tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import all functions from utils.py\n",
    "from utils import *\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# first, let us define a molecule using pySCF notation\n",
    "\n",
    "atom = \"H 0 0 0; H 0 0 0.74\" # equilibrium bond length H2\n",
    "basis = \"sto-3g\"\n",
    "charge = 0\n",
    "spin = 0\n",
    "\n",
    "# and construct its Hamiltonian in qubit form using the Jordan-Wigner transform\n",
    "unsimplified_hamiltonian = get_unsimplified_hamiltonian(atom, basis, charge, spin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'openfermion.ops.operators.qubit_operator.QubitOperator'> \n",
      "\n",
      "(-0.09706626816763164+0j) [] +\n",
      "(-0.04530261550379926+0j) [X0 X1 Y2 Y3] +\n",
      "(0.04530261550379926+0j) [X0 Y1 Y2 X3] +\n",
      "(0.04530261550379926+0j) [Y0 X1 X2 Y3] +\n",
      "(-0.04530261550379926+0j) [Y0 Y1 X2 X3] +\n",
      "(0.17141282644776912+0j) [Z0] +\n",
      "(0.16868898170361205+0j) [Z0 Z1] +\n",
      "(0.12062523483390412+0j) [Z0 Z2] +\n",
      "(0.1659278503377034+0j) [Z0 Z3] +\n",
      "(0.17141282644776917+0j) [Z1] +\n",
      "(0.16592785033770338+0j) [Z1 Z2] +\n",
      "(0.12062523483390412+0j) [Z1 Z3] +\n",
      "(-0.22343153690813441+0j) [Z2] +\n",
      "(0.17441287612261572+0j) [Z2 Z3] +\n",
      "(-0.22343153690813444+0j) [Z3]\n"
     ]
    }
   ],
   "source": [
    "# we can inspect our Hamiltonian, which is of OpenFermion QubitOperator type\n",
    "print(type(unsimplified_hamiltonian),\"\\n\")\n",
    "print(unsimplified_hamiltonian)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n"
     ]
    }
   ],
   "source": [
    "# we can use OpenFermion's QubitOperator functions to get details about our unsimplified Hamiltonian, e.g.,\n",
    "\n",
    "from openfermion.utils import count_qubits\n",
    "print(count_qubits(unsimplified_hamiltonian))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 \n",
      "\n",
      "(-0.3270705806846189+0j) [] +\n",
      "(0.18121046201519705+0j) [X0] +\n",
      "(-0.7896887267118071+0j) [Z0]\n"
     ]
    }
   ],
   "source": [
    "# lets now construct a symmetry adapted version of our Hamiltonian and compare\n",
    "\n",
    "simplified_hamiltonian = get_simplified_hamiltonian(atom, basis, charge, spin)\n",
    "\n",
    "print(count_qubits(simplified_hamiltonian),\"\\n\")\n",
    "print(simplified_hamiltonian)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No Symmetry-Adapted Encoding:\n",
      "Ground State Energy -1.1167593073964284, Number of Qubits: 8\n",
      "\n",
      "With Symmetry-Adapted Encoding:\n",
      "Ground State Energy -1.1167593073964284, Number of Qubits: 8\n"
     ]
    }
   ],
   "source": [
    "# now let's apply the XBK method to both of our Hamiltonians\n",
    "\n",
    "r_value = 2\n",
    "\n",
    "unsimplified_ground_state_energy, unsimplified_ground_state, unsimplified_ising_hamiltonian = calculate_ising_ground_state(unsimplified_hamiltonian, r_value)\n",
    "simplified_ground_state_energy, simplified_ground_state, simplified_ising_hamiltonian = calculate_ising_ground_state(simplified_hamiltonian, r_value)\n",
    "\n",
    "# and compare the energies and number of qubits each Hamiltonian uses\n",
    "\n",
    "print(f\"No Symmetry-Adapted Encoding:\\nGround State Energy {unsimplified_ground_state_energy}, Number of Qubits: {count_qubits(unsimplified_ising_hamiltonian)}\\n\")\n",
    "print(f\"With Symmetry-Adapted Encoding:\\nGround State Energy {unsimplified_ground_state_energy}, Number of Qubits: {count_qubits(unsimplified_ising_hamiltonian)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Exception ignored in: <function _TemporaryFileCloser.__del__ at 0x7f3c21ce79c0>\n",
      "Traceback (most recent call last):\n",
      "  File \"/home/jwdesroches/miniconda3/envs/qis_conda/lib/python3.11/tempfile.py\", line 450, in __del__\n",
      "    self.close()\n",
      "  File \"/home/jwdesroches/miniconda3/envs/qis_conda/lib/python3.11/tempfile.py\", line 446, in close\n",
      "    unlink(self.name)\n",
      "FileNotFoundError: [Errno 2] No such file or directory: '/home/jwdesroches/python/Ga2QuAMES/symmetry/final_product/tmpr10ktj8x'\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "converged SCF energy = -7.02841009454055  <S^2> = 2.8515412e-11  2S+1 = 1\n",
      "converged SCF energy = -7.30874165394089  <S^2> = 5.7953642e-14  2S+1 = 1\n",
      "converged SCF energy = -7.49864507381235  <S^2> = 5.6177285e-14  2S+1 = 1\n",
      "converged SCF energy = -7.62892302744456  <S^2> = 4.4408921e-15  2S+1 = 1\n",
      "converged SCF energy = -7.71773656838278  <S^2> = 2.8315128e-12  2S+1 = 1\n",
      "converged SCF energy = -7.77743000202365  <S^2> = 5.7544369e-10  2S+1 = 1\n",
      "converged SCF energy = -7.81664121927656  <S^2> = 1.9570234e-10  2S+1 = 1\n",
      "converged SCF energy = -7.84132702654149  <S^2> = 6.2144068e-11  2S+1 = 1\n",
      "converged SCF energy = -7.85556546081298  <S^2> = 8.1421536e-12  2S+1 = 1\n",
      "converged SCF energy = -7.86218376662212  <S^2> = 1.6544988e-11  2S+1 = 1\n",
      "converged SCF energy = -7.86319032294314  <S^2> = 2.0092972e-10  2S+1 = 1\n",
      "converged SCF energy = -7.86004735984908  <S^2> = 5.3194538e-10  2S+1 = 1\n",
      "converged SCF energy = -7.85383960184028  <S^2> = 8.2578389e-13  2S+1 = 1\n",
      "converged SCF energy = -7.84538169559151  <S^2> = 3.1881164e-12  2S+1 = 1\n",
      "converged SCF energy = -7.83529030520272  <S^2> = 1.6477042e-11  2S+1 = 1\n",
      "converged SCF energy = -7.82403501652659  <S^2> = 1.8174799e-09  2S+1 = 1\n",
      "converged SCF energy = -7.81197577845831  <S^2> = 2.5230928e-12  2S+1 = 1\n",
      "converged SCF energy = -7.79939126012932  <S^2> = 5.9463545e-13  2S+1 = 1\n",
      "converged SCF energy = -7.7865006252816  <S^2> = 1.1822765e-11  2S+1 = 1\n",
      "converged SCF energy = -7.77348011629784  <S^2> = 3.6646242e-12  2S+1 = 1\n",
      "converged SCF energy = -7.76047524048894  <S^2> = 2.2635227e-12  2S+1 = 1\n",
      "converged SCF energy = -7.74760912877292  <S^2> = 2.5661695e-12  2S+1 = 1\n",
      "converged SCF energy = -7.73498766083524  <S^2> = 2.4846791e-13  2S+1 = 1\n",
      "converged SCF energy = -7.72270207743331  <S^2> = 1.2041479e-12  2S+1 = 1\n",
      "converged SCF energy = -7.71082990021766  <S^2> = 6.5316641e-12  2S+1 = 1\n"
     ]
    }
   ],
   "source": [
    "# we can compare with FCI for a range of bond lengths for a different molecule (LiH)\n",
    "\n",
    "from pyscf import gto, scf, fci\n",
    "from openfermion.linalg import get_ground_state, get_sparse_operator\n",
    "\n",
    "bond_lengths = np.linspace(0.5, 3.0, 25)\n",
    "\n",
    "fci_energies = []\n",
    "unsimp_qubit_energies = []\n",
    "simp_qubit_energies = []\n",
    "unsimp_ising_energies = []\n",
