{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Omnibus Embedding for Multiple Graphs\n", "\n", "This demo shows you how to simultaneously embed two graphs using omnibus embedding from two graphs sampled from different stochastic block models (SBM). We will also compare the results to that of adjacency spectral embedding, and show why it is useful to embed the graphs simultaneously." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import graspologic\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulate two different graphs using stochastic block models (SBM)\n", "\n", "We sample 2-block SBMs (undirected, no self-loops) with 50 vertices, each block containing 25 vertices (n = [25, 25]), and the following block probabilities:\n", "\n", "\\begin{align*}\n", "P_1 = \n", "\\begin{bmatrix}0.3 & 0.1\\\\\n", "0.1 & 0.7\n", "\\end{bmatrix},~\n", "P_2 = \\begin{bmatrix}0.3 & 0.1\\\\\n", "0.1 & 0.3\n", "\\end{bmatrix}\n", "\\end{align*}\n", "\n", "The only difference between the two are the block probability for the second block. We sample $G_1 \\sim \\text{SBM}(n, P_1)$ and $G_2 \\sim \\text{SBM}(n, P_2)$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from graspologic.simulations import sbm\n", "\n", "m = 50\n", "n = [m, m]\n", "P1 = [[.3, .1], \n", " [.1, .7]]\n", "P2 = [[.3, .1], \n", " [.1, .3]]\n", "\n", "np.random.seed(8)\n", "G1 = sbm(n, P1)\n", "G2 = sbm(n, P2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualize the graphs using heatmap\n", "\n", "We visualize the sampled graphs using heatmap function. Heatmap will plot the adjacency matrix, where the colors represent the weight of the edge. In this case, we have binary graphs so the values will be either 0 or 1. \n", "\n", "There is clear block structure to the graphs, and we see that the second, lower right, block of $G_1$ has more edges than that of $G_2$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
", "image/svg+xml": "\n\n\n\n \n \n \n \n 2021-03-11T12:26:53.281814\n image/svg+xml\n \n \n Matplotlib v3.3.0, https://matplotlib.org/\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n 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\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n 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\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n", "image/png": 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", "image/svg+xml": "\n\n\n\n \n \n \n \n 2021-03-11T12:26:54.530980\n image/svg+xml\n \n \n Matplotlib v3.3.0, https://matplotlib.org/\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n 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\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n", "image/png": 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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "from graspologic.plot import heatmap\n", "\n", "heatmap(G1, figsize=(7, 7), title='Visualization of Graph 1')\n", "_ = heatmap(G2, figsize=(7, 7), title='Visualization of Graph 2')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Embed the two graphs using omnibus embedding\n", "\n", "The purpose of embedding graphs is to obtain a Euclidean representation, sometimes called latent positions, of the adjacency matrices. Again, we assume that the probability matrix of a graph is given by $P = XX^T$ and we are trying to estimate $X$. The benefit of omnibus embedding is that the latent positions of all embedded graphs live in the same canonical space, thus eliminating the need to align the results.\n", "\n", "We use all of the default parameters. Underneath, the select_dimension algorithm will automatically find the optimal embedding dimension for us. In this example, we get the following estimate,\n", "\n", "\\begin{align*}\n", "\\hat{Z} = \n", "\\begin{bmatrix}\n", "\\hat{X_1}\\\\\n", "\\hat{X_2}\n", "\\end{bmatrix}\n", "\\end{align*}\n", "\n", "where the first block, $\\hat{X_1}$, are the latent positions of the first graph, and the second block, $\\hat{X_2}$, are the latent positions of the second graph." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "tags": [] }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "(2, 100, 2)\n" ] } ], "source": [ "from graspologic.embed import OmnibusEmbed\n", "\n", "embedder = OmnibusEmbed()\n", "Zhat = embedder.fit_transform([G1, G2])\n", "\n", "print(Zhat.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualize the latent positions\n", "\n", "Since the two graphs have clear block structures, we should see two \"clusters\" when we visualize the latent positions. The vertices that form the first block should be close together since they have the same block probabilities, while those that form the second block should be further apart since they have different block probabilities." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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S6qPV4Vcp1Y5uf/E8dM3fekw3rxcn8PHyP6Bm65L/gp52+1LZsUfR/2m42Ww/Yh3fAfxV9QMr3V+tVv+3dnRpQ7opr2Dj/IH5O7Pch9BTb/cbhpGFVf9+/H/Rv2vqfS0qlP1O2IkePSx/7New8vquhpk/g99Gf7+/req5X4nUd62a1HidR9TS+5S9A13T9T7gfyrdIPBX6GH/V6OLzV9f436Pmvf5vFLqQSCOLhC+07z9ZnQh9BeUUv8F3S9nHj1CtAc9VfUSzB5Nq7TcOayZYRjfVUr9Fbon0s/Mgvkkeln0i9CFouW9jN4PXKeU+r/oVVMJ4DLz+AiNjXY8CrxBKfVP6BGcPPCEYRhPLHGft6OL3T9h9n06ykIfrxK68Di+xP2X8wrzsb8H/BL9dRtAj0qUqHwPms4wjIT5R+orwBGl1FfQRfT70b2TzlL1S36jGIYxYb7nj6BD2BuVUt9AB0Vry6B2dOj63ToFx+eqn6D7hz2llPpXFvp4taFbCNjF3oZhnFFKHUbXNR5XSv0zuofdf0SvGK4OJXuBf1RKPYkeDZpAF5a/Bl1H9XFW5rV1RudAr9S7Z4WPt1JfB/5NKfUP6JrDa8zLCPAnVceu9PfjX6NHlf8TcEwp9X9Y+Fo8ga67rPZOdB+v/2l+f/4YHYZ+B9265LfX9nKX9E7076PPKKX+Iwt9vP4TehGF9XtDrMRmLaeUS+MXll9ibWD2BkI3w3sE/YOeRK+i+n+o0zfKvM970L8ws+YxI1W3h9D9Z55CB5A0Ooz8M7qJZLDs2FtYwVL0Rs+hzmMdqPd4S9znDeiQFUdPGzyNLqD3VR3379H/O/05us4iCZwA/gYYqjr2Q9Rext+Dnr6aRE+nGsCHzNuW+nr0o+tiRtEF3DPokaIX1zh2Re83eoXVp9CBbtp8v0fQIzm/uYL3seZrNm/7Nsu0P0E3kHzIPIccOnx9Fuircew91G95stR5LPneLHFuQfP78Tss9Lk6C3wN/QdS1bnfSL3v26Xek1qvr+x7+0ONPtcS34eG+fx96JGtKfT3/jHg5jqP70WH8HHz9T+LHjV31fieGkA3If43833Kmvf7OnDDCt53631Y6lL+vMPU+Rmq9b2/kvfP/N45jv5dN43+XbC9zmM1/PvRPD6M/hk8bX4dfgG8Fx1o6v1OeB76Z3Qe/bvoe+j/CNzCyttJNPS7ouz6S9H/ca9+7v9KVYsPuTR2UeYbK4QQQgjREHNU9GZ0U9tGd1AQSI2XEEIIIWpQSjlUjT0qlVLXo0tXfi6ha+WkxksIIYQQtXiAU0qpx9FTogV0resr0FPQ79zEcztvyVSjEEIIIRYxV33/T+A6dC1fAF1z+gTwMcMwflT/3qIeCV5CCCGEEBvknJ1q7OrqMoaHhzf7NIQQQgghlvXUU0/NGIbRvdxx52zwGh4e5ujRWnt5CiGEEEKcW5RSo40cJ6sahRBCCCE2iAQvIYQQQogNIsFLCCGEEGKDnLM1XkIIIcT5Lp/PMz4+TiaT2exTEU3i8/kYGBjA7Xav6v4SvIQQQoh1Mj4+TigUYnh4GKXUZp+OWCPDMJidnWV8fJydO3eu6jFkqlEIIYRYJ5lMhs7OTgldW4RSis7OzjWNYErwEkIIIdaRhK6tZa1fTwleQgghhBAbRIKXEEIIsYVNTk5y8803c9FFF7F//35e8pKX8NBDDzXt8YeHh5mZmVnymNnZWa699lpaWlp417ve1dDj3nLLLezcuZPLL7+cSy+9lA9/+MP2bQcOHFhVk/UPfehDfPKTn1zymCeeeIJ9+/bhcrl44IEHVvwcy5HgJYQQQmxRhmHw2te+lpe+9KWcPHmSp556ii9/+cuMj48vOrZQKKzbefh8Pj760Y8uG3qqfeITn+D48eMcP36cL37xizz33HPrdIYLBgcHueeee7j55pvX5fEleAkhhBDnisOHYXgYHA798fDhNT3cY489hsfj4e1vf7t93dDQEO9+97sBuOeee7jxxhu57rrruP7660kkElx//fXs27eP3bt389WvfhWAkZERLr30Ug4ePMiuXbu46aabSKVS9mN++tOftu/zi1/8YtF5BINBrrnmGnw+36peh1XMHgwGF912//33s3v3bl70ohdx++2329d/4xvfYN++fezdu5frr79+0f0+//nPc8MNN5BOpyuuHx4eZs+ePTgc6xORJHgJIYQQ54LDh+HWW2F0FAxDf7z11jWFr6effpp9+/YtecyxY8d44IEHOHLkCD6fj4ceeohjx47x+OOP8973vhfDMAA4ceIE73jHO3jmmWcIh8N85jOfsR+jq6uLY8eOcdttt614VGsp73vf+7j88ssZGBjgDW94Az09PRW3T0xMcPvtt/PYY49x/PhxnnzySR5++GGmp6d561vfyoMPPsiPf/xjvvKVr1Tc78477+RrX/saDz/8MH6/v2nn2wgJXkIIIcS54NAhKBtFAvTnhw417Sne+c53snfvXl784hfb173iFa+go6MD0FOTH/jAB9izZw8vf/nLOX36NJOTkwDs2LGD3/qt3wLgjW98I9/5znfsx3jd614HwP79+xkZGWna+VpTjWfPnuXRRx/lu9/9bsXtTz75JAcOHKC7uxuXy8XBgwd54okn+P73v89LX/pSu9eW9foA7r33Xr7+9a/zwAMP4PV6m3aujZLgJYQQQpwLxsZWdn0DLrvsMo4dO2Z/ftddd/Hoo48yPT1tX1c+fXf48GGmp6d56qmnOH78OL29vfY0X3UbhfLPrQDjdDrXpVaspaWFAwcOVIS91dq9ezcjIyM169w2ggQvIYQQ4lwwOLiy6xtw3XXXkclk+OxnP2tfl6oeVSsTjUbp6enB7Xbz+OOPMzo6at82NjbG9773PQDuu+8+rrnmmlWfV7k3velN/PCHP1zymEKhwA9+8AMuvvjiiuuvuuoqjhw5wszMDMVikfvvv5+XvexlXH311TzxxBN2Mf7c3Jx9nyuuuILPfe5z3HjjjUxMTDTlNayEBC8hhBDiXHDHHRAIVF4XCOjrV0kpxcMPP8yRI0fYuXMnV111FW9+85v5+Mc/XvP4gwcPcvToUXbv3s29997LpZdeat92ySWXcNddd7Fr1y4ikQi33Xbbis5leHiY97znPdxzzz0MDAzw85//HICf/OQn9PX11byPVeO1Z88edu/ebU9pWrZv387HPvYxrr32Wvbu3cv+/ft5zWteQ3d3N3fffTeve93r2Lt3L69//esr7nfNNdfwyU9+kle96lWLWmE8+eSTDAwM8JWvfIW3ve1tXHbZZSt6nctRVtHcuebKK680VtOjQwghhDhXPPPMM+zatavxOxw+rGu6xsb0SNcdd8DBg+t3gg0aGRnh1a9+NT/72c+a+rixWIy3vOUti4rfz3W1vq5KqacMw7hyufvKJtlCCCHEueLgwXMiaG2UcDh83oWutZKpRiGEEEIsaXh4uOmjXRcqCV5CCCGEEBtEgtdWFA6DUosv4fBmn5kQQghxQZPgtRXF4wAsWjZhXi+EEEKIzSHBa4sqAWNAZLNPRAghhBA2CV5blALcwDQwRY3RLyGEEBeEyclJbr75Zi666CL279/PS17yEh566KGmPf7w8PCiXljVZmdnufbaa2lpaeFd73pXQ497yy23sHPnTi6//HIuvfRSPvzhD9u3HThwgNW0nPrQhz607F6Sn/rUp3jhC1/Inj17uP766yuayDaDBK8tSgF9QDswD0ygR8GEEEJcOAzD4LWvfS0vfelLOXnyJE899RRf/vKXa26Xsx5b/Vh8Ph8f/ehHV7yBtrVX4/Hjx/niF79od6JfT1dccQVHjx7lJz/5CTfddBPvf//7m/r4Ery2uG6gB0gCp1jfHywhhBBrc/gwDA+Dw6E/Hj68tsd77LHH8Hg8vP3tb7evGxoa4t3vfjcA99xzDzfeeCPXXXcd119/PYlEguuvv559+/axe/duvvrVrwK6geqll17KwYMH2bVrFzfddFPF1kOf/vSn7fv84he/WHQewWCQa665Bp/Pt6rXYe0XWb6vpOX+++9n9+7dvOhFL+L222+3r//GN77Bvn372Lt3L9dff/2i+33+85/nhhtuIJ1OV1x/7bXXEjB3ELj66qubvqejBK+tKBSq+LQN6AfywSBjY2Nks9nNOCshhBBLOHwYbr0VRkfBMPTHW29dW/h6+umn2bdv35LHHDt2jAceeIAjR47g8/l46KGHOHbsGI8//jjvfe97sXa4OXHiBO94xzt45plnCIfDfOYzn7Efo6uri2PHjnHbbbeteFRrKdaWQQMDA7zhDW+gp6en4vaJiQluv/12HnvsMY4fP86TTz7Jww8/zPT0NG9961t58MEH+fGPf7yoSeudd97J1772NR5++GH8fn/d5//CF77ADTfc0LTXAxK8tqZYTP/Ull2ChsGO2VkATp06teQmqRWkNYUQQmyIQ4eg+ldzKqWvb5Z3vvOd7N27lxe/+MX2da94xSvo6OgA9NTkBz7wAfbs2cPLX/5yTp8+zeTkJAA7duzgt37rtwB44xvfyHe+8x37Maw9FPfv38/IyEjTzteaajx79iyPPvoo3/3udytuf/LJJzlw4ADd3d24XC4OHjzIE088wfe//31e+tKXsnPnTgD79QHce++9fP3rX+eBBx7A6/XWfe4vfelLHD16lPe9731Nez0gweuC4vV6GRwcxO12Mz4+TjQaXf5O9VpQSGsKIYRoqrGxlV3fiMsuu4xjx47Zn9911108+uijTE9P29eVT98dPnyY6elpnnrqKY4fP05vb689zaeUqnjs8s+tAON0OtelpKWlpYUDBw5UhL3V2r17NyMjI0tOIX7rW9/ijjvu4JFHHlkynK2GBK8LjMvlYseOHQSDQSYnJ5ddiQK6KH8SSCGrI4UQYr0MDq7s+kZcd911ZDIZPvvZz9rXLTXjEY1G6enpwe128/jjj1es6BsbG+N73/seAPfddx/XXHPN6k+szJve9CZ++MMfLnlMoVDgBz/4ARdffHHF9VdddRVHjhxhZmaGYrHI/fffz8te9jKuvvpqnnjiCbsYf25uzr7PFVdcwec+9zluvPFGJiYmFj3Xj370I972trfxyCOPLJrabAYJXhcgh8NBX18fra2tzM3NcebMGXsOv5YsEAfGgZOUhbAl7iOEEGJl7rgDzJpuWyCgr18tpRQPP/wwR44cYefOnVx11VW8+c1v5uMf/3jN4w8ePMjRo0fZvXs39957L5deeql92yWXXMJdd93Frl27iEQi3HbbbSs6l+HhYd7znvdwzz33MDAwwM9//nMAfvKTn9DX11fzPlaN1549e9i9e7c9pWnZvn07H/vYx7j22mvZu3cv+/fv5zWveQ3d3d3cfffdvO51r2Pv3r28/vWvr7jfNddcwyc/+Ule9apXLRqAeN/73kcikeB3f/d3ufzyy7nxxhtX9DqXo87VP55XXnmlsZoeHWJl5ubmmJmZwe/309fXh9PprDzAHEo20Csj4+bHEuB89llCoRAtLS32ChAhhBALnnnmGXbt2tXw8YcP65qusTE90nXHHXDw4DqeYINGRkZ49atf3fSNsmOxGG95y1sWFb+f62p9XZVSTxmGceVy93Wt21mJ80JHRwdut5uzZ88yNjZGf38/Ho9n0XEKaDEvdggLBIhGo8zPz+NyuWhpaSEUCi25QkQIIUR9Bw+eG0Fro4TD4fMudK2VTDVuZQ02hAmFQgwMDFAqlTh16lRlT5Oq1hRghrBQiO3bt3PxxRezfft2fD4f0WiUU6dOcfLkSaanpxf1RhFCCHF+Gh4ebvpo14VKRry2KqshjFVEaTWEgZr/nfL7/QwODnL69GnGx8fZtm0boVBIt6ZYgsPhIBQKEQqFKJVKJJNJ4vE48/PzRCIRXC6XfftqG+cJIYQQW4UEr63KbAiTBDJAJyw0hKkzju12u9mxYwcTExOcOXOGfD5f0ftkOdUhLJFIVIQwt9ttT0dKCBNCCHEhkuC1WcLh2r2wGhhlaojZ+CUDzAKtmF/sZRrCOJ1OBgYGOHv2LDMzM+TzeXp6ehb1b1mOw+EgHA4TDofrhjArpDW7R4oQQghxrpLgtVnWuzHp4CCMjhJCB68EeuugRhrCKKXYvn07brebubk58vk8fX19OByrKwksD2HFYtGejoxEIszNzUkIE0IIccGQ4vpNlkP3xGqqw4chkQDAY17isOKGMF1dXfT29pJOpzl16lRTuhE7nU7C4TD9/f1cdNFF9Pb22gFvdHSUkZERZmdnyeVya34uIYQQMDk5yc0338xFF13E/v37eclLXsJDDz3UtMcfHh5ethn3N7/5Tfbv38/u3bvZv38/jz322LKPe8stt7Bz504uv/xyLr30Uj784Q/btx04cIDVtJz60Ic+tOxekk888QT79u3D5XLxwAMPrPg5liMjXptsHogBz2vWA1YX1YMe9Wpro/C//heuFa5Tbm1txe12MzExYbebaNaolNPppLW1ldbWVorFoj0dOTs7y+zsLB6Pxx4Jq9XiQgghxNIMw+C1r30tb37zm7nvvvsAGB0d5ZFHHll0bKFQwOVan1jQ1dXFP/3TP9HX18fPfvYz/sN/+A+cPn162ft94hOf4KabbiKTyfDCF76QN73pTfb+i+tlcHCQe+65p6mbfZeTEa9NtrLKqQaYRfVFdK8tAx28CARIrLL7biAQYMeOHYDeYDuZTDbpZBdYIWxgYICLLrqInp4enE4ns7OzjIyMMDo6ytzcnIyECSG2rnBYN62uvoTDq37Ixx57DI/Hw9vf/nb7uqGhId797ncDcM8993DjjTdy3XXXcf3115NIJLj++uvZt28fu3fv5qtf/SqgG6heeumlHDx4kF27dnHTTTdVbD306U9/2r7PL37xi0XnccUVV9jd6S+77DLS6TTZbLbh12HtF1m+r6Tl/vvvZ/fu3bzoRS/i9ttvt6//xje+wb59+9i7dy/XX3/9ovt9/vOf54YbbljU+mh4eJg9e/asurxmORK8zgFN3TvALJ5PAKfRU5kewDsxQby8fmyFP+DlG2yfPn2a+fn5Zp51BZfLRVtbGzt27LBDmMPhYGZmpiKE5fP5dTsHIYTYcOtQ+/v000+zb9++JY85duwYDzzwAEeOHMHn8/HQQw9x7NgxHn/8cd773vfa28OdOHGCd7zjHTzzzDOEw2E+85nP2I/R1dXFsWPHuO2225YdKXrwwQfZt29fQ7Mn1pZBAwMDvOENb1i0d+LExAS33347jz32GMePH+fJJ5/k4YcfZnp6mre+9a08+OCD/PjHP17UpPXOO+/ka1/7Gg8//PCGN/2W4LVZzMaki0a8ajQsXRGzeD4BuAHr2zo0MEA6nV6o01rFD3j5BttTU1MVu9uvl+oQ1t3djVKKmZkZnnvuOcbGxiSECSFEg975zneyd+9eXvziF9vXveIVr7BbBxmGwQc+8AH27NnDy1/+ck6fPs3k5CQAO3bs4Ld+67cAeOMb38h3vvMd+zGsPRT379/PyMhI3ed/+umnuf322/nc5z7X0Pl+4hOf4Pjx45w9e5ZHH32U7373uxW3P/nkkxw4cIDu7m5cLhcHDx7kiSee4Pvf/z4vfelL7WnJ8tZI9957L1//+td54IEHNmVBlwSvzRKLgWHA9DT88pf634ax9lYSd9xBye8nBdgDsoEALf/tvwFUjHqVgLPokNYoh8NBf38/bW1tRCIRJiYmNmyzbJfLRXt7O4ODg+zcuZPu7m6AihAWiUSasghACCG2gssuu4xjx47Zn9911108+uijFf9xLp++O3z4MNPT0zz11FMcP36c3t5ee5qvuq1Q+edWgHE6nXV/B4+Pj/M7v/M73HvvvVx88cUreh0tLS0cOHCgIuyt1u7duxkZGWF8fHzNj7UaErzOAU0NLgcPkvr0pzH6+mgBGBqCu+/G8+Y34/V6K4KXQvf5mmHl0509PT10d3eTSCQ4deoUxb//+4a2J2oWt9tdEcK6uroAmJ6e5uTJkxLChBACuO6668hkMnz2s5+1ryuvzaoWjUbp6enB7Xbz+OOPMzo6at82NjbG9773PQDuu+8+rrnmmobPY35+nle96lV87GMfs0fNLG9605v44Q9/uOT9C4UCP/jBDxYFtquuuoojR44wMzNDsVjk/vvv52UvexlXX301TzzxBM899xwAc3Nz9n2uuOIKPve5z3HjjTcyMTHR8GtoFglem2yljUkbkXjVq3AcOYK/VIKREbtTfSgUIpPJ2GFEAd3oOrDoKp6nvb2dvr4+sl/5CmO33kpudFSP2lnbE61z+LK43W46OjoqQphhGHYIO3XqFPPz8wshrME9LIUQ4nynlOLhhx/myJEj7Ny5k6uuuoo3v/nNfPzjH695/MGDBzl69Ci7d+/m3nvv5dJLL7Vvu+SSS7jrrrvYtWsXkUiE2267reHzuPPOO3n22Wf5yEc+wuWXX87ll1/O1NQUAD/5yU/swvtqVo3Xnj172L17tz2ladm+fTsf+9jHuPbaa9m7dy/79+/nNa95Dd3d3dx999287nWvY+/evbz+9a+vuN8111zDJz/5SV71qlctaoXx5JNPMjAwwFe+8hXe9ra3cdlllzX8OhuhNmqaaKWuvPJKYzU9Os43VuuEF7zgBU15PMMwOHnyJMFgkG3btlXcls/nee655+ju7qa9bL57HMgCOzGT+Aq/JzJDQ5weG8MA+oCAdcPQkA5+mySXy9ktKqzVM/5vfIPQn/wJoXQap3VgIAB33113KyUhhFitZ555hl27djV28HrvaLIGIyMjvPrVr276RtmxWIy3vOUti4rfz3W1vq5KqacMw7hyufvKiNcmUw88ANdei6FUU0ZfMpkMxWKx5pJbt9u9MN1YVsTfDRQBeyB2hUuXfadOMYhuClexOHiZ7YnWm8fjoaOjg6GhIYaHh+ns7KT4V3/FVDrNrzGbysLCHpZCCLGZrNrf6ssmh671FA6Hz7vQtVYSvDbT4cPwx38M1hxzE6boEokESqmawQsWphvzs7P2dV4gDESAPKx86fLgIG5gEGivuv5c4fF46OzsZHhigmH0puEV23RvckgUQohz2fDwcNNHuy5UTQleSqlXKqVOKKWeVUr9SZ1jfk8p9XOl1NNKqfua8bznvUOHIJ1mDpiyrlvj6EsikSAQCNRt/BYyR7oSiYW1jFPoOi/QhfYrdscdEAhUfjOtcHuiDTM4iAcdvNxV1wshhBDrbc3BSynlBO4CbgBeCPy+UuqFVcc8H/hT4LcMw7gM+KO1Pu+WMDaGQk/PNWOKLpfLkc/n6452gZ5u9Pl8Fasb04ATPVoVR690XJGDB3WN1NCQbsJqrqRsqGZqowvdzZBY4VwNiUIIIbacZox4XQU8axjGScMwcsCXgddUHfNW4C7DMCIAhmFMIexRlgJVm2Y6HKsKINYoVktLy5LH2dON6DYSOfR0Ywc6gK2qLerBg7qQvmol5ZKsfSU3cjXkWkKiEEIIsUbNCF79wKmyz8fN68q9AHiBUurflFLfV0q9stYDKaVuVUodVUod3Yiu6JvujjvA76cICyvsAIrFVQWQRCKBz+fTm5wuMZJkBbM4OnQZ6ODlALrQI2DlU5Hr5tAhiqkUpykbZduIQvfVhEQhhBCiCTaquN4FPB84APw+8HmlVFv1QYZh3G0YxpWGYVxpdSXf0g4epPSpT2EohQuIUdbMdIUBpFAokMlkdKgqG0nK1BhJsqcbg0F7itPaNCEMeIJBpqen178j/dgYCfRm3qrqeiGEEM0xOTnJzTffzEUXXcT+/ft5yUtewkMPPdS0xx8eHl7UC6vaN7/5Tfbv38/u3bvZv38/jz322LKPe8stt7Bz504uv/xyLr30Uj784Q/btx04cIDVtJz60Ic+tOxekp/61Kd44QtfyJ49e7j++usrmsg2QzOC12lgR9nnA+Z15caBRwzDyBuG8RzwS3QQu+AVfud3wDDsVgxzwAiQghUFkGQyCZhbPxw6BKkU08AYegSrOsiFQiGyx46ROH0a9ctf4i6VwDBQhkH35CT5fH5dN8IGYHCQOJV7SlrXCyGEWDvDMHjta1/LS1/6Uk6ePMlTTz3Fl7/85Zrb5aznTh9dXV380z/9Ez/96U/54he/yB/8wR80dD9rr8bjx4/zxS9+0e5Ev56uuOIKjh49yk9+8hNuuukm3v/+9zf18ZsRvJ4Enq+U2qmU8gBvAB6pOuZh9GgXSqku9NTjySY893mvWCxCTw9OdD+tAfP6ceBsf7++vQGJRMLu02WMjnIW3R6iDbD3XS8LctbqxtnZWTweT0UH/WAwSCAQYG5uruHnX43iRz9KyuejYltwKXQXQlygwmFdelp9WWFrxQqPPfYYHo+Ht7/97fZ1Q0NDvPvd7wbgnnvu4cYbb+S6667j+uuvJ5FIcP3117Nv3z52797NV7/6VUA3UL300ks5ePAgu3bt4qabbqrYeujTn/60fZ9f/OIXi87jiiuusLvTX3bZZaTTabuxdSOs/SJrLR67//772b17Ny960Yu4/fbb7eu/8Y1vsG/fPvbu3cv111+/6H6f//znueGGG0in0xXXX3vttQTMRVhXX3110/d0XHPwMgyjALwL+D/AM8A/GIbxtFLqI0qpG83D/g8wq5T6OfA48D7DMGZrP+KFpVAowC234PLprlIBYBjo8PuJ/9EfMTIyQmyZ5nmlUolUKkVLSwuGYXCmv58YumVCT/mBZSNJLpcLn89HJBKpuTt7d3c3xWKxYn+rZov/9m/DRz9KaHBQCt2FEBe8ei0UV9pasdzTTz/Nvn37ljzm2LFjPPDAAxw5cgSfz8dDDz3EsWPHePzxx3nve99rl52cOHGCd7zjHTzzzDOEw2E+85nP2I/R1dXFsWPHuO2225adynvwwQfZt29fzb891awtgwYGBnjDG95AT0/FXzUmJia4/fbbeeyxxzh+/DhPPvkkDz/8MNPT07z1rW/lwQcf5Mc//vGiJq133nknX/va13j44Yfx+/3U84UvfIEbbrhh2fNcCdfyhyzPMIx/Af6l6roPlv3bAN5jXkSZYrEI112H84UvhL/4C91iYnCQrjvuIHTTTUxOTnL27FlisRi9vb243e5Fj5FKpTCuuAJ/Mslp9DRlD3q0y1Y9khQOE4jHSVNVX2VuTeH1emltbWV+fp62traaz7tW8Xgcz0034f2v/7Xpjy2EEGKxd77znXznO9/B4/Hw5JNPAvCKV7yCDnMbOcMw+MAHPsATTzyBw+Hg9OnTTE5OArBjxw57g+s3vvGN/M3f/A3/1fz9be2huH//fv7xH/+x7vM//fTT3H777fzrv/5rQ+f7iU98gptuuskeifvud7/Lb/7mb9q3P/nkkxw4cACrLvzgwYM88cQTOJ1OXvrSl7Jz504A+/UB3HvvvezYsYOHH354yb9tX/rSlzh69ChHjhxp6FwbJZ3rN1mxWNSrEG++edFKO6/Xy+DgID09PWQyGUZGRohEIouK3hOJBCSTzKJD1zaqQletkaR4HI/5z3z5sWX/ters7ARYtmhyNQqFAul02p7yFEII0XyXXXYZx44dsz+/6667ePTRRynvHFA+fXf48GGmp6d56qmnOH78OL29vfY0X3lJSvXn1uiV0+msWys2Pj7O7/zO73Dvvfdy8cUXr+h1tLS0cODAAb7zne+s6H617N69m5GRkSWnEL/1rW9xxx138MgjjzQ0MrcSErw2WaFQwOl0LnlMW1sbw8PDBM3VhmNjY/YPgmEYRKNRouiWDB5qDGPWaZlQRG+bk1t0i+Zyuejo6CAej9vP1yxWA1cJXkIIsX6uu+46MpkMn/3sZ+3rymuzqkWjUXp6enC73Tz++OMVK/rGxsb43ve+B8B9993HNddc0/B5zM/P86pXvYqPfexj9qiZ5U1vehM//OEPl7x/oVDgBz/4waLAdtVVV3HkyBFmZmYoFovcf//9vOxlL+Pqq6/miSeesIvxy8tmrrjiCj73uc9x4403MmFt2VfmRz/6EW9729t45JFHFk1tNoMEr01mBa/lWje4XC76+vro6+ujWCwyNjbG9PQ0kUiE8fFxPOjC/AJlmz9b6lRnZtEjYz7MFhY1tLe343K5mJpqbs/beDyO1+vF4/Esf7AQQohVUUrx8MMPc+TIEXbu3MlVV13Fm9/8Zj7+8Y/XPP7gwYMcPXqU3bt3c++993LppZfat11yySXcdddd7Nq1i0gkwm233dbwedx55508++yzfOQjH+Hyyy/n8ssvt/+u/OQnP7EL76tZNV579uxh9+7d9pSmZfv27XzsYx/j2muvZe/evezfv5/XvOY1dHd3c/fdd/O6172OvXv38vrXv77iftdccw2f/OQnedWrXrVoVud973sfiUSC3/3d3+Xyyy/nxhtvpJnUuvdqWqUrr7zSWE2PjvPK4cP8+H3vI3XmDPsHB/H89/++eGQqHF5UWVkCZoJBpr7/fX71q1/hdru57rd/mwC6j0cO2Fnr+cq/1koxih4dq+52S9X3RDQaZXJyku3btzdlhKpQKHDy5Em6uroq5t2FEGKreeaZZ9i1a1dDx9b4dQ/YpbebamRkhFe/+tVN3yg7Fovxlre8ZVHx+7mu1tdVKfWUYRhXLndfGfHaLIcPY7z1rRTPnNFd68fGanerr/FT6ABCZt+uXC6H3+8nih7tCqJrtrLoxqT1lG8VtJzW1la8Xi8zMzNNaaoq04xCCLFYLKb/31t92ezQtZ7C4fB5F7rWSoLXZjl0iEI6jUKPOi3XrT4DWJv4JNF9vtxuN5dddhkXX3wxiWCQEXT4Ar2HkzX6VUuupcXeKqhCnTDU3d3dtKaq8Xgcn8+3LislhRBCNN/w8HDTR7suVBK8NsvYmB2SnFXX1zIHTAC/RgcqD3p5rMfjYWBggKG5ObxjY/Zxp4BW87hasqdPw4kTeLPZhv5rFQgECAaDzM7Orqmpaj6fJ5PJyGiXEOKCca6W9IjVWevXU4LXRrNaExsGBXRX+YsoC0h1tsvZjh4Zexa9n2MPkO7pwXfJJbjcbjxdXezYsYNedHG9Fd/qfXtks1mUUisaderq6qJUKq2pqao1zWht1C2EEFuZz+djdnZWwtcWYRgGs7Oz+Mym56vRlAaqYgXM4GGgpwUd6LosBUtulxMxj7/YPHYEPfVoL6w1H9fV0kJfIoELmETv09gL+KtGmLLZ7KKtgpazqKlqZ+eKK0FlmlEIcSEZGBhgfHy8om+WOL/5fD4GBgaWP7AOCV5LOXxY11yNjemRqDvuaMp2NiX0yJVCBy972LHWdjmhENPxOBEghG6OWgJOoKcfu9BTik50Ep/+6U9pL5Voyefx+XyUSiVO5fO0trbSXSrhcOhny2azBL/xDfjEJ1b0+jo7O4nH40xPT9O3wv0tcrkc2WzW7jAshBBbndvttrunCwESvOo7fBhuvRUjlcIAHKOjetUhrDl8lco+VhS313jcyV/9img0Sltbm27kphRO9NRjET0KNoIOZLn5eXK5HP39/czNzWEYBkNDQ8zOzhKJREgmk3R3dxMIBCg+9BDeD34Qwyzwp8HX53K5aG9vZ3Z2ljS6B9g8OhRWfDOVj6SZI2CymlEIIcSFTmq86jl0CFIpUujRqQwsuepwJcqDV73kaxgGZ86cIRqN0tHRsah7bjuwGxg0H2MM+OUvf2kXwQcCATKZDIZh0N3dzeDgIE6nkzNnzjAyMkLhU5/Cm04zCpyxHrTB19fR0YHL5eKU+bzTQPnEYpGq1ZRm4IrH4/j9fr1FkhBCCHEBkuBVj7m6MIWeErRHpkZHYXgYHA79sbrvVgOWC16lUonTp08Tj8fp7u6mq6ur7mN50eGrCET/8R9Jp9Pkcjl77y1rawifz8fg4CDd3d1EIhFOnzlD2rxfI6sqyxWLRYrFIs8BUaAPsNqgptAjcGeq7pPNZsnlcjLaJYQQ4oImwasec3VhCr3y0J44U0qHL8NYmJ5bSfgKhWoHLzOQFItFxsfHSaVS9Pb20t7evuj+lghwFr2K0QO84EtfwuFwMDo6Sjabxel0kkwutFFVStHe3k5vby/B3l5m0W0nKrYzrbOqEvQoXCQSYWRkBNArK1vQiwMM9GrLcXSQ21Z1X5lmFEIIISR41XfHHRT9frLo4AXYbSDmWWjXsOLpx1iMYixG8ec/R/30p7giEbt/VqFQYHx8nGw2S19fH62trTXvb9VPGejQ9SN0of32iQmGhobw+/1MTk4SK6urKlcqlRg6dIgen48CenRqxnw8Rkf141sXc4/HdDpt7w/p9/sZGhriEnRom0YHuDl0of8QixuzJhIJAoHAshuCCyGEEFuZBK96Dh4k/elPQ18fAYChIXsPQwe65itjHdvA9Fy5UqlEsVjE4XDY9U75fJ5Tp06Rz+fp7+9fus+VOSrVAXSjQ44HGO3rY2Zmht7eXrq7uzEMg7GxMSKRiH1XwzDI5XJ4f//3Cfzt39K/fTtt6NA0gh7hK1eIxzl79iynTp2iWCzS19dHf38/Ho+HgFIEzful0VOOvZSNDpqyINOMQgghBBK8lpT67d/GceQIvlIJRkZ0+EJPrynKCsqXmJ6rpVQqUSgU7OCVzWY5deoUpVKJgYEBAoHA0g9wxx0QCFBCB6Y+YI/fT/uf/RnxeJyRkRFyuRwXXXQRSimeffZZe5/FXC6HYRh4vV6Kv/d7OL/9bbYnk1gdScZZGP2KoENVPB6no6ODnTt3VgbCwUG60aNcIfN9qSVu1ptJ01QhhBAXOgleS0ilUvj9/oUmo2bgcaBDRhww/P66TU/rKR/xsqYXQTfaa6gb7sGDcPfdzA0MUAC6d+zA9fnP033bbezcuZPW1lZisRjT09N2kf3c3BynTp0ikdA7Pnq9XnvrH6fTSQAYZqFI3lqt6AeGhobo6upa3Gz1jjvwBAK0ofePzIFuAvulL1VsQxT/6U8JBoMyzSiEEOKCJ8GrjkKhQC6Xqxx9MgMPQ0OEgWJfH8lPf3rFfb1KpRKlUol0Os2ZM2dwOBzs2LEDr3fRltV15X/v94g89hihiQn8Y2P2ObhcLnp6eti5bx/hF7wArr6a+auuwnnJJaSGhnh2xw6SX/kK7uc/n2IoBNdei/N//29goS/YnPnvPqAf8Hjq7Ph48CCUSnShRwBnQNe8vfGNdm1YJpMhn8/LNKMQQgiBBK+6rDYMi6b9Dh6EkRECpRLOJ54gdsMNK37sUqlEMplkZmYGj8fDjh07VryFjrX9RL0u8K5Egl7gEvSqwwR6+nA+nWb2wx/m7NgYeYCJCRxve9vCtCJ61GsnZVOHS63azGRwmvdJoGu9gIreXUope+RNCCGEuJBJJ8s6UqkUTqez7iiUUopwOMz8/DzFYnHpabRwuGIbnXlgCtjh9zMQj694Ci6VSpFIJOjq6lqyGWkRHYbazIsTOA0U8nlG0V98LzCWyZBDB7RuyjbstizT0T6PDmzWCsfyird4PC6rGYUQQgiTjHjVYdV3LSUUCmEYhl03VVdZ6IqgN6/2ADvS6RUHEsMwmJ6exu12L+7xVX4cMIEegfKg66+60FsNDaMD13PAL9GBqQ/oNww8Q0MUzPva3eeXaZlRRK9cbEev9LQWHaTTaQqFgkwzCiGEECYJXjXk83kKhcKyqwt9Ph8ej4dYLLbkcZYZFgrWO6kxstSAaDRqbzS9qNi9zFl06NpmPlcOXQDvRocsqwWFEx3SMg4HxWKR6OgoI+ax2fIHXKJlhmF+bDUf11oVaU0zympGIYQQQpOpxhrq1nfVEA6HmZmZIZ/PL1un5UKHEzd6ym+lb36xWGR2dpZAILBkmJmZmSGOHuEKsRCgrG5eQXQg86KL4v3AZKnEM9/9Lp7eXrZNTtJnnqdtiZYZVid+B3qqctx8rkQiQTAYxOGQfC+EEEKAjHjVlEqlcLlc9VfzlQmbq/caGfVqQzcYzaHf+JUGr