{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9f3b2367",
   "metadata": {},
   "source": [
    "Install qiskit\n",
    "and also matplotlib and pylatexenc (for nicer circuit plots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "57d23af3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: qiskit in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (2.2.1)\n",
      "Collecting qiskit_aer\n",
      "  Downloading qiskit_aer-0.17.2-cp313-cp313-macosx_10_13_x86_64.whl.metadata (8.3 kB)\n",
      "Requirement already satisfied: qiskit_ibm_runtime in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (0.42.0)\n",
      "Requirement already satisfied: matplotlib in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (3.10.6)\n",
      "Collecting pylatexenc\n",
      "  Using cached pylatexenc-2.10.tar.gz (162 kB)\n",
      "  Preparing metadata (setup.py) ... \u001b[?25ldone\n",
      "\u001b[?25hRequirement already satisfied: rustworkx>=0.15.0 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from qiskit) (0.17.1)\n",
      "Requirement already satisfied: numpy<3,>=1.17 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from qiskit) (2.3.3)\n",
      "Requirement already satisfied: scipy>=1.5 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from qiskit) (1.16.2)\n",
      "Requirement already satisfied: dill>=0.3 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from qiskit) (0.4.0)\n",
      "Requirement already satisfied: stevedore>=3.0.0 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from qiskit) (5.5.0)\n",
      "Requirement already satisfied: typing-extensions in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from qiskit) (4.15.0)\n",
      "Requirement already satisfied: psutil>=5 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from qiskit_aer) (7.1.0)\n",
      "Requirement already satisfied: python-dateutil>=2.8.0 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from qiskit_aer) (2.9.0.post0)\n",
      "Requirement already satisfied: requests>=2.19 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from qiskit_ibm_runtime) (2.32.5)\n",
      "Requirement already satisfied: requests-ntlm>=1.1.0 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from qiskit_ibm_runtime) (1.3.0)\n",
      "Requirement already satisfied: urllib3>=1.21.1 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from qiskit_ibm_runtime) (2.5.0)\n",
      "Requirement already satisfied: ibm-platform-services>=0.22.6 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from qiskit_ibm_runtime) (0.68.3)\n",
      "Requirement already satisfied: pydantic>=2.5.0 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from qiskit_ibm_runtime) (2.11.9)\n",
      "Requirement already satisfied: packaging in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from qiskit_ibm_runtime) (25.0)\n",
      "Requirement already satisfied: contourpy>=1.0.1 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from matplotlib) (1.3.3)\n",
      "Requirement already satisfied: cycler>=0.10 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from matplotlib) (0.12.1)\n",
      "Requirement already satisfied: fonttools>=4.22.0 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from matplotlib) (4.60.0)\n",
      "Requirement already satisfied: kiwisolver>=1.3.1 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from matplotlib) (1.4.9)\n",
      "Requirement already satisfied: pillow>=8 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from matplotlib) (11.3.0)\n",
      "Requirement already satisfied: pyparsing>=2.3.1 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from matplotlib) (3.2.5)\n",
      "Requirement already satisfied: ibm_cloud_sdk_core<4.0.0,>=3.24.2 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from ibm-platform-services>=0.22.6->qiskit_ibm_runtime) (3.24.2)\n",
      "Requirement already satisfied: PyJWT<3.0.0,>=2.10.1 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from ibm_cloud_sdk_core<4.0.0,>=3.24.2->ibm-platform-services>=0.22.6->qiskit_ibm_runtime) (2.10.1)\n",
      "Requirement already satisfied: six>=1.5 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from python-dateutil>=2.8.0->qiskit_aer) (1.17.0)\n",
      "Requirement already satisfied: charset_normalizer<4,>=2 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from requests>=2.19->qiskit_ibm_runtime) (3.4.3)\n",
      "Requirement already satisfied: idna<4,>=2.5 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from requests>=2.19->qiskit_ibm_runtime) (3.10)\n",
      "Requirement already satisfied: certifi>=2017.4.17 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from requests>=2.19->qiskit_ibm_runtime) (2025.8.3)\n",
      "Requirement already satisfied: annotated-types>=0.6.0 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from pydantic>=2.5.0->qiskit_ibm_runtime) (0.7.0)\n",
      "Requirement already satisfied: pydantic-core==2.33.2 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from pydantic>=2.5.0->qiskit_ibm_runtime) (2.33.2)\n",
      "Requirement already satisfied: typing-inspection>=0.4.0 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from pydantic>=2.5.0->qiskit_ibm_runtime) (0.4.1)\n",
      "Requirement already satisfied: cryptography>=1.3 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from requests-ntlm>=1.1.0->qiskit_ibm_runtime) (46.0.1)\n",
      "Requirement already satisfied: pyspnego>=0.4.0 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from requests-ntlm>=1.1.0->qiskit_ibm_runtime) (0.12.0)\n",
      "Requirement already satisfied: cffi>=2.0.0 in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from cryptography>=1.3->requests-ntlm>=1.1.0->qiskit_ibm_runtime) (2.0.0)\n",
      "Requirement already satisfied: pycparser in /opt/anaconda3/envs/qiskit_povm/lib/python3.13/site-packages (from cffi>=2.0.0->cryptography>=1.3->requests-ntlm>=1.1.0->qiskit_ibm_runtime) (2.23)\n",
      "Downloading qiskit_aer-0.17.2-cp313-cp313-macosx_10_13_x86_64.whl (2.5 MB)\n",
      "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m2.5/2.5 MB\u001b[0m \u001b[31m1.2 MB/s\u001b[0m  \u001b[33m0:00:02\u001b[0m eta \u001b[36m0:00:01\u001b[0m\n",
      "\u001b[?25hBuilding wheels for collected packages: pylatexenc\n",
      "\u001b[33m  DEPRECATION: Building 'pylatexenc' using the legacy setup.py bdist_wheel mechanism, which will be removed in a future version. pip 25.3 will enforce this behaviour change. A possible replacement is to use the standardized build interface by setting the `--use-pep517` option, (possibly combined with `--no-build-isolation`), or adding a `pyproject.toml` file to the source tree of 'pylatexenc'. Discussion can be found at https://github.com/pypa/pip/issues/6334\u001b[0m\u001b[33m\n",
      "\u001b[0m  Building wheel for pylatexenc (setup.py) ... \u001b[?25ldone\n",
      "\u001b[?25h  Created wheel for pylatexenc: filename=pylatexenc-2.10-py3-none-any.whl size=136896 sha256=1b7a087044a53e52f356b2da5adc9c6bb8e470405cb9000aedfdcda320339d25\n",
      "  Stored in directory: /Users/saraalvesdossantos/Library/Caches/pip/wheels/3c/d9/c1/bb2a15d13c742b9035ef7ae6ebe236af270b1d1d9b386dcd5e\n",
      "Successfully built pylatexenc\n",
      "Installing collected packages: pylatexenc, qiskit_aer\n",
      "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m2/2\u001b[0m [qiskit_aer]\n",
      "\u001b[1A\u001b[2KSuccessfully installed pylatexenc-2.10 qiskit_aer-0.17.2\n"
     ]
    }
   ],
   "source": [
    "!pip install qiskit qiskit_aer qiskit_ibm_runtime matplotlib pylatexenc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33b8652b",
   "metadata": {},
   "source": [
    "### Import Qiskit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9e16a55a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import qiskit\n",
    "import numpy as np\n",
    "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, transpile\n",
    "from qiskit_aer import QasmSimulator, StatevectorSimulator\n",
    "from qiskit.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb0b3c71",
   "metadata": {},
   "source": [
    "## Problem 1: A first quantum circuit in Qiskit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41b8c372",
   "metadata": {},
   "source": [
    "Initialise a simple circuit with 1 qubit and 1 classical bit for the output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e033a2f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Every quantum circuit is initialised with every qubit in |0>\n",
    "qc1a = QuantumCircuit(QuantumRegister(1), ClassicalRegister(1))\n",
    "# qc1a = QuantumCircuit(1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e5b56410",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x11c563b80>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# In Qiskit, standard gates are methods of the circuit object\n",
    "\n",
    "\n",
    "# TODO apply a single qubit gate to qubit 0\n",
    "\n",
    "qc1a.x(0)\n",
    "#qc1a.h(0)\n",
    "#qc1a.s(0)\n",
    "#qc1a.t(0)\n",
    "\n",
    "\n",
    "qc1a.measure(qubit=0, cbit=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ec639c1",
   "metadata": {},
   "source": [
    "we can also draw the circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "66079976",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 287.093x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc1a.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7e2d24e",
   "metadata": {},
   "source": [
    "Finially we run the circuit on a simulator (1000 times)\n",
    "and plot the measurement results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3ca4cddb",
   "metadata": {},
   "outputs": [],
   "source": [
    "simulator = QasmSimulator()\n",
    "results1a = simulator.run(qc1a, shots=1000).result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "729224e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram(results1a.get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a428675",
   "metadata": {},
   "source": [
    "#### Preparing Bell states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f6fe087a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 454.517x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Shortcut for QuantumCircuit(QuantumRegister(2), ClassicalRegister(2))\n",
    "qc1b = QuantumCircuit(2,2)\n",
    "\n",
    "\n",
    "# TODO prepare a Bell state\n",
    "# e.g. by doing a h gate on qubit 0 followed by a cnot on qubits 0 and 1\n",
    "\n",
    "qc1b.h(0)\n",
    "qc1b.cx(0,1)\n",
    "\n",
    "\n",
    "qc1b.measure([0,1], [0,1])\n",
    "# Shortcut:\n",
    "#qc1b.measure_all()\n",
    "\n",
    "qc1b.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b88dd0d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results1b = simulator.run(qc1b, shots=1000000).result()\n",
    "plot_histogram(results1b.get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7f2e321",
   "metadata": {},
   "source": [
    "## Problem 2: Use different simulators in Qiskit\n",
    "\n",
    "We are going to see how the use of different simulators affects the final result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "229b32e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_aer import QasmSimulator, StatevectorSimulator"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2db868a8",
   "metadata": {},
   "source": [
    "We'll use a fake backend from qiskit to simulate realistic noise without needing an IBM account.\n",
    "\n",
    "Fake backends provide realistic device configurations and noise models based on real IBM quantum devices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5c7cfac8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using fake backend: fake_manila\n",
      "Number of qubits: 5\n"
     ]
    }
   ],
   "source": [
    "# Use a fake backend instead of connecting to IBM\n",
    "from qiskit_aer.noise import NoiseModel\n",
    "from qiskit_ibm_runtime.fake_provider import FakeManilaV2\n",
    "\n",
    "# Create a fake backend (simulates IBM Manila quantum computer)\n",
    "fake_backend = FakeManilaV2()\n",
    "print(f\"Using fake backend: {fake_backend.name}\")\n",
    "print(f\"Number of qubits: {fake_backend.num_qubits}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82f4127c",
   "metadata": {},
   "source": [
    "Get the noise model from the fake backend\n",
    "\n",
    "This noise model approximates the real device's behavior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0fe61a9c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NoiseModel:\n",
      "  Basis gates: ['cx', 'delay', 'for_loop', 'id', 'if_else', 'measure', 'reset', 'rz', 'switch_case', 'sx', 'x']\n",
      "  Instructions with noise: ['sx', 'id', 'reset', 'measure', 'cx', 'x']\n",
      "  Qubits with noise: [0, 1, 2, 3, 4]\n",
      "  Specific qubit errors: [('sx', (0,)), ('sx', (1,)), ('sx', (2,)), ('sx', (3,)), ('sx', (4,)), ('id', (0,)), ('id', (1,)), ('id', (2,)), ('id', (3,)), ('id', (4,)), ('reset', (0,)), ('reset', (1,)), ('reset', (2,)), ('reset', (3,)), ('reset', (4,)), ('cx', (0, 1)), ('cx', (1, 0)), ('cx', (1, 2)), ('cx', (2, 1)), ('cx', (2, 3)), ('cx', (3, 2)), ('cx', (3, 4)), ('cx', (4, 3)), ('x', (0,)), ('x', (1,)), ('x', (2,)), ('x', (3,)), ('x', (4,)), ('measure', (0,)), ('measure', (1,)), ('measure', (2,)), ('measure', (3,)), ('measure', (4,))]\n"
     ]
    }
   ],
   "source": [
    "# Generate noise model from the fake backend\n",
    "noise_model = NoiseModel.from_backend(fake_backend)\n",
    "print(noise_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3accc60d",
   "metadata": {},
   "source": [
    "You can also try other fake backends like FakeLimaV2, FakeQuitoV2, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "dd803733",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Available fake backends:\n",
      "  - fake_algiers\n",
      "  - fake_almaden\n",
