term_grouping_plots.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using Bron-Kerbosch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from term_grouping import *\n",
    "from print_cliques import print_cliques\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import Counter\n",
    "import time\n",
    "import numpy as np\n",
    "\n",
    "plt.rcParams[\"font.size\"] = 13\n",
    "plt.rcParams[\"axes.labelsize\"] = 15\n",
    "plt.rcParams[\"axes.titlesize\"] = 15\n",
    "plt.rcParams[\"font.family\"] = 'sans-serif'\n",
    "plt.rcParams[\"xtick.labelsize\"] = 13\n",
    "plt.rcParams[\"ytick.labelsize\"] = 15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8 qubits\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 69 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.12s\n",
      "{'Z**Z****', '**Z*****', '**Z***Z*', '**ZZ****', '***Z****', '*Z****Z*', '***ZZ***', '****Z**Z', '*Z**Z***', 'Z*****Z*', 'Z******Z', '*ZZ*****', '***Z*Z**', '**Z****Z', 'Z*Z*****', '*****ZZ*', '*Z***Z**', '****ZZ**', 'ZZ******', '***Z**Z*', '*Z*Z****', '***Z***Z', '******ZZ', '****Z***', '*****Z**', '******Z*', '*Z*****Z', '****Z*Z*', '*Z******', '**Z**Z**', '**Z*Z***', '*******Z', '*****Z*Z', 'Z****Z**', 'Z*******', 'Z***Z***'}\n",
      "{'*XYYX***', 'XX****YY', '***YXXY*', '**YYXX**', 'XXYY****', '****XXYY'}\n",
      "{'***XYYX*', '**XXYY**', 'YY****XX', '*YXXY***', '****YYXX', 'YYXX****'}\n",
      "{'*YYXX***', '**YXXY**', '****XYYX', 'XY****YX', 'XYYX****', '***XXYY*'}\n",
      "{'****YXXY', '**XYYX**', 'YX****XY', '*XXYY***', 'YXXY****', '***YYXX*'}\n",
      "{'XZZZX*Z*', 'XZ*ZX***', 'XZZZX***', 'XZZZXZ**', 'X*ZZX***', 'XZZZX**Z', 'XZZ*X***'}\n",
      "{'YZZZY**Z', 'YZZZY*Z*', 'YZ*ZY***', 'YZZ*Y***', 'YZZZYZ**', 'Y*ZZY***', 'YZZZY***'}\n",
      "{'**ZXZZZX', '***XZ*ZX', '***XZZZX', '***XZZ*X', '*Z*XZZZX', '***X*ZZX', 'Z**XZZZX'}\n",
      "{'***YZ*ZY', '*Z*YZZZY', '**ZYZZZY', '***Y*ZZY', 'Z**YZZZY', '***YZZ*Y', '***YZZZY'}\n",
      "{'**YX**XY', '*XY**YX*', 'XX**YY**'}\n",
      "{'**XX**YY', '*YX**XY*', 'XY**YX**'}\n",
      "{'*XZZ*X**', '*XZ*ZX**', 'ZXZZZX**', '*XZZZXZ*', '*XZZZX*Z', '*X*ZZX**', '*XZZZX**'}\n",
      "{'*YZ*ZY**', '*YZZ*Y**', '*Y*ZZY**', '*YZZZY**', 'ZYZZZY**', '*YZZZY*Z', '*YZZZYZ*'}\n",
      "{'**XZ*ZX*', '**XZZ*X*', '**X*ZZX*', '*ZXZZZX*', '**XZZZX*', 'Z*XZZZX*', '**XZZZXZ'}\n",
      "{'**YZ*ZY*', '**YZZZYZ', '**YZZZY*', 'Z*YZZZY*', '*ZYZZZY*', '**YZZ*Y*', '**Y*ZZY*'}\n",
      "{'YX**XY**', '**XY**YX', '*XX**YY*'}\n",
      "{'*YY**XX*', 'YY**XX**', '**YY**XX'}\n",
      "{'**XZXXZX', 'XZX**XZX'}\n",
      "{'**XZXYZY', 'XZX**YZY'}\n",
      "{'**YZYXZX', 'YZY**XZX'}\n",
      "{'YZYYZY**', 'YZY**YZY'}\n",
      "{'XXYZZZZY'}\n",
      "{'XX*XZZX*'}\n",
      "{'XYYZZZZX'}\n",
      "{'XY*YZZX*'}\n",
      "{'XZXXZX**'}\n",
      "{'XZXYZY**'}\n",
      "{'XZX*XZX*'}\n",
      "{'XZX*YZY*'}\n",
      "{'XZY*YZX*'}\n",
      "{'XZZXYZZY'}\n",
      "{'XZZX*XX*'}\n",
      "{'XZZYYZZX'}\n",
      "{'XZZY*YX*'}\n",
      "{'XZZZZXYY'}\n",
      "{'XZZZZYYX'}\n",
      "{'YXXZZZZY'}\n",
      "{'YX*XZZY*'}\n",
      "{'YYXZZZZX'}\n",
      "{'YY*YZZY*'}\n",
      "{'YZX*XZY*'}\n",
      "{'YZYXZX**'}\n",
      "{'YZY*XZX*'}\n",
      "{'YZY*YZY*'}\n",
      "{'YZZXXZZY'}\n",
      "{'YZZX*XY*'}\n",
      "{'YZZYXZZX'}\n",
      "{'YZZY*YY*'}\n",
      "{'YZZZZXXY'}\n",
      "{'YZZZZYXX'}\n",
      "{'*XX*XZZX'}\n",
      "{'*XY*YZZX'}\n",
      "{'*XZXXZX*'}\n",
      "{'*XZXYZY*'}\n",
      "{'*XZX*XZX'}\n",
      "{'*XZX*YZY'}\n",
      "{'*XZY*YZX'}\n",
      "{'*XZZX*XX'}\n",
      "{'*XZZY*YX'}\n",
      "{'*YX*XZZY'}\n",
      "{'*YY*YZZY'}\n",
      "{'*YZX*XZY'}\n",
      "{'*YZYXZX*'}\n",
      "{'*YZYYZY*'}\n",
      "{'*YZY*XZX'}\n",
      "{'*YZY*YZY'}\n",
      "{'*YZZX*XY'}\n",
      "{'*YZZY*YY'}\n",
      "{'**YZYYZY'}\n",
      "\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 8 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 1.14s\n",
      "{'**Z*****', '**Z***Z*', '**ZZ****', '*Z****Z*', '***Z****', 'XZZZX*Z*', 'YZZZY**Z', '*ZZ*****', '***Z*Z**', '**Z****Z', '*****ZZ*', 'XZZ*X***', '*Z***Z**', 'XZ*ZX***', 'YZZZY***', 'Y*ZZY***', '***Z**Z*', 'YZZZYZ**', '*Z*Z****', 'XZZZX***', '***Z***Z', '******ZZ', 'X*ZZX***', '*****Z**', '******Z*', 'XZZZX**Z', '*Z*****Z', '*Z******', 'YZ*ZY***', 'YZZ*Y***', '**Z**Z**', '*******Z', 'YZZZY*Z*', 'XZZZXZ**', '*****Z*Z', 'Z***Z***'}\n",
      "{'*YX**XY*', '*XY**YX*', '***XZZZX', '***Y*ZZY', 'Z*XZZZX*', '**XX**YY', '**YX**XY', '*XZZZX**', '**YZ*ZY*', '**YZZZY*', '***YZZZY', '**XY**YX', '**XZZZX*', '****Z***', 'Z**YZZZY', '**XZ*ZX*', '*YZZ*Y**', '*YZX*XZY', '*XX**YY*', 'ZXZZZX**', 'Z*YZZZY*', '*YZY*XZX', '*XZY*YZX', '*YZZZY**', '***X*ZZX', '*XZZ*X**', '*XZX*YZY', '**YY**XX', 'ZYZZZY**', '*YY**XX*', 'Z*******', 'Z**XZZZX'}\n",
      "{'YZY**YZY', 'XYYZZZZX', 'YZYYZY**', '*YZY*YZY', '*XZZZX*Z', 'YXXY****', '*Z*XZZZX', 'XZX**YZY', '*YZ*ZY**', '****YXXY', '****XXYY', 'XZX*YZY*', '*XZZY*YX', 'YZY*YZY*', '*YZYYZY*', '****Z*Z*', 'YYXZZZZX', 'YZY*XZX*', '*XZZX*XX', 'XZXYZY**', 'XXYY****', '*YZYXZX*', '***YYXX*', '***YZ*ZY', '***YXXY*', '*XZX*XZX', 'XZX*XZX*', 'Z*Z*****'}\n",
      "{'YZZZZYXX', 'YY*YZZY*', 'YX****XY', '*XXYY***', '**YZYXZX', '*YY*YZZY', 'XY*YZZX*', 'XX****YY', 'YZZY*YY*', '**XYYX**', 'YZX*XZY*', '*XYYX***', 'Z*****Z*', '***XZ*ZX', '**YYXX**', '**Z*Z***', '*YZZZY*Z', '**XZXXZX', 'XZY*YZX*', '*YX*XZZY', 'XZZY*YX*', '*Z*YZZZY', '*XZ*ZX**', 'XZZZZYYX'}\n",
      "{'***XYYX*', 'YZZX*XY*', 'XZZZZXYY', '**YZYYZY', '*XZXYZY*', 'XX*XZZX*', '*YXXY***', '*YZZY*YY', 'XXYZZZZY', 'XZXXZX**', '**XXYY**', '*XY*YZZX', 'YY****XX', '****YYXX', 'YZY**XZX', 'YYXX****'}\n",
      "{'YX**XY**', 'YZZXXZZY', '**ZXZZZX', '**ZYZZZY', 'YZZYXZZX', '*XZZZXZ*', 'XZZXYZZY', '***YZZ*Y', '*YZZZYZ*', '*Y*ZZY**', 'YY**XX**', 'XY**YX**', 'XX**YY**', '*X*ZZX**', '***XZZ*X', 'XZZYYZZX'}\n",
      "{'XZZX*XX*', 'YZYXZX**', '****XYYX', 'XY****YX', 'YZZZZXXY', '*XX*XZZX', '***XXYY*', 'XZX**XZX', '*YYXX***', '**XZXYZY', 'YX*XZZY*', '**YXXY**', '*XZXXZX*', 'YXXZZZZY', 'XYYX****', '*YZZX*XY'}\n",
      "{'Z**Z****', '****ZZ**', '**YZZZYZ', '*ZXZZZX*', 'Z******Z', 'ZZ******', '**Y*ZZY*', '**XZZ*X*', '**X*ZZX*', '***ZZ***', '**XZZZXZ', 'Z****Z**', '****Z**Z', '**YZZ*Y*', '*Z**Z***', '*ZYZZZY*'}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "hfile = 'hamiltonians/sampleH2.txt'\n",
    "H = parseHamiltonian(hfile)\n",
    "\n",
    "ops = [term[1] for term in H]\n",
    "Nq = max([len(op) for op in ops])\n",
    "print('{} qubits'.format(Nq))\n",
    "\n",
    "for commutativity_type in [QWCCommutativity, FullCommutativity]:\n",
    "    cliques = genMeasureCircuit(H, Nq, commutativity_type)\n",
    "    for cliq in cliques:\n",
    "        print(cliq)\n",
    "    print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_cliques_loc(filelist):\n",
    "    for file in filelist:\n",
    "        print('--------------')\n",
    "        print(file)\n",
    "        H = parseHamiltonian(file)\n",
    "    \n",
    "        # For some qubit encodings, there isn't a single term acting on all qubits\n",
    "        # so this will report the wrong qubit#\n",
    "        # Instead, look for the largest index being operated on.\n",
    "        ops = [term[1] for term in H]\n",
    "        #Nq = max([len(op) for op in ops])\n",
    "        Nq = max([int(op[-1][1:]) for op in ops]) + 1\n",
    "        print('{} qubits'.format(Nq))\n",
    "    \n",
    "        print('{} total terms\\n'.format(len(H)))\n",
    "\n",
    "        for commutativity_type, type_str in zip([QWCCommutativity, FullCommutativity],['QWC','FULL']):\n",
    "            print(type_str + 'Commutation:')\n",
    "            cliques = genMeasureCircuit(H, Nq, commutativity_type)\n",
    "            print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def many_trials(filename, commutativity_type, numtrials):\n",
    "    H = parseHamiltonian(filename)\n",
    "    ops = [term[1] for term in H]\n",
    "    Nq = max([int(op[-1][1:]) for op in ops]) + 1\n",
    "    print('--------------')\n",
    "    print(filename)\n",
    "    results = []\n",
    "    runtimes = []\n",
    "    for i in range(numtrials):\n",
    "        start_time = time.time()\n",
    "        cliques = genMeasureCircuit(H, Nq, commutativity_type)\n",
    "        end_time = time.time()\n",
    "        results += [len(cliques)]\n",
    "        runtimes += [end_time - start_time]\n",
    "    return Counter(results), runtimes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What is the effect of term grouping across basis representations?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What is the effect of term grouping across qubit encodings?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--------------\n",
      "hamiltonians/H2_6-31g_JW_0.7_AS4.txt\n",
      "8 qubits\n",
      "185 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 69 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.13s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 8 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 1.08s\n",
      "\n",
      "--------------\n",
      "hamiltonians/H2_6-31g_BK_0.7_AS4.txt\n",
      "8 qubits\n",
      "185 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 56 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.09s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 8 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.88s\n",
      "\n",
      "--------------\n",
      "hamiltonians/H2_6-31g_BKSF_0.7_AS4.txt\n",
      "28 qubits\n",
      "461 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 460 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 29 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 3.12s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 460 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 16 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 38.49s\n",
      "\n",
      "--------------\n",
      "hamiltonians/H2_6-31g_BKT_0.7_AS4.txt\n",
      "8 qubits\n",
      "185 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 56 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.09s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 8 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.89s\n",
      "\n",
      "--------------\n",
      "hamiltonians/H2_6-31g_PC_0.7_AS4.txt\n",
      "8 qubits\n",
      "185 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 61 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.09s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 8 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.96s\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# First look at H2 molecule\n",
    "Hfiles = ['hamiltonians/H2_6-31g_{}_0.7_AS4.txt'.format(e) for e in ['JW','BK','BKSF','BKT','PC']]\n",
    "\n",
    "print_cliques_loc(Hfiles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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P+VSyYaHP5vU1s26H1/LYpbP9SspuAx4pK6uZ7VnrLM2ybYcDfyX7p7qI7A/4X4EDWXZ273L7Lqk7nGzyw0Kyf/bnUzb7k+yqCS8A88nOBfsctc+6vTi/zST7B/x7oHvJNnXNuj22bH+1zfTdi+zcso/J/pntSpZYntDAc7TcrNsix72Cr8Myx1Xf61lyv7bbtQ3sZ0Oyf67b11J3FFlPysL8Z4MzboFPk52EPy1/Xt8gm+Syfdl2q9cT804l2/UhS2Lnk30ROjt/DzzWQBy3kfVCfY1s0sHHZKcnbFq23TFkn7mPyJKJgSw7i3bL/HjeLDmeq1l2pnzp9uuTJZJTyT7Pb+fxrl+y/an58azRwDHsQDapaCbZqRyPkS1gXd9j6nr/1zZTvLbPxPbAQ/nz8R7Z36beZdsMIFs8ewFZ7+JRZH8j7i/bbguyxPD9vL2XgGvIElzIhm2fJEvc55Jd5Wa/sjYOzR9f56xnb23vFvmLL6mNi4jpwK9TSj9opv0NJ/sHtnNK6dHm2GdrENmVK55NKVWrp6hi8qH2F4EHUkp19QK3ahHxB7JJJrVNPFCJiLgLmJZS+m5Lx6Lm49CtpIrIh6ceJ+tN3ZxsuOkJmv+Sai3tx8BfIuL8VHLyf2uQTzDpRdZT2oPscm0bkg19rqx2ou5zUpXLZ0XvTTaqoXbERE9SpaxBNoOyD9nQ0X3AaamdDRuklB7Jz2PrR9kyKa3AfLLh2o3JJuNNBr6QStZxW9mklGpdmkXLWY9sCLrO5YTUNjl0K0mS1Ea5vIokSVIbZaInSZLURrWbc/R69+6d+vfv39JhSJIkNdnEiRPfTSk1eGWbdpPo9e/fnwkTJrR0GJIkSU0WEa8V2c6hW0mSpDbKRE+SJKmNMtGTJElqo0z0JK1UlixZws4770xE8Oabby4tf+WVVxgxYgQ9evSgR48e7LTTTixatGhp/YQJE9hhhx3o0qULG2+8MTfddFNLhC9JzardTMaQ1Db88pe/pEuXLsuUzZw5kyFDhnD88cczcuRIunbtylNPPUWHDh0AmDNnDvvuuy+nn34648aN4+GHH2bEiBFsvPHGDB48uCUOQ2qz5s6dy4wZM5b5oqUVt8Yaa7DBBhuwyipN65Mz0ZO00pgyZQrXXHMNd9xxB9tuu+3S8ssvv5x+/fpx/vnnLy0bNGjQ0t/vvPNOOnfuzJlnnklEsOeeezJixAiuu+46Ez2pgubOncs777zD+uuvT+fOnYmIlg5ppbRkyRKmTZvGu+++S9++fZvUlkO3klYKS5Ys4eijj+bSSy+lZ8+ey9Q9+OCDbLLJJnz5y1+mV69ebLXVVtx8881L6ydPnszAgQOX+aczcOBAJk+e3GzxS+3BjBkzWH/99enSpYtJXhOsssoqrL322syZM6fpbVUgHkmquiuvvJJ11lmHAw44YLm6d999l1tuuYVvfOMbzJgxg8suu4xjjjmGRx55BIB58+bRo0ePZR7Ts2dP5s6d2yyxS+3FokWL6Ny5c0uH0SasuuqqLF68uMntmOhJavVefvllLrvsMq666qpa67t168bgwYM58MAD6dixI3vuuSf77LMP99xzz9L68m/Gs2fPpnv37lWPXWpv7MmrjEo9jyZ6klq9Rx55hJkzZ7LlllvSu3dvBg4cCMBWW23FNddcwzbbbFPrH8Wasq233pqnnnpqmbqnnnqKrbfeuvrBS1ILcjKGpFbv4IMPZvjw4Uvvv/nmmwwePJhRo0ax6aabMnDgQIYMGcLdd9/Nl770JR566CFGjRrFWWedBcCIESM488wzufTSSzn55JMZN24cd955Jw888EBLHZLUbvQ/+2/Nsp9Xf/aFZtlPjXHjxrH//vsze/bsZt3virJHT1Kr16VLFzbYYIOlt3XWWQeAddZZh65du7LTTjtxyy23cNZZZ9GtWzdOOukkfve73y2dUduzZ0/uvfdebr/9dnr06MFxxx3Htdde64xbqR0bOnQoEcHDDz+8TPmnP/1pRo4c2eDjhwwZ0uqTPLBHT9JKqH///qSUlik76KCDOOigg+p8zPbbb8/jjz9e7dAkrUTWWmstTj/9dMaPH99mzy20R0+SJLVLxx13HG+++Sa33nrrcnXz58/ngAMOYJ111qF79+4MHDhwmdM9xo4dS8eOWX/Zs88+S6dOnZg5c+bS+pQSG220ETfeeOPS9k4//XQ22mgjevXqxT777MPLL79c5SM00ZMkSe3UGmuswYUXXsj3v/99Pv7442XqlixZwgEHHMBLL73ErFmzOPTQQ/nqV7+6TDJXY8stt2SbbbZZZv3OsWPHMmvWLA488EAAjj32WF588UUee+wxpk+fzo477sgXv/jFql9BxERPkiS1W0cddRTdunXjyiuvXKa8a9euHH744XTr1o1VV12VM844g06dOvHEE0/U2c4NN9yw9P4NN9zA1772Nbp06cK7777LrbfeyjXXXMPaa69Np06dOO+883j77bcZP358VY/PRE+SJLVbHTp04JJLLuEnP/kJs2bNWlr+0UcfcdJJJzFgwAC6d+9Oz549ef/992vt0QM49NBDmTJlCk8++STz5s3jjjvu4OijjwZg6tSpQLYkVM+ePenZsye9evVi0aJFvPHGG1U9PidjSGp1mms5hto09xINklrevvvuyw477MCFF164tOzyyy/noYceYvTo0fTv35+IoHfv3stNBKvRs2dPvvKVrzBy5Ei23npr+vXrt3Rm/6c+9SkAXnrpJfr06VP9Ayphj54kSWr3Lr30Uq677rqlPXZz585ltdVWY6211mLhwoVceOGFDS6nctRRR3HLLbdw3XXXcdRRRy0t79u3L4cddhgnnngi06ZNA7Kr89x111188MEH1TsoTPQkSZLYeuutOeSQQ5ZeA/vUU0+lZ8+erLfeemy88cZ06dKF/v3719vG8OHD6dKlCxMnTuSII45Ypu7666/