb0+PB298NJ4f82LMnj472hZmo6F7QzT/562CrTV3Zsvi5xPHT47nH3oxZk3LrdUWjd27xKrrDYr1RqyT39Wtmtn6HwAAAIBP06tfj/jaj/eNL5+wRzz8j8fiiXuejZnvzoz5LQvyGdt7b0+PeXPmFWStOTPmLH4+9c334ql7nov3p86IBfNao0v3hhi42oqx0Y7rR+eG4hfkypk8DwAqn1IaAMBy6r1ir/jiMbvkHx9oa2uLb2/xw4Ku88g/n4j7rxsTE55741Pn2PrLW8TW+2yeP56gWgmyAAAAAFiaXClsh//ZOv/4sF985eyC3Wiau3n0uQfH5/O8Fx58MX8awsdde2aXGL7nZrHt/ltGv0F9o1r9d8e0yfI8AKhA1b2lBgBAgdXU1ERjj8aCXe9fl42MK077+6cW0nJyO7bddv6/4uf7nRX/eWpCVDNb/wMAAACwrLr37lqwa4175OU4/zuXxvMPjl9iIS1n7qy5ce/VD8T/HfC7eOT2J6La5TI9eR4AVB6lNACAAssdp1kImcjEOxOnLtPRAOd+68J4cewrUc0U0wAAAABYFuttNaRg11qWHdcWti6MK37297j/uoej2immAUDlUUoDACiw7fYbXpDrfNqdlEvTuqA1LvjelTHljfaX2SqRYhoAAAAA7TX8S5tFp851ia1/7Zk3xwsPvRjVTjENACqLUhoAQIGttsGqMWidRaWoJLTMbok7Lr4nqp1iGgAAAADt0bVnY2z6hY0SWz+bzcbN592Ru0u16n1QTJPpAUD6KaUBABRaJmLv43ePTE1y32o9cfczMWv67Kh2imkAAAAAtMdu39gxunTrktj6k19pjleffT2x9cuJTA8AKoNSGgBAEQzZfM34nx/sk9j6uWM8x9z6WGLrl1uIZet/AAAAAJamb1OfOOqsQ5brGM9M7i7VArj/ujEFuU4lUEwDgPRTSgMAKJIR+2weh53+1ajr1P4ga+W1BhZs/RfGvFiwa1UCxTQAAAAAlmatTVaPE/58VHTv1a3d71lxcL/IFujczecfkud9mGIaAKSbUhoAQBFttsvn4rQbvhe7fH2H6Nar6xJfkzvmc6MdNohv//GIWGfYmgVb2/Gdn6SYBgAAAMDSrLbBKvGTG06KfY7fI/qu3GepBbbDf/m12OXg7Qu29pwZc6Ktra1g16sEimkAkF7Lvv8sAADLZIWBvWKv43aNPY7cKZ6574V467UpMWdWS3Sqr4uefbrHRjuuH73698y/9rkHxhVs3bZWAdanF9Mmx+CmTw8VAQAAAKheXXs0xk4Hbxuf/9o2Mf7RV+L15yfG7Blzora2Nrr1aoyhI9aJldYYkH/tmFsfK+ja2basbUWWkOc1t07OF9NkegCQHkppAAAlUte5LjbZecOlvqaxe5eCrdelR2PBrlWpxbQcQRYAAAAAS5KpycS6W66Vf3yaxh6Fy/M6N3SO2rragl2vkiimAUD66NkDAJSRwesPKti1VluvcNeqRLb+BwAAAKCjVll35chEpiDXGrz+KgW5TqWS5wFAuiilAQCUkSFbrhV9VlqhINfaet8tCnKdSibIAgAAAKAjeq/YK9bfZkhBrrXNvlsW5DqVTJ4HAOnh+E4AgDJSU1OTD59uPu+fHbrOOsPWjBVX7bfEz818b1Y8ePPYeOXJV2P2+3Pyv9e1Z2OsvekasdVem0W33t2imtj6HwAAAICO2Hb/reLZB8Z16Bo9+vaIz20/dImfmzdnXoy986l47oFxMXP67FjYujC6dOsSq67bFFt/efPoW2WZljwPANJBKQ0AoMxstdewuOfK+2Pm9FnLfY1dvr79J35v8stvxb8uGxlP3ftsPrj6uHEPvxS3/+Xu2HjnDfLvX2mNAVEtBFkAAAAALK91t1grBg1pionjJy33NXY+eLuorav9yO9Nn/J+3HXZqHjk9ieiZU7LJ97z0mOvxN1Xjoqhw9eJnQ/ZLtbebI2oFvI8ACh/ju8EACgzuV3Ljvrd16NT5+W7f2Cf4/eIIVus9ZHfe+re5+I3Xz8vHr/rqSUW0j7Q2toaY+94Mn7z9T/EM/e9ENXE1v8AAAAALI9MTSaOPuuQ6NWv53K9f/PdN4kd/2frj/ze6y9Mil8dfG7cd91DSyykfdgLY16M3x9zQfz7yvsjslE15HkAUN6U0gAAytBqG6wSx/3hiGjs3mWZC2k7HbTtR37vqZHPxUXf/2u0Lmht93UWzFsQF3zvinjugfFRTQRZAAAAACyPXv17xokXHBX9BvVdpvcN/9KwOOgn+0VkPnriwbnHXBgz31u2kxRuOvf2uOuKUVFN5HkAUL6U0gAAytSaGw+O7195fD6Y6lTfaamvze2M9u0/HhE7HbztRwKstya8E5f9+OrILsctktlsNi4+9W8xtcoCHUEWAAAAAMujb1Of+N5lx8bOB28fXXt2XeprB62zchzy8wPjoB/v95FjO1vmzIvzv3PpZ+6O9mlu+cMd8cJDL0Y1kecBQHlavjOhAAAoib4rr5C/U/LLJ+wRY257LF54aHzMmj4nFi5si67du8Sq6w2Krb+8RfRfZcl3YN77t/tjwfz275D2cfNb5se9V42OA07ZK6otyGpunZwPsgY39Ul6HAAAAABSomuPxtj7+N3ii0fvHI/f/Uw88e+n4/2ps6J13oJo6N4lBgzuF1vvs0UMXm/QR24u/cAj/3gipk2Z3qEZ/nXZyBi61TpRTeR5AFB+lNIAAFKgsUeX+PzXtsk/2mvuzJYYe+dTHV77kdufiL2O2zXqG+tj9ow5MWXCOzF3VkvUda6LHn26x4DB/ZcYoKWdIAsAAACA5ZXLzrbYY5P8o92yEQ9cP6bDa7/y5Gvx5n/eipXWGBDzWxZE86tvx5wZcyNTk4luvRpj4OorfmR3tkohzwOA8qKUBgBQoR6544n8TmcdlTsq4J8X3RPvvzMjnvj3M7GwdeFHPr/i4P6x7X7DY8s9NomGbg1RSQRZAAAAAJTKK09NiObX3i7Itf516ajo1rMxHr798WiZ/dGjQHv07ZHfrW3E3sOiV/+eUUnkeQBQPmqSHqBaTJgwIc4777zYd999Y6211orGxsZoaGiIpqam2HvvveOaa66J1tblP1oLAODjJjz7RsGu9e8r74uxdz75iUJaztsTpsR1v70lfrjb6XHftR2/k7Mcg6ycXJAFAED1kOcBAKX22rOvF+xaj/3ryRh17YOfKKTlzJg6I/554d3x4z1/Fdf/7h/RtrAtKok8DwDKg53SSuAnP/lJnH766ZHNZj/xucmTJ+cft9xyS/zud7+L66+/PlZZZZVE5gQAKsvsGXNLul5uV7Zrz7w5pr09PfY+breKOtLTHZYAANVFngcAJCF3xGYpZdvaYuTVD8TUye/GN3/1tajrVDl/dSzPA4Dk2SmtBJqbm/MBVteuXeOggw6KSy+9NEaPHh2PPfZYXHnllTFs2LD868aOHRs77bRTzJo1K+mRAYAKUFuTTCvs7itGxT1XPRCVxh2WAADVQ54HACShJqE879n7X4irfnljxCf7+KkmzwOAZCmllUCfPn3i17/+dT7MyoVWhx56aIwYMSI23XTTfKg1ZsyYOOCAA/Kvffnll/N3WAIAdFTX3l0TW/umc/8Z7zVPj0ojyAIAqA7yPAAgCd16JZfnPfKPx+OFMS9GJeZ5uYc8DwBKTymtBHIB1imnnBLdu3df4udra2vjT3/6U3Tu3Dn/cW7LfwCAjlp3i7USWzu39f/omx6OSqSYBgBQ+eR5AEAShmyZXJ6Xc/91Y6JSKaYBQOkppZXR3Zcbbrhh/vl//vOfpMcBACrARjusH917d0ts/QdvGhutC1qjEimmAQAgzwMACm3g6ivGWpusntj6z44eF+++OS0qlWIaAJSWUloZmTdv3uI7LQEAOqquc12M2HvzxNafNX1WPPyPx6NSKaYBACDPAwAKbdv9t0p0/Tsuvicq2QfFNJkeABRfXQnWoB2mTJkS48aNyz9fd911l/n9kyZNWurnm5ubl3s2ACC9tv/KiBhz22Px/tQZiax/w+/+kb+7c8VV+0WlhljNrZPzIdbgpj5JjwMAQIryvByZHgDwcRvtsF4MXn+VmPDcG4ms//Btj8UmO20YQ4evHZVKpgcApaGUVibOPPPMaG1ddLzVAQccsMzvHzRoUBGmAgDSrvsK3eJbvz8szj7yL9Eyu6Xk689vmR9/PP6SOPVvJ0RDt4ao7B3TJguxAACqSEfzvByZHgDwcTW1NXH0WV+Psw7/U7yTwG5e2Ww2Lvr+X+OUK74dAwZX5o2mOYppAFB8ju8sA4888kicc845+edNTU1xzDHHJD0SAFBBmtZeKb574THRu3+vRNZ/9833YvTNY6PSfbD1PwAAlU+eBwAU+0bT7150TKyyblMi68+bOy/uumxkVLr/3mwq0wOAYrBTWsLefvvt2G+//fJ3VWYymbj88sujsbFxma8zceLEz9zqf/PNN+/ApABAmq281oD40TUnxoO3jI3RN4z51Lss+w3qG60LWmPaW9MLun5uzc9/devI1GSi8otpdkwDAKhkhcrzcmR6AMCn6dGne5x00THx2L+eivuvHxOvvzDpUwtsvfr2iIkvvVnQ9R+/6+n48nf2iG69ukYls2MaABSPUtqH5EKkjrr00kvj0EMPbddrZ86cGXvssUdMmrTom8hf/epXseOOOy7Xurk7MgEAlqZL94bY6aBt8uWwcY+8HC8/8WrMeX9u/nONPbvEOsPWjHU2WyMevPnRuPqMGwu6dq4El1tz6PC1o9IppgEAlE6a87wcmR4AsDR1netiyz03yz9ypbTnRo+PmdNmxcIFC6Nrjy6xytBBseF268bE8W/Gb7/xx4Kunbtxdcytj8XOh2wXlU4xDQCKQyktIS0tLbHXXnvF448/nv/45JNPjlNOOSXpsQCAKpDbrSxXDvu0gtiwXTeKm37/z2iZ01LQdcdXSSntw8W0HEEWAEBlkOcBAEladWhT/rEkq62/SgxaZ+WY+OKiPKpQxj/yUlWU0nIU0wCg8JTSPmTcuHEdvsbAgQM/8zW5rf0POOCAGDly0Vns3/zmN+PMM8/s8NoAAIVQ31gfw/caFiOvfqCg1501fXZUE0EWAEDxyfMAAHJ3oUZsf+BWceX/XlfQy86aPieqiTwPAApLKe1DhgwZUvQ12tra4uCDD47bbrst//GBBx4Yf/nLX4q+LgDAstjz6J3jlSdfjYnjJxf0+6BqI8gCACgueR4AwCJb7LFpvDDmpXj87qcLds1sWzaqjTwPAAqnpoDXoh2OOuqouOaaa/LP99xzz/jrX/8aNTX+NQAA5bdb2rfOOSwaujYU7JpdezQuepKNePM/b8VzD46PJ+5+Jp5/6MWY8sbUqOQgKycXZAEAkD7yPAAgDTI1mTjkZwdEv0F9C3bNxh5dFj9/981p+dJbLs977oHxMenFN/M5XyWS5wFAYdgprYS++93vxkUXXZR//vnPfz6uu+66qKvzrwAAKE89+nSPz39tm7j9grsLcr1BQ1aOB296NO6/fkxMeunNT3x+tQ0Hx7b7bhmb7LRB1HWurO+R3GEJAJBO8jwAIE1ymdp+3/1inH/iZQW53uD1V4mn7n0un+e9OPaVT3x+xVX7xTb7bhlbfnGz6NK9cDe3lgN5HgB0nFv6SuRnP/tZnH322fnnW221Vdxyyy1RX1+f9FgAAEuVC5UK8ZduDd0a4vqzbo2rfnnDEgtpOa89MyEuP+2a+PGeZ8RLj/0nKo07LAEA0kWeBwCk0dCt1ok+K61QkGuNvfOpuPD7Vy6xkJbz9uvvxPW/uy1O3f30eOiWsVFp5HkA0DFu6yuB8847L37+85/nn6+88srxm9/8Jl577bWlvmedddaJTp06lWhCAIAl675Ct9h45w1i7B1Pdug6LbNa2v3ame/Nij98++L4xulfjY12XD8qiTssAQDSQZ4HAKRV7pjx3GkEN533zw5dJ1NTE9OnTG/Xa+e3zI+//eL6mDF1Zux6+I5RSeR5ALD8lNJK4IYbblj8fPLkybH11lt/5ntyIdfgwYOLPBkAwGfb6aDt4sm7n43W1taSrbmwdWFc+qOr49t/OiLW3LiyvicSZAEAlD95HgCQZsP3Hhb//tv9+Zs/l1e2rW2Z33Pbn/8VPfp2j632GhaVRJ4HAMvH8Z0AACxV09oD4+Cf7V/ydXMluNxxn5GNimPrfwAAAACKpWuPxjjm7MOic0Pnkq993W9vjTkz5kalkecBwLJTSiuBUaNGRTabXaaHuyoBgHKy2Rc2isN+8T9RV9f+jXY71Xf86KK3J0yJx+95JiqRIAsAoHzJ8wCAtFt1aFMc/8dvRrdeXdv9nkwm0+F1c0d53n3lfVGJ5HkAsGyU0gAAaHcx7XuXH5v/tbau9lNfl7sDc+t9togBq61YkHUv+eHf4oLvXRHjH3k5sm2VtW2aIAsAAACAYlltw1XjB1ceH9vtv1U0NDZ86usyNTWx0Q4bxOe2X78g69512cj43RHnx2N3PR2tC1qjksjzAKD9MtncbXxUvEmTJsWgQYPyz0c+8HgMGLhS0iMBACk2871Z8dAtj8V/nn4t5rw/J6KmJrr17BJDtlg7ttxjk5g7uyV+/MUzCr5uv0F9Y5UhK8fc2fNiwbwF0di9IVYc3D9G7DUs+jb1ibRqbp2c/3Vwiv8ZAOADzZObY8Q6W+WfT5w4MZqampIeCVJLpgcAFMq8OfPi0TuejBfGvBSzps+OtoVt0di9S6y2/iqx1d7Dolf/nvG9HX8Wc2YW9ujN7it0i7U2XSMWtMyPljnzo6FL51hhYO/Y4oub5ndzSyt5HgCVpLlIeV77z18CAIAPhUlfOGz7iMg9Pqn5tSlFWfediVPzj496Pn/35dDh68SOX90m1t1yrUjjHZa5ICt3h6UgCwAAAIBCq2+sj2323TL/WJLcDaCFLqR9cHPrE3c//Ynfv++6h/KltO0OGBGb77ZxZGo6fnRoKcnzAOCzOb4TAICCm98yv+RrvjDmxfjDty+KW/54ZyqP+bT1PwAAAABJmd+yoORrvv7CpLjiZ3+Pi37wt3wpLm3keQCwdEppAAAUXJduDYmtnds17YZzbo80EmQBAAAAkISGrvWJrf3UyGfjLydfEQtbF0bayPMA4NMppQEAUHB9Vl4hamprE1t/5NUPxEO3jI00EmQBAAAAUGq1dbXRZ6UVElt/3MMvxY0pvtE095DnAcBHKaUBAFBwXXs0xkY7rpfoDHdefE+0tbVFGimmAQAAAFBqW+01LNH1H7jh4Zj53qxIK8U0APiouo99DAAABbHtvsPjibufSWz9d5unxQsPvhT1XTvHY3c+FdOmvB/z587PH0XQf5V+MfxLm8XA1VeMcg6xmlsn54OswU19kh4HAAAAgCoopf3zwn8ndoxmbt0Hbx4bG263boy59bF4Z+LUaJk9Lzp36Ry9+/eKYbtuFGtuvFpEJsq8mDZZngcASmkAABTLWpusHiuvNTAmv9yc2AyX/OiqmDd33hI+My7u+dv9+RBrh69sHRvtsH5ZhlmKaQAAAACUSo8+3WPTXT4Xj/7zicRmuOOif8dt59+5xM+NvunhGLj6gNhu/+Gx1d7D8keOlnMxLUemB0A1c3wnAADFkYn4xi+/Fo3duyQ2wpILaf/1ypOvxYXfvzKu+uUN0bawPI/6dJQnAAAAAKWy/0lfigGD+ye2fuuC1qV+vvnVt+KaX98Uf/j2JTF3ZkuUK5keACilAQBQRAMG94tjzz08uvXqGuXswZsfjSt+fm1ENsqSEAsAAACAUmjs0SWOO+/wRItp7fHSY6/EecddGPPmzo9yJdMDoNoppQEAUFSD1x8UJ1/yrVh3y7WjnI2948m46/JRUc4h1qKt/4VYAAAAABRP7wG94qSLvxXDdts4amrL84jMnNdfmBR/+8UNUc4U0wCoZkppAAAUXb9BffN3WP70+pNj2/23yp3sWZbuvmJUzG9ZEOVMMQ0AAACAUuyYduj/fiVOv/2HsefRX4jaurooR4/f9VS8NeGdKGeKaQBUK6U0AABKZsVV+8WBp+wVO35t2yhHc2bOjcfvejrKnWIaAAAAAKXQo0/32PXwHeNrP943ytXoGx6OcqeYBkA1UkoDAKDktt1/eNTWlefW//dfPybS4INimiALAAAAgGLbdOcNo0ffHlGOHv7HY2V/+kGOYhoA1UYpDQCAkuu78grxtR/vF+XojXGTYsG88g+xcgRZAAAAAJRCXee6OPLXB0WnzuV3jOfcWS3x5itvRRrI8wCoJkppAAAkYos9NokDvrd3ZCIT5Wb2jLmRFoIsAAAAAEphtQ1XjSN/+/Wo71If5Wb2jDmRFvI8AKqFUhoAAInZ7oDhcfQ5h8bANQZEOampKb+i3NIIsgAAAAAohaHD147vXnRMrLXpGlFOMhl5HgCUG6U0AAAStf6IIfHjq0+M7154TGy6y0bR0LVh8edq6+qiS7f/flwqjd27RNoIsgAAAAAohaa1B8Z3/nxk/OTv343t9t8quvfutvhzmZqaaOzRWPKZuvYs/ZodJc8DoNKV36HfAABUn0zEGhsNzj9yWhe0RrYtG53qO0XbwrZ49J9PxP3Xj4nXX5hU9FFW/9zgqOuczm+Tc0FWc+vkfJA1uKlP0uMAAAAAUMEGrL5iHHDKXvlHW1tbLJjXGvUNnfOfe+7B8XHftQ/FC2NeLPoc3Xp1jZXXLK+TGNpLngdAJbNTGgAAZaeuU12+kJZTU1sTW+65WZxy+bfjmLMPK/ra2+0/PNLMHZYAAAAAlFpNTU3Ud+mcv/k091h/6yFx7LnfiJ/d+L3FOV+xDP/SsNTeZJojzwOgUimlAQCQqqM+V15zYNGunztqYKMd1o+0E2QBAAAAUA76DeobG39+g6JdPxOZ2HrfLSLt5HkAVCKlNAAA0iMTsW0RdzLb7Zs7pfquyg8TZAEAAABQDrbdr3h53lZ7D4u+K60QlUCeB0ClUUoDACBVhu26UTR0bSj4dbfbf6vUH935cYIsAAAAAJK22vqrxKAhi3KqQlp7szXjgFP2ikoizwOgkiilAQCQKvWN9fHFo3Yu6DV3OXSH2P/kL+V3Yqs0giwAAAAAEpWJ2Pvbu0empnB/Nb3RDhvEt845NOo6VcapBx8mzwOgUiilAQCQOjt8ZevY/sARHbpGLgTLhVff+fNRsdexu0ampgIbaf+fIAsAAACAJA3ZfM34nx/s0+HrrLXJ6nH4GQfFN3/1tehU3ykqlTwPgEpQedVxAAAqXyZi/5O+FF17NMbtF97d7rcNGNw/Vttgleg3qF9sscfG0at/z6gWuSCruXVyPsga3NQn6XEAAAAAqDIj9tk86rvWx5U/uzZaF7S26z29V+wVa26yWqwwoFcM23XjGLj6ilEt5HkApJ1SGgAA6ZSJ2P3InWLD7YfG/deNibF3PhXzW+Z/4mWdGzrHsF03im33Hx5Na68U1UyQBQAAAECSNtvlc7H6BqvGAzc8HA/d8mjMmj57iSccfG679WKb/baMIcPWzOeA1UqeB0CaKaUBAJBquaLZV3+0b+xz/B7x5L3PxntvTouWOfOiobE+Vlipd2y84wbRpXtD0mOWDUEWAAAAAElaYWCv2Ou4XWOPI3eKZ+57Id56bUrMmdUSnerromef7rHRjutX1QkH7T/Kc7I8D4BUUUoDAKAi5IpnW+01LOkxUkExDQAAAICk1XWui0123jDpMVKV6SmmAZAmNUkPAAAAJHmH5btJjwIAAAAAtLuYJs8DIB2U0gAAoEoppgEAAABAOotpMj0Ayp1SGgAAVDHFNAAAAABIF5keAGmglAYAAFVOiAUAAAAA6SLTA6DcKaUBAABCLAAAAABIGZkeAOVMKQ0AAFgcYuUeQiwAAAAASAfFNADKlVIaAADwEYppAAAAAJAeimkAlCOlNAAA4BMU0wAAAAAgPRTTACg3SmkAAMBSi2mCLAAAAAAof4ppAJQTpTQAAOBTCbIAAAAAID3keQCUC6U0AABgqQRZAAAAAJAe8jwAyoFSGgAA8JkEWQAAAACQHvI8AJKmlAYAALSLIAsAAAAA0kOeB0CSlNIAAIB2E2QBAAAAQHrI8wBIilIaAACwTARZAAAAAJAe8jwAkqCUBgAALDNBFgAAAACkhzwPgFJTSgMAAJaLIAsAAAAA0kOeB0ApKaUBAADLTZAFAAAAAOkhzwOgVJTSAACADhFkAQAAAEB6yPMAKAWlNAAAoMMEWQAAAACQHvI8AIpNKQ0AACgIQRYAAAAApIc8D4BiUkoDAAAKRpAFAAAAAOnK83IPeR4AhaaUBgAAFJRiGgAAAACki2IaAIWmlAYAABScYhoAAAAApItiGgCFpJQGAAAUhWIaAAAAAKSzmCbTA6CjlNIAAICiUUwDAAAAgHSR6QFQCEppAABAUQmxAAAAACBdZHoAdJRSGgAAUHRCLAAAAABIF5keAB2hlAYAAJQsxMo9hFgAAAAAkA6KaQAsL6U0AACgpBTTAAAAACA9FNMAWB5KaQAAQMkppgEAAABAeiimAbCslNIAAIBEKKYBAAAAQHoopgGwLJTSAACAxItpgiwAAAAAKH+KaQC0l1IaAACQKEEWAAAAAKSHPA+A9lBKAwAAEifIAgAAAID0kOcB8FmU0gAAgLIgyAIAAACA9JDnAbA0SmkAAEDZEGQBAAAAQHrI8wD4NEppAABAWRFkAQAAAEB6yPMAWBKlNAAAoOwIsgAAAAAgPeR5AHycUhoAAFCWBFkAAAAAkB7yPAA+TCkNAAAoW4IsAAAAAEgPeR4AH1BKAwAAypogCwAAAADSQ54HQI5SGgAAUPYEWQAAAACQHvI8AJTSAACAVBBkAQAAAEB6yPMAqptSGgAAkBqCLAAAAABIV56Xe8jzAKqPUhoAAJAqimkAAAAAkC6KaQDVRykNAABIHcU0AAAAAEgXxTSA6qKUBgAApJJiGgAAAACks5gm0wOofEppAABAaimmAQAAAEC6yPQAqoNSGgAAkGpCLAAAAABIF5keQOVTSgMAAFJPiAUAAAAA6SLTA6hsSmkAAEDFhFi5hxALAAAAANJBMQ2gcimlAQAAFUUxDQAAAADSQzENoDIppQEAABVHMQ0AAAAA0kMxDaDyKKUBAAAVSTENAAAAANJDMQ2gsiilAQAAFV9ME2QBAAAAQPlTTAOoHEppAABARRNkAQAAAEB6yPMAKoNSGgAAUPEEWQAAAACQHvI8gPRTSgMAAKqCIAsAAAAA0kOeB5BuSmkAAEDVEGQBAAAAQHrI8wDSSykNAACoKoIsAAAAAEgPeR5AOimlAQAAVUeQBQAAAADpIc8DSB+lNAAAoCoJsgAAAAAgPeR5AOmilAYAAFQtQRYAAAAApIc8DyA9lNIAAICqJsgCAAAAgPSQ5wGkg1IaAABQ9QRZAAAAAJAe8jyA8qeUBgAAIMgCAAAAgFSR5wGUN6U0AACA/0+QBQAAAADpIc8DKF9KaQAAAB8iyAIAAACAdOV5uYc8D6C8KKUBAAB8jGIaAAAAAKSLYhpAeVFKAwAAWALFNAAAAABIF8U0gPKhlAYAAPApFNMAAAAAIJ3FNJkeQLKU0gAAAJZCMQ0AAAAA0kWmB5A8pTQAAIDPIMQCAAAAgHSR6QEkSykNAACgHYRYAAAAAJAuMj2A5CilAQAAtJMQCwAAAADSRaYHkAylNAAAgGUMsXIPIRYAAAAApINiGkDpKaUBAAAsB8U0AAAAAEgPxTSA0lJKAwAAWE6KaQAAAACQHoppAKWjlAYAAFCAYpogCwAAAADKn2IaQGkopQEAAHSQIAsAAAAA0kOeB1B8SmkAAAAFIMgCAAAAgPSQ5wEUl1IaAABAgQiyAAAAACA95HkAxaOUBgAAUECCLAAAAABID3keQHEopQEAABSYIAsAAAAA0kOeB1B4SmkAAABFIMgCAAAAgPSQ5wEUllIaAABAkQiyAAAAACA95HkAhaOUBgAAUESCLAAAAABID3keQGEopQEAABSZIAsAAAAA0kOeB9BxSmkAAAAlIMgCAAAAgPSQ5wF0jFIaAABAiQiyAAAAACA95HkAy08pDQAAoIQEWQAAAACQrjwv95DnASwbpTQAAIASU0wDAAAAgHRRTANYNkppAAAACVBMAwAAAIB0UUwDaD+lNAAAgIQopgEAAABAuiimAbSPUhoAAECCFNMAAAAAIJ3FNJkewKdTSgMAAEiYYhoAAAAApItMD2DplNIAAADKgBALAAAAANJFpgfw6ZTSAAAAyoQQCwAAAADSRaYHsGRKaQAAAGVEiAUAAAAA6SLTA/gkpTQAAIAyDLFyDyEWAAAAAKSDYhrARymlAQAAlCnFNAAAAABID8U0gP9SSkvYHXfcEZlMZvHjZz/7WdIjAQAAZUQxDQDKizwPAABYGsU0gEWU0hI0e/bsOOaYY5IeAwAASEkxTZAFAMmS5wEAAO2hmAaglJaon/zkJ/H6669H//79kx4FAAAoc4IsAEiePA8AAGgveR5Q7ZTSEvL444/HueeeG/X19XH66acnPQ4AAJACgiwASI48DwAAWFbyPKCaKaUlYOHChXHEEUfkfz311FNjzTXXTHokAAAgJQRZAFB68jwAAGB5yfOAaqWUloCzzz47nnzyyVh77bXj+9//ftLjAAAAKSPIAoDSkucBAAAdIc8DqpFSWolNmDAhTjvttPzz888/P7/dPwAAwLISZAFAacjzAACAQpDnAdWmLukBqs0xxxwTc+bMia997Wux4447Fuy6kyZNWurnm5ubC7YWAABQPkFWc+vkfJA1uKlP0uMAQEUqVp6XI9MDAIDqIs8DqolSWgldddVVceedd0avXr3id7/7XUGvPWjQoIJeDwAASAdBFgCkM8/LkekBAED1kecB1cLxnSXy3nvvxYknnph/fsYZZ0T//v2THgkAAKgQtv4HgMKT5wEAAMUizwOqgZ3SSuTkk0+OKVOmxBZbbBFHHnlkwa8/ceLEz9zqf/PNNy/4ugAAQHlwhyUApCvPy5HpAQBA9ZLnAZVOKe1DMplMh69x6aWXxqGHHvqR3xs1alT+92tra+PPf/5z1NQUfoO6pqamgl8TAABIF0EWANUmzXlejkwPAACqmzwPqGSO7yyyefPmxVFHHZV/fvzxx8dGG22U9EgAAEAFs/U/AHSMPA8AACh1npd7yPOASmOntA8ZN25ch68xcODAj3x84403xksvvRSdOnWKoUOHxjXXXPOJ97zwwguLnz/33HOLX5M7GmC11Vbr8EwAAEB1cYclANVCngcAAFSKRcW0yfI8oGIopX3IkCFDinJnZc6CBQviiCOO+MzX33DDDflHTu6IACEWAACwPBTTAKgG8jwAAKCSKKYBlcTxnQAAABXKUZ4AAAAAkC4fHOUp0wPSTimtyA499NDIZrNLfYwcOXLx60877bTFv597LwAAQEcopgHAspHnAQAASZPpAZVAKQ0AAKDCCbEAAAAAIF1kekDaKaUBAABUASEWAAAAAKS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            "text/plain": [
              "<Figure size 1500x500 with 2 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 472,
              "width": 1234
            }
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# number of training points\n",
