{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Creating a model of SERCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we will create a bond graph model of a more complicated system - the model of SERCA described in Tran et al. (2009), which was later represented as a bond graph in Pan et al. (2018). The reaction scheme for the network is shown below.\n",
    "\n",
    "![](Tran_SERCA.svg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To create this model, we make lists of the reactions and chemostats."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from BondGraphTools import reaction_builder\n",
    "from BondGraphTools.reaction_builder import Reaction_Network\n",
    "\n",
    "from BondGraphTools import draw, simulate\n",
    "from numpy import log\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy import init_printing, SparseMatrix, Eq, Symbol, lambdify\n",
    "init_printing()\n",
    "\n",
    "reactions = [\n",
    "    (\"P1 + MgATP = P2\", 'R1,2'),\n",
    "    (\"P2 + H = P2a\", 'R2,2a'),\n",
    "    (\"P2 + 2*Cai = P4\", 'R2,4'),\n",
    "    (\"P4 = P5 + 2*H\", 'R4,5'),\n",
    "    (\"P5 = P6 + MgADP\", 'R5,6'),\n",
    "    (\"P6 = P8 + 2*Casr\", 'R6,8'),\n",
    "    (\"P8 + 2*H = P9\", 'R8,9'),\n",
    "    (\"P9 = P10 + H\", 'R9,10'),\n",
    "    (\"P10 = P1 + Pi\", 'R10,1')\n",
    "]\n",
    "\n",
    "metabolites = ['MgATP', 'MgADP', 'Pi', 'H', 'Cai', 'Casr']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then use for loops to sequentially add the reactions and chemostats to the model using the Reaction Builder."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Species:\n",
      "['P1', 'MgATP', 'P2', 'H', 'P2a', 'Cai', 'P4', 'P5', 'P6', 'MgADP', 'P8', 'Casr', 'P9', 'P10', 'Pi']\n",
      "\n",
      "\n",
      "Reactions:\n",
      "R1,2 ({'P1': 1, 'MgATP': 1}, {'P2': 1}, None, None)\n",
      "R2,2a ({'P2': 1, 'H': 1}, {'P2a': 1}, None, None)\n",
      "R2,4 ({'P2': 1, 'Cai': 2}, {'P4': 1}, None, None)\n",
      "R4,5 ({'P4': 1}, {'P5': 1, 'H': 2}, None, None)\n",
      "R5,6 ({'P5': 1}, {'P6': 1, 'MgADP': 1}, None, None)\n",
      "R6,8 ({'P6': 1}, {'P8': 1, 'Casr': 2}, None, None)\n",
      "R8,9 ({'P8': 1, 'H': 2}, {'P9': 1}, None, None)\n",
      "R9,10 ({'P9': 1}, {'P10': 1, 'H': 1}, None, None)\n",
      "R10,1 ({'P10': 1}, {'P1': 1, 'Pi': 1}, None, None)\n"
     ]
    }
   ],
   "source": [
    "# Create a new reaction network\n",
    "rn_SERCA = Reaction_Network(name=\"SERCA Network\")\n",
    "\n",
    "# Add reactions to the reaction network\n",
    "for reaction, Re_name in reactions:\n",
    "    rn_SERCA.add_reaction(reaction=reaction, name=Re_name)\n",
    "\n",
    "# Add chemostats to the reaction network\n",
    "for metabolite in metabolites:\n",
    "    rn_SERCA.add_chemostat(metabolite)\n",
    "    \n",
    "# Print the species and reactions\n",
    "print('Species:')\n",
    "print(rn_SERCA.species)\n",
    "print('\\n')\n",
    "print('Reactions:')\n",
    "for reaction in rn_SERCA._reactions.keys():\n",
    "    print(reaction, rn_SERCA._reactions[reaction])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then convert the reaction network into a bond graph, and draw the bond graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = rn_SERCA.as_network_model(normalised=True)\n",
    "draw(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also derive the differential equations for the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ dx_{0} + u_{0} u_{15} x_{0} e^{u_{1}} + u_{0} u_{23} x_{0} e^{u_{14}} - u_{13} u_{23} x_{8} - u_{15} u_{2} x_{1}, \\  dx_{1} - u_{0} u_{15} x_{0} e^{u_{1}} + u_{15} u_{2} x_{1} + u_{16} u_{2} x_{1} e^{u_{3}} - u_{16} u_{4} x_{2} + u_{17} u_{2} x_{1} e^{2 u_{5}} - u_{17} u_{6} x_{3}, \\  dx_{2} - u_{16} u_{2} x_{1} e^{u_{3}} + u_{16} u_{4} x_{2}, \\  dx_{3} - u_{17} u_{2} x_{1} e^{2 u_{5}} + u_{17} u_{6} x_{3} + u_{18} u_{6} x_{3} - u_{18} u_{7} x_{4} e^{2 u_{3}}, \\  dx_{4} - u_{18} u_{6} x_{3} + u_{18} u_{7} x_{4} e^{2 u_{3}} + u_{19} u_{7} x_{4} - u_{19} u_{8} x_{5} e^{u_{9}}, \\  dx_{5} - u_{10} u_{20} x_{6} e^{2 u_{11}} - u_{19} u_{7} x_{4} + u_{19} u_{8} x_{5} e^{u_{9}} + u_{20} u_{8} x_{5}, \\  dx_{6} + u_{10} u_{20} x_{6} e^{2 u_{11}} + u_{10} u_{21} x_{6} e^{2 u_{3}} - u_{12} u_{21} x_{7} - u_{20} u_{8} x_{5}, \\  dx_{7} - u_{10} u_{21} x_{6} e^{2 u_{3}} + u_{12} u_{21} x_{7} + u_{12} u_{22} x_{7} - u_{13} u_{22} x_{8} e^{u_{3}}, \\  dx_{8} - u_{0} u_{23} x_{0} e^{u_{14}} - u_{12} u_{22} x_{7} + u_{13} u_{22} x_{8} e^{u_{3}} + u_{13} u_{23} x_{8}\\right]$"
      ],
      "text/plain": [
       "⎡                 u₁              u₁₄                                         \n",
       "⎣dx₀ + u₀⋅u₁₅⋅x₀⋅ℯ   + u₀⋅u₂₃⋅x₀⋅ℯ    - u₁₃⋅u₂₃⋅x₈ - u₁₅⋅u₂⋅x₁, dx₁ - u₀⋅u₁₅⋅x\n",
       "\n",
       "   u₁                          u₃                          2⋅u₅               \n",
       "₀⋅ℯ   + u₁₅⋅u₂⋅x₁ + u₁₆⋅u₂⋅x₁⋅ℯ   - u₁₆⋅u₄⋅x₂ + u₁₇⋅u₂⋅x₁⋅ℯ     - u₁₇⋅u₆⋅x₃, d\n",
       "\n",
       "                u₃                               2⋅u₅                         \n",
       "x₂ - u₁₆⋅u₂⋅x₁⋅ℯ   + u₁₆⋅u₄⋅x₂, dx₃ - u₁₇⋅u₂⋅x₁⋅ℯ     + u₁₇⋅u₆⋅x₃ + u₁₈⋅u₆⋅x₃ \n",
       "\n",
       "             2⋅u₃                               2⋅u₃                          \n",
       "- u₁₈⋅u₇⋅x₄⋅ℯ    , dx₄ - u₁₈⋅u₆⋅x₃ + u₁₈⋅u₇⋅x₄⋅ℯ     + u₁₉⋅u₇⋅x₄ - u₁₉⋅u₈⋅x₅⋅ℯ\n",
       "\n",
       "u₉                    2⋅u₁₁                          u₉                       \n",
       "  , dx₅ - u₁₀⋅u₂₀⋅x₆⋅ℯ      - u₁₉⋅u₇⋅x₄ + u₁₉⋅u₈⋅x₅⋅ℯ   + u₂₀⋅u₈⋅x₅, dx₆ + u₁₀\n",
       "\n",
       "         2⋅u₁₁               2⋅u₃                                             \n",
       "⋅u₂₀⋅x₆⋅ℯ      + u₁₀⋅u₂₁⋅x₆⋅ℯ     - u₁₂⋅u₂₁⋅x₇ - u₂₀⋅u₈⋅x₅, dx₇ - u₁₀⋅u₂₁⋅x₆⋅ℯ\n",
       "\n",
       "2⋅u₃                                         u₃                   u₁₄         \n",
       "     + u₁₂⋅u₂₁⋅x₇ + u₁₂⋅u₂₂⋅x₇ - u₁₃⋅u₂₂⋅x₈⋅ℯ  , dx₈ - u₀⋅u₂₃⋅x₀⋅ℯ    - u₁₂⋅u₂\n",
       "\n",
       "                   u₃             ⎤\n",
       "₂⋅x₇ + u₁₃⋅u₂₂⋅x₈⋅ℯ   + u₁₃⋅u₂₃⋅x₈⎦"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.constitutive_relations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The parameters for the model have not been set. We can define these parameters using a list and use a for loop to set these parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "reaction_rates = {\n",
    "    \"R1,2\": 0.00053004, \n",
    "    \"R2,2a\": 8326784.0537,\n",
    "    \"R2,4\": 1567.7476,\n",
    "    \"R4,5\": 1567.7476,\n",
    "    \"R5,6\": 3063.4006,\n",
    "    \"R6,8\": 130852.3839,\n",
    "    \"R8,9\": 11612934.8748,\n",
    "    \"R9,10\": 11612934.8748,\n",
    "    \"R10,1\": 0.049926\n",
    "}\n",
    "\n",
    "species_affinities = {\"P1\": 5263.6085,\n",
    "                   \"P2\": 3803.6518,\n",
    "                   \"P2a\": 3110.4445,\n",
    "                   \"P4\": 16520516.1239,\n",
    "                   \"P5\": 0.82914,\n",
    "                   \"P6\": 993148.433,\n",
    "                   \"P8\": 37.7379,\n",
    "                   \"P9\": 2230.2717,\n",
    "                   \"P10\": 410.6048,\n",
    "                   \"Cai\": 1.9058,\n",
    "                   \"Casr\": 31.764,\n",
    "                   \"MgATP\": 244.3021,\n",
    "                   \"MgADP\": 5.8126e-7,\n",
    "                   \"Pi\": 0.014921,\n",
    "                   \"H\": 1862.5406}\n",
    "\n",
    "R = reaction_builder.R\n",
    "T = 310\n",
    "\n",
    "# Set reaction rate constants\n",
    "for reaction,rate in reaction_rates.items():\n",
    "    comp = model/f\"R:{reaction}\"\n",
    "    comp.set_param('r',rate)\n",
    "    comp.set_param('R',R)\n",
    "    comp.set_param('T',T)\n",
    "\n",
    "# Set species constants\n",
    "for species,affinity in species_affinities.items():\n",
    "    if species not in metabolites:\n",
    "        comp = model/f\"C:{species}\"\n",
    "        comp.set_param('k',affinity)\n",
    "        comp.set_param('R',R)\n",
    "        comp.set_param('T',T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also set the efforts of the chemostats automatically using a function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the fixed amounts for each chemostat\n",
    "chemostat_amounts = {\n",
    "    \"Cai\": 0.0057,\n",
    "    \"Casr\": None,\n",
    "    \"H\": 0.004028,\n",
    "    \"MgADP\": 1.3794,\n",
    "    \"MgATP\": 3.8,\n",
    "    \"Pi\": 570\n",
    "}\n",
    "\n",
    "for species in metabolites:\n",
    "    affinity = species_affinities[species]\n",
    "    comp = model/f\"SS:{species}\"\n",
    "    if chemostat_amounts[species]:\n",
    "        effort = R*T*log(species_affinities[species]*chemostat_amounts[species])\n",
