{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# A Network Tour of Data Science\n", "\n", "[Pierre Vandergheynst](https://people.epfl.ch/pierre.vandergheynst), *Full Professor*, and [Michaƫl Defferrard](http://deff.ch), *PhD student*, [EPFL](http://epfl.ch) [LTS2](http://lts2.epfl.ch).\n", "\n", "# Exercise 5: Graph Signals and Fourier Transform\n", "\n", "The goal of this exercise is to experiment with the notions of graph signals, graph Fourier transform and smoothness and illustrate these concepts in the light of clustering." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import scipy.spatial\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1 Graph\n", "\n", "**Goal**: compute the combinatorial Laplacian $L$ of a graph formed with $c=2$ clusters.\n", "\n", "**Step 1**: construct and visualize a fabricated data matrix $X = [x_1, \\ldots, x_n]^t \\in \\mathbb{R}^{n \\times d}$ whose lines are $n$ samples embedded in a $d$-dimensional Euclidean space." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWQAAAFdCAYAAAA0bhdFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTERkCAZkIiJDMCATERni/wMlyt9zWfyTYgAAAABJRU5ErkJggg==\n", "text/plain": [ "<matplotlib.figure.Figure at 0x7f48d7342470>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "d = 2 # Dimensionality.\n", "n = 100 # Number of samples.\n", "c = 2 # Number of communities.\n", "\n", "# Data matrix, structured in communities.\n", "X = np.random.normal(0, 1, (n, d))\n", "X += np.linspace(0, 2, c).repeat(n//c)[:, np.newaxis]\n", "\n", "fig, ax = plt.subplots(1, 1, squeeze=True)\n", "ax.scatter(X[:n//c, 0], X[:n//c, 1], c='b', s=40, linewidths=0, label='class 0');\n", "ax.scatter(X[n//c:, 0], X[n//c:, 1], c='r', s=40, linewidths=0, label='class 1');\n", "lim1 = X.min() - 0.5\n", "lim2 = X.max() + 0.5\n", "ax.set_xlim(lim1, lim2)\n", "ax.set_ylim(lim1, lim2)\n", "ax.set_aspect('equal')\n", "ax.legend(loc='upper left');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Step 2**: compute all $n^2$ pairwise euclidean distances $\\operatorname{dist}(i, j) = \\|x_i - x_j\\|_2$.\n", "\n", "Hint: you may use the function `scipy.spatial.distance.pdist()` and `scipy.spatial.distance.squareform()`." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABMIAAAGyCAYAAAAGbWjGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n", "text/plain": [ "<matplotlib.figure.Figure at 0x7f48d732fbe0>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Pairwise distances.\n", "dist = YOUR CODE\n", "\n", "plt.figure(figsize=(15, 5))\n", "plt.hist(dist.flatten(), bins=40);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Step 3: order the distances and, for each sample, solely keep the $k=10$ closest samples to form a $k$ nearest neighbor ($k$-NN) graph.\n", "\n", "Hint: you may sort a numpy array with `np.sort() or np.argsort()`." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "k = 10 # Miminum number of edges per node.\n", "\n", "dist = YOUR CODE\n", "\n", "assert dist.shape == (n, k)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Step 4: compute the weights using a Gaussian kernel, i.e. $$\\operatorname{weight}(i, j) = \\exp\\left(-\\frac{\\operatorname{dist}(i,j)^2}{\\sigma^2}\\right) = \\exp\\left(-\\frac{\\|x_i - x_j\\|_2^2}{\\sigma^2}\\right).$$\n", "\n", "Hint: you may use the below definition of $\\sigma^2$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABMAAAAGyCAYAAAACmLj7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAYAAABA1/4//Pq0EfHqYvYAAAAASUVORK5CYII=\n", "text/plain": [ "<matplotlib.figure.Figure at 0x7f48d6f74be0>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Scaling factor.\n", "sigma2 = np.mean(dist[:, -1])**2\n", "\n", "# Weights with Gaussian kernel.\n", "dist = YOUR CODE\n", "\n", "plt.figure(figsize=(15, 5))\n", "plt.hist(dist.flatten(), bins=40);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Step 5: construct and visualize the sparse weight matrix $W_{ij} = \\operatorname{weight}(i, j)$.\n", "\n", "Hint: you may use the function `scipy.sparse.coo_matrix()` to create a sparse matrix." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n = |V| = 100, k|V| < |E| = 1242\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWEAAAFdCAYAAADSR9wBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "<matplotlib.figure.Figure at 0x7f48d6e73ef0>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Weight matrix.\n", "I = YOUR CODE\n", "J = YOUR CODE\n", "V = YOUR CODE\n", "W = scipy.sparse.coo_matrix((V, (I, J)), shape=(n, n))\n", "\n", "# No self-connections.\n", "W.setdiag(0)\n", "\n", "# Non-directed graph.\n", "bigger = W.T > W\n", "W = W - W.multiply(bigger) + W.T.multiply(bigger)\n", "assert type(W) == scipy.sparse.csr_matrix\n", "\n", "print('n = |V| = {}, k|V| < |E| = {}'.format(n, W.nnz))\n", "plt.spy(W, markersize=2, color='black');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Step 6: compute the combinatorial graph Laplacian $L = D - W$ where $D$ is the diagonal degree matrix $D_{ii} = \\sum_j W_{ij}$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABHwAAAG+CAYAAADhkBM3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTgAAAABJRU5ErkJggg==\n", "text/plain": [ "<matplotlib.figure.Figure at 0x7f48d732f400>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Degree matrix.\n", "D = YOUR CODE\n", "\n", "# Laplacian matrix.\n", "L = D - W\n", "\n", "fig, axes = plt.subplots(1, 2, squeeze=True, figsize=(15, 5))\n", "axes[0].spy(L, markersize=2, color='black');\n", "axes[1].plot(D.diagonal(), '.');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2 Fourier Basis\n", "\n", "Compute the eigendecomposition $L=U \\Lambda U^t$ of the Laplacian, where $\\Lambda$ is the diagonal matrix of eigenvalues $\\Lambda_{\\ell\\ell} = \\lambda_\\ell$ and $U = [u_1, \\ldots, u_n]^t$ is the graph Fourier basis.\n", "\n", "Hint: you may use the function `np.linalg.eigh()`." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABMIAAAGyCAYAAAAGbWjGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkiRJVcFCmCRJkiRJkqrC/wPqeaPuM3JeuwAAAABJRU5ErkJggg==\n", "text/plain": [ "<matplotlib.figure.Figure at 0x7f48d731b3c8>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lamb, U = YOUR CODE\n", "\n", "#print(lamb)\n", "plt.figure(figsize=(15, 5))\n", "plt.plot(lamb, '.-');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. Visualize the eigenvectors $u_\\ell$ corresponding to the first eight non-zero eigenvalues $\\lambda_\\ell$.\n", "2. Can you explain what you observe and relate it to the structure of the graph ?\n", "\n", "Hint: you may use the function `plt.scatter()`." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABI8AAAINCAYAAAC3XV/rAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAIABJREFUeJzs3Xd4FGXXwOHfs5teCBBC6CUU6SJBBOmgUlQQBAEpIk3s\nWLB/r9hFFCtVQKSI0qVYEKSIgGJoofcOAUIS0svufH9s2ibbQnY3hXNfV643O8/szFnf7GHmzFOU\npmkIIYQQQgghhBBCCGGJrqgDEEIIIYQQQgghhBDFlxSPhBBCCCGEEEIIIYRVUjwSQgghhBBCCCGE\nEFZJ8UgIIYQQQgghhBBCWCXFIyGEEEIIIYQQQghhlRSPhBBCCCGEEEIIIYRVUjwSQgghhBBCCCGE\nEFZJ8UgIIYQQQgghhBBCWCXFIyGEEEIIIYQQQghhlRSPhBBCCCGEEEIIIYRVUjwSTqGUqqSU+lgp\n9adS6oZSyqiU6lDUcQkhhD1KqS5KqdlKqSNKqUSl1Aml1LdKqUpFHZsQQlijlGqvlPpZKXVWKZWs\nlLqklPpVKXV3UccmhBCOUkrNyrx3XFXUsQjbPIo6AFFq3AaMB44B+4A2RRuOEEI4bCJQDliCKYeF\nAc8C9yulmmuadqUogxNCCCvqAwZgGnAZUx4bAmxRSvXUNG1dUQYnhBD2KKXCgWFAclHHIuxTmqYV\ndQyiFFBK+QOemqbFKqUeBhYDnTVN21LEoQkhhE1KqXaapm3Ns609sBl4X9O0/xVNZEIIUTBKKV/g\nJLBb07SeRR2PEELYopT6GzgI3ANEaprWq4hDEjbIsLVbnFJqrlLqlIXtE5RSRkePo2laoqZpsc6N\nTgghrHNi/tpqYdtfwHWgYeGiFEIIc87KXZZompYMXAXKFuY4QgiRl7Nzl1JqGNAYeNMZ8QnXk2Fr\nQsv8cXS7EEIUFy7LX5m9KQOAa4U5jhBCWODU3KWUCgS8gArAY5huxj4oTIBCCGGB03KXUioA+Aj4\nQNO0K0opJ4QnXE2KR0IIIUR+LwCewI9FHYgQQtixGOiW+XsaMAN4v+jCEUIIu97GNM/RF0UdiHCc\nFI+EEEKIXDJXivwf8JOmaZuLOh4hhLDjVeBToDqmnkdemIrfaUUZlBBCWKKUqg88BwzQNC29qOMR\njpPikRBCCJFJKdUAWI5p1cjRRRyOEELYpWnavqzflVILgV3Ad8AjRRaUEEJY9wXwt6ZpK4s6EFEw\nUjwS1san6t0ahRBCFJxT85dSqjqwDogB7tc0LfFmAxNCCBtcdu2laVq6UmoV8KpSylvTtNTCHlMI\nITIVOncppboA3YE+SqmaWZsx1SV8M7dd1zQtvlCRCpeQ4pGIwfKKHLXcHIcQQhSU0/KXUqo8psKR\nJ9BJ07SowoUmhBBWufrayw/TzVggIMUjIYSzOCN3VcdUhFqRZ7sGVAVOYpp38qubiE+4mBSPxAkg\nSCnVRNO0/QBKqcrAQ0UblhBC2OWU/KWU8gN+BSpjKhyddHqkQgiRw1m5K0TTtKt5tpUFHgbOapom\nq0UKIZzJGblrA9DHwvZvgdOYJvvfX8g4hYsoTZPV2G9lSqlywFkgClOF1x8YC1wBWmiaVpBuiG9h\nqho3BgYCc4BTAJqmyZKxQginclb+UkqtBHoBs4FNeZoTNE372VkxCyGEE3PXf8B54J/M99YEhmMq\nhD+iaVreJ/tCCHHTnHnfaOHYp4BITdN6OSNW4RpSPBIopboCk4H6mIo972X+/r8CFo+MWB4Lq2ma\nJr3chBBO54z8lXnBUsNK8xlN08KcEasQQmRxUu56EtPDugaYhpLEANuBSZqmbXNF3EKIW5uz7hst\nHPckpuJRb6cEKlxCikdCCCGEEEIIIYQQwipdUQcghBBCCCGEEEIIIYovGUokbFJKlQF8be0jqxIJ\nIYojyV9CiJJIcpcQoiSS3FX6ybA1YZNS6jvgMRu7aIUZ3yqEEK4i+UsIURJJ7hJClESSu0o/KR4J\nm5RSDYAqtvbRNO1PN4UjhBAOk/wlhCiJJHcJIUoiyV2lX7EqHimlgoFuwGkgpWijEaJE8wFqAb9r\nmhZdxLGUepK7hHAqyV9uJPlLCKeR3OVGkruEcBqHc1dxm/OoG7CwqIMQohQZDPxQ1EHcAiR3CeF8\nkr/cQ/KXEM4lucs9JHcJ4Vx2c1dxKx6dBliwYAENGzZ06A0vvPACn3/+uStjcut5Suu5SuNnKs7n\nOnToEEOGDIHM75RwudNQPHOXO89VGj+TO89VGj/TzZxL8pfbnQbH81dx/tspCecqjZ/Jnecqzp9J\ncpfbnQbJXfLdk3MV9jwFyV3FrXiUAtCwYUNatGjh0BuCgoIc3rcw3HWe0nqu0viZSsi5pBuvexTb\n3OXOc5XGz+TOc5XGz1TIc0n+co8C5a8S8rdTbM9VGj+TO89VQj6T5C73kNzlxnOVxs9UWs/lytyl\nu5mjCiGEEEIIIYQQQohbgxSPhBBCCCGEEEIIIYRVUjwSQgghhBBCCCGEEFaV+OLRoEGDStV5Suu5\nSuNnKs3nEq5XGv92SuNncue5SuNncve5hOuV1r8d+Z6XjHOVxs8k3KO0/u3Id0/O5c7zKE3TXHbw\nglJKtQAiIiIi3DZxlRCl0a5duwgPDwcI1zRtV1HHU9pJ7hLCeSR/uZfkLyGcQ3KXe0nuEsI5CpK7\n3NbzSCn1ulLKqJSa7K5zCiGEM0j+EkKURJK7hBAlkeQuIYontxSPlFJ3AqOBve44nxBCOIvkLyFE\nSSS5SwhREknuEqL4cnnxSCkVACwARgGxrj6fEEI4i+QvIURJJLlLCFESSe4SonhzR8+jKcBqTdP+\ndMO5hBDCmSR/CSFKIsldQoiSSHKXEMWYhysPrpQaCDQHWrryPEII4WySv4QQJZHkLiFESSS5S4ji\nz2XFI6VUNeAL4F5N09IL8t4XXniBoKAgs22DBg2SJTOFsGDRokUsWrTIbFtcXFwRRVM63Gz+ktwl\nRMFI/nIuufYSwj0kdzmX5C4h3KOwuUtpmubsmEwHVqo3sBwwACpzsx7QMrd5a3lOLksuCuEcslxs\n4RQ0f0nuEsJ5JH/dPLn2EqLoSO66eZK7hCg6Bcldrhy2th5ommfbXOAQ8HHeBCCEEMWI5C8hREkk\nuUsIURJJ7hKiBHBZ8UjTtETgYO5tSqlEIFrTtEOuOq8QQhSW5C8hREkkuUsIURJJ7hKiZHDHamu5\nSdVYCFFSSf4SQpREkruEECWR5C4hihmXrraWl6ZpXdx5PiGEcBbJX0KIkkhylxCiJJLcJUTx4+6e\nR0IIIYQQQgghhBCiBJHikRBCCCGEEEIIIYSwSopHQgghhBBCCCGEEMIqt855JMStLiEqiv+mTePo\n6tUYMzKo1aULdz37LOXCwoo6NCGEsE5LhZT5kDofjNHg0QR8ngav9kUdmRBC2PT775eYPv0Ex47F\nU6mSL8OH12LgwBp4eMgzdCFE8XX14EH+/eYbzm7dioePDw0ffpjwMWPwLVeuyGKS4pEQbnL10CG+\n79yZxKio7G1R+/axe9YsBq1ZQ62OHYswOiGEsEJLgthukLE1Z5vhAKT+BP4Twe+VootNCCFsGD9+\nD59+eiT79YEDN9iwIYoffzzLihXt8PSUApIQovg5/PPPLH3kEQxpadnbLu7cScSMGQzfvJmg6tWL\nJC7JmEK4yaoRI8wKR1nSEhJYPngwxoyMIohKCCHsSPrQvHCUW+KrkBHp3niEEMIBGzdGmRWOclu7\n9hJTpx53c0RCCGFfanw8K4cNMyscZYk9dYpfn3mmCKIykeKRuCUYU1O5OG8eu3v25L/27TkybhyJ\nR4+67fxRkZGc37HDanv8hQscXbvWbfEIIUqQS3/C5kfhl7am/7200X3n1jRInmV7n5Rv3ROLEKJE\nOXr0BuPG/Uf79uvo2XMj8+adJC3N4Lbzz5x50k77CTdFIoQoSa5fh0mToHMX6NQZPvoIrl513/kP\n/PQTqTduWG0/umYN8Rcvui+gXGTYmij1MuLj2X3ffcTlKt7Ebt3K+alTafLDD4T26+fyGGJPnbK7\nT8xJ2xc5Qohb0D/PwaGvc23YBqcWQcPn4K4v3RBAEmj5e0yaMUjuEkKYW7z4DEOGbCM93Zi97ddf\nLzJt2jHWretCYKCny2M4eTLBZvupU4kuj0EIUbIcOQJdukLu2szmzfDFl7D+D2ja1PUx2Lsn1IxG\nYs+cIbBKFdcHk4f0PBKl3vHXXzcrHGXR0tM5MHQoaW4oJQdWrWp3nzLVqrk8DiFECXJmRZ7CUS6H\nvoKzP7shCF9QdiZm1EnuEkLkuHIlhWHDzAtHWXbsuMabb+51SxxVq/oWql0IcesZMtS8cJTlyhUY\nOMg9Mdi9b1SqSApHIMUjUcoZkpK4NG+e1XZjSgoX5851eRxVwsMJvf12q+1+FSpwW69eLo9DCFGC\nHJluu/3wNNfHoHTg87jtfXxGuD4OIUSJMXfuCVJT8xeOsnz//UmSk10/z+PIkbZXsh0xorbLYxBC\nlBwREfDff9bbDx6ELVtcH0fTQYPw8LVe3A7r2pWyNWu6PhALpHgkSrXUS5cwxMfb3CfpiOXJFJ3t\nwZkz8S5TJt92nacnD86ahYe3t1viEEKUEHF2ctMN9+Qu/N4CfRPLbb4vgWcr98QhhCgRjhyxfd11\n40Y6ly4luzyOnj0rM2xYLYttd98dzPPP13d5DEKIksORW0J33Db6li9PzylTULr8pRr/ihXp8bWV\nXuluIMUjUap5BgejPGxP7eUVGuqWWKq2asWYiAhaPvkkgVWr4h8aStNHH2Xk9u006N3bLTEIIUoQ\nXzu5ycc9uQtdOSj7N/h9APrbQIWAZ2cosxQCPnVPDEKIEiM01Mdmu4eHIjjY9Q/MlFLMnduK779v\nxd13B1OhgjdNmwbx2WfNWb++E35+MvWrECKHI7eEbrpt5I7HH2f45s007NsX/4oVCapRg9Yvvsjo\n//6jQoMG7gnCAsmaolTzLFuWCr16cXX5css7KEXlxx5zWzzl69bl/qlTuX/qVLedUwhRQtV9DK79\na6N9uNtCQVcG/N8w/QghhA2PPRbGRx8dsNr+0EPVCQryckssSimGDavNsGEyRE0IYVvnzlCzJpw5\nY7k9NBR69HBfPDXataNGu3buO6EDpOeRKPXqffIJXpUqWWyr9cYb+NeXbstCiGKo3kio1MlyW6VO\nUM/OXERCCFEEbrutDG+80dhiW+XKvkyc2NzNEQkhhH06HUyfBl4WatseHjBtKni6fqHIYk2KR6LU\n86tTh1b//ku1p582DWPz9CSoTRua/Pgjdd9/v6jDE0IIy/TecM+v0OIjCAwD5QGBdUyv7/nV1C6E\nEMXQBx8058cf29KmTQU8PXUEB3vz9NP1+eefboSFBRZ1eEIIYVH37rD1L+jXD/z8wMcHeveGzZug\nT5+ijq7ouXTYmlJqLPAkUCtz0wHgXU3TfnPleYX7pR06RMykSSSsWgUZGfh26UK5l1/G9+67izo0\nAHyqV6fBN9/Q4JtvijoUUQJI7rqFJMXAlskQMR+SoqFSE7j7KQgfWtSRmXj4QLPXTD9C2CG569Zh\nNGrMnn2M6dOPcPRoHKGhvgwfXpdx4xoREFA8Ho0PGFCLAQNqFXUYooSQ/HXr+PPPU0yevJ2//jqL\nj48Hffs2YPz4toSFlSvq0AC4805YsriooyieXD3n0TngVeB45uvhwM9Kqeaaph1y8bmFmyRv386F\n++5DS0jI3pa4YgWJq1ZRaeFCAgcMKMLohLgpkrtuBYnRMKU9XMn1f+mZHaaf09vhYZmbTJQ4krtu\nAZqmMXToX/zww8nsbQkJ8fzf/+1m5cqzbNzYncDA4lFAEqIAJH/dAmbOjGDs2DVomun1jRupTJ8e\nwU8/HWDTpuE0a+amGanFTXHpsDVN09ZqmvabpmnHM3/eAhKA1q48r3CvK088YVY4ymYwcOXJJzEm\nu345ViGcSXLXLWL9++aFo9y2T4NTf7s3HiEKSXLXrWHNmvNmhaPcIiKi+fxz65NVC1FcSf4q/aKj\nk3j++d+yC0e5xcSk8Oyzv7o/KFEgbpvzSCmlU0oNBPyA7e46r3CtlIgI0iIjrbYbY2JIWLHCjREJ\n4VySu0opTYP/5treZ+cct4QihCtI7iq95s49brN9zpxjbopECNeQ/FU6/fjjflJSMqy2b9lyhpMn\nY9wYkSgoVw9bQynVBNOX3geIB/pomnbY1ecV7pFx6ZLdfQwO7CNEcSO5q5TLSIHkWNv73JDcJUoe\nyV2l36VLSTbbL1+WHt+iZJL8VbpdumRhpEq+feKLzdxHIj939Dw6DNwO3AVMA+YppRq44bzCDbzq\n1rW7jzE5mYsPPcSpGjU407Qp1z/8EEOsnZs2IYqe5K7SzNMXgqra3sc/BFY+DZ/UMf2sfBquyRN9\nUexJ7irl6tYtY7O9du1APvxwH02brqRGjSU89NAG/vxTiuGiRJD8VYrVrVveZrter4iIuEyHDvOo\nUeNr2rb9njlz9mAwGN0UobBHaZYGHbryhEr9ARzXNO1JC20tgIgOHToQFBRk1jZo0CAGDRrkpihF\nQZzv1InkzZsttumCgjDGxeXb7tmgAdW2bMEjJMTV4ZV6ixYtYtGiRWbb4uLi2LJlC0C4pmm7iiSw\nUkZyVym07l1Y97aVRmVanzUjzxN8rwAY8SvUaufy8G4Fkr9cz1buymyX/FXCbN0aRfv21ucGqVjR\nhytXUvJt//TTlrz0UhNXhnbLkNzlHnLtVbokJaVTrdpkYmLy5yeAqlXLcOFC/p6VvXrVY9myfnh4\nuG3GnVKrsLmrKIpHG4AzmqaNsNDWAoiIiIigRYsWbo1L3Ly0Eye40LkzGefOmW1XAQGWJ9LOVGbU\nKEK//dbV4d2Sdu3aRXh4OMgFjNNI7iqFMlJh9gNwbL35dqXAvzykRFt+X/kwGH/ctJ9wOslfzmUr\nd2W2S/4qgSZM2M077+zNt71mTX/OnEm0+B6l4PjxhwkLC3R1eLckyV3OJ9depc/vvx+nT5+fSE42\nn/uoUqWAzCG3lq+tZs26n5Ejm7shwltPQXKXS8t3SqkPlFLtlFI1lVJNlFIfAR2BBa48r3Avrzp1\nqLFnD8ETJ+LTti3erVpR7rXXKDN8uM33xf/wA8Yk2+P2hSgKkrtuER7eMOoXeHQB3NYNqoVDy8fg\noa+tF44Arp+EExvdF6cQDpLcdeuYMOEOtmzpwaBBtQkPD+b++6uxYEF7iz2OsmiaTKYtii/JX7eG\nbt3qEhn5JC++2Jo776xC+/Y1+OKLbtSvXxFrhSOAWbP2uC9IYZWrJ8wOBeYBlYE4YB9wn6Zpf7r4\nvMLN9OXLU/6VVyj/yivZ2y4PHWrzPVpSEoboaHR+fq4OT4iCktx1q9B7QovBpp8s9lZhA4g7Z38f\nIdxPctctpH37UNq3D81+ffZsAsnJBpvvOXvWcq8kIYoByV+3iDp1yvPZZ93Mtn3zje3OemfP5p8G\nRbifS4tHmqaNcuXxRfHmWauWzXbl74++QgWb+yTv20dyRAT6oCACe/RA5+vrxAiFsExy1y2uXE37\n+5S1s0/8JTi1wfR77a4QWLnwcQlhh+SuW1tIiA/+/h4kJlpfCrtWrQCbx0hOzuC33y4QG5tGixbB\n3H677QluhXAWyV+3tlq1ynL8eIzNdls0TWPTpoucPh1PtWr+dO1aDZ1OphdwNlf3PBK3sDIjRnD9\nww/BaHmG/MDBg60Wg9IvXuTso4+SmGsibn25clT68EOCx451Sbx5GdPSuLh0KZdXrMCYmkpwhw5U\nHzECr/JyISVEqRbWCYLrQvRxy+0V6kFYR8tthnT4/TnYPRuM6aZtOg9oPgK6f2Pq6eQOUZvh5PeQ\ncgXK3Ab1noAy9d1zbiFEkfD19WDw4DBmzjxqsV2nU4wYYX2V3Jkzj/DaaxHExKRlb+vQIZQffuhA\n1ar+To/XkuPH45k58yQHD8YREuLN0KG16NIl1P4bhRAl2ujRzVm//pTV9lGjrM939M8/UQwduoFj\nx3J6J9WqFch333WmUyc7K+s6SWwsfPcdbNoEnp7Quzc88gh4e7vl9G4jU5YLl/GsXZuQzz+32ObV\nuDEVPvzQYpuWkcHJ++4zKxwBGGJiuPDkkxxp0oTrs2djTE11esxZ0qKj+euuu9g9eDCXli4lavVq\nDo4fz5/16xO7c6fLziuEKAaUgkfmgbeF5bC9y0D/761Plv37cxAxPadwBGDMgF0z4YtqsOVdSIhy\nTdxgmtRk+wj4oxOc+A4urIVDk2F1Qzg203XnFUIUCx9+2ILGjfM/oVcKPv/8TmrVsjxZ9tKlp3ni\nie1mhSOALVuiqFt3OaNH/01kpPVeAc4wd+4pGjT4lUmTDrN27SXmzj1N166bGDJkB0ajexf4EUK4\nV//+DRkyxPJqkH373sawYU0ttp0+fYNu3daYFY5M2+Pp2nU199yzlrVrzzo93tz27IH69eHFF2HV\nKli2DIYNg5Yt4coVl57a7aR4JApFy8gg4+BBMo5ZnoCx7HPPUW3LFgL698ezTh28W7SgwqRJVNu2\nDX1wsMX3xK1YQeqBA1bPmXrgAOdHjeJk584YbKzmVhiRTz3FjT35J2ZLj45mZ9++GDOsdwkXQpQQ\nV0/AxQOQkZa/rWYbeG43tB0HIbeZftqOM22r2cby8RIum3ocWZN0BTa/DTObwZX9zvkMeR3/1lQ0\nykszwr9PQkyka84rhHCbqKgkIiOvExub/yFacLAP27b1ZNKklrRoEUydOoH071+LzZt78Nxzjawe\n8/3386/cliUlxcCsWcdo0WIVCxaccMpnyOvIkRuMGrUTgyF/kWjhwjNMmSITfQtR0iUkpBEZGcWF\nCzfytSmlmDevFz/+2IcuXWoRFlaWjh1rMH9+L5YseRi93nLZ4uuv9xMXZ+E6DjAaNTZsOM8DD6xj\nzJi/nPpZcs4BffvC1av52/bvhzFjXHLaIiPD1sRN0TSNpM8+I+nzzzFevAiAvlEjAt59F5+HHzbb\nTx8SQvD//odngwYoD/t/cvG//+5QDEnbtxP19ttU+eyzm/sQVqRcvsyl5cutt58/T9SqVVTu29ep\n5xVCuMn+X2DVW3But+l1QAh0egZ6vAW6XBcnei9oMRzufQd8LPRCyuvUn+Y9jqxJvAIrh8AYF6wc\ncmSK9TbNCMemQysb+wghiq1jx+J48cUd/PLLeYxGDW9vPQMGhPHZZ3dRoYJP9n4Gg8a991Zh8OAw\nKle2vyhJVFQye/fa71WUkaExYsTf3HNPZSpVcu5iJzNmnLBYOMoyZcpxnn1Wht4KURIlJqbx6qvr\n+f77vSQkmAo9nTrV4tNP7yU8vEr2funpRho1qsD06T2oV8+xaUJ+/91eryIjoOfbb49w771V6d8/\n7CY/hWW//AKnrI+2Y/VqOHsWatRw6mmLjPQ8Ejcl4ZVXSBg/PrtwBGA4eJC4/v1J/uEH0z6LFnGh\nQQMuNmzIxaZNOV+zJnGTJxfqvFquH4CY775DS3fgZq0AEg4fRrPTsyh+v4t6DQghXCtyDUx9MKdw\nBJBwFda8DT88YXp9fjd80xkmVIdJzeF/leGnJyAl3nlxRO2FC/8473hZ4uzkpljJXUKUROfOJdC+\n/RrWrDmXPYQrNdXAvHnH6Nx5LYmJ6URHp/DYY39RufJPNG++iqpVF9Ojxx8cPhzrtDjS0418952V\n+eAKYf9+2yspHTkST0aG5Tk0hRDFl8Fg5P77f2DKlJ3ZhSOATZtO06nT9+zbF4XRqPHee39RrdpX\nNGv2LfXrT6NZs29Ztcry/G0FkzPNwIwZh51wPHM2BssApp5Jh51/2iIjPY9udfv3wsLZcPY0VK8J\nQ0ZBk9ttvsVw4QJJX3xhuVHTSHjjDTJSUogeOdL8fRcvEvPSS6Rs306FadOsrrQW2L07MbPNh35k\nFYzyXjYYY2LIiI7GIzQUQ2wsOj8/dIWcmczLynC63Dxl0mwhilbMZVj3LZyIAN9AaD8QWvQw7zlk\nyYrXTD1wLNk2G27vDQsehdRchaK0JNg+E05sgRFLoVJjy++v3RV0nvl7HylMj2qyrl+yktn1E1D1\nLkiLNzV62V4FySFewZBqoe90Fm/JXUIUpeTkDBYtOsYvv5xF0zTuu686Q4bUx9/f9mT6n34aSVRU\nssW2/ftjmDXrMN99d9KsB5GmwW+/XWDbtivMnt2Whx+uibIwX1toqC933FGe3buvWzi6HlPyUmQl\nr0OHTIWe1FQDSUkZlC3rZfG4BREcbPvarUwZTzw85Jm3EEVF0zT++OMUCxfuJzY2hebNQxk9+g6q\nVbPdM3vNmqNs3nzGYltCQhrvvruZChUCmDFjt1lbZOQV+vRZwptvtuONN9ri42O5bNG9ew0OHLDU\nc9KTnPxlupM8dMhUSDcYNOLi0ilTxqPQecWRW8LSdNsoWfhWNuld6NQcvv0afl8Ns74xvf7kHZtv\nS12+HGz0zDGcOUPMq69abU9aupRTVaty5amn0NLyj1ENeughfJqaT4pmJH/hCMAAnHvzTfbWqUNE\n+fL8V6YMxwcNIvnozVeqyzRtSpnbrRfQdN7eVBkw4KaPL4QopN3rYGxd+OF/8M/PsGkBvPcAvNMD\n0lKsv+/SQbhk4xGRpsHa180LR7ldOQyfNIEZ90Ds+fztAaHQYrT5tryFo6xteiByJvzYFr4pA98E\nwk/t4dRv1uNzRNhQ2+21hxXu+EKIm3buXAK3376YkSM3sWzZSZYvP8XYsVto3Pgnjh+33fNm8eKT\nNtunTj1idejZjRvp9O+/iQYNVrBx4yWL+7z1lqXrHg/ME5gpea1bF0W/flsIDFxM+fJLqVdvFV9+\neRhNu/lJrYcMqWmzfehQ2+1CCNdJTzfQp89SunVbxLx5kaxadYx3391K3bpT+fnnIzbfu3jxQZvt\nK1ceYebM3RbbjEZ4772tVK36FV988a/FfZ59tilly3rl2eqNKX/lzl06oqIyGDVqLyEhGwgO3kBI\nyAbGjTtIbOzNj2Lp1w+sLB4OQMOGpomzSwspHt2qNq6DiW9bbvtkAvxpfd4hLTHR5qGNgPHaNavt\nClBpacQPyM21AAAgAElEQVRNm0bU6NH52z08qL1uHf4dTUth5x6mlpcBuDpnDqmZg021tDSif/yR\ng23akFyIPoJNvvoKnY+Pxbbb3nsP75CQmz62EKIQEmJhYj9IsZCH9qwzFZSsSbWduwCIsn2RgwYc\n2wDTu5h6JOXV7Uto+TSozH9e8xaOsuiAS5vh4racbRe2wsr74dAP9uO0pvGrEGBlPH/V+6Far5s/\nthCiUPIuJZ3lzJl4BgxYZ/O9iYm2h9NfvmyjcJ7p6NEb9Oy5nj17ovO19e1bk1mz7iYgIOvpftYT\n+/yiolJZtuwc6emmx3onTiQwblwEY8bc/FDcHj0q06eP5SW1a9b04403rE/2LYRwrY8+2sbPP+d/\nMJ+aamDgwJVcvmx9AaOkJNuFGYNBw17d+fr1ZF544Q+mTv0vX1vNmoGsW/cgtWtnrSSpx1qJw2Ao\ny+zZF4mJMcUUG5vBl1+eoVOnf4iPv7nFkMqVg48/ttzm5QVffXVThy22pHh0q5r1je322dYnVPVs\n3dr2ex2YFDtL/Pz5pJ/M/zTNs1IlArt3B6wXjow22jKuX+fcW285HEdewR060Pavvwjt3Rul1wNQ\n9s47CV+8mLrjx9/0cYUQhbTxe0i2MffQH7MgPf8KRABUamh/4mtrQ9ryunYMdlso8ug8oOkwSDea\nkpS1kRweVto0I2x+EQyWVw6xy6cidNsG9Z8Cz8wLKb/q0PwD6LgCdPqbO64QolD2749m8+aLVtt3\n7brGjh2Xrba3bl3R5vH9/By79kpJMTBxouW5z4YMqYO3d9atQcGHoc2adYJduywNfbNPp1MsXnw3\nEyc2o2ZN02TcAQEePPFEHbZtu4cqVWw82hdCuIzBYGT69F1W21NSMpg92/oCIHfdZbkonKVCBX+H\nY/ngg78tzn12550VadYsa9oRa9c5vpiGsuW3d28806fbm3jbuueeg2XL4K67TK91OnjgAdiyBe65\n56YPWyxJ8ehWdcjOcs022r06dcLjjjustvv27w+etsfuZxd9NI2osWNJszDMLHbRIvN9rR3Ditif\nf8aQYL0Sbk/Zli1ptXIlPZOT6ZmURPt//6VK//43fTwhhBOctpO7EmIg+oLlNp8AaJe/t2O2kLpQ\nxfacb2b3U39+CMf/zL9P5CLbx7DWGylLUhSc+cP2MWzxDTWtqPZILAxMgL5nockbpvmYhBBFIjLS\nflHF1j7jxjWx2ublpaNbN9s3aLktXXqa+fNPkJpqMNv+xx8XiY7OKlzf3BxGCxbYWHbIDg8PHa+8\n0pDTpx8kMfFh4uL6Mn16SykcCVGEoqOTuXTJ9v1UZKT1uRZHjryDMmWsz2k2cKDjvQovXkzghRfW\nc/Wqec/v+Pg01qyxPK9SDtt5ZMEC68V9R/TtCzt2QHIypKSYVlnLKiaVJlI8ulUFlbPdXtb2zF5l\nV65E37Bhvu1e3btTdtYs/AcNsvrevD2Gkv/4gzMNGnDttdfM9jPEmiY1s3b5Yq94pGVkYIgv/OpI\nOk9P9LYGswoh3CfQzqyDOh34BVlv7/0htOiXf3uFMHh6LXR60fbxcyek66dgVlf4tiuk5rqwSs0c\nlmKre6Q9KfaXzbZL6cDD8Sd6QgjXCQ62PBQ+t/Llrd9g9exZnU8/bYWHh/lVkZ+fB4sWdeatt27P\n1WvItowMjWHD/qJeveUcPJizEltsbO4ejzeXvGJibrLXZB5+fh7odIWbhFsIUXgBAV54etrOLeXL\nW89vISH+rFo1kPLlze+llIKXX27Dl192p0ED+4sVZfnmm11Urz6Nn346lL0tISEdgyErZ1nrQW47\nn2QNZSssHx+7fShKNFlt7VY05QM4a2dej/5DbDbra9QgODKS1DVrSN+0CTw98e7TB682bQAInjIF\nw+XLpKwzH8OvYZqnKB9NI2biRLyaNKHMENO5fVu0IP3sWatf9ay5863xrFQJz0LOTWRMS+PUV19x\n5ttvSTp1Ct9q1ag+ciRhL7yAh59foY4thCigbWth9QLb+7ToAWVsXIR4eMHoJXAmAnYvhbRkqNMW\nmvcBvQeE1oerR2D9x/mHsFma+BrgxJ+w6jnoP8f0utIdwHem343k70HtyD1ZSFP7+9hzfgUc+Ryi\n/zUVkar3h4avQUCtwh9bCOGwEyfimDBhp819ypf3pmdP25NCv/RSMwYOrMO8ece4dCmJevWCGDKk\nLuXKmYpOS5Z05tFHN5OQ4NjcHefOJfLAA+s5erQvHh467rgjd3HewM3cJjRrVrbA78lrz54YJk48\nzJo1FzEYNLp2DeWVVxrQvr3MNymEOyUlpfPUUxvIyLBdeBkyxPY1S8eOtTh7dhyLFu0nMjKK8uV9\nGTy4GXXrmnLOmjUD6NHjR44dc2TYqyI11cDQoWtp2jSERo0qULGiL1Wr+nPhQiI5uStvzBnYymnN\nmgVabXPUlSsan3ySwcKFGVy/Dk2aKJ55xoPHHy89JRfpeXSrmfEJTH4LtFTrQ0KbtYBhY+weSun1\n+PTuTeDnnxP4ySfZhSMAXUAAlX7/nUpbt+LZqhUGTF9Ze5czsV9+mf17hWefNZ0Hy6Ha++OtOHYs\nqgDzL+VlTE/n3169ODh+PIlHj6Klp5N06hRH3nqLHffeiyHZ8pK5QggX2L8d3ugDUZfA2ryw/mVh\nmJVZC/OqGQ4PfQSPfAHh/U2Foyz3fwBvHYc7h5oSjQ7L8y/mvi7ZsxASMrttNx8GPpm9n9LJXzE3\nrXZtXdX2EGJn+Jw9Bz6ArX3h6l9gTIW063BiBvzRCm7YXhlFCOE8cXGpdOmyiu3bo6zuoxR89tnd\n+Prav2apWtWf119vzldf3c2zzzbOLhwBPPhgdS5ceISPPmqBt7dj85udOpXA6tXnAGjcuBxdu1bO\nbMl63Od4D6SAAA8ee8zKhP0O2rgxijZtNvDjj2dJSMggOdnAmjUX6dx5Iz/9dPNzkgghCm7IkF/5\n/vuDaJr13DRsWFPuvrua3WP5+3sxalQLvvyyB2+/3Sm7cARQp045Dh16guXLH6Zq1QAbR8l5ipee\nbmTqVNMqbXq9jqefzhraqwFp5M9dFhY5yeWZZwq3ouPlyxpt2qTy2WcZXL4MaWmwa5fGiBHpPPmk\nc3pkFgdSPLqVpKbAt5+YfleAP+CF+SqGg0fAzxvB3zlDHXzatqXKtm0EjB2LpjP/c7NUw06NiMhe\n6jWgSxeCn3kGjZwCUv4FY0FZ6BtYrndvqrzxRqFiv7BwIVd/t7zqXMy2bZyZMaNQxxdCFMD8jyAj\ns0txIpBATlFGA2qFwyfboab1eUEKJLg2DJ4HA2aBt595wspKSrm3GdLg8j7T7z5BMOjnnLZ0IBVT\n9TzrXiwd0FsYDlu2HvSw07vKnsQzsN/KqnOpV2HPy4U7vhDCYXPnHuHsWevzhQQHe7NmTU+GD2/g\nlPOVKePFa681Y+vWHlSr5lgP6Z07c1bInT+/PYGBWddVRnISV04hSVm4gPP392DZsg42h97Zo2ka\nY8dGkJKSv4+6waDx1FOW24QQzrd//zVWrDie+UoHeJP7cb5Op2PSpK58992DTjmfXq+jT58G7N07\nmo4da1jZyzz57NyZs8jAK680p0WLrIUFjJieNKZhymFGTBdelqczmTChLt27F65n44QJ6Zw8abnY\nPn26ge3bS0fuKj19qIR9u3dATK7lWRWmucNyD1Nt2ggC7axGVFA6HZ7R0fgYjdn3elllpKx7qKyv\nmvL3R+W6KqnyxRdEL12K8XJOcsj9tdQpxW2bN3NjwwYSd+/GIyiI4MGDCera1WZIyWfOcGH6dGK3\nbkXn40PFvn2pPGwY+lxFs3Nz59o8xrm5cwkbN87mPkIIJ9A02PGL+bbUzJ8s9StCNefcfJlJT4Pk\npPzV7qz5jHL/K+qdq8tzrY5wez84sDRn1bWsXkxZ2n4CPn5w+nfT3VitHnDbAPCwMTdKWjwc/x7O\nrARDKlTqAA2fBP9cT/1OzbO9atylXyDlimllNiGES61da3sS1/j4dLvD1W6GUnnnMLIup1gElSv7\n8dlnrRgzZgc5XSQVuSvm/fpVZ9SoeixadJobN9IJDy/PyJF1CA21Pj+k0aixatUFvv/+NFeupNCg\nQRmefLIuLVvm9D7Yvj2ao0etz1V5/Xoaq1Zd4JFHrN1YCiGcZe3avKth6zD1OjDdiRmNitatqzt9\nbjIPDx3R0XlHd2TlH42cJ3gQGOiVvYder2PZsvsIC1uCpmXkep8+e//KlTV+/bUt339/gdOnk6lR\nw4eRI6vTtKntIWsRESlMmxbHoUNphIToGTasDA895J/92TMyNBYutF0cmjvXQJs2JX/FWykelXYZ\nGaYrCL0ejFZuJnJ/563tUwip69aRvGRJdq+hrPpvFg9Mz7OMQODAgeah6fVU/egjzjz+uMVjBw8f\nTmCbNgTmGjJnz/UNG9jbuzeGxMScbevXc+7rr2mxcSPeoaGmuKOsdzEHSL1sfUldIUQhaZopf3l6\nmn7X7AydcEHuIjkOVo3PjIf8xR8wJS8dUKEOVLvTvK3DO3Dqd1PBJ6/ghnD7CPD0gyYjHIsn8QL8\n0hluHMvZFrUVDn4N966Byh1M21Jt5y40o6kHkhSPhHCJtDQDXl6mmwSj0XbuspfabtaLL+50aO4j\npWDAgNpm24YODePrr48SGRmbb39/fw/eeqspzZqV4777KudrtyQjw0j//ttYuTJnJcxt26KZM+cU\nkybdzssvmwr/UVHWxiTnuHzZ/j5CiJuTnm7Aw0OHUsrGZVXOjaO9/HYzvvxyJ/v3Z63eZl78Mck5\n58CB5g8Na9UKZMyYBsyYkX8Vb4AJE5pz++1lmDzZ8Y4Sn38ew0svXTPL1T//nEivXv4sW1YZDw9F\nUhLYW+A7KspFyd7NXDpsTSn1ulLqX6XUDaVUlFJqhVKqvivPKTJt/x2e7AJ3e5l+XngAPDQIsPNl\naX+f00NJmj8fMH3VrV3G6AG9vz/lX389X1vw8OHU/O47vGrkPGnSlSlD6KuvUmPmzALFknLuHPse\nftiscJQl8dAhjjz9dPZr//q2/1T9b7utQOcWJYfkriJ06ii8NBQa+0EDL3jwDli5AMJt9yaklfNz\nF/uWQ1pmrrBUOIKc+Yt6fJJ/LEeFRjBoPVTJtVar0sNtfWHwRlPhyFEZybDxUfPCUZb0eNj4iGno\nHECgnT9VvS/4VXf83KLEkNxVdOLj03jjjW2Ehs7C23sqVarM4e23d9CxYxWb77v3XvtzhRTUmTMJ\nbNlip4icacyY+oSFmT919/HRs2FDV/r3r2G2utuddwbzxx9daNbMzoq9uWiaxptvRpoVjnIbP34v\nu3aZJsmtX9/+hLW33Vb4SW1F8ST5q+jMnHmQJk1+xMtrJgEBsxg5ciONG1ew+Z5y5by5885Qp8cy\nf35krld5C0dkv77ttnIMHtwo3/unTGnNm282Iygop0dl9er+fPvt3YwZU7B7t99+S8hXOMqyalUi\nX3xhKrAHBkJlO7X0+vVLx2xBru551B74Gvgv81wfAeuUUg01TZPZhl1lzffw7uM5j7M0DbauhR3r\n4J6+sPIny+/r2AMaFnKSVguM0aahcvbqrZ7lyuFRq5bFtuDhwyk/bBhJERFoqan43nGH2RAze1Iv\nXuTUuHFcWbaMDBs9FK6uXEnq5ct4V6pEzbFjiVq1yuq+tcaOdfj8osSR3FUUjuyHQR0gLtcy9Qf3\nwPjHoPdA0Oks9zAKrgQ9LfdOLJTEPMN8rdEUVGpmua1KK3hsB0QfhsQrUK4uBNq+mTRjSId//wcH\npgI3rMeRHGUayhb2CNQaCvvegIz8RXIAaj4Knk4eniyKC8ldRSAxMZ3OnVcQEXEle9ulS4m8++5O\nWrcOJSTEh6tX8/eY0esVr7xyh9PjiY5Otb9TpjvusLw6ZUiID4sXt+fy5WSOHYunQgVvGjYMKlAc\n8+ef5t13D3D8uO1H8jNmnGDGjPI0bhxEu3YV2Lr1msX9wsL8uffeSgWKQZQokr+KwNNPb2Hq1APZ\nr5OSMpgz5zBr1pyhbduq/P235cLvuHEt8PV1/pr0165l/V+dd4lbc40aVbB4fr1ex/vvt+CNN5qx\ne3c0np46wsOD0esdL97s3JnISy9d4K+/0jEN1bNs+vQ4Xn65HEopxozx4J13LHeT0Olg9OiSP2QN\nXNzzSNO0npqmzdc07ZCmaZHAcKAGEO7K897SUpJg8jjL/aAz0uH4vzDiBfDK9UVQCu7pDV/+6JKQ\nPBs3BmwvLgRgOH8ewwXLCQpA6XT433knAe3aoff3J+30aS488wwHK1fmQLlynHrgARL+/DPf+zJi\nY9nfsSPRS5ZgtDO0RTMYSD5pGuMb2qMHdcaPt7hfjVGjqDpokJ1PJEoqyV1F5OPx5oWj3Fb9BGMm\nQVCeG51ajeDz9VDG8SfhDquU+UQr7+TY+WhwaqvtYwU3gBodTIWjtETY9hHMuA0mB8F3LWHPLMvz\nFK0fArs+hnQbhaMscZmrqHmVg9YLQWdh4tpyLaD5p3YOJEoqyV1FY9q0SLPCUW47dkTx5JONaNDA\nfAn7ChV8WLjwHrs9k25GWFgAPj6O3ahs3Wq7h1KlSr60b18xu3C0aNFp2rb9nbJlFxMW9jP/+99e\nYmLyF6tmzDjOsGH/2C0cARw5kjO0d+7cu6hePX+vzPLlvVi8+G6nz68iig/JX+63e/dVs8JRbleu\nJFOxYhAPPmi+gqKXl56XXw7n//6vtUtiyunxZLtM8c8/l2y2+/l50LZtKK1ahaDX69ix4zr9+/9D\ncPAaKlZcy8iRERw+nH9agb17k+jc+Rh//ZVgN4YTJ9IxGEz33K+/7sG99+bfX6eDadM8qVdPeh7d\njLKYOqBcd/N5bx1bVkF8/jHq2S6egh4PwROvwqZfID0d7uoIYa4bguU3ZgwJX3yBMhjs9j5SPjYm\nis0lKSKCk506Ycw1wDR+7Vrif/mFqtOnEzxmTPb2yzNmkHLctFqAI5ccXqE5XTAbTpyId5UqXFq8\nmIz4eAIaNqTGyJFU7NbNoThFqSG5y9WuXYG/LK9uCJgK4tfiYPl52L4WYq9CzYZwR0fXxdSgOwSH\nwfW8k0ZaYGuS69zSEuG7cLh+JGfb5Qj4dTSc2Qi9FuQMf7vyHxxfbPrdkaHyPrlWCqnWG9oth6Nf\nQeJZ8KsKNQZCrcGgdzBWURpI7nKDefMO22zfsOEcBw8OZNOmixw+HEPFir488EAtvL1d8yS6bFlv\nBg8OY/ZsC8Nc83C0yAQwZMjfLFx4Ovt1XFw67723n6VLz/LXX/cRHGwqWKelGfi//9vv8HH9/HJu\nR+rUCWD9+o68995BIiJiKFPGk549KzNmTBiVKlmfkFuUSpK/XGzePMtzA2VZs+YM16+P4Ny5G2zZ\ncgFvbz3331+bkJACDLsvoKefbsnff5+3u19B8uecOacZPXqXWef1OXPOsHjxBdata0ubNjkPJidM\nuERiYtaOti++AgIUer3KjEexfLkn77yTwvr1BpTS06qVB08+6cHtt5eOwhG4sXikTEtofQFs1TTt\noLvOe8uJjXZgn2vQogP0c8EwDws869en7KxZxI4cYXNiNe927dCH2F8m0RAbm69wlE3TuPj88wQ9\n/DAewaZEEL10aXaz3Sl1lcoeDhe9ZQt7Rowg6cSJnMMbDHgFW+7iLUonyV1uEhttf+bYmGvg7QOd\nHnZPTDodPL4MvukC6THWq8+efqZCkyMWdjIvHOV28AdoNADq9TK9PrHU8n7WeGbeWCVfhO1D4MrG\nnLa0q6bhalI4umVI7nKfa9dsT+J87VoySik6d65K585V3RLT5Ml3Ehl5nX//tX1d2LevYyu9TZiw\nz6xwlNuhQzd4991IvvyyJQCbN1/l6lXHh85l1cvT0408//wuZs06RXq66YrNy0tHq1blqVDBQk9K\nUWpJ/nIPe7krPd1IXFwqDRsG07Che+5/Bg1qzN9/n2PKlN2Y5jyyrG9fx6bDioi4zqhRuyxeYiYk\nZDBmzG4iI+8BIDXVyOrVcbn2sH1d6ump0DQNpRTffpvEa68lcP16znuCg70IDS1d0wS4sww2FWgE\nDLS3oyiE2g2ds4+TeTdtio+vF3prN18eHpR9912HjnX+ySctF44yaSkpxC5alP06a3JsDdPCSDZp\nGjGbNhF/+DD/9OxpVjgCSDh0iB333UfyuXMOxSpKBcld7lClBvgH2N6nbv6JEV2uQh3QVwBb90Gd\nxoNvWRs7ZDr4I1z+z/Y++77L+T0915xF9qYVUMCVv8GYDhvvNS8cAaReg39HwPmV9uMUpYXkLjdp\n1Mj2sNlGjcrbbHeFMmW8qFPH9k1Lhw6hdO9uv5h14UIS770XaXOf778/mf2AMDHR/ipvuR06ZLpZ\ne+65XUybdiK7cASQlmbk66+P8dJLewp0TFHiSf5yA3u5KzjYh4oV3d/jLzy8KrYKRxUr+jFuXEuH\njtWnzz82n03u33+DnTtNndvS0jQM2TeLWSulWOt6oBETY+TMmQyWLElhzJh4s8IRwPr1aXTrFps9\ntK00cEvPI6XUN0BPoL2mabYHKAIvvPACQUHmk/INGjSIQTLHjLkTu2HPBtB7QKsHoEpdaNnZVBw6\ndcjye8I7FUnxKPn9d1CpqfjpIMUI6bm+Qzqg7Jtv4tu5s93jGBISiFuxwu5+6RcvZv8e2KYNyYcO\n2S8cZVJ6PScnT7a4IhtAekwMp6dMoeHHHzt4RNdatGgRi3IVywDi4uKs7C0KQnKXaxgvXCDt55Vo\nSYl4tG6DZ7v24OcPfYbBgqmW3xQQCA8NcW+gAFvnwJXMoR8a4E3OYxcjUKMddJvg2LF2T7e/T3xO\n7qJSG4j8xlQYcuhRjw7OL4cbNh7SHvwAqj3kyMHcQvKXaxQ0d4HkL0ckJaWzbNkxLl5MICysLL17\n18HLS89TTzVlwwbrwyyeeqqpG6M0iYyMYdGiU1bby5b1Yu3ae1B5V4m0YM6cEzaW7TaJi0snKSmD\ngABP7ryzPHq9cviGSa/XcelSMrNnW493xowTvPVWI0JCikfvScldriPXXs6naRrr1l1hz55YypXz\n4uGHqxAc7M2IEQ14993/SEmxfJc0enRDPD3dO9FzRoaRt976y2q7UrB4cS+qVbO/8uK2bdGcO2d/\nrvVLl0w9sAID9TRq5MPBgynkFK+MmC4Ac1+IZS2164FOB++/b2WBEmDfvgxWrUqlT5/SkbtcXjzK\nTAC9gY6app115D2ff/45LVq0cG1gJVl8DEwcALv/yNk260XoMhSemwUfLYGn74Hoy+bvq1YHJnzv\n3lgBLTmZ9F/WAqYvvK8efDRTLyAF6BXoTp2weYws6RcuQKr9rtDedetm/1752We5Om8eWob9J2HK\ny4vyXbuy78UXbe535ddfs4tHxowMolavJuHwYbwrVqRyv354BhVsRZLCsPQP5K5duwgPl/kFC0Ny\nl/Npmkbya6+Q8tUXkOv7qA9vSeDSFehemQiH9kLE3+Zv9PWDr5dAoPu+V9kicg0dS8v8ybqeMADn\nHctdAFy3P/8I5XJyF3X6wfbXIMnBno7VH4ALdoa6Xf/P1AvJO3NCymvb4eoW0+TaVXtDQG3HzuUk\nkr+c72ZyF0j+smfJkqOMHv0HcXE51yChoX788ENP+vaty4svNmfy5Py9Y95+uxX33FPDnaECsGzZ\naZvtsbFpnDuXSMOG9ntNHjuWf1LZvEJCvPH3N91WVK3qxyOPVGfRIsf+/B54oArr10eZ9TjKKzXV\nyJ9/XmHAANN/y9OnE/n550ukpBho164Cbdu6d0oByV2uIddeznfw4A369NnB0aM5ozaef34v777b\niPHj67Nw4T0MGvQHaWnm3797763G22871rvHmbZtu8DFizZGmGiwf/81Ona0n1ePHbM/YT+Y5lrL\n8uKLFRk16izmcxVYHr/SrJkXHh469u2zfY/5669p2cWjGzc0li5NIyrKSP36enr18sTT030LARQ2\nd7m0eKSUmgoMAnoBiUqprJmI4zRNsz3IUlj3yUDzwhGYvkkb5oFfEIz9CpYcgtVz4d8/QKeHdg9A\nj8Hg6/jy9s6ipabmW15bKfM/Pi3FsRU4PSpUAL2eXH0K81He3pQdMCD7dUDz5tSbP59Dw4aZJgi3\nocqIEXiWt9+9XMvs/xizYwf/9etHSq5V4vY//zyNP/+cmqNH2z2OKJ4kd7lGymeTSJmcf6UvQ8R/\nxD/YkzIRe1A/bIJ1K2DtT5CYALe3goFjoHI1t8cLQFpS/m250096AVYPDqgECRdt73PHEzm/673g\ngV9hzb2QYefha2BtqNbTfvEITP9epFyBrQ/DtVyrxO15CWqPgJbTQOfu9TSEM0juco1//rnEo4/+\nQkaG+bVMVFQSvXr9zN69Q/nss/b061eX2bMPcu5cArVrl2H06MaEh1cskpiTkuz3t7bW2yCvSpXs\nPzEfObKOWS+mGTNacvVqKuvX217NzctL8dxz9di69Zrdc2gaGAwazz67hxkzTpldWrZuXZ7ly++i\ncmWZVLukkvzlfImJGdx331YuXDD/z5eSYuSVV/ZTpYoPgweHcfToo8yYcYBdu64RFOTFo4/W44EH\nahZoeXtnSUqyfa8GkJzs2NBYR3JXo0aBNG6cM8R35MgKHDuWysSJ9udp/7//c2xIctawublzU3n2\n2URyz75SubJi8eIA2rWzNz9B8eDqq8OxmEp1m/JsfxyY5+JzlyxHNsH2eXDjClRuAB2egNB6+fc7\nsQd2rbN+nHWzYPAECCwPj44z/RQxXdmy6Bs1wnDQ+lAKj9Z3O3Qsj+Bgyjz4IDdWWp+3o+qUKej8\nzYtkIQMH4h8ezvZGjaz2QPINC6PBlCkAVOzWjbOzZ1s9R8Xu3Um5dIl/evQgPdZ8dTtDYiL7nngC\n3xo1qNitG8kXLhD1229oRiMVu3bFPyzMylFFMSK5y0HJx45xeeZMkg8dwjMkhJBhwyhrYQiqlp5O\nys1TIXkAACAASURBVJefWz2OYX8k6b/9ilfP+6Fnf9NPcVDnbji7y3a7o5oOh8u2jnU/1Ohgvi24\nMQw5A8saQryVXk46T+ixGZQOKneD0zZ6mJYLN63Ktr4tXNtm3qYZ4eQs8A6G2z+GjES4tBrSYiCo\nGVRo69DHFEVKcpeDYmJSmDNnH5s3n8PLS89DD9Wjf//b8PbOf2n82WcR+QpHWRIT05kyZQ+TJ3ei\nTZvKtGlT2dWhO+Tuu20vQFKunBcNGjjWm3P48DpMmmRlOgQgNNSHt99uZrYtMNCTP/7oxNChO1iw\n4IzV906d2pLatQPw9tbj4aHIyLA81M3LS0eXLhWZMOEg06blH962Y8d1evfewb//dsZo1Fi//gon\nTiRSpYoPPXtWwtOz9Kx2VIpJ/nJAerrG8uUxLFsWS0qKRtu2/owcWYEKFfLnrgULzuYrHOU2adIx\nBg+uQc2agXz4YWtXhu2w8PBKeHvrSU21Xty++27HFh64556KVKvmy/nzlh/06XSwbFn+z/3xx1Vp\n3NiPYcMuW3iXyUMPBdKvn2noXNOmHkRGWi9ode/uxZ9/pjNiRGK++ZcuXdK4//4EDhwIolo1Uy+m\n7dsz8PVVPPCAJ+XLF6/c5dJoNE3TaZqmt/AjCSCLpsGc4fBpZ/j7O4hcC+s+g/81hL8sFC8iN9k+\nXmoyHN7hikgLxed568PAVLlyeA93fOW3yp9+ikdoqMW24Oefp/zIkRbb/OrVo8GMGaZMkYdX5crc\nsW4dKrMt7MUX0ftZXobSIyiIWk8/zZmZM/MVjrJpGscnTmRr9+78WqMGu0aNYveYMfxety7/DhpE\nRpKF3gyi2JDc5ZioOXPY1bAhFz/9lJi1a7kydy4HunTh6GOPoeXpbWg4fBjtsvV/hAEyNm202V4k\nujwDHlZW+VEK7nnB8WM1Hw3VO1huqxQOD1uZz03vCV2XgbeFJ1zKEzr/BAHVTa+rPQxlGliPodEb\ncHVr/sJRbsenwZ4XYXUI/DMIdj8Fm9rB+haQUIBhesLtJHc5ZvfuKOrX/5aXX97E6tUnWLbsKEOH\nruWuuxZw9Wr+f583bbI9dHTjxuK3iMaDD1anXj3rE2aPHXsbvr6OPUNu1CiI119vbLGtXDkvtm69\nDx8fy/OiTJkSTni45Ul5X3ihPiNHmh6oVaniy+OPWx82O2pUGAEBHnzzzUmr++zcGcN77x2kUqW1\ndOv2N089tYeHHtpB9eq/smaNQ1N/iSIk+cu+2NgM2rU7wsCBp1myJJbVq+N47bWL1Kt3gO3b8w/R\n2rTJdo++vXvjuH49zVXh3pSQED+GDrWcbwBat67icPFIr1fMmHEHXl757/30esX8+S1p0MDy3ElD\nh5Zj7FjLw3pbt/Zl4cIq2a/feMP6yJ4mTTzo3dubTz9NsTpx940bGh99lEyTJrHcfvsNxo5N4rHH\nEqlaNZYJE4rXPWPxKmXdijZPh+0WnhIbDTB/DFzM01vHw4EubR5ezonNibxHjMTnldfyFW5UxYr4\nv/8B2t9bMJ6yfkFgdqw6dai7cyfBzzyDPiQE5euLf4cO1Fy+nKpffGHzvVVHjKDlli1U7NcP7ypV\n8K1Th1qvvcZdERH41amTvV9go0a0WrMG35rmS9j616tH63Xr8KtZk+jNm22e69rGjVz5/XfzIXua\nxvkff2SXlQKXECVF0sGDHB8zxuIQ0qvz5nF5uvnk0Mrz/9k77/Coii4Ov9vSKyGEkEAivUPooRcp\n0kFBREBAEBBBkaZ8CHZUiqKAgA2p0qSG3qv03hNSISQhPaRu+f5Ywmaze+8mkAbc93nyyN6ZO3c2\nZs/OnDnnd/Jgu/LSp6gpWw1GrQObXIsLpRV0ngapjyDoTN7GUtrAgN3Q9jtwraJ/XaoatJ8DQ07o\nnURCuNWDXueg1ofg4At2XlBpEPT8D3z7GPoprKDtXijd0vh+K1dotATK94VocdtFVhLc+RE0uU7q\nEi7AkVdBXbIWMhIS+UGj0dKnzyYePjQ9ib50KZrRo02juy1FrZTEqBaFQs6OHa9StaqpA6lvXx+a\nNCnDvn2RZGbmLXXt22/r888/LWjevDS2tgo8PGz46KPqXL3ajcqVhYVrnZxUHD7cntmz61GnjjOe\nnjZ06ODBxo0tmDfPz6jvggUNGDmyIkqlIf1NpZIzZkwlfvrJj8uXk0hIEE9pmTHjJjExxpvhqKgM\nXn/9FOfOxefpvUpIlFQ+/DCC06dNv4MTEjT06XOXjAzjg7u82Kacn7eSws8/d6BHj0om1+vWdeeD\nDxqyfXswsbF5kw3o2rUsx4+3oV8/LxwdlTg4KHnjDS9OnmzDwIHiukm//urJP/940batHWXLKqhX\nz5off/TgwIEK2NkZfrcDBtiwaJEjLi7Gv8s2bVTs2eOCUinj8GFx27VoUQbXrhn//0tPhy++SGf+\n/JKTtSnTidWuK2JkMlkD4Ny5c+deHuGzmbXh/jXh9vbj4K2fDa+jQ+HdiiYaQk9wLAXL74FVyVB0\nz40mNJTMf1aji49HrsmCgE3owh6HM8tkyDt3xWrRn8jKFI9GQG50Wi0P9+8nLTwcu1dewa1t2yc5\n/f917kzMHuEUQh0gGMAol9P5zp1CS2HLIXzWUKfTieTJSBQEL6Ptuvvhh0T+/LNgu23NmjS4ZrBt\nOp2OxDo10N66JXiP09GTKJuVjLBpE9KT4dRqiA4EmVJf6fJuDqdR+dow4jeoUoLmH38B4i+Cyhk8\nXwPlYy2QGz/Apani9yow1orMScPf4ZXCc4BL9qtoedns15Ytd+jdW7hqq0IhIzR0NF5eBofImDH7\nWLz4suA9X3/dgv/9r2mBzrOg0Gi0bN8ewYkT0SgUMq5eTWbnzvtP0sM8PGz46qt6jBxZ2cJIRcf9\n+2ns3x+FTAYdOng80TE6dy6eRo2ePkL1rbe8Wb26SUFN0wTJdhUtL5vtio1V4+V1hYwM4b37qlW+\nDBxoiFLesOEe/fqdEuzfrp07Bw60KtB5FiRnz0ayZUsgWVlaYmIy+fffYBIS9EULbGwUvPtuTebN\na4WVVdFWhBMiNVXHzp0ZJCXpaNhQSd26hkNBF5d4EhOfzu/i5SUjJMSl0Bx9+bFdJe+o5GVCp4NI\nkZLKAPeuGr8u4wMdRRbt/acVn+NIq4Vt62FwN+jcAEa/CceNv+QVPj7YTv0U6y5d0C39xeA4AtDp\n0O4KIKNnR3QWhK2fPDIuDk1sbEG+CyNkcjnuHTtSYfhwSrdrZyQGWbZXL9F7Rc2DVkv0vn0FM0kJ\niWIg9epV0fa069eNUtdkMhm2M74Q7K96rWvxOo5unoLZQ2BsA/i0I+z9G7JynF7bOEKbUdB5Chz4\n29hxBBB+Fb7rBPeFnWNGZDyC5Cjhg4CCwNUPKg7TRxspc4jIeonbLotEiejuSUiUcK5eFU/j0Gh0\n3LxpLJQ6aVIjnJ3Np696eTkwalRds21FQVhYCp98cpbGjbfh7x/AN99c4uFDwym1QiGnV68KfP99\nI86fT2TbtntGukJRUem8994pVqzIW/R3ZqaGqKh0UT2SZ6VcOVsGD/Zl0CBfIwFsPz8XfHzMSwrk\nhT17ogtiehISxcKdOxmijiOAq1eNo3F69/akQQPzqVdKpYwZM0TS3AuZlJRMFiy4ROvWG2nY8B/G\njj3E9evGtrdRI0+++qoVbm6O/PnnzSeOI9AL/i9ceIX33juQp+fpdDqio9NJTs7bHvNpsLOT8frr\nNgwbZmvkOALo1evpo+vv3dNx7Vrh2dz8IDmPihOZDOzM54E/wd6MxsXYRfD6ZLA1lBXEqTSMmAt9\nJxbsHPOKRgPvvQGj+8OBHXD1AmxbB/3bw6xpJt3V338lWDFNd/Uymi3/6ocNDyfr4AHUOTaqmpAQ\nHi1eTHSTJkS6ufGgdGmiGzcmbZPwSWJh4D1kCPZVq5ptM1/QMRdmtJdyk3D1Kje++47r33zDw/9K\nnpaVxMuL0k28LLLS1fWJhlg21v3fxP6v5ci9c1ROs7bGeti7OPyzvjCmmTc2/QQT/GH/Cgi6ABf2\nwdyhMK2TXkcuJ/uXQIKAdkZaMgTMffzvJH0hhKCToHkcg5gUDVe3w2+94FMX+KwsfOkDe2fpU5WL\nCqdq4DNIuF2OcNQR6IW5LZERDUEL4OaXcO9f0OatMoqERGHj5mb5gK1UKeM+lSq5cODAGzRqZKy3\n2LatN4cO9aN06eKp8HXiRDR16mzh+++vcvZsLP/9F8P06ReoV28rt28nGvU9eTKG3buFdX++/PIq\nOp0OjUbLf/895NChKBIT9Q70lJQszpyJZeTIM5Qps4WyZbfg5raZ0aPPEhNTdOkUcrmMzz+v8Uz3\nWyI9XcPq1eF88cUNli4NJiGhZOnBSLy8uLlZjq4pVcpYx0yplLNnTwveeMMLhcLw91+ligObNzej\nbVtxYf3CIiYmjWbN1jNu3BGOHr3P+fMxLFp0hfr117BhQ6BR3/R0Nd99d05wrBUrbnH3rt7eXb8e\nx4EDEYSFJQP6yMtbtxKYOfMSlStvxcNjIy4u6+nW7SDnzhVe8IE5pk61xcHBcj8hFHkIrtq/P4uv\nvkpjzpw0goIKZ10p1eItbpoNhv3zhdv9h5heUyhh+A8wYDrcOqXXyajhDyoBUdeiYMUS2CngvFkw\nC9p2Bv82AOiSk9EePSQ6nHrDWtJWryYrYPuTk3l5pUpotDIy7wSS+6w+6+xZ4vr2xWXpUuxHjnzG\nNyOOTqcjZvduIpYvx6pMGbQZGaSFhRnqMKpUaCxETskUCjy6dBFs16Sn89/gwURsyFF2e/p0yrRt\nS/ONG7EulbfSkBIShYX7oEHErhd2+LgPHmz2uvWgwVi9NRD1yZOQloqivh9y9+JZvAAQdgOWfoxZ\nFcMrh2HtLBjypeHa+W3i453bAi5OcHgJZDwWr3TyAOcy8OAqqHTGjpmECAiYBvcvwztrnvntWCTh\nKgQtgbR74FgVHoWC9vFJnsIWdGmWj5U8u4u33/4ebswAbY5Nl215aLYZXF781AKJkk2/ftWZMOEg\n6enmHZq1a5fGz8+0KEeDBh6cOfM2V67EcO9eChUrulC1qoUDwEJEo9EyYMBhkpJM1xv376cybNhx\njh/v+uTatm33RMcLDEzm22+vsmRJIOHhek0Ve3slFSs6Ehj4iLQ045XXo0dqliwJ4tChaE6efBVX\n18LV24yOTue330I4fPghdeo4ER6e9kT/yMpKTmam5SjO7t3Lirbv3x/NgAGnefjQYLsmTLjML7/U\nY/hw32eav4TEs1Klig1Nm9px6pR53UGlEgYONLVJbm7WrF/flIiIVK5dS8bVVUXjxq5G2RRFzcSJ\nR7l2Lc7kelaWlnfe2UuHDt64uuqd+MePRxIXJ+yk1mp1LFx4hSNHHnD2bAygdxRXq+ZKQoKWyMgs\n9Ln4hv47dtzn0KEoDhx4laZNSxfsm8tFerqOtWvT2bgxnZo1ITxcRmSkfs0pk5lffubG11dOzZrC\n3qPwcA29eqVw4YLBYTRlShojR1qzaJGdkePwWZEij4qbrp+Cm6/5tno9oK7IIt3OCfw6Qt22xes4\nAli52EL7EsO/BSKOstHpIG3PPrK2bTVK6dAGBcHdQNF0sMSpU9Gl5U1A7WnQaTScf+stTr32GvfW\nrCH+2DHSQkNBp8Nn7FhaX7yI97vviqesAT7Dh2OXM/oiF+fHjTN2HD0m+tAh/nvrrWd8FxISz06p\n7t0p1bOn2TZrX1+8P/1U8F6ZQoGqZUtUHTsVr+MIYOdS8W/unb8Zt2ssRNBoEvUVMzNyVD1JioLw\nK/pxhL6/L/wDwSIV0AqCO4tgV124swCiD0Lybb3jyL0NtDsITf+wvCpwrAHe/YTbw9fAtU+MHUcA\naeFwvDNkSoK1EsWLm5st335rXuPD2lrB/PkdRO+vU8edLl1eKVbHEcDOnfcID38k2H7iRDRXrxo+\nb2q1ZefK9OmXnziOQO8gunIlnrQ04QOxW7eSWbDgTh5n/XScPh1H9ep7mT79Onv3RnPlil4428fH\nlrVrm3DpUgdUKvHNkZ2dgokTqwi2Bwc/omfPk0aOI4DUVA0jRpzn0KGYAnkvEhLPwo8/ehsJNedk\nxgxPypUTduJ6e9vRubMHTZqUKlbHUXx8OuvWBQq2p6aqWbHCIAGQF9u1cOH1J44j0DuIbtyIIzIy\nEaGFTWqqhqlTL+R94k9BbKwWf/84hg5NYtu2TE6fziIyMhM7OzWzZ9sQFORM/fqWQ4qmT7cVjJzU\n6XR0727sONJfh6VLM/jyy4LdF0vOo+LGyQM+OQFtxxiq+ZSqAH2+hdEb85TaVCIIsVC+OcRgJGQu\nLsj8Ggp21Wj10UnmkMlAKfIr0cXHk75zp/hcnoGQRYu4v3at2bbQRYuQyeVUnjABpaNw5ZEK77xD\n/YULBdvTo6MJWS5clfTBnj0kXBYW7pSQKApkcjnVNmzAZ9YsrCvoq1UoHB0pO2YMdU+cwKqs+Alv\nieG+BdsV/wDScjiCaotsLGUAGcLtGsTF0M6tEp/Ls5BwFc6PMz+BmMOQcEnvFHIW0W5x8YPW+0Au\nEmFwZ7ZwW+ZDCFuW1xlLSBQaEyY0ZsOGXjRp4gnoT6l79KjEkSMDad/ex8LdJYPAwCSLfYKCDGup\nDh3EbbL4ybQOMeO1alWoYNuzolZref31U8THmzqwQkPTWLkyjOrVHRk16hXBMVxdVezc2YJatUwr\nz2WzaNFdUlMF5BR0MHdu4TrIJCTygr+/A8ePV6VvXxeUj/OH/PxsWbXKl88+8yzeyeWRiIgUi5pp\ngYEJT/7drFlZ7O3F9ILkIuPpAGHn9+HD0UREFF4F2fHjk7l40fTQMTVVx/ffp+DpKWfGDOG0Z4UC\n5s+35d13hYNEdu/O4vJl4d/nggUZpKcXXIG058Qz8YLj4glvL4L5CbAgBb4P1UckKUtg2WohPCwY\nLI9yRi9VE4Qr/WhU4noEliLvtAkJ4h2egZBFi4QbdTpCFy/GsWpVWuzejUO1akbNdj4+tDx4kEbL\nliEXKUke+99/aDPFc+yjD1sotS0hUQTIVSq8P/mERqGhNEtJoWlCApUWLcLK8/lYwABQysJc7Z3B\nxt7wuuNYsBVwDlsqiasDk5zbnKQVnu0iaDHoRB4e+CvIldBqD3h0Nt4nqlygzg/w6nmwLSc4BOpH\nkGjhFO/hkXxNW0KisHj99WqcOjWYtLSPSU//mK1bX3/iTHoe8PS0LBxdrpyhT6dOnjRoIJzyrtFY\n2lwIt2enjxUGW7dGEhEhfHIeEPCAsLBUfvyxLh9+WAlra8MiUaWSMWCAN9HR3WjdWjw15cgRcSH1\nw4fF2yUkior69e3YuLEiaWl+pKbW5/z5GkYV1ko6Hh52FvXHypUzrLucna0ZPbq2YF+l0lLkjrh9\nMpf6WxDExGhZv1443e7hQx3r16fTp48Vf/1lT+5A/MaNFYSEODN+vLim3pEj4hHxcXE6rlwpOP0j\nyXlUkpDLwdrecr+CJuIOXD4C0eFPP0a318Xb3xxm9FLRtx+q2T+DvfH7ldWsjbz2s1UtUdWv/0z3\nC6HT6UgRKTMOkHzjBg+2buXmlClk3L6NlUqFu78/jVeupEtICGXatrX4HLm15RRERR76SEgUJQp7\nexOB7EInJhpOHIEb4pXfROlgXpvJ0D7EOALU3Qcm7wC38sb9HNyg2ZtPPw8Ar8KxXQAk3hBvT74F\n8Zfg/IcQeQg0MrCrBtVmQI9oqDbZ8jNkSiwuK8SiliQkigEbGyUqVdGWeU5LU3PixAP+++8BWVlP\nt6jv1as89vbC0qW1a7vQuLHBYSKTyQgIaEvLlsY7FCsrOYMHC0ftGBB2HtWvb76aU0Fw86b5SPRs\ntFo4ezaeTz65xqpV4WRk6PDwsGbIkApERLzGmjVNUIqFrD/G2lq8j6V2CYmiRqmUYWtbtH+XOp2O\nCxfiOHo0+qnF5MuUscPfXzgSUqmUM3iwcRW4775rzqhRtU0iJLt180Vl6eBOBGdnFb6+hbP3DgpS\nY6l4+PXrWfzySyrffZdMTEwWDg5qunSRc+KEI6dPO+Ptbfm7KafDXLhPXmdtGUkw+2Um6BL8PBau\nHde/lsuhSVf48FeICIJ1P8H1U2BjB+37Q78PoZSpiCRpqXBkk16LzNwaqG0n6JRLG+W/IyhLOaJY\ntgJNbCIkJiKrXRdFm3Zov5iJ+sxpwWlrRQ7HrJo3x6pB4QiyymQyrNzcyHwofPqUFR/PmV6GMti6\nrCwSTp7kyqVL2L/yCqWaN7f4HPfWrbEqVYrMOFMhOdBHe5Tr0SP/b0BC4kUhMQGmfgBb1vHkm7lO\nffjqR/AuD0vnwb7ten21Fu3hvY+htoBjZvMf+kwzc1+szmXg7RnG18JvQXgQvDEbVDJIvA+u5aBh\nLwg+BecsiF4LrXGs7KHJMIHGAsDGgraU0gn2t9BHD2WTdAuufQkqJ6ieh0qeCmvweA2iAoT7lOub\nt/lKSLyA6HQ6vvrqHPPnXyYuTp/i6ulpx7RpDRgypBoLF15n5cpA4uIyqFXLlQ8+qEnv3r5mx1q/\nPpRHj8yfOCsUMpYsMV5vxMZmcPBgFO+9V5kpU2oSHJyCnZ2Snj29cXBQsnVrBImJYjsd4Q3KuHHC\nWkLPSunSlnc9kydf4e5dQ+pJVFQGy5eHER+fyaZN/nkSi+3TpxxHjwpXX+rbVyTqUkLiJWDz5nCm\nTr3A7dt6h66trYKhQysyZ44fmzaFsXjxLe7cScLT046hQyszalRVbGxMXQ23bsVz8aL5PQ7AzJlN\n8PIylCXLzNSwZ084zZp50r37K0REJJOVpaV9e29q1XKjc+ft7NkjFgAh7IAZPrwSdnaF4w5xd7fs\n1NqzJ4vz5w2RlSkpOnbtyuDmzSxOnCiFp6dl51GfPio+/1w4OrNKFTl16hTcAYnkRn9ZuR8Ek9oZ\nHEegP775bzuM9IPx7eDoZoiNhHtBsGIWjGgED8zktQeshrA7YA/YYPirUgC2gIuNXqwI4Mp5aFsT\nXm8DHw9DNqIvyl8+R1mnFoo27QCwGTkKmbOz2WnrdMLOI0WVKriuKdxqRd5DzFS/y0HytWtmr2tS\nU7k6fnyenqG0taXm9OmC7ZXefx/b5yktSEKiIFGr4Y1OsGEVRkc6Vy7Cm52gU334exHcC4MH92Dj\nCujRFPZuNx3r3l3Y8TekA6mAGkNqWTqQqDakqCXHwYzuMLI6zB0KswbAnBGQkgXN+uuLFlRtDRWb\nCc9dhvm0NSt7GP4vOBRixQ9fcduF0s7YcZSTy9MgPY9isdVngFxgs+fSQHIeSbzUTJ58kpkzzzxx\nHAFERqYybtwxqldfz7RpZ7l+PYEHD9LYv/8+ffrs45NPTA/TdDodn39+UfA5Go3uyWm8Vqtj6tQL\neHtvYuDA4wwZcpI+fY5w5kwsAwf6UqaMDXZ2SsaOrWph9ua3DF98UZtu3QrPsdKvnxe2tsIbnzJl\nrI0cRznZtu0BW7bcz9Nzhg/3pVIl8xEIzs4qJk+29PuRkHhxCQi4x+uvH33iOAJIS9Pw6693qFZt\nM4MGHeXYsWiiotK5eDGOjz46TefOe81WtZw9+yKPHmnQbxRzOnZlgNwoDW3t2kDKl19Bjx47GTbs\nID167OTPP2/TtasvtWq5ATB5cn3E9b/lmIuc7NzZk2+/LbyI70qVlDRvLixTolDA+fPmDwBCQrR8\n/bVwQYSc1K2rpH9/4ajuL7+0LVCBdMl59LKybg4km6l6owMePjRffSg6An6eYHr94Fb9f2XoT+8d\nAWfAAbACjgToHVOR92BAR7iTK30iIhSG9YDrehFoeblyOGzdgSyXg0Sne1x8Tac3N3JA7uiITe/e\nuK5YgceVKygfC/cWFpU/+QT7KuZP2Jz8/NCJxCcmnjtH8vXreXpOtQkT8Pv5Z2xyiA6rXFyoNWMG\nfvPm5W/SEhIvEjs2w4Uz5tu0WfAoxfR6ZiZMHK7/b06ObTPYuizgEZAEJKOPRkqMgyuPK6DN7AGn\nc0XUpCbDH1MgIEc1ybGbzTuQ9GsivYMqE0AJFVtDj+9hRghU7yTypgsAz9egvECVNHsfSH8gfK82\nE8L+ydtzSjWB5jvBKUf6sUwF3gOgxV6QP0dafhISBUhUVCo//3xFoFVOZKT5k+Pvv79sVEUI4Nq1\nBO7eFU/n2ro1DICZMy/zww/XSU83hIZrNDpWrgxh6NCTT659+WVdRo6sLLAJM3be1KzpxMSJ1bh+\n/TVmzKglOo9nxdXVijlzzOud2Noq0Fmoc718eVienuPsrOLQoVZ061bWKFPZ378UBw60pHJlB+Gb\nJSRecD777BJas6f3WiIizDs5jhyJ4uefTVPmt24NefwvGXrbonz8o9/dZbfv3x/BwIH7iI42to1n\nzkTTocM2UlL0e65XX/Vm6dI2AhFEVo+fowY0eHhYM3ToK+zZ056dO9thY1O4Kcvz5zvi6GjecVOv\nnnjE04oV6Rbtm6GvPePHWxupwfj6ylm50p4BAwpW6kRKW3tZOfav+euWUu+Pb4WEh+BSGkJuQPB1\niIsWv0ej0Xt9lv8KCQJhiunp+lSTn5YBoGreHIflK3nU2VDZSCbTRx1pHs9RWd4b5zvByJRF92ds\n7e5Oi+PHCZw1i/C//yYrLg77KlXwGTMGdUICSRfExWIzYmIQrsNmTNVx46g8ejRxZ8+iU6txbdgQ\npZ1lgUwJiRea7QK2K9s5I0RsDOzdptdnexgN50/ArTxULVRnwcUDcP2EcJ+1s+C1kfrUXycP+Hgf\nfOgBmY8XVDoMa6Tsyf7vIngV7qbLCJkM/NdA6eZ6cezk22BVSh+R5NEejvYUvz8jH2Wq3dtBh0uQ\neAWy4sChGtg8J9X3JCQKie3bQ8nKEhKtFz/L/fPP2zRq5E5GhoaDB+9z9aqZw79cZGVpSUnJYv78\nm4J9NmwI49atJKpVc0KhkLN0aVNu3Ejh2LHsdZ2M3Olqc+bUY+LE6iZjFSbvv1+JChXsmD37UFCf\nHAAAIABJREFUDkePPkSlktOrlyfTplWjadNDovfGxIhUwMyFt7cd27c3Jzw8laCgR3h62lCtWl5X\nbRISLybBwSlcuCBkc8SqgMCff95hypQ6AJw4EU1kZCoZGeL3ZNvJWbPOCzisIDQ0mZUrbzN6tH4d\nNWJETe7dS+Pzz89hWHRl2y79eK+95smOHZ1Fn13QNGqk4uTJUnz77SP+/TedjAxo1kzFpEl2/P67\ncKoZQHKyjowMsBGvIwWAlZWM+fPt+fJLWy5d0mBrK6NhQ4VFYfKnQXIevaxkCXyZWnJwajRw6zws\nnwXnD+mvWfpebtQalEo4tEu838Gdxo/atYPc+rsKGSiyrz2IQBcagqxSZQsTKFis3d2pNW8etebN\nQ6fRIFPod4T3160TvU+mUOAgELUkhFylorS//1PPVULihSNTwODk5fsxLBimj4aNf+mjkJSAWIES\nW3uo1RTWfis+bnQohF0H38en47eOQEaukzgd+oOv7Be3jxWt8whAroBqH+l/dFqQPTam6VF6sWud\nSMUOpxr5f55znaebp4TEC4h4aWpxAxYR8YhFi64zY8Y5YmOzbWDulA9j2rf35PjxGJKThT/XOh3s\n3n2fatX0JezT0zUcP/4QMWfW6dPCWiWFSffunnTv7olWqzPaENWo4cilS4mC99WokX/nT/nydpQv\nLx3WSUiAJdslTnh4KseORTFy5Alu3sz+nIpXB2vf3ousLA0HDtwT7bdzZ9gT5xHA3r33MbVdOrI3\nt6dPWwh2KCRq1VKyapUz4Gxkv44fz2LnTmHRcV9fOTY2+XP+ODvLad26cBPLpLS1l5U6rcxft/Q3\nqrKC70cZHEcAKgv3vTslf3PLRi1uXADRNLGCRqfTkR4WRsZ9Q/58tuMIoGzv3liLaBF59OqFTTlJ\ncFFC4ploJmC78hLZe2gbrFliSF97kkImQO9R4GBef00UrWXblac+BUlaNCSHgPbxIlCW4+vfxgO8\nRbSILLVLSEhYpGVLMa1CcQOWmqpm7NgTORxHIHbi7+dXio4d87/e0Gp1ZlULciIcPVU4JCdnERz8\niNRUvc3MfZL+/vsVBe+VyWD0aOF2CQkJy