{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1-Choose the right distance cutoffs \n",
    "\n",
    "In this notebook, we introduce the concept of dual-cutoff for, eps. coarse-grained simulations, and how to determine the two cutoff values for PyLipID. In this dual-cutoff scheme, a contact starts when any atom/bead of a molecule moves closer to the target than the lower cutoff, and ends when all of the atom/bead moves farther than the upper cutoff. The duration between the start and end points is considered as the duration of a continuous contact. \n",
    "\n",
    "PyLipID uses this dual-cutoff scheme to deal with the 'rattling in the cage' effect in coarse-grained simulations, in which the coarse-grained beads, due to the smoothened potentials, could have large jigglings around their positions. Thus the choice of the cutoff values will affect the accuracy of PyLipID calculation. \n",
    "\n",
    "We will first illustrate the 'rattling in cage' effect, then look at ways to determine the optimal dual cutoffs for a system. We will also have a brief look at how the choice of cutoff values affects binding site calculation. Finally we will test the dual-cutoff on atomistic simulations. We recommend users to test on cutoffs when applying PyLipID to a new system, esp. to different types of lipid. \n",
    "\n",
    "PyLipID also accepts using the usual single cutoff scheme. Users only need to provide a single cutoff value to shift to the single cutoff. \n",
    "\n",
    "The trajectories used in this tutorials can be downloaded [here](https://github.com/wlsong/PyLipID/tree/master/docs/tutorials/traj_data).\n",
    "\n",
    "For those of you who are impatient, PyLipID documentation website has provided a **no-brainer script** that runs all PyLipID analysis in one run. The script can be downloaded [here](https://pylipid.readthedocs.io/en/master/demo.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pylipid\n",
    "from pylipid.api import LipidInteraction\n",
    "print(pylipid.__version__)  # the following script works for versions later than 1.4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The \"rattling in cage\" effect in MARTINI force field\n",
    "\n",
    "MARTINI force field often generates large jigglings of beads, with deviations from their positions as large as 0.4 nm. As these deviations would come back very quick, they should not be considered as dissociations. To check on these jigglings, we can plot the minimum distances of protein residues to their contacting lipid molecules. \n",
    "\n",
    "Here we still use the simulation trajectories of Adenosine 2a receptor (A2aR) that was used in the previous 'walk-through' tutorial. In these trajectories, a single copy of A2aR was embedded in a complex membrane containing 7 lipid species, including PC, PE, PS, PIP2, CHOL, GM3, Sph (See figure 1 in the previous tutorial). Let's use the following script to look at the minimum distances of the contacting cholesterol molecules with protein residues. \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Minimum distances of cholesterol to A2aR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import product\n",
    "import mdtraj as md\n",
    "from pylipid.util import get_traj_info, check_dir\n",
    "\n",
    "def plot_minimum_distances(distances, times, title, fn):\n",
    "    fig, ax = plt.subplots(1, 1, figsize=(3, 2.5))\n",
    "    ax.plot(times, distances)\n",
    "    ax.set_xlabel(r\"Time ($\\mu$s)\")\n",
    "    ax.set_ylabel(\"Minimum distances (nm)\")\n",
    "    ax.set_title(title)\n",
    "    ax.set_ylim(0, 1.0)\n",
    "    plt.tight_layout()\n",
    "    plt.savefig(fn, dpi=200)\n",
    "    plt.close()\n",
    "    return\n",
    "\n",
    "\n",
    "def compute_minimum_distance(traj, lipid, fig_dir, lipid_atoms=None, \n",
    "                            contact_frames=10, distance_threshold=0.65):\n",
    "    DIST_CONTACT_ALL = []\n",
    "    traj_info, _, _ = get_traj_info(traj, lipid, lipid_atoms=lipid_atoms)\n",
    "    for protein_idx in np.arange(nprot, dtype=int):\n",
    "        for residue_idx, residue_atom_indices in enumerate(\n",
    "            traj_info[\"protein_residue_atomid_list\"][protein_idx]):\n",
    "            dist_matrix = np.array([np.min(\n",
    "                            md.compute_distances(traj, np.array(list(product(residue_atom_indices, lipid_atom_indices)))),\n",
    "                            axis=1) for lipid_atom_indices in traj_info[\"lipid_residue_atomid_list\"]])\n",
    "            # plot distances\n",
    "            for lipid_idx in np.arange(len(dist_matrix)):\n",
    "                if sum(dist_matrix[lipid_idx] < distance_threshold) >= contact_frames:\n",
    "                    DIST_CONTACT_ALL.append(dist_matrix[lipid_idx])\n",
    "                    plot_minimum_distances(dist_matrix[lipid_idx], traj.time/1000000.0, \n",
    "                                           \"{}-{}{}\".format(traj_info[\"residue_list\"][residue_idx], lipid, lipid_idx), \n",
    "                                           \"{}/dist_{}_{}{}.png\".format(fig_dir, traj_info[\"residue_list\"][residue_idx], \n",
    "                                                                        lipid, lipid_idx))\n",
    "    \n",
    "    return DIST_CONTACT_ALL\n",
    "\n",
    "\n",
    "trajfile = \"./traj_data/A2a/run1/protein_lipids.xtc\"\n",
    "topfile = \"./traj_data/A2a/run1/protein_lipids.gro\"\n",
    "lipid = \"CHOL\"\n",
    "lipid_atoms = None # all lipid atom/bead will be considered\n",
    "nprot = 1\n",
    "save_dir = \"test_minimum_dist_A2a_{}\".format(lipid)\n",
    "fig_dir = check_dir(save_dir, \"Figures\", print_info=False)\n",
    "contact_frames = 30  # will only plot data if the contact was formed over ${contact_frames} frames.\n",
    "distance_threshold = 0.65\n",
    "\n",
    "traj = md.load(trajfile, top=topfile)\n",
    "minimum_distance_set = compute_minimum_distance(traj, lipid, fig_dir, lipid_atoms=lipid_atoms,\n",
    "                                               contact_frames=10, distance_threshold=0.65)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this script, we plotted the minimum distances of a cholesterol molecule to a protein residue if their minimum distance stayed below 0.65nm (controled by `distance_threshold`) over 10 frames (controled by `contact_frames`). We made these two parameters of `distance_threshold` and `contact_frames` in the script to screen out the noises, otherwise it could have generate loads of figures. \n",
    "\n",
    "We can check the generated figures and find different contact activities. For example, we can find some contacts with small jigglings, in which cases the minimum distances stayed around 0.475 nm: \n",
    "\n",
    "<img src=\"statics/dist_9THR_CHOL224.png\" />\n",
    "\n",
    "and some with larger jigglings, in which cases the minimum distances can shift to 0.7-0.8 nm:\n",
    "\n",
    "<img src=\"statics/dist_10VAL_CHOL6.png\" />\n",
    "\n",
    "For some messier situations, we can find that lipids came close to the target without forming an effective contact, in which cases the minimum distances still can reach as low as 0.65-0.7 nm: \n",
    "\n",
    "<img src=\"statics/dist_27TRP_CHOL166.png\" />\n",
    "\n",
    "**Therefore, we want to use the lower cutoff of the dual-cutoff scheme to pick out the effective contacts and use the upper one to deal with the jigglings.**\n",
    "\n",
    "We can also look at the distribution of the minimum distances: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.ticker as ticker\n",
    "\n",
    "def plot_PDF(distance_set, num_of_bins, fn):\n",
    "    fig, ax = plt.subplots(1,1)\n",
    "    ax.hist(distance_set, bins=num_of_bins, density=True)\n",
    "    ax.set_xlim(0, 1.0)\n",
    "    ax.set_xlabel(\"Minimum distance (nm)\")\n",
    "    ax.set_ylabel(\"Probablity Density\")\n",
    "    ax.set_title(lipid)\n",
    "    ax.xaxis.set_major_locator(ticker.MultipleLocator(0.2))\n",
    "    ax.xaxis.set_minor_locator(ticker.MultipleLocator(0.05))\n",
    "    plt.tight_layout()\n",
    "    plt.savefig(fn, dpi=200)\n",
    "    return\n",
    "\n",
    "distance_set = np.concatenate(minimum_distance_set)\n",
    "num_of_bins = 1000\n",
    "fig_fn = \"{}/dist_distribut_{}.png\".format(save_dir, lipid)\n",
    "plot_PDF(distance_set, num_of_bins, fig_fn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From this probability distribution plot, we can see that the first contact layer of cholesterol starts at ~ 0.4 nm, peaks at ~0.5 nm and ends at ~0.7 nm. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Minimum distances of PIP2 to A2aR\n",
    "\n",
    "Let's check the contact activities of some phospholipids. In this case, we chose to look at PIP2 molecules, the residue name of which is \"POP2\" in MARTINI force field. PIP2 lipids have been shown to bind to a couple of GPCRs and exert allosteric modulation on the receptor functions. Let's use the functions defined above to plot minimum distances of PIP2 with A2aR. Considering the lipid acyl tails are often too dynamic, we decided to only include the lipid headgroup beads for calculation, to produce better defined binding events. Thus, we provide to the `lipid_atoms` a list of atom names of PIP2 headgroup beads. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "trajfile = \"./traj_data/A2a/run1/protein_lipids.xtc\"\n",
    "topfile = \"./traj_data/A2a/run1/protein_lipids.gro\"\n",
    "lipid = \"POP2\" # residue name of PIP2\n",
    "lipid_atoms = [\"C1\", \"C2\", \"C3\", \"PO4\", \"P1\", \"P2\"] # PIP2 headgroup beads\n",
    "nprot = 1\n",
    "save_dir = \"test_minimum_dist_A2a_{}\".format(lipid)\n",
    "fig_dir = check_dir(save_dir, \"Figures\", print_info=False)\n",
    "contact_frames = 10  # will only plot data if the contact was formed over ${contact_frames} frames.\n",
    "distance_threshold = 0.65\n",
    "\n",
    "traj = md.load(trajfile, top=topfile)\n",
    "minimum_distance_set = compute_minimum_distance(traj, lipid, fig_dir, lipid_atoms=lipid_atoms,\n",
    "                                               contact_frames=10, distance_threshold=0.65)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similar to what we have seen from cholesterol bindings, we can find some interactions with small jigglings:\n",
    "\n",
    "<img src=\"statics/dist_203ARG_POP229.png\" />\n",
    "\n",
    "and some with larger jigglings: \n",
    "\n",
    "<img src=\"statics/dist_120LYS_POP211.png\" />\n",
    "\n",
    "We can even find that the bindings of PIP2 are more stable, i.e. the durations of the bindings are longer. One PIP2 molecule bound to A2aR without dissociation in the 3 micro-second simulation:\n",
    "\n",
    "<img src=\"statics/dist_197ARG_POP218.png\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check the distribution of PIP2 minimum distances:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "distance_set = np.concatenate(minimum_distance_set)\n",
    "num_of_bins = 1000\n",
    "fig_fn = \"{}/dist_distribut_{}.png\".format(save_dir, lipid)\n",
    "plot_PDF(distance_set, num_of_bins, fig_fn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparing to that of cholesterols, the distance distribution of PIP2 has a narrower first peak, which starts at ~0.425 nm and ends at ~0.675 nm. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Determining the cutoff values\n",
