Egan_two_qubit_errors.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Two qubit errors validated against Egan paper\n",
    "===============\n",
    "\n",
    "This is a simulation of two qubit errors in an ion trap quantum computer to compare a qiskit noise model with experiments by Egan [1].  The noise model will be used on our simulation of the Steane code.  Different numbers of consecutive RXX gates are set up and the ground state probability simulated is compared with that observed by Egan.\n",
    "\n",
    "Our simulation shows results broadly aligned with Egan.  For 16 gates we found a ground state probability of around 0.81(3) whilst Egan has a worst case of 0.78 and a best case of 0.87.\n",
    "\n",
    "[1] Egan L, Debroy DM, Noel C, Risinger A, Zhu D, Biswas D, et al. Fault-Tolerant Operation of a Quantum Error-Correction Code. arXiv Available from: http://arxiv.org/abs/2009.11482\n",
    "\n",
    "This is part of an MSc project on the Steane code.  Please see https://goldsmdn.github.io/ for full details."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import the necessary function modules."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import(\n",
    "  QuantumCircuit,\n",
    "  QuantumRegister,\n",
    "  ClassicalRegister,\n",
    "  execute,\n",
    "  Aer)\n",
    "\n",
    "from qiskit.providers.aer.noise import NoiseModel\n",
    "from qiskit.providers.aer.noise.errors import pauli_error, depolarizing_error\n",
    "from qiskit.visualization import plot_histogram\n",
    "\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from helper_functions import (get_noise, mean_of_list, calculate_standard_error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define constants so the process flow can be controlled from one place:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "SINGLE_GATE_SET = ['id', 'ry', 'rx']\n",
    "TWO_GATE_SET = ['rxx']\n",
    "BASIS_GATE_SET = SINGLE_GATE_SET + TWO_GATE_SET\n",
    "\n",
    "SHOTS = 10000                             #Number of shots to run \n",
    "ITERATIONS  = 4                           #Number of runs\n",
    "MEASURE_NOISE = 0.0046                    #Measurement noise \n",
    "SINGLE_GATE_DEPOLARISING = 0.0            #Single gate noise not relevant \n",
    "TWO_GATE_DEPOLARISING = 0.011             #Two gate noise\n",
    "NOISE = True                              #Test with noise\n",
    "GATE_DEPTH_REVERSE_LIST = [2, 4, 6, 8, 10, 12, 14, 16]               \n",
    "GATES_DEPTH_NO_REVERSE_LIST = [8, 16]\n",
    "GATE_DEPTH_CALCULATION = [0, 2, 4, 6, 8, 10, 12, 14, 16]  \n",
    "PI = math.pi\n",
    "\n",
    "SIMULATOR = Aer.get_backend('qasm_simulator')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Qubit 1 and Qubit 2 will each be unchanged with probability (1-p).  Both Qbit 1 and Qbit 2 will be unchanged with probability (1-p) ^ 2 which is close to 1-2p for small p.  When the qubits are changed then half the time this won't be detected by a projective measurement.  So the probability of the ground state after d gate is close to (1 - p) ^ d."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We simulate for both reversals and no reversals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Define lists used in simulations for graphs\n",
    "simulation_probability_reverse = []\n",
    "standard_error_reverse = []\n",
    "simulation_probability_no_reverse = []\n",
    "standard_error_no_reverse = []\n",
    "gate_depth_plot_reverse = []\n",
    "gate_depth_plot_no_reverse = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 2 gates with reversal simulated mean ground state population is 0.9649\n",
      "  The standard error is 0.0008\n",
      "For 4 gates with reversal simulated mean ground state population is 0.9447\n",
      "  The standard error is 0.0011\n",
      "For 6 gates with reversal simulated mean ground state population is 0.9230\n",
      "  The standard error is 0.0009\n",
      "For 8 gates with reversal simulated mean ground state population is 0.9008\n",
      "  The standard error is 0.0008\n",
      "For 10 gates with reversal simulated mean ground state population is 0.8844\n",
      "  The standard error is 0.0022\n",
      "For 12 gates with reversal simulated mean ground state population is 0.8537\n",
      "  The standard error is 0.0015\n",
      "For 14 gates with reversal simulated mean ground state population is 0.8386\n",
      "  The standard error is 0.0015\n",
      "For 16 gates with reversal simulated mean ground state population is 0.8153\n",
      "  The standard error is 0.0027\n",
      "For 8 gates with no reversal simulated mean ground state population is 0.8930. \n",
      "  The standard error is 0.0008\n",
      "For 16 gates with no reversal simulated mean ground state population is 0.7964. \n",
      "  The standard error is 0.0012\n"
     ]
    }
   ],
   "source": [
    "for reverse in [True, False]:\n",
    "    probability_list = []\n",
    "    if reverse:\n",
    "        gate_depth_list = GATE_DEPTH_REVERSE_LIST\n",
    "    else:\n",
    "        gate_depth_list = GATES_DEPTH_NO_REVERSE_LIST\n",
    "    for gate_depth in gate_depth_list:\n",
    "        probability_list = []\n",
    "        for iteration in range(ITERATIONS):\n",
    "            qr = QuantumRegister(2,'code_qubit')     # Two qubits\n",
    "            cr = ClassicalRegister(2,'syndrome_bit') # two Syndrome bit\n",