    "simp_ising_energies = []\n",
    "\n",
    "for bond_length in bond_lengths:\n",
    "    \n",
    "    # FCI calculation\n",
    "    mol = gto.Mole()\n",
    "    mol.build(\n",
    "        atom = f'Li 0 0 0; H 0 0 {bond_length}', \n",
    "        basis = 'sto-3g', \n",
    "        unit = 'angstrom'\n",
    "    )\n",
    "\n",
    "    mf = scf.UHF(mol)\n",
    "    mf.kernel()\n",
    "\n",
    "    cisolver = fci.FCI(mf)\n",
    "    fci_energy = cisolver.kernel()[0]\n",
    "    fci_energies+= [fci_energy]\n",
    "     \n",
    "    # construct pySCF geometry using our return_geomtery() function\n",
    "    atom = return_geometry(\"LiH\", bond_length)\n",
    "    \n",
    "    # construct hamiltonians\n",
    "    unsimp_ham = get_unsimplified_hamiltonian(atom, basis, charge, spin)\n",
    "    simp_ham = get_simplified_hamiltonian(atom, basis, charge, spin)\n",
    "    \n",
    "    # do diagonalization on qubit Hamiltonians before XBK transform\n",
    "    \n",
    "    unsimp_qubit_energy, _ = get_ground_state(get_sparse_operator(unsimp_ham))\n",
    "    simp_qubit_energy, _ = get_ground_state(get_sparse_operator(simp_ham))\n",
    "    \n",
    "    unsimp_qubit_energies += [unsimp_qubit_energy]\n",
    "    simp_qubit_energies += [simp_qubit_energy]\n",
    "    \n",
    "    # apply XBK method\n",
    "    \n",
    "    unsimp_ising_energy, _, _ = calculate_ising_ground_state(unsimp_ham, r_value = 1)\n",
    "    simp_ising_energy, _, _ = calculate_ising_ground_state(simp_ham, r_value = 1)\n",
    "    \n",
    "    unsimp_ising_energies += [unsimp_ising_energy]\n",
    "    simp_ising_energies += [simp_ising_energy]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f3ba41ef6d0>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkYAAAHNCAYAAAD7QrTqAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9hAAAPYQGoP6dpAACE0UlEQVR4nO3deXhM1//A8fdkmeyLbGKJLELsuyCKWENRqq2iRWIpilrrR/u1V3VFW0oXDdqqorW0Wqokttoq9iW2jAixhSQist/fH5gaWSQxyUySz+t55nnMveee+7l3rplPzjn3XJWiKApCCCGEEAITQwcghBBCCGEsJDESQgghhHhIEiMhhBBCiIckMRJCCCGEeEgSIyGEEEKIhyQxEkIIIYR4SBIjIYQQQoiHJDESQgghhHhIEiMhhBBCiIckMRJCD1QqFTNmzCjwduHh4ahUKsLDw/UekygZPv74Y3x8fDA1NaVBgwaGDodly5ahUqnQaDR6r7uw/0+EKE6SGIli9ehL99HL0tKS6tWrM2rUKK5fv17g+r788kuWLVum/0Bz8McffxjsS/3J8/bka9++fQaJqzilpKQwf/58mjVrhoODg861c/bsWUOHVyh//fUXkyZNomXLloSGhvL+++8X6f6Cg4OxtbUt8HaBgYHUqVMnx3UajQaVSsUnn3zyrOEVym+//UabNm1wc3PD2toaHx8fevfuzebNm4EHsef1f+fR6/H/2+np6Xz++ec0bdoUOzs7bG1tadq0KZ9//jnp6en5jm3nzp288MILeHh4YGlpibu7O507d2bPnj05ls/KymLFihV07NgRFxcXzM3NcXNzo1OnTnz99dekpqY+07kS+WNm6ABE2TRr1iy8vb1JSUlh9+7dLF68mD/++IMTJ05gbW2d73q+/PJLXFxcCA4OLrpgH/rjjz9YtGhRjsnR/fv3MTMr+v9Oj87bk3x9fYt834Z069YtOnfuzKFDh+jWrRv9+vXD1taWyMhIVq1axddff01aWpqhwyyw7du3Y2JiwtKlS1Gr1YYOB4D+/fvTp08fLCws9F63vv+ffPLJJ7z99tu0adOGKVOmYG1tzfnz5/n7779ZtWoVnTt35t1332XIkCHabQ4ePMjnn3/OO++8Q82aNbXL69WrB8C9e/fo2rUrO3bsoFu3bgQHB2NiYsLmzZsZM2YMv/76K5s2bcLGxuap8Z09exYTExOGDx+Ou7s7d+7c4YcffqB169Zs2rSJzp0765ybF198kS1bthAQEMDEiRMpX748t2/fZseOHbz55pvs37+fpUuX6u38iVwoQhSj0NBQBVAOHjyos3z8+PEKoKxcubJA9dWuXVtp06aNHiPM3ciRIxV9/5cJCwtTACUsLCzPcrmdN0NJSkoq1v117dpVMTExUdauXZttXUpKijJhwgS97Cc9PV1JTU3VS135ERISotjY2OitvqysLCU5OTnX9QMHDizU/tq0aaPUrl07x3VRUVEKoHz88ccFrvdZpKenK/b29krHjh1zXH/9+vUcl69ZsybP/3NvvPGGAihffPFFtnULFy5UAGX48OGFjvvevXtK+fLllaCgIJ3lw4YNUwBlwYIFOW539uxZZdGiRYXer8g/6UoTRqFdu3YAREVFAZCRkcHs2bOpWrUqFhYWeHl58c477+g0JXt5eXHy5El27NihbQ4PDAzUro+Pj2fs2LF4eHhgYWGBr68vH374IVlZWdoyj3cDfP3119r9NW3alIMHD2rLBQcHs2jRIgCd5vdHnmyKv3TpEm+++SZ+fn5YWVnh7OzMK6+8UiTjNh6X3+N55MyZM7z88ss4OTlhaWlJkyZN2Lhxo06ZR914j/5qdXNzo3Llytr1ixYtwsfHBysrK/z9/dm1axeBgYHazyIpKQkbGxvGjBmTbf8xMTGYmpoyd+7cXI9p//79bNq0icGDB/PSSy9lW29hYaHTjfP4vh8XHByMl5dXjudqwYIF2nN1+PBhzMzMmDlzZrY6IiMjUalULFy4ULssP9dZTlQqFaGhody7d097PT3qFs7P9Q8P/g9069aNLVu20KRJE6ysrPjqq6/y3O/TFOcYoxkzZqBSqTh//jzBwcE4Ojri4OBASEgIycnJedZ169YtEhMTadmyZY7r3dzcChxfTEwMS5cupV27dowaNSrb+pEjR9K2bVu+/fZbYmJiClw/gLW1Na6ursTHx2uXXb58mW+//ZbOnTvn+P8EoFq1arz55puF2qcoGOlKE0bhwoULADg7OwMwZMgQli9fzssvv8yECRPYv38/c+fO5fTp06xbtw6ABQsWMHr0aGxtbXn33XcBKF++PADJycm0adOGK1euMGzYMKpUqcI///zDlClTiI2NZcGCBTr7X7lyJXfv3mXYsGGoVCo++ugjevXqxcWLFzE3N2fYsGFcvXqVrVu38v333z/1eA4ePMg///xDnz59qFy5MhqNhsWLFxMYGMipU6cK1F34uISEBG7duqWzTKVSac9bfo8H4OTJk7Rs2ZJKlSoxefJkbGxsWL16NT179uSXX37hxRdf1KnzzTffxNXVlWnTpnHv3j0AFi9ezKhRo2jVqhXjxo1Do9HQs2dPypUrp02ebG1tefHFF/n555+ZN28epqam2jp/+uknFEXhtddey/WYHyVq/fv3L9Q5e5rQ0FBSUlJ44403sLCwoEKFCrRp04bVq1czffp0nbI///wzpqamvPLKK0DBr7PHff/993z99dccOHCAb7/9FoCAgAAgf9f/I5GRkfTt25dhw4YxdOhQ/Pz89Hh2/pOZmZnt2gO4c+fOM9fdu3dvvL29mTt3LhEREXz77be4ubnx4Ycf5rqNm5sbVlZW/Pbbb4wePRonJ6dnjuPPP/8kMzOTAQMG5FpmwIABhIWFsXnzZp0uurwkJiaSlpbGrVu3WLFiBSdOnOCdd97Jtt/XX3/9mY9B6IGhm6xE2fKoS+jvv/9Wbt68qVy+fFlZtWqV4uzsrFhZWSkxMTHKkSNHFEAZMmSIzrYTJ05UAGX79u3aZbl1pc2ePVuxsbFRzp49q7N88uTJiqmpqRIdHa0oyn/dAM7Ozsrt27e15TZs2KAAym+//aZdlldXGqBMnz5d+z6n7oy9e/cqgLJixQrtsoJ2peX0srCw0JYryPG0b99eqVu3rpKSkqJdlpWVpQQEBCjVqlXLtu/nnntOycjI0C5PTU1VnJ2dlaZNmyrp6ena5cuWLVMAnc9ly5YtCqD8+eefOsdVr169p3aFvvjiiwqg3LlzJ89yj7Rp0ybHOgcOHKh4enpq3z86V/b29sqNGzd0yn711VcKoBw/flxnea1atZR27dpp3+f3OstNTl1bBbn+PT09FUDZvHlznvvJa39PevR5R0VFaZe1adMm1+vv0Ss/XWlP/j+ZPn26AiiDBg3SKffiiy8qzs7OT61v2rRpCqDY2NgoXbp0UebMmaMcOnQoz23y6kobO3asAiiHDx/OdfuIiAgFUMaPH//U+B4JCgrSnie1Wq0MGzZMuX//vnb9uHHjFEA5cuSIznapqanKzZs3ta9bt27le5+i8KQrTRhEhw4dcHV1xcPDgz59+mBra8u6deuoVKkSf/zxBwDjx4/X2WbChAkAbNq06an1r1mzhlatWlGuXDlu3bqlfXXo0IHMzEx27typU/7VV1+lXLly2vetWrUC4OLFi4U6PisrK+2/09PTiYuLw9fXF0dHRyIiIgpVJzzottq6davO688//8xW7mnHc/v2bbZv307v3r25e/eu9vzExcURFBTEuXPnuHLlik6dQ4cO1Wnt+ffff4mLi2Po0KE6A2pfe+01nX3Dg8+7YsWK/Pjjj9plJ06c4NixY0/9KzkxMREAOzu7PMsV1ksvvYSrq6vOsl69emFmZsbPP/+sXXbixAlOnTrFq6++ql1W0OssPwp6/Xt7exMUFFTg/RSUl5dXtmtv69at/PDDD89c9/Dhw3Xet2rViri4OO1nn5uZM2eycuVKGjZsyJYtW3j33Xdp3LgxjRo14vTp0wWO4+7du0De19qjdU+L7XEffPABf/31F0uXLqV58+akpaWRkZGhXf+orifvGPzjjz9wdXXVvjw9PfO9T1F40pUmDGLRokVUr14dMzMzypcvj5+fHyYmD/L0S5cuYWJiku1OK3d3dxwdHbl06dJT6z937hzHjh3L9oP3yI0bN3TeV6lSRef9ox/2wnYT3L9/n7lz5xIaGsqVK1dQFEW7LiEhoVB1Avj7+9OkSZOnlnva8Zw/fx5FUZg6dSpTp07NsY4bN25QqVIl7fsn74Z79Dk8+TmZmZnpjOUBMDEx4bXXXmPx4sUkJydjbW3Njz/+iKWlpbZbKjf29vbAgx8tR0fHPMsWRk53+bm4uNC+fXtWr17N7NmzgQfdaGZmZvTq1UtbrqDXWX4U9PrPKf6iYGNjQ4cOHbIt18dYpLyu10eff2769u1L3759SUxMZP/+/SxbtoyVK1fSvXt3Tpw4gaWlZb7jeJT0PEqQcvJk8pSWlsbt27d1yri6uur8EfH4/FSvv/46jRo1Ijg4mLVr1+rUlZSUpFNPy5Yt2bp1K/BgvqvcbvMX+iWJkTCI/PzAPz64uaCysrLo2LEjkyZNynF99erVdd4//iX2uMcTmoIYPXo0oaGhjB07lhYtWuDg4IBKpaJPnz5PHZSrD087nkcxTJw4MdfWhid/mB9vBSuMAQMG8PHHH7N+/Xr69u3LypUr6datGw4ODnluV6NGDQCOHz+ubfnKi0qlyvFzy8zMzLF8bsfVp08fQkJCOHLkCA0aNGD16tW0b98eFxcXbZmCXmcFkd/r/1k/F2Ogj/9/9vb2dOzYkY4dO2Jubs7y5cvZv38/bdq0yXcdj27fP3bsWK6TbR47dgyAWrVqAfDPP//Qtm1bnTJRUVHZ/jh4RK1W88ILL/DBBx9w//59rKystNf4iRMnqF+/vrasq6urNhnVR8ucyB9JjITR8fT0JCsri3PnzunMM3L9+nXi4+N1mpNz+/GoWrUqSUlJOf6FW1gFSdTWrl3LwIED+fTTT7XLUlJSdO5EMSQfHx8AzM3NC32OHn0O58+f1/lhyMjIQKPRaOeFeaROnTo0bNiQH3/8kcqVKxMdHc0XX3zx1P10796duXPn8sMPP+QrMSpXrlyOXaD5aWl8XM+ePRk2bJi2O+3s2bNMmTJFp0xRXGcFuf5Fzpo0acLy5cuJjY0t0HZdunTB1NSU77//PtcB2CtWrMDMzEw7B1H9+vW1rTqPuLu757mf+/fvoygKd+/excrKSrvfH3/8Mc8bEUTxkDFGwug8//zzANnu6Jk3bx4AXbt21S6zsbHJMdno3bs3e/fuZcuWLdnWxcfH6/Tv59ejCd3yk9yYmppm+2v3iy++yLXVori5ubkRGBjIV199leOPx82bN59aR5MmTXB2duabb77ROZ8//vhjrl2Q/fv356+//mLBggU4OzvTpUuXp+6nRYsWdO7cmW+//Zb169dnW5+WlsbEiRO176tWrcqZM2d0juHo0aMF7oZwdHQkKCiI1atXs2rVKtRqNT179tQpUxTXWUGu/7IsOTmZvXv35rju0bi7gt6h5+HhQUhICH///TeLFy/Otn7JkiVs376dwYMHa++6LFeuHB06dNB5Peq+y6krNT4+nl9++QUPDw/tlAJVqlRh0KBB/PnnnzpTQTyusK3XouCkxUgYnfr16zNw4EC+/vpr4uPjadOmDQcOHGD58uX07NlTp3WicePGLF68mPfeew9fX1/c3Nxo164db7/9Nhs3btTOXNu4cWPu3bvH8ePHWbt2LRqNRqdLJD8aN24MwFtvvUVQUBCmpqb06dMnx7LdunXj+++/x8HBgVq1arF3717+/vvvbLfVF9Sff/7JmTNnsi0PCAjQtgLl16JFi3juueeoW7cuQ4cOxcfHh+vXr7N3715iYmI4evRontur1WpmzJjB6NGjadeuHb1790aj0bBs2TKqVq2aYwtbv379mDRpEuvWrWPEiBHaqQOeZsWKFXTq1IlevXrRvXt32rdvj42NDefOnWPVqlXExsZq5zIaNGgQ8+bNIygoiMGDB3Pjxg2WLFlC7dq1CzRgFh4MYn/99df58ssvCQoKyjbGqSius4Jc/4WRnp7Oe++9l225k5NTiZonJzk5mYCAAJo3b07nzp3x8PAgPj6e9evXs2vXLnr27EnDhg0LXO/8+fM5c+YMb775Jps3b9a2DG3ZsoUNGzbQpk0bnZbgvHTp0oXKlSvTrFkz3NzciI6OJjQ0lKtXr+oM7IcHiXBUVBSjR49m1apVdO/eHTc3N27dusWePXv47bffimwqBvEEg90PJ8qk/M7gnJ6ersycOVPx9vZWzM3NFQ8PD2XKlCk6t5YriqJcu3ZN6dq1q2JnZ5ftFvG7d+8qU6ZMUXx9fRW1Wq24uLgoAQEByieffKKkpaUpipL3rL08cWtxRkaGMnr0aMXV1VVRqVQ6t+4/WfbOnTtKSEiI4uLiotja2ipBQUHKmTNnFE9PT2XgwIHacvq4XR9QQkNDC3w8iqIoFy5cUAYMGKC4u7sr5ubmSqVKlZRu3brpzDD9tM/s888/Vzw9PRULCwvF399f2bNnj9K4cWOlc+fOOZZ//vnnFUD5559/8jzmJyUnJyuffPKJ0rRpU8XW1lZRq9VKtWrVlNGjRyvnz5/XKfvDDz8oPj4+ilqtVho0aKBs2bIl19v187rNPDExUbGyslIA5YcffsixTH6us9zkdvt8fq9/T09PpWvXrnnu48n95XYNVa1aVVGU3G/X18fM109eg49u179586ZOuZxieFJ6erryzTffKD179tRef9bW1krDhg2Vjz/+ONcZzJ8287WiPLhNfv78+Urjxo0VGxsbxdraWmnUqJGyYMGCp36mj1u4cKHy3HPPKS4uLoqZmZni6uqqdO/eXdm5c2eO5TMyMpTQ0FClXbt2ipOTk2JmZqa4uLgo7du3V5YsWaJzi78oOipFkfY5IYT+ZGVl4erqSq9evfjmm2+yrX/xxRc5fvw458+fN0B0QgiRNxljJIQotJSUlGxjH1asWMHt27dzfCxHbGwsmzZtKrJZrIUQ4llJi5EQotDCw8MZN24cr7zyCs7OzkRERLB06VJq1qzJoUOHtE+Mj4qKYs+ePXz77bccPHiQCxcuPPXOHSGEMAQZfC2EKDQvLy88PDz4/PPPuX37Nk5OTgwYMIAPPvhAmxQB7Nixg5CQEKpUqcLy5cslKRJCGC1pMRJCCCGEeEjGGAkhhBBCPCSJkRBCCCHEQzLGqICysrK4evUqdnZ2z/QsLyGEEEIUH+XhY1gqVqyofWh5TiQxKqCrV6/i4eFh6DCEEEIIUQiXL1/WPtIlJyUyMQoPD891WvwDBw7QtGnTHNelpKQwYcIEVq1aRWpqKkFBQXz55ZeUL18+3/u2s7MDHpxYe3v7ggcvhBBCiGKXmJiIh4eH9nc8NyXyrrS0tDRu376ts2zq1Kls27aNCxcu5NrFNWLECDZt2sSyZctwcHBg1KhRmJiYFOjhkomJiTg4OJCQkCCJkRBCCFFC5Pf3u0S2GKnVap15UNLT09mwYQOjR4/ONSlKSEhg6dKlrFy5knbt2gEQGhpKzZo12bdvH82bNy+W2IUQQghhvErFXWkbN24kLi6OkJCQXMscOnSI9PR0OnTooF1Wo0YNqlSpwt69e4sjTCGEEEIYuRLZYvSkpUuXEhQUlOdgqmvXrqFWq3F0dNRZXr58ea5du5brdqmpqaSmpmrfJyYmPnO8QgghhDBORpUYTZ48mQ8//DDPMqdPn6ZGjRra9zExMWzZsoXVq1cXSUxz585l5syZRVK3EEIYi8zMTNLT0w0dhhCFZm5ujqmp6TPXY1SJ0YQJEwgODs6zjI+Pj8770NBQnJ2deeGFF/Lczt3dnbS0NOLj43Vaja5fv57nc5umTJnC+PHjte8fjWoXQojSQFEUrl27Rnx8vKFDEeKZOTo64u7u/kzzDBpVYuTq6oqrq2u+yyuKQmhoKAMGDMDc3DzPso0bN8bc3Jxt27bx0ksvARAZGUl0dDQtWrTIdTsLCwssLCzyHZMQQpQkj5IiNzc3rK2tZeJaUSIpikJycjI3btwAoEKFCoWuy6gSo4Lavn07UVFRDBkyJNu6K1eu0L59e1asWIG/vz8ODg4MHjyY8ePH4+TkhL29PaNHj6ZFixZyR5oQokzKzMzUJkXOzs6GDkeIZ2JlZQXAjRs3cHNzK3S3WolOjJYuXUpAQIDOmKNH0tPTiYyMJDk5Wbts/vz5mJiY8NJLL+lM8CiEEGXRozFF1tbWBo5ECP14dC2np6cXOjEqkRM8GpJM8CiEKC1SUlKIiorC29sbS0tLQ4cjxDPL65rO7+93qZjHSAghhBBCHyQxMqCoGVFoZmtyXKeZrSFqRlTxBiSEEEKUcZIYGZDKVIVmmgbNbA0xiTGERYURkxiDZrYGzTQNKlO5O0QIIXISHByMSqXK9jp//jzw4G670aNH4+Pjg4WFBR4eHnTv3p1t27Zp6/Dy8mLBggUGOgJhrEr04OuSzmuqFwCaaRpCw0JZ0WYFA3YMICQsBK9ZXtr1QgghsuvcuTOhoaE6y1xdXdFoNLRs2RJHR0c+/vhj6tatS3p6Olu2bGHkyJGcOXPGQBGLkkASIwMzG2NGaFgoIWEhvLbzNdSZakLbhjJnzBxDhyaEEEbNwsIixwl633zzTVQqFQcOHMDGxka7vHbt2gwaNKg4QxQlkCRGBnYu7hwr2qzQJkVppmmsaLOCkNshVLbP/dlvQghRFB5NlGcI+phg8vbt22zevJk5c+boJEWPPPm8TCGeJImRgVVzrsaAHQO0SZE6U82AHQPwHedr6NCEEGVQcnIytra2Btl3UlJSjslMbn7//XedWLt06cLbb7+Noig5zm8nRH5IYmRgGZ9lEBIWQmhb3TFGGZ9lwFRDRyeEEMarbdu2LF68WPvexsaG6OhoA0YkSgNJjAzo0d1nXrO8mDNmDiG3Q/Ad50vGZxlopmkAZAC2EKJYWVtbk5SUZLB9F4SNjQ2+vrqt6xYWFqhUKhlgLQpNEiMDUjIVnbvPtGOKpv63XgghipNKpSpQd5axcXJyIigoiEWLFvHWW29lO5b4+HgZZyTyJImRAXnP8M51nbQUCSFE4SxatIiWLVvi7+/PrFmzqFevHhkZGWzdupXFixdz+vRpQ4cojJgkRkIIIUoVHx8fIiIimDNnDhMmTCA2NhZXV1caN26sMyZJiJzIQ2QLqKgeIrv/3XdJ2bQJh5AQGowZo7d6hRAiN/IQWVHayENkS5GjP0Sy7Wgvfv0qwdChCCGEEGWWdKUZiWP2XVjEYAKj/jB0KEIIIUSZJS1GRqJ28weTlF1KkYkdhRBCCEORxMhItOpbF4BLVOVObLxhgxFCCCHKKEmMjEStNjVw4hZZmBK+fL+hwxFCCCHKJEmMjISJqQnepg9maj289aqBoxFCCCHKJkmMjIiHQwwA50+bGjgSIYQQomySxMiIeHvfA+BKnKuBIxFCCCHKJrld34i88LLCm4d8Mc+IBtIMHY4QQghR5kiLkRGp/0pbfLmAZ1Y6iTExhg5HCCHKvMDAQMaOHWvoMPROo9GgUqk4cuRIrmXCw8NRqVTEx8cXW1zGQBIjI1KualViTR58JNGbNxs4GiGEMF65JSzLli3D0dFRb/v59ddfmT17tt7qe1aXL19m0KBBVKxYEbVajaenJ2PGjCEuLk7v+woICCA2NhYHBwdA/+fWWEliZGRCrQfRl5Vs+DHZ0KEIIUSZ5+TkhJ2dnaHDAODixYs0adKEc+fO8dNPP3H+/HmWLFnCtm3baNGiBbdv39br/tRqNe7u7qhUKr3Wa+wkMTIyR6zbsIq+HD7hbOhQhBCixAsODqZnz5588sknVKhQAWdnZ0aOHEl6erq2zJdffkm1atWwtLSkfPnyvPzyy9p1T7ZMeXl58d577zFgwABsbW3x9PRk48aN3Lx5kx49emBra0u9evX4999/tds8amlZv369dj9BQUFcvny5QMcycuRI1Go1f/31F23atKFKlSp06dKFv//+mytXrvDuu+9qy6pUKtavX6+zvaOjI8uWLdNZdubMGQICArC0tKROnTrs2LFDu+7xrrTw8HBCQkJISEhApVKhUqmYMWNGgeIvKSQxMjJVqz8YdH05vpKBIxFClEmKAvfuGealKEVySGFhYVy4cIGwsDCWL1/OsmXLtAnCv//+y1tvvcWsWbOIjIxk8+bNtG7dOs/65s+fT8uWLTl8+DBdu3alf//+DBgwgNdff52IiAiqVq3KgAEDUB47nuTkZObMmcOKFSvYs2cP8fHx9OnTJ9/HcPv2bbZs2cKbb76JlZWVzjp3d3dee+01fv75Z5195sfbb7/NhAkTOHz4MC1atKB79+45dssFBASwYMEC7O3tiY2NJTY2lokTJxZoXyWF3JVmZBq0c4PdEJVRw9ChCCHKouRksLU1zL6TksDGRu/VlitXjoULF2JqakqNGjXo2rUr27ZtY+jQoURHR2NjY0O3bt2ws7PD09OThg0b5lnf888/z7BhwwCYNm0aixcvpmnTprzyyisA/N///R8tWrTg+vXruLu7A5Cens7ChQtp1qwZAMuXL6dmzZocOHAAf3//px7DuXPnUBSFmjVr5ri+Zs2a3Llzh5s3b+Lm5pbvczNq1CheeuklABYvXszmzZtZunQpkyZN0imnVqtxcHBApVJpj6m0khYjI9M2+MF/kJu4c2bPWQNHI4QQJV/t2rUxNf1v4twKFSpw48YNADp27Iinpyc+Pj7079+fH3/8keTkvMd41qtXT/vv8uXLA1C3bt1syx7tA8DMzIymTZtq39eoUQNHR0dOnz5doGN5WouQWq0uUH0tWrTQibFJkyYFjqm0kcTIyLh5u1GFCwDs/umYgaMRQpQ51tYPWm4M8bK2zneY9vb2JCQkZFseHx+vvYvqEXNzc533KpWKrKwsAOzs7IiIiOCnn36iQoUKTJs2jfr16+d5i/rj9T0amJzTskf70AdfX19UKlWuScvp06dxdXXV3jWmUqmyJVGPj6sSuZPEyAh5WpwD4Pie7P/phRCiSKlUD7qzDPEqwN1Pfn5+REREZFseERFB9erVC3TIZmZmdOjQgY8++ohjx46h0WjYvn17gep4moyMDJ0B2ZGRkcTHx+faNfYkZ2dnOnbsyJdffsn9+/d11l27do0ff/yR4OBg7TJXV1diY2O178+dO5djS9i+fft0Yjx06FCuManVajIzM/MVb0kmiZERquJyHTPSSYhJNXQoQghhlEaMGMHZs2d56623OHbsGJGRkcybN4+ffvqJCRMm5Lue33//nc8//5wjR45w6dIlVqxYQVZWFn5+fnqN19zcnNGjR7N//34OHTpEcHAwzZs3144vOnDgADVq1ODKlSu51rFw4UJSU1MJCgpi586dXL58mc2bN9OxY0eqV6/OtGnTtGXbtWvHwoULOXz4MP/++y/Dhw/P1nIGsGjRItatW8eZM2cYOXIkd+7cYdCgQTnu38vLi6SkJLZt28atW7ee2uVYUkliZIQGdj3BPWwYnzrZ0KEIIYRR8vHxYefOnZw5c4YOHTrQrFkzVq9ezZo1a+jcuXO+63F0dOTXX3+lXbt21KxZkyVLlvDTTz9Ru3ZtvcZrbW3N//3f/9GvXz9atmyJra0tP//8s3Z9cnIykZGReXZ3VatWjYMHD+Lj40Pv3r3x9PSkS5cuVK9enT179mD72KD5Tz/9FA8PD1q1akW/fv2YOHEi1jl0VX7wwQd88MEH1K9fn927d7Nx40ZcXFxy3H9AQADDhw/n1VdfxdXVlY8++ugZzojxUikFvbevjEtMTMTBwYGEhATs7e2LZB9nf/mF6i+/TAJgn5mJykTyVyGE/qWkpBAVFYW3tzeWlpaGDqfUWrZsGWPHji2SR2tMnz6defPmsXXrVpo3b673+kuavK7p/P5+yy+uEfIKCiIdcACuHTpk6HCEEEIYqZkzZ/L555+zb98+vQ72LstkHiMjpLa1ZbTpe+zP7Ejw4rO8+dgtnkIIIcTjQkJCDB1CqSItRkbqtLoeB/Hn+D4ZgC2EECVZcHBwmXtCfUkmiZGRquJ+E4BLMQ5PKSmEEEIIfZHEyEhVr/eglzP6npdhAxFCCCHKEEmMjFTT7t4AXMyqSUZahoGjEUIIIcoGSYyMVKt+zbAghftY88/qg4YORwghhCgTJDEyUmorNT6qMwDsX3/ewNEIIYQQZYPcrm/EPG0ukJZkS9JZjaFDEUIIIcoEaTEyYm8/9x3nqUZQwreGDkUIIUoclUrF+vXrDR2G3i1btgxHR8c8y8yYMYMGDRoUSzyljSRGRsyu+YOHC7pev27gSIQQwrjcvHmTESNGUKVKFSwsLHB3dycoKIg9e/Zoy8TGxtKlSxcDRqnrn3/+4fnnn6dcuXJYWlpSt25d5s2bVyRPrJ84cSLbtm3Tvg8ODqZnz556309pJImREavYqRMAnqmppN5NMnA0QghhPF566SUOHz7M8uXLOXv2LBs3biQwMJC4uDhtGXd3dywsLAwY5X/WrVtHmzZtqFy5MmFhYZw5c4YxY8bw3nvv0adPH/T92FJbW1ucnZ31WmeZoYgCSUhIUAAlISGhyPeVlZmpBPGbUo445Y/PtxX5/oQQZcv9+/eVU6dOKffv3zd0KAVy584dBVDCw8PzLAco69atUxRFUaKiohRA+fnnn5XnnntOsbS0VJo0aaJERkYqBw4cUBo3bqzY2NgonTt3Vm7cuKGtY+DAgUqPHj2UGTNmKC4uLoqdnZ0ybNgwJTU1Nd/xJiUlKc7OzkqvXr2yrdu4caMCKKtWrVIURVHCwsIUQLlz5462zOHDhxVAiYqKUhRFUUJDQxUHBwdl3bp1iq+vr2JhYaF06tRJiY6O1m4zffp0pX79+tp/AzqvsLCwfMdfkuR1Tef391tajIyYysSEayau3MGJg39EGzocIUQZcu9e7q+UlPyXvX8/f2ULwtbWFltbW9avX09qasEemzR9+nT+97//ERERgZmZGf369WPSpEl89tln7Nq1i/PnzzNt2jSdbbZt28bp06cJDw/np59+4tdff2XmzJn53udff/1FXFwcEydOzLaue/fuVK9enZ9++qlAx5GcnMycOXNYsWIFe/bsIT4+nj59+uRYduLEifTu3ZvOnTsTGxtLbGwsAQEBBdpfWSKJkZHzsLsEwPmTBg5ECFGm2Nrm/nrpJd2ybm65l31yiI+XV87lCsLMzIxly5axfPlyHB0dadmyJe+88w7Hjh176rYTJ04kKCiImjVrMmbMGA4dOsTUqVNp2bIlDRs2ZPDgwYSFhelso1ar+e6776hduzZdu3Zl1qxZfP755/l+mv3Zs2cBqFmzZo7ra9SooS2TX+np6SxcuJAWLVrQuHFjli9fzj///MOBAweylbW1tcXKyko7Fsvd3R21Wl2g/ZUlkhgZOW/PuwBculHewJEIIYTxeOmll7h69SobN26kc+fOhIeH06hRI5YtW5bndvXq1dP+u3z5B9+rdevW1Vl248YNnW3q16+PtbW19n2LFi1ISkri8uXLBYpZyWMcUUETFTMzM5o2bap9X6NGDRwdHTl9+nSB6hHZyTxGRq52Czs4BtGpvoYORQhRhiTlcb+Hqanu+yfyCB0mT/z5rdEUOqRsLC0t6dixIx07dmTq1KkMGTKE6dOnExwcnOs25ubm2n+rVKocl+W3JSi/qlWrBsDp06dz7MI6ffq09tZ6k4cn7PEkKj09Xa/xiLxJi5GRa9XvwV83l6jKrehbBo5GCFFW2Njk/rK0zH9ZK6v8ldWHWrVqca+gA5by4ejRo9x/bLDUvn37sLW1xcPDI1/bBwUF4eTkxKeffppt3caNGzl37pw2mXN1dQUeTDXwyJEjR7Jtl5GRwb///qt9HxkZSXx8fK7ddWq1ukimBSiNJDEycrVa18CFGyiYsGNF9r5jIYQoa+Li4mjXrh0//PADx44dIyoqijVr1vDRRx/Ro0cPve8vLS2NwYMHc+rUKf744w+mT5/OqFGjtK07CxcupH379rlub2Njw1dffcWGDRt44403OHbsGBqNhqVLlxIcHMzQoUN5/vnnAfD19cXDw4MZM2Zw7tw5Nm3alGNCZW5uzujRo9m/fz+HDh0iODiY5s2b4+/vn2MMXl5eHDt2jMjISG7duiWtUHmQrrQSoLH5Lki34c6/EcDzhg5HCCEMytbWlmbNmjF//nwuXLhAeno6Hh4eDB06lHfeeUfv+2vfvj3VqlWjdevWpKam0rdvX2bMmKFdf+vWLS5cuJBnHS+//DJhYWHMmTOHVq1akZiYCMCHH37IpEmTtOXMzc356aefGDFiBPXq1aNp06a89957vPLKKzr1WVtb83//93/069ePK1eu0KpVK5YuXZrr/ocOHUp4eDhNmjQhKSmJsLAwAgMDC34yygCVktdoMJFNYmIiDg4OJCQkYG9vXyz73FGvHm2OHye8SRMCDx4sln0KIUq/lJQUoqKi8Pb2xvLJ/jEBPJgxOj4+Xu+PFklJSaFHjx5cvnyZHTt2aLvQxLPJ65rO7++3dKWVAKqHd0zY6HPUohBCCIOxtLRkw4YNDBgwgJ07dxo6HPEY6UorARyfew5WrsTmtjTuCSFEaWFpacnkyZMNHYZ4giRGJYBbu65U5AqxWRXRHIvGs14VQ4ckhBBlwtPmRRKlj3SllQDuflWAB7dZhq84ZNhghBBCiFJMEqMSwsv8wXTxx3feNnAkQgghROkliVEJUcXpKgAXL1o/paQQQgghCksSoxKiqt+DybguJ1Q2cCRCCCFE6SWJUQnRsIM7ABczaiIzTwkhhBBFQxKjEiJwoD8qsriNC6d2njF0OEIIIUSpJLfrlxAuVVzorlpFZSWOmG1m1G5Tw9AhCSGEEKWOtBiVIFPcx7OIUVie/MvQoQghhBClkiRGJUhK1aoAqE6dMnAkQghRdgQGBjJ27FhDh1FgJTVuQ5PEqARRN2pEEjbcjrYxdChCCGFwuf3wL1u2DEdHR73t59dff2X27Nl6q+9ZBAcH07Nnz3yVNaa4C2vu3Lk0bdoUOzs73Nzc6NmzJ5GRkUW6zxKZGIWHh6NSqXJ8Hczl6fO3b99m9OjR+Pn5YWVlRZUqVXjrrbdISEgo5ugLL8nvBexIYkDydrIyswwdjhBClAlOTk7Y2dkZOowCM2TcGRkZeqlnx44djBw5kn379rF161bS09Pp1KkT9+7d00v9OSmRiVFAQACxsbE6ryFDhuDt7U2TJk1y3Obq1atcvXqVTz75hBMnTrBs2TI2b97M4MGDizn6wgvo0wwz0rmLPf9uPGzocIQQQkdMYgxhUWHEJMYYOhQdgYGBvPXWW0yaNAknJyfc3d2ZMWOGdv3atWupW7cuVlZWODs706FDB50f3idbpgIDAxk9ejRjx46lXLlylC9fnm+++YZ79+4REhKCnZ0dvr6+/PnnnzrbjBo1ilGjRuHg4ICLiwtTp05Fecb5V/KKPae48zoPAHfv3uW1117DxsaGChUqMH/+/Kd2yWk0GlQqFatXr6ZVq1ZYWFiwcePGZzquRzZv3kxwcDC1a9emfv36LFu2jOjoaA4dKrrHY5XIxEitVuPu7q59OTs7s2HDBkJCQlCpVDluU6dOHX755Re6d+9O1apVadeuHXPmzOG3337TW2Zb1GydbPFWPXg0yD9r5ZZ9IYTxWBqxFM8FnrRb0Q7PBZ4sjVhq6JB0LF++HBsbG/bv389HH33ErFmz2Lp1K7GxsfTt25dBgwZx+vRpwsPD6dWr11MTluXLl+Pi4sKBAwcYPXo0I0aM4JVXXiEgIICIiAg6depE//79SU5O1tnGzMyMAwcO8NlnnzFv3jy+/fbbQh9TYWLP7Tw8Mn78ePbs2cPGjRvZunUru3btIiIiIs84jh49CsDHH3/MtGnTOHnyJO3bt9euf//997G1tc3zFR0dna9jftTL4+TklK/yhVEqbtffuHEjcXFxhISEFGi7hIQE7O3tMTPL/TSkpqaSmpqqfZ+YmFjoOPWhitUFziXX5vSh1KcXFkKIYhCTGMMbv79BlvKgiz9LyWLY78MI8g2isr1xzNZfr149pk+fDkC1atVYuHAh27Ztw9nZmYyMDHr16oWnpycAdevWfWp99evX53//+x8AU6ZM4YMPPsDFxYWhQ4cCMG3aNBYvXsyxY8do3rw5AB4eHsyfPx+VSoWfnx/Hjx9n/vz52m0KKjY2tsCx53YeOnbsyN27d1m+fDkrV67UJjahoaFUrFgxzzqPHDmCjY0Na9aswcvLK9v64cOH07t37zzreNo+ALKyshg7diwtW7akTp06Ty1fWKUiMVq6dClBQUFUrpz//4C3bt1i9uzZvPHGG3mWmzt3LjNnznzWEPXG0z0OLsKlK+UMHYoQQgBwLu6cNil6JFPJ5Pzt80aVGD2uQoUK3Lhxg/r169O+fXvq1q1LUFAQnTp14uWXX6Zcuby/Yx+vz9TUFGdnZ52kpHz58gDcuHFDu6x58+Y6vRotWrTg008/JTMzE1NT0wIfU2Fiz+08AFy8eJH09HT8/f216x0cHPDz88szjqNHj/LCCy/kmBTBg9YdfbTwjBw5khMnTrB79+5nrisvRtWVNnny5FwHVT96nTmj24UUExPDli1bCjRWKDExka5du1KrVq1s/atPmjJlCgkJCdrX5cuXC3NoeuPX4EEuG33P26BxCCHEI9Wcq2Gi0v05MVWZ4uvkW6T7tbe3z/EGmvj4eBwcHHSWmZub67xXqVRkZWVhamrK1q1b+fPPP6lVqxZffPEFfn5+REVF5bnvnOp7fNmjBCgrq+hulClM7Lmdh2dx5MgRAgMDc12vj660UaNG8fvvvxMWFlagRpDCMKoWowkTJhAcHJxnGR8fH533oaGhODs788ILL+RrH3fv3qVz587Y2dmxbt26bBfJkywsLLCwsMhX3cWhWY+q8CtcVGqQdj8NtZXa0CEJIcq4yvaV+brb1wz7fRiZSiamKlO+6vZVkbcW+fn58ddf2Se8jYiIoHr16vmuR6VS0bJlS1q2bMm0adPw9PRk3bp1jB8/Xp/hsn//fp33+/bto1q1aoVqLXpEn7H7+Phgbm7OwYMHqVKlCvBgyMnZs2dp3bp1jtskJiai0Who2LBhrvU+S1eaoiiMHj2adevWER4ejrd30TcKGFVi5Orqiqura77LK4pCaGgoAwYMeGqCAw8+wKCgIO2IeUtLy2cJ1yBavNKEkIFfU5fTXNj6PDVf6GjokIQQgsGNBhPkG8T52+fxdfItli60ESNGsHDhQt566y2GDBmChYUFmzZt4qeffuK3337LVx379+9n27ZtdOrUCTc3N/bv38/NmzepWbOm3uONjo5m/PjxDBs2jIiICL744gs+/fRT7fqFCxeybt06tm3bZpDY7ezsGDhwIG+//TZOTk64ubkxffp0TExMcr2x6ejRo5iamuY5tulZutJGjhzJypUr2bBhA3Z2dly7dg140MVnZWVVqDqfxqgSo4Lavn07UVFRDBkyJNu6K1eu0L59e1asWIG/vz+JiYl06tSJ5ORkfvjhBxITE7UDqV1dXZ8pYy9Oais1E63HUSs5mX27zUESIyGEkahsX7lYxxT5+Piwc+dO3n33XTp06EBaWho1atRgzZo1dO7cOV912Nvbs3PnThYsWEBiYiKenp58+umndOnSRe/xDhgwgPv37+Pv74+pqSljxozRGed669YtLly4kO/6iiL2efPmMXz4cLp164a9vT2TJk3i8uXLuTYkHD16FD8/vyJraFi8eDFAtq660NDQp/YwFZZKedZJFAyoX79+XLp0iT179mRbp9Fo8Pb2JiwsjMDAQMLDw2nbtm2O9URFReU6aOxJiYmJODg4aO9oM4Tdvr48d+EC4W3bErh9u0FiEEKUfCkpKURFReHt7V0iW9BLksDAQBo0aMCCBQsMHUqB3Lt3j0qVKvHpp5+WiHn/8rqm8/v7XaJbjFauXJnrOi8vL525HAIDA595Ii1jcb96HY5dsObMCUcCDR2MEEKIUuPw4cOcOXMGf39/EhISmDVrFgA9evQwcGTFp0QnRmXVGdfedKIfvrdOMdzQwQghhChVPvnkEyIjI1Gr1TRu3Jhdu3bh4uJi6LCKjSRGJVDL3rVgBWiUaiTeTMTe1TBdekIIIfInPDzc0CHkS8OGDYv0cRslgVHNYyTyp0HnejhwhwzM2bFin6HDEUIIIUoNSYxKIBNTE3xMTwNwaItxPaxRCCGEKMkkMSqhPOwezBJ6/lTJmGZACCGEKAkkMSqhvLzuARB9q7yBIxFCCCFKD0mMSqi6LR88B+hSajUDRyKEEEKUHpIYlVCBr9flfaawiDHce+zpzUIIIYQoPEmMSijf5n4MNvmIbmzi0p9/GjocIYQQolSQxKgEi3F40J0Wt2OHgSMRQgghSgeZ4LEE01RsxKU7dlzYbUUrQwcjhBBClALSYlSC7bfvRy/W8YvmJUOHIoQQQpQKkhiVYHVbOwGgSfczcCRCCGF8AgMDGTt2rKHDKJSSHHtJJ4lRCRY4sCkA16jExUNRBo5GCCGK182bNxkxYgRVqlTBwsICd3d3goKC2LNnDwC//vors2fPNnCUDwQHB9OzZ898lzem2Atj7ty5NG3aFDs7O9zc3OjZsyeRkZGGDitfJDEqwSrXrERlNADs+D7CsMEIIcqkqBlRaGZrclynma0hakbR/dH20ksvcfjwYZYvX87Zs2fZuHEjgYGBxMXFAeDk5ISdnV2R7b8oGSr2jIwMvdSzY8cORo4cyb59+9i6dSvp6el06tSJe/fu6aX+oiSJUQnnqT4LwPHd8YYNRAhRJqlMVWimabIlR5rZGjTTNKhMVUWy3/j4eHbt2sWHH35I27Zt8fT0xN/fnylTpvDCCy8A2bujAgMDGT16NGPHjqVcuXKUL1+eb775hnv37hESEoKdnR2+vr78+cQUKIGBgYwaNYpRo0bh4OCAi4sLU6dORVGUQse/du1a6tati5WVFc7OznTo0EEnaXg89sDAQN566y0mTZqEk5MT7u7uzJgxQ6e+u3fv8tprr2FjY0OFChWYP3/+U7vjNBoNKpWK1atX06pVKywsLNi4cWOhj+lxmzdvJjg4mNq1a1O/fn2WLVtGdHQ0hw4d0kv9RUkSoxKuinMsAFFR1gaORAhRFnlN9cJrlpdOcvQoKfKa5YXXVK8i2a+trS22trasX7+e1NTUfG+3fPlyXFxcOHDgAKNHj2bEiBG88sorBAQEEBERQadOnejfvz/JycnZtjMzM+PAgQN89tlnzJs3j2+//bZQscfGxtK3b18GDRrE6dOnCQ8Pp1evXnkmWsuXL8fGxob9+/fz0UcfMWvWLLZu3apdP378ePbs2cPGjRvZunUru3btIiIi756Eo0ePAvDxxx8zbdo0Tp48Sfv27XXKvP/++9pzndsrOjr6qceckJAAPGgJM3Zyu34JV7VGJsTC5QQPQ4cihCijHiU/mmkaLr13CSVNKdKkCMDMzIxly5YxdOhQlixZQqNGjWjTpg19+vShXr16uW5Xv359/ve//wEwZcoUPvjgA1xcXBg6dCgA06ZNY/HixRw7dozmzZtrt/Pw8GD+/PmoVCr8/Pw4fvw48+fP125XELGxsWRkZNCrVy88PT0BqFu3bp7b1KtXj+nTpwNQrVo1Fi5cyLZt2+jYsSN3795l+fLlrFy5UpvYhIaGUrFixTzrPHLkCDY2NqxZswYvL68cywwfPpzevXvnWc/T9pOVlcXYsWNp2bIlderUybOsMZAWoxKuw0tOrOYVvswcjJKVZehwhBBllNdUL1RqFUqagkqtKtKk6JGXXnqJq1evsnHjRjp37kx4eDiNGjVi2bJluW7zeNJkamqKs7OzTlJSvvyDB3PfeOJRS82bN0el+q9bsEWLFpw7d47MzMwCx12/fn3at29P3bp1eeWVV/jmm2+4c+dOnts8mexVqFBBG+PFixdJT0/H399fu97BwQE/v7zvWD569CgvvPBCrkkRPGjh8fX1zfNlZpZ3G8vIkSM5ceIEq1atyrOcsZDEqITz79uaXqzFn7PcOHbM0OEIIcoozWyNNilS0pRcB2Trm6WlJR07dmTq1Kn8888/BAcHa1tWcmJubq7zXqVS6Sx7lPxkFeEfmqampmzdupU///yTWrVq8cUXX+Dn50dUVO4D1XOK+1ljPHLkCIGBgXmWedautFGjRvH7778TFhZG5cqVnyne4iKJUQln5eRE9MP/MDGbNxs4GiFEWfT4mKI2qW2yjTkqTrVq1SqSO5/279+v837fvn1Uq1YNU1PTQtWnUqlo2bIlM2fO5PDhw6jVatatW1eounx8fDA3N+fgwYPaZQkJCZw9ezbXbRITE9FoNDRs2DDPuocPH86RI0fyfOXUlaYoCqNGjWLdunVs374db2/vQh2bIcgYo1Jgp0Nb1t6qh7IxhcaTDR2NEKIsyWmg9eNjjh5/r09xcXG88sorDBo0iHr16mFnZ8e///7LRx99RI8ePfS+v+joaMaPH8+wYcOIiIjgiy++4NNPPwVg4cKFrFu3jm3btuWrrv3797Nt2zY6deqEm5sb+/fv5+bNm9SsWbNQsdnZ2TFw4EDefvttnJyccHNzY/r06ZiYmOh0/z3u6NGjmJqaPnVsk5OTU6EGTI8cOZKVK1eyYcMG7OzsuHbtGvCgi8/KyqrA9RUnSYxKge3WfVlBMF1PrmGSoYMRQpQpSmbOA60fvVcyC39Le15sbW1p1qwZ8+fP58KFC6Snp+Ph4cHQoUN555139L6/AQMGcP/+ffz9/TE1NWXMmDG88cYbANy6dYsLFy7kuy57e3t27tzJggULSExMxNPTk08//ZQuXboUOr558+YxfPhwunXrhr29PZMmTeLy5ctYWlrmWP7o0aP4+fnluv5ZLV68GCBbV11oaCjBwcFFsk99USnPMhFDGZSYmIiDgwMJCQnY29sbOhwA5nRbzv82DaSeyQGOZvo/fQMhhABSUlKIiorC29u7yH4gS4PAwEAaNGjAggULDB1Kvt27d49KlSrx6aefMnjwYEOHU2zyuqbz+/stLUalQJOunrAJLmbVJCMtAzO1fKxCCFGWHD58mDNnzuDv709CQgKzZs0CKJJuxdJOBl+XAq36+aMmlSTsOLDO+GcVFUIIoX+ffPIJ9evX186ivWvXLlxcXAwdVokjTQulgLWDNd6qY0Qq9di37iwBrzYzdEhCCFFqhIeHGzqEp2rYsGGJeNxGSSAtRqVEFauLAJyJSDNwJEIIIUTJJYlRKeFZ8TYAmivOBo5ECCGEKLkkMSolXugSRwQN+TgzxNChCCGEECWWJEalRIOXm9GQI9RIjScjJcXQ4QghShCZtUWUFvq4liUxKiUqBQRwD7AAordvN3Q4QogS4NHzt5KTkw0ciRD68ehafvLZcgUhd6WVEpfeu8xe048Jz7SnXqiGUc//t04zW4OSqeA9o+Q8q0YIUfRMTU1xdHTUPqXd2to610dICGHMFEUhOTmZGzdu4OjoWOhn2IEkRqWGylRFxcwmpODFjpO/UjsqjGrO1cj4LEP7HCMhhHiSu7s7gDY5EqIkc3R01F7ThSWJUSnhNdWL37+IYNBN+K78EdqtmMCAHQMICQvJ8TlGQggBD57yXqFCBdzc3EhPTzd0OEIUmrm5+TO1FD0iiVEpEt/jKt+d38Cg8EG8vut11JlqQtuGMmfMHEOHJoQwcqampnr5URGipJPB16VI+Y5WfB+4gjTTNNSZatJM01jRZgXnb583dGhCCCFEiSCJUSkS1LEj/cMHaJMidaaaATsG4Ovka+jQhBBCiBJBEqNSJGthFoPCQ/guMJSgqUGEtg0lJCyEjM8yDB2aEEIIUSLIGKNSQjNbg2aahn8s7/J9xByev+fMnL/Ha+9KA2QAthBCCPEUkhiVEkqmgtcsL+4cmkv8hteJvGRJZft5MPW/9UIIIYTImyRGpcSjyRsTvqiDw4ZEKsbd066TliIhhBAif2SMUSnj0bkzAJUzM0mMiTFwNEIIIUTJIolRKeNUrRpvq6bTjm38+eV+Q4cjhBBClCiSGJVC+8wDCKMd4eviDR2KEEIIUaJIYlQK1a16GYDjF6sYOBIhhBCiZJHEqBRq368CAMfSmpGSlGLgaIQQQoiSQxKjUqj7hA44cIe72LP+w62GDkcIIYQoMSQxKoXUVmrqWTwYeB22+oaBoxFCCCFKDkmMSql61a4AcDzKy7CBCCGEECWIJEalVMf+lXEiDq/0GNKTkw0djhBCCFEiSGJUSnUb155I3FhJMGd++MHQ4QghhBAlgiRGpZSpuRnnK5QHIO6XXwwcjRBCCFEySGJUiqW2aIECpB64bOhQhBBCiBJBEqNSzKTzIDy4TK/4gyTdTjJ0OEIIIYTRk8SoFGsxMIgULEjGhl/el/mMhBBCiKcxK0jhjRs3FngHHTt2xMrKqsDbiWdnpjajnuV+wlK6sWvdHQZ+YuiIhBBCCONWoMSoZ8+eBapcpVJx7tw5fHx8CrSd0J96Na8TdhiOR8tnIIQQQjxNgbvSrl27RlZWVr5e1tbWRRGzKICgQd4AHM/wJ/FmooGjEUIIIYxbgRKjgQMHFqhb7PXXX8fe3r7AQQn9CRoRiAvXuY81v8yRcUZCCCFEXgqUGIWGhmJnZ5fv8osXL8bFxaXAQQn9MTE1oZ7VAQB2bpAWIyGEECIvBRpjlJdTp06xYcMGHB0dqV27NnXr1qVcuXL6ql48g7aNz1Nv93zq3doChBg6HCGEEMJo6e12/RdeeAFra2vu3bvH0qVLad++PVWrVtVX9eIZ9Jvix3zG0zdpCynx8YYORwghhDBaemsxcnd3Z8yYMTrLMjMz9VW9eAbenTtz3cSE8llZHFm2jAZjxxo6JCGEEMIoPXOL0fjx41mxYgVt2rRh6dKlOutMTU2ftXqhByoTE05W8mU7bdn+ncbQ4QghhBBG65kTo8DAQKKjozl37hwff/wx1atXp1+/fsydO5fff/9dHzEKPfijwiTas50fT71i6FCEEEIIo6VSFEXRZ4UpKSmcOHGCY8eOcfz4cebPn6/P6g0uMTERBwcHEhISStRUBGHL9tAupCVqUomNuYdTJSdDhySEEEIUm/z+fhe4xSg4OJjk5ORc11taWtKkSRMGDRpU6pKikqxN/xZUIIY0LFg9S+YzEkIIIXJS4MTo+++/Jynpvye1jxgxgvgn7nTKyMh45sDyEh4ejkqlyvF18ODBp26vKApdunRBpVKxfv36Io3VWJiYmlDX5l8A/vnzvoGjEUIIIYxTgROjJ3vefvzxR27fvq19f/369SLvYgoICCA2NlbnNWTIELy9vWnSpMlTt1+wYAEqlapIYzRGDeo/+JyOX/UzcCRCCCGEcXrmwdc5DVFKSUl51mrzpFarcXd3176cnZ3ZsGEDISEhT014jhw5wqeffsp3331XpDEao64jagJwMrMxN6JuGDgaIYQQwvjobYLHxxV3a8zGjRuJi4sjJCTvWZ2Tk5Pp168fixYtwt3dPV91p6amkpiYqPMqqZ7r24yKRJOOmrVzthk6HCGEEMLoFCoxWrlyJREREaSnp+s7nkJZunQpQUFBVK5cOc9y48aNIyAggB49euS77rlz5+Lg4KB9eXh4PGu4BmNiasJ49+kcpgE1Ti40dDhCCCGE0SlwYtSqVSumT59OkyZNsLW1JTk5menTp7NkyRL27dunMzC7oCZPnpzroOpHrzNnzuhsExMTw5YtWxg8eHCedW/cuJHt27ezYMGCAsU0ZcoUEhIStK/Lly8X9LCMin8XFQ04iuuJY4YORQghhDA6hZ7H6Ny5cxw6dIiIiAjtKz4+XtuNVpjHgdy8eZO4uLg8y/j4+KBWq7XvZ8+ezRdffMGVK1cwNzfPdbuxY8fy+eefY2LyXy6YmZmJiYkJrVq1Ijw8PF8xltR5jB6J2b2byq1akQ6kxsZim88uRSGEEKIky+/vt14neIyKiuLff//l8OHDvP/++/qqNleKolC1alV69erFJ598kmfZa9eucevWLZ1ldevW5bPPPqN79+54e3vna58lPTEC+Mb0ZfZkdaPlYBVDvx1o6HCEEEKIIlckEzweO3aMrKysXNd7e3vzyiuvaJOikydPFumcRtu3bycqKoohQ4ZkW3flyhVq1KjBgQMHgAcPua1Tp47OC6BKlSr5TopKi3U2fVlOMGF/lL0pC4QQQoi8FCgxatiw4VO7uh7XokULoqOjCxxUfi1dupSAgABq1KiRbV16ejqRkZF5ztJdVjVqlADAies1DRyJEEIIYVzMClJYURSmTp2KtbV1vsqnpaUVKqj8WrlyZa7rvLy8cpxj6XF6fkxcifHCmPrM2QGnshoSc/oKlWtWMnRIQgghhFEoUGLUunVrIiMj812+RYsWWFlZFTgoUbT8X2xMFS4QTVXWvhfO2B9fM3RIQgghhFEoUGKU3zu3hPGrax9BdGJV9m0r+N2DQgghRGlVJDNfC+PXqOk9AE7crG3gSIQQQgjjIYlRGdVzfEMAzLNMuHWh6AbICyGEECWJJEZlVKPn63PIzJ3DNOLism8MHY4QQghhFCQxKsOSfMsBkPznnwaORAghhDAOkhiVYWYdOgBQ7uQ5A0cihBBCGIdCJ0YDBw5k586d+oxFFLNKrw+hHdsISLmK5sglQ4cjhBBCGFyhE6OEhAQ6dOhAtWrVeP/997ly5Yo+4xLFwLNZfS5RiWRsWPOeJLlCCCFEoROj9evXc+XKFUaMGMHPP/+Ml5cXXbp0Ye3ataSnp+szRlGE6pQ7DMD+HdKrKoQQQjzTr6Grqyvjx4/n6NGj7N+/H19fX/r370/FihUZN24c587J2BVj16RFKgAn4+oYOBIhhBDC8PTSTBAbG8vWrVvZunUrpqamPP/88xw/fpxatWoxf/58fexCFJFeb/sDcEapz/kDFwwcjRBCCGFYhU6M0tPT+eWXX+jWrRuenp6sWbOGsWPHcvXqVZYvX87ff//N6tWrmTVrlj7jFXpWO7AmvqpTAKx9f7eBoxFCCCEMq0DPSntchQoVyMrKom/fvhw4cIAGDRpkK9O2bVscHR2fITxRHOqUO8r527U4uNvc0KEIIYQQBlXoxGj+/Pm88sorWFpa5lrG0dGRqKiowu5CFJOWre+Rvv53mif8DfQzdDhCCCGEwagURVEMHURJkpiYiIODAwkJCdjb2xs6HL2Ii4zEuUYNAG6dOoVLzZoGjkgIIYTQr/z+fhe6xWj8+PE5LlepVFhaWuLr60uPHj1wcnIq7C5EMXH28+OspSXVU1I49+23uHz6qaFDEkIIIQyi0InR4cOHiYiIIDMzEz8/PwDOnj2LqakpNWrU4Msvv2TChAns3r2bWrVq6S1gUTRiq1fH6thtjq6/SgvJi4QQQpRRhb4rrUePHnTo0IGrV69y6NAhDh06RExMDB07dqRv375cuXKF1q1bM27cOH3GK4rIoWpjqMJlPo2aauhQhBBCCIMp9BijSpUqsXXr1mytQSdPnqRTp05cuXKFiIgIOnXqxK1bt/QSrDEojWOMAM4fuED1Zt4omHAi7DS1A2WckRBCiNIjv7/fz/SstBs3bmRbfvPmTRITE4EHd6WlpaUVdheiGPn6V8VPdRyAXz7cb+BohBBCCMN4pq60QYMGsW7dOmJiYoiJiWHdunUMHjyYnj17AnDgwAGqV6+ur1hFEavjcgKAQ/tzn4JBCCGEKM0