        "N = 100\n",
        "\n",
        "# number of outlier points\n",
        "n_outliers = 5\n",
        "\n",
        "x_train, t = make_classification(\n",
        "    n_features=2, n_informative=2, n_redundant=0, n_classes=2, n_clusters_per_class=1, n_samples=N, random_state=12\n",
        ")\n",
        "\n",
        "x1, x2 = np.meshgrid(np.linspace(-5, 5, 100), np.linspace(-5, 5, 100))\n",
        "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
        "\n",
        "outliers = np.random.random_sample((n_outliers, 2)) + 3\n",
        "x_train_outliers = np.vstack((x_train, outliers))\n",
        "t_outliers = np.hstack((t, np.ones(n_outliers, dtype=int)))\n",
        "\n",
        "feature = LinearFeature()\n",
        "x_train_linear = feature.transform(x_train)\n",
        "x_train_linear_outliers = feature.transform(x_train_outliers)\n",
        "x_test_linear = feature.transform(x_test)\n",
        "\n",
        "model = LogisticRegression()\n",
        "model.fit_lms(x_train_linear, t, 0.01)\n",
        "predicted = model.predict(x_test_linear)\n",
        "\n",
        "plt.figure(figsize=(15, 5))\n",
        "\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
        "plt.contourf(x1, x2, predicted.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)\n",
        "plt.xlabel(\"$x_1$\", fontsize=12)\n",
        "plt.ylabel(\"$x_2$\", fontsize=12)\n",
        "plt.title(\"Original decision boundary\")\n",
        "\n",
        "model.fit_lms(x_train_linear_outliers, t_outliers, 0.01)\n",
        "predicted_outliers = model.predict(x_test_linear)\n",
        "\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.scatter(x_train_outliers[:, 0], x_train_outliers[:, 1], c=t_outliers)\n",
        "plt.contourf(x1, x2, predicted_outliers.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)\n",
        "plt.xlabel(\"$x_1$\", fontsize=12)\n",
        "plt.ylabel(\"$x_2$\", fontsize=12)\n",
        "plt.title(\"Outliers decision boundary\")\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "5f4b21e3",
      "metadata": {},
      "source": [
        "Note that logistic regression is robust to outliers in contrast to linear discriminants presented in section [4.1](#4.1-Discriminant-Functions)."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "9b1a37d8",
      "metadata": {},
      "source": [
        "### 4.3.3 Iterative reweighted least squares\n",
        "\n",
        "In linear regression models, the maximum likelihood solution, on the assumption of Gaussian noise model, leads to a closed-form solution. For logistic regression, there is no longer a closed-form solution, due to the nonlinearity of the logistic sigmoid function. However, the error function is still convex and can be minimized by an efficient iterative technique based on *Newton-Raphson* iterative optimization scheme. This algorithm uses a local quadratic approximation to the log-likelihood, and takes the form\n",
        "\n",
        "$$\n",
        "\\mathbf{w}^{new} = \\mathbf{w}^{old} - \\mathbf{H}^{-1}\\nabla E(\\mathbf{w})\n",
        "$$\n",
        "\n",
        "where $\\mathbf{H}$ is the Hessian matrix whose elements comprise the second derivatives of $E(\\mathbf{w})$ over $\\mathbf{w}$.\n",
        "\n",
        "Note that, if we apply the *Newton-Raphson* algorithm to the linear regression model, we derive the standard least squares solution (see $4.94$ and $4.95$).\n",
        "\n",
        "Applying the *Newton-Raphson* update to the cross-entropy error function for the logistic regression model, we obtain,\n",
        "\n",
        "$$\n",
        "\\nabla E(\\mathbf{w}) = \\sum_{n=1}^N(y_n-t_n)\\boldsymbol\\phi_n = \\boldsymbol\\Phi^T(\\mathsf{y}-\\mathsf{t})\n",
        "$$\n",
        "\n",
        "and\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "\\mathbf{H} &= \\nabla\\nabla E(\\mathbf{w}) \\\\\n",
        "&= \\nabla\\sum_{n=1}^N(y_n-t_n)\\boldsymbol\\phi_n \\\\\n",
        "&= \\nabla\\sum_{n=1}^N y_n\\boldsymbol\\phi_n \\\\\n",
        "&\\overset{(4.88)}{=} \\sum_{n=1}^N y_n(1-y_n)\\boldsymbol\\phi_n\\frac{d}{d\\mathbf{w}}\\mathbf{w}^T\\boldsymbol\\phi_n \\\\ \n",
        "&= \\sum_{n=1}^N y_n(1-y_n)\\boldsymbol\\phi_n\\boldsymbol\\phi_n^T \\\\\n",
        "&= \\mathbf{\\Phi}^T\\mathbf{R}\\mathbf{\\Phi}\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "where $\\mathbf{R}$ is a diagonal matrix whose elements are $R_{nn}=y_n(1-y_n)$. Then, the update formula becomes,\n",
        "\n",
        "$$\n",