    "            qc = QuantumCircuit(qr,cr)\n",
    "            qc.reset(qr[0])\n",
    "            qc.reset(qr[1])\n",
    "            for i in range(gate_depth):\n",
    "                #if reversals apply XX gate if gate number is odd or inverse otherwise\n",
    "                if i % 2 == 0:\n",
    "                    qc.rxx(PI/4,qr[0],qr[1])\n",
    "                else:\n",
    "                    if reverse:\n",
    "                        qc.rxx(-PI/4,qr[0],qr[1])\n",
    "                    else:\n",
    "                        qc.rxx(PI/4,qr[0],qr[1])\n",
    "\n",
    "            qc.measure(qr, cr)\n",
    "            noise_model = get_noise(MEASURE_NOISE, SINGLE_GATE_DEPOLARISING, TWO_GATE_DEPOLARISING,\n",
    "                                    SINGLE_GATE_SET, TWO_GATE_SET)\n",
    "            if NOISE:\n",
    "                result = execute(qc, SIMULATOR, noise_model=noise_model, shots=SHOTS).result()\n",
    "            else:\n",
    "                result = execute(qc, SIMULATOR, shots=SHOTS).result()     \n",
    "            counts = result.get_counts(qc)\n",
    "            probability = counts.get('00') / SHOTS\n",
    "            probability_list.append(probability)\n",
    "        mean = mean_of_list(probability_list)  \n",
    "        standard_deviation, standard_error = calculate_standard_error(probability_list)\n",
    "        if reverse:\n",
    "            simulation_probability_reverse.append(mean)\n",
    "            standard_error_reverse.append(standard_error)\n",
    "            gate_depth_plot_reverse.append(gate_depth)\n",
    "            print(f'For {gate_depth} gates with reversal simulated mean ground state population is {probability:.4f}')\n",
    "        else:\n",
    "            simulation_probability_no_reverse.append(mean)\n",
    "            standard_error_no_reverse.append(standard_error)\n",
    "            gate_depth_plot_no_reverse.append(gate_depth)\n",
    "            print(f'For {gate_depth} gates with no reversal simulated mean ground state population is {probability:.4f}. ')   \n",
    "        print(f'  The standard error is {standard_error:.4f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set up Egan's best fit lines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 0 gates\n",
      "Egan  echoed best fit line is 0.9954\n",
      "Egan cumulative best fit line is 0.9954\n",
      "Calculation based on depolarising noise is 0.9954\n",
      "For 2 gates\n",
      "Egan  echoed best fit line is 0.9814\n",
      "Egan cumulative best fit line is 0.9654\n",
      "Calculation based on depolarising noise is 0.9736\n",
      "For 4 gates\n",
      "Egan  echoed best fit line is 0.9674\n",
      "Egan cumulative best fit line is 0.9354\n",
      "Calculation based on depolarising noise is 0.9523\n",
      "For 6 gates\n",
      "Egan  echoed best fit line is 0.9534\n",
      "Egan cumulative best fit line is 0.9054\n",
      "Calculation based on depolarising noise is 0.9315\n",
      "For 8 gates\n",
      "Egan  echoed best fit line is 0.9394\n",
      "Egan cumulative best fit line is 0.8754\n",
      "Calculation based on depolarising noise is 0.9111\n",
      "For 10 gates\n",
      "Egan  echoed best fit line is 0.9254\n",
      "Egan cumulative best fit line is 0.8454\n",
      "Calculation based on depolarising noise is 0.8912\n",
      "For 12 gates\n",
      "Egan  echoed best fit line is 0.9114\n",
      "Egan cumulative best fit line is 0.8154\n",
      "Calculation based on depolarising noise is 0.8717\n",
      "For 14 gates\n",
      "Egan  echoed best fit line is 0.8974\n",
      "Egan cumulative best fit line is 0.7854\n",
      "Calculation based on depolarising noise is 0.8526\n",
      "For 16 gates\n",
      "Egan  echoed best fit line is 0.8834\n",
      "Egan cumulative best fit line is 0.7554\n",
      "Calculation based on depolarising noise is 0.8339\n"
     ]
    }
   ],
   "source": [
    "echoed_calculation = []\n",
    "cumulative_calculation = []\n",
    "theory_calculation = []\n",
    "expected = (1 - TWO_GATE_DEPOLARISING)** gate_depth * (1 - MEASURE_NOISE)\n",
    "for gate_depth in GATE_DEPTH_CALCULATION:\n",
    "    echoed = (1 - MEASURE_NOISE) -  gate_depth * 0.007\n",
    "    cumulative = (1 - MEASURE_NOISE) - gate_depth * 0.015\n",
    "    theory = (1 - TWO_GATE_DEPOLARISING)** gate_depth * (1 - MEASURE_NOISE)\n",
    "    echoed_calculation.append(echoed)\n",
    "    cumulative_calculation.append(cumulative)\n",
    "    theory_calculation.append(theory)\n",
    "    print(f'For {gate_depth} gates')\n",
    "    print(f'Egan  echoed best fit line is {echoed:.4f}')\n",
    "    print(f'Egan cumulative best fit line is {cumulative:.4f}')\n",