1Su7Iinp3i5eCHKlbOlS5e9ORxHIBa74uio4v33zaep\nWkKtzltEU1GRmakjODiLuDiD8y2n/Ro1yhaFSNbcmDEl04EtOY9eVt6YiNnEdkupn5XqQWSI8TU5\nerHs3H9Ndg4wczG06aZ/3baL+NjtXoMTh+HHb+DXuShq1RTtLvPyRl6laAQM7/3+OyerVeOYjw9H\nvbw41agRMdu2GfWRW1nRaONGVC6mJWsda9Wi7q+/FslcJSReaN4aCm5mhKWzha6FKF0Gzh4xvZ6I\nafSkXA49R8D73+tfN7Jgu8r4gFIF/86Gdd+ARg4qC3HG1duJtxcUD45BQFtY7QHrXoG1PnD5B33k\nUU4aLQSXuqb3q5yhxQZ9JTUJCYmnpm5dNzp1Ki/QKr6puXHDXMpIttEz9vb4+7sTEPAqMpmMFi3c\ncXQU3qjJZNCsWWmWLAnkq6+uERAQSaNGrqJzad/eTNXdQuDevTQGDTpD6dIBVKy4mzJlAhg16jzx\n8cYe/5EjfRk82FTvUiaDuXPrWHw/EhIS4iiVcj76qJpAq7groVQpazNVIRXoIw+M8fKyJyCgKz4+\njqhUCtq39xIdu1MnbzZsCOarry6wePEN/P3LiPZv375oDvAzM3VMn/4QL69gKlYMwd39Ll273uPS\nJePFZtWqShYvdjTrQOrTx5qPPy6ZzqNCTVuTyWStgMlAQ8AT6K3T6bYW5jOfS4IPwNlFEHsL7MtA\n3XegzkCQF+L/nvpt4ePfYOF4SM9RpcLZDTqNgDVzDOJC2XhXATuBU3gFeoFsrRxGfw+l3KFjX7DP\nES78zvvCukdWNnD+LKz5+8klpVyOracraZHm82ytPppkFPlTWAR/8w1BuaqfJZ87x6Vevai9ejVl\nBwx4cr2Uvz/tbt4k9PffiT18GIW1NWX79sVrwAAUtk/ntZcoeiTblTcSbt/myi+/EHnkCApra3x7\n96bWqFHYuLkV3kOdXWDtLninD9zLUZpVpYJhoyFgrV7TKCd29tCzH6xeaDqeDr0DSQkMHQOVa0LL\nHuDpY+hTrx3UbC6se+ThCR/UMC40UKosaB+YX1fV7wFe4s7xAiHyMOzqpBe8zib1HpyZCklB0DKH\n0Ld1aeh4CkL/gYh/QZMO7q2g0kiwlfSKnick+2WZuLg0li49x6ZNN0lPV9OqVQU++KAJ1asXYsVD\nYM2aV+nbdzeHDxtXAOvevTwxMVmcOmWqLfbhh7WYP998Jddsp1PnzuXp1Mmb5s3dadbMsIFycFDx\n0UfV+eqrq2bvrl/fjbZtD5GWZljvlSolXLXH09OGIUN8BdsLipiYDFq2PExIiGF9+uiRhqVLQzh1\nKp7jx9tgb69fI8tkMpYvb8SQIRVYtiyUBw/SqVrVgVGjXqFePdPDPImSi2S7LKNW6/jnHw3LlmmI\nitJRtaqM0aOVdOxYuPuhyZP1mkILFtw20iGqXt2FZs1cWbYs0OSerl29OXVKKFVML5BdubI9o0ZV\npXJlZ7p390GpNCyapk1rwMGD983qHpUta88331w2KjRgba3AxkZOerqpM16hkDFpUtGk0vfrF8nW\nrQbpAq0Wdu5M5fjxCI4d86ZOHcNh3IgRdrRsacXixWlcvaqmdGkZQ4bY0qWLVaHoFRUEsryqeD/V\n4DJZF6A5cB7YCPQRMwIymawBcO7cuXM0aNCg0OZVojg0A45+ZXrdsxF0+AF8WhWuEyklAQ6thdj7\nUK4ytH4DrG3h9gXY8DNcPwU29tC+P/QYCZ+/DSd2CI8nk8GRTL3GkTmuXoBxg+B2jqpj3j76ajzB\npoYHILNUOdJDciy0rKyw+mgSNl988xRvOH9kxsZyzNsbbXq62Xbr8uVpGRxcJE6s/HD+/HkaNmwI\n0FCn050v7vk8b0i2yzJhu3axq08fNLk+G7YeHrSYO5cK3bphbSYKr8BQq2HnFrh+BVxLQe83oYwH\nREXCsoWwbzto1NCyAwwbBwe2wrcTxcf8ew+07Gi+LTkO5ryjr7iW/b1p5wRV68MNMxFNAK7uII81\njvKp1w1GrQZbp/y/5/yytRnEnBJuf/06uDyFllEhI9mvZ0OyX+KEhyfSuvUyQkISjK5bWSmYPr01\nQ4bUw8fnKdJV88HJkw/Yty8ChUJG9+6+1K3rRnq6mmXL7rByZSCxsenUrl2KsWNr4OJijZ/fJtHx\npk6ty3ffNTHbptXqmDbtIvPn33pScU2hkNG6tQcHDz40e4+trQLQkZZmsF1VqzqycWNzatcufIfM\n//53jW+/vSXYvmBBPcaOrVTo88gvku16NiTbJU5Wlo4+fTIJCDB1jrz5ppxPPlFSv37h7kdCQlLY\nsCGMlBQ1TZu60aVLOWQyGQEB4SxZcps7d5IoW9aWYcMqM3BgRTw81hIXJyyO27hxaU6f7i7Yvm5d\nIOPHHyMqyuAk8vMrTVBQKklJ5qVL3NysjVJ8XVys+PXXFgwYUPg248CBVDp0ENZq6tPHnn//LXkS\nJvmxXYXqPDJ6kEymxYIH+WUzAkSchL+ai/dxLAdtvgC/EUUzJ0usmQc/i2zAGraDBQcsj3P6GIQE\nQVkv/SbwrdeE+7q4ol68Ac3li8gcHFD26I28jHhoYkFx7/ffuTFypGifhocP49q6dZHMJ69IC5iC\nQ7JdpqjT0lju7U1GnHnhVBlgY2dHtZEjaTp7NnJVCSjPfuMSdK8v3G7vACfug4MFcdWI23DzFNjY\nQQ1/eL8qpJsvUwvA1HWQGqXXOKr5Kng/XS5/vkkOhnUWtD78ZkCDL4pmPvlAsl8Fh2S/TOnefTUB\nAXdEeijo2rUyS5d2xcurCJy8FsjK0lKhwhoePBCuzLN372u8+qp4ikdcXAZ790aSlaWjTZsyDB58\nisOHhasofvppDapWdSQuLpPatZ3p2NEDmTm5g0KgYsVdBAenCra3aOHGsWNtimQu+UGyXQWHZLtM\n+fFHNR9/LKb1qqZOHRm//GJDmzYloyZW//6HWL8+RLD900/r8O23DUXHyMrSsGdPBA8fplG7thsB\nAeHMnCn88WrVqiyTJtXhzp1EPD3t6N3bFzu7ovl9jBwZxe+/Jwm2KxSQmFgJe/uSpRyUH9tVMv6y\nXiSiLsLp2RCyW//6lS7QZDKUqWfa9/xSy+Ml34ftI0GmgPrDCnauT0O3YbBqNsQ+MG2TyWDQ1LyN\n06Sl/gdg1nTxvgnxKJ3sUX74cf7mWgCok5Mt90kSNhISEs8Lj6KiODNvHjfWrCEjMZGyDRvScPx4\nqvTubdL37saNgo4j0GeCZaWmcm3+fNIfPqTdypWFOPM8UqMetO0KhwQiJweNtew4AvCuqv8BuHxQ\n3HEEcO8O9JuWv7kWBFmWbReZku2SeP7JytKwZMk5fvvtPMHB8VSo4My77/rx/vuNsbY2XuZGRCSx\nc6f5KGcDOnbsCKJdu1WcP/8uDg7CaVxFgUolZ9KkOkyadNpse+PG7nToYPkku1Qpa9580xfQFwA5\ndsx81FE2p07F8u23ZnTQigCxCnGAYMSBhMTzRkAA/PQTnDkDDg7w5pswcSKYq6+zdKmlQhtyrlzR\n0KVLKseP29OgQfFnRUyeXJvNm8PMilU7O6sYM6a6xTFUKgXduhmkBD755Ixo/+PHozh8uFuRObtz\nkpwsrl+n0UBqqrbEOY/yw/M785JI8G5Y2QxurIa0WP3P9VWwoikE7zHtH38372Mf+dxU4LQ4cHKF\n+XvBN1eqg6ML/O8vaNY5/2Na5WFhZl08Yq1ODcW94TKFAsf6ItEMEhLPAckREaxo2pTTP/xAcng4\nmUlJhB08yKY+fTj2+ecm/ZPuWrZd2TGtQatWkXDzZsFO+Gn5aQ282tP4mlIJgz+AiU+RBqvKg+1S\nFZPQtFNlsLKQelO6UdHMRUKikFCrtfTuvZZx43Zy+XIUycmZXLsWw8cf76Fr19VkZhprN4aEJJjV\nzzBG337nThzLl18upJnnj4kT6/K//9XH2tp4M9iunSfbt3fK9yZJJpOhUolvAXI/qyhp2FA8NU4S\nwZZ4Efj+e+jeHfbtg8REuHcP5s2Dxo0hONi0/927ecsWSk+Hb78VThUrSho3Ls26dW1wdzcuIuLr\n68CuXR0pX94+32NaWYnbJpVKXiyOI4CGDcWLpfj6KnFzK36n3rNQIiOPJkyYgLOz8aL3rbfe4q23\n3iqmGeUBrQZ2jQSNmQ+rJgN2j4RRwcblkR3FQ4yNSAyDyPNQrgQs9ivVhtXX4PwhCL4OLqX1ArM2\nT6kK/1of+GGmcLtPRahlJnKrCHBt3RpHPz+SL1ww217m9dex8fYu4lkZs2bNGtasWWN0LTExUaC3\nRGHyXNou4PCnn5IUGmq27cQXX1BjwADcqhtOh+y9LNuunF/boVu24FLd8ulSoePoBEu2QOANOHVI\nXyGtXTcoI1ZCW4SqTaFUOYi7b75dJoOmppFbRYLSDqqOgKtzzbfblYNX3ijaOZlBsl8lh+fRfq1c\neZkdO8ynoB04EMzvv5/n/fcbP7lWrlweogtzWK/Nm2/z/vslYN0FfP11Iz76qDbbtoWRlqbG378M\nfn5PL/Ddu7cX//wTJtjep08+1qgFzIcfVmb3bvNCu3I5fPCBhZTcIkCyXSWH59F2hYTANIGg5Pv3\nYfJk2LDB+LqXl4zg4Lw5kLZuVaPT6YrNiZKT3r196NrVm+3bI7h/P5XKlR3p1MnrqQWhe/f2YceO\ncNH24mL4cCe++ipOMAJp3DiXYhfCflbbJWkeFRTBu2G9hXLO/feAbw4x1rv7YJWAOKs5hh6H8hY0\nkp5X3hsAW9aab1u4At4YVLTzyUFaSAgXOnUi9Y7xAtXZ35/6O3agKkxR4KdEyrsvOF5025X56BG/\nuLmhyRA+pWo6dSptvvvOcE9SEsu9vMhKSTHbX4bxyUTDL7/E77PPCmjGJYw9v8HC98y3dRgG4/8s\n2vnkRJMBB/pDWK4/XVsP6LQTSvsVz7wsINmvguNFt19t2izjyBHzjm+ARo3KceaMsW5hu3Z/c+hQ\niMioCrIdSG3aVODQocHPPtESyJUrCfj77zdTRhtq1HDi7NmORaYTYo7vvrvFtGnXjIpYKpUyli71\nY9gw3+KaliiS7So4XnTb9cUXYCaw+wlKJURFQalShmtff53FZ5+Jpa6pMcR9g1rtiEJR/M6jgiY1\nVU2jRpu5cSPBpM3OTsnJkz2oW7cQq/5a4MCBVPr0iSQpydiBNHy4E7/9VqbYnUfmyI/tktLWCoqU\nyDz0yXU6XfFV8BMXY36CjQuUfYHTo76ZD23bgIMKsjNBvCvAL38Xq+MIwNbXl2bXrlF7zRrKjRiB\n95gx1N+5k0bHj5dIx5GERH5Ij4sTdRwBpNw3tl1WTk60XrxYsMpg7quebds+wwxLOO2HQtv3QOsA\nqYAGsHWE3pNgbB507QoThTV03ALdjkLNcVD1XWj5G/S/W2IdRxIS+SEyUlzby1z7woVdKV1aKFJa\nTs7Io7Zti+8Eu7CpU8eFOXPqUbasIc1CLpfRq5cXBw60LVbHEcAnn1QjMLAz06dXY9gwH77+uiah\noV1KrONIQiI/RFrYNqrVEJNLz37CBCXNmgk5HrTkdBy1aqV4IR1HoHcQLVvWmpo1SyGTGWx2gwZu\n7N37WrE6jgDat7cjLMyX+fPdGT7ciY8/duHcufL88YdHiXQc5ZdC/WaQyWT2QGUM38QVZTJZPSBO\np9MJx5s9j7hWttzHxUyf7kvBpw2c+xXundJX5DFHo7Ggesq0sJLOlpXw2XuQnqbfddoCLjYwcxb0\nHFjcswNArlJRdsAAyg4YUNxTkSgCXibbZefujpWTE5kiwu8ulU1tV9W338apYkUuzZtH2I4dqFNT\nkZN76wVlmjWjbKtWBT7vEkHgZZjaA6JypH6ky6Dt2zD0B33aWkmgbEv9j8RLwctkvypXLsWdO8Li\n/ZUqlTK5VrOmO+fOvce8eSdZvfoKMTGp6H9VxtbL2dma9957MZ2siYmZ9O17nAMHjFPDGjd25a+/\nmuDqWrwi4dlUrGjPV1/VKu5pSBQRL5ftEm+3tTUVzba3l7F/vzWLFqn54w8Nt25p0WcQGTuOACZP\nLhmf4cJg0qQz/Pjj9cf6dfo4mDJlbPj999b4+RWv4ygbZ2cF48e/mAEGhR151Ai4AJxD/1c9FzgP\nlLzawM+Kd0twqyncXro2eLcw31bnbRh6DD4MB29/4zaZHBq8B21K6K8sOQ5Wfw3v14d3KsLo+jC+\nJXzeHw6uA7WFihiXTsMnQ/WOo5xkpMMn78A1KepXolh4aWyX0saG2u+8I9guVyqpO3y42bay/v50\nXr+ed5OSqD1yJEq53Nhx1Lw5r27eXMAzLhh0ajXaVctQv9aarPqVUPvXRtulCbzTA5bMg4R48QHS\nU2FiF2PHEYBOB5sXw/r5hTZ3CQkLvDT26733xItajBplvr1CBWd++qkL0dGTWbq0J/b2NuR0HJUr\n58COHQPyqJFU9Bw6FMkbbxykcuWNVKv2L40bb6NTp91MnnyGwEDLVRSHDz9j4jgCOHUqjiFDThXG\nlCUk8sJLY7veeUe8FtDAgeBoxvzY2cmYNEnFjRs2nDplTfnyxo4jW1v45RcbevRQFfykC4DAwBTG\njbtI9ep7qFRpFw0b7qNdu4MMG3aKw4fN65zlZOHCG8yde82k8EF0dDpduuwlOVmqxFjYFGrkkU6n\nO8zLlBrXfRWs6whpucqf2paG7nkoVe1QFoadgPDjEHYUlDZQrTe4+BbKdE24tg+OLYOkB+BRBdqO\nggoiqXIxETC5NTzIVRJAB2QBh9ZDLX/4YRfYO5kfY/l8fd1Cc6jVsPxn+H5Z/t/LM5Bx+TLa5GSs\natVCIaWlvZS8bLar1ddfc/+//3hwxrj8qUyhoPNvv+FoQRRerlDQaulS6n/6KaFbtqBJT6dsmzZ4\n+PuL3ldQZNy8SfzixWRcvYrCzQ3nQYNw6NYNmdz8/0KdWo3m7T7odm83XEOfcaZVgnLfdlj0PazZ\nCzUFSlXv+wdiReLO1/0Eb4zXq7sWFfGhkBgOLhX0PxIvJS+T/erduzpjxjTi11/PmrQNHVqft96q\nbXGMkSP9ePPNmqxff4OoqEdUr+5Gz55VUSoL/1cYG5vOH3/cYP/+eyiVMnr08GXw4KrY2wtv/GbP\nvsqUKabvF2Dv3kh++uk6f/zRgiFDzIc23L2bwubN9wTHDwi4z61bSVSrJrBuKwTi47O4fv0RTk5K\n6tRxKLLnSpQsXibb5e4Oy5bB4MH67U5O6tWDH36wPEbjxgru3nUgIEDN9etaSpeW8cYbKlxdCz/q\nOTNTy/r1MaxfH82jR1qaNXNi1ChPvL2Fq40dPfqQrl1PkJKSO8tGB0SzbFkII0ZUZOnSRmaFvnU6\nHT/+eF1w/OjodFauDGLMmKIr0JKVpeXChWR0OvDzc8TK6sX/8y2R1daeWzzqw7DLcHExBO/SX3vl\nNag/Wu8YyivlW+h/igqdDv4crnccZXN9PxxcDG/OgS4Tzd+35CNTxxHoD+9UQAZw7ST8OgkmCWh/\nnD8uPjdL7XlEl5EBcjkylfCC7NGOHTycPJnM63rDJLO1xXHIENznzUNu94KmDEpIANZOTrx1+DDX\nV67kxpo1ZCQm4tGgAX5jx+JRP+9aa46vvELtjz4qxJmakvDXX0SOHGnkhE5etw6HXr3w3rABmdL0\na077929GjqOc6NSgVYD8YTSMfB2O3jLvALpiwTY9CIXoCCj7jE4cjRo0WWBlK9wnNhC2vg9B+/T2\nXCaDSh2h5yJwq/Rsz5eQKOEsWtSNnj2rsXTpOUJCEihf3pkRI/zo0aNansdwcrLm3XeLVlfy4sWH\ndOq0jZiY9CfXduwIY+7cSxw82BNvb1Mnys2bCUydat5xlI1arePdd4/TvHkZKlc2dQD991+syal9\nTnQ6OHHi4TM7j3Q6HWlpWuzshMtSp6ZqmDDhNitWRJKWpheXrVXLntmzq/Daa09fSU5C4nlgwACo\nXRsWLoTTp/WRRm++qY9Kyuu2Q6mU0auXil69CneuOUlKUtOx4yVOnzZoyu3bF8+8eeFs2lSbTp1M\n04U1Gh2DBp0x4zgCQ5kVNb//fpdmzdx4913TiopRUWkEBYnr3J04EV0gzqPUVDU2NgpRjaKffgrj\nu+9CiIrKBMDdXcXkyT5Mnuz7zM8vybz47rGixsETmn8GDcaAlTXcWgG7BsPt9VBEle3yzdE/jR1H\nOVk7Ce6eNr2eEAMntwiPKcOgmrt3JaQIlAC0EvZQAxAfC/39YVQP2LleOEpJAM32LWR0aE66mw3p\nbjZkvN4NzamTJv0e7d3L/Z49nziOAHRpaSQtWUJknz75eqaExPOIytaWeiNH0uyzz7D39SXowAG2\njxjBqXnzyBSoqlbcZAYGmjiOsknZsoXYOXPM3qf9+zfRcZ9Iz4UEwuE95jtZsl0An70BH7SFtT8K\n20AhIq7Cgv4wwk7/M70+HFtu2i/5AfzWGgL3Gr5jdDoI3KO/nhKVv+dKSDyHdOlSme+/f5UWLcpz\n8+ZDpkzZx8SJuwkNNa3GUxLQanW88cZuI8dRNoGBiQwbdtDsfX/8cSdPS0m1WseSJbfMttnYCDtz\n9MiZOzeI5s0PMWnSFe7efWT5gTmIi8vk449v4Oa2H3v7PZQrd4CZM++QlmZqp3v1usTSpfeeOI4A\nrl17RM+el9i/X1jLSkLiRaF2bZg1C/r1g8REmDsXhg+HEyeKe2bCTJwYZOQ4yiY1VUv//tdITjZ1\nEO3ZE0VYWJrJdQMyslOHFy68Y7aHjY3CgpSkjKNHY2nWbBeDBh3n2DHLaXA50Wp1/PzzbapUCcDe\nfiMODhsZPvw0ISGmNnDWrGAmTLj9xHEEEBOTxZQpgcycGZSv5z5vSM6jgkarhq19YPcwuHcUEu9C\n2D7Y3h/2jCju2ZnnwCLx9oO/ml57GKE/ERcj+wOekQaRd8336fKG+BhJ8XDxPzi4HT7sD+/3hqy8\n5bOqf/uVzAG90WY7i7RatLt3kPlaWzT7jTeEsdOnCzqmUvfsIfXQoTw9U0Lieebk7Nmsat+eW//+\nS8Lduzw4d459Eyfyd8uWpCeUvE1Y/NKlog7l+F/N2C6AsBDRcXU5q6veumq+UzsLtgvgxhm4eBh+\n+RiG+cGDMMv3AASfgy+bw+n1+qgjgLBLsPQd2PCZcd+TP0OyQPpc8n34b2Henikh8Rxz5Egofn5L\nWLDgDLdvx3Lz5kPmzfuP+vWXcPbsfcsDFDF79oQTFCSsTbRvXwR37pja3JCQvDvyr141b7M7dfLA\nyUkoClsJKLh2LZmTJ+OYO/cOtWvvY9euB3l6ZmJiFm3anOLHH0OIj9fbrsjIDL78MpCuXc+SmWkw\nrvv3x7Fvn3kHkVqtY8aMF3sDJiEBEB0NzZrBp5/CxYsQFARr10LLlrB4cXHPzpSkJDWrVgkfSiUm\nali92tRpExqamudnXLtm3ja6uFjTvr2nwF0KQEloaCqnTsWyalUIrVrtZebMy3l+7vDhp/nwwwsE\nBurtbFqahr/+Csbffx/BwQbbm5ysZtasEMFxZs8OfWL/XkQk51FBc+V3uGs+HYJrf0KgSLROYWHJ\nyRN5Q7z9vpn20l4gt3B6lfN0zElA/X7wOPDwEh8nJwe3w7IfLXbTJSaSNX2y+cbMTLImjXtcoQDU\n9++TcdpMdFUOUv79N+9zlJB4Dom9dYsDU6eabYu+dInDM2YU8YxAp9E8+ZyaI/OGuO1Sh4WhfWTm\n1NxbPJVMlvOb0VUgdaJBO2jSWXQcIyKD4Yf38tZ39ceQLhCave1beBhqeH19k/hY1yTbJfFio9Xq\nGDJkE48emS7WExLSGTq06EX7dTodGo1WsP3mTQuC/OhT1HJToULe9YBKlzavxuvgoOJ0qdSjAAAg\nAElEQVR//6thpkWBca1MPWlpGgYMOMOjRxbWksD8+SFcvWrewXXoUByrVxsceZs2iUcFnDiRSFRU\nhsVnSkg8z0yZArfMBAnqdDBuHNwTlicrNNRq4XVXSEi6UaSgOW7cMF13lS8vknqfCzc34UpxX37p\nZ0ZXKLtaprn+VzhyxHIE9vHjMfz9d4jZtgcP0pkxw3CQuG9fHMnJwgeXaWladu6MtfjM5xXJeVTQ\nXBFPh+Dq70UzD60Gjv0Ec6rC/1TwuStsHQ/JURByClYMhTlNYXF3sLMXH8vR3fSaHKgjUn47W30W\noF4b8BDYrJX2gNVHoW23vAvLrrHgin8Yg+aX2chShUOtdXduozurdxjp0k3Dxk36Z0gLGIkXm4t/\n/CGaWntl+XI0eYz6e1aiAgI43qYN21UqAqysONO3LwnnzpERFkbYJ59wzd+f623akBodjVgGh9zB\nAZmNcXqZ9tEjtO27iD5fni2TZGcPXfsKd5y1CV7/AGwt2NBszuyB+2Z04rLJTIOz2+DGkdxVdw3o\ntHBileG12oL9stQuIfGcs2dPEKGhwmmh167FcPJk0VT5vn49lrff3oGt7c8olT/RtOlq1q27RUpK\nFgsWXKFduy34+//Lnj0RFscqXTqX7dLqaN26TJ7nMniwsN7ZlCk1WLiwAd7eOTd0wmuwxMQs/vlH\neM46nY7Ll5P57Tfx97VihcF5lJ4uvgHNax8JieeV5GR9lJEQarVeVLsoSEjQMGXKQ9zd76JSBeLr\nG8ysWXGkp2vZvDmB3r2DaNr0Jl98EYVBl8Q87u6mzp/q1Z3x8BApL4eO7IXP4MG+gr2aNy/D7t0d\nadjQEJQgk4nPZ/Fi82lw2QQHpzBnzk2EF16wfn046en6jW3ebFf+ZFaeJyTB7IImKUS8PdFCe0Gg\n08E/A+HyOsO19AQ48QucXgmJZk68bAChPUaLIYZ/x4bDyg/hwlbI0ujXGrk/Qzog+4DKzhHenys+\n3/KvwNLt8OAeRN2D7yfB2aPC/SOC9akqilzG4mEMfDIOAv5FmZWF0ho0Wn2Wm7k9sS5WXxVP6eOD\nsnx51OHCi0vbli3F34OExHNOYkiIaHtGYiLpCQnYu5txJhcgIYsXc2XMmCevdWo1DzZtIi4gAFeZ\nzMSRKwPsMb/tcXr7bWSP7YQ2I4PYadNI+v13tElJeNiBrZnMDZkSnqxDps8GRxHRWGtbmPALvPcN\nhN2CfWv0+kZC6HQQcQfKvWJ8XauBdTNh9yJ4FG94Y/oMElOSc1T09GkF8SHCz/QVcfJLSLwA5EXX\nKDQ0EX//8oU6j/Pno2jbdj3JyQYNjNOnH/DmmwG4ujoTH58pcrcxVas606yZx5PXf/xxi2++uUhw\ncDLGopLm6dfPl44dy4n2ef/9KowaVYkrVxK5ciWJIUPOifa/fdt8RNE//zzgs8+CCAzM1jNRol8Y\nmm6wHj40/A5atXLhjz+EUwp9fW0oXz4P2nISEs8pDx6ApfNrC0uzAiExUUPr1hFcuWL4fIaGqpk2\n7SE//RRJdLRh3aVP1LBHXxXJ9GBdLodBgwy268SJBCZNusPJk4kI2y1DxEGVKg5MniwueN22rSdn\nz/bg9u1EEhOzaN9+v4AQt57bt81Hcl+8GMf48Wc5ejQmx9XsKCbjKMyMDC0pKXoR7ebNnZHLQSvg\nQ5LJoGXLF7datxR5VNA4Wqis41QE5ZPv7DF2HGWjwbzjCPTf9eZS4Ot1g4aPT96TH8I3reDcJv1m\nRwGUAuwAKyU4uIKtC2QCMhW0exMWnIBqDfM277JeUK8JlPMR7+da2tRxlJoKfdrD5rVGmkgKOVhb\nYSqwJpMhq15T/0+FApcJEwQfp6xQAYf+/fP2HiQknlOcKojbJitHR2ycnQt1DlmJiVyfNMlsm2Nm\nptkIQB1gToJR5eND6Rypdg/69ydh3jy0Sfpc+qhUeJgKGRoZOmcXZG6lUNjIUFiBrEkL+GsrvDPG\nzMhmsHeCGo2hYh3Lfd3M5OsvHQ3/fmNwHGW/sSwMEZw58c5Rfrz5hzlCpXKhUIH/h5bnJCHxHFO+\nvGW7VKFC4dougAkTDhk5jgxY5ctxZG2tYMGCVk9KVf/881VGjDj62HEEho2WFkdHJW5u1k/SOCpW\ndGTOnEasWdPabKnr3CgUcurXd6V1a8uHAp6epo6cNWse8NZbV3M4jsDg3DLdKNaubUi7e/NND7y9\nhSMRJkyoIFrpSELiecfDA6zFgnEAC0uzAmH+/AQjx5GBLCPHkTHWmPuMf/aZDz4+eltx5kwir756\n/rHjCPSbTXtAhY2NAldXFQ4OckCNs7OS8eOrcPx4B8GU29xUrepM48alKVtWPCXO09O0/fbtJNq1\n25/LcQQG+2ocdVCunC2lSukjqnx8bOnXzwMhevQoTdWqeYxIfw6RnEd5QSMQumKOOgKi2E/SMbMg\nZFfhVl47b6YiDxiigYRwdgGHx/oe7hWh3/fwwSaDttH+RcZaG6B/Tw6AixoGjodN8bA7HXanwcx/\noGJt8k2fd8Tb+w41vbZ+JdwwL2wrk4Eyl32Td+6K3Ndw+u/y0Ud6B1Ku1DlVpUp47dqF3JJ1l5Ao\ngWg1GrRqyzoVAPXffVe03dHLiysrVpCVmnfRw/wSuXEjGjMaReaXKAY0MhmKSvoUDbmzM64ffIDP\nyZOoyulP3tOOH+fR1q0m96VkQWSKjqgKtVEGxSKPyEQWkgGbj0GnHvl/A+3eAFsRTZJqDaFSLgdT\n5B04+IfwPWqM1zAObtBsgOG1V0PotxKscj3XygH6r4ZyRVt+XEKiINDpdGRm5i3sv3PnSpQvLxwh\n6OxszcGDwURGipd4fhZCQhI5ckRInER8qV2jhgtyuQyVSk6fPq9w9GhvOnbUR0mlpan5/PMLZu7S\nAVo0GjWBgX1JTx9MauoggoJeZ+LE2igU+Vve+/jY0a6dsAPJykrOwIHeRte0Wh3/+5+YqLWp42fs\nWMPhoI2Ngt27/ahY0XhjJ5fDxx9XYPz4Itg1S0gUAnlVunBy0ldZE0Img7AwvZB2YbJ8uZBtFJcq\neOUVJ2xt5chk0LixI2vW1ODzzw17q5kz75rRR1IAtqSn27NqlT/Jyb1JTX2d+Pg+zJ/fAHf3/Ecb\nDh1aMd/t3313jYQEMae+8T599OhKRs7s336rQefOpnq+7du78vfftcQn/JwjOY/EuLkc1vrBYitY\nYgt7B0H8TfF76rwHvq8ZX8s+gJED4Xth62uwsS1kFtJC5tFD89ctpWimJ8D8KPhDDT8EQdcpoMwR\njnRmg/j9Z9br/2tlbRoZlB9avGreQQRQuSaM+tT0+vaNokPmnI6sek2sFhprT8lkMtznzcM3KIjS\nP/xAqc8+w3PLFnxu3cKqhjlhSQmJkkv4iROs7t6dr62s+EqlYlnbtgTu2iV6T+ka/2fvvMOjqrY+\n/J6ZSTJppFICCYGQEHoJHSSIgtI7gQiICIIFReDaQD+8qGAFKRcsSJWOFAVEKSJIl9B7h0AghJBA\nejIz3x9DSCYz58ykF/b7PHlkztpnnxUhK/usvfZv1ebpKVNk7ffOnmXTiBHMCQoi+qRMB7J8knY3\n5w6QEavRxGCg4nffUSsjg+C4OCrNmoWdT1aFT8Ia5diV8s8/ZNy+DRoN2MsLNVrFyRXGzbas3+bo\nAuMsdD47uE55MyFLBgAcy8Fbv4CDk+mYBgPgvZvQ6wd4+kPo9SO8fwvq2dARTiAoQURGPmDUqN8o\nV+5zHBw+pWbNWcyceQC9Xv5nRK1WsWhRL5ycLHcQi49P5cMP/6JatRksW3aiUPyOiZFrQZ3VflqO\nnj2rk54+itTUkaxd24lmzbJ0jbZvv8X9+/JvoklJGWzadANJknB0zJ8SxcyZDR7vrOfkq6/qUaGC\n6UtdRMRDrlyx1no7KxZ+9VUwrVt7mIyoU8eF8+dbs359Az76qDpffRXE5ctt+Oabmnn9NgSCYiE1\nFT77zFgppNWClxeMHw+xlhsKPuarryAw0LLNYIB586BxY3j99cKrO7h7Vy5Rr/zi6OnpQFJSKOnp\n7Th4sAkDB2ZV4zx8mMEffyiLRq9ebRSydnTU2FQpKceYMcE0bepp0danjx+9e5sfWf7lF2s6eFn/\ns3v0qMz775u+C7q6atiypTGHDjVn8uQAPv44gH37mrF9exPc3eW6WZYNhOaRHPs+gIjPsz7rUuH8\nUri2CXrvAi+Z4wlqO+i5AU4thJM/wb3DYLCw839rF+waAx3mF7zvFWobj67lxNrPpbacsmh1qpWK\nA2v23DB1PoS0geVz4dIZ41G1Xi/Cy+PBzcN8vLVDwyoJVY/eqLv2QN13gJmIbiZ21arh8Y5MlzaB\noBRwYfNmVvTqhT7b8c1rf//NtV276PHTTzQeNkz23jYffIBP06b8O2sWV3fsIN1CFVDCrVus7tmT\n186fR5WfJLEFXOrUsXjdFslUOx+fx/pGZvfbUC1lKKiKqs5DjQ0CVnwDR3YafyeE9oLwd6C6he8v\nTenl6xGBrSGkC7QbAW4ypdLactDslXy5LhAUJzduxNOq1U/cvJm1sXbhQixjxmzh339vsXhxb9l7\n27evzuHDI5kxYz+//HKGu3fNf57T0nQMHbqekBAfatWS6aKYRwIC3HBwUJOamnuRVB8fJ9njWUlJ\n1itHbRljC/XquXHw4NN89dUF1qy5SXKyjtatvRg3LpDOnSuZjbdFNDYoyJlOnTwZOdKPevVcLY5R\nqyV69qxAz562i4ELBCWJjAzo0QP+zPbqFRsL06bBli2wZw+4y0jgVKoEBw7AnDmweDFckNF2njsX\nGjaEUaMK3v86dezZv9/Se5SEkoi0m5vxnVGtNo9fqal6WU2gTKx1bbMVFxc7/vqrA9Onn2XBgstE\nRSUTGOjCqFFBvPZakMX4ak3Q2tPTni5dfBk0yJ/nn68km9xq2rQcTZsqaGOWQUTlkSXiLkLEF5Zt\nqXGwx7Imx2PUdtDgFWg5wXLiKJNzyyBZpkooPzSXaQdtLVUY3EHZHtjSir2VlQfkAkmCsBGw7jAc\nT4K/r8PYTy0njgBatFGernU7HJb9gmbQUNnEkUBQ2jHo9WwePdokcZRlNPDH2LGkWWpdn42Ajh3p\ntmCB4nG3uMuXubBxY37dNaNily6oXcyPfaWinEDSVKiAU135MmFtS+XYpa5cGU1BCguEtIcvN8LW\nBNhyHyYssJw4AghWjl1oXeDd36HHRPnEkUBQBpg0aadJ4ig7S5YcZ9euaxZtmdSq5c3cud0ICJBZ\nJwAZGXrmzDmULz8t4enpSIsWFvTMTFrPmiNJEB4eJGtv3ry8Vd2fli0LLulSo4YL333XmJiYbiQm\n9mTr1qcsJo4AGjRwwcVFeQNhzpzazJxZRzZxJBCUBVauNE0cZef0aZiu0EcDwNMTPvxQ+QgbwMyZ\nefPPGi+8IHfcXrmCZvBgy9U+AF5edgQGKmsRtWxZcFp0Li52fPRRfS5f7kly8kBOnOjG6NHBskd4\n27RR1nkbObIGS5a0pFMnn3xVRZVFRPLIEud/RinTyo2tkHjb+jzREcp2XSrEnja9ptcZk1cP89FW\nVqWyXGWkQf5vXKWG/haOVGTnuTFZ+kc5kVTwfDEKs770KjgriJO9Pr7ofBEIionre/YQd0W+FXxq\nfDznLGj/5CTm9Gl0Vg7t344wj28PIyO5f/Eiel3eWpRKajVqC8ldA5CI5ahsAPy+/FJxXteBA1H7\nWHqxM+L+1ltImmIqxK3/LPg3lLc/MwKcnqxdLcGTR3q6jhUrlI/DLllyzKa5IiKicm2PjU3m/Pl7\nJCbaLmydk0qVXLG8+EpHbk3ZvXtVypeXf8GqVs2V3r3lm4h07FiF+vXlX+AKk3LlNLzyShVZe8OG\nLjz7bPH4JhAUJUuW5M+eiYVllQmnT0NajhCVnAznz4PMqX+bcHWVSwLbI3dspUIFDUOHmmv+ZCJJ\nEmPHym/KeXraMXSo/LqssBk/Xl6SxMlJzauvyif1n3RE8sgSKdaqgQyQauUQK4CDDRlV+0djUuNh\nUz/43h0WB8GCqrCiKVzdbH0OM/f0xr/Z7J0GVZhqZ+Sk30xws7y79JiAZvDKQrDL8XJn5wAj5kON\nFrn3taDwrQqL14N7jh1He3v4dDo83614/BIIipCkGOuVjLaMcbChq1pm5zV9Rga7P/qI2ZUqMdfP\njx+Dgvi+WjUOfv01hjwc0M+ZxMkMWyqymj9nXtMD7r16UWGossi+ytGRKlu2oPH1NbOVGzmyeI+q\nShK89xv4NzC3tR4Ag2WqYAWCMkRycgbJycrHr+R1hUxxc1OuLs5uX7PmDDVrzsXbexrBwd9RocJ0\nXn11M/HxVo7CW0CjUZElcpmpdZR5zdgdLXv08vd3YsmSjlbn/emnUJ5+2vwlq0WL8ixb1j7XfhYk\nX3wRaKJzkkn9+i789lsjsWMveCKwtqyyYdkFgLWll6Mj2D0qBjp3Dlq3Nh6HCw42dm7r0gXyIklp\nWVNOwlLXMQAHB4mNG2tYrYp8/XU/xo2ratbxumJFezZvblSs2kBdu1Zh+vQmjztVZuLhYc/69e3w\n91dofvKEIzSPLOFpRSXdzgVcLGRTdalw6ReIOQYO7lClvbGFsl5mQeRZB8o3hCsbYVMf0Oc4ahJ9\nGH7rDl3WQA35s/5meAeDmy/ER5omkewwti1KBxIejXWvAmFzob4NnYV0GeDsCG16wa2L4OgFtTtA\n25fA1YJ+wM0zsPMHuHMR3H2M44Ja2/595JZ2HeB4JKxfCZfOg3cF6PsCVBBHPQRPBuVlNINsGXN1\n504ubd2KJEkEdelC+bp1uXvqlMWxklpN7bAw4i5fZlnbtiTcumVifxgZyc533uHhjRs8O2NGrr4H\n72ef5ebSpWbNUuMwvoK58aiQ2sEB/08+ocp426oKM5KTUXfvjv7YMdQqFU4tW+I+fDj2tWqZjdXF\nxJA0fz5pe/YgabU49uuHtnfvwqtO8vaDL4/CsT/gzG5jQr55b6gqo60nEJQxXF3t8fUtR2TkA9kx\ndepY1im6cOEeK1ee4uHDVJo2rUxYWB3mzPlXdp7w8HqkpGTQo8cqtm41rdRMSsrg+++PcPjwbXbv\nfhGt1vaf+Wef9WPZsvPkFIrOwnj4VpJgyJBaTJv2FOXKWRfoj49PIzS0EhqNRHx8OvXqeTBoUA2e\nfda86ic1Vcfq1dfZsCGS9HQ97dpVYNiwGri756MRgAJ2diqWL6/PxInVWbs2mtRUPW3buvP8814i\ncSR4YqhbFw4flrfLLc3u34elS40d1fz9oXt34xE4OQYMMMaPTz+Fjz4ytRkM8PvvsG8f7N9vTCjZ\nSvv2TqhUPNIoyv7iqAG0QApgTN43b+7MDz/40bChk8xsWTx8qCMw0I0ePaoQGZmEv789PXp4MWBA\nRbRa82qnnTtjWbw4irt306ld25mRI6sQGGj9OXnl7bdrER7uz7JlV4mOTqFmzXIMGOCPk5NIjygh\n/u9YouYg2Pc+pMksYoJfNG+LHP0vbOoBSdnKoSUVVGwOUfvN51Bp4KmvIf4ybO5nnjjKxKCHPe9B\nQC/MUrdyqNTw1DuweYx5myIJYxWiuxpavw+dPrFt3od3Yc7zEJmjZWzCBWjexzx59OdMWPq2aWuA\nnT9Ch9Hw4izbvo+84OQEL8gLAgsEZRnv4GCqP/MMV3bssGyvVYvqzzxjci3p3j1W9OzJjT17Hl/b\n/dlnVGrUCEmtxmDhCFqrd97BtUoV5terZ5Y4yk7E7Nk0eftt3KtXlx2Tk4Bx47i1ahXpFnSbdMB9\nwL9rV+ovWYKdh7y2SSYGvZ5rw4cTu3ChyfX7hw/j0K6dWfIode9e7nXtiiEu7vG15FWrsGvRAu8/\n/kBlQ1VWnpAkaNTJ+CUQPGFIksRrrzVl4kTLsUujUfHKK01MrhkMBt5883fmzDlkstTw9S1HhQpO\nREebi2Y/9VRVwsLqMm7cVrPEUXb+/TeKZctO8vLLjWz+HsLDazJ58kGuXZPvpBsc7MaKFZ1o1Mg2\nnaL5888xatQ/ZGRkfYOHDt2lUiVHs+TR3bspdOiwnePHs2LXhg2RfP75af74oz2NGhXeEbJ69Vyo\nV0/s1AueTF57zSh2Lccbb5hf+/lnGDnSeOwsE0dHqFfPcvVQ+fLGhNG6deaJo+zExcEnnxjnt5Xq\n1e0YMMCF5cuTsPzi6Ei5cvbMnu3FkCEyyt85OHIkkU6dzhIdnVVAcfhwBnFxGvr1M93U1+sNDBt2\nmsWLs96hN26MYdq068ybV5uXXqps+zeTSypWdGTsWNFVOzcUybE1SZLekCTpiiRJyZIk7ZckqVlR\nPDfP2JeD51eDxkK206cNtMpxjCA1Hn7rbJo4AmPiJ3o/BL8Abtn6MFZuCz3/hGqd4cRcY8WSEnEX\n4K6Vg7A5af0WuCosTlQ6qN3R9oTUsuHmiSOAmMvwU4520JcPmSeOMtk2G/bkIqIJBMVIqYtdQM+F\nC/EMMj+r7VKpEv1XrzbbDV43eLBJ4iiT20ePUuWpp6gaGvr4mkeNGnSaM4f2U6dy5Y8/uHf6tNl9\n2THo9ZxbvTpX/ruHhODVST6BYgC0ISE2JY4A7s6caZY4AjAkJ3M5LIy0bMkvQ0oKsb17mySOMkk/\ncID4t9+26ZkCQXFTGmPXO++0pmdP8+1yjUbFwoU9qVbN9KXl66/38r//HTJbakRGPkClUjFgQF3s\n7Y0vQu7uWsaObcmWLYNISkpnwYLjVv1ZufJMrvx3dNTwwQdNFcd4ezvZnDg6evQer7ximjjKZOrU\nY/zyi2nya9SogyaJo0yio1Po02c3Ol3BdDYSCAqT0hi7WraEr7+2/Eo1ciQMGWJ67dAheOkl08QR\nGD+fOQNDh4LXIzkhjQb69TN2bAsIsC6+DbBmDVY7neXkyy+9USt00E1P19Ctm23C92lperp3P2eS\nOMpkx44HvPPOdZNrc+dGmiSOMtHpDIwYcYZz55QbvQiKlkKvPJIkaQDwDTASOAiMBf6QJKmmwWAo\nhFZjBUTV52DQeTj9I9w5YDyqFhgGAb2NVUPZObdYWScp5l8Ycs6YXFI7gGO2Kp3bB2zzJ01+J8si\nsZchKVp5zNkNUK2d9bliLsMphc5KkUfg0j9Q4ynj5+1zLCeOMtn2P2gz2PpzBYJipLTGLjc/P149\nepTjS5dyYeNG9DodAR060HDoUBxzJFyiT53i4pYtsnNd272bty5fxt7ZmYzUVFwrV36cfLq130JF\npQXSHuYydgHxJ04o2qM2bKDO5MlW5zEYDETPkq90NCQnc+/HH/GZNAmA5DVr0EfLx82k5ctx++Yb\nVJ5CBFZQcimtscvOTs3atQP444+L/PzzCWJjk6lfvwIjRzYhMND0Z06n0zNz5kHZuW7fTqBTp0Dm\nzevB/fvJVKjgjIODce22e/d1kpJkqr2zkZCQe/HsgwfvKNr37Ini3r1kvLyUuxAB/O9/p2W0SIzM\nnHmKvn2NVZ03biSyYUOk7NgrVxL4/fdbdOtmrvsmEJQUSmvsAhg/Hjp2hB9+gIsXwccHhg2DbPtv\nj5kxA+T6iuh0xq9bt+DOHaOmkWu2nI0tS6/UVKOwdm6aS+/alSrrE0BysoGtW1MIC1NoTvSItWvv\nc/OmfIxdtCiGqVP9cHMzxuTZs+WbROl0Br77LpLp03NxDk9QqBTFsbWxwPcGg2ExgCRJrwJdgZcB\n5RY5xY1LFWj+sfVxt/cq2+POGwW2XSx0pbBU3ZQTtRa8cql9IaezlB2d9cUTADePKSeDwJhAykwe\nRVpRa7uZBzU3gaDoKbWxy87JiSavvEKTV15RHBe5b5+i3aDXE7l/P/UGDDB/hlJ3w2z4NG9u07js\n6C0cWTOxZ9gQ3wD9w4ekXb6sOCbp6NHHf063pjSZmkrGxYvY5+F7EgiKkFIbu1Qqic6dg+jcWbnT\nzfXr8Yr6SAB7997gpZca4eJiqvfj7GybSGuzZrnvBJSRYX27Pz3dtpKAI0fu2Ww/e/aBYqIJ4OTJ\neJE8EpR0Sm3sAmjQAGbPtj5ur5XXxr17jf1+/PzMbc7OxqNpStSvn7vEEYAty6r0dNuaoBw5olwp\nlJSk5/z5FJo1c0GnM3D2rPkR4+ycPCkqj0oShXpsTZIkO6AJsD3zmsHYfmcb0Kown12kqK3tIEnG\niiNLBPW3Pn+twUZx6tzgWQPc5FskAhDwjLI9E0cbzrdqs+mAuFjx1Vns2gtKNk9K7NI4Wt/9tpMZ\nE9y3L5JK+VeIe2AgNbp2zbVf5dsrdxCyZs9E0mqR7JWFYtXZNIxUXtbjrKg6EpRknpTYZYuQtaOj\n5TGNG1ciMFD52KudnYrXXmuiOMYS7dsrJ2fq1PGkUiXbEu/WRK7d3LLsnp7WBbFtGSMQFBdPSuwC\no7ZRXu39bXhtHDMmd/4AtGunRWlJp1Ybx9iCu7v88bdM3NzUj+aVHlcgyeHpWXxd2QTmFLbmkTdG\n5a2cdbx3ACt94UsRNfoq26s+D/Yy50SDB0H5xvL3+rSB0Nx1KwKMotmtFboQla8NwT1smyswFNwV\nFkT2ztCgV9bn1laOpLUZomwXCIqfJyJ2BXXpophA0rq7E9Chg0Wbe0AAjV57TfZeR29v+m7caDXB\nZNGvceOQ7CwvFtSOjtR4802b5lHZ2+Per5/iGM8XXnj8Z6fwcOMKSQa7li3RBAbK2gWCEsATEbt8\nfFxp3drCtnw2+vWz3OJIkiQ+//wZWclHtVpi+fLeBAfnctMOGDgwCH9/eV2Qd98NsXmuF16ooWgf\nNCjL3qSJF7Vrl5Mdq9Wq6dfPyoaiQFC8PBGxC6CvlddGpWXL++9n6SFZ4q23YPjw3Pvk769hwAD5\nxPYLLzjj62vbgaWBA70UE1FNmzpTs2bW2nPwYOW/3iFDytRff6mnSASzLSCR1YG59OPfGao8bdmm\ndoBmH8vfq9FC7+1QZ5jxeFomrv7QcRH0/wfs8timsOVbEDoR1Dl2m3xCYPAWY/E0oTEAACAASURB\nVILJFlRq6P2NsXucJbp9Co7ZFi0tBkAdmaomn2DoNM625woEJY8yFbscPTxo8957svbQjz7Czkk+\n/nSYNYvQKVNwrpjVOUPr6UnTsWN5/eZNvHLTKzYb7o0b02L1auxzVPk4VKxIq19/xTUX8/p8/DFq\nmZWWW/fuuHbs+Piz2tcX1w8/tDhWcnLC3RalSoGgZFKmYhfAp5+2R6OxvC7p2jWItm39Ze/t27cW\n69b1o379LPFqR0cNnTvXICpqDH371pK9VwmtVsPWrb2oW9czx3U1U6a0YuhQ27v6DBoUSMuWlsW1\nq1VzYdw4UzmDmTObYm9v+f/HlCkN8fSUqYAXCEo2ZS52jR5t+UgaGK9b6s6WSUAA7N4NnTplCXSr\n1cYjc/v3G/WU8sq8eV707Wu+5uvf34nvv7c9mV69upaxYy0nfBwcJL76yjSRPXFidfz9LVc19ejh\nTZcu3hZtguJBMljTssnP5MYSxCSgr8Fg+DXb9YWAm8Fg6J1jfAhwODQ0FLcc7ZDDw8MJDw8vNF/z\nTXoi/DMOzi+BjEfy+RWaQZtvjN3VbCE1Hh5eB8fy4FyAWdaEO3BmHaQlgG8L8G9rvHZiBSTfgwr1\noHZvUFspCzz1O/zxCVx5pJNSuQF0fA+avmA+Ni0FNn4OO3+AuChwcoM2L0Kv/wPXXAaBgxtgyxyI\nPA3lykO7IfDcKHDIY1KtjLF8+XKWL19uci0+Pp5du3YBNDEYDLls1Sd4omIXsG/6dPZ+9RUJUcZu\nF+X8/Gg7YQJNX33Vpvt16encP38etYMDHgVYmaNLSeHW+vUk37iBc/Xq+PTogUGv5+bq1SRcuIBD\npUr4DRxolmTKScq5c9z68EPi1q+HjAw0FSviPWoUPh9+aLHCKennn0n45hvSjx4FjQZtjx64fvQR\n9o1sb9sNYDhxDN2c6Rj+2Ql2dqg690D16hgkP1EBkImIXwVLbmPXI1upjV9bt17i3Xe3cfTobQBc\nXOx5+eVGfPFFR5uOtgFcvBhLaqqOoCDPx93Z8ovBYGDHjkiOHLmLm5s9ffrUwNNTy/btN/jnnyi0\nWjV9+tSgZk3l43MJCen83/8dZsGC88TFpaHVqhk4MIDPPmtK5crmVQL798fw6acn+P33KPR6A82b\ne/Huu3Xo2zd3MefOnTRmzYpizZp7JCXpaN26HG+/XZmWLW3rtvQkIGJXwfKkxa6rV+HNN2HzZmNn\nNJUKunQxaib5y+e9Tbh9G+7ehapVIce3ny/OnEnjjz+M77KdOzsRHGzHmTNprF+fRGqqgdBQLc88\nY4vo/22mT7/NpUupSBI8+2w5/vtfX1q3No8jt26lMnnyZZYuvU1Cgo6qVbW8+moV/vMff+zsbK91\nSUvT89NPt1iw4BZRUanUqOHIq6/6MmBARbNuw08q+Y1dhZo8ApAkaT9wwGAwjHn0WQKuAzMNBsNX\nOcaGAIcPHz5MSIjtpb0litQ4iL8I9m7griz4WGzs/gL++shUMNu1MgxcB742CMEm3gO9DlwrQPQZ\nOPA93D0HLhUgZCgEZqs6MhggNRHsnVCsYZRj8buw4Svz60HNYdJ2cHTJ/ZxPABERETRp0gTEAibP\nPGmxS5eeTvTJk0iSRIX69VEpHN8qLqK3b+fgwIGkxWQ1XVFptTT49lsCRo2yer8uIQH9w4doypcn\nIy6Ouz/9xMNdu5AcHPDo1QuvAQNQOWTtzuuTkpDs7GSP0Cmh3/wrupf6G1ueZMfTC81vfyHVzWUT\nhCcIEb/yR25i1yN7qY9fZ8/GkJCQRnCwF66uJa/CJjIyge7df+Po0azYJUnw0ku1+eGHZ2QrqDJJ\nS9MRE5OCh4cDarXE6tXXWbv2BikpOtq2rcDw4TUoX15rMl6nM8jqPilx5UoKoaEniIw0jV0qFcyf\nH8TQoZaroQQiduWXJzF23boFN29ClSpQuXJxe2NOerqBYcNiWLrUVLS6aVN7fv21Aj4+yjHGYDBw\n5046Wq0Kd3cNO3c+ZOHCe9y5k0HNmg6MHOlN3bpZiSidzkBKih5n59yvQVNT9XTrdpRt22LNbMOG\n+TB/ft1cz/mkkJvYVRTd1qYBiyRJOkxW20UnYGERPLvocXCHCk2L9pkJt+DsYki4CW4BUOtFeYHt\nkyth2/vm1x/egp87w1vnwcma4PUj+/7vYMMbYMjWOSRiMYS8CP0XGldGkgTaPCZ4zu+3nDgCuHAQ\n1k6FQZ/lbW6BwDpPVOxS29nh01hBf60QSE9K4uLy5cQcPYqDuztBgwbhUcvycZGka9fY17MnukTT\nBYw+JYWjr72Gc0AAFbMdQbOE2sUFtYsLCYcOca5TJzJisxYY99et4/a0adTatg07b2N1pErhyJ4S\nhuRkdG8MM08cAcTeQzfmFTTbbOi3KxDkjScqdgHUqlW0xxoMBgNbtlzhzz+vIEkSXboE0KFDNdmx\n3br9xrFjMTmuw4IFZ6hY0YmpU1srPs/eXk3lys7ExqbSseMOIiKyYtfmzbf44ovTbN78NK1alX88\nPq+89dZls8QRGKsjXn31Et27ewgBW0Fh8cTFrsqViz5pdOKEgRUr9Dx8CE2bSoSFSWi1lqty3n33\nvlniCODff9Po1SuaAweUnZckiUqV7DEYDIwYcY2ffsrqErllC8yadZcZM3x5801jUlqtlvKUOAKY\nOzfSYuIIYMGCKHr3rkD37uXzNLcgi0LXPDIYDKuA8cBk4AjQAHjeYDDcLexnPxEcmwUL/WHvB3B8\nNuweB/N94dxyy+P3fC0/V3IsRPxk23NvnzBPHGUSsdhYjZRfts1Ttu+w0VeBIA+I2FW43N67l5/9\n/dk5YgQnZ8/m8KefsqJ2bXa/+SaWKmIvz51rljh6jMHAha8VYlv2oRkZXOjTxyRxlEnSsWNcVRAB\ntxXDxnVw3/ICBsDw7wEMZ07l+zkCgSVE7CpcoqMTadZsMV26rOHbbw8zffq/dOy4ijZtlnL/forZ\n+K1bb5gljrIzd+4JEhPTZe3ZefPNf00SR5nExaXRp88u0tJ0tn8jFoiKSmPz5vuy9pQUPUuXin9G\ngsJBxK7CRa838PLLGTRokMGUKXpmzdIzdKiOgIAMIiLM110PHuj58ceHsvMdPJjGrl3mMc8S8+ff\nM0kcZWIwwJgxkUREJNn+jcgwb95NRftPP93K9zMERVN5hMFgmAPMKYpnlXmSouHsIoi/AOnJcPZn\n8zG6FNj6InjWgfINs66np8Ctf5Xnv7YbnnrXuh/751pOHGWy73/Q0ja9FFlirivb4+5AehrYifaz\ngsJBxK6CIyMlhfOrVnFr714Ari5dSnpCgtm4k7Nn416zJvVzdFSL2b1bcf57VuyZ3N+wgbTISFl7\n7Lp1pEVFYe/jY9N8ljDcvGHTGKm2KKEWFA4idhUsO3ZcZf36c6Sl6fjnnyhOnTJ/Cdq79yYvv/w7\n69aZSrP884/yC0t8fBonTtyjZUtlrcu7d1NYvVp+XXT7dgq//HKD8PBqivMoERmZil5haQdw/Xpq\nnucXCKwhYlfBcvYsLFli1Ea6eVPP5s3mSaKoKOjSJYPLlzU4OWVVIEVEpJKYqCxvs3t3CqGhlsWu\ns/O//8nn/wwGmDv3Lj/+aKPYkwzXrysnsqzZBbZRJMkjQQFxfhlsHwr6DONnpQ0mfYaxKqlDtuod\nlcbYOU2vcKPGegAA4I6VXfPo07bNo0T5asp2Dx+ROBIISgH3Tp9m1dNPk3zXuHhQA0o/uce//ZZ6\no0ebiBuqHZR1TFRa22JX0ikrsUunI/ns2XwljyQ/6wsgW8YIBILiJSEhjY4dl7J/f/YEkPyRrQ0b\nLnD5chwBAe6Przk4WD+CYcuY8+cfkJ6unNk5dSrO6jxK+Pk5oFaDTmGZWK2ajetEgUBQrLz9dvbu\nawZAPn7cuQPLlhkYMSJr3eXgYF1gWu64W05On1ZO3Jw6lf/ETrVqjpw4Yb4pmWUXsasgKPRja4J8\nont07vzeSdg6OCtxZAt3Dph+VmugZnfle+r0sW1uJyv6AtoCkP3v+IqyvYMVu0AgKDZ0j/R+9BkZ\nrGrX7nHiCKz/4nlw+TIpMabHPCr3UY5N1uyZZOoZ5SRzWWUANF62t6S1hNStN3jJx0ipZRukYNtb\ndgsEgqIjPV2HXm/cbQ8PX58jcaT8omQwwMGDUSbXeveuoXhPQEA5GjWyrtnk7W39xadcufxtqFWq\nZE+3bvLdK52cVAwaJDRDBIKSiF4PGY9eE7//PnviyDYOHDBNLjVv7oCvr3xiW5Kgd2/btCG9vJTr\nVVxc8p+SeOUVZf2lV16pku9nCETyqGSSeBP2vAaLy8FCB1hdE7aGYXytyQV2FoSq230EdjLtFX1C\nwL8dbJsA06vBVHdY0B5OrzUfGzJE+dnJ9+H7dhB7NXc+ZyewGfSdaNkW3Bp6v5f3uQUCQYGjS0tj\n35QpfOfvzzcODsz08uKXrl1JjpHX+7CEpFKhcTSNU1WHDsWlZk2L4+3c3AgaP55rc+fyT+PGbHV3\nZ3fdulyZNg1diululmdYGFK2KiYDxiJOHcbkkQ4426cP9//4I1c+m/jv4ID6u8VgqVqqfAXUM37M\n89wCgaBwWLXqNC1aLMDe/nO02s/p2XMVmzZdyPU8Li6mlUl16ngyaFCw7PhPPmnJn3/eonPnrXh4\nLMPXdxXjxh3k5k1Tjbfg4HI0a6ac2J4y5SRffpk/PbVZswLw9zePXRqNxLx5gbi7i0MLAkFJ4vBh\n6NPHuOSws4OnnoL3LfRGsoaLi2lyXK2WmDzZXWY0vPyyC2lpBoYPv0PFipfx8rpEWFgUBw+aVxEN\nGSKflAbYseMhL754lcTEvOu2vfqqL507W46Ro0ZVoXPnom2sUFYRyaOSRmIk/NYKzn4H6Y9Eyh5c\ngNgz5mOtVQoGhZlfqxwCQ/6Eyk2yrqntoH449PkZFoTC7qkQdw1S4uHqTljZF7Z/aDpP7R5Q20oV\n05Vd8GN7SHlgxVEFXvgUPtwCzXpApUCo2RJemQMfbweHvHVCEggEBY8+I4O1PXqwe+JEHlw36nKk\nxMZy7c8/zcZaWxpU7dwZOxfT5Ledqyttd+7Ep1cvJHXWTphXmzY8tW0bFydM4PTrr/Pw6FEy4uNJ\nOH2as+PH82/nzuhSszQ67Ly98ZsyBchKHOVMy6dcusSZHj14eCBH9WYuUHXsjObvCFTDRkFgTahd\nF9X4CWh2HRFVRwJBCWPKlD0MGLCOgweNVUbp6Xp+/fUC5tr9BpQ28jw9tRa7ri1Y8Cz/+U9jXF2z\nEksBAeVYuvQ5oqMz6NRpK1u23CQuLo2bN5OYPv00zZpt5NIl0/XTjBlNcHKSrwSIj0/nvfeO8s03\nFtaMNuLn58Dhww355JOqNGjgRFCQlqFDK3DgQAPCw0XVkUBQkvj7b2OyaN26rKqjPXsgzuwEq4S1\nF8ewMHP7sGGuLFzojb9/Vtxxc5P44AM3XnrJiWbNrjN//gOio3XExupZvTqBNm1usHat6fGxd96p\nSM2a8vIDOh0sWRJLWNgVRR+VsLNT8euvDZk/vw5t27pTo4Yjzz/vxdq1DfjuO7HuKigkS11tigtJ\nkkKAw4cPHyYkJKS43Skedr8C5y10GUvD/Kiq0vFVj1oQdgAcysk/6+4ZSLoHXjXBpQKsHw5H5suP\nf+MkVMgm8KpLh93TYPtkSFdQye8+E3waQtRRcPSAOj1Bq+CXIN9ERETQpEkTgCYGgyGiuP0p64jY\nBWdWrOC38HCz6xJGjaOc2Mtc1zg50WvXLso3aWLBaiT51i0SL11CW6kSLkFB3Fq2jGODBsmOrz1j\nBtXeesvkWuzatVwdP57kq1dl7/Ps2ZPqX31F/NatoFLh3qkTDtWqyY4XFAwifhUtT3r8unXrIf7+\ns8nIsKIU/RgVlqMXzJ7dgTfekP9/mJCQxrFjMWi1Gho3Lk9UVBLVqq0hI8PyWrxHDz82bHjW5NrR\no7G8995R/vwzyuI9AN7eDhw/3oU//rjDw4fpNG3qSatWYte9sBGxq2h50mMXQIMGcOKEraMz66vN\n6d1bYu1a+apCvd5AREQaqakGGjWyx9lZRb161zh1Ks3ieC8vFZGR1dFqs+pU7t5N55NPopg9O8ZC\nYj6LvXtrcudOBteupVGtmj1du7qh0dimrSTIG7mJXaL2tCSh18HlZZZtKswTRZKF62oHCOwHbacp\nJ44AymfLwqanwMnlyuMj5kOnb7I9yw6efg+2TVK+748JkJYtA23vAs9PgTZvyt8jEAhKFacWL7Z4\nPXOfPuev/TSMsrPqbLbK7drR8osvFBNHAI6VK+NYOetse+SCBYrjI+fPN0seefbpw+158xSTR7G/\n/kr8hg1ZvqtUeA8ZQvUffkBlL8T6BYKywPLlp3KROIKsRZeKzOgVFOTBhx+24sUX6yne6eJiT5s2\nWbFryZJLsokjgE2bIomOTqZChaxjvI0aefLccz6KyaOYmFSqVdtIWlrW3M2be7JmTRv8/ETVtkBQ\nFjhyJDeJI8g6cJSp8AgeHjBqlIr//lf5MJJKJdG0aVbl0MGDKbKJI4B79/T8+msiYWGuj6+VL2/H\nsGHezJqlLGXQseMFky5vPj52LF7sT4cOovCgJCCSRyWJjCTjlyXUWD5fkbmt3+Q9CBoMzlVA66H8\nnPRkODIDTsyDhBvg6g81BxqvK/FQpt2sUvc2ME0cZX7+7S1wrQQN+ivfKxAISgVJCrpGlpJHAOmA\nV/PmdJo/H3s3N1x8fa0+5/rKlZyfMYP7ERHYlStH1fBwkq5dU7wn9Zbl2GVQaikEmG2N6fXELFqE\nSqul+nffWfVVIBCUfGJirKx9LKJHq9Vw4MBQtFoNQUEeJt0hLXHoUDRffHGELVuMx3qff94PtVo5\nCa3TGbhzJ8UkeWS8bj3ZlZamI7s6xcGDsTz//N8cP/48Go1QrRAISjv37uXlLhWgYu1aAzVrQkAA\nODoqx65bt/R8+WUyy5enER9voHFjNa1bW39SVJR5kyedzvqJp+yJI+M86fTocYmIiNrUqiU6phU3\nInlUkrBzAWc/SLxhbpMwnvNIx7TSSAKqPgfNPwOV9VavZKTA2k5wc1fWtbgLcPATcNXAQ4Vubp4y\nHUMCn4XzeRCX/ftzkTwSCMoI3nXqcPvQIYu27Pv02XGuUoUe69bhUlm5Q0YmxydM4MzUqY8/p969\ny4WZM1FrtThamD8TpxqWY5dbhw7EWdBkykROIeDuggX4Tp6MXYUKNvktEAhKLnXq5P44l729HRs3\nhtGggW0xYPPma/TuvYW0tKwF3Nq1V1CrJbJqMM1xcFDh62teKdShgw9w1MpTzaPXmTMP2LDhJn37\n+tnkt0AgKLkEB4NKZeyylhsmTTIeU7OF69d1tGnzkMjIrIfs369j/34AJ0BetqRGDTuzaw0aOFKh\ngobo6Fx0DweSkw3MnBnNnDlVc3WfoOARWw8lCUmC2q/J21Ua6LgcavaH8vXA/znotAa6/m5b4giM\n1UbZE0cm82cY1zAWbWoIGWHZ1u49kPLwT+lmBCTF5v4+gUBQ4mj8+uuK9rZffEHI22/j3aABlVq0\n4Olvv+Wl06dtThzFnz5tkjjKji4lBfPeHln4jRpl8XrF4cMVE0BySytDWhoP/v5b4YkCgaC00L9/\nbcqXlz/KFRZWh2++eY5mzfxo0KAy48e34uzZkTz7rL9N8+t0ekaN+tskcZRlM2DcFbS8G9+/fzU8\nPMxFZkNCPOnYsZLCU+XFcbduvWPdaYFAUOLx84Nu3ZTty5dDhw5Qrx4MGAD//AMff2z7MyZMSDZJ\nHJniiFzi289PQ+fOzmbX7e1VjBuXt423rVsf5uk+QcEiKo9KGvXfgVs74ZaF3XDvphDQFwIH5n3+\n0wuV7a4uEJvjmJmkgq5zwKOa5XtqtIewRfDrW5B8P3f+qMQ/QYGgLODTvDmhn3/OLgv9YbWentQa\nOBC3qnnfMbq6aJGiXadSYdDrzV6XfF54gSpDh1q8x87Tk7pbt3K2f39Szp83salQ3l2RNCJ2CQRl\nAa1Wwy+/9KVjx2WkppoeZVWrJcLD69CrVzDjxjXL0/zbtkUSGZmoMMKAWm1ApzONXnXquDNtWnPZ\nu1atasugQXvYvDnnsdxMQUzLCOFZgaDs8MMPcOwYWDq93707DBxo/MoLiYkG1qyR1zUCcHbWkpho\nGt/KlVOxfHmlR5WV5rz7bkXi4nRMmxZtostmDbHsKhmIyqOShqSCxOuWbXf3w78T8zd/opUdJ5eK\n0ONHqN4efBpD42Ew8iA0HWl5fFoS3D0LQR1hwk3o+rW1dUsW1UNF1zWBoAzxQEZ8OiU2lvW9e+dr\n7pTbtxXtBr2e+osXU7FPH1wbNaJ8t240XruWhj//bFGLxKDXk3zhAmpXV0LOnqXOli3Yubs/7qOk\nFMJUzs6Ue+aZfH0/AoGg5HDnTqJZ4giMlUGDB28gMvJBPua2rqn03/824rXXggkJ8aJt24rMmtWC\nAwe6Ur68ZX2PyMgk7txJYd26UE6e7EqzZt5kdYHL3obAnO7dbav2FAgEJZ+0NJCTnJwzB9asyfvc\ncXEGUlOVx3Tq5Mqnn3rRooWWJk0ceO89D06cqEqbNo4Wx8fGZnDuXCrvv1+JGzfq8dJLnjb70727\nW27cFxQSIodX0rixGeLPyttPfAP3jkDN4VC9v+3H1TLxqAkJkcr2JiOMX0qkJcH2CXBkAaQ+MB65\nC+gIbtWz3rosdYjLRKWGZz7Kne8CgaDEkhwby8mFC2XtdyIimF+vHvVeeokGI0agdXfP1fyuNWsq\n2u3c3KgcFobfkCFW54qaM4ebX31F6qNkl1PduniHhWGIi7Mp713p7bfRuIlFjEBQVpg27YCsLTEx\nnWbN5jNwYF1Gj25KjRpWmpLkoGZN67Hi6ad9aNPGx+q4nTvvMGHCUfbtM74tVqig5fXXgzh2LB5b\ndu1atfLiueeUjrsJBILSxPffQ6JCYePQocYE0muvQbt2uZu7fHkJDw+J+/flq4MaNNAwcaIrEycq\nJ4GuX0/jP/+JYt26eDIyQKuVCAtz58aNdJt88fJS8+abQmeyJCAqj0oa0fusDNDDrW2wMxxWB0DU\nX7mbv+GrVuwKmkuPXdDDsm6wf4YxcQTGrkSX/oRj2Vpmy1UguVaC8JUQ1MFWrwUCQQkn+uhRMlKU\nlIcg5tQpdr7zDnP9/Ij43//Qpdu2aACo/vLLqOzlOxNVe+kl1A7m2iA5uT55MpffeONx4ggg6dQp\nrk+aJJvrzkRycKDKRx/h+8knNnotEAhKOgaDgf37byqOuX07kW+/PUhw8FxGjdpEbKztHdpatqxE\no0byotz163valDj666/bPPfcjseJI4Do6BQ+/vgEaWnWxWf79vVl8+ZQq13hBAJB6WGfldfGpCRY\nuRKefhratIEcJ/QVsbeXGDZMfl1lZwfDh1tfd925k85TT11i9Wpj4gggJcXA4sX32b9fed0IEBLi\nyPbtQfj5KXenFBQNInlU0lBbLvOzSMJ1+P0Z2DnAvKW0HDX7QwOZBFLjMVCju/U5zm+EKzJJK12a\n6b8qiawzICpA6wzjz0P9vrb5KxAISgUaR9tjV3pCAttGj2Z+vXok29hr1tHHh+YLFljUGvJq1Yr6\nn35q/bkxMUROmSJr1yMnW2skaMMGfCdPFi9fAkEZQpIktFrbCvF1OgM//HAUP7+ZHDignHDKztKl\nz1KxonmMrFDBkWXLbNtIe//9o6Sny6W4DShFr7ffDmLNmja4u4uXL4GgLJGLpRd79xo7tE2fbvs9\nkyc70qaNeXzUaGD+fGeqVLGeSpgxI0a2wig52YDSMdvGjR05fLg2DRvKNzUQFC0ieVTSqN4vd+MN\nwNVVcCwXO+Ed5kLfPyF4APi0guBw6Lcd2n9r2/0nVyrbLf2rymz80fJ10Lra7qtAICgV+DRvTrlc\nCmLfP3+eX5RaheTA/4UX6HT8OIGjR+PVujWVOnWi+aJFtP/rL+xcXKzeH7thAwYrB/jlXr+cQkLw\neP55m30VCASlh379audqfFJSBs88s5S0NHOdJEvUqePJyZMDmDq1Be3aVSY01IcpU1pw8uQA6tXz\nsnr/1asJHDxoLdFuObHk5KTmP/+pZZOfAoGgdNEvl6+NAOPGGbuu2YKzs8SOHa4sWeJM5852tG6t\n4Y03HDh2zI3Bg61XHQGsXBmvaJcUOnZPnCiO2ZY0hOZRScO9FgQNgwsLrI/NzsmvoNH/2T7ev6Px\nKy+kJVgf4+oDD6NMr9XpDR2sVwcIBILSh0qtpu1nn7HJBs2h7Nzav5/YS5fwrFHDpvHlatemyaxZ\neXERnZIwwCMc69Yl9dQpk2va4GBqrl2bp2cKBIKSz8SJbfj11/PEx1tRh81GUlI6U6b8w8cf2yYk\n4u3tyPvvh/D++yG59i8hwfqxtMaNPThyxFTY29VVw+rVralSRezaCwRlkYEDYeZMOHIkd/e99RZE\nRNg21t5eYvBgB5uTRTlJSFAWBfD1tSMmRv+oCsmISgWTJvnQt2/uNOYEhU+hVR5JkjRBkqQ9kiQl\nSpIUW1jPKZM89SM0+ggcbFegJyNBWQi7IKki3zoWgPJ1YPxl6LcImr8GT42HV/fDoLWgESXTgpKP\niF95o+7gwXRfvhwPK+LWOTkxb14heWSKSzMrrbbVampv2UKt7dupNGYMFV5/naA1a2hw8iQO/v5F\n4qNAkB9E7MobwcFe7Nw5mPbtc/dzvm7duULyyJTAQFc8PZXXT+PH1+Ls2c5MnFiHUaNqMGtWCDdu\ndOf5563rKQkExY2IXXlDq4Xt2+HFF8EG2cfH5NgjK1SaN1c+W9ehgys3btRn2rQqjBrlzaRJlbhw\noS7/938idpVECrPyyA5YBewDXi7E55Q9VGpoMhkaToCzP8CBMfJjsx8TTYkCF99Cd48mI+Cfz+Ur\nkFq+DXZaaPyi8UsgKH2I+JVHag8cSK0BA7i1fz8rnnkGnRURbYB0GyqC8IYS0AAAIABJREFUCoJy\nrVrh0rw5CQcPWrR79+uHg68vDr6+uD3zTJH4JBAUMCJ25ZFGjSqxY8dgrl+Pp3v3VRw/Hm31nuRk\n246t5RetVs2oUUFMnWr5ja9KFUf696+Kvb2aTz+tXyQ+CQQFjIhdecTDAxYtMmoZvfsu/PST9XvS\n0grfr0zGjPFm48aHFm1qNbz5pjdeXhrGjq1YdE4J8kyhVR4ZDIb/GgyGGcCJwnpGmUejhbpvQqDC\nMZDHySMVOOdObyTPuFSE8PWgtdB+tuXb0PSVovFDICgkRPzKH5IkUaVVKzrOng02iEv7tm1bBF4Z\nqfXLLzjWqWN2vVxoKDW+/77I/BAICgMRu/JP1apuLF7cAw8PrdWxLVpULgKPjPz3vw0ICzNf51Wu\n7MimTe2xt1cXmS8CQUEjYlf+8fQ0JpBCbDgZW7EI8zQdOrgyfboP6hwhyt5eYv58Pxo3zoXqt6DY\nEZpHJR1JgtBF4N0c9r+Z7Xq2LwDfzuBYhJEg4FkYex2O/wzRJ8HRExoMhvJClFEgEBhpMHw47oGB\nrOnShYykJItjHNzdCerZs8h8cvD1pfHx48T+9htx27YhaTR49uiBu6g0EggEj2jYsCL//vsy3bqt\n4syZGNlxb79t5Rh/AWJnp2Llyra88849Vq26RmJiBi1aeBMW5o9WKxJHAoEAXF1h504YPRoWL5Yf\n9/bbRebSo+eVp18/NxYtuk9kZDoBAfYMHepJhQoiFVHaEH9jpQFJgrqjwaki7AoHQ44yaZdq0PqH\novdLWw6av170zy0q4m7CgSXG/3oHQIsXwcV6VxSBQJBF1XbtGHbsGEtatCAl1lTGQK3V0mvNGtT2\nRauFJqnVePXqhVevXkX63KIiPSmJ88uXE3PsGA7u7tR84QU8a4nEvkCQGwICPIiIGE5o6GIOHYoy\ns3/ySTuaNCl6TY6mTb1o2rRsrkUMBgMXt2zh8tatIEkEde5MQIcOxe2WQFCqcHU1HmPz8jJWIuWk\nY0djx7WixtfXnokTy+7RtBMn0lmxIpWHD/U0bWpHWJgWrdZ69X1pI1fJI0mSpgLvKQwxALUNBsP5\nfHklsEz1/uBRF07PhOg9oHGCav0haAQ4uBefX3eOQtId8AgC94Di86Mg+WsWrBkH+mwdTjZMgCHz\noVl48fklyDMifhUfHoGBjDh3jmPff8/5tWvRZ2RQtX17QkaPxiMwsNj8Sr1+naQzZ9B4eeHatGmx\n+VGQRO3dy8aePUmJyaqWOPTJJzQYPZrQmTORbDhGKChZiNhVfGi1GvbsGcqyZadYsOAYMTFJ1K1b\nntdfb0K7dsUnov/gQToHD95Do1HRqpUXDg6lv/IoMTqapV26EHX48ONr+6dNw69NG8J/+w1HD9F1\nqbQhYlfxMm0adOsGc+bAmTPg4wNDh0J4OGiKqXxEpzOwf38yiYl6QkK0eHuX/joWvd7AiBEPWLAg\nu8ZnMu+/n8CmTe40bmxXbL4VBpLBYLA+KnOwJHkB1rY7LhsMhsdv3JIkDQWmGwwGq63DJEkKAQ6H\nhobi5maqpxMeHk54uHhpL1Hc3AdbX4foo48uSFCtA3SaB+WKSH+pMDi7HWbI7HSpNPDBYfBtULQ+\nKbB8+XKWL19uci0+Pp5du3YBNDEYDDY24yzbFGb8ErGrdJF25w6XRo4kduNG0BtbyDrWrk3AzJm4\nl+Jd7tS4OBYFBJB6/75Fe+isWTQcPbqIvVJGxC/riLWXIJOMDD0ffHCc7767REKC8a/b29uBDz6o\nzbhxwcXsXf5Y3KEDV7Zvt2ir1asXA9atK2KPlBGxyzoidgmys2RJPBMmRBMZafzrdnCQGDy4HDNn\nVsLJqdBkmAudqVMTmTDBchOpihVVXL7sjZNTydm4y2/sylXyKC/kJQgcPnyYEFvUvgTFR8xpWNIc\n0i10SXIPgKER4GBBULs0MKc7nNgob28zAgb/WHT+5IGIiAiaNGkCYgGTL3KbPBKxq+SjT03lWNOm\nJJ08aWaTHByo//ffuLZoUQye5Z+j337L7rFjZe1ugYEMOX++xFcfifiVf8Taq2wyatQhfvjhskXb\nN980KrUJpDvHj/Ndw4aydkml4s0LF/AIKNnV7SJ25R8Ru8omK1c+YODAmxZtXbo4s2lT6Sw6yMgw\nULVqDFFRetkx8+aVY/jwki0KnpvYVWhpPkmS/CRJagj4A2pJkho++nIurGcKipADX1hOHAHEXYYT\nC4vUnQLlygFl+1UrdkGpR8SvskvMypUWE0cAhtRUbnz2WRF7VHDc3r9f0R5/8SIp9+4VkTeC4kDE\nrrLLtWuJzJt3RdY+ZcppUlJ0svaSTOQB5XWVQa/n5qFDReSNoDgQsatsM2nSXVnb5s2JHDiQXITe\nFBzXr+sUE0cABw6kF5E3RUNh1ohNBiKASYDLoz9HAE0K8ZmCouLiBmX7hfVF40dh4GDl95S9+D32\nBCDiVxkldoNy7Lq/aRP69NL5i97OWTk2SSoVaq319uOCUo2IXWWUjRtvodfLnxa4dy+Nf/6Rf0Er\nydhbiV22jhGUakTsKqOcPZvKuXNpimPWr39YRN4ULM7O1iu5bRlTmii05JHBYBhmMBjUFr52FdYz\nBUWI3srLlTV7SSakv7K9SVjR+CEoNkT8KrtYTQzp9Y91kEobgWHKscm/SxfsXVyKyBtBcSBiV9kl\nPd16XEpLK52xK6hrV8Xkt6Onp+i6VsYRsavskp5uXSLHljElkYoV1YSGKgtih4U5FJE3RUPpVacS\nFC9+Tyvbq7YvEjcKhWfHgnsVy7ZKtaD18KL1RyAQFBhuTz+taHdt1QqVQ+n8RV/1ueeo+txzFm0a\nJyda/Pe/ReyRQCAoKNq3r6Bod3RU07KlNW3ikonWzY3QDz+UtT89eTIaUTUpEJRKatVyoFIl5Y6Q\n7ds7FZE3Bc9nn7lgb2/Z1ru3A61ayRhLKSJ5VJLQZ5i2hi/JNPsPSDL/fOzLQaNRRetPQeLmA+N3\nQ8OeoHoU7DT20OwFGPs3OJYrXv8EghKGQa8nIyXF+sASQMVhw7ArX17WXuXdd4vQm4JFkiS6rl9P\nwzFjsC+XFacqh4bSe8cOKghBUYHAjOTk0lEp3bChB889V0nWPnx4dTw9S2fiG+Cp99+n69y5uFer\n9viaZ2AgPRcupPkbbxSfYwJBCSU1tXQUStvZSYwdK5/YrlfPgc6dS29V9FNP2bN1qwetWmVVIHl4\nSLz3nhMrV5bS5lEKaIrbAQFwezucmQp3dhg/V3wW6nwAFZ8pXr+U8G8PnefDtjchLds5VZfK0GMV\nuPoWn28FgXd1eHU9PLwLD+4YK5GcPYrbK4GgRHH/0iX2ffIJZ1euJCMlBa/atQl56y0ajRpVYjt6\naTw8qPPnn5zt04fUK1nisypHR/y/+AKvXr2K0bv8o3F0JPTbb2n12Wc8uHoVBzc3XHxLeTwWCAqY\nxMQ0pk7dy7x5R7lzJxFvbydefrkhEye2oVy5kpuAWbGiFQMG7GXr1juPr0kSDBlSjW++aVSMnhUM\nTV99lSYjR3Lv/HmQJLxq1iyxv0sEguJi/gL4diacOAkODtCvD3w0EYJLcLPFd97xJDo6gxkzYsnI\nVifRpImW9et9UalK9895aKg9e/d6cu2ajoQEAwEBahwdS/f3JIdIHhU311fBvnAwZEsd39kG0Tug\n1XKoWoL1deoNhaA+cP4XSLoDHkEQ2ANUZeiflWt545dAIDAh9vx5lrZpQ3JMzONr986cYetrr3H3\n+HGemzOnGL1TxqVRI5pcuMD9338n6dQpNF5eePfrh8bdvbhdKzDsnJ3xqlu3uN0QCEocKSkZdOy4\njH37stpGx8Qk8eWX+9i+/Qo7dw7BxaVkHjPw8LDnzz+fJiIilh07otFoJLp1q0xgoGtxu1ZgSCoV\n3rVqFbcbAkGJ5D/vwjfTsz6npsLS5bDpd9j9F9SrV3y+KSFJEl9/XZGxYz1Zv/4hSUkGWrRwJDS0\n9B5Xs4S/v/LxvLJAGXrLL4Hc3QWRKyEjETyagf8QsMt25EmXBhFvmSaOMjHoIWIM+PYGlbIQV7Hi\n4Ar1XypuLwQCQQESe/EiRxYs4MGNG7hXq0bjl182OUoAsGvCBJPEUXaOzp1Lw5Ejqdio5O6ES2o1\nnt264dmtW3G7IhAICoi4uBQWLjzKkSO3cXNzYODAerRu7WcyZsGCYyaJo+wcPnyb77+PYPz4lkXh\nbp4JCfEkJMSzuN0QCAQFREYGrPsNtmwzfu7UAXp3B022N/WzZ00TR9mJi4N3P4DNvxW+r/mhShU7\n3nhDxK7SjEgeFQb6NNgfBreytYS+tghO/x+02QRejxYlt/+ElDuW5wBIuW0cU7lr4forEAgEj9jz\n1Vdse+89MGR1vtj92Wd0mjnzse5E6oMHXLTS8v7U4sUlOnkkEAjKFjt3XqVXrxXEx6c+vjZr1kEG\nDqzHzz/3Rq026jQuWXJCcZ7Fi0+U+OSRQCAoO0Tdho494dSZrGvzl0Dd2rB1A/g8kjr7eZnyPH/8\nCdHRUEFZW18gyBdCMLswODXJNHGUSVos7OkOGUnGz6mWd+1NsGWMQCAQFACXtm5l27vvmiSOwCiI\n/fubb3Jj714AUuPj0Wcoi/vLVSUJBAJBQRMXl2KWOMpkxYqTTJ36z+PPMTHJinPFxCQVuH8CgUAg\nx6ARpomjTE6dgReyNXi+d095Hr0e7t8vWN8EgpyI5FFBo0uBKz/I29Ni4Maj1LGbDXoUtowRCASC\nAuDgrFnyRoPhsd25YkUcvb0V5/IWejsCgaCIWLToqMXEUSZz5hwiI8MoEVC3rnLsqltX6BwKBIKi\n4cQp+GuXvH3nbuMYgDq1ledydQU/P+UxAkF+EcmjgibxqrHCSIn7Ecb/ejUDz2by4zybg2fTAnNN\nIBAIlIg6fFjZHmGMXWp7exqMGCE7TuPoSP2XXy5Q3wQCgUCOw4ejFO1RUQncvp0AwBtvKK+r3nij\nSYH5JRAIBEpEHLV9zItDjAkiOV56EZzKlv60oAQikkcFjZ1b7sa0Wg5O/uZjnPyhlZXDrZlEr4Ej\nHWFvdfi3Ndz8EfTptt0rEAgEj3BwU45f2e1tJk2iWseOZmM0Wi3dV6zAqbz13fvYf/9l/5AhbAwI\n4Pd69Tg5aRIpd+/m3nGBQPBE4+bmoGhXqaTHHdQ6dKjOxx+3tTju3Xdb0bOn9X7XN28+4P33d1C7\n9ncEBs5hxIiNnDwZnXvHBQLBE42VZZfJGDc3WL3CcoIotC1M/cz6XMnJMGs2NG8F1YOgaw/YtDl3\nPguebIRgdkHj6APe7SDmb/kxfuFZf3atAZ1PwNWfIep34zWfzlBtCNi5WH/e2ZFw68eszylX4cE+\nuPsLNPgVVCWs3aw+HS7OhMvfQ8Il0FaCasMg+F3TTnQCgaDIqRcezs7/+z9FeyYarZb+W7ZwceNG\nzixfTtqDB1Rs3JiGI0dSrmpVq8+6unQpB4cOxaDTPb526tQprixcyDO7duHsbyGpXsykbVhPyrfT\nyNi3Fxwdse/dF8f3PkAdbP1lUyAQFB7h4fWZPfuQrL1z50Dc3bWPP0+aFEr37kH8+ONRrl2Lx9fX\nleHDG9GiRRWrzzp9+i5PP/0zd+9maSNduvT/7N13mFTl3f/x9z0zW2FZWIpUQbCAoCLYE0s09q4x\nivpoFGOJJv54TEyMxhi7PtFoYtQoNkSJLYqxo2hUxAYGUCkivcMCy/bdmbl/f8wAu8u03T3nTNnP\n67rmAs6ZOfd3YPbDzHfuc59NTJz4NS+9dCYnnrhb+56MC2bPruGOO1YxefImGhsthx9ewrXX9uGY\nY7qmuzSRDu3Yo6CsG2yMs1ZRWbfIfbbd/xj4bi48Mh6++BI6d4azz4JTWlyZLZbqajj6OJj+6fZt\nS5bAG2/Cdb+F229t99Nx3IYNQe66ax0TJmxmw4Ygw4YV8ItfdOfyy7vj85l0l9chGdtiYdR0MsaM\nAmbMmDGDUaNGpbuctiv/DD78EYRiLMo46GLY7zFnxtnwBsxOcCW23e6DAVc7M5YTbAg+OQ1Wv7bj\nvq4j4fD/qIHkkJkzZzJ69GiA0dbamemuJ9flSnbVbtrEYwcdRPmCBTvs6zViBBd/8gkFieZMp6h+\n40b+3b8/odrYC9f2PflkDn311XaP46Tae/9M7W9/s8N2U1pKybsfENCV5Ryj/PJWruTXOee8yHPP\nfbPD9pKSfD788CJGjuztyDg/+MFTfPLJipj7uncvYsWKX1FYmDnfzX78cSXHHjuPmppws+3GwCOP\n7MIll+jSTE5RdnkrV7LrkSfgsjgf1/5xP1x6kTPj3HgT3JJgdtKnH8OBBzozlhPWrw/ywx8uZMGC\nhh32nXdeV55+egDGqIHkhNZkl05bc0P3A+HwD2CnY4Doi7qoP+x1F4x+NNEjW2dVkmOtGu/cWE5Y\n8WLsxhHA5v/Cd/d7W4+INFPUrRsXffQRIy++mEBREQB5nTox+rLL+Nl//uNI4whg2bPPxm0cAax+\n/XVqVydew8RL4dWrqb3+upj7bEUFNdf8P48rEpGWJk48g5tvPoLevSOztn0+wwkn7OZo4+jbb9fH\nbRwBlJfX8sor8x0ZyylXXrlkh8YRRC6qOW7cUrZsSXzlTBFx16UXwfNPwT57bd+2z16RbU41jgDG\nP96+/V67/fZ1MRtHAM88s5l3363yuCIBnbbmnrID4NC3I4tnB2sip7MZv7Nj1C1t336vLX0q+f49\n/+BNLSISU6devTj1scc44W9/o6a8nOIePciLNpKcUr00cTbZcJjalSsp6tPH0XHbqn7SMxCM/wEr\n+OF/CC1Zgn/QIO+KEpFmAgEff/jD4Vx33aGsWVNF5875zU5Vc8KyZVuS3mfp0gpHx2yPr76qZvbs\nmrj7q6rCvPTSJi66SFeYE0mns06P3Favify5jzP97m0aGiDZd3JLlzk7Zns99VScc/ma7D/6aGe+\n1JTUaeaR2/LLoLi/840jgMIka4IUJl93xFP1SRaTrF/rTR0iklRecTGlAwY43jgCkq5nZHw+ivol\nX3vEK3Zd8oVwrRb6FskIgYCP/v27ON44Ath55+Sn1u+8cwor4Hpk3brkF09Zu1YXWBHJFH16O984\nAsjPh95JjrvzAOfHbatg0LJpUyjhfdau1azJdFDzKJv1jX+p7Mj+n3tTR6o6J1lUtmSoN3WISFrt\nfO65+BM0pfqceGLGzDoC8O+eJLvy8/Htsos3xYhI2uy5Z08OPjh+Y7t79yJOPz1zFtDfffdCki0J\nMnSo8002Eck8l1yceP/Px3pTRyoCAcPgwYkv+jR0aOKrbIo7XGseGWMGGmPGG2MWGWNqjDHfGWNu\nMsbkuTVmh9PjROgTp4FUdgz0u8LbepIZkqSewRlWr3RIyi73FZSVsd8jj2D8O87ILB4wgFF//Wsa\nqoov/+xzMN26xd9/xk/w9ejhYUUiO1J2eePRR0+kZ88dr5VdUODnySdPzqjFsnfZpZDjjos/E6p/\n/3xOOil+tol4Qdnljd9dCwfFWRD7t7/JrMWyAX7xi+5x9xkDl10Wf7+4x82ZR0OJrBb9c2BPYBxw\nOZBgnXdptWGPwojnodtRkdPYuhwMezwCe78GvsQdW8/1+CEMvyX2voEXwiAHV4UTaTtllwcGnX8+\nR02fzsDzzqPTLrvQZc89GX7jjRz95Zd0yrC1g0ynTnSe9DwU7/iB0b/X3hTfl1nNLumwlF0eGD68\nJzNnjuXaaw9mjz26M3hwV8aO3YcvvriYk07aLd3l7eDRRwez2247zi7q2tXPCy/sSiCgqxVJ2im7\nPNCpE0ydAn/9C+w3GgYNguOPg9cmw523p7u6HV19dQ9OO23HU4WNgb/+tS8jRmjWZDoYa613gxnz\na+Bya+2ucfbnxCUXJYmNn8Oif0DVQijsE2ka7XQMSedWS8p0uVhnKbsEILRsGfWP/oPg9E8wRUXk\nn/ET8s8Zg3FhXaiOTPnlnGTZFb2P8ivHVVWFePrpDbzyyiYaGy1HHFHCpZf2onfvDPuSMcspu5yj\n7BKAcNjy2mtbmDBhMxs2BBk2rIDLL+/OPvvofZeTWpNdXs+t7Qps9HhMyTRlB0RuItlD2SX4d96Z\n4lv0RahkFWWX0Lmznyuu2Ikrrtgp3aWIpErZJfh8hlNOKeWUUzLnQgQdnWcLZhtjdgWuAh72akwR\nkfZSdolINlJ2iUg2UnaJZK5WN4+MMXcYY8IJbiFjzO4tHtMPeBN4zlr7uFPFi4ikStklItlI2SUi\n2UjZJZJ72nLa2p+BJ5LcZ9HW3xhj+gJTgY+ttZelMsC4ceMoLW0+PW3MmDGMGTOmlaWK5L5JkyYx\nadKkZtsqKirSVE1GU3aJZBjlV0pczy5Qfom0hrIrJcoukQzT3uxydcHsaPd4KvAF8D82yWBa+EzE\nGVq0sX2UXSLpo/xqu9ZmV/Qxyi8RByi72k7ZJZI+GbFgtjGmD/ABsAS4FuhlolfTstaudWtcEZH2\nUHaJSDZSdolINlJ2iWQPN6+2dgwwOHpbHt1mAAv4XRxXRKQ9lF0iko2UXSKSjZRdIlnCtautWWuf\nstb6W9x81lqFgIhkLGWXiGQjZZeIZCNll0j2cK15JCIiIiIiIiIi2U/NIxERERERERERiUvNIxER\nERERERERiUvNIxERERERERERiUvNIxERERERERERiUvNIxERERERERERiUvNIxERERERERERiUvN\nIxERERERERERiUvNIxERERERERERiUvNIxERERERERERiUvNIxERERERERERiUvNIxERERERERER\niUvNIxERERERERERiUvNIxERERERERERiUvNIxERERERERERiUvNI2lmzZoqfvvbKQwadB89etzN\n8cc/w9tvL0x3WSIiCTU0hPjb3z5j5MiHKSu7i9GjH+Hhh78kGAynuzQRkYRee20jRx/9Nd27f8bg\nwV9y/fVLWb++Md1liYgkNGdOFT/72Vx6955G797T+NnP5jJnTlW6yxIXudo8MsZMNsYsNcbUGmNW\nGWMmGGP6uDmmtN3SpZvZf/9HufvuT1i6tILy8lreemshxx33DPfeOz3d5Yl4RtmVXRobQ5x88iR+\n9au3mDVrLZs21TFz5mquuOJ1zjzzeUIhNZCkY1B2ZZ9bb13OySfP5d13K9i4McjixfXcfvsKDjpo\nNqtW1ae7PBFPKLuyz3vvbeLAA2fy1FNrWbu2kbVrG3nqqbUceOBM3ntvU7rLE5e4PfNoKnAWsDtw\nBjAEeMHlMaWNrrnmHVas2BJz37XXTmHZsgqPKxJJG2VXFhk/fibvvPN9zH2vvjqfZ5+d43FFImmj\n7Moi8+fXcOONy2LuW7Sojt//PvY+kRyk7Moi4bBl7Nh51Nbu+OVcbW2YsWPnEQ7bNFQmbnO1eWSt\nvd9a+7m1drm19lPgTuAgY4zfzXGl9TZurGXy5Plx94dClqee+q+HFYmkj7IruzzxROJsevxxZZd0\nDMqu7PLkk+uwCT5fPffcBqqrQ94VJJImyq7sMnXqJpYujT8zcunSes0+ylGerXlkjCkDzgOmWWv1\nP2GGWbeuOunaIKtWVXpUjUjmUHZlvpUrE2fTypWxZ1SK5DJlV+ZbubIh4f66ujAbNwY9qkYkMyi7\nMl+y7IrcR6fd5iLXm0fGmDuNMVXABmAAcJrbY0rr9e1bQmFhIOF9Bg/u5lE1Iumn7MoeybJpyJAy\njyoRST9lV/YYPLgw4f6SEj89e+Z5VI1Ieim7skey7AIYMqTIg0rEa4m7BTEYY+4AfpvgLhYYZq1d\nEP3z3cB4YCDwR+Bp4KREY4wbN47S0tJm28aMGcOYMWNaW66kqEuXAs4+ezhPPTUr5v6CAj8XXjjS\n46okFZMmTWLSpEnNtlVUaH2qlpRduevSS0fx8cfx1wa59NJRHlYjraH8Ss6L7ALlVzqMHbsTt966\nnFCcuRUXXNCTwkJdGDkTKbuSU3blrkMP7cqwYcXMnVsTc/+wYcUcemhXj6uSVLQ3u4xNdLJ1rAcY\n0x3onuRui6y1O8yzNcb0A5YDB1trP4uxfxQwY8aMGYwapTf7XtuwoYYjjniSb75Z32y732948snT\nOP/8vdNUmbTWzJkzGT16NMBoa+3MdNeTCZRductaywUXvMLEibN32HfppaP4xz9OTkNV0lbKr+bc\nzK7ofZRfaTR+/Bouu+x7wi1WDhg1qhNTp46gtLTV3/NKmii7mlN25baZMys5+uhZO5xaW1YWYMqU\nfRg1qiRNlUlrtSa7Wv0/krW2HChvY21bFz0raOPjxUU9ehTz6aeX8MQTX/Hcc99QWdnAAQf05aqr\nDmCffXqnuzyRdlF25S5jDBMmnMYZZwxl/PivWL68gkGDunLppaM56aTd012eSLsou3LbJZf0Zt99\nO/PAA6uZObOK0tIAY8b04MILe1FcrLWCJXspu3LbqFElzJ69Pw89tJI339wIwPHHl3HFFf3o10//\nbLnKta8zjDH7AwcAHwObgF2Bm4HvgOlujSvt07lzPr/85YH88pcHprsUkbRQdmUnYwynnz6M008f\nlu5SRNJC2ZW9Ro/uzBNP7JbuMkTSQtmVvfr1K+DWWwdz662D012KeMTNE6lrgTOAd4F5wKPAf4Ej\nrLWNLo4rItIeyi4RyUbKLhHJRsoukSzh2swja+3XwFFuHV9ExA3KLhHJRsouEclGyi6R7JH1l3Bo\nuVp4to+Tq2Pl4nPK5bHEfbn42snF5+TlWLn4nLweS9yXq68d/Zxnx1i5+JzEG7n62tHPnsbychw1\njzJsnFwdKxefUy6PJe7LxddOLj4nL8fKxefk9Vjivlx97ejnPDvGysXnJN7I1deOfvY0lpfjZH3z\nSERERERERERE3KPmkYiIiIiIiIiIxKXmkYiIiIiIiIiIxOXa1dbaqBBg7ty5KT+goqKCmTNnulaQ\n1+Pk6li5+JwyeawmP0OFrhUkTWVsdnk5Vi4+Jy/HysXn1JaxlF+Ps/D1AAAgAElEQVSea1V+ZfJr\nJxvGysXn5OVYmfyclF2eU3Z5OFYuPqdcHcvN7DLW2jaW5TxjzLnAM+muQySHnGetfTbdReQ6ZZeI\nK5RfHlB+iThO2eUBZZeI45JmV6Y1j7oDxwJLgLr0ViOS1QqBQcDb1tryNNeS85RdIo5SfnlI+SXi\nGGWXh5RdIo5JObsyqnkkIiIiIiIiIiKZRQtmi4iIiIiIiIhIXGoeiYiIiIiIiIhIXGoeiYiIiIiI\niIhIXGoeiYiIiIiIiIhIXDnTPDLGTDbGLDXG1BpjVhljJhhj+rgwzkBjzHhjzCJjTI0x5jtjzE3G\nmDwXxvq9MWaaMabaGLPR4WNfaYxZHP37+tQYs7+Tx28yzqHGmFeNMSuNMWFjzCkujXOdMeZzY8wW\nY8xaY8zLxpjdXRrrcmPMLGNMRfT2iTHmODfGajHuddG/w3vdHku8o+xq9bGVXW0fS9kljsnF7IqO\nl9X5pexydFxlV47yIr+UXa0ew5Psio7lSX6lK7uiY7uSXznTPAKmAmcBuwNnAEOAF1wYZyhggJ8D\newLjgMuB21wYKw94HnjIyYMaY84G7gH+COwLzALeNsb0cHKcqE7Af4ErATcv7Xco8DfgQODHRP7u\n3jHGFLkw1nLgt8Do6G0qMNkYM8yFsQCIhvTPifxbSW5RdqVI2dVuyi5xUi5mF2R/fim7HKDsynle\n5Jeyq3W8yi7wLr88zy5wOb+stTl5A04GgoDfg7F+DSx08fgXAhsdPN6nwP1N/myAFcC1Lv89hYFT\nPPr37xEd74cejVcOXOTSsTsD84EjgfeBe714Trql56bsSng8ZZfz4ym7dHPq3ztnsis6Rtbnl7Kr\nzcdWdnWwm1f5pexKeUzPsis6nmf55WZ2RY/van7l0syjbYwxZcB5wDRrbciDIbsCjk4PdEt0quRo\n4L2t22zklfYucHC66nJBVyJda1f/XYwxPmPMOUAxMN2lYf4O/NtaO9Wl40uGUHbFp+xylrJLnKTs\nSqyD5JeyS7KSx/ml7MpMrueXR9kFLudXTjWPjDF3GmOqgA3AAOA0D8bcFbgKeNjtsRzSA/ADa1ts\nXwv09r4c5xljDHAf8LG19luXxhhhjKkE6oEHgdOttfNcGOccYCRwndPHlsyh7EqJssuZMZRd4hhl\nV8pyOr+UXZKNvM4vZVdmcju/vMqu6Fiu51dGN4+MMXdEF3qKdwu1WNzqbiJ/YUcDIeBpF8fCGNMP\neBN4zlr7uFvjeMTg/vmlXnmQyLnF57g4xjxgHyLnyj4ETDDGDHVyAGNMfyJhdr61ttHJY4u7lF2e\nUna1jrJL4srF7GrrWB7JlfxSdknaeZVfyq5IaeRGdoH7+eV6doF3+WWi58ZlJGNMd6B7krststYG\nYzy2H5FFqg621n7m9FjGmL5EziP8xFp7UbLjt3Wc6GMuBP5irS1LdZwE4+cBNcCZ1tpXm2x/Eii1\n1p7e3jESjB0GTms6rgtjPEDkvOVDrbXL3BonxrhTiJzDfIWDxzwV+BeR/9BMdLOfSFiHgAKbyT/A\nHZiya9tjlF2pj6HskrTLxexqy1jRx2R9fim7Wn1MZVcW8yq/lF25kV3RcTzPLzeyK3pcT/Ir0N4D\nuMlaW05kUam28Ed/LXB6rGjATAW+AC5uTVHtfE7tZq1tNMbMAI4CXoVt0/WOAv6arrqcEA2AU4HD\nvXwDE+UjxddaK7wL7NVi25PAXOBOvYHJXMou5ym7XKPskm1yMbtaO5YbcjW/lF2SSbzKL2VX9mcX\npDW/3Mgu8Ci/Mrp5lCoTuRzdAcDHwCZgV+Bm4DscXpDKGNMH+ABYAlwL9Ir8DIG1tuX5oO0dawBQ\nBgwE/MaYfaK7Flprq9tx6HuBp6Jh8DmRS0cWE3mBOcoY04nIv8fWDujg6PPYaK1d7uA4DwJjgFOA\namPMTtFdFdbaOqfGiY51G5Gpp8uBEiKL7B0OHOPkONF/42bn3hpjqoFya+1cJ8eS9FB2tZqyq31j\nKbvEEbmaXdHxsjq/lF1tp+zqGLzKL2VX63iVXdGxPMkvr7ILPMwv69El8Ny8ASOIrAK/nsjUuu+B\nB4A+Lox1IZGpX01vYSDkwlhPxBgrBBzmwLF/QSTMaokE5X4u/dscvvXvp8XtcYfHiTVGCLjAhec0\nHlgU/btbA7wDHOnG31+MsaeiS8bmzE3Z1aZjK7vaPpaySzen/j1zMrui42V1fim7HB9b2ZVjN6/y\nS9nV6jE8ya7oWJ7kVzqzKzq+4/mV0WseiYiIiIiIiIhIemX01dZERERERERERCS91DwSERERERER\nEZG41DwSEREREREREZG41DwSEREREREREZG41DwSEREREREREZG41DwSRxhjLjTGhGPcQsaYXumu\nT0QkGWPMj40x7xljNhtjthhjvjTGnJXuukREYjHGvB/nvVfYGFOf7vpEROIxxow2xrxmjFltjKk0\nxswyxvzSGKP+RAYLpLsAySkW+AOwpMX2zd6XIiKSOmPMRcB44B3gOiAE7AEMSGddIiIJ3Ao82mJb\nJ+AfwNvelyMikpwxZhQwDVgA3AnUAMcD9wODgXHpq04SUfNInPaWtXZmuosQEUmVMWYg8ABwv7X2\nf9Ndj4hIKqy177XcZow5L/rbZzwuR0QkVZcTmXRwqLW2IrrtUWPMB8DPUPMoY2laWAdnjHnSGLM4\nxvabjDHhNh6zs6YciojbHMyvK4j8f/jH6OM7OVSiiMgO3Hjv1cR5QBXwajuPIyLSjIPZVQLUNWkc\nbbUGqG1PjeIufcAXG72luj0RA3wAbAFqjDGTjTG7tq88EZG4nMqvo4B5wInGmOVApTGm3BhzszHG\nOFCniEhTTr732sYY0wP4MfCytVYfwETEaU5l1wdAF2PMI8aYocaYnY0xlwOnAXe0v0xxi05bE6fU\nAE8A7xNpHo0GrgGmGWNGWWtXprM4EZEEdiOyxtHjwF3AbOAM4AbAD1yfvtJERFJ2DpHM0ilrIpLJ\nHgWGA5cBl0S3BYGrrLWPpK0qSUrNI3GEtfYF4IUmm141xrwDfEjkg9cv0lKYiEhynYnMnPyttfbP\n0W0vG2O6A1cbY2631lanrzwRkZScC6wH3k13ISIi8Vhrw8aY74G3gOeBemAM8IAxZo21VqfdZiid\ntiausdZOAz4jMoVaRCRTbT29458ttk8CioB9vS1HRKR1jDG7AAcB/7TWtnfdJBER1xhjfgdcC4yx\n1j5jrX3RWnsm8DHwd62dm7n0DyPxzk/1O3T85UCZQ8cSEWnKqfxaFf11bYvt64jMSOrWyuOJiCTi\nxnuv86LHfbYdxxARScSp7LoCmGqtrWmx/VWgLzColccTj6h5JJuArjG2D3Lo+IOJTKEWEXGaU/k1\nI/prvxbb+xF5o6QMExEnufHeawywyFr7eTuOISKSiFPZtROxG0550V+1tE6GUvNIvgdKjTEjtm4w\nxvQhstp9yqJX+Gi57QQiC2e/2d4iRURicCS/gOeIzDAa2+Q4BrgI2Mj25pKIiBOcyq6tjx0JDAMm\nOlOeiEhMTmXXAuBoY8y2md3RU9XOBiqj40gGMta2+YqgkgOiP7TLiJyu8VegE3A5kdM1RllrU5qG\naIxZAHwFfAlUEGkaXQSsBA6w1uqbexFxlFP5FT3WFOBHwHhgFnA6cBRwqbX2MYdLF5EOzMnsih7v\nz8A4YJi1doHD5YqIAI5+bjwXeBpYBDxCZO3Jc4EDgeuttXc6X704Qc0jwRhzFHAvsDuwGLgl+vsb\nWxECNwMnArsAxcBq4DXgZjWORMQtTuRX9DjFwK1EvvUqA+YDd1prWy6iLSLSbg5mlyHyYW61tfYA\nN2oVEdnKwew6GrgOGA50IfK+6+/W2kcdL1oco+aRiIiIiIiIiIjEpTWPREREREREREQkLq1kLgkZ\nY7oARYnuY61teXlrEZG0U36JSDZSdolINlJ25T6dtiYJGWOeAC5McBfb2oUdRUS8oPwSkWyk7BKR\nbKTsyn1qHklCxpihQN9E97HWTvWoHBGRlCm/RCQbKbtEJBspu3JfRjWPjDHdgWOBJUBdeqsRyWqF\nwCDgbWtteZpryXnKLhFHKb88pPwScYyyy0PKLhHHpJxdmbbm0bHAM+kuQiSHnAc8m+4iOgBll4jz\nlF/eUH6JOEvZ5Q1ll4izkmZXpjWPlgBMnDiRYcOGpfSAcePG8Ze//MXNmjwdJ1fHysXnlMljzZ07\nl/PPPx+iP1PiuiWQmdnl5Vi5+Jy8HCsXn1NbxlJ+eW4JpJ5fmfzayYaxcvE5eTlWJj8nZZfnloCy\nSz97Gqu947QmuzKteVQHMGzYMEaNGpXSA0pLS1O+b3t4NU6ujpWLzylLxtI0Xm9kbHZ5OVYuPicv\nx8rF59TOsZRf3mhVfmXJaydjx8rF5+TlWFnynJRd3lB2eThWLj6nXB3LzezyteWoIiIiIiIiIiLS\nMah5JCIiIiIiIiIical5JCIiIiIiIiIicWV982jMmDE5NU6ujpWLzymXxxL35eJrJxefk5dj5eJz\n8noscV+uvnb0c54dY+XicxJv5OprRz97GsvLcYy11rWDNxvImOuA24D7rLX/G+c+o4AZM2bM8Gzh\nKpFcNHPmTEaPHg0w2lo7M931ZLtk+aXsEnGO8ss5eu8l4h1ll3OUXSLeaU12eTLzyBizP/BzYJYX\n44mIOEX5JSLZSNklItlI2SWSuVxvHhljOgMTgUuAzW6PJyLiFOWXiGQjZZeIZCNll0hm82Lm0d+B\nf1trp3owloiIk5RfIpKNlF0iko2UXSIZLODmwY0x5wAjgf3cHEdExGnKLxHJRsouEclGyi6RzOda\n88gY0x+4DzjaWtvo1jgiIk5TfolINlJ2iUg2UnaJZAc3Zx6NBnoCM4wxJrrNDxxmjLkKKLBxLvU2\nbtw4SktLm20bM2aMLpkpEsOkSZOYNGlSs20VFRVpqiZntCm/lF0iraP8cpzee4l4QNnlOGWXiAfa\nm10mzs9huxljOgEDW2x+EpgL3GmtnRvjMbrkoogDdLnY9mltfim7RJyj/Go7vfcSSR9lV9spu0TS\npzXZ5drMI2ttNfBt023GmGqgPFYAiIhkCuWXiGQjZZeIZCNll0h28OJqa025M81JRMR9yi8RyUbK\nLhHJRsoukQzj6tXWWrLWHunleCIiTlF+iUg2UnaJSDZSdolkHq9nHomIiIiIiIiISBZR80hERERE\nREREROJS80hEREREREREROJS80jEY9Zavv12PbNnr6WxMZTuckREUrasCr4qh4qGdFciIpK6jUH4\nqgZWKbtEJIvU18Os2TB/QboriVDzSMRDEyfOZvfdH2D48AfZZ5+HGTjwPu6555N0lyUiktCXG+Dw\nt2Hgv2DU69D3Rbh0OlQ2prsyEZH41jfC+YuhzxwYNQ/6fw3Hfgdza9NdmYhIfKEQ3HQr9NsVRh4E\nQ0fCXvvD5H+nty41j0Q8Mn78TP7nf15m4cKN27atXl3Fr389hd///r00ViYiEt+cTfCjd+DDtdu3\n1QTh0e/guHchGE5fbSIi8VSH4Mjv4JlN0BC96LsF3qmEw76DxfVpLU9EJK7Lfwl/uh3Ky7dv+/ob\nOP0ceHly+upS80g6lA3hMEvDIRqt9XTcxsYQN9wwNe7+e+6Zzrp11R5WJCJZJVwFjYsiv3rs5tlQ\nFYy975P1MHm5t/WISPYIE6SW1TSw2fOxJ2yEr+ti79sQhP9bG3ufiAjAikZYnoYZ1vMXwGNPxd5n\nLfz+Jk/LaUbNI+kQvggFOam6koFVFQyr2sLuVRXcXl9LyKMm0kcfLWPt2vjNoYaGEJMnz/OkFhHJ\nIqG1sP4iWNYTVgyBZb0ifw6t82T4YBheWZb4Pi8s9aQUEckiYYIs5nGmcxqfcibTOJH/cjVb+Naz\nGl5M0q96wft+lohkgecrYe8lMGAx7LwYhi+BiVu8G/+lVyJNonjmzYc5X3tXT1OB9Awr4p0vQkGO\nq66k6enta63l1vo6vguFeaK4k+s11NQkb1unch8R6UBCm2H14dA4f/s2WwtVT0L9dOjzKfi7ulpC\nYxiCSXrsNXFmJYlIxzWXW1jHlCZbLJv4gq+Yw748QBf2dL2GmiSn1NbqlFsRaWF8Bfy8xazEbxvg\nf9bAxhD8qpv7NdTUOHMfN2jmkeS8m+pqibcu4nPBBmaE3P/kM3p0HwKBxD9uBx88wPU6RCSLVD7U\nvHHUVON8qPyH6yUUBWDvJG+UDu7pehkikkW28G2LxtF2YepYhPvZBXBQku8Gk+0XkY6lPgzXbYi/\n/w/lUOVB0/mgAxLvLymB4e7332NS80hy2rpwmPeTNIdeaHT/uq19+pQwZsyIuPt/8IMBHHBAP9fr\nEJEsUjUp8f7qJPsd8r8J3qB0yYOxu3pShohkibVxGkdbbeJLT9ZA+kUPKDDx94/r5XoJIpJFptTA\nhlD8/VvC8IYHS9SecBwM3SP+/ksvhs6d3a8jFjWPJKdVk3xNoy0erXv04IMncuyxQ3bYvu++vXnx\nxZ96UoOIZBFbmXh/2JsT8C8cAtfvBb4WH8K6F8BrR0KvIk/KEJEsESLZ+RQ2hfu0326F8OJgKGnx\naScA3NsPTix1vQQRySKVKcwq2uLBzCOfD157CXbfbcd9Pz0Tbv+T+zXEozWPJKf1Nz56GcO6BA2i\nUX5vfgw6d87nrbfOZ/r05bz66nyCwTBHHTWYY48dgjEJvhoTkY4pfzQEl8TfX7CfZ6Xcui9cshs8\nswg2NsCIrnD2ICjWuwgRaaGEPVjNv+Puz6eMAryZ9nNSKazYC57dCAvqoU8enF8W+VVEpKlRhcnv\ns1+B+3UADBkM386Ef78OH0+HwgI48zTYd6Q348ejt32S0/KM4ZK8Am5viH2t1u7GcE5evqc1HXzw\nAK1vJCLJdfkV1PwLYs6gNNDll56WM6gzXL+3p0OKSBbaiWNZxCMEiT07si9n4PPwI0gXP1yutdlE\nJIk98uG4YngrzsTIw4pgZAoNJqf4/XDaKZFbptBpa5LzfldQyE8CO37F1N0YXizqTGfN+hGRTFR0\nGHT/K+BvscMf2V54aDqqEhFJKEAn9ub/CNBlh329+DEDuSANVYmIJPdUb9g3xuyi4fkwqY/39WQa\nzTwSx1RXw4cfQjAIhxwC3bunu6KIgDFMKO7MVcEgLwYbqLSWff0Bzs3LV+NIRLA2TNhOw9pyfGY4\nPl+Mk8zTpctVUHQyVD0JwWUQ2BlKLor8KiIdXhWLqWE5+ZTRlfgX5vBaKXtxMC+xlrepZD5+iunF\njylleLpLE5EMsLYePquAQh8cXgYFGTKlpVcAvtgZXq+OLI5tgWOL4ZTOENDHRnebR8aYy4ErgEHR\nTd8AN1tr33JzXPHe7bfD3f8HFRWRPxcWwiVj4Z57IN/bs8LiOiAQ4ICA+qWSnLKr4wiG3qAheDWW\nRdu2+cyPKch7HJ/JkCsg5g2Ebn9MdxWSBZRdHUcNK/mGO9jMrG3bOjGQoVxDGfumsbLtAnSiH2ek\nuwzJEsqvjqEmBFfNhYmroTF6Vn6PPLhxCPwyQ74X85tIs+iUNF3RLJO53eNbDvwWGB29TQUmG2OG\nuTyueOjOO+H6G7Y3jgDq6uCBv8Nll6evLpF2UHZ1AKHwNOqDZzRrHAGE7bvUNR6NtbVpqkykzZRd\nHUAjlczgV80aRwDVLOUrfkMlC9NUmUi7KL86gHNnwxOrtjeOADY0wq/mwcPL01eXpMbV5pG19nVr\n7VvW2oXR2w1AFXCQm+OKd2pq4K674++fMAEWL/auHhEnKLs6hsbQ7UBjzH3WzicYnuRtQSLtpOzq\nGFbyOnWsi7kvTD1LeNbjikTaT/mV+77aApPXx99/2yIIxb9AtmQAz84uNMb4jDHnAMXAdK/GFXdN\nmwabN8ffHw7D6697V4+I05RducnaIKHwOwnvEwq/5lE1Is5TduWuDXyScP96pnlUiYg7lF+56bUE\njSOAFfWRBpNkLtcXgDHGjCDyQ18IVAKnW2vnuT2ueCMYTO0+GzbCN99BaQmM3NP9ukTaS9mV68LR\nWyJBrK0nbGcA4DOjMSbGJThEMoiyK/dZQkn2R7KtgoUEqaaEQeRT6kVpIu2i/MptqcwqClpYUg1L\na6B/EQzRukMZxYvVg+cB+wBdgTOBCcaYwxQEueHgg6G4OHL6Wjz/mQW/OwTqGyJ/3nM3+PN1cPwR\nnpQo0lbKrhxmTD4+80PC9uO497HWUNMwENj6VVlP8vzXkB/4jSc1irSRsivHlTGazcyOu78zg/kP\nF1PFMgB85NGXIxnOlQQo9qpMkbZQfuWwI8vgT4vi7+8WgBvmwNT1kaucARzRAx7aF4aWeFKiJGGs\n9fbEQmPMFGChtfaKGPtGATMOO+wwSkubf0MyZswYxowZ41GV0hrXXAP3/iX2vrI+sDHGF/WBALzz\nFPzoYHdr6wgmTZrEpEnN12apqKjgww8/BBhtrZ2ZlsJyjLIr9wRDr1MfPJXtb1Ga6kxkqYUd5flv\nJD+gq585QfnlvkTZFd2v/Moy9WzgEy4gSGWMvT6C5MWcV1nG3hzEPRh0ven2UnZ5Q++9cs8PP4dp\ncZY8KQlBZYxrlfQqgJlHQr8id2vrCNqbXeloHr0HLLXWXhxj3yhgxowZMxg1apSndUnbBYNw1VUw\n/jEINZlJfeAh8NkK4q6sdej+8OFznpTY4cycOZPRo0eD3sA4RtmVmxpD42kI/gbYfpK9YTcsy4G6\nOI8qpjh/BcboNBA3KL+clSi7ovuVX1mogrnM4Y/Usnrbtjy64KM7layK+7gDuIOe7O9FiR2Osst5\neu+VezY0wNmzYerG7dvyDOzXCaavif+43+wGd+/lfn0dUWuyy9XT1owxtwFvErn0YglwHnA4cIyb\n44q3AgF4+GG4/np44w1obIQjj4T7n4HPElys6KMvImsh9SjzrlaRVCi7Oo48/yUEfOcQCk/G2nJ8\nvuGEwxtoCJ2b4FE1hMJvE/D/1LM6RVKh7Oo4ShnGD/gn5XxODcvJp4xS9mIqibIL1jBNzSPJSMqv\njqFHPry3X2Rh7I83Q6EPTukJx8RfRQCAl1epeZQJ3F7zaCdgAtAHqABmA8dYa6e6PK6kwYABcNll\n2/+8dY2jRFK5j0gaKLs6EGM6E/Cft+3PYft00sdY6t0sSaStlF0diMFHDw5i65XM69iQ9DFh9MZL\nMpbyqwPZt0vktlV94usAUJfsGifiCVebR9baS9w8vmS2Q/eDp16Kv3/XgdB3p/j7vy+Hhz+HGSuh\ntBDG7A1nDIeA3/laE7G2BmjUKSodiLKrY/P7fgAYYq+FBOCL3ic2azdjG57ABt8CwASOxeRfjDFd\nHa81oXAjhKogUAomzvnDklOUXR1bAd0ppi81CU5bKyP+V/dhQqxhGiv4gCBVlLIrAzmRzvRzo9wE\ndViqCFGEj7x4ax9IzlF+dWyH9oD5sZeaBOCwHokfP30DPLoocqW2/kVwyWA4rJezNaZiSz34DXTK\n935sL3hxtTXpoM49Ff54P6yMc/7qNZeAibNm44tz4LznoaFJF/qVb2H/ATBpDAzx4DNYKDydxuAt\nhOw7gMVn9iHP/78E/Oe7P7iIpI3PDMbvO4NQOHb32+87HZ8ZHHOfDc0nVHMU2JVNtr0DDXfhK5yA\nCRyDiRd8TqlbBd/dCKsnQagGCnrDgEth8O/BH+MKBiKSEwyGwZzF19wfc38hPenLkTH3hajnM/7A\nBmZt27aBWSziFYbxc3bhRPy4+2mokTBPsIoXWct6GinExzF05wr60xtll0guu3oITFgGDTFmGAUM\njNs1/mOvnw23z22+7emlcO7O8MAo6OZBfPzza/i/6TBzdeTrxx8PhhsPgx/u7P7YXlI7X1xTVBi5\notqQgc23BwLw+1/A5efFftzaSjj/heaNo62+WA67PghHvAKfr3W+5q1C4feoazySkH2brbMPwnYW\n9cELaQje7t7AIpIRCgKP4fcdt8N2v+84CgKPxX1cqPbcZo2jbew6wrXHEaoeSrgh+WlxbVa/Bj49\nBFY8Fmkcbd228GaYeQrYJPPCRSSrDeRkhnAuhubTtIvpywHciT9OE2YeTzdrHG1lCfEND/MaFzKH\nCYQJulJ3GMs1LOAhVrCeRgDqCPMq67mQb1irU4VFctqIUnjhACjNa769JAAT94f9usV+3Nurd2wc\nbfXsMuj5IpzzIayqcbbepu6ZDmP+FWkcQeST45RFcOQEeGuhe+Omg2YeSZtZC2+/C/+ZBnkBOO0k\nGDWy+X323A3mvwtvfAAzv4bSEjjrBOjXO/5xH58B9Ynem1TDf1bCjybDR6fDqJ5OPJvm6oPXQJx1\nARpDt5DnH4sxCc65E5GMFuIbGngZSz0BDiSPEzBNvk8xpoTCvNcJhWcSCkdOP/P7jsPvi39FFxv8\nDMJJLrATXkC47gJgC778K514Ks19fyfULo29b8M7sOZl6PMT58cVEU9UU8k3zKCaLXSjB8MYRQGF\nze4zlIsZxCms5j80Uk0pu9GLA5tlXFNhGlnGW3HHNECQCubxIpWs5BCuc/IpAfARm/mI2NfvXkcD\n41nJ9cSe8Skima8uCC8sgTmboCwfzh0CO3dufp9T+sLKXvDCysjpZwOK4af9oCQv5iEBeDBJcybk\ng+eWwBcb4IsToczhWUjlNXDD+7H3NYbh/70N8xLMmso2ah5Jm6xcBSeeBbPmbN92y92RBtKkx6Ew\n+j7m01nw7/chGIIjD4RjfhD/VLWt5q1PMrgFQlBj4MbP4bUT2/NMdhQOz8baOQnu0UAw/AJ5/quc\nHVhEXGcJUsOlNPDPbdvqAR+705mX8bMLAGGWU88/sb6N+H17ks9PMBQlPnZ4fsp1hOtvxORdjDGJ\nj9lqq55Jsn+imkciWWoGHzGVyYTYPoPwff7NyZzPrgwHoJFavmc6W1hNEaUM4UiKifOVfVQ9m2mk\nMuF9THQW9kqmU848ujO0nc+muTeSLPb9JuVqHolkqU/WwncGf/EAACAASURBVOnvwbq67dtumAnX\n7Q23jI78ORSG11fAx2uh0A9nDoR9uic/9rzE0RXpfgOLquDB+XDD3m16CnG9NDfSGItnfjl8sRL2\n93bpONeoeSSEw5bKSktJicHnS20tjtPPbd442uqV12DcdfDn2+Cn/wtvfLh9392Pwb7D4PWHoU+C\n2UK9OsffR0+gK9AJ2AJvLoPKBihx8DR8y8bk97GbnBtQRNouXAmmAExqIVDLn5o1jrYdhgVUcQZd\nmEEdt1HH3dDkA1otv6cTk8jjh/EPbhIEmwVjI79aA5iN2OC7mLyTU6o7ZcEk2dSo7BLJBHWEsUBR\niitILGYeU/jXDtvrqeNlnmQs11LNSj7gARqp3bZ/Bs+zH2MYwfFxj51HZwwBbIxT0kL4qKOQIH58\nWPJoZDkfOd482pLkdLhqQgSxBHB5zTgRSagxDLVB6JLiZ6/yOjhxCmxucUJHyMKts2BIFzi8N5zw\nDsyr2L7/lv/CT3eBpw+D/AQXS+pVAAtiNZAskW8HQ0AYCERmIDndPNpU58x9soXWPOrAtmyx/PrX\nNfTsuZmuXTfTs+dmfv3rGioqEl8L8aNP4IsEZ2Y8+Qz8/MbmjaOtvpoLe50BD74MlXHOPb1g3xgb\ni4AfAqOBIUBvYHcI94XKRviacl5hEVNYTnX0XPm28plhQIL5kYDPxL9aiYi4zFqo/Dus3gNWdoEV\nnWHD2dAY56T3rQ+jhgbGx90fZj61XEcdd9C0cRR5bDlVnEAN1xJmeczHm8DRYPq0HBRfCPwh8IXB\nZ8EfjmwjvAIaFkLFQ5Fb46JUnn1inZNkUxeH3zWJSKtMo4rzWMwI5rIXczmbxbyfZNYPwBf8J+6+\nEEE+4y2mcl+zxhFErqD2ORN5h7tZx3cxHx+giD7seAXJaorZQA+qKKGOYmroxBa6sJn11FLHDP7L\nND5jCcuS1p/MbhQn3L8LRWociaTRwi1w/kdQ8iyU/hOG/Avu/RbC8S5MG/X4dzs2jpr68xw4aUrz\nxtFWzy+GfV6GlxZBMM7H0wsGxdjYCGwCqoE6IiuR1MDKishxJi+A+z+Hl+dDYzuXgtwryRXd/Ab2\ndGGJlXTRzKMOqrracuSRW5gxY/tPzMaNlnvuqeP99xv58MMudOoU+z/paZ8mPnZdA7zwdvz95eVw\n5d1w29Mw5V7Yc1Dz/Xv1hnE/gL9Ma7JxNBBjRlJRn2quDHxJDdsTpxA/FzCUMxmSuNA4jNkJv+9M\nQuEdZycAGAbi9zk8W0BEUrf5Kqh6sMmGRqh9HuregV4fQf6ImA8L8S2WGO9OmmjguQR7g9TzAPX8\ng06MJ5+zmu01JoCv8EHCtWdB9Ft0E47OOGrBWGDd76H+SrYuyg8+KDkXej4KvsIdH5SKgVfB13Gu\ndmz8MODyth1XRNrtDSr4f6yg6WegGdRwKcu4k76cmeD0shUsTnjsNXyFTfDl2QpmsYJZDOXHHMJF\nO+wfxsWUM4f66OzrOgqoomSH+1l8fMk63uMeGpvMFupHH87jp5TRtsvhnkkvJrGGILE/iZ6D1pkU\nSZfvtsAhb8KGJuvWL6qCa76E/26ECQkmZX+S5AJH38Re6mybeRXwk3fhwF7w1vHQtcWaRRcOiiyM\n/cG66IYQsCX2sTZthJ3uh41Neuy9O8GTJ8OxbTwr9rhdYdcyWBjnxJVT94D+Xdp27EykmUcd1COP\n1DdrHDU1c2aIRx6Jf1WL4mRLdORH1jhKKAirNsDp10cmEbR074lwy3GRs1HoSczGkTEhRu81nZqC\n5h8G6wjxCN8wlRVJioivIPAAPrN/jD29KMj7F8YkmD8pIu5pmN2icdSE3QwVv4v7UJPkm20Ay7qk\n94FGqrmEUIwPc7680/AVvYM1RVgbu3EEQDWY+s3Q7INSGConwvp2LKQ9YGzsBpHxw4jxUDK87ccW\nkTYLYrmVNcT68twCd7CWuph7I/JIdo5IapcSmse7fBdjFlMnenMo95PPIMIYqukU8/FbKGED3Zo1\njgBWsprHebrZekytMZAi/sSQmLOLTqUnZ6l5JJI2N3zVvHHU1NOL4JMEb52KkkxVSTqfMHqHz9bB\nL6ftuDvfD28eBmf0JtI4ivcRNgRUN28cAayphtNehG+Srbkbh8/Ayz+FPjE+q+7bG/5xUtuOm6nU\nPOqgJk5MfMnTRPtPOwn8CXonPVJY3GyrBcthyhex9y0yYAdAdP3aHfTuuYriovhvlp6PMz07FcZ0\nozDvYwoCz+H3jcHvO4P8wP0U58/H7xuZ/AAi4o6aiYn3170JofKYu/zsiY89kgyQ6oTcRup5LOYe\na1YS9tdifXHeFIWIdzHHiMoJEFyVYh0xjHgIDpoeaSLtdDoMvg4O+w76/6ztxxSRdvmEatYlWNdn\nMyE+oCru/j1IfMppJ1L/avtbpsTcbvGzmhrK6U4wzun7mxPMLNrARr4m8enDiZxADyYzkkvox5GU\ncSa9eILh3MQQjE5ZE0mLmiC8HPts/W0mJjjr/sxBiR87tDT1Wp5fBOtrd9xe6Id5q4DNQIz9QPym\nEpEFr++L83k0FSN6wfwr4e/Hw0+GwZgR8NyZ8NlY6JH8e8usouZRB7VxY+ITVBPt33kAXPnz+I+9\n8zro3SNJAU2mHP70LrjhWdjU4j3TB6sTH6J7t8Qt4sVUsom2r1BmTICA/ycU5k2kMC9ydTVjcmje\noUg2Cidb0D4MNv6paUX8iXjfc+VzHnmcknIp9fyVai4lxLzmFYQ+iPwm3medYLJv2oJQ+0HKdcTU\n7aBIE2nUv2CP26E4ThdeRDxRkcKMnM0JmksHcCRFcWYDdacXwzgy5VrKWcw73MZK/tts+xrmY7fN\nftrxfWAQP41JZkB9x/cp1xFLXwq4kgHcw+7cwGBGxjh1TkS8U9UYWSQ7kU0JvhA7dWc4JM66QMUB\nuH2/JO+JmkRRQxgOegn+Pidydbat1tXAt8muB5J4TX6mJD4zOKmSAvjF/vDCWfDsGfDT4ZCXgyeq\nqHnUAdXXQ7duiV/Ne+2VeP99d8EtN0DPJk2iXQfDM+Nh7AVwy68SPLiIZq+8ilq47UU49PrmDaS8\nrfeJ80Wctcm/hfI79RJf9Tl8+xysiDFfUkQ8E/YnWQvIVwb++NdDzecUOjEJH8O2bTN0o5DfUMxD\nFPE7Yp4nG1OQBiayhcMJ0uQrKxP5xt6aWB+/UuXQkoRbFsP3L8CyNyCYQ5f7EMkyBTUFSe+zB/Hz\nrStlnMcvGcTubP2o5cPPUEZyLlcxjB/Rjf4pVmNZzWze5Q7m8ta2rT4i7/0MYNqYXj6H3ndVhC2v\n1AV5qS7IumQr8oqIa0wIuiRpgoxIsNRZwAdvHQtjd4eiJsc5uBe8dxycNjCyLyYLLc/mXbQFrvoI\nzn5n+2LdAQdix4ljQGTplncXwPP/hW/XOHPMTKIFszuY9evhqB/DnNmFkGBhxSuvTPwmxxi44Vr4\nzdXwzVzIy4MRe0a2A1zyEyjIh5sfhIVbL8JhiDSOWq6ZFP0S65vlcOe/4K4LIn8+dSD83xwip3dU\nQssvn9aX70S/3vHnUQ6jG12SrhGQxNpZ8NqFsG7W9m3dh8IJj0H/Q9p3bBFJmbVhgg0/I+x/mnyT\nYC2hTmOji6XFl88p5HMKIeZiqcXPMEw0mPyMoIQ3qeV3BEm1WVxJDePowseRY/hPJRx8GAyEAhBo\n+W1XXuT9UNz2tymC4h+nOHYc9Zvgg7GwdDLY6Duvwu6w/62wpxbNFvHSo0vh8lmF9D6kmKIesU+3\nH04h+yZZl60HO3EOV7CFTVRTSSllFDdpdh/PDXzKBBbzaZMZRDtq2hj6konswiEU0oV+7EWAAoLU\nY7DYFkkVIEQBddQnaHINS3pqcGLWWm6sbuT+mkaqo2XmAxcVBbivJJ98o9PXRLwyYzkc+whs6Qz0\niX2fQj+M3S3xcUryYPwP4c/7w8JKKMuHwU1O5nj4EOhbDH/7tskspq2No6bv95r8/qVFMHkxnD4Y\nygrh0D7wUaKzVvJIeOraybsmfg6peGkWXP1K5KpuW/1oV5hwLvRv27UEMo5mHnUwl10Oc+YQ/WY8\n9srXN91UxLHHptZ0KSiAUSNhr+HbG0db/c8psOBNePBm8JcBZUAxzT8xdaLZq/DJ97f//ld7QmlB\nNCXWErnkYpNZ3+s292ZLbezTyHzAecRrY6eociVMOqp54wigfB48dxyUL2jf8UUkZeHgQ4RDT4MP\nGjvHmdFTeAyU3pzyMf0MI8CobY2jrQKMpoQplDAVSHYObkSImYT4FgDjOxbji1x6JByAYF5kFtJW\n1kezU3d3UHpVNDTbyFp462RY8vL2xhFAXTl8dAUsSLJulIg45pstcPmsyGegtTP701C14/urfuTx\nVwakfMwudKMPOzdrHAEUUsIRXMnZ/I0eca84azFNGkthGlkcbZTnU8wITgAib9V8LT65WaCELcSb\nU9mfvuxBkk+RSdxU3cjt1dsbRxD5DvEftUGu2JJosTgRcVIwBGc8CeXVRD6HxVgRoMAH/zwUeie7\nmFJU1wLYr0fzxhGA3wd/GgWrzoErdidyilmIHRtHLXriTzZZNeCP+ydpbCSYPdW1EK6OdZ2kVnhv\nAZz9dPPGEcD7C+Goh6Au/pyNrKLmUQeyfDlMntxkgykCuhD5FJMHFHD//V344x9TTIAUGANX/ASe\n/CN0bhoUfiKNpBYfoNZVbL/6Wv9OMOkYoEt0QzmwBNhkI9v6GGasPYh+jTs1eyH3oJDfMZr9k1yZ\nw9oQYbuEsI0zp3DGA1Abe+FdGirhi78kPL6IOCcUfGDb720+NHSDYBGE8iCUD6Gup0KPN8G08RL3\nMQQ4iBKmEGbItvcvYQy1FFBLwQ4fn8JEssQYQ17B6/hCncBC2A+N+dAYgLCJ9s+LwXbaE0yTmQam\nM3S7Drrfmby4utVQs6R5c2irle/BmgSzpmbeEvsylyLiuIeWbP+8E6rLY8UHQ1j3VV+qVnWhalUX\n8uf14U12ZWB7Z0o3UUxXTuAGytiHUPQdUuQKakVsopRwi7f/NWxfLGRfzqQLuxGOLlHtJ4whRBA/\n1XTCB/QkSJcm08ENhj0ZysWcjy/Jim5bCLKc+phXlqsMW+6rif8Ja0JdkKWhJIuviIgj/v0NLGu6\njtBiYCGwEdgMZi18cnRkTSOnFAbgwR/CNXs0mbVtiVxMcj07zBxa3WQi51H9YdwImjeYLJFGVFX0\nsT7Ys8V3giN3gvfOhUFJZgbVNcKiDbApzrWabnu3+TpMTS1YD//8KvHxs4VOW+tA5s2DcMsXtQnQ\n9GVQk9qVXltlSw387lmo8gOlQCHbe1ZhIoFQDVjYtU/zGUzH9zQccYjlg3Ib+aEvgKbrRRZTwN/8\nB1BJDYvYQjF57EV3/AnevFhrCYbupzF0P5bIOXU+czD5gT/h9x21/Y7fv5H4iX3/eup/CSLSZtaG\nsLb5otT4INS07+Krxm+c/z6knLuooZxIeG09hSOSL43k0Yka/IQBg6/JN/3GdCEQ+B229g+RmUY2\ncqrdtmQyQI8HwTcS6j6KbCg6FHxJFuVf/zZ8dyNUfB75c9EusMs1MPDK7fdZliS7KhbAloVQ2r4Z\nAiKS3NeVzf9swz4ql3ejcnk3ANYBxUOdH/crPudr1gG9ojONDL5oy3sdvShjIwXRyz52aXI+isFw\nCBfwT/5MILrCbJAATaeNH8RBHMQJLGYp9dTTh96UJbgKG8BS6rmXlbxPBUGgMz5OoztX04dO0SkB\nHzaGqErQ1w4Db9aHuLxY332LuO3rWN+tV7FtLVoLVGyBJN/Vt9pXq+Bv70ZmPgGRGUghIgGwGegG\ndAUM7N7iSm23HAyPfwWbaiP7W572dkh/mHY+fLUGllTAzl1gdJzT8baqrocbXocnPous0+v3wckj\n4K5TYPfoQuC1DZEZRom88f/ZO+/wKKr1j39mtqYXIAkhQOi9N5EiRRAQ6YhIuSr3Wn5i7xevIvfa\nu9gV7A0BEcRC76L03iEBAgTS+9b5/TEp22Z2gWwIMJ/n2cdkzpkzZzH77jnf85Z9cFvXQP4Fqjea\neHQFc/wkrFwHogg39IXYAKIgAulzvnyxAtLKHHgigRoeHYzIgtA5uGuA9/0f1oTrbJDuUajEAMyu\nBWGiQBhhJChUIfHE6ngEu+Ntt2tO6U9KbEMw6Reg1w2WL/o60XfFX7uGhsaF4cyHkt/AWQDGrgjG\n1sjijXIVNUGofONl5QBF5clkK0Sj8mmiJ58IwinATH901HcfwPwIgu0PBPs678FNDyAYrpN/Dhsa\n2ITSf4ato3A7Vis+BnunQslJaPaifC0Q26TZLw2NSsfphKVb4GQGJMdDvw5Qw49DUWzlORxVzAMH\nG6jIAyDimQBbJIuaRJBLLNAA9xyOiTSkE9ezheVeY9emAV0ZgA6RxgRWxTENCxM5SKZLuaMCnHzN\nOfZSxGc0weAWTKeM5jOpoREctqXA1lSIDoXBbaFGANuq2CCUoX9tLVjLQtZsuHsSOZEjUUqABLi7\ntfu9IQb4fAiM/bl0DBdqhcLHN8g/d0iQX/6wO2DIh7DGpYikwwkLdsL6o7DxYWhYMzC7dKU4TQZV\nPBIE4SlgJNAcKAY2AE9IkqQliwkixcVw16Pw7TxwlH5wjEa4azI0by57IPnCbIYxYyp/PkvK3PT0\nyHmPfGGAeo3gAR97qGZGga11JGbmwU+FYJHgOjM8GAXtTYEnTrSTS470GWbHOwp+SXasjicrxKPk\nAXBut/KADQYG/GyNywvNdl1C8t+A3OkguRzXm/ojRozCKX2meJuon1TpUylmTQC9BIqIIpZ3vFuE\nEKSIpWCZBZYvQEoHsTmY70Ewjgh8IpINsn+C3XfjFfBfxrHXoP59YE6EpAGw+23f/QAiGmheR1co\nmu26dKzcDre/BqnpFdcaJcI/p8B8lfsmBVog7Tw4Rzr5pWK7iKToi51PJP0Yhd5HErbrGEUSTdjB\nGrI4QwjhtKQbrbkWw3mE2G0nn/9ywk04cmUrhSwhmxuJpadBRwjyH64vBOB64xVY+1oD0OzXpeJk\nFox/H9a5/CtHh8K/h4FJDxaFEvdta0M75eK2F8ySQ6U/OFFc8lAIN8VCTx9eQ8OawKbJ8NZmWHUc\nDDoY0QTu6whJfpy7XTl2Fp76yV04cuVcAbywBD69FUKNcG0ybEhRHm/gxdUSqDYE2/OoFzAT2Fz6\nrBeBJYIgtJAkSem7QeMi+edDsnDkitUKMz+FMTfCsWNg8ZFt/sUXguN5VB6GFo5KeSE4ZwebU/Yo\n8iRRL/BiLLzoMT87Dg5wGhsOGhJHpEIS8Gx+4zhPE+U4SYiKPixJu3E6dyOKraHzfbDjUzm/kSd6\nM3R9WPnNaFzuaLbrUlAwG3Ie8b5uWY7e2QZrZD3guFezqBuOKA4JwoQCE6edOLGSQgjegf+CYAbz\nvfLLA4fzbyTpDKLQBFFs4Xvw4r1w+EYoTAG1XLGSHc7MheT7od5gqNkBMhQC7Ns/AUEI8dOoFmi2\n6xKwLxWG/geKStyvHzkFL74Ofe+BlT4+vw1C4clKqPDjiVBuuyQPjyPvnunkoWB9aEQbGtHG6/pp\nCjhOHhEYaUENl+dVUIiDRznIRnKxYETNnv5KDjcSS4wocFeonreKfO9WR5t0NKmsetoa1RHNflUx\nNjsMeBn2e1QpyymCx7+HiX3gax/n6CY9vD0yOHMq3zc6VLuRnq7c1jYOZvtYFmbnw4Z9oNdBr1YQ\nqpAm86nv4ZVF4AxHtcDJ91tl8Qjgqf4wbLbvlJL1YmBiJ+VxLieCKh5JkuT2v00QhNuQw7s7AT78\n+DUulqMp8J3KEdfiFbBwEbzzNvz2m+xi3bUrPP4YjB4dnDkN6QSL/sbvX1uxTVZx6wcoYK1gDz/x\nNwWl2dP0iHSnKRPpidE1jxP7SeEJwF5aOUQdiVKxKLoBjPsNFk6E3JSKDuGJcONsqNXa5/0alz+a\n7boESBLkv6DYLNh2YeRL7Pr1OO3fAAUg1EOnvwed/lGEIIghofQlC4FAHJLtpAU8rsO5Dov9TiTp\nQPk1UeiNyTALUWhY0dFphcODwXo8MJ9oe578X0GEwb/Cslvg9OqKdn0odJgGLe8KeK4alxea7bo0\nvDHPWzgqI68I2h2D6/vDh6lwohgi9DAxCZ5pCvGVl+O/nFrEE0UMuaUWTI08sv30qCCLYt5mE9tJ\nLzdJCYRxJx3o7FHH+3mOslEl1NiVQpdd4svhRiwSfFJsL/dVEoAxJh2zo9TKVGpc7mj2q+qZt9lb\nOHJl11H4YTK8uhI2nwBRgBtbwtPXQ9f6yvddDEOawRdb8bvuOR646cJmh8dmwUe/QUmpkB8dDo+P\nhqfGufedvQpeWlj6ix8DWmiVw9F0IgxtBZ+MhUcXQY6L1Nm+DsyZDGFXiPmq6pxH0ch/CllV/Nyr\nhqWr1YvoFBdDiR1+WSR7IzkcEFJ5xdV8MrEPvDIfjvnwdnIl1Ai1wtX7lDGXDSxmp9s1O07Wsp8C\nSrifQeXXM/gGSpcgFsHPJ9cpIAouZ3AWILwP5O2EkFDoOAp63Aeili7sKkOzXcHGfhjsCr7BpQiW\nzRhCP0QyvAeUIAiB5Tm7UAw0IoybKGSh3756Aos9sTtWYLEPwvNIzSmtocTanxDjVgRBTqRLzjxZ\nOJIf4J8Ql9LctmKo0Q1KLLIIVacXdH4GQoLgXqpRndFsVxXwx2b19qVbYfc98O+mUGiHEJ28CQsW\nAiI96M+v/Fie5l+JKMV8Au4UYeM+lpLvUe7oDIW8wHr+Rx9aIpcxOouVJVRUq3VKIqKgvDg1S8by\nSRY6BZraTPQsMZLhlGgVIvFEjEA7k+ZxdBWi2a8g88cu9fYdx+G6BnBzezkptE4EY5C3QI/2hDm7\n5OepCUj1YgIfc+C/YZWHB1VOAfz7C/lnVwHpDdeaI368n2qGyf8mIItI0SboWw+OZEDtaPhXDxjd\nPvB5Xg5U2Q5YEAQBeAtYJ0nS3qp67tWGEMBipKyPMQhJGn0RHgIr/gfd3oWzKodQ4zvKApI/DnGS\nX9mB0nJoGymkkkH90kVMIdvL2+JPZCPUlJAMvu/Vn3MiRB+EyK4w50FY6ZE3ZP86yM2FodP9T1Tj\nikCzXVVFIDspuY8g6CDABPkXS03eIpdinKzCiO8S0nrqY6an37GcUiYljlEICqsRiePYHbMx6EtD\n9wr+rGhU8GqoGBzIS4E6wKG58McEWTQq4+xWyNgLNy2Uw241rng021V1+Ft7uTaHVdHKuyPXcIZC\nVrKBGop7b4G2dAtovCdZ5yUclWFHYg77mE4vAPZQUG7lbOgpJJQICn3eK0mQJplAgAMW6J8KaXZ5\nbiCwsxjW58OK+tCoitatGpcezX5VDQGtvEo7hVTR5691Asy9GUY+A1YV76Z/Bma6+O9XsGoXim/2\nlXnwwHA5hC2/GPacdGm0IVcJV7g3vwiKrHLzje/DSpe8UTvTYNUB0E+B4e0Cm+vlQFW6T7wPtAR6\n+Ov40EMPERXlXntv/PjxjB8/PkhTu3IY2EeuruZUiM4KC4Xe3at0SgD8cRrOlnkV+RCQmtSCF28K\nbKw5rFZJ/yiznZRy8UgszYNkLikhsqQIZzqUJICkdx9DVyhhTJXAdAgOH/cWjspY/Bw07gXN+wc2\n4SDz3Xff8d1337ldy80NzFVcIyA021UV6BuBvinYVfJimgdX3XxKKeI0qRzHRBy1OY3OK/TVTC3e\n8pnzwxOr9L57InAf2J2/YKBUPBJLy5hIoLDvqmi3AIWHoPAMLJnoLhyVcWIp/P1fuPZ5v3OtKjT7\nFVQCtl2g2a+LYXAX+GixSvslKM/swMliCsigHqEUEeJDge7HMGJK10pq7CKTI2Shlqp6G2ew4cSA\niJkKL6ECwrEKZopxeM1BAvKkCE6U/j4+rUw4cue4DSakwcbAirtVCZrtCjra2qsKGNwOPlur3N4p\nGeLOI8l0ZfHjN2Ddh6xU+EjKPbw13BGAeFRUAi/+gKpKllMAa/fADZ1kryqdWFoZTUA+mCtEPq/0\nHMMKFhFO5cBH69yFozIsdhg/G1L/B7Ui/M+3KrhY21Ul4pEgCO8CQ4BekiSpRFbKvPnmm3Ts2DH4\nE7uMOXIS3p0HK7bISb9u6gH3jILkejBpLHzxg+/7pk6BqEtgBN7aVPpDOHJG7AJkNVcEQuTQtkA+\nVDkUcIJzyDKwMg6XDV40AyliN9H58qZNtEHISQl7mITTLIAT9EUSupLS+RjjYbVy7hUAVr9fbcQj\nX1+QW7dupVOnKyQz2yVEs11BwJoLBz+BlLlgL4S47tDiPohpA5FPQ9Zk3/cZu4K56iscnuAnJOyU\nYOYESUSTSyhFABQRikAvGgR4cm+Xfgygl4t3U8xYSH9ZvqSe81a2XaYE2DsLHCoxwrs/hm7TQeer\nNEHVo9mv4HC+tgs0++UPp1Nizhwrs2dbOHVKomFDkTvvNDF0qJGHRsM3K6DAR0rf6HCYOrzq57uJ\nk6RTAOjZRwtqcY4aZKLDQRGh5JJIuwA8JgFWB5DTTQKcpYaqE5HEoCcLO8WlB3hFhFGCGTMlCEg4\n0GHBhFMQiZNENhbBNhUPy7+KYUsxdApyqoVA0WxX8NDWXpXPn8fgvbWwPQ1iQmBCZ/hHVxjZCVon\nwe6Tvu+bNqxq5wlwNhO+LRPjdwHngLpACLIXdho8eEtFuJgaf2yCYgu+qzG5YC91lTQZ4KaOsGAz\nFWKRHcgDjMhrLQm5gIkT9JEQboZZG5THLrbBZ3/C49WkSPfF2q6gi0elBmA4cJ0kSd5lcjTOm1Vb\nYehjUOiySNl6AD76GVbOhI9eB4NBFpBspfuQkBBZOHrh6aqfb04J7Hf1mDbhlbl+Z0ZgY1mwlSa9\nVo/ib+kiU9dgLBn8iChVpOUXJDAUAAUeOzJjAkT3gzMT1SdyZl/FzxuXwLwPIXU/xMTBjf+AIRNB\nXz02ZxoXhma7gkDRGfj9OshzOZ7J2Q2HPoPeX0ODjNe+DQAAIABJREFUSeDMg7z/gLMsE6IA5iEQ\n+0VgcbmVTC57yn+2YyDD45ReX35m7h+JAgRBUE1MpxP7VfwS1kkWkM4EIDoJQPJtsOE59X4lGfIr\nrDZk7IPNM+HEGtCboMkI6Hg3hNYK6P1oVE8021X5OBwS48YVMG9ehbi7Z4+DRYts3HuviXffDeO3\nF+D2V+HwqYr7WtSDLx+HenFVP+dDVCysnOhIJ4F0Etz6pJFHwwByHhVj9+vx3YgYTKW+SUZE7qEu\nz3MM17WaEx1FPkKObxFC2esnLybAPossHmVa4cOT8NNZKHFAzxi4rx60CjBvpkb1RbNflc87q+HB\n+e5Lj3VH4bO/YNm9sORxmPQhLHcJDqwZAa+Mg5Gdq36+W/eC1TVLwJnSlwubd0OfADw684vBX60k\nox66u6S7fXYULN0l56crp8zD24Ph7cBig+wi9WfsK52/3QHf/AWfb4D0PGgaD3f1hsHeRS2rLUEV\njwRBeB8YDwwDCgVBiC9typUkyV8Gh6sOmx0KSiAqVA49U+pz63R34aiMM5kw5UVY/xF88ib890lY\ntUFWZvv3htjzSCxWmZj1oBPAoXJyHhZgHG0NIokgBDs2bPi+KY4ImruIR3qiaMpXZIVMAX5RHtwJ\nNPxQrlQUXgvyVGpAhpduIN+fBp+5eCkd2wdbV8Mf38Kbv4DxCkmtf5Wh2a7zxOmEglwICZeVayX+\nftBdOCpDssP6OyBxIETcC2F3gGUJOAvA2AUMTYM3dz/oUD/m9tfu3rcjdvEkosOhsA0zotd5VEJr\n8A2I8ZD7rvrgSZMhoimE+BF+RCMYI+HwrzB/lLuX0pmtsP1jmLAaYhoqj6FRbdFs1/mTm1uCwaAj\nNFTZds2ebXETjlx57z0LQ4YYGDLEyMHPYc1OOHEOGiRAj0tYlNUUwBI/kD4ATYlmGTp0KNkuuJkW\nbr+PJR4TIg+ST6HKc+pKeiYIYSwJYCo19ZBaDL03wXGXv+Y9hfBZGsxpB8MvgVCnUTlo9uv8KLaD\n1QlRKnuoQ2e9haMy/k6F6b/B6yNh2ZOwNw22pUJUCAxoLXvhXArCAlhWhYUGNlbnpsjCjwOU4m7H\n9oRYl+iX9smwYhqMfgdO5iiPbTTCKyMhOhT0IthVRKqa4fIefth78LtL4u59p+Hn7fDoQHh1bGDv\n6VIT7NIFdwORwCrglMvr5iA/97IiLQumfAzR/4LYOyFpKjw3D6w+4r5/WQ+nVbx0NuyCPUflnxPi\n4ZaRMHb4pROOQBaPhjZW7zO2WWBj6dHRi7bosaP3EcthAB7DO3mSgTjiwxcgGRt5tZUTeTvUKPUt\n7zZJfSLdJsOO9e7CkSt/L4Nv38SZlUXhq6+S1acPWb17UzBjBo50FVFKo7qg2a5AsFnhoxlwQxJc\nFwu9o2H6FEj34f9ckgHH5yuPZS+Co1/LP4shEDIcwiZcUuEIIJ4+F9XuilGcCoKAJIpeUWgSYNC/\niyh4BPcLBkieCUm3Kw8c0gQ6lZYMaa4Q9ldG41GACIsm+g5vyz8Jv98NDhts+w5mDYWZ18Lcu+HU\nTu/+GtUNzXYFyHff7aJDh4+Ijn6Z8PAXuOGGr1m/3rejw8cfq7vFlLULAlzXDiZef2mFI4DuqNfR\nrk80dQgsj8H11CUcIzYMOD3kIwnoQhLdfSQmGUYtXife63oZRgnmC3GYBIEbwiFOJalSoh6uD4N7\n97kLR2VYJZi8GwrssO4sTNoA1y6BMWthcZp6JWKNaoNmvwJgcyYMXQXhP0L0XGi9GD5TKFY7a6P6\n3/5nf1WEbLWsAxOuhaEdLp1wBHBtB6ijbDYw6GFEgJlDWibDgE7I4f+etUokSIyGzx72vq9rY1j3\njHqS8PcnQ8Oastg2rK36PCZ3g3dXugtHrry2RE6ufTQDHpsPPV+HAe/AR2vlhNzViaCKR5IkiZIk\n6Xy8vgzmcy8nTmXDtdNh9iooKl2bnM6B6fNgxOulCbtcOOo/7JxjAWU3qFqm94AwBUPUpx4MUdF0\nPBlMdzrRFCM2QijGiAUDVmKBaYygptJiSNAhJP0BRh+b0chJUOfjit97/x/UU4j9bHKdLC799Inq\nPJ1fvU5GUhIFjz+ObfVqbGvXUvjss2S2aoVt27bA3qzGJUGzXQHgcMBDI+DDZyGj1OiUFMHPs+G2\na+HsKff+hSfB6fvkvpz8o8GZ60WQyBDCSPbZZiSW+twS8Fh6oQ8m4XUk0YBTp8MpijhFEYdowKD/\nEKNuivLNLd+DOB/JByI7wDWrKn6P6wht/s/3GKHx0P152D8XSrJ99wFIWQYv1IVvboV9iyH1T9j4\nEbzZAf6aFdB71bg0aLYrMF55ZT233jqf7dvlWAJJgiVLjtCv35csWeK9Czt6VD3uwV/7paAuUfTF\ntwehiMAEAq8fHYaBGXQjHBM2DFgxYEeHDT09aMg0rlG8dyRhPEmUl+9RLCI/CHHUF+QWowAzE3w7\nB+iBdxPgjAV+UzlAzbND55XQaxl8nQJ/ZsC8EzB0NdzmZxOtcenR7Jd/1p2V/74XnwJn6d/znly4\n4y94xsf5zlE/aUGyi/yHXFU1Oh28+JBy+0P/gNrnEV3/9b+hQ2NkAclS+l8btKwNW9+VxShf1K8J\nCx6QPYtcMejgtfEwpXfFtZdGQC2FsNkH+kKbOvDxGvV53v01NHkWXlsG64/Asv1w93dwzSuQURDY\ne60KqrLamoYPXvwZjit8sH/bAQu3wMguFdfqBPBhqeO/cEaV0z4eVo6Hx1bC6tIUIeFGGNDNQXRL\nO+NyJdrpRaaE6KntJwOaDpEpDOV6zrCFA5RgJZkEOtMco7+MaMZG0GAvFCyG4g2yh0PEGDC1cu9n\nDocHV8AfL8GGWZB/FqLrQM87YcBjYDDBqWOqjxJyM5B8hBdKmZnkjhtHjQMH5PwnGhqXI2sWwfrf\nfLedOQGzX4AnXUKtQhLkkFBJZZMVmlS5c6wE9ITSmXc4yLukswonVkAknM7YackafiSUaJrTi5rU\n8zueSZyKQRqOTfoKJycQScYgTEIUEtVv1IVAp58hdwuk/wySDWL7Qs0B3rmg+r4HtdrDjncgczcY\nwqDpeOjyNETWh9yv/cxSgkIfHpKSE+bdBY37Qg0trE3j8uTcuUKeeWalzzar1cFDD/3Bnj3uAmyd\nOiJZWZ7H1hUkJQXbkf/CuJtu1CSMPzhIXmnCjkSpJpG05j0pBDNZDBNCGIAZ0c96pBWxfMUAVnCS\nw+QShp4+JNGYKNX7AB4iilsIYz5FZOGgKQaGEUqIxxn2zVEQp4eXMmBpaYXJG8LhyRrQOwzWZ/tN\nX8IBhcqUXx6DPnFw+3kcVmpoVDce2irn+fLFC3vgzsaQ5CJ21IlWHy/cJHvOVDcmDZO9n6a/B/tK\nzxVr15To36qIk1uLGDdOom9fMxMnhhMerm5/42Jg84eweCP8XlrAaVAXuPEa5TQxZQxsAyffhu83\nwoHTEB8FE7pDgse/a5M42Pg4PP8bfL9F9hZqW0cWju64Vu5zzI+QdyAdn8rMrlPw4I/wtYoDelUi\nSNVIhhcEoSOwZcuWLVdN1vzYf0G2SgnmUV1gnov6WmKBOsMhK893//ZNYNsXlTvH8+WcFc5aIckE\nUT60nJN5kFEi8bzewnybuwU0A99FmRhmrma6psPmXZ3o6QlybiOlW6yQoRLlEb10Kabrr6+kCbrj\nkjW/kyRJW4PyEI1yrkbbxWNjYdlc5fbwKFjrESy+fBicWOS7v2iAsScgRMVXOcjYsJBHJmbCCPOx\nIbKRTwnpHGEvf7EAySP4rD1DuIZqFrTutIPoYU93zIZfVbycALJR3qX1exKGvFgZs/OJZr+qlqvN\nfn3wwSb+7/9+Ve2zZcuddOxYu/z3t98u4cEHlY/nf/wxnDFjAkzeGAQcksQhG+gFaGzwFoFsODhN\nPvskiXulYnI8bFcPjHwr1CBMqD4imEMqLSTp8nZSiqGBSllxQK7mq5Adp0ss/D2okiboA812VS1X\nm+06mAfNVFK3ArzSHh5rWfH77lPQ5iXl/nf3gA/GVc78LpTUVDuFhU4aNTJgMnnbr4MpcDbdwdS7\n0tmxwz2Gq04dHUuXxtOixaWzv76wO+Rq6K40/jccOadyk4CiW49RD6degBpBKgpwPrar+nxLXIVI\nEuT4cRX0FJbMJvj0Kd8udlHh8MmTlTe/8+VQIQzbBgmroPUGSFgNd+yGLI9IlaRI+CPM5iUcgfx9\nPz7XwmnPeD0fpJPNSraygq2cIbNy3oQSvspaD1fffBX7UZgdB30kDtbQuFzIy1JvL8yTE2m70uVN\nCKnto7MAXd++ZMKRDQur+I5PeIyveY5PeYL5vMlZ3POfGIigCJGNPoQjgO38ylE2+32elTxOsJhj\n/EAmW3yOVWl4CkcAzceCMcL7ehk21I/3z2m2S+PyJSvLh0uwB9nZ7n3uvttE376+V/U332xk1KhL\nlyBkZq5EwxPQ4iQ0OQEtT0j8UOCZD1JHnBTFg1KJl3AEsB4r0yWFU0kXbJLEz3YLb9uKmGu3UBLE\nA2id4C4cASSHQH+14nAKFZHKOJhfGTPT0Lg0ZAWQ+ybbo0/rRHj6Bt99m8XBjCEXP68LZfnyYrp1\nO0Vy8klatTpFUtIJnn02G7vd3a40TYbXX8r0Eo4A0tIcjBp1jkCcYdats/L664V8+GER6enKnqSV\ngadwBDClp5+bVFQZqx1S/Sy7q4pq5t5xdSEI0DoJdqlUem7rIwpi5HXw58fwxvewfLMsJN3UAx4e\nD40vUdTH8WLouUn2OCqjxAmfnYKt+bChK4SWfpCcksQHRT6ygZfdB8wqtnNPuMB8MjmGhRroGU4s\nBixsIJV97CaTirCKeUB7GjOZwZj8ha5VFq26wZDJ8Kt3KLatUK5KroaYkKDannfyJH/NnMmhX37B\nabfToH9/uj3wADWbBZhdXEMjmDRpC3+vUG5v1MrbHziyEdy0Gfa+BSk/ykmya10DLR+C2n2COl0l\nnDj5mXdJw1UQkTjBfubxOmN5nJouiWD3sBzPRP2u7GIZ9WnLMf4knX3o0FOXLsRSlxOsJYN15LMd\niQobGE4yHZhBGHWD8A59oDdD35dhyX0geSygnICKNywAEeq2C0sRrJgFa7+G/Eyo1wYGTYU2AWa4\n1NAIIm3bqovUer1IixbuOQJMJoHffovgo48szJ5tIS3NSaNGInfeaea224yInipHFfFslsQMDwfP\nfTa45SwUSRK3R1TM62eKOaeiCs+hiGekSLZiZbFUggWJawQjg6QQfndaWWq38rvTRr6L/YtB4D1j\nODfpq66y7PSGsDMfznmm0JOQvY5U9pAJAYTnLNgHH22CQ1lQOxxu6wCT28t5TjQ0LiVNI8CsUw5b\nA2jrI0ztvzdCl3owcw3sSIOYUJjQCe67Tv75UrB8eTGDBqVjd9kOZmQ4mTEjl6NH7Xz1VYUNPn7c\nzsKFyt4W+/fbWLq0hHr1dHz+eQHp6U6aNtVz223h7N5tY9GiYubNs3PqVIVxuP/+fB59NJQXXlA5\nSKtk/tEdftoGm1J8NAqoikeCAHF+prrtJLyzFtanyMWqRreFe3vIld4qE008usRMHQh3KeQf1Ylw\nt8Jau1Nz+GZ60KZ13rya4i4cubIjH746BXeV7ouyJTjhVFeI1wo5zOUUVpdVwCzOEkMWTTlIKN4n\nh9s5jI4l3MGNF/o2AuNkCrzxb/hjnlxtKiocasXIlYti4yk+mEHRodOqqV2EWrUw3ag8z/SdO/mi\nXz+KMys8qjIPHmTHF18wftEiGvTrV4lvSEPjAhhzN/zwLm7f/K6Mm+r7emgidH5FflUDjrHTQziq\nwEoJf7OYIdxZfi0TFbUfyCKFn3iIQipcDw+wFBEnYRQQ6iOeooAUNvEYvfgCHUHchNlLYN1zsP0T\nKM6UvZIi6snXDSGgi4Uj2/wnFel8m3JbcT7M6A9HNlVcSz8CmxbALf+DUdMq451oaFwwQ4Y0oWHD\nGI4e9Z00fuTI5iQmeq/STSaB++83c//95mBPMSDOOSRezlVun5YFE8MlDKW5jHZL6gULCpEYI2Ww\nhYp+30hFCFIOFpsBSfLe2WQj8Q9rPitEHe19eTlWIrNS4bUjsL80cWydcHCKgAANTbD+OKB8LgnA\nbQ3U26f+Au/9XfH7kSxYdxx+3AMLb5VDRzQ0LhWxJhhfHz5TqC1SOwRGKZxBDWsjv6oLTz6Zrbh8\n/PrrQh59NIp27eRQtN27rV6O7J68/HIuK1a4r6+mTcspTZJvwlOZsdngxReLiIsTefDBsAt7EwGy\n/iA8Mx9W7JV/rxkFJhPYJbla298n5DBdNfo3gySVyuk/bIOJ34Dd5d9p12mY/TesuRfqq3lsnida\n2Nol5l/94J99va/rdTD7TmjuXfm0WjLHT/V51/YwAdQiUw06KydD09yEozKyiSVPpbTsVg6Sicpq\n6mI5fQJuuRZ++U4WjgByC+DwCYhvDV9tRZj0GAKy+OcTnY7I999HMClvEn++4w434agMW1ER8ydO\nxKlkcTU0qorkZvDMLND7WE2PmAKj7/S+Xg056CfM7AjbcbjUdzWhtsiQEMl3E47KcCJiVbF8JaRz\nGhVProvFaYcfh8KfL8nCUdm1vOMg6mDCGrjpM//CUY+pUK+Lcvu8/7oLR658/zSkqiSC09CoAnQ6\nkZ9+Gkd8vPdnuWPH2nzwQZAPoCqJhYVgUdlwnHbAWpe9VHQABTpchaMyJAEMBhtKLj024F2b/1DA\ni2HGAfjnjgrhCCCtAM7lw8fNYGVXqO3H6bxLLNyn4rj9xyF34cit7TB8oGDWNDSqkrc6wbU+CiPV\nMMGCXmC8DDzkjh2zsXmzegzenDkVLtAxMf7lCk/hCAKrrvj660U4/Ck3F8HKvdDvpQrhCCAjF9LO\nwuQusOEpGN0R2fNIgagQeGuMcntuMUz5wV04KuN4Ntz30wVP3yeaeHSJEQT45F+wYTrc1V+urPbv\n4XDoDZjc2+/t1YZCP6GjBS5ah1kQGGlStm7RITlIKh+ikyjH5klIHOSk+mQuho9ehLOnfbdtXAHL\nFmC662703a9FFGUR0HW9pouPI2bFCsxjlK3A6W3bOL1li2J7wenTHFy8+ELfgYZG5XHTZPj5EEz5\nN/QbCaPvgs83wLOfelcAq6bYUV/AOHHgcNlQNVEpSS3iRO3o24IJp8oKIYttqnO5KA7+DCnLfbcV\nnIY/X4TEdnDdI7776Iww7A0YOVP5GU4nrJytPo/lnwY2Xw2NINK2bTwHD97HzJmDGTOmJbfe2oY5\nc8bw11//pEaNSxTHcZ4UBrDfKXDZTIwmVG1/orohEEQQRWVlebVT3avpYkgvgf8ppFmzS/DIHjlR\n+IddwKDwJiYmw4r+EKbiOfSJ8rIroHYNjaog0gBrroefesl/16Prwhsd4fBN0LUaVtv2RWEAxqvA\nxXhdc42JRo2UP7z+KqaprctOnnRy6FDw8h898p2cr8gXr/8GqRnw8khIVCha2T4Jtj4FrVQK8n67\nFQpVlrKL98KpSvSr0Bwwqwndm8qvy5VuUbBCJZFXN48Y3BnhRpZbi8nwYT/qmqyqKTfyUQ/61AVT\nE12kXF0NgIXfIAwag/mDjyl4bjqOdWvQ5WSja9gQ05Q7Md87FcGoXhEgJyXF7zQC6aOhUSUkJsPU\n5y/1LC6YeJI5yg7F9hokYqQiTKUp17KfdaRz2KtvKCE41LK1ImBHj9HH6b7cGsQjw71+bNfeb2HQ\nBzDgPyBZYf+vkHUCzNHQcQL0eQwifSU7d6GkQM5xpEZG6vnNW0MjSERGmpg6tStTp3a91FO5ILr6\niXDVA51c+iQLev5PCuc9Crz6GsGPjA6CKCl6JgYz0+Tc02BT2WseLIQtuTAkEV5uDd8cgz35slPs\n4ER4vAV0ruH/OSk5F9euoVFV6EQYUVd+XY40bqwnNlYkK0tZkO7WrcJ4CYLAW2/FMnLkWZ+hbqLo\nXZ/FHXWxypcDfWWw/xRsU1nyOCX4fiM8MRQ+vgXeWgZ/p0KJBJ3rwwN94eZO/p+T4ieRtlOCEznK\nAtX5oolHVzlHS+Dzs3DaCo3NcFscxJdqGxkOiR02iVBBoJsRRBVPgq51bKzI8r18MAoS99Z1v7ex\nXmRdbAjTC63ML3FgBeqKAv8XqidFp2eVypz1KgqyHh0tSVa5+yKQJChQr0bizM4kY+xYiubPL7dk\nQmgokaPHEfLQwwE9JqqejyzpF9BHQ+NKxkIxe/mLc6RhJowWdKFWaWJrO3ZSSUNCoi6JmFTCxeJo\njZNFpV5D3rTHPfGcDgNDeZQt/Mx+1lJCAQbMNKE7UYSznR9U5y2oLGLi6KF670VR4mfnY8mH5c/B\n2lfAVpqYUi9A054wcDqYlcOFyzGHQ1gMFPrOJQNAjct0tauhUUnYHbBgGyzfK1cTG9oOBrWpcNbc\nmgZZxdC8FiSpLPbb6AUiLRJ5CiLSmDCoo3dfez0nRtFQ0vOhVMAh7IjAAMyMIYR/ofK5BdX91xBd\n8Mpk5wbg1PTHcRixC9JcTh7bxsKzLaFVgLk+6kXBllPq7RoaVzsbNxYzZ04BBQVOunUzM358BKGh\n8qH9sWPFHD5cTO3aRlq3Vs7SbDaLNG9ezIYNvo1X3bo6xoxxDyseOjSUZcsSmDEjpzxErUMHI088\nEcV992Vy7pz/Kt2+aNlSR+PGwZFD/FVUBziWAV2nwyaXPFbxUXB/z8CEI4B6KrmQQP6eUfsuOV80\n8egq5oWT8PRx9/XAMyfgw0YSG3ROviqUys/Q6+vgpWiRW8K8vXpSnA7eDytAX8+E/XgIboGbosQd\nLew0C6sQlnZRxByyOK63khil5/fIWNpIYUQLskD1CzGsQlmkiVFZ4FxHe8IJoJzGhSAI0Lwd7Nuu\n2OXc1hMUH1zrdk0qKiJ3xgzE0FCinnjC72MSO3UioX17zmz3/Zyw+HiaDh16fnPX0LiCSGU/i/gE\nq0vy6c0spR290VOfFWygEPlb24SRHnRmEH0QPbwSJSS+ZAV51CGRNHQuApIEGGlIaypqq+aQx0a2\nkspJjBhpwxSak0wI4ejQU0gWO5iLhG8XaBGHovgdSTPi6H6h/yT+ie8AqSo5lYwJsGK6+zVJgj3z\nZWHp9iX+nyGK0Pd2+OUN5T79pgQ0XQ2NK5ETWXDD67DPJfr9/ZVwTSN4YjhMWwZ7z8rXdSIMbwEf\njYCaPlKtPbZdTllGU8Aj0s5YAO+46LSFDvjqHCzMArsUxvCoMMbGO6mth1BBtotvOPPZp2CfJAkc\nDt+ekdEI3KsP0roLaO9n06OzwXN/g81j77gzC/ovht1joWYAOc7/2Ql+2qfcPqWj/zE0NK5UbDaJ\nW289w9y5FZ6Ln3ySx7RpmcyaVYN33klh6dLs8jxDnTtH8P77TejSxfvgad68E2zYsB1oBHjG2ll4\n9dVYjEZ5L+l0Svz66xm++uo4GRlWWrWK5KWXkmnSJJzoaNkmrV9fwsyZ+SqzV3Z+mD69kkuRudC8\nNoQYoVjFrXPeJsjwmHp6Ltz6AdSMgP6t/D/n1o7w2CIoVhDab2gGdXxU4btQtJxHVykLs2Dace+D\nJKsEU3KcfOoiHAGkOuDWTCfzi7yV3U+tFmyAIdGCqUMu+rrF6OJLMNQvwtwxl7+jKqTX90lnDIeZ\nQxYbKWAhOdwpHOVtMa3cs+kGYuiokJRWh50I8sgjwi13iBkjg+jGCIKcKGry/YpNFrue4oMpiu25\nr72GZFELaalg2KxZmKO9P+l6s5kRn3+OzhBMJ3ENjepLEfks5GM34aiM9WxhEcvKhSMAC1ZWsIEF\neIsf+0klnSyKCeUojUgnnmyiyaQGKTRgH0aykb/VD3KUV/iAZazjECns4SDf8wufMg9r6YYrjFha\nc5PCzCUM2CnB7Ga7BETi6U1nXglu2FqHu0FUsBsSUKgSLHx4KZxQyCTryZhnILm977bR/4EGHQIb\nR0PjCmTs++7CURkbj8PobyuEIwCHE+bvgetne+fMyLPBFymATYA9wEEgHTgD7AfrPoElabKdOWmB\nDjvgnqPwWw4szYWnjsM120T2F1ZsA54TohRPlGXhyHsD1kHUs8gcRQMxeLZrUBw0ValTkOjwFo7K\nSC+GT1QEIVeGNJUFJF/0awBTuwU2jobGlcj06ZluwlEZ6ek2hg/fyZIl2W4Jqjdvzqd//x0cOODt\nfvPOO4dKfzoC7AJOIRuvw8AOliw5BoDd7mT06I3cdNOfzJmTxooV55g58wjXXLOcuXOPl4/3xBNR\nJCaq2SAHct6jignWqSPy5ZeRjB0bvOqZ0WEwScWhPDrUWzgqwynBi4sCe05MKHw01nehpsRImDkq\nsHECRROPrlLeVsj5jFFCMvv2TZaAZ3O9v6F3OipO2UWThKFOCcYGxehrWxD0EvucTmySxN8U8Da+\ny7J9TxYLSz2KDAh8TCMmUANd6Qm+gJMocqhPCgYcFBBBJrVpRUfuYSTPcyc30QNRNR1kJTD6dph0\nn/d1g5HiXqNVb3VmZGDZrF7ZqYzaHTty17ZtdHvwQWIaNSKqfn06TJnCvzZtovGgQRcycw2NK4Jd\nrMfmI6+QBOSjfIK0ka3keng0nuScy/0iuURzjngyqYkNI04kTpGBBStfMg+rj1xFJznNQpaW/96R\n8XTjDgSXPEl2dIg40eHEjoECwgnnGtryH3rzHR14DqNKFclKIbYxDPtaTnztSdMxYFEPyeXQ74E9\nJzQKZqyFia9C/XZymFqHIfDkYhg34/znraFxhbDxCPylUGKbMOVChztOw9zd7tcO5UNR+dJLgFwB\njgtwQoB8eR20ozRB6pQjcMhbayfDDmMOyJsUgH6CmR+FmtS1V9gIh02HpdCE3VYhKzVHx0v6UDaY\no1ljjqa9GNwgBlGABV0hycce75oYyPLez7rx+3nUUPlkOHw/Fvo2gKRI6FIH3h8Kv00CkxaroXGV\nUlLi5MMPlTIuF+Jw+Pa2zs938Oqrx72ub9/RLU5kAAAgAElEQVTuGkZfBJwAUoFMQCpvf+ONwyxY\n4L1hdTrh7ru3c/CgrLzUqaNn/foEBg40UCEQOUrHLpubjRo1Snj4YROrV8eQklKTSZOC5zFZxhu3\nQp8W3tfjIqGdnwwkK/aBLcDi2pM6w4b7YHwHOYytWRz8+3rY8jA0quRE6popvErZrPRlG6IeM7rb\nBodtEgadk8/sJeyXHByW1O8JQ/5D+w71RKrfkckw5MDNUHT0oITd7MKGAT12dDiRAAkBCYEwdEyh\nJ6aq/jP+zzuyiPTTF5B1Dho2hzFTYNbn4CffyfkQnZzMoDffZNCbb1bamBoalzvpeC9EACwYkVTO\nQ5w42csh2tOGDeznAGnk4D8DaigmtrGbEpVE2NvYwzAGEFIqGCXQiQwWIhJSaq/keemwo8OBHT3d\nuYNEmvh9fqXS4mZI6gk7Z0PGPgitBW0mg80G2+ZW3nPM4TDsUfmloaEBwOYUlUY/ya8X7IVxbWHh\nYZh7AM75y24NRBvgcDEsVTFzxyzwRw4MLs2Z0UswkZdWiyynA0GQcNpLPY5EJ6LegeQQGRKl494q\nrurUIgIO9INv02B1JhhFGJEAN8ZD5CH/958P49rILw0NDZljx+wqya19KNMuLFiQwaefwt9/Z/HZ\nZ6mcPl2CJKknsI6Olr2k339fSW0Hh0Pi449TeO01+cOanGygXr0sZC8mHRWeRgKygZVo1iyU119P\nVn12ZRNmghVPwh+75BC1Ehtc20T2SJrwQeU+q2t9+HZS5Y7pC008ukqJ0EHeBVYmXGC38LytoDwy\nXjYByu6CNxuMCILAEdUqRHDUoz2VTEQkTC41QATKEs5KlODkHPkk4SdTWDBo2UF+uRAyeDA506Yp\n3iLWqoWpc+dgz0xD44rGtfKZO/69DjPJ52m+Ibc8rE3CqHJnLaJJpja72KM6rh07WeRQhwQAMkgD\nwOlhFx3ocZR+7WaQRt2qFo8AIhKhx9Pu1+xWCI+HAt+eoQA0HRzceWloXOFEqEVH+DFfRTa47ltY\nn+ZysTaKopMowC31YF+xvzpDcp8y8SjfCUdtADr3+5wiTqssgu8ILPq+0gnVwz/ryy9XBtWFeceU\n7xus5ejX0LgowsPVDJS6hbFaJR5+eCdvvulaoVbd6WDChPoUFztITVXPOL1vn7vH9Pbt+aVju44v\nUSZw7dwZoBtPJSMIMKit/HJlUFtYuE35vv4twVANlRotbO0qZZxS2VKL+gomXoT/OQvcUyoKgODb\neMQLAk+Y5BVTrB+tMsajPVSlQlIZIQH0qTR2/AmfPg+fvQxH9no1mzp0IGTIEMXbox59FMHk53hR\nQ0NDlab4zlpqwIq/Rcw6jroIRwACDgXhW0RkNNchIBDmmY3WB659TAEk7Q+kT6VRmAIH34C9/4X0\npeB56qc3Qq/Hle9vPBCSugR1ihoaVzrD2svJU33ip6JYps1DOALIQnEP9lBTaBgONQNIj1jLZell\nFsDkR8iKDmJqNk/yrDBrL8zYBF8fgGIfe78n2smeSL5ICIF/Ng/uHDU0rnTq1jVw7bVK6rf6vqZJ\nE5OHcARq8kP37jWYMKE+ZrNIRIT6vrFWLfdnR0er9y/zaKoKHA74eSXM+BBmfgtnMrz7TOoB9RW8\nOHUiPKWUQvMSE1TxSBCEXoIgLBQEIU0QBKcgCMOC+bzLmRynxHabkzSHvzOiyuHROlDH1yKmRMCs\n4pHUKsyOw2NhIQggik4EoeKc3QTcYjCyMiyCeqWJFEf48RDqi5E32c4UVnAPq8hE75ZY1pMWJFBD\nIbF2pZKTCVOug9uuhfeehneehDGt4IlxYHU/gqv1ww+Ejh0rVx0qRQgLI+rZZ4l6XGVzplGt0GxX\n4EhWK5adO7EeOFAlz2tAS+rjHUCuQyIC5ViOOiSSQbHXdQd6bB62pglJTGUUbWgEQEdaI6jYomTq\n8ifbeYVZvMjHbOAIRpTrQxsw0oi2iu2VhiTBtvvgt0aw8xHY+wysHQjL2smCkis9H4br/wtGF5sq\niNBqNIz/Mfhz1ag0NPsVOAcPFrFzZwEWy4WVeT4fYsLgGaXNgErenpqhsN1XkVkLco7ZogrHpSbh\n8EEneK00Z323CGiuolOHi5BtgZ5boOmfMHoXqOR3BWBChJ8OlcTXB6DOF/DPVfDsJpi0HJK+gN89\nIpe7xMH8gZDksRxsVwOWDw2s0ppG9UCzXYFzqki2C9kBhLBWBi+/XBOTT2U5DL3et5wgimC1+vIe\nEpCDnwT0ennMmBgjjzzSjCVLrsNk0iEIAhMnqrsNtmhhZvjwJTRtOocePRaSmOieFNuTCRMSVcer\nLHYehCZDYcQD8Oz7cP9LUG+gLCS5Em6WQ9q6NnS/nhAF394D/VpWyXTPm2A7Q4UB24HZwLwgP+uy\nJNsp8XCune+LnZQgf5z6GwXejNLT2hA8ba+2Eda1hidS4acssEkQJsKEWgL31tYxOdvBDpeTMB3w\nQITAYbPF5+dSEEDQSUiSg8PmGGJEkRDB3cjcSDQLyWa9j1VSU6ysYTd2l8GPkkcotTCR4VZCG8CE\nnvFU0Un4E+Ng6xrv60vmQGQsTKsIWhXDw4mbMwdbSgqWtWsRzGZCBg5EjPJTa1ajuqHZLj9ITifZ\nL71Ezttv4zgrlwgytmxJ7IwZRIxWTx5/MQiIDOcuNvALu9iAhSIEBJJpyTUMZQVb2OYRZtaEZGrT\nhD34Tlgvp7LWcRcDaE19QjxO0mKIYiC9+YPVXvcaMXKGHI6wofzaWbLQEUEsxZh9CFY9GFY1nkcH\nXoIj73pfz90F6wbDwN0guLgR9H0aut8Ph/4AewnU7wGxDb3v16juaPbLDwsWnOPpp4+xZ4+8salV\ny8B999Vh2rT6iGLwCm88eSPUioCXf4NDpVGi7erCf26C1BKYtgRKXLxrkmPg+UEw4VeFAa3AWbiv\nMzzdA2qa5PWYK+81hCF7weK5dpMgEXjAJWfQoVJzFRIJxT5y+A8Pg+v9O2JeNBtOw20rwPM8NcsC\nI3+DHeOgqUtB2hvrQcp4WJYGZ4qhaRR0jw/+PDUqHc12+WFvLjy0BZaekbdjJhFurgdvdoIaQQxu\n6NkzhOXL6zBtWiarV8uGIiFBx9SpNejePYFbb91LenrFxjE8XMe77zbh/vuVKrXKAlLr1lH8/nsP\nYmONGDz2vc8804Lff0/n2DFvAapVKz1PPrmx/PdDh/LYsOEskZGh5OVF4xkL3KBBCI88knwhb/28\nKCiCG+729jSy2WUhqV5tuG14xfWGcfDXdNhyDHafhJoRMLB19QxXKyOoU5Mk6XfgdwBB8Pw60yiR\nJPpn2thmq/h2lIBlVolO52yMCoXbQnQMNMoKbGWTbIYfmkGOHTJssqAUpgMQ2F5bz8oSJ39ZZFFp\nZIhAkl7gdotQkbjeBxGCQKLOt0+zAYEPSeZzMvieTNKwUQs9w4liHdux+lClinCSQBIhZJNOPgIC\n7UliNB1oQBVkbNy3Ff5erty+8DO4938Q7R4HaEhOxpCcHNy5aQQNzXb559z995P73ntu16x793Jm\nzBgY3JuISZNhxK0QUvkiiR4DvRnJtQylgBxMhBBSWmltAvUYQG/2cggnTprSgCRqswbvUFNPahDl\nJRyVMYBe1KIGa/iLE6ShR09bWpBODql4VwNx4CSf2jQATiMnfYyjLl0YQDMU6kFXJk4rHHpbuT1/\nP5z+BRKHu183R0KbscGdm0ZQ0eyXOvPmnWPs2D1u0Zvnztl45pkUvvoqh3/8ox533BFJ7drBWSJP\n6Q139ILUTDk0oa6Lk+I/OsLcXZBVDK3jYUgzSPVTCBEgIRRqKXjY9IuC9W3gxZOwMFsWZPpEQV0R\nvlCovFucB9fHwBonWCVI1MHd0fBkrLc4FQze2OEtHJVR4oB3d8E7vdyv60S4QctvdFmj2S51jhZA\n72WQ6RL0YHHCVynwy0mYWBumtIB2Qdoe9egRwqpVSaSn2ykocFKvngGDQf7fdPx4d37+OYNDh4qp\nXdvImDG1iIjQM326kbw85VxDNWuaiI/3bbwSEsxs2NCHl146wJdfHic720aLFhEMHlyDN97Y6vOe\nvLwievasyb59IpmZNkJDdYwfX5v//reJV5hbMPhqke8QtTJe+9xdPCqjUwP5dTlQjXWty5c8SeJP\nu/xBuVavJ0LB/n1X7HQTjlyxAt8XO5ljsdPHIPJztJnwIJ2GRevllyd9zSJ9PT7P4/Rm5jqUfSTH\n6dU/mEZE7iSOO4nDiYSIwK+ksExFkUqhiC+5ERMCRvSYqbqYVZ8eR65YLbBrI/S6sWrmo6ERRJwO\nBxnr1mHLzSW6fXvC6vmuI2pLSSH3A+UyEZlL1hC+fQ3C69Ph2z+gaXB8b/UYiKaW1/U4ahCHu6Db\niYZ8z1qs+F7EJBBNA+JUn9eelrSnZbntOkc2L/CRYv8SbDRhKKNohBNHucBVJeQfAItKAmyAc6u9\nxSMNjcuUnTvzOHasiHr1QujQwbe3ryRJPPXUUa+0X2UcOpTD00+bmDEjiy+/jGfcuODEaAkCJPvY\n4NUIhbu6uV9rGA3dE+HPU77HEgW41Y+J7RQOc0tz/0hS6fM3qN+TZIGc5lDghFgd6KpwK79GQdQq\nY7XCv4WGxuVIWglszYVwPfSKAYUoMF7e6y4cuZJth5kHYOYumNoGZvby3a8yiI/XE+/h2Wc0iowd\n672GmjixLv/7n3JaA3+haQkJZt56qx1vvdUOp1NCFAXuuEN9b5aamsmZM+PIyrIRFaXHZKq6RG1r\ntqi37zkCGdlQ8xLUeqostITZlYhTknimpJjG+TmMLC5gZHEBjfJzeLakGKePlcrcYj8x9pL8Tb3K\n5uSh/CoKavXDQNHAEJ3vjI91BJHH9IF7GYilLoVnUM+m7wTOUUIkIVUrHAEYAlCpA+mjoVHNOf7D\nDyxu0ICVffqwbvhwFjdowLpRo7BkZXn1LZg/H5zK9svmAIsNOH0Sbh+m2reqCMPMSK7x2aZD5BZ6\nquY1cqXMdmWR67dvFrlunlFVhhiAXQqkj4ZGNWf37jy6dl1Lu3arGTFiEx07rqFjx9Vs3epdo37H\njgIOHfIOJXWnGKtVYtKkMxw4UD3WXm/0g1CF5c+T10D984iMFwRZQEpVr7BNSgmEiHJC7aoUjkAO\nxVFtr8Kk3RoawSLXBrdsg/orYdgW6PeX/POXJ333n3vc9/VySm3Eu7vgU//O1lXCQw81oVkz3+uf\n3r1rMn584O6CZSHFKSn5qv1OnChEFAXi4kxVKhwBmPzUcRIEMFbxVray0cSjSuRpSzGvWUvcMvoU\nAK9aS/iPxXuxUqh09OWDb0vsZDmrJpm2GqIg8LUxgmcModQR5D+fUGCyzsQyUxR1xPP/kNbyk/tD\nAGpWZWUiV667CRTC8ACIrgkdgyjva2hUAad+/ZU/x4+n6MSJ8muS00naTz+xZtAgJA/xx1lY6HfM\ncnOVcgSWLa7M6V4wA2jH3dxAcqmHkQC0oh6PMoLW1Fe/2Qcx+EgK4kF0AH2CQkRTiPTjjlBnZNXM\nRUMjSKSlFdOv359s2uQuFG3blsf1128kJcX9cKqoKBAhWzZeNht88IF/gbgquKYOrJsAI5pUCDmt\na8LswfB87/MfTxAgyY92XPcSJpoe4SfV2sjLJLxDQ0MJSYKbNsMPp91DNE9Z4B87YZ4P77tCf5Xm\nXUTed3ZWyjQvmthYI2vXXse99zYkMlIOc4mLMzFtWjP+n73zDo+qaPvwfbYlm94IoSf03kERBAWl\ng6go4qci9ooolteCBTuKir2LhaIiKopIE+kgvbdAQkslvexm2/n+2IRsOefsJqTCua8rl2Rmds5s\nzD6Z+c1T/v67Pwa5UokKNGumfBnXuHFQteauU2LcYOX+wX0hrIbvEquaOhm29uijjxLukWB44sSJ\nTJw4sZZW5Jssh4NPLDK+hMAnlhKmBQQSJZR/SPoZNKyxKCQQcsEMHLA5GGCo/esWvSDwhD6Ix3VG\nChAJQkB3HqHJV9KULzhAiUzoWk8aEFtb4lHDpjD+fvhRIukswN3TwVC7t/fz589n/vz5bm15eXVj\nw3uxUR9tF8D+l17yLt9eSvbWraQsWUKTMeVlggIvlfbgKUMQIMD1ZmXfDhhaN2qO9qY1vWmNGQsa\nNBjO489gLFEk0JQkpK8JAwmgG+0qPf950+ll2DQeySoHjcZCVN8aX5Inqv2qO9RH+/XRR8lkZkp7\nB+XkWHnvveO8917nc22dOwcTHKyhqEhJRCq/Ot65U35fV9P0aAi/XgclNrDYIfQ8tx53NoKXkuX7\n72p0fvOfD9O6wbwjzgTZnjQPgXs61fyaPFFtV92hPtquVVmwTqqKYikzEuF6j89gvxj4N0NhUhdx\naW822BzyIXA1SYMGAXz4YXdmz+5GYaGN0FDdeYk7d97Zlu++Oyrbf9ddtbfvGjMILu0KmyXEO70O\nXriv5tfkyfnaLkGsgPfL+SAIggMYJ4riYoUxPYHt27dvp2fPnjWyrqriJ6uF203Kt/HfGoO5QV++\nKTlhE+mQacEk879A0NgRhPLOXVFGulRjBbbaZBWneJtdODwOOVEE8Db9aVLTIR+uOBzwyQuw4AMo\nLP1wxTSCu56FCQ/W3roU2LFjB7169QLoJYqidFY5Fb+40G2XOSOD3z2D1z1oeddd9Pnii3Pfi6LI\nyW7dsOzdKzk+PAhiXSrh8OK7cPfUqlhunSOVTD5iHkUeVdU0aLiVsXSnfS2trJRTP8G+p6HImbQb\nrRHiJ0PXWaCtmzWsVftVdVzo9qtLl3/Zt08+hKFlyyCOHRvi1jZ16lFmzz4j8wodEEvZFf7o0cH8\n8UfNlHeuaYrsMGQnbJFIyD2lKcxuW/NrcmVvFty/BjakOb8XgKHN4NNBEF9LDp2+UG1X1XGh265H\nDsD7ycpjkq6AeJfqhotPwzVy6X5EoADKilMH6aDonvNeZp1l6tRNzJ6936v9kksasGrVSIKDay82\nLK8AHnwNflrmrLIG0KkVvPMEDL2s1palSEVsV7V6HgmCEAy0ptyRrqUgCN2AbFEUT8m/sv5h80OE\n8xzTQiewKFLPhBwr+W5dIoLgcBOOOuuEC1Y4suNATz69KCKTfKxogQj6055xtCKaWj7gaDTw4Mtw\nx9NwcDtoddCxN+jredCqiiwXk+0Sbb78oMHhMUYQBBovXkzKyJFYDh506wsOhBjXC0CdDkZfuNW7\nUgE7vUkmGxELMRTTj3CG0pdmxNX28qDZjdD0BsjZDvZiCO8ChnqcqVHFJxeT/bLZlPdeUv1vvtmK\nU6dKWLTIsySODojGNfZj4sR6Hl+gwOlC6GyBI5lQaAe9EbrGweOt4Hrl2gE1QpdoWH8dHMmFlCKI\nD627opFK1XBR2S4/Img9zdfYpjCzOzyz26NPBIo4JxwBTGxTBYuso+TkmImJEWjaVCQjw4QgaGnS\nJIKHHurKvfd2ICiodgOrwkPhh9dh1uNw8DhEhEL3Wr5HrEqq+6fbG1iN89daBGaVtn8L3FHNz65R\nBur0aJGvYq8FLtd5iw3DAzWcbmhgnsnBl8U2ttvsIIhupVB1wMwQHxm4aplk8jBjowXhpWKQhgA/\nfr3sOPiEpewi+VybBiuQRglBRNKh+hZdUYxBan6ji4eLxnYZGzcmrEMH8j1EIFcaXnWVV5s+Pp7m\ne/dStGQJpu/nICz/jRCDSKCnqbr/SWjUpIpXXXWkYeIsJcRhxIgWByKhfibmX0giX+CalVLPKcKx\nE8y1RMi+rsYRBIjqXdurUKk5Lhr7NXhwDIcOFcr2DxniXdIsIEDDL790Zvv2AubMSeebb/IoKtID\ngbgKR5dfHsgNN1RPtbWqINsEh3MgMhASwqDQ6vy3P9Eg69Nh+Cr3HCrWAthjgug6lk+obYTzS+Wi\n4KKxXUNi4GOFBNgJRmgZ5N3+REe4OR6+S4JPDsCpPJwlul2INcKzvapytVWLxeJg9+58NBro3DmE\nwkI7oaE6DH6kZsnMLObyy3/k8GHXmD8bx4+nYzabal04cqVhtPPrQqNaf8KiKK7hIknK3VSjYYLe\nwDyrdOz9TXoDTTXSP4pQjcC9wVruDdbySbGVd4utHCvNnjZQr+GFEANX1FCuIws2irAQSiA6P/7X\nbeYM37GX0zjdxgWc1l4AetOIm+lEK+RvuTdxyE04cmUHx9nCUfrVZs4QlYuSi8l2AbR/6in+u/12\nyb6QVq1oNn68ZJ+g1RIydiwhY8fC+n/gnRdhyzpnZ3xruHca3FYzAd52HBRgxoieAD/En2QKeZfD\n7KC8mpyIgAMNbQnlFppzFfLhfKkU8RXS5UxSKOJrDvI4PSr+RlRUzpOLyX5NmZLAnDmnKC72vroL\nCNAwdap85uVevULp1SuUadOsPPPMWX75pQiLRSQyUsPkyWHMmBGNXl8zSVczTKATIMoPR+sCC0xd\nDfMOgbn0bQsCiBpoHAL3dYH/9QK9zLZRFGHyRunku8U2uH0DHL/OPxFKRaUquZhs19hY6BACB2W0\n7ydayn8GmwTB053g0Xbw4lb48iBkmUGvgXEJ8NqlTkG5JsjLs2MyOYiN9S+P0cyZicyadYyMDOd5\nWaMRcTisBAWJTJzYnJdf7kKjRvJ5bp99doOHcOTat57rrmtNu3ZRlXszKn5Rd+S5C4APAoOwiCK/\n2KznMvcIwHidnvcDJeRjCe4P0nOfUUeKQyRAEIipob/e2RQxn51sIhkrdoIxcCWtuYHuBMocxLaQ\nwhtsdPWSPPe+RWArqewhg5cZRHukpdd1yHs7OPsP1Kx4lL0dTi5wXsFF9YYWN4POv/93Kir1lYRJ\nkzCnp7P/xRexm8pz90R0707/RYvQBviRmXXAYOdX9lkoKYG4xnAeifT9xYadxexiNQfJw4QWDb1o\nwXj6EId0/ep0TDzENvKwurULiGiwc4QCnucAZ7FwE9JlZJdzCiWv8zWc4UG6YKyhP7NW0slmEVZS\nMNCESK5FryB+qahcCLRrF8LixX245ZadpKWVZ1du0MDAnDnd6drV9wkqPl7PvHmNKCx0kJNjJzZW\nS4CvWvFVxNyj8MYu2Fd6FrqsIbzQC4Y2lR7vEGHEItiQ4t4uioAdUgrh+c2wNR1+Gy19+FybDokK\nla5PFMHKVBhaQ6meiiwwbw9sT3EmAZ/YBXpemGmmVFTOodPAsj5w/Q7Y6pKrOEADz7SC+/0oABuo\ngzf6wYy+TgE63AChNRSosnVrMdOnp7F8eSGiCAkJBh55JIYpU6IRZPZ+zz13iFdfdU907XAIgIHi\nYgtffZXEqlUZbN58FQ0beivpZrONuXPlz42iCF9/vY8336xECcpK4HCILF2aydKlmYgiDBsWw+jR\nsbVW6a2mUMWjKsQoCHwXFMLzdjsr7FbysNJRJ9BXE4AR/3+RBEGgibbmfvFyMfE8S8mkPOF3ERb+\n5ABHOcvzDEWH9xXWD+xVPDwBlGDnG3bzJtK1C3OQdzd39ueTTSZGgjAS7PO9SGHmJAVsRUBLOAPQ\n4+3GjsMOW26HEz+Utx37DPY8AwOXQHSfSj1bRaW+0OHJJ2l1992c/u03SlJTMUREEHvllYQkVDCG\nIUri81VNiIjMZgW7KU+FYMfBfyRxkFSe5xoa4n14/JGTXsJRGQJOEUlE4DOOM4o4yTC2TI8E2Z6U\n4OAIeTQiqNLVIk2YOMwRLFhpTjPiZMSgLOZxhldxLbWSxgc0YTrR3FSpZ6uo1BeGDGnAyZNX8eef\n6Rw7ZsJmMzJoUDR9+lQsL2FIiIaQkJpzepi1Bx7f7N62MR1GLIWfhsD1Ek5Tfx73Fo7ccABa+CMJ\n/j4BI+O9h5wq9r22PVnQKghahFWuWpPVDn8nO3MVtQqHIc2l7xK2nILRc+Gsy5re3gC3doNvrgXt\nReGDonKx0swI//WHjTmwNRfySqBPOFxWwVAngxaa1mB6tk2bihgy5Dgml4pPSUkWpk5NITGxhA8+\n8E5VkJVlYdasYwqz6gEbyclFzJx5kFmzvD23s7PNFBcr5+k8fjyXo0ezadQohJBKpnzZvPk0u3en\nERlpZPTotgQFef8tOXvWwogR29i2rVz5+/jjk3TrFsqyZX1o2LB2K3FXJ6p4VB1obazTZrAR519D\nDTCYEGbQkMZ+5tKoSf5gn5tw5MphMthAMoNo5dZ+hgJOIFGiQ4KDZJFBEbES4k80oWRLCEgCDqLJ\nIpwkPmcXAgKt6MiVjCHaz9t0O8Uk8Rw5rKTMJ0pARyw30YwnEFw9Yw+86i4clVGSCWtHwZgk0FVO\nvFJRqS9odDry16/nzLx5OMxmDgBhPXrQ6Z13iLniitpenhd7OO0mHLlSgJnf2MG9XOHVt4Z0xXkF\nHIhoKMHBGs4yGu+a1XHIeyTa0eBAy1S2AtCGMCbTmn74n4V2Nf+yhnVYXUSuVrRkAjcQ7GJLi9jG\nGWaAR6VKsHGGFwmkLcHUryo0KioVRa/XcPRoBLNmBZKRIQKFNG4s8PTTRh56qO5VFcwtgelbpfsc\nIkzbDNcmeHsOLZKvTu2kLFOMAHMPS4tH8UpbGStghidWwxNA42B4pDs80dN/R9KlSXDnckh12Va2\nCod5I6GviyktLPEWjsr4fje0i4FnB/n3TBWV+kyeGb44BPtLj1VBWrg9Ad7uBsY6eFJ/4olUN+HI\nlY8+yuKhh6Jp187d7i5Zko7ZrORyIEBp9uC5c09KikfR0YGEhhooKJBKEeMArCxatI+FC/cSFKTn\nlls68+abg4mI8O9vQFJSDjfeuJBt28oV+oiIQGbOvIq773ZPIjVp0h434aiM3bsLuPnm3axa1dev\nZ9ZHVE2/ijmDlQmcPCccgfPXeSWFTOAkebIptWuPDST56D/u1Wap4PsolLnlH0gniVaRxqQQQR5l\nKchFRBLZzw98QA6eFVKkOc7T5LAC10OViI10fuAMH5QPdFgh8WP5iUoy4cQ8v56polJfER0Otowc\nyamvv8ZhNp9rz9+5ky3DhpG9aVMtrriTwToAACAASURBVE6aTSQq9v/HcewS/pElPn0my8mXsV1D\naY5GwqPUhhY7OkSXvqPk8xw7WEOaX8/cxBZW8o+bcARwjON8z1y3trN8h7dwVIbIWSREcRWVC4zp\n04t56ilTqXDkJCVF5OGHi3nrLWUvwdrg12QwKWyjThSWl6h3xVyBrVeOWbp9QEPoIBXRa8VZscnl\nGSlF8NQGeOhf/565MwPGLXYXjgCO5cGwRXDKJVzuhz3SwlEZH/0Htrq3ZVZRqVJWpsGYdeXCEUCx\nHT5OhOs21N665Dh50sKGDfIfXFGE+fNzvdqVhSN3cnKk8wcHBOi49VapQkoiUAI4cDicfwOKi618\n/vlOBg/+AZNJeh/nislkZciQ79yEI4DcXDP33PMnv/126FzbkSNFLF2aKTvXP/9ksWePfw4W9RFV\nPKpiviSbLBlh5RRW5uP9gapOkklhM3vZxzFsLuuyYCWdHAoxUeSZpt8Dqf6mhBKGf+6AgWiJkwk5\nu4S29MW9nmQIhRiR3vWYKGIjK3w+08QxcvlHtj+d+djLvK2KToJZ2ROBLJkrQhWVC4T0JUvIXr9e\nss9hsXDkxRdrdD2FZJDEak6wjhIXL0cHDjLIJZt8in3YLit2N7tXRhcfldBchZ/WSPuCx2LkQbq4\nyUci4JD5s+oAPucwDlmhp2ycg3Wsk+0/xWmOUe76Xcw+xflM7FHsV1Gp72RlOXj7bRmlBHj1VTNF\nRcqfu6ok3wo/nYA5x+Gwx/nhdLEz31B2ifRrXcmVMG/9/ckFVGqUuipEEH/XHyI8t3AKGtsneyHR\nj+3rrG1gkRF8ckvgk93l3289ozxXagGcvnDPXyoqADy3F+wy5unvNFibUXNrsdvh77/hm29gncc2\nJDvbwZEjVlJSlMPGAHJzvYWi/v19JbF27qAAunaVzlcJ8Mor/enWrYFHq7w4tHNnOt9/v9fHs2HB\ngn0kJckbuddfL98fb9uW58wzp8DWrd5eSRcKddAZrn6zDIUshMBSCrhPJnl0VZJBNnP4k9Mu4Rmh\nBDGWQSSTzhYOUoIFAYFogslAh10irxFAPO4f+EJMbOUgCejY7ePwBjCYeIJkwvU0CNzF1XQngXUc\nIJtCwslT9As4xC5GMVGyz0o+6fzNWVZgwYAOKxqJw5qDIgrZRTj9Qe9HoLA/Y1RU6jFpixYp9meu\nWIGtoABdaPWWrrZh5j8+4hQbEUstgRYDbRhFFl1YyU6yS+1sKMFosOOQsV0NCXOrvGbFwSqy0CgI\n386oD6cA1IIg+ihUixxNPK0I43eSOEoeJkRSFTYxKZg4RB4dJcQrO3Z2cow9JJKCDQM69Ehv0o6S\nSKvSUGKNQvics18Nt1W5sPnrLytmee2IvDyRVausjB1b/ZlkX9vv/HKtZDaqMUxuBTMPwX+lxR1j\nDIABrxLbZWgE6Opx1lqTAseKnWEsJrnzW6l2rdfAvZ3l19k7BnaPhg8Pw9IzYLYoi0Mi8ONReFYm\n/ePGFPj1qO+wumXJ8NoA5799pSMRBN9jVFTqMykm2JKtPOaX0zDQ/4j3SvP333D33XD6dHlbhw7w\n5ps25szJY/FiEzYbBAUJ6PXBWK3FyHk9d+/uHiaWmGhh0SIL8fHhJCfLiSr2c/M9/HAbmTEQGRnI\n+vUT+Prrfcyde4i8vBJOnszEpODKuWDBAe65Rzp8Pykph++/38P33ytftP333xlyc81ERAQSEuK7\nAnpo6IUrsVy476yWKPFxq+yrvyowUcKH/ESuh5CVTzHfsQxc7spFRKwUEo5ALuFehzANAsNof+77\nLRxgPiuwYkcEgomkiGC3OV3pQgNup6viejUI9KXNOQ+kBXxCMvLugFYsOHCg8bjhP8s6DvAi9nPX\nZwFYMGDAgkFyh1a65sCG0GAQZK6RX2TzCYrvQUWlvmNXOn0BiCIOi2+x+HzZxHucYYtbmx0LS9jF\nSdzLsxZQVHr+MuCQ+HN2tUtY7BGKeJQDpJfaAi0G9FhkPIcEGhDA63RG8FHsoANRdCgV2OdxnC84\noji+WEIQyiCX9/mNTMo2VUZMGNFjIYwCrxW4rimCEaQjf2KLYKTielRU6jtms+99lT9jzpcPD8Oz\nu73bl6TAEg/n5rMWwIhT7JEwvWOaQ4tSnT7PAtcsgzWppZ16XM9Z5QjO+Qwa+H4oJMhf3gPQPARm\n9nJ+bU2Hvj8qj5dKM2Kywg1/whLl7AfncM3hNKEzvL9ZfuzgBIhRtW+VCxh/wlArEqpaWXbtgnHj\nnIVyXTl40M4112QgiuVX+sXFIhCAMz+Rt2tgbKyOCRPKL8imTcvk3XdzSz11YnEq5p5ujnbKlPSH\nH27DbbcpF2oJCTEwZUpPpkxxCkJhYW8pjpfOkQSvvLKWF17491yomy/KqqhdfXUMUVF6srOlLwtD\nQ7WMHOnpHXXhoIpHVUxvjCxTqCDWp5JVdyrCf+zzEo6gLBRD+iCkQSQIE4UuIRpaBO7hMpqX3ryf\nII0fWHYu7EIAosghlAJMBNGTDmgJoBgLgejoTzN6ESeZF0SJRjQnWeEA1pAmXsKRiTPsZzoOL5FI\nwEIAGhzoXA5tWkIJwSUZW7fXYfVgsEvs4prdCNGXVOg9qKjUN6IGDCBlwQLZ/pD27TFEV6/XZB4n\nvYQjgBIMnKKZ5GucRV6tmNHiat8G0vaceGTGzhT2c9bFK8he6m2pxUZvwojHSB52BAR6EcEw4jDK\neDTJ0U6ispsregRa4e655UDkIxa7CEflWDFQRDAhHgUN2tH23L+j+T9y+B0LJ7xebyCeaBkvTRWV\nC4X+/ZULkWi10K9f9W53bQ5444BMp1KCiDLvIxd3654x8KVLoug717gIR+A8swUBNkgIhpHNnSFu\nZjt0joa7OkHTCjqIto+EED0UKqQG6SNRq2TaWv+FI4BRLmfCy5rD+E6wcL/3uEAdvDrE/3lVVOoj\nLYKgqRFOK4SMDqgBDeKtt7yFIycFbsKROzqcIlL5C6OjtSxeHI/R6DR6H3+cyzvvuLo0aoEWQDGB\ngcVMmhRMSUkJBQUW4uICuf32BHr39hXe5k3v3o1Yvdp7D1RGnz7eRU9++eUA06ev9vsZAwY0JyzM\nWUHNaNTyyitteOABaaP/0kttCAm5cCWWC/edVRFHMLMLE8FoGEQIIT4OE3cSxQoK3cKu9FgJwIwO\nO8vJw04Bd9CE1j7CDSrLQZIl20UfIk4odgbRkVxMNCKMK2lDjEvIw2p2SObr0GNDTz7h5HIHo85r\n7QDd6cdW1mCTCf/ojXf5jTP8KiEclWNB7yYexTEJrauQF9MPrvwH9jwDGf862wIaQOv7odP0Sr0P\nFZXapDA9nWPLluGw20kYPJiIFi0Uxze99VaOvPQSlsxyrz8tEIxzeyAcOcKBK66g0bRpRI4ZUy1r\nTmWnZHsmDc6FkkkhIHIV7SnCRjAB9KcNrVwqmy3nrJtw5PpKO3qOY2c27dFVUOj2pCfRJBBCkswF\nwmAaEYl7+dYDnCDNw6PKFTMBBFF8Lvw2gXjiiT/XryOCVvxAKjPJYxkiFgQMhDOCRjyJ1oegpaJS\n1zCbHfz1Vw7Z2Va6dg2mb19lJaRjRy0jRuhZutTlMy4IYAyEwADsGoGrbhC473Z4+C7QVcPOd38e\nnJE7ACqZFQHGt4VAG+g0MLaF86usRH1ygTO5tuScekiywL3doUvFz1tuhBrgjo7wvoTnFEB8GFzT\n0r0t1wxzJIQfORoY4b5u7m3zxkOHGPhka3ny7CsT4LWr4BLp+wIVlTqLKMKaPEg0QSMDDIsCncLn\nX6uBqW3hcdfPnQjYcKbxEeGxDbAzHf7XFWKryf9g2TK5HoWM9kCPHmH06WOnqMjBJZcEMWlSJGFh\nznOyKIq8+65cLGwQZnMQ7dvHMHWqfGoAf5k6ta+seKTTaXjwwd5e7e+9531RKYdGI/Dcc5e7td1/\nfwvCw/W88koiBw86L/jatg3mmWdaMmlS0wqsvv6hikcyZGHjMU6zweXGNxgND9OAu5DPQtiXIN4g\njudJx4xIACUEubjnWRBZShZryOFTOtCF6s0fUhGs2LiV3rJhGkmkSraXkeyj31/CiWIck/id77B6\nCEKXcCVd8A66z0d5B1MWjqchiDhuoxH3eA+K6QeDV4MpDWwFENQCtGrAvUr9wmG3s+yxx9j+6afY\nS8PMBI2GzhMnMuaLL9AbpXcf+rAwLl22jP/GjsV8+jQ6IAKXS3OHg4I1ayhYs4YWs2cTN2VKTbwd\nwFnBzBd9iKcDzSX79vrIRZeJhTRKaMr5lfQWEHiFnjzJNs54bLp6EMUUOnq9JslnBTah1EPKTkc6\ncB3jvEboiaU5b2PnBWycRUcDtDKJvlVU6jLffpvBY48lkZ1dftnTp08ICxa0o2VL+c/n3LnBXHtt\nIWvW2JzCUXiom0p05Bg8Nh3WbYaFX4OmDpWLaRMBr8lE92/JAF8RFZvTz188AnizPxzPgz+T3dub\nhsCfY5zilit7zyrkXvKgewP4fgTEeYSh6bUwYwg8NwhO5DlFrLi6sy1WUfGbnYVw80E45CIiNzbA\n521glILT9mPt4FQxfJBY+lkvwa3i4dkSeHc/LD4JG0ZDw+oPYHFB2fgIgobPPvP26gFnIYPEROUq\nZ5s3+0iX4Cdjx7bllVcG8fzza91C0AICtHzzzRg6dfJ239qy5bRXmxSNGoXwzjvDGDastVffzTc3\n5uabG5OcXIzDAQkJRgTh/C4h6wOqeCSBiMidnGCfRyB6EQ7eIJ1QtExQSKJ6IxEMI5QfyeFzjknW\nXivGwUyS+Z4uVbx66EACBzju1S4gKnofRROmmN/DIJP0ugy9j/6K0JpOPMDz7GMbWaQTRAid6E00\n0lnjtD68uLQYac0rhHGJ70OVMQ6Iq+TKVVRql5VPPcV/77/v1iY6HOydOxfRbuf6+fNlXxveowdD\njh8n7bffSJk6FXtKiuS4k08+SfTNN6OPUSjnUwka0ZNdzPFqD/Mh/ggINFUQ9QP9KCzqzxh/aEwQ\ncxjAWtLZTTZaBAbQkJ4yhRIC/LCbw7iKnnQgUuHvDjjDcbV16EJCRaUi/PVXNpMnH/WqYrN1ayFD\nhuxj374eBAdLC8mRkRr+/TeMjRutPPUSrN8hvb39dQn8sQyuGVG1a+8cDo2NzgS4Xogoeh/1URB+\ngv3YpQdV0U4+UAd/jIUNKbAw0SkMXdYIJrSBAIln+JPM+v/awyM9oY+PLZVBB22qv5aMikq1kFoC\nV++BLA8xNcUC1x2Ajd2hl8yfZkGA93rCI23htX3wpUz467ECeHU3vH9p1a4dYPhwmDtXqseAa1ia\nJx06yO9fAgMFNBpwKFRACgqqOhX/2WcHMHFiJ779dg+pqYW0aRPFpEldiY2VTpwWEmIgJ0devOrW\nrSEzZ17N4MEJ6DyVcw/i46snkqiuUofuXuoOayn0Eo5c+ZRMRB9qbDhaIrCVppWWZh9FHFeqjVpJ\nutMGQeK5QmkdITn6uSSXlaIH8tnvAXr66K8oRoLpwyCGcyMDGSkrHAHEMlhxroYMJ5Ih6m28ygWN\nOTeXbZ98Itu/78cfyT52TLYfQKPXE9m1q6xwBCCWlJClkB+psoTTDAPeWV4jySHYI++PK81pQKiC\ngDxEQVgC6E4YMQoV2CqKDg2DacSjdGIKHWWFI3DaTSXRviERDKafT+FIRaW+89prp2XLHycnlzB/\nvnwhjTIuu0xPUqqyIDun6k0XWg30ksgJBChe3hu1MLaxfP+QJhAZIN8fpINR0g6XlaZ/Y3h3IHw6\nGG7rIC0cgdObqK2CWdII8OoA38KRikp959NUb+GoDIsIb/vh5JIQAr5qknzro5phZRk2TK5H+cz0\n2GPy/SEhGoYNUxZVbrihas9kLVtG8tJLg/j881E88UQ/WeEI4MYblc+8U6deytChrXwKRxcj6k9E\ngnUKCa8BTmEl2Y8S9dkKJZulxoiI7OMMC9nBb+zitEIeDCWKKSYAMxoPnycBES02vHcyIhEEMoJ+\nivMOpDvRMvkzIgllIN0rtd6qoCFXE+pSFc4VPRE055YaXpGKSs1zYt06rMUKMeqiyLHly33OY83I\n8DnG5jnmxEGY9xrMeR62r0D2FOgDOwIOD/lbRCCSLKROYQIC9/ioKNadMAYhfb2vQ+B+mXC3miCG\nMK6km2SfgMC19PdZ8U1Fpb5TXGxnwwZlD8NlyxRqybuQcdZHv4cGddbsrJT23G747rj/oVieBIXg\nTGTtXR5R1vPore7l+Y2kMOrgxV7y/U93hwgFcak6EQR483L3CmquPNQdWqgp11QuApb5OK756i8j\nw4c/Qb4VSlyOdhYbLNgC0xfBe8shzbvuhl+YZJ+rRy5IafhwIz17Kl+6zZgRjdEobSAGDzYyfHjt\neez8738DaNBA+vm9ejXipps61/CK6g9q2Fol8WcrH++jspoWaE4gIiJ/s5+f2IHFJanzz+ygHy25\nj4HoKqDzBWFEg0ggJTgAHTaCMCEgYiaAQkKwozsXwhaJkSl+VOQJwcijTOBnVrOXYzgQ0SDQhZaM\n50rJm38RB1ZM6AhEU8HKRRVBg4FuzOYYH5LOchyUABqiuZRWPIQRhas9FZULBH9irf0ZE9i6NYJO\nh2iTP0UFdujg/Me2f+HF2yDllPN7A84S1G27wct/QGzFsp4GEIqFAkREHAiUEIgdDVocGLBgcUk4\nrUHDvYwkRsJbyZPXacfHnOA3MZ1Cwbn76kgID9OCXjKvz7eBXgPGar5muZGBRBDMKnaRV+ph1YwG\njOFSutHSx6tVVC4O/E0l0b4N7JWrfAZ0KC1WmFQAt2+EtellDwA08NhO+LE/DKmgx0ykDqd4ZARB\ndKBvbEIbYUW0CFhPG7GfNZTr3wI82gYe9E6j4cWUzs7wtVd3OtcM0CwYnuwGD8mcb4rtYBchtJp3\n+eNaw+/XwPQNsKtUlGsUDI/0gCe901OqqFyQ+DJN/l7/tI+Av8/I98eHQIAWCs3wxCL4YgPYHTjt\nih2e+BleHgf/q2DtoijZ0FkB54bOhGtJyH79Ali40Heitd69A1m1qgmPP36WjRudET0hIQKTJoUx\nc2aM5H7UaoWiYggLrd7cdPHxEaxbN5lp05azdGkiDoeI0ajj//6vC2+9NZTAQFUikUP9yUgwiFDm\nkC3bH4+BFhIhDpvI5BdOkUgBIegZTEOi0JItmfUIBhFFLAY+Yx1rkfZF3MRxIjByC/6Xig8njARa\nkEQykeQR4OIlZcRMOPlkE4WNAPrTh2EMIhDfV1fpHGcnS4DdtEcggrb0Zgjt6Ok11kYJ+1jEMVZi\nJg8dgSQwkK5MINCPg15l0BNKe56mNVMoIQM94RhkvA1UVC5EWgwciD44GGuRdIiXoNHQSsI/uXj/\nfs688w65K1YgCAIRI0YQMngwBTJeSrrYWKKuuw4WfwsvTnb3MirBWXr68G6YPgY+3en/qQ9I4HL2\n8CNmAjG7CPDhFBBGAWeJJoNY2tKM2xhOlB/VxFJFO++JBfxMAAU0obUocqMQzFSiJDcvczJhVirs\nMzndc0dFwAtNoZe8B/R5ISAwjN5cRU8yyUWH1i9BTEXlQiEoSMvAgWGsXZsvO2bECO8YqbM58MEC\nWLAcCoqgd0e4coiyeHTf7bA3B/r/DQWuDuKlB7AsE1yzFvaPghYV+Mzf0gg+PQ26qBKCOuUi6FwS\ntzY3YU0LoHhPBM2MAvO7Q38/cvxYHPDuGfgsH5IaQ5QDxkXDzPYQLXHpvyEbZiTCirPOt9MzDJ5s\nCROq8f5sdEvnV1Ke0yuiVbgzEbaKysXCiCjYrOA4OULiKGJzwDeH4ctDcLIQWoQ6Q1AF5CNd72/v\nFI4ufwd2lYXClXk2asBmg6d/gZYN4Ma+/q9/1CiIjIScMg+pc9siLRAOYgiQS1CQyLvvBnPHHYHo\nlMrIlfLLEpj1qZHNyc0wNLUy5DIHM/6np3cPb1XodAq88DYs+B2KTdA4Du67Ff73EOirLqWuG+3a\nxfDnnzeTkVHE2bPFNG0aRlhYLbly1iNU8UiCAQTTHSO7ZPIRPUADrzCCORznK8pziWRh4RuO05BA\nLBgo9DAFLTHyDPHs4pSscFTGag5zHT0IqkBOjlEM5TtmuwlHZWgQiSWfG3mcxvhXTvAU+1jKbByl\nnlFaoIAD/MtB4E7a0f/cWAc2VvMqGZTv3myYOcpy0tjLMF4joBqTuuoIRkdCtc2volJXCQgL45Ip\nU1j/+uuS/V3+7/+ITHD/bOSuXMnBsWNxuPgtp3/2GZrgYAITErAkJbmN14SG0ubnn9FYTPD6A9Lh\naSJQBBzbDTtWQq+r/X4P7RjJIdaQK5F3TgAakMUIRnAJV/g1X6poZ4SYyelzIr6Go8Cropnj5PKB\n4H4gnX4KXnFJ9+QA/siFlfmwoj30r8Z81Fo0xKmCt8pFynPPNWP48P2SCVZbtw7kppvcc5elZMLl\nd8Jxl3wif6x1/rdnf9ixwXuet1+C3t3hck/hyBUHFFnhk6PwRgWi8ftHwo1NHPyd4C4claGPK2F8\naBHzI0IUy3eXYRNh3H5Y6nKgy9bC17mwdS+s6wbhLrv45ZkwehtYXR69Ix9u2gWnzPB4NTsxJqh6\nt8pFyn2N4KMUyJCwKYEaeMLjqGV3wPUrYLFLdfk0k7O6Yrdo2JPnLSBd0xwe6wyv/OUiHHmiAxzw\n9rKKiUdGI8yaBXfcKTNA0NK8eSTbtkKDBv65A735IfzvtfLvLXY9S9fB+p3w70Lo6VJh8kwqXDYW\nTrnsvVLS4Pm3YMtOWDyner2QYmODFfMjqbhTIzmPBEF4UBCEJEEQTIIgbBYEoU47swoIfElzBhPq\nJhGFo+V54riOCLfxSRS6CUeupGNmGCHcSxP6EkZ/IphOAj/QmWgMPoUjADM2TpBVoffQkBhCkQ85\ncWDlLCdk+10REVnH9+eEI8++DczD6pKNP5kNbsKRKwWkcpA//HquikptU99sF8DgV16h/1NPoTOW\ne+1o9Hp63HUXY774wm2saLdzdPJkN+GoDEdREQ69noQvviB8xAjCBg+myfPP0+3QIcIGDoRlP4JZ\nIb+SDWe52b3rKrR+A8EYfIi/uRz2e743xHwX4cid+RSzSSy3XSdL4HWZPOEmB0zzz2SqqNQ69dF2\nXX11BPPmtSUuzv2aeeDAMFat6ozR6O7O8tRsd+HIlV2nYc4nMGEcXNEf7rkNdqyCaQ9AYj6s95XW\nTYT1vvNze9G/nUlSOCpjb3Axvspfl/Fzpotw5DlPEbznEd7yyAF34ciV6Ucgy3eqThWVWqc+2q5Y\nA6zqCt099IeEQPijE3TzyAv9/VF34ciV3Vnwcg94oD1cEQfj4+H3q2DRENBp4JvNPhajha1JUOI7\n7a4bPXoo9588qSEtzT/ZICUNnpsp3VdQCFNfcG977X134ciVJSudXyp1h2r3PBIEYQIwC7gH+A94\nFFgmCEJbURR9pDWsPSLQ8TnNSaaEPZgIQsMAQiTLOS9BIUAVWEc6f9IBvcRrc/2stqavYL6gfLKx\nKlSMA8jEj/T/QBpHyUd+p2WhmBPsonVpaF0yaxXnS2It3bnZr2erqNQW9dV2CRoNV73xBv2feoqk\nVatw2O3EDxpESJx3Ao+cZcuwnJa3A+YjRwhs3572f/3l3ZkpX43tHA7AEFiB1TvJRnnuLE75NY9N\nFPnVh439USymn+B0U16QhYzM5GRLESSaoXXF35KKSo1RX20XwIQJDbjuumhWrcojO9tGly5BdOni\nfSOcXwg/KxwoHA5IzoIFX3j3pfiz7RIhoBLXq/t8FEpJw0EmDhr5saf7Lt13/wstnP/elguH5AtS\nYnbAwjS4t/ZqA6io+KQ+267OwbCzF/yXD0dN0MgAV0RIJ5T/8pDyXMtOwdqx0n0pvuoGCKDTOr8q\nws6dvsfs2gVduvgeN+9XZwidHOu2QNJJSCi1Rz8sUp7vh19gzFDfz1WpGWoibO1R4DNRFL8DEATh\nPmAUcAcgo0vWHeIJIN5HPqBMF68bKYqxU4iNSImws1hCOYzyDiGaYFr6KDXtSYCPZN3+jgEwo1wB\nBcDkMqbER7U6i49+FZU6Qr22XcbISDqOH684Rkk4KqPklIxQ07SV70VogAHX+R7nQQBGipEvG2KQ\nSM4vhQmRYh+3/FkuSSCz/aiylFPJSkwqKjVIvbZder2G4cMVasADmTlQ4sOT5pTM1iohxHmgcyiZ\nBgGuq1iufwDCfTj0a4FgP9PnZvrwHHDtz/HDy8CfMSoqtUy9tl0AfcOcX0qcVhB6AU4p9LdqAIeV\njo0ijPVRxVGKiIiqGQOQ6UewzNlsp3hkt0O+j2Nmtn+FNlVqiGoNWxMEQQ/0AlaVtYmiKAIrwUdd\n+HpEIx8iTAg6QmV0uitp53P+8fREU8H/VSGE05Q2imPa09uvuSL8qFQWSSOXf7fwMZ969aVSt7lY\nbFdggu/cYLJjrr4BwhQOeHpg+G3QvH2F19XGR4GANvgXzB+CQCMftrOti23u4kOTChRUryOVus3F\nYrsaRoPRx2cxQWbr0iwYRvjY1rQNh0mVSJ04XqO8qGFCAGGCf/u5Dj7skWt/x1DQ+tCkulRjvjYV\nlfPlYrFdAAk+PotK/fcOUH5tgADPja74moYPV6q6BjExMNRP758OysdPDAZoWXoU1GqhY1vl8V06\n+PdclZqhunMexeC8aPHUSNOBChZBrbuMorHiPdIIGqOT+VG3oyHXIp2R0YCWuxnAQB8ikBwDuRad\nTJLtrgwgxs/y9ZE0ojHyB8Bw4mhCx3Pft2EYSoUp2zLCr+eqqNQiF4XtCh8yhAAFASmoSxdCL71U\nujPQCK/NgwCJw5JWgJvug8e/qtS6ujKESJkfcwzN6cjlfs0jCAK3C/JJEHXArS7946MgTqGqx80x\npeW4VVTqLheF7QoJgonehSPPodPB5Gvk+z++xFn2WorLYmHNVRBSiQo/l2gM3CAjIIUh8JxW5qES\n3N/I//4mgTCuofzYlkEwooHfmGk15AAAIABJREFUj1ZRqQ0uCtsFcLcPMeRuhTu3h66AkZ2k+xoF\nwz+PQw/lO3xJjEaY+aZ0nyDAWzMhwM9CZBPGQrTC3eKNYyDaRah6aLL8WJ3OWXVNpe5QIwmzJVCq\nRFjvaEYwDyEtm7YllDtQLnExnp48wwguIZ5mRNKSGG6gJ59zC1fIzOsPcbRgAo+SQOdz1eHCieYK\nrmcIN1Voriu5izC8dx5GwhjKA27V56JpRR/uRJD49WrHKBL8PPi5YiGDfLZiIrHCr1VRqUIuKNsl\naDS0/eEHtKHe11y6qCjafPut8gT9h8OPe2DiFGjXA9p0gZsegCUn4LFPQFs5pSWAIK7lKToxCH1p\n2LABI10YzDgeP9fmD1MIZSjehzkt8J4QQbxQvsYADfzWFqIkln1ZCLxXiQ1ZkQ3W5cDmXGdpXhWV\nWuKCsl0Ab06BjhLbK40GPnkaGiuIJc1DYMcoeLMnXBoDHcNhfAtYPxw2DIc4/6L6JflUG84L2hCa\nlO6BtMBoIYBluig6avxXpC4LhzdktP0742CSh1j0aWfoIREu09AAv/aUzr2ihEOErTmw5izkqSFv\nKrXHBWe7JraCm1tL993SGm5SyAqg18Lv98HcyXB1e+jUCK5sA3NuhZS34DKZef3hzjvh10XQ2yUw\npU8f+O1XuP12/+cxGmHhFxAicXfXozPMnuHedt9tMHmC91idDr5+B9r6kSXBk8OJ8O9GOOlfel+V\nCiCIUmWWq2pypwtiMXC9KIqLXdrnAOGiKF7rMb4nsH3gwIGEh7vX/Jw4cSITJ06strVWBXvI4RdO\ncYxCQtBxNXGMpAnGCia7rg4smLFiIYgQ7FhJZCVJrKGEQiJoRluG0xjlVPtWzBxhI8nsQsRBUzrR\nnssJwIiNfLQEo3HxdMonlURWUkAqRiJpxZVEUzGrZiWbE7xCDv9Qlso2iA4052lCfaz3YmH+/PnM\nnz/frS0vL4+1a9cC9BJFcUetLKwec7HZLnNSEqkffkjusmWg0RA5ciSNHnyQgGaVSPpRxdixYqaY\nQILRomMPh9nILjLJJpRg+tKFvnRFp2BnHaLIMswsFE3k4KADOm4Xgmkj6Mm2gEEDIS6CUY4NvsmE\nDQVg1Dg9ksZE+g4LcVu3CNMT4aNTkF+aJ6lxADzfEu6t/R9rnUG1X1VLRW1XaV+9tV/5hfDlb7Bg\nGRQUQe+O8PBN0Ldzba/MaXfO4iAIgRBBwz5MfEsW2ygmAA3DCOVWoonxkX50RwF8nlaehPeOhjA4\nEgpFEYsIUS6qkNUBi9Lgt3Rn5bUrouC2JhBWQS+q+afh2UOQVFpQM0gLdzaHtzpCQO1vaesEqu2q\nWi422yWK8PNxZ/Lsk4XQIhTuag/jE5yePrVNVmneouhoSM2ED+bBb6udueYG9oKpt0A3H5lXUtLg\ns+9h4zZnmPH40U6vJLRQUAKRRvfcTBv+g+8WOnMmdWgDd/8fxFdwv7RrHzzwNGza7vxeEGDEYPjk\ndWjetGJzXaicr+2qVvEIQBCEzcAWURQfKf1eAE4C74ui+JbH2J7A9u3bt9OzZ89qXdfFihUTq3iJ\nLAkPni7cQFckpF8ZHJSQwudkshAb2WgIJIphNOEhDFXgYeqghANMxMRRrz4NgXTge4IUwukuZnbs\n2EGvXr1A3cBUGtV21T1+YTnr8f51bkML7uEGdBWoAfHdaXjrOOwrdF5rDomGF9tAf4WY/4pw3wH4\nTObG66P28ICa+k0W1X6dHxWxXaX9qv2qZpaQxzRO45lvvyE65pNAc5kUA1Jssdl42VTCSqsdEeig\n1TA10MDtAf7PocRPZ2DCdum+6xvBwjpfOL32UG3X+aHarrrH4SS44k5I86h1Z9DDj2/BuMH+z5WS\nD9NXwII9UGyFBsFwV2+YPhiMlQgT9uRYMvQZCTkSCbbjm8HO5RAR7t2nUjHbVRNha+8A9wiCcJsg\nCO2BT4EgYE4NPPuCx46F/fzJb0xjHpP5g6c4zAocSMdH7GORpHAEsJefyea4X88VsXGUh0jlc2xk\nA+DAzFl+5yC3YiGjcm/IhWz+lhSOyp6Vwufn/QwVFQVU21XdmBZB1hWQFgEZ8ZD/LDikq/EeJllS\nOAI4ygnWInPakeCVRJi0xykcgdMffmUWDP4PVmRW7C1IkWyCLxRcpWccB4sawqZSfai2q5o5TSpz\n+ZXnmcULvMN8fidVZt9TgJ1nSPESjgDSsfECqX4/d43VxtX5xawoFY4ADtod3FtkZkaxueJvxANR\nhOkKZcR/SYVd8oUwVVTOF9V2VTNpGfDkq9D8UojsDFdNhD9Xyo+/7xVv4QjAYoXJ06HY5N9z0wug\n/2fw9XancASQWQSvr4GRc8Bqr/Bb8eLtT6WFI4DkU/DVfOk+lYpR7eKRKIo/AdOAGcBOoCswTBTF\nKtiiX9zYsbCC19jG9+RxGivFZJPMZr5kDe94CUgiIsfKixhIkuijv4wcVpHPZsk+C2mk8rV/b8LH\nM5TIZTWijEimonK+qLarmsl/BnKvB8saEPPAfgKKXoOzl4I9zWv4FnYrTrfZR38Z6SUwQ1qTxuKA\nxw76NY0iizNQtEzpFtiklp5VqSZU21W9HCSRD5jDTvZTjIkiitnOXt7naxJJ9hq/hDyKFCzCegpJ\nweLXs58sNlMi0/em2cIZx/ntiQ4UwBEfZcQX+a91qahUCNV2VS8nz0DfsfDWZ3AqBXLzYdUGGHMH\nvPah9/jEk/DvVvn5cgtg4Qr/nj1zHSTnSPf9mwQL9/k3jxK/LlXuX/TX+T9DhQr4+J8Hoih+DHxc\nE8+6kHHg4BArOcDfFHIWHTrsSP+VP8lWTrCJBPqfa7NTQgn5is8owj/7nMUSxf5sltCC//k1lxyi\nj82UiA3nEa228r6rXOiotqsKOb0U9r4BmZshTAeXFEuPsx+DgukQ8YVbczbK1905PvrL+CnVmQtE\njn2FsDsfukkknvUXix/R4CWq7q1Sjai2q+rIIo3NLOcoe7Dj4CzR2CXy91qxsZAlPOVRROQMytmm\nRSANG419hK4dtNvZZZc3HDbg5xIrU43+FxTwxB+7pNoulepEtV1VR04evPUNfLXQKfQEOKBAZqs0\n/W24aQy0dCkMciLF9zNO+Ckmz93lu39iN//mkqPEhwbvq1/FP9RTdz1BxMEKZrKZb8knHQd2bDLC\nURlH+dftey0BBKB8Igomxq/12H2IUDYf/f4QQm8f/d0Rakb/VFFROR/2zYKVIyF9LTgs0FBGOCrD\nPA9E9/v1SB+2y1d/GTl+VA3yZ4wSl0co9xs10EeNu1dRqfOkcoJveZMDbMOKBRMarAqFn86Sw3FO\nurU1RjmZhwDE+bGXyXH4VqVzzzOPacdQiPaROmlQ9Hk9QkVFpQbIzoUe18Hrn0NGNlgs8sIRgMMB\ncxa6t7Vo7Ps5zf1McZvrI6o2x8/wNyUGXqLcP6jf+T9DRRWP6ix2rCSznUOsIYNjJLKeM+yt0Bym\n0lxEZQgItEI5s1krhiDioJBt5LEaC2ckxxnxTrGvwU4AZgIxEUwQFk5VaL2eNOA6tAoHwjhuP6/5\nVVRUqomja2HDV7DvLyhMgW1Puvf7uhgXi8Hhvsu5FOUrqUvpDsA+m4M/SmzskAmgl/QosgNFQD4I\nhZB/npuYSyKUBaQ7m0BkFSSHVFFRqVpySeUQ6zjKZkooZjFfYKfcltj92DbnU+D2/WjCCVJ43QBC\naIyBDKz8QwGbKMImIVC102okTKeIRmtHp7ei1dswaexYz0NACtTCwwny/Z1DYXhspadXUVGpJrJy\nYe4f8M0iOHYSpr7u4RXkh1