{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "# Non-linear dimension reduction to diffusion maps\n", "\n", "Here we reduce the dimensions of a trajectory into a diffusion map.\n", "\n", "**Last updated:** December 2022 with MDAnalysis 2.4.0-dev0\n", "\n", "**Minimum version of MDAnalysis:** 0.17.0\n", "\n", "**Packages required:**\n", " \n", "* MDAnalysis (Michaud-Agrawal *et al.*, 2011, Gowers *et al.*, 2016)\n", "* MDAnalysisTests\n", "\n", "
\n", " \n", "**Note**\n", "\n", "Please cite Coifman and Lafon, 2006 if you use the ``MDAnalysis.analysis.diffusionmap.DiffusionMap`` in published work.\n", "\n", "
\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T15:45:37.571182346Z", "start_time": "2023-12-01T15:45:37.278542715Z" } }, "outputs": [], "source": [ "import MDAnalysis as mda\n", "from MDAnalysis.tests.datafiles import PSF, DCD\n", "from MDAnalysis.analysis import diffusionmap\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Loading files\n", "\n", "The test files we will be working with here feature adenylate kinase (AdK), a phosophotransferase enzyme (Beckstein *et al.*, 2009). The trajectory ``DCD`` samples a transition from a closed to an open conformation." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T15:45:40.137367027Z", "start_time": "2023-12-01T15:45:39.752599056Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/pbarletta/mambaforge/envs/mda-user-guide/lib/python3.9/site-packages/MDAnalysis/coordinates/DCD.py:165: DeprecationWarning: DCDReader currently makes independent timesteps by copying self.ts while other readers update self.ts inplace. This behavior will be changed in 3.0 to be the same as other readers. Read more at https://github.com/MDAnalysis/mdanalysis/issues/3889 to learn if this change in behavior might affect you.\n", " warnings.warn(\"DCDReader currently makes independent timesteps\"\n" ] } ], "source": [ "u = mda.Universe(PSF, DCD)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Diffusion maps\n", "\n", "Diffusion maps are a non-linear dimensionality reduction technique that embeds the coordinates of each frame onto a lower-dimensional space, such that the distance between each frame in the lower-dimensional space represents their “diffusion distance”, or similarity. It integrates local information about the similarity of each point to its neighours, into a global geometry of the intrinsic manifold. This means that this technique is not suitable for trajectories where the transitions between conformational states are not well-sampled (e.g. replica exchange simulations), as the regions may become disconnected and a meaningful global geometry cannot be approximated. Unlike [principal component analysis](pca.ipynb), there is no explicit mapping between the components of the lower-dimensional space and the original atomic coordinates; no physical interpretation of the eigenvectors is immediately available. \n", "Please see Coifman and Lafon, 2006, Porte *et al.*, 2008, Rohrdanz *et al.*, 2011 and Ferguson *et al.*, 2011 for more information.\n", "\n", "The default distance metric implemented in MDAnalysis' DiffusionMap class is RMSD.\n", "\n", "
\n", " \n", "**Note**\n", "\n", "MDAnalysis implements RMSD calculation using the fast QCP algorithm (Theobald, 2005). Please cite Theobald, 2005 if you use the default distance metric in published work.\n", "\n", "
\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T15:45:46.600061010Z", "start_time": "2023-12-01T15:45:45.485997717Z" } }, "outputs": [ { "data": { "text/plain": "" }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dmap = diffusionmap.DiffusionMap(u, select='backbone', epsilon=2)\n", "dmap.run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first eigenvector in a diffusion map is always essentially all ones (when divided by a constant):" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T15:45:48.442257804Z", "start_time": "2023-12-01T15:45:48.414223207Z" } }, "outputs": [ { "data": { "text/plain": "array([0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525, 0.10101525, 0.10101525,\n 0.10101525, 0.10101525, 0.10101525])" }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dmap._eigenvectors[:, 0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Therefore, when we embed the trajectory onto the dominant eigenvectors, we ignore the first eigenvector. In order to determine which vectors are dominant, we can examine the eigenvalues for a **spectral gap**: where the eigenvalues stop decreasing constantly in value." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "scrolled": true, "ExecuteTime": { "end_time": "2023-12-01T15:46:14.302609772Z", "start_time": "2023-12-01T15:46:13.922625868Z" } }, "outputs": [ { "data": { "text/plain": "[]" }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": "
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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.plot(dmap.eigenvalues[1:16])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From this plot, we take the first *k* dominant eigenvectors to be the first five. Below, we transform the trajectory onto these eigenvectors. The ``time`` argument is the exponent that the eigenvalues are raised to for embedding. As values increase for ``time``, more dominant eigenvectors (with lower eigenvalues) dominate the diffusion distance more. The ``transform`` method returns an array of shape (# frames, # eigenvectors)." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T15:46:15.659657778Z", "start_time": "2023-12-01T15:46:15.608628221Z" } }, "outputs": [ { "data": { "text/plain": "(98, 5)" }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "transformed = dmap.transform(5, # number of eigenvectors\n", " time=1)\n", "transformed.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For easier analysis and plotting we can turn the array into a DataFrame." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T15:46:16.586512021Z", "start_time": "2023-12-01T15:46:16.569047940Z" } }, "outputs": [ { "data": { "text/plain": " Mode2 Mode3 Mode4 Mode5 Mode6 Time (ps)\n0 0.094795 0.075950 0.054708 0.035526 0.022757 0.0\n1 0.166068 0.132017 0.094409 0.060914 0.038667 1.0\n2 0.199960 0.154475 0.107425 0.067632 0.041445 2.0\n3 0.228815 0.168694 0.111460 0.067112 0.038469 3.0\n4 0.250384 0.171873 0.103407 0.057143 0.028398 4.0", "text/html": "