ns5/9LEOHDqVbt2587nOf4/bbb6/6si5RVxdkWzNo0KA0YcKElg5DUgEO3UorpxdeeIHNNtuspcNoM+p7PiNiYkppUENt2KMnSZLURpnoSZIktVEmepIkSW2UiZ4kSVIbZaInSZLURpnoSZIktVEmepIkSW2UiZ4kSVIbZaInSZLURnVs6QAkSVIbdn6PZtrPnObZz0rGHj1JktRuPfroo+yzzz706NGDrl27st122/H73/8egMmTJxMRvPHGG0u3f/rpp4kIzj777GXa2W233TjttNOW3n/ppZc4/PDDWXfddenatSsDBgzg6KOP5qWXXmqeA8uZ6EmSpHZp1KhR7L777gwePJj//Oc/zJgxg7POOovvfe97/PjHP2arrbaib9++jBkzZuljxowZwxZbbMHo0aOXls2fP5/x48czfPhwAJ555hkGDRrEqquuyj//+U/mzZvHhAkTGDhwIH/7W/Ney9uhW0mS1C595zvf4dBDD+W8885bWnbwwQczf/58jjvuOI488kj22GMPRo8ezTe/+U0ARo8ezZlnnsl3v/td3n//fdZcc03GjRtHSonddtsNgFNOOYXtttuOG264YWm7vXr14rvf/W7zHiD26EmSpHZoypQpvPzyyxx++OHL1R122GEsWbKEUaNGMWzYsKW9d4sXL+bhhx9m7733ZvDgwYwdOxbIkr/BgwezxhprMH/+fMaOHcthhx3WnIdTJxM9SZLU7sycOROA9ddff7m6Tp060bt3b2bMmMHw4cN56623ePHFF3niiSfYYIMNWHvttZf29EGW6NUM277//vt88skntbbbEkz0JElSu9OnTx8Apk2btlzdwoULeffdd+nbty/9+/dnwIABjBkzhjFjxrDHHnsAsPvuuzNmzBjef/99Jk2atDTRW3PNNenQoUOt7bYEEz1JktTubLLJJgwYMIBbbrllubrbbrsNgGHDhgEwfPhwRo8ezejRo5cmettttx1vvfUWN998M127dmX77bcHoEuXLgwdOpRbb721mY6kfiZ6kiSp3YkIrrrqKm666SYuuugi3nvvPT766CP+9Kc/8T//8z+ceuqp9O/fH8gSvjFjxjB+/HiGDh0KQIcOHRgyZAgXX3wxQ4cOpWPH/85vvfzyy5kwYQLHHnssU6dOJaXE7Nmzufbaa7nyyiub9TiddStJkqqnFS9kvO+++zJ69GguvPBCLrnkEj788ENSSvzyl7/kpJNOWrrdsGHDmDNnDttuuy1rrrnm0vI99tiDv/71r0uHbWtstdVWPPHEE1xwwQUMHjyYDz74gD59+jBs2LDl1t+rNhM9SZLUbu26666MGjUKgNmzZ/P5z3+e5557johYus1aa63FkiVLlnvsKaecwimnnFJru5/5zGe4+eabqxP0CnDoVpIkCejZsyd///vfWX/99XnuuedaOpyKsEdPkiQpt8466yyzgPLKzh49SZKkNspET5IkqY0y0ZMkSWqjTPQkSZLaKBM9SZKkNspET5IkqY1yeRVJklQ1n/vd55plP89885lm2c+rr77KRhttxBtvvMEGG2zAyJEjueiii3j55ZebZf8ryh49SZLU7gwdOpTVVluNrl27Lr0de+yxLR1WxdmjJ0mS2qUf/vCH/OAHP2jpMKrKHj1JkqTc+eefz/Dhw5cpGzp0KBdddFELRdQ0JnqSJEltlImeJElqly6++GJ69uy59PbYY4+1dEgVZ6InSZLapXPPPZfZs2cvve20004tHVLFmehJkiTlunbtyocffrhM2VtvvdVC0TSdiZ4kSVJu0KBBPPnkk0ycOJHFixdz1VVXMXXq1JYOq9FM9CRJknJDhw7ltNNOY5999mHdddflnXfeYZdddmnpsBotUkotHUOzGDRoUJowYUJLhyGpgP5n/63F9v3qz77QYvuWVnYvvPACm222WUuH0WbU93xGxMSU0qCG2rBHT5IkqY0y0ZMkSWqjTPQkSZLaKBM9SZKkNspET5IkVUx7meRZbZV6Hlss0YuIVSLiXxGRImKDkvIjIuKViJgfEeMjYruyxw2KiMfz+lci4vDmj16SJJVbddVV+eijj1o6jDZh0aJFdOzYscnttGSP3inA/NKCiNgV+F/g28CawB3AvRHRPa/vAdyXl68JnABcGxGDmzFuSZJUi759+zJt2jTmz59vz14TLFmyhHfeeYcePXo0ua2mp4qNEBGfAU4Evgo8VVJ1HHBnSmlUvt2lwHeBEcDvgAOAj4BLUvYOeiAi7gKOBx5tviOQJEnlunfvDmSXDFu0aFELR7NyW2ONNejdu3eT22n2RC8iVgF+C5wBzC6r3hoYWXMnpZQi4qm8vKb+ybTs14QngW/Usa/jyZJA+vXrV4nwJUlSPbp377404VPLa4mh25OB6SmlO2up6wbMKSubDXQvWL+MlNJ1KaVBKaVBffr0aULIkiRJK59m7dGLiE8DpwF1XbJjHlA+IN0TeKWkvn8t9XMrFKIkSVKb0dw9ersCfYBnI+JdsmFXgKcj4kRgMjCwZuOICGCbvJz857ZlbW5bUi9JkqRccyd6fwQ2JkvetgH2y8v3Am4ErgcOiIhhEdGJrPdvdeCufLu7gC4RcUZEdIqIYWQTNK5rxmOQJElaKTTr0G1KaT4lS6pERM3+p6eUPgAeyXv2rgfWBZ4B9kspzc0fPzsi9gOuBi4E3gZOSCk541aSJKlMiyyvUiOl9CoQZWU3kvXu1fWYJ4AdqhuZJEnSys9LoEmSJLVRJnqSJEltlImeJElSG2WiJ0mS1EY1KdGLiJ6VCkSSJEmVVSjRi4hvR8SZJfe3iYg3gVkRMTEiNqhahJIkSWqUoj16J7HsZcZ+BbwFfD1v42cVjkuSJElNVHQdvX7AvwEiog+wCzAspTQ2IhYCV1UpPkmSJDVS0R69j4FO+e+7k13dYlx+/z3Ac/UkSZJamaI9eo8D38nPy/secH9K6ZO8bgDZMK4kSZJakaI9eqcDm5Nde3ZD4NySuq8B/6xwXJIkSWqiQj16KaXngE9HxFrAeymlVFJ9OvB2NYKTJElS4xVdXuW3EbFRSmlWWZIH2WzcSyofmiRJkpqi6NDtkUCfOup6A9+sSDSSJEmqmBW5MkZ5T16NLYGZFYhFkiRJFVTnOXoRcTJwcn43AXdHxMdlm60OrA2qZSrgAAAgAElEQVSMrEp0kiRJarT6JmM8D9wBBHAq8CDLT7pYCLwI/LEq0UmSJKnR6kz0UkoPAA8ARMQ84NcppWnNFZgkSZKapujyKhdUOxBJkiRVVn3n6P0ROCel9Er+e31SSulrlQ1NkiRJTVFfj14fYNX8977UPetWkiRJrVB95+jtXvL70GaJRpIkSRWzIuvoSZIkaSVSaDJGRDR4ibOU0plND0eSJEmVUijRAw6qpWxNoDswB3gfMNGTJElqRYour7JRbeURsSNwHXBCJYOSJElS0zXpHL2U0njgUuCqyoQjSZKkSqnEZIxZwGcr0I4kSZIqqOhkjC61FHcCNgMuBJ6rZFCSJElquqKTMT6g9gWTA5gGfKViEUmSJKkiiiZ6R7N8orcAeBN4PKW0qKJRSZIkqcmKzrodWeU4JEmSVGGFJmNExLCIOLKOuiMjYvfa6iRJktRyis66vRhYu4663sBPKhOOJEmSKqVoorcFMKGOuqeAzSsTjiRJkiqlaKK3GOhVR91aFYpFkiRJFVQ00XsEOCMiOpUW5vdPA8ZVOjBJkiQ1TdHlVc4lS/Zejog/AG8D6wIHAz2AY6oTniRJkhqr6PIqT0fE9sD5wDfIhmtnAaOBC1JKU6oWoSRJkhqlwUQvIlYh672bllI6tPohSZIkqRKKnKO3CvAqsGt1Q5EkSVIlNZjopZQWA68BXaofjiRJkiql6KzbnwPnRkSfagYjSZKkyik663YvsvP0Xo2IicA7QCqpTymlr1U6OEmSJDVe0USvN/DvsvuSJElqxYour7J7tQORJElSZRU9R0+SJEkrmTp79CLiROD2lNLM/Pd6pZSuqWhkkiRJapL6hm6vAiYAM/Pf65MAEz1JkqRWpM5EL6W0Sm2/S5IkaeVgAidJktRG1ZnoRcSGETExIvarZ5t9820GVCc8SZIkNVZ9PXqnAx+klO6ta4OU0n3AXOCMSgcmSZKkpqkv0fsS8NsCbfwW2Lsy4UiSJKlS6kv01gNeKdDGVGD9yoQjSZKkSqkv0ZsL9CnQRu98W0mSJLUi9SV6jwFfK9DGIfm2kiRJakXqWzD5MmB0RLwAXJRS+qS0MiJWAX4AHAgMq16IkiRJaoz6FkweGxGnkCV834qI0cDrZFfB6EeW3PUBTkkpPdQcwUqSJKm4+nr0SCn9KiLGAScBu5H13gFMA+4D/l9KaXJ1Q5QkSVJj1JvoAaSUngKOboZYJEmSVEFeAk2SJKmNMtGTJElqo0z0JEmS2igTPUmSpDbKRE+SJKmNKpToRcQnEbFDHXXbRcQntdVJkiSp5RTt0Yt66lYFFlcgFkmSJFVQnevoRUQ/oH9J0bYRsXrZZqsD3wSmVj40SZIkNUV9CyYfBZxHdsmzBPxvHdt9BBxb4bgkSZLURPUletcAfyIbtn0a+Hr+s9RC4PWU0sfVCU+SJEmNVWeil1KaCcwEiIiNgLdTSgubKzBJkiQ1TYPXugVIKb0GEBGrAeuTnZtXvs3zlQ1NkiRJTVEo0YuI9YDrgH1rqyY7h69DBeOSJElSExVK9IBfAwOBU4Hnyc7NkyRJUitWdB29XYDvpZSuTCk9kFJ6qPxWdIcRcXFETI2IuRExIyL+lC/lUlN/RES8EhHzI2J8RGxX9vhBEfF4Xv9KRBxedN+SJEntSdFEbwbZMiqV8Htgm5RSd7J1+l4HbgOIiF3JlnH5NrAmcAdwb0R0z+t7APfl5WsCJwDXRsTgCsUmSZLUZhRN9H4EnFWTcDVFSunFlNKc/G4AS4DP5vePA+5MKY3Kl2y5FPgYGJHXH0CWcF6SUvo4pfQAcBdwfFPjkiRJamuKnqN3ANAPeC0ingBml9WnlNLXiu40Ig4j67nrTnb5tFPzqq2BkaWNRsRTeXlN/ZMppVTS3JPAN+rYz/HkSWC/fv1q20SSJKnNKpro9QZeyX9fFejTlJ2mlG4BbomIdYBjgGfyqm7AnLLNZ5MlhEXqy/dzHdlsYQYNGpRq20aSJKmtKrqO3u7V2HlKaXpEXA/8J5+QMQ/oUbZZT/6bZM5j2evv1tTPrUZ8kiRJK7Oi5+gtFZn1IqJob2BDOgJrAOsBk8mWcVm6L2CbvJz857Zlj9+2pF6SJEm5woleROwXEeOBBcAbwFZ5+fVFlziJiFUi4rsR0Te/vwFwNfAq8CJwPXBARAyLiE7AaWRX4bgrb+IuoEtEnBERnSJiGNn5g9cVPQ5JkqT2olCiFxFHAPeQJWPHk82WrTGF7Dy7ovYDno2ID4HxwHxgeEppcUrpEeBEsoRvDnAwsF9KaS5ASml2/viD8vrrgRNSSo+uwP4lSZLahaLDr+cCl6aUzomIDsANJXXPAacXaSSltIQsUatvmxuBG+upfwLYocj+JEmS2rOiQ7efAh6oo24Bdcx6lSRJUsspmui9wfKTIGoMAl6uTDiSJEmqlKKJ3m+A8/JJF53zssgnQ5xJdq6cJEmSWpGi5+j9HNgQ+B3wSV72L6AD8H8ppV9VITZJkiQ1QdEFkxPwnYi4HBgOrAW8B4xJKU2pYnySJElqpBVa9Dil9Ar/vUqFJEmSWrEVSvQi4rPA+mSLGC8jpXRvpYKSJElS0xVK9CLic8CtwGYsu1hyjUR2vp4kSZJaiaI9er8FFgFfJFtKZWHVIpIkSVJFFE30NgO+mlL6ezWDkSRJUuUUXUfvcaBfNQORJElSZRXt0TseuDUi5gMPArPLN0gpza9kYJIkSWqaooneu8CrwI31bONkDEmSpFakaKJ3EzAY+AVOxpAkSVopFE30dgeOSyndUs1gJEmSVDlFJ2O8CngOniRJ0kqkaKJ3BnBuRPSvXiiSJEmqpKJDtxeQLa8yJSJepfZZtztUMC5JkiQ1UdFE79n8JkmSpJVEoUQvpXRUtQORJElSZRU9Rw+AyGwYETtHxBrVCkqSJElNVzjRi4gTgWnAa8A44LN5+Z0R8T/VCU+SJEmNVSjRi4gzgMuB64E9gCipHgt8reKRSZIkqUmKTsb4DvCjlNIlEVF+qbN/A5+pbFiSJElqqqJDt+sAE+uoWwKsXplwJEmSVClFE72Xgc/XUbcb8HxlwpEkSVKlFB26vQK4JiIWAn/Ky/pGxDHAqcBx1QhOkiRJjVd0Hb1fR8SawI/IrpIBcC/Z9W/PTyndUqX4JEmS1EhFe/RIKV0aEdcCg4HewHvAoymlOdUKTpIkSY3XYKIXEasD9wA/SSmNBUZVOyhJkiQ1XYOTMVJKC4DtgfJlVSRJktSKFZ11ew/wlWoGIkmSpMoqeo7e34FLI2JdskkY7wCpdIOU0r0Vjk2SJElNUDTRuyn/eUB+K5dwaFeSJKlVKZrobVTVKCRJklRxRdfRe63agUiSJKmyCiV6EbF5Q9uklLwMmiRJUitSdOj2WcomX9TCc/QkSZJakaKJ3u61lPUC9spvJ1csIkmSJFVE0XP0Hqqj6q6IuAg4GPhrxaKSJElSkxVdMLk+DwJfrkA7kiRJqqBKJHpfAGZXoB1JkiRVUNFZt3+spbgTsCmwCfD9SgYlSZKkpis6GaNPLWULgHHAqV7+TJIkqfUpOhmjtlm3kiRJasUafY5eRKwZEdtExGqVDEiSJEmVUSjRi4gLIuJnJff3AF4HJgL/iYgtqhSfJEmSGqloj97XgRdL7l8GPALskpf/tMJxSZIkqYmKJnrrAf8BiIgNga2B81JKjwGXAztVJzxJkiQ1VtFEbx7QI/99D+D9lNLj+f0FQJdKByZJkqSmKbq8ykPA2RGxBDgd+HNJ3WeANyodmCRJkpqmaI/eKcDHwG1kV8E4t6TuCODhCsclSZKkJiq6jt40siHb2uxNNnwrSZKkVqTo0G2dUkpzKxGIJEmSKqtwohcRg4FjyM7JW728PqW0QwXjkiRJUhMVXTB5T7Lz8DYAdgVmAh+QLbOyFvBstQKUJElS4xSdjHEhcCXwhfz+D1NKe5D17i0CxlY+NEmSJDVF0URvc+A+YAmQgDUAUkqvAeez7CxcSZIktQJFE70FwCoppQS8DWxcUjeXbEhXkiRJrUjRyRiTgc8CDwCjgXMiYhqwkGxY95nqhCdJkqTGKtqjdwXZkC3A94EPgb8DDwJ9ge9UPjRJkiQ1RdEFk+8t+X1aRGwHfBroDLyYUlpYpfgkSZLUSCu8YHJEBLAuMDWltLjyIUmSJKkSig7dEhH7RcR4sokZbwBb5eXXR8ThVYpPkiRJjVR0weQjgHuAF4HjgSipnkJ2xQxJkiS1IkV79M4FLk0pfRO4qazuObJ19iRJktSKFE30PkW2tEptFgDdKxOOJEmSKqVoovcGsG0ddYOAlysTjiRJkiqlaKL3G+C8fNJF57wsImIYcCZwfTWCkyRJUuMVXV7l58CGwO+AT/KyfwEdgP9LKf2qCrFJkiSpCYoumJyA70TE5cAwoDfwHjAmpTSlivFJkiSpkVZoweSU0ivAK1WKRZIkSRVUZ6IXEf1WpKGU0utND0eSJEmVUl+P3tSCbQSQyM7XkyRJUitRX6IXwAfAn8muijG/WSKSJElSRdS3vMpuwI3AnsBvga+T9dqNSin9rfxWZGcR8fOIeC4i5kbEW/l1cnuVbXNERLwSEfMjYnxEbFdWPygiHs/rX/E6u5IkSbWrM9FLKT2SUvousB5wAPARMBJ4JyJ+GxF7RUTRdfhqfAIcDqwFbA1sANxQUxkRuwL/C3wbWBO4A7g3Irrn9T2A+/LyNYETgGsjYvAKxiFJktTmNZiopZSWpJQeSCkdA6wNfJNs0eS/ATevyM5SSt9PKT2VUlqUUpoJXAUMLdnkOODOlNKolNLHwKXAx8CIvL4m4bwkpfRxSukB4C7g+BWJo7nddtttDBkyhO7du9Ox4/Kj5b/4xS/YeOON6datG5tssgnXXHNNre08/fTTdOrUieHDh1c75HbF10dqOj9HrZ+vUfu0QsurAFuRDenuQtY79+8m7n8Y8HTJ/a3Jeg2BbP2+iHgqL6+pfzJf16/Gk8A3ams8Io4nTwL79VuhScQVteaaa3LiiSfy0Ucfcfzxy+ak99xzD+eddx6jR49mp5124tFHH2X48OFssskm7Lnnnku3W7x4MUcffTRDhgxp7vDbPF8fqen8HLV+vkbtU4M9ehGxeURcGBEvAY8CnwN+BPRNKZ3f2B1HxFfJevBOLinuBswp23Q20L1g/TJSStellAallAb16dOnsaE22d57782hhx7KgAEDlqt7+eWX2Xrrrdlpp50AGDx4MFtttRWTJ09eZruf/vSnbL/99n64qsDXR2o6P0etn69R+1RnohcR50TE02Q9brsBlwHrpZT2SSmNTCnNbexOI+Igsuvjfiml9GRJ1TygR9nmPYG5BetXOocccghz587ln//8J0uWLGHcuHFMmTKFffbZZ+k2zzzzDCNHjuTnP/95C0baPvn6SE3n56j18zVqu+obur2YLLH6AzANGACcGRG1bZtSSmcV2WFEHEWWNO6fUvpnWfVkYGDJtgFsA9xZUj+i7DHb5uUrpb59+3LggQey++67s2TJEgCuuOIKttxySyDrJj/qqKO44oor6N691o5LVZGvj9R0fo5aP1+jtqu+RO91soWQdy7QTgIaTPQi4nvAecDeKaUnatnkeuD+iPgdMA74HrA62YQL8p+XRMQZwJXAELIJGnvW0tZK4cc//jG33norkyZNYrPNNuP555/nS1/6Ep07d+aYY47hkksuYZNNNmH//fdv6VDbJV8fqen8HLV+vkZtV52JXkqpfxX2dyWwGHiwtGcwpdQ1//lIRJxIlvCtCzwD7FczTJxSmh0R+wFXAxcCbwMnpJQerUKszWLixImMGDGCzTffHIAtttiCr3zlK/z1r3/lmGOOYdSoUTz55JP07t0bgPnz57N48WJ69+7NlClT6NWrV33Nq4l8faSm83PU+vkatV0rug5ek6SUIqW0akqpa+mtbJsbU0oDUkqdU0o7pJQmltU/kZd3zre7qTmPoTE++eQTFixYwMKFCwFYsGABCxYsIKXELrvswt13381LL70EwAsvvMDdd9/NwIHZCPbtt9/O888/z6RJk5g0aRInnHACO+64I5MmTaJnz54tdkxtia+P1HR+jlo/X6P2aUWXV1Ej/P73v+eoo45aer9z584ATJ06lTPOOIM5c+aw55578u6779KrVy8OOuggzj77bADKZwt3796d1VZbjQ022KD5DqCN8/WRms7PUevna9Q+xbJL0rVdgwYNShMmTGjpMCQV0P/sQldVrIpXf/aFFtu3JBUVERNTSoMa2q5Zh24lSZLUfOpbR69fRKzanMFIkiSpcurr0ZtKtkYdETEmIjZtnpAkSZJUCfUleh8BXfLfh1LHZcYkSZLUOtU36/Yp4MqIeCC/f1JEvF3HtoWvjCFJkqTmUV+idxxwKfBlsitfDAM+rmPbQlfGaA+cLdj6+RpJTefnqHVrydcHfI1ak/qujPEisD9ARCwBvpJSery5ApMkSVLTFF0weSOyy41JkiRpJVEo0UspvRYRHSPia8CuQC/gPWAccGdKaXEVY5QkSVIjFEr0IqIvMArYCngVeAcYDHwHmBwRe6WUZlYrSEmSJK24olfGuBxYC9gxpTQgpTQ4pTQA2DEvv7xaAUqSJKlxiiZ6+wFnpZSeKC3M758DOL1GkiSplSma6K0GzKujbh7QqTLhSJIkqVKKJnqPAWdFxBqlhfn9s/J6SZIktSJFl1c5DXgQeCMiRpFNxugL7A0E2SXSJEmS1IoU6tFLKU0CNgGuA/oAe5IletcCm6SUJlctQkmSJDVK0R49UkrvAmdXMRZJkiRVUNFz9CRJkrSSMdGTJElqo0z0JEmS2igTPUmSpDaqwUQvIlaLiHMjYuvmCEiSJEmV0WCil1L6GDgX6Fn9cCRJklQpRYduxwPbVTMQSZIkVVbRdfTOBG6JiIXAvWRXxkilG6SU5lc4NkmSJDVB0URvfP7zV8CVdWzToenhSJIkqVKKJnpHU9aDJ0mSpNatUKKXUhpZ5TgkSZJUYYWvdQsQEZuTTcrYEPhtSml6RHwaeCelNK8aAUqSJKlxCiV6EdEV+C1wILAof9z9wHTgJ8DrwOlVilGSJEmNUHR5lcuBnYFhQDcgSuruBfapcFySJElqoqJDtwcAJ6eUHoyI8tm1rwGfqmxYkiRJaqqiPXqdgVl11HUDPqlMOJIkSaqUooneE8ARddQdCPyrMuFIkiSpUooO3f4A+EdE/AO4nWxNvf0i4hSyRG+3KsUnSZKkRirUo5dSeoRsIsZqwFVkkzEuAAYAw1NKT1QtQkmSJDVK4XX0Ukr/BIZERGdgTWC217eVJElqvYqeo1dqAdlaeh9VOBZJkiRVUOFELyL2i4h/kSV604EFEfGviPhC1aKTJElSoxVK9CLiW8BfgA+Ak4GD8p8fAPfk9ZIkSWpFip6j933gupTSt8vKr42Ia4Fzgf+raGSSJElqkqJDt2sBd9ZRdwfQqzLhSJIkqVKKJnoPAp+vo+7zwMOVCUeSJEmVUufQbURsXnL3V8CvI2It4G5gBtAXGAHsCxxbzSAlSZK04uo7R+9Zsitg1AjgW/kt5fdr3A90qHh0kiRJarT6Er3dmy0KSZIkVVydiV5K6aHmDESSJEmVVfgSaDUioiPQqbzcy6FJkiS1LkUXTO4REddExNtkV8aYV8tNkiRJrUjRHr2RZMuoXA+8DCysVkCSJEmqjKKJ3jDgWymlW6sZjCRJkiqn6ILJrwOegydJkrQSKZronQn8ICL6VTMYSZIkVU6hoduU0r0RMRx4OSJeBWbXss0OFY5NkiRJTVAo0YuIXwD/AzyBkzEkSZJWCkUnYxwLnJtS+mk1g5EkSVLlFD1Hbz4wsZqBSJIkqbKKJnpXAsdHRFQzGEmSJFVO0aHb3sCOwL8jYizLT8ZIKaWzKhmYJEmSmqZooncgsBhYFdizlvoEmOhJkiS1IkWXV9mo2oFIkiSpsoqeoydJkqSVTNF19E5saJuU0jVND0eSJEmVUvQcvavqqUv5TxM9SZKkVqTQ0G1KaZXyG9ALOBSYDGxezSAlSZK04or26C0npTQb+ENE9AD+DxhaqaAkSZLUdJWYjDEVGFSBdiRJklRBTUr0ImJd4DSyZE+SJEmtSNFZtzP576SLGp2AbsAC4IAKxyVJkqQmKnqO3tUsn+gtAN4E7k8pzapoVJIkSWqyolfGOL/KcUiSJKnCvDKGJElSG1Vnj15EjFmBdlJKaVgF4pEkSVKF1NejN6vArRPZ+nlDi+4wIg6JiHERMTciFtdSv09EPBcRH0XEsxGxV1n9pyPiHxHxYUS8GRGnFd23JElSe1Jnj15K6aC66iKiH3AW8EXgXeCXK7DP98kul9YZuK6s3QHAncDxwB+Bg4C7ImKLlNKrEdEB+AvwD+BLwKbA/RHxZkrpDysQgyRJUpu3Qufo5b1pvwFeIku0zgE+lVL6adE2Ukp/TyndCvynlupvAhNTSjellBamlG4GnszLAXYDPgWck1Kan1J6kuyqHCesyHFIkiS1B4USvYjYIiJuAV4AdgdOBjZOKV2RUvqogvFsDUwsK3syL6+pn5JS+qCO+vK4j4+ICRExYebMmRUMU5IkqfWrN9GLiO0i4k7gaWBb4Fhgk5TStSmlhVWIpxswp6xsNtC9YP0yUkrXpZQGpZQG9enTp6KBSpIktXb1zbq9D9iLLMk7JKV0ezPEMw/oUVbWE5hbsF6SJEm5+hZM3jv/uSFwdURcXV9DKaW+FYhnMtnQcKltgdEl9Z+JiDVSSh+W1E+uwL4lSZLalPoSvQuqscN85uyqZEuzEBGr51UfAzcCZ0TEocCfgAOB7YAj8m0eBl4DfhIRZwOfBb5Fds6gJEmSStS3vEpVEj3gG8ANJfdrJnNslFJ6JSIOAC4Dfks2M3dESunVPKZPImJ/spm2s8jOz7s0pXRblWKVJElaaRW61m0lpZRGAiPrqb8fuL+e+pcBr8IhSZLUAK91K0mS1EaZ6EmSJLVRJnqSJEltlImeJElSG2WiJ0mS1EaZ6LVT//jHP9hpp53o2rUrvXv35sQTTwTgk08+4cc//jEbbbQRXbt2ZciQITz99NMtHK0kSWoME712aOzYsRx44IGcfvrpzJo1izfffJNjjz0WgMsvv5ybbrqJ0aNH89577zFkyBD23ntv5s2b18JRS5KkFWWi1w6dc845nHDCCRx44IGsttpqrL766gwcOBCA22+/nRNPPJEBAwbQqVMnLrjgAmbNmsVdd93VwlFLkqQVZaLXznz44Yc8/vjjS5O73r17M3ToUCZMmADAkiVLSCkt85iUEpMmTWqJcCVJUhOY6LUz77//PkuWLOH6669n5MiRvPXWW+y1117st99+zJ49m/3335+rr76al156iQULFvCDH/yATz75hLlz57Z06JIkaQWZ6LUz3bp1A+Coo45iq622olOnTpxzzjksWrSIf/3rX5x99tmMGDGCvfbai379+gGw2Wab0bt375YMW5IkNYKJXjvTo0cP+vfvT0QsVxcRrLbaalxyySVMnTqVGTNmcMYZZ/Cf//yHoUOHNn+wkiSpSUz02qETTzyRG264geeff57Fixdz6aWXsvrqq7Pzzjszffp0Xn31VQDeeOMNjjzySAYPHszee+/dskFLktqcupb6mjx5Mvvuuy/rrrsuEcEjjzzSwpGuvEz02qHTTz+do48+mj322IPevXtz33338f/bu+84qcrrj+OfQ1OQYgGNlRI1YkWDLUhEUTF2UWJiLNiiYuGXRMREY7DGErGXiIqoWIMiGmsIxFgj9kQl2CUKCkixrODu+f1xnoHLsEvbZe/s7Pf9eu0L5t47s8/OnTtz5jzPc55HH32Udu3aMXnyZHbffXdatWpF9+7d6dSpE2PGjKk2AygiIrK8Flfqq0WLFvTt25cxY8bk3MqGr1neDZD6Z2ace+65nHvuuYvs6969O5MmTcqhVSIi0phkS30VFEp9de3ala5du+bVtLKijJ6IiIjUqyWV+pK6o0BPpMT079+f5s2b07p16/k/11133ULHvPvuuxx44IG0a9eOdu3ascMOOzBv3rycWixSenQdlbYllfqSuqNAT6QEHXnkkXz55ZfzfwoDlAE+//xzevbsyVZbbcVHH33EjBkzuOaaa2jatGmOLRYpPbqOSteSSn1J3dEYPZEGZujQoWywwQYMGTJk/rbu3bvn1yCRBkjXUb6WVOpL6o4yeiIlaNSoUay++upsvPHGDBo0iC+//HL+vnHjxrHRRhux//77s/rqq7PlllsycuTIHFsrUpp0HZW2xZX6cncqKiqoqKgAYO7cuVRUVFBZWZlzqxseZfTKyZB2Of/+Wfn+/jJxyimncPHFF9OhQwfeeustjjrqKI477jjuuusuAKZNm8aLL77IPffcw6hRoxg3bhz77rsvHTt2ZKeddsq59SKlQddR6TvttNOYM2cOu+66KxUVFWy99dbzS3198MEHdO7cef6xvXv3BmD48OH0798/pxY3TMroiZSYH/7wh6y11lo0adKEzTbbjMsvv5y//OUvfPvtt0CMbdlxxx05+OCDadasGbvvvjt77rmn6k2JZOg6Kn2FUl9Tpkxh5syZjBs3jm7dugHQqVMn3H2RHwV5y06BnkiJa9IkLlN3B6Bbt24a1yKyjHQdSWOlQE+kxNx9993zywtMmjSJ3/zmN+y3336svPLKABx//PE8//zzjB49mqqqKsaNG8cTTzzBAQcckGezRUqKriORoEBPpMTccMMNdOnShVVWWYU99tiDHXbYgeHDh8/fv8MOO3DnnXcyePBg2rRpwymnnMKIESPYcccdc2y1SGnRdSQSNBlDpMSMHz9+icf069ePfv36rfjGiDRQuo5EgjJ6IiIiImVKGT0RERGpW3mW+1Kpr4UooyciIiJSphToiYiIiJQpBXoiIiIiZUpj9ETqk5Iy2WoAACAASURBVJapE6k9XUciS00ZPREREZEypUBPREREpEwp0BMREREpUwr0RERERMqUAj0RERGRMqVAT0RERKRMKdATERERKVMK9EREltHgwYPZbLPNaNu2Leussw7HHXccM2bMmL+/srKS8847j86dO9O6dWt69uzJ66+/nmOLRaSxUqAnIrKMmjZtyh133MH06dN57bXXmDx5MkcdddT8/UOHDuWOO+5g7NixzJgxg549e9KnTx/mzJmTY6tFpDFSoCcisowuvPBCtt56a5o3b06HDh04+eSTGT9+/Pz99913HwMGDKBLly60aNGCc845h+nTp/PAAw/k12gRaZQU6ImI1NLYsWPZcsst59+uqqrC3Rc6xt159dVX67tpItLIKdATEamFUaNGMWzYMK688sr52/bdd1+uvfZaJk2aREVFBWeddRaVlZXMnj07x5aKSGOkQE9EZDndd999HHfccYwZM4Ztttlm/vYzzjiDAw88kD322IMNNtgAgK5du9K+ffu8mioijZQCPRGR5TB8+HCOP/54HnroIXbZZZeF9q200kpccsklvP/++3z22WcMGjSI9957j169euXTWBFptBToiYgso6uuuorTTjuNxx9/nB49eiyyf8qUKXzwwQcAfPzxx/Tv358dd9yRPn361HNLRaSxU6AnIrKMBg4cyOzZs9lll11o3br1/J+CyZMns/vuu9OqVSu6d+9Op06dGDNmDGaWY6tFpDFqlncDREQamuIZtcW6d+/OpEmT6qk1IiI1U0ZPREREpEwp0BMRaUDuvvtuevbsSdu2bWnWbNFOmc8++4wjjzySNdZYg7Zt29KtWzc++eSTHFoqIqVAgZ6ISAOy2mqrMWDAAK644opF9lVUVNC7d29atGjBxIkTmTlzJiNHjlxo/KCINC4aoyci0oAUZu5ml1wrGDFiBDNnzuS6666jefPmAGy22Wb12TwRKTHK6ImIlIlx48ax6aabcvzxx7PGGmuwySabMHTo0LybJSI5UkZPRCRrSLucf/+s5b7rtGnTGDt2LFdccQU33HADr7/+OnvuuSdrrbUWv/jFL+qwkSLSUCijJyJSJtq0acO6667LwIEDadGiBd27d+ewww7jwQcfzLtpIpITBXoiImWiW7du1RZlVqFmkcZLgZ7kasqUKRxyyCF06NCB1VZbjV133ZXXXnst72ZJhs5RaamsrKSiooK5c+cCMdO2oqICd6d///5Mnz6da6+9lsrKSl577TVGjhxJ3759c2616DoqfeV6jhToSa4GDBjAjBkzmDhxIlOnTqV79+7ss88+S1x5QOqPzlFpuf3222nZsiV9+vShsrKSli1b0rJlSz788EM6duzII488wk033UTbtm05+OCDGTJkCIccckjezW70dB2VvnI9Rwr0JFfvvPMO/fr1Y/XVV6dFixYcc8wxTJ48menTp+fdNEl0jkpL//79cfdFfjp16gRAr169eOWVV/jqq6+YNGkSJ510Ur4NFkDXUUNQrudIgZ7katCgQYwaNYpp06ZRUVHBjTfeyE477UT79u3zbpokOkcitafrqPSV6zlSoCe56tGjB5WVlXTo0IHWrVtz//33M2zYsLybJRk6RyK1p+uo9JXrOVKgJ7mpqqpit912Y+ONN2bWrFl8/fXXnHnmmfTs2ZOpU6fm3TxB50ikLug6Kn3lfI4U6EluZsyYwfvvv88pp5xC27ZtadGiBcceeyxVVVU8//zzeTdP0DkSqQu6jkpfOZ8jBXqSm/bt27Pxxhtz3XXX8dVXX/Hdd99xyy23MGfOHLbYYou8myfoHInUBV1Hpa+cz5GWQJNcjR49mkGDBtGxY0fmzZvHhhtuyH333UeXLl3ybpokOkf1a4sR+X2ovHHkG7n97nKn66j0les5UqAnueratSsPP/xw3s2QxdA5Eqk9XUelr1zPkbpuRURERMqUAj0RERGRMqVAT0RERKRMKdATERERKVMK9ERERETKlGbdSp1RWYjSp3MkUnu6jkpbnucHSu8cKaMnIiIiUqYU6ImIiIiUqQYZ6JlZUzO71Mw+N7M5ZjbKzNrn3S4RERGRUtIgAz3gDGB/YHtgvbTt9vyaIyIiIlJ6GupkjF8C57r7ewBmdjrwjpl1cvcPcm2ZiIiISIkwd8+7DcvEzNoBM4Gt3f3VzPZZwOHuPiaz7ZdEUAjwA2Bifba1AWoPTMu7EbJYOkelT+eo9OkclT6doyXr6O4dlnRQQ8zotU3/ziraPjOzDwB3vxG4sT4aVQ7MbIK7d8+7HVIznaPSp3NU+nSOSp/OUd1piGP05qR/2xVtXxWYXc9tERERESlZDS7Qc/eZwEfANoVtZtaFyOa9nle7REREREpNgwv0khuBwWbW2czaAhcDj2siRq2pm7v06RyVPp2j0qdzVPp0jupIg5uMAVFHjwju+gMrAU8Cv3R3DdwUERERSRpkoCciIiIiS9ZQu25FREREZAkU6ImIiIiUKQV6kgszs8z/9TpsYNJ607bkI2VFSuOVRURqpA9YqXdm1sTd3cy6mNka7l6Vd5tk6ZnZLsBdwC1mtrWZrZp3mxobM2sG4O6VZraemX0/7zaVq6IvpfpyIw2OAj2pVynIqzKzjYDngJ3ybpMsncyH3LPACOAL4G7gIjPbM7eGNTIpyHvGzE4ws7WBV4H1c25WWTKzZp5mLJrZSsAaOTdJUCZ7WWnWrdQbM7OUyVsLOBGY6e5X5N0uWbLMuWsNNHH32Wn73sDeRMB+sbuPzLOdjYGZtQQOA64AKoBB7n5L4UtUvq0rH2bWNGVMmwCjiSVDNwOuBu5298m5NrCRS8mCrd393sK5yrtNpUoZPak3KVBYDbgcOA6YCGBmLXJtmCxROnfNiWzenpntfwUuAx4ETjezPjk1sdFw92+I2qEtiaUg5xb2Fbp0pfZSkGfAU8TymqcCxwOXAHvl2TYB4ADgRjNrrSBv8RToSX2rAl5L/x4G4O5zNSGjQWhNvGc8Cwu6ct39XaIr91lgfzNrq7FMda/QXWVmrYDPgR8DhwPDzOxUd69y9+/SMd/Lr6VlZTegwt0Pc/d3gF2B/wA3mdkq+Tat8Sl6XxkBvAjsk/bpM6QGemJkhcp8OFka7zILuAr4I7CxmV0CkMbtadxFCcm+caY32NWAVsC3EFm+wv70IfhXoDfQKbtPai/Tjbg5MBzYGniG6FIcDPzRzE5Ox95C+hIltbYyUAie7yCy2T9MXeRDzGyzPBvXWGS+VGbfcz4DpgJHpNsatlADBXqywmQ+nDYlxrX81cwGAhsCNwC3Adub2UUQXSX5tVaKpeC7lZltm95gmxGBXsvUjTs/gE/HPww8CpyijF7dSeMjK81sS2Ac8BbwgodviGvrDOAqM3sR6AFcmV+LG6YavmjOAXY2s7FAJ2C71ANxCtCH6NKVOlZcfisNHVnHzJ4ys13MrHPafSbQxcwOzqelDYMCPVlhMkHeeGAmMAb4CbFY9feI1Pt9RHffgLzaKYt1CjDWzHoSs2ynAVPdfR7EN+xCd2EyFlgFUKBXR9KH3KrAn4Gz3X0I8J2Z9TWzw4Dvu/vVwDbEBI1N3X2exustvdTbUJm+uHQ3sx5p7Nd44EJgF2Is6lpm9itgCHCEu3+cX6vLU2biVzMza5e+cHYGNgfeIcZI3mJmvwGaAs8DG6X7Kqapht4IZIVJHzSnApe7+x/Ttl8BY9z9k3RRjiDS7/fn11JZjIeBdYFbgFFAC+CgNE5sFaCS6N7aCLgHeAKYpm6UOjcXmAW4mXUhrpdZxGSML8zsQHd/lSi1Usimf1fjo8l8KWP0XXo/Gk+8xpsBa6ZA+mpiuML5wPvETOdd3P31nJpc1lKQtzKRBLjLzD4k3ltOcPejzWxrYFPgPCL42w+oMrNR7v7f3BpewlReRVYoM3sMGO7u95jZK8B/3f2Q9GG1pbuPzhyrKfI5qqk8h5l1BX4J/AJoD9wObAE0B6YQH3xNgb7uXlF/LS5fhaxG5nYb4A/EbM+PievoFDP7KXAQkV36Np/WlgczexCY7u5Hp9tfEnUij0vBx9rAdKC5u3+VY1PLlpl1dvf30/8vAg4h3nMuLCQLMseuA2wF9E3HXejuF9X0PtaYKdCTOlPNh1NLYuLFx8TMqLfd/Yi0715girufmktjZSGZ8ZStgXOIwG1m6iYkdcEfRbyhHuXuY82shbvPLXocvcnWUuZcrAl0IWbYvkeMj1yPqGP4Vjr2NqANEWTrzXwZZF+rKYi7HfiZu09LE1q2AboTxag/1ZeYFcvMfgycDJzs7p+lLzfvp93HAOPdfVYaS1lV9FlzFnENbFPvDW8A1J8tdSJ9OLlFaY3VYX69r38S41kqiW5czOx2oqvv1zk1VzIygUVb4GVgAyLQO8HMLgRw9zeBm4GHgBvMbNfqyuIoyKudzLnYEniaGM/6d2Kc2FruPhF4z8w2NLMHiGDkp+na07jIpZSe5yoza2Fm7YnPws7ALDO7DtiWmHjxHRF8HJNjcxuLKcCZKchrS/QU7ElMLLoM6Gdmq7l7ZXq9Z1cpuQholr6QShGN0ZNaK5oVOBKYbWZVwL7ufluaoTkA+JuZTSEKvW6XxsWouzZn6dy1IWpSPZ66BJsD/wN+kN50v3b3t83sj0QNxNFmtou7v5Rj08tOOhcbEWMdh7r7JWmi0mCgQ3r+/0dMavqKWBlgXppMoDF5S6HwXKXA+HVgpLufZ2bvE9nTSe6+RTp2IHAgsEd+LS5/6TPkv+n/6xDjIke5+53AhNTTMJgYo3oXMSGjipQ8IALxdYmudSmirlupFVuwdu06ROZhJDEg/HTiwtvZ3T82s42JAK+CeCOt0odTaUhdIQ8C27r7WpntFwI/IybLtAbO81huaFOitMRVCtJrL32Ire/ub6UJTEOI7tnfpf0vELXcmhKByYVEsPddYXairqOlY2bNU2BswMHE+1Oh/mAP4rltTgQSOwBHAnu5+yt5tbkxyGSyOxBDFIYSr/f7PC2rmL7k7E98hjQh3q/mpX2HAv9x99dy+QNKnAI9qTUz24DIMKzv7melbS2Jbr7OxJvp5KL7aCxXzlI3yBdphtv+RPmOm9z9NDPbH7iL+KY8gei2bUuqI5Z5DGVkayFlS98nguZz0rZNiBnNLwPPAe+4+2FmNgr4EXClu1+Ujl1oXKzUzMwuA55098fM7ErgUODSlDUt9G51Ak4jgr3PgVvd/e1cGtxIFF7DZrYFsWrSD4jnfxCwJnBnJtjrTczyfywFhs0LwZ7UTIGeLJf0jdhSZu5a4ERiTcgD3H1mOmYV4AFgR6CLu3+eW4NlvnTutiBWWOjl7nNSVm8/4A5ibFg34FB3H5vuszuRaTpA57FupCBvAvBEIauU2deEWH7r/9x9r7TtCuADIijUl6RlYGZjgPXcfZv0+j+c6Aqc7u4/TscoaK5nmSCvLXAskcn+U9q3CWnIAtG9flfRffUlcylpMoYss8wb4moA7n4SMWB2fWBXixprpBIEfYkabDNyaq4U8fA6MZOzR9pWSXTf/gLYhFh5YWzmbscS3YXT6rm5ZSl9CXoDuCcb5JnZVma2UgrkmgK7mdk+ZjaSWPbsqvTlSu/dSymN6Vq1MCMzvXfdC/weaG9mIwrbzaxF5n6a3LKCped8daIQ8tHENVEI4t4GLiaGjgw0s92K7qsgbynpzUKWiS1YjqYd8LjFtHbc/VfEDNtzgJ9kgr0v3X1gSrNrLdsSYKE5sbzTQYXtKbh4hBjgvKuZFb5ZDycKlP5CszvrzAHEF6PxhQ1m1o9Yu7ZL2vQikWE9D1gL2K0Q5Cmjt3QsyjgdQnyJwcyapy+qFcRr/WxgUzO7GSA7LEHZvfrh7jOIREFXoLB2cFU6T28DlxPDgP6eUxMbPHXdylLLDJjtSmR49ic+gC7IjBkaTpR8uJQYSKsiriUqze78F3CWu1+b2d6E6Ma9NW36EOiu2Z11J3VV/R+RVdoDmEd8mP3c3R/LHNcUWJ1YbUQTL5aBmT1EjCu9nlhX++zisY1pLPFeROboCXfXUowrWE1fVMzsTCJR8HN3v6/whTIbcOtLzvJReRVZainI24QFmbvfEzPTTkxB4AXufpSZjQb6uPsdebZXapbeMCeZ2TnAUWY23d3vhsjspQ/JXwL9iLF6CvLqkLvPThnTJkQplaZEqZTX0sSAKnevSt1Tn8OCpbrya3XDkWaMr+3u3dPtFsBwM6t090sLmWl3/8bMHiFmNWtJsxUskyzYkBjW05p4/T/v7hek1/7IFIf/pfj+CvKWjwI9qZFFXbxP3D07Lutg4GGPRdQxs78Bk4HTzWy2u1/t7gekrkEpUZk3zIeILsTTzGyNQmYvvRk/6O73woLaYzk1tyy5+9dpJuhsIqO0atpVBSzS1aIPuWXyhC8oT9Pco55nJXCbmVEc7JG6dmXFyQR5WwF/Ax4n1qrdDvi7mV3u7udY1GC918x6u/u4PNtcLhToSbUsFo6+FOif2WbEEkyrF7a5++fpG/HpwFlmtnJ6E52nWVGlKTu70N3fTbOmPwLOT+f9AeCZwuzpdJyCvFrKdBca0Mzd57n7HGComa0GPGlmh1aXyZClU+jac/fx6XZTT+U33H1k6g28zcyq3P0yjcNbcYq7WVOQty5wJ3CRu19mZqsCbwFrEytbXOpRvHoy0XMkdUBj9GQh2SDAzNb0WI5mDWLa++dp5tNw4DeFbE869hZgErAvsVbhy3m0XxZlC4pat3X32Ys57vvAGURmqRMx+H9WPTWzbGUyGe081uosrMzQjFjibCCRwfsVMSRi10KgInXPzH5GBBu/cvcr825POcq85lchlpDbAHgUMKKu6mmpO/0Z4G2iKkNfYvLR7wtfLNWTUDc061YWkjIOrc1sF2C6xcLqdwInp/8/R5Qm+J2ZDTazLSxKP6xLdH+sDWyYV/tlUSnIWxMYZlGUdBEpGHwXONHd+wGHKcirvfTFqdLMugEvm9kPUpDXhFhBZhV3n+PuXxKrARxD1DGUZWBmV5jZroUB/IuTxqL+lBgbJnXMFl47ewLQm6jbeT8xFvXKdJ7uAt5z98OJISSziDXR5/cCKcirG+q6lepcCuzksd7jZ2b2KnGxfg1cC/yJ6Or7HbEUVhNgD49F7icBLap/WMnRmkBPour8G9nMLSw0/qvwJjupnttXdjJdtasSNcKucveJafdQ4HV3PzRz7FdEtlyZjGVgsbziQcTs/6XqolL3+IqTgrzWRJD3oLsPgvlFq48jgroOwBrpNsR6wncCf8yMnVR3Yx1R160swmLd2leBW9z9jLTtLKJb9n7gRo+ls9oRZSG+SRfnr4FfE0HiB/m0XqD6Kv9m9lti7do93H1qPi1rXMxsLWLM4xxivOvUlGHd1N3fTMdoLGstpEljjxKzlj/Luz2NXcpWjyYKr2/nC1ZKGkp03f6aWMbsn8BKwLukGnqFbLcmHtUtdd02cpaKGGe7PNz9E+Bcoir/rmnb+cAYotDrcWa2rrvPcvevgY3M7PfAWcB+CvLylwLvtmbWJrP5CWAmkdUrvCHLirUWMAXoBXQsfIBlgrwmCvKWT8qUAnxDrNjy9dJ03cqKlV7j5wKfAYPSUKA9iLWF7/PwDTCACNDfBTZPQV5TBXl1Txk9KSzHdDXwD2JNwe/MbDNgGPBPdx+cOfa3xDiiIZ7q5FkUHd0HeMXd36n3P0AWkgK4dsDzxOoKz7j79WnfcGBjd++RYxPLVnXZiNS1+Ccia3GQu7+urEXtWFq1hXheNybev7oV9qvbL39mtg0x1OdTYt3mfdz9qZqGJWi4woqjQE8ws32JiRQvEV2xh6eyG/sRKfhe7v5U5vgjiICwUmMpSkfxuTCzvsTEmDOAZ4Enie6Sy4Hz3f3JXBpapjKD0L8P/BhoTyzb9ApRq/BCYEui8v+/de0sPzM7gRgjfC3wFXAaEei1JuoQfg20Ab5PjIXUWts5SJOQ7iGugf7uXlHUe6TXfz1QoNcIFS60TBmV9YgJGOOAjsCuwMPEoNm+xLexfu7+adHjaGxRicgEGWsQM59nAZ+m7Ox6wIlEYdIdgVZEeZzL82txeclMvNiCKAY7mlgf+EtiZuFJaSzZacCewA7u/l5+LW74zOwoohzN+8CPgNeIMh5NiECvORH07ejuH+XVzsbOojbndUSP0bA0u1/qkQK9RibzgbRQmjxl6c4HtiKmwu9FTL54k8hGXA/cpm9gpSdTJ29LovTNdGKNz38BN7j7i5lA8GRi4fBT1E1St9JMw0eB0R7FYNsC/wVudvcz0zFbEeNcz9eXpGVjZr2JwftvF4JkMzsUuIoo+3Qb0SvRgijj8SVQoYlH+UvduNcQmb0L0jhwqScK9Bohi+XJ/kG8KV5R+IZlZlcTY7tOAL4lMnt/IgK/W9396HxaLEuSsnZPEyU8hprZQSwobD2shvtoTEwdSjNsxwA9Uib1RWCSux9qsUZ0c3d/I3O8MuJLycxGAesAGxHjTi9w96fTvsOA84Bbidf/F3m1U2pmZtsDxwK/VMKgfmnWXePUCriZqF10XZoxC/GNq5L4oKpMY7j2JSZf/DKXlsrS2gR41t2HptunA6PcfZiZbVQ0+xZQMdIVYC7wHbC/mU0gMk+Hpn1nE92L8ynIWzpm9iBRB7IHsHX6/76F/WlS2AXAkcDgFHBLiXH3F0hBnmZH1y8Feo1QKotyM7AD8AZwoJn9i+juM+INs3DsR+4+3Bcs2SSlqQOwiZl9LwUZ77v7UWkG7glotZI6lSlL1KTwf2JSwHvEl6j/eVT8x8xuJ57/m/Noa0NmsbTiVu7e02MN24+Jwf2bmtk5ZnZNGo5yEzHOeG8yKytIaSkEecro1S913TZSmXFdLYl1TS8ngoV/AccDZ7j7JTk2UWpQQwmP7YBLgPWA5939sLT9dmJyxh4q51E3MtfO5sCpxPXzGNFtO40YJzmL+OI0E+hMZMnnqbt26ZnZ6sRz+hnRJTvezNYm6q7dTqwPvDvwH3ffL92nnWvpPpGFKKPXeDUBcPdv3P0td9+TGNO1ctrfrcZ7Sm4KBUXNbF0z62lmPwFw938RC4S3BF4xs4PM7A5gc+An6T663mspZSOqUgmVvxMB3QTgYOAyInPXD7iBmHk7gpj1OS+NiVSQt5RSSZQjiNmzJ5rZ0cALxPi844kg+x6geaa3YXYujRUpYcroNUKFQfipy+l8YqLFxLTve0QJjoc0hqu0FM2uHQNMJSbKPAEc6+7TzOwUojBvO2AycGah213ns26kEja/Bma6+6VpWzdiZZgZ7r7IeFZl8pZfCqqvJMbo/bWQrU77LiQmaBzm7t/m1ESRkqZAr8wVd/Nly6sQdadeLowlqua+Cg5KjJltRGSSLnb3a8ysC/AOUfPwWHf/vJr7KMioAykj2orIIu1ArPn828w1tTdReLyru0/Ks63lxsw2YEFx5BHu/qiZHU8Uod7Z3f+dawNFSpgCvTKWqZ22HtGF979CeQczu5cYG3tIuq0BsiUkez6yAbeZnQRsmgrwrgSMJyYA9CJWv/itaxm6OlXNl6X9iezdF8Tz/VLa3ooYq3eku7+fS2PLWMrsXUU8798SVQN2c/eXc22YSIlToFemiir1PwVMJFZGOIPoBmnt7tPTscr4lJDMuWsBzEv/70wM9F+ZWNrpfSKzN8Xdf25mVwKnAJe5+6DcGl+mzKwjMQFgl/TlaR/gTOK6ehAYS6y3ujmwrSa+rBgpg30rMRZyL3d/Nd8WiZQ+lcsoQ5mxXO2B3wJnu/vVaTDzOcR6kH9Ox5qCvNKRCfKaE+foszRz9nXig+0x4HMz+xExSL1Qp62CmIE4PodmNwYtiIK9/zKz7dz94TTG9SxiwsBfiCzTdoWJLwr26p67v2dmPyeSFJPzbo9IQ6BZeGUofdCsDZwLrEIsX4a730IsBH4kcIyZrafu2pKzRvq3FfAysc7wP4GB7v5YpmabE+U7zjKze4gCsuNStqlp8YPKsil+DtOYu72JtVNfTlnwB4nraQLwCXB5ev4V5K1A7v4/BXkiS0+BXvn6ATEjsxeR6QHA3W8nPpzOAvbIpWVSLTPbCXjDzNqkWmCPAh2BOURQl11N4U2i5mE3IkO7VSaTpAxtLaWArYvFguyFbROBw4kVMJ5Pz/WTxISA7YgvT9spyBORUqIxemWihiK6PYFBxAfTVe7+VGZfH+BvCgryl+muXRXo4O6TzKylu39jsZD7BsDRRCHkQZn7rUoEgVWFmdSaJb380kz0Du7+abp9F7AfMatzQua4A4D7gQ+ADVOAvScwlAjOf6dSHyJSKhTolYHM7Nr1gc2Atu5+b9q3GzAAmAdc7Wkh8OL71nujBVgoyFsJaJNq4a1NFIb9mbs/m+q2HUkEHf9y99NTd+277v677OPk9oc0cBZrAd8EPA/8xWOprcI6q1sTBZEn+IJiyb8llto62d3npWN3Bya5+wc5/AkiItVSoNfAFRXRfZhYLqg9MJ1Y9mp6ygqdCKwK/MbdX8uvxVIsza4dB1zr7nemTN11wF7Anu7+fAr2fgEcRcy6nQ1sXwgyZPmZWVvgRaI8zcVEXUIvfAEys0eBTYgvTM8Bf0z7B6T9zXUeRKRUKdBrgMxsZXevyNwuLMd0ibtfmzJ7HxJjuA5w9ylmthewE3CWxhCVlpTNe4XI4L2etq0GXAQcBvROwV5bYubnZsDolMVVd20tpOf+H0Th8AGZ7S2B5u4+O92+F+hOzKytIGbXzlMmVURKnQK9BsbM9iOyc8e6+//StiOALd39tDRb8AXg38RkjG+AQwrHpuM1KzBHxcGBmXUiZtbu5O4fZravRmSPCsHeC0WPo273WjKzbYEL3X33zLa+wDHAWsS4yJPT9h0BA15QkC0iDYVm3TY8rxJrPl5lZuukbX8DrjczAx4HJrp7/7T9R0R31HwK8vKVxuStbGa90qZviGvR6L0hGwAAEsNJREFUio77ghgLdgfwnJltWrRfQV7tOdDVzPqY2RZmdhGxxNkHwNPETNqzANz9OXd/tlDCRkGeiDQEKpjcgKQMwkcW652+RgR7p7r7J2l/N6ApsUICRNmNXYgPLCktFwI7mNn5wBtEV/si69S6+xdmdjYwCfhv/TaxUZhKDHu4Of1/FrGs1j9St24n4jpaiIJsEWko1HXbgGRm1zYlBubfSmR7znD3T8xsB2KZptuBbYCNiC7dSnXzlZY0jvIKYnWLd4D/A35OdBdCjAVbE1gfuK0wW1rdhXXPzDYkrpUvgI8KX5zSvseAx9398rzaJyJSGwr0Ghgz2xx4BriEGIPXh8jYHe3un5vZNUAHYCWgXxowrjF5JSQzU3pd4FqgMzGr8xliLdsmRNAB8BUxSUPBXS0ta5BsZrcRE1+21/MvIg2VAr0GIo2/W5lYU/N5dz8vbd+AWILpGeAod5+ZLfegDFBpygR7awNXEitf3Oju99dwvDKytWBmrYB7iTGP/65ppmw6rhcxGaMTsEP6sqTnX0QaJE3GKHGFNTc9fJM2z0r7Wrj7R8AJwP7APWbWIRPkmYK8fJnZejXsagKQVmE4mSjZcZyZ7ZeC+uxjmIKMWusGdGExQV7yPWBzYjLG9inIa6bnX0QaKgV6JazwAW9m25rZFSnbUAVsmw4pFGn9GLgb+I4olAxEcFivDZaFpNIdr5jZqtngrZBlNbOmZvYbYBpwEvA1MJiYVT2fzmOdWJN4v1vse567vwf82d1/UzhH+rIkIg2ZAr0SlT5gPBXJvQ2Y4e5fA2cAB5vZFcQAcoiK/f92971Td6DOawlw9xeBbd19JtAKFmRZU6b2NWArd69KdQ7/D3iKWKFBasnMmptZh3TzWyKg9kKWvCbuXsiYK5MqIg2exuiVMDPbmBgrhLsPzozr6kGMN5oFzCUyeTuqUn/pSZm8NYn6hye4+4Np2zPAZ+5+QDpuoWW0NIGmdlIw9zDwJlHKpjdwhLvvk/brOhGRRkGBXgkzswOA+4kaa1u5++xMsLcWMVh8JeAZVeovLZnzZCkzez2xwsVP3f1RM+tYWAVDA/1XDDM7ATgdGEbMRN8L2A1Yg7huviImOG0F3J8yryIiZUWBXgmpLstgZgcS2bs/uPuFadsigYGChdKTZkSPAPZ092/N7GKie/Ygd384HaPztgKZ2dHAECL7vQEwGVidKCz+DVAJfAr0VAZVRMqRVsYoEZliyGsSmbp5RPHWB8zsKODWFAf+sbrAQMFCSWpOBBW7AI+l7ncH7jOzA939MZ23upMmKx0EtCDWo/23u99iZl8R9QrvBkYCLxPjk1cihj7MTllXdZeLSNlRoFcC0gdMpZltSXwYzQbaABVmdri735EChJvNrI27/y7XBku1qsnIfkpkkPoBjwG4+xlmVgU8YmY/cvfnc2hq2UmTll4glorbDnjJzH7v7i+7+z1mtjKR2ZtCrAU9NRvYKcgTkXKl2Zk5KJ4Vm8ZyrQM8AFxNlNc4GvgP8KSZdXb3kcTs2p2K66xJ/jJj8doVtqVZ0kOAPma2S2b774hyKhPqvaFlyMzaAC8BT7j7fsTyfxsCOxeOcfcRwPnAEcBpZrZ6NrBTkCci5Upj9HKSMgyHAI+6+2dm1h24wN37ZI5Zh1hsfRxwaTZbpFmDpSMz8WJN4HoiGzuQKIkz1cxGAU+7++XFY/I0gaZ2zGwlYgnA2e7eO7N9GNCOGIfXDDgsBeIDiAkZB+n6EZHGQBm9/BwJnAUcbmbtidl/u6QlsQrlNj4h1jxds/hDSR9SpSOTkV0fuIEYX/lnYqWSnkSJj4FmtkbxmDwFebW2KjHObqqZ9QEws32JskRPAx8RGfIRAO5+nbv3TUGfMuMiUvY0Ri8n7v7nlAE6CDDgDqLr9nozO8LdZ6dDm5BZ7UJKSyZYGA38x92PIrrbf0R0HY4A3iBmfPYFhikbW3dSxvRw4Cqgv5ntTCwJuLu7jzWzZsSyZtUtK6dzICJlT123OSgaBP4HYE8iyJsB9AEKkzK2AjoDP1Tmp7SZ2V7EeLwB7j4hs31TYrzYecBMd9+5+keQ2jCz7wNXAj8mhjmcl9n3APCuu5+WV/tERPKirtscFArppv+fAzwB/IQo5HoNcDuRhXiTFOQtadkmqT81nItJxDrEm2ePcfc33X0M0BNYJwWEUsfc/V1istJTwGZmtgeAmQ0HuhBLB4qINDrK6OUo231kZucS9dZGA9e5+zeZ41RUt8SkDNKexGSZb9OYr8HAycCP3P3jzLGFGoljgStT4CcrQCazNwfoCLQmvizN03UkIo2RMno5yg4Id/ezgbFEzbUTU12wwnH6cCohKVu3M3ApMAq4zMxWJTKxzxKD/+eX0UlB3s5EIP92Lo1uJFJm71RiTOR3LAjymuk6EpHGSBm9ElCU2fsDsSbnr939GQ0aLw3VFdRNwd2RwL5E9+AdwKHA2+6+T9GxKwNru/v79dTkRi1NdJqWhkmohI2INFoK9EpEUbD3GPEhdVjOzRIW6nrtDOxNrI/6sru/kNl3EjHpYiDwX6Br5nwqWM+JVrwQkcZOgV4JyRTeHQKsC5yoTES+MudkS2IZs7cBJyZd/Nzd/549FtgE+G+aQKMgQ0REcqUxeiUkBRSrAr2AqxTk5S+dk/WBB4FL3H1X4HBgJaJe3p6w0Hi8N1OQ10xBnoiI5E0ZvRJkZiu7e0Xe7WjMMl2yLYjSKD3c/dw0eeYV4FXga2IFhoPc/eEcmysiIlItZfRKkIK8fKUxdZVmtjXwK6JG3j1p90PEChj9iYBvMjC4cL8cmisiIlIjBXoiGSmT52a2BlHTsMrdP3L3iWa2FrGU1kXp8O2As4nVGLT+sIiIlBx13YoUMbONgf2BDu5+etpmxHJ0E4AxwNrpZxtNvBARkVKljJ40WoUJFNXoDVwMHGhmHSCyde7+HnAisdTZu2SWp1OQJyIipUgZPWmUMpMtWgEHAS2A59z9zbT/KGJ5swHATdkZ0NkCvCrGKyIipaxZ3g0QqW+ZIK8t8AIx2WI74CUzO9vdX3L34Wa2GnAtUGVmNxeW0MoGdgryRESklCnQk0YlM6O2DfAS8Ii7DzSzdYBxxMSKlwDcfWha1/ZqYBUzu1JdtCIi0pCo61YaHTNbCXgamO3uvTPbhwHtgG+IL0GHpRm4ZwO7Az/WzFoREWlINBlDGqNVgbnAVDPrA2Bm+xLFj58GPgJ6ALcBuPu5pCBPtfJERKQhUUZPGiUz6wJcBcwB3gdOAPq5+1gzawZcT1wfx2buY8roiYhIQ6KMnjRKqVTKQKANcDJwubuPTfu+A9oDM4vuoyBPREQaFGX0pFEzsw2A64AvgVvc/QkzGw5sQ6qTl2sDRUREakGBnjR6ZvZ94EqiG7cj0JoI8uYVSrHk2kAREZHlpEBPhPlj9m4HKoHeKchTMWQREWnQFOiJJGa2JjDN3asU5ImISDlQoCdSxMyaqDCyiIiUAwV6IiIiImVK5VVEREREypQCPREREZEypUBPREREpEwp0BMREREpUwr0RBowMxtiZl7Nz99KoG0fmNmf6vH3bZyej1VXwGP3N7MXzOwrM5ttZuPMbO/lfKxe6RxtvoTjbjWzCZnb25nZkKX8HbfW8LpwM9tpedq9IpjZX8xsfOb2EDOblmOTRMpOs7wbICK1NgvYs5pteTsQmF6Pv29j4A/ArRStU1wbZnY9cByxVN5ZxPvmz4CHzezX7n55Xf2uIucBLTO3tyP+viFLef+3gaOq2f6f2jVrhboJeCjvRoiUEwV6Ig3fd+7+fF0+oJk1B6pqs/ybu79Sh03KhZkdAJwAnOjuN2R2PWpmU4BLzWysu79e17/b3d+t5UN8VdevixXN3ScDk/Nuh0g5UdetSJkzsyZmdoaZvWNm35rZf83syKJjxqdutF+a2btABbBOoSvNzLY3swlm9o2ZPW1mnc1sTTMbbWZfmtlbZrZr0WMu0nVrZj81szdSOz42swvMrFlmf//UvbiFmT2ZukrfNrO+S/gbe7EgE/R+eowPMvu7mdlYM/vazL4ws5FmttZSPH0DgXeAYdXsuxD4Ejh5CX9z4W9qXXT/dczs4fQ3fmRmJxTdb37XrZn1B65O/y90wY5fivbXKNOF3MvM7kvn8T0zG1DNsT9O3dVfmtms9HrZOrN/ic+vma1vZo+k19AHZnZsNb9noa7bZWzjyek19VV6XfYu3Lc2z5NIQ6dAT6QMmFmzoh/L7L6a6HK8EdgbeAC4xcz2KXqYHsCJwGBgXxZ0/7ZK970c+DmwAbEu8F3A00Bf4H/AfWbWajFt3AO4B3gZ2D+16zTgmmoOvxMYQ3T/TgLuNrP1FvMUvJwei9SeHdN9MbMOwPj0dxwKnALsDDxpZi0W095m6XEeqi6z6e6zgHHpsZbHzcDrqb2PAtdXc04K/gpclv6/Y/pZJNgpVs3rorpenGHAa8TzNR641sy2yzxGL2AsMA84EjgE+Cewbtq/xOc3vR4fBDYHjgF+TQTROy7pb1jKNh5IvJ4Kr5nXiedXRNxdP/rRTwP9IcZreTU/u6X9GwJVwJFF97sNeDFzezzwDfC9Gh5/58y2AWnb2Zltm6ZtP8ls+wD4U+b288C4osc/HagE1ku3+6fHOTpzzBrAd8AJS3gu9kn37VS0/SJizF7bzLbt0rE/X8zjfS8dM3Axx1xBdJFW+zcX/U2t0+1e6faNRcc9CTyfuX0rMCFz++R4y16q18WtNbwuPHNMoR3nZrY1Bz4HLspsew6YQFpJqZrftcTnF9gr3d4+c0zHdF7HF73epi1HG18E/lrUruvSfXvV5zWpH/2U2o8yeiIN3yxg26KfF9K+3kSg90BRVmcs0M3MmmYe5yV3n1LN488lMjgF76R//17NtnWra2D6PdsA9xXtuofoWSjO7DxR+I+7Twc+A9ZLj2VFWaolvY9tBzzh7rMzj/kvIijbqdC+xWREl2R515F8oOj2/cAPi85JbbzFoq+Lbas5LvtczyMyqIXnehVge2CEu9f0dy7x+U3HTHX3FzLHfAi8tJR/y+La2BToRmTzsopvizRKmowh0vB95+4TatjXHmhKzbNw12bB4PepNRwzx92rMrfnpn/nz2x197kpNlp5Me1oXs3vKNxevWh78azZuZnHPhIYntk3gsia1WRtqp9pOjXze8eycBfsLkS39LdE5qkmHYFPF7N/cT6r5nYz4rmq6Vwsi68X87rIWtxzvRpgLP5vXJrn93ss+veStrWpZRs7EM/b50XHFN8WaZQU6ImUtxlE91gPIrNXLPvhu7yZqaUxjRjjtWbR9sKA/RnL8FgPsXBmakl11z6t5vcWfncho3Q8CwccE939OzN7FtjbzE4rCnYxs7ZE12I2c1QBFI/7Kw5iC4rbtCZxrkqpjtwXxOtm7cUcszTP75QajlmTGDJQG58Tz1uHou3Ft0UaJXXdipS3vxMZvXbuPqGan7lLeoC64DGZ4SWgX9GunxKBxHPL8FjTi/6GD9Kuwt9SnFV8AehjZvMDOTPbFuhEZO1w94lFjzknHXoVUZ9vkRmiwBnAqiycXZwMdC06bvca/pQDq7n9ktdc0mZuantNWdM65+5fEc/fEYvpzl7i80uMoVvLzLbPHLMB0Z1f2zZWAq8SE3yy9qvtY4uUA2X0RMqYu080sxuIWauXEIPqVwY2AzZ29+oCmBXlD8DjZjYcuBvYgigKPMyjflptTUz/Hm9mdxNdl28AQ4nZxI+b2cVAa2ICwRvAqMU9oLuPTs/ftWa2KfAw8b55CNFdfI27j8/c5QHgajP7HRHc9CWe6+r8xMwuAP6RjtudRYOVrLfTvwPN7O/AbHefuJjjVzGzHarZ/o67L0vW8Azgb0TtwBuBr4gxlRPc/WGW7vl9hJg1e5+ZDSYyn+dSfXfu8rgQuN/MriEyrD2IGeZQfSZbpNFQRk+k/J1EBFRHEB+4txIfgk/VZyPc/QliRYnuRPfr/xElQ05e3P2W4fE/JEqs9AWeSb8Dd/+cGHNXQZSEuZaYXLL7UmY0BxArY+xIlAh5lAjyfgucWnTsjcRM3FOBe4ks3Pk1PO6xREZrNDFj+CR3X9wEgn8ClxJlSV4A/ryEdm9CZEqLf4pXUVksd3+KCEJbAXcQE2h2Jo3tXJrnN03k2A94E7iFeI6uYRkyuUto4wPEc34A8Xxuy4JyO7Nrup9IY2A1T6QSEZFiqZ7fi8ArwL6L6WqVHJnZWcCZwOruXttxgCINlrpuRUSWgbtPTgV6xxNj+E7Kt0WSijb/lihg/TXQkyj8fbOCPGnslNETEZEGzczaEd3G2wHtiJnAdwK/T3X3RBotBXoiIiIiZUqTMURERETKlAI9ERERkTKlQE9ERESkTCnQExERESlTCvREREREypQCPREREZEy9f8d0206jBxysQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 648x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# copying the data printed out above\n",
    "naive = (184,184,460,184,184)\n",
    "qwc   = (69,56,29,56,61)\n",
    "full  = (8,8,16,8,8)\n",
    "\n",
    "xaxis = np.array((1,2,3,4,5))\n",
    "\n",
    "width = 0.3\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(9,8))\n",
    "rects1 = ax.bar(xaxis - width, naive, width, label='Naive')\n",
    "rects2 = ax.bar(xaxis, qwc, width, label='QWC')\n",
    "rects3 = ax.bar(xaxis + width, full, width, label='Full')\n",
    "\n",
    "ax.set_ylabel('Number of Measurement Circuits')\n",
    "ax.set_xlabel('Fermion-to-Qubit Encoding')\n",
    "ax.set_title('Term Grouping for H2 (6-31g basis, 8 modes)')\n",
    "ax.set_xticks(xaxis)\n",
    "ax.set_xticklabels(('Jordan-Wigner', 'Bravyi-Kitaev (BK)', 'BK Super-Fast', 'BK Tree', 'Parity'),\n",
    "                  rotation=30)\n",
    "ax.legend()\n",
    "\n",
    "\n",
    "def autolabel(rects, xpos='center'):\n",
    "    \"\"\"\n",
    "    Attach a text label above each bar in *rects*, displaying its height.\n",
    "\n",
    "    *xpos* indicates which side to place the text w.r.t. the center of\n",
    "    the bar. It can be one of the following {'center', 'right', 'left'}.\n",
    "    \"\"\"\n",
    "\n",
    "    ha = {'center': 'center', 'right': 'left', 'left': 'right'}\n",
    "    offset = {'center': 0, 'right': 1, 'left': -1}\n",
    "\n",
    "    for rect in rects:\n",
    "        height = rect.get_height()\n",
    "        ax.annotate('{}'.format(height),\n",
    "                    xy=(rect.get_x() + rect.get_width() / 2, height),\n",
    "                    xytext=(offset[xpos]*3, 3),  # use 3 points offset\n",
    "                    textcoords=\"offset points\",  # in both directions\n",
    "                    ha=ha[xpos], va='bottom')\n",
    "\n",
    "\n",
    "autolabel(rects1)\n",
    "autolabel(rects2)\n",
    "autolabel(rects3)\n",
    "\n",
    "fig.tight_layout()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What is the effect of term grouping across increasing Active Spaces?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--------------\n",
      "hamiltonians/H2_6-31g_JW_0.7_AS1.txt\n",
      "2 qubits\n",
      "4 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 3 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 1 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.000222s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 3 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 1 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.000149s\n",
      "\n",
      "--------------\n",
      "hamiltonians/H2_6-31g_JW_0.7_AS2.txt\n",
      "4 qubits\n",
      "15 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 14 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 5 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.001745s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 14 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 2 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.002355s\n",
      "\n",
      "--------------\n",
      "hamiltonians/H2_6-31g_JW_0.7_AS3.txt\n",
      "6 qubits\n",
      "62 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 61 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 17 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.016043s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 61 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 6 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.045602s\n",
      "\n",
      "--------------\n",
      "hamiltonians/H2_6-31g_JW_0.7_AS4.txt\n",
      "8 qubits\n",
      "185 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 69 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.130932s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 8 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 1.129214s\n",
      "\n"
     ]
    }
   ],
   "source": [
    "Hfiles = ['hamiltonians/H2_6-31g_JW_0.7_AS{}.txt'.format(a) for a in [1,2,3,4]]\n",
    "\n",
    "print_cliques_loc(Hfiles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# copying the data printed out above\n",
    "naive = (3,14,61,184)\n",
    "qwc   = (1,5,17,69)\n",
    "full  = (1,2,6,8)\n",
    "\n",
    "# active spaces (x-axis)\n",
    "# There is a weird naming convention...\n",
    "# Openfermion lists active spaces as 1,2,3,4\n",
    "# But, active spaces always come in pairs so there are actually\n",
    "# twice as many spaces as what Openfermion says there is... its confusing\n",
    "AS = np.array((1,2,3,4))\n",
    "\n",
    "width = 0.3\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(9,7))\n",
    "rects1 = ax.bar(AS - width, naive, width, label='Naive')\n",
    "rects2 = ax.bar(AS, qwc, width, label='QWC')\n",
    "rects3 = ax.bar(AS + width, full, width, label='Full')\n",
    "\n",
    "ax.set_ylabel('Number of Measurement Circuits')\n",
    "ax.set_xlabel('Number of Active Spaces')\n",
    "ax.set_title('Term Grouping for H2 (6-31g basis, JW encoding)')\n",
    "ax.set_xticks(AS)\n",
    "ax.set_xticklabels(('2', '4', '6', '8'))\n",
    "ax.legend()\n",
    "\n",
    "\n",
    "def autolabel(rects, xpos='center'):\n",
    "    \"\"\"\n",
    "    Attach a text label above each bar in *rects*, displaying its height.\n",
    "\n",
    "    *xpos* indicates which side to place the text w.r.t. the center of\n",
    "    the bar. It can be one of the following {'center', 'right', 'left'}.\n",
    "    \"\"\"\n",
    "\n",
    "    ha = {'center': 'center', 'right': 'left', 'left': 'right'}\n",
    "    offset = {'center': 0, 'right': 1, 'left': -1}\n",
    "\n",
    "    for rect in rects:\n",
    "        height = rect.get_height()\n",
    "        ax.annotate('{}'.format(height),\n",
    "                    xy=(rect.get_x() + rect.get_width() / 2, height),\n",
    "                    xytext=(offset[xpos]*3, 3),  # use 3 points offset\n",
    "                    textcoords=\"offset points\",  # in both directions\n",
    "                    ha=ha[xpos], va='bottom')\n",
    "\n",
    "\n",
    "autolabel(rects1)\n",
    "autolabel(rects2)\n",
    "autolabel(rects3)\n",
    "\n",
    "fig.tight_layout()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def complexity(C,xx):\n",
    "    return [C*(3**((2*x)/3)) for x in xx]\n",
    "\n",
    "def complexity2(qq,xx,A,B,C):\n",
    "    return [A*(3**((2*x)/3)) + B*3*q*x + C*(x**2)*(2*q+2) for q,x in zip(qq,xx)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 0.000149 1.6555555555555556e-05\n",
      "14 0.002355 8.295817716281784e-08\n",
      "61 0.045602 1.803237228579473e-21\n",
      "184 1.129214 3.356621265069175e-59\n",
      "3 0.000222 2.4666666666666665e-05\n",
      "14 0.001745 6.147007182552746e-08\n",
      "61 0.016043 6.343874141068481e-22\n",
      "184 0.130932 3.891991557650164e-60\n"
     ]
    }
   ],
   "source": [
    "nterms = (3,14,61,184)\n",
    "fulltime = (0.000149,0.002355,0.045602,1.129214)\n",
    "for h,t in zip(nterms,fulltime):\n",
    "    print(h,t,t/complexity(1,[h])[0])\n",
    "    \n",
    "qwctime = (0.000222,0.001745,0.016043,0.130932)\n",
    "for h,t in zip(nterms,qwctime):\n",
    "    print(h,t,t/complexity(1,[h])[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1059bf9b0>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# copying runtime data from above\n",
    "nterms = (3,14,61)#,184)\n",
    "qq = (2,4,6,8)\n",
    "xx = np.arange(nterms[0],nterms[-1],0.1)\n",
    "cc = complexity(2e-21,xx)\n",
    "cc2 = complexity2(qq,nterms,2e-21,1e-10,1e-10)\n",
    "qwctime = (0.000222,0.001745,0.016043)#,0.130932)\n",
    "fulltime = (0.000149,0.002355,0.045602)#,1.129214)\n",
    "\n",
    "plt.subplots(figsize=[6,6])\n",
    "\n",
    "# QWC commutation\n",
    "plt.scatter(nterms,qwctime,c='blue',s=30)\n",
    "plt.plot(nterms,qwctime,c='blue',lw=2,label='QWC')\n",
    "\n",
    "# Full commutation\n",
    "plt.scatter(nterms,fulltime,c='orange',s=30)\n",
    "plt.plot(nterms,fulltime,c='orange',lw=2,label='FULL')\n",
    "\n",
    "# Complexity bounds\n",
    "plt.plot(xx,cc,c='green',lw=2,label=r'$O(3^{2n/3})$')\n",
    "\n",
    "#plt.plot(nterms,cc2,c='red',lw=2,label='exact')\n",
    "\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How does runtime vary across qubit encodings?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# I will generate this data later (will take ~60 minutes to complete).\n",
    "# Then we can compare average runtimes.\n",
    "results = []\n",
    "for file in Hfiles:\n",
    "    for comm_type, comm_str in zip([QWCCommutativity, FullCommutativity], ['QWC','FULL']):\n",
    "        ret, times = many_trials(file, comm_type, 100)\n",
    "        results += [(file,comm_str,ret,times)]\n",
    "\n",
    "print('\\n\\n-------------------')\n",
    "print('All trials finished')\n",
    "for r in results:\n",
    "    print(r[0],r[1],r[2],np.mean(r[3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How does runtime vary across size of Hamiltonian?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "def myfunc(filename, commutativity_type):\n",
    "    H = parseHamiltonian(filename)\n",
    "    numterms = len(H) - 1\n",
    "    \n",
    "    ops = [term[1] for term in H]\n",
    "    Nq = max([int(op[-1][1:]) for op in ops]) + 1\n",
    "    \n",
    "    print('--------------')\n",
    "    print(filename)\n",
    "    \n",
    "    start_time = time.time()\n",
    "    cliques = genMeasureCircuit(H, Nq, commutativity_type)\n",
    "    end_time = time.time()\n",
    "    \n",
    "    numcliques = [len(cliques)]\n",
    "    runtime = [end_time - start_time]\n",
    "    \n",
    "    return numterms, numcliques, runtime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['hamiltonians/H2O_6-31g_BK_104_AS1.txt', 'hamiltonians/H2O_6-31g_BK_104_AS2.txt', 'hamiltonians/H2O_6-31g_BK_104_AS3.txt', 'hamiltonians/H2O_6-31g_BK_104_AS4.txt', 'hamiltonians/H2O_6-31g_BK_104_AS5.txt', 'hamiltonians/H2O_6-31g_BK_104_AS6.txt']\n"
     ]
    }
   ],
   "source": [
    "# try looking at H2O for more datapoints\n",
    "h2ofiles = ['hamiltonians/H2O_6-31g_BK_104_AS{}.txt'.format(a) for a in [1,2,3,4,5,6]]\n",