KPfj6q6++Yty4cfTp04eMjIwHlZmZMXDgQO1jQGrUqMG3336rn0hFkfNvncXaX+DEnYaGDkUIIYQwiEKNMUpPT6dz584sWbKEChUqcPHiRQB8fHywtbXVe5DGpLSOMQLQHLmET0MPFEw4suUE9TvJg2WFEEKUDkU6xsjc3Jxjx44BYGtrS7169ahXr16pT4pKO68GntRQPfhc13/6r4GjEUIIIYpfoccYvf766yxdulSfsQgj8Kr3Sn6mN42ivjJ0KEIIIUSxK/QYo4yMDL777jv+/vtvGjdujI2Njc76efPmPXNwovh1ec0S/9lriNLIA2WFEEKUPYWex6ht27a5V6pSsX379kIHZcxK8xgjgIToaGw9PTEFYg8epEKTJoYOSQghhHhmRf6stLCwsMJuKoyYQ5Uq/GH6LjczvYifuZsxv+kmRprZGpRMBe8Z3gaKUAghhCg6hR5jJEqvE1ZN8cSXu1urEZMYQ1hUGDGJMWhma9BM06AyVRk6RCGEEKJIPFNitGvXLl5//XVatGjBlStXAPj+++/ZvXu3XoIThqHucY/v8OK5VBve7fku7Va0492e76KZpsFrlhdeU70MHaIQQghRJAqdGP3yyy8EBQVhZWXF4cOHSU1NBR48KuT999/XW4Ci+PWe1pYf7eG7wFBCwkLYMnsLIWEhhLYNxWxMoXtfhRBCCKNX6MTovffeY8mSJXzzzTeYm/93B1PLli2JiIjQS3DCMCpWr4CXyx98H7iCNNM01Jlq0kzTWNFmBedvnzd0eEIIIUSRKXRiFBkZSevWrbMtd3BwID4+/lliEkagrkka/cMHaJMidaaaATsG4Ovka+jQhBBCiCJT6MTI3d2d8+eztx7s3r0bHx+fZwpKGF5f26oMCg/hu8BQgqYGEdr2QbdaxmcZhg5NCCGEKDKFHjAydOhQxowZw3fffYdKpeLq1avs3buXiRMnMnXqVH3GKIqZZraG8kfsWEYVfomYwjdDm9F53AtkfJaBZpoGQAZgCyGEKJUKnRhNnjyZrKws2rdvT3JyMq1bt8bCwoKJEycyevRofcYoipmSqeA1y4vuc1/lm8QI9m8fSOV+b8LU/9YLIYQQpVGhZ75+JC0tjfPnz5OUlEStWrVK/YNkS/vM148Lb9mSwH/+YbePD89duGDocIQQQohCK/KZrx9Rq9XUqlXrWasRRsi+Rw/45x+8L11CycpCZSLzgQohhCjdnikx2rZtG9u2bePGjRtkZWXprPvuu++eKTBheH4hg3jz/yz5O7MzH364hRendDF0SEIIIUSRKnQTwMyZM+nUqRPbtm3j1q1b3LlzR+clSj4bVxcirbw5R3VWLogzdDhCCCFEkSt0i9GSJUtYtmwZ/fv312c8wsh0fSGB7T9D+I2OJCckY+1gbeiQhBBCiCJT6BajtLQ0AgIC9BmLMELDv+qFC9e5RXm+GrHO0OEIIYQQRarQidGQIUNYuXKlPmMRRsjawZpA178B+H29g4GjEUIIIYpWobvSUlJS+Prrr/n777+pV6+ezvPSAObNm/fMwQnj0HecM2vfgT33O6A5cgmvBp6GDkkIIYQoEoWex6ht27Z5rg8LCytUQMauLM1j9EhWZhY1zU9yVqnLBP+lfLJ/sKFDEkIIIQqkyOcxKq2Jj8jOxNSEbnXCST8eRsCJHwBJjIQQQpROBR5j9Pzzz5OQkKB9/8EHHxAfH699HxcXJxM+lkKTVrRiPmPolXyQS9u2GTocIYQQokgUODHasmULqamp2vfvv/8+t2/f1r7PyMggMjJSP9EJo1G+QQMiXFwAiJo508DRCCGEEEWjwInRk0OSnvFRa6IESe3Tjx20ZuXuF8lIyzB0OEIIIYTeycOvRL7VmjydF9jIN8o4lk/cYOhwhBBCCL0rcGKkUqlQqVTZlonSz6mSE63s/wLg1+VZTykthBBClDwFvitNURSCg4OxsLAAHsxnNHz4cGxsbAB0xh+J0qdXiCmbPoNdiUHcir6FSxUXQ4ckhBBC6E2B5zEKCQnJV7nQ0NBCBWTsyuI8Ro/LSMvAxyKay/gwrUMoM7fm73oQQgghDKnI5jEqrQmPyB8ztRltPXey4pIPf+2ogtyfJoQQojSRwdeiwAa/5wfAgfRAjmw5buBohBBCCP2RxEgUWOvXW9DAdC9eaNg9c7mhwxFCCCH0RhIjUSgze/3AeXwJiliIkiV3qAkhhCgdJDEShdLm40mkAtVSUznz00+GDkcIIYTQC0mMRKE4eHoS4eFBKmr2zpbJHoUQQpQOkhiJQovuPpkKxDIpchHJCcmGDkcIIYR4ZpIYiULr+eEgTEknDle+fGOdocMRQgghnpkkRqLQLG0tCXT7G4BNGx0NG4wQQgihB5IYiWfS/203AP5J6cDFQ1EGjkYIIYR4NpIYiWfywsSO+KmOkYYFC4eHGTocIYQQ4plIYiSeWbtaBwHYFlHHwJEIIYQQz0YSI/HM3vy8BaZkcCzLn13Ldxg6HCGEEKLQSmRiFB4ejkqlyvF18ODBPLfdu3cv7dq1w8bGBnt7e1q3bs39+/eLKfLSqU67WrxjN55T1CTz2/8ZOhwhhBCi0MwMHUBhBAQEEBsbq7Ns6tSpbNu2jSZNmuS63d69e+ncuTNTpkzhiy++wMzMjKNHj2JiUiLzQ6PSebApNRecwW6vKVkZGZiYlchLSwghRBmnUhRFMXQQzyo9PZ1KlSoxevRopk6dmmu55s2b07FjR2bPnl3ofSUmJuLg4EBCQgL29vaFrqe0uX/7NmnOzjgAh+fNp+G4sYYOSQghhNDK7+93qWgq2bhxI3FxcYSEhORa5saNG+zfvx83NzcCAgIoX748bdq0Yffu3cUYaell5eTEL149eJVVzJzhZuhwhBBCiEIpFYnR0qVLCQoKonLlyrmWuXjxIgAzZsxg6NChbN68mUaNGtG+fXvOnTuX63apqakkJibqvETOTHoNZDWvsi2xOzeibhg6HCGEEKLAjCoxmjx5cq6Dqh+9zpw5o7NNTEwMW7ZsYfDgwXnWnZWVBcCwYcMICQmhYcOGzJ8/Hz8/P7777rtct5s7dy4ODg7al4eHx7MfaCk14KMeVOECSdixcOgfhg5HCCGEKDCjGiE7YcIEgoOD8yzj4+Oj8z40NBRnZ2deeOGFPLerUKECALVq1dJZXrNmTaKjo3PdbsqUKYwfP177PjExUZKjXJiYmtDOaxfLNFXZssOLWYYOSAghhCggo0qMXF1dcXV1zXd5RVEIDQ1lwIABmJub51nWy8uLihUrEhkZqbP87NmzdOnSJdftLCwssLCwyHdMZd3gubVY1hcOZrTm0KajNO5a39AhCSGEEPlmVF1pBbV9+3aioqIYMmRItnVXrlyhRo0aHDhwAACVSsXbb7/N559/ztq1azl//jxTp07lzJkzT+2GE/n3XB9/Gpr+g4IJX48/ZOhwhBBCiAIxqhajglq6dCkBAQHUqFEj27r09HQiIyNJTk7WLhs7diwpKSmMGzeO27dvU79+fbZu3UrVqlWLM+xSr6P/GQ7vDWDbuRZkZWZhYlqi828hhBBlSKmYx6g4yTxGTxd94jIv1b1KH1bTMbQR9YJfM3RIQgghyrgyNY+RMC5V6niwwPNVJjCPO/M/MnQ4QgghRL5JYiSKhMXDcV8uxxpxYerZHMtoZmuImhFVnGEJIYQQeZLESBSJBhMnckFlxznqcPm9q2hma4hJjCEsKoyYxBg0szVopmlQmaoMHaoQQgihJYmRKBJmlpb8r/wXvMgEtpuloZmm4d2e79JuRTve7fkummkavGZ54TXVy9ChCiGEEFqSGIki89r/PXhEy1xrX0LbhhISFsKW2VsICQshtG0oZmNK9E2RQgghSiFJjESR6Ta2PTVVR8hwusSKNitIM01DnakmzTSNFW1WcP72eUOHKIQQQuiQxEgUqXa1D8HtavQPH6BNitSZagbsGICvk6+hwxNCCCF0SGIkitSIhS0ZkJjGoPAH3WdBU4O03WoZn2UYOjwhhBBChwzyEEXKZqclIWj4Di/uXmlI2MAQfMf5kvFZBpppGgAZgC2EEMJoSGIkipSSqXCpejzfn/XixXOutK78HCZmZjD1v/VCCCGEsZBHghSQPBKk4OKvxRNdoQH1uMThTz6h4YQJhg5JCCFEGSOPBBFGw9Hdkfia1gDc+/JLA0cjhBBC5E4SI1EsnB62EjlcNGPvz3sNHI0QQgiRM0mMRLGoM3gw/2czkYacZOqgm4YORwghhMiRJEai2LSY2oEsTNiW/AJrZ/9h6HCEEEKIbCQxEsWm5/8F0dFmAwAfz7ImKzPLwBEJIYQQuiQxEsVqRmhl1KRyICOQRYN/NnQ4QgghhA5JjESxavFKU15wWwPAlytqkZEms18LIYQwHpIYiWI397cW2BPPGaU+Mzp/b+hwhBBCCC1JjESx8/WvyqvVfsWBeOzD95ESH2/okIQQQghAEiNhIB+E9WSPqhqTlK/ZN3CgocMRQgghAEmMhIE4VXLi9sBuANT77TcSLl0ycERCCCGEJEbCgAK++oqzagv2K0FMa7Pa0OEIIYQQkhgJwzFVqwnv8wXP8ydfXRrNwY2HDR2SEEKIMk4SI2FQQ74bTCPTPaRiyYz+FwwdjhBCiDJOEiNhUCamJox/+xYAmxNfZNOCvw0ckRBCiLJMEiNhcK/N7UGg5SayMGXu/ymGDkcIIUQZJomRMAr/W2iPKRnsSevIt6PXGjocIYQQZZQkRsIotB/cim7lHiREn3/pKQ+YFUIIYRCSGAmjMefX+jTkX2Zmvc++t982dDhCCCHKIJWiKDKoowASExNxcHAgISEBe3t7Q4dT6oS1CaTtzh1EmZtTOT4ec2trQ4ckhBCiFMjv77e0GAmj0uSnldxUqfBOT2d3yGBDhyOEEKKMkcRIGBW7ihU51utVFjCGEav/x9WzsYYOSQghRBkiiZEwOi2WLuUzRhJJbd7ptMXQ4QghhChCUTOi0MzW5LhOM1tD1IyoYo1HEiNhdKwdrBnSdQ8Aay+9zIntpwwckRBCiKKiMlWhmaZBM1tDTGIMYVFhxCTGoJmtQTNNg8pUVazxSGIkjNKUDQOoa3KQe9jyv1eOGTocIYQQRcRrqhdes7zQTNPwbs93abeiHe/2fBfNNA1es7zwmupVrPFIYiSMkompCW+9eQmA32+/zPbQPUbX3CqEEEI/zMaYEdo2lJCwELbM3kJIWAihbUMxG2NW7LFIYiSM1pAvXqaleiuZmDH7zXija24VQgihH+fizrGizQrSTNNQZ6pJM01jRZsVnL99vthjkcRIGLUpH6owIZOdKZ05bX7AqJpbhRCiLNNnK34152oM2DFAmxSpM9UM2DEAXydfPUWbf5IYCaPWdWwHRrvM4TANqfDBG5iONjGa5lYhhCjL9NmKn/FZhvb7PGhqkPZ7PuOzjCI8gpxJYiSM3qTfg6jGcRokJPDbvP8ZTXOrEEKUZfoaNP0okfKa5cWc9XMIGxjGnPVztHXn1ipVVOTPbGH0KjZrRri/P4EHDuD05V4G1MuhuXVc8Te3CiFEWWc2xozQsAetO6/tfA11pprQtqHMGTMn33UomYpOIlXZvvKDFVP/W1+cpMVIlAgNVq1iAnP4M26L0TS3CiFEWaePQdPeM7xzbV3ymuqF9wxvPUWbP9JiJEoER29vvF1q0P1WNGtwYuLiiYRYhOA7zpeMzzLQTNMAyABsIYTIQ9SMKFSmqhy/KzWzNSiZSoESkVwHTZfgVnxJjESJ0X5gTRZ9msqX1CP9he/4OnLQgxUGam4VQoiS5tGAaXjQDXYu7hzVnKtp/8D0muVVoPoeHzS9os0KBuwY8F8r/lT9x18cVIqiyK9JASQmJuLg4EBCQgL29vaGDqfM+V+7UOaEhWBPPIf2x+HrX9XQIQkhRInyaLDzk8lMQac9eXzQtNkYM87fPo+vk69OkmVMrfj5/f2WFiNRoszY3J9fLI9yRqnP2I5b+T1BEiMhhCgIfQyYBuMbNK0vMvhalChmajPGDT+Liiw2Jb7CxGZLDR2SEEKUKPqaZdrYBk3riyRGosR548tXGOy7DFvu0vzARo4tXmzokIQQosjo+zmRxjTLtDGSxEiUSF+dCWa5e0deZiPuo0YRe/CgoUMSQogioe/nRBrTLNPGSAZfF5AMvjYe927cIMbTE7+UFLZb+tLg/H6cKjkZOiwhhNC7sjpgWp9k8LUo9Wzc3LDesoXf2/yPQSlraVRjB3/E98DEVBpChRCliwyYLj7yCyJKNI/WrbkybBS3cWJL0ou81SDU0CEJIYTeyYDp4iOJkSjxhi3pzYi6ywFYcmIgS9742cARCSHKOhkwXXJJYiRKhc8Oh9DZ7hcyMeOdbzqwe+U+Q4ckhCjDZMB0ySWDrwtIBl8br/hr8bSudI7jWU2prjrOrgvlcfN2M3RYQogySgZMGxcZfC3KHEd3R5ZtNKdzt2ucVeoysf5Clse/icpEGkaFEMVPBkyXTPKLIUqVRl0b8Onb+3id5Sy5O4kdnTsbOiQhRBklA6ZLJkmMRKnT/6OeDO2/DWvu03rrVg7OmGHokIQQJYAMmBYgiZEopVqvWMHOWrUAFZtmprD1qx3adfr+8hNClA4yYFqAjDESpVjz/fsZ6fI5S1LfwWd4JGEtL1Oljof2yw8ejAE4F3eOas7VdAYyCiHKnkfdVZppGkLD9Ddges6YOYTcDsF33H8Dph/fnzAukhiJUktta8uozS+yoe1lLuJHv8ZbCUusoNcvPyFE6SIDpoV0pYlSrXZgTT6fdRxL7rMnrSODfH8EHn75PWzW3jJ7i7a522yM/K0gRFkmA6aFJEai1Ht56vNMavcTAD/EDGRO9+V6+/ITQhiePscNyoBpIYmRKBNmbhtE7/LfA/D+7y8TtTZWvvyEKCX0OWhaBkwLmfm6gGTm65IrJSmFwHJ7OZwRwPeqz3FTmj7zjLRCCOOgj1mmZYbp0k1mvhbiCZa2lqzc50Vk09lYKR2wsPyJmaumEpIsd4sIUdLpY9C0DJgWIImRKGN8Gntz++UA7Nd8R/WU79kcdILOh/c8WClffkKUWI/GDT5Kih6NGwy5HfJfgvMUeQ2Ilj+Wyo4SOcYoPDwclUqV4+vgwYO5bnft2jX69++Pu7s7NjY2NGrUiF9++aUYIxfGoMnq54mbWJ6j1GPEkR/4X+B32nVyt4gQxUNmmRbGqkQmRgEBAcTGxuq8hgwZgre3N02aNMl1uwEDBhAZGcnGjRs5fvw4vXr1onfv3hw+fLgYoxfGoMXHH7Ogylto8OaTHf1YNHiVoUMSokyRWaaF0VJKgbS0NMXV1VWZNWtWnuVsbGyUFStW6CxzcnJSvvnmm3zvKyEhQQGUhISEQsUqjEd6arrSyuJPBRTFlHRlVN1vlcyMTEOHJUSZETUrSgkjTBnQdoDCDJQBbQcoYYQpUbOiClVP1Kwo5XLCZSUsKky5nHBZZ7kwfpkZmcql49HKmT/DlHiNRu/15/f3u1SMMdq4cSNxcXGEhITkWS4gIICff/6Zrl274ujoyOrVq0lJSSEwMDDXbVJTU0lNTdW+T0xM1FfYwsDM1GZs1DSnb/Vf2Hz3JRYeH8xFp7X8dL4T9q5yx6EQRU1mmS7dEm8mcuHQJaKPXeXq+QTuXLlLS+vNKDdvooqL44fogRxNbkpCphMJijO3cSEdD9YylptDnXnu668NEnepuF3/+eefB+CPP/7Is1x8fDyvvvoqf/31F2ZmZlhbW7NmzRo6deqU6zYzZsxg5syZ2ZbL7fqlR1ZmFm81CGXxiWCyMKWeyQFWbbOiZmBdQ4cmRKkWFhVGuxXt2DJ7i3ZsUNDUIMIGhhHoFWjo8MQTsjKziDl9hbN7o9AcvcHV80kkXLtPd8vlmN26hfruXebdns3ejPbcwZW76P5GmpBJOuaY8CDt6M3PrKF3tv18zlDqv3af1j/8oNf4S+Tt+pMnT+bDDz/Ms8zp06epUaOG9n1MTAxbtmxh9erVT61/6tSpxMfH8/fff+Pi4sL69evp3bs3u3btom7dnH8Ep0yZwvjx47XvExMT8fDwyOcRiZLAxNSEhccHU3PQT/wvNAjHrPvYtGvFqdCvqTVwoKHDE8JoRM2IQmWqyvEOLc1sDUqmUqCbF3IdMD1OBkwXp8SbiZzZfY6LEVe5fCaeO1eS6WT5MyY3bqC+fZvPbk1nT3onbuJOCh7Af7+BJmTyEaMwJQsABQeiqapdb0oGTtzCURWHvckdwtx8MS9nTpazMwGcpKZFKG5VrKjg64hnXXe8G1bBqdI3xX0KdBhVi9HNmzeJi4vLs4yPjw9qtVr7fvbs2XzxxRdcuXIFc3PzXLe7cOECvr6+nDhxgtq1a2uXd+jQAV9fX5YsWZKvGGWCx9ItfNlurN94Ff/0q6QA/w4fwXOLvzR0WEIYhScnQDwXd45qztUKPQGiPiZlFLnLyszi8skYTmw/S/Sxa9TJ3ErmpUuYxsbydfRo9qe25aZSgXicdLYzIZM01Npkpx8/8hP9tOvticeF65QzvYmj+jYTfD/AqqI9pu7uRJs3QnGqQqWarng3qEzlWpUwUxtHG0yJbDFydXXF1dU13+UVRSE0NJQBAwbkmRQBJCcnA2BionsjnqmpKVlZWQUPVpRKgcHPkdhhP/ubNKHZ9eusXVKdheu/Z8XFV1FbqbOV1/df0EIYs0fXuWaahtCwZ0tmHk+y5oyZQ8htmWi1ILIys9AcjiL94iEST53i/rlz/H6gDieuVyfuvjNxGe5cpxJJVAGqoCKLVEIw58Fdeksoxzn+ayRQk4or13AyuYGjeRxbqzTAsoItJhUr8rzVdZ4vvxGfhhXwC6iKc2UnwBHwe7j1C8V89EXLqBKjgtq+fTtRUVEMGTIk27orV67Qvn17VqxYgb+/PzVq1MDX15dhw4bxySef4OzszPr169m6dSu///67AaIXxsq+cmWaxsTwdeOhfHZsLFyDaIdt/PRvNTzrVdEp++iWYyDXv6CFKE1kwHTxyExL48bRo+xed5Hj+5O5ooFrt+y4mezKzYyKXKcSKXiTSg1tsvMVP/AnL2WrqxxxuKmuEObsi6WriqyKFWlrc5Hn3H7Gq74rfi288WrgiYmpJ+D5cKvOxXasxsaoutIKql+/fly6dIk9e/ZkW6fRaPD29iYsLEx719m5c+eYPHkyu3fvJikpCV9fXyZOnEj//v3zvU/pSitbZnVZxgebe3Mfa7w5y9dfX6PD0NY6ZaQ7QJQlMmBaPzLSMjgRdppjW89x4Uj8w8THllv3XPlR6YJHZipqsndjPekIHqit4ki0t2er+lU0Fg1w94AqNWyp5l+Ruu38cKniUmzHZczy+/tdohMjQ5DEqOz55b0/eGtqHa5SBXsSmPnaJsb+8N8XVUxiDO/2fJeQsBDtANLQtqHMWT8n348iEKKo6Lu7V673/Is+cZkD645z6p8bPJe5CrPLl7C5cYNF8dP4MWs4aVjkuJ0GTzyJJgOYaTKRzSbdcbO+gZvTXSp5g1ctO6o3r0S9DjVxdHcs1mMqyUrkGCMhjNFL/3ueGs+dpn+HfzicGcD4H/twPuIrvjgxFJWJiV6e0SREUdF3d+/jM0w/3kKa8VmGthusrFCysrh97hyxu3ax8/cEDh514upNR67dr8SVLG/iHruD6xLTqMJlANy5RxoWmJJBRS5T3iwGV6sblHdOpGIVhejOkzELbED5hg2ZbWnJbAMeY1kkiZEQ+VA7sCY7byTRr+rP/Bb/Ku1Pb+afqh/Q6NAhueVYGDUZMP1ssjKzOLXzDId+P8PZf+O5fNGEq3FOXEutzNqsbtQgFmfgB+ayjOyTDLtyjUqmUeysUIPKVX0w8/WlrYcL3WsdpGGXuljaegNyg4YxkcRIiHyydbJl/a1X+KbLO3Tbuh5zDZzy8CDj9b/kL2hh1GTA9NNdPRvL7p8icL68BdPIw1hoNGy81peFGVNJohZQK9s216lGDWK5ampKRcvDdDVdQ8Xyd/H0M6X2c+74v1iPitUrAO7AX8V9SKKQZIxRAckYIwFwZMECPMaPJ0YZyR1eIqHlfRr/UZfzt8/j6+Rb6HldhAD9jwuSAdMPZKalceyPg+z6RcPZIylcvmLD1bsVicmoyjUqAbCL53iOBzf0fM1QhvE1JmRSiWgqmF3C3e4aldzv4V1LTWAPZ+p0bY6Vk1NeuxVGQsYYCVGEGowdy+VGjfizTTyn8OLnPRUY9/yPfLB70IMCpeAvaGE4+h4XVNa6e6OPR7Nn1WFO7olDc96UbulLaZxwAI/UVPYygjHkPGmrK9eIsK5EVpUaZPn64uXnw1a/nfj3bIC9q3R5lRWSGAlRSB6tWxN8/jp96/xLWooXH+4ZxFmXlXy+qw2Va1aSliJRaPocFwSlc8C0kpXFrVOniPnrLyI2x/L7oUbEJFbiUkZ1bj6c1PCRjmynGrsAqMZJqqlOUslCQyXnW3j5ZlKrpQstX23wcJ6ynw1zQMJoSFdaAUlXmnhSRloGQ/2+Z5nmwcBLJ27Ru8YG5vz9Ik6V8t/ELrNoi8fp67b4Jx/jUdK6e7Myszi06SgH1kdy+uA9Ll22IybJg/GZH9Gf9QBsoROd2aKzXXmu4mF2gYp2V+lY5wjNOlhRvnVrKgUEYKrOPou9KP2kK02IYmKmNiM0KoT6r/3IFyubcBE/lpwZTFWPYTTtnUCLb79FbWv71HpkFu2ST5/Jrb6mgSgpA6Yz0jK4GPYP8Xv+Jvnff7l4wowFV6aiyfLjLg2Bhjrlz9KILNZz2cyMTMcr9DH/Hp9q6dRt7cpz/RpRuWYloOLD0q8W9+GIEkwSIyH0ZOyPrzH8qxRmPf8d4bt9eEsJRf1zOjFr17LnxQn0CJ2Jpa1lrtvru/tEFD99Jrf6GheUVyJmiGsqIy2DfWv/Zf+G80QeTuPS1XJcTvZGo1TnHf7ifzy4U64yVRlMUwDMSMeT83hYRuHheoOqNaFlt0akvhaHp5MTnsDzxX4korSSrrQCkq40kR9pSUnsHTIEvzVrcM4yoSanUchkYOe9vLPh9VyfNi2zCpd8+npETEl/1ExWZhYH1kdwbdceHM/9hdmZM9y7akmvlAMkY5PjNn34gRmWQ4lzc+N+1erss+1Po06VadXPH1unp7e6CpEXeSRIEZHESBRE8q1brOo1nbd3zeQ2D55XVEN1lCGvHGfcyn6YmJrolJfbqks+fSS3JWlcUFZmFof/PMY/a09z+uB9LsXYcznJk6isGiRhx0CWaSc+TMMcG+5hQhY+qjN4WEVRpeJt/Oqb06SbDy1fbYraSsb/iKIhY4yEMALWLi4M2rmITqevMPX5UH7V9OKMUp+Jq+uzYu1+RgzWMPzr/8Y/6Kv7RAZy55++z5U+xgYZ47igrMwsTmw/xZ7VJ0k5c5LGt9ZQLiYGl6RMmpKEQoNs25iTxk0Ta/6p5EFatWpYNm7M3zX30OyV5lja1gfqF/txCPE0khgJUQwq16xEaFQI//s3iqkvbGB97Mscy2rGiG+aYfdTW+p90oe6w4bp7bZqGcidf8Y4Z5ChxwXdOn2a9YtOcnxPAppLNsQkenAxsybx1AHq8By7GPfYE7z8iCQdqGJ5gSrlb1GtjopGnT1o07851g69gd5FHrMQ+iJdaQUkXWlCH05sP8X03ke4F+fIZroCsMd6OOnJr+qt+6Skj1HJi75befR5rkrSeb94KIod30dwYk88GVduEHz/IyonJOCqKHgQTczDB6A+YkImVbhIbasIJjZeiLphQ1zatKFyu45Yl5PvQ2HcpCtNCCNWp10tfrlVi8t79rJrUHVanD2LY7KKBVTgwvsn+D8XW4JGBD4oXMjuE309H0tfSYg+kxl9t/Lo61wZ60NW71y4wOW//uKXlVmcinQk+s6DiRCv899szu7E8hnvaLdpqdrKFfNKVHG5jm+NDBp2qkSb/k0pV7EaUA25BV6UVpIYCWFAHi1b4BEZiWbrVlb3/Z2lcdVQUvzY8WYmrcdvovVzNxj0aftC/Zjqax4cfSUh+kxm9D21QWmYMygrM4vTuyL5Z/VxTu2/i0ZjTfJdC77PfAW3rCzKAWPYTjhtdbarxCW81Gep7HSNHc8PxbXNc3h27swqN7cii1UIYyZdaQUkXWmiKP02byufvJPBztQu2mVmpNPIbA9j2q+hzfTXqdSiRb7q0uet/8Z4C7o+j68kTZOQlZnF9YhDXP37b5IOHGDVngD2326JJtOPOzhnK5+IHXYkEWNqyueW44myqYePbxr12zjTZkATKtWoZICjEKL4ye36RUQSI1Ec1n+4hTWfX2f/1aZcoCZqUrmFC3YkccbKis3Vh1Ll1S70nNQp2y3/jxhjEqLPBESfUxsY47igpNtJ7F1ziCN/R3P+eDqXrzoQc68K0Vm+XKMClqQCMIRvWMoQAFRkUYWLeKgv4OF8De9qmbz4mgV+3dpiV7FiXrsTotSTxKiISGIkilvYsj3s/GInPc9/QJ3EREyBxvxLBI2pxCWaOe+mYy9TBnz8AtYO1oD+58HRVxKiz2SmNDxLLCMtg4hNRzn0x3mqxW/E/PwprK9c4dtb/8e3yliyMM1xu3+ph6M6kpsuLhx06cFtd38atK9Aq9eaFuj5fEKUJTL4WohSom1wS9oGtwSmcOv0aY59MA+7n29glZrMFTz5Nc6TX7+Byd/cwd/6L9q3u0mPav56Heuir/mV9FUP6O+J8cUxLuj2uXPsWRXBvr/vcemCKVfiXLiaWoVoxZcUGgONOcUManIGgL+5RRam2HKXKqrzVLSKprLbbXzrmNAoyIMar/2DTTlbqgLNnzk6IcTjpMWogKTFSBiLW9G3CJ3wJ+F/WXIgsQ23eDBYtg8/sZx+HHN25l6HjtgPnEzDLs82kZ6xjTEytpmh78Unc/iPY5zcGU3UiSRiL5tw/bYD47Lepen9MzgpCrP5H9Mem/vnEXPSqMJFpjiNp6rPTUxq1iTTryXO/i2p065Wrl2lQoiCka60IiKJkTBGaffT+GnqJv78MYnON38mOHMTACeoTV1O4EEUlc0vUqlcLJ5eqdRq7kjzl2pTo2X1p/7w6isJ0WcyU9wze9+9lcjhP09walc0Hnd3YRNzDLMrVwiL7cTilHe5TsUcu71+pytd+QOAFSbdWWQyngp216hc6R6+9Sxp1Nkb/xcb5flwYSGEfkhiVEQkMRIlwcU//yT6iy/YGebJjJRFKOSc/HzMm3Sy+4EEd3duePijce1C4y7eNH/pvx9rY5zHSJ8SbyYSf/4s9y5Gci8qiiP7UtlxtCo37jhwI8Wd65keXKOi9hz+QRe6sBmAH+nH6/wIgAUpVOISbuYxuNncws3lHh1aXafh89WoHBiItYtLsR+bEOI/khgVEUmMRElz/sAFdq08wsm98VzSWHA13p3LaT7E4MUWgujI34Duj7yaVDxV56lkocHD9Sbe1RXa97Sn0cstsXV3N+ThPFVGWgYXIzSkXT5DxpXzJF+6xOkTpuyIrEPCXSsS7tuRkFGO+EwXbuNKIo5s4AVe4DcAfuA1+vNDtnqtSKYil3jT/j2aVD5CVpUq3KvckHjX5tTvVJ2az1XH1Ey6vYQwVjL4WggBgK9/VXz9q2Zbfiv6FrG7h/HP/lqkHTvGheOO1Lx9BI1SnftYc06pzbmU2nAZuAzNtj2P7eiXSQO+YhAfMB1rVRJWqntYmiRjaXofS7MUrMxTebHiWrxcb4KdHVeoztn7dbB1NMPexQIHVyscyttg52TNvYQUXK3jUKffISMpicsxppyOciQlOZPU5CxS7yukpkBaqoq0NBVtHbdQxeQcJqmpnEiow/rbfUjPMic5w4b4TGfuKK7cxoVMfFnPBHqwEYBL9OF7Psn1HMXixjUTExLUasysLtFTtYrybveo7GOKbyNn6nWs9rDbsSY8TB6FEKWTJEZClFEuVVxw6fcy9HsZgEBgGg9aXA5uOMjB388RGXGfyzG2XLlbmfKZpwFQA8m4cJUqoPDglQVkwMOpdRgbv4RAdgCwmOHMIiTXOLbQiU5sBeAgQ/g/vsm1bHd+I5AIAK5Sh630zLVsDE5cVKu5a2lJhuUteqSvwtE+hXLOmbhUNKNiVVs8arlQtUkVqtRdgqn5t7gDfkCfp5w7IUTpJYmREEKHmdqMFq80pcUrTZ9YE0ViTAz3YmNpey6BVZG/k3DzPnfjUkmKz+BufCbJ9+D+PRNu2NuyM6MWJvfvkxCfSrO74dzPsua+YsN9xYZ72JGKJRakEKcyJdrUjHQTEzKJo37GfsxNUlGr0jAzSUdtmoa5aQbmpunccrMkvFwzsLQkPdOGkfFLUVuAtb0JFbysqORXDq8GFfFt6o2tUygQCkB9oH8xn0chRMkkY4wKSMYYCSGEECVPfn+/ZaSgEEIIIcRDkhgJIYQQQjwkiZEQQgghxEOSGAkhhBBCPCSJkRBCCCHEQ5IYCSGEEEI8JImREEIIIcRDkhgJIYQQQjwkiZEQQgghxEOSGAkhhBBCPCSJkRBCCCHEQ5IYCSGEEEI8JImREEIIIcRDkhgJIYQQQjxkZugAShpFUQBITEw0cCRCCCGEyK9Hv9uPfsdzI4lRAd29excADw8PA0cihBBCiIK6e/cuDg4Oua5XKU9LnYSOrKwsrl69ip2dHSqVSm/1JiYm4uHhweXLl7G3t9dbvSI7OdfFQ85z8ZDzXDzkPBePojzPiqJw9+5dKlasiIlJ7iOJpMWogExMTKhcuXKR1W9vby//6YqJnOviIee5eMh5Lh5ynotHUZ3nvFqKHpHB10IIIYQQD0liJIQQQgjxkCRGRsLCwoLp06djYWFh6FBKPTnXxUPOc/GQ81w85DwXD2M4zzL4WgghhBDiIWkxEkIIIYR4SBIjIYQQQoiHJDESQgghhHhIEiMhhBBCiIckMSpGixYtwsvLC0tLS5o1a8aBAwdyLbts2TJUKpXOy9LSshijLZl27txJ9+7dqVixIiqVivXr1z91m/DwcBo1aoSFhQW+vr4sW7asyOMs6Qp6nsPDw7NdzyqVimvXrhVPwCXU3Llzadq0KXZ2dri5udGzZ08iIyOfut2aNWuoUaMGlpaW1K1blz/++KMYoi25CnOe5Tu64BYvXky9evW0kze2aNGCP//8M89tDHEtS2JUTH7++WfGjx/P9OnTiYiIoH79+gQFBXHjxo1ct7G3tyc2Nlb7unTpUjFGXDLdu3eP+vXrs2jRonyVj4qKomvXrrRt25YjR44wduxYhgwZwpYtW4o40pKtoOf5kcjISJ1r2s3NrYgiLB127NjByJEj2bdvH1u3biU9PZ1OnTpx7969XLf5559/6Nu3L4MHD+bw4cP07NmTnj17cuLEiWKMvGQpzHkG+Y4uqMqVK/PBBx9w6NAh/v33X9q1a0ePHj04efJkjuUNdi0rolj4+/srI0eO1L7PzMxUKlasqMydOzfH8qGhoYqDg0MxRVc6Acq6devyLDNp0iSldu3aOsteffVVJSgoqAgjK13yc57DwsIUQLlz506xxFRa3bhxQwGUHTt25Fqmd+/eSteuXXWWNWvWTBk2bFhRh1dq5Oc8y3e0fpQrV0759ttvc1xnqGtZWoyKQVpaGocOHaJDhw7aZSYmJnTo0IG9e/fmul1SUhKenp54eHjkmVWLwtu7d6/O5wIQFBSU5+ciCq9BgwZUqFCBjh07smfPHkOHU+IkJCQA4OTklGsZuaafXX7OM8h39LPIzMxk1apV3Lt3jxYtWuRYxlDXsiRGxeDWrVtkZmZSvnx5neXly5fPdYyFn58f3333HRs2bOCHH34gKyuLgIAAYmJiiiPkMuPatWs5fi6JiYncv3/fQFGVPhUqVGDJkiX88ssv/PLLL3h4eBAYGEhERIShQysxsrKyGDt2LC1btqROnTq5lsvtmpbxXPmT3/Ms39GFc/z4cWxtbbGwsGD48OGsW7eOWrVq5VjWUNeyWZHWLgqtRYsWOll0QEAANWvW5KuvvmL27NkGjEyIgvPz88PPz0/7PiAggAsXLjB//ny+//57A0ZWcowcOZITJ06we/duQ4dSquX3PMt3dOH4+flx5MgREhISWLt2LQMHDmTHjh25JkeGIC1GxcDFxQVTU1OuX7+us/z69eu4u7vnqw5zc3MaNmzI+fPniyLEMsvd3T3Hz8Xe3h4rKysDRVU2+Pv7y/WcT6NGjeL3338nLCyMypUr51k2t2s6v981ZVlBzvOT5Ds6f9RqNb6+vjRu3Ji5c+dSv359PvvssxzLGupalsSoGKjVaho3bsy2bdu0y7Kysti2bVuufatPyszM5Pjx41SoUKGowiyTWrRoofO5AGzdujXfn4sovCNHjsj1/BSKojBq1CjWrVvH9u3b8fb2fuo2ck0XXGHO85PkO7pwsrKySE1NzXGdwa7lIh3aLbRWrVqlWFhYKMuWLVNOnTqlvPHGG4qjo6Ny7do1RVEUpX///srkyZO15WfOnKls2bJFuXDhgnLo0CGlT58+iqWlpXLy5ElDHUKJcPfuXeXw4cPK4cOHFUCZN2+ecvjwYeXSpUuKoijK5MmTlf79+2vLX7x4UbG2tlbefvtt5fTp08qiRYsUU1NTZfPmzYY6hBKhoOd5/vz5yvr165Vz584px48fV8aMGaOYmJgof//9t6EOoUQYMWKE4uDgoISHhyuxsbHaV3JysrbMk98de/bsUczMzJRPPvlEOX36tDJ9+nTF3NxcOX78uCEOoUQozHmW7+iCmzx5srJjxw4lKipKOXbsmDJ58mRFpVIpf/31l6IoxnMtS2JUjL744gulSpUqilqtVvz9/ZV9+/Zp17Vp00YZOHCg9v3YsWO1ZcuXL688//zzSkREhAGiLlke3Rb+5OvRuR04cKDSpk2bbNs0aNBAUavVio+PjxIaGlrscZc0BT3PH374oVK1alXF0tJScXJyUgIDA5Xt27cbJvgSJKdzDOhco09+dyiKoqxevVqpXr26olarldq1ayubNm0q3sBLmMKcZ/mOLrhBgwYpnp6eilqtVlxdXZX27dtrkyJFMZ5rWaUoilK0bVJCCCGEECWDjDESQgghhHhIEiMhhBBCiIckMRJCCCGEeEgSIyGEEEKIhyQxEkIIIYR4SBIjIYQQQoiHJDESQgghhHhIEiMhhBBCiIckMRJCCCGEeEgSIyGEKOF+//13vL298ff359y5c4YOR4gSTR4JIoQQJZyfnx+LFi3i5MmT7N27l1WrVhk6JCFKLGkxEkKUKIGBgYwdO9bQYRRaYeIPDAxEpVKhUqk4cuRItvXOzs74+vri5eWFWq3WWRccHKzddv369YUPXIgyQhIjIUSBPf5jq1KpcHZ2pnPnzhw7dszQoQEP4uvZs6dBY9B3Ajd06FBiY2OpU6dOtnUhISFUrVqVESNGsGDBAp11n332GbGxsXqLQ4jSThIjIUShdO7cmdjYWGJjY9m2bRtmZmZ069bN0GGVWtbW1ri7u2NmZqazPCMjg88++4xJkyaRlJREuXLldNY7ODjg7u5enKEKUaJJYiSEKBQLCwvc3d1xd3enQYMGTJ48mcuXL3Pz5k0AUlNTeeutt3Bzc8PS0pLnnnuOgwcP6tQRGBjIW2+9xaRJk3BycsLd3Z0ZM2Zo19+7d48BAwZga2tLhQoV+PTTT5857qysLObOnYu3tzdWVlbUr1+ftWvXFigugLt37/Laa69hY2NDhQoVmD9/vraVKDg4mB07dvDZZ59pW9U0Go1ODHnVXRBLlizBx8eHkSNHcvfuXS5evFjouoQQkhgJIfQgKSmJH374AV9fX5ydnQGYNGkSv/zyC8uXLyciIgJfX1+CgoK4ffu2zrbLly/HxsaG/fv389FHHzFr1iy2bt0KwNtvv82OHTvYsGEDf/31F+Hh4URERDxTrHPnzmXFihUsWbKEkydPMm7cOF5//XV27NiR77gAxo8fz549e9i4cSNbt25l165d2tg+++wzWrRooe3+io2NxcPDI99159ft27eZPXs2H374IZUrV8bBwSHHMUhCiAJQhBCigAYOHKiYmpoqNjY2io2NjQIoFSpUUA4dOqQoiqIkJSUp5ubmyo8//qjdJi0tTalYsaLy0UcfaZe1adNGee6553Tqbtq0qfJ///d/yt27dxW1Wq2sXr1auy4uLk6xsrJSxowZ89T4evTokW15SkqKYm1trfzzzz86ywcPHqz07ds3X3EpiqIkJiYq5ubmypo1a7Tr4+PjFWtra21sbdq0yTHOp9Wdk9zqGjVqlDJs2DDt+xYtWihTp07NsQ5AWbduXa77EEI8YPa0xEkIIXLStm1bFi9eDMCdO3f48ssv6dKlCwcOHCAhIYH09HRatmypLW9ubo6/vz+nT5/WqadevXo67ytUqMCNGze4cOECaWlpNGvWTLvOyckJPz+/Qsd8/vx5kpOT6dixo87ytLQ0GjZsmK+4AC5evEh6ejr+/v7a9Q4ODvmOLa+68+vUqVP88MMPOuezTp060mIkxDOSxEgIUSg2Njb4+vpq33/77bc4ODjwzTff0Lt373zXY25urvNepVKRlZWltzgfl5SUBMCmTZuoVKmSzjoLC4tii0sfdY8bN474+HgqV66sXZaVlaXTZSeEKDgZYySE0AuVSoWJiQn379+natWqqNVq9uzZo12fnp7OwYMHqVWrVr7qq1q1Kubm5uzfv1+77M6dO5w9e7bQMdaqVQsLCwuio6Px9fXVeRUkofDx8cHc3FxnMHlCQoJObGq1mszMzELHmpfff/+dQ4cOcfjwYY4cOaJ9LV26lOjoaO7cuVMk+xWiLJAWIyFEoaSmpnLt2jXgQcKycOFCkpKS6N69OzY2NowYMYK3334bJycnqlSpwkcffURycjKDBw/OV/22trYMHjyYt99+G2dnZ9zc3Hj33XcxMcnf33MJCQnZupWcnZ2ZOHEi48aNIysri+eee46EhAT27NmDvb09AwcOzFfddnZ2DBw4UHt8bm5uTJ8+HRMTE1QqFQBeXl7s378fjUaDra0tTk5O+Y49L+np6UyYMIG3336bBg0a6Kyzt7cH4OjRowQGBj7zvoQoiyQxEkIUyubNm6lQoQLwIFGoUaMGa9as0f4gf/DBB2RlZdG/f3/u3r1LkyZN2LJlS7Z5dvLy8ccfa5MtOzs7JkyYQEJCQr62DQ8PzzZuaPDgwXzzzTe4uroyd+5cLl68iKOjI40aNeKdd97Jd1wA8+bNY/jw4XTr1g17e3smTZrE5cuXsbS0BGDixIkMHDiQWrVqcf/+faKiovDy8irQPnLyxRdfEB8fz6hRo7Kt8/DwwNramiNHjkhiJEQhybPShBBCD+7du0elSpX49NNP890qll+BgYE0aNAg26zWBaFSqVi3bp3BZwQXwtjJGCMhhCiEw4cP89NPP3HhwgUiIiJ47bXXAOjRo0eR7O/LL7/E1taW48ePF2i74cOHY2trWyQxCVEaSYuREEIUwuHDhxkyZAiRkZGo1WoaN27MvHnzqFu3rt73deXKFe7fvw9AlSpVsj0oNi83btwgMTEReDAtgI2Njd7jE6I0kcRICCGEEOIh6UoTQgghhHhIEiMhhBBCiIckMRJCCCGEeEgSIyGEEEKIhyQxEkIIIYR4SBIjIYQQQoiHJDESQgghhHhIEiMhhBBCiIckMRJCCCGEeEgSIyGEEEKIhyQxEkIIIYR46P8B10mIIR2lKY8AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# and plot the results to compare\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(bond_lengths, fci_energies, \"-k\", label = \"FCI\")\n",
    "ax.plot(bond_lengths, unsimp_qubit_energies, \"-r\", label = \"Unsimp. Qubit\")\n",
    "ax.plot(bond_lengths, simp_qubit_energies, \"--b\", label = \"Simp. Qubit\")\n",
    "ax.plot(bond_lengths, unsimp_ising_energies, \".g\", label = \"Unsimp. Ising $r=2$\")\n",
    "ax.plot(bond_lengths, simp_ising_energies, \"xm\", label = \"Simp. Ising $r=2$\")\n",
    "\n",
    "ax.set_ylabel(\"Energy [$E_h$]\")\n",
    "ax.set_xlabel(\"Bond Length [$\\\\AA$]\")\n",
    "ax.set_title(\"Potential Energy Curve for LiH in STO-3G\")\n",
    "ax.legend(loc = \"upper right\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "qis_conda",
   "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": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}