{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "# Calculating the RDF atom-to-atom\n", "\n", "We calculate the site-specific radial distribution functions of solvent around certain atoms.\n", "\n", "**Last updated:** December 2022 with MDAnalysis 2.4.0-dev0\n", "\n", "**Minimum version of MDAnalysis:** 0.19.0\n", "\n", "**Packages required:**\n", " \n", "* MDAnalysis (Michaud-Agrawal *et al.*, 2011, Gowers *et al.*, 2016)\n", "* MDAnalysisTests\n", "\n", "**Optional packages for visualisation:**\n", "\n", "* [matplotlib](https://matplotlib.org)\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:58:29.353011Z", "iopub.status.busy": "2021-05-19T05:58:29.352352Z", "iopub.status.idle": "2021-05-19T05:58:30.289550Z", "shell.execute_reply": "2021-05-19T05:58:30.290032Z" } }, "outputs": [], "source": [ "import MDAnalysis as mda\n", "from MDAnalysis.tests.datafiles import TPR, XTC\n", "from MDAnalysis.analysis import rdf\n", "import matplotlib.pyplot as plt\n", "import numpy as np\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": { "execution": { "iopub.execute_input": "2021-05-19T05:58:30.294493Z", "iopub.status.busy": "2021-05-19T05:58:30.293625Z", "iopub.status.idle": "2021-05-19T05:58:31.229943Z", "shell.execute_reply": "2021-05-19T05:58:31.229178Z" } }, "outputs": [], "source": [ "u = mda.Universe(TPR, XTC)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculating the site-specific radial distribution function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A radial distribution function $g_{ab}(r)$ describes the time-averaged density of particles in $b$ from the reference group $a$ at distance $r$. It is normalised so that it becomes 1 for large separations in a homogenous system. See [the tutorial on averaged RDFs](average_rdf.ipynb) for more information. The `InterRDF_s` class ([API docs](https://docs.mdanalysis.org/stable/documentation_pages/analysis/rdf.html#MDAnalysis.analysis.rdf.InterRDF_s)) allows you to compute RDFs on an atom-to-atom basis, rather than simply giving the averaged RDF as in `InterRDF`.\n", "\n", "Below, I calculate the RDF between selected alpha-carbons and the water atoms within 15 angstroms of CA60, *in the first frame of the trajectory*. The water group does not update over the trajectory as the water moves towards and away from the alpha-carbon. \n", "\n", "The RDF is limited to a spherical shell around each atom by `range`. Note that the range is defined around *each atom*, rather than the center-of-mass of the entire group.\n", "\n", "If `density=True`, the final RDF is over the average density of the selected atoms in the trajectory box, making it comparable to the output of `rdf.InterRDF`. If `density=False`, the density is not taken into account. This can make it difficult to compare RDFs between AtomGroups that contain different numbers of atoms." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:58:31.235366Z", "iopub.status.busy": "2021-05-19T05:58:31.234786Z", "iopub.status.idle": "2021-05-19T05:58:31.854793Z", "shell.execute_reply": "2021-05-19T05:58:31.855177Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/pbarletta/mambaforge/envs/guide/lib/python3.9/site-packages/MDAnalysis/analysis/rdf.py:531: DeprecationWarning: The `u` attribute is superflous and will be removed in MDAnalysis 3.0.0.\n", " warnings.warn(\"The `u` attribute is superflous and will be removed \"\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ca60 = u.select_atoms('resid 61 and name CA')\n", "ca61 = u.select_atoms('resid 62 and name CA')\n", "ca62 = u.select_atoms('resid 63 and name CA')\n", "water = u.select_atoms('resname SOL and sphzone 15 group sel_a', sel_a=ca60)\n", "\n", "ags = [[ca60+ca61, water], [ca62, water]]\n", "\n", "ss_rdf = rdf.InterRDF_s(u, ags,\n", " nbins=75, # default\n", " range=(0.0, 15.0), # distance\n", " norm='density',\n", " )\n", "ss_rdf.run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Like `rdf.InterRDF`, the distance bins are available at `ss_rdf.bins`." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:58:31.859860Z", "iopub.status.busy": "2021-05-19T05:58:31.859307Z", "iopub.status.idle": "2021-05-19T05:58:31.861752Z", "shell.execute_reply": "2021-05-19T05:58:31.862184Z" } }, "outputs": [ { "data": { "text/plain": [ "array([ 0.1, 0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5, 1.7, 1.9, 2.1,\n", " 2.3, 2.5, 2.7, 2.9, 3.1, 3.3, 3.5, 3.7, 3.9, 4.1, 4.3,\n", " 4.5, 4.7, 4.9, 5.1, 5.3, 5.5, 5.7, 5.9, 6.1, 6.3, 6.5,\n", " 6.7, 6.9, 7.1, 7.3, 7.5, 7.7, 7.9, 8.1, 8.3, 8.5, 8.7,\n", " 8.9, 9.1, 9.3, 9.5, 9.7, 9.9, 10.1, 10.3, 10.5, 10.7, 10.9,\n", " 11.1, 11.3, 11.5, 11.7, 11.9, 12.1, 12.3, 12.5, 12.7, 12.9, 13.1,\n", " 13.3, 13.5, 13.7, 13.9, 14.1, 14.3, 14.5, 14.7, 14.9])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ss_rdf.results.bins" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`ss_rdf.rdf` contains the atom-pairwise RDF for each of your pairs of AtomGroups. It is a list with the same length as your list of pairs `ags`. A result array has the shape `(len(ag1), len(ag2), nbins)` for the AtomGroup pair `(ag1, ag2)`. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:58:31.867176Z", "iopub.status.busy": "2021-05-19T05:58:31.866041Z", "iopub.status.idle": "2021-05-19T05:58:31.868917Z", "shell.execute_reply": "2021-05-19T05:58:31.868467Z" }, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "There are 1041 water atoms\n", "The first result array has shape: (2, 1041, 75)\n", "The second result array has shape: (1, 1041, 75)\n" ] } ], "source": [ "print('There are {} water atoms'.format(len(water)))\n", "print('The first result array has shape: {}'.format(ss_rdf.results.rdf[0].shape))\n", "print('The second result array has shape: {}'.format(ss_rdf.results.rdf[1].shape))" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "Index the results array to get the RDF for a particular pair of atoms. `ss_rdf.rdf[i][j][k]` will return the RDF between atoms $j$ and $k$ in the $i$-th pair of atom groups. For example, below we get the RDF between the alpha-carbon in residue 61 (i.e. the second atom of the first atom group) and the 571st atom of water." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:58:31.872815Z", "iopub.status.busy": "2021-05-19T05:58:31.872315Z", "iopub.status.idle": "2021-05-19T05:58:31.874585Z", "shell.execute_reply": "2021-05-19T05:58:31.874939Z" }, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "array([0. , 0. , 0. , 0. , 0. ,\n", " 0. , 0. , 0. , 0. , 0. ,\n", " 0. , 0. , 0. , 0. , 0. ,\n", " 0. , 0. , 0. , 0. , 0. ,\n", " 0.0023665 , 0. , 0. , 0. , 0. ,\n", " 0. , 0. , 0. , 0. , 0.00114292,\n", " 0.00106921, 0. , 0.00094167, 0. , 0. ,\n", " 0. , 0.0007466 , 0. , 0. , 0. ,\n", " 0. , 0. , 0.00055068, 0. , 0. ,\n", " 0. , 0. , 0. , 0. , 0. ,\n", " 0. , 0. , 0. , 0. , 0. ,\n", " 0. , 0.0003116 , 0. , 0. , 0. ,\n", " 0. , 0. , 0.00025464, 0.00024669, 0. ,\n", " 0. , 0. , 0. , 0. , 0. ,\n", " 0. , 0. , 0. , 0. , 0. ])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ca61_h2o_571 = ss_rdf.results.rdf[0][1][570]\n", "ca61_h2o_571" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:58:31.889621Z", "iopub.status.busy": "2021-05-19T05:58:31.888908Z", "iopub.status.idle": "2021-05-19T05:58:31.994719Z", "shell.execute_reply": "2021-05-19T05:58:31.995133Z" } }, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'RDF between CA61 and MW6365')" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(ss_rdf.results.bins, ca61_h2o_571)\n", "w570 = water[570]\n", "plt.xlabel('Radius (angstrom)')\n", "plt.ylabel('Radial distribution')\n", "plt.title('RDF between CA61 and {}{}'.format(w570.name, w570.resid))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you are having trouble finding pairs of atoms where the results are not simply 0, you can use Numpy functions to find the indices of the nonzero values. Below we count the nonzero entries in the first `rdf` array." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:58:31.999184Z", "iopub.status.busy": "2021-05-19T05:58:31.998414Z", "iopub.status.idle": "2021-05-19T05:58:32.002173Z", "shell.execute_reply": "2021-05-19T05:58:32.002636Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4374 4374 4374\n" ] } ], "source": [ "j, k, nbin = np.nonzero(ss_rdf.results.rdf[0])\n", "print(len(j), len(k), len(nbin))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Each triplet of `[j, k, nbin]` indices is a nonzero value, corresponding to the `nbin`th bin between atoms $j$ and $k$. For example:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:58:32.007000Z", "iopub.status.busy": "2021-05-19T05:58:32.006227Z", "iopub.status.idle": "2021-05-19T05:58:32.009198Z", "shell.execute_reply": "2021-05-19T05:58:32.009731Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 0.00028\n" ] } ], "source": [ "print(f\"{ss_rdf.results.rdf[0][j[0], k[0], nbin[0]]: .5f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Right now, we don't care which particular bin has a nonzero value. Let's find which water atom is the most present around the alpha-carbon of residue 60, i.e. the first atom." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:58:32.014116Z", "iopub.status.busy": "2021-05-19T05:58:32.013437Z", "iopub.status.idle": "2021-05-19T05:58:32.016651Z", "shell.execute_reply": "2021-05-19T05:58:32.017050Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The water atom with the highest distribution around CA60 has index 568\n" ] } ], "source": [ "# where j == 0, representing the first atom\n", "water_for_ca60 = k[j==0]\n", "# count how many of each atom index are in array\n", "k_values, k_counts = np.unique(water_for_ca60, \n", " return_counts=True)\n", "# get the first k value with the most counts\n", "k_max = k_values[np.argmax(k_counts)]\n", "print('The water atom with the highest distribution '\n", " 'around CA60 has index {}'.format(k_max))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can also calculate a cumulative distribution function for each of your results with `ss_rdf.get_cdf()`. This is the actual count of atoms within the given range, averaged over the trajectory; the volume of each radial shell is not taken into account. The result then gets saved into `ss_rdf.cdf`. The CDF has the same shape as the corresponding RDF array." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:58:32.020554Z", "iopub.status.busy": "2021-05-19T05:58:32.019986Z", "iopub.status.idle": "2021-05-19T05:58:32.023642Z", "shell.execute_reply": "2021-05-19T05:58:32.024163Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(2, 1041, 75)\n" ] } ], "source": [ "cdf = ss_rdf.get_cdf()\n", "print(cdf[0].shape)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:58:32.037826Z", "iopub.status.busy": "2021-05-19T05:58:32.037243Z", "iopub.status.idle": "2021-05-19T05:58:32.136373Z", "shell.execute_reply": "2021-05-19T05:58:32.137071Z" }, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'RDF between CA60 and HW16365')" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(ss_rdf.results.bins, ss_rdf.results.cdf[0][0][568])\n", "w568 = water[568]\n", "plt.xlabel('Radius (angstrom)')\n", "plt.ylabel('Radial cumulative distribution')\n", "plt.title('RDF between CA60 and {}{}'.format(w568.name, w568.resid))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The site-specific RDF without densities" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When the `density` of the selected atom groups over the box volume is not accounted for, your distribution values will be proportionally lower." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "[array([[[0. , 0. , 0. , ..., 0.1, 0.1, 0.1],\n", " [0. , 0. , 0. , ..., 0.1, 0.1, 0.1],\n", " [0. , 0. , 0. , ..., 0.1, 0.1, 0.1],\n", " ...,\n", " [0. , 0. , 0. , ..., 0.1, 0.1, 0.1],\n", " [0. , 0. , 0. , ..., 0.1, 0.1, 0.1],\n", " [0. , 0. , 0. , ..., 0.1, 0.1, 0.1]],\n", " \n", " [[0. , 0. , 0. , ..., 0. , 0.1, 0.1],\n", " [0. , 0. , 0. , ..., 0. , 0. , 0. ],\n", " [0. , 0. , 0. , ..., 0.1, 0.1, 0.1],\n", " ...,\n", " [0. , 0. , 0. , ..., 0.1, 0.1, 0.1],\n", " [0. , 0. , 0. , ..., 0.1, 0.1, 0.1],\n", " [0. , 0. , 0. , ..., 0.1, 0.1, 0.1]]]),\n", " array([[[0. , 0. , 0. , ..., 0. , 0.1, 0.1],\n", " [0. , 0. , 0. , ..., 0. , 0. , 0. ],\n", " [0. , 0. , 0. , ..., 0.1, 0.1, 0.1],\n", " ...,\n", " [0. , 0. , 0. , ..., 0. , 0. , 0.1],\n", " [0. , 0. , 0. , ..., 0. , 0. , 0. ],\n", " [0. , 0. , 0. , ..., 0. , 0. , 0. ]]])]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ss_rdf_nodensity = rdf.InterRDF_s(u, ags,\n", " nbins=75, # default\n", " range=(0.0, 15.0), # distance\n", " density=False,\n", " )\n", "ss_rdf_nodensity.run()\n", "ss_rdf_nodensity.get_cdf()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2021-05-19T05:58:32.717827Z", "iopub.status.busy": "2021-05-19T05:58:32.717256Z", "iopub.status.idle": "2021-05-19T05:58:32.823568Z", "shell.execute_reply": "2021-05-19T05:58:32.823941Z" } }, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'RDF between CA61 and MW6365')" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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8fJfSqrOHH34YAErtjaLgwq3nFDSaNWumNCX37NkTVqsVH3zwAT799FPcd999qp9n/fr1kCQJ3bp189naMjIySr0m/yNQs2ZNAMCLL76IQYMGlfocTZo08fh55K3EW7ZsQVpaGvr27atc//e//43vvvsOBQUFDsFOzZo1UaNGDWzcuLHU55T/cZLX+OmnnzoECr7Ws2dPGI1GrFu3TtUZKFu2bFECVOeAASj6h+zw4cNo3rw5GjZs6PaoAFHc41GRpmR7y5YtQ48ePfDee+85XLdv5PWG/NrcfS+Vx2OPPYZ///vfkCQJw4YNK/Penj17IjU1Fdu2bcO2bdtw5513Ko/Jgc13332nNC7LgRAAl2Zye0IIVV/zTp06AQCOHTuGtm3bIiwsDCkpKaW+drV/lr7+Myft4p8wBa0ZM2agevXqmDRpkupG4kWLFmHDhg148MEHlQyDL6xYscKhYfLMmTPYtWuXckhdkyZNkJKSgp9++skleyS/yUGH8//47dWpUwfNmzfHZ599hvT0dCXY6du3L/7880+kpqYiOjoaHTt2VD7mrrvuwuXLl2G1Wkv9vHKQ1b9/fxgMBpw4ccLtGn0hPj4eTz75JDZt2uR2p9GJEydw8OBBAEWNtTqdDuvWrcPWrVsd3pYuXQqg6PwYADAYDLj77rtx5MgRh0MZhRDYuHEjGjZsqAR1FSVJkvJnJTt48CB2795drudr0qQJ6tSp4/Z7qTyGDRuGv/3tb3j++edx0003lXlvt27doNfr8emnn+LQoUMOByzGxMSgTZs2WLJkCU6fPq00NMvq1KmDzp074/vvv3c4wyc3Nxfbt29XtTNu69atAIBGjRop1/7+978jKyvL5fV//fXXiIyMRIsWLcp8Tvn7S83npwDnxxIakU+4O2dHCCFmzJghAIilS5cq17p37y4aNGggdu/eLXbv3i2+/fZb8cEHH4i77rpLABDdu3d36CsQouLn7CQmJoq7775bfPnll+Ljjz8WjRo1ElFRUeK3335T7v3222+FyWQS/fr1E8uXLxfbt28Xa9euFVOnThX33Xefct/JkycFAHHPPfeIHTt2iL1794q//vpLeXzUqFECgAgLC3PomUlOThYAxMCBAx3WaLFYxB133CFiY2PFq6++KjZs2CC2bNkiFi9eLIYNGybWrFmj3Dt16lRhMBjE8OHDxdq1a8W2bdvEqlWrxPjx48WkSZOU+4YNGyYiIiJcvh5yb40neXl5on///kKSJPHQQw+J1atXi++++06sWbNGPPXUUyI0NFSsW7dO/PXXX8JkMok77rjD7XO1a9dO1KpVSxQWFgohhPjtt99EtWrVRJMmTcSKFSvEV199Je69914hSZLLeUh79+4Vq1evFqtXrxaJiYmiefPmyvv2PT+lmTRpkpAkSUyaNEl88803Yt68eSI+Pl40bNjQob9G7tn573//6/IcAMTkyZOV9z/44AMBQPleWrZsmWjUqJFITEz0umfHHXc9O0II0bFjRyFJktDr9SIzM9PhsbFjxwpJkgQAkZaW5vKx33//vQgJCRG33nqrWLt2rVi3bp24/fbbhdFoFLt27VLumzRpkhg+fLj4+OOPxbZt28S6devEiBEjhF6vF/fff7/Dc16+fFnUq1dPJCQkiA8//FBs2rRJOSfIvrfp448/Fn//+9/FwoULxTfffCM+++wzMWTIEAFAPProox6/bhT4GOxQwCsr2MnLyxP16tUTKSkpyk6X7t27OzSLRkREiAYNGoj77rtPrF692uEgOVlFg52lS5eK0aNHi1q1agmTySRuv/128eOPP7rc/9NPP4nBgweL2rVrC6PRKOLj40WvXr3E/PnzHe6bNWuWSE5OFnq93uUfps8//1wAEH379nX4GPkfgdmzZ7t8XrPZLN566y1x8803i9DQUBEZGSmaNm0qhg8fLo4fP+5w77p160TPnj1FdHS0MJlMIikpSdx3331iy5Ytyj0VDXaEKArClixZInr16iViY2OFwWAQtWrVEnfccYdYvny5sFqtYtasWQKAWLdundvnmT9/vstus59//lkMGDBAREVFidDQUHHrrbc6HIBn/zrsv1fs30oLBuwVFBSI5557Ttx0000iNDRUtGvXTqxbt87lAEBvgh0higKelJQUERISIho3biwWLlzo9aGCZSkr2JkwYYIAoOzisrdu3Tql+TsnJ6fU596xY4fo3r27CA8PF+Hh4aJXr17i+++/d7hn/fr1ok+fPiIuLk4YDAYRGRkpOnXqJGbPnu2yU1GIot1fQ4YMEdWrVxchISGidevWLgeJ7t69W/Tu3VvEx8cLo9EowsPDRceOHcW8efNK/ftOwUcSopTDCIiIiIiCBHt2iIiIKKgx2CEiIqKgxmCHiIiIghqDHSIiIgpqDHaIiIgoqDHYISIioqDGcREomq1z4cIFREVFlTkbhoiIiLRDCIHs7GwkJCSUOfaDwQ6ACxcuIDEx0d/LICIionI4d+4c6tat6/ZxBjsoGXR47tw5REdH+3k1REREpEZWVhYSExOVf8fdYbADKKWr6OhoBjtEREQBxlMLChuUiYiIKKgx2CEiIqKgxmCHiIiIghqDHSIiIgpqDHaIiIgoqDHYISIioqDGYIeIiIiCGoMdIiIiCmoMdoiIiCioMdghIiKioMZgh4iIiIIagx0iIiIKagx2iHwgr9Dq7yUQEZEbDHaIKui/m37Fza9txuELWf5eChERlYLBDlEF7TtzDYUWG45cZLBDRKRFDHaIKshqEw6/EhGRtjDYIaogs83m8CsREWkLgx2iCrJYhcOvRESkLQx2iCrIUly+srCMRUSkSQx2iCrIYrU5/EpERNrCYIeogqzM7BARaRqDHaIKkhuT2bNDRKRNDHaIKkhpUOZuLCIiTWKwQ1RBbFAmItI2BjtEFcQGZSIibWOwQ1RBchnLzJ4dIiJNYrBDVEEWjosgItI0BjtEFSQ3JrNBmYhImxjsEFWAEEIpX7GMRUSkTQx2iCrAvnLFMhYRkTYx2CGqALPdDiwzd2MREWkSgx2iCrA/W4cnKBMRaZNfgx2LxYJ///vfSE5ORlhYGBo0aIDXXnsNNrtGTyEEpkyZgoSEBISFhaFHjx44dOiQw/MUFBRg1KhRqFmzJiIiIjBw4ED8/vvvVf1y6AZktQtweKggEZE2+TXYefPNNzF//nzMnTsXR44cwYwZM/Df//4Xc+bMUe6ZMWMGUlNTMXfuXOzduxfx8fHo27cvsrOzlXvGjBmDtWvXYuXKldi5cyeuX7+Ou+66C1ar1R8vi24gZrvAnLuxiIi0yeDPT757927cfffdGDBgAACgfv36WLFiBX788UcARVmdWbNm4eWXX8agQYMAAEuWLEFcXByWL1+O4cOHIzMzEx9++CGWLl2KPn36AACWLVuGxMREbNmyBf379/fPi6MbgpVlLCIizfNrZue2227DN998g2PHjgEAfvrpJ+zcuRN33nknAODUqVPIyMhAv379lI8xmUzo3r07du3aBQBIT0+H2Wx2uCchIQEtW7ZU7iGqLPZNyczsEBFpk18zOxMnTkRmZiaaNm0KvV4Pq9WKN954Aw8++CAAICMjAwAQFxfn8HFxcXE4c+aMck9ISAiqV6/uco/88c4KCgpQUFCgvJ+VleWz10Q3FvtsDjM7RETa5NfMzqpVq7Bs2TIsX74c+/btw5IlS/DWW29hyZIlDvdJkuTwvhDC5Zqzsu6ZNm0aYmJilLfExMSKvRC6YTnsxmKDMhGRJvk12Hn++efxwgsvYMiQIWjVqhUeeeQRjB07FtOmTQMAxMfHA4BLhubSpUtKtic+Ph6FhYW4evWq23ucvfjii8jMzFTezp075+uXRjcICxuUiYg0z6/BTm5uLnQ6xyXo9Xpl63lycjLi4+ORlpamPF5YWIjt27ejS5cuAID27dvDaDQ63HPx4kX88ssvyj3OTCYToqOjHd6IyoNlLCIi7fNrz87f/vY3vPHGG6hXrx5atGiB/fv3IzU1FY8//jiAovLVmDFjMHXqVKSkpCAlJQVTp05FeHg4HnroIQBATEwMnnjiCYwfPx41atRAbGwsnnvuObRq1UrZnUVUWVjGIiLSPr8GO3PmzMErr7yCkSNH4tKlS0hISMDw4cMxadIk5Z4JEyYgLy8PI0eOxNWrV3HLLbdg8+bNiIqKUu6ZOXMmDAYDBg8ejLy8PPTu3RuLFy+GXq/3x8uiG4jFfjcWx0UQEWmSJIS44f87mpWVhZiYGGRmZrKkRV7ZfeIyHnx/DwDgpmph+P6FXn5eERHRjUPtv9+cjUVUAfaHCnLqORGRNjHYIaoAjosgItI+BjtEFWC/A8vM3VhERJrEYIeoAqx22RyWsYiItInBDlEFmB0yOyxjERFpEYMdogqw8pwdIiLNY7BDVAH22RyrTYAnORARaQ+DHaIKcM7mMLtDRKQ9DHaIKsA5uGGTMhGR9jDYIaoA5xERbFImItIeBjtEFeA86ZyTz4mItIfBDlEFsGeHiEj7GOwQVYBzGYsjI4iItIfBDlEFmJ0zOyxjERFpDoMdogqw2pwzOwx2iIi0hsEOUQW4NiizjEVEpDUMdogqwDmTw8nnRETaw2CHqAKcMzk8VJCISHsY7BBVgHODspm7sYiINIfBDlEFWHmoIBGR5jHYIaoA50wOz9khItIeBjtEFcBxEURE2sdgh6gCnBuS2aBMRKQ9DHaIKsB5yjmnnhMRaQ+DHaIK4CBQIiLtY7BDVAEMdoiItI/BDlEFuEw9ZxmLiEhzGOwQVQB3YxERaR+DHaIKcD5Xh2UsIiLtYbBDVAFycBNq1BW/zzIWEZHWMNghqgC5bBVm1APg1HMiIi1isENUAXImJ7Q42LEys0NEpDkMdogqQM7shDKzQ0SkWQx2iCqgpGenKNjhbiwiIu1hsENUAfK5OnKDMstYRETaw2CHqALMcmbHoHd4n4iItIPBDlEFyFPOw0LkMhYzO0REWsNgh6gCzE5lLB4qSESkPQx2iCpA2Y1lYIMyEZFWMdghqgC5jGWSd2Mxs0NEpDkMdogqwGxzKmOxZ4eISHMY7BCVk9UmIIoTOWHM7BARaRaDHaJysh/6Gcpgh4hIsxjsEJWTfTMyy1hERNrFYIeonOyzOJx6TkSkXQx2iMrJPotjMnDqORGRVjHYISonObOjkwCjQXK4RkRE2sFgh6ic5MDGoNfBoCv6q2Rmzw4RkeYw2CEqJ7mMZdRJMOqLMjtWZnaIiDSHwQ5ROcnNyHqdBL2S2WGwQ0SkNQx2iMpJzuIY9ToY9HLPDstYRERaw2CHqJzk/hyDXoJRJ5+zw8wOEZHWMNghKielQVmng17H3VhERFrFYIeonOQzdQx6NigTEWkZgx2icnJsUJaKr7Fnh4hIaxjsEJWT3J9j1Olg1LNnh4hIqxjsEJWTxa6MVbIbi8EOEZHWMNghKic5i2PQSTDouPWciEirGOwQlVNp4yJYxiIi0h4GO0TlpJSxdBIPFSQi0jAGO0TlpJSx9BIzO0REGsZgh6ic7A8VtG9QFoIBDxGRljDYISonZeq53bgIgAcLEhFpDYMdonIy2+wOFSzO7ADcfk5EpDUMdojKyaoMAtUpW88BnqJMRKQ1DHaIyknO4Bh1knKCMsAyFhGR1jDYISqnktlYOtgldpTrRESkDQx2iMpJnnpu1EuQpJLJ5zxrh4hIW/we7Jw/fx4PP/wwatSogfDwcLRp0wbp6enK40IITJkyBQkJCQgLC0OPHj1w6NAhh+coKCjAqFGjULNmTURERGDgwIH4/fffq/ql0A3Gfuq5/a88a4eISFv8GuxcvXoVXbt2hdFoxIYNG3D48GG8/fbbqFatmnLPjBkzkJqairlz52Lv3r2Ij49H3759kZ2drdwzZswYrF27FitXrsTOnTtx/fp13HXXXbBarX54VXSjsCiZnaK/RvL2c+7GIiLSFoM/P/mbb76JxMRELFq0SLlWv3595fdCCMyaNQsvv/wyBg0aBABYsmQJ4uLisHz5cgwfPhyZmZn48MMPsXTpUvTp0wcAsGzZMiQmJmLLli3o379/lb4munGUHCpYlNGRDxa0soxFRKQpfs3srF+/Hh06dMD999+P2rVro23btnj//feVx0+dOoWMjAz069dPuWYymdC9e3fs2rULAJCeng6z2exwT0JCAlq2bKnc46ygoABZWVkOb0TekstV8hk7+uLMDhuUiYi0xa/BzsmTJ/Hee+8hJSUFmzZtwogRIzB69Gh89NFHAICMjAwAQFxcnMPHxcXFKY9lZGQgJCQE1atXd3uPs2nTpiEmJkZ5S0xM9PVLoxuAVdl6XlzG0rNnh4hIi/wa7NhsNrRr1w5Tp05F27ZtMXz4cPzzn//Ee++953CfJEkO7wshXK45K+ueF198EZmZmcrbuXPnKvZC6IZkVg4VdCxjcTcWEZG2+DXYqVOnDpo3b+5wrVmzZjh79iwAID4+HgBcMjSXLl1Ssj3x8fEoLCzE1atX3d7jzGQyITo62uGNyFvK1HO5Z4cNykREmuTXYKdr1644evSow7Vjx44hKSkJAJCcnIz4+HikpaUpjxcWFmL79u3o0qULAKB9+/YwGo0O91y8eBG//PKLcg9RZVAalIt3Y8lBD8dFEBFpi193Y40dOxZdunTB1KlTMXjwYPzwww9YsGABFixYAKCofDVmzBhMnToVKSkpSElJwdSpUxEeHo6HHnoIABATE4MnnngC48ePR40aNRAbG4vnnnsOrVq1UnZnEVUGuVxVshurKOjhuAgiIm3xa7DTsWNHrF27Fi+++CJee+01JCcnY9asWRg6dKhyz4QJE5CXl4eRI0fi6tWruOWWW7B582ZERUUp98ycORMGgwGDBw9GXl4eevfujcWLF0Ov1/vjZdENwrWMxQZlIiItkoQQXv1kzsnJwfTp0/HNN9/g0qVLsDk1Y548edKnC6wKWVlZiImJQWZmJvt3SLXhS3/EpkN/4D/3tMTDtybh3nnfY//Za1jwSHv0axHv7+UREQU9tf9+e53ZefLJJ7F9+3Y88sgjqFOnjsddUUTByl1mh2UsIiJt8TrY2bBhA7766it07dq1MtZDFDDMLg3KOofrRESkDV7vxqpevTpiY2MrYy1EAcV+6jlgd84Od2MREWmK18HO66+/jkmTJiE3N7cy1kMUMJynnisNyszsEBFpitdlrLfffhsnTpxAXFwc6tevD6PR6PD4vn37fLY4Ii2TMzhy+UouZ3E3FhGRtngd7Nxzzz2VsAyiwKPMxiouXxk59ZyISJO8DnYmT55cGesgCjjOZSxOPSci0qZyHyqYnp6OI0eOQJIkNG/eHG3btvXluog0rySzUzz1XMdBoEREWuR1sHPp0iUMGTIE27ZtQ7Vq1SCEQGZmJnr27ImVK1eiVq1albFOIs0xu4yLYIMyEZEWeb0ba9SoUcjKysKhQ4dw5coVXL16Fb/88guysrIwevToylgjkSYphwrqHctYbFAmItIWrzM7GzduxJYtW9CsWTPlWvPmzfHuu++iX79+Pl0ckZbJZSx5N5aR5+wQEWmS15kdm83mst0cAIxGo8ucLKJgZpa3nsuHCsqZHZaxiIg0xetgp1evXnj22Wdx4cIF5dr58+cxduxY9O7d26eLI9Iyi1Nmhz07RETa5HWwM3fuXGRnZ6N+/fpo2LAhGjVqhOTkZGRnZ2POnDmVsUYiTbK4ZHaKfjWzjEVEpCle9+wkJiZi3759SEtLw6+//gohBJo3b44+ffpUxvqINKsks8Op50REWlbuc3b69u2Lvn37+nItRAGlZDeW47gIHipIRKQtqoKd2bNn41//+hdCQ0Mxe/bsMu/l9nO6UciHBxqdz9lhGYuISFNUBTszZ87E0KFDERoaipkzZ7q9T5IkBjt0Q7DZBORqlfPUc5axiIi0RVWwc+rUqVJ/T3SjMtsds6CUseTZWAx2iIg0xevdWK+99hpyc3Ndrufl5eG1117zyaKItM4+e+M89ZxlLCIibfE62Hn11Vdx/fp1l+u5ubl49dVXfbIoIq2zb0J2nnrOc3aIiLTF62BHCAFJklyu//TTT4iNjfXJooi0ziGz43yoIDM7RESaonrrefXq1SFJEiRJQuPGjR0CHqvViuvXr2PEiBGVskgirZEDGp0E6HROZSxmdoiINEV1sDNr1iwIIfD444/j1VdfRUxMjPJYSEgI6tevj86dO1fKIom0xuw0KgLg1HMiIq1SHewMGzYMAJCcnIwuXbqUOgyU6EZhVQ4ULMlwyuftWDgQl4hIU7w+QTk5ORkXL150+3i9evUqtCCiQCBvPZfP1gFKtqCzjEVEpC1eBzv169cvtUFZZrVaK7QgokDgPCoCKAl8WMYiItIWr4Od/fv3O7xvNpuxf/9+pKam4o033vDZwoi0zFJqZodTz4mItMjrYOfmm292udahQwckJCTgv//9LwYNGuSThRFpmZLZsQt29BwXQUSkSV6fs+NO48aNsXfvXl89HZGmKZkduzKWkT07RESa5HVmJysry+F9IQQuXryIKVOmICUlxWcLI9IySym7seQsD8tYRETa4nWwU61aNZcGZSEEEhMTsXLlSp8tjEjLLDbXMpZ85g7LWERE2uJ1sLN161aH93U6HWrVqoVGjRrBYPD66YgCkqWUQwVLGpQZ7BARaYnX0Un37t0rYx1EAUUeF2G0P1RQz0MFiYi0qFypmKNHj2LOnDk4cuQIJElC06ZN8cwzz6Bp06a+Xh+RJsnZG73DbqziMhYzO0REmuL1bqxPP/0ULVu2RHp6Om6++Wa0bt0a+/btQ6tWrbB69erKWCOR5sh9OaUdKmhmZoeISFO8zuxMmDABL774Il577TWH65MnT8bEiRNx//33+2xxRFoll6ocy1hsUCYi0iKvMzsZGRn4xz/+4XL94YcfRkZGhk8WRaR1JWUs+6nnJQ3KQjDgISLSCq+DnR49emDHjh0u13fu3Inbb7/dJ4si0jqrnNnRuTYoFz3OYIeISCtUlbHWr1+v/H7gwIGYOHEi0tPTceuttwIA9uzZg9WrV+PVV1+tnFUSaYy5tEMF7fp3LDYBg77Kl0VERKVQFezcc889LtfmzZuHefPmOVx7+umnMWLECJ8sjEjL5K3nDufs2GV5ODKCiEg7VAU7Nu4uIXKgHCpYyrgIoCQYIiIi//PZIFCiG4kc7OhLmXpu/zgREfmfqszO7Nmz8a9//QuhoaGYPXt2mfeOHj3aJwsj0jLlBGW7MpYkSTDoJFhsQhkUSkRE/qcq2Jk5cyaGDh2K0NBQzJw50+19kiQx2KEbQmllLPl9i01w8jkRkYaoCnZOnTpV6u+JblRy5sa+T6fofR0AG7eeExFpiFc9O2azGQ0aNMDhw4craz1EAcFSyriIovc5DJSISGu8CnaMRiMKCgogSZLnm4mCmLL13LmMVdzDY2bPDhGRZni9G2vUqFF48803YbFYKmM9RAFByey4lLGK3mcZi4hIO7weBPq///0P33zzDTZv3oxWrVohIiLC4fE1a9b4bHFEWiWXqewPFQRKMj1sUCYi0g6vg51q1arh73//e2WshShgyA3KRqcyljz5nOfsEBFph9fBzqJFiypjHUQBpbSp50XvFzcos2eHiEgzvO7Z6dWrF65du+ZyPSsrC7169fLFmog0T5l67tKgzN1YRERa43Wws23bNhQWFrpcz8/Px44dO3yyKCKtM5cyLgKw33rOzA4RkVaoLmMdPHhQ+f3hw4eRkZGhvG+1WrFx40bcdNNNvl0dkUaVbD13alAuLmuxjEVEpB2qg502bdpAkiRIklRquSosLAxz5szx6eKItEreWm7UOTcoyz07LGMREWmF6mDn1KlTEEKgQYMG+OGHH1CrVi3lsZCQENSuXRt6vb5SFkmkNSUNyo7BjtKgzDIWEZFmqA52kpKSAAA2Nl4SKQ3IRqcyVsnWc/49ISLSCq8blJcsWYKvvvpKeX/ChAmoVq0aunTpgjNnzvh0cURapQwCdbMbi+MiiIi0w+tgZ+rUqQgLCwMA7N69G3PnzsWMGTNQs2ZNjB071ucLJNIid+Mi5HN3OC6CiEg7vD5U8Ny5c2jUqBEAYN26dbjvvvvwr3/9C127dkWPHj18vT4iTSoJdpzLWGxQJiLSGq8zO5GRkbh8+TIAYPPmzejTpw8AIDQ0FHl5eb5dHZFGuZ16rufUcyIirfE6s9O3b188+eSTaNu2LY4dO4YBAwYAAA4dOoT69ev7en1EmqT07DgPAuXUcyIizfE6s/Puu++ic+fO+PPPP/HZZ5+hRo0aAID09HQ8+OCDPl8gkRYpU8/dNShzNxYRkWaUa+r53LlzXa6/+uqrPlkQUSCQe3ZcZmPpg+sE5d+v5uLP7AK0rVfd30shIio3VcHOwYMH0bJlS+h0OoexEaVp3bq1TxZGpGUWN1PPDUF2qOCIZen45XwWPnq8E7o1ruX5A4iINEhVsNOmTRtkZGSgdu3aytgIIUp+mMvvS5IEq9VaaYsl0gqljOVuEGiQ7MY6f7Vo08FrXx7GhmdvdzlEkYgoEKj6yXXq1CllPMSpU6dw8uRJnDp1SnmT3z958mS5FzJt2jRIkoQxY8Yo14QQmDJlChISEhAWFoYePXrg0KFDDh9XUFCAUaNGoWbNmoiIiMDAgQPx+++/l3sdRGp4OlQwWBqU88xF/3n57dJ1fLSbh4YSUWBSFewkJSVBkiTl92W9lcfevXuxYMEClxLYjBkzkJqairlz52Lv3r2Ij49H3759kZ2drdwzZswYrF27FitXrsTOnTtx/fp13HXXXcwwUaUyy1vPnctYQbT1XAiBfHNJhmrWlmO4fL3AjysiIiofVWWs9evXq37CgQMHerWA69evY+jQoXj//ffxn//8R7kuhMCsWbPw8ssvY9CgQQCKRlXExcVh+fLlGD58ODIzM/Hhhx9i6dKlynk/y5YtQ2JiIrZs2YL+/ft7tRYitaxuGpSNSs9O4JexCiwlr6FhrQic+DMHb20+immD2JdHRIFFVbBzzz33OLxfWs+OzNuMytNPP40BAwagT58+DsHOqVOnkJGRgX79+inXTCYTunfvjl27dmH48OFIT0+H2Wx2uCchIQEtW7bErl273AY7BQUFKCgo+R9qVlaWV2smMtvcTT2XB4EGfmYnr7Dk7/J/7mmFB9/fg5V7z2HoLUloeVOMH1dGROQdVWUsm82mvG3evBlt2rTBhg0bcO3aNWRmZuLrr79Gu3btsHHjRq8++cqVK7Fv3z5MmzbN5bGMjAwAQFxcnMP1uLg45bGMjAyEhISgevXqbu8pzbRp0xATE6O8JSYmerVuIrkB2blhN5galPMtRcGOUS+hc8MaGHhzAoQApqw/5PCfHSIirfN6a8WYMWPwzjvvoH///oiOjkZUVBT69++P1NRUjB49WvXznDt3Ds8++yyWLVuG0NBQt/fZZ40AKLu+yuLpnhdffBGZmZnK27lz51Svm8hmE5ATN867sUpmYwV+MCBndkINegDAi3c2RZhRjx/PXMX6ny74c2lERF7xOtg5ceIEYmJcU9gxMTE4ffq06udJT0/HpUuX0L59exgMBhgMBmzfvh2zZ8+GwWBQMjrOGZpLly4pj8XHx6OwsBBXr151e09pTCYToqOjHd6I1LIvUTk3KAdVGat4J1ZoSFGwUycmDE/3bAgAmPb1r8gttPhtbURE3vA62OnYsSPGjBmDixcvKtcyMjIwfvx4dOrUSfXz9O7dGz///DMOHDigvHXo0AFDhw7FgQMH0KBBA8THxyMtLU35mMLCQmzfvh1dunQBALRv3x5Go9HhnosXL+KXX35R7iHyNftt5c5bz5XMThA0KMs7scKMeuXak7c3QGJsGDKy8jFv6wl/LY2IyCtej4tYuHAh7r33XiQlJaFevXoAgLNnz6Jx48ZYt26d6ueJiopCy5YtHa5FRESgRo0ayvUxY8Zg6tSpSElJQUpKCqZOnYrw8HA89NBDAIqySU888QTGjx+PGjVqIDY2Fs899xxatWql7M4i8jX7uVeu5+wEz9bzfDmzYyz5P1GoUY+X72yOEcvSsWDHSTx8axLiY9yXoYmItMDrYKdRo0Y4ePAg0tLS8Ouvv0IIgebNm6NPnz4ee2m8NWHCBOTl5WHkyJG4evUqbrnlFmzevBlRUVHKPTNnzoTBYMDgwYORl5eH3r17Y/HixdDr9WU8M1H52ffjBPPUcznYsc/sAED/FnFoEheFo39k4+fzmQx2iEjzvA52gKKm4X79+jls+faFbdu2uXyeKVOmYMqUKW4/JjQ0FHPmzMGcOXN8uhYid+QSlSS5bj2XMz3mINiNJffsmJyCHUmSUCMyBPij5B4iIi3joBsiL8mZHaPO9a9PME09l3djOWd27K/lsUmZiAIAgx0iL5VMPHct2wZVGcvi2qAsk3do2R88SESkVQx2iLykTDzXuw92zMGwG6vQtUFZpmR2zIH/Ooko+DHYIfKSfIaO84GCgP0JykGQ2ZEblENcMzvhcmaHPTtEFABUNSh7MzuKB/RRsFMmnutL6dkJwkMFTQb27BBRYFMV7FSrVk31iAZvB4ESBRpl4nmZmZ3AL+/klZHZCTUys0NEgUNVsLN169bKXgdRwJAPDNSX2rNTlNkJigblUk5QloUpDcqBH9QRUfBTFex07969stdBFDCUieelbj0PogblUk5QlpX07LCMRUTaV65DBQEgNzcXZ8+eRWFhocP11q1bV3hRRFomZ21K240lB0BB1aBc2tZzI7eeE1Hg8DrY+fPPP/HYY49hw4YNpT7Onh0KdmabfM6Oa8ZDPnsnmBqUQ8s6VJA9O0QUALzeej5mzBhcvXoVe/bsQVhYGDZu3IglS5YgJSUF69evr4w1EmmKtbhEZSwtsxNMDcqF7oOdkjJW4L9OIgp+Xmd2vv32W3z++efo2LEjdDodkpKS0LdvX0RHR2PatGkYMGBAZayTSDPkBuXSz9kJojJWGScoc+s5EQUSrzM7OTk5qF27NgAgNjYWf/75JwCgVatW2Ldvn29XR6RBFiXYKe2cneApY+WXkdkJ5aGCRBRAvA52mjRpgqNHjwIA2rRpg//3//4fzp8/j/nz56NOnTo+XyCR1pQ5LkIuYwXBbqySc3bKGBfBredEFAC8LmONGTMGFy9eBABMnjwZ/fv3x8cff4yQkBAsXrzY1+sj0hwls1PGCcpmq1AO2gxU+WU0KCs9OyxjEVEA8DrYGTp0qPL7tm3b4vTp0/j1119Rr1491KxZ06eLI9IiJbNTxtRzALAJoJTkT8BQuxtLTVC39/QVzP7mOKYMbIGGtSJ9v1giojJUeBBoeHg42rVrx0CHbhhqBoECJTO0AlVBGScoyz07NgEUqnidn+w9hx3H/8LXBy/6dpFERCqoyuyMGzcOr7/+OiIiIjBu3Lgy701NTfXJwoi0qqSM5X5cBBDYTcoWq00JYsrK7ABAfqGt1GGh9nKKy13XWfYiIj9QFezs378fZrNZ+b07gdyfQKSWMvW8jHERAGAN4O3n8rZzoPTMjlGvg1EvwWwVyDVbEANjmc+XU1BUEsst4O4tIqp6Xg8C5VBQutGVNS7CvrQVyPOx8u22lJsMpVe7Q416mK0WVSMj5HtyOV6CiPygwj07RDeasnp2JElSRkYE8uRzOTgxGXTQlfI6Ae9GRshlrFyWsYjID1RldgYNGqT6CdesWVPuxRAFAqWMVcrWc6AoCLLaREA3KBdY5DN23PfiyNvP81UEO3JGJ4eZHSLyA1WZnZiYGOUtOjoa33zzDX788Ufl8fT0dHzzzTeIiYmptIUSaYWcsTG6yXgYg2BkhHxYYGn9OjK5cVlNaUrO6PBcHiLyB1WZnUWLFim/nzhxIgYPHoz58+dDry/6YWe1WjFy5EhER0dXziqJNESejVXa1POi64E/MqKsM3ZkYcrBgiqCneLG5Bw2KBORH3jds7Nw4UI899xzSqADAHq9HuPGjcPChQt9ujgiLSpr6rn99UAeGVHW6ckytT07Qgj27BCRX3kd7FgsFhw5csTl+pEjR2AL4B/uRGqZyzhnByjZkh7QZSwl2HH/IyJcZWanwGKDnOTibiwi8gevx0U89thjePzxx/Hbb7/h1ltvBQDs2bMH06dPx2OPPebzBRJpjZyxCeYylpzZUdOz4ymzYx/gMNghIn/wOth56623EB8fj5kzZyoDQevUqYMJEyZg/PjxPl8gkdZ4blAuDnYCeDeWmmBHbRkrp6CkdJVTaAn4AalEFHi8DnZ0Oh0mTJiACRMmICsrCwDYmEw3FHMZU8/tr5sDuYxVqL5BOd9DtsY+GBKiqKxV1vMSEfma18GOPQY5dCOyWN1PPbe/HsiHCsrjItQEO55KU/aZHfl9BjtEVJXKFex8+umn+OSTT3D27FkUFhY6PLZv3z6fLIxIqyxljIuwvx7I4yJKMjvuG5TVlrGcg6HcQitqVHB9RETe8Ho31uzZs/HYY4+hdu3a2L9/Pzp16oQaNWrg5MmTuOOOOypjjUSaokw9d5PZ0QfBbixf9uyUFuwQEVUlr4OdefPmYcGCBZg7dy5CQkIwYcIEpKWlYfTo0cjMzKyMNRJpirwby13PjlEpYwVuZkcJdlSMi/C09dz5bJ0cnrVDRFXM62Dn7Nmz6NKlCwAgLCwM2dnZAIBHHnkEK1as8O3qiDSorEGggF0ZK4AzO2pOUFa79dz51ORcnqJMRFXM62AnPj4ely9fBgAkJSVhz549AIBTp05BiMD94U6klkXtoYIBndlR36DsbWaHpygTUVXzOtjp1asXvvjiCwDAE088gbFjx6Jv37544IEHcO+99/p8gURao0w9d3OooEE5Zydwg/88L3p2PE09Z88OEfmb17uxFixYoIyFGDFiBGJjY7Fz50787W9/w4gRI3y+QCKtUQ4V9JjZCdxgJ1/FuAjVW8/Zs0NEflauQwV1dv+jHTx4MAYPHgwAOH/+PG666SbfrY5Ig8y2sqeeG26QcRFqd2M5l7nUTEknIvIlr8tYpcnIyMCoUaPQqFEjXzwdkaZZld1YZTcoB/K4CDUNysoJyl42KDu/T0RU2VQHO9euXcPQoUNRq1YtJCQkYPbs2bDZbJg0aRIaNGiAPXv2YOHChZW5ViJNkHtxjG4yO0Z9MJyzo6JB2aiujCU3JJsMOof3iYiqiuoy1ksvvYTvvvsOw4YNw8aNGzF27Fhs3LgR+fn52LBhA7p3716Z6yTSDLlBWe/2UMHAL2PJpaayztlRdmOZrWUO95SDoVpRJvx+NY8NykRU5VRndr766issWrQIb731FtavXw8hBBo3boxvv/2WgQ7dUDw1KAfT1HM14yLk4Z7uyJmcmpEmAGxQJqKqpzrYuXDhApo3bw4AaNCgAUJDQ/Hkk09W2sKItEo+LNBTZsccwJkdbxqU7e8vjdyjIwc7lXWoYH5xhomIyJnqYMdms8FoNCrv6/V6REREVMqiiLRMPizQ6GZchLz1PFDHRQghVJ2zY9DrEKKX+3DcBzDyc9WKKg52PDQ0l8el7Hx0+M8WjF55wOfPTUSBT3XPjhACjz76KEymoh9Y+fn5GDFihEvAs2bNGt+ukEhjrB6mnhsD/FBBs1VATkqZygh2gKIyV6HVVub285yCorJVrcgQAEBuge/LWEczsnG9wIL001d8/txEFPhUBzvDhg1zeP/hhx/2+WKIAoFZ5dTzQJ2NZR+4lJXZAYqalLPyLWWenSNnfWpGyT07vs/sZOdbHH4lIrKnOthZtGhRZa6DKGBYPIyLkDM7gVrGkvtvdJL7JmyZp5ERQgilQblWcc9OXiU0KGfnmwEA1wstsNkEdG4CUSK6MfnkUEGiG4nFQxlLDoICtUHZvjnZ3XZyWVhI0f+X3PXsFFhsSkmsKjI7QnC3FxG5YrBD5CUl2PE4CDQwMztKc3IZZ+zIwoq3prvr2cmx68+pEVF5PTv25SuWsojIGYMdIi8IITw2KAf6bCy5/8ZkUBHseBgZIWd8Qo06RIUW7ebMrYQt4gx2iKgsDHaIvGAfwLgbF2EI8HER8qgIdZmdskdGyNfDQwwIDyk5hFD+HL4i9+w4/56ICGCwQ+QV+wBG7yGzYw3QzI6a05Nlcs+Ou91Ycv9MeIjeYWeXr/tqrtuVxrIroUxGRIGNwQ6RFyx2O6zcbT2Xy1vmAO3ZUXN6ssxTz44cBEWEGKDTSUp2p6yt6uXBMhYRlYXBDpEX7DM77k5QlstbAduzo2R21Jex3PXsyA3KcklMDnZ8ndlhGYuIysJgh8gLZrvMjrujXAJ96rlXwY6Hrefy9QiTHOwU3Z/j4/lY9qUrZnaIyBmDHSIv2E88d3cGTaBvPVcalL3I7LgrY9k3KBf9WvllrOsMdojICYMdIi9YPEw8B0rO3wnc3Vhe9OyEFL3WfLeZnZIGZftfWcYioqrEYIfIC3LTsbtt54BdZifAx0Wo2o3lYeu5XK6SMzsRJrns5btgx2y1OWxlZxmLiJwx2CHygqcDBQG7qeeB2rMjHwSo5pwdeeu5uzKWuSjwiHDK7LgLjsrDuWzFredE5IzBDpEXzEoZy/1fnWCZeh6q5gRlTz07SmbHsUE514cNys6ZHJaxiMgZgx0iL8ilqbKmgRt1gT713IsTlOWeHXdbz+WeHZNjg7Ive3aynIIblrGIyBmDHSIveJp4XvTYjdOgHOqhZ6fkUMGi++SeHV/uxrpe4JzZYbBDRI4Y7BB5QQ5g3E08B0p2apkDNrOjvkE53OO4CHmCetF9cgDly8yOHNzIWSPn4IeIiMEOkRfkMpa7URFASYnLGqCZHV+eoJxb4NigLB8u6NuenaIyVkK1MOV9X09VJ6LAxmCHyAtKZsfNqAigJOtjDtTdWOUIdjxOPVd6dso+cbk85MyOHOyYrQIFlsDMqhFR5WCwQ+QFNZmdG+oE5ZCS3VilZVOq4lBBuWwVF2WCfKg1+3aIyB6DHSIvlGR2yjpBObDP2VEalFXtxiq5p7RsSk6hm63nPszsyLuxosOMiCx+fm4/JyJ7fg12pk2bho4dOyIqKgq1a9fGPffcg6NHjzrcI4TAlClTkJCQgLCwMPTo0QOHDh1yuKegoACjRo1CzZo1ERERgYEDB+L333+vypdCNwg5gCnrBGVjgO/GUg4VVHHOTqih5OtQWpNyyW4s+QRl3x8qKGdxokINiAo1OFwjIgL8HOxs374dTz/9NPbs2YO0tDRYLBb069cPOTk5yj0zZsxAamoq5s6di7179yI+Ph59+/ZFdna2cs+YMWOwdu1arFy5Ejt37sT169dx1113wWr17bBBInlcRFmzsfTKOTuBGezkW+TMjucfDwa9DiHFwV2uU5OyEKLknB2XE5R9WMZSgh0jokKNABjsEJEjgz8/+caNGx3eX7RoEWrXro309HR069YNQgjMmjULL7/8MgYNGgQAWLJkCeLi4rB8+XIMHz4cmZmZ+PDDD7F06VL06dMHALBs2TIkJiZiy5Yt6N+/f5W/LgpeasZFyI8F6tZzJbOjomcHKCplFebZXDI7+WYb5DYe5wblnErYjRVlKsnsXC9gGYuISmiqZyczMxMAEBsbCwA4deoUMjIy0K9fP+Uek8mE7t27Y9euXQCA9PR0mM1mh3sSEhLQsmVL5R4iXyk5Z8fz1HMhAi+7Y7OV7GRSHey42X5un72R74lQzuXx/Tk7UaEGRBYHO1kayOzkm604+Ps1boMn0gDNBDtCCIwbNw633XYbWrZsCQDIyMgAAMTFxTncGxcXpzyWkZGBkJAQVK9e3e09zgoKCpCVleXwRqSGnK0pc+u5XdYn0Caf2zcZq9mNBZQ0KTv34eQWlhxOKJf2lHvNVth8FAjKu7G0VsaavuFXDJz7PdIO/+HvpRDd8DQT7DzzzDM4ePAgVqxY4fKYJDn+L1oI4XLNWVn3TJs2DTExMcpbYmJi+RdONxQ5U1P2bKySv1aB1qRsP9DT28yO8zBQuV9HzuYAJQ3KQpT0BlVUaQ3KzpPQ/eH4paK+wt/+vO7nlRCRJoKdUaNGYf369di6dSvq1q2rXI+PjwcAlwzNpUuXlGxPfHw8CgsLcfXqVbf3OHvxxReRmZmpvJ07d86XL4eCmLqp53aZnQALduRSVIheV2YTtj3lrB03mZ1wU0nQFGrQK2fh+GpHlrz1PDLUgCiTdraeX8kpWsPVnEI/r4SI/BrsCCHwzDPPYM2aNfj222+RnJzs8HhycjLi4+ORlpamXCssLMT27dvRpUsXAED79u1hNBod7rl48SJ++eUX5R5nJpMJ0dHRDm9EasgHBRpVjIsAAq+MlefFXCyZ256d4ibkcGNJZkenk0pOXfZBk7LNJuzKWNraei4HOXLQQ0T+49fdWE8//TSWL1+Ozz//HFFRUUoGJyYmBmFhYZAkCWPGjMHUqVORkpKClJQUTJ06FeHh4XjooYeUe5944gmMHz8eNWrUQGxsLJ577jm0atVK2Z1F5Ctqpp5LkgS9ToLVJgLuYMF8L0ZFyNxNPldOTzY5Pld4iAG5hVafnKKca7YqO76i7Xt2/LwbSwiBK7lFwc7VXGZ2iPzNr8HOe++9BwDo0aOHw/VFixbh0UcfBQBMmDABeXl5GDlyJK5evYpbbrkFmzdvRlRUlHL/zJkzYTAYMHjwYOTl5aF3795YvHgx9Hr1P7CJ1LCoKGMVPV4U7JgDbGSEN6cny8JDSu/ZyXU6UND5fl+UseRylUEnwWTQaSazk1toRWFxs/cVlrGI/M6vwY6aLZmSJGHKlCmYMmWK23tCQ0MxZ84czJkzx4erI3JlLS5LldWgDBSVuQoReFvP8wqLt52rOD1Z5q6M5XygoMyXBwvaNydLkoRIkzaCHfsAh5kdIv/TRIMyUaCQJ5kbPGR25K3p5gBtUA71IrPjrkE5z2kulizC5LuDBbPtTk+2/9XfDcr2AQ4zO0T+x2CHyAtyg3JZPTuA/TDQwCpjyaWoMC8alN317MjBjHx6sqyk7OWLzE7x6cnF5SutlLHsA5zsfEvAlTOJgg2DHSIvKA3KHrZly8FQoG4996ZB2X3PjnzOTullLF9mduTyVcm4CP8GO86lK5ayiPyLwQ6RF5RxEWWcoAyUlLkCdTeW2tOT7e91HRchNzs7ZnbkhmXf9uw4lrFyC61KFs4fnLebX+X2cyK/YrBD5AW5LKU2s2MN2DKWF1vP3TQc57jJ7LgbL1Ee8sDPaKcyVtFj/svuOB8kyL4dIv9isEPkhZLMjrqencBrUC4KzkzelLGUcRGOgV2um54duUHZN1vPi8tYxUGOUa9TDkT0Z9/OFZaxiDSFwQ6RF1T37MhlrAALdsqT2ZEzNfnOhwqa5ROU3fXs+HbruSzS5P9hoMzsEGkLgx0iL8i7ajxvPQ/Q3ViF5R8X4dKgXBzMRLicoFz6VvXycO7ZAUpKWv7cfi4HN/KsLs7HIvIvBjtEXlAz9RwoaWAOtMxOgaUcPTtGdz078jk7zlvPi8/Z8UmDcvEQULtSmRa2n8tlqwa1IwG4lrWIqGox2CHygpqp50AAn7NTWP5xEflOPTt5bk5QljM9vuzZcShjaWD7ubwbq2GtCADM7BD5G4MdIi8ou7FUHyoYWJmd8jQoh7k5Z8ddZifM6MMGZWU3VkkZK8rk31OUhRBKZqdhLTmzw63nRP7EYIfIC2rLWMYALWOVq0HZTRnLXc+O/L4vGpSvl5LZkX+f5acyVla+Rfk+Sa7JzA6RFjDYIfKC3KCsZuq5/f2BIs/sfYNyqLGkjGUr/kdeCKHsxnIuiYWHVN7Wc6CkWdlfZSw5sAkP0aNOTCgA7sYi8jcGO0ReUDI7HraeG5VDBQMrs1NQjsyOfU9OgaUouMs32yCKX3qES4NyZfTslJSxIv28G0tuRq4eHoLYiBAAPGeHyN8Y7BB5wezluAhzgAU75TpB2e5e+ePtd1o5P5evxkUUWKwoLM6c2Zexov28G0vO7MRGhKB6cbCTW2h1GadBRFWHwQ6RF9SOi9Arg0ADq4xVngZlvU5CiKHoR4kcwCi7uox66Jy+VuF2u7FsFQgG7YMZ++yRv7eeXy1uRq4eEYIok0H5XrnGJmUiv2GwQ+QFteMi5DJXoJWxypPZAey3nztmdpybk+3vBYB8S/mzHfYTz/V2AZV8gvJ1f2d2wo2QJEnJ7rBvh8h/GOwQeUHeSq73lNmRy1gBthsrvxzn7AB2pygXFmWGcgpK33YOAKEGPaTiL598X3nIPTn2JSz797P83bNTHOTEhrNvh8jfGOwQeUEuSxk99OwYA7WMZfF+Nxbguv08TzljxzVo0ukkZV5WRfp2Stt2bv++33t2ioOc6hFFmSZmdoj8h8EOkRdUDwLVB96hgharTclEeVvGCnWaj5Xj5vRkWZgPtp9n2ZWx7Mk7s/y2GyvHKbPDHVlEfsdgh8gLSs+Ox3ERxYcKBtC4iHxLyVpDK9izk6v07LiWsYquVzyzU1LGMjpcj7IbFyFE1QebclAjBznVw9mzQ+RvDHaIvBDM4yLsp5CbDF6WsZxGRuQWlt3orAwDrUDPjnxooLsylk345iwfbymZnXCnzA6DHSK/YbBD5AVLEE89z7fbiSVJZb8+ZyWTz4uDneIgxl1mxxcHC5Y2BBQoWr/cQO6Pvh1567lLZodbz4n8hsEOkRcs3k49D6AG5fxyjIqQlezGUtezUxLs+L6MJUmSXSmragMMq03gmrIbq2hdzOwQ+R+DHSIvyLOugrFBubxn7ACuPTtl7cYCSg4BzPFFZqeU7JHctFzVw0Cz8syQ/8irK7ux2LND5G8Mdoi8UDL13NPW88ArY8kBSqiXZ+wAZe3GKruMlVeRzI6bnp2ia/KOrKoNduQzdqJCDcr3AM/ZIfI/BjtEKgkhvDhUsHjqeQDuxgo1eB/shIW469lxU8Yqvl6xQwXliedGl8ei/DQM1H4ulsz+nB1/7A4LJjabwK7f/kIm+5/ISwx2iFSyH/3gsUE5AMdF5JXz9GQAyiGB+c67sdxkdnwxDNTdCcpASWmrqkdGOO/EAkoCnwKLTcl8UflsO3YJD33wP0xa/4u/l0IBhsEOkUr2/Teepp4HYhmroJynJwN2W8+dGpQj3B4qWPHdWO5OULa/VtVlLOczdoCiHih5Kz/7dirm59+zAAC/nM/080oo0DDYIVLJbLezyuPUc7mMFUC7sfI8nI1TFpet50qDsqfMji8alEsrY/nnFOUrOcUTz+0yO5Ik2e3IYvmlIs5cyQEAnLuaB1sAZU3J/xjsEKlkX5LyFOzIZa6AKmMpW8/L0bNjLP1QQbdbz5WenUoqY8mZnQo8f3nImZ3q4Y4BWDXlrB1mdiri7OVcAEChxYaMrHw/r4YCCYMdIpXsJ5irnnoeQMFOvrm4QdkHW89LxkWUfc5OeXtYrDahbFsvLdiJ9FMZy3kuliy2uEmZZ+1UzOniYKfo9zl+XAkFGgY7RCopoyJ0kscThgNx6nlFztkJdQpe5F1W7reey+MiyheMXLf7uMgyt577fzcWwPlYvpBTYMFf1wuU98/aBT5EnjDYIVJJGQLqYScWYD8INHAyOwU+OEFZLl/leThBuaI9O3IQE2LQwVTKVvlof2V2cl13YwGcfO4LZ684BjdnrjDYIfUY7BCpJAcuniaeAyVlrhslsyN/TH6hFTabQK657MxORXdjyUFMdClZHaDkBOXrVd2zw8xOpTnjlMnRSmbneoEFB85dQ2Yem8+1rPSfFETkQg5c1GR2ArJBuQInKNv34ORbrJDPznPXsyNfL+85OyUTz113Ytlf91fPjtyjI2Nmp+LOFPfoRIUakJ1v0UzPzpiV+7HlyCUAwE3VwtA8IRrN6kSjeZ1otEmshviYUD+vkAAGO0SqeZPZkc/hMQfQOTsVOUHZfuu5fbbG3XMps7HKeYKyXMaKdDNV3R8nKFusNmUWl3MZi/OxKk4uW93WqCY2/JKBs5dzIYTw2D9XmYQQ+N/JK8r756/l4fy1PKQd/gMAoJOA1SM6o31SrL+WSMUY7BCppPTseNiJZX+PJYDGRVTkBGX5YwosNuWwv/AQPXRuvlZhdpkgm024vc+d7DIOFLS/XpWZnWvFZQxJAmLCnDI7xcHPNY45KDe5bNW1ONjJLrDgaq7ZpWRYlS5m5iO7wAKDTsKel3rjt0vXceRiFg5fyMKO438hIysfO49fZrCjAQx2iFSS51ypa1AOvKnn8gnKFZl6DgCXi7MX7vp1gJLMDlAU8ES4ydC4k+Up2Ck+aLDAYkOhxYYQQ+W3J8r9OjFhRpcTtu3nY1H5yAcKNo6LQnx0KDKy8nH6co5fg51jf2QDAOrXjEDNSBNqRppwa4MaAID3vzuJN74+otxD/sUGZSKV1E48B0rKWIE0LkLp2SnHbiz7ctUVJdhxHzSFGnWQqw855ejbkbNHkaWcngw4bkevqlKW0q8T7vqPr33PDoeBeq/QYsP5q3kAgPo1wpFUIxyA/5uU5UCmSVyUy2ON44uu/ZqRVaVrotIx2CFSSR794