final_submission_latest.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0ov8nlwIjxBB"
      },
      "source": [
        "QHack2022 Open Hackathon - FEYNMAN PRODIGIES TEAM\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "Project Name: Efficient ground state computation methodologies for BeH2\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "In this notebook, we describe the implementation of different methodologies to find the ground state of the molecule BeH2, each with their own merits and drawbacks. The methods used consider only single and double excitations. Some of the methodologies that we implement greatly simplify the model while sacrificing chemical accuracy while others use error mitigation more efficiently through qiskit runtime which works well with hybrid algorithms such as VQE.\n",
        "\n",
        "\n",
        "We are trying to find the ground state of BeH2, so it is worth knowing more on its physical chemistry. Beryllium has chemical formula 1s2 2s2 and the two hydrogens 1s1 in electron configuration notation. When the molecule BeH2 is formed, the s orbitals from the two hydrogens hybridize with the p orbitals from beryllium to form two sp molecular orbital bonds that want to be as far away from each other as possible due to electron repulsion and this results in a linear molecule. We use the sto3g basis to approximate slater type orbitals."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GKqckBHOj3ZR"
      },
      "source": [
        "The following module need installation: qiskit for testing our quantum simulations, pyscf as an open source collection of electronic structure modules, qiskit_nature, and qiskit_ibm_runtime."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "ExG_XkTuXRuu",
        "collapsed": true
      },
      "outputs": [],
      "source": [
        "#Install the required packages\n",
        "!pip install pennylane --q\n",
        "!pip install qiskit qiskit_nature --quiet\n",
        "!pip install pyscf qiskit_ibm_runtime --quiet\n",
        "!pip install prototype-zne --quiet\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "id": "KXq32iAaJjxk"
      },
      "outputs": [],
      "source": [
        "# Import necessary libraries and packages\n",
        "import math\n",
        "import matplotlib.pyplot as plt\n",
        "import pennylane.numpy as np\n",
        "import pennylane as qml\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')\n",
        "from qiskit_ibm_runtime import QiskitRuntimeService, Session, Options, Sampler, Estimator\n",
        "from qiskit_nature.second_q.circuit.library import UCC, UCCSD, HartreeFock\n",
        "from qiskit_nature.second_q.mappers import JordanWignerMapper, ParityMapper, QubitMapper\n",
        "\n",
        "from qiskit_nature.units import DistanceUnit\n",
        "from qiskit_nature.second_q.drivers import PySCFDriver\n",
        "\n",
        "from qiskit.primitives import Estimator\n",
        "\n",
        "from qiskit_nature.settings import settings\n",
        "from qiskit.circuit import QuantumCircuit\n",
        "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
        "from qiskit_ibm_runtime import SamplerV2 as Sampler\n",
        "from qiskit_ibm_runtime.fake_provider import FakeManilaV2\n",
        "from qiskit_algorithms.optimizers import SLSQP\n",
        "\n",
        "from qiskit_algorithms import NumPyMinimumEigensolver, VQE\n",
        "from qiskit_nature.second_q.algorithms import GroundStateEigensolver\n",
        "from qiskit_nature.second_q.transformers.active_space_transformer import ActiveSpaceTransformer\n",
        "from qiskit_nature.second_q.problems.electronic_structure_problem import ElectronicStructureProblem\n",
        "settings.dict_aux_operators = True"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "PwlLlmZNPPk2"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rWDx-56GJjxk"
      },
      "source": [
        "VQE"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4NNJVn95Jjxk"
      },
      "source": [
        "First we do the usual hybrid VQE algorithm using single and double excitations UCCSD strategy. We use all such excitations to come up with the ground state energy calculation.\n",
        "\n",
        "For this setup we use 4 electrons in 6 orbitals inside the molecule. The pair of electrons in the 1s orbital(core) of Be atom are stable, therefore we don't include them in our active space. We use the sto-3g basis set and two-qubit reduction method using parity mapping to reduce the system size without affecting the calculation due to symmetry. We first find the true ground state energy which we will use throughout the file for reference, as the target. Note that this is calculated using NumpyEigenSolver.\n",
        "\n",
        "We then make a circuit and find the expected value of the hamiltonian using ADAM optimizer.\n",
        "\n",
        "We calculate the time taken for this method, along with the number of CNOT gates that are in the circuit. This number is calculated using the formula 13 x double_excitations + 2 x single_excitations. This is because of the number of CNOT gates using in the ansatz for the respective excitation schemes. Finally we plot the graph of the GS Energy calculation over time."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "oTFl4EdGJjxk"
      },
      "outputs": [],
      "source": [
        "# Create an instance of the PySCFDriver with the specified molecular configuration\n",
        "driver = PySCFDriver(\n",
        "    atom=\"Be 0 0 0; H -1.291 0 0; H 1.291 0 0\",  # Defines the positions of the atoms\n",
        "    basis=\"sto3g\",                             # Specifies the basis set for the calculation\n",
        "    charge=0,                                  # The total charge of the molecule\n",
        "    spin=0,                                    # The total spin of the molecule\n",
        "    unit=DistanceUnit.ANGSTROM,                # The unit of measurement for atomic positions\n",
        ")\n",
        "\n",
        "# Execute the driver to compute the molecular properties\n",
        "properties = driver.run()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "MHPtJQC_Jjxk",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f1ce65e1-7b6c-4543-bc96-5dfd5da67875"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "number of alpha electrons:  3\n",
            "number of beta electrons:  3\n",
            "number of spin orbitals:  14\n"
          ]
        }
      ],
      "source": [
        "# Retrieve the number of alpha electrons from the molecular properties\n",
        "num_alpha_electrons = properties.num_alpha\n",
        "# Retrieve the number of beta electrons from the molecular properties\n",
        "num_beta_electrons = properties.num_beta\n",
        "# Convert the number of spin orbitals to an integer for further calculations\n",
        "num_spin_orbitals = int(properties.num_spin_orbitals)\n",
        "\n",
        "# Get the nuclear repulsion energy from the molecular properties\n",
        "nuclear_rep_energy = properties.nuclear_repulsion_energy\n",
        "\n",
        "print(\"number of alpha electrons: \", num_alpha_electrons)\n",
        "\n",
        "print(\"number of beta electrons: \", num_beta_electrons)\n",
        "\n",
        "print(\"number of spin orbitals: \", num_spin_orbitals)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Define the active space around the Fermi level (selected automatically around the HOMO and LUMO, ordered by energy)\n",
        "transformer = ActiveSpaceTransformer(\n",
        "    num_electrons=4, #Number of electrons in our active space\n",
        "    num_spatial_orbitals = 6, #Numer of orbitals in our active space\n",
        ")\n",
        "\n",
        "# Define the reduced problem using this transformer\n",
        "problem = transformer.transform(properties)\n",
        "\n",
        "# The second quantized Hamiltonian of the reduce problem\n",
        "second_q_ops_reduced = problem.second_q_ops()"
      ],
      "metadata": {
        "id": "PXIVsId9MpF1"
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "YdkoU6V9Jjxk"
      },
      "outputs": [],
      "source": [
        "# # Check the occupation of the spin orbitals\n",
        "# PN_property = properties.get_property(\"ParticleNumber\")\n",
        "\n",
        "\n",
        "# #Now we remove/freeze the core orbital 1s of Be for the calculations\n",
        "# # Define the active space around the Fermi level\n",
        "# transformer = ActiveSpaceTransformer(\n",
        "#     num_electrons=4, # Number of electrons in our active space\n",
        "#     num_molecular_orbitals=6, # Number of orbitals in our active space\n",
        "# )\n",
        "\n",
        "# # Now we can get the reduced electronic structure problem\n",
        "# problem_reduced = ElectronicStructureProblem(driver, transformers=[transformer])\n",
        "\n",
        "# # The second quantized Hamiltonian of the reduce problem\n",
        "# second_q_ops_reduced = problem_reduced.second_q_ops()"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Setup the mapper and qubit converter\n",
        "mapper_type = 'ParityMapper'\n",
        "\n",
        "if mapper_type == 'ParityMapper':\n",
        "    mapper = ParityMapper()\n",
        "elif mapper_type == 'JordanWignerMapper':\n",
        "    mapper = JordanWignerMapper()\n",
        "\n",
        "# Use Parity mapper to map the problem\n",
        "qubit_op_parity = mapper.map(problem.hamiltonian.second_q_op())\n",
        "print(qubit_op_parity)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "collapsed": true,
        "id": "OGuf5ei6JZ91",
        "outputId": "f2535bd9-a97d-4277-b29f-2252ec30ac01"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "SparsePauliOp(['IIIIIIIIIIII', 'IIIIIIIIIIIZ', 'IIIIIIIIIIZZ', 'IIIIIIIIIIZI', 'IIIIIIZXXXXZ', 'IIIIIIZXXXXI', 'IIIIIIIYXXYI', 'IIIIIIIYXXYZ', 'IIIIIIIIIZZI', 'IIIIIIIIIZZZ', 'IIIIIIIIZZII', 'IIIIIIIIZZIZ', 'IIIIIIIZZIII', 'IIIIIIIZZIIZ', 'IIIIIIZZIIII', 'IIIIIIZZIIIZ', 'IIIIIZZIIIII', 'IIIIIZZIIIIZ', 'IZXXXXZIIIII', 'IZXXXXZIIIIZ', 'IIYXXYIIIIII', 'IIYXXYIIIIIZ', 'IIIIZZIIIIII', 'IIIIZZIIIIIZ', 'ZXXXXZIIIIII', 'ZXXXXZIIIIIZ', 'IYXXYIIIIIII', 'IYXXYIIIIIIZ', 'IIIZZIIIIIII', 'IIIZZIIIIIIZ', 'IIZZIIIIIIII', 'IIZZIIIIIIIZ', 'IZZIIIIIIIII', 'IZZIIIIIIIIZ', 'ZZIIIIIIIIII', 'ZZIIIIIIIIIZ', 'IIIIIIIZXXXX', 'IIIIIIIZXXYY', 'IIIIIIIIYXXY', 'IIIIIIIIYXYX', 'IIIIIIZXZIZX', 'IIIIIIIXIIZX', 'IIIIIIZYIIIY', 'IIIIIIIYZIZY', 'IIIIIIZXZIIX', 'IIIIIIIXIIIX', 'IIIIZXZIIIZX', 'IIIIIXIIIIZX', 'IIIIZXZIIIIX', 'IIIIIXIIIIIX', 'ZXXXXXZIIIZX', 'IYXXXYIIIIZX', 'ZXXXXXZIIIIX', 'IYXXXYIIIIIX', 'IZXXXZIIIIZX', 'IIYXYIIIIIZX', 'IZXXXZIIIIIX', 'IIYXYIIIIIIX', 'ZXZIIIIIIIZX', 'IXIIIIIIIIZX', 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            "              coeffs=[-9.07239108e-01+0.j, -2.30901642e-01+0.j, -2.51849340e-01+0.j,\n",
            "  6.28202291e-02+0.j, -5.44227918e-02+0.j,  9.48854680e-03+0.j,\n",
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            " -6.67939302e-03+0.j, -6.67939302e-03+0.j,  1.92135809e-02+0.j,\n",
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            "  1.80211133e-02+0.j,  1.80211133e-02+0.j,  1.80211133e-02+0.j,\n",
            "  1.23249745e-02+0.j,  1.23249745e-02+0.j,  1.23249745e-02+0.j,\n",
            "  1.23249745e-02+0.j, -9.15801322e-03+0.j, -9.15801322e-03+0.j,\n",
            " -1.00925613e-02+0.j, -1.00925613e-02+0.j, -1.13445156e-02+0.j,\n",
            "  1.13445156e-02+0.j, -1.13445156e-02+0.j,  1.13445156e-02+0.j,\n",
            "  1.41342551e-02+0.j,  1.41342551e-02+0.j,  1.41342551e-02+0.j,\n",
            "  1.41342551e-02+0.j,  1.52803958e-02+0.j,  1.52803958e-02+0.j,\n",
            "  1.52803958e-02+0.j,  1.52803958e-02+0.j, -1.43361010e-02+0.j,\n",
            "  1.43361010e-02+0.j, -1.43361010e-02+0.j,  1.43361010e-02+0.j,\n",
            "  8.62916558e-02+0.j,  8.62916558e-02+0.j,  8.21012011e-02+0.j,\n",
            "  9.27110681e-02+0.j,  1.04118712e-01+0.j, -1.23438690e-02+0.j,\n",
            " -1.23438690e-02+0.j,  1.09889220e-01+0.j, -5.59829189e-03+0.j,\n",
            " -5.59829189e-03+0.j,  9.00569277e-02+0.j,  9.00569277e-02+0.j,\n",
            "  1.02906304e-01+0.j,  1.13110732e-01+0.j, -1.07701191e-02+0.j,\n",
            "  1.07701191e-02+0.j,  3.76527189e-03+0.j, -3.76527189e-03+0.j,\n",
            " -3.76527189e-03+0.j,  3.76527189e-03+0.j,  3.45882864e-03+0.j,\n",
            "  3.45882864e-03+0.j, -3.45882864e-03+0.j, -3.45882864e-03+0.j,\n",
            " -1.07701191e-02+0.j, -1.07701191e-02+0.j,  3.76527189e-03+0.j,\n",
            "  3.76527189e-03+0.j,  3.76527189e-03+0.j,  3.76527189e-03+0.j,\n",
            "  3.45882864e-03+0.j,  3.45882864e-03+0.j,  3.45882864e-03+0.j,\n",
            "  3.45882864e-03+0.j, -1.70795064e-02+0.j,  1.70795064e-02+0.j,\n",
            " -2.38709174e-02+0.j,  2.38709174e-02+0.j, -2.38709174e-02+0.j,\n",
            "  2.38709174e-02+0.j,  1.52803958e-02+0.j,  1.52803958e-02+0.j,\n",
            "  1.52803958e-02+0.j,  1.52803958e-02+0.j,  2.08051029e-02+0.j,\n",
            "  2.08051029e-02+0.j,  2.08051029e-02+0.j,  2.08051029e-02+0.j,\n",
            " -2.40849928e-02+0.j,  2.40849928e-02+0.j, -2.40849928e-02+0.j,\n",
            "  2.40849928e-02+0.j, -1.85596875e-03+0.j, -1.85596875e-03+0.j,\n",
            "  1.80211133e-02+0.j,  1.80211133e-02+0.j,  1.80211133e-02+0.j,\n",
            "  1.80211133e-02+0.j, -5.59829189e-03+0.j, -5.59829189e-03+0.j,\n",
            "  2.03996636e-02+0.j,  2.03996636e-02+0.j,  2.03996636e-02+0.j,\n",
            "  2.03996636e-02+0.j,  1.42289477e-02+0.j,  1.42289477e-02+0.j,\n",
            "  1.42289477e-02+0.j,  1.42289477e-02+0.j, -7.00548636e-03+0.j,\n",
            " -7.00548636e-03+0.j, -3.61514725e-03+0.j, -3.61514725e-03+0.j,\n",
            "  9.42777259e-02+0.j,  7.96719958e-02+0.j,  9.42484566e-02+0.j,\n",
            "  9.30443319e-02+0.j,  1.23249745e-02+0.j,  1.23249745e-02+0.j,\n",
            "  9.00569277e-02+0.j,  1.42289477e-02+0.j,  1.42289477e-02+0.j,\n",
            "  1.12464760e-01+0.j,  1.00340071e-01+0.j,  9.24328880e-02+0.j,\n",
            "  9.83561505e-02+0.j,  6.06234481e-03+0.j, -6.06234481e-03+0.j,\n",
            " -6.06234481e-03+0.j,  6.06234481e-03+0.j,  1.18846517e-02+0.j,\n",
            "  1.18846517e-02+0.j,  1.18846517e-02+0.j,  1.18846517e-02+0.j,\n",
            "  1.27608922e-02+0.j,  1.27608922e-02+0.j,  1.27608922e-02+0.j,\n",
            "  1.27608922e-02+0.j,  3.45882864e-03+0.j, -3.45882864e-03+0.j,\n",
            "  3.45882864e-03+0.j, -3.45882864e-03+0.j,  4.10769391e-03+0.j,\n",
            "  4.10769391e-03+0.j,  4.10769391e-03+0.j,  4.10769391e-03+0.j,\n",
            "  7.96719958e-02+0.j,  9.42484566e-02+0.j,  9.30443319e-02+0.j,\n",
            "  1.23249745e-02+0.j,  1.23249745e-02+0.j,  9.00569277e-02+0.j,\n",
            "  1.42289477e-02+0.j,  1.42289477e-02+0.j,  1.00340071e-01+0.j,\n",
            "  1.12464760e-01+0.j,  9.24328880e-02+0.j,  9.83561505e-02+0.j,\n",
            "  1.18846517e-02+0.j,  1.18846517e-02+0.j, -1.18846517e-02+0.j,\n",
            " -1.18846517e-02+0.j,  1.27608922e-02+0.j, -1.27608922e-02+0.j,\n",
            " -1.27608922e-02+0.j,  1.27608922e-02+0.j,  3.45882864e-03+0.j,\n",
            "  3.45882864e-03+0.j,  3.45882864e-03+0.j,  3.45882864e-03+0.j,\n",
            "  4.10769391e-03+0.j,  4.10769391e-03+0.j,  4.10769391e-03+0.j,\n",
            "  4.10769391e-03+0.j,  7.47368488e-02+0.j,  1.00156597e-01+0.j,\n",
            " -9.15801322e-03+0.j, -9.15801322e-03+0.j,  1.02906304e-01+0.j,\n",
            " -7.00548636e-03+0.j, -7.00548636e-03+0.j,  9.24328880e-02+0.j,\n",
            "  9.24328880e-02+0.j,  1.03716191e-01+0.j,  1.10113825e-01+0.j,\n",
            "  3.58172747e-02+0.j, -3.58172747e-02+0.j, -3.58172747e-02+0.j,\n",
            "  3.58172747e-02+0.j, -1.43361010e-02+0.j, -1.43361010e-02+0.j,\n",
            "  1.43361010e-02+0.j,  1.43361010e-02+0.j, -2.40849928e-02+0.j,\n",
            " -2.40849928e-02+0.j,  2.40849928e-02+0.j,  2.40849928e-02+0.j,\n",
            "  3.53769758e-02+0.j, -3.53769758e-02+0.j, -3.53769758e-02+0.j,\n",
            "  3.53769758e-02+0.j,  1.08334887e-01+0.j, -1.00925613e-02+0.j,\n",
            " -1.00925613e-02+0.j,  1.13110732e-01+0.j, -3.61514725e-03+0.j,\n",
            " -3.61514725e-03+0.j,  9.83561505e-02+0.j,  9.83561505e-02+0.j,\n",
            "  1.10113825e-01+0.j,  1.23806959e-01+0.j,  6.28202291e-02+0.j,\n",
            "  9.48854680e-03+0.j,  9.48854680e-03+0.j,  8.05654306e-02+0.j,\n",
            "  8.05654306e-02+0.j,  8.09430161e-02+0.j,  9.42006317e-02+0.j,\n",
            " -1.15270484e-02+0.j,  1.15270484e-02+0.j,  2.05368789e-02+0.j,\n",
            " -1.77961614e-02+0.j,  2.74071754e-03+0.j,  2.74071754e-03+0.j,\n",
            " -1.77961614e-02+0.j,  2.05368789e-02+0.j, -4.40322854e-04+0.j,\n",
            " -4.40322854e-04+0.j, -4.40322854e-04+0.j,  4.40322854e-04+0.j,\n",
            "  4.24353966e-03+0.j,  4.24353966e-03+0.j,  8.62916558e-02+0.j,\n",
            "  8.62916558e-02+0.j,  8.21012011e-02+0.j,  9.27110681e-02+0.j,\n",
            " -1.07701191e-02+0.j,  1.07701191e-02+0.j, -1.07701191e-02+0.j,\n",
            " -1.07701191e-02+0.j, -1.70795064e-02+0.j,  1.70795064e-02+0.j,\n",
            "  9.42777259e-02+0.j,  7.96719958e-02+0.j,  9.42484566e-02+0.j,\n",
            "  7.96719958e-02+0.j,  9.42484566e-02+0.j,  7.47368488e-02+0.j])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uWZZySjGJjxl"
      },
      "outputs": [],
      "source": [
        "# #Using paritymapper to take advantage of the Z2 symmetry of the system\n",
        "# mapper = ParityMapper()\n",
        "\n",
        "# converter = QubitConverter(mapper)\n",
        "\n",
        "# qubit_op = converter.convert(second_q_ops_reduced[\"ElectronicEnergy\"])\n",
        "# #reduces the qubit number by 2\n",
        "# parity_converter = QubitConverter(mapper, two_qubit_reduction=True)\n",
        "\n",
        "# # Compute the Hamitonian in qubit form\n",
        "# qubit_op_parity = parity_converter.convert(second_q_ops_reduced.get('ElectronicEnergy'), num_particles=problem_reduced.num_particles)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "numpy_solver = NumPyMinimumEigensolver()\n",
        "\n",
        "# Create a ground state eigensolver using the given mapper and Numpy solver.\n",
        "calc = GroundStateEigensolver(mapper, numpy_solver)\n",
        "# Solve the problem to find the ground state energy of the molecule.\n",
        "res = calc.solve(problem)\n",
        "\n",
        "real_solution = res.total_energies[0]\n",
        "# Output the computed total energy of the molecule's ground state.\n",
        "print('Reference_energy:', real_solution)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c9DnnpGIWHct",
        "outputId": "a37d6e9d-c5a0-4f90-b532-073fa2137b22"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Reference_energy: -15.594427466321315\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Fnl49VbsJjxl"
      },
      "outputs": [],
      "source": [
        "# #Use UCCSD ansatz to look for single and double excitation on noiseless simulator\n",
        "# vqe_factory = VQEUCCFactory(\n",
        "#     quantum_instance=Aer.get_backend(\"aer_simulator_statevector\"),\n",
        "#     optimizer=SLSQP(maxiter=6,ftol = 1e-4),\n",
        "#     ansatz=UCC(excitations='sd')\n",
        "# )\n",
        "\n",
        "# from qiskit.algorithms import NumPyMinimumEigensolver\n",
        "\n",
        "# numpy_solver = NumPyMinimumEigensolver()\n",
        "\n",
        "# #Find the real solution using classical method\n",
        "# solver = GroundStateEigensolver(parity_converter, vqe_factory)\n",
        "# real_solution_t = solver.solve(problem_reduced).total_energies[0]\n",
        "# print('Reference energy : ', real_solution_t)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "id": "ObtuYRKsJjxl"
      },
      "outputs": [],
      "source": [
        "symbols = [\"H\",\"Be\",\"H\"]\n",
        "geometry = np.array([ -1.291/0.529, 0.0, 0.0,0.0, 0.0, 0.0, 1.291/0.529, 0.0, 0.0])\n",
        "#define the hamiltonian of the system\n",
        "hamil = qml.qchem.molecular_hamiltonian(symbols,geometry,charge = 0,basis = 'sto-3g', active_electrons=4, active_orbitals=6)[0]\n",
        "#number of qubits\n",
        "n_qubits = len(hamil.wires)\n",
        "\n",
        "#define the hf state\n",
        "hf_state = qml.qchem.hf_state(electrons=4, orbitals=n_qubits)\n",
        "# singles and doubles are used to make the AllSinglesDoubles template\n",
        "singles, doubles = qml.qchem.excitations(4, n_qubits)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Number of qubits:\" ,n_qubits)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "g8qQekJLXTPN",
        "outputId": "0299312e-c872-4f00-9f10-84cde305d454"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Number of qubits: 12\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "id": "xs3yTQuxJjxl",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "df16018b-6d44-4524-9a3a-accffc1a1fac"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "iter: 0  cost_fn: -15.573666991620525\n",
            "iter: 10  cost_fn: -15.590281520394653\n",
            "iter: 20  cost_fn: -15.593307278314382\n",
            "CPU times: user 1min 36s, sys: 405 ms, total: 1min 37s\n",
            "Wall time: 1min 40s\n"
          ]
        }
      ],
      "source": [
        "%%time\n",
        "np.random_seed = 10\n",
        "\n",
        "dev = qml.device(\"default.qubit\", wires=n_qubits)\n",
        "@qml.qnode(dev)\n",
        "\n",
        "\n",
        "def cost(weights):\n",
        "    qml.BasisState(hf_state, wires=list(range(n_qubits)))\n",
        "    for i in range(len(singles)):\n",
        "        qml.SingleExcitation(weights[i+len(doubles)], wires=singles[i])\n",
        "    for i in range(len(doubles)):\n",
        "        qml.DoubleExcitation(weights[i], wires=doubles[i])\n",
        "    return qml.expval(hamil)\n",
        "\n",
        "weights = np.zeros(len(doubles + singles), requires_grad=True)\n",
        "opt = qml.AdamOptimizer(stepsize=0.02)\n",
        "i=0\n",
        "iter=[]\n",
        "cost_val=[]\n",
        "Lowest_E=0\n",
        "best_weights=0\n",
        "for _ in range(30):\n",
        "    weights = opt.step(cost, weights)\n",
        "    iter.append(i)\n",
        "    cost_fn=cost(weights)\n",
        "    if Lowest_E>cost_fn:\n",
        "        Lowest_E=cost_fn\n",
        "        best_weights=weights\n",
        "    cost_val.append(cost_fn)\n",
        "    if i%10==0:\n",
        "      print('iter:',i,' cost_fn:',cost_fn)\n",
        "    i=i+1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "id": "gwWUb2HtJjxl",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "102a662c-13c6-4da8-a018-2119dc3a0592"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Total number of CNOT gates used =  1020\n"
          ]
        }
      ],
      "source": [
        "#Total number of 2-qubit (CNOT) gates\n",
        "print(\"Total number of CNOT gates used = \", 13*len(doubles) + 2*len(singles))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "id": "qr728euyJjxl",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 578
        },
        "outputId": "59209503-43ef-4004-8f27-3724235bd733"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# The following plot is of full VQE\n",
        "import matplotlib.pyplot as plt\n",
        "plt.rcParams[\"font.size\"] = 14\n",
        "\n",
        "# plot loss and reference value\n",
        "plt.figure(figsize=(12, 6), facecolor='white')\n",
        "plt.plot(cost_val, label=\"Estimator VQE BeH2 IDEAL\")\n",
        "plt.axhline(y=real_solution.real, color=\"tab:red\", ls=\"--\", label=\"Target\")\n",
        "\n",
        "plt.legend(loc=\"best\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Energy [H]\")\n",
        "plt.title(\"VQE energy\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IYqocdAnJjxl"
      },
      "source": [
        "ADAPT_VQE"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GeLpEteeJjxl"
      },
      "source": [
        "In the previous calculation, we used all the single and double excitations, however, one can reduce their number by looking at the gradient w.r.t. parameters for those schemes. The idea is that if the parameters remain constant, then we can train the schemes where parameters need to change in order to reduce the time as well as the number of gates required.\n",
        "\n",
        "The same is demonstrated using ADAPT_VQE, where we 'ADAPT' to non-vanishing gradients and using a similar ansatz with restricted number of schemes, we get much faster and better results. This is basically due to the classical preprocessing of data.\n",
        "\n",
        "The convergence can be seen after merely 10 iterations and the time taken is less than a minute for optimization. The number of CNOT gates already reduce by a factor of 10."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "id": "zGUXkVe-Jjxl",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a3a06b56-ebb5-434c-87a7-ab023b9c63b3"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Total number of excitations = 92\n"
          ]
        }
      ],
      "source": [
        "#We use pennylane for faster computation\n",
        "\n",
        "#Define the symbol and geometry\n",
        "symbols = [\"H\",\"Be\",\"H\"]\n",
        "#Geometry in atomic distance for pennylane\n",
        "geometry = np.array([ -1.291/0.529, 0.0, 0.0,0.0, 0.0, 0.0, 1.291/0.529, 0.0, 0.0])\n",
        "active_electrons = 4\n",
        "H, qubits = qml.qchem.molecular_hamiltonian(\n",
        "    symbols,\n",
        "    geometry,\n",
        "    active_electrons=active_electrons,\n",
        "    active_orbitals=6\n",