    "\n",
    "As we have shown above, the binding activities of cholesterol and PIP2 are different, when they bind to the same receptor A2aR. The situation could be more complex if we compare the binding activities of lipids to different receptors. We therefore need to do a systematic check on the suitable cutoffs whenever we apply PyLipID to different systems and different lipids. \n",
    "\n",
    "To illustrate that the contact distances could be different with different proteins, we include testings of cutoffs on two systems: one on a Class A GPCR, A2aR and the other on the ligand-gated ion channel GABAA. Each receptor had two simulation repeats. \n",
    "\n",
    "We start by checking the impact of different cutoffs on a couple of contact metrics, including num. of binding sites, num. of contacting residues, and the average interaction durations. By plotting these metrics as a function of different cutoffs, we will try to find the cutoffs that optimize the calculation of contacts and binding sites. \n",
    "\n",
    "Let's first define a test function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import product\n",
    "import shutil\n",
    "\n",
    "def test_cutoffs(cutoff_list, trajfile_list, topfile_list, lipid, lipid_atons, nprot=1,\n",
    "                 stride=1, save_dir=None, timeunit=\"us\"):\n",
    "    num_of_binding_sites = {}\n",
    "    duration_avgs = {}\n",
    "    num_of_contacting_residues = {}\n",
    "    for cutoffs in cutoff_list:\n",
    "        li = LipidInteraction(trajfile_list, topfile_list=topfile_list, cutoffs=cutoffs, lipid=lipid,\n",
    "                              lipid_atoms=lipid_atoms, nprot=1, timeunit=timeunit, \n",
    "                              save_dir=save_dir, stride=stride)\n",
    "        li.collect_residue_contacts()\n",
    "        li.compute_residue_duration()\n",
    "        li.compute_binding_nodes(print_data=False) # switch print and write to False for cleaner output.\n",
    "        num_of_binding_sites[cutoffs] = len(li.node_list)\n",
    "        duration_avgs[cutoffs] = li.dataset[\"Duration\"].mean()\n",
    "        num_of_contacting_residues[cutoffs] = sum(li.dataset[\"Duration\"]>0)\n",
    "    shutil.rmtree(li.save_dir)\n",
    "    return num_of_binding_sites, duration_avgs, num_of_contacting_residues\n",
    "\n",
    "\n",
    "lower_cutoff = [0.375, 0.40, 0.425, 0.45, 0.475, 0.5]\n",
    "upper_cutoff = [0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85]\n",
    "cutoff_list = list(product(lower_cutoff, upper_cutoff))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we used interaction durations instead of interaction residence time to speed up the testing. We defined a couple of lower cutoffs and upper cutoffs to test on. \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cholesterol interactions with A2a\n",
    "\n",
    "Let's check how cholesterol contacts and binding sites change with different cutoffs in A2a simulations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "\n",
    "stride = 1   # use this to speed up if you have too many frames.\n",
    "lipid = \"CHOL\"\n",
    "lipid_atoms = None\n",
    "nprot = 1\n",
    "timeunit = \"us\"\n",
    "\n",
    "# A2aR simulations\n",
    "save_dir = check_dir(suffix=\"test_cutoffs_A2a\", print_info=False)\n",
    "\n",
    "trajfile_list = [\"./traj_data/A2a/run1/protein_lipids.xtc\", \n",
    "                 \"./traj_data/A2a/run2/protein_lipids.xtc\"]\n",
    "topfile_list = [\"./traj_data/A2a/run1/protein_lipids.gro\", \n",
    "                 \"./traj_data/A2a/run2/protein_lipids.gro\"]\n",
    "num_of_binding_sites, duration_avgs, num_of_contacting_residues = test_cutoffs(\n",
    "                                 cutoff_list, trajfile_list, topfile_list, lipid, lipid_atoms, \n",
    "                                 nprot=nprot, stride=stride, save_dir=save_dir, timeunit=timeunit)\n",
    "\n",
    "\n",
    "test_data = {\"num_of_binding_sites\": num_of_binding_sites,\n",
    "             \"duration_avgs\": duration_avgs,\n",
    "             \"num_of_contacting_residues\": num_of_contacting_residues,\n",
    "             \"test_cutoff_list\": cutoff_list}\n",
    "\n",
    "with open(f\"{save_dir}/test_cutoff_data_{lipid}.pickle\", \"wb\") as f:\n",
    "    pickle.dump(test_data, f, 2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use the following function to plot the contact metrics as a function of the cutoff values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1270.08x259.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1270.08x259.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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n7Tdvy1atWpVr164ddzMkSZIkSZKkgUXEOZm5avb0fsa4+wiwqXH/WuCMUTVMkiRJkiRJ0g31s+NueWb+pXen/n2b9pokSZIkSZIkqZ8dd5dGxEN7dyLiYcBl7TVJkiRJkiRJ0pYuTtHzNOADEfEmIIBfAo9rtVWSJEmSJEnSErfgjrvMvAC4a0TsSHUxiw3tN0uSJEmSJEla2vo54o6IeBBwELBdRACQma9qsV2SJEmSJEnSkrbgGHcR8TZgDfBsqlNlHwncvOV2SZIkSZIkSUtaPxenuHtmPg74XWa+ErgbsG+7zZIkSZIkSZKWtn523P2p/vnHiNgLuBq4RXtNkiRJkiRJktTPGHefiYhdgNcB3wMSeEebjZIkSZIkSZKWun523P1LZl4FfCwiPgNsB/y53WZJkiRJkiRJS1s/p8p+s/dLZl6VmVc0p0mSJEmSJEkavXmPuIuImwJ7A9tHxF9RXVEWYCdghw7aJkmSJEmSJC1ZWzpV9v7AscA+wImN6RuAE1pskyRJkiRJkrTkzbvjLjNPA06LiCMz82MdtkmSJEmSJEla8vq9quyjgf2a82fmq9pqlCRJkiRJkrTU9bPj7lPAFcA5wFXtNkeSJEmSJEkS9Lfjbp/MfEDrLZEkSZIkSZJ0nWV9zPONiLhd6y2RJEmSJEmSdJ1+jrhbDRwbERdSnSobQGbm7VttmSRJkiRJkrSE9bPj7oGtt0KSJEmSJEnS9Sx4qmxm/g+wC/CQ+rZLPU2SJEmSJElSSxbccRcRzwU+ANy4vr0/Ip7ddsMkSZIkSZKkpayfU2WfBNwlMzcCRMQ/A98E/q3NhkmSJEmSJElLWT9XlQ3g2sb9a+tpkiRJkiRJklrSzxF37wa+HRGfqO8/HHhnay2SJEmSJEmStPCOu8w8MSK+CqymOtLuCZn5/bYbJkmSJEmSJC1lC+64i4i7Aj/KzO/V92ci4i6Z+e3WWydJkiRJkiQtUf2McfdW4MrG/Y31tIFFxM8j4ryI+EFErK2n7RoRX4yIdfXPGw1TQ5IkSZIkSZpmfV2cIjOzdyczN9Hf2HgLuXdmHpKZq+r7LwG+nJkrgS/X9yVJkiRJkqQlqZ8ddz+LiOdExNb17bnAz1poy8OA0+rfT6O6CIYkSZIkSZK0JPWz4+5pwN2BXwEXAXcBjhuybgL/HhHnRERvWTfJzEsA6p83nuuJEXFcRKyNiLWXXnrpkM2QJEmSJEmSJlM/V5X9DXDUiOveIzMvjogbA1+MiJ/0+8TMPAU4BWDVqlW5wOySJEmSJEnSVOrniLuRy8yL65+/AT4B3Bn4dUTsCVD//M042iZJkiRJkiRNgs533EXEioiY6f0OHA6cD5wJPL6e7fHAp7pumyRJkiRJkjQp5t1xV1+Egoi4x4hr3gQ4OyJ+CHwH+Gxmfh54LXC/iFgH3K++L0mSJEmSJC1JWxrj7gnAG4F/A+4wqoKZ+TPg4DmmXw7cd1R1JEmSJEmSpGm2pR13/xURPwf2iIhzG9MDyMy8fastkyRJkiRJkpaweXfcZebREXFT4AvAQ7trkiRJkiRJkqQtHXFHZv4/4OCI2AY4sJ7808y8uvWWSZIkSZIkSUvYFnfcAUTEocB7gZ9TnSa7b0Q8PjO/1nLbJEmSJEmSpCVrwR13wInA4Zn5U4CIOBD4EHDHNhsmSZIkSZIkLWX97LjburfTDiAz/zsitm6xTZIklWXDBjj9dFi3DlauhDVrYGbGWku9VomZJEmSNFKRmVueIeJdQALvqyc9BliemU9ouW0LWrVqVa5du3bczZAkaX5nnw1HHAGbNsHGjbBiBSxbBmedBatXW2up1ioxkyRJkgYWEedk5qobTO9jx922wDOB1VRj3H0NeEtmXtVGQxfDHXeSpIm2YQPsvXf1c7aZGbj4YthxR2sttVolZpIkSdJQ5ttxt2yhJ2bmVZl5Ymb+bWb+TWaeNAk77SRJmninn14d5TSXTZuqx6219GqVmEmSJEmtWHDHnSRJGtC6ddWpiXPZuBHWr7fWUqxVYiZJkiS1wh13kiS1ZeXKajyxuaxYAQccYK2lWKvETJIkSWrFgmPcTTLHuJMkTbRSxzKz1nTU6bqWJEmSBjbwGHfzLOy44ZskSVLhZmaqK3fOzGw+6mnFis3TR7nDxFrTU6vETJIkSWrFQEfcRcRTM/PtLbRnUTziTpI0Fa68sroIwPr11amJa9a0t8PEWtNTq8RMkiRJGsh8R9x5qqwkSZIkSZI0RvPtuFvexxN3AR4H7NecPzOfM8L2SZIkSZIkSWpYcMcdcBbwLeA8YFO7zZEkSZIkSZIE/e242y4zj2+9JZIkSZIkSZKu089VZd8XEU+JiD0jYtferfWWSZIkSZIkSUtYP0fc/QV4HfAyoHcliwRu2VajJEmSJEmSpKWunx13xwMHZOZlbTdG0hKzYQOcfjqsWwcrV8KaNTAzM921SsxkLUmSJEkai8jMLc8QcSZwVGb+sZsm9W/VqlW5du3acTdD0iDOPhuOOAI2bYKNG2HFCli2DM46C1avns5aJWayliRJkiS1LiLOycxVN5jex467TwAHAV8BrupNz8znjLqRi+WOO2lKbdgAe+9d/ZxtZgYuvhh23HG6apWYyVqjqSVJkiRJC5hvx10/F6f4JPAa4BvAOY2bJA3m9NOro5zmsmlT9fi01Soxk7UkSZIkaawWHOMuM0/roiGSlpB166pTE+eycSOsXz99tUrMZC1JkiRJGqsFj7iLiAsj4mezb100TlKhVq6sxhOby4oVcMAB01erxEzWkiRJkqSx6meMu90ad7cDHgnsmpkvb7Nh/XCMO2lKlTiWWYmZrDWaWpIkSZK0gIHHuMvMyxu3X2XmycB92mikpCViZqa6cufMzOajnlas2Dx9lDtMuqpVYiZrSZIkSdJY9XPE3R0ad5cBq4CnZ+bBbTasH0UecbdhQzUo+rp11alca9ZU/0haa/JqlZip61pXXlnVWr++OjVxzZr2dph0VavETNaSJEmSpFbNd8RdPzvuvtK4ew3wc+D1mfnTkbZwc70HAG8EtgLekZmvnW/e4nbcnX02HHFEdUXDjRuroz+WLauO/li92lqTVKvETF3XkiRJkiRJwBA77roUEVsB/w3cD7gI+C5wdGb+eK75i9pxV+rYTiXWKjFT17UkSZIkSdJ1Bh7jLiK2jYhHR8QJEfHy3q2dZnJnYH1m/iwz/wJ8GHhYS7Umy+mnV0c5zWXTpupxa01GrRIzdV1LkiRJkiQtaMEdd8CnqHaeXQNsbNzasDfwy8b9i+pp14mI4yJibUSsvfTSS1tqxhisW1edmjiXjRur8ZesNRm1SszUdS1JkiRJkrSg5X3Ms09mPqD1llRijmnXO5c3M08BToHqVNkuGtWJlSur8cTm2nGyYkU1aLq1JqNWiZm6riVJkiRJkhbUz8UpTgH+LTPPa70xEXcDXpGZ96/vvxQgM/9prvkd485aY6lVYqaua0mSJEmSpOsMPMYdsBo4JyJ+GhHnRsR5EXHu6JsIVBejWBkRt4iIbYCjgDNbqjVZZmaqK3fOzFRHN0H1szd9lDtMrDUddUquJUmSJEmSFtTPEXc3n2t6Zv5PKw2KOAI4GdgKeFdmvma+eYs64q7nyiuriwCsX1+dmrhmTXs7TKw1HXVKriVJkiRJkuY94m7BHXeTrMgdd5IkSZIkSVpShjlVVpIkSZIkSVLHpvqIu4i4FGjllN0JsDtwmbWmolaJmaw1PXWsNV21SsxkrempY63pqWOt6apVYiZrTU8da01XrRIzlVyrazfPzD1mT5zqHXcli4i1cx0iaa3Jq1ViJmtNTx1rTVetEjNZa3rqWGt66lhrumqVmMla01PHWtNVq8RMJdeaFJ4qK0mSJEmSJE0gd9xJkiRJkiRJE8gdd5PrFGtNTa0SM1lreupYa7pqlZjJWtNTx1rTU8da01WrxEzWmp461pquWiVmKrnWRHCMO0mSJEmSJGkCecSdJEmSJEmSNIHccSdJkiRJkiRNIHfcjVlEtL4OIiLarjGrXievqxJzdZ2prlnU+hrD66L1emN6XRSXq8t69hdD1bBvH03N4nL5OTLZNcZRz/5iZDWLy1Xa9m2jXmf/v9s3TW6NcdQscV1NE3fcjUFE/G1ErIqI3TJzU8u1ds8OBjLsMlNdr7hcXWWqa3WSKyLuFRGPAOgqW69Omxs2XefqIlO9/OJydZnJ/mIktezbh6tVXK6IuHeX/VKJuTrM1OlniP3F0LWKy+X/IyOp5bbgkNxuH9w4/necFu6461i95/gQ4H7AFyLijhGxXUu1/hr4ZEQ8OiLu1UaNuk5nmep6h1JYrohYTQeZ6lqd5IqIPYC9gcdGxNsi4rCI2HnUdRr1jo2I90bESyLi9m1t2HSZKyIe10WmulaXuUpcV8X17XWtLnPZtw9Xq8tc96SbdbULsBfdfY50lWsFHeXqMNONqfrbYwpbV/btw9cqrm+v63XSv3e8rtwWHK6W2+3D1en0f8dp41VlOxQRB2fmDxv3nw48CDgDOCszLx1hrWWZuSki7gHcnqqzPz8zXz6qGnWdzjLVy1+emdfUGzcHUUiuusahwG1oKVNdo5NcEbFvZv6ycf94qn9S/gC8KTN/O4o6c9S9E9Xr/QTgOcDnRvnh0mWuiNguM/8cEXejel20kqmu1fn6iog7A7ejjHVVXN9e1+oyl337cDXGkevuwMG0t64OB76emRvr+119jrSd65nA5zPzgvp+F/1t25l2yMw/Nu4/H9iT6V9X9u3D1yq2b6/rtNq/d7yuxrEt6Hb7YLXcbl+KMtNbBzfgbcCp9e9bNaY/BPgg8Df1/WUjqHUy8NzG/eXALYHzgZOnMVO9nA8D3wC2LiUX8CjgscD29f1t2sjUZS7gvcBb69+3bkw/DPgXqs5+uxHmei/w+FnT/qZ+rRw9wnXVWa56fZzedqYx5DoSeERh66q4vn0MuezbpyfX84G7tv0aBE4HPgTcCNimMf1+o34Pd5zrFOBK4OGzpt+3hb6pq0z/CnwMeD3wVwWtK/v24WsV17fXy+mkf+94XXW53eR2+/TkKm67fZpvY2/AUrgB7wLesYXHjwK+C9xyBLXeDZwJrJjjsd2A7wDPmqZM9fLeDHylzre6nrZ8mnPVH8ifp9qw+dasD+WRZeoyF/BW4CNbePxvgTcCNxlRrlPr1/uOczx2BNVG1F/X92MaclFtwH8ZOA94yKzHHjCqTGPI9T7gLOD71BuiBayr4vr2MeSyb5+eXG8BPj7PY6NcV0+i+ia/d39Z7zVR3z9yxJ8jXeV6M/BO4KnAucAusx5/+Aj7pq4ynQJ8FFhd/7561uPTuq7s24evVVzfXi+vk/6943XV5XaT2+3Ts66K226f9tvYG1D6DbgLsAm4Y33/scDxVHuOb9mY73iqDbpth6i1M/Dhxv27AvcGdm1Muwdw0qAvfiDq5XaSqV7OycBHqL6pewPwr43HehsBo8h1tw7X1THAlxv33wTsy/WPLBgqU2M5d+4iF/Bg4FfArev7jwBeDDweuFNjvlOANw6TqV7OtsAHGvfvBvx1/XfsvS4eDXwd2GeIOp3lotrQ/WT9+9OAFzVf5/XvRw2bqV7OA4GLO8p1LNWpYb332vuBW1H9Q94bsuHoEayrB3W4rorq2xvrprP+Hfv2qejb62X8I7CucX9/4KZc/5vxUeX6G+CE+vfn1m1/G/C4xjynDvse7jIX1c66LzbuvxN4av178x//UfRN/9RRphmqvrx3NNWpVEedPB84ooV19ZqOctm327fPV7OT/p1u+/Yut3Hdbh+ultvtQ2Qq4ebFKVoUEZGZ3waOA86MiDfVv18O3B84LiJ2qGc/A7iQqqMe1JXAzhFxaEQ8jer0hacBn67Pt6eusQtw8wFrLMvMb1FthLaeKSJuAlyUmY/KzGuoOsj7R8SDAeppAOsZLtfyzPwm8Ay6WVcXAWsjYu+IeDHVxsDrgG9HxD71PMOuKwAy8zvAM2k5V2Z+hmqj/QUR8VrgRVSd/R2AJ0fEAfWsLwCykXPR6oF6twNuGxG3j4je3+9lwP8BHlWPF/NB4HPATQat1VWu+nnnZebD60m/AJ4eEbfJanyYZXV7Pjxspno8os9RfWPc+vqqs/y+XsYLgUOpNjbfQrXhRmZ+iOHX1Wep1tULW15XJfbt0GH/bt8+PX17RGxP9R7+ckTcMyKOo9qIfjPw9fpxgJ8xglxU/xjcJSJWUZ0m82GqoxmeHxEPqed5PsN/jiynyvUfHeQ6NTPvV9fdGvgB1T+sZOa1dVtgNP3t/9BBpszcQLXj6RsR8Tqqfyo/T/U6e3Y9/hyMZl2tAH4JfKXNXPbtgH37lnTSv3fVt9e1utrGdbvd7fYb6Gq7vRjj3nNY6o1qQ+XujfvHAb8BDqjv70F1SO09GvM8FpgZsF5v7/dzqTrBU4Ab19NeBJxD/Y0Q8FDg6SzynHSqb9D+d6NWq5nmqN9r/wuBF9a/N7+pHjRX73D33vJbzwX8L6oxYd5J1TnuU08/Cfh24288UKb6uY+k2qjojcHxtDZyUX3gNpfxBqqxD/au798C+CRwUH1/OdWh40N981kv6ylU33h+src84Nk0Dumucx87wLKvNwYHcGKHubaqf76a6miFHWY9PlCm+rnXG4eji1zAres6HwX+i+pIjW2o+pS3jmBdHQk8snH/pLYyUWDfXj/3ZMbUv2PfvtganfTt9fP2rX/uVi/jq8BPgZX1++idVP88Dp1rVt2PU/1j/5jGtBdQv8+HeQ/Xzz8cWEH1D3aruXrLaL6uga2B71EfndGbr54+aN/0TKqj0HbuONMzqD7371nfn6HqTw4b0braof65TZu5sG+3b1+4bqv9O9327WPZdsft9kGW7Xb7CNfVNN/G3oASb8wzBgezDpsGPg3cHYY7333WMm9Xv9DXAoc2pp8B7NG4v8Mil/tu5hiDo4tMc7Tl/lQbbQfW95c1HltsruYYHPdsTN+9g3V1I+DGVAM690412Q74QPPvvNhM9XOaY3B8h82HoN90lLmoPnzPmGP6AbPu/zv1Rnx9f+tB6s1R5xCqQUsvAO5cT9uF6hugfRrz3WiRy51zDA7g5h3l6m38rab6wN6tvt/c4F1Upvo5J7N5HI6HN6bfou1cwI7AgVSnz+xeT9ur7q92G2JdNcfgeFdj+i1nzTd0Jgrs2+vnTET/jn17P8vupG+vl3HdYNG9vx2wBrhVY9odgRNnPW+x62quHVvbAl+kukpj77GzaIwdNWi/xOYLX+w6K9et28o1a3ov4wPqPmVm1uOD9E29i170Bqu/cZ3pwLbXVf37y6iu+te7/0XgCSNYV70LX7wBOIDq872N16B9u317v/Vb6d/ptm8f27Y7brcvdrkn43b7SNfVNN88VXbEIuI1wP0y82/r+/tHxF4RsXVm/ro+VJiI+ChweWZ+I+tX4xA1e8uMzDwP+DuqDvE+EfGUiDgD+HM2LhmemX9cxPJ3pvr256GZuTEi7hoR942I3TLz1435RpapmWu2zPwC1TcAJ0TE9tm4FPUic51M9e3V/YDfUn3T1VvOZY35Rrquerky83fAtVRjBjwmIg6k2hC5KjM3DpKprnEMsDIzH5CZR1FtAOwdEdtk5v8bVa6IOJVqI/OR9f29I2K/us3r62krIuJDwK8y80uNTFcvtt6s2r3Dz39A9YHyWeD4+jSqdwAXZuZFjXq/W8Syt6Xa4HpoZl4ZEXeLiHtHxJ5Up+oQETOjztV8vffWR2aeDexE9c8LWZ1S1Xz9LGb5bwb2y8z7Um34Htiod2E9z8jXV0RsVf+6keoUrguAh0fEbak2fC/OzMsbtRazro6l+sfmCKrD6reJiNvUy/lZPc+Oo8hUYt9eL7vz/t2+ffGZ6hqd9O31Mt5KdQW3pzfae1lmnp6ZP23M+uLZz13kutoW2L7+PXp9XGZeldWppesj4t0RcRZwSWa+qVFn0f1SRDwJ2Ckzj87M30bEVo1cP2kr16zlXFv/eiHV+D63nvX4YvumNwNbUR0x9sqIuFFm/oZq3KX/bszayrqqH34nsE9E/HtEfJqqX3/3oJnqGqdQ/ZN4EtXn4J6Z+fsWXoP27fbtC9VttX/vuG8fy7a72+1ut9fLPpaOtttLtHzhWdSviNiOqoP4ckTck+qQ6jXA74F9I+LQzPxTRDwZ+ENmPrF+Xiy2A46IR1BtQH2U6gPkL/WiyMzzI+IEqjf4XYAfZOZrBq1FYwyOOtMTqTY494mI52fmtyLiKcNm2kKu5uPL6g/8b1GdUvCnxdaol9Mbg+N59f03A5+LiAdnNTYCUY0hcfSwuWZnyszrMmXm5RHxRqrTCB5M9YH81EFr1a4bg4PqEPpjqI4ouFVEPCQzLxrR+voG1ThEB1INpPtY4KYR8TXg1fUG57PqzE8YJlO9UfNb4KeZuT4zN0XE8sy8JjPXRsTFVB8Aq4EfZuarB6lXf7heNwYHcDDVmDC9D6//qDeonzFsrjkyZeP1Tf0P5bVUG/SH9Z434N+vNw7HM+tJvwDeHBGfycwf17mD6lSrUee6tpHrqoj4MdX4GEcBP8nMZw1ai+uPwfFoqjE49ouI84H3UJ26MopMpfbt0FH/bt8+PX17RBxBdarXfRs59wd+DZybmd+LiN2prvL2x8w8fpBaEXEaVX+7LCJO662fui/cOjOvzsyHR8T+VP+UnVc/77p+cgC/Bf5vvZznAgdHxF+AszPz/XWuf20jV29ZvYyZ+dOIeFRmfnfALETEU6mOYuqNn3dnYE1EvD0zr6qntb2uguq18Xiqfv0PWY19NPC6iogZYAfg6My8OiIeTzV21F2ojsL8/Ihy2bfbt/eVq+X+vavtduho232ObUG32xdXy+32If93LFH4dxitiNiNaoDeJwN7UnXoFwJvpzp8d01E7JyZV9TzL3qjJiI+QjWGyUaqD8gvAZ/KzEt7neI8zxukVtQd03OpDpm9OfB3mfmbiHgR1bddd6f6Zn7DoHX6yNXrDOdt42LrNZ6/TWb+JSJeCJCZr+tliIidMvMPg+bqd13VG49bZf1t3TD/mETE/wL+gWrD835UY7ZcFBEnAXfLzLsOm6tRaw3VN+2/pDoV4mqqU3Z+mpkvmDXvMK+LGaq/4aXArzPzFfVj2zQ3pqL+Z28EuZ5C9eG/D7AmM6+KiGcDt8vM44bNtUCm6zLMzjiKD6/eeykiXk11Rb7n5hzfDLeQa9veP5L1/T3qDcRhXhu3phrb5mbAQVQboVdRnYaxbTaOFhqmTv3covr2+nmd9O/27VPZt7+O6pSwy4D7UI05tyfVP0ivAa4BDs/M9wxSq359HQo8Drg31albL8hq59m8630Er4kj65qvBv6eaifdLlT/aL2Iaty5B40h16Dv4eY/jVtTjTd018x8TGOevRjPuhpmBytRHbl3U6ox7Y4GTqAaa/FwqvG5fgk8cNBcjTr27e3kmsq+vY9cI+/fu+zb6+e3uu3udrvb7Vuo19l2e5FyAs7XLe0G7MrcY4ucNGu+RY9PQHXawJmN+0dTDR75HK5/+fgH0Dj/fASZ5huD46Nc/zz3QcdKG0uuWW243hgcHa6rB866P/R4HMw/BscHqTbURlnrYcDBjft/RTVezPJh61Bdqegz9e/bAHel+kbmn2fN9zgGGP9lC3UPob8xOAZ5XfSb6ZhRZprdZrY8DkfbuXYcptas5fU7BscoXuvF9e31Mlvr38eZq7Fs+/b+l9/sB+YarPxTwG1H8Dc8DnhV4/69gJ8ARzWmndq8P8LXw3wXvlgzTbma7WMLF73oMNPRI1o//Vz44vBhc816vn37FOVqLHukffsic420f6fD7fZ6Oa1su+N2u9vtC9ftbLu9tJtj3I1IxPXOc/8t8Im84dgi2XxO1q/KRfod1eH7j62X8SHga1Qb1Ler27KKakP78nmX0odepvrbgvnG4PhTXv8890EywRhyzZazxuCY9Vib62qv+jUzTC2iVi/jd8w9BsefM/PPI6h1Xd+RmZ/KzB82Hn4psDEb3yAP8boIqkP4V2X17dU5VBvtN4rq1BmiGhvhL7nI8V/mLLb4MTgGydVvpqtHkaleXl/jcMyeZ7Fl6D/XlUPWIhY/BsfA76vGMoro2+tlddW/27cPV6uTvr2x/Gsb/eDzqXZu/aq+fyHVqWM3bT53wFy/AvaMiBvVy/gq1dFir6//dgDHZ+aHB1j2dZqviUafcTTVEVUvbcx6H6p/mq8zqbka6+q69tXrbausjvo4gerUo5nZz20504cGWPZ1mrl66yoz30J1Ctea+v4GqqM09mk+d5Bc9u327fPorH/vcru9rtfFtrvb7SPgdvtwr/VSearsEGKO8Q/qD8pszNMbg+PqzDy2njboeAu9Q98fQXWu+ccy8xv1Y/+H6vSIB7WQaRn1kCxRjTXTG4Pj6hx+DI6x5Zr1eO8Q+4dQjcHxziHrtZ6pXtZCuQ6jGoNjA0OMwRGzxj+op113GkT9AbMT1YfklTnCcQki4plU/2g9MTP/OyJ2pBoXYf/MfPGseUeRq3kaxF5sHoNjYw44BkeXmbaQ6wbjcETEIVRXbHr9oFlm1e16XTUzHUP1XjuQIcfgKLFv30Ku1vp3+/ah6nTSt9fP2Zbqm/s/NvJd7/SUiFhB1b//ude/D6N+3X0YuILN4yldExEvB9Zm5lmNeQd9/c2V67plRcQnqf5JvwnVhS+eNOm55so0xzy3oroa3yNyiPHzGssb67qKiJtSXXFzB6pTqn6bmY8fMIt9u337lmpOQq5R9u1j2XZ3u93t9j4zjWy7falwx92Aos9xHSJiD4YYL2We2vtTval2AL6Ymf9RT/84cFw2rqw0wkwjH4NjjuWMI1drY3DUy2glU72MTsbgiD7Hdahf64flkINSN+r2NqCWU10t7x7AC7Ma0Htv4F3AMVldPW+Q5Y9jDI5WM/WRq5VxOMa8rkY6BkeJfXu9jLH17/bti152Z+MrReOiA8BpOetCCvX7ehnV+G+3zczHNh8bMF/vH+7lVKfe/hI4jerb/i8BH8jMtw+y7D5zNfvzkV34ou1cC60r2HyEQkTcJTO/PWitxnLHva56R53sxJAXvrBvv8HzJjbXOPv2ejlj/T9rRH1759vubrcPxu324cfOWyo8VXYAUe3N3y4z75/V5eM/BdwGODoidm18+D8Q2ND48I9RvBgz8wKqb2ouB54XEa+NiM9RHfo+6IfJQpl6HyYPiGog32Z7RvIGG1Ou3rqaK9fQH/5tZIJFra8HUv1T0vvwX9RrMKqreO2QmQ+k2og5jeoUnH+u8/U+FB/DCK4k19T7+9dZ3kF1qsJnIuJxdTt+PsQHykK5eh+Kj4uIHZofmsPkajNT3d5+19cxda7rNnKGeb2PeV31rpx4TETs2PjwX3R/W2LfXrdvrP27fXv/uurb6+e8iOrKhc8ATgfeEfXpYc1/CDJzU2a+NjfvtFs2ZH+xqf7n+xqqcZauAI4F/gO4IIffEbRQrmZ/fkFu3mk31Pu4zVz9rKvmOsl6p100To0bxASsq54rMvPtg25j2Lfbty/GmHKNsm8fy7a72+2L53b7cNvtS4077gazmHEdRjIuwWyZ+V9UV7x6IfAH4LNZX0UsYu6xIBbQ6Rgc8ykxVwuZoLsxOPod/2BTNr49GXXHm5mXZ3VY+Euovq38ajZOHxhgkZ2OwTGXFjJB/7lGNg7HbGNcV6MYg6PEvh3K7AdLzATdjp/3e+Cc+j37Uaojmv4uIo7qLS8iTo2IR/eeMOA/kTfY1szNY7Jdk9XpOM+jOlXnCfM9ZxF+T3+5jprVpsWe2tRlrt8zWKZS1tXRs9q02G0M+/bp6QfHnqmuO65co+jbx77t7nZ739xu39wOTwNdSI7xyhjTeIPrTi9+BNWVru7eeOz/UHXso6izot+2zJq2bFIzlZqry0xdr696mc8Ezqa+ahfV1YCOY9ZVh+bL2eZt0L/hJOcaJlOpubrIZH8xPblKzNRlrsYyH0R1NdAbNabdC7gIWFXfnxli+U9c6G8x1+PD9ksl5ioxUxe5mm20v5j8XF32gaXmaiy31e0m6quBDvC8id0WHEemUnO1nWmp3jzibpGyfoUB36f6pvAhEXGf+rFXA1dFNbDtwCLiVODhc0xvXh1tzlNVcoBvS7rIBGXm6jpT/byu1lcvw9uBT1NdQe5WWX078lngkIgY+ip89bfpD4uIbeapP+83+oP8DbvI1XWmWcsuJldXr8FZz7O/WCT79hu0b2LX1Syfo/p2/V8iYtuoxlj6KnAK9RVWs7qK56K/dY+INwMPbv4tolb/vm29/Bv8rQZ9DzeUmKvETNBirjnaaH+xSCX27VBuLuhsW/BE4Igt1J66bcGuM81adjG5utxuX4rccTegbG+8ircBu2bmB+aomRGxX1RjIWwadCNmPm1lgjJzjTNTXaO19VUvP+ufrYzrABAROwOHU42ZszoaO4Tqv+Et6t83zffBslht5xpHpt6y65/F5OriNThHTfuLRbBvn5511RSbxzJ6NLAX1VU071S/rw8D9p3Vpr43rCPiDGDHrMZxIiK2j+pUy6z/fvsCx0R1tdCRKjFXiZnqWq3lmov9xeKU2LdDubkaNdreFjwF2Ccz3ztX7YjYr/59arYFx5Gpt+z6ZzG5xrHdvpR4VdkhRcQM1QbHkVQDfL6pnj7IpaCfQXVo6eGZ+auIuDcQVO+Dr9TzvAT4X8DTs6Vz3UeZqX5ecbkmJVNdZ6Tra4FaR9a1ds7MfxhFnfqDZRuqjfR/yMyvRMRMZm6IiDOpBop+zCjav4U2jDTXJGSq21FcrjZeg/PUGXV/8Qzg/iX1F5OSq8RMdZ1W+/Z6B821UV1V7jXALsBBwLqsxy8bcLk/BdZm5mMi4inAnajGcToJ+E/gAODlwCmZ+YUhY8xVv7hcJWaq67eSa4GabgsuvKyJyOX/IyOrN5Ltpog4FngdcHBmXhwR9wX+DGybm6+8+xngimnZFpykTHWt4nJ1td2+FLjjbgsiYkXWV/XZwjw3eOHFgFfliYi7UH2gfBY4BDgUuADYGvhZZp4QEQcCTwJOzMxfD1Cj00z1c4vL1UWmuk7n62sxhnxdLMvqW55nA9+mOi3mmVQbUZ/NzH+L6hSd9wInZ+Y3R9bwPts26PMmMVOzfYM+bxJzDZJpDP3FaqqxPc4CDqaQ/qKLXCVmqut0nWvO5/V2nNS/bw/sm5n/PUitXnsjIoDvAHsC66j6iiOAuwD/lJnfqzfkHwk8hmqA9EG/TCguV4mZOszltuD1p01sLv8fGT5XROyeAxypN8Tr4s7AQ4ErgZ2oxqP8DvAo4PWZeeKw24IlZqrrFJer60zCi1PMd6MaLPcxc0yPxu9DDUbZWM5rqcYXgeqNdSbwderBeoG7Ah8EZqj+UX42jYF8JzFTqbm6ytRlrrrOw4BtunhdzFH/4cBJ9e9fAa4Ajmg8/kCqb2mmJldbmUrN1WWmjvuL3YCt699Xl9BfdJmrxExjyNXJRQca7+EVjWkfA/6qcf+NwAsb93c0V9mZxpDLbcEpyNVlplJzAScCj+vqb9hY5p2BtwE/Bm5STzuY6sqh+1INwzXotmBxmUrNNa5MS/029gZM4q1+kX9sC4/vRzU+wvVeoAPWehPwJ+AHvRd4/aY6qDHPbsC/Azefhkyl5uoqU5e5qAaF/h/gE8B9uOGOk1s0fm9rZ9DN6r/tScAXgadRfSt0SP34VtOWq41MpebqMlPH/cU7gDOoNpAOqqfdYZr7iy5zlZhpDLneDHx81rToLZfqlJmBl99Y5uz38Jw7eerHn9xsi7nKzdRxLrcFpyRXl5lKzUV18ZaPbKlW4/dR7Shs7pC5LXBA4/4uwMeB3QatWWKmUnONI5O3+u857gZM2o1qbJsfAXvX9+9NtXFz78Y8L6EaYHGHIWu9B3h//fupzL3nehnwPuCt05Cp1FxdZRrT+jqlzvflXg1gpv55JvCBYWvUy9pq1v3mB8vngLVs3qi6zzTk6jpTqbk6yvQM4PyO+otTqTfggX8EvgksnzXPKPuLonKVmGkMuc4ATmvc3775vqb6tv3JwE2HqdNY3lzv4RX1z22BzwCnjqBOcblKzNRlLtwWnJpcXWYqNRfVBcIuBfaq798XuAeNbbH6PdzGtmDz/dvcLvwg8HYzlZ+ry0zebnjzqrI3dE59Wx0R/0Q1WO4TgKdGxD/W83wc+H9Uh1QPJCIOBn6fmY+tJ/2S6pDW3uMREdsBHwL+kplP700foFwnmer2FZer40zQXa7e+/884C1UR1G9KCI+T9UxQzWuzfKIuNugdeparwBOjIijImIvuO6KRsvrWR4K3DnrKxvl5oFTF/037CpXl5nq5xWXq8vXIHAu8D3gni2/r24GXAU8BSAzTwAuBm7dmGeU/UWJuUrMBB3lqt0eWA4Q1UUH3gh8PiKOiIgVwK5Up8gcPEyRhd7D9eO3o7oAwlNmPWcQJeYqMRN0lAu3Bacpl/+PDN+3/xh4O/C4etmvptpOen9EHF/PcyTtbAte2/v71NuFu0TEm4E/Z+ZT6+cN8vcrMVOpuTrJpHmMe8/hpNzocLyKeerfBPg58IRZ02/f+H1Rh5uOO1OpudrINM5ctDgeW/38k6lOQXg48EngH4D7jvJ11nWucWUqNVfLmTobu6xe3lZUV2KMRt0vA0fOmu92jd8H6S+Ky1Vipq5zsfkUxAC+C1xUv6duA7yA6iioO9TzHAl8uP47DHvq1rzv4eayB/n7lZqrxExd5qLjbSZueCRuEduCXeTqOlPJuerltj0m28n0uS0I3GmY13vJmUrN1XYmb1v424+7AZNwo9vxKp5P9S3MwxrTtqp/HkU12OMMWzhVbdIylZqrq0zjWF+zarcyHlv93B2Ad7N53KgDgJcC/wzcozHfE4FbT0OucWYqNVeLmbocu+xUqg2nZY1pyxrtOLT+/WTgVo15BukvistVYqYx5XoYHV10YFbtLb6HzVV+pi5z0e22YK+/2KYxbeq3BbvK1WWmknPNbiPtjcnW77bgk2fVH3QczOIylZqri0zetnxb8qfKRsR7gF0yc3uqbwYfC5CZP8zMH9XzLKPagL8gM/9niFpvBw4DtgFeGREH1LWurWf5b+AuVP8UX9t8btbvgknLVC+ruFxdZaprvYcOckXEVrPu9w6h/gWwP3BP4P6Z+TbgJZn5g/rxaxlQZv6R6tv2F0XELpm5nurbxz9TjYlARGwPXJGZPxmkRte5ushUL6O4XF1miohTqb7ZfiTwBeAdEbE8M7/XQn+xM3A41em994qIbet29y53/wvgZvV7/SaZ+dPecwfoL4rLVWKmMee6S0TsWLf5yMz8fmPWmwG/a9zfuMg6A72HB1VirhIz1cvvKtd76G5bsJfp8VSnQW5T1+p9Jq1jyrYF6+V0kmsM/48Ul6v5Ps7M7N3PzPOBCxqzvgW4NDMvrx/fxAAWsS34u/qx69q2lDOVmqvrTNqyJb3jLjoc/yAingHcODMfmJlvB74P7BYRd+zNk5nfozrE+pHTkKl+XnG5uspU1+okV3Q/HtsxUe38hGrQ398AR0fEjvUGzEeBp0XErTPzT5n5sUnP1VWmUnN1nKnTscsy8wqqHTO/B14G3L1e3k71LLtQDUp9eWYePWitEnOVmKl+zrhyXVHnulO9vBX1z20j4jPAZZn5jsbzFrMB/wo6/BwpNVeJmTrM1ek27hyZev8M93ZKnsMUbQv2dJGr60x1u4vKNc/7uJWxy8a8LTjVmUrN1WUm9Skn4LC/SbnR0ngV9fPuAGxX/34c8AfgVcBPgOc35hv60uddZSo117gytZWLMYxbBuwOvILqMO5lwKOpTk84ns1XCz0LOHiIGp3m6iJTqbnGkKmTscuaz6Mau+bOwIOprrz7eeDZ9WMPAU5uPGfQ0xSKy1VipgnL9cz6fb0KeMWgtbp+D5eaq8RMXeWqn9PJOHN9ZHpWY76htwVLzNVlphJzLeZ9zAjGLmPCtgWnJVOpubrO5K2/25I84i4inh8RT4iIhzWmbZWZv6a6XPftImImNh8Oem49T+Tgh7N+LzP/HNW3+ttQnRf+cuBo4JiI2LueL3u1Jj1TqbnaztRlrojYAdgZ+N+Z+UmqgaE3AodHxD0a8z0xIm4991IGci1wEHBs3d4PA18D9gG+ERFnAZsy84eDLHxMuVrNBGXm6jJTRJwaEQ+nenuur9+jvdNhLgQuq+c7OSJulZnn1feH6S96z/slcHRmfgbYDrgbm08j+FJmPq+utazXdyzlXCVmmtBcF9aPn5OZr2jkmvjPkRJzlZgJOsnVe18ta0xre1twS5l+1phvmG3B4nKNI1NpuRbxPn5yRByQmd8dtFbDpGwLTk2mUnONKZP6sOR23EWHY5fNJTP/ALwtM39TT7qgvl01aK1xZ6qXU1yuNjJBt7myo/HY5qj7O6pvZ14aEcdk5qbM/GRmHg88C/jnzHxwXX/RG7vjyNV2prpGcbm6yhQdjl02j+8BW0fEScA1wIuBV0TEIZn5p0atxW7AF5erxEww8bmuW/5ic43rc6ShxFwlZoIWckWH48zNY75MBw9Tq8RcE5AJCsi1iPfx73KIMdlm1ZyUbcGpyVRqrnFkUp9yAg776+oGPAP4ROP+u6k62jvOmu9fgH8ZslZfVysCPkC1c2jiM5Waq6tMXeYCjgHeXv9+IPA64OnUV28Dbkf1DeStZz1v1Kc0H0Z1ufDZpxBE/XOxpwCNPdeoM5WaaxyZgFOA91CdknjvetpO9c8TgU3AG4aptaX+guq0nLVsPmXnPiNaN8XlKjFTabm6fg+XmKvETF3maixzrvfVjo3HW90W7Li/mOpcXWQqNVfX7+N52jD124JtZyo11yRk8rbAOhp3AzoN29HYZVTnnb+R6rLje821XGBP4F3Au4ap21WmUnN1manjXJ2M69BnW1ZTnSL2HOBBJeQaZaZSc3WZie7GY5uvv1he/9y60ZZlw9QqNVeJmUrNRbfv4eJylZhpDLm6Gress0yl5uoqU+G53Bacgkyl5pqUTN7mvy2pU2Wzm7HLTqa6St1XqD5QnhER920ut/79EuAdmfnE+nmLHkunq0yl5uo6U1e5aq2P69CvzDyb6hSDq4F7R8SxQyxuInKNOBOUmauzTNnN2GUnM39/cU398+peWxptYoj+orhcJWYqOFcn7+ESc5WYCSauvxjVOHOdZpq1jGJydZGpft7JFJir5rZgS9xu78tEZNIW5ATsPRzHjcZVgYCdgI8Buw+5zB2oTn08qL5/APBS4J+BezTmezKwf+P+SA4xbSNTqbnGnanN9dVY5sFUGxrHzJp+KHBoG5n6bNdOpeUaNlOpubrOBNwMeBNwEvBF4GnAd4BDhlxuv/3FE5l1CoG5lk6mEnO1/R4uMVeJmcaZq17mfO+rg4dc7qT2F1Obq61MJeeaVcdtwSnIVGquSczkrbEext2AVsN1OHZZY1mvBk4Ddqnv3xx4JfCi+v72wJHTlKnUXG1nGuf6aix35OM6TMLNXNNzayPTlt5XtDcW0Vj7i2nNVWKmknPNU7fVfqnEXCVm6iJXqe+rEnONI1PJuWbVdFtwSm4l5ioxUym3sTegtWDdjsfWyWCOXWYqNVdXmcaxvrbQjpGO6zApN3NNz22UmbbwvmpjbJtJ6C+mNleJmUrOtUA7Rj0+UHG5SszUZa5S31cl5uoyU8m5FmiL24JTcisxV4mZSrgVOcbdGMYu+xxwSUTsAKwHvg+sBI6LiJnMPI/q4gPbNp+0mFrjGI+t0FytZxpTrnnl6Md1mAjmmh6jyjSGsYgmob+YylwlZio510Ja6JdKzFViJrC/GChTqbnGMSZgwbnm5bbg9CgxV4mZSrB83A0YtbpT3xn435n5o4g4H3gkcHhE/Dkzv17P92TgK5n5jfp+NDvhRWoO5viWiPgw8Efgr6kGc/wlQwzmOKZMpeZqNdMYc21RZq4D1tV1dmqjxjiYa3oMm2kR76snAt/IzJ+MoNmT1F9MTa4SM9XtLTJXv0bcL5WYq8RMYH8xkBJzjSkTlJtri9wWnB4l5iox09TLCTjsb9Q3xjC2CO0PCjyu8VKKy9V2pnGuL2/eSr7ZX0xPrhIzlZxrHLcSc5WYqYtcpb6vSsw1jkwl5/LmzZu3fm9jb8DIgkzA2CKMeDDHSchUaq5RZ5qUXN68lXabhPdVqf2FffvSzjUJtxJzlZipjVylvq9KzDUJmUrO5c2bN2/93Eoa427sY4tk5peA44CXR8RzIuJBzRq5+NMgx56pXl5xuVrIBBOQSyrQ2N9XpfYX9u19KzXX2JWYq8RMYH+xCCXmGnumenlF5pKkfpS04645/sEm4MPA14B9qMY/OIsOxhbJ0Q7mOBGZoMxcI84EE5JLKsxEvK9K7S/s2/tSaq6JUGKuEjOB/UWfSsw1EZmg3FyStJDeocVFiIiDgc8AJ2Tm+xrTDwXIzP+s70dX35ZExE6Z+Ychnj9xmep6xeUaNlO9jInLJU27SXxfldpf2LfPu4wic02iEnOVmAnsL7awjOJyTWKmul6RuSRptqJ23AFExGHAvwKvy8x3N6ZHZmZELBvw0PexKTETmGt8LZSmT6nvqxJzlZgJys0ljVOp76sSc5WYCcrNJaksxe24A4iI1cD7gJOACzLzs2Nu0tBKzATmktS/Ut9XJeYqMROUm0sap1LfVyXmKjETlJtLUjmK3HEHEBErqa4+tD9wfma+Z7wtGl6JmcBckvpX6vuqxFwlZoJyc0njVOr7qsRcJWaCcnNJKkOxO+6aShxbpMRMYC5J/Sv1fVVirhIzQbm5pHEq9X1VYq4SM0G5uSRNryWx406SJEmSJEmaNsvG3QBJkiRJkiRJN+SOO0mSJEmSJGkCueNOkiRJkiRJmkDuuJMkSZIkSZImkDvuJEmSplBEXBsRP4iIH0XEDyPi+IgYeNsuIr4aEatG0K4T+pzvORHxXxHxgYjYNiK+VOdZM2wbJEmSSrF83A2QJEnSQP6UmYcARMSNgQ8COwN/P85GAScA/9jHfM8AHpiZF0bEXYGte3kkSZJU8Yg7SZKkKZeZvwGOA54VlWMj4k29xyPiMxFxr/r3t0bE2vpIvVcutOyIuFNEfKM+qu87ETEz3/Ij4rXA9vWRcx+oHzs+Is6vb8+rp70NuCVwZkS8GHg/cEj9vP1H9XeRJEmadh5xJ0mSVIDM/Fl9quyNF5j1ZZn524jYCvhyRNw+M8+da8aI2AY4HViTmd+NiJ2AP22hDS+JiGc1jgS8I/AE4C5AAN+OiP/MzKdFxAOAe2fmZRHxbeAFmfngRcaWJEkqmkfcSZIklSP6mOdREfE94PvAQcBttjDvrYBLMvO7AJn5h8y8ZhHtWQ18IjM3ZuaVwMeBey7i+ZIkSUuaR9xJkiQVICJuCVwL/Aa4hut/QbtdPc8tgBcAd8rM30XEe3qPzbdYIOeYPufy53m+JEmSBuQRd5IkSVMuIvYA3ga8KTMT+DnVmHHLImJf4M71rDsBG4ErIuImwAMXWPRPgL0i4k51nZmIWL6F5QNcHRFb179/DXh4ROwQESuAvwH+75BxJUmSlgyPuJMkSZpO20fED4CtqY6Aex9wYv3Y14ELgfOA84HvAWTmDyPi+8CPgJ/V880rM/8SEWuAf4uI7anGtztsvuXXTgHOjYjvZeZj6qP6vlM/9o7M/P4woSVJkpaSqL6UlSRJkiRJkjRJPFVWkiRJkiRJmkDuuJMkSZIkSZImkDvuJEmSJEmSpAnkjjtJkiRJkiRpArnjTpIkSZIkSZpA7riTJEmSJEmSJpA77iRJkiRJkqQJ9P8BguJMRwxVWxIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1270.08x259.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def graph(cutoff_list, metric_values, ylabel, title, fn):\n",
    "    fig, ax = plt.subplots(1, 1, figsize=(len(cutoff_list)*0.42, 3.6))\n",
    "    ax.scatter(np.arange(len(cutoff_list)), metric_values, s=50, color='red')\n",
    "    ax.set_xticks(np.arange(len(cutoff_list)))\n",
    "    ax.set_xticklabels(cutoff_list, rotation=45, ha='right')\n",
    "    ax.set_xlabel(\"Dual cutoff\")\n",
    "    ax.set_ylabel(ylabel)\n",
    "    ax.set_title(title)\n",
    "    plt.tight_layout()\n",
    "    plt.savefig(fn, dpi=200)\n",
    "    return\n",
    "\n",
    "graph(cutoff_list, [num_of_binding_sites[cutoffs] for cutoffs in cutoff_list], \n",
    "      \"num. of binding sites\", lipid, f\"{save_dir}/test_cutoff_num_of_bs_{lipid}.png\")\n",
    "\n",
    "graph(cutoff_list, [duration_avgs[cutoffs] for cutoffs in cutoff_list], \n",
    "      f\"Durations ({timeunit})\", lipid, f\"{save_dir}/test_cutoff_durations_{lipid}.png\")\n",
    "\n",
    "graph(cutoff_list, [num_of_contacting_residues[cutoffs] for cutoffs in cutoff_list], \n",
    "      \"num. of contacting residues\", lipid, \n",
    "      f\"{save_dir}/test_cutoff_num_of_contacting_residues_{lipid}.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the plot of durations and num. of contacting residues, we can see that contacts started to emerge with at the lower cutoff of 0.425 nm but saw a prominent jump at 0.45 nm of the lower cutoff, suggesting that effect contacts start at 0.45 nm. This also agrees with the distribution of the minimum distances which starts 0.4 nm. \n",
    "\n",
    "With the same lower cutoff, we saw a positive correlation of the larger upper cutoff and the longer interaction durations. This correlation was almost linear when the upper cutoff is smaller than 0.65 nm, but flattened out after 0.65 nm, suggesting that the impact of increasing the upper cutoff on interaction durations is marginal after this point. Further increase the lower cutoff (data not shown in this test) will see a decrease of interaction durations, regardless of the upper cutoffs, suggesting that too big a lower cutoff will include unnecessary noises which could lead to inaccurate results. \n",
    "\n",
    "The impact on binding site calculation was a bit more complex. No effective binding site was detected for lower cutoffs smaller than 0.45 nm, even though some contacts started to emerge at the lower cutoff of 0.425 nm. When the lower cutoff is at 0.45 nm, the binding site calculation was very unstable. The number of detected binding sites flickered with increasing upper cutoffs, suggesting that these dual-cutoffs cannot effectively differentiate binding and unbinding events. The num. of binding sites flattened at the dual cutoff of 0.475-0.7 nm, indicating that this is a good cutoff to effectively separate binding/unbinding activities. \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PIP<sub>2</sub> interactions with A2a\n",
    "\n",
    "As we have shown above that PIP<sub>2</sub> and cholesterols have interaction dynamics with A2a receptor, let's see if interaction metrics would responded differently to the change of cutoffs than those of cholesterols. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "lipid = \"POP2\"\n",
    "lipid_atoms = [\"C1\", \"C2\", \"C3\", \"PO4\", \"P1\", \"P2\"]\n",
    "num_of_binding_sites, duration_avgs, num_of_contacting_residues = test_cutoffs(\n",
    "                                 cutoff_list, trajfile_list, topfile_list, lipid, lipid_atoms, \n",
    "                                 nprot=nprot, stride=stride, save_dir=save_dir, timeunit=timeunit)\n",
    "test_data = {\"num_of_binding_sites\": num_of_binding_sites,\n",
    "             \"duration_avgs\": duration_avgs,\n",
    "             \"num_of_contacting_residues\": num_of_contacting_residues,\n",
    "             \"test_cutoff_list\": cutoff_list}\n",
    "\n",
    "with open(f\"{save_dir}/test_cutoff_data_{lipid}.pickle\", \"wb\") as f:\n",
    "    pickle.dump(test_data, f, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similar to cholesterol analysis, let's plot the interaction metrics as a function of cutoffs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1270.08x259.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Is63ty92d3Kg6dtxJkiRJ0jTzUm1pdnm5u4a06ktlI+I6wOHNOHRTxUtlJUmSJElSXxYXS4f41q2lg21hoZzlOuoyvNxdfRjqUtmI+BjwkGb9zwOXRcS/ZuYyU5ZIkiRJkiRNqTZmegUvd9fQ+r1U9qDMvCIiHg+8ITP/KCKm7ow7SZIkSZKkFbU102uHl7trCP123K2JiEOB3wJ+f4zHI0mSJPWvjcucJEl12by5nP22lJ07y+OjnuDBSSM0oH477v4E+BBwYWZ+JiJuDmwd32FJkiRJu9HWZU6SpLq0PdOrNIS+Ou4y853AO7vufws4cVwHJUmSJK2o7cucJEn1cKZXzZC5flaKiEMi4vkRcU5EvL5zG/fBSZIkSUvq5zInSZKWsrBQJodYytxceVyaEv1eKvsPwL8DHwauHt/hSJIkSX3wMidJ0qCc6VUzpN+OuwMy8zljPRJJkiSpX17mJEl1amvSIWd61YyIzNz9ShF/CnwiMy8Y/yENbuPGjblly5ZJH4YkSZLGbXER1q+/9hh3HfPzjnEnSbNoqUmHOmfBOemQKhcRF2Xmxt7lfY1xBzwNeH9E/DQiFpvbFaM9REmSJKlPncuc5ufLBzsoPzvL7bSTpNnSPelQ52zqHTt2Ld++fbLHJ01Iv7PKjuG8VEmSJGkIXuYkSfXoZ9KhU09t95ikKdDvGHdExEOA32jufiwz3z+eQ5IkSZL6tG6dH+QkqQZOOiQtqa9LZSPixZTLZb/a3J7WLJMkSZIkSRpOZ9KhpTjpkPZg/U5O8UXg6Mzc2dzfC/hcZt5+zMe3Kk5OIUmSJEnSDHLSIe3hhp2cAuDgrt8PGvqIJEmSJEmSwEmHpGX0O8bdXwCfi4iPAkEZ6+55YzsqSZIkSZoFi4tl0PytW8ulfgsLpaNB0uo56ZD0S/q6VBYgIg4F7kTpuPtUZv5vH9s8AHglsBdwXma+uOfxaB4/HrgSOCUzPxsRhwNvBm4E7ATOycxX7q48L5WVJEmS1JoLL4Tjjy8zXu7YUc4OmpsrZwdt2jTpo5MkzZCBLpWNiFs3P+8AHApcDHwHuHGzbKVt9wLOAo4DbgOcFBG36VntOGBDczsNeE2z/CrgGZn5K8CdgScvsa0kSZIkTcbiYum0W1zcNRPmjh27lm/fPtnjkyRVYXeXyp5B6VB72RKPJXCvFbY9BtiWmd8CiIi3AydQZqXtOAF4c5bT/j4ZEQdHxKGZeSlwKUBmLkbEfwLre7aVJEmSpMnYvLmcabeUnTvL46ee2u4xSZKqs2LHXWae1vx6XGb+tPuxiNhvN/teTzk7r+Ni4Ng+1llP02nXlHME8GvAp5YqJCJOo3QucpOb3GQ3hyRJkiRJI7B1664z7Xrt2FHG55IkaUj9zir7iT6XdYsllvUOqLfiOhGxDng38PTMvGKpQjLznMzcmJkbDznkkN0ckiRJkiSNwIYNu2a+7LV2bRlUX5KkIe1ujLsbRcQdgf0j4tci4g7N7R7AAbvZ98XA4V33DwMu6XediNib0mn3lsx8z+6CSJIkSVJrFhbKRBRLmZsrj0uSNKTdjXF3f+AUSofay7uWLwLP3822nwE2RMTNgO8CjwAe2bPO+cBTmvHvjgUuz8xLm9lmXwf8Z2a+HEmSJEmaJvPzZfbY5WaVXbdu0kcoSarA7sa4exPwpog4MTPfvZodZ+ZVEfEU4EPAXsDrM/MrEXF68/jZwAXA8cA24Ergsc3mdwVOBr4UEZ9vlj0/My9YzTFIkiRJ0ths2gSXXFImoti2rVweu7Bgp53qtLhYXutbt5ZLxRcWSge2pLGKMqFrHytGPBC4LXDNpBSZ+SdjOq6BbNy4Mbds2TLpw5AkSZIkqR4XXrj82aWbNk366KQqRMRFmbmxd3lfk1NExNnAAvBUyoQSDwduOtIjlCRJkiRJ02VxsXTaLS7umkl5x45dy7dvn+zxSZXrd1bZX8/MxwA/ysw/Bu7CtSeVkCRJkiRJtdm8uZxpt5SdO8vjksam3467nzY/r4yIGwO/AG42nkOSJEmSJElTYevWXWfa9dqxo4zvKGls+u24e19EHAy8FPgs8F/A28Z0TJIkSZIkaRps2FDGtFvK2rVlUhZJY7PbjruImAM+kpk/bmaWvSlw68x8wdiPTpIkSZIkTc7CQpmIYilzc+VxSWOz2467zNwJvKzr/s8y8/KxHpUkSZIkSZq8+fkye+z8/K4z79au3bV83brJHp9UuTV9rvdPEXEi8J7MzHEekCRJkmbc4mIZrHzr1nKJ1cJC+YAnSZpNmzbBJZeUun3btnJ57MKCnXZSC6KffriIWATWAldRJqoIIDPzwPEe3ups3Lgxt2zZMunDkCRJ2nNdeCEcf3yZaXDHjnJWxtxcOStj06ZJH50kSdJUioiLMnNj7/K+zrjLTL8ilSRJ0soWF0un3eLirmWdmQiPP76creHZGZIkSX3rq+MuIn5jqeWZ+W+jPRxJkiTNrM2by5l2S9m5szx+6qntHpMkSdIM63eMu2d1/b4fcAxwEXCvkR+RJEmSZtPWrbvOsOu1Y0cZF0mSJEl96/dS2Qd334+Iw4GXjOWIJEmSNJs2bChj2i3Vebd2bRnMXJIkSX2bG3C7i4FfHeWBSJIkacYtLJSJKJYyN1celyRJUt/6HePur4HO9LNzwNHAF8Z0TJIkSZpF8/Nl9tjlZpV1YgpJkqRV6XeMuy1dv18FvC0zPz6G45EkSdIs27SpzB67eXMZ0+7II8uZdnbaSZIkrVq/Y9y9KSIOaX6/bLyHJEmSpJm2bp2zx0qSJI3AimPcRfHCiPg+8DXgGxFxWUS8oJ3DkyRJkiRJkvZMu5uc4unAXYE7Zeb1MvM6wLHAXSPi98Z9cJIkSZIkSdKeancdd48BTsrMb3cWZOa3gEc3j0mSJEmSJEkag9113O2dmd/vXdiMc7f3eA5JkiRJkiRJ0u467n4+4GMARMQDIuLrEbEtIp67xOMREa9qHv9iRNyh67HXR8T3IuLLuytHkiRJkiRJqs3uOu6OiogrlrgtArdbacOI2As4CzgOuA1wUkTcpme144ANze004DVdj70ReED/USRJkiRJkqR6rFnpwczca4h9HwNsa8bEIyLeDpwAfLVrnROAN2dmAp+MiIMj4tDMvDQz/y0ijhiifEmSJEmSJGlm7e6Mu2GsB77Tdf/iZtlq11lRRJwWEVsiYstll1020IFKkiRJkiRJ02acHXexxLIcYJ0VZeY5mbkxMzcecsghq9lUkiRJkiRJmlrj7Li7GDi86/5hwCUDrCNJkiRJkiTtccbZcfcZYENE3Cwi9gEeAZzfs875wGOa2WXvDFyemZeO8ZgkSZIkSZKkmTC2jrvMvAp4CvAh4D+Bd2TmVyLi9Ig4vVntAuBbwDbgXOBJne0j4m3AfwC3ioiLI+LUcR2rJEmSJEmSNG2iTOhah40bN+aWLVsmfRiSJEmSJElS3yLioszc2Lt8nJfKSpIkSZIkSRqQHXeSJEmSJEnSFLLjTpIkSZIkSZpCdtxJkiRJkiRJU8iOO0mSJEmSJGkK2XEnSZIkSZIkTSE77iRJkiRJkqQpZMedJEmSJEmSNIXsuJMkSZIkSZKmkB13kiRJkiRJ0hSy406SJEmSJEmaQnbcSZIkSZIkSVPIjjtJkiRJkiRpCtlxJ0mSJEmSJE0hO+4kSZIkSZKkKWTHnSRJkiRJkjSF7LiTJEmSJEmSppAdd5IkSZIkSdIUsuNOkiRJkiRJmkJrJn0AWsHiImzeDFu3woYNsLAA8/OWNY1l1ZipzbJqzFRrWTVmarOsGjPVWlaNmdouS5IkScPLzLHdgAcAXwe2Ac9d4vEAXtU8/kXgDv1uu9Ttjne8Y1bj3/89c34+c+3aTCg/5+fLcsuarrJqzNRmWTVmqrWsGjO1WVaNmWotq8ZMbZclSZKkVQG25BJ9XVEeG72I2Av4BnBf4GLgM8BJmfnVrnWOB54KHA8cC7wyM4/tZ9ulbNy4Mbds2TKOOO1aXIT168vPXvPzcMklsG6dZU1DWTVmarOsGjPVWlaNmdosq8ZMtZZVY6a2y5IkSdKqRcRFmbmxd/k4x7g7BtiWmd/KzJ8DbwdO6FnnBODNTefiJ4GDI+LQPret1+bNsHPn0o/t3Fket6zpKKvGTG2WVWOmWsuqMVObZdWYqdayaszUdlmSJEkamXF23K0HvtN1/+JmWT/r9LMtABFxWkRsiYgtl1122dAHPRW2boUdO5Z+bMcO2LbNsqalrBoztVlWjZlqLavGTG2WVWOmWsuqMVPbZUmSJGlkxtlxF0ss670ud7l1+tm2LMw8JzM3ZubGQw45ZJWHOKU2bIC1a5d+bO1aOPJIy5qWsmrM1GZZNWaqtawaM7VZVo2Zai2rxkxtlyVJkqSRGecYd3cBXpiZ92/uPw8gM/+ia53XAh/LzLc1978O3AM4YnfbLsUx7iyr9bJqzNRmWTVmqrWsGjO1WVaNmWotq8ZMbZclSZKkVZvEGHefATZExM0iYh/gEcD5PeucDzwmijsDl2fmpX1uW6/5ebjggvKz8+342rW7lo+yYW1Zs1FOrWXVmKnWsmrM1GZZNWaqtawaM7VdliRJkkZmbGfcwTWzxp4J7AW8PjP/LCJOB8jMsyMigFcDDwCuBB6bmVuW23Z35VVzxl3H9u1lsOht28olLAsL42tYW9ZslFNrWTVmqrWsGjO1WVaNmWotq8ZMbZclSZKkvi13xt1YO+7aVl3HnSRJkiRJkqo3iUtlJUmSJEmSJA2oqjPuIuIy4L8nfRxjcH3g+5Y1E2XVmKnNsmrMVGtZNWZqs6waM9VaVo2Z2iyrxky1llVjplrLqjFTm2XVmKnWsmrM1GZZNWZqu6y23TQzD+ldWFXHXa0iYstSp0ta1vSVVWOmNsuqMVOtZdWYqc2yasxUa1k1ZmqzrBoz1VpWjZlqLavGTG2WVWOmWsuqMVObZdWYqe2ypoWXykqSJEmSJElTyI47SZIkSZIkaQrZcTcbzrGsmSmrxkxtllVjplrLqjFTm2XVmKnWsmrM1GZZNWaqtawaM9VaVo2Z2iyrxky1llVjpjbLqjFT22VNBce4kyRJkiRJkqaQZ9xJkiRJkiRJU8iOO0mSJEmSJGkK2XE3RSJi7M9HRMS4y+gpr5XXWI25aszUVdbYs03g79dKeTXmqjFTV1nWFYOXU12uGjM15VT3HjbT7JRZ4/tqQs9VdbnMNHRZ1b1/2yrT/yGzW+a0suNuwiLi/0XExoi4XmbuHHNZ188WBjVsM1NTXnW5Ks10j4h4GEAb2TpljLOB03am7nJqylVbJuuKkZRXXa4aMzXltZXrni2+h800XFlt1rfVva9afq6qy2Wmocuqrg3Y7L+6XDVmavbf+uerWWDH3QQ1PchHA/cFPhQRd4yI/cZU1m8A742IR0bEPcZRRlNOa5ma8u5OZbkiYhP1ZToEWA88OiLOjoj7RMRBYyrrlIh4c0Q8NyJuP64GTpuZmvIeU1uuGp8r6/WRlGe9Png5bT9Xd6OdXAcDN6ad93BbmdZSWaamrBtQ6tuTa8lVY73elNVmLuv1wcuxvT58WW3msr0+XFmtfr6aJc4qOyERcVRmfqHr/hOBBwLvBC7IzMtGWNZcZu6MiLsCt6dU/F/OzBeMqoymnNYyNftfk5lXNY2c21JJrqaMuwO3oYJMEXF4Zn6n6/4ZlA8rVwCvzswfjqqsrjLuRHmtPx/4XeCDo/wn03amiNgvM38aEXehvC6qyNWUcQxwOyrIZL0+kvKs1wfff+uZmnJ+HTiK8eW6H/DxzNzR3G+jXhp3picD/5iZ32zuz3ympowDMvPKrvvPAA5lhnPVWK83ZbWZy3p98P3bXh++jDbbgbbXhyuj9VwzJTO9tXwDzgbObX7fq2v5g4G3Ar/Z3J8bQVlnAk/rur8GuDnwZeDMWczU7OftwCeAvWvJBfwW8Ghg/+b+PhVkejPwmub3vbuW3wd4CaXi329Eud4M/HbPst9sXicnzWKmZr9vBTbXlAs4EXhYZZms14cvz3p9BjI1+3kGcOcWXoObgbcB1wH26Vp+3zG8h9vKdA6wHXhoz/J7z2qmZt+vAt4N/BXwa5U8V9XV6xPIZb0+G5mqa69PIJft9RnJNau3iR/AnnYDXg+ct8LjjwA+A9x8BGW9ATgfWLvEY9cDPg08ZZYyNfs7C/hok29Ts2zNLOdq/jn/I6WB88mef9Czmuk1wDtWePz/Aa8EbjiCss5tXuvrlnjseEpj6jea+zELmZr9nQl8BPgS8OCexx4wi7mAvwUuAD5H0yCd9efKen24spr9Wa/PQKZmf38DvGeZx0aZ61TKN/qd+3Od10Rz/8QRvofbynQW8Drgd4AvAgf3PP7QWcvU7O8c4F3Apub3TT2Pz+JzVV29PoFc1uuzkam69voEcp2J7fWZeK5m+TbxA9iTbsCxwE7gjs39RwNnUHqQb9613hmUht2+Q5R1EPD2rvt3Bu4JXLdr2V2BVwz6JgCi2W8rmZr9nAm8g/KN3cuAV3U91mkMjCLXXVp8rk4GPtJ1/9XA4Vz77IKhMjX7OKbFTA8Cvgvcurn/MOA5wG8Dd+pa7xzglUO+JvYF3tJ1/y7AbzR/w85r4pHAx4HDZiFTs5+zgPc2v58OPLv7dd78/ogR5DoOuKSl5+oUyuVhnffZ3wG3onwg7wzdcNIIMj2wxdef9br1+lLlVVevN/v5c2Br1/1bADfi2t+OD52r2c9vAs9vfn9ac/xnA4/pWufcEbyHW8lE6az75677rwN+p/m9+8P/KOqlv2jxeZqn1OWdM6rOpZx58gzg+BE/V3/W0nNVVb3e7KPVuh3r9Zmo16mwvT6BXLbXhyurtTb7rN+cnKIlERGZ+SngNOD8iHh18/sPgPsDp0XEAc3q7wS+Tam0B7UdOCgi7h4Rp1MuYTgdeF9z3T1NGQcDNx2wjLnM/CSlMTr2TBFxQ+DizPytzLyKUlHePyIeBNAsA9jGcLnWZOZ/AE+inefqYmBLRKyPiOdQGgYvBT4VEYc16wz7XJGZnwaeTAuZMvP9lIb7MyPixcCzKRX/HYDHR8SRzarPBLIr56o0A/buB/xqRNw+Ijp/u98H/hD4rWbMmLcCHwRuOO2ZmlyHAV/KzIc2i/4HeGJE3CbLODFzzTG9nSFyNeMRfZDyzfHYczU5ftzs41nA3SmNzr+hNODIzLcx/HP1Acpz9axxv/6s163Xl1FdvR4R+1Pewx+JiLtFxGmUhvRZwMebxwG+xZC5GnPAsRGxkXKpzNspZzQ8IyIe3KzzDIZ7D6+hZPqXFjKdm5n3bcrdG/g85UMrmXl1cywwmrr2v2knE5m5SOl8+kREvJTy4fIfKa+1pzZj0MHwz9Va4DvAR8eZq9J6HVqs263XZ6der7G93nIu2+vDP1ettNmrMOmewz3hRmms/HrX/dOA7wFHNvcPoZxae9eudR4NzA9YXqcn/GmUCvEc4AbNsmcDF9F8OwQ8BHgiq7w+nfJN2u91lTXWTEuU3zn+ZwHPan7v/sZ60FydU987+x97LuBXKOPCvI5SUR7WLH8F8Kmuv/GgmR5OaVx0xuI4fVyZKP98u/fzMso4COub+zcD3gvctrm/hnIK+bBngTyB8s3nezv7Ap5K16ndTe5TBtj3tcbiAF7eRqau8vZqfr6IcsbCAT2PD5rrWmNxtJELuHVTzruA/6ScqbEPpT55zQgynQg8vOv+K8aVCev1oTMtUb71ev/7b61eb7Y9vPl5vWY/HwO+Dmxo3kevo3yIHCrXEuW+h/Lh/lFdy55J8z4f8j18P2At5UP2WDN19tH9mgb2Bj5Lc3ZGZ71m+aCZnkw5C+2gNp6nnlxPovzPv1tzf55Sp9xnBM/VAc3PfcaZiwrr9WbbM5lQ3Y71+mr2b3t9V+5TBtz/xNrs2F5fbRmttdlruU38AGq/scxYHPScQg28D/h1GO4a8Z593q55wW8B7t61/J3AIV33D1jlft/AEmNxtJFpiWO5P6Xxdsvm/lzXY6vN1T0Wx926ll+/hefqOsANKIM6dy432Q94S/ffeYBM3WNxfJpdp6LfaNSZKP+I37nE8iN77v8TTUO+ub/3oGV27eNoysCl3wSOaZYdTPkm6LCu9a6zyv0uORYHcNNxZ+raV6chuInyz/t6zf3uhu9qc53JrrE4Htq1/GYtPFfrgFtSLqG5frPsxk1ddb0hMnWPxfH6ruU371lv6ExYr1uv91f2zNfrzX6uGTC687cDFoBbdS27I/Dynu1Wm2upzq19gX+mzNbYeewCusaQGvA93Jn04ro9mW49rkw9yzv5HtDUJ/M9jw+SqTPpRWfA+hs0mW45ykzLPVfN779Pmfmvc/+fgccOmasz6cXLgCMp/9vH8fqrrl5vtpmKuh3r9d3t1/b6EO31ZpuJttmxvb6afbfWZq/p5qWyYxQRfwbcNzP/X3P/FhFx44jYOzP/rzltmIh4F/CDzPxENq/KIcrs7DMy80vAH1Aqx3tFxBMi4p3AT7Nr+vDMvHIV+z+I8k3QQzJzR0TcOSLuHRHXy8z/61pvZJm6c/XKzA9Rvg14fkTsn13TUq8y15mUb7LuC/yQ8q1XZz/f71pvpM9VJ1dm/gi4mjJ+wKMi4paUBsnPMnPHgJlOBjZk5gMy8xGUhsD6iNgnM/93lJki4lxKY/Phzf31EXFEc8zbmmVrI+JtwHcz88NdmX4xSJnNPjunoH+e8o/lA8AZzWVU5wHfzsyLu8r60Sr2vS+l4fWQzNweEXeJiHtGxKGUy3WIiPlRZ2r2e83rvfOcZOaFwIGUDzFkubSq+/XT777PAo7IzHtTGr+37Crr280643iu9mp+3UG5jOubwEMj4lcpDeBLMvMHXWWtJtMplA83x1NOrd8nIm7T7OdbzTrrRpHJet16fTdlVlOvN/t5DWUWtyd2He/3M3NzZn69a9Xn9G67ylz7Avs3v0enfsvMn2W5vHRbRLwhIi4ALs3MV3eVs9r38KnAgZl5Umb+MCL26sr0tXFl6tnP1c2v36aM73PrnsdXm+ksYC/KGWN/HBHXyczvUcZd+kbXqkNlaspa8rlqHn4dcFhE/FNEvI9Sr79hiFznUD4ovoLy/+/QzPzxGF5/1dXrzb5br9ut1wfKZHt9iPZ6s/+JtNltrw/0XJ1CS2322qzZ/SoaRETsR6koPhIRd6OcXr0A/Bg4PCLunpk/iYjHA1dk5uOa7WK1lXFEPIzSiHoX5Z/Jz5tdkZlfjojnU97sxwKfz8w/G7QsusbiaDI9jtLwPCwinpGZn4yIJwybaYVc3Y/PNf/4P0m5tOAnqy2j2U9nLI6nN/fPAj4YEQ/KMkYCUcaTOGnYXL2ZMvOaTJn5g4h4JeVyggdR/jn/zqBl0TUWB+VU+pMpZxXcKiIenJkXj+q5opzafGzTgDmmKe9GEfFvwIuahudTmsyPHbSspnHzQ+DrmbktM3dGxJrMvCozt0TEJZR/ApuAL2TmiwYpq/kHe81YHMBRlHFhOv/E/qVpVD9p2EzL5Mqu1zfNB8urKQ37+3S2G+Dv1xmL48nNov8BzoqI92fmV5vcQbncatTP1dVdmX4WEV+ljJPxCOBrmfmUQcvi2mNxPJIyFscREfFl4I2US1hGkcl63Xp9t5lqqdcj4njKJV/37sp5C+D/gC9m5mcj4vqUmd6uzMwzBikvIt5EqW/nIuJNneenqQf3zsxfZOZDI+IWlA9mX2q2u6aOXKUfAv/e7ONpwFER8XPgwsz8uybTq8aRqbOvTr7M/HpE/FZmfmaAHJ39/Q7lLKbO+HnHAAsR8drM/FmzbOjnaaVczXMVlNfGb1Pq9SuyjIE00HMVEfPAAcBJmfmLiPhtythRx1LOwPzHEb3+aq3XoaW63Xp9dup1Kmuvd7ahpTb7Erlsr69eK232GoV/g/GJiOtRBul9PHAopXL/NvBaymm8CxFxUGZe3qw/SMPmHZSxTHZQ/lF+GPiHzLysU0Eus90gZUVTQT2NcvrsTYE/yMzvRcSzKd96/Trl2/nFQcvpI1enUlz2GFdbXtf2+2TmzyPiWQCZ+dJOhog4MDOvGDRXv89V04jcK5tv7ob4G/4K8KeUxud9KeO2XBwRrwDukpl3HjZTT3kLlG/bv0O5JOIXlEt3vp6Zz+xZd9C/3zzl73cZ8H+Z+cLmsX26G1XRfNgbNlfTUDoKOAxYyMyfRcRTgdtl5mnDZuoj1zU5mvvX5BzBa32v5p/ziyiz8j0tl/iGeAzP1b6dD5PN/UOahuIwf8NbU8a3uQlwW0pj9GeUyzH2za6zhYYpp9nWet16vd9MNdTrL6VcGvZ94F6UMecOpXxI+jPgKuB+mfnGQcprXmN3Bx4D3JNyCdczs3SgLfu8D/OaiIgTm/JeBPwRpZPuYMoHrWdTxp174AQyDfqa6P7QuDdlzKE7Z+ajuta5MUM8T5PI1Wz7Psr/p49ROmOeTxln8X6UMbq+Axw3TK5mu6rq9Wa7Vup26/WZrNera68324+1zW57ffj2erNta2326uQUXK9b8w24LkuPMfKKnvVWPVYB5fKB87vun0QZSPJ3ufY08g+g61r0EWRabiyOd3Hta94HGn9hUrl6juFaY3G0+Fwd13N/2LGJlhuL462UxtpIyunazwnAUV33f40ybsyaYcqizFj0/ub3fYA7U76V+cue9R7DAGPArFDu0fQ3Fsegr/V+c508ylzdx8zKY3GM87k6ma5xSEbwWu93LI6hX+tYrw+yf+v1Eb0GaaFe76kHlhq0/B+AXx3B3/A04E+67t8D+BrwiK5l53bfH9FrYblJLxZmKVP38bHCpBfDZlplrpNGnGu5SS/uN4pcXdtXV683+xxb3T7JXF37tl4frLyq2uvNPo9mTG32VeSyvd5f2a212Wu6OcbdGERc63r3HwJ/n788xkh2b5PNq3OVfkQ5jf/RzT7eBvwbpVF9u+ZYNlIa2z9Ydi996GRqvjVYbiyOn+S1r3kfJBNMIFev7BmLo+excT5XN25eMwOXFY1m+x+x9FgcP83Mnw6ZqVPeNfVIZv5DZn6h6+HnATuy65vkAcsKyqn8G7N8g3URpeF+nSiXzxBlfISf5yrHgFmysNWPxTHo36/fXL8YUa6+xuLoXWe1xdB/pu1DlkWsfiyOQcuxXh88E1ivz0S93lXG1V314DMoHVzfbe5/m3IJ2Y26tx3wb/hd4NCIuE6zj49Rzhj7q+ZvB3BGZr59gH0D1349dNUXJ1HOqHpe16r3onxwvsa0Z+o+vuY52yvLWR/Pp1x6NN+77RDv4X5zvW3A/V8rV+e5ysy/oVzGtdDcX6ScpXFY97bDvN6b7auo15t9tVW3W68PUZbt9eHbtc3+2miz214friya/bXSZq+Vl8qOSCwxFkLzDzO71umMxfGLzDylWTbo2DOdU+AfRrnu/N2Z+YnmsT+kXCbxwDFkmqMZmiXKeDOdsTh+kcOPxTGxXD2Pd061fzBlLI7XDVneNGS6D2UsjkWGHIsjesZCaJZdczlE88/mQMo/y+05ovEJIuLJlA9bj8vMb0TEOsrYCLfIzOf0rLvaMW6WytR9OcSN2TUWx44cYiyOKcj1S2NxRMTRlFmb/mqYLFOS6WTK++yWDDkWh/W69foK5U1DppHV6812+1K+wb+yK9+1LlGJiLWUuv2nnbp9GM1r7+3A5ewaV+mqiHgBsCUzL+had5D38FKZrtlPRLyX8kH9hpRJL06dxUxLrHMrymx8D8shxs/r2efEnquIuBFl1s0DKJdU/TAzf3vAHNXV6yvkGlvdPiV1oPX6ymVV115fIdfY2+y210f2XI2lzb4nsONuBKLP8R0i4hCGGDdlmbJvQXmDHQD8c2b+S7P8PcBp2TXD0ggzjXwsjiX2M4lcYxuLo9nHRJ+rGMFYHNHn+A7Na/0+OcTA1F1ldhpSaygz5t0VeFaWQb3XA68HTs4yg94g+5/UWByTzDWWsTgmnGmkY3FYr19rO+v15cue+Xq92e6aSQeAN2XPZArN+3qOMgbcr2bmo7sfGzBj50P3Gsqlt98B3kT51v/DwFsy87WD7LuPTN11+agmvZh0pmudhRcRx2bmpwYtq6fcieeidDAMNelFjfV6s4+J1e3W66var+31IdqAfeQa13jXttdHn2ss4+fVzktlhxSlV3+/zLx/lmnk/wG4DXBSRFy3qxFwHLDY1QiIUbwoM/OblG9tfgA8PSJeHBEfpJwCP+g/lt1l6vxjeUCUAX27j2ckb7QJ5eo8V0vlGrqHe8LP1XGUDyadRsCqX39RZvM6IDOPozRo3kS5FOcvm3ydf46PYsjZ5Lp1/vZNlvMolyy8PyIe0xzDfw3xz3J3mTr/HB8TEQd0//Mc9rU+4Vyd5+rkJtc1DZ1hXusTztSZPfHkiFjX1QAY5LVuvX7t47FeX8as1+vNds+mzGD4JGAzcF40l4l1fzDIzJ2Z+eLc1Wk3N2R9sbP5AH4VZbyly4FTgH8BvpnDdQTtLlN3Xf7N3NVpN9R7eMKZsvv5yKbTLroujxvUNOTKzMsz87WDti1qrNeb45to3W693h/b68O1AfvMNZY2u+311Wuzzb4nseNueKsZ32EkYxT0ysz/pMx89SzgCuAD2cwmFrH0mBC70epYHMupMdcEMw09Fgf0PRbCzuz6FmWUFXBm/iDL6eHPpXxr+bHsuoxggF22PhbHUiaYayRjcSxlwpmGHYvDen1Masw14/U6lJkML2res++inNX0BxHxiM4+I+LciHhkZ4MBP0z+Upszd43LdlWWy3KeTrlk57HLbTPiTI/oOZ7VXgY0C5kG6cydxlwn9RzPanPVWK/Dnl0H1pjJ9vryJt5mt73et9bHz9sj5ARnxpj1G1xzqfHDKDNe/XrXY39IqeRHUc7afo+lZ9nctGaqNVeNmXrKfDJwIc3sXZRZgU6jZwai5XKO6zbI32/aM9Waa9ozWVeYa0/I1FPmAymzgV6na9k9gIuBjc39+SH2/7jd/S2WenyYeslM5lrq+GqqK2rNZabR3Bhze4lmJtABthu4DVhrrhoztZFrT7x5xt0QsnmlAZ+jfGP44Ii4V/PYi4CfRRngdmARcS7w0CWWd8+StuTlKjnANydtZII6c9WYqaMrw2uB91FmkbtVlm9JPgAcHRFDzcbXfKN+QkTss0zZy36jP8jfr41MTTnV5aox0xLbWVesUo25asy0hA9SvmV/SUTsG2WspY8B59DMspplJs9Vf/seEWcBD+r+W0Sj+X3fZv+/9Lca9D3cMNMq1Zqr5/iqqSua7arLZabhtNQGfDlw/Aplj7QN2LPvanLVmKln32Nvs+9p7LgbgRzfuBVnA9fNzLcsUWZGxBFRxkXYOWhjZjnjygR15qoxU08Z2fwc11gIBwH3o4yZsym6OoSav9/Nmt93LvcPZrXGnQnqzFVjpmXKtK5YhRpz1ZipV+wa0+iRwI0pM2neqXlf3wc4vOe4+m5cR8Q7gXVZxnMiIvaPcqllNn+/w4GTo8wYOjJmGujDXZW5etVYVzRlVJfLTAOXMe424DnAYZn55qXKjogjmt9H1gbs7Lv5WU2uGjN19t38bK3NvqdwVtkRioh5SsPjRMpgn69ulg8yffKTKKeY3i8zvxsR9wSC8n74aLPOc4FfAZ6YY7rufZSZmu2qy1Vjpj7LO7Ep76DM/NNhy2r+wexDaaj/aWZ+NCLmM3MxIs6nDBb9qFEd/zLHMNJMzfbV5aox0wrljLqueBJw/5rqihpz1ZhphTL2yjJ+2Rrgz4CDgdsCW7MZv2zA/X4d2JKZj4qIJwB3oozn9ArgX4EjgRcA52Tmh4aM0Vu2mVa37ypzrVBmdW3AppzqcplpJOWNpL0UEacALwWOysxLIuLewE+BfXPXzLvvBy4fdxuwKau6XDVmaspqpc1eOzvu+hQRa7OZ4WeFdX7pBRgDztATEcdS/rl8ADgauDvwTWBv4FuZ+fyIuCVwKvDyzPy/AcpoNVOzbXW5asw0iCH+fnNZvu15KvApyqUxT6Y0pj6QmX8d5RKdNwNnZuZ/jPTA+zi2YbatKVdtmSZQV2yijO9xAXAUldQVNeaqMdNK23Y6T5rf9wcOz8xvDFJe55gjIoBPA4cCWyl1xfHAscBfZOZnm8b8w4FHUQZKH6Tj2EwDZKo1V41twKac6nKZ6VrLBnn/Xj8HOFNviL/fMcBDgO3AgZSxKD8N/BbwV5n58lG0AWvMVWOmppxWc+3xcgoG2pv2G2XQ3EctsTy6fh9qAMeu/byYMsYIlDfZ+cDHaQbtBe4MvBWYp3xYfipdA/pOY6Zac1Wa6VzgBGCfNl4XPWU8FHhF8/tHgcuB47seP47yTc3MZKo1Vw2ZWn5fXQ/Yu/l9Uw11Ra25aszU7KuVSQe63sNru5a9G/i1rvuvBJ7VdX+dmdrNVGuuluuKVtqAteYy09CZXg48po2yevZ/DHA28FXghs2yoyizhh5OGYZroDZgrblqzDTJXHvybeIHMO235gX/7hUeP4IyVsK1XqgDlvVq4CfA5zsv9OYNdtuuda4H/BNw01nIVGuuSjMdBPw38PfAvfjlzpObdf0+jn8wN2n+rq8A/hk4nfLt0NHN43vNWqZac816ppbfV+cB76Q0lG7bLLvDLNcVteaqMVOzj7OA9/Qsi86+KZfODFVGs5/e9/CSnTzN44/vPhYztZep1lwt1xWttAFrzWWmoTOdA7xjpbK6fh9VR2F3Z8yvAkd23T8YeA9wvWHKrDFXjZkmlctb2nG34h+njG/zFWB9c/+elAbOPbvWeS5loMUDhizrjcDfNb+fy9I92HPA3wKvmYVMteaqMVPX/s5p8n2kUw4w3/w8H3jLCMrYq+d+9z+YDwJb2NW4utcsZKo1V6WZngR8uaW64lyahjzw58B/AGt61hlVXdFKplpz1Zip2dc7gTd13d+/+31N+db98cCNhi2r2d9S7+G1zc99gfcD55ppsplqy0WFbcBac5lp6EynAJcBN27u3xu4K11tsOa9O442YPd7t7s9+FbgteaqP1Pbubxd++assiu7qLltioi/oAya+1jgdyLiz5t13gP8L+X06oFExFHAjzPz0c2i71BOb+08HhGxH/A24OeZ+cTO8gGKayVTc3zV5aoxU3N8nbrgS8DfUM6kenZE/COlgoYyts2aiLjLEOW8EHh5RDwiIm4M18xstKZZ5SHAMdnMcJS7BlBd9d+vrUxNWS+kslw1Zmp8EfgscLcx1xU3AX4GPAEgM58PXALcumudUdUVrWRqjq+6XDVm6nJ7YA1AlEkHXgn8Y0QcHxFrgetSLpU5aphCdvcebh6/HWUChCf0bLNaZhpCpblqbANCnbnMNJyvAq8FHtPs+0WU9tHfRcQZzTonMp424NWdv0/THjw4Is4CfpqZv9NsN+hrvcZcNWZqLZeWMOmew2m80eK4FcuUf0Pgv4DH9iy/fdfvqzrtdNKZas1VWybGNHZZs+2ZlEsRHgq8F/hT4N6jfI21nanWXJVmamXssq7y9qLMxBhd5X4EOLFnvdt1/b7auqLVTLXmqjRT5zLEAD4DXNy8p24DPJNyJtQdmnVOBN7e/B2GvYRr2fdw975X+/cz02gz1ZKLlttL/PJZuCNvA9aay0yja68z/rHLzqTPNiBwp2Fe67XnqjFTG7m8LfN3n/QBTNuNdseteAblG5kTupbt1fx8BGXQx3lWuFxt2jLVmqvGTMuUP/Kxy5rtDgDewK5xo44Engf8JXDXrvUeB9x6FjLVmqvSTK2MXdbs51xKA2qua9lc13Hcvfn9TOBWXeustq5oLVOtuWrM1JXrBFqYdGCJsld8D5tpOjLVkIt224CdumKfrmUjbwPWmstMo2mvc+0O9XGNXdZvG/DxPeUP/GVCjblqzNRWLm/L37xUtktEvBE4ODP3p3xD+GiAzPxCZn6lWWeO0oj/Zmb+9xBlvRa4D7AP8McRcWRT1tXNKt8AjqV8ML66e9ts3g3TlqnZV3W5Ks20V8/9zunU/wPcArgbcP/MPBt4bmZ+vnn8agaQmVdSvnF/dkQcnJnbKN9C/pQyLgIRsT9weWZ+bRYyNdtWl6u2TBFxLuUb7ocDHwLOi4g1mfnZMbyvDgLuR7m89x4RsW9z3J0p7/8HuEnzXr9hZn69s+0q64rWMtWaq8ZMS+Q6NiLWNcd8YmZ+rmvVmwA/6rq/Y5XlDPQeHoSZBs/UlFVdrpbbS51Mv025FHKfpqzO/6OtjKAN2JT1RirLZabRtdczMzv3M/PLwDe7Vv0b4LLM/EHz+E4GsIo24I+ax645tj09V42ZJpFLy7PjrhEtjoUQEU8CbpCZx2Xma4HPAdeLiDt21snMz1JOt374LGRqtqsuV6WZXkh7Y5edHKXjE8rgv98DToqIdU1D5l3A6RFx68z8SWa+e5Cy2sxUa65KM7U5dhmZeTmlc+bHwO8Dv97s78BmlYMpg1P/IDNPGqSstjM1ZVSXq8ZMTRmdXJc3ue7U7HNt83PfiHg/8P3MPK9ru9V8OHkhLda3ZhosU6252mwvLZOp84G40yl5EUO2AZv9VZfLTGNpr49l7LK22oC15qoxU9u51IecgtP+pvHGmMataLa7A7Bf8/tpwBXAnwBfA57Rtd7QY5i0lanWXLVlouWxy4DrAy+knM49BzyScpnCGeyaLfQC4Kghymg1U625Ks009rHLerejjGFzDPAgysy7/wg8tXnswcCZXdsMchlVa5lqzVVjpj5yPbl5X28EXjhoeRN4D5tpwNdFxblaGWeuj0xP6VpvFGMOVpfLTEO9zvt+/zKCsctooQ1Ya64aM00il7fd3/b4M+4i4hkR8diIOKFr2V6Z+X+UqbtvFxHzseu00C8260QOfmrrZzPzp1G+2d+Hcn34C4CTgJMjYn2zXnbKmvZMteaqKVNEHAAcBPxeZr6XMkD0DuB+EXHXrvUeFxG3Xnovq3Y1cFvglOZ43w78G3AY8ImIuADYmZlfGGTnE8oEdeaqJlNEnBsRD6W8Nbc178/OZTHfBr7frHdmRNwqM7/U3B+mruhs9x3gpMx8P7AfcBd2XUrw4cx8elPWXKfemNZMteaqMVMfub7dPH5RZr6wK1ff5U2iXjLT6jM121SXq+t9Nde1bNxtwJUyfatrvYHagLXmMlNr7fXHR8SRmfmZQcvqMtY2YK25asw0wVzajT264y5aGrtsOZl5BXB2Zn6vWfTN5vazQcuadKZmP9XlqiFTtjB22RJl/ojyDc3zIuLkzNyZme/NzDOApwB/mZkPaspedYN3EpmacqvLVUumaGnsshV8Ftg7Il4BXAU8B3hhRBydmT/pKms1H1gnnQnqzFVjJlg51zVlrLZxPan6tmGmVagtV7Q4ztwylst01DBl1ZjLTK2213+UQ4xd1lPmWNuAteaqMdOkcqkPOQWn/U3iBjwJ+Puu+2+gVLp37FnvJcBLhiyrr5mLgLdQOoemPlOtuSrNdDLw2ub3WwIvBZ5IM4sbcDvKt5G37tluZJf/Ujoov8ovX0oQzc/VXto08Uy15qohE3AO8EbKZYn3bJYd2Px8ObATeNkwZa1UV1Auz9nCrkt37jWC52XsmWrNVWOmNnO1+R4203Cvv1pzNftY6n21ruvxsbYBx5Gp1lxmGriM6tqAteaqMdO05PK2wvMz6QOYWPCWxi6jXIP+SsoU5Ddear/AocDrgdcPU25bmWrNVWOmZh+tjIXQx3Fsolwm9rvAA2vIVGuuWc1Ee2OXLVdXrGl+7t11LHNDltVKplpz1ZhpArnaGk/HTMO/LqrLtZv31SjHLmv7uaoul5kGz9Tso7o2YK25asw0Tbm8LX3bYy+VzTGPXdZscyZlprqPUv65PCki7t293+b3S4HzMvNxzXarGk+nzUy15qoxU5exj4XQj8y8kHKpwS+Ae0bEKUPsbioyQZ25ZjVTjnnssmabM1m+rriq+fmLzrF0HRMD1hVjz1RrrhozTSIX7YynY6bhM0GFuXbzvhrVOHOtZurZRzW5zGR7fRk15qoxE0xJLi0jp6D3cNI3umYIAg4E3g1cf8h9HkC5/PG2zf0jgecBfwnctWu9xwO36Lo/klNNx5Gp1lw1ZlqijKMojY6Te5bfHbj7qDP1eUwH1pap1lyzlgm4CfBq4BXAPwOnA58Gjh5yv/3WFY+j5zKCac1Ua64aM00y1zjfw2Ya+euv1lzLva+OGnK/E8tUay4zDVVOdW3AWnPVmGlac3lr/uaTPoDWgrY0dlnPvl4EvAk4uLl/U+CPgWc39/cHTpylTLXmqjHTEvse+VgIk77VmKnWXOPItNL7ivGNRzSxumJcmWrNVWOmNnKtUO7Y6iUzmatr/9XVFbXmMtPo6vWeMqtrA9aaq8ZMNeea9dvED6CVkO2OXdbKoI5tZqo1V42Z+jiWkY6FMA23GjPVmmuUmVZ4X41jjJtJ1xXjGmOpulw1ZmozVx/HMcr3sJnGlGlWc9VYV9Say0zD1+u7OZbq2oC15qoxU825ZvlW/Rh3bY9dRvk25tKIOADYBnwO2ACcFhHzmfklygQE+3ZvtJqyJpCp1lw1ZlpRjn4shImrMRPUmWtUmSYwHtGk64pxjYdVY64aM7WSqx8jrpfMtOsYpv3/fY3vq1aeqxpzmWlk9fqyamwDQp25aswE9eaaZWsmfQDj1FTwBwG/l5lfiYgvAw8H7hcRP83MjzfrPR74aGZ+orkf3RXyKnUP6vg3EfF24ErgNyiDOn6HIQZ1nFCmWnPVmGm3MnMrsLUp68BxldOmGjNBnbmGzbSK99XjgE9k5tdGcNjTUleMMhPUmavGTDDmXKsxwnrJTGM2K7lqrCua460ul5lGWq+vqMY2INSZq8ZMUG+umZVTcNrfOG9MYIwRxjyo4yQy1ZqrxkzevNV+s64w156WqY1ck7iZafLHOy25aqwras1lJm/evHlr/zbxAxhLqCkYY4QRD+o4DZlqzVVjJm/eartNw/uq1rqixlw1ZhpHrmm4mWl2bjW+r8bxXNWYy0zjyeTNmzdv/d5qHeNu4mOMZOaHgdOAF0TE70bEA7vLyNVfCjnxTM3+qstVYyapQhN/X9VaV9SYq8ZMzf5GnWvizDQ7anxfjem5qjGXmXYdh+11Sa2rteOueyyEncDbgX8DDqOMhXABLYwxkqMd1HEqMkGduWrMJFVmKt5XtdYVNeaqMRPUOWC0mWZHje+rMTxXNeYykyRNUOfU4upExFHA+4HnZ+bfdi2/O0Bm/mtzP9r65iQiDszMK4bYfuoyNeVVl6vGTNKsm8b3Va11RY25aszUlDdUrmlkptlR4/tqFM9VjbnMZHtd0uRU23EHEBH3AV4FvDQz39C1PDIzI2JuwFPgJ6bGTFBnrhozSZNW4/uqxkxQZ64aM0mTVuv7qsZcZpKkyai64w4gIjYBfwu8AvhmZn5gwoc0tBozQZ25aswkTVqN76saM0GduWrMJE1are+rGnOZSZLaV33HHUBEbKDMRHQL4MuZ+cbJHtHwaswEdeaqMZM0aTW+r2rMBHXmqjGTNGm1vq9qzGUmSWrXHtFx163GMUZqzAR15qoxkzRpNb6vaswEdeaqMZM0abW+r2rMZSZJGr89ruNOkiRJkiRJmgVzkz4ASZIkSZIkSb/MjjtJkiRJkiRpCtlxJ0mSJEmSJE0hO+4kSZIkSZKkKWTHnSRJ0gyLiKsj4vMR8ZWI+EJEnBERA7fxIuJjEbFxBMf1/D7X+92I+M+IeEtE7BsRH27yLAx7DJIkSbNuzaQPQJIkSUP5SWYeDRARNwDeChwE/NEkDwp4PvDnfaz3JOC4zPx2RNwZ2LuTR5IkaU/nGXeSJEmVyMzvAacBT4nilIh4defxiHh/RNyj+f01EbGlOVPvj3e374i4U0R8ojmr79MRMb/c/iPixcD+zZlzb2keOyMivtzcnt4sOxu4OXB+RDwH+Dvg6Ga7W4zq7yJJkjSrPONOkiSpIpn5reZS2RvsZtXfz8wfRsRewEci4vaZ+cWlVoyIfYDNwEJmfiYiDgR+ssIxPDcintJ1JuAdgccCxwIBfCoi/jUzT4+IBwD3zMzvR8SngGdm5oNWGVuSJKlKnnEnSZJUn+hjnd+KiM8CnwNuC9xmhXVvBVyamZ8ByMwrMvOqVRzPJuDvM3NHZm4H3gPcbRXbS5Ik7ZE8406SJKkiEXFz4Grge8BVXPuL2v2adW4GPBO4U2b+KCLe2Hlsud0CucTyJfe/zPaSJElaJc+4kyRJqkREHAKcDbw6MxP4L8qYcXMRcThwTLPqgcAO4PKIuCFw3G52/TXgxhFxp6ac+YhYs8L+AX4REXs3v/8b8NCIOCAi1gK/Cfz7kHElSZKq5xl3kiRJs23/iPg8sDflDLi/BV7ePPZx4NvAl4AvA58FyMwvRMTngK8A32rWW1Zm/jwiFoC/joj9KePb3We5/TfOAb4YEZ/NzEc1Z/V9unnsvMz83DChJUmS9gRRvoyVJEmSJEmSNE28VFaSJEmSJEmaQnbcSZIkSZIkSVPIjjtJkiRJkiRpCtlxJ0mSJEmSJE0hO+4kSZIkSZKkKWTHnSRJkiRJkjSF7LiTJEmSJEmSptD/By06sVfQHxk0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1270.08x259.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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xROCSzPwDQERsC+wB/LSVFkqSJEmSJEnLUD9z3H0Y2Fi7fT1wejPNkSRJkiRJkgT9bbhbmZl/7N0o17dqrkmSJEmSJEmS+tlwd1lEPLp3IyIeA1zeXJMkSZIkSZIkLXRyip5nAqdGxFuAAH4OPLnRVkmSJEmSJEnL3KIb7jLzQuBeEbE9EJm5vvlmSZIkSZIkSctbP3vcERGPBO4IbBMRAGTmaxtslyRJkiRJkrSsLTrHXUS8A1gDPI/qUNnHAbdquF2SJEmSJEnSstbPySnuk5lPBn6Tma8B7g3s2WyzJEmSJEmSpOWtnw13vy8/fxcRtwSuBW7dXJMkSZIkSZIk9TPH3ZkRsRPwBuCbQALvarJRkiRJkiRJ0nLXz4a7f8rMa4CPRsSZwDbAH5ptliRJkiRJkrS89XOo7P/0rmTmNZl5Zf0+SZIkSZIkSaM37x53EXELYHdg24j4U6ozygLsAGzXQtskSZIkSZKkZWuhQ2UfBhwN7AEcX7t/PfCKBtskSZIkSZIkLXvzbrjLzFOAUyLi8Mz8aIttkiRJkiRJkpa9fs8q+wRg7/rzM/O1TTVKkiRJkiRJWu762XD3CeBK4FzgmmabI0mSJEmSJAn623C3R2Y+vPGWSJIkSZIkSbrBij6e85WIuHPjLZEkSZIkSZJ0g372uDsQODoiLqI6VDaAzMy7NNoySZIkSZIkaRnrZ8PdIxpvhSRJkiRJkqTNLHqobGb+DNgJeFS57FTukyRJkiRJktSQRTfcRcQLgFOBm5XL+yPieU03TJIkSZIkSVrO+jlU9i+Ae2bmBoCI+Efgf4B/bbJhkiRJkiRJ0nLWz1llA7i+dvv6ct/CC0XsGRFfiIgfRsT3y557RMTOEfG5iFhXft5ksKZLkiRJkiRJ3dXPhruTga9FxKsj4tXAV4F397HcdcBxmfknwL2A50TEHYCXAWdn5r7A2eW2JEmSJEmSpJpFD5XNzOMj4hzgQKo97Z6amd/qY7lLgUvL9fUR8UNgd+AxwAPK004BzgFeOkDbJUmSJEmSpM5adMNdRNwL+H5mfrPcnomIe2bm1/otEhF7A38KfA24edmoR2ZeGhE3m2eZY4BjAPbaa69+S0mSJEmSJEmd0M+hsm8Hrq7d3lDu60tEbA98FHhhZl7V73KZeWJmrs7M1bvuumu/i0mSJEmSJEmd0NfJKTIzezcycyP9nY2WiNiSaqPdqZn5sXL3LyNit/L4bsCvltZkSZIkSZIkqfv62XD3k4h4fkRsWS4vAH6y2EIREVQnsfhhZh5fe+gM4Cnl+lOATyy10ZIkSZIkSVLX9bPh7pnAfYBfABcD96TMPbeI+wJHAQ+KiG+XyyHA64GHRMQ64CHltiRJkiRJkqSafs4q+yvgiKWuODO/RHUW2rk8eKnrkyRJkiRJkpaTfva4kyRJkiRJktQyN9xJkiRJkiRJE2jeDXflJBRExH3ba44kSZIkSZIkWHiPu6eWn//aRkMkSZIkSZIkbbLQySl+GBE/BXaNiPNq9weQmXmXRlsmSZIkSZIkLWPzbrjLzCMj4hbAZ4FHt9ckSZIkSZIkSQvtcUdm/h+wf0RsBdyu3H1+Zl7beMskSZIkSZKkZWzBDXcAEXEQ8G/AT6kOk90zIp6SmV9suG2SJEmSJEnSsrXohjvgeOChmXk+QETcDvggcECTDZMkSZIkSZKWs4XOKtuzZW+jHUBm/hjYsrkmSZIkSZIkSepnj7u1EfFu4H3l9hOBc5trkiRJkiRJkqR+Ntw9C3gO8HyqOe6+CLytyUZJkiRJkiRJy92iG+4y8xqqee6Ob745kiRJkiRJkqC/Oe4kSZIkSZIktcwNd5IkSZIkSdIEcsOdJEmSJEmSNIEG2nAXEceMuiGSJEmSJEmSNhl0j7sYaSskSZIkSZIkbWagDXeZ+c5RN0SSJEmSJEnSJisXe0JE7AQ8Gdi7/vzMfH5jrZIkSZIkSZKWuUU33AFnAV8FvgtsbLY5kiRJkiRJkqC/DXfbZOaxjbdEkiRJkiRJ0g36mePufRHxjIjYLSJ27l0ab5kkSZIkSZK0jPWzx90fgTcAfw1kuS+B2zTVKEmSJEmSJGm562fD3bHAPpl5edONkSRJkiRJklTp51DZ7wO/a7ohkiRJkiRJkjbpZ4+764FvR8QXgGt6d2bm8xtrlSRJkiRJkrTM9bPh7uPlIkmSJEmSJKkli264y8xT2miIJEmSJEmSpE0W3XAXERex6WyyN8hMzyorSZIkSZIkNaSfQ2VX165vAzwO2LmZ5kiSJEmSJEmCPs4qm5lX1C6/yMwTgAc13zRJkiRJkiRp+ernUNm71W6uoNoDb6axFi0X69fDaafBunWw776wZg3MNPRrtZa1rGWtSaxjLWtZqzu1JEmS1IzMXPACfKF2+RxwEnD7xZZbZJ0PB84HLgBettjzDzjggOyU//7vzJmZzFWrMqH6OTNT3W8ta1nLWuOs1cVM1rKWtZqtJUmSpKEBa3OObWJRPdaeiNgC+DHwEOBi4BvAkZn5g/mWWb16da5du7alFjZs/XrYfffq52wzM3DJJbD99taylrWs1X6tLmaylrWs1WwtSZIkjUREnJuZq2ffv+gcdxGxdUQ8ISJeERGv7F2GaMs9gAsy8yeZ+UfgQ8BjhljfdDntNNi4ce7HNm6sHreWtaxlrXHU6mIma1nLWs3WkiRJUqMW3XAHfIJqw9p1wIbaZVC7Az+v3b643LeZiDgmItZGxNrLLrtsiHITZt062DDPr2/DBrjgAmtZy1rWGk+tLmaylrWs1WwtSZIkNaqfDXd7ZOaazPynzHxj7zJEzZjjvhsdr5uZJ2bm6sxcveuuuw5RbsLsuy+sWjX3Y6tWwT77WMta1rLWeGp1MZO1rGWtZmtJkiSpUYvOcRcRJwL/mpnfHUnBiHsDr87Mh5XbLwfIzH+YbxnnuLOWtaxlLee4s5a1rDWBtSRJkjQSA89xBxwInBsR50fEeRHx3Yg4b4i2fAPYNyJuHRFbAUcAZwyxvukyMwNnnVX97H0bvmrVpvtHOZC2lrWsZa1JrGMta1mrO7UkSZLUqH72uLvVXPdn5s8GLhpxCHACsAXwnsz8u4We36k97nquvrqaHPqCC6pDVtasaW4gbS1rWctak1jHWtayVndqSZIkaSjz7XG36Ia7SdDJDXeSJEmSJEkSwx0qK0mSJEmSJKllU7HHXURcBgx8aO6E2wW43FrWspa1JrBWFzNZy1rWspa12q/VxUzWspa1rGWt9mu1mWkcbpWZu86+cyo23HVZRKyda1dIa1nLWtYad60uZrKWtaxlLWu1X6uLmaxlLWtZy1rt12oz0yTxUFlJkiRJkiRpArnhTpIkSZIkSZpAbrgbvxOtZS1rWWtCa3Uxk7WsZS1rWav9Wl3MZC1rWcta1mq/VpuZJoZz3EmSJEmSJEkTyD3uJEmSJEmSpAnkhjtJkiRJkiRpArnhriUR0fjvOiKi6Rpz1OxcrjYylTqdzFVqtZJtDL9Dc01wjXHW7GJfWGqaa/Aanezju9g/tVmn7XpdzGWfMdKa5hq8RidzlTr2T1NQp+16Xc01Ldxw16CI+POIWB0RN83MjQ3X2iVbmrCwi7nazFTqdS5XRDwgIh4L0NbfYq9OkwMZc41GG5nK+lvL1cW+sNQy1/C1OtfHl3pt5Xpgm/2TuYau02a/a58xfC1zDV+rc7kc746OuQY3jlzTwg13DSlbiO8KPAT4bEQcEBHbNFTr/sDHI+IJEfGAJmrUarWZ6yBayNVmplLvQDqWKyJ2BXYHnhQR74iIgyNixyZqlXpHR8S/RcTLIuIuTQ1kxpDryV3L1dZrVWq1mcs+fvharfTxpVabuTrXx5d696OdXDsBt6S9fretXKvoZq6bUfW7R7XQ77aSqdSyjx++ln388LVayeU4fmT1OjeOL/U6+XpNG88q24CI2D8zv1O7/SzgkcDpwFmZedkIa63IzI0RcV/gLlQd+/cy85WjqlGr1WaulZl5XRnM3JGGcrWZaVbdg4A70IFcEbFnZv68dvtYqn9OrgLekpm/HlWtWXXvTvU3/wrg+cCnR/lB0nauiNgmM/8QEfem+tvoRK5S4x7AnWkoU6nRWi77+JHUaqWPL7Va7+e71MfPqnsfYH+ay/VQ4MuZuaHcbuvzpOlczwE+k5kXlttdybVdZv6udvs4YDea/TxpNFOpYR8/fC37+OFrtJLLcfzI6nV2HF/qNDqWH1euqZKZXkZ4Ad4BnFSub1G7/1HAB4A/K7dXjKDWCcALardXArcBvgecMMW5PgR8BdiyyVxtZirreTzwJGDbcnurac8F/Bvw9nJ9y9r9BwP/RNWxbzPCbP8GPGXWfX9W/l6OnOJcHwBO61Iu4HDgsU1nGkMu+/jha7XSx48hV+f6+LKe44B7Nf13CJwGfBC4CbBV7f6HNNTvtpXrROBq4LBZ9z94ynP9C/BR4J+BP23y9WorU1m3ffzwtezjpyQXjuNHlatz4/iy3lbG8m3nmtbL2BvQpQvwHuBdCzx+BPAN4DYjqHUycAawao7Hbgp8HXjuFOZ6K/CFku/Act/KUedqM1NZ3zuAz1ANZr4660N4KnMBbwc+vMDjfw68Gbj5iH6HJ5W/+e3neOwQqoHT/cvtmKJcJwBnA98FHjXrsYdPYy7gfcBZwLcoA88mXqsx5LKPH75WK338GHJ1ro8v63sb8LF5Hhtlrr+g+va+d3tF7++i3D58xP1uW7neCrwb+EvgPGCnWY8fNqW5TgQ+AhxYrh846/GRvV5tZSrrs48fvpZ9/JTkwnG84/iF67Uylm871zRfxt6ArlyAewIbgQPK7ScBx1JtIb5N7XnHUg3ith6i1o7Ah2q37wU8ENi5dt99gTcN80cORFl3W7lOAD5M9c3cG4F/qT3W+9AfKlfJdO+2MpX1HAWcXbv9FmBPNt+jYBSv1z1afK0OBX4B7FduPxZ4KfAU4O61550IvHmY319Zz9bAqbXb9wbuX36Pvb+NJwBfBvaYolxvBT5erj8TeEn9771cP2IEuR4BXNJGLuBoqkPCeu+39wO3p/pHvDc9w5HDZirreWRbrxf28VPRx9dytdbP08E+vqzn74F1tdu3BW7B5t+GD52rrOfPgFeU6y8o7X8H8OTac04a9n3cZi6qjXWfq91+N/CX5Xr9n/5RfZ78Q0u5Zqj69d7eVCdR7W1yHHDIKF8v4O9a/Bu0j7ePn69eK318WU8r/TyO4x3HL1zvaFoYy9PiOL4LF09OMQIREZn5NeAY4IyIeEu5fgXwMOCYiNiuPP104CKqTnlQVwM7RsRBEfFMqsMVngl8shxXT6mxE3CrIeqsyMyvUg0+G80VETcHLs7Mx2fmdVQd4cMi4lCAch/ABQyXa2Vm/g/wbNp5rQAuBtZGxO4R8VKqAcAbgK9FxB7lOUO/Xpn5deA5tJArM8+kGqi/KCJeD7yEqmO/G/D0iNinPPVFQNZyLlmZmHcb4E4RcZeI6P3+/hr4f8DjyxwxHwA+Ddx8SnLtAXw3Mw8rd/0v8KyIuENW88KsKG36EEPkKnMQfZrqW+LGc5Ucvy3reDFwENXg8m1UAzUy84MM+VqV9XyK6vV6cZO57OOB6enjof1+vnN9fERsS/VePjsi7hcRx1ANnN8KfLk8DvAThn+9oPpn4J4RsZrq0JgPUe3BcFxEPKo85ziG73dXUuX6zxZynZSZDyl1twS+TfWPKpl5fWkLjKbfBfgZLeTKzPVUG56+EhFvoPqH8jNUf2/PK3PQwZCvV1Qn8/g58IWmM9nHA/bxC2mlj4f2+nnH8Y7jF9HKWL6tcXxnjHvL4bRfqAYm96ndPgb4FbBPub0r1a6z960950nAzID1elu5X0DV4Z0I3Kzc9xLgXMo3QMCjgWcxwLHnVN+a/VWtXqO5ZtXutf/FwIvL9fq30wPlYtPu7b31t5IJ+BOqeWDeTdUR7lHufxPwtdrveNBcj6MaRPTm3HhmU7moPmDr63kj1TwHu5fbtwY+Dtyx3F5JtZv4UHt+lHU9g+pbzo/31gc8j9ru2yX70QOse7M5N4Dj28pV//sGXke1l8J2sx4fNNdmc260kQvYr9T5CPBDqr0ztqLqU94+bKay7OHA42q339RULuzjp6aPL8u23s/ToT6+LLtn+XnTsp5zgPOBfct76d1U/zQOlWuOuh+j+qf+ibX7XkR5rw/zPi7LPxRYRfXPdaO5euuo/20DWwLfpOyR0XteuX+YXM+h2hNtx5ZzPZtqDHC/cnuGql85eNjXi/IZSPXZ0XQm+/gR5JpV2z5+6TVa6edxHO84vr+6jY7laXEc36XL2BswzRfmmXeDWbtJA58E7gPDzeU0a513Ln/Qa4GDavefDuxau73dAOs+mTnm3Wgj16z1P4xqoHa7cntF7bEl5WLzOTfuV7t/lzYyUU22fTOqSZx7h5dsA5xa/z0PkKs+58bX2bS7+S1GnYvqw/b0Oe7fZ9bt/6AM3MvtLQetOWu9d6WaoPRC4B7lvp2ovu3Zo/a8myxxvXPOuQHcqo1cZV29Qd+BVB/SNy236wPdpeY6gU1zbhxWu//WTecCtgduR3XIzC7lvluWPuumg2Yqy9Tn3HhP7f7bzHre0Lmwj5+aPr4sM7Z+ng708WU9N0wQ3fvdAWuA29fuOwA4ftZyS80114atrYHPUZ2hsffYWdTmjRq0f2LTiS92npVrv6Zyzbq/l/HhpV+ZmfX4oLl6J77oTVR/s5Lrdk2/XuX6X1Od7a93+3PAU4fJxaaTXrwR2Ifqc37kf4NlGft4+/h+azfSx5dlWunncRzvOH5p9RsZy9PiOL5rFw+VHVBE/B3wkMz883L7thFxy4jYMjN/WXYLJiI+AlyRmV/J8lc3RM3eOiMzvwv8DVXn96CIeEZEnA78IWunB8/M3y2xxo5U3/Y8OjM3RMS9IuLBEXHTzPxl7XkjzzVbZn6Wakv/KyJi26ydcnopuSLiBKpvqh4C/JrqW63eei6vPW9kmcr6opctM38DXE81P8ATI+J2VAOPazJzQ609S8l1FLBvZj48M4+g+rDfPSK2ysz/G2WuiDiJamD5uHJ794jYu7T5gnLfqoj4IPCLzPx8LdO1g9Ss1e7tav5tqg+PTwHHlsOn3gVclJkX1+r9Zgnr3ppqkPXozLw6Iu4dEQ+MiN2oDtEhImYaynXD333vdcnMLwE7UP3jQlaHU9X/hvpd91uBvTPzwVQD3dvVal1UnjPy1ysitihXN1AdtnUhcFhE3IlqsHtJZl5Rq9V3prL+o6n+oTmEajf6rSLiDmVdPynP2X4Uuezjp6ePLzVOoOV+vkt9fFnP26nO2vasWnsvz8zTMvP82lNfOnvZJebaGti2XI9eP5eZ12R1aOkFEXFyRJwFXJqZb6nVWXL/FBF/AeyQmUdm5q8jYotarh81lWvWeq4vVy+imtNnv1mPD5LrrcAWVHuMvSYibpKZv6Kab+nHtac28nqVh98N7BER/xERn6Tq408eNFdEnEj1j+GbqD4Ld8vM3476b7DUso+3j1+sZqN9fKnRSj/vON5x/BJqNzaWb3Mc30UrF3+KZouIbag6g7Mj4n5Uu1CvAX4L7BkRB2Xm7yPi6cBVmfm0slwstbONiMdSDZg+QvWB8ceyKjLzexHxCqo38z2Bb2fm3w1aq7hh3o2S62lUA809IuK4zPxqRDyjoVz1x1eUD/ivUh1C8PsBstTn3Hhhuf1W4NMRcWhW8yAQ1XwRRw6baa5cmXlDrsy8IiLeTHXowKFUH8B/OUS9G+bcoNpd/iiqvQhuHxGPysyLR/FaFV+hmn/odlQT5z4JuEVEfBF4XRlkPrdkfuowtcog5tfA+Zl5QWZujIiVmXldZq6NiEuoOvsDge9k5usGqVc+SG+YcwPYn2oemN4H1X+WQfSzG8qVtb9zyj+T11MN5A/uLTfAe6s358Zzyl3/C7w1Is7MzB+U3EF1eNVQuebIdH0t0zUR8QOquTCOAH6Umc8dtFYtS2/OjSdQzbmxd0R8D3gv1SEro8hlHz8lfXxZV2v9fFf7+Ig4hOowrwfXct4W+CVwXmZ+MyJ2oTqz2+8y89hB6kXEKVT97oqIOKX3+pT+cMvMvDYzD4uI21L9M/bdstwNfeUAfg38d1nPC4D9I+KPwJcy8/0l1780kau3rl7GzDw/Ih6fmd8YMEtvnX9JtRdTbw69ewBrIuKdmXlNua/p1yuo/j6eQtXHX5XVnEcDvV4RMQNsBxyZmddGxFOo5ou6J9VemJ8ZRaayjH28fXxfuRru46G9ft5xvOP4fnM1OZZvZRzfVeHvYTARcVOqCXmfDuxG1YFfBLyTalfdNRGxY2ZeWZ4/yCDmw1Rzlmyg+kD8PPCJzLys1wHOs9xAA9zeG6MMbLenmmD1bzLzVxHxEqpvt+5D9Y38+oZy9Tq9edu31Fy15bfKzD9GxIsBMvMNvfZHxA6ZedWgmfrIdcPrVQaMW2T5hm6Ien8C/C3VQPMhVHO0XBwRbwLunZn3GkWuWr01VN+u/5zq8IdrqQ7TOT8zXzTrucP8DmeofoeXAb/MzFeXx7aqD6Ci/JM3TL2y7DOoPuz3ANZk5jUR8Tzgzpl5TAu5bshRbt+QcwR/81uUD+DXUZ2J7wU5x7fBQ7yP58u0de+fx3J71zIoHPa12o9qPpu9gDtSDT6voTr0Yuus7Sk0glr28c3kaqyPL+torJ9fBn38G6gOB7sceBDVnHO7Uf1j9HfAdcBDM/O9g9Qrf2MHAU8GHkh12NaLstp4Nu9rP4J+8PBS83XAq6g20u1E9c/VS6jmnXvkGHIN0z/V/1nckmqeoXtl5hNrz7kl43m9hsn1SarPqnOoNsK8gmquxYdSzc31c+ARg2aaVcs+vplc9vFLq9laP+843nH8HMu1OpZvcxzfSTkBx+tO6wXYmbnnEnnTrOcteS4CqkMFzqjdPpJqksjns/np4h9O7TjzEeWab96Nj7D5Me1Tlau27s3m3Bj2tVpirkfMuj3sfETzzbnxAaqB2Ujq1NbzGGD/2u0/pZojZuWwtajOSnRmub4VcC+qb1/+cdbznswAc4gsUPeu9DfnRtO5jhplrnqbWXjOjUHex0vJtP0wteao3e+cG6OoZR8/RblmtWOk/fwSck1dHz+rP5hrovJPAHcawe/wGOC1tdsPAH4EHFG776T67RH+Pcx34os105ar3kYWOPFFi7mOHHGm+U568dBhM81R1z5+inLNakcn+viyjtbG8jiObzLX1IzjB8g1srE8LY7ju3ZxjrslitjsePZfA/+eN55LJOvLZPnrW6LfUO2u/6Syjg8CX6QaRN+5tGU11eD6innX0qdervLNwHzzbvw+Nz+mfaJz1V+rupw158asxwbJBP3numX5uxm4XhRl+d8w95wbf8jMP4wgF1Hmpijr+URmfqf28MuBDVn71niIWkG12/7qrL6pOpdqsH6TqA6ZIap5EP6YS5xDZM5iS59zo+lc144oV19zbsx+zlLL0H+mq4esRVnfUufcGKiWffz09PFlXW31853r42s1rq/1h8dRbdz6Rbl9EdVhY7eoLzvg7/AXwG4RcZOyjnOo9hT75/K7Azg2Mz80wLpvUP+bqPUbR1LtTfXy2lMfRPXP8g2mIVe9jeW12yKrvT1eQXXI0czsZRvO9cEB1g1snqn3WmXm26gO21pTbq+n2jNjj/qy9vGbs4/f7LGJ7uPLulobyzuOrziOv3EpWhzLtzWO7zIPle1DzDHfQflgzNpzevNuXJuZR5f7Bj3WvLer+2Opjin/aGZ+pTz2/6gOh3hkQ7lWUKZiiWqOmd68G9fmkPNutJFrrkyzHu/tTv8oqjk33j1MvbLOSch1MNWcG+sZcs6NmDXXQbnvhkMfygfKDlQfilfnCOcgiIjnUP2D9bTM/HFEbE81B8JtM/Ols5671Lkw5spVP/Thlmyac2NDDjjnxoTkutGcGxFxV6qzM/3zMFnayFSWWSzXUVTvt9sx5Jwb9vHT08fPl2vW4yPt57vWx5fltqb6xv53tXybHZISEauo+vk/9Pr5YZS/vQ8BV7JpLqXrIuKVwNrMPKv23FHmumFdEfFxqn/Qb0514ou/mNZcczzn9lRn4XtsDjmHXllfo7kWeq0i4hZUZ9rcjuowql9n5lOGyGIfbx+/UL1JyTWSft5xvOP4JdQeZ66RjeOXCzfcLSL6nMchInZliDlS5ql9W6o3z3bA5zLzP8v9HwOOydpZlAZYd6vzbsxaRyO5+n2t5lhuJB3EmHKNdM6N6HMOh/L3fnAOMRH1rLq9QdNKqjPk3Rd4cVYTee8OvAc4Kqsz5g2y/tbn3JiAXI3MudF0pj5yjXTODfv4Gy03zbmanltp6vv4stwNJxwATslZJ1Io7+8VVPO/3Skzn1R/bMCMvX+0V1Idevtz4BSqb/g/D5yame8cZN195qr36yM78cUE5NpsL7yIuGdmfm2YemU9jebqJxPVhoVRnPTCPn7z5aY511T28WUdrfTzjuMdx09BrkbmwV4OPFR2AVFtud8mMx+W1eniPwHcATgyInaufdg/Alhf+7CPUfzRZeaFVN/KXAG8MCJeHxGfptrVfZgPj8Vy9T48Hh7V5L31Nk1kriW8VnNlGsnW6zHl6r1Wj6D6R6T3Qb/kv8Goztq1XWY+gmrgcgrVYTf/WPL1PgSfyJAD6dl6r0HJ8y6qwxPOjIgnl3b8dIgPj8Vy9T4EnxwR29U/JKc8V+/1OqrkumFQM8zffJOZSnsXy9U7Y+JREbF97cN+kL95+/gp6eNh/P38tPfxZbmXUJ2x8NnAacC7ohwaVv9HIDM3Zubrc9NGuxVD9hsbyz/d11HNsXQlcDTwn8CFOfzGrcVy1fv1C3PTRruh3ssTkCvrr0uWjXZROzRuEE3m6jdTZl6Zme8cZqxhH28fvxQT8HoN1c87jncc368x5xrZOH65ccPdwpYyj8NI5hObLTN/SHWGqxcDVwGfynLWsIi5533oQ6vzU8ylgVxjz1TqjivXKObc6Heug41Z+6Zk1J1sZl6R1W7gL6P6dvKcrB0uMMAqW51zYz5jzDWSOTfm0kAmWFquYefcsI+fnj4eupmr1XmVqM5ceG55736Eao+mv4mII3rrjIiTIuIJvQUGGUzPteEoN83Hdl1Wh+C8kOrwnKfOt8wS/Jb+ch0xq01LPbxzWnJN8uv1W/rLdOSs9gwy1rCPn56+EMw1bD/vON5x/JKNOddI5sFeNnKMZ8aY5AvccBjxY6nObnWf2mP/j6ojH0WdVf22ZdZ9K8zVbqYu56qt9znAlyhn6aI6888xzDrD0Hw5m7wM+jdvrvZzDZOprVxd7AvNNV25xtTHP5LqTKA3qd33AOBiYHW5PTPE+p+22O9irseH7Z/MNT25ms40u41d6jPMZa4+6rUxftplwOUmerxrrunKtRwv7nE3jyx/ScC3qL4dfFREPKg89jrgmqgmsh1YRJwEHDbH/fUzos15eEoO+O1IF3O1kQm6mws2y/BO4JNUZ427fVbfhHwKuGtEDH32vfIt+mMiYqt56s/7Lf4gv0NzbVZnSbnazjRr3Y2+XrOW60xfWJYz14C63MfXfJrqG/V/ioito5pb6RzgRMoZVrM6i+eSv2mPiLcCh9Z/F1GU61uX9d/odzXo+7jGXNOTq7FM87SxM31GWc5cA+pqLmh1vHs8cMgC9aduvFvqmGuWSc61XLnhbhHZ3HwH7wB2zsxT56iZEbF3VPMebBxm4DKfLuZqKhN0N1etRpafjcxbBhAROwIPpZon58CobRAqv8Nbl+sb5/sQWSpzDWYcmXrrLj8be73mqNm5vrDUMNcSdL2Phxv+Id1INefMLanOoHn38v4+GNhzVrv6HkxHxOnA9lnN30REbBvVYZZZfn97AkdFdbbQkTJXZRpyNZlpPl3sM0oNcy1BV3PV1t/GePdEYI/M/Le56kfE3uX61Ix3wVzTlms586yyfYqIGapBxuFUE3q+pdy/5LO6RMSzqXYhfWhm/iIiHggE1d/7F8pzXgb8CfCsbPC49i7mGmWmslwnc/VR7/BSb8fM/NtR1CofIltRDc7/NjO/EBEzmbk+Is6gmhz6iaNo/wJtMFd/6xt7ptKOkb9e89QZdV/4bOBhHezjzTXFfXzZOHN9VGeS+ztgJ+COwLosc5cNuN7zgbWZ+cSIeAZwd6r5m94E/BewD/BK4MTM/OyQMeaqb66lrXdsuZrK1Efdzo13Sx1zLb6uTubqo9bIxk8RcTTwBmD/zLwkIh4M/AHYOjedffdM4MppGu+aa7pyLXduuAMiYlWWM/gs8Jwb/YHFgGfhiYh7Un2AfAq4K3AQcCGwJfCTzHxFRNwO+Avg+Mz85VJrlDqdy9V2prJsJ3Mt1ZC/wxVZfaPzPOBrVIfDPIdq4PSpzPzXqA7L+TfghMz8n5E1vM+2DbNsl3JNcqZ6+5a4TNt94YFUc3mcBexPd/p4c01RHz/fsr0NJ+X6tsCemfnjQer12hwRAXwd2A1YR9VnHALcE/iHzPxmGbw/Dngi1eTog36pYK4pydVGprJM58a7pY65Nr/PXNXzd8kB9tIb8vPkHsCjgauBHajmpfw68HjgnzPz+GHHhua60XLm0uZyAibaG+eFaoLcJ85xf9SuDzXRem09r6eaTwSqN9AZwJcpE/QC9wI+AMxQ/ZP8PGqT9y73XG1m6mquUusxwFZt/A7nqH8Y8KZy/QvAlcAhtccfQfWNjLnGnKupTG3navn9dVNgy3L9wKb6DHNNV642M5V1tXLCgdr7eFXtvo8Cf1q7/WbgxbXb25ur+7naylTL1anxrrnMtUCd44Ent/H7m6PGPYB3AD8Abl7u25/qrKF7Uk3BNeh411zm8rLY733cDRhr+OqP+aMLPL431XwIm/0hDljrLcDvgW/3/pDLm+eOtefcFPgP4FbmGl+mruaimgz6Z8C/Aw/ixhtNbl273tSHyF7ld/sm4HPAM6m+AbpreXwLc01GriYytZ2r5ffXu4DTqQZEdyz33W3UfYa5pitXm5nKOt4KfGzWfdFbN9VhMkPVKOuZ/T6ecwNPefzp9baYq9u52spU1tW58a65zLXAek4EPrxQndr1UX4ZVN8Ycydgn9rtnYCPATcdtK65zOWlz9/9uBswtuDVfDbfB3Yvtx9INZh5YO05L6OaSHG7IWu9F3h/uX4Sc2+hXgG8D3i7ucaXqcu5yvpOLPnO7tUBZsrPM4BTR1Rni1m36x8inwbWsmkg9SBzjS9X25lazPVs4HttvL9KP/HRcv3vgf8BVs56zij7eHNNQa42M5V1nQ6cUru9bf39TfUN+9OBWwxbq6xvrvfxqvJza+BM4CRzLZ9cbWaig+Ndc5lrgTpHA5cBtyy3Hwzcl9q4rLyHmxrv1t/H9XHiB4B3mstcTeTysvllOZ9V9txyOTAi/oFqgtynAn8ZEX9fnvMx4P+odqEeSETsD/w2M59U7vo51a6rvccjIrYBPgj8MTOf1bt/wJJdzNVKptK+rubqvde/C7yNai+ql0TEZ6g6YajmslkZEfcestargeMj4oiIuCXccPaileUpjwbukeUsRrlpktQl/w7NNVyuNjOV5Vp7vYDzgG8C92u4L9wLuAZ4BkBmvgK4BNiv9pxR9vHmmp5crWSquQuwEiCqEw68GfhMRBwSEauAnakOi9l/mCKLvY/L43emOvnBM2YtMwhzDaHlXK1kKro43gVzmWtuPwDeCTy5rPd1VOOl90fEseU5h9PcePf63u+ojBN3ioi3An/IzL8syw3yOzSXudSvcW85bPtCi/MdzFP/5sBPgafOuv8uteuD7LbauVzjztTFXDQ4b1lZ/gSqww4OAz4O/C3w4FG+JuYa2TxzY8nUQq7W5mMr69uC6gyMUat7NnD4rOfduXZ9kD7eXFOSawyZeocgBvAN4OLyvroD8CKqvaDuVp5zOPCh8nsY9lC0ed/H9XUP8ndhrunK1WYmWh5DceO9cTsxjjfXdOUq62xszrJajRPoc2wI3H2Y36G5zOVlib/7cTeg1bDtzndwHNU3Lo+p3bdF+XkE1aSOMyxwmNpyztVmpi7nmqN+I/OWlWW3A05m03xR+wAvB/4RuG/teU8D9jPX+HKNM1PDudqcj+0kqoHSitp9K2rtOKhcPwG4fe05g/Tx5pqSXG1mquV6DC2dSGFW7QXfx+ZaHrnazES7491en7FV7b4ujOPNNUW5ZreRBuYsq62r37Hh02e1YdA5Ps1lLi9LuCybQ2Uj4r3ATpm5LdW3gU8CyMzvZOb3y3NWUA3aL8zMnw1R653AwcBWwGsiYp9S6/rylB8D96T6h/j6+rJZ/tqXUOu9dCxXm5nKujqXKyK2mHW7t7v0/wK3Be4HPCwz3wG8LDO/XR6/ngFl5u+ovmV/SUTslJkXUH3b+Aeq+Q+IiG2BKzPzR4PUMNdocrWRqayjtVwRcRLVt9mPAz4LvCsiVmbmNxt4f+0IPJTq8N4HRMTWpd2909v/L7BXec/fPDPP7y07QB9vrinJ1WamOXLdMyK2L20+PDO/VXvqXsBvarc3LLHOQO/jQZlrenK1lanUei/tjaF6uZ5CdQjkVqVW77NpHdM5jjfXlOSqv48zM3u3M/N7wIW1p74NuCwzryiPb2RASxgb/qY8dkP7zGWuUeXS/JbFhrtocb6DiHg2cLPMfERmvhP4FnDTiDig95zM/CbV7tSPGzRTqdW5XG1mKst1Lle0P2/ZUVFt/IRqot9fAUdGxPZlwPIR4JkRsV9m/j4zPzpIPXONZO68VjKNIVer87Fl5pVUG2Z+C/w1cJ+yvh3KU3aimoj6isw8ctBa5pqeXG1nKjV6ua4sue5e1rmq/Nw6Is4ELs/Md9WWW8qg/dW02O+aa7pytZGprKfVseEcuXr/BPc2TJ7LlI3jS7vNNYS2cs3zPm5qzrJxj3fNZS71Kydgt7+2LzQ030FZ7m7ANuX6McBVwGuBHwHH1Z431FwlyyVXk5m6mIsxzFsG7AK8mmqX7RXAE6gOSTiWTWcKPQvYf4ga5pqSTGPK1cp8bPXlqOaruQdwKNXZdz8DPK889ijghNoygx6WYK4pydVmpj5yPae8v1cDrx60XtvvY3NNV642MtWWa2Xesj5yPbf2vKHHheYy1xw1+n4fM7o5yyZqvGuu5ZnLy+KXTu9xFxHHRcRTI+Ixtfu2yMxfUp2a+84RMRObdvs8rzwncsBdPLM6JOYPUX2TvxXV8d+vBI4EjoqI3cvzslfLXOPJ1LVcEbEdsCPwV5n5caoJoTcAD42I+9ae97SI2G/utQzkeuCOwNGlzR8CvgjsAXwlIs4CNmbmdwZZublGmqvRTNBurog4KSIOo3qLXlDep73DYC4CLi/POyEibp+Z3y23h+kLe8v9HDgyM88EtgHuzabDBj6fmS8stVb0+g9zdS/XODL1keui8vi5mfnqWq6+642r3zXX9ORqOlNZpvf+WlG7r+nx7kK5flJ73jDjeHOZa646/b6Pnx4R+2TmNwapM4dJGe+aa3nn0iI6u+EuWpxnbi6ZeRXwjsz8VbnrwnK5ZphaXcw17kxlPVOfK1uat2yOur+h+ibm5RFxVGZuzMyPZ+axwHOBf8zMQ0v9JQ+YzDW6XE1nKjXamj9vR1qaj20e3wS2jIg3AdcBLwVeHRF3zczf12ot9R9Vc01JrgnIBAvnuqHGUl+vcfW7NeZagjHnaiRTtDhv2Tzmy7X/MLXMZa75LOF9/JsccM6yeepOynjXXMs4l/qQE7Db36gvwLOBf6/dPpmqUz1g1vP+CfinIWv1dXYi4FSqDUPmGlOmruYCjgLeWa7fDngD8CzKWduAO1N967jfrOVGffjvwVSnBp99yECUn0s9XMBcDeUadaZx5QJOBN5LdUjiA8t9O5SfxwMbgTcOU2uhPoPqcJy1bDpU50Ejen3MNSW52sjUZq6238fmmp5cE9RnbF97vNHxrrnM1UautvunBdrRufGuuaYvl5cFXqNxN6CRUC3NW0Z1fPmbqU4zfsu51gvsBrwHeM+wdbuYq61MHc/VyrxlfbblQKrDw54PPNJck5trlJnazkV785bN12esLD+3rLVlxTC1zDVdudrKNIZcbb6PzTUludrMVF/HPO+vkc1bZi5zTUiuiRgXljqdG++aa/pyeZn70slDZbOdeeZOoDoz3ReoPkCeHREPrq+3XL8UeFdmPq0st+R5gbqcq41MXc5VND5vWb8y80tUhxRcCzwwIo4eYnXmatCIM0GLubKd+dhOYP4+47ry89peW2ptYpA+w1zTlauNTOPIRUvvY3NNT64J7DNGNW/ZCZjLXAtoI1cxEeNC6OZ4F8zVp4nJpXnkBGw9bPJC7QxAwA7AR4FdhlzndlSHPt6x3N4HeDnwj8B9a897OnDb2u1RHurWuVxNZOpyrlk19qcaWBw16/6DgIOa+Bvss107mGs6cg2baRy5gL2AtwBvAj4HPBP4OnDXIdfbb5/xNGYdMmCu5ZWrqUzjzNX0+9hc05NrgvuM/Ydcr7nMNfZcs2pM3Liw1OvceNdc05fLS/m9j7sBIwnR4jxztXW9DjgF2KncvhXwGuAl5fa2wOHmGn+mLueate6Rz1s2CRdzTdeliVwLvb9obk6bsfbx5pqsXOPI1NbrNU/dRvsnc01PLvsMc5mr2X6+VsNx4RRdzOWl9ddm3A0YOkC785a1OQlw53K1manLuRZpy0jnLZuUi7mm6zLKXAu8v5qYL2oS+nhzTViuNjO1/Xot0o5Rz4NprinJZZ9hLnM1l2uRdjgunKKLuby0eZnqOe7GMM/cp4FLI2I74ALgW8C+wDERMZOZ36U6+cDW9YWWWquLucYxJ2CHc80rRz9v2UQw13QZVa4xzGkzCX28uSYo1zjmVWojVz8a6J/MtXk7JjmXfYa5zNVcrnk5Lpwu5lKbVo67AYMqnfiOwF9l5vcj4nvA44CHRsQfMvPL5XlPB76QmV8pt6Pe4S5RfdLGt0XEh4DfAfenmrTx5ww/CXDnco0pU5dzLSgz1wHrSq0dmqrTNnNNl2FzLeH99TTgK5n5oxE0e5L6eHMtblL6+FFmghZer36NuH8yV8NGmMs+Y0DmMtewHBdOF3OpNTkBu/0NemEMc4nQwqSNXcw1jkxdzuXFy3K4dLEvNNd05erqZ9e4Luaanlz2GeYyl2N5L168TM5l7A1YcoMnYC4Rmpl8vXO5JiFTl3N58dLFyyS8v+zjl3euScjU1Os1CRdzTc/FPsNc5nIs78WLl8m4TOMcd2OfSyQzPw8cA7wyIp4fEY+s18jBDoPsYq6xZyrr62QuqaPG/v6yj1+SLuYae6ayviZer7Ez1/Swz1gSc23eFnNJ0ghN44a7+nwHG4EPAV8E9qCa7+AsWphLJEc/aWMXc01EJuhuLqmDJuL9ZR/fty7mmohM0N0Jos01Pewz+mauBnU1lyT1q7eL8VSJiP2BM4FXZOb7avcfBJCZ/1VuR1vfjETEDpl51ZDr6FyuScxU6nUyl9QFk/j+so9fcB2dyzWJmUq9oV+vSWSu6WGfseA6zGUuSWrEVG64A4iIg4F/Ad6QmSfX7o/MzIhYMeCu02PVxVxdzATdzSVNgq6+v8w1PbqYSZoUXX1/mWu6dDWXpO6Z2g13ABFxIPA+4E3AhZn5qTE3aSS6mKuLmaC7uaRJ0NX3l7mmRxczSZOiq+8vc02XruaS1C1TveEOICL2pTrb0G2B72Xme8fbotHoYq4uZoLu5pImQVffX+aaHl3MJE2Krr6/zDVduppLUndM/Ya7ui7OJQLdzNXFTNDdXNIk6Or7y1zTo4uZpEnR1feXuaZLV3NJmm6d2nAnSZIkSZIkdcWKcTdAkiRJkiRJ0o254U6SJEmSJEmaQG64kyRJkiRJkiaQG+4kSZIkSZKkCeSGO0mSpCkREddHxLcj4vsR8Z2IODYiBh7PRcQ5EbF6BO16RZ/Pe35E/DAiTo2IrSPi8yXPmmHbIEmS1EUrx90ASZIk9e33mXlXgIi4GfABYEfgVeNsFPAK4O/7eN6zgUdk5kURcS9gy14eSZIk3Zh73EmSJE2hzPwVcAzw3KgcHRFv6T0eEWdGxAPK9bdHxNqyp95rFlt3RNw9Ir5S9ur7ekTMzLf+iHg9sG3Zc+7U8tixEfG9cnlhue8dwG2AMyLipcD7gbuW5W47qt+LJElSl7jHnSRJ0pTKzJ+UQ2VvtshT/zozfx0RWwBnR8RdMvO8uZ4YEVsBpwFrMvMbEbED8PsF2vCyiHhubU/AA4CnAvcEAvhaRPxXZj4zIh4OPDAzL4+IrwEvysxDlxhbkiRp2XCPO0mSpOkWfTzn8RHxTeBbwB2BOyzw3NsDl2bmNwAy86rMvG4J7TkQ+PfM3JCZVwMfA+63hOUlSZJUuMedJEnSlIqI2wDXA78CrmPzL2W3Kc+5NfAi4O6Z+ZuIeG/vsflWC+Qc98+5/nmWlyRJ0gi4x50kSdIUiohdgXcAb8nMBH5KNWfciojYE7hHeeoOwAbgyoi4OfCIRVb9I+CWEXH3UmcmIlYusH6AayNiy3L9i8BhEbFdRKwC/gz47yHjSpIkLUvucSdJkjQ9to2IbwNbUu0B9z7g+PLYl4GLgO8C3wO+CZCZ34mIbwHfB35SnjevzPxjRKwB/jUitqWa3+7g+dZfnAicFxHfzMwnlr36vl4ee1dmfmuY0JIkSctVVF/QSpIkSZIkSZokHiorSZIkSZIkTSA33EmSJEmSJEkTyA13kiRJkiRJ0gRyw50kSZIkSZI0gdxwJ0mSJEmSJE0gN9xJkiRJkiRJE8gNd5IkSZIkSdIE+v81oLupNZon2QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1270.08x259.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph(cutoff_list, [num_of_binding_sites[cutoffs] for cutoffs in cutoff_list], \n",
