{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Calculating the Dimension Reduction Ensemble Similarity between ensembles\n", "\n", "Here we compare the conformational ensembles of proteins in four trajectories, using the dimension reduction ensemble similarity method.\n", "\n", "**Last executed:** Sep 25, 2020 with MDAnalysis 1.0.0\n", "\n", "**Last updated:** September 2020\n", "\n", "**Minimum version of MDAnalysis:** 1.0.0\n", "\n", "**Packages required:**\n", " \n", "* MDAnalysis (Michaud-Agrawal *et al.*, 2011, Gowers *et al.*, 2016)\n", "* MDAnalysisTests\n", "* [scikit-learn](https://scikit-learn.org/stable/)\n", " \n", "**Optional packages for visualisation:**\n", "\n", "* [matplotlib](https://matplotlib.org)\n", "\n", "\n", "
\n", " \n", "**Note**\n", "\n", "The metrics and methods in the `encore` module are from (Tiberti *et al.*, 2015). Please cite them when using the ``MDAnalysis.analysis.encore`` module in published work.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:45:02.786638Z", "start_time": "2020-09-25T05:44:48.314302Z" } }, "outputs": [], "source": [ "import MDAnalysis as mda\n", "from MDAnalysis.tests.datafiles import (PSF, DCD, DCD2, GRO, XTC, \n", " PSF_NAMD_GBIS, DCD_NAMD_GBIS)\n", "from MDAnalysis.analysis import encore\n", "from MDAnalysis.analysis.encore.dimensionality_reduction import DimensionalityReductionMethod as drm\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "# This import registers a 3D projection, but is otherwise unused.\n", "from mpl_toolkits.mplot3d import Axes3D \n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Loading files" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The test files we will be working with here feature adenylate kinase (AdK), a phosophotransferase enzyme. (Beckstein *et al.*, 2009)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:45:04.030896Z", "start_time": "2020-09-25T05:45:03.770613Z" } }, "outputs": [], "source": [ "u1 = mda.Universe(PSF, DCD)\n", "u2 = mda.Universe(PSF, DCD2)\n", "u3 = mda.Universe(PSF_NAMD_GBIS, DCD_NAMD_GBIS)\n", "\n", "labels = ['DCD', 'DCD2', 'NAMD']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The trajectories can have different lengths, as seen below." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:45:04.880256Z", "start_time": "2020-09-25T05:45:04.874762Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "98 102 100\n" ] } ], "source": [ "print(len(u1.trajectory), len(u2.trajectory), len(u3.trajectory))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculating dimension reduction similarity with default settings" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The dimension reduction similarity method projects ensembles onto a lower-dimensional space using your chosen dimension reduction algorithm (by default: stochastic proximity embedding). A probability density function is estimated with [Gaussian-based kernel-density estimation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gaussian_kde.html), using Scott's rule to select the bandwidth.\n", "\n", "The similarity of each probability density function is compared using the Jensen-Shannon divergence. This divergence has an upper bound of $\\ln{(2)}$ and a lower bound of 0.0. Normally, $\\ln{(2)}$ represents no similarity between the ensembles, and 0.0 represents identical conformational ensembles. However, due to the stochastic nature of the dimension reduction, two identical symbols will not necessarily result in an exact divergence of 0.0. In addition, calculating the similarity with `dres()` twice will result in similar but not identical numbers.\n", "\n", "You do not need to align your trajectories, as the function will align it for you (along your `select`ion atoms, which are `select='name CA'` by default). The function we use is `dres` ([API docs](https://docs.mdanalysis.org/stable/documentation_pages/analysis/encore/similarity.html#MDAnalysis.analysis.encore.similarity.dres))." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:45:18.839369Z", "start_time": "2020-09-25T05:45:06.267428Z" } }, "outputs": [], "source": [ "dres0, details0 = encore.dres([u1, u2, u3])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`encore.dres` returns two outputs. `dres0` is the similarity matrix for the ensemble of trajectories." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:45:22.215208Z", "start_time": "2020-09-25T05:45:22.205167Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[0. , 0.68690372, 0.68942142],\n", " [0.68690372, 0. , 0.66357751],\n", " [0.68942142, 0.66357751, 0. ]])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dres0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`details0` contains information on the dimensionality reduction, as well as the associated reduced coordinates. Each frame is in the conformational ensemble is reduced to 3 dimensions." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:45:28.395157Z", "start_time": "2020-09-25T05:45:28.390077Z" }, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "(3, 300)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "reduced = details0['reduced_coordinates'][0]\n", "reduced.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As with the other ensemble similarity methods, we can plot a flat matrix of similarity values." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:45:50.363936Z", "start_time": "2020-09-25T05:45:50.193591Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig0, ax0 = plt.subplots()\n", "im0 = plt.imshow(dres0, vmax=np.log(2), vmin=0)\n", "plt.xticks(np.arange(3), labels)\n", "plt.yticks(np.arange(3), labels)\n", "plt.title('Dimension reduction ensemble similarity')\n", "cbar0 = fig0.colorbar(im0)\n", "cbar0.set_label('Jensen-Shannon divergence')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also plot the reduced coordinates to directly visualise where each trajectory lies in the lower-dimensional space.\n", "\n", "For the plotting of the reduced dimensions, we define a helper function to make it easier to partition the data." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:45:52.491727Z", "start_time": "2020-09-25T05:45:52.487124Z" } }, "outputs": [], "source": [ "def zip_data_with_labels(reduced):\n", " rd_dcd = reduced[:, :98] # first 98 frames\n", " rd_dcd2 = reduced[:, 98:(98+102)] # next 102 frames\n", " rd_namd = reduced[:,(98+102):] # last 100 frames\n", " return zip([rd_dcd, rd_dcd2, rd_namd], labels)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:45:53.072538Z", "start_time": "2020-09-25T05:45:52.879726Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rdfig0 = plt.figure()\n", "rdax0 = rdfig0.add_subplot(111, projection='3d')\n", "for data, label in zip_data_with_labels(reduced):\n", " rdax0.scatter(*data, label=label)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculating dimension reduction similarity with one method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dimension reduction methods should be subclasses of `analysis.encore.dimensionality_reduction.DimensionalityReductionMethod`, initialised with your chosen parameters. \n", "\n", "Below, we set up stochastic proximity embedding scheme, which maps data to lower dimensions by iteratively adjusting the distance between a pair of points on the lower-dimensional map to match their full-dimensional proximity. The learning rate controls the magnitude of these adjustments, and decreases over the mapping from `max_lam` (default: 2.0) to `min_lam` (default: 0.1) to avoid numerical oscillation. The learning rate is updated every cycle for `ncycle`s, over which `nstep` adjustments are performed.\n", "\n", "The number of dimensions to map to is controlled by the keyword `dimension` (default: 2)." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:45:54.583864Z", "start_time": "2020-09-25T05:45:54.579746Z" } }, "outputs": [], "source": [ "dim_red_method = drm.StochasticProximityEmbeddingNative(dimension=3,\n", " min_lam=0.2,\n", " max_lam=1.0,\n", " ncycle=50,\n", " nstep=1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can also control the number of samples `nsamples` drawn from the ensembles used to calculate the Jensen-Shannon divergence.\n", "\n", "By default, MDAnalysis will run the job on one core. If it is taking too long and you have the resources, you can increase the number of cores used." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:46:15.038125Z", "start_time": "2020-09-25T05:45:58.170234Z" } }, "outputs": [], "source": [ "dres1, details1 = encore.dres([u1, u2, u3],\n", " select='name CA',\n", " dimensionality_reduction_method=dim_red_method,\n", " nsamples=1000,\n", " ncores=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Reducing the learning rate, number of cycles, and number of steps for the stochastic proximity embedding seems to have left our trajectories closer on the lower-dimensional map." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:46:15.164726Z", "start_time": "2020-09-25T05:46:15.040249Z" }, "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig1, ax1 = plt.subplots()\n", "im1 = plt.imshow(dres1, vmax=np.log(2), vmin=0)\n", "plt.xticks(np.arange(3), labels)\n", "plt.yticks(np.arange(3), labels)\n", "plt.title('Dimension reduction ensemble similarity')\n", "cbar1 = fig1.colorbar(im1)\n", "cbar1.set_label('Jensen-Shannon divergence')" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:46:15.356420Z", "start_time": "2020-09-25T05:46:15.166979Z" }, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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cifczqa1NHquvry9R2Tdv3rwh0dHxiJFKeNOZ20DmbB+nEseK7OOLYBUVFSmvj9btI1NkHK/qG24RbyyFH/GgZiLGTUcLJyTpOhwO/vKXv/Cd73wnrYZy//79WJbFP//5TwKBQIr937x589i8eTNXXHEFlmXx/PPPp6wSj2QbOR4kk+3evXtZsmTJmEt1p02bxpo1a9LKgVRVTdseZyIQQhCJRBIuYwsXLhzS0eFExHDmNiN58A4mD5fL9a6NdMeL0bp9+P3+Id0+0l3P0a7lSPnksRR+ADz55JPs2rWLW265ZYKfdupxVEi3L9xHm7+NGbkzKHYOnxscKzRN45prruHOO+/k5ptvHvL+H/7wB6688kr279/Po48+ysc//vHEex//+Md5+OGHueKKK3jhhRc4/fTTeeKJJ9IeZ7Bt5FhuwHQaW4/HM2KpblNTE21tbWlLdQcjE5Fucp44Go1y8sknvydMb0by4I1Hcj6fj46ODkKhEJFIhHA4TGFhYUYiubFiohVpRxsjdfsYfD3D4TBA2j548c9qGMa4vSoGk7HH4znuZ2lTTrqP1z3O9VuvR1M0DMvgxtNu5JyacyY97he+8AVWrFjBN7/5zSHvPfzwwzz99NO8/fbb3H333SmkO3/+fDZv3kx/fz8PPvggV1xxxbCkC6m2keXl5cNuN1JBQzpEo1EaGxvp6uqisrIypdHjSJgM6Uop6e7upq6ujpycHJYtW8auXbveE4Q7EuLdKQZfh/379yfUFemm1ckFH5NZcBqMTC2kTQSZ0EMPdz2TZxp+vz+l9ZLL5SIQCOByudA0bcJpH4/Hc1ysQ4yEKSXdvnAf12+9nrAZhsMz4uu3Xs+6GesmHfHm5+dz1VVXcdddd6XkPLdv3860adOYPXs2lZWVfPrTn6a/vz9FmnTxxRfz0EMP8frrr6f10h2MkX6IYyloSEY4HKahoYG+vj6qqqpYv379uH5cE0kvJC/K5efns2LFiuPS0Od4RE5OzrAdjf1+f8rqv6qqQ8h4NF1sOhyr9MJUF6CM1u1j3759iVL2wQbzY10QjVdlHs+YUtJt87ehKVqCcAE0RaPN35aRNMNXvvIVVq1axac+9anEaw8++CAHDhxgzpw5QKzn1yOPPMJnPvOZxDb/9m//xqpVq7j66qtH/XEn20YmI65GiE+bRiPb5LLZOXPmsHDhwglFM+OJdKWUtLe3J/xzTz75ZJxO57iP+V7FcDnd4XKccSmW3++nt7eXpqamlCKFwWQ83uNONY4V2cfJWFVVqqurEykGy7JS1Cnpun0k54xVVc1GujNyZ2BYqQbMhmUwI3dGRsYvLi7mYx/7GPfddx+f/vSnsSyLP/3pT+zevTuxOPb8889z0003pZBuVVUVN998c1q7x2QMto2EI2Qbx2iSFZ/PRygUYvfu3Ymy2cncUGPZN1kBUVxcnPDPnSpYloXH48HtdmfM5OZExHBSrOQihZHKd3Nzc7HZbMeM/OIlwMcKgxfS4mmcdN0+kvvg9fb24vf7ufbaa1FVNeH/sWzZMlauXDnpc1qzZg0zZ87ksccem9RYcUwp6RY7i7nxtBuH5HQzEeXG8bWvfS3RaPKf//wnM2fOTFEjbNy4kX379tHe3p6y3+c+97m04w1nGzmYbOMYjgQ9Hg91dXUYhoHL5WLVqlVTTkiWZdHa2kpTUxOlpaXDKiAyebyWlhaamprIy8sjHA6j63rCVyE5spuImfexRqYizuGKFAZ7KdTX12MYRmKKnZ+fPyZfikxhXNVoRhgRDSJdhSAy94AYy/VOVqckq5deffVVrrjiCtatW0dbWxs7duxIyEonih//+McsXrwYr9c7qXGSMeXf5Dk157BuxrqMqhf8fn/iv8vLyxMaTIDXXnstZVtVVROEe//996cdr6GhIfHfyfnSOMkOR7iDIaVM0bvW1NRQWFjIjh07ptS3NlluVlZWxtq1a48K2TY3NzN9+nROPfXUlMWfeCmv3+9P8Y91OBwJEomvXh/Pq/RTPc0fzkthx44dlJSUEI1G6ejoSJgEpfOlmCwZ1zU10dDSRn5RKYuqKsb0fWj7/4r91R8hsLDyZxH+8B3IvIpR95tqxH1JLrrooiHpwImgpaWFf/zjH3z3u9/lhz/8YQbOMIajEn4UO4szGt1ONZLJdqzbxyMVp9PJokWLUvJ9qqoO6XOVCZimSXNzMy0tLWOSm00W6chW07SEZ0Icw/kqRCIR/H5/Yko4uGAhTshj0XS+a2AZKD1vgzSxShaCFksDFRcXpxDqYF+KRGcKI0p15xOU97wK9jyCa7+Abd6mMUWsL73wND95rQeJQNLAmgo7X3Q/i+tAP2bFyURP/SJoqWsASvd+7K/eCTY3UrWheJpxPPdfhC+4L7PXZYLIZE73K1/5Cj/4wQ8S5cmZwok355tCxCPa8eTU4gtV+fn5LF++PK0qIJMFDfHzrK+vp7W1lRkzZgzbGSJTGI5sx4PkNjfJU8JkGVGyRnawLMuyrKO+wDSZ40kpqe8NEYqaVBW7yHOmuV56ENfmz6L0vgMCrLyZhC78zbBtgtL5Uti2/Qxb81/BiICU2J7+Km+2/1987tkj+lLIiI+fv96JWxg4FAtpWbzR6qTNcZAyRwtK5y6U7gOEL/gVJPvp9tUCMtYJBpDOApSufaiHngJFxaw8FeyDJIimjjJQj1TtyILZKePFkamZoGmaGQk8HnvsMcrKyli9ejUvvPDC5E8sCRO6U4/V6upUITmyja+YjiapikQiRCIRdF0fVRWQKdLVdZ2mpiYCgQDAmLW9o2G47zMTZDsakmVEyVPCwbKscDjM9u3bE4L8wYtPU4GJSqhMS/KzfzbwWv0AiiJw21T+66w51NQ9gFb7FNJZRHT9V1EbX0Tp3ge2mORRGWjA8eqdWHnnpz70I17U9jdBc2LOWA3K4e9cD2Hb9QBKeIBYowKJYoZZKQ4QWXvpyL4URj9hy0auEgEEQoCChY8cUO0gJVrr64hgNzInqTFnzrTYsaQVy+VGvCjBHpzP/3fsffc0Qhf9FtNVSJ23jpC3nVUv3ILd1wZIzMr1hM+9O0HaiWtmmpP+bWVS8vbKK6/w6KOP8vjjjxMOh/F6vVxxxRX87ne/m/TY4/6UTqeT3t5eSkpKTnjiTZdGGKlZY9ywJt4NNjc3l6qqqlGPM1nSTS6kmDVrFnl5eVRVVWWEcOMStOSxjgbZjobBsqz+/n7Wrl2bUALEV6jji0+D852Zsn6cyG/8jSYPW+v6KcuLaXT7Azq/evBh7ojeSrwDltb4T4zKU2NcGT+GosYiybwkU5i+Otx/vBTMKEgLa9pSQhf/L44XbsD21kMg478rESNBaaF07R3VlyLo6WWx9gYHjOkUyiBhaUPFoka0xfLzsY0Z3HXGnHkKxrz/g3ZoCygqItSHtLmRtliQInztqDt+yffs8OSbLlx908m1ruBTzhf5uHMbavMr2HY9gL7q06njTsBScjDi920meOnWW2/l1ltvBeCFF17g9ttvzwjhwgRIt7KykpaWFrq7uzNyAscKIz0VI5FIisQqXm0W/2FomobD4WDGjLFJ3yZKutFolIaGBrq7u1MKKTo6OjIm70m2d5wM2R6tB3A6JUD8YRjPF6ezfowT8XgW74abAYhAF2rDi4DArP4A0l2S8n5fMGbkHd83T4To9BtghwSJmRGUgab4gWL/WhZm+fKUsZxPfwsRGgBFASlRO3fj3HIdWt0ziMOEe/jbA6kAAqsgNRDQ3v479m0/Ayyiqz6LWHopbrebb118Oj/620u8pc+gRA3wFfcWppseMMASgr6C5ezdW487pyslTSE3fBtj8UWIiBfba3eh9NcduWaKQmvHWzzZfzJBz2xmyW4UBL8Mf5BqrZ91Yg9K9/4h13QiJcCDMZYZ6vGAcX9Km81GdXX1VJzLlCNdh4Z0N9XWrVs57bTTUkivsrKSysrKCRHdeEk3EolQX19PX18fs2fPZt68eSlEER8vE9NqIQSGYdDW1nZMI9vJIN5vrLi4OCXfmWz96Pf7h7iNJSsphvNUGJJbHWjE/afLQA/GyPLVHxL82J+R+UcewFVFsbF000JTBAMhgzVqMzF6TBrPkYc5YxVq08uAwKw4iei6L8GbexObKJ6mI7sIESPrrj0II3TknA6PLFU72F0Yyy5LvKceehLnU9+I5XwB53P/RVizY1R/kNLmJ7h11j6MornoG75BR+f7OLTz9/iDIaZXVlO44TOsFlrC1CY55x6TbeUyu2AF07r3gxJrD/RseDE3Nn0Ub9gFQuJXvRSbIZCS3cYs1jn205FbQr+njll5s7Apsd9wJtILAwMDU+IutmnTJjZt2pSx8U6cO2sSGG+HBsuy2L9/P/39/RMq1R2MsZJuvLPuwMDAiFVrmbJ3tCyLSCTC9u3bmTFjxglHtqNhuCl2fPEuTiTt7e0JT4XkFEW8tDsZ9lfvhLAXbIdz+OEB7NvuJnLGEVerJWUOrirezx/qnFg2F3MqZ/IfbAV/nB4BoRJdcTnGissRgU6QFjK3Ysgikzl9JVr987EcKoDmxCqZj+JrRZgxxYhEgD0Xq3w50VO/hDVj9ZHz3f17MMKxRS4pMHQT264HsG/7GUrfITCiqO070PoP8ez0G/lN0//BZtOQ/fD1ci9nLCod0STIX3Q5arCTguZnaTJLuTn6MUyHA6HoWKadZsrJoQmJQgl9/FM1ua7jUczOxyhzlXHnhjuZnTcbwzAmPXM7EarR4F1OuuPp0ACxpov19fWEQiGKiopYtGhRRqbNqqoOMWVORigUoq6uDq/XS3V19agNJlVVnRTpJqcRpJSsXLly0hHCibS4OpwHgGmaKe1t/H4/b775Zkqxx2xPO5o4vJBkRsHUEZ6mI4NIifPRz3Fpy6ucD4SsHHKNxUQuux/zsf9A7TmA1BxE134BY8XlIAQyd/qw5xo+8zbcj1wRI0hpoS/5KJEN38T9h4+g+Npi+ys2gp/YjCyqGbK/PCz5uj/6IX6hn4MpFU5p6+D74qfkGtEYyRsR+lsP8ZvWbjTNhkNV0LG4/Zla1s4uoMA1dEaVYmpzwQ+JWiaHavtRn62n1CYw6KXHb2FaGofspSzNtfGn4lYOaIUIoSCRdIY6uWHbDfzmQ7/JSE73RHAYg3ch6Y63QwPESnXr6uoIh8PU1NTg8XgoLy/PGIkMF+mm66w7lmMqijKhHHG6nO3evXuP6wKFKYOUQ6LKeNeC+API5/OxfHksxxoIBAj1tqAHvTgifsBMzPqVth2EGt/AXnkSmrcRrfV1kODQBA4ZgI4dRM0IoSv+Mf7zdBURvPwxRKArRqDOGKkEr9yC2vwKwojGFuRcRWl3j57yBV6t7eGe6Dk40FGEZJsxjx9YF/M99Yi2tosiBKCpsU9lUxUsadEb0NOSbr23ngcPPkjACLBpxibOqDyD0jwnFiCEysz8cvLtUQJ6hJMXd2F3t/Bat4UwY8QqEEgkTd4m9u3fh2Va2O12otHohAt7BgYGspHu0cR4OzRA7Euqq6vDsqxEV12ImdxkIscUx2DSHamz7lgw3vTCSAtkI6k1xosTIdrV9jyM47W7wIxgzD2TyKbrhxQAJEMIgaZpFOY4mPHodSjB1iNJVEDacpBSYnvxZnYu+U9cvgZWmxaKtEBREMiYqsCcRHGMEMjcQbaimgOz+oOj7mpNX8n2xd/B2NWPWzOQjnzsaPwrsAhULXZemp3pxcXIXhXdlGgqRAwLRUB5XowAu0Pd3LrjVg56DlJgK8Cn+7CwUFHZ07uH1zpe482eXQzYT6Lfu5YSVzGGNIiU/IpXvAchqYpWEUri+rntbn7f93scUQdn5J9BYG9gRF+KkZBNLxwlJCsL4qWoo/Uei5fqaprG3Llzh0xJNE3LyGpqHHHSHWtn3bGONxrGokbIRH44fr2n2hpwslCbt+J45XakYgPNhXboKaQtl+j7vo329maU7gNYJQswFl8IipbyEFHbdyAC3UjNEculGiFAgN2NYpnkixBr1qxBmiuh6V7EQD3SMpBAyF7K9voBXN17U5QUR8MQHaB0eiXK2waWTUUIQVQ3Kamcj15yIWrP25jTV2Df+F0+91od9+0KEjYsVCG44Zx55Ajsg6QAACAASURBVDhi1+G/t/03Lf4WnJqTrlAXQSNIhbsCVVHx636eanmKQnshxdO3E8x/m3zHPPqsA5hmY8q5CESCcG3CRsgMsbVnK0IK9kb2cv8Z9+PSXMP6UsRTPcnXMf6b9nq9WdKdSsTJtrOzM0Feo5Ft/MtzuVwsXrx4WPPuTJfthsNhurq6CAaDKRH1RDEaUY5H+jVZ0k0uRdY0LZHni98UU+paJSVK9z5EeACrdDHSnea6Wia2f/0C2/6/IEL9MdXBYbG/VB1oTS8jnv42Wu1TYBmgaGhNLxH+Pz9Kd0BAxIoH4uoBaYGUGLPfB4BQbYQ/9jDOF25E6d6HVboINl3PKmdRothjsCH6YHOgTOOcpWU8tb+HQ90BFCFw2VS+dtZCItNS/QTmFEe485JpuJ3TKctz4rLFvjtv1EtroBWXFivP1pTYbylqRXEpLiJmBCll4nVda6ZOr0My9CG8oHABH5/3cTRF46Y3bkIgsCk2LNNiIDrAv7r+xftmvG9YX4rkUuhkX4q77rqLQCDA3Llzef3111myZMmkWk+Fw2E2btxIJBLBMAwuvfTScbfsGg4nHOkO7tDwzjvvcNpppw27vWVZdHR00NjYOGKpbjI0TctIBVm8s65pmrjdbtasWTPpMWF4opyIznakNuwjIflYFRUVrF69OmUhKtnoxul0ppBxRppBSgvHc/+NVvs0KCpS0Qif+1OsQTpX2477sL9xLwgVoQcgGkDa82JVYFYUac9Bq3s6RqSaI6aFbXgxFqkmRbpmxSpkTjmKtyVGvZorRriWiTHvbKKnfe3IQV1FhM9OJW0F0nZTGOzB29jYSCAQYMeOHSkPr8k4jTltKj/52FLeaPIQ1i2WzcijNDeWNgjoAfb17WNL8xa2tm7F0eRges50PrXwU9QU1DDNNS1GtghMaaIJDafqxCd8RM0kvw0lNp4lLaJW7HVFxPLCifNQnVxUcxFnVZ2Vsi+QIGhd6iN+luF8PW655Ra+//3vI4Tg17/+NQcOHOCZZ56ZsKzS4XDw3HPPkZubi67rbNiwgbPPPpt169ZNaLxknHCka5omuq6PahqebHNYUlIyLgPveHphoujv76e2thZFUZg3bx5Op5M9e/ZMeLzBGJxemGxRw3jzw/HrWl5enjhWNBpFURSKioqG3BDhcDhRuBBvBhm350smlvF0WVAbX46V1GquWM5UD+J89j8JfuLvKdtpB/8Re1+1IZV8hB5CiQzEbnLVTvTkT+N47v8mX5BYCew7/yDPX4QQh+VXNhfBjz6E/dUfoXgaMWesQV99TSwvOglrw8EevIZhsHv3bpYtW5YS0fn9/oRT2+Bij7HMJg56DtBq7afQXUi+631EzAib6zfzv2//LxEzQsgIoRLrqPtW71t8+7Vv41AdLCxcyILCBSwtXspL7S/FLoU+G3vfVwlEXdgLBviP0wr5W9ND9IR7MK3DSqHD/1OIKRWKncVcteAqzp99PgB21c6Gig282vEqpmViShO36mZV6apxX0MhBFVVVYnu3evXrx/3GOnGjD8gdV1PcE4mcMKRbrzfffL/TzaoMQyDlpYWWltbKS8vn5DN4URIN54rrq2tHdJZN7kgIxOIf+ZMlOuONb0QN0ZvaGigrKxszI5myVrZZCPqwd4Kzc3NRKPRISmKtBGeGUVp3xGTbGluhBFGBLrB347z0c8SOeP7R6rEbLlgmaACQkHa8zBnvw9j3lmYM09B5pRh33Y3wtMc8wOI+BBmFPv2e1hpmpjOdvTTvxEby1VE9IPjn2J2+yI8daAH05Jsml9CVbFr2G3jv+WRnNrixR59fX3savXxRL2OicLZCws4a/E0cnNzU5zanml5hrvfuhvDMlCEwuONjxMxI+zp24NuxSJLefh//dF+zEgpISuHsL2T7d3b+Vf3v5BINKFhGTn0NV5MrlZCvt2Jb6CIV97K52fn/4xXOl4hbIT5S91faPA1JI5X7CzmD2f+AbeWOsP87urv8st9v2RH9w4cUQffPPWbFDomnpPN9EKaaZqsXr2aQ4cO8YUvfIFTTz01I+OecKQ7GJqmoes6iqLQ1NREe3s7M2fOnJTQfzykm9xZ1+VysWTJkiFTyMnqagdDCEFPTw9NTU2TriAbjXSTW/6UlJRkzKt3uJY3yeW8ySmKeOFIvqYz45X/RPM2IUL9iGgQzEhsqq86UFv/hfPxLxG69PcARNZ/FdffPwdRPyDAVURk03+n+L+GLrofx3PXo3TvQwn1gc0ZU5NJiWPn/RhLP4YsnFjfrXZPmCt/+yb+SKzQ4r6tzfzi48tZND39esJInYCTndpKSkrY2+7j50/uIWoIhLD4+fZ+TEuyelpsNtEWbWO3vptn2g8Q6jkXYeVgL9jD9sgrqELBtMyEdAvAkpJI19kYntUgTEDiqvwdqqsldm5IRGQOUqoY+NFUNzmKZEezF024OGvWWQB8qPJD/GjXj9jbv5dZubO4buV1QwgXwKE6uHb5tQC88cYbVOWP7mMyErxeb8pDarJQVZU333yTgYEBLrroIvbs2cOyZcsmPe4JT7qKonDw4EE8Hg+zZs3KiPPWWNQB6TrrDrcIkqmV/XhkGz9mJirIhsvpxptZ1tXVHZWWP3HYbLa0KYpt27bFSPqVm5B99QTVHGy2QhzRPkAiFTvSXYwQGkr33tiCmc2NNXMNoUt+h1r3LGgOjIUfGSK/kjllhM//OUrvQVwPX5LwNIgVHmiIYM+ESff+11rwhU1smgAEId3kJy828NPL0t+8O5o9PHcoTK3s4NylZdi1VAIORk0MS5LnUNm8q5OIYeK0qSAhqIe55639nLzyefJsebza9SrRSCGBhs+BpYGAYPB92KMmjtKXUFCwsGKKAsAMzUH3rCKuQZaWRrjto+TMvTN2nZAoig5SxP4AS4KqgKYcmXrn2HL47prvjus6ZaJF0VRJxgoLC9m0aRNbtmx5b5JufMoUCoWor6/PWKluMjRNS7SGHoxj0Vl3cBph4cKFBAKBjEjaBud04w+T2tpaCgoKWLVq1dFtZikttENPovQdwiqqxph3NkJRURSFadOm4TK6Ea48bJoTiQvLB+gBDHshliExzAh+y01zbQMF+YWxFEXRfLRTF496aCu/ElQHRDygaAjLAOHCKp6bdnu17llsBzYj7XlE134eWTBryDaesHE4koz9bhUh8ISOLBZ1h7rZ1bsLRSi0t1fzsxfbiOgmj9fX8bddHfzq8hWHCxUkP3i6lr+/1YUQsGpWPiXuWAssbzSAJS0sS8FhRWnwNeCJepBIor3vA+twMCABIugDp+IofQkLCw0NAwMVlQrrJJoVJ1HCsSIjYWIZ+SjShiX02P6uWmyubhzmQrxhA00RfPq0WajK5POdk82Z6rqescCgu7s7oaAIhUI888wzfOtb38rI2Ccc6ZqmyVtvvUUgEGDOnDmoqkphYWFGq6rSpReklHR0dFBfX3/UOusOl7Pt6enJmCl6PL0QT5PU1taSl5fHSSedlNLafjSMO5qXFkrHm4iIF6tseSIH63j+RrR3HgNLB8WG2vgSkTO+n9jNnLYUrb8OVEes8MDuQhZWYvN18Hp0Dl/xX0VYy8P5pIdvb7RT6fKOWUUhNSehi36L6+/XIAJd6LZcrAt+Bc6h0ZO29084n/1uzNcAgfb2ZoJXPonMn5my3RkLS3jpUB+mJRGAqgjOWBTzgWj2N/O97d8jaARBCvbvvAqH4sKuxib9h7oDPPdOJx9eXMFfd3Xwjz1dSHQMy+D1hij5RS3oshhpaoACioVa9GIiP2sZbnTvSlKrORwIAuRquYTMEIWOQk4uPZlrl1/Lcy8f4qc9Fg5pR2IR0g2w91JiL2Rd4ToMNaaTPXfD6dS3F9Hli7BsRh7rqjM3pZ8oMq0Rb29v5+qrr07o/z/2sY9x3nnnZWTsE450VVWlsrKSwsJChBAEg8GMt8JJJt3BnXWPRuQ32gJZpgxvIEaWPp+Pbdu24Xa7j0rkjmXifOJLqE1bYyv/ikrogvuQ7tIY4WoOEK6YiqDuWaIDDYldo+u+iNJ/CKXnHQQSo/qDRDZdj//A83xxi52oTcOmKoSCAW57aoDHLrLjWP2htCoKXyDI32oNtndaDIQtFEWwdHout330Gaa7YfuO3axNMo9JhmPrD2POXYeVCyLqx7bnYaKnXZey3RmLptEb0Lnn5UY8IYM8h4YvbNAV7OU7r36HzlAnJY4SSpxlmJaCIQxUoRAygkgJd+78OUHHybxSV4U/GsQSMQ8PKRWiXgVX1X3ofRuQloat8F9ouYeQMi+Wq9VLEEJHYueIVZnEVfQWAAsLF3LP++9J6GurC+r53Puq+MXLTWgCinLc/PjSdVTknJ9QUvj9foINPirwUVPgIgeT7m5jUm2WMkmYmVIYrFixgp07d2ZkrME44UhXCEFxcXHii7LZbOj6yNq+8SK+ONfc3JzRzrqjlcmOVY2QqU4UfX19NDY2oigKK1eunBJhfjK8YYODXQEKOl9jReMroGgxiZYewvn0twmd85NYV4S4BEuImL42ycYQRz7hC+5D+NpiVWM55SAEdUWngbYXzTIhPIANiWFA3xO3M8vyYSy6cIiK4r8fe5vnWroJ64cfYJZkb5uPa367nRtOzyEcidDW1pZeRWEN+s1JC13382TzkwxEBlhUuIgVJSsQQrCgwsQTDmFYCp6QyQPbWnjo7R0wrR6JJGgECRgB7DmNRINVSGkiUBGKhV/dxQ93PU+o+/0YnA5SHl7kUxBaL5qzA/vMv2BJ63B8C4Y0yLPlYUhJCAFKCFU4UaSKVEwWzG5nUckmrl1+bYJw47h87UzOW1aGN2wwPd+BTY19F8M5tY3WZmksUsBM5HPD4fBRWXPIBE440h2MkfKvE0G8yq27uxu3253R1frh/BzGK/2abKQ7MDDAwYMHsdlszJw5EynllBNubXeAL/1pLxHDworaeL/1b9ya/xfUw3pZ4W9HFsxCuqfFCFVzgBFB5pZhFVYDSTpnoSDzK1PGL8uzY1gSoYcRSEypIIRgGn3Yt/0MY9GFKdtLKXlibze6mXodhSLoDCvMW7iEvbt3JmY6g1MUs6rPp3D/7xFmBJCgOblP9rP1wBaCgTIeVfbyyZN7WFt2Cv/19BZ0Yy5gYQkI6RbhvkVMm+6MVXMh6Y30Yq94CNF5CWF/JZotgLvi7yj2AUwpsRW/jB5YgIyWxIhXC+Ce/hQ2xU7UiiKRqEIl35bPJTWXcN6c89AUjQf/1coft/tQFQXTknz9jIWcv/yeId9PckBQ4LKlNblJxljbLLW0tBCJRFLaLMX/jUsO30sOY/AuIF2bzZaRnvTxctbW1lZKS0vJy8tj/vz5GTjDGNKRrmmatLS00NLSMi7p10RJ1+PxcOjQIYQQiY7FnZ2dGe92mgy19hlsu3/HLQ1n4zen43I6kZrGi8GlPBPZz4cde8GMYlWsAtVG6IJf4XjhBpSed7CmLSXywe8leoiNhOn5Tj57ehW/euEA4rCB2Dccf6VQBLBk+rJrVREYFol0ZxyaIshxOdA0jcrKI+SenKJonX8lvrBOSeuzmJqb16vPZktvFwcPnnU4hSq4qaWXIu1NmntriAmFJTKhjDCxq3YkkrAZBqAsJxf3/JdoDjTHvmNpwWFJl6oauGf/Eis4G6SKzdVKWV4+q0o/xL7+fSgorJ++nisXXkm+/YhN5xc2FHPu4iBtnjCzilzMKkp/LTMRbcLIUsB4iqKrqwu/359os+RwONB1Ha/XO+E2SyeK2Q2coKSbvGgz2eoxwzASZBs38lYUhddffz1TpwukpgQmSrbpxhoLfD4fBw8eRErJvHnzUiKCiZYBjwVq3XM4n/k2mDqtwfNx0IMwNHCXoms5tJoFYOlYxTWEz/oBADKvgvD5vxh17LBu8vjeLjwhg1NmF7J0Rh5XnVrJhoJeurZ8n2rZjEMYXBb8Jocic6l+YBe3fGQhMwpi+XghBJ9cV8n9r7VgRs2EvsCuKnzjjJq0q/FDCj2qb0JyE9I0Gah7inf+NhfTVEFIkNA/MA0vJhKD2K0mABWUKM7SF4mYEVShogoVgSDfkY9hGBTYCvCaXhShYEqTXFsuAT2AKiSOvBYMaTDDPYM7Tr+DWblDFRODMafEzZySkfP0pmlOqcVnOi+FeFv57u7utG2WkiPj0UrHvV5vNtI9WphoTjfeWbe9vZ3Kysoh+t5ME5Gqqui6TmNj44TJNo6xRrp+v59Dhw5hGAbz5s1LGwlkYlEuGAxSW1sLgOpw86sdHt5oDZAf8fGf9gW839zKIqWZndZcXGYUGehFc02j6tz/JDjzBqSrKG1b7uEQ1k0uv/9NWvpDGJZEUwTfO28BH15SRs2ilczL/zq88hM+VPtRuqxcLFMw0Ozhqv/dxT/+v7U4DmtfP7ehisoiJy8e7CNimKyqLGDtnEKWVozdKCUYNTnY5eUPB5/D1M8CDl9LIZBSQSqHY1URBsuGUAO4yx9nXZWDulAuYSvMsqJlDEQH8Ok+sGKeBZ9d/FlKnCX85sBvsGRMS6sIBbfm5sxZZ/KZJZ9BFZkzE8pUz73xIN5WPicnh4KCgsTMcqQ2S263O61T28DAQJZ0pxLJSfnxRrq6rtPQ0JDorJupNuYjwTRNQqEQu3btmnS1HIwe6QYCAQ4dOpRiITkcxuu9kIxwOExtbS0+n4/Zs2ejKAr/76l6Xm8OYBOSft3Gt6KXcb+9kZvt9/P5yJdooxRLqly+zMW6eeXIpO+ydSDMdzYfoLYnSGWhk5s/spB504bmmrfs66ZlIETEiFl5RgyLW56s5cNLYrlFa8Zq9m34Cb6G3ViHr5MlwR82qOsJsvhwNZgQgvOWlXPesvIhxxgNpjR5u6uPr/6pDm8kQkA/A0UxsEx7onBAVUAVAksqgEQoBu7i3eQUv8PFVddTZavC5/MRDofpcfSwNbyVgBHgpPyTuHT2pTgcDjbO2EhHsIN8ez7TXNNGPqlJIBN51Uwdeyxtlrxeb8Kp7b777qOjowOn08kzzzzDsmXLJtWEoLm5mauuuoqOjg4UReGaa67hy1/+8qQ/ZxwnJOkmY6yR7nCddacSyWkETdNYtGhRyqLDRDFcdBqPOIPBIPPmzaOkpCTN3mMba1gYYaIm1NU30N/fn+h4Efc03t0ZJddhR1EEwiYI+j3sMOfxCe05/uT4Hi3abHKUKC3ld9Ha2prQzUqh8Nk/7KbbF0URUNsT4HN/eItHP7+GHEfqz9QbNjDNVCVIMJr6EHLZVQwrdbZiWBK3ffLE0hfu44G3H+CRl6rw+vOBWImvREFoAbDcIAUfOdnJoQ6V/Z0RpATN1UF++au8f+YH2Th/Y8qYpmmyIbiB1tZWgsEgBw4cSPGi0HN1PFHPpNzGRkKmcroTwVi9q4drs7R48WJ+/OMf09raypYtW7j99tv59a9/PeZu3YOhaRp33HEHq1atwufzsXr1as4880yWLFkyofGGjJ+RUY4ykm+20XKSo3XWHQkT7YSQLmfb0NAw7nGGw+BzCoVC1NbW4vf7mTt37rg6UYw5pxvsRXn8a8jWnShSYfraL7HwtE8OOU7uYR2qXRFYih3hLCAnpwxCdjShMFvtIbT+65RVLcDv99PZ2UltbS2tXp0+v35YTSpQFUHUtDjYHeSkytT+bafMLkRVFAwjRrSaKjh1TmrqZE6xiw1zi3ilrp+wbuG0KWyoKaKqaPIa6wfeeYBtXdvwBRdgSgMhYoUPUqrYCl/HWfQGp81YxY2n34wl4dXmWrY0PYFl6+Ck0qu4sPrCIWMmL0Dl5eUxc2asyGI4L4pM22UeT5HueJGXl4fb7ebss8/m8ssvn/T5VFRUUFFRkRh78eLFtLa2vrdJdywIh8OJMuGROusOh5EkXsNhpAWyTBujw5HuwR6Ph7lz57J06dJxPyTGEukahoH+t69i79yB4irGpYHrrZ9jzFuDHORfe90Hq7nxiYMEoyaKAnOm5fOBqjLkW05a9TwejG4i9HqAD5VZrJx1pHqryhdBbt9ObIVfIi1JxLJoPHQAhy+PaDRKf38/ubm5LJqey/cvXMT/e+Ig/ojBqXMKueUji1LOQwjBHRcv4W+7OninK8CCshwuXDk9lk6RVqxlzBgQMSN4o15ybbm4NBemNHmj6w0saeFye/H7ikGaSARCGNidveQ4Lc6s2oQQAlXAhtnz2DD7i2M63mDDm+G8KNLZZQIp+c7x2GUe60h3sgVHU6VeaGhoYOfOnRlzGIN3IekO7qw70Y6+42nZMxY1QqYKGiAWvYfDYXbs2EFNTc2o3YNHwkg5XcuyaG5uprm5mQ19+9HypiHUw59LDyG69qWQrpSSjfNL+Fm+g10tXvKcGh+ospP32/tppZwLQ1/DLx3IqODPD77F/1yyjNPnxvLN0/IcfHTVDP7yZjtRU2LXFD6woIRzN8wjGAzS39+f0ral2OHg3nNLE9Ge2x4jjKa+EL95tRlfxOC8ZeVccvIRN7GAHuDpxqdp8beQZ8vjzMozqcipGPbatUfbeXzH4wT0AEIIrlhwBctLlscWtoSgZu4r7Nv7AQzDiZAKBSXvkF/SQrGzHFWZWORmWdaov7mpsMs81pHuZFMmU9Gqx+/3c8kll/CjH/1o0t2yk3FCku7gm0RRFHw+Hw0NDePurDscxhKZjkf6FVcvTAbRaJT6+np6e3tRVZX169dPuuwxXaRrWRZtbW00NjYyffp01q1bh62hAgI9MdNueVhg5S5NO+bC8lwWluciBhpxbf4UIurjd9Fz8UsHmrBAQtS08ZMXGxKkC/C1D1WzdnYBh7qDzCpycsaiUhQhyM/Px2azsWDBAuCI1Mjv9yc6LgSDQbqDFje+HiVsSKSEfx7q4zsfnsdFK2Mtzrc0baEz2Emps5Tdvbt5vPFxbIqNUlcpq0pXcUH1BRQ4YivgUTPKM95nMNwGPeEeLGlx079u4vbTb2dR4SJean8JRemnclEzvqATlDBuZ5R8ez5FjiKWFE9sKjqZiHO8dpnJKYp4NdmxgGEYx11xhK7rXHLJJVx++eVcfPHFGRsXTlDSTYbf7ycUCrFnzx7mzZs37s66w2Gklj0T0dmqqko4HJ7QuSQrLubMmcP8+fN57bXXMvI5k3O6yaY+paWlKdV4xgdvQHvsSzFfWmlhzVqPVb0pNkh/PUqgD/JmgetItOF8+psQ7gebm0DUEatBkBwu7xVE9EHVYELw/vklvH/+yAuAcamRw+FIWSy8+4V6Ikbz4W0grFvc9cw7zLHacbgdHOw7SGV+JfXeepr9zfh0H3m2PDqCHezp20PIDCWkWD7dh9fyEggHyNFyYrKkyAD377+frlAXObYcImYEnTCXLfkw013T2d23myJnEefPOZ8Kd8Vwpz8ipqKj8lhSFN3d3USjUbq6uiacopgoMtEE1uPxZMxLV0rJv//7v7N48WKuu+660XcYJ05I0o2btMQ76+bk5LB48eJJNaIbjHRStMkUNUwkvWAYBg0NDXR2djJ79uwhiotM3KBCCEzTpKuri9raWgoLC9N658oZq9A//meUzj1IZz5y5hpAoL70Pyj7/oKJhqLaMc65M9aM0dRR+uuRziIsWw7nWW+x2X86OhqodmyqwnnLx67kiFgRXmp7idZAK5a0mF8wn5qCGkqcR0jXkDFpmBIzgwUkWmSA1cE36Kq6ErVPpauvi4PegwSMAFErGpvRCIN2fzs9oR5OLj2ZtWVrybXlxuwSD6cSTMvEptio9dZS6ixlddlqwmYYf9SPqqhcOPdCLpw7dIFsvDhaudXBKQpVjbXqKS8vn3hHjwkiU2XAmSLdV155hQceeIDly5dz0kknAXDLLbdwzjnnZGT8E5J0o9Eo77zzDtXV1RQXF7Nv376M5UvjSCbdyVaQwfhI1zCMROFGXEs8+EaMpwUm+2MdGBjA6/XS1dU1up1j3nSsvNhUXdQ+g/bS/0DXfn4kL+O34Y1YUnD2g8/z7f9YgE21IV0loAfA5mZtUZA71D9zh/pJIsLBBcvL+dT60aupIKaJ3RXaRaGvkNZAKz7dR723nvm++Wys2Mj0nNg5nb1kGn/Y3kpYNxBInOj8m/Iczn89QfmMlVy65FI2N2zGF/DhM31YwiJkhfBEPdiFHVWo3PPGPbSUt7CuYh3r3evZEt5CQA+gCIVyV3midFdBwa26iSgRFDJHklMR6Y4FlmVht9snlaKYqIoiE5FuJBIZlxXpSNiwYcOUVWnCCUq6drud1auPWO7FXcEyiUxWkMXHG410TdOkqamJtrY2Zs6cybp164Yl1cmSrsfj4Z133sFms+F0OsfliC/adqK9eCvoYf6ir+d/o6ejYKIIwZO+aopeauTaTdWEz7gF55brYl0cLJP3r1pM5aJVfP/pOh7b00V9b4hvnlkzqrlKUA8SMAPoYZ23B97GrbnJt+djU2y8PfB2gnQXludyz8eX85Pf/xm/ZecC5RU+qz2OMCz6ap+kuvo2KnMrqSmooT3QjjfqpT/SjxCCPFces/Nmk6Pm8GbkTdaaa1mqLcV0mewM7sShOSgTZXyw4oP8ufXPdIe7Y50XpMWmmZsm9B2kw7FSEYwWbU6limKyke5UEuRU4IQk3cFfns1my6gcyzRNPB5PoitFJtrijES6cZVAS0sLM2bMGJFsB4833hbTcR8GzAjLbe24LB97PGGQpyH66lB2/Q4R8WPNeR/WovPTdroVrdtiqVlXES9bSzFQcAgTKcBC49WGAa4FrIqTCV32CErfIaSrGE/OHP7jNzvxhHQ0VeGfh3rp9EX45SeWjxjd2RQbfUYfnT2dRK0opjTpDneztHgplj01L7xqVgH3l9yL29tK3LzbUG0ctIKsATwRD/Py57GgcAEDkQH29O4haARZVLSIXFsuYSMMKlRWVtLR0cG1a6/FE/HgDXjRdI1QIMQ5rnPY4dkBAtaWrMXhHRQPbgAAIABJREFUc+AhM4ULI/VIm0pMhOwzpaLI1Gc+FjOEieCEJF0YanqTiUg3OY2Qk5NDZWUlc+emb9UyXqQj3cl08x1PJZlo2Y65dzN93gAd0zZSvXwDpXvvQzTuQ6pOqrpaUbZZKI3/BBR6yWfPS8/h7LBYufECNHXQDeEoQEgL6cijwmki/BBbIVOxVCdluUesMKW7GNN9CgAHGgcI6od7egGqUDjUHaAvqFOSM7x9plNzIpHYhI0oUaJmFKfipMHXwIaKDSnb+nU/f523nqvf/CsCgSoUunJLeadqNWuA6e7pHBg4QJmrjFJnKXPy59AX7iNshLGkhV/3c2H1halWh46ChKoBoKamhjM5E8MwEv4AyW3Sk6fcgzvzjgbLso4JeWRSMjbRpqMTTVHouj7u4ONY4oQl3WTYbLaEIcZEkC5n29/fT39/f8bOMZl0kyVZ5eXlY25nnoyxkm70nefQnvwWppSU2WxU+HZjVBUiug8g82eBEIS8EYr3P4q0OTgUyuVzrRuJoGF1Cpa07+auj61IaZBoLTgb5e1/ILyt/HuBh6fCi+kRRVhCw6Up/PvaaWlvYrsW6/WlcPihCUQMi827Ophd4uYDC0pQhiGcEq2EwoKYMiKgBwgYARYXLaYqL7WD7F9r/8rBnHyuW3Q6c3xd+BWFwMzVXD09Rs6bZm6iJ9xDR6gDJKwvX8/ykuU83/o8fsPPypKVnFJ2ypimrJqmUVBQkCJVSp5y+/3+xJRbCJGYasf/0n3nxyq9cDSOO1rT0YmmKDweT0Z1tFONE5Z0MxHpjrRANlnLyMGIn2NbWxsNDQ1DJFnjxWg54kgkQl1dHRVbf0ah3YUj5/APPdiDUvsMIJKcvRQQAuFt56buTxCQNtxEkYbOnuY+Ht/TwYUnJdWxOwswPvIzaHiZSGcr357tpNExE0XVWFysooX62LmzCcuyEl0EcnNzmVeUw7KKPHa1+jAtC920kBJ+tbUZm6rwwju9fO+8Bf8/e28eJddZXnv/zlCnhq6qrp5ndUvd6pbUmmUJ2ZYxeAQbTMxlMiSEGD6cBBKSrPiG+3EJOFmOF7kkN/Fi5YPrhDAk4ADBMWDHXNt4Eh5ky7Ys262e57m6a57O+P1ROqXq7uq5JFle2WuxbDddp06drrPP8+73efY+d2OZBvKZBxDDw9yQzPBIQEYSZXyKj0p35RItVTM1huJDlCvlDMoSp1wCmqmyW4sxGBukxd9CiaOET7R/gnAmjCzKBJxZIv94+8cXHGujFedKS267Ks4f8nA6nQuI+O1Q6a4XdujoeiQKm4g9Hs8l5aULlzDp5mO9mu5auhGKSbp2/2s8HicWixUl+me5Sje/p3fr1q1UlpchzC+q2J1+LJ+JEBvHUny4MrMYu65FeukfmTTLUCw9y8migK6pTEUzSz7PRDDKUNBPbUM7VzQ3c6UgoGnakpY2+8aJRCKMj49z25Y0rU6RWVXiscE0HkVEkrK9ws/0z9Mzk6CjxguWhetnn0UePQ5amstFhU7lFp7uvAmH6GBnYDenRy1i6Rn2NfpoDLiRBAlFVHg5+DIxLYYiKkhIzKXneG3uNWo8Neyt2IssylS6Cw925J97MclPkiT8fv+Ciix/yCMWixEMBgmFQrz++usLiNiu8s4nLoa1IyxP9muVKL773e/y8MMPA/Dnf/7n7Nmzh+uuu27D7WO33347v/jFL6iurub1119f/QUbwCVLuovtHddS6a53gmyzbWiWZTEzM8PAwACBQACPx0NHR8emjpl/fvmkm99mlu+iZu75CNKvvgoZM9u7KsqYO2/B8tYivvFThNgEs1W1+I9+HnHkOfYnRnlS24UkaJhYOETYXe/PfR47nr28vHxBpV7oWtlL6pKSEmpqztknHtY0+ibmeHqkD8s00QzdfgH9I+NUypUEUsPIo78GXQVRQjRUys48yHVX/b+ozjJ+7/7X6Z6OZ1+GwP/+0C4ObSnlhqYbeG76OQzTwMSk1FWKQ3RgWibBVLAo175YKDTkcerUKTo6OnLkMjc3x/DwcE639Pl8C5bdxZIEzreJ+Urvu57Nx8USxT333MM111zDQw89xGWXXcbp06c5cODAhkn3U5/6FJ///Of55Cc/uaHXrwWXLOnmY7VKdyN9tpupdPPJqbS0NBfX/uyzz27oeIUgimIuHtr2R2hsbFzS+WC2XY8liEhdD2LJCua+38Kq2pn9/y77NADTzz5Lq+zEuOIL/M/w/2Q+5OM1rQlBFPido40ca6tgfn6e3t5eSkpKzsXPWxZqaJzHesLMG2521PpoKvcQTmk0lLpyOrAQHsLR9R+Ahd7+fhwVbWxvqqEuMM5EOIPDIaHpFh5FpL3aSygUIjLyOrtMCylPW7UECTMd5f8OGHRNxYFsNaoZBnc93MPPfvcweyv30l7aznx6noSeoFQpJabFMDGpdK1c3ebjYvbLSpKEy+VaUuXljz6Pjo6SSCQAFkg4G50gu1jyQjFGgGOxGC0tLdxyyy3ccsstmzrWO9/5zqI6AhbC24J0l6t0NzPUsBHStSyLubk5+vv7KSkpWX3YYBMQBIHZ2Vl6e3tz/gjLfTar9Vr01mtXPabVchWeW/+e/9P/GHFhCqnzA6RFLydPnkQURTo7O/F6swbgmAbaiW/zh79WOJMKYAoyScFNRrdwOSQ8isQ3P7ab7eIE7h99JNuri4Xjle+Q+tAPkKs7uffDnXzloV56ZxK0VLj46s3t50zLm6qRzvxNNvjRsjAFAdUR4GTfNK+OWKiank2qFUAUBELJ7N9fEiRu3Xor3+v5HoIuMJeZY6tvK/sr9m/YD+FCYqUNLUVRKC8vX2BKb5pmTsIJh8O5IMj89iy7Kl6J3C7WQ6ZYZjf/tZF2AbCSp24xJsjWmx1mk63L5WLPnj14PIUzqTb75bb14dHRUfx+/4Y6H1Y6L6tuP0bdfqxkkq7eXlR1nPb29iVmIsLYCV7oGqIncxSfwyStq8xkFEBAlizmEyqfuf95vl35dXaqUSTHWTLV0yjP30v6lm9R63fxrdv2EFNjpI00PkceKTj9pD76Y1wPfwExMkLU1YD04X/mstIGhJoQDw29mQ1uNE0ME7aViZw6dYoxxnho7iEQwC27ubb2Wj7U+iH8in9d1/1ikdB631cUxRyx5sOWJ+Lx+ILsMTvuxpYp7Libi/V5i2V2s2XLltV/8S2CS5Z0C6EYZLtehEIh+vr6UBSFXbt2Lfny52MzU2T5kkUgEKC5uRmHw1EUws2/6TKZDP39/USj0ZyBUMHXxCeJ4wQEBAESppIL1U2pBqJgMB+XUEpVdMvkZ6k9/EC7DhP40Mwo7z/7fq/Pv84LU9kQUEVSuLHpRqo9Z2N3KtpJ/tZ/AvDqSy9x0FeHABxqLuNPr2vlbx8fQDNM9jX5+evf2IFDyPCPJ/4RJ05EXcShO3hm6Bl2GDtoLmvOkdNavhOXCukuh+XaswrF3UiSRCaTySV5nK90ikIoxghwOBxm7969RTqj849LlnTzv5iGYaCqKs899xx1dXUXhGzD4TB9fX1IkpSLM18N9ubcekl3bm6Ovr6+BZLF2NhY0borRFFEVVVGRkYIBoNr8ui1/E3sdz2OLJgkdJGwfo78LcCwRPxunf7G/QzN+vnfmVtxoSMI8P/FjiG/OcvlbQ6eGHuCmBbDsiwCSoDHxx/nY20fK/je+SuPD+6v5dZ9NeimlZUZgKiaRpTFBSY4YkrEU+ZBEIRcSoVhGLjd7gXLb7viy8fFmnA6X+8rCAIejwePx7MgNkrXdV588cUFXTb2NcrvLV7PkMdaUQwt+Xx46Z5PXLKkCwsrW4DDhw8vccfaLBZXHtFolN7eXgRBoL29fV1a0no7IsLhML29vTgcDnbv3r0gG0qSJFRVXfOxloNhGGQyGV566SWam5s5evTomnaxrYZD1Hf287fGcf587DKmBCcOQUAzs8MPFhbv3d5Pf/1uXurbiaWCUwLLXYEq+/hV9xyt9SKvzb2GU3YiCRLjiXG2aFvQTA1FWtgiVehmFwQBh3Tu516Hl3JnOaFMiDJnGUk9iSRKbKvatmCiLL/ii8ViTE5O5iq+/M2oS22mf6OQZRlJkmhsbMz9bPGQx/T0dM5zd7FWvJnVVrFsHYtFurfddhtPPvkkwWCQxsZG7rrrLj796U8X5dg2LlnSTSaTnDhxIicjnDp16rzEpttCfywWo6+vD9M0aWtr25Bh8lpJN+ePAHR0dBQk9s1Gp+dPxQmCwMGDB5fVoQtCEDH3fozd7e/lb4Ixfvv+QRQjgWFZ6JZIxtA4kHqankgrs97tpFPVmGelFz2t43VKTKen0E2dMqkMWZSJmBHmM/NLCHetEAWR3+38Xe578z5mUjN4HB7u6LxjAeHCyhVfPslEIhFOnDixoDvA5/Odd3/ZC41CksZahjxmZmaIx+MFhzzWOsprGMamC6Vi2jr+8Ic/LMpxVsIlS7oej+e8TpDZx4xEIoyOjqJpGm1tbZv6464nOn379u0rPr032kdsWRbT09MMDAxQWVnJkSNHOH369MZJxFVKS4Of9+yK88ircQxEJEHg9naDy8u301h5gCsad/HXD0cIn+0wcCsSv3mkgTBRGkoaiOtx0kYa0VKolttJZPQlCcBrRY2nhi8d+hJpI41TchbMQuuP9PPo2KOohsoVtVdwqOoQgiAgyzKBQIBAIEB5eTmWZdHZ2Zmriu0Bj0wmg8PhWFLxXazkhc1iPT26yw15ZDKZ3ANrdnY2N/rs8XgW9BYvHvIoRqUbjUaLRroXApcs6do3iY21RrGvFYlEglgsRk9PDx0dHQvadDaK5YjSTvNNJBLnLzqdrDbc29uLz+fj4MGDuFwuQukQT4Sf4Ndv/pp9tfs4VrEfaewFhMQslq8Oq+koOFZuexMEgT+7wss7M0OMqV62Vno5XJFBiFdRUXcFlqeSf/hohqf65jBMi2Ot5TQGXDwzUEcs1I7bE8XlMDk1WI3hbuGvpvq4dX8dl20pXfAea13JCIKAWy58zqPxUf7h9X9AFmUkQeL73d/HwuJw9eGCx8mP/c4f8FipZ9bn812wSbJiYLPTaIIg4HK5cLlcCzZe80d584c8FEXJXZ90Or3ph1UymTxvrZnnA5c06eajWJVuPgF6vV7a2tqKphctJl3bHyEcDtPa2kpVVdWaK87FE2krIRKJ5LThPXv25LThuBbn3lP3MpocpVwqp7+nm1J+yYHSNnD6Eeb7QY1hdbyvoMWjDbPvcRKv/oy9c/0c1efIsAeVVsStV4Gnkv7ZBK+MRfEoEle1luN3yfz9E4M8/MYsptVGxlCp8Bm0VpbSXFqBqpv8+yuTtJS7qfQWl7ReDb6KhZXzXBAEgeOTx5eQ7mpdBCv1zMZisWVJxvYLeCtVxedrMKLQKG/+6HMikSAajdLd3Y0oihsa8rAfxG+l67kaLlnShYXVz2Yr3XQ6TX9/P7FYjNbWViorK+nu7i5qIoVNupqmMTg4SDAY3HBisT2RthISiQS9vb3oul5w068/0k84HaZcKcfn8OE1FYbHXmF/3eVZLxxfLUJ0EktLgrK0Fc40Tca7X0Z+8YdUWPM4vG5MrRpnqIfBqquZmbTo73qB+3v07FScJPGL09P87rFm/vPNWdyKiChIOHWZiXmVq7ZmCUyRRQQBQkmt6KQrC/LCnm4rG8NTDBTqmV0uRHOtrmMXAhfS2Wzx6HM4HKajoyPnFLjY4GaxjOPxeAo+IC4ljf2SJt18bLTStb08I5HIkhThlcIpNwJBEJiYmKC/v39dnQKFsJK8YD9A4vH4inKFgICFlfunLgrn8sUEEUwdsEBc+DXJBVj297I98xq1+giCnsRwb0X0lCPI0OaJ0XzwMD/66ZuUuFO4JAvDMBidjfBvz7yOrpnoSAiCePZMYD6uUuN3oupZ97EyT/FJ6HD1YZ6ZfIaZ5AyiIGJhcX3T9Ut+r1j9ssuFaC7nOpZKpXLesuerTWsxLqbDmD0csdyQh6qques0NjZGIpHAsizcbjdzc3NMTEzkjNCLcZ0eeeQRvvCFL2AYBp/5zGf44he/uOljLsbbhnQdDkdOV1sLVFVlYGCA+fn5ZftS1xLDvhYYhsHo6CjDw8MEAoE1JUOshkL6sKZpDAwMMDc3R2tr66ox9NsD26nyVDEUH0LNqARFg3dvew9CbDxLtKaR1XRlV+41ti4ccoQQMk8yFxqmAgunoSFGRrA81VhKKVgm4vRpMokYLsmJ4nSS1kwcisj2lmpOhSYJp3QSqo5hgQT0TASJxBRk2cF7dlZyaixMQjXZWetDEARmYhkmY3FEQaC1qgS/a/1f30p3JX+87495YfoFNFPjQOUBWvwtS37vfA9HFNqQMgyDkydP4vP5FrRpSZKUq4rtTali9qFfLA9fWJ3wFUVBUZQlQx7JZJJwOMyzzz7L5OQkBw4cwO/385WvfIVrr1195H25c/nc5z7Ho48+SmNjI4cPH+aWW25h167ijo9f0qS72FN3LQSpqipDQ0MEg0FaWlro6OhY9ubarE6c35ZVW1vL9u3b0TStKFVFfqVrGAbDw8NMTk7S3NxMe3v7mgjDLbv5w31/yA9f+iGm0+RQwyEOVR/CjI0jZOJYrlLwZ310Y7EY3d3dyLKM3CRz/xv38/6pQV6QJPolg5sFASkdAVcAy9OQNbmZ7+MasYnvB1uYJ0BaBxOLvmCKQ1vKePC16WzsD+B2SsRNid/ZXUOt0+CHr04STKjIgsDPRYn9ZRpKZIwyfwkIEoNzKa7fUYlvA8Rb5a7ifS3vW/frzjcsy0KW5SXessslVKxlwGMtuJiVLqxfGrClmWPHjlFfX08kEuGBBx4gHA5v6jxOnDhBW1sb27ZtA+BjH/sYDz744H+R7nJYTdPN95ld69JeluWci/16kFt+Dw7m2rIcDscCV/zNwq50R0ZGGB0dXTXIcjn4FB/vrno3gUDg3I1e2nRupDeVore3l0wmk/NguPvFu1EkBdnpIwBMCSlOVXayP5nErDuA5alEmnwFq3QL/80Px6NJpmMefG4PLRVuRuZTjMynkMWsWY1uWiQyBqYFM2mR6vJSTCXNnhoXlmURSaR5dmKOq91JItMRDNMgYci8oIfZ11yxKcJZDhdjDHi591wuoaLQgMd6jW7g4la6m0UkEsldl81ueI+Pj9PUdC6hurGxkRdeeGFTxyyES5p087+gy9k76rrO8PAwU1NTC3xm14L1VrqL/REOHTq0oPG7GB699vtMT08TjUYpCZTQvr+dCk9FwZ7UtUAQhCX6sC2/hEKhnAeDfb11Q0cURN4sb+DwzAAVWgZHJobR+h70nbciDT4BUlaPlQSocFnsFxOU1GRTezXdRLey47sZ3cR+Z90w+b9ds9T5nQvOzeVUsASJ6upqAiXZvLTJ+QRuj0AsEoLn/wFp5gSm7GZ++0cRth7bdO/sxSDd9ZDfcgMeKxnd2PLE4s6Ai13pbgb5pLtZFGpJPB/fgUuadPOx2N5R13VGR0eZmJigsbFxXWSbf8y1km4hf4TF2Czp2taRvb29BAIBuunmJ+M/wRq3qC+p5wv7v0C5a/39xMtJFcvJL9dtuY5vvf4thiQXwfI6/Jk4h/Z+Cq3qEGJ8EkvxZK0ctSSIMu2OWc5oe/BYFhZgAs1lbqZjGVKamauqvU6ZeNogmtZxKxLBuIpTFgmndC6rlYllDARRw7AsFKfCnm1VVLz5PeTIC1hlFViair/vnxnzVzMaqspp/Lar1sXuElgNxag4CxndmKZJKpUiFosV7AzQNA2n03nBK95iRBMVcwS4sbGR0dHR3H/b6dzFxiVNuovTI3Rdz21ajY+Pb3jJbWMtJGn7IyiKssQfYSPHW+19nE4n+/btY0Kd4JmuZ9hSvQWH6GAyMck/vfFP3HnoznUf2ybdsbExhoeHV42Bv6LuCgCeHH8SRVR4/7b301iyBeuVf0VMTgMClisAehqAWw6/g6HRel6fzJLgsW3lfPhgHd88PszPX5vGwkKWJFwOkXBK44meef7wXc08NxhmNq6iSALxmEWNAAG3jNcl03Z2I00aeQbLXQaSgiApiHqCeqao3nU1kL2xC3UJ2Im9NhkvlifeSvLCZpE/4JEPu5VtbGyMVCrFyZMnAZa0sp2vAY9iVNjFJN3Dhw/T29vL4OAgDQ0N3H///fzgBz8oyrHzcUmT7mJkMhmef/75ojmNrVTp2tNqgiCs22VsPYjH4/T29mKa5oL3GQ+Ng0CuxzTgDDAQGVjXsSF7oycSCYLBILW1tTn9+c35N3lq7ClcsoubWm6ixnNuGksQBK6sv5Ir6688d6Ch45CYxvKfNU2JTWA2HMZouRoH8CftFuGUjiiA3yUjCAJfvKGNY63lfPWhHkzLwjAtKkoUHBLMxjU+dlk9Pzo5gSyJzKnzxFWDSNrg6vY8u0nFD7GJXIeFYFmgnPtbiKKYa9Cvq6vLfWbbzGU5PfRimN1c6ErTHvCIRqM5mSL/IbXcgIfP51t3THohFMvWsaGhYVPHsCHLMt/4xje48cYbMQyD22+/nc7OzqIce8H7FP2IFximaTI+Ps7IyAiWZRXV1rEQ6doDB5qmreqPsBjrId1UKkVfXx/JZJL29vYls+Xlzqw3gGmZiIJITItRW1K75nOBbJXQ09ODYRg0NjbS2toKwEvTL/Gl576EamRdzB7of4D7rr1vAfEuhpAKYTnyDHMcHoTUuUBMQRAK9t0eay3n0JZSpqIZ/C6ZhoCL2ZiKblqEkxqqYVFeIhMWRapKHExH02R0E+fZKCD10Gdw/urLEJtCAMzSJvSWq1f83MuZueTroXNzczm/hfx2rfMpT1zMiCCbQPMfUvnntThAcz2x8suhWLaOxSTGm266iZtuuqloxyuES5p04/E4J0+epLq6miNHjvDiiy8WdUMgn3Q34o+wGGsh3fwNrJVGg3dX7GavZy/D6WEkJNwON5/etTYLOvvBYRgGO3bsIBqNLtDD73