{ "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:** May 18, 2021 with MDAnalysis 1.1.1\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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:06.881320Z", "iopub.status.busy": "2021-05-19T06:00:06.880313Z", "iopub.status.idle": "2021-05-19T06:00:08.072432Z", "shell.execute_reply": "2021-05-19T06:00:08.072918Z" } }, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:08.077053Z", "iopub.status.busy": "2021-05-19T06:00:08.076510Z", "iopub.status.idle": "2021-05-19T06:00:08.484693Z", "shell.execute_reply": "2021-05-19T06:00:08.485506Z" } }, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:08.491135Z", "iopub.status.busy": "2021-05-19T06:00:08.490196Z", "iopub.status.idle": "2021-05-19T06:00:08.493573Z", "shell.execute_reply": "2021-05-19T06:00:08.493950Z" } }, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:08.498333Z", "iopub.status.busy": "2021-05-19T06:00:08.497787Z", "iopub.status.idle": "2021-05-19T06:00:24.011315Z", "shell.execute_reply": "2021-05-19T06:00:24.011935Z" } }, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:24.017757Z", "iopub.status.busy": "2021-05-19T06:00:24.016938Z", "iopub.status.idle": "2021-05-19T06:00:24.019497Z", "shell.execute_reply": "2021-05-19T06:00:24.019879Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[0. , 0.68814591, 0.67615372],\n", " [0.68814591, 0. , 0.66800132],\n", " [0.67615372, 0.66800132, 0. ]])" ] }, "execution_count": 1, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:24.023682Z", "iopub.status.busy": "2021-05-19T06:00:24.023139Z", "iopub.status.idle": "2021-05-19T06:00:24.025461Z", "shell.execute_reply": "2021-05-19T06:00:24.025824Z" }, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "(3, 300)" ] }, "execution_count": 1, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:24.054640Z", "iopub.status.busy": "2021-05-19T06:00:24.053951Z", "iopub.status.idle": "2021-05-19T06:00:24.151384Z", "shell.execute_reply": "2021-05-19T06:00:24.152022Z" } }, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:24.156522Z", "iopub.status.busy": "2021-05-19T06:00:24.155878Z", "iopub.status.idle": "2021-05-19T06:00:24.157706Z", "shell.execute_reply": "2021-05-19T06:00:24.158114Z" } }, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:24.178746Z", "iopub.status.busy": "2021-05-19T06:00:24.175595Z", "iopub.status.idle": "2021-05-19T06:00:24.275066Z", "shell.execute_reply": "2021-05-19T06:00:24.275432Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:24.279049Z", "iopub.status.busy": "2021-05-19T06:00:24.278415Z", "iopub.status.idle": "2021-05-19T06:00:24.280192Z", "shell.execute_reply": "2021-05-19T06:00:24.280691Z" } }, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:24.284097Z", "iopub.status.busy": "2021-05-19T06:00:24.283537Z", "iopub.status.idle": "2021-05-19T06:00:38.823133Z", "shell.execute_reply": "2021-05-19T06:00:38.823635Z" } }, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:38.856904Z", "iopub.status.busy": "2021-05-19T06:00:38.856153Z", "iopub.status.idle": "2021-05-19T06:00:38.942546Z", "shell.execute_reply": "2021-05-19T06:00:38.943132Z" }, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:38.970010Z", "iopub.status.busy": "2021-05-19T06:00:38.963707Z", "iopub.status.idle": "2021-05-19T06:00:39.078026Z", "shell.execute_reply": "2021-05-19T06:00:39.078392Z" }, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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0NzczMjLCokWLWLJkCbIs09TUdMSwuGyi6zqtra2JerozSSGeDVb8aFFRUcqCoWVlBYNBAoEAfX194/yPyWJ8tC/GuSy6pmnO6jdOLhaUjPU0MzAwQDAYpKurK+FamsjPn+4YTjXxwzJqJorqORaYk6LrcDj4zW9+wze+8Y2Uu63F/v37MU2TF198kWAwmHLhLlmyhMcff5wrr7wS0zR5/vnnmT9/fuL1ycpGTofJEhoCgQDNzc0Eg0EWL17MihUrxnUqeD9EV9M0Wltb6e3tTdRreOONN94XH2u6C2+ikozJxcqtlfmxbXwsMc4mc1l0DcPIivvGeppxu90UFhbS0NAAjPfzT1SfIjkC5khiDPDHP/6RXbt28e1vfzvj3yVTHBXRHYoM0RXootpTTYmz5MgfOAKqqnL99dfzwx/+kDvvvHPc67/61a+46qqr2L9/P7///e+5/PLLE69dfvnlPPzww1x55ZX85S9/4ZRTTuGpp55Ku5+xZSOnckFNltCQnD1WV1dHaWlp2jEVRTmqSQmxWCxRr2Em3X7fb5KLlVdUVCS2W2FSgUAgEbMaCoWIxWLs27cvIcRWNtdsBfNoRC9ki6mEo82Gse6Lifz8wIQRMOnqU4wtFuT1esd1nT7WyLroPtn0JLe9ehuqrKKbOnecfAfn1p0763FvuOEGjjvuOG699dZxrz388MM888wzvPvuu9x9990potvQ0MDjjz/O8PAwDz74IFdeeeWEogupZSMrKysnfJ/l07JOLssHBfEQsKamJiRJSps9NhZZlseF3mQDq7X6wMAAixYtOqbENlMLgWPDpMLhMAcPHmTBggUEAoGU1u9Wam2yGKerADYRc9lfPFWf7tEYfyr1KdIVC3r55ZdpbGxkwYIFGTlekUiELVu2EI1G0XWdiy++eNpPvOnIqugORYa47dXbiBgRGH1avu3V29hUvWnWFm9BQQFXX301P/rRj1L8SG+++Sbl5eUsWrSImpoarrvuOoaHh1N+wAsvvJCHHnqIN954I20t3bFMdvEnd2hobW3FZrNRU1ODEIL+/n6amppwOp0sW7ZsXMD6RGTbvRCJRGhubmZ4eJja2loaGhqOGbE9GkiSlDaBwEqtDQQCDA4O0tbWRiwWm9DCGks2hdFyUWWL2fp0j0QmRH2i+hSapiUiKPbt28fLL7/Mgw8+iMfj4cknn5zydTcWh8PBc889h8fjQdM0Tj31VM455xw2bdo0q++RVdHtCnShympCcAFUWaUr0JURN8OXv/xlNmzYwGc+85nEtgcffJADBw5QW1sLgM/n47HHHuNzn/tc4j2XXXYZGzZs4Jprrjmi2CSXjUzGikawsnokSUJVVQzDoLu7m5aWFvLz81m9evW0fYlWp4dMkCwEkUiEpqYmRkZGWLx4McuXL5+zPsiZMpkwTpRaa13UgUBgnIWVbBXrup5VSzfbj//ZTOO2fLXZwGazUVhYyN/8zd/Q3NzMxz/+cc466yz8fv+4ZJDpIElS4vOapqFpWkZ+36yKbrWnGt1MjcPTTZ1qT3VGxi8pKeGSSy7h3nvv5brrrsM0TR555BF2796dWBx7/vnn+da3vpUiugsXLuTOO+9MW+4xmbFlI+Gw2FpY/lrTNPF6vfT391NVVTWt7LGxZMqna8XZRqNRmpub8fl8aRfujkWOpTRg66Ie6ysc63scGRkhFovh9/sznn13tH2u2Rh/ol58mcTn8yUs4ZlauMkYhsHGjRs5dOgQN9xwQ6Jc7GzIquiWOEu44+Q7xvl0M2HlWnzlK19JNJp88cUXmT9/fko0wpYtW9i3bx/d3d0pn/v85z+fdryJykaOFVsLK0urs7MTt9tNVVUVy5cvn9V3ypR7QQjB3r17CYfD1NXVsXLlymNebOcSY32P/f39+P3+RLfpybLvrL+pCl22RXeui7qFz+fL6EKaoijs3LmTkZERLrjgAvbu3ZvI2pspWV9IO7fuXDZVb8po9EIgEEj8u7KyklAolPj/119/PeW9iqIkBPf+++9PO15LS0vi38liZ4lsOsG1fLmvv/468+fP56STTkpYurNltim8gUCApqYmQqEQixYtoqqqak6KbbZKO2YLywVgt9spKSmZNPuus7MzkTwwNpPL7XaPE8CjIboDIYNtPX247Qqb64qxKUfenzl6POUjnF9HS3S9Xu8RF6pnQlFREaeffjpPP/30sS+6ELd4M2ndZptksU33mrWaCaQkDmTKQp3pOH6/n6amJqLRKPX19ei6TlFR0ZwU3LlWwwAmF8bJsu8mavueXHAm2wud7/ZH+N7r/ZgAAurL8/ifTx+HXU3db9tQmOGwxoIiJ/e/3sHju3sBuGDtPL50ei2KnHps5b59OF78FisHW6F6A+ZH70DkZU8LvF7vuIW2mdLf359YvAuHwzz77LN8/etfn/W4czI5IltMJrZWPQBd13E4HDidzkR+uIWqquNyyWfCdEXX5/PR2NiIruvU19cnLKz29vaM+IbnctD/0WQmxyk5k2tsWq2V8BEMBhkZGcHv9/Pmm29mJfvunrd9RDSBTY2XEj3YF+SJPb1ctL4qMZ8fv9DCb3f2oMoSYc0AJFz2uCj/bncP8wodXLbx8HqNFBrE+fRNYGgYkkpez3bMZ24l8on/gSydT4ZhZGzBrru7m2uuuSZR5P2SSy7hYx/72KzHnZHoftAuwiOJbTQaxTRN7HZ7YnEs3XszZelO1b3g9XppbGzENE3q6+vTdo+Y7eN0cmuXo0k2O0dki0wep7HZd16vl56eHhoaGlJSocfWxXW73SiOPPI9bgo9eQz4Qoz0d1JZWkJB8cSNBEaiZsJKlSSJmG7SHzicbruzw8dvd/VgUyRkSSKkmRimwK7aUSWQTYPXm4dTRFfu3x9v0WX3IPQQwulGHjgAsQA4Zr/INZZM/7bHHXccO3bsyOiYMAPRdTqdDA4OTphNNZewfiQrFjP5+1jl6IQQOByOlNVnIQRDQ0M4HI6U8Y6WeyG5VU99ff2Ej1OZiIKYivgFAgE6OztTHoeP5fKMczGBwXJdJGffjX192Bfgm08e4s32dkCwLm+Q6yP3UoYXr2TSsfwyaj/6OR5/Z4hXm4apyHdw/SkLqSxwsLRYZe+ggWGaRHUTIeBQf5CwZuCyKXR5o0gi7ruNp94KTAEbwq/wFeURXFKUpp5VtHTdRe28MuSmPzP83muUhv3ISh4IAcIASQZ1ZlE9R8I6T491XZq26NbU1NDR0ZGRBaP3k2QhiUajicwjq14CkKhmlA6Hw8G8efNStmXKvTCRhTo0NERjYyOqqk7aqid5nNneBCyrO52IBgIBGhsbiUajVFVVEY1GUxaIZlMR7Fi/cNKRzVjaIyVHyLLMz7cPsKMrTIUaYL7RzXXh31LOCEPkowiD4v0Pce9gCb/sXYApQELipff6+cnF9Zy3WCYsOdjTFUAAEvDsgQEaB0L89KQBPr79Lk41htlpruBfxDUYwsFyqY2/V35FBDtDwkNddB87HrqV0sVliLbXieoaUfwY4TB2mw3JtKFt/Gy8SW0WiEQix2QX77FMW3RtNhuLFy/OxlyyztgODVaM7dtvv01+fj5dXV04nU7q6upmFOOXjUdiy6pubGzEbrezfPnyKc8tW90jgsEgjY2NRCKRhA95bNryZBXBkouWT1b34MPsXkg3tizLxHSTpgM7mP/eA5QqIcy6reirLwVJZnu7l6WihX+QfoYsGSyV2ugTRQyJfAwUBIK+vl7stsUJizUYM7jl8SY6fDFMDpdTFIAhgIH3kJ75AZE8Fw53IeuD+7hZ/Jxbpes5xd2BqpnEhA0ZCEseNog9+A85GBIeiqUAQclBASGimozLXYBt36OI/Cr05Z/M+DEaGRk5pquLWXwoFtIm6tAghKC7u5vh4WFkWWbNmjWzulNm8oJLTiN2uVysXLly2tk1me6TFgqFOHToEOFwmPr6+oSLKZ2QTVQRLLlx4ti6B5YIezye2S8AGjHUA4+j9OxC5JWjrb4EkV+VmFs2mI7oSv5ubLv+FynUh1F5HOG6c3B2vooUHsasWI1ZvSFlsck0TQKa4O/u/RPfCHwHHzo+xUH94EEkPYK2/jNUFzr59MCDCCSGyScgnFRIIwxRQEjEXWH90mG/vyRJaCa0+w2EkECKi20yq6UWEAbdIagpEOQVFrE1cohSm42wUoDQZRACWRJUiAEcIkqpBPOkIZzEMAAnOrpQeDeYR6lLpuyNu9EX/RW4MhvalcnIhWzygRbdiTo0mKZJR0dHogFkRUUFNTU1x8SjiSW2oVCInp6eGaURW2TK0g2FQhw8eJBQKJQitmPnPRXBmahxoq7riYSC3t5eBgcHGRoaSilAM512PradD6A0P4