    "        comp.set_param('e',effort)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We check the parameters have been set by deriving the differential equation again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAGJwAAABACAYAAAD7cTuXAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAgAElEQVR4Aeyd7dXrxPX2nSwKODmp4IEOIFQAdABJBUAHsPiU/zcWdHCgAgIdQCrgpQNIBZDTQZ7r0j3jM5Y1M9eWJVuWL62lW29b++U3e8+MfdvWn/73v/8dvJiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiAQuD//u//nkHuOba/lfvKvUvLlPbL/aXtWJ8JmIAJmIAJmIAJ3IJAOb8p9x/dl1vEb5smYAImYAImYAImYAImYAImYAImYAImYAImYAImYAImYAImYAImsFUCr+Gfie/Cue8nHOQHvN6YOO9TJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACVySA7/2+CXN/SybfwvYFzv3CY2xfx4bXn2PlwyB+wbkfsOW1b7F5gfUn7L/kubzgmPf8A+uvWPm9Yur8DdsDttX7cPnvSZaitPMBd8YLdPA7zB9gO9ht6cQ1xvA+Vtrn/nc4l32pxg65qi8dnfyONVnRFmP/FvKZWc+XSWbQ4cUETMAETMAETGAHBDAnqM490vyC159j9bwrtbfnXTtIfIdgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiawaQL4n9zPcJD/qxwvH7xWnHmv2OfuH6NjH5qACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACdyGwBcw+ym+OMyHSfDBDF9j5YMnuHyBc8eHPmCfD4sYHp6ALb9kzAc/HHCeGy58CMR32P4b27/wBLb8weR/Y806W/dR/k+8r7bg+ke4xgc3lEtLJ31+B/flh1PwC9LZl1bsLV9aOvmAiTL2/8Jejql1X4tZGav3TcAETMAETMAE7pdAa+7hedd0u7bmT553TTPzWRMwARMwARMwARMwARMwARMwARMwARMwARMwARMwARMwARMwAROIEPgQws9HNwyfCzs+cAIfiMofGhvJ+dAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETODGBPiQiJdY+RCHf2B9UfjzI87/iuNP07lvimsvcO1LHmPLBz68ju13WPmACa7DgmPqfpPnuY+Tk/cl8QPlsP83rL9h/7d8nlsc84EY/O5y9oenuUzqTLroF+3mhcfZl1bsh3T/iS/pXEtnfpgF7ZHpYLt1X3KMcQ8LZE+Y4Zhxv431d+xn5oz546c7/NcETMAETMAETOBOCLTmHp53jeaAmOtwfuR5150kt900ARMwARMwARMwARMwARMwARMwARMwARMwARMwARMwARMwARO4TwL4v9wvY89xbvjM05/HF3xsAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiawLQL8cjBWPhjhXax/YP2p8PAr7PMLxV+k9fgACNyTH3ww3Ivj73gftvyy8ZfY8iEJPB622H2ejifv4zUstP8u7uFDJd7H9iOe5IJ9PtSCvh59GC48XavppE3qLBce02fqbMVe86Wns/SP3D6gLSzV++gHrleZDXcfDj9i+wb3IU8W1HdccI4/xvwJVnLjdojxKOAdEzABEzABEzCBmxPA+Nyae3jedT4HrM6f2Jjg6XnXzbPaDpiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACZiACeyZwJ/3HJxjMwETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMAETMIE9EOCDCfhjvVj5I8d8QMLP2H+WYvsa+x9g5YMOPsX67+JaEjl8i3PDAx/yCRxT9hds+RALPjxi6kERZ/dRFvcMD67APv15gfWAc/Tnb9hSV2sZ6+RDI04ezJCO+YAH6m3FPukLbmvqpF4u0E3fP8U2+9y8D3JVZrhGJv/A+i1WLuTKB1CUC699RVmsbI8sW8p43wRMwARMwARM4IYEMEa35h6edz21zXEOiMPm/Ck3Jbh63pVheGsCJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACCxLwAycWhGlVJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJrA0Afw4Lx/k8GuhNz9o4pCuHS/hmA89+NfxBHZw7k1sjvfkazj/Pfb/wJYPW/gI6+f5Gre1+3DpP6Uc9ocHQ2DLh0Y8w32fcMX+61g/wz63wzKlE+d4/29JJG/4cA2u9Hsy9iQ46UtLZzYAGT64gw+b4EM36O8B26ov6XqTGWTehI788Ir3cMwHYryf7mUs/AFr2sgLj3neiwmYgAmYgAmYwAYIpHF5cu4xHrNx7HkX2gwcmvMnNitkPO/aQH7bBRMwARMwARMwARMwARMwARMwARMwARMwARMwARMwARMwARMwgX0SeG2fYTkqEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABEzABE9gHAf6IL9aPsfKhEHw4wdtY3+N5RojtN1j5wAQe8/q3+Rr2ufBBEL8Me6d/vsXhR5D9K7a/YvvV6eXqfR9Clg9RoN43sL7D+3COD434Elv6QF+nlpovH+A+xkAdlPmAN+NcM3aITPrCe7FM6uQF6P0Zmzex8uEY2Ax2v+QOlup9uNZj9gL6cluQ+T+w8iEVXBjXH8Peqz885gM5ptrnlZT3TMAETMAETMAErkIA43hz7oHrnneN5oCpYarzJzDzvOsq2WsjJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACJmACj0rgT//85z/fRfDf459zf3pUCFuJG23wJtaTD4PhmB+oe44tPxznxQR2QeBRc/1R495F0m4kCDWHVLmNhGU3TEAmsPXchn/8YD/n1v/CPr+ccffL1pnfPeALAthjvl2Aw7eawME10U+Crffpj96GS7bPo7PsV4MlTMAEVALuT1RSltsqAedwv2WWnIP0rcUl3IZxZvd4x9bz8F6Y3rJebmn7Xton6ueSdeH2idK3/L0ScK7fa8ud+q32f6rcqXYf7ZXAkvngvmSvWfI4cUVyWKmdiL7HoTwvUrOcx813xQlEck3pB6IerKEz6oPlTcAE7p9ApC+7/2jvLwK1fVS5+yOwXY/NfLttcy+e3TKHbmn7XtrHfu6TAHKf3xv+D7Z/yRFi/7/Yfwtbf5c4Q3nQLXJA+q65KvegGIewzeiRW3+bsSMnb/b9w1va3mZr2KtHIYDc97zrURr7wjg9b7gQ4E5vd17so2E9D9pHOzqK6xBwv3cdznOtuH3mkvN9JqATUOpMnVuocrp3t5XcWzy3pWnreyeg9CX3wuBean9PzO8lN9bw0+24BtXr6ryXPuO6VOZZuyeW91C7io/3xLyVVYiDnz368LWWkK89EWBiYO9jbD8umeCY/1z8rDjH429x/ofi3AHH/Of/p+nc37D9g8c4f/JwCZz7N85RRz7PfS5vPW1e/YXcF+nod2zfwPoFznU/SAaZi2KhTehgPJkFfeQx7Z/EjXOUlfwMyNHekszpZunncIw/38Cn3A75XClX5Y77ZD5HxTvZSbEvlusBfVLblJihm7XwLVZ+CPNleS3v47yavy/yPdg+x/phRecqNR7wc+l4irD3swue3dxgtAX3HPxZv1HIVPuMfLNoV80hVW4wL9qWZaFPrQlZZ+bk7bYI9HIH19U50EHMGzm3oU/t8yQ5khd8ZP/B/H8BWWzOlpc4f/wyQL6Kc81+B9dDcwvI55iyibP+iRcKuVYfJTPPxqC3GU9ULsvvYQs2S9ZEKN/E9h4wK20Imci8XHrtULZx8uHsNRhlVNtJdtUxqeVnsi/VY1SW8ntawFHmxLgr3EM1UfKr6BtEcE3KIVUu+b+4zqS31/+G+nTE1G0XyNysXyvbcCf70fZptXe4HtQcXlpujZoocrc1xxnSRpGFjDTm5TxUdBayrXbMYgfolOSON3hnMwTUtuvJ4bqUh6pcBgT53NfX6iXUn0Cf9NpFlaOfkFXHTXlMSnqbdRXxMenrsaTYsEB303aW4zYiW963h33EnpnmcCZf2+aLidX4NUQoh7Mubiv6BhFcU/NSkkv2JFnV9uDoqzha74NH5yDddoGPcj0K8cxuw8zA29sRSLmgvCcQzcNuPwrb0tg5poP7qHvcl4zFDi25iG3Idms/oC9cLymOVh9xgIxS0yHb0NmNm9CTbSWHztpoByeWrIu12kdtR0kutbkkq+ZQ0pnHrtqcd0gX6OzKQSbUtyg6c65Clu3UrMdgPBLLbH8nWznXwVt67ZK5zGiffOvJHDZqNyvhNvkwOUbhWre959hONqt5mXQqnw85BOyr/Z8ql213/Qz4WDaN97dBQM4Huou2bvW5cl+SdHXrLyOCXUl2abmIn7DdHQ+TPlVOHjtV2wXPVjtmsQP0SnLHG+5/J5LDSu1E9JF3NzcgExqHyyZJ7Xk2HuK8nGtZX9JVHecoB5luPElOqe9NsCxiyigWm69khfe6BRvl9e9ZeLiPbTuVl3KuQ4eSQ4fkY+91ciTXlH5giDnZ7s6pICzrLGFC/yRHyuCaXOOQlViWtpONlv1uXwC7cnuPbft4GwTQhrmds0OL9I/QW80tGsJ1KWdVuaSzGUsOUNWpyEFGrgFRNtKX5ZAO0M37muP7UXhHO4hbavMccuJ0NnbxOq4pOam2jyo3uCbapo+hMRvyzbyI6EuyvbE4oz70bGdByHW5Q0YZD0PMs/29bhP/2bmO+6W+TWybI2bI55rtvWfdzYuj0mKnFTfF0vVaXxnKIehS8pI2FZYh2ymWLiPVxwIh/W32G6Ws903gUgLIN36/ZPx94N8mzl1qyvdXCPRqHtfluQdku/0S3VDlIKq+xlblaFvqu8e4cB/7xtq4Ko1t1Ak9XVnIyMwDfkYYSe2Y4pFlx77u6biTH11Gqc2782zIyfkL2W6uXdKGrZiT3t58Qp77qHFDTplz0T3ZtspI9ZH68pIY1ualWcxbE1iMAHJuN/OuVD+1cXnJflfqV+BPRE75P8PQ7tDbjSUnCGRzv59Pnby/m0+W2wbHyLwh2+29xpfHMPqoxAMZmU8Z9172U/tVxxFcl+eUIks5L0Zt2MsNKYfW0Im4F7UdYZ7zsPAhnzqr3UKmyTIrSKxqr19C86BSp/e3RwC5UWvnA651+0jIRMYv5fWKpC/l6NJ91NBAiCnXdW6ws5rKF/IW99Q4yv1eYbdZp5BbfDxkHNDbbe8c7462cvskRmzn1rg5t216bZ5zchG5FMuiOtX8zbkD+SbLiI9ZZ94m3ZPz/KS3aRv3R9vxEWvnAE5qf63UGduEHHu/L6XKRfzLqXPcIjbaOcshnJdyI7FRXrPJ8WTnkm+tfkgeG4M6u2M49QViH8z34sk+ersdAmobB+WU/FL6kpxX6hgn1QtikWqfxkVZufYTR4XPMUlwT44/n5ucy0KOflT7E1yLMJcZ0SnBNsV2ufRix3UpLwkHssocRG7HpDPnzyLzTvgo6VvDtqozwnykk4dcajUmx/6k5lgb4zmI3GdkPXveor3IY8zoLOSKXJhl0tPqK4+2IZvbPJ87yQ1cj/SVUu1Cpzonzz4N2xRXk2OSacWu+DiHudK3ncRzrQM/cEIjzaQ5e/gAzn2BpMqTmkETjvnAiWdYv+MJbJnQfFH43iDwdI6F9TPPYS0f0vBHkmGS8cNi1PE5ZF6m88MGxz+n89kGCzHrG3/IrLyV+7Nj4c2wTVt8WMYxbuy/j3PfY/sB1sGnJCv5iXskOerEsihz2Gb7kAljGtoCWx5z5YM8joviJ2RkPkfFO9lB7IvmekSf0jbEDDm2z9dYWWt8+At9nlwUnUkf85c1/iUVYcv6/Q+2fJDFuB4Xr3HYkOpHkYPM0JcE4mHIu1hS7GpuSP1GgLlkN4GWcgiyXblgzFLtRHIoYn8XSbajINS2g5w0LkTyRsltoobOxfrGpE/tH9+GPOcT4/6fat7Fmt9cp4+RulLnXlL/RGdURhDt9idJXySeSL9H9btYwHzpmojkW7cm1JwsGkOZlzMvpPwt9Obd2usWXldtS/O0GbFnH7md9DO1N68przPk2i0N72E/wmkU7xR3uSZGunh4pi/lRTeHVDkaUWVVuUKn2q+qfbqUk/DzZv0aY9/h0m2flBtKe8v1oObb0nJsv5V0dse8nDuwr8p2x52IzhR3tx1VuWzb2+0QUNtOlUuRqXmoyh1gX6mBaH/SnfuluFW57lhMPtAZGZPU+uv6mLNOYZni7tpO8Uivr7L9vW1Te0pz6VHsZ3M6XJdzeKSLh2f6Ujt281KVoxFVVpUrdEr5BvnuHCTp9ByRILzIBFLOqn1pNw+TPjWv6ac8Jo6COqv90fV82JLr2o7UdCAWqc+LsISsNMbCx4jtbj9KyMlPNYd4y96WJeti0fZJbdNtR1WODafKqnI5GSBPP/l5i+bnKlQ56OrWd8R2ikfu2xQ/k85u+2Q/d7aN5Hq3f4m0D2S7c6Wkr2u30SZnY4/a3hHbSbabl5BTx4hDxD7i7/Z/iZEkp/oZ9LHRTL50IwLdfEht3M1t+B/pS6T+Ntnuyi4tx7ZQdSbZpcdNqpXGTvip2pbeM0lxK+1NH/e2SDmcgu7WDuRkfUo7prZZdDxMsai5JuUQdQbi6dZ38vGmLBHPNeYrKdT72yQ+6ue8xwHW5mndXIdd5qSUQ0m2qxP65FyDrNIPHIJ8JJ1jiDg+41jIdGs8wrLQW+5O2ofe7hiVbCttU9rz/kYIpPxm+7MNJ79HcGEb13JLqv9kW+0nun09sas6g3JSDSSdiqzclyWdDzn3Q+xSm0+U21lequ2ddKntI8lFbKeYu2N20tnNC1VfUTvd/FVtFzqlGod8dzyEjMScth9kmZ3rqR277Z04Km0ziEKvOrdQ82KqKWtxd2sCyqI51I09wFK2nXSqjLo+EmLSqTCaYu5zJnApAX4f9xMo4XdQnmP94FKFvr9NQK15yEn/C0n6uv2SKld4r77GVuWoWuoXCx/y7tn4wguIqTu2ZQWKLGQk5lnnxHbST8h1GcG29DqNNiOyEz7u8dQZd5VRklt03gWd3bxU/Ws0Vi1mdT4hz33gQ7dugxwl20FGXR/JMulUGTXw+5IJzCawl3lXrQ9S5yPdflftVwJy8hifdHZjYRZAdu77Y7z9jCNPYunOGygE293xhnJpUfvJbjywK89ZsvG9bFPs3XEEclK+BVlKeUHW0Cvlhiq3hs6lbUOfxDznYpJnDbI/mvzfTCTurLfY1upbmgcVery7bQJn7Yx8kvrIJHf18ZA4YVuqFzWWQme3pirNecYxyUn9HvyU+rykc7HxMMUttXcl7ns/3W2flEPdcTPSNom71OZqbqhyt7QdYRmJZyIJz+oxYhv61Bp72NpJPLv9f2qbbp1BTp1bSHJB/yZSqPoap5sbsC2NT8loJJ5uPxSxnRgpOpnnUlur9lXbUw3jc7clEGhjqQ5SLkj5hciVvuQAner4KvmYiHdrv2gZRTZS+yofxs6YmnNZyLCmu7Wf4pGYJ9lu3EHbSe0+NmrsqQ3Vz3Ix15Xf65XbEfbV+llUjq28tG1Vp8o86evWGOW4qPE8SZ/8PZvH4qrUZ5xo2ffBFKOpiKfkJJZov0hfyfZWc6PbVxaBdGs3+SmPE4Vu7k7xYSyR2Ls+wo7EnA4l22rfxluuvviBEx3kaER+YOtswfmPcJKNO14+xIl/Y80PXuDDJY4PZ6Aw7mWS834m7V94Li2/4PwH+WBqm+47PtCCMjj3Eivt8ckmxwdb8Fq5QObSWKiOfn8EXXzARI5xeBMf5z/Dmn+sgXJdP6FDkoOuQ5Jdmjnb4BvozjHQFDuNkx+KDvgp8aGRHS6L5jr4SPoCbXOA7EvoHWoM+6wHPhzibAno5IuQ55AfHjZBRdhnHf+E3al6XLTGYUeqH1UOPkfjYci7WMBIyo0UbLffUJkH7dJ8N4eSj125iO2ArJxDAZ0pJG+2QiDQdlI/jrjkvIGskttL941EL/sIPmdzMZzji6sDtnnuxH2134nMLbr9U/JDYkRZLF3mFFLjUeWoc4fL4jUBnt18g4zU3pG2STqVeXkkf49NDv2Tr1soELAdqVu1Ho8+Jl+qfuK6VI9JYUT2xIcdHIRj7+RHtybGzBr61BxS5WhalVXlWBOR/JX6dPiptstN+rVxG+7ouNs+kfaGrFoPar4tLcemW1QnYpbGPBpWZZOcMuZFdEp1C9uSHOPxsi0CatsF5Jjb3TyEPkmOtJJs973bJKv2J+rcT5VT+wi6KY1JKnPoU32UWQZsU+ej1786F2HbDwuYVefmuKbmcFbHNqjpU/NSlaNNVVaVo/+RHOrOQRIYtV2kegzEzXjCbZh89ua2BOS+FG528zCS15Cl7e7YOcaD+2q1fyLakgvYlmo6oG/wEfLdeoFMpI9Qa/qg2IaTUtwJeCSHTtpoJwdL10U3NwLto7ajKscmU2VVOeYkc6g75w3KSX1LQKdcj6rOAEty390CTkquS/0LdMntA5DKXEmyO9Uo8KU2Rqk1IdsOxC2PEYhJtg/Zbv+XGKlyqp8RH6eayeduS6CbD4HcPkBW6UvU+iMZVXZpOdk2YmYNLDZu0nDS2R07VdtJp9Q3Q6ckR517XBC/ksMMvVs7FFL0QUbKIaib3d/CxuR4mGx3cy3FIuVGIB61bmn+AL3dtgnYjrJcdb4yBHjff9Q5w0mUaK/JvISQ2j6RHFJ1SrmWApH6AchG+Kg6jywbHBkL41ZqPMLyaJs7NfvJdnd8hAq5bU4M+2ArBFbrH2u5lQJXc1aVo1olFsqpOlW5SA3IsuDXHTcZDOSk8Z2yO1zUNj+G3shLtb0HXYH2UdoxYlsakwJ5IelLAKX8DdimWil26KRtZTw8QFZhnkLa7wYcavM0iTnIqO0daRvKKnML1cezBqzFjfNyX6nmEOTU2CWWDEa1DVGJUcBH2pYZnYG/8gn4+r8rm7S5GxBAO09axfk/TV7wyRCBQM2rcwWpX4KTqlyOR32NLckhbrXvzvaHLe6bHFeTPmVsOwRkVeYnPvIANib9TIIKo0j7RGTPfN3TiQZ3lZE0V0g51J0TJzklL1X/zpqrFjPOh+YTkO/O3VM83bjhpMQxB6PYhqzEKODjAbIhRtnfW23hr+ddt4J/Rbto50lrOL/JeRf8qo13Us0iWLW/WFouMsarsbDtwu+P8aYGR17uzhtwP/ko4w1tUVbpy2lbiSfChzp3s4ClOo6o+RZh2c0Lgk7t3c0NVW4NnWvYhp8qc4bEpZvrET+fVD79xX21fnIQwPXuHKzU5/1tEmi0s1rXS49zqj4CVetFjYU6uzVFofHS4EjRbr+H+285HtLHCCPK72lR2kcaN1M7SnMVtc2XlmPDLa1T1ZdsR1h25wFTiQh/JscvnI/YltoR9h+5diL9dbfOUn5Icwu0pSIX8e8klRo5RJ1Kbqjj02BXiUfNXyiUbQd0RlhK9gO2T9rGB5sgILVxIBcj+dXtS5Bb1KeOH1IsSadS+4eg7Bp9WXcuCx+l8TBlW5c55dS4g7aTC/vYBGKX8hJUInOQSDt26ye192JybOFb6oR5lTld7dYYhdR4KFsuuG9yHksZXFP6jFLdLvdbjMqAW3IKS8hE+kqa7uYGdKpzyRyKUruRcTTrPcCXVq5FYld8pD01fyN92zGea+74gRMN2mho/hg9E4jreHkDJ/jjwV+NL4yO38Xxr9D1F6ylHj7g4H2cex3rycMNRvePD/lj+b+MT+L4R6yfQBcHtNLOIIpzS8RCXbR9woT2sPJauah+qnLUvShz+Pw+dJLLO1SeF5w/K3BcU/1U+WRze9ouneuqPrVtIqxVncyhqXrkuWo9dhxRbVONKqvKrRFPJ9z7uhzoN1Tm9wWg761zqM/okSTUfnzpvFHrT5Vjm6k+cj42tfApfbQ3Z5HmFoH+iT5EYp/js++ZJrB0Taj5tkZ7q/NyKX9LXMjl1usWiqq21botzcv7LT8j9RiRlZ27E8E5sbe4I2y1Jo6EOvrUHFLlaFeVVeWOsSy1E2yXW/VrS4W7Zz2RelDzbWk58l9aZ2TMU2XVcYfxqDop68UEIgTUPFTlaFvN10h/os79VDm1j2A86phEWWVRfaQulaVi9+FlgnORgVdnThfJYUWfmpeqHG2qsqrcEMeSf4LtotajGk+4DZeM3bouIhDpSy8yNHFzZEwcbu/0JUcTgpxqW60BVR99XKNe1JpWbatxM55b5hDt72lZun3UdlTlyFqVVeWoU52nqXKRelR10k91UXVGGKm270VOzfVF+5fAXGmW3c7Yo7b3LNudhlfHCKpZw37HveNl1c9b+nh01jubIKD2JWr9MShVdmm5iG11nFHlaFsdOyM6qddLm4Caw20tr66q+tR2nNXfdsZDNddeRdXfU+NR65YWb8Zy7Q1sUAUAACAASURBVPlKH+ddSKhzhmMwnbxUcz2SQ6pONdeOsQg7YT6CzkGkw5Eyao1HWB7d69hX+wK1bY52vbMNAmv2j53cIgA1ZyW5QCyL24bCSA2osmv0ZYx9N0uwzYe4O3kp5VoCqLaPKhexvfSYFNGn5m8kz9TY1fFQZR7x8e5kF8p1tb3VtiFHdW6h5sVJ23TiPpFtHERySI1dZRmxrTJSfWwg2d4ltPUmf/h2e6TskQksQkCdK6j9kiq3iPMTSsL9Ymd8Ucc2uqLKqsxPwuv4eSLbOIi0T0S2YfK+L3W4q4zUuYKav2quqf6dNFIn5hPZzoE691HjVjnSLdW2ykj1sYNke5fR3p53ba9ZHtqjTh+k1qzaXywtFxnjpVjAg3Lq78Qcc6fD8SjX2VHHG6qR+slAPBKfjv97v6zm2xos1dxQ5dhWquzSchHbKvNDINfVeI75LNS3Og866vTO9gh02lmt66XHOVUfgar1IsUSqKmTxuxwPJFtHETqdOnxkG5JjBr++9ITAaltEiy1zZeWo/mldar6UujSZpbOheox0o6PXDuR/lppdHVuocrN8q+TQ2puqOMTuajxKAwpE7Gt6oywXMO+6qflrkNAbWNVLpJfSoSR8UP1Ua19+qfKqrUv85k7l1WgCjJq3IKqhxdR83KNOYhaP0vLsdFvqVNiHqwxNZ5jwnfmIGqfcdS3x50Oo2PIHbnFWQZyY42+Uh4nMqAOnyy25DbCfI2+bclYDn9eVNv+lP0DCVZ7oAQTgQ+M+B7rsyJ0PvXnRXHMB0v8Bpmzh0AkmfLe4rbqLjv5Pyau5odW8PrUskQsB8TxA1Y+PINxDQv2mehcyrhVP1U56l+a+cfQyYdl1NqGNvMi+UkuWBU+We+etkvnuqpPapsg6K5OtHOu3al6/D3Z+1vQLsW7tgudqmxXbsV4Cnd3sav2G13mu6BRBOEcKmB4NxPo9uMr5Y1af5JcxEfIfpeDz1uc49zw83wc3eJ+dW6h9k90QYo96qvluwQWrYlAvq3R3tK8PJC/JbzW6xbKdW3D7lrzNNXPSD1GZEv7e9ifE3s1PwI1UbKb1KfmkCpHg6qsKlcGsfB+pF1u1a8tHPL+1CGPpDmJmm9Ly5H4GjqhNjLmqbLdcafIIFVncYt3TUAioOahKkejUr6iVqX+hAohK712UeQgE53Pdcck+qguio+FLollIe/dNoHIXCRrmpzT8SLaUs7hrAzbSX1qXqpyyT8p1yM6iziW3I20S7ceI/FAdk4bLhm7dc0kgLaTxoWZ6nu3RcbErGuy9vPFYtuT69qO1ADsdvVl31aql25N075iOxg3dd4yhzLWXWyXbB+1HVW5lD9rjYfqPE2Vk+sRcak6IznW1RnhHjF8L7JKrjMWyC3dv0hzpQvsTo490CfVzkoxU600Rqxon6qVRfLzgvZRfLDMHRFALnRfgwTrT6pVVacqR+QRWYh3x5nUjKocxdWxM6IzueFNjQDavZvDtXunzgf0Se0IfXPH4cnxMPms5tpUiLVz3XiCNXa4Mcu15ys1jvd0XpozjAKq5qWS6zNySKqfQK6NwmkezuHTVFhcrHJMMt0aj7IsbHO3Zb/bF1AB7EttQ1kvmyOwZv9YzS01Z1W5RFWNZdH5KW1HakCVhdyic5rNZd4yDkltPjI1mZfgLeVF1qW2jyIXtQ0flh6TZH3wddH+Phh7dzxk+0Cna+cpUS/O9UB7S23z5Fb/tXcwL5La42Yy7uNVYSeYQ1LsKkvVdpCR5KOAZnMi5ID1dTpW7m/OUTtkAvdPoDtXYA2mMJvfL1XlVkY2p19sjS/S6+YUkyrbZV5h1PKzcsur05H2ici+srDbvUnuEUaQVefZav52cy3i30TLTcY8Idc8BR/UubsUd4DjQbENGalvS0FKPjaBbPgiWWD1vGvDbfRgrk32QZGahazU7y4th3aSxvhILNA55/0xpswkR14ILN3xptCl9pPdeIJ8ChcebrebbyuyVHNDlWPjqbJLy0Vsd5kXWdjN9SSrxlOobtc32l2dg5U6vb89ApP9eKSuIXur8ZA0u/USiQX61Joat+Qkx7FQ5zhSp4uNh/QpyKgTxsNfVtuGoNQ2X1ru1rbVJFHjHutboh6ldnz02kH8Uv8/bqDaMfRJc4uA3Fz/Wjkk5QZi7I5PmYMaT5YXtrJtQdcgEmzrxe2rflruagTUNpbkgvmlBBkZPyQfYVStffonyaq1H+Qzdy6rcO3JSHH3lPj6QKCbl8iLyP8cIljV+llajj7eUmeXeYIYqTE1nrJ9qnMQtc8ole10v8poFG9VbiWWam4s3lcGx4mMqconCyy5VZlDbq2+bclwDq8tqm1HytCAnyCc8gEKJ9ExEVIy8GEL/8X+p9jyKSx8AMXxxSD2+cSeqYVPTD/gOp+yclxw/BEOmDx/xcp/Qn+eZbDNSYXT1eX5+AruWySWsV4eQzcHCP6Q8sfYHx7Oga3kpypHO1wgvzRzPgyADwNhW/wDKx8SwDb8Fuc4mA4L9qV4sny5xb1nfEbXqZttzuVtrB9iZbvTHy4/Qscxn55ObfMv/Fws1xmhog8ys9umRlHVCTk+rIRqzmoO51i/XIYPkjztPv3FPYvUeMBPidGceJIPu8jfso06+91+Q22bjp3qZeiv5lB5kypX3nPJPuzNqgnFZmL6aLmmoNm0DNpNGhcgxzjkvhTy1RpIudLj8lyVoyLIzs5t3Mtx4E1sOU9cZIGu2tyi2z/RAdwvjQuls7inyryUW3o/+bqb2kc8q9RE5g79Z/mWGGaR2naq/mqyw3noleblYyW4r5a/WW/zdQuFFNuQmV23Y5+njqG/56dUj0m3LAu7u3ntEI2d8gL3pPZpA/mzmigFWvpwTcohyPEft1Q7VUcnrwnW0FnGo+7Dj16fHsnJq/drZZyIZW81cRDap0Qg70PvZD3g/KK5Dn03qwnYluc4QVlpzIvolBsuKJh82M3cKRj+rsXRtmoeqnJyvYzBwpfJ/mQsx2PINud++Z4pOZyT+qdChzQmZfnodspH6sD52SyjPtTkkw97qn15LpLaoDc3P0EHXs0cxvWqPlyT8hJyNxsPT4INHMBnzxEDvCw6jwDyrDkuCHkoG4YuaUzMCiFfrf0sw60ip9iGjNSfJJuhWEb+Nvu8Ura2D19njbG478x2JO4pf3B/NYdwbXevD8kAcfX65ylU3XPQO7t9cK80zqlyKU6pJoI6pXkadEpyyU+pHiM6u42VBFSdkJNYZrtJ757mkjm0YYv4znL9RCAdQK7av0zJT5wLzWHz/YpdyFTHKFwLtXe2y61iu5Sf2oeOWWOEYh+6pf5PkZvrJ+6r5gWu7XLcmWrnezqn5MOceKD3rC/BObn+VFnI3XKMlcZD+CjJZc6Q746dUZ1Z95Lb5MPDjoeIX+pzM3PIT9VEKDeyLm6hr9rfZjnIVMfDpKOba1mXsoU9KR7IyX3BlF3cf02Wq8xXEqtd1A9iCc1tIN/My3GbQ/4s13Hu0hw60zm2y2PYOcu1Ug7Xu/0AZKJ8ujqTb12OsN2tccjMYon7qvZxTeoLSpZ5H/c22ybp3kXt5JjveLtW/1jNLbJCDkg5Czlpjpj4S7GsZPskBWCjWQOlsCoLuWZfVups7UMPa3sv9Se1eeaB2Kt5iWtSTmZd463aPlNyUduQD41JY1/Hx5fow71yro/t8hj3y9wh2x0PKzaatQO9e6qJAQFiWiXXoXeyvdW2Saynmqk8x8+3y3lR3oj7qnGXctF96K3mEK7NzctJlmPfarZxXmY018exL+Nj6F2tdpLuz2CT32/kwu84fsq4h6NXf/6O3Rc4zzP8/uOxf8Q5ttv7WH/Dyn22FfcPvnbfXNiGXq5LADVzrK2R5Td5jOvD98Kx5WHzs+SQiczvqW9YcJ/6GrsrB12hvhvy1fEF19gX9paBSVBWYl4abvk5kqsygo7I+CLL0n6Kfy+vQ45IW9wjPI8K0w7unZwr4Hw3fyEj5eVc/3BftSbGcUSPoXty3oXz3binbOG+SY4V2TPbuF/O87k+TvlSnoPeLcy56JLnXQ84ryxzcSv7qIlqHxSp2XE8uFfqLy6Vw/3SGB+MJfT+GGOH/irHkg3kWvMGabzJ+qBL7cu78UCX3D8X9lfrT7ONrW3BSc03ut6cx5extfKCcrgu5YYqt4bONWwnPyXmlMWi5LrE8knd01/EJtX36J6zeVC+nljtbh6f47vXbaudcS3cR2YOuPcq4yHtwZZUL5CjuNJHdWuKisoFuqV6gdwmx0PGAt9C7Q353Y2HrfYp27u3Dz3SXCUx7KmTf8dH1UeDquzScr1gy+uq7fIe7uM+qR7H942PoUdtx4evnZIduDX7f1yv9oOlnrwP+ercIstwG5Br+pd0NXMIttTckManMo68r8aT5cdb3D/b9lhX7Rg2qizXsA+duxt3amzv4bzaxqrcOGbcV80vyuJ6tS/BtdBrH8hL9QI5qfaTf7JsGTtsqH1ei094Llv6UNuHb1Xm+Z4Io3yPsoXeh6t/xKzmJREqr3EG1L12TKx7zXIX81MGocaTZCXmkJVqLGKb9rngnuYc5Enq1V/IN/uM5ANrl8vbWO/297iHCPBHZaTKFXqbLLNcZ6vmRniMQDzdPrj0DfKtceIQ5VPqru3P8HGSOfTcxeurP9dAPPJ5NB4blQ04fKCuxgLX2eEOD1nAlg9dYMKePEACx2cL7nsTJ2lj/OPDnCj8C9e/xMprXH/GPvVyyQPly6fDyb8nE0jcu0os0MsfT2ZnzyfUMOafCm9UP1W5o2rYXJJ5ZvU36OUHMMmd8fCBE+8fjc7j3uJTqD58kex+iZN8is/XWN/FObY9/WNe3e2COObm+mTME/rCOTSp+PRkRCcfBsIaGy+Mm0vOsaejp+Olalz1U5Wjj9F4dp2/udFG29ymrX4jwnykvntI+60cygpUuSy/1DaaQ6rdR8w1lc1dyU304/Q/kje93FbrT5XLfCM+5nu45Ti+yFhOdlhrcy/aUvonykVj7zGnzrWW3df+AjVRsp/Kt2h7l/qa+/BdnpcL+XuAjPS6hU5BVrE9t257cSt+qvVIWxHZvdWEHHskP4oGnKqJ4bKoT80hVY62VVlVrghX2lX6dLldpiyC7Zs4zzop3++YG0+1DZPtPdaEMtefQt8712Kpts/ScvR5SZ2RMS8ie0BeK+NOSGevwWZe31tNzMSwz9vEPLxGvrb6kwE+fO29dlHl1D5istHpBy6Mx6RJ2dpJIRbXfg3e/PPyXATto8zNx55Uc1jUp+alKkf/VFlVbhxz79hzxB4hX7+IgNCXUr+ShyE/YFeZwx3E2pfl6CR0Krblmhb1TfGp9nlTwuo5+KOMsTXbctzZH9rD2npflKJ7nAsvXheZKXmltTg17Krts7QcjS+tU52nqXIDILEeQzoHxf0/EZ0qS1rdY+2UNGu5PsiI/Uupr7Yvz2GpQLULOWW+G2lv2XYt0N55xgaZ6uswMXa1/1Plztxu+Sn6uPfaOWN2Bydm54MQW60vidSfKru0HMNTdKrjjCp3xIqa6s2NwzqPypfb2XtN13KYBOfUzpS+cDuK/e0Bcsp4SLlerkUyJhKPUmM129dkybbm0vq825ME/oKn8jqM8ruuH3JAjGdzG5yX8pKABJbhHBJ00nS5TOVavj6nHxjupR/YOeODc5JO3B/hqNR4iKVgP9IXHJlAb+89DMruunYGGPfzZ/H+UcitTEfNWVUuEouqU5UbYkLs6vhxiMgmYK2+LDNVtnuqP7nNxbwMtfcItto+NblLbA/5BH+mxqSRm9oh87Olb0b+tgzLscOuMh6ObdWYZ7k91QRzQZlfyMwJCTq7fRtklLaJzC2iPipx5zaPbps5JMY+2FRYjpxr2ZYZRXwc2W8drlI78JXfHf0Z6zfY5/cb+T3DF1j5AIqzBdf/lNb3sH1ZCHyL/a9wjl/8pg4e58XX7ptLbkdvb0gAdTU1V1D7JVUuR8g5n/K5YlXuAP+VcYtyvfElMrZFZHPsxy18mWI+XBf8zHoURpH2iciuMm7kwG6xFblHGB3Yzlib76vgei9/I7kW9a9XE5c2RXXuI8R9tK1wPAq/2qnZlhlFfHxltru3Su3A19Cci17iHs+7Hm9e2U3QawogB5U+SK7ZlNfdfncNuZIb4qqN8WosHN+5qP//UjhSX2/eEBlvqI/9SG8Mo5gaj8qHOrms0p8+qb6fv5V8i7Ds5QVhqLmhyq2hcw3bk4lQYU5ZJdcjfrLG1Poe+1qbB1FOrp1kf6zbxwsTENs5UtfMnZuPh8REP7BhHs/5TrZSUzQzLLCl1kuv3wvVKY3D9pLjIVVG2luuaSq+g6XXPqEQxLZR23xpOcaytE5VX4RjWGegHiU/xHakrlVqJ8Uj+XprIfiq9P9z6qw1tyjDbsqJ/h0S81v8RmoZC/eb8YyFlWMygNx4bFRuPZFRWZ7chIMF7O9t3BkjuvtjtY1bcryGtfmeNkD1+pLw+DGGX/MR55W516AuIlvYb9Y+/cKq8KFK6b2dwnZrt8f8eO/MuI/3V3Zc/wDD9sdm3I9H5iBKO6r1s7Qcm/6WOmn/bKkwJ0cuvRpT4xmUwZb6unKQT3+afQZk5NpJ9kvdm9tXGalyowB7LEfik4dqbhzgozyewJJSu4ND0NsdJ2bymQy4OCn7WNzTYh7p2+Q8L2xfvPvnizXsU8HHSLD8IIlqhJDhQwleYn0D6w9Y2QH+ms5jt7rwA3r5g3tHIdx38iE/HPOBF9TLDwiqy19HgqvEAt9+wcoPMLIT+AYrH4xRPqRh5MbZ4djPM4F04kQu2biYOfSw2Lmwsxm39b9w/utCZhDs/Bn72eUD/XwCDzuQvDAuMsz+cAAurx9wDzsKrp9wm2/c8HbpXJ/U14n/pG06surlrJNPwDqgLfJDYbj/Jk6xLbmcPLQG19ao8SdL03+zn9NXX53NcnI8iGVO/j7jfVj5Iei7W+D3kv1GZh7iAB+kHFLlQsY1YTmHNHVDfc3JNebZ0E9i+wIrx2cv2yAw1Y/LebNQbqv1V8rJPmbMKe/exZZzuYsX6KnOLXBtyf6Jvh5jh26p37k4wJEC2J1T+/c2T2LUF9VExgZe7Ofm5tuxvbM+ZQub8mshyFbzt7AlvW6hvGg7XLeFL63dpp/wTa7HoOycmtjs3CsSe2qMJvdxg0F/ryYUfWoOqXJ0U5VV5cahN4/Bpdmnz2iXKXtX6dfga6gmGBvWPE7wIZNcc71OxXH1c/Cn2T5zHYLeXj2o+ba0HENaQ2cLVWTMO8qCoTzmtYzj2lFnRy58GT5Ga+J13sPYsPK1E2uC72d42SgBthVce4m1+T60KieEeZav0N3rTwa1kFPmfgdBTu0jauFMjUk12cnzgo+T941OnrEcXZ99CP9CtU9DuMdzxPrrdM8Rn3Lk5P9SzJmUpJf8L2WqHsM1Dl+a/RCuh2oi1cOm54iJ/V1vwLk7LkBm8bkwdEpjJ+Aqtc82UOUOom25BkR9J3mCe5r1ciIcP5iq6aOWjm057qwQ+po5hOuh2qde3LPZ8bCIe/G6SLG3ckNtn6Xl6NoaOjPO2ladpx3lkDtq31Kzmc8fdeYTC2yzTolltHYgf1evI+kvmDbfM4dMs39R2gQ6wnOlgF1l7JHaO8cSsJ1viW57Y0SXOXyU+j9VrhJA1c8eI1wPjzulD7j/Lj8rUcawxf0L86EaEvS2+pJI/amyS8sxNlVnlUO6kMeZkBwYLjF2qrZ7vp1dh3+hmmZO8B7GhXXz76vSXwRdHQ9xXepzM7ievixX2Z60I3R1x4SkRxkPD9C3RK5VXJ88neOZVWPXZAlbq8xXoDdUP