    "    print(f'Calculation based on depolarising noise is {theory:.4f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 1345.49x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.draw(output='mpl', filename = 'Egan_two_qubit_circuit.jpg', fold=60)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6NH47d5I6ZAhnHnsMR0gIVttp01F8ajiKakOMMYqABm7LycrK4rfffiM6OppVq1aRmJhIYGAgN954I1FRUQwcOJCwsLASPTaNRlO+0Q6iBBCbDdvjj+O3YAH26tWJmzePjGuvBTAcRexbhJz+FCU5pFYbTGKdu/N1FAA5OTls3ryZ6Ojo82Itevfu7Yy1iIiIKKGj02g05RXtIEqQnI0bkbFj8T1wgOTRozn74INIpUoAWG1xhMW+6XQUadUGkVjnHrILcBQADoeDnTt3XhBr0a1bN2esRf369Uvg6DQaTXlDO4gSRtLTsc2ahf9rr2Fr0IC4BQvIatfOmW61xRuOIu5TlMNmOIra95Ad2PDiZYu4jbVo3749w4YNY9iwYTrWQqPRFBrtILxEdnQ0auJErLGxJE2aRMK0aeAyO8lwFG8REveJ4Siq3my0KAIbFboOHWuh0WguB+0gvIgkJ2O75x78P/6YrObNiVu4EFvTpuflsWafIezkW4TEfWw6ioGmo2hcpLp0rIVGoykq2kGUArK/+grLpElYUlJImDmTpNtvhzwPa2v2GcJi3ybk9McoR6bZorib7MAri1yfjrXQaDSFQTuIUoLExWGbOBH/778no0MH4ubPJ8fN4LI1+yyhsW8TevojlCOTc1VuJLH2PdgqX9rYQn6xFgMHDnTGWlQyB9I1Gk3FQjuI0oQItsWL8ZkxA+x2zs6eTcrIkeBmnMCSfZawU+8ReupDLI5znAvrQ2Kde8gKirzk6rOysvj111+dsRZJSUk61kKjqcBoB1EKcfzzDzljx+K3di3p3bsT98wz2PNZQ8KSk0zoqfcJPbUYqz2F9NDrSKwzlczgDpdlg4610Gg02kGUVkTIeuEFfB95BPH358wTT5A2cGC+2VVOKqFxHxMW+w7WnEQyQjqTWPseMkI6u22BFAWHw8GOHTucsRb//POPjrXQaCoA2kGUcux//mlIdWzdSlr//sQ/8QSO8PB88yt7OiFxnxIW+zY+2fFkBLUnsc49ZIR2v2xHAUasxf79+1mxYgUrV67UsRYaTTlGO4iyQE4OWU89hd8zz2APC+Ptzp3Zm2cluhkzZpz3WzmyCI77nLDYN/G1xZJZuTWJte8mPfz6YnEUuRw5coSVK1cSHR19QazFLbfcQrt27XSshUZTRtEOogyRs3UrMno0vn/+yZvA/UCamXbgwAH3OzlsBJ/5mvCTi/DNOkZWpWYk1r6bc1VuBFW8cQ+nTp0iOjqalStXsmnTJux2O1dccQVDhw7VsRYaTRlEO4gyhmRmsrZnT7pv2kRCcDAfX389B+vUuaAFceGOOQSd+Y7wk6/jl3kIW0BjEutMIa3qQFA+xW5nQkKCM9Ziw4YNOtZCoymDaAdRRslZtw4ZOxaff/4h+fbbSbj3XsTf/+I7ip3KCT8RfuJV/DP+Itv/ChJrTya12hCweOaBnRtrsWLFCtasWUN6erqOtdBoygDaQZRhJDWVrJkzCXj3XWxNmnB6wQJsrVoVcmcHlRJ/psqJV/BP30O2X22Sak8itfotiKUQjuYSycrKYsOGDURHR/Pzzz87Yy369etHVFQUAwYM0LEWGk0pQTuIckD28uWoO+7AevYsiVOnkjh5MvgUsttIhErJawk/8QoBaTHk+EaQVOsOUmqMQKyBHrXbXayFr68vvXr10rEWGk0pQDuIcoIkJGC76y78v/ySzDZtiFuwgOxGhVd+RYTAlI2En3iFwNRN2H2qkFTrdpIjRiHWIM8ZbqJjLTSa0od2EOUM28cfY502DZWeTsKDD5I8ZgxYLEUqIyBlM+EnX6VS8gbsPmEk1xxPcsRYHD4hHrL6fFxjLaKjo9m/fz/wv1iLqKgomjVrViK2aDQVGe0gyiGOkyfJnjAB/+ho0rt0If6558ipXbvI5fin7SD8xKtUTvoFuzWIlIixJNUcj8O3igeszp8jR444u6FiYmIAaNasmdNZ6FgLjcYzaAdRXhHBtmgRPrNmIUpx9rHHSB069JKC5PzO7SX8xKsEJa7AYalESsRtJNW8HbtfdQ8YXjCnTp1yBua5xlrkOosuXbroWAuNppjQDqKc4zh4kJzRo/H7/XfOXX898U8/jb1q1Usqyzf9L8JPLiLo7HJE+ZJSYwRJte/E7udeSNDTuIu1qFGjBoMHD9axFhpNMaAdREXA4SDruefwnTMHCQoi/qmnOHfDDZdcnG/mEcJOLiL4zDeAIqX6LSTVnkSOf91iM7mopKamsm7dOh1rodEUI9pBVCDsu3ZhHzUKv127SB06lDOPPooj5NIHnn2yjhN28g1C4pcCQmq1ISTVnkx2QINis/lSyMzMdK5roWMtNJpLx2sOQinVD3gRsAJvi8i8POn1gXeB6kACMFpEjptpdmCXmfUfERlUUF3aQfwPsdmwPfYYfgsXYq9enbjnniOjW7fLKtOaFWsshxr3GUqySas6gKTak7FVanrxnT1Mdnb2ebEWcXFx+Pr6nreuRY0aNbxtpkZTKvGKg1BKWYG/gL7AcWAzMFJE9rrk+QJYLiLvK6V6AxNEZIyZliYihZ6crx3EheRs3IiMGYPvwYMkjR1LwqxZSODlBcZZs88QGvsOoac/MVe5601i7SlkBbcrJqsvD4fDQUxMDCtXrjwv1uLaa69l2LBhOtZCo8mDtxxEF2COiNxo/n4YQESedcmzB+gnIseUMYcxWURCzDTtIIoBSU/Hdv/9+C9ahK1hQ+IWLCCrbdvLLteSk0ToqQ8JPf0+1pwkc/GiKWSEdC1WqfHLQcdaaDQXx1sO4haMh/8d5u8xwDUiMtUlzyfAHyLyolJqGPAlUE1EziqlcoAYIAeYJyLfuKnjLuAugCuuuKLD0aNHPXIs5YHs6GjUxIlYY2NJmjyZhKlToRhm/yj7OULiPiMs9h18suPIrBxJUu3JnAu/HlTRgvc8jY610GgupDQ7iNrAK0BDYB0QBbQSkSSlVB0ROaGUagT8AvQRkYP51adbEBdHkpKw3XMP/p98Qlbz5sT95z/YrrqqeAp3ZJlrUryBb9YxbIFXklhrEmnVbvaI1PjlEhsbe16shcPh0LEWmgpJqe1iypM/CPhTRC6YR6mUWowxVrE0v/q0gyg82V9+iWXyZCwpKSTcey9JEydCcT0MJYegsz8QdnKRKTVel6Rad3pcQfZy0LEWmoqMtxyED8YgdR/gBMYg9W0issclTzUgQUQcSqmnAbuIPKaUCgfSRSTLzLMRGOw6wJ0X7SCKhsTFYZs4Ef/vvyejY0fi5s8n54orirECB5WSVhN+4jUCzu0gx7c6yTUnkhwxskSEAS8VHWuhqWh4c5prf+AFjGmu74rI00qpucAWEVlmdkM9CwhGF9M9plPoCrwBOAAL8IKIvFNQXdpBXAIi2N57D5+ZM8Fu58wjj5A6fHjxDjKLEJDyO+EnF1Ep5Vfs1lCSa44hOWIcDt/w4qvHA+hYC01FQAfKaQrEcfQoOWPH4rduHed69CD+mWew57NGw4svvnjBtosuhWrin7aDsJOLCEpcaeg91RhBUq2JXpPxKAo61kJTXtEOQnNxHA6yXngB33//G/H3J37uXM4NGHBBtiuvvPKCbQcOHChSVYbe0xsEnV0OykJK9SiSat1JTkDZiE9wF2thsVjOW9fiiuLsrtNoPIh2EJpCY9+3D/uYMfht3UrqgAGcmTMHR/j/uoIupwWRF5/Mf4zo7PgvQOykVR1IUu1JpSI6u7DkF2vRoUMHhg0bxrBhw3SshaZUox2Epmjk5JD15JP4Pfss9vBw4p99lvQePTxWndUWR9ipdwk5/QkWR3qpi84uCjrWQlPW0A5Cc0nkbNmCjB6N7/79JI8YwdmHH0YqV/ZYfUZ09geEnv6g1EZnF4XcWIsVK1awefNmHWuhKZVoB6G5ZCQzE9vs2fi99BI5desSt2ABmR3d3kvFhrvo7MTaU0gP71PqorMLS0JCAj///DPR0dH8+uuvzliLIUOGEBUVRc+ePXWshcYraAehuWxy1qyBceOwHjtG8u23k3DvvYi/ZwPflCOLoLzR2bUnk1Z1YKmMzi4sqamprF27lujoaGesRVhYmDPW4oYbbtCxFpoSQzsITbEgqanYZszA/733sDVpwumFC7G1bFkCFRvR2eEnX8cv42+y/euZ0dlRpTY6u7C4xlqsWrWK5ORkKlWqdF6sRWhoqLfN1JRjtIPQFCvZ332HuuMOrAkJJEybRtKkSeBTAm/04qBS0i+En3jdGZ2dVOt2UmqMKNXR2YVFx1povIF2EJpiR86exXbXXfh/9RWZbdoQt2AB2Y0alVDlQmDK74SdfJ1KKb+VqejswpIba5HrLHSshcZTaAeh8Ri2jz7COm0aKjOTsw8+SMro0WApuYFk/7QYwk8uonLiKjM6ezhJNSdg969dYjZ4GhHhzz//ZMWKFaxcufKCWIuoqCiaNi07sSOa0oV2EBqP4jhxguzx4/FftYr0rl2JmzcPe+2SfUD7pf9lyHic/R6UIrXqYJJq30l24IWR32Udd7EWzZs3dzqLtm3b6lgLTaHRDkLjeUSwvfYaPg89hCjF2cceI3Xo0BKPX/DJOk5Y7DsEx3+BxZHJubA+JNaeRFZw+xK1o6Rwt65F/fr1z4u1sJRgi05T9tAOQlNi2P/+25Dq+OMP0vr25cxTT2GvWrXE7bBknyX09IeEnv7ICLoL7kRSrbtID+tZJoPuCoO7WIuIiIjzYi18fX29baamlKEdhKZksdvJeu45/J54AkdQEHFPP016375eMcUIuvuc0FPv4muLJSvwKpJq3WnEUljK78Myv1iLm2++mWHDhulYC40T7SA0XsG+cyf2UaPw272blGHDOPvooziCg71jjCOboLPLCY9904il8KtNcq3bSal+K2It3w9KHWuhKQjtIDReQ7KysD32GH7/+Q85NWoQ/9xzZHTt6kWDjJXuwk6+SWDaVuw+4SRHjCY5YgwO3yres6uEyC/Wok+fPs5Yi+rVq3vbTE0Joh2Exuvk/PYbMnYsvgcPkjRuHAkPPIAEBnrVpoDUrYSdfIPKSb/gsASSUv1fJNeaSI5/Ha/aVVLkF2tx7bXXOmMt6tWr520zNR5GOwhNqUDOncP2wAP4L1qErWFD4hYsIKttW2+bZUyRjX2LoLPfgQhp1W4mqdZd2Cpd5W3TSgzXWIvo6Gj++usvADp27OicEXXVVRXnfFQktIPQlCqyV6xATZyI9dQpEqdMIfGee+AylUyLYyEjn6yThJ56l5C4JVgcGZwL60VS7UlkBntWvbY0cvjwYWfLYseOHQC0aNHCuQiSjrUoP2gHoSl1SFIStilT8P/sM7JatCBu4UJsl/GGWhxLoeZiyU4k9PRH5roUiWQEtSep9l2kh/Uus3Ljl4OOtSjfaAehKbVkf/EFlilTsKSmknDvvSRNnAiXsIhOcS6FmouyZxAc/wVhse/gazuBLfBKkmrdRWrVgWCpmGs3nD17ll9++UXHWpQjtIPQlGrk9Glst9+O//ffk9GxI3Hz55NTmoToHNkEJfxA2Mk38c/YT45fTZJqTiSlxnDE6rkV9ko7BcVa5K5rEejliQiai6MdhKb0I4LtnXfwue8+sNs588gjpA4fXrqinkWolLyOsJOLCEzd7KIiOwaHb8lHi5cmMjMz2bBhA9HR0fz888/OWIubbrrJGWsREhLibTM1btAOQlNmcBw5Qs7YsfitX8+5Hj