vjPgzTwCNnSTSuxvmP/v/gjj13LHtMK9AM4y/DWUcvIRPFaLpiTedz675a/u3kJD6XRCSlo8ginXVeJFHANC3Ms1VnRjeRJRFZPHc9zJo9pN/790jTp7FkF0bT5aAsL/GshHw9tKSkJNfDbVd+wWBwzfLERnCxughWI7/1DnjY12a1AY9imd0UayPtQuGSJl2Px7Mgkdb2IygW8dqjtl1dXRvyR1iMlUg3v8ti69atK/YPQ/ZGuMZ3DY5WB4+PPo5LchFWwzTSuOxr8lMhtm/fnruB4vH4guV0Sk8t6ISwsBiLj/HxRz7OTGqGHWU7+Oo7vrogxtyq6USNTOOcfBEAo/EoZu3a3Pzf0RJAFgVeGongdohcu6OSal+2g2Fvo59TY1HmUiZCSuc9nTVI+aRrWczLddBQR0WJo2iVol11Llf55XvN5vvx2iRsDzGsh0QvFulu9H2Xcxwr5MOb71Vsd5a81TTdC4VLmnRlWV4g8tsdDMUgXdsfIZlM0trauiF/hMUo9Ho7zXdsbGzdXRbz5jz/8sq/kNEzIMAzk8/w5cNf5kD1gQW/p+t6rkd569at7Ny5k5gW41/P/CvBdJBmqZnd7t2537+x+Ua+8+Z30EwNy7KQRInjE8fRTA1REDkVPMUfP/3HfO+G7yEIAvF4nJ6eHpJJN8hXZisdqxRfcA6fz4fT6Vz1AXJZc4DLms/dPNneXZ2DjX5ayt28+vocB3ZVU1t2rorN6CY/fnmSgbkEWAIdNSV8cH9tLknifGEt8kS+81j+Etzn8y27BL+Y4ZDFKlSWuzb2gIetoScSCTKZzJIR4PWuGIrppXuhcEmT7mKsFsW+FuRXnM3NzZSUlOQ2YIoJy7KYnJxkcHCQmpqaDWnRJ5MnSevpnGNWQktwf+/9OdK1OxLy49lFUSSlp/gfv/4fTCYmkUWZJ/QnuK7iOj7f9nkAbmu/DcuyeHjoYZySk8vrLudHPT/CEq3cuY/ER5iOTTM/Nk8sFmP79u253fF0Ok1ifgqr+z8JRyZI4iFefRB3oCZXNXo8nsI3l2UxFVP591cmiWcMHJLA+/dU0+CTCbgXXp/nBubpDyZoCGSHKLqm4rw0HObybZu34dwIAS7XrpW/MTU0NLRkCe7z+XC5XJdcpbseFBrwGB8fR1VVSkpKNjzg8V+ke5GxXBT7WmC3mo2NjdHU1JSrOO0NumIuW2dmZujv76esrGyBPLJeJM0k4UyYmBrD4/Dgklzopr7AqLyqqmoJoZ+aPcVMaibX05sixaOzj/L71u8jCiKiIPKbO36T39zxmwC8Ovsq9/fcfy4xGAvTMOk61cXO7TvZuXMnkNWjBUHA7VTwxU5DqYJVewAhHUG3Jpkv204skc5txORXOD6PE3/oNEJ0nAf6KrD8jdT4AsQyOg+cmuKd5Uu7CaaiKiWKyFxCJa0aaIbJdGzzEUbFxHLyRCaTIRaLLViCm6aJLMu4XK7cg+lCDC1crOEIe5S5urp61QEPy7IWWD+WlJSgKArxeHzFMNi3Ii5p0l1MhBupdPO7H+rq6jh69OgCgsqP7NksQqEQyWSS6enpZQco1oqoGqUr1UXaSCMgkNSTuGU3n2z9JCdOnMDr9S6ZiLOhWwuvkSRIWJaVHb7IzGFaJpWucxNoeyv3sq9yH6/OvkrGyCBZEh9s/CBXX351rkKyLOucnq4lIR3G8p1t0ZJdOCZfpkqWqazaibllFwgiejKMOnmGRHCE+NwgsdgMIamCybAHV/QMz1tbQHSAINDuXOqoVlfq5Ffds8QyBqIAsYxBU9k6IodWwPlc6uebfucvwScmJohGo7nsv3yyydeKi909cbFIV9f1ghFRaxnwOH78OF/5yldIp9Pceeed7N+/n2PHjuV8EzaDH//4x3z1q1+lq6uLEydOcNlll236mPm4pEkXlprerLXStZf3Q0NDVFVV5fpTF6MYpGv39Ip3id0iAAAgAElEQVSiiNvtprOzc9PLuVOzpzAsg3pPPREtkt2gM6E+Uc+Ozh0rPv33VOzB6/ASyURQJIWEluCg/yB/evxPeWHqBUzLZItvC9++7tt4FS+iIPLF9j/lZ8l/JaloHGq/mmONx3LHs0wTKzqBkIyiu8qwJCeiaWLpKoJlIk+8iJAKY+oq0uhzoGcwy7biOvNT3GqCUgHE+OvobddTJ/twxwRenTFwutLoVoZoxuTZIZFdtSOUl5fj9XpxOp3srPWiGlbW+xeBbZUe5hIqsbS+ISOcfFwMfdVuwcqf/19sjG7LE06nc8GU3WYsIN+qXRP5WDzg0dbWxi233MKVV17Je9/7Xk6dOsWpU6eKQrq7d+/mpz/9KXfcsXy3zmZwyZNuPtZS6a7mj7AYdtvYRsLzkskkfX19pNNp2tvbCQQCnDhxYl2ZVMtBEAQQwCk6KRPL0C0dUzY5ePDgqh4Mpc5S/uqKv+L7Z77PXGqOnb6dDM4McnzieO53BqODfOGpL/B3R/+OvjdeoXL+RX4n4ENxOLAEFxZnq1vDgMGnkKZfwylKgIDadhNG4zuQRp9HSIew4jNodZdhKn5ExYs4/TqCmkTQU1ilZxvbgz2Is104mo5ydaPAK7MCgqWjZKJc5YkSi4GL8gU5ZQlDosZpUelzozgV/B4nU1EVzdh4YOfFRCGiX84Y3c4ki8ViCzoE8ol4LWY3cPFId7MtY7Ycc/3113P99Us9kTcKWy47X7jkSXdxpbuSp67tW+D1ejlw4AAul2vZ37WxEXvH/BiexWYxduW82SXi7sBuvHiZT87jUlygwAe3fTBHuJZl8fzU8wxHh6n31nOs/tgCMq4rqeO/H/rvQLYSv33wdiwsJCF7k5qWyZvzb9LV1cUeV5CSukrwVGYNzsdfwiypwfTWQXQCeeY1KG3MGpKrCZwjT2Ic+BSU1kGwFxwuxLJmsCzQVAbjCuF0ioqkk0a3kb025a0I0QmE2BQdkkBneRWB1BDuyhI0XKDO0zT7BJkjv8+zAyEmMmlKPSKV/gjhZApXKsHQhEaZU2RqVCd1VkddK/EsxlvZ8Ga5TDI7zTgWiy3RQt+KuW2blTVisdiaJkHfarjkSTcfy1W6oVCIvr4+FEVZkBG2FqyHdHVdZ3BwkJmZGbZt21awzWyzpjemaTIyMsL4+Di/V/97nBJPESfOoepD3Nh8Y+737nv9Ph4aegjDMpAEiRenX+TGLTfyt6/8LXPpOfZW7uXOA3+CPxNHGTnJB8Ih3jSSvOJ0EZQlLCyckpPDhw8jneoGZynZZ5uIZZiY0SlwVyKaGoIgY9mE7vAgxCaz5OypgAY/JINIiWkk2cmvxuB4phVRkrGCIa7RNN5RlcEyDDKdHwV3OaWSwrsZ5vhpBylNQRbh5qpZpGiMn52eZjCYpNTtYDKaIeD30FTtZyaqsnObi2vbyxC09BLiyTe98fl8q1ZYl6L3Qn6asY3lctvy5QnTNC/K591spRsOhzfco3vdddcxNTW15Od33303H/jABzZ8TmvBJU+6i01v8jXdaDRKb2/vuvwRFmMtJJlvspPf+bDR4xWCZVlMTEzwfO/z+Mp9HD10lOnRaTpLOxfs/ALMp+d5ePhhvI6sHmtZFk+OPcljo4+BBQ7JwcmpF/jpI3fwaW8HzuAA11sBwvo4lXqCX3i9JGSZPzrwR9mVhLcWIqNYnirMRBB5/EUcahRr6lXMLVdkCVdNZAk3PoUZaD4XZCk5MNuuR5jvJxRL8JzhoL6mHEkU0D0CT01PcKA2hqvzA8jl23Mbcse2J9gb/BlxVz0VThN1cpyQ0sFgMEl9qRNBEPE6ZSYiaW7dV7coS821hHjsHtHZ2VkGBgYWmIDb3QX5dodvF++FtcgTmUwmN82ZP2W30VXCWrHZSnczgxGPPfbYht93s7jkSTcfdqUbj8fp6+vbkD/CYqxU6VqWxfj4OMPDw7nOh9W+RBsh3WAwyJmeMzySfIQBbQBpUuKBuQf4ZM0n8ZlLHyQpPYWImJMTBEFAt3QM06DEka3yGwyBdKQHw7mFlLMKIz7Nh8uupkuYxVNaxf7dn+Ro/RVYloXRcBQxFYHwKPLky5iVHVC5A7QkYvfPsSraEIM94CjBLN+GufVdiy6iE6t6F6o7g9A3kiVcw6Qn5mQwVcN34p3c6qyj+izhSJIEtTup6nw3ZW8+RHgmRsRZj9r6QYyuDLphIggmWFmiskwjZ01ZiLSWa9uyTcAjkQhjY2OoqpozdrE3Ty9kBVgMq8O1YLE8MTs7y5EjRy64PLHZh0wxvXQvJN5WpKtpGqFQiDfeeGPD/giLUYh083ttKyoq1tVrux7SjUaj9PT04HA4eFp8msfmHkNAoNxdjoXFv0/+O38S+JMlr6vx1FDjqWEiMYFH9pDUk3gdXuJqPEcisqFhCRKzwRCSKCArHuo8Thq0ANc6WzDnRtH9s5jOAMgurB23IMSnEU0NAs0A2f8eO4GppUCSsbw1mG03glj4wRPwOCh1O5iNZxgLpRieT1HhVYhndP7lhTE+e1UzXmf2K5lIJOhN1iM1fIQ3y0p5I+xA6NJIZEz0cAafSyalGnTWeQm4zwWIGoaBZVmIorjAxGUxljMBt/tnJyYmiEQizM3NbXq8d62wz/tCIp/oV5InFruOOZ3OBVXxRrsnNvOQOV8jwA888AB/8Ad/wOzsLDfffDP79+/nl7/8ZdGOf8mTriAIOU+BSCSCJEkcOXKkaBXD4sie+fl5ent7KSkp4eDBg2vajMvHWkg3mUzS29uLqqq0t7fTleri0eOPIiAgiRKhdAgBAdkonFYsizJ/eflfcu+r99If7WdX+S7+oO1j/OSlv6EvOsiQw8GUZfBR5078Ww7gnu8iPD2MEA5iVrRjVu7AUuOIvY9idf43BOns16SkKuskpiVBdiFOvYrlCmCVNoGkIM73Y8Ymsv9dAIok8tHL6nn49DTPD4ZoKnOzo9aLyyExGUkzFc3QHLA409tP/1SYluZm0lIzr52aorEsOx46EU5R7XOys85HpVehs85/1hgnW+mappnTKG0Ctr8LgiDk/rccudnGLqqqYpomjY2N6LqeG2RYPN5rV9Ber3fTvdwXo4tgNa+SfHmitjbrYrdS98SFlCfOl9nNrbfeyq233lr049q45El3dnaWrq6unKfAc889V9Qlml3p2lWnLMurmpWvhJVIV1VV+vv7CYfDbN++Pbcz/fLwy4iiiGAK2DEL4UyYw4HDmKZJVI0yGhulyl2FS3bxQN8DzKXnuG7LddxVfxdCbBLx9R/zOf8+TsdgLpXBdfh2rqzejjj6HJa0g1DGR6DKi1HViSVICK5ShPg0gpEBm3QlB2bbDYh9v0RIzoGWxGo8ClK2yrcEEcyVHyhlHoWPH2lkIpLB55ZxylnN2TAtgjNTjJyZ5lTchyZV0NOfYD4ZwiEJub9pqduBKIpc01G14LjLVbU2Aef/E8j9DZYj4nyylmV52fFem3T6+/tzOnE+Ea+n1fBidUyslxhX655YbpIsPyqoGJp5OBxeMFxyqeCSJ92Kioo1hUxuFLquMzU1RSQSyQUzbgaFSDc/Imfr1q1Luh4qXZU4RAeyIhNTY5iWScAZ4LaW2zg1f4q/O/l3CAhohkapsxTd0hEEgcfHHmcqOcVHMjLzsTTBuEpz7eUcdKSx/FVY5duyGqxhMJJ6lHKrC6emITtlBD2dnQaTF5KGVdqIse8ToMYRfXWIwTOgpRDUOCheLO/CTb1CmImpbCl38+zAHOUehYyaIWDGKFdqSFS2YmZiNPizK4i5RIbxsEqd34UoCkRSOh01ax/7FPN14rPIJ2D7f/bfAc5lxq1EgCvpxItjcRRFWUDEyy3FL0alW4yecRvrkScURUFVVWZmZjYsT0SjUdra2opy7hcSlzzp2naO+ShGxZBOp3NVp9vt5vDhw5s6ng1JknIdFvkbcbmInPQc4hs/ATWBVb0Lq+Eybt56M4+NPsZEYoKAM4AiKnz9qq8zOj3KX3X/FYZl4BAdmJbJVHKKSndlVh9E5Ptvfp9D6iGqrSnanRJCIojlKoOzHg026Wzv3M/sqIBj8NfomoHsUNBa3oVrdg6/37/Q/Ul2gezC7LgZXGUI4QHMwJbsBppj5THckfkkPz89jSgIlLslwvNBrmxyc+ORg/hKPJx5bQqXfI4gG8vc+JwyU9EMAFsrPUuq3PViNSIOhUJMTk6ybdu2Bd0woijmrsFqOnFNTdbw3TYAj8ViC5bi+aYutk58oTbS8nG+R4CXkyfi8ThnzpzJjcUvtn9cS4/1pWh2A28D0l2MzY7t2paOwWCQbdu20dLSQk9PT1HPL5VKMTMzQ19fHxUVFedGkNMRpJPfxjINkN2IXQ9iGiolzce49+p7OTF9AtVU2Ve5j0hylq93fR3d0vEbBlWqiiGIjMkic+k5BARMy8QjeWhu3oJrsAdLroV0GDE0hLr13RhnNwgFQcgu06qug86joCZI4yCa0nObSul0Olex+f3+nCGLue1dwLvW/PmfHwzhlgXS0RBeLYmnqoLOHY34SrJk3VLh5o3JKF6XBBbEMwa/sb+O5nIPhmlR6pbPW45YOp2mp6cHy7LYv39/ThqwteHF8sRaN+xsnTh/KW6busRisZxOnE6n0TQtN+pcDJ14NVyM6loQBCRJwu1209LSkvv5euQJuDS9dOFtQLqLb0Bbg13vl9UwDEZGRpiYmKC5uTknWaiqumm7yHyk02nGxsaoqKhYshEnhIez/a5nuwMs2Yk48hzalit4cOBBnhx7kmok9vY9TXrmNT4eHedxh8n+dBoRC9ESmHBIPF5SgiGIWeLFRHBImM3HEEaex0zOYspupJ6HwVGCVb/QexenF5xeXIDLR8GdfbtiSyaTyLKcI2G/34/H41n2JjZNk9m5eUKhEPU1VdTW1jAZzaDn6Xu1fhdeReaFwTBVXgfv7ayhs853XitAW96ZmZlZYO5uI//z5G/Y2SSc3zkBa9uwK2Tqcvr0aWpqatA0bYFOnE86dj9xMT/7xTK7WXyPriZPzM/PMzw8TDqd5q677sIwDJ599ll8Ph9tbW1FeXjceeed/PznP0dRFFpbW/nnf/7nohP7JU+6i+FwONA0bc1dBfkuY4VScDcyBlwIiUSCnp4eMpkMgUCAPXv2LP0lQQDyyMU0QHJwf8/9/LD7hzhFB1fMjHDcNCir2IEF/F40xTMukZCY/VNu0WGbKTGkyLgkF4qokHF4ENUML6abeEm7HFIqB/wejg49jVXTmdsIWw1OwcAde4NqLYHV0IZVuY9oMk0oEiOdjjM3OEgikcjpnTYZe73e3FRgi9+LKtbhcLsIpTQkUaAxkP1bhZIqP3l5AlEU2NfoJ57RqfAq541wbR+OgYGBXCjnajfuRjbs7Ip4NSIGcqGP+edoT5SFQiFGRkaWtGzZfrwbuU5vdbObQsMdpmnyzW9+kzvuuIOpqSm+9KUvUVdXx7333rvp87r++uu55557kGWZP/uzP+Oee+7ha1/72qaPm49LnnSXq3RXQ77nbGVl5bIuY6IobmqnNZPJ0NfXRywWo729HVmWGR4eXvqLagIioxCfzuqupQ0IWgpzz0f45Wt/g1Ny4kek0hIYlURqRQXN4cKZiOIXSkgLEldWX8nw7HOUyiXUuAMk9ST13nqU5qvp+vWDPBcJ0OCOgs/PiXgVfkllh6EXJN1ISuNX3UGmoxnqSp1cs81L2RvfRUjMYMlOhJFnecZ/M0/MZ6vCulIXHz64kxKnnGuxisViDAwMMD8/jyAIVFRUsCfgoyIlMxo3KfM4OdJSRpkn+/79swk0w6KuNEvCsijySt8YO3t/gRgZwww0o+/7LSipXHK+64X9EHQ4HBw4cGBDhkb52MiGnf06m4gLEaDtPJbfLbPYj3dqaipn/p3fT7zSqsPGW6nSXStEUaSlpSVX8RZTgrnhhhty/3706FF+8pOfFO3YNi550oWFpjd2pbsSgsEgfX19+P3+VV3GNgrbh2F2dpZt27axa9cuBEEgkUgsbRnT04gn/wkhPg3eaoTQMJbiwdx7G1b5NpQ3FGJqDE2SMQQBp2nhVbxcW/4uIvHHaXeUc33bu9laUs90SYDnUt2k9CjbA9v54oEvYrnKGKm+Bt/scUSHCs4A/mSUUWrZ4Vjq6aubJj97bYpISqfMIzMSSvMfJ8b5pDWDFMj24A5GTB57bZjaHXXIkshUNMMvu2b44P763CbRzMwMmqZx8OBBfD4f8XicaDSK3wizRY9haRYzw0HSZyvixdfFMjXk4V8hlI9hucsQQ4M4XvgG2rv+J4gb++raf5dQKJRzfjtfWI2I83ViVVVJp9M5Mlptw66QH6+maTkiHh4eJplM5kg7v3si/3yK2b2wHhSD7IuZh1gI3/72t/noRz9a9OO+LUg3HytVunbkuKIo7N27t6CB8maRH5HT1NS0pJ2tUMuYEBrKEq6/AVXT0XwCnmA/ljur9/32zt/mr0/+NSFN5T9LSrg5GqMsmKTEYZFq+3+4etduhNlukBQqD32Wb3jrclWVvaQtLS2lt/ogpZl+xEyMpFKJb9ves5LGQkRTOnMJNVdxVvsUpiZ0ooqMrUDOaQ5Esum8AOUeB6OhdE6uGRsbo7m5mfb29nM9toviWkzTzG0mTU1NkZiLMj2lEpx14HE5EcwMNyhDUJIlFstbgxCdgOQ8rKE1LR+WZTE1NcXQ0BBNTU20tbVdlDyyQkRsr7jq6+txuVwb2rCDbMFRXl5Oefm5uCI7sdeOw4nH45immRvtzWQy56XoWA2bNbvZzOpzLWY3d999N7Is84lPfGLD77Mc3haku1qlG4/H6e3txTRNOjo6FqSXrhWrtaHlyxXV1dXLZp4VHI6wTITwCG8MTXA8VI4hOqhxOLjh2ftwH/kkx+qP4Vf8PDn8JMlQEn/DTiq2tODwltHfP4215