OlAQcAusxOAu7HKc6igTicp85/ks1DKCnYkSVKGh+aVY0dWWacnA0V/RvJcrqoqZSmnJ5eSaZB7eMxWUeU7xILB+Wt5sImirGOtKJMS7Djv0Kpqx/64DgBIiYt0eaxpcbBz+nKuctgm+Q+DHSKVrDYvenb0gVfGyq9AsAOU9OFcLg52PJWmwk3lb1L2tPUcKMnuVFVwUdpcLFmoUa8Ef5yP5T15J1a92HBIkoSkGhFF16/4d0fW8eLMTuNSMju1o0yICTPCahM48ef1ql4aOWGwQ6SSXJJSU8ZSpp4HVLBTlIUqT88OACVTc1lFGQsomYhenu3nnrae2z+WVUVlrJKJ56WvqTrnY5WbfKBgveKMTr1Y/2d2bDaB45eKgpjGpWR2JElCk+LsDvt2/I/BDpFK3pSxAnLqubn8u7GAkvN5/rquLtgJq8ApysrW8zIyO1W9I8vdXCxZyeRzBjveOv1XUVBTvzjYqS9ndvwY7Jy/lofcQiuM+pJMk7OmSt8Ogx1/Y7BDpFJJg7KKQwWLz+IJpEMFlTJWOc7ZAUoyQkoZq4zdWEWPlz+z42k3VtFjVXuw4NUyGpQBnrVTEWeLy1X1ioMKOcPz1/WCcs9Xq6jjl4oCmAY1I91me+Xy1jEGO37HYIdIJXmCuarMjjIINDCCHSFESYNySPl+LMjBjvyPuacMUUV6dq7nqyhjySMjqmo3VhkNygAQG148+ZxlLK/JGZyk4vJVTJgR1Yq/nv7K7sjNyfKuq9LImZ2jDHb8jsEOkUryzipVPTtyGStADhUstNqUEQ8VbVCWy1geG5TlU5fLsVMlu6DsE5SBqi9jMbNTOWw2ofTsyLuwin5flOU566cmZTlb07i2a7+OLKU4s3MhM5+zs/yMwQ6RShavdmMV/dUSouiHtdblF5YEZeVtUC7J7Hjeeg4A4fJ8rHKUIdTsxlKCnarajeUxs8P5WOXxR3Y+Ciw26HUSEqqFKdeT/NykfKy4jJVSyk4sWUyYEQnFs7GOs0nZrxjsEKkkl6T0Xkw9BwIjuyOXsAw6SVXmqjRyZkeO7TzvxiouY3nZoCyEsBsX4Xk3VtVldor+5+7uRF9mdspHDmbqVg9z+N5Uztq5UvXBjs0m8FsZO7HsNWaTsiYw2CFSSZ5zpapB2e6eQOjbqegZO4BrcFPWuAj7+/O8bFDON9uUxu+ydmPJJa6qOEG5wGJVtsO7K2OV7MZiOcMb8inJ8nZzWcn286ovY527mot8c9EYEnc7sWTcfq4NDHaIVFIGgaoZF2GX/QmEs3YqcnqyzPljI0weyljlzOzIwYtOKtnRVZqq7NmRB3zqJPc7xOSGWp6z4x354ED7fh2gaB4V4J8yltyc3LBWpMcNC/IoCWZ2/IvBDpFKcmbHm6nnQGCMjMhXztgp/48E516fMKOHrefl7NnJUuZiGSBJ7v8sSspYlZ9JUc7YCQ9xO8Gd5+yUz2llJ5ZjBkXu2blwLQ+Flqr9O3ZMOTm57BIW4JjZ4Vw0/2GwQ6SS2aq+QVmnkyDfFghn7eRV8IwdwDXY8ZTZCVPO2fEus6Pm9OSix6tuXMRVDwcKAo4NyoHQtK4VchnLObNTK8qEMKMeNlF0wF9VOlbGmAhncvbnWq4Zl7ILKntp5AaDHSKVlNlYKht45fvMAfAPW34FT08u7WM99exElPMEZU9DQGVVWcaSS1Pu+nUAoFrxYzZRdSMsgoHck+PcGyNJktK3c7qK+3aUM3ZUBDuhRr1y8jPP2/EfBjtEKsnlKDWZHfv7AqOMVbTGCmV2XIIdTz07RY/neNmgnK3i9OSix6tuN1ZJZsd9tinEoFMOOuSOLHWu5RYqZUvnBmWgJNtztgr7duwHe6opYwElpSwGO/7DYIdIJeWcHRW7sQC7YCcAMjt5hfLpyT4sY3ncjWVw+NxqlWR21JexKrtsdMXDtnOZXObiWTvqyP06taNMpWYdle3nVRjsnLmcg0KLDaFGHRKruwZgpWkSFw2ATcr+xGCHSCWLTf3Uc/v7AmLruaW4jGX0XYNyuKfdWKaKZXbKOj3Z+fHr5Zi/5Q05eKleRhkLsD9rh2UsNeQSVn0327vrKQNBq66MJZewGtWOdNuM7qxJfGTxxzLY8RcGO0QqeTP13P6+QJh8rmR2KrD13NsyltKz4+VsLLVlrFCjHiHFAWdll7LkspSnzI4yH4tlLFWUM3ZqlJ5Bqe+HgwXlk5Ab1/bcryNrEl+U2Tn2R3ZAbFgIRgx2iFRSpp6rDHbkzE4g/HBTGpQrEuzYfawkee7/CS/nbiw1pyfLSpqUKzeT4nVmh2UsVeQgJqmUfp2i6/J8rNwq2+F29A/PYyKc1YsNR6hRhwKLTZnzRVWLwQ6RSmYvxkUU3Sf37Gg/s6M0KPsosxNu1HtM8SsnKJutXgWE1wvU7cYCSk5Yvl7JmR052PGc2WHPjjfk8pS7zE5CtVAYdBIKLTb8kZ1fJWs6XlzGkktTauh1ElJqy03KWZWyLiobgx0ilZTdWGoblPVyGUv7mR1fnKBsX7YK89CcDDhORc/zYvK52jKW/T2VXcaSR0CUdc6O/eMsY6kjNx6769kx6HW4qXrRcNDTf1V+xsRsteHkX0XBTooXZSzAfkfWdZ+vizxjsEOkklLGUhnsGHWBU8bK80EZyz5Q8nSgIACYDDrIByDnetFA7FWwYyoqdVX2uTZKz46HMlYsG5RVyyu0KofwOR8oaE8+f+fslcpvUj5zOQdmq0B4iB432U1gV0MeG3H0D2Z2/IHBDpFK8uGA3paxAqFBuWQQqG92Y3k6UBAoOhSuPE3KytZzkzc9O5WX2ckrtCrBYlnn7AAlPT0sY3km97ZEhxqUAxlLkxRbddvP5Z1YKV7sxJLxrB3/YrBDpJJcxlKd2dHLhwpqP7Pj6xOUPe3Ecr7Pm+3n2cXjH8qaeC6LrIKREXLgYtRLHrfDcz6WeqfdnJzsrCrP2jlWjuZkmRzsnL6cq/x9o6rDYIdIJeVQQZWZHXlcRCAcKuiLBmX73VfeBjveHCzoTRkrugqGgdoPAS1rMCkAxEZw8rla7mZiOZNPVj5TBWUsbwaAOqsdZUK1cCOsNoHfLrFvp6ox2CFSydtxEYG0G8sX5+zodJJSBvN0erJMLnfleBXsFAUu0V5tPa/8zI6nnVhASRkrM88cEGNE/EkOXjwFO/VrygcL5lb6VHFvZmI5kyRJ+TgeLlj1GOwQqeTtuAi5jHWjNCjbf7yn05NlciNzrsoyk9lqU7JQqraemyp/67l9ZseTmDAjJAkQoijgIffkspR8lo47cmYnO9+Ca7mV9zUttNhw+q+iAKw8wQ4ANGXfjt8w2CFSSe69UT31vLjcFQhbz33RoAzYBTsqy1hhXk4+tw9aIjz0xwAlBw9mVWZmR+XpyUDR905MWPEpyixllemMh9OTZaFGPeKiTQAqd/r5qb9yYLEJRJkMqBMTWq7naKzsyGKwU9WCJtiZN28ekpOTERoaivbt22PHjh3+XhIFGbkcFZxTz32U2SkOctSWsSKUU5TVBSNyOSrMqFc1o6wqTlC+kiufseO5rAaUbE/n9nP3zFYbzl/LA+D+jB179icpVxa59NQoLtJjb5Y7zOz4T1AEO6tWrcKYMWPw8ssvY//+/bj99ttxxx134OzZs/5eGgWRkgZl7w4VvFEalIGSYEfN1nP7+9T27GTlqz892f6+Su3ZUXnGjqxkGCgzO+5cuJYHq03AZNChdpTJ4/1VsSOrPDOxnMm7uC5m5rOMWcXU/cTQuNTUVDzxxBN48sknAQCzZs3Cpk2b8N5772HatGl+W9fVnEKvJzqTdslNvKpPUC4uY/11vQC/X9X2PBz5+7TCwY6XZSz5vj+y8lV9jeQyhZpt50BJsJOZZ660P4MLxRmIss6CsVe9eBjoqb9yNP994S/7z14DUNSPo+Y8GznYOZqRXWlf05/PZwIAUsqxE0sWE2ZEQkwoLmTmY/eJv9DyphhfLS8gVAsP8Xg8Q2UJ+GCnsLAQ6enpeOGFFxyu9+vXD7t27Sr1YwoKClBQUKC8n5VVOSda/nfzUSz/H7NLwUb91vOiH9KzthzHrC3HK3NJPlPhnp3iTI3a83rkRuZF35/Gou9Pq/48aoaA2t93/loebntzq+rnLw81PTtASSPzmxt/xZsbf63MJQU8TzuxZPWKS11f/XwRX/18sTKXVO7mZOXj46NwITMfI5bt89GKAsfUe1vhoVvq+eVzB3yw89dff8FqtSIuLs7helxcHDIyMkr9mGnTpuHVV1+t9LUZdRJMhqCoFFKxutXDcHPdaqru7dc8HtuO/hkwB4i1rVcNCTHeHYHvbECreJy9nIMuDWuour9Xk9r4LP13r8pMBp2EgTcnqLo3uWYE2tWrhkMXKveI/rjoUNzaQN1r/r+W8Ug78odXZwvdiEwGHe5uc5Oqe7s2rIHkmhFKlq2yNKwViQ71q1foOe5rXxf7zlxFgUX7vXy+pnJvR6WQRGUfTFDJLly4gJtuugm7du1C586dletvvPEGli5dil9/df2fU2mZncTERGRmZiI6OrpK1k1EREQVk5WVhZiYGI//fgd8ZqdmzZrQ6/UuWZxLly65ZHtkJpMJJpPnpjciIiIKfAFfYwkJCUH79u2RlpbmcD0tLQ1dunTx06qIiIhIKwI+swMA48aNwyOPPIIOHTqgc+fOWLBgAc6ePYsRI0b4e2lERETkZ0ER7DzwwAO4fPkyXnvtNVy8eBEtW7bE119/jaSkJH8vjYiIiPws4BuUfUFtgxMRERFph9p/vwO+Z4eIiIioLAx2iIiIKKgx2CEiIqKgxmCHiIiIghqDHSIiIgpqDHaIiIgoqDHYISIioqDGYIeIiIiCGoMdIiIiCmpBMS6iouRDpLOysvy8EiIiIlJL/nfb0zAIBjsAsrOzAQCJiYl+XgkRERF5Kzs7GzExMW4f52wsADabDRcuXEBUVBQkSarQc2VlZSExMRHnzp27YeZs8TXzNQcrvma+5mAVLK9ZCIHs7GwkJCRAp3PfmcPMDgCdToe6dev69Dmjo6MD+huoPPiabwx8zTcGvuYbQzC85rIyOjI2KBMREVFQY7BDREREQY3Bjo+ZTCZMnjwZJpPJ30upMnzNNwa+5hsDX/ON4UZ7zWxQJiIioqDGzA4REREFNQY7REREFNQY7BAREVFQY7BDREREQY3Bjo/NmzcPycnJCA0NRfv27bFjxw5/L6nSTJs2DR07dkRUVBRq166Ne+65B0ePHvX3sqrUtGnTIEkSxowZ4++lVKrz58/j4YcfRo0aNRAeHo42bdogPT3d38uqNBaLBf/+97+RnJyMsLAwNGjQAK+99hpsNpu/l+Yz3333Hf72t78hISEBkiRh3bp1Do8LITBlyhQkJCQgLCwMPXr0wKFDh/yzWB8p6zWbzWZMnDgRrVq1QkREBBISEvCPf/wDFy5c8N+CfcDTn7O94cOHQ5IkzJo1q8rWV1UY7PjQqlWrMGbMGLz88svYv38/br/9dtxxxx04e/asv5dWKbZv346nn34ae/bsQVpaGiwWC/r164ecnBx/L61K7N27FwsWLEDr1q39vZRKdfXqVXTt2hVGoxEbNmzA4cOH8fbbb6NatWr+XlqlefPNNzF//nzMnTsXR44cwYwZM/Df//4Xc+bM8ffSfCYnJwc333wz5s6dW+rjM2bMQGpqKubOnYu9e/ciPj4effv2VWYJBqKyXnNubi727duHV155Bfv27cOaNWtw7NgxDBw40A8r9R1Pf86ydevW4X//+x8SEhKqaGVVTJDPdOrUSYwYMcLhWtOmTcULL7zgpxVVrUuXLgkAYvv27f5eSqXLzs4WKSkpIi0tTXTv3l08++yz/l5SpZk4caK47bbb/L2MKjVgwADx+OOPO1wbNGiQePjhh/20osoFQKxdu1Z532azifj4eDF9+nTlWn5+voiJiRHz58/3wwp9z/k1l+aHH34QAMSZM2eqZlGVzN1r/v3338VNN90kfvnlF5GUlCRmzpxZ5WurbMzs+EhhYSHS09PRr18/h+v9+vXDrl27/LSqqpWZmQkAiI2N9fNKKt/TTz+NAQMGoE+fPv5eSqVbv349OnTogPvvvx+1a9dG27Zt8f777/t7WZXqtttuwzfffINjx44BAH766Sfs3LkTd955p59XVjVOnTqFjIwMh59nJpMJ3bt3v2F+ngFFP9MkSQrqLKbNZsMjjzyC559/Hi1atPD3cioNB4H6yF9//QWr1Yq4uDiH63FxccjIyPDTqqqOEALjxo3DbbfdhpYtW/p7OZVq5cqV2LdvH/bu3evvpVSJkydP4r333sO4cePw0ksv4YcffsDo0aNhMpnwj3/8w9/LqxQTJ05EZmYmmjZtCr1eD6vVijfeeAMPPvigv5dWJeSfWaX9PDtz5ow/llTl8vPz8cILL+Chhx4K+EGZZXnzzTdhMBgwevRofy+lUjHY8TFJkhzeF0K4XAtGzzzzDA4ePIidO3f6eymV6ty5c3j22WexefNmhIaG+ns5VcJms6FDhw6YOnUqAKBt27Y4dOgQ3nvvvaANdlatWoVly5Zh+fLlaNGiBQ4cOIAxY8YgISEBw4YN8/fyqsyN+vPMbDZjyJAhsNlsmDdvnr+XU2nS09PxzjvvYN++fUH/58oylo/UrFkTer3eJYtz6dIll/8dBZtRo0Zh/fr12Lp1K+rWrevv5VSq9PR0XLp0Ce3bt4fBYIDBYMD27dsxe/ZsGAwGWK1Wfy/R5+rUqYPmzZs7XGvWrFnQNt4DwPPPP48XXngBQ4YMQatWrfDII49g7NixmDZtmr+XViXi4+MB4Ib8eWY2mzF48GCcOnUKaWlpQZ3V2bFjBy5duoR69eopP8/OnDmD8ePHo379+v5enk8x2PGRkJAQtG/fHmlpaQ7X09LS0KVLFz+tqnIJIfDMM89gzZo1+Pbbb5GcnOzvJVW63r174+eff8aBAweUtw4dOmDo0KE4cOAA9Hq9v5foc127dnU5UuDYsWNISkry04oqX25uLnQ6xx+Per0+qLaelyU5ORnx8fEOP88KCwuxffv2oP15BpQEOsePH8eWLVtQo0YNfy+pUj3yyCM4ePCgw8+zhIQEPP/889i0aZO/l+dTLGP50Lhx4/DII4+gQ4cO6Ny5MxYsWICzZ89ixIgR/l5apXj66aexfPlyfP7554iKilL+FxgTE4OwsDA/r65yREVFufQkRUREoEaNGkHbqzR27Fh06dIFU6dOxeDBg/HDDz9gwYIFWLBggb+XVmn+9re/4Y033kC9evXQokUL7N+/H6mpqXj88cf9vTSfuX79On777Tfl/VOnTuHAgQOIjY1FvXr1MGbMGEydOhUpKSlISUnB1KlTER4ejoceesiPq66Ysl5zQkIC7rvvPuzbtw9ffvklrFar8jMtNjYWISEh/lp2hXj6c3YO6IxGI+Lj49GkSZOqXmrl8u9msODz7rvviqSkJBESEiLatWsX1NuwAZT6tmjRIn8vrUoF+9ZzIYT44osvRMuWLYXJZBJNmzYVCxYs8PeSKlVWVpZ49tlnRb169URoaKho0KCBePnll0VBQYG/l+YzW7duLfXv77Bhw4QQRdvPJ0+eLOLj44XJZBLdunUTP//8s38XXUFlveZTp065/Zm2detWfy+93Dz9OTsL1q3nkhBCVFFcRURERFTl2LNDREREQY3BDhEREQU1BjtEREQU1BjsEBERUVBjsENERERBjcEOERERBTUGO0RERBTUGOwQUYU9+uijuOeee5T3e/TogTFjxlTq5ywsLESjRo3w/fffV+rnCUT33XcfUlNT/b0MIs1gsEN0g3j00UchSRIkSYLBYEC9evXw1FNP4erVqz7/XGvWrMHrr7/u8+e1t2DBAiQlJaFr166V+nm8VRWBnieTJk3CG2+8gaysLL+ug0grGOwQ3UD+7//+DxcvXsTp06fxwQcf4IsvvsDIkSN9/nliY2MRFRXl8+e1N2fOHDz55JOV+jkqixACFoul0p6/devWqF+/Pj7++ONK+xxEgYTBDtENxGQyIT4+HnXr1kW/fv3wwAMPYPPmzcrjVqsVTzzxBJKTkxEWFoYmTZrgnXfecXgOq9WKcePGoVq1aqhRowYmTJgA56kzztkNSZKwbt06h3uqVauGxYsXAygqST3zzDOoU6cOQkNDUb9+fUybNs3t69i3bx9+++03DBgwwOH6xIkT0bhxY4SHh6NBgwZ45ZVXYDablcenTJmCNm3aYOnSpahfvz5iYmIwZMgQZGdnK/dkZ2dj6NChiIiIQJ06dTBz5kyX1zNv3jykpKQgNDQUcXFxuO+++wAUZc+2b9+Od955R8minT59Gtu2bYMkSdi0aRM6dOgAk8mEHTt2oKCgAKNHj0bt2rURGhqK2267DXv37lU+j/3HtW3bFmFhYejVqxcuXbqEDRs2oFmzZoiOjsaDDz6I3Nxch6/FwIEDsWLFCrdfQ6IbCYMdohvUyZMnsXHjRhiNRuWazWZD3bp18cknn+Dw4cOYNGkSXnrpJXzyySfKPW+//TYWLlyIDz/8EDt37sSVK1ewdu3aCq1l9uzZWL9+PT755BMcPXoUy5YtQ/369d3e/91336Fx48aIjo52uB4VFYXFixfj8OHDeOedd/D+++9j5syZDvecOHEC69atw5dffokvv/wS27dvx/Tp05XHx40bh++//x7r169HWloaduzYgX379imP//jjjxg9ejRee+01HD16FBs3bkS3bt0AAO+88w46d+6Mf/7zn7h48SIuXryIxMRE5WMnTJiAadOm4ciRI2jdujUmTJiAzz77DEuWLMG+ffvQqFEj9O/fH1euXHFY85QpUzB37lzs2rUL586dw+DBgzFr1iwsX74cX331FdLS0jBnzhyHj+nUqRN++OEHFBQUqPtDIApm/p1DSkRVZdiwYUKv14uIiAgRGhqqTD9OTU0t8+NGjhwp/v73vyvv16lTR0yfPl1532w2i7p164q7775bueY8CR6AWLt2rcPzxsTEiEWLFgkhhBg1apTo1auXsNlsql7Ls88+K3r16uXxvhkzZoj27dsr70+ePFmEh4eLrKws5drzzz8vbrnlFiFE0bRzo9EoVq9erTx+7do1ER4erryezz77TERHRzs8hz3n1y5EyeTpdevWKdeuX78ujEaj+Pjjj5VrhYWFIiEhQcyYMcPh47Zs2aLcM23aNAFAnDhxQrk2fPhw0b9/f4fP+dNPPwkA4vTp02V+jYhuBMzsEN1AevbsiQMHDuB///sfRo0ahf79+2PUqFEO98yfPx8dOnRArVq1EBkZiffffx9nz54FAGRmZuLixYvo3Lmzcr/BYECHDh0qtK5HH30UBw4cQJMmTTB69GiH0lpp8vLyEBoa6nL9008/xW233Yb4+HhERkbilVdeUdYuq1+/vkM/UZ06dXDp0iUARdkus9mMTp06KY/HxMSgSZMmyvt9+/ZFUlISGjRogEceeQQff/yxSwnJHfuv04kTJ2A2mx0arI1GIzp16oQjR444fFzr1q2V38fFxSllOvtr8muQhYWFAYDqtREFMwY7RDeQiIgINGrUCK1bt8bs2bNRUFCAV199VXn8k08+wdixY/H4449j8+bNOHDgAB577DEUFhZW6PNKkuTS12PfS9OuXTucOnUKr7/+OvLy8jB48GClD6Y0NWvWdNlFtmfPHgwZMgR33HEHvvzyS+zfvx8vv/yyy9rty3by2mw2GwAoa5QkyeEe+7VHRUVh3759WLFiBerUqYNJkybh5ptvxrVr1zx8FYq+/s7PWdrncr5mv2ZJksp8DTK5FFarVi2P6yIKdgx2iG5gkydPxltvvYULFy4AAHbs2IEuXbpg5MiRaNu2LRo1aoQTJ04o98fExKBOnTrYs2ePcs1isSA9Pb3Mz1OrVi1cvHhRef/48eMuGYfo6Gg88MADeP/997Fq1Sp89tlnLr0rsrZt2+LXX391CEK+//57JCUl4eWXX0aHDh2QkpKCM2fOqP9iAGjYsCGMRiN++OEH5VpWVhaOHz/ucJ/BYECfPn0wY8YMHDx4EKdPn8a3334LAAgJCYHVavX4uRo1aoSQkBDs3LlTuWY2m/Hjjz+iWbNmXq27NL/88gvq1q2LmjVrVvi5iAKdwd8LICL/6dGjB1q0aIGpU6di7ty5aNSoET766CNs2rQJycnJWLp0Kfbu3Yvk5GTlY5599llMnz4dKSkpaNasGVJTUz1mNXr16oW5c+fi1ltvhc1mw8SJEx2yEzNnzkSdOnXQpk0b6HQ6rF69GvHx8ahWrVqpz9ezZ0/k5OTg0KFDaNmyJYCi4OHs2bNYuXIlOnbsiK+++srrxumoqCgMGzYMzz//PGJjY1G7dm1MnjwZOp1OybZ8+eWXOHnyJLp164bq1avj66+/hs1mU0pd9evXx//+9z+cPn0akZGRiI2NLfVzRURE4KmnnlI+V7169TBjxgzk5ubiiSee8GrdpdmxYwf69etX4echCgbM7BDd4MaNG4f3338f586dw4gRIzBo0CA88MADuOWWW3D58mWXc3jGjx+Pf/zjH3j00UfRuXNnREVF4d577y3zc7z99ttITExEt27d8NBDD+G5555DeHi48nhkZCTefPNNdOjQAR07dsTp06fx9ddfQ6cr/UdUjRo1MGjQIIdzZO6++26MHTsWzzzzDNq0aYNdu3bhlVde8frrkZqais6dO+Ouu+5Cnz590LVrVzRr1kzpEapWrRrWrFmDXr16oVmzZpg/fz5WrFiBFi1aAACee+456PV6NG/eHLVq1XLpGbI3ffp0/P3vf8cjjzyCdu3a4bfffsOmTZtQvXp1r9dtLz8/H2vXrsU///nPCj0PUbCQhHMhnYgoAPz888/o06cPfvvtt0o9wDAnJwc33XQT3n77bZ9kXKrCu+++i88//9xjozfRjYKZHSIKSK1atcKMGTNw+vRpnz7v/v37sWLFCpw4cQL79u3D0KFDARRljgKF0Wh0OXeH6EbGzA4RkZ39+/fjySefxNGjRxESEoL27dsjNTUVrVq18vfSiKicGOwQERFRUGMZi4iIiIIagx0iIiIKagx2iIiIKKgx2CEiIqKgxmCHiIiIghqDHSIiIgpqDHaIiIgoqDHYISIioqDGYIeIiIiC2v8Hsec1+Xt9cw0AAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(ss_rdf_nodensity.results.bins, \n", " ss_rdf_nodensity.results.rdf[0][1][570])\n", "plt.xlabel('Radius (angstrom)')\n", "plt.ylabel('Radial distribution')\n", "plt.title('RDF between CA61 and {}{}'.format(w570.name, w570.resid))" ] }, { "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." ] } ], "metadata": { "celltoolbar": "Raw Cell Format", "kernelspec": { "display_name": "guide", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.15" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "vscode": { "interpreter": { "hash": "5edc5d8d8cbc0935a054a8e44024f729bc376180aae27775d15f2ff38c68f892" } } }, "nbformat": 4, "nbformat_minor": 2 }