        ")\n",
        "\n",
        "print(f\"Total number of excitations = {len(singles) + len(doubles)}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "id": "CTowOdLzJjxm"
      },
      "outputs": [],
      "source": [
        "def circuit_1(params, excitations):\n",
        "    qml.BasisState(hf_state, wires=range(qubits))\n",
        "\n",
        "    for i, excitation in enumerate(excitations):\n",
        "        if len(excitation) == 4:\n",
        "            qml.DoubleExcitation(params[i], wires=excitation)\n",
        "        else:\n",
        "            qml.SingleExcitation(params[i], wires=excitation)\n",
        "    return qml.expval(H)\n",
        "dev = qml.device(\"default.qubit\", wires=qubits)\n",
        "cost_fn = qml.QNode(circuit_1, dev)\n",
        "\n",
        "circuit_gradient = qml.grad(cost_fn, argnum=0)\n",
        "\n",
        "params = [0.0] * len(doubles)\n",
        "grads = circuit_gradient(params, excitations=doubles)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "id": "GNxlH1KNJjxm"
      },
      "outputs": [],
      "source": [
        "doubles_select = [doubles[i] for i in range(len(doubles)) if abs(grads[i]) > 1.0e-5]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "id": "QpecDr64Jjxm"
      },
      "outputs": [],
      "source": [
        "opt = qml.GradientDescentOptimizer(stepsize=0.5)\n",
        "\n",
        "params_doubles = np.zeros(len(doubles_select), requires_grad=True)\n",
        "\n",
        "for n in range(20):\n",
        "    params_doubles = opt.step(cost_fn, params_doubles, excitations=doubles_select)\n",
        "def circuit_2(params, excitations, gates_select, params_select):\n",
        "    qml.BasisState(hf_state, wires=range(qubits))\n",
        "\n",
        "    for i, gate in enumerate(gates_select):\n",
        "        if len(gate) == 4:\n",
        "            qml.DoubleExcitation(params_select[i], wires=gate)\n",
        "        elif len(gate) == 2:\n",
        "            qml.SingleExcitation(params_select[i], wires=gate)\n",
        "\n",
        "    for i, gate in enumerate(excitations):\n",
        "        if len(gate) == 4:\n",
        "            qml.DoubleExcitation(params[i], wires=gate)\n",
        "        elif len(gate) == 2:\n",
        "            qml.SingleExcitation(params[i], wires=gate)\n",
        "    return qml.expval(H)\n",
        "cost_fn = qml.QNode(circuit_2, dev)\n",
        "circuit_gradient = qml.grad(cost_fn, argnum=0)\n",
        "params = [0.0] * len(singles)\n",
        "\n",
        "grads = circuit_gradient(\n",
        "    params,\n",
        "    excitations=singles,\n",
        "    gates_select=doubles_select,\n",
        "    params_select=params_doubles\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "id": "JZUmV8AdJjxm"
      },
      "outputs": [],
      "source": [
        "singles_select = [singles[i] for i in range(len(singles)) if abs(grads[i]) > 1.0e-5 ]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "id": "G_-bDOhVJjxm",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "55894f49-a632-4863-984d-852891056208"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "n = 0,  E = -15.56135211 H, t = 1.67 s\n",
            "n = 1,  E = -15.58014760 H, t = 1.90 s\n",
            "n = 2,  E = -15.58775020 H, t = 1.82 s\n",
            "n = 3,  E = -15.59102148 H, t = 1.79 s\n",
            "n = 4,  E = -15.59250983 H, t = 1.83 s\n",
            "n = 5,  E = -15.59322462 H, t = 2.25 s\n",
            "n = 6,  E = -15.59358749 H, t = 2.49 s\n",
            "n = 7,  E = -15.59378268 H, t = 1.86 s\n",
            "n = 8,  E = -15.59389401 H, t = 1.90 s\n",
            "n = 9,  E = -15.59396115 H, t = 1.96 s\n",
            "n = 10,  E = -15.59400369 H, t = 1.69 s\n",
            "n = 11,  E = -15.59403176 H, t = 1.85 s\n",
            "n = 12,  E = -15.59405087 H, t = 2.51 s\n",
            "n = 13,  E = -15.59406418 H, t = 2.62 s\n",
            "n = 14,  E = -15.59407361 H, t = 1.64 s\n",
            "n = 15,  E = -15.59408036 H, t = 1.85 s\n",
            "n = 16,  E = -15.59408523 H, t = 1.91 s\n",
            "n = 17,  E = -15.59408878 H, t = 1.79 s\n",
            "n = 18,  E = -15.59409136 H, t = 2.13 s\n",
            "n = 19,  E = -15.59409325 H, t = 2.76 s\n"
          ]
        }
      ],
      "source": [
        "cost_fn = qml.QNode(circuit_1, dev)\n",
        "\n",
        "params = np.zeros(len(doubles_select + singles_select), requires_grad=True)\n",
        "\n",
        "gates_select = doubles_select + singles_select\n",
        "energy_vals = []\n",
        "import time\n",
        "for n in range(20):\n",
        "    t1 = time.time()\n",
        "    params, energy = opt.step_and_cost(cost_fn, params, excitations=gates_select)\n",
        "    t2 = time.time()\n",
        "    energy_vals.append(energy)\n",
        "    print(\"n = {:},  E = {:.8f} H, t = {:.2f} s\".format(n, energy, t2 - t1))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "fT8yAnTCJjxm",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "461d153e-51ae-4af7-9711-9df45dde342d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Total number of CNOT qubit gates used = 190\n"
          ]
        }
      ],
      "source": [
        "#Total number of 2 qubit gates used\n",
        "print('Total number of CNOT qubit gates used =', 13*len(doubles_select) + 2*len(singles_select))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "id": "PisRhPFOJjxm",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 578
        },
        "outputId": "7744df26-9e55-4015-a3b5-77ccd624e0da"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x600 with 1 Axes>"
            ],
            "image/png": 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uuEP169dXnTp1FBgYqIceekgnT54s1DY1NVUTJkyQv7+/zGazAgIC9MwzzxRYcR0AAOBq/fr10/vvv6+YmBilpKQoJydHZ86c0Zo1a4oNLKQr/69kGIbOnDmjBQsWyNPT8wZWDQCo7WrcSIs1a9Zo9uzZcnJyUqtWrZSYmFiq6zp27KjBgwcXOn6twKM4gwYNUqdOnQodL2q/dsMw9Je//EXvvPOOmjdvrgcffFDu7u6Kj49XVFSUTpw4UWCv9IyMDPXs2VN79uxRv3799NBDDyk6OlqvvvqqoqKitGXLFtWpU6fMNQMAAAAAUNXUuNBi6NChGjhwoNq3b6+kpCT5+PiU6rpOnTqVaVTFtQwePFjh4eGlavvWW2/pnXfe0RNPPKG33npL9vb2Bc7n5uYWeP/KK69oz549mjx5subMmWM9PmXKFL388st6/fXX9eyzz5a61ry8PMXHx8vd3Z291gEAAAAAlc4wDKWlpcnX11d2diVMADFqsDNnzhiSjJ49exbbJjY21pBkjBw58rrvFxERYUgyIiIiStU+MzPTqFu3rhEUFGRcvny5xPZ5eXmGr6+v4ebmZqSnpxc4l56ebri5uRlBQUFlqvnkyZOGJF68ePHixYsXL168ePHixeuGvk6ePFniM2uNG2lRXvHx8Zo/f75SUlLk7e2tsLAwNW/evFx9RUdHKykpSbm5uQoICFDfvn1Vv379Qu3WrVunCxcuaNSoUbJYLPr888915MgReXl5qW/fvmrRokWB9kePHlV8fLz69+8vV1fXAudcXV3VvXt3rV27VidPniwwpeRa3N3dJUknT56Uh4dHuT4vAAAAAACllZqaqqZNm1qfR6+F0OI369ev1/r1663vTSaThg0bpgULFhQKCEqSv4d5PmdnZ02fPl2TJ08ucHzXrl2SJHt7e3Xo0EFHjhyxnrOzs9P48eP16quvWo8dPXpUktSyZcsi79uyZUutXbtWR48eLTa0yM7OVnZ2tvV9WlqaJMnDw4PQAgAAAABww5RmiYIat3tIWbm4uGjatGnatWuXLl68qOTkZG3YsEFdu3bV8uXLNWLEiFL3FRgYqHnz5unIkSPKzMzUqVOntGzZMtWrV09TpkzRvHnzCrQ/d+6cJOm1116Tp6enfvzxR6WlpWnLli1q1aqV5s6dq//+97/W9ikpKZJU7Krd+aFDfruizJ49W56entZXaUdkAAAAAABwo1XJkRYTJ04sMBqgJE8//XSxow9K0qhRI82cObPAsT59+qhbt24KDQ3V6tWrtXv3boWGhpbYV8+ePdWzZ0/rez8/Pw0fPlyhoaHq3LmzZsyYoccff1wODle+9ry8PEmSk5OT1qxZI19fX0nSbbfdpo8//lgdO3bU3Llz9fjjj5frsxXl2Wef1YQJE6zv84flAAAAAABQ1VTJ0GLhwoXKyMgodfshQ4aUO7QojouLi4YPH67nn39e27ZtK1VoUZy2bduqR48e2rBhgw4ePKj27dtL+n3EROfOna2BRb527dopKChIMTExunjxory8vKztixtJkZqaWqDfopjNZpnN5nJ/FgAAAAAAbpQqGVqkp6fbugRJUoMGDSSpTAFKWfpq3bq1JMnLy6vIa/KPZ2VlycvLyxrM5K9t8UclrXkBAAAAAEB1UuvXtLiWHTt2SJICAgKuqx+LxaKdO3dKkvz9/a3He/XqJUk6ePBgoWsuX76smJgYubq6qmHDhpKuhBG+vr7atm1boSAlIyND27ZtU2BgINM9AAAAAAA1QpUcaXEjRUdHq1OnToVWLV29erWWLl2qunXr6s477yxw7syZM0pJSZGPj0+BqRi7du3STTfdVKCtxWLRlClTFBMTo169esnHx8d6rnnz5urXr5/WrVunRYsWacyYMdZzc+bM0cWLF/XII49Y18AwmUwaM2aMZs6cqVmzZmnOnDnW9rNmzVJ6erqmTp16/V8KAAAAqgyLxaLLly/bugwAuCZHR0fZ29tXeL8mwzCMCu/Vhg4dOmR9mM/KytLKlSvl7e2tAQMGWNtERkZa/xwWFqZjx46pW7duatKkiSwWi3bv3q2tW7fKbDZr5cqVGjhwYIF7hIeHa+nSpYqIiFB4eLj1uMlkUocOHdShQwf5+fkpOTlZUVFROnLkiJo0aaKoqCgFBQUV6OvYsWO69dZbde7cOd19991q06aNoqOjtXHjRvn7+2v79u1q3LixtX1GRoa6d++uvXv3ql+/fgoNDdXu3bu1bt06denSRVFRUXJ2di7195WamipPT0+lpKSw5SkAAEAVYhiGEhISlJKSohr2v+wAaiCTySRPT081bty4xK1My/IcWuNCi82bN1unXRTn6o+8aNEirVq1Svv371diYqLy8vLk5+en3r17a+LEiWrTpk2h64sLLSZNmqTt27crJiZGycnJcnJyUosWLXTvvfdqwoQJqlu3bpH1nDx5Uv/85z/1zTffKCkpSY0bN9bAgQP1z3/+U40aNSrUPiUlRTNmzNCqVauUkJAgHx8fDR06VNOnT5e7u3spv6krCC0AAACqposXL+rMmTNq2LChXF1dS3wIAABbMQxDGRkZOn/+vHx8fIpdtzFfrQ4tUDaEFgAAAFWPYRg6evSoXF1d5efnZ+tyAKBUTp8+rYyMDLVs2fKaQWtZnkNZiBMAAACoYiwWiywWC/+oBKBa8fDwsP7+qiiEFgAAAEAVk5ubK0nWBdkBoDrI/52V/zusIhBaAAAAAFUU61gAqE4q43cWoQUAAAAAAKiSCC0AAAAAAECVRGgBAAAAAACqJEILAAAAAABQJRFaoFo4fj5da6JP6/j5dFuXAgAAgBvs0UcflclkUv369ZWdnV1su7CwMJlMJuvL0dFR9evXV6dOnTR69Gh98803ysvLK/F+vXv3lslkUrt27a7ZLiAgoMD97O3t1aBBA/Xr10+fffaZJCkuLq5Am5JeAQEBxd5v6tSpMplMmj179jXrysvLU7NmzWRvb6+TJ08WOJeSkqJZs2apS5cu8vLykrOzs4KCgvToo49q3759Rfa3efPmEusOCwu7Zk35/vgzyv85NW3aVA8//LB+/vnnUvVzLZGRkTKZTJozZ06xbWbMmCGTyaQPP/zQeiwjI0PLly/X/fffr1atWsnZ2VleXl7q2bOnPvjggzLVkP+d/eUvfylwPDw8vMBnd3BwUN26dRUSEqJhw4bpk08+UU5OTpF9FvXd/fG1efPmIq/NyMiQh4eHTCaT/vrXvxZbd/7f1wEDBpTp81Ym9lBCtfDyN4e0dv9ZPX93sIIautm6HAAAANwgaWlpWrlypUwmk5KTk7VmzRo98MAD17xm4sSJcnNzU15eni5evKiDBw/q/fff15IlS3Trrbfqgw8+ULNmzYq89vjx49YHzv3792vHjh26+eabi72Xvb29nn/+eUlSTk6ODh06pM8//1zr16/Xq6++qtGjR2v69OmFrnvhhRfk6empv//97wWOe3l5FXuvRx99VLNnz1ZERISeffbZYtutX79eJ0+e1IABA9S0aVPr8Z9++kkDBw5UQkKC2rVrpxEjRsjFxcX6/SxdulRz5szRM888U2S/N910k+65554iz10rbClK/s9IktLT07Vnzx59+OGHWrNmjbZs2aLOnTuXqb+K8N1332n48OGqX7+++vTpoz//+c86d+6cVq9erYcffljbtm3T22+/XSH3Gj16tJo0aSLDMJSamqqjR4/qiy++0IoVKxQcHKwPP/xQHTp0KPLaq7+7Pyru57By5UqlpaXJZDJpxYoVmjt3rurUqVMhn6XSGajVUlJSDElGSkqKrUu5ptfXHzb8J39pjP8o2talAAAAVLqsrCzjwIEDRlZWlq1Lsbl3333XkGRMmDDBsLOzM+64445i2/bs2dOQZJw5c6bQufPnzxsPPfSQIclo06aNkZ6eXmQfzz33nCHJmDRpkiHJGDt2bLH38/f3N8xmc6Hja9euNUwmk+Hi4mJkZGQUea0kw9/fv9i+i5P/Gbds2VJsm/vvv9+QZHz88cfWYydOnDDq1atn2NnZGf/9738LXXPo0CGjefPmhiRj6dKlBc5t2rTJkGSMGzeuzPUWV39RP6NXXnnFkGQMHz78uu4RERFhSDJmz55dbJvp06cbkowPPvjAeiw6Otp47733jOzs7AJtExISDH9/f0OSsWPHjlLVUNx3NnLkSEOS8cMPPxS6JjU11Rg/frwhyfD29jZOnz5d4Py1vruSdO/e3XBwcDD+/ve/G5KM999/v8h2sbGxhiSjf//+Zb6HYZT+d1dZnkOZHoJqIcTHQ5J08EyajSsBAADAjbR48WI5ODjoH//4h3r16qVvv/1WJ06cKHM/DRo00PLly9W7d28dOnRI8+fPL9TGYrEoMjJS9evX10svvaQWLVroww8/VEZGRpnu1a9fP7Vu3VqZmZnav39/mWu9ltGjR0uSlixZUuT55ORkffbZZ2rQoIEGDhxoPT516lQlJyfr2WefLTRlQZJat26tzz77TI6Ojho/fnyZP3NFyJ+SkJiYWOicYRhasmSJunfvLg8PD7m4uKhz587Ffg/l0alTJz3yyCNycnIqcNzb21vjxo2TJG3ZsqXC7vdH7u7ueu211xQeHq6zZ8/qxRdfrJB+Dx8+rG3btmnAgAEaP368TCaTFi9eXCF93wiEFqgWgn8LLWLOpSknt+R5iAAAADWRYRjKzMmt8i/DMCrk8x44cEDbt29Xv3795O3trREjRigvL08RERHl6s/Ozk7PPfecJOmjjz4qdH7t2rU6ffq0HnjgATk5OWn48OFKS0vTxx9/XO7PYDKZyn1tUYYMGSJPT099/PHHSk8vvN7bihUrlJ2dreHDh1sfvjMyMrRy5UrVqVNHkyZNKrbvtm3b6k9/+pOSk5O1evXqCq27NNatWydJCg0NLXDcMAwNGzZMo0eP1vnz5/Xwww9rzJgxysjI0OjRo6/5mSqKo6OjJMnBofJXWJg2bZqkK1M6KuK/pfyAYsSIEWrWrJnCwsK0adMmxcbGXnffNwJrWqBaaFLXWe51HJR2KVcx59IV4uth65IAAABuuKzLFoX8c62tyyjRgZn95eJ0/Y8a+Q9bw4cPlyT96U9/0hNPPKGIiAj985//lJ1d2f8Ntnv37nJwcNCePXuUm5tb4CH0j/d75JFHNGPGDC1evFjh4eGlvse3336rw4cPy9XVVW3bti1zjdfi7Oyshx56SAsWLNBHH31kHXmRL3/kwdXHd+7cqcuXL6tr167XXDNDkvr06aOPPvpI27Zts34PV/czY8aMIq8bMGCAbrnlllJ/jldffdW6LkNGRob27dunDRs2qE+fPoVCiEWLFumDDz7QqFGjtHDhQmuAkJOToyFDhmju3Ll66KGHdNNNNxW4bsOGDbp06VKR9y9uwcqiWCwWLVu2TCaTSX379i31deUVFBSkpk2b6uTJk4qNjVVQUFCB81d/d1erU6eOpkyZUuBYbm6uli1bJi8vL917772Srvz93rRpk5YsWaJZs2ZV3gepIIQWqBZMJpOCG3vox7hkHTyTSmgBAABQw12+fFnvvfeePDw8NHjwYEmSm5ub7rvvPi1fvlwbNmxQv379ytyv2WxW/fr1dfbsWSUnJ6tRo0aSpPPnz+uLL75Qq1atrA/fQUFB6t69u7Zu3arDhw+rdevWhfrLzc21PshfvnxZhw8f1meffSbDMDRr1iw5OzuX7wu4htGjR2vBggVasmRJgXBi7969io6OVteuXQuEJQkJCZJUYFHO4uS3OX36dKFzu3bt0q5du4q8zsvLq0yhxdy5cwsdCwgI0EMPPVQoWHn77bfl6uqq+fPnWwMLSXJyctJLL72kL774Qh988EGh0OLbb7/Vt99+W+qaijNt2jT9/PPPevTRR0vcUaai+Pr66uTJk0pMTCwUWhT13UmSp6dnodDiyy+/1NmzZzV27FjrwptDhgzRk08+qcjISL3wwgvlCv9uJEILVBshvr+HFgAAALWRs6O9Dszsb+sySuTsaH/dfXz22Wc6f/68Ro8eXWCXgxEjRmj58uVavHhxuUKL4ixdulSXL18uNLpgxIgR2rp1q5YsWaKXX3650HUWi0UvvPCCpCvTT+rWravevXvrr3/9a4E1JSpS586d1bFjR33//fcFwpT8kSJ/HH1RHkVtDTtu3DgtWLDguvuWpDNnzqhx48aSpKysLMXExGjmzJkaM2aMDhw4YH0wz8zM1M8//yxfX98iv//Lly9Lkg4dOlTo3OzZsws9xOebMWOG9ed2LQsWLNDs2bP1f//3f3rzzTdL/fkq09XfXUkWLVok6crf43zu7u4aPHiwVqxYobVr1+rOO++slDorCqEFqo1gH3dJ0sEEQgsAAFA7mUymCpl2UR1cPQ//an369JGfn58+++wzJScnq169emXqNzs7W0lJSbK3ty9w7eLFi2UymQqFFvfff7+eeuopLVu2TC+99FKhNQ3MZnOxUxAq0+jRo/XUU09Zw5ScnBytWLFCLi4uevDBBwu0zX/APXnyZIn95rfx8/Or+KKL4ezsrPbt22vFihXauXOn3nzzTT311FPy9/fXhQsXZBiGTp8+fc2QoTIWDl20aJGeeOIJtW/fXuvXry92m9HKEB8fL0lq2LDhdfXxzTffKCgoSD169ChwbsSIEVqxYoWWLFlS5UOLqj0OBLhK/mKcB+JTK2xxJwAAAFQ9J0+etC7K2LNnT5lMJuvL3t5ep0+fVnZ2tpYvX17mvrdt26bc3Fx16tTJGkB8//33OnTokAzDUEBAQIH7eXl56dKlS0pISNBXX31VoZ/zegwbNkxms1nLli1Tbm6uPvvsMyUlJWno0KHy8Cg4lbpz585ydHTUrl27lJKScs1+86dThISEVFrtxXF0dFRoaKgsFouio6MlyfpZbrrpJhmGUexr06ZNFVrLu+++q8cee0whISH69ttvVb9+/Qrt/1qOHz+ukydPqmHDhgoICCh3P5GRkbJYLDp+/HiBv9Mmk8m6U8vnn39e5G4tVUntiGlRI7TydpedSbqQeVlnU7PV2LNOyRcBAACg2omMjFReXp569OhR7DoSS5cu1eLFi/XUU0+Vut+8vDy99NJLkqSHHnrIejx/VMedd94pX1/fQtddvHhRq1at0uLFiyttykdZ1atXT/fdd58+/PBDffXVV0UuwJnP1dVVDzzwgJYvX665c+dq5syZRfZ58OBBffrpp3J0dCzw/dxIFy5ckPT79BR3d3cFBwfr4MGDunjxYokLiVaEd999V+PGjVNwcLA2btx4XaMdyiN/ccwHHnig3LvP5G8RK0nh4eGyty88ZevgwYP6/vvv9d5772n8+PHlL7iSEVqg2qjjaK/mDd109Fy6Dp5JJbQAAACogQzDUEREhEwmk5YuXVpoEcJ8R44c0Q8//KCdO3eqc+fOJfabmJiop556Shs3blRISIgef/xxSVJ6erpWrlwpV1dXrVy5ssgpAHl5efL399dXX32lhISEUq8nUNlGjx6tDz/8ULNnz9aPP/6oVq1a6bbbbiuy7UsvvaSvvvpK//rXv9SsWTONGTOmwPmjR49q0KBBysnJ0VNPPSVvb+8b8REK+Omnn/Tdd9/J0dFR3bp1sx5/6qmn9Pjjj2vs2LGKjIyUq6trgetiY2NlMpmua1RCvkWLFmncuHFq06aNNm7caF2o9UZIT0/X9OnTFRkZKR8fH02dOrXcfUVFRenYsWO6/fbbi90i+PDhw2rTpo0WL15MaAFUlGAfDx09l64DZ1LVq82N+wUCAACAG2Pjxo2KjY1Vz549iw0sJGnUqFH64YcftHjx4kKhRf6WkHl5eUpNTdWBAwf03Xff6dKlS+revbs++OADubi4SJI++ugjpaena+TIkcWuWWBnZ6cRI0boX//6l5YuXarJkydX3Ae+Dn369FFAQIC2b98uSXr00UeLbdusWTN9/fXXGjhwoMaOHat58+YpLCxMLi4uOnjwoL7++mvl5OTojjvuKHZ3imtteVrUdpvXcvW2nZcuXdLRo0f1xRdfKDc3V//617/k4+NjbTtu3Dht375dS5cu1bZt29S3b1/5+vrq7NmzOnTokHbs2KEVK1Zcd2ixceNGPfbYYzIMQ7fffrv++9//FmrTqVMn624212PRokX65ptvZBiG0tLSdPToUUVFRSktLU1t27bVhx9+WOA7uFpxW55Kv289mz96aNSoUcXW0Lp1a9166636/vvvtWPHDt18883Wcz///HOx2/y2adOmTD/r62agVktJSTEkGSkpKbYupVT+synG8J/8pfHE+7tsXQoAAEClycrKMg4cOGBkZWXZupQb7qGHHjIkGREREddsl5KSYjg7Oxuenp5GZmamYRiG0bNnT0OS9eXg4GDUrVvX6Nixo/Hoo48a33zzjWGxWAr0061bN0OSsWnTpmve78iRI4Yko1WrVtZj/v7+htlsLtfnlGT4+/uX69qrvfDCC4Ykw97e3oiPjy+x/YULF4yZM2caN910k+Hh4WH9ruzs7Iy333670PdjGIaxadOmAt9rUS9PT89S1fvHn1H+vRs2bGjceeedxpdfflnstR999JHRt29fo27duoajo6Ph5+dnhIWFGXPnzjXOnz9vbRcREWFIMmbPnl1sX9OnTzckGR988EGh6671GjlyZKk+Z/53Nm7cuALHR44cWaA/e3t7w8vLywgJCTGGDRtmfPzxx0ZOTk6pv7s/vl5//XXj4sWLhrOzs+Hq6mqkpaVds853333XkGSMHTvWMAzDiI2NLfEePXv2LLa/0v7uKstzqMkwWNGwNktNTZWnp6dSUlIKLdhTFW0+fE7hET8pqKGrNk4Ms3U5AAAAleLSpUuKjY1VYGBgge0+gcrw5JNPav78+Zo0aZL+/e9/27ocVGOl/d1VludQpoegWgnxvfIXOi4xQ1k5Fjk7Xf8e4AAAAEBt9uabbyomJkavvvqqPD099fzzz9u6JMCKLU9RrTRyr6MGbk7KM6TDZ9NsXQ4AAABQ7dnb22vlypV64YUXZLFYlJCQYOuSACtGWqDaCfbx0HdHE3UgPlWdmnrZuhwAAACg2vPw8NA///lPW5cBFMJIC1Q7wT5XpogcPJNq40oAAAAAAJWJ0ALVTgihBQAAAADUCoQWqHbyR1ocSkhTXh6b3wAAAABATUVogWonqKGrnOztlJ6dq5MXMm1dDgAAAACgkhBaoNpxtLdTS283SUwRAQAAAICajNAC1VL+uhYHzrDtKQAAAADUVIQWqJbYQQQAAAAAaj5CC1RL+aHFgXhCCwAAAACoqQgtUC3lTw85fTFLKVmXbVwNAAAAAKAyEFqgWvJ0cZSfl7Mk6RBTRAAAAACgRiK0QLUV7OMuiXUtAAAAAKCmIrRAtWVd14LQAgAAoMYwmUxlelUXM2bMkMlk0ubNm21dClCtONi6AKC8ft9BhG1PAQAAaorp06cXOvbGG28oJSWlyHMAajZCC1Rb+YtxHj6bplxLnhzsGTgEAABQ3c2YMaPQscjISKWkpBR5DkDNxlMeqq1m9Vzk6mSvnNw8xSZm2LocAAAA3EDx8fGaPn26brnlFjVq1Ehms1kBAQF64okndO7cuULtw8PDZTKZdPz4cc2dO1chISEym80KDw+3tomKitLtt98uV1dX1a9fXw888IBOnjypsLCwIqeiGIahJUuWqHv37vLw8JCLi4s6d+6sJUuWFGgXFhamF154QZLUq1cv69SWgICACv1OgJqIkRaotuzsTGrd2F27f72oA2dS1dLb3dYlAQAA3BB5mZnFn7S3l53ZXLq2dnayq1OnfG2zsiTDKNzMxaX4PirQli1bNHfuXPXp00c333yzHB0dFR0drf/+979au3atdu/eLU9Pz0LX/e1vf9P27dt19913695771WjRo0kSevWrdPdd98te3t7PfDAA/L19dWmTZvUo0cP1a1bt1A/hmFo2LBh+uCDD9SyZUs9/PDDcnJy0vr16zV69GgdOHBAr776qiRZg5GoqCiNHDnSGlZ4eXlVyncD1CSEFqjWgn08rKHFoE5+ti4HAADghjgcelOx51x73q5mCxda3x/p3kNGVlaRbV26dJH/e8us72P69JXlwoUi29Zp106Bn3xsfX/87nt0OT6+ULvgQwdLrL8i9O7dWwkJCXJzcytwfNmyZRo5cqTefvttPffcc4Wu27dvn6Kjo9WsWTPrMYvFoscee0wWi8UaVOQbOXKkli1bVqifRYsW6YMPPtCoUaO0cOFCOTo6SpJycnI0ZMgQzZ07Vw899JBuuukmhYeHKy4uTlFRUQoPD1dYWFgFfQtAzcf0EFRrLMYJAABQOzVq1KhQYCFJw4cPl4eHhzZs2FDkdc8880yBwEKStm7dqhMnTujee+8tEFhI0osvvih7e/tC/bz99ttydXXV/PnzrYGFJDk5Oemll16SJH3wwQdl/lwACmKkBaq1EN/80IJtTwEAQO3Reveu4k/+4QG71batxbe1K/hvmC2+LfpBv6i2Qf/7ssjpITfS6tWrtXDhQu3evVsXLlyQxWKxnosvYhSIJHXt2rXQsb1790pSocBCkpo2bapmzZopNjbWeiwzM1M///yzfH199fLLLxe65vLly5KkQ4cOle0DASiE0ALVWpvG7jKZpPNp2Tqflq2G7uaSLwIAAKjmyrJuRKW1dXYuddvKMHfuXE2aNEkNGzZUv3791KRJEzn/VtMbb7yh7OzsIq/z9vYudCw19co/gOWvb1HUNVeHFhcuXJBhGDp9+rR1gc2iZGSwWDxwvQgtUK25ODkooL6rYhMzdPBMqhq6N7R1SQAAAKhkubm5mjVrlnx8fLRnz54CYYNhGHrllVeKvbaoXUA8PK6M3i1q1xFJOnv2bJHtb7rpJu3cubPM9QMoPda0QLUX7HNl1xCmiAAAANQOiYmJSklJUbdu3QqNjti5c6eyill4tDgdO3aUJG3btq3QuVOnTunXX38tcMzd3V3BwcE6ePCgLl68WKp75K+LcfUUFgAlI7RAtRfiw7oWAAAAtUmjRo3k7Oys3bt3K/OqbVovXLigv/3tb2Xur0ePHmrWrJm++OIL/fDDDwXOTZs2rcig4amnnlJmZqbGjh1b5DSQ2NhYxcXFWd/Xq1dPknTy5Mky1wfUZkwPQbWXv4PIAUILAACAWsHOzk5PPPGE5s6dq44dO+ree+9Vamqqvv76a/n7+8vX17dM/dnb22vBggUaOHCgevfurQceeEA+Pj6KiorS6dOn1bFjR+3bt6/ANePGjdP27du1dOlSbdu2TX379pWvr6/Onj2rQ4cOaceOHVqxYoUCAgIkSb169ZLJZNLUqVO1f/9+eXp6ysvLS08++WRFfS1AjcRIC1R7+aHFsfMZunSZ4XYAAAC1wezZs/XSSy/JZDLpP//5j9avX6+HHnpI69atK7AFaWndeeedWrdunTp37qyVK1fqnXfeUZMmTbR161ZZLBbrOhb5TCaTIiMj9dFHH6lt27b68ssv9dprr2n9+vWqU6eOXn31VfXt29faPiQkRBEREWrQoIHmzZunadOm6dVXX73u7wGo6UyGYeN9iirYnj17tHLlSu3atUu7d+9WYmKievbsqc2bNxfZPi4uToGBgcX2N336dM2YMaNU946MjNSoUaOKPb9p0yaFhYUVee7TTz/Vf/7zH+3evVsZGRny8fHRLbfcoldeeUVNmza1tpsxY8Y1VyiOjY21prmlkZqaKk9PT6WkpBT6RVxdGIahTjPXKyXrsr78Ww+18/O0dUkAAADX5dKlS4qNjVVgYKDq1Klj63JqtbS0NHl7e6t9+/basWOHrcsBqrTS/u4qy3NojZsesmbNGs2ePVtOTk5q1aqVEhMTS3Vdx44dNXjw4ELHiwsZrmXQoEHq1KlToeNFhQmGYegvf/mL3nnnHTVv3lwPPvig3N3dFR8fr6ioKJ04caJAaJFv5MiRRfbn5eVV5nqrO5PJpBAfD/1wPEkHzqQSWgAAAKDMMjIylJeXJ3d3d+sxi8WiZ555RllZWUU+KwCofDUutBg6dKgGDhyo9u3bKykpST4+PqW6rlOnTqUeUVGSwYMHKzw8vFRt33rrLb3zzjt64okn9NZbb1lXFc6Xm5tb5HXh4eHlClRqquD80CKedS0AAABQdkePHlWPHj3Uv39/BQUFKS0tTd99950OHDigtm3b6qmnnrJ1iUCtVONCi7Zt29q6hFLLysrSCy+8oKCgIL355puFAgtJcnCocT+iSsG2pwAAALgefn5+Gjp0qKKiovTNN98oNzdXzZo106RJk/Tcc8/J1dXV1iUCtRJPxL+Jj4/X/PnzlZKSIm9vb4WFhal58+bl6is6OlpJSUnKzc1VQECA+vbtq/r16xdqt27dOl24cEGjRo2SxWLR559/riNHjsjLy0t9+/ZVixYtir3Hli1btGPHDtnZ2ally5bq27ev3NzcylVvTRB81banhmHIZDLZuCIAAABUJw0bNlRERIStywDwB4QWv1m/fr3Wr19vfW8ymTRs2DAtWLCgzKnqW2+9VeC9s7Ozpk+frsmTJxc4vmvXLklXtljq0KGDjhw5Yj1nZ2en8ePHF7ui8PTp0wu89/Ly0ptvvqkRI0Zcs7bs7GxlZ2db36em1oyRCS293eRgZ1LqpVzFp1ySn5ezrUsCAAAAAFynWr/lqYuLi6ZNm6Zdu3bp4sWLSk5O1oYNG9S1a1ctX768xBDgaoGBgZo3b56OHDmizMxMnTp1SsuWLVO9evU0ZcoUzZs3r0D7c+fOSZJee+01eXp66scff1RaWpq2bNmiVq1aae7cufrvf/9b4JqOHTtqyZIlOn78uLKyshQbG6t58+bJZDIpPDxcn3/++TVrnD17tjw9Pa2vohb5rI7MDvZq0ejKSBPWtQAAAACAmqFKbnk6ceLEAqMBSvL000+rZcuWhY4nJCTIx8fnmlueFiczM1OhoaE6fPiwdu3apdDQ0DJdf7X9+/erc+fOcnFx0dmzZ63rVDz22GN699135ezsrJiYGPn6+lqv+eWXX9SxY0cFBgYqJiamxHt8++23uuOOO9SuXTvt27ev2HZFjbRo2rRptd7yNN/4j/bo0+jTmnBHKz3Vp/DfBwAAgOoif9vAgIAAOTszghRA9ZCVlaW4uLiav+XpwoULlZGRUer2Q4YMKTK0uB4uLi4aPny4nn/+eW3btu26Qou2bduqR48e2rBhgw4ePKj27dtLkjw9r2zN2blz5wKBhSS1a9dOQUFBiomJ0cWLF0vcyrRPnz5q3ry5fv75Z6Wmphb7gzebzTKbzeX+LFVZsI+7Po1mMU4AAFD95f8jV3E7yQFAVZT/O6siN5SoktND0tPTZRhGqV+VtfVngwYNJKlMAUpZ+mrdurUkFRtI5B/Pysoq0z0yMzPLWWX1FuJzJQQitAAAANWdvb297O3ta8z6YwBqh9TUVOvvr4pSJUdaVBU7duyQJAUEBFxXPxaLRTt37pQk+fv7W4/36tVLknTw4MFC11y+fFkxMTFydXVVw4YNS7xHRkaG9u/fL1dXV2t4Udvkb3sal5Sp9OxcuZn56w0AAKonk8mkRo0a6cyZMzKbzXJ1dWV3NABVlmEYysjIUGpqqnx8fCr091Wtf6qLjo5Wp06dCn2pq1ev1tKlS1W3bl3deeedBc6dOXNGKSkp8vHxsU7xkK7sBnLTTTcVaGuxWDRlyhTFxMSoV69e8vHxsZ5r3ry5+vXrp3Xr1mnRokUaM2aM9dycOXN08eJFPfLII9ahNWlpaTpz5oxatWpV4B5ZWVkaO3as0tLSNGrUqAodilOd1Hczq5G7WefSsnU4IVU3+dezdUkAAADl5unpqaysLCUmJur8+fO2LgcArslkMsnLy6vAM3KF9FsVF+K8HocOHdKcOXMkXXmYX7lypby9vTVgwABrm8jISOufw8LCdOzYMXXr1k1NmjSRxWLR7t27tXXrVpnNZq1cuVIDBw4scI/w8HAtXbpUERERCg8Ptx43mUzq0KGDOnToID8/PyUnJysqKkpHjhxRkyZNFBUVpaCgoAJ9HTt2TLfeeqvOnTunu+++W23atFF0dLQ2btwof39/bd++XY0bN5YkxcXFKSgoSF26dFFwcLAaN26ss2fPasOGDTp16pTat2+vTZs2qX79+qX+vsqyAEp1MHLJj4o6cl6zBrfT8Fv8S74AAACgirNYLLp8+bKtywCAa3J0dCz1tJBqvxDn9UhISNDSpUsLHDt79myBY1eHFo888ohWrVql7du3KzExUXl5efLz89OYMWM0ceJEtWnTptT3njhxorZv367169crOTlZTk5OatGihZ5//nlNmDBBdevWLXRN8+bNtXPnTv3zn//UN998o3Xr1qlx48b661//qn/+859q1KiRtW29evX0xBNP6Mcff9RXX32lCxcuyNnZWcHBwXrqqaf05JNP1vrVpUN8PRR15DzrWgAAgBqjoueHA0B1UuNGWqBsatpIi8/3xuupD6LVqamX1vy1u63LAQAAAAD8QVmeQ6vk7iFAeYX8thjn4YQ0WfLI4wAAAACgOiO0QI0SUN9VZgc7ZV226ETS9W9VCwAAAACwHUIL1CgO9nZq0/jKaIuDZ9JsXA0AAAAA4HoQWqDGCfa5MifqwJkUG1cCAAAAALgehBaocfJDC0ZaAAAAAED1RmiBGuf30IJtTwEAAACgOiO0QI3T5rcdRM6kXNKFjBwbVwMAAAAAKC9CC9Q4HnUc1bSesyRGWwAAAABAdUZogRopuHH+YpyEFgAAAABQXRFaoEZiMU4AAAAAqP4ILVAjhfiyGCcAAAAAVHeEFqiRQn4baXH0XJpycvNsXA0AAAAAoDwILVAjNanrLHezgy5bDB07n27rcgAAAAAA5UBogRrJZDJZtz5liggAAAAAVE+EFqixQnxY1wIAAAAAqjNCC9RY+TuIsO0pAAAAAFRPhBaosa7e9tQwDBtXAwAAAAAoK0IL1FitG7vLziQlZ+ToXFq2rcsBAAAAAJQRoQVqrDqO9gpq6CaJKSIAAAAAUB0RWqBGs65rEU9oAQAAAADVDaEFarRgtj0FAAAAgGqL0AI1WjDbngIAAABAtUVogRqt7W+hRWxihrJyLDauBgAAAABQFoQWqNEauptV39VJeYZ0+GyarcsBAAAAAJQBoQVqNJPJxBQRAAAAAKimCC1Q47EYJwAAAABUT4QWqPFCfBlpAQAAAADVEaEFarzfp4ekKS/PsHE1AAAAAIDSIrRAjde8oZuc7O2Unp2rUxeybF0OAAAAAKCUCC1Q4zna26lFIzdJ0gGmiAAAAABAtUFogVqBdS0AAAAAoPohtECtkL+uBSMtAAAAAKD6ILRArcC2pwAAAABQ/RBaoFYI+W2kxakLWUq9dNnG1QAAAAAASoPQArWCl4uTfD3rSJIOnUmzcTUAAAAAgNIgtECtkb+uBVNEAAAAAKB6ILRArWFdjDOe0AIAAAAAqgNCC9Qa1pEWCYQWAAAAAFAdEFqg1gjxvRJaHE5IU64lz8bVAAAAAABKQmiBWsO/notcnOyVnZunuKQMW5cDAAAAACgBoQVqDTs7k1o3dpck7WddCwAAAACo8ggtUKv8voMI254CAAAAQFVHaIFaJYRtTwEAAACg2iC0QK0STGgBAAAAANUGoQVqlTaN3WUySefSspWYnm3rcgAAAAAA10BogVrF1ewg/3oukhhtAQAAAABVHaEFap0QX6aIAAAAAEB1QGiBWie4MTuIAAAAAEB1QGiBWid/Mc4D8Yy0AAAAAICqrMaFFnv27NHUqVPVv39/NWzYUCaTSWFhYcW2j4uLk8lkKvY1Y8aMUt87MjLymn1t3ry5TO1NJpP69OlT6D6pqamaMGGC/P39ZTabFRAQoGeeeUbp6emlrrU2C/5tesix8+nKzrXYuBoAAAAAQHEcbF1ARVuzZo1mz54tJycntWrVSomJiaW6rmPHjho8eHCh49cKPIozaNAgderUqdDxgICAAu87deqk6dOnF9nHJ598ov3796t///4FjmdkZKhnz57as2eP+vXrp4ceekjR0dF69dVXFRUVpS1btqhOnTplrrk28fWsI09nR6VkXdbRs+lq5+dp65IAAAAAAEWocaHF0KFDNXDgQLVv315JSUny8fEp1XWdOnUq06iKaxk8eLDCw8NLdc+iwo2cnBy9/fbbcnBw0MiRIwuce+WVV7Rnzx5NnjxZc+bMsR6fMmWKXn75Zb3++ut69tlnr/cj1Ggmk0nBPu7afjxZB8+kEloAAAAAQBVV46aHtG3bVqGhoXJ0dLR1KeW2Zs0aJSUl6Z577pG3t7f1uGEYWrRokdzc3DRt2rQC10ybNk1ubm5atGjRjS63WrKua8EOIgAAAABQZdW4kRblFR8fr/nz5yslJUXe3t4KCwtT8+bNy9VXdHS0kpKSlJubq4CAAPXt21f169cv9fX5wcOYMWMKHD969Kji4+PVv39/ubq6Fjjn6uqq7t27a+3atTp58qSaNm1artpri/zQgm1PAQAAAKDqIrT4zfr167V+/Xrre5PJpGHDhmnBggWFAoKSvPXWWwXeOzs7a/r06Zo8eXKJ1544cULffvutmjRpogEDBhQ4d/ToUUlSy5Yti7y2ZcuWWrt2rY4ePVpsaJGdna3s7Gzr+9TU2vnQHuLz+7anhmHIZDLZuCIAAAAAwB/VuOkhZeXi4qJp06Zp165dunjxopKTk7VhwwZ17dpVy5cv14gRI0rdV2BgoObNm6cjR44oMzNTp06d0rJly1SvXj1NmTJF8+bNK7GPiIgI5eXlKTw8XPb29gXOpaSkSJI8PYteg8HDw6NAu6LMnj1bnp6e1ldtHZHRopGbHOxMSsm6rDMpl2xdDgAAAACgCFVypMXEiRMLjAYoydNPP13s6IOSNGrUSDNnzixwrE+fPurWrZtCQ0O1evVq7d69W6GhoSX21bNnT/Xs2dP63s/PT8OHD1doaKg6d+6sGTNm6PHHH5eDQ9Ffe15eniIiImQymfToo4+W6/OU5Nlnn9WECROs71NTU2tlcFHH0V7NG7rp8Nk0HYhPla+Xs61LAgAAAAD8QZUMLRYuXKiMjIxStx8yZEi5Q4viuLi4aPjw4Xr++ee1bdu2UoUWxWnbtq169OihDRs26ODBg2rfvn2R7TZs2KBff/1Vffr0UWBgYKHz+SMsihtJkT/Vo7iRGJJkNptlNpvL+hFqpGAfdx0+m6aDZ1LVN8S75AsAAAAAADdUlQwt0tPTbV2CJKlBgwaSVKYA5Xr6Km4Bznz5wUz+2hZ/VNKaFygo2MdDa/bE62BC7VzXAwAAAACqulq/psW17NixQ5IUEBBwXf1YLBbt3LlTkuTv719km6SkJH322WeqV6+e7rvvviLbtGzZUr6+vtq2bVuh8CMjI0Pbtm1TYGBgrZzuUR4hvr8vxgkAAAAAqHpqfWgRHR0twzAKHV+9erWWLl2qunXr6s477yxw7syZMzp06FChaRq7du0q1I/FYtGUKVMUExOjXr16ycfHp8g63nvvPeXk5OiRRx4pdvqGyWTSmDFjlJ6erlmzZhU4N2vWLKWnp2vs2LHX/Lz4Xf62p3FJGcrIzrVxNQAAAACAPzIZRT2xV2OHDh3SnDlzJElZWVlauXKlvL29C2wfGhkZaf1zWFiYjh07pm7duqlJkyayWCzavXu3tm7dKrPZrJUrV2rgwIEF7hEeHq6lS5cqIiJC4eHh1uMmk0kdOnRQhw4d5Ofnp+TkZEVFRenIkSNq0qSJoqKiFBQUVGTd7du31y+//KJ9+/YVu+aFdGVERffu3bV3717169dPoaGh2r17t9atW6cuXbooKipKzs6lX1QyNTVVnp6eSklJse4+Upt0eWmDzqdla9Xjt+om/7q2LgcAAAAAaryyPIdWyTUtrkdCQoKWLl1a4NjZs2cLHLs6tHjkkUe0atUqbd++XYmJicrLy5Ofn5/GjBmjiRMnqk2bNqW+98SJE7V9+3atX79eycnJcnJyUosWLfT8889rwoQJqlu36IfiH3/8Ub/88ou6du16zcBCklxdXRUVFaUZM2Zo1apV2rRpk3x8fDRx4kRNnz69TIEFroy2OJ92XgfPpBJaAAAAAEAVU+NGWqBsavtIizlfH9KCqGMadnMzvXTftQMjAAAAAMD1K8tzaK1f0wK1W7CPuyTpwBl2EAEAAACAqobQArVayG+LcR5OSFNeHoOOAAAAAKAqIbRArRbYwFVODnbKzLHoRHKmrcsBAAAAAFyF0AK1moO9ndo0vjJF5CBTRAAAAACgSiG0QK0X3PjKFJED8YQWAAAAAFCVEFqg1stfjJORFgAAAABQtRBaoNYL/m0xTkILAAAAAKhaCC1Q6wX7Xgkt4lMu6WJmjo2rAQAAAADkI7RAredRx1FN6jpLkg4w2gIAAAAAqgxCC0BXTxFJs3ElAAAAAIB8hBaAWNcCAAAAAKoiQgtAUgihBQAAAABUOYQWgH4PLY6eTddlS56NqwEAAAAASIQWgCSpSV1nuZkdlGPJ07Hz6bYuBwAAAAAgQgtAkmRnZ1Kbxu6SmCICAAAAAFUFoQXwmxBfdhABAAAAgKqE0AL4Tf4OIgfiGWkBAAAAAFUBoQXwm6u3PTUMw8bVAAAAAAAILYDftPZ2l51JSsrI0fm0bFuXAwAAAAC1HqEF8BtnJ3sFNnCVJB1gMU4AAAAAsDlCC+Aq1nUtCC0AAAAAwOYILYCr/L6uBTuIAAAAAICtEVoAVwm5ajFOAAAAAIBtEVoAVwnxvRJaHD+frkuXLTauBgAAAABqN0IL4CqN3M2q5+qkPEM6nMAUEQAAAACwJUIL4Comk0nBPu6SmCICAAAAALZGaAH8QXBj1rUAAAAAgKqA0AL4g/x1LdhBBAAAAABsi9AC+IPgq3YQMQzDxtUAAAAAQO1FaAH8QfOGbnK0NyktO1enLmTZuhwAAAAAqLUILYA/cHKwU4tGVxbjPMC6FgAAAABgM4QWQBFCfFiMEwAAAABsjdACKEL+tqcH4gktAAAAAMBWCC2AIlhHWiQQWgAAAACArRBaAEXI30HkZHKW0i5dtnE1AAAAAFA7EVoARajr6iQfzzqSpEMJaTauBgAAAABqJ0ILoBj5oy1Y1wIAAAAAbIPQAihG/mKc7CACAAAAALZBaAEUI5htTwEAAADApggtgGLk7yByKCFNuZY8G1cDAAAAALWPQ2kabdmy5bpvFBAQoGbNml13P8CN4l/fVc6O9sq6bFFcUoZaNHK3dUkAAAAAUKuUKrQICwuTyWS6rhtNnz5d//znP6+rD+BGsrczqXVjd+05eVEHzqQRWgAAAADADVaq0EKSevbsqZ49e5b5BoZhaObMmWW+DqgKgn08tOfkRR08k6qBHX1tXQ4AAAAA1CqlDi3CwsLKPVKC0ALVVYgvi3ECAAAAgK2UaiHOm2++WU2aNCn3Ta73esBWQn7b9vRAPKEFAAAAANxopRpp8cMPP1zXTa73esBWWje+MtLiXFq2ktKzVd/NbOOKAAAAAKD2YMtT4BrczA7yr+8iSTp4Js3G1QAAAABA7UJoAZQgxId1LQAAAADAFkq9EOcrr7xSrhv84x//KNd1QFUR7OOhr39J0AFCCwAAAAC4oUodWkyZMkUmk0mGYViPmUwmSSpw7Gomk+mGhxZ79uzRypUrtWvXLu3evVuJiYnq2bOnNm/eXGT7uLg4BQYGFtvf9OnTNWPGjFLdOzIyUqNGjSr2/KZNmxQWFlbq9pLUu3dvffvtt9b3M2bM0AsvvFBs+9jYWAUEBJSqXpROMCMtAAAAAMAmSh1aREREFDq2Zs0aff7550Wes5U1a9Zo9uzZcnJyUqtWrZSYmFiq6zp27KjBgwcXOn51yFBagwYNUqdOnQod/2OY0KlTJ02fPr3IPj755BPt379f/fv3L/L8yJEjiwwnvLy8ylgtShL82w4iMefSlZ1rkdnB3sYVAQAAAEDtUOrQYuTIkYWOxcXF6fPPPy/ynK0MHTpUAwcOVPv27ZWUlCQfH59SXdepU6dSj6goyeDBgxUeHl6qexYVbuTk5Ojtt9+Wg4NDsd9teHh4uQIVlJ2fl7M86jgo9VKuYs6lq62vp61LAgAAAIBaocYtxNm2bVuFhobK0dHR1qWU25o1a5SUlKR77rlH3t7eti6n1jOZTNYpIgfimSICAAAAADdKqUda1HTx8fGaP3++UlJS5O3trbCwMDVv3rxcfUVHRyspKUm5ubkKCAhQ3759Vb9+/VJfv2jRIknSmDFjim2zZcsW