TBm0+XnqqezrUf557u3wc/QXIrx+G7wQqVXYW9LYeJySCKWBYZpIYkChmlhOgM4FC9CfApLdlOqqpjeyzEtC1EQiKZ1Ag6DF198MSfXrFaFiKKYS5NtaGhgJ7AvnuGlgVmi8QR1Qpqy7mHGx8pwKE4Uh4RHz6BZIuvZSrIHW7xeL5dddlnRkxc2ilQqRXd3N7Isc/DgwSXklz9dt9ENu0KJvYt7Z+fn55menj4vsfLLwTCMTW0I2vf7Rs5vNbOb7373u/ziF7/g8ccfPy+f/21BuvlwOBxkMtmeznQ6TV9fH4lEgu3bty+oANaD1aLd7dFgn8+3slwRm0J546ds6XsN0T2IueP92b7WVJjZSJwnoruoFWZwWBpTyk6eCpVx08CvSO/8EPKMzBHtCO0H23OfQ9d1BlLP8YOnf0BSS3Jd43X8xrbfKHgDuhwSv7G/ltlY9tpU+Zwoi1JzwymVR96YJRjLmsoMzSVxOyRMC45tr8ZV89uYQ0+DGmVr8w4OR5t5aSSKoeuk4iEMl8yvkqVU6TI3VWpUlgg4JIGxcJr/ODVFJKWxo8bLTbtr8CiFr2WF18mNe8/FyEuBWSp6H0LXk+gZlemadzLeM4yq9uamv+wNu8Wpw/aEXzKZpKOj4y3jvWqaJsPDw0xPT9Pe3r7s9zK/us1/7WY37PI3p9LpNB6Ph6qqqlx0+uKQyHxpYi068Vqg6/qmpIF4PH5e/p6PPPIIX/va13jqqafOy0oY3oakK8sy6XSa7u5u5ubmaGtro6qqalNPLEmSCn5J8mN4Vh0NVuNIL/4fwMAQnYjjJ0FLYh78HYTYJKGqw4gpC4cuYTm8VCgG4xkPc5MjvBl/kW3btrFz584Fn2MwNsi3pr6FIAlIgsR90fvQLZ2PbP9IwVNQJJGGQOFctvmkyl2/6GYuoeJxSDSUuyhzKby7o5KAx0FTWfZ1xq5zM+nXaBql2hzhaJwRXxXBdJbM5+IZvvyzLjrrfDgkkfFImgqPgzKPg9fGo+imxccua1jTtTd2vB+zegdCcg7JU0lteRu1Z1c26XSaaDRKJBJhdHQ0t1T2+Xyoqko4HF7W1/hiwTbSX2u3xGKsRSdebcMuH7a2ulx0uqqqOSKem5vLdafkV8SLdeK1YLMRWJFIZEMr1tXw+c9/nkwmk0uiOHr0KN/85jeL+h5vC9K1byhd15menmZqaoodO3Ys0BM3g8WRPel0mt7eXlKpVG4zRpg9g9D3MjjcmC3vzBp4559jbCprFFPagCUmsEobMadf5+TEc5RmgriFDIZ/G0YiiohBMC3hSA2QadvF5YcX+vPaN9YTo09giRaKoGCZFpqp8aOuH3GZdFluSbnWJdzPTk0xn1CpK3WjGyZj82mclRINARflJQuPYevW4+PjtLS0cGD3Dr7+aD/1ARdYMB7JkFIN3IpEPKPTP5ugoa0CWRSoL3XSNRXLyRKrQhCwKtqxKhb/+BxJ5E9/zczM0Nvbi9PpxOPxMDQ0xMTExJKhjgtNwvmDF/v27dtUKOlirGfDziZiy7JyUtdK10JRlII6cX5FbOvEi43iV5JxNlvpni9bx76+vqIfczHeFqRrpymMjIxQU1NDWVkZDQ1rq6TWApt0NU1jYGBgSQUtTLyM9Pw3sCQHgqEjDj2D/u4vg/tc47slKdk0hbNaVCoZ5OWxp/l7YwjJsvhQNMw+p4NX49XoqTBOn5tbrzxERec1OUNwy7JIqAm+1/U9esI9xLU4KSNF2kyjiApO2YnXnV0ChkIhhoeHUVUVt9uN3+9HdHpwukuoLC3BkSctGKbJ8HwSScj+uyyJWAikdQNFXlgZ2Z0fdpinJEmYloUiiWQ0A0kUSWR0FIeIQxLxOR0YJqRUHUVWSGsmboe0NsJdB+wHoWEYHDx4cMHSUFVVotHohoc6NgP7ATUxMUFra+sFM2hZjojtf5qmSSQSYX5+ntra2tw+SH41vJJOXGhTtFCAZr5OnC8BbbbS3UxqxMXG24J0JyYmyGQyHD16FMuyePXVV4t6fFEUGRsbIxwOL9mRBxC7HsRylYLTjwUI4RGEyVewtl1z7iCljVh1+xDGX6Y0/Abp2VEE0eTDoVl+VdXMv/oMrhZmeUfNtVR3vIO66qoc4dlVimZofPZXn6U30pv9uW05ZoFu6miixp0776S2tnbBnHsqleJ4zxS/7htDVTM4RYNrt3lpqAzgLvHy/HiGobkU4bROMKFR7VNIaiZHWmpy/rb2ZqQsy+zfv3/B8IkoCNy8p5qfvjqFhUUiY9Bc4SbgltFNqPY5CSY0EqoJAty2RmlhLcjXR+08usVQFIXKysolY7ixWIxoNMrgoqEOm4i9Xu+miDgcDtPT05PzXL4Y/bD5sD+LaZoMDAyQSCTYv38/brd7QUW8kQ275RIq0ul0rmfbvk8dDgfJZJK5uTkCgcCGVh6X6ggwvE1It6mpKdcmZlnWmmPYV4Md0z41NUVlZeXyyRCmDkLezwUBwdBZ0NQiiJh7b0Nwl2GO9fB62RaejJeRnqvAGdZIVKeYqvdx+Nj7c8ewz8HeJDk9d5q+SHb5IyDkSNcpZmUPWZR5R807sqdkWWiGiSKJhFWBp0ainEqeYF4bxyX4cceu5FPNDbw4MMOv+8PUSyaaIBAxBVRN5MP767hpd7YC6u/vJxaLrZjCsavOT3mJwmxM5V1tlbw2EWUqmsG04PYrmijzOEiqBrV+FzX+4rQo2anOG9FHC7VX2bP/0WiUkZER4vE4giAsIeLVyFNVVXp7e8lkMnR2dm7YBvR8wDbfb25upqOjY9l+4GJs2OVLQPnj5KqqcvLkyZzPSTKZzD3w1mN281+k+xZBsbS6YDBIb28vZWVlbNmyBY/Hs+yXwGy9Funl72GZOhgqyE7M2r0FTk4EVzmqq5IzVjNvRAV8QgpTcxILNXFzWRz5578PgoSx4xbijVfzdP8kx8dex6Wkwd2PydJ4cYfkwCk50UwNSZAYnU/yZO8cmmFR7nEQTak8PtCNhoQotIB7mp8PPM2nLt+Ot6KWlkwJlV4HrWmV8fk4LjRamOHppwfRdZ2Kigqam5tX1SFr/S5qz1oy7m8qJZzScDukRfllm0cymaS7uxuHw7Gk6t4MCs3+2/plNBplfHw8p196vd6cPGEHXdqucaOjo2zbto3q6uq3zAZeOp3mzJkzyLLMoUOHVtX6i71hlw9FUZBleYnZjd1PXCgqyCZkWyf+L9K9yCjmF9seoHA6nezbtw+Px8Po6OiKo8XW1ndjSArC8LOglGDseB/4agv/rrsMU00zFCpljzRJyowz6vCxRW9GmTyD1VDFXHKWwcf+jP8lXU2/6UWSM6TTPlQNRM9eJNcYknM+d0zDNDAFk5uab0LTZR7vnsDvknE5JAbnkrwyOo9qRVAcOiCiJRvwlPbQG+6l2reXtGZgWg7cTgVPSQk7y0Q0dZr6+npqa2tJJBK5HLFMJoPL5cpt1Nlz/4vhc8n4XMX9el3IaTIby+mXiUSCaDTK9PQ0fX19qKqKpmmUlJTQ2tpKWVnZW4JwLctidHSUiYmJgmY+68FmNuxWmrCD7ANvuescj8eZnZ1lcDBbBHznO99hfn6e3bt3MzY2RkNDQ1Gu9Ze//GUefPBBRFGkurqa73znO9TX12/6uIvxtiDdQlivp64dkaNp2pIBisWRPUsgCFjNx7CajzEdTfPQ6Snmk71sKXNzuKUMn0umokQhGAwycGaCbaaG14pTKToI0YDlPEwmkeRndJCen2Iu8jyyISCnRTKeaRx6KVrGj6lLiKKGnmrACjyP0x3laO1Ryp3l7K3cy/ta3sdkJINpWbgc2RvD55QBEZdnDi1dhUBWC/YE+vArfnZU+JiMZnhtLEpGVXFrYeoqvezMqyC9Xu+CDoFCrVprIeKNIn+arLGxkcOHD19UQsvXfvPll7a2tpwfr21M4/F4FmzYFdMhbDXEYjG6urooLy8/b5ryWjbsCskTtmy2mk5sX+e6ujucGfoAACAASURBVDog+13w+Xx8/etfZ3R0lDvuuAPDMHjkkUc2/VnuvPNO/vIv/xKAe++9l7/4i78oersYvE1Id/ENuB5P3eUicvIhy4WzyBYjkdH5t5PjyKJARYmD/3xjmp+fnmJrmRO/GeWabV72t5SRHKvkWFUljwYDdMc8SKko9SUybdIcjwU9bBedNKCSESUsC9KqB8sASw9gZkQUyYMQc3H7wWo+03n7gnNwnR1msKfJRAFcssS1LYd5cvxxdM2H2zXPFY172V2xG1EQuGprKeXqLNFYnH27dq5YQS7XqmVvmBQiYptwFg8vrAWxWIzu7m5KSkrWtCy+UMh/ECzWR/MJIt8hzO4mKcZ1WQmGYeQyA3ft2rVgc+tCYCUntkQiwZkzZ6isrFxzdFI+BEFg586duN1uPve5z3HkyJGinXd+oZVIJM7bg/1tQbqLYUexr0S6hmEwNDTE1NRUwYicfNjDEQVhWblNr/mEiqqbVJS66J6Koeom6VQSnEnC7gBGoAmXc4IoBn7jWa5KJplNH6PJY1G/8wZcQ4O40mn8QMItEHMmIFyGoimoWhWICWQlhWWAoJfT7rlqyelUlCgc2hLg5EgYURCQJYHPXtXMa+PlOAhgiHNc01HKVU1HwIKR0ZFcv+3+3Ts39EUrtGFiO2FFo1Gi0egCacImm5UIR9O03DThW2maDLKdHN3d3Xg8nhXHivMdwvK7SewHlK0Tp9Pp3FCHTcYbTde1W/oaGhrYvn37W0LigHMyx9TUFB0dHbkH+1qikwoR8flKjfjSl77E9773PUpLS3niiSeKfnx4m5BuIXvH5Tx18/1zGxoauPzyy1fd9S5oohMaRH7hHyA6gVXZjvGO38fp8GOaoBsGE7MhkvE0Hk8Jzc21hBIawXiGWFUVL8Re5ZrQGDtMGDU8pOI+XOM+ws3voSQ6w8vWa7xoBBGtPj6atCgxSnmUCiRRICLVIDlk9tdtxe8o7J1woKmUrRUe0rqB3+XAo0j4nDKRN1R0o5z+UYlaa5rQ5DDV1dVr8klYL/KdsFYjYqfTuUCaCAaDjI2N0dLS8paaJjMMg4GBAUKhEB0dHRtqzl9uR9++LvbAQSqVWpCtZvcSL3ctMpkM3d3dAEWxqiwm4vE4XV1dlJWVcfjw4QX320Y37Kanpzek6a9mdnP33Xdz9913c8899/CNb3yDu+66a93vsRreFqS7GHalmw/bsLqvr29F/9xCWEK6mTjyU/dkW8V8NQhzfcjP/DWVl/8RHcmTPNtnIjgbQClhT1MZApBUDWr8Lp6dPcGULCBbkJIlrvr/2zvz8DjqM89/qg+11Dpasi3L1mHLsty6fFuYIwFCwHE4BhIzPAPMjFmOJcDjxFljjzkyXEkMIQHMLjzBJBCGENgBAgwbSFgIa05bli986bRk675a6kNSn1W1f4gqqnXYstRSt6X6PI//AEP3r1uqb731Ht/XtJcPg+fS0lBLXOZFOGZ+RZVHQAgl8G1PL7ekzaQjIwFPawUne3NZkZpJek4JHm+I9KSRL6xUqxkY+Hy9/hB/OdxOSoIZgxTkeGMz7e0mNl6+DGsEJ6NOx+mEuLOzk6NHj6ptWn19fXR2dk7II/iZoPzuHD9+fMJyyhaLhfT09CEjuEpE3NnZSX9/P0ajcch0XWtrK42NjerATqwgSRL19fU4HA6KiopG/bRyqjyxz+fjySefpLGxcUw3ltOZ3SjceOONXHnllbrongqt05gS6Sr09PRQU1OD1WodsiJnNAwWXcHTPDDS+3WHgpyUQbDlCKE/XM01coDV5hxcliK+zPtvtPqgxeljeXYKxRlWPmzyIxqMBI1G+swWEvDzA8NOZglJvBDKZZ/jI9Li0phtnk1GsJuv+upoF0Tmmc0ETT1UtnfwUd8xFmX5Ecy3AKevrrq8IUKiiMvhxOfzsSArA2dAGPXGiIlEeXRUvHdXr16N1WoNi/y0j+CDi3UTLcTa9rTJzinHxcUxc+bMsI4DZajD4/FQW1tLT08PRqORWbNmqd/ZeIc6IoHL5aKyspKMjAxKS0vHfR6DwcDBgwfZuHEjV199NfX19RF3i6upqWHRokUAvPvuuxQWFkb09RWmjOhqUSJdZYpKluVxFRQGF9Jkc+LASK8kEgiKuBztzOg4hAkJyRTHPEM9uFopLCzCWbwGwdtFYko8GA0sT1/OB6mz8TmaSQoG8AsCqYKROPulJGWnkBRKwmq2EgqFcBitZPhawJyMWQhyvvlLnNZE3DNz6JIN3Lerlue+8xzxppFvIpIk0dPRQktrK3lzZ5ExJ4N+v0i8WcJiiu6FqYxvt7W1DRmRHRwRAyPmQrVFqUgJsSRJnDhxgs7OTux2e8xsnTWbzdhsNrq7uwkGg5SWlmK1WtVe4sbGRnp7ewGG9BJPxkScUsRzu92nN4EaJX6/n8cff5ydO3fywgsvsHTpMD3wEeCee+6hqqoKg8HA/PnzJ6RzAUA4jRnw2J2CJ5lgMKg+gtTX19Pe3o4gCOOydNTy5ZdfcsEFFwz8gywT2vN7gofeQZJlBO8JkvodgIwBkBEwmOIJLfw+mC0IggGQEAuvQVrwHaqd1Xyx61Eur91FghjkSPIM3rd/h9VZ3+b12tdJMaXT1ZWF0yNT2F/NVXGHiBe8HDRK/Dk5hURTKgmGBEKE+Leif2Pp3KVDohtZlunq6uL48ePMnj0bj3kGO2sHenvNBoFrls0Z0XFsMlAKPhkZGcyfP3/MkZBWiN1u95Ci1FiEWOsENm/evKhHjVq6u7uprq5m7ty55OTkjHg2rSmN2+0OG+rQpiciueqmp6eHqqoqsrKyyM7OjsjN78CBA2zcuJF169axZcuWmPFCHgUjfvgpJbqBQID6+npaWlpITU1l6dKlEXv8VERXMb3pdjgomiGRZPbR+pc7yfZ6MMsS8tcDugIG5NkliHnfBVMccihAU9tedszJxmZM5K6uDpq6K+n0d2MUDOywFdIQLKQgrYCj7Z2IITPpSVaMUjJd3iPMmrmLk6ILg2whjZVIoSREYxc/X3ErSSFr2MhqXFwcDoeDhIQEFi1apKZT3L4g/YFvimvRoL+/n+rqaoxGY9jZIom2WKcIcVxcnCrCIwmx1gmsoKBgQs42VgKBANXV1QSDQQoLC8fkUqYd6lBSFMq2Ye3TwpkKWygUUl33lHau8eL3+3nsscf4/PPP2bFjB4sXLx73a04yIwrPlEkvtLS0cPz4cXJyciguLsbhcEQ03yfLMidOnKC5uTnM9KY/0Ee/0UTAYMYoBRG+vokF41MwmuLBNJADPOqqps1VQ1eCiK23hyPubpqNAhZLIj5fMmLrSnoTLPjjsrD6F3L+wiQykgb6BnfWJ9LkbQcc+PqyaAnOwBpnICfxuziC8zh38UC/rLKJwOFwYLVa6evr49ChQ2Fik5GcGJWClCiKalFloh/XhytKaYVY2x2g+CkoRbuRerWjheL/cfLkyXGPFmuHDbSvr4zfdnV1UV9frw51DDaIHw5lXH7+/PkR6zTZt28fP/3pT7nuuuv45JNPIhqNxwJT5tOkpKSoK3LcbndETW/a29vp6+sjFAoNWcMTb0qgYd65zKrdiRiQ+X+hlRyQC7AazFwpOSns7wLrLFq7jiKaLATjU0j29hNCQpSgV+rliLcIWexDMPqZmWiio8eAwyMwJ1mg1x+ipceA31RIvGAh2J+MJbmCOcmz+Ye886ho83DhwjS6O1ppaWlhwYIFZGRkhHkMD3bT0q5wOV0rUqS+v/r6erXyH43H9ZGEuKWlhZqaGoxGIwaDgZMnT9LT0zPuftlIoAwSnK4feDwIgqC6g2mHOrxeL263e8Shjvj4eE6ePIkkScOuGhoLPp+PRx99lF27dvHyyy9TUlIy7teMRaaM6Gq3yY52DfvpcDqdVFVVqb+UCxYsUIsR2jnz8y57mgPxj+DaX8duuYRMwUkwGORPbVn8aEaInGATAZOZ99IyCBqMHE9KZWl3M2myTL8cxCpJtJoN+KUAM6025qTIdPcFaXP7qO3ow2LxQpwTE8kIfTMwirMxYMDtE9l/wsGDzS2smJfGdd8qJT4u/MI0mUykpaWFRZZaW0NlnY3iL6v8iYTYKJs1EhISYmqaDAYe1xXPBKUYBairzYeLiJXIb6KFWFvE0w4STBaCIGC1WrFarUOGOpTvxeFwYDabSUxMpKGhYdw3qfLycjZt2sQ//dM/sXPnzikX3WqZMp9M+4MezRr2U6HkHUVRpKSkhKSkJPbu3au63WvtFoWgl6TmMi6aewHbTclkSB7ixABxcpCeYB+N7R6yF9s5r+soqc3VvJ2eTVV8Av+VWcCSrnossoWTVifO3lTiZJmTPT1k2uZw8aJZGARIspho7LWxzyEjCH7MJh8Bv5VEeSb/Z38DaQlG5i+YS22fyEdVDq5aMrzRjpbhbA21PaGK0fdo8qDDofUjGOsi0IlC6wSmdExoP5PFYsFisYSlGBQTdLfbTVtbW9jgQiRvUvDNjX727NlReyoYDmUirK2tDZPJxIUXXqjuI1RyxG1tbfT392M2m4cYxI/03Xi9XrZt20Z5eTmvvPIKRUVFk/zJJp8pI7paxhrpKj4MLpdriCOT0vtrMpm+WW8e7MPy100I7kaQJZL9+ThEKwmCDMhIskBy92FMh8qZbU4kSUiEZgNvzL2KOXNKeEV6EpPZjyfgwRT3KaHePNKs53HuvDTyZ1vJSk3AZjXx3uEQi9OWc7jrKEKcgwKbhWzSscyysip3JgZBID5O5kCjmysXZ4zp4h+uJ1SbB21paRnSK6sIsYJW0HJzc8P8CGIBt9tNVVUVqampZzSFN5wJulaItTepsQpxMBikpqYGn8/HkiVLJmwp4liQZZmWlhYaGhqG5LzHMtQRDAaZM2cOBw8eZPPmzdx44418/