2If+YZ7BER3jbrAvxTtxMW+yZBiStxWAJIrX4LSTVvJydATwvNzs5m06ZNzkHu+Ph4/Pz8nLEWgwYN0rEWpQjtIDRlC4eDrP/+F99HH0X8/YmfO5dzAwZ42yq3+GYcICz2bYLPfAviIK3qAJJq3YmtcnNvm1YqyI21yJ0+e+zYMR1rUcrQDkJTJrHv3Yt99Gj8tm8ndeBAzsyZgyMszNtmucWaFUvYqcWExH2GxXGO9NDuJNaeRGbw1aWrm8yLiAj79u0jOjqaFStW8PfffwM61sLbaAehKbvk5JA1dy5+zz6LvUoV4p99lvQePbxtVb5YcpIJOf0xYacWY81JILNyG5JqT+Jc+PUVcopsQRw6dIjo6GhWrlx5QaxFVFQUbdq00bEWJYB2EJoyT87mzciYMfju30/yiBGcffhhpHLpnUGkHJkEx39JWOzb+GYdwxbQkKRat5NWbShi8fe2eaWOkydPsmrVKlasWMHmzZtxOBw0aNDA6Sw6d+6sYy08hHYQmnKBZGRgmz0bv5dfJqduXeIWLCCzYymPcpYcghJ+IuzkW/in7yHHpyrJNceSUuO2crN+dnFz9uzZ89a1yM7O1rEWHkQ7CE25Imf1ahg3Duvx4yTdcQeJM2ci/qX8rVyEgJTfCYt9m8rJa3FYAs2ZTxPICShFMR+ljNTUVNasWeOMtcjIyNCxFsWMdhCacoekpGCbPh3/99/H1qQJpxcuxNaypbfNKhR+6X8RGvsOwWeXgdg5V+VGkmrdSVZQpLdNK9VkZmayfv16Z6xFSkqKjrUoBrSD0JRbsr/9FnXXXVgTEkiYNo2kSZPAx8fbZhUKq+0Uoac+ICTuU6z2VHNZ1DvNZVF1f3tBZGdn88cffzgHuXWsxaWjHYSmXCNnzmC78078v/mGzDZtiFuwgOxGjbxtVqFROamExH9O6KnF+NpisQU0JqnWHaRWGwR6QPuiuMZarFixguPHj+tYiyKgHYSmQmD74AOs06ejsrI4++CDpIweDWVp5kuu5lPs2/in7yPHtzrJEWNJibgNh49eErQw6FiLouM1B6GU6ge8CFiBt0VkXp70+sC7QHUgARgtIsfNtHHA/5lZnxKR9wuqSzsIDYDj+HGyx4/H/+efSe/albh587DXru1ts4qGCIEpvxIW+zaVkjfgsFQipca/SK45ocKsdldc5MZaREdHs3PnTkDHWuTFKw5CKWUF/gL6AseBzcBIEdnrkucLYLmIvK+U6g1MEJExSqkqwBagIyDAVqCDiCTmV592EBonImS9+iq+Dz2EWCycefxx0oYMKZMRzX7n9hF26h2Czi43Vrur2p+kWrdjq9zK26aVOU6ePOlc10LHWvwPbzmILsAcEbnR/P0wgIg865JnD9BPRI4pw40ni0iIUmok0FNEJpn53gDWiMin+dWnHYQmL/a//sI+Zgx+mzaRdsMNxD/5JI6qJau6WlzrVFizThJ26v3/SXmEdCGp1h1khHYvk47P2+QXazF06FCioqLo0aNHhYm1KMhBeNJd1gGOufw+bm5zZQcwzPw+FAhWSlUt5L4ope5SSm1RSm2Jj48vNsM15QPrVVfh99tvZD35JJXXrOGKm26i0sqV3jbrkrD71+Zs/Yc52m4DZ+s9hF/GIWrvv526uwYQHP8VOGzeNrFMUbVqVf71r3/x9ttvs2nTJp5//nnat2/P+++/T9++falRowZjx47l22+/JSMjw9vmeg1PtiBuwWgd3GH+HgNcIyJTXfLUBl4BGgLrgCigFXAHECAiT5n5HgUyRGRhfvXpFoSmIHJiYpDRo/Hds4eUYcM4++ijOIKDvW3WpeOwEXx2OaGxb+Of8Rc5vhEk1xxHSo2ROHzK8HF5GXexFpUrV6Zfv37lNtai1HYx5ckfBPwpInV1F5PGE0hWFrZHH8XvP/8hJyKC+PnzyejSxdtmXR4iBCavIyz2HSql/IbDUpmUGiNIqjkOu38ZG5wvZVSUWAtvOQgfjEHqPsAJjEHq20Rkj0ueakCCiDiUUk8DdhF5zByk3gq0N7NuwxikTsivPu0gNIUlZ8MGZOxYfA8fJmncOBIeeAApB3INfud2Exb7DkFnfwClSKsygKRad+i1KYoBh8PB9u3bndNnc2MtrrvuOqKiohgyZEiZjbXw5jTX/sALGNNc3xWRp5VSc4EtIrLM7IZ6FmOm0jrgHhHJMvedCDxiFvW0iLxXUF3aQWiKgpw7h+2++/B/801sjRoRt2ABWW3aeNusYsEn6wShp94jJO5zLI500kO6kVT7TjJCuukB7WJARNi7dy8rV648L9aiU6dOzkHushRroQPlNJp8yP7pJ9TEiVjj4kicMoXEu+8GPz9vm1UsGGtTfELo6Q/wyY4nq1JzQ3K8ygCwVIwZOiVBWY+10A5CoykASUzENmUK/kuWkNWiBacXLiS7DL0BXhRHFsFnlhEW+zZ+mQfJ9qtFcs3xpFT/F6IHtIuVshhrcdkOQik1DfiooEA1b6MdhOZyyf78cyx3341KTSXhvvtInjABrNbLKjPcTRxE4iXEQRQL4qBS0lrCYt8iMHUTdmswKTVGkBwxFrt/Le/YVI45e/Ysq1atIjo6mt9++43s7Gxq1qzpXNeitMRaFIeDeAoYgTFY/C6wQkpZ00M7CE1x4Dh1iuwJE/D/6ScyOnUibv58ci5j8LHxlVdesO3ggQOXY2Kx4J+201ibIuEnUBbSqvQnqdZEHaHtIVJTU1m9ejXR0dGsXbvWua7FoEGDiIqKom/fvl5b16JYupjMSOcbgAkYEhifA++IyMHiMvRy0A5CU2yIYHv7bXzuvx8cDs48/DCpw4df0gBvqWpBuMEn67gpOb4Ei+OcITlecyLp4b1BXV7rSeOejIwMNmzYcEGsxU033cSwYcNKPNai2MYglFJtMBxEP2A10BlYKSIPFoehl4N2EJrixnHkCNljxuC/YQPnevYk/plnsNeo4W2zPIIhOf4Foafex9d2Apt/fZJrjie1ehRireRt88otrrEW0dHRnDlzpsRjLYqji2kGMBY4A7wNfCMi2UopC/C3iDQuToMvBe0gNB7B4SDrP//B99FHkcBA4p94gnMDBnjbKs8hOVROWEFY7LsEnNuB3RpKSsRIkiPGYPeL8LZ15Rq73U5MTEyJx1oUh4N4AiOO4aibtOYisu/yzbw8tIPQeBL7nj3YR4/GLyaG1Jtv5szjj+MIC/O2WZ5DBP+07YTFvkPlxJWgrKRVHUBSzYnYKrfwtnXlntxYi9yWhWusRe6MqCZNmhRLXcXhID4UkTEX2+ZNtIPQeJycHLLmzMHvueewV61K3DPPkNGjh7et8jg+mf8QevoDQuK+MMYpQjob4xR6adQS4+DBg05nsWvXLgBatmzpdBaRkZGXHGtRHA5im4i0d/ltBXaJSKl5ldAOQlNS5GzahIwZg+9ff5E8ciRnZ89GKlf2tlkex5KTQnD854SdWoyP7RS2gIYk15xAarWhiLXsS5WUFU6ePOl0Flu2bMHhcNClSxd+++23Syrvkh2EKbD3CBAIpOduBmzAmyLy8CVZ5AG0g9CUJJKRge3BB/F79VVy6tYlbuFCMjt08LZZJYMjm6CEnwg99Q4B53Zj9wknucZtpESMxu5X9sXryhK5sRY5OTk8+uijl9SKKI4WxLOlyRm4QzsIjTfI+eUXGD8e6/HjJN15JwkzZoC/v7fNKhlECEjdQuipd6mcuAqUD6lVB5FcawK2Ss28bV2Fo2HDhpcUpX05LYhmIvKnUqq9u3QR2VZkazyEdhAabyEpKdimTcP/gw/IatqUuAULsLUoNb2vbimule5y8ck8Qtip9wmOX4rFkUF6SDeSa00kPfQ6PU5RQnjDQbwlIncqpVa7SRYR6V1kazyEdhAab5P9zTeou+7CmpREwrRpJN11F/j4eNsst1zpJsL7QDFEeFtykgiJ+4zQUx/ik30aW0BjkmpNJK3aYMQScNnla/KnxB1EWUI7CE1pQM6cwXbHHfh/+y2ZbdsSt3Ah2Q0aeNusC/CUg3DisBGU8ANhse/in74Xu08VkiNGGeMUviW7LnhFwRstiGH5JgIi8lWRrfEQ2kFoShO2Dz7AOn06KiuLsw89RMqoUVCKVDw97iByESEg9Q/CYt+lctIvOJQfadUGk1RzAtmVypFibinAEw7iYu3fmwtIE6DUOAiNpjThN3Ysjl69yB43jupPPEHlVauIe/ZZ7LVLxzKg06ZNK5mKlCIzpDOnQjrjm3GI0FOLCT7zFSHxX5Aeeh1JNSeSEXqtXsiolKK7mDQaTyKC7ZVX8Jk9G7FaOfPYY6QNGVKhH4iW7ERC4j4l9PSHxkJGgVeRXGsiqVVvBksFmQHmATzRgihUaUqpCKXUO0qpH83fLZRStxfZEo2moqEUftOmIdu3Y2/WjIhZs4iYOhXL2bPetsxrOHzDSapzN0fbriGu0XxQFmocmk39mB6En3gFS3bFPTeljcK6m8XACiC3ffwXMNMD9mg05RLrVVfht3EjWXPnUnn1aur170+lVau8bZZ3sfiTWn0Yx1t9x8lmH5BVuRVVjr9A/e3dqX7o3/im/+VtCys8hXUQ1UTkc8ABICI5gN1jVmk05RGrFf9HH8X+++9IRAS1Jk+m+uzZqNRUb1vmXZQiI7Qrp5q+zT+RP5FWbQhBZ77hil39qbVvHJUSV4M4vG1lhaSwDuKcUqoqxsA0SqnOQLLHrNJoyjE+7drhs20bWfffT/BXX1FvwAACNm70tlmlguzAK4lv9DRH263nbN378cs4QK2/7qTezhsIOfUByn7O2yZWKAortdEeeBloBewGqgO3iMhOz5pXePQgtaYskrNhAzJ2LL6HD5M0fjwJDzyABOiAMieObIISVxAa+565PkUwqdVvJTliDDkBxb82QlnGq4FySikfoCmGWN9+EckusiUeRDsITVlF0tKw3Xcf/m+9ha1xY+IWLCArMtLbZpU6/FO3E3r6fYISfgJxcC68L8k1x5EZ3KlCzwrLRQfKFYB2EJqyTvYPP6Buvx1rfDyJU6aQeM894OvrbbNKHdasWELjPiYk7jOsOUlkVWpBUs0JpFXtX6GnyXrDQbxnfq0BdAV+MX/3An4TkYFFtsZDaAehKQ9IYiK2yZPx//xzslq25PTChWQX08ph5Q1lzyDo7LeEnVqMX8YBcnyrkVLjNlIibsPuW83b5pU4JR4HISITRGQC4Au0EJEoEYkCWprbNBpNMaLCw/FfsoTszz7DJzaWuoMHE/rOO+DQs3jyItZAUmuM4FjrHznZbDFZlVtT5cRL1N9+HdUPPojfuT3eNrHMU1h3U09EYl1+nwau8IA9Go0G8B0+HLV7N9m9e1Pt2WepPXo0PsePe9us0olSZIRey6mmb/FP5EpSagwnKOEn6u0eTO29I6mcEA