DNA_flux_example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import mdtraj as md\n",
    "import openpathsampling as paths\n",
    "import numpy as np\n",
    "\n",
    "from openpathsampling.engines.openmm.tools import ops_load_trajectory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example: Analyzing flux out of Watson-Crick DNA\n",
    "\n",
    "This example comes from a project studying the transition between the Watson-Crick and Hoogsteen base pairing motifs in DNA (Vreede, Bolhuis, Swenson. In prep.) To calculate the rate of the transtion, we used TIS, which requires the calculation of the flux out of the state and through an innermost interface. This notebook shows how to calculate that flux from an existing MD calculation, and how to select the location for the innermost interface.\n",
    "\n",
    "In this particular case, we had already begun path sampling, and so we didn't want to change the definition of our states. This makes it a bit more challenging to find a good interface, but, as shown below, the problem can still be solved.\n",
    "\n",
    "The calculations below focus on the `run0-dna.xtc` file, although they could easily be extended to include the other runs as well. At the end, we will calculate things using all the runs.\n",
    "\n",
    "The data for this was provided by Jocelyne Vreede and David Swenson, and can be downloaded from https://figshare.com/articles/Molecular_dynamics_simulations_of_DNA/4508975. In order to run this notebook, download the zip file for that data and unzip it such that the resulting directory, named `4508975`, is in the same directory that you started Jupyter from."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1min 10s, sys: 827 ms, total: 1min 11s\n",
      "Wall time: 1min 13s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "directory = \"4508975/\"\n",
    "files = ['run0-dna.xtc', 'run1-dna.xtc', 'run2-dna.xtc', 'run3-dna.xtc', 'run4-dna.xtc']\n",
    "# load the data\n",
    "runs = [ops_load_trajectory(directory + f, top=directory + 'dna.gro') for f in files]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll start by looking in some details at `run0.xtc`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "run0 = runs[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# use an mdtraj-style topology for its magic features\n",
    "topology = run0.topology.mdtraj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DT9-N3 DA4-N1\n",
      "DT9-N3 DA4-N7\n",
      "DT9-O4 DA4-N6\n"
     ]
    }
   ],
   "source": [
    "print(topology.atom(275), topology.atom(494))\n",
    "print(topology.atom(275), topology.atom(488))\n",
    "print(topology.atom(274), topology.atom(491))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That was just a little check that we're looking at the right atoms. The MDTraj `Topology` makes that really easy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the CVs, states, and interfaces\n",
    "\n",
    "We'll use these CVs for the entire simulation. `d_bp` measures a distance repesenting a hydrogen bond common to both the WC and HG states. `d_WC` is a distance that represents a hydrogen bond formed in the WC state (but which is not formed in HG), and `d_HG` is a distance for a hydrogen bond formed in the HG state (which not in WC). The specific atoms involved are shown in the previous section, using the topology."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# first we define the CVs that we'll be using\n",
    "d_WC = paths.MDTrajFunctionCV(\"d_WC\", md.compute_distances, run0.topology, atom_pairs=[[275, 494]])\n",
    "d_HG = paths.MDTrajFunctionCV(\"d_HG\", md.compute_distances, run0.topology, atom_pairs=[[275, 488]])\n",
    "d_bp = paths.MDTrajFunctionCV(\"d_bp\", md.compute_distances, run0.topology, atom_pairs=[[491, 274]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To combine both the WC and HG bonds, we use the `atan2` function. Note that, if you want to make a CV that is composed of other CVs, you can do this by using the other CVs as input variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def atan2_cv_fcn(snapshot, d_WC, d_HG):\n",
    "    import math\n",
    "    wc = d_WC(snapshot)\n",
    "    hg = d_HG(snapshot)\n",
    "    return math.atan2(wc, hg)\n",
    "\n",
    "atan2_cv = paths.CoordinateFunctionCV(\"atan2\", atan2_cv_fcn, d_WC=d_WC, d_HG=d_HG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we define our WC and HG states."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the states are a combination of volumes defined by these CVs\n",
    "state_WC = (paths.CVDefinedVolume(d_WC, lambda_min=0.0, lambda_max=0.35) &\n",
    "            paths.CVDefinedVolume(d_bp, lambda_min=0.0, lambda_max=0.35)).named(\"WC\")\n",
    "\n",
    "state_HG = (paths.CVDefinedVolume(d_HG, lambda_min=0.0, lambda_max=0.35) &\n",