\n\n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
Mode2Mode3Mode4Mode5Mode6Time (ps)
00.0947950.0759500.0547080.0355260.0227570.0
10.1660680.1320170.0944090.0609140.0386671.0
20.1999600.1544750.1074250.0676320.0414452.0
30.2288150.1686940.1114600.0671120.0384693.0
40.2503840.1718730.1034070.0571430.0283984.0
\n
" }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.DataFrame(transformed, \n", " columns=['Mode{}'.format(i+2) for i in range(5)])\n", "df['Time (ps)'] = df.index * u.trajectory.dt\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are several ways we can visualise the data. Using the Seaborn's `PairGrid` tool is the quickest and easiest way, if you have seaborn already installed. Each of the subplots below illustrates axes of the lower-dimensional embedding of the higher-dimensional data, such that dots (frames) that are close are kinetically close (connected by a large number of short pathways), whereas greater distance indicates states that are connected by a smaller number of long pathways. Please see Ferguson *et al.*, 2011 for more information.\n", "\n", "
\n", " \n", "**Note**\n", "\n", "You will need to install the data visualisation library [Seaborn](https://seaborn.pydata.org/installing.html) for this function.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2023-12-01T15:46:56.819570418Z", "start_time": "2023-12-01T15:46:17.713372425Z" } }, "outputs": [ { "data": { "text/plain": "" }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": "
", "image/png": 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C1AnzIRvLIbKKmbdszi3fV8T4EQIifeD+RD2Y6RNXw95uSjaUOadDf2dL6MbW4sDlPb/gg7/Wk+01jpmPiYu/CdFc5bgcEC3ukV4AoDXi3xgZ/wPaEyEfBMdjPqjAfqwa/2IZr6KJXkw2/2mlg/XziG1l3zcUC2pE/eh7Xof+9qMA5IBL+QFAqF54DjvLcTerJKLYiNQcqAtWQ3trU+8EZdY3ob/b54bRwIBfAfU9r0N+8K+efykQBy63/AbISka+I+/Blajc8H1Fih91/uqIY2fUg5kR/rqu7LcQonB64Iexhq8gP3gKMnSj5hVQ4nAJDtFoiPR8qFljrG5GzKLFvRzkoN3o+O+vbz4IFhD6zvWZF+zFivEvlvEq6ntELSbnA2gxuskDROrnkbDvG48FNaI+Ajd1DCaZnkv5vT6guxuAhISAMu/bLKYRJQhl0iKIMQdAttRApOdDpOZA+NKg7dzcO+matyqUE8JyiAicxSY/fApy7Fz+CkgJJ1L8RCJSc6DOXxU1rkYiGG/6K39B+I2aH4UomMZ4JDJJpLjXNC3q+mbE/4BtpGSHYr7/XJ95gYDhj1fRROvHgxWTjda3n0fCvm8OFtSI+oh0U0ehqBCLzoJUU/DBl5WYOfEwaxpHRJYQqTlhE6vQpCv4K2Cf16LfGLaWkxVKSP3jJ5rB4mqkGI9E1hhu3AeZEf/RMC9QNLH22/4i9ePBisnxxr5vDtMKahUVFcjIyEBaWlrY8u7ubpSWluKQQw4xa9NEI9Z7U8fw03WV3InQfRno3mf+KbtEZH/RJl3RcohIyxuwLhGFG+3BzID3YzwSOYbR8R91O8wLZKJ49eORYN83h+FP+ayqqsLpp5+OJUuW4JBDDsEVV1yB1tbem1A2Njbi7LPPNnqzRIYI3NRxRehSrcBNHVewak9Ew8IcQmQfjEci6o95gRIV+745DD9Dbf369VBVFY888giam5uxfv16nHXWWdiwYQOysrIAADLSnd6JbEKZcChEwbTA6a9peUwyRBQT5hAi+2A8ElF/zAuUqNj3jWf4GWo7duzA2rVrMXv2bBx++OHYtGkTioqKcM4556ChoQEAIIJVUZNs3LgRxx57LGbPno3TTjsNb775ZtR1n3nmGZx77rk47LDDMH/+fHz729/GSy+9ZGr7yP5ESjaU/MlMMkQ0IswhRPbBeCSi/pgXKFGx7xvL8IJaS0sLMjMzQ//2+Xz44x//iLFjx+Lss89GbW2t0ZsMs23bNqxbtw4XXXQRHn/8cSxYsAAXXHABysrKIq7/xhtv4PDDD8fdd9+Nxx57DAsXLsRFF12E999/39R2kj3I9kbImt2Q7Y1WN4WIHIy5hMieGJtEFAlzAxHjwAiGX/I5btw4fPTRR5g4cWLvRjwe3Hrrrbjkkkvwve99z+hNhtmwYQNWrFiBlStXAgDWrl2L7du3Y9OmTbjssssGrL927dqwf1966aV47rnn8Pzzz2PGjBmmtpWspe95A3LXYwjcmFFAzD4NygQ+LIOIYsNcQmRPjE0iioS5gYhxYBTDC2pHHXUUHnnkESxbtix8Qz1FtYsvvhgVFRVGbxYA0NXVhffeew8XXnhh2PLFixdj586dw3oPXdfR2tqK7OzsmLc/2GNxg6/Z6dG5RnPSPurVuyF33AuRlALFlwRAQu56DFreZCA5K+LfOGn/RsrofVRV1ZD3MYPTv0ejviu9qQqy7iuI3HFQMguNaJqpbBeHHY1AaDICDCeXjES89juRYtZ2fckh9KYq+Gv2wNPebO/PLk6xORJG9b1Eitdo72/rPjgC3K84MCg3BOdPMqsYwPD2LVFj1mlzTSPZqu/3ZeMx0kij+fyHG69CGvyEAL/fj46ODqSnp0d8XdM0VFRUYOzYsUZuFgBQWVmJo446Cps2bcL8+fNDy++8805s3boVTz/99JDvcc899+Avf/kLtm3bhry84T1CVtM0lJaWjrTZFGeZe19B4a5NED0JxDdhKrz5gcHw05yj0ZKUWIneTAsWLLC6CQMwXnv1jQUJgarZq9E0fpHVzXKU9M4qTKn/z4DlTs0ljFkajJNyhttiMxLGK1HsjMgNI82FiRizTho3EkkijJGjNdx4NfwMNY/HE1ZM6+rqwldffYUJEybA4/FAVVVTiml99X/ogZRyWA9CeOKJJ3D77bfjjjvuGHYxra/Zs2dHrWRqmoZdu3YNuo7TOWEf9aYqtD+1Gb3VeKBrzydQM3Oh+JIxZc7CQc9Qs/v+jVYi7GOQ0/dxtN9V/1gQkBjz7mZMPHqFrX89tF0f7WgEXvwv+uYUQAyaS0bCdvttAaP3nZ9pbByXM+IUmyORCH3P7H1z62fI/YqDUeaGSLmwcNcmTDjiFHhyik1pcjyY8d04btwwga36fl82HiONFI/P3/CCWlB7eztuuOEGPP744wCAp59+GuPHj8evfvUrFBYWDrgs0wg5OTlQVRU1NTVhy2tra5Gfnz/o327btg1r167FrbfeisMPP3xE21dVdcgvajjrOJ2d91E2lgFSH7i8qwNiwRlQ0nKHfA87759RuI/OMdL9iBgLUodoLIfqgAmhbb6/tFzos0+DfPcxQEpACIhZpw0rl4yEbfbbAmbteyJ/prFwXM6Ic2yOhJv7Xrz2za2fIffLRKPMDZFyoYCEaKqAmj/OjBbHhRnfjePGDRPZou/35YAx0khmfv6mFdTWr1+PDz/8EA888AAuuOCC0PJFixbhtttuM6Wg5vP5MHPmTLz88ss4/vjjQ8t37NiBpUuXRv27J554AldddRVuueUWHHPMMYa3i+xDyR0PCCU8uQsF6pLLoBROsa5hRHEWLRaUXOdOBq2iTDgEsmAa0FYDpOZDpLjnlz2iICfmDMYmEUUymtwQKRdKCIgcc6/AciInjhuJhGOkMRSz3vi5557DNddcg4MPPjhs+ZQpU7Bnzx6zNotzzz0XW7ZswZYtW7B7927ceOONKC8vx6pVqwAECn2XX355aP0nnngCV1xxBa644grMmTMH1dXVqK6uRnNzs2ltJOsomYVI/voVgeQOAEJB8tevgMpiGiWYaLGQKKfgG02kZEHkTeZkhFyrf86QEPB97We2zxmMTSKKZKS5IdL8qWr2atvnQitwrml/HCNHz7Qz1Orq6iLeh6y9vX1Y9zMbqeXLl6O+vh533HEHqqqqMG3aNNx9992h+7ZVV1ejvLw8tP7DDz8Mv9+P66+/Htdff31o+amnnoqbbrrJtHZSfMj2xgFVd9+8b8AzeSH0uq+gJODTZoiCGAsjEymvECWCYM7w1+zBB2UNmDV3idVNCsPYJKLBGJUj+s6fZFYxmj4rM7CV7sK5pv1wrDSWaQW12bNn48UXX8RZZ50VtvyRRx7B3LlzzdosAGDNmjVYs2ZNxNf6F8kefPBBU9tC1vF/8Ay00kehpKRCSUqFmHUqlPGBMyaVzEImdCKMPBb0xkpoNV9Czd8PStYYE1pmT/reNyHf3YrATVxFWF4hSgRKZiHUtDz460utbkoYN8Wm2/Or2/eP7MnoHBGcP2maBoAFtcHwuMs+3DRWjpTRY5BpBbVLL70U559/Pj799FNomoYHHngAn376KUpLS1nEItN17tiI9id+G/p30tTZ8GErZP5UVuKJRqnzzcfQvvWGwD0xhIKUU3+BpINPs7pZppPtjX0mIQAgId9lXiGympti0+351e37R/bkphxBNFKMA3PGINPuoTZ//nxs2rQJHR0dmDBhAl5++WXk5eVh8+bNmDVrllmbJYLeWIn2J38Xtqzzk3ehd7YBbbUWtYrIHfTGyt6BCACkjvatN0BvrLS2YfHQVoPwx4sj8G/mFSJruSQ23Z5f3b5/ZGMuyRFEo5LgcWDWGGTaGWoAMH36dPzmN78xcxNEYWRbPfyfbA88/jf8FejtbUDqwPv6EdHwaTVfRnwEula7x9JLd2RbPWRzFURGIURqjjkbSc0HIBA+GRHMK+RYcYmbeHBJbNo1vxrF7fvnVK7JA4NxSY6goSVEfx6pBI8Ds8YgQwtqLS0tw143PT3dyE0TQdv9MrQ3/ga9qyPCqwLq3BUJczorkVnU/P0iPgJdzZtgWZuCsR+8H4R6yJlQJy82fDsiJQti1qkD7j3BvEJOFK+4iQe3xKYd86uR3L5/TuSmPDAYt+QIGlyi9OeRSvQ4MGsMMrSgdvDBBw/7CZ4ffPCBkZumBCfb6uF//UFA6hBeH3zj9kfXV58FXhQKUr7+U3gOPMHaRhK5gJI1Bimn/mLA/QeCv+zI1rreXwbTck1vj2yr7zN5AgAJ7c2NUIpnmPLLpDL+YMj8qYHT41PzEmYSQpHFu78bJd5xEw9uiM2h8qvTuX3/RsLKHOLGPDAYN+SIRDdYvCRafx6pRI4Ds8YgQwtqDzzwQOi/9+3bh/Xr1+PUU08NPdWztLQUW7duxWWXXWbkZomgffgsoHWH/q1mFyA5PRvKzG/AM2VxQk/WiIyWdPBp8E5dDK12D9S8CaH40j59Cf5X/4rgr16ew86BOuVIU9sim6sw4H4QUg9MuEyaQImULCCBJiAUmRX93ShWxE08uCE2o+VXt3D7/sUiUg7BpMPjtn235oHBuCFHJKqhxtxE7M8jlchxYMYYZGhB7dBDDw399znnnIMrr7wSJ510UmjZ0qVLMW3aNDzyyCM49dRTjdw0JTDZWgft/afDF+oahC8Z3gOXMIkSmUDJGhM2CMnWuj4THQCQ8L/2AJTimab+6i4yCjHgfhBC6VlOZA6r+rtRGDf21j+/uo3b9284ouUQdcyBcWsD8wA5xXDGXPZnGi6jxyDTnvJZWloa8Wmes2bNwjvvvGPWZikBRfxFAoAybSmLaURxMtgvg2YSqTlQDzkzcE8EIHAvhIPXMPbJVFb1d6MwboisZYccwjxATjGceGF/JquY9pTPoqIibN68GVdeeWXY8ocffhhFRUVmbZYSUORfJAQ804+1qklECcfKXwbVyYuhFM/gU50obtzwSzjjhsg6g+aQ8i/j1g7mAXKC4Y657M9kBdMKaldddRUuvvhibN++HXPmzAEAvP3229izZw9uu+02szZLCSLwSORKiIwxEGm58Bx2DvyvPRC6waBn4dmOuOyGyC2MjsOwGB/GhEik5nDiRHFjp3En1ljpi3FDZI1oOQSpOQCMK6gNJz8wD5DdDXfMHc14SDRSphXUjj76aDzzzDN46KGH8Nlnn0FKiaVLl2LVqlUoLi42a7OUALTd26G99iBCj0ReeBbUKUdCKZ7pyKetEbmFUXEYMcYnH2FoW4lGyw7jDmOFyLki5RBN0wx7f+YHcpOhxlz2d7KKaQU1IHDZ56WXXmrmJijByLb6PskSACS01/8WuiklC2lE1hptHA4a4/y1kWzGynGHsULkfGblEOYHcqNo8cL+TlYytaDW1NSELVu2YPfu3RBCYMqUKVixYgUyMjLM3Cy5mGyuBB+JTORejHGi4WGsEFE0zA+USNjfyUqmPeVz165dOP7443H//fejsbER9fX12LBhA4477ji89957Zm2WXE5kjEHgppR9FzrrRtBEFB1jnGh4GCtEFA3zAyUS9neykmkFtXXr1uHYY4/F888/j9tvvx1/+tOf8Nxzz2HJkiW48cYbzdosuZxIzYG68KzwRyIfeiZ/fSByCcY40fAwVogoGuYHSiTs72Ql0y75fPfdd3HDDTfA4+ndhMfjwfnnn48VK1aYtVlyGdnRCLTWAml5EMlZAAB18hHhN6VksiRylXjFeKT8QuQkbhsPGZNExnFbfuiLuYL6c3N/j4QxYB+mFdTS09NRXl6OyZMnhy0vLy9HWlqaWZslF5Ff/Q/yvX8g+LQWzDwZYtwCAHzEN5HbmR3jg+UXIidxy3jImCQynlvyQ1/MFRSNG/t7JIwBezHtks/ly5dj7dq12LZtG8rLy1FRUYEnn3wSV199Nb7+9a+btVlyCdnR2CdRAICEfO8fgWo8EdEoML8Q2QtjkoiGg7mCEh1jwH5MO0Pt8ssvD/2/pmmQUsLr9WL16tX46U9/atZmySVkzWfQO9ogPF6I0GXDEmirA3haKxGNRmstBjwNyub5RbbWIbV5D2TrBCCzwOrmEBkrzjEpW2uhN1ZAySqCSMsz/P2JaCBPVzP08veh5JSMPO4cOH5T7JijB8EYsB3TCmo+nw9XX301LrvsMuzZswdSSuy3335ISUkxa5PkEv6PXoB/+z0IJgs1pwBqWiYAAaTmWto2InKBtDwEngbVd0Ji3/zi/+gF+F++B5OkhP+zLcDi8+GZvsTqZhEZJ44xGYwnSAkIAQ/jich0+scvYtr790F7X0IbTdw5bPym2DFHD4ExYDuGF9R+/vOfD2u9devWGb1pcgHZWhtIon2ShFZfDSUpDcqcFbzpIhGNmkjOAmaeHHb/CTHzZFvml1BOlD05UUr4X74X6riD+KstuUa8YpLxRBR/srUW2iv3QWD0ceek8Ztixxw9NMaA/RheUNu6dStKSkowY8YMSNn/dESi6GRLLfyfvQKp6xBChL8461TebJGIDCPGLQDypwROkU/NjXkiIltqoTeWQ8kqhkg3b5KnN1b0TixDG9ehN1VC5eSSbC6WOBltTA4H44lo9GId/4yOu3jkCrKGWTk6XnO2eGEM2IvhBbVVq1Zh27Zt2Lt3L1asWIFvfvObyM7ONnoz5DL+D59H93/vCiVRqSgQSs8zM4QCJX9/C1tHRG4kkrNGdL+JsHwlBLxHfReeA441oYWAklUECBE+wRQKlMwxpmyPyCgjiZORxuRwMZ6IRmckcW1G3JmdK8gaZvSVeM7Z4okxYB+GP+Xz2muvxfbt23HBBRfghRdewDHHHINLLrkEL730Es9Yo4hkS21YMQ0AoOuB/iIUeBb/P57mS0S2MCBfSYnu/94N2VJryvZEWh48i88HRO8PDMyJZHfxjpPhYjwRjdxI41qk5UFddB4keq4+YdxRFEbnaLuOReQupjyUwOfz4aSTTsJJJ52Effv2YevWrbjuuuvg9/vx5JNPIi0tzYzNkkPpjeUDT+8F4Fl4Jjz7H8YBl4hsI2K+kjr0pgqoJl1G4Jm+BCiehU/eehlT5y+Gh0/5JJuzIk6GyzN9CdRxB0FvqoSSOYZzDKJhGk1cK9OOwccNKmaMz4cnp5hxR1EZmaPtPBaRe5j2lM+g4L2wpJTQdd3szZEDKVnFEU/v9UxiMY2I7CVavlIyi0zdrkjLRVvGeIg0PsWJ7M+qOBkukZbHe6YRxWi0ce33ZUApPhBCVU1qIbmFUTna7mMRuYPhl3wCQFdXF5544gmce+65OPHEE/Hxxx/jmmuuwYsvvsiz02gAkZ4H71HfDTu913vUha64aSQRuQvzFdHQGCdE7sO4Jqdhn6V4MPwMtWuvvRbbtm1DcXExTjvtNNxyyy3IyckxejPkMp4DjoU6bg70pgoomUVMdERkW8xXRENjnBC5D+OanIZ9lsxmeEFt8+bNKCkpwbhx4/DGG2/gjTfeiLje7bffbvSmyeFEeh6vZyciR2C+Ihoa44TIfRjX5DTss2Qmwwtqp5xySui+aURERERERERERG5jeEHtpptuMvotySVka13v6ba8sTYRuRRzHZF9MB6JnIdxS2ZgvyIzmP6UTyIA6N71BPxvbAYACEWB5/Dz4Jl2jLWNIqKEJFtroTdWQMkqMvxJwv6PX4R/x32BJ0oJwVxHCcnMGIsF45HIGqPJAYxbMsNo+pVdxjSyJxbUyHTd7/wT/tc3hv4tpQr/jg1Qxx7EXweIKK78Hz2P7u1/CU2ovEdcAM/0Yw15b9la1ztZAwApmeso4ZgZY7FgPBJZI1IOEFOOHtbfMm7JDKPpV3YZ08i+FKsbQO7W/O6LKPv7TWhrbOpdKDVIXYPeVGldw4jIttpqylC162W01ZQBALS6MnR9+BK0urJRva9sre2dFAGAlOjefg9ka+1omwwA0Jsqet87tFGduY4cbTjxF4zZ1j3vmRpjsWA8EsVfcJzVO9rhb6yD3tEelgPaa8vDxvf+GLdkhpH2q0jzxs7nbkdn6ZPDGhOj9XNyF56hRqb5+I4fYde/twAQACRmTCzAxJkH9rwqoGSOsbB1RGRHnz+7CW/dcTkgdUAomH3cqcjZuTn077QzbwbSZ47ovfXGKBOqxgqoBpzCr2QWAUKEb0MozHXkWO0v/Q0tD1wair/0s29BypFnhq0zIGZnTcb4CUW9KxgYY7FgPBLFn95Yge7Kr9D52QehZUn7HwhPUyWadz6Dp399RyhXzP/+bzHpuNVhf8+4JTOMtF/1nzd2V+0L9O23/jvsMXHu924C8g4wdH/IXniGGpmi5dOdfYppACDw/hfVoTPVPId8m6duE1GYtpqy3kkIAEgdu/69BZ3+3n+3bvwZ1JbqEb2/ktUzoepLKIHlBhBpufAcfh4glNB7ew4/l7mOHEmrK+stpgGA1NHy4GVhv8q315YPjNl3P0F7e2fvGxkYY7FgPBLFn5QIK6YBgX+31VWhdtufwnLFzj9fMeAMHsYtmWGk/arvvFHv7Ajv2xHGxEjz2Lfv+jn8TTWG7g/ZC89QI8Pp9eWo374ZvcW0IIGWxkZkHn8RvLNPsqJpRGRjLeWf905CQgTadYEktecXQl2Dr/IDAMfH/P4iLQ/eIy5A9/Z7Qr8ceo8439AbzHqmHQN17EHQmyqhZI7hQQA5lla1e2A86hq6P3sD3nmBMTxizEqgra0TKSlJpsRYLBiPRPGlN9dFXN704ZsDzhCXuobWii+Qml8StpxxS2YYSb/qO2/UO9oGrqBr0Ko+g5ob6MNNH785YEyUuobuunJD9oHsiQU1MlTLtlvxj50voiS5G4GCWt+imkTut34N76xjrGkcEdlaevGkwK+HfSYjLZrAZ21elCT5UeDToAgg9emb8FlTOYpP+QnS84tj2oZn+rFQx80x9WlNIi0XKg8AyOHUwslh8dimCTT7FbTd9QPkrdiLpPoOIDcbLboHjd0CWR4N6aoOoajIWf07+DywxRPRGI9E8dM3b0gpoekSmgT0Z24FoECTEo1+Fa2agtwkibSiiRHfh3FLZhhJvwrOG/173kHHh98OL5gpKtTC/QEAHS9vgvbAz0IvtWgK6rtVpHskirrb0f3hS0DxVKi5Y8Pev7t2H7oqPoOvaH9488JfI2dwZUFt48aNuPfee1FdXY2pU6fiqquuwsEHHxx1/ddffx033XQTPvnkExQWFuL888/H6tWro65Pkf3qtEOxvdIPIBeAxPE5TZic3IngPdRmH386MlhMI6IoUvNLMP/7v8XOP18BqWv4sD0F/2lIhwQgILEkqwnZqh/1mgdpjz0Cz+N/x5KLb8KMZd+OaTsiLS/u93Micho1twTpZ9+ClgcuxWetCt5oTEJwPJ909w1o1wTeaU3Fqy3ZkBAQkDg6uxVn/PQGpE0Y2X0OicjZgnmj+f5L0N6loUXr+XG9qwPNWhpebkjHF12BXCIAZD/zNI48aCpSivdHcl7JEO9OZA2RlgfvgUsCY+KDlwXO1oYK5ZiL0C0B1JehZePlSFIkpmUCj5UnY3tTOoJj5vS7fo+u/AbMTO9GxnduRcrRZwMA6l94EGX3/CR01UTJ+b9HzpKzrNxVGgHXFdS2bduGdevW4Ze//CXmz5+PzZs344ILLsCTTz6JkpKBiXrv3r248MILsXLlSvzud7/DW2+9heuuuw65ublYtmyZBXvgTJccPwtvN6jQIKAC8KoCz9Zn4oj9qzB+2TnIWfwtpE+ZZ3UziSgC2Vpnm0srJh23GmPmHo097+/EXVdcDYnAJSISAs/UZwIycOCeo3RhXlYHnrvt55iw4KiYz1QjMoKdYscMKUeeibYuDW/ccg10KaBJoE1TcE91HhqkDzoAjwIoIhCj/23KxIUHHWt1s4loEGbnLd/MJdC03mLavk4v7inPRbPfgw6pBI4VRCB33P7HPwDFVcj0AtO/ezOKl64xvD1ERkk58kz4Zh6Lsqfuxu5/3AVs/TPw+F2YfPL3kNJz5tqXHZ5QMU3XAb8UeLslFfvaVXynuB6L7r8EvtlLoUv0FtMAQOoou/dSpB90bOhMNbfPMdzCdQW1DRs2YMWKFVi5ciUAYO3atdi+fTs2bdqEyy67bMD6mzdvRnFxMdauXQsAmDx5Mnbt2oX77ruPBbVhuubE6XizIRX+0CWeEt2aRKoKlHd6sfCbF0PN4a9ORHbk/+Q/8L+yIXBvEyHgWXQuPFOPtrRNqfkl6EjbB9nnfisdukCXVBDMMR16MhobfViU0YLXH78fR592NvwVu+EpmjzgdHoiM9gxdmKh1e0bVsy0JueiU1fQrgt06gpeakxHp1SgB2/poEskCwmfIqHrOsr27kFBIZ/IR2RH8chbWuVuaLoEoODv1Tl4vjETgIBfSmjBYwUp4dMlkhWg3u9BpqcLH939M+TMXYLkvJJh5yeieOuWCBTT+hTCdv/fnZieraJTl3i+OnAGpl8HOqUI9fkyLQV/2OdDslKBRY//Gph5QsT7lHZVfg5v3ljHzzESiasKal1dXXjvvfdw4YUXhi1fvHgxdu7cGfFvSktLsXjx4rBlRx55JB599FF0d3fD6/UOe/uapg352mDrONHfzzwIr9d6+xTTAEDAD6Bb0zFt6WlA5hhX7Ldbv8O+jN5HVVUNeR8zOP17NOK7kq118O/YAPScBQYp4X/lfmDMDMt/CSsqGQshBKSU8OtAlwzPMRqADl3Bxy0+KA/fg3Ev/g5pigYIBZnf+T1Sj3LXKfPxyj+JFLOj+UztHDvD0fbfB9F0f+9lJoPFjJo7Fu26gC4FPmjyoatvMQ0AINAhAY+UUIVETsVb0LT58dkRhzIqnhMpXqO9v9PH8v7M3K945C29uRp6ZytURcHrTSmhYpou0VtMAwAIdEnAq+vI8fh7/lhD677d6H7nmWHnJzuI5TtL5Jh1i7qn/hyhEKbDf+iZ2Pvvh5CsSOi6RHfP2Zh9+3ybVLGxMhvTXv0n0t56KvAE0b4P61BUqAX7wd9U7eg5hp2MJqcON15dVVCrr6+HpmnIywu/N05+fj6qq6sj/k1NTQ3y8/PDluXl5cHv96O+vh6FhYXD3v6uXbsMWccp1P/cidcqutGOVER6oqeEQNfCs1BaWmpB68zjpu8wGqP2ccGCBYa8jxnc8j2OZj9SW/ZiEmT4Qqnjk5070JY+bpQtG73TzjgHjz10PwLTlkg5BmiGF37ZjYpOFZNTNEDqaLz/J/hUFEHPKIh7m81mdr9NxJgdyfvaPXYGozRXo+D+n0D0+XU9UsyobXXwNlegvLYRgIAOoAleyAGxiNDr505oR+ozv8WujEnQeJ/CIY22TydivFq1nXgzY7/MzluZX72KMe//HQISXVlj8OYXgTugAsGywMBxfHpqBzI9PblIKPhiz16M+fvQ+cmOhvOdMWadTWmuRs7TtwPwom9/1iHw0b/+hk4NSFJ0pCg6OjQVkfp8TbcPTV1tyEwGMtOS0djaCSF1SKHAf9wleG9PlaPnGHY1kv493Hh1VUEtSIjwziulHLBsqPUjLR/K7Nmzo1YyNU3Drl27Bl3HSfTmavz7d8/Ap/iQIvzoCF2KFSQxPlXD3LlzLWqh8dz2HUaSCPsY5PR9NOK7kq0T4P/icaDvoC0UTJ13uC1+AZs7dy5OOf1b2Hz7jdj0zA70zzECEhnohoBATbcHk1O6AABC6phekIKkA+Za0WxTJFJsRmP0vo/mM7V77Aym84OXUN/v1/X+MdP1xmPoeOJ6QOrI7AZeA6AAyEQ3WhDpIEFiTUkzvlakAxI4YEwavFPmmr8zDpUI8Wz2vrn1MzRzv8zMW3pzNTr+vSX03s3eTKQqDT3/Fn3KauHj+KKMlsB/Kiqmnv8b5BSXDJmf7MYtfdHp7Y+Hzg9eQr3QUej1o6rbAyBwJYUOBYBEkgJMSe5EWYeKhvZgmSW8z+d7u9DWc7JUarIPyWlpUBefjdSjz4E3N3CLJCfPMewmHvHpqoJaTk4OVFVFTU1N2PLa2toBZ6EFRTp7ra6uDh6PB9nZ2TFtX1XVIb+o4azjBM3v/xfVrRp8isTkVD/ebvWiG0Dw/kY+6Pjbf9z5S4dbvsPBcB+dY1T7kVkAHH5u4DTynksrPIu+A0+mfX4FLiouwY9/fTtqOi7Gv//7MoI5RoVEsqJjcrofQkg0ayo6dYEkJTD58KZmueL77c8t/XYkzNr3Eb2vA2InmqSSqYBQwi9ZUVQkFU+BqqrQGyrQsfX60OvpXuCoEhX/LfPjwMwu1Db60BF22afE4ZmtOHV88CwTFd7C/RO2n8bCzfEcr31z62doyn6ZmLdkY1lYTslJUZGiSkxJ7sSnHUlQhIAqJQJ1hMA4Pj+tDQeld2HcxfcgffohoXunDZaf7MzpfdHp7Y+H4PiZ5dGQqmro1hV0Q0FZpxJaZ4zPj2/mN6OsPAm1fk9Yn08TGg7JaMfnTRITMiSSPQKqR4V442H4jjsfSvDzd/Acw67M7N+uKqj5fD7MnDkTL7/8Mo4//vjQ8h07dmDp0qUR/2bu3Ll44YUXwpZt374ds2bNiun+aYlCqy9Dy46/Y9+OJ+FVgGJfoIy2OLMFHzZ70QwfCn1d2Lz9fYtbSkTD4Zl6NNSS2dCbK6Fk2PcpQr9afxtO3/wH/OLWe9CpKchVujAlXYMQEsW+bngVoF1XkKRo8GXmAHqX1U0ml3NK7PSn5o5F9nm3omHDjwFdAxQV2ef+IXTjb63mywH3h5lV4EXGlPn43ysvIy3Hj7caUlAnfUiChoVZbTh/cjekVCAUL9JW/RpqTjG0+jJoVZ9BLdyfDyYisgmz8paSMy6sEOaDHwvydMjaLuR5/PiqQ0W7LgAJ5Pk0HJndinFJ3Ri75hrkH34ytPoydH24HeqY/QfNT0RW6jt+enUNXq9Ayspfouz+m8LGzSRFx28mfYV7y/PxXmsSNAiM8XZjXkYH8nyB9dr8Esk+L6TfD6gSWu0eKNlFofeIFqscW+3HVQU1ADj33HNx+eWXY9asWZg3bx4efvhhlJeXY9WqVQCA9evXo7KyEr/97W8BAKtWrcLGjRuxbt06fOtb38LOnTvx6KOPYv369Vbuhi11bH8Ie//yY1S0A34JAF5kezSkKRraNQWTk9sx4aDDcfyvNlndVCKKgUjLheqAYsDcVT/GY8efjhdv+h4+f78UulSQourwKgAgIZJTkZyTBsXjg5o3wermUgJwSuz0l3b02UievRT+ys/gGbN/2MGqmr/fwDNEhMCYlk+QokpMUP0oKGhGh64iWdEwK70LXh2QXQKpp12O5EXfRsf2h9Dyt5+GfllPP/NmeGcugV79OZSCSVBzii3YayICzMlbSmYhkr72U3Q+dTNqa+qwd085MiUwJdmHDl3B1BSJJEXCIyTyvRpUITEuTSC1sx5tT/8JrY/d0JsvzlqPolt2RcxPRFaLNH4emJyPD+76WU8RWMHkb3wXYyZNwrXbN+D9r+rw5mcNSFY0pPQ5QSrFK6C3NYb+3b37TXgnHxq2rb6xqtWXo+P5v6D933eGja3JR5wRl/2m6FxXUFu+fDnq6+txxx13oKqqCtOmTcPdd9+NsWMDybi6uhrl5eWh9cePH4+7774b69atw8aNG1FYWIi1a9di2bJlVu2CLWn1Zai7/yeoaA/82yOAHI+Ger8KryLgVXTMPvYb6DrifGsbSkSupmQXY9LkKcja9yY+bQ3ey0kix6OhtkVHfnY60pZfGvqVT2+ogFbzBdT8iWG//BElOqGoULxeCCX8EggluwipK65F26PXhibtwutFqkfFjJIMvF/WhBRVIEX1I0fV0KUD3TrgVSRat/4K3mmH9xbTAEDqaPnbZYA3KfAoEaEgbfU6JC9aFf+dJiLT+OZ8HVrWeOy94gQAgWOFQp8f9f7e+y5OT9eRmwQkKQI+FWh7+k8Iu0+U1NHyt58id93/kHTgkfHfCaJhUHPHhhV6xy49A3lzj0Fb+edILZ6E5LzAmWP6QSdixu63UPer7/SJg8CcVensCtyctEfrYzcg6ZBTIp511vHKZrQ8dCXQ1dG7sCdWvDOP4ZlqFnNdQQ0A1qxZgzVr1kR87aabbhqw7NBDD8XWrVvNbpajtf3f79ClhT9tJF3VkazoGDPnCEw445dI2W+W657oSUT2ojeUI+udv8OTpKO1W4dfCniEhKfndk5dwgPPhIOgN1ai46UH0PmfDaGiQOrp1yNp4enW7gCRDXS+tgVtW66JGBt6YyXU/AnI+OEmyK42yLYGtD96NQCgIN2DYl/3wLjTEDhTVNfQvfu1AZeMQsrQL/eQOlo3XQXvAUfzTDUil+lsaQqL/+CxQn5WGvLSffC1Nw7y1z10DVrV5ywSkKMk55WECmlBSmYhutXUUBz0HTtD42aQrsH/+VuQ9fug5E2AkjUGQODMtNZNPw+Mof1JHR3/uR9pp1xl4p7RUFxZUCNjdbz0V3Tt/D/4ItzHzyOACd/4PtL3nwNNixDoREQG0qq/AIQCnxrIPx4RXuhPSkmGf9976Lj3QsiO1t4XpI62LdfAO/0InqlGCU1vqOgtpgFhseHf/Sra//HrUKEt5eS18ExZFLoE1OfzRoy70PxAUeGdvHDgJaMA0PfJ6VKDXvMFC2pELpNSvP+A+PcIYEy6Fx5FQh/kb0MUFWrhJNPaSBRPyUWTACHggQwbOwccVwsF7Y/+AkJRQuOvb8Ep0Ks/7xmT+z9dO6DzpQeQcsx5nNtaSBl6FUpkemMlOv71BwjVA5/Ph6KU8NfHzVqA9DnHWdM4Iko4asFECFWF16MOzEcl+cj82iXofOa2qL/kaTVfxqehRDal1XwR4QwyHf4vS3uLaT3L2v/xawBAyjd+Hihkez0YV5IfOGAGACFQlCYCv7IrauBeaZPmIf3Mm4HgpaRCATxeiL4HA0KFkj/RzN0kIgsk5ZVg6nfX9+YIACW5afB6FAhFgZKWGba+8HghPH0eAteTR3h2GrlFUl4JfMsuCYuJcSX5yFxydtg4qWZkB4ppQGj81RsroRRMCtx6QQhADT8XSiSlQAhwbmsxnqFGg9Jr9wACEEJASUpGjqIgLVlDl6Yj86gzkHs2H95ARPGjZBejdtFFyH/lLmSr3UhL1oHZJyJr8Uqk7D8vkLOkDigRfskTSuCG60QJTM2fGOGhA0rg1+8IhTa9bi9880+GZ/Jh0Ou+QkbuOIzp7MK7Lz+LWYuPQ5JXDVyeVTgpdBCcfMQZ8M48JrS8+8P/onXTVYDUAKEibfWNPDuNyKWKjl2DrEkzUXPL6UhSFXg9vYUEJTUNqStvgL/8Y3S8cG/PfRVVpJ52NTzjDwrLI0Ru4ZmzDLNPOgudX7wNn9eDlP3nQckag5Tll0Kr+hxobwrdWiGkZ/z1TDoYaavXoXXTVRAqIJVAcVp4fKGz2Ti3tRYLajQoJW8ChOIBvL7AvxUVyT4d2cf9AKnLf2xt44goIbVMOw77n7AGqNsLJX/iwANzoQRuf+z1QXZ3hZalnn49T4mnhKdkFyH19OsH3EPNs9/ciIU2JXd84O+yxoTu6ZKkaVAnHISkvBKoqhrxAFjNKQktVxetgveAo6HXfBE5ZonIVVImzUXBiqvQ/sRvQ8uE1weheOCbcQySF30bKUvOZ06ghJGUV4LUwvFhy4LjpN5YOej4m9xnDPXvfQ8dT90SNn5zbmstFtRoUErWGKScvDZw2YeqQkgg+cQfI/nIc6xuGhElMCW7GGreuIHL++Qs4fECqhdJh5+BpMPXcMJB1CNp4enwTj8CWs2XUPP3C8VGaLzvcw+1YBFttNScYh40EyWQ5GPOA1QVHf/6Q+DhhooHSd/4eSinMCcQBYQdb0cZf4Px4p26CEnzTxowfpN1WFCjIfkWnALPlEXQ6/ZCyR1v2OSaiMgMzFlEQ1OyiwZMxBk7RGSk5CPPge+gE9Fd/SU+qGjC7PlLrG4SkS3FMv5GGr/JOiyo0bD0vdSDiMjumLOIRoaxQ0RGUrLGwJOeD62x1OqmENkax19n4lM+KUS21kGv+ACytc7qphARWYr5kCjxMO6JEhfjn+yOfdSeeIYaAQC0T/4L/6v3A5AABDyHfQfq1KMsbhURUfwxHxIlHsY9UeJi/JPdsY/aF89QI8jWuj4BCgAS/tf+yuo3ESUc5kOixMO4J0pcjH+yO/ZRe2NBLcHpzdXwf7IdUvOHvyB1yOYqaxpFRAlDb66Gf08p9OZqq5sCAJDNleidsAQXMh8SmcEu8c+4J7KXeOYGxj8ZyYy+yz5qb7zkM4F173oKnc/cGng8LwA1MxtKSlrgRaFAZBRa2DoicruwHCQUJJ1wCbyzv2Zpm0TGGAACYRMX5kMiw9kp/hn3RPYR79zA+CejROq7yowTRv2+7KP2xjPUEpTeXB1WTAMArakBUtMAocCz8ByItFwLW0hEbjYgB0kdnc/cavmZKiItF57DvgOInuGR+ZDIcHaLf8Y9kT1YkRsY/2SEaH1XGtB32UftjWeoJSi9fl9YMS1InbsSnqmLGaBEZKqIOUjq0OvLoGQUWNOoHurUo6CUzIJsroLIKGQ+JDKYHeOfcU9kPatyA+OfRitq320oN+T92UftiwW1BKXkjA1UufsGvlCgTj6MAUpEpouWg5ScEusa1YdIy2UuJDKJXeOfcU9kLStzA+OfRiNq380uBmr3GbIN9lF74iWfCURvqYW2bxf0llooGQVIOuGSsFNHk064xPIzQ4jIWn3zhJmYg4jcYSQ5g/FPRJGMJDfEa95CNJhofVfYYFxjjJiLZ6gliO6dj6P7lQcC/1AU+I7+HryzvwZ14sGB06hzSjiRJUpw/g+eRdd/7gSkBISA7+jvQRk/F7KhDCK7BEp6vqHbYw4icjbtw+fhf+musJzhOfC4iOvqLTVhuYTxT0SRxJIb/B88i64X/xy6CbzvmIui5iAis0Xqu5qmxWXb/cfYoEhze8aIsVhQSwBdb22Ff8f9vQukRNd/7oIyfh6UjAJOYokIektt74ALBPLEC3cEJqnBQXjJD+CZcbyh22UOInImT1cT/G/cFZ4zgnOL9Lywdf3v/xtdL/xpQC5h/BNRJMPJDXpLbWCeogcLFjq6XrgjYg4iihcrxrVoY2zEuX2UcZpGjpd8ulz3pzvQ+ezt0DvbIfXep45A1yAbjblJIhE5n17xAaDrYYMudG1AgU1vqTF+283V8H+5M+5P+NMbKtD96avQGyriul2ikbJTn/V11PXmhyCph+YWeksNtH27oFV+3DvRB4aVS6zKCURkH/3zQP/8F5i39Dv7R9fgf+8ZU+YqREFD9c24tqWlJuoYKxvLAsvD/qezBmAwnqHmYm1br0PH9o2hf6uZOVCz8qB4vAAERFaxdY0jItvwv/8suv5zB4DgYIze/+5L6pAN5YCBl352vbMNnU//PnS5RtKyn8B30HLD3j+aztf+jta//yK03bSVNyBp4UrTt0s0Unbrs13JuYAQ4UU1oUBkFffmlL4F+r4GySVW5QQiso/+eUDZfxE6X3kkLP8puZGPY/xvPgz/W3+H7+jvwzODl7aRsYbTN+M5NsuGsqhjrMguQWA+3/d11gCMxjPUXMq/7/2wYhoAaE310NtbIXUd3kVn8VRPIgr8stX3wBdAYOBVAIjwlYUCkW3cIKw3V/dOSgBA6uh8+vemn5WiN1T0FiZ6ttv691/Y4qwfokjs2Gf9vkx4jvxu2A2YfUd/F4AcvJjWs26kXGJVTiAi++ifB6S/C507Ng/IfyI1FwPmKUFSous/f+aZamSo4fbNeI7NIrsk8ONW2MLgGCsH/j4u+xfYaLRYUHMpbU9pxOVS80OdcQK8806Ja3uIyJ5kY3nEA17vCZfCd+wPwg+Wl3zf0AcT6HVfhT9eHACkDr3emMeLR6PVfBFxu1rNl6Zul2ik7Npn1QOORfKZdyLpm9ch+cw74TnwuIE5RYje/wGD5hKrcgIR2Uf/PCA1/8CVpA7Z3hw+TwHCc43UIRv5QxkZZ7h9M55js5KeD9+SyPP1wKWdAypqjAuD8ZJPl1InzI24XHh88C1cFd/GEJFtiaziiJdtqUXToaTnQ5kwr+e08WLDn/Kp5I4LTAD6HkALBUrOWEO305+aPzHidtX8/UzdLtFI2bnPKul5QJ8z3iPmFEVF0mnrgO7OQXOJVTmBiOyjfx4QaoTD1Z78p2QXQZkwD1r5h+j+9/oB64isoji0mBJFLH0znjwzjo84X482x2dcGItnqLmUZ+wMJB+xJmyZmpmL5OU/4xO1iChESc+H7+jv97ts66LQYKyk50MdN9vwYhoQeBJS0rKfhG07adlPTM9RSnYR0lbeELbdtJU3QMnmBIPsyUl9NlpOUcdMGzKXWJUTiMg++ucB4fEh6fBVUfOfkp4P79Qj4DvmB1HnMkRGiLVvxrVtEebrQ83xyRg8Q83FUk/9JXyHrkT3JzugZOTBO+0ITkqJaADPjOOgTJgL2VgBkVUU14HWd9ByeCYdAr1+H5ScsXHLUUkLV8I7/UhoNV+GfuUmsjMn9dnR5BSrcgIR2UekPJCy9PuD5j8r5zKUOEbSN63EuDAfC2ou5xk7A56xM6xuBhHZnJKeb+jTO2PadkaBJQfNSnaR7SY+RINxUp8dTU6xKicQkX30zwPDyX9WzmUocYykb1qJcWEuXvLpAnpzDbS9b0Nv5pNsiMh4zDFEZDXmISKKBXMGOR37sDPwDDWH6373aXQ998fAzQaFgG/pj+CdtczqZhGRSzDHEJHVmIeIKBbMGeR07MPOwTPUHExvrukNNACQEl3P3cYqNhEZgjmGiKzGPEREsWDOIKdjH3YWFtQcTDbsC38MLgBIHbKhzJoGEZGrMMcQkdWYh4goFswZ5HTsw87CgpqDieyxgBD9FioQ2SXWNIiIXIU5hoisxjxERLFgziCnYx92FhbUHEzJyIdv6Y8A0fM1CgW+pRdDyeBTPIho9JhjiMhqzENEFAvmDHI69mFn4UMJHM47axnU/RZANpRBZJcw0IjIUMwxRGQ15iEiigVzBjkd+7BzsKDmAkpGPsAgIyKTMMcQkdWYh4goFswZ5HTsw87ASz6JiIiIiIiIiIhiwIIaERERERERERFRDFhQIyIiIiIiIiIiigELakRERERERERERDFwVUGtsbERP/vZz7BgwQIsWLAAP/vZz9DU1BR1/e7ubvzud7/DN77xDcydOxdHHHEELr/8clRWVsax1URERERERERE5CSuKqhddtll+PDDD3HPPffgnnvuwYcffojLL7886vodHR14//33cdFFF+Gxxx7D7bffji+++AIXXXRRHFtNRERERERERERO4rG6AUbZvXs3XnrpJTzyyCOYM2cOAOCGG27At7/9bXz22WfYf//9B/xNRkYGNmzYELbs6quvxsqVK1FWVoaSkpK4tJ2IiIiIiIiIiJzDNQW1nTt3IiMjI1RMA4C5c+ciIyMDO3fujFhQi6SlpQVCCGRmZsbcBk3ThnxtsHWczu376Pb9A4zfR1VVDXkfMzj9e0yE/hgJ99vc/U6kmE3UvmQEfnajY9Tnl0jxGu393dYHuV/OE8u+JXLMJio3930nGM3nP9x4FVJKGfO729Cdd96JrVu34umnnw5bvmzZMpx22mn47ne/O+R7dHZ2YvXq1dh///1x8803D3vbmqahtLQ01iaH8fhbkdTdiE5vFvyetFG9F5FdLFiwwOomDGBEvFJsmN+cgzFLsWJ8W4fxSonIyTmHMUtWcXLcWGW48Wr7M9Ruu+023H777YOus2XLlqivSSkhhBhyO93d3fjJT34CKSWuvfbaWJsJAJg9e3bUSqamadi1a1fEdfTPX4F862EAEoCAmL8ayqRFI2qDlQbbRzdw+/4BibGPQU7fR6d8V0bnN6fst9ESdb/7Mnrf+ZmOXOizy2gFSp0/f4m3ROh7Zu+bWz9D7tfg7HjM5JbvzOnttys79A87xk28xOPzt31Bbc2aNVi+fPmg64wbNw4fffQRamtrB7xWV1eHvLy8Qf++u7sbP/7xj/HVV1/hr3/9K9LT00fUVlVVh/yi+q8j2+qhvbUJgQ4OABJy52YoJTMhUnNG1A6rDedzcDK37x/AfXQSO++HmfnNzvttpkTdb8C8fU/kz3Q0PP6+xTTADfOXeHNz34vXvrn1M+R+DWT3Yyanf2dOb7/dWfX52j1u4sXMz9/2BbXc3Fzk5uYOud68efPQ3NyMd955BwcddBAA4O2330ZzczPmzZsX9e+CxbQvv/wSDzzwAHJy4tuxZEsVejt4cKEO2VKdUJ2ciNyH+Y3IvZK6G8H4JqJ44ZyCKHaMG/MpVjfAKJMnT8aRRx6Jq6++GqWlpSgtLcXVV1+NJUuWhD2Q4MQTT8S///1vAIDf78ePfvQjvPvuu7j55puhaRqqq6tRXV2Nrq6uuLRbpBcC6HdJqlAg0gvisn0iIrMwvxG5V6c3C4xvIooXzimIYse4MZ9rCmoAcPPNN2PatGk477zzcN5552H69On47W9/G7bO559/jubmZgBARUUFnn/+eVRUVODkk0/GEUccEfrfzp0749JmkZoD9eAzANHzVQgF6oLVrBgTkeMxvxG5l9+TBjF/NeObiOKCcwqi2DFuzGf7Sz5jkZ2dPeTTOT/66KPQfwfvvWY1df/FUIpmBE69TC9gByci12B+I3IvZdIiKCUzGd9EFBecUxDFjnFjLlcV1JxMpOawcxORKzG/EbkX45uI4ok5hyh2jBvzuOqSTyIiIiIiIiIiIrOxoBYnsr0BaR0VkO0NVjeFiGhQsr0BevUnzFdENsUYJSIzMccQDcS4oEh4yWcc6F+8CpQ+gimQwLPPQZ/7LSgTD7O6WUREA+hfvAq99BEEHrEtoDBfEdkKY5SIzMQcQzQQ44Ki4RlqJpPtDX2CDwAk9LcfYWWbiGyH+YrI3hijRGQm5hiigRgXNBgW1EwmW6rRG3zBhRKypcaS9hARRcN8RWRvjFEiMhNzDNFAjAsaDAtqJhPpBQBEv4UCIj3fkvYQEUXDfEVkb4xRIjITcwzRQIwLGgwLaiYTKdlQ5n4LED1BKASUOd+CSMm2tF1ERP0xXxHZG2OUiMzEHEM0EOOCBsOHEsSBMvEw6PlT8enbr2LKnMOgpOdZ3SQiooiUiYdBjDkAsqUGIj2fkwUim2GMEpGZmGOIBmJcUDQsqMWJSMlGa3IRg4+IbE+kZDNXEdkYY5SIzMQcQzQQ44Ii4SWfREREREREREREMWBBjYiIiIiIiIiIKAYsqBEREREREREREcWABTUiIiIiIiIiIqIY8KEEBpBSAgA0TYu6TvC1wdZxOrfvo9v3DzBnHxVFgQg+ZtoGhhOvTpAI/TES7rf5+50oMZuofckI/OxGx8jPL1HitT+39kHul/PEum+JGrOJys193wlG+/kPJ16FDEYRjVhXVxd27dpldTOIbGnu3LlQVdXqZoQwXokGx5glcg7GK5GzMGaJnGM48cqCmgF0XYff77fdLw5EdmC3uGC8Eg3ObrHBmCWKzm5xwXglGpzdYoMxSxQdz1AjIiIiIiIiIiIyGB9KQEREREREREREFAMW1IiIiIiIiIiIiGLAghoREREREREREVEMWFAjIiIiIiIiIiKKAQtqREREREREREREMWBBjYiIiIiIiIiIKAYsqBEREREREREREcWABTUiIiIiIiIiIqIYsKBGREREREREREQUAxbUiIiIiIiIiIiIYsCCGhERERERERERUQxYUCMiIiIiIiIiIooBC2pEREREREREREQxYEGNiIiIiIiIiIgoBiyoERERERERERERxYAFNSIiIiIiIiIiohiwoEZERERERERERBQDFtQMIKWEpmmQUlrdFCIaAuOVyFkYs0TOwXglchbGLNHosKBmAF3XUVpaCl3XB13nnXfeGXQdp3P7Prp9/4DE2ceh4tUJEuG7ioT7nVj7DZgXs4n8mY4WP7vRcfPnF68x1q2fIffLeZy+b26ZF9uV0/uH08Xj82dBLU6klOju7nZ19d/t++j2/QMSYx/dIlG/K+53Yu23mfiZjhw/u9Hh5zd6bv0MuV/O4+Z9o9Fj/7BWPD5/FtSIiIiIiIiIiIhiwIIaERERERERERFRDFhQIyIiIiIiIiIiigELakRERERERERERDFgQY2IiIiIiIiIiCgGLKgRxUi21EDb+w705hqrm0JENCx6M/OWk/D7IkpsnGtSouL4R07jsboBRE6SVfkWOndcB0gJCAHfsT+Ed+YJVjeLiCiq7veeQdfztzNvOQS/L6LExrkmJSqOf+REPEONaJhkSw2KPv1nIMkDgJToev5P/AWFiGxLb67pnZwCzFs2x++LKLFxrkmJiuMfORULakTDpDeUQ0CGL5Q6ZGO5NQ0iIhqCbCjrnZyGFjJv2RW/L6LExrkmJSqOf+RULKgRDZOSXQwJEb5QKBBZxdY0iIhoCCK7BBDMW07B74sosXGuSYmK4x85FQtqRMMk0vNRMeUbgOgJG6HAd+wPoGTkW9swIqIolIx8+I79IfOWQ/D7IkpsnGtSouL4R07FhxIQxaBxzHxMXPxNiOYqiKxiJnkisj3vzBOgTpgP2VjOvOUA/L6IEhvnmpSoOP6RE7GgRhQjkZ4PNWuM1c0gIho2JSMf4MTUMfh9ESU2zjUpUXH8I6fhJZ9EREREREREREQxYEGNiIiIiIiIiIgoBiyoERERERERERERxYAFNSIiIiIiIiIiohiwoEZERERERERERBQDFtSIiIiIiIiIiIhiwIIaERERERERERFRDFhQIyIiIiIiIiIiigELakRERERERERERDFgQY1sSbbWQit7D7K11uqmEBFZTrbWIbV5D2RrndVNIXI8zjGI4s/T1Qy9/H3GHQ2JOZqcxGN1A4j683/0Avwv3wNICQgBz+Lz4Zm+xOpmERFZIpgTJ0kJ/2dbAOZEohHjHIMo/vSPX8S09++D9r6ExrijQTBHk9PwDDWyFdla25tEAUBK+F++l79QEFFCYk4kMg7jiSj+ZGsttFfugwDjjgbHHE1OxIIa2YreWNGbRIOkDr2p0poGERFZiDmRyDiMJ6L4Y9zRcLGvkBOxoEa2omQVAUKELxQKlMwx1jSIiMhCzIlExmE8EcUf446Gi32FnIgFNbIVkZYHz+LzAdHTNYUCz+L/B5GWZ23DiIgswJxIZBzGE1H8ibQ8qIvOg0RPoYRxR1EwR5MT8aEEZDue6UugjjsIelMllMwxTKJElNA805cAxbPwyVsvY+r8xfBkFljdJCLH4hyDKP6Uacfg4wYVM8bnw5NTzLijqJijyWlYUCNbEml5UJlAiYgAACItF20Z4yHScq1uCpHjcY5BFH9+XwaU4gMhVNXqppDNMUeTk/CSTyIiIiIiIiIiohiwoEZERERERERERBQDFtSIiIiIiIiIiIhiwIIaERERERERERFRDFhQIyIiIiIiIiIiioErC2obN27Esccei9mzZ+O0007Dm2++GXXdZ555Bueeey4OO+wwzJ8/H9/+9rfx0ksvxbG1RERERERERETkJK4rqG3btg3r1q3DRRddhMcffxwLFizABRdcgLKysojrv/HGGzj88MNx991347HHHsPChQtx0UUX4f33349zy4mIiIiIiIiIyAlcV1DbsGEDVqxYgZUrV2Ly5MlYu3YtioqKsGnTpojrr127FhdccAEOOuggTJw4EZdeein2228/PP/883FuOREREREREREROYHH6gYYqaurC++99x4uvPDCsOWLFy/Gzp07h/Ueuq6jtbUV2dnZMW9f07QhXxtsHadz+z66ff8A4/dRVVVD3scMTv8eE6E/RsL9Nne/EylmE7UvGYGf3egY9fklUrxGe3+39UHul/PEsm+JHLOJys193wlG8/kPN16FlFLG/O42VVlZiaOOOgqbNm3C/PnzQ8vvvPNObN26FU8//fSQ73HPPffgL3/5C7Zt24a8vLxhbVfTNJSWlo602USutWDBAqubMADjlSg6xiyRczBeiZyFMUvkHMONV1edoRYkhAj7t5RywLJInnjiCdx+++244447hl1M62v27NlRK5mapmHXrl2DruN0bt9Ht+8fkBj7GOT0fUyk76ov7ndi7XdfRu87P9OR42c3Oonw+Zm9b279DLlfzuOWfXN6++3KLf3DqeLx+buqoJaTkwNVVVFTUxO2vLa2Fvn5+YP+7bZt27B27VrceuutOPzww0e0fVVVh/yihrOO07l9H92+fwD30Uncsh+x4n4nHrP2PZE/09HiZzc6bv784rVvbv0MuV/O4/R9c3r77Y6fr7XM/Pxd9VACn8+HmTNn4uWXXw5bvmPHDsybNy/q3z3xxBO48sorsX79ehxzzDEmt5KIiIiIiIiIiJzMVQU1ADj33HOxZcsWbNmyBbt378aNN96I8vJyrFq1CgCwfv16XH755aH1n3jiCVxxxRW44oorMGfOHFRXV6O6uhrNzc1W7QLZlGxvQFpnJWR7g9VNISIHkO0N0Gs+Zc4gsgDjj4iCmA8oEbCfW8NVl3wCwPLly1FfX4877rgDVVVVmDZtGu6++26MHTsWAFBdXY3y8vLQ+g8//DD8fj+uv/56XH/99aHlp556Km666aa4t5/sQbY3QLbWQKTlQ6RkQ//yNeDtLZgCCTz/AvQ5p0PZb6HVzSQim9I+fQHy/W0AJAABhTmDKG70L1+D/vYWBONPzFgOkT0+NKYTUeLonw+C43H/uT6Rk0Xr55Gw7xvLdQU1AFizZg3WrFkT8bX+RbIHH3wwHk0iALK1DnpTBZTMIoi0XKubE5W+53Xobz+K0ET8wK9Bvv9kz78BQEJ/ZwtE4XQmISIawP/ek9A/fBpCUSFUFcwZRPEj2xv6HFQAUvNDf3srhOKB8HihzFkBZcKh1jaSiAZl1DFD/3wQHI9ldzvkB0+ht/jAvJAInHIsGqto/TzSvLP/cS77/ui5sqBG9uP/+EX4d9wHSAkIAc/h58Ez7RirmzVAICEFkwwASMgPtvX5d3CxDFT2eXBMRH34330K/jc2h/6tpGVCSU5hziCKE9lag+CYrXe0Q29tCr2mpGcB7zwKUTCNsUhkU0YeM/TNB70LZeAMchFaAJ15wfWcciw6ElH7eb95Z6TjXPb90XPdPdTIfmRrXW8CAwAp4d+xAbK1ztqGRRAtIfUZdQOEgEgb/MmxRJRYZGsd/G9sClumtzZBahoA5gyieAjEmYDUtLBiGgDoLY2Qfj9ka601jSOiQRl9zBDMB/2WInLxgXnBrZx0LDoSEft5hGPV6IU39v3RYEGNTKc3VfQmsCCpQ2+qtKZBfZvR3ghZsxuyvRFAlISkKBAzlgOiZ7kQUA46nZV8IgqR7Y3Q976FARMVAFLXAvdwYs4gMp1IyYYy53RIXYv4utQ1iLS8OLeKiIbD6GOGYD7oO4cPzOn7HQILwbzgYnY+FjVCpH4e6Vg1aoG5syV0LEyx4yWfZDolsygQ4H0TmVCgZI6xrlEA9D1vQO56DKF7pc0+DcqEQ6DMWQH9nUdDpwQrBwWuLfcXHYRP33kNUw5aCCWdgy4RBQRzidT8EV9XDlgGdcqSOLeKKHEp+y2EJ70QXf93zYDX1FnfZHGbyKbMOGZQ9lsIUTg97CbsWnM15Fdv9m5i7ALmBRez67GokSL18/4Chbc+x7kQgABk6SbIPsfCFBueoUamE2m58Bx+Xu+vQUKB5/BzLb0ZpGxv7FNMAwAJ+e5jkO2NUCYcCnXpz6Es+m7g/3tu1ChSstGaNIYDLhGF9M0lQlWhZmT3vigEPIecAc/Mr1vVPKKEJVJzoWbkhC1TMrKhjF9gUYuIaChmHTOIlGwo+VMgUrIDZ+KU7QwUWIL/K9/JM3RczI7Hombo28+jCR3nzj8zcGZm8Ky2PsfCFBueoUZx4Zl2DNSxB0FvqoSSOcb6BBbtXmltNUBKFkRKNgtnRDS0frlESUmD8CVDTF8GZdx863MdUaJqrYGSkgrhS4LU/BCqJ/DU3Z5xnojsyfRjhp5xu7eQgLBjAHIn2x2LWkikZANJtRD9r/5kHIwIC2oUNyItF+ogyUu21EJvLIeSVQxh9iWVoWvI+576K4BU3jSciIYWzFciKQ39c4nweKBMOASCExJKcHEd1/vrGeeFqgYKaQDHeSIDxCOuhzpmGBUeAyScvn1WLT7Q6ubYA+PAMCyokS34P3we3f+9K3TfMu9R34XngGNN255IyYKYfRrku4+FtilmnRb1AFi21UM2VcLrbzWtTUTkDP4Pn0f3f+5C8P6LnlknQGn8dFi5hChRjGRcl231kC3VEOkFEKk5g647lFjHeSIampnzdSPjfzDMDYkl3seY8erHo8U4MA4LamQ52VLbm+gAQEp0//duqOPmjPqXL9neGDh1NTV/QIJQJhwCWTAt6utB+uevQHtrMwCJAyAg81Vg8uJRtYuInEm21PYppgGAhP/dZ5C04iYIoQ+aS4gSxUjG9b5jLSCgzl8FZdKi2Lbbb8wf7jhPREMzc75uRPwPRzBHiIJpEEuuZG5wOTP7bCSR+jF67sVtJ4wDY7GgRpbTG8ujPMq4Auookp2+903Id7ci9BTPWadCGX9w2DoiJWvQ68RlW32fxAgISMi3H4EsnmHrXx2IyBz+D/6FAfdfhITeVAnP/odZ0SQi24l1XO8/1gIS2s7NEGMOGPZYG23MH2qcJ6LhMWu+bkT8D8dwjgvIXczqs5FE7ccF0wzdzmgxDozHp3yS5ZSsYgy4K6JQAo84HiHZ3tgnWQCBJ5dsjfnJJbKlGgMOnqWEbK0ZcduIyJkCTwZ7K+JrQuXvU0RBsY7rox1rjRrziSg6M+brQHzm2swRicmsPhtJtH6MFvscMzIOzMGCGllOpOfBe9R3wx5l7D3qwtGditsW4SmekEBbbYxtK0Dgho19FwqINN6wkSjhtNVAeLxQ0jPDFivpWVAKJlvUKCL7iXVcH/VYa9CYT0TRmTJfR5zm2swRCcmsPht5W5H7MdJtdMzIODAFf1InW/AccCzUcXOgN1VAySwafaJLjfDkEgggNbb3Fak5UOevgvbWpsCvZRBQ5n6Ll3sSJZDgDWbhSYZQVKiZORDeJEjND6F6oM5dwZxA1E9wXNeqPoFQVSgFU6KuGxprd24O3RxZnbdq+HFl0JhPRIMb7nw9lhuzjzr+h4M5ImHFcow5mgcKROvHMiV7lHtgIMaBKVhQI9sQ6XmGXc8uUrIgZp064BrxEd9sUQ74DyJKAPrnr0D73yaE8sikRRBV70JJUwEpIQ5cDnXy0VY3k8iWZPXHkG9tgoSEDgF1weqoNxpXJi2CGHMAZGsNRFp+TAczho/5RBTVUPP1/uOmumD1kDdmH038D6vNzBEJbTjHmJH6bawPxojUjzVNG3nDDcY4MAcLauRayviDIfOnBk5jTc0bUbKQbfV9kmtPTb/0YT6UgCgB9I9/QEJ+8QqUJT+FIv0jzitEiSBS/GhvbRr0RuMiNWfEY6sRYz4RjU7UuB/GjdlHE//DwRxB0YxkvIrG7H48WowD47GgRiGytQ6yuRIiYwxEWq7VzTHEaJ/uFfVGqS01EKk50JurodeXQckpgZJRMLrGEpFtaJWfwP/Jf4HuTiheX+8LUgL+TojCqdY1jmyN40LAUOOnGUY95rtwHkSJyao8FP3G7NVxa8NgBssRjP/EZcV4NRJG9VHp74Le2gzFl9H/rm80AiyoEQBA++S/8L96P4Knf3oO+w7UqUdZ3Crr9d5gsk+SFQIiPR/du/6FzmdvDV0nn3TcJfDOPtGqphKRQTqf+yO6394W+realQdPVs/EpSf+iSLhuNBrsPHTjjgPIrewMg9Fi3ukFwBojUsbRoLxn9icMF4Z1Uc5TzEen/JJkK11fQIUACT8r/0VsrXOwlbZg0jNCdz7oeeRyxICYu63ITV/bzICACnR+ewfoTfb4xc4IhoZrfKTsGIaAGiNtdC7uwI3mJ2/2la/VpJ96M3VHBf66D9+2jl+OA8it7A6D0WNezvdmL0fxj/Zfbwyqo9anR/cimeoEWRzJQae5qpDNlfxlGf03mBSa6rEB19WYebEw6Dve7c3GQVJHXpDWUJf4kPkdHrFB5FfmLAQnnmn2mZyRfaj15dxXOgndIPmlhqIdONvNG4UzoPILeyQhyLFvZ1uzN4f458Ae49XRvVRO+QHN2JBjSAyxmDgaa4KREahVU2yHZGaA5GUie59gdPVlZySwK8YMvwzU7JLLGohERlBKTow4nLPlCNtNbki++G4EJndb9AMcB5E7mGXPOSEuA9i/FOQXfutUX3ULvnBbXjJJ0Gk5cJz2HcA0dMdhALPwnP4q8wglIwCJB13SdhnlnTcj1jdJ3I4dcxUeOcsD1vmnbMc6hg+hIAGx3HBuTgPIrdgHood45/szqg+yvxgDp6hRgAAdepRUEpmBU4dzSjkIDIM3tknQp24IHCabHZiP82NyE2Slv4Inllfg17xIZSiA1hMo2HjuOBcnAeRWzAPxY7xT3ZnVB9lfjAeC2oupzdUQKv5Amr+RCjZRYOuK9JyOYDESMkoYCIicqjB8qM6ZioLaTQiZo4LsYzpFDvOg8gt3Dg/NTv/Mf5ppOI1NhvVR92YH6zEgpqLdb72d7T+/ReA1AGhIG3lDUhauNLqZsVEdjQCrbVAWh5EcpbVzSEil3BDfqTEkgh9lmM+EUXSP/+lnnIVkg48grmCLGfV2Mzx0j5YUHMpvaGiN7gBQOpo/fsv4J1+pGN+1ZZf/Q/yvX8gcANGAcw8GWLcAqubRUQOF8iPV/d5bLjz8iMlFjeM6UPhmE9EkUTKf21bfw1P7UlQktOYK8gyVo3NHC/thQ8lcCmt5ove4A6SOrSaLy1pj2ythVb2HmRr7fDW72jskygAQEK+949ANZ6IaBS6d78a8bHh/rL3rWkQ0RDsNqYPhWM+UWKLNQcMJmL+g4TW1gLmCoqHaP3ZirGZ46X98Aw1l1LzJwae4NE3yIUCNX+/uLfF/9Hz6N7+l8ABrBDwHnEBPNOPHfyPWmsR9mhgIPDvtjqAp7US0Qj5P3oe2usPRnhFQE1Nj3t7iIbDTmP6UDjmEyW2SDlATDl6xO8XMf+FjdnMFWSewcY0S8Zmjpe2wzPUXErJLkLayhvCHoubtvKGuF8aIltre5MQAEiJ7u33DP2LVVoeANFvoQBSebNQIhqZYD4SXi+8xRP6vCKQMuNgKEXTLWsb0WDsMqYPhWM+UWIbcQ4YxID8Fxyzk1ND/2auIDMM1Z8tGZs5XtoOz1BzsaSFK+GdfiS0mi+h5u9nycRbb6yIeGmV3lgBNS0v6t+J5Cxg5slh14eLmSfzpotENGJ985EnOx9qWib0rk74iifCe/h5zC9ka3YY04fCMZ8osUXLAbKpclTv2zf/Kd2NEHu2g7mCzDacMS3eYzPHS/thQc3llOwiSyfdSlYRIER4MhJKYPkQxLgFQP6UwCmsqblMFEQ0Kv3zkfD6oPqS4Fn6M4i8idY2jmgYrB7Th8IxnyixRcsBInMMULl3dO/dJ//JSQuZK8h0wx3T4j02c7y0F17yScOmN1Sg+9NXoTdUDPtvRFoevEdcEHYqrPeI8yEG+aU67O+TsyByJzFRENGI9M1bkfPRBVBYTKMENJIxfSgc84kSW/8cIP1+iP2PhOzuNnY7zBUUB6Md08yiN1TA/9UHkEoKY8AGeIYaDUvna1vQtuWawE0XhYLU069H0sLTh/W3nunHQh03B3pjBZSsIsuTEBElhmh5i/mIEt1oxvShcMwnSmzBHNCx/W/ofPYu4NN3gW23IeOQ/wfMnWt184hiYrcxzczxm0aGZ6jRkPSGit7ABQCpo23LNTGfqaaWzLQ8CRFRYhgsbzEfUSIzYkwfCmOMKLHJ7m50PHtXWJ7Jf+NeQ/MMUbzYZUyLx/hNsWNBjYak1XzR71HVAKQOreZLS9pDRDQU/5c7mbeIIhhqTNcbK+H/7A3ojaO7iTgRJa5IeUZIHXrtHmsaROQAQ42/PCa3J17ySUPSyj8auFAoUPP3i39jiIiG0PW/x9G29YaBLzBvEUHNnxi4H0zfSXlPbHT973G0/+PXoUtJUk5eC9+CU6xqKhE5VMQ8A0Av/xCYtsiaRhHZ2HDG38HGb7IOz1CjQemNlej89+0QXl/Y8pSv/9TWTxojosSkN1ai/R+/hhAIz1s995lg3qJEp2QXIfX068Nushz4t+idzAOA1NH+j1/zTDUiipmSXYSUr/80bJnw+tD13B3MKUT9BOeuQ42/0cZvzm2txTPUaFB67R5A6hAeL6CqgC4BRcCz30GhdbS6ffBX7IYomGhdQ4kooQXzEDpbQhOSvnkrdfVv4Ju9zOJWEtlD0sLToRROQdenr8E3ZSG8k+bC/9kbES8l0ev2QskaY01DicixPBNmQySnhI4dRM+ZNcPJKcEx3VM0GWru2Di1mGh4