{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "**Chapter 8 – Dimensionality Reduction**\n", "\n", "_This notebook contains all the sample code and solutions to the exercises in chapter 8._" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", " \n", "
 \n", " Run in Google Colab\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Setup" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, let's import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures. We also check that Python 3.5 or later is installed (although Python 2.x may work, it is deprecated so we strongly recommend you use Python 3 instead), as well as Scikit-Learn ≥0.20." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Python ≥3.5 is required\n", "import sys\n", "assert sys.version_info >= (3, 5)\n", "\n", "# Scikit-Learn ≥0.20 is required\n", "import sklearn\n", "assert sklearn.__version__ >= \"0.20\"\n", "\n", "# Common imports\n", "import numpy as np\n", "import os\n", "\n", "# to make this notebook's output stable across runs\n", "np.random.seed(42)\n", "\n", "# To plot pretty figures\n", "%matplotlib inline\n", "import matplotlib as mpl\n", "import matplotlib.pyplot as plt\n", "mpl.rc('axes', labelsize=14)\n", "mpl.rc('xtick', labelsize=12)\n", "mpl.rc('ytick', labelsize=12)\n", "\n", "# Where to save the figures\n", "PROJECT_ROOT_DIR = \".\"\n", "CHAPTER_ID = \"dim_reduction\"\n", "IMAGES_PATH = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID)\n", "os.makedirs(IMAGES_PATH, exist_ok=True)\n", "\n", "def save_fig(fig_id, tight_layout=True, fig_extension=\"png\", resolution=300):\n", " path = os.path.join(IMAGES_PATH, fig_id + \".\" + fig_extension)\n", " print(\"Saving figure\", fig_id)\n", " if tight_layout:\n", " plt.tight_layout()\n", " plt.savefig(path, format=fig_extension, dpi=resolution)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Projection methods\n", "Build 3D dataset:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "np.random.seed(4)\n", "m = 60\n", "w1, w2 = 0.1, 0.3\n", "noise = 0.1\n", "\n", "angles = np.random.rand(m) * 3 * np.pi / 2 - 0.5\n", "X = np.empty((m, 3))\n", "X[:, 0] = np.cos(angles) + np.sin(angles)/2 + noise * np.random.randn(m) / 2\n", "X[:, 1] = np.sin(angles) * 0.7 + noise * np.random.randn(m) / 2\n", "X[:, 2] = X[:, 0] * w1 + X[:, 1] * w2 + noise * np.random.randn(m)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## PCA using SVD decomposition" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "X_centered = X - X.mean(axis=0)\n", "U, s, Vt = np.linalg.svd(X_centered)\n", "c1 = Vt.T[:, 0]\n", "c2 = Vt.T[:, 1]" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "m, n = X.shape\n", "\n", "S = np.zeros(X_centered.shape)\n", "S[:n, :n] = np.diag(s)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.allclose(X_centered, U.dot(S).dot(Vt))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "W2 = Vt.T[:, :2]\n", "X2D = X_centered.dot(W2)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "X2D_using_svd = X2D" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## PCA using Scikit-Learn" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With Scikit-Learn, PCA is really trivial. It even takes care of mean centering for you:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "from sklearn.decomposition import PCA\n", "\n", "pca = PCA(n_components=2)\n", "X2D = pca.fit_transform(X)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 1.26203346, 0.42067648],\n", " [-0.08001485, -0.35272239],\n", " [ 1.17545763, 0.36085729],\n", " [ 0.89305601, -0.30862856],\n", " [ 0.73016287, -0.25404049]])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X2D[:5]" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[-1.26203346, -0.42067648],\n", " [ 0.08001485, 0.35272239],\n", " [-1.17545763, -0.36085729],\n", " [-0.89305601, 0.30862856],\n", " [-0.73016287, 0.25404049]])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X2D_using_svd[:5]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that running PCA multiple times on slightly different datasets may result in different results. In general the only difference is that some axes may be flipped. In this example, PCA using Scikit-Learn gives the same projection as the one given by the SVD approach, except both axes are flipped:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.allclose(X2D, -X2D_using_svd)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recover the 3D points projected on the plane (PCA 2D subspace)." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "X3D_inv = pca.inverse_transform(X2D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course, there was some loss of information during the projection step, so the recovered 3D points are not exactly equal to the original 3D points:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.allclose(X3D_inv, X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can compute the reconstruction error:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.01017033779284855" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(np.sum(np.square(X3D_inv - X), axis=1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The inverse transform in the SVD approach looks like this:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "X3D_inv_using_svd = X2D_using_svd.dot(Vt[:2, :])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The reconstructions from both methods are not identical because Scikit-Learn's PCA class automatically takes care of reversing the mean centering, but if we subtract the mean, we get the same reconstruction:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.allclose(X3D_inv_using_svd, X3D_inv - pca.mean_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The PCA object gives access to the principal components that it computed:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[-0.93636116, -0.29854881, -0.18465208],\n", " [ 0.34027485, -0.90119108, -0.2684542 ]])" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pca.components_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare to the first two principal components computed using the SVD method:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0.93636116, 0.29854881, 0.18465208],\n", " [-0.34027485, 0.90119108, 0.2684542 ]])" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Vt[:2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice how the axes are flipped." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's look at the explained variance ratio:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.84248607, 0.14631839])" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pca.explained_variance_ratio_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first dimension explains 84.2% of the variance, while the second explains 14.6%." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By projecting down to 2D, we lost about 1.1% of the variance:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.011195535570688975" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "1 - pca.explained_variance_ratio_.sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is how to compute the explained variance ratio using the SVD approach (recall that s is the diagonal of the matrix S):" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.84248607, 0.14631839, 0.01119554])" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.square(s) / np.square(s).sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, let's generate some nice figures! :)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Utility class to draw 3D arrows (copied from http://stackoverflow.com/questions/11140163)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "from matplotlib.patches import FancyArrowPatch\n", "from mpl_toolkits.mplot3d import proj3d\n", "\n", "class Arrow3D(FancyArrowPatch):\n", " def __init__(self, xs, ys, zs, *args, **kwargs):\n", " FancyArrowPatch.__init__(self, (0,0), (0,0), *args, **kwargs)\n", " self._verts3d = xs, ys, zs\n", "\n", " def draw(self, renderer):\n", " xs3d, ys3d, zs3d = self._verts3d\n", " xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n", " self.set_positions((xs[0],ys[0]),(xs[1],ys[1]))\n", " FancyArrowPatch.draw(self, renderer)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Express the plane as a function of x and y." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "axes = [-1.8, 1.8, -1.3, 1.3, -1.0, 1.0]\n", "\n", "x1s = np.linspace(axes[0], axes[1], 10)\n", "x2s = np.linspace(axes[2], axes[3], 10)\n", "x1, x2 = np.meshgrid(x1s, x2s)\n", "\n", "C = pca.components_\n", "R = C.T.dot(C)\n", "z = (R[0, 2] * x1 + R[1, 2] * x2) / (1 - R[2, 2])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the 3D dataset, the plane and the projections on that plane." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Saving figure dataset_3d_plot\n" ] }, { "data": { "image/png": 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VFWlpaZNvQEEsLDelQPX19dHc3ExVVdWk5VzhitvIyAiDg4NhH5OU12exWCbsR6vV+gie0vKbjfw1/1QH/xbgUlfcrKwskpKS5uz81rlyTG63ezqFfx9QA/zl0O81QP9cWpLCESxu/stQk8nE8PBw0KXfZMTKcpMmYo2Pj7N+/fqwhCIccZOaIE71+CTcbjcWi0UWPiVardZH8CTLT0qAngmULcCVwYmWlhasVispKSnY7fY5VzkxV8RNCuBEgiAIOryaoAW0giAkAC5RFP0/+CeAbYIgPAX0ArcB26Z80DHmiBQ3ZYrH2NgY9fX1aDQaqquro96mRqMJurwL9/V2u52PP/6YvLy8iJbE4TSrbG1tjVp8Iw1YuN1urFar7NeThLGlpYWkpCQf4fO3/qaDYMGJgwcP0t7eTmtrq0+nk9msnJgrS2WpU3CE3Ab8WPH71cBPBUF4DKgHVoii2CGK4quCIPwK+CeH89x+PGFrs8wRJW7+JVQdHR309fVRU1PDnj17prTtqS5LTSYTfX19rF69OmJrYrJIq+Rni4apWhH+wujxeBgfH2d8fHzCczUaDfHx8bKlJy1zpcdiZdFIwQmpK25ycrIcnJCKziV/XbjBiVhxJIubKIo/AX4S5M8+ZqAoir8BfhPNsc0UR4y4+ZdQSW2B1q9fH5MvU7Ti5vF4aGpqwmAwUFxcHPOJ86OjowwMDES8TSVTaaIZCVJto81mY2xszOc9FQRhQkRX+Xs0wictAYMFJ6TSJOXMCWk+6XQxV8TNbDZH3eFmvjDnxc2/hErKk1J2p40F0YibzWZj7969ZGdns2jRInkZFynBlo1OpzOmfrZomEpag38DTmVvMiWS8AVKZwklfMH8W8GCE11dXZhMJhITE+Xifyk4ESvmirhFuSydV8xpcRNFUU5YFUWRlpYWRkZGOPbYY2OS4a4kUiEYHh7mwIED8oyFgYGBmHXihcN+tmid+DNZKzvV1yuFz2QyTXi9UviUPj632x2WMAUKTkj1sFarldTUVNmyC7etfDBUcZs7zFlxU/Zds9ls1NbWkpOTw9q1a6dlWRFuVxBpEpXBYPAR2am2Gfenp6cHs9kc1fak44yW2RZG//dSmjPg/340NTXJlQ7Kpa7k7wskMsrghDTFyr/9t7JJZKTBibkkbv6VMEcbc07clEEDQRAYHBykqamJFStWTOrPmkoYPpwLUppElZaWNqFONZbF72NjY/T39094XBRFBgcHcTgcZGRkyOPj/JmquEzlPKZaJxvJ5ye5LMxms4/wScfgX72hFD4pyCAIAmlpafKsA7fbzdjYGAaDgY6ODgCfVkKTBSek+QmzjWq5zTFxU+aueTweeXpTOPliUuF7NDluMLkgBJpEFcnrw8XpdNLW1jZhgK/b7aa5uRmApKQkent7sVqtJCcnyxdnXFzcrFtdMPXyo0he7y+GyuMPt3rD38enDE74902bLDgxlyy3aGaBzCfmjLhJQQNpNF1dXR3FxcUsX748rLv5dF3U4U6iilVnj7a2NtnPJm3PZrPR0NBAQUEBOTk5uFyuCTNLW1pacLvd8sSlaPqpzbYwRvp6//c7ktf7V29ISNFX/7K1oqIiysvL8Xg8crNOk8lEUlKSLHaJiYlzStyKi4tn+zBmlVkXN//ctZ6eHjo6OgJ2zwjFdLQscjqd1NbWkpiYOOkkqlhYPL29vbJDXULK3Vq8eDEpKSnyPqQLOyEhgcLCQgoLC2X/0djYGD09PWi1WtLT00lNTSUxMTHkTWKq/eymq/FAKPzdEFO9uUjn4J/E7P8cvV5PYmIi6enpcqXHwMAALpcLnU5HfHw8drt9ysGJqRBNhcJ8Y1bFTcpZ+/jjj6mpqaG+vh6dThdVCVWsrYZIJ1FN1edmtVrp7e2VfxdFUbYOVqxYMemyXDp+aYkKXnEeHR2lr68Pq9VKUlISGRkZpKWlydUEsVhKS8c70yitpJmyGoMlMQuCgF6vZ2BgAKfTSXd3NxqNhuzsbLnHXbQuk2iQStSOZmZF3Pxz18bHx/nvf/9LeXl51MMsYmG5SSknHR0d9Pb2RjSJaiqWj8vlore3V+4553K5aGxsJCkpKaxlebALMy4uTs73klIgRkdHaW5u9lnCpqWlycsxCVEUwxas2VzOSr7J2fYTSucgiiI6nY7c3Fx5EHN3dzcmk4n4+Hiys7PJy8sjNzdXDm7EsnpDQg0ozIK4KXPXANrb27Hb7axdu3ZKI+1icYG53W727NlDXFwc69atiyjqNRXLra2tTX4/rFYrTU1NlJSUTNpgE8L39SlTIAoLC+ULT7r4tFotaWlppKen+yxhlf8rgxzSPmdjOSoRK2sxlh1hPB6P/L3RaDQ+lrTL5cJkMtHY2Mju3bt93vPMzEyfaO5UqzfUCoUZFjdl7po0WT01NVW+6KbCVC03s9mMxWKhvLycoqKiiF8f7UXa19fH2NgYAIODg/T29lJRURHR+xHNRa6cRC/dcPyXsNKFFxcXJ1tyyn1Jgi5ZfNLfZnKJOlV3QCysPsBH3IK5EJQ96uCw26C/v5/W1lb0er0shpKoCYIgp7QEKlsL5gdW89xmSNz8238bDAYOHjzI0qVLycnJYXh4eMqtYqYibl1dXXR2dsrzOqMhmru/2Wymt7dXnvVgNBpZuXJl2BZjLCK00uuDLWGVUVi32+3j5wokeMpjU/7v8XgmHG+se+jNBv7nEMn3WHrP8/LycLvd2Gw2TCYTnZ2dOBwO+QaTlpaGw+GYEGyCw9UbZWVlPl1ZVJ/bDIibf9+1xsZGTCYTa9eulaNJ0hdkKsmP0Vwobreb+vp6RFFk3bp1fPTRR1PafyQXmsvlorW1FbvdTmNjI4IgsGTJkpi1SZqMUO9XsCXs0NAQBw4ckGdkhorCBrLipJ+Vz/cXynCJhbBNh7hGmgoiWY6CIMgDsfPy8hBFEavVytjYmHyDSUlJkdN8pGvF4XCQkpIyod2UGi2dZnFTLkPHx8epq6sjNzeXY4891ucLLlldUxG3SC23YJOooiXS5U17ezvDw8O0traycOFC2tvbZ6zJYaQXtUajkUucVqxYIXfdCLaEDRf/Y/C39oI9LxbEKuk6UE1wLPLcBEEgOTmZ5ORk+QZjNpsZGxuTo+ppaWlkZWUFDMK5XK5Z7Ws3F5gWcfMvoerv76elpYWVK1fKA32VTNVfBpF9WUNNopqJ/ff19XHgwAGGh4dZvny5fNcNd0kzVatlqhZPOEvYyRKJAx1DKJ9dMOGLhum0+iKx3CL5zgQLTsTFxbF7927i4+MntGE/2om5uPmXUB04cACXyxWyhCoW4qbVaiftpBvOJKpoCffLNDo6ynvvvYdGo2HlypUTklDDSfuQbhrREOu0jWBL2LGxsYBR2HAbFPijXNJOZvGFE9iYriBEuOI21UCGTqejvLyc8vJywFvFYjQaqaur48Ybb8Tj8fDQQw9xxhlnsHjx4km/LwaDgezs7BeAs4Ah4AeiKD4d4LivAf4IKBP9LhBF8e2oT2aaiLm4SW+i2Wymrq5OXvaFenNnwnKzWq3s3buXwsJCSktLI+4RFgtMJhM7d+6Uc50kpBwzZa5ZIB+UJGzRMhNpG9ISVqprVEZhx8fHSUxMjGoJKzFVi2+6AxCS/2y60el0Pu4UZaXKrl27OOmkk3A6ndx666386le/orKyMuT2tmzZAuAA8oHVwMuCIOwRDw1e9uPfoiieHLOTmSamxXLr7Oykq6uL6urqsJyaWq12ysNHQglkf38/TU1Nk06ikpYr0/HlHBgY4J133mHBggUT3hNlGoH/vqV0AGVeWTTHOFVLIdqlnHIJC96bTKRLWIloxFkpfP4CF43FN9kxhGO5xcLfV1RUFPTm4PF4SExM5KabbuKmm26adFsWi4UdO3YA3C6Kohl4XxCEl4AvMsemyEfCtPjcBEFg/fr1YQcIdDpdTJal/tuQOotYrdawO4vEuvBZFEWamppoa2ujtLQ06DEEEw/JglNO11Im0/ova2c7NSIY0vFHsoRVnlus89GUP09m8Sn/PtkxTHbjicV5pKWlkZ2dHfTvkVYnNDQ0oNVqcTgcDYqH