    "      \"num. of binding sites\", lipid, f\"{save_dir}/test_cutoff_num_of_bs_{lipid}.png\")\n",
    "\n",
    "graph(cutoff_list, [duration_avgs[cutoffs] for cutoffs in cutoff_list], \n",
    "      f\"Durations ({timeunit})\", lipid, f\"{save_dir}/test_cutoff_durations_{lipid}.png\")\n",
    "\n",
    "graph(cutoff_list, [num_of_contacting_residues[cutoffs] for cutoffs in cutoff_list], \n",
    "      \"num. of contacting residues\", lipid, \n",
    "      f\"{save_dir}/test_cutoff_num_of_contacting_residues_{lipid}.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of major differrence, when comparing to cholesterol interactions, is that larger lower cutoffs were required to calculate contacts or binding sites. This observation agreed with the analysis of the minimum distance distribution, which started at 0.425 nm instead of 0.4 nm in that of the cholesterols. Another difference is that the duration plot does not show an obvious plateau as the upper cutoff increased from 0.55 nm to 0.8 nm, but has a little turn at 0.7 nm. This could suggest that the 'gap' between the first and second layers of PIP<sub>2</sub>s is narrower than that of cholesterols. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compare results with A2a and GABAA\n",
    "\n",
    "We have shown that different lipid species may require different cutoff values, now let's check if the cutoff values will change for different proteins. Below we will first calculate the interaction metrics mentioned above for our GABAA simulations, then we will plot results from the two systems together for comparison. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# GABAA simulations\n",
    "save_dir = check_dir(suffix=\"test_cutoffs_GABAA\", print_info=False)\n",
    "lipid = \"CHOL\"\n",
    "trajfile_list = [\"./traj_data/GABAA/run1/protein_lipids.xtc\", \n",
    "                 \"./traj_data/GABAA/run2/protein_lipids.xtc\"]\n",
    "topfile_list = [\"./traj_data/GABAA/run1/protein_lipids.gro\", \n",
    "                 \"./traj_data/GABAA/run2/protein_lipids.gro\"]\n",
    "\n",
    "num_of_binding_sites, duration_avgs, num_of_contacting_residues = test_cutoffs(\n",
    "                                 cutoff_list, trajfile_list, topfile_list, lipid, lipid_atoms, \n",
    "                                 nprot=nprot, stride=stride, save_dir=save_dir, timeunit=timeunit)\n",
    "\n",
    "test_data = {\"num_of_binding_sites\": num_of_binding_sites,\n",
    "             \"duration_avgs\": duration_avgs,\n",
    "             \"num_of_contacting_residues\": num_of_contacting_residues,\n",
    "             \"test_cutoff_list\": cutoff_list}\n",
    "\n",
    "with open(f\"{save_dir}/test_cutoff_data_{lipid}.pickle\", \"wb\") as f:\n",
    "    pickle.dump(test_data, f, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've generated data for the GABAA simulations, let's use the following script to compare the two sets of data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1270.08x259.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1270.08x259.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1270.08x259.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def graph_compare(cutoff_list, data1, data2, label1, label2, ylabel, title, fn):\n",
    "    colors = [\"#20639B\", \"#ED553B\"]\n",
    "    fig, ax = plt.subplots(1, 1, figsize=(len(cutoff_list)*0.42, 3.6))\n",
    "    m1 = ax.scatter(np.arange(len(cutoff_list)), data1, s=50, color=colors[0])\n",
    "    m2 = ax.scatter(np.arange(len(cutoff_list)), data2, s=50, color=colors[1])\n",
    "    ax.set_xticks(np.arange(len(cutoff_list)))\n",
    "    ax.set_xticklabels(cutoff_list, rotation=45, ha='right')\n",
    "    ax.set_xlabel(\"Dual cutoff\")\n",
    "    ax.set_ylabel(ylabel)\n",
    "    ax.set_title(title)\n",
    "    ax.legend([m1, m2], [label1, label2], loc=\"upper left\")\n",
    "    plt.tight_layout()\n",
    "    plt.savefig(fn, dpi=200)\n",
    "    return\n",
    "\n",
    "\n",
    "lipid = \"CHOL\"\n",
    "with open(f\"./test_cutoffs_A2a/test_cutoff_data_{lipid}.pickle\", \"rb\") as f:\n",
    "    data_A2a = pickle.load(f)\n",
    "with open(f\"./test_cutoffs_GABAA/test_cutoff_data_{lipid}.pickle\", \"rb\") as f:\n",
    "    data_GABAA = pickle.load(f)\n",
    "    \n",
    "if data_A2a[\"test_cutoff_list\"] == data_GABAA[\"test_cutoff_list\"]:\n",
    "    cutoff_list = data_A2a[\"test_cutoff_list\"]\n",
    "    # plot 1 \n",
    "    graph_compare(cutoff_list, \n",
    "                  [data_A2a[\"num_of_binding_sites\"][cutoffs] for cutoffs in cutoff_list], \n",
    "                  [data_GABAA[\"num_of_binding_sites\"][cutoffs] for cutoffs in cutoff_list],\n",
    "                  \"A2a\", \"GABAA\", \"Num. of binding sites\",\n",
    "                 lipid, f\"cmp_num_of_bs_{lipid}.png\")\n",
    "\n",
    "    # plot 2\n",
    "    graph_compare(cutoff_list, \n",
    "                  [data_A2a[\"duration_avgs\"][cutoffs] for cutoffs in cutoff_list], \n",
    "                 [data_GABAA[\"duration_avgs\"][cutoffs] for cutoffs in cutoff_list], \n",
    "                  \"A2a\", \"GABAA\", f\"Average Durations ({timeunit})\",\n",
    "                 lipid, f\"cmp_durations_{lipid}.png\")\n",
    "\n",
    "    # plot 3\n",
    "    graph_compare(cutoff_list, \n",
    "                  [data_A2a[\"num_of_contacting_residues\"][cutoffs] for cutoffs in cutoff_list],\n",
    "                 [data_GABAA[\"num_of_contacting_residues\"][cutoffs] for cutoffs in cutoff_list], \n",
    "                  \"A2a\", \"GABAA\", \"num. of contacting residues\",\n",
    "                 lipid, f\"cmp_num_of_contacting_residues_{lipid}.png\")\n"
   ]
  },
  {
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    "In both cases, we saw cholesterol contacts started to come up at 0.4 nm and cholesterol binding sites at 0.45 nm. However, the average interaction durations of cholesterols are much shorter with GABAA than with A2aR, even though the total number of contacting residues are similar. These data revealed that the interactions of cholesterols with GABAA is much weaker than those with A2aR. The scenario in binding site calculation is less straight-forward. The number of calculated binding sites showed a big jump beetween 0.45 nm and 0.475 nm in GABAA whereas the variance of binding sites is less significant in A2aR after 0.45 nm. For A2a, the dual cutoff of 0.475-0.7 seems a good choice, whereas for GABAA, 0.475-0.75 seems better. "
   ]
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    "## The impact of cutoff values on binding site caluclation\n",
    "\n",
    "We have seen that unsuitable cutoffs may lead to inaccurate calculation of binding sites, in particular the number of binding sites may vary with different cutoff values. In the following session, we will look into these differences and check how much an impact cutoff will make. \n",
    "\n",
    "We will check the cholesterol interactions and binding sites with GABAA using three dual-cutoffs, i.e. 0.45-0.7, 0.475-0.7 and 0.5-0.7. Based on the figure above, the three dual-cutoffs illustrate three progressive steps of cholesterol contacts starting to come up, binding site calculation is unstable and the calculation reaching plateau. \n",
    "\n",
    "To save time for this test, we will only calculate binding site and the binding site residence time for comparison, whereas skip the other functionalities of PyLipID, including pose analysis. We will use the following script to run the calculation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "COLLECT INTERACTIONS FROM TRAJECTORIES: 100%|██████████| 2/2 [02:58<00:00, 89.43s/it]\n",
      "CALCULATE INTERACTIONS FOR BINDING SITES: 100%|██████████| 23/23 [00:13<00:00,  1.69it/s]\n",
      "COLLECT INTERACTIONS FROM TRAJECTORIES: 100%|██████████| 2/2 [03:12<00:00, 96.04s/it]\n",
      "CALCULATE INTERACTIONS FOR BINDING SITES: 100%|██████████| 16/16 [00:09<00:00,  1.62it/s]\n",
      "COLLECT INTERACTIONS FROM TRAJECTORIES: 100%|██████████| 2/2 [03:06<00:00, 93.01s/it]\n",
      "CALCULATE INTERACTIONS FOR BINDING SITES: 100%|██████████| 11/11 [00:07<00:00,  1.43it/s]\n"
     ]
    }
   ],
   "source": [
    "from pylipid.api import LipidInteraction\n",
    "\n",
    "lipid = \"CHOL\"\n",
    "trajfile_list = [\"./traj_data/GABAA/run1/protein_lipids.xtc\", \n",
    "                 \"./traj_data/GABAA/run2/protein_lipids.xtc\"]\n",
    "topfile_list = [\"./traj_data/GABAA/run1/protein_lipids.gro\", \n",
    "                 \"./traj_data/GABAA/run2/protein_lipids.gro\"]\n",
    "\n",
    "atomistic_structure = \"./traj_data/GABAA/GABAA_atomistic.pdb\" # use `save_pymol_script` to map \n",
    "                                                              # binding sites to this atomistic structure. \n",
    "\n",
    "cutoffs_list = [[0.45, 0.7], [0.475, 0.7], [0.5, 0.7]]\n",
    "\n",
    "for cutoffs in cutoffs_list:\n",
    "    save_dir = \"GABAA_cutoffs_{}\".format(\"_\".join([str(cutoff) for cutoff in cutoffs]))\n",
    "    li = LipidInteraction(trajfile_list, topfile_list=topfile_list, lipid=lipid, cutoffs=cutoffs, \n",
    "                         save_dir=save_dir, timeunit=\"us\")\n",
    "    li.collect_residue_contacts()\n",
    "    li.compute_residue_koff(plot_data=False)  # plot_data=False to save time and disc space\n",
    "    li.compute_binding_nodes(print_data=False) \n",
    "    li.compute_site_koff(plot_data=True)\n",
    "    li.write_site_info()\n",
    "    li.save_pymol_script(atomistic_structure)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `save_pymol_script()` function mapped the bindings to a provided atomistic structure of the receptor and generated a python script `show_binding_site_info.py` that can show such infomation in a PyMol session. Run the script using python will open the PyMol session from which we can check the binding site locations and make comparisons easily. \n",
    "\n",
    "<img src=\"statics/binding_site_comparisons_cutoffs.png\" />\n",
    "\n",
    "Above we showed the calculated binding sites at the same locations from two dual-cutoffs. Comapring the two showed that using a larger lower cutoff tends to merge binding sites, as illustrated by the binding site colored in maroon in the larger dual-cutoff (left), which concatenated the green and blue binding sites in the case of using the smaller dual-cutoffs (right). Whether this maroon binding site should be split can be subjective, as the two binding sites (blue and green) detected by using the smaller cutoffs can be considered as two bound poses at the same binding site. Thus, users need to check the calculated results and adjust the cutoffs according to their needs. "
   ]
  }
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