7dixQ3Z2dmrZsqX69u0rNze3ctWLkgX7eGhHbDLbngIAAADADURo8Zv169dr/fr11vcmk0nDhg3TggUL5OrqWqa+3nrrrQLvnZ2dNX36dE2ePLnEa0+cOKFvv/1WTZo00YABA4pt98e1MLy8vPTmm29qxIgR1+w/Oztb2dnZ1vepqYwcKA22PQUAAACAG6/GTQ8pKxcXF02bNk27du3SxYsXlZycrA0bNqhr165avnx5iSHA1QIDAzVv3jwdOXJEmZmZOnXqlJYtW6Z69eppypQpmjdvXol9REREKC8vT+Hh4bK3L7zgY8eOHbVkyRIdP35cWVlZio2N1bx582QymRQeHq7PP//8mv3Pnj1bnp6e1lfTpk1L/flqsxDf30KLhNRid8sBAAAAAFQsk3EdT2AvvPCCZs6cKYvFUpE1aeLEiQVGA5Tk6aefVsuWLQsdT0hIkI+PzzW3PC1OZmamQkNDdfjwYe3atUuhoaFluv5q+/fvV+fOneXi4qKzZ8/KwaHoAS55eXkKDAzUyZMndezYsWtuxfpH3377re644w61a9dO+/btK7ZdUSMtmjZtqpSUFHl4eJT+Q9Uyly5b1Hb6WlnyDH0/pbd8vZxtXRIAAAAAVEupqany9PQs1XNoqaeHPPHEE4WO7dy5s9hz0pUpFvPnzy/tLawWLlyojIyMUrcfMmRIkaHF9XBxcdHw4cP1/PPPa9u2bdcVWrRt21Y9evTQhg0bdPDgQbVv377Idhs2bNCvv/6qPn36lCmwkKQ+ffqoefPm+vnnn5WamlrsD95sNstsNpf5M9R2dRzt1byhq46cTdfBM6mEFgAAAABwA5Q6tFiwYEGZz5U3tEhPTy/zNZWhQYMGklSmAOV6+irNApwl3SMmJkaZmZmMmqgEwT4e1tCiTzC7ugAAAABAZSt1aLFp06bKrKNK2rFjhyQpICDguvqxWCzWUSn+/v5FtklKStJnn32mevXq6b777ivzPTIyMrR//365urpaAxJUrBAfD322J54dRAAAAADgBil1aNGzZ8/KrMNmoqOj1alTJ5lMpgLHV69eraVLl6pu3bq68847C5w7c+aMUlJS5OPjI09PT+vxXbt26aabbirQ1mKxaMqUKYqJiVGvXr3k4+NTZB3vvfeecnJy9MgjjxQ7fSMtLU1nzpxRq1atChzPysrS2LFjlZaWplGjRhW7ZgauTzA7iAAAAADADVXjnm4PHTqkOXPmSLryMJ9/LDw83NomMjLS+ufx48fr2LFj6tatm5o0aSKLxaLdu3dr69atMpvNioyMLBBMSNKzzz6rpUuXKiIiokC/nTt3VocOHdShQwf5+fkpOTlZUVFROnLkiJo0aWKd/lGUxYsXS7r21JCkpCS1adNGXbp0UXBwsBo3bqyzZ89qw4YNOnXqlNq3b69///vfpf2qUEb5oUVsUoYyc3Ll4lTj/vMBAAAAgCqlVE9dOTk5cnBwkJ1d+XZIvd7ryyIhIUFLly4tcOzs2bMFjl0dWjzyyCNatWqVtm/frsTEROXl5cnPz09jxozRxIkT1aZNm1Lfe+LEidq+fbvWr1+v5ORkOTk5qUWLFnr++ec1YcIE1a1bt8jrfvzxR/3yyy/q2rVrsYt0SlK9evX0xBNP6Mcff9RXX32lCxcuyNnZWcHBwXrqqaf05JNPytmZBSIrS0N3sxq4mZWYnq1DCWkKbVb0zxMAAAAAUDFKteWpvb29ZsyYoWnTppXrJtd7PSpPWbaagTRiyY/acuS8XrqvnYbdXPT6JAAAAACA4pXlObRUQx8Mw1Apso1Kux6oKoJ93CWxrgUAAAAA3AilnpQfGRmpzZs3l+smf1zkEqiuQn5b1+JAPKEFAAAAAFS2UocWcXFxiouLq8RSgKovfzHOQwlpysszZGdHIAcAAAAAlaVUoUVeXl5l1wFUC0ENXOXkYKfMHIt+Tc5UQANXW5cEAAAAADVW5W/nAdQgDvZ2au3NuhYAAAAAcCMQWgBllL8Y5wFCCwAAAACoVIQWQBnlr2vBSAsAAAAAqFyEFkAZ/R5apNm4EgAAAACo2QgtgDLKDy1OX8xSSuZlG1cDAAAAADUXoQVQRp7OjvLzcpbEuhYAAAAAUJkILYByYF0LAAAAAKh85QotPvroI12+zLB41F4hPmx7CgAAAACVrVyhxUMPPSQ/Pz9NmjRJhw4dquiagCovxPe3kRYJhBYAAAAAUFnKFVo8//zzqlOnjl577TW1bdtWt99+u9577z1dunSpousDqqT86SFHEtJ12ZJn42oAAAAAoGYqV2gxc+ZMxcXF6YsvvtDAgQO1fft2hYeHy8fHR3/729+0d+/eiq4TqFKa1nWRq5O9cix5On4+w9blAAAAAECNVO6FOO3s7HT33Xfr008/1alTp/Svf/1LDRs21Pz58xUaGqquXbtq0aJFSk9Pr8h6gSrBzs6kNizGCQAAAACVqkJ2D2nUqJEmT56sI0eOaO3atfLx8dGuXbs0btw4+fr66oknntCJEycq4lZAlRFCaAEAAAAAlarCtjw9cOCAxo8fr4cffljx8fFycXHRsGHDFBAQoAULFigkJERff/11Rd0OsLn8dS0OEFoAAAAAQKW4rtAiKytLERERuvXWW9W+fXu9+eab8vPz0/z58xUfH69ly5Zp3759+t///ic3NzdNnjy5ouoGbC6YbU8BAAAAoFI5lOeinTt3atGiRfrwww+VlpamOnXqaMSIEfrLX/6im2++uVD7O++8U6NHj9arr7563QUDVUXrxu4ymaTE9BydS7ukRu51bF0SAAAAANQo5QotunbtKkkKCQnRuHHjNGLECHl6el7zmmbNmsnPz688twOqJBcnBwU2cNXx8xk6eCaN0AIAAAAAKli5pocMGzZMW7Zs0S+//KK//e1vJQYWkvSXv/xFsbGx5bkdUGVZ17WIZ4oIAAAAAFS0co20eO+99yq6DqBaCvHx0P/2nWFdCwAAAACoBBW2ewhQG7EYJwAAAABUnnKNtAgKCiqxjZ2dnTw8PNS6dWvdd999uv/++8tzK6BKC/G5MjXqeGKGLl22qI6jvY0rAgAAAICao1yhRV5ennJzcxUfH3+lEwcHNWjQQImJicrNzZUk+fr66ty5c9qzZ49WrlypRYsW6csvv5STk1PFVQ/YmLeHWXVdHHUh87KOnE1ThyZeti4JAAAAAGqMck0P2bNnj3x8fNS7d299//33ys7OVnx8vLKzs/X999+rT58+8vX11a+//qojR47orrvu0rfffqu5c+dWdP2ATZlMJutinEwRAQAAAICKVa7QYvLkycrOzta6det0yy23yGQySbryAHfLLbfom2++0aVLlzRlyhS1aNFCH3/8sfz9/fXhhx9WaPFAVfB7aJFm40oAAAAAoGYpV2jx2Wef6a677pKdXdGX29vb66677tJnn30mSapTp4569+6tmJiY8lcKVFEh+dueMtICAAAAACpUuUKL1NRUpaZe+wEtJSVFKSkp1vcNGjQoz62AKu/q6SGGYdi4GgAAAACoOcoVWoSEhOiDDz7Q8ePHizx//PhxffjhhwoJCbEe+/XXX9WwYcPyVQlUYS0aucnR3qS0S7k6dSHL1uUAAAAAQI1Rrt1Dpk6dqiFDhqhTp04aM2aMunfvrkaNGuncuXPatm2bFi9erPT0dE2dOlWSlJOTo3Xr1qlfv34VWjxQFTg52Kl5QzcdSkjTwTOpalrPxdYlAQAAAECNUK7Q4k9/+pMWLVqkv//973rjjTf05ptvWs8ZhiE3NzctXLhQf/rTnyRJmZmZWrx4sdq2bVsxVQNVTIivx2+hRZr6tW1s63IAAAAAoEYoV2ghSY8++qj+/Oc/67PPPtPevXuVmpoqDw8PdezYUYMGDZKnp6e1rZeXlwYNGlQhBQNVUYiPh1brtA6cSSm5MQAAAACgVMoVWsycOVOBgYEaPny4RowYUdE1AdUO254CAAAAQMUr10KcL774on7++eeKrgWotvJDi1+TM5V26bKNqwEAAACAmqFcoUWzZs108eLFCi4FqL7quTqpsUcdSdLhBEZbAAAAAEBFKFdo8eCDD+qbb75RSgrz94F8wT7ukqQDZ1JtXAkAAAAA1AzlCi2mTZumDh06qHfv3vrf//6nc+fOVXRdQLXz+7oWhBYAAAAAUBHKtRCni4uLpCvbmw4cOLDYdiaTSbm5ueWrDKhm8kOLAyzGCQAAAAAVolyhxW233SaTyVTRtQDVWojvldDicEKqLHmG7O34bwQAAAAArke5QovNmzdXcBlA9RdQ31V1HO106XKeYhMz1KKRm61LAgAAAIBqrVxrWgAozN7OpNaNWdcCAAAAACrKdYUWOTk5+uqrr/Taa69p1qxZ1uOXLl3SuXPnlJeXd90FAtVJyG87iBBaAAAAAMD1K3do8fnnn6tZs2a69957NWnSJM2YMcN6bt++ffLx8dGHH35YETUC1UYIO4gAAAAAQIUpV2ixbds2DRkyRGazWW+++aYefvjhAue7du2qFi1aaNWqVRVSJFBd/L6DCKEFAAAAAFyvci3EOWvWLHl5eWnXrl1q0KCBkpKSCrXp3LmzduzYcd0FAtVJm99Ci7Op2UrOyFE9VycbVwQAAAAA1Ve5Rlrs2LFDgwYNUoMGDYpt07RpUyUkJJS7MKA6cjM7qFk9F0lMEQEAAACA61Wu0CI7O1seHh7XbHPx4kXZ2bE5CWof1rUAAAAAgIpRrlQhKChIP/300zXb/PDDD2rTpk25iroee/bs0dSpU9W/f381bNhQJpNJYWFhxbaPi4uTyWQq9nX1AqMliYyMvGZfmzdvLnSNYRhavXq1evXqJR8fH7m4uKh169YaN26cjh8/XuR9UlNTNWHCBPn7+8tsNisgIEDPPPOM0tPTS10rKo91XYt4QgsAAAAAuB7lWtPiz3/+s1588UVFRERo1KhRhc6/+uqr+uWXX/TKK69cd4FltWbNGs2ePVtOTk5q1aqVEhMTS3Vdx44dNXjw4ELHrxV4FGfQoEHq1KlToeMBAQGFjk2aNEmvvfaafHx8NHjwYHl4eGjv3r1699139cEHH+j7779Xu3btrO0zMjLUs2dP7dmzR/369dNDDz2k6Ohovfrqq4qKitKWLVtUp06dMteMihP827anLMYJAAAAANenXKHFM888o1WrVmnMmDFasWKFsrOzJUn/+Mc/9MMPP+j7779Xp06d9OSTT1ZosaUxdOhQDRw4UO3bt1dSUpJ8fHxKdV2nTp3KNKriWgYPHqzw8PAS2yUkJOiNN96Qv7+/9u7dK09PT+u5119/XRMmTNBrr72mJUuWWI+/8sor2rNnjyZPnqw5c+ZYj0+ZMkUvv/yyXn/9dT377LMV8jlQPvkjLY6dT1dObp6cHJgmBQAAAADlUa6nKTc3N3333Xd68MEHtXnzZm3dulWGYejVV1/V999/r/vvv18bNmyQ2Wyu6HpL1LZtW4WGhsrR0fGG37us4uLilJeXp+7duxcILCTpnnvukSSdP3/eeswwDC1atEhubm6aNm1agfbTpk2Tm5ubFi1aVPmF45qa1HWWex0HXbYYijnHlB0AAAAAKK9yjbSQpLp16+r999/XW2+9pZ9++knJycny8PBQly5d5O3tXZE13hDx8fGaP3++UlJS5O3trbCwMDVv3rxcfUVHRyspKUm5ubkKCAhQ3759Vb9+/ULtWrZsKScnJ23btk2pqakFFjf98ssvJUl9+vSxHjt69Kji4+PVv39/ubq6FujL1dVV3bt319q1a3Xy5Ek1bdq0XLXj+plMJgX7eOjH2GQdOJOqEN9rL1oLAAAAAChauUOLfPXr19eAAQMqohabWr9+vdavX299bzKZNGzYMC1YsKBQQFCSt956q8B7Z2dnTZ8+XZMnTy5wvH79+pozZ44mTpyoNm3aaNCgQdY1LTZu3KgnnniiwBSbo0ePSroSdhSlZcuWWrt2rY4ePVpsaJGdnW2dziNdWdQTFS/kt9CCHUQAAAAAoPxq/WR7FxcXTZs2Tbt27dLFixeVnJysDRs2qGvXrlq+fLlGjBhR6r4CAwM1b948HTlyRJmZmTp16pSWLVumevXqacqUKZo3b16ha8aPH68PP/xQ6enpWrBggV555RWtXbtWN998sx5++GE5OPyeK6WkpEhSoakk+fJHauS3K8rs2bPl6elpfTEio3LkL8ZJaAEAAAAA5VfukRYHDhzQ22+/rZ9++kkXL16UxWIp1MZkMunYsWNl7nvixIkFRgOU5Omnny529EFJGjVqpJkzZxY41qdPH3Xr1k2hoaFavXq1du/erdDQ0BL76tmzp3r27Gl97+fnp+HDhys0NFSdO3fWjBkz9PjjjxcIImbOnKkXX3xRM2fO1COPPCIvLy/t2bNH48ePV1hYmFatWqWBAweW67MV5dlnn9WECROs71NTUwkuKkGIz5Vg6ZfTKcrOtcjsYG/jigAAAACg+ilXaBEVFaUBAwYoOztbDg4O8vb2LvAgns8wjHIVtXDhQmVkZJS6/ZAhQ8odWhTHxcVFw4cP1/PPP69t27aVKrQoTtu2bdWjRw9t2LBBBw8eVPv27SVJGzZs0PTp0zV+/HhNmTLF2r5Hjx764osvFBQUpIkTJ1pDi/wRFsWNpMif6lHcSAxJMpvNNlkgtbZp4+Mubw+zzqZm6/M98RramWAIAAAAAMqqXKHFlClTlJubq0WLFmnkyJGyt6/Yf0VOT68aOy40aNBAksoUoJSlr6+//lqS1KtXr0LtGzdurDZt2ig6Olrp6elyc3OzBjP5a1v8UUlrXuDGcbS306jugZrz9SG9+91xDbmpiUwmk63LAgAAAIBqpVxrWuzdu1cPPvigHn300QoPLKqSHTt2SJICAgKuqx+LxaKdO3dKkvz9/a3Hc3JyJBXc1vRq58+fl52dnXX71pYtW8rX11fbtm0rFKRkZGRo27ZtCgwMZLpHFfHwzc3kZnbQkbPp2ny46J8xAAAAAKB45QotXF1d1ahRo4quxSaio6OLnMayevVqLV26VHXr1tWdd95Z4NyZM2d06NChQtM0du3aVagfi8WiKVOmKCYmRr169ZKPj4/1XPfu3SVJr732WqG+FixYoFOnTqlbt27W6Rwmk0ljxoxRenq6Zs2aVaD9rFmzlJ6errFjx5bh06MyedRx1INdrgRIC7eUfW0XAAAAAKjtTEY5Fp4YOXKkDh48qB9//LEyarouhw4d0pw5cyRJWVlZWrlypby9vQtsyxoZGWn9c1hYmI4dO6Zu3bqpSZMmslgs2r17t7Zu3Sqz2ayVK1cWWggzPDxcS5cuVUREhMLDw63HTSaTOnTooA4dOsjPz0/JycmKiorSkSNH1KRJE0VFRSkoKMja3mKxqHfv3tqyZYsaNWqkgQMHysvLS7t379bGjRvl7OyszZs3q2vXrtZrMjIy1L17d+3du1f9+vVTaGiodu/erXXr1qlLly6KioqSs7Nzqb+v1NRUeXp6KiUlxbr7CCpO/MUs3f7KJuXmGfr8ye7q0MTL1iUBAAAAgE2V5Tm0XKHFuXPn1KNHDw0YMEBz5syRi4tLuYutaJs3by5yjYirXf2RFy1apFWrVmn//v1KTExUXl6e/Pz81Lt3b02cOFFt2rQpdH1xocWkSZO0fft2xcTEKDk5WU5OTmrRooXuvfdeTZgwQXXr1i3UV3Z2tl5//XWtXLlShw8fVk5Ojry9vdWrVy9NnTpVwcHBha5JSUnRjBkztGrVKiUkJMjHx0dDhw7V9OnT5e7uXoZvi9DiRhj/0R59Gn1a93Tw0dsPl39BVwAAAACoCSo9tOjdu7cuXryovXv3ytXVVa1atSryRiaTSd9++21Zu8cNRGhR+Q7Ep+qut76TnUmKeqaXmtarOiEfAAAAANxoZXkOLdfuIZs3b7b+OT09Xbt37y6yHbslAFKIr4dua9lA3x1N1OKtsZoxsK2tSwIAAACAaqFcC3Hm5eWV6mWxWCq6XqBaeuz2K2uZfPTTSV3IyLFxNQAAAABQPZQrtABQNj1aNFCIj4eyLlu0fPsJW5cDAAAAANVCpYUWOTk5Sk1NrazugWrFZDJZR1ss/SFOly4zCgkAAAAASlLq0CIoKEhvvfVWgWNr167VhAkTimw/e/bsInfLAGqruzv4yNezjhLTc/Rp9GlblwMAAAAAVV6pQ4u4uDhdvHixwLHt27frzTffrOiagBrJ0d5Oj/YIlCS9+91x5eWVeeMeAAAAAKhVWNMCuIEe7NpM7nUcdPx8hjYcPGvrcgAAAACgSiO0AG4gN7ODht3sL0l6Z8txG1cDAAAAAFUboQVwg43qHiBHe5N2nrigXScu2LocAAAAAKiyCC2AG8zbo44Gd/KTJL3LaAsAAAAAKBahBWADY3/b/nTtgQTFJmbYuBoAAAAAqJocytJ4+fLl2r59u/V9TEyMJOmuu+4q1Db/HIDCWnm7q1frhtp0+LwWfXdcL93X3tYlAQAAAECVYzIMo1T7LtrZlX1QhslkksViKfN1uHFSU1Pl6emplJQUeXh42LqcWuWHY0l66N3tMjvYaduU3mrgZrZ1SQAAAABQ6cryHFrqkRaxsbHXXRiA390SVE8dmnhq36kUvffDCY2/o5WtSwIAAACAKqXUoYW/v39l1gHUOiaTSY/dHqQnV0Rr2Q9x+kvP5nJ2srd1WQAAAABQZbAQJ2BDA9o2VtN6zrqQeVmf7Dpp63IAAAAAoEohtABsyMHeTqO7B0qSFm2NlSWvVEvMAAAAAECtQGgB2Nj9XZrKy8VRJ5IytXZ/gq3LAQAAAIAqg9ACsDEXJwcNv+XKmjELtxxXKTf0AQAAAIAaj9ACqAJGdAuQk4Od9p68qJ/iLti6HAAAAACoEggtgCqgobtZfw5tIkl6Z8sxG1cDAAAAAFUDoQVQRYy5LVAmk7Th4DnFnEuzdTkAAAAAYHOEFkAV0byhm/oGe0uS3t0Sa+NqAAAAAMD2CC2AKmTc7UGSpE+jT+tc2iUbVwMAAAAAtkVoAVQhnQPqKbSZl3IseVr6fZytywEAAAAAmyK0AKqYx25vLklavv1XZWTn2rgaAAAAALAdQgugirkjxFsB9V2UknVZH/100tblAAAAAIDNEFoAVYy9nUljbruytsXirbHKteTZuCIAAAAAsA1CC6AKGnJTE9V3ddLpi1n66pcEW5cDAAAAADZBaAFUQXUc7TWiW4Ak6Z0tx2QYhm0LAgAAAAAbILQAqqjh3fxVx9FOv5xO1Q/HkmxdDgAAAADccIQWQBVVz9VJQ29qKklauOW4jasBAAAAgBuP0AKowsbcFig7kxR15LwOJaTauhwAAAAAuKEILYAqzL++qwa0ayxJendLrI2rAQAAAIAbi9ACqOIeu725JOnzvaeVkHLJxtUAAAAAwI1DaAFUcZ2aeqlrYD1dthiK2MZoCwAAAAC1B6EFUA08dluQJGnFjl+VdumyjasBAAAAgBuD0AKoBnq3aaTmDV2Vlp2rD3781dblAAAAAMANQWgBVAN2diY9dvuV0RZLtsYpJzfPxhUBAAAAQOUjtACqicH/56eG7mYlpF7Sl/vibV0OAAAAAFQ6QgugmjA72Cv81gBJ0jtbjsswDNsWBAAAAACVjNACqEYeudlfLk72OpSQpi1HE21dDgAAAABUKkILoBrxdHHUA12aSpLe2XLMxtUAAAAAQOUitACqmdE9AmVvZ9K2mCT9cjrF1uUAAAAAQKUhtACqmSZ1XXR3ex9J0rvfHbdxNQAAAABQeQgtgGoof/vTL/ed0akLmTauBgAAAAAqB6EFUA218/PUrc3ry5JnaMnWOFuXAwAAAACVgtACqKbyR1t8+NOvSsm8bONqAAAAAKDiEVoA1VTPVg3VprG7MnMsWr7jhK3LAQAAAIAKV+NCiz179mjq1Knq37+/GjZsKJPJpLCwsGLbx8XFyWQyFfuaMWNGqe8dGRl5zb42b95c6BrDMLR69Wr16tVLPj4+cnFxUevWrTVu3DgdP154kcUZM2Zc8x5xcXGlrhfVm8lk0tjbroy2iPw+Ttm5FhtXBAAAAAAVy8HWBVS0NWvWaPbs2XJyclKrVq2UmJhYqus6duyowYMHFzp+rcCjOIMGDVKnTp0KHQ8ICCh0bNKkSXrttdfk4+OjwYMHy8PDQ3v37tW7776rDz74QN9//73atWtX6LqRI0cW2Z+Xl1eZ60X1dW9HX/177WElpF7SZ9Hxur9LU1uXBAAAAAAVpsaFFkOHDtXAgQPVvn17JSUlycfHp1TXderUqUyjKq5l8ODBCg8PL7FdQkKC3njjDfn7+2vv3r3y9PS0nnv99dc1YcIEvfbaa1qyZEmha8PDw8sVqKBmcXKw06juAZr99SG9891xDbmpiezsTLYuCwAAAAAqRI2bHtK2bVuFhobK0dHR1qWUKC4uTnl5eerevXuBwEKS7rnnHknS+fPnbVEaqpGHbm4mN7ODYs6la9Phc7YuBwAAAAAqTI0baVFe8fHxmj9/vlJSUuTt7a2wsDA1b968XH1FR0crKSlJubm5CggIUN++fVW/fv1C7Vq2bCknJydt27ZNqamp8vDwsJ778ssvJUl9+vQp8h5btmzRjh07ZGdnp5YtW6pv375yc3MrV72o3jzqOOrhm5vpnS3HtXDLcfUJ9rZ1SQAAAABQIQgtfrN+/XqtX7/e+t5kMmnYsGFasGCBXF1dy9TXW2+9VeC9s7Ozpk+frsmTJxc4Xr9+fc2ZM0cTJ05UmzZtNGjQIOuaFhs3btQTTzyhJ598ssh7TJ8+vcB7Ly8vvfnmmxoxYsQ1a8vOzlZ2drb1fWpqalk+GqqoUd0DtGRrrH6MTdaekxfVqamXrUsCAAAAgOtW46aHlJWLi4umTZumXbt26eLFi0pOTtaGDRvUtWtXLV++vMQQ4GqBgYGaN2+ejhw5oszMTJ06dUrLli1TvXr1NGXKFM2bN6/QNePHj9eHH36o9PR0LViwQK+88orWrl2rm2++WQ8//LAcHArmSh07dtSSJUt0/PhxZWVlKTY2VvPmzZPJZFJ4eLg+//zza9Y4e/ZseXp6Wl9Nm7JwY03g4+msgZ18JUnvbim86wwAAAAAVEcmwzAMWxfxRxMnTiwwGqAkTz/9tFq2bFnoeEJCgnx8fNSzZ88itxu9lszMTIWGhurw4cPatWuXQkNDy3T91fbv36/OnTvLxcVFZ8+eLRBEzJw5Uy+++KJmzpypRx55RF5eXtqzZ4/Gjx+vPXv2aNWqVRo4cGCJ9/j22291xx13qF27dtq3b1+x7YoaadG0aVOlpKQUmJ6C6udQQqoGvPGd7EzS5km91Ky+i61LAgAAAIBCUlNT5enpWarn0CoZWri5uSkjI6PU7Tdt2lTkThrXE1pI0ksvvaTnn39eb731lv72t7+V+fqr3XHHHdqwYYP27dun9u3bS5I2bNigO+64Q+PHj9drr71WqPagoCD5+fnp6NGjpbpHy5YtFRMTU6YAoix/WVD1jVjyo7YcOa8R3fw1c1DhrXIBAAAAwNbK8hxaJaeHpKenyzCMUr8qa+vPBg0aSFKZApSy9PX1119Lknr16lWofePGjdWmTRvFxMQoPT29TPfIzMy83nJRTY27PUiStHLnSSVn5Ni4GgAAAAC4PlUytKgqduzYIUkKCAi4rn4sFot27twpSfL397cez8m58lBZ3Lam58+fl52dXam2b83IyND+/fvl6upqDS9Q+9zavL7a+nro0uU8Ld9+wtblAAAAAMB1qfWhRXR0tIqaIbN69WotXbpUdevW1Z133lng3JkzZ3To0CGlpKQUOL5r165C/VgsFk2ZMkUxMTHq1auXfHx8rOe6d+8uSXrttdcK9bVgwQKdOnVK3bp1k9lsliSlpaXpyJEjhe6RlZWlsWPHKi0tTffff3+hxTtRe5hMJj3222iLpd/H6dJli40rAgAAAIDyq5JrWlyPQ4cOac6cOZKuPMyvXLlS3t7eGjBggLVNZGSk9c9hYWE6duyYunXrpiZNmshisWj37t3aunWrzGazVq5cWWghzPDwcC1dulQREREKDw+3HjeZTOrQoYM6dOggPz8/JScnKyoqSkeOHFGTJk0UFRWloKAga3uLxaLevXtry5YtatSokQYOHCgvLy/t3r1bGzdulLOzszZv3qyuXbtKkuLi4hQUFKQuXbooODhYjRs31tmzZ7VhwwadOnVK7du316ZNm1S/fv1Sf1+saVHz5Fry1PPfm3X6YpZeuq+dht3sX/JFAAAAAHCDVPuFOK/H5s2bi1wj4mpXf+RFixZp1apV2r9/vxITE5WXlyc/Pz/17t1bEydOVJs2bQpdX1xoMWnSJG3fvl0xMTFKTk6Wk5OTWrRooXvvvVcTJkxQ3bp1C/WVnZ2t119/XStXrtThw4eVk5Mjb29v9erVS1OnTlVwcLC1bWpqqqZOnaoff/xRcXFxunDhgpydnRUcHKwhQ4boySeflLOzc5m+L0KLmmnx1ljN+vKAAhu4asOEnrK3M9m6JAAAAACQVMtDC5QNoUXNlJGdq26zv1XqpVwteOQmDWjX2NYlAQAAAICkGrB7CIDr42p20CO3XJkW8u53x21cDQAAAACUD6EFUEOF3xogJ3s77TpxQbtOJNu6HAAAAAAoM0ILoIZq5FFH9/2fnyRpYRSjLQAAAABUP4QWQA029vZASdL6g2d1/Hy6jasBAAAAgLIhtABqsBaN3NWnTSMZhvTud7G2LgcAAAAAyoTQAqjhHrs9SJK0avcpJaZn27gaAAAAACg9QgughusaWE8dm3opJzdPy76Ps3U5AAAAAFBqhBZADWcymTTut9EWy7afUGZOro0rAgAAAIDSIbQAaoH+bRurWT0XXcy8rI93nrJ1OQAAAABQKoQWQC1gb2fSmNuu7CSyaOtx5VrybFwRAAAAAJSM0AKoJYbe1FR1XRx1MjlLa/eftXU5AAAAAFAiQguglnB2stfwbgGSpHe2HJNhGLYtCAAAAABKQGgB1CIjuvnL7GCnvadStCM22dblAAAAAMA1EVoAtUgDN7P+fFMTSdI7W47buBoAAAAAuDZCC6CWGXtbkEwmaeOhczp6Ns3W5QAAAABAsQgtgFomsIGr+oV4S5Le/Y7RFgAAAACqLkILoBZ67PbmkqQ10fE6l3rJxtUAAAAAQNEILYBa6Cb/uursX1c5ljxFfB9n63IAAAAAoEiEFkAtNfb2IEnS8u0nlJ6da+NqAAAAAKAwQguglroj2FtBDVyVdilXH/74q63LAQAAAIBCCC2AWsrOzqQxt10ZbbFka6wuW/JsXBEAAAAAFERoAdRifwr1UwM3J8WnXNJXP5+xdTkAAAAAUAChBVCL1XG018huAZKkhVHHZRiGbQsCAAAAgKsQWgC13CO3+MvZ0V4HzqRqW0ySrcsBAAAAACtCC6CWq+vqpPs7N5EkLdxyzMbVAAAAAMDvCC0AaMxtQbIzSd8dTdS+UxdtXQ4AAAAASCK0ACCpaT0X3d3BV5I0KuIn7Y9PsXFFAAAAAEBoAeA3Lwxsq7a+HkrKyNGD72zXrhMXbF0SAAAAgFqO0AKAJKmeq5NWjL1Fnf3rKu1SroYv3qGtRxNtXRYAAACAWozQAoCVp7Ojlo3uqttaNlBmjkWPRv6kdfsTbF0WAAAAgFqK0AJAAS5ODlo0srP6t/VWjiVPj7+/W2uiT9u6LAAAAAC1EKEFgELMDvaa/3Co/hTqJ0ueofEr92j59hO2LgsAAABALUNoAaBIDvZ2enVIR43o5i/DkJ5f84v+u/mYrcsCAAAAUIsQWgAolp2dSS8MbKu/9mouSXr5m0P699pDMgzDxpUBAAAAqA0ILQBck8lk0jP922jygDaSpPmbjmnG5/uVl0dwAQAAAKByEVoAKJXHw5pr1uB2MpmkpT+c0KRP9irXkmfrsgAAAADUYIQWAEpt+C3+eu3+jrK3M2n17tN6ckW0snMtti4LAAAAQA1FaAGgTO77vyb6z7BQOdnb6Zv9CRqzdKcyc3JtXRYAAACAGojQAkCZ9W/bWEvCu8jZ0V7fHU3UiMU/KvXSZVuXBQAAAKCGIbQAUC49WjbQ8jFd5V7HQTtPXNDD725XUnq2rcsCAAAAUIMQWgAot5v86+nDx25RfVcn/XI6Vfcv/EEJKZdsXRYAAACAGoLQAsB1aevrqY/GdZOPZx0dO5+hoQu/169JmbYuCwAAAEANQGgB4Lq1aOSmj//STf71XXQyOUtDFnyvI2fTbF0WAAAAgGqO0AJAhWhS10Ufj+um1t7uOpeWrQcW/qB9py7auiwAAAAA1RihBYAK08ijjj4ad4s6NvHUhczLevjdHdpxPMnWZQEAAACopggtAFQoLxcnvT/2Ft0cWE/p2bkaseRHbT58ztZlAQAAAKiGCC0AVDg3s4OWPtpVvds0UnZunsYu26mvfj5j67IAAAAAVDOEFgAqRR1Hey145Cbd08FHly2GnlyxWyt3nrR1WQAAAACqEUILAJXGycFObz74f3qwS1PlGdI/PtmniG2xti4LAAAAQDVR40KLPXv2aOrUqerfv78aNmwok8mksLCwYtvHxcXJZDIV+5oxY0ap7x0ZGXnNvjZv3lzomry8PL399tsKDQ2Vi4uLPDw8dPvtt+vzzz8v9j6pqamaMGGC/P39ZTabFRAQoGeeeUbp6emlrhW4UeztTJr9p/Ya3SNQkvTCFwc079ujMgzDxpUBAAAAqOocbF1ARVuzZo1mz54tJycntWrVSomJiaW6rmPHjho8eHCh49cKPIozaNAgderUqdDxgICAAu8Nw9D999+vVatWqXnz5ho9erSys7P12WefadCgQZo3b56efPLJAtdkZGSoZ8+e2rNnj/r166eHHnpI0dHRevXVVxUVFaUtW7aoTp06Za4ZqEwmk0nP3x0s9zoOemPDUc1df0Rp2bl69s42MplMti4PAAAAQBVV40KLoUOHauDAgWrfvr2SkpLk4+NTqus6depUplEV1zJ48GCFh4eX2G7VqlVatWqVunfvrvXr18vZ2VmS9K9//UudO3fWpEmTdM899xQIO1555RXt2bNHkydP1pw5c6zHp0yZopdfflmvv/66nn322Qr5HEBFMplM+nvfVnIzO+jF/x3UO1uOK+1Srl4c3E72dgQXAAAAAAqrcdND2rZtq9DQUDk6Otq6lBJ99tlnkqSpU6daAwtJatCggcaPH6/s7GxFRERYjxuGoUWLFsnNzU3Tpk0r0Ne0adPk5uamRYsW3ZjigXIac1uQXv5ze5lM0gc//qrxH+3RZUuercsCAAAAUAXVuJEW5RUfH6/58+crJSVF3t7eCgsLU/PmzcvVV3R0tJKSkpSbm6uAgAD17dtX9evXL9QuISFBkhQYGFjoXP6xjRs36oUXXpAkHT16VPHx8erfv79cXV0LtHd1dVX37t21du1anTx5Uk2bNi1X7cCN8ECXZnJxctD4j/bo873xyszJ1dsPh6qOo72tSwMAAABQhRBa/Gb9+vVav3699b3JZNKwYcO0YMGCQgFBSd56660C752dnTV9+nRNnjy5wPEGDRpIkmJjYxUcHFzgXGzslR0Wjhw5Yj129OhRSVLLli2LvG/Lli21du1aHT16tNjQIjs7W9nZ2db3qamppflIQIW7t6OvXM32enz5bm04eE6PRv6kd0d0lquZX0sAAAAArqhx00PKysXFRdOmTdOuXbt08eJFJScna8OGDeratauWL1+uESNGlLqvwMBAzZs3T0eOHFFmZqZOnTqlZcuWqV69epoyZYrmzZtXoP2dd94pSZozZ44uXbpkPZ6UlKQ33nhDknTx4kXr8ZSUFEmSp6dnkff38PAo0K4os2fPlqenp/XFiAzYUu823lr6aFe5Otnr+2NJGrZohy5m5ti6LAAAAABVhMmogvsOTpw4scBogJI8/fTTRY4+SEhIkI+Pj3r27FnkdqPXkpmZqdDQUB0+fFi7du1SaGhoma6/2v79+9W5c2e5uLjo7NmzcnC48i/Jubm56tevnzZt2qQWLVpowIABunz5stasWSNvb2/t27dPderUUVZWliRpxYoVGjZsmJ577jm9+OKLhe7z3HPP6V//+pdWr16t++67r8haihpp0bRpU6WkpFhDD+BG23PyosIjftTFzMtq09hd742+WQ3dzbYuCwAAAEAlSE1NlaenZ6meQ6vkOOyFCxcqIyOj1O2HDBlS7JSJ8nJxcdHw4cP1/PPPa9u2bdcVWrRt21Y9evTQhg0bdPDgQbVv316S5ODgoK+//lpz5szRihUr9M4778jT01P33XefJk2apFatWqlRo0bWfvJHWBQ3kiJ/qkdxIzEkyWw2y2zmYRBVS6emXvrosW56ZPEOHUpI0/0Lf9DyMTfLz8u55IsBAAAA1FhVcnpIenq6DMMo9SssLKxS6shfc6IsAUpZ+zKbzZo+fboOHz6s7OxsnTt3TgsXLtTp06clSZ07d7a2zQ9m8te2+KOS1rwAqrLWjd318bhu8vNyVmxihob+93sdP59u67IAAAAA2FCVDC2qih07dkiSAgICrqsfi8WinTt3SpL8/f1Ldc37778vSXrwwQetx1q2bClfX19t27atUPiRkZGhbdu2KTAwkHUqUG0FNHDVJ493U1BDV8WnXNL9C3/QwTMsFgsAAADUVrU+tIiOjlZRy3qsXr1aS5cuVd26da0LZuY7c+aMDh06VGiaxq5duwr1Y7FYNGXKFMXExKhXr17y8fEpcL6o3Ts++eQTLVmyRF26dNGf/vQn63GTyaQxY8YoPT1ds2bNKnDNrFmzlJ6errFjx5b8oYEqzMfTWSvHdVOIj4cS03P0wMIftPvXC7YuCwAAAIANVMmFOK/HoUOHNGfOHElSVlaWVq5cKW9vbw0YMMDaJjIy0vrnsLAwHTt2TN26dVOTJk1ksVi0e/dubd26VWazWStXrtTAgQML3CM8PFxLly5VRESEwsPDrcdNJpM6dOigDh06yM/PT8nJyYqKitKRI0fUpEkTRUVFKSgoqEBfwcHBatq0qYKDg1WnTh39+OOP2rx5s4KCgrRx48ZCIzMyMjLUvXt37d27V/369VNoaKh2796tdevWqUuXLoqKipKzc+nXASjLAijAjZSSdVmPRv6kXScuyMXJXotGdNatLRrYuiwAAAAA16ksz6E1LrTYvHmzevXqdc02V3/kRYsWadWqVdq/f78SExOVl5cnPz8/9e7dWxMnTlSbNm0KXV9caDFp0iRt375dMTExSk5OlpOTk1q0aKF7771XEyZMUN26dQv1NWPGDK1evVpxcXG6fPmyAgMD9ec//1nPPPNMsT+8lJQUzZgxQ6tWrbLukDJ06FBNnz5d7u7upfymriC0QFWWmZOrce/t0ndHE+XkYKf/PByqviHeti4LAAAAwHWo1aEFyobQAlVddq5Ff1sRrXUHzsrezqTX7u+oQZ38bF0WAAAAgHIqy3NorV/TAkDVZnaw13+Gheq+//OTJc/Q3z/aoxU7frV1WQAAAABuAEILAFWeg72d5g7tqEduaSbDkKZ++rPe2XLM1mUBAAAAqGSEFgCqBTs7k2YNaqfHw5pLkv711SHNXXe4yN1/AAAAANQMhBYAqg2TyaTJA9roHwNaS5LmbYzRxJV7FZuYYePKAAAAAFQGFuKs5ViIE9XVez/Eadpn+63vw1o3VPitAbq9ZUPZ2ZlsWBkAAACAa2H3EJQaoQWqs+3Hk/TuluPaePic8n+TBTVw1chbA/Tnm5rIzexg2wIBAAAAFEJogVIjtEBNcCIpQ8t+OKGVP51UWnauJMnN7KAhNzXRyFsDFNjA1cYVAgAAAMhHaIFSI7RATZKRnavVu08p4vs4HT//+zoXvVo3VHj3QN3WogFTRwAAAAAbI7RAqRFaoCbKyzO0NSZRkd/HadPVU0cauir81gD9KZSpIwAAAICtEFqg1AgtUNPFJV6ZOvLxzt+njribHTSkcxON7BagAKaOAAAAADcUoQVKjdACtUX6b1NHIq+aOmIySb1aN1L4rQG6rWUDmUxMHQEAAAAqG6EFSo3QArVNXp6h72ISFbktVpsOn7ceb97wyq4jTB0BAAAAKhehBUqN0AK1WWxihpZ+H6dPdp1S+lVTR4Z2bqoR/9/evcdFVef/A3+dmYEBGS4iCigKiGhkKPkDrbTwbvpzxfK+ZWJZ7a91Vzdz3fpa2LaVXdzNdfu2lV9BUzPTvlammRfQNGVLzVshiECQQoHKnWGY8/n9wcwww1yYkbu8no+HD2Y+5/35nM+Z4+cDvDmfc+4O5dIRIiIiIqJWwKQFOY1JC6L6pSM7TxZg4ze5uFzcsHRk7KBeSBwZhlEDuHSEiIiIiKilMGlBTmPSgqiBLAscyfoVKd/kIs1s6ciAXhosuDsUDw4LgReXjhARERERNQuTFuQ0Ji2IbLv8awU2Hc+zXDriocJsw9KR0B5cOkJEREREdDOYtCCnMWlB5Fh5ja5+6cjxPOSYLR0Zd1svJN4TjpEDenDpCBERERGRC5i0IKcxaUHkHFkWOJz1K1KO5eJwZqOlI/eE4cE7+3DpCBERERGRE5i0IKcxaUHkuuxfK/DB8Tx8/F0+Kmv1AOqXjsyJ7YtH7g5Dvx7d2rmHREREREQdF5MW5DQmLYhuXnmNDjsMTx3JLakCYFw6EojEe8K4dISIiIiIyAYmLchpTFoQNZ8sCxzO/BXJ3+TiiNnSkUjj0pFhfdDNnUtHiIiIiIgAJi3IBUxaELWs7F8rsOmbXOw4WWBaOuLjocKcuPqlI339uXSEiIiIiLo2Ji3IaUxaELWOshoddnxXgI3Hc5FntnRk7KBeGDkgAEP7+uL2YF94uivbuadERERERG2LSQtyGpMWRK1LlgXSMn9B8rFcfJ1VbLFNqZAQ2UuDoSF+GNLXF0P6+GFQkDfcVYp26i0RERERUetj0oKcxqQFUdu59EsF9py7irMFN3CmoBS/lmutYtxVCkQF+2BoiC+GhPhhSIgvInpqoFTwhp5EREREdGtg0oKcxqQFUfsQQqCwrAZnC0pxtuCG4WspSqt1VrFe7koM7uOLoSG+iA7xw9AQX/Tz78YnkxARERFRp8SkBTmNSQuijkMIgbySKpz9uRRn8+sTGeevlKLKcENPc37d3BDdxxdDDFdkDA3xQ5CvRzv0moiIiIjINUxakNOYtCDq2PSyQPavFTiTf8N0VcaPV8tRq5etYnt5q01JDONXfy/3dug1EREREZF9TFqQ05i0IOp8autkXCwsx5mCG6alJZlF5ZBtzOZ9/T0xpE9DEiM6xBcatartO01EREREZMCkBTmNSQuiW0N1rR4XrpTijOFqjHMFpbhcXGkVJ0lA/wCv+ieWhPhiSF8/3B7sAw83PnqViIiIiNoGkxbkNCYtiG5dpdU6nP+5tP6KjPxSnPu5FD/fqLaKUykkDAz0xtC+DUtLBgZ6w03JR68SERERUctj0oKcxqQFUdfya7kW536+gTOGJMbZghsorqi1ilOrFLi9tw+GhvghopcGQT4eCPLxQKCvGgFeaij4CFYiIiIiuklMWpDTmLQg6tqEELhSWoOz+TdwpqAU536uv0dGeU2d3ToqhYSe3moEGhIZQb4e6OWjNkts1H/14r0ziIiIiMgGV34P5U+URERdmCRJ6OPniT5+npgcHQwAkGWB3JJKnPu5FGfyS/HTtSr8Ul6DwtIaFFdoUScLXC2twdXSGodta9QqBPqoEeTrgUAfD1OSI9CQ6Aj0UaOnRg0Vl6EQERERkR280qKL45UWROSKOr2MXyu0KCrTorC0BkVlNSgsq0FRaQ2KDImNojItKrT2r9Qwp5CAAI15YkPdKLFR/8/HQwVJ4pIUIiIiolsBr7QgIqJWoVIqEOzriWBfT6Cv/bgKbR2KDMmMQvPERpm2/nVZDX4p10IvC/xSrsUv5VoApXbb83RT1i9D8a5PcBgTG/XJjfqlKr28PeCu4lUbRERERLcSJi2IiKjFadQqaHpqENFTYzdGLwuUVGpRVKo1JTZ+Kau/WsOY2CgsrUFZTR2qdXrkFFcix8ZjXM0FaNzR07v+ygxvDxW8Pdzq+2J8r24o8/YwlKvdTK/5xBQiIiKijoVJCyIiahdKhYRe3vVXSETD125cda2+YRmKKZmhtSj7pUyLWr2M4opam09DcZaHmwIaQxLD20PVkNywKnOzToQYtmnUKij5dBUiIiKiFsGkBRERdWie7kqEBXghLMDLbowsC1yvqkVhWQ1+LdeivKYOFdo6VNTUobxGh3JtXX2ZobxxWbVODwCo0cmo0WlRXKFtVp+93JUWiQxvU4KjIdnRUO4GT3cl1CoF1ColPNzqv6pVCqjdGsrclQre14OIiIi6HCYtiIio01MoJPTQqNFDo76p+nV62ZDMqDP7qkN5jXmZzpAEqUO5MSGitSyrrZMBAJW1elTW6oGyljxKGBIbCqjdGiU3Gic83GyUNUqCOCxr1Ja7UgEFrx4hIiKidsCkBRERdXkqpQJ+3dzh1829We1o6/RmV3M0SnhYlOlMV3mUG6700Nbpoa2TUaOr/6rVyaip08P8GV/aOhnaOhmoce7pLC3JXdmQ4FCrFFApJagUEtyUxtcKuBm+qpSGclvbjTEKCSpl4zrmcfbqK+BmqKtUOK7jZmjXWF8hgVerEBERdTJMWhAREbUQtUoJtUZ501d8NCaEQJ0sGhIZdTK0Oj1qdLIpyWEqM3w1ljXU0UOra4gzlTVKkDQuq9HpIZslTGr1Mmr1MsrR9gmTlqSQ6u+nopDqky4KhQSlQoJSMryWDO8N/8zjlQqzOo3iFcZtkgSlwrKOeZsWdUyxivqvUqO2DftXSBIkqeG1MfmikMy3N+xTMsWZxxrKFHbqGvZpr2277RnaNMZJqN8GY11YbpMUsC6TYNqHxTYmmIiICExaEBERdViSVH8lgZtSAe922H+dXrZKhmjr6pMmdXoZOr2AXhbQyTLq9KK+TK7/WqdvKNfpZdQZynV6gTpTef1rnaFunWyINS+32i6glxu3b95mfZzePONiRhaArBcABJp35xJqC/WJjaaTHDDGKSwTH4Ax0dIQL0kNbZjaM5bXV7F4bx6HxuWN2oBFHes2Gtq2PBa77Td6b9hLw/7M227UJ5gdi3m7aNS2qVVTFbO+mPZr2V9TiaM4s/02PqfGOMv3jbab961R/xzWs7MdjdprMh7mx2o/ida4Hat6LsRatmsW02S7tj/jxnG2dmjveBv30/Z25+vCUZ9Mbdj5jG3G2mvDVn3H584ZjpKoTTXT1H7s9c+5ura5KRUYf3ug48qdCJMWREREZJNKqYBGqYBG3fl+XJDl+qtUjEkPvSGRIQvL13WygCwL6A3lsoyG10KgTm9WRxhiTe0AdbJsem3Rjtl+LOui4XWjGFk0/grIQkAYvja8b+inMCuXBQzv67eb19U3sd0qVob9ts36Zeyv8b1AQ72WYGxTNq2TaqGGiYhuYd27ueH0CxPbuxstpvP9FEJERETUBIVCgrtCgjsU7d2VLkvYSGQIGMoMrxuSIQBslIn6Qou6pgRJ47JG+zRPxBhzHhZlgKHcvJ+GNtDQPsy3wfKYDNUbHZdlG1btN2oDjcsdtG94a/bashzGOmbHYl2nodx83w2vbZcDjfvroL7Zfi3qN27PznZYbXeunvk9gCzqudgPy1LLcovXNvZr3oStWNiNFXbKnY+1bt9yq/Xn40Js493Y+ayaqisab7TTvr22HMfa2+Jsu3b6ZqdZR7tzta36Oq5usL+fzvjHBkduraMhIiIiog7BuAzD8K49u0JERJ0YkxYEAJCrqiCrbPx3UCqhUKst4uxSKKDw8Li52Opq+6lHSYLC0/PmYmtqAFm2341u3W4uVqsF9PoWiZU8PU3r5OTaWqDO/k3uXIr18ICkqP8Lo6ithWipWLUaklLpeqxOB6HT2Y91d4dk+D/oUmxdHURtrf1YNzdIbm6ux+r1EFr7K94llQqSu7vrsbIMUVPTIrFQqaAwxgoBUV3dMrGujHvOEbZjOUe4Hss5oj6Wc8TNxXKOqI/lHOF6LOeI+ljOETcXyzkCwM3NEQ7PXyNMWhAAIOve+6AxfFMw5xV/H/q9+67pfebIUXYnqW5xcQj9YJPp/aVx46G/ft1mrMcddyB8x8em95f/71TorlyxGes+IAIRu3eb3ufMmoXaS9k2Y91698aAQwdN7/Meno+a8+dtxiq7d8fA49+Y3uc//gSqvv3WZqzk6YnbTp8yvS/44x9RefiIzVgAiMr40fT6yp9XoHzfPruxg06dhGSYeApfSELprl12YyO/OQaVvz8A4JfVq3F964d2YyMOHIB7SJ/62LfW4tqGDXZj+3/+GdSRkQCA4nffQ/Hbb9uNDft4OzyjowEA1z74AL+88abd2H4bN8JrxHAAwPXt21H00t/sxob8+x14jx4NACj9fDeuPvec3dg+b/0DPvffDwAoP3AAPy/9k93Y4Fdegd+DDwAAKo4eRcHv/p/d2MDnV8L/oYcAAFXfncRPCxbYje21/Bn0eOwxAEDNDz8gd9Zsu7EBv/89ev5hMQCgNjsbl38zzW6s/6OPIvDPywEAuitXkT1+vN3Y7r+dh6AXXgAA6K9fR9Y9I+3G+k6fjt6rXwUAiOpqXBz2f+zGek+ahJC1b5neO4rlHFGPc0QDzhH1OEfU4xxRj3NEA84R9ThH1OMcUa8rzhEVDhItjXGhJxERERERERF1SJJw5Y4lncD333+P7du34+TJkzh16hSKi4sRHx+PtLQ0m/G5ubkIDw+3215SUhJWrVrl1L5TUlKwcOFCu9tTU1Mx2pABNpJlGf/93/+NDRs2ICMjAyqVCjExMXjmmWcwbZp1FnXVqlV48cUX7e4jJycHYWFhTvUXAMrKyuDr64vrV6/Cx8fHOoCXbNmO7QKXbNmN5WWd9bG8rNP1WM4RNxXLOcIQyznC5VjOEQacI24ulnNEfSznCNdjOUc0dINzhN3YsrIydA8ORmlpqe3fQ83ccstDdu3ahVdffRXu7u4YOHAgiouLnao3dOhQTJ8+3aq8cZLBGQkJCYiJibEqb5xMEEJg9uzZ2LlzJyIiIvDYY49Bq9Xi008/RUJCAtatW4fFixfb3MeCBQtsJif8/Pxc7i9Q/x/f/D+/ozhX2nQ61mzwt2is2WTVorFmk2uLxrq7A4ZvCC0ZK7m7m76BtVus2TfyFo1VqUw/eLRorFJpupSuRWMVitaJlaRWiQVacdxzjnA9lnOE67GcI+pjOUfcXCznCACcI24qlnOECeeIm4jtAnOEwkGSo7FbLmkxa9YsTJs2DdHR0SgpKUFwcLBT9WJiYpy+oqIp06dPR2JiYpNxO3fuxM6dOzFy5Ejs378fnoYB8sorryA2NhbPPPMMpk6dajM5kZiYeFMJFSIiIiIiIqLO4pa7p8XgwYMxbNgwuDmZXW1Pn376KQDgueeeMyUsACAgIAB/+tOfoNVqkZyc3F7dIyIiIiIiImpXt9yVFjfrypUrePvtt1FaWorAwECMHj0aERERN9XW6dOnUVJSgrq6OoSFhWH8+PHo0aOHVVxhYSEA2LynhrHs0KFDNu9hceTIEaSnp0OhUCAyMhLjx4+HRqO5qf4SERERERERdURMWhjs378f+/fvN72XJAkPPfQQ/v3vf8PLy8ultv75z39avPf09ERSUhJWrFhhUR4QEACg/uaZUVFRFttycnIAAJmZmTb3kZSUZPHez88Pa9euxSOPPOKwb1qtFlqzG/2UlZU5jCciIiIiIiJqL7fc8hBXdevWDc8//zxOnjyJGzdu4Nq1azhw4ACGDx+OzZs3N5kEMBceHo5169YhMzMTVVVVKCgowKZNm+Dv74+//OUvWLdunUX85MmTAQCrV69GjdmdfUtKSvDWW28BAG7cuGFRZ+jQodiwYQMuX76M6upq5OTkYN26dZAkCYmJifjss88c9vHVV1+Fr6+v6V/fvn2dPj4iIiIiIiKittQhH3m6bNkyi6sBmrJkyRJERkZalRcWFiI4ONjhI0/tqaqqwrBhw3Dx4kWcPHkSw4YNc6m+uQsXLiA2NhbdunVDUVERVIa7DtfV1WHixIlITU3FgAEDcP/990On02HXrl0IDAzE2bNn4eHhgWpHjxQyOHjwICZMmIA77rgDZ8+etRtn60qLvn37OvWoGSIiIiIiIqLmKisrg6+vb+d95Om7776LyspKp+NnzpxpM2nRHN26dcP8+fOxcuVKHDt2rFlJi8GDB2PUqFE4cOAAfvzxR0RHRwMAVCoV9u7di9WrV2Pr1q1477334OvriwceeADPPPMMBg4ciF69ejm1j3HjxiEiIgLnzp1DWVmZ3ROvVquhduGxOERERERERETtpUMmLSoqKtq7CwAa7jnhSgLF1bbUajWSkpKs7lFhvDIkNjbWpX1cunQJVVVVvGqCiIiIiIiIOr0uf08LR9LT0wEAYWFhzWpHr9fju+++AwCEhoY6VWfLli0AgLlz5zoVX1lZiQsXLsDLy8uUICEiIiIiIiLqzLp80uL06dOwdVuPTz75BBs3bkT37t1NN8w0unr1KjIyMlBaWmpRfvLkSat29Ho9/vKXv+DSpUsYM2YMgoODLbbbenrHjh07sGHDBsTFxeHBBx80lZeXl9t8mkh1dTUef/xxlJeXY/bs2aZ7ZhARERERERF1Zrfcb7cZGRlYvXo1AJhuYJmRkYHExERTTEpKiun1n/70J2RnZ+Puu+9GSEgI9Ho9Tp06haNHj0KtViMlJQW+vr4W+3j22WexceNGJCcnW7QbGxuLIUOGYMiQIejTpw+uXbuGw4cPIzMzEyEhIVi/fr1Vf0eMGIG+ffsiKioKHh4e+M9//oO0tDT0798fH3/8MZRKpSm2pKQEt912G+Li4hAVFYWgoCAUFRXhwIEDKCgoQHR0NN54440W+BSJiIiIiIiI2t8tl7QoLCzExo0bLcqKioosysyTFg8//DB27tyJEydOoLi4GLIso0+fPli0aBGWLVuG2267zel9L1u2DCdOnMD+/ftx7do1uLu7Y8CAAVi5ciWefvppdO/e3arOnDlz8Mknn+DEiRPQ6XQIDw/HypUrsXz5cqv7Uvj7++Opp57Cf/7zH+zZswfXr1+Hp6cnoqKi8Mc//hGLFy+Gp6en0/0lIiIiIiIi6sg65CNPqe248qgZIiIiIiIioubq9I88pbZjzFnZurcGERERERERUUsz/v7pzDUUTFp0ceXl5QCAvn37tnNPiIiIiIiIqCspLy+3uodkY1we0sXJsowrV67A29sbkiS1d3fsKisrQ9++fZGfn89lLJ0Qz1/nxXPXefHcdV48d50bz1/nxXPXefHcdT5CCJSXl6N3795QKBw/1JRXWnRxCoUCISEh7d0Np/n4+HAi6sR4/jovnrvOi+eu8+K569x4/jovnrvOi+euc2nqCgsjxykNIiIiIiIiIqJ2wqQFEREREREREXVITFpQp6BWq5GUlAS1Wt3eXaGbwPPXefHcdV48d50Xz13nxvPXefHcdV48d7c23oiTiIiIiIiIiDokXmlBRERERERERB0SkxZERERERERE1CExaUFEREREREREHRKTFkRERERERETUITFpQe3m22+/xZQpU+Dn5wcvLy/cdddd2L59u0ttaLVa/PWvf0VkZCQ8PDzQu3dvPPHEE/jll19aqddd288//4y33noLEydORL9+/eDu7o6goCDMmDED6enpTreTlpYGSZLs/ktJSWm9g+jiwsLC7H7uo0ePdqmtLVu2YPjw4fDy8kL37t0xdepUnDp1qnU63sWlpKQ4HDOSJGHcuHFNtsOx17o2b96MJ598ErGxsVCr1U1+pmVlZXj66acRGhoKtVqNsLAwLF++HBUVFS7ve9++fYiPj4e3tzd8fHwwZswYHDx4sBlH07U4e+50Oh127tyJBQsWICoqChqNBt7e3hgxYgTeeecd6PV6l/bbknNyV+XKuFu1apXDOTA3N9elfWdmZmL27NkICAiAp6cnhg4dinfeeQd8zoHzXDl/TX0flCQJ+fn5Tu2XY69zUbV3B6hrSk1NxaRJk+Dh4YG5c+fC29sbO3fuxJw5c5Cfn49ly5Y12YYsy0hISMC+fftw1113YcaMGcjKysL69etx8OBBnDhxAj179myDo+k61q1bh9deew0RERGYOHEievbsiaysLOzatQu7du3C1q1bMWfOHKfbi4+Pt/mNISYmpuU6TVZ8fX2xdOlSq/KwsDCn23j55ZexcuVKhIaG4ne/+x3Ky8uxbds23HPPPTh48CBGjhzZch0mxMTEICkpyea2HTt24MKFC5g0aZLT7XHstY6VK1ciLy8PAQEBCA4ORl5ent3YyspKxMfH4/vvv8fEiRMxb948nD59Gm+++SYOHz6MI0eOwMPDw6n9bt68GfPnz0fPnj2RmJgIAPjoo48wYcIEbN++HTNnzmyJw7ulOXvusrOzMXPmTGg0GowbNw7Tpk1DaWkpPv/8czz11FPYs2cPPvvsM0iS5PS+W2JO7spcGXdGCxYssPn5+vn5Ob3fH374Affccw+qq6sxe/Zs9O7dG1988QWeeuop/PDDD1i3bp0LR9F1uXL+7H0fvHTpErZs2YLbb78dffv2dXrfHHudiCBqYzqdTkRERAi1Wi1Onz5tKr9x44YYOHCgcHd3F7m5uU22s2HDBgFAzJs3T8iybCp/5513BADxxBNPtEb3u7SdO3eKtLQ0q/IjR44INzc30b17d1FTU9NkO6mpqQKASEpKaoVekiOhoaEiNDS0WW1kZmYKlUolBg4cKG7cuGEqP336tFCr1SIqKkro9fpm9pScodVqRY8ePYRKpRKFhYVNxnPsta79+/ebvn+9+uqrAoBITk62GfvCCy8IAGLFihUW5StWrBAAxCuvvOLUPq9duyb8/PxEQECAyM/PN5Xn5+eLgIAAERAQIMrKym7ugLoQZ89dQUGBePvtt0VFRYVFeUVFhYiNjRUAxPbt253eb0vMyV2dK+MuKSlJABCpqanN3u99990nAIg9e/aYyrRarbj33nsFAPHNN980ex9dgSvnz57FixcLAGLNmjVO1+HY61y4PITa3KFDh5CdnY3f/va3Fn/V8/X1xXPPPYfa2lps3LixyXbef/99AMCrr75q8ReNJ598Ev3798eWLVtQXV3d4v3vyh588EHEx8dbld97770YM2YMrl+/jnPnzrVDz6gtJScno66uDv/1X/8FX19fU3lMTAzmzZuHH3/8EUePHm3HHnYdu3btQklJCaZOnYrAwMD27k6XN378eISGhjYZJ4TA+vXrodFo8Pzzz1tse/7556HRaLB+/Xqn9vnxxx/jxo0b+MMf/oCQkBBTeUhICBYvXozi4mL87//+r2sH0gU5e+769OmDp556Cl5eXhblXl5eePrppwEAhw8fbpU+km3OnruWlJmZiSNHjmDMmDGYPHmyqdzd3R0vvfQSgIafU8mx5p6/mpoabNmyBe7u7pg/f34L9ow6Ei4PoTaXlpYGAJg4caLVNuPlzU19w6+pqUF6ejoGDRpkNdFJkoQJEybg3XffxXfffYd77723ZTpODrm5uQEAVCrnp5WsrCy89dZbqK6uRkhICMaOHYs+ffq0VhfJQKvVIiUlBVeuXIGPjw/i4uIwYsQIp+s3NYZTUlJw+PBh3HfffS3VZbLD+IvtokWLXKrHsde+srKycOXKFUyaNMnmL78jR47Evn37kJ+f3+Slzk2Nx1WrVuHw4cN45JFHWqz/ZNvNfB8Emj8nk+uOHDmC9PR0KBQKREZGYvz48dBoNE7XdzTuRo0aBS8vLyav2sgnn3yC69evY+bMmS4vC+fY6zyYtKA2l5WVBQCIjIy02hYUFASNRmOKsSc7OxuyLNtsw7ztrKwsJi3awE8//YQDBw4gODgY0dHRTtfbunUrtm7danqvUqnwhz/8AW+88QaUSmVrdJUAFBYWYuHChRZlcXFx+PDDDxEREdFk/aysLGg0GgQFBVltMx971Lry8vJw8OBBhISE4P7773epLsde+3L0fdBYvm/fPmRlZTWZtHDUFsdj29qwYQMA27/IOtLcOZlc1/jeCH5+fli7dq3TyT1H406pVCI8PBw//PAD6urqXE5ikWv+53/+B4DryXuAY68z4fIQanOlpaUAYHFZuTkfHx9TTHPaMI+j1qPT6TB//nxotVq89tprTv3C07NnT6xevRrnz59HRUUFioqKsGvXLgwYMAD/+Mc/8Oc//7kNet41LVy4EAcPHkRRUREqKytx+vRpzJ8/H99++y3GjRuH8vLyJtsoLS3l2OsAkpOTIcsyEhMTnU40cOx1DC35PcxRWxyPbee9997D3r17MXbsWEyZMsXpei0xJ5Pzhg4dig0bNuDy5cuorq5GTk4O1q1bB0mSkJiYiM8++8ypdpwZw7Is8/y1spycHKSmpqJfv36YMGGCS3U59joXpv6I6KYZf2E6cuQIHn/8cafXEg4ePBiDBw82vffy8kJCQgJGjBiBIUOG4J///CdWrFiBXr16tVbXu6zGf12KiYnBpk2bAAAffPAB3n//fdO6bOq4ZFlGcnIyJEnCo48+6nQ9jj2ilrd7924sXrwYoaGh2Lx5s0t1OSe3rQceeMDifVhYGBYvXoyoqChMmDABK1euxLRp09qpd+SqDRs2QAiBhQsXQqFw7W/xHHudC6+0oDZnzErb+8tPWVmZ3cy1K22Yx1HLk2UZjz76KLZu3YqHH34Y//73v5vdZlBQEBISElBXV4f09PQW6CU568knnwQAHDt2rMlYX19fjr12duDAAfz0008YO3YswsPDm90ex17basnvYY7a4nhsfXv27MHMmTMRGBiIQ4cOITg4uEXadWVOpuYbN24cIiIicO7cOdO4ccSZMSxJEry9vVu0n9RAlmWkpKRAoVC4lLxvCsdex8SkBbU5R2tsCwsLUVFRYXedr1H//v2hUCjsrtNtar0wNY8sy1i4cCE2btyIefPmmb5ptISAgAAAQGVlZYu0R85x5XOPjIxERUUFCgsLrbZx7LWNm70BpyMce22nqXtNuDKOHLXF8di6vvjiCzz44IMICAhAamoq+vfv32Jtczy2PeNnXlVV1WSso3Gn1+uRk5OD8PBw3s+iFX355ZcoKCjAhAkT0K9fvxZrl2OvY2LSgtqc8ZGZX331ldW2ffv2WcTY4+npieHDh+PixYvIy8uz2CaEwP79++Hl5YXY2NgW6jUZGRMWmzZtwpw5c/DBBx+06I37jH/lDQsLa7E2qWmufO4tMYbp5pWUlODTTz+Fv7+/1aXOzcGx13YiIyPRu3dvHDt2zOoH48rKShw7dgzh4eFN3oQT4HhsL1988QVmzJgBf39/pKamYsCAAS3aPsdj26qsrMSFCxfg5eVl+qXVEUfj7ujRo6isrOS4a2XNuQGnIxx7HROTFtTmxo0bh/79+2Pr1q34/vvvTeWlpaV45ZVX4O7ubnH35qtXryIjI8PqErwnnngCAPDss89CCGEqf/fdd3H58mU89NBD8PT0bN2D6WKMS0I2bdqEWbNmYfPmzQ4TFsXFxcjIyEBxcbFF+cmTJ23Gr127FqmpqYiMjERcXFyL9p2AjIwMm39BysjIwIoVKwAAv/3tb03lpaWlyMjIwNWrVy3iFy5cCJVKhZdfftliXH7//ff48MMPERUVhVGjRrXSUdAHH3yA2tpaPPzww1Cr1TZjOPY6NkmSsGjRIlRUVOCll16y2PbSSy+hoqICjz/+uEV5VVUVMjIy8NNPP1mUz549G76+vli3bh0KCgpM5QUFBfjXv/6FgICAFk1uEbB3717MmDED3bt3N40bR3Q6HTIyMpCdnW1R7uqcTM1TXl6OzMxMq/Lq6mo8/vjjKC8vx+zZs62ujsjIyEBGRoZF2aBBg3DfffchNTUVe/fuNZXX1tbi+eefB9Dyv0xTg19//RWff/45evbs6fAeJBx7tw5JmP+2R9RGUlNTMWnSJHh4eGDu3Lnw9vbGzp07kZeXhzfffBPLli0zxSYmJmLjxo1ITk5GYmKiqVyWZUyZMgX79u3DXXfdhfj4eFy6dAmffPIJwsLCkJ6e7vLzmsmxVatW4cUXX4RGo8GSJUtsXvY4ffp0xMTEWMQnJSVh1apVppiwsDC4ubkhNjYWISEhqKysxIkTJ3D69Gn4+flh3759GD58eBsdVdexatUq/P3vf8d9992H0NBQeHl5ITMzE3v27IFOp8Ozzz6LV155xRSfkpKChQsXYsGCBUhJSbFo6+WXX8bKlSsRGhqKGTNmoLy8HNu2bUNtbS0OHjyIkSNHtvHRdR3R0dE4f/48zp49a/cRwxx77WP9+vU4evQoAODcuXM4deoURo4cafor/KhRo0y/yFRWVmLkyJE4c+YMJk6ciGHDhuHUqVP46quvEBcXh8OHD1sk3tPS0jBmzBjEx8cjLS3NYr+bN2/G/Pnz0bNnT8yZMwcA8NFHH6G4uBgfffQRZs2a1QZH37k5e+4yMjIQExMDrVaLuXPnYtCgQVZthYWFWfy8kpubi/DwcISGhiI3N9dU7uqcTLY5e+5yc3PRv39/xMXFISoqCkFBQSgqKsKBAwdQUFCA6OhopKamokePHhbtS5IEAGj8K9OFCxcwcuRIVFdXY86cOQgODsYXX3yBCxcuYPHixVi3bl0bHH3n58q8abRmzRo888wzePrpp7FmzRq7bXPs3UIEUTtJT08X999/v/Dx8RGenp5i+PDhYtu2bVZxCxYsEABEcnKy1baamhqxatUqERERIdzd3UVQUJBYtGiRKCwsbIMj6HqM58LRP/PzlJSUJACIpKQki3ZWr14txowZI3r37i3UarXw9PQUt912m1i6dKnIz89v24PqQtLS0sTs2bNFZGSk8PHxESqVSgQFBYmEhASxb98+q/jk5GQBQCxYsMBme5s3bxaxsbHC09NT+Pr6iilTpoiTJ0+28lF0benp6QKAGD58uMM4jr320dQc2Xgs3bhxQyxdulT07dtXuLm5iX79+olly5aJsrIyq7ZTU1MFABEfH29z33v37hX33nuv8PLyEhqNRsTHx4v9+/e3wlHempw9d8bz4Ohf43OUk5MjAIjQ0FCLclfnZLLN2XNXWloqfv/734u4uDjRs2dPoVKphLe3txg+fLh4/fXXRVVVlc32je3YkpGRIWbOnCn8/f2FWq0W0dHR4u233xayLLfW4d5yXJ03hRAiKipKABA//PCDw7Y59m4dvNKCiIiIiIiIiDok3tOCiIiIiIiIiDokJi2IiIiIiIiIqENi0oKIiIiIiIiIOiQmLYiIiIiIiIioQ2LSgoiIiIiIiIg6JCYtiIiIiIiIiKhDYtKCiIiIiIiIiDokJi2IiIiIiIiIqENi0oKIiIiIiIiIOiQmLYiIiIjaUFpaGiRJwqpVq9q7K0RERB0ekxZERETUoeXm5kKSJNx///2mssTEREiShNzc3PbrmAOSJGH06NHt3Q0iIqJOT9XeHSAiIiLqSoYPH44ff/wRAQEB7d0VIiKiDo9JCyIiIqI21K1bN9x2223t3Q0iIqJOgctDiIiIqFMJCwvDxo0bAQDh4eGQJMnmcoycnBwsWrQI/fr1g1qtRnBwMBITE5GXl2fVprH+zz//jEceeQRBQUFQKBRIS0sDAKSmpuLRRx/FoEGDoNFooNFoEBsbi/fee8+iHeP9KgDg8OHDpr5JkoSUlBSLGFv3tDh//jxmz56NXr16Qa1WIzw8HEuXLkVJSYnNzyEsLAwVFRVYsmQJevfuDbVajSFDhmDHjh0ufqpEREQdE6+0ICIiok5l6dKlSElJwZkzZ7BkyRL4+fkBqP8l3ig9PR2TJk1CZWUlpk6disjISOTm5mLLli3Yu3cvjh8/jv79+1u0W1JSgrvvvhv+/v6YO3cuampq4OPjAwB47bXXcOnSJdx111144IEHcOPGDXz55Zd48skncfHiRaxZs8bUh6SkJLz44osIDQ1FYmKiqf2YmBiHx3X06FFMmjQJtbW1mDlzJsLCwnD8+HGsXbsWu3fvxokTJ6yWlOh0OkycOBHXr1/HjBkzUFVVhW3btmH27Nn48ssvMXHixJv7kImIiDoKQURERNSB5eTkCABi0qRJprIFCxYIACInJ8cqvra2VoSFhQlvb29x6tQpi21ff/21UCqVYurUqRblAAQAsXDhQlFXV2fV5uXLl63KdDqdmDBhglAqlSIvL8+qvfj4eJvHk5qaKgCIpKQkU5lerxcRERECgPjyyy8t4pcvXy4AiEcffdSiPDQ0VAAQCQkJQqvVmsoPHDhg9XkRERF1VlweQkRERLeU3bt3Izc3F8uXL8edd95psW3UqFFISEjAnj17UFZWZrHN3d0dr7/+OpRKpVWb4eHhVmUqlQq/+93voNfrkZqa2qw+Hzt2DNnZ2Zg8eTImTZpkse2FF16Av78/tm7ditraWqu6//jHP+Du7m56P27cOISGhuLbb79tVp+IiIg6Ai4PISIiolvKiRMnAAAXL160ed+IwsJCyLKMzMxMxMbGmsrDw8PtPtGjvLwcb775Jnbt2oXs7GxUVlZabL9y5Uqz+nz69GkAsPmYVOP9M7766itcvHgR0dHRpm1+fn42EyohISE4fvx4s/pERETUETBpQURERLeUa9euAQC2bNniMK5x4iEwMNBmXG1tLUaPHo1Tp07hzjvvxPz589GjRw+oVCrk5uZi48aN0Gq1zeqz8aoPe30IDg62iDPy9fW1Ga9SqSDLcrP6RERE1BEwaUFERES3FOPNMz///HNMnTrV6XrGp3409umnn+LUqVN47LHHsH79eott27ZtMz3JpDmMfS4qKrK5vbCw0CKOiIioq+A9LYiIiKjTMd53Qq/XW20bMWIEALTY8ojs7GwAQEJCgtW2r7/+2mYdhUJhs2/2GO+9YXzEqrnKykp899138PT0xKBBg5xuk4iI6FbApAURERF1Ov7+/gCA/Px8q20JCQno168f/v73v+PIkSNW23U6HY4ePer0vkJDQwHAqs7hw4fx/vvv2+1fQUGB0/sYOXIkIiIisHfvXhw4cMBi29/+9jeUlJRg3rx5FjfcJCIi6gq4PISIiIg6nbFjx+LNN9/EE088gRkzZsDLywuhoaGYP38+1Go1duzYgcmTJyM+Ph5jx45FdHQ0JElCXl4evv76a/To0QMZGRlO7es3v/kNwsLC8Prrr+P8+fO44447cPHiRezevRsPPPAAduzYYbN/27dvx/Tp03HnnXdCqVRi2rRpGDJkiM19KBQKpKSkYNKkSZgyZQpmzZqF0NBQHD9+HGlpaYiIiMDq1aub9ZkRERF1RkxaEBERUaczefJkvP7663j//fexZs0a6HQ6xMfHY/78+QCAuLg4nDlzBm+88Qb27NmDY8eOQa1Wo0+fPpg+fTrmzZvn9L40Gg0OHTqE5cuX48iRI0hLS8PgwYOxZcsWBAYG2kxarF27FgBw6NAhfP7555BlGSEhIXaTFkD941hPnDiBv/71r/jqq69QWlqK3r17Y8mSJVi5cqXdJ5sQERHdyiQhhGjvThARERERERERNcZ7WhARERERERFRh8SkBRERERERERF1SExaEBEREREREVGHxKQFEREREREREXVITFoQERERERERUYfEpAURERERERERdUhMWhARERERERFRh8SkBRERERERERF1SExaEBEREREREVGHxKQFEREREREREXVITFoQERERERERUYfEpAURERERERERdUj/H8WlTg0b4kSGAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# The following plot is of ADAPT_VQE\n",
        "import matplotlib.pyplot as plt\n",
        "plt.rcParams[\"font.size\"] = 14\n",
        "\n",
        "# plot loss and reference value\n",
        "plt.figure(figsize=(12, 6), facecolor='white')\n",
        "plt.plot(energy_vals, label=\"ADAPT VQE BeH2 IDEAL\")\n",
        "plt.axhline(y=real_solution.real, color=\"tab:red\", ls=\"--\", label=\"Target\")\n",
        "\n",
        "plt.legend(loc=\"best\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Energy [H]\")\n",
        "plt.title(\"VQE energy\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ID8Hm5lQJjxm"
      },
      "source": [
        "TETRIS_VQE"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W2vc2hi9Jjxn"
      },
      "source": [
        "TETRIS_VQE is a dynamic circuit design based on the idea of ADAPT VQE.\n",
        "\n",
        "Instead of using the same number of gates to begin with, the idea is to keep adding gates until we converge. We start with some scheme with non-zero gradient sorted in an order. We run the optimization method for that fixed circuit and calulcate the GS Energy. After each iteration, we add more schemes from the bigger pool in a constrained manner.\n",
        "\n",
        "In this work, we look at the closeness to the actual solution. By this, we mean that we stop if the GS Energy we get after dynamic addition of schemes to circuits is close to the real energy calculated above. Another method could be to use the different in the energy values and decide convergence on that.\n",
        "\n",
        "This method could be useful for large circuits where the number of schemes is large so that a step by step addition results in a better convergence.\n",
        "\n",
        "In our code, we get the convergence we want, with time and CNOT gates in between VQE and ADAPT VQE."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {
        "id": "VPRqOuXyJjxn",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e3e64064-b78f-4f47-9ace-ecf55fadaa57"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "time_iteration = 0,  Energy = -15.56135211 Ha\n",
            "Number of gates = 14\n",
            "\n",
            "Circuit Depth = 8\n",
            "\n",
            "time_iteration = 1, Energy = -15.57366875 Ha\n",
            "Number of gates = 16\n",
            "\n",
            "Circuit Depth = 9\n",
            "\n",
            "time_iteration = 2, Energy = -15.58113881 Ha\n",
            "Number of gates = 18\n",
            "\n",
            "Circuit Depth = 10\n",
            "\n",
            "time_iteration = 3, Energy = -15.58573604 Ha\n",
            "Number of gates = 20\n",
            "\n",
            "Circuit Depth = 11\n",
            "\n",
            "time_iteration = 4, Energy = -15.58860691 Ha\n",
            "Number of gates = 22\n",
            "\n",
            "Circuit Depth = 12\n",
            "\n",
            "time_iteration = 5, Energy = -15.59042490 Ha\n",
            "Number of gates = 24\n",
            "\n",
            "Circuit Depth = 13\n",
            "\n",
            "time_iteration = 6, Energy = -15.59159140 Ha\n",
            "Number of gates = 26\n",
            "\n",
            "Circuit Depth = 14\n",
            "\n",
            "time_iteration = 7, Energy = -15.59234926 Ha\n",
            "Number of gates = 28\n",
            "\n",
            "Circuit Depth = 15\n",
            "\n",
            "time_iteration = 8, Energy = -15.59284751 Ha\n",
            "Number of gates = 30\n",
            "\n",
            "Circuit Depth = 16\n",
            "\n",
            "time_iteration = 9, Energy = -15.59317890 Ha\n",
            "Number of gates = 32\n",
            "\n",
            "Circuit Depth = 17\n",
            "\n",
            "time_iteration = 10, Energy = -15.59340185 Ha\n",
            "Number of gates = 34\n",
            "\n",
            "Circuit Depth = 18\n",
            "\n",
            "time_iteration = 11, Energy = -15.59355358 Ha\n",
            "Number of gates = 36\n",
            "\n",
            "Circuit Depth = 19\n",
            "\n",
            "time_iteration = 12, Energy = -15.59365804 Ha\n",
            "Number of gates = 38\n",
            "\n",
            "Circuit Depth = 20\n",
            "\n",
            "time_iteration = 13, Energy = -15.59373080 Ha\n",
            "Number of gates = 40\n",
            "\n",
            "Circuit Depth = 21\n",
            "\n",
            "time_iteration = 14, Energy = -15.59378211 Ha\n",
            "Number of gates = 42\n",
            "\n",
            "Circuit Depth = 22\n",
            "\n",
            "time_iteration = 15, Energy = -15.59382244 Ha\n",
            "Number of gates = 45\n",
            "\n",
            "Circuit Depth = 23\n",
            "\n",
            "time_iteration = 16, Energy = -15.59386377 Ha\n",
            "Number of gates = 49\n",
            "\n",
            "Circuit Depth = 24\n",
            "\n",
            "time_iteration = 17, Energy = -15.59390224 Ha\n",
            "Number of gates = 53\n",
            "\n",
            "Circuit Depth = 25\n",
            "\n",
            "time_iteration = 18, Energy = -15.59393330 Ha\n",
            "Number of gates = 57\n",
            "\n",
            "Circuit Depth = 26\n",
            "\n",
            "time_iteration = 19, Energy = -15.59395571 Ha\n",
            "Number of gates = 61\n",
            "\n",
            "Circuit Depth = 27\n",
            "\n",
            "time_iteration = 20, Energy = -15.59397077 Ha\n",
            "Number of gates = 65\n",
            "\n",
            "Circuit Depth = 28\n",
            "\n"
          ]
        }
      ],
      "source": [
        "\n",
        "#Define the symbol and geometry\n",
        "symbols = [\"H\",\"Be\",\"H\"]\n",
        "#Geometry in atomic distance for pennylane\n",
        "geometry = np.array([ -1.291/0.529, 0.0, 0.0,0.0, 0.0, 0.0, 1.291/0.529, 0.0, 0.0])\n",
        "active_electrons = 4\n",
        "H, qubits = qml.qchem.molecular_hamiltonian(\n",
        "    symbols,\n",
        "    geometry,\n",
        "    charge = 0,\n",
        "    active_electrons=active_electrons,\n",
        "    basis = 'sto-3g',\n",
        "    active_orbitals=6\n",
        ")\n",
        "n_qubits = qubits\n",
        "#HF State\n",
        "hf_state= qml.qchem.hf_state(electrons=active_electrons, orbitals=n_qubits)\n",
        "\n",
        "\n",
        "#all the operators together\n",
        "all_operators=singles+doubles\n",
        "\n",
        "params = [0.0] * len(doubles+singles)\n",
        "params=np.array(params )\n",
        "\n",
        "#define the circuit again\n",
        "def circuit_1(params, excitations):\n",
        "        qml.BasisState(hf_state, wires=range(n_qubits))\n",
        "\n",
        "        for i, excitation in enumerate(excitations):\n",
        "            if len(excitation) == 4:\n",
        "                qml.DoubleExcitation(params[i], wires=excitation)\n",
        "            else:\n",
        "                qml.SingleExcitation(params[i], wires=excitation)\n",
        "        return qml.expval(H )\n",
        "\n",
        "\n",
        "\n",
        "dev = qml.device(\"default.qubit\", wires=n_qubits)\n",
        "cost_fn = qml.QNode(circuit_1, dev)\n",
        "circuit_gradient = qml.grad(cost_fn, argnum=0)\n",
        "grads = circuit_gradient(params, excitations=doubles+singles)\n",
        "\n",
        "#operators in the opposite manner\n",
        "opposite_pool=doubles+singles\n",
        "\n",
        "#Thresholding the excitations\n",
        "new_opposite_pool=[opposite_pool[idx] for idx in range(len(grads)) if abs(grads[idx]) >1e-5]\n",
        "#gradients for the excitations thresholded\n",
        "new_grads=[grads[idx] for idx in range(len(grads)) if abs(grads[idx]) > 1e-5]\n",
        "\n",
        "#Now we sort these gradients and we will apply it sequentially\n",
        "indx=np.argsort(np.abs(new_grads))\n",
        "sorted_opposite_pool=[new_opposite_pool[idx] for idx in indx]\n",
        "\n",
        "#For the shallower circuit, we will use this\n",
        "shallow_circuits=[]\n",
        "while len(sorted_opposite_pool) !=0:\n",
        "    q_layer=[]\n",
        "    ind_left=[]\n",
        "    for idx, op in enumerate(sorted_opposite_pool):\n",
        "        if shallow_circuits==[]:\n",
        "            shallow_circuits.append(op)\n",
        "            q_layer=q_layer+op\n",
        "        else:\n",
        "            Stack=True\n",
        "            for k in op:\n",
        "                if k in q_layer:\n",
        "                    Stack=False\n",
        "                    ind_left.append(idx)\n",
        "                    break\n",
        "            if Stack:\n",
        "                shallow_circuits.append(op)\n",
        "                q_layer=q_layer+op\n",
        "    sorted_opposite_pool=[sorted_opposite_pool[idx] for idx in ind_left]\n",
        "\n",
        "params = [0.0] * len(doubles_select+singles_select)\n",
        "params=np.array(params )\n",
        "\n",
        "q_layer=[]\n",
        "time_iterations=20\n",
        "conv_tol=1e-4\n",
        "energy=[]\n",
        "\n",
        "opt = qml.GradientDescentOptimizer(stepsize=0.3)\n",
        "dev = qml.device(\"default.qubit\", wires=n_qubits)\n",
        "\n",
        "cost_fn = qml.QNode(circuit_1, dev, expansion_strategy=\"device\")\n",
        "circuit_gradient = qml.grad(cost_fn, argnum=0) # step 2.\n",
        "\n",
        "energy = [cost_fn(params, shallow_circuits)] # step 2.\n",
        "print(f\"time_iteration = 0,  Energy = {energy[-1]:.8f} Ha\")\n",
        "print(\"Number of gates = {}\\n\".format(len(shallow_circuits)))\n",
        "configs=qml.specs(cost_fn)(params, excitations=shallow_circuits)\n",
        "print(\"Circuit Depth = {}\\n\".format(configs['resources'].depth,))\n",
        "t1 = time.time()\n",
        "for n in range(time_iterations):\n",
        "\n",
        "    Test_set=shallow_circuits+all_operators\n",
        "    Test_parameters=list(params)+[0.0]*len(all_operators)\n",
        "    Test_parameters=np.array(Test_parameters)\n",
        "\n",
        "    test_grads = circuit_gradient(Test_parameters,Test_set)\n",
        "    test_grads = test_grads[len(params):]\n",
        "\n",
        "    test_sorted_indx=np.argsort(np.abs(test_grads))[::-1]\n",
        "    maxpos=test_sorted_indx[0]\n",
        "    Larger_sorted_indx=[]\n",
        "    for ind in test_sorted_indx:\n",
        "        Larger_sorted_indx.append(ind)\n",
        "\n",
        "    for k,ind in enumerate(Larger_sorted_indx):\n",
        "        op_set=set(all_operators[ind])\n",
        "        q_layer_set=set(q_layer)\n",
        "        if not bool(op_set & q_layer_set):\n",
        "            q_layer=q_layer+all_operators[ind]\n",
        "            shallow_circuits.append(all_operators[ind])\n",
        "            params=np.append(params, 0.0)\n",
        "        if (len(q_layer)>=n_qubits-4): # It is hard to find the operators with non-zero gradient fill all qubit layers.\n",
        "            q_layer=[]                                 # We leave at maximum 4 idle qubits\n",
        "            break\n",
        "\n",
        "\n",
        "    params,_ = opt.step(cost_fn, params, shallow_circuits) # Step 5.\n",
        "    E_val=cost_fn(params, shallow_circuits)\n",
        "    energy.append(E_val)\n",
        "    conv = np.abs(real_solution.real - E_val) #step 3.\n",
        "\n",
        "    print(f\"time_iteration = {n+1}, Energy = {energy[-1]:.8f} Ha\")\n",
        "    print(\"Number of gates = {}\\n\".format(len(shallow_circuits)))\n",
        "    configs=qml.specs(cost_fn)(params, excitations=shallow_circuits)\n",
        "    print(\"Circuit Depth = {}\\n\".format(configs['resources'].depth,))\n",
        "    if conv <= conv_tol:\n",
        "        break\n",
        "t2 = time.time()"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "HRHxRRE8aRVg"
      },
      "execution_count": 44,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "id": "CgaDGxScJjxn",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 578
        },
        "outputId": "addb8255-456d-43c2-f890-0d65d865329c"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# The following plot is of ADAPT_VQE\n",
        "import matplotlib.pyplot as plt\n",
        "plt.rcParams[\"font.size\"] = 14\n",
        "\n",
        "# plot loss and reference value\n",
        "plt.figure(figsize=(12, 6), facecolor='white')\n",
        "plt.plot(energy, label=\"TETRIS ADAPT VQE BeH2 IDEAL\")\n",
        "plt.axhline(y=real_solution.real, color=\"tab:red\", ls=\"--\", label=\"Target\")\n",
        "\n",
        "plt.legend(loc=\"best\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Energy [H]\")\n",
        "plt.title(\"TETRIS ADAPT VQE energy\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "id": "qxxAfluFJjxn",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "81058d53-186f-49fb-8f71-cb9432dc2ad9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Number of two qubit CNOT gates for TETRIS ADAPT VQE is 603\n"
          ]
        }
      ],
      "source": [
        "num_two_gates = 0\n",
        "for ele in shallow_circuits:\n",
        "    if len(ele)==2:\n",
        "        num_two_gates+=2\n",
        "    else:\n",
        "        num_two_gates+=13\n",
        "print('Number of two qubit CNOT gates for TETRIS ADAPT VQE is', num_two_gates)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {
        "id": "VFv3PMNhJjxn",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ae92d2cb-136c-4fa0-8b89-6965de6265a8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time taken = 114.38073205947876\n"
          ]
        }
      ],
      "source": [
        "print('Time taken =', t2-t1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a_HfjvoiJjxn"
      },
      "source": [
        "Plotting the three different techniques overlaid on each other for comparison"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {
        "id": "WxPHZBRMJjxn",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 578
        },
        "outputId": "9f26496b-2546-4655-f631-98c61b61ce8d"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x600 with 1 Axes>"
            ],