9wCnBnnJGkEQhgAD8CRwpzhxQtasMy3LUmmieLhMx7J0fHycvXv3kpeXx9KlS2eks4g/TqeTvXv3otVqQ34ZIbRlFOi4JrMy/AVwLhbFh1rCKqOwUlKrxBtvaHnkkXj6+9eSny9yww0Ozjwz9PcnUssz0PvrX62hRDq/6e4KotVqWbBgQcjnmM3miMTNbDYHWtGM4p0g78+7QBXQDqwEngVcwJ1h73CGmPWuIBC7gIK0jcHBQRoaGsJqcKkkluI2NjZGXV0dCxcuxGg0BpwdoCTYxRetMElWnP/rQ12YgYiFsIWLfxTWZrMxOjoqt4FKTU1l1658tm7NwG73bre/X+Cee/SAPajAxTo6GipxWaotVZ639LpYfL+Ki4snHaEYaY5bSkqKXCWjII0AE+RFUWxR/ForCMLPgO+giltgYmW5ud1uGhoaGBsbY926dRHP0ZS2MVV6enpob2+npqaGvr6+SYUNYpPiEA7hVhRMpZTq3nvjeeklHR4PCIKGjRsd3HKLI6JtSEmtycnJFBQUyHleTzyRIgubhN0ucN998Zx55sRxg7Eg3BuM9N4G8p36l6pJRCJ2KSkpk64AIPJlaWVlpRSBXyKKYuOhh2vwTpafDBGYk3kn02I/R3qhxkLcXC4Xw8PDaDQajj322KgGBMeiPXd9fT0DAwOsW7cOi8XC6OhoWK8NdAHFom5S+fo33tBy+eWJnHpqEpdfnsgbbxz2iSovTKmaRBlgkf5pNJqQy657743nxRd1eDwCoEUURV58Uce990b+efgHUtLS0hgaCnw/HhsTeP55Kw6Hw+88k3n99ZltHhmsYkP5/kr/pOcr39tA1rVGo6G0tDSs/UdaNJ+cnMzFF18M8DNBEJIFQTgJ2IjXn+Z/bucKgpB/6OdlwO3AX8Pe2Qwy+y1Dmbq4DQ8PU1dXR2JiIhUVFbOSA2az2bBarSQmJlJTU4PD4aC7uzvs1/sLUSz8ZP7Cds89evr7NYBAf7+Ge+7R+wic/+v9l2HKi1M6Rv80lr/+NQ7vjVwApOMXeOml6BYJ/uKenx9M7AWeeiqDZ58d5e674w6dp4b+fkKe52TEYjbGZNsIdGNRRnQFQaCwsDDs5pfRtDv6wx/+AN7p8QPAM8BXRVHcJwhCqSAIZkEQJGU9HdgrCIIFeAV4HvhlRDubIY5ocRNF7ySq5uZm1qxZM+XBHNGKm8Fg4JNPPiEhIYGysjI8Hg+tra0RXxTKL3Ss60YfeSQ+4HLukUcmWlTh7l95USr/PyxuGvmfx6OZ9Kbz+OOP+5xDoGO44QYH3pXQRIaGdPztb6U4nb7fA7td4MEHtVgslojrV6fqI5vqNkRRJDk52ScvcjKiqSvNyspCFMVNoigmi6JYKiXwiqLYIYpiiiiKHYd+v1UUxfxDz1skiuKPRFEMnT0/Sxyx4uZwOPjkk09wu92sXbtW7l8/FaLp4d/W1kZjYyPHHnus3BpI6lEXCbH0uQW6gPv7A28/2OPRiqt3xSpZbYf/aTQeH/GWlmCS1VdXV8e2bduoq6sLKQhnnukmLS3wseXni4rz0aAUwaEhHQMDA+zbt4/m5mZ5ithcRxCESaOj/qgdQbwckT43o9HIxx9/TFlZGZWVlfJFMl31goFwuVzs3bsXq9XKunXrSEhIQKPRMDAwwMjISMT7lqylqZ5HsNcHW875Py69PpR/LhQXXugG/D9LkZNO8o4qfPzxxyf4nmpra7n55psBuPnmm6mtrQ3qewL4xjcc6PW+x63Xe1NCvOejXBJ7SU42UV5eTm9vDd/73gouvbSMz38+iccf76Ojo4ORkRGf7+BMLEfDobCwMOIB5POhUaUgCMcKgrD20M/aQ7+vEgQhLdxtHFGWmyh6p7A3NDRwzDHHBByxNxXCFTeLxcLHH39MTk4OK1askB3sDoeDzs5OHwd8JPuGyaNnRqORtrY2hoeHJ9TShjr+G24ILgj+rw/mn/vPfybvDPytbzlYunQv3tQn8dD/f+G99y7g7rvvlq0ziccff5wtW7bI5+J0OtmyZQv33PPHgL4njUbD2WeLfOtbNjIyxvGKWA+nn/5vzjzTzQ03OIiP9xeUcSyWu3n88V7uuUfP4KAOEDAY9DzzzCJ27y7AZDLR0NDAgQMH6Ovrw2QyRe1WkI53qiuJpKSkiJajEkdyuyNBEOIEQbgMuBf4jSAI1wHnAVuBlw49FpbzcU6Im06nm7T8yul08umnn2Kz2Vi3bl3QEXtTIRxxGxgYYPfu3axcudJndJrH45EbTyod8P74Rx6Vj4fat1TW1t/fT05ODna7naamJvbv3093dzdmsznk68880813vmMnP9+DV3R62LSpzic3TDreYP65v/718Pkq/WMSkqXy8MMVbN36CYKwHjgeuAetVsvf//53AL7xjW/IArd582Z++MMH0Gh0h7YRx4YND2Gz/Q/NzRNnOkjW3umn2/nc5x4G1gMX8sor32Dnzp2ccw4sX74d6EESPrgDeI1t25IDntf//V86CxYsYPny5SxevJj4+PiolrCxLN2TkuGj2d6RLG7AIuDbwFPAQeB+IAPYDHwTWAPcAiBM8uZMW/lVJExmuUmTqBYvXkxBQcFUDy8oocRNKqMaHR0NmEPX3t6Oy+UKqzwn0M/S78paUunvbrebpqYm9Ho9y5YtkxNai4qKcLlcjI2NMTQ0RFtbm1yYnpGRMaHU68wz3Zx55jhOp5MLL7wCi+U0Hn88h82bN/ucezA/nNGoB6yyf2zdunVUVVUFfO8+/vhjn/NTfr5ut5stW7ZwzTXXsHnzZnp6qjn55Lt4991b+cxnvsLChaswmUTefVfD4sWB389bbrmF2tpan8fuueceXnjhBdrbO4C7AryqEO+S1fd9V56vXq8nLi5OcrBPSCQO1DBSQqpOiEWybn5+ftQ38CPR5yYIgiB6vzAlQKIoig8JgtAKnCOKopSSsl8QhDjgZrwfsIaJPhCZOZHEG+zLIFkr3d3dEU2iivVxOBwO9u7dS3p6+oRGmwBDQ0MYjcaoo5ySfymQxWez2WhsbKSoqEjO3Fei0+nIycmZcDEqC9MzMjJISUmRjzsuLo7jjjuOt99+G7PZzPr161m5cqW8zeRkExbLRNdGQsIodXUH+cY3vgHATTd9i3PO+R2XXbaSxYt9j2vz5s1kZGTw29/+NuA5C4KOoqLjAOjv1zAysp/y8hVIGQzJyRxaFgdmy5Z7uf323zE4+Defx5uamoK+BnrxChwcjuhCfr5Htjr9qzmk7rjKROLR0VF6e3sRBIH09HTS0tJISkryqQGeCgkJCVO6iR+hk6+ku04qIA2M1QEfAgiCkCiK4jjgBMJyQs6JZWkgS8/lcrFnzx5MJhPr168PW9hinUIxNjbGf//7X0pLSwO2AR8fH6erqwuILoVD2meg146OjnLw4EHKy8vJzs6eIHxvvhnHZZcl85nPJHPZZcm8+WacfCEuXbqUpUuXkpqaisFgoL6+nsbGRgYGBrDb7ZSXl2M2mwGvE1/pB7vllnji4nxviHFxbpYte5MtW7bIVpjHY+eVV27kZz/bRlOT7/tSV1fH1q1bg563KLr45S+/yv/+7+MIQi179/6RpUtvIDf3SgAsFg4toQPz618/NUHYDr2jCIL3ni0IOlJSlJ157ufwjV4EPOj1bm64weaTuwf4RHLlLR9KJA62hG1tbcXhcEw5ChvtclTiCA0oSF9sJ9Bx6OddwK8ADgkbQCXeXLxJmRPLUn9MJhO1tbUsXLgwooEtU53F4N/wsru7m46ODmpqagLeCaV8NmXtYKR5VIFy20RRpLe3F4PB4NOpV8kbb2j51a/i8F5HHgYG4J574hEEOOMMl3xxStOWJKtubGyM3//+9/ztb4eFweFw+CwTJT/c1q1OjMZ4EhLGuPXWBIqLy/jb3x7k1Ve/gcfjQKuN4+yzt5KYWMW774ryEvLxxx9n27Ztk5y9juzsB+nttbNr19cAeP3173PWWfeRnLwKk0ng/PODuyo8nq+QnZ3B8PC9/n9BFL3HUVZ2Em1tHyj+9hoQh1b7A9zueKCXr341njPPTJxwYwtkffmXqOn1erKzs+Ubz9jYGF1dXbS1teF0On3aOYX7nczLy5uy1WW1Wo/EyVeS5bYLGD1kqfUBfdKSVRCEAiAPePXQa0JebHPCclPS1dVFXV0d1dXVEU+iisVgZslhXV9fz9DQEOvWrQv6Zevo6MBms8m/Rxoh87fWpGVRU1MT4+PjrFixImgZ2SOPxONwTExWffhhr58tULZ7QkIC+fn5fOc73+H++++XOxFrNOeTlvYO27Zt4bLLvNn8Z57p5sUX3Zx33k+w2c6gsHDPoWOs4ayz7gPgjDN+RW5u1YQl5ObNm9m6davs8xOEOAoKNgOQnX0NAMuWnYnN9iEff7wFt9t16JjtvPrq/9DU9ChXXOEK6m8DMBgeDSBsAFo2bHiIzMyVtLW9g9cQULITt/skFi68A7iQpKR3w15KBiqh8p6fgFarRa/Xk5KSwrJly1i+fDnp6ek+Udje3t6QicR6vT7qoeRKjqSAgiAIhYIg5Imi6BEEQSuKYq8oiu8rLDUO+eIQRbFPFMXviqL4+0O/h/zQ5oy4iaJIbW0tBoOBdevWRfXhxELcHA4HH3/8MUlJSVRXVwdtRT48PIzBYPB5LJJlqf8FJXXZra+vJzU1lUWLFoWs4ezv1+Kfy+V9PLTVLF2g1dXV/O53vwPORqP5EWNjKYCWgYF47rpLzzPPGPm//3uDV199DYBvfONbfPhhN/n5HpKTq6muvpbCwuMRhMBLyKqqKu655x4AqquvIinpejIyziMu7hqys88kLm4FmZnXc845f0AQvOep1+vZunUr99335ZDCBnDiiV8mO/tBQBJ/7+e0Zs1NxMdXk5//R0pLH0EQfG8AghDHeec9xGc+8x3i4jL473//y6OPPhpyX5MhvadS+3cpsJCenk5paSkrVqxgyZIl6PV6BgYGqK+vl6OwymTvBQsWxKRd0hHmc7sWb9oHoii6BcmncIjJIqKhmBNJvGazGavVSnp6OqtWrYp6tsFUnblms5menh6WLFnCwoULg56HzWajs7NzwuPhilug45Ry5EpLSykoKJi04WFeXmARD5SsGyhtA7wClJz8PVwuLZIPCjy4XALbtqXyyCN34PF49+N22/nTn+6gtfVRTCaBJUu+gscjYjKBySRwyikT3/c1a9ZQVbWG1FQzVqsOp/MnmM1J6HR3YDJdTlaWQHLyao477kIAfvOb38jR18k477xxFixYRlmZ169XVvYApaWVZGe7sFgE+vsFPJ5qli79FgAFBd8DoKjoAfLyVmG1aiguPpYPP/yQP/3pTz4+x0hRBiP8PzdJ+LRaLVlZWZSXl7NixQqKiorweDx0dnZSX1+PyWTCbrdPuSM1eK32WM4HmWYMwBWCIPxKEASNKIouQRB0kqgdWo4uFAQhJ9INz7rl1tvby969e+URZlPx102lRrWtrY2enh5yc3PJygqerOrvZ1MSyfJGycDAAEajkaamCq65JpsTT4zj4ovjJnSzeP11DRddFMeppyZjs4FOFzopF/Apa1Iep3QMFktg34zNlsaGDQ+h0XgtH602npqau0hO3shnPtOBVmuhv18gLU3gyis9LFkycRvNzRry869CpxsiNXWIzEwRUYS4OG8rpNxcDyaTQHX1ZygrK+Nvfyvh8cd1PvltwSgvd3HZZf189rMrqKi4jpqaKkpLL8TlamLRIhf5+SKCAJWVF1NZeR3JyReTkXE92dlVsiCvWFEo9zH71re+FZXAKV0RkQyHSUxMJD8/n4qKCqqrq1m+fDkjIyPs3r2bXbt20draytjYWFSJxLEs5ZsBHgJ+BmwBfn1oaeqSfGyCIFyKt0Hm5QCCZOaHwbSJ22RvsMfjYd++ffT397N+/Xr0ev2MjveTkKKyVqvVp9ogGJ2dnYyPB+8bNtmXUSksHo+HlpYWRkZGaGxczIMPZtPX501R6OsTuOsurSxwr7+u4a67tAwMeO/IY2Pex9PSpKTcXm66adQnKXfXrl1885vfBA5fvMr3yGvR9QY8zoQEKC1dxckn3wDAmWfeS1HRcjyeAo49NpWLLhrgoov2cNxxe9Dr2+ULUZmg/O67OlJTlwOwaFE92dkiqakiDoeGoiI3CxZ4OOkkN62tyykvLych4SAmk8Cf/xyewJWVOdm82cUf//glsrI8ZGRUADaczi4qK73vcUODwPHHX8fChR6ysq4nNRVSU0USEh7ilVf+T96W3W5ny5YtQa3ccJBSQSKlrKyM3NxcKioqWLt2LVVVVSQmJtLV1cVHH31EbW0t3d3dIb93/sdxpAjcIb/Zz4H/BW4AfioIQrUgCF8BdgJ/AeKA/ZFue1Zs10CTqKZ7SEwgLBYLe/fupbS0lOLiYkwmU0hxNBqNE/xsSiaLliqFxel00tjYSHp6OuXl5dx6qxa73ffCsNm83SzOOsvDgw9qsdl8/Wwul0Bioshdd33M1772NeLjfwicDUyMWEoXrxQRBQ7938u2beN4u914iYtzs26dB4sFysuvZnTUQUHBGtraDCxcKMrDgqUkYpPJxODg4IQk4v5+Hbm5mZjNucAB1qw5GVEUGBjw8MMfeh39jz6qIS0tg9HRPGy2BgoKTgZCJ/AGuon192vIzq7AbAaHo5usrFJqajwcOCAwOCiwYIGHq67ysHixt7zslVe+jtdY6APuR69/O6JlcaDjiGbyVVZWljyLVCI+Pp6CggIKCgoQRe/keYPBQENDA3a7nfT0dLKyssjMzDySlp8BEQQh7lBXkR8dWnpuwdtLLhfvh3Mb8IAoikaYPIigZMbfmWCTqKKdZ6kkEstNOo5Vq1bJX65Qr7fb7XR0dPjcFZVf5MkSOJXLF6vVSmNjI6WlpXIb9KGhwKkCfX3S/xOLwb3nIbBixQpycnJ499136enpYfPmzWzevJl169bxzW9+E5fLRXx8PL/97W99knW9vIrXetsCFAB9OJ1bycwsxGT6H0BDTc31mEwwPh7HKaf43oB0Ot2EdBMpiVijyaOvL4mMjItISPAmIJvNHvLzD0caBwZ05OaC07kUm60ZEEhOFujvB29dauD30d86yc/3YDIlsWDBbWi13pxIvV7k5JM9bN58eDveFJpEHA6pwL4QuI0rr9xMVVX4kcpAn3Wk8xPi4uJ8xvMFQhAOT55fsGABHo+H0dFRDAYD7e3tcrqPJJIOhyOqRq2zwaEUD6cgCAuBy/AOpEnEO5vhPWCTJGrRMGPLUo/HO6C5q6uLdevWTRhIEes5CsEQRZGGhgb5OJR3zVCVEq2trfK2A6UEKC02/46qyvdieHiYpqYmlixZ4jPfIScn8HFLier5+YEtAq9vSeCUU07hww8/9PGvVVVV8eUvex3qq1f/kI8+qpmw3POmbVyIIGwE1qPVXsTWrRfy7W9v5oorXKSmigwOCqSkwOmn94SMYkq+JCmJ+KKLMnA49IyOZjM0ZKWra5TBQRvHH394eZWf78FiEcnMPJuioq8DIhaLh/x8d8gOtf7idsopXv+d1ZqEx0PAQMcbb2j5xS/0TMyxTeTvf18U9LwCEchCj3Q5WFJSEnFOpiRmixcvlpewSUlJ9PT08Mwzz3DJJZfgcrloa2sLa3sGg4GLLrqI5ORkBEFoFwThC8GeKwjCLYIg9AmCMCoIwmPhFrAH45Bf7XbgDeBuYBj4CvAwsAS4Yirbn5GAwvj4OB9//DF6vZ5jjjkm4J0lFsvSySw3qQecIAgBjyPY6zs7O7FarRMeD7Z//xwzKYra2dnJ4OCg/IVU8sUvjhIf77vvhASRG290o9FoSEh4GN8h3wDjVFa+AXiz2qX3T/KvNTdr6Og4n7KycvLybEH9WVVVVfz4xz8GoKamhiWHogOLF3utnu9/38F117lYsMBGJCxZIvClL2koLk5BoymgsDCZCy8cRadrY9++fXR0dLBmzShjY2A2ayaIkv9NxD+PUNkTbskSfMQ4NVX0yZWTOp2IohQZ9mWyFBolwdwPkVhuGRkZZGRkhL3PYMTHx5Ofn8/y5cu54oor+MY3viHX7q5bt25C5xh/tmzZQnx8PP1eU/kq4AFBEPzNewRBOBvvDNPTgYV4C9x/OuUTgP8BBoErgctFUXwCb4H834GtgiDcGO2Gp31ZGu4kqumaXSohFd8vWbIkaBuZQOJmNBoZGhoKa/+BXi8IAi+/7GbrVjAYFpGfL/LVr3o46yzfVt2nnebA4zHw5z9n098voteP8P3vp3HOObBnzx7a2x/iggtWsXPnQrxJ2gNcc42ZzZtPDupfq6m5lsWLr2fFinMZH68nO/sCQBPQn7VhwwbKyytIS0vjppvaSUhYxcUXu9iwwT2lFJvFi71+LkFwHxKETCBTrtMUBAPr1w+wZ08Ww8MplJRoOe88YUKtqv8xKIMyh/cFFRUi4FZYeN7/vZ1OAucGQqj25b5M1lwhHHHT6XQRN6AMB41GI5eG/fnPf8blcoX0yUnDmOvq6khJSUEUxVDDmL8M/FE8NIFeEISf4+3cMdWhzZ8H2kRR7D60Xa0oinZBEL6K98P6gyAITuAxMdAdJQTTark1NjbS1tbG2rVrJx2xN53L0q6uLurr61mzZk3I/lj+fj/JzxYJ/oXXf/ubk7vu0mEw6JF6oymjoJJlIooiJ59s4oUXnFx++a9xu8+juXkrr7xSx1e/+nUAXnnlW1xzzXvAerZubWfzZq+PSKoIkHrsS8mwRUU3kJKiITm5mvj4YjweW9CC9Hfe0ZGefgmiCJmZtZjN8OCDcbzzji4mvlD/76WyTvOss8r55jcT+frXDXz2s03Y7XW0tbVhNBp9XAFKgn3P/a096XevZSaibH1+eGjTOOee2xJwe4G2H4xwAwrFxcXTFgiwWq1yAu9k+5CGMVdWViof3oPX5+XPykN/Uz4vXxCEycdxhUAUxX+JotityGtzH/rfAXwVeBx4BO9dMSKmTdwaGhoQBIG1a9eGNdhiOgYzS+kmw8PDYRXfK5c9Uu5bJMfkf9c2Go088IBmQk9/KQrqv2/pwjnttNNwuVw8+eST/Oxn1+PxOA+dj4Nt2+6msrKG6upqn55wVVVV/OY3vwEOJ8Pm54PF4iElpZr8/C+i1SYFLUh//nkdTudKBAHi4/eTkuImMVFk+/aZmUsRHx8vp0OsWLGC7OxsLBYLDQ0NHDx4kJ6eHqxWq0/9bST+rbw8SdyU7c+lZpp3sG3bFWzbti3kdK/JkrTDWZampaWFzKOcKpEMZI5wGHPKob8pn0eQ54aNMlnX/2+H8t2uA3ZwuFNI2EzbsrSysjKiO75Wq4147kCgbUhiZLPZ2LNnDwUFBWF3WVA+p6urC4vFEtH+lZG83t5ejEYjRmPgbsFSFFT52kAXjkYTB3jweNxotfGceupWSktX4PF4/WvKwvtVq1axefNmqqur8Xg8nHKKmz//2etjSk72lkkFK0gfGhLIylqEw1GB210MeEhOjmN4OPouK9F0SZFel5qaSmpqKoIg4HA4fCbRH3J+o9frFdPnhaDT5zUaDV/5io177tH7Nav0ADsOpYFspaqqaoLlLf0vfbahzmmyZalWqw17PF+0RNIRJJJhzID50N+UzyPIc8MmzKXm5ZEuSWEaxS1SP00sLbfh4WEOHDgQ8cR5iZGREQYHByN+nSAIcmNJrVbL8uXLKSiYKGRwOAqqRBRFHn30UR577DH5MclqAzjzzF9RULCKvr7AkTqAa665Rr4IFy92c8UVIu++q6O/X0N+vofPfc7NokXeSgElOTkiZrMOjeb6Q49osFo95ERc9BL4uKaC/yR6q9VKT08P//hHPE8/HYfT6RWUYNPnRVHkzDM91NW5ePFFb4txLxrgQq688tiAaSD+VqLyXPyj4OBtwhlK3IqLiyc0EI01kRTNS8OYGxsb5SASwYcx7zv0t78ontcviuLwFA95UqIRNpgD5VcSsRI3o9FIc3Mzxx57bFTC5nQ6aW9vj2r/LpeLwcFB0tPT5cL3G290k5Dg+9lIUVAlygvl4YcfliO5Wq2eCy54hNWrr6eo6HgsFigoCH3TUPq4vBFPB9//vo3Nmx2Ul7t9rD1paXvJJW6sVgGTCdxuAZNJxGoVuPji6CLY0zVgRcr7ysjI4OWXy4OM8dPJUULlNt54Y5yJw9ETee650HMKAh2HfyqQZLErZ7gq01dSU1PDmhY/VSLpwisNY/7Rj36ExWJBCDGMGXgCuE4QhBWCIGTiTa7dFqvjng7mjbi5XC6am5txuVysXbs24olBcLiPWjTHMTY2RmdnJ2lpaT5Bi7PO8vD977spKPD6e3S6Qb7/fbccLZVoa4vjD39o4rHHHuOllwS+9737AVi3biuJiatYvfr6Q2kS8JnPBD8+/3SJyc5XukhPPdXFjTc6SUkRMBi0pKbCV7/q5rTTIi/lieQYot2GKIpBE5+HhrS0tLSwf/9+nn7ayKWX6jn11KSgdbTBHofIViDKZatS8IRD8xBmgkgbVf7hD39gfHxc+s4GHcYsiuKreBtH/hNoP/TvxzE/gRgybcvSSC+IqYib2Wxm7969FBR4pxhF2zamu7vbpz9buPT19TE4OMiiRYswGicmVJ91ljf145lnnuH3v/89y5c/CxxOBWhqEnjssWY++eQ2AF555asMDT3Ipk3XcfHFK3nnHe/StqAALrjAQ1mZh4kWyNTZsMErZr5BmcN/D5SUPFURixZRFMnJcTM0NPErnJ8vsmzZMl59FR57LGFCWZs/yckmILBQRmJ9BvO5FRUVzVjVQKS93LKysnjxxRelX2UFFr1DmH02JIrib4DfTP0oZ4Y5U5gWrbj19/fT3Nwst0qKZmYoeC2vwcHBiL7MHo9HjqhWVVXJbbuDcfrpp/P73/+eN998E7fbzfXXe/1bv/nNH9m9+3BPMY/HxYcfXs/q1ddTUSEeyt06vM+xMSuJiYkTLqRoHfgSk1kpkqUXaB9K4Qv2nHAJ5zxEUeTqq0d44IFsnyCBVuvkhhu836P7759c2OLiXNx8szdo40+kfuNAqSApKSkxH0EZiiNxOMx0ccSKm1RGZTabWbduHXFxcdjt9qgsCYfDQVtb24QSKmk/yv+Vr2lsbCQzM5PCwsKwph7l5eVRXV3Nzp076e3t5bjjjmPVKu+kp0AM+7lqpS69LpcLp9NJXFwcGRkZpKWlkZiYOGUraiqCJC2/lJ9hoBrcyY4xkrZRGzbYSEmxH4qWgiAM4Hb/nqKijbz+ejVjY8GsWxEQyciwc+WVBkpKemho0MnDXhISEqKqdfZPBZGSameSI6xR5bQyZ8QtnNmlEg6Hgz179pCZmckxxxwjXzzRWH9SPpu078kuLo1Gg9lspqmpibKyMtLT00MOefFnxYoV/PnPfwa88zvvu+8+PvvZ/yEtbR2ffvp1vHlXOkpKHkSvr6apyU1FhYjD4aChoYGcnBw5UGK32zGZTPJYwUCTrsIlFlObgiXaBgoKKP9X/j1cgZWeJ40rfPTRR3nySa8f/Oab/0ly8j8IvnTvpabmdu677z68IzEz5HQTyTUhzT9IS0sLu/7TP/euoKAgKt/vVDiSWoxPN0ecz00qo6qsrJxg7kdzgfb09PgsJ6VtBPPb9ff309vbS2Vlpc8dXqPRyBdBMJF79NFHZWEDrzj9z//8D5s2XcvIyFcoKPhf+vq+yfLlV+F0VlNeLvLOOwJFRRYaGxspKysjNTUVt9uN2+1Gp9ORlZVFbm4ubrcbs9mMwWCgo6MDvV5Penp6wPml/sQiABDJez+Z6E1mNUuPSc9//PHHZWEDDk2gCubjEqms/OCQsB1GSiKWvlMmk0nOrRME7wi/9PR0EhMTJ+2SDNFPi58qqrgdZs5YbuGIYVdXF52dnUFnmEaafjA2NiYVDPscR7DOIO3t7djtdlauXIlWq/VZhilrHf1TLaS/33DDDRx33HF8/etfx+l0Eh8fz/33309VVRXf/raH4eEatNp15ORYyM72kJEB7e0OuYuIXq9HPNSyWjpXQRBkqzM5OZmUlBQ0Gg12u11uPeTxeEhLSyM9PV1OgFWebyjq6urYvXs3q1evDpm5H0txDOXT8881A+T2TjfffDNOpxO9Xo/LZcTtDpR6MYLHs5jm5sD94qTjkJKIwZse5J9ELC1hA5U4SdHRSG/wscBisRyJk6+mhTkjbqGQplF5PB7Wr18f9eg+JU6nM2BbmEAC6XK5aGhoIDU1lcrKyqBfWv+LPJBjfdWqVWzdupWvfOUrbN26lVWrViGKIhUVblJSbBQW3oFGk4RGA319FhITrSxfvly+sCWBUV7s8fHxE3KupMTXvLw82aqTGkomJSXJlkhcXByiKOJ0Ounq6qK9vZ2Ojg6GhoY47bTT+O53vyv792666SZWrFgxxXd+8vctEP7vpdJ5r9Fo5IE3X/va17j88q/z5JP3Av8PZRNOb1eVX9PU9Bp33HEdt912zQSBCySsgZKIR0dH5RujdOOQXjuVafFTRbXcDjNnlqXBGB8fZ8+ePT5de6eKv59Nif/yymq10tTURElJiU9NYLAOIOFYjlVVVVx33XWsXLlS3sYpp7h4/HEdNlsaSUkinZ1jWK0arr8+E0HwTEjBCFSILgmfsmDc7XbLSaRpaWlyveaHH35IS0sL/f39DAwMMDw8TEFBAWVlZZSWllJTU8PevXtxOp14PB65c7A/U43QTgXp/ZCEbuXKlVRWrubJJ//30DNE4Ca8TTh7gd8D/6Ci4hFqalb6zFqF8JbWUhJxoE7ENpuNrq4u8vPzsdvtYdVUx5rx8fGwB5jPd+a05TbVMqpg9Pb2YjIFLolTXqwGg4Guri4qKip8vjBKS+P11zU8+KCWvj7Iz9fxuc9lEMi48X2ewI033oAy/aCiQuSccwY4eDCODz/sYdWqXK66Ss+iRR6fTHdJtEItwQVBkK20jo4O2traaG9vp729nfHxcUpLS1mwYAELFy7khBNOIDs7m6SkJBwOh5z9n5aWxo9+9CNZMOPi4pQlOkBsghDRbsM/si1t48QTt1JUVMe7727B43kNb87p2cTHb8LheJ2FC7/BihWrSEnhUITVLb+f0RyHshPx+Pg4xx13HOPj49TX1+NyucjMzCQ7O1sOPE03kttCZZrFLZq7uvT81tZWhoaGwu4qEi4mk4m+QMWeh9BoNLjdbjo7OzGZTCxfvtzHIa88J2loi83mtSD6+wUef7yUv/xFYGzMm3QrlVn5P+/uu7UIAj593Wy2Onbu/Cqjo6Ns3foWcXGHl17KZZl0IbpcLnkp2d7eTmtrKx0dHXR0dJCUlERpaSllZWWUl5dz6qmnsnDhQrkESLLqlOclCIK85Ors7GTXrl3cfPPN8nBq5cU500EIfyR/o/9x9PdrKC1dxWmn/Yw33/wh5eW309t7Ni4XZGVdT3X1lWRleTCZvMm+/vWjgd7vcMnMzJSDCGVlZbhcLkZGRhgYGKCxsZGEhASys7PJysqalmXrVPML5xtzynKTOoPs37+fhIQE1q5dG9XdLlg7nGB+NiWCINDe3i5PDg+1f+/QFv/iaQ1So4W+Pq+oxcejeJ4G8PgMf/F4PDzyyCM8++yzuFwuEhMT6ezsZPHixQiCIKd7+P/r7++Xl5JlZWWsXbuWSy+9VI6qKkuB/IMIoiii0+km+OoSEhJISEigqamJiooKjj/+eEZHR7Hb7djtdkZGRiJKjwhFLPLq/PHOUhAoLj6VmpprWbPmdLq63LS0CKxZcy3JyYdnrUrdUUIFM4Klrfg/T/LLKdHpdD6+uvHxcYaHh2loaMDhcJCRkUFWVhYZGRkxtbZmI5AxF5lT4iaKIp988gnl5eUUFRVFtQ3pixroy9Le3h6y7bLNZmN4eJi8vDzKysqCblsihAGo2KaAzSZdCF5hU76+v7+f73znO3R0dMg+QJfLxf3334/b7aa9vR2r1Sr7whYuXMi5555LWVkZxcXFQct6lHdx/wtU6asK5KvzeDy8+eabnHHGGWRkZJCdnY0oivLw4N7eXnQ6nRyUiMayjtRq829ttGlTGhddNHFpfsopHv78Z+/XWhpso9HAl7/sorVVkLujnH++m8WLPWFVZSj/l/Bvh1RSUkJLS/CGl4IgkJSURFJSEgsWLMDtdjM6Osrw8DAtLS3ExcXJVl1SUlJUAqVabb7MmWVpX18fZrOZmpqaKZWrSPly/uLW29sbqHeVzOjoKG1tbWRmZk4YtQaBl2HB2hkFx/f1er2RSy65ZMJ2nU4nGo2GL3zhC5SVlZGXlxcwFSJS/BON/cVOp9MhiiImk4lPPvmE7373u7J153Q6EQSBoqIiNBoNNpsNk8lER0cHTqeT1NRU0tPTZYsxFNEIm7IXW3+/wGOPFZOWZuaCC3yfu3ixhyuucPHuu5oJQrZhw8RtR/t+KkUvJyeHpKSkiFYZ0gR6KUgl3VhbWloYHx+Panyfw+GY8aThucysW24ej4fGxkYsFgs5OTlT/nACXThmszmon03qBGIwGFi+fDkDAwNhR0FvvNHt40sLzgiCkIooHn674+LcbNiwj4MHS+nu7kan0/kM3bVarWRkZCAIgpy7NR0thGCidfLee++xevVqOYhjs9lobW2luLhY9knGxcWRlZVFTk4OHo8Hi8XCyMgInZ2dkyYQR3oe3vkHvu+x06nlT39K4oILJjY4leY2TEYsAiLx8fEUFxfjcDimFDBISEiguLiY4uLiQ/XDYwwPD8vj+ySrLlT1idlsViOlCmZV3KQyqqysLNasWcP+/ftjPpjZ5XLR2toa0GHsdrtpaWlBEAR52nwkX3gpGHDffW4Mhji8nZCT8S37ETn1VCef/Szcd58dgyGOzEwHmzZ1c8klS8jI+D/sdjuffvopb775Ju+99x4OhwOj0ciCBQswGo00NTXh8XjkiUn+ibjhEInV98Ybb3DeeechiiJms5mWlhYWLVpEamqqTzRO8tPB4QRiQRAmJBBLVl1KSkpUNZsTJ1N5l/cDA9H7qWIhbAALFiyYtKolUjQajc90LIfDwfDwMB0dHZjNZrk3XFZWls/NI9J2R/OdaV+WBmNkZIR9+/b5lFFNxxyFtrY22c+m9EMpazXz8/PlC1ar1QZNMwhER8fDGAxS59yX8OsSA2g4cCCXO+90ctZZAvff/1tOOeUUKioq0Ov1eDwe4uPjOf744zn++OPluQ8Gg4HExEQSExMpLi7G6XQyMjLikyWfkZFBenp6WMuWcIVteHiY+vp6fvGLX2A0Gunu7qayspLExMQJy1mtViuLldIhr9fryc3N9UkgHh4eprOzk4SEBDm7P9yutPn5okLglMOpe3n88efZvHlzWNtREgv/lHJafCzFzZ/4+HgKCwspLCyU3QbDw8N0dXXJx5GUlMTo6GjU4mYwGMjOzn4BOAsYAn4giuLTgZ4rCMI1wB/xnTV5gSiKb0e182liViy3zs5Ourq6JpRRxXoCVl9fX0A/m8lkoqWlhfLycp8vp4T0syR4ylpHURR9ctYKCr7Ktdeew1NPfRG7PUDvcLz5VKIo0tfXx2c/+1mWLFkiLxH9LwiNRsOqVat8fvd4PBMib2azmZGREXp7e9FqtWRmZpKRkRFwWR+J1fbPf/6TE044gdHRUYxGI8uWLZsg+P4EC0pIF7wUeNBqtVitVrlbsiiK8t/8neiPP/64LFo33OAIMP9gnC9+0RSVsMXCavOfFj+d4qZEEAS5oL+8vByn04nRaOS1117jV7/6FfHx8Wzbto2zzz6bwsKJrdODsWXLFgAHkA+sBl4WBGGPeGiUXwD+LYriyVM9n+lEmORLP6Xbm8vl8hErt9vN/v378Xg8cn2mktbWVvR6fdSRUoADBw6Qm5uLXq+nsbFxwkU5MDBAX18fS5cuDRjlGxgYwOVyUVxcDEy8w7/+uoY774xTXGgier2Hq65q5bHHEgDlsXuXT/n5Hv73fxvweDwsXLgQCNyDP1qkFA2j0Sg79zMzM0lNTZUDAuFy4403cs4551BVVSW3Sp9KIEMSOakGVtqOZPFJBeoWi4XExEReffVVyss/w113fZ3jj3+YZctWcsopHlpaBB55JIH+fhHo5YILOrj55mURzySI1XK0vLzcZ6iyNHfDP9F5Jnnrrbd47rnnWL16NY2NjTz88MNhvc5isZCZmYnT6VwqimIDgCAITwLdoihOmEt6yHK7fq6L24wtS6UyqqKiIhYsWBDwwo7VstThcNDb2zuhFlFKBamqqgp6l1UWpAe6CB58UIvd7u0HJmG3C7z88iJOPfVN3n03D1GULjgPguDkxBMH0Ov1FBQUTPD9BWOyKgQler2e/Px88vPzcbvdmEwmDAYD7e3tJCQkyFbdZELQ1dVFW1sb1dXVlJeXxyRCK3VLkc5badWBt5ljWloagiCwa9cunn32WbyT3OA//9mCTncf3d2r+cIX3PzlL95pZI8//jwnnnjirKVLBJoWP1OWWyisVivl5eV85zvfieh10vxSh8PRoHh4D3BqiJetEQRhCDDgnblwpyiKU3OYx5gZ+TSGhobYtWsXS5cuDVkfGqtlaXt7Ow6HQ37M6XRy4MAB4uPj5SVhMJTLq0AES/3o7xe54op0RPHHxMXZATfQgyj+hPb2HqzW4rCFTTqOaC5ErVZLRkYGCxcupLq6mpKSEtm/WFdXR1dXF2azOWBzgD//+c+ceOKJLFq0KGCvtWh4/XUtF10Uz8kn67nssgTeeiuOuLg49Ho9cXFxsr+wrq6OW2+VLkppbKGT99//KgcO/I4XXxyTXQzXXXcdEHmyaiyG1gSbFj/Z5KuZINouvBHOLwV4F6gC8oBLgCuByBR1BpjWT0MURVpaWmhpaZmxqfMGg4HR0cOzY61WK/X19RQWFlJcXBxWDlaoYwg0kk/iq18tAUSczlOA9cCFwGvs3v0Nnn221kfYpJ+lZZ+SWBSjSxdaUlISxcXFrFy5kmXLlpGQkEBfXx+1tbW0tLRgMBiwWq3s37+fTz/9lAsvvNDnOKaCtzwtnoEBAfAm0N59dxyvv66Rj1Gn0/Hkk09y0003IYr+NxQtJ5/8EBs2fAOLJYXR0VHq6+s5cOAAdrsdh8Mhv4fK+ttg70cslqPBpsXPBcst2EDmDRs2yO+N/7+TTz450vmliKLYIopiqyiKHlEUa4GfAZfG+nymyrQuSwcHB3E4HGGXUU1V3CwWC0NDQ/Lvw8PDdHd3s2TJkrDzfyarmQye2yYAhcCPDv38mvwXj8fJK6/8D/n5m2WrI5zMd+9rJ/blD+ccAomjMijh8Xgwm80MDAxgMBgwGo2YzWaWLl0KxEYMHnooHofD9zjsdoGtW3WcddZhy/q6665jYOAEXn31JtxuO5KvsqzsQUZHV2E2uykq0lBYWChbogcPHqSrqwuHwyGnmkjLW+k9iJX1KSEl1gZiLoibxWKRfcVK3n777Ulf53K5EARhiSiKUuuXYPNLAyEyHROLpsi0fhr5+fmT1mcqmYq4ud1uWltbEQRvA8mOjg4GBgZYsWJF2MIm3f1DXdTSqL6EhBEmxls0QALwdZTTlAQhjvPPf1gWtsmQorLK+knl3VZ6TqjXToZkoY6Pj1NdXU1TUxMnn3wy7e3t1NXV0draytjY2JQEzuv8n8jwsEBTk/9xV3P22d5xhgsX/pCcnOtJS6tmbEyD1arl1FM98mcrWWqLFi1i6dKlZGRkyFZdY2Mjg4OD8jwN6eYgnUe4lp4/Wq025DyEuSBuUopQpEjzS4GfCYKQLISeX4ogCOcKgpB/6OdlwO3AX6M+8GlizswthamJW1tbm+xnk5oILlu2LOzSFWUi5mTikJv7CS7XOUwUN0kI8lm06Bfyo0VFD3DZZZM3eQy1b6Xgga/YKZe24V5gfX199Pb2snz5cvR6Pf/85z/ZuHEjS5cuZcWKFaSlpTE0NERdXR2NjY0MDQ2FrMv1RxCEQyPzJqLTmXjnHd9IeX6+SFLSKlavvo6amgsoKbkBk0lDZqaHK690sXSphvj4eHQ6HX19fSQnJ8vvhbT0XrFiBQsWLECaSlZfX09XVxejo6M+lrIkev7vZyjRm2xa/FwQt6l04f3DH/4A3s6eAyjmlwIIfjNMgdOBvYIgWIBXgOeBX07x8GPOrCXxBiJacRsYGGB0dJTx8XG6urpITk6OaAiu8s4+2XLs0Ucf5bHHpKTdPg6nfhwuitdqh8nMzCcz83ri46G8vIqKiskDSZFaSf5LW+WgGum8/LuCiKJIZ2cndrtdtqpra2tJSEjwyb+TepSJhzrPGo1G+aYhRQuDFXhLx/Htbyfw85+7EUWt4m9uTjghCb/u7px6qptnntFRUXEDKSkQFwcmk5srr3RRUXH4/Wlra0On08kdU5RC5T9XQlp6S3MlpARiqQOx/3sZzEUQzrT4uSJu0U6+ysrKQhTFTYH+JvrNMBVF8Vbg1qh2NIPMem2pEp1OF7G4Wa1Wuru7MRqNdHR0UFRUhN0+sd4wXCaz3K6//nqOO+44tmzZgsu1FbgNb8mVJEzuQyVScNJJF+JyJZKTY0cUJwYOJCJJ+wiFf9se/4oCURRpbm5Gr9ezZMkS+e9SB5BAx+C1wLydZ0tKSuRKiZ6eHsbHx+WJW8o2SNJxnHWWh7ff1vCf/9ix2+NISHCyfr2WvDxITfXdT0UFXHmli3fe0dLfD/n5cMEFh4XN7XbT1NRESkoKRUVFPpZqqATilJQUuZhfygeUEoiDzZXw/1zCGc83V8RNLb86zJwSt8kilf5ItaHd3d2MjIxQVVWF1WrFarVGtE+lxRSOIz0xsZq8vFPo6ZGCBlvwtrLuIympnszMzzI6mkVOjhuz2UFlZQ+1tUZSUlLkriPKBOapCls44uhyueQ5qwWHQr6SD+utt97ioYceki09pa/Pn7i4OHlKlJSEOzIyQldXF3FxcWRmZpKeni5XSlx7rYvERB0dHQ9x3HE3YDaDyQQXXDDxc66ogIqKiY9Lx56VlUV+fn7Qc5TERSmySutV6rkm5QMq50oEG/oS7rT4uSBuVqtVHQ6jYE6JWySzS8Fb0VBXV4dOp5OXWNKX2X9pBoEjk4E6gEwmbm+/LVBV9X1stn0YDK/hjYwKLF/+bSorL6WtzTtQ+ZhjBC68UEdFxQI8nmJMJhNGo5Guri7i4+PJzMwkKysrbL9gMCYTNpvNRlNTE8XFxRPScT7++GMKCgooKSnxcbr7v3+Btq8srQJvpYTRaJTnU6SlpZGfn8mVV6byzjvXH7LIRC64wC1bZP74R3qdTicHDx6ksLBw0qWhhCT2oaw6QRB8EojHx8floS+C4B3lV1hYOKEBZTDmgrgFSwU5WplTPrdI8rs6Ozv517/+RV5ens/dXLL+QgmaMvPe/++TWW5ut5uDB03odPsxGg+PhC8u/h5O50VkZYnExYkcc4zIddcdtkL8hWB8fByj0UhDQ4Pc8SMzMzPiRoWTvWfKrh6BlixvvvkmZ5999oRthJOqovTnCYIgV2EUFBTgcrkYGxtjYGAAq7WVU09Nkn11wcTcf182m