jO6fwePtMFFiJWnh6fBOPwJazZdQ8/djMc0GWFCjQSl5E0KnlgqhACoAoUDJHQ8AaHnqNjRu7n3SSMqxl1r6BB/ZVg/ZXAWRUQiRmmNZO4goflr/8wAa7rukJw8JJOUWwpueAQCBvOVR4Jkw19pGEtlIeMwoyDpzHVIPPTXsUhIpJSABeJKtbSwRmcqsuXPoGEJoAERgYZ9jiGj656fs825F2tFnG9YucjezjwWN6p96Q0VvUazP8XbIILGiZBexkGYjLKjRoJSsMUg5eW3YNd1JJ1wMvW4v2l9+CI2br+1dWerIfP4WaMvPgVowIe5t1Xa/DO2NvyFwBCCgHnIm1MmL494OIoofrW4fGu79EQJxD0BKdNZWQU1JhaKqoftQ8AwbogCtbl/vwQAASB2ND14JX35xaLyX/i5Ivx8A0Hz7aqSuuBbe6UcEfi3PHQ+k51u4B0RkFDPnzt0fbYfs7ERwfJYeL3xHnjl4eyLkp4YNP0by7KU8U42GZPax4Gj7p95YCb1uL/x7dqF92y2hY+vUFdcOON7m3NU5WFCjIfkWnALPlEXQ6/ZCK/sATU/dis72DqidrQPWFVKHv+pz+OJcUJNt9X0SKABIaG9uhFI8g2eqEblY/cPXoF0DvArgEcGlEr4l30PSlIOh5I7nhISoD3/F7oGXlkCi65UHkPade6AUTkHz7av6vKSj7dFfQiSnQggAQoE46kKgsgVtSjXSJs+HklkYz10gIgOYMXfWm6qg13+FzuYm1P3tKiR5BLweNfCivxvdr2yE//WHkfKNn8M3/+QBfx8xP+ka/JWfsaBGg4rHsWCs/VNvqoJWsweejka0/vevaH7qVvhUAY/W3afhOtoevRZZP/83Mi57IvTDFeeuzsGCGg1LMKj3/P5M7KuoCy3PVFSoCpCq6EhSJKRQ4CmcFPf2yeYq9CbQ4EI9cMovC2pErvTxutPx5f9egkf44BES+R4/Mj2BiY7iUeGZdLDFLSSyH0/R5AhP3xNQU9Igm6sgO1sB2X88lYCuAaqK8qp67P3Tz+EREqUCGDduDMYsPQdJh58BNack9CdafRm0qs+gFu4ftpyI7MHouXPX20+i86mbUVtTh717ykPL87LT4PP5kOpVkJokIf1daN1yDZS8SaF7Mmv1ZdAqP4NISR+YnxQVnjH7j2QXKYHE41gw4vgZpX8G4wFSR2ZNPf63pwJ+KeAREhPy05GbkQKpa5CaBqGq0Gr3wDv50KHvL8ix1XZMKajV19fjo48+wgEHHIDs7GzU1dVhy5Yt6Orqwte+9jVMnjzZjM2SyRqf/ENYMa1FU7C3MwXdukCXFJiY1ImUOccjTVfhG+R9zCAyChG4P0OfRCqUnuVE5DYvXLQQH35VjRTVixRFIsejAQBS1S6kZuXAd8BRFreQyJ7U3LHIOnMdGh+8EsHLYtJnHwI1NR0ioxBqUlaEghvQ0iXxQXk9yhvaIKUXXVKgwOsHvqpE0tbfwvt/NyP9rPVIOWINOrY/hJa//TR06Ur6mTfDO3MJ9OrPoRRMgppTbMm+E1EvI+fOelMVOp+6GV2dnWHFtNpuFR+W+aGIbkAKzCrswiS1BZou0f3rE5C27PsQ6XlofeyGUL5IO3I1WrdvDhTxFRXZ5/6BZ6fRkOJxLKjmjkX2ebeiYcOPo/bP7tp96Pzsf/D/6zdQPR7UNndg+8d1aNOTkKJKeIRER1Ub5qk61K623r/b/Sa8kw+Num2tvhwdz/8F7f++M2xsTT7iDMP2j0bG8ILaO++8g/POOw8tLS3IzMzEfffdh0suuQQejwdSSvzlL3/BQw89hJkzZxq96ZCNGzfi3nvvRXV1NaZOnYqrrroKBx8c/UyF119/HTfddBM++eQTFBYW4vzzz8fq1atNa58TafVlaPz3faF/+yVQ71fR4PegvMsLKQW+6EiC56VX8Z8dR2Pp+VfgsNMviFv7RGoO1EPOhPbmxlCSUQ9ew7PTiFzo1V+tQVmzHwI+CCGRrQbu9ZSs6BCZeUg79iyoxdMtbiWRfaUf/z348ovR9coDUFPSoKamh8ZMkQqkrrgWbY9eGxpPP2iQeP6LRgBAt54MvxQQENjTKXFASjvGp3XDq+ho+dtP4Rk7o7eYBgBSR8vfLgO8SRCQgQPm1euQvGhV9AYSkemMnDvr9V8BUkdnZ1do2Z4OLz5sT4GUAhKBQkL5PonJSR5MT21HuirR9cQfkeRVet9I6uh+cysKfvksZEcrPGP2ZzGNhiVex4JpR5+N5NlL4a/8LKx/dtSWofqpu9D81O3wIDD+7RZ5eLkCkEiBgIRXkRjjDVzu2djchtyk3vdtfewGJB1ySsSzzjpe2YyWh64Eujp6F0odLRt/Bu/MY3immsUML6j9/ve/x4knnogrr7wSDz/8MH7wgx/gyCOPxK9+9SsAwNq1a3HHHXfgT3/6k9GbBgBs27YN69atwy9/+UvMnz8fmzdvxgUXXIAnn3wSJSUDO9vevXtx4YUXYuXKlfjd736Ht956C9dddx1yc3OxbNkyU9roRN2734RP7a34+6VAty5Q3uWFJgU6JFDW5kWLVJGr+iH/sg4eSBx8+oVxa6M6eTGU4hl8yieRi513zAzUdvuQKQTGpfnhkQINmgfZuh9+KZC15Gyknnat1c0ksj3fvJPhnX5UxDEz6dAV8E5bDK12D1qRjOe/fyoAoFMX6JQCX7V60CQ9yBaBYvYh0o80BC4L7d792sB7zAQvGVUCZ761broK3gOO5plqRBYzau6s5IwLPLgsKXCNSocu8GF7CjQp0KoL1HR60KYLJAuJZr9Atd+DqcmdmIxOeFUBRRG9b6ZrQFc7kg480ohdpAQSr2NBNXdsWKF333MP4YM7gz8keZDr8aOiy4MnahRUdHkhBZDv8aMgSUN1twepqg6/7Hc2na5Bq/p8QHFMqy9H66afB+Kivyh/Q/GlDL1KbN577z2ce+65SE9Px9lnn42qqip861vfCr2+Zs0a7Nq1y+jNhmzYsAErVqzAypUrMXnyZKxduxZFRUXYtGlTxPU3b96M4uJirF27FpMnT8bKlStx2mmn4b777ou4fqISAvAqAkUpgX97hESXFJBSoN6v4p2WNHzlT0a95sNnXSl4qSEd2zfchJaa8sHf2Oh2puZAGTOdxTQiF1pyyEH4tCMVDZoXX2nJ2NmcAj8AKQXaNRX7LTgSWadfa3UziRxjsDFTyS6Cd/KhKP9qLwBAl0CnFNjZnIK9WjIaNC8+9ydjR2Mqqtp7/05vawpcMjpgY30OmKUGveYLg/eGiEbCiLmzklmIpK/9FL6kJIyfUIw2TYGUAmVdXuxsScPe7hTUaknY152MHU0ZeLkpDbs7k9DkF2julujuW4NXVKgW3I+Z3CFex4IdtWWof3c7Gj/d2aeYBgACld0e3FtRgHc70lClJaHK78PHHSn4sC0ZWs9JKZnefvd7i9Lv9erPe864EwNeY6zYg+FnqHV3dyMpKXD+otfrRXJyMnJyejt0dnY2GhoajN4sAKCrqwvvvfceLrww/KyoxYsXY+fOnRH/prS0FIsXhz9O98gjj8Sjjz6K7u5ueL3eYW9f0yJUjvu9Ntg6dqZMnA/h9SEbXUjzSnRpgI5ufNKehH0dgV+dNAgErl0HmnUV7zZ7UPmve5Cy+iprG28Qp3+Hw2H0Pqqqasj7mMHp32Mi9Me+vrZ4HtrgQfD+GKoUAFR81erBpLRuTC7MxOTLH3bt5xGv7zuRYjbRYmjEpAZAQkfgzLR2qUKTAnrPmN8iBX79ZQH+OrsSijcJnc/dhZRTr0L74+sCv6gLBVBViL4HA0IFcscn7GdvVN9LpHiN9v5u60NO3i911olI3m8BSur3Af9+EC9tfhKfdSQheGzglwKBvVLwRWcyuhsE9vN1okWXACRKUoGcFBVpZ/wWyBzjmM8glu8skWPWTSqefwif/OVyQOqBsbBfbezt5lRU+71hfd4PiepuLyo7u7CsCEhJ8kH6ey6RVgbp93kTAveCgw6pegAtcGY4hILU1b9xVKxYYTQ5dbjxanhBraioCHv37sW4ceMABC4BLSgoCL1eXV0dVmAzUn19PTRNQ15eXtjy/Px8VFdXR/ybmpoa5Ofnhy3Ly8uD3+9HfX09CguHfyPD4Zx5Z+bZeWZLP+KHyNvxZ3g1P7xCYMKMo5DxzA60ampYMQ0IJI+9HT6oL/4ZH/nS0DVmBrT0guhv7iBO/g6Hy6h9XLBggSHvYwa3fI9u2Y/BvPS3W9GoBYtpQCDHSChSoEF6kK22I/+cm1FaWmphK+PD7O87EWM2EWJoNPTqfUhRdLRqCup1D/RQMS1IoE7z4Z9V6ThlPwBSxxf+DHSvug+epjL4M0uQUlaKvFfuhJA6pFBQu+i7+OKLSgCVFu2VPYy27yVivFq1nXhz8n6pLdUo3nE/SnzZCI7bukRPYaF3HN/XlYSabg8yPN0ABMraBVq+tR4ybTrgwPF8ON8ZY9b5RMVHaLr/ZwhW0YQMPNwnqLLLg50tKdBDxbTePt8FoLLbg8lpGoQnCVBV1B18DtomHg4trSBqv09f9L3AGKoCUvWg8cCT0DzzG9DS8h0ZK1YYSf8ebrwaXlD7+te/jrq63idBHnPMMWGvP//88zjooIOM3mwY0e+USCnlgGVDrR9p+VBmz54dtZKpaRp27do16Dq2N3cu9BPWQKv+EmrBfsgGcPTbi/BiQ3giCRAQQiBV70DaMzcGbkJ85s1IOmJN/NttEFd8h0NIhH0Mcvo+Jsp3VbPtz3j9jTcBpPR7RUBCRzr8+MY5F2HqUcdZ0by4SZTvezBG7zs/06F1bt+I1meugZ6j4tX6JCQJHXLAeA8AAi/VpeC4knak+xRMO2wplOy+90c7Lmz+kJOd2PdOS4S+Z/a+ufUzdMN+tf79l+iAxNHZLXi8LgeB8RqIdKywrysJk1ICN2mHlNhv/Hhkz5wbz+aOmhu+M8D58+J46Ny+EVV//yma+vRlIQBFBs7i7tQFPu1Igk+RkJAYeHctEXiAVvBfigfjFn8T/vZW+IoK4c2Nci+0fsfgiT6GxiIe8Wl4Qe2HP/zhoK9/73vfM21ncnJyoKoqampqwpbX1tYOOAstKNLZa3V1dfB4PMjOzo5p+6qqDrlvw1nHztS8cfDmjQv9+5Bzf4EDrl+PN9v6nj0CABLHZDb3Xu8tdbRu/BmSZh8HNVqycAinf4fDwX10DrfsRyRaXRnefuBGJIksBH4JDM8xPkicMrcEB5xxhUUtjD83f99DMWvfE/kzHYxWV4bWv/0UkBL7p/pRlKRBgcSmmt5LuHpJpCoaGrpVjDn712HzhKD+8wdyd9+L17659TN06n5pdWXoePYuAEC+14/jshrxbGMWBII3YA8fx/dL6uz9p6IibexkR+434NzvLMjp7TdbcEz0KToChbLevqyoCqZkKNjXLoAWgcIkP77q1OEPu4ILACTOKaqD8KQAQoU2ezk+/+WJoaeSlpz/e+QsOSvi9jmGjo6Z/dvwhxL019XVhc8++wx+f+B635SUFPh8PlO25fP5MHPmTLz88sthy3fs2IF58+ZF/Ju5c+dix44dYcu2b9+OWbNmxXT/tESVsvRC/PInFyJTCdxjJUDCJySyvDr0vteU6xq0qs8saCUROdE/H/wzbt5bgK+6k+ATgXusBEikQMOiPD/OuPM5K5tI5Fpa1e6wp3WmqhKrxrZhXnorlLAbxkgkC4lPOpPx6WE/QvKib8e/sURkC1rVbghIaEJFiyawoqABp+XVIVvtRhJ09D9WqNV6jgkVFdMv/B2S85z9ozu5V3BM9CpASUqfOalQMP3Cm1F47s0oTlMgINGmqfCogAfhc9f5aa044swfI+uSh5F2yd9R/cJDveOs1FF276Xort1nwd7RaJhWUGtvb8dVV12FuXPn4qSTTkJ5eeBpj7/61a9w9913m7VZnHvuudiyZQu2bNmC3bt348Ybb0R5eTlWrVoFAFi/fj0uv/zy0PqrVq1CWVkZ1q1bh927d2PLli149NFHcd5555nWRrcpPOUyXHr6EqQKDclCQ6rQkaxIbK3LQXVXn0qwokIt3N+Qbcq2euiVH0K21RvyfkRkL1Vffow7Nj8RurwsWZFIFRrGeTuxMKsLN353BW7817sWt5LIemaNh2rh5IFP6xQKbrz6ClxWUo7Zya1IFhrSFR0+JXDmyd333Y/qqsS+LxqRncR7vhzMG3qfM3OOz2nG2WNqMSu1bcCxwlMN2Rj3o3tx2B1vonipc28LQ/ZgZn/vOybm+CSmZeiYmA4cum4bipeuQfLi1Rj/m1dx+DfPwKc9D+NIVWWgrwsNvzjr67j9seeRdupV8E49DFp7S9iPVgAAXUNX5eeGt53MZfgln0Hr16/Hhx9+iAceeAAXXHBBaPmiRYtw2223DXgSp1GWL1+O+vp63HHHHaiqqsK0adNw9913Y+zYsQACD0UIFvcAYPz48bj77ruxbt06bNy4EYWFhVi7di2WLVtmSvvcqmDBCfA8+mLYMgmBsi4fktVOpHgU5J213pDLPbXd26G99iCCp46rC8+COvmIUb8vEdlDy//+gV1b7grdzzLIowh8q6AeU35yL+YeebxFrSOyDzPHQzW3BOln34KWBy8LPK1TUZF+1np4ZizBgemXw6M04k/lyWF/o+s6yvbuQUHhGEPaQEQjZ8V8OZg3Gv96KQB/aPnMtA7oEPikMzVsfV3X0Zo6hmem0aiZ3d/7j4lej4qcs9YjZXLvVXBqTgnyF30T+Ns/Q8s8Pb9LlSw6CWru2NByX9H+gQJd36KaosI3ZpJhbab4MK2g9txzz+H3v/895s6dG7Z8ypQp2LNnj1mbBQCsWbMGa9ZE/pXjpptuGrDs0EMPxdatW01tk9vtN2sBhBBhB8BCABWdKlq6fYBQML9TxWhThGyr75MsAUBCe/1vUIpnQqSa8/RYIoqfz7fdg7f+8ku0aAoEcsNugC4gMe+cn6M5wx1PDCYajXiMhylHngnfzGOhVX0GtXD/0I9iReetR/3dl0NADohR7Yu3gAWHGLJ9IhoZK+fLwbyhPn0nqp68A9D1QEH+wMUQlR+F5QxFUVAyfoKp7SH3i1d/jzYm9qV/8dbAsVFRUDJufNh63ryxKDn/9yi799LQj1Yl/+8WePPG9n9LsjnTLvmsq6tDXl7egOXt7e0xPz2T7K+gcAwuueLq0HerKAqOymxButLz65TUsfPPV6CtpmxU25HNlQBkv4U6ZHPVqN6XiKzXVlOGt+65DgCQruo4Kqsl9GwwRQj86EeXYPLJF1nZRCLbiNd4qOaWwHfAEWEHDtnHnImUi/6K87/1zT7P75M4KqsFXzz061GP9UQ0OlbPl9XcEhSsvh7Tbn0bE6/+P5Rc8y90frwjbFwXkPj+Dy/mGa00avHs75HGxKC2mjJ8vvFXA/r5yaecGrGf5yw5C9NuLcXEq/8P024tjfpAArI3085Qmz17Nl588UWcdVZ4x3jkkUcGnLVG7nDiN05BSnomsrMykdJWjff/8N2w16WuobXiC6Tmj/y0bpExBgg9KSi4UIHIKBzxexKRPbSUfx526vuBqR0Yn9SFcbNmY/Z3/4DC/aZB0zQLW0hkH5aPhxkFOGrpCWh/8X40+lVkeTSkqzqkjlGP9UQ0Opbnhx7evLHw5o1F89svAVKGxvVgzjj8oOlxbQ+5k136e3Ae27+fT548PurfBGOEnMu0gtqll16K888/H59++ik0TcMDDzyATz/9FKWlpXjwwQfN2ixFoDdXQ6/7CkruOCgmXyqVlZOLOXPnorO+Eu/3uy5cKCrSiiaO6v1Fag7UhWdBe/1voUcMq4eeycs9iRwsmKPSMrMG3E8iwyOxcMV3kb7fNAtbSGQ/dhgP04snId0DpKvdve0yYKyP57yFyI3skB/6Si+eFLgXjJRIV3Wkq/qQuYJ5gIYr3v09Wt8M9PPAPLZvP/fmFpvSDrIH0wpq8+fPx6ZNm3DfffdhwoQJePnllzFjxgxs3rwZ06fz14h46XpnGzqf/n0ouSQt+wl8By0Pva43V0Ov3wclZ6yhg1Vqfgnmf/+32PnnKyB1DUJRMe+i3xjyi7U6+QgoxTMhm6sgMgpZTCNysM7XH0bXi38BIAGhYM43zsQ7T2zsyRsK5v2/XyJ9wclWN5PIlqweD1Pyikc11keagww1byGi4bE6P/SVkleMvOU/QN1Tfx5Wrug/N2AeoKHEq78PNkal5pdg3nm/QOl9N0DKQDFtznfXoSEz35S2kD2YVlADgOnTp+M3v/mNmZugQejN1b0BDwBSR+fTv4dn0iFQMgrQvespdD5za29COOESeGd/zbDtTzpuNcbMPRqtFV8grWiioZd/iNQcFtKIHK7r9UfQ9eLdvQukjjE1b2LZLdvQ1txkeN4gciOrx8ORjvWR5iDqxIMHnbcQUWyszg99Zcw7AQd/8yy0V+0ZNFdEmhswD9BwmN3fh3NsXfjRYzhqwRS0dXQje9lFSFu0CqWlpaa1iaxnaEGtpaVl2Oump6cbuWmKQK/7KvxRvAAgdej1+wCgdyLbs7zzmVuhTjzY8DPVeEBMRP3pzdXo/O89A1+QOpKEH2mzDo9/o4hoRGId6/Xm6ohzkKSvXxl13sIDaSLnS8krRnrhuKivDzY3YB4gqw332Do5yYvkJC/w2oOQs5Za0FKKJ0MLagcffPCwn+D5wQcfGLlpikDJHTfgfkQQCpScsYHAj5gQyjhYEZHpAjlIDnxBCCg5vDkrkZtFm4MAIuq8hYjcj3MDsrMRHVs3lMe3kRR3hhbUHnjggdB/79u3D+vXr8epp54aeqpnaWkptm7dissuu8zIzVIUSkYBkpb9ZMB13qGCWcSEwLPJiMh8Ss5YCEWF1GXY5Nl39AUs6hO5nJIzNuIcRB07Y/B5CxG5GucGZGcjOrbOLgZq91nTYIoLQwtqhx56aOi/zznnHFx55ZU46aSTQsuWLl2KadOm4ZFHHsGpp55q5KYpCt9By+GZdMiAm/4qGQVIOuGSAfcv4WBFRPHQNwdJXQOEQNJR58N36LesbhoRmWywOUi0eQsRuR/nBmR3sR5bi4wCACyouZlpDyUoLS3FddddN2D5rFmzcPXVV5u1WYpAySiIOCH1zv4a1IkHBy7zzCnhpJWI4oo5iChxDRb/0eYtROR+nBuQ3cVybK1pmgUtpHgyraBWVFSEzZs348orrwxb/vDDD6OoqMiszVKMOGklIisxBxElLsY/EUXC3EBOxb6beEwrqF111VW4+OKLsX37dsyZMwcA8Pbbb2PPnj247bbbzNqsY8m2esiWKoj0Qts83pqIyAjMb0TuxfgmonhiziGKHePGPKYV1I4++mg888wzeOihh/DZZ59BSomlS5di1apVKC4uNmuzjqR99jK0Nx8CIAEIqAefAXX/xVY3i4ho1JjfiNxL//wVaG9tAuObiOKBcwqi2DFuzGVaQQ0IXPZ56aWXmrkJx5Nt9X06OABIaP/bBKVoBqvHRORozG9E7uXxt0K+9TAY30QUD5xTEMWOcWM+UwtqTU1N2LJlC3bv3g0hBKZMmYIVK1YgIyPDzM0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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "import seaborn as sns\n", "\n", "g = sns.PairGrid(df, hue='Time (ps)', \n", " palette=sns.color_palette('Oranges_d',\n", " n_colors=len(df)))\n", "g.map(plt.scatter, marker='.')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "[1] Oliver Beckstein, Elizabeth J. Denning, Juan R. Perilla, and Thomas B. Woolf.\n", "Zipping and Unzipping of Adenylate Kinase: Atomistic Insights into the Ensemble of OpenClosed Transitions.\n", "Journal of Molecular Biology, 394(1):160–176, November 2009.\n", "00107.\n", "URL: https://linkinghub.elsevier.com/retrieve/pii/S0022283609011164, doi:10.1016/j.jmb.2009.09.009.\n", "\n", "[2] Ronald R. Coifman and Stéphane Lafon.\n", "Diffusion maps.\n", "Applied and Computational Harmonic Analysis, 21(1):5–30, July 2006.\n", "02271.\n", "doi:10.1016/j.acha.2006.04.006.\n", "\n", "[3] J. de la Porte, B. M. Herbst, W. Hereman, and S. J. van der Walt.\n", "An introduction to diffusion maps.\n", "In In The 19th Symposium of the Pattern Recognition Association of South Africa. 2008.\n", "00038.\n", "\n", "[4] Andrew Ferguson, Athanassios Z. Panagiotopoulos, Ioannis G. Kevrekidis, and Pablo G. Debenedetti.\n", "Nonlinear dimensionality reduction in molecular simulation: The diffusion map approach.\n", "Chemical Physics Letters, 509(1-3):1–11, June 2011.\n", "00085.\n", "doi:10.1016/j.cplett.2011.04.066.\n", "\n", "[5] Richard J. Gowers, Max Linke, Jonathan Barnoud, Tyler J. E. Reddy, Manuel N. Melo, Sean L. Seyler, Jan Domański, David L. Dotson, Sébastien Buchoux, Ian M. Kenney, and Oliver Beckstein.\n", "MDAnalysis: A Python Package for the Rapid Analysis of Molecular Dynamics Simulations.\n", "Proceedings of the 15th Python in Science Conference, pages 98–105, 2016.\n", "00152.\n", "URL: https://conference.scipy.org/proceedings/scipy2016/oliver_beckstein.html, doi:10.25080/Majora-629e541a-00e.\n", "\n", "[6] Naveen Michaud-Agrawal, Elizabeth J. Denning, Thomas B. Woolf, and Oliver Beckstein.\n", "MDAnalysis: A toolkit for the analysis of molecular dynamics simulations.\n", "Journal of Computational Chemistry, 32(10):2319–2327, July 2011.\n", "00778.\n", "URL: http://doi.wiley.com/10.1002/jcc.21787, doi:10.1002/jcc.21787.\n", "\n", "[7] Mary A. Rohrdanz, Wenwei Zheng, Mauro Maggioni, and Cecilia Clementi.\n", "Determination of reaction coordinates via locally scaled diffusion map.\n", "The Journal of Chemical Physics, 134(12):124116, March 2011.\n", "00220.\n", "doi:10.1063/1.3569857.\n", "\n", "[8] Douglas L. Theobald.\n", "Rapid calculation of RMSDs using a quaternion-based characteristic polynomial.\n", "Acta Crystallographica Section A Foundations of Crystallography, 61(4):478–480, July 2005.\n", "00127.\n", "URL: http://scripts.iucr.org/cgi-bin/paper?S0108767305015266, doi:10.1107/S0108767305015266." ] } ], "metadata": { "kernelspec": { "display_name": "guide", "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": "3.9.15" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "vscode": { "interpreter": { "hash": "5edc5d8d8cbc0935a054a8e44024f729bc376180aae27775d15f2ff38c68f892" } } }, "nbformat": 4, "nbformat_minor": 2 }