            "image/png": 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7fHx8eP7557NVXBcRERG50YABA/juu+8IDQ0lJiaGlJQUIiIiWL58eZ4JC8j8byXDMIiIiOCrr77Czc2tDKMWEZHqrsqttFi+fDnvvPMOdnZ2tGjRgsjISIv6dejQgSFDhuS4nl/CIy+DBw+mY8eOOa7ndl67YRg8+uijfPPNNzRt2pThw4dTo0YNwsPD2bx5M2fOnMl2VnpCQgK9e/dm7969DBgwgIceeog9e/bwwQcfsHnzZv744w8cHBwKHbOIiIiIiIhIRVPlkhZDhw5l0KBBtGvXjqioKLy8vCzq17Fjx0KtqsjPkCFDCAgIsKjtp59+yjfffMPjjz/Op59+irW1dbb7aWlp2d6///777N27lylTpvDuu++ar0+dOpX33nuP//3vf7z44osWx5qRkUF4eDg1atTQWesiIiIiIiJS6gzDIC4ujvr162NlVcAGEKMKi4iIMACjd+/eebY5deqUARhjx44t9nxz5swxAGPOnDkWtb927ZpRs2ZNo0mTJkZqamqB7TMyMoz69esbLi4uRnx8fLZ78fHxhouLi9GkSZNCxRwWFmYAeumll1566aWXXnrppZdeeulVpq+wsLACv7NWuZUWRRUeHs4XX3xBTEwMnp6e+Pv707Rp0yKNtWfPHqKiokhLS8PHx4f+/ftTu3btHO3Wrl3LlStXGDduHOnp6axcuZJjx47h7u5O//79adasWbb2x48fJzw8nIEDB+Ls7JztnrOzMz179mTNmjWEhYVl21KSnxo1agAQFhaGq6trkZ5XRERERERExFKxsbF4e3ubv4/mR0mL69atW8e6devM700mEyNHjuSrr77KkSAoSNYZ5lkcHR2ZNm0aU6ZMyXZ99+7dAFhbW9O+fXuOHTtmvmdlZcWzzz7LBx98YL52/PhxAJo3b57rvM2bN2fNmjUcP348z6RFcnIyycnJ5vdxcXEAuLq6KmkhIiIiIiIiZcaSEgVV7vSQwnJycuLVV19l9+7dXL16lejoaNavX0/Xrl1ZsGABY8aMsXgsX19fPvvsM44dO8a1a9c4d+4c8+bNo1atWkydOpXPPvssW/tLly4B8NFHH+Hm5saOHTuIi4vjjz/+oEWLFnz44Yf83//9n7l9TEwMQJ5Vu7OSDlntcvPOO+/g5uZmflm6IkNERERERESkrFXIlRaTJ0/OthqgIM8880yeqw8K4uHhwYwZM7Jd69evHz169KBTp04sW7aMkJAQOnXqVOBYvXv3pnfv3ub3DRo0YPTo0XTq1InOnTszffp0HnvsMWxsMj/2jIwMAOzs7Fi+fDn169cH4NZbb+WHH36gQ4cOfPjhhzz22GNFerbcvPjii0yaNMn8PmtZjoiIiIiIiEhFUyGTFl9//TUJCQkWt3/ggQeKnLTIi5OTE6NHj+aVV14hKCjIoqRFXtq0aUOvXr1Yv349hw8fpl27dsDfKyY6d+5sTlhkadu2LU2aNCE0NJSrV6/i7u5ubp/XSorY2Nhs4+bG3t4ee3v7Ij+LiIiIiIiISFmpkEmL+Pj48g4BgDp16gAUKoFSmLFatmwJgLu7e659sq4nJibi7u5uTsxk1bb4p4JqXoiIiIiIiIhUJtW+pkV+tm/fDoCPj0+xxklPT2fXrl0ANG7c2Hy9T58+ABw+fDhHn9TUVEJDQ3F2dqZu3bpAZjKifv36BAUF5UikJCQkEBQUhK+vr7Z7iIiIiIiISJVQIVdalKU9e/bQsWPHHFVLly1bxty5c6lZsyZ33nlntnsRERHExMTg5eWVbSvG7t27ufnmm7O1TU9PZ+rUqYSGhtKnTx+8vLzM95o2bcqAAQNYu3YtM2fOZMKECeZ77777LlevXmXUqFHmGhgmk4kJEyYwY8YM3njjDd59911z+zfeeIP4+Hheeuml4n8oIiIiIiKFkJqaSnp6enmHISLlyNbWFmtr6xIf12QYhlHio5ajI0eOmL/MJyYmsmTJEjw9PbnjjjvMbQIDA82/+/v7c+LECXr06EHDhg1JT08nJCSELVu2YG9vz5IlSxg0aFC2OQICApg7dy5z5swhICDAfN1kMtG+fXvat29PgwYNiI6OZvPmzRw7doyGDRuyefNmmjRpkm2sEydOcMstt3Dp0iXuvvtu/Pz82LNnDxs3bqRx48YEBwdTr149c/uEhAR69uzJvn37GDBgAJ06dSIkJIS1a9fSpUsXNm/ejKOjo8WfV2xsLG5ubsTExOjIUxEREREplNjYWCIjIwtVRF9EqiaTyYSbmxv16tUr8CjTwnwPrXJJi02bNpm3XeTlxkeeOXMmS5cu5eDBg0RGRpKRkUGDBg3o27cvkydPxs/PL0f/vJIWzz33HMHBwYSGhhIdHY2dnR3NmjXj3nvvZdKkSdSsWTPXeMLCwnjttdf47bffiIqKol69egwaNIjXXnsNDw+PHO1jYmKYPn06S5cu5cKFC3h5eTF06FCmTZtGjRo1LPykMilpISIiIiJFERsby/nz53FxccHNzQ1bW9sCv6iISNVkGAYJCQlcvnwZLy+vPOs2ZqnWSQspHCUtRERERKQoTp48ia2tLQ0bNlSyQkQAOH/+PAkJCTRv3jzffxcK8z1UhThFRERERKRQUlNTSU5Oxs3NTQkLETFzdXUlPT29RGvcKGkhIiIiIiKFkvWFxNbWtpwjEZGKJOsQibS0tBIbU0kLEREREREpEq2yEJEblca/CUpaiIiIiIiIiEiFpKSFiIiIiIiIiFRISlqIiIiIiIiISIWkpIWIiIiIiIiIVEhKWkilcCFsGz/9/jLnzgaVdygiIiIiUo2NGDECk8nEokWL8m0XGxuLk5MT7u7uJCYmmq9fuHCBKVOm0L59e2rUqIGTkxMtW7bkqaee4tSpU7mOFRgYiMlkyvcVEBBQko8pUmHYlHcAIpaYvmkyQRlxPHftMmMb9SzvcERERESkmho/fjyLFi1i9uzZPPTQQ3m2W7RoEYmJiYwdOxZHR0cAfvnlF4YPH05cXBzdu3dn4sSJ2NjYsHfvXr788ku+/fZbZs+ezYgRI3Ids1+/fvTq1SvXex07diz2s4lUREpaSKXQw7UZQVf3EHz1CGPLOxgRERERqbb69u2Lr68vGzdu5OzZszRq1CjXdrNnzwYykxwAu3fv5v7778fKyorly5czePDgbO23bdvGoEGDGD16NF5eXvTp0yfHmP3792fq1Kkl/EQiFZu2h0il0L1B5uqK3alXSElPKedoRERERKS6MplMjBs3joyMDObMmZNrm4MHD7Jjxw7at29P586dAXjmmWdITk7m008/zZGwAOjRowcLFy4kIyODJ554AsMwSvU5RCoLJS2kUmjeuA+10tNJNMG+S3vKOxwRERERyYNhGFxLSavwr+IkBQICArCysiIwMDDXcbKSGVmrLI4fP05QUBANGjRg3LhxeY57++23061bNw4fPsyWLVuKHJ9IVaLtIVIpWNVuSvekVH5xtmbbyd/o4tWtvEMSERERkVwkpqbT+rU15R1GgQ7NGIiTXdG+Dnl7ezNgwAB+++03Nm7cSL9+/cz30tLSWLBgAfb29owaNQqArVu3AuDv74+1tXW+Y/fr14/t27cTFBTErbfemu3e+vXrSUpKyrXf8OHD8fPzK9LziFRkSlpI5WBlTXe72vxCAtsjgss7GhERERGp5saPH89vv/3G7NmzsyUtVq1axcWLF3nwwQepVasWkHliCGQmOwqS1eb8+fM57m3YsIENGzbk2q9jx45KWkiVpKSFVBo9araG+J0cSDhPTHIMbvZu5R2SiIiIiPyDo601h2YMLO8wCuRom/+Kh4IMHjyYunXr8tNPPxETE4ObW+Z/m/6zAGdRZWRk5Lj2zjvvqBCnVDuqaSGVRj2vm/BJSSUDg10XdpV3OCIiIiKSC5PJhJOdTYV/mUymYj2nra0to0ePJjExkYULFwKZKyp+/fVXGjVqRP/+/c1t69WrB0BYWFiB42a1adCgQbHiE6kqlLSQysOjNT0SM/fwbYvYVs7BiIiIiEh1l7WaYtasWQDMnz+ftLQ0xo0bh5XV31+1brnlFgA2bdpEenp6vmNmbf9o3bp1aYQsUukoaSGVh2cbul8vPBQcvrWcgxERERGR6q5169Z0796d3bt3s3//fubMmWM+EvVGzZs3p1evXpw/f565c+fmOd6GDRvYvn07derU4a677irt8EUqBSUtpPJw8aQLjlgbBmfiwgiPDy/viERERESkmstabfH4449z+PBh+vfvT+PGjXO0++STT7C3t+epp55i1apVOe7v2LGDESNGAPDSSy9hZ2dXuoGLVBIqxCmVh8lEDY82tE0+xj4He4Ijgrm/+f3lHZWIiIiIVGPDhg3jP//5D0FBQUDeBTg7derE0qVLGT58OPfeey89evSgR48e2NjYsHfvXtavX09GRgbjxo3j2WefzXWM/I48rVevHo8++mjJPJRIBaKkhVQuHq3pcWw/+xzs2Ra+TUkLERERESlXNWrU4MEHH2TOnDnUqlWLIUOG5Nn27rvv5tixY/zvf//jl19+4euvvyYhIQEAZ2dnZs2axbBhw/Lsn9+Rpx06dFDSQqokbQ+RysWzNd2vF+PcHrGdDCPnUVAiIiIiImVp9uzZGIZBVFQU9vb2+bb18vLi/fff58CBA8THx5Oens6gQYNISEjg8uXLufYJCAjAMIx8X3v37i2FJxMpf0paSOXi0Zr2yck4ZRhcSb7C0eij5R2RiIiIiEiRWVlZ8d1339GhQweefvpp5s+fX94hiVQoSlpI5eLRClugc9YpIhHB5RuPiIiIiEgxubi48PPPP/Paa69x9uxZ4uPjyzskkQpDNS2kcrGvAe6N6J54hT+cHNkWvo1xbccV3E9EREREpALz9vZm+vTp5R2GSIWjlRZS+Xi0ocf1uhYhl0JITk8u54BERERERESkNChpIZWPZ2uapqZS12RHcnoyey7tKe+IREREREREpBQoaSGVj0drTED39My/vsHhqmshIiIiIiJSFSlpIZWPZxsAul+NBGBbxLbyjEZERERERERKiZIWUvnUbgZWtnSPjwHgcNRhriZdLd+YREREREREpMQpaSGVj7Ut1G2JR3o6TR09MDDYfmF7eUclIiIiIiIiJUxJC6mcPFoB0MO2NgDBEaprISIiIiIiUtUoaSGVk0drALonpwGwLVx1LURERERERKoaJS2kcrpejLNz1HlsTDacjz9PWFxYOQclIiIiIiIiJUlJC6mcrq+0cI4KpX2dtoBWW4iIiIiIiFQ1SlpI5eTWEOzdICON7q7NANW1EBERERERqWqUtJDKyWT6uxinlQsA2yO2k56RXp5RiYiIiEg19PDDD2MymahduzbJycm5tvH398dkMplftra21K5dm44dOzJ+/Hh+++03MjIyCpyrb9++mEwm2rZtm287Hx+fbPNZW1tTp04dBgwYwIoVKwA4ffp0tjYFvXx8fCz6PDIyMvD29sba2prz58/n23bdunWYTCYGDBiQ496ePXsYN24cTZo0wdHREXd3d7p06cJbb71FXFxcruMFBAQU+ByBgYEWPYdUDDblHYBIkXm2hrBg2sZfxdnWmdiUWI5EH6FNnTblHZmIiIiIVBNxcXEsWbIEk8lEdHQ0y5cvZ9iwYXm2nzx5Mi4uLmRkZHD16lUOHz7Md999x+zZs7nllltYtGgRjRo1yrXvyZMn2bRpEyaTiYMHD7J9+3a6deuW51zW1ta88sorAKSkpHDkyBFWrlzJunXr+OCDDxg/fjzTpk3L0e/111/Hzc2N//znP9muu7u7F/yBAFZWVgQEBPDmm28SGBjIyy+/nGfb2bNnAzB+/Phs12fMmMH06dOxsbFh4MCBPPjggyQmJrJp0yZeeeUVvvrqK1avXk379u1zHXf8+PE0bNgw13sdO3a06DmkgjCkWouJiTEAIyYmprxDKbzt3xjGNFfDWPCA8eSGJ422gW2Nb/d/W95RiYiIiFR5iYmJxqFDh4zExMTyDqXcffvttwZgTJo0ybCysjJuv/32XNv17t3bAIyIiIgc9y5fvmw89NBDBmD4+fkZ8fHxuY7x8ssvG4Dx3HPPGYAxceLEPONq3LixYW9vn+P6mjVrDJPJZDg5ORkJCQm59gWMxo0b5zm2JU6cOGGYTCajWbNmebaJjo42HBwcjFq1ahlJSUnm659//rkBGE2aNDEOHz6co99XX31lWFtbG/Xq1TMuXryY7d7YsWMNwNi2bVux4peisfTfhsJ8D9X2EKm8rp8gwqXD9PDqAUBwuOpaiIiIiEjZmTVrFjY2Nrzwwgv06dOHDRs2cObMmUKNUadOHRYsWEDfvn05cuQIX3zxRY426enpBAYGUrt2bd566y2aNWvG999/T0JCQqHmGjBgAC1btuTatWscPHiwUH0Lo0mTJvTp04fQ0FA2b96ca5uFCxeSlJTEqFGjsLe3B+DKlSu8+OKL2NnZ8fPPP+Pn55ej3yOPPMKUKVO4cOECr732Wqk9g1QMSlpI5XW9pgUxYXSvnbmnL+RSCIlpieUYlIiIiEg1ZxiQklDxX4ZR7Ec9dOgQwcHBDBgwAE9PT8aMGUNGRgZz5swp9FhWVlbmbRSLFy/OcX/NmjWcP3+eYcOGYWdnx+jRo4mLi+OHH34ocvwmk6nIfS2RteUjawvIP2V9TjduDfnxxx+Ji4vj/vvvp3Xr1nmO/fzzz+Pg4MC8efNISUkpwailolFNC6m8HGtCjfoQF45vYgKeTp5cvHaRPRf3cEuDW8o7OhEREZHqKfUavF2/vKMo2EvhYOdcrCFmzZoFwOjRowG4//77efzxx5kzZw6vvfYaVlaF+9+Ie/bsiY2NDXv37iUtLQ0bm7+/rv1zrlGjRjF9+nRmzZpFQECAxXNs2LCBo0eP4uzsTJs2pVsL7v7778fd3Z0ff/yRzz//nBo1apjv7d+/n927d9O5c+dsdSm2bt0KQL9+/fId293dnU6dOrF161ZCQkLo3r17tvszZ87kt99+y7Xv1KlTcXBwKOpjSRlT0kIqN8/WEBeO6dIhunt1Z8WJFWyL2KakhYiIiIiUqtTUVObPn4+rqytDhgwBwMXFhfvuu48FCxawfv36XE/EyI+9vT21a9fm4sWLREdH4+HhAcDly5f5+eefadGihfnLeZMmTejZsydbtmzh6NGjtGzZMsd4aWlpTJ8+3Rzv0aNHWbFiBYZh8MYbb+Do6Fj0D8ACDg4OjBw5ki+++ILvv/+eiRMnmu9lrb54+OGHs/W5cOECAN7e3gWOn9UmtxNKspI8ufnPf/6jpEUloqSFVG4erSF0PVw6RI9WfVlxYgXBEaprISIiIlJubJ0yVzFUdLZOxeq+YsUKLl++zPjx47N9AR4zZgwLFixg1qxZhU5a5GXu3LmkpqaaV1ncONeWLVuYPXs27733Xo5+6enpvP7660Dm9pOaNWvSt29fnnjiCQYNGlQisRVkwoQJfPHFF8yePductEhJSeG7777D0dGRESNGFHuO3I6K3bZtW47VF1I5KWkhlVtWMc6Lh+jW90UAjkQfISoxitqOtcsxMBEREZFqymQq9raLyiDrf8kfM2ZMtuv9+vWjQYMGrFixgujoaGrVqmXxmMnJyURFRWFtbZ2t36xZszCZTDmSFg8++CBPP/008+bN46233sq2nQQyV24kJSUV9tFKVMeOHenUqRPBwcEcPnyYVq1asXLlSiIjIxk1ahRubm7Z2terVw+AsLCwAsfOatOgQYOSD1wqDBXilMrN43pxnksHqeNQmxY1WwCw48KOcgxKRERERKqysLAw1q5dC0Dv3r0xmUzml7W1NefPnyc5OZkFCxYUatygoCDS0tLo2LGjOQGxdetWjhw5gmEY+Pj4ZJvL3d2dpKQkLly4wC+//FLiz1lSsgptZiV6civAmeWWWzK3eW/YsCHfMa9evUpISAjW1ta0aNGiJMOVCkYrLaRyq9sSTNaQFAOx4XT36s6xK8fYFr6NO33vLO/oRERERKQKCgwMJCMjg169euVZS2Lu3LnMmjWLp59+2qIxMzIyeOuttwB46KGHzNezvujfeeed1K+fs8Dp1atXWbp0KbNmzSqzLR+FNWLECCZPnsyCBQt46qmnWLNmDU2bNqV379452g4dOpTJkyezbNkyjhw5kuuRpwAffvghSUlJ3HvvvdSpU6e0H0HKkZIWUrnZ2EPtZhB5NLOuRf0ezDs0j20R2zAMo9SPcRIRERGR6sUwDObMmYPJZGLu3Lk0adIk13bHjh1j27Zt7Nq1i86dO+c7ZmRkJE8//TQbN26kdevWPPbYYwDEx8ezZMkSnJ2dWbJkCS4uLjn6ZmRk0LhxY3755RcuXLhg3l5Rkbi7u/Ovf/2L7777jpEjR5Kens7DDz+c63+ru7u788477/Dkk09y7733snr16hwrKWbNmsU777yDnZ2d+ZhYqbqUtJDKz6OVOWnRqetEbK1suZBwgTOxZ/Bx8ynv6ERERESkCtm4cSOnTp2id+/eeSYsAMaNG8e2bduYNWtWtqTFBx98gIuLCxkZGcTGxnLo0CH+/PNPkpKS6NmzJ4sWLcLJKbNI6OLFi4mPj2fs2LG5Jiwgs8DmmDFjePvtt5k7dy5Tpkwp2QcuIePHj+e7774jKCgIa2vrfI9pfeKJJ4iMjOT111+nXbt23HHHHbRq1YqkpCQ2bdrEvn37sLa25v/+7//o1q1brmPkd+Rp9+7dueOOO0risaQMKGkhlZ9nGzi0HC4ewsnWiY4eHdl5YSfBEcFKWoiIiIhIicrarpHfl26AYcOG8cwzz7Bo0SI++ugj8/UPP/wQABsbG2rUqEGjRo0YMWIEDz74ILfffjtWVn+XHbR0roCAAN5++21mz55dYZMW/v7+NG3alBMnTjBw4MBct7rcaNq0adx77718+umnbNq0iTVr1pCcnAxAixYtWLRoEZ06dcqzf35Hnj7zzDNKWlQiVa4Q5969e3nppZcYOHAgdevWxWQy4e/vn2f706dPZytm889X1rnGlggMDMx3rE2bNuXZ96effuL222+ndu3aODg44Ovry0MPPZSjau706dPzneP06dMWx1tl3FCME6C7V+bRRtvCt5VXRCIiIiJSRS1cuBDDMApMJLi6unLt2jWuXr2Ko6MjmzZtwjAM8ys1NZXo6Gj27t3LrFmzGDhwYLaEBWQW4TQMI9/vMwDNmzfHMAyOHj1qvnb69OkinxxiGEaJf68wmUyEhoZiGAarV6+2qE+nTp0IDAw0P8ulS5fw9fUlPDyc1NTUXPsEBgZm+5xze3388ccl+GRS2qrcSovly5eb9ze1aNGCyMhIi/p16NCBIUOG5Lhe0D8QuRk8eDAdO3bMcd3HxyfHNcMwePTRR/nmm29o2rQpw4cPp0aNGoSHh7N582bOnDmDt7d3jn5jx47NdTx3d/dCx1vpeV5PWlw+Bulp9PDqwWd7PmPnhZ2kZaRhY1Xl/pqLiIiIiFQ7devW5eeff+aWW27hzjvvZPPmzbRr1668w5JSVuW+zQ0dOpRBgwbRrl07oqKi8PLysqhfx44dC7WqIj9DhgwpMPOa5dNPP+Wbb77h8ccf59NPP8Xa2jrb/bS0tFz7BQQEFCmhUiW5+4CtM6QmQPQJWtduTQ27GsSlxHEw6iAd6nYo7whFRERERKQEtGnThlWrVrFhwwa2bt2qpEU1UOWSFm3atCnvECyWmJjI66+/TpMmTfjkk09yJCwA8/nMkg8rK/Dwg/O74eJBrOu2pFu9bqw/u57g8GAlLURERERESsDp06cJDAwssJ27uzv/+c9/Si2OW2+9lVtvvbXUxpeKRd+IrwsPD+eLL74gJiYGT09Pc6GYotizZw9RUVGkpaXh4+ND//79qV27do52a9eu5cqVK4wbN4709HRWrlzJsWPHcHd3p3///jRr1izPOf744w+2b9+OlZUVzZs3p3///nlWFK4WPFpnJi0uHQLup7tXd9afXc+2iG080uGR8o5ORERERKTSO336NK+//nqB7Ro3blyqSQupXpS0uG7dunWsW7fO/N5kMjFy5Ei++uornJ2dCzXWp59+mu29o6Mj06ZNy1HJd/fu3QBYW1vTvn17jh07Zr5nZWXFs88+ywcffJDrHNOmTcv23t3dnU8++YQxY8bkG1tycrK56i5AbGxswQ9UGXheX2Fz8RAAPer3AGDf5X1cS72Gk61TeUUmIiIiIlIl+Pv7YxhGeYch1UyVOz2ksJycnHj11VfZvXs3V69eJTo6mvXr19O1a1cWLFhQYBLgRr6+vnz22WccO3aMa9euce7cOebNm0etWrWYOnUqn332Wbb2ly5dAuCjjz7Czc2NHTt2EBcXxx9//EGLFi348MMP+b//+79sfTp06MDs2bM5efIkiYmJnDp1is8++wyTyURAQAArV67MN8Z33nkHNzc38yu3Ip+VkvkEkcykhXcNb+o71yctI41dF3eVY2AiIiIiIiJSVCajAqbKJk+enG01QEGeeeYZmjdvnuP6hQsX8PLyonfv3vkeN5qba9eu0alTJ44ePcru3bvzPQO4IAcPHqRz5844OTlx8eJFc52Kf//733z77bc4OjoSGhqa7aziAwcO0KFDB3x9fQkNDS1wjg0bNnD77bfTtm1b9u/fn2e73FZaeHt7ExMTg6ura5GfsdzFX4YPmgEmeOk82Dkzfet0lh5fyujWo3mhywvlHaGIiIhIlZGUlMSpU6fw9fXFwcGhvMMRkQrC0n8bYmNjcXNzs+h7aIXcHvL111+TkJBgcfsHHngg16RFcTg5OTF69GheeeUVgoKCipW0aNOmDb169WL9+vUcPnzYXOHWzc0NgM6dO2dLWAC0bduWJk2aEBoaytWrVws8yrRfv340bdqUv/76i9jY2Dz/4O3t7bG3ty/ys1RYLnXBuS4kXIZLR6DhzXT36s7S40vZFr6tvKMTERERERGRIqiQ20Pi4+MxDMPiV2kd/VmnTh2AQiVQCjNWy5YtAfJMSGRdT0xMLNQc165dK2KUlZx5i8hBALp5dQMg9GookYmR5RWViIiIiIiIFFGFTFpUFNu3bwfAx8enWOOkp6eza1dmXYXGjRubr/fp0weAw4cP5+iTmppKaGgozs7O1K1bt8A5EhISOHjwIM7OzubkRbXzj2KcNR1q0qpWKwCtthAREREREamEqn3SYs+ePblWwF22bBlz586lZs2a3HnnndnuRUREcOTIEWJiYrJdzzoN5Ebp6elMnTqV0NBQ+vTpg5eXl/le06ZNGTBgAKGhocycOTNbv3fffZerV69y3333mWtgxMXFZTthJEtiYiITJ04kLi6OBx980Ny+2vnHSguA7vW7AxAcEVweEYmIiIiIiEgxVLlvt0eOHOHdd98F/t5WceTIEQICAsxtAgMDzb8/++yznDhxgh49etCwYUPS09MJCQlhy5Yt2NvbExgYaK49keXFF19k7ty5zJkzJ9u4nTt3pn379rRv354GDRoQHR3N5s2bOXbsGA0bNsyRmAD48ssvueWWW5g4cSLLly/Hz8+PPXv2sHHjRho3bsx///tfc9uoqCj8/Pzo0qULrVq1ol69ely8eJH169dz7tw52rVrl619teN5PWlxfaUFQHev7sw5MIfg8GAMw8BkMpVTcCIiIiIiIlJYVS5pceHCBebOnZvt2sWLF7NduzFpMWrUKJYuXUpwcDCRkZFkZGTQoEEDJkyYwOTJk/Hz87N47smTJxMcHMy6deuIjo7Gzs6OZs2a8corrzBp0iRq1qyZo0/Tpk3ZtWsXr732Gr/99htr166lXr16PPHEE7z22mt4eHiY29aqVYvHH3+cHTt28Msvv3DlyhUcHR1p1aoVTz/9NE8++SSOjo6F+LSqmLqtABNci4T4S+DiQSePTthZ2XEp8RKnYk7RxL1JeUcpIiIiIiIiFqqQR55K2SnMUTOVwqc3QfRJGL0cmmbWDJmwdgLbI7YztetURrYaWb7xiYiIiFQBOvJURHJTGkeeVvuaFlLFmOta/F3ctIdXDwCCw1XXQkRERESKx2QyFeoFcPr06QLbZRX/9/f3L9T4mzZtAjIPD7jxurW1NbVr16Zfv3788MMPuT5LYGAgJpPJvL3+RqtXr+buu+/Gw8MDW1tb6tSpQ9u2bXn44YdZsWJFsT/HhIQEXF1dMZlMPPHEE3m2y+2zc3Jyon79+vTr14/XXnuNEydOFDjfmTNnsLa2xmQy5bulftOmTTnmc3BwoEmTJkycOJHTp08DMH369EL9OU2fPt2iz2Xt2rWYTCYGDhxYYNuRI0diMplYuHBhtuvp6enMmTOH22+/nbp162JnZ4eXlxeDBw9m5cqVeY5n6d/nslbltodINefRGo6sylmMMwR2XtxJakYqtla25RigiIiIiFRm06ZNy3Ht448/JiYmJtd7N2ratCmjRo3K9Z67uzsAAQEB+Pv7Z7u3fPly9u3bx9ixY3OcbHjje2tra1555RXg79MIf/rpJzZu3Mjbb7/Niy++mP/DXff6668zffp0nJycuOeee/Dx8SEtLY2DBw+yePFijh07xuDBgy0aKy9LliwhLi7O/KX7ww8/zPd/mb/xs0tOTubSpUvs2LGDN954g7fffpsXXniBt956K88v1rNnzyYjIwOTycTs2bN5/vnn843v5ptv5p577gHg6tWrbNq0iZkzZ7J06VK2b9+e488IYO/evaxYsYLevXvnuJ9b+9z079+fRo0asX79esLCwvD29s61XUxMDD/99BPu7u7cf//95uuXLl1i8ODBBAcHmxMVHh4enDt3jtWrV7Ny5UqGDh3KvHnzcv28a9euzZNPPmlRrGXGkGotJibGAIyYmJjyDqVkHFhmGNNcDeNrf/Ol9Ix0o+einkbbwLZGyMWQcgxOREREpGpITEw0Dh06ZCQmJpZ3KBVC48aNjfy+Wp06dcoAjIEDBxZp/LFjxxqA8fvvv+cbg729fY7rW7ZsMaysrAxHR0cjISEh2705c+YYgPHOO+9ki9XKysrw9vY2zp8/n2O8a9eu5RuHpXr27GnY2NgY//nPfwzA+O6773JtV9Bn9+effxo+Pj4GYLzyyiu5tklPTzcaNWpk1KlTxwgICDAAIygoKNe2v//+uwEYjzzySLbrGRkZxujRow3AGDt2bK59sz7PadOm5f7QFpo2bZoBGDNmzMizzZdffmkAxhNPPGG+lpKSYvTo0cMAjPHjxxvXrl3L1ufKlSvG3XffbQDGuHHjcowJGC1btixW7Jb+21CY76HaHiJVi0ebzJ+Xj0BGBgBWJiu61esGaIuIiIiIiFQvPXv2xM/Pj8TERA4dOlRg+x07dpCRkcH9999P/fr1c9x3dHS0eNVAXo4ePUpQUBB33HEHzz77LCaTiVmzZhVprF69evHbb79hb2/P+++/T1hYWI4269at4+zZswwfPpzx48cDFHq+G7ex7Ny5s0ixWmrcuHGYTCYCAwMx8ihBOXv2bADz8wDMnTuXbdu2ceutt/Ltt9/mOKTB3d2dH374gWbNmjFnzhyCgyvHdyMlLaRqqdUErO0h9RpcOWW+3KN+Zl2LbRHbyisyEREREZFyZWNTcHWA2rVrA3D8+PFSiyMrYTBmzBgaNWqEv78/v//+O6dOnSqgZ+5atmzJgw8+SEpKCsuXL893vl69etGkSROWLFlCfHx8keYr7doOjRs3pn///pw8edJcs+RGBw4cYNeuXdx0003cdNNN5utz5swB4OWXX84zRkdHRyZPngzAt99+W/LBlwLVtJCqxdoG6raEC/vh0iGo3RSA7l7dAdh/eT/xKfG42LmUZ5QiIiIiVZZhGCSmJZZ3GAVytHEs88KCoaGheRZk7N69O3fccUeJzxkUFMSRI0eoXbs2fn5+Bbbv1q0bjRo14pdffuGee+5h+PDhdO3alebNm5fI55WWlsa8efNwd3fn3nvvBWD06NH8/vvvzJ49mzfeeKNI4/r7+zN//vwcqyCioqJYsWIFfn5+dOnSBYBRo0YxY8YMFi9enG2lQn4Mw+D//u//AOjatWuRYiyM8ePHs27dOmbPnk2fPn2y3cttlUVaWho7d+7ExsaG3r175zt2v379gMy/G/8UGRmZ599RPz8/hg8fXpjHKBFKWkjV49kmM2lx8RC0yvyHsGGNhnjX8CYsLoxdF3fh7+1fvjGKiIiIVFGJaYl0W9itvMMo0PYR23GydSrTOU+cOMHrr7+e671nnnmm2EmLtLQ08xfOGwtxWllZ8eWXX1p0PK2LiwvLly9n9OjRrF69mtWrVwPg5ubGrbfeysMPP8x9991X5BhXrVrFxYsXmThxojmeBx54gCeffJLAwEBef/11rKwKvyEgaytLZGRktuvz588nJSWF0aNHm6+NGTOGGTNmMGvWrDyTFrt27TJ/ljExMWzatIm9e/dSq1YtXn755ULHV1hDhgyhdu3aLF26lC+++MJ8LGhqaioLFizAwcGBESNGmNtHRUWRmppKvXr1Cvxzziruef78+Rz3oqKi8vw7OnjwYCUtREqE+djTg9kud/fqTlhcGMERwUpaiIiIiEiZGzhwIL/99lupjZ+enp7jC6eNjQ0//PADQ4YMsXicm266ib/++ott27bx+++/s3v3brZs2cKqVatYtWoVI0eOZP78+UVaeTFz5kwgM3GQpUaNGgwZMoSFCxeyZs0a7rzzzkKPm5dZs2ZhMpmyndrStGlTbrnlFrZu3crhw4dp1apVjn67d+9m9+7dANjZ2dGgQQMmTpzIyy+/TOPGjUssvrzY29szatQoPvnkExYtWsQjjzwCwM8//8zly5d56KGHqFmzZrHmyLheA/BGLVu25MiRI8Uat6QpaSFVj2dW0uJwtss96vfgh2M/sC1cdS1ERERESoujjSPbR2wv7zAK5GjjWHCjSsbe3p6kpCQA4uPj2bhxIw8//DCjR49my5YtdOjQweKxTCYTt9xyC7fccguQuT1ixYoVjBkzhu+++45//etfhV5xER4ezm+//UaTJk3o1atXtntjxoxh4cKFzJ49u0hJi/DwcADq1q1rvrZ9+3YOHDhAnz59aNSoUY75tm7dyuzZs/nvf/+bY7xHHnmEr776qtBxlKTx48fzySefMHv2bHPSIretIZBZi8TW1pbIyEiSkpLyXW2RVay0QYMGpRR5yVIhTql6slZaRJ2A1CTz5a71umLCxMmYk1xMuFhOwYmIiIhUbSaTCSdbpwr/Kut6FmXNxcWFQYMGsXjxYuLj4xk3blyeJ1FYwmQyMWTIEJ599lkANm7cWOgxAgMDSU9P5+TJk5hMpmyvrK0xK1euzLHFwxJZBSuz6lbA3wU4f//99xzzPfroowDMmzeP1NTUQs9XFtq1a0eXLl3YsWMHBw8eJCIigt9++w1fX1/69u2bra2NjQ1dunQhLS2NzZs35zvuhg0bAGjdunWpxV6StNJCqp4aXuDgDklXIfIoeGVmlN3s3WhTuw0Hog4QHBHM4GaDyzVMEREREZHS1q9fP4YMGcLy5ctZtGhRtjoIReHiUrSC9oZhmFcJBAQEYG1tnaPN4cOH2bp1K/PnzzcnRyxx7NgxlixZgr29vXn1R0JCAt9//z1OTk489NBDufbbuXMn+/fvZ9WqVcWq01Gaxo8fz86dO5k1axaenp6kp6ebj0T9p4cffpitW7fyzjvvMGDAgFzbJCUl8dFHHwHZt+hUZEpaSNVjMmUW4zwTlFmM0+vvZXDd63dX0kJEREREqpXp06ezYsUKXn/9dYYNG5ZrwiDLjh07OHLkCA8++GCOLQaXL18216T45/aOgmzevJkTJ05w2223mY/m/KejR4/i5+fHrFmzLE5aBAUFMWrUKJKTk5k2bZp5y8MPP/xAXFwcY8aMMcf8T2vXrmXgwIHMmjWrwiYtHnroISZNmsSCBQuoWbMmVlZWBAQE5Np27NixzJo1i82bN/Poo4/yySefZPszjImJYcyYMRw/fpybb77ZfHpLRaekhVRNHq0zkxb/KMbZw6sHM/+aSXBEMIZhVPllgSIiIiJSceR35CnA1KlTLTrho7A6dOjAfffdx7Jly1iwYAFjx47Ns214eDhjx47lySef5LbbbsPPzw8bGxvOnDnDqlWriI+P5+6772bo0KGFiiFrq8a4cePybNOyZUtzgczt27fTrdvfp9Dc+NmlpKRw6dIlduzYwV9//YW1tTWvvPIK06ZNK9R8/fv3p2HDhvz222+Eh4ebTyCpSFxdXXnggQeYN28ely9f5o477jCf/vFPNjY2LF++nEGDBvHNN9+watUq7rrrLjw8PDh//jyrVq0iKioKb29vli9fjq2tbY4x8jvyFODRRx+lXr16JfV4FlHSQqqmrGKcFw9lu9zRoyMO1g5EJkYSejWU5jWbl0NwIiIiIlId5XfkKcB//vOfUklaAEybNo2ffvqJGTNmMHLkSGxscv8q2K9fPxYsWMCaNWsICQkhKCiI+Ph4atasSbdu3RgxYgRjx44t1LGkMTExLF26FGdnZx544IF8244bN46tW7cya9asbEmLGz87R0dH3N3d8fPz49VXX2Xs2LE0bdrU3Pbo0aNs2bIFX19fevfunedcVlZWjB07lrfeeovAwEBeeukli5+pLI0fP5558+YBmVtA8uPh4UFQUBBz585l4cKF/PTTT1y5csV8UsjDDz/M//73P/MRqv+U35GnkHkUa1knLUxGcaqxSKUXGxuLm5sbMTExef7FrZTObofZAzLrW0zOfmTPo+seJSg8iOc7P8+YNpVjH5eIiIhIRZKUlMSpU6fw9fUttS/ZIlJyfvjhB4YNG0avXr1Ys2YNjo6lc3qOpf82FOZ7qE4PkarJ4/pZy3ERcC06263uXt0BCI4ILuuoREREREREytzQoUOZMWMGf/75J//6178q7IkpudH2EKmaHFzBrRHEnIVLh8Dn70JBPer3gN2w6+IuUtNTsbXOuZdLRERERESkKnnllVdwd3cnMjKS3bt307179/IOySJKWkjV5dn6etLicLakRfOazanlUIvopGj2Xd5H53qdyzFIEREREZHKae/evSxfvrzAdj4+PnmeeFFdLF++nL179xbYzt/fH39//1KL48knnyy1sUuLkhZSdXm0gmO/wcXsJ4hYmazo5tWNX0/9yraIbUpaiIiIiIgUwd69e/Mt2pild+/eSlosX87cuXMtaluaSYvKSDUtpOryaJP589KhHLd6ePUAVNdCRERERKSoAgICMAyjwNemTZvKO9RyFxgYaNFnld9xo9WVkhZSdWUde3rpMPzjkJysYpwHIg8QmxJb1pGJiIiIiIiIBZS0kKqrdnOwsoHkWIgJy3bLy8ULH1cfMowMdl7YWU4BioiIiIiISH6UtJCqy8YO6rTI/P1izi0iWasttoVvK8uoRERERERExEJKWkjV5pG1ReRgjlvd62cmLbZHbC/LiERERERERMRCSlpI1ZZV1yKXlRZd63XFymTF6djTRMRHlHFgIiIiIiIiUhAlLaRqM58gcjjHrRp2NWhbpy2gU0REREREREQqIiUtpGrLWmkReQzSU3Pczjr6VHUtREREREREKh4lLaRqc/MGuxqQkQqRx3PczirGuf3CdjKMjLKOTkRERERERPKhpIVUbSYTeLTK/P1SzroWHep2wNHGkeikaI5dOVbGwYmIiIiIiEh+lLSQqs9cjDPnCSK21rZ09uwMQHC46lqIiIiIiIhUJEpaSNVnLsaZc6UFQI/61+taRKiuhYiIiIjkz2QyFepVWUyfPh2TycSmTZvKOxSRbGzKOwCRUpfPsafwd12LkIshJKcnY29tX1aRiYiIiEglM23atBzXPv74Y2JiYnK9JyLFo6SFVH0e15MWMWchKRYcXLPdbubejDqOdYhMjGTvpb108+pWDkGKiIiISGUwffr0HNcCAwOJiYnJ9Z6IFI+2h0jV51QLanhl/n7pcI7bJpPJvNoiOEJ1LURERESk+MLDw5k2bRrdu3fHw8MDe3t7fHx8ePzxx7l06VKO9gEBAZhMJk6ePMmHH35I69atsbe3JyAgwNxm8+bN3HbbbTg7O1O7dm2GDRtGWFgY/v7+uW5FMQyD2bNn07NnT1xdXXFycqJz587Mnj07Wzt/f39ef/11APr06WPe2uLj41Oin4lIUWilhVQPHq0hLiKzrkWjnCspetTvwaqTq9gWvo1nOj1TDgGKiIiISFXyxx9/8OGHH9KvXz+6deuGra0te/bs4f/+7/9Ys2YNISEhuLm55ej31FNPERwczN133829996Lh4cHAGvXruXuu+/G2tqaYcOGUb9+fX7//Xd69epFzZo1c4xjGAYjR45k0aJFNG/enBEjRmBnZ8e6desYP348hw4d4oMPPgAwJ0Y2b97M2LFjzckKd3f3UvlsRApDSQupHjxawYkNeRbj7FYvM5FxKOoQMckxuNnn/H8gIiIiImK5jGvX8r5pbY2Vvb1lba2ssHJwKFrbxEQwjJzNnJzyHqOE9O3blwsXLuDi4pLt+rx58xg7diyff/45L7/8co5++/fvZ8+ePTRq1Mh8LT09nX//+9+kp6ebExVZxo4dy7x583KMM3PmTBYtWsS4ceP4+uuvsbW1BSAlJYUHHniADz/8kIceeoibb76ZgIAATp8+zebNmwkICMDf37+EPgWR4lPSQqoHz+sniORRjNPT2ZOmbk05EXOC7RHbGeAzoAyDExEREal6jna6Oc97zr1vo9HXX5vfH+vZCyMxMde2Tl260Hj+31/KQ/v1J/3KlVzbOrRti++PP5jfn7z7HlLDw3O0a3Uk55bhkpa1QuKfRo8ezVNPPcX69etzTVo8//zz2RIWAFu2bOHMmTMMGjQoW8IC4M033+S7774jPT092/XPP/8cZ2dnvvjiC3PCAsDOzo633nqLn3/+mUWLFnHzzXn/OYlUBEpaSPWQVYzz0sHMbHsue/661+/OiZgTBEcEK2khIiIiIsW2bNkyvv76a0JCQrhy5Uq2xEJ4LskUgK5du+a4tm/fPoAcCQsAb29vGjVqxKlTp8zXrl27xl9//UX9+vV57733cvRJTU0F4MiRI4V7IJFyoKSFVA91W4LJChKvQNwFcPXK0aSHVw++O/wd28K3lUOAIiIiIlVLy5Dded+0ts72tkXQlrzbWmU/O6DZhvUWt22yelWu20PKwocffshzzz1H3bp1GTBgAA0bNsTR0RHIPCI1OTk5136enp45rsXGxgJ5r97w9PTMlrS4cuUKhmFw/vx5c4HN3CQkJFj8PCLlRUkLqR5sHaFWU4g6nrnaIpekRed6nbEx2XAu/hxhcWF41/Auh0BFREREqobC1I0otbbXkwRlLS0tjTfeeAMvLy/27t2bLdlgGAbvv/9+nn1zOwXE1dUVINdTRwAuXryYa/ubb76ZXbt2FTp+kYpER55K9eF5fYtIHnUtnG2daV+3PaCjT0VERESk6CIjI4mJiaFHjx45Vkfs2rWLxDzqd+SlQ4cOAAQFBeW4d+7cOc6ePZvtWo0aNWjVqhWHDx/m6tWrFs1hfX31yz9rY4iUNyUtpPrwuF6MM48TRAC6e3UHIDhcSQsRERERKRoPDw8cHR0JCQnh2g2nnVy5coWnnnqq0OP16tWLRo0a8fPPP7NtW/atzK+++mquiYann36aa9euMXHixFy3gZw6dYrTp0+b39eqVQuAsLCwQscnUpq0PUSqj6yVFvkkLXrU78GX+75k+4XtpGekY21lnWdbEREREZHcWFlZ8fjjj/Phhx/SoUMH7r33XmJjY/n1119p3Lgx9evXL9R41tbWfPXVVwwaNIi+ffsybNgwvLy82Lx5M+fPn6dDhw7s378/W59HHnmE4OBg5s6dS1BQEP3796d+/fpcvHiRI0eOsH37dhYuXIiPjw8Affr0wWQy8dJLL3Hw4EHc3Nxwd3fnySefLKmPRaRItNJCqo+sE0QuH4WM3Je9tanTBmdbZ2KSYzhyRdWURURERKRo3nnnHd566y1MJhNffvkl69at46GHHmLt2rXZjiC11J133snatWvp3LkzS5Ys4ZtvvqFhw4Zs2bKF9PR0cx2LLCaTicDAQBYvXkybNm1YtWoVH330EevWrcPBwYEPPviA/v37m9u3bt2aOXPmUKdOHT777DNeffVVPvjgg2J/DiLFZTKMciqnKxVCbGwsbm5uxMTE5PiHrsrJSIe3G0BaIjy5C+o0z7XZUxufYlPYJp7p9AwT2k0o2xhFREREKoGkpCROnTqFr68vDg4O5R1OtRYXF4enpyft2rVj+/bt5R2OVHOW/ttQmO+hWmkh1YeVNXj4Zf5+8WCezcx1LVSMU0REREQqiISEBOLi4rJdS09P5/nnnycxMZEhQ4aUT2AipUw1LaR68WgD4Xsy61q0GZJrkx71ewCw5+IektKScLDR/3ogIiIiIuXr+PHj9OrVi4EDB9KkSRPi4uL4888/OXToEG3atOHpp58u7xBFSoVWWkj1Yj72NO+VFr6uvng4eZCSkULIpZAyCkxEREREJG8NGjRg6NCh7Nmzhy+//JI5c+aQkpLCc889x5YtW3B2di7vEEVKhVZaSPXiUfAJIiaTiR5ePVhxYgXB4cHcUv+WMgpORERERCR3devWZc6cOeUdhkiZq3IrLfbu3ctLL73EwIEDqVu3LiaTCX9//zzbnz59GpPJlOdr+vTpFs8dGBiY71ibNm0qVHuTyUS/fv1yzBMbG8ukSZNo3Lgx9vb2+Pj48PzzzxMfH29xrNWWZ5vMn9GnICXnedVZutdXXQsREREREZHyVuVWWixfvpx33nkHOzs7WrRoQWRkpEX9OnTokGvxmvwSHnkZPHgwHTt2zHE96wzkLB07dmTatGm5jvHjjz9y8OBBBg4cmO16QkICvXv3Zu/evQwYMICHHnqIPXv28MEHH7B582b++OMPVXDOj4sHONWBa5Fw+Qg0uDnXZlnFOA9HHyY6KZpaDrXKMkoRERERERGhCiYthg4dyqBBg2jXrh1RUVF4eXlZ1K9jx46FWlWRnyFDhhAQEGDRnLklN1JSUvj888+xsbFh7Nix2e69//777N27lylTpvDuu++ar0+dOpX33nuP//3vf7z44ovFfYSqzbM1nPoDLh3OM2lRx7EOzWs25/iV4+yI2MEdvneUcZAiIiIiFZ9hGOUdgohUIKXxb0KV2x7Spk0bOnXqhK2tbXmHUmTLly8nKiqKe+65B09PT/N1wzCYOXMmLi4uvPrqq9n6vPrqq7i4uDBz5syyDrfy8bi+ReRi3nUtAHp4ZZ4isi1iW2lHJCIiIlKpWFtbA5CamlrOkYhIRZKWlgaAjU3JrY+ocistiio8PJwvvviCmJgYPD098ff3p2nTpkUaa8+ePURFRZGWloaPjw/9+/endu3aFvfPSjxMmDAh2/Xjx48THh7OwIEDc1QHdnZ2pmfPnqxZs4awsDC8vb2LFHu14NEq8+elvE8QgcwtIvMOzWNb+DYMw8BkMpVBcCIiIiIVn62tLfb29sTExFCjRg39d5KIAJn1F62trc2JzZKgpMV169atY926deb3JpOJkSNH8tVXXxX6+KBPP/0023tHR0emTZvGlClTCux75swZNmzYQMOGDbnjjuxbEo4fPw5A8+bNc+3bvHlz1qxZw/Hjx/NMWiQnJ5OcnGx+HxsbW2BMVY6nZSstbva8GRsrGyISIgiLC6ORa6MyCE5ERESkcqhTpw7nz5/n3LlzuLm5YWtrq+SFSDVlGAYJCQnExsbi5eVVov8WVPukhZOTE6+++ipDhgyhadOmZGRkEBISwssvv8yCBQu4du0aS5cutWgsX19fPvvsMwYOHEjDhg2Jjo5m48aNvPjii0ydOhUnJyeeeuqpfMeYM2cOGRkZBAQE5MhOxcTEAODm5pZrX1dX12ztcvPOO+/w+uuvW/Q8VVZdv8yfCZcgIRKc6+TazMnWiY51O7Lr4i62hW9T0kJERETkBln/7RkZGcn58+fLORoRKW8mkwl3d/c8v68WVYVMWkyePDnbaoCCPPPMM3muPiiIh4cHM2bMyHatX79+9OjRg06dOrFs2TJCQkLo1KlTgWP17t2b3r17m983aNCA0aNH06lTJzp37sz06dN57LHH8tzfk5GRwZw5czCZTDz88MNFep6CvPjii0yaNMn8PjY2tvptJbF3gZo+cOU0XDwITXrn2bRH/R7suriL4IhghvkNK7MQRURERCoDV1dXXF1dSU1NJT09vbzDEZFyZGtrW6LbQrJUyKTF119/TUJCgsXtH3jggSInLfLi5OTE6NGjeeWVVwgKCrIoaZGXNm3a0KtXL9avX8/hw4dp165dru3Wr1/P2bNn6devH76+vjnuZ2Ws8lpJkbXVI7/Mlr29Pfb29oV9hKrHo01m0uLSoXyTFt29uvPZns/YfmE76RnpWFuV/P8RioiIiFR2tra2lboQvohUXBXy9JD4+HgMw7D45e/vXypx1KmTuW2gMAmU4oyVVwHOLFmJmazaFv9UUM0LuYFn68yfF/Mvxtmmdhtq2NYgLiWOQ1H518AQERERERGRklUhkxYVxfbt2wHw8fEp1jjp6ens2rULgMaNG+faJioqihUrVlCrVi3uu+++XNs0b96c+vXrExQUlCP5kZCQQFBQEL6+vtVvu0dReFxPWlw6nG8zaytrunp1BXT0qYiIiIiISFmr9kmLPXv2YBhGjuvLli1j7ty51KxZkzvvvDPbvYiICI4cOZJjm8bu3btzjJOens7UqVMJDQ2lT58+eHl55RrH/PnzSUlJYdSoUXlu3zCZTEyYMIH4+HjeeOONbPfeeOMN4uPjmThxYr7PK9dlnSBy6TBkZOTbtIdXDwCCI4JLOyoRERERERG5gcnI7Rt7JXbkyBHeffddABITE1myZAmenp7Zjg8NDAw0/+7v78+JEyfo0aMHDRs2JD09nZCQELZs2YK9vT1Llixh0KBB2eYICAhg7ty5zJkzh4CAAPN1k8lE+/btad++PQ0aNCA6OprNmzdz7NgxGjZsyObNm2nSpEmucbdr144DBw6wf//+PGteQOaKip49e7Jv3z4GDBhAp06dCAkJYe3atXTp0oXNmzfj6Oho8ecVGxuLm5sbMTEx5grQ1UJ6KrxdH9JT4Om9UCtnDZEsZ2LPcM9P92BjZUPQ8CCcbJ3KLk4REREREZEqpjDfQytkIc7iuHDhAnPnzs127eLFi9mu3Zi0GDVqFEuXLiU4OJjIyEgyMjJo0KABEyZMYPLkyfj5+Vk89+TJkwkODmbdunVER0djZ2dHs2bNeOWVV5g0aRI1a9bMtd+OHTs4cOAAXbt2zTdhAeDs7MzmzZuZPn06S5cu5ffff8fLy4vJkyczbdq0QiUsqjVrW6jTEi7+lVmMM5+kRaMajfBy9iIiIYKQSyH0atCrDAMVERERERGpvqrcSgspnGq70gJg2b9h/2Lo8wr0fj7fptO2TmPZ8WWMaT2G57vk31ZERERERETyVpjvodW+poVUY+ZinPmfIAKZR5+C6lqIiIiIiIiUJSUtpPrKKsZ5seCjTLt5dQPg2JVjRCZGlmZUIiIiIiIicp2SFlJ9Za20iAqFtOR8m9ZyqIVfrcz6Jtsjtpd2ZCIiIiIiIoKSFlKdudYHBzcw0uHy0QKbZx19ui18W2lHJiIiIiIiIihpIdWZyQQe17eIXDpcYPMb61qofq2IiIiIiEjpU9JCqjdPy4txdvLshJ2VHRevXeRU7KlSDkxERERERESUtJDqzaNV5k8LinE62Dhwk8dNAASH6xQRERERERGR0qakhVRv5u0hBSctALrXz9wisi1CdS1ERERERERKm5IWUr1lrbSIPQ+JVwpsnlWMc+eFnaRlpJVmZCIiIiIiItWekhZSvTm6g2vDzN8tKMbpV8sPN3s3ElITOBB5oHRjExERERERqeaUtBDJKsZ5seBinNZW1nSt1xXQFhEREREREZHSpqSFiEfWCSKW1bXoUT9zi4iKcYqIiIiIiJQuJS1EPLOKcRa8PQSgu1dmMc79l/eTkJpQWlGJiIiIiIhUe0paiGSttLh4CAyjwObeNbxp6NKQNCONXRd2lXJwIiIiIiIi1ZeSFiJ1WoCVDSTHZJ4iYoGso0+DI7RFREREREREpLQoaSFiYwe1m2X+ftHCuhbXjz7dFq5inCIiIiIiIqVFSQsRuKEYZ8EniAB0rdcVEyZOxJzg0rVLpRiYiIiIiIhI9aWkhQjccOypZSst3B3caV07s4+2iIiIiIiIiJQOJS1EADyyThCxLGkBf58ioqNPRURERERESoeSFiLw90qLy0chPdWiLj3qZ9a1CI4IxrDg1BEREREREREpHCUtRADcGoGdC2SkQlSoRV06enTE3tqey4mXOXH1RCkHKCIiIiIiUv0oaSECYGUFHq0yf7dwi4i9tT03e94MwLYInSIiIiIiIiJS0pS0EMniUbhinHBDXQsV4xQRERERESlxSlqIZDEfe2p50iKrrsXOCztJtbAWhoiIiIiIiFhGSQuRLOZjTw9a3KVFzRbUcqhFYloi+yP3l1JgIiIiIiIi1ZOSFiJZso49vXoGkuMs6mJlsqJbvW4AbAtXXQsREREREZGSpKSFSBbn2uDimfn7pSMWd+teX3UtRERERERESoOSFiI3Mte1sHyLSA+vzLoWByIPEJdi2QoNERERERERKZiSFiI38ry+RaQQJ4h4uXjR2LUx6UY6Oy/sLKXAREREREREqh8lLURuVIQTRODvo09V10JERERERKTkKGkhciPPG5IWhmFxt6wtIqprISIiIiIiUnKUtBC5UV0/wATXoiD+ksXdunh1wcpkxenY01xIuFB68YmIiIiIiFQjSlqI3MjWEWo1yfy9EMU4Xe1caVu7LaAtIiIiIiIiIiVFSQuRf8raIlKIYpzw99Gn2yKUtBARERERESkJSlqI/JPH9RNEiliMc3vEdjKMjJKOSkREREREpNpR0kLkn8wrLSzfHgLQsW5HHG0ciU6K5viV46UQmIiIiIiISPWipIVUCpHxyXzzxwkuxSaV/mRZKy0uH4GMdIu72VrbcrPnzYBOERERERERESkJSlpIpfD4dyG8/csRfgw5V/qT1fIFG0dIS4IrpwvVNevo09/Dfi+FwERERERERKoXJS2kUnigU0MAluwMwzCM0p3Myhrqtsz8vZBbRAb4DMDaZM3ui7s5Gn20FIITERERERGpPpS0kErh7vZeONtZczrqGttPRZf+hJ5FK8ZZz7ketze+HYD5h+aXdFQiIiIiIiLVio0ljf74449iT+Tj40OjRo2KPY5UT872NgzqWJ9FO8JYvDOM7k1ql+6EHkUrxgkwqvUofjv9G7+c+oX/3Pwf6jjWKeHgREREREREqgeLkhb+/v6YTKZiTTRt2jRee+21Yo0h1duDnb1ZtCOMX/6KYPqgNrg52pbeZB6tMn8WcqUFQIe6HWhftz37L+9n8dHFPNHxiRIOTkREREREpHqwKGkB0Lt3b3r37l3oCQzDYMaMGYXuJ/JPHb3daelZg6MX41i59zyje/iU3mRZ20OiT0JqItg6Fqr76NajeX7z8yw5uoQJ7SZgb21fCkGKiIiIiIhUbRYnLfz9/Yu8UkJJCykJJpOJYV28mbHqEN/vDCvdpIWLJzjWgsTozKNP699UqO79G/XHy9mLiIQIVp9czf3N7y+lQEVERERERKouiwpxduvWjYYNGxZ5kuL2F8ly300NsLO24mB4LAfOx5TeRCbT36stLhZ+i4iNlQ0j/EYAmQU5S/3EExERERERkSrIoqTFtm3bePjhh4s8SXH7i2Sp6WzHgDaeACzeGVa6k2UV4yxCXQuA+1vcj6ONI6FXQ9kWsa0EAxMREREREakedOSpVDrDu2SeQrN873mSUtNLbyLP4iUtXO1cua/ZfYCOPxURERERESkKJS2k0rmlaW0a1nQkLimNXw9ElN5EHkXfHpJlVKtRmDCx5fwWTl49WUKBiYiIiIiIVA8WF+J8//33izTBCy+8UKR+InmxsjLxYGdvPlp3jO93hHHfTaVUL8XDL/Nn/AW4Fg1OtQo9hLerN/7e/vwe9jsLDi/gtR469ldERERERMRSJsPCCoFWVlaYTKZsBQVNJhNAnkUGTSYT6emluHw/F3v37mXJkiXs3r2bkJAQIiMj6d27N5s2bcq1/enTp/H19c1zvGnTpjF9+nSL5g4MDGTcuHF53v/999/x9/e3uD1A37592bBhg/n99OnTef311/Nsf+rUKXx8fCyKFyA2NhY3NzdiYmJwdXW1uF95C7+aSK/3NpJhwO/P+eNbx7l0Jvq4HVw9C2NXge+tRRpi54WdPLzmYRysHVj3wDrcHdxLNkYREREREZFKpDDfQy1eaTFnzpwc15YvX87KlStzvVdeli9fzjvvvIOdnR0tWrQgMjLSon4dOnRgyJAhOa7fmGSw1ODBg+nYsWOO6/9MJnTs2JFp06blOsaPP/7IwYMHGThwYK73x44dm2tywt3dvZDRVk713R3p3aIuvx+9zJJdYUy5w690JvJok5m0uHSoyEmLzp6daVWrFYejD/PDsR+Y2H5iCQcpIiIiIiJSNVmctBg7dmyOa6dPn2blypW53isvQ4cOZdCgQbRr146oqCi8vLws6texY0eLV1QUZMiQIQQEBFg0Z27JjZSUFD7//HNsbGzy/GwDAgKKlFCpSoZ18eb3o5f5cfc5Jt3eAlvrUijR4tkajv0KFw8WeQiTycTo1qN5actLLDqyiIA2Adha25ZgkCIiIiIiIlVTlSvE2aZNGzp16oStbeX9Urh8+XKioqK455578PT0LO9wKqy+fp7UcbHjclwyvx+5VDqTFPPY0yx3+NxBXce6XE68zJoza0ogMBERERERkarP4pUWVV14eDhffPEFMTExeHp64u/vT9OmTYs01p49e4iKiiItLQ0fHx/69+9P7dq1Le4/c+ZMACZMmJBnmz/++IPt27djZWVF8+bN6d+/Py4uLkWKt7Kys7HiX50a8vUfJ1myK4wBbeqV/CSe108QuXQYMjLAqmh5PltrW4b7DeezPZ8x/9B87va921wTRkRERERERHKnpMV169atY926deb3JpOJkSNH8tVXX+HsXLgij59++mm2946OjkybNo0pU6YU2PfMmTNs2LCBhg0bcscdd+TZ7p+1MNzd3fnkk08YM2ZMvuMnJyeTnJxsfh8bG1tgTBXZ0M7efP3HSTYeucSFmCTquTmU7AS1m4GVLaTEQ0wY1Gxc5KGGthjKN/u/4VDUIUIuhXCz580lGKiIiIiIiEjVU+W2hxSWk5MTr776Krt37+bq1atER0ezfv16unbtyoIFCwpMAtzI19eXzz77jGPHjnHt2jXOnTvHvHnzqFWrFlOnTuWzzz4rcIw5c+aQkZFBQEAA1tbWOe536NCB2bNnc/LkSRITEzl16hSfffYZJpOJgIAAVq5cme/477zzDm5ubuaXt7e3xc9XETXzcKGLT00yDFgacq7kJ7C2hbotM38v5haRmg41ubfpvQDMPzS/uJGJiIiIiIhUeRYfeZqb119/nRkzZpT4saaTJ0/OthqgIM888wzNmzfPcf3ChQt4eXnle+RpXq5du0anTp04evQou3fvplOnToXqf6ODBw/SuXNnnJycuHjxIjY2uS9wycjIwNfXl7CwME6cOJHvUaz/tGHDBm6//Xbatm3L/v3782yX20oLb2/vSnfk6Y1+3H2O537YR6NaTmx6zh8rqxLedrF0Ivy1BPq+Crc9V6yhTlw9wZAVQzBhYvX9q/GuUbmTRiIiIiIiIoVVKkeePv744zmu7dq1K897kLnF4osvvrB0CrOvv/6ahIQEi9s/8MADuSYtisPJyYnRo0fzyiuvEBQUVKykRZs2bejVqxfr16/n8OHDtGvXLtd269ev5+zZs/Tr169QCQuAfv360bRpU/766y9iY2Pz/IO3t7fH3t6+0M9Qkd3Vrh7TVx7kbPQ1gk9FcUvTOiU7gWdr+Itir7QAaOrelJ71exIUHsTCwwuZ0rXgLUMiIiIiIiLVlcVJi6+++qrQ94qatIiPjy90n9JQp07ml9/CJFCKM5YlBTgLmiM0NJRr165V2lUTReFkZ8OgjvVZuP0si3eGlXzSIusEkYvFT1oAjG49mqDwIJYdX8bjHR+nhl2NEhlXRERERESkqrE4afH777+XZhwV0vbt2wHw8fEp1jjp6enmVSmNG+deyDEqKooVK1ZQq1Yt7rvvvkLPkZCQwMGDB3F2djYnSKqT4V28Wbj9LL8euMCMa6m4OZXgkbdZSYuo45CWAjZ2xRrulvq30NStKSdiTrDs+DLGthlbAkGKiIiIiIhUPRYnLXr37l2acZSbPXv20LFjxxzHTy5btoy5c+dSs2ZN7rzzzmz3IiIiiImJwcvLCzc3N/P13bt3c/PN2U+ESE9PZ+rUqYSGhtKnTx+8vLxyjWP+/PmkpKQwatSoPLdvxMXFERERQYsWLbJdT0xMZOLEicTFxTFu3Lg8a2ZUZe0auOFXrwZHLsSxfO95xt7iU3KDuzUEezdIjoHIY1CvbbGGM5lMjGo9ite3vc7CwwsZ2WokNlbV789MRERERESkIFXum9KRI0d49913gcwv81nXAgICzG0CAwPNvz/77LOcOHGCHj160LBhQ9LT0wkJCWHLli3Y29sTGBiYLTEB8OKLLzJ37lzmzJmTbdzOnTvTvn172rdvT4MGDYiOjmbz5s0cO3aMhg0bmrd/5GbWrFlA/ltDoqKi8PPzo0uXLrRq1Yp69epx8eJF1q9fz7lz52jXrh3//e9/Lf2oqhSTycTwLt5M//kQi3acZUyPxjkSUcUYHDxaQVhwZl2LYiYtAO5pcg+fhnxKeEI4G89uZIDPgBIIVEREREREpGqxKGmRkpKCjY0NVlZFOyG1uP0L48KFC8ydOzfbtYsXL2a7dmPSYtSoUSxdupTg4GAiIyPJyMigQYMGTJgwgcmTJ+Pn52fx3JMnTyY4OJh169YRHR2NnZ0dzZo145VXXmHSpEnUrFkz1347duzgwIEDdO3aNc8inQC1atXi8ccfZ8eOHfzyyy9cuXIFR0dHWrVqxdNPP82TTz6Jo6OjxfFWNUNuasDbvx7hyIU4/jofQ/uG7iU3uGfrzKTFxYMlMpyDjQNDWw7lm/3fMP/QfCUtREREREREcmHRkafW1tZMnz6dV199tUiTFLe/lJ7CHDVTGTzz/R5W7A1nZLdGvHVf3gmgQtvxLfzyHDQfCCOXlMiQl69dZsDSAaRlpLHwroW0q1uC8YqIiIiIiFRQhfkeatHSB8MwsCC3UWr9RSw1rLM3ACv3hnMtJa3kBvZsk/mzBI49zVLXqS53+d4FwPxD80tsXBERERERkarC4poWgYGBbNq0qUiTlFhtAZECdG9Sm0a1nDgbfY1f/rrAAzc3LJmBPVpl/owJg6QYcHDLv72FRrcezcoTK1l7Zi2TEiZRz7leiYwrIiIiIiJSFVictDh9+jSnT58uxVBEis/KysSwLt78d81RluwMK7mkhWNNcG0Asefh0mFo1L1EhvWr5UeXel3YeWEni44s4tmbny2RcUVERERERKoCi7aHZGRkFPv12muvlfaziADwr04NsTLBjtPRnLgcX3IDZ622KKFinFlGtxoNwI/HfuRa6rUSHVtERERERKQyK/3jPETKWD03B/q09ABgyc6wkhvYo3XmzxKsawHQ27s3jWo0IjYllpUnVpbo2CIiIiIiIpWZkhZSJQ3rklmQc2nIOVLTM0pm0KxinBdLNmlhZbJiZKuRACw4vIAMo4TiFRERERERqeSUtJAqqY+fB3Vc7ImMT2HD4UslM6h5pcVBKOHTcIY0G0INuxqciT3Dn+f+LNGxRUREREREKislLaRKsrW2MhfhXLzzbMkMWrclmKwzTw+JiyiZMa9zsnXigeYPADr+VEREREREJIuSFlJlZW0R2XzsMhExicUf0MYeajfL/L2Et4gAPOT3ENYma7Zf2M7R6KMlPr6IiIiIiEhlo6SFVFm+dZzp6luLDAN+3HWuZAb1vGGLSAnzcvGif+P+gFZbiIiIiIiIgJIWUsUNv77aYvGuMDIySqAOhUfpFOPMMrp15vGnv5z6hcjEyFKZQ0REREREpLIoUtJi8eLFpKamlnQsIiXuzrZe1HCw4dyVRLadjCr+gB6tMn+WwkoLgA51O9C+bntSM1JZfHRxqcwhIiIiIiJSWRQpafHQQw/RoEEDnnvuOY4cOVLSMYmUGEc7awZ3rA/A9zvDij9g1vaQy8cgPa344+Uia7XFkqNLSE5PLpU5REREREREKoMiJS1eeeUVHBwc+Oijj2jTpg233XYb8+fPJykpqaTjEym24V0aAbDmwAWuJKQUbzB3H7B1hvRkiD5R/OBy0b9Rf7ycvYhOimb1ydWlMoeIiIiIiEhlUKSkxYwZMzh9+jQ///wzgwYNIjg4mICAALy8vHjqqafYt29fSccpUmRtG7jRpr4rKekZ/LTnfPEGs7ICD7/M3y+WzhYRGysbRviNADILchpGCdTiEBERERERqYSKXIjTysqKu+++m59++olz587x9ttvU7duXb744gs6depE165dmTlzJvHx8SUZr0iRmAty7gwrfhLAI+sEkdIpxglwf4v7cbRxJPRqKNsitpXaPCIiIiIiIhVZiZwe4uHhwZQpUzh27Bhr1qzBy8uL3bt388gjj1C/fn0ef/xxzpw5UxJTiRTJoI4NsLex4ujFOPadiyneYJ7XTxC5dLj4geXB1c6V+5rdB+j4UxERERERqb5K7MjTQ4cO8eyzzzJixAjCw8NxcnJi5MiR+Pj48NVXX9G6dWt+/fXXkppOpFDcHG25q50XAIt3ni3eYFkrLUppe0iWUa1GYcLElvNbOBlzslTnEhERERERqYiKlbRITExkzpw53HLLLbRr145PPvmEBg0a8MUXXxAeHs68efPYv38/q1evxsXFhSlTppRU3CKFNuz6FpGVe8NJSC7GyR9ZKy2unIaUhOIHlgdvV2/8vf0B+O7Qd6U2j4iIiIiISEVVpKTFrl27ePTRR/Hy8mLChAns27ePMWPGsG3bNvbu3ctjjz1GjRo1zO3vvPNOxo8fr+NRpVx1862FT20nElLSWf1XRNEHcq4Dzh6AAZdK9+901vGnK0+s5GrS1VKdS0REREREpKIpUtKia9eufPPNNzRs2JCPP/6Y8PBw5syZQ7du3fLs06hRIxo0aFDkQEWKy2Qy8eANBTmLxaNV5s9LpbtFpLNnZ1rVakVSehI/Hv+xVOcSERERERGpaIqUtBg5ciR//PEHBw4c4KmnnsLNza3APo8++iinTp0qynQiJeaBTg2xtjKx+8wVQi/FFX2grC0iF0vvBBHITLRkrbZYdHgRqemppTqfiIiIiIhIRVKkpMX8+fPp1atXScciUuo8XB3o09IDKOZqC/Oxp6W70gLgDp87qONYh0uJl1hzZk2pzyciIiIiIlJRlNjpISKVxfDrW0SWhpwnJS2jaIN4Zp0gUrorLQBsrW0Z3nI4kHn8qWEYpT6niIiIiIhIRWBTlE5NmjQpsI2VlRWurq60bNmS++67jwcffLAoU4mUOP+WdfGoYc+luGQ2HL7IndePQi2Uuq0AE1yLhPjL4FK3xOO80YMtH+Tbv77lUNQhQi6FcLPnzaU6n4iIiIiISEVQpJUWGRkZpKSkcPr0aU6fPs25c+dISkri3Llz5mtJSUmEhoayePFiHnroIQYMGEBKSkpJxy9SaDbWVjxwc0MAvi/qFhE7J6jlm/l7GWwRqelQk3ua3ANkrrYQERERERGpDoqUtNi7dy9eXl707duXrVu3kpycTHh4OMnJyWzdupV+/fpRv359zp49y7Fjx7jrrrvYsGEDH374YUnHL1IkD3bO3CLyx/HLnL+aWLRBPMpuiwj8ffzpxrMbCYsr5uknIiIiIiIilUCRkhZTpkwhOTmZtWvX0r17d0wmE5B50kH37t357bffSEpKYurUqTRr1owffviBxo0b8/3335do8CJF5VPHmR5NamMY8OOuc0UbJOsEkTJYaQHQ1L0pPev3xMBg4eGFZTKniIiIiIhIeSpS0mLFihXcddddWFnl3t3a2pq77rqLFStWAODg4EDfvn0JDQ0teqQiJWzY9YKcS3aFkZ5RhOKWZbzSAv5ebbHs+DLiUopxZKuIiIiIiEglUKSkRWxsLLGxsfm2iYmJISYmxvy+Tp06RZlKpNTc0bYerg42nL+aSFBoZOEHyEpaXD4CGUU8haSQbql/C03dmnIt7RrLji8rkzlFRERERETKS5GSFq1bt2bRokWcPHky1/snT57k+++/p3Xr1uZrZ8+epW7d0j1hQaQwHGytue+mBgAs3lWEGhG1moC1PaRegyunSji63JlMJka1HgXAwsMLSctIK5N5RUREREREykORkhYvvfQSMTExdOzYkUmTJrF06VL+/PNPli5dyqRJk7jpppuIjY3lpZdeAiAlJYW1a9dyyy23lGjwIsX14PUtImsPXiA6oZCn21jbQN2Wmb9fKrstIvc0uYea9jUJTwjn97Dfy2xeERERERGRslakpMX999/PzJkzAfj444958MEH8ff358EHH+Tjjz/GMAy+/vpr7r//fgCuXbvGrFmzmDFjRslFLlIC2tR3o10DN1LTDZaFFKEgZ1YxzjKsa+Fg48DQlkMBHX8qIiIiIiJVm01ROz788MP861//YsWKFezbt4/Y2FhcXV3p0KEDgwcPxs3NzdzW3d2dwYMHl0jAIiVtWBdv/jofw+KdYYzv5Ws+DcciWXUtynClBcDwlsOZfWA2ey7t4UDkAdrWaVum84uIiIiIiJSFIiUtZsyYga+vL6NHj2bMmDElHZNImRrUsT5vrj7E8Uvx7Am7SqdGNS3v7Fk+SYu6TnW5y/cuVp5YybxD83j/tvfLdH4REREREZGyUKTtIW+++SZ//fVXScciUi5cHWy5q50XAIt3FLIgp8f17SFRJyA1qYQjy1/W8afrTq/jQsKFMp1bRERERESkLBQpadGoUSOuXr1awqGIlJ/hXRoB8PP+cOKTC3EiR4164FgTjHSIPFpK0eXOr5YfXep1Ic1IY9GRRWU6t4iIiIiISFkoUtJi+PDh/Pbbb8TExJR0PCLlootPTZrUceZaSjqr94db3tFk+ruuRRkW48wyulXmaosfj/3ItdRrZT6/iIiIiIhIaSpS0uLVV1+lffv29O3bl9WrV3Pp0qWSjkukTJlMJvPxp9/vLOwWkay6FgdLOKqC9fbujXcNb2JTYll5YmWZzy8iIiIiIlKaipS0cHJy4tdff2XPnj0MGjQILy8vrK2tc7xsbIp8OIlImbu/UwNsrEzsOXuVYxfjLO/oWX4rLaxMVoxsNRKABYcXkGFklHkMIiIiIiIipaVIWYVbb721cMdCilQCHjUc6NfKgzUHL7J4Zxiv3tPawo7Xi3GW8QkiWe5rdh9f7PmCM7Fn+PPcn/T27l0ucYiIiIiIiJS0IiUtNm3aVMJhiFQMw7p4s+bgRZaFnOOFO1pib2NdcCePVpk/4yLgWjQ41SrdIP/BydaJf7X4F4EHA5l/aL6SFiIiIiIiUmUUaXuISFV1W/O61HN14Mq1VNYdumhZJwdXcMs8fYRLh0svuHyM8BuBtcma7Re2czS6bE8xERERERERKS3FSlqkpKTwyy+/8NFHH/HGG2+YryclJXHp0iUyMrS/XioXG2srhnZuCMDiwhTkzKprUU5bRLxcvOjfuD8A8w/NL5cYRERERERESlqRkxYrV66kUaNG3HvvvTz33HNMnz7dfG///v14eXnx/fffl0SMImVq6M2Zp4hsCY0kLNrCY0TNx56W/QkiWUa3zjz+9JdTvxCZGFlucYiIiIiIiJSUIiUtgoKCeOCBB7C3t+eTTz5hxIgR2e537dqVZs2asXTp0hIJUqQsNartRM9mtTEM+GH3Ocs6eZZvMU6ADnU70L5ue1IzUllydEm5xSEiIiIiIlJSipS0eOONN3B3d2f37t08+eSTNG/ePEebzp07s2/fvmIHKFIehnXJrFHx464w0jOMgjtkFeO8dBgMC9qXkqzVFouPLiY5Pbnc4hARERERESkJRUpabN++ncGDB1OnTp0823h7e3PhwoUiByZSnga09sTN0ZbwmCT+PH654A61m4OVDSTHQkwhamGUsP6N+uPl7EV0UjS/nPyl3OIQEREREREpCUVKWiQnJ+Pq6ppvm6tXr2JlpcNJpHJysLXmvpsaABYW5LSxgzotMn+/WH5bRGysbBjhl7lda/7h+RjluOpDRERERESkuIqUVWjSpAk7d+7Mt822bdvw8/MrUlDFsXfvXl566SUGDhxI3bp1MZlM+Pv759n+9OnTmEymPF83FhgtSGBgYL5jbdq0KUcfwzBYtmwZffr0wcvLCycnJ1q2bMkjjzzCyZMnc50nNjaWSZMm0bhxY+zt7fHx8eH5558nPj7e4lilYMO6ZBbkXH/4IpHxFmy1yCrGean8inEC3N/ifhxtHDl+5TjBEcHlGouIiIiIiEhx2BSl07/+9S/efPNN5syZw7hx43Lc/+CDDzhw4ADvv/9+sQMsrOXLl/POO+9gZ2dHixYtiIy07BSFDh06MGTIkBzX80t45GXw4MF07Ngxx3UfH58c15577jk++ugjvLy8GDJkCK6uruzbt49vv/2WRYsWsXXrVtq2bWtun5CQQO/evdm7dy8DBgzgoYceYs+ePXzwwQds3ryZP/74AwcHh0LHLDm18nKlg7c7+8Ku8lPIeSbe1iT/Dp6t4QCZdS3KkaudK/c1u4+FRxYy/9B8etTvUa7xiIiIiIiIFFWRkhbPP/88S5cuZcKECSxcuJDk5Mz/FfqFF15g27ZtbN26lY4dO/Lkk0+WaLCWGDp0KIMGDaJdu3ZERUXh5eVlUb+OHTsWalVFfoYMGUJAQECB7S5cuMDHH39M48aN2bdvH25ubuZ7//vf/5g0aRIfffQRs2fPNl9///332bt3L1OmTOHdd981X586dSrvvfce//vf/3jxxRdL5DkEhnX2Zl/YVb7feZYJt/piMpnybuxx/QSRctwekmVUq1EsOrKIP8//ycmYkzRxKyDhIiIiIiIiUgEVaXuIi4sLf/75J8OHD2fTpk1s2bIFwzD44IMP2Lp1Kw8++CDr16/H3t6+pOMtUJs2bejUqRO2trZlPndhnT59moyMDHr27JktYQFwzz33AHD58t9FIA3DYObMmbi4uPDqq69ma//qq6/i4uLCzJkzSz/wauTeDl442lpz4nICIWev5N/Y8/r2kMhjkJ5a+sHlw9vVG39vfwC+O/RducYiIiIiIiJSVEVaaQFQs2ZNvvvuOz799FN27txJdHQ0rq6udOnSBU9Pz5KMsUyEh4fzxRdfEBMTg6enJ/7+/jRt2rRIY+3Zs4eoqCjS0tLw8fGhf//+1K5dO0e75s2bY2dnR1BQELGxsdmKm65atQqAfv36ma8dP36c8PBwBg4ciLOzc7axnJ2d6dmzJ2vWrCEsLAxvb+8ixS7Z1XCw5Z72Xvyw+xzf7wjj5sa18m7s5g12NSAlDiKP/53EKCejW4/m97DfWXliJU/d9BTuDu7lGo+IiIiIiEhhFTlpkaV27drccccdJRFLuVq3bh3r1q0zvzeZTIwcOZKvvvoqR4KgIJ9++mm2946OjkybNo0pU6Zku167dm3effddJk+ejJ+fH4MHDzbXtNi4cSOPP/54ti02x48fBzKTHblp3rw5a9as4fjx43kmLZKTk83beSCzqKfkb1gXb37YfY5V+yN47d7W1HDIYxWPyQQereDcDrh0qNyTFp09O+NXy48j0Uf48fiPTGg3oVzjERERERERKaxqfyapk5MTr776Krt37+bq1atER0ezfv16unbtyoIFCxgzZozFY/n6+vLZZ59x7Ngxrl27xrlz55g3bx61atVi6tSpfPbZZzn6PPvss3z//ffEx8fz1Vdf8f7777NmzRq6devGiBEjsLH5O68UExMDkGMrSZaslRpZ7XLzzjvv4ObmZn5pRUbBbm5ck6Z1nUlMTefnfRH5N85KVFws3xNEIDPxNrr1aAAWHV5EajlvWRERERERESmsIq+0OHToEJ9//jk7d+7k6tWrpKen52hjMpk4ceJEoceePHlyttUABXnmmWfyXH1QEA8PD2bMmJHtWr9+/ejRowedOnVi2bJlhISE0KlTpwLH6t27N7179za/b9CgAaNHj6ZTp0507tyZ6dOn89hjj2VLRMyYMYM333yTGTNmMGrUKNzd3dm7dy/PPvss/v7+LF26lEGDBhXp2XLz4osvMmnSJPP72NhYJS4KYDKZGN6lEW/9cpjFu8IY0a1R3o2zinGG7ymb4Apwp8+d/G/3/7iUeIk1Z9ZwT5N7yjskERERERERixUpabF582buuOMOkpOTsbGxwdPTM9sX8SyGYRQpqK+//pqEhASL2z/wwANFTlrkxcnJidGjR/PKK68QFBRkUdIiL23atKFXr16sX7+ew4cP065dOwDWr1/PtGnTePbZZ5k6daq5fa9evfj5559p0qQJkydPNictslZY5LWSImurR14rMQDs7e3LpUBqZXdfpwa899sR9oVd5XBELK28XHNv2LRv5s+TmyD6JNQq31M7bK1tGd5yOJ/v/Zz5h+Zzt+/d+Z+AIiIiIiIiUoEUaXvI1KlTSUtLY+bMmSQmJhIWFsapU6dyfRVFfHw8hmFY/PL39y/SPAWpU6cOQKESKIUZ69dffwWgT58+OdrXq1cPPz8/QkNDiY+PB/6uZZFV2+KfCqp5IUVXx8We21tnFphdvDMsn4bNoFl/wIAd35ZNcAV4sOWD2FvbcyjqECGXQso7HBEREREREYsVKWmxb98+hg8fzsMPP4y1tXVJx1RhbN++HQAfH59ijZOens6uXbsAaNy4sfl6SkoKkP1Y0xtdvnwZKysr8/GtzZs3p379+gQFBeVIpCQkJBAUFISvr6+2e5SSYV0yP9fle8+TlJpzO5RZt8cyf+5ZAMlxZRBZ/mo61DRvC1lwaEE5RyMiIiIiImK5IiUtnJ2d8fDwKOlYysWePXty3caybNky5s6dS82aNbnzzjuz3YuIiODIkSM5tmns3r07xzjp6elMnTqV0NBQ+vTpg5eXl/lez549Afjoo49yjPXVV19x7tw5evToYd7OYTKZmDBhAvHx8bzxxhvZ2r/xxhvEx8czceLEQjy9FMatzetS382Bq9dSWXvoYt4Nm/aF2s0hORb2Liy7APORVZBzY9hGzsWdK+doRERERERELGMyilB4YuzYsRw+fJgdO3aURkzFcuTIEd59910AEhMTWbJkCZ6entmOZQ0MDDT/7u/vz4kTJ+jRowcNGzYkPT2dkJAQtmzZgr29PUuWLMlRCDMgIIC5c+cyZ84cAgICzNdNJhPt27enffv2NGjQgOjoaDZv3syxY8do2LAhmzdvpkmTv2scpKen07dvX/744w88PDwYNGgQ7u7uhISEsHHjRhwdHdm0aRNdu3Y190lISKBnz57s27ePAQMG0KlTJ0JCQli7di1dunRh8+bNODo6Wvx5xcbG4ubmRkxMjPn0EcnbR+uO8emG4/RsVpvvJnTPu+GOb+GX56BWU3hyF1iV/0E9j657lKDwIEa1GsWUrlMK7iAiIiIiIlIKCvM9tEhJi0uXLtGrVy/uuOMO3n33XZycnIocbEnbtGlTrjUibnTjI8+cOZOlS5dy8OBBIiMjycjIoEGDBvTt25fJkyfj5+eXo39eSYvnnnuO4OBgQkNDiY6Oxs7OjmbNmnHvvfcyadIkatasmWOs5ORk/ve//7FkyRKOHj1KSkoKnp6e9OnTh5deeolWrVrl6BMTE8P06dNZunQpFy5cwMvLi6FDhzJt2jRq1KhRiE9LSYvCCou+xm3//R3DgD9f6IN3rTz+7ifHw0etITkGRiyBFgPLNtBcBJ0P4tH1j+Js68z6B9bjYudS3iGJiIiIiEg1VOpJi759+3L16lX27duHs7MzLVq0yHUik8nEhg0bCju8lCElLQpv9Kzt/Hk8kqf6NmPygJZ5N1zzMmz7HJr0gTHLyyy+vBiGwX0r7uNEzAme7/w8Y9qMKe+QRERERESkGir1pIWVhUvdTSYT6en5FCyUcqekReGt2h/Okwv3UM/VgaCpfbG2yuMI0Sun4dObwMiAx7eDR85VO2Xtx2M/8vq212ng0oDV963G2qrqFtIVEREREZGKqTDfQ4u00T4jI8OilxIWUhXd3tqTmk62XIhN4o9juZ/8AkBNH2h5V+bv278qk9gKck+Te6hpX5Pz8efZGLaxvMMRERERERHJV/lXBxSpZOxtrLm/U0MAvt95Nv/G3R7N/Lnve7gWXcqRFczBxoGhLYcCMP/Q/HKORkREREREJH+llrRISUkhNja2tIYXKVfDungDsOHwJS7HJefd0KcXeLaFtEQImVdG0eVveMvh2FjZsOfSHg5EHijvcERERERERPJkcdKiSZMmfPrpp9murVmzhkmTJuXa/p133sn1tAyRqqCFZw1uauROWobBspBzeTc0mf5ebbHjW0hPK5sA81HXqS53+WZuW5l3qGIkUkRERERERHJjcdLi9OnTXL16Ndu14OBgPvnkk5KOSaRSGH59tcXinWHkW8+23VBwqg2x5+Do6jKKLn+jW48GYM3pNYRcDCnnaERERERERHKnmhYiRXR3+/o42VlzMjKBnaev5N3Q1gFuHpf5e3DFKMjpV8uPQU0HkWFkMPXPqcSmaCuXiIiIiIhUPEpaiBSRi70N97avD2SutshXlwlgZQNnt0LEvjKIrmAvdXuJhi4NiUiI4I1tb+S/WkRERERERKQcKGkhUgzDumZuEVn9VzixSal5N3T1gtZDMn+vIKstnG2dee+297A2WfPb6d9YeWJleYckIiIiIiKSjZIWIsVwk7c7zT1cSErNYOXe8Pwbd38s8+eBHyH+UukHZ4H2ddvzRMcnAHh7+9ucjS3gCFcREREREZEypKSFSDGYTCbz8acFbhFp2BkadIb0FNg1pwyis8zDbR+ms2dnrqVdY8ofU0jNyGfFiIiIiIiISBkyGRZuZLeysqJZs2Y0a9bMfC00NJQTJ04wcODAHO2z7qWnp5dctFLiYmNjcXNzIyYmBldX1/IOp1KKTkih29vrSU03WP10L9rUd8u78V8/wtLx4OIJ/zkANnZlF2g+LiRc4P6V9xOXEsfEdhN5utPT5R2SiIiIiIhUUYX5HlqopEVhmUwmJS0qOCUtSsYT34Ww+q8IxvZozOuD2+bdMD0VPm4HcRFw3zfQYVjZBVmAtafXMnnzZEyYmDVwFl3qdSnvkEREREREpAoqzPdQG0sHPXXqVLEDE6mqhnXxZvVfEfy05zwv3tUKB1vr3Bta20KX8bDxTdj+f9D+QTCZyjbYPAzwGcD94fez7PgyXvzzRZYOWoqbfT6rRkREREREREqZxUmLxo0bl2YcIpVar2Z1aODuyPmriaw5eIHBHRvk3fjmcbD5vxC+B8J2QKNuZRdoAaZ0mcLui7s5E3uG17e9zoe9P8RUQZIqIiIiIiJS/agQp0gJsLIyMbRzQwC+31FAQU7nOtB+aObv2/+vlCMrHCdbJ9677T1srGxYd2YdP4X+VN4hiYiIiIhINaakhUgJGdrZG5MJtp38//buO76pcv8D+OdkNuledEIHlCEUCjJUVEBkynKAoiLgvl5coBev4i16FdAriqI/F0JRQEXh4gBENhcUZBSQyiq0QCktdLdpm2ac3x8ZTdq0TbrS8Xm/zCvJc55z8g0xafrpc54nFxdyNbV3HmRe/vSvH4HCjKYvzgU9A3vi6b5PAwAW/bEIaYU8NYyIiIiIiNyDoQVRI4nwU+HWuGAAwDd1LX8a2guIvgUQDcDBZc1QnWtm9JyBQaGDUKYvMy2DauAyqERERERE1PwYWhA1oqkDOwEAvvr9Aq4Wl9feedCTpuvDSUBFadMW5iKJIMGbN78JX6UvTuadxNLkpe4uiYiIiIiI2iGGFkSNaOR1IegT6YsSrR6Lt5ypvXO3MYBfFFCWD/y5tnkKdEGIZwheu+k1AMCKlBX4PfN3N1dERERERETtDUMLokYkkQj41/jrAABrD1/CicuFtXSWAgMfN93e/wkgis1QoWuGdxqOyV1Nk4a+svcV5Jfnu7kiIiIiIiJqTxhaEDWy66MCMKFPOEQR+PfPf0GsLYzo+yAg9wSunQTSdjdfkS54ccCLiPGNwbWya0j8LbH250NERERERNSIGFoQNYG5Y7pDKZPgQFoetqRk1dxR5Qck3G+6vf+TZqnNVSqZCm/f+jbkEjl2XtqJ78585+6SiIiIiIionWBoQdQEIvxUeOLWWADAm5tOolxnqLnzoCdM12d+AfLON0N1ruse0B3P9XsOAPCfg//BuYJz7i2IiIiIiIjaBYYWRE3kyaGdEeKjxKW8MqzYl15zx6A4oMsIACJw4LPmKs9lD173IG4KvwnlhnLM3TMXFYYKd5dERERERERtHEMLoiaiVsgwd3R3AMBHO1NrXwLVsvxp8iqgvKgZqnOdZRnUAI8AnM4/jSVHlri7JCIiIiIiauMYWhA1oUkJEdYlUN/9tZYlUDvfBgTGARXFwNE1zVegi4JUQXj9ptcBAF/99RX2Xt7r5oqIiIiIiKgtY2hB1IRsl0D99lAtS6BKJJVzW/zxKWA0NlOFrhvScQimdp8KAJi3dx5yy3LdXBEREREREbVVDC2ImpjTS6D2mQoofU2TcZ79tXmLdNHs62eji18X5Jbn4tV9r3IZVCIiIiIiahIMLYiagVNLoCq9gH7TTLcPfNx8xdWDh8wDb936FhQSBf53+X/4+tTX7i6JiIiIiIjaIIYWRM2g6hKoWn0NS6AOfBwQJMD5XcDVk81XYD109e+K2f1nAwAWH1qMM/m1zNlBRERERERUDwwtiJrJE0Mql0BdvjfdcSf/KKDbWNPtA580W231dX/3+3FLxC2oMFZg7p65KNfXskIKERERERGRixhaEDUTT6WTS6De8DfT9bFvgdK8ZqqufgRBwL8H/xuBHoFILUjFu4ffdXdJRERERETUhjC0IGpGTi2BGjUYCIkH9GXAkS+bt8B6CFQF4o2b3wAAfH3qa+zJ2OPmioiIiIiIqK1gaEHUjKougZqS6WAJVEEAbnjSdPuPzwGDvhkrrJ+bI27Ggz0eBGBaBjWnLMfNFRERERERUVvA0IKomV0fFYDx5iVQX/+phiVQe90DqIOAogzg1M/NX2Q9PH/98+jm3w352ny8svcVGEWju0siIiIiIqJWjqEFkRu8VNcSqHIPoP9M0+1WMCEnACikCrx161tQSpX4LfM3rPprlbtLIiIiIiKiVo6hBZEbOLUEav9HAIkMuPg7kHm0eQusp85+nfGPAf8AACw5sgSn8k65uSIiIiIiImrNGFoQuYntEqgr9qVX7+ATBvS803S7lYy2AIDJXSdjWMdh0Bl1+Meef6BMX+bukoiIiIiIqJViaEHkJp5KGf4xyrQE6oc7UnGtWFu90yDz8qcn1gElV5uxuvoTBAGv3fQaglXBSCtMwzsH33F3SURERERE1EoxtCByozv7Vi6BuvjX09U7RF4PRA4ADBXAoeXNX2A9+Xv4482b3wQArD2zFtsvbndzRURERERE1BoxtCByI6eWQB1kXv704BeA3sFojBbqxvAbMbOnaTLRxN8Ska3JdnNFRERERETU2jC0IHKzOpdAvW4i4B0OaK4CKf91T5H19HTfp9EjoAcKtYV4ZR+XQSUiIiIiItcwtCBqAWpdAlUqBwY8Yrq9/2OgaqjRgsmlcrx161tQyVQ4cOUAVqasdHdJRERERETUijC0IGoB6lwC9fqZgMwDuHIUuHSg+QtsgBjfGMwdMBcA8MGRD5CSm+LmioiIiIiIqLVgaEHUQtS6BKpnIBA/2XR7/8fNXltD3RV3F0ZEjYBe1GPunrko1ZW6uyQiIiIiImoFGFoQtRB1LoF6g3n505M/AYUZzVxdwwiCgMQbExGiDsGFogt46+Bb7i6JiIiIiIhaAYYWRC1IrUughvQEom8BRAPwx+fuKbABfJW+WHjLQggQsP7sevya/qu7SyIiIiIiohaOoQVRC1LnEqiW0RaHk4CK1neKxYDQAXgk3jSp6Pzf5yNLk1XHHkRERERE1J61udDi6NGjePnllzFq1CgEBwdDEAQMHTq0xv7p6ekQBKHGy/z5851+7KSkpFqPtWvXrmr7iKKI9evXY9iwYQgLC4NarUa3bt3wxBNP4Pz589X6z58/v9bHSE9Pd7peaplqXQK162jALwooLwCOf+u2GhviqYSn0CuwF4orivHP//0TBqOh7p2IiIiIiKhdkrm7gMa2YcMGLFy4EAqFAl27dkVOTo5T+/Xp0weTJk2q1l5b4FGTiRMnIiEhoVp7dHR0tbYXXngB7777LsLCwjBp0iT4+Pjg2LFj+Pzzz/H111/jt99+Q69evartN336dIfH8/Pzc7leannmju6GX1OyrEugju4VZtogkQKDngC2vAwc+BS4fgYgCG6t1VVyiWkZ1Mk/Tcah7ENYfmI5Huv9mLvLIiIiIiKiFqjNhRaTJ0/GhAkTEB8fj9zcXISFhTm1X0JCgkujKmozadIkzJgxo85+WVlZWLJkCaKionDs2DH4+vpat7333nuYPXs23n33XSxfvrzavjNmzKhXoEKtQ6S/Go/fGoulO1Lx5qaTGNa9A5QyqWlj3weBHW8C104C53cBnYe5tdb66OTTCS8Pehnz9s3DR0c/wqCwQegd3NvdZRERERERUQvT5k4P6dmzJ/r16we5XO7uUuqUnp4Oo9GIwYMH2wUWADBu3DgAwLVr19xRGrUAT9a0BKqHL5Bwv+n2gU/cUltjmNB5AkZHj4ZBNGDunrnQ6DTuLomIiIiIiFqYNjfSor4yMzPx0UcfobCwECEhIRg6dCg6d+5cr2MlJycjNzcXer0e0dHRuP322xEYGFitX1xcHBQKBfbt24eioiL4+PhYt/38888AgOHDhzt8jD179uDAgQOQSCSIi4vD7bffDi8vr3rVSy2TZQnUOd8dw4c7UnF3v0gEeytNGwc9ARz8HDizBcg9BwTW7/9VdxIEAa/e+CqOXTuGjJIMLDiwAG/e/Ka7yyIiIiIiohaEoYXZ1q1bsXXrVut9QRDwwAMP4JNPPoGnp6dLx/rggw/s7qtUKiQmJmLu3Ll27YGBgVi0aBHmzJmD7t27Y+LEidY5LXbs2IGnnnoKs2bNcvgYiYmJdvf9/Pzw/vvv46GHHqq1Nq1WC61Wa71fVFTkylOjZnZn3wh8+Xs6jmUUYvGvp7HobvMpFEFxQJcRQOpW4I/PgDFvubfQevJR+GDRLYswc8tM/HjuR9wccTPGxIxxd1lERERERNRCtLnTQ1ylVqvx6quv4vDhwygoKEBeXh62bduGgQMHYtWqVXWGALZiYmKwdOlSnDlzBqWlpcjIyMCXX36JgIAAvPTSS1i6dGm1fZ5//nl88803KCkpwSeffIK3334bW7ZswaBBg3D//fdDJrPPlfr06YPly5fj/PnzKCsrQ1paGpYuXQpBEDBjxgz8+OOPtda4cOFC+Pr6Wi8dO3Z0+vlR86t1CdQbnjRdJ68Gyltv+NQvpB8e7/04AODfv/8bl0suu7kiIiIiIiJqKQTRbj3FlmHOnDl2owHq8uyzzyIuLq5ae1ZWFsLCwjBkyBCHy43WprS0FP369cPp06dx+PBh9OvXz6X9baWkpKB///5Qq9XIzs62CyJef/11vPHGG3j99dfx4IMPws/PD0ePHsXzzz+Po0ePYt26dZgwYUKdj7F9+3aMGDECvXr1wvHjx2vs52ikRceOHVFYWGh3egq1LE9/nYyfjmViUEwAvnn8BgiCAIgi8NFAIOcMMHoRcMPf3F1mvemNesz4ZQaOXTuGvh36Yvmo5ZBJOBCMiIiIiKgtKioqgq+vr1O/h7bI0MLLywsajfOT8u3cudPhShoNCS0A4M0338S8efPwwQcf4Omnn3Z5f1sjRozAtm3bcPz4ccTHxwMAtm3bhhEjRuD555/Hu+++W6322NhYRERE4OzZs049RlxcHFJTU10KIFz5n4XcJyO/FMMX74ZWb8QnD16P0b1CTRsOLgM2zgH8Y4CnD5uWRG2lMoozcM9P90Cj0+CphKfwtz6tN4QhIiIiIqKaufJ7aIs8PaSkpASiKDp9aaqlP4OCggDApQDFlWNt3rwZADBsWPUlK0NDQ9G9e3ekpqaipKTEpccoLS1taLnUwliWQAWABZtOQqs3mDb0mWpaTSQ/DTj7qxsrbLhI70i8esOrAIBPjn2Co1ePurcgIiIiIiJyuxYZWrQUBw4cAABER0c36DgGgwGHDh0CAERFRVnbKyoqANS8rOm1a9cgkUicWr5Vo9EgJSUFnp6e1vCC2hbLEqgX80orl0BVeAL9zPOutOLlTy3uiL0D42LHwSga8dL/XkJxRbG7SyIiIiIiIjdq96FFcnIyHJ0hs379eqxcuRL+/v4YM8Z+NYMrV67g1KlTKCwstGs/fPhwteMYDAa89NJLSE1NxbBhwxAWFmbdNnjwYADAu+++W+1Yn3zyCTIyMnDjjTdCqTQtc1lcXIwzZ85Ue4yysjI89thjKC4uxpQpU6pN3kltg2UJVAD4cEcqrhWb5yYZ+DggSIDzu4CrJ91XYCN5ZdAriPCKwOWSy3hj/xvuLoeIiIiIiNyoRc5p0RCnTp3CokWLAJh+mV+7di1CQkIwevRoa5+kpCTr7aFDh+LcuXO48cYbERkZCYPBgCNHjmDv3r1QKpVYu3ZttYkwZ8yYgZUrV2LFihWYMWOGtV0QBPTu3Ru9e/dGREQE8vLysHv3bpw5cwaRkZHYvXs3YmNjrf0NBgNuu+027NmzBx06dMCECRPg5+eHI0eOYMeOHVCpVNi1axcGDhwIAEhPT0dsbCwGDBiAHj16IDQ0FNnZ2di2bRsyMjIQHx+PnTt3IjAw0Ol/L85p0boYjSIm/d8+HM8oxNSBHbHwLvMSqN8+CJz8Cbh+BjD+fbfW2BiOXTuG6ZunwyAasODmBRjfeby7SyIiIiIiokbS6ifibIhdu3Y5nCPClu1TXrZsGdatW4eUlBTk5OTAaDQiIiICt912G+bMmYPu3btX27+m0OKFF17A/v37kZqairy8PCgUCnTp0gXjx4/H7Nmz4e/vX+1YWq0W7733HtauXYvTp0+joqICISEhGDZsGF5++WX06NHD2reoqAgvv/wy/vjjD6SnpyM/Px8qlQo9evTAPffcg1mzZkGlUrn078XQovU5lJ6Hez75HYIA/Pz0zegZ7guk7wOSxgIyFTD7L0Ad4O4yG+zTY5/iw6MfwlPuie/Gf4eO3lyel4iIiIioLWjXoQW5hqFF61RtCVQA+PQWIOtP4Pb5wM3Pu7nChjMYDXh4y8M4cvUIegf1xorRK6CQKtxdFhERERERNVCrXz2EiGo3d3Q3KGUSHEjLw5aUbEAQgEHmJUL/WAYY9O4tsBFIJVIsumURvOXeOJ5zHE9uexKF2sK6dyQiIiIiojaDoQVRK+RwCdRedwPqIKAoAzj1k5srbBxhXmF4b9h78JR74mDWQTy0+SFcLrns7rKIiIiIiKiZMLQgaqWeHNIZHbxtlkCVewD9HzZt3N/6lz+1GBQ2CCtHr0QHdQecLzyPBzY+gJScFHeXRUREREREzYChBVEr5amUYe7oKkugDngEkMiBS/uBzGQ3V9h4ugV0w5qxa9DNvxtyy3Mxc8tM7L60291lERERERFRE2NoQdSK3dk3Ar0jfVGi1ePdracB71Cg552mjW1otAUAhHiGIGl0EgaHD0aZvgzP7HwG35z6xt1lERERERFRE2JoQdSKSSQC/jXuOgDANwcvISWzELjhSdPGE+uA4mw3Vtf4vBReWDp8Ke6OuxtG0Yg3D7yJxYcWwyga3V0aERERERE1AYYWRK1c/+gAjOsdBlEE/v3zXxDD+wGRAwGjDji03N3lNTq5RI7EGxPxdN+nAQBJKUl4YfcLKNeXu7kyIiIiIiJqbAwtiNqAl8Z0h1Imwf7z5iVQLaMtDn0B6LXuLa4JCIKAx3s/joW3LIRMIsPWC1vx2K+PIb88392lERERERFRI2JoQdQGVFsCNe4OwDsc0FwDTqx3c3VNZ1zsOHw24jN4K7xx9NpRPLjpQVwsuujusoiIiIiIqJEwtCBqI2yXQE3afxkY+Khpw4GPAVF0b3FNaEDoAKwaswoRXhG4WHwRD256EEevHnV3WURERERE1AgYWhC1EZ5KGf5hXgJ16Y5U5HS7H5B5AFeOARf3u7m6phXrF4tVY1ehZ2BP5Gvz8eivj2Lrha3uLouIiIiIiBqIoQVRG3KXzRKoi/deA3pPMW048LF7C2sGQaogLB+1HEMjh0Jr0GLOrjlYmbISYhseZUJERERE1NYxtCBqQ6ougZoa+6Bpw8mfgYJLbqyseajlaiwZtgT3dbsPIkS8c+gdLPxjIQxGg7tLIyIiIiKiemBoQdTG2C6BOu83I8SYWwHRABz83N2lNQupRIqXB72MF/q/AAD4+tTXeG7XcyjVlbq5MiIiIiIichVDC6I2yHYJ1CNh95kaD68EKjTuLayZCIKA6T2nY/GQxVBIFNh1aRce3vIwcspy3F0aERERERG5gKEFURtkuwTqnOQQiH7RQHkBcPxbt9bV3EZGj8QXo76An9IPKbkpeHDTgzhfcN7dZRERERERkZMYWhC1UZYlUNPztfg96C5T44FP2/Typ44kdEjAqrGr0Mm7Ey6XXMaDmx/EwayD7i6LiIiIiIicwNCCqI2yXQJ19tneMMo9gWungPM73VxZ84vyicKqsavQJ7gPiiuK8fjWx7Hx/EZ3l0VERERERHVgaEHUhlmWQM3SKrDfZ5Spcf8n7i3KTfw9/LFs5DKMiBoBvVGPl/73Ej4//jmXRCUiIiIiasEYWhC1YbZLoM67MtjUeHYLkHvOjVW5j4fMA+8MeQfTr5sOAPgg+QO89vtr0Bl1bq6MiIiIiIgcYWhB1MZZlkA9bwzDEeUAU+OBT91blBtJBAleGPACXh70MiSCBOvOrsPT25+GRtc+VlYhIiIiImpNGFoQtQOWJVDfKx5uaji6GigvdG9Rbja1+1S8P+x9qGQq7Mvch+mbpyNbk+3usoiIiIiIyAZDC6J2wLIE6v+M8UgXIoGKEuDoGneX5XZDOw7FilErEOgRiNP5p/HApgdwOu+0u8siIiIiIiIzhhZE7YRpCVQPfF4x0tRw4FPAaHBvUS1Az6CeWH3HasT6xiK7NBvTf5mO3y7/5u6yiIiIiIgIDC2I2g3LEqjrDTejUPQE8tOAs7+6u6wWIcIrAl+O+RL9Q/pDo9Pg79v/jv+e/a+7yyIiIiIiavcYWhC1I3f1jUBcZAi+NgwzNfz2IWA0ureoFsJX6YtPR3yKsTFjoRf1+Ndv/8KHyR9ySVQiIiIiIjdiaEHUjliWQP1SPxI6UQpc2AtsmsPgwkwhVWDRLYvwWPxjAIBPj3+KV/a+Ap2BS6ISEREREbkDQwuidqZ/dAD69Y7HP3SPwwgBOLQc2Pg8gwszQRDwTL9nMP/G+ZAKUvx0/ic8ue1JFFUUubs0IiIiIqJ2h6EFUTv00pju2CwdgtkVf4MREuBwEvDzswwubNzd9W58NPwjqGVq/JH1Bx7a9BAySzLdXRYRERERUbvC0IKoHYr0V2P59AHYKhuC5yuehAES4MiXwE9PM7iwMThiML4c8yU6qDvgXOE5PLDpAaTkpri7LCIiIiKidoOhBVE7dVOXIHzz+I3Yq7oNz1c8ZQouklcBPzK4sNUtoBtWj12Nrv5dkVOWg5m/zMTuS7vdXRYRERERUbvA0IKoHYuP9MV3T96Iwz7D8WzF36GHBDi6CvhxFmA0uLu8FiPUMxQrR6/EjWE3okxfhmd2PoNvT33r7rKIiIiIiNo8hhZE7VxssBfW/e0mnAkegWcrZpmDi9XAD39ncGHDS+GFj27/CHd2uRNG0Yg3DryBxYcWwyhyVAoRERERUVNhaEFECPX1wNonbkRWxzF4uuJp6EUJcOxrYMPfGFzYkEvkeO2m1zArYRYAICklCS/ufhFag9bNlRERERERtU0MLYgIAOCnVmDVI4Og7Toes3TPQCdKgePfAv99AjDo3V1eiyEIAp7o8wQW3LwAMokMv174FY/9+hgKygvcXRoRERERUZvD0IKIrFQKKT6ddj3Ufe7ELN3TpuDiz+8YXDgwvvN4fHr7p/CWeyP5ajIe3PwgLhVdcndZRERERERtCkMLIrIjl0rwzuQ+iLzpXvzdMuLixPcQ1z/G4KKKgWED8dXYrxDuGY4LRRfwwKYHsOPiDoii6O7SiIiIiIjaBIYWRFSNRCJg3h09kDDyQTylexYVohRCynoYv38EMOjcXV6L0tmvM1bfsRrXBV6HfG0+nt35LGZumYkTOSfcXRoRERERUavH0IKIHBIEAU8N7YLhk2biKf1zqBClkJzcAMN3DzO4qCJIFYQVo1bgkV6PQClV4nD2YUzdOBX/2P0PZBRnuLs8IiIiIqJWSxA5jrldKyoqgq+vLwoLC+Hj4+PucqiF+uVEFtZ/uwxLJe9BKeih6zYe8ikrAKnc3aW1OFdKrmBp8lL8fP5niBAhl8hxf/f78Vjvx+Cr9HV3eUREREREbufK76EMLdo5hhbkrN/P5eLLLz/DErwDpaCHtstYKO9bCcgU7i6tRTqZexKLDy/GgSsHAAA+Ch883vtxTO0+FQop/82IiIiIqP1iaEFOY2hBrjhxuRCffvEp3jG8DaWgQ2nsaKjv/4rBRQ1EUcTey3vx7uF3kVqQCgCI8IrAc/2ew6joURAEwc0VEhERERE1P4YW5DSGFuSq9BwNln7+CRaUL4RS0KE4agS8p61hcFELvVGPH1J/wEdHP8K1smsAgPigeMzpPwfXh1zv5uqIiIiIiJoXQwtyGkMLqo+rReVY8ukn+FfJG/AQdMiPHA7/GV8DMqW7S2vRSnWlWPnXSqw4sQJl+jIAwLCOw/D89c8jxjfGzdURERERETUPhhbkNIYWVF+FZTp88NmneDFvPjwEHa6FDUXwI2sZXDghpywHHx39COvProdRNEIqSHFP13vwtz5/Q6Aq0N3lERERERE1KYYW5DSGFtQQ5ToDPvxiGf5+ZR5UQgWudLgFYY99D8g93F1aq3Cu4BzeO/wedmfsBgB4yj3xcK+HMe26aVDJVG6ujoiIiIioaTC0IKcxtKCG0huM+PzLJMxInwuVUIGLATeh09/+y+DCBX9c+QPvHHoHJ/NOAgA6qDvg6b5PY3zseEglUjdXR0RERETUuBhakNMYWlBjEEURq79djbtOzoZa0OK8zyDEzNoAQaF2d2mthlE0YlPaJnxw5ANc0VwBAHT174o518/BTRE3ubk6IiIiIqLGw9CCnMbQghrTjxvW4vbkWVALWpz27I/OT/8ImYenu8tqVbQGLdacXIPPj3+OYl0xAOCm8Jsw+/rZ6BbQzc3VERERERE1nCu/h0qaqaZmc/ToUbz88ssYNWoUgoODIQgChg4dWmP/9PR0CIJQ42X+/PlOP3ZSUlKtx9q1a1e1fYxGIz788EP069cParUaPj4+uPXWW/Hjjz/W+DhFRUWYPXs2oqKioFQqER0djRdffBElJSVO10rUFCZMmoL9N30KjahEN80hnFkyDuWlxe4uq1VRSpWY2WsmNt21CQ/2eBAyiQy/Zf6GyT9Nxqv7XkW2JtvdJRIRERERNRuZuwtobBs2bMDChQuhUCjQtWtX5OTkOLVfnz59MGnSpGrttQUeNZk4cSISEhKqtUdHR9vdF0URU6ZMwbp169C5c2c88sgj0Gq1+OGHHzBx4kQsXboUs2bNsttHo9FgyJAhOHr0KEaOHImpU6ciOTkZ77zzDnbv3o09e/bAw4NzCZD73DbqThz0UOC6HQ/juvIjOL5kHKJm/QhfH193l9aq+Hn4Ye7Aubi/+/1YcmQJfr3wKzakbsAvab9g2nXT8Ej8I/CUcxQLEREREbVtbe70kJSUFGi1WsTHxyM3NxdhYWEYMmSIw1EOgGmkRUxMDKZPn46kpKQGPXZSUhJmzpyJFStWYMaMGXX2//777zF58mQMHjwYW7duhUplWi0gJycH/fv3R1ZWFk6dOmUXdiQmJuL111/H3LlzsWjRImv7Sy+9hLfeegsLFizAP//5T6dr5ukh1FRS9m9B9OaH4CmU46isN8L/tgEdArmcZ30du3YMiw8tRvLVZABAgEcAnurzFO7qehfkErmbqyMiIiIicl67Pj2kZ8+e6NevH+Tylv8l/ocffgAAvPzyy9bAAgCCgoLw/PPPQ6vVYsWKFdZ2URSxbNkyeHl54dVXX7U71quvvgovLy8sW7aseYonqkPPG0bh6sSvUQIVEvTHkfHRBFzMuubuslqtPsF9sHL0Srw39D1E+UQhrzwPbxx4A3f9cBd2XNyBNpY/ExEREREBaIOhRX1lZmbio48+woIFC/DFF1/g3Llz9T5WcnIyFi9ejLfeegvffvstcnNzHfbLysoCAMTExFTbZmnbsWOHte3s2bPIzMzE4MGD4elpPyzc09MTgwcPxvnz53Hp0qV6107UmGL63YaSe9ZCAxX6GU/g2icT8Fd6prvLarUEQcDtUbfjvxP/i38O/Cf8lf5IL0rHszufxcwtM3Ei54S7SyQiIiIialRtbk6L+tq6dSu2bt1qvS8IAh544AF88skn1QKCunzwwQd291UqFRITEzF37ly79qCgIABAWloaevToYbctLS0NAHDmzBlr29mzZwEAcXFxDh83Li4OW7ZswdmzZ9GxY0eHfbRaLbRarfV+UVGRM0+JqN5Ce92KPPn3wNeTcT3+wuEVd+GP+9diYLdO7i6t1ZJL5Li/x/0Y33k8vvjzC6w6uQqHsw9j6sapGBM9Bs/0ewaR3pHuLpOIiIiIqMHa/UgLtVqNV199FYcPH0ZBQQHy8vKwbds2DBw4EKtWrcJDDz3k9LFiYmKwdOlSnDlzBqWlpcjIyMCXX36JgIAAvPTSS1i6dKld/zFjxgAAFi1ahPLycmt7bm4ulixZAgAoKCiwthcWFgIAfH0dT2hoORfI0s+RhQsXwtfX13qpKdwgakwB3W6G+NAGaARPXC+chGTNPdh2NNXdZbV63gpvPHf9c/j5zp8xofMECBCwOX0zJmyYgHcOvoNCbc2fBURERERErUGLnIhzzpw5dqMB6vLss886HH2QlZVV50ScNSktLUW/fv1w+vRpHD58GP369XNpf1spKSno378/1Go1srOzIZOZBrjo9XqMHDkSO3fuRJcuXTB69GjodDps2LABISEhOH78ODw8PFBWVgYAWLNmDR544AG88soreOONN6o9ziuvvIIFCxZg/fr1uPPOOx3W4mikRceOHTkRJzUL7YWDMKycCLVRg0PGrrgweiXuvuk6d5fVZpzMPYnFhxfjwJUDAAAfhQ8e7/04pnafCoVU4ebqiCqJogit3giNVg+N1oASrR6aCr3p2nwBAIVMAoVUarqWSaA0XyukNrdlEihlUmu7XGpaZpyIiIhaLlcm4myRp4d8+umn0Gg0Tve/5557ajxlor7UajWmTZuGefPmYd++fQ0KLXr27Imbb74Z27Ztw8mTJxEfHw8AkMlk2Lx5MxYtWoQ1a9bgs88+g6+vL+6880688MIL6Nq1Kzp06GA9jmWERU0jKSynetQ0EgMAlEollEplvZ8LUUMoowZAP/MnlK6YgP44A+GXh7Cs9As8Mrw3f8loBD0Ce+DzEZ9j7+W9ePfwu0gtSMU7h97B16e+xrP9nsXo6NH8d6Z60xuMpoChwhQq2AYMJVpDjW32YYTBeltvbLq/mVgCDqU5yFBUDTiqtkklUMqr9JVKq7VZjmdqNwUlaoUUQV5KBHgqoJC1+wGsREREja5FhhYlJSXuLgFA5ZwTrgQorh5LqVQiMTERiYmJdu2WkSH9+/e3tlmCGcvcFlXVNecFUUsg63g9pI/+jLIvJuB6nIWw52G8U/Ix5kwYAImEv1A3lCAIuCXyFtwUfhN+OPcDPkz+EJdLLuMfe/6BL1O+xJz+c9A/tH/dB6I2xWgUkVVUjkt5pSgqryV0qHAQOpj7avXGJqlNrZDCUymDl1IGT6UUngrTbUEAtHojtHojKiwXgxFavaHyvrlNZ7APQCzbipuk4pr5quQI9FIgyEuJIC8FAj2VCPJS2reZr03PkZ95REREdWmRoUVLceCAaYh1dHR0g45jMBhw6NAhAEBUVJRT+6xevRoAcN9991nb4uLiEB4ejn379kGj0dhNEKrRaLBv3z7ExMRwngpq8YTwvlA98hPKl49HP30qhCN/w7yy9/HalJsgl/IvlY1BKpHirri7MDp6NFb+tRIrTqzAidwTmLllJoZ1HIYn+zyJHgE9+EtTG2IwisgsKMOF3FKk52qQnqNBem4pLuRqcCGvFBWNFDooZJJqAYNd6KCsbDPdtu9n21etkEHaCGGl0SiaAw2bcENnQIXBaBdwWEMQg22bwS4AsetnbTNUC08s/YrL9cgvrYDBKKKwTIfCMh3OX6v7jx0KmQRBngoEeSsR6KkwhxumQMMSdAR6KhHkrUCAWgEZPxuJiKidavehRXJyMhISEqp9cV+/fj1WrlwJf39/64SZFleuXEFhYSHCwsLsTsU4fPgwrr/+eru+BoMBL730ElJTUzFs2DCEhYXZbS8qKqp2Ds/333+P5cuXY8CAAbjrrrus7YIg4NFHH8Xrr7+Of//731i0aJF127///W+UlJTg5Zdfrt8/BFFzC0+AxyM/Q7t8PPrqUiGcfAbPJS3GO9NuhUohdXd1bYZarsbf+vwNk7tOxv8d/T+sO7sOOy/txM5LOxHrG4uxMWMxNnYsOnoz7GwNdAYjLueXIT1XYw0nLNeX8kqrjTiwJZMIiPBXwU+tqCFIkFYJFUzXloDBSymDWiFrkadASCQCPCRSeMjd89lhNIooKNMht0SLnJIK5JRokVuiRa7GdDunpMK6LbdEC02FKSjJLCxHZmF5nccXBMBfrUCgp8Jm1IY57PCuvA7yNIUdnsp2//WOiIjakBY5EWdDnDp1yvrLfFlZGdauXYuQkBCMHj3a2icpKcl6e+jQoTh37hxuvPFGREZGwmAw4MiRI9i7dy+USiXWrl2LCRMm2D3GjBkzsHLlSqxYsQIzZsywtguCgN69e6N3796IiIhAXl4edu/ejTNnziAyMhK7d+9GbGys3bF69OiBjh07okePHvDw8MAff/yBXbt2ITY2Fjt27Kg2MkOj0WDw4ME4duwYRo4ciX79+uHIkSP49ddfMWDAAOzevRsqlcrpfy9XJkAhahJZf6Ji+TgoKgpwzBiLxSGLsHTmbfBVy91dWZt0vuA8Pj72MXZc3IEKY4W1vXdwb9wRcwdGRY9CoCrQjRVShd6IS/mmERLpOeZr84iJjPyyWueCUEgl6BigQnSgJ6KDPBEdqEZUoCeiAz0R7ufBv9a3EGUVBlOwoalATrEWuRrbsKPCdL/YdJ2nqYCr03+o5FLTSA0vJYLNIzaCvZUI91Mh0t90CfdTuS3kISIicuX30DYXWuzatQvDhg2rtY/tU162bBnWrVuHlJQU5OTkwGg0IiIiArfddhvmzJmD7t27V9u/ptDihRdewP79+5Gamoq8vDwoFAp06dIF48ePx+zZs+Hv71/tWPPnz8f69euRnp4OnU6HmJgY3H333XjxxRdrfPEKCwsxf/58rFu3zrpCyuTJk5GYmAhvb28n/6VMGFpQi5B1AroV4yHX5uG4MQav+S3A/z16G0J8PNxdWZtVXFGM7Re3Y+P5jfgj6w8YRdOpA1JBihvCb8AdMXdgeKfhUMvVbq60bSrXGXApr9QaRqTlVI6YyCwoq/WXVKVMguhAT0QFqhEdZL423w/zVTXK6RbUchiMIvJLK0xhRokW18zBhm3Acc06kkOLcp3zpwEFeyvNIYYaETaBhuU+R70REVFTadehBbmGoQW1GNkp0K8YB1l5Hv40RuNF1ev4+LHbERPkWfe+1CDXSq/hl/RfsPH8RqTkpljbPaQeGNZxGO6IvQM3hd8EuZSjX1xRWqHHhVz7kRKWkRNXispR209ftUJqHiGhtruOCfJEB28lJ62lGmm0elOoodGaR3GYAo2rxVpczi9DRn4ZMvJLoakw1HmsIC8FIvzVpiDDrzLQiPRXIcJfBbWCp6EQEVH9MLQgpzG0oBYl+y8YksZBWpaLFGMUnpbNxwePDEeviJqX8aXGlV6Yjk1pm7Dx/EZcLL5obfdT+mFk1EjcEXsHEjokQCLwNAPANJdBeq4GJ68Um+eXqAwosou0te7rrZQhKsgcRlQZORHspeQkqdRkRFFEQakOlwtMAUaGNcyovF+i1dd5nABPhXV0hmmkhrpypIa/Cl6cW4OIiGrA0IKcxtCCWpyrJ2FMGgdJaQ7+MkbhceFVvD1tGG7qEuTuytoVURSRkpuCjec3YnPaZuSW51q3hXuGY0zMGNwRewfi/NvPEsuiKCIjvwzHMwpx/HIBjl8qxInLhSiu5Zc7P7Xc4YiJ6EA1AjwVDCaoRRJFEUVlelzKLzUHG5VhxmXz7aLyukMNP7XcPErDFGLYnYoSoIKPB0dvERG1VwwtyGkMLahFunoKxpXjIdFcxUljJ0zTv4LrusRifO8wjOoVyi+6zUxv1OOPrD+w8fxGbL+4HRpd5XKOcf5xuCPmDoyNGYswr7BajtL6ZBeVmwKKjAIczyjEn5cLkaepqNZPKZOge5gPOgd5mgKJoMpgwk+tcEPlRE2vsEyHy/llVUZrVIYcBaW6Oo/h4yGzjsqwPfWkU4AaUYFqnn5CRNSGMbQgpzG0oBbr2hmISeMgaLJx2hiJ1/QP4TdjTyikUgztFozxfcJxe48QThTXzMr15didsRubzm/Cnst7oDdW/rW1X4d+uCP2DoyMGgk/Dz/3FVkPeZoKazhhCigKHJ7eIZcK6B7qg/hIX/SO8EXvSD/EhXhBzlU5iOwUl5tPP8mrGmyY7jsKAKsK9lZaRydFBagRFWS6jg705ApTREStHEMLchpDC2rRrp0BVo4DSrIBAKmSGCwtH4ONxhughwxqhRS39wjB+D7huLVrEJQyBhjNqVBbiK0XtmJT2iYcyjoEEaYfJzKJDDeH34w7Yu/AkI5DoJI5vwxzcygq1+FERiGOX64cRZGRX1atn0QA4jp4o3ekr/nih26h3lwmkqgRaLR6a5hx2WZOjUv5pbiYV1rnSA0/tdwUZJhHNXWyXnNOGCKi1oChBTmNoQW1eIWXgX1LgORVgK4UAFCk6ICvxDH4pPgWFMO0JKePhwyje4VifJ9w3BgbCBn/8t2ssjRZ+CXtF2xM24hTeaes7WqZGsM7DccdsXdgUNggyCTNO9y7tEKPlMwi62kef2YU4nyOxmHf2CBP9I70RXykH3pH+qJnuA+HpxO5SWGpDhfyzBPb5mhwIc80we2F3FJcLa59klvL6jum0RlqRAWY55MJ8kSYjwdX3yEiagEYWpDTGFpQq1GaBxxaDhz4FNBcBQAY5F74I2A8FuYNwfHiyv9/g7wUGBsfhvF9wnF9J39+QW1m5wrOYeP5jdiUtgmXSy5b2wM8AjA6ejTuiL0D8UHxjf6XUK3egFNXiu1O8zh7tRhGBz/lIv1V1tETvSN80SvSl3OlELUSGq0eF/NKrUsKWwKN9JxSZBaW1bqcsEIqQccAFaIDPdEpUG13Hemv4qleRETNhKEFOY2hBbU6ei1wfC3w+4fANdNf9EVBityosfhWPgnLzvkg32ZYcbivB8b1Ccf43uHoFeHDIcPNSBRFHLt2DBvPb8SW9C3I1+Zbt3X07oixMWNxR+wdiPGNcfnYOoMRZ7NL8OflAhzLKMSfGYU4lVUEnaH6j7QQHyXiI/zQJ9LXNBdFpB8CPDlBJlFbpNUbkJFfZh2VYQ02cktxKb/U4WeEhVQiINzPA9HmJYijAszXgZ7oFKDmHEpERI2IoQU5jaEFtVqiCKRuA35bCqTttjYbo2/BiU7T8OW1rtjy11W75ShjgjwxvrdpBEZciLc7qm63dEYd9mfux8a0jdhxcQfK9JVzSPQI6IE7Yu/AmJgx6KDuUG1fo1HE+ZwS6+iJ4xkFSMksglZvrNbXXy03jZ6wjKKI9EWIj0eTPjciah0MRhGZBWWmICPPFGSk52hwMa8U6bkalOuqf6bYCvXxMI/KME8Oag42OgWq4aviSC0iIlcwtCCnMbSgNuHKMeC3D4GU9YBlNYugbtAN/Bt2Km/DDym52H4y2+4LafdQb4w3j8DoFKh2U+HtU6muFLsu7cLGtI347fJv0Ium10yAgH4dBiAhYBj8xX64mAOcuFyIlMwilNiETxbeShnizaMn+kT6IT7CF5H+Ko6mISKXiaKIa8VapOeaAoyLluu8UqTlaFBcXv0zyJZlYtBO5rk0OgWqrUu3hnhzHg0ioqoYWpDTGFpQm1KYARz4BDiUBFQUm9o8g4GBT0DTezq2XdDhp2OZ2H3mmt0Q4T4d/TChTzjuiA9DqC//Kt8cynUGpF4tQfLlDOy8tA0ni3ehREi1bheNMuhLukFfHA9DaQw8hAD0ivAxnebR0RfxEb6IDvTkLwJE1OREUURBqc5uMtB06+SgpcgpqX1iUKVMgo4BphEancynnHQKVCMqQI1IfzUUMs6jQUTtD0MLchpDC2qTyouAI18C+z8GijJMbTIV0PcB4IanUKjqhC0pWfjxWCZ+O5djnahREICB0QGYkBCOMb3COO9BI6jQG5GWo8GZ7GKcyS7G6axinL1aggu5mmoTZAryPMh9jsHD/xhEeZbdtlDPMPQNTkBChwT07dAXXf27Qirh+eVE5H62E4NeNJ92Yrl/uaAMBkezAZtJBCDMV2WeO8MUalhGaHQKVHOCYCJqsxhakNMYWlCbZtABKRuA35eaTiEBAAhA9zuAm54BOg3CtWItNp+4gh+PZuLQhcqJIqUSATd3CcL4PuEY2TOEXxzrYDCKuJCrwZnsElM4kV2Ms9nFOH9NA30NX9j91XJ0DfFGt1BvxIV4o1uIN7qGeMFPrcDpvNPYlLYJv2f+jjP5Z2AQDXb7qmVq9A7ujb4d+iKhQwL6BPeBp9yzOZ4qEZHTdAajzTwapbiYax9qlOkMte7vr5ZbTzmJsp5yYhqt0cFbydPhiKjVYmhBTmNoQe2CKALp/zPNe3F2S2V75EDgpllA93GARIrLBWXYeDwTPx7LxInLRdZuCpkEw7oFY3yfcAzvHtKuZ5A3GkVcLigzj5wosY6eOHetxOHEmIBp7om4EC90C/VG15DKS5CXwqkv3KW6UvyZ8yeSrybj6NWjOHbtGEp0JXZ9JIIEXf27ok9wH/Tt0Bd9O/RFmGcYv9ATUYsliiKulWhx0bLKiSXUyCvFxdxS5Goqat3fQy5Bp4DKU05sQw0u30pELR1DC3IaQwtqd66eMi2XevxbwGD+QugfDdzwd9PpIwrTX+vPXyvBz8ev4MdjmUi9WvkLslohxYjrQjC+dzhu7RrcZs9FFkURV4u1OJ1VXHlqR3YJUrOLoalw/JdBD7kEXUO8EdfBG91CvayjJ8J8PRo1PDAYDUgtSMXRq0eRfM0UZFwuuVytXwd1B2uAkdAhAd38u0EmkTVaHURETalEq8cF86SgF6qcfpJZUFbtFDtbEgEI91NZTzmJ9Fch0l+FCD8VIvxV6ODtASnnBCIiN2JoQU5jaEHtVnE2cPBz4OAyoMx8WoiHHzDgEWDg44B3KADTL++nsorx07FM/HQ8E5fyKpfq9PGQYUwv0xKqN8QGQNZK/6qVW6K1jpqwnXuiqIbZ8hVSCWKDPa2ndnQ1n9bR0V/ttokxr5ZeNYUY5tEYp/JOWVclsVDJVIgPirfOi9EnuA+8FVz6lohanwq9EZcLykyhhjnQsIQaF/NK61y+VS4VEOZbGWLYBhod/dUI9fXgSA0ialIMLchpDC2o3avQAEfXAL9/BOSnmdqkCqD3FODGWUCHHtauoiji6KUC/HTsCn4+nomrxZUzxgd5KTCyZyiCLJN3mkcWWH6Ftx1oIJhbLW1V+1QdlVDZz/F+tfWp3F5Zj1EUkZFfZg0ockocD0GWSgREB6pNc050qAwoogPVLT6gKdOX4UTOCWuIcfTaURRbVpQxEyCgi38X9A02jcRI6JCASK9InlJCRK2aZaScKcjQ4FJ+GS7nlyEj3zQx6JXC8lonBwVMIzVCfDzswoxIf7X1doSfCh7y9nuqJBE1HEMLchpDCyIzowE4vQn4bSlw6UBle5cRwE1PAzG32iUBBqOIg+l5+PFYJjb/eQX5pTo3FN04BAHo6K82j5zwss45ERvsCaWsbXwpNYpGnC84bz2dJPlqMi4VX6rWL0gVZDqdJNg0GqN7YHfIJZyElYjaDr3BiOxiLS7nl+FyQSky8spwucB0ycg3XVfUMEeRrSAvpSnM8DOP1DCHGZH+akT4q+Cl5Ol4RFQzhhbkNIYWRA5cPGBaceTkzwDMH5Gh8aYVR3reCUjtf4nVGYzYl5qDvWdzoDMYLXvA8ukqmltsP22r9kGVPjXtW32/yj6o1kd0uI8IIMzXA3EdTJNjdungBbWi/X25zCnLMY3CMM+N8VfuX9Ab7U8p8ZB6oGdQT+vcGH2C+8BX6eumiomImp7RKCJHozUFGPmWMKPU5nYZSmuY28iWr0rucKSGZX4NX5WcI9uI2jGGFuQ0hhZEtcg9B+z/GDi6GtCVmtp8IoBBTwLXTwc8+MtrW1KuL0dKbordKSWF2sJq/Tr7drbOi9G3Q1909O7IL95E1G6IooiCUp01zMiwCTMswUZhWd2jDz0V0mqnnYT4KNHB2wMhPkoEe3vAx0PGz1eiNoqhBTmNoQWRE0rzgENfAAc+AzRXTW0Kb1NwMehJwK+je+ujJmEUjUgvSreb4DO9KL1avwCPAPQO7o3Ovp0R5ROFGN8YRPtEw8/Dr9lrJiJqCYrLTaGGaS6NMpvbpnk1appLqSqlTIIOPkqEeHuggznQCPZWIsTHAx28ldY2fzVHbRC1NgwtyGkMLYhcoCsH/vzONO9FzmlTmyA1nTJy09NAeIJby6Oml1eeV3lKydVkpOSmQGd0/BdFX6Uvon2iTRffaOvtTj6doJAqmrlyIqKWo6zCYJ1HwxJmZBaUIbtIi6vF5bharEVxDStYOaKQShDsrTQHGqYgwxpqWAIObw8EeirctsoVEdljaEFOY2hBVA9GI5C6zTTvRdqeyvboW4Cuo4HI/kBYH0Cucl+N1CwqDBX4K/cvpOSmIL0wHelFpkuWJqvGfSSCBGGeYYj2jUaMTwyifKKsoUaIOoR/LSQiginYsAQYV81hhiXUuGZuyy4uR4ELE2FLJQKCvSwjNEynoFQNOUJ8TOFGS18li6i1Y2hBTmNoQdRAmUeB3z8ETqwHRJuJySQyIKQXEDnAfOkPBMRWX4uU2qRSXSkuFV9CWlGaNcy4UHgB6UXpKNGV1LifSqYyhRjm0RlRPlHWYMNL4dWMz4CIqHXQ6g2mEKNYi6tFjkIOLa4VlyNXUwFnf+sRBCDQ0xRsWEMNc9DRwRxq+Knl8FMr4KuSQ86Ag8hlDC3IaQwtiBpJwSXTqSMZB4GMQ5VzX9hS+QMR/c0hxvVAxPWmNmo3RFFEbnlu5agMS6BRdAGXii/BINY8I3+QKqjaqSbRvtGI8IqATNL+Vn8hInKFzmBETokl0KgMNa4Vl1vbsovKkVOihdHF3468lTL4quXwV1eGGX4qOfzVcviqFfBXy6u0K+CjkkPKU1WoHWNoQU5jaEHUBEQRKLgIXD5kCjAyDgFXjgEGbfW+gXGVIUbkAKBDT0DKX0DbI51Rh4ziDFwoumANM9IK03Ch6AJyy3Nr3E8myBDpHVktzIj2iUaARwBPNyEicoHBKCJXUzlao2rIcbVYi3xNBQpKK1DkwrwbVQkC4ONRNcww33YYgCjgq5ZzRRVqMxhakNMYWhA1E30FkP1nZYiRcRDIT6veT6YCwvuaTieJNI/K8Alv/nqpRSmqKLKeXmI7QuNi0UWUG8pr3M9b7m0NMCxzZ4R6hqKDqgOCVEGQS+XN+CyIiNoWvcGIonI98ksrUFCqQ2FZBfI1OhSU6VBgbssvrUBhmc7ap6BUhxJt/cMOqUSAr8ocdtiEGf7mcMPP0ybkUMnhqZTCy0MGb6UcHnIJAw9qMRhakNMYWhC5kSYHuHy4MsS4fATQFlbv5x1uH2KEJQAKdbOXSy2PUTQiW5ONtKI0uxEaF4ouILMkEyJq/xHvr/RHsDrYdFGZLh3UHaz3O6g7IFAVCLmE4QYRUWPRGYyVIYc5yMgvrUCh+do+9NChsNTUr0xX8ymEzpBKBHgqpPD2kMNLKYOXhwyeShm8lTLrfa+qt23blDJ4m/fhPB7UUAwtyGkMLYhaEKMRyD1bGWJkHAKupgCi0b6fIAVCelaGGBH9gcAugIRfIKhSub4cF4svIr3QFGJYwoyrpVdxrewa9Ebn/tInQIC/h78p1FCbQw1zwGF7P1AVyLk1iIiaULnOgMKyypDDNHLDFHLYhR7mIKSo3DSqo0Srd3oSUmcpZRJ42wQbngqZ/X27MEReLQyxhB9quZTL0LZTDC3IaQwtiFo4bQlw5ah9kFHiYDlND1/zJJ+WION6QB3Q7OVS62AUjSjUFloDjGul13Ct7Jrpvvn2tbJryCnNgV50PtwI8AhAB7Xp1BPbERu2IzgCPAIYbhARNSNRFFFaYbAGGCXlpuvicj00lrYq94vL9SjRmkIPjdZgvV+uM9b9gC4QBMBTIYNaIYWnUgaVXApPpRRqc5v1Wim19qvcZt5HYbvNtJ2nwrR8DC3IaQwtiFoZUQSKLtucUnIYyEwG9A7mNQjobB9ihPQCZIrmr5laLaNoRH55fs3BRuk1XC27ityy3FpXPrElESQI8AiodipKsDoYHVSV9/09/BluEBG1MHqD0RRimAMNSwBS0+1i8237MMR0Mbi6TIsLLGGIKdCQQqWQwVMhhdo8ukOtNIceCpldMGIJPaz7KqVQy2XWbSq5lGFII2FoQU5jaEHUBhh0QHZKZYiRcRDITa3eT+YBhPUxhRhBXQGfCNMknz7hppEa/CFM9WQwGpCvza8WZlwrvWbXllOeA2PV051q4Sn3hI/CBz4KH/gqfU23lT7wVfjCR+ljve+jsG/zVnhDIvB0KSKilkoURWj1RmuIUVqhR1mFAZoKA0q1epRWGFBaoTfdt7TpTNeaCoO5r956Xao19WvovB91GdMrFB8/eH2TPkZ7wdCCnMbQgqiNKs0zTeyZcbBy6dXygpr7K7wqAwzbMMMnsvK2yp/BBjWIwWhAXnmeXbCRU5pjDTiull5FTlkOcstzXQo3qhIgwFvh7TDksIYfNQQhapmaf0UjImqljEYRZTr7IMMSfpRVmE51sQ8/bEIQm7CktMJmX21lGHJXvwi8OyXBvU+yjWBoQU5jaEHUTogikHvOFGJkHgHyLwBFmaZTTcrynDuGTFUZYPhGOgg5Ik3zaPAXPmogvVGP4opiFFUUoVBbiKKKIhRpi1BYUYgibZF9u83t4opilOnLGvTYMkFWOYrDZiRHTSGHt8IbapkaKpkKarkaHlIPhh5ERG2MJQwRAXgpeepiY2BoQU5jaEFEqCgFiq+YAgxLkFFoc7soEyjNce5YUmX10RpVAw51EFc6oSZTYahwOuSo2kdn1DX48QUIUMvVdkGGWqaGSq6qbJOpHfapqU0lU0EukTMMISKiNoOhBTmNoQUROUVXDhRnmoMMmzCj8HLlbc1V544lVQDeYVVOQzHf9o0w3fYMBiTSpn1ORDZEUUSZvsxhsOHovqWtRFeCMn1Zg0d41EUmyKzBhyXIsA06qrZZbtuGJR5SDyikCiilSiilysrbMiVkgoyhCBERNRuGFuQ0hhZE1Gj0FdVHbFQduVGSDcCJHzsSmSnY8Aw2TRLq4QMofUy3LdfWNptrDz/TbSmHblLzMhgNKDeUo0xfhlJdKUr1pdbrqm1l+jL77bqy6m3mfSqMFc1Sv0SQVAYZkspAwzbYqBp2KCSVfTxkHvbbHIUjDu5bbnPiVCKi9sWV30P5rY6IiBqHTAH4R5kuNTHogOIsc5iRYT9ywxpsZAFGPVB4yXSpD7m6SqBRNeTwrSX4MAcjHOlBLpBKpPCUeMJT7gmoGu+4OqPOGmDYBhuW22U6x2GHo4CkwlABrUFbeW0TiBhFY7OMGKmJTCKzBhlyiRwyiQxyiRxyqRwyQQa5VG7fXtNtaeXtWvuaj1d1W7X70ur7yiQyhixERM2IoQURETUfqRzw62i6YJDjPga9aURG0WVAkwNoi4DyIkBbCJQXmm8XObguBHSlpmPoSk2Xkqz616rwqiP4sLT5Akpv05KyMg9A7mGatFSmBOSqynaZkpOUksvkEjnkCjl8FI0/GtIoGqEz6qxBRrm+3Bpo2IUbNm21bavar65jGcTKpQn1Rj30Rj00Ok2jP8+mIBMqwwupRAqZIINUIoVUkEImkUEqSB3et+1nve9gm7PHqKufpT6pIDXdNl9ba6/SXts2R8eRSuzvExE1BYYWRETUskhlprktfCNc39egA7TFpgCjaqBhe9uyrVq/IsDyl+aKEtOlOLORnphQGV7YhhlyD5vb5rBDpqq53eH+NbV7mIIiIgcsp4QopUq3PL7eqK8WbJQbyqE36qEz6qAz6KAX9dAZdNAZdZXttrdt+rjSt8Y+Vfubb4tVTmvTi3roDXq3/Lu1VAKEamGGRJBUhieCFBKJfRjiqM26TWLfz1FQUmubTZhTW/jiTB/bMMdhoFPL86gt5HEUGnFuGaLqGFoQEVHbIZWbll1VB9T/GPoKc/BRUMOIDkvYYROEaIsBvRbQlQH6ctNFV24KQESj+cCi6b6+zHTs5iJI7UMPqdx0kchNAZFEbpoc1XpbbppTRKqou591u2Ufcx+7far2M2+rs58MECQcndKGWU61UMvV7i6lVqIowiAarAGGJWwxiAYYjAboRT0MRoOpj+1to97ap+r9Ju1nc9uyzWg0wiAaYBTtrw3G6m121+bjWNpq/XeCCL2oN01bZKy1K9Wi1mDEvM3VIMRyXxAEuzaJIIEEkuptji519BMgmGpx5ngwhTNVwxoBgt3xrPVCAgiwHtu2r6WP9b5Ne03Hs96ux/Gs15bbVe9DsL6OtttM/9k/PjmPoQUREZEtmQKQBQKegQ0/liia5udwFGY4DDkst83b9WX1azdobWowVI4aaY0EqWl+EUFqCjIkEpvb0srtdn2kpsBDYr5frY9tu6RKH1nlvtWOJ3NciyCx2UdicxHst9teJFLz9qrbpFX2d3TcOi7W/g6OD8F+GwTzbaGW7TX0bycEQbCeDuIBD3eX41a1BRqWNtv7VQMTR6GJs2FKTY9n18dmX0dtlvvWYxht+tTQXmfAU0fwU7VP1VE7jv6NjaIRenAkT3tgG6BYgg27cMRBWFJTAGLbz1fpi/9O/K+bn13jYWhBRETUVAShcgQBmnGFJqPRFFzYhhmWkMSgA4w687UeMFTY3NaZ7ht1prlFLP1q3Me2X4WT++jtt1luG2v4gi4aAEPtf+ElN3E15Ki6vdZApD7XcHB8V67hQn/bUUBVQhxLn2rHg/0xXO5b9bGcOK7tdmt71ftVt6HGvhIAklqPVdexnbxvd7Pqv22VdkdtACBIAUir7y/Y7CN19ZgO6qzWH7VsE0wjdyCaQgwBMIoiDDDCKKKyHSKMgLnd0r9yP9ttRogw2F4L5r6iEUZUtovmY1jarPtChCjat9n1s943VtluDlgs94Wq+5uek9Fac+V20aZmy/MFRFPOj8paRfPji9b9UFkrRMBSh7mPo/5Vj2O5bTQvoGm0eSy7xxXN+9sdr/EX3RStxzc6tbias3RGXeMdrAVgaEFERNTWSCSARGU6LaS1EMUqQYfBFFgY9Ta3DVVu6823jU72NVbZz1FfyzEc9LXtb+1rNPWtdjEfQxQr2yzHretidLCv6GBfh49dy+NCrNzWGN+OLac+1XHaABFVEsBfwFozsefdEO9ZZhc0WCMPsYZry+2q9x1cA7Ae29pm8xhG0WjfZtMXqGxraxPj8j1DRERE7icIplNzoHB3Je2HKNoHHFVDjWrbRMd9a923pmM5ug/7x6rXNRzU4so1nOtnO1eNZT/bPtbjoI7tjh6zlr522+F836p1OHz8uvraaJJj2zxGrW22+6J6W4OP6aCtpv1r6+/SNtSyra79ano+Dvat8XGd7dfAYzZK31rU2t/Vx3DcLgR3hSCYTuWQgkujNxeGFkRERETtkWXODSIiohaMoQUBAIylpTDKHPzvIJVColTa9auRRAKJh0f9+paV1Zx0CgIkKlX9+paXm4bP1lSGWl2/vlptredYu9JXUKmsE+gYKyoAfc0TL7nU18MDgsQ0NEysqIDYWH2VSghSqet9dTqIuprPrxMUCgjm/wdd6qvXQ6yoqLmvXA5BLne9r8EAUautua9MBkGhcL2v0QixvLxR+kImg8TSVxQhlpU1Tl9X3vf8jHDcl58RrvflZ4SpLz8j6teXnxGmvvyMcL0vPyNMffkZUb++/IwAUL/PiFpfvyoYWhAA4Owtt8JLWv2vLZ5DbkWnTz+13j8z+OYaP6TUAwYg6qsvrfdTh98OQ36+w74evXoh5vvvrPfP3zEOusxMh30VXTqj888/W++nTZ6MitRzDvvKw8PRZcd26/0LD05D+YkTDvtK/f3R9fffrPcvPfY4Sg8edNhXUKnQPfmI9X7GM89As3uPw74A0OPUSevtzH/MRfGWLTX27XbkMATzB0/WvxJRuGFDjX3jftsHWYBpKcerixYhf83XNfbtvG0bFJERpr5L3kfe8uU19o396Uco4+IAADmffoacjz6qsW/0d2uhio8HAOR99RWu/uedGvt2WrkSnoMGAgDy165F9r/fqLFv5Ccfw3voUABA4U8/48rLL9fYN2LJe/AZPRoAULxtGy4/93yNfcMWLIDfXXcCAEr27kXGk3+rsW/Iq/MQ8MADAIDSQ4dxcfr0Gvt2ePEFBD7yCACg/K+/kD55So19g/7+dwQ/PQsAUHHuHM6Pn1Bj34CHH0bIP14EAOgyr+Dc7bfX2Nf//qkI/de/AACG/HycvWlwjX19J01C+KKFAACxrAyn+11fY1/vUaMQ+f4S6/3a+vIzwoSfEZX4GWHCzwgTfkaY8DOiEj8jTPgZYcLPCJP2+BlR4sIk221rhg4iIiIiIiIiajMEUXR1hpOW7ejRo1i7di0OHz6MI0eOICcnB0OGDMGuXbsc9k9PT0dMTEyNx0tMTMT8+fOdeuykpCTMnDmzxu07d+7EUHMCbGE0GvF///d/WL58OU6dOgWZTIaEhAS88MILmDCheoo6f/58vPbaazU+RlpaGqKjo52qFwCKiorg6+uL/CtX4OPjYDk+Dtly3LcdDNmqsS+HdZr6clin6335GVGvvvyMMPflZ4TLffkZYcbPiPr15WeEqS8/I1zvy8+IyjL4GVFj36KiIviHhaGwsNDx76E22tzpIRs2bMDChQuhUCjQtWtX5OTkOLVfnz59MGnSpGrtVUMGZ0ycOBEJCQnV2quGCaIoYsqUKVi3bh06d+6MRx55BFqtFj/88AMmTpyIpUuXYtasWQ4fY/r06Q7DCT8/P5frBUz/49v+z19bP1eO6XRfmzd/o/a1+bBq1L42H66N2lehABTOzZzvSl9BobD+AHNbX5sf5I3aVyazfvFo1L5SqXUoXaP2lUiapq8gNElfoAnf9/yMcL0vPyNc78vPCFNffkbUry8/IwDwM6JeffkZYcXPiHr0bQefEZJaQo6q2lxoMXnyZEyYMAHx8fHIzc1FWFiYU/slJCQ4PaKiLpMmTcKMGTPq7Ldu3TqsW7cOgwcPxtatW6Eyv0EWLFiA/v3744UXXsC4ceMchhMzZsyoV6BCRERERERE1Fq0uTktevbsiX79+kHuZLrqTj/88AMA4OWXX7YGFgAQFBSE559/HlqtFitWrHBXeURERERERERu1eZGWtRXZmYmPvroIxQWFiIkJARDhw5F586d63Ws5ORk5ObmQq/XIzo6GrfffjsCAwOr9cvKygIAh3NqWNp27NjhcA6LPXv24MCBA5BIJIiLi8Ptt98OLy+vetVLRERERERE1BIxtDDbunUrtm7dar0vCAIeeOABfPLJJ/D09HTpWB988IHdfZVKhcTERMydO9euPSgoCIBp8swePXrYbUtLSwMAnDlzxuFjJCYm2t338/PD+++/j4ceeqjW2rRaLbQ2E/0UFRXV2p+IiIiIiIjIXdrc6SGuUqvVePXVV3H48GEUFBQgLy8P27Ztw8CBA7Fq1ao6QwBbMTExWLp0Kc6cOYPS0lJkZGTgyy+/REBAAF566SUsXbrUrv+YMWMAAIsWLUK5zcy+ubm5WLJkCQCgoKDAbp8+ffpg+fLlOH/+PMrKypCWloalS5dCEATMmDEDP/74Y601Lly4EL6+vtZLx44dnX5+RERERERERM2pRS55OmfOHLvRAHV59tlnERcXV609KysLYWFhtS55WpPS0lL069cPp0+fxuHDh9GvXz+X9reVkpKC/v37Q61WIzs7GzLzrMN6vR4jR47Ezp070aVLF4wePRo6nQ4bNmxASEgIjh8/Dg8PD5TVtqSQ2fbt2zFixAj06tULx48fr7Gfo5EWHTt2dGqpGSIiIiIiIqKGKioqgq+vb+td8vTTTz+FRqNxuv8999zjMLRoCLVajWnTpmHevHnYt29fg0KLnj174uabb8a2bdtw8uRJxMfHAwBkMhk2b96MRYsWYc2aNfjss8/g6+uLO++8Ey+88AK6du2KDh06OPUYw4cPR+fOnfHnn3+iqKioxhdeqVRC6cKyOERERERERETu0iJDi5KSEneXAKByzglXAhRXj6VUKpGYmFhtjgrLyJD+/fu79BipqakoLS3lqAkiIiIiIiJq9dr9nBa1OXDgAAAgOjq6QccxGAw4dOgQACAqKsqpfVavXg0AuO+++5zqr9FokJKSAk9PT2tAQkRERERERNSatfvQIjk5GY6m9Vi/fj1WrlwJf39/64SZFleuXMGpU6dQWFho13748OFqxzEYDHjppZeQmpqKYcOGISwszG67o9U7vv/+eyxfvhwDBgzAXXfdZW0vLi52uJpIWVkZHnvsMRQXF2PKlCnWOTOIiIiIiIiIWrM299vtqVOnsGjRIgCwTmB56tQpzJgxw9onKSnJevv555/HuXPncOONNyIyMhIGgwFHjhzB3r17oVQqkZSUBF9fX7vH+Oc//4mVK1dixYoVdsft378/evfujd69eyMiIgJ5eXnYvXs3zpw5g8jISCxbtqxavYMGDULHjh3Ro0cPeHh44I8//sCuXbsQGxuL7777DlKp1No3NzcX3bt3x4ABA9CjRw+EhoYiOzsb27ZtQ0ZGBuLj4/Gf//ynEf4ViYiIiIiIiNyvzYUWWVlZWLlypV1bdna2XZttaPHggw9i3bp12L9/P3JycmA0GhEREYFHH30Uc+bMQffu3Z1+7Dlz5mD//v3YunUr8vLyoFAo0KVLF8ybNw+zZ8+Gv79/tX3uvfderF+/Hvv374dOp0NMTAzmzZuHF198sdq8FAEBAXjqqafwxx9/YNOmTcjPz4dKpUKPHj3wzDPPYNasWVCpVE7XS0RERERERNSStcglT6n5uLLUDBEREREREVFDtfolT6n5WDIrR3NrEBERERERETU2y++fzoyhYGjRzhUXFwMAOnbs6OZKiIiIiIiIqD0pLi6uNodkVTw9pJ0zGo3IzMyEt7c3BEFwdzk1KioqQseOHXHp0iWextKC8XVqHfg6tXx8jVoHvk6tA1+n1oGvU8vH16h1aC2vkyiKKC4uRnh4OCSS2hc15UiLdk4ikSAyMtLdZTjNx8enRb/5yISvU+vA16nl42vUOvB1ah34OrUOfJ1aPr5GrUNreJ3qGmFhUXukQURERERERETkJgwtiIiIiIiIiKhFYmhBrYJSqURiYiKUSqW7S6Fa8HVqHfg6tXx8jVoHvk6tA1+n1oGvU8vH16h1aIuvEyfiJCIiIiIiIqIWiSMtiIiIiIiIiKhFYmhBRERERERERC0SQwsiIiIiIiIiapEYWhARERERERFRi8TQgtzm4MGDGDt2LPz8/ODp6YkbbrgBa9eudekYWq0Wr7/+OuLi4uDh4YHw8HA8/vjjuHr1ahNV3X5cvnwZS5YswciRI9GpUycoFAqEhobi7rvvxoEDB5w+zq5duyAIQo2XpKSkpnsS7UR0dHSN/75Dhw516VirV6/GwIED4enpCX9/f4wbNw5HjhxpmsLbkaSkpFrfB4IgYPjw4XUeh++nxrFq1So88cQT6N+/P5RKZZ3/dkVFRZg9ezaioqKgVCoRHR2NF198ESUlJS4/9pYtWzBkyBB4e3vDx8cHw4YNw/bt2xvwbNomZ18jnU6HdevWYfr06ejRowe8vLzg7e2NQYMG4eOPP4bBYHDpcRvz87Q9cOW9NH/+/Fo/v9LT01167DNnzmDKlCkICgqCSqVCnz598PHHH4NrDFTnyutU188qQRBw6dIlpx6X7yfn1ed7d3v62SRzdwHUPu3cuROjRo2Ch4cH7rvvPnh7e2PdunW49957cenSJcyZM6fOYxiNRkycOBFbtmzBDTfcgLvvvhtnz57FsmXLsH37duzfvx/BwcHN8GzapqVLl+Ktt95C586dMXLkSAQHB+Ps2bPYsGEDNmzYgDVr1uDee+91+nhDhgxx+AMqISGh8Ypux3x9ffHcc89Va4+Ojnb6GG+++SbmzZuHqKgoPPnkkyguLsY333yDm266Cdu3b8fgwYMbr+B2JiEhAYmJiQ63ff/990hJScGoUaOcPh7fTw0zb948XLhwAUFBQQgLC8OFCxdq7KvRaDBkyBAcPXoUI0eOxNSpU5GcnIx33nkHu3fvxp49e+Dh4eHU465atQrTpk1DcHAwZsyYAQD49ttvMWLECKxduxb33HNPYzy9NsHZ1+jcuXO455574OXlheHDh2PChAkoLCzETz/9hKeeegqbNm3Cjz/+CEEQnH7sxvg8bS9ceS9ZTJ8+3eG/pZ+fn9OP+9dff+Gmm25CWVkZpkyZgvDwcGzcuBFPPfUU/vrrLyxdutSFZ9H2ufI61fSzKjU1FatXr8Z1112Hjh07Ov3YfD85x9Xv3e3uZ5NI1Mx0Op3YuXNnUalUisnJydb2goICsWvXrqJCoRDT09PrPM7y5ctFAOLUqVNFo9Fobf/4449FAOLjjz/eFOW3G+vWrRN37dpVrX3Pnj2iXC4X/f39xfLy8jqPs3PnThGAmJiY2ARVkiiKYlRUlBgVFdWgY5w5c0aUyWRi165dxYKCAmt7cnKyqFQqxR49eogGg6GBlVJVWq1WDAwMFGUymZiVlVVnf76fGsfWrVutP2cWLlwoAhBXrFjhsO+//vUvEYA4d+5cu/a5c+eKAMQFCxY49Zh5eXmin5+fGBQUJF66dMnafunSJTEoKEgMCgoSi4qK6veE2iBnX6OMjAzxo48+EktKSuzaS0pKxP79+4sAxLVr1zr9uI3xedqeuPJeSkxMFAGIO3fubPDj3nrrrSIAcdOmTdY2rVYr3nLLLSIA8bfffmvwY7QlrrxONZk1a5YIQFy8eLHT+/D95DxXv3e3t59NPD2Emt2OHTtw7tw53H///XZ/FfT19cXLL7+MiooKrFy5ss7jfP755wCAhQsX2v0F5YknnkBsbCxWr16NsrKyRq+/vbjrrrswZMiQau233HILhg0bhvz8fPz5559uqIyawooVK6DX6/HKK6/A19fX2p6QkICpU6fi5MmT2Lt3rxsrbJs2bNiA3NxcjBs3DiEhIe4up924/fbbERUVVWc/URSxbNkyeHl54dVXX7Xb9uqrr8LLywvLli1z6jG/++47FBQU4Omnn0ZkZKS1PTIyErNmzUJOTg7++9//uvZE2jBnX6OIiAg89dRT8PT0tGv39PTE7NmzAQC7d+9ukhrJ+depMZ05cwZ79uzBsGHDMGbMGGu7QqHAv//9bwCV3xHJpKGvU3l5OVavXg2FQoFp06Y1YmVk4cr37vb4s4mhBTW7Xbt2AQBGjhxZbZtleHRdXzDKy8tx4MABdOvWrdqHsCAIGDFiBDQaDQ4dOtQ4RZMduVwOAJDJnD/D7OzZs1iyZAkWLlyIr776CpcvX26q8tolrVaLpKQkLFiwAB9++KFL844AjfO+JNdZvlQ8+uijLu3H91PzOHv2LDIzMzF48GCHvxQPHjwY58+fd+r8br7Hml99flYBDf88pdrt2bMHb731Fv7zn/9gw4YNLp9/X9t76eabb4anpyffS41s/fr1yM/Px4QJE1w+9Zrvp4ar+lnWHn82cU4LanZnz54FAMTFxVXbFhoaCi8vL2ufmpw7dw5Go9HhMWyPffbsWdxyyy0NrJhsXbx4Edu2bUNYWBji4+Od3m/NmjVYs2aN9b5MJsPTTz+N//znP5BKpU1RaruSlZWFmTNn2rUNGDAAX3/9NTp37lzn/mfPnoWXlxdCQ0OrbbN9P1HjuXDhArZv347IyEiMHj3apX35fmoetf28srRv2bIFZ8+erfMc79qOxfdY01i+fDkAx1/Ga9PQz1OqXdU5E/z8/PD+++/joYcecmr/2t5LUqkUMTEx+Ouvv6DX610OrMixL774AoDrATvA91NDOfre3R5/NnGkBTW7wsJCALAbgm7Lx8fH2qchx7DtR41Dp9Nh2rRp0Gq1eOutt5z65Sg4OBiLFi3CiRMnUFJSguzsbGzYsAFdunTBe++9h3/84x/NUHnbNnPmTGzfvh3Z2dnQaDRITk7GtGnTcPDgQQwfPhzFxcV1HqOwsJDvp2a2YsUKGI1GzJgxw+mgge+n5tWYP2tqOxbfY43vs88+w+bNm3Hbbbdh7NixTu/XGJ+n5FifPn2wfPlynD9/HmVlZUhLS8PSpUshCAJmzJiBH3/80anjOPO+NBqNfK0aSVpaGnbu3IlOnTphxIgRLu3L91PD1PS9uz3+bGL8SEROsfxytWfPHjz22GNOn9PYs2dP9OzZ03rf09MTEydOxKBBg9C7d2988MEHmDt3Ljp06NBUpbd5Vf9qlZCQgC+//BIA8NVXX+Hzzz+3nttNLYPRaMSKFSsgCAIefvhhp/fj+4mobj///DNmzZqFqKgorFq1yqV9+XnadO688067+9HR0Zg1axZ69OiBESNGYN68eZgwYYKbqqOaLF++HKIoYubMmZBIXPt7N99P9Vff791tFUdaULOzJHk1pXZFRUU1JoeuHMO2HzWM0WjEww8/jDVr1uDBBx/EJ5980uBjhoaGYuLEidDr9Ty/sYk88cQTAIB9+/bV2dfX15fvp2a0bds2XLx4EbfddhtiYmIafDy+n5pGY/6sqe1YfI81nk2bNuGee+5BSEgIduzYgbCwsEY5riufp+Sa4cOHo3Pnzvjzzz+t74XaOPO+FAQB3t7ejVpne2Q0GpGUlASJROJSwF4Xvp9qV9f37vb4s4mhBTW72s6PysrKQklJSY3naFnExsZCIpHUeI5VXed6kfOMRiNmzpyJlStXYurUqdYfXo0hKCgIgGmtaWp8rvz7xsXFoaSkBFlZWdW28f3U+Oo7AWdt+H5qfHWdz+vKe6O2Y/E91jg2btyIu+66C0FBQdi5cydiY2Mb7dh8fzUty79vaWlpnX1rey8ZDAakpaUhJiaG81k0gl9++QUZGRkYMWIEOnXq1GjH5fupZs58726PP5sYWlCzsyzn8+uvv1bbtmXLFrs+NVGpVBg4cCBOnz6NCxcu2G0TRRFbt26Fp6cn+vfv30hVt0+WD84vv/wS9957L7766qtGneTP8hfh6OjoRjsmVXLl37cx3pfknNzcXPzwww8ICAioNly6Ifh+anxxcXEIDw/Hvn37qn251mg02LdvH2JiYuqc6Azge6ypbdy4EXfffTcCAgKwc+dOdOnSpVGPz/dX09FoNEhJSYGnp6f1l9na1PZe2rt3LzQaDd9LjaQhE3DWhu8nx5z93t0ufzaJRM1Mp9OJsbGxolKpFJOTk63tBQUFYteuXUWFQiGmpaVZ2zMzM8WTJ0+KBQUFdsdZvny5CECcOnWqaDQare0ff/yxCEB8/PHHm/qptGkGg0GcPn26CECcPHmyqNPpau1/7do18eTJk+K1a9fs2g8dOuSw/5IlS0QAYlxcnKjX6xut7vbm5MmTokajcdgeGhoqAhB3795tbS8oKBBPnjwpZmZm2vU/ffq0KJPJxK5du9q915KTk0WlUin26NFDNBgMTfdE2pH33ntPBCA+88wzNfbh+6n5LFy4UAQgrlixwuH2f/3rXyIAce7cuXbtc+fOFQGICxYssGvXaDTiyZMnxQsXLti15+Xlib6+vmJQUJB46dIla/ulS5fEoKAgMSgoSCwqKmqcJ9XG1PUabdq0SVQqlWJoaKh46tSpOo9XUVEhnjx5UkxNTbVrd/XzlOzV9joVFRWJp0+frtZeWloqTp06VQQgzpw5s9r2kydPiidPnqzWfuutt4oAxE2bNlnbtFqteMstt4gAxH379jXsybRhdb2fLK5evSrK5XIxODhY1Gq1Nfbj+6lxuPq9u739bBJEURSbNSUhArBz506MGjUKHh4euO++++Dt7Y1169bhwoULeOeddzBnzhxr3xkzZmDlypVYsWIFZsyYYW03Go0YO3YstmzZghtuuAFDhgxBamoq1q9fj+joaBw4cMDltaSp0vz58/Haa6/By8sLzz77rMNhlpMmTUJCQoJd/8TERMyfP9/aJzo6GnK5HP3790dkZCQ0Gg3279+P5ORk+Pn5YcuWLRg4cGAzPau2Z/78+Xj33Xdx6623IioqCp6enjhz5gw2bdoEnU6Hf/7zn1iwYIG1f1JSEmbOnInp06cjKSnJ7lhvvvkm5s2bh6ioKNx9990oLi7GN998g4qKCmzfvh2DBw9u5mfXNsXHx+PEiRM4fvx4jcsG8/3UtJYtW4a9e/cCAP78808cOXIEgwcPtv51/uabb7b+ZVGj0WDw4ME4duwYRo4ciX79+uHIkSP49ddfMWDAAOzevRsqlcp67F27dmHYsGEYMmQIdu3aZfe4q1atwrRp0xAcHIx7770XAPDtt98iJycH3377LSZPntwMz751cPY1OnXqFBISEqDVanHfffehW7du1Y4VHR1t9/0hPT0dMTExiIqKQnp6urXd1c9Tcv51Sk9PR2xsLAYMGIAePXogNDQU2dnZ2LZtGzIyMhAfH4+dO3ciMDDQ7viCIAAwjaK1lZKSgsGDB6OsrAz33nsvwsLCsHHjRqSkpGDWrFlYunRpMzz71sOVzzyLxYsX44UXXsDs2bOxePHiGo/N91PjcPV7d7v72eTm0ITasQMHDoijR48WfXx8RJVKJQ4cOFD85ptvqvWzpI6OEuHy8nJx/vz5YufOnUWFQiGGhoaKjz76qJiVldUMz6Bts/y713axfU0SExNFAGJiYqLdcRYtWiQOGzZMDA8PF5VKpahSqcTu3buLzz33nF2iS/Wza9cuccqUKWJcXJzo4+MjymQyMTQ0VJw4caK4ZcuWav1XrFghAhCnT5/u8HirVq0S+/fvL6pUKtHX11ccO3asePjw4SZ+Fu3HgQMHRADiwIEDa+3H91PTquvzrer7o6CgQHzuuefEjh07inK5XOzUqZM4Z84ch3992rlzpwhAHDJkiMPH3rx5s3jLLbeInp6eopeXlzhkyBBx69atTfAsWzdnXyPLv3dtl6qvRVpamghAjIqKsmt39fOUnH+dCgsLxb///e/igAEDxODgYFEmk4ne3t7iwIEDxbffflssLS11eHzLcRw5deqUeM8994gBAQGiUqkU4+PjxY8++shu9C2ZuPqZJ4qi2KNHDxGA+Ndff9V6bL6fGoer37tFsX39bOJICyIiIiIiIiJqkTgRJxERERERERG1SAwtiIiIiIiIiKhFYmhBRERERERERC0SQwsiIiIiIiIiapEYWhARERERERFRi8TQgoiIiIiIiIhaJIYWRERERERERNQiMbQgIiIiIiIiohaJoQURERERERERtUgMLYiIiIia0a5duyAIAubPn+/uUoiIiFo8hhZERETUoqWnp0MQBIwePdraNmPGDAiCgPT0dPcVVgtBEDB06FB3l0FERNTqydxdABEREVF7MnDgQJw8eRJBQUHuLoWIiKjFY2hBRERE1IzUajW6d+/u7jKIiIhaBZ4eQkRERK1KdHQ0Vq5cCQCIiYmBIAgOT8dIS0vDo48+ik6dOkGpVCIsLAwzZszAhQsXqh3Tsv/ly5fx0EMPITQ0FBKJBLt27QIA7Ny5Ew8//DC6desGLy8veHl5oX///vjss8/sjmOZrwIAdu/eba1NEAQkJSXZ9XE0p8WJEycwZcoUdOjQAUqlEjExMXjuueeQm5vr8N8hOjoaJSUlePbZZxEeHg6lUonevXvj+++/d/FflYiIqGXiSAsiIiJqVZ577jkkJSXh2LFjePbZZ+Hn5wfA9Eu8xYEDBzBq1ChoNBqMGzcOcXFxSE9Px+rVq7F582b8/vvviI2NtTtubm4ubrzxRgQEBOC+++5DeXk5fHx8AABvvfUWUlNTccMNN+DOO+9EQUEBfvnlFzzxxBM4ffo0Fi9ebK0hMTERr732GqKiojBjxgzr8RMSEmp9Xnv37sWoUaNQUVGBe+65B9HR0fj999/x/vvv4+eff8b+/furnVKi0+kwcuRI5Ofn4+6770ZpaSm++eYbTJkyBb/88gtGjhxZv39kIiKilkIkIiIiasHS0tJEAOKoUaOsbdOnTxcBiGlpadX6V1RUiNHR0aK3t7d45MgRu23/+9//RKlUKo4bN86uHYAIQJw5c6ao1+urHfP8+fPV2nQ6nThixAhRKpWKFy5cqHa8IUOGOHw+O3fuFAGIiYmJ1jaDwSB27txZBCD+8ssvdv1ffPFFEYD48MMP27VHRUWJAMSJEyeKWq3W2r5t27Zq/15EREStFU8PISIiojbl559/Rnp6Ol588UX07dvXbtvNN9+MiRMnYtOmTSgqKrLbplAo8Pbbb0MqlVY7ZkxMTLU2mUyGJ598EgaDATt37mxQzfv27cO5c+cwZswYjBo1ym7bv/71LwQEBGDNmjWoqKiotu97770HhUJhvT98+HBERUXh4MGDDaqJiIioJeDpIURERNSm7N+/HwBw+vRph/NGZGVlwWg04syZM+jfv7+1PSYmpsYVPYqLi/HOO+9gw4YNOHfuHDQajd32zMzMBtWcnJwMAA6XSbXMn/Hrr7/i9OnTiI+Pt27z8/NzGKhERkbi999/b1BNRERELQFDCyIiImpT8vLyAACrV6+utV/V4CEkJMRhv4qKCgwdOhRHjhxB3759MW3aNAQGBkImkyE9PR0rV66EVqttUM2WUR811RAWFmbXz8LX19dhf5lMBqPR2KCaiIiIWgKGFkRERNSmWCbP/OmnnzBu3Din97Os+lHVDz/8gCNHjuCRRx7BsmXL7LZ988031pVMGsJSc3Z2tsPtWVlZdv2IiIjaC85pQURERK2OZd4Jg8FQbdugQYMAoNFOjzh37hwAYOLEidW2/e9//3O4j0QicVhbTSxzb1iWWLWl0Whw6NAhqFQqdOvWzeljEhERtQUMLYiIiKjVCQgIAABcunSp2raJEyeiU6dOePfdd7Fnz55q23U6Hfbu3ev0Y0VFRQFAtX12796Nzz//vMb6MjIynH6MwYMHo3Pnzti8eTO2bdtmt+2NN95Abm4upk6dajfhJhERUXvA00OIiIio1bntttvwzjvv4PHHH8fdd98NT09PREVFYdq0aVAqlfj+++8xZswYDBkyBLfddhvi4+MhCAIuXLiA//3vfwgMDMSpU6eceqzx48cjOjoab7/9Nk6cOIFevXrh9OnT+Pnnn3HnnXfi+++/d1jf2rVrMWnSJPTt2xdSqRQTJkxA7969HT6GRCJBUlISRo0ahbFjx2Ly5MmIiorC77//jl27dqFz585YtGhRg/7NiIiIWiOGFkRERNTqjBkzBm+//TY+//xzLF68GDqdDkOGDMG0adMAAAMGDMCxY8fwn//8B5s2bcK+ffugVCoRERGBSZMmYerUqU4/lpeXF3bs2IEXX3wRe/bswa5du9CzZ0+sXr0aISEhDkOL999/HwCwY8cO/PTTTzAajYiMjKwxtABMy7Hu378fr7/+On799VcUFhYiPDwczz77LObNm1fjyiZERERtmSCKoujuIoiIiIiIiIiIquKcFkRERERERETUIjG0ICIiIiIiIqIWiaEFEREREREREbVIDC2IiIiIiIiIqEViaEFERERERERELRJDCyIiIiIiIiJqkRhaEBEREREREVGLxNCCiIiIiIiIiFokhhZERERERERE1CIxtCAiIiIiIiKiFomhBRERERERERG1SAwtiIiIiIiIiKhF+n8N1G4yKsV8lwAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.rcParams[\"font.size\"] = 14\n",
        "\n",
        "# plot loss and reference value\n",
        "plt.figure(figsize=(12, 6), facecolor='white')\n",
        "plt.plot(cost_val[:20], label=\"VQE\")\n",
        "plt.plot(energy_vals, label=\"ADAPT_VQE\")\n",
        "plt.plot(energy, label=\"TETRIS_ADAPT_VQE\")\n",
        "plt.axhline(y=real_solution.real, color=\"tab:red\", ls=\"--\", label=\"Target\")\n",
        "\n",
        "plt.legend(loc=\"best\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Energy [H]\")\n",
        "plt.title(\"VQE energy\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EdAc58BJJjxn"
      },
      "source": [
        "So far we used hybrid algorithm VQE with different techniques to get estimates on a noiseless (simulated) quantum backend. However, on real quantum devices, the errors propagate pretty fast. Therefore, we need error mitigation techniques.\n",
        "\n",
        "Furthermore, we need to apply it to systems where the number of two qubit gates (most prone to error after toffoli) are minimized. To resolve this issue, we look at a smaller system"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IWOmur2eJjxn"
      },
      "source": [
        "Now using error mitigation with qiskit runtime and just VQE. This method is based on a crude approximation, restricting the Hilbert space to an active space of unbonded electrons within the BeH2 molecule.. The circuits take longer to run depending on how available the ibm backend is but achieve error mitigated results."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {
        "id": "JZ-AUnYJJjxn"
      },
      "outputs": [],
      "source": [
        "# Import necessary libraries and packages\n",
        "import math\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')\n",
        "from qiskit_ibm_runtime import QiskitRuntimeService, Session, Options, Estimator\n",
        "from qiskit_nature.second_q.circuit.library import UCC, UCCSD, HartreeFock\n",
        "from qiskit_nature.second_q.mappers import JordanWignerMapper, ParityMapper, QubitMapper\n",
        "\n",
        "from qiskit_nature.units import DistanceUnit\n",
        "from qiskit_nature.second_q.drivers import PySCFDriver\n",
        "\n",
        "\n",
        "from qiskit_nature.settings import settings\n",
        "from qiskit.circuit import QuantumCircuit\n",
        "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
        "from qiskit_ibm_runtime import SamplerV2 as Sampler\n",
        "from qiskit_ibm_runtime.fake_provider import FakeManilaV2\n",
        "from qiskit_algorithms.optimizers import SLSQP\n",
        "\n",
        "from qiskit_algorithms import NumPyMinimumEigensolver, VQE\n",
        "from qiskit_nature.second_q.algorithms import GroundStateEigensolver\n",
        "from qiskit_nature.second_q.transformers.active_space_transformer import ActiveSpaceTransformer\n",
        "from qiskit_nature.second_q.problems.electronic_structure_problem import ElectronicStructureProblem\n",
        "settings.dict_aux_operators = True"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U7CpsxQuj_gd"
      },
      "source": [
        "We use the linear geometry of the molecule and set a distance d as rougly the equilibrium distance of the two hydrogen atoms from beryllium which is 1.29 Angstroms."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "metadata": {
        "id": "JimUdlD6XzAr"
      },
      "outputs": [],
      "source": [
        "# Create an instance of the PySCFDriver with the specified molecular configuration\n",
        "driver = PySCFDriver(\n",
        "    atom=\"Be 0 0 0; H -1.291 0 0; H 1.291 0 0\",  # Defines the positions of the atoms\n",
        "    basis=\"sto3g\",                             # Specifies the basis set for the calculation\n",
        "    charge=0,                                  # The total charge of the molecule\n",
        "    spin=0,                                    # The total spin of the molecule\n",
        "    unit=DistanceUnit.ANGSTROM,                # The unit of measurement for atomic positions\n",
        ")\n",
        "\n",
        "# Execute the driver to compute the molecular properties\n",
        "properties = driver.run()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {
        "id": "FMnsCkB5Jjxo",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8a14fd35-a5f3-43a7-a304-22c93601f6bb"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "number of alpha electrons:  3\n",
            "number of beta electrons:  3\n",
            "number of spin orbitals:  14\n"
          ]
        }
      ],
      "source": [
        "# Retrieve the number of alpha electrons from the molecular properties\n",
        "num_alpha_electrons = properties.num_alpha\n",
        "# Retrieve the number of beta electrons from the molecular properties\n",
        "num_beta_electrons = properties.num_beta\n",
        "# Convert the number of spin orbitals to an integer for further calculations\n",
        "num_spin_orbitals = int(properties.num_spin_orbitals)\n",
        "\n",
        "# Get the nuclear repulsion energy from the molecular properties\n",
        "nuclear_rep_energy = properties.nuclear_repulsion_energy\n",