      "  - fake_armonk\n",
      "  - fake_athens\n",
      "  - fake_auckland\n",
      "  - fake_belem\n",
      "  - fake_boeblingen\n",
      "  - fake_bogota\n",
      "  - fake_brisbane\n",
      "  - fake_brooklyn\n",
      "  - fake_burlington\n",
      "  - fake_cairo\n",
      "  - fake_cambridge\n",
      "  - fake_casablanca\n",
      "  - fake_cusco\n",
      "  - fake_essex\n",
      "  - fake_fez\n",
      "  - fake_fractional\n",
      "  - fake_geneva\n",
      "  - fake_guadalupe\n",
      "  - fake_hanoi\n",
      "  - fake_jakarta\n",
      "  - fake_johannesburg\n",
      "  - fake_kawasaki\n",
      "  - fake_kolkata\n",
      "  - fake_kyiv\n",
      "  - fake_kyoto\n",
      "  - fake_lagos\n",
      "  - fake_lima\n",
      "  - fake_london\n",
      "  - fake_manhattan\n",
      "  - fake_manila\n",
      "  - fake_melbourne\n",
      "  - fake_marrakesh\n",
      "  - fake_montreal\n",
      "  - fake_mumbai\n",
      "  - fake_nairobi\n",
      "  - fake_osaka\n",
      "  - fake_oslo\n",
      "  - fake_ourense\n",
      "  - fake_paris\n",
      "  - fake_peekskill\n",
      "  - fake_perth\n",
      "  - fake_prague\n",
      "  - fake_poughkeepsie\n",
      "  - fake_quebec\n",
      "  - fake_quito\n",
      "  - fake_rochester\n",
      "  - fake_rome\n",
      "  - fake_santiago\n",
      "  - fake_sherbrooke\n",
      "  - fake_singapore\n",
      "  - fake_sydney\n",
      "  - fake_torino\n",
      "  - fake_toronto\n",
      "  - fake_valencia\n",
      "  - fake_vigo\n",
      "  - fake_washington\n",
      "  - fake_yorktown\n"
     ]
    }
   ],
   "source": [
    "# Optional: List available fake backends\n",
    "from qiskit_ibm_runtime.fake_provider import FakeProviderForBackendV2\n",
    "fake_provider = FakeProviderForBackendV2()\n",
    "print(\"Available fake backends:\")\n",
    "for backend in fake_provider.backends():\n",
    "    print(f\"  - {backend.name}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4b7ab2b",
   "metadata": {},
   "source": [
    "prepare the simulators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "68fa4385",
   "metadata": {},
   "outputs": [],
   "source": [
    "statevector_simulator = StatevectorSimulator()\n",
    "qasm_simulator        = QasmSimulator()\n",
    "noisy_qasm_simulator  = QasmSimulator(noise_model=noise_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0e1a3b70",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 454.719x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc2 = QuantumCircuit(4)\n",
    "\n",
    "\n",
    "# TODO implement a circuit that prepares 1/√2 (|0000⟩ + |1111⟩)\n",
    "\n",
    "qc2.h(0)\n",
    "qc2.cx(0,1)\n",
    "qc2.cx(0,2)\n",
    "qc2.cx(0,3)\n",
    "\n",
    "\n",
    "qc2.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4538e2f",
   "metadata": {},
   "source": [
    "If we use the statevector_simulator we can directly extract the coefficients in the computational basis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "8a8e01de",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statevector([0.70710678+0.j, 0.        +0.j, 0.        +0.j,\n",
      "             0.        +0.j, 0.        +0.j, 0.        +0.j,\n",
      "             0.        +0.j, 0.        +0.j, 0.        +0.j,\n",
      "             0.        +0.j, 0.        +0.j, 0.        +0.j,\n",
      "             0.        +0.j, 0.        +0.j, 0.        +0.j,\n",
      "             0.70710678+0.j],\n",
      "            dims=(2, 2, 2, 2))\n"
     ]
    }
   ],
   "source": [
    "# Statevector simulator is the exact state at the end of the circuit, then shots=1 by default\n",
    "results2 = statevector_simulator.run(qc2).result()\n",
    "results2.get_statevector()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f94d65a4",
   "metadata": {},
   "source": [
    "As we can see, we obtain the vector describing the state of the quantum computer.\n",
    "\n",
    "Now we add the missing measurements of the end of the circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "51c23e7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 914.831x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc2.measure_all()\n",
    "qc2.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "84229bb9",
   "metadata": {},
   "outputs": [],
   "source": [
    "results2 = qasm_simulator.run(qc2, shots=1000).result()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57489989",
   "metadata": {},
   "source": [
    "plot the result of 1000 runs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "eb85b1a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram(results2.get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a2ace08",
   "metadata": {},
   "source": [
    "and finally we run it using the simulated noise model from the device we selected"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6bd0675e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yZIlrcStWrFi6xyuJW7dunfu3fsYmdd793n2Z2bt3r7t5lAiKEkndJHfu3JYnTx6XcB46dCj6WG+7xvHFNoBqm+7LbLv3d09U7N/JlSuXpaWlufgUZ8btmcXu1z7pOSXjGMfMtufNmzfT2Nkn9ol9Yp/YJ/Ypu/cpOyRin3J0Yle9enWXxKnJ8b333rNbbrnFjafz07Bhw2zw4MGHbf/kk0/cJAxRy2C9evVs6dKlboJGbLxqOVywYIHr7vXUrVvXKlWqZLNnz7bt27dHtytp1aQO/e3sMHny5Oi/Cxcu7MYlrlmzxh1Dj7qwmzRpYitWrLDly5dHt/uxT7EnYPPmza1AgQLpYpTLLrvMdu/ebTNnzoxu05tA4yM3bdoUbYFln9gn9ol9Yp/YJz/3KTv4vU9z5swJ1xg7db2efvrpdu2111rLli3tjz/+SNdqp53u2bOnm1ihSRITJ05Md4BXrlxpVatWtS+//NId0Ky22FWoUMGdmF5/th9XD9UeOPHkbsVDrQN/RRTGqzz2iX1in9gn9inn71OV/umT1ePx0yNtfd2nzZs3u2ogWRljF8gWu4y080q6GjRo4E6W6dOnuzInokxYWa8yctHPhx9+2DZs2OAydJk2bZo7EOrOzUy+fPncLSM9n26xdKB1yyizZt3Mtmf8u8cr3t/RiaBbRpnF7vc+Hcv2zGJnn9inI21nn9gn9ol9SsR3bjzJ2qe4j7WA6d+/v7Vt29Y1V6opVTNgZ82aZVOnTnUzQrp06WK9e/d2M2WVrPXo0cMlc5oRK61bt3YJ3E033WQjRoxw4+oGDBjgat/FS9wAAADCInCJnVrabr75Zvvtt99cIqdixUrqLrnkEnf/yJEjXVasFju14mnG6wsvvBD9/8qAJ02aZN26dXMJX6FChdwYvSFDhiRxrwAAAPyXI8bYJQN17AAACL/KOeB7ODR17AAAAJB1JHYAAAAhQWIHAAAQEiR2AAAAIUFiBwAAEBIkdgAAACFBYgcAABASJHYAAAAhQWIHAAAQEiR2AAAAIUFiBwAAEBIkdgAAACFBYgcAABASJHYAAAAhQWIHAAAQEiR2AAAAIUFiBwAAEBIkdgAAACFBYgcAABASJHYAAAAhQWIHAAAQEiR2AAAAIUFiBwAAkOqJ3ezZs2316tVHfMyaNWvc4wAAABDgxK558+Y2evToIz7mzTffdI8DAABAgBO7SCRy1MccOnTIcuXKdbxPAQAAgKCMsVuxYoUVLVrUz6cAAADA/0mzY3Dbbbel+33ChAm2atWqwx538ODB6Pi6tm3bHstTAAAAIBGJXeyYOnWxLlmyxN3i0f0NGza0kSNHHm9sAAAA8CuxW7lyZXR8XdWqVa1nz552zz33HPa4PHnyWPHixa1QoULH8ucBAACQqMSuUqVK0X+PGjXK6tWrl24bAAAAckhiF+uWW27J3kgAAACQnMTOs2DBAlu4cKFt2bLFTZqIN9bugQceONGnAQAAgF+J3ebNm61Dhw42Z86cI9a0I7EDAAAIeGLXu3dv+/zzz61Zs2auW7Z8+fKWlnbCDYAAAAA4TsediU2aNMkaNWpk06dPZ3UJAACAnLzyxO7du61p06YkdQAAADk9satbt27cVScAAACQwxK7QYMG2cSJE23+/PnZGxEAAAASO8Zu3bp11q5dO7v44outU6dOVr9+fStSpEjcx958883H+zQAAADwO7G79dZb3fg6lTrRGrK6ZRxvp/u0jcQOAAAgwImdlhQDAABAcLCkGAAAQKpPngAAAEBIWuxWr16d5cdWrFjxeJ8GAAAAfid2lStXzlJxYj3mwIEDx/s0AAAA8Dux00zXeInd1q1b7euvv7aVK1e6UihKAAEAABDgxE7lTTKjMidPPPGEjRgxwl577bXjfQoAAAAke/KEWvLuu+8+O+uss6xPnz5+PAUAAAASOSv23HPPtRkzZvj5FAAAAEhEYvfjjz8ycQIAACDoY+wyc+jQIfv111/dGLwPPvjAWrZsmd1PAQAAgOxM7HLnzn3EcieaQFG8eHE3iQIAAAABTuyaNm0aN7FTwqeErmHDhta5c2crXbr0icYIAAAAPxO7WbNmHe9/BQAAgA9YKxYAACAksmXyxJw5c2zJkiW2bds2K1KkiNWtW9cuuOCC7PjTAAAASERiN3fuXDeO7ocffohOmPDG3VWrVs1GjRpljRs3PpGnAAAAgN+J3bfffmutW7e2Xbt22SWXXGLNmze3U0891datW2czZ860Tz75xNq0aWPz58+3WrVqHe/TAAAAwO/EbsiQIbZv3z6bPHmyXXrppenu69u3r02ZMsX+9Kc/uceNHTv2eJ8GAAAAfk+e0KzYq6666rCkzqPtul+tdwAAAAhwYrd161arUqXKER+j+/U4AAAABDixK1eunBs/dyRffPGFexwAAAACnNhp/Jy6Yx944AHbs2dPuvv0+6BBg1w3bPv27bMjTgAAAPg1eUIJ3aRJk+yRRx6xl19+2Ro1amRlypSx9evX28KFC23jxo1WtWpV9zgAAAAEOLErWbKk64q9//773axXzY715M+f39W3e/TRR61EiRLZFSsAAAD8KlB8yimn2Ouvv+5a7L7//vvoyhM1atSwvHnznsifBgAAgN+J3cMPP2w7d+60wYMHR5M3/Tz77LOjj1F9u7/97W9WuHBh69ev37E+BQAAAPyePPHpp5/awIEDXTfskVrkTjrpJPcYJXfUsQMAAAhgYvfmm29a8eLF7a677jrqY7t37+7G12m9WAAAAAQssZs7d661atXK8uXLd9TH6jF67Jw5c04kPgAAAPiR2K1du9aVMMkqrTzx22+/HctTAAAAIBGJXe7cuW3//v1Zfrweq/8DAAAA/x1T1qXlwb755pssP16PPe20044nLgAAAPiZ2F100UU2Y8YMW7Vq1VEfq8fosU2bNj3WmAAAAOB3YqeZrupeveqqq2zTpk2ZPu7333+3q6++2g4cOGDdunU7poCGDRtmDRs2dDXwSpcubR06dLDly5cfthatYlFJlZNPPtk6duzoljKLtXr1amvXrp0VLFjQ/Z0+ffq4eAAAAMLqmBK7+vXrW8+ePe3LL7+0WrVquZp2qlO3YsUKd5s1a5ZbG1b3LV682Hr16uX+z7H47LPPXNKm5cqmTZvmEsnWrVu7osge/d0PP/zQxo0b5x6vSR1XXnll9P6DBw+6pE6FkjWT94033rDRo0e7eAEAAMIqVyQSiRzLf9DDVXj4scces0OHDsW9P0+ePG4N2aFDh1quXLlOKMCNGze6FjclcOrW3bp1q5UqVcrGjBnjWg5Fy5nVrFnT5s2bZ+eff759/PHHdvnll7uEr0yZMu4xL730kvXt29f9PRVQPhotj1a0aFH3fFomzS+V+310wn9j1fB22RILAACppnIO+B4+lpzkmJcUU6L2yCOPWJcuXVzxYbWIrVu3zt1XtmxZu+CCC+zWW2+1008/3bKDdkJU7FjUEqhWPNXI82ht2ooVK0YTO/3UEmdeUidt2rRx3cLffvut1atX77Dn2bt3r7vFHkTRc3kzgTXDV0mrWgRjk1pvu7p6Y/NkbdN9mW0/lhnGRxL7d/T6pKWlufgUZ8btmcXu1z7pOSVjN3hm27WiSWaxs0/sE/vEPrFP7FN271N2SMQ+ZdVx75USN7XI+Uk7ra5fJYu1a9d225REqsWtWLFi6R6rJM5LMPUzNqnz7vfuy2xsn9a/zeiTTz5x4/REyaOSwqVLl7oxfJ7q1au75HLBggWuRdBTt25dq1Spks2ePdu2b98e3d64cWPXCqm/nR0mT54c/bfGJrZo0cLWrFljS5YsiW5XK2eTJk1cl3nsmEU/9in2BGzevLkVKFAgXYxy2WWX2e7du9MtOac3gbrQNX5TyTn7xD6xT+wT+8Q++b1P2cHvfTqWxR6OuSs2kdTCpm7Vzz//3MqXL++2qQu2c+fO6VrXpFGjRu5FevTRR61r1672888/29SpU6P379q1ywoVKuROyrZt22apxa5ChQruxPSaPf24eqj2wIkndyseah34K6IwXuWxT+wT+8Q+sU85f5+q9E+frB6Pnx5p6+s+bd682U0Y9aUrNlG0Hu2kSZNc5u0ldV53ryZFbNmyJV2rnWbF6j7vMcp6Y3mzZr3HxFsCLd5SaTo5dYulA61bRpk162a2PePfPV7x/o5OhHjFoTOL3e99OpbtmcXOPrFPR9rOPrFP7BP7lIjv3HiStU9xY7GAUaaqpG78+PGuDp6WJYvVoEED9+JMnz49uk3NnGrSVHOr6OeyZctsw4YN0cdohq2yXM3YBQAACKPAtdip1Im6Wz/44APXH++NidNsEPWF66cmbvTu3dtNqFCy1qNHD5fMaeKEqDyKEribbrrJRowY4f7GgAED3N+O1yoHAAAQBoFL7F588UX3s1mzZum2awauZtvKyJEjXZOnChNrXJxmvL7wwgvRx6p5U924GqOnhE9j62655RYbMmRIgvcGAAAghRO7rMzlyJ8/vz3//PPulhnNIsk4ewcAACDMAjfGDgAAAMeHxA4AACAkSOwAAABCgsQOAAAgJEjsAAAAQoLEDgAAICRI7AAAAEKCxA4AACAkSOwAAABCgsQOAAAgJEjsAAAAQoLEDgAAICRI7AAAAEKCxA4AACAkSOwAAABCgsQOAAAgJEjsAAAAQoLEDgAAICRI7AAAAEKCxA4AACAkSOwAAABCgsQOAAAgJEjsAAAAQoLEDgAAICRI7AAAAEKCxA4AACAkSOwAAABCgsQOAAAgJEjsAAAAQoLEDgAAICRI7AAAAEKCxA4AACAkSOwAAABCgsQOAAAgJEjsAAAAQoLEDgAAICRI7AAAAEKCxA4AACAkSOwAAABCgsQOAAAgJEjsAAAAQoLEDgAAICRI7AAAAEKCxA4AACAkSOwAAABCgsQOAAAgJEjsAAAAQoLEDgAAICRI7AAAAEKCxA4AACAkSOwAAABCgsQOAAAgJEjsAAAAQoLEDgAAICRI7AAAAEKCxA4AACAkSOwAAABCgsQOAAAgJEjsAAAAQoLEDgAAICRI7AAAAEKCxA4AACAkSOwAAABCgsQOAAAgJEjsAAAAQoLEDgAAICRI7AAAAEKCxA4AACAkSOwAAABCgsQOAAAgJEjsAAAAQoLEDgAAICRI7AAAAEKCxA4AACAkApfYzZ4926644gorV66c5cqVyyZMmJDu/kgkYgMHDrRTTz3VChQoYK1atbIVK1ake8zmzZutU6dOVqRIEStWrJh16dLFduzYkeA9AQAASPHEbufOnXbOOefY888/H/f+ESNG2DPPPGMvvfSSffHFF1aoUCFr06aN7dmzJ/oYJXXffvutTZs2zSZNmuSSxa5duyZwLwAAABIvzQKmbdu27haPWuueeuopGzBggLVv395te/PNN61MmTKuZe+6666z//znPzZlyhRbuHChnXvuue4xzz77rF122WX2+OOPu5ZAAACAMApci92RrFy50tatW+e6Xz1Fixa18847z+bNm+d+1091v3pJnejxuXPndi18AAAAYRW4FrsjUVInaqGLpd+9+/SzdOnS6e5PS0uzEiVKRB8Tz969e93Ns23bNvdz//797iZKDvPkyWMHDx60Q4cORR/rbT9w4IBrVfRom+7LbLv3d09U7N/RuETtr+JTnBm3Zxa7X/uk5xQ9Pivb8+bNm2ns7BP7xD6xT+wT+5Td+5QdErFPoUzs/DRs2DAbPHjwYds/+eQTK1iwoPt3xYoVrV69erZ06VJbvXp19DHVq1e3GjVq2IIFC2zjxo3R7XXr1rVKlSq5MX7bt2+Pbm/cuLFLPvW3s8PkyZOj/y5cuLC1aNHC1qxZY0uWLIluL1WqlDVp0sRNNFm+fHl0ux/7FHsCNm/e3E1yiY1R1DW+e/dumzlzZnSb3gTt2rWzTZs2RVtg2Sf2iX1in9gn9snPfcoOfu/TnDlzshxLrkhsahgwynjHjx9vHTp0cL//9NNPdvrpp9tXX33ldtZz8cUXu9+ffvppe/311+3ee++1P/74I3q/Xsj8+fPbuHHj7M9//nOWW+wqVKjgTkzNrvXr6qHaAyee3K14qHXgr4jCeJXHPrFP7BP7xD7l/H2q0j99sno8fnqkra/7pGofJUuWtK1bt0ZzklC02FWpUsXKli1r06dPjyZ2SsA0dq5bt27RzHzLli22ePFia9Cggds2Y8YMdwA1Fi8z+fLlc7eMdHLqFksHWreMMmvWzWx7xr97vOL9HZ0IumWUWex+79OxbM8sdvaJfTrSdvaJfWKf2KdEfOfGk6x9ivtYCxjVm/vhhx/STZhQ86bGyKkJs2fPnjZ06FCrVq2aS/QeeOABN9PVa9WrWbOmXXrppXb77be7kijK0O+66y43Y5YZsQAAIMwCl9gtWrTI9Xt7evfu7X7ecsstNnr0aLv//vtdrTvVpVPL3IUXXujKm6ir1fP222+7ZK5ly5Yug+7YsaOrfQcAABBmgR5jl0zq4lUplaz0Z5+Iyv0+OuG/sWp4u2yJBQCAVFM5B3wPH0tOkqPq2AEAACBzJHYAAAAhQWIHAAAQEiR2AAAAIUFiBwAAEBIkdgAAACFBYgcAABASJHYAAAAhQWIHAAAQEiR2AAAAIUFiBwAAEBIkdgAAACFBYgcAABASJHYAAAAhQWIHAAAQEiR2AAAAIUFiBwAAEBIkdgAAACFBYgfkAA8++KDlypUr3a1GjRqHPS4SiVjbtm3d/RMmTEhKrACA5ElL4nMDOAZnnXWWffrpp9Hf09IOf/s+9dRTLqkDAKQmEjsgh1AiV7Zs2UzvX7JkiT3xxBO2aNEiO/XUUxMaGwAgGOiKBXKIFStWWLly5axq1arWqVMnW716dfS+Xbt22Q033GDPP//8EZM/AEC4kdgBOcB5551no0ePtilTptiLL75oK1eutIsuusi2b9/u7u/Vq5c1adLE2rdvn+xQAQBJRFcskANoQoSnTp06LtGrVKmSvfvuu1aqVCmbMWOGffXVV0mNEQCQfLTYATlQsWLF7Mwzz7QffvjBJXU//vij26ZxeN6kio4dO1qzZs2SHSoAIIFosQNyoB07drhk7qabbrJrrrnG/vKXv6S7/+yzz7aRI0faFVdckbQYAQCJR2IH5AD33XefS9LU/bp27VobNGiQ5cmTx66//nrXFRtvwkTFihWtSpUqSYkXAJAcJHZADvDLL7+4JO733393idyFF15o8+fPd/8GAMBDYgfkAGPHjj2mx2sFCgBA6mHyBAAAQEiQ2AEAAIQEiR0AAEBIkNgBAACEBJMngICr3O+jbPk7q4a3y5a/AwAILlrsAAAAQoLEDgAAICRI7AAAAEKCxA4AACAkSOwAAABCgsQOAAAgJEjsAAAAQoLEDgAAICRI7AAAAEKCxA4AACAkSOwAAABCgsQOABBaw4YNs4YNG1rhwoWtdOnS1qFDB1u+fHncx0YiEWvbtq3lypXLJkyYkPBYgexAYgcACK3PPvvMunfvbvPnz7dp06bZ/v37rXXr1rZz587DHvvUU0+5pA7IydKSHQAAAH6ZMmVKut9Hjx7tWu4WL15sTZs2jW5fsmSJPfHEE7Zo0SI79dRTkxApkD1osQMApIytW7e6nyVKlIhu27Vrl91www32/PPPW9myZZMYHXDiSOwAACnh0KFD1rNnT7vgggusdu3a0e29evWyJk2aWPv27ZMaH5Ad6IoFAKQEjbX75ptv7PPPP49umzhxos2YMcO++uqrpMYGZBda7AAAoXfXXXfZpEmTbObMmVa+fPnodiV1P/74oxUrVszS0tLcTTp27GjNmjVLYsTA8aHFDgAQWiph0qNHDxs/frzNmjXLqlSpku7+fv362V/+8pd0284++2wbOXKkXXHFFQmOFjhxtNgBAELd/frWW2/ZmDFjXC27devWudvu3bvd/ZosofF2sTepWLHiYUkgst/s2bNdAl2uXLm49QNvvfVWtz32dumllyYt3pyAxA5ZfoM9+OCDVqNGDStUqJAVL17cWrVqZV988UXoYwGQc7344otuJqy6VVXGxLu98847lqqO9vka64477nCPUY0/P6ie4DnnnONmJGdGidxvv/0Wvf3zn//0JZawoCsWh73BbrvtNrvyyisPu//MM8+05557zqpWrequdtVVoUKfP/zwg5UqVSq0sQDI2V2xifg/OcnRPl896r5WYWclgH7RSh+6HUm+fPkoQ3MMSOyQ5TeY6jzFevLJJ+21116zpUuXWsuWLUMbCwCESVaSqV9//dWNTZw6daq1a9cuYbHFo7GRKiqt3pkWLVrY0KFDrWTJkkmNKcjoisVx2bdvn73yyitWtGhRd+VHLEhlR+vaUgvQwIEDXRdggQIF3NCBFStWJC1e4Gj1/m666Sbr06ePnXXWWUmNRd2wb775pk2fPt0effRRt0ScktKDBw8mNa4gI7HDMVG5gJNPPtny58/vuj+19uIpp5yS8rEgtR1tnNCIESPsmWeesZdeesmNBdXY0DZt2tiePXsSHitwNEqgVPbl7rvvTnYodt1119mf/vQnN1O5Q4cO7nN/4cKFrhUP8dEVi2PSvHlzt6bipk2b7NVXX7VrrrnGfVGpmTyVY0FqO1LXllrrNPB8wIAB0ZUN1AJRpkwZ17KnLy74o3K/j074b6wantxuyETTGrpPP/20ffnll671OWg0rloX8BpPzbCb+GixwzFRS8MZZ5xh559/vhvTpqs6/Uz1WIDMrFy50pXXUPerR8MGzjvvPJs3b15SYwMy+ve//20bNmxw5V68gs0///yz3XvvvVa5cuVkh2e//PKL/f77725YA+IjscMJj8XYu3evBUGQYgE8SupELXSx9Lt3n580CP7GG290g801vk9dWosWLfL9eZEzaWydJqGpN8S7aeyoxttpIkV227FjR/R5vAsh/Xv16tXuPj2vZuauWrXKjbNTq7cu6DWUAfHRFYsovYnUvO3x3mAlSpRwXwoPP/ywG+ugKyV1f2o8kb40rr766lDHAuRUf/zxh1vwXsMWPv74Y1cKSJM2NLsQqetIn69qqcs44zRv3ryu3Ej16tWzPRZdZOj89PTu3dv9vOWWW1wNQiWZb7zxhm3ZssUlmCpr9dBDD7kSKIiPxA5ZeoNp0Pf333/v3mBKpPTGb9iwoWu292PWVJBiwbEZPny49e/f3+655x7fiprmJF79rfXr16frPtLvdevW9X0QfIUKFWzUqFHRbaymEBxKXHRTa5To80uzp49WisTPz9fRo0dbIqlw9JHqBvrRShh2JHbI8hvs/fffT8lYkHWarfbyyy9bnTp1kh1KYCiRUnKnbiQvkdu2bZub6NOtWzdfn3vixImuy0ot2SoTcdppp9mdd95pt99+uyXasGHD3PtWF2XqEm7SpIlLPP1oBcopypcv7y6EqlWr5j7vdLGqrsavvvrK14vUo32+ZuQlnsgZGGMH+LgcT6p173Tq1MnNUE5WV1+yXpsjjRNSHD179nRFVZVoLVu2zG6++WYXo8o3+Omnn35yLUJKHNTyoURSJSyUQCSaEkut26rxUipNtH//ftetplIxqUrn6mWXXeZeH62moyEmKuGkYwQcL1rsAJ+W40k1+tJWhXrN/lQSk0qvzdG6tu6//34XW9euXd1YoQsvvNCmTJniajD6PaHo3HPPtUceecT9Xq9ePfvmm2/ccAbFlkja31g6LipNpPIaTZs2tVSngrvjxo1z50njxo0t7LKjFE0qlqPJChI7wIfleFLN2LFjXd0rdcWm4mtztK4ttdoNGTLE3RJJY/pq1aqVblvNmjXtX//6lyXb1q1b3U8N2E9lasFVIqdi1Wqt0/qsGV+z7ERtv/AjsUPg3uxBigVHt2bNGjdRQt1rfrdA4dhoRuzy5cvTbfvvf/9rlSpVsmRSS6K6pxVf7dq1LZVpjKG67ZXovvfee64lVd3WfiZ3CDcSOwAnRF1pKmhav379dN1KGu/23HPPudqCefLkSWqMqapXr15ukoK6YrUyy4IFC9y6yrolu9teXcKff/65pbqTTjrJ1WWTBg0auFZvrfygSUjA8SCxA3BCtKyPupNide7c2WrUqGF9+/YlqUsilQFS157Kz6gbWDN0VYJGk1yS5a677nLrfSrx16xQpEehdZwoEjsAJ6Rw4cKHdadpuTfVF0yFbragDx24/PLL3S3ZNAaxR48eLtHUAu7U0zOXcGtMqIoCb9++3caMGeOODbXbcCJI7AAACel+VeLywQcfuIsBbzk1rZurunapSEMYVPrmt99+c8dB9R+V1F1yySXJDg05GIkdkM3L8cBcq0My8NoEl+rpeTOIY2lVjFtvvdVS0WuvvZbsEBBCJHZADl6OB+ml8msT9C7hY1npAMDxC/XKE1oYvnLlyq4Ew3nnnedmhAHZVbMs4y3siUNOwGsDINWFtsXunXfecVfrqrCupE4zwbRmomo6qdo5gPC1CgFAqgttYvfkk0+6ha5VdkGU4H300Uf2+uuvW79+/ZIdHgCEFhcA6bF8FhIplIndvn37XNFUTSX35M6d261hOW/evLj/R3WDYmsHecvdbN682S1W7f0N1eRS8VXVGor929p+4MCBdONItE33ZbZdf/fQ3l0nvL+///57uqWL0tLSXHyKM+P2zGLPjji2bdsWPVYePafoGGRle968ebMtlhN9neoNnXHCcXw1oMX/7lMmr0dWXqfsOB7eeRJ77h3P65Sd5+uJvJ/qPjQ9W16bWMf9OmXDMdHnTGafEVl9nfx+3xzL65QdsXifwXE/I7L4OmXX+ZqVz3K/3zdeLEf7LD/a65Td3zlH/Cw/wuuUncfEc7yv06FsiEVrQB/Ld+6xfu7pMyLLY1UjIfTrr79qzyNz585Nt71Pnz6RRo0axf0/gwYNcv+HGzdu3Lhx48bNAnhbs2bNUXOgULbYHQ+17nkz6ESZtDJkFVlV5p0MunquUKGCW4uzSJEiSYkhaLEEJY4gxUIcwY0lKHEEKZagxBGkWIISR5BiIY701FKnItblypWzowllYnfKKae45sv169en267fy5YtG/f/5MuXz91iFStWzIJAJ1Oy3+xBiyUocQQpFuIIbixBiSNIsQQljiDFEpQ4ghQLcfx/KmKdsuVOtKiyFlOePn16uhY4/d64ceOkxgYAAOCXULbYibpVVZT03HPPtUaNGrlyJzt37ozOkgUAAAib0CZ21157rW3cuNEGDhzo1iSsW7euTZkyxcqUKWM5hbqGBw0adFgXcSrHEpQ4ghQLcQQ3lqDEEaRYghJHkGIJShxBioU4jl8uzaA4gf8PAACAgAjlGDsAAIBURGIHAAAQEiR2AAAAIUFiBwAAEBIkdgAAACFBYpeDxC4YnMpiJ3JzTP4Xx+RwHAcAqYjELgc4ePCg+5k7d+7ol3gyvrSC8kWptXtVbDr2mEgyKvdwTIJ7THQcfv/99+jvyars5L1/g8I7DvpJtatg4nXBiaCOXYBt2rTJ3n//ffv2229txYoVbpm0Tp06WY0aNZIal3fKKJmId1+87dll1apV9s4779jcuXPtxx9/tAsuuMA6dOhgzZs3t/z581uyeF+SsUlV7H0ck8Qek2+++cbeeust++STT2zt2rV23nnnWdu2ba1ly5ZWrVq1hMSQWcIb73gkkvZ7x44dVrhw4cO2J/p4JPtYeIm31hYPgl27drmb1jtPZlxBOib6HtRFq9Zu37t3rxUvXtzy5s2b8DgOHDhgaWk5Y00HErsAa9++vUvqqlSpYhUqVLAvvvjC/vOf/1idOnWsX79+dvXVVyfszffmm2+6hFLPHZss6MNZXwaJ+kJo0aKFa4XRUnFly5a1WbNm2aJFi+zUU0+1Pn362B133JGwYzJ8+HB3PC6++GIrVKhQug9FfWFxTJJ3TJTI6UO4TZs2Vrp0abfqzNSpU+3kk092x2PAgAGukrzfyczdd99tDRs2tD/96U/pFvDW8dDzJjqxmTlzpo0aNcq+//57l9zp+HTs2NEuvPBCS5bMEt4jXUAmMo5Eee+992z06NH21VdfuX2/6KKL3Hmj97fey8mQ7GPy97//3Z2vS5YscTForXddsOqY6D2ejAuSg//XAh+UxDcuJXYInunTp0dKliwZ+emnn9zv27dvj/z222+RqVOnRm666aZIjRo1Iq+++mpCYvn3v/8dyZ07d6RVq1aR7t27R0aPHh35z3/+k+4xe/bsiQwZMiSydu1a3+KYMWOGOyabNm1yvx86dMj9XL58eeS+++6LVKhQIdKvX79Ioo5Jrly5Iueff37k8ssvd/s+b968dI/ZtWtXpEePHpGff/7Ztzg4JoebOXNm5JRTTons3Lkz3fa9e/dGnn766Uj58uUjV199dWT37t2RRByP2rVrR84+++xIly5dIh9//PFhx6Nz586Rb7/9NuK3zz//PFKzZs1I06ZNI8OHD4/07ds3cs4557j3dv369SMTJ06MJMJ3333nzkkdnwMHDqS7T79757Dfvvrqq8gNN9wQ+fDDDyP79+9PWhzy2WefRapUqRK56qqrIu+8807kueeeizRr1sy9Nqeffnrk9ddfT7ljovfxaaedFrn77rsjCxYsiEyYMCFy3XXXRU499VR3e+SRRxISz7x58yIXXnhh5M0333SfIbF0jA4ePOji+P333xN6fI6ExC6gBg4c6BKpeDZu3Og+GAsVKhRZunSp77Hcc889kYYNG0Z69+4dufjiiyP16tWLtG3b1n0xjB8/PvLLL7+4k19fYkpA/fLoo49GGjduHH1zeW8o2bdvX+TFF1+MFC5c2H1h+K1Pnz6Riy66KPLEE09EbrnlFvdvxXbNNddEnn32WZdYzZ8/3x2Tbdu2+RYHx+Rwzz//vDtHvWRXx0bHwvPRRx+5ZFhfXn7661//GmnZsmVkzJgxkUGDBkUuvfRSl1jpvaT3zuLFi90Xlt/Hw3PllVe65DKWzpeFCxdGOnXq5BKI999/3/c4br75ZvfZpfOjY8eO7nxZtmxZusfMnTs30rVrV1+/KBVH/vz5I3Xq1Ik0aNAg0qtXL/e8sebMmRO59tprD0tAs5sSuttvvz3uZ70u0EqVKhUZOXJkxG9BOiZK4nQOZKT3so6F3sP6bkrEMcmbN2+kUqVKkRIlSrjXSg0sGS+a2rRpc1gynCx0xQbUv//9b7vqqqvsH//4h7Vu3fqw+/ft2+fGDP35z3+2u+66y9dYbrrpJjfmY+TIkW6Mg7q1PvroI1u6dKlrqq9ataob06RuwE8//dS3ONQtrSb4Z5991q655pro9tim+CuuuMI10aurzU+33Xaba4p/9dVX3diL+fPn2+zZs+3LL790Y7rUXa1xkbVr17aPP/7Ytzg4Jof75ZdfrEmTJnb//fene2/EjunSMAYNcRgxYoRvcfTs2dO2b9/ujoeeV8Mo1M22YMECd0w2b95sP//8szVt2tS9n/ym7nGNMRw4cOBhx2Pr1q3WtWtXW7lypXttSpYs6Vsc9erVs1atWlmpUqVs8eLF7vVSHKeffrrrZrvkkkvsoYcess8++8y+++473+LQe0KfrTofNXRBt99++83KlCnjPlt1jjz55JMuDn2++UldrpUqVXLvY+/zXcfEG9N13333uaEEkydPdsNyUuGY3HzzzbZ//35744037KSTTrI9e/a4zxdvfN0zzzxjL774ok2YMMGqV6/uWxxNmzZ156TO2YULF7r3qo5LwYIF7corr3Tvm5deesl91n399dcWCMnOLBGfumh0pVCrVq3IY489FlmyZElkx44d0fu3bt3qmqn/9a9/+R6LrqYnT5582HZ1u7722mvuqlutDmoJ8ZOuENVqWLp06cidd94ZmTJlimv+9qxfv951s7333nsRv6lbXF0FGSmeSZMmuSvdRB4TXdFzTP5/V7S6Gk8++WTXSqahA7FDBFatWuW6qN99992In9R6rRbKeNsXLVrkWh0ScY549Hz6zPjhhx/iHjMN+6hWrZr7rPHLf//7X9fqP2rUKPf7li1bXOvH3/72N9d9f95557n7dVzU9eYX7Wu7du0iL7/8svtd3fbqhvz73//uWs4Uh4a7KI4PPvgg4re33nrLvYfVgpuxRdVruVNXbbzzKazHRJ9l+qxXr1Asr1VM34d6H8+ePdu3GH799VfXyu0Ne1JrobZpqJR61Ro1ahQpXry4OyaJGsqQFbTYBdjq1att2LBhNmPGDNdi1qhRI9cqpis5tYYsW7bM/vvf/yYkFl056UpJV/nelb53tT9p0iS78cYbbcuWLb7HoRZDXdV++OGH7qpWV68lSpSwIkWKuJYQxaCBtsmY/Rk7iUTxXX/99W6Aut80Y0xXrh988IE7JrryT/QxyTiA2TtPdIWdjGMimlH+z3/+07WKqeVDx0OD0NVqpkkUn3/+uSVSxmOk46EWELVEJMLGjRvdrHp9rlx33XWuBeKcc86Jzo4dP368ayVRK6OffvjhB3dunHnmmem2q1V33rx59sorr7jz9o8//vA1jvXr17v3jnocYul5NblE76mJEyf6/rmm80Jx/OUvf7Fp06bZ5ZdfHp3Vrpmgolnvut/v1yZIx0Sf9f3797fnn3/etSSq50gTfdSarOfX551a5P0+Jr///rubqZyxpVTxrVu3zp577jnXKp+I77+sIrHLAfSlrC5ZJXN6ufQm04neu3dvNwMxWbyERl3G27Zt87UbNiN9yCih1LHRG0rdBeqS7Nat22EfSommL60777zTdbW9++67CXtedaMpWfC+FPWhE4Rj4p0nyTgma9ascQmcuqx//fVX1+2nmaC6ENFFUrLoeAwaNMh9kb788ssJe15dCOrLWcdE3Vv6slKXkr7M1e156aWX2mOPPZbQGYY6FrFlJJTUaEb122+/bclMvBWHhg+MHTs2Ic+vCx7NilXipBIfen2UdCsunbsaajF48GBL9muTyGMi+pzXBZqG/ujiRF34mtGuc7Zz585uyEWyz5O0tDQ3qzkoSOwCRi1j+oDVyaxWBdWu05gUr3SEEhp9Sav1zO8p3l4sGlOg1g7FUblyZTfeQieyV+tI46k0RsfPcTmZfdCI92ZPpKOVq9D9upL0rrizm64glegrSdJzaEyMXp+zzjrL3a+EQa9TInixjBs3zrUU1qxZ08444wzXIqPfE3VMPDofJeN5oitsfSEE5RzRBYC+nDLWk0sEtfbrM0afJ7oI0GuoMYG6EFCilwx6b6t1RBetKq+keozJootFjZ969NFHXbmaRFLLpcZraUymLkx03nbv3t19FyTi/PV6ZzKeq7p4T+QxiU2gdOGuizMdD13A7t69243pVU3KZNaW27Fjh/Xo0cPuueceq1u3rgUFiV3AaJCsrk5Ue0utGzqRK1as6LpOdGUS+0WZjFiUVKo7TSeyuocTQVdqGVsm1eWoN32iC1XGiyXRNdrE67ZRoq2re702ep1Uj6xXr16uiy2ZsajLU3W49IWkhDMRVOfRq22V2XmSiCKj8eLQ88YOX0hkcV4lCnofq5tTCbe+gBSfJo/o3FVSl4jk0otDx0dfyLoI0UWA/q2LWO+YKNmNrYGYrMRbx8XvJFfd0urK0yQS72Lo/PPPd69PIhNsLw5N6lEM+pw/++yzXQIX27KthKpAgQIpUUMvq7VaE33BmCVJHuOHGKplpdIUGkytwd4aOKuB3hqkqUHPRYoUibzxxhuBiKVo0aKRf/zjH+6xfpYkWLFiRSQtLS1ywQUXuOfOWBZBz61yFl988cVhNYYSHYs3uNbvWPTaaGKApthrko1s3rw58swzz0TOOussV/tKZVBiS58kM5YRI0b4Hsv333/vBjDr3NRg54yDzL3zRAOc161bF/o4PCtXrnTlVVTKRLX7qlevHilWrJiblHXvvfemm2iT6Dg06Fz1/e6//343OSCWX+eKSuCoXEfG58pYo80r5eHnOfvjjz+68jcagK9abSqNo5qHqi2oiXMqQ5MI8eLQ66LahrfeeuthEzr8PCaa7KWJGbGlVPR8Xr040U/VTfXT+jhxeM8dy6uFGZT6dR4SuwAZOnSoKx7qiT2pNANINXv0htuwYUPKxPLggw9GKlasGLnjjjsiTZo0cV8IqhekAp6anSRr1qxxX6b6mQqxqO6XCmZ6MiaRmkWtGXRecWs/BSWWhx56yCWSSrgVjy48zjzzzMgDDzzgkgpv1q5em9WrV4c+Ds///M//uJmOseej4lBdPc3CLFu2rJt9mOw4VHA2Y20wPyhx0bHXa6K6i0rEM35xq3i2Zkz7XZNMnyNXXHFF5I8//ohu0+fICy+84Oow6sJas2X9drQ41KCQiDhEBfD1+qjAuGphxkvCdd7oc8XP5K57QOI4XiR2AaLSJZpOHluVXx8u3pelSgWocKSKzqZKLNdff32kZ8+e7oNGV44qdHvjjTe6Dxy1OqiwaocOHdy//RaUWD799NNI5cqV0xUd1mvjtZipJUirP6gyu9+CEku3bt3ciha60FDyoPIqKgOjFhB9QaqV9ZJLLvH9tQlKHB5dgCj59lqTY5MVJTHt27d356zfrQ5BiUOtULfddpsr8O4lT9r25JNPupZmGTx4sLsY8ZsuCvVc3oVzxtYhJVwq4qzEwc9jEpQ4RCVV9H5Ri7/eK3ny5HEX03q91LLoXWCr5TcV4jheJHYBom4CJVP60FfdsXhXAkqmvDpDYY9FH/66Uhw2bFi67UoWpk2b5pIFfRnoysrv5dWCFIuSJq1KUq5cucgrr7wSTaJiqTtHKzD4LQix6ItIQwYyPodalrX03T//+U931a3XRnUXwx5HLLUcnnvuuenev0qsvNdJ9bjOOOOMw7rbwhiHhpIoifGWhtLF6bhx41yNNn1Bq2VK92tFAyV6ftNzKIH0EgVRXN4xUj1B3a/lxlIhDq1gpFUdvM9Prcaieo8DBgyI1s9TEq5k3M9VOH4JSBwngsQuYNQapOValDRddtllrqti1qxZrtlXVxD60IktVJwqsUjsslAefVnqjZZxXdCwx6IvRBX81Qeuuv7UCqGCrnp9tJawEq1EvTZBiiXeOBjR8mGJPk+CEIfGaam7VUlVvCXUtMxbvnz5fI8nCHGoqLuKVeu8jKUiyUpelGyrZUqtM/EuULKbEqm6detGqlat6uLK6JtvvnFLWfn92gQlDv19jT3NOC5V7yM1NCj5VxFrv1+fnQGJ40QwKzaANmzY4JaOUV04FVddvny5m23YrFkzNwPxhhtuSIlYMps5GDvDsE+fPm6Zl1mzZvkWR1BjUekQ1SPTTc+rZW4UjwrPdunSxdq1a+drHEGJxauTd6TZc6r/NXfuXLcsU9jjiDfjsW/fvu41UUkilRG57LLL3HtZs1RVyy4RNbiCEofoddKs2IwzpK+99lr3mTdz5syExKH3Tb9+/VxdOL1ftHSVaglquS59jmhmqmqYpkocR6oXJypSrO8hlYNJtTiOBYldQKjumOrzaNq0ppNrurm+IH788Uc37V7T/1VeJBHlToISixeHCnXqNFU5jdhaedqm6uOnnXaa73WVghJLvARTJT1Uy0+vlVYxKFq0aELKRQQllqyUDtGXk2odenX+whxHPCohMn36dLeKjRJv1bHT+aukW8WadT6nUhyx71vvdVMpD62nqwRHKxz4zXtevU90HJQk6Lio9Ik+c7VKiOrGqXRQqsRxpLIien3at2/vCq5rjfSwx3EiSOwCQMuRjBo1ytUQ0hWkFjRWfSct2K3Fof0u/BvEWDLGUatWLatRo4a7ylfrT/ny5RMSR9BiydjiELtkV7IEJZastJilUhxqaVfxYb02ag3TkoRKsnVxptdKrTSJqEUZtDjUIqXkWrXiYj/PVI9MPROJaOmOJ7Yepgq+66IoleOIVzhZrb2NGzcmjqMgsUsyVVpXgU4Vcr399ttddW99AOmqdsWKFW5FgaefftoVE43XJBzGWI4Uh7pz1C0wcuRIF4ffBWeDEou+kOrXr+9aErSMTmyLT2yhVVWrV6LpZ8HZoMRypDhir7oVh1ob/FrxIihxeJQo3XHHHa5otM5JPacSKSUxrVu3duvTehcjfhZKDmoc5cqVcwWRFYeGlGipLq2vnAh6fhV7VzHxZApKHEGK5UBA4sgWSR7jl/KefvppN7U6nhkzZriinpqZGltjKOyxBCWOIMWiODToXhNZ9FMFRVX4N7bIrcpraBB07Oy2MMdCHJnXoFSNydmzZ7vfVUj7pZdecuV4FKMKBGvCAHF0cjO2r7nmmoTEIZpFqQLRd911l4sn3oQETfKYPHly3AlaYYvjWGJR6SA/C7+PDEgc2YHELslUBFIzCVUOwatkHXvSaLuKaapgZqrEEpQ4ghSLVjHo2rWrqyuoYpmqlVahQgW3ssPFF1/sZuQ+9dRTkYIFC/oaR5BiIY74VHdLz5eRZvWpCLDqcXk144gjcXGIVndQTT9dEOr8UPkMVRtQsunVj9NnTmYXk2GLI0ixNApIHNmBxC7JtJSOribvvPPO6PIkGUslNG7c2FW4TpVYghJHUGJRPSnVmoot8qsPGi31Nn78eFeSRhXS1VrkFRoNeyzEEZ9aV5RkKqFUaQavBmNs0VmVG1HB5HhL4hGHf1S0WquReEsxfvfdd5H+/ftHKlWq5EpnKAFVwXfFohUywh5HkGLZEJA4sguJXRJ562dqlYfy5cu7Apkqlvnll1+6+/XlMGbMGLcWp7ccUdhjCUocQYtFCYS3bFnG+mj68lKXiZIHFdf0W1BiIY745s2b54r9qqCql8zEUrdwoUKFfI+HONLT54UuAjIunaYkU11/WpdVS9D5vSRhUOIIUixrAxJHdiGxCwB9MWgxdTXzqvK5PmSULGgtUhWN1DqTqRZLUOIIUiz68In3xSRDhgxJyDJIQYuFONLThYiSSa0IowLiGjOkFquZM2e69Xrff/999yXVoEED4khgHB4VtPWK2sZbnuvee+91S52lShxBimVXQOLIDsyKTRIV+X3nnXfssccec7OzVBOuePHirhRAvXr1XCmAn376ydq2betmZfo5GzYosQQljiDF4sXx+OOPuxINRYoUcbP6VHpGZRlUL04zCv/+97+77ZdffrkvcQQpFuLImi1bttjo0aNtzJgxtmTJEle2In/+/G4Gb//+/e38888njiTEkRnVkatbt66bWa1CzqkeR5Bi2ROQOLKKxC5JbrvtNvv6669dYqCp9yqrofIZv/76q5t6rwr1qpeWSrEEJY4gxRIbh8qGKA6VzVizZo1LKHv37p2wekpBiYU4LNPCqUomY+njXdt37Njhis/qXFb9NuJIXByZxRLvMe+++65df/31rhB6mOMIUiy7AxJHtkp2k2EqUjOvZsjFrlmobVqUWusVajC+uvn8HswbpFiCEkeQYsksjhUrVkRef/11F4dKrWgtR78FJRbiyJzWb9Z4UC127y3gntHmzZujsRJHYuLIaiyJKN8UlDiCFEvvgMSRnUjskkAf9ppdo4Wx41E/v+o8aap1qsQSlDiCFEtQ4ghSLMQR39tvv+0Gdmuxdo3n69Wrl6uzqFp6Xh0y1eBq3759ZOnSpcSRoDiOFMv69evdDF3ZsWNH5IorrvD1YjEocQQplrcDEkd2I7FLAn3ot2jRItK0aVM3gDfe1eITTzyRkAG9QYklKHEEKZagxBGkWIgj81p63bp1cwWQVZC3cuXK7gurfv36kWHDhrmZ3GpJTEtLI44ExhGkWIISR5Bi6RKQOLIbiV2SzJ0711WiV32ct956y82q82bkqDlYVdlvuOGGlIolKHEEKZagxBGkWIgjPbUsPPzww67uVqyvv/7azQBVmQbN4larROfOnYkjQXEEKZagxBGkWPYHJA4/kNglkboA9OGfP39+V8RU1c/vuOMO1ySs6tc6wVItlqDEEaRYghJHkGIhjsPHAH3//ffu31oZJWMLohJPtUQsWbKEOBIYR5BiCUocQYrlj4DEkd2YFRsAGzZssEmTJtmECRPc7JzatWvbVVddZTVr1kzZWIISR5BiCUocQYqFODKnUiv6eM+TJ4+9+uqrds8997gyPcSR3DiCFEtQ4ghSLIcCEseJILELGJ1UuXPntiAISixBiSNIsQQljiDFQhyZe/LJJ+3gwYPWp08f4ghQHEGKJShxBCmWJwMSx7EisQOAkNu/f79rgUh2wkkcwY0lKHEEKZb9AYnjWJHYAQAAhETOSkMBAACQKRI7AACAkCCxAwAACAkSOwAAgJAgsQMAAAgJEjsAAICQILEDAAAICRI7AACAkCCxAwAAsHD4fwd+fbaR9ABqAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results2 = noisy_qasm_simulator.run(qc2, shots=1000).result()\n",
    "plot_histogram(results2.get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adec89db",
   "metadata": {},
   "source": [
    "## Problem 3: Transpile a quantum Circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "89c6f6ce",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.compiler import transpile"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f94d3da",
   "metadata": {},
   "source": [
    "First we select a backend (in this case a real device) to transpile for"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "827bbd71",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.providers.fake_provider import GenericBackendV2\n",
    "fake_hardware_backend = GenericBackendV2(num_qubits=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "3a3cc9d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1249.28x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc3 = QuantumCircuit(5)\n",
    "\n",
    "\n",
    "# TODO implement a cirquit of your choice using 5 qubits\n",
    "\n",
    "thetas = [0.1, 0.2, 0.3, 0.4, 0.5]\n",
    "\n",
    "for i,theta  in enumerate(thetas):\n",
    "    qc3.ry(theta, i)\n",
    "qc3.cx(0,1)\n",
    "qc3.cx(0,2)\n",
    "qc3.cx(0,3)\n",
    "qc3.cx(0,4)\n",
    "\n",
    "qc3.barrier() # to put a barrier in the circuit for visualisation purposes\n",
    "for i in range(5):\n",
    "    qc3.h(i)\n",
    "\n",
    "\n",
    "qc3.measure_all()\n",
    "qc3.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b52e7de",
   "metadata": {},
   "source": [