43GxkYWLFgwoSIgFIE6jwSy6pT/9Ho9eXl58rFbLBY8Hg8fffQR6enpZGdnh+ytFqxB6kyijvXzZdott0gEK9yLuru7m7feeouFCxdOaCw5mRWjXHb5Rx6VzwmEzWajoaGB0dEPqKt7wu+Y7iI/fwiT6fqgyy4liYmJJCUlyROU/P1Y0vI1lDUw2fsqWYnSAOlA5/P+++9z4403htxOoH36+/MkpPdf2YxRFEW539uBAwd8WvoohxwrPztp6lgwUQ5FOIEZf6tOadkJgkBlZaXchUPqatLe3o5WqyU7O1seqiMd+1yoULDZbLM2UnAuMqeWpeHQ1tbGv//9b5YtWxbQFxKO387fOlNacIHSLcA7wLm5uZlFixZx661VPPDAZ/j446/j8djRaLQUFj5EeXkVqamhl12BjsE/uVZavkoRvmC1oaGEvL+/n+HhYZYvXx7U2vj3v/9NZWVl2EuvYChvFMqlrfS/IHhHC6akpMjtm0ZHR+nq6sJms5GWlkZmZqbc702yNv2njk1GtIEZf6FLTEyUhU0URZKSkkhOTpa7cCg75kpt2OeCuEH4qUBHA0eMuHk8Hvbv309HR0fI+tDJmiFO5lPzt+BEUWRgYID+/n45b27xYpGvfW0Ff/nLVl5++Xqqq1fxla8UU10dvr8w2DEol6+iKPosXwF5+arM81KiTPVYunRpyKXSG2+8wVlnnRX2MQdiMss80LJWWgJKjv3R0VFGRkbo6OhAEAQcDkdEVSUS0TTC9Eej0VBeXi7fOCWrzu12ywKWm5tLfn4+oijKHXMNBgMul4vc3Fyys7Nn3IIKN3n7aGJOLUsl/KN1drudPXv2EBcXJ88TCLW/YF/wSH2AoijS0dGBzWZj+fLlPttYvFjkBz9YRkrK5w/Nf6hFEE6S9x8s4hiJdSEIh4eKKBtWdnd3Mz4+TlpampyGIVmCLS0txMfHU1FREfJ8TSYT//3vf/nBD34Q0Xvify5TeZ30HkmWqcFgoLu7m4KCArq7u3G5XKSnp8tiPtnnF4va0YKCAh9hkqw6qXWUtHSVVgfKYdeLFi1ibGxMnm410zNLQZ18pWTOWW7SRSpZHKOjo9TV1VFaWsrw8HBYhe+hCPeCdLvdNDY2kpSUREVFhSxK/tx0003ce+8fePPN3bz99ink54uceipUVPjWiEr7nop1IaVhSB1ux8bGZItHr9djs9nIyckJWF/oz7vvvsuxxx47JQd0LHLzpJtff3+/PMdCp9PJvsjR0dFDQQkriYmJcp865RI9VnmCCQkJcppMIJRBibi4OFnkbDYb4+PjxMfHk5eXR2FhIR6PRz72xsZGEhMTZV/ddEyiD5W+c7Qy58RNOb2qp6eHtrY2ampq6OjomNKdOZJCcKnVd0FBgewHC/bFaWqC0dFjcLl2kpPTj8mUzzPP6OTMeuUFJ1l1/tuK5KJUlolJTnmbzcbBgwdJTk5mZGSEkZER2RpSOuyV23jjjTd8OoBESjQWuT/SUqqnpweLxUJlZaXPMlqn08mCIAUljEYjPT09cmunrKwseXjOVC/wsrKyiF6v0Wiw2+3s27ePlStXkpCQgNvtlr9n0pAcQRDk6Vb19fW43W4yMzPJycnxKfafCjabTZ185cecFDdpqIvVamX9+vWy4zlaIhG2sbExbDYbK1asICUlRRajYJbBO+9oSUurwWDYidW6m8zMs+XH/RNSg6VXSEiCIR1voIvV/zwk5/vixYvlqKLUetrfYZ+amopGo2FgYIADBw5w1113hfWe+BMr344gCLS1teF2u6moqAhpdUt5aSkpKSxYsECuNmhvb8dut8uVEtISMFR+XiDy8/Mj9vFZrVb27t3L8uXL5RQfZaqJJHTSnAyp7Zbb7Zaj4wcOHCAlJUUe+BJOwnAg1By3icyIzy3S59fW1pKdnc3q1asxGAwYDIYpHUO4X/DBwUF6e3tJSEggOTlZFrZQS8n+foG8vFSs1iXYbO0ApKRMnNgUjqUTKOIYKpk2WKqH5JuUlq/KzryJiYn861//4sQTT4z6Th+LJSBAU1MTcXFxPs0xw8U/L02qlJAizJJVK4lFqHpbKT8vEiwWC7W1tXKTAX8CJRBLYicIghxlBa9IDg8PU1tbCyCPTAw1xs8fdfLVROaU5SYVOS9atIjy8nJsNhudnZ1T2mY4VpsUYRwfH2fFihU0Nzdz8OBBuYIg1BcsP1/EZBLIz78SQUg8dB7exyM5hlDHFujngYEBOdVD8v8EOk5p+SYlwVosFt5++23OPfdc6uvr5ehruNG9WPR5k+pEU1NTpzQvQ7rpKM9RijCPjIyEHImo/L+0tDQih7/ZbKa2tpaqqqqwfJaBEogloRNFUZ5ZWlpaKlvd0hi/tLQ02aoLVckSbbuj+cycETfJ8Sr5IaQOENESrvNeutASEhLkwEFFRQV2ux2DwUBjYyMej0fukuHvw5K6WUASKSneukn/JN6pioF/CZmU6iH5qPyXr5JlJb3m4MGDPPnkk5xzzjmUlJQwNDQkT7qXLiSHwyFHX6XlayCmei4ul4umpiYyMzND1omGQ6BjUUaYlQnSypGIUoK0lF8YicVjNpupq6tj1apVUVtKgRKIJcETBIHs7Gx53KWUQNzR0YFG4x3OLE24V37mU+kIMl+Z9WWpKHpbkRuNRtatW0d7eztut5vOzk6fAnj/O24of4r0nMkuRIfDwYEDByYEDgRBkO+mRUVFcgpGIB9WRYVG0c1C8KmdjEUUT/laKdUjLi4uZKqH/3mPjo7yzjvv8NFHH2G32yksLGTv3r3U1NT4DJZRTjlPSppYLjXVIILT6aSxsZH8/Pyw60QDEcn7GmwkYk9PD3q9nszMTKxWa1j+NpPJxL59+1i1alXMhCRU/asygXjhwoUTEoiVZWHqsnQi0zraD7yWUbBieJfLRW1tLYmJiVRWVqLRaGhpacFutzM+Ph7wNUqUPimlZVNfX09lZWVIM145u1QZOAhUcO9/PmNjY3Jb7qSkJLkThv/+YhFRlLYRqKtHuHR1dXHNNdf4BGUSExPR6XQ89thjFBUVTej5JpVLjYyMyMu+zMzMqP10UulaWVlZoGEkERHLeQh2u52hoSHsdjuZmZnk5uaSkZExwXIdHR1l//79VFdXRxx4iBb/5auEJOzScOa//OUvvPrqqxQWFvL73/+exYsXR7Sf+++/n23btvHJJ584gGdEUbwm1PMFQbgF+B7e5pY78Da2jL7P2DQxa+JmtVrZs2cPpaWlPnlZjY2NtLa2Tqkk6ODBgyxevNgny1zJ0NAQPT09VFZWEhcXJy/roknyldITRkZG5JY/0nDkqQqbdBFLXT2KioqC9vAPhtTH7IwzzvB5H/R6PVVVVdxzzz0+EbpAjnfJDyTNRZVSHKQ+aZMh1YkuXrx4ziydsrOzfRqaut1uDAYDQ0NDjIyMkJycLFt8VquVAwcOUFNTM2u1m/5BCQkpkv/ggw/y4Ycf4na7KS4u5oEHHgh7288//zwajYaLLrroQSAxlLgJgnA28ARwGtADvAB8KAaYbzrbzMqydHh4mAMHDlBVVeVzFxdFke7u7ojaWQfanyAIOJ1OH0tKOo7Ozk7MZjMrVqyQ96m8S0daQaBMT7DZbBOmqWdlZQXMNQsHqZNsqK4ekyGKIvHx8SQlJWE2mwGvsK1Zs4Y777wzYEda5f/S86VuHx6Ph5GREYaGhmhrawtpucLhVJVgxfuRnkssIrU6nW5CorNWq5X71EnL16GhIT755BOsVisLFizA6XSSkJAwK8mywYISkuC1trayePFifv3rX0f8/hyanwAwDJRM8vQvA38UD7cg/znwFHD0iZsSURRpb2+nv7+ftWvXTsjU7uzsxOFwRL3kkKyNQMtBKXCg7EIr3fWUxzeVpWRCQgKFhYUUFRXhcDiC+unCqaLQaDQYjUY6OzujFgblueTk5GA2m4mPj+e4447jZz/7WVh95PyDMlK5lNQXTlq+9vb2otVqfSzXkZEROjs7Wbp0aUyy8mOVglJaWhqy5lYq9Hc6nQwMDHDcccdhMplob2+XZ3zm5OSQnZ09a22OlL66d999lw8++IA//elP8vFPIyvxHQazB8gXBCFbFMXhIK+ZFWZM3NxuN/X19QiCwLp16yZc4EajkaGhoYi78QbCfxaDNAouLy9P7iCr7Okm4S+OoZJpgyG9RtmxVso1UzrrQ1k7Go2Gvr4+hoeHWbZs2aST4kMdh4SUsnDyySfz4x//OOyLcrIbjdSCXPJfGY1G2tvbsdlseDweysvLY1ZuFAthk973yRgeHqapqYnVq1ej1+tJSUnxKasaGhqS63hzcnLIzc2dlSXrBx98wA9+8AP+/ve/h1V2FwNS8A5slpB+TsVr+c0ZZmRZarPZ2LNnD4WFhSxYsGCCUNjtdjo6OoDoOzsoL2Zl8bzZbKa5uZmFCxeSmpo6IXAgESifLFD7nsmsu0DH7p+HJfnpent70el0srUjiYBUrD9ZV49Q+B9HSUkJGo2Gn/zkJ2HldEWzBFQmw7rdbvLy8uRUE6nFenp6upy+EgmxCM5otVpKSiZbdXmTuVtbW1mzZs2EigGNRiNbrkuWLGF8fJyhoSH279+Pw+GQUzVmolj+448/5tZbb+Wll14KKmwbNmzgnXfeCfi3k046iffffz/S3ZrxDmyWkH4OPOpsFpn2gILVauXDDz9k2bJlAcP/oihy8OBBOe3DZDIxODjIokWLwt6H/xe/o6NDFjJpKHN8fHzIwMFULh6l+Em5SuEi+emMRqPsP0lKSmLRokVRXRyx8ktF282lu7sbq9XK4sWLZWFWpmCMjo6i0+l8oq+TWcmxio4uXLhwQpt1fwYGBmhvb2f16tURW8xut5vh4WGGhoYYHR0lJSVFXr5GW1YVjE8//ZSvfe1rvPjii5SXl8dkm4Ig/AIomSSg8DTQKori/zv0+2nA06IoRhbCnwGmXdwkp3iwpUlnZyeDg4Py79I0qyVLloS1/UAXoVRtINUsShdLMLGIZcqG8mf/ZNpQuFwuGhoaiI+PlyOkkfjpputcwkXyp7rdbsrLy33qO/2x2Wxymkmgtkb+boFYkJ6ePukNs7+/n46OjqiEzR9J0AcHBxke9q7WpOhrJGVVgaitreWGG25gx44dYV8noXC5XLhcLhITE+/CG1C4AXCJojghzUEQhHOAbXijpb14U0E+movR0mkXNyDoqL2RkRFaWlp8HrPZbLS3t7N06dKwtu1/AXk8Hmpra4mLi6OyslJ+znQ6WcMVA//2R5KVYrPZaG5uprCwUE71kPx0RqMRk8k0qZ8ukuMIRST+RQllHznJ7RCuMEltjYxGo08FgbR8DeQXDVQfGgqNRsOKFStCClZvby/d3d2sXr16ygN7AuFwOBgaGmJoaAiLxUJGRgY5OTlkZWVF5Hqor6/n2muv5S9/+QvLli2LybH95Cc/4ac//an/wz8VRfEngncQcz2wQvTOL0UQhG/hm+d241GZ5waBxc3hcLB///4JwQMpi11K1QiF/wXkcDhk6yc1NZXc3NyQwharJdxUsFqtAZOJlSj9dP7LOskijkaUAhGpQMaqThQOWzvSeer1etl6DRWUUApeoGMvLS0NWRHR09NDb28vq1evnpHopzKdxmAwoNfr5aBEqKj4wYMH+fKXv8zTTz9NVVXVdBzavGoINyPi5nA4JjjsGxoasFgsE57r8Xior6+f9MPzFzaLxUJTUxNlZWV4PB46OjrkguPpjGJNxVqSUiUqKysnXLyhLBSln04qDM/Ozp5yDlak5yItpXNycsjLy4t6O8GQlq9GoxG32x2wAD4UUh5iRYiBFl1dXQwMDFBTUzNraR1Wq1W26pxOJ1lZWeTm5pKeni6fZ3NzM1dddRVPPPEEq1evnq5DUcUtUvzFzePxMDY2htVqZXx8HKvVKifuiqJIbW0t1dXVwQ/ar+TKYDDQ1dVFRUWF3LhQKpg2GAw4nU6f2QOB0kCiYSo+IWmAy2RlYkoCLWul3mAGgyFqP520vUiEUbKS/eeJxspP5v/5SJ/nyMgIVqs16IBrJRqNhuXLlwd15nd2djI0NER1dfWsj+WTcLlcGAwGBgcHGRsb44MPPkCj0fDMM8+wbds21q5dO527V8UtUvzFLRAul0ueFv/++++zfPnyoL46ZWStp6eH0dFReWhMoIiov18nWgFQEq04iqJIV1cX4+PjLFmyJGa+QI1GI5/nyMhI2H46iUjOR5onWlpaOuU60WiORQpSGY1GxsbG5LK3zMxMHyErKSmRu2v4097ezsjICKtWrZqzE6NEUeTvf/87d955J06nk+zsbG655ZYpdVCeBFXcIsXpdEZ0N//ggw848cQTcbvdsmUnWXkOh0Our2tubkar1co1guEEDqQLY3h4WBaArKws2YEdDtH6tyTHu06no6ysbNpTNpR1r4H8dOFsw59g80Rn038p9W9TLtOLi4tZs2ZNwM+ptbUVk8lEVVXVnBU28AY5LrvsMn77299yyimn0NfXh8