        "\n",
        "# Print the number of alpha electrons to the console\n",
        "print(\"number of alpha electrons: \", num_alpha_electrons)\n",
        "# Print the number of beta electrons to the console\n",
        "print(\"number of beta electrons: \", num_beta_electrons)\n",
        "# Print the number of spin orbitals to the console\n",
        "print(\"number of spin orbitals: \", num_spin_orbitals)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {
        "id": "Nqe3nv1fJjxq"
      },
      "outputs": [],
      "source": [
        "# Define the active space around the Fermi level (selected automatically around the HOMO and LUMO, ordered by energy)\n",
        "transformer = ActiveSpaceTransformer(\n",
        "    num_electrons=2, #Number of electrons in our active space\n",
        "    num_spatial_orbitals = 2, #Numer of orbitals in our active space\n",
        ")\n",
        "\n",
        "# Define the reduced problem using this transformer\n",
        "problem = transformer.transform(properties)\n",
        "\n",
        "# The second quantized Hamiltonian of the reduce problem\n",
        "second_q_ops_reduced = problem.second_q_ops()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {
        "id": "YOuQ5jZ3Jjxq"
      },
      "outputs": [],
      "source": [
        "# Setup the mapper and qubit converter\n",
        "mapper_type = 'ParityMapper'\n",
        "\n",
        "if mapper_type == 'ParityMapper':\n",
        "    mapper = ParityMapper()\n",
        "elif mapper_type == 'JordanWignerMapper':\n",
        "    mapper = JordanWignerMapper()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 55,
      "metadata": {
        "id": "GjSEjD5oJjxr",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3564d3a1-4f14-4c75-800e-2783fc9f31f6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "SparsePauliOp(['IIII', 'IIIZ', 'IIZZ', 'IIZI', 'IZZI', 'IZZZ', 'ZZII', 'ZZIZ', 'ZXIX', 'IXZX', 'ZXZX', 'IXIX', 'IZIZ', 'ZZZZ', 'ZIZI'],\n",
            "              coeffs=[-0.78880753+0.j,  0.14838961+0.j, -0.04151142+0.j,  0.08629166+0.j,\n",
            "  0.14838961+0.j,  0.10988922+0.j, -0.04151142+0.j,  0.09005693+0.j,\n",
            "  0.00376527+0.j, -0.00376527+0.j, -0.00376527+0.j,  0.00376527+0.j,\n",
            "  0.09005693+0.j,  0.11246476+0.j,  0.08629166+0.j])\n"
          ]
        }
      ],
      "source": [
        "# Use Parity mapper to map the problem\n",
        "qubit_op_parity = mapper.map(problem.hamiltonian.second_q_op())\n",
        "print(qubit_op_parity)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 56,
      "metadata": {
        "id": "uyHLVQ-WJjxr"
      },
      "outputs": [],
      "source": [
        "# Run the sampler job locally using FakeManilaV2\n",
        "fake_manila = FakeManilaV2()\n",
        "\n",
        "# Define options for the simulator\n",
        "options = {\"simulator\": {\"seed_simulator\": 42}}\n",
        "\n",
        "# Create a Sampler object with the fake backend and the defined options\n",
        "sampler = Sampler(backend=fake_manila, options=options)\n",
        "\n",
        "# Create an Estimator object with the fake backend and the defined options\n",
        "estimator = Estimator(backend=fake_manila, options=options)\n",
        "\n",
        "# Define the ansatz (trial wavefunction) using the UCCSD (Unitary Coupled Cluster Singles and Doubles) method\n",
        "ansatz = UCCSD(\n",
        "    problem.num_spatial_orbitals,  # Number of spatial orbitals in the molecule\n",
        "    problem.num_particles,         # Number of particles (electrons) in the molecule\n",
        "    mapper,                        # Object that maps fermionic operators to qubit operators\n",
        "    initial_state=HartreeFock(     # The initial state is set to the Hartree-Fock state\n",
        "        problem.num_spatial_orbitals,  # Number of spatial orbitals\n",
        "        problem.num_particles,         # Number of particles (electrons)\n",
        "        mapper,                        # Mapper for fermionic to qubit operator conversion\n",
        "    ),\n",
        ")\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Number of particles after parity reduction (Z_2 symmetry reduction)\n",
        "problem.num_particles"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WIBIVsJqeQxn",
        "outputId": "d19b7c4d-bbca-4b02-ab11-23e5aa9b32cc"
      },
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1, 1)"
            ]
          },
          "metadata": {},
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 58,
      "metadata": {
        "id": "QolXYbOVJjxr",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "64647068-e8e6-4d07-a9ee-c4829ea720b5"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-15.561043875545712\n"
          ]
        }
      ],
      "source": [
        "\n",
        "# Set up the VQE solver with the estimator, ansatz, and SLSQP optimizer.\n",
        "vqe_solver = VQE(estimator, ansatz, SLSQP(maxiter=6,ftol = 1e-4))\n",
        "#vqe_solver = VQE(sampler, ansatz, SLSQP(maxiter=6,ftol = 1e-4))\n",
        "\n",
        "# Initialize the parameters for the VQE solver to zeros.\n",
        "vqe_solver.initial_point = [0.0] * ansatz.num_parameters\n",
        "\n",
        "# Create a ground state eigensolver using the given mapper and VQE solver.\n",
        "solver = GroundStateEigensolver(mapper, vqe_solver)\n",
        "\n",
        "# Solve the problem to find the ground state energy of the molecule.\n",
        "res = solver.solve(problem)\n",
        "\n",
        "# Output the computed total energy of the molecule's ground state.\n",
        "print(res.total_energies[0])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3QndcCn0Jjxr"
      },
      "outputs": [],
      "source": [
        "token = ''\n",
        "IBMQ.save_account(token)\n",
        "service = QiskitRuntimeService()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Tvogx28dJjxr"
      },
      "outputs": [],
      "source": [
        "#using qasm simulator\n",
        "backend = service.backends(simulator=True)[0]\n",
        "noisy_sim = FakeManilaV2()\n",
        "#noisy_sim = FakeGuadalupe()\n",
        "#for running on real quantum device\n",
        "#backend = 'ibmq_lima'\n",
        "#backend = 'ibmq_guadalupe'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uLT0Z2cOJjxr"
      },
      "outputs": [],
      "source": [
        "service = QiskitRuntimeService(\n",
        "    channel='ibm_quantum',\n",
        "    instance='qhack-event/main/level-2-team-1',\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xuIcOeGpJjxr"
      },
      "outputs": [],
      "source": [
        "#for noisy simulator\n",
        "noise_model = NoiseModel.from_backend(noisy_sim)\n",
        "\n",
        "options_with_em = Options(\n",
        "    simulator={\n",
        "        \"noise_model\": noise_model,\n",
        "        \"seed_simulator\": 42,\n",
        "    },\n",
        "    resilience_level=1 # You may change the value here. resilience_level = 1 will activate TREX\n",
        ")\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WybLtibQJjxr"
      },
      "outputs": [],
      "source": [
        "%%time\n",
        "from qiskit.utils import algorithm_globals\n",
        "algorithm_globals.random_seed = 1024\n",
        "\n",
        "# Define convergence list\n",
        "convergence = []\n",
        "\n",
        "# Keep track of jobs\n",
        "job_list = []\n",
        "\n",
        "# Initialize estimator object\n",
        "#estimator = Estimator()\n",
        "\n",
        "# Define evaluate_expectation function\n",
        "def evaluate_expectation(x):\n",
        "    x = list(x)\n",
        "\n",
        "    # Define estimator run parameters\n",
        "\n",
        "    with Session(service=service, backend=backend):\n",
        "      estimator = Estimator(options=options_with_em)\n",
        "      job = estimator.run(circuits=[ansatz], parameter_values=[x],observables=qubit_op_parity).result()\n",
        "      results = job.values[0]\n",
        "      job_list.append(job)\n",
        "\n",
        "\n",
        "    # Pass results back to callback function\n",
        "    return np.real(results)\n",
        "\n",
        "\n",
        "\n",
        "# Call back function\n",
        "def callback(x,fx,ax,tx,nx):\n",
        "    # Callback function to get a view on internal states and statistics of the optimizer for visualization\n",
        "    convergence.append(evaluate_expectation(fx))\n",
        "\n",
        "np.random.seed(10)\n",
        "\n",
        "# Define initial point. We shall define a random point here based on the number of parameters in our ansatz\n",
        "initial_point = np.random.random(ansatz.num_parameters)\n",
        "\n",
        "\n",
        "# Define optimizer and pass callback function\n",
        "optimizer = SPSA(maxiter = 50, callback=callback)\n",
        "\n",
        "# Define minimize function\n",
        "result =  optimizer.minimize(evaluate_expectation, x0=initial_point)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1CViEqIzJjxr"
      },
      "source": [
        "The energy is measured in Hartrees."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "8TcF1hwfJjxr"
      },
      "outputs": [],
      "source": [
        "Energy_H_t = []\n",
        "for i in range(len(convergence)):\n",
        "    sol = MinimumEigensolverResult()\n",
        "    sol.eigenvalue = convergence[i]\n",
        "    sol = problem_reduced.interpret(sol).total_energies[0]\n",
        "    Energy_H_t.append(sol)\n",
        "print(\"Computed Energy:\", Energy_H_t[-1])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9X1_-tHxJjxr"
      },
      "outputs": [],
      "source": [
        "# The following plot compares the two Estimators - with and without noise\n",
        "\n",
        "plt.rcParams[\"font.size\"] = 14\n",
        "\n",
        "# plot loss and reference value\n",
        "plt.figure(figsize=(12, 6), facecolor='white')\n",
        "plt.plot(Energy_H_t, label=\"Estimator VQE BeH2+NOISY+TREX\")\n",
        "plt.axhline(y=real_solution_t.real, color=\"tab:red\", ls=\"--\", label=\"Target\")\n",
        "\n",
        "plt.legend(loc=\"best\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Energy [H]\")\n",
        "plt.title(\"VQE energy\")\n",
        "plt.show()\n",
        "\n",
        "print(Energy_H_t)\n",
        "print(real_solution_t.real)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vGA7AvuBJjxr"
      },
      "source": [
        "The graph below shows the use of Twirled Readout Error eXtinction (TREX) error mitgation with FakeManila. resilience_level=2 uses zero-noise extrapolation (ZNE) and resilience_level=3 probabilistic error cancellation."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "TbFVxDMRJjxr"
      },
      "outputs": [],
      "source": [
        "#the list below is obtained from running the above code using FakeManila() backend with TREX\n",
        "\n",
        "Energy = [(-15.308589894649552+0j), (-15.376219303406794+0j), (-15.39387021095869+0j), (-15.41320988016764+0j), (-15.424979665346248+0j), (-15.43005680849908+0j), (-15.458793700847162+0j), (-15.446448283806754+0j), (-15.4898171094885+0j), (-15.476441721587053+0j), (-15.474969955813778+0j), (-15.502844077303289+0j), (-15.497264640785085+0j), (-15.50411400536762+0j), (-15.522390027528557+0j), (-15.511767919548054+0j), (-15.546447335850596+0j), (-15.507244766958324+0j), (-15.514498135878798+0j), (-15.528440541600068+0j), (-15.505466876966013+0j), (-15.534659182874288+0j), (-15.506999906756407+0j), (-15.510933484293696+0j), (-15.523721688697963+0j), (-15.510674314602634+0j), (-15.527421789425498+0j), (-15.533565249430302+0j), (-15.505068081695628+0j), (-15.52178684825123+0j), (-15.517105482753143+0j), (-15.51841838222561+0j), (-15.515969684471115+0j), (-15.52842328809817+0j), (-15.531562898320603+0j), (-15.530992698664287+0j), (-15.551054905020186+0j), (-15.519531658012843+0j), (-15.507667899741014+0j), (-15.515193693691847+0j), (-15.533802941657433+0j), (-15.528088837443674+0j), (-15.504669734193806+0j), (-15.539639668296635+0j), (-15.510747126847535+0j), (-15.513427925056904+0j), (-15.52002162186678+0j), (-15.526629340135559+0j), (-15.516375594669652+0j), (-15.505610970793215+0j)]\n",
        "\n",
        "Target_E = -15.561651427447169\n",
        "\n",
        "E = []\n",
        "for i in range(len(Energy)):\n",
        "    E.append(np.real(Energy[i]))\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "613RXvgzJjxr",
        "outputId": "b5bef3b7-4136-4567-a9b8-18b2924e9019"
      },
      "outputs": [
        {
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",
            "text/plain": [
              "<pyolite.display.Image at 0x318af68>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.rcParams[\"font.size\"] = 14\n",
        "\n",
        "# plot loss and reference value\n",
        "plt.figure(figsize=(12, 6), facecolor='white')\n",
        "plt.plot(E, label=\"Estimator VQE BeH2+NOISY+TREX\")\n",
        "plt.axhline(y=Target_E, color=\"tab:red\", ls=\"--\", label=\"Target, d = 1.291 Angstroms\")\n",
        "\n",
        "plt.legend(loc=\"best\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Energy [H]\")\n",
        "plt.title(\"VQE energy\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3Q8qHSycJjxs"
      },
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tSKR_6GmJjxs"
      },
      "source": [
        "Additionally we have error mitigated results from the real backend ibmq_lima using TREX and ZNE. While TREX results show monotonic convergence to the ground state, we show ZNE results."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3HYdg5IXJjxs"
      },
      "outputs": [],
      "source": [
        "backend = 'ibmq_lima'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gqLnVNRNJjxs"
      },
      "outputs": [],
      "source": [
        "service = QiskitRuntimeService(\n",
        "    channel='ibm_quantum',\n",
        "    instance='qhack-event/main/level-2-team-1',\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_f9oHVRnJjxs"
      },
      "outputs": [],
      "source": [
        "options_with_em = Options(resilience_level=2 # You may change the value here. resilience_level = 1 will activate TREX\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7064QXAeJjxs"
      },
      "outputs": [],
      "source": [
        "%%time\n",
        "from qiskit.utils import algorithm_globals\n",
        "algorithm_globals.random_seed = 1024\n",
        "\n",
        "# Define convergence list\n",
        "convergence = []\n",
        "\n",
        "# Keep track of jobs (Do-not-modify)\n",
        "job_list = []\n",
        "\n",
        "# Initialize estimator object\n",
        "#estimator = Estimator()# Enter your code here\n",
        "\n",
        "# Define evaluate_expectation function\n",
        "def evaluate_expectation(x):\n",
        "    x = list(x)\n",
        "\n",
        "    # Define estimator run parameters\n",
        "    #### enter your code below ####\n",
        "\n",
        "\n",
        "\n",
        "    with Session(service=service, backend=backend):\n",
        "      estimator = Estimator(options=options_with_em)\n",
        "      job = estimator.run(circuits=[ansatz], parameter_values=[x],observables=qubit_op_parity).result()\n",
        "      results = job.values[0]\n",
        "      job_list.append(job)\n",
        "\n",
        "\n",
        "    # Pass results back to callback function\n",
        "    return np.real(results)\n",
        "\n",
        "\n",
        "\n",
        "# Call back function\n",
        "def callback(x,fx,ax,tx,nx):\n",
        "    # Callback function to get a view on internal states and statistics of the optimizer for visualization\n",
        "    convergence.append(evaluate_expectation(fx))\n",
        "\n",
        "np.random.seed(10)\n",
        "\n",
        "# Define initial point. We shall define a random point here based on the number of parameters in our ansatz\n",
        "initial_point = np.random.random(ansatz.num_parameters)\n",
        "\n",
        "#### enter your code below ####\n",
        "# Define optimizer and pass callback function\n",
        "optimizer = SPSA(maxiter = 50, callback=callback) # ----------- Enter your code here\n",
        "\n",
        "# Define minimize function\n",
        "result =  optimizer.minimize(evaluate_expectation, x0=initial_point) # ----------- Enter your code here"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "TfJobxOlJjxs"
      },
      "outputs": [],
      "source": [
        "Energy_H_t = []\n",
        "for i in range(len(convergence)):\n",
        "    sol = MinimumEigensolverResult()\n",
        "    sol.eigenvalue = convergence[i]\n",
        "    sol = problem_reduced.interpret(sol).total_energies[0]\n",
        "    Energy_H_t.append(sol)\n",
        "print(\"Computed Energy:\", Energy_H_t[-1])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1ZwDffXfJjxs"
      },
      "outputs": [],
      "source": [
        "#the list below is obtained from running the above code using ibmq_lima backend with ZNE.\n",
        "\n",
        "Energy = [(-15.299725496726987+0j), (-15.404457371901044+0j), (-15.432048634488877+0j), (-15.479413567324093+0j), (-15.484154453097942+0j), (-15.498274731551897+0j), (-15.502134849652316+0j), (-15.501013354303835+0j), (-15.519383560872486+0j), (-15.525552730938573+0j), (-15.554337105185438+0j), (-15.554400483338556+0j), (-15.551891864562178+0j), (-15.545635016923596+0j), (-15.555698525879142+0j), (-15.551595355187027+0j), (-15.550354849219326+0j), (-15.551810351294685+0j), (-15.551651191275324+0j), (-15.54715839405482+0j), (-15.551579926022692+0j), (-15.549270670410346+0j), (-15.550742270040319+0j), (-15.558344780907598+0j), (-15.549046655882846+0j), (-15.554513011088916+0j), (-15.552365255003002+0j), (-15.552115439722515+0j), (-15.552561179281044+0j), (-15.548556478987896+0j), (-15.548150337736507+0j), (-15.550477227254524+0j), (-15.552545202356784+0j), (-15.549357297389344+0j), (-15.553080711408695+0j), (-15.553468837096995+0j), (-15.550786010522367+0j), (-15.550639970088818+0j), (-15.551100054992032+0j), (-15.551329759565471+0j), (-15.547600770146323+0j), (-15.5489985182846+0j), (-15.55645182159987+0j), (-15.55738365191599+0j), (-15.551482890586493+0j), (-15.551267266507073+0j), (-15.553622111797393+0j), (-15.553782805606561+0j), (-15.55176306113025+0j), (-15.550018243753359+0j)]\n",
        "\n",
        "Target_E = -15.561651427447183\n",
        "\n",
        "E = []\n",
        "for i in range(len(Energy)):\n",
        "    E.append(np.real(Energy[i]))\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "oxRIoJxUJjxs",
        "outputId": "06ca8d2c-a552-4fcf-99b9-0780314f4010"
      },
      "outputs": [
        {
          "data": {
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",
            "text/plain": [
              "<pyolite.display.Image at 0x3894850>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.rcParams[\"font.size\"] = 14\n",
        "\n",
        "# plot loss and reference value\n",
        "plt.figure(figsize=(12, 6), facecolor='white')\n",
        "plt.plot(E, label=\"Estimator VQE BeH2+ibmq_lima+ZNE\")\n",
        "plt.axhline(y=Target_E, color=\"tab:red\", ls=\"--\", label=\"Target d = 1.291 Angstroms\")\n",
        "\n",
        "plt.legend(loc=\"best\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Energy [H]\")\n",
        "plt.title(\"VQE energy\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xGuH0rOZJjxs"
      },
      "source": [
        "The results show that the qiskit runtime error mitigation works quite well."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TgDZZCf7Jjxt"
      },
      "source": [
        "We also use entanglement forging from circuit knitting toolbox to reduce the complexity of the problem while sacrificing chemical accuracy."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "A41yIGuQJjxt"
      },
      "outputs": [],
      "source": [
        "from qiskit_nature.drivers import Molecule\n",
        "from qiskit_nature.drivers.second_quantization import PySCFDriver\n",
        "from qiskit_nature.problems.second_quantization import ElectronicStructureProblem\n",
        "from qiskit_nature.transformers.second_quantization.electronic import ActiveSpaceTransformer\n",
        "molecule = Molecule(\n",
        "    geometry=[\n",
        "        (\"Be\",[0.0,0.0,0.0]),\n",
        "        (\"H\", [0.0, 0.0, -1.3]),\n",
        "        (\"H\", [0.0, 0.0, 1.3]),\n",
        "    ],\n",
        "    charge=0,\n",
        "    multiplicity=1,\n",
        ")\n",
        "driver = PySCFDriver.from_molecule(molecule=molecule, basis=\"sto3g\")\n",
        "\n",
        "\n",
        "transformer = ActiveSpaceTransformer(\n",
        "    num_electrons=6, # Number of electrons in our active space\n",
        "    num_molecular_orbitals=2, # Number of orbitals in our active space\n",
        ")\n",
        "problem = ElectronicStructureProblem(\n",
        "        driver,\n",
        "        [transformer])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "vn5P3xhdJjxt"
      },
      "outputs": [],
      "source": [
        "from circuit_knitting_toolbox.entanglement_forging import EntanglementForgingAnsatz\n",
        "from qiskit.circuit.library import TwoLocal\n",
        "\n",
        "ansatz = EntanglementForgingAnsatz(\n",
        "    circuit_u=TwoLocal(2, [], \"cry\", [[0, 1], [1,0]], reps=1),\n",
        "    bitstrings_u=[(0,1),(1,0)],\n",
        ")\n",
        "\n",
        "ansatz.circuit_u.draw()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zlWV3RCcJjxt"
      },
      "outputs": [],
      "source": [
        "from qiskit_ibm_runtime import QiskitRuntimeService, Options\n",
        "\n",
        "# By default, use a local simulator to implement the Qiskit Runtime Primitives\n",
        "service = None\n",
        "\n",
        "# Uncomment the following line to instead use the Qiskit Runtime Service.\n",
        "# service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
        "\n",
        "backend_names = [\"ibmq_qasm_simulator\"] * 4\n",
        "\n",
        "# If a single set of options are passed, it will be applied to all backends\n",
        "options = [Options(execution={\"shots\": 1000}), Options(execution={\"shots\": 2000}), Options(execution={\"shots\":2000}),Options(execution={\"shots\":1000})]\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LLw1DF7CJjxt"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "from qiskit.algorithms.optimizers import COBYLA\n",
        "from circuit_knitting_toolbox.entanglement_forging import (\n",
        "    EntanglementForgingGroundStateSolver,\n",
        ")\n",
        "\n",
        "optimizer = COBYLA(maxiter=50,tol = 1e-5)\n",
        "\n",
        "solver = EntanglementForgingGroundStateSolver(\n",
        "    ansatz=ansatz,\n",
        "    optimizer=optimizer,\n",
        "    service=service,\n",
        "    backend_names=backend_names,\n",
        "    options=options,\n",
        "    initial_point=[0.0, np.pi / 2],\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3bpdmb5rJjxt"
      },
      "outputs": [],
      "source": [
        "%%capture\n",
        "\n",
        "results = solver.solve(problem)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a4F378xlJjxt"
      },
      "source": [
        "The following results are obtained from running the above code. We also explored applying entanglement forging differently by a different choice of used bitstrings. The procedure is explained here. https://github.com/qiskit-community/prototype-entanglement-forging/blob/main/docs/3-explanatory_material/explanatory_material.md#picking-the-bitstrings"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ouPBjPgHJjxt"
      },
      "outputs": [],
      "source": [
        "eigenvalue = [-15.067677961867169, -14.43349358705019, -16.850469941463, -17.35366210680921, -15.923394623984477, -17.39183988919921, -15.819941135220622, -17.66749851343628, -16.604922689851417, -17.666004725250048, -16.603020233190847, -17.29859516235202, -17.72566408267279, -17.69888982692018, -17.725690220806747, -17.69877309532289, -17.707285219181852, -17.72692685156067, -17.72285154687804, -17.72692548497306, -17.722851428629223, -17.725553090234015, -17.727115720551243, -17.726972567291043, -17.72711573111239, -17.72697242358583, -17.72706287631097, -17.727111031352962, -17.727110299209098, -17.7271157340197, -17.72711597275354, -17.727114147285853, -17.72711598580272, -17.72711650046225, -17.727115718768687, -17.72711627160566, -17.727116501379225, -17.727116401603, -17.72711642982655, -17.727116506819804, -17.72711649203592, -17.727116506782636, -17.727116492007838, -17.727116501944796, -17.72711650735905, -17.72711650663199, -17.727116507358662, -17.727116506631813, -17.727116507025464]\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "HyL4U9dTJjxt",
        "outputId": "5ce7c689-cbef-418d-8c2b-c6a27fdf3e01"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Energy:\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<pyolite.display.Image at 0xc289e0>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "print(\"Energy:\")\n",
        "plt.plot(eigenvalue)\n",
        "plt.xlabel(\"Iterations\")\n",
        "plt.ylabel(\"Energy (Hartrees)\")\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rGZbuEAkJjxt"
      },
      "source": [
        "We also used orbital freezing through the following from IBM, problem = ElectronicStructureProblem(driver,[FreezeCoreTransformer(freeze_core=True, remove_orbitals=[-3,-2, -1])]) where we checked that excluding the orbitals we listed did not influence the chemical accuracy as much as excluding more orbitals.\n"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}