    "            paths.CVDefinedVolume(d_bp, lambda_min=0.0, lambda_max=0.35)).named(\"HG\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's plot these CVs. Since this trajectory is of the WC state, the `d_WC` should be small, and `d_HG` should be large."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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5iTcvz25LEyzpXvnvShpWDHwPGGdPHmdClhPnTT6PDbs30KB8g6DLBSplOXzs\nMB3f7Mi8v+b5nR+OYJ/hc/Of851YFJIKJXH99ddHvU/JO8lFkjla1LcksfLzlf0snfeUrJB99XxZ\nvcu4b0b2VfWERRM8Bmd7edHLrsfuB4VYjFMQqM1CJDbs3kD7Se2B4MOw/7rjV5+qBX+27Nviiss9\nOfPuybR6+2pOr+jZfiAahZ4s5PF8/M/jeW+lY5C5r//4mqvev4p+rfu5TrqhOE/2321wNIzu9lE3\nvlz3pccyl065lKV3LA2a2LlzbzgLMHHZRLo37g7gt3tuoG7yHSYH7gXw82ZH9VGgrsTe7SXG/zye\nR7951PV86ZalHgnk60teB/A7evE90+/xeL5622pu+ewWwPP1nDf5PLrU78J/B/+jYrGKHuu4V2lE\nq+0bbQHoPb03vaf39pjnPNn7a/TtXrI2cM5Abj7jZgZ9OyjgfkJ1ifcuIciwjsTM30n+9P+dzrre\ngYdBCNaQftehXZghhgdbPhg0HmebImdD+2h72dw7/d6oEpWMzAz2H93PV79/5XGM8i5l8XuLkNKQ\neVcmRHjnhe97fU/b19t6TGtUqZFPQ97nL3ieB2Y9ENY2F92+iFm/zXKNAxNsudSXU13Pr2xwpWu8\nHndXnXYVZ1U7i4dmBR9ArUxKGY+qcu/t+9OtUTemLJ/CxC4TeXHhi/z8z8/Mu3keP//zM32m9+HU\ncqdybcNreXLuk0FfBzjG0/r2z2/p0aQHLSa0CFgK903Pbxjy0xC+2xW4l1u8KVnx4jyxLdmyxCNR\nCWbT3pyPihluL5lwBTsw1XuxXsB5d35+p+vxA7MecPVMCnZV9cjXj/BZt/BuqPfHrvC6yFosd36R\nHcuew3vYfXg3j37zaNgNMlf8u8LjuXeiArBsq6PhY7Q3g5y9fjaDvx3MVaddFXrhMIUav2fId0M8\nnru/TwAv/vQiFsuLF70IRHaCazy+ccB5U9dM9Xju3O5F71wUcB1nr7mt+7ZSuXhlen/ZO+Cy0Rj3\n0zi6Nswegdn7tbrfoiAcxzKPMfS7ofQ5y/F73HN4j0+C6m7A1wMCznO2WQrm1SWv0rF28J5g+4/s\nd72uUFU+2/ZvY/uB7ZQpUsZj+tKtSwOsEVyfGX38Xvh4V68FPD6UzvqLQOU6lcFrrLQ9pfaAV+Ft\n8VrFfZYLJPWzrAQhxPLNmjXzWOaj3R/5XefDXR/y4a4PQ27vP/4Dt4/Ce/v+VDq1EuyAeo3qUeLf\nEgCcccaHtU5vAAAgAElEQVQZtJ7eGqpA0UpFqX1abQhcS+zYD3D9uOtZvX01o24ahaliCHQo+Pbw\ntyw7FF4j8HhRsuImkvtiuN88MBbdfGN1T46cco7DAp5VI8HqKyM9IYTD+0rN/SA9Yv4I78VzJKd1\nsUO+G+K391g8jftpHIPbD6Z80fK5Wtcc6nU7T9hPpz9N6+qtY36n7CSTxPcbswf38x7fZMPuDRFt\nb9raaUxbO82jzZp3F1537iNLe1dhRnNrjlDcewc2/p9vYjn6x9GM/nG0K9lyivYGm94JqpMzyQfH\ndy2crv3hCjTQnLdwLyYjkQijGjtLrZztx7xZa8Oudne+nmDjesHx0YNLyYqbSO44+una8G6EGK6/\n9vwV0+3FWrDusxk2I+Z32fXuBZWb9xoJp1tyKC/9/FIMIomtCiMq8OHVH+baAF3WWio+VzH0gmQn\nAbG269Auj5K2X7b+4jG/wbjgbTwCeemn7M8z3ATrsncvi3g/B48e9Bhh1x/3sVfcT6bL/10eaBWf\ntlDRjiAcTqlxLBMVgOav+DZYj0XpdThiMRhmMM5bQwQzcsFIwPOY5/3bCTdRi8Vo7YlC/c/cxOoe\nGZFavX21q246UX2+7vOA845lHqP9xPa5uv/cTFaCjVFxvLvqg6v4cNWHubLtSJL7aHm3U8gr7re8\nCJe/IfZDOZxxmMWbFwddJtFK7eIhr0o8cjpydij+ErFA3I957r3/lv+7POS56sapN4ZdQnW8MPHu\njpRXjDHNgEXcRsA6Q2eXUYlMh5M7eIwKKxIrJxU/ydUlWyQ/aVezHUkmyeMWMXH1DzABgFRrbfAM\nOxcoWXFTpkiZkEPhi4iI5DtxTlZUDeRGiYqIiEjiUbIiIiIiCU3JioiIiCQ0JSsiIiKS0JSsiIiI\nSEJTsiIiIiIJTcmKiIiIJDQlKyIiIpLQlKyIiIhIQlOyIiIiIglNyYqIiIgkNCUrIiIiktCUrIiI\niEhCU7JynJjXa168QxCRfK5YcrF4hyD5lJKVXFKkYJGYbq9V9VYx3V5e6XNWn3iHAMArl74S7xD8\nivX35LJ6l8V0eyLuxnQaE+8QJJ9SshIDZ1U9K94hJCxnstK2Rtu4xnFLs1viuv9ArmxwZUy3d/7J\n58d0eyeyG5rcEO8QEtZNTW/yO33JliVhrX9Pi3tiFssfff6I2bYkMt/c8E28Q3BRshIDZ1Y902da\nlRJVAPi82+ce0+8/+/6Y7HNi54khl5nfaz4jOo6Iyf5GpY3ymXZOzXNCrmeMCWv77Wu1jzSkuKhQ\ntEJMt9e0clOP5zO6z4hqO4tvW4wdZLHYWISVZ0ZeMJIShUrEZd+TukzyeF6+aPmI1t/Vfxe1y9R2\nPa9aompM4opUxuMZPNjywYDz7aDIvxOX1r3U7/RQr/Gu5nfRsXZHxl40Nuhyfc/uS79W/cKK5aTi\nJ4W1nPh3cumTXY8bVWwU0brnnnwuP97yY6xDioqSlRhoUL4BANO7T3dN69eqHzOvn8nFdS92TfOX\n1ETizuZ3uh73bNrT7zKnVTgNgC71u9CyekvKpZQLus1wT773nX2fz7S6ZeuGtS5Akgn8Vbv5jJsp\nm1I24PxyKeVCxvnule+GHYs/4Z5o1vVeF/U+6pary8TOE7n5jJsBuD31du5veT8zr58JOD6ztFPT\nPNaZ32s+q+9eHXS7BsMZJ50RdVzx1LdlX4+k4camN8Zs21/f8LXPtBc6vQA43jOAw48dds3b9tA2\nNt2/yfX87SveDrr9UkVKeZxI45UoJpkkRlwwgvrl64dc9pc7fglrm/4uMoafN5zkAslB1xt38Thm\n9ZgVcvsD2g6gXvl6UcfiT8bjGTx+zuO80fmNsJbPL56/4HnXY/f3ZuA5A4Ou99JFLwE5P2/FSr5N\nVrrU78K4i8bFZFu3pd7G590+p13Ndq5pvc7oxQWnXOB6Xr1k9aAZ6o5+O0Lu56WLX/J47jzwOp1Z\n9Uxm95gddBtzes7xeP7vQ/+G3G8g7geRU8ueyqb7N3HhqRd6LJOclMyT5z7J5Msn+91G2xptearD\nUz7T3ZObX3v/GvQH81jbx+h6elfX8/Sb0l2PU09K9buO99V8OAf6YsnFKFWklM/0UD96p1nXz6Jn\n056uqp+qJaqSZJICXu2MvXAsLau39Iitc73OrsfXnn4tBwYc4OCjB0Pu+7Zmt4UVY6RaVmsZ8Tpl\nipTxeH56xdNdj8+o7D/pKmAKeDxvWKEh3U7vFnQ/HU7u4DPt+sbX88PNP7C+z3oAChUo5DG/YrGK\nrscFkwoG3T5ArdK1Qi4TrjY12gSc90nXT0KuHyqpBWhUqRHnnXye6/kldS9xPa5RqobrsfP317p6\na9e04oWKk2kzA277h5t/8Hj+8iUvA77t1q5scCXlUspRvWT1kPFCdmIZSpJJYsi5Q4ImvIH26bzI\nSwSVi1emXrnwErlA3I+BJQpnH+tSq6Ty6bWfsuWBLQw9dyh1ywW+4CyTUibgvHjIt8nKvWfey10t\n7vI7r1fTXgHX+/iaj32mFUgq4FGC0r5We58rEOfVdK8zHNsuXaS0a94X133ht2TBvSTFyb3qpfdZ\nvV2PDz16yOML6tS4UmMAiiYXdcXWvVF3P68sm7MKKxT3g8gHV39AlRJV6FK/i89yj57zqMeB0N3z\nFzxPpeKVuKD2BR7Te5/Zmz/7/MmYTmMom1KW969+32O+8/X8es+vDD13qMe81jVac99Z95F2Shrp\nvdLZ/fBuAL678TtXtVywkp5AAl05Dz13KHaQ5cULX+Tbnt+6pt/Z/E72PbLP9TzQ+xpou/ec6Vvv\nP/Xaqa7H7Wu2JyU5hcIFC/tdf3C7wa7HBZIK+F0mHjY/sDnidRbcssDj+SV1L2FA2wGu584SjiW3\ne7apcE9ym1RqQpmUMpxd7eyASUbBpIKuhCmlYIrHvGYnNfNZ3ploFy9UHGsjL1lx/4zql6vPRXUu\n8lkmySR5THdfx9veR/aG3Kf79839WOf+m3CWyLono8aYoMnK2dXO9njepFITAJ91PrzmQ4wxdDyl\nY8Dqq0DVUDnlr/2LeyP3VXetYkj7IQAMbT/UZ9lYcu9Z5dwnOL6za+5Zk6NS3NY1spPMFlVaANnn\nnMvqXUal4pUAWHbHMvY8vMe17ND2Q10lndVKVot6/7kh3yYr5558rsdz94NBsBPZ5Q0u93jev3X/\nkPuygyyD2g8CoGHFhgCULFySuTfOZcsDW/weoABevOhFn2lzes7h2MBjPtMLFyzst4g2tUoqBwYc\nYON9G/niui8AeOuKtyhcIPsEd2zgMS6v73hdk7tMZuntS/3uw1vVko6qkyST5NP2IlzO0pnbUj2v\n/K211Cxdk3vPuhfITk7c5wPUKVfHbzHxqE6jmHH9DIoULELJwiUBR6LnTCq9i6DdD+CBispDnYzu\nPvNu2tRow71n3stl9S7jsXMec233/Nrn+3w+3klKsCvIP/r8wcq7VnpM837P3GMsllzM9Z2D8HqT\nOUvFRl4wMuAy1zS8JuR2vEssk5OyX3e5lHKu5MpZfeou0HvgPn3kBSN54twnPEpk/nngH/7r/5/P\n93DujXN57bLXgsY79sKxHiUqzs/l4roX+5S8eKtZuqYrvna12nnMuyP1Do/n7vE6VS5e2fU47dQ0\nvrjuC1e7pVPKnOLatvP1N6/S3ONzff8qzyS+eKHiQeMFR7sSgNk9ZkdcdRVJQuY8jlprA5b6jLjA\nf5u6T7p+QvMqzSOKLRwFkgr4tPdzT1YaVGjAwHMGsuLOFQxsF16JaTTm9JzD3/f/7Xr+aNtHXRen\nzvf41LKnhtxOj8Y9Qi7j/Bzcf4dORQoWoUThEpQvWp6uDbsysN1AbmhyAyvuXBG0pC8e8m2yEg73\napxA3L8AzqvXxhUbh7X9tjXbujJcJ/crQX9JU5JJivgqOSU5hXJFy3kkRRk2wyNu5zbPPflcKhSr\nEFY98SNtHvGZ5n2yCXUwdC5vjGHfI/tCVmPFQvpN6Xx53Zce064+7WrX40aVGnHo0UMcHXiUrg27\n+lxhB1MgqQBjLhzDp9d+SpUSVVwHnnCLsgOpVbqWT1F1sM/Iu6t2oOqw21Nvp07ZOoCjGsIOsvRt\n2dc13/vk/95V73k899fuwLvUokGF7KTklLKOE/Duh3ez+PbFPq/DX7G0wXgs07RyU7+JufPK8fNu\nn7u+R4ULFnaVZnr/1pzuOfMetj641fXcWcqXZJJYe89awPE+BTtR9zqjFxM7T2TjfRtdJWje1bb+\nSkqTTBLDzxvONQ2v4arTrnLsP+u4UyalDI0qNmLcReMokFSA2mVqu0pynCWYbWv69rL7tue3/HTr\nTwFjvfK0K7GDLOfVPs9j+oA2AwKs4WAIXLLirxGv8yLhpBInhVXNCvBX37/49Z5fKZBUwG+3/hnd\nZ3Bs4DGPJC9S3u39PrrmI4/fpzHGdVHpFKy0PRrJSckeiXCBpAIMbj8Y8H/M3D9gv+u7GCnneSTY\n8WLbQ9t496rsdn/erz8RhK6UzYecH2qD8g2oWqIqrau35pbP/Hd9df9BFSpQiJV3rQwrI/Zn3yP7\nSC6QTOEn/Rfr+/Nb79/CboDm7limZ8mJ88fqPCCHqiYpUahEyMZ2gTSt3JSlW5b6TC9WqJiroah7\nG5RYcxaR/tb7N3Ye3EmLqo5i0lPKnOK6wnZe/Tt/wGaI8aj7bVujLd9v/D7kvpwHpPNrZ3cpdh6M\ncprARKJuubrc2PRGtuzbwozfsnscjb9kPHP+mEOHyR38NsYOdSX9/AXPc2fzO3lvxXuMXOAokbmo\nzkX0bNKTScsmBVzPeSJz171RdyoU821IXSaljEdPHfeDeZ2ydVi307O43L1K1mnatdPCHqvo6fOe\npl9rR0+VWqVrkfF4BgZDswnZ1UC3p97ueuycb4yheqnq/HDzD6zatsrnd+nv8zbG0L9Nf59p4Hjv\nf7kzu5Tv93t/913fzza9S3jC8cz5z3Br6q2s27mOVxe/6qoCaFm9JfyQHZd7spL5eCbT1k4L2Iuq\nXvl6fNXjq4h6+gWqevjmhm8oV7Scq1q7cvHKbNm3JeT2Fty8gLNfO9tn+iNtHmFY+jDAf9smd40r\nNaZ9rfa8vvT1kPsL5OjAoyQ/kX28NCa7tMxZTeN9DAZH1fE/e/+haHJRj0T+wlMvZPpv030uYGqX\nqc36/9Z7THMlK3l4vMkNCVOyYoy52xjzhzHmoDFmgTGmRYjlSxljxhlj/slaZ40xplMsYnG26bi0\n7qW83vl1bm52s9/lRl4wkvtbenZFPq3CaSGLjisXr8yT5z7pM71YoWIUKlCIj6/52FWUXiy5mEcj\nOG+nlD3Fo/tktEaljeK+s+5zVe2A4+p3fq/5vHPFOx7LDjxnIF/1+Cqs7fr7gXxzwzcBD2BlU8pi\nB9k8GQTvlLKnuBIVgI6ndKRJ5SZ+l33nineY32s+4DjwfHvjt2Hto3DBwuzqv4uHWj2U43idutTv\nEnCwvUAlWQWSCvBG5zf89npqX6s9H13zkd+xaJzbc+/+6K54oeKcWfVMHmj1AO1rtXc1FJ/YZaJr\nmd5nZretcvYwiCT2mdfPpEapGn4b1IabqF9a71LKFQ3eM86pQFIBj2WTTBLGGO49817XNPeThHO+\nU41SNeh0quNQdE7Nc1yNot2Xeeb8ZxzTojyBOHvihTrWhGqo6Z2MPtvxWXb230nN0jXZ/fBurmhw\nhWte08pNPZIVYwyd63f2aB/h7fza54fVUBl8e1+Nu2gc1zW6joJJBTn35HNdiUo43r/qfb6/6XvO\nquZ/DCxnqXCgBt1O+wfsD1pK5c29N5n79z7Ye+C8CHJVm4VRNecsvbuk7iUenRo+vfZTn2rsaC8q\nE01ClKwYY7oCzwO3AQuBvsBMY0xda+12P8snA7OBLcAVwD9ATWBXpPteeMtCznz1TI8Skna12oU1\nNoF7cXkkQjUwdG8Xs2/AviBLxk7VklUZ1clzLJWShUvSsnpLx9WVG+8GrZHWY5dJKUPDCg359s9v\nIyoVcl5FF00uGrShX27o1ij7RBnuwdfJuweRT1WZ1/s3vft0vl7v2+3WKZyeIYHeV+e+qpeszl97\n/nIt635Scrq8/uX8tvM3wNHTxP09TzJJ7Oq/y3WyrFKiik9PsyfPfZIiBYu4ep9c1+g6Uqv4r45y\nxe3n5O1su3Bm1TOZsmKKR/ulvLxavOmMm7jpjJtYtmUZjSqFN17Fdzd+x97De+k/uz89m/Rk6Zal\nPNTqIX7Z6jih+CtJcnLvtePtyQ5PcnXDq4P22HD/fAJpXaM1BuNqs+bOva3X3A1zObva2UxfN91n\nuVi5rtF1Hs8bV2ocsPt4qGPO1Q2v9pnm3mC1ROESbLp/k98SPnfebeXcfzf+uDeij7SBqnuJmmua\n1/d7UpdJVC9ZnXeWOy4gM20mX3b/EjPEsVztMrV9Ynb2pAvVsSKYRbctYva82fSfELqNZm5JiGQF\nR3LysrV2MoAx5g7gYqAX8Kyf5W8GSgNnW+tqfLExmh23qNqCMZ3G0O30bny82renj1Ojio3C7iUT\nTynJjvYVoQb/ebDlgzz3w3Mx2We4jfSmXDnFdXUUTc+J9F7pTF83nbRT0zh5jP8r/eOBs52Hd3sD\n58Gq06mdXFfmOfXs+c/6VPkBrjY1gex7ZB+FCxamxyc9WP7vcp8eRwbPajF/Hj3nUQD++C/8EUiD\nJa/3nHkP1UtW9+l1ktcClb4FUqJwCVf7lfGXjAccJ5WZ18+kY+2OftfZ9tA2ny7e7pILJIdsgOqv\nm723ysUrkzkoeOL/4dUfkr7R0dMwNy4SHm79cMQXANHwrp6P5nj+UKuH+HbDt0HPFYG8f9X7PJ3+\ntKsKPFADe/fp7m0LIXvU5SkrpjiWzTqOPnnuk6zavsonUQHHb+rIY0dy9B43O6kZ5LwAP0finqxk\nlZKkAk87p1lrrTFmNhBoEIdLcdSkvmSM6QxsA94BnrE28l+Ts8fJTU1vCnivFve640RWukhpVt21\nKmj/eXC0wg/UEj+W3BsDX3v6ta7H0bSzqVisYsDB8MDRq6NU4dAH6HirXaY2mY9nut4DZ/FvJA15\nw/VQa8/qJ+eBsEjBIgEbnIKjShLgtcteC3uk0UCcVSqX1PFfnel+9Rjs8yuYVJArT/O8PcEz5z9D\nv9k5iy8ejDFBG/BHOppubqpQrIKrtNffyTCnhp0/LOJ1ojl+5GR7aaemUbtMba5ocEXAtjJ9z/Ys\nafcuFbm64dXM/2u+T3s9904G4JkQ3nfWfTz89cO+8XolNs4Lg0BOhKqguCcrQHmgALDVa/pWIFCF\na22gA/AWcCFQB3gpazu+jUHC9Hrn6BtQJRL33hfxMiptFGWKlAnYan/ouUMpmlw06i7PLau1ZM6f\nntUO/sYlyU01S9Vkw+4NUa3rfnA8qcRJjL1wrE8xeDRClVi5GveGebAvmlzUZ3Tcvmf3DdqOylvJ\nwiWDVqvWKFWDdjXb8Vjbxzi5jKPELFRxu1Pn+p3pXL9zyOUkNu5veT8Dvgneaygvrb1nLfVezNkA\nauGoWKyi3wbO4GjP5RxkMJTzap/H6B9HU7NUTZ/fqr8Gtv3b9PdpgA2e3cLzi0RIVgIxELB+IQlH\nMnObdXxaS4wxVYEHCZGsPNDqAXqkhe6bLr5evuRljmYcDbqMs468bErZoDeKK5tSlmc7+qvhC8+0\nbtPYvDfywcViacVdKzh87HDoBcMQ60QrVFuOnLT1GJkWeByWaCQXSPZosHx3i7vp0biH314cEl+B\nBiDMa62qtWLplqUhS5DDNanLJMYtjHxE85EXjIzot3tJ3Us4NvAYBZIKYK3l0baPcmuzW4HstnDB\nbj3i5GrfEqQK/tjAY1ENfpmoEiFZ2Q5kAN5l0hXxLW1x2gwcsZ5p5WqgsjGmoLU24IhmP7z6A79+\n9KvHtG7dutGtW/Chu8X/IGQGw6Nts4sgr2t0HVv2bQk5FHpOFS9UnDrl6uTqPsKJIZxBuPKSsz2M\nc7Ayb8fDlZi/wRDl+Ne8SnNuOSM2dz8f3Wm0q3t5LDQ7qRmvdQ4+eKCTe6lkoME4wVEqOeXKKT63\npHBWjRtjeLJD9rV1sULFmHLllLDaq/krhfGWk1Grp0yZwpQpUzym7d69O+rtxULckxVr7VFjzCLg\nPGAagHF8G84DXgiw2jzA+2xYD9gcLFEBGD5iOG3P9h1ISaLj3TgvuUCy32JLyRsX1bmI9feud1Wn\nBBLrOn/JX0L1ovEnki7AoSQXSA6YkOc291JJf8nCxXUu5ot1X3BFgys4qURkd4x2b9cXjLPEJLd6\nRfq7gF+8eDGpqcF78+WmuCcrWUYCk7KSFmfX5aLARABjzGTgb2uts7L0f8A9xpgxwItAXeARYHSo\nHcXiID2161Rmr8/9kVZFohEsUYnXnYHlxPHB1R+47vsjvpwlGrlZBeOvMe6JLiEqtKy17wMPAEOB\nJUBjIM1auy1rkWpAZbfl/wYuAFoAy3AkKaOAZ/Ii3s71OzP2orF5sSuRmOrZxNGb6njohi+x432X\n8Zy46rSr4l4FG0+JUCrZ64xepBRMCfs2BieCRClZwVr7Eo4ePf7m+YyHbK39EYh4mNPjoc5eJLd0\nOLlDWAMeyoll+Z3LfYZhl+NX08pNOfDogXiHkaeiKlkxxiQbY6obY+oZY0I3XU4gKgYXkfymZuma\nPneal+g4b58geSvsZMUYU8IYc6cx5jtgD/Anjh4424wxG4wxr4S6n08iUMmKyPGh06mdXHcZFkkU\nqVVSmdxlcsD5zmHto2mELIGFVQ1kjOkLPAb8DnyGY7TZf4CDQFngdKAtMMsY8yPQ21q7LsDm4irU\nvTJEJDFM755796ERyYnL6l3GBadc4Lf3zjUNr+GahtfEIaoTW7htVs4CzrHWrgwwfyHwetY9fW7C\nkbgkZLKSKIMaiYhI3ihdpHRMt1eqSClmXj8zptuU4MJKVqy1YXX+ttYeBsbnKCIREZEYmd9rPtVL\nVY93GJJDCdMbSEREJNZaVg90P1w5nkScrBhjigC9gXNxDInv0UjXWtssNqGJiIiIRFey8hqOAdk+\nxNFWRd1rREREJNdEk6xcAlxkrZ0X62BEREREvEWTrGwC9sY6EBERkUjNvH4mB47mr9Fc86NokpUH\ngGeMMXdYazfEOiAREZFwXXDKBfEOQfJANMnKz0ARYL0x5gBw1H2mtfa4Gn5fREREEls0ycoUoCow\nANiKGtiKiIhILoomWWkFtLTWLot1MCIiIiLeornr8hogJdaBiIiIiPgTTbLyMPC8Maa9MaacMaak\n+1+sAxQREZH8LZpqoBlZ/7/2mm5wtF8pkKOIRERERNxEk6ycG/MoRERERAKIOFmx1n6XG4GIiIiI\n+BPVXZeNMaWBM/F/I8PJMYhLREREBIjursuXAm8DxXAMu+8+zooFlKyIiIhIzETTG+h54HWghLW2\ntLW2jNufRq8VERGRmIomWakKvGCt1Z2jREREJNdFk6zMBJrHOhARERERf6JpYPsFMMIYcxqwHN8b\nGU6LRWAiIiIiEF2y8krW/8f9zNOgcCIiIhJT0YyzEk3VkYiIiEhUlHiIiIhIQgsrWTHGXBvuBo0x\n1Y0xraMPSURERCRbuCUrdxljVhtj+hlj6nvPNMaUMsZcZIx5B1gMlItplCIiIpJvhdVmxVp7jjHm\nMqA3MMwYsx/YChwCygCVge3ARKChtfbf3AlXRERE8puwG9hmdUmeZowpD7QBagIpOJKUJcASa21m\nrkQpIiIi+VY0vYG2A1NzIRYRERERH+oNJCIiIglNyYqIiIgkNCUrIiIiktCUrIiIiEhCizpZMcYU\nMsbUM8ZEc38hERERkbBEnKwYY4oaY14DDgArgRpZ08caYx6OcXwiIiKSz0VTsjIMaAK0xzEonNNs\noGsMYhIRERFxiaYKpwvQ1Vq7wBhj3aavBE6JTVgiIiIiDtGUrFQA/A2nXwywfqaHxRhztzHmD2PM\nQWPMAmNMiyDL9jTGZBpjMrL+ZxpjDkS7bxEREUlc0SQrPwMXuz13Jii3AD9EE4QxpivwPDAIOANY\nBszMGto/kN047knk/KsZzb5FREQksUVTDTQAmG6MOS1r/T7GmIZAS6BdlHH0BV621k4GMMbcgSMh\n6gU8G2Ada63dFuX+RERE5DgRccmKtTYdaIojUVkOXIDjDswtrbWLIt2eMSYZSAW+dtuHxdFgt2WQ\nVYsbY/40xmw0xkzNSp5ERETkBBPVGCnW2t+BW2MUQ3mgAI6Ex91WoF6AddbiKHX5BSgFPATMN8Y0\ntNZuilFcIiIikgAiTlaMMRcBGdbamV7T04Aka+30GMVmCNBg11q7AFjgtu8fgNXAbTjavYiIiMgJ\nIpqSleGAv8HfTNa8SJOV7UAGUMlrekV8S1v8stYeM8YsAU4NtWzfvn0pVaqUx7Ru3brRrVu38KIV\nERE5gU2ZMoUpU6Z4TNu9e3econEwjuYhEaxgzEGggbX2T6/ptYCV1tpiEQdhzALgR2ttn6znBtgI\nvGCtHRHG+knACuBLa+2DAZZpBixatGgRzZo1izREERGRfGvx4sWkpqYCpFprF+f1/qPpurwbqO1n\n+qnA/ijjGAncZoy5wRhTHxgPFAUmAhhjJhtjnnYubIwZaIzpaIw52RhzBvA2jq7Lr0a5fxEREUlQ\n0VQDfQqMNsZcntXQFmPMqTjGSZkWTRDW2vezxlQZiqM6aCmQ5tY1uRpwzG2VMsAEHOOr/AcswtEb\naU00+xcREZHEFU2y0g+YAawxxvydNa0a8D3gtwomHNbal4CXAszr4PX8fuD+aPclIiIix4+IkxVr\n7W5jTCugI44bGh4EfrHWzo11cCIiIiLRjrNigVlZfyIiIiK5JqpkxRhzHnAeju7FHo10rbW9YhCX\niIiICBDdoHCDgMdx3NBwMzm407KIiIhIKNGUrNwB3GitfTPWwYiIiIh4i2aclULA/FgHIiIiIuJP\nNBLqPeYAACAASURBVMnKq8B1sQ5ERERExJ9oqoGK4Bht9nwcdz0+6j4zawwUERERkZiIJllpjGOE\nWYDTveapsa2IiIjEVDSDwp2bG4GIiIiI+BNNmxURERGRPBPtoHAtgKuBGjh6B7lYa6+IQVwiIiIi\nQBQlK8aYa4F5QAPgciAZOA3oAOyOaXQiIiKS70VTDTQA6GutvRQ4AvTBkbi8D2yMYWwiIiIiUSUr\npwBfZD0+AhTLurHhKOC2WAUmIiIiAtElKzuBElmPN5Hdfbk0UDQWQYmIiIg4RdPA9nugI7Ac+AAY\nY4zpkDXt6xjGJiIiIhJVsnIPjlFsAZ7CMYJtK+Aj4MkYxSUiIiICRDco3E63x5nA8JhGJCIiIuIm\nmq7LGcaYin6mlzPGZMQmLBERERGHaBrYmgDTC+PoHSQiIiISM2FXAxlj7s16aIFbjDH73GYXAM4B\n1sQwNhEREZGI2qz0zfpvgDsA9yqfI8CfWdNFREREYibsZMVaezKAMWYOcIW19r9ci0pEREQkS8Rt\nVqy157onKsaYAsaYpsaYMrENTURERCS63kCjjTE3Zz0uAMwFFgN/GWPaxzY8ERERye+i6Q10NbAs\n6/GlQC2gPo57Az0Vm7BEREREHKJJVsoBW7IeXwR8YK39FXgdaBSrwEREREQgumRlK3BaVhVQJ2B2\n1vSiePYQEhEREcmxaO4N9AbwPrAZx5grX2VNPwuNsyIiIiIxFs29gQYbY1YA1XFUAR3OmpWB7hMk\nIiIiMRZNyQrW2g/9TJuU83BEREREPIWVrGQNtT/BWnvIbdh9v6y1L8QkMhERERHCL1npC7wNHCJ7\n2H1/LKBkRURERGImrGTFOdS+92MRERGR3BZN12URERGRPBNum5WR4W7QWnt/9OGIiIiIeAq3zcoZ\nXs9TgQLA2qzndXF0XV4Uo7hEREREgPDbrJzrfGyMuR/YC/R03n05647LbwDf50aQIiIikn9F02bl\nAeARZ6ICkPX4sax5IiIiIjETTbJSEqjgZ3oFoETOwhERERHxFE2y8gnwhjHmCmNMNWNMVWPMlcBr\nwMfRBmKMudsY84cx5qAxZoExpkWY611rjMk0xkS9bxEREUlc0SQrdwDTgXeADcDGrMczgLuiCcIY\n0xV4HhiEozHvMmCmMaZ8iPVqAiOAudHsV0RERBJfxMmKtfaAtfYuoByOxKIZUNZae5e1dn+UcfQF\nXrbWTrbWrsGREB0AegVawRiTBLwFPA78EeV+RUREJMFFPSictXa/tfYXa+2yHCQpGGOScXSF/tpt\n2xaYDbQMsuog4F9r7RvR7ltEREQSX1R3XY6x8jjGbNnqNX0rUM/fCsaY1sBNQJPcDU1ERETiLRGS\nlUAMjhsjek40pjjwJnCre/fpcPXt25dSpUp5TOvWrRvdunWLNk4REZETxpQpU5gyZYrHtN27d8cp\nGgfjqHGJYwCOaqADwJXW2mlu0ycCpay1l3st3wRYjGPEXJM12VmdlQHUs9b6tGExxjQDFi1atIhm\nzZrF/HWIiIicqBYvXkxqaipAqrV2cV7vP+43MrTWHsUxTP95zmnGGJP1fL6fVVYDjYCmOKqBmgDT\ngG+yHv+VyyGLiIhIHkqUaqCRwCRjzCJgIY7eQUWBiQDGmMnA39baAdbaI8Aq95WNMbtwtMtdnadR\ni4iISK5LiGTFWvt+1pgqQ4FKwFIgzVq7LWuRasCxeMUnIiIi8ZMQyQqAtfYl4KUA8zqEWPemXAlK\nRERE4i7ubVZEREREglGyIiIiIglNyYqIiIgkNCUrIiIiktCUrIiIiEhCU7IiIiIiCU3JioiIiCQ0\nJSsiIiKS0JSsiIiISEJTsiIiIiIJTcmKiIiIJDQlKyIiIpLQlKyIiIhIQlOyIiIiIglNyYqInHBe\nfRUWLIh3FCISK0pWEkjXrjBpUryjEDn+3XortGwZ7yhEJFaUrISQmQl9+8LWrbm/r/ffhxtvzP39\nnKi2b493BCIiie+dd2DDhnhHERklKyGsXg2jR8OAAfGORIL55ReoUAFmzIh3JCIiia17d0hLi3cU\nkVGykovGjoW2bXN3H++9B7t25e4+jge//+74v2xZfOMQETkeHG/nDSUrIVgb/br33gvp6bGLxdv+\n/XDttXDHHbm3DxERkXhTspKHfvkFqlVzJBmxkJHh+L9zZ2y2Jye+Rx6BH36IdxTibts2GDgwZxdG\nIie6fJes/P13ZMsbE/k+1q3zv964cbBpE/z2W+htbNniSGw2bQq8jPPgFk2Mkj8NHw6dOsU7CnH3\n0EPw5JPhHRe8degAb78d+5hEEk2+S1auvDKy5aO52pk9O/J1vM2Y4UhUpk0LvIySFZHjn7OENBpz\n5kCvXrGLRSRR5btk5dix6NZ7/XU4dCi2sQQTTiKiYuPEcvgwrF8f7ygkv0nE48D8+Y5j1+bN8Y5E\nThT5LlnJiTlz8n6fxsDu3fDMM74HJZWsJJY774RTTol3FMeX336Dr7+OdxTxlYjJRk598YXj/5o1\n8Y3jRJaZGf3F9/FIyUoEcpoURHJQci772Wdw003w8MOwcmXuxCWxoYarkatTB84/P95RJIZ//jkx\nExfJHddeC8nJ8Ouv8Y4kb+TLZGXePLj++sjXC5YUbN2afbLKafJw9Gj24y++gE8+cTwOVLIyfToc\nORLZPjZvdjQEPhFMm+YYuC+39OnjGM8m0fz+e/66ssoNBw/mvHp3797YVBG3bw+TJ0e+nhKcvHX0\naGKMUfLBB47/9erFbpurVsG+fbHbXizly2TlhhtCt6Bv08b3BPXmm57PV650JCZr1kCrVo6/QDZt\ngldeCS++Xbv8H4AyMx3/9+517Hfq1Ox506eHt22A5s2hShWoWzf8dRJZ584wd67j8cqVjmqzWHrh\nBcdVTCh5edI4cABOPRUGD875trZudXyn8qMyZaBSpdDLZWQ4euj5U7IkNGkSm3iWLInNdhLFiZhI\n3XCD43uTiAYPzj4WRqNhQ7jmmpiFE1P5MlkJp+Rj3jzfwdbefhvWrvVcBhwlKu4NK1ev9t3eqlXZ\njwcPDn5FfPAg/Pyz7/SmTR3/nft66qnA2whm0aLo1suJlSsd7TliNcbM88/Dv//6Tn/zzfh1zc3t\nA/OCBY7v7p9/Ohrzgv/vSaQqV47dyTYvjBkTfuIfyuHDsGeP/3n33QeLFzseP/44nHRS4J47OSmK\nPxFP6InirbdiP6y8s6Q7pw4fjn3J6JAh0K5dzraRqAmzkhUcg6r5K8b1dxCpXx/uv9/xJUvKeve8\n133hheD7nzo1eJfkO++E8eP9z1u4MDtp+eOP4Ptxd+QIXHEFbNwY/jqx9NJLjiQrVIO7w4ehRg34\n8cfAy2zfDg8+6Hif/Annx/bDD47kyb3KLV4uvBAuuyz0cs6GqCtWxL6dUiTfpZwaMMBRqvfEE5Gv\ne+iQI4m47bbwB0P86y/H++V+wQCh38MxYxx3Qgf47jvHf2sdN4GLpromHOEkLtdee/y0U4tHnK++\nmn1B16MHzJqV9zGEo0gROO+8+O0/0HfN32d21lmxS9KipWQFKFcOOnYMf/1RoxylKs5kJdL2IhD8\nJOmvZMbprLMi3xc4fsCffOIYFCy3hHOlEOpgvGWL4+QycmTobQR638M5QA4b5jigJcLovzNmOBpS\nh+LvdSXiVXmDBsFPEMOGOdpLPf54ZNtdtQpSUrKflysX3noLFjj+h7rJ5U8/Bf5dur/P3f/f3pmH\nSVFd/f9zABVFcCPILwlKoiKKERUxmhg3DC6Ie4QYRU3MQ9RXs6kR4xuU+IoQYxa3oMZ9RXElGpQY\nt6gQQQRFWVRAkB0EhhlwYM7vj9NlVVdXbzM93Q1zPs9zn666dbc6feveb917q+pHcM45heXdHCSt\nn1qxwtYuVOpmpJr46U+hb9/Sp6tqIjU6ujZ6dPjEZjEE1/Krr9pTptV4HUeZOLHxI/mlokWKlYC6\nunAqIfoNn6lT88dVDdeQxO/YksI+8ki638CBpvqDO7Yopb4bqauDiy5qXNwJE2DXXQsTZG3b2ihB\nwHvvwSmnmJ2q9U6wWsuVC9WmlXv1amtkS8lLL9mr/MFGz666yqb+SplPLhGfi+BdHzU19mr7JJYv\nh4MOgoMPhhdfzDye1JmsWFH69VGN7bReecWmoh5+OH/Yhoaw7VKFYcOKf7N3McyYYTd2SdO20TKV\nctFqXV3j4zY02HTKqaem+w8bZiI1ekP29NP2G9QrEXO5bkbjdeaoo9LXHzYXkybZjfamSosUK8FT\nMMcfn7y4rpD5+/nz4Q9/sO3bb88ddvx4e6lcnAcesCcAZs5MX+DYqhH/Sq5GLnpxJYmjXNxwg92t\nZVtcGGf8eOjVC8aOhV//2i7C6LmpwrRpzft15MZ25DNmWENSVxc2OqVm8WKzTbmZMwdeey3cD6Y3\nGsuaNWGHBzacHR21U4V99ml6PqXgqqvsd+hQ6NQpOUwwlTt5cvJdedL1tdNOuRfnfvih1aFSrCsa\nN84e8c72+oKAQsTOdtvB/vvbdm2t2SX6Ftxly9LX5hXDJ59k1oMnnrDfYIQrid/+tumLVlXDdYRN\nYe+9bV1hfNrjllsyw2ZrI3Ld3HXsmOkXFXILFtj/sWGDucZ8hiGJ3r1tCUNATU2yqArO6dZbq+sj\nuS1SrAS8/HLu46tWJVdQsFGRQhfV5XsUbM89i5uGSuKUU5L96+pC9Q/5R4HAHokN1H9QcVVNuHTu\nnD/+5MkmVKJEL+p997V1N7fdlnvtTmOJNyCzZsGYMfnjde9udznZFlzmo5COol8/6N+/+LRHjrTp\nMUg/v0LvxLt3h8MOKz7fbHToAL/5Tfbj1T6sXSzB+cTPK1jonESwdqqY9+9ks9vgwbZm6aWXCo+T\njZqazNHjII316+367N69uDTB0jzyyHCELSCpQx87Nr0TDgRO0rl8+KH5H3qoTZnMnGnXQ5x777Uw\nYO+syZZ3PrIJtWyjclDcf5A0VT5nTug/dCjcfbeVY8gQexdRc6ytq60NR49mzcocXbvoIhg1qvT5\nNpYWLVaSiK9hyLbQtdRMmRJul/IV1TvtZMIqG+PGZYqu3XcPV5QHozyqcPnlNjJQLIsW2d1akE7A\nhRfaY8fZuPlmu4iLpbY2/e7lwAPh9NMLixs8/dEYCmmwGvPf1tebMAjq4tq14d16oW9VztWp5mP/\n/cNOIErSOptSiJTnnoN77iksbF2d/d/x1woUW6Z8nVpTzquYuNEOsUcP64CjaeQSiMXy0kuw/fa2\nPXGi2aBt2+x19LXX7FhNja3vidOzJ8ydm17eKFG//v1t5C1OdLQOrG3aay/4+99t1OSoo2wxepId\nktbrNLdoLkYMHX98+G6UONdfby94E0kvc3Cdx59CK2SNWyGMHWuCpFs36NLF/OLnFB2RrSQuViLM\nn1/4or1sJF3EhRDtTErxeO/GjbaAMd/c7bHHJr9UKJimiY6sxBk3Dtq0sc4017Bx9+6Za3YK4eKL\n4eSTi48HtgYhIBgpmTMnc5SrmEWrwTt18pEtfq47s2IYODB862v8Lq2Yl5OJFNYQTZmSPLwerNuK\n5hmce7RxXboUdtwx93eTolME/frZW5uT8ovTpYvV80GDso90lqLDyjaykotCX5Hw0EPh/qOPhvac\nPt1eSBjNN3o9R//7QjvNadPC7T59wjQKGU087DB7l9TZZ9v6nii5PgVSW2vb8anwJAEdr89B3Gi7\nGm1r1q83IVNTk3+KbN683OtmmkL8/JP+j+efL2xhdtRO0fZ34sRQDL73XmZ+udqXf/0re91NmuqJ\nLuIORmQrvb7PxUqEUrzRNX4RV4rx4xv3aGiUCy4IRUa0og8ebBfUn/9snVJNTeZamJkzk4esc7F+\nvc3XRsm3sDffeoDHHw+3v/GNcLqtse+aCb55kou1a62RnTrVRghmzbIpr06dwuHpUjJmjJ3n2LH2\ntEwxgjm6PuO737UGacSIwuNfckn6EzoB0ZHC11+HlStzT8UdcojVp2wNal1d8vD58uWWNhQ+VC6S\nKVqzdTazZ1u9LEak1NSki7WGBptaBetQginWuXOTR6yS6nx8xAHsTrxQVMMpnkK59NJwuigQSXPm\nhII9eBHlypWZC6mD/2Lq1PDm65ln4Lrrco+WRu129NF2QwTZ24EhQ+D886F9+9yLuUXsQYH4GqOG\nBptyaeyXr4N68tRTuafyg5unYjv8aPhvfxu6drXtpOUJvXtnT6eYT1osWFDYSzDLjqq2CAccAChM\nUrt0Nz8XMGKE6rXXNi6uavLx2bOzx12+XHXUqMLymTAhe94DBoR+Z5xhv3vvnV62iRPDMCeckP+c\nkvzHjw+3Fy/OPO/Ro8Ptd99Nj3vQQZrBsceq3nyz6u67W5jWrVW33rp4ewd8/LHqkUeq1tXZ/hdf\nFPdf3nmn/Seg+vjj2e0Aqltumbt83bun+z3/vOrFF9t+t26qO+6YHm/Dhux5jRyZuyyg+s9/ZpZh\nzpzCznvcONWhQ1UbGkK/jRtV27XLDDt3bvr+/PnZ0+3XT3XnnW17/fr8/ymonnee6sMPpx9fuNB+\nt9tO9YknVIcMSU4ner4dOliaX/1q9nxbt1Z98knbHj48s36qql53XXF1KH5eAweG+926hdvxc0xy\nv/lNYTYD1dWrM/1AdaedMuNu3Ji/3LnyVA3tdtddyfmqqi5ZorpsWXI6Z52VnMfatXa8vl71iitC\n/223Ldzu772netRRYXqF1NWkc4yf0/XXN64etGo1Sa0P5QDVCvThlci0IifaQsTK73/f+LhJFTtw\ns2Zlj7t0qerf/lZYPkli5dprVT/4IN3v5JPtt0eP9LINHRqGySdWxoxJ9r/vvnA7ECv19clhX3gh\n0+9Xv7IOMZe98rmf/lR1t93S48+YYQLliCNCW6k2TqxMn27b552Xu1Fv0ybZf9WqUPBE60h0f489\nVHfYId0vmx2hMLGSVCfbty8sfNeuYX0M/NatU91mm8ywcbFy4YWF5bFuXfZjK1eqfvSRbbdvn17P\nQHXw4MLyeOONcLt9e7NB587Zw7dqZXUJTEi2b6/64ovp182BBzaunkLmf1ysu/LK/P9xsL9ihdWh\n/fbLn27//vnrT5J/0rV72mmqN95YeBr5jgViZdy4dP9C6zKYWOnTJ0yvGJtHiYr3pjkXK+U50RYg\nVpriPvvMfkeOTD6eT6zcdlth+Vx6abJ/0NjGXVys/O//hsfyiZVs7tZbw+1ArGQL269fsv+SJSYu\nVq1qmt2jeY8apXruueH+hAmqa9ZkioZ87rLLVAcNsu3zzssdtlWrxpUVbCRp++3T/RYvzp3Ga68V\nnl8wslSsTV9+Odxevz5ZrBxzTOP+r1ydfpcuTasLgQv+u6jd27Yt/j88++zwuilFuRrrOnbMfuy9\n99LLt3RpppAstQtGcPONzIBdf9mO1dRkP7Z2rcXdf//Gl3PyZNWePfPnleRUTaQsW6b67LOlsp2L\nFVJi4iLgE6AOeAvonSPsKcB/gZVADfAOcJaLlca7XMPMoHr77dmPLVlSuFgp1u2zT3jhNTTYNExw\nrLFiJeoeeaT4uxYI794POKBp+R96aPZjN93U9PM75JDS/RfxTi9JYH7zm6XL7xe/aHpH+/HHpStP\npdy//pX7eC7BOXNm5cVKPvfHP4bbixYVPu3XVPfII/nDXHJJ9mOBkEhya9cWPxVfSrdggS0HgHDa\ntunOxQrAAGAdMAjoDowCVgAds4Q/DDgJ2BP4BnAJUA9838VK87h99sl+rDnFyo47hlMVf/pT+rG+\nfUuTx513Fh/nBz+o/H9Sbjd2bPnzrPaOthwu1zTK5mDD6DqOd95R/eST6rFrdKSzGFdTozpsWOVt\nW1rnYoXUSMpfIvsCzAcuLyKNScA1Llaax+29d/Zjo0ernnhi85fhlFMqbwd35XW5phDcFeZKd2dd\nHvfQQ5UvQ1Pd5jCil+kqK1Yk1ZFXDBHZAqgFTlPVZyL+9wDbqWqWd7OmpdEHeAo4SVUTH5gVkQOA\nSaZpDihF0R3HcRynhTAZ6AXQS1Wb8PrMxtGm3Bkm0BFoDcTfjboYm+ZJREQ6AAuArYANwIXZhIrj\nOI7jOJsu1SBWsiHYkFM21gA9gW2BPsCfRORjVX21HIVzHMdxHKc8VINYWQZsBOLfL+1E5mjLl9ii\nMYIXeE8Vkb2BIUAesfJLYLuY3w9TznEcx3FaOg+nXJRVlSjIl1RcrKhqvYhMwkZHngEQEUnt/7WI\npFphU0J5+BO+ZsVxHMdxspF0A//lmpWKUHGxkuJG4N6UaJmIDX9sA9wDICL3AfNV9crU/hXA28BH\nmEDpB5wFJHySyXEcx3GcTZmqECuqOlpEOgLDsOmgKcAxqhp8R/Lr2CLagHbALSn/OuBD4EeqGvls\nneM4juM4mwMVf3S5XPijy47jOI7TWCr76HKrcmfoOI7jOI5TDC5WHMdxHMepalysbMK0qYoVR47j\nOI7TvLhYaSYOOaR0afXK8rTYr39dujwcx4H77690CaqXs86qdAmcloyLlWbi9dfhrrtKk9Yuu8AJ\nJ8Dhh9vnpJ57zvwLWRv97rtNy3uLLZoW33GKoW/fyuZ/1lmwZElly5DEuecm+++4I2yzTXnK0K1b\nefJx8jNgQNPTWL++6WmUkxYpVv7nf2DlyuzHd9ghd/zjjsufR6tWsGFDut8//pE7zgknJAuQNm3g\n2Wfh5Zdtv317+21ogNmzs6c3dy7suy9cdVX+8sZZuNB+Bw0qPm7PnuF2hw7QtWvxaTSV995L3z/m\nmPKXodyoQk1N8+dz8cWFhRsypPA0H30UFi8Or70FC/LHeeqpwtMvhq98Be64o7g4P/5x+v6jj5au\nPAB33x1uP/88fPIJfPEFLF8Oa9c2Le3vfS/Tr2dPuPrqdL8ttywsve23b1y7USkqPWL05z9nP3bb\nbcn+N99sv336wCOPNC7fQv9PgMGDG5dHSanEp54r4bDnlRUm6bJlqhs2qB5xhOrkyarXXZf+Key3\n3krf/+gj1YYG2+7dW/VnPwuP7btvuL1yZbitqvr66+npvP666iuvqL7/vh2Pf4K7oSHZf+BATWPJ\nEvN/7bXk8IFbscKOb9ig+tvfJod5+mnVN95I92vXzuJNmKBaWxv633+/avv24X7//pnpjRpl+dXX\nqx55pOro0aqrV6eHue22zHi//KXq1KmqItnPJ+569Ur2f+wxK/+rr6q+/bZtT59eeLpR169fpt/X\nv646bZpqp06q3/9+9rjHH5++//776fb8y19UDzqo+DKdeqrZ9/770/0Deve2/Z/9TPXnP7ftqVPD\ncJ07J6e7zTbJ/vvtp/r3v6fnE2zfeafqxo2ql19u+yNGqPbpo7p0qYWbO1d13DjVd95JTnuXXVRP\nOy0s+8qVVmdy1evALV0abv/kJ+H2kCHJ57T11snpRK/ngJdeSg/zwgvmv+22yWnEyztvXvr+brvZ\n75NPNq4eRtN/9VXNIBq2b9/Gpb3LLpl2iIarqwv/52zu3XeT40bdqlXW1t14Y+j3ta+p7r57ZtjP\nPw+3ly9PTq9dO/t99FHV997LPL733vZ7442q3/525vG5c+13r73y2+rMM+33u9/NHuaGG8Lt1q1z\npzdtmtlqzpx0/z59rB7fdZftn3yy6tixdi1GbdGvX/5r5eWXC6uzcbfrruG29ZGT1PpQDlCtQB9e\niUwrcqIpsdKz5ySNE29AZs603+22U91ppzDcccdZx/7pp6oHHKD617+q7rOPpjUgoPrNb4Zx3n/f\n3F13hWIkIKnyJPl/+mlGkdN47LHMOBdfnB7m7ruzV1jV9EahQ4fkcgYsW6Z61VV2PhMmqA4apPqL\nX+QuI6j+8IeqixZZ53bSSba9Zo3q8OEmaFTDBuOZZ1Rnzw7z7tQp3H7oIfuNNjxHHx1ur1uXvQwQ\nCq7zzw/9br/dzivYP/FEixMN07q16sKF6Wn+9Kfhfx5vZFVVL73U9rt0MRGnqvrHP5p/wOLFqkOH\nWqc+fLgJgCCd9983ARhN+/TTw7inn575/wTh//53s/X69ennf+GFyXXh978Ptz/+ODPdxx+3ziCp\nTlx2mX7ZMCaxbp3qoYdm5vnRR8nhVVUfeCAz/KmnhtvBDQRYBzh0qJ1v0Pk880y6fQ4+OPm8X301\n83waGuyaOecc8//Pf8x/yhTrjFatss571izViRPtWLQOxMVKcGzsWPu9+mrVPfdMD/PEE8nl23bb\ndJu/8UamraLXyssvqz7/fHJaQd7Dh6efM1jn1LWr6g47hOlGxbpqeNMzfLjquefa9lZbqY4ZE9oh\nIJpnjx6ZNlYNb/Y+/9xuWIIwy5ebrYN0dt45M8333zfR/vHHJlSy5f3002Ebun59pj0aGux8otf/\nqFHp9SJwL7xgv7/7XXb7RoXHLbeovvmmtW8XXGB+V16ZXN9vvjnTRrW1Fq+mxvbXrjWRHgj1/v0z\nzxfCdgdU//vfcHuPPazsU6davJEjw2NnnGHXT7Af7Vfq61X/9jcXK+U50ZRYefzxTLHS0GAdxVZb\nhRVlypRMcZHEjBnWSAasWBFWrHwEFeHOO61Cxf2DTqMQRoxIjxcnUOhgZU4KF/jdc0+6/x572GhC\nOfjOd6wMGzdaZxCUacMGG/F68UW7ULt3twYSrFNRVb3vPvPPRpBWcIE++aTqggWWZjzM4sW2H4iV\n//43uT4Ex6dNC+N++GHT7QDpncaaNTbiAKoPPxz6f/GFNarBHZpquliJct11qt26hf//mDFmgxtv\ntE532DDzf/ZZCz9gQHJdCsoXPRY0jkl3/VE+/9wE39y51jnko3NnE5IBCxdaPoGYnDIl/f8LqK21\n30Cs/O53qvPnW0cejLJ166Z6663poidOMDL11lv5y3rxxRZ2/PjM0cSgHBs2qP7f/1ndvvrq9DDx\nUYGNG62jDdqTaOeaRHB85Urb797d9pcts3py5ZW2P2FCevhge9ddrVOqr89+jvPm2TW6Zk24vBXs\noAAAEVZJREFUv2RJctiGBhOpQQedZOPVqy0N1fAav+GG9DB/+EM4Gr3TTtn/qyRbgNW1KNdcY+d6\n3302sh5ljz3S0w6EVqtW6f7x9vbee8Ptmhr7bds2HN1WDYVeMEqXxOzZuQV8wKJFltbJJ9t+fJQ5\naoOGBtU77jDhmXQzEYxKBjz1VDhCNm9eODo9aZKLlfKcaA6xEhAME5eLwYOT83v77cIuyCSyxYtO\nbWULN2eONehxGhoKE26lYPZsu6iD/Dp21C8b7iTiDVEuHnhA9aabrDG57DJrwOPE7RKMNmRrQIIp\ntDVr7Dc+KtVYpk+3BqkxBMI0EHGFcs01Fu8f/7D92loTNkkEUycBwchKMDXZXHz2meVz0kmFhf/B\nD5I7rDPPDDttVRs5SRIkgQiblL3Z+JK1a21UNiAYvRg0yI4Fo1IBQUcOqv/+twmYHj1U27SxEds4\nYCOP2ejVS/XBB8P9pUvTO+OaGhMC8elmVbPHK6/kP8fG0NBg109j27Qo0dGPXDQ2r0WL0uvBmjX2\nP61eHY7+qlo93Hlny2PAAPMLptGysXChjYQEQropBHUnLtSffNKmMFXDUat81NfbSFY+XKyUWayM\nGZO91Rk92qYTqoHGXmw33JB9dCGa5gknpDds1crcuarXX1++/OJ2r68vvBFfvtymByrN+vUmPILp\nn0IJ1pV89lnxea5cqXrFFeFUV3OxapWV8brrCgt/000WPnqHWwyrV9tddGPE+h13WN5jx2YPE0xl\n5hrNCBgxIl0MNZWRI21qrxzMmmXn+aMfNT2tYI1KLp56yqZfmpv588O6kWskshLU1ZW2Paq0WGlx\n3wZ6++1J9OpV/d8G+vRT++3SpXRpithvC/nLG4XbqPr59FP42tfsibt8qNoTMx07Nn+54mzcCA88\nYE/GBPUqziGHwFtv2ZODrVuXt3zlJPgP7r47+2PYhbLDDvD559V3ja5bB/Pnw+67V7okzcPkyZPp\n1aty3wZqce9AzdZoVBulFCkBt95avncybKpMmZL5yLlTXRRzbYhURqiAiY9zzskdJmiPNpV2qbHs\ntJM9Vt+uXdPTev318DUO1UTbtpuvUKkGWpxYaclccEGlS1D9RN8R4zjNzaWXwmmnbf5iBUojVAB6\n9DDntCxcrDiO41SIU0+tvukMx6lGWuQbbB3HcRzH2XRwseI4juM4TlXjYsVxHMdxnKrGxYrjOI7j\nOFWNixXHcRzHcaoaFyuO4ziO41Q1LlYcx3Ecx6lqXKw4juM4jlPVuFhxHMdxHKeqcbHiOI7jOE5V\n42LFcRzHcZyqxsWK4ziO4zhVjYsVx3Ecx3GqGhcrjuM4juNUNS5WHMdxHMepalysOI7jOI5T1bhY\ncRzHcRynqnGx4jiO4zhOVeNixXEcx3GcqsbFiuM4juM4VY2LFcdxHMdxqhoXK47jOI7jVDUuVhzH\ncRzHqWpcrDiO4ziOU9W4WHEcx3Ecp6pxseI4juM4TlVTNWJFRC4SkU9EpE5E3hKR3jnCni8ir4rI\nipR7MVd4p3I8/PDDlS5Ci8NtXn7c5uXHbd6yqAqxIiIDgD8CQ4H9gXeBcSLSMUuUw4GHgCOAg4FP\ngRdE5P81f2mdYvAGpfy4zcuP27z8uM1bFlUhVoBfAqNU9T5V/RD4GVAL/DgpsKqerap/U9WpqjoT\nOB87lz5lK7HjOI7jOGWh4mJFRLYAegH/CvxUVYHxwCEFJtMO2AJYUfICOo7jOI5TUSouVoCOQGtg\nccx/MdC5wDRGAAswgeM4juM4zmZEm0oXIAcCaN5AIlcAZwCHq+oXOYK2Bfjggw9KUzqnIFatWsXk\nyZMrXYwWhdu8/LjNy4/bvLxE+s62lchfbMalcqSmgWqB01T1mYj/PcB2qnpKjriXAlcCfVT1nTz5\nnAk8WJJCO47jOE7L5Eeq+lC5M634yIqq1ovIJGxx7DMAIiKp/b9miycil2FCpW8+oZJiHPAjYA6w\nronFdhzHcZyWRFugK9aXlp2Kj6wAiMgZwL3AYGAi9nTQ6UB3VV0qIvcB81X1ylT4y4FhwA+BNyJJ\n1ajq2rIW3nEcx3GcZqXiIysAqjo69U6VYcDOwBTgGFVdmgrydWBDJMoF2NM/j8eSuiaVhuM4juM4\nmwlVMbLiOI7jOI6TjWp4dNlxHMdxHCcrLlYcx3Ecx6lqWoRYKeYjiU6IiAwRkYkislpEFovIkyLS\nLRZmKxG5RUSWicgaEXlcRDrFwnQRkX+IyFoRWSQiI0WkVSzMESIySUTWichMETmnHOdY7aT+gwYR\nuTHi5zYvMSLyVRG5P2XTWhF5V0QOiIUZJiKfpY6/KCK7x47vICIPisgqEVkpIneKSLtYmH1TH2Gt\nE5G5qacaWxwi0kpEfi8iH6fsOVtErkoI5zZvJCLyPRF5RkQWpNqQExPClMW+IvIDEfkgFeZdETmu\n6BNS1c3aAQOwR5UHAd2BUdhr+TtWumzV7oDngLOBvYBvAWOxR7+3joS5LeV3OPYRyjeA1yLHWwHT\nsMfdvgUcAywBro2E6QrUACOBPYGLgHrg+5W2QYXt3xv4GHgHuNFt3mx23h74BLgT+/THrsDRwDci\nYX6Tajf6A/sATwEfAVtGwjwPTAYOBL4DzAQeiBxvDyzEnnzcC3uZ5Vrg/ErboAI2vzJVJ48FdgFO\nBVYD/+M2L5mNj8UeODkZ2AicGDteFvtin82pB36VamuuAdYDexd1PpU2aBn+sLeAv0T2BZgPXF7p\nsm1qDvs0QgNwaGq/Q6rSnRIJs2cqzEGp/eNSFbVjJMxgYCXQJrU/Apgay+th4LlKn3MFbb0tMAM4\nCvg3KbHiNm8WW18PvJInzGfALyP7HYA64IzU/l6p/2D/SJhjsKcYO6f2LwCWBf9Bym84ML3SNqiA\nzZ8F7oj5PQ7c5zZvFns3kClWymJf4BHgmVjebwK3FnMOm/U0kJTmI4lOyPbYJxCCD0b2wh5/j9p3\nBjCP0L4HA9NUdVkknXHAdkCPSJj4d53G0bL/o1uAZ1X1pZj/gbjNS01/4G0RGZ2a7pwsIucHB0Xk\nG9h3yqI2Xw1MIN3mKzX9BZXjsevl25Ewr6pq9DUM44A9RWS7Up9UlfMG0EdE9gAQkZ7Ad7HRXLd5\nM1Nm+x5CCdqazVqsUJqPJDp8+VbhPwOvq+r0lHdn4ItUJY8StW9nku1PAWE6iMhWTS37poaIDAT2\nA4YkHN4Zt3mp+SZ2hzgD6Av8DfiriJyVOt4Za6BztSOdsWmNL1HVjZiwL+Z/aSlcDzwKfCgiXwCT\ngD+r6iOp427z5qWc9s0Wpij7V8VL4SpAQR9JdNK4FdgbOLSAsIXaN1cYKSDMZoeIfB0Thd9X1fpi\nouI2byytgImq+r+p/XdFpAcmYB7IEa8Qm+cL01JtPgA4ExgITMfE+V9E5DNVvT9HPLd581Iq+xYS\npij7b+4jK8uwhUU7x/w7kan0nCyIyM3A8cARqvpZ5NAiYEsR6RCLErXvIjLtv3PkWLYwnYDVmvtL\n2psjvYCvAJNEpF5E6rGFtD9P3YEuBrZym5eUhUD8c+wfYAs/wWwl5G5HFqX2v0REWgM7kN/m0PLa\no5HAcFV9TFXfV9UHgT8Rjia6zZuX5rZvdNQmW5ii7L9Zi5XUnWnwkUQg7SOJb2SL54SkhMpJwJGq\nOi92eBK22Cpq325YIx/Y903gW2KfUwjoC6wi7CDejKYRCfNmKc5hE2M89gTPfkDPlHsbu8MPtutx\nm5eS/2CLlKPsCcwFUNVPsAY3avMO2Lx91Obbi8j+kTT6YB3CxEiYw1INfkBfYIaqrirNqWwybEPm\nnXUDqT7Jbd68lNm+SW3N9ym2ran0KuUyrII+A1vhHH10eTnwlUqXrdodNvWzEvgepowD1zYW5hPg\nCGxU4D9kPkb7LvYI3L7YavLFwO8jYbpij9GOwDqJC4EvgKMrbYNqcESeBnKbN4t9D8SesBoC7IZN\nT6wBBkbCXJ5qN/pjYvIpYBbpj3k+h4nJ3thi0RnA/ZHjHbAnMO7FplQHpP6Dn1TaBhWw+d3YovDj\nsUfFT8HWR1znNi+ZjdthNzj7YULwF6n9LuW0L7aQ9gvCR5evxl4n4o8uJ/xpF2LvpajD1NyBlS7T\npuBSFXxjghsUCbMVcBM25bYGeAzoFEunC/aOlhqs0xwBtIqFORwbqalLXTBnV/r8q8UBL5EuVtzm\npbfx8cBUoBZ4H/hxQpirUw1zLfY0w+6x49tjI2CrMJF/B7BNLMy3gFdSacwDLq30uVfI3u2AGzHR\nvTZV/64h8gis27zJNj48Sxt+V7ntC5wGfJhqa6ZiHyou6nz8Q4aO4ziO41Q1m/WaFcdxHMdxNn1c\nrDiO4ziOU9W4WHEcx3Ecp6pxseI4juM4TlXjYsVxHMdxnKrGxYrjOI7jOFWNixXHcRzHcaoaFyuO\n4ziO41Q1LlYcx3Ecx6lqXKw4zmaCiNwuIstFZKOI7Fvp8lQ7ItIgIidWuhyO4+SnTaUL4DhO0xGR\nY7GPdR6OfW9lWWVL5DiOUzpcrDjO5sHuwEJVnZAtgIhsoar1ZSxTi8Nt7DjNg08DOc4mjojcDfwV\n2CU1tfFxyv/fInKTiPxJRJYC/0z5/1JEpopIjYjME5FbRKRdJL1zRGSliPQTkQ9FZK2IjBaRrVPH\nPhGRFSLyFxGRSLwtReQGEZmfSvtNETk8T9kbROQnIvJEKp+ZItI/XpZYnJNEpCGyP1RE3hGR80Rk\nroisEZGbRaSViFwuIgtFZLGIXJlQhK+KyHMiUisiH4nIabG8vi4ij6bssUxEnhKRXaO2F5EnReRK\nEVmAfVnWcZwS42LFcTZ9LgF+B8wHdgZ6R44NAtYD3wF+lvLbCFwM9EgdPxIYEUtzm1SYM4BjUmGe\nBI4FjgPOAgYDp0fi3AJ8OxXnW8BjwPMislue8v8OeCQV5zngQRHZPnI86dPwcb/dUmU7BhgInA/8\nA/gqcBjwG+BaEekdizcsVc59gQeBR0RkTwARaQOMA1YB3025NcA/U8cC+gDdgKOBE/Kcq+M4jUFV\n3blzt4k74OfAxzG/fwOTCoh7GrAksn8OJmi6RvxuwzrqrSN+zwO3prZ3AeqBzrG0XwSuzZF3A3B1\nZH+bVN59I2VZEYtzErAxsj