        "\\mathbf{w}^{new} = \\mathbf{w}^{old} - (\\mathbf{\\Phi}^T\\mathbf{R}\\mathbf{\\Phi})^{-1}\\boldsymbol\\Phi^T(\\mathsf{y}-\\mathsf{t})\n",
        "$$\n",
        "\n",
        "Note that Hessian depends on $\\mathbf{w}$ through the weighting matrix $\\mathbf{R}$, corresponding to the fact that the error function is no longer quadratic. Thus, we must apply the update formula iteratively, each time using the new weight vector $\\mathbf{w}$ to compute the revised weighting matrix $\\mathbf{R}$. To that end, the algorithm is known as *iterative reweighted least squares* or *IRLS*.\n",
        "\n",
        "The elements of $\\mathbf{R}$ can be interpreted as variances, given by,\n",
        "\n",
        "$$\n",
        "\\mathbb{E}[t] = \\sum_{t\\in\\{0,1\\}} t p(t|\\mathbf{x}) = \\sigma(x)\n",
        "$$\n",
        "\n",
        "and\n",
        "\n",
        "$$\n",
        "\\text{var}[t] = \\mathbb{E}[t^2] - \\mathbb{E}[t]^2 \\overset{t^2 = t}{=} \\mathbb{E}[t] - \\mathbb{E}[t]^2 =\n",
        "\\sigma(x) - \\sigma(x)^2 = y(1-y)\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "id": "7b0d5774",
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1500x500 with 2 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 472,
              "width": 1234
            }
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# number of training points\n",
        "N = 100\n",
        "\n",
        "# number of outlier points\n",
        "n_outliers = 5\n",
        "\n",
        "x_train, t = make_classification(\n",
        "    n_features=2, n_informative=2, n_redundant=0, n_classes=2, n_clusters_per_class=1, n_samples=N, random_state=12\n",
        ")\n",
        "\n",
        "x1, x2 = np.meshgrid(np.linspace(-5, 5, 100), np.linspace(-5, 5, 100))\n",
        "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
        "\n",
        "outliers = np.random.random_sample((n_outliers, 2)) + 3\n",
        "x_train_outliers = np.vstack((x_train, outliers))\n",
        "t_outliers = np.hstack((t, np.ones(n_outliers, dtype=int)))\n",
        "\n",
        "feature = LinearFeature()\n",
        "x_train_linear = feature.transform(x_train)\n",
        "x_train_linear_outliers = feature.transform(x_train_outliers)\n",
        "x_test_linear = feature.transform(x_test)\n",
        "\n",
        "model = LogisticRegression()\n",
        "model.fit(x_train_linear, t)\n",
        "predicted = model.predict(x_test_linear)\n",
        "\n",
        "plt.figure(figsize=(15, 5))\n",
        "\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
        "plt.contourf(x1, x2, predicted.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)\n",
        "plt.xlabel(\"$x_1$\", fontsize=12)\n",
        "plt.ylabel(\"$x_2$\", fontsize=12)\n",
        "plt.title(\"Original decision boundary\")\n",
        "\n",
        "model.fit_lms(x_train_linear_outliers, t_outliers, 0.01)\n",
        "predicted_outliers = model.predict(x_test_linear)\n",
        "\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.scatter(x_train_outliers[:, 0], x_train_outliers[:, 1], c=t_outliers)\n",
        "plt.contourf(x1, x2, predicted_outliers.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)\n",
        "plt.xlabel(\"$x_1$\", fontsize=12)\n",
        "plt.ylabel(\"$x_2$\", fontsize=12)\n",
        "plt.title(\"Outliers decision boundary\")\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8cffab22",
      "metadata": {},
      "source": [
        "### [Gradient Descent vs Newton-Raphson](https://www.youtube.com/watch?v=iwO0JPt59YQ)\n",
        "\n",
        "Newton-Raphson method requires to compute the Hessian (through solving a set of linear equations) and thus, the computational cost for each iteration is higher than that of gradient descent. However, it usually converges faster than gradient descent in the sense that the number of iterations required is much smaller."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "85d7707d",
      "metadata": {},
      "source": [
        "### 4.3.4 Multiclass logistic regression\n",
        "\n",
        "We have seen that for $K>2$ classes, the posterior probabilities are given by a softmax transformation of linear functions of feature variables. Here, we consider the maximum likelihood to determine the parameters $\\mathbf{w}_k$ of the model directly. To that end, we need to calculate the derivatives of $y_k$ (see $4.104$) over the activation functions $\\alpha_j$ (see $4.68$ and $4.105$).\n",
        "\n",
        "In order to find the derivatives, we need to consider $k\\neq j$ and $k=j$.\n",
        "\n",