PHHUzq61TJlPqX2l/tML3RRFGloaFBzooMLAoo9XWNjI7NmzSIlJQWTyYTx0GsYWvYhW5KRrelcadzDC+JlNEmzCMpG0gwebKIDuT+AweCkIpjH//ZdwslQH5+2HEQUVmNI/ZRg3xKCrhXIoWT+r8tJ0N/JZ8cd/OOKTJZlp+APSew9sZxsIZecOA+XrijALSTypz1N6tqbgDjQdxtJkRt8QZ3KTyEuLg6n06k6WsXSBaRE3n19fRQVFUXEAOZUQqysBfJ6vWFpm+H2s2lz3rm5ucyZMyemblRer5eKigqsVuuof66nG+r4/e9/z1tvvUVPTw+XX345KSkpeL3emPLXmEimTMuYJElhKYWwvtoRUCrD9fX1zJ07l/nz54dFP1ojDr/fT3d3t3pRWfpbWXn4Qcx+JxhNA724UhBH0MxX0kL+M3TJgN24AOebj3O9dS83e+6gJZRE0CTiS+mlvz+NkNyPIZCBUZYIEYeEAVt8HN+1zyLOZOBnV9hxdHVRV1dHRkYG8+bNw2g0EhQlXi1vpq6rD6MgIMnwjyvnsjhzch/lFXNsr9eLzWbD6/USCATUNiTlTzT6K7VOYNESNG3U53a7w4Q4Pj6ejo4O4uPjsdvtMZXz1vrwFhQURKzbZNeuXWzZsoV//dd/5dZbb+Xo0aPs37+f9evXTzXRnfp9urIsEwgE1H/+8ssvOf/880e8yJQm85SUFPLz88N+4bVFMsWXd4h95BdPYjj8nxj6u5AEI4ghDHIQQZbYHlxHjZzFbMGJJAs0kc58oZ0PxFLi8OMxmXFjRULEjBtDaAYBLIgo+TsDZoNA/qwENq8wkJJkJT8/f0iFOCBKVLX10hcQyUqNV9ekTwbaabK8vLyw3Ki2+q38CYVCYUJ8um2x40VxAlNMxWOpqd7v91NbW0tXVxdWq1W1IdWmJqKxsVihr6+PiooKbDYbeXl5EZlk6+/v55FHHuHQoUM8//zz2O32CJw0ppn6fbqDGclTt7e3l+rqagRBYMmSJUPGFMOKZKfy9RT9GOJTID4Zk7sZEBFtiwjKAi3ts0nBiySYkI0mDCIclBaRL7RQw1z8AkiSCcEgkS730kY64W69EiHJQLOzH8OMQkoWzR32DHFGA0uyJr9IpUxsKcWewRflSNXv/v5+Nc93/PhxRFEkMTExTIjHm5ZQtks4nc6YK+LBgCdBVVUVM2fO5MILL1R/v7QRcUdHhxoRT6YQK0s+Ozs7KSwsjMh3J8uyGt3efPPNPPXUU1Ff0BltpqzoKh0MykXs9/vVivpwzfnaVAIwbHSrRcr/HsbjH4HRgpSWhxDyErroPqR532LB3/ezvy1Epusgks+DDMwUXFjlfhbEWdkvJCLIXoxmD4I4AylkBLS/iDImA6QmxtMnxc6PyOv1qjesM91NpvWWVfpBlbXdSjGqpqYmbP+YIsSjuUhlWaajo4O6ujpycnLIz8+PqdxoKBRSf/+GW1Y5Uh5UeVJQClITJcRut1s1F4+EQQ0MRMwPP/wwx44d44033iA/P3/crzkVmDLpBRgQVoXDhw+Tm5uL1WpVzcoXLlwYNjgAZy62Wgwnv8B06BWQRELF1yLlfw8EAY8vxPOfn6Dh8GfQ380/WL4ix9DF//KuQbTOxj+zgNSEfvq9IpVtIr2+IH5ManrBgIEki5GcmXH894tTuSgvl3hj9EZSFcP3rq6uiHlZjIQyqupyuVTPAFmWhwixVhQUJ7C4uDgWLVoUU7lR+GYD77x588jMzByXSCpCrETFSmeA9rtJTBz91KEyKdjT0xOxIqMsy3z++eds3bqV2267jTvvvHM6RrdTP6cLA49oyuc5duwYRqORrq4usrKyhhiXjEdsR4Mky/R/+j+xHnyRRAZuBifj8jmeuBzzxZtZmp3Cy7sbqWhxsr++kzjJi1uMo08yAwIJcX3Ep3/BzPRqUi02HjnvEbJTsiN2vtGgjR4VE5No9I1KkhRWjFJ8JhITEwkEAni9XgoLCyf0ZjAWfD6f6lpVUFAwYTcD7bDLYCFWouLhhNjpdFJZWUlmZiY5OTkR+f3v7e3lwQcfpLq6mueff56FCxeO+zXPUqaX6HZ1dXH48GFsNhtLliwJK6KMpkgWKQz1OzF/8kuw2MBgAl8P4qLvE7rgfxAIBPjzF0d5v7oXc7yV+m4foiyTkWzBaPLSb3sZmzUAsow74CbDmMFts28jKSkJm82mXkgTJYJKISohIWFIoTEW6OjooKamhsTERIxGI319fRgMhrCOiTOJ+CKJLMs0NTXR3NxMfn5+VLwcRhJiZZV5T08Pfr+f4uLiiPQEy7LMZ599xj333MPtt9/OHXfcETODHVFieohud3c3lZWVGI1GrFYriYmJZGVlqX8/uEg24RekLGPc9wKmY38GZKQ5y/FfdD8NbQ5aW1vJXbCAA13wcVUXnZ4AyQkmlmWlkDjjGG+e+D1ploG8syiL+EU/r1z2inohuVyuIT4KNptt3JNRioua2+3GbrePaSXNRKJEj4IgYLfbw/LKWp8Jt9s96T4TMDD6XFlZSWpqasQq/5EiGAyqq6osFovaf67NEY/lRuXxeHjggQeoq6vjd7/7Hbm5uRPzAc4upofoKuumU1NTaW5uJhgMkpubO+GphNMS6EcWA3S6/dTV14f12wJqSkQ50/7O/Wzbu41kczIGwYAn4CHPlsdjFzw25KW1xRYloomLi1Oj4cFTYyOhnTqaP38+c+fOjalClLZFbfC04KkYHPH19fWpY6qRHOFV9qc5nU4KCwtjruc0GAyGWUMqvxPa78fj8ag3qsHFuuGiVlmW+eSTT7j33nu58847uf3226d7dKtleoiu1si8vb0dt9tNXl5e9MT2a7TGLwsXLjytI5Msy/xH5X/w3on3MApGbBYbD61+iLmJw7eODUaZGlOKUX6/n4SEBDUaHjys4HK5qK6uxmazsWDBgpjqaYUBc+zq6mrS09PJzc0d94U9eGBhPD4TEL6BN1Lm3ZFEKeQNdqAbiVAoFFas0wpxcnKymjZ5+OGHaWho4Pnnn2f+/PmT9GnOGqaH6IZCITV90N3dTVVVFdnZ2dhstqjk95Q2Na/Xi91uP+Pop9PbSX+onznWOViMY7fOUxyiFBFWhhXi4+PVjo/CwsKYSyX4/X5qamrGZdx9Ju812Pj8VD4Tyv9TXV2NJEkxZ3oO32wIFgRh3IU8JXXT0tLC5s2bqaysJDk5mbVr13L55Zdz1VVXRfDkU4LpIbrBYJBQKKSmEpQLyOVyhbkfKdHeRF0k2kfhBQsWjMt4eiJQztfU1MSsWbOQZRmPx4MkSepjpc1mi9qCQ6UQ1dTUNKwT2GShWBkqfxSfCcW0xeFwsGjRorA9brGAdvw5khuC3W43P/vZz2hubmbHjh2kpaVx4MAB/H4/a9asich7DEdjYyPr16+nra0Ng8HA7bffzsaNGyfs/SLE9BDdLVu2kJSURGlpKatWrSI5OTnsYg0EAmq053K58Pv96miqIsTjmYhSWqzq6+tjcr8WDBQba2pqmDVrFrm5uUPWXGsfuz0ez6R3BCgTW2lpaTFXiNI+QRmNxgEPjK+3LGj7ZKPZ6eHz+aioqMBisbBo0aKIpIpkWebjjz/m/vvvZ+PGjdx8882T+nvd2tpKa2srK1euxOPxsGrVKt555x2Ki4sn7QxjYHqIblVVFbt376asrIz9+/cTCARYvHgxq1at4pxzzqGkpGRI+5jX6w177BZFcUzRntvtpqamZtR528lGmSYDsNvto35UVx4rle9Ia3iufWIYrxAHg0Fqa2vp7++nsLAwIltkI4kyIOJwOCgoKFBTMcP5TASDwSHjzROdJ9e2qdnt9oj1LLtcLu677z46Ojp47rnnyMnJicjrjodrrrmGDRs2TGh0HQGmh+gOxufzcfDgQXbv3k15eTlHjx7FarWyatUqSktLKS0tHbKJVpIkent7VZHxeDynbMtSzEt8Pt+Y8rYTjXaaLD8/f9RV/1Oh9ZJ1uVxq/lPbMTHam452B1gsWhvCN+ZIo3160fpMaG/mkfaZUFDW+iQlJZGfnx+RpwNZlvnwww954IEH2LRpE+vXr4+Jp7YTJ05w0UUXceTIkZjz1RjE9BTdwSiPh+Xl5aoQnzx5Ut3dpYhxWlpa2IWvtNVooz2LxYIkSfh8PvLy8mKuxUqWZTo7O6mrqzvtuu5IvNfgjgmtvaPNZhs22vN4PFRVVZGcnExeXl7MdU0EAgFqamoIBALjLuQpCyC1QjxWnwkFJTff3t4e0UKo0+nk3nvvpbu7m+eeey6s1z2a9Pb2cvHFF3P//fezbt26aB/ndOiiOxLKPqqysjLKysrYu3cvHo+HoqIiVYSXLVumFt0kSVJHY1NSUoiLi8Pj8RAIBEhMTMRms6kiE618ZF9fH1VVVVgslmEtISeDkaI9Zd+cx+NRV3bH2tOBthA12jarsTAWnwkFZQhjxowZLFiwICI3VFmW+eCDD3jooYfYvHkz//Iv/xIT0S0MBD5XXXUVa9euZdOmTdE+zmjQRfdMCAaDHD58WBXiQ4cOYTKZmD9/PhUVFdxxxx3ccMMNYZGPNpJxuVx4PB5kWSY5OVkV4okuQoVCIerq6nC5XDE5TSaKIo2NjTQ0NJCQkKD2T2tz6BM52jwa+vv7qaysJD4+PmKFqDNhOJ8J+OY7Sk5OprOzk+7u7ojesHp6erjnnntwu9389re/JTMzMyKvGwlkWeamm25ixowZbN++PdrHGS266I6HYDDILbfcwrFjx7jooos4ceIEtbW1zJ49Oyw/PDgiEkVxyNiuyWRSc582mw2LxTJuIdbmRSPhZDURKNF3fHx8mJeD9jtSRGayR3fhGy/Zjo6OqGzgPRXKd9Te3k5raysGgyGsh9hms404NXY6ZFnmr3/9Kw8//DBbt27lxhtvjJnoVuHzzz/nwgsvZMmSJerZtm3bxhVXXBHlk50SXXTHy65duzjvvPPCtiO0tLSo0fCePXtU60OlZW3lypVDBEMpQimPlD6fj4SEhLAi1JlEV8qyxZSUlJjMiyrWgd3d3djt9lGJ2XA5dGViTPmeInGzUlA28EZq4i3SiKLI8ePHcbvdFBUVkZiYGBGfie7ubrZu3YrX6+XZZ59VfY51IoIuupOBKIpUVFRQVlZGeXk5+/fvRxRFli5dqkbDRUVFYVVr7bSYIjJK7lMRmOHyeoFAgNraWrxeLwUFBRHxQY00yoaIzMzMcdtCaifGlB7r+Pj4sJvVmfbHxnqbGnzTOTGaEePhnMW0izG17X3vvfceP//5z7nvvvu4/vrrY+7JaAqgi240UHo49+3bx549eygrK6OyshKbzab2DpeWlpKVlTWkbU0psLhcLtU/VhFgr9dLR0cHCxcujLlpN/imJ9hgMGC32yekkKfcrLRPDdr+WKWYOVxbltYnOBbNfWAgP19dXY3f76eoqGjM05OD16HfdtttwMA6qy1btvC9732PefPmRfLoOgPoohsrKH6/2rREc3Mzubm5ajS8cuVKbDZbmBCEQiGam5s5efIkJpMJQRBUNzHtI3c0UfKi7e3tEW3QHy0jtWVpHbNMJhM1NTWYTKaY28Cr0NnZSW1tbUT7lmVZ5t1332Xbtm1s2LCBnJwc9u3bRzAY5JFHHonAqUfmlltu4S9/+QuzZ8/myJEjE/peMYQuurGMJEnU1taqIrxv3z76+/spKSmhtLSU7Oxs3nnnHe66666wflG/3x821qz0xmrb1iLVgH86lPHi2bNnDxk4iSbKsIvT6aS1tZXe3l4SEhJIS0sLM4OPhUg3EAhQVVWFLMsUFBRE7Cba1dXF3XffjSAIPPPMM5PuFfHpp5+SlJTE+vXrddFFF92YJRAIUFZWxq9+9Sv27NlDQUEBoVCIFStWqBFxXl7ekBVE/f39YWPNSt+ntm0tkoKoOG2JokhBQcGEOoGNFWXpotLTqhj8aM2QBuc+I+GxO1pkWaa9vZ36+no1ZRSp133nnXd47LHH+Pd//3euu+66qN1cTpw4wVVXXaWLLlN4vcDs6AAADDBJREFUG/DZjlKtv+SSS3jrrbcwm804nU7Ky8spKyvjnXfeUXeXrVy5Up2omzVrFomJiWqfpdL36XK5OHnyZFhLliLEY/FOkGWZxsZGWlpaVCewWEO7gbe4uDis2JiWlha2EVoxg3e5XLS1teH1etW2rIlM3/h8PiorKzGbzZSWlkas+6Sjo4O7774bs9nMxx9/HJM/n+mKHumexUiSRGNjI7t372bPnj2Ul5fjdDopKChQC3XLli0bErVpBcbtduP1elXLQkWIT3XxK05gSuQYS05gCkpeNCcnh6ysrDFFeFprR236RhsRj1UklZbDxsbGM9qEMZrXfeutt3j88cd56KGHWLduXUykTvRIV/MXuuhOLUKhEEePHlW9JQ4ePIggCCxfvlwd5CgoKAgTSsU7Qdu2FgqF1LFmpWtCFEXV3KegoCAmW6z8fj+VlZWqcXcko9ORXOkGf0+nuwl5vV6OHTtGYmIi+fn5Ecu7t7e3c/fdd5OQkMDTTz8dlYWYI6GLruYvdNGd2siyTG9vL/v27VP7h6urq5k5cyarVq1i1apVrF69ekiVXOkEUITY4XAQCARITU1lzpw5UdvGMRJa4/NFixZNmuAo7X1KNKz4Jww32qxNyRQWFkZs6k2SJP785z/zm9/8hkceeYQf/OAHMfNzUdBFV/MXuuhOPxRDlz179qgRcVtbG/n5+WpaYsWKFSQlJfHVV18RCASw2Wzk5uaqJjaTvY3jVPT29lJRUYHNZmPhwoVRT3cMN9oMA1F4SkoKCxcuHGKwP1ba2trYtGkTycnJbN++PWJpikhyww03sHPnTrq6usjIyODhhx/m1ltvjfaxJhpddHVOjSiKVFdXh+WH29raSExM5Pbbb+eCCy6guLh4SA5zordxnO7MdXV19PT0xKRbGXzjYtfZ2UlmZiaiKKo3LO0yzDP14ZAkiddff52nnnqKX/ziF1x99dUxF91Oc3TR1Rk9PT09XHLJJdx1110UFxdTXl6umsAnJSWFmfwMNvWO5DaOU+FwOKipqSEzM5OcnJyYFBylVS09PX3Y3mXtDUvx4dAWNEcabW5ra2Pjxo3MmDGDp556atKHUHRGhS66Z8Ibb7zBQw89REVFBXv27KG0tDTaR5p0+vr6hhTKZFnG4XCEmcA3NDQwb9481eRn1apVQ0zgz3Qbx6kIBAJUV1cTCoUoLCyMuQ288E0E7nQ6KS4uHnXBUTvarDw5KKPNTU1Naj/v888/z7Zt27jyyitj8majA+iie2ZUVFRgMBj40Y9+xG9+85tpKbqjRZIk6uvrw0zge3t7KS4uViPipUuXDhHHUCgU1rambOPQ2l5qozylxaqhoSGiAwSRpqenh6qqqohF4EpB89133+XFF1+kvr6ejIwMVqxYwebNmykpKYnQyUfmb3/7Gxs3bkQURW677TbuueeeCX/PKYAuumPhO9/5ji66YyAQCISZwB8+fBiz2cyKFSvUQl1+fv6Qx+3BBjbKNo6EhAQcDgcpKSnY7fZJG20+E0KhkOpYVlRUFLHJPEmSePXVV3nmmWd49NFHueKKKwgGgxw5coSsrCwyMjIi8j4jIYoidrudDz/8UF1r9dprr8X6Jt5YQBfdsaCLbmSQZRm3283evXtVf4njx4+TkZERlh8e7JimFPe6urpISUnB7/dP+jaO0eBwOKiuro64gXxLSws/+clPmDt3Lk888URUjNV37drFQw89xAcffADAo48+CsC999476Wc5y9DHgAdz2WWX0dbWNuTf//KXv+Saa66JwommLoIgYLPZuPTSS7n00kuBASFubm6mrKyM3bt38+yzz+JwOLDb7eo4bHl5OQ888ADf+ta31KhY245VX1+vbuPQTtNF0uD8VASDQaqrqwkGg6xYsSJi+WVJknjllVf47W9/y69+9SvWrl0btRtLc3Nz2Nr17OxsysrKonKWqcK0Fd2PPvoo2keY1giCQHZ2NtnZ2Vx77bXAgKDu3r2be++9l6amJjIzM7npppvCTOCVoQJt1KfdxtHS0qJu49B2AUR6o0Z7ezt1dXXk5eVF1NO4qamJn/zkJ+Tk5PDpp59Gfc/dcE/C0X6yONuZtqIbK+hFim8wGo2Iosidd97J9ddfDwwsilRM4H/9619TVVVFWlqa2ilxzjnnkJWVxaxZs9QpNO02jq6uLurq6tRtHFqD87G0rSljxkajkVWrVkXMj1eSJF5++WV27NjBr3/9a9asWRMT4padnU1jY6P6z8rNUGfs6DndYXj77bf58Y9/TGdnJ6mpqSxfvlzNaUUSvUhx5siyTGdnZ5gJfEtLCwsWLAgzgU9JSRnStjbSNg7tcseRhE67/DM/Pz+irl2NjY38+Mc/Ji8vj8cff5yUlJSIvfZ4CYVC2O12/v73v5OVlcU555zDq6++OildE2c5eiEtFtGLFJFBMYFXpun27duHz+dTTeBLS0tZvHjxkKhUWe6oCLEyJTZ4W7PX66WiooKEhAQWLVoUse4JSZJ46aWX+N3vfscTTzzBpZdeGhPR7WDef/99fvrTnyKKIrfccgv3339/tI90NqAX0mIRvUgRGZRdbHa7nfXr1wMDaYCDBw9SVlbGjh07OHLkCPHx8axcuVIV4gULFgzx1VUWYLpcLhobG+nr60MURTIyMiLantXQ0MCGDRuw2+188cUXMblYVOGKK66I9XXnZxW66EYRvUgxcVgsFs4991zOPfdcYOC7djqd6oLQt956i/r6erKyslQRXrVqFTNnziQ9PR1RFHE6nWRkZJCZmUlvby8dHR3U1taOaxuHJEm88MIL/OEPf+CJJ57gu9/9rv4zn2boohtF9CLF5CEIAmlpaaxdu5a1a9cCAwLY0NDA7t27+eyzz3