80VbZtYmX7KBbvA+DyWN43x8K8Gfhhgmx67PiWwFrg6NT+3cBnQJtK\n1wF37jZn52tWHGfz5u24h4gcDVwBdAc6YGvXthKRrVW1LhWsVlXnRKItBuZEjgd+nVLb+wCtgZnR\nqSGsc8+32HdasKGqtSKyJpJuocxR1dpY2TbEwkTLG/BWbP9NoGdqe19gj1R5omyFjeSMT+1PU9V4\nXo7jlBAXK46zebM2upNab/EsNmVzJbAC+B5wJ7AFEIiR+CJRzeIXTCVvi4mDA7ARiyg1ecqYK90G\nQGLHtygwjVzp5iKYYtoWE3tnJpRhaWR7LY7jNCsuVhynZdELaKWqlwYeIjKwBOm+g42s7Kyq/ylB\negFLgfaxUZ/9S5j+wcADsf3Jqe3J2PqbpaqaT3A5jtOM+AJbx2lZzAbaiMglIvINETkbWyjbJFR1\nFvAQcJ+InCIiXUXkIBG5QkSOa0LSE4BaYLiIfFNEzsTWsZSKH6SeItpDRK7BFiffnDr2IDaF9bSI\nHJo6pyNST0F9tYRlcBwnDy5WHGfzJeMpGlWdCvwKuBxbK/JDbP1KKTgXuA+4AXuE90ngQGBeMWWM\n+qnqSmyh63FYeQdgC2obQzwvTaU1EHg3lc9AVf0wlXcd9iTRPGAMMB24A1uzsrqRZXAcpxGIalJb\n4TiO4ziOUx34yIrjOI7jOFWNixXHcRzHcaoaFyuO4ziO41Q1LlYcx3Ecx6lqXKw4juM4jlPVuFhx\nHMdxHKeqcbHiOI7jOE5V42LFcRzHcZyqxsWK4ziO4zhVjYsVx3Ecx3GqGhcrjuM4juNUNf8fO5kx\nY/gr7OIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10acb7d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(wc_line,) = plt.plot(d_WC(run0), label=\"d_WC\")\n",
    "(hg_line,) = plt.plot(d_HG(run0), label=\"d_HG\")\n",
    "plt.xlabel('frame number')\n",
    "plt.ylabel('distance (nm)')\n",
    "plt.legend(handles=[wc_line, hg_line]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Okay, that looks good. Now we'll plot the atan2 values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xW3akCtJc6KJOmDgnxk03td/mAw/497PcQZ19dv/nEydW66TN+8cl6Wfr5o9v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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12da7cc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(atan2_cv(run0))\n",
    "plt.xlabel('frame number')\n",
    "plt.ylabel('atan2(wc, hg)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Originally, the original innermost interface was at 0.5: it doesn't look like this trajectory ever crosses that interface. To be very sure, we'll check the interface itself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now we define the interfaces. First we define the contribution from the atan2 part:\n",
    "# (for now I only include the innermost interface, since that's the one I care about)\n",
    "\n",
    "atan2_vals = paths.VolumeInterfaceSet(atan2_cv, 0.0, [0.5])\n",
    "\n",
    "# The actual interface volumes are the atan2-based volumes combined with state\n",
    "# (to be outside the interface you must also be outside the state!)\n",
    "interfaces = [iface | state_WC for iface in atan2_vals]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analyze the frames based on these states/interfaces\n",
    "\n",
    "Now we count how many frames are outside the interface:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "out_interface_frames = [frame for frame in run0 if not interfaces[0](frame)]\n",
    "print(len(out_interface_frames))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Okay, 0 frames outside the interface. That's not good. Just for fun, let's do the same and see how many frames are outside the state:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "257\n"
     ]
    }
   ],
   "source": [
    "out_state_frames = [frame for frame in run0 if not state_WC(frame)]\n",
    "print(len(out_state_frames))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, 257/10000 is reasonable, but still rather small, actually. But we can work with that.\n",
    "\n",
    "One last thing: let's see what the values of atan2 are for those frames. We need those frames to also be outside our interface."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x12e3568d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(atan2_cv(out_state_frames));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So some frames are outside the state with atan2 a bit over 0.4. Based on the histogram, it looks to me like we should put an interface around 0.43 or so, to make sure we have enough frames outside the interface and the state.\n",
    "\n",
    "Let's compare this distribution with the atan2 distribution for the whole trajectory:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JklSdgUOSJFVn4JAkSdXtRffhkKQdGxkZ6fcQJm3+/PksWrSo38OQJs3AoV00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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1024672d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(atan2_cv(run0));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the frames that are outside the state have the (about) same atan2 distribution as the whole trajectory, which means that (in the vicinity of the WC state) there's no correlation between atan2 and being outside the state.\n",
    "\n",
    "We can still define an interface around 0.43, because the trajectory will only be outside the interface if it is also outside the state, but this does mean that some frames *inside* the state will have a larger order parameter than frames *outside* the state, which seems odd from an intuitive perspective."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rrxpafd4rPipaJzeyHTdpEktcRgDjJk1mwgT/jlz/938wY0b1d07PSTf5T3RW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\nDAgpAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12e319110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(atan2_cv(run0))\n",
    "input_index = [run0.index(s) for s in out_state_frames]\n",
    "plt.plot(input_index, atan2_cv(run0[input_index]), 'ro');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The picture above shows the issue in another way: the blue shows `atan2` for *all* frames. The red dots are the frames that are outside the state. The correlation with `atan2` is not very strong when we're near the Watson-Crick state. You would much rather see something where all the red dots are clustered near the top of the blue.\n",