fIK0H2d2MfOkT0jDuJPzhPgB5BPfQ08lAjZkEN+tKPgX3qx37Kohv14/jLP0HMT0xx0/LCL9GfuRef5KE4P5/KvKdwnXgtYulfJz5imiYP7vEx378LpxRlQBQiNDjoN1mw93ew/jPcvHURNHvpNgsxBRxiPmukZorw45A0trm3Ut9wGnv39KGbcb8tkoRpCmTJuhmlyq4XNwIJWQLFiOIID2KXFC70vMNvRpZziqhnJY0USUFcRGgRlSyROnGiIQDLkeAiysJYI3LMJCSpRLoP4KzbPOVjOxXmQoUx+ACK7mQdGnRdT2SPVVZWJnqPHTx4MCO+2NnOu6+vj6amJvLz83G5XKxZs2ZWY85WdEOhEH6/nwMHDtDQ0EBZWVnWrERVVVOKmciyTGlpKW63OyHGye18XC5XihinhE2ZBkrri4jCGpBkhN2D5O9CHjwI+UvTT0AIbG/fi9K9E+EoJNK5j307d/Bs5Wc4fVklGxYe2YKaqujKQwch6gVPFdubhxExlTX08JR+Ii3DMh6/wYJn76O+/izU0QQF0zTp9OnUCgUhgSnia1ORmMa+vij+lmFOqi1GbliP9t4ueinAQKFFzOPf9QuRK1fz7avPQJUlqgqdvNI0TJnbRo8vyrZWL4YAmyKQgeQz5iVzDbtFHSeKd3GHfUiA6SzkVuMerjjvXxko/C8O7HmO+r0/QhcSZdIQBhIyInF7E4CdeIiZgYxNaHT96V+o/vxv4wtrGWJkZCRn6R5NJuvQEIvFaGtro6enJ5E9lhyNkKkFsOS5TKccYE9PDy0tLRQWFrJu3TpcLhevvvrqrH2EMxXdcDhMY2MjgUAAp9PJypUrp+RHzoZP06q5OjahIBwOp1jG4XA40dfL486j1jCRtRiKLf5YLQkBsjrxHCMjKL17EAUL8EZ1Xu2LUGq20Ks3c1dHiJu31nJC7eSPw1P6/iKultKocTAUilEumZhCisuUBAYSgXCM594d4KyV8UJLpmmyvNzBi0NruNT8E6V4MZBRJZP/EOfz3p+b+fVnixFb/4GegzdQLvVhIPNv+kU8Z27kusULcIwmOlx5Yg1XnljDPz7xLjs7/Jijxm3MhMp8GwNBHX10o47KLdrf8mL1f0FwH0Eln8GwwCHCDL/yM2o/cz9Lqj6F03wNuX8/wb7euKsCkbCZTUABJAQmMm2iDFewk1DHXhwVS1AcmXnCzLkXjhJW0XArgDm5aHgkEqG1tZWBgQEWLlzIySefnHZ1WVGUjImuFe51pAInpmkmxDZde3Ur3Gs2oVfTFd1wOExTUxM+n4/6+npWrVrF3r17j7j4lOwjzxSTiVeyvzgZy18cCATordxKUePv0FFQMNALFzMSKwAzkP6YSPKoIJoM9XVSoQ9TqMTwOGy4DJkn9/XPWnTlzu3Y37wbKRaE8AiSEaVKjqGYMZpEFRXSCCEclBHkT8YJdLzTz8rqfGqKXAghuGJdKT1hhZuabuIcXqZYDrFDWsNL0aXQG+Affv8u/+/set4+/i6eeH0Pqh5gUBThtMmcs7I8ZS6hmMETe/swTIGKTjEBgkoRf392A7s7fTz4VhcSYAjB3562hDL/IrRDjYSCAQqIL5q2DoX5zfPNfOWjdURPvAHX07cQQ8VFXGhNJGQghAMXUQaFh2HykZCoZBDp8asRSDQuuhxv7TnjmlpONxIkudjNscycFd3JOjSEQqFEVa1FixYdsV6sqqrjGuHNlCOJrmmadHV10dbWRmlpKbOGM40AACAASURBVBs3bhwX7wuHw71mK7pTKYZulXz0er3jCuMcS9W+jkSKv3jeZ5CXrMM1cADdXkC47HjMiM7w4CBer5dt27YlCtB4PB48bjdKzSbsex+iZqSHCsMgKvJYHX6TZttfT+YJTjCZ6Eq+Lhyv/wBhL0DkF4/Gq7ooWHcK392h8p5RzCd4iTLJx7PaRp42T8TT5uULD+7hPy9dgzBNnE47//6plbxwcB7/8EQxhmkSipgIQAb+dKCfwWCMn5xh49KD9+P1+1EkCbHpbyktcvK9Zxo52B9kTVU+V5w4HwnYKr/Nj213I2MSwcnu4f/g5o9s5aPLymgf8LHKNcTiajvayCU49j5KGXHjRCBhM6M8+U4fX/loHaKknvD5P+U3v/0dp/XcR53UgSoEw8KNIsVvcpWSl3l4EUAMF6q7GEyNFd2PMbzuDLzOfILBIAMDA4l6Ksmx30cKO/R6vVRVVU3vpHkfmHOim05srR/B7/fT3NxMOBxm8eLFU66qpaoqwWAwI/OzXBVjhdQ0TTo7O2lra6O8vDzhT56ITCRaHMnSTRbbiUo+ZmIxbibMWuwlCbNqPVKoD8fBp6hoeY6SFReSv3ANPT09LF26NFGAxiparoXnc1w4iuYspyXkZFAqYWXgNZ5xn8THVtem3U1YM3inOy5uTn3iWFrZ1xZ3btri1nnAXoHp7SJ2yiXcus7GGy0j/GbnQg70BjBMQanbjtuuEPANcf3PXsDtLuSmLfOprJQ4fWkpt53bwLf/eIhQzESRQFVkTFOwvXUI24v3Ul1op7piMehRaLqf63a7eHMoj5hhsqvDx54uP2fO17mr724cxBBI2KUAp23/O0LHv8XaggCbnrkGKTQAegRJj5BcGFtD5kTlXapUf2KbcBZxjf3PyFI3ihAISWAXMQQKGirSqGArCGySDqYOsg2MGHmBVuwLNkzY+y4YDKaEHVrZd9ZN0+Fw5NwL2cIwjEQxYUtsR0ZGEh106+rqKCkpmZZvMZM+3bFiaRgGnZ2dtLe3U1FRwQknnDClYtGZDvdKJhqN0tTUxPDwMHV1dZPW151Llu5YlJYXsO+4H9NVAiKKfdvd2NbdAFSkLUAjeYtwdM1Dc5ZTHREYI2GcMTh3XgCz7xD7g+6UxTtfDL740B6GQ/GniTInfP/89C4IoThAj4DQ6fBqdPQNIFD4zu/f4/Lj53Px+iouXl/FDQ/v5WBfALdN4jL/fZwq70AC3gys5J//eDW/qKmgqtDJWSvKsSsy3/j9AWL64d/YI0WQoz7IH20tpToIawJ9pAvNqEMeTfHd3enj92drSM+pYGpIgCLJ8X/7u3D++f9D8neBrCJpIRJRDaMBDrbRyN8bNh8u7q+0voi9dyeggywjhIlHihFFQUVgIAMSCjpCmEh6FGzxbcIzvhXWZNl3Vtih3++nu7ubz3/+8wSDQd577z327t3Lcccdx9lnnz3tc8aivb2dq6++mp6eHmRZ5vrrr+emm26a8XjJzDnRtVIhhRAMDg7S1NSEqqrU19fPOFwkG6JrGAbt7e10dHRQVVXFiSeeOK1CHNmwdJPFdqqdI6wQu2MOIVDaX0FpfQWhOjCWfgyzdAkYcdFAklHaXkHY8xPWpdAjOHrfhvK/Hj9eLIDjpTtRenahmjr2olrKS6sRnqUs+ujZGCgpVnFrayv37g7RNRxPk5UkaPeaPLJrgC+fVYY/ovNOtx+7KrNe7Me+6+dIUR+0voI/UoZbcfJo4TUUKHYe3N7NaUtKKfPYOW91BT/4c4DTI8+xhe1EsaFIcLK0h07xDDs7VlBVGPf9b64rprrQSdtwGN0QOFSZC4+vRxrOR0T98foGRgyEkRKfm6BwPi7FBGFJqgDTQOSVIQ++B7ICZppzcPSUUfMr2bz2cJlDKepLvP/wMpqEikHcAQIygjA2HFI8LVjSI+hLzsaomXr4WLred6+99hpXXXUVV199NeFwmD179sxKdFVV5fvf/z4bNmzA7/ezceNGzjzzTFauXDnjMRNjz3qEo4wVWtXc3IzL5WLFihWzaskBmRVdSZLo7OzknXfeobq6mk2bNs2oa0AmRdfqHDE0NERtbe202vRkomjOTDiSha20vYRtx/0IVzGyoaG8+n2im/4O296HkEfaAAFaGBQ7MHozNjRMJS/td7e/cTdyzy5E4UII9qN4W9GLaomecisaKu/2Btne5qXAZeOMZYvJd6pE9+3GYQuiKNaNSTDQuo/mB3/K9p4Yz3ECgxTzTdsDrFmyGNvCU4j0N+LtifJg0d/iVUtRAUUCb1ijzGPnnJXlRDWDspebKdW9iVArhGCjtI+w7bCP36HKPHDNOn71Vifd3ignLCri7BVlRAf+H44X/gmCA4BA2vRFxF8qUEciaIaJXZFZWumhoqwco2gxysB+QAHVRmTrP4EjH7OoFrlv74QhXZJsR1x8X1yYRzGqNsRTfPVIIkojhsrb5hKWSR0USkE0VIblUkqWn4ZY+UmEqwSzYnVGqo4FAgFOPvnkcen5M6GqqirhH87Pz2fFihV0dnZ+OEU3FArR398/6+yxZDIhurqu09bWRnd3N2VlZTMWW4tMuBcMw0gkGdTW1rJs2bIZlR7MpujKvXuQ+95BOAsxFp0G9qndQJXmFxCuEnDkx2sF+Dqxb/8pUngIkV8dD8saOogUGQFTjz8VO4sI124F//jjqnS9Ffcx6mGEpwIRy6NFms8lPzmIP3oASYJyjx1VlvjFGx2ct7qCUredg/1BShmhUhrAJo3wTe0h6A1RZgrOlF7lAfl8/BGNne3DLMiXkZUiZNFNZ1ghz20S1EwcqpywXiVJ4oJ1VTg67MjvRfELB6aQcRFhgTJMeX2qxZpnV/jcyQtTtpnlKwh/4qdIgV6Eqxhcxfy8Jswvn36RphGd0vlLuem0ebgf+SRSoBtTcSGEgag+IZ5SDETO+h55j10JWhChOJDE6PVhGoj8asIX3IcoqU/ssz3Qzr/v+zGl8+v4+9a9uA2dGDb2ihq+pH+WQVHBcUorn10hsWXNEvTFp2Q0RheyFzLW0tLCjh07MtKqB+ag6Ho8HlatWpXRMWcjupqm0draSm9vLzU1NdTW1o6rSjYTZmPpxmIxmpub6e3txeFwcMIJJ8y4EEs2F9KUlhex7fhZ3Bo1NNS2V4hu+QewxXtpTSr2ii1etcpCmEiRkbg7AeKWk7MYrXI1omwpSApm1UbMmAz+vpShJH8XUmgAKToCmh3CI+iKk1+8pxDSDYzRmNXBYAyXTSEQ1XngjQ7y7ArHO7s5J/Q7JGGywdZMkTFCC6XokiCPCFvFm4RkG6rNQWVlCXpwCLmqHMVvo2vIj0eFS1Y4aGs6mPAVF3c+h9r0LJLQKUJHUxxokov5VfMRE3VzMGKo7z6BFB7CqNqAWb0RUVIX/36hQap+fRG3BnpAmBihTcT6P4sUHgTFAbKJMAyU3l0QGQFXMWrLXyAWBCOKvvJCtNWXI/s7MUsbMMuWpezaF/Nx8ys3E4gFQIUnFlZTbBgow2tpGz4PU1FQ7R0Urn2Pj3zkX6Z+gkwTTdPSRgLNhkAgwEUXXcS//du/Zayuw5wT3Wwwk0foWCxGa2srfX19LFiwgM2bNyPLMu3t7Rkr7zhdsYvFYrS0tNDf38+iRYtYt24dLS0ts6p8NVVLdyYWsbrvMUReeUJkJV8Hct87mPOPP6JFri/7OPbX/i3uQjANhKMAo2IVtpYXMe0eQMSt1srjMBafnviciA6PG1tpfgGjfDWqFhodT8PnmM+T0hYa5E5W8h4jwsNz+npCIp5plWdXKXCqfNT/R/5qVS2KKx8O9iMF+shXDYaiMiYSpiTxlLSFm9S3kQMx7IqdgjO+yv3FdfT5o+zrCYAQFJQooEUYaXuHyhdvRxMStlE/qIpJxFWGWb2RtAGEhobr0StQ+veBoSEUG9G/+kf0NZcB4Hj2/yF728AYjR5ofx2lYH7c/61HAAlJtiMJCSQZ9d0ncLxwJxjxOr22vb9GeCqJnfyVw8dRCP7Q+gde6HyB7lA3g+FBbIoNZXSGw4oCZXtxlRxAmHYUJcKysk9N7cSYAdl4GtM0jYsuuogrrriCCy+8MGPjzjnRfb9L/llW5MDAAIsWLUqIrYWiKBmJ+Z1OWUZN02hpaaGvry9lTlaJxdnOI1uWrmRqCFuqiyjxGDsGpenP2N59AqE60dZejVmxiuhp30DpfhtUB8aCkxG2POTwEHL/PhACY/HpcZfFkeZhRMBZgLb8AqTwIFLEy0DB8Zy0fRe3y/cgy/GMsT1iMX9rfAVJtpFnV5ARuAmjOt3YVZkR9wI8wRZKbDEMQ8HUdZ7kVEo3nk/hhsuJxgIITwXYPfT6Inz50X34InHXR6nbzr9/ahULjBZsdmf80VtTkWIBhDAZzqunST0ec9s2nE5nShRFftfLyAP7435UxYZkGjhe/NZo9TEpfjwM/bDfVA+jDBxAivqQRhe8FCOCvuSvwVmIeuDxhOACIHTsb/2E2OZbEmP8685/5YmWJzCSnjaiZhRVSpUUSdaRZJ0iezGfW/E5sk2m9EEIwWc/+1lWrFjBLbfckpExLeac6ML7E8aUvBg1WcJFpmJ+p+JeSHZtLFy4cNwNIFulHdMRCAQSrWemeuLri7eivvd/CFcJkh4GuxujpAG5dy/uwUYkZTlQjnrwaRwvfgshKSBMlM43iHz8HszSBvTRR2iL2MlfRQoPI2QZHIVTWqAx5p+I3L0DJAWhusCmUbNqC7fvvgY0iGFHSIJ1cgtnybt5y7EJWQJv1MBfuBxHuAehVmOoLmLzjkdVJMoA/5JPctOKT+K0xy8zQQV7On08+U4jb7WNMBzSKHXHwwf7/FEe3t7FF4+rifuWkcGWh5BtICt0rvoCa1atxW63E4lEEinQ/f39FLbsokGPi7d17GU9ijA0JNWOWbYU2ddxOBJBdSKPtCYE1ypzI/JKmRA9QmTwXfzuUgYiAzze/HhShELS24SOQ3YQNQ8bHgVKAf+5+T9x22ZWuGkqRCKRjLoWXnnlFR544AHWrFnDunXrAPj2t7/NueeeO+ux56ToZot0GUWRSITm5uZEmNWRFqMy2T0iFoulfU3XdVpaWujt7U1xbaQbI9uWrtfr5eDBg4n/j0QiKIpyONNr1CJLFy6nr7gQobpQenZgOhejL/skjpe+g9L6EjWGiekqQ5xxB7bt/xO/vO0ekCSk8BDKwacwSxvGT0iSJm18mLYlU8UqtA3XoTQ/D8joqy9BlC+nTA0TVZ0YgE2JF2q5dUMp/9SRT48vyqn1hWzZfAPmoceQ+99BIBE85evY5x8HxCtsJX/rt9u9/NNv3+Zs7XkuMPr4i7mOPsfxOFQZRZbo90Ww7XwkHnplxEB1IBxFRM6+C33YhizLKT3VrEQCqcaD0voL0GMIZDANRgqX8fbbO1EUheKay1nV9hqKHgZJxqjagBTohuBh37YESHr8fNNWXox66OnU30pSuOmlL9HtcGEKM63gqpKKIilctewqtlZv5eWelylyFFE5UklFXsW492eSTFcYO/XUU7Nm2OVEd5Sx6bvJdQimGtOaPM5sSede0HWd1tZWenp6JhXb5DEyYemmG8Pv93Po0CFM06ShoYG8vLxE7Qtd1xMxrb29vQSDwUSWniXEVmUwln0MY1m82Z+66wFs+3+LkCRUUyBFhxF/jPsRpUg8BlS4RgV1hivfg0GN/zsYxNnTyvoFBZy4KN4t2Zy3DnPeupT3GvNPxNH1JihOMDWQJEqWnMQPTkoVe23DdSAELXv2sGzMIlMyj7x+iJ9qf88iukARfFZ+kv8KXMIfCi7HEPAp+Tlsex4E1QGKAyEMtOWfwKj9K8zB7ROef6Kolsgn7sHxzN8jh4fQF25GPfsHnOgqRg/78fzqPGQ9gjB1TNlGs7wYuWw5tb4ulFE3gqk40FbHfa5G3UfiIWPedhACU1Y4aLfRa3cR1IJEkl0PSdgUGyWOEi5dcilum5vFhfFmBzt27Jj1wvKRmCvZaDBHRTcb7gUrgiEWi9HU1EQgEJhWKnHyOJnuk5YcjlZTU3NEsbXIVLue5PoNwWCQQ4cOEY1GaWhoSDTDTH6PqqoUFhbGLQ8hwIghZBvRWIxAIEAgEKC/vz+lk4TH46F+98Px31V1gGTG00/DQ+grL0R99wmI+pGEibB70JeeN+3vMhLS+PEr3XhDUYqCAba3eQnFDLYuTd+wMXL2XTj/9DWUzm3gKCSy9Y5x1nXHSJiXDw0hgJKYzvJJzpUTfM/GBXe0IY6MyRfEI/wmdhGXbKhh7eAeJFOLR3NIIJkmatd2Yhy5FZCx4GRC1704bruz9XnUUB8IE2QVRZgs6XyMwet3432zCPeBR4gZEocWXspQt4prZA9ut5uCM++lctfdOLyNHHJ6uEkdZiA6hJlU+FFGTli8RY4iVhav5Ja1t4xzI8y2hshU8Pl8c6KWLsxR0c0W+/btQ9M06urqWLVq1Yyc8pmqWGaJXVNTE93d3cyfP59NmzZN6+TNxM3JGiO53OOSJUum1JhU8nVgf/UHyL5ORF4pyuabcZbF6/IiBER9mFqUoHAQCIbQDBObEJi6BkgowkRXXITy63AuuwC183VE6VJiJ30JUTz9llF7u/34owalLoWCPBsum8wf9/dPKLq4iomc/9P4XNN817ahMN96+hAxw0ACwsEwtXVhls1Ln+Z9ln1nwo8KAiHFIxMev7oWKb8K8eL8FAteCIGZHw/0P1KPtAnRw+Pnb+o4HHbYcjOxLTfT1NREUUEB9aWliVoH/kCAnsWf5+3Bt/nl8C/xm+PXKWyyjVOqTuHcRedy8ryTJ5xCNnvHWYyMjOREN5tkMoLBaq7o8/moq6tj4cKFsxo/E+4FwzDo7e2lp6eH+vr6aYutRSaOkzWX3t7eRLnHKY1raDhe/E589T2/GqI+7C//C5Fz/h1seajvPIra+iIg4SypJ3/j36BuuBLple+hxgKYpoGQbYRKVjI80Ise0VGcKxmcdwFOv4pHDCQKnWQ9omWC8Z850I9umlTmxxdwWgJBnjkwyLJ54y9+KTRE5fDO1G0Qr20w2rZGO/6LqI3PIIUG429wFsbjlhPTGF0k69+PuvchJCHQVl+GWTFxlpSx8NTRspVmfI+Kir7wlNRMslFLdGyLpd2Du/lF0y8ImaFx48rIOHBwVdFVuHU3IyMjE/rujwY598IcwO/309jYiKZp1NfX43Q6cbvds76AZyO6Vr2Gzs5OSktLKS0tpba2dlbzmSlWaFxPTw8FBQWsW7fuiDVuU/4/PIQUGUZ45sUzwqI+pNAA6qFnMQtrUJufxyyId3aQhw6hvvsE+prLkEwNdf9vicZ0vCuuoKi8iqr+fQjbPLTareTZywgEAni9Xjo7O1P6qyUv3KXzIa6uyiffodDlC7NvcJiIbnLW8jJ0U6DK0//dNUOgSBJLQ2/TENlDu6bii16c/vj4u8DuAjMGxuGV/eimmxItyUVeCaEr/oDa+hKYRjwMbnRRMCG4vXtwPXo5khZ3zdj2PUboov/FrFqfdr+iYD6hTz2I85lvIIX6MRaeSuSjd6a8Z6K6zc+2P0tIHy+4AE7VyfmLz6eysjJRSD7Zd59cAexoRBrNla4RMEdFdzbC6PV6aWxsxDRN6uvrEz7J4eHhjLkFprt4lSy21dXVnHTSSUSj0ZSogKNFcmTEokWLWLFiBcPD4xMKjoSwe+IWViyEPLAfKeoF08C26+cYlWsQqiNhbZnOYuThJpBktHXXoK27hvb2dlRVJb+qKpHcIAFu4j7gysrDVak0TUss3HV3dxMMBjEMIxHPav0Vulx8em0p3/xTG8gSFR47LzcN0/XIXj65toqtS0tRpii+3d4IvojOiv6nuUj8BmSZNYaOp+8ARO+LF5tJwiyYD8JE2N0g8uILc7INbf21qQPbPegN50y4X/u2/4wLrjLqwtCj2N+4m8gn753wM+a8dYSuemrC1w3DQJZlWvwt/LHtjwgEZ9ScMeFv7lAcXLv8Wj7d8GlkSU4ROyEEsVHffXKLpW3btiXKMVo3xumEFx4Jn8/HkiVLMjJWtpmTojsTRkZGaGxsBKC+vn7cXTFTRW+mcxIZhkFHR0eiEllyG6HkhppHA8MwaGtro6urKyUyYnBwcGaWit1NbP112F/7wWi6qR2ztB6RX4XS9TaisAYhTJBkpOgIRtkEvcumgM1mS+mvBvGL34pntaIowuEwO3t1nLLJvEI77T6NgaBGny9K00CYN1tH+Puz6o/4G/b6ovzzU4eI6AZ38iQjpgu7zUm+3aBQHyTa/hrGkrNSP+QqJnLWv+L809fiNyNZIXLWXeCcnnUm6eFUd4fEaFbZzDFNk+ZAM7e+dSthPYwiKTzV9hRfXvNlHm18dFx42FfWfoWP1X4s/fwkKaXFklWGcePGjSnlGHt6ehItlpKtYrfbjd1un7YY59wLxxDDw8M0NjaiKApLliyZ0NmuquqUuixkguRuxPPmzRvXsw0yF3o2lblYJSitqmjJj5rTsdzHxjkbdR8hpoVwvPlfmAXVYM+PB+g7POjzT0TtfhuBhCioRl9+/rTnHtYMfGGdApeKK6n61kAgRvNgiDy7wop5ZSmFsfu2N6G096AZ0B+IIQGyBKqI8pd3e/nrxXYaqksmbRfzesswoZjOvEInrmEBsh1FlnDZAMSEWXVG/ZkEr3sR2d+NmV89zhqeCtrqS+PRFMbouSrb0dZcOq0xInqEV3teJaSHWF2yGsMwuHPXnXhjXgAkJLSoxl+6/sIXV32R/9n3P5jCRJEVNpZv5NxFU08QSPYXW+JaUVGR8rrVYmlwcJC2tjZisRiqqqZk3U3kMrKYK616YI6K7pHugkIIhoaGaGpqwmazsWzZsiM2VlRVlUhkdhbDkZiK2FpkIrHhSHPp6uqitbWVysrKCecyYQREoBd516+Qgv2IqnWw9OMIwTj/qLHoNMx3f4+khRDISJFh9MUfQV//GYyl54GpI9wV8QI2U9nvKAd6/Nz3egeaIbApEtdtXsCySg8HegJ895lGdFNgCsEJC4v40um1CbfBcVVuKjw2+iMSjDaCrMh3kOdQMCIa/nCU1tbWRLsYqwW89We32+ONHEfPwR2e0zje9yy6mYeqRcBZFC9xOBGOAkzH9AunWMdCbziHiB7B/tZP4qUTN3wOfdknpjxOWA/z9de+TkewA1OY2GQbpztOpyPYcXhfCAzTYCAywB0n3sEJlSdwYPgAZc4yNs/bjDyNGGld1ycVy5QWS0lompZwUfT09BAIBDAMIxHrbYmxdXOcK+3XYY6K7kRYhc0bGxtxOp3TqrWbzY7Aya16Kisrp1TQPJPFw5PnYnUfbm5uprS09IidLNKKX9SP+uw/QtQPtjykPQ/T0tzKt4e3ohmwcWEhn9lcg8umEFE8iNNvx7H7l0ihfvTFW9FXXhjPHEvTLWAqhGIGP3utA5dNoSRPIRgzuPfVdm4/byn//XIrqixR5LIhhODN1hF2dfrYsCB+QbpsMl86qYT3wnnc91oHYc3AaVPwRw0qC11sWlWPXT3c9tyywoaHh2lvbycWi5EXk9GjOl2DMR62nU+vw8En8t/Dj4J0zj/GFw8zyNjjr6+4AH3FBTMa66Xul2gPtGNX7HhjXgKxAL8N/nb8PhFsLN8IwLKiZSwrmjjpYzJmGqNrs9koLi5OrLlA/DhEo9GEGA8ODjI4OMjNN9+Moig88MADnHzyyaxbt45FixbNaL4A1113HX/4wx+oqKhg7969Mx5nIuak6I61dIUQDAwM0NTURF5eHqtXrx7X4uNIZKN7hCzLCWuyoqJiWt0jMrXAYLkHZFmmv7+fxsZGioqKJmyIOdHnU+bWfyBeAjC/GoARw4528M/kV30EW57KW60jCAR7u/w0DYRw2mS++tHrOG3JJLn908Ab1tAMQak7fjG77Qq+iEbLYIj+QIzSvPhNJN6oFHzh1N/VbZe5cFkVpzeU8uMXWmjsD7GyysOX/qo2IbjWdx/boQDiVti86kH+b28fgUiUWMWZ7Ck6i2g0ygKvjMfox+Px4HQ6M/I7ZjLONagF0UyN4ehw3FcrQGO8W01G5rKGy2a9v0wmRiS3WCorOxxb/eqrr3LuueeyevVqtm/fzq5du/jmN7854/1ce+213HjjjVx99dWZmPY45qToWiR3kfB4PLMqbJ7JNuyyLNPR0UFnZ+e0+qJlA0mSGBgYSByjdevWxdNvp/H5cRa3rMYD7kfxhyLxxoaqEk+Vddt4bEcPdkWmwKmiGYJ/+VMji0ryWFgy8b7lwUMoHW8gZAW7vR7NU532fYUuG6oc9+m6bAresMZ7fQF++Fwz/f4oQ0GNpRV5aIZAQqK2NP0+S9x2bjs3dQGvaSBElzfCvAIHS8rT37htNhtr6+axtu6wRSuEYNu2bbjd7kTfrnR1KDwez7RTYq2bZiZYXbIazdTiPlpJwcRERk7JNIO4dZunzr5JgK7rWc9GczgcxGIxrrzyyozc5LZs2UJLS8vsJzYBc1J0kx+RCwsLWbt27bSEJB2ZsHRN06S7uxuv10teXt77KrYQX0QMBAJ0dXWxZs2aaVv/kL7WsKhYCcW1SENNCNVBgebnd86PYCIhA4GoTjBmUFpsQ5Ik7KqEZpgc7A9OKLry4EFs2++J9zMTghLfqwyuvBaYP+69eXaFqzfV8PPXO/BFdJoGgpTk2akqcFCUZ2NHm5e24QjFLhtf3LKQ2tLD4iGEwBTw25097Or0UVXo4LKN1RS6bPx+dy8/e60dKd4dh0+fUM0lG9IL/1isRqkVFRUpC0Vj61A0NjYmwtmSxXiy1uIzzUaL6BF+/u7P2d6/HbfNzdVLr2Z9+XpOqzqNZ9qfQSAosBcQiobQJR2bYsMUJqqkJlwLsyW5nkm2mGuNU+ek6EI8k2z9+vU4nc6MjDcb0RVC0N3dTUtLRrjV/AAAIABJREFUC6WlpZSVlbFgwYL3TXC9Xi+HDh1ClmXy8/NZvnz5jG9KaX26qgP9I7cjH/oTBPtxlq1iaF8Jfb3x8o5OVaIi305MN3HYFIQQCAEleRO7VpS2l8HuOVzQxu/FObAblm4gohnsaPfxVtsIeTaFzXXFrKku4PbzljIS1rjrmabR5pASeTaFuvI8Llw3j7NXlKcVqwf3eHm9awC7IvFWm+DtNi93fGwp973Wjtsuoyoyuin41ZtdbG0opTx/5iUDU+pQjJLsm0yuQ2FlhI1duJupe+EX7/2CV3tepdheTFSP8uM9P+a2E27j2uXX8t7Ie0SNKLIkI3SBalMToWEF9gIurk+f5DFdjkbdBYv3u9b2VJmToivLMg0NDRm9w80kRGus2B5//PHY7Xb27duXsXCvdOUmJyK58pcVHrdz585ZLchZPt0eb4SmgSAOVWZFVQF5djfmyvhijgJ8raSH1v2NaKiU1x/PgSGDf376EKGYgSkEWxpKWFczyaq9ZV4mIZAIawb//VIrf9zXT0gzkCWJPx0Y4Eun13JqfQkeh8rCEhc7O3yjrcgFqiJT5LLROBDCbVf+f/bePDyyuz73/Jy19lJJpV1qqbW01Oq93ZsNtsFgw8VgwJAQAncyQ9juABlPhuuHZIbMJOQSrvNHksnk5ubmYQmExQEuYFaDbbzvu9t2d0tq7XtJqn05dbb5o3yqS2otJakkW75+/eih3Vi/Oqfq1Ht+5/t9v+9LY/DSqHDetHhoNENt0IP4yt/NJjWeGUsgCCC/EocjiwKSKBDLGlsi3ZVPdeXa5HL51OjoKLquF20+p6enix37cojs2cizhNQQkijhET1kjAwD8QGub72eL535Er8Y+QWapdGYaOT6E9fzxNwTSILEmYYz1LhXt8fcCHaCdHVdf9XGjzeDXUm624GN3CVLyxs1NTWXNaUqae+42ohmKTKZDIODg+RyuSXOX6VrbBYLaZ3nZvP8dGoYRRIxbZvHhqN87E3teNVXjis+jnr3n9OVSyHLEnb0Hqqu+VP++SOHGZxLE/IqHG4OrPkeG23XoM6dQ0hHCtlngkCu9jCDU0lenk5h2jZhn4pu2mR1kx88M83VXQViOL03xK9ensMqpInjd4v800NjmJaNadlcv7+Wj13ZWti1WyvdqAWqfTJeVSKZMwi4ZdKagSpLNFdVlnDXwmryqVgsxtDQELquMz4+Tjqdxrbty3bFy30oAkqARD6BLMrFDYpTp90b2MtnD38W27Z56qmnqPfWrzrwsBUYhlGxANnVEI/HK5ZfthPYtaT7aqRH2LbN7OwsQ0NDVFdXr6oAqKS941qkW47z11ZI997zEX76wjRnR7OYokl3g5/uOh+RpMb5mSRXtIUKI5+//S+I0UUsTy1GzsAde4noQ9/D6H4nh8J+VLfKr16KcG4mic8lc+PB+stqu1Z1J3OHPo4y/TR+j4uoqxNdDZPLW0vmoUQBLLuwYzUsmztfnuOHz05T61PZW+vFLYs8OhRlLqmxr86HZdncdS7CFXuCHGutQpVFrtrj5ckZHVUS0C2bhoCLoy1VfOk9vfynOweIpPLUeBX+z3d243O9+l8RSZLweDy0tV1K/bUsi2w2u6IPhaZqZJUsb617K/99/L+zkCsY6HQGOzlZd3LJ2uXc1LeCndjpVnoa7fd///e57777mJ+fp7W1lb/4i7/g4x//eMXWf/WvqF0Ah2yHh4cJhUJcccUVa9aSK2nvaJrmZY9OmqYxNDRELBZb1/lrs6Q7E8/xs7MzhDwyKd0GyeTl6STRdJ7WkIdsXmdwcJDZ2VlOCBrehhYs2Vs4jqSJHHQRURQWFhb49fkBLizq1PoUUqLCV++P88mr22itrUIQBEzL5l8fn+CxEQ1BOERnrZcP9LhRseis9RLyyIwhkMmbGJaNT5W4truGf3xghHv7F0hkdbK6RSZvcnV3DVndpO6VGBxRLJgpziULqQi2bfPvj4Xoi6o8P5GgucrNR0614FUlOmu9fO2jR9CMQiz6a6VGuFIjrXR8ttSH4t6xe/nGhW9gmRY5I0dYDOMRPPT6e3lH9TuILcSKjTtBEIrSxu3CTpFuJQcjvve971VsrZWwa0l3O74QpZpWuCRJGxoaoqqqquzGXSUje0rXcZy/FhYWyk6z2CzpxrI6oiiQ1ExkERAFrFeeLIYjcaKjCfbsK+SyyRcWEF64HXwy2CaCZaC2n6SprgmAn4xc5HB3ITBR0zTGFzM8c36EaVceURQZSMn8ol9DN8FCIJLK47U9vHd/gOYqN5++up3bn5ri7FQCn0vmPYfruW5fmE9+9yw1PgWfKjEezRJJ5xmKZPC7ZCSp8L4Ylo2IQEvVpc9NkUQ+dMXKygRBEHArO9P4KRflSsZSeop/HfxXfIqPOHEi2QgRIrT523hae5pjwjHUtFr0oRBFEbfbTT6fJxqN4vf7K14b3QnJ2G5yGINdTLrbAUfBoChKcZDAsTXcSPe/konAlmVd5vy1WijmWmtsFHV+V8GY27BwSSCpMtm8jp5N0unT2Csk8MxFEMNurN53Qz6DcPEekFX0E5/Eqrvk8ep1SWi6id8lF5zDdIkDvc3sq/dhmiaP3HuRuVQatwTYFtGUzUNGljfVarhcLlr8fr74ru4lN5hopiDoFwCPKtFW42UmoXGkJcDn3trO1x+ZYDaVx7ZtPnhFIweayptMfC2iXPVCPB/Hsi2ms9Ms5haLSb0ZM0PYHeaB2AP8Xycu+fOapsn8/Dzj4+NEIhGGh4eXWDM6teK1fCjWw05IxuLx+JI+xmsdb5BuCSRJYnZ2lsnJSQKBwIbJ1kGlEoEFQWB8fJxoNLqhmJ5SbJZ0w36VPzizh68/MopugpDPcazeg5ZO8T+lvo7nbI444Dr3I4Lvuw3r8IfI975/xeN714F6bn96ikTOwLRs9tX76KgtNFckSUJxuRAEEV/BMQZbMzDFgltVKpViZmamOGhQ6pl7rCXAMxMJPIqEZljsb/Dzh29qwyWL3HZzH/OpPF5VIuje/st8O/sL5e50a921CAjEtfiSgYeYFqPGVYNuLp08kySp2Izr6SkMiZRaMzoqirV8KNZ70tqpqJ43Gmk7gEqWF5wx4mg0im3bHDlyZEsd162WFxxjnLm5ORoaGjadHAFba6S1+ix+Z0+Gk24QGzqZTZk0n7+TWpdFSm3BsmzmYnOEzv8U6+SnVl2ns9bLp97cxvzMGFXJizTVBMEIgVoY1jjWEuDXLytk8gXVgleV2V+n4vP5lszQG4ZRJIOZmRneFk5ip3QmMyIH6t185EQttpHHllzIokBj8PIm50YkeBvBdq0Law9H2LbNb8Z/w3f7v8uCtoBH8mBjI4gCmIVIHdu2yRpZ3tb6tst+f3lNd7k1Y+kxrORD4biBld4MS6/VnarpljYZX+vYtaRbCSz3bKitraW1tXXLEpfNku5y56+WlhbC4fCWLtrNkG4ymaS/vx9RFDl6+BDCCy/wpjMdvDSVYOpiHtNUXllbQEfBzq+/q6/TJ2m98HeFaPExG3uwEe2aL4Dq52hrFVd1hBhdzBbLBe/a74dlPq6yLF/mm/um03aRDFKpFBcuzKBp2hIyCAQC+Hy+bW0YbTfprnbsD00/xFfPfZWoFkUWZBaNRQDCrjBu2U0kG8Gv+PnUgU9xTdM1l/1+uaS4mg9FPp8vTtxNTk6STqexLKtoWK5pGpqmVdSwfDlisRhHjhzZlrW3A7uWdLfyAZa6kXm93qJnw8DAQEVUBxsl3dWcv5yR0a1gI6Tr6H2dpN/lzYk91R4eCxxnX+QsMgo5w6RJ0aH9zQAI2ShifAQEEaumC0osDJVzPwZBxg4WOu1CfAxp4nHMzrfjVSX+6K0dnJ1MkDUs9tX5UPKJ4mPtWij1aV2eJpFMJkmlUkVtq/Pfq6qK1+slEAhUbGpwO0l3eU3Xsi3i+TguycXDMw8TyUYwLANREFFFFa/iJeQK4ZbcnKo/xcf2f4yguvLj91Z9HVRVRVXVy9zAHDmbZVlFDblTHiqtF1ei3rubvHRhF5PuZuD47A4ODuLxeC5zI6uU01i5Ol3bttd0/qqEp64oiuuek6ZpXLx4kXg8zr59+1ZN+g16FN71797LM/ebtM/eTXWVQvVVn8JuPQOpOZQXb0fAAttGmnwSvec9yJNPIqRnECMvY7tLmh2ijFCyQ/aqEmc6Lv3/c3OJLZ23oijU1NRQU3NpssqyLEZGRshms0Sj0aJhtuPRupXG0U7tdGNajL9/4e+L/rcL2QVMy0QoxFySM3O4ZBfv2/s+buq4ad21t+PxvzTgcnR0tLgLrYQPxUrYTakR8D8Q6Tpk63K5OHjw4Io+u5Ui3fV0uqU7bZ/Pt2rDztHpbvVYVkvEMAyD4eFhIpEIHR0d9PX1rW8QL8CeEzficb2Xllof4ivm4OLUM1iCWPTIFeKTuB7+68LvqD7IRJHiY5jNJ8E0wDYx6w9u6dw2Ckcipaoqra2thWNbo3FUSsTryam2M2a8dIDhWxe+xURqghp3DaZtMhAbQJEU8lYeyy7coENqiGubry177e2OR3ewmg9FLpcrkvF6PhQr4Q31wg6h3F3F4uIiFy9eRFVVDhw4sKapuSzLZLPZLR/bWuWFaDTK4OAgqqqu6/u7FmGWi5XKC6VBmHv27OHKK68s64v3/HiMO1+eQxQETNvmcHOQGw81FD4LUytYPr4CQU8jpGaxmgspClbrSZh8GgytkJ925DPYNV2rvtZOTRyu1jgyTXMJEZTKqZw6cemQwXbtdA3LoD/Rz7w1T7vYzoXYBYKuIIIgIAsyiqgQUAK4JBdZo3Dt/oeD/4EqV3nDAtsp6SrHHU0QBDweDx6PpywfClVVi7tij8eDy+UikUi8QbqvBTjkpigK+/fvXzeuByq3012J6Eqdv8o9HkmSthwhVHostm0zOTnJ6OgoTU1NG1JFmJbNPRfmaQi6UKSC3eNL00lOtIVorHJj1x9CmDuPLclouomRyeKRfci2XTCzEUTsqla0t/9lwb7xVUK5RC5JEsFgcIkUqdQdLJlMLhky8Hg85HI5YrFYxWqVC9kFvvDoFxiIDWBiolxUcIkuGn2NNPmasG2bOk8h/80tuXHJLo7XHudNTW8q+zW2c6e7ldLFaj4UpU8lFy5c4NZbb2VxcZFPfvKTHD16lOuuu44zZ85s+pjvvPNObrnlFkzT5BOf+AR/8id/sum1VsOuJd3V7qClQZTlkpuD7UgETqVSDAwMYJom+/bt29C44lbNapw1DMMo1tDKiehZCcYrXgeJrM7ZySSaaRFwSeT0wo7erunE7HkPsYtP8vxUiknvO+jN/Zb908NUh6ogn8Jsv3ZDhLtdO93N7khXcwczDIPFxUUymcySWqXH41nyeLyRJAnLtvirZ/6K4eQwBoVrMm/lMS2TqcwULsmFZVtc13Id7+94P6OpUbyyl95Q74YyzLZT0rUda6uqWqzVt7W18cQTT3DNNdfwxS9+kbNnzxKJRDa9tmmafPazn+Wuu+6itbWVU6dO8d73vpcDBw6s/8sbwK4lXVj6CBqLxRgcHESSpLKCKFdCJSN7LMvihRdeIJfL0d3dvaShUy4qMU7saFpN01zXMwJgNpYmN/QI/uwE4fpW2Hs1giCgSAJ1fpV/e2oSj1LY6c4lLJ6fiLO3tlAiyYe6+IHhxtsq4VEkRmpamZt6iLdVmXgaujD3lL8De634HpQDR57m9Xrp7S1kiZV28EuTJNbStY4mR/n12K+xsDhac5SZzEyxQSYKhfdcFERkQeaWI7cQUAO0+gruabWe2lWPby28Vne6G4EgCBw8eJCDB7fWI3jiiSfo7u6ms7MTgA9/+MPccccdb5DucjiP7YIg0NPTs6XJlEq4g+VyOQYHB8lms+zfv39VJUA52Ip6IZFIMDAwgGVZhEIhDh06tO7vnJ9JMv7gd9mTfJqY6CM//gwti4MI9hFs26a1SqVWyaFLPtyqwr6AyhOjMd53rOBhoFs2edMirLySUaZ4GKq+hiO9jTRXVcZsfqvYqeGI0g5+aZKEk3K7XNc6xRRfnfkqpmAiCiIPTT2EaZtLAkVtbCRBwit7OVBTGSLYTmJcLwm4Uq9RqeN3ehwOWltbefzxxyuydil2Nem++OKLaJpWNOzeKray0y11/urs7CQej2+JcGFz6oVMJsPAwAD5fJ6enh5EUWR4eHjd37Msm0fOT3Jd7gVyVW2ogshY1qBm9iJptZnpcw9z8tmv0azF0X0N3F/zB8yYblyvBDkWEiNEarwKi+k8NT6VTN5EEgWq3DLoWZBUEMv7gmxnI+3VnEhbKeXWsiw+c/9nsLDwiQU/ikgqQq1SS0AIkCWLhYWMjEfx8OHurQdGlr72bt7pVnIEeKXrbTuulV1Nur29vRW9k27GklHXdYaHh5mfn1/i/DUyMrLlzvBGyguO1jaRSBS1tkBxJ7UeLNvGsKyiBAwKMdwvTyf5TSZC+Ny/EHEF0d0NuDILnBj7F75b8xk+fLIDKJR35ubmONXg4dFJnal4Do8i8d4eL6Hz30NITIEoY/S+G6t2/ybejdc21iPdZD7JQm6BgBog7A6zmFvkzrE7iWpRjtcdJ2NmUBUVVS48JRh5g9bqVj7Y8kEevvgwE8YEsi3T4+5hv7afsbGxdaVU5WC31XSXo5Ia3dbWVsbHx4v/PjExQXNzeRl5G8GuJl1VVbfcaCrFSiGMq8EwDEZHR5mZmaG9vf0y2ZVDmFsl3fXOr5T0Ozs7L9PaltuMkyWRtoYwAwsH6U6/QFr0ISbjXDDqCLnAbQrMGCoNQYVQdSstqSn+43V7aAgqPPvss1iWRV1dHZlMhiPeFEk7i0uVUV94iLS5iFy9B1W0kc/9BP3EJ7C9m6tBvlaxGulatsVLCy/xw6EfYtkWNjbXNl/LDwZ/wHByGBGRX4z+ghZvC5Zd8MAFMGyDt7e+ndNtp/GlfOzduxefz4dlWUUpW6mUaqUBj3J2adtpYr4Tto6V9NI9deoUAwMDDA8P09LSwu233853v/vdiqxdil1Nuq9Gs8U0TcbGxor1n9WcvyrRBFurvOAcx9TUFG1tbatqbTeigLiup5ZHxffTP1xHgznDgi/Aw6keqrKTiIaJS7TI6iaHakUstZq5xRnOjqbo6emhurqafD6/5DPR83nE+39GRqkhvrBIPp/Hrc2TfPFJpKZDRa3rSjem7Sov7KThzWhylH+98K88HXkat+TmcPgwHtnDd/q/w3hqHL/iR0AgZ+aI5CIcqjnESHIEy7b4YNcHuWHPDcBSvasTNlraKHYGPJyx50gkQiaTKRqdrzXgsZ0m5jtl61gp0pVlmX/4h3/gne98J6Zp8od/+Idbbs6t+DoVX/F1Csf5a3x8nObmZq666qo17+KVIN2V1ig1xWlubl5Xa7sR0nUpEm/ta4K+QhJsrH+e5COjaFI9z/jfwsHYfdS63KSjAufrb6IxXEvfgYOrEqSiqijVzbhNHcJhsC3suIC7ZS9xQVpRXuUQym6L1V4+CJA1snzzwjexbRtVVBEFkZcWX+JU/Sl0Uy84gb2iTFBEhZyZ40unv0RMi+GRPfiUS0Mz6027lQ54LB8wSKfTJJPJohm/M3brkLCu69u2eVkp9aTSqPQI8I033siNN95YsfVWwq4m3e24WJZPFy13/jpz5kxZd+9KyM+WDzY4+Wy1tbWcPn26rAt6K1rfq7vDDM2n+dWzKX7lvZrplgNcHZzH6DrMke7Dl4jAyEEqgmCY4G9Y0iwzem9CefHfIDkJtoW15yp8LX2UzuGVyqucvC8nfBEokvFGZ/J3ErZtk7Ny/GToJ0ykJ/BKXhJagjpPHaqkYtompm0Sz8cJuUJEchHyZh5RENEsjY5AB7Ioryj92myza7UBj1wuV1RQ5HI5nnnmmSVexc7PVksDu62mu1PY1aS7HXCaabIsr+j8tZF1trrTdYh/YWGBgYEBAoFAWVrbUmyFdCVR4H++cg/t5gSxxSkaGprYf/Q6Ap4Sn9pcHPHcHaAlsQ0dO9SO2f3O4kiwHWgif+KTCNkFkN3YvvrLXmcleVU0GmV2dpbq6mpSqRTz8/PFR+ZSy8aNksN27aANy+AXkV+QlJMElABPRZ9iIj1B2B3GK3sxbAPN1DAtk88d/hz3TNzD3RN3Y2PT5G7iz07+2aprV1JhUDp2W1dXx/z8PKdOnVriVTw9PV10CCt9AlkpcXjN92SHonpaWlq29TUqjTdIdxmc9Ijx8XGqqqpWTfwtZ52tkm48HiedTjM+Ps7hw4fX9GlYDRt5GhBGH0Z68K8hG8VuPMLCyf/IxcF+al68nRZBQ41IPBO5gSNv+xDVvsJ7Iow9BoaGHWzGNgyk2Aj24hBWbc+lhVVfwfRmg5AkiXA4fJknwkrk4JijOOWJtW6Q2/GEFNNizOZn6Qh2sJBbIGtl8ck+LNsilo8RUkN87tjnONNwBlmU6avu4/2d7yejZ2j1ty4pJyzHTpjSrORVbNuXvIpLE4eXexV7vd4VyXUnarqJRGJb6q7biV1NupX+8iwsLBCPxxFFcdNRPQ62MmiRTqeL3r5ut5tjx45t+jhWRS6BkJrBtgwEQcRORZB/8ycgCJiSC3PwPsS5KdoajjNrZqG6FUEW6Jj7DS+d7ebqK68CQNBixQQIAFtUQU9t+fBWqxNLkrSiU1UmkyGZTF5m2ejs0JzyRCVh2RYTqQmm09NMxiZJG2lM2yRjZBAFEa/i5Uj4CDkzR1AN8uamNy85vz3+PWusfgnbaRu5FtbyKnZufKVexctdwXZKp1vJJOCdwK4m3Uqh1PkrHA7T1ta25S/oZjS/uVyOixcvkkql6O7uJhwO88gjj2zpOFZEahbp7O2QTSBMPAqiAraNnY6Q9bZg6gbuYBPh/ATRdB1pOUQIG1tUkEURPTlXXMquakecehJbbgZTByuP7WtY48Urj1JyKB7Xso7+3Nwc2WwWwzDweDyYpllMlNgMMVi2xU+Hf8rD0w8zmhrFNExUQeWZyDOE1BAZPcPewF6qXdVEshE6g52bPr9Xi3RXw2oDHqVxPmNjYyQSCfL5PMFgsCIhlyvhjZruDmOrF6IzKlvq/NXf318xT91yE4F1XWdoaIiFhQW6uro4cODAknOr9JdOHLoXW1QRklMgqdg2ZHXw5LMobg1voKY4QSbVtOOdfwnT8oJlkjdMwnWXBON2ywksPYMQOYdg2Zh734od3HqNbavnu1pHf3h4uDBS+4rjmtOwc5IknF2x06TUTI2oFsUtuhlPjzMQH8Av+2n0NvLc/HOF0oErhCZoYEHYHeZQ+BBdVV1EtSiz2VnqPfVc33r9ls5nO1DJ+vZKcT5PP/00fX19SywaHa9in89XfL+3Ev2+27x0YZeT7maxlvNXJfwXnHXWi5sxTZPR0VGmp6dpb2+np6fnMrLZFq9WLQmKF0GLkzUE8ukEQrgTwRdGyS9ip/II2BinP4On7yZqZv8fsukZ0CSyXe9i/8ErLq0lKdhdb8Pae21BflTmmG852I6ml9O0K31cTmpJZuIzpLIptAWtOHAwb8/zy+QvWTQW0W0dn+rjQPWBQlPM0LCxMWwDj+jBEiwydoY6Tx1XNlxJX3Uf87l5TNuk1l2LLL72vmrbXSu2LAu3243H49mQV3FpOWi96/4N0n2Nw8kAW8v5ayfSIyzLYnJykrGxsXW1tk5DrlJfjrxhoQc6EYYeIJOyCeWjBANVEG7Adl+FFe5GEGXM5uPY7deAIJA9+TlCikFNQwuif5VJMlECYes3q+1ESk+xmF+kzlVX/LuZzAy/GfsNhm1g2RaHw4c5s+8MqXyK256+jaSZJCSHGEmPkMgl8Ot+2vxtLOgLGKJBUAkS1aLopo5P8iGJEo3eRgRBKHrdbhWvRuBlpbDSsZfjVeyUg0p30CvlqqVSqTWDCV6L2NWkW+7F6NRKk8lksVa62u/Kskw+n9/ysa2kXigNoKyrqytLa1uJnDTntSeiWX7y9CizsyKHzHpubFVxJV0ICNj5NNbBD2J3X/4YLChuDJ8P0V/Lc+NxfnshgkcRuelIE63Vl2rflRwprfRE2oXoBR6dfZRYNIY76eb9Ve+n0dvI/ZP345bd+JSC0uDswlk6g52YtklEi5CwEmTIIEhCwRfBAz6vDzWpsl/Zz7nkOQzdQESkxdfCjfU3EpA2biv6amCnrBfLwVpexSvlqsXjce666y5EUWRsbIy9e/dW7Ob0gx/8gD//8z/n3LlzPPHEE5w8ebIi6zrY1aQLa385lzt/La+VroRyygLloJR0nUy0wcFBgsHghmRolchJEwSB+ViCr931Ei7R5kBXO3mhix+YNn/w9j0oVg4LmUjWxozlqPEpuBVpye/bts2jQwv81a8GEISCQc69/fP83e8eoanKhWVZ2La9JF5IFEUEQXjVBxoS+QSPzj5K2BVGVEVsyebeyXv5na7fIW2kqfcUtMEZI8O56DniWpywJ8xsdhbd0pFFGcMyMG0TSZRI2Amaq5v5SN9H8MpedFNnfHS8IKdKy5w9e7bYsCt9XN6IxrUU26Ut3k7fhUphtVy12dlZpqenufvuu/njP/5jRkZG+NSnPsVnPvOZLb/moUOH+NGPfsSnP/3pLa+1EnY96a6EUhOYvXv3Fp2/ysFmVAerrePckfv7+1FVlSNHjuD1biyqZkt6X9tCXxyH+ARPPWfgC1bTUB0ka1ioCuR0k0zexO/ycH9/hOGFLKIAHlXi3x1oIOQt7MIFQcCyLP7tqUlUWcDvKlw286k8d52b4SMnC40zRVGwbbtIwM6fS28+kiQt8RFY8/ArQDaGZRQjyiVBImNkQICx2Bj3jN+DgMB8bp4