    "print(h2ofiles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--------------\n",
      "hamiltonians/H2O_6-31g_BK_104_AS1.txt\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 3 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 1 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.000127s\n",
      "--------------\n",
      "hamiltonians/H2O_6-31g_BK_104_AS2.txt\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 26 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 8 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.002170s\n",
      "--------------\n",
      "hamiltonians/H2O_6-31g_BK_104_AS3.txt\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 61 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 12 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.014395s\n",
      "--------------\n",
      "hamiltonians/H2O_6-31g_BK_104_AS4.txt\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 192 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 43 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.169738s\n",
      "--------------\n",
      "hamiltonians/H2O_6-31g_BK_104_AS5.txt\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 275 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 43 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.937246s\n",
      "--------------\n",
      "hamiltonians/H2O_6-31g_BK_104_AS6.txt\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 630 nodes.\n"
     ]
    }
   ],
   "source": [
    "comtype = QWCCommutativity\n",
    "numterms, numcliques, runtimes = [], [], []\n",
    "for f in h2ofiles:\n",
    "    nt, nc, t = myfunc(f,comtype)\n",
    "    numterms += [nt]\n",
    "    numcliques += [nc]\n",
    "    runtimes += [t]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot multiple molecules together"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# first we need to choose a tractable active space for each molecule\n",
    "h2files = ['hamiltonians/H2_sto-3g_BK_0.7_AS{}.txt'.format(a) for a in [1,2]]\n",
    "lihfiles = ['hamiltonians/LiH_sto-3g_BK_1.45_AS{}.txt'.format(a) for a in [1,2,3,4,5,6]]\n",
    "h2ofiles = ['hamiltonians/H2O_sto-3g_BK_104_AS{}.txt'.format(a) for a in [1,2,3,4,5,6]]\n",
    "ch4files = ['hamiltonians/CH4_sto-3g_BK_grnd_AS{}.txt'.format(a) for a in [1,2,3,4,5,6,7,8,9]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "molecule_files = (h2files,lihfiles,h2ofiles,ch4files)\n",
    "\n",
    "for molecule, mol_name in zip(molecule_files, ['H2','LiH','H2O','CH4']):\n",
    "    active_spaces, num_terms, nqubits = [], [], []\n",
    "    for ASnum, asfile in enumerate(molecule):\n",
    "        ASnum += 1\n",
    "        #print(ASnum,asfile)\n",
    "        \n",
    "        H = parseHamiltonian(asfile)\n",
    "\n",
    "        ops = [term[1] for term in H]\n",
    "        Nq = max([len(op) for op in ops])\n",
    "        \n",
    "        nqubits += [Nq]\n",
    "        num_terms += [len(H)-1]\n",
    "        active_spaces += [ASnum]\n",
    "        \n",
    "\n",
    "    width = 0.5\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(9,7))\n",
    "    rects1 = ax.bar(active_spaces, num_terms, width)\n",
    "\n",
    "    ax.set_ylabel('Number of terms')\n",
    "    ax.set_xlabel('Number of Active Spaces')\n",
    "    ax.set_title('Number of terms for {} (sto-3g basis, BK encoding)'.format(mol_name))\n",
    "    ax.set_xticks(active_spaces)\n",
    "\n",
    "    def autolabel(rects, qubits, xpos='center'):\n",
    "        \"\"\"\n",
    "        Attach a text label above each bar in *rects*, displaying its height.\n",
    "\n",
    "        *xpos* indicates which side to place the text w.r.t. the center of\n",
    "        the bar. It can be one of the following {'center', 'right', 'left'}.\n",
    "        \"\"\"\n",
    "\n",
    "        ha = {'center': 'center', 'right': 'left', 'left': 'right'}\n",
    "        offset = {'center': 0, 'right': 1, 'left': -1}\n",
    "\n",
    "        for rect, nq in zip(rects,qubits):\n",
    "            height = rect.get_height()\n",
    "            ax.annotate('Nq={}'.format(nq),\n",
    "                        xy=(rect.get_x() + rect.get_width() / 2, height),\n",
    "                        xytext=(offset[xpos]*3, 3),  # use 3 points offset\n",
    "                        textcoords=\"offset points\",  # in both directions\n",
    "                        ha=ha[xpos], va='bottom')\n",
    "\n",
    "\n",
    "    autolabel(rects1, nqubits)\n",
    "\n",
    "    fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['hamiltonians/H2_sto-3g_BK_0.7_AS2.txt', 'hamiltonians/LiH_sto-3g_BK_1.45_AS3.txt', 'hamiltonians/H2O_sto-3g_BK_104_AS4.txt', 'hamiltonians/CH4_sto-3g_BK_grnd_AS4.txt']\n",
      "--------------\n",
      "hamiltonians/H2_sto-3g_BK_0.7_AS2.txt\n",
      "4 qubits\n",
      "15 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 14 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 3 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.001482s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 14 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 2 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.001200s\n",
      "\n",
      "--------------\n",
      "hamiltonians/LiH_sto-3g_BK_1.45_AS3.txt\n",
      "6 qubits\n",
      "118 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 117 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 38 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.040986s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 117 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 9 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.109233s\n",
      "\n",
      "--------------\n",
      "hamiltonians/H2O_sto-3g_BK_104_AS4.txt\n",
      "8 qubits\n",
      "193 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 192 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 42 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.187812s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 192 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 9 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 9.416595s\n",
      "\n",
      "--------------\n",
      "hamiltonians/CH4_sto-3g_BK_grnd_AS4.txt\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "8 qubits\n",
      "241 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 240 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 62 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.259468s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 240 nodes.\n",
      "MEASURECIRCUIT: BronKerbosch found 19 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 15.331529s\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Based on the above results we will look at:\n",
    "# H2: AS = 2\n",
    "# LiH: AS = 3\n",
    "# H2O: AS = 4\n",
    "# CH4: AS = 4\n",
    "\n",
    "fs = [h2files[1],lihfiles[2],h2ofiles[3],ch4files[3]]\n",
    "print(fs)\n",
    "\n",
    "for f in fs:\n",
    "    print_cliques(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# copying the data printed out above\n",
    "naive = (14,117,192,240)\n",
    "qwc   = (3,38,42,62)\n",
    "full  = (2,9,9,19)\n",
    "\n",
    "xaxis = np.array((1,2,3,4))\n",
    "\n",
    "width = 0.3\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(9,7))\n",
    "rects1 = ax.bar(xaxis - width, naive, width, label='Naive')\n",
    "rects2 = ax.bar(xaxis, qwc, width, label='QWC')\n",
    "rects3 = ax.bar(xaxis + width, full, width, label='GC')\n",
    "\n",
    "ax.set_ylabel('Number of Partitions',fontsize=19)\n",
    "ax.set_xlabel('Molecule [AS#]',fontsize=19)\n",
    "ax.set_title('Bron-Kerbosch Simultaneous Measurement',fontsize=19)\n",
    "ax.set_xticks(xaxis)\n",
    "ax.set_xticklabels((r'$\\mathrm{H}_2$ [2]', 'LiH [3]', r'$\\mathrm{H}_2\\mathrm{O}$ [4]', r'$\\mathrm{CH}_4$ [4]'),\n",
    "                   fontsize=15)\n",
    "ax.legend(fontsize=15,loc='upper left')\n",
    "\n",
    "\n",
    "def autolabel(rects, xpos='center'):\n",
    "    \"\"\"\n",
    "    Attach a text label above each bar in *rects*, displaying its height.\n",
    "\n",
    "    *xpos* indicates which side to place the text w.r.t. the center of\n",
    "    the bar. It can be one of the following {'center', 'right', 'left'}.\n",
    "    \"\"\"\n",
    "\n",
    "    ha = {'center': 'center', 'right': 'left', 'left': 'right'}\n",
    "    offset = {'center': 0, 'right': 1, 'left': -1}\n",
    "\n",
    "    for rect in rects:\n",
    "        height = rect.get_height()\n",
    "        ax.annotate('{}'.format(height),\n",
    "                    xy=(rect.get_x() + rect.get_width() / 2, height),\n",
    "                    xytext=(offset[xpos]*3, 3),  # use 3 points offset\n",
    "                    textcoords=\"offset points\",  # in both directions\n",
    "                    ha=ha[xpos], va='bottom',fontsize=15)\n",
    "\n",
    "\n",
    "autolabel(rects1)\n",
    "autolabel(rects2)\n",
    "autolabel(rects3)\n",
    "\n",
    "fig.tight_layout()\n",
    "\n",
    "plt.savefig('Figures/BronKerbosch.pdf', format='pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Using NetworkX Poly-Time Heuristic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_cliques_x(filelist):\n",
    "    for file in filelist:\n",
    "        print('--------------')\n",
    "        print(file)\n",
    "        H = parseHamiltonian(file)\n",
    "    \n",
    "        # For some qubit encodings, there isn't a single term acting on all qubits\n",
    "        # so this will report the wrong qubit#\n",
    "        # Instead, look for the largest index being operated on.\n",
    "        ops = [term[1] for term in H]\n",
    "        #Nq = max([len(op) for op in ops])\n",
    "        Nq = max([int(op[-1][1:]) for op in ops]) + 1\n",
    "        print('{} qubits'.format(Nq))\n",
    "    \n",
    "        print('{} total terms\\n'.format(len(H)))\n",
    "\n",
    "        for commutativity_type, type_str in zip([QWCCommutativity, FullCommutativity],['QWC','FULL']):\n",
    "            print(type_str + 'Commutation:')\n",
    "            cliques = genMeasureCircuit(H, Nq, commutativity_type, clique_cover_method=NetworkX_approximate_clique_cover)\n",
    "            print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def many_trials(filename, commutativity_type, numtrials):\n",
    "    H = parseHamiltonian(filename)\n",
    "    ops = [term[1] for term in H]\n",
    "    Nq = max([int(op[-1][1:]) for op in ops]) + 1\n",
    "    print('--------------')\n",
    "    print(filename)\n",
    "    results = []\n",
    "    runtimes = []\n",
    "    for i in range(numtrials):\n",
    "        start_time = time.time()\n",
    "        cliques = genMeasureCircuit(H, Nq, commutativity_type, clique_cover_method=NetworkX_approximate_clique_cover)\n",
    "        end_time = time.time()\n",
    "        results += [len(cliques)]\n",
    "        runtimes += [end_time - start_time]\n",
    "    return Counter(results), runtimes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# What is the effect of term grouping across basis representations?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--------------\n",
      "hamiltonians/H2_6-31g_JW_0.7_AS4.txt\n",
      "8 qubits\n",
      "185 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 72 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 1.11s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 15 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.84s\n",
      "\n",
      "--------------\n",
      "hamiltonians/H2_6-31g_BK_0.7_AS4.txt\n",
      "8 qubits\n",
      "185 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 57 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 2.68s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 13 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 1.37s\n",
      "\n",
      "--------------\n",
      "hamiltonians/H2_6-31g_BKSF_0.7_AS4.txt\n",
      "28 qubits\n",
      "461 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 460 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 53 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 9.63s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 460 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 24 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 10.43s\n",
      "\n",
      "--------------\n",
      "hamiltonians/H2_6-31g_BKT_0.7_AS4.txt\n",
      "8 qubits\n",
      "185 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 57 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 2.34s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 13 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.99s\n",
      "\n",
      "--------------\n",
      "hamiltonians/H2_6-31g_PC_0.7_AS4.txt\n",
      "8 qubits\n",
      "185 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 62 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 1.68s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 19 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 1.13s\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# What is the effect of term grouping across qubit encodings?\n",
    "# First look at H2 molecule\n",
    "Hfiles = ['hamiltonians/H2_6-31g_{}_0.7_AS4.txt'.format(e) for e in ['JW','BK','BKSF','BKT','PC']]\n",
    "\n",
    "print_cliques_x(Hfiles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# copying the data printed out above\n",
    "naive = (184,184,460,184,184)\n",
    "qwc   = (72,57,53,57,62)\n",
    "full  = (15,13,24,13,19)\n",
    "\n",
    "xaxis = np.array((1,2,3,4,5))\n",
    "\n",
    "width = 0.3\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(9,8))\n",
    "rects1 = ax.bar(xaxis - width, naive, width, label='Naive')\n",
    "rects2 = ax.bar(xaxis, qwc, width, label='QWC')\n",
    "rects3 = ax.bar(xaxis + width, full, width, label='GC')\n",
    "\n",