    "\n",
    "The best thing to do here would be to change the states to have more strict boundaries. However, we had already started sampling at this point, so the state definitions were fixed (whereas new interfaces can easily be added to a simple TIS simulation).\n",
    "\n",
    "Now we'll do some flux analysis for this transition:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "wc_hg = paths.TISTransition(stateA=state_WC, \n",
    "                            stateB=state_HG, \n",
    "                            interfaces=interfaces, \n",
    "                            orderparameter=atan2_cv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "analyzer = paths.TrajectoryTransitionAnalysis(wc_hg, dt=2.0) # time in picoseconds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next cells will create a couple interfaces (you are inside the interface if you are inside the value for `atan2` ***or*** if you are inside the state) and then figure out how many flux events there are through each of those interfaces. The `analyze_flux` method returns a dictionary with keys `'in` and `'out'`, corresponding to the parts of each flux that are in and out of the interface, respectively. We'll focus on the times that the trajectory is out of the interface."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "137\n",
      "CPU times: user 22.3 s, sys: 269 ms, total: 22.6 s\n",
      "Wall time: 22.6 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "iface_43 = state_WC | paths.CVDefinedVolume(atan2_cv, lambda_min=0.0, lambda_max=0.43)\n",
    "out_43 = analyzer.analyze_flux(trajectories=run0,\n",
    "                               state=state_WC,\n",
    "                               interface=iface_43)['out']\n",
    "print(len(out_43))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25\n"
     ]
    }
   ],
   "source": [
    "iface_45 = state_WC | paths.CVDefinedVolume(atan2_cv, lambda_min=0.0, lambda_max=0.45)\n",
    "out_45 = analyzer.analyze_flux(trajectories=run0,\n",
    "                               state=state_WC,\n",
    "                               interface=iface_45)['out']\n",
    "print(len(out_45))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So if we set the interface at `atan2=0.43`, and at `0.45` we get 25. The next question to ask is *how long* do each of these flux events last. In the next cells, I'll plot a histogram of that for the interface at 0.43."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x12f9f4290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist([len(traj) for traj in out_43]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "All of these are dominated by having a single frame outside the interface; however, the ones with interfaces closer in are better (only 0.43 is shown).\n",
    "\n",
    "An even better thing to look at would be same kind of analysis, but for the whole trajectory that would be sampled by TIS. (There could be frames outside the state, but not outside the interface, that are part of this trajectory.) This basically amounts to finding all the possible shooting points that each segment would have.\n",
    "\n",
    "The ensemble defined below requires that all frame from the subtrajectories it finds be outside the state and at least one be outside the interface. This gives us the segments that can be used as shooting points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Segments: 137\n",
      "Longer than 1 frame: 8\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x12fa4ec10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "all_shooting_ensemble_43 = paths.AllOutXEnsemble(state_WC) & paths.PartOutXEnsemble(iface_43)\n",
    "segments_43 = all_shooting_ensemble_43.split(run0)\n",
    "plt.hist([len(s) for s in segments_43])\n",
    "print(\"Segments:\", len(segments_43))\n",
    "print(\"Longer than 1 frame:\", len([s for s in segments_43 if len(s) > 1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is just as easy to calculate the flux"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "flux_dict_43 = analyzer.analyze_flux(trajectories=runs,\n",
    "                                     state=state_WC,\n",
    "                                     interface=iface_43)\n",
    "\n",
    "all_shooting_43 = [all_shooting_ensemble_43.split(run) for run in runs]\n",
    "all_shooting_43 = sum(all_shooting_43, [])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "567\n"
     ]
    }
   ],
   "source": [
    "print(len(flux_dict_43['out']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "562\n"
     ]
    }
   ],
   "source": [
    "print(len(flux_dict_43['in']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Segments: 569\n",
      "Longer than 1 frame: 33\n"
     ]
    }
   ],
   "source": [
    "print(\"Segments:\", len(all_shooting_43))\n",
    "print(\"Longer than 1 frame:\", len([s for s in all_shooting_43 if len(s) > 1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can directly calculate the flux. Since the `analyzer` knows that the time between frames is 0.2 ps, the result is in units of events/picosecond. We could do this for just one run in the same way, but we'll go ahead and calculate it for all of them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00572665248916\n"
     ]
    }
   ],
   "source": [
    "print(analyzer.flux(trajectories=runs,\n",
    "                    state=state_WC,\n",
    "                    interface=iface_43))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.10"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": true,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": true
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}