qtYrHZx5HMzVC7hAvLrxIQAmQMTJk9SySIFHnruNMwxlq3bVc2XhlUVuryioulwuPx1N0pXImv5LJJMlkkqmpKTRNQ1GBubRWAAAgAElEQVSUyzSua70P2zkOvZ2+C9t53IIg0NjYyEc/+lG++tWv8pOf/ASgYuZXfX19FVlnNex60i3d6a7n/FUOKlXT1TStKEXr7e3dtOfnZssLppYhdeeXEKef4xDg3nuKZ/UP8uxYDEUWyesWDVUuPIrEeDTL0HyGlldKBdF0nidHF7mhr9BsctzXDMtGLDXVtm10o+A5UHpTK909OcduWVaRjJ2/c8jY+f3SXXElHhUXc4v8cvSXRLUo56PnGXWPEk1EmTPmMDFxy24My8AjeVjMLZIzcxyrPUZACVDrqWUqM8V1LdeR0lOk9TR9NX38/r7fX/G1VjIxdya/Sk3MSzO+RkdHyWQyRclbaTffqVtud7T7brZ1TCaTS4x/Xu0nqnKx60kXynf+KgdbJV0nOSKVSqGqKidOnNj0WrDx8oKmm1wYHkc6+316Ey/h2nOAhYV55IVzXCndzy/kt2HaNrIkEPIUdrK5vEk0ozO8kMG0bJqCLhRpKYFYlsV7DjXw/903jGlZmJaNKou8pad2TVJwPofln0cpAa9ExKZpFv++nM/SsAxkUS6kLbzyz6/Hf41pm+zx70EzNR6ZeYRqoRrLttgT2ENMi7G/Zj+RTISbO27mjpE7qFILj7H17nq8spcFbQERkYAa4LqW61Z9/XLJsTTjy0GpMU1p3dIZjTZNE03TUFW1ogS83Q5jOzECvFmN7vXXX8/MzMxlf//lL3+Z973vfVs9tDWx60l3enqawcFBmpqa1nX+KgebJd18Ps/Q0BCLi4t0d3dz4MABHnvssS0dC5RfXrBtm5dHpvjWQ4NIqpsbc0nyShC3KIAoYkhemu1prt9fT84w8cgS0axO3rTImxZzk0NcyzN4hDxPLuzDPHJ1cW0n3PL6/bUI2Nx1fh63IvLhky101m58vNdZ0zk/Bw4BLy4uMjQ0RENDA6ZprrkjjmpRHpx6kFg+RlpPo4hKcTAhko3Q5m8DoEqtot5bT7PQzJQ+hU/1kTNyiBTWafQ20lfdx8vRlwvBjjZ85tBnUEQFwzJoD7RT41495249J7C1sFo3P5vNEovFsCyLc+fOkc/nUVV1iRdCub65K2G7vXR3wtZxs6R79913V/hoyseuJ12/31+241Y52CjplpY09u7dS29vb0V3I+WUF+LxOBcuXOCXoyatzU3UBDwY0x0sjj+LK1iHAChGmlxoLznDJOCWiWV0qjwyXkXCTs3xMf3fyOs6uqDwAc4xlwoCbcU67OjoKPl8nqO1Qa65sWtTfhTrQdM0+vv7ATh8+DBer7dQE7ZMFrILxLU4yXwSVVRp9bWiSAp3jd1VCG20bIbiQyxqi7T4WhhODqNbOj7ZR9gdRhEL10dQDpKwE8xl5qhz1zGdmeZA9QE8iocb9tzAvtA+skaWGncNTd6mso+90mUAR08sSRKRSISjR48W3yNHVlXqm1tamijXBGi373Qr6aW7k9j1pBsMBisyzOCgXFeuUn/dlpaWLZU01jue1c4vk8kUJ+g6unvxxeaoCRQcyKYb3oo7NkBj4iIuLYPRegUdb/oIs2NZ5pN5av0qV3bWIIoC1YlzWGIeT10bNmBmE3QsPoJpvgvLsgiHw/h8PpLJJLFYrOht4Ha7CQQCBINBAoHAhiLGS2EYBsPDw0Sj0cv00xYWD848yLnFczwx+wRZI0u9t579of3c1H4TmqlR76lnMjVZdPHyil5Ul4pu6cxmZzFsA9u2ubnjZl6eeJkWbwtNchNNviY6gh2cqj9VeK8FcdPjuttVe11eXnGm7EqHDRxZlZM6nEqlilN2pU275SZAb0T1rIwf//jH/NEf/RGRSIR3v/vdHDt2jF//+tcVW3/Xk26lL/T11rNtm+npaYaHhzfkr7tZrFReyOfzXLx4kVgsxr59+6itrcW2bao8UeJZnSqPQs6SeKjpYxw47mVmbIi6joNUB4K882DwMoJoDnmJyALZxCQeI45kG1SHDxSNuZ0EAp/PR2NjY/F90DSNRCJBMplkcnKSXC6HqqpFp69gMLjm468zijs+Pk5bWxvd3d0IgoBpmzw09RCPTD9CWk/jVbzEcjGS+SSKpJDMJ3lu/jm6qrqQZRlbtPGpPnRbRxIlJFkip+cIKkFO159mX9U+3JIbv+qnQ+vAF/TR0lBZO8DtJN1yZI7LZVWWZZHNZpeYAJXG+gQCAXK53LY8scDO2Dpul9nNzTffzM0331zxdR3setLdKdi2zfz8PIODg4RCobL9dbf6ZSzd6ZaODZeGYELhZvG+o0386NlJpuM5REHg3YebCNYFmFpIYZUoeJYfj9x6nGbPv2DGxzBVLy5bw5YljHwC3CvvJErF7Mu78w4RO1NFkiQt2RH7fD5isRgDAwPU1NRw6tSpJTeuh6Ye4vsD3y+S7YK2gEty4ZbdKKJSqLkKsJBb4HTjaR6feRxFVvDJPgQE4vk4XtlLtbeaA7UHCLvDWJbF4uIi0cUodbV1RT3xSnXizWA7Y4A2c1ylN8rStZaXJ0zTZGZmZkl5YrMmQKXYCVvHWCxGXV1lpv52EruedLdLTlP6JYpGowwMDOB2uzl69GjZWttKhVNqmsbExEQxome1UkZD0MXH37yXlGbgUSQ8auGLs17JxPbUQMtJJF89EiZWdQeCKCGk57BXId3VoKoqtbW1S6aKdF1nJjrDL0Z/wWhsFDWvctxznPbadtxuN+l0ekkd8snZJ1FEBZfoosZdw4K2gG7oIIBpmwTVIHkzT4uvhZ5QDw3eBtJ6mvd1vI/h+DAXExcJqkGO1x2n3ltPNpst1oqPHz+Oy+UqKiOcH1hbwrYedqq8sBWsNPXl9/uLRvHOE4tjAuTkqzmEvJG+yU7ZOnZ3d2/ra2wHdj3pbgec5lXpl7Wvr2+JJrDcdbZCurZtk0qlilHQ5TQMVVmkRl66A1+NdEuJR/aGsb3VCOor55gYL1g+VgCSLPHb+d8ynhzHjRt3nZsx1xinW06Tz+SZnJwkmUxi2zZ+v5/R+VFGciO4FTcu0YVH9uCVvGSMDBYWoiBytPYoVzZdCRSUCY7UK+wOc7KhMLZpmiaDg4MsLCwUx7+XHNcKyonVJGzO+7jaYMduIN3lcIhxJQPz0tTh+fn5oimNk6/mEPFqdXzTNLcUDV8OdqPZDbxBuitCEATOnj1LPp9n3759m/5gtzJN5kyyAdTX19Pb27updeBy0tV0k3PTCRK5PC1VHtrDXuyOa5HO/7zgQGaZWFUt2FXlmWyvBtM2ubB4gedHn+ehqYc4Wn8Ul9fFaGqU52efJ2tmeWf7Ozm85zBQ+KIPzA0QG4+RyWfI5DNYtkVACfDpfZ+mKlBFQkjgc/voDfXikVf2PHbGRJ0o7VOnTq1LXKtJ2OCSZng5GTuP/s77+2rVdLey9mrvy2qpw06+mtO0y+VyyLJ8WXnCMIwNT19uFLvRSxdeB6RbyQvSaVAlk0l6enpobW3d0vqbId1MJsPAwAC6rtPb24tpmkxPT2/6GOAS6dq2Td4wuOP5GSaiWVyyyJOjca7rqeVoayvGod9FSM0V7BpD7cWcs83inoF7eHzkcUL+EHjgXPYc2WSWaDaKIAgoksLd43dTpVbRFmhDFEVGtVGCniDNwWYiuQiaqVGj1NAR6iCbzmIkDbS8xoBnYEnDzvE1SCQS9Pf34/P5OHHixJZ2WysNdpRO2DkknE6nicfjNDQ0FNN1K1Enhq3pf9fDRksAy/PVHDhJEslkspgk4TRZs9lskZArXeN9Y6e7i2EYBiMjI8zOztLR0YFhGASDwS0T+kY0v85wRTQaLSoSoFC32upMudOMM02TqWiWyViW1urCLkQ3LR4ZinKkJYjgDWN7w+ustjZmM7NMRieZGp/ipexLHOs8hqqqWFGLe8bvKTTCRJGwO8x8dp4mXxOT6UnaAoUhBkUqNMo8iocuVxcL2QXC7jB7Wi7tup0dVyKRIJFIMDExQS6XwzCMQgzOnj3U19dvS/x3KRE7ssHZ2Vm6u7sJhUIrlicc4twMEW9neaFSa6+UJHHu3DlCoRC2bTM3N1ecsttK0OVy7MaoHngdkO5WiNGyLMbHxxkfH18yPpxIJCpqerMWnBHmqakpOjo6lgxXJPNJfjP5GybnJ/HEPXRVdW34GGw9iz/yNIvDzzNT1cBU6ChjsQxpW6DKVUXYXYtpWdjARt9J27YxbbNo0P387PP85OWfoOd1AqEAaU8aUbo08dXqb8UjechbeRq8DSTyCTRTw69c8kPtq+mjfa6dmcwMlm1hY/Oejvcsed3lO66JiQkmJyfp6OjA7XaTTCYZGBggk8mgKMplErZKEI2jZGlsbOT06dNrTtit1rCD9Z3YdqKmux2wLItgMHiZeiKbzV4WdOl8RqXm5eWcczKZfIN0Xy1s1Hu1VGvb2NjIlVdeueTRp5JG5quRrm3bTE1NMTIysqKReSKf4PMPfp659Bz5fJ4HH36QL576IsfqloZUOi5aLslFtau6SNjF3dbQ/VRbiwT27OHcxMOcH/0mT2hvQp/xIUo6kh2ipUajb/gqrtt7XdHcxsYuSLNWwYOTD/Lz0Z9j2Ran609zRDrCD/p/QFttG+FQmIXcAo+NPsZLiy8VhxnqPfX01fTx/PzzzKRnkEWZFn8LvaFL9epGbyO/2/27PDX3FHkzz9Hao/TVrOz65ETTO97Ezvu3/NHXkbANDw+TTqeX1Cud/K5yiS2bzXLhwoVieKnb7V71v12PiMtxYtsNO92VsNIYsDNl5/V6L5MZOll2TqSPIAhLBjt8Pt9l6+0Ga8qV8Log3XJh2zaRSISLFy9SXV29qtZ2u0l3fn6egYGBNY/h3vF7iWQjhNwhMmYGEZH/dva/8alDn+JXo79iPjtPR7CD6cw089l5LCwOeG6gTrwKy7I51OzncIMbJTmFmIuSmXqabLyfvtwiR/wP8ZhxEMH2EfBEaKqu4tvnvs3k6CRJO8mAPoCoiJxpOMPNvTcXzLtL8GzkWf7xxX8s+BLoBt+a/RbXN15PY2MjtYFaNFPj0ZlHcUtumn3NpIwUU5kpPnHgEzwbebZIsqfqT7Gvel9xRNdBe7Cd9mD7qu+rM4kniiJHjx5dM0RUUZTLYtwNwyCVSpFIJBgfHyeVKqQXO19wh4hLv+SmaTIyMsL8/Dz79u1bMXWkHGy0YZdOp1EUBcMwVjUP2ixeKxNpTiDs8kgfx41tZmaGZDKJZVl4vV5yuRyjo6Pbcuy33norP/vZz1BVla6uLr7xjW9UvFn3uiDdcna60WiU/v5+vF7vuvHqlSLd5eskEgkuXLiAy+VaV++bMTJgU0h1sG2SepLJ9CS3PHALAG3+Nl6YfwFZlDlef5xE0sWvzo/xrs5W2gNtPDkaw6NUc8DUEBYGGdJjRLQofsvkTHaBZ2rOYgkCqhoi4D/DpJHhXvNeFnOLNLgaaJFbuG/8PqIzUa4IXIHf7y8ON/x24rfYpo2QF0hbaXJijvtj93NIPAQiSIJEzszhU3w0+ZqQRInZzCz13no+0PUBDMvAJW28lueMCy8uLm6J+FaSSDlOX4lEgunp6eKX3OfzIYoi0WiU5ubmspQQG8VKZJrL5Th//nyxRu0cY+n/brVh91ouXUiStKJ5eSaT4dy5c9x3331MTExw7Ngxmpub+fznP8/11289/POGG27gK1/5CrIs84UvfIGvfOUr3HbbbVtetxSvC9JdC8lksrgrOnjwYFl5SrIsl53kuxayVpbB2CAROYIYETHyxmXeugu5Bc4vnietp3lx4UUi2Qg91T1cUXcFklggr4yZIapHC7tePYONzVy2EIOeNbKYlkkm50GSDFJGDJe8lwYpSWQqiV13kNzQb3EvDNJt5IkLAu26QdAyiUkyNjYL2gJpPU1IDeFX/KSsFHklT3tdO5ZqceLAiaIZ99jYGFMTU2TyGQzJIE8eERGv5EUSJbBBtwtpC3sDe5FECc3UkEQJj+RBFuUNhzQ6MUcjIyO0trZuC/Gt5PSVTqd5+eWXsW2bmpoaFhcXmZ2dLSYHlyonKgXLshgbG2NmZoZ9+/Zdpi1eS0+8mYbdTgwXVQqO7/DJkyfp6enh4sWLPPDAA8zMzFTsenjHO95R/POVV17JD3/4w4qsW4rXLemWhlD29PRs6BGhEjvdgegAX3juC6TzadQBlaN1R/nj03+MS3WRN/M8F3mOidQEvxr9FbqpM5Yaw7Zt3JKbx2cf57Hpx/j88c/znQvfIZFOUOWqosHbwFB8CFmQyZk5/IofzdQKdUBRx7IUql1BmmbvxT37PNV+F6IWJqV4sSWVEQlsU8cQRfZpGs/63ATVIHPZOeo8dYXmVjxRsEc0MsiiTHugvUhIsViMdDrNTb038c3RbzKXmUO3dARboM6qI7OQodZfy/vb30+bq41H5h8hbaSxsfnwvg+jShuXbzlPB4FAgJMnT26LImE5TNNkeHiYhYUFenp6lnTlnWZQIpEgFosxPl6I6XHMfxwi3oz5j/M05tSoVyKScurEm2nYVRrbReYO4vF4UWHU1FS+G9xG8PWvf53f+73fq/i6rwvSLf2AS3PRuru7qa1d22R7JWw1hj2ei/O5336OhJ5AFESyQpYH5h7gmV8/g0f2EFADGLbBXGaOvJkvOFvZkNbTaKYGNjw7/yzBi0H+/i1/z/fv/z4/036GR/LgU3wktASKpOCW3IT8IeL5OKaa4FDd22hI67jmniXnayHcXAXaArI7RFxxUSN4GbZSjMgSNcgcDB/kD3r/gNHkKMOJYeq99cxmZpnNzuKVvTR4Grhhzw3FQYOGhgZOnTpVePSrruLbF77NZHqSozVHafQ1MpWeYn94P6Io0mv3oggKKT1Fc7CZ6kw10WiUQCBQll4zn88zMDBALpejr69vRxJfS2v+qw1VlDaDVjP/mZ6eJpvNlm3+45yrpmlFS8uNYLMNu1KCrjQZb2dcD2zN1rEcA/Mvf/nLyLLMRz/60S0d50p4XZAuXKr3zc3N0dnZuaFctOXYyE73mblnuL3/djRT49rmazntPc1PX/4paTONS3Yh2AI5K4dhGVS7qrGw6I/10xPqKQQemgZT6amC/SA2hnXpdR+efpjvXPgOXWoXNzXfxM+Hf07YFSagBLiq4SpO1p/kRP0JIrkIqqRSJYeJX3wcn+XDWxt6Jf0hSJVHI9j2Zh5KDKITpimXoKbnJt589NNUuao4aZ7kx0M/Zjg+TFuwjeP1x7m66WrCQpjRl0fxeDxFzwIHx+uOcyh8iDuG7mAwPshMZoa+mj6u3XttsTHWR19xeMBJRRgcHMQ0zWI8jVMndnawjoxvamqKzs5O6uvrt33XBIVSglNvv+KKKzZUMljL/CeZTJJIJIret475j/MTj8eZmJio+Lmu1bBzxttLbVFL68RbbdhtZ8SQg62kRqxnYP7Nb36Tn//859xzzz3bch6vC9Kdm5vj3LlztLW1VcTXtlzSHYgN8HfP/R2yIDOfmef52ec5XnWcmBBDszQ0S0MRFEy7cEF7FA+aUdjJ5owcVWoVaT2NaZm4JFeheUaheaaICqqkcvf43XT4OvhQ94d4W8vbSOVTNPgalozAtvpbi39uaGxBnhGxBROQITOP1XiIvtr97Bm+G03P4G05g7vtzfCKJMwlufhQ94eIabGCBtb2cPHiRaZyU/T09KzqOaGICh/s+iCxfAwBgSq16rKLtFSeVRra6DStnJ2l03jJZDKEw2GOHz++phyrUjBNsziUstEy1HpYqSuv6zrJZLKoYBEEAZfLxcLCAvl8vqic2I7OvCAIxRtaab24NL/Otu0tN+y20xzdwXaNAN95553cdttt3H///ds2xvy6IN1QKHSZ1nYrcEjXsAy+9tLX+M3Yb1AllY/1fYx3tL8D27b5/sD3+ecX/5m0nkawBRAKZPlw9GE8sgdVLJho5+08AgJe2Vu0HnSmEGrcNcTzcVRRpdnXzMXYReL5OJJY0Gk2+gqPr4IgMDAwQDAYpCHYgFtanYzsUDtm1w1IQ7+F5BSCkQPZgxlsxXfyf8VXWPCy3xMFkSqlirGxMS7MXqCzs5O6urp17/SCIFDt2tgoZqkGEwr19/PnzwPQ0dFBLpfjxRdfRNf1YtPKaXJVykTFmZQaGhoqNud2YkctCAKRSIREIsGJEycIBAJFeVQikWBycpJUKoVlWUUJm/OzlXp2Mpnk/PnzRVvSUlJ3/CNKsZWG3U7YOm4X6X7uc59D0zRuuOEGoNBM+6d/+qeKvsbrgnRdLldFJF4OJEkiltH5/J3f5cGJZ8ATRVKS/OUTf8lgfJD2QDtff/nrGIaBZVtYWCjCKz6vJmimRqu/lYXcAlk9yxX1V5DUk6T0FBYWJ+tOolkaKT3Fezrew8cPfBy37GY2PcstD9xCTIsRVINIgsR1LddxfO/xYr1wamqqaD7tEFGp9wCAtedKbElB6v81VmgvCBbS0G8xXX7scM9l5+sYxIyMjNDU1LRqE6fSKE2MWMlYqLRpFY1Gi5FBHo9nCRFvVD2QSqXo7+/H7XZv2Z+hXJSa8LS1tdHT01P8vFaSRzllmUQiURyjNQyjWJZxzn+9YzdNk4sXLxKPx9m/f3/ZTnlbadjpur5rUyMGBwcrvuZyCOsUvLe3Gl4hWJZVNKWuBJ6cvMD/8b2XmNc0bGwEMY+n+XZE1zwuyYWMjGAL+FU/C/mFQgcfAZdU+PLnrTw9oR6wIZKMcOuVt3K64TRD8SHcspueUE8h12uF2lcsF+OOoTuYy8xxsOYgb9/z9sskVssbN4lE4jIiDs88iKotgOeVCzOzgF3ThdX9jiVrOW5mfr+frq6uHSOg6elpRkdH2bNnDy0tLWXvMkt9F5xzd9QDTn14+U3IgWEYxSZrb2/vjo2QOvVit9tNd3f3pt9jR6fqnHsymSzGJq107s6ocktLy5bNm1bDciJ2jPZN06Srq+uyCbtK3cxvu+02jhw5woc+9KGKrLcNWPXNfl3sdCuJx6Yf4zN3/JisdhRBTiEAtuklv3g17qafYFs2BoXpIEVWqBVrmcnMIAsyNe4aNFNDtVQyRgbbtmlT23hL81tQJOWyEd7SL4Fz4fokHx/Z95Hio9tKWKlxU0rEiUSC5GwUz2I/lr8Rj8eN34wj1hzAeUB1ouLz+fyOqQPgEskHg8FNScBKfRcaGhqAy8/diQ5ybkJONM3k5CRtbW3s27dvR0oJpVNsvb29W96ZOTpVn89XlEk5NyHnBjQ5OUk2m0XXdWRZpr29fdNDJOWgdEecSCQ4f/484XC4aC6+2q54q4Mdu9XWEV4npFupL5Bpmfznp/8zhnEYhBJnL8HANguNK7/qLzbGskYWgAZPA301fWSMDMfrjvOejvcwlBjCI3lIDaRQpNWJZbmsZwnZ2jZCbBQhM4/trsKu6So2v5ajSMSiSaM5hd3RhqS/hJ19kbzmI+7by1hUIfvoo1iWhWEYVNU1MWxX8dJLUVpCWXwuCRGBvqYAfldlLw1N0xgcHETTtIqT/GrqgVwuRyQSYWBgoLjjmp2dLdoNBoNBPB7PthCws8tsamralmEOB8vNfyYnJ5mYmGDfvn2oqkoikSia/8iyvGRHXCnzH6cZGYvFOHDgwKqf7XrliY0QcSKReIN0dzNs2+arL32Vb53/Flkji+h1Q3I/tiWDYGNbKpJvAAEBVVIxLINbr7gV3dIxbIPTDaep99YvWdNpgj0y+Miar+s0Jla60MSJxxFHHwJJBTOP1XAEq/uGFRthAKQjqPf8GUJqFlJz2L5arM63oebThNtOo7k7iiY/ksvDt5+cJpmJYJoG34jYSKJEjU8hHPDwpZv6qPVvvdRQOmFVbnOuEtB1ndHRURKJBEeOHClOmmmaVtwVzs7OFp3IlpPRZo8xl8vR39+PbdvrGuJUEqlUivPnzxMMBpc0ypbHJjnnvpL5j+P0tZF67OLiIv39/TQ3N3Py5Mk137fNOLGtRsS71UsXXieku9Uv8T3j9/CdC98BGyQk8A9im/eQj14FtoRa/RhK6Oki6X7y0Cd5e9vbN/16pReZc/yXnYORQxx/DDvYwkRC5/mxGMGL9+O1uznWs3JMuPz8t1/ZFQcR8mmEbBQhs0A8sJ/os/eQPtjIqVOnUBSF4fkMii/DoeYGnh6LIkoJBAECCkzNx/nbOx7jdw8WiMgfCDCdlUgbUB9w0V3nK+s9d+RgpUMV243SevHyhhVcijAvJaPV9LROfdxxuVrrnB198fT0dHEoZyfgTM8tLi6yf//+JWPMy6EoCjU1NUvKDaXmPxMTE2WZ/0CBwJ2BjvVMh9bCZht2s7Ozb+x0dzOemH2CvJlHFmVUJHpyWYLK44y1PM3oKzVHURA5UX+C/3rdf93w+s5OtiyydWCZgM1UUueXZ2eRJQHdMPjug0P8obuGK9ouv+CE5DS24gMKabkmIucHBnlS8FDtDdDsayzWUEXx0tRQWrOQRBFJEgj4/diKgafaQ29vG/F4nB89M8WT40mwLURJ4q1dVbzzYOOqyoF0Ok1/fz+Kouzobi+ZTHLhwgX8fv+G6sVr6WlXGmwoJWJRFInFYly4cIHa2todu7nAJWtLx4hnM5uP1fLRHCJebv7jSNwcw//GxsaKP7msNdiRy+X4m7/5G8bHx7ctPn678boh3Y166pai1lWLgICp63wiHuNkNoMquhFEk38OSjzpC+CSPLwj/L/z3SfG2Rv2clVnTVkXm2PvKAhCeWTrQPFihdqZfO553IJKrZgl665BV0LcfX5+RdK1Go8gv/RDTG89+byNnogS9+6jtwYuhM7w5AszhP0qLSEPLSE3bdUeRqMZvKpIVjdpD3gxbZu0ZnBsTxUej4ekITKcXeRwZzOCAFre4MnpFEfqFxkbGytKuBzD6sXFxWLc0U7tRHRd5+LFi6RSKXp7ezccILoSVtsVOkQ8OjpaVA8IgkBra+umRs43g3w+T39/P4ZhbMtNTRt9TIkAACAASURBVBTFy8x/LMsiFosxMDCAYRgoisLIyAhzc3PbZv6z/Jiee+45brnlFt773vcyPDy8Iz4c24HXDeluBk69sSveRaO7kVBqipO5LPOKi4OBg4Rdfv5Sn+fsm/9v7j1bxbceiSEKMSwb3nWwnk9d07Hm+o6IPB6PEwgElqTJrgtBwOq5kYWLGnb8IrPKHs66jnF+SuPF2WlemExwy1vbOSNdQJx8CkQJo+VKUjXHEEcewuVy8UL9TYzVXoPhrSenhhFjOWYSGi0hD7Io8jtXNPPiVIJ4Vqe3wc+jw1EW0zrvOtjAuw4WlAF5w0IUBMRXjtulyHg8Htr2dhLyKkUZ0+joKGNjY6iqiiAIjI6Osri4WPGhhuXv79TUFGNjY7S3ty9J3dgOyLJMdXU1oVCIqakpkskk3d3deL3eogNbOp0uDn84O2Lns98qSs+3q6trSdNwO+G4vI2OjtLd3V00iXd01Mlkcon5T6lqZLPmP6XQNI2//uu/5r777uNrX/saR44cqdSpvSp4Xeh0obDbKTdLbHlyxN69e9FtnXNnv0nnc7fjr+5Gy2ioioJHjzJyw9e45UcD1PgVFAwatFESWYM//ffvIVxV6NSmNYNkzqDGp6LKYrFJFolEmJ6eXtKwcX4k1UUsY+B3SfhWUQuMLmb4i1/0Y5gWIwsZ0nmTfXU+RFGgPXeOP+saIlDXRjoVZ2F8gGzvB2g/eApFdfGtp2aJJDWqPAqabjKf0vm9ky3sb1ylu2zb2DZIYomBkGHyt/cMkdIMqtwKi5k8zSE3n31LB6IgEIvF6O/vp6qqis7OThRFWTLU4GhK8/k8Xq93SZ10K0TsuI8Fg8Hi6+4EnBJGIBCgq6trxckr0zSLOtpEIrGkTuqc/0YbVul0mvPnz+Pz+eju7t72iS8H2WyWc+fO4fV6y3pdR77nnHsymSSbzS5pVpZTI3fw7LPPcsstt/CBD3yAW2+9dTftblc9uf/hSNepg1VVVV0+DJBZQP75/waCQCovoOajKHuO0X/0T/nTn7xEi0fnf1n4W+r1KUzLoqHjAMp7/1/uGcryXx4YBhsCbvn/b+/Mo5uq87//vkmabklX2lK6b2lDaekK6CAigo4oMOLzO6AiDuDDMIdtfhUOAj4jKoLMgMKMHAFFZXTUo46IAwIqHmQZuwBWFtt0p2260S1Jl6z3Pn9kvpeb0j3JTWnv65yeIxxMvkmT9/3cz/L+4M9zFYj0t97ycVMJRqMR2vY2MMUn0VV3Haebx+E/kqmg3DywKFmGB0N0kIoBJiAekFmjGKqtEm0l/8GvDZ14szQIEr8IeP1XoLPaT2J2hAhi0LjSaIKnpQPVnkpMvn8+7o0NRJPOgL9+V4afazRgGCBYLsVfFiYjwn9oRY+WTiO+KmxAvVaP6EAvLEgdDzeY2T7fxMREm11YvdFTiLVaLTvmy70QDfSlMplMKCsrQ1dXFxITE3nrLyaDFRqN5g5P5MFARn25QswwDLy9vW0uRD2FmKZp1maSz4EOhmFQXV2N+vp6JCUl2Z0q4hYrdTrdHeY/JD1F7ggMBgNef/11XLhwAQcPHsSkSZMc8bL4ZPSLrtls7teOkZiZi8ViKBSKPs0sqGYVxLlvQd9cA0NAIrwf2gKjRI7//fwaftP4MWaZzqIFvvB0E0Mh60Zb/EIsLZ4Kb6kYYgqoaOmCwUxjarQflt8bhdQw27yY+vNNGK8+CaOFgogCVD734Be3dKS2f49IHzEsHv6QSKToUC6G3NsDgRVHIXKXAQyNk1dr8W/3+ej0HA+apqFoOYN5AXWoFYVCawQixM247pmFK0wStvw2Ae4SETZ/VQQ3MQVPqRgGkwX+3lJsnzd8BzaapnHz5k00NjYiLi7Orjxmzwmr/oSYYRio1WrU1NQgJiYGISEhvORPuR4NQ52eGwhSsOKKEddzgaIoqNVqhIaGIjIykjcvXOLT4O/vj5iYGKcVBkmOnLz+zs5OfPzxx6itrYVKpcJvf/tbvP7660O+wI0Qxq7o6vV6lJaWoru7e0jFnbq6OhgMBsTEWPO2zR0G1H28FgG6IsDDF+F+nnAzaVHvrcT/bVkMP0831LR1o63TBIBBcqgcZgbYuUCJ8P9Glp9+dxHzCldCx3hDz4jhQRkRQmnR6BEDibkD/nIZPMYnwuQdhk6xHN1GM5iWChjEMrhJpejuaMNnt6JwTjQFRpMJM8KA/xdxFd/+UgVvdzE6JAG4HDAXNToKv78nAh5uYuw/W4lgn9vFjXqNHn9flAJPt6F9kYjXbEVFBcaPH+80EeAKMREig8EAk8kEb29vREVFwd/fn5fbzK6uLqhUKkilUnbYwNnQNA2NRsMa8EulUjAMc0dqxhmvn6ZpVFRUoLW1FUql0iEFyaGg1+uxfft2FBYWYvr06WhsbMTVq1dx4sQJp07VOYmxNwZsMplQWVmJ5uZmNvk/lAhFIpGgs7OT/fM4mTuCs6dDfFkFeHuAoc2AXgtRRAzoWwzMNANNtxkikbW9zMdDgk5dG8rV9Qj3i4GRZvCzqhILQIESu0FkYWBmRBDDBC3tDjfGDJnUD15tFZD4RcLXwx0+/kGgpN1gvAJhMhnRadbg/vFmeEvNkLu7ITVMhpteD+KGbxkMjAQW3wgYIAXNGODn6QZPqRg0rGeTiCh0GMyQuUvgIRmaWBKDGKlUeoevrqPhjroGBgairKwMFEVBoVDAbDazxjcWi8VpQkTTNKqqqnDr1q07Nkc4E67xEDea78sKk+vAZm+OvL29HcXFxRg/fjyysrJ4i6oJBQUFyMnJwaJFi/Dtt9/ylrN2BaPmlXFXVldXV7Nz9tOmTRvWB6g3T106dTGo1nKIyr4D1dEExjMAQS352BATjD1VMf8d5QVSQt0xR/svTOi4gYRfvCE2zgQmLYFaFAKdSA5vugMikTuklg7oGTF+6QpAmkSH6lttiJPT8OhqgSXmATDewZDc+hWmdjXaWlsgoihMnvU/mBoUbfNFTE2Iwz9+boVJ2waIxLgv1g9BUhN8fDyxIHU8jl1thAiARExh3QOxg774mEwmVFRUQKvVQqFQ8JpPrK2t7dXcm+s5QMzRewqRPUJMcv7jx4936vhuT4i9pYeHxx09xj2tMAHbO4KWlhZUVlYOywrTbLbm5js7O5Gamuo0D9m+6O7uxo4dO1BQUICPPvoISqWS1+d3BaMqvVBbW8ve/kZFRdl1tSS9mCkpKezfMQwD2myC29errO5jXuMA2gSq8xZq73kFFxql+OxKPX5jOI/7DOdglIVjWowfJLpamCcvwZs3o9F87QcsN/0THpYOaBhPlDHhcBMBYopCgkiNdpE/0v7PZjDh2TCZzai5/h9QtZcRGhYOz4T7wMh73wel05tR194NymKAJ21t4yHFGoPIE5B6IWa8P8KC/AcUEm7+NCoqCqGhobzkTwGw3RD+/v6IjY0dUj6ReyEiecKeQuzj49Pr58JgMKCkpMSaK1cohj1hNVRIjrypqcluUxxusZK8/v6sMImRemRkJCZMmMDb75iQl5eHDRs24KmnnsL69etHW3Q7+nO6TU1NUKvViIuLc8jtL8nnpaen206SGTvgcWINGJ8w9t9SugaYfpMDJiQFTdfOwDtvLySMAV6R6RBJvazbG0ImQ5++HF8W1uNqWQ3qm5rg7RuE4kYdZlOXMI5uRpc8CmeZTHyy8h401KmhVqvtFj2uQTapmlMUZfMl5FaNuaIXExPD2xeBuydsMN0Qg4UrxESMyLogEg1rNBq2MEh6UPmATLIFBwcjKirKaTnynlaYer0eZrMZYrEY0dHRCAwM7NUK01l0d3dj+/btuHLlCg4dOoTExERenpdnRr/oOtpT12g04pdffkFGRobtJBkYuJ38X8BsADz9AbMeVHcbjA/tglhdAEnu30B1awB9O+AuhyVuNqjOWzAnLwSteBQA0NZlxEvHVfB2F+NcaSvEFGBhAH9PCaL9pVgSa0RQUBCio6OdUjkmfaQ9hdhstlpWDneh53CgaRq1tbXsTjQ+DHFomkZXVxcaGhqgVqtBURTc3Nxs+mgHu0BzOHDb3pRKJW+39GTIgRipS6XSXv2YHTXU0Bs//fQTNm7ciGeeeQbr1q3jbWTaBYx+0WUYBkaj0WGPZbFYcOHCBURERMDHxwe+vr7sB4Rqq4Lbxd2AsQOgRDBnrgAd+Ru4f7YYsJgBsRuotipA3womUAFLzEyYp64GJB7s439ySY2L5a3o0JtR3NgBNzGFeB8Gz2X4IWuSgje/AmI63djYyM7Ra7VaGytA8uNoG0SycnzcuHFOu8D0Blf0kpKS4O3tbbNAk1yMiN+Ao4SY237Gd9pGr9ejqKgI7u7uSEhI6DXXbePH/N+hBqlUaiPEw/0MdHV14ZVXXsHVq1dx6NAhKBR3bjAZZQiiO5THIXaL3d3d0Gg00Gg00Ol0YBiGjYZ8ZZ6QiwygPP0AqfVW2P3T/wFAARJ3gKEBTQ3MGctgSVsKiGwFxUIzuFTdjpu3OkB3tiDM3YDUiUm8FqsGagHjNrRrNBqbL6Gvr2+fGxoGwmAwoLS0FCaTCYmJibxGesSBLDo6ekCzFu7KnJ59tFwhGszForu7G8XFxby2nwG3i5JqtRoKhWLIrVdGo/EOIe7Nl7ev95FhGDa6XbZsGVavXj2ao1sugugO5v8fyAGMpmmbSEin09mYgwTXfAPvok8BNxlAGwGxFMZ5B8DIx9/xfNxV43w2+wPWFjDu+pih5MC50RC5LSXrYgbaWca1P+Q7f0pes7e3N+Li4obdXjaQEPecLOO+5uGInj10dnaiqKgIPj4+iIuLc5jY9TZdJpFIbNIScrkcBoMBL7/8Mn799VccOnSI3SYxRhj9ogtYBWGoDMlusRfMZvNtEdK0Q3bzO4zTXIXIKwCG1GfgHTHJJhrkRpikgMLnbXV5eTnrAuaIqJq7Kkej0dhUzEk0LJfL0dHRgdLSUgQFBfH6mrkr1gfymx0uRIjJHRERYnd3d3R0dCAgIIDX6Jb0GTc3NzvtNfeEa4WZn5+PV199FTqdDkqlEkuXLsXs2bMRFRXl9HOMIMaG6BqNxkHbO9ortgOdgwgQNxr08PBAe3s7ZDIZFAoFb36g3L7XwdxWO+L5SOtSa2srmpqawDAM/Pz84O/v32/rliMhW3TDw8OdtpixN0jva3t7O4KDg6HX69m16lyvgd68FuxFo9GguLjYqR0R/dHR0YGXXnoJJSUl2L17N3Q6HS5fvoyUlBTMnj2b17O4GEF0CWQXGXGld6TY9gVZ4dLR0QEfHx+2ZYf0j5KI0BnRX1tbG0pLS3lvAeOu6YmPj0dgYCC6urrYixFp3errttweuru7oVKpIJFIkJCQwKvZNRH63npfuebg5D1gGMamfW+o7mMEsmpdq9VCqVQ6rOVusDAMg/Pnz+OFF17AypUrsWrVKl4Ev6amBkuXLkVDQwNEIhFWrlyJ9evXO/15B8HYEN2BnMZ67iTjozWJCE9MTIzNZFXP/lFSLSdfQF9fX8hksmF/cLu7u1FaWso2+/M5aUSmukJCQvqNtvrKj3JFaChetFwzHr7zp3q9HiqVCiKRCImJiYNOJfQmxMDQbCDJ++3MVev9odPp8Oc//xkVFRV45513EB0dzdtz19fXo76+HhkZGdDpdMjMzMRXX32FiRMn8naGPhjbouvMVEJvkNYg4tc7WHOYgQp1vr6+Ay5NJGu/b926hYSEBJsVNM6mu7sbJSUlADDsqa6e7wHpIZbJZOwdAXeYg0AWJA4k9I6GYRi2IOqo95v7HpAcMXCnENM0jZKSEhiNRiiVSt7aDAkMw+DHH3/E5s2b8cc//hErV67kPZ3RkwULFmDNmjWYM2eOS8+BsSq6fIstYB0fLikpgZeXl0Om44j9Hbkt780MnXzZSA/ohAkTEBERwdsXgBthOkPoexvmIF6sXl5eaGlpAcMwUCqVvI3vArctEP38/IY8sjxUek4WtrW1wWAwwNfXFyEhIUO+K7AXnU6HF198EdXV1Th06NCIKJJVVVVhxowZuH79+kiwgxwbokvsHV0htnq9HuXl5dDr9VAoFE61xSO9k1whNplM8PDwQFRUFAIDA3mrlDc3N6OsrMypdo+9Qcx4Ghoa4OXlBYvF4vRhDgLJn2o0GiQlJfFqgWgwGFBcXAyxWIy4uDibPlqyoaJnjtiRvxOGYXD27Fls2bIFa9aswYoVK1we3QLWAt7999+PrVu3YuHCha4+DjBWRNdkMsFsNvNaJCMTXU1NTXabeg8Vo9HILmSMjo4GTdPsF9BoNLLTVL6+vg4fayXFKrFYjISEBF5vbbVaLWuyzY0wTSaTTY68q6uLHebg3hXY8/shJjF8d0RwTYgSEhL6XPHe26og7s42e4RYq9XixRdfhFqtxsGDBxEZGWnvy3IIJpMJjz32GB5++GHk5OS4+jiEsSG6GzduZNdvZ2Zmsu77zoB4n1ZWVrrkdl6tVvfbAkas/7ita/YUqQgkZ9zc3IyEhARei1Xcrb9JSUmDWtVjzzBHz8dRqVQAgMTERF47Irq6ulBUVDTs/Wi9pWdEItGghZhhGPzwww/YunUr1q9fj2XLlo2I6Bawnu3ZZ59FQEAA9u7d6+rjcBkboqtSqZCbm4u8vDxcuXIFRqMRkyZNQmZmJrKzs5GcnOwQo2uNRoOSkhLI5XLExsbydisPWAtGpaWlCAwMHPIqFVIpJ0JMoiCuAPW3MJD41oaGhvJ6kSFGLVVVVXZ7FnCHOciPwWBg18j39KHlRpjcTbh8QLpfGhsb7bZ97ElfQsxdpS6Xy6HX67FlyxY0NTXhwIEDiIiIcNgZHMGFCxdw3333ISUlhf087tixA3PnznXxycaI6PZEr9ejsLAQubm5KCgowI0bN+Dl5YXMzExkZWUhKytrSJVusvrHbDYjISGBt6WIgGM6A3qjt0KdRCJhOwV8fHzYKrmbmxvvfa9kCy7ZRuuMNTV9Lc10d3dHV1cXfHx8oFDwZ0IEWAtVRUVF7MWVjwscV4jPnz+PXbt2QaPRICUlBU899RTmzJkzIgpmdwljU3R7wjAMWltbUVBQwArxzZs3ER4ejuzsbFaM/f39bSIpbhsWsT3kC4vFwm6DJUMGzoYUZ9rb29HQ0ACDwQC5XI7AwEA2R+zs6J687tbWVl634JLnrqioQHNzM0JCQthcMdeHl+TJHd2xQF53W1sblEolrxd2Qnt7OzZv3ozW1lbs2bMHTU1N7FTZrFmzeD/PXYogun1B5tTz8vKQl5eHS5cusTPj6enpaG5uRldXF9atW4ewsDBeb6lJzpg0vfP53MQfYsKECQgLC4PJZLLJD3MLdY4e6yVpjAkTJvD6uoHbgwYkT99zosyRwxw9aWtrg0qlYrf/8j3kwDAMTp8+jW3btmHDhg1YsmQJb+/98uXLcfz4cQQHB+P69eu8PKeTEUR3KJhMJnz00UfYvn07/P1vr7fJyMhARkYGsrKykJCQ4LS+TJ1OZ+OIxWfOuLOzEyqVivVd7eu5nVGo40518elNAVij+5KSEpjNZiQlJQ06ldDXRBl3srC3YQ4uZrOZ3VjNd68xoa2tDS+88AK0Wi3efvttTJgwgdfnP3fuHGQyGZYuXSqIruPPcnfw6aefIiMjAwqFAgzDQKfT4dKlS8jLy0N+fj7KysoQHBxskx+2157RaDSy5tqJiYm89n9y3biGsqqeS1+FOrlcbjNN1ptlJhmX5nuKjmEY1NXVobq6GnFxcQgODrb7MfsqUvVWsLx16xbKysp4NzUnMAyDkydP4uWXX8amTZvw1FNPuawzoaqqCo899pgguo4/y+iAfFlJWiI/P59toyItaxkZGQOO7QK3V9ao1WrevXW52wyc0XtqsVhY8dFoNDYbKXx9fcEwDKqqqhAcHIzo6Ghev/CkSDfcVqyhQAqW5H3o7OyEwWCAm5sbIiMjERgY6LRhjr5obW3Fpk2b0N3djf3797Obll2FILpWBNEdAhaLBUVFRcjLy0NBQQGuXLkCi8WC1NRUNhpWKpU2X+7m5maUl5fzvrIGsE7xlJSUsGbmfKUxjEYjWltbUVVVBYPBAIlEYrOx19mFOpqm2eIk30U67vaKqKgouLu7O3WYo68znDhxAq+++iq2bNmCxYsX8x5h94YgulYE0bUD0op0+fJl5OfnIy8vD8XFxfD19UV8fDxu3LiBxYsX45lnnuHVis9sNqOiogIajcZhZuaDhdv3Ghsby97OGwwGXgp1pFjF99gyYG37KyoqgqenZ5/tbz1HvLkLI7krkoZLS0sLNm7cCLPZjP379yMkJMSel+RQBNG1Ioiug6FpGhs2bMCJEycwffp0Nq0QHR3NRsMZGRnw9fV1SoRDhgwiIiIQFhbGa4RDDGJ8fX0RGxvbr4iSQh0RIK7/LncjxWBF02QysY5cSUlJvBaruE5kw7GcJCvUBzPM0d8Zvv76a+zYsQNbt27FokWLRkR0y0UQXSuC6DqBb7/9FrNmzWJFh6ZplJWVsbnhy5cvo6urC8nJyawQT5o0ya4Ih+wIc+aQQV+YzWZ2TZA9BUJup4BGoxlUoY57oeE7Xw5Y3/eioiKHOpExDHOHEBuNRnh5edlckMjvuLm5Gc8//zwoisJbb73lkGKho3nyySdx9uxZtjf65ZdfxooVK1x9LHsQRPduw2g0orCwkBXi69evw8PDA+np6awQx8bGDhjpETcurVaLxMREXi3vuL3GvW1ScATcQp1Wq0VnZydbqPPw8EBjYyO8vLygUCh4vdBw88Z87Cnj3hmQn507d6KzsxPl5eVYtWoVcnJyXDJsMUYRRPduh2EYtLe3o6CggC3UVVRUICwsDBkZGexEHXE543ZEuKIdifT78l2kA6z54bKyMrS0tMDT0xNmsxnu7u5sFOjsQh3ZUxYSEsJ73pjQ1NSEnJwcUBSFmTNnori4GIWFhfj+++9d0gc8BhFEdzRC1nvn5uYiPz8fBQUFaG9vR0hICGpra7FkyRKsWLHCqW5rPeG6kDnapGUwtLe3Q6VSISgoiG1B62tjMfd23BGFOovFgrKyMtYFje89ZYD14vzll1/iL3/5C7Zt24aFCxfyerE9deoU1q9fD4vFgueeew4vvPACb889whBEd6yQk5ODc+fO4ZFHHkF9fT0KCwtBURTS0tLYQY7ExESntKYRQ3O+XcgAaxqFDJYolcoBd8I5ulBHxofDw8N5L1ASGhsb8fzzz8PT0xP79u3j1SMEsF50FAoFvvvuO9bP5JNPPhkJ+8pcgSC6Y4XCwkJMnjzZZgFmR0cHLl++zKYlSkpKEBgYiMzMTGRmZmLKlCl2rWUn244B8O7GxR3usDeN0ttILynUcUd6uY9vMpmgUqmGPD7sSGiaxr/+9S/s3r0br7zyCn73u9+5RPR/+uknbNu2DadPnwYA7Ny5EwCwefNm3s8yAujzF8DPPm4B3khLS7P5MxGNmTNnYubMmQBuV/Tz8/ORm5uLw4cPs6vSifdweno6ZDJZv19ekt6or6/n3X0NsPa9FhcXQyqVIjMz0+48LXdUl0BGejUaDSorK9lCnVwuB8MwaGlpQVxcHO9dEYSGhgbk5ORALpfj7NmzvI5Q90StVtv47YaHhyMvL89l5xmpCKI7BqEoCqGhoViwYAEWLFgAwCouJSUlyM3NxbFjx7Bt2zYYjUakpKSwQjxx4kS2A6C+vh7V1dUYN24csrOzeZ2k44q9s1eti8Vi+Pn52eSmidctTdPw9PREZWUl6urqbPLDzjbroWkan332Gd58801s374d8+fPd3nfbW93za4+00hEEF1Y1/z8+9//hlQqRVxcHN5//33eC0CuRiwWQ6lUQqlUYtmyZQCsaYOff/4Zubm5+Pvf/44bN26wYjJu3Djs2LGDN4NtgkajgUqlQmBgIO9iT6bpamtr7zDmIX2zGo0G1dXVbKGOO0nmKG+HhoYGrF+/HgEBAfjxxx95XZnUH+Hh4aipqWH/XFtby7tb2d2AkNOF7bDCpk2bAAC7du1y8alGHidPnsTGjRsxb948uLm54dKlS6iurkZkZCRr8pOZmXmHCbwj4A5YKJVK3jsDiDmOTCZDfHz8gGLfW98sKdQRIZbJZENet/Tpp5/ib3/7G3bs2IFHH310REWSZrMZCoUCZ86cQVhYGLKzs/Hxxx8jOTnZ1UdzBUIhbbAcPXoUX3zxBf75z3+6+igjjpqaGjZqI5AhAK4JfEdHByZOnMh2S6SmptpVYGpqakJ5ebnTBiz6g6ZpdttzUlKSXT4VxASdtK0NplBHqK+vx/r16xEUFIQ33ngD/v7+9rwsp/HNN9/gT3/6EywWC5YvX46tW7e6+kiuQhDdwTJv3jwsWrQIS5YscfVR7lqMRiOuXbvGCvG1a9fg5uaG9PR0Nj8cHx8/YFqCa2qemJjI64AFcHvVO3GAc0Yaheu9SywfxWIxfHx8oFarERISgitXrmD//v3YuXMn5s6dO6KiW4E+EUR39uzZaGhouOPvX3vtNbaY9Nprr+HSpUv48ssvhQ+2A2EYBlqt1sYEvry8HCEhITYm8MHBwaAoCmazGdXV1WhqauLd1By4beje3t7ukj1lZCfbu+++i6NHj0KtViM9PR333nsv1qxZMyK9EwTuQBDdgThy5AgOHDiAM2fODNhYPxQ+//xzbNu2DUVFRcjPz0dWVpbDHvtuhhSl8vLy2CWhLS0tCA4ORm1tLX7/+99j2bJlvE7TAVZj75KSkl53pPEFTdP46KOP8Pbbb2PXrl14+OGHUVdXh4KCAsycOXPMFXnvUgTR7Y9Tp04hJycHP/74I4KCghz62EVFRRCJRPjDH/6A3bt3C6LbDy+++CJOnjyJ+fPnQ61W4+effwbDMDYm8ElJSU7Z8GAymVBaWgqDwcC79SOX2tparFu3DhEREdi9ezevXsc9EQIGuxBEtz/i4+Nh5J5ZAQAABbhJREFUMBjY29hp06bhwIEDDn2OmTNnCqI7AFeuXEFaWhqbOyUdAFwTeJVKBX9/f7ZTIjs72+6xW1Koi46Otmsyzx5omsY//vEPHDx4EH/9618xZ84cl6e4hIDBLoSJtP4oKytz9REEYN22zIWiKHh7e2PGjBmYMWMGgNvr4UmR7siRI6irq0NMTIyNCbyPj8+AomUwGKBSqUBRlEMm2oZLTU0N1q5di9jYWJw/f55X+83+UCqVrj7CqEQQXQcwmCKdgGOgKArBwcGYN28e5s2bB+C2CXxubi5OnjyJ7du3Q6/X32ECT0SVpml2oi4+Pt7hKaXBQtM0PvjgA7zzzjvYs2cPHnzwQZdHtwLORxBdB/D999/z+nyCfZ4tIpEICoUCCoUCS5cuBWCNYokJ/MGDB1kT+Pj4eFy7dg3PPfcclixZ4rLotrq6GmvWrIFCocDFixddZi4uBAz8I4juXYbFYsHq1att7PPmz58/Vu3z+sTd3R1Tp07F1KlTAVjTErt27cJ7772HBx54AKdPn8aBAwcQFhbGRsOZmZkIDAx0arRJ0zQOHz6M999/H3v27MGsWbNcGt3yHTAICKLrdI4ePYq1a9fi1q1bePTRR5GWlsZa3w2H/Px8xMfHIzY2FgCwePFiHDt2TBDdAaAoCqmpqbh69So7HUfTNKqrq5Gbm4vz58/jjTfegEajQVJSElukmzx5ssM6GaqqqrBmzRpMnDgRFy5cEFbnjFGE7oW7jC+++AKnTp3Cu+++CwD48MMPkZeXh7feesvFJxsdmEwm3Lhxg+0dLiwshEgkYqfpsrKyoFAohuSZYLFYcPjwYXzwwQfYu3cv7r///rsid8sNGPz8/OwOGMYYQvfCaEGwz3Mubm5uSEtLQ1paGlatWmVjAp+bm4sdO3agpKQEQUFBrAhnZ2f36adbWVmJtWvXIiUlBRcvXnTJCp/h8vjjj+Pxxx939TFGHYLo3mU42z5v+fLlOH78OIKDg3H9+nWHPe7dSl8m8PX19awJ/KFDh9DU1MSawGdlZWHy5Mn45JNP8OGHH2Lfvn247777hIujAAAhvXDX4Wz7vHPnzkEmk2Hp0qWC6A4Bi8UClUrF9g+fOnUKU6ZMwQcffODQsfKhIPhEuxRhIm004Wz7vKqqKjz22GOC6NoBwzAuj2wFn2iXIuR0RxNz587F3LlzXX0MgX5wteACwEMPPcT+97Rp0/DFF1+48DQCBP72rAgICLiM9957D4888oirjyEAQXQFeKSmpgYPPPAAlEolkpOTsW/fPlcf6a5n9uzZmDRp0h0/x44dY//Na6+9BolEgqefftqFJxUgCOkFAd6QSCTYs2cPMjIyoNPpkJmZiTlz5giDHXYw0ETZkSNHcPz4cZw5c2ZEpDwEhEhXoAdPPvkk7rnnHqhUKoSHh+Pw4cMOe+zQ0FDWSUwul0OpVEKtVjvs8QVsOXXqFHbt2oWvv/7aZR0UAncidC8IuISqqirMmDED169fHzFWhqMNPnyiBfpE6F4QGDl0dHTgiSeewN69ewXBdSKCT/TIREgvCPCKyWTCE088gaeffhoLFy506GPr9XpMmTIFkydPRnJyMl566SWHPr6AgCMQ0gsCvMEwDJ599lkEBARg7969Tnn8zs5OyGQymEwmTJ8+Hfv27cO0adMc/lwCAgPQZ3pBiHQFeOPixYv48MMP8cMPP7CmMt98843DHp+iKNYu0WQywWQyCRV7gRGHkNMV4I3p06f36pLmSCwWCzIzM1FWVobVq1ezJuYCAiMFIdIVGFWIxWIUFhaitrYW+fn5gn+EwIhjoJyugMBdC0VRLwHoZBhmt6vPIiBAECJdgVEDRVFBFEX5/fe/PQHMBlDs2lMJCNgi5HQFRhOhAI5QFCWGNaD4jGGY4y4+k4CADUJ6QUBAQIBHhPSCgICAAI8IoisgICDAI4LoCggICPDI/we0iZgIpXkroQAAAABJRU5ErkJggg==\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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:39.082218Z", "iopub.status.busy": "2021-05-19T06:00:39.081719Z", "iopub.status.idle": "2021-05-19T06:00:39.083899Z", "shell.execute_reply": "2021-05-19T06:00:39.084316Z" } }, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:39.088976Z", "iopub.status.busy": "2021-05-19T06:00:39.088150Z", "iopub.status.idle": "2021-05-19T06:00:39.639886Z", "shell.execute_reply": "2021-05-19T06:00:39.640376Z" } }, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:39.652901Z", "iopub.status.busy": "2021-05-19T06:00:39.651599Z", "iopub.status.idle": "2021-05-19T06:00:39.877708Z", "shell.execute_reply": "2021-05-19T06:00:39.878291Z" } }, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:39.882023Z", "iopub.status.busy": "2021-05-19T06:00:39.881458Z", "iopub.status.idle": "2021-05-19T06:00:39.883385Z", "shell.execute_reply": "2021-05-19T06:00:39.883838Z" } }, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:39.891861Z", "iopub.status.busy": "2021-05-19T06:00:39.887760Z", "iopub.status.idle": "2021-05-19T06:00:39.967652Z", "shell.execute_reply": "2021-05-19T06:00:39.968250Z" } }, "outputs": [ { "data": { "text/plain": [ "[Text(0, 0, 'DCD'), Text(0, 0, 'DCD2'), Text(0, 0, 'NAMD')]" ] }, "execution_count": 1, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:39.986837Z", "iopub.status.busy": "2021-05-19T06:00:39.986321Z", "iopub.status.idle": "2021-05-19T06:00:40.086598Z", "shell.execute_reply": "2021-05-19T06:00:40.086980Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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DaPoMEZFOFA4iIpKh14ZDXtNn9DuppLWIiHRHV1cjndq/fLM59NpwyGv6jL79S1qLiEh3/OipHTmXb7l9apkq6cXhkBf1OYhIDLy9/3DUJbRTOIAm3hORyJVzgFt3KBxAE++JSORu/822nMuz96KWjsIBYNCIqCsQkYT78FBrzuVfHX92mSpJUThUnQCTbou6ChGRnH447fNl3Z7C4YSToW5G1FWIiMSKwkEzsoqIZIgsHMxsqpntMLNdZrYgqjoYeHpkmxYR6Y6B/cr/pzqScDCzKuCnwOXA+cAsMzs/ilpEROLujul1Zd9mVEcOlwC73H23u/8dWAFcGUklOq0kIjE37aLqsm8zqnCoBt5K+7kpaOvAzOaaWaOZNba0tJSmEp1WEhHJEFU4ZBvPkTHtkbsvcfd6d68fMmRIGcoSERGILhyagPSRZzXAO5FUotNKIiIZogqHl4BaMxtlZicAM4F1xdxAt6fs1mklEZEMkYSDu38CzAOeArYDq9w998Qi+W4jnym7RURiLIpJ+SIb5+Duj7v7ue5+jrsvjqoOTdctInHX1X0eSkEjpDVdt4jEQPVpA0OXRXGfB4WDpusWkRi4ecqY0GV9yj1fNwoHHTmISCzkGujWFkFnqcJBRw4iIhkUDgMHR12BiEjsKBxERCSDwkEjpEVEMigcNEJaRCSDwkFEJAaiGAWdi8JBp5VEJAZyjYI+MSl3gouVQTVRVyAiEsko6FwSHg4Gk26LuggREaosfBj0oda2MlaSkvBwcKibEXURIiIc83jNGZ3scNAAOBGJiVwT70Uh2eEgIhITuSbei0Kyw0FXKolITDT+NV73lkl2OGgAnIjEwPcefY1fvfifUZfRQbLDQUQkBpbFLBgg6eGg00oiEgNdXac0UIPgykynlUSkAtwxva7s20x2OIiIVIBcd4krlWSHw+F4XR0gIhIXyQ4H3T9aRGLuf4w/O5LtJjscdP9oEYmBsACoHXoSP5z2+TJXk9I3kq3GhY4cRCQGjgfA8o1vccydKjNm/dOIyIIBkh4OOnIQkZj44bTPRxoGnSX7tJIm3hMRySrZ4SAiIlklOxw0QlpEJKtkh4NuESoiklWyw6G2IeoKRERiKdnhsPPpqCsQEYmlZIfDgaaoKxARiaVEhsP6k05MPVCfg4hIVr02HAadMCj7AjPuPCOYqnvSbeUrSESkgvTacFj4TwtDl+3v0wcwqJtRvoJERCpIQeFgZleb2TYzazOz+k7LFprZLjPbYWZT0tovNrPXgmX3mpkVUkOYK0Zf0cUzurr3kohIchV65LAVmA48n95oZucDM4GxwFTgZ2bts9z9HJgL1AZfUwusoWc0dYaISKiCwsHdt7v7jiyLrgRWuPtRd38T2AVcYmbDgVPd/U/u7sAvgWmF1CAiIsVXqj6HauCttJ+bgrbq4HHn9qzMbK6ZNZpZY0tLS3Er1NQZIiKhupyy28x+C5yVZdEt7r42bLUsbZ6jPSt3XwIsAaivry9uJ8HA04v6ciIivUmX4eDul/XgdZuAEWk/1wDvBO01WdpFRCRGSnVaaR0w08z6m9koUh3Pm9y9GfjYzMYHVyldB4QdfZTW4Q8i2ayISCUo9FLWq8ysCZgArDezpwDcfRuwCngdeBK4wb39tmv/CvxfUp3UfwGeKKSGHtMtQkVEQhV0m1B3fwR4JGTZYmBxlvZG4HOFbLcodItQEZFQvXaEdJd05CAiEiq54aAjBxGRUMkNB42QFhEJldxwEBGRUMkNB42QFhEJldxw0AhpEZFQyQ0HEREJldxw0AhpEZFQyQ0HjXMQEQmV3HDQOAcRkVDJDQeNcxARCZXccBARkVDJDQd1SIuIhEpuOKhDWkQkVHLDQR3SIiKhkhsO6pAWEQmV3HAQEZFQyQ0HTbwnIhIqueGgifdEREIlNxxERCRUcsNB4xxEREIlNxw0zkFEJFRyw0HjHEREQiU3HDTOQUQkVHLDQUREQiU3HNQhLSISKrnhoA5pEZFQyQ0HdUiLiIRKbjjoyEFEJFRyw0FHDiIioZIbDrqUVUQkVHLDQUREQiU3HDRlt4hIqOSGw6CaqCsQEYmt5IZDbUPUFYiIxFZyw2Hn01FXICISWwWFg5n9yMzeMLMtZvaImZ2Wtmyhme0ysx1mNiWt/WIzey1Ydq+ZWSE19NiBtyLZrIhIJSj0yOEZ4HPuXgf8GVgIYGbnAzOBscBU4Gdm7aPOfg7MBWqDr6kF1tAzGgQnIhKqoHBw96fd/ZPgxxeB4728VwIr3P2ou78J7AIuMbPhwKnu/id3d+CXwLRCaugxDYITEQlVzD6HfwGeCB5XA+nnbZqCturgcef2rMxsrpk1mlljS0tLEUsFBo0o7uuJiPQifbt6gpn9Fjgry6Jb3H1t8JxbgE+AZcdXy/J8z9GelbsvAZYA1NfXhz6vRybdVtSXExHpTboMB3e/LNdyM5sN/DdgUnCqCFJHBOn/Na8B3gnaa7K0l5cZ1M0o+2ZFRCpFoVcrTQX+Dfjv7n4obdE6YKaZ9TezUaQ6nje5ezPwsZmND65Sug5YW0gNIiJSfF0eOXThPqA/8ExwReqL7v5Nd99mZquA10mdbrrBvb0H+F+BB4GBpPoonsh4VRERiVRB4eDun8mxbDGwOEt7I/C5QrYrIiKlldwR0iIiEkrhICIiGXp1OFwz5pq82kVEJKXQDulY+9747wHw0J8fos3b6GN9uPrcq9vbRUQkO/vH0IR4q6+v98bGxqjLEBGpKGb2srvX57terz6tJCIiPaNwEBGRDAoHERHJoHAQEZEMCgcREclQMVcrmVkL8NcINn0m8H4E2+2JSqm1UuoE1VoqlVJrpdQJ4bV+2t2H5PtiFRMOUTGzxp5cBhaFSqm1UuoE1VoqlVJrpdQJxa9Vp5VERCSDwkFERDIoHLq2JOoC8lAptVZKnaBaS6VSaq2UOqHItarPQUREMujIQUREMigcREQkQ6LDwcyuNrNtZtZmZvWdli00s11mtsPMpqS1X2xmrwXL7rXg5tlm1t/MVgbtG81sZAnrXmRmb5vZq8HXl3pad7mZ2dSgtl1mtiCKGjrVsyfYL6+aWWPQNtjMnjGzncH309Oen3X/lqi2B8xsr5ltTWvLu7ZyvPchtcbuc2pmI8xsg5ltD/7tzw/aY7dfc9Ranv3q7on9Aj4LjAGeA+rT2s8H/gPoD4wC/gJUBcs2ARMAA54ALg/avwX8Ing8E1hZwroXAd/N0p533WXe31VBTaOBE4Jaz4/4M7AHOLNT2/8CFgSPFwB3dbV/S1TbRGAcsLWQ2srx3ofUGrvPKTAcGBc8PgX4c1BP7PZrjlrLsl8TfeTg7tvdfUeWRVcCK9z9qLu/CewCLjGz4cCp7v4nT+3xXwLT0tZZGjx+GJgUwf/Oe1J3OV0C7HL33e7+d2BFUHPcpL+XS+n4Hmfs31IV4e7PAx8UUlu53vuQWsNEVqu7N7v7K8Hjj4HtQDUx3K85ag1T1FoTHQ45VANvpf3cFLRVB487t3dYx90/AQ4AZ5SwxnlmtiU4nD9+CNyTussprL4oOfC0mb1sZnODtmHu3gypf6DA0KA9DvXnW1vU731sP6fBqd+LgI3EfL92qhXKsF97fTiY2W/NbGuWr1z/Y832P37P0Z5rnR7pou6fA+cAFwLNwP8uoO5yiksd6S5193HA5cANZjYxx3PjWP9xcXzvY/s5NbOTgdXAje7+Ua6nhtQUZa1l2a+9+h7SAO5+WQ9WawJGpP1cA7wTtNdkaU9fp8nM+gKD6P5hdobu1m1m/wd4rIC6yymsvsi4+zvB971m9gip00Tvmdlwd28ODsn3Bk+PQ/351hbZe+/u7x1/HKfPqZn1I/XHdpm7rwmaY7lfs9Varv3a648cemgdMNNSVyCNAmqBTcHh5sdmNj7oT7gOWJu2zuzg8ZeB3wXn94ou+PAedxVw/AqRntRdTi8BtWY2ysxOINVxvy6COgAws5PM7JTjj4EGUvsy/b2cTcf3OGP/lrfq/GqL8r2P4+c0eN37ge3ufnfaotjt17Bay7Zfi9m7XmlfwY5tAo4C7wFPpS27hVRv/w7SevaB+uDN+AtwH/8YZT4AeIhUJ9AmYHQJ6/5/wGvAluADMbyndUewz79E6qqLvwC3RPz+jyZ1dcd/ANuO10Oqr+hZYGfwfXBX+7dE9S0nddqgNficfq0ntZXjvQ+pNXafU+C/kDqlsgV4Nfj6Uhz3a45ay7JfNX2GiIhk0GklERHJoHAQEZEMCgcREcmgcBARkQwKBxERyaBwEBGRDAoHERHJ8P8ByVLPZti2WjMAAAAASUVORK5CYII=\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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:40.096943Z", "iopub.status.busy": "2021-05-19T06:00:40.096283Z", "iopub.status.idle": "2021-05-19T06:00:40.226034Z", "shell.execute_reply": "2021-05-19T06:00:40.226379Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:00:40.230299Z", "iopub.status.busy": "2021-05-19T06:00:40.229747Z", "iopub.status.idle": "2021-05-19T06:01:08.831730Z", "shell.execute_reply": "2021-05-19T06:01:08.832264Z" } }, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:01:08.837023Z", "iopub.status.busy": "2021-05-19T06:01:08.836407Z", "iopub.status.idle": "2021-05-19T06:01:08.838722Z", "shell.execute_reply": "2021-05-19T06:01:08.839117Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[0. , 0.25148565, 0.59436574],\n", " [0.25148565, 0. , 0.59185462],\n", " [0.59436574, 0.59185462, 0. ]])" ] }, "execution_count": 1, "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" }, "execution": { "iopub.execute_input": "2021-05-19T06:01:08.842891Z", "iopub.status.busy": "2021-05-19T06:01:08.842304Z", "iopub.status.idle": "2021-05-19T06:01:08.844397Z", "shell.execute_reply": "2021-05-19T06:01:08.844736Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[0. , 0.07238521, 0.05236259],\n", " [0.07238521, 0. , 0.05092071],\n", " [0.05236259, 0.05092071, 0. ]])" ] }, "execution_count": 1, "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 }