lISXf/vnVzGKRwjx8RCjcMdeYwWn4M/joqLxJ1lRKZgoAYoAEQBjly\nMbl+Mu0+0MiY2iAjPDDp/OZXcaK6bdRBjrKBTcylhMJzbfpK6HyhEhXPOnM9aewlm2MSfePRksQB\n7nMRjTSEcyXNmYGOyHNjY5lABj/iPHWJBFCCwc01O5XjXEEcbxDBDRVeO4CeKNryMYk8htUlEaWA\ngaY8QiRDKjWviopKNXFqF3x9M6S5JA5qEQxxHnEOPhyPECJBE+nW1I4E+tOTDRJJs1vTnAa2HgzI\nN7HJWv6s7joNn4UZ6K0vry09OhYSjJBUJhCZwcXUIgLX/AN3tIYv+1W+ZO4v3eHaXbDBI7fRxDiY\n5aO8rYqKSs1SQhH/8AUnXHKnCQSQ7xFKpsV3Vtdo3G1XKFpep7FstbUnacg0TrOEvHP9DdHxGLFc\n7zJXtEbDBIOe7yzOvZYgONAZbC42SuRjh4kNZgu/B4YTLVTufnh6W0gzw+cn3HO3dQuDxX1BUwfK\niKuoqDgRRXjmXXjvezCXii+CAF4fUz8+t60kqsB+Nh0G3QHpWe7teh18PQNmb4eZG8tFoyA93NMT\n3roadC4m6OF+cNvPLmtpCASW928shNYL4K8RcEklBeqBl8JXs+ChZ6HIZZ8ZHQnzP4ZW8ZWbV8Ud\nVTyqY5xiD//yOZ4SsR2r1+deRIOgkISxLVd5tekxcjUzSGQlSayhhELCaUpbhhOKmWPcC26bIwd5\nrCKRVNqx4FyYmJGWJDCDZF5AR7GHcFS+6jT+h5EeBNDar/fvSQjd6Mrf5LIaE8fQE0kkw9B7bM5U\nVFRqmbw0eP9qKPQoy+GQCK89A7REfjMTNBkEb9ec8QylLS3YwE4yySaMEPrShRb2LvTJsZDuEdax\ny+ZgaI6ZrVFGWpXuYrQC/NoLhv0H6SbchCNXvk6E3tFwfyWFngYGWN8XNuTA6hzQC3BNLLQPrtx8\nKioq1cfffEAqh93arNjAQzwyYEWLDbvM9rkxDWlOE6/2UYTTAgNzyGI7xRjQMJxQbiWaxzjNRo80\nBOnYeIoUAtEwivIY11nBgRx1ONhks6HT2yTF7d2inUcshfwQULnEbRoBPukGT7Z2Vlcz2eGyKBjS\noFLTqaioVCMvfwJvfOneJooSjkYCzlO/VNlHwGCAyTd6t7dLgB0/wofz4dd/nHmDBvWGqbfAkgx4\n9h/38cVWeG8LFFnh89Hl7bf2gG2n4f1NQBRuwlEZ2SUwbhmcuBkMWu9+f7h9Alw7An76A1LSoHUC\nXD8SAiWep1I5VPGojrGLP5DyLRQREDzaRQQcCGgkxndgBE3pIfkMHQG0ZxTtGeXWfoRbQOZWzcQB\n8lhNBFefa4thLKH05gTX4JBNtG0ni9noCcDCfjSEE8K1hHAtgo/kkGVo0BPFUL/Gqqio1BLrPvMW\njsDp2eOJCTgAdMRbQNL3g5CXZB/TlXZ09QibfdHkLRyVkSfCu8VWPgwrD/joFgZHr4Bxa+Afmeof\nALMPQmoarEh2HqhGtoJ7ukODCghA/SOdXyoqKnWTVI54CUcAGhw492PlRkoAwsknhwhED4/wEIKZ\nyDWyz+mMkbdp6tb2H0VewpEr75PhJh6FCQKrQoN4ucTELId8crY/7RbeNplZYbVTKIr01Gm5P8BA\nR53/J7KEYHi8cvd+KioqNUCxCd79rgIvCMDpTujhd6DVwlczIU7G46dxLLz2iPOrjCILzPxN/lFf\n74TnLofmLvkdZ4+BcV3g6uVyp01IM8H0nZBogxPF8P/t3XecVNXdx/HPmZnd2cqyS1t6RxCRXkVQ\nxIbYsIHdqHlUTPKYx2hssSRGkxgTE3uiURJFk1hQ1GBBNAhYQLEBgoAgve0C22fmPn/MAlum7TL3\nTuH7fr3mpXvvnXvOsLvfvfObc8/plgNXdIOTYpxbCaCgBVx5QezHS9OoeJREfFSzOcQFDAQLRY2L\nSgYLF34sssgkn2LyaEsfjqNj7fwfkexhKVVsxksHsulCWYjbQepqWDwCyKQ9AUK8YazXziwy65S6\nK3mfPcykmGdxkRO1nyKSApbNCb19B9CFxn9tvgd2A11d0OXI4G1q2RcEHybyR0Q72MFGNpGFlx70\nYHZV5FtJZlf5abgKbb4HTJQ7UFbshl9+feDrBd/Dg5/AO+fD4foUXiQtrCf0GtEuLNz4G40yysBH\nK3ZSQRb5dCaDbPrRi9EMIZ+8iG2VU8kqvgOgJ12Y22B+pIa+pZq1VNGtzmxHbmPIc9PoDWBdfuDW\nqkqsQLDA9Yk/wJNVNTyZm815Xk24JpIOPvoCSpqyPpEBsgEfdCiEdq1h2AC49lI4sl/kp9b44N1l\nUFIOg7vCqj1QGmGOIr8VnAPpqgZzJuXkhC8c7fPbZUDth3SLS+CFjXB1d3g49JgIcZiKRykj3Cij\n4LbjuJF2HB7TmfbyJd9yBxV15j3KpkfYUUz7WCHGOhoMLgoIUBLiGfuOaayKjyjhfoq4NaY+i0iy\nC3MPWgBYBfSh8RINewD3DdDmnphaKKOMf/MiK1mFVZtVeeTRLvMY8PUP+7xwn88XRZu4O8Sbs81l\ncPGr8MkPYuqyiCQ5E2EykCwqKSen0SgjDz4G4OVspsfURoAArzKPD1hSezscZODBTR8i38NLyNXd\nCmOZwKTB03zAlWUVHJvhpm24WWVFJGU0a05GEyzgfPYGtIlx5cRnFsD1M2Fz6YF2h/QgWAWKUEnw\nhbiGinrdVdvHhh5ZAxPbwpTGdwWLw/TXI4l4yKQ94Uu/Fi68eHHhxxDAhZ9s3IxnesyFo0rWs4yr\n6xWOACpYjY+siJPx5zMq5PYCzojYpitMjXkPM0MWpEQkBfU/Ofy+UmB7a3ATvChwARku6P8jGPjr\nmE4fIMDfmME3rNxfOALYy14G5s2mt/ebsM+dkBn6T92FPaI0GmZi78WbYfGm0PtEJLV0ZkDYfS4s\nWuIjh3I81OChhmzKOYz2nMrPYm7jFd5lHh/tLxxBcE6lSr6mP1+FfV4xHnqEWGPtdI834qKVVgAs\nq3HuVQEzqsLf7iYiqWPEACgqiHxMlotgkScA+KBjEcx/NvbC0aufwkWPHSgcQXBOpcXfgtlExFXc\nJoRYubF3AYyINnI7TLg9tiZab8UJGnmUZAZzKptZjocqcigno/Yz80qycNGFKdzLNpazm41kU0gn\nhuGOce4ggM08iz/MDLEWAfy48YQo9mTSgUImhXxeK65hD2/h279C2wHBIlfoZAmwiwCluIkxwUQk\neY39Ibz3IOzdElx+dd8f/xqgOhOmvQl5BrbNB3cWdDwVstrFfPrlrGAToSs2xsDY3IWsrOrTaF8G\ncF1O6Ns0JneCUzrCa42jK/gxfYTh4Ct3wtD20fstIsmtmF505HA28zndWU0X1pFJNXvJZw3d6c6N\n9GAo6/kUPz6K6UsRIZYlCmMv5SFXidynG9+xkt5Uh3jHdAWtcYf4GL61cXFbRg631jSucFsW+Hzh\nL++/DUS4301EUkZ2Flx/Gdz8R4JzSZYTLBS5gGyYPAmevx9eeRu27oC+PeH4sU0bsfTLWcFMCcWq\nAsog1N26p/YJf3v//aPh+NeCk/E3flEEP2gMYWWYBU7EWSoeJZmOHMEgRrOBl+pdLuRSTiabqGIH\nHRhMhzCTYUezi/kR97toi2EXVp1ZbrPoTXcewBVqanzAQ1u68gLbeYDdvIxFBQYLNz5ctbM1hWLI\nxhVlfgARSREt2sKFD8O/z6XeHe1uINsPpSuh87lQGH0+tlBWEH5kEUC7jM10d5exxn9gNutWBh5v\n4WVIRugrEZeBF4+B33wFj30DG8oJfjpXQbBwFOE9VntFl0jaOIFL2cAx5NT5ECyLKlqznRzmkMNE\nDmNCs879DWvxRZjlw0WAoZSykAOz1WZguJJWXBrhw7WfZOTQ0bh5oKacz6zg+S0LfNXukKOO9ilu\n1r0uIpKMbvohvPgCfPJxnY0BYA9sWgF+H0w9tXnn3rYbPl4d+ZjeWfCtgbprlkzuDf84M/xzjiqG\n/54Gdy6G19bXPjeT4ApsEcZDtNeKaUlBxaMkU81utvB6yIJLNSV8xu8Yzu14KWpmC5E/cXLTgiN4\nkVLewc8esulLPiNDHmtRTRmvUc0K3BTShp/QgqPYzuV1Wgu/skcuZ2IiDrwWkZTy4e8JORWi5YfX\nfwAdDoeiI5p1aiviTbVBH7Xy8n6VlzV+i45uw+leN94wb5Te2wDvbACPgVO7wVU9odNDUB3DnbQ9\nC2Fc7AMPRCTJVfN4vcJRXVX+R6nmSDJcUzGm6ZNNx5JdP6YN19GdpVSQjeF4WtAqzCX6Gmp4hXLK\nsRjq8fKepyXjK0r4zPIHRxQYE/ZWEgNc5I19tLqIJLd58xsUjupY/Cn87Bfw2zuhRYumnzvMIrb1\njOkEb54Lr60MznE0sTv0D7Nq264amLkFNlRB92x4diLcuRruW0dwtFQVwQ/vwrisa9Nfg8SfikdJ\nZgPz8NNw+nqLDKpx46eCJbzPmRQxlD5cSz7RJu2or4CRbOWlsPtbMgoPBbRiSsTzVLKErVyOny37\nt+3kbrIYVK/wZQg0mmgSwENXCrmhSX0XkSS2bRmsX9B4ewHQAvCUwSsDoHAADLwDukXOmIZ60ZPF\nEW79aEtbikwBZ0T5ZGpbBZz+Oiw8EF3c/jGMahNb4SjbA4+f3MyJKkUkKVXwj0bbvNU15FZUkuEP\nABeDuRHLexVk34ZpQgD0ogsuXATCfHjnwkVvutKSHIZEWIE2gMXP2cUM9tarDfW0PHyJh33TmHo8\nPmqqMwg16+wd2V56uDXdqUi6eKJxdAWLx4Hgfx97AmY8C+ecAQ/8Blq2jP3c7QpgQGf4Yn34Y044\nArq1hOnDI5/rqU1wzQqoqBOD/7cSOng5MANzJsGpDkJci53YFi5R8Sgp6C9IkqlotOy9hZdKPPjr\nXAYE2MnHLOISvuBWqtgW8/mLuSDs7WcusilmWtRz+NnJFi6sVzgK8lHJJwTq9DR421ptgtU+8jmf\nDszGQ5jStIiknt0hPrVvBRRR/2OKXV/Au2fBCwNhy6KYT9+fw2lN67D7x3N0TOc5d079wtE+i7YR\nvNc+guHtYdGlMKFbTE2JSAqwCBBoMJ+at7qGgr3ltYWjfQdugsrbYVsrKPt7zOcvIJ8RESblHkZ/\nWpIf9Tx/ZDdPNygcAXxrfGR5q9g33Mi4IMNbg8vtZ991VxsX/Csvm59na7S3SDr5fmODDRbBAeB1\ngqKiAmbMhNbd4JbbobKSmN0c4Za33u3g7BHRz/FBCVy+rH7hCGC3H1bUnbbNALkEb1+rrVC43PCH\nI+GVMcF1ViTx9G1IMjkU1/vajT/shNMAW3iXj7iIqkZFp3Dn78lh/IHMBoWbTIrpy5/IimESyL08\nT4CSsPsbznLkwsJNADcBsuhDa+7TJNki6aZlt/pfeyDs+yEDlH4OLx8F6+bEdHo3bi7jYjrTqd52\nL14mcRKDGBj1HIu3wryGF1p1ZRJ2xWyPC146G45UzVskrRhcuOh8YINlkVdeGXa+Rty7sLZfDLuu\nj7mNszieEQzAVeesBsMwjuAcToz6/GosnmBP2P3GZeF2H7hl2BjwZPjJzKohM6uG+/MyOS2z6bfc\niUhy697wbVuE2Un8Afj1fXDUBKiJcdHFqaPgTxdCfoNxByN6wFs3QmYM9zD9YX34bjV6h2sIFo9a\nAC3h0j7wv70gzKK5kgC6bS3JdGQ8X/MXfLVrRLujLGVvYfCxm2X8ikH8MaY2ChjFYF6jhIVUsQkv\nHWjJaEyE+YnqquSjKEcYLEK9BzMUcGNMbYhIimnVC7pPgDVzg1/nErYQAwQ/ujABeGcqXLYrpiZa\n0pKr+CHr+Z6NbCILL305jMiLVh/wweYoBxiCE3yHiN1rhkDH6IMDRCQF5XApe/klAB6/H0+kFckM\nwavnkt9D7lWQ2Svq+T14mMYpnMRYVrAWgD50o4go62zXWk0N26PMWel1BSgPMeXcIOPmDLdGHImk\noysvhr89W2dDtHmKDCz5DO77I9z0s9ja+NEJcOnRMPszKK2AwV1hZM/Y+zi/NPJ+r4GqEP0u8MCN\nulUt6aiOl2QyyGUw1+OiaZ8Q7eLjmCZl3MfgoZCjKeZcChkbc+Eo+NxoFyFu8rkCw4FVjzz0pDVP\nkMOkmNsRkRRz2uPQomPw/2OdEqS6BNbOblIznenESIYzkCNjLhwBZMUQc9eNgM51JpYsyoY7joY/\nHN+kLopICsnlWjIZB4CJ5VJqX76V3NykdgopYBQDGcXAmAtHAFkxBOpZbi/DXAc+E84AznV7mZVV\nQKYmaRNJS6NHwG2xD4Lcn11/fqRp7eRnw7TRcNWEphWOALKiVBv65sJZbcBdJ6bGFsC7g6FP+Gng\nJEFsKx4ZY242xnxgjCkzxuy0q5101J6jGMeDdGUSHmKd2cxiL9/a2q99ohWAcphIEXfTkc9px2yK\nmUt7PiCHUxzpn8jBUn41U1FPuOpTOPYuyI1ydbFvGjSA9W/Y3TMguKpapHvmW2fBPUfDmmvgk8tg\n4SWw4Udw+9Hg0nsvSQHKruYxeCnk37TgQYx7TMiFPurZN8Kn+lPb+wbQjQz6R/lQ8UpXHu9mtWRx\nVkve9BawIruIJ7z5FBl9TizJT9nVfHfdDG+9CFMmQ3aUuRv3XXdt2Wp7t/ab0iby/qlt4d8D4Psx\nMH8IrBwF/x0KgzXaOynZ+RclA/gn0MTapgC0oBsD+QljeAgX4ZdVddUbxhxivLINcjkZL4ND7jNk\n0ZLrAHCRh5fhZNIfE/MwBJGkoPxqrtw2cMxtcOU3UNA3/HF148pbZHu3ANrnwo/Dz1vL7cPB6wa3\nC4a2h1EdIUs3d0tqUXY1kyGTHC6kyPUmxvvD8Af6OXBrq3HuY/GbaBn2on0S2QyuHYXZx+VhtDuD\nNioaSWpRdh2EicfACzPg6UcjHLRvFTaHXdcZ2oapfXfLgh/WDlgv9sJRLaGXRhslNdv+sliWdadl\nWQ8AX9jVxqEgh04M4E5Mo0+cLFwE9n8D3eSQSw9H+mTIoB3Pksc5UKewlckginkOL0c60g8Ruyi/\n4sC44LhXIS9ELvmpXzzqfoZTveJ3Y+BXI4KjjPbpnAePHwPXRigsiaQCZVec5NwPGSFGS/uBsjp3\n5eae51iXjiebJ2lNnzq2fdCqAAAgAElEQVTTleZiuJJ8Ho2wEqVIKlB2xcc5Z8Kdoe6mbVA4Gj7U\nqR5B5yx4bwgcV3ggO13Aqa3h/SFQpLn8U4o+U00BbRnLOF5mIedSwx4MwSmp647l6cKFTZ4n6WC4\nKaAND1DEL6hhDS5akkn0SSNF5BDSohdMWQGvT4DN/w1uC1B/Qsfio6GNc1cxxsAtw+D6wfDZdvAY\nGNQ6ONpIRATAmGzIn421527Ye2twoy/42H/t5WoJ+RFGKNngZHI4mRy+pppyLA4jg3xNXyoidfzi\n53DyRBh9HPj91J8mgOB10C9/4Wyf+ubC24PhuwrYUA1ds6Cj5vFPSfqLkyIyacEo/kEBvXDVKxy5\n6MR5dOWShPTLTSuyGJZ2haMqAjzJNk5hBcP4kjP5hpnswN+ESclFBHB5YNJc6HER+E39wlGHCXDi\nywnpltcNI9vB0LZpWDj65gX45zHwUCH8tTvMvwUqtie6VyIpx+Tfgsl9CFPlxdQtHLm7QPE74E7M\niJ/DyWQY3rQrHH1FOf/HOkbxFaP5ihtZzzdUJrpbIiln+DD44C1o15p61125ufDXh+H44xLTr67Z\nMKYg/QpHm7fDDX+CLpOhcAIcPx1m/zfRvbJHk0YeGWPugYhrrVtAP8uyvjmoXklIXloznKcp5QtK\n+QIXXtowDi9RZiKzUSDwBQHfU1jWZoyrD2735RhXp4T1Jx6qCHAFa/iIsv3bvqaSO9jAB+zhAbri\n1hxOKUf5lUAuD0yYAcPuhO9ehUANdDgW2gxJWJe27IYnF8FXm6FVLlw0HIZ1SVh34mf+zfDRPQe+\nriqBj34N3/wTzvsv5BYnrm/SLMquBGtxDeRdCGUvgH87ZPaD7JPBxL5KbTxVEWAO2/mY3bgxjKeQ\ncRSm/HXJe+xmOt9RU+ed7svs4j+U8DjdGUleAnsnzaHsSqyRI2DDt/DaG7D8G2jXFqacDvkJmoja\nwuJDSnmH7VQSYAD5TKINeSl+I9S6zTD2Cli/5cC2tz8KPn59Ddx0WeL6ZgdjWU1Y3t2YVkCrKIet\ntixr31SCGGMuAf5gWVbUGVGNMUOAxePGjaOgoP4SptOmTWPatGkx91Xs56u+Ab/vdw22ZuDJfAK3\n56KE9CkenmIb97Ap7P776cIpMa+CZ7+ZM2cyc+bMettKS0t5//33AYZalrUkIR1LMnbml7Irtcz6\nHKY+DZU19bdfOQYeOy84pDslbfsc/j4w/P4BV8LxjzvXnxgov6LTtZfss45KrmYZG6mqt/1wcnmY\nfhSk6JswHxbHsIxt+2cir68rmczhsKRafEXZFZ2yS/apxM/PWM5CSuptb4mHBzic/qTu0mpTb4bn\n3wq9z+WClS9AjyQaV3Gw2dWk4lFzNCcEFi9ezJAhiftEWqLz+2biqz4/zF43GVlLcbn6O9qneDmV\nbyIOkx5LHk84NDl5cy1ZsoShQ4eCLmAOSlOLR8qu5LduJ/T5FVSFfo/CQ+fANUc726e4mXcdLPlj\n+P0ZuXD1DvAk93hx5dfB07VXejqHpayiIuS+CRTxe/o43KP4eJfdXMXaiMf8nR6MSPLRR8qug6fs\nSk/3sZrnwnww34oMXmEY3hS8Dbd0L7Q5HmrCXFMC3HY53HWVc31qjqZkl23fJWNMZ2PMQKAr4DbG\nDKx95NrVpjjH7/tzpL34fQ871pd420ZNxP1bw3wyJulD+ZW+/rIwfOEI4E/vOdeXuNu7MfL+mjKo\nLnWmL5IQyq709TGlYQtHAPPYyaYGI5JSxdYo112xHiOpS9mVvsrx8ypbw+7fQQ1vk5rzMm4viVw4\nAtiYmi8tLDvHt94FXFzn631VrGOB921sVxxgBSJ/oGIFPnWoJ/HXmUx2RbhA60ymg72RBFF+pakl\n6yPvX7EVKqohOxV/zVv2jLw/qwi8hc70RRJF2ZWmllMecX8AWEU57UnukYWhdInhuqpLCr4uaRJl\nV5paTwVl+CMes4IyTnGoP/FU3Apys6Es/NtGenZ0rj9OsG3kkWVZl1mW5Q7xUACkhWhz/hRE2Z+8\nzotye/Z5RB1JKylO+ZW+WmZH3p+VAd7UnDYEjrgCTIQ/6/0vA3eGc/0Rxym70lce0Sfozo3hmGQ0\nijy6RSgg9SOLI8lxsEfiNGVX+sqPYaxKLPmWjHKz4YKTwu/PzIDLTnWuP05IvZsLJSm4PZEnoXN7\nws2HlPymUMgpYYpfF9GK8bRwuEciEi/Thkbef97g4ASHKallD5jwEISaVLb9KBh9h9M9EpE4mUAR\n3ggTRrcnk0EpOumswXAfXSgI8QayCDe/JR2WwhQ5NHUgiwERsskAJyZw5fCDde+1MLB34+1uN/z1\nVihu7Xyf7JSqn6+mnRo2sZcPAMjjKDJon+AeRebOuAG//wWwGt8DYlxjcbnPS0Cv4sNVexFzErt5\ngZ1soYbOZHIOrRiXohdmIrap3AtfvgaVu6HzEOgapTqTYJMOh5MPhze+bryvTR78IsInSClh4FXQ\nbhgsfQi2LQVvS+h7AfS7ADxZie6dSPIIBODDt2HjWmjXGUafELzaT1IFeLiKzjzAukb7XMBP6Yor\niVYja6oB5PAKvZnJTuazBxcwnhacRxFt0IhJkbqWLq3h449ryM01nHKKlxYtkvtTr5/Qjel8RRWB\nRvvOoT1diTIsPIkVtoAFT8LTs+G5N2FPOQzrB9PPgYGpuYZBRCoeJViAajbxC0p4CfbfD+qmJVNo\nz524knR+HWPak+n9AF/NLQT8/wSqgELcnstwZ9yFMcnZ71i5MJxAASek8O13Irab9yDMuiVYONqn\nxxi4/Dko6py4fkXgcsFLl8Mv58DjC2DbXshwwxkD4O7J0CMdPiEqHgbFf0t0L0SS12cfwK0XwYY1\nB7YVd4Y7n4IRExLWrWgupQOtyeApNvJt7dyMR5LH/9CJMVGnE0h+xWRyHcVcR3GiuyKSlDZv9jNt\nWinz5h2YQD4vz3D77blcf33yzi0+iBY8yhE8yjo+ogQL6IiXqXRgapIPmIhFThZcfXbwke5UPEqw\nTdxBCf9usNVPCf/C4KIDdyekX7Ewrs5keGdgWY+CVQKmdcoXjUQkRh8/B8//qPH21QvgzyfArZ8n\n7fw63gz41WS4/eRg8ahFFuRpLlaRQ8P3q+Hak6FsT/3tm9fDTybDM4uhR7/E9C0Gk2nDZNqwg2rc\nGFpqVI7IISEQsDjppBKWLq2/vNfevRY/+9leCgtdXH558o7gGUA+D9GfPfioIkARGSk9WvJQldxj\n3FKYj7Xs4n/ZSDc20JatnEg5L9Y7poYtlDTYVlcJL1ITYWnDZGFMDsbVQYUjkXRQWQbP3gmXdoHJ\nLvhBd3j+11BdWf+4Ob8Of47Ny+HT8NmWLDLc0KFAhSORdLF0xgweHzqUu9xuflNYyOyrr6Z0fYPb\n62f+qXHhaJ/KCnjmD/Z3NA5akanCkUiaWLCghNNO+wyv9x283nc47bTPWLCgpN4xs2dXNSoc1XXv\nvWVYlmV3Vw9aPh5ak6nCUYpS8cgGNaxkGydSzj+w2AsEqGExu/ghu7ln/3FlLATCh4BFTe0xIiIO\nqKqAW46HZ+6AbevBsmDLWphxC/ziZKipDh5Xugk2fBH5XF/Psbu3IiL7zfm//+PlSy5h05IlWIEA\nlSUlLH70Uf46ciS71tS5PW3hm5FPtEDZJSLOmTVrK+PHL+bVV7dTXW1RXW3x6qvbGT9+MS+/fGAQ\nwVtvVUc8z6pVflav9kc8RuRgqXhkg93cToAdIfft4X58rK39KnrF1ehbJCJOeeMxWB6mYP3FPJg7\no/aLGD4tirRkvIhIHG354gsW3X9/yH17N21i7s03H9hgouRXyi63KCKpxucLcM01K/D5Go8Y8vks\npk9fgc8XnGQ6WnTFeozIwdBfyDjzs51K3o5whEU5zwPBVdVMhCHHhgxyGRPnHoqIhPHO07HtLygO\nrqwWyRGT4tMnEZEolj4dObu+fuEFqvfuDX4xNko2RdsvIhInb721k40bq8Lu37ixirfe2gnAySdH\nvse+b183PXpoOmOxl4pHcRZgF4RYhrD+MdsA8NCaQqaGPa6Q8/HQKqZ2fWyikg+p2T+qSUSkiUqj\nzLG2a8uB/590a/jjOg2EgafH1mbVHvj+A9j8afA2ORGRJirbGjm7AjU1VOzaFfxi6o+gRWHoA3Pz\n4fz/jalNy+/Hv/gTfIsWYlVUNKW7IiIAbN0a+VY0gC1bgsecdFImI0aELw7ddlvsq62tWOFn/vwa\ntmyJ/J5VpCEVj+LMTXsMkX95PfTZ///F3EIRl2I4MNm0IZMiLqWYm6K252MjW7iU9QxnE2fyPWPY\nyJlUs6z5L8IJOz6Etc/AlrlgKbhEkkKnvpH3d66zAtGgM+Hiv0Fem/rH9DsBfjQHXO7I5/JXw9s/\nhQc7wN/Hwt+GwGN9YNk/m9d3h6xZs4uZM7/g5ZeXU1YW/aJPROzXum/k7MoqLCSvXbvgF+27wCNv\nQc/+9Q/qdhg8NAe69o7aXvVTT7C3b3fKxg6n/Ngx7OnZkcq7foEVSN7rmT34+Q+7mU0pm6iJ/gQR\nsV3fvtELPv36BY8xxvD664WcempmvdvTWrUyPPJIPuefH32ltUWLfIwYUUrfvqUcffQeOnUqYerU\nvWzfnrzZFfD5+PbNN/n8mWfY9Omnie7OIU9j2+LMRR45nEMZT4Xcb8glh3PrfO2hPbfShmsoYxEA\nuYzCQ1HUtgLsZhNn15lDKaiKD9nEWXTgDTLo2uzXYouSL2HRRVDy2YFtud1h+F+g+LjE9UtEYNLV\nsHRu5P11jb4Uhp8Py9+Git3QeRAURylA7fPqRY0LRbtWwctTg/Ml9T27SV23W2lpJZdf/govvbSc\nQCA4QqpFCy+33TaO66/X7cUiiTT4Bz/gvbvuwl8V+vaPwZdfjjuzzoqwhw+Ff38Jny2ATd9BcWcY\nPDamtqqfeJzKa/+n/sZdu6i+55dYO7aT/cDDzX0ZtrCweIBtPMkOymtHxruB0yjgl3QgS58jiyTM\nyJEFDB6cz6efhl4BcvDgfEaOLNj/datWLl55pZCVK30sXuwjL88wcWImWVnRJzv6/HMfEyfupqzs\nwDafD55/vprly/18+GELvN7kmjRp+axZvD59Ons2bNi/rdOoUZz5j39Q1LNnAnt26NJfDBu04HYy\nGBpij5dCHsNFy0Z7PBRRwCQKmBRT4QhgDzMbFY72CVBCKY82odcOqNwK7x5Xv3AEULYG/jsZdi1N\nTL9EJGjs2TD52tD7zr4Rhp3UeLsnMzi/0fCpsReOtiyNMMLIgvci3BKXIFOm/JMXXli2v3AEsHt3\nFT/72Vs88sjHCeyZiOQVF3PmjBm4MhrPI9l13DiOvfPO0E8cNAZOnhZz4ciqqaHqV7eH3V/zxOME\n1q2L6VxOeYTtPMi2/YUjAD/wEqVcz4bwTxQRRzz77BF06NB4PqMOHbw8++wRIZ/Tu7eHqVOzmDzZ\nG1PhCOBXv6qsVziqa+lSP88/n1yjqdfNn8+/zj67XuEI4PtFi5gxYQJVe0IX3MReKh7ZwEU+bXiV\nQh4hixPJ5Cjy+BHtWEA2Id58NVMZb0TcX87rcWsrLlY9BlVh5iXwV8Ly+5ztj4g0dvWf4Z534dgL\nYcB4OO4S+N18uOze+LXxzUuR9+9cAdu+il97B+mDD9Yxd+6asPvvuWc+fn/yDvkWORT0P/dcrvnq\nK0Zddx3djjmGw04/nbOee46L3n6bjJycuLTh/3Ah1ubNEQ7w45s9Ky5txUMlAZ4Is/ovwH/YzbeE\nn6xXROzXt28uX345it//vjcTJxYxcWIR993Xmy+/HBXTbW2xsCyLl1+OXBx68cXkKh7Nv+ceAj5f\nyH2l69axdMaMkPvEXrptzSaGTHI4hxzOsa0NK8of/Gj7HbcpSjEr2n4RccaRxwQfdvFVRj/Gnzz5\n9cYbqyLuX79+N198sZVBg4od6pGIhNKqd29OvP9++xqojJ5dVgzHOOVTyinFH/GYeeyhJ5FXcRIR\nexUWZvDTn3blpz+1Z7oRvx9qokx1lkTRhRUIsGrOnIjHrHr9dUZMn+5Qj2QfjTxKYVmMjLjfywiH\nehKrKCspaeJskUNDpyi3iGQVQevDnelLDKwYVoGL5RgRSW3uIcMgKyvyMUcd7VBvoosllZRcIunP\n4zGMHh15zMjRRyfZmJIo11XJvEBBOrOteGSM6WqM+asxZrUxptwYs9IYc4cxpvEN6dIsLbgEQ7iL\nGEMB/xNmX4IUnxh5f/v43dIn0lzKLgf0mgSt+oXfP3Q6eCK/QXPSCSdEnpSxQ4d8Bgxo51BvREJT\ndtnPFBWRcckPwu53jxqDZ+QoB3sU2SByyI9yqT+OPId6IxKasssZ118f/rqqoMBwxRXJMwLRuFz0\nmDgx4jE9T9L7xkSwc+RRX8AAVwKHA9cBVwF329jmISWD7rTliUYTcBuyaM1vyeaoBPUsjF5XQWar\n0PtcmdD3emf7IxKasstuxgXnvg5tGk4EaWDgFTA2/IS0iTB+fDfGju0Sdv8NN4zB49FAXkk4ZZcD\nsn5zP56zzm203T18JNnPvZiAHoWXg4tLCHPdBRxHPn3Cfggp4hhllwOmTMnkd7/Lpu7CkwDt2hle\ney2Pdu2S6zrmqJ//HON2h9yX37Ejgy691NkOCWDjnEeWZc0B6t6suNYYcx/BMLjBrnYPNTkcS2c+\noYzZ+FiLm3bkcjruECu6JVx2ezjmTVh0AexeXmd7Rxj+GBSFWqFOxFnKLoe07AaXfw5r3oTvF0BG\nNhx2FhT1TnTPQpo1ayoXXfQSr7++cv+2nJwMfv7zo/jJT5JnpIEcupRdzjBeLzn/eB7/Tbfhmz0L\nq6YGz/hj8Rw9PtFdC+nHtKGaAE+xk+ram9RcwIm04F46JLZzIii7nHT99dlcfLGX556rZvv2AP36\nuTnrrEwyM2Nbsc1J3Y89linPPMN/fvxjyrYeWHCp3cCBnP3cc2QVFCSwd4cup29ubAnsdLjNtOci\nh3wafwqWlIqGwKRlsPU92LMSsjtA8QngSrL7bEXqU3bZwRjocWLwkeSKirJ57bXzWbZsGwsXfk92\ntodJk3pTUKBP7SWpKbts4u5/BO7+oZfRTiYuDDdQzBW05n324sNiBLl0ITP6k0USR9llk7ZtXfz4\nx6lx7XLEeefR78wzWfnGG5Rv306bfv3oPGZMort1SHPsHbsxphdwLfBTp9qUJNZ2fPAhkuSUXVJX\nv35t6NevTaK7IRKVskvqKsLDGck4Kl2kAWWX1OXOzKTv6acnuhtSq8k3Nxpj7jHGBCI8/MaYPg2e\n0xF4A3jesqwn49V5EZFYKbtEJBUpu0QkFSm7RNJPc0Ye3Qf8Lcoxq/f9jzGmAzAXmG9ZVkzLf113\n3XUUNLiPcdq0aUybNq2JXRVJfzNnzmTmzJn1tpWWliaoN0lN2SWSZJRfMbE9u0D5JdIUyq6YKLtE\nkszBZpexLCvefTpw8mD1eC7wMXCRFaUxY8wQYPHixYsZMmSIbf0SSXdLlixh6NChAEMty1qS6P6k\nGmWXSOIov5qvqdlV+xzll0gcKLuaT9klkjhNyS7b5jwyxrQH5gFrCc6U39aY4EzulmVtsatdEZGD\noewSkVSk7BKRVKTsEkkddk6YfQLQo/axvnabASzAbWO7IiIHQ9klIqlI2SUiqUjZJZIimjxhdqws\ny3rasix3g4fLsiyFgIgkLWWXiKQiZZeIpCJll0jqsK14JCIiIiIiIiIiqU/FIxERERERERERCUvF\nIxERERERERERCUvFIxERERERERERCUvFIxERERERERERCUvFIxERERERERERCUvFIxERERERERER\nCUvFIxERERERERERCUvFIxERERERERERCUvFIxERERERERERCUvFIxERERERERERCUvFIxERERER\nERERCUvFIxERERERERERCUvFIxERERERERERCUvFIxERERERERERCcuT6A5I8vFjsZQ9lOOnL7m0\nJjPRXRIRiU3VF+BbBxndIfPwRPdGRCQmG6pgaTkUuGF0PrhMonskIhJdWRks+Dj4/2OGQ25uYvsj\n9rJ15JExZpYx5jtjTIUxZqMxZoYxpr2dbcrBeYPtTOZTLudrfsQKTuZTbmUVZfgT3TURxyi7UlDV\nUlg/AtYfCZsmw7r+8P1RUL0s0T0TcYyyK/WU+OC8FdB1MZyyDMZ+CT2XwIs7Et0zEecou1KPZcEd\nv4UOA+CEc4KPDgPg9t8E90l6svu2tbnAOUAfYArQE/iXzW1KM81lJ7ewis1U79/mw+I1tvO/rEhg\nz0Qcp+xKJTXfwYYJUPVx/e2VC2DDseDblJh+iThP2ZVCAhac/DX8cwf1PqJbWwXnrIA5uxLWNRGn\nKbtSzM2/gjt/B7v3HNi2ew/cdV9wn6QnW4tHlmU9YFnWR5ZlrbcsaxFwLzDKGOO2s11pnkf5nnCF\n4k/YzceUOtofkURRdqWYkj9CYGfoff4tUPqws/0RSRBlV2p5fRcs2ht6XwC483tHuyOSMMqu1LJz\nFzzwl/D7H/hL8BhJP45NmG2MKQIuAD6wLEv3QCWZjVSykvKIx8xDKSCHHmVXCih7Jcr+Wc70QySJ\nKLuS3ytRLqsW7oFtNc70RSRZKLuS31vzoKIi/P6KCnhznlO9ESfZXjwyxtxrjNkLbAc6A2fY3aY0\nXU3YMUcH+GI4RiRdKLtSSZR3V5befcmhQ9mVOmoCMRyjSy85RCi7UkeNL4ZjdOmVlppcPDLG3GOM\nCUR4+I0xfeo85bfAIOB4grd0/z1OfZc46kQWxVFWVRtOC4d6IxJ/yq40ln1s5P05E5zph4gNlF3p\n69iCyPv7ZkMHLXgrKUrZlb7GjQZ3hBsK3W4YP8a5/ohzjNXE6dCNMa2AVlEOW21ZVqOapDGmI7Ae\nGG1Z1och9g8BFo8bN46Cgvp/UadNm8a0adOa1Fdpmpls5resDbmvG1n8i4F40NqxyWbmzJnMnDmz\n3rbS0lLef/99gKGWZS1JSMeSjLIrjVV9ButHQp3J/vcz2dD5U8g8zPFuSXTKr+jszK7aY5RfCVIV\ngL6fBifIDuXJnnBZO2f7JLFRdkWn7EpvF14Nz/w79L4LzoZ/POJsfyQ2B5tdTS4eHQxjTBdgLXCM\nZVnvh9g/BFi8ePFihgwZ4li/5ICHWM/TbKx3G1tfcvg9h9EBbwJ7Jk2xZMkShg4dCrqAiQtlVwoo\newW2/AACdda3dreFdn+HnBMS1y9pMuVX/ETLrtpjlF8JtKoCzlwBX9aZdtJr4LbOcEunxPVLmk7Z\nFT/KruRXXg6XXAv/frX+9rMmw4yHICcnMf2SpmtKdnns6oQxZjgwApgP7AJ6AXcBK4GFdrUrB2c6\nnZlGMXPZSTl++pPHUN2uJocQZVeKyj0Nun0PZS+Dbz1kdIPc08Hong85NCi7UlOvbPhiEMwthSV7\nocADU4qgVUaieybiDGVXasrJgX89CctXwn/eCW476Tjo2zux/RJ72VY8AiqAKcAdQC6wCXgDuNuy\nNHtpMisig7PROGk5ZCm7UpUrC/KnJroXIomi7EphEwqCD5FDkLIrhfXtrYLRocS24pFlWV8Cx9l1\nfhEROyi7RCQVKbtEJBUpu0RSR5NXW0s2DSd8SvV20rWtdHxN6dyW2C8df3bS8TU52VY6vian2xL7\npevPjn7PU6OtdHxN4ox0/dnR757acrIdFY+SrJ10bSsdX1M6tyX2S8efnXR8TU62lY6vyem2xH7p\n+rOj3/PUaCsdX5M4I11/dvS7p7acbCfli0ciIiIiIiIiImIfFY9ERERERERERCQsFY9ERERERERE\nRCQs21Zba6YsgGXLlsX8hNLSUpYsWWJbh5xuJ13bSsfXlMxt1fkdyrKtQ1JX0maXk22l42tysq10\nfE3NaUv55bgm5Vcy/+ykQlvp+JqcbCuZX5Oyy3HKLgfbSsfXlK5t2ZldxrKsZnYr/owx5wPPJLof\nImnkAsuynk10J9KdskvEFsovByi/ROJO2eUAZZdI3EXNrmQrHrUCTgTWApWJ7Y1ISssCugFzLMva\nkeC+pD1ll0hcKb8cpPwSiRtll4OUXSJxE3N2JVXxSEREREREREREkosmzBYRERERERERkbBUPBIR\nERERERERkbBUPBIRERERERERkbBUPBIRERERERERkbDSpnhkjJlljPnOGFNhjNlojJlhjGlvQztd\njTF/NcasNsaUG2NWGmPuMMZk2NDWzcaYD4wxZcaYnXE+93RjzJraf69Fxpjh8Tx/nXaONsa8YozZ\nYIwJGGNOs6mdm4wxHxljdhtjthhjXjLG9LGprauMMUuNMaW1jwXGmJPsaKtBuzfV/hveb3db4hxl\nV5PPrexqflvKLombdMyu2vZSOr+UXXFtV9mVppzIL2VXk9twJLtq23IkvxKVXbVt25JfaVM8AuYC\n5wB9gClAT+BfNrTTFzDAlcDhwHXAVcDdNrSVAfwTeCSeJzXGnAf8HrgdGAwsBeYYY1rHs51aucBn\nwHTAzqX9jgb+DIwEJhL8t3vTGJNtQ1vrgRuBobWPucAsY0w/G9oCoDakryT4vZL0ouyKkbLroCm7\nJJ7SMbsg9fNL2RUHyq6050R+KbuaxqnsAufyy/HsApvzy7KstHwApwI+wO1AW9cDq2w8/yXAzjie\nbxHwQJ2vDfA9cIPN/04B4DSHvv+ta9sb61B7O4DLbDp3HrACmAC8C9zvxGvSIzEPZVfE8ym74t+e\nskuPeH2/0ya7attI+fxSdjX73MquQ+zhVH4pu2Ju07Hsqm3PsfyyM7tqz29rfqXTyKP9jDFFwAXA\nB5Zl+R1osiUQ1+GBdqkdKjkUeGffNiv4k/Y2MDpR/bJBS4JVa1u/L8YYlzFmKpADLLSpmYeAVy3L\nmmvT+SVJKLvCU3bFl7JL4knZFdkhkl/KLklJDueXsis52Z5fDmUX2JxfaVU8Msbca4zZC2wHOgNn\nONBmL+Ba4FG72/C6VCAAAAQlSURBVIqT1oAb2NJg+xag2PnuxJ8xxgB/BOZblvW1TW0cYYzZA1QB\nDwNnWpa13IZ2pgKDgJvifW5JHsqumCi74tOGskviRtkVs7TOL2WXpCKn80vZlZzszi+nsqu2Ldvz\nK6mLR8aYe2onegr38DeY3Oq3BP/Bjgf8wN9tbAtjTEfgDeB5y7KetKsdhxjsv7/UKQ8TvLd4qo1t\nLAcGErxX9hFghjGmbzwbMMZ0IhhmF1qWVRPPc4u9lF2OUnY1jbJLwkrH7GpuWw5Jl/xSdknCOZVf\nyq5g10iP7AL788v27ALn8svU3huXlIwxrYBWUQ5bbVmWL8RzOxKcpGq0ZVkfxrstY0wHgvcRLrAs\n67Jo529uO7XPuQT4g2VZRbG2E6H9DKAcOMuyrFfqbH8KKLAs68yDbSNC2wHgjLrt2tDGgwTvWz7a\nsqx1drUTot23CN7DfHUcz3k68CLBP2imdrObYFj7Aa+VzL/AhzBl1/7nKLtib0PZJQmXjtnVnLZq\nn5Py+aXsavI5lV0pzKn8UnalR3bVtuN4ftmRXbXndSS/PAd7AjtZlrWD4KRSzeGu/a833m3VBsxc\n4GPgB03p1EG+poNmWVaNMWYxcBzwCuwfrncc8KdE9SseagPgdGC8kxcwtVzE+LPWBG8DAxpsewpY\nBtyrC5jkpeyKP2WXbZRdsl86ZldT27JDuuaXskuSiVP5pexK/eyChOaXHdkFDuVXUhePYmWCy9GN\nAOYDu4BewF3ASuI8IZUxpj0wD1gL3AC0Df4OgWVZDe8HPdi2OgNFQFfAbYwZWLtrlWVZZQdx6vuB\np2vD4COCS0fmEPwBiytjTC7B78e+CmiP2tex07Ks9XFs52FgGnAaUGaMaVe7q9SyrMp4tVPb1t0E\nh56uB/IJTrI3Hjghnu3Ufo/r3XtrjCkDdliWtSyebUliKLuaTNl1cG0puyQu0jW7attL6fxSdjWf\nsuvQ4FR+Kbuaxqnsqm3LkfxyKrvAwfyyHFoCz84HcATBWeC3ERxa9y3wINDehrYuITj0q+4jAPht\naOtvIdryA+PicO5rCIZZBcGgHGbT92b8vn+fBo8n49xOqDb8wMU2vKa/Aqtr/+02A28CE+z49wvR\n9ly0ZGzaPJRdzTq3sqv5bSm79IjX9zMts6u2vZTOL2VX3NtWdqXZw6n8UnY1uQ1Hsqu2LUfyK5HZ\nVdt+3PMrqec8EhERERERERGRxErq1dZERERERERERCSxVDwSEREREREREZGwVDwSEREREREREZGw\nVDwSEREREREREZGwVDwSEREREREREZGwVDwSEREREREREZGwVDwSEREREREREZGwVDwSERERERER\nEZGwVDwSEREREREREZGwVDwSEREREREREZGwVDwSEREREREREZGwVDwSEREREREREZGw/h+9y2e+\nBqlpYgAAAABJRU5ErkJggg==\n", "text/plain": [ "<matplotlib.figure.Figure at 0x7f48d6cf8908>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "YOUR CODE" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3 Graph Signals\n", "\n", "1. Let $f(u)$ be a positive and non-increasing function of $u$.\n", "2. Compute the graph signal $x$ whose graph Fourier transform satisfies $\\hat{x}(\\ell) = f(\\lambda_\\ell)$.\n", "3. Visualize the result.\n", "4. Can you interpret it ? How does the choice of $f$ influence the result ? " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def f1(u):\n", " YOUR CODE\n", " return y\n", "\n", "xhat = f(lamb)\n", "\n", "x = YOUR CODE" ] } ], "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 1 }