9nZWYrFYt2CetAjYnNzc7QGg3ZrCBe6DmvO/LdVDO9Ehy4fwPbtOJ1OXO98J3mfjxgLgQqo7GhvvmYAQiF7xEsBAXRR/ulAgGw2K9OMQgghRBkZ8aohlUo1vArP5XIRCASIx+N0dnY2dJ88Kw9euVyO+fl52tra6hb8p1IppqamCAQC9MTjeiNv9JTjvPmxp+z4NDqMtfh8tP3pn3LJVVdR3L+f2fZ2Zv/yL4lMTNCBDowVCb18G6JYjFIsBmfP4ti5E9xuunI5Ro4exRGNcskll6zgVQohhBBbm4x4VclmsxSLxWUL68uFQiFyuRyZTKbeARWf5tCjQ64V1D5NTU3hcDjqhrtcLsfExAQej4e+vr6K+q8selSrgK69MoDZ/n5OAaVt29j2N39D/7vfjcvlwuv10veudzF08iQBdL3Wc+jgVo9hbqVkPafb7cblclEoFCgUCkvcUwghhLiwyIhXlXRad6JqpL7LEgqFmJqaIhaL1e48XzYNWSqVKD71lB7x2r+/ocdPJBKkUil6enoWr4IMhynE44yjU3S/+bE87OXQwUuh92IcA1Lf/CaB2Vl27tpFuEaY83q99KFXKc5SNe1YpVTSt1q1XOl02g6j09PT9Pf3N/Q6hRBCiK1ORryqpFIp3G73ihqaOhwOWlpaiMfj9uiP7fBhGB7W037Dw5S+9CWKxSIul2uh6DwcXqifKr+Ew3b7CI/HQ2tr66LnNuJxJljoNG8n6XjcDl9ZdD1XBh26isEgvb299PT0LFvH5kOHuY7qG8rO0+jogH377BGveDyO2+1mYGCAZDJpL1YQQgghLnQSvKqkUqkVjXYBEA4T7uuj+LznkXI4FkKJ36+bj46O6n0LR0cpvv3tFP7lXyqDXXnNVLl4nEgkQj6fp6enp2b7iDPoWi03OlxViMUoFYvEfvxjTn/rW+T+4R/w/d//y45IxJ5KbUZj0xJAMolSyu5r1tLSQkdHB2632+6yX1dVOF2yU74QQghxHpPgVSaTyVAqlVYevOJxAujgU7G2MZOBVIooCy0dSuk0xbvvrlkgPwmcKvu8gN7cuqWlpeY5TU9PM2c+ttWnq1ypVGJ8fJwzZ84A8PznP5+enh67jg2WCV5LrEicNi+z6NYRSfTKzqmpKRKJBG63m1wuR2trK6lUimg0WvuBDh9eFE659VYJX0IIIbYkqfEqs5L+XdUUumdWFD0CZCVaAx2oOtF9s0pAYXKy5lRmisqmqjPowvVa7SPm5+cZM/db7Eb35Spfh5kCJkdHmZubIxwO09bWRltbG8lkkmQyadeiLRm8arXIsKYT0dObhnmeKSB49izT09OkUil8Ph+zs7MATE5OMjExwcDAAE6nE4fDgcPhQCmF4/bbcaRSKPR0pg8WOuWvcPNxIYQQ4lwnwatMKpXC4/GsevotjB75sYrZQYcTWHijS0CxRm1V3rxYmwBZW+90tLcvCmnxeJyf/exnGIbBTnToKn/8aXQA9ChFV1cXmUwGpRQ+nw/DMOw6Nlj9VONF5kcD3bcrCQwODZHP5+nr66Onp4dSqYRhGIRCIU6dOoXD4aC1tZVSqWRfjNOnKZrnXVHAv0SnfCGEEOJ8JVONJsMwSKfTqxrtsviAnSyELoCCWUtlBaO8z4dxyy2LgpdVfm49+5R5n46OyrL2aDTK0aNHyefz7Nq1i4FQyH7sJDCCDl0dwSBDQ0MVXeO9Xi+BQID8gw+S2bMHxyWXoHbuXNO0nlV15ga7e39PTw/BYJBQKEQ4HGb79u0MDAyglKK9vZ3e3l62b99Of38/A0NDDKL3j6x455folC+EEEKcryR4mTKZDIZhrCl41VL49Kehr08Xvg8NkfvkJ+G66yqDVyhECh20POiRrgzQ1dKig5NZfD6lFEfb2nBcdx0vvu46urq7IR6nCJwJBjl94gTOkREG02m6EgmUUmSzCzsuer1egl/9Kvz5nxM/fVpfudKaqhp1XwbgCAaJx+M4nc6a72FXVxeGYdjTj7Y77oDq4wMBfb0QQgixxUjwMq2lvqtuEXooRPGmm+Dxx3Hl8zAyQu63fxugMnjFYqSefZbAmTOUikVmfv1rfKOjhONxOHyYwlvfytjoKE+jt/i5Cj29B7rWagRIJJN0dnYyODho128VCgW7x5bL5cLpdKI++EFSmQy/AiYwp/esmqpGxGK6CL7sUhobg5//nGQySUtLS83Vl1Y7jGg0Si6XW7jh4EG4+24YGtL1Y0ND+nOp7xJCCLEFSfAyWQXhq9rQuUYYwTAgFrM7tzudTjh8mNxLXoLjla/Edckl9iiTtcowEAgwNzdHoVCgp0dv7pP80z9lJJ1mFF1Ddjk6fBXQwekMeppvEOjs7ETdd5/dmiF70UXwyCMUCgXS6TRjY2OcHBsjhZ7abC9/DWuoqbKmaUul0pJ7M3Z2duJwOBa3lzh4EEZGoFTSHyV0CSGE2KKkuB7ddiGTydDe3r78wStULBb1SNN998Gtt5JLpXAAzrExPcUHpP7jfwT0VjuTk5OEw2G8Xi9TU1PMnzqFE725di8LdVBZdE1XN3ovRQX2ikPQwWzq1CkmDh0iMzVF2+teR0tLC10DA3SPj5NGr4K0Y+YaaqpKpRKpVIpwOLzkiKHT6aSzs9Ne+djsaV0hhBDiXCcjXugtbtajvgv0dJ/T6dRTeakUeXQdlwJ7is9aTRmJRFBKEQ6HGRsbY35+nvaBAS4Cng+U960PolcWtrNQ4F5EF9b/CngKGAeKuRzt997L85//fIaGhuj42Mdo9fspsdBbbK01VcVi0d4maDltbW2NNVUVQgghtiAJXujgZbVbaLZCoYDL5aqYyit/FmN01K4vSyQSuFwuTp8+TaFQoL+/n+6PfQwVCLC4amqhU30GHbJ+je4ZZvXB7wUGgPbJyYVQdPAg6u678fT2koOm1FQlk7p1ayPBS5ktLrLZLLFafcKEEEKILUymGlljfdcyisWiLqQfHITRUdrQNVmWzI4dlEol4vE4qVSKtrY2gsEg27Zt04HNCkSHDi2Et6r9IBW6B1gHuonrPJBgoYeY6uur6AVWfMMb8L/gBeQdDopXXLHmbYPi8Tgej8fehmg5oVCISCTCzMwMLdbKTSGEEOICcMH/xSsWi2QymXWrN7KnGs22CQXK0m4gQGpqiplLL2Vyzx48V19N96WXMrBjB67y/l3lxeel0kLxvsmL7h/WZf67iK7xAsDnw/P+91esNCwWi/j9fhwOx5o3sLbquxoZ7SrX3d1NoVAgEoms/Ellb0chhBDnqQs+eKXTaWCVbSSWYXVut0aujM99jmJfnw5e5hTfWDbLCLpofhd61Aqov3F2AwqYo119fRgf+Qje17++4vZisYjX68Xj8djThKsV/8IXKL3xjYR37VpRCPL7/YRCIXsVZ8PMvR3zsrejEEKI89AFP9WYSqXWtb4LFrblKbz+9XDVVbi2baMQCDAxMcEv0UXzz6dyChKoWKVIKLR478RQqGZAKwaDlL7/fUouFw6HY9GG3NYG2S0tLWsb8Tp8mNh/+S+4Mhn8sBCCoKGasa6uLhKJBLOzs/T29jb2nIcOkUmlGEeH1A6QvR2FEEKcNy74ES+rrUGtpp9rZQUcl0vnWyuIZb/0JUaHhjg7NIQbuBSImJdy2fJPao2A1ekfVjx+nGKxaL+m6uBlNVUNhUIUCoWK7vaLKFX3UvzAB0hkMpVtKVbQjNXtdtPW1kY0Gl36HMpkR0c5jV5YEC6/QfZ2FEIIcR64oEe8CoUCuVyOcDi8/MGrfHwAV28vJBLkgVn0JtohdFF8K7o1RALdj8sSRa9Q3G4e2yhr8+ny6bt6I17hcJjZ2VlSqdSiY6oZ5qU8qSfMsNNN1WjdCkJQR0cHsViM6elpBgYGljw2l8sx3teHmphggKpvXtnbUQghxHngwhzxCodBKdJuN1xyCYHOTj2K0+QAZk81JhLk0Fv7xNBBpR3d9qEX3Qi1hcogEUJ3qD9j3qdRxWKxInRZWwVVH6OUwul04nQ67W18stksmUyGdDpNKpUimUySMJ//l8DTmFsMmeL9/fiAi1n9BtdOp5OOjg77+erJ5/OMj4/De9/LgN9fGfRkb0chhBDniQtzxMuctkuhk6ev6vpmsQJOAphC99vajg5bcXQj1QC6GL66Z34ePRqWQDdE7QJCc3MYhlH3UiqV7K2BDMMgGo3aiwbKj5uamrI3BZ+bmyMWi5HNZpecbk0B0+Y59VvX/dEf0fHBD4K5QAFYVQhqa2tj/p57mP7rvyZw+vSinmUFYDwYpHT8ODve+U48vb0L7TUGB/XzSX2XEEKI88CFGbxMKapGaposl8sxOzuLYT5PH3q6DvNjN7qOqwXwDQ3plhFm+Imi+3E5zPP8BdB58qQ9LepwOFBKofbuRSWTKPTUZQEd2nxeL+5vfpOWlha7hk0phcPhIJvNEgqF6O7uJhgMcvbsWcLhsN1TyzpWKWU/rnUek+hmrSGA971Pf7QC2ypDkLrvProPHWIinSaGDneG+bxF8/mKySQDAwN6SvTgQQlaQgghzksXbPAy0LVVjbX8XLlMJsPo6CjZbJYuytpEmFLoETA/5mjX6GjFKsYOFvZgvAg4CyRvvJGuv/gLOt72toUHqpqeiwIzQGs2i7e3l+3bty/02AqHIR4nhS5ObzefIxUM4nruuWV7cYXN+02gpx670X3DqvuKrdihQ7Sk0/jNcw+hA57VjyyPHmVbj5WnQgghxEa6MGu80IGmh5UVrjdqbm6OsbExisUiO3bsWBS6QAevHLoovaXG7S70VKTLPNc+IHzmDDN/9EfMfe5zi45Po8NZ3nxcK1F7PJ6Fg8yp1CIL2w0pwJ9MkrziioYakgbRU6Ux9HRpse6RK1BWpO80X4MHvQXSKJWbgwshhBDnsws2eDVNWRf1wtAQ43/zN8zMzBAKhejt7aWlpUX32yqTQ9duOVio7cqj20lMo0eUxoCT6PqukyzUh4UyGWY+8hFmZ2crHrOIDkMp898KvS9iRfAqO7a83D4I5E6fplCrIWl5qwpTCR2G3MApmhC+zGJ8HzCMDl1p9AhbKwsrQYUQQojz3YUZvOpNqa1w2xurizqjoyQNg9GxMdK3307vkSNs27ZtoWu91W/LnErMoKcEgyz0oiqgQ1cUHTIc6FGeTnTI8aLD1HYgPDHB7OwsMzMz9qlY8Spm3lehR7uqC+YNdHAqb5tqjSbZk5bL9OJqBV6A3qYojw5fK+o+X83cTsk6vwnz/C5G9zgrmc+RLi/iF0IIIc5DF2bwqtN4dFFn+OUcOoSRSjEFnEZP7w1lMrTecYfdK6uilYM5suNHr1LsYuEL4AOeZ16GgQFg29AQneigU16Mt21oiNbWVubm5pg2r3Ojw1YMPZplsLh/F+Yx7eiifivGeM3Hr2hhukQvLmW+hoB5ngVgfHx89eHr4EG4+24YGtK1bOhp4DD6fRkEnMEg4+PjxJu88lQIIYTYSBdm8GqWsTGK6FqndnRA8FjXV3WtB+yRnQg66LSVPZS1crBC2UiQzWzX0NvbS1tbG5FgkGnz/m7zXBTgCAbrNkXtNI+dZGGV5RA67Nhq9eKqMSLoB/pbWigUCmsOX2e//33iJ07QPTdHW1kgdhsGO6JRfD4fZ86cYW5ubnXPIYQQQmwyCV5rMTiICz1C1Q0L/acGBxe61pcHr4MHKf3t3xLr6yMEuIaGoN5KvVCoYiQIpeyNta1WCj09PbQ/9xyREyeYmpzEc/o0sX/4B1zf+Q4cO1Y3eDnQ05c5dP0UVNZ81e3FVWek0B+P09/fT6FQ4NSpU6sKX1NTU8RiMTo7O2lvr+5qpkcOBwYGCIVCzMzMMDk5ibGWlZRCCCHEJpDgtRbmiFSt0FJzqhGIvvrVlB5/nPZMRvftSqeXnvY8eFAfVyrpj1X9q7q7u+no6GB+fp5oNEoymay7R2P5iFUAPZU3B2S93rrhrlF+v5+BgQGKxSKnTp0in883fN+ZmRnm5+dpb2+ns7Oz7nFKKbZv305HRwfRaJSJiQl730khhBDifCDBay2WGJGqNeJlGAaRSIRAILDs3ogNO3yYriuvpPOSS4geOMDcN79pF/VXh77qEavuQgHns89y9sQJjOeeqxvuGuXz+ezwNT4+3lD4mpubY25ujtbWVrq7uxt6nq6uLnp7e0kmk6seYRNCCCE2gwSvtaozIlUoFOwu8JZEIkGhUKg5lbYq5qpKY3RUF+FPTZG+7z4mX/lKPF/72rJ3dzqd9Pb2ks1miUQiTTklK3yVSqVlR74ikQgzMzOEw2F6e3tX9Dytra0MDAyQz+cZGxsjm80ufychhBBik0nwWifFYrGyvgs9uuPxeAgGg815kkOHIJViDr2tTot5SSYSzL///Rhf+tKyD9HS0kJLSwuzs7Pkcs3plmWFL8Mw6oavaDTK9PQ0LS0tKw5dlkAgwI4dOwA4derUkptsCyGEEOcCCV7rpFAo6Kk+s8FqWimyv/mbtH/zm817krExsug6LasdhNV0NJfNMvEHf4ChlJ4GtS7h8KKH6enpQSnF5ORk007N6/VWhK/yUBePx5mcnCQYDLJ9+/YlN+du5HkGBwdxu92cPn2aaDTajNMXQggh1oUEr3VSLBZxffWrdoPVCOCcmCD8h3+45JY8K2Hs2MFZ9IrEbvRoVyu6MWs/uh/WBAstIwB726ByLpeL7u5u0ul0U4OLHb727GHc6yWnFAmlOBMO47/kEvouvXRNocvicrnYsWMHwWCQyclJZv72b+3dBJbbAkkIIYTYSBK81kmhUMD18Y9DKmVvEdQKqHR6ya7wKzH3p39K1uejBx2+XOjViiV0EGsDRtB7Hi639q+1tZVAIMD09HRTi9W9Xi87kkkM9Mbao+imqP2ASiSa9jwOh4O+vj5av/Ut5v74jzkzOqrbTVRvgSSEEEJsIgle66BUKlEqlXCOjwN6iyAHZQ1Tl+gK36hsNsvc9dcT/uQnaTFbMBTN5ymgA848OojF0J31lwtfvb29GIbB1NTUms+vnAcdBCfRfcPKO/Y3k1KK3r/6K7oyGeLo1wwsuwWSEEIIsVEkeK1WOFxZO1VWQ2V3rTcLv8PARZRt+1OrK/wKGIbB2bNncTqddL/97TAzA1/6EtHt25lGB644OuDsAZ6P3h5oufDldrvp6uoikUg0fWueEHp/x+3AGaq2J2qmsTE6zOcJV10vhBBCbDYJXqtVL5jE4/ZUnfMv/sLe8sd+o+t1hV+B2dlZstksvb29OBwOotEoz/3mbzJ+yy0ot5tt6Km8DvQUZAjoQ4+8jYMdDGtpa2vD5/MxNTW15HErpYAd6K2JlHke6xK+zFAboip4rTHsCiGEEM0gwWsNisBZ9NY7FddbI15vfOOSW/6sRiaTYW5ujmAwSDab5eTJk0xOTuJ0Ogn93d8xmM/TA1Q3cGhBjwJlzc2m64UqpRS9vb2USiWmp6drHrMWHnQAs8NXs/tvLbG/pRBCCLHZJHitQRJdP1W9Y6A94uV0Lrvlz7LKpjQNpRj3+4lecgnJF7yAmZkZfD4fO3bsYHBwEMfkJE70aFdr+WMoBYZBi2HQNzlJLpdbMnx5vV7a29uJxWLN6Y1Vtbm2Gx2+HMEgp+68k8zQUPNWIC6zv6UQQgixmSR4rUECXbdVvflPxXZBS9SCNcSc0swCP0evUPQA4VSKoaEh+vv78fv9GIZBprcXL7qI31/+GGXTbMFgkP7+fnK53JLb7XR2duLxeJicnFz7fog1Ntd2GwYDd92F88/+jPGxMTLNXIG41rArhBBCrBMJXqtkACl0z6xqFV3ry2rBKiJOg8XrKXRR/C/RPbkGgMuAbVRugl0sFsm95S34fb7KB6gxzRYIBBgYGKBQKDA+Pl4zfFlTjoVCgZmZmYbOdaXcf/EX7MhkcFJW8yUrEIUQQmxhErxWKd3SQgldO1UhFFroWl8miu6pNcfiqcla4vE4Y2NjjLPQjmIY2EXZ6sgy+Xye/Mtehv8v/7KhaTa/309/fz+FQqHutj5+v5+2tjbm5+fJZDINnPUKjY3hQk87htEjedb1QgghxFYkwWuVEr/+NeqXvyRQKlVOo8ViNfdpDJiXGXSPrVSNxzQMQ69QfO45zpw5Q7FYpBfdiuKF6BWB9b5g6XQawzAI3Hxzw9Nsfr+fgYEBisUi4+PjNcNXV1cXLpeLs2fP6oakzWROgbqAHnTBffn1QgghxFYjwWuVkskkwWCw5pY3tUa83OiWDv3oEa9x4MzAAAWlKA4NMfe5z1WsUOzr62Pnzp2627158VBfOp0G9DTiSljF+aVSadGeiqA7wvf29pLL5Zibm1vRYy9LViAKIYS4wEjwWoVsNks+nycYrFXhRc0RL0sQPWXYBcyfPs1TwI/Gxpj+wz/E9+EPs+PlL2dweJiWF71IF5lXrQi0VV2fSqVQSuH3+2sfv4TyDa3Hx8cXha9gMEg4HGbunnvIygpEIYQQYtUkeK2C1WKhVvAqFosYhrEw4lUjOCn0ykMD3W8rC5DN0v73f4//1Ck9ZWmt8PvsZxetCLSmNMul02k8Hs+ikbZGeb1eduzYgWEYnDp1alF/re5vfhPHn/0Zk2NjlecnKxCFEEKIhknwWoVEIoHP56s5qlXRSgJ0cAoEFjU0daBXKF4NXI6eRhxHr1y01xiuYIVfOp1e8TRjNY/Hw44dO1BKMT4+XhG+nH/+5/RkMmSAyCrOTwghhBASvFasWCySyWSWnGaEsuB16BDZVIoxoLoPfBhdWF4+/ZhE76toW26F3+HDFIeGyF59Nf7XvnbNI1Dl4evUqVMLqxnHxgiZ51ox1iYrEIUQQoiGSfBaIWuasaVlUSMJoKprPZAfHeU0C9OL9Sil6AB2ovcZtC21wu/wYbj1VrJjYxQB/5kzTZn+c7vd7NixA6fTyfj4uA5f5nlsAyrOSFYgCiGEEA2T4LVCiUQCl8tV0by0XPmIV6FQYLyvDwM9reguP7Czs7Ko/O1vh0CgskfXciv8Dh2CVIosUEK3q2jW9F91+EqbG347KWv7ICsQhRBCiBWR4LUChmGQSqXqTjOCHvFSStkrBIvveQ/9fn9lK4hAAP7X/6osKv/MZ1a+ws+c5vOgpwCb3YDU5XKxY8cOXC4X49dcQ+rTn5YViEIIIcQaSPBagVQqRalUqjvNCDp4ORwOTp8+TT6fp++22/B9/vONBZaVrvAzp/l8QAdgr2c0jMb3glyGFb48Hg+n/92/I/nnf66fd2xMj6ytdVWjEEIIcQGR4LUCyWQSpdSSqwetvQ0zmQzbt2/Xx65XywRzmq9ofloxTdngXpCNcDqdDAwM4PmXf2HiXe8iOTra3JYSQgghxAWiKcFLKfVKpdQJpdSzSqk/WeK4/6SUMpRSVzbjeTdaIpGo260e9FTkxMQEuVyObdu2LTky1hRmgLOC1+o6eDXG6XQy8KlP4c1kmAAS1g3SUkIIIYRo2JqDl1LKCdwF3IDeUvD3lVIvrHFcCPhD4Adrfc7NkM1mKRQKS9Z3TU5OEo/H2bZtG+EmTfU1wo1ebVi73L95nKdOMWA+zxRlm31LSwkhhBCiIc0Y8boKeNYwjJOGYeSALwOvqXHcR4GPA5kmPOeGW6pbPcDU1BTRaJRQKERHR8dGnhoudE+w9RzxAmBw0G78OoBsai2EEEKsVDOCVz9wquzzcfM6m1JqH7DDMIx/XuqBlFK3KqWOKqWOTk9XtxvdXEt1q5+dnWV+fp5wOEx7e3vdfRrPe+am1g7KVlBKSwkhhBCiYeteXK+UcgCfAt673LGGYdxtGMaVhmFc2d3dvd6n1rBCoUAmk6lZsxWJRJidnbVDF7CxwavBTbSbQja1FkIIIdakGQnhNLCj7PMB8zpLCHgR8G2zKH0b8IhS6kbDMI424fnXXb1pxlgsxvT0NC0tLfT29trHrXaj6lWp2ix73R08KEFLCCGEWKVmjHg9CTxfKbVTKeUB3gA8Yt1oGEbUMIwuwzCGDcMYBr4PnDehC3Twqu5Wn0gkOHv2LIFAgO3bt6OUWrxPoxBCCCFEmTUHL8MwCsC7gP8DPAP8g2EYTyulPqKUunGtj7/ZDMMgmUxWTDOmUinOnDmDz+ejr6/Pbi9RvU+jEEIIIUS5pgzNGIbxL8C/VF33wTrHHmjGc26UVCqFYRj2NGMmk2FiYgKPx0N/fz8Ox0J2LRaLOJ3Oun2+hBBCCHFhk871y0gkEjgcDgKBANlsltOnT+N0Ounv7180slUoFGS0SwghhBB1SfBaRjKZJBAIUCgUOH36NEopBgYGatZxFQoFqe8SQgghRF0SvOo5fJjs0BCFiy/G9xu/wfidd2IYBgMDA7jd7spjw2FQiuLQEK4dO3SrBaWatlG12GSHD8PwMDgc+qPsTSmEEGKVJHjVcvgw3HoribExikBkfJziBz5A/xNP4PF4