2OKuP8exsTanEHKS8aMOHu5Hs4hQecRN2QX7QeOip92JvnAptq3RDgqNR5lKdsfxV0e5r5gOKe0DWRCtcM2xMr3MNmfcx3GodIJ788jAJar9I/wRs0tNWe7cjNi6epMVFW5QRx+9Pq8Y2MFZZt92VFpZwc2Q/U3Vof7NzN2wZdo/ip5GWrvzAe+SO3TkZtlO/uA7eSYVFyP7jb1IRY51wXDcuywq4yHR5Md5gdcD9UE9WHd+pi0eK4j5m57QybUNsdGOt/Jcws5L5IKJe5za50zbHOIVF9T8vZI7JDtsswuCbZlRhEfs/3WFvpCtZN14T7WD99L4EodJwvOkff3WCn3S3GR31Xj+bMFcvx/F9uI9w4Lz2GH9foyneKGx5T1tTvmUrSnd29PYGquoPZLqtwQJepWeo2tylEpZNVxa4nxJY9tSqu1ZKeYZ52SnyKjSPtIsrAbGjcgfw9zLrJXuEuMckMi9u5cATJq/ma1U9ucayH/xJin7HXPsd0hVJ13ReJWOJYOdWzLjCI+lvZr+9AXqp2sB/ctPueibuj1vOsJ8kPMK3M+bWx7k36XDJD/3f45IjfiWhvju/0P6zLpiny2WeHImKU52CiW8WEeb4bz0Nkcw4LxdPlkZ6B3lf4067+z7VS+RVgukRdEdpIbDYaq3Bo6l7J9xjyY6w08w6XST6m+S4XwpToHm1E7n+Ke77HysyTsl45radP7FxNQ2lmua3qDtlp0nFP1TZA4qxfIdGOBvUceD4mxy4hC4LS78RAxLTUuEREZNecqg5D2p+ybW3csLUdbS+tU9bXiHF8b61T6tbGO6nGgHdeqnbsZD8Gq2/9DJlRnkK/OLcpGU+QU/5JOKYegb26NT41PZTgHJZ6TG/SDrm1FVYDlWN1s+7AZHnd4D1b+D5Hvbfl38satsc6x2sZVObTV4n1JJdTx+DEWm/QR/sm1H5Glcch3+zzINPng+py57Dj2s2PolftvyMqMzgxNnIC+OfXPus/va9/DbwpPRD55aiovpTkItYGJ3I6T1l+d7NVPllxajnqvrfOEORguXWNlPNIcJMOFL80+A9ejtXMP806VkSo34OyxzMxb22huQF7uKyEr1y5km+NEiiHEpxV3vhbxkfdAvpm/EJH6NuiJ5jltLzJH/HMO3tsnAqkxug94SHJManY6v2F9Dxr48AUu1YcVQI66KZ9lhxsaf/jjPvwnLJPtj4ZcfjrQ71kG9zCxVoulsMMnq7zEmn+wUfVTlRtMpXiWZn7yQIAUE78QwIHyb+k45Ge657iB32M++dpPuFbafwsX2PmR5QHbD7Dmh0/wmO35O7bMuS+xz386TH5wlPffeoFvl+T6mfsVfRe1zZmRpxOyTvjEtvp/WNlWw4t27LNWf8TKpWzfpzPnf+fWuOqnKncIxhPNX/5wJXOYtcX1npepdi37DZn5QhDKHGqpVOVaOprXgjnU1FVcjOYan2z5A3zhQ5H4FHeu3bGwsOfdlQigPSbHhQXypsxttf5UuYHGTB8/xs1T/cXFhOFPbW4xZa/sn2g7FHvF2ZJ5ReTi09Hav6t5EumgHZesiVq+LdHeZ40J38k7PC9PcZ/lb9In9dWqbcgtMU87iT3iJ25U6jHrV2SjNXEvc69u7EHumWmtJg6qPshJOaTK0TFVVpXLwV64nerTu+0yZRN+X6Nfy6ZDNYGb+E8Wvpbmyvdj2D9yjNz6MtU+UZ+r9UBF4LForqv6VrAdGfNkWcSjjnmyzmgDivLhmoDeNxDfd1j5HhPfx/i3aMtiVyag5qEqB/fn5muzP5nCwhzDefYz+X3jKbHDlBzOSf3TlELcOzkmTcmq56Z8xL1zWapme3Kh2kcMniNOz9MPYMP+vvuaBHJSXqpybGBVVpXrJY14fWoO4jmiCM9idQLIY2lcSBqm8rCuvLgCO9IcLskptS/1EXQhYFvtT6RYivDzbnjczje2tohPGWOrtnG/FHfNB9w/lUN7HQ+nMMyui0LZxe2jtqMqR99UWVUOKtV5mipHH9V6lHUW7dLblXUGGIVqBw7yg6v39DqymutTsMFtqn+ZEq2dmztXmrSb8k0Zo2b3qwvEfMIC+pQx4nhP0L7a/3XlIn5WfIzWThkz/4/N12VerkOgmw+CG9W+BPkh158qu7Qc4xN1quOMKjeghW1l7AzpFNosKhKt6V2Phwleq3ZqNXFROyJXLh0PlVyL5IYcj1hjU7avyrJo27Ev48+TjK8fau0DwWj9HHVD5+bHRPg4ObfBeeZbd552DLbYmWKJc/J4Uqg67k7pPF582qnl2kjs5LDVDwyCsDvJ50TL6cGJTtwvc0yy3c+nQE5mKdqX+4LTUJ+OYGOyb8PVaO3w88jkxc+Kk/vwugxbL8sRYH6Ol1n9o5hbgy01Z1W5FIAUi6pTlRvD4zHurdXAmbggO6cvO7ODE9H6O+qAj1sdu7ptDt+lPhdycj96BPO0o7ZPVe4C2wfcGx2TRu6fHkb1QV7O9VNLT0e4X+IOObZjdzwc2agyT3LRmtj0mJQYdedpKvMRy+EQ9561d6Bt5LlFxMdkvxv3VDzCuWYOBWI/M4V7z1iOhHq216ydkStnh9HaOSBezi2+wZaf0foB61Sb5XP8MeP8YAq+D8HvGPKe8cKcejdd448Zsp/g8hzrON94zBr2NUAolnvjUrju3VsRQK2xVs++F47zar8kyXXiO3mN3ZA9k0t9RXdOkeRyv1QzMe5rSjn2N1x+f9qc9Uvp9LAZy5bXDvBlkjmFRD9P9I0OThhBn9w+AdnouLHpOVeEe4DRqFmmX1Om9u7lr5yXEf+S7V5NnMUROFGd+4hxT5rCvb05F+9r2ZZq4hIfJx1/OhmtnQP8WGPORW+YV553PbXLvc2f5s5/n6LdyN9UY90+CHJSzU6FhXuV/uKwpBx0tcb4SCzd98cYM+xJ75FN8UnnynmDPN4UtntjWDbdjQexRPis1Z9mf+9iW8u3IMupWMu84HU1N1S5NXSuYfuMTY15IdjLddlP2Jpb39V5EPyM1g7n8XxoKH/ckXOSvNKGlwUIqO18SV3j3quPh0QDu5NjYjCWXk0NrQCdc+slt2LZ78l1muKk7cXGWuq29AAAIABJREFUw6RTHROjNc12UV5fZC5b2ZbtI/uU8kJpG7XNl5ZjLEvrVPXJHAM+DjoXqMcT3wLteIDsWrVzl+MheEj9fwLeqrPW3KJsL1Uu58qkf6nNldeKkf736Cf0T45PR4FXO6F4Xt1W3wvYriuZuKK29QL2Q+MO7Pl38ibaa81TahurcvQVspO1Womj7EsuGpNqPuK8XPsR2SKeUO13+JDHeOFc7BnW/BvA4+vR45L5cO/MuHt2o/XPdrqb3xTuBZ+vg+3kGILz6hwkqxpvx+2o1s/ScvTrljrHXA415klQqTE1Htpi3nbnICMne31GqHage9PzTpWRKhdkORJvHnZzI/movF5sGRrX7pks7JyNozP5nOkWT7R8bOYv/FT7tlCeQ+9ic8TXRAgPIQaw7ED44bypAhgz4Af3+EPzxwX3fYf1DZz4FSvfEGbyHhdcYyf5HFs+nOJkwTl+GYTX+NCBqWXwC9d5jROh8ZLPDb5DbpVYoPdNGsb2l5EDP+GYMb+La+TAy9kn7ucln+OHq14qcvlGbBdjXth+Wegf75LhoZDNvpdy+Vzm3uWDm4e8gN4xw7/j2uel8tE+438nn8P9/EF1PnSCDyRRcjbfuvoW/lyU62MHa/pwPppDY9Vnx1GdlIcSDgbHBefYVlyO7YJzS9e4FPuK8YTyF35Qnh925pOq7nIpWDb7DcixNhlj7h/KePO5Y26UF1v70NnNId6vyrVsXXIN9qWaUG1AXyjXoJdjLO/J/TJrJX8AVTVruYUJoA2q4wJN4Xo3byDTrQHIcH5BlbnWuJ+XfG7OHOQAvV0fs6G0ZX8XrvWRDtrtzi0gk+de9LG2zJnXdJnXjF16HjFFa/9u5klkg/gurokR48l8gx1pvjDSpRxK83LYV/KXbf0Msmq9SLYZBOPHpjtPo2xvgS7p9RVtYqW6SD0qsqGagA+U3+zcS+UEOYk7gY+WWk2E9NFP6O3mkCpHH1VZVW4Ud/UQ+rp9OmTyONrNybEh3HuVfi3bhb1QTeA+PrWVP3aev3zJvoTn3pzQlc1cbQsfuu1zgTOT9VDqg/1Fc13VRx9U2Z4cr2Olymf8M1ryufI1AkXy+VI8n8vjkjTuROyXxpbah/1oTYzff+ITxf9Yyh/rWZyAlIewKsldkK/N/gR6u3M/+MjXLpIcKdJXbLpjMWXzgnuaY1KWa21VH+kfVqrKfUepNp/L/Ul5bZF92A7VfpL3HHFEH1w8R9T+L8V6rC1keLaAbbMecT1a471+KFQTcHjTc8QzoHd2Au0r9feQW2Mu3B0TYZf50n0/AnKhPgI6u7Yhk/9PqNSArG+UIs16GclKh2DRrOlCSdM29ChxHyCn5lCo9qGX8psdD8kRPq5RF7mJlmoftR0luRS3JAs+XTnKYKXaZ/wzWvK56P8KpHpUbY98ah5GdVIeCpvzaMiEagf67u11ZDXXEbvUvzQbJV0s2obMa8swV1LtQi409tAHGO6192IxTwUJH5pjRCB2qf+DPklu7GvLz4CP0doZ3ID+d7Gz2uvDcayPdDw3H0RG1b6E98N2t/6yHVV2aTnFT9rEStFn/DNa8rnouEk13bETdvP/ubOd0nw+t1rtwH60pvc0Hs7pSydrQs0hNi5kpTEJcpHxsJtrMH3yOd4y0cb7kXh4L+WxaY7FYxs4vibLXOP0s7aE5itUgrij9TPYxn2bHxPh4+TcBuflvISslOuJpZRDEZ0D7Kc/k7mW7M7pBw7wY5KPqhP3yxxTHHKNQ3eXpWqfurDShWfJj3KTzw1jFOQi7T2ndt6BjfF9pT/en0GgaGPmTW2R+8fURs+wlecu9AGGu2NIT47XsTKGbiwU4tLT+SSlyUFXpAZk2ewDttW+rJDp7sLPcR31vrcx6MR9mxu72H5Y6V+zzSET6nOpFzq7OUnDxaK2T1Nujm3cUx2TCv/k3Z4+XJ+Tv137YuzyeFgY7DGfUxObHJPAcPFcD7S31DZsZ6xsnmdFG+XdfO44hlAeF5v1CJlQ3NlYYNvMIehRY59TOz3bB4WR6mOACe2Gagfy5PRTvo9brGffKYUMxxu+T8KHUigLv7PEPOHyFdb/pu0f2D7HWi48pqyvlVSeON0Tl1PvfXR1Aqi55twj1WSz76bTATnpdTv0SXIJWLfvhj72c93XNowDK9U+45/Rks/l182ybKkH+qvMcU0eByErM4Is+4VuO9JPRRYyoXEjxb/JOVeKWeYeYKTOFZT8Df3PQWzDUMypDaOb1tynGzeMMW6V49i3lu2DwggKJR/HhlvHsBuqHcjThzXmXHTT865XjfUo88pXEd94D7kd6oOUmoWM1F8sLVeihO7qGJ/lerHwOlaKc+yuLeR3gJzMEbLdeQNk8nfv8pyntJ/PHV/j42K3n4TOPIZ140kxUa47Z4HetfrTMuZN74NBM99wvcsSMt28yO0CWe7mPOB+XvK50Gcv6N+SOlV9dDoim4NM91WZFzrJvbbwt5Ok32qBnFzfE8aq8yDoDdUOdLNd/1TawPELrCd1Wl73vk4AHEPtDHmlrm8+HpIAfK3WS7rejIWxYqVos6aSLpkjdHb7PcjcfDxMcTUZJZlQTSM29fUF1V99Udon6FR3rgJ9nKvkfHs2oT+fk8c5VR9tqbJLy03EWT2l2k7xyPVYNXh+QWrHfBv9xf7JOIVz1MElv6cXqh3eBx2bHg/hn9r/d/vBgdTpn+rc4lSs/vmHgH+RHArlBn2FH83xSY1nJCcdBm1XdaosxwqWsA8d0drx7+SNG2LFY7WNW3K4tlhfAl3ROdWRTstHCEVqPyKb7Vf7vACfPLfgmFRb2N/JC2xH+u85cTd9gf1o/dOHu/hN4WbgxcVOXh5wXZmDSO1IXVhpPc9FC0+O5+5ifkrH1XjKINN9k+N2oa9bY4Vsj2VkDlK6Wu0zUgzR2tnsvBMsJUaqXAkx7TdZTsifnSrau5sbuFnuK6FXrd3uOApdzIln2Jbvs5/FEj2h+jjS22UOvWS59OurxeaIr40CevRDFunbaDQ+ObhcmJh8Y5rnmXifY2USnhUKzrET4hfUnmM9LjjHZHkD2w/ySewPkxlsqfNvWP/I14rtoAcyuTPkjyMO9xUy3M328o8nrhULn/x1gD9/wXoWP6+lRfVTkoOtZ9C7NPOa7RxD2cnUZMfcVT7ZxrBFfO8yPqzHLzemmA/YclLD9uT10iccHtgGb06c57WbLPB1qVwf/Bf0qW0T4XGpTrZJ+UES2l66xqlT9VOVo86pZSqeoxzaqJm/R8F97NRY5uhyjdbkxn1Gvk/Zqjmkyik2l5Jp5pBqRMw1Tjr5MJ4vsX6KlS+Iok/EU12ynEAAbdAbF2paxnmj5rZaf6pczT+eH/s4yCJmjtkcu/P8bTg/8486t6jFk83m/onHNdlxH6UyzzZW2YJnc5zB9buZJxEQ/F2qJgbe0NfLN7W9pfZL9tR5uZK/0usW2GWfzlhV27V4Juu2Jlycl/3EPTXmWZ1Sj1OywzlwaNZEvvEOtgqnCPfMp1UTYX0THNUcUuVoQpVV5Sbcvvj1SNZZ5u9wDjl57X4t+5LtKzXBN+Z+OrlxWwerjLmp32Tez5mTqPm2tBxbZq7OWr/yPDU3r+elKztj3OnqzMbX3CrjBGTGOcE65pv9XjZGQM1DVa4IL5SvSX+vP1HmfnRBlSvcPdmt9hHwc+6YdGIg6GOI5djQUseIXRkPlzK3pp4az2yTc5HwnK6Tw2F92ZliW83LQoa7qlxENqJz5I7niACy5TniuL3u7Vjt7xedC6d6V947kGof0Pl+c/d/x7C7+PsWgVhOcqPT553IqgfQKY2xF9ie6svUHDqGAft7GQ8XrYsMaOH2yWrL7VQ7ltfzvipHeVV2Sq42r3ieHOF1Ll25xE7pW540CjqzYGDb9bOja4rRcItSO5C5m9eRQq6H+5cO21rb5Nvy+2mqXWmMQpyfZgMT23F7q7YnVLVPwQ9ljFDtq/2fKnd0XvBT9bHUKY07KSfZJvzhNy/LEwjng+JCajfW47j/690+rr+WvCq7tBx9Guus9WXPUwC8zkWSS/zUsVPS+WR+vb/wuVvTkBnnA/vATb6vKuRwqHYEfWo7qv2tNB6Cf/hzvGIWqfHU1I1r7Ch3A5a0XYsn+xWdr+T7hi1i6tYPBVPsZLPZMRE+sq4nP+eN81JeQgfnaWquQ3RymcqhkM7EuzWWhfoBetnig2vMo65OyDFfbvJeC2PAEmnHWu2Mx8dQ2zy5MfCUaofyiRs/CzH+XHJW5+08ArU2ztoi/WMkt7L+qe1U/StyaixTuvK5ubYjNRCRZe63PgOU/Q5vi5qa/N5GVpjsk8sWxy6lzZfIy2peqO2jymXuxbZluzpmw16u3UJVexf3KPpC+du22L16jD3xU19fDYqjzCF/72PSGrnebe8ZbVOr2+cpI3i9tRzzIgktEfekvV4OBWPvsiyd6NkuZSf2j4yCPk6o6p+CDaV2+F2WDyDL9sr+1dr6x77Vo8R/sPeX41H6UTnYeYl13A/ye67Dubwt7vM1wLgXLkW7effKBJAjylxhyqtc9y+nLhbnpuS6r7HT/ZIcYuDcWplTRMaXyNgWkWVd9phH/JQYFe0x3p1qn7FMPq7KIiZl3Bj0FLJbex8gwj0zGW/HjLpzBfBQ85e2Qrk2dg7HY/+WiHnCzNOpFBttjP//cAjG3eU4dqJleyw7Oj4yCvo4UqMdwoZSO2vNueik512vmuph5o6vQr753hJ90LFmUzRqf7G03GAeNd0b41vQx7HU+vysI782inBU5w0128+TcV4/BPvJms5xPPl4vB3zObm+Qn96on+LBxfk25ilmhfEUGvHk9wIyK2hU/UxYpuyzHmlxmv2Bx34k2u3JleyZNtI/3fMyrmFn/L/HiCrzEVOPjeCe3jc+mxf6Y73+wQi/XhN27iulx7nVH1H/5AnSr0c5YudcSy1Wsm35JqKcFT7vZrtsk4PiHWJ13TjePLx1HbM6CgDX5Sajry+OOq+4o7aPl2Xgm1DfVKbryB3a9u0rywqn0g9du3OaMeazktr5x7GQ7W/DtVZagO269n7OyVsQU71T8oh2A5/thI+yuOTEE8Zfnc/YrurbMZn9xa2P7gIncq449/JExp0CRG1jQU5tVbVvkQdP44YWj5C6A+syv+DDtATmacN9tM9rT5P5UN9tdgHW/iT57L5uLeVmM+Ju2d4fB02mvWP62RI/uMYX+Icx+TxeZza9oKY5DFkFMl4DiK1Y9JRy6HnxXXuLi13a51DeALzWtzD/fhT5llNtmTJtgm9DwMfmeetPiP7Mmwh36ydJLzleac6T5N/tyADirLM91W2tfbO4vx/UHSMUGtXGSckjvAx+v6b6uPA4ULm474tsz1Ar5Lni80RXzta9g7hM/m5niw4/1+c4IczyodF8EN4fAhF2Vnm+1ggRz2QYYOzgxwn5fs4nz+A/tXEdepjQhx1YZ8PvTjp6HDM5S2sv0AHJwsHbFeJBaqpf+qDKiwgLtlXyU/IS3KMK61LMucPkNP+eCFL2sux8LrkJ+/D2uUD3cyRQWeywx+/pM0ynz7Dcc4Zyk8tnNznwXjq+lXPwd8lc/0g6lPbJsJC0gn/WMNfY/1/2Gfb02e2FeuWeVQui9Z4Uiz5CVlJTo0nxTjoxD7rpJe/JYd731f7DYl5EIaaQ6pc0HxfXM2hvqYniTm5hnv4oAkq+ALbT7AdHjzBE16uTwBt0B0XIKP2pWpuq/Wnyh0CPmbIeV7EcfrSheNLd24BGbV/oj9q7Cpz6lxsAW+OpYOP2FfGGcpPLZuaJ9FBxLNkTeSYe/mmtnfW19wihsi8vJu/1AeD5bx7sI/ztddgtN99TQAZtW9pxpsvQh99lPyEXKQeu7KwHa2J7PbWt93YUwAq9xxvtSYi7ajmkCpH51RZVS4HLG7VPl1tl8EsfL16vwab4ZrAPfm9l4yLr2H4Bucv+cSNt2r7RN2s1kNWBAZSf7m0HO2voDMy5kmy8FEadxJPSWdmv9QWPoZrItvGvXzN9A+sL7A/rpMs5u0