2iZ+VfCoV1ED8rpVYopcYrpcYD3wMVPMpHo/Esllq18P/hB2xvvIH/3r3UGzCA4M8/h3Iij+MJsgMbcqbBHI6228CZK2bjk3WSmn/fzRU7+hAa+w6WnAoec1JEijKLaRhwnflznYh87TGrLgE9BqEpzzgOHyZnzBj8fv2Vc716Ef/MM9ir6+U9L4rkUDnxZ0JPLSYwdTMOS2VSqw8jueY4sgMaeNu6YkWvB1EA2kFoyj0OB1kLF+L72GNIpUrEz53LuZtu8rZVZQa/c7sJO/U+QWeXg+SQHtaT5JrjyQjpWi6myXpjFtMGEblWKZWKGUWdm4SxolxIka3xENpBaCoK9j17sI8ahd+OHaQOGsSZxx/HERrqbbOKheJeCtUdVls8IXGfEHL6E3xyzmILbEJSzXGkVRtSple984aDqC8iR4tcoxfQDkJTocjOJmvOHPzmz8detSpxzz5LRvfu3rbqsimxhYwAHFkEn/2e0FPv4Z++D7tPOCk1RpAcMQq7X03P1OlBvOEgtolIe/P7l+YU11KJdhCaikjOH38YUh1//UXybbdxdvZspFIlb5t1yZREC+ICRAhI3UzoqcVUTlwJykpalZtIrjmOrKC2nq27GPGGg9guIu3yfi+NaAehqahIRga2Bx/E79VXyalXj9MLF5LVvr23zSqT+GQeI/T0hwTHf47VnkZmUFuSak7gXPgNYCndoV/eWDBI8vmu0WhKCSowEP+XX8a+ciVKhDojRlBl/nzIyvK2aWWOnIB6nK3/CEfbbSC+/mNYshOpeWAG9WN6EnZyEZbsRG+bWKJczEG0UUqlmIPUkeb3FKVUqlIq5WKFK6X6KaX2K6UOKKVmu0m/Qim1Wim1XSm1UynV39zeQCmVoZSKMT+LLu3wNJqKg0+fPlh37yZr1CjC33yTusOG4bdvn7fNKpOINYiUmmM51mYlsVe9iS3wSqoeW0j97ddS/dDD+J2rGOfVY9NclVJWjJXn+gLHgc3ASBHZ65LnTWC7iLyulGoB/CAiDZRSDYDlItKqsPXpLiaN5n9kf/MNljvvxJKcTML06STdeSf4+HjbrDKNX/pfhJz+gOAz32BxZJIR3InkiDGcq3IDKO+fW6+tSX2JXA0cEJFDImIDPgMG58kjQO5U2VDgpAft0WgqDL5DhmDZuxdbv35U/c9/qDNyJL5HjnjbrDKNrdJVnGn4FEfb/WpEadtOUfPAdKP76cRr5XItbU86iDrAMZffx81trswBRiuljgM/ANNc0hqaXU9rlVLX4Qal1F1KqS1KqS3x8fHFaLpGU/ZR1avj/+232N57D9+DB6l7882EfPSRluq4TBw+oSTXuoN/2qwi9qpF2AIaU/X4f11EAnd728Riw5MOojCMBBaLSF2gP/ChUsoCxAJXmLOm7gM+UUpdEJQnIm+KSEcR6Vhdyw5oNBeiFH7jxxvCf507U33OHGqNH481Nvbi+2oKRllJD7+e2Obv80/kT6RWv9UUCRxCnT23GhHbjlK1rlqR8aSDOAG4rglY19zmyu3A5wAishEIAKqJSJaInDW3bwUOAld50FaNplxjqVcP/59/xvbiiwRs20a9/v0J+vZb3ZooJrIDr+RMwyeM7qf6/4clO4GIAzOpH9OD8OMvY7WVzR4OTzqIzUATpVRDpZQfMAJYlifPP0AfAKVUcwwHEa+Uqm4OcqOUagQ0AQ550FaNpvyjFH7TpyPbt2Nv1oyI++8nYupULAkJ3ras3ODwCSa55nhj9lPTt7FVakaVEy9SP6Y7NQ7ch39ajLdNLBIeG3oXkRyl1FRgBWAF3hWRPUqpucAWEVkG3A+8pZS6F2PAeryIiFKqOzBXKZUNOIDJIlLkuzg7O5vjx4+TmZlZbMel0ZQLFi9GkpNRyclIYiIOERwB3tEhUkphsVjw8/O7pFk4pRJlIT2sJ+lhPfHNOEzI6Y8IiV9K8NllZFZuQ3LNMaRVuanUL5FartVcDx8+THBwMFWrVkWVA7VGjaa4kXPnkMOHsWRmYg8PJ6dWLaSEH9IiQlJSEgkJCQR4yUmVBMqeRnD814Se/hC/zEPk+FQlJWIkKTVGYveLuOzyy9o0V6+TmZmpnYNGUwCqcmVUixY4IiKwJCbi+/ffWM6dK1kblCIsLAxHOV9W1Qi+G8OxyJ842fQ9soIiCT/xKvVjelDj7xn4p24rdWNC3o/u8DDaOWg0BaMsFlS9ekhYGBw+jN/hw+RUq4Y9IgIpof8fpRTlpTfjoigLGWHXkRF2HT6ZRwk9/THB8V8QnPA9WZVaklxzLGlVByKloPupXLcgNBpN4VHBwaiWLXFUq4bPmTP4HjiAJSPD22aVa3IC6v9P+6nBXJRkUePQQ9Tffi1Vji3EmuXd2GHtIDyM1Wqlbdu2zs+8efM8Wl+DBg04c+bMZZVx5MgRPvnkk3zTZ82aRcuWLZk1axaLFi3igw8+AGDx4sWcPOn+hh4/fjxLly4F4I477mDv3r1u8xWVkSNHEhkZyfPPP18s5ZU0a9asYeDAgSVap+u1yIuyWrE0aICjSROUw4HvwYP4xMWVuq6PkubFF1+84FOciLUyKRG3caz1j5xs9iEZwR0JO/km9WN6EfHXPQSkbPLKNSj3XUzeJjAwkJiYGG+bUSRyHcRtt93mNv3NN98kISEBq9V63vbFixfTqlUrateuXWD5b7/9drHYeerUKTZv3lykBWVycnLw8aImkbfrLyyW0FCkZUvk6FF84uKwpKaSXbcu4u/9bg9v8PLLL1+wzSPrVChFRmgXMkK74JN1nJDTHxMS9zlBiSvIqtSM5IgxpFUdhFgDi79uN5T+O7WYmDlzZrE/qNu2bcsLL7xwSfv+8MMP3HfffVSuXJlu3bpx6NAhli9fzqZNm5gxYwaZmZkEBgby3nvv0bRpUxYvXsyyZctIT0/n4MGDDB06lPnz57ste/78+fz4448EBgbyySefcOWVVxIfH8/kyZP5559/AHjhhRfo1q0ba9eudd7oSinWrVvH7Nmz2bdvH23btmXcuHHce++9zrIHDRpEWloaHTp04OGHH2bfvn0EBQXRoEEDtmzZwqhRowgMDGTjxo0EBrq/iXv27MnChQvp2LEjQUFBzJgxg+XLlxMYGMi3335LREREvva6csMNN3DixAnatm3Lyy+/THBwMJMnTyY9PZ3GjRvz7rvvEh4eTs+ePWnbti0bNmxg5MiR3H///c4y5syZQ1BQEA888AAArVq1Yvny5QD069ePDh06sG3bNlq2bMkHH3xApUqVaNCgAf/6178KfY7nzJnDwYMHOXToEFdccQWffvrpeceRkpLCgAEDOHDgAL169eK1117DYrHw6aef8swzzyAiDBgwgOeeew6AoKAg0tLSAFi6dCnLly9n8eLFjB8/npCQELZs2cKpU6eYP38+t9xyCyLCtGnTWLlyJfXq1cPPz+9it6dxP/j4oBo3xpGQgDp6FL8DB8ipWRN71aqF2r88MW3atItnKmZy/OuScMVDJNaZTtDZZYSe/pAah/9N1WMLSKl+KykRo8jxr+tRG3QXk4fJyMg4r4tpyZIlZGZmMmnSJH788Ue2bt2Kq45Us2bNWL9+Pdu3b2fu3Lk88sgjzrSYmBiWLFnCrl27WLJkCceOHXNXJaGhoezatYupU6cyc+ZMwHjbuffee9m8eTNffvkld9xxBwALFy7k1VdfJSYmhvXr1xMYGMi8efO47rrriImJOc85ACxbtszZKho+fLhz+y233ELHjh35+OOPiYmJydc55OXcuXN07tyZHTt20L17d956660C7c1rS+PGjYmJieG6665j7NixPPfcc+zcuZPWrVvzxBNPOPPabDa2bNlynnO4GPv37+fuu+9m3759hISE8NprrznTinKOAfbu3cuqVasucA4AmzZt4uWXX2bv3r0cPHiQr776ipMnT/LQQw/xyy+/EBMTw+bNm/nmm28uanNsbCwbNmxg+fLlzJ5tKOx//fXX7N+/n7179/LBBx/w22+/FfocAFiqVIGWLZHgYHxjY/E7fBiVXbYlJIrKjBkzLviUFGINJLXGcI63+o4TzT8hI6QzYbHvckVMbyL+mkJg8kaPdT9VmBbEpb7pXy7uuphiYmJo1KgRDRs2BIx+9DfffBOA5ORkxo0bx99//41SimyXf8Q+ffoQai5O36JFC44ePUq9evXIy8iRI51/cx/wq1atOq/fPyUlhbS0NLp168Z9993HqFGjGDZsGHXrevaNJC9+fn7OPvgOHTqwcuXKAu0NCgpyW05ycjJJSUn06NEDgHHjxnHrrbc6012dWWGpV6+es9UyevRoXnrpJWdLoyjnGIyWV35O8+qrr6ZRo0bO8jZs2ICvry89e/YkV2Ns1KhRrFu3jiFDhhRo85AhQ7BYLLRo0YLTp08DsG7dOkaOHInVaqV27dr07t27yOdC+fmhmjTBceYM6tgx/P7+m5xatbCHhxe5LM0lohSZIVeTGXI11qyThMZ9QkjcEoISV5IR3Akabiz2KiuMgygrPProo/Tq1Yuvv/6aI0eO0LNnT2eav0v/r9VqJScnx20ZrlN7c787HA5+//33CwKRZs+ezYABA/jhhx/o1q0bK1asKMajuTi+vr5OG12PKT97L5XKlSu73e7j43Pe/HvXqPu8U6TdnVfX7wXZnF/9F6vnYvnzqgS43iPFPm1UKSzVqyMhIcihQ/ieOIElJYWcOnWQMjCuUp6w+9cmod4DJNaZRtDZ5Sh7Ov4emJKsu5i8QNOmTTl06BBHTH3+JUuWONOSk5OpU8dQRV+8ePEllZ9b3pIlS+jSpQtg9Ne7DrTltmoOHjxI69ateeihh+jUqRN//vknwcHBpKamFrneS93PHfnZmx+hoaGEh4ezfv16AD788ENna6IgGjRowLZt2wDYtm0bhw8fdqb9888/bNxovJV98sknXHvttc60opzji7Fp0yYOHz6Mw+FgyZIlXHvttVx99dWsXbuWM2fOYLfb+fTTT53HExERwb59+3A4HHz99dcXLb979+4sWbIEu91ObGwsq1evLpRd+aH8/bE0a4ajbl0saWn4/f031pSLLjCp8QBi8Se1ehQpNcd4pHztIDxM3jGI2bNnExgYyGuvveYcBA0ODnZ2HT344IM8/PDDtGvXLt8WwsVITEwkMjKSF1980Tn986WXXmLLli1ERkbSokULFi0yVnF94YUXaNWqFZGRkfj6+nLTTTcRGRmJ1WqlTZs2RZo+On78eCZPnkzbtm3JuMz58/nZWxDvv/8+s2bNIjIykpiYGB577LGL7hMVFUVCQgItW7bklVde4aqr/ica3LRpU1599VWaN29OYmIiU6ZMcaYV5RxfjE6dOjF16lSaN29Ow4YNGTp0KLVq1WLevHn06tWLNm3a0KFDBwYPNtbbmjdvHgMHDqRr167UqlXrouUPHTqUJk2a0KJFC8aOHet0aJeFUlhq1oQWLRA/P3z/+Qff48dR5TwauqJRrrWY9u3bR/Pmzb1kUcHk9qeLCPfccw9NmjS5YEBY4z2OHDnCwIED2b37wsVfcmdsVatWzQuWlT7E4UBOnkSdOgW+vmTXqYMjn7Gigvjrr78K7IrTFIzWYipHvPXWW7Rt25aWLVuSnJzMpEmTvG2SRnNJKIsFS9260KwZYrHgd+QIPidP6tZEOUC3IDQaTbEhdjty4gQqLg7x8yOnbl0clSoVal/dgrg8dAtCo9GUapTViuWKK+Cqq1CA76FD+Jw+XeGlOsoq2kFoNJpiR4WEGAPYVargEx+P38GDWPTCXWUO7SA0Go1HUD4+WBo1wtG4MSonxxD+u0whSU3JoqNbNBqNR7GEhyNBQciRI/icOoUlJcUQ/iukJpQmf1xVZcPDw1FKMWfOnGIrX7cgPIyW+zYorXLfixcvZurUqcViS1E4cuQIrVq1KtE658yZw8KFC0u0zlyUry+WK6/E0aABKisLvwMHsCYUeZl5TR5efvll52fu3Lnn6Y8VB7oF4WG03PeFVES577Ii8+1RlMJSrRoSHIwcOYLvyZOGVEfdulqqo5RScVoQM2dCz57F+zFVPC+FH374gWbNmtGhQwemT5/uFKzbtGkTXbp0oV27dnTt2pX9+/cDxsN32LBh9OvXjyZNmvDggw/mW/b8+fNp3bo1V199tfPhGR8fT1RUFJ06daJTp078+uuvAKxdu9bZumnXrh2pqanMnj2b9evX07Zt2wvezF3lvpcsWeJ8K126dKlT7vtikdQ9e/Ykd0pyUFAQ//73v2nTpg2dO3d2CszlZ68rrnLf69evJyYmhs6dOxMZGcnQoUNJTEx01jdz5kw6duxY4EIvR44coXfv3kRGRtKnTx/++ecf7HY7DRs2RERISkrCarWybt06wJCw+Pvvvzl37hwTJ07k6quvpl27dnz77bfOazZo0CB69+5Nnz59LqgvJyeHUaNG0bx5c2655RbS09MB+Pnnn2nXrh2tW7dm4sSJZGVlAee3Drds2eLU6ZozZw4TJ06kZ8+eNGrUiJdeeslZx9NPP81VV13Ftdde67yXvI3y98dy1VU46tXDkp5uSHUkJ3vbLI0bKo6D8BJa7rtgSpPc97Rp0xg3bhw7d+5k1KhRTJ8+HavVStOmTdm7dy8bNmygffv2rF+/nqysLI4dO0aTJk14+umn6d27N5s2bWL16tXMmjWLc+fOAYa+09KlS1m7du0F9bmTE8/MzGT8+PHO65yTk8Prr79+0fP4559/smLFCjZt2sQTTzxBdnY2W7du5bPPPiMmJoYffviBzZs3X7ScEkMpLBERxkwnf398jx3DmpiIRXc7lSoqTrtOy31rue+LsHHjRr766isAxowZ42ylXXfddaxbt47Dhw/z8MMP89Zbb9GjRw86deoEQHR0NMuWLXP272dmZjoXDerbty9VqlRxW587OfG+ffvSsGFDpybUuHHjePXVV52OPj8GDBiAv78//v7+1KhRg9OnT7N+/XqGDh1KJTNQbdCgQRc9ByWNCghANW+OIzYWy86d1Lv1VuKfeYb0Xr28bVqZwHUho9xB6uKk4jiIMoKW+y5Zue/C0L17d15//XVOnjzJ3LlzWbBgAWvWrOG6664DDFntL7/8kqZNm5633x9//FGsMt+u0uQFyXwXdG+USpTCUrs2Eh+PVKtGrTvvJOXWWznzyCNIcLC3rSvVuC5cdKmR1AWhu5i8gJb7vjglJfftSteuXfnss88A+Pjjj50O4Oqrr+a3337DYrEQEBBA27ZteeONN+jevTsAN954Iy+//LJz/YXt27cXqj53cuJNmzblyJEjzrEj1+No0KABW7duBeDLL7+8aPndu3fnm2++ISMjg9TUVL777rvCngqvoPz88Nm2jax77yX4yy+pd/PNBPzxh7fNqtBoB+FhtNz3pVFSct+uvPzyy7z33ntERkby4YcfOge0/f39qVevHp07dwaMLqfU1FRat24NGK2+7OxsIiMjadmyJY8++mih6nMnJx4QEMB7773HrbfeSuvWrbFYLEyePBmAxx9/nBkzZtCxY8cLZpC5o3379gwfPpw2bdpw0003ObvESjMqIAD///4X++rVKKuV2qNHU/WZZ1DmQL2mZNFifV5Cy31rNOeT9/9V0tKwzZyJ/zvvYLvySk4vXIithGNHyhJarK8coeW+NZqCUUFB+L/9NtnLl2NJS6PuLbcQ/vLL4DJxQ+NZtIPwEvfeey8xMTHs3buXjz/+2DnTRKPRnI/vgAFY9+zBNmQIVV58kTr/+he+Bw9626wKgXYQGo2m1KOqVMH/iy/I/uQTfI8fp+6gQYQuXgx6USKPoh2ERqMpM/iOHInavZvsHj2o9tRT1B47Fp8TJ7xtVrlFOwiNRlOmsNSujf9PP2F7/XX8d++mXv/+BC9dqhcl8gDaQWg0mrKHUvhNngw7dpATGUmN2bOpOXkyVr3eRLGiHYSHOXXqFCNGjKBx48Z06NCB/v3789dffxW4T35yEhdjzZo1TtmK/MjV5cll2bJlxSJBXtLy1a6Cf2WpjkuR3L7YNdqyZQvTp0+/XNMuiZMnT3LLLbd4pW4AS6NG+G3YQNazzxK4fj31brqJyj/95DV7yhsedRBKqX5Kqf1KqQNKqdlu0q9QSq1WSm1XSu1USvV3SXvY3G+/UupGT9rpKUSEoUOH0rNnTw4ePMjWrVt59tlnnYql3iCvgxg0aBCzZ19waTSlhJycnIteo44dO56n4FqS1K5d27nOh9ewWPCfPRvZsgV7vXrUnDqVGvffjyUlxbt2lQM85iCUUlbgVeAmoAUwUinVIk+2/wM+F5F2wAjgNXPfFubvlkA/4DWzvEtn60xY1bN4P1tnFljl6tWr8fX1dUbCArRp04brrruOtLQ0+vTpQ/v27WndurVTIjovzz33HK1bt6ZNmzbOh4Trm+2ZM2do0KDBBfu5kw232Ww89thjLFmyxKks67pgjju5azAipKdPn07Xrl1p1KhRvg+E/OSr586dS6dOnWjVqhV33XWXU5LipZdeokWLFkRGRjJixAiAfKWzMzIyGDFiBM2bN2fo0KH5RmoXJJX9+OOPO8/3n3/+ecG+BdURHR1Nly5daN++PbfeeitpaWnOch988MEL5NXzO5euvPXWW3Tq1Ik2bdoQFRXlPF+5EenXXHMNDz744HnX6IsvvqBVq1a0adPGKfXh2nIsSPr7ySefpGnTplx77bWMHDnSbUsmv2stIsyaNYtWrVrRunVrp5yLa8txz549XH311bRt25bIyEj+/vtvAD766CPn9kmTJmG3291eu8vF2ro1vps3k/XwwwQtX069/v0J3LDBI3VVFDzZgrgaOCAih0TEBnwGDM6TR4AQ83sokLsc2WDgMxHJEpHDwAGzvDLF7t276dChg9u0gIAAvv76a7Zt28bq1au5//77yRvV/uOPP/Ltt9/yxx9/sGPHjgLXgMiLO9lwPz8/5s6dy/Dhwy+Q6wb3cte5xMbGsmHDBpYvX57v26w7+WqAqVOnsnnzZnbv3k1GRgbLly8HYN68eWzfvp2dO3c6pTTyk85+/fXXqVSpEvv27eOJJ55wahK5cjGp7GrVqrFt2zamTJni9uGYXx1nzpzhqaeeYtWqVWzbto2OHTvy3//+17mfO3n1gs5lLsOGDWPz5s3s2LGD5s2b88477zjTjh8/zm+//XZePWA42xUrVrBjxw6WLVvm9jq4k/7OlU3fsWMHP/74Y4FdZ+6u9VdffUVMTAw7duxg1apVzJo1i9jY2PP2W7RoETNmzCAmJoYtW7ZQt25d9u3bx5IlS/j111+JiYnBarXy8ccf51v35aL8/PB/5hnsGzYgQUHUHj+eanPmoEznqykanlRzrQO4LlhwHLgmT545QLRSahpQGbjeZd/f8+xbJ28FSqm7gLsArrjiioKt6fBCYe0uEUSERx55hHXr1mGxWDhx4gSnT5+mZs2azjyrVq1iwoQJziC6/GSj3VGQbHh+5Cd3DTBkyBAsFgstWrTIt4vMnXz1Aw88wOrVq5k/fz7p6ekkJCTQsmVLbr75ZiIjIxk1ahRDhgxhyJAhQP7S2evWrXM+ZCMjI4mMjLyg/v379xcolT1s2DDAkBXPPU5X8qvj999/Z+/evc5js9lsThFEcC+vXtC5zGX37t383//9H0lJSaSlpXHjjf/rSb311lvd6i1169aN8ePH869//ct5PHlxJ/3966+/MnjwYAICAggICODmm292uy+4v9YbNmxg5MiRWK1WIiIi6NGjB5s3bz7vOnTp0oWnn36a48ePM2zYMJo0acLPP//M1q1bnTpQGRkZ1KhRI9+6iwufzp2RHTvImjWLkNdfJ3D9euIWLCCrfXuP112ShLssgKXCw0EpKMY1qb0t9z0SWCwi/1FKdQE+VEoVeqRTRN4E3gRDi8lDNl4yLVu2zLc75uOPPyY+Pp6tW7fi6+tLgwYNLpBwzo+CZJ9zKUg2/FJwlZPOT7/LnXx1ZmYmd999N1u2bKFevXrMmTPHafP333/PunXr+O6773j66afZtWtXvtLZxUHuMRRVDltE6Nu3L59++qnbdHfy6oVh/PjxfPPNN7Rp04bFixezZs0aZ1p+MuGLFi3ijz/+4Pvvv6dDhw5uW1KXK/1dmGvtjttuu41rrrmG77//nv79+/PGG28gIowbN45nn322SDYUB6pSJfxffZWcoUOxTJhAnREjSJo0iYRp08DPr8Tt8QRVXBSPnRSjg/BkF9MJwHU1m7rmNlduBz4HEJGNQABQrZD7lnp69+5NVlaWczEggJ07d7J+/XqSk5OpUaMGvr6+rF69mqNHj16wf9++fXnvvfecfdMJ5mpbrrLP+Tmg/GTDC5Lkzk/uurC4k6/OdQbVqlUjLS3Naa/D4eDYsWP06tWL5557juTkZOdbtDvp7O7du/PJJ58Axpv3zp07L6i/IKnswpBfHZ07d+bXX391lnvu3LnzZqK5k1cvzLlMTU2lVq1aZGdnF7rb5eDBg1xzzTXMnTuX6tWr57uqYF66devGd999R2ZmJmlpac5uvsJy3XXXsWTJEux2O/Hx8axbt46rrz6/1/fQoUM0atSI6dOnM3jwYHbu3EmfPn1YunQpcXFxgHEPu7vXPYnP9ddj3b0b28iRhL/+OnWjovBzMwZVFkmYNs35kcceg8cfL9byPekgNgNNlFINlVJ+GIPOeTtN/wH6ACilmmM4iHgz3willL9SqiHQBNjkQVs9glKKr7/+mlWrVtG4cWNatmzJww8/TM2aNRk1ahRbtmyhdevWfPDBBzRr1uyC/fv168egQYPo2LEjbdu2dXa7PPDAA7z++uu0a