Fh9vbkhdoKp7fBM3qhabxPxeQDYGF0II0QTKMIzlj9oEV155pXH06CZ1nBgehtFRRoAzQBe6FX9gaAhGRhYfrxQl4FmgG2gvv+0cfX9Fg4aHKY2OkkGHaruhSL3vBSGEEBckpdRThmFcudxxUpBULhy2R6mK6H2QvEAfEIAlN4Muov8wyxt6fjMMg2w2SyaT0ZfRUXLmba1Ar3WgbAwuhBBiFWSqsZwZugxgEugBXgDY/eqX2AzaDVyMbtN/XrnA65dyuRyxWIypqSnGxsZ49tlnGRsbY2pqimQyibu/n070iGdX+R1lY3AhhBCrIAM0NUwCCfToRpt15VbcDNqqX0qlKAEOq34JtuS2QNaem+WXUqkEgMPhwOfz0d7ejtfrxe/36xWqH/+4/R7ZtuL3ghBCiA0hNV7llCIHjKHrtDrLb/vSl+qHkbIpygqh0MbvpbgSZi1bDJgGhjEXB2yB+qVisVg5ZZjJ2DsLKKXwer34fD77UnPRhOXwYTh0SE8vDg7q0LUFg6kQQojVa7TGS4JXObPjfB49dVjhHH2f1sThAMMgB4ygw2Y36PfBHAk6Hyyqy8pkyOVy9u0ej6ciZHm9XtldQAghRFNJcf0aLApdW9XgIIyO4gHCwDw6fLnO8fqlWiHL+g+Ey+XC5/MRDoftoFW+rZMQQgixmSR4lQuF6k8ZbkV33GHXL3UCcWDW76d3I+qXGpyezefzFSErm83WrMuyQpbsHCCEEOJcJn+lyp3L9ViNWGmtmVWndOgQ7rExWvv7mf/DP6T9d3+XJSqemqPGeRaBTDxOZnbWDlrFYhFYqMsqH8lasi5LCCGEOAdJ8NpKzDCTQ/cJcVVdX9PBg3YA6ywWiZ48yezsLNu3b1/PMwV02455IGNe8tYNs7N4vV5aWloqQpbUZQkhhDjfSfDagiYBBQys8H5Op5P29nbm5ubo6OjA6/Uuf6c1UMAseiWlD926wwd4n/c8qcsSQgixJclfty3I6qK/Gu3t7TgcDmZmZpp5SnVdBOwEtqML+/0goUsIIcSWJX/htqAiq//COp1OOjo6SCaTpNPpZp5WTfINKIQQ4kIif/e2oLWMeAG0tbXhdDrXd9Sr3krRrbqCVAghhECC19YSClE0/+msun4lHA4HnZ2dpNNpkslks86uUiymm9JWX873laVCCCHEEiR4bSWxGMVsFk6cwBmNrinMtLa24na7N6zWSwghhLgQSPDaYqy+V07nWiYbdd+szs5Ostks8aXaUQghhBCiYRK8tphmBS+AcDiMx+NhdnaWc3VPTyGEEOJ8IsFri2lm8ALo6uoil8vJqJcQQgjRBBK8tphmBy+re/zMzIyMegkhhBBrJMFriykWiyilmtqEtOuyyyhcfDFRhwOUWriEwyt/sHC48jHW8lhCCCHEeUaC1xZTLBabNtplCSQSBNDb+5TKb1jN9GO9+8hUphBCiAuABK8tZj2CF0AXujHrfJMeLw6MAWeBOSAJ5PP5Je8jhBBCnO9kk+wtZr2Clw/oBoJNejyFTv0pwO4y9txzKKXweDx4PB68Xq/9b7fbjVKqSc8uhBBCbA4JXltMsVjE7Xavy2O3N/GxWswL6OnLHJDt7SWXy5HL5chkMhUrKcsDWXkwk0AmhBDifCLBa4tZrxGv9eRAj6j5Wlsrri+VSnYQy+VyZLPZmoHM7XYvGiHzeDz1A9nhw3DoEIyNweAg3HEHHDy4fi9QCCGEMEnw2kIMw6BUKjU/eIVCtYvfV7Oh9Qoey+Fw4PP58Pl8FdcbhmEHsfJglkgkKo6rNULm+cpXUG97G6RS+qDRUbj1Vv1vCV9CCCHWmQSvLaRU0msOmx68mrlxdRMeSymF1+vF6/VWXG8FsupRsmQyudCD7PbbcadSeAAPevrUlUrpETAJXkIIIdaZBK8tpNnNU883SwWyfD6vg9jEBDl0TVkKaLMOGhvb0HMVQghxYZLgtYVc6MGrnvLC/JahIT29CBjo1ZWArvUSQggh1pn08dpCJHg14I47IBAAykJXIKCvF0IIIdaZBK8tZMOC1/m87c/Bg3D33TA0pM95aEh/LvVdQgghNoBMNW4hGxa8zvdtfw4elKAlhBBiU8iI1xZSLBZxOBwb1lA0DRQ25JmEEEKIrUGC1xaykc1Ti8A4euNsIYQQQjRGgtcWspHBywmE0fssyqiXEEII0RgJXlvIRm8X1IFuyRDZsGcUQgghzm8SvLaQDQte5vY+bvSo1zx66nFVWwgJIYQQFxAJXlvIhgWvWAwMAwyDjmwW48QJItPTzd1aSAghhNiCJHhtEeu2QfYyPB4PoVCI+fl5e69IIYQQQtQmwWuL2Myu9R0dHZRKJebn5zf8uYUQQojziQSvLWIzg5fX6yUYDBKJRGTUSwghhFiCBK8tYrP3aezo6KBYLBKNRjfl+YUQQojzgQSvLWKzg5ff7ycQCBCJRDAMY1POQQghhDjXSfDaIjY7eIEe9SoUCsRkdaMQQghRkwSvLcIKXg7H5n1JA4EAPp+Pubk5GfUSQgghapDgtUVYPbw2aoPsejo7O8nn88Tj8U09DyGEEOJcJMFri9jo7YLqCQaDeL1e5ubmNvtUhBBCiHOOBK+t4PBhii9+MY6dO2F4GA4f3tTT6ejoIJfLyaiXEEIIUUWC1/nu8GG49VaKp0/jBBgdhVtv3dTwFQqF8Hg8MuolhBBCVJHgdb47dAhSKYqAy7ouldLXb6KOjg6y2SzJZHJTz0MIIYQ4l0jwOt+NjQHQCYRqXL9ZQqEQLpdLRr2EEEKIMhK8zneDgwC0AoEa128WpRQdHR2k02lSqdSmnosQQghxrpDgdb674w4IBCqvCwT09ZustbUVp9Mpo15CCCGESYLX+e7gQbj7bhgaAqX0x7vv1tdvMmvUK5VKkclkNvt0hBBCiE3nWv4Qcc47ePCcCFq1tLa2Mjc3x9zcHH19fZt9OkIIIcSmkhEvsa4cDgdtbW0kEgmy2exmn44QQgixqSR4iXXX1taGw+GQWi8hhBAXPAleYt05nU7a2tqIx+PkcrnNPh0hhBBi00jwEhuivb0dpZSMegkhhLigSfASG8LpdNLa2ko8Hiefz2/26QghhBCbQoKX2DAdHR0ARCKRTT4TIYQQYnNI8BIbxuVyEQ6HiUajFAqFzT4dIYQQYsNJ8BIbqqOjA8MwZNRLCCHEBUmCl9hQbrebUChENBqlWCxu9ukIIYQQG0qCl9hwHR0dlEol5ufnN/tUhBBCiA0lwUtsOK/XS0tLC/Pz85RKpc0+HSGEEGLDSPASm6Kjo4NisSijXkIIIS4oErzEpvD5fAQCASKRCIZhbPbpCCGEEBtCgpfYNJ2dnRQfeojo0BA4HDA8DIcPb/ZpCSGEEOvGtdknIC5c/n/8R/x//ufMZTK0Amp0FG69Vd948OCmnpsQQgixHmTES2yeQ4foyGQoADHrulQKDh3axJMSQggh1o8EL7F5xsYIAl4gXXW9EEIIsRVJ8BKbZ3AQgB3AthrXCyGEEFuNBC+xee64AwKBym/CQEBfL4QQQmxBErzE5jl4EO6+G4aGQCn98e67pbBeCCHEliWrGsXmOnhQgpYQQogLhox4CSGEEEJskKYEL6XUK5VSJ5RSzyql/qTG7e9RSv1cKfUTpdSjSqmhZjyvEEIIIcT5ZM3BSynlBO4CbgBeCPy+UuqFVYf9CLjSMIw9wAPAX631eYUQQgghzjfNGPG6CnjWMIyThmHkgC8Dryk/wDCMxw3DSJmffh8YaMLzCiGEEEKcV5oRvPqBU2Wfj5vX1fMW4Ou1blBK3aqUOqqUOjo9Pd2EUxNCCCGEOHdsaHG9UuqNwJXAJ2rdbhjG3YZhXGkYxpXd3d0beWpCCCGEEOuuGe0kTqObj1sGzOsqKKVeDhwCXmYYRrYJzyuEEEIIcV5pxojXk8DzlVI7lVIe4A3AI+UHKKWuAD4H3GgYxlQTnlMIIYQQ4ryz5uBlGEYBeBfwf4BngH8wDONppdRHlFI3mod9AmgBvqKUOq6UeqTOwwkhhBBCbFlN6VxvGMa/AP9Sdd0Hy/798mY8jxBCCCHE+Uw61wshhBBCbBAJXkIIIYQQG0SClxBCCCHEBpHgJYQQQgixQSR4CSGEEEJsEAleQgghhBAbRIKXEEIIIcQGkeAlhBBCCLFBJHgJIYQQQmwQCV5CCCGEEBtEgpcQQgghxAaR4CWEEEIIsUEkeAkhhBBCbBAJXkIIIYQQG0SClxBCCCHEBpHgJYQQQgixQSR4CSGEEEJsEAleQgghhBAbRIKXEEIIIcQGkeAlhBBCCLFBJHgJIYQQQmwQCV5CCCGEEBtEgpcQQgghxAaR4CWEEEIIsUEkeAkhhBBCbBAJXkIIIYQQG0SClxBCCCHEBpHgJYQQQgixQSR4CSGEEEJsEAleQgghhBAbRIKXEEIIIcQGkeAlhBBCCLFBJHgJIYQQQmwQCV5CCCGEEBtEgpcQQgghxAaR4CWEEEIIsUEkeAkhhBBCbBAJXkIIIYQQG0SClxBCCCHEBpHgJYQQQgixQSR4CSGEEEJsEAleQgghhBAbRIKXEEIIIcQGkeAlhBBCCLFBJHgJIYQQQmwQCV5CCCGEEBtEgpcQQgghxAaR4CWEEEIIsUEkeAkhhBBCbBAJXkIIIYQQG0SClxBCCCHEBpHgJYQQQgixQSR4CSGEEEJsEAleQgghhBAbRIKXEEIIIcQGkeAlhBBCCLFBJHgJIYQQQmwQCV5CCCGEEBtEgpcQQmyAcBiUWnwJhzf7zIQQG0mClxBCbIB4vPyzZJ3rhRBbnWuzT0AIIS4sCWACcAPtQBj5P7AQFw75aRdCiA3VAvSh/987BZxkZmaGQqGwuaclhNgQMuIlhBAbrsW8ZIAIc3NzRCIRQqEQ7e3teL3eTT4/IcR6keAlhBCbxgdsZ+fOLubn54lGo8RiMQKBAO3t7QSDwc0+QSFEk8lUoxBCmNZz5WEoVP96t9tNd3c3F110Ed3d3eRyOU6fPs3IyAjRaBTDMNZ+AkKIc4KMeAkhhKneCsNmrDyMxZY/xuFw0N7eTltbG4lEgrm5OSYnJ5mZmaGtrY22tjacTufaT0YIsWkkeAkhxCIR82MboDb82ZVShEIhQqEQ6XSaSCTC7Owsc3NzhMNh2tvb8Xg8G35eQoi1k+AlhBCLpNFtH+aBbqAFpfS0YCMjV83k9/vx+/3kcjm7DiwajRIMBmlvbycQCGzsCQkh1kSClxBCLNKHbnI6je655Qd6iMc3b7Whx+Ohp6eHzs5OotEokUiE8fFxvF4v7e3thEIhlNr40TkhxMpI8BJCiJqC6F+R0+i2D6NAmEKhC5dr8351Op1OOjo6aG9vJx6PE4lEOHv2rF0H1traKnVgQpzDJHgJIYQpFKoupI8DKRYWgEd47rm4HXwcjs1bGK6UIhwOEw6HSaVSRCIRZmZmmJ2dpbW1lfb2dtxu96adnxCiNgleQghhsuq3FmbsutDTjPPoqccSiUSCZDJJNBqlq6uL8Dmwy3UgECAQCJDNZu06sPn5eVpaWmhvb8fv92/2KQohTBK8hBBiSUHzkgeihMNRkskkExMTzM7O0tnZybZt286JInev10tvb69dBzY/P08ikcDn89He3k5LS4vUgQmxySR4CSFElcVTjgBuQqEuLrqok0Qiwfz8PNPT0zz33HOcOXOGbdu2sWPHjnOizYPL5aKzs5OOjg5isRiRSIQzZ87gcrlob2+ntbV1U6dJhbiQqXO1I/KVV15pHD16dLNPQwgh6rKm9k6dOkUkEsHtdjMwMMDQ0NA5V1+VTCaJRCKkUikcDgetra20tbWdc+cpxPlKKfWUYRhXLnecjHgJIcQqWVN73d3dzM/Pc/LkSX79618zOjrKjh07GBwcxOfzbfZpAhAMBgkGg2SzWSKRCPPz8xUbc58r5ynEVifBSwgh1sjhcNDR0UFHRwfRaJSTJ08yMjLCqVOn6O/vp6+v75zps+X1etm2bRtdXXpj7vn5eeLxOH6/364DE0KsH5lqFEKIdRCLxXjuueeYmZnB5XLR3d1Nd3f3OTe9VyqV7DqwfD6P2+2mvb2dcDgsdWBCrIBMNQohxCYKh8Ps2bOHWCzGqVOnmJ2dJRKJ2MXtra2tBIPBTR8Fczgc9gbc1sbcU1NTdj+wtra2TW0YK8RWIz9NQgixTpRStLa2EgqFmJubY3p6mng8TjqdJh6P4/F47BB2LoSblpYWWlpayGQyRCIR5ubmKurAvN7N2zJJiK1i83/ShRBii3M4HHR1ddHa2srMzAyxWIxcLkepVKJQKDA3N0dLSwutra3nRD8wn8/H9u3b7TqwaDRKLBYjEAjQ3t5OMBjc7FMU4rwlwUsIITaI2+1m+/bttLe3MzU1RSaTQSmFx+MhlUpVjIKFw+FN33PR7XbT3d1dsTH36dOn8Xg8dh3YZk+VCnG+aUrlpFLqlUqpE0qpZ5VSf1Ljdq9S6n+bt/9AKTXcjOcVQojzkc/nY3BwkO3bt+Nyuchms3i9Xjo6OnA4HExPT3Py5EnOnj1LJpPZ7NPF4XDQ3t7Ozp072b59O0opJicnOXnyJLOzsxSLxc0+RSHOG2se8VJKOYG7gFcA48CTSqlHDMP4edlhbwEihmE8Tyn1BuDjwOvX+txCCLFewuFa3et1V3trT8e1CoVCtLS02PVUqVSKtrY2urq6iMfjxONxYrEYPp/PrhXb7I25Q6EQoVCIdDrN3Nwcs7OzzM3NEQ6HaW9vPyc69wtxLmvGVONVwLOGYZwEUEp9GXgNUB68XgN8yPz3A8CdSillnKu9LIQQW9JKwlSt45a6frWUUnR0dNDa2srs7Czz8/PEYjE6OzvZuXMn8Xic+fl5JicnmZ6eJhwO09bWtukBx+/309/fTy6XIxKJEIvFiEajBINB2tvbz4laNSHORc0IXv3AqbLPx4HfqHeMYRgFpVQU6ARmyg9SSt0K3AowODjYhFMTQogFC6GpiK60UFXX1zIPBID1DTpOp5Oenh7a2tqYnp5menqa+fl5uru7GR4eJp1O24Xu8/Pz+P1+2traNn3ja4/HQ29vL11dXXYd2Pj4OF6vl/b29nOmcawQ54pzqrjeMIy7gbtBN1Dd5NMRQmxZp4AcOny5ACdnzrhwOp24XC6zqN0FGMAE4AR8QBgIsZ6/Oj0eD/39/SSTSaanp5mYmMDv99Pd3c327dspFotEo1Gi0ShnzpzB6XTaLSk2szGr0+mko6OD9vZ24vE4kUiEs2fPMjMzQ1tbG62trZu+WECIc0EzfnucBnaUfT5gXlfrmHGllAtoBWab8NxCCLEKnUAeKKBHvwpks1kKhQKlUqnG8TFgyryPi6eeCtqNUN1utx3WFkLb2gWDQQKBALFYjJmZGcbGxgiHw3R1ddnbEyWTSebn55mbm2Nubo5gMEhbW9umtntQShEOhwmHw/bG3DMzM3ZD1vb29nOqc78QG60ZwetJ4PlKqZ3ogPUG4OaqYx4B3gx8D7gJeEzqu4QQmye06JrhYf3RMAwKhYVAtvCxAKSBeZLJGLOz+v+O1ubTfr/fnlKrDmL1Pi4X0qobsEYiEeLxOO3t7XR0dNjPnc/n7VGw06dP43a77VGwzRxlqt6Y25ombWlpob29Hb/fv2nnJsRmacpejUqp/wj8T/R4/N8ZhnGHUuojwFHDMB5RSvmAvweuAOaAN1jF+PXIXo1CiGZbqtSo+lfhcoX4Vs3V/Pw8+XwewzAIBoP4fD7cbjeFQoFisWh/rPW7Vim1bECz/u1wOMjn88zMzBCPx3E6nXZT1oXXYJBIJIhGo6RSKZRStLS00NbWdk6EnEKhYNepFYtFfD6fvTG31IGJ812jezXKJtlCiAvGerSIMAyDZDJJLBYjmUxiGAYej4dwOEwoFLKn1YrFYkUQW+pjLUopO4hZI1y5XI5AIEBvb6/dcNXlcqGUIpfL2SskS6USHo+Htra2c2Lza8Mw7I25c7kcLpfLnrrd7HMTYrUkeAkhtqSN6K+1WsVikUQiQSwWI51OA7rtQjgcpqWlpeFpv+ogVi+kWasIC4WCvZ2Px+PB4XBUjJSl02lSqRT5fB63201bWxudnZ0EAoFNH2lKJpPMzc2RTqdxOBz2xtxSBybON40Gr3NqVaMQQlSrF7SqNbu/1mqUrzDM5/N2A9TJyUmmpqYIBoN209SlAk8j9V+wUI82MzPD9PQ02WwWt9ttF9cXCgXy+Tygu+UrpYjFYpw9exbDMPB6vfaKw1qLBNZj0UA1qw7M2pjbulgbc/t8vnV5XiE2i4x4CSHOafXzSQbdYyuE7rOlFtVpnSuy2SyxWIx4PE6hUMDhcBAKhQiHw02rvSoWi3YDVofDQWdnJ21tbXbAs0JasVgkm83aqyHLR+YCgQAOh6NmPRo0b9HAUgqFgl2IXyqV8Pv9dh2YEOcymWoUQmwJC8FrBt3wtBU9WB8HJoESel1PC8lk6JzvmJ5KpYjFYiQSCUqlEi6Xy26/0Ixu9LlcjunpaZLJJG63m66uLkKhxas4y88nGo2SSCQwDINAIEA4HMbr9VIqlZatSVvpooHq6+rVdJVKJXsVpDVFam3MLXVg4lwkwUsIsSUsBK8z6LClgBagDd3UNGVen+DEiRJOp9PeT/BcWMlXT6lUqijKB/B6vXZRvsu1tkqQVCplTz9aDViXmrYrFArEYjHm5+cpFAq4XC572nSpc2lk0YD171ocDseyo2fpdJp4PE42m7Wnc9va2tb8HgnRTBK8hBBbQuVUYw6ImpcS4AXasfpyxWIJ4vG4vbrQ5XLZIexcrhUqFot2PVgmkwGwR55aWlrWNMITjUaZmZmhWCwSCoXo7u5eMrBYqzSj0agdCK2WFGsdTWx00UC9kJbL5Ugmk2QyGTsYdnZ2EgwGF4W1zV40IC48EryEEFtC7b+fJXQ3+Xl0GHMSDLYyP69HQUqlEomEDmGpVArDMHC73XYI83q9G/gKViaXy9khLJ/P2724wuHwqlchlkoluwErYDdgXS7QlTdmLRaL9opIq3XFejEMY8lRtHQ6zdzcHNFolEKhYK8cLQ+GjdSirWTRwOHDcOgQjI3B4CDccQccPLhe74A4H0nwEkJsCcu1j0ilUszPz5NIJIDFozNWiwcrhIHeD9EKYc2oq1ov1hRbPB6nWCza06jhcHhVI3jWCshYLFazAWs9VmPW+fl50uk0SilCoRBtbW2bOpJYLBaZn59nZmaGXC5nL1oIBAI1p0BXu2jgK19xcdttLtLphaAaCMDdd0v4EgskeAkhLijVozMej4f29nZCoZA9smNN6cXjcXs1n1VXNTjYQiKxuHfUudAfzJr+i8fjdhG8FR7D4fCKe15lMhmmp6dJp9N4vV66u7sbnkbMZrNEo1G7MavVkqL8fd5ohmHYG3NbdWBtbW20tbVVjGg1slig1qKBa6+FiQlYqC/cDsDQEIyMbOQrFecyCV5CiPPaahulVv8RrteUs1Ao2CEsk8lwySWgi/VbzIun7DGbd35rVSqV7PO2RvB8Pp9dlL+SKcBEIsH09DT5fJ5gMEh3d3fDI4DWeczPz9vvczgcprW1dVOnclOpFJFIhGQyaW/YbTWWXYnyEbNgsHzfTjd6Za2eBq+5p7q4IEnwEkKc11ayr2I91n6K1ihRMBikra3NbjBqyefzeDxx9OrIGfPSCnQCXeRyLYtGlRbOrwRUjvRs1K9VayViLBYjl8uhlKooym+kHswwDObn55mdnaVUKtld7VcS4DKZDPPz88TjcQzDwO/325t7b1aRey6XIxKJEIvF7K99e3v7qhYIDA/D6Oji62XES5ST4CWE2HRrGRVa+Hs9jw5EIfRIlGvFwaZQKNg9oaxpSKtVgjU9tvB8CeAsOnzFgRJPPKHDTFdXF4FAAL/fj9/vRU89TQBJ9AiZvsRiHrxeL263u2bwWI/RsnpNWq2ap+VUN2Dt6Oigvb19RcGpWCzaLSny+XxFJ//N2gLIqgOzvvZer9eegm70tR0+DLfeCuYAIyA1XmIxCV5CiE23llGrhfvGgAiQNT/3E4mEVjytpp9TF4lHIhEymYw9PdbW1obXW2sqKgvMcPz4DPF4nFwuZ2/Js39/EAiip58MdBPXApDnxAnrNSjcbjcejwePR4cxj8eDz+dBh7Za57iil1RTvSatjazoXGkD1qXOoXzRQzAYpLW1ddM60NfamNvaLqmR7yNZ1SiWI8FLCLHpdHgygNPo0apWrMDRePCy5NAjUHFOnMgButeVtffhcn88F48y6S2HgsE4x44ZXHJJAN2UdXEwMAw9nWbVjiUSCfbv120sdBf9gPm6vICX6WkXDoeDUqlELpezLxZdT+Y2X1PevL8P8BOLLfSiWmtPKitoxmIxu61Go01ayxuw+nw+enp6Vr2S0lr0YDVmtVpSbFYD1GQySSQSIZVKoZSitbWV9vZ22ZhbrIkELyHEptN5oYDuOp9GB5U2oA3DWDooLZU1MpmsXWBu9boqD2G1VtfVf7wis7NRBgfnSSYLLBRPt5rnu8CaCkyn0wQCVk1Y3rxYIUxx4oT+vepyucxpST8+nw+Hw0E2myUczqFD1zR6SrOIrhWDb33LhdvttkfK3G63PVJWHcjKL1YH+HphbbVNWqPRKLOzsxQKBUKhEF1dXasKKNbKzPn5eTvwtLS00NraumnbPGWzWSKRiF2b1tLSQnt7+zm944E4d0nwEkKsu+VqlSr/9qeBOXQ9lIOpKT3KUG/Uo9E6qGx2cQgLBoOEQiGCwWCNGq5J9OhUG9bKRcNYCAaRSITBwbR5TNg8bmF6zvqVqc/PMF+XFcJKBAIOnnnGg8vlQilFOp2mUCgAenscn8/Hjh1+wI8e5VLo4JYF0oyMpMlkMqTTaXtlXclcOmcFLJfLVbHVTi3VQaz8UiwWSaVSpFIpisWiPRVphaDq0FYqlYhEIszNzQGNN2CtJ5fL2S0pymvu1rsxaz2FQoH5+Xm7FYnP57M35pYO+KJREryEEOtuuRqu2rdngQi//KVOVaFQiI6OjqY0MrWmA60C8/IQFg63oEPOJLpuzEBP8bVRKgUr/sAqpWu7YAQ9khUGuoGOuiN1hmGQSqXsXlul0sK+kT6fzw5h6XSa4eFs2T296BCmL4axEKQKhQLZbLZiujKXy9lb6hiGgWEYdqAq3zLHCljVl1JV/4NsNksikbC3WXK73XYIs7bisS6GYditGjweDz09PbS2tq5pKtRqSZHJZDa9MathGPYiDKsOrL29vWIRhhD1SPASQqy7hb+3Z9GjRwF0kFAYxtKjVnNzBSKRCPPz8/Zy/46OjqZN81R3fb/kEge6GD6EHmmythwqoKcI24BWQiGnec4ZYBxd2B+zj3vyyVa6urrw+/32VKD10QogtRqelu8b2d3tIZFIo0fLMuZHg2AQfvpTtz016ff7axbDF4vFmoHMGlkDXdhfXdTv8XjsLZWqA5nV1ywajVasjLRWcZYH42w2y9zcHJlMBp/PR3d3t11n18illmw2y/z8vN3+wefz2aNgmzHqZC3CSKfTdi+4pUZohZDgJYRYd/rvYRE4ha5ZAj2q5GdmprK2qZ7q5f5+v5+Ojo5FvbbWIpVKEQzG0a0iiui+W1ajVAO96XbKPPcQOoRZIy4GeiowAkzxb/+mQ4nH4yEYDFYEo/IVjFYYc7lcdquHevtGGoZBNpslnV6YZiyfniyvE/P7/XWDSLFYXBTGstnsokBWXjdWfrEe19rrsvqcg8FgxVZM0WiUqakpstms3cHeGmlb6m/LcrVpyWSSRCJBoVDA7XbT3t5OW1vbpmzvlMlk7Dow0CO07e3t5/Sm62JzSPASQqy7yr//RfTITRpIceLEwnSaFRisS61RD2uaJxKJmA1NPXR0dDStCWftmqwiMItulBpCB7IEutDdhw5gIcpbP2SzOXtkxupVFQgE8Hq9FAoFO/CU/251OBy43W6cTieFQoFMJkM+n8ftduPz+WruG5nP5+2pyXQ6ba+KVErh9XorwthyozDVqytrrbSEheBYHsocDgfJZJJYLEY2m13UpBWoaMDa2qpHBB0OR82pzqUu1X+PMpmMHf4cDofdANdaEbncAoNmKhT0CG00GqVUKuH3++06MGk1IUCClxBiAyyVh4rFUkVwyGQy9h9Wj8dTEcTKV8lVb/mzXnU2ShnoqcZnzY9z6JGtfqALa4XiwirHNkIhl13YXyqV7GahuVzObha6c2cbiYQLPTWZsy/BYJ6f/jRHPp83358iyWSSTCZj99qyVtV1dHQsKnIvFov2aFj1++l2uyvez0ZHhgzDqBvIyv82uFwu+zFzuZxdj+V2u2lpaSEcDuP1epmdnSUajaKUWlUDVmsKtHoq1OpCb21PBHpFZiAQWDJ0Njr1WR7YGjlHqw4sn8/zz//s5tChdtLpMNYOBtJc9cIkwUsIse5W0oHdMIyK4JBOp+1C7/K2C+V1Tclkkrm5OdLptB1s2tvbmzKaUZkH8sAY8Gtgyvw8xL/+ays+n8+emuvq6qKzs3NR+4PyZqG6R1cIHdYqj7NWT+ZyOoBZIce6vzWqBHqUsK2tzW5vUD4laBW6W9OT1sUqunc6nRWjjFZxf6MMw6g4P2vKsjyQWeHPKkK3RoDC4TDpdJpEIrGmBqz1WC0pkskkAH6/317AUGshQSMja+VWEtbS6TSXXRbl9OkMehGGtc2Uku2ELkASvIQQ57zq4GDVIlnBwSrstlbTJRKJpjW8rJ9DMugQNso//MN8Rfd5q+g7FAqxbds2ent7F00Pejzz6GL8GfS0Zhf6j7GPZNJrF7jXYo2Czc3N2a83n8/jcrns+irrj351LZl1HuXvab3pyXrTvY2oDmTlNVDpdNp+j6waKGvrov7+/qYGsHw+bzdmLRaLuN1ue3ui5V5bvUC2VGir97fykksUelQzga4HHESHMCdzc/VDm9h6JHgJIc47Vl1TKpUinU7b03JKKTssWKMsVuuBjo6ORSv/GhmJq3fMgiJTU3NMTEwQjUZJpVK43W57ys/hcNgF5b29vbS2tpqjdR70H+Cz6MaxCfS0Y4Cf/Sxk13qV11KVN0gtl8vl7JWZyWSyoi7M7XZTKBQqCudhYVrQerxCoUCpVLJry6qne62RsbUWrhcKBdLpNHNzc8zNzdk1cFZQ83g8hMNhtm3bRjAYXBQc19qdf35+nnQ6bTdmbWtra2oj1Hphbc+eIuPjRXS9YAFdH1ikr6/I44/XfiylVN26tKVG2MS5TYKXEOK8Z/0xty7WNJwVfqw/6J2dnfYG1lA+mlXCqruxVP/KWy6kWTVnVqCwpj2VUsTjcTKZDE6n0+4Xtm9fCD3FaPXmKqFXTc7z4x/n7Wk5a7VjeV8tKzRVBzKr432tRrFWiCkUCotGo8ofWyllt5IoDxHlf/jLpyZXOj1ZLZ/P2zVw1vuXTqdxuVz2oomF5raqIojVWmnZiFxuYeFDqVTC4/HYxfjrFVyW2kD7939/+ZG16ks95WGt0dDWrNcsiwcaI8FLCLHllEqVBfupVMrugG71Wtq+fTv9/T3mPZ5D9+4Kmx/VmjahTqfTduuLlPmX1uFwkM/n7XYDL3+5B92mwoeecnKY//YwNpa1w5YVCgKBgB2YrDqqbDZbMbVVvdrQqu+yWi5YozxWt34rrFS3l7CeJ5/P249v9f8qFAp2Q1br+UKhkD3d6/P5Vj09aa1OjEQizMzMkE6naWlpYfv27bS1tZHP5+3Xbo1yWuoFsqVCRalUsnuSWaOTVmPW5TYJX41mBpPl6tPWGtaWC2/V7+tSwVLCVyUJXkKILc8q2E+lUkxNTXH27FlyuRyvfKW1EtHLQoNUPxAinQ6vuQdT+RYzVnCxRqWuuSZBOl1koR1FEN0cNcuxYwv3t+qvAoEAbW1ti/pUlYeR8map5b+zPR4Pl11WJJWythxymq85REtLiFhs8fY/1vtWPg1YHsqy2SyZTMb+WCqV7H5k1qhea2sroVBoxTV2Vnf/qakpTp06Ze55GWBoaIht27bZobJWUX95WITFPdPKp1fLZTIZe9TNqj9ra2trWpuSc0GjiwpWE9auvtrJ6dO6Zm1hFweHLB6oQYKXEOKCNDMzQ3f3BLrAPY+e9nOjg0mRH/7QSzgcpquri9bW1jV1IrdGViKRiB2kXC4XhUKB2dlZEokELpeLzs5Otm3bRiAQqJg2tUaC8vk8Xq+X9vZ2tm/fTmtra83nswJTeSDr77daVhjohQEprE27jx7Vew52dnY23AHe6vlVHsSsKU5rJWOpVEIpVdGDLBwO2w1hG5niKpVKnD17lpGREeLxOIFAgG3bttHd3U0oFFoUoKpXWtYLo+U1buWd+wFisZgdlp1Op7010mY0Zt1sjYyklUolBget+jUrrF0EuFAKqnafuuBJ8BJCXLB0vkihe3PNo4OIB3Bx9GiCRCJBLpezw053dzfd3d1ralNR3ubAWgzgcDiYnZ1lenqafD5PIBBg+/btDAwM4PF47PYaiUSCqakpYrEYhUIBv99PT08Pvb29tLS0LDmypF+rAZw2r3Gi/0jO853v6EUBVp8wq0dYa2urPW25kuBpjdQlEgni8TixWMwOZPpc9OpJq8Gq1d9rqSJ6wzCYmZlhbGyMWCxmf02s+5dvdF5PvUBWXuNmLWiw6uGsGkGrAW5bW1vFNK3QhodhdBT091gJ/f2FjHjVIMFLCHHBqiyYz6C3+4kTDCpOnAjg8/nIZDJMT08zOztrTxVaIayzs7PhlguLi/NzwDzBYIxjx3SH85aWFpLJJBMTE0QiEQA6Ojro7++np6cHl8tlT5tOT08zOTlpd0i3mqpaq/Sq929c2LbpOfQfRtBTqz5mZrx25/n5+Xm7KW15YX4gEGhoheVSrEL6WCxmhzJrKtPpdOL1evH5fHYoq9UKQynF3NwcU1NTJJNJe2rT6XTaTVqr+6ctp3wngfJAZk21FQoFUqmU3RDW7/fT2dlJT09PU1dEns+kxqtxEryEEOeV5ds7VKrVpHUp+XzebnNgGIa9557H47H/4M/OztqrFq3A09raaheY1xodqj9AUmJubqHDudvtpq2tDZfLxdmzZzlz5gzpdBq3201vby99fX2Ew2E78GSzWaamppienrYL+QOBgB1GrBDW2elH15Mp9HTqwsbbJ04stOOwgo+1wXYsFrNHhbxeLy6Xq2JkbakVlssplUr2aF4qlbIbw1rTsdW9yJRS9rZKAPF43G4Z0tLSglLKHrWzpjXXUiRfvuggm83aG3SXL5oIBoP2dHT5lOVaWl+cr2RVY2MkeAkhzisLf8sM81L9B96gfM9EWNwaohFWYfz8/DylUolAIGBv0WO1jpiammJubs5eXWgFnuo9J3VosB45gq4nWwgEVqf6ZDJJJBIhnU7jcDjs2qJ4PM7p06eZnZ2lWCzS0tJCb28vnZ2dtLS02BtOW20ZUqkUhULBDgDFYtHslK/Q4ctvnoMPcJDPFyp2CyhfLelyuSgWixQKBYrFoh2qrIBhFbkvt8LS+rhcGKnVLNd6bmtlncvlQilFsVi0e4LlcjkCgYBdDG81lA0EAnbt2loa6ZYrlUokk0lmZmaYnp62X7s1ammF4lo1ZCttfSG2HgleQojzysLfrBgwjV491YYujC8BJ9GhojmtIaw99yKRiB1mOjo67BEWK/BEo1Hi8TjZbBaHw4HL5cLr9dqrv573PD96am8SXUfmQW8Z1IJhVK6ezGazdpd3wzAIBoO0t7fjcDiYnJzk7Nmz9lY74XDYLjRvaWnB4XDYjUJTqZS9WfUll3hJJq3NvzP2cwWDPp57rrJTffm2TdZHq5A6m83aKwd9Pp9dY2V1m29khWV1GFtqdKhejzbrsaxNsFOpFDMzM2QyGTweD8FgkHw+TyKRsPfytBrpWtsrWasw18IK4Vbz3EKhYDeddTgcS24yXh3IpPnphUGClxDivLLw93mhJktrQYetNDqUFdEFvs1pDWEYht1jKpfL4Xa77SlGKzRYU3PxeNwepbH+uO/caaCL94vmuRfQo3Nefv3rkB2cymuGisWiPepmjTa1t7cTDAaJxWJ2jVc2m8Xv91eEoGAwaI/aWY1CrRYJwWCQbDZrd/5vZGNya9uf8t5oyWSSVCpVEcK6u7tpb2+3A02tFZbVYcRqjForkFUrn54sXz0J2K06MpkMbrfbDsjWqFgkErGnCK3RqZaWlornK68pW2kQymazdr84a2q2ra2NlpYWO7Q2ssl4+Xuw0jo6ce6T4CWEOK8sHhgpoFckRtGhxoseAXOiQ1mCEycMe3SoGVNOiUSCubk5uxu9FcDK/0Amk0m7iNwwDC65xIMeiXOZ55xGr6hM88QTSTsYBYNBOjs77a2FlFL2qIpV9G5tBN7a2mrXHZWHikBALwywmqX6/X7i8Tjz8/P2Cr22tja7TUYjG5Nb9WtWSwVrV4B0Ok0sFrPbYlibYbe2ttqrQK3XUa58irI8lJVvbVQ+pVn+sXyUynqc8nO39oVMpVL4/X76+vro7e3F7/eTy+WYm5tjdnaWbDZrB1qrfq1ceRCqDmVL+fu/L3HoUJxTp+bp68vynvc4+IM/CNurRMtVN8VdbqVlvfdBnD8keAkhziv1y2MM9EhXBL1i0IlujhomGtV9sMpHO6yRobVM76RSKSKRCMlk0u6IXz7aA3qEJpFI0NcXI5m0lnxZU6F+WlpyPPecbhVhbXhtFdNbIayrq8vur2V1xbc64Fud1p1Opz26ZU15ORwOe/rQamoKEI1G7XYW9fYrXGpj8vIRMWs61eqSH41GmZmZsRcgAHadVVdXF8Fg0J6Gq6VUKi0aHbMCkmW5PSytvTyj0SinT58mGo3aI2AdHR32VkeGYZBOp+0pXWt62NoGaaltlaqnC63Pv/xlZ9Xqvgx+/zwf/Wic3/5tXQdmjYItVetVKBRqjpCVvw/lCw+q23GIc5cELyFE0zSy6fR6PUelFHoULEEwqPjVr1rsQGS1MyhfDWe1IFht0XM2m2Vubo54PF6xKXd1w01ry6Bazx8MBu0gkEwm7VGZZDJpbx3U2dlpBxiHw2F3xa+eRrRGt6x6LKso3VoV2NLSgs/nI5fLLZoWq9dAdbmNycsv1v0TiYRdgJ5IJMjn8/j9frtmzRpFK5/SrKd8qq78Y709LMuDSCKRYHx8nHg8jsPhIBAI2M/ndrvtVZz5fN4OmOVNX60FBsttq8T/196bR8mWlmW+zxfzPGfkcDLzDAXUom1FoRbqsl2XUlvbVgvUC+tCCeiyL8tuLy1w+4JQgzRFgSINSl8HoJe3lS4QBJHDWCoi0DSoCEpruwqqzpDzEMOO2DHvHfu7f3z5frEjMiIzMjMyMs8572+tXJknT2bEjr3z5H7OOzwPgHvv9WJjww81w5cGLVEsL3fxd39X1dur7qrlUYTSqJalu1LozrQ8zB+NmT4svBiGmRgH/U4/6a+Q44g6y7KGipN4PN43j9XtduH1erUFwXHnwSzLQrlcRqVSgZQSsVhMV1gGITd6ev5hFgjUAiwWi7qKRJWsWCyGbDaLdDoNx3HQaDT0Jl8ymUQqldJtSGp3kj0DBWCTKSjQG4ofVxCMGnonc1RqT1J2Y6vV0tUwaklS9SwSieiW5mAl7TDclaGDMiz9fj9arZauTtIcnGVZaLVaWri4Y3QAIBgM6pYtLS+4kVL2+YBlMh2oWb4OgHmoDVL0Obg3Gg19XQBlSZFMJhGLxQ59vaMYFIZugUgMVurcoowF2fRg4cUwzMTo/e62ABSgWmphAIETC6+TiDrHcbTVgnsGKZVKwePxaA8pEiiBQEC3Io/TtonHu6jVDKiqWxfqHGQQj0f3iUSykahWq6jX65BSIhgM6nk099yYlBKGYWgRVq/X0e12EQ6HEY/HEQqFYNu2FpmJREJvQ1YqFVQqFT3wTzdbcqynzD236KA25DiGpIPB5O6BfRJi9EaVP3KzpwqQ2yqCPMUoeHtco1picKCfqn+2besB+EAggHw+j3w+3/fam82mFi71el0L2nA4jFwup8/JMLHSc3DvZ5iDOx1LpVKBbdvw+Xy66jip+S2Kdhr25mbQ/mOckHHmeLDwYhhmYvTuQ00Am1BD5ADgxcZGpK+acfzHbkMJGhJ1viOJusHIHjJIDQaDOlOxWq3q+aTjzIP1jtWBGvovQ52LICqV9Mjg5W63q5+/1VKWD9FoFIlEYt9MELUlSYjV63U9eE/eXe5NyPn5ecTj8b4hfar8+P1+tNttLTzpWCj4OhAIaEEw7jlwD+yT6zu1Bf1+v/5ZoNmwWq2mn9M9r+Xe/AsEAn0eaUfNTnRvWJqmia2tLZ0QkE6n9TmmwXWqDHa7XdTrdZimqS06otGoXh5IJBL6OY7j4E7i220BEovFtCnvaTAYMn7YpuWgIONNy+PDwothmImxX0tYoM29p55qDB3QjkQiYwmx3mObUF5YNNvjx+Zm+Mg3406n02e1MDj0TPE2g+7o48yD9f5qG8qkNAagDqCEJ57oWVEcJGRo/opyGUkkJRKJoTE1lOVIopLmn6jqQ35glO3o9Xp1bA+Zv9J8l2maeraMBBNVfKgNeRzRMziwT5U1r9erh91p1oqqcO4MSrenmPv7qCoWCoWOXKFpNpvY3t7W818UvD24YUkLBCTO3Z5toVAI2WxWi7CPfCSEBx8Ux3Jw73Q6uiJHwpnO+TSqT4Mh427nfrcOGFxwoLdxKnV3usM9Cy+GYSbGYe3AUQPa4wix/Y/dBom6J5/svxm7h7YPE3VkkEpDz9TucdtDDM5jeb3evnDn4cfqAFiD8uyiDcsUajU1iE+RQ6lUSm8ljsLdCqUq1EHWGK1WS4sqt9UCzYGRoCGfK5pzojieZDKJeDyuN/6oYuWOyaFcyGg0euD5PYhBGwj3wD7NTpH48Pv9etjd4/H02V+422YkwOj6j9uyq1arKBQKsG0b8XgcuVxOC7BRG5ZkpUEtUxLnlOVJG5xHbZMCPWNWwzB0RiQlGZzUk+64jBJk7gWHQQuQwU1LznRk4cUwzAQ56gA8hQ+7RQEAbYNAAioYDMLjGa3qpMQ+gUHVimGPNapaNej4nkgkkEql+obdB+exaB7MPZfT//BNqNaoOjEbG6q1KaVEqVTSLU+yojhopoysKY5ijUFtPBJhtFRAIdiBQEBvObqrY2QBkUql4Pf7davN7dBPm5D5fH4iFRka2KefCbJxIDsL2r6Mx+NaHNJG4qDTvjvyaH980/Dr7zgOyuUySqUSACCVSiGbze57XYMblu12W7cK6Zp2u12EQiFdrXJvr4ZCoSNVDGlJgvJD6XFHbaBOG/dygVuQua0v6GftX/yLINbWKLkhBOVrN3wG7naFhRfDMIcyDZsIYPiNF1Di6Tu/M4x6nTIGg6A8xlHHQNW1warIQfYHxOCNLhKJ6DYk0e12tQhy+1WpqkQM+zMkLQAGvvWt3oYlhW+744FoIP6wSp1t20e2xuh0OlqEuUOpqWVHbTZ3pYtaXbOzs5iZmYGUUr/u3d1dXQWMxWKYn59HPp8/UTC1Gxp0dwtqcsy3bVsfcz6fRyqV0mKG2pruqphbiA8O7Q8KK9u2USgUUK1W4fV6taHtYSKHNixN00ShUECpVEKlUtELHT6fT4sut3iiKpb78Ye141784v4lEcrzdL/288SwTcvFxTZ6s5/Zvbf+rc/bHRZeDMMcSu9+QDE8PU7zV4PbsqDRaPQJsVAopKtYgzetYXS7XS3oBu0PBkOt6Ubc7XZ1G9K2bfj9ft2GdN+saR6sWq3Csiw8+9kC9XocKoux14qLxwHDcHT0kLu1STFAZH0RjUaRyWSGznMNctRWKB0zCahisYhKpbJ3jHGd/dhut7G7u4tCoaCPNZfLYXZ2FvF4HIFAQIdFb29vo16vw+/348d/PIdGYxEqQaB3XU4q1N1xQbVaTbvlk+FsIpFALpdDPp/fN5R+UOYjmaYOeorR6ycBSu3Do0AZkuVyGa1Wq8+MlQLAhRD4/Of9+L3fi2NrK4F0OolqNYFut3ftB9txtFhBCxGRSERX1s5DFWwUauvTQc/kWJ1rrngN+ToWXgxz59L7Pb6y9z4HVXmanPAap6p2kHhyz4iNI8Tc9geNRqNveDgYDPbNibmDp5vN5oGVBvfcDw2lD/pzEfV6XUfbULsxHo9rnydqV9Es1mEcZE1BRqDDsG0btVoNu7u72NraQqPRgN/vRz6fx4ULF5BIJFAsFrG1tYVSqYROp6NbnOR6T5uROzs7eNazdkFbnMASgEWQkegkbyVU2TJNUwtEqj6S6z+JyMFz7xZx9J4E0aA7P1XAOp0OIpEIZmZmjlzVcxxn37Wh9ttHPmLjwQebaLUqUHOLdJIoSP0CgCCWloK4dq0/2oj+c1CpVPqMWVOp1LmMFOIZLxZeDMOMQU/DVAAUoW6qYQBZSDmZdffj+HS5W1EkntRjib6K2LB24v7nkH0VEfeckDs42uv16q022hQcNmR+FBEUj7dRq1Hgt4SqkqUQi1n4xjdUZSwQCCCTyYy0ohh2bsa1pnBDwdrr6+vY2dnR1beFhQXMz8/D5/OhXC5jZ2dHbz6SUKXh/CtXvABqAP4JapszA2AOwCIsK3eqgsDtlk8boeRpls1mEYvF9ALHsBazuz3pHvYPBoPodDpalGYyGWSz2WO9lsFrc++9wMZGL0ZKnbsKVARWA0Ae1J574on+AXZ3bFKr1dJbrQBG/myeNbzVyMKLYZhD6L8/SaibQgmAjZUVZSo5TktsvOeoQG0CRqFuQt6xqySHCTF3ReywQXCqprgrbG4fqkAggLvv7qBeb0PNcwWgWmsJxOOevpbaMBFE82CxWAxeLx1LF2oQ39j7OIByWZm