lkikmENAiquEVKtOIWCClD/KOPPiItLY309HSsVmvYgqO8kCVHvcFgYHR0lPj4eLKysgLOCA22jXDx7+ox0ykbyvQLSQDS09MjKmQ3mUy0trayZMmSCX7M6VqORopkvWZkZMjuCGVUsqWlBYvFwsqVK+e0sPX393PJJZfw61//mtNOO22mdquKW6TEUtxMJhN79+6lsrKSrKwsebt2ux2r1YrNZpMtPf99TnbhjI+PYzAYGBkZkTPRpTrJcLcRCLvdTmNjo9zVI1YO92iR/FdGoxGbzSbnmUmWWKCbRKjgR6yIlUAWFRWRn58vRyUHBwcxGAxyWVx1dfWcHqYyNDTExRdfzC9+8QvOPvvsmdy1Km6R4nK5IqoX/fe//81xxx034c46MDBAU1OT/OUMVXEAhwVvfHxc/hduxxGpTlJKNJUmLUXa4cNisdDc3Ex5eTmpqamzlrIRCMlPJ/WnU/rpMjMz5WX60NAQvb29LF26NGAXkdlOp1GSlJREZWXlhOBLQ0ODHHAZHh5GFEW54+1Uk2pjicFg4JJLLuH222/nggsumOndz403IUbMSXH76KOPWLNmjXwhiaJIW1ubT2RrMmELhtPp9PHhSX68yY5fEjrpAsnKypr0opCsnSVLlsiWwmxHaUMRKJ9Oq9XicDhYtmwZOp1uQqlUrIQtVtbssmXLfJbMkrCJosjSpUvlz8vhcDA8PMzg4CAWi0UetZeVlTVry9WRkREuueQSvvvd73LRRRfNxiGo4hYpkYrbJ598Is+BlGaICoLgU7UQyy+g2+32ETyr1TohUitd0FInXoPBgMViISUlhaysLHnqu8TAwACDg4NyQ0zlNuYCk4mJVE41NjYmT1uXAhLK/v3+4h5u1YCSWL0vBQUFFBYW+pzDgQMH0Gg0E6w5JdIsicHBQYxGI0lJSeTm5pKTkxPzmtBgjI2Ncemll/KNb3yDyy+/fEb2GQBV3CIlUnHbvXs3S5YsIS4ujt27d5OXl0dJSUnU1lo0eDweWeiU/ysRRVEemzc2NiZPRLdYLNjtdp/i8VgQK0tpMjFR1olKY/eUfrrx8XEf6zVUza60vekmISGBZcuW+eyzvr6e+Pj4kPMm/JGs18HBQYaGhgDk6oFwk4cjxWw2c/nll3PDDTdw1VVXxXz7EaCKW6SEmqMQiLq6OnJycmhubmbJkiVkZ2cHbVU0k4iiKAcslCkqUkKtxWKhpaUFp9Mp10hmZmYSFxc3p/xSoQhUJxroOZKoR5JPF6ihQKyWo0uXLpVnG4iiyL59+0hMTIxqJqoSqSZ0cHAQq9Uqz1nIzMyMyerBarXy+c9/nquvvprNmzdPeXtTRBW3SIlU3Hbt2oXZbGbNmjUkJibOqMUWDTabDZPJxCeffCJPjZJ8V0ajESDi+aD+xKooPpTIut1uGhsbSUtLC1knGiidJlTdazCkpqKT1YZORn5+vny8khsjOTk5orZZ4eC/fFXOWYhm+Wqz2bjyyiu55JJLuOGGG+bC93vWDyCWzClxk5ZDbW1tLF26VO5nP5eFDZCbcS5cuFCexelwOGTLzmQy0d3dTX9/f8BSsMmIVYQ11HI0WJ1ooGMJJZCB6kH9/XThEKyDij96vZ5ly5bJ51ZbW0t6ejoLFy4Me1/REKilkeSnC+dztdvtXH311Zx77rls2bJlrny/58RBxIoZETdpgtJkz6mvr0cURbkAfMGCBdPSfiaWmEwm6urqWL58uTzVPRhS2kVPTw9dXV0YjUYSEhImLQWb7rw4qU40nOlakRxLID+ddK7RduNVHoPH46GyslLuprJ3716ysrJ8plrNFNKIwMHBQcbHx+Xi90BjAp1OJ1/+8pc55ZRTuOWWW+aKsIEqbpEzmbg5HA727NlDTk4OCxYswGq10tHRwcjICGlpaeTl5ZGdnT3nMsqHh4dpbGyMekivx+ORp4n39/ej0+lITk4mISFBPtfpXo5GUic6lWORmiVI816l4Es4da/ByM3NpaSkBLfbzd69e+Xvz2zjdrvl5as0JjA3N5e0tDT0ej3XXXcdxx57LN/73vfmkrCBKm6RE0rczGYze/fuZfHixROmvouiyOjoKAMDAwwPD5OcnCxPK59ti667u5uenh5qampiki4giiJjY2MMDAwwNDQkt+tJSkrC6XQyPj4etbAEE6VgdaLBji9WF+JU/HQS8fHxLF++HFEU2bNnD/n5+TM1ICUipOXrwMAAW7Zsoaenh8WLF3PfffeF3ZB1BlHFLVJEUQyYKDs0NMTBgwdlyydURFT6kvT39zM0NERCQoI8zWqqLaEjQRRFWlpaMJvNVFVVTVurHIvFIufKabVacnJySEtLQxRFn0jtZPlhwYTNZDLR1tZGRUVFWEGOWC2NA20nGj+ddNzS4KGpNsqcbtxuNzfddBNpaWlUVVWxc+dOrr32WjZt2hTV9qQp8bW1tVx55ZVs27Yt6HPvvfde7r77bsbHx7nkkkt44IEHgt1EVHGLlEDi1t7eTl9fHzU1NXLmeySBA+XFr9PpZKGbrrpHOOwXlFqYz9SSwmazMTg4yMDAAG63W3b6JycnyxUXSsGTgjfBrK1I60RjJWzhJOuG8tNJS/Xs7GyKiorYvXs3JSUl8sStuYrH4+Hmm28mIyODX/3qVzFxr0hT4l977TXGx8eDittrr73Gl770Jf7xj39QVFTERRddxPHHH89dd90V6OmquEWKUtw8Hg8HDhzA5XKxcuVK+cs+lQ98fHxcFjrw+mLy8vJi2oHX6XRSW1tLdnY2ZWVlMdtuNMcxNDTEwMCA7LjOy8vz6dqqFDxJ9KT3f2hoiP7+fp/KiVDEcjkaKUo/nZRPl5uby9q1a9m/fz+lpaVydHqu4vF4+O53v4tWq+V3v/tdzP3Gt912G11dXUHF7Qtf+AILFy7kl7/8JQBvvfUWV111FX19fYGePq/EbUYcV8qLbs+ePXJEK1aJuYmJiZSVlVFWVobdbmdwcJD9+/fjcrlkoYvG4S8RKNVjtoiLi6OwsJDCwkLcbjcGg4Hu7m72799Peno6eXl5cn86ZYDA7XbT0NAAwAknnIDD4cBms026v9msHdVoNBPmvSYmJvLRRx+RlJQkn8Nc7fDh8Xi4/fbb8Xg83H///bMSENu3bx8bN26Uf6+pqZG7QIeaKzEfmDGvvMViYc+ePSxatGjC1PdYotfrKSkpoaSkBKfTyeDgII2NjdhsNnJycsjPz4+oC0QkqR4zjVarlafai6LIyMgIAwMDNDY2kpycTF5eHjk5OWi1Wtrb23E4HJx++unyRTZZidlMLkcnQxAECgoKMBqNVFdXk5yczODgIPv27ZOX6nOpw4coivz85z9nZGSERx99dNYi/Waz2ecmJ/1sMplUcYsFUtb4ypUrfSY8TfeXMC4ujqKiIoqKinC5XAwPD9Pa2orFYiE7O3vCcs4fKdVDupjmMoIgyOVeygidJGoJCQkTWmprNBqSk5N9zk1ZYmaz2bBYLIyPj09JnGJRFO/xeBgcHGTp0qXyRVlaWkppaam8VJc+28zMTPLy8gLmmM0Eoihy11130dPTw7Zt22Z1PkNKSgpjY2Py79LPqamps3VIM8aMiJtGo2HdunVye/DZqDjQ6XTk5+eTn58/YTmXkZFBfn6+z8UgpXocc8wxM9YZIlYIgkBqairJycmMj4+TmppKUlISdXV1iKIoL9WlWkz/1yYmJk7wVyp740mBi3CaIcTC+rPb7ZhMJo499tiAScbKpbpUItXf38/BgwdJSUmRKwdmIn1IFEXuvfdeGhoaeOqpp2Z98MzKlSvZs2eP3GlESpuZ71YbzJC4dXd387//+79ceOGFrF27dtaXDcrlnNStVboYUlNT8Xg8eDwejjnmmFn/ckaLlNiamZkplyItXLgQh8PB4OAgBw8exOFwyBZsampqyM9Fr9ej1+vJzMyUH/PvjaecYgaxETabzUZvby+nnXZaWG4BjUZDdnY22dnZcteWwcFB2tvbiYuLkz/36fDTiaLI1q1b2bVrF88+++y0iqk0Jd7tduN2u7HZbOh0ugn7/NKXvsQ111zDVVddRWFhIXfccQfXXHPNtB3XXGJGoqU2m42//e1vvPDCC9TV1XHqqaeyadMm1q9fP6fEQxIEu92OKIpzKmk4EqTATWFhYcjEVmmpPjAwgNlsjslyTppipozUBptiNhk2m43m5mbOOecccnJyotqGkvHxcQYHBxkcHMTtdsvCHgs/nSiKPPLII7z11lvs2LFj2q39QFPif/zjH3PttdeyYsUK6uvr5TK03/zmNz55bg8++KCa50aMxE2JzWbj9ddfZ/v27Xz66aecdNJJbNq0iRNPPHFWBcTlcrF3716ys7PlL8VcSBqOFLvdLkd2QxXA+yMt5wYGBhgZGSE1NVUue5vqDcjj8cgWnrJlVCiksrBTTjllWorgJT+dshNvtK2MRFFk27Zt7Ny5kxdeeGHORm/DQBW3WOFwOOQ73Ycffsjxxx/Ppk2b+MxnPjOjAhJOqsdsJA1Hyvj4OHv27JGH50SLshRseHh4WoRdWWmhtPKkxxsbG1m9ejU1NTUx2V8o/IU9Uj/dk08+yfbt23nppZdimls5C6jiNh04nU7effddnnvuOd5//32OPfZYNm7cyGc/+9lpFZBoUj1mImk4UqTzWLlyJWlpaTHdtn8pmHS+02GhDA0N8cknn1BeXs7ChQtnPJij9NMNDQ1N6qd79tln+dOf/sTLL7885yPqYaCK23Tjdrt5//332b59O2+//TarVq1i48aNnHHGGTEVkKl29QDkpOGBgYGYJQ1HysjICAcOHJjSeYRLqFKwqfqtJIGeS6k3gfx0qamp5OTk8OKLL/Lwww/z8ssvz5fUClXcZhKPx8OHH37I9u3beeutt6isrGTTpk2cddZZU7oAenp66O7ujllXD0BOGh4YGIg6aThShoaGaG5upqamZsZ9PeGUgoXL2NgY9fX1VFdXB0xRmQtI5/unP/2JJ554Arfbzf3338955503p/2wEaCK22zh8XjYtWsX27dv57XXXmPhwoVceOGFnHvuuWEvxaSuHiaTiVWrVk1btFaKRPb394edNBwpvb29dHV1xVSgo0XKHRwYGGBsbMynFGwyB/3o6Cj79++npqbmiPBZvfbaa9x9993ceuutvP3225jN5pBdOSbDYDBw3XXX8frrr5OTk8Odd97JF77whQnP27ZtG9ddd53Pe7Rz5042bNgQ9b79UMVtLiC1lN6+fTuvvPIKBQUFbNy4kfPPP98nF8v/Nfv370er1frMsJxu/C/8jIwM8vLypjRkpLOzk8HBQaqrq+dcmorH45H78BkMBp9SMP9jNRqNHDx48IgRtrfeeouf//znvPzyy+Tm5sZkm1deeSUej4c//vGP7N69m/PPP58PPviAlStX+jxv27ZtPProo7z//vsx2W8AVHGba4iiyP79+9m+fTs7d+4kMzOTjRs3csEFF8j5UVJXj6ysLMrKyma104WUNKzsNJyVlRWWFansJ+dfTjUXUZaCSQ56KfJqsVhoaGhg9erVR0T6xLvvvsttt93Gzp07Y9ZmSUpDqauro7KyEoAvfvGLFBcXT2hLpIpbZMwLcVMiiiJNTU0+ofkNGzbwwgsv8MQTT7B48eLZPkSZSDsNi6LIwYMH8Xg8LF++fNYrPaLBarUyODhIT08P4+PjlJaWUlRUNGf9bBIffPAB3/3ud9m5c2dMG2N++umnnHjiiT55f7/+9a955513+Nvf/ubz3G3btrFlyxYSExPJysrii1/8Ij/4wQ9iabkfeV+oEMw7cVMiiiKvvvoq1113nTyY94ILLmDTpk0UFRXNKXGYrNOw1HwgISEhoiHDc5GhoSFaWlpYsWKFLO6RlILNNB999BG33HILL730UsxnNLz33ntcdtllPv3VHnnkEZ566inefvttn+e2tLQgCAJlZWXs27ePz3/+87LAxYi586bHgLnlrJkGtm3bxj//+U8qKyvp6elhx44d3HDDDTidTi644AI2btw4q8tUCanYPTU1lYqKCjm37NNPP0Wr1WK328nLy6OiomJWj3OqDAwM0NbWxurVq4mPjyclJYXi4mI5ANPe3h6zUrBYsGvXLr75zW/y17/+dVqGz/h37QBv5DhQaolyDuuqVav40Y9+xD333BNLcZtXzGvLLRiiKNLf388LL7zAjh07MJlMnH/++WzcuHHOWUVOp5Ndu3aRlJQk12jOhaThaOjv76ejo4PVq1eHTJ2YzlKwSNi7dy9f+cpX2LFjB0uWLJmWfUg+t3379sn7+NKXvkRRUVGwVuAyzz77LHfffTe7du2K1eHMnS9+DDgqxc2foaEhXnzxRXbs2MHQ0BDnnnsuF1544az7tQLVic6FpOFo6O3tpbu7m9WrV0fkI/IvBUtMTJQrBqYzt6y+vp5rr72Wv/zlLyxbtmza9gNwxRVXIAgCjz76KLt37+a8884LGC39+9//zjHHHEN+fj4HDhzg0ksv5bLLLuPHP/5xrA5FFbf5jNFo5KWXXmLHjh10dXVx1llnsWnTJqqqqmZ0eWS1Wtm7d2/IOtHZSBqOhp6eHnp7e+VhQFNBmvI+naVgBw8e5Mtf/jJPP/00VVVVMdtuMAwGA9deey1vvPEG2dnZ3HXXXXzhC1+go6PDp8PHrbfeypNPPonZbCY/P5+rr76a22+/PZYiP3e+NDFAFbcQjI2NsXPnTnbs2EFzczOnn346mzZtYs2aNdMqdNHUic5E0nA0dHd309/fT01NTcyXlNNRCtbc3MxVV13FE088werVq2N6vEcAqrgdjVgsFl555RV27NhBfX09GzZsYNOmTaxbty6mF+3IyAj79++fUn3ldCQNR0NnZydDQ0NUV1dPu6/MvxQsOzub3NzciMS9vb2dK664gj/+8Y+sXbt2Wo93jqKK29GO1JPuueeeY/fu3Zx88sls2rSJE044YUrLrumoE51q0nC0dHR0YDAYqK6unvFoZzSlYF1dXVx++eU8+OCDHH/88TN6vHMIVdxUDiP1pHvuuef46KOPOOGEE9i0aRMnn3xyRL6QmagTjTRpOFra2toYHR2dExUUkrgPDg4GLQXr7e3l0ksv5b777uMzn/nMrB7vLKOKm0pgnE4n77zzDtu3b+f9999n7dq1bNy4kQ0bNoTsSTcbdaKTJQ1Hi1QaNtMBmHDwLwX75z//idvtZufOndx7772cdtpps32Is40qbiqT43K55J5077zzDtXV1WzcuJHTTz9dzk+T6kQtFsusi8FUOw2LokhzczM2m42VK1fOqWhtMP7zn//wwx/+EIvFQkZGBtdee+2Uh6eE2+ED4N577/WZbfDAAw/Mdmfnuf+hRYAqbjOA2+3mww8/ZMeOHbz55pssW7aMz33uc/z973/noosu4rzzzptTYqDsNCyKInl5eSGThqV6XofDwYoVK+bUuQTDYDBwySWX8KMf/Yjzzz+fgYEBWltbOe6446a03XA7fLz22mt86Utf4h//+AdFRUVcdNFFHH/88ZMm7k4zc/+DiwBV3GYYj8fDf/7zH6677jq0Wi0VFRVs3LiRc889d052c50saVgURRoaGvB4PCxbtuyIELaRkREuueQSvve977Fp06aYbTeSDh9f+MIXWLhwIb/85S8Bbyulq666yqfGdBaY+x9eBMz72tK5hkajYfv27dxwww1885vfpLa2lueee47zzjuPwsJCuSdduPMcphu9Xk9JSQklJSVy0nBjY6OcNGy1WomPjz9ihG1sbIzLL7+cb33rWzEVNoCGhga0Wq0sbAA1NTW88847E567b98+Nm7c6PO8/v5+hoeHj4qByTOBKm6zwC9/+UvZt1JTU0NNTQ0///nPqa+vZ/v27WzatInMzEw2bdrE+eefH5OZnbEgLi6OoqIiioqKcDqd7N27F5vNhkajobGxcU4kDYfCbDZzxRVX8NWvfpXLLrtsWrafnp7u81h6ejomk2nS50o/m0wmVdxihCpus0Agp7EgCKxcuZKVK1fyox/9iMbGRrZv387nP/95EhMT2bhxIxdeeCF5eXmzLh5SX7n09HSOOeYYPB4PBoOB7u5u9u/fP2tJw6GwWq1cccUV8vT16SCSDh/+z5V+nouuiSOVufHNU/FBEAQqKyv54Q9/yAcffMCjjz6Kw+Hgi1/8Iueddx5/+MMf6OnpYRJ/6bTg8Xioq6sjKSlJ7qAi1XiuXLmS4447jvz8fAYGBvjPf/7Dvn375MlRs4XNZuMLX/iCLG7TRWVlJS6Xi8bGRvmxPXv2TAgmAKxcuZI9e/b4PE/KOVSJDfMuoHD//fezbds2amtrufLKK6c0uGOuIYoi3d3d7Nixg+effx632y33pCstLZ12i06aW5GWlkZ5eXlYxzsTScOhsNvtXH311Zx77rls2bJl2t+jcDt8vPrqq1xzzTX84x//oLCwkEsuuYT169er0dIYMu/E7fnnn0ej0fDaa68xPj4+r8RNidST7vnnn+f555/HbDbLPekWL14c84vY4/Gwd+9eMjMzKSsri+p4pyNpOBQOh4Mvf/nLnHrqqdxyyy0zspwPt8MHwG9+8xufPLcHH3xQzXOLIfNO3CRuu+02urq65q24+TM4OCj3pBseHua8887jwgsvjEkU0+12s3fvXnJycmLWjdZ/ir2USxeri9vpdHLdddexdu1avve97826n/IIYV69Saq4zUMMBoPck667u5uzzz6bTZs2sXLlyogd/G63mz179pCXl0dJScm0HG+kScOT4XK5+J//+R+WL1/O7bffrgpb+MyrN0oVt3nO6OgoO3fu5Pnnn6e5uZkzzjiDTZs2sXr16kmFzuVysWfPHgoLC2M68SkUU+007Ha7+frXv05JSQl33HGHKmyRMa/erCNK3DZs2BAwIRLgpJNO8pnnqIrbRMxms9yTbv/+/Xz2s5+Ve9L5C53L5WL37t0UFxdTWFg4K8cbqNNwqOlYHo+Hm2++mczMTO6+++45k4Yy04iiGK2oq+J2JKCKW2jGx8d5/fXX2b59O7t37+Yzn/mM3JPOYDDwn//8h3Xr1pGfnz/bhwpM3mnY4/Hw3e9+F51Ox29/+9ujStjcbnesevOp4jaXcblcuFwufvrTn9LV1cUjjzyCTqebsdSDIxG73S73pPv3v/+Nw+HgS1/6Erfccsu0DmGJFmUzysbGRp5//nni4+NJTk7moYceOmqF7Xe/+x29vb2sWLGCDRs2yFHZCJhX4jbvvgV33HEHiYmJ3HXXXfzf//0fiYmJ3HHHHbN9WHMavV7Peeedx69+9SvS09PZvHkzvb29nHTSSWzZsoXXX38dh8Mx24cpo0waPvfcc0lLS2Pfvn1yQ4Le3t6Y7s9gMHDRRReRnJxMWVkZTz/9dNDnbtu2Da1WS0pKivzPf7jyVGhqasJmswHeZbgkbCeeeCL/+Mc/aGpq4qmnnuKRRx7B6XTOSqL3XGHeWW4q0bNr1y6GhoY466yzgIk96WpqauSedLGcNhUtoihy55130t7ezrZt2xAEgf/85z/U1NSQlJQUs/2E28YIvOL26KOP+vh/Y8Wzzz7Lbbfdxscff+zTWOGLX/wiY2Nj/PWvfwXg4Ycf5ne/+x2ffPJJpJ+TarmpzE+OOeYYWdgAdDodGzZs4P7772f37t3ceOONfPDBB2zYsIHNmzfz4osvYrVaZ+VYRVHkN7/5DU1NTTz++ONotVo0Gg0nnHBCTIXNYrGwY8cOfv7zn5OSksLJJ5/MhRdeyJNPPhmzfUyGZIC899576HQ6n4lozc3NGI1GfvrTn8qPXX311YiiSHt7Ox6PZ8aOc66hiptKWGi1Wk4++WTuvfdedu/ezbe//W12797NGWecwdVXX81zzz0XsPvFdCCKIvfffz+ffvopTz755LT6U4O1Mdq3b1/Q13z66afk5ORQWVnJz3/+c1wu15SOQRK33NxcrFarT8H94sWLue2223xyEDUaDaIoMjw8LPsf29rapnQMRyKql10lYjQaDevXr5drIffu3ctzzz3HfffdR1FRERs3buS8886blp50oijy8MMP8/7777Njx45pD3hE0sYI4JRTTqGuro6ysjL27dvH5z//eXQ6HT/4wQ+iPgZJoPR6PaOjoxPEUprWJYqibKlJdbwAt956K83NzWzfvn3aRyzOJVTLbZqIxAl9JKPRaFi9ejW/+MUv+O9//8udd95JV1cXmzZt4uKLL+aJJ55geHg4JvsSRZHHH39cHqsYiylhGzZsQBCEgP9OPvnkiNoYASxatIjy8nI0Gg2rVq3iRz/6Edu3b4/q2P71r3/xyiuv0N7eDsCCBQvQ6XQ+AQUlgiDIVptGoyEzM5Pbb7+dZ599lkcfffSoEjZQLbdpY8uWLcTHx9Pf3y87oWtqagI6oecLgiBQVVVFVVUVP/7xj2loaGD79u1cfvnlJCcnc+GFF/K5z30u6p50Tz75JH/961956aWXYhbQmCySabFY5DZGS5YsAYK3MQqEIAhRRSxbWlrkMYMFBQWceOKJJCYmIggCTU1NlJSUyBadx+ORRU0QBBISEkhNTeWCCy6gra2NTz75hOzsbFwu11GVEqVGS6eBSHrpHw2Iokhrays7duzgxRdfJC4ujs997nNs3LiRwsLCsITu2Wef5YknnmDnzp1hl2LFinDbGAH8/e9/55hjjiE/P58DBw5w6aWXctlll/HjH/844v2+/vrrjIyMsG3bNhoaGujr68NqtXLKKaewatUqzjvvPKqrqykuLpZfI4oiFouF5cuX43A4+PTTTykqKgo30XdeRUsRRTHUP5Uo2LVrl5iQkODz2D333CNecMEFs3REcwePxyN2dHSI9957r3jKKaeIJ510knjnnXeKBw4cEM1ms2ixWCb8e/LJJ8VTTjlFHBsbm5VjHh4eFjdu3CgmJSWJCxYsEJ966in5b+3t7WJycrLY3t4uiqIofvvb3xbz8vLEpKQksby8XLz99ttFh8MR0f48Ho/P73a7XXQ6neLPfvYzURAEcd26dWJqaqooCIKYl5cnHnvsseJLL73k85odO3bIx+RyucLd9WR6cET9Uy23aeC9997jsssu85lk9Mgjj/DUU0/FNKHzSEcURfr6+uSedFarVe5Jt2jRIgRB4G9/+xv33XcfL7/88pwZmjOTSBeqRqPhX//6F5dffjkPP/ww69ev5+mnn2bXrl00NTXx9ttvBwyuRFiaNa8st6NnAT6DROqEPloRBIHCwkK2bNnCli1bGBwc5IUXXuDWW2/FYDCwZMkSGhoaeP31149KYQPk4AZ4o6W9vb0kJSWRm5vLN7/5TeBwoXwgn9rRFkRQokZLp4FIeumrHCY3N5evfOUrvPbaa7z22mvk5+fz9NNPk5WVNduHNieQosOB5lGIonhUBQvCQV2WThOROKFVVMKhp6eHhQsX8qc//Ykrr7xyOnYxr5alquU2TfzhD39gfHycvLw8rrzySh544AFV2FSmREZGBi6XC4PBMNuHckSgWm4qKkcI+/fv5/Of/zyvvfbadDUQVS03FZUjkfvvv5+1a9ei1+vDml967733UlBQQHp6Otdeey12u336DzIEy5cv58MPP6SwsHDK9apHA6q4qRw1FBUVcdttt3HttddO+tzXXnuNu+66i7feeou2tjZaWlqiSsSNNVLHEzV4MDmquKkcNVx88cVs2rQprKnuf/rTn7juuutYuXKlXKOptqw/slDF7Sgj0qXZ0cq+ffuoqamRf6+pqaG/vz9mTQBUph9V3I4yIlmaHc34tzqSfp6pnnUqU0cVt6OMSJZmRxKTtS6KFP8qE+lntcrkyEEVN5V5wdtvvx20gDqaeQYrV65kz5498u979uwhPz9/3t0U5jOquKkcNbhcLmw2G263G7fbjc1mC5pS8aUvfYk//vGP1NfXYzQaueOOO1Qf5RGGKm5BMJvNE4rfVY5sQo197OjoICUlhY6ODgDOOeccvvvd7/LZz36WsrIyysrKfIawqMx91AoFP6QOC8888wxXXXUV999/P1/72tdm+7Bizm233UZXV5ea3qCiRK1QmM9I7WVOP/108vLyaGpqApCXL+Pj40d0bV8kSzMVlSMZVdyCkJubS2pqKv/6178Ab0b4xx9/zJVXXklOTg633367PKjjSCLU0kxFZT4x2bL0qEQQBEn0HwHOBM4DvgTcCAwCPwfeFEWxa3aOUEVFZTLUAjU/BEEQRFH0HPq5E8gB3gXswAPA70RR7FE8V707qKjMQVRx80MURVEQhHTgMuAmIAF4A/ieKIoHpOcphU0QBO2hl3oCbVNFRWXmUX1uCgRB0AqCcDHwKvA74CDQBdSLonhAsVyVRDDr0M9uVdhUVOYWqrgBgiDEC4LwWeBlYDvgBi4EPgeMAUsDvCYT+LYgCP8WBOExQRDUNrsqKnMIdVnqpQR4CEgErhZF8WnpD4IgGIEVgiBkiaKozAGJB94CzMA3gGHgO6ofTkVlbqCKGyCKYgtQKQhCmiiKY4IgaEVRlEYMfYg3Sur2e00/0C8Igh6oB/5+6E8CR2Hys4rKXENdliL72oRDwiYohA3gUyAZuCTA6+KAVXgF7T0A1femojI3UC03vAEBxc+y1XVI6J4WBOFtDpWmHAoqiIeeVwJUA7tFUXQKgqBRxU1FZW6gilsIDkVENVJe26HHPJLAAZVAKfDkbB2jiopKYNRl6SQEssQUj63CK3LvB3uuiorK7KBabhEiCMIqYAPQijdF5D1RFC1+QQgVFZVZRhW3yBkCjgXuwZsO8r4gCBWiKDbN7mGpqKgoUQvnp4AgCOuBW4BFwEZRFPtm+ZBUVFQOoYpbhAjehm9aURTVJmgqKnMYVdymwKGoqUYVOhWVuYcqbioqKvMSNRVERUVlXqKKm4qKyrxEFTcVFZV5iSpuKioq8xJV3FRUVOYlqripqKjMS/4/bx5cmbIRFP8AAAAASUVORK5CYII=\n", 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