9fOuUZxXvKTDe/Vqxd79+51DlK7kp/cdWFxJ18dFhbGnXfeSatWrbjxxhudXQ12u53Ro0fTunVr2rVrx/Tp0wkLC8tXOnvKlCmkpaXRvHlzHnvsMbdjOwVJZReG/OqoXr06ixcvZuTIkURGRtKlS5fzBrndyasX5lw++eSTXHPNNXTr1s3t9XfHrFmzaN26Na1ataJr1660adOmUPt16tSJQYMGERkZyU033UTr1q2dEvOFYejQoURGRtKmTRt69+7N/Pnzz+sOBfj8889p1aoVbdu2Zffu3YwdO5YWLVrw1FNPccMNNxAZGUnfvn0vGLsoCVRoKP4ffUT2l1/iEx9P3WHDCHvjDfDQgHlJkThjhvMjjz9erK0H8LDctzlt9QXACrwrIk8rpeYCW0RkmTlb6S0gCGPA+kERiTb3/TcwEcgBZorIjwXVVdbkvjXlgwYNGrBlyxaqVavmbVMuSq7EfHp6Ot27d+fNN9+kfSnqky+p/1eJi8N2++34L19ORocOxM2fT079+h6v19N4Qu7bo2MQIvID8EOebY+5fN8LdMtn36eBpz1pn0ZTkbjrrrvYu3cvmZmZjBs3rlQ5h5JE1aiB/7Jl2BYvxn/GDOrdfDNnZ88mZeRIY5BX48Tbg9QaTZkmd9nYskDu+IoGQ6pjwgQcffqQM3Ys1R97jMorVxL37LPY83SdVWS01IZGo6mwWK64Ar/Vq8n6738J2LyZev37E/Tdd1r4z0Q7CI1GU7FRCv9770W2b8d+1VVE3HsvEdOnYzFnDVZkdBeTK+5mABTzrACNRlM6sTZrhvX338l66ikqP/00AVu2EP/MM6T36uVt07yGdhCuPPHEhdu0g9BoKg5WK/6PP07OwIHImDHUuvNOUv71L8488ghyiSrLZRndxeRhnn76aVq2bElkZCRt27bljz/+AOCOO+5g7969xVJHgwYN8o2HyOWZZ54573fXrl2LpW5PkSt5fuTIET24SuGusab48OnQAZ9t28icOZPgpUupN3AgAeb/bkVCOwgPsnHjRpYvX862bdvYuXMnq1atol49I0D87bffpkWLvOK2niOvg/jtt9+KvY6iSjoUBm86CE8cjyfL1RQvKiCAgOefx/7LL2C1Unv0aKo+8wzKVAiuCGgH4UFiY2OpVq2aU9umWrVq1K5dGzhfsjsoKIhZs2bRsmVLrr/+ejZt2uSUa85V7HSVfAYYOHDgedo9uQwZMoQOHTrQsmVLp8TH7NmzycjIoG3btowaNcpZJ+Qv47xmzRp69uzJLbfcQrNmzRg1apRbXZ6ePXsyc+ZMOnbsyIsvvsjWrVvp0aMHHTp04MYbb3RGzbqT9s67eE6rVq0umDY6e/Zs1q9fT9u2bXn++efzlZR2JSgoiH//+9+0adOGzp07OwXnCiPBPWfOHMaMGUO3bt0YM2YM8fHxREVF0alTJzp16sSvv/6Kw+GgQYMGJCUlOfdr0qQJp0+fdpvfXbn5HYe766fxLj49euCzaxdZEyYQ9u671B08GL/du71tVskgIuXi06FDB8nL3r17L9hWIMbktvM/l0Fqaqq0adNGmjRpIlOmTJE1a9Y403r06CGbN282q0V++OEHEREZMmSI9O3bV2w2m8TExEibNm1EROS9996Te+65x7n/gAEDZPXq1SIiUr9+fYmPjxcRkbNnz4qISHp6urRs2VLOnDkjIiKVK1c+z7bc30uXLpXrr79ecnJy5NSpU1KvXj05efKkrF69WkJCQuTYsWNit9ulc+fOsn79+guOsUePHjJlyhQREbHZbNKlSxeJi4sTEZHPPvtMJkyYICIitWrVkszMTBERSUxMFBGRxx9/XBYsWOAsq2XLlnL48OHz7Fu9erUMGDDAmWfq1Kny0UcfiYhIVlaWpKenX2ATIMuWLRMRkVmzZsmTTz4pIiIDBw6UxYsXi4jIO++8I4MHD75g38cff1zat2/vLHfkyJHO4z569Kg0a9ZMRESmT58u7777roiI/P7779KnT58C8+ctN7/jyO/6uV7j8kqR/1+9gO277yQ7IkIcPj5ydsYMObBvnxw4cKBUfOx2+yUdE4ayhdvnqh6k9iBBQUFs3bqV9evXs3r1aoYPH868efMYP378efn8/Pzo168fAK1bt8bf3x9fX19at25d5ECsl156ia+//hqAY8eO8ffff1O1atV88+cn4xwSEsLVV19N3bp1AWjbti1Hjhzh2muvvaCM3HUl9u/fz+7du+nbty9g6C3VqlULwK2096XgTlI6L35+fs4FdDp06MDKlSuBwklwg7HKXmBgIGBIrruOFaWkpJCWlsbw4cOZO3cuEyZM4LPPPnOeg/zy5y03v+Mo6vXTlCy+Awcie/diu+suqrz4IpVWryZuwQKyGzf2tmkeQTsID2O1WunZsyc9e/akdevWvP/++xc4CF9fX6dMtMVicXZJWSwWZ3+1q8Q3uJf5XrNmDatWrWLjxo1UqlSJnj17FlpC3B2FlY3OlaYWEVq2bOlUdHXFnbR3YY4pL+4kpXv37n1eHtfzeSly165S2w6Hg99//52AgIDz8nTp0oUDBw4QHx/PN998w//93/8VmD9vue6Ow2KxFOv103gGVaUK/kuXYvv4Y3ynTaPuoEEkzJpF8tixcAlaSKWZ8nU0pYz9+/ef10ceExND/UsUBWvQoAExMTFOmexNmy4Ut01OTiY8PJxKlSrx559/8vvv/1tzydfX1+2iQYWRcS4sTZs2JT4+3ukgsrOz2bNnT77S3g0aNGDbtm0AbNu2jcOHD19QZl55cneS0oXlUuTMb7jhBl520dyPiYkBDKXeoUOHct9999G8eXPnW35++fPi7jgKun6a0offqFGo3bvJ7tGDak89Re2xY/E5UeZWJSgQ3YLwIGlpaUybNo2kpCR8fHy48sorL3ngsVu3bjRs2JAWLVrQvHlzt0Jr/fr1Y9GiRTRv3pymTZvSuXNnZ9pdd91FZGQk7du3P2/tgaFDh7Jx40batGmDUsop4+xuzeaL4efnx9KlS5k+fTrJycnk5OQwc+ZMrrrqKkaPHk1ycjIi4pT2joqK4oMPPqBly5Zcc801zpXgXImMjMRqtdKmTRvGjx9PVlYWH374Ib6+vtSsWZNHHnmk0Pa9/PLLTJgwgQULFlC9enXee++9i+7z0ksvcc899xAZGUlOTg7du3d3Lo86fPhwOnXqdN56GwXld+Xzzz+/4DgqV66c7/XTlE4stWvj/9NP2BYtwn/WLOr178+Zxx4jddiwciH851G575KkWOS+dSS1RuM1yro8v+PgQXJGj8bv998516cP8U8/jb0EZeDLnNx3mUM7A41Gc4lYGjfG79dfyXruOQLnzKHeTTcR/9RTnHNZa7ysoccgNBqNpriwWPB/+GFkyxbsdetS8557qPHAA1hSUrxt2SWhHYRGo9EUM9bWrfHdsoWshx4i6LvvqNe/P4Fm0GRZQjsIjUaj8QDKzw//efOwr1+PBAVRe9w4qj3xBCojw9umFRo9BuHCHDdjEO62aTQaTWHx6dIF2bGDzAceIPT11wlcv564BQvIatfO26ZdFD2LyQXlZlpaeTk/Gk1pp6zPYioM2dHRqIkTscbGkjR5MglTp4KfX7GU7YlZTLqLycNoue9Lo7zJfecVW9RUTHxvuAHr7t3YRowg/LXXqBsVhd/+/d42K1+0g/AgWu778rlcB2G324vRGs+Xqyn/qLAw/D/+mOylS/GJj6fu0KGEvfUWlMJ7SjsID6Llvr0n933//ffTpk0bNm7cyEcffeTcZ9KkSdjtdhYtWsSsWbOc+7ieX3f53ZU7e/Zs5zE98MADAHz33Xdcc801tGvXjuuvv94pNa7R5MU3KgrLnj3Y+val6nPPUXvUKHyOHvW2WeeTn8xrWfsUh9w3cMHnctBy396T+16yZImIGPfAwIEDxWaziYjIlClT5P3335e4uDhp3Lixc59+/frJ+vXr882ft9wzZ87IVVddJQ6H47xjSkhIcG5766235L777hORC6+f5kLKgty3R3A4JOvdd8UeHCz2SpUk7skn5cDff2u57/KOlvv2jty31WolKioKgJ9//pmtW7fSqVMnADIyMqhRowbVq1enUaNG/P777zRp0oQ///yTbt268eqrr7rNn7fc0NBQAgICuP322xk4cKBTXvz48eMMHz6c2NhYbDYbDRs2vORj1VQQlMJvwgQcvXuTM3Ys1R99lMorVxL37LPYIyK8apruYvIwuXLfTzzxBK+88gpffvnlBXk8Ife9Y8cO2rVr5xW575iYGGJiYti1axfR0dGAIfd9zz33sG3bNjp16kROTs4ly30vW7aMwMBA+vfvzy+//HJBnoCAAKxWq9OmcePGOW3av3+/c+ryiBEj+Pzzz/nyyy8ZOnQoSqkC87uW6+Pjw6ZNm7jllltYvny508FPmzaNqVOnsmvXLt544w0t160pNJb69fFbvZqs//yHgE2bqNe/P0HLl3vXJq/WXs7Rct/el/vu06cPS5cuJS4uDoCEhASOmv28Q4cO5dtvv+XTTz91josUlN+VtLQ0kpOT6d+/P88//zw7duwAjGtQp04dAN5///3CnzyNBgypjvvuQ7Ztw37llUTMnEnE9OlYEhO9Yo7uYvIgWu7b+3LfLVq04KmnnuKGG27A4XDg6+vLq6++Sv369QkPD6d58+bs3bvX6RQLyu9KamoqgwcPJjMzExHhv//9L2AMvN96662Eh4fTu3dvt05Po7kY1ubNsf7+O1lPPUXlZ54hYPNm4p99lvSePUvUDh0o54KOpNZovEdFCJS7FHK2bEFGj8Z3/35Shg/nzMMPI+YsRFe03LeH0c5Ao9GUNnw6dkRiYsh8+GGCX3yRwN9+I27+fDLNiRSeRI9BaDQaTSlHBQQQ8Pzz2FevBouF2rfdRtV581BZWR6tt9w7iPLShabRlGf0/2nh8OnRA59du7CNH0/Y229Td8gQ/Hbv9lh95dpBBAQEcPbsWX3zaTSlGBHh7NmzBAQEeNuUMoEKDsb/3XfJXrYMS0oKdW+5hfBXXgGXKePFRbkeg6hbty7Hjx8nPj7e26ZoNJoCCAgIcAZlagqH7803I3v2YLvrLvz270ddwgD1xSjXDsLX11dHsmo0mnKLqloV/y+/xC8ryyMOwqNdTEqpfkqp/UqpA0qp2W7Sn1dKxZifv5RSSS5pdpe0ZZ60U6PRaMoyykX1oDjxWAtCKWUFXgX6AseBzUqpZSLiXARBRO51yT8NcF1iKUNE2nrKPo1Go9EUjCdbEFcDB0TkkIjYgM+AwQXkHwl86kF7NBqNRlMEPDkGUQc45vL7OHCNu4xKqfpAQ8BVeS1AKbUFyAHmicg3bva7C7jL/JmmlLqcpZmqAQUvy+YdtF1FQ9tVNLRdRaM82pWvQFxpGaQeASwVEdclleqLyAmlVCPgF6XULhE56LqTiLwJXJq4UR6UUlvyCzf3JtquoqHtKhrarqJR0ezyZBfTCaCey++65jZ3jCBP95KInDD/HgLWcP74hEaj0Wg8jCcdxGagiVKqoVLKD8MJXDAbSSnVDAgHNrpsC1dK+ZvfqwHdgL1599VoNBqN5/BYF5OI5CilpgIrACvwrojsUUrNxVjiLtdZjAA+k/PDnZsDbyilHBhObJ7r7CcPUSxdVR5A21U0tF1FQ9tVNCqUXeVG7luj0Wg0xUu51mLSaDQazaWjHYRGo9Fo3FLhHcTF5EC8gVKqnlJqtVJqr1Jqj1JqhrdtckUpZVVKbVdKeXdFdReUUmFKqaVKqT+VUvuUUl28bROAUupe8xruVkp9qpTymmSpUupdpVScUmq3y7YqSqmVSqm/zb/hpcSuBea13KmU+lopFVYa7HJJu18pJeYkmlJhl1JqmnnO9iil5hdHXRXaQbjIgdwEtABGKqVaeNcqwAgOvF9EWgCdgXtKiV25zAD2eduIPLwI/CQizYA2lAL7lFJ1gOlARxFphTFZY4QXTVoM9MuzbTbws4g0AX42f5c0i7nQrpVAKxGJBP4CHi5po3BvF0qpesANwD8lbZDJYvLYpZTqhaFU0UZEWgILi6OiCu0gKLocSIkgIrEiss38norxsKvjXasMlFJ1gQHA2962JRelVCjQHXgHQERsIpLkVaP+hw8QqJTyASoBJ71liIisAxLybB4MvG9+fx8YUpI2gXu7RCRaRHLMn79jxFF53S6T54EHAa/M8MnHrikYsz2zzDxxxVFXRXcQ7uRASsWDOBelVAOMIME/vGxKLi9g/HMU/+okl05DIB54z+z6elspVdnbRpnBngsx3jRjgWQRifauVRcQISKx5vdTQIQ3jcmHicCP3jYCQCk1GDghIju8bUsergKuU0r9oZRaq5QqlgWrK7qDKNUopYKAL4GZIpJSCuwZCMSJyFZv25IHH6A98LqItAPO4Z2ukvMw+/MHYziw2kBlpdRo71qVP2YsUqma966U+jdGl+vHpcCWSsAjwGPetsUNPkAVjC7pWcDnSil1uYVWdAdRFDmQEkUp5YvhHD4Wka+8bY9JN2CQUuoIRndcb6XUR941CTBafsdFJLeVtRTDYXib64HDIhIvItnAV0BXL9uUl9NKqVoA5t9i6ZooDpRS44GBwKg8gbTeojGGs99h/g/UBbYppWp61SqD48BXYrAJo4V/2QPoFd1BFEoOpKQxPf87wD4R+a+37clFRB4Wkboi0gDjXP0iIl5/IxaRU8AxpVRTc1MfSoc0yz9AZ6VUJfOa9qEUDJ7nYRkwzvw+DvjWi7Y4UUr1w+jKHCQi6d62B0BEdolIDRFpYP4PHAfam/eft/kG6AWglLoK8KMYVGcrtIMwB8Fy5UD2AZ+LyB7vWgUYb+pjMN7Qc1fV6+9to0o504CPlVI7gbbAM941B8wWzVJgG7AL4//Na1INSqlPMTTPmiqljiulbgfmAX2VUn9jtHjmlRK7XgGCgZXm/b+olNjldfKx612gkTn19TNgXHG0urTUhkaj0WjcUqFbEBqNRqPJH+0gNBqNRuMW7SA0Go1G4xbtIDQajUbjFu0gNBqNRuMW7SA0pRpTMfM/Lr8fUErNKaayFyulbimOsi5Sz62mwuzqPNs7msqbfubvxkqpQ0qpEKXUMKXUzy55rzWne16wCqRS6mql1BpTkXWbUup7pVTri9jUUylV2oL2NKUM7SA0pZ0sYJg3ZJULwt2DugBuB+4UkV6uG0VkC7AWeMDc9CrwbxFJMaPns5RSt5lR9a8Bd7sI2OXaEQF8DjwiIk1EpD3wLEbUb0H0pPRFdWtKGdpBaEo7ORjBZffmTcjbAlBKpZl/e5qCZd+ab+TzlFKjlFKblFK7lFKuD8/rlVJblFJ/mVpTuetdLFBKbVbGegSTXMpdr5RahptIbaXUSLP83Uqp58xtjwHXAu8opRa4Ob5HgDuVUg8CPiLyqUvaVOApYA6wWUR+c7P/VOB91zQR2SAi35j132wKuG1XSq1SSkWYApCTgXvNVsl1SqnqSqkvzWPerJTqZu7fwyVYc7tSKtiNDZryiojoj/6U2g+QBoQAR4BQjLftOWbaYuAW17zm355AElAL8MfQ13rCTJsBvOCy/08YL0pNMKQTAoC7gP8z8/gDWzA0eHpiCAE2dGNnbQxpjeoYwmm/AEPMtDUYa0Lkd4yTADvQ1E3as0AyUC2ffb8CBhdQdjj/C4i9A/iP+X0O8IBLvk+Aa83vV2DIvAB8B3QzvwdhODGv3xf6UzKfojSTNRqvICIpSqkPMBbfySjkbpvFlLFWSh0EcmW2d2Fq1ph8LiIO4G+l1CGgGcZiMJEurZNQDAdiAzaJyGE39XUC1ohIvFnnxxhrVHxTCFtvAk5jLFq1P3ejMha06ovhJOtTCG0dpdQfGA41WkRmYAjKLTGF+PwAd7aDIbPRQv1PADREGWrCvwL/NY/nKxE5Xojj0ZQTdBeTpqzwAkZfvus6DzmY97BSyoLxAMwly+W7w+W3A857McqrNSOAAqaJSFvz01D+t47Ducs5iLyY3VqhwI3AAmVISudyN4ZDux14VSm38s17cFGuFZFrgEfNMgFeBl4RkdYYLZX8ljy1AJ1djrmOiKSJyDyMlkcg8KtSqtmlHqum7KEdhKZMICIJGIOxroJpR4AO5vdBgO8lFH2rUspijks0wniDXwFMMQeHUUpdpS6+ANEmoIdSqpr55j8SYwA6X5RSgcB/gXtEZBeGkuq/zbSawH3AgyLyE0Y32R1uinkVGJ9nRpKrkwnlfxL241y2p2KI4eUSjSF4mGtbW/NvYzFUTJ/DUD/WDqICoR2EpizxH87XuH8L46G8A+jCpb3d/4PxcP8RmCwimRjLqe7F0PrfDbwBBXfHmt1Zs4HVwA5gq4hcTDr7UeBrEckd8J6DsS56EwzHMT+3ywqYCfxbKVUlT72ngOHAs0qpA0qp34BbMNRQc8v8Qim1lfO7qL4DhuYOUmOunW0Oyu/FGMQGmGkOuu8EsiklK7tpSgat5qrRaDQat+gWhEaj0Wjcoh2ERqPRaNyiHYRGo9Fo3KIdhEaj0Wjcoh2ERqPRaNyiHYRGo9Fo3KIdhEaj0Wjc8v+tqKO5w8zR1wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#graph constants\n",
    "YMIN = 0.75\n",
    "YMAX = 1.000\n",
    "YTICK = 0.05\n",
    "BAR_WIDTH = 5\n",
    "\n",
    "#graph\n",
    "title_text = \"Ground state probabilty against number of Clifford Gates\"\n",
    "plt.errorbar(gate_depth_plot_no_reverse, simulation_probability_no_reverse, yerr = standard_error_no_reverse, \n",
    "             fmt = 'none', elinewidth = BAR_WIDTH, label =  'Simulation results no reversal', color = 'red')           \n",
    "plt.errorbar(gate_depth_plot_reverse, simulation_probability_reverse, yerr = standard_error_reverse, \n",
    "            fmt = 'none', elinewidth = BAR_WIDTH, label = 'Simulation results reversal', color = 'black')\n",
    "plt.plot(GATE_DEPTH_CALCULATION, echoed_calculation, label = \"Egan best fit line for upper bound\" , color=\"black\")\n",
    "plt.plot(GATE_DEPTH_CALCULATION, cumulative_calculation, label = \"Egan best fit line for lower bound\" , color=\"red\")\n",
    "plt.plot(GATE_DEPTH_CALCULATION, theory_calculation, label = \"Calculation based on depolarising noise\", color=\"orange\")\n",
    "plt.fill_between(GATE_DEPTH_CALCULATION, echoed_calculation, cumulative_calculation, color = '#dcdcdc')\n",
    "\n",
    "plt.title('Simulation of two qubit errors with RXX gates')\n",
    "plt.xlabel('Number of XX Gates')\n",
    "plt.ylabel('Fidelity')  \n",
    "plt.legend()\n",
    "plt.ylim(YMIN, YMAX)\n",
    "plt.xticks(np.arange(0, 18, 2))\n",
    "plt.yticks(np.arange(YMIN, YMAX, YTICK))\n",
    "fname = \"RXX_gate_two_qubit_errors_graph.png\"\n",
    "plt.savefig(fname)"
   ]
  },
  {
   "attachments": {
    "Egan%20Figure%20S2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results from Egan for comparison are shown below.  We expected that since we have used an average error our results are intermediate between the bands shown by Egan.\n",
    "\n",
    "![Egan%20Figure%20S2.png](attachment:Egan%20Figure%20S2.png)"
   ]
  }
 ],
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  "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",
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 },
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 "nbformat_minor": 4
}