    "then we transpile the circuit for the selected backend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "3cf632bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zTxWMlP+At956K9zc3IoFH0VycjIuXrzIACQRORUGIDXg1VdfVQ2TcePG5QcfhZwF+/jjj9GtWze8++67KhtSDkha4e7rjcyUvO4FRhO77GV1KSjopiGo/dA7MBKWAZYBk5i4K/hw5WH8uDUGSSkZ8PPxwE03VscjdzVB0/r6zXwwycjMxsqfT2Lpd0cRc+4KXFyAOqGV8J/bG2Fw99pwdy+e6aA3uw9dxKLlB/HPgXikpWcjyN8TA28Ox31DGqNGVe1l+FvqUlI6lnwbhdUbonExKR3enm5o3rAyHrkrEh1aVFMnIUlfeBzIw7YAy4DRSBfrRYsWqWSSgjw8PBAREYG6devC398/P5B48uRJdcnIyFD3SSBy6dKl2Lx5Mx555BE1UU/B4KM8z6RJk9CsWTMHvDsiIh0EIOPj4/HGG29g1apViImJQbVq1TBkyBDMmDEDTzzxBBYvXowFCxbgsccegzOQgKEt/izIQUfGfhQPPPBAscclDb9Ro0aIiorCmjVrcP/990MranZrgTO//wsjCr71QVTuNAy52ZlIi96LuFWvIyM+Bi4e3vnrJO/fhKPTig++nZuVgdycbLRZnQ2tYxlgGbianoVHZ/yJ/605guzs3EKPSSBq4bIDuLVTGD6d0Q3VqugzCPX1Tyfw2IytOH+p8B/wvUcSsPaP0wir7osPXu6C/l3Dodfg88jnf8Mf/xTPfvrz3/N45d1dePiuJnjzmQ7w8NBfIDYnJxdT3vkHby7dh6vphX/Tuw5dVEHpts2C8cWs7mhYJ9Bh+0m2x+NAHrYFWAaMRLpaf/TRR8jMzMy/T7qZ9+7dG61bt4a7u3upGZO7du1SWZP//pv3ezl+/DieffZZhIeHIzo6ulDwUZ6TiMjZaKIlv3v3blWJyjggcXFxaNq0qaq03377bQwfPhwHDx5U67Vs2dJu+9C9e3cVUJSzT9ezZ88etGrVCkePHi3368qBRs52yQDEbdu2LXGdLl26qOVff/0FLanergkubD9c6L7Wz9+jZkFsMKJnidv0XTkVo08uQ1Bjbf8R9wptiICWvRDYph9ChkxCgxe+Q+rR7Tj17sP56/g364pWy1MKXZotioK7fzBq3vMq9IBlwNhlID0jGwMe/QmLV0cVCz4W9OPWM+g8Zi3OX0yD3ny86jDu+u/GYsHHgs6cT8XgJ35WgUq9ORWbgptGf1di8NEkMysHC744gGH/3YCsrBzoiZysvP+VTXjtw3+LBR8L2rE/Xn1OB48nwgh8fX3RoUMHtdQzHgfysC3AMmCUekCSSqTXmin4WLNmTUybNg0vvPAC2rdvX2rwUUhXa/kvKMNuTZ8+XU1MYxpDksFHItIKVy1kPg4aNEgFHmW259jYWDWortx+/fXXsW7dOjUrtAQHW7RoAWcg4zTKmakePXqoM1PlIZmNpolnSjsoSVfsgutqgmSHugC5OYX/TO6e8xUSDkaj/Stj4BtaePDtpg8OREinZtg9ZzkSD5+GnlSK7IQq3UcjYfNypBzcWuI6OZnpOD5rCCo17YLQYZOheSwDMHoZmPTWNmzcFmvWukeiL2PEpF+hJzv2X8BDr24xa10J0I6e/BsOn0jUVfDt9gm/qC7n5vj211N49f3d0BPJ8P3kmyNmrXsxMR0DH/sJmZn6CsKWRCbak14tsjQSIx4H2BYozJBlwCD1gIzdKD32TGR271mzZqmebJZq0KCBClwWHXqrf//+DD4SkVNz+gCkdK+WLtfStXrOnDn542EIOcMjs4DJoLsyXkZAQACcZcbq0aNHq/2WIKQ5WZOlSUhIUMuyZn8zPWZaVwuqtWqA+F3FM0RzMrOwacJCuPt6ofNb4/PvD6hfE62fuxsX/onCvkVroEehw18CXN1w9ospJT5+atHDyMm8iogJS6AHLAPGLgOJl9Px4arCGS/X8+v2WOw8EA+9mP/5/jIzP4tKz8jBO8vzMv714NdtsaqLsSUWfnkAaVezoAfZ2Tl4a+k+i7Y5HpOMb37Ny3TRM+lqmJKSopZGY6TjgGBboDijlQEj1AOXLl3Chx9+mH978ODBuO++++Dp6WnV88l/XxlDUsaCLJphKck7RETOyqkDkNK1evny5QgODsbMmTNLXKdNmzZqKYHIgk6cOKEqdwlYSoDu3nvvVTOBlZcEFU0DAZd2OXXqFF555RX07NlTXZcgpCytcfVqXre8sg5Q0j1bpKU5Z/fEGh0j4eJWuKiF9WiFM7+WnMlyae8J7FmwGmHdW6LRqF5wcXVF17cfV49JY7ToWXK98A5tgCpdRyB5zwY13k9B5797G0k71qL+89/A1Ut7XVFYBsyj5zJQlIz5mHbV8j8VMkmJHly4lIavfjxh1eeWknpt3Cgte+fLg1ZN1GLN5+aMftgSg5NnUyze7p0vD0Dvjhw5otpQsjQaPR8H2BYwj57LgBHrAcn2/+CDD5Camqpud+rUCXfffbfVcwUUne1aul2bsh7lv+D777+vXpOIyBk59SQ0y5YtU+NajBw5EpUqVSpxHR8fn2IBSJm4RYJ+VapUUc8hlbFkSw4cOBBbtmyBq6v1cdeuXbtavI0EJUeNGoU//vjD4m29vfMGoTbNelaS9PT0Qp+FpWQ8EenSbgmPXFe8jPbXXS9icCd0fvMRbBgzC3Fb91/bPsAXmcl5B+KS/Dt3BWr3aYu2U+5FlWYRqNa6Iba9sgSXj52FtRo1bIRMF9s1Vl08fVBjnm0bRSHDXsClTcvUWe/Gr+V1N03e8ytilj6LhlPWw6tGhNXP3ahRQ+Rm2C5IbfQyYI/vX2tloDwuVroL8LR8dsb/rdiCHz6+G1p31aMhMvxHWbzd5ZRM1G16M7yytN/tMDZoIuBa8rG9LOMnzsULj2o/8ynJpxfgY3mb4vftZxBWq5b0WtWUO++80+x1TVk969evxz///GP2dnfccQcqGtsCbAuwLWD7OsDaesARdYAkiZSWKGMaz1/mMxCSFDNu3DibBh/lP64Mx/Xf//5XZVru3btXPd6uXbtSn0e6fZf135KIqCwhISH59ZCuApAbN25USwkmlpWRWDQAKWeZzpw5owJ+pnFDZKBeOeMkM0XffvvtVu+TnGEyN11eMi5N3a8jIyOtej1zuleb0027LBJ8lM/LEp4ubkCN6693cs1WBNQNQfit7fIbnH5hwbgSc6HM7XKzstXZ7YHrZ6HJ2L449/dBHPhgHcrjbOxZZOTarhuHnHk24yMoxL95d7T5tvSzkj7hkYVmM0w/dxLHZ9+FWmNnq23L4+zZs8hJL72RbymjlwFrvn+9lYFyicgFrOh5lJXjbnF95ZQCawLXRhSxSPzFy0CKDj6DIA+rNku9mo1UPZSBmpmANecNXdxw9ux5IFdbmbBXrpg31mfBHh2ytGQ7R9QNbAuwLcC2gHks+S1bWw84og4w9UQrjXSLNhkzZkypSTXWBh9N2Y8S2JThykyvWVYAUsqAKYGFiKgiOXUA0jSjl0zAUlpFLBmNRQOQa9euVTNDFxy0+KabbkK9evXw3XfflSsAKQFMGW/yeiQw2q1bN3VdZuqWcTqsYRqYWD4Leb8lTURz7NixQutaE8G25ow3zDx5HL1+G25Z8iy2v5w3Vk1477Y4/dP1I+aZl1ORk5EFN08PxGzYKX0YUB41Q2vaPAPSnqRxeGzm7QhsPxjVBzxW7ueTmfZsnfVg5DJg7+9fC2WgPC55AtbsibtrFmqEhUHrrnr4wtpBQYKr+sMrUPufQSwykIOy/7iVxNfbFZV1UAaSfNxheQdsichko2bN6prLgPTz8zN7XVOwQXp2WLJdmAPKBdsCbAvYm7OXAXNZ8lu2th5wRB1QVmKKJHnIxKRChhSTma7tEXwUrVu3Ro0aNXDu3DmVBSlBRvmuSyL3MwOSiKxlTfxIEwFI04GntLENZXxIGWhXxnmsW7du/v0HDhzAsGHDiq3frFkz9Zi9ydk30wzY0t3gs88+g5ubm1XP1apVK3Vgk7NUctDp2LFjsXU2b96slh06dLDqNaxJn81MvYrP65vXfTApKgbIBYIa1UJiVAz864Ygecm5627Xed6jcPVwR2LUabR4cqg6e54cff3tShN1JAoevnld2m0hLQvo+j3sJmHrSqSd+BdXz0Sp2RCLarbwADyrmT8zYFTUEfjY8Bdv9DJg7+9fC2WgPN776iAemV7yDJ9leWjkzVg4+TloXcLldIT1WmbxOJiVAzxxattm+Hg7yRdZDvc8+yuWrT9u8XaL356I4X3fhdb98tcZ9H7wB4u369O5Nn58L6/3h5Zs377d7HUPHTqkhtDp168fmjRpYvZ28ge9orEtwLYA2wK2rwOsrQccUQdIcHDlypUlPiZdx03jMcqs19YMA2ZO8FHIc/fu3Vv97zR93rfddluJzxkVFVViUgsRkb25O3tkVboX79y5U2UwFhQbG4uJEyeq6y1atCg0loZsExQUVOz5ZEzIw4ctm3XVGlOnTsXRo0fVOCRy4CxPBS/BVTmYrFu3Ts2eVjQAKd3M5SAiQcrSDjLO4PTPO1S3m5SYeGSmXP+sa+R9/RHa+Qb8M/MLnP5hGwb9NBud547HD0NehlFU7TFaXfSCZcByeisDBY0cUB+T5m5H8hXLupE+cpd1w1k4m8oBXri7X30sXh1l0Xbjbm+ki+CjGD880uIAZI2qPrjjlpJ7RWhNz/Y10ahOIKKikyz+3PSuQYMG+PHHH1UbyOj0dhxgW8ByeisDRqoHTL3USpow1ZbBx4KvYQpASiIMEZGzcepZsOVMkXj99ddVkM1EzuhIhqFkP4qWLVvafV+kO/XQoUPN6gIwf/58FYSUDE1bnF168cUXVYD1k08+wf/+979CB7X77rtPXX/ooYdQvXp1OCvpYhPepy1qdr8RZ//YU+a6cka89eR7cGHXEexb+I06S777za8QclMz1RAlbWIZoIL8/Tzx6AjLAikDbg5HswbWjXXrjJ4c2QyeHuYfhv183DHews/MmXVuVUNdLPHUaPnMrOtR4GxcXV0w6T8l/4ksTdP6QRjQNRx6J20nGdeaGTr6w7YAGakeOHHihFrKewgPD7dr8NHUBd00JqXptYmInIlTByClkq1atSpOnz6tuk9LhduwYUM1foaM59izZ88SzyjJwSoxMbHY88nMYJIFaQ0JKK5YsQLVqlW77royVsmUKVPUgcIWJOtx1qxZKoV/7NixagxK6Zot3REk01K6XsvjzkwGDQ+oF4o6/drjwvYyslBdXNBl3mOqG8HmCQuRm5M3Rs++d75F/O6jqiHqX8ea4b7J0VgGqKhXH22D23qY123sxsZV8NmMvHF19aJ5oyr4dEY3uLldfzQ/CVR+Pacn6tUKgF7IibWVb92ChnXMe0+jBzbAxLEtoCfj7miEJ0eZNxt8WHVfrF3QB+7uTt10swkZR/uZZ57Jn2iQ9INtATJSPSDjMZrGXLQkkGpN8FHI78U0DqbMIp7z/78bIiJn4dStWJm5etOmTRgwYAC8vb3VjNISQHz//fdVl2RTVmTRAKTMOF3SWI9yn7WzUTuaHHR++OEH1R07KSlJjYsik8689tpr+P333+Hr6wtnlpudgzO/5Q3CbGpElqTZw4NQo30T7Jq9HElHrs1kJ9tIA9TVzU11vSHtYRmgoiSQsuLNW/DMvTfAx9ut1CyxEX3r4ffFAxAUYPmEJc7urlvrqaBS/fDSu5hF1gvCLx/0Qz8dZr5Jl+qtSwdhcPfaEm8oUSVfd0x5qBWWTL9ZlQc9kSDsWxM7YM4z7dX4nqXp1bEm/vpsMOrW0m5XREukpKSo9p8sSV/YFiCj1AMS/JOAofz3lO7klnj33XctDj6ayGvJa8r/4+xs28z2TkRkK06f0y4VqMxqXZQcjCQgKWd6brjhhkKPDRw4EJMnT1ZnzCSIKf7++2/VZXn27NnQqltvvVVdtOrU+m1lzlwY2DAMrSeNwPkdh7H/ve+KPW7qetNm8kjV9ebgx3Ye9ZtsjmWASgpCzvlvB7zwYEv879sj+GFLDH7dFouMrBz4+7pj/zdDER5SCXrWt0stRH03DD9tPYP/rTmCVRtOIiMzBz5eblj3Th90bxdaaJxjvQmu7I1v3+6N4zGX8f7XhzD/s/1Iz8yBl6cr5k7siFED66su+3ol3+0zY5qr8U2X/3gcq345iZ/+PKPKgHS7377sNhWEJtILtgXICOQ/6vPPP2/VtrfccosKQEoQ05Lgoxg3bpxVr0lEVBGcPgBZmv3796suyZIFWDT778EHH8SCBQvUpCzSdfrq1auq8pau2848UYveRa/9s8zH5Qz3p3XvKXOdvQtWqwtpE8sAlTUpy5Ojb1CXWr2W4cz5VARU8tR98NFEMvskECkX0/uvEuiFHu1rwiike/nrT7XH5+uOqfcfHOSNRwww4YqJr487/nN7I3UxlYEgf08GH0l32BYgKlvTpk3x7LPPqgxGS4KPRETOTrMByL1795Y6o1hAQAA2btyICRMmYMSIEWrMDcmKnDt3rjobReQIUS/3QVZCnEQa4Objj/AH3oZvvVaF1rm8ZyPOLH0OOWkpavyjwLYDEHbvLLgUKbcn54/FxY3/w42fJ8C9Ev+cEhER6UnClhW4vGcDwu+bi+NzRuDq6QNw9fSBe2B11H7kXXiHWtalk7SHZcDYJAhJRKQ3ugxAivr165fYdZvIUepN/Co/WJjw52oVRGw6P28cJBP3SpVR779fwiukHnIyriJqSi9c/HUpgm8Zm79Owp+r4OJmmwmOyPmD0kRERiMT/slJZHMm/tOrxL9Wo0qPe9X1an0eRECbfqq7/vl1CxG98H40fu03R+8i2ZnRywDrASIi/dFtAJLI2RTMVMxOTVIZjkUVDD65enrDt25LZJw/mX9fZuI5xH09A42m/4r4nz+qgL0mRweliYiMpmrVqhg5ciT0LCslEQeeuAE5GWnwDA5HbmY60uOOo0r30ajzyLtIObQFEROWwMXdA4Ft++dv59eoI859M8eh+062wTJQNiPUA0RERqPZAKR0sSbSmhNz70Xy3l/V9YZTyh40PTMhDglbV6DBi9cyeaMXPoCwsW/AzdcYM6EaNShd1p+SiMcZeCYifbt8+TK2bdumxu6WYXX0Wv9Xufkelf0eOvwlJO38EXErZqg6/vKun+DXpJMKPBV1fu18BLXneOZ6wDJQNiPUA0RERsMBEYkqUN2nlqLF4tMIGzUdMUufLXW97NTLODp9EEKGTIJfw7bqvvifPoJntdoIaNGzAveYKiIovWdcOM5+/hLqPvlpoT8lNQY9iabzdqPWffPg17gjg49EZAhnz57F5MmT1VLPUk/shs//93xIPfZPfi+IxL+/QeWOdxRbP/brGUiPPYqwe2dW+L6SfbAMlM4o9QARkZEwAEnkAFV7jlGZkFmXLxZ7LDs1GUde6YugDrehxm1P598v6yf+/S32PhChLuLAhBZIPb6rQvedKiYoXdqfEiIi0oe0E7vz63ZTPZ+bm4ukXT8ioHW/QuvGrZ6DxD9XocGU9XD18nXQHpOtsQwQEZGRMABJVAGkS23GxWtncBP/+gbu/lXh5l+l0HrZaSk4MrUvAlr3RehdLxZ6rO4zn6tAVfMPT6qLaDp/DwNTOg1Kl/SnhIiI9CHj4hkALvCsGqZup53cA586zZEatQ0+tSLh5lMpf91z376FhE3L0HDaz4WG7iBtYxkgIiKj0ewYkERaIuP7HX9jmBrTz8XFFe4B1dTYjjKb4ckF9yOo/WAEdRiM89/Nx5Uj25CTfgWJf61S21buNAyhd73g6LdAdghK56SnwrNqzWJB6ZL+lIQOYxkgItIL6b1Q8MSSm18Qzn+/CO4BwQjqcHv+/RnxMYhZ/Aw8Q+oh6sUe6j4Xdy9EzvnbIftNtsMyQERERsMAJFEF8KpeB5FztpX4WMFx/STQaG6wsc23uTbbP3KuoHRpf0o4BiQRGYGXlxcaN26slnoV1G6guphEvrldLfc/1gw1pudNVic8g2vxeK9TLANlM0I9QERkNAxAEhE5WVC6tD8lRERGULduXXz6ad6kXEbTbOF+R+8CORjLQB4j1wNERHrFMSCJiIiIiIiIiIjIbhiAJCIiIiKncfjwYXTu3FkticiYWA8QEekPA5BERERE5DRyc3ORmZmplkRkTKwHiIj0h2NAklXcfbww8thn0No+25K3G7CpPzRD9teWjF4GtPb926MMEBEZndaOBWwLsC3AtoBtubm5YejQoTZ7vtnvL0fylSvw9/PDxIeGF7ttq30mInIEBiDJKjJTr4evN4zMxQXwMfAvyOhlwOjfPxER8VjAtoCxv3/K+w24u9uuEEi+Z05u3lKet+htIiItYxdsIiIiIiIiIiIishueRiEiIiIipxEREYFly5YhLCzM0btCRA7CeoCISH8YgCQiIiIip+Ht7Y369es7ejeIyIFYDxAR6Q+7YBMRERGR04iNjcX06dPVkoiMifUAEZH+MABJRERERE4jKSkJa9asUUsiMibWA0RE+sMAJBEREREREREREdkNA5BERERERERERERkNwxAEhERERERERERkd0wAElERERETqNKlSoYM2aMWhKRMbEeICLSHwYgiYiIiMhpuLq6wsPDQy2JyJhYDxAR6Q9rdCIiIiJyGvHx8fjoo4/UkoiMifUAEZH+MABJREREREREREREdsMAJBEREREREREREdkNA5BERERERERERERkNwxAEhEREZHT8Pf3R9++fdWSiIyJ9QARkf64O3oHiIiIiIhMwsLCMG3aNEfvBhE5EOsBIiL9YQYkERERETmN9PR0nD59Wi2JyJhYDxAR6Q8DkERERETkNE6cOIGhQ4eqJREZE+sBIiL9YRdsskpubi6y0rR1RtLdxwsuLi42e77cXOBqNjTD2w2w4ds3fBnQ2vdvjzJARGR0WjsWsC3AtgDbAmRLUgdkZ2vrR+Dm5mbT/4REZD4GIMkq0tj8vP4oaMnIY5/Bw9fbZs8nDc6u30MzNvUHfGz4izd6GdDa92+PMkBEZHRaOxawLcC2ANsCZEsSfFy5ciW0RDJr3d35IyByBHbBJiIiIiIiIiIiIrthAJKIiIiIiIiIiIjshrnHREREROQ0mjRpgm3btjl6N4jIgVgPEBHpDzMgiYiIiIiIiIiIyG4YgCQiIqeQfCUDh08kIjMrR93Ozsl19C4RkQNER0dj3LhxaklExsR6gIhIf9gFm4iIHCI9Ixsrfz6J7zefxj8H4nH4ZBJyC8Qc4+LTENF3OdpEBqNnh1CMGtAAgf6ejtxlIqoAaWlp2Ldvn1oSkTGxHiAi0h8GIImIqEJdTLyKN/+3Dx+tOowLCVfLXDf6bIq6rNpwEs/O3Y6RA+pj0n9aoH54QIXtLxEREREREZUPA5BEFSh572+IerFHoftcvf3gVbMRqnYfjeoDH4eLG3+Wemb0MvDNxpN4+NWtOHfR8oyGK2lZ+GDFYXy29hhmPdkWj45oCldXF7vsJxGRvRj9OEAsA0REZEw8shE5QOWb70Zgm/6Q/qaZCXG4+NtSxCx+GldjDqLOox84eveoAhitDGRkZuOhaVuw5Nsj5X6u1KtZeGLWX1i1IRor37oFVQK9bLKPREQVyWjHASqOZYCIiIyEk9AQOYBvvdao2n0UqvYYjZAhE9Hkjb/gUbUW4n/+CJlJFxy9e1QBjFQGZKzHIU9tsEnwsaDftsei+7h1uHCJ40MR6UloaCimTp2qlnpmpOMAlYxloHRGqQeIiIyEGZAacfLkSWzYsAHbt29Xl7179yIzMxNjxozBkiVLoGVjY1fY7LmWhN4JLXLz9oNf445I3LoC6XHH4BFYDUbCMqDfMpCbm4vRk3/Huj9O2+X59x5JQN9HfsQfnwyAn6+HXV6DiCpWYGAg+vXrB6PR63HAXGwLsAwUZNR6gMrv0qVLyMjIQEhIiKN3hYiKYABSI+bNm4f58+dDb/zCgrHt5SU48MFaGJ00NIV7pSowEpYBfZeBD1cextc/nbBom+3LBiMk2Bdx8alod/ea666/8+BFPP/2Drz93E3l2FMichYJCQn45Zdf0KtXL1SuXBlGosfjgDnYFrjGqGWgKCPXA0Z09uxZHDhwAMePH1eJN0lJScjOzoa7uzuCg4NRt25d1KtXD82bN0dQUFCZwcdXX30V6enpmDJlCoOQRE6GAUiNkIq3f//+aNeuHdq2bYv169dj0aJF0Lrw3m1x+qcdMJqc9FRkXY5X2WFZCXG48MN7SDu+C74N28M7rBGMhGVAv2Ug+mwynpmzzeLtJPhYq4afRdss+OIAhvaKQLe27KpFpHXnzp3D7Nmz1R9NPQcejHAcMBfbAiwDRq0HjCwrKws7duzAzz//jP3795e6Xnx8PA4dOqSuu7m5oUOHDujduzeaNGkCFxeXYsHH2NhYdfv9999XQciC6xCRYzEAqREvvvhiodt//fUX9CCgXggOLYmD0cQue1ldCgq6aQhqP/QOjIZlQL9l4L9vbkNKamaFvd4j07di/+ohbGgSkSYY4ThgLrYFrjFqGSBjkSzHd999F9HR0cUek3acdMGXYKN0pU5OTs5/TLIit27dqi6SlHP//ferjMiiwcfq1atj/PjxbBMSORlNBSDl7Mcbb7yBVatWISYmBtWqVcOQIUMwY8YMPPHEE1i8eDEWLFiAxx57zNG7qsjZTFZ6pXP39UZmylUYUfCtD6Jyp2HIzc5EWvRexK16HRnxMXDx8M5fJ3n/JhydVnzsm9ysDOTmZKPN6mxoHcuAfstATNwVrN5YvFFpTwePJ2Lj37G4pWPNCn1dIiJr6P04YC62BVgGyDhycnKwevVq9X9egokm0lW6R48eaNy4MSIiIuDtfe03cPnyZZw4cQL79u3Db7/9lh+QlOzJgwcP4u6778a6desKBR9feuklFSsgIueimQDk7t271UDEcXFx8PPzQ9OmTdVYEW+//TaOHTumznqIli1b2m0funfvjt9//11VgFIxlmXPnj249957sWLFCjRo0MBu+6RlNbu1wJnf/4UReYU2REDLXup6YJt+qBTZBYef74JT7z6MehO/VPf7N+uKVstTCm2XcfEsDj3TFtUGOEeQvbxYBvRbBmTsx+zs3Ap/3UXLDzIASUSaoPfjgLnYFmAZIOMEH9977z388ccf+feFh4dj1KhRqqu9q6tridsFBATgxhtvVJe77roLW7ZswRdffKECk1euXMFHH32Uvy6Dj0TOreRfuRNmPg4aNEgFH5955hl1dmPnzp3q9uuvv67OeMjM0JJt2KJFCziDTz75BP/++686kyOD6VJx1ds1wYXthwvd1/r5e9QsiA1G9Cxxm74rp2L0yWUIahwOPakU2QlVuo9GwublSDm4tcR1cjLTcXzWEFRq2gWhwyZDD1gG9FsGvvzBMfXet79FIzUtyyGvTUS24evrq8b4kqWR6O04YC62Ba4xahkoiVHrAb2SnoEffvhhfvBR/rffcccdqiejBBZLCz4W5eHhoZKC5syZg9atWxd6zN/fn8FHIieniQCkdK+WLtfStVoqG6lcTCZNmqQqLRnEVrIS5QyJM3jzzTcxevRotd8ShJRxLqgA6ZruAuTm5BS6e/ecr5BwMBrtXxkD39DCs/81fXAgQjo1w+45y5F4+DT0JnT4S4CrG85+MaXEx08tehg5mVcRMWEJdIFlQLdlICk5A1HRSQ55bcm6/DfqokNem4hso3bt2mpIHVkajV6OA2ZjW6AYw5WBUhi5HtAjmdH8119/VddlbMennnoKw4cPVwFFa8h/f1OXaxPpmi1ZkUTkvJw+ACnjOixfvlzNAj1z5swS12nTpo1aSiDSxBSwbN++Pby8vGw6FqM8twQUy7qcOnUKr7zyCnr27KmuSxBSlpSnWqsGiN91tNj9OZlZ2DRhIdx9vdD5rfH59wfUr4nWz92NC/9EYd+iNdAj79AGqNJ1BJL3bFDj/RR0/ru3kbRjLeo//w1cvfRxJphlQL9lYNchxwYA/znAACSRlsm4YCkpKYXGBzMKvRwHzMW2QHFGKwOlMXI9oDfnz5/H559/nn/b9B/dWkUnnPHx8cl/TCa2kYlriMg5OX0ActmyZWq8iJEjR6JSpUolrmOqdAoGII8ePYqVK1eqAW3btWtn033q2rUr6tate91L/fr1sXHjRrWNBCVlfAsjqtExEi5uhYtaWI9WOPPr7hLXv7T3BPYsWI2w7i3RaFQvuLi6ouvbj6vHpDFa9Cy5noQMewFwdS101jt5z6+IWfos6k36Gl41yh571FmxDBirDBw+mWTo1yei8jly5Ig6gStLI9LDcaAkbAuYT69lwBJGrwf05OOPP8bVq3kTTcl3etNNN1n9XCXNdi1JSvLf25Qo9O2339poz4nIcJPQmAJ4kkFYGqloigYgb7755vyKSTIRZbBaW5FBcj09Pc1a9+LFi/ndryMjI+GM2rZtq8bTtIRHritexvXPXEUM7oTObz6CDWNmIW7r/mvbB/giMzm11O3+nbsCtfu0Rdsp96JKswhUa90Q215ZgsvHzsJajRo2QqaL7RqrLp4+qDHPskaRf/PuaPNt6RNz+IRHFprNMP3cSRyffRdqjZ2tti2PRo0aIjcjDbZi9DJgzfevtzJQmhSvjoBf8Rk7xfZlgxESXHbWRkiwT/7y9M8jSl0vLj4V7e4ungGzeMlnWP3OMGhVbNDTgGsgYuNiUatWLRiN0d+/Xj+DO++806JsGbF+/Xr8888/Zm8n44lVNLYF2BZgW8D2dYC19YAj6gBbu+M/T8KvUkB+/V/0trOR/8Sl9VIUp0+fVvMiiKpVq5YrIaek4KNpzMfx48fjueeeUxmzP/74I2677bZS/683atSIWZJE5SBJfjILvS4DkNHR0WpZp06dUsd/MAUXCwYgzR3I1hpr1qy57izYpsBot27d1HUZ42LRokVwRhJ8PHPmjEXbeLq4ATWuv97JNVsRUDcE4be2y29w+oUF40rMhTK3y83KVme3B66fhSZj++Lc3wdx4IN1KI+zsWeRkWu7bhzS9cWMj8BqOempODbzdgS2H4zqNpjlUGaNl+e0FaOXAXt//1ooA6Wqmgj4lfyQBB9r1SjlwSLc3VzNXreg1CvJSLWwTnMq/tmqf0JOdrbFdbMuGP396/QzkJlKzZWWlpa/tGQ7R3xWbAuwLcC2gHks+S1bWw/oob6Uet+0lPdT9LazkaHOyvLzzz/nX5dJZa2dVKis4KNpNm3JrNy8ebPquv/XX3+phKTSfgPp6elW7QcRlY/TByBNBxzTQagoGR9SZsmWiWlMqdfOQA4Qphmw5YzfZ599pgbcddYItjVnvGHmyePo9dtwy5Jnsf3lvMGyw3u3xemfrh8xz7ycipyMLLh5eiBmw06ZPg3lUTO0ps0zIO0pYetKpJ34F1fPRKnZEItqtvAAPKuZPzB3zZo1bZ71YOQyYO/vXwtloDRXPL2QWEbW4vVI5qMEH7OycxAXX/r+lvZclXzcERgWBq2KdXNTPy1XNzeEavh9WMvo71+vn4Gfn5/FbT8ZYseS7cIc8FmxLcC2gL05exkwlyW/ZWvrAUfUAbYm9b5pKe+n6G1nU1avQEkUMs16LYHK0gKC5Q0+mvTu3VsFIIVMeFPa68lvgBmQRBUbP9JMAFLeXEJCAnbu3FlsvAiphCZOnKiut2jRwqYTzZTX1KlT1TiU0hVAxrF0d3fej9qa9NnM1Kv4vL55KfRJUTFALhDUqBYSo2LgXzcEyUvOXXe7zvMehauHOxKjTqPFk0PV2fPk6OtvV5qoI1Hw8PWGraRlAV2/h91U7TFaXWwlKuoIfGxYDI1eBuz9/WuhDJRm18F4tB5e8vg7JXWZLkq6XUvmowQfw3t/afHrL3rreYwetBhaVavXMpw5n4rQkFDE7MsbYsRIjP7+9foZbN++3ex1Dx06pNpO/fr1Q5MmTczebt68eahobAuwLcC2gO3rAGvrAUfUAbY2453PcTnlSl79HxNT7LazkSCjzLtQWvdr09iPrVu3tir70dzgo6lrtdx/4cIFHDt2THXHLikBKCoqyqn/mxPpmdNPQtOrVy+1fP3111VlUfAgJhmGkv0oWrZsafd9ke7UQ4cONess3Pz581UQUjI0WcFJQGGH6nbj7uuNzJTrn3WNvK8/QjvfgN1vfY3fHnhTnfXrPPfaLIikPSwDxtGsQWV4eTou47tts+KNUiLSjgYNGqgxvGRJ+sK2AJmL9YD2nThxIv+6Nd+jJcFHIclIMgmskAxH6WpNRM7F6QOQkyZNUgPWyhmUZs2aqQlgGjZsiPbt26NevXpqJq2i4z/aiwQUV6xYUWqlV5B0F5gyZQo8PDxs8toyzmVwcHD+5a233lL3f/nll4Xut+VkO7YkXWzC+7RFze434uwfe8pcV86It558Dy7sOoJ9C79RZ8l3v/kVQm5qphqipE0sA8bh6eGGts2CHfLalQM80ahOgENem4hsQ07cVq5cmSdwdYhtATIX6wHtO3XqVP51c+ZPKE/w0UTiA0XnkiAi5+H0AUiZ7WvTpk0YMGAAvL291YzSVapUwfvvv49169blZ0VWRADSkTIzM9WM2qaLaUxMGUC34P2ynjOSQcMD6oWiTr/2uLD9cOkrurigy7zH1CRCmycsRG5O3hg9+975FvG7j6qGqH8dew/3TfbAMmAs993RyCGv+5/bG8HNzekPbURUBulm+Mwzzzhld0MqH7YFyFysB7QvNfXaWN1BQUF2Dz6KwMDAEl+fiJyDJv6lRUZGYu3atUhOTlaXv//+Gw8++KAanFgCktI4ueGGG6Bn3bt3R25u7nUvsp4zys3OwZnf/s27/v+NyJI0e3gQarRvgl2zlyPpyLWZ3mQbaYCy6412sQwYy/Bb66lsxIr28DDzx4sjIuckM5jKyWdZkr6wLUDmYj2gfWPGjMHChQtVz70aNcw/YSBjOEoQ0tLgo2jXrh3mzp2Ld955Rw2fRkTORRMByNLs379fBd2kS3ZJg9pKd2m5HDhwoNBtayZdofI7tX4bTv1Q+gDUgQ3D0HrSCJzfcRj73/uu2OPseqN9LAPG4evjjsfublqhr3l7zzpoWOfamW8iInI+bAsQGYPMmyBDhMms05Z0pW/cuDGee+45hIeHWxR8FBITCA0NVUO4yczbRORcND2oxt69e8vsfj1s2LASb8vZmCVLllTAHlJB0Wv/LPNxOcP9ad17ylxn74LV6qJFUS/3QVZCHODqCjcff4Q/8DZ867UqtE7KoT9x6r1H1PXcrExUatpFrefqce0AKkH3Iy/dgtTjO9Hyi0RoidHLgNFMvv9GrPzlJA4cs385DfL3xDuTb7L76xARVYSELStwec8GhN83F8fnjMDV0wfg6ukD98DqqP3Iu/AO1e7EHGwLmEfPZYDInB6QMgmt9HQkIv3QdQBSAjVEzqLexK/gXilv/JOEP1fj5PyxaDo/rxuSiW/dGxE5Zztc3D1UN6Pjs4biwveLUOO2p/LXOb9mLrxC6qsAJGmbOUFpLfP2cscn027GTaO/Q06O+fVxXHxqoaU55j/bETWr+1m1n0REzibxr9Wo0uNedb1anwcR0KafmuH1/LqFiF54Pxq/9pujd5HsjGWAjI7BRyL90XUAksiZmIKPIjs1SQ2wXpSr17WhBHKzMpCTkVZovbRT+5H41zeIeOITJGz9ugL2mhwdlNa69s2r4d0XO+GhaVvM3qbd3Wsseo3H72mK0YOYCUKkF9LdbsKECRZ1u9OarJREHHjiBnWc9wwOR25mOtLjjqNK99Go88i7SDm0BRETlqgTkoFtr3Uz9mvUEee+mePQfSfbYBkomxHqASIio9F0AHLjxo2O3gUii5yYey+S9/6qrjec8n2J66SfO4ljM25DetwxBLYZgGr9xud3yY5e+ADqPP4x4OpWoftNFRuULutPScTjH0FrHryzCTIyc/D4zLK73VnjkbuaYN6kjiorhIj0QcbuGjlyJPRe/1e5+R6V/R46/CUk7fwRcStmqDr+8q6f4Nekkwo8FXV+7XwEtb/NIftMtsUyUDYj1ANEREbDvGaiClT3qaVosfg0wkZNR8zSZ0tcx6tGhMqCa7EkDjlZ6Uj8c5W6/+yXUxF00xD4hEdW8F6TvYPSe8aF4+znL6Huk58W+lNSY9CTaDpvN2rdNw9+jTtqMvhoIhPSrHizJ6oG2WZAcC9PN8x5pj3eeaETXF0ZfCTSk8uXL+OXX35RSz1LPbEbPv8/7EbqsX/yh+BI/PsbVO54R7H1Y7+egfTYowi7d2aF7yvZB8tA6YxSDxARGQkDkEQOULXnGJUJmXX5YqnruPlUQpUuI3Dpj8/V7ZT9v+PCugXY+0AEDj/fBdmpl9X1zKQLFbjnVFFB6dL+lGjZ0N51sX/1UAy5JaJcz9OxRTXs/vp2PDOmOTMfiXTo7NmzmDx5slrqWdqJ3fl1u6mel/HLk3b9iIDW/QqtG7d6jjoh2WDK+kLDtZC2sQyUzij1ABGRkTAASVQBpEttxsVrDSgZx9Hdvyrc/KsUWu9q7FHV1VrkZGaoAch96rRQtxvP3ITmH0Wj+Ycn0XjmZrj5BqjrHoEcG0ePQemS/pToQY2qPljxVk9s/XQgRg9sAE8P8w5DEmcccHM41i7sjc3/G4gmda91Xyci0pqMi2ekZoNn1TB1O+3kHvjUaY7UqG3wqRWpTkKanPv2LSRsWoaG034uNHQHaRvLABERGY2mx4Ak0goZ3+/4G8PUmH4uLq5wD6iGBi+uVdlbJxfcj6D2gxHUYTCS92zEsbVvw8XVDbnZWfBvcYsaF4j0GZTOSU+FZ9WaxYLSJf0pCR32AvRCyv1NN9ZQl7cmdsDGbWfxz4F47Ngfj5hzqbiakQVPDzdUr+KNNk2D0SYyGN3ahiAizN/Ru05EZBOpx3cVOrHk5heE898vgntAMII63J5/f0Z8DGIWPwPPkHqIerGHus/F3QuRc/52yH6T7bAMEBGR0TAASVQBvKrXQeScbSU+VnBcv2q3Pqgu132+GhFo+UWiTfeRnCcoXdqfEi2PAVma4MreuOvWeupCRGQUQe0GqotJ5Jvb1XL/Y81QY3reZHXCM7gW2nyb65B9JPtiGSAiIqNhAJKIyMmC0qX9KSEiMgIvLy80btxYLY2m2cL9jt4FcjCWgTxGrgeIiPSKAUgiIiIichp169bFp59+6ujdICIHYj1ARKQ/nISGiIiIiIiIiIiI7IYBSCIiIiJyGocPH0bnzp3VkoiMifUAEZH+MABJRERERE4jNzcXmZmZaklExsR6gIhIfzgGJFnF3ccLI499Bq3tsy15uwGb+kMzZH9tyehlQGvfvz3KABGR0WntWMC2ANsCbAuQLbm5uWHo0KE2e77Z7y9H8pUr8Pfzw8SHhhe7bat9JiLHYACSrOLi4gIPX28YmYsL4GPgX5DRy4DRv38iIuKxgG0BY3//RFIHuLvb7kcg+a45uXlLed6it4lI29gFm4iIiIiIiIiIiOyGpxGIiIiIyGlERERg2bJlCAsLc/SuEJGDsB4gItIfBiCJiIiIyGl4e3ujfv36jt4NInIg1gNERPrDLthERERE5DRiY2Mxffp0tSQiY2I9QESkPwxAEhEREZHTSEpKwpo1a9SSiIyJ9QARkf4wAElERERERERERER2wwAkERERERERERER2Q0DkERERERERERERGQ3DEASERERkdNwdXVFq1at1JKIjIn1ABGR/rBGJyIiIiKnkZOTg127dqklERkT6wEiIv1hAJKIiIiIiIiIiIjshgFIIiIiIiIiIiIishsGIImIiIiIiIiIiMhuGIAkIiIiIqfh7++Pvn37qiURGRPrASIi/XF39A4QEREREZmEhYVh2rRpjt4NInIg1gNERPrDDEgiIiIichrp6ek4ffq0WhKRMbEeICLSHwYgiYiIiMhpnDhxAkOHDlVLIjIm1gNERPrDLthkldzcXGSlaeuMpLuPF1xcXGz2fLm5wNVsaIa3G2DDt2/4MqC1798eZYCIyOi0dixgW4BtAbYFiGxL6sHsbG1VBG5ubjb9X0xkLgYgySrS2Py8/ihoychjn8HD19tmzycNzq7fQzM29Qd8bPiLN3oZ0Nr3b48yQERkdFo7FrAtwLYA2wJEtiXBx5UrV0JLJLvY3Z0VAVU8dsEmIiIiIiIiIiIiu2EAkoiIiIiIiIiIiOyGebdERERE5DSaNGmCbdu2OXo3iMiBWA8QEekPMyCJiIiIiIiIiIjIbhiAJCIiIiKnER0djXHjxqklERkT6wEiIv1hF2wiIiIHyc3Nxb4jCdi27wL+ORCPA8cTcf7SVfXYhYSreHzmn2jbNBgdWlRDk7pBjt5dogqRlpaGffv2qSURGRPrASIi/WEAkoiIqIKlpGbii++PYdHyg/j38KUS18nIzMHCZQfyb7e/oRrGD4/EXbfWhY83D99ERERERKQd/AdDVIGS9/6GqBd7FLrP1dsPXjUboWr30ag+8HG4uPFnqWcsA8YmGY/LfziOx2b+iYuJ6RZtK1mScnn+7R34YEpnDOxW2277SUT2w+MAsQwQEZER8chG5ACVb74bgW36SzQCmQlxuPjbUsQsfhpXYw6izqMfOHr3qAKwDBhPfMJVPDRtC1ZtOFmu54m9kIpBj/+M0QMbYMHzNyHQ39Nm+0hEFYfHAWIZICIiI2EAksgBfOu1RtXuo/JvV+s/HvvHN0H8zx+h5qjX4BFYzaH7R/bHMmAsp+NS0PvBH3D4ZJLNnvPTtUex9+gl/PhuX1Sv6mOz5yVytNDQUEydOlUt9YzHAWIZKJ1R6gEiIiNhAJIcbmzsCps915LQO6FFbt5+8GvcEYlbVyA97pjhGpwsAywDehYXn4qe96/H0VOXbf7cuw9dQu+HfsBvi/ujcoCXzZ+fyBECAwPRr18/GI3RjwNsC7AMFGTUeoDIFnJycuDq6uro3SAqhgFIjYwZtnXrVqxZswabNm3CoUOHkJycjCpVqqBdu3Z48MEHMXjwYGiRX1gwtr28BAc+WAujk4amcK9UBUbCMnCNUcuAnuXk5OKu/260S/DRZE/UJdw7+XesWdAbLi4udnsdooqSkJCAX375Bb169ULlypVhJEY9DrAtcI1Ry0BRRq4HyLhBw7i4OJw4cUItMzMzVRDRz88PderUQd26ddX165FYwQcffIBJkyYhJCSkQvadyFwMQGrAxo0b1cFXyJ/L+vXro169ejh69CjWrVunLuPGjcNHH32kuT+f4b3b4vRPO2A0OempyLocr4LLWQlxuPDDe0g7vgu+DdvDO6wRjIRlgGVAz2QW6007z1m0zfZlgxES7KsyJ9vdvcasbdb+cRqfrT2K0YMaWrmnRM7j3LlzmD17Npo3b67rwAOPA9ewLcAyYNR6gOjYsWP4+eef8ffffyMtLa3MdcPDw9GzZ09069YNvr6+JQYfZ86cifT0dEybNk0NY1CtmnEzqcn5MACpAdIokYDjU089hREjRiA4OFjdn52djQULFuDpp5/G4sWL0aZNG4wfPx5aElAvBIeWxMFoYpe9rC4FBd00BLUfegdGwzJwjVHLgF6dPJOM5+Zvt3g7CT7WqnH9M9xFPTHrL9zaqRbHgyTSCB4HrmFb4BqjlgEio5FkoiVLlqiluU6fPo3//e9/+PLLL1WC0l133QUvL69iwUdTsFKGMiByJgxAakD79u1VheLh4VHofjc3Nzz55JPqsffff1+lWmspAOnu643MlKswouBbH0TlTsOQm52JtOi9iFv1OjLiY+Di4Z2/TvL+TTg6rfjYN7lZGcjNyUab1dnQOpYBlgE9W7DsANKuVtx3lJicgQ9WHsKLD7aqsNckIuvxOJCHbQGWASIjycjIwMqVK9XwapJoZOLj44OmTZuqxKPatWvD29tbdcuW4QiOHz+uApWyFBJklF6Q//zzDx5++GF1X8Hg44033ohnnnkGnp6eDnqXRDoIQMbHx+ONN97AqlWrEBMTo9KJhwwZghkzZuCJJ55QWYCSEfjYY4/BGUiFYosu0QEBAWU+fuutt6oA5OHDh6ElNbu1wJnf/4UReYU2REDLvG71gW36oVJkFxx+vgtOvfsw6k38Ut3v36wrWi1PKbRdxsWzOPRMW1Qb4BxlvLxYBlgG9Co1LQuffBNV4a/7/teH8dy4G+HuzoHHiZwdjwN52BZgGSAyipSUFMyaNatQ1mOtWrXQv39/dOrUSQUdS9K9e/f8DEjprv3rr7+qMSJlrMhXXnkF7u7uyMrKUusw+EjOTDP/UHbv3q3GAJGxQOSHJmcH5Ef39ttvY/jw4Th48KBar2XLlnbbB/nhS0Dx5MmT1113z549aNWqlUUp1da6ejXvrHFJ40A4s+rtmuDC9sJB09bP36NmQWwwomeJ2/RdORWjTy5DUONw6EmlyE6o0n00EjYvR8rBrSWuk5OZjuOzhqBS0y4IHTYZesAycI1Ry4BerdpwEgmXMyr8dWPOXcEPW2Iq/HWJbEnaMx06dNBcu6a8jHocYFvgGqOWgZIYtR4gfQcfX3311fz4gPRmlDiGBCRlXMfSgo8FSbdqmfvh9ddfR8OG18b9ZvCRtMJVK5mPgwYNUoFH+UHFxsZi586d6rb8+CT9ePv27So42KJFCziDTz75BP/++y969OiRnyptL8uXL1fLrl27QjMkM9QFyM3JKXT37jlfIeFgNNq/Mga+oYVn/2v64ECEdGqG3XOWI/HwaehN6PCXAFc3nP1iSomPn1r0MHIyryJiwhLoAstAMYYrAzq2eZdlE8/Y0pbdjnttIluQrmfSo0WWRmO44wDbAsUYrgyUwsj1AOmPdKV+8803ER0drW4HBQVh+vTpuOOOO1T2oqVq1qyJu+++WwUxC5LYA4OP5Mw0EYCU7tXS5Vq6Vs+ZMwf+/v75j8n08hLpl6h/RETEdbsrVxSpYEaPHq32WyoCc7ImrfH999/j22+/zf8stKJaqwaI31U8OzQnMwubJiyEu68XOr91bTzLgPo10fq5u3HhnyjsW2TerLBa4x3aAFW6jkDyng1qvJ+Czn/3NpJ2rEX957+Bq5c+zgSzDBRntDKgZ/8ciDfkaxPZgkyyJ5kisjQaox0H2BYozmhloDRGrgdIf9avX5/fY1MmhpkyZQrq1q1r9fPJHBCSiFX09yFJUJcvXy73/hIZNgApP1TJ8JOZn2Vg1ZLI7M9CApEmK1aswNChQ1GnTh2Vut+kSRO88MIL6kBWXhJUlIBiWZdTp06p8RgknVquSxBSlrZ07NgxFeQ0BWll3AhnVKNjJFzcChe1sB6tcObX3SWuf2nvCexZsBph3Vui0ahecHF1Rde3H1ePSWO06FlyPQkZ9gLg6lrorHfynl8Rs/RZ1Jv0NbxqRECLWAbMp9cyYCTZ2TnYE3XJYa+/+5DjXpvIFo4cOaLaT7I0Ir0eB9gWMJ9ey4AljF4PkH5I702ZtdpEJpGVDEZrFZ3tWnqAytBvIikpSc2sTeSsnH4SmmXLlqmU5ZEjR6JSpUolriMzRhUNQEqmpKTsywQ1MrCrjCE5depU/P777/jjjz/g6mp97NWars4SlBw1apR6bVuQ7ud9+/bFpUuX0KdPH/V+rdW2bVv1fJbwyHXFy2h/3fUiBndC5zcfwYYxsxC3df+17QN8kZmcWup2/85dgdp92qLtlHtRpVkEqrVuiG2vLMHlY2dhrUYNGyHTxXaNVRdPH9SYZ1mjyL95d7T59tpsZ0X5hEcWms0w/dxJHJ99F2qNna22LY9GjRoiNyMNtmL0MmDN96+3MkAly4EnMqq8UOrj25cNRkhw6ZkrIcE++cvTP48odb24+FS0u7t4BtCFS1fUcU+rYoOeBlwDERsXq+n3UR56/AzuvPNOs9c9f/58fsaIzPBpLunKVtHYFmBbgG0B29cB1tYDjqgDbO2O/zwJv0oB+fV/0dt6p8X3L12eS0uUEjKBrsxdIeT/e2RkpM2Cj6YxH69cuYL//ve/arl161bcdtttKhGrNI0aNVKzcRNZIyQkBDt27NBnAHLjxo1qKRmEZWUkFg1Afvfdd2qWbJNu3bqp2xLI3Lx5M26++War90kmwzF3bIWLFy/md78uT2VTkCnoKAPYdu7cGatXr4aHh4fVzyfBxzNnzli0jaeLG1Dj+uudXLMVAXVDEH5ru/wGp19YMK7EXChzu9ysbHV2e+D6WWgyti/O/X0QBz5Yh/I4G3sWGbm268YhXV/M+AislpOeimMzb0dg+8GoboNZDs+ePaue01aMXgbs/f1roQxQKVx9gMJDlhUiwcdaNfyu+zTubq5mrVeci8V1ulPxz1b9M3Kys7X9PspDh5+B/CkyV1paWv7Sku0c8VmxLcC2ANsC5rHkt2xtPaCH+lLqfdNS3k/R23qnxffv5eVV6mPSHfrPP/9U1/38/DBiROknlq0NPkpcQi7Dhg3Lz36UmbLvv//+MusB0/MQVSSnD0CaBmotLYIvYz9u2bKlWACyYPCxYKafKG/ltWbNGjXe5PVIYFQCn0JmuFq0aBHKSyoxOXOyd+9etG7dWk3AU97Z4SSCbc0Zb5h58jh6/TbcsuRZbH85r0IM790Wp3+6fsQ883IqcjKy4ObpgZgNO4Hc0s8Um6NmaE2bZ0DaU8LWlUg78S+unolSsyEW1WzhAXhWM39gbkn1t3XWg5HLgL2/fy2UASpZLtxQVm6OZC6WRTIfJfiYlZ2DuPg0i5/HBVmoGRYGrYp1c1NVi6ubG0I1/D7KQ4+fgfzxMpcp2CA9XCzZLswBnxXbAmwL2JuzlwFzWfJbtrYecEQdYGtS75uW8n6K3tY7Lb7/shKTpPelaYbq7t27mzXTtaXBRxNJsJLeo7LOpk2bcM8995QaJ5B6gBmQVJHxI80EIE0HH9NZsKJkfEiZJVsmprneQK6//vqrTTMRyyJBTtMM2NLl4LPPPis2S5WlUlNTMXDgQDXjt7yHH3/8UQ1iW17WpM9mpl7F5/VHmbVuUlSM/CNHUKNaSIyKgX/dECQvuf4srZ3nPQpXD3ckRp1GiyeHqrPnydHWz+4adSQKHr7WVfolScsCun4Pu6naY7S62EpU1BH42PAXb/QyYO/vXwtlgEoX3vtLxJwrOWOjpG7TBUm3a8l8lOCjPI+lbmhUA3tW5vUM0KJavZbhzPlUhIaEImafdt9HeejxM5C2iyV/tORPVL9+/dQY3uaaN28eKhrbAmwLsC1g+zrA2nrAEXWArc1453NcTrmSV//HxBS7rXdafP8SYFy5cmWJj/3777/512+55Ra7BR+FBBuld6T0IJV1ZfzUgglaBUVFRVk1+zaR7iehMUVXd+7cWeKArhMnTswffNXFxaXMgOBLL72ksgdbtmwJe5PxJqWLtIxFIgfP8v7A5QyFPJeczahfvz5++eUXNTGPVpz+eYfqduPu643MlOufdY28rz9CO9+A3W99jd8eeFOd9eo899osiKQ9LANkJG2aVnXga2vn2EBUkgYNGqiTrLIkfWFbgMzFeoC0Ljc3FydOnFDXg4KCrJp4xtzgo0nBRCtJhCJyNk4fgOzVq5dayjTzEqkveBZNMgwl+1GUFVSUma9lIFb5oS5evNjqfZHu1DKztjndAObPn6+CkJKhWd7gY3Z2tkqh/umnn9TguxJ8LM/MWY4gXWzC+7RFze434uwfe8pcV86It558Dy7sOoJ9C79RZ8l3v/kVQm5qphqipE0sA2QkbZs5LgjIACRpnbSbKleuzOwMHWJbgMzFeoC07sKFC/m9Oa/XU9MWwUdRr169/OsMQJIzcvoA5KRJk1C1alWcPn0azZo1UxPANGzYEO3bt1c/sJ49e6r1Sksvlq7bgwYNUmcfJIAXGhpq9b5IQHHFihUlji9ZlIxXMmXKlHJNDmPy1Vdf5ad1S4Ujs2l36dKlxIuls1lXFBk0PKBeKOr0a48L2w+XvqKLC7rMe0zNUr55wkLk5uSN0bPvnW8Rv/uoaoj617H3cN9kDywDZCRDe1ne0LQFNzcX3N6j9FkPibRAutnJnyxn7W5H1mNbgMzFeoC0LiEhIf+6pTEIa4KPRV8nMTHR4n0mgtEDkJLxJ92OBwwYoAZtlRmlq1Spgvfff19NwGLKiiwpACnT3cv4izLG4fr169G0aVNoUcEZquRMhky6U9rl6tWrcEa52Tk481veGBimRmRJmj08CDXaN8Gu2cuRdOTaZEGyjTRA2fVGu1gGyEgi6wWhRzvrT3hZ67budVArxJqZs4mch/RckbafLElf2BYgc7EeIK2TmMVdd92F22+/XSVRWfLff+7cuRYHH4WctJGen9Jr09oxJ4nsSRM57TKWwdq1a4vdLwckCUjKD+2GG24o9FhOTg5GjhyJDRs24Pvvv1cZk1o1duxYddG6U+u3lTlzYWDDMLSeNALndxzG/ve+K/a4qetNm8kjVdebgx/bedRvsjmWATKSR0dE4tftsRX+mkREzoxtASIyAuk1OWTIEIu38/LywoQJE9QQdDIBk7nBR5O7777b4tckqiiaCECWZv/+/Wpw10aNGhWbYv7RRx/F119/jeeee0499tdff+U/JpO4mNONmmwreu2fZT4uZ7g/rXtPmevsXbBaXbQo6uU+yEqIk1NTcPPxR/gDb8O3XqsS15VyfeSlW5B6fCdaflE8ff7k/LG4uPF/uPHzBLhXCoJWGL0MkLEM6RWBXh1r4pe/zlbI693ZOwI9O2hrfGAiMh62BYiIyiY9N1955RWEhYVZFHwkcnaaDkDu3bu31O7X0uVazJo1S10K+uSTT3SRUUjaUm/iV/nBwoQ/V6sgYtP5ed2Qijq/Zi68QuqrAGRRCX+ugotb+ccWJW0FpUl7XFxc8NErXXDDkNVISc2062sFV/bGO5M72fU1iKjiJGxZgct7NiD8vrk4PmcErp4+AFdPH7gHVkftR96FdyhnBtY7lgEiY7Nm4hoiZ+f0Y0BaG4CUrtmSRVbShcFHcoSCmYrZqUlqgPWSpJ3aj8S/vkHI0OeKPZaZeA5xX89ArXFv2XVfqeKC0k3f3oOm83aj+uCnVVCa9KVOTX+8+6JlgcG4+FTEnLuiluZwdXXB4qldUb2qj5V7SeRcpJeKdD8zcm+VxL9WI6jD7ep6tT4Potmiw+qkZVCH2xC98H5H7x5VAKOXAdYDRET6o9sMSCJndGLuvUje+6u63nBK8TGLcrMyEb3wAdR5/GPA1a3Y4/JY2Ng34ObrXyH7S44JSmelJOLAEzcgJyMNnsHhyM1MR3rccVTpPhoRj3/kwD0ma4wa2ACXktIx4fVrQ4GUpd3da8x+bikyH0/tgkHda5djD4mcS9WqVdU43npWVj1f55F3kXJoCyImLIGLuwcC2/bP386vUUec+2aOQ/edbINloGxGqAeIiIxG0wHIjRs3OnoXiCxS96mlainjN8YsfbZYEPLsl1MRdNMQ+IRHIv3cyUKPxf/0ETyr1UZAi54Vus9U8UFpCUxWufke1S07dPhLSNr5I+JWzGDwUcOeGNkMfj7uGP/aVmRklj7zqyV8vd3xyatdcdet9WzyfETO4vLly9i2bZuaQDAgIAB6VFY9f3nXT/Br0kkFnoo6v3Y+gtrf5pB9JttiGSibEeoBIiKj0XQXbCKtqtpzjAo6ZV2+WOj+lP2/48K6Bdj7QAQOP98F2amX1fXMpAtq/cS/v1W35SIOTGiB1OO7HPQuyFZB6RaLTyNs1HQVlDZJPbEbPv8/HmTqsX84NqQO3DekMXYuvx3tbggu93N1axuCPSvvYPCRdOns2bOYPHmyWupZafV84t/foHLHO4qtH/v1DKTHHkXYvTMrfF/JPlgGSmeUeoCIyEg0nQFJpKVuNjnpqfCsmjdDrYzx6O5fFW7+VQqt13jmpvzrkgF58KmWaP5hXiZk3Wc+L7TuP7e5oOn8PZqaBZvKDkpHv/uwCkq7B1RF2ond+X9E5E9JUPvBjt5FsoFmDSpj69JBeO/rQ5j/+X4cPXXZsu3rB+Gp0TfgP7c3UmM/EpF2lVTPy1jlSbt+RNiYNwqtG7d6DhL/XIWG036Bq5evg/aYbI1lgIiIjIQBSKIKIOP7HX9jmBrnx8XFFe4B1dDgxbVqltyTC+5XDc6gDgwwGUlZQemMi2dkdD94Vg1Tj6Wd3IPQYS84eI/JVtzdXfHY3U0xfngkNvx9Fp9+dxTb91/A4ZNJyM0tvK4EGSPrBqJ982oYO7ghurYJUfUGEWlbafV8atQ2+NSKhJtPpfx1z337FhI2LVOBJ5501A+WASIiMhoGIIkqgFf1Ooics63Ex0ob18+rRgRafpFY6nO2+bZIpIJ0E5SWbvUFu1y7+QXh/PeLOAakzkhwsfdNYeoikq9k4NCJJFxJy1KTy1Ty9UCTiED4+RYfA4yItK20et49IDh/5mORER+DmMXPwDOkHqJe7KHuc3H3QuScvx2y32Q7LANERGQ0DEASETlZUDqo3UB1MYl8c3sF7hk5ir+fJ9rdUM3Ru0HkcF5eXmjcuLFa6lVp9fz+x5qhxvS8icmEZ3AtnnDUKZaBshmhHiAiMhoGIImIiIjIadStWxeffvopjKjZwv2O3gVyMJaBPEauB4iI9IqzYBMREREREREREZHdMABJRERERE7j8OHD6Ny5s1oSkTGxHiAi0h8GIImIiIjIaeTm5iIzM1MticiYWA8QEekPx4Akq7j7eGHksc+gtX22JW83YFN/aIbsry0ZvQxo7fu3RxkgIjI6rR0L2BZgW4BtASLbcnNzw9ChQ232fLPfX47kK1fg7+eHiQ8NL3bbVvtM5AgMQJJVXFxc4OHrDSNzcQF8DPwLMnoZMPr3T0REPBawLWDs75+I8upBd3fbVQSS85uTm7eU5y16m0jL2AWbiIiIiIiIiIiI7IYhdCIiIiJyGhEREVi2bBnCwsIcvStE5CCsB4iI9IcBSCIiIiJyGt7e3qhfv76jd4OIHIj1ABGR/rALNhERERE5jdjYWEyfPl0ticiYWA8QEekPA5BERERE5DSSkpKwZs0atSQiY2I9QESkPwxAEhERERERERERkd0wAElERERERERERER2wwAkERERERERERER2Q0DkERERETkNFxdXdGqVSu1JCJjYj1ARKQ/rNGJiIiIyGnk5ORg165daklExsR6gIhIfxiAJCIiIiIiIiIiIrthAJKIiIiIiIiIiIjshgFIIiIiIiIiIiIishsGIImIiIjIafj7+6Nv375qSUTGxHqAiEh/3B29A0REREREJmFhYZg2bZqjd4OIHIj1ABGR/jADkoiIiIicRnp6Ok6fPq2WRGRMrAeIiPSHAUgiIiIichonTpzA0KFD1ZKIjIn1ABGR/jAASURERERERERERHbDMSDJKrm5uchK01aXCHcfL7i4uNjs+XJzgavZ0AxvN8CGb9/wZUBr3789ygARkdFp7VjAtgDbAmwLEJEtyXEgO1tbFaGbm5tN4wJkPgYgySrS2Py8/ihoychjn8HD19tmzycNzq7fQzM29Qd8bPiLN3oZ0Nr3b48yQERkdFo7FrAtwLYA2wJEZEsSfFy5ciW0RIZ3cHdnRegI7IJNREREREREREREdsOwLxERERE5jSZNmmDbtm2O3g0iciDWA0RE+sMMSCIiIiIiIiIiIrIbBiCJiIiIyGlER0dj3LhxaklExsR6gIhIfxiAJCIiIofPoHgiJhmrfjmJK2lZ6j5Z/vznGVxK0tYMu1R+aWlp2Ldvn1oSkTGxHiAi0h+OAUlEREQVLicnVwUY319xCL/viCsWaExMzkCfh35Q1yNqVsLg7rXxyPBINKkb5KA9JiIiIiIiazEASURERBWa7bh0zVFM/3A3jp66bNY2J8+m4O0vDqhLz/ahmP10e7RuGmz3fSUiIiIiIttgAJKoAiXv/Q1RL/YodJ+rtx+8ajZC1e6jUX3g43Bx489Sz1gGyMjOnLuCB6dtxvebYqx+jo3bYtF+5BpMvv9GvPhgS3h6uNl0H4nsjccBYhkgIiIj4pGNyAEq33w3Atv0l1QgZCbE4eJvSxGz+GlcjTmIOo9+4OjdowrAMkBGs3lnHAY9/rPqWl1e2dm5ePX93fhxyxmse6cPgit722QfyTmEhoZi6tSpaqlnPA4Qy0DpjFIPEBEZCQOQ5HBjY1fY7LmWhN4JLfCt1xpVu4/Kv12t/3jsH98E8T9/hJqjXoNHYDUYCcsAywDp2+87YtFv/I9Iu5pt0+fdtu8Cuo9bh98/GYCqQQxC6kVgYCD69esHveNxoDC2BVgGjFgPEBEZCQOQGrFmzRqsX78e//zzD86cOYP4+Hh4enqifv366N+/P55++mkEB2tvPCy/sGBse3kJDnywFkbm5u0Hv8Ydkbh1BdLjjhmqwckykMfIZYD07eDxRJX5aOvgo8n+Y4kY+NhP+OOTgfDwcLXLa1DFSkhIwC+//IJevXqhcuXKMAojHwfYFshj5DJQlFHrASICUlJSkJqaipycHBXzCAoKgqur+W28jRs3omnTpggJCbHrfpLlGIDUiLfeegu///67+gHWrFkTLVq0wPnz57Fnzx78+++/+Oijj/DTTz+hZcuW0JLw3m1x+qcdjt4NpyANTeFeqQqMhGXgGqOWAdKvrKwcjH3xDyRfyTR7m+3LBiMk2Bdx8alod/cas7b5a88FzPz4X0x5uFU59pacxblz5zB79mw0b97ccIEHox4H2Ba4xqhloCgj1wNERnPp0iVs2rQJUVFROHHihLpdkI+PDyIiIlCvXj106tRJJWGV5ocffsCSJUtQpUoVTJkyhUFIJ8MApEaMGzdO/YC6dOmigpAme/fuxT333IN9+/ap5YEDB6AlAfVCcGhJHIwmJz0VWZfj1WywWQlxuPDDe0g7vgu+DdvDO6wRjIRlgGWA9OvNpXtVN2lLSPCxVg0/i1/r1Q924bYetXFj46oWb0vkCDwOXMO2AMsAERnPkSNHsG7dOmzfvh3Z2aX3lElLS8PBgwfVRdaXQGTfvn1VbKRgZqQp+CgkiLljxw4MHDiwQt4LmYcBSI249957S7xfzgp+/PHH6NChQ/6PMjIyElrg7uuNzJSrMKLYZS+rS0FBNw1B7YfegZGwDLAMkH4lXk7HtPd2V9jrZWXl4vn5O/D9olsr7DWJyoPHgTxsC7AMEJGxpKen48svv1QBQzkBUzTbsW7duqrbtYuLiwo+RkdH4+LFi/nrHD9+HIsWLVJdrR9++GGV5Vgw+CiGDBmCAQMGVOj7Ip0FIGXcwzfeeAOrVq1CTEwMqlWrpgrWjBkz8MQTT2Dx4sVYsGABHnvsMTgD+THJj8beCgYcZawErajZrQXO/P4vjCj41gdRudMw5GZnIi16L+JWvY6M+Bi4eFybRCF5/yYcnVZ88O3crAzk5mSjzWr7jKdWkVgGWAZIv5Z+dxSpV7Mq9DV/2BKD4zGXUa9WQIW+LpE1eBzIw7YAywARGcfp06cxZ84cNcxCwUmnevbsqTIaZeb7ksZ7TEpKUvNhyLBzJ0+eVPcdOnQIkyZNQrt27bBly5b8dSVGNGzYsAqJxZBlNDNa++7du1W2n4wFEhcXpwYVzczMxNtvv43hw4erzD9hzzEQu3fvrgqxqcCXRcZmbNWqFY4ePQp7M/3Y/Pz80LhxY2hF9XZNcGH74UL3tX7+HjULYoMRPUvcpu/KqRh9chmCGodDy7xCGyKgZS8EtumHkCGT0OCF75B6dDtOvftw/jr+zbqi1fKUQpdmi6Lg7h+Mmve8Cj1gGWAZIH2SE3CLlh90wOsC7311qMJfl2zL19dX9eyQpZ7xOJCHbQGWASPXA0RGIpmLr7zySn7w0cPDA6NGjcI777yjYjphYWGlTjZjClLOnDkTL7zwAqpXr67uz8jIYPBRQ1y1kvk4aNAgFXh85plnEBsbi507d6rbr7/+ev64AVLIZHIWZ/DJJ5+oyWF69Oihfmi2JjNCyeewdOlSjB07Vt0nmaCVKlWCJkiF4ALk5uQUunv3nK+QcDAa7V8ZA9/QwoNvN31wIEI6NcPuOcuRePh0Be+wfVWK7IQq3UcjYfNypBzcWuI6OZnpOD5rCCo17YLQYZOheSwDhRiyDJBuHTudjMMnkxzy2us26atuMKLatWurHi2yNBJDHgfYFijEkGWgFEatB4j06uzZsyp4eOXKFXVbullLLEfGaHR3N79jrsR8JDFNesY2bNiw0GNt2rRh8NHJaSIAKd2rpcu1dK2WdF1/f//8xyTl9sYbb0RWVpaaGSkgwDm6Xb355psYPXq02m8JQpqTNWmO9957T/2g3Nzc1GzYY8aMQa1atfDdd9+pz0krqrVqgPhdxbNDczKzsGnCQrj7eqHzW+Pz7w+oXxOtn7sbF/6Jwr5F5s2KqjWhw18CXN1w9ospJT5+atHDyMm8iogJ18a20DKWgeKMVgZIv/45EO+w1z50IglXUs2fdZucjwxEn5KSUuaA9HpltOMA2wLFGa0MlMbI9QCR3sjveOHChUhOTla3pdemTLAr8Qxr/fbbb2oSm4IkAUyStMh5OX0AUrpWL1++HMHBwSpiXhKJdAsJRJrINO69evVSYwh4eXmpIF3BrtrlIUFFCSiWdTl16pRKL5Y0YbkuQUhZlpe8n86dO6suCfKDlWCkdPf+4osv1LgIzqhGx0i4uBUuamE9WuHMryVPTnBp7wnsWbAaYd1botGoXnBxdUXXtx9Xj0ljtOhZcr3wDm2AKl1HIHnPBjXeT0Hnv3sbSTvWov7z38DVS3tdUVgGzKPnMkDGsvOg4wKQOTm52H34ksNen8pP/lBI+6noHwsj0PNxgG0B8+i5DFjCyPUAkd5IspSpV6jEMJ599lk12Yy1ik44I9mUQpLSJGFLeouSc3L6AOSyZctUARo5cmSp3YtNhbdgADIhIUGl5soYkTJQqaT37t+/HzfddJMKIJZH165dVSG/3qV+/fpqZiYhQUkZ36C8brvtNmzevBl//fUXzpw5o6L8HTt2VJ+TM87yFDG4E3p9Ohk1OhSemdsjwBeZyaVPmPPv3BW4tO8E2k65Fx1eG4dqrRti5+vLcPnYWehZyLAXAFfXQme9k/f8ipilz6LepK/hVSMCWsMyYBk9lgEynlOxVxz8+ikOfX2i8tDjcYBtAcvosQwQkTHJ7NUrVqxQ1yV56pFHHinX2K4lzXYt2ZQ1atRQt6OiolR2JDknp58F2xTAkwzC0pgCigUDkIMHD1aXgmR2JEn3XblyJSZMmGD1Pklg09PT0+wfnKn7dcHZqm1F9kXGwKxXr54afPWXX35RmZ+WaNu2rRpP0xIeua54Ge2vu97JNVsRUDcE4be2Q9zW/eo+v7BgXIm5UOZ2uVnZ6uz2wPWz0GRsX5z7+yAOfLAO5dGoYSNkutjubIiLpw9qzLPsrKx/8+5o821uqY/7hEcWms0w/dxJHJ99F2qNna22LY9GjRoiNyMNtmL0MmDN96+3MkBUmouVhgOeTUt8bPuywQgJLr3hGRLsk788/fOIMl8nLj4V7e4u3g1z/GMTMDGj5KwqLYgNehpwDURsXKzqwaEHd955p9nrnj9/Xi3Xr1+vZrw01x133IGKxrYA2wJsC9i+DrC2HnBEHWBrd/znSfhVCsiv/4ve1jujv38tfgYSFymtp6rYsGGDykwU/fr1KzZuY3mDj6YxHx966CFMmzYtfz2JH5U2FmSjRo3U5DVknZCQEOzYsUOfAcjo6Gi1rFOnTomPS2E2zXpUMABZkqpVq6qlJYOclmTNmjVqvMnrkcBot27d1HXp/r1o0SLYg4yJKa8jgVXJiLQ0ACnBR8mmtISnixuQd5LhuqLXb8MtS57F9pfzKovw3m1x+qfrF9jMy6nIyciCm6cHYjbszJvetBzOxp5FRq7txpGRri9mfgRWyUlPxbGZtyOw/WBUH/CYTQb+lee0FaOXAXt//1ooA0SlCr8ClHKeToKPtWr4Xfcp3N1czVqvJIkJ8UhMtOy45lT8s1UflZzsbIuPz87KNOi8OdLS0vKXlmzniM+KbQG2BdgWMI8lv2Vr6wE91JdS75uW8n6K3tY7o79/LX4GMtxdaSRWY0ook9mtZcIZewQfRdOmTdGgQQMcPXpUDX0nmZCSfFZaPZienm71vpD1nD4AaTrgmA5CRcn4kDJLtgThTH3/iw54Kl24JZD5/PPPq2jtXXfdZff9lsrBNAO2nPH77LPP1MQx9mI6q2DNQM3ymVhzxhtmnjxOiooBcoGgRrWQGBUD/7ohSF5y7rrbdZ73KFw93JEYdRotnhyqzp4nR19/u9LUDK1p8wxIe0rYuhJpJ/7F1TNRajbEopotPADPaubPDCjjbdg668HIZcDe378WygBRaRK9c3CljKzFskjmowQfs7JzEBdfdnkt7bmqBnrB2y8MWhXr5qaqV1c3N4SGafd9FOTn52dx20+G2LFkuzAHfFZsC7AtYG/OXgbMZclv2dp6wBF1gK1JvW9ayvspelvvjP7+tfgZlNUz9MCBA0hMTMzvdVmlShW7BB9N+vTpowKQQpLUSgtASj3IDEjrWRM/0kwAUt6cjOe4c+dONX5jQTLD0cSJE9X1Fi1alJhiK5mBpgxJiYhLBL5atWp23++pU6eqwi9dAWR8xvJmXZbl0qVL+P3339X1li1bWry9NemzmalX8Xl988e0PP3zDtXtJiUmHpkp12/0RN7XH6Gdb8A/M7/A6R+2YdBPs9F57nj8MORlWCvqSBQ8fL1hK2lZQNfvYTdVe4xWF1uJijoCHxsWQ6OXAXt//1ooA0SlWbw6Cve9XHjyBJOSukwXJN2uJfNRgo/hvb+06vUP7foRwZVtV99XtFq9luHM+VSEhoQiZl/5xq12Ftu3b7fopOrYsWPVyWVL2k/z5s1DRWNbgG0BtgVsXwdYWw84og6wtRnvfI7LKVfy6v+YmGK39c7o71+Ln4H8VqUnZkmOHTtWaDg8ewYfTUFOE9OkNyWR7Eh7xmdIw5PQmLoTyyQyUlAKHsQkw1CyH8sKvH388cdqwhYJAgYEBKiouLWzUUswc+jQoWadhZs/f74KQkqGZnkLtwQIZWBVUzS/oF27dqmxFOTMgowHecstt8AZSReb8D5tUbP7jTj7x54y15Uz4q0n34MLu45g38Jv1Fny3W9+hZCbmqmGKGkTywCRcbRpmjfkiSPUqVlJ08FHyhsqp3LlyvxzoENsC5C5WA8Qad+JEyfyr8ucFfYMPgqZ3MaUnSc9YK3pHUoGD0BOmjRJjd14+vRpNGvWTAXZZODS9u3bq0Lcs2fPMsd/lLTbDh06YMSIEWoA1OTkZLzxxhtW7YsEFGUGJ3MyKKW7gAQNPTw8UF4pKSl49dVX1fuW2Z0ksi/vSVKwW7dujW3btqmBVL/55hu7dvMuDxk0PKBeKOr0a48L2w+XvqKLC7rMe0yNEbF5wkLk5uR1kdn3zreI331UNUT969h7tB2yB5YBIuNoWq8yqjkoCNijXahDXpdsRzI8nnnmGafM9KDyYVuAzMV6gEj7ZKxFITGR0NBQuwYfTUxzh2RmZuLChbInOqOK5/QBSJnpadOmTRgwYAC8vb3VjNIydsD777+vZn82ZUVebwIaERQUlD8wqZbIe5OMyttvv11lccp7lsxHiehLhug777yjJp+x5qxCRcnNzsGZ3/7Nu/7/jciSNHt4EGq0b4Jds5cj6ci1QXZlG2mAytgX0vWGtIdlgMg4PDxccf+QksfdsbeHhzVxyOuS7ciJV2n7yZL0hW0BMhfrASLtCwwMVLGb6tWrqxNK5vrpp5+sCj4KeT3JnpbXlLlAyLloIqc9MjISa9euLXa/HJAkICmF+YYbbrju85w/fx6HDx9W2YNaIj+gJ554Ql207NT6bWXOXBjYMAytJ43A+R2Hsf+974o9bup602bySNX15uDHdh50h2yOZYDIOB4a1hivf7IHOTnlm7HWEq0jq6J9c/uP80xE1mNbgIjIGF566SWrtgsPD1eza8tM1ZYEH8WYMWPUhZyTJgKQpdm/fz9yc3NV92Pp71/QqFGjVLajjA0pmY9HjhzB3Llz1TgiTz31lMP22cii1/5Z5uNyhvvTuveUuc7eBavVhbSJZYDIOOrU9Me42xvio1XXxm+2t5cfbmV2A5WIHINtASIiul4C2nPPPYeDBw+qSX3ZttMPTQcg9+7dW2r3644dO2Lp0qWq6/LVq1dVFF0mrZk8eXL+uABEFSnq5T7ISogDXF3h5uOP8Afehm+9VoXWSd77G45M6wfvsGtdF5u8/idcvXzyb0vQ/chLtyD1+E60/CKxQt8DEZEl5jzTAT9sOYOYc1fs/lojB9TH4B48vpM+JGxZgct7NiD8vrk4PmcErp4+AFdPH7gHVkftR96Fd2gDR+8i2RnLABEZPQgpF9IX3QYgH3vsMXUhchb1Jn4F90pB6nrCn6txcv5YNJ2fNw5SQRJ8bDpvd6nPc37NXHiF1FcBSNJ/UJpIywL9PfHRK13Q95Efzd4mLj610NIcNav74u3nbrJqH8n5yGR/EyZMMGvSP71K/Gs1qvS4V12v1udBBLTppzJAzq9biOiF96Pxa785ehfJzoxeBlgPEBHpj24DkETOxhR8FNmpSWqGR0ulndqPxL++QcQTnyBh69c23kNy1qA0kZbd2rkW3pl8Ex6dUXa3S5N2d6+x6PmD/D2xftGtqBLoZeUekrOpWrUqRo4cCT3LSknEgSduQE5GGjyDw5GbmY70uOOo0n006jzyLlIObUHEhCVwcfdAYNv++dv5NeqIc9/Mcei+k22wDJTNCPUAEZHRaDoAuXHjRkfvApFFTsy9F8l7f1XXG04pedD09NhjOPBUa7i4uqHqLf9B9f55szzmZmUieuEDqPP4x4CrW4XuN1VsULqsPyURj3/kwD0mss74EU3V8rGZf5Y194TFqlX2xk/v90WLRlVs96TkcJcvX8a2bdvQvn17BAQEQK/1f5Wb71HZ76HDX0LSzh8Rt2KGquMv7/oJfk06qcBTUefXzkdQ+9scss9kWywDZTNCPUBEZDTmz4VOROVW96mlaLH4NMJGTUfM0meLPe5bvzVaLI5B07k7Uf/51Yj/4T1c2vyVeuzsl1MRdNMQ+IRzLAy9BaX3jAvH2c9fQt0nPy30p6TGoCdVd/xa982DX+OODD6S5oOQEiysHepnk+frfVNN7PjyNrRsUtUmz0fO4+zZs2rMblnqWeqJ3fD5/2E3Uo/9kz8ER+Lf36ByxzuKrR/79Qykxx5F2L0zK3xfyT5YBkpnlHqAiMhIGIAkcoCqPceoTMisyxcL3e/mGwA3v0B13TO4FirffDdSDmxSt1P2/44L6xZg7wMROPx8F2SnXlbXM5MuOOQ9kH2D0qX9KSHSsl4dw7B35RA8PKwJ3N2tm9FQulp/MKUzfnxPgpmVbL6PRBUl7cTu/LrdVM/LRHNJu35EQOt+hdaNWz0HiX+uQoMp6+Hq5eugPSZbYxkgIiIjYQCSqAJIl9qMi9fO4Mo4ju7+VeHmX7jbYOalWOTm5Kjr2anJSNq+Nr9h2njmJjT/KBrNPzyJxjM3q2ClXPcI5ODcegxKl/SnhEgPAip54t2XOiP6h+GYOr61mkDGHO1vqIb/Tb8ZMT+PwAN3NlGTMRBpVcbFMwBc4Fk1TN1OO7kHPnWaIzVqG3xqRcLN51pw/dy3byFh0zI0nPZzoaE7SNtYBoiIyGg0PQYkkVbI+H7H3ximxvRzcXGFe0A1NHhxrfoDfXLB/QhqPxhBHQYj4c+VuLD+Xbi4uSM3OwuVOw9T40CSPoPSOemp8Kxas1hQuqQ/JaHDXnDwHhPZVs3qfpjycCu8+GBLHDt9GTv2x2PnwYu4mHQVGZk58PZ0Q0RYJbSJDEabpsGoXtXH0btMZDOpx3cVOrHk5heE898vgntAMII63J5/f0Z8DGIWPwPPkHqIerGHus/F3QuRc/52yH6T7bAMEBGR0TAASVQBvKrXQeScbSU+VnBcv+oDHlOX6z5fjQi0/CLRpvtIzhOULu1PCceAJD1ydXVBwzqB6nJ3//qO3h1yAl5eXmjcuLFa6lVQu4HqYhL55na13P9YM9SYnjdZnWk4ljbf2nDmJnIaLANlM0I9QERkNAxAEhE5WVC6tD8lRERGULduXXz6ad6kXEbTbOF+R+8CORjLQB4j1wNERHrFMSCJiIiIiIiIiIjIbhiAJCIiIiKncfjwYXTu3FkticiYWA8QEekPA5BERERE5DRyc3ORmZmplkRkTKwHiIj0hwFIIiIiIiIiIiIishtOQkNWcffxwshjn0Fr+2xL3m7Apv7QDNlfWzJ6GdDa92+PMkBEZHRaOxawLcC2ANsCRGRLbm5uGDp0qM2eb/b7y5F85Qr8/fww8aHhxW7bap/JMRiAJKu4uLjAw9cbRubiAvgY+Bdk9DJg9O+fiIh4LGBbwNjfPxGRHAfc3W1XEcqgCzm5eUt53qK3Sdv4DRIRERGR04iIiMCyZcsQFhbm6F0hIgdhPUBEpD8MQBIRERGR0/D29kb9+vUdvRtE5ECsB4iI9IeT0BARERGR04iNjcX06dPVkoiMifUAEZH+MABJRERERE4jKSkJa9asUUsiMibWA0RE+sMAJBEREREREREREdkNA5BERERERERERERkNwxAEhERERERERERkd0wAElERERETqNKlSoYM2aMWhKRMbEeICLSHwYgiYiIiMhpuLq6wsPDQy2JyJhYDxAR6Q9rdCIiIiJyGvHx8fjoo4/UkoiMifUAEZH+MABJREREREREREREdsMAJBEREREREREREdkNA5BERERERERERERkNwxAEhEREZHT8Pf3R9++fdWSiIyJ9QARkf64O3oHiIiIiIhMwsLCMG3aNEfvBhE5EOsBIiL9YQYkERERETmN9PR0nD59Wi2JyJhYDxAR6Q8DkERERETkNE6cOIGhQ4eqJREZE+sBIiL9YRdsskpubi6y0rR1RtLdxwsuLi42e77cXOBqNjTD2w2w4ds3fBnQ2vdvjzJARGR0WjsWsC3AtgDbAkREtiXHwuxs7RwM3NzcbBoXsQQDkGQVaWx+Xn8UtGTksc/g4etts+eTBmfX76EZm/oDPjb8xRu9DGjt+7dHGSAiMjqtHQvYFmBbgG0BIiLbkuDjypUroRVDhw6Fu7tjDgTsgk1ERERERERERER2wwAkERERERERERER2Q0T8ImIiIjIaTRp0gTbtm1z9G4QkQOxHiAi0h9mQBIREREREREREZHdMABJRERE5CRycnKRI1Pr/v+sikYUHR2NcePGqSURGRPrASIi/WEXbCIiIiIHOXQiEd9sjMaO/fH450A8Tp5NyX8sNj4NXcesRZumwejaugYGda8NTw836F1aWhr27dunlkRkTKwHiIj0hwFIIiIiogrOcpSg4ztfHsDGbbGlricJkJt3nVOX+Z/vR42qPnhgaGOMHx6J0Gq+FbrPRERERETlwQAkUQVK3vsbol7sUeg+V28/eNVshKrdR6P6wMfh4safpZ6xDBAZ28kzyRg3ZRN+3V564LE05y6mYfoHu7Fg2QHMndgBY29rCBcXF7vsJ9kPjwPEMkBEREbEIxuRA1S++W4Etumv0lsyE+Jw8beliFn8NK7GHESdRz9w9O5RBWAZIDKepWuOYPxrW3ElLatcz5OUnKGCmCt+PoHPZnZH5QAvm+0jVRweB4hlgIiIjIST0BA5gG+91qjafRSq9hiNkCET0eSNv+BRtRbif/4ImUkXHL17VAFYBoiM5a2lezHmxT/KHXws6PtNMeg+7nucv6ivMdJCQ0MxdepUtdQzHgeIZaB0RqkHiIiMhBmQ5HBjY1fY7LmWhN4JLXLz9oNf445I3LoC6XHH4BFYDUbCMsAyQKRn7311EM/M2WaX594TdQm3PvIDfvt4AAL9PaEHgYGB6NevH4zG6McBtgVYBgoyaj1ARFRe2dnZSEpKQpUqVeBsGIDUqA8//BAPPvigut6tWzf89ttv0CK/sGBse3kJDnywFkYnDU3hXsn5Kgp7Yhm4xqhlgEjP/j18EY/P+tOur7H70CU8NfsvLJ52M/QgISEBv/zyC3r16oXKlSvDSIx6HGBb4BqjloGijFwPEJHxZGRk4Pjx4+py4sQJXLp0CVlZWXB3d0dQUBDq1auHunXron79+vDy8ioz+PjOO+/g0KFDmDJlCkJCQuBMGIDUoLi4OEyaNAl6EN67LU7/tANGk5OeiqzL8cjNzUVWQhwu/PAe0o7vgm/D9vAOawQjYRlgGSDSq8zMHIx96Q9kZeVatN32ZYMREuyLuPhUtLt7jVnbfPLNEdzZuy76dw2H1p07dw6zZ89G8+bNdR144HHgGrYFWAaMWg8QkbHFxcWpky2///47kpOTS11vy5Ytaunj46MS0Hr37o2wsLASg49bt25Vt2fOnIk333xTBTGdhfPsCZnt8ccfx+XLlzFw4ECsXavtM8UB9UJwaEkcjCZ22cvqUlDQTUNQ+6F3YDQsA9cYtQwQ6dX8z/er7ERLSfCxVg0/i7d7aNoWHPt+GDw93CzelioejwPXsC1wjVHLABGRkaSlpeGzzz7Dhg0bLN7uhx9+UJcuXbpg7NixqFSpUrHgowQd7733XqcKPgrn2hu6rjVr1mDFihUqCCl9+rUcgHT39UZmylUYUfCtD6Jyp2HIzc5EWvRexK16HRnxMXDx8M5fJ3n/JhydVnzsm9ysDOTmZKPN6mxoHcsAywCRXmVn52DBsv0V+pox565g1S8nMaJf/Qp9XbIOjwN52BZgGSAiMpJ9+/bhvffeQ3x8fP59Eihs3749mjZtqrpa16xZEx4eHqobtmRJStds6Vb9119/qe7aYvPmzeq57rvvPvz555+Fgo9PPfUU2rRpA2ejmQCkfDlvvPEGVq1ahZiYGFSrVg1DhgzBjBkz8MQTT2Dx4sVYsGABHnvsMTgD6Urh4uJi0+eUlNxHH31UFcbp06fjrbfegpbV7NYCZ37/F0bkFdoQAS17qeuBbfqhUmQXHH6+C069+zDqTfxS3e/frCtaLU8ptF3GxbM49ExbVBvgHOW8vFgGWAaI9GrdH6dxKvZKhb/uO18eZABSI3gcyMO2AMsAEZFR/PHHHyr4mJOTo27LeI633347brnlFgQEBBRbX4KJERER6tKzZ0+V1SjdtSUuduXKFSQmJqpu1gXXd9bgo3CFBuzevVuN/yHjgEj0V6LCmZmZePvttzF8+HAcPHhQrdeyZUu77UP37t1VQPHkyZPXXXfPnj1o1aoVjh49atN9eP7551Xwdd68eSUWTq2p3q4JLmw/XOi+1s/fo2ZBbDCiZ4nb9F05FaNPLkNQY+2PcVVQpchOqNJ9NBI2L0fKwbwzF0XlZKbj+KwhqNS0C0KHTYYesAxcY9QyQKRXn661bRvAXJt3ncOJmNLHENICX19fdOjQQS2NxKjHAbYFrjFqGSiJUesBItKvzZs34913380PPkpcS2Jcd9xxh9nxHeluPWDAALVd0fiXq6urUwcfNRGAlMzHQYMGqcDjM888g9jYWOzcuVPdfv3117Fu3Tps375dBQdbtGgBZ/DJJ5/g33//RY8ePVSqrC1ISq0U1n79+mHYsGHQPMkOdQFy///HZ7J7zldIOBiN9q+MgW9o4dn/mj44ECGdmmH3nOVIPHwaehM6/CXA1Q1nv5hS4uOnFj2MnMyriJiwBLrAMlCM4coAkY5t23fBYa+9fb/jXtsWateurXq1yNJoDHccYFugGMOVgVIYuR4gIv2Rma3fffdd1VNW9OnTBy+++CKqV69u1fMFBgYWO0EjgU2ZpMaZOX0AUrpXS9afdK2eM2cO/P398x+TmaBvvPFG1S9eUlKdJStQUmBHjx6t9luCkOZkTZZFsj0feOABlZ67cOFC6EG1Vg0Qv6t4dkhOZhY2TVgId18vdH5rfP79AfVrovVzd+PCP1HYt8i8GUG1xju0Aap0HYHkPRvUeD8Fnf/ubSTtWIv6z38DVy99nAlmGSjOaGWASK8uXEpzSPdrk38OXBtTSItkIPWUlBS1NBqjHQfYFijOaGWgNEauB4hIXyReJcHH7P+vz3r16oX//Oc/KmPRGkUnnCn4PNK9++pV5x1X2akDkNK1evny5QgODlZTiJfElF4qgcjSSNagZEi+8sor5d4nCSpKQLGsy6lTp9RrSR99uS5BSFlaa9asWdi/f7+KkNerVw9aU6NjJFzcChe1sB6tcObX3SWuf2nvCexZsBph3Vui0ahecHF1Rde3H1ePSWO06FlyPQkZ9oLUIIXOeifv+RUxS59FvUlfw6tGBLSIZcB8ei0DREay/1iioV+/vI4cOaLaULI0Ir0eB9gWMJ9ey4AljF4PEJF+fPvtt/nxoDp16qiZq62dL6Sk2a6ffvppNG7cWN0+f/68iqE5K6eehGbZsmUqjXTkyJGqr3tJTCmmpQUgv/rqKzWGpK107drV4m0kKDlq1Cg14KilDh8+jNdeew2RkZGYOHEi7KFt27aqS7slPHJd8TLaX3e9iMGd0PnNR7BhzCzEbb02G6hHgC8yk1NL3e7fuStQu09btJ1yL6o0i0C11g2x7ZUluHzsLKzVqGEjZLrYrrHq4umDGvMsaxT5N++ONt/mpV2XxCc8stBshunnTuL47LtQa+xstW15NGrUELkZabAVo5cBa75/vZUBIirZVY+GgP+oEh/bvmwwQoLLzlwKCfbJX57+eUSp68XFp6Ld3cWzwH7e8Adq1RoHZ3LnnXeava40nsX69evxzz//mL2djKFU0dgWYFuAbQHb1wHW1gOOqANs7Y7/PAm/SgGIjYtFrVq1it3WO6O/f2H0z0CL79/T07PUhLn09HR8//336rqbmxseeeQRFTS0VfDRNOZjWFgYnn32WTVD9i+//KImbC7Ye7igRo0a5c+kbY2QkBDs2LFDfwHIjRs3qqVkEJaVkVhaAPLy5ct48sknVddtCQDagkyGIwXMHBcvXszvfi0BRGtIAZVCK6m0Mg27PUjw8cyZMxZt4+niBtS4/non12xFQN0QhN/aLr/B6RcWjCsxZY9PlZuVrc5uD1w/C03G9sW5vw/iwAfrUB5nY88iI9d23Tik64sZH4HVctJTcWzm7QhsPxjVbTDL4dmzZ9Vz2orRy4C9v38tlAEiKoV/FaDkNp8KPtaq4WfW07i7uZq9bkEZ6ekWH9ftTWZqNFdaWlr+0pLtHPGe2RZgW4BtAfNY8lu2th5wtnrPGjn/30VTlvJ+it7WO6O/f2H0z0CL71+GyiuNBAtNdVjnzp3V0IG2Dj6K0NBQNZO2nLSRIfxkpuyBAweWehyQGJMjOHUAMjo6Oj9NtbS+9Fu2bCk1APnCCy+o6K5kUNoqALlmzRqzCo0ERrt166auy0zdixYtsur1ZMId6dN/1113FXtMxkURUgglCi2ioqIsHgvTtK2lZ7xh5snj6PXbcMuSZ7H95bzBssN7t8Xpn64fMc+8nIqcjCy4eXogZsNO4P8HbLVWzdCaNs+AtKeErSuRduJfXD0TpWZDLKrZwgPwrGb+wNw1a9a0edaDkcuAvb9/LZQBIipZurs/4svIWrweyXyU4GNWdg7i4kv/zZb2XF6eLggOC4Mz8fMzP5BqaqhLLxdLtpOz/xWNbQG2BezN2cuAuSz5LVtbDziiDrA1Vze3/KW8n6K39c7o718Y/TPQ4vsvK0Ftw4YN+df79Oljl+CjSe/evVUA0vS6pQUg5ThQ3gxIXQYgTQce0xmwoqRvu8ySLamldevWLfSYpIR++OGHFnXdsRWJzJtmwJbuBp999plKt7WWdEM/d+5cqY9LhNv0uGlKd0tYkz6bmXoVn9c3L6ibFBUD5AJBjWohMSoG/nVDkLyk9Pdj0nneo3D1cEdi1Gm0eHKoOnueHH397UoTdSQKHr7esJW0LKBrXja1XVTtMVpdbCUq6gh8bPiLN3oZsPf3r4UyQEQli0+4imrdPi/xsZK6TBcl3a4l81GCj+G9v7T49Z98eBhmPfkGnMn27dvNXvfQoUNqGB4Zw7tJkyZmbzdv3jxUNLYF2BZgW8D2dYC19YAj6gBbm/HO57iccgWhIaEqoaXobb0z+vsXRv8MtPj+JTFu5cqVxe6XIJ/EhIQET+vXr2+34KMpsCgJeJKUFhsbi6SkJDVbdlHyuLXdwHU9CY0psipZgEXJB2oaE7FFixaFBvGUL+mhhx5SM2c3a9YMFW3q1Kk4evSoGodEDpzl+XITExPVVO0lXV5++WW1jmRamu4LCgqCMzr98w7V7cbd1xuZKdc/6xp5X3+Edr4Bu9/6Gr898KY649F57rVZEEl7WAaIyCiCK3ujdqjlXadtpU3TYGhZgwYN8OOPP6ol6QvbAmQu1gNEpHXSo9eUINawYUOLJ56xJPhoIq9jYgp+OhOnDkDK9OTi9ddfV1HagmfQJMNQsh9Fy5YtC223cOFClRFoi1mvTSTIN3ToULO6AMyfP18FISVD01GRZWcjXWzC+7RFze434uwfe8pcV86It558Dy7sOoJ9C79RZ8l3v/kVQm5qphqipE0sA0RkJB2aV3fYa7drpu0ApLSdKleuzDaUDrEtQOZiPUBEWnfixIn860V77Noj+Cjq1auXf900H4kzceoA5KRJk1C1alWcPn1aZTLKBDAS0W3fvr36YHv27Fls/EcJSr700kuYMmWKSoWVDEK5iKtXr6rr1nRTloDiihUrUK1ateuuK2OVyOvba9IYLZJBwwPqhaJOv/a4sP1w6Su6uKDLvMfUuJebJyxE7v9/V/ve+Rbxu4+qhqh/HXsP9032wDJAREZy7yDHZO3c3CYEEWGlzICjEdLF6plnnnHarlZkPbYFyFysB4hI6wpOoBUcbP7JYWuDj0LiZ0XnDHEmTh2AlGnWN23ahAEDBsDb21tFcKtUqYL3338f69aty8+KLBiAlINUcnKy6oItZ81MF1MmpVw/deqUw96TUeVm5+DMb//mXS8jANzs4UGo0b4Jds1ejqQj12a5km2kAcquN9rFMkBERtKvSy3UqVmpwl93/PBIaJ00mKX954wNZyoftgXIXKwHiEjrunbtqpLjnn32WYvGfzx79mz+XCaWBB9NMTR5vRdffNHqSW/syelz2iMjI7F27dpi98vBSAKScmb0hhtuyL9fxgn59ddfi60vXbbHjBmDsWPHlmvWHmciXcxt2c3c3k6t31bmzIWBDcPQetIInN9xGPvf+67Y46auN20mj1Rdbw5+bOdRv8nmWAaIyCjc3FwxYWQzPD377wp7TRl38o5b6lTY6xFZg20BIiIyAsl6tCTz0SQ8PFwFEd98802MHz/e7OCjqFSpElq1agVn5fQByNLs379fTbois/z4+voW+sC7d+9e4jYRERGlPkb2F732zzIflzPcn9a9p8x19i5YrS5aFPVyH2QlxAGurnDz8Uf4A2/Dt17xyiHt5F6c+vBxZCXmzfBYc9RrqHzTkPzHpdwfeekWpB7fiZZf5A0voBVGLwNEZCyPjWiKz9Yexc6DFyvk9T6Y0gWeHm4V8lpE1mJbgIiIqGxNmzbFggULCsW69ECzAci9e/cW635N5MzqTfwK7pXyZilP+HM1Ts4fi6bz87ohmeSkp+LojNtQ98mlqNS0C3Kzs5GVcqnQOufXzIVXSH0VgCRtMzcoTUTa5OHhiiWv3ow2I75FZpb540/HxacWWprj/iGNcGvnWlbtJzmfhC0rcHnPBoTfNxfH54zA1dMH4OrpA/fA6qj9yLvwDuXMwHrHMkBEZGy+Ogs+GioAKVljRI5kCj6K7NQkNcB6UZd+/wJ+jTuq4KNwcXODR+C1iY/STu1H4l/fIOKJT5Cw9esK2nNyZFCaiLSteaMqWPRCJzwwdbPZ27S7e41Fr9GmaTDemtgBeiET/k2YMMGsif/0KvGv1ajS4151vVqfBxHQph9cXFxwft1CRC+8H41f+83Ru0h2ZvQywHqAiEh/DBOAJHIGJ+bei+S9eWOUNpxSfMyiNDm77e6Fo68ORMbFGPjUaYFa495UQcjcrExEL3wAdR7/GHBlFzs9B6WzUhJx4IkbkJORBs/gcORmpiM97jiqdB+NiMc/cuAeE5E17h/aGKlXszDh9b9s/tytmlTFD+/eCn8/T+iFzOA4cuRI6FlZ9XydR95FyqEtiJiwBC7uHghs2z9/O79GHXHumzkO3XeyDZaBshmhHiAiMhrNBiA3btzo6F0gsljdp5aq5cWN/0PM0meLBSFzs7Nw+d9f0GT2X/CoUhNnP52MU+8+gvrPrcDZL6ci6KYh8AmPRPq5kw56B1QRQWkJTFa5+R7VLTt0+EtI2vkj4lbMYPCRSMOeGNkMwUHeeHj6FiRfybTJcw7uXhtLX+uGQH/9BB/F5cuXsW3bNrRv3x4BAQHQo7Lq+cu7foJfk04q8FTU+bXzEdT+NofsM9kWy0DZjFAPEBEZjaujd4DIiKr2HKOCTlmXC09M4FmtNvyb94Bn1TDVzaZK91G4EpWXMZOy/3dcWLcAex+IwOHnuyA79bK6npl0wUHvgmwVlG6x+DTCRk1XQWmT1BO74fP/40GmHvuHY0MS6cA9A+pj36oh6NMprFzPUznAE5/O6IZv5vfSXfBRnD17FpMnT1ZLPSutnk/8+xtU7nhHsfVjv56B9NijCLt3ZoXvK9kHy0DpjFIPEBEZCQOQRBXUzSbj4rUGlIzj6O5fFW7+VQqtV6XLXUg9ul0FF0XSju/hE5E3zEDjmZvQ/KNoNP/wJBrP3Aw33wB1veAYkaSfoHTaid35f0QYgCTSj9qhlVSX6TVv90ZfCyeNqVndF1PHt8bBb+/EqIEN1Ikq0q6S6nkZszxp148IaN2v0Lpxq+cg8c9VaDBlPVy99DcovVGxDBARkZFotgs2kZbI+H7H3ximxvlxcXGFe0A1NHhxrfrzeHLB/QhqPxhBHQarDMiQOyfj0LOd1HoeVcNQZ/wHjt59slNQWmY996xas1hQOuPiGZmCSGXCirSTexA67AUH7zER2YrU/YO611aXo6cu45uN0fjnQDz+ORiPY6eTkZOTN3FekL+nGuNRJpnp2roG+nUJVzNrk/aVVs+nRm2DT61IuPlUyl/33LdvIWHTMjSc9kuhsYNJ21gGiIjIaBiAJKoAXtXrIHLOthIfKzquX9Ueo9WlzOerEYGWXyTadB/JeYLSqcd3Fcp4dPMLwvnvF3EMSCIdalA7AP8d27zQfZmZOXBzc4GrKzMc9aq0et49IBhBHW7Pvz8jPgYxi5+BZ0g9RL3YQ93n4u6FyDl/O2S/yXZYBoiIyGgYgCQicrKgdFC7gepiEvnm9grcMyJyNKNnOXp5eaFx48ZqqVel1fP7H2uGGtPzJiYTnsG10ObbvIxY0heWgbIZoR4gIjIaBiCJiIiIyGnUrVsXn376qaN3wyGaLdzv6F0gB2MZyGPkeoCISK+MfYqdiIiIiIiIiIiI7IoBSCIiIiJyGocPH0bnzp3VkoiMifUAEZH+MABJRERERE4jNzcXmZmZaklExsR6gIhIfzgGJFnF3ccLI499Bq3tsy15uwGb+kMzZH9tyehlQGvfvz3KABGR0WntWMC2ANsCbAsQEdmWm5sbhg4dapPnmv3+ciRfuQJ/Pz9MfGh4qfeVd38dhQFIsoqLiws8fL1hZC4ugI+Bf0FGLwNG//6JiIjHArYFjP39ExFR3rHQ3d02B4NcADm5eUvTc5Z0n1axCzYRERERERERERHZjbbDp0RERESkKxEREVi2bBnCwsIcvStE5CCsB4iI9IcBSCIiIiJyGt7e3qhfv76jd4OIHIj1ABGR/rALNhERERE5jdjYWEyfPl0ticiYWA8QEekPA5BERERE5DSSkpKwZs0atSQiY2I9QESkPwxAEhERERERERERkd0wAElERERERERERER2wwAkERERERERERER2Q1nwSYiIiIiu2rXrp3Z69aqVQsvv/wyevXqhdDQULvuFxE5Xx0gWA8QEekPA5BERERE5DQk2PDKK684ejeIyIFYDxAR6Q+7YBMREREREREREZHdMABJREREREREREREdsMAJBEREREREREREdkNA5BERERERERERERkNwxAEhERERERERERkd0wAElERERERERERER2wwAkERERERERERER2Q0DkERERERERERERGQ3DEASERERERERERGR3TAASURERERERERERHbDACQRERERERERERHZDQOQZJZXXnkFLi4uxS5Hjx519K4RERERERFRCb7//nu0bNkSXl5eiIiIwFtvvQUj+eOPP3DbbbehTp066v/r9OnTYSSzZ8/GTTfdhMqVKyMoKAhdunTBDz/8AKP49NNP0aZNG/X+fXx8EBkZqX4Dubm5MKKNGzfCzc0NDRo0cMjruzvkVUmT5ID1559/FrqvWrVqDtsfIiIiIiIiKtmOHTtU8O2///0vli1bhr///hsPP/wwfH191dIIUlJS0LRpU9xzzz148sknYcSA07hx49CuXTv1vX/00UcYOHAgfv/9d3Tu3Bl6V716dbz00kto3LixCsJv2rQJ48ePV0G4CRMmwEji4uIwZswY9OnTB0eOHHHIPjAASWaTH2lISIijd4OIiIiIiIiuQzK9JPA0c+ZMdVuyv/bv349Zs2YZJgDZv39/dRHPPvssjGb9+vWFbr/xxhsqA3LVqlWGCEDeeuuthW7Xq1cP33zzDX777TdDBSBzcnIwatQoPProo7h69arDApDsgk1mi4mJQa1atdSlX79+2Lp1q6N3iYiIiIiIiEqwZcsW9O3bt9B9cjs6Olr9tyPjkUDU5cuX4efnB6ORbtfbtm1Tv4sePXrASF599VU1BIGjg/DMgCSztG/fHp988olKX5cK6/3330fXrl3V2ZPevXs7eveIiIiIiIg04UraVZyJiy92f1Z2dv4y6kRMsdsF1axRFZV8fcp8ndjY2GI92Ey35TFJLHGU46djkZWV9/6sef+V/HxQs3pVaNXFhMu4mHi52P2WfAb169SEm6tlOWUzZsxAYmIiHnzwQThSZmYWTsTElev9V68ahKCAStd9raSkJISFhSEjI0MFYF9++WU88cQTcLSY2AtIvZpe6L6S3m9pn4GXpwfqhNW47uv8+uuveO+997Br1y4VhHQkBiDJLKa0dRMJPspZMxnUlgFIIiIiIiIi80jg4Iff/8bZcxdLfDw17SoWf/V9qbdDqlXBY/feAS07E3cB6zb+ZdX7lxDKg/cMgpa5urrg829+RnpGplWfQbsWTdCormUB5EWLFqkA5Jo1axwafBbu7m74e/cB7I86adX7lwD0k+PuNOu1/P39sXv3bqSmpqpenM8//zxq1qyJ++67D450OeUKlq76qcTHir7fku4bNqD7dQOQ8fHxquu1JJM5w3B67IJNVpPZtE6eLLnCICIiIiIiouLc3dwwfGBPtbSUm5srhg/soQI41xMaGqomnijo3Llz+Y85Uue2zVGvdk2rtr25w42oG+7Y/S+vyoH+GNzbujEYqwT6Y2DPjhZtM2fOHEycOFEFH3v16gVHk0y8O27tqgKJ1hja9+brZgCbuLq6qlmfW7RoocY+nTRpEl544QU4WtOGEWjborFV2zZrFIHWzRped719+/bh7NmzauIhd3d3dZk2bRqOHTumrn/xxReoSAxAktV27tyJ8PBwR+8GERERERGRptQIroy+3dpbvF2fru0QambXY5lk5Mcffyx0nwyhVadOHYdnwLm6uOCuAd1VNqglJPuzd5e20AMJIEkgydLA3V0De8DLy9PsbaZMmYKpU6fi+++/d4rgo4kEECWQaKn2NzZBZIM6Vr+udMOWiVicwaCeN6mAsiUkaDvk1pvN6k4tk1Dt3btXZYCaLhKElTiOXB8wYAAqErtgk1mefvppFTWPiIhQY0B++OGH+Pnnn/Htt986eteIiIiIiIg0p1PbG3DwWDSORZ81a/2IWiHo2q652c//1FNPoVOnTirba/To0fj777+xYMECzJ07F85Axu+7rXdnfLXuN7OzP0cM6mlW9qdJSkoKjh49qq7LGICSESqBl0qVKqmsOEeSAJIEkqLPnEPKlTSztunW4UZVDsz15JNPqvkbli1bhsaNG+dnxPr4+CAwMBCOJoFECShu+/eQWetXCfLHgJ43mf38Mt6jDB8ns19nZmbijz/+wOuvv47//Oc/cAZeXp4qoPz+52uQa+Y2d/brBj9fb7PWlcmGbrjhhkL3Va9eHZ6ensXurwjMgCSzyCDF9957LyIjI9GnTx8cPnwYv/zyCwYN0vbYG0RERERERI7KAhzWvzu8zchmk0xBCVRId1JzSfbTN998g7Vr1+LGG29UmXCvvfaayoByFq2aNUTzxnXNWvfWru1UBqQlduzYgVatWqmL/Kd955131PX7778fzkACSRJQModkvvbq0sai558/f77K9rvjjjtUt3vTZcKECXAWElCUwKI5AdvhA3pYlDUryVNS3ps1a4aOHTuqyVhmzpyJt956C84iolYIunVsada6HVpGokn92tAql1yZi5yIiIiIiIiIKtyu/UewfO2vZa4jQSprx4vTwqzg8z7+GsllZAHKmI8PjBhgUQBWS1b/uAl/7z5YZvbn42OGWByA1YromDi898V3KCs81eOmlrj1ZsuHLdCCrOxsvLP0G8SeL3liKlE1KABP/GeoxcMWOBN9/nrJYXJyc3HkZEyZFQcRERERERHladm0AZo3rlfmZBVtmjeCXvn5lJ0FqLI/B3TXbfBR9O/RUQWYStP35va6DT6KOrVC0L3jjaU+XrNGVdzS2bLsT+1NTNVDBZrLHPtTw8FHod9fMDnEvkPH8fHy77H4q/UMQhIREREREV2HBBduv7UL/Cv5ljhRx5C+Xc2acELLGtevrbqXlmRwr85q1mg9M3WxL+l7rlc7FJ0tGPtTqyTAKIHGEoNzA3pYNWu8loRUq1Jqhmf3ji1RJ6wGtM4wAUj5IZt+zN99950aiDQgIADBwcG488471TTkJjJGRrdu3RAUFKTWue2223DkyJFSnzs9PV2NrSAD/Mo23t7eaoBXmeY+Pj6+xG1kAOBnn31WjcsREhICLy8vhIWF4a677sL27dtLfS2Zuap///9r7/5Du67zAI6/KlcNFVkZy9PLNG9KTkE9NdG8znN5dodwV6FWIBhcVxT+UedF2X9RFEWS4B/RVSO6oh+SEiTogdKMPMpUKk/IZVlCll2cS9O5PN7v+I6vW0s399Ha9/GA4bav+34nNYNnr/f7dU2+OLSqqiouvPDCfC/j4sWLY9OmTXGmpx/Xb9qS3x8+rLbP/0cSAACgyCnAP8+dmSNkJfhDmgKsOX4KMG2Jnlj/q6gEKTCl0NQxTKZ7QtN9oX1dV6Fxzm8mR20fnv4sN2PyuBycyw2tHRy/mz4x+oKKCZAl6dLZefPmRXNzc956dfDgwXjllVdycPziiy9i+fLlebFKCo5pU9LRo0djzZo1MXPmzPx4R59//nlMmzYtb5dKUTEFyLq6uvj444/jkUceiUmTJuXX6ujGG2+Mhx9+OD+WImi6FDWFzJdeeimHzPQ9dbRy5cq8Jv3111/Pq+PHjx8ftbW18emnn8bTTz8dzz77bJzp6cd9+/+bL1GePun0b1QCAAD4uRo98pdxxYTL2z+ePH5MXD5qeFSKc8+tygGqNMgyoH91/GlO35/+LJdCUwpOJfMa+v70Z7kUGlNwLBl5yS9i+q/7/vRnx8VUpaPWKcamydi+Mv1ZcQFy6dKl0djYGJ999lls2bIlx7s0hZg+TlOE99xzT3587969+fE9e/bkiJjW1T/66KPHPVc6Yjx//vx49913cxhMU5S7d++O7du358nH9HyffPJJ3HTTTZ2+j7SBLEXO/fv3x3vvvZdfa9++fbFq1ao8QZm2crW0tLT//hRCly1b1h4iU/h855134oMPPsibnTZu3Bhz5syJn8L0Y6r21eefd8a+FwAAgJ+ja66aGoNrBuWtwH+cdUVUmkuG1sZvp03I76eJ0EqZ/iwpD071dSNi4tjKmP4sl4JjCo/td39WUIBOUnBO4Tn5/VVTonZwTfQVFbMFu/R/Te644454/PHHj3ts7dq1MXfu3C4fTxOH6dhzmjjctm3bccehU3isr6/Px6ZTOCzX1tYWU6ZMyXGxqakppk///l+iE7nvvvvi/vvvj+effz4WLFiQP5cC6JAhQ6Kmpia++uqr6E0rGlfFgZauN46djNajR+PQt4fz++nukrOisv6SAAAA6K2NuElfmXrqrpQoWluP5onISnWktTX69etXcfGtJJ34bPvuu6jq1y8q9WfgSPoZqOr3k5sAHjigOm9k74mK+6eZJgs7mjhx4kk93vEodemY9KJFizrFx+Scc87Jx71TgNywYUOnAJkmIF944YUcNdMkZGtra/58moRMtm7d2h4gL7roovwaX3/9daxbty4aGhqit6T4+L+Wb3rx+Q722nMBAABQeb49ciQq2uEK//NHxKH4fsipUh3uYz8DFRcgL7vssk6fS3Hvxx5PC1+S8iPRSTpqnaT7F1999dUffL10VDpJR7zLpePcd999dz5a3ZUUJctj5pIlS+Khhx6Kq6++OkfR2bNnx4wZM/L9lWlZzqkU7FNh+hEAAACgbxt4Cv2o4gJk//79O32ufKT1RI+XS9OISbqH8UTSspuStK36rrvuylExHbVOW7YvvfTS/NrptZ566qm4+eab2yciSx544IEYNmxYXqSTpirTW1pkkzZo33DDDXnpzQUXdH87VE/HZ0t3Py7/x8s5QM6eMSlmT5/U4+cCAAAAoO+puADZmwYMGJB/TVuy0+bsk1XaVn3nnXfGvffe+6OTj+XOPvvsuP322/NbWp7zxhtv5OPYL774Yp7CTAtz0sen8w7I8unHzVt3xL+3/qdHzwMAAADAT5c7IM+QsWPH5nsa0xbr7gTIjz76KP+ajk//kLfeeuuEz5EmIRcuXJjfUsgcN25crF+/Pj/3iBEjzsgdkO5+BAAAAKAjAfIUXHfddfHcc8/FE088kbdnlyYiT6S6urp9s3VHaTHNa6+91u0QOmjQoHwkfO/evd0OkD09w+/uRwAAAIDKMNAdkGdGursxLYDZuHFjXgyTQmR9ff1xq+M3b94cjY2NsXTp0hg5cmT+/JVXXhmrV6+OBx98MGbNmtW++Ob999+Pa6+9Nh+17ijdM/nYY4/luyGnTp3afi9lW1tbrFixIsfHtCU7xcju6sn4rLsfAQAAADgZZx07duxYVIBSsOvqj9vTx7/88sscIt9888388fDhw+Piiy+OQ4cOxa5du+Kbb74/2rxjx44YM2ZMfv/AgQN5i/WHH34YVVVVMXr06Bwr0+8ZMmRI3HbbbbFs2bJYtGhRPPPMM/lr0lHvCRMm5PcHDhyYo2VaYrN79+72OyNXrlwZt956a5wO23fsin+u+Vecf9658fe/Lozq8887La8LAAAAwM9L51E7umXw4MF5AjKFwoaGhhwc33777XwX46hRo2LJkiX58bq6uvavSQGxqakpFi9eHDU1NbFz585oaWmJW265JW+2Hjp0aKfXSV//5JNPxvz583OkbG5ujm3btuWpx+uvvz4vpDld8TFNP67ftCW/P2PyOPERAAAAgC5VzAQkvefbw0di9bqm2Nm8J/72lwUCJAAAAABdEiA5pRCZjmADAAAAQFcESAAAAACgMO6ABAAAAAAKI0ACAAAAAIURIAEAAACAwgiQAAAAAEBhBEgAAAAAoDACJAAAAABQGAESAAAAACiMAAkAAAAAFEaABAAAAAAKI0ACAAAAAIURIAEAAACAwgiQAAAAAEBhBEgAAAAAoDACJAAAAABQGAESAAAAACiMAAkAAAAAFEaABAAAAAAKI0ACAAAAAIURIAEAAACAwgiQAAAAAEBhBEgAAAAAoDACJAAAAABQGAESAAAAACiMAAkAAAAAFEaABAAAAAAKI0ACAAAAAIURIAEAAACAwgiQAAAAAEBhBEgAAAAAoDACJAAAAABQGAESAAAAACiMAAkAAAAAFEaABAAAAAAKI0ACAAAAAIURIAEAAACAwgiQAAAAAEBhBEgAAAAAoDACJAAAAABQGAESAAAAAIii/B9OPWk/L3yCyQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1677.96x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transpiled_qc3 = transpile(qc3, backend = fake_hardware_backend)\n",
    "transpiled_qc3.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd800b55",
   "metadata": {},
   "source": [
    "As you can see, transpilation greatly extend the depth of your circuit. You can use the options in the transpile function to reduce the depth of the transpiled circuit."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86a5d06b",
   "metadata": {},
   "source": [
    "## Problem 4:  Quantum Fourier Transform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "85526dde",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.circuit.library import SGate, TGate\n",
    "CS = SGate().control()\n",
    "CT = TGate().control()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "a54410af",
   "metadata": {},
   "outputs": [],
   "source": [
    "def qft(qc):\n",
    "    # TODO implement the QFT for 3 qubits\n",
    "    qc.h(0)\n",
    "    qc.append(CS, [1,0])\n",
    "    qc.append(CT, [2,0])\n",
    "    qc.h(1)\n",
    "    qc.append(CS, [2,1])\n",
    "    qc.h(2)\n",
    "    qc.swap(0,2)\n",
    "\n",
    "\n",
    "def initialize(qc):\n",
    "    # TODO initialize to states different from |000⟩ here\n",
    "    qc.h(0)\n",
    "    qc.x(1)\n",
    "    qc.h(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "00880250",
   "metadata": {},
   "outputs": [],
   "source": [
    "# HINT:\n",
    "\n",
    "# you can use\n",
    "\n",
    "#from qiskit.circuit.library import SGate, TGate\n",
    "#CS = SGate().control()\n",
    "#CT = TGate().control()\n",
    "#qc.append(CS, [control,target])\n",
    "#qc.append(CT, [control,target])\n",
    "\n",
    "# or a controlled phase gate specifying the angles for S and T in terms of π\n",
    "\n",
    "# from math import pi\n",
    "# qc.cp(angle, control, target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "8259d0bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1165.66x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc4 = QuantumCircuit(3)\n",
    "\n",
    "initialize(qc4)\n",
    "qft(qc4)\n",
    "qc4.measure_all()\n",
    "\n",
    "qc4.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "98832636",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1092.68x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc4_transpiled = transpile(qc4, simulator)\n",