jyySdxOp1YrVZcLhfbt2+npKSEhIQEkpOTmTt3rvr/KW1rZ7KN48SJE2zYsIHi4mI+//zzmI5udSYOPacbRfQiRWzR3t7OD3/4Q5YuXcrixYs5cOAABw8exGAwqNN0paWl2O32IfaRyjYOJTWhbOOoqalBEASam5t5/fXX2b59OxdffLEe3U599EJarBKtIsU0XYt9SpTNGAUFBeq/05rAKyY/1dXVpKenqyJ8zjnnkJGRMcQE3u/38+abb/LSSy/R1NREWloaixcvZuvWrSxdunRSP5tu4jTp6KKrE840XYsdEZT2Ma0JfEdHh2oCX1payrJly3jttdf44x//yNNPP82FF16IJEkcO3aMjIyMSTfs0U2cJh1ddHWGMg1XqEwYoihSVVWl9g//7W9/Y/Xq1bz00ktYrdZoH09F9xOZNPSWMR2dicRoNFJcXExxcTE333wzsizreVudYdFFV0dnAoiG4OomTmcHuujq6EwRdBOns4PxLarS0TlDGhsbueSSSygqKqKkpISnn3462kfS0ZlUdNGdptxwww2cf/75VFVVkZ2dzQsvvDAp72symXjiiSeoqKhQfXSPHTs2Ke89nXn77bfJzs5m165dXHnlleqAiM7ko3cv6ESVa665hg0bNrBmzZpoH0VHJ5KMmNTXI12dqHHixAkOHDig+iPo6EwHdNHViQq9vb1ce+21bN++Pab8Y3V0JhpddHUmnWAwyLXXXss///M/s27dumgfR0dnUtFFV2dSkWWZW2+9laKiIjZt2hTt48Q8W7ZsobCwkKVLl/LDH/4Qp9MZ7SPpjBNddHUmlS+++II//vGPfPzxxyxfvpzly5fz/vvvT9r7+3w+Vq9ezbJlyygpKeHBBx+ctPceC2vWrOHIkSMcOnQIu92ubhfROXvRuxd0phWyLNPX10dSUhLBYJBvf/vbPP3005x33nnRPtppefvtt3nzzTf505/+FO2j6JwevXtBRwcGxnMV8/BgMEgwGDxrPBJefPFFLr/88mgfQ2ecnC7S1dGZcgiCYAT2AfnAs7Isb43yeT4C5gzzV/fLsvxfX/839wOlwDpZv2jPanTR1Zm2CIKQCrwN/FiW5Zj1txQE4SbgDuBSWZb7o30enfGhpxd0pi2yLDuBncD3o3yUEREE4fvAVuBqXXCnBrro6kwrBEFI/zrCRRCEBOAyoDK6pzolzwDJwIeCIBwUBOG5aB9IZ3zo1o460425wH98ndc1AK/LsvyXKJ9pRGRZzo/2GXQii57T1dHR0ZlE9PSCjo6OziTy/wG5au6SKRySuQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "reduced1 = details1['reduced_coordinates'][0]\n", "\n", "rdfig1 = plt.figure()\n", "rdax1 = rdfig1.add_subplot(111, projection='3d')\n", "for data, label in zip_data_with_labels(reduced1):\n", " rdax1.scatter(*data, label=label)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculating dimension reduction similarity with multiple methods" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You may want to try different dimension reduction methods, or use different parameters within the methods. `encore.dres` allows you to pass a list of `dimensionality_reduction_method`s to be applied.\n", "\n", "
\n", " \n", "**Note**\n", "\n", "To use the other ENCORE methods available, you need to install [scikit-learn](https://scikit-learn.org/stable/).\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Trying out different dimension reduction parameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Principal component analysis uses singular value decomposition to project data onto a lower dimensional space. [(See the scikit-learn user guide for more information.)](https://scikit-learn.org/stable/modules/decomposition.html#pca)\n", "\n", "The method provided by MDAnalysis.encore accepts any of the keyword arguments of [sklearn.decomposition.PCA](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html) *except* `n_components`. Instead, use `dimension` to specify how many components to keep." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:46:15.363617Z", "start_time": "2020-09-25T05:46:15.358770Z" } }, "outputs": [], "source": [ "pc1 = drm.PrincipalComponentAnalysis(dimension=1,\n", " svd_solver='auto')\n", "pc2 = drm.PrincipalComponentAnalysis(dimension=2,\n", " svd_solver='auto')\n", "pc3 = drm.PrincipalComponentAnalysis(dimension=3,\n", " svd_solver='auto')\n", "pc4 = drm.PrincipalComponentAnalysis(dimension=4,\n", " svd_solver='auto')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When we pass a list of clustering methods to `encore.dres`, the results get saved in `dres2` and `details2` in order." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:46:19.006309Z", "start_time": "2020-09-25T05:46:15.366299Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4 4\n" ] } ], "source": [ "dres2, details2 = encore.dres([u1, u2, u3],\n", " select='name CA',\n", " dimensionality_reduction_method=[pc1, pc2, pc3, pc4],\n", " ncores=4)\n", "print(len(dres2), len(details2['reduced_coordinates']))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:46:19.278170Z", "start_time": "2020-09-25T05:46:19.008083Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "titles = ['Dim = {}'.format(n) for n in range(1, 5)]\n", "fig2, axes = plt.subplots(1, 4, sharey=True, figsize=(15, 3))\n", "for i, (data, title) in enumerate(zip(dres2, titles)):\n", " imi = axes[i].imshow(data, vmax=np.log(2), vmin=0)\n", " axes[i].set_xticks(np.arange(3))\n", " axes[i].set_xticklabels(labels)\n", " axes[i].set_title(title)\n", "plt.yticks(np.arange(3), labels)\n", "cbar2 = fig2.colorbar(imi, ax=axes.ravel().tolist())\n", "cbar2.set_label('Jensen-Shannon divergence')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, adding more dimensions to the principal component analysis has little difference in how similar each ensemble is over its resulting probability distribution (i.e. not similar at all!)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:46:19.283763Z", "start_time": "2020-09-25T05:46:19.280140Z" } }, "outputs": [], "source": [ "rd_p1, rd_p2, rd_p3, _ = details2['reduced_coordinates']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we plot how the trajectories vary on one dimension with a violin plot, we can see that DCD is indeed very distant from DCD2 and NAMD on the first principal component." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:46:21.066390Z", "start_time": "2020-09-25T05:46:20.954724Z" } }, "outputs": [ { "data": { "text/plain": [ "[Text(0, 0, 'DCD'), Text(0, 0, 'DCD2'), Text(0, 0, 'NAMD')]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rd_p1_fig, rd_p1_ax = plt.subplots(figsize=(4, 8))\n", "split_data = [x[0].reshape((-1,)) for x in zip_data_with_labels(rd_p1)]\n", "rd_p1_ax.violinplot(split_data, showextrema=False)\n", "rd_p1_ax.set_xticks(np.arange(1, 4))\n", "rd_p1_ax.set_xticklabels(labels)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Expanding out to the second principal component shows that DCD2 and NAMD mainly vary on the second axis." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:46:22.711419Z", "start_time": "2020-09-25T05:46:22.570112Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rd_p2_fig, rd_p2_ax = plt.subplots()\n", "for data, label in zip_data_with_labels(rd_p2):\n", " rd_p2_ax.scatter(*data, label=label)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting over the top three principal components gives quite a different result to the reduced coordinates given by stochastic proximity embedding." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:46:24.217241Z", "start_time": "2020-09-25T05:46:24.022300Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rd_p3_fig = plt.figure(figsize=(8, 6))\n", "rd_p3_ax = rd_p3_fig.add_subplot(111, projection='3d')\n", "for data, label in zip_data_with_labels(rd_p3):\n", " rd_p3_ax.scatter(*data, label=label)\n", "rd_p3_ax.set_xlabel('PC 1')\n", "rd_p3_ax.set_ylabel('PC 2')\n", "rd_p3_ax.set_zlabel('PC 3')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimating the error in a dimension reduction ensemble similarity analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`encore.dres` also allows for error estimation using a bootstrapping method. This returns the average Jensen-Shannon divergence, and standard deviation over the samples. " ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:47:03.114880Z", "start_time": "2020-09-25T05:46:27.863556Z" } }, "outputs": [], "source": [ "avgs, stds = encore.dres([u1, u2, u3],\n", " select='name CA',\n", " dimensionality_reduction_method=dim_red_method,\n", " estimate_error=True,\n", " ncores=4)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:47:03.121704Z", "start_time": "2020-09-25T05:47:03.117153Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[0. , 0.23991747, 0.59734865],\n", " [0.23991747, 0. , 0.59311978],\n", " [0.59734865, 0.59311978, 0. ]])" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "avgs" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "ExecuteTime": { "end_time": "2020-09-25T05:47:03.128656Z", "start_time": "2020-09-25T05:47:03.123726Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[0. , 0.06776036, 0.04572998],\n", " [0.06776036, 0. , 0.04178307],\n", " [0.04572998, 0.04178307, 0. ]])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stds" ] }, { "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] 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", "[3] 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", "[4] Matteo Tiberti, Elena Papaleo, Tone Bengtsen, Wouter Boomsma, and Kresten Lindorff-Larsen.\n", "ENCORE: Software for Quantitative Ensemble Comparison.\n", "PLOS Computational Biology, 11(10):e1004415, October 2015.\n", "00031.\n", "URL: https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004415, doi:10.1371/journal.pcbi.1004415." ] } ], "metadata": { "kernelspec": { "display_name": "Python (mda-user-guide)", "language": "python", "name": "mda-user-guide" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.3" }, "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 } }, "nbformat": 4, "nbformat_minor": 2 }