NCaQc7OahKleEEs3Xbn8C3cO8jr4Udrib781juiQHPVL/lG1BvjsmZVlhK/mY9ERZCub7Ioj3GaQG29gn2728P6fORXI+HWGBw9lriOPFV3l49jo98ZP0QVbKS1WO/qmyqlwRs7KrzkHUdhlswtduPc6IJ/clZ21Io9AXrgncMx77tjZHVNpwyzJqX6rmoRQr2lV63wJy/H+cVPuqnGqbgUC2259E9FFnsTTrpZCTduFHt6YLRU3bStyFrm4OQV+49gv9W95dtC6KQBdpH7UdVTn6p8qqcilmdZ4mycF2d15esJZ0FvLKrqRTYQSZ2bWDe+/hdWQz1wG7278oDVLIqHMlyS4Yc3ySxiilvZOfku0iJmkX9tUxQrWv9n+q3BCH6GfXR+h5BoVDLWKfbaS+DvsI8vyfNe/3sjyBUD4EzDf7ErTn+9AlfV5IlV1ajrGqOiEqjTOqHOxK83L6iEW1/SS90F/4OLemyXUP42G0dpo1EWjHbn/LJgbjyHgYmaepGSTlJfyU+4LC8FVZJrtLz1fm1s+mx0S0Z3Nug+uR9xLUXI/kkKQzkGuhfqDHJ9nt6oSeaH1LNQ69EsuIfcQk9QWQk9oGtufWzmewwc+S873Rr6HnG6zHH8nHOS/zCSzWP6JNhjwYu4Lzk/+7wHk1ZyU52FVjOaxgW6qBxCYiy1v+lu6b/N9AutbdIOa59bflsUtt86XfYyh5q+3TlFNzMhuGfHPMznLqNqAvmr9dF5TYIRN5fZVt9pjPrYlNjklgFJlfvA9Iyuv5bnvPaBtpbqHkBRs6EndOjMC2l0ORvOyyHPnVtE1ZhRFkIj6OXJg+hM5Q7SR53vMe1m+wMlf5HZefsY7/V83XG3/FerZA9n2s4/nfhzwP4edY38D6TnEjH3DB9y6ok9eP34Xlvq/dNRc0oZdrE0DNdOceqR6744sql2LsvsaOyMG21C9CLvL+hzS2JT9lWfigMJfHf9iXWEbaR5GFTGjcSJy42eSci44hJpm7wog6sXTnCtAl5e+TOu39HNW/SMzJfnRTnfsE4+5ynHCsapuyCqOgjxMunJ+CzlDtJHnes8aciw563vWY88rz5LzBGeT3TfrdFKrar6hyB8TTHeNpG3J8rdOdW0FGen8M+mSO0CnNGyAnzW1gOzKGqfFIfGB7zf4UCLa9IP5uvkFGYolI1bwgFCk3AnJr6FR9jNg+KMypEIuU65BT/IzU92A8/anOgxBHqHaoD/fwddSwYJ959T227B+9LEAALOV2TvyVMUQdv5aWG4jAzyX7KKmmIhzhpNrvKXV6gO3Fx0OChN5uPw6ZUE0ned6jvL6gG7dY1Pbp+oZ4I21DfVKbryB3a9u0rywSH3CX+zXFaLQdIb947dBP6L2H8VDt16N1Vp1bjNqwJyf5B9ZyDkGWdd79bZ7Uht3xKRjPSLx+CB+jtuvKnq5ILLOSpexDD8eQoS/APtup+10DyPl38nJDrLhV21iUU/NL7Uuk8SPj6fmI6/L4HpHN9rFdpC9L+qS5bGG7tysxnxl30zZ0Ruuf8lMLPyP3fOrCls8h/m4/DpnuHCTFKLVjklXrZ2k5mr+lzoPCHD5GakyJR56DpPbhptlnII5o7TD2zc474VuEEWVPFtw/+XnjJNRkeaKofyDlBvyR55IwqdZudxylXeiL8ulHrfuYdXWZw9du3waZOXm+2Bzxzzkab5sE2Ehcy4UfuPs2NeDxPI75pFK+ATx0RtjyCSnsRJ9hnz/edlxx7mMcM6G5DOefdp/+4ho/4Mfl+OE+nOOHCv/Alsk1LNinb3/H+uHTmebf2bEkrfzSyvelheQL9R7jUf1U5ZK9RZnDNj9wyR9wPj7AA/uTLAN+Snxglw8k4Mq2pM2TL0LgHK/9iLW3cGLI+2++wOelc13SF2ibMaP8YdyzyXVAJ308aTscs95ZC7+MDC5e46qfqhz8VeNZKn9HiDZz2MoNqd8IMC+DrtpNQlIOQVaVi9hWZdUcKvVxvxZ7ONfAfnjxCZ1vYWV7fYJznNx6WYdAre0O4C7143BLzRspt2FXmiupcgmb6mOmnMfml/lEZ1vliPukuQXikfon+hGIXWI+EVsrnlK8Jheu/VJpsb+ZeRJ9AvelayKH2sy3QHtnfdzW2ibLSPNyCEv5m5WOtowrx1ZeUm1H6zbb6MWe5fL2zE8wj9SjIrtUTWSfN7GNcJpw+Ix7IZPz5mVxrrc7pU/NIVWOPqiyqtw4rlb+Sn16pF0gSz+V9zui8fTa8KKagN+cL/I9lbfGAG94LLXPyL9We2fRHkvKqe2ztNzittG20jyQhgOy6rgT0UkX8qK0I2VbcrNrAhy+hG5+4fg97Of3IWnPy3IEWm1XWmnJqXmoys3JV6U/Ued+qpza7zAeyipjkspc9XEOS/rQau/Sx5bs7NofG9jSMdpSmR/XXJ6a02VZJYezbN5O6VPzUpWjLVVWlcv+520r36Q5SKRdAvUYjafXhhfVBPze4hwxt+G9btW+VMrDEYRWXlNUHhNHenk4VfsTYlU51bZaA6q+0sdevZSyTZaBms46e7bVuKlPyaGLaj87vcHtGnXBMJdqH7UdVTn6psqqcgfkr/QaUZWDj3I9BnQy9rz06lGKB8oURrNrB7Hdw+vIXq4r/Utul7yttg+YqHPYOXazfW4ZV44tn1fam7Jzbbfipm31dZhqX+3/VLkD2kf1U/ExXDuwz/chmSNe1iMg50PhQjW3C5lcby+Lc+WuWn+8R5VdWk62jVyVxhlVLoGSxs6gzqR62CjtSMGaXLims3H4vIfxMFo7zZoItKPS32bUU1v6kX3J16Vcy8LFtpYbh0A8at0WZo/+T/YvAdsyS+hcer4Srh/4sOkxEf6xLdW5Tdme3J/KS7V9Ijmk6sz+5VqZzDUIyf1AgI+sMztZbKc48rJa4xGWhdnj7pl9xC2Nj9Cgts2c2uFn3PmjwL9hZVt+jpW56mUBAmC6dP845dVZbiUhNWcluUAsNC/pDMipNUDbEVnKkx8X5r+y1Mb3OfW39bFLzd8pblN5qeZFqU9tn56cbBu5TtnomF3Li0NQXzR/yapqO4FUY1fHw6S2WztzauIex6RLcl1tb7ltkG/q3ELNi9ze4+1U3KVMLy8p26tbyqixqyypk4tiW2Wk+vhk+dXfGqNo7fBz7Fx+Rfv/gvUl9smD82bGUC78XiP1HxfIDN9DxYnxd9MOuPZdWocvbGP/KIN9zh35xWPK8Hr5ZXtfu2Mux+TwztIEajV/QP2wVpW5h9ovqXKMUX2NrcpR59x+kfeejS/sY3Be+p67KhtgTp+mljM/IaQyirSPIhsdNw6I/x7nXGyHKe4KI96rzhWk/FVzDXZV/+jj1DIVcylX7VtKIexTD5eXT5uzv1LcuEvlWBro2VYZqT6WtrlfYxStndXmXHQSOeV51x3Pn9B+s+a/bPuNL1N9kFqzan+xqBzagv4p8yqil2JhfUJW+p0YKp1YpjhK8wbYludBsCv1k4F4JD6wu2Z/OoHz6qdq48gBLNV8U1lKeUECsC3lhiq3hs6VbKvMyUiq3YifE9k3Vd+lWGseFK2do174TL38naGzH8Q7CnlnSQJT7azW9aLjHIJS9R2QH2q9SLFAn1RTDfBTHKV+D7alPi/ZXno8pFqFUbSmI68vGlhXvSS1z8iD6rgJOaltqE9t86Xlbm2b9oulylKNu9A13p2qx1KmahtCcjtCdo3aOfoJDlseD9X+OlpnjJnLy6dN9W9PTvWvZoD6s40sI+UG2k0dn7JebrOtl+XJyn41f2fappmqTlyTWc60X7MdHXcOsM/vtL6N9S2sHNf9O3mAsOSitrEqB9/U/JL6EtiV51QBH6XaT5wjsrylV/sqnwPimTOXrdUffZOYUxBLNG7e07Idrn8qnFg4H82MJy7f7FQ19kBeKnMQBii3I2xL9bO0HJ28sU5p3IaPco2p8TD2iYU5W8vbfP7lxH08Nbt24DN138v7MPQ1s2DctaUll+9/Wbu5OF+tWcoEciPSV6q1K48TRTx5t8Uny7RiV33MuhTmSt8WznO00WJzxD/985//pAN8QMKfcmTePhEAE/5ANRuRjLiw4/wR5/mlwQO2bIjPsJY/OM+HUBzfAMb+r7hOHVMLPzD4Vr6AfcqxCLhw0KfeT3H+pLBxzOTjhwl5/nesb2P9HOePHxDE8cmCaxfHkhVCF3mwA8gL/f4C549x8wKOJT9VuaRzUeZJJ1nSVy7kPslS9RNyXT6FLubHAcf8MCe/mMCn3P6MlR+2Yr4NC/bJmLJ/wT7bfViw/z/s8MtER9l06eob+LBorgf1SblGKNCbv2zFduJ9rBt+gJb9ICePw4J9SSfk8gNLKM/lpA94OvX0F7KL13jAz8XiKWxK+TtiwDxnf/FGeX4L+/BJyg36CtluvwEZlXnErppDqlzEtiSb2BCTUhNNnQVDOddwz89Yy7GVtU477+B8dZykw150AmDZbDtqgkxkXJD6UuhUc1utP0kuxSP5mGTpJ8fzD+FzdYzGtS7HpK87t6AcF+js9k9JTood+iTmSacaT1MONrNvUu0nHym72XlS4rN4TSS93XwrmL7EPdXXD5Brtg3t5QWy3Xk5ZSEn52+Sb75uSTKq7UjdyrEH/JTqMemryoJhqCaoLy+4d7Nzr8LHauxZJm8Rj5If3ZpQ9cGelEOqHO2qsqpc0inlL3RG+vRuu0DfTfo12L2kJsiAecTX0ewTN7Oo7QM5qb0ZWNKpzEkWzXXYlfQlHyVZVSfkcn6wfatjXrItyUKnNO4EdUrtCNtduSJmae5EP8dLipG58hb2/bppDGjGsdJ2VBuQk/IQ+iS5ZFuqgSQrja+wL839AnJqHxEZk7p1lWKWYomwVNs76Wz6CV25/cK1j3uymbLxAAAgAElEQVQ9RyTkygI+zTknrqt5KcnRjZV0NnMohw/bniM+MdjkHDG3071ukV9SX6rmIeSkvCYvyMpjYpJv1n5uA+jtyqm2ISf1E6q+wsfuuA2dEkvIyWNs4qjYluJO+po5BP92Ox4iNql/Vtty6faBXakdVbnk3xo6c468hI3qa0T4qcrJfUtAp1SPiZHqZ5Nl4Vt4Lkk/uEAHWWzydSR8U/qiZv8yBPkUZ6R9yJ1txOU51rPPncA3ye6gIf3BPc2xB9eb7Z11RWxDths3ZKJjhBQ79Kr9nyon+9ljhOu5BqXaSbG8i+3wOZR0/3+x9efzcmIutE2slc/bdXM7u5R0sp+r/r8XMlL9Uacqu7Rc0HbO8Ze47+JxM9mWxk7ELdlOOqV2hM6mXGFTqmnaHi/Qce/jodSXMm7EqoyvUjtClzQmlLxxT288lHItxdLMjWwXNtV45L4g2b8ZS8S0yHylYCPVD+QZ86bHRPgozxmKHOnlpZTrqV2oljnHpfX5U0knlSTuvbGMbaOMoTKfZLerkz5ygXyTY5KRahy6QvWo2IdOtS/otk2hS6qd5N/7uO/42bOk47+4xofJn3xmn/Je5hEAy0X6x9I6dCq5LeVs8o/qlX6iGwsVqToDct0aoF0u0BmR7Y6bSWdzfIfNXMtS/UF+82PXAPOJp9TmiVMzLxG3lJOFbbV9unKqbchFxqRmXiQmsr4kL+Uv/OzaLjhK3KFTGg+Tn03m0BWqiaTzbsYkxLdIrkOP2t6RtsnsX4Jr67W3lBc5j1Ib9eKO5GUzh7JdNS9VlikO1bbESPUx2W4ygq7cftJ4knTyO38nn8eCHp7jl96P319Lsp9gyy8+D/qx5QMnhu+v8roXEzCBZQmgvpo1T2uQkecKkFX7JUku2Wef2H2NDduSXNIpj1tJvje+5L6xObYlXV3ZCHPqzAvu6/kpMVLbkXZ7srie442MG3cz50oMetylfAerReddBftmXvbaMOdXucU9vZi7fctIX3fuA5tS3UJO4pjtQ16xrbah5CNtw26TEa7PqR3PuXLDertrAqiPXh+k1qzUX8DeYnLQJc+r2IiQl2IpZNl3cHmO9ezzOsOV9Ae6exzVeUPur5rjDc3CZqSfZOzNeBQ+kMn+ReYicn+acF59g7ia4wgdgoycb5CVcg1yUl4k+5l9MzegU5JbQ+fStqFPZs54uOAeJddlRklns74Hw0+2q/Oggo1cO4Xej7D/BnTk13H5krcLEgDfZjun3KJF5g+Xyf+/Q26xcY5GAvrkelFjSfa7NUW5vEB3j6PU70GPXKeQXXQ8ZCzQ2ezHC//kmsY99zAequ3THTcTx0jbSG1esH8JG63/h0j6kp+S7Eq2VZaSj4wnL/C3V4+q7Ug7Ll47RTybHg/BW+3/pTpj3NBZnVtkLqqc6t9Iby+HurkBu/L4lG0rcUOmm79R24rOxFttazn2nm1cz31AZNzx7+TlpFppq+aYKhfML6kvKXLnJfS3xs1IvnZrPyOH/Yhst8+DPqn+CvvduSx0dvuT1DYS8yQrxa3Yhkyo/iFPP9meW/+tvC53xBLJy+YchO3CJfHJr62f49QfWM9+jzvJZva9+llUbg3bqs4I86SzW2OqbcrlBX405yCUS21Z/Sw7rud2kcfOwv6m550p/i4jVa7HMunp1mzml+S7uQG7Ul+Z9El9MHRGx4kuR+iUYk8c1f6lO+YVHLnLfOZy8l4UbIbzHPdcPEeEDn7f4MPZD5yAAjb+11gJ4l84/hhbLyZgAisRSEV78oPpOMc3KvlPBz4wwYsJbJ4AcnXzP2i3eYh2sEoA+cU5CZ8gxof3HBccc1L7I7bHL18eL664A3ueK63I16pNoCSAeuOLG8+TSijeNwEQQG147uVMMIFEAPUwvDGJ7fD+VTo+YOvX086ShyKAnOeb0f/Bepw7pXrgP2HOvsy8JhzY9WumNQFbtwlUCKD2PEessPHpxyOQxkB+0OSmc0SPiY+Xe4749gQ8Ht6+DezB/RBAvWzmdeT9ULOnJjC8P8/3Pf5RsGAt8QOt/JE4/++6AONdE7gHAh4P76GV7ONWCaT3PTYzJm6Vk/0ygSkCqJ+TH7PAMf/nzf/pXf1z46mW/b2RqYbyud0R8Ni1uyZ1QAsQ2NKYtEA4VmECVyOA2smfxzo+LCzVkx8gdrVWsKFLCaS5kV8LXArS95uAQMBzLgGSRUxggoDnXBNQfMoETMAEZhBwfzoDmm8xgYIAaog/oMjfOTl5yGghsvoubPt7eqtTtoG9E/B4uPcWdnxrE9jCeLh2jNZvAksRQL34d/KWgmk9JnCHBNAH+Lfy7rDd7PJ2CHjeuZ22sCfLElhqjpjGmQ9fm+seFPyCe9/Cll9m+H6uHt9nAiYgE/gcknwiD2vvgNrj/nfY+scxCcSLCZjAwxNgf4j1OdZnWF8WQPgGG/vQqy7wwXOlqxK3sQcn4HnSgyeAwzcBEzCBFgHMy4Z/uEKGPybMD85x4Y8K56fODif8xwQegQBfK2HlU9zL95P4HhNfQ/3rmgzgh18zXRO4bZmACZiACZwQwDi0mTmix8STpvGBCZiACZjAxghgnNrM68iNobE7JtAkkOZ4w+d7KIhjzj/5wInPWVc8d80l+ePP+V0Tum3tigDrFusm3lfdFVgH8xAE0hi0mTHxIaA7yD0R4A/SlP/T4wOlb/K5cc8n95RWjqVHwGNXj5CvPyiBzYxJD8rfYd8vgS/g+gdYhwdOYIzhZxf5nZfjAyjuNzR7/igE/FrgUVracW6EgOdcG2kIu3F3BDznursms8MmYAIbJeD+dKMNY7fuhkD+zurNHPZr+Juht+F9EfB4uK/2dDTXJ3Dz8fD6IduiCcwjgLmbfydvHjrfZQJ7IeDfyttLSzqOWxHwvPNW5G13VQJLzxFnP3CCUcIZ/hgZl0180C358zq2N3vi7xMO/zWB5Qkgr7/E+gVXaP8d6xtYP1zekjWawPIEkLf88QT+oCvHDfbTQx5j++Xy1qzxwQnwA/nsK39NHP6KLX9Y+Oo/2kH7sLupuVJi4o0J7I4Aam3VeVKqZb/O2F3m7Dcg5KznXvttXkc2j8DPuO0ZVm6PC2qFr1G8mMAjEuDrps9QA3x/icvbWPmDg1d/3QSbfs00NIH/mMD6BFBvq80RUy37NdP6zWgLyxLY1BzRY+KyjWttJlAj4PGwRsbnTaBLYDOvI7ueWsAENkgA4w8fNPFeco3/y/4e63fXdhU2/T7MtaHb3t4IrDoephr1+yt7yxrHc0IAeb6JMfHEKR+YwLYJfAr38v/0+DnIA+qI49FNljRW0fYmvjdyEwg2+nAE1hi7Ui153vdw2XT3AW9qTLp7mg7gYQigz/8K6ydYy+8BvvUwABzobgik+Qvj8WuB3bSqA9kogdXmXKmO/Tpkow1vty4jgPz2nOsyhL57BQLud1eAapWrE3B/ujpiG9g/AT5E/qdbh5nGILrh1/C3bgzbv0sCa46HniPeZUrY6TiBTYyHcbd9hwncjAA/B+bfybsZfhs2gdsRwNxw1d/Ku11ktmwCVyOw+LzTr9mu1nY21Cew2Bzxtb6tpgS/DMunpF39x8gqXvHHA7l6MYFdEkCt8UNDXkzg7gggdzkxc/7eXcvdn8Mp17b0w8FbmyvdX6PaYxMQCaw8T/LrDLEdLLYNAp57baMd7MV2CKAm/rIdb+yJCdyeAGriF3jBdQuLXzNtoRXsw0MQWHmO6NdMD5FF+wpyg3NEj4n7SjFHs1ECHg832jB2a/MENvY6cvO87KAJjAmghr7COa63XjznvHUL2P5dE7jCeOj3V+46Q+y8QmBDY6LirmVM4OYEUDMv4cSWPnfr+eTNs8IOXJvASmOX533Xbkjbu5jABseki2OyAhO4FgHUz5fXsmU7JrAiAb8WWBGuVZtAJrDynMuvQzJob3dJwHOuXTbrvQflfvfeW/BB/Xd/+qAN77AXIYD6eWMRRZcr8Wv4yxlaw4MTWHE89BzxwXPrEcLf0Hj4CLgd4w4IoGb4m4z+nbwdtKVDMIE5BNAHbOmzoXNC8D0mcDMCK807/ZrtZi1qwyWBJeeIfy4Vz9h/F/f4qbYzwPkWEzABEzABEzCBhyDgudJDNLODNAETMAETMAETMAETMAETmEnAr5lmgvNtJmACJmACuyPgMXF3TeqATMAETMAETMAETGBzBDzn3FyT2CETMAETMAETMAETuCsCnk/eVXPZWRMwARMwARMwARMwARNYjIBfCyyG0opMwARMwARMwARMwARMwARMwARMYFUCfg2/Kl4rNwETMAETMAETMIFdE/BcctfN6+BMwARMwARMwAQejcBrasB4ysXrkP0CK5+I9jtWPmjiTayfYz0ukOOTWT5KJ97G9kOsvPcf6dyPkPku7XtjAiZgAiZgAiZgArsg4LnSLprRQZiACZiACZiACZiACZiACaxEwK+ZVgJrtSZgAiZgAndHwGPi3TWZHTYBEzABEzABEzCBuyPgOefdNZkdNgETMAETMAETMIFNEfB8clPNYWdMwARMwARMwARMwARM4GoE/FrgaqhtyARMwARMwARMwARMwARMwARMwAQuIuDX8Bfh880mYAImYAImYAIm8NAEPJd86OZ38CZgAiZgAiZgAg9C4M9KnJgY8qljP2P9FPtcv8Q+Hz7BhQ+eKJcveD3J/IgLX2N9l/dhy4dR5Puw68UETMAETMAETMAE7p8A5jmeK91/MzoCEzABEzABEzABEzABEzCBlQj4NdNKYK3WBEzABEzg7gh4TLy7JrPDJmACJmACJmACJnB3BDznvLsms8MmYAImYAImYAImsCkCnk9uqjnsjAmYgAmYgAmYgAmYgAlcjYBfC1wNtQ2ZgAmYgAmYgAmYgAmYgAmYgAmYwEUE1noND72vX+SYbzYBEzABEzABEzABE9g8gbXmkpsP3A6agAmYgAmYgAmYwIMReK0XLyaGfEjEt1j5oInfCnnu/4JzL/M57H+E/fKBErz2PtYPk8zz0fUD7snyv+PaX3HMB1N4MQETMAETMAETMIG7IIC5y9pzJer/O9aPYeutu4BiJ03ABEzABEzABEzABEzABEwgEVjzNVPS/VkylT/U+iHOH9+zdkOYgAmYgAmYwFYIrDwmchzkQ3H/wMr9t7F+Dpu/YOvFBEzABEzABEzABEzgQQisOeccI4Stn7H6/9djMD42ARMwARMwARMwgTsmsOZ8Err5vuXHWL9PiHj8B85/l469MQETMAETMAETMAETMAETuBGBNV8L5JBgg98j53fIubzE8VdPu/5rAiZgAiZgAiZgAiZgAiZgAiZgAiagElj5NTx/W47/w3uBtfyNuQPO+3sJaiNZzgRMwARMwARMwAQ2SmDluSTnjPwdYv5W3l/T9gucO5lXbhSN3TIBEzABEzABEzCB3RHoPnACEfODPM8wYRt/gIc/WjL+gP9Po4kdv1R6fCgFrn2A4+OCY04Mf8f2S57E9l2s32N97yg0sYPrfGOS9scLH2hxwHV+GWG80I8T+2MBH5vA3gmgBvhC7N9YuVWXD3Cf3/hXaVluNQLO39XQWvHlBNacK70J9/KcR+q7XSuXN6g1PC4B1I9fZzxu8zvyEQGPJyMgPnx4Aq6Jh08BA7iMwGqvmeAWP2hwfC84zed+xvk3Wi67plt0fM0E6gRSjeX3KUpB/2+mpOF9E6gTWHVMhNnfUKfD/3Ox/QTH/H/QX2rueDyskfF5E2gT8HjY5uOrJtAi4LGnRcfXTGAxAmvOOY9Opvkm/5fdXVz7XUQWeDACnk8+WIM73MUIeDxZDKUVmUCPwJrzSf44Db87wvcu+UXi71Db4++n4PSrxbX/ioX37o+A533312b2eF0C7tPX5WvtJmACJrAAgTVfCxwwDvAzfR9iy+94871lHldfD0DG34FdoFGt4vEIoHb8najHa3ZHbAImcEMC7ndvCN+mN0nA8/hNNoud2ieBNV/D8/95/M7Q+HtDfA1//P5eidW1X9LwvgkMv3vo1+ZOBBOYQcDjyQxovsUE5hFYbS6JOuZnwvh5sOEBE6muv8W53m8K+39C89rSdz04AY+dD54ADn82AdSOX7PNpucb743Aa4LDf4fMD6VcGmD4JuH3o/PjH6XnvZ+XMqN9Tjzfyeeg9wesfODE61irTyTDtdqbkO9DF+8dHmCR9apb3Pc/VdZyJrBFAsjhP7X8wvWXuM4HwSy6uHYWxfmwypy/D9v0Vw+8l2szHFptrgRfObfiB6o5x5EWyK7S19M4dHuuJLWChbZKADncmyv5dcZWG89+rUKgVRO45vFkFepWumUCt6gJ2PT8astJ8cC+tephBpbVXjPBl4/g67dY8/vXfL+Z597EOn6v+ug6rq0yzkGva/pI2Tv3SAA5fJPXTGTl+rnHjHkMn3t1EaSw5pg4/n/sX+HbHy3/EJvHwxYgX3tYAr26x/VV3kMkcOj2fPJhM28fgQv147FnH03tKBYm0KudoLk155yDK/CXXyiufq5v7C/kXftjKD7eNYFeTeP6KvNJ6PVccteZtf/ghNrxeLL/NHCEMwj0ameGyrXnk+/A5+r/8Mb+Qta1P4bi480Q6NUfrnvet5nWsiPXICDUhPv0azSEbZiACTwMgV6/OwPEaq8F4Cs/0/cTtsNrAW6x9n5cyOPGjEb0LfsngNrx5/v238yO0ARMYGMEWn0vrq3y/g8RQLf/97exXLA7TwQ6NeF5vBPFBCYItOpmQlw5tdpreBj/bewvjl9gnRzz6CyurVL7SbfHQ4LwsjkCyPvq6/NaveC8fxdxcy1ph65JoFU39APXPZ5cs0Fs664I9OonGMyac0n+74f/C8oPnHgJ35/3/Fur/qHXc8kefF/fNIFe7bt2Nt18du6GBITamXyPA/f5NdsN282m4wR6uU6NzQdOQMEzyHA9ebAEjjlhPOB6/iEvHp4suMYvl/Le7/KFpI/3cRLIB1bw+vgLqC9x7s2J8zi17gKfqm/mrGvZ2k3gvgm4du67/R7de+fvo2fAZfEjfziX4br4XOkyz9a52/WyDldr3T8B187+29gRxgi4JmK8LL1vAq6HfbevoxveP177NRP/mfPTVli7prfSEvbjHgm4fu6x1exzhAByfNUxEfrHP9LGDzbwRxuuvrier47cBndEwPWzo8Z0KFcl4Nq5Km4b2zAB1MKqc06Gnmzwc31f3RqFa//WLWD7WyPgmthai9ifeyHg2rmXlrKf1yCQ5nqrfxYSdvJ3TH7A/strxDa24dofE/HxPRFw/t5Ta9nXaxBwTVyDsm2YgAnsnQD60rXfW/4IDD+AHX6fnO8v87VA9Xvpa/L2uLEmXeveOwHXz95b2PGZgAlsjYD73a21iP25JQHXwy3p2/bWCKAe1n4Nf/L9A9jj8ae34uD6vxV5290iAdfDFlvFPt0LAdfPvbSU/VybAGph7bkkf3/ve9j5EuunWPn/oRdrx1XTD/v+TeEaHJ83gQYB104Dji+ZQIOAa6cBx5duRqD5wInCq/FDIfJTxA5IbP5gCX/E5A+s32L9Auf4gR/+2BcfLFHe+xmO8xuJnHhOLdTTfSLZ1I0+ZwImYAImYAImYAJzCGB+8gzryzn3pnvK+Q5PLTFXusAd32oCJmACJmACJmACJmACJmACyxHY6msm+DX+cUO+J/0bzo9/dHs5GNZkAiZgAibwsAQWGA/JbtX3EeHjJ7DxD6wvJsZJ2vdiAiZgAiZgAiZgAiawcQILzDvXnHN+BP/4JZDa5/42TtfumYAJmIAJmIAJmMC+CSwwlySgNeeTn0E/v0vC74t8DX+/wfod9r2YgAmYgAmYgAmYgAmYgAlcQGCrrwXoF8Liyu9YfYOV3zvn989/xjr+7B8ueTEBEzABEzABEzABEzABEzABEzCB/RNY4HX8Kv/Pg19Hvdjn78nxB4Mv+Q2W/TemIzQBEzABEzABEzCBKxPY8FyS3zEgDf4fiN9xHR48wRNeTMAETMAETMAETMAErk/gzy2T6U0/fojn9SyHc3xD8E2sP6Vz7+Ec3zB8N61/4JgfAuIXAY4LzvH6j8cT9R0+bIL3ezEBEzABEzABEzCB1Qmkect/sf05agz38B+k154rRd20vAmYgAmYgAmYgAmYgAmYgAnMJnAvr5ngJ9+z5nvXb80O1jeagAmYgAmYQIXAJeMhVeL+q7yPCDtfwtw7WPn/W34wz4sJmIAJmIAJmIAJmMAdEcAcjp+Z2+T/ruEb33fxjwHfUT7ZVRMwARMwARMwgccicMlckqRw/6rvYUL/D1g/wMqHx9PW51i/pW0vJmACJmACJmACJmACJmAC8wlgfj37fWVaTfPztb4Xxe+Kc/kVdn5JtvgQuhfYP35nfZDwHxMwARMwARMwARMwARMwARMwARN4AAJ4PTz7dXx6Xb3Wa/gj/eTjx9jSlhcTMAETMAETMAETMIGNENjyXBK+8Xce3sbK33ngdw4+wbkX2HoxARMwARMwARMwARO4AYHmAyeSPx9g+zYmbZy4fYF9PlziPazPeQ7bPJnjm4RfYeWDJT7CtY+x/RBbfvjnI+w/w7b80im/KDC18I3R4xNvpwR8zgRMwARMwARMwASWIoD5CecknHtwrsJ5SHRZa64U9cPyJmACJmACJmACJmACJmACJrA4gXt4zQQf+eVTvnf9VvJ3cQ5WaAImYAIm8NgEFhgPCfAq7yMmX/kDDV9gnx/U82ICJmACJmACJmACJnAnBBaYd64y54RffO+FnxX0Z/ruJJfspgmYgAmYgAmYwOMRWGAuSWirzCepGP7xAWblMswtcZ7fPfFiAiZgAiZgAiZgAiZgAiYwk8CWXwvAt/ye8k85vOQvD/1aIEPx1gRMwARMwARMwARMwARMwARM4GEILPA6frX/5xWN8Hfs/1Ice9cETMAETMAETMAETGADBDY+l/wa/n2AlQ8g55yVv1X8d+z7+60byB27YAImYAImYAIm8HgEXuuFjIkaf4SZE7fxcnIuyfEhE8cF5/iAifIhE+W139I9/ELq+E3G8fHxPu+YgAmYwBQB9CdvYj3pO3DMH473F96ngPnc6gSQfxzf+OHXf2GfY+kmF/jm2kHLgMMbWMdfaJTaDPetMleSjD+gEHg7Zx+w3R2yCfQIuG/oEfL1eyTgvL7HVrPPJrBfAuiTNvuaCb7x9fen2PKDB4d0zG3+sup+G+aOI0P7+LXdHbefXb8dAdfO7djTMvjPHg/T/au8jwi/+L+Q/2B9B/v5/yT5Pem/4Xw+Rzd2uSBujyu7bFkHZQImYAImYAKPSeCSeSfuXWXOiZbgnJPzYT7wkwuPD+n4R2wnPx9IGS8mYAImYAImYAImYALXI4B52Sbfw0wEvoV/fHh8fr/yeTrv/+kVKQI+fq+z4OFdE1AJuHZUUpYzARMwARPYKwGMhVt+LcA5f57/l03g1wIlDe+bgAmYgAmYgAmYgAmYgAmYQICA3xMNwNqg6CWv43HvWp8PK0nx9+NelCe8bwImYAImYAImYAImsA0CW5xLwif+1sMfJSGc+wHrVzg39TvDpaj3TcAETGDzBNCf+XOdm28lO7g3Aq67y1u0+8CJy000NXyOq/wx7uGLA2hQ7n+H7dwPC/FNUa53tTCR4fC3WPklikn/cT5/Yfd3yL2B9YspTkvLwc5haZ2qvr3ZZjxezgkgH5r5j+vDjwamO/nDSHxRyR8RzF84ykr/jXPPcJDPc5/LW0+bV38ht2g9UfPSOlV992L7Ff2H2mNu859oL9CeU4G/xPm/8AK2zNfPCiEe88t1PxTnjrs4v1TdUOdd1M4x+HV33gZb/xDGuoyX0H6znEV+bH78IOCl/VT1RWwvkQhX1vES9rh6WZgA8mupMU3uGxYOwepMIEwAeX8Xr3HCgfkGE5hJIFATB8guOh9T9c0MbY+3be41U8ofvvbme0WcV3Dhh1o/Hfb8Z8sE5PmbWquq3Jah3LFvfs10YeOl/iz3XZt9H/zCMPdy+xbHQ77XzP+dlP9f5f9cWZv/2gv4Thw3G1fU8WdpOfK4B52qj5F4Orlwy8seDxeij7xpvmcYyRc1B1W5iO2FcFjNnRHYS/6qNaHKRWrn1jo3lHKbmneiXfhZnPx5nAOO+T73R1g/x77/h3ajxEntoLyWZJv5vdUbtVPA7G7mk8i3Xczn1LphG6uyS8utYTuQsxa9gABywXXyIJ+DvyBNLrl1U3PJIhB+gbh8D/N9HF/yvZFC9fZ3Ufeb/6zIvYxTqp8bzordzPs2xvhm/yfYGAe7YwJ3T+AWc2VCU8eXpeVubfvuE8YBjAls9bUA35v8AOvwHblU57/9//bu9tqNYkvjOLBuAB6TAc7ADBnYGcBMBIYMLut+Mt9YkAHcCO5ABpDBXJwBZIBxBjN7292yzjkt6SlpV+96+Wst+ehla1fVr3Z1t/ocS/Zz8//M3R8U9/cTWOam2f/nvp/EkC3xPmTIab1tUC2veeub9HstF1Bjo+NK2r5tpnh1pwJsd2+cOFuz6vnU1O3AjcPk5QjcKpB2TlTdr946wAle3+r7eKdf/4/eBNPQ7hDZH7Y7N1f2jGPEK+Huv8zWRrN/c8M+8v5scb8lgZbXjjuxfoqrpaljSZs//73PY7s+sqvv89aLv7/3zxqe5mLjb3Y/5ZNg/ZPOvUbHjdb2NAXNQI8FOA9zrDHmbd6zBc3rpX2hPa+e/5fXXVDXh0vz4cuXL/0DR34x9A8zRrdxQOEfDnZ8sJjRrept2hgfWSP/tKt/AIx/eJAfIP7H1tjtsd/sOf8Pum8/BHt5rT/23G4f/uNFdJzl/yA6p5pvtLZ9PFzeC1gdSPVvcb4z8A/rf76+2m77m5W/29Xr//CHhXb7d3vssV09t68LXy8P/mO7xYWuJ2vjg+icar5e2vZ+znixefRa9W37YTt95OD7Xt/frdt1r3P/QEh9dq0AACAASURBVMzDxe77H2j+6ygmfN14Y5a/+bVzQKl4wxzc90v7+X3FZopTW398O+i14TXj9eT9+7O1flqfdrvY2FNq1tptfv/hkxDdTzVfSdu7FQsNNStgdRW+T7Oc0rahWRQ6No2A1WoX73GmmRAGmi5QuCZCj8esbSlfOlIjHTCvVt8z/WVE3rc7F+tvyrnuO53gzlkBmyPp+E1dq2rc2U7xJAJJAla/HCMm2Zc2a3PV5P7Qx2F983OH/23XP/2+XT6zq5+D3jo//TZgpH9snCn7FWtXOqaMjvO56yGn2seS8YxUt4zlroDVi3TOsKRe1BpU40ravjs67o0uMFr9qmtCjStZO9k5W6nVpaaa+9316mP98y+a8L/j8Q8I9g8N9r87fPu3D3aby04CZl7yXjLtuHUnDpppQGDZdk3397BOb2NPW2PRbTdQSkN3gXUy39/BZxT0UmdNHksuffuHufg5zI/dxx5bvzzL7w57sXGWHLsNca7TJ9PGHbqPLMk5bDExsJMCVm8pa+dkh3gCAQSKBGwNp/2OwDsavc9S82W3XTRJBDcvsKyjJt8LLLXu/xfU3wf4+4Endp3i/5DbOJu/LLXT/Hm95iHpIAKdCPSw5ns5lirpZyflQTcRaEbA1lfJ+dTQc5Cs7WbKgI4IAlavKedEWSfC5Agh5tjs/0vw7i/19YX9fCUMh5AKAmbP/rCCKyn7FbA1kfZ7BGs79Jiz31mg5z0K9LB23FVdZz3OQY0+L/Pa3O+ErF9+/OJ/C+bvVfzivxfyz1Uc/v+3LnPS/O9arJ+h+zQ1nxeDGhsdV6Ntz8llPgGrTc7DzDftjLhAwNaI9J7N4krOd0jrrqCb04Sas38W14uPskdsHfE/DvLr93b9yq5vsvu0R/s+Trv6yVX/EOl/nWrTnvf/pOvf2Hb4j7l22438/g/r66LjPG90TjXfaG2vc8TP9wJWC1L92yv8A/vvfwi/v6H0NeAfxn98eWV5/UtbPrTrE7s++MNDeyx0PXnj0TnVfL20fTxBM962+fQvRvF92+FqDl7Xv9pj65dNeF36G/H7lxf2gP/nurcXi6+xbjx302vn3eh3+be5k2g+apt3//ZW3559alffvr09ZtpFpN1Gdq9Zc29+/7HUS2g/1XGXtN1uWdGzPQWstmrs0y5uG/YcI20hcEag+fc4Z/rOUwjUEJDWhHpcEh1XY8Ad52z1PdN6LsjfLx2uHTvP1PWLx2+s6ZnKYfqxSvvDRYm1k1suTe4PncS2mV4b6+9b/Xeu/jvI4f8Y76gcdl8b5tv8uTi1j0sNNT+eo/nm5oACVq/SOUO1rqPjStbJgNPDkC4IjFS/mWtHbbtkPZbkvDDNez/d7HHn4v+j2frxpp+L8b+FOPxN295Qk7cnvZe0+Uk7zpt8fqYbvtXaMMdz6rrxSVZjo+NqtD1d0SYM2OqAdbK4u4XdHPrv4BNKbG2y2WPJZQ2s5zD95xRfNrFMjHTstsR2f67Tx2HzG3ocWpJzceTHfAK7r535iBkxAvUEluOE3f+PpY8oep+l5stuu95skjlRoNn3Aku9+98xrO8Hpvk/5In1IDdt89L8+Qp5MAQigMBFgdbXfC/HUiX9vDgpBCCAwJaAdD5VXYvRcVsd5jEEkgR2Pyeqrqckj96abf19vH9mE182kVtV7A9z/Wm9MQHbJjV9Dot9ZGMFQ3cOAq2vHe8o6+cwXSU3mjyWtLn0z8nz3wH574TW3wtN8f9bbbxN76dK1pqNJe1vvnpou2ShEjucAOdhhptSBhQpoO4LrU3pfMfSt4vrLnIMI+ZK/8KJEVGDx/SF5ds6Cfu/9vgzW1iPlvai4zxtdE4132htL1PEjysEntlrfj+q8zXFr3bjkT3u31BUclFrUI3zttXY6Lhe2i6Zn9FifTu9dfnOavf4i1SeWNDzrcArH4teN96NzPq9kqHsZTYn35e9gujGBaJrNjqf8/WQU+1jyXgaLx2615hAjX1aY0OkOxMKRNe1uq1W4yacEoacLKCuCbWGo+OSedppnvdM7czFZD1hTU824RMPV90fqkSsHVWqMI79YSFYe+HRayMrn8tGt10jp9rHkrY9lgsCam1Fx7m8mpNZQuCUgFpD0XHen+icar4abdfK6XmbuHDc2cQ09NAJ9b2kul6j43owpI85AtG1pubz0aqxalyNnJlt51QErW4JqHUQHVejpmvkVMed3fbW3FZ/jGPJ6sTXNqAeu6n51XWQFefjiG67JKfqSNx8AjXqcj5FRoxArkCNdRydU83nkmpsdFzuLNJ6FQHeC1RhJeldgehtkZrvbi+4hwACewmoazQrzh16aHuv+aIdBEYTUM+nZm4HRjNnPOMKsE4anVvexzc6MW11i/1hW/NBb/oRyNr3qe32I0lPZxNQazg6zp3VnLPNycnxcix5kqaHJ9R6j45zm+icar7R2u6hzuhjnoC6LqLj8kZMywiUC6jnO8oz84oHAnzhxAOS5h7wBfF6o1frt7b5836JjquRU+3jaG37eLhcJ+BfLOHfWvjmxMvXL1w58fSDh9UaVOO8ATU2Oq6Xth9MwiwPWN3+fH+s9ph/q9a39x73L6b43J77xa7HNe2xP9yLVe5GrxtvM7N+lTETg8B9geiajc7n/e0hp9rHkvHcnyvuI3BOoMY+7Vx7PIfAHgLRda1uq9W4PQxoA4FjAXVNqDUcHXfcV24jgMD+Aqzp/c1pMUdA3R+qvWPtqFLEzSYQvTay8vm8RbddI6fax5K2PZYLAmptRce5vJqTWULglIBaQ9Fx3p/onGq+Gm3Xyul5uSDQk4D6XlJdr9FxPVnS130FomtNzeejVGPVuBo5M9vetxJo7ZyAWgfRcTVqukZOddzZbZ+bY56bT0A9dlNl1HWQFefjiG67JKfqSNx8AjXqcj5FRoxArkCNdRydU83nkmpsdFzuLNI6Agj0KhC9LVLz9epFvxHoXUBdo1lx7ttD273XAf1HIEtAPZ+auR3IsqFdBEoFWCelYsQj0I4A+8N25oKe9CWQte9T2+1Lk97OJKDWcHScG6s5Z5oPxjqugFrv0XEuGp1TzTda2+NWJyOLEFDXRXRcRN/JgcBeAur5jr36M3Q7fxt6dJ0P7t4Hj58azePoOG8oOqeab7S2T00aj2sCVjf+DVxbl6f+oD3/6vhJu/+l3fcP7P/Yrp/Y9ds1xn4ef5C/PbV5kdeTvzo6p5qvl7Y3hSd+0ObXa/Kp/fz6mMHu/+xXe+xzu/61PP/EbvsXUDz40orj127dttcUrRvPYa9pcu1sjY/HEHCBPWvW2mp+/7GYhPZTHXdJ2x7LBYESAavDon3auW1DSbvEIlBTILKu1W21Gldz3ORG4JSAsibUGo6OO9VnHkcAgTgBW7e7no+I6zmZEIgVUPaHxy2ydo41uI3Ae4E914a11fy5OLWPLqjGRseVtP1+prk1s0B0Dar5qNWZqy5u7Gq9RceV1G8PbdcYT9wskwmBfQVszV78PVr0ulbz7StBaz0JqDUUHedGPeRU+1hrPD3V0sh9VesgOq5WXUX3U81XYzwlbY9co4ztOgGrn4vHbseZLX6336Gpta3G+TjUWDWuJOexI7fnE7Ca2m3tzKfLiBHIF1D3G2qcj0iNjY7Lbjt/NukBAgj0JhC9HVTz9eZEfxEYRUBdo1lx7txD26PUA+NAIEPA1vjF86mZ24EME9pE4JSArYXdzomq6+5UX3kcAQTKBNgflnkRjYALqPuqrDhmCYFWBTLXhNp2q3b0C4ESAbXeo+O8j9E51XyjtV0y38SOKWC1z3mYMaeWUe0oYOvo4vn/4+6cW3fHcdzeFvho+2EebUTg8dKPN2f64x9oEh3nzUXnVPON1raPh0uggG30n1o6/+D+Ox/ab/d9LfyPPf+9Xf05v/5mt/1bvPyi1qAaVyPnaG2/heefg8B3dsuvDy5Wp37w8+PyhMd43d75QpXluat+WP5T68bztbx2rhovLxpeYO+aVbfNapxPkBqrxtXIWaPt4YuTAdYXOLNPu7RtqN85WkDgSoEb6lrdVqtxV46AlyEQK7CxJtQajo6LHRjZEEDgvsCl4zfW9H0x7k8lsLE/XMfP2lkl+InAXYG910b0fkrN56NWY9W4GjlrtH13xrk3q4BaW9FxJetk1rlh3JcFoutSzVdSv2pONa5G27VyXp5BIhDoQGDjvaS6XqPjOtCii0kC0bWm5vPhqrFqXI2cmW0nlQTNbgiodRAdV6Oma+RUx53d9sbU8hACdwU2jt3WgN7Pdfo41LWqxpXkXB35OZ/A3mtnPmFGjEC+gLrfUON8RGpsdFx22/mzSQ8QQKA3gejtoJqvNyf6i8AoAuoazYpz5x7aHqUeGAcCTQhsnE/N3A40YUInEDCBvc+JquuOyUEAgUoC7A8rwZJ2JAF1X5UVN5I1YxlLIHNNqG2PJc5oZhVQ6z06zr2jc6r5Rmt71tpl3O8EOA9DJSBQSWDjfMfa0qV1t8bx84QAXzhxAqajhz8W+xod581G51Tzjda2OIWELQI/2c+fbcfw/bGI3X9u1zfrY3b7D7v9q11/WB8Tfqo1qMZ5k2psdFwvbQvT0n+I1aN/Scoz++k1+eBij39uD3r9PrGrx3j878vjdvPmy+a68azWRu9r52YcEvQl0GjN9rAN94mO7qear6TtvgqS3mYIbO7TgrYNGeOhTQRcoGZdq9tqNY4ZQ2APgc01caFhtYaj4y50i6cRQOCUQNDxG2v6FDCPjyCwuT9k7YwwtYyhhkCjayN6P6Xmc2I1Vo2rkbNG2zXKi5z9Cai1FR1Xsk76U6XHewlE16War6R+1ZxqXI22a+Xcqw5oB4FbBDbfS15IqK7X6LgL3eLpiQWia03N5+RqrBpXI2dm2xOXZXNDV+sgOq5GTdfIqY47u+3mCosO7S6weew2ybnOGuuvJOfuk02D9QUaXTv1B04LCCBwX0A9FlTjPL8aGx2X3fZ9W+4jgAAClwSit4Nqvkv94nkEEKgjoK7RrDgfdQ9t15kdsiIwpsDm+dQLQ83cDlzoGk8jcLtAo+dE1XV3OwAZEJhTgP3hnPPOqGMF1H1VVlzsaMmGQJxA5ppQ244bLZkQyBNQ6z06zkccnVPNN1rbedVDy1UFOA9TlZfkCGye7whad1Pr8oUTbU//6zPdW7/d60+LiY7zZqNzqvlGa9vHwyVIwDb6/uURf9jPL8SU/qUTn1i8f3i/WoNqnHdBjY2O66Vt7yeXdwJf2Q+vxwcXq88v7UH/0oev7er1/dzurzX+T7vv36519cVeX7puvK1W1s7V4+aF0wnUrNketuE+4dH9VPOVtD1dYTLgWIEr9mnH24bYzpANgSCBG+ta3VarcUGjIg0C1wucWBNqDUfHXT8QXokAAtcKHB+/saavVeR13Quc2B+eGxdr55wOz80sUHNtRO+n1Hw+n2qsGlcjZ422Z65lxv5eQK2t6LiSdfK+t9xC4K5AdF2q+bwXamx0XI22a+X0vFwQ6FrgxHvJ6HWt5uvaks5XFVBrKDrOB9VDTrWPtcZTdfJJLguodRAdV6uuovup5qsxnpK25QkncE6BE8du5zB6Otfp41DXixpXkvOcI8/NJ1Bz7cynyYgRyBdQ9xtqnI9IjY2Oy247fzbpAQII9CYQvR1U8/XmRH8RGEVAXaNZce7cQ9uj1APjQCBd4MT51MztQLoJHUDgjEDNc6LqujvTPZ5CAIFrBdgfXivH6yYTUPdVWXGTTQfD7Uggc02obXfESVcROCmg1nt0nHcoOqeab7S2T04uT0wrwHmYaaeegUcJnDjfcS798bo7F8dzJsAXTjRcBlb8b5bubX3Y+PqYfzh5aJy3GZ1TzTda28v88SNAwGrIP5T/sf30D+O/c7HHfrHrb3cevHvnkT3POrlr4veKtyP+ItXSY7kcBD63W6feJH9nz319iLQbZvyz/XhiV5+jZ3a96mJ5Tq4bT2jPN712rho0LxpaIKNmrc3m9x8+6dH9VPOVtD10cTK46gJWkyf3afbcxf1Z9Q7SAAJXCNxa1+q2Wo27Ygi8BIFQgVNrQq3h6LjQwZEMAQTuCNh6vXj8xpq+Q8adiQSs9m9678PamahYGOpBIGO/Er3W1Hw+aDVWjauRs0bbhwnnxtQCam1Fx5Wsk6kniMGfFYiuSzVfSf2qOdW4Gm3Xynl28ngSgQ4EbF1uvpdU12t0XAdkdDFJILrW1Hw+XDVWjauRM7PtpJKg2Q0BtQ6i42rUdI2c6riz296YWh5C4CBgdbx57OYB9tzuv0NT15Uat4wj7W8uD9DcmEogY+1MBcxgEWhEQN0XqXE+LDU2Oi677UamlG4ggEBHAtHbQTVfR0R0FYGhBNQ1mhXn2D20PVRRMBgEEgVsvW+eT83cDiRy0DQCBwFbA83+PuHQSW4ggECYAPvDMEoSDS6QdYyotjs4P8PrWECt4eg4J1NzdsxL1xE4CKj1Hh3nHYjOqeYbre3DZHJjOgGrec7DTDfrDHgPAVtbm+f/vW1l3e3Rx97b4Asn2p/BX62Ln2x08/HymD/vl+i4GjnVPo7Wto+Hyw0CtsH3D+t/Yj+/WNPY7U/8utz/T/u5fnnCGuI/364Ti3u1PKjWoBrnadXY6Lhe2l7o5/1h9ee16bW6/geqA8by3PEXohw/59+g5V88sW7vD88pNyz3pXXjaXpYO8pwiZlHIKtme9iGexVE91PNV9L2PNXKSMMEhH2aum0I6xOJELhVILCu1W21Gnfr0Hg9AlcJCGtCreHouKvGw4sQQOCigHr8xpq+SEnASALC/pC1M9KEM5ZIgay1Eb2fUvO5nRqrxtXIWaPtyLohV78Cam1Fx5Wsk3516Xltgei6VPOV1K+aU42r0XatnLXnn/wIVBEQ3kuq6zU6rsp4STqEQHStqfkcT41V42rkzGx7iAIbZBBqHUTH1ajpGjnVcWe3PUg5MoxIAeHYbZRznTXWX0nOyGkjVx8CWWunDx16icBYAuqxoBrnOmpsdFx222NVBqNBAIE9BKK3g2q+PcZGGwgg8FBAXaNZcd7jHtp+KMsjCCAgCwjnUzO3A/I4CESgkkDWOVF13VUaNmkRmE+A/eF8c86IbxZQ91VZcTcPkAQIVBLIXBNq25WGTloEdhVQ6z06zgcZnVPNN1rbuxYMjTUjwHmYZqaCjowiIJzvUNfdKCRVxsEXTlRhDU36k2XzYr9/+dQeeGULZf0A8+g4by86p5pvtLZ9PFyuFLAaf2ov/cx+fn0vxed2//Xy2I/2/JN7z/vdZ3b1NyXrRa1BNc7zqrHRcb20vdrP/HPdhq/1erBYtuFv7Of65SmH55Yb/mUVxzV8//nN+5ZPWTf+2h7WzuYYeXBagaya7WEb7kUR3U81X0nb0xYvA79OQNynqduG6zrBqxAIFgiua3VbrcYFj5Z0CFwWENeEWsPRcZcHQAQCCFwjoB6/saav0eU1XQqI+0PWTpezS6d3EMhaG9H7KTWfk6qxalyNnDXa3qGcaKIDAbW2ouNK1kkHjHQxSSC6LtV8JfWr5lTjarRdK2dSWdAsAtcLiO8l1fUaHXf9wHjl6ALRtabmc1c1Vo2rkTOz7dFrr6fxqXUQHVejpmvkVMed3XZPNUdfdxAQj91GOddZY/2V5NxhRmmiMYGstdMYA91BYAoB9VhQjXM0NTY6LrvtKQqGQSKAQKhA9HZQzRc6CJIhgIAsoK7RrDgfSA9ty+AEIoDAXQHxfGrmduBuh7mHwP4CWedE1XW3vwgtIjCgAPvDASeVIe0hoO6rsuL2MKANBK4RyFwTatvXjIvXINCagFrv0XHuEJ1TzTda263VFP3ZR4DzMPs408okAuL5DnXdTaJ23TD5wonr3KJf9fGS8PH9xLYYfrTHXttP/3D9txe77R9A/l92ffHukQ8+iI7zvNE51Xyjtb3OET9PCpyrf/8Qfn9T8cjq54fjqz32ld1fv3Dl7XPHLdhzf1/uf7E+bo+FrifPG51TzddL26v95D99m+2XtV7f3Xv/r9foTzb3a9zbZ+z+l3bjF/v5x/vQw62IdePJml87hxFzA4F3Aik1q26b1TgfihqrxtXIWaPtd9PIvwjcEYjYp0nbhjutcgeBJAHbtjb/HieJhmYnFVDXhHpcEh036bQwbAT2EJCO31jTe0wFbbQgoO4Pra+snRYmjD60KJCyNqL3U2o+nwA1Vo2rkbNG2y0WH32qJnDunGHo73up1WpzOHPirutXXRNqnBeCGqvG1co5c9Ey9j4FbM1Iv29Q11Z0XJ+q9DpQYIr9oXtFrx01X422A+efVJoA62Twv4PXyoCoWQRs+y4du5nHEOc6fV7VfZoaV5LTY7lMJ5CydqZTZsAI7Cew27GyD0ndF0XHZbe933TSEgIIdCaw2zZY3a525kd3EehNoLk1X7JtUGOj43yS1Zy9FQT9RaAVAVtj0vlUdS1Gx7XiRD+mF0g5J6qup+lnBwAEAgTYHwYgkmJkga7fz448MYyteYHm1o6LcYzZfN3QwXKBrteauibVOOdTY6PjarRdXg68YhABzsMMMpEMYzeBc/tC6fy/9VRad7uNqNOGPnz58uUz67t/oPWHnY6h226buX+Qvl98DvyDxl/Z1T9Y3OfDPyjh7cVu+3Pf2dU/rPxPu35m12/tcY8/XKLjPHF0TjXfaG0fJokbBwGrhYv1bzG/2wt8p7B1eWXPf7o+Ybc97uvlvn95y2u/b4/7ujlc7H7oevLE0TnVfL20fcCf9IbNp9fmb3Z9Ybd/3mKwx5/a4/+wq9ftevEvofh1veM/7X7oullyNr92jg24jYCtg5SatXab338sazq0n+q4S9qmihFY6iV0n6ZuG9BHIFvAarWL9zjZTrQ/j0Dhmkg7zplnRhgpAvsJqMdvFhe69vcbIS0hoAsU7g9TzovooyESgRyBrP1K9H5KzefKaqwaVyNnjbZzKoxW9xKwmrl4zpBa3Ws2aKdUYKT6VbffalyNdVsrZ+m8E49ApoCtwZLfN4SeXylZ/5lGtL2/gNXGMMdzJXWuxkbH+QzXyLl/5czVos0Z62Siv4Ofq7oZ7TkBW/slx24pvweosU/JzHluPnhuTAGrt5S1M6Ymo0IgR8DWccqxso82ep+l5stuO2emaRUBBFoUyNoGl2wvW3SjTwj0KtD6mi/ZNqix0XE+92rOXuuEfiOQKWDrq+R8Kr8Lz5ws2k4VsLWSck6UfWDqtNP4RALsDyeabIYqC9i6SPk9grrvU+PkAROIQJBA62vHh8n6CZps0qQKjLTW1DWpxvnEqLHRcTXaTi00Gk8TsNrkPEyaPg33ImDr5OJ7NospOf8vrbtefPbspzn/Ze294Asn9lSnLQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEDgBoH1Cyc+uiEHL0UAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEgQ4AsnEtBpEgEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBC4RYAvnLhFj9cigAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgkCfOFEAjpNIoAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAK3CPCFE7fo8VoEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAIEGAL5xIQKdJBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQOAWAb5w4hY9XosAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIJAjwhRMJ6DSJAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCNwiwBdO3KLHaxFAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAA8ZFciwAAAYFJREFUAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQACBBIG/rW1+8803/7feXn7+YY89ufcYdxFAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBHYQsO+N+M2aebrVlH/hxL/t+nzjydcbj/EQAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIDAPgIvrJnHG039+/8BaE/j5ebzrSIAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle \\left[ dx_{0} + \\frac{482504830082603 x_{0}}{100000000000} - \\frac{252010950009 x_{1}}{125000000000} - \\frac{1601551191 x_{8}}{78125000}, \\  dx_{1} - \\frac{129500971360511 x_{0}}{50000000000} + \\frac{29701834891466 x_{1}}{125} - \\frac{64749999156297 x_{2}}{2500} - \\frac{51799999008011 x_{3}}{2000}, \\  dx_{2} - \\frac{118807339213011 x_{1}}{500} + \\frac{64749999156297 x_{2}}{2500}, \\  dx_{3} - \\frac{351844898712793 x_{1}}{500000000000} + \\frac{517999990080109 x_{3}}{10000} - \\frac{731634931235523 x_{4}}{10000000000}, \\  dx_{4} - \\frac{51799999008011 x_{3}}{2000} + \\frac{757034810970363 x_{4}}{10000000000} - \\frac{243937525489403 x_{5}}{100000000000}, \\  dx_{5} - \\frac{634996993371 x_{4}}{250000000} + \\frac{64977921231987 x_{5}}{500} - \\frac{493809417837981 x_{6} e^{\\frac{387975470350209 u_{0}}{500000000000000000}}}{100000000}, \\  dx_{6} - \\frac{129955840024599 x_{5}}{1000} + \\frac{493809417837981 x_{6} e^{\\frac{387975470350209 u_{0}}{500000000000000000}}}{100000000} + \\frac{49333296450869 x_{6}}{2000} - \\frac{129500000026047 x_{7}}{5000}, \\  dx_{7} - \\frac{49333296450869 x_{6}}{2000} + \\frac{518000000104189 x_{7}}{10000} - \\frac{357734827121321 x_{8}}{10000}, \\  dx_{8} - \\frac{223502887361581 x_{0}}{100000000000} - \\frac{129500000026047 x_{7}}{5000} + \\frac{4471685341579 x_{8}}{125}\\right]$"