        "1. $k\\neq j$\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "\\frac{\\partial y_k}{\\partial\\alpha_k} \n",
        "&= \\frac{\\partial}{\\partial\\alpha_k} \\frac{\\exp(\\alpha_k)}{\\sum_j \\exp(\\alpha_j)} \\\\\n",
        "&= \\frac{-\\exp(\\alpha_k)\\exp(\\alpha_j)}{\\big(\\sum_j \\exp(\\alpha_j)\\big)^2} \\\\\n",
        "&= -\\frac{\\exp(\\alpha_k)}{\\sum_j \\exp(\\alpha_j)}\\frac{\\exp(\\alpha_j)}{\\sum_j \\exp(\\alpha_j)} \\\\\n",
        "&\\overset{4.104}{=} -y_k y_j\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "2. $k=j$\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "\\frac{\\partial y_k}{\\partial\\alpha_k} \n",
        "&= \\frac{\\partial}{\\partial\\alpha_k} \\frac{\\exp(\\alpha_k)}{\\sum_j \\exp(\\alpha_j)} \\\\\n",
        "&= \\frac{\\exp(\\alpha_k)\\sum_j \\exp(\\alpha_j) - \\exp(\\alpha_k)^2}{\\big(\\sum_j \\exp(\\alpha_j)\\big)^2} \\\\\n",
        "&= \\frac{\\exp(\\alpha_k)\\sum_j \\exp(\\alpha_j)}{\\big(\\sum_j \\exp(\\alpha_j)\\big)^2} - \\frac{\\exp(\\alpha_k)^2}{\\big(\\sum_j \\exp(\\alpha_j)\\big)^2}\\\\\n",
        "&= \\frac{\\exp(\\alpha_k)}{\\sum_j \\exp(\\alpha_j)} - \\bigg(\\frac{\\exp(\\alpha_k)}{\\sum_j \\exp(\\alpha_j)}\\bigg)^2\\\\\n",
        "&=  y_k - y_k^2 \\\\\n",
        "&= y_k(1-y_k)\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "where we have used the quotient rule $\\big(\\frac{f}{g}\\big)'=\\frac{f'g-fg'}{g^2}$.\n",
        "\n",
        "\n",
        "Combining $(1)$ and $(2)$, we obtain,\n",
        "\n",
        "$$\n",
        "\\frac{\\partial y_k}{\\partial\\alpha_k} = y_k(I_{kj}-y_j)\n",
        "$$\n",
        "\n",
        "where $I_{kj}$ are the elements of the identity matrix.\n",
        "\n",
        "Assuming a $1$-of-$K$ coding scheme in which the target vector $\\mathbf{t}_k$ is a binary vector having all elements zero except for element $k$, which equals to one, then ,the likelihood function is then given by,\n",
        "\n",
        "$$\n",
        "p(\\mathbf{T}|\\mathbf{w}_1,\\dots,\\mathbf{w}_k) = \n",
        "\\prod_{n=1}^N \\prod_{k=1}^K p(\\mathbf{C}_k|\\boldsymbol\\phi_n)^{t_{nk}} =\n",
        "\\prod_{n=1}^N \\prod_{k=1}^K y_k(\\boldsymbol\\phi_n)^{t_{nk}}\n",
        "$$\n",
        "\n",
        "where $\\mathbf{T}$ is a $N\\times K$ matrix of target variables with elements $t_{nk}$. Taking the negative logarithm the gives,\n",
        "\n",
        "$$\n",
        "E(\\mathbf{w}_1,\\dots,\\mathbf{w}_k) = -\\ln p(\\mathbf{T}|\\mathbf{w}_1,\\dots,\\mathbf{w}_k) = \n",
        "-\\sum_{n=1}^N \\sum_{k=1}^K t_{nk}\\ln y_k(\\boldsymbol\\phi_n)\n",
        "$$\n",
        "\n",
        "which is the *cross-entropy* error function for the multiclass problem.\n",
        "\n",
        "Taking the gradient of the error function over the parameter vector $\\mathbf{w}_j$, we obtain\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "\\nabla_{\\mathbf{w}_j} E(\\mathbf{w}_1,\\dots,\\mathbf{w}_K) \n",
        "&= - \\nabla_{\\mathbf{w}_j} \\sum_{n=1}^N \\sum_{k=1}^K t_{nk}\\ln y_k(\\boldsymbol\\phi_n) \\\\\n",
        "&= - \\sum_{n=1}^N \\sum_{k=1}^K t_{nk}\\frac{1}{y_{nk}}y_{nk}(I_{kj}-y_{nj})\\boldsymbol\\phi_n \\\\\n",
        "&= - \\sum_{n=1}^N \\sum_{k=1}^K t_{nk}(I_{kj}-y_{nj})\\boldsymbol\\phi_n \\\\\n",
        "&= \\sum_{n=1}^N \\sum_{k=1}^K t_{nk}y_{nj}\\boldsymbol\\phi_n - \\sum_{n=1}^N \\sum_{k=1}^K t_{nk}I_{kj}\\boldsymbol\\phi_n \\\\\n",
        "&= \\sum_{n=1}^N \\sum_{k=1}^K t_{nk}y_{nj}\\boldsymbol\\phi_n - \\sum_{n=1}^N t_{nj}\\boldsymbol\\phi_n \\\\\n",
        "&\\overset{\\sum_k t_{nk}=1}{=} \\sum_{n=1}^N y_{nj}\\boldsymbol\\phi_n - \\sum_{n=1}^N t_{nj}\\boldsymbol\\phi_n \\\\\n",
        "&= \\sum_{n=1}^N (y_{nj} - t_{nj})\\boldsymbol\\phi_n\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "The Newton-Raphson update formula, requires the evaluation of the Hessian matrix, given by\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "\\nabla_{\\mathbf{w}_k} \\nabla_{\\mathbf{w}_j} E(\\mathbf{w}_1,\\dots,\\mathbf{w}_K) \n",
        "&= - \\nabla_{\\mathbf{w}_k} \\nabla_{\\mathbf{w}_j} \\ln p(\\mathbf{T}|\\mathbf{w}_1,\\dots,\\mathbf{w}_k) \\\\\n",
        "&= - \\nabla_{\\mathbf{w}_k} \\sum_{n=1}^N (y_{nj} - t_{nj})\\boldsymbol\\phi_n \\\\\n",
        "&= - \\nabla_{\\mathbf{w}_k} \\sum_{n=1}^N y_{nj}\\boldsymbol\\phi_n \\\\\n",
        "&= \\sum_{n=1}^N \\frac{\\partial}{\\partial\\mathbf{w}_k}y_{nj}\\boldsymbol\\phi_n \\\\\n",
        "&= \\sum_{n=1}^N y_{nk}(I_{kj}-y_{nj})\\boldsymbol\\phi_n\\boldsymbol\\phi_n^T \\\\\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "Below we present a softmax regression example trained using gradient descent."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "id": "ba3b77ec",