    "ax.set_ylabel('Number of Partitions',fontsize=19)\n",
    "ax.set_xlabel('Fermion-to-Qubit Encoding',fontsize=19)\n",
    "ax.set_title(r'Simultaneous Measurement for $\\mathrm{H}_2$',fontsize=19)\n",
    "ax.set_xticks(xaxis)\n",
    "ax.set_xticklabels(('Jordan-Wigner', 'Bravyi-Kitaev (BK)', 'BK Super-Fast', 'BK Tree', 'Parity'),\n",
    "                  rotation=30,fontsize=15)\n",
    "#ax.set_yticklabels(fontsize=15)\n",
    "ax.legend(fontsize=19)\n",
    "\n",
    "\n",
    "def autolabel(rects, xpos='center'):\n",
    "    \"\"\"\n",
    "    Attach a text label above each bar in *rects*, displaying its height.\n",
    "\n",
    "    *xpos* indicates which side to place the text w.r.t. the center of\n",
    "    the bar. It can be one of the following {'center', 'right', 'left'}.\n",
    "    \"\"\"\n",
    "\n",
    "    ha = {'center': 'center', 'right': 'left', 'left': 'right'}\n",
    "    offset = {'center': 0, 'right': 1, 'left': -1}\n",
    "\n",
    "    for rect in rects:\n",
    "        height = rect.get_height()\n",
    "        ax.annotate('{}'.format(height),\n",
    "                    xy=(rect.get_x() + rect.get_width() / 2, height),\n",
    "                    xytext=(offset[xpos]*3, 3),  # use 3 points offset\n",
    "                    textcoords=\"offset points\",  # in both directions\n",
    "                    ha=ha[xpos], va='bottom',fontsize=15)\n",
    "\n",
    "\n",
    "autolabel(rects1)\n",
    "autolabel(rects2)\n",
    "autolabel(rects3)\n",
    "\n",
    "fig.tight_layout()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--------------\n",
      "hamiltonians/H2_6-31g_JW_0.7_AS1.txt\n",
      "2 qubits\n",
      "4 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 3 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 1 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.00s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 3 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 1 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.00s\n",
      "\n",
      "--------------\n",
      "hamiltonians/H2_6-31g_JW_0.7_AS2.txt\n",
      "4 qubits\n",
      "15 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 14 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 1 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.00s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 14 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 2 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.01s\n",
      "\n",
      "--------------\n",
      "hamiltonians/H2_6-31g_JW_0.7_AS3.txt\n",
      "6 qubits\n",
      "62 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 61 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 17 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.11s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 61 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 9 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.08s\n",
      "\n",
      "--------------\n",
      "hamiltonians/H2_6-31g_JW_0.7_AS4.txt\n",
      "8 qubits\n",
      "185 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 72 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 1.31s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 184 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 15 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.83s\n",
      "\n"
     ]
    }
   ],
   "source": [
    "Hfiles = ['hamiltonians/H2_6-31g_JW_0.7_AS{}.txt'.format(a) for a in [1,2,3,4]]\n",
    "\n",
    "print_cliques_x(Hfiles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IVNrs2bOXuXt505mWUgIYatu2LbNmzcp1GCIiIiKVZmbzU2mnU8AiIiIieUYJoIiISA3x9ddfc8EFF9CpUydq165Nr169tmizdOlSzjnnHFq1akWjRo3o3LkzTz311JYrCy1evJhGjRphZvz0U15MgiHoFLCIiEiN8emnnzJp0iS6du3KunVbTqG7adMmTjjhBJYvX85tt93GDjvswLhx4zjjjDMoKCigb9++WyxzxRVX0KhRI37++edsbIJUE+oBFBERqSH69OnDwoULefbZZ9l77723qP/yyy+ZNWsWd999N6effjqHH344o0aNonPnzowZM2aL9m+//TaTJ0/m8ssvz0b4Uo2oB1BERKSGqFWr4n6b9evXA9CkSZMy5U2bNiV+4oeNGzcyZMgQrr/+epo2bZreQKXaUw+giIjIVmKfffahS5cuXH/99Xz11VesXr2a0aNH8+677zJo0KAybe+//35++eUXLrroohxFK7mkHsAUrV69mu+//770vyvJjrp169KyZUsaN26c61BERKo9M+Pll1/mxBNPpH379kDwOfroo49y2GGHlbZbvnw51113HU8++SR169bNVbiSQ0oAU7B69Wq+++47WrVqRYMGDTCzXIeUF9ydNWvWsHjxYgAlgSIiSWzatIkzzzyT5cuXM3bsWFq2bMmkSZM477zzaNasGb179wbg2muvpUuXLhx77LE5jlhyRQlgCr7//ntatWpFQUFBrkPJK2ZGQUEBrVq1YsmSJUoARUSSeOmll5g4cSJffvkle+yxBwC9evVi4cKFDB06lN69e/Ppp5/yyCOP8NZbb7Fy5UoAiouLAVi1ahW1a9emQYMGOdsGyQ4lgClYv3693gw51KBBA516FxFJweeff05BQUFp8leic+fOvPjiiwB89dVXrF+/nm7dum2x/M4778x5553Hww8/nJV4JXeUAKZIp31zR/teRCQ1bdq0obi4mC+++II999yztHz27NmUzHffs2dP3nzzzTLLTZ48mVtvvZVJkyax2267ZTNkyRElgCIiIjVEcXExkyZNAoIZPFavXs24ceMAOPbYYzn22GNp3bo1J510Etdffz0tWrRg4sSJPPPMM9x3330ANG/efIsZRObNmwfAQQcdRKNGjbK2PZI7SgBFRERqiO+//55TTz21TFnJ8//85z+0bduWKVOmcPXVV/PHP/6R1atXs/vuu3P//fczcODAXIQs1ZTFDwyZrwoLC33WrFkJ6z777DM6dOiwRXnbqyZmOqyE5o04rlLLDR8+nBtuuIGjjjqKV155pUzdKaecwrJly5g6dWpqMcybx6677sqECRM4/vjjKxVPFOX9DURERGQzM5vt7oXJ2mkg6Dz06quvMnPmzCqtY8cdd2T69On07NkzTVGJiIhItigBzDPbbbcd++23H3/+85+rtJ769evTtWtXTR8kIiJSAykBzDNmxjXXXMOLL77Ixx9/nLDN0qVLOffcc9ltt91o0KAB7du3Z9iwYaxbt660zbx58zAzXnrpJQAGDBjAgQceuMW67r33Xho0aMBPP/0EBIOUjhgxgnbt2lG/fn3at2/PY489loEtFRERkfIoAcxDp556Ku3bty+3F3DZsmVst9123HHHHUyePJkrrriCRx99lCFDhpS7zv79+zNz5ky++eabMuXPPPMMxx13XOldZUOGDOHmm29m4MCBTJw4kb59+3LuueeWJpIiIiKSeboLOA/VqlWLq666ivPOO48bb7yxdL7IEvvuuy+333576fMePXrQsGFDzj33XO655x7q1au3xTqPPPJImjVrxjPPPMNVV10FBEMUvPPOOzzzzDMAfP3114waNYpHH32UAQMGAHDEEUewdOlSbrjhhqzcTCIiUt3l6gbDVFX2RkSpXtQDmKfOOOMMWrduzS233LJFnbtz11130bFjRxo0aEDdunU5/fTTWbt2LQsWLEi4vjp16nDyySczduzY0rJnn32Whg0bctxxwYfFlClTqFWrFn379mXDhg2lj8MPP5wPP/yQjRs3ZmZjRUREpAwlgHmqTp06DB06lCeffJL58+eXqbvrrrv44x//SN++fRk/fjzvv/9+6QCiv/zyS7nr7N+/Px9++CFffvklAGPHjuWEE04onUZv2bJlbNy4kSZNmlC3bt3Sx9lnn82GDRtYunRphrZWREREYukUcB4799xzufnmm7n11lvLlD/77LOceuqpZa4RnDt3btL19erVix122IGxY8dy1llnMWPGDK6++urS+u222446derw7rvvUqvWlv97tGzZsgpbIyIiIqlSApjH6tevz+WXX87VV1/N/vvvT926dQFYs2YN9evXL9P2qaeeSrq+WrVqccoppzB27Fh+9atf0bhxY3r37l1af9hhh7Fx40ZWrVrFkUcemd6NERERkZTpFHCeu+CCC9hmm20oKioqLTvyyCMZO3YsI0eO5JVXXuGss87i66+/Tml9/fr149NPP+XOO++kb9++ZW4Y2XPPPRk0aBD9+/fn1ltvZcqUKUycOJHbbruN888/P+3bJiIiIompB7AKtoY7oQoKCrjsssu49tprS8uuv/56fvjhB4YNGwbAySefzN///nf69OmTdH09evRgl112YeHChfTv33+L+vvuu4/27dvz0EMPcf3119O4cWM6duzIeeedl76NEhERkQppLuBQZeYCluzR30BE8oWGgZGq0FzAIiIiIpKQEkARERGRPKMEUERERCTPKAEUERERyTNKAEVERETyjBJAERERkTyT8wTQzNqZ2QNmNsfMNprZ1Lj6Xmbm5TxeiWl3djltBmV9o0RERESqseowEPTewLHAe0C9BPX/ArrFlbUGxgIvJ2h/GLAm5vk3aYhRREREZKtRHRLACe4+HsDMxgHNYyvdfTVBcljKzA4CNgHPJFjfTHf/KUOxioiIiNR4OT8F7O6bKrHYacA0d1+S7njywejRo+nSpQsNGzakcePGHHrooUycuHnk+euuu46CggLWr19fZrl+/fphZrzzzjtlyh966CHMjCVLNv851q5dy+23307nzp1p2LAhBQUFHHDAATz44IOsW7cusxsoIiIiFaoOPYCRmNkeQGdgYDlN/m1mzYB/A3e4+wMZC2Z4k4ytuuLXXVXpRS+88EIeeughfv/733PzzTezYcMGxowZw/HHH88dd9zBZZddRvfu3bn55pv54IMPOPDAA0uXLSoqoqCggKKiInr27FmmvG3btuy0004ArFmzhqOOOoqPP/6YSy+9tLTt9OnTGTZsGGvWrOGSSy6p9DaIiIhI1dS4BJCg92898Fxc+VLgOuB9oHbY7n4zK3D3OxOtyMwGEiaSrVu3zljA1cULL7zA/fffz6hRoxg0aPO9Mccccww77LADV1xxBYcffjjdunXDzCgqKipNABctWsSiRYsYNGgQRUVFZdZbVFREjx49Sp8PGzaMf/3rX8yYMYN99tmntPyII47goosu4vPPP8/wloqIiEhFcn4KuBL6A6+6+39jC939FXe/2d1fdfeX3f0sgmsEh5lZwu109wfdvdDdC1u0aJGF0HPr7rvvpl27dvzud7/bou6aa66hUaNG3HvvvTRt2pSOHTuWSfSKiorYbbfdOOmkk5g+fXpp+fLly/nyyy/p3r07AMXFxTzwwAMMGjSoTPJXYrvttittKyIiIrlRoxJAM+sEdACeTnGRccB2QNtMxVRTbNiwgenTp9OnTx9q1669RX2TJk049NBDmTZtGgDdu3cvkwBOnz6dbt260aVLF3744Qe+/vprgNI2JT2As2fP5ueff6Z3796Z3iQRERGppBqVABL0/q0BxkdczjMQS42ybNky1q5dS5s2bcpt06ZNGxYtWgQECeDixYtZsGABECR63bp1o2nTpnTo0KE08SsqKmKbbbZh3333BWDx4sVAfpxSFxERqalqWgLYj2DYmFSHefktsAyYn7mQti5mBmzu0SsqKuKXX37hgw8+oFu3YDjGrl27lkkAu3btSq1atRKuR0RERKqfnCeAZlZgZqeY2SlAK6BFyXMzK4hp1xXYlXJO/5rZc2Z2pZkdY2bHm9kTBAnjjZUcamar0rx5c+rXr8/8+eXnwvPnz2fHHXcEYI899qBFixYUFRUxa9Ys6tWrx3777QdAt27dKCoqYsOGDcyaNavMDSCtWrUCKO05FBERkeon5wkg0BJ4Nnx0BTrGPG8Z064/sIrEs38AfAGcS3B38LPhes5y93syE3bNUqdOHbp3787EiRPZtGnLfHj16tVMnTq1zA0aJYleUVERBxxwAHXq1Ckt//TTT5k2bRrFxcVlEsDCwkIaNmzIK6+8ssVriIiISPWQ8wTQ3ee5u5XzmBfT7lJ3b+rua8tZzzXuvqe7F7h7A3ff392fyNqG1AAXX3wxX375JQ8//PAWdSNGjGDlypWcc845pWU9evRgzpw5vP7666WnfwE6duzINttswx133EHt2rXp0qVLaV2DBg244IILGDVqFHPnzt3idVauXFnmLmIRERHJvpo4DqBU0kknncSgQYO46KKLmDt3LscffzwbNmxg7NixjB49msGDB9OrV6/S9t27d2fDhg28/vrrDBkypLTczOjSpQsvv/wynTp1YptttinzOjfffDPvv/8+PXr04LLLLivtIZwxYwb33HMPV111VZmEUkRERLJLCWBVVGFGjlwZOXIkXbp0YdSoUTz00EMUFxcDcMstt3DllVeWaVtYWEi9evVYt24dXbt2LVPXrVs3Xn311YRj+jVo0IDXX3+de+65hyeffJIRI0YAsPfeezN06FAuuOCCDG2diIiIpMLc836EFAAKCwt91qxZCes+++wzOnTokOWIsmPRokUccMABdO7cmQkTJiQcI7A62Jr/BiIisdpeNTF5oxyaN+K4XIcgFTCz2e5emKxdzq8BlNzaeeedef7553njjTe4+OKLcx2OiIiIZIFOAQtdu3bll19+yXUYIiIikiXqARQRERHJM0oARURERPKMEkARERGRPKMEUERERCTPKAEUERERyTNKAEVERETyjBJAERERkTyjBFBEREQkz2gg6CrY97F9c/K6Hw/4uErLv/DCC4wcOZLZs2fz448/0qJFCw466CCGDBlCjx49StutXr2a22+/nXHjxvGf//yHOnXq0LlzZwYPHswpp5xCrVr6/0FERKQmUgKYZy677DL+/ve/c9ZZZ3HhhRfSrFkz5s+fz5gxY+jZsydff/01u+++O99//z29evVi5cqV/OEPf2D//fdn7dq1vPHGG5x//vnUr1+fE088MdebIyIiIpWgBDCPjB8/nrvuuotHH32Us88+u0zdmWeeyYQJE2jQoAEAF154IStWrGDWrFm0atWqtF3v3r0ZPHgwq1atymboIiIikkZKAPPIXXfdxQEHHLBF8leiT58+AMyfP5/nn3+eu+++u0zyV6J169aZDFNEREQyTBdx5YkNGzYwffp0jjrqqKRt33rrLdyd3r17ZyEyERERyTb1AOaJ5cuXs3btWnbZZZcy5e7Oxo0bS5/Xrl2bxYsXA+rpExER2VqpBzBPuDsAZlam/G9/+xt169Ytfdx3332ldfFtRUREZOugBDBPNG/enPr167No0aIy5WeeeSYzZ85k5syZpWUl1/0tWLAgqzGKiIhIdigBzBN16tShW7duvPrqq2XKt99+ewoLCyksLCwtO/jggzEzXnnllWyHKSIiIlmgBDCPXHrppcyYMYMnnniiwnZt2rShb9++/OUvf2Hp0qVb1C9cuJCPP67aYNQiIiKSO7oJJI+ceOKJXHrppZx99tm8+eab9OnTh+bNm7N8+XJee+01ABo1agTAqFGjOOSQQygsLCwzEPS0adO47777ePzxx9l339zMhCIiIiJVowSwCqo6JVsu3HnnnRx88MGMHDmS8847r3QquG7dujFp0iSOOeYYAFq2bMl7773H7bffzkMPPcS1115L3bp16dy5M3feeSfHH398jrdEREREKksJYB7q27cvffv2TdquSZMm3HTTTdx0001ZiEpERESyRdcAioiIiOQZJYAiIiIieUYJoIiIiEieUQIoIiIikmeUAKaoZCo1yT7texERkfRSApiCunXrsmbNmlxoMThLAAAgAElEQVSHkbfWrFlD3bp1cx2GiIjIVkMJYApatmzJ4sWLKS4uVm9UFrk7xcXFLF68mJYtW+Y6HBERka2GxgFMQePGjQFYsmQJ69evz3E0+aVu3bpsv/32pX8DERERqTolgClq3LixkhARERHZKugUsIiIiEieUQIoIiIikmeUAIqIiIjkGSWAIiIiInlGCaCIiIhInlECKCIiIpJncp4Amlk7M3vAzOaY2UYzm5qgzTwz87jHtwnadTSzKWZWbGZLzOxGM6udlQ0RERERqSGqwziAewPHAu8B9Spo90/gnpjn62IrzWxb4HVgLnAisDvwN4Ikd1ga4xURERGp0apDAjjB3ccDmNk4oHk57Za6+3sVrGcQ0AA42d1XA6+ZWWNguJndFpaJiIiI5L2cnwJ2901pWtUxwCtxid4YgqTwkDS9hoiIiEiNl/MEMIJzzWydma0ys3Fm1iaufi/g89gCd18AFId1IiIiIkL1OAWcivEE1wguAjoAfwLeNrN93X1V2GZbYGWCZVeEdVsws4HAQIDWrVunO2YRERGRaqlG9AC6+yXu/rS7v+3uDwJHAzsB58Q3TbC4lVOOuz/o7oXuXtiiRYv0Bi0iIiJSTdWIBDCeu38CfAH8JqZ4BdA0QfMmJO4ZFBEREclLNTIBjBHbs/c5cdf6mdkuQEPirg0UERERyWc1MgE0s32APYHZMcUvA0eb2TYxZf2ANcC0LIYnIiIiUq3l/CYQMysgGAgaoBXQ2MxOCZ9PAg4FzgBeApYQ9PINAxYAo2NWdT9wMfB/ZnYrsBswHLhDYwCKiIiIbJbzBBBoCTwbV1byfFdgYdjmLoJr/JYDk4FrYhM7d19hZocD9wITCK77u5MgCRQRERGRUM4TQHefR3CnbkUOT3Fdc4HDqhqTiIiIyNasRl4DKCIiIiKVpwRQREREJM8oARQRERHJM0oARURERPKMEkARERGRPKMEUERERCTPKAEUERERyTNKAEVERETyjBJAERERkTyjBFBEREQkz6QlATSzxmZWkI51iYiIiEhmpZwAmtnhZnabmTWNKdvBzKYCK4AVZnZvBmIUERERkTSK0gN4OXCCu6+MKbsLOBh4H/gGuNDMBqQxPhERERFJsygJ4H5AUckTM2sEnAQ85+7dgF8DXwAD0xqhiIiIiKRVlARwO2BpzPMeQD3gCQB3Xwu8AuyRtuhEREREJO2iJICrgG1jnh8KbATeiilbD+hmEBEREZFqLEoC+Alwgpk1M7PGwP8CM+KuCdwV+DadAYqIiIhIekVJAG8DdgIWhY9WwN9KKs2sHnAIMDudAYqIiIhIetVJtaG7v2pmJwEld/mOdffnY5r0ABYDz6UxPhERERFJs5QTQAB3fxF4sZy6N4HO6QhKRERERDJHU8GJiIiI5JlIPYAAZtYFKASaArUTNHF3v6mqgYmIiIhIZqScAJpZc2A80BWwCpo6oARQREREpJqK0gN4F9ANeAN4nOCGjw2ZCEpEREREMidKAngMMN3dj8hUMCIiIiKSeVFuAqkHvJupQEREREQkO6IkgLOA9pkKRERERESyI0oCeBVwVDgYtIiIiIjUUFGuATwaeBN4zszeBD4EVidop2FgRERERKqxKAng8JjfDwsfiWgYGBEREZFqLEoCeGjGohARERGRrEk5AXT3aZkMRERERESyQ3MBi4iIiOSZyAmgmR1jZmPM7DMzWxz+/KeZ9c5EgCIiIiKSXlHmAjbgEeAsgrmANwDLgd2BPYF+Zva4u5+TiUBFREREJD2i9ABeBAwgmA3kEOBX7r4j8CvgYOAd4CwzuyjtUYqIiIhI2kRJAM8DPgcOd/e33X0TgLtvcvd3gCOAL4DfpT9MEREREUmXKAngnsAEd1+fqDIsn4CmixMRERGp1qIkgGuBJknaNA7biYiIiEg1FSUBnAX8j5ntmqgyLO8HzExHYCIiIiKSGVESwBEEPXz/MrO/mFlvM+sc/vwLMDusvyVKAGbWzsweMLM5ZrbRzKbG1e9oZn8N638ys4Vm9piZ7RTXrpeZeYLHiCjxiIiIiGztoswEMsXMBgCjgKuAK2OqDfgRGODub0aMYW/gWOA9oF6C+v2BvsDDwAxge4J5iYvMbB93/ymu/enANzHPF0eMR0RERGSrFmUuYNz9KTObAJwEdCLo8VsNzAFecPfVlYhhgruPBzCzcUDzuPp3gL3cfUNJgZn9i+CO498Cj8W1/8jdP6lEHCIiIiJ5IVICCBAmeY+nK4CS4WQqqF+ZoOxLMysGWqYrDhEREZF8USPnAjaz/YACYG6C6jfCawnnmdkwM6ud5fBEREREqrVyewDN7BHAgWvc/bvweSrc3c9LS3SJ46oF3A18BbwaU7WK4EaVt4F1wPHADUAL4JJMxSMiIiJS01R0CvhsggTwVuC78HkqnGDWkEy5BegGHBI7KLW7fwB8ENPudTNbC/zBzG5y92XxKzKzgcBAgNatW2cwZBEREZHqo6IEsGS8v8Vxz3PGzH4PXAGc5u4zUlhkHDAU2A94I77S3R8EHgQoLCz0NIYqIiIiUm2VmwC6+/yKnmebmf0WuAcY6u5jIy6u5E5EREQklPJNIGb2iJmdkKTN8RGuFUyZmfUCngLudffbIyz6W2AD8FG6YxIRERGpqaIMA3M2MA94sYI2nYABwLmprtTMCggGggZoBTQ2s1PC55OANsALwOfAWDPrGrP4D+7+73A9o4AfCKaiWxeuczBwl7svTzUeERERka1d5HEAkygg6HGLoiXwbFxZyfNdgS5AE4Lk8t24do+x+eaUz4DzgcsIZhT5Gvgj8PeI8YiIiIhs1SpMAM0s/tbYpgnKAGoT9N6dDCyIEoC7zyOYSq48o8NHsvX8HSV7IiIiIkkl6wGcx+YbKJxgPL2KxtQz4OqqhyUiIiIimZIsAXycIPEz4CyCOX8/TNBuI/Bf4E13fzmtEYqIiIhIWlWYALr72SW/m9khwKPhqVYRERERqaFSvgnE3XM+ELSIiIiIVF3K4wCKiIiIyNah3B5AM/uG4Pq/I9z9P+HzVLi7756W6EREREQk7So6BVyLslOoxT8vT0VDuoiIiIhIjlU0F3Dbip6LiIiISM2kawBFRERE8kzKCaCZfWNmFydpc1GEawVFREREJAei9AC2BZomadMUaFPpaEREREQk49J9Crg58Eua1ykiIiIiaVThQNBmdlZc0a8TlAHUBloRTBc3N02xiYiIiEgGJJsJZDSbh35x4MTwEa9k6JdfgBvSEpmIiIiIZESyBPCc8KcBjwDjgRcStNsI/Bd4z93/m77wRERERCTdKkwA3f2xkt/N7BDgeXd/MeNRiYiIiEjGRLkJ5NfAQZkKRERERESyI0oCuDuwIVOBiIiIiEh2REkAPwA6ZCoQEREREcmOKAngcOAYM/ufDMUiIiIiIlmQ7C7gWAcBbwFPm9kfgVnA92weJqaEu/tNaYpPRERERNIsSgI4POb3A8JHIg4oARQRERGppqIkgIdmLAoRERERyZqUE0B3n5bJQEREREQkO6LcBCIiIiIiW4Eop4BLmVlrYEegfqJ6d3+rKkGJiIiISOZESgDN7LfACGC3JE1rVzoiEREREcmolE8Bm9nRwDMEvX73AEYwLMwDwEfh80nAjekPU0RERETSJco1gFcCK4HfuPulYdmb7v57d+8MXAwcAbyc5hhFREREJI2iJIC/AZ5392UxZaWnet39XuAdNAagiIiISLUWJQGsC3wX8/wXoGlcmw+ALlUNSkREREQyJ0oCuAjYKeb5f9gy2dsDWF/VoEREREQkc6IkgEWUTfgmAAeY2X1mdqyZ3Qz0CduJiIiISDUVZRiYx4EdzKy1uy8AbgGOBS4EBhHcBbwY+GPaoxQRERGRtIkyFdybwJsxz1eZWSFwIsG4gAuBCe7+Y9qjFBEREZG0qdRMICXcfR3wbJpiEREREZEsSJoAmtl2wBCgEHDgfeA+d1+R4dhEREREJAMqTADNrAVBwtea4Bo/gOOAc8zsQHdfnuH4RERERCTNkt0FPAxoA7wB9AP6h7/vClyT2dBEREREJBOSnQI+BvgS6O3uGwHMbBzwKUFPoO74FREREalhkvUA7gK8WpL8Abj7JuBVgtPCIiIiIlLDJEsA6wPLEpT/N6yrMjNrZ2YPmNkcM9toZlMTtDEzu8bMFprZGjN7y8x+naBdRzObYmbFZrbEzG40s9rx7URERETyWZSZQDJlb4IBpb8MH4