8kveWz+fTodzjDrMf1ZqCsCwLm5ub2NjY0PNOqVQKCwsLSCQS6Ha7uoVGrdhAIIDLl7t7x9+A8nMr7T1iAn/5lwnk83nMzc3tM4idNJ1OR4tE0zTRarXg8/kQjUYRjUYRi8W0oB72M+H+eWq1Wvp1VioVHcA9Pz+P+fn5Y8+1dTodBIMmlMiyoKrJmSFf6WBpqY3/+T8PzrAkQUnWHfQ5GvJn/62zh4UXwzCHMrw4ogTYU0+VYNu23oI7rgDrPUcBSnjQpG0IhUJ07BaiG2onkngi0UMVjMF24mG4fagajQae9rQu1HloQc2sCCixmEenkxq6oUgiyDRNnaP49KfHoKodALADNfvSBFDDX/91V1dYwuGwFpQejwepVArpdPpIN9NBa4pnP9uPej0B1dLqtU0H57FM08T6+jp2d3fRarUQiUSQTqeRzWb3GbDefXcESjh7oKp461Diq44PfrAnXrPZLJaWlnQr9TRFAbUkKWCc5gX9fr+u1g3O+g0eD5nC0kzd+vo6TNOEz+dDJpNBPp8/lqdYz+2+CTXztL+KNqodRxuWg7YXjuPoqmuj0dAbuGR1kUqlzvUs2O0MCy+GYQ7loPmrSkXqNfput4tIJIJcLndkr6H9VbUWVMWkjieeUIKJAo6j0Whf0PG4HDTX5a6IjSvEhOhA3SwLUPNv7b3jtvGpTyln86WlJeTz+aE3OZoHm5szoYQmVYpCUOLLxt/9XUPbR5Bjejgc1jdbGs6nqqPP59PROxSMPepc1Go1JJPUzsLe8yahDF+HVxo7nQ5KpRI2Nzd1C5W2KUOhEBzHwfJyZ+91+PceLwklwG7iS1+q67YuVcui0ShyuRzm5+e1CelpmoW2Wi3dLiaxQpFFXq8XV68C73wnsLERwOJiGA8/HMbP/VxkaFuxWq1idXVV53NSdBMwvqfYsLmnQED9+yqVjteOow1LEmKmaaJYLOrZQ2pdZ7NZhEIhzm2cIiy8GIaZCGRESgKMhpvHFWAH/a637a62ErjrrjrqdVpHD0AN+UcRi4Vhmke7WdOAtbsidhQh1h9jRIPRJgADf/zHBZ2NGAgEMDc3h7m5Oe1BRaaSfr8f6qFrUO2m+t5jBgEk0G6r+Zxms4lisai3IamtR9UX27b1TI974N8twsjSwP1xJEJVnW0oASn3njuNWi050pqi2+3q7Uz3YHc0GsVznuPdExFdqCqgB0Ac0WgSTz2lNjdpgL1SqeDZz15Hq1WGarWFAKQBZBCN5lAu54+VlzkuZJ1BG6Ef/7jAgw960Wr59469hVDIwSOPAD/1U76+Kqn7PJMBa7vdht/vRzQa1a3KYZ5iJHbo3E5r7skdum6aJmzb1l50JLr8fn/f7BgJMmYysPBiGGaiOI4DwzBQLpePJMDG9QpT96kOqBrW2wITWFkJ6WrYcdy93QP25NY+atNRVZNGP5ZlKXPYjY0NbGxsoFgs7s3zqMehYwyFQviu74pDiR0/lEhpQ1XSuohGPajXo1CtyBioxRuNGvja15QAi8Vi6Ha72n3ffSMl93eyLuh2u33RL3ffTR+VocSfA6rcffSjSmhQG43anX/4h14tEpaWJB5+uI4f/uFyXxuUqkcUTE2xTJFIRNtQdLtdpNNp5PMZKOG6BbW8Udm7xiE8/rgKNM/lcshms4hGo6cmxBqNBu6+28TaWg1KNM5AicA2lpaa+Ku/Uj8X7pSEQXNWqv5KKZFKpZDJZHQywKCnGG3juqti0wylpmF88oIjs+FAIIBOp6OXC+hYhw30n8fNyfMOCy+GYU6FQQEWi8WQzWZPbK7ZEztlqJtzEEqMdHHjRl0P1FN0EAmx49wgaKbHPWDvFmKXLrkNXQHyJFLf2/9YVLEqFApoNBo6i9Dj8eDee200mwJqtscPajVGIh00Gk0oISTQG+DPAkjCNFW7jiwu4vE4AOjAaTJppc8TJMSUMLahNua66GVrqjbvn/5pRTvVkzXG3/5tFO9+dwqdTmzvOMMIhcJ4xzvCeNGLPNp41ePx6Kqa4zjodDp4znNqaDRs9CqVNMcXATALNd/WRU98VvH5z/dc6x3H0X5V2Wy2L41gUng82LvGDajr2ksjIIPPUVFHNCfm9/u175zP59tnwOr2FKOZMcK9Qev2FDtNqHpJZq9uHzgK03bPkLkzLD0ez77qWDAY5CH+A2DhxTDMqUIxLOVyGY7jnFiA9YTXLlRrjra6PFhZCcLv9+ubdKfT0TeJQCCgRdhhIdejICFGFbGlpSZ6W54m1Nr/HIAUpBztmWUYBiqVCmzb1hEwXq8XrVZLiyJAtaae+Uwf1LzXBtSAOg3xB/DFL6pIG6ogtVot7eMUCAR0DBO5z5MAk1JqAZlIyL3XQG/QH29vd/WsUKFQQKFQwEtfWkGxSELQC1UVksjngfe9T7Wp6LWQ8KDtzWc9ywclqOpQ4k6gN0wehRJkdMMOA/DhySdVhclxHH0slEQQDAb1huJnPhPB294WxtpaGMvLIbzlLeJYrbreoPt+Ll4c3gIcZc5KJrWAMqZdWlraJ4KBXsvbXRUb5ilGFdLTnMFqNBqoVCp9xqxkSUHP63akd8+RDduwHBRk06zonVdYeDEMM5VIoEEBFo/HtWg4CvvvOR2om3gLN2+2+gbmfT6fDlymm7cQQrd4aFA9GAxqMeIWJYd9Lh6ntlwVqk1WgKoahfHlL6sqBz0+VQDoex3H6asyCCHwL/9lDK1WcO8xmqB2o6KMnjBSAeHveIfy0aIWUTAYhGVZOoeRRCadh2AwiHQ6jUwmo4/n2c8G6jRW5iIaBb72NejzRW933WVDtSTrUBWrOSjx5MfqquhbXKBYI3L+f+lLadjeQq/K1tl7PR0oATYHVf1yAHjx5JMphEIhbeVAHlZerxe1Wg2NRgNXr3bwq7/qRbvthxJsqvL0zneG8bKX9exDxpmjGjbo7mYcs093dmSj0UC5XEaxWIRlWUgmk7hw4YI2nh1ViT0oQHxwaP80qktkm0H/QfD5fNqS4iAj3sHqmNupH1D/JocJsjtpoJ+FF8MwxzIv7f+a4UJl2Odt20a5XNbO7LFYTGcWjiN+Zmf7qzLuSs3qquyrHtD/xqkC4TiOFmD0v3MacD/Ojaw3H0XYUDNKBTz2WM9BnVpGNNfl3sgUQugB+ec+twlVBVIGqkpEkLCkjUnafAS+9CUPbNvWlTKa0/H5fNq2gubUqK1JG23ZbBb5fF4birrbdgdtQ/ZXhJpQotPEwoKDL37Rp1tUfr+/L6OvUqngrrsKUFW7XShhFdp7vR0oMWdCCboQgIsAZvD4447eFiQTU9pCpHP7Qz/kwcYGVR8dqMqjxMJCC5/7nDrST386hNe/PoxmMwzyh4tEgHe/W+LFL1Y/D/T2gQ84eNObulhbo3PtQNltqPSAo8bbSCnRaDSwvb2NjY0NNJtNvQgxmBs66j8iwzzF6N+I3+/fN7Q/KciSolKpaGPWWCyGVCq1L5ZpFJZlDRVkbl0xONAfDKrq9bSXD6YBCy+GYVzCax2Dgub69cOrP8eB5kqq1apuQVKLbP/xCf3+O79ToF4XUDdsOnCBaFTgn/5J9H0tvTmOs8/riESg+3/kFGIciUT6BAm1RwarP2p+Xwy8AYBEqWSiXC5rywWq0gzeLEnwqJuMCtIGvrn3WDkA81A3fHpssrBo4tq1XiWEhuepOhEIBBCJRPSNs1wu63YQeVrZto1gMNg3S0QtosGqCr19+MNB/MIvePoqQuGwxLveVcOP/mhV35zJLZ6Ct9X5A1S1axeqOmhCiVUP1M+bCVXZuwmgBJ8vhN/6rYvI5XLaroKqiPV6HaVSCZZl4Ud+xAcljOTeuUnr6/DXf62u90/9VAe7u5TPGN87twILC0KLs0Huvps2Mr17j5nUr+O4gc6O46BQKGBnZwftdlufa/fPoPt8jxJRbk8xEmT0nwmqgLrDwCfR4rMsS1fBaFuXgr6PWnWTUo4UZAQN9H/84wG89rVBNJsB0BLKrRwzxMKLYRiX8Fqlz4Bu9Ovr/WJDfb3Y9zbs8+N8jlqQhmEAgN5gIwF2Wi0I2jSjG5c7LoYqZHRTpAF12sgjDmvRSilhmqbONyTXdL/fr5+LbpY+nw933RWBqsYYUMKksveIKai8vhxoBoqew7btvuF/alHR1mAgENAWFrS1KaWE3+/XIowqZaFQqG+Ojea03Hg8Hnz+80H8l/8SwvZ2CAsLIbzudWG85CVhbZ5Lz08tT4oqisej6AlIB6paZgDo4Kmn1LmhSKabN2/i61//OtbX1yGl1NUgMm6dnZ3FzMwMut0uXvACE7u7LSiR1Kto5fM2PvQhVcX6wR+ke5gN1dIkrzQPvv71gLZMoMpLMBjEs57lx+qqb+/rvfrYJxHobFmWtnSgOTi/36/bkzTnRyLKXdEa9W/Csqy+qthgELj7cU6yjUg/15VKBc1mE0IIxONxpFKpY20TDz724PzYc5/bwcYGbVjGof4zcusGa7PwYhjmxK3GSdDtdlEqlWAYBqSUOltvGltdQC8iiMQYObzTjQyAHuZOp9NIp9NaKIwDVWgoxiWVSiGVSvUNZi8sNOBeFuiJkyo+8xkLkUgE8/PzWFxcHHmDc7ekarUayuUyarUaWq2WFmHuNg4dPwlAEjaU7zdoOus+PzTH5bZH8Pl82mMMgL6JCiHw4z/uR7NJLv1hKCHjIBKp4bOfLWs3/Wg0qmeJCoUCrl+/ju3tbX19aPMuFAohn8/jW9+6gP/8n/2wrF64dDCYwtveNotXvEKZ+aoWKZnU9jY5Fxdt/M3f7LfcAICrV4GHHgJ6S4dehEJe/Nqv+fCiF432RjtKdanZbOo0gFAohJmZGYTD4T4RRYKazvFgJdL9fO6W3NKSg4cfbuIFL+gJ6WGVtUFPsaPQbrdRqVR05ToYDCKVSiEej09skF5tmjroLZaoKuBJKo9nCQsvhmHOhfAi3DNgAJBIJJDJZPoE2DSWAYBeHAvNYFHcDM3XUOg1DayPE2DdbDZRKpVQr9fh8XiQTCaRTqf3BuCBnkdZc++9snn4H/+jqvMag8GgFmC5XO7A5yThZJomdnd3USwWdSWEKjzU7iTrBxrEpygfOhf0RjNybnf0er2u42lIpFmWpb+OKom2betNPRLXyWRSt9SoUuP3+5FIqFzHUCikbTi6XWWmWyqVUCwW0Wq1IITAN76RxIc+lMPurg8zMw28+MVN/MAPePVW3n//71k88EB4r12l3sLhAN773v3bj7SMYds2Hnusi//4H22srtpYXOzida+zcd99PaE27N5IAvQg41r6mCADVtu2EYvF8Gd/NoNf+RW/nml65JEufvInm30VLYK84a5eDeOVrwyj2ez9Z8DdkqNqklvQjfIUo03bcXEcR0cykZdbIpHYZ+h7HEZtmnLF64xg4cUwJ2daQuYo2LaNUqmESkW12+gm3RMoQG/Lryc8TvtXFVUiKpWK3tKkmyDF92QymUPzB9vtNsrlMqrVqm7VPP3pGdRqgzepDmKxJr75zYZ+3q2tLRSLRS3crly5gitXrhw6VE2ColgsYmtrCzs7O7olSLmR1AolYSCE0LNawwQeVc1oeN8dvUO2HiTUBs8dCSkSf1RBJDsKqjRSu5dapX6/H/F4HJZlwTAMFAoFHYAdj8eRTqd1fmSpVNI2G3/913H83u8lsb0dx8KCwKtfDfz0T/t1m5EGu+n1jwOJUXe1bNjHzojSzGDEk2ma+OAHTbz5zR602xmoRYEgIhHRN9NESyRuEfW850lsbABKWIah/N58BwqUcT3FQqHQ2AKKrrFpmrpNnEqlEIvFjlVVG7ZpyjNeZwgLL4a5vRkUYMlkErOzGai5mzLUjFAWavZDTL1CRzNRFOdjGAYae3cIWsGn1mQkEtnX0rEsS8fuUO5hJpMZ2Uq0LEu3Qa9du4a1tTVUKhUIIZDP57G0tIS5uTk9w+WuUA3e/Gnbjs4vtScB6JmqcDissxjJvZ4WBQ7afjwMqlzReSMRFggEdLvStm2YptnnrE6fp3ZtLBbTW3c0S0dbm4lEQi9HNBoN7U3l9hYjcUnng/B6vX2C7KRO7bTMMY5Ie97zbGxuGlDLBmEoiw0PLlzw4ctfHt3eDIdt9JYvWgAuA/CM3ZJ77DHgDW9wsLLSwuJiC699bRM/+qP7PcXcVbGDrj8t0FCiAnnMJZPJI48Q8FbjOYKFF8PcGViWhVKphGq1imc8A1AbZkEo4dWG8pLKwnEOb/eNw0mqgK1WC6VSqU/QkJM8Oa+TlUAgEIDH40Gn0+nLYqR5rHA43NfmGxRQlmWhWCxiZWUFW1tbaLfbiEQimJubw9LSkp7Xikaj+ypS7j8DyvG+Wq3qNp65dwKEENqmIhaLIZ/PY2FhQc+BTQIKDKfMRIoYCofDEELokGeyIaG2ZTAYxMzMDAKBAGq1GiqVCgzDQK1W03FKFJ/k9Xq1xxbZGVCFjK4FfR1Zbwwag9Kmnbs6NulwaSFoDq2O3jKAmklbWekJtUEhfe+9wMYGGdv2lgIWF334h3/Y3+p0H+9BVaUXvrDTVxVzz5sNDu2PqhQ2Gg19XQBoO41J/gzdKrDwYhjmlkKJkhLUxp+A2vgLgATYtWt+ZLPZseatDuKoc2+DHmHuN7JzICHmdnUnMRaNRvXMVafTQb1e1+Ijk8nolf1RwomsKtbX13Ht2jUUCgVYloVEIoHZ2VldHXL7dY06P2R8StUKyplUr11qL7B4PI65uTlt8TAJV3UppRaAw6wpHMdBsVjE7u6uFonuWB5ACchSqYTd3V00Gg1te0Aijs4XbXSSBQctHNB5pWUKarNRlYaqV+4sQwB9IswdLn3UIfNxZ5rIzZ+qZR/4gI1XvaqLZrO3PBAK2XjkkS7uu2//47lbnN/7vT6srdH2pg9kYTKsTUkLHO7t13E9xYYZs6ZSKSQSiTsm95GFF8Mwtxw9P6gi1NZfT4DduGHo4eyTCLDetzSh2jc9M8319f2D5gf9jvR4PPpmDvRcyWu1Wl/2nd/v7wv5puoMWTJkMpm+zL9RSClRqVSwtraG7e1tXf1JJBL68d1RNMNaoESr1dKD+YZh6FxIeh46bhI2g9YHJ9lsc3u9DVpTRCIRLbC2trZQq9WQSqVw+fJlRCIR7Tm1tbWF1dVVVCqVvo07ejwSkhTdROdDCIFGo6E3OQmymxg0wnXPs1GaAAkJEnEkzEiUjRIaJ5lpGtaSe8lLessC7pam+88XL1KSAP0cPw3jtilpI9g9b3aYpxj5y1FrXgihvfzGNWa9VWHhxTDMLUd/G7AD5YZeRTTqwY0baouKNgCPK8B6X7oB5aoOUD7hjRvDK06j/nzQ87bbbX2DJ9sHsl+geBzLslCtVnV2Xj6fx9zc3FieSa1WC9vb29ja2oJpmn0bhe5jIx8vqogNVq9oHqxcLmNzc1MfD1XtqLLjFlvuVhSJyePG25Dpa7Va1TNedKOWUmJzcxM3btyAZVmYm5vDXXfdpTcybdtGoVDAtWvXUCwW9TxcMpnU82FUvbFtW4vUbDarY60GDXipUkYiixIQSGBZltUX7k0CjypuVGFzD667v//97xdTnWnqVdnoPxhqkP64m4NH8RRzHEdbUtCcH1XBbsdsRxZeDMPcFtCMlGma8Hg8eo3dMAy0Wi34/X7dshtHgPW+xN573zPQHPXr8KTbobS1R7YMbp8sao2RnQVtNM7OziIWi2mn+VHCptvtolwuY2trC+VyGbZta9NLGhonUaFev+iriLmFGOVMbmxsYHt7W7eaIpEIcrmcbs/5fL598TaTMPKk5QLamiOhFAqFsLq6itXVVXg8Hly4cAELCwtadEspUSqVcOPGDRQKBXg8HiwsLODy5cv67wzDgGEY2umfRIDbHJTEwGB7WUqpzxHNUlErj5zaqUXpfqPvdQ/Mu889nf+D2pYnHT4/7c1BsjVxtycHPcWCwWCf9Qht1CaTyRMbs54nWHgxDHNbMSjAKAeSbB/GFWDH8TabtB8audKTEKMbtGVZME1Tu4aTnxhVTdxxP4MtRHIdLxaLKBaLqNfrfX5k0WhU50eS+FOvTfRVxGheyrIs7OzsYG1tbV+VMZfL6XNN7VVq3dFN121Z4I4uGgfHcfQ8GG2S0mNsb2+jWCwiGAwin8/rGTASpqZp4saNG9jc3AQAzM7O4uLFi0gmk1rg0lwe/SzFYjHMzMwgFov1CSeKzqIIHBJjjuP0VbbIvJYElrvt5/bXarVa+x7fPXdGVTJqG1+9GsErXxka6d8FjCfMprk5OOgpRq8Z6CVbdDodvWhCprrj/sfpPMPCi2GY25J2u41isYharXYsAXac6lXvYUyodf4YKAh6Er9CyaiUTEo7nQ5M09SGlfF4HIlEAgD6jDHd2YtuP6ZWq9UnLsg1Ph6P65ghr9fbN7tD805uB3WqyNTrdayurmJzcxO1Wg2WZSGVSmF+fh5zc3NIpVK6+jNqJoiqHyTwxvWOIjFK1hPuz9m2jWg0ilgsprcY3Yat169fx8bGBhzHQSqVwsWLF5HJZODz+dBut1GtVrG5uamXDGhrdHFxEeFwWAsnt1ii6uGwsHa/36/jo+iYaIMV6A3vU3WMBKv7fDWbPZuHl70M2NnxoOfftQwghuXlAG7cUG3LW8EHi6pd7uiubrerW/A0L5bP5/Um660ICy+GYW5r3ALM6/Vqc82jVsDGofftRai5MwnVooyiVovroe1JQK2ber0O0zRRKBRQrVbh8XiQyWSQz+d1ZYbafXSjplksEk4+n0+7jpumqT2XYrEYwuEwksmkjoCh5yUh4BZi5KBOLd7NzU3s7Oyg0WggFAppi4uZmZl9la1BIUbC0b0EcNg2JkFJA1QVLJfLAKA9yTwej3a0pzmwTqeD1dVVbGxsoNVqIZFI4MKFC8hms1oQdTod7OzsYHNzE6VSCQCQTqexsLCA2dnZodU6Mo4lYUZLFXRs7Xa7r+UWi8X0G4kxsrhwQxWjRqOBTIaSDppQFhRJUKbnE08AP/ADAayvk2N/COo/BOff+d2dG9psNnULuNFo6HGCmZkZHbN0q1TCWHgxDHNH0G63USgUUK/XT02A9X+bA3UTrAOo4YknHH3Dj8ViR8p5HAfLslCr1bC1tYXNzU3dopmdnUU+n9c+XiTCBgeeabCbhJp7o5IGvskTy+29NJjl2G639TxXKBTSBrGlUgnlchlCCGSzWSwvL+uK0ajX4xZ41IY6Smg0bc5VKhWsr6/DMAz4/X7MzMwgGAzq+bA/+7MUHn00idVVD5aWOnjNa7bw3d+9gXq9jmg0qluV7vzBRqOB9fV1bG1todFowO/3I5fLYWFhQbd9D8NxHFiWpcWzaZo6eoler8/n6zOypXk+Gub3+/14+tP9A/YTDgALS0sdfO1rbczMWFBedxaACFTg+q2ZddjpdFCr1bC9va1jpEiwzszM4PHH43jrW8NYXQ3h4kXfuTRaZeHFMMwdBbnMkwCjltIkBNjoL5eo11Wlo1arwbZtPbxON9NJehhJKbGzs4ONjQ29BUhbYjQXRMLPHQzurjTR5+hYg8GgFmDk/D5MYFCUjbsiRtUZsn8olUo6JmlxcRHLy8vIZrMHnm93tE2j0dgXGu3exhw2gN7tdlEoFPDUU0/BNE29CPDxjwMPP+xBu+2FCu9OIRIJ4Ld+q40f/uGibpuGQiEdB5VKpfo8vUqlEjY2NrRzfiwWQzab1fmdh0U5Dbt+ZONBPzOUfWlZljZxpWvy+ONBPPRQAK2WH8pIOIBw2I/f+R0/XvYyPy5fFnvCTEKJMiX4z3vFaxyq1apeGPn4x1t4+9u9aLdjUAJTzdb95m+G8bKX7fcUOytYeDEMc0cyTID5/X6d7UemnEcRYOPOhbVaLX1DJQERCoW0CJvk7EqtVkOhUNCO+DToTRYIJMIoWse27b6qGM1N0QyY1+vVvl+hUEjPlbmrQW5oU5MEEw3D7+zs6HMdi8WwsLCAS5cuYWFhYawbJJl4DguNphbqMDd1KSW2t7dx8+ZNNBoNvOQlSWxthaAsFACVhhDF0lIaKysR3aouFAqo1WpadNJGqLv612q1UCgUsL29rc1faSsvHo/ratVxcAe2U7uShLFt23j8cQ9+53c82NryYH4+gNe8xq9NUz/5SR/e8Aa3MPMjHA7g3e/246UvvT3sGizLwpUrFaytGVAt1y6ADAALCwtdfO5zvRb7MJ+5aS4WsPBiGOaOptlsolgs6pYFtSBPIsCOAlWC6EYKqE0/d1tpElAmozsTkVzyacaIhtrJDsJ9jI1GA7u7u9je3kaj0dAijDINQ6EQstms3vobBVVz6vU6dnd3sbm5qQfXaRtyeXkZV65c0dXIcRhVaQOGW1i0221sb2/j4sUyVCUoDCW64lApCF1cvx5AOp3WW5kUWVSv13WgOJmyki8aoERSpVJBsVjUw/5kjhsMBrUIG9VmHRf3/J7btoO2X92+ch/7mMDb3+5gY6OLhQXg1a8G7rtPzdCRsSu1LunjSbbCp4HHQ6a+NagW/9ze31ioVEZ7in3yk2H8h/8QRrMZghKmp7t8wMKLYRgG+wUYVcCKxeJUBBig2mkkwprNpvZ2IhE2iQFi2mQ0TVO3+yKRiBZXJP5IWJCPlHtwvF6vY3NzU3tdkYs/GYZGo1Etwg5rtblbdSsrK1hbW4NlWdoGYmlpCbOzs0feYnMPZg9aWFClLxQK4du+rYX1dSpHZqGqJBJLSya++EVlj0HhzqlUCt1uV9uVkIs/Db8nEgnti0bHUKvVdEYhzcyRwJn0taWW7kFzfO4sSq/XqzcnyRDWDVVF3aKM/nwe432OErXkHtr/7u9uYWODht2CAC4O/b5JwcKLYRjGRaPRQLFYRLPZ1GLL5/P1CbBxo3tOAmU81mo11Ot1XcEgCwIalj8unU4H5XJZO9DH43FdYSIn/Xq9rm/GgUBAV8OoVWlZFgzDQKVS0cPg3W4XjUYDlUoFjuPonMVsNqvFDpmrjjomEmAUiJ1MJhGLxZDL5fTbUc1XR1lYXL0KPPigg3bbhDLIzSEcXsR73+vD/fdDb0VSuDPZUQgh9LasbdvweDzafyocDuuNSSEEHnsMeMMb2lhZMbCwUMUv/VIXP/ETsq+iRFuklKc5ye1X9xyf2y8LQJ/VSDAY1Nd10B6D/MQIt4AcFGaUeTltjmsCqyplbagWpQSQBnB6ywcsvBiGYYYwSoCVSiX9uWkIMKAX10Nbb91uF0IIvSEZi8WO3RaybVu7tTuOg0gkgkwmo/PyKLCbxBi5s7vbkn6/XwdqU/g3WVmUSiXt6UWfJ+Hl9hZzz9tQhMzW1hZ2d3dRKpV0lA8FT0ejUaRSKaTTaX0sR63CUJXvv/23Jt761iY2NorI58v4+Z/34eUvv4B8Pt/nqE4ikwQlDdmXSiU90+Xz+XS7z+fz4U//NInXvCaJZpOOrYtwuIpHHzXwYz9m6VYfbZxSBBFdVzK0nSS2bWsROsxqhMQYzUHReR0UYm5x5gwolMEKmfvPpxkDdJxZrXErZZOChRfDMMwB1Ot1Xe2ijcezEmBAr4VGLUmqXrg3JI/i/k44jqN9krrdLkKhEDKZTN+8Fg3KUzWM2lg0cB+NRrUzPgUfx+NxhEIhbURKVhV0E3YzaPTq9/tRr9exs7OjB9ap/eXz+bRDvLsS5zZfPep5oGDtGzduoFKpIBAI6KxGt49Yp9NBpVLRIpPaizT/RXNvAPA939PExoaA8s5KQc2SqZv6P/xDbV9INGVzksCeZJXzIIa1KOm+f5BIJrrd7lATWYpEckPnZ5gwG+c/EJMehD/tuKRBWHgxDMOMwaAAy2az8Hq9ZybAiHa7rUUYCaFgMKhF2HGsDKrVKkqlkvYCowHzwddFkUYkxOgGS7E4dPMFoI1Y3cKMvpZuvNQSo8chqwga9K/VatjZ2UG1Wu1bQCDPL4/Ho0WCEAI+n0+LsME5tcOgXMt2u414PK4H8t3HRT5clKVJhqfUHvZ6vXja00i4mlA2Dpf3HqPXxup0OjAMA9VqVVfTkskkfD6fvrZU5SQRRkawpwW1Zt1ijK4lAL1Q4W5Tjvq5p/M0TJgdda7stEQSbzUeARZeDMNMk3q9jkKhgHa7jUAgoCtg7rbkWQgwQFVsMpna3jxSc++zfgDqRm2a42/R0WB4qVRCu93WG5/JZHLkDb/dbmsRRssB7nBoEkKpVAqRSAT1eh3VahWWZfVFHnm93pHVF6Bn29BoNBAOh7W3FkXtUFuTWmTHjSPqdDrY3t5Gs9lENBpFLpfTIs9tYdHpdPpyBTOZDKLRKNrtNp773Do2NrxQc0NhuCteg20sCh+nlq3X60UqlUIymdTxR24fuEgkgng8PnEz3lHQULrb980tkkdFUx0E/XyMO1d2771+rK8rrzJ1Lm8NF343LLwYhmGOQa1WQ7FY1AKMKmBnLcB6T9WFWquvAWgAkHjyyeMNcLutKCiqJZ1OH3izp7k0EmLuWTEAiEQimJ2dRTab1TNdpmlCSolAIKANWmlmarD6QkHWGxsbME1Tu/RfuHBBizoKqaY5JfL+oioLCTESY6OEgmEY2N3dhRAC+Xxe52EOWliQAz1FN8ViMXzhC0k88IAP7bYNVfHKAEghmxX4zd8cXVWp1+u6dUltyFQqhXA43GeuSq1mEmEnmfc7Du58RbouNO81GOodCoWOdGxuIU3CLJ+3oBz4O1CGt7MAbi0X/qkILyFEBsAHAVwCcAPAi6SU5YGv+U4AvwN1JrsAHpVSfvCwx2bhxTDMWUIGpZ1OZ+IC7GRB3RX0svkkgDo2NmpakLjji8ZtW7VaLT0sL4RAMpnUvmeHYdu2Fl7lcllbLFCFaG5uDtlsVkf8NJuqYheNRpFIJPSGIEGRRnRMN27cwNbWFizLQjwex6VLl5DJZLTBKEUiJRIJhEIhPVg/mAtJ1TCa5yIsy8LW1paufs3Ozu4b5qf5u0ajgUKhoHMqP/c5D377t0MwzQBUBTICYBbhcArvfa84sKXl3hx1HKfPN0wIMdSMNxwOaxE2bduHcSwtBufFjvLvon8QXkJtonLFa9iTvA1ASUr5q0KIXwaQllK+buBrngFASim/JYRYAPC3AJ4ppTQOemwWXgzDnAdM00SxWESn00EwGEQ2m4XH4zmRAOt9We8Goz8z4ley+h4J4Mm99x6oG30E7baacyIHebKLOGp80aAVRSKRQDqdPtI8GVVttra2sLOzA9u2EQgEkM/nMT8/j2AwiFarhUqlou0a4vE4ksnkSFPZer2Oa9eu4caNGzAMA16vF3Nzc8jn87qNRS0xak/GYjE9q0aLA8MCusmt3zAMFAoFAMDMzAySyeTI1yil1NuZz3teAdvb5K5PsT1RXLgwhyefnDvUKNdxHB1k7vYWSyaTWvgOm/ejdIHjLl1MgqNYWtC82CimPQh/GkxLeD0B4HlSyk0hxDyAv5RS3n3I9/w9gP9dSvmtg76OhRfDMOeJcQRYOp1GKpU6VID1/roGYBOUwwf4YRiBoWaW/a3GhuvNwhNPqPaa2xiVwrWPE19k2zbK5bKuxkSjUWQymSM7sne7Xezs7GBrawulUgmO4yAWi2lxJISAZVnaziIQCOgYnmEikR7vxo0bWiRlMhnkcjn8yZ9YeOc769jeriGfF/iFXwjj/vuV2av7uYYFdJMQ8/l8ehCeWqaHiRohbKgq5A6U8ApDXdMa/vzPlSjP5/O64nbQsHqj0dAVQwC6DUkWIEAvEcE0zb6lCxJhk4ylOg7uiiW90byY29KCbC3c13mag/CnwbSElyGlTO19LACU6c8jvv65AH4fwLdJKfd1bYUQrwDwCgBYXl5+zs1hBhwMwzBnSLVaRbFY1C7suVwOQgg9KzWOAOt9ug21FdcBzbc88UTvd7J7E2xhgcQZtbVopsaCYTR0u4/mcILBoBZiXq9Xm7YeJb6IInIOsqIYl1arhd3dXezu7vbNN9EMFs39OI6jt/yGtSIBVXEql8tagP3FXwi88515dDrzAHwASggGC3jVq0zce6+j7UJmZmZ0S9Lv9++riJEQq9frqNfrCIfDWFxcRD6fH3ktey0yCcAGRdMsLlbw+OPrMAwDtm3rWa1PfMKLd74zhPX1CJaWwnjLW0L4mZ/Zv1VKbUiKgaI2pLt1TOLaNM2+60oi7LyERx9kaUGi9yBLi1uFiQkvIcSfoxeM5OYBAL/vFlpCiLKUMj3iceYB/CWAl0spv3LYgXHFi2GY8wpZJ5AAozzDuTkParUiVCXKB7XxlkI8Lvpmtw4qiHU6/ZtgtFn37d9uYc/Lcw8vAD+i0QBWVnpVMqo41Ot1nfFHLcdoNKr9pGq1mh6IPyzihlprFMhN81vxePzI8222bevHonxJn8+nDThJfNHnqaWWTCaHColarYZnPOMGNjc3oSpOeQDPBBDC0lIbX/5yAcViEeVyWS9MxGIxJBIJnV1Jb24/s2q1is3NTTSbTUQiESwtLSGRSOjWJL3uw1pkZNhrmiY+9jEbb3pTeC/UmqqQAr/2ayG85CW9zEkSHvRzZhgGWq0WPB6PbkMOVrYolooij4DTyQadBJO0tDhPnKtWoxAiASW63iKl/PA4j83Ci2GY886gN9bdd4cA5KDmtkiAqY03x+lVwA66h4z6lRyPS9Rq7s0vVSWLRjv42tf6PZN8Pp/O7qOsxU6no0UYDZuT2CChRvFF7g1Jd/XhOFYUB507t6igViMFfFM1isK+afh8MLgacEfDrACoQgVihwCk4TiqYmbbNqrVKgqFgm7Tkbs8ucgP3vC9Xi+2t7exvr6OZrOpBZvH40EoFNLtw498JIQHHxQHtsgajQae8Ywi1teb6InyAIAGLlxo4i/+oqW/ltpw9EY2HBRxJKXUDv/RaHTfue12u1qEkbj2+/194vq8MWhp0Wq19EzecS0tps20hNevAyi6huszUsrXDnxNAMCnAXxcSvkb4z42Cy+GYW4VSIClUkWodlMTyocoCtVObOPJJ716timZFCfYahyGg1jMwsZGf5Vs0F2cNgG73a722KJgabJSIGuGw+KL6vW6NpklX6pUKnUsy4NBUUGij56HLBYovicSiSCbzSKfzyMajeLyZeHaiHOgxJeBhYUOvvhFn/bMomMjt33TNPV5IkPPq1cF3v52GxsbwMKCwGtfG8QLX6hmvzqdDvx+PxKJhI7nUddG9A3rj9roUwKxASXKI1Dh3era2nZ/wDP5pQHQDvtkFksborTVSa9vmPilbFASYacR0H5a2La9T4y5I5Dcs2LDLC2mPTM2LeGVBfAhAMsAbkLZSZSEEPcA+AUp5b8RQvwMgP8PwD+6vvVnpZR/d9Bjs/BiGOZWQwgJNWh9DUAZvcpGCN/4RlvfoN3D5eM/Nn1kQFXSolA3797w97Bf5ySy3GKM3tONnm5qFPlCm3KDg+XD4ovcYdNCCO0Fdhy7g8HZJqpyxeNxbedQLpdRLBZ1hS4ajeLLX57FAw/MotXqVX8iEeBd76rjR36krKN7aEvTXS2htqJqBUo89JAfrRad1y5CoRbe/OYWfuInehW6QCCACxcuIJfLaZuFRqOxzwHfbWEhhDiSZQJVIt1CjEQHWTdQnI97O3Tw9blxHEeLMDp/pxXifVoM830j3JYWf/InIfziLwbRbPbE6GlvSbKBKsMwzJTpt4moQG23qRLW3/+9au/UajXdzltYWEAqlRqrTdcvvMoA6lDtxjSouuY4R6teUAvSsixtXEqGpzSsTVUxr9er36g9l8lkkEgkdM5hqVSCuVfKi8fjyGQyx2oJUQVx0GIhlUppw1RKGtje3oZpmvjsZyV+//ej2N6ew+JiHm99a1wPrbfbbR3dQ2ItnU73bQs6joNLl2pYXa2i1yK+AkBgeVnim9/saG+ttbU1GIahZ/toVoyWBNxtM3XtBD796RDe+MYwyuUIVBtUXfNxxYBb4JEQo2qmW4C5W7IHBXGTCKNKojvEOx6P3xIiDOgJ1EFLi3vvBTY2ACAIajsDgVP1BWPhxTAMM2X236cklFAq4R//sbf6T5WbdruNWCyGCxcuYH5+/kDrgv2PvQlgDaqV6QEQxTe/GdHB0tFo9Nj+TjT8TGKFjE/JaZy+huayKK8xnU4jGo32De4f14qCcFfUACXoyOmdaDQa2raiuterjUQiyOfzyOVyiEajCAaD6Ha7MAwDhmHobUF3XqVqBQKqXdyBqigOd083DAOrq6totVpaeA3OJJEQ+/CHHbz2tV0txFSlK4h0OoJf//Uwfu7nwsfa5Ot0On32GCSe6/W6bifOzs4in88fWIGUUmoRVqvVtAiLRqNahN1Km4ZqMaMFwP22CCB4qk74LLwYhmFOmVEO9IPEYhIrKwZKpRK63a6eA6LqCQUvz83NYX5+HolEYp9oGl58aEJV1KoA6virv+roOBcaVCcR5t6WOw6WZWmbhUqlgna7rds+1L70er06t5HCpqmFSSKA2pBHraYMc3pPp9P7NitbrRa2t7exvb2tKzk0iE6eWJFIpE/8UkXtOc9JYWVlv0AZVSWxbVs/Tzgc1jFJ1CKkmB1VfVFbqIoggDYWFtr43OfUPZhmlag9eZxr5fYpKxaL2mPO6/XqFIF0Oq1n0IbNQL3kJVIb8Q6GeFN+5K0gwvrbuj244nUALLwYhjnvHHU70XEcGIahfbGi0Siy2SyazSZWV1dRLBbR7XaRTCaRzWa15UE4HD5E5KnooPX1qs5P7Ha78Hg88Hg8WuiQpQTZShwXqoiRdxiZZNKcEznJ+3w+vZFHIoQ8qVKpFAKBgH4bZho7DHJ6L5fL+wKn3d9LVZxSqdQ3E0bngCqDFM9Tr9fx8Y8LPPRQHM1mCqo9NV4rsFqtYnd3F47jIJfLIZ3uuSq1222EQu7KSwfAXVBVSgf1ei8TkrY7geGbjUeFrDs2Nzd1AHwoFEIikcAXvpDF618fQbNJAd+efa+V7DVIhJ1ViPdxOAsnfBZeDMMwp0xPeJWhqk8eqNkgD8plNQ/l8Xj63nu93n0CLBaLIZvNQkqJra0tFAoFtFot7UhOlatYLIb5+Qhqtf0VB9qIJCuBarWqN+PIQgKAngsip3sSISepYjiOo8OkSXxRxcdtE0HByzTUTZWx/nMq9okxej94k6eqFRmyUhty8DG73S6q1ap+I08sCtMWQsDv98OyLPzxH1t417t82NgIY2kpjbe+NTbWjdq2bezs7KBWqyEUCmFubk6L23GH6knoUNXKLcSCwWDfsP5RBY/jOCiVSnom7gUvsLG9HYCaD8xB+Z8dXBEiEWaaZl8k1VmEeI/DbbnVeJqw8GIY5rzTE14lKAf6LpSdgYMnnhj9fSTCAOgbGQAkEgkdRVSpVHTmIkWreDweXXEgIXZQhciyLJimqa0QaPaInps25WgLj4TYSR3PyYOLhBh9bFmWPl7HUY7y8Xgc2WwW4XC4bwOT3ruhwX63GCNxQ7NojuMgFAohnU4Pdb1vt9t6gcCyLNi2rQUxHRfNs/l8Pn1NxvUqM00TOzs7cBwH2WwW6XQa73+/OFb1xR3OPWgxEQwG+ywsjmKlUK/XEYsZ6KUmJKB80kNjz0DRogGdR+BsQ7zPAyy8GIZhTpnRrUYJ21bu6+TCftDHtm2jVCrpoW+aSZJSwjAMNBoN7VsUCAR0K9Hr9Wpnd3JVH1Zh83g86HQ62jaB7Aco24823Gg1n+a03JFDJ6HdbmvxRYKSKmKdTkcbsS4sLGB+fl7ftKWUeqB/0A6DBtkJamvSc1FbkbIaB18DtSLpeICesPN4PDrsmzYhKbtxfn7+0DZtt9vF9vZ2X/Xrj/4ocOLqi9tigsSY2+uLKmIf/WgY//bf+g4UeqoK14Havq1A/YchhKWlFG7ePFoiAYV4ky8acD5CvKcNCy+GYZhT5jgO9AfR7Xb1TBJVutLpNCzL0o7r1FILBAJ6E40yGql1Rjdg982T5r28Xi86nY6OFAKg566i0ahud7Varb1NP49+TNreOwnuWB6KDjIMQ8+3RaNRLC8v4/Lly0gmkyMFANkrDBNlNG9G7Va/3490Oo1cLqdbt1Q1A1SFjqw0qDJIWYdSSpRKJezs7OiWpoqHmsPMzMyBomJY9WuSFg00a+euiPWG+QNQs1uRvTdvXxuxfwZKmc6GQgYeeaSDn/zJfvuOozAsxHvccPZbHRZeDMMwp8yogfeDHOjHodvtakHiOI5uxzmOowfFvV6vDuN2V29oCFpK2efsTY87WGkjV3iyfyAD1Ugkol3sSdhQRYhuonQjHTXLNo7IIJFkmiY2Nzexvr6OYrEIj8eDTCaDy5cvY2lpCfF4fOw5NHfLkvy+KFczEAj0VQc/+Uk/3v72ANbX/VhaCuCBBxz8xE80+8RsMplELBZDs9nExsYGdnZ2dO5jNpvF7OzsyFm5breLnZ0dmKaJUCiE2dnZUwuvJiEWDjehvMiaUKJqGcPaiMPakT/5kw0YhqHtO2KxGFKpFD760ciRK3bDQryDwaD+2TkvId6TgoUXwzDMLQ4JsHK5DCmlnjfqdrtDBZjH44GUUrf1SIQBB1cdqHpUqVRgGIbeAAwEAnqrkkKY3Rtu5C5PFbHBGykN9Q+2PQc/dr8nc9SnnnoKKysrqNfr8Pv9yGazWFxcRC6XQy6XO3IlhgbsC4WCbtH9+Z9H8cADQbTbXagMTIlQCHjkEeD5zxfodDp6S5Pm0XK5HBKJBEqlEjY3N3WVjHIcSbQOVgfd1a9MJoNMJnNqBqX9w/wtKPsKcSQrBcuyUKlUUKlU8NGPdvHQQ0G0WimoHMz9G5CH4Rb5gyHe8Xj8thBhLLwYhmFuE6gFaRjG2AKMoPkbd2uRqlYkqgYFQKfT0fNNZA1BwoIczcmCgYSYe+g7FAohGAxCCKErbIPzbc4hE9z0GkqlEtbX17XnFomabDaLmZkZ5PN5ncNI7dTDqNVqMAwD3/3dDWxsCKjh8jTUtqGFpaUOvvrVXuvSbalAQ/epVAqZTAZ+v79PjPp8Pj2LR5ubbusKqn4Fg0HMzc2diuCYpJWClBIXL5pYXS1DmfX6AFzGUYWcG7eIHwzxjsfjJ25nnxUsvBiGYW4zbNvWLUhAbUFmMpmxBBh9v3suTEqpHcpJiA1+T6vV0kP5NNBPw/x0g6R2IW0xUpUtGAzqTcnB4GiK1hlnAYH8qIrFIgqFQp+nFFkakBBKJpP72p+jPo7FLKjNvjqU8JoFsN+pnob8aUGhVCppHzEAum1Gs2sUsxQOh7Ww8vv9+nw4jqMd9k+r+jVJK4Weo38TagsyCWC4o/9RIfsT988kue7H4/FjJx6cBSy8GIZhpsRpzXqNgrYgK5XK3vOrCpht22MJMEDZJpBDeb1e1w7lZDA6uI1GLcxqtaorXH6/H4lEQg/7E2SuSlU2EnjuOKPj2g3UajUUCgU9UE45k4ZhwLIsva2ZTqeRTCb1ayAh56aX59eF8tcKAPDgwgUvvvKV4XNr9LEQQs+m1Wo1dDodHSze6XRQLBb1xibNfpGAo81JqibmcjlcvHjx3LbbpuUC7ziOFmGDId4kwt7/fjFVb66jwMKLYRhmSvSKFQ4o/Jg4zV+xgwIsmUwik8noz1MgdzqdRjqdPrANR75MJCKA3gxOLBbra//QDbJarepWETmix+PxPusGEngkxKgaRvNjo9qdh+E2TyWx5TgOyuUySqUSms2mruZlMhmd2ej3+3Ul7bHHunjlKx00m+S/1kU43MXb3ubg+c/vr7oddK90R/XQQD4tA5D4dBwHsVgM4XBYRy1RBa1SqcDr9WJxcRHLy8s6i3KYaexRmFTV6yxc4IeFeH/iE148+GAUzWYcalNTnPpxHAUWXgzDMFNCaQYJ4DpU1EwSQBTA6Qovgipd1L4iAUYtyKMIMKC3jUZ+W1R5oEqYe3uPhqar1aq2D4hGozruaPC5aNPQ/dhuU9ijhnu3222USiVttZFIJJBMJtHpdLC7u6srgGTPQRuiFP78oQ/5xxInUsqx2qL1eh2GYejWLLUdKcMRgH6t5DtmmiY2NjZQKpUghEAqldLHR1uF1LZ0b6oedB0nLZam7QLvhrZ2n/nMGtbWalAiObv3drr5i0eBhRfDMMyUUMLLgXKwr0C1rvwAUrDtxNSiVCzL0hUwuoGn0+ljCzBgeOWBhBLNhVHbkCo41Wq1z6Q1kUgMrWq5o4bI2R7omYGSRcM41TB67WR4Go/HkU6nEQwGtWfY7u6uFnz0HIlEoi8Tc1LXiqqCZNDa7Xbh8/ngOA7a7Ta63a4eKI9EIvrrV1ZWUC6XAaitUBJ21OoMhUJamNIgfzAY1NulJM6e/Wwf1tYowioICug+LyLlOKhZMwlllREAvaZJzJpNAhZeDMMwU6JfF0gANQAGgCa++c3RGYKnhWVZugJGAoxakMcVYEDP/JSEGAklihtyezM1m009lO9uvyUSiZGzTJ1Op29I310NIyF2mAGnbdswDEN7oEUiEWQyGUQiEX1ctVpNV8mo6hYKhbQQo+c7Tgt0GJZlaUFK54w2PilMnIK+hRDY3d3V7cd4PK4rkJSDSZU0mjUj81jaFnUcBz/yI14oYeIHsACVxxgA4IOUp2NjcdpMa9bsuLDwYhiGmRKj781tbG9XUK1WdYYgtZFOy8PJTafT0VUgIYQWWicVYO7Hd7ckAeiNNKpWASobsFqt9vmD0TzYqLYiDfOTEKO5M7/f31cNG3XMFERuGAZs20YoFEImk0EsFtNf4466IZd7qi5RgDeJsGE+ZceBFhRM04SUUvuhkTltIpHQaQXb29uwbRuZTEbbh7jzLynwnNqPfr8fXq8XlmXhO76jhY2NNvrD24GFBYEvfck/NIT8vOcrnsWs2VFg4cUwDDMlDttqJPsAwzC0AzzNIk0jQoW27EzThMfj0S3IYQJsWK7hOJAocG+k0SYjCTEAeiifhFo4HNbGowc9r2VZfdUwqhbRFuYoYSSl1BYQ5FyfTqeRSCT6xK9lWX2+ZLQxSTNaoVAIn/qUH+94RwRraxEsL0fwlrf4jn3DdxynT/BR/iTlQkajUSSTSd0mDQQCmJub66uakpcabXgC0BFPn/xkFK96VQTNZgCq9d1BONzBO95h4b77eh5lbg1Ar3UwhJwE3UFMawbsLGfNDoOFF8MwzDmk2WzqSBa6yVJO4mlXwQYFGAmtSQowoFetIhFGm4xuqwohhBYelI/oHso/6Fy4W57UfgNUtY0G9IdVw0zTRKlUQrvd1sHcyWRyaMyPW0RaloWPfrSDN79ZoNUSINuJUCiId7wjgpe9LHLosPtBuGfjKHux2+3qZYBgMKjn6yhzcti8nLtCaFkWrl4F3vlOPzY2IlhaiuLRRyN46Ut7x/jYY8Ab3mBhZUWZxr7+9UqUUevSDVXk3GKM3n/gA55zXYmaFiy8GIZhzjFkClqpVLTjOc35nPYwvnsT0N1qpNmwSQkw9/NRJYlEkts93+PxwDRNmKaph/Lj8bje7DsMMoYl0UF+XST0otFoXzWs0WigVCpps1OqAA57nSRo1EZdHap6ZEEZrjpYWGjic5+TuvpGbcnjzvNRhYv8wVqtlo4rotcViUQwOzt7oLkoVfBIjLnPSSQSwdWrUfziLwbRbPYEnFsskefYsBByEtLEvff69kK5/VA2D3EA52f2alqw8GIYhrkFoFV5wzDQaDR0PA9ZCJwm7Xa7T2hlMhmkUim9ITjYmpyEIKS4GPcAPc1UUSWMRBoN5dM82DgzVlJK3YKr1+ta6JEdBlXDvF4vWq0WyuWytqJIJpNIp9ND5856G3VNKKf7HFTEkES9vr/65o4LikQiR7LIAHqtSMrPpG1NMnGNRqOYm5sbWv066Jw0Gg20Wq0981gPlFCKQcUmjSeWHMfRIsyyLGSzHShHe2vv8eYBnJ9tw2nBwothGOYWg4KqK5UKHMdBMBhEMplEIpE4dhtrHNwCzO14f5oCDDjcPd/dUgRUBBGJsHEHwaltSKLDPZBOQszj8aBcLvdZUWQymT6hN+5G3aj4pHGXAoZBrchisaiFImVGzs/P42/+5i686U2RseeelLVFA8qWoQ4gjJOIpf5zI6EEKVe8Rn4dCy+GYZjzBQ2EG4aBdrsNj8ejh/FPM1am1WoNjRw6bQFGuK0qaIuRfKmklOh0On0mpDSUfxQR466G0WNRdSoYDOpNTcdxtOt9OBw+9kad2yKj2Wzqlh9tTA7LsRwFzc4ZhoGtrS1sbW3hU5+q4L3vjcKyng7g6SBvq2wW+M3fHH1s/WKpl7hwHLF03rcNpwULL4ZhmNuAVqulndCllDoQmtpyp/WcbgFGLUiypzhtAQb0u+dTLJHX60UgEIDjONqGgVqz5L91lHPirk5RxQ1QQ/rdbldnLYbDYWQyGXzsY7ETbdRRy4+ek4QfbSKO61VGx26aJp75zHVsbT0JoAjl5P4dUL5dwQPFz+3kbH9eYOHFMAxzG9HtdnUVzLIseL1eJJNJpFKpU/NfarVaOpDaLcBoCH8aAgzoCaRB93wKniYBRoajiUTiWMPt7nBvMlalDUGfz4dkMol8Pj8xHzb3JmKj0dBVPgrWdkcLjULNnrUBrADYhmofegHcDSCDixcjIytYLJYmCwsvhmGY2xQaxqfZJxrGH2cD8Dg0m00Ui0U0Gg34fD5kMhl84hNJPPCAhZWVIhYWTLzmNR68/OWnK8CAnpWE2+pBSqkFGKDmqciMNB6PH8srzR3uTdE/FEYei8WwsLCAubm5ib5W8iobNEgNBoN9g/pu0bd/vqoKYBdqzqoLIAjDSO3zLWMmDwsvhmGY2xzLsrQgeNazuqjXA1AB3QmQUzmZuE6CRqOBYrGID36wiYce8qHVyuw9n4VwuIg3vcnEC15w+hUwN1SlIusFykKke1s4HNYmrfF4/NjHRP5au7u72N7e1iJ0dnYWCwsLB7rwHxdqS5JBKkUouW0rPvKR0L6WoUICMHHhQhl/8RftqVRI73RYeDEMw9whKJd4EyqguwlV7UhAiaIQJv1rfnm5gdXV4t5z+QBcABDE8nIHX/nK9FqQg3S7XV0Jo2oYDbR7vV4twMik9biboo7joFQqYX19HYVCAd1uF/F4HLlcTlcejzpvdhjuCKVB24pPfzqChx+OoFyOgIbrATWz9fKXA5/4RAOrqwYWFmp4zWsE7r9fBYh/+MNBbjVOEBZeDMMwdxC9e3wFwAZUULcAEMb6uorIIQ8oj8ejZ6SOIz7UXBGg5onKUMPcQlsRjIoompYAA/a759PHtm0jGAzqjUUyaT2uSOp0Otja2sLOzg6azaaOg6L2INlHTDoaajC30bZtXL0K/MZvBLC+HsHSUgQ/9mMR/MEfeFzVsA7CYQOPPFKFlA4eeiiMVisN5eN1Z24iThIWXgzDMHcQPd1gANiBsgioAajiM59Rw/ixWGxoS8wtwgZF2bA/P+tZAqurHigLAg+UwPNgedmDp57qfe1gSHcqlUImk5mqACPIRoLmtciyIhQKIR6PY2ZmBolEAh/5SOhYVSDbtlEul/XsnRACwWBQC1u/3699w04SLzSKYbYVyiQ1BCAKZWwaAiCwvOzAcSpYWzPQMz1dBHDneW9NEhZeDMMwdxD7CzYO1JyPg1Kppo03HcfRGYCRSASO4+g3KeWhfwaAq1eBhx4C9twQAAChEPDII8B997mPSYkw27ZRrVa1PQUJMJ/PdyTBR38+KeSeX6vVUCgUYJomOp0OPv/5EN72tiTa7TmoNq3/yFWgbrcLwzBgGMaeUalPe6+RU7/bJHZc+4ijQLYVkQgZpNKFugLAp39W1PWs7/2dqnrdaW7zk4SFF8MwzB3EQZ0y+jU/mA/p9/uRTCaPlA9JIuyxxyQeftjByoqDpSWJX/kVBy984cECrtVqaR8wKaX23zqqmDpMpA3+3WEirtlswjRN3HPPLra2KgDaAPJQvlgJLC/HcPPm0ap0juOgWq2iVCrBtm0EAgGk02n4fD5dmXLbRxwU7n1cehuPDpT4UluvFy+qvx/HiZ8ZHxZeDMMwdxCJBGCa+z8/bKvxLPMhAQxtQaZSKQghxqq6jfrzqArduNx9twdKdJlQQ+ptADYAD77+9Zh2yh81KzfszwBgmibK5TLa7ba240gkEnAcpy/OiPzJ3HFGR00qcHtzZTLq2ltW7++pggew2/ykGVd48U4pwzDMbcBRLCNIaMViMXQ6HR3CbJomgsEgUqkU4vH4qeVDBgIBzM3NIZPJoFQq6dkoGsKfZCzSUUTb4qKDtTUHQAbUpgWamJurolKpoFAoAIAemh9XpJIII+PZ1dVVbchKodyJREJHIhmGgd3dXQghEAgEEI1G9fXy+/1a4A0y6EZfLAKBgIoPKpWGz6zxVuP04YoXwzAMA8dxYJrmvnzIVCo18RmkQYZVwKgtN00Oi9FpNBqoVqt6O9Lj8fQJonGrdI1GA+VyGbVaDUIIRKPRfR5jtm1rHy93xmMwGNQ+XjSkT1W27/s+D9bXadkhvvfG7cNpwa1GhmEY5lgM5kNGIhEkk8lTzYcEoCtCZynAxonRkVKiVquhWq3qgflgMKhNWsc93na7jXK5rF9vLBbDZz6Txhvf6MPKioPlZYk3vtHBC1/Y1bYRpmnuM1OlIPGLFz1QVToHajkgDYAH5qcFCy+GYRjmRHS7XT2M784rTCaTpyqGzoMAGxcKq65Wqzr0OhKJ6Hmwcdq1lmWhXC7jfe+r4MEHJVqtGFS7MzR07srt4eUO9/6BHwhhfb3fOgLgite0YOHFMAzDTIxp50MCt5YAA9TxVqtVVKtVWJalq1jxeBzRaPTQauHFi12srBhQXmxdAJcB+A8VTuRR9thjDbzudc09mw8vgAjC4Sh+93cj8Hp9PM91yrDwYhiGYSaOOx+y2+0iEAgglUodyxbiKM9ZKpVQqVQghEAymdQ+YOeVVqulFxa63S68Xi/i8Tji8fjIofxeIoADlQpwdG+t972viwceaGB1tY6FhQZe/WobAPDQQ0G0WlEoM9UQIhHBG4wThoUXwzAMc2pIKfUwfqvVghBCD+NPcivRza0owCi6iIbypZR6izEej/ctLvR8t/o5Sauw3W7jaU+rY22NjFQlgEsAAtyCnDAsvBiGYZip0Gq1UKlUUK1WIaVEKBTSlhSnMYxPAqy656FxKwgwQG2OuofyAejIokQigT/8Q++peGv1V9KaUFUvHrqfNCy8GIZhmKnS7XZRrSrPq06nA6/Xq4fxB/MhJ8GtKsAAZRdBQ/ntdhsAEI1G8alPxfHmN8ewuuqZ2CzWaVTSmP2w8GIYhmHOjEajAcMwUKvVAChRkUqlEI1GJ/5ct7IAA5SPGc2DWZal/cEoT/OkVcPD/MmYycDCi2EYhjlzJpEPOS63ugADVG4kzYPRUD7Ng4VCoWM/7jj+ZMzJYOHFMAzDnBvIdNQwDDSbTQghEI/HkUqlTiQohnE7CDDK06xWq6jX65BSIhAIaBF2Gq1b5mSMK7xOZ/eXYRiGYVyQ0FpaWsKlS5eQTCZRq9WwsrKCmzdvolKp6Fick+L3+zE7O4tLly4hkUigUqng+vXr2NnZgW3bE3mO04Y8wBYWFnDlyhXMzs7C6/WiUCjg+vXrWF1d1ZYexGOPqXkuj0e9f+yxMzt85gC44sUwDMOcCcPyIakNOcl8SNu2tRErACQSCWSz2VuqAkbYtq1NWjudjs56/NSn4vj3/z6GZrM3D8ZzXNOFW40MwzDMLUOz2dTD+JQPScP4k7KksG1b+4ABSoBlMplbtm3Xbrf1UP73f7+NjQ0PVDB2AoAyaeXNxenBwothGIa55aB8SMMwYNv2qeRD3m4CDACEaACoAqhBia/Zvc+zV9e0GFd43Xp1VoZhGOa2xev1IpPJIJPJoFaroVKpoFgsolQqIRaLIZlMnjgf0ufzIZ/PI5PJaAFWrVZvaQF28WIEN29GoJzpe0prefnMDokZAQsvhmEY5lwSi8UQi8VgWRYMw9BttUnlQ95OAuzRR8mrS0AFZKsZr0cfPdvjYvbDwothGIY51/j9fszMzCCXy+lh/J2dHRQKBW1JcZJ8yNtBgNEAPXt1nX94xothGIa55Wi1WjAMA6ZpQkqJcDiMVCqFWCx24mH823EGjDl9eMaLYRiGuW0JhUKYm5vDzMwMqtUqDMPA5ubmRPIhb4cKGHN+YQNVhmEY5pbF6/UinU7j8uXLWFxcRDgcRqlUwvXr17G+vo56vX7sxyYBdvnyZSSTSVSrVVy/fh3b29uwLIsNS5ljwRUvhmEY5rYgEokgEonAtm0YhoFKpYL19XX4/X49jH+cfEh3BaxcLsMwDLzvfRU8/HACzWYWgB83b6rhdoDnqpiD4RkvhmEY5rbktPIhbdvG5ctlrK0ZUPYN2b03Niy9k+EZL4ZhGOaOhoRWPB5Hu93Ws1rVahWhUAipVArxePzIw/g+nw/r6zMA0gDKAHoblSsrE30JzG0Iz3gxDMMwtz3BYBD5fB5XrlxBPp+H4zjY2trCtWvXsLu7i06nc6THU8akPgAzAGIDn2eY0bDwYhiGYe4YPB4PUqkULl26hKWlJUQiERiGgRs3bmBtbU1nRR7Go48qg1I3bFjKjAO3GhmGYZg7knA4jHA4DNu2tSXFxsYGfD6fHsYflQ/JhqXMceHheoZhGIaBGsav1+swDAONRgNCCMRiMaRSKYTD4bM+POacw8P1DMMwDHMESGjFYjF0Oh1UKhVUKhWYpolgMIhkMnnifEiGYeHFMAzDMAMEAgGdD0ltSMqHTCQSSCaTJ8qHZO5cWHgxDMMwzAiEEDqCiPIhK5UKDMOYaD4kc+fAwothGIZhxuCwfMhUKjVyGJ9hCP4JYRiGYZgjQPmQ6XRaD+OXSiWUSiU9jB8Z9JpgmD1YeDEMwzDMMYlGo4hGo7AsSw/j12o1BAIBPYx/nHxI5vaFhRfDMAzDnBC/349cLodsNgvTNFGpVLC7u9s3jH+SfEjm9oGFF8MwDMNMCCEEEokEEokE2u02DMNAtVpFpVI5UT4kc/vAwothGIZhToFgMIjZ2dm+YfytrS3s7u4ikUgglUrB7/ef9WEyU4aFF8MwDMOcIpQPmUql0Gg0UKlUUC6XUS6XEY1GkUqlEI1Gz/owmSnBwothGIZhpkQkEkEkEsHMzIwexl9fX4ff79d+YTyMf3vDwothGIZhpozP50M2m0Umk9GWFIVCAcVikfMhb3NYeDEMwzDMGTGYD0nD+JQPScP4nA95+8DCi2EYhmHOAYFAAPl8HrlcDqZpwjAMbG9v9w3jBwKBsz5M5oSw8GIYhmGYc4TH4xmZDxmJRJBMJjkf8haGhRfDMAzDnFPc+ZA0jL+5uQmfz6fFGedD3lrw1WIYhmGYc47X60Umk+kbxi8Wi33D+JwPeWvAwothGIZhbiEOy4dMJpM8jH+OYeHFMAzDMLcgg/mQhmH05UOmUikEg8GzPkxmABZeDMMwDHMLw/mQtxYnqkUKITJCiD8TQnxr7336gK9NCCHWhBD/70mek2EYhmGY4VA+5JUrVzAzMwPHcbC1tYVr166hUCjAsqyzPsQ7npM2gX8ZwGellE8H8Nm9P4/iEQBfOOHzMQzDMAxzCF6vF+l0GpcuXcLi4iLC4TBKpRKuX7+O9fV11Ov1sz7EO5aTthqfD+B5ex//PoC/BPC6wS8SQjwHwCyAzwC454TPyTAMwzDMmFA+pG3bnA95Djip8JqVUm7ufbwFJa76EEJ4APwnAD8D4IcOejAhxCsAvAIAlpeXT3hoDMMwDMMQ7nzIWq3Wlw8Zj8eRSqUQCoXO+jBvew4VXkKIPwcwN+SvHnD/QUophRByyNf9OwCfklKuHTbYJ6V8D4D3AMA999wz7LEYhmEYhjkBQgjE43HE4/G+fMhqtcr5kFPgUOElpRxZpRJCbAsh5qWUm0KIeQA7Q77sewF8vxDi3wGIAQgIIWpSyoPmwRiGYRiGOWUOyoekNiTnQ06Wk7YarwJ4OYBf3Xv/scEvkFLeTx8LIX4WwD0suhiGYRjm/ODOh2w2mzAMA4ZhoFwuIxKJIJVKIRqNsiXFBDip8PpVAB8SQvw8gJsAXgQAQoh7APyClPLfnPDxGYZhGIaZIuFwGOFwGN1uV4dzb2xscD7khBBSns9RqnvuuUd+9atfPevDYBiGYZg7nlqthkqlgnq9DiEEYrEYkskk50O6EEL8rZTyUOcGlqwMwzAMwxxILBZDLBaDZVl6GN80TQQCAaRSKSQSCR7GHxMWXgzDMAzDjIXf78fMzEzfMP7Ozg4KhYK2pOB8yINhecowDMMwzJGgfMjl5WUsLy8jFouhWq3i5s2bWF1dhWmakFLisceAS5cAj0e9f+yxsz7ys4crXgzDMAzDHJtQKIS5uTnMzMygWq3CMAxsbm7iE5/w4sEHk2g2kwD8uHkTeMUr1Pfcf/+BD3lbw8P1DMMwDMNMlEajgWc8w8D6em3vM1EAMwACuHgRuHHj7I7ttODheoZhGIZhzoRIJIKNjQgAG4ABoAqablpZObvjOg/wjBfDMAzDMBNHRS77AOQAXAHVeu70KGYWXgzDMAzDTJxHHwUGbb4iEfX5OxkWXgzDMAzDTJz77wfe8x7g4kVACPX+Pe+5swfrAZ7xYhiGYRjmlLj/fhZag3DFi2EYhmEYZkqw8GIYhmEYhpkSLLwYhmEYhmGmBAsvhmEYhmGYKcHCi2EYhmEYZkqw8GIYhmEYhpkSLLwYhmEYhmGmBAsvhmEYhmGYKcHCi2EYhmEYZkqw8GIYhmEYhpkSLLwYhmEYhmGmBAsvhmEYhmGYKcHCi2EYhmEYZkqw8GIYhmEYhpkSLLwYhmEYhmGmBAsvhmEYhmGYKcHCi2EYhmEYZkqw8GIYhmEYhpkSLLwYhmEYhmGmBAsvhmEYhmGYKSGklGd9DEMRQuwCuHnWx3EG5AAUzvogmKnA1/rOga/1nQNf6zuHwWt9UUo5c9g3nVvhdacihPiqlPKesz4O5vTha33nwNf6zoGv9Z3Dca81txoZhmEYhmGmBAsvhmEYhmGYKcHC6/zxnrM+AGZq8LW+c+BrfefA1/rO4VjXmme8GIZhGIZhpgRXvBiGYRiGYaYECy+GYRiGYZgpwcLrjBBC/CshxBNCiCeFEL885O9fI4T4X0KIbwghPiuEuHgWx8mcnMOutevrfloIIYUQvIp+izLOtRZCvGjv3/Y/CiHeP+1jZE7OGL+/l4UQnxNCfH3vd/i/PovjZE6OEOL3hBA7Qoh/GPH3Qgjxrr2fhW8IIZ592GOy8DoDhBBeAL8F4EcB/DMALxZC/LOBL/s6gHuklN8B4MMA3jbdo2QmwZjXGkKIOIBfAvBX0z1CZlKMc62FEE8H8HoA3yel/DYAr5r2cTInY8x/0w8C+JCU8rsA/B8Afnu6R8lMkP8K4F8d8Pc/CuDpe2+vAPA7hz0gC6+z4bkAnpRSXpNSdgD8IYDnu79ASvk5KWVj749fAbA45WNkJsOh13qPRwD8GoDWNA+OmSjjXOv/E8BvSSnLACCl3JnyMTInZ5zrLAEk9j5OAtiY4vExE0RK+QUApQO+5PkA/kAqvgIgJYSYP+gxWXidDRcArLr+vLb3uVH8PIBPn+oRMafFodd6rzS9JKX85DQPjJk44/y7fgaAZwghviSE+IoQ4qD/STPnk3Gu8xsB/IwQYg3ApwC8cjqHxpwBR72fw3eqh8OcGCHEzwC4B8D/dtbHwkweIYQHwDsA/OwZHwozHXxQLYnnQVWxvyCE+HYppXGWB8VMnBcD+K9Syv8khPheAO8TQvxzKaVz1gfGnD1c8Tob1gEsuf68uPe5PoQQPwTgAQD3SSnbUzo2ZrIcdq3jAP45gL8UQtwA8D0ArvKA/S3JOP+u1wBclVJaUsrrAL4JJcSYW4dxrvPPA/gQAEgpvwwgBBWozNx+jHU/d8PC62z4GwBPF0JcFkIEoIYvr7q/QAjxXQDeDSW6eA7k1uXAay2lrEgpc1LKS1LKS1DzfPdJKb96NofLnIBD/10D+BOoaheEEDmo1uO1KR4jc3LGuc4rAH4QAIQQz4QSXrtTPUpmWlwF8LK97cbvAVCRUm4e9A3cajwDpJS2EOL/AvA4AC+A35NS/qMQ4k0AviqlvArg1wHEAPyREAIAVqSU953ZQTPHYsxrzdwGjHmtHwfww0KI/wWgC+D/kVIWz+6omaMy5nX+vwG8VwjxaqhB+5+VHBNzSyKE+ADUf5ZyezN7vwLADwBSyt+FmuH71wCeBNAA8HOHPib/LDAMwzAMw0wHbjUyDMMwDMNMCRZeDMMwDMMwU4KFF8MwDMMwzJRg4cUwDMMwDDMlWHgxDMMwDMNMCRZeDMMwDMMwU4KFF8MwDMMwzJT4/wGwzmVgGNeiegAAAABJRU5ErkJggg==\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "Xhat1 = Zhat[0]\n", "Xhat2 = Zhat[1]\n", "\n", "# Plot the points\n", "fig, ax = plt.subplots(figsize=(10, 10))\n", "ax.scatter(Xhat1[:m, 0], Xhat1[:m, 1], marker='o', c='red', label = 'Graph 1, Block 1')\n", "ax.scatter(Xhat1[m:, 0], Xhat1[m:, 1], marker='o', c='blue', label = 'Graph 1, Block 2')\n", "ax.scatter(Xhat2[:m, 0], Xhat2[:m, 1], marker='s', c='red', label = 'Graph 2, Block 1')\n", "ax.scatter(Xhat2[m:, 0], Xhat2[m:, 1], marker='s', c='blue', label= 'Graph 2, Block 2')\n", "ax.legend()\n", "\n", "# Plot lines between matched pairs of points\n", "for i in range(2*m):\n", " ax.plot([Xhat1[i, 0], Xhat2[i, 0]], [Xhat1[i, 1], Xhat2[i, 1]], 'black', alpha = 0.15)\n", " \n", "_ = ax.set_title('Latent Positions from Omnibus Embedding', fontsize=20)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.9-final" } }, "nbformat": 4, "nbformat_minor": 4 }