      "metadata": {},
      "outputs": [
        {
          "data": {
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            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 435,
              "width": 568
            }
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# number of training points\n",
        "N = 100\n",
        "\n",
        "x_train, t = make_classification(\n",
        "    n_features=2, n_informative=2, n_redundant=0, n_classes=3, n_clusters_per_class=1, n_samples=N, random_state=21\n",
        ")\n",
        "\n",
        "x1, x2 = np.meshgrid(np.linspace(-5, 5, 100), np.linspace(-5, 5, 100))\n",
        "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
        "\n",
        "model = SoftmaxRegression()\n",
        "model.fit(x_train, t)\n",
        "predicted = model.predict(x_test)\n",
        "\n",
        "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
        "plt.contourf(x1, x2, predicted.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 2, 4))\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)\n",
        "plt.xlabel(\"$x_1$\", fontsize=12)\n",
        "plt.ylabel(\"$x_2$\", fontsize=12)\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "e6676eb8",
      "metadata": {},
      "source": [
        "## 4.4 Laplace Approximation\n",
        "\n",
        "In contrast to the [Bayesian treatment of linear regression](ch3_linear_models_for_regression.ipynb#3.3-Bayesian-Linear-Regression), in the Bayesian treatment of logistic regression, we cannot integrate exactly over the parameter vector $\\mathbf{w}$ since the posterior distribution is no longer Gaussian. To that end, we may use a widely used framework called the Laplace approximation, that aims to find a Gaussian approximation to a probability density defined over a set of continuous variables. Consider a single continuous variable $z$, having a distribution $p(z)$ defined by\n",
        "\n",
        "$$\n",
        "p(z) = \\frac{1}{Z}f(z)\n",
        "$$\n",
        "\n",
        "where $Z=\\int f(z)\\text{d}z$ is the normalization coefficient. The goal is to find a Gaussian approximation $q(z)$ centered on a mode of the distribution $p(z)$. The first step is to find a mode of $p(z)$, that is, a point $z_0$ such that $p'(z_0)=0$ or equivalently\n",
        "\n",
        "$$\n",
        "\\frac{df(z)}{dz}\\bigg|_{z=z_0} = 0\n",
        "$$\n",
        "\n",
        "Then, we use a second-order Taylor expansion to approximate $g(z) = \\ln f(z)$ (because the logarithm of any Gaussian distribution is a quadratic function of the variables), centered on the mode $z_0$ so that,\n",
        "\n",
        "$$\n",
        "g(z) = \\ln f(z) \\approx \\sum_{n=0}^{2} \\frac{g^{(n)}(z_0)}{n!}(z-z_0)^n = g(z_0) - \\frac{1}{2}g''(z_0)(z-z_0)^2\n",
        "$$\n",
        "\n",
        "Note that the first-order term is omitted since $z_0$ is a local maximum of the distribution and thus the derivative is zero. Then, taking the exponential on both sides of the expansion, we obtain\n",
        "\n",
        "$$\n",
        "f(z) \\approx f(z_0)\\exp\\Big\\{ -\\frac{A}{2}(z-z_0)^2 \\Big\\}\n",
        "$$\n",
        "\n",
        "where $A=-\\frac{d^2f(z)}{d^2z}$ on $z_0$. Therefore, using the standard result for the normalization of a Gaussian, the final normalized distribution $q(z)$ has the form,\n",
        "\n",
        "$$\n",
        "q(z) = \\Big(\\frac{A}{2\\pi}\\Big)^{1/2} \\exp\\Big\\{ -\\frac{A}{2}(z-z_0)^2 \\Big\\} = \\mathcal{N}(z|z_0,A)\n",
        "$$\n",
        "\n",
        "Note that the Gaussian approximation is well defined only when its precision $A>0$, which implies that $z_0$ must be a local maximum, not a minimum! In practice a mode may be found by running some form of numerical optimization. The Laplace approximation is depicted in the next Figure,\n",
        "\n",
        "<img src=\"../images/fg4_14a.png\" width=\"400\"/>\n",
        "\n",
        "The same approximation can be applied to an $M$-dimentional space $\\mathbf{z}$.\n",
        "\n",
        "## 4.5 Bayesian Logistic Regression\n",
        "\n",
        "Exact Bayesian inference for logistic regression, as well as, the evaluation of the predictive distribution are intractable. Thus, here, we consider the application of Laplace approximation for the problem of Bayesian logistic regression.\n",
        "\n",
        "### 4.5.1 Laplace approximation\n",
        "\n",