lcBVwH3Eow28hPwOtmtkNJAzPbFnid4E7lE4EbCU5R35CxyEVERERqoFTGATzKzBrFlXUHMLNb2Xx3cAl39ysjxDDB3ceH6xsHNI+tNLNfESSAt7j7vWHZdGAeMJjgRhUIZiNpAJzs7quB18ysMTDczG4Ly0RERETyXioJYPfwkcgVCcocSDkBDK8pTPb6jYFnYpb52cwmENykUpIAHgO8EpfojSHoNTyEYO5iERERkbyXLAE8NCtRVGwvYCPwVVz5ZwRD08S2eyO2gbsvMLPisE4JoIiIiAhJEkB3n5atQCqwLfBT7J3IoRVAgZnVC6ek2xZYmWD5FWHdFsxsIDAQoHVr3dQsIiIi+aE63ASSCk9QZgnqymuXqBx3f9DdC929sEWLFlUMUURERKRmqAkJ4ApgmwTDuTQFit19fUy7pgmWb0LinkERERGRvFQTEsDPgdpAu7jyvcK62HZ7xTYws12AhnHtRERERPJaTUgAi4DVwKklBWZWQDAe4Msx7V4GjjazbWLK+gFrgOpwLaOIiIhItZDKMDAZFSZzx4ZPWwGNzeyU8Pkkdy82sxHAdWa2gqA37w8Eyes9Mau6H7gY+L9wfMLdgOHAHRoDUERERGSzchNAMzsYmOfuCzIcQ0vg2biykue7Egz4PIIg4bsaaAbMAo509+9KFnD3FWZ2OHAvwZAvK4E7CZJAEREREQlV1AP4JsE0ajcCmNkbwGh3fzydAbj7PLacTSS+jQN/Dh8VtZsLHJa24ERERES2QhVdA7geqBvzvBfQNpPBiIiIiEjmVZQAzie4qSJ2gLyE4+mJiIiISM1RUQL4MFAIfGtmGwmSv+FmtjHJY0NWIhcRERGRSin3GkB3/6uZLQV6AzsSzAs8n+CmDBERERGpoZLNBfwk8CSAmW0CHnX3G7MRmIiIiIhkRpRxAM8BPshUICIiIiKSHSkngO7+WOxzM9seaAysjh2PT0RERESqt0hTwZlZQzO7Nbw2cAnBrBxLzGypmY0ws4YZiVJERERE0iblHkAzawK8DewDrCKYX/c7YHvg18BQ4BgzO0hTr4mIiIhUX1F6AK8jSP7+Cuzi7oe5+2nufhiwC3ArsC8wLP1hioiIiEi6REkATwbecPcr3f2n2Ap3/9ndryaYPu6UdAYoIiIiIukVJQHcCZiRpM17YTsRERERqaaiJIArgN2TtNk9bCciIiIi1VSUBHAK8Fsz+22iSjPrC/wWeD0dgYmIiIhIZkQZCPpPwLHAM2Y2A3iLzXcBHwx0Iej9+1O6gxQRERGR9IkyEPS/zewgYBTQE+ga1+Rt4EJ3/yaN8YmIiIhImkXpAcTdPwUONrPWQCfCmUCAOe6+IAPxiYiIiEiaRUoAS4TJnhI+ERERkRoo0lRwIiIiIlLzKQEUERERyTNKAEVERETyjBJAERERkTyjBFBEREQkz6ScAJrZHWY2MJPBiIiIiEjmRekB/D2wa6YCEREREZHsiJIAfgW0ylQgIiIiIpIdURLA+4A+ZtYuU8GIiIiISOZFmQlkLjADmGlmDwCzge8Bj2/o7m+lJzwRERERSbcoCeBUgmTPgKEkSPxi1K5CTCIiIiKSQVESwBupOOkTERERkRog5QTQ3YdnMA4RERERyRINBC0iIiKSZ6KcAgbAzAqBfsCeQIG7HxGWtwG6AK+7+3/TGqWIiIiIpE2kBNDM7gYGE9wIAmWvCXTgaeBy4M60RCciIiIiaRdlKrjfA0OA54F9gFti6919AVAEnJjOAEVEREQkvaJcA3gB8BHwP+4+F1iXoM3ngAaKFhEREXr16oWZJXxMnz6dpUuXcsUVV9CpUycaNWrELrvswoABA1iyZEmuQ9/qRTkF3B4Y6e6bKmizDGhetZBERERkazBy5EhWr15dpuz666/ngw8+4IADDmDy5Mk8//zznH/++XTp0oXvvvuO4cOH0717dz755BMaNWqUo8i3flESwDXANknatAFWVD4cERER2Vp07NixzPN169Yxa9Ys+vXrR506dejZsyeff/45depsTkd+85vfsOeee/Lcc88xYMCAbIecN6KcAp4FHGtmBYkqzawFcAzwbjoCExERka3L5MmTWbFiBaeddhoATZs2LZP8AbRv356CggK+//77XISYN6IkgLcDOwGTzGw/wjuBzayWmR0ATCToIbwj7VGKiIhIjTdmzBhatWrFQQcdVG6bjz76iOLi4i16DyW9oswE8qqZ/QH4K/ABsDGsKgbqApuAS9y9KO1RioiISI1WXFzMhAkTGDhwIGaWsM2mTZu45JJL2GOPPTjqqKOyHGF+iTQOoLvfZWavAYOAA4DtgNXA+8D97v5R+kMEM5sKHFJOdXd3n25m8wiuQYz1nbvvkImYREREJHUTJkzgp59+Kj39m8jVV1/N9OnTmTZtGnXr1s1idPkn8kwg7v4pwXiA2fR7oHFc2Y1AZ2BmTNk/gXtinicaqkZERESybMyYMbRr147CwsKE9SNHjuSvf/0rTz/9NF26dMlydPkncgIYy8zquvv6dAVTnnDcwdjXrQcUAmPdfUNM1VJ3fy/T8YiIiEjqVq1axcsvv8zQoUMT1j/33HMMGTKE2267jX79+mU5uvwU5SYQzKyOmQ0xsxlmtgb4xczWhM+HmFmVEsoIegPbEkw9JyIiItXY888/z9q1axOe/p06dSqnn346gwcP5vLLL89BdPkp5YTNzJoArxL0vG0C5gPfAy0JTsUWAqeb2VHuvrrcFaVHf2Ax8HZc+blmdjHBmIWvAX909/kZjkVEREQqMGbMGDp16kSHDh3KlH/22WecdNJJ7LXXXvTr14/33tt8Eq9Fixbsvvvu2Q41b0TpsbuF4MaPR4A/ufvikgoza0VwTd45YbuL0hlkrHAcwj7Ag+7uMVXjgfeARUAH4E/A22a2r7uvKmddA4GBAK1bt85UyCIiInlr2bJlTJkyhZtuummLuhkzZrBq1SrmzJlDjx49ytQNGDCA0aNHZynK/GNlc6gKGpp9C3zp7gdX0OYdYA933z5N8SV6jX7AGOAAd59VQbt9gA+By939rmTrLSws9Fmzyl2diIhIVrS9amKuQ6jQvBHH5ToEqYCZzXb3xHfaxIhyDeA2bHnKNd40oGGEdVZGf+DripI/AHf/BPgC+E2G4xERERGpUaIkgB8CyU7GtwPmVD6cioXXIR5DtJs/UuviFBEREckTURLA64GTzOx/E1Wa2RnACcB16QisHH2B+qSQAIangPcEZmcwHhEREZEap9ybQMzs+gTF04AnzOxa4F3gB6AF0J3gxovXgB7AG+kPFQhO/85x98/iYj0OOAN4CVgC7AUMAxYAozMUi4iIiEiNVNFdwMMrqOsQPuIdBRwJbHmrTxWZWXPgcBL3MC4kGI7mLqApsByYDFyThSFpRERE8sfwJrmOoHzDEw76IQlUlAAemrUoUuDuy4CEEwOGcxAfnt2IRERERGqmchNAd5+WzUBEREREJDsiTQUnIiIiIjVf5Ll7zawlwfV/O1H+KdnHqxiXiIiIiGRIlLmAGwL3Av9bwXJGMO6eEkARERGRaipKD+C9wACCAaGfA74FNmQiKBERERHJnCjXAPYF3gcK3f3P7v4Pd38s0SNDsYqISGjDhg2MGDGCPfbYg/r167Pzzjtz2WWXlWkzcuRIjjvuOJo1a4aZMXXq1NwEKyLVTpQeQAfedvdNmQpGRERSc8455zBlyhT+9Kc/sddee7Fw4ULmzp1bps3jjz+OmXH00Ufz9NNRZtAUka1dlATwXaBjpgIREZHUTJ48mTFjxjBnzhw6diz/Y7moqIhatWrxySefKAEUkTKinAK+EuhuZhdkKhgREUnukUce4bDDDqsw+QOoVUsjfYlIYil/Orj7p0BP4BYz+8LMxpnZIwke/8hcuCIiMmPGDNq3b8/gwYNp3LgxBQUFnHzyySxZsiTXoYlIDRFlGJh2wASCuXabAnuU09SB86oemoiIJPLtt98yevRoOnXqxJgxY/jxxx8ZOnQoffv25b333sPMch2iiFRzUYeBaRv+HAssBTZmICYREamAu+PujB8/nmbNmgGw4447csghh/DGG29w+OGaGl1EKhYlAewBPO/uF2cqGBERSW7bbbdlt912K03+AHr27Em9evWYO3euEkARSSrKFcI/A/MyFIeIiKSoQ4cOCcvdXTd+iEhKonxSjAd6mS4uERHJqeOPP56PPvqIZcuWlZa99dZbrF+/nk6dOuUwMhGpKaIkgEMJrvl7wsx2ylA8IiKSxMCBA2nWrBl9+vRhwoQJ/POf/+TMM8/kiCOOoGfPnqXtZs2axbhx43jttdcAmDZtGuPGjWPWrFm5Cl1Eqoko1wB+ANQD9gdOM7MVwOoE7dzdd09HcCIisqXGjRvzxhtvcPHFF9O/f3/q1avHiSeeyJ133lmm3b333stjj22enXP48OEADBgwgNGjR2cxYhGpbqIkgLWA9cCCmLJEp4N1ilhEJMPatWvHpEmTKmwzevRoJXoiklDKCaC7t81gHCIiIiKSJbpdTERERCTPKAEUERERyTNRpoJ7JMWm7u6aCk5ERESkmopyE8jZSeqd4AYQzQUsIhJR26sm5jqEcs0bcVyuQxCRNIuSAO5aTnlj4DfANcBHwBVVDUpEREREMifKXcDzK6j+2MwmESSAfYB7qhqYiIiIiGRG2m4CcfcfgAnAkHStU0RERETSL913Aa8FWqd5nSIiIiKSRmlLAM2sLXAqsDBd6xQRERGR9EvHMDB1gJ2AngRzBf85DXGJiIiISIakcxiYr4A73f3+yocjIiIiIpmWjmFgNgEr3f3HNMQjIiIiIhmWrmFgRERERKSG0FzAIiIiInmmwh5AMzurMit198crF46IiIiIZFqyU8CjCeb2rYiFPz3mpxJAERERkWoqWQKY6qweDYALgN2rFo6IiIiIZFqFCaC731dRvZnVAs4HrgJaAUuAm9IWnYiIiIikXaVvAjGzfsBnwCiCHsArgXbu/kCaYhMRERGRDIgyDiAAZnYMwWwfnYBi4C/AX919dZpjExEREZEMiDIVXHfgFoIp39YD9wE3u/v3GYpNRERERDIg6SlgM9vPzCYAbwM9gCeAPd394mwlf2Z2tpl5gsegmDZmZteY2UIzW2Nmb5nZr7MRn4iIiEhNkmwcwKeAfgRDvbwADHP3z7IRWDkOA9bEPP8m5vergOuAK4DPgT8Ar5vZPu7+bfZCFBEREanekp0CPo1gXL9vgI3ADWZW8RLg7t4vDbElMtPdf4ovNLNfESSAt7j7vWHZdGAeMBgYlqF4RERERGqcVK4BNILx/VId4y/ZwNGZ0B1oDDxTGoT7z+Gp62NQAigiIiJSKlkCuGtWokjdv82sGfBv4I6YIWf2Iuih/Cqu/WcEp7BFREREJJRsIOj52QokiaUE1/e9D9QmODV9v5kVuPudwLbAT+6+MW65FUCBmdVz93VZjVhERESkmoo8DmAuuPsrwCsxRS+bWX1gmJndXdIswaLx8xSXrTQbCAwEaN26dZqiFREREaneKj0TSDUwDtgOaEvQ07eNmdWOa9MUKHb39YlW4O4Punuhuxe2aNEio8GKiIiIVBc1OQEs4QTDvtQG2sXV7RXWiYiIiEioJieAvwWWAfOBImA1cGpJpZkVAH2Al3MSnYiIiEg1VSOuATSz5whuAPmIoKevX/i42N03Ab+Y2QjgOjNbweaBoGsB9+QmahEREZHqqUYkgMAXwLnALgQ3dswFznL3J2LajCBI+K4GmgGzgCPd/bssxyoiIiJSrdWIBNDdrwGuSdLGgT+HDxEREREpR02+BlBEREREKkEJoIiIiEieUQIoIiIikmeUAIqIiIjkGSWAIiIiInlGCaCIiIhInlECKCIiIpJnlACKiIiI5BklgCIiIiJ5RgmgiIiISJ5RAigiIiKSZ5QAioiIiOQZJYAiIiIieUYJoIiIiEieUQIoIiIikmeUAIqIiIj8f3t3Hi5Fda97/Pu6FRAUZHCARLNRI0Y0jomEiPNBUQlGRYRrlHjvUTASiEM05+QYRBM1iIKgJ9cYQuKABqKSKLlqiOQggsQBIgpEj2wHPIpMEoNClHX/WNXSNL0HYO+u7l3v53nqKXrV6upfVxe7f73WqlUZ4wTQzMzMLGOcAJqZmZlljBNAMzMzs4xxAmhmZmaWMU4AzczMzDLGCaCZmZlZxjgBNDMzM8sYJ4BmZmZmGeME0MzMzCxjnACamZmZZYwTQDMzM7OMcQJoZmZmljFOAM3MzMwyxgmgmZmZWcY4ATQzMzPLGCeAZmZmZhnjBNDMzMwsY5wAmpmZmWWME0AzMzOzjHECaGZmZpYxTgDNzMzMMsYJoJmZmVnGOAE0MzMzyxgngGZmZmYZ4wTQzMzMLGMqIgGU1F/S7yQtk/ShpOclDSyoM1NSKLK0SituMzMzs3K0Y9oBNNDlwFLge8AK4DTgfkmdQgjj8+o9BfxbwXPXlyZEMzMzs8pQKQlg3xDCirzHf5LUhZgY5ieAq0IIc0sbmpmZmVllqYgu4ILkL+dFYI9Sx2JmZmZW6SoiAaxFT+CVgrLektYly+OSvpxGYGZmZmblrCITQEknAf2AO/KK/wwMB04BLgb2AWZJqq5jPxdLek7Sc++//37TBWxmliGvvfYal1xyCYceeihVVVUcf/zxm22fOXMmkooup5xySjpBm2VMpWU3fpMAABscSURBVIwB/EyS0N0PTAshTMqVhxB+lFdtlqQ/AouBEcmyhRDCXcBdAEcddVRomojNzLLl5ZdfZvr06fTo0YMNGzZssf2II45gzpw5m5W9+eabDBgwgD59+pQqTLNMq6gEUFIH4A/Am8D5ddUNIbwraTZwRCliMzOzqG/fvvTr1w+Ac845hxUrNh/G3bZtW3r06LFZ2axZs9hhhx0499xzSxanWZZVTBewpNbAo0AL4PQQwj8a+FS37JmZldAOO2z9V8vkyZM57rjj6NKlSxNEZGaFKiIBlLQjMAX4ItAnhLC8Ac/ZE/g68HwTh2dmZtvh1Vdf5cUXX2TgwIH1VzZrRPWNVwWorq7eYqzqXnvtVfpgG1mldAHfSZz8eTjQQVJ+38GLQDfgRmKS+AbxApAfABuBsaUN1czMtsbkyZPZaaedOPvss9MOxTKmvvGqOYMGDWLYsGGfPW7RokUpwmtSlZIA9k7W44ps6wqsBERMAjsCfwdmAmeGEN4sRYBmZrZtHnjgAXr37k2HDh3SDsUypr7xqjmdO3feYtxqpauILuAQQnUIQbUsNSGEZSGE00IInUMILUIIHUMIZ4cQFqcdu1ljaUhXRb4RI0YgiSuvvLI0AZptgwULFrBo0SJ3/1oqtmW8anOR3XduVmFyXRUHHHAABxxwQJ11X3nlFSZOnEjbtm1LFJ3ZtnnggQfYeeedP2uFMStHEydOpEWLFrRr145zzjmHN954I+2QtpsTQLMK0bdvX9566y2mTJlC9+7d66z73e9+l+HDh9O+ffsSRWe2bR588EH69u3LLrvsknYoZkX169ePO+64gxkzZjB69GjmzJlDr169+OCDD9IObbtUyhhAs8xraFfF1KlTWbRoEdOmTeOee+5p4qjMtrRu3TqmT58OwLJly1i7di1Tp04F4LTTTqN169YAzJ07l6VLl3LrrbemFqtZfcaN23T5Qa9evejZsyeHHXYYv/zlLxkxouh9JiqCE0CzZuSjjz7iiiuu4KabbqJNmzZph2MZtXz5cvr3779ZWe7x0qVLqa6uBmL3b7t27Xz3D6soBx98MN26deOFF15IO5Tt4i5gs2bkxhtvpHPnzpx/fp03yjFrUtXV1YQQii655A9g7NixrFmzhpYtW6YXrNk2kpR2CNvFCaBZM7F06VJuueUWxo4dW/F/mMzMytXChQtZsmQJRx55ZNqhbBd3AZs1E9dccw19+vThwAMPZM2aNQBs3LiR9evXs2bNGtq1a+fE0MwsT33jVZ966inuvfdezjjjDLp06cLixYu54YYb2GeffRg8eHCKkW8/J4BmzcSSJUtYsGABDz300GblEyZMYMKECbz11lt8/vOfTyk6M7PyU9941b333pvly5czYsQI1qxZQ8eOHTn11FP5yU9+UvHTbDkBNGsm7r77bj788MPNys477zyOO+44hg4dyu67755SZGZm5Sk3XrUuM2bMKFE0peUE0KxC1NdVcdRRR23xnFatWrH33nvXe9cQszqNbJd2BLUbuf1zsT3yyCNce+21LFmyhC5dujBs2DAuv/zyRgjOrHw5ATSrEA2dWsPMGm727NmcddZZXHTRRdxyyy08++yzXH311eywww4VPcebWX2cAJpViIZ0VRSqqalpmmDMmolRo0ZxzDHHcPfddwPQu3dvVq9ezahRo7j00ktp0aJFyhGaNQ1PA2NmZpk1f/58Tj755M3KckngnDlzUorKrOk5ATQzs8z6+OOPt2jly01MvWjRojRCMisJdwGbmVlm7b///vzlL3/ZrGzevHkArFq1Ko2QbDsc8qtD0g6hVi9d+FLaIWzGLYBmZpZZQ4YMYdq0afz85z9n9erVPP7444wZMwaAqqqqlKMzazpuATRLSfU1j6UdQq1qbjo97RDMSuKiiy5iwYIFDB06lIsvvpjWrVtz8803M2zYMPbcc8+0wzNrMm4BNDOzzKqqqmLChAm8//77/PWvf+W9996jR48eAJ+tzZojtwCamVnmtW/fnvbt2wNw55130rNnTw488MCUozJrOk4Azcwss+bOncvTTz/NYYcdxtq1a5k8eTKPP/44Tz/9dNqhmTUpdwGbmVlm7bTTTjz44IOceeaZDB48mHXr1jF79my+/OUvpx2aWZNyC6CZmWXWkUceucU0MGZZ4BbACjN16lR69uxJx44dadWqFd26deOGG25gw4YNaYdmZmZmFcItgBVm5cqVnHDCCVx11VXstttuzJs3j5EjR/Luu+8yYcKEtMMzMzOzCuAEsMJccsklmz0+4YQTWLt2LXfccQfjx49HUkqRmVWOKVOmcM899/D888/zwQcf0K1bN6688koGDhyYdmhmZiXhBLAZ6Nixo7uAzbbCrbfeSteuXbntttvo1KkT06dPZ9CgQaxYsYJhw4alHZ6ZWZNzAlihPv30U9avX88LL7zA7bffztChQ8ui9e+1115j9OjRzJ07l4ULF9KrVy9mzpyZdlhAecfWHJXz8f79739Pp06dPnt84okn8s4773Drrbc6Aaww5XzvVyi/+7+a5TgBrFBt2rRh/fr1AFxwwQWMHj065Yiil19+menTp9OjR4+ya5Us59iao3I+3vnJX87hhx/OtGnTUojGzKz0fBVwhXrmmWeYNWsWY8aMYdq0aVx22WVphwRA3759eeutt5gyZQrdu3dPO5zNlHNszVGlHe9nnnmGgw46KO0wzMxKwi2AFeqII44A4JhjjqFTp05ceOGFXHHFFey3336pxrXDDuX7m6KcY2uOKul4z5gxg2nTpjFx4sS0QzEzK4nK+Qtttcolg0uXLk05ErPKU1NTw6BBg+jXrx+DBw9OOxwzs5JwAtgMzJ49G4CuXbumHIlZZVm1ahV9+vRhn3324d577007HDOzknEXcIU59dRTOfnkk+nevTtVVVXMnj2bMWPGMGDAgNS7f80qybp16zjjjDPYsGEDjz32GG3atEk7JDOzknECWGG+8pWvMGnSJGpqathxxx3Zd999ufHGGxkyZEjaoZlVjE8++YT+/fvz6quvMnv2bPbYY4+0QzIzKykngBXm+uuv5/rrr087DLOKdumllzJ9+nTGjRvHqlWrmDt37mfbDj/8cFq2bJlidGZmTc8JoJllzhNPPAHA8OHDt9i2dOlSqqurSxyRmVlpOQG0RrVu3TqmT58OwLJly1i7di1Tp04F4LTTTqN169aOLSPK+XjX1NSk9tpmZuXACaA1quXLl9O/f//NynKP025ZKefYmiMfbzOz8uUE0BpVdXU1IYS0wyiqnGNrjny8zczKlxPAEqq+5rG0Q6hTzU2npx2CmZmZlYAngjYzMzPLmGaVAEo6SNIMSeskvSNplKSqtOMyMzMzKyfNpgtYUnvgj8ArQD9gP2AMMcn9YYqhmVkjO+RXh6QdQq1euvCltEMwM6tXs0kAgSHAzsBZIYS1wJOS2gIjJf00KTMzMzPLvOaUAPYBHi9I9B4AbgaOA36fSlSVZGS7tCOo1SFd90k7hDo1u1afMj4XACjz88HMrNw1pzGABwKL8wtCCG8C65JtZmZmZgaouczTJemfwFUhhLEF5W8Dvw4h/FuR51wMXJw87AYsafJAs6UTsCLtIKws+FywfD4fLMfnQuP7Qghh9/oqNacuYIBi2axqKSeEcBdwV5NGlGGSngshHJV2HJY+nwuWz+eD5fhcSE9z6gJeDexWpLwdsKbEsZiZmZmVreaUAC6mYKyfpL2BNhSMDTQzMzPLsuaUAP4BOEXSrnllA4CPgD+nE1LmuXvdcnwuWD6fD5bjcyElzekikPbESaAXEqd+2Re4FRgbQvBE0GZmZmaJZpMAQrwVHDAB+Bpx3N/dwMgQwqepBmZmZmZWRppVAmhmZmZm9WtOYwAtZZL6S/qdpGWSPpT0vKSBacdl6ZP0ueScCJJ2STseKz1JO0q6RtKrktZLelvSbWnHZemQdJ6kF5K/C8sk/VpSl7TjypLmNg+gpetyYCnwPeLEnqcB90vqFEIYn2pklrbRwIfEq/Itm34JnARcR5yZYW/goFQjslRI+gYwGbgDuAroDNwAPCrpqBDCxjTjywp3AVujSRK9FQVl9wNfCyF0TSksS5mkXsA04CfERHDXEMKH6UZlpSTpVOL92A8NIbySdjyWLkkPAF8MIRyZV/YN4t+Jg0IIi1ILLkPcBWyNpjD5S7wI7FHqWKw8SKoCxgOj8O2esuwi4E9O/iyxE/BBQVnuhg0qcSyZ5QTQmlpP4vQ8lk1DgFbErh7LrqOBv0maIGmtpHWSHvKYr8yaCPSSdIGktpIOIHYBP+UfCaXjBNCajKSTgH74yz+TJHUErgcuDyH8M+14LFV7AYOBw4DzgG8DRwIPS3KLT8aEEB4jng93EVsClwBVwFkphpU5vgjEmoSkauB+YFoIYVKqwVhafgw8G0KYnnYgljolS78QwkoASf9DvEvTicCMFGOzEpN0AvAzYBzxLl57AiOJPwhO9ty9peEE0BqdpA7E/9RvAuenHI6lQFJ34rivYyXtlhS3TtbtJH0aQvgonegsBauB13PJX+JpYAPxSmAngNkyBvhdCOHqXIGk+cSrw/sBD6UVWJa4C9galaTWwKNAC+D0EMI/Ug7J0vFF4kDvOcQv/9VsGgrwNvHCEMuO2q7qFOApP7LnQGB+fkEIYQnwEbBfKhFlkFsArdFI2hGYQvzy/3oIYXnKIVl6ngZOKCg7FbiaOD/k6yWPyNL0KHBdwVRRxxJ/JCxILyxLyRvAEfkFkr4E7AzUpBFQFnkeQGs0ku4C/hUYDswr2PxiCGF96aOyciFpMHEyYM8DmDGS2gILgWXE+SB3BW4GFocQ/iXN2Kz0JA0HbkuW3BjAa4k9Rwe756g03AJojal3sh5XZFtX/MvOLJNCCGslnQjcDjxAHPs3jXjXIMue24nnwFDiVFFriL0GP3DyVzpuATQzMzPLGF8EYmZmZpYxTgDNzMzMMsYJoJmZmVnGOAE0MzMzyxgngGZmZmYZ4wTQzMzMLGOcAJrZdpN0vKQgaWTasWwPRVdJ+puk9cl7Oj7tuIqRNLKc4zOz8uYE0KzMSKpOvtiDpMm11Lks2T64xOE1d/8L+CmwFrgFuI4GTmCeJI9Lk8/ll40RTLKvmY2xr6YkaS9JYyUtkfSxpA8l/bekRySNkKS0YzSzzflOIGblbYCkm0MI8+uvao2gT7I+I4Tw7lY+93igGghAf0nDmviWdxOId9V4swlfo16SvgDMBfYC/gL8HFgP7AccDfQjxvpJWjGa2ZacAJqVr9eBfYEfA6enHEtWdAbYhuQP4NvJeizxFmf9ifc+bhIhhBXAiqba/1a4jpj8/SCEcFP+hqTl72Tg0zQCM7PauQvYrHy9CDwCnCbpmPoq53UdT2roNkk1ybKbpP8r6b2k++5xSV9M6nSX9KikNZI+kDRJ0q51xHGypGckrUv295+Sdqulbm9JT0hanXQd/lXSdwq7DPPHu0kaImlhMkZvbAOOy/6S7pX0bvKcpZLG5MckabCkAJyQPM51wc+sb/9J/V2Bs4DngBuI9zkdXEf9KklDJc2VtDY55gsl/VRSm9yYyqT6cXnxfDbmr3AMoKSTkse31PKa30i2X1tQ/hVJD0t6Pzk+SyT9UFKLhrx34KvJ+meFG0L0ZMi752juWCfrAZLmS/pI0tuSfiKpZUF8LSR9V9IfJS2TtCGp+wtJn6vlvbZP9rUo2ffK5Jy8tEjdgZJmJZ/DPyQ9K+ncIvU6SLopOT7rkv8PL0saL2mnBh4rs7LhBNCsvP0Q2Ajc2ISv0QJ4kvhFfn/y797Ak5IOBmYDVcAvgCXAhcQuvWJ6Ao8BbwPjgFeJN3t/sjChkDQCeBw4GPgt8J/JpgnEm8UX8wPgZmA+saVtcV1vTFJ3YB4wEJgF3AosBS4Hns5LZOcTW7LeSB5flyyT6tp/nnOBNsC9IYRVwB+AXpL2KxJTFfAwcCewO/ArYvL0OjAsKatJXp8kpuvylppaYngKeAc4T1Kxv+2DkvX9ebGcAzxDTHynA+OBlcD1wNTCRLwWq5L1/g2om+9c4nufTzxXVhI/398U1OtA/NwAphE/94XEFtdnJHXIryypM7Er+gfAauJ7mkzsgr6yoO5txOPRGbgPmAh0Ah6UdEVePRHP1e8TP6fxSew1wL8CmyWtZhUhhODFi5cyWtg0jmxq8vhXyePT8+pclpQNLvK8SXXsc1JBeU1SPhmoyisfn5SvBi7NK9+R2DL5T2CvvPLjk/oB+FbBa/wiKR+eV3Yw8Qt5FrBrwf5/m9T/al75yKTsA6DbVhzL/0qed25B+U+T8tEF5TPjn8Wt/sxmJe9nz+Rx/2T/o4rUHZFsexjYqWBbR6BV3uMAzKzlNXPH5Pi8sjFJ2QkFdXcB/gE8m1e2O/B34G/AHgX1xxU7brXE8b2k7nJigtoLaF1H/cF558pxeeVVwBNJeb+88pZA5yL7GZjU/Y+C8keS8iuLPOdzef/uk9T7DdAir7w1MIfYivu5pOzLSd3biuxzN2CHrT1nvHhJe3ELoFn5+xHxy+jHDWyR2RbfDyHkj9N6MFmvYFPLHCGET4gJ2o7Al4rsZzFwb0HZj4hjwM7PK7uE+IU/LITw94L957ooBxTZ/10hhCX1vhs+uzihFzAvhFDYqnQ9MZm8oCH7qud19geOAf4YQngvKf59sv8Li3xmQ4gXSVwWQvhn/oYQwsoQwsfbEc59yXpQQfmZxMTmvryyC4iJ4fdDCMsL6v+QmPAU+wwKjSP+YGhP/Oz+C1gr6TlJ35fUppbnPR5C+HPuQXL+5T778/PK14cQ/qfwySGEycRjfFKuLGn9+wbwEptaDfOfsyzv4aXE1vWhIYQNeXXWEbvxdyJ26+f7R5F9rgkhbKzlPZqVLV8EYlbmQgg1ku4itvqdR2yta0yrQwhvFZTlvnBfCiGEgm25CyS6FNnX7ML6IYS3Jb1BbEXJ+SoxKfympDML9pEbT9WtyP6fK/YGanFosv5z4YYQwt8lvQgcL6lzsQRjK+Qu/vgsuQohfCzpoWTbicAMAEm7EN/XiwXJSKMIIbwgaTFwtqTv5CU2g4jH+8G86rmxe8dKOqzI7j6i+GdQ+Jobge9KuhE4A+iRLEcmy7clHR1CWFvw1KeL7G4esXU5/1xB0tHE7tevEVsu87+7Ouf9+0hAxGS8vqTsq8QEcliR31W7J+vc+3+F2O38b5IOJQ5zmBlCqHMIglk5cwJoVhluICYToyRNaeR9F34xw6arNotty03nUWzg+/u1vMZyYF9JLUMI64njuqrY1OJTTLGWo8KWqrq0Tdbv1bL9vbx625QAJmPtvgWsI3bp5ruX+Jl9myQBBNol63e25fUa6D5iC2cfYJqkTsC/ADPyWighfgYQu3BrU1vr3RaSJPrnyUIyfvR+4BDgP4CrCp6yxbkSQtgoaSWbPjskHUccl/oJ8P+A/yYe70DsTs8ff7c1x7cD8TvwR3XUaZPE9YmkE4FRwNnERBdJrwPXhRB+3YDXMysrTgDNKkAI4T3FK17/HfjftVTLtXgU+3/dtkhZU9i9lvI9gA1J8gcxsfwn0KawG7Qeha2Rdcklr3vWsn3Pgnrb4mRg7+Tff6+lh/4sSW2TFrAPkrJiraeN5X5iAjiIeNHEucRz4v6Cern3XR1CeINGFkJYKGk48Cfg2CJVtjhXkoS6I/FCnZyriT82jg0hzM2rK7ZMKtck64Yc37XA2hBC1wbUJYTwPjBU0neILZSnEBPQX0laFkKYUecOzMqMxwCaVY7RxCsurwV2LrK9ri+/w5sqqAI9C8e8Sfo8sA/w17ziecQv9SOaMJYFyXqL5CPpij0MWL6d3b+Dk/UjxItdCpc5xM9qAECIE0MvAg6qbQqTAhuJLaUNFkJ4PXndvsn7HETszn2ooOq8ZN1ja/a/lXITYRdrSSw2tdFXiedF/rmyL7AyP/lLHEoc15jveeKPhJNquRI63zzgC8m4wQYLIWwMIcwPIdzMpu7/M7ZmH2blwAmgWYUIIXxAnAKlC/EiisLta4nTrhwjad9cuaTdiS2HpfAlNr/YA+KVoTuy+QUIPyN2M98haY/CnUj6gqTq7QkkadWaBRwtqXAw/78Tr97c5q47Se2AbxK7MvuHEP5P4UKcIgQ2JQoQL6ppCUwonD8umWuuVV7RKqAhiWKh+4iJ5wji1DyP5l9sk5hEvKjhZklbtIJJ2kNSsQt9CutdnlwIU1heBeSmUik23u8USccW1B+VF3/OW0AHSd3y6u5CnA5mMyFO4P0wsYXu8iIx5R/LCcTxgneryLyWkg7KnZuSuua/fp5cK/L6ItvMypq7gM0qy3hgOPE2W8XcRpxfbk4yVrAl0Jc4l98XSxDfk8Qv1L7Aa8TWt68TL964M1cphLAgmQfwduBvkv5AnO+uE3AgMWkZRAPvw1uHocQk8DeSfkscP3Y08cKMl9mUcGyL84BWwM+Sq5e3EEJ4WdLzwNckdUuuYL6DeOXqmcBiSY8SE4j9gVOBg9j0vp8i3lbut8RWsU+BexrQZfsbYoJ0LTHJua+wQjKs4FvEi4oWSXqMeHzaEs+VY4lj9xbV81oXAGMkvUCcf28lsXu3N/AF4q3qih3nPwBPSHqAeGFRH2Li9rsQwiN59X5G7GqfLenB5P2cSky8i431uzTZz2hJ3yQmnzsTpx6qJrYoEkJ4TNJoYjfyq5KeSPa3F3Hc4hHEi06WE1sbH5Y0h3jerCD+H+xH7Er+RT3HyKz8pD0PjRcvXjZfKJgHsMj2IWyaR21wke3DiV/kG4hJ2AigK7XPA1hTRwyTimwbXPjabJoHcCTxy3oOcaD++8Qv8N1qeS/HELsm30vifYc4jciVQKe8eiMpmPNuK47n/sQEKPcaNcT58raIia2YB5B4/9sAHFpPvdycjTfmlVUB3yEmxuuI8/EtBG4ibw49YmvvVGJStTH/GNR3TIhXqgZiK2KLOuI7BLgHWJYcn/eAZ4nJ4z4NOA5HJLHMIrbWbUjez4vEi5c61Hb+ELvG5wMfJ69/I3nzIOY953xiAvxRUm8CMVGt7fxtT2wtf5WYXK8g/ggaUqRuX+LFJSuTum8S5yMcShyjCvD55LOZl5zTHxH/j90N7F+qvw1evDTmohC2Zky1mZnZtpM0mHiP5G+HECalG41ZdnkMoJmZmVnGOAE0MzMzyxgngGZmZmYZ4zGAZmZmZhnjFkAzMzOzjHECaGZmZpYxTgDNzMzMMsYJoJmZmVnGOAE0MzMzy5j/D5frmTs+KC9UAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 648x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# copying the data printed out above\n",
    "naive = (3,14,61,184)\n",
    "qwc   = (1,1,17,72)\n",
    "full  = (1,2,9,15)\n",
    "\n",
    "# active spaces (x-axis)\n",
    "# There is a weird naming convention...\n",
    "# Openfermion lists active spaces as 1,2,3,4\n",
    "# But, active spaces always come in pairs so there are actually\n",
    "# twice as many spaces as what Openfermion says there is... its confusing\n",
    "AS = np.array((1,2,3,4))\n",
    "\n",
    "width = 0.3\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(9,7))\n",
    "rects1 = ax.bar(AS - width, naive, width, label='Naive')\n",
    "rects2 = ax.bar(AS, qwc, width, label='QWC')\n",
    "rects3 = ax.bar(AS + width, full, width, label='GC')\n",
    "\n",
    "ax.set_ylabel('Number of Partitions',fontsize=19)\n",
    "ax.set_xlabel('Number of Active Spaces',fontsize=19)\n",
    "ax.set_title(r'Bron-Kerbosch Simultaneous Measurement for $\\mathrm{H}_2$',fontsize=19)\n",
    "ax.set_xticks(AS)\n",
    "ax.set_xticklabels(('2', '4', '6', '8'),fontsize=15)\n",
    "ax.legend(fontsize=15,loc='upper left')\n",
    "\n",
    "\n",
    "def autolabel(rects, xpos='center'):\n",
    "    \"\"\"\n",
    "    Attach a text label above each bar in *rects*, displaying its height.\n",
    "\n",
    "    *xpos* indicates which side to place the text w.r.t. the center of\n",
    "    the bar. It can be one of the following {'center', 'right', 'left'}.\n",
    "    \"\"\"\n",
    "\n",
    "    ha = {'center': 'center', 'right': 'left', 'left': 'right'}\n",
    "    offset = {'center': 0, 'right': 1, 'left': -1}\n",
    "\n",
    "    for rect in rects:\n",
    "        height = rect.get_height()\n",
    "        ax.annotate('{}'.format(height),\n",
    "                    xy=(rect.get_x() + rect.get_width() / 2, height),\n",
    "                    xytext=(offset[xpos]*3, 3),  # use 3 points offset\n",
    "                    textcoords=\"offset points\",  # in both directions\n",
    "                    ha=ha[xpos], va='bottom',fontsize=15)\n",
    "\n",
    "\n",
    "autolabel(rects1)\n",
    "autolabel(rects2)\n",
    "autolabel(rects3)\n",
    "\n",
    "fig.tight_layout()\n",
    "\n",
    "plt.savefig('Figures/ActiveSpaces.pdf',format='pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot multiple molecules together"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# first we need to choose a tractable active space for each molecule\n",
    "h2files = ['hamiltonians/H2_sto-3g_BK_0.7_AS{}.txt'.format(a) for a in [1,2]]\n",
    "lihfiles = ['hamiltonians/LiH_sto-3g_BK_1.45_AS{}.txt'.format(a) for a in [1,2,3,4,5,6]]\n",
    "h2ofiles = ['hamiltonians/H2O_sto-3g_BK_104_AS{}.txt'.format(a) for a in [1,2,3,4,5,6]]\n",
    "ch4files = ['hamiltonians/CH4_sto-3g_BK_grnd_AS{}.txt'.format(a) for a in [1,2,3,4,5,6,7,8,9]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['hamiltonians/H2_sto-3g_BK_0.7_AS2.txt', 'hamiltonians/LiH_sto-3g_BK_1.45_AS3.txt', 'hamiltonians/H2O_sto-3g_BK_104_AS4.txt', 'hamiltonians/CH4_sto-3g_BK_grnd_AS4.txt']\n",
      "--------------\n",
      "hamiltonians/H2_sto-3g_BK_0.7_AS2.txt\n",
      "4 qubits\n",
      "15 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 14 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 3 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.003326s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 14 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 2 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.003340s\n",
      "\n",
      "--------------\n",
      "hamiltonians/LiH_sto-3g_BK_1.45_AS3.txt\n",
      "6 qubits\n",
      "118 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 117 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 39 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.251704s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 117 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 13 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.167520s\n",
      "\n",
      "--------------\n",
      "hamiltonians/H2O_sto-3g_BK_104_AS4.txt\n",
      "8 qubits\n",
      "193 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 192 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 45 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.641773s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 192 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 19 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 0.581299s\n",
      "\n",
      "--------------\n",
      "hamiltonians/CH4_sto-3g_BK_grnd_AS4.txt\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "Imaginary coefficient! -- skipping for now\n",
      "8 qubits\n",
      "241 total terms\n",
      "\n",
      "QWCCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 240 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 68 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 1.589233s\n",
      "\n",
      "FULLCommutation:\n",
      "MEASURECIRCUIT: Generated graph for the Hamiltonian with 240 nodes.\n",
      "MEASURECIRCUIT: NetworkX_approximate_clique_cover found 25 unique circuits\n",
      "MEASURECIRCUIT: Elapsed time: 1.007746s\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Based on the above results we will look at:\n",
    "# H2: AS = 2\n",
    "# LiH: AS = 3\n",
    "# H2O: AS = 4\n",
    "# CH4: AS = 4\n",
    "\n",
    "fs = [h2files[1],lihfiles[2],h2ofiles[3],ch4files[3]]\n",
    "print(fs)\n",
    "print_cliques_x(fs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# copying the data printed out above\n",
    "naive = (14,117,192,240)\n",
    "qwc   = (3,39,45,68)\n",
    "full  = (2,13,19,25)\n",
    "\n",
    "xaxis = np.array((1,2,3,4))\n",
    "\n",
    "width = 0.3\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(9,7))\n",
    "rects1 = ax.bar(xaxis - width, naive, width, label='Naive')\n",
    "rects2 = ax.bar(xaxis, qwc, width, label='QWC')\n",
    "rects3 = ax.bar(xaxis + width, full, width, label='Full')\n",
    "\n",
    "ax.set_ylabel('Number of Measurement Circuits')\n",
    "ax.set_xlabel('Molecule [AS#]')\n",
    "ax.set_title('NetworkX Term Grouping (sto-3g basis, BK encoding)')\n",
    "ax.set_xticks(xaxis)\n",
    "ax.set_xticklabels(('H2 [2]', 'LiH [3]', 'H2O [4]', 'CH4 [4]'))\n",
    "ax.legend()\n",
    "\n",
    "\n",
    "def autolabel(rects, xpos='center'):\n",
    "    \"\"\"\n",
    "    Attach a text label above each bar in *rects*, displaying its height.\n",
    "\n",
    "    *xpos* indicates which side to place the text w.r.t. the center of\n",
    "    the bar. It can be one of the following {'center', 'right', 'left'}.\n",
    "    \"\"\"\n",
    "\n",
    "    ha = {'center': 'center', 'right': 'left', 'left': 'right'}\n",
    "    offset = {'center': 0, 'right': 1, 'left': -1}\n",
    "\n",
    "    for rect in rects:\n",
    "        height = rect.get_height()\n",
    "        ax.annotate('{}'.format(height),\n",
    "                    xy=(rect.get_x() + rect.get_width() / 2, height),\n",
    "                    xytext=(offset[xpos]*3, 3),  # use 3 points offset\n",
    "                    textcoords=\"offset points\",  # in both directions\n",
    "                    ha=ha[xpos], va='bottom')\n",
    "\n",
    "\n",
    "autolabel(rects1)\n",
    "autolabel(rects2)\n",
    "autolabel(rects3)\n",
    "\n",
    "fig.tight_layout()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compare the runtimes between Bron-Kerbosch and NetworkX for the different Molecules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# copying the data printed out above\n",
    "bk_qwc  = (0.001482,0.040986,0.187812,0.259468)\n",
    "bk_full = (0.001200,0.109233,9.416595,15.331529)\n",
    "nx_qwc  = (0.003326,0.251704,0.641773,1.589233)\n",
    "nx_full = (0.003340,0.167520,0.581299,1.007746)\n",
    "\n",
    "xaxis = np.array((1,2,3,4))\n",
    "\n",
    "width = 0.2\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12,7))\n",
    "rects1 = ax.bar(xaxis - 1.5*width, bk_qwc, width, label='BK QWC')\n",
    "rects2 = ax.bar(xaxis - 0.5*width, bk_full, width, label='BK FULL')\n",
    "rects3 = ax.bar(xaxis + 0.5*width, nx_qwc, width, label='NX QWC')\n",
    "rects4 = ax.bar(xaxis + 1.5*width, nx_full, width, label='NX FULL')\n",
    "\n",
    "ax.set_ylabel('Time for Max-Clique-Cover')\n",
    "ax.set_xlabel('Molecule [AS#]')\n",
    "ax.set_title('Bron-Kerbosch vs. NetworkX Runtimes')\n",
    "ax.set_xticks(xaxis)\n",
    "ax.set_xticklabels(('H2 [2]', 'LiH [3]', 'H2O [4]', 'CH4 [4]'))\n",
    "ax.legend(loc='upper left')\n",
    "\n",
    "\n",
    "def autolabel(rects, xpos='center'):\n",
    "    \"\"\"\n",
    "    Attach a text label above each bar in *rects*, displaying its height.\n",
    "\n",
    "    *xpos* indicates which side to place the text w.r.t. the center of\n",
    "    the bar. It can be one of the following {'center', 'right', 'left'}.\n",
    "    \"\"\"\n",
    "\n",
    "    ha = {'center': 'center', 'right': 'left', 'left': 'right'}\n",
    "    offset = {'center': 0, 'right': 1, 'left': -1}\n",
    "\n",
    "    for rect in rects:\n",
    "        height = rect.get_height()\n",
    "        ax.annotate('{:.2f}'.format(height),\n",
    "                    xy=(rect.get_x() + rect.get_width() / 2, height),\n",
    "                    xytext=(offset[xpos]*3, 3),  # use 3 points offset\n",
    "                    textcoords=\"offset points\",  # in both directions\n",
    "                    ha=ha[xpos], va='bottom')\n",
    "\n",
    "\n",
    "autolabel(rects1)\n",
    "autolabel(rects2)\n",
    "autolabel(rects3)\n",
    "autolabel(rects4)\n",
    "\n",
    "fig.tight_layout()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0, 0, 'H2 [2]'),\n",
       " Text(0, 0, 'LiH [3]'),\n",
       " Text(0, 0, 'H2O [4]'),\n",
       " Text(0, 0, 'CH4 [4]')]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot same data as a line plot instead\n",
    "bk_qwc  = (0.001482,0.040986,0.187812,0.259468)\n",
    "bk_full = (0.001200,0.109233,9.416595,15.331529)\n",
    "nx_qwc  = (0.003326,0.251704,0.641773,1.589233)\n",
    "nx_full = (0.003340,0.167520,0.581299,1.007746)\n",
    "\n",
    "xaxis = np.array((1,2,3,4))\n",
    "\n",
    "colors = ['blue','orange','green','red']\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12,7))\n",
    "ax.scatter(xaxis,bk_qwc,c=colors[0],s=25)\n",
    "ax.plot(xaxis,bk_qwc,c=colors[0],lw=1,label='BK QWC')\n",
    "ax.scatter(xaxis,bk_full,c=colors[1],s=25)\n",
    "ax.plot(xaxis,bk_full,c=colors[1],lw=1,label='BK FULL')\n",
    "ax.scatter(xaxis,nx_qwc,c=colors[2],s=25)\n",
    "ax.plot(xaxis,nx_qwc,c=colors[2],lw=1,label='NX QWC')\n",
    "ax.scatter(xaxis,nx_full,c=colors[3],s=25)\n",
    "ax.plot(xaxis,nx_full,c=colors[3],lw=1,label='NX FULL')\n",
    "\n",
    "plt.legend()\n",
    "ax.set_ylim([0,2])\n",
    "ax.set_ylabel('Time for Max-Clique-Cover')\n",
    "ax.set_xlabel('Molecule [AS#]')\n",
    "ax.set_title('Bron-Kerbosch vs. NetworkX Runtimes')\n",
    "ax.set_xticks(xaxis)\n",
    "ax.set_xticklabels(('H2 [2]', 'LiH [3]', 'H2O [4]', 'CH4 [4]'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# I will generate this data later (will take ~60 minutes to complete).\n",
    "# Then we can compare average runtimes.\n",
    "results = []\n",
    "for file in Hfiles:\n",
    "    for comm_type, comm_str in zip([QWCCommutativity, FullCommutativity], ['QWC','FULL']):\n",
    "        ret, times = many_trials(file, comm_type, 100)\n",
    "        results += [(file,comm_str,ret,times)]\n",
    "\n",
    "print('\\n\\n-------------------')\n",
    "print('All trials finished')\n",
    "for r in results:\n",
    "    print(r[0],r[1],r[2],np.mean(r[3]))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}