      ],
      "text/plain": [
       "⎡                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢      482504830082603⋅x₀   252010950009⋅x₁   1601551191⋅x₈        12950097136\n",
       "⎢dx₀ + ────────────────── - ─────────────── - ─────────────, dx₁ - ───────────\n",
       "⎣         100000000000        125000000000       78125000             50000000\n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "0511⋅x₀   29701834891466⋅x₁   64749999156297⋅x₂   51799999008011⋅x₃        118\n",
       "─────── + ───────────────── - ───────────────── - ─────────────────, dx₂ - ───\n",
       "000              125                 2500                2000                 \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "807339213011⋅x₁   64749999156297⋅x₂        351844898712793⋅x₁   51799999008010\n",
       "─────────────── + ─────────────────, dx₃ - ────────────────── + ──────────────\n",
       "    500                  2500                 500000000000            10000   \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "9⋅x₃   731634931235523⋅x₄        51799999008011⋅x₃   757034810970363⋅x₄   2439\n",
       "──── - ──────────────────, dx₄ - ───────────────── + ────────────────── - ────\n",
       "          10000000000                   2000            10000000000          1\n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "37525489403⋅x₅        634996993371⋅x₄   64977921231987⋅x₅   493809417837981⋅x₆\n",
       "──────────────, dx₅ - ─────────────── + ───────────────── - ──────────────────\n",
       "00000000000              250000000             500                        1000\n",
       "\n",
       "  387975470350209⋅u₀                                                 387975470\n",
       "  ──────────────────                                                 ─────────\n",
       "  500000000000000000                                                 500000000\n",
       "⋅ℯ                          129955840024599⋅x₅   493809417837981⋅x₆⋅ℯ         \n",
       "────────────────────, dx₆ - ────────────────── + ─────────────────────────────\n",
       "00000                              1000                        100000000      \n",
       "\n",
       "350209⋅u₀                                                                     \n",
       "─────────                                                                     \n",
       "000000000                                                                     \n",
       "            49333296450869⋅x₆   129500000026047⋅x₇        49333296450869⋅x₆   \n",
       "───────── + ───────────────── - ──────────────────, dx₇ - ───────────────── + \n",
       "                   2000                5000                      2000         \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "518000000104189⋅x₇   357734827121321⋅x₈        223502887361581⋅x₀   1295000000\n",
       "────────────────── - ──────────────────, dx₈ - ────────────────── - ──────────\n",
       "      10000                10000                  100000000000             500\n",
       "\n",
       "                           ⎤\n",
       "                           ⎥\n",
       "                           ⎥\n",
       "26047⋅x₇   4471685341579⋅x₈⎥\n",
       "──────── + ────────────────⎥\n",
       "0                125       ⎦"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.constitutive_relations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will next simulate this model. We first set the initial conditions of the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ 0.000483061870385487, \\  0.0574915174273067, \\  0.527445119834607, \\  1.51818391164022 \\cdot 10^{-9}, \\  0.000521923287622898, \\  7.80721128535043 \\cdot 10^{-5}, \\  0.156693953834181, \\  0.149232225342376, \\  0.108044124948978\\right]$"
      ],
      "text/plain": [
       "[0.000483061870385487, 0.0574915174273067, 0.527445119834607, 1.51818391164022\n",
       "e-09, 0.000521923287622898, 7.80721128535043e-05, 0.156693953834181, 0.1492322\n",
       "25342376, 0.108044124948978]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Initial Conditions\n",
    "initial_conditions = {\n",
    "    \"P1\": 0.000483061870385487,\n",
    "    \"P2\": 0.0574915174273067,\n",
    "    \"P2a\": 0.527445119834607,\n",
    "    \"P4\": 1.51818391164022e-09,\n",
    "    \"P5\": 0.000521923287622898,\n",
    "    \"P6\": 7.80721128535043e-05,\n",
    "    \"P8\": 0.156693953834181,\n",
    "    \"P9\": 0.149232225342376,\n",
    "    \"P10\": 0.108044124948978\n",
    "}\n",
    "\n",
    "def simulation_ic(model,initial_conditions):\n",
    "    num_states = len(model.state_vars)\n",
    "    array_initial_conditions = [0]*num_states\n",
    "    state_order = [[]]*num_states\n",
    "    for i in range(num_states):\n",
    "        comp = model.state_vars['x_'+str(i)][0]\n",
    "        array_initial_conditions[i] = initial_conditions[comp.name]\n",
    "        state_order[i] = comp.name\n",
    "    return array_initial_conditions, state_order\n",
    "\n",
    "array_initial_conditions, state_order = simulation_ic(model,initial_conditions)\n",
    "array_initial_conditions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We finally simulate and plot the model. The amount of SR calcium was left as a control variable, and we allow it to gradually increase over time, according to the function $[\\mathrm{ Ca_{sr}^{2+}}] = 0.05+0.01t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x196fc5a8bb0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "vol_sr = 2.28\n",
    "K_Casr = species_affinities['Casr']\n",
    "\n",
    "t,x = simulate(model, timespan = (0.0,195.0), x0 = array_initial_conditions, dt=1, \n",
    "                   control_vars={'u_0':f'{R}*{T}*log({K_Casr}*(0.05+0.01*t)*{vol_sr})'})\n",
    "plt.plot(t,x)\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Amount')\n",
    "plt.legend(state_order)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the functions defined in the previous notebook, we can also find the flux through R1,2 to calculate the cycling rate of the pump, which we plot against SR calcium concentration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Cycling rate')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "def full_equations(model):\n",
    "    # Load full equations of model\n",
    "    X, mapping, A, F, G = model.system_model()\n",
    "    # AX + F(X) = 0\n",
    "    # G(X) = 0\n",
    "    AX = A*SparseMatrix(X) + F\n",
    "    full_model_equations = {}\n",
    "    for i in range(AX.rows):\n",
    "        xi = X[i]\n",
    "        eqn = xi - AX[i,0]\n",
    "        full_model_equations[str(xi)] = eqn\n",
    "    return full_model_equations\n",
    "\n",
    "# Define a function that returns the port for a component\n",
    "def find_port(component,direction):\n",
    "    if direction in ['f', 'forward']:\n",
    "        index = 0\n",
    "    elif direction in ['r', 'reverse']:\n",
    "        index = 1\n",
    "    return list(component.ports.keys())[index]\n",
    "\n",
    "# Returns the mathematical expression for a flux\n",
    "def reaction_flux_expression(model,Re_comp,direction):\n",
    "    mapping = model.system_model()[1]\n",
    "    port = find_port(Re_comp,direction)\n",
    "    bond_index = mapping[1][port]\n",
    "    \n",
    "    full_model_equations = full_equations(model)\n",
    "    V = full_model_equations[f'f_{bond_index}']\n",
    "    return V\n",
    "\n",
    "# Returns a function that can be used to compute flux\n",
    "def flux_function(model,Re_comp):\n",
    "    V = reaction_flux_expression(model,Re_comp,'f')\n",
    "    return convert_to_function(V,model)\n",
    "\n",
    "# Converts a symbolic expression to a function\n",
    "def convert_to_function(expression,model):\n",
    "    states = [Symbol(x) for x in model.state_vars.keys()]\n",
    "    return lambdify(([states]),expression)\n",
    "\n",
    "# Calculate the flow through the reaction using states from the simulation\n",
    "R12 = model/'R:R1,2'\n",
    "V_R12_func = flux_function(model,R12)\n",
    "cyc_rate = [V_R12_func(s) for s in x]\n",
    "\n",
    "# Generate a vector for SR calcium concentration\n",
    "Casr = [0.05+0.01*time for time in t]\n",
    "\n",
    "# Plot the cycling rate\n",
    "plt.plot(Casr,cyc_rate)\n",
    "plt.xlabel('SR calcium concentration')\n",
    "plt.ylabel('Cycling rate')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "Tran, K., Smith, N.P., Loiselle, D.S. and Crampin, E.J., 2009. A thermodynamic model of the cardiac sarcoplasmic/endoplasmic Ca2+ (SERCA) pump. *Biophysical journal*, 96(5), pp.2029-2042. https://doi.org/10.1016/j.bpj.2008.11.045\n",
    "\n",
    "Pan, M., Gawthrop, P.J., Tran, K., Cursons, J. and Crampin, E.J., 2019. A thermodynamic framework for modelling membrane transporters. *Journal of Theoretical Biology*, 481, pp.10-23. https://doi.org/10.1016/j.jtbi.2018.09.034"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}