        "Similar to the Bayesian linear regression, we seek a Gaussian representation for the posterior distribution of the parameters, thus, we use a Gaussian (conjugate) prior in the general form,\n",
        "\n",
        "$$\n",
        "p(\\mathbf{w}) = \\mathcal{N}(\\mathbf{w}|\\mathbf{m}_0,\\mathbf{S}_0)\n",
        "$$\n",
        "\n",
        "where $\\mathbf{m}_0,\\mathbf{S}_0$ are fixed hyperparameters. Then, the posterior over $\\mathbf{w}$ is given by\n",
        "\n",
        "$$\n",
        "p(\\mathbf{w}|\\mathsf{t}) \\propto p(\\mathsf{t}|\\mathbf{w})p(\\mathbf{w})\n",
        "$$\n",
        "\n",
        "Taking the natural logarithm on both sides, and substituting for the prior and the likelihood, we obtain\n",
        "\n",
        "$$\n",
        "\\ln p(\\mathbf{w}|\\mathsf{t}) = \\ln\\Big(\\prod_{n=1}^N y_n^{t_n}\\{1-y_n\\}^{1-t_n}\\Big)\\ln \\mathcal{N}(\\mathbf{w}|\\mathbf{m}_0,\\mathbf{S}_0) = \\sum_{n=1}^N\\{t_n\\ln y_n + (1-t_n)\\ln(1-y_n)\\} + \\frac{1}{(2\\pi)^{D/2}|\\mathbf{S}_0|^{1/2}} -\\frac{1}{2}(\\mathbf{w}-\\mathbf{m}_0)^T\\mathbf{S}_0^{-1}(\\mathbf{w}-\\mathbf{m}_0)\n",
        "$$\n",
        "\n",
        "Then, to obtain the Gaussian approximation of the posterior, first, we maximize the posterior to give the MAP solution $\\mathbf{w}_{MAP}$, which corresponds to the mean of the approximated Gaussian. The covariance matrix is then given by the Hessian matrix of the negative log-likelihood,\n",
        "\n",
        "$$\n",
        "\\mathbf{S}_N^{-1} = -\\nabla\\nabla\\ln p(\\mathbf{w}|\\mathsf{t}) = \\mathbf{S}_0^{-1} + \\sum_{n=1}^N y_n(1-y_n)\\boldsymbol\\phi_n\\boldsymbol\\phi_n^T\n",
        "$$\n",
        "\n",
        "where we make use of $(4.97)$. Thus, the Gaussian approximation of the posterior takes the form,\n",
        "\n",
        "$$\n",
        "q(\\mathbf{w}) = \\mathcal{N}(\\mathbf{w}|\\mathbf{w}_{MAP},\\mathbf{S}_N)\n",
        "$$\n",
        "\n",
        "### 4.5.2 Predictive distribution\n",
        "\n",
        "The predictive distribution for class $\\mathcal{C}_1$, given a new feature vector $\\boldsymbol\\phi_{unseen}$, is obtained by marginalizing over the posterior distribution $p(\\mathbf{w}|\\mathsf{t})$, which is approximated by $q(\\mathbf{w})$, so that,\n",
        "\n",
        "$$\n",
        "p(\\mathcal{C}_1|\\boldsymbol\\phi_{unseen},\\mathsf{t},\\boldsymbol\\Phi) = \\int p(\\mathcal{C}_1|\\boldsymbol\\phi_{unseen},\\mathbf{w})p(\\mathbf{w}|\\mathsf{t},\\boldsymbol\\Phi)\\text{d}\\mathbf{w} \\approx \\int \\sigma(\\mathbf{w}^T\\boldsymbol\\phi)q(\\mathbf{w})\\text{d}\\mathbf{w}\n",
        "$$\n",
        "\n",
        "The evalution of the above integral is fairly complex and involves a significant number of steps. For more details see the corresponding section in the book. The final approximate predictive distribution has the form,\n",
        "\n",
        "$$\n",
        "p(\\mathcal{C}_1|\\boldsymbol\\phi_{unseen},\\mathsf{t}) = \\sigma\\big(\\kappa(\\sigma_{\\alpha}^2)\\mu_{\\alpha}\\big)\n",
        "$$\n",
        "\n",
        "where $\\kappa(\\sigma_{\\alpha}^2) = (1+ \\pi\\sigma_{\\alpha}^2/8)^{-1/2}$, $\\mu_a = \\mathbf{w}_{MAP}^T\\boldsymbol\\phi_{unseen}$, and $\\sigma_{\\alpha} = \\boldsymbol\\phi_{unseen}^T\\mathbf{S}_N\\boldsymbol\\phi_{unseen}$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "id": "14be25ca",
      "metadata": {},
      "outputs": [
        {
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",
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 418,
              "width": 531
            }
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# number of training points\n",
        "N = 100\n",
        "\n",
        "x_train, t = make_classification(\n",
        "    n_features=2, n_informative=2, n_redundant=0, n_classes=2, n_clusters_per_class=1, n_samples=N, random_state=21\n",
        ")\n",
        "\n",
        "x1, x2 = np.meshgrid(np.linspace(-5, 5, N), np.linspace(-5, 5, N))\n",
        "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
        "\n",
        "model = BayesianLogisticRegression()\n",
        "model.fit(x_train, t)\n",
        "predicted = model.predict(x_test)\n",
        "\n",
        "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
        "plt.contourf(x1, x2, predicted.reshape(N, N), alpha=0.2, levels=np.linspace(0, 1, 5))\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)\n",
        "plt.colorbar()\n",
        "plt.show()"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": ".venv",
      "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": "3.10.16"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}