    "qc4_transpiled.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "c46091b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vwZZbbplaNOMkkrlz5xa3x9DapUuX9NqUl3vuuafG96lqpYprM7Zu3bravtGee+4Z5s+fnybtFMSKHcd8zpw5M7UmF7Rt2zbsvvvuaZJR1XGqcajBDjvskGaUT548ubi9Ic49x+SYHJNjckytV4ljKswjWOlj7KqaNWtW2G+//dIvW95LxGBXU+Crj9j1uuGGG4YDDzwwDB48OHz22WfVWu3iQcfxfnFiRZxBe/fdd1f7A7/77rtpTOCLL75Ya1dsTS123bt3T29ioT+7Ia4eNj5LuCsnb523R3ZXeTleuTomx+SYHFMlHdOsWbNCp06dVv4Yu6pGjhwZnnzyybDbbrulFrU4m7WhlhOJBx9D19Zbb53+sA899FAYPnx4ei4m4Zh6YyKP4r+jR48O06dPTwk9euCBB9IfInbn1qZVq1bpsbT4++KjqviHjo+l1Xb8tW1f+nUpvZrek9rep/psjxUzPuq6vbZzrKHPPcfkmByTY6pv2Wvb7phCgx9TjfuGFTRu3Liw3XbbpZC1Mu8uccYZZ6Q162JzZWxKjTNgH3300XDfffelGSFHHXVUCpVxpmwMa8cff3wKc3HiRLTHHnukAHfIIYeEiy++OI2rO/PMM8Nxxx1XY3ADAMjFCge72P+8yy67rPRbhsWWtrjuXFx/Lga5/v37p1D3/e9/Pz0f18WLqTi22FVdoLggJuAYOuMs2Bj44pIrsUXx3HPPXanlBAAoNys8xm7HHXcM6667brj11ltDjqxjV5msYwfAqpxJVvheseecc06apPD000+v6EsAAFAOXbFx7Fqc+rvrrruGgw8+OGy11Va1psjYtQoAQJl2xcZxbnF8XdUfX3q8XXxuZSx3Ugq6YiuTrlgAKuaWYlXFW4oBAFA+yvKWYgAA1N8KT54AACCTFruq9zj7NnGxYQAAyjTYrb/++nVanDjus/T91gAAKKNgF5cwqSnYxRkbL7/8cnj33XfTUigxAALk4sILLwx33HFHePPNN0Pr1q3DDjvsEH7961+H3r17F/eJ99B+7LHHqv3cv/3bv4Wrrrqq+P3Pf/7zMGHChPDaa6+Fvn37hpdeeqlRjwPI0woHu+uuu67W5+IyJ7/5zW/SvVqvueaaFf0VAGUnBrZ47+ltt9029Ub88pe/TPeofv3119MtDAuOPvroarcybNOmzTKvdeSRR4ZnnnkmvPLKK41WfiBvKxzslie25J1yyilh/Pjx4dRTTw1///vfG+LXADS6e++9d5mL3C5duoQXXngh3T+7apDr2rVrra/zu9/9Lv07Y8YMwQ5YNWbFbrPNNuHhhx9uyF8BUFJx+EnUsWPHattvuumm0Llz57DZZpuFM844I3z55ZclKiE07lCF2Jrdtm3bdMGz3377hcmTJ9fauzds2LDUGDR27NhqF0txW02P6dOnN+LRrJoapMWuYMqUKSZOANlavHhxOPHEE8OOO+6YAlzBQQcdFHr27Bm6deuWWuNOP/309OEWx+ZBzuo6VCG6/PLLaxyrf+CBB4Yf/OAH1bYdfvjh4auvvkphkUYOdvE/ug8//DAl7rvuuisMHjx4Zf8KgLIQP8Di5Icnn3yy2vZjjjmm+PXmm28e1llnnfR/YbzY3XDDDUtQUiivoQpxslAci//888+n+lFVnJQUHwVxuELs/TNmv4GDXeFesbWJTawdOnRIbxxAbkaMGBHGjRsXHn/88bDeeustd9/tt98+/fv2228LdoRKH6oQhyXEVu0rrrhiueNQC2644YY0ZvWAAw5o0LKGSg92MXnXFOxi4IuBLjbDHnHEEZpNgazEi9bjjz8+3HnnneHRRx8NG2ywwbf+TGEpk6VbJqAShyqcdNJJaZmgfffdt06vE1vqYhCs2opHAwS7+B8aQCV2v44ZMyYNNYkDxKdNm5a2r7nmmumDJ3a3xuf33HPP0KlTpzTGLn6QxYvh/v37F18ntt598cUX6efnz59fDH/9+vULLVu2LNnxQUMOVbj77rtTt+o//vGPOr3GxIkTwxtvvBH++te/NmBJ89KgkycAcvOHP/yhuAhxVddee20a4B1D2YMPPpgGhs+bNy907949DB8+PJx55pnV9v/pT39abRHjAQMGpH/j4u4WdifXoQox1MWLn/bt21fbP9aRnXfeeZlGoz//+c9hyy23DFtvvXWjlX1Vt1KCXVw9PV5tzpkzJ7Rr1y69CbHpFSDHrtjliUFu6btO1ESvB5U4VOEXv/hFuqipKk4wuuyyy8Lee+9dbXts0b711lvTEio0UrB76qmn0ji62KVQeEML4+423njjdAU7cODA7/IrAIBMhirEyRI1TZjo0aPHMiHwlltuSUum/OQnP2m08ld0sJs0aVJamybObvn+978fBg0alAYGxzfxkUceCffff38YOnRoePrpp9OYEQCgsocq1EecNLH//vsv021LAwW7eA/Er7/+Otxzzz3LLCQYF+OMa9nss88+ab+bb755RX8NAJDJUIX6/EzsFaQRbykW+87jmjJLh7qCuD0+H1vvAAAo42AXFx38tvWb4vOFxQkBACjTYBfvgRjHzy3PM888k/YDAKCMg10cPxe7Y88666x0Y96q4vfnnHNO6oat68rSAAB8N02WrMhIxxDCp59+mu5/GBfTjKurb7fddmHttdcOn3zySXjuuefSTXt79eoVnn322Wr3iFtVxDX54vTs2JUc1+ZrKOv/YnyDvTb1995Fe5W6CACwwplkhWfFxjAXu2JPO+20NOs1zo4tWG211dL6dr/+9a9XyVAHAFBxCxR37tw5/OUvfwl//OMfw5tvvlm880SfPn1CixYtVl4pAQBY+cFu9OjR6f6Ho0aNKoa3+G+8JUhBXN/uV7/6VVp1Ot4+BACAMgt28cbWZ599drj44ouX2yIXb4Idu2pPPfXUNA4v3pUCoD6MPy0vxp9ChrNib7jhhtChQ4cwYsSIOt0vLo6vi7cRAQCgzIJdvL3HkCFDQqtWrb5137hP3HfChAnfpXwAADREV+xHH32UljCpq3jnibvuuqs+vwIA+BaGKpSX98poqEK9WuyaNm0aFi5cWOf9477xZwAAaHj1Sl3x9mCvvfZanfeP+6677rorUi4AABoy2O28887h4YcfDu+999637hv3ifvusssu9S0TAAANHeziTNfYvXrAAQeEmTNnLvd2Yz/+8Y/DokWLwrHHHrsi5QIAoCEnT2y11VbhxBNPDJdffnno169f+NnPfpbWqFtvvfXS8x9++GF46KGHwtVXX53uFTty5Mj0MwAAlOGdJ37zm9+ke8Fecskl6S4U8VHVkiVLQrNmzcIZZ5wRzj///JVZVgAAVmawa9KkSbjgggvCUUcdlRYfjmvbTZs2LT3XtWvXsOOOO4bDDz88bLjhhvV9aQAAGjPYFcTgpkUOAKB8WGQOACATgh0AQCYEOwCATAh2AACZEOwAADIh2AEAZEKwAwDIhGAHAJAJwQ4AIBOCHQBAJgQ7AIBMCHYAAJkQ7AAAMiHYAQBkQrADAMiEYAcAkAnBDgAgE4IdAEAmBDsAgEwIdgAAmRDsAAAyIdgBAGRCsAMAyIRgBwCQCcEOACATgh0AQCYEOwCATAh2AACZEOwAADIh2AEAZEKwAwDIhGAHAJAJwQ4AIBOCHQBAJgQ7AIBMCHYAAJkQ7AAAMiHYAQBkQrADAMiEYAcAkAnBDgAgE4IdAEAmBDsAgEwIdgAAmRDsAAAyIdgBAGRCsAMAyIRgBwCQCcEOACATgh0AQCYEOwCATAh2AACZEOwAADIh2AEAZEKwAwDIhGAHAJAJwQ4AIBOCHQBAJgQ7AIBMlF2we/zxx8Pee+8dunXrFpo0aRLGjh1b7fnDDz88ba/6+MEPflBtn1mzZoWDDz44tGvXLrRv3z4cddRR4YsvvmjkIwEAqPBgN2/evLDFFluEK664otZ9YpD7+OOPi4+//e1v1Z6PoW7SpEnhgQceCOPGjUth8ZhjjmmE0gMAlE7zUGaGDRuWHsvTqlWr0LVr1xqfe+ONN8K9994bnnvuubDNNtukbb///e/DnnvuGS699NLUEggAkKOyC3Z18eijj4YuXbqEDh06hN133z2cf/75oVOnTum5iRMnpu7XQqiLhgwZEpo2bRqeeeaZ8KMf/ajG11ywYEF6FMyZMyf9u3DhwvSI4ms0a9YsfPPNN2Hx4sXFfQvbFy1aFJYsWVLcHrfF52rbXnhdykfV96S296l58/+tNvF9rcv2Fi1apPMlnjcFcQhB3L+27bWdYw117pXjMVFeKuncWxWOifKyuBHOvbpa5c6O2A27//77hw022CBMmTIl/PKXv0wtfDHQxT/AtGnTUuirKv5xO3bsmJ6rzYUXXhhGjRq1zPb7778/tGnTJn3do0ePMGDAgPDKK6+E999/v7hP7969Q58+fcKzzz4bZsyYUdy+5ZZbhp49e6au4Llz5xa3Dxw4MJUxvjbl5Z577qnxfapaqQYNGhRat25dbd8otgrPnz8/PPLII9XOvb322ivMnDkznaMFbdu2TRclU6dODS+99FJx+1prrRV22GGH8NZbb4XJkycXtzfEuVfux0R5qaRzb1U4JsrL1AY+9yZMmFDnsjRZUjUalpmYeO+8886w33771brPO++8EzbccMPw4IMPhsGDB4cLLrggXH/99dX+kFGsfDG4HXvssXVusevevXuqbHESRkNd5W18lnBXTt46b4/i11oYSntM6/9ifLXfSWlNGf2Dijn3VoVjUj/KyzsXDGvQcy9OCo09k7Nnzy5mkmxa7JbWq1ev0Llz5/D222+nYBfH3k2fPr3aPvEPFf8otY3LK4zbi4+lxQoXH1XFP3RNXUW1NY/Xtn3p16X0anpPanuf6rM9Vsz4qOv22s6xhj73yumYKC+VdO6tCsdEeWlaonOvxrKEVdwHH3wQPv3007DOOusUm8Y///zz8MILLxT3efjhh1My3n777UtYUgCAhlV2LXZxvbnY+lbw7rvvpn7rOEYuPmJ36vDhw1PrWxxjd9ppp4WNNtooDB06NO3ft2/fNA7v6KOPDldddVVqIh8xYkT4l3/5FzNiAYCslV2L3fPPP58GFsZHNHLkyPT12WefnZot44DDffbZJ2yyySZp4eGtt946PPHEE9W6UW+66aY0CDF2zcbBqjvttFO4+uqrS3hUAAAV2GK32267VRs4uLT77rvvW18jtuyNGTNmJZcMAKC8lV2LHQAAK0awAwDIhGAHAJAJwQ4AIBOCHQBAJgQ7AIBMCHYAAJkQ7AAAMiHYAQBkQrADAMiEYAcAkAnBDgAgE4IdAEAmBDsAgEwIdgAAmRDsAAAyIdgBAGRCsAMAyIRgBwCQCcEOACATgh0AQCYEOwCATAh2AACZEOwAADIh2AEAZEKwAwDIhGAHAJAJwQ4AIBOCHQBAJgQ7AIBMCHYAAJkQ7AAAMiHYAQBkQrADAMiEYAcAkAnBDgAgE4IdAEAmBDsAgEwIdgAAmRDsAAAyIdgBAGRCsAMAyIRgBwCQCcEOACATgh0AQCYEOwCATAh2AACZEOwAADIh2AEAZEKwAwDIhGAHAJAJwQ4AIBOCHQBAJgQ7AIBMCHYAAJkQ7AAAMiHYAQBkQrADAMiEYAcAkAnBDgAgE4IdAEAmBDsAgEwIdgAAmRDsAAAyIdgBAGRCsAMAyIRgBwCQCcEOACATgh0AQCYEOwCATAh2AACZEOwAADIh2AEAZEKwAwDIhGAHAJAJwQ4AIBOCHQBAJgQ7AIBMCHYAAJkQ7AAAMiHYAQBkQrADAMiEYAcAkAnBDgAgE4IdAEAmBDsAgEwIdgAAmRDsAAAyIdgBAGRCsAMAyIRgBwCQCcEOACATgh0AQCYEOwCATAh2AACZEOwAADIh2AEAZEKwAwDIhGAHAJAJwQ4AIBNZB7srrrgirL/++mG11VYL22+/fXj22WdLXSQAgAaTbbC75ZZbwsiRI8M555wTXnzxxbDFFluEoUOHhunTp5e6aAAADSLbYPfb3/42HH300eGII44I/fr1C1dddVVo06ZN+Mtf/lLqogEANIgsg93XX38dXnjhhTBkyJDitqZNm6bvJ06cWNKyAQA0lOYhQzNnzgzffPNNWHvttattj9+/+eabNf7MggUL0qNg9uzZ6d9Zs2aFhQsXFsNhs2bN0msvXry4uG9h+6JFi8KSJUuK2+O2+Fxt2+PrLl7w5Uo8cr6rTz/9tMb3qarmzf+32sT3tS7bW7Rokc6XeN4UNGnSJO1f2/bazrGVee6V+zGpG+Xls88+q5hzb1U4JvWjvHz++ecNeu7FLBJVfa6igt2KuPDCC8OoUaOW2b7BBhuUpDyURufLS10CKE8d1Q2oVYdGqh9z584Na665ZuUFu86dO6eU+8knn1TbHr/v2rVrjT9zxhlnpMkWBTFJx4TcqVOnlLyp3Zw5c0L37t3D1KlTQ7t27UpdHCgb6gbUTv2ou9hSF0Ndt27dvnXfLINdy5Ytw9Zbbx0eeuihsN9++xWDWvx+xIgRNf5Mq1at0qOq9u3bN0p5cxErpsoJy1I3oHbqR918W0td1sEuiq1vhx12WNhmm23CdtttFy6//PIwb968NEsWACBH2Qa7Aw88MMyYMSOcffbZYdq0aWHLLbcM99577zITKgAAcpFtsItit2ttXa+sPLELOy4EvXRXNlQ6dQNqp340jCZL6jJ3FgCAspflAsUAAJVIsAMAyIRgBwCQCcEOACATgh0rlbk4UDv1A2hoZsUCAGQi63XsaBwLFy4Mr7/+ehg/fny6LcyAAQPC+uuvnxaDbt68ebqdW9OmGoepTF9++WV4+umnw2233RY6duwY+vbtGzbaaKOwySabpO+h0n3zzTfpnuw+J1YOLXZ8Z6ecckr429/+Frp06RI+++yz8P7774cNNtggHHTQQeHnP/95WGuttUpdRCiZn/70p+GBBx5IFzuffvppqh9du3YNu+yyS/j3f//3sNVWW5W6iFASzzzzTNh+++2rbVu0aFEKeELeivOX4zuJLXVXX311+NOf/hTuueee8M4774R33303/OQnPwnXXntt2HjjjcONN95Y6mJCyerHLbfcEsaMGZNuafjaa6+Ff/7zn+H4449PrXjbbrttuOSSS1KrtmtsKsnkyZPDwIEDw3rrrZcufmLIi2IvTwx1sT58/fXX4b/+67/CJ598UurirlK02PGdjB49Otx///3hscceKzapN2vWLH09b9688Ktf/So8/PDD4aGHHtJyR8X57W9/G+68887wxBNPpO/jB1XLli2Lz1966aXhyiuvTPUjtnJDpTj//PPDzTffHIYPH54+I1599dU0fCfe5/3II49MLdzxPu/dunVLF0Pdu3cvdZFXGVrs+E7ieKHp06en7qUohrrYlB4/wFZfffVw3HHHpbETf//730tdVGh0W2yxRfjggw/Ck08+mb6PoS7Wj/nz56fvDznkkPRhFj/goJJ89NFHYffdd0/3c49DeW666abwwx/+MF0I9e/fP+y0007h0EMPTZ8xQl39CHZ8J7vuumv6d9iwYSm8LViwIDWlF1olYldsZLwElWiHHXZIEyViK0QcrhADXawfrVu3Ts/HUBe3rbnmmqUuKjSa2LMTQ1yfPn1ST07sjt1rr73CueeemyYZxeE9sd48+OCD4eSTTy51cVc5umJZKVdeI0eODG+88UaqoHHc0KBBg0LPnj3D73//+3D99denpvTYggeVJga3OCRh7NixoU2bNmmw+D777BPat28frrnmmtQN+z//8z/qBxWrppUTxo0bl+rJF198keoNdSfYsVLE7tg4eSJeYcUQFwfGzpw5M+y2225pYGycIQuV+oE1d+7c1B0bH88991x4/vnnU5fskCFDwlFHHZVaK6BSxNgRH8vryRk1alR46qmnwn333deoZcuBYMcKizOV4gzYVq1apa6lXr16pYo6ZcqUtHZXbIHo3LmztbqoSDW1QsSxpzNmzEj15auvvkpdsFrqqDR1Wdv00UcfTd20m266aaOVKxeCHSskjheKy5m8+OKLacxQ79690yDXwYMHp+bzTp06lbqIUBbif7GF2eJxIhFQ95Y76s9fk3qLi6yefvrpKcTFsUFxPa44ODy2RJx33nnhiCOOSC15kesGKk1cpDsuXRIX7p40aVIKc/HiJ/4bA15srYjimNTYRQuVXDcKoa7qWo6xbnz++eclLu2qS7Cj3uK09Hg7pBjievToETbbbLNw2mmnpbEQcTB4XHsozniKFVMLBZXmr3/9axpnGu82sfnmm4d+/fqlRYjj0IXYahc/yOISKHHcabwYgkqxvLoR60X8vCjUjVmzZpW6uKsswY56a9GiRZqp9Oabb6bv41ihOHYoirNhb7jhhjQwPFZeqDSvvPJKOProo9OK+XGyRJwgEWeHx4VW42SiuGZdXBootnbHcalQKdSNxiHYUW8//vGP09VVrJAx1K222mpp3bpCF1NcmyiOsYtXZlBJ4jqOcbB3XDU/tmbHdewuu+yydLuk+IEV7xEbbyd20kknpeEMUCnUjcZj8gT1EsNbbC6Pq4OfcMIJYc6cOWl83bHHHhsGDBgQPv744zSb6Zhjjkm3iImVGCrtAyyOQ42tEEvP/lu4cGFaEigubzJ16tSw7rrrlrSs0JjUjcbRvJF+D5koVMRY+WLLXLxH7F133RV23nnnFPhiZYwVNF51CXVUorj8T6wL8QNs6dnhcRhDXMMu1g0fXFQadaNxCHbUWVxw+JZbbkmDXWOljOvTdejQIY2TOPXUU9Pade+88066vVjhVmJQafXj0ksvTetvtWvXLrVMxOV/4oVQXLsutlLE24j97ne/K3VxodGoG41LVyx1duSRR4aXX345Bbc11lgjXXW9/fbb4cMPP0y3D4srhcdZTlDp9aNt27apfsRlG2K3UrzQibfdGzhwYKmLCY1O3Whcgh11Ek+TGObibcN23XXX4rYY7J544onw5z//OU1Pv/3229PyJ1BJaqsf8S4ssX7EBb1nz54dbr31VivpU1HUjcZnVix18vrrr6fp51VvfxTHSsSrrXg1Fm9kHsdPxGAHlaa2+rHRRhulBbtj/YiLFN92220lLSc0NnWj8Ql21EmsmF26dAknn3xyuqvE0g29cYzEYYcdFsaNG1eyMkKpqB9QM3Wj8Ql21EmsfOeff35a3uSQQw4JY8aMSUubzJ8/vziNPd5aLN4zFiqN+gE1UzcanzF21Etcmy7eSiyuHB7HTey0005pYcl4O7HOnTunsXb9+/cvdTGhJNQPqJm60XgEO1bI9OnTU9P52LFj0xVZnDBxwAEHhL59+5a6aFBy6gfUTN1oeIId39nSK4gD/5/6ATVTNxqGYAcAkAlRGQAgE4IdAEAmBDsAgEwIdgAAmRDsAAAyIdgBAGRCsAMAyIRgBwCQCcEOACATgh0AQMjD/wPqpfk2AwDQLgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results4 = simulator.run(qc4_transpiled, shots=1000).result()\n",
    "plot_histogram(results4.get_counts())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "32dc8b95",
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO also run the qft cirquit with a noise model like in Problem 3 and plot the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "ac0efb8a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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I17lz53r+XhNwTEyMDBs2zAS+4sWLmz56kydP9mOpAAAA8l5A9LHzB+axYx47AACcwJp57AAAAJB9BDsAAABLEOwAAAAsQbADAACwBMEOAADAEgQ7AAAASxDsAAAALEGwAwAAsATBDgAAwBIEOyCITZs2TVq3bi0lS5aUihUrSp8+feTAgQNe23Tq1ElCQkK8bk888YRnfXR09DXr3Te9RCAAIIivFQsg/2zYsEGGDx9uwl1KSor84Q9/kG7dusk333xjrrPsNnToUK/rLRcrVszz84ABA6RHjx5ejzt48GC5cuWKCYsAgPxDsAOC2MqVK71+19Y3DWOxsbHSsWNHryBXuXLlTB+jaNGi5uZ28uRJWbduncyfPz8P9xwAkBlOxQLw0AtMq7Jly3otf+edd6R8+fLSuHFjef755+XSpUtZPsaiRYtMEOzfv3+e7y8AwBstdgCMtLQ0GTVqlHTo0MEEOLeHHnpIatasKVWrVpU9e/bIs88+a/rhffDBB5k+jrbU6d+kb8UDAOQPgh0AQ/va7d27VzZt2uS1/LHHHvP83KRJE6lSpYp06dJFDh8+LHXr1vXaduvWrfLtt9/KW2+9lW/7DQD4H07FApARI0ZITEyMrF+/XqpVq3bdbdu0aWPuDx06dM26v//979KsWTNp2bJlnu0rACBrBDsgiLlcLhPqli5dagY81K5d+xf/Zvfu3eZeW+7Su3Dhgrz33nsyZMiQPNtfAMD1cSoWCPLTr4sXL5YPP/zQzGWXkJBgloeHh5s+cnq6Vdf37NlTypUrZ/rYjR492oyYbdq0qddjvfvuu2bKlN/85jd+Kg0AgGAHBLF58+Z5JiFOb8GCBWYuukKFCsmnn34qs2fPlosXL0r16tWlX79+Mm7cuEwHTfTt21dKly6db/sPAPBGsAOC/FTs9WiQ00mMs2PLli25tFcAgJyijx0AAIAlCHYAAACWINgBAABYgmAHAABgCYIdAPhg2rRp0rp1azM9TMWKFaVPnz7mEmtZDU6JiIiQkJAQWbZsmde6J5980kzkXLhwYTOpMwDkBoIdAPhARwnr/H/btm2TNWvWSHJysnTr1s1MB5ORThOjoS4rjz76qAwYMCCP9xhAMGG6EwDwwcqVK71+j46ONi13sbGxZuLm9FfomDlzpuzcufOaq3So119/3dyfPHnSTPwMALmBFjsAuAGJiYnmvmzZsp5lly5dkoceekjmzJkjlStX9uPeAQg2BDsAyKG0tDQZNWqUdOjQQRo3buxZrpdda9++vfTu3duv+wcg+HAqFgBySPva7d27VzZt2uRZtnz5clm3bp18+eWXft03AMGJFjsAyIERI0ZITEyMrF+/XqpVq+ZZrqHu8OHD5pq5YWFh5qb0GrsZr8kLALmNFjsA8IFOYTJy5EhZunSpfPbZZ1K7dm2v9c8995z89re/9VrWpEkTmTVrlvTq1Suf9xZAsCHYAYCPp18XL14sH374oZnLLiEhwSwPDw+XokWLmsESmQ2YqFGjhlcIPHTokFy4cMH8/eXLl80oWtWoUSMpVKhQPpYIgE0IdgDgg3nz5pn7jKdVFyxYIIMHD87242irns6J59a8eXNzHxcXJ7Vq1cq1/QUQXAh2gOVqPfexONWR6ZESiKdic+Nv9DQuAOQ2Bk8AAABYgmAHAABgCYIdAACAJQh2AAAAliDYAQAAWIJgBwAAYAmCHQAAQLAHu40bN0p8fPx1tzl69KjZDgAAAA4Odp07d5bo6OjrbrNo0SKzHQAAABwc7LIz+3paWpqEhITk9F8AAADAKX3sDh48aC6MDQAAAIddK/bRRx/1+n3ZsmVy5MiRa7ZLTU319K+LiIi48b0EAABA7ga79H3q9BTr7t27zS0zur5169Yya9YsX/4FAAAA8iPYxcXFefrX1alTR0aNGiVPPfXUNdsVKFBAypQpI8WLF8/pfgEAACAvg13NmjU9Py9YsECaN2/utQwAbFDruY/FqY5Mj/T3LgCwJdilFxUVlbt7AgAAAP8EO7ft27fLjh075OzZs2bQRGZ97caPH3+j/wYAAAB5FexOnz4tffr0kc2bN193TjuCHQAAgMOD3ZgxY2TTpk3SqVMnc1q2WrVqEhZ2ww2AAAAAyKEcJ7GYmBi5/fbbZe3atVxdAgAAIJCvPHH58mXp2LEjoQ4AACDQg12zZs0yveoEAAAAAizYTZw4UZYvXy7btm3L3T0CAABA/vaxS0hIkMjISPnVr34lAwcOlBYtWkipUqUy3fbhhx/O6b8BAABAXge7wYMHm/51OtWJXkNWbxn72+k6XUawAwAAcHCw00uKAQAAwDm4pBgAAECwD54AAACAJS128fHx2d62Ro0aOf03AAAAyOtgV6tWrWxNTqzbpKSk5PTfAAAAIK+DnY50zSzYJSYmyldffSVxcXFmKhQNgAAAAHBwsNPpTbKi05zMnDlTZsyYIfPnz8/pvwAAAIC/B09oS97TTz8tt956q4wdOzYv/gUAAADyc1Rsq1atZN26dXn5LwAAAJAfwe7w4cMMnAAAAHB6H7uspKWlyQ8//GD64H344YfSpUuX3P4XAAAAyM1gFxoaet3pTnQARZkyZcwgCgAAADg42HXs2DHTYKeBTwNd69at5ZFHHpGKFSve6D4CAAAgL4PdZ599ltM/BQAAQB7gWrEAAACWyJXBE5s3b5bdu3fLuXPnpFSpUtKsWTPp0KFDbjw0AAAA8iPYbdmyxfSjO3TokGfAhLvfXb169WTBggXSrl27G/kXAAAAyOtgt2/fPunWrZtcunRJ7r77buncubNUqVJFEhISZP369bJ69Wrp3r27bNu2TRo1apTTfwMAAIC8DnaTJ0+Wq1evyooVK6RHjx5e65599llZuXKl3HvvvWa7JUuW5PTfAAAAIK8HT+io2P79+18T6tx0ua7X1jsAAAA4ONglJiZK7dq1r7uNrtftAAAA4OBgV7VqVdN/7nq++OILsx0AAAAcHOy0/5yejh0/frxcuXLFa53+PnHiRHMatnfv3j497rRp08xVK0qWLGmuWtGnTx85cODANY8/fPhwKVeunJQoUUL69esnx48f99omPj5eIiMjpVixYuZxxo4dKykpKTktLgAAgL3BTgOdnmp9+eWXpUaNGnLPPffIkCFDzH3NmjVlypQpZr1u54sNGzaY0KatgWvWrJHk5GQz+vbixYuebUaPHi0fffSRvP/++2b7Y8eOSd++fT3rU1NTTajTwR06JcvChQslOjpaJkyYkNPiAgAA2DsqVlvLNHw988wzZtSrjo51K1KkiJnf7pVXXpGyZcv69Lg6mjY9DWTa4hYbG2uuT6t99ubPny+LFy+Wu+66y2yj8+U1bNjQ7E/btm3NVCvffPONfPrpp1KpUiUzYbIGTR2t++KLL0qhQoVyWmwAAAA7LylWvnx5+cc//mHC1ldffSWff/65uXeHL11/o9yDL9wBUQOetuJ17drVs02DBg1Mq+HWrVvN73rfpEkTE+rcdE49vTKGzr8HAABgI59b7F566SVzWnTSpElSsGBBs0zvNUi56SnQF154wfSTe+6553K8c2lpaTJq1ChzebLGjRubZToBsra4lS5d2mtbDXG6zr1N+lDnXu9el5mkpCRzc9MQqDRE6k2FhoZKgQIFzKle3Tc393Ltw6dX33DTZbouq+Xux3UiLWNulCks7OdDLGP/xqyW67Gkdav/302vZqLbZ7U8q+cjr56nQCuT0zn5eXIiLXugHHs2vp4oE2Vy+nu5T8FOT21qP7UZM2Z4Ql1mNHjpqVodsNCmTRtzVYqc0L52e/fulU2bNkle00EbGlYz0tO6OgBDaatg8+bNZc+ePWZwhlv9+vVNq+H27dvl5MmTnuV6Clj7G27cuFHOnz/vWa6XWdPTy/rYTnXw4MEclyn9AajPfdGiRb1O1auePXvK5cuXveY51BeB9o08deqUp/VV6RcEPe1+9OhRc01itwoVKkj79u3NvqYfYJMXz1Mgl8npnPk85cpltPOEljFQjj0bX0+UiTJt9UOZNm/eLNkV4kofDX/Bww8/bCrghx9+kMKFC193W239qlatmkRERMiiRYvEVyNGjJAPP/zQPEHp58tbt26ddOnSRc6cOePVaqcF19Y9HVih4XP58uVelRwXFyd16tSRXbt2mUrNTotd9erVzZNYqlSpPPv2UG+8M8Pd4Zd6BOU3IhvLdPO4VeJUR6ZHOvJ5currUsVN6xkwx56NryfKRJlS/VCm06dPmwYz7Z7mziRZ8elrqY4w1b5tvxTqlG6j2/qSMpUWaOTIkbJ06VIznUrGSZBbtmxpKnft2rVmmhOlaViTr6Zypfd6yvjEiRMmpSsdYauVkdV1a3V/MyuX/q+MrZNa0XrLyH0wZHf59Vo9/c1dvtwqky/L9SDWW3aXZ/V85PXzFMhlcpJAeJ6cRD8wAvnYs/H1RJkoU6iD3st9etfXaUW01Su7NJRpq5uvp191xKv+nTZxuvvEhYeHmyZTvddpVcaMGWMGVGhY0yCoYU5HxCqdHkUD3KBBg8xpY32McePGmcfOTigFAAAIRD4FO187/Ou2vn77nTdvnrnv1KmT13Kd0mTw4MHm51mzZpnH1RY7PX2qI17nzp3r2VZTcExMjAwbNswEvuLFi0tUVJRMnjzZp30BAACwNtjp5cF0MEN26bY33XSTTzuUnS5/Ok/enDlzzC0r2ucuY4dIAAAAm/nUnHbnnXeawQtHjhz5xW11G91WJxUGAACAw4Kd9lHT06v9+/c3o0Wz8tNPP8n9999vRnfo6VAAAAA47FRsixYtzJQis2fPNoMTnnjiCTMPjE5ronQaFB2t+re//c3Mw6IDHPRvAAAAkPd8ngth5syZpo/bq6++aqYU0VvGPnI6eOH555+XqVOn5ua+AgAAIDeDnc6h9PLLL5spR3Skqs5t556SpHLlyubyXzp6tW7dur4+NAAAAG5Ajmcv1eBGixwAAIBzOHuKdQAAAGQbwQ4AAMASBDsAAABLEOwAAAAsQbADAACwBMEOAADAEgQ7AAAASxDsAAAALEGwAwAAsATBDgAAwBIEOwAAAEsQ7AAAACxBsAMAALAEwQ4AAMASBDsAAABLEOwAAAAsQbADAACwBMEOAADAEgQ7AAAASxDsAAAALEGwAwAAsATBDgAAwBIEOwAAAEsQ7AAAACxBsAMAALAEwQ4AAMASBDsAAABLEOwAAAAsQbADAACwBMEOAADAEgQ7AAAASxDsAAAALEGwAwAAsATBDgAAwBIEOwAAAEsQ7AAAACxBsAMAALAEwQ4AAMASBDsAAABLEOwAAAAsQbADAACwBMEOAADAEgQ7AAAASxDsAAAALEGwAwAAsATBDgAAwBIEOwAAAEsQ7AAAACxBsAMAALAEwQ4AAMASBDsAAABLEOwAAAAsQbADAACwBMEOAADAEgQ7AAAASxDsAAAALEGwAwAAsATBDgAAwBIEOwAAAEsQ7AAAACxBsAMAALAEwQ4AAMASBDsAAABLEOwAAAAsQbADAACwBMEOAADAEgQ7AAAASxDsAAAALEGwAwAAsATBDgAAwBIEOwAAAEsQ7AAAACxBsAMAALAEwQ4AAMASBDsAAABLEOwAAAAsQbADAACwhOOC3caNG6VXr15StWpVCQkJkWXLlnmtd7lcMmHCBKlSpYoULVpUunbtKgcPHvTa5vTp0zJw4EApVaqUlC5dWoYMGSIXLlzI55IAAAAEebC7ePGi3HbbbTJnzpxM18+YMUNef/11eeONN+SLL76Q4sWLS/fu3eXKlSuebTTU7du3T9asWSMxMTEmLD722GP5WAoAAID8FyYOExERYW6Z0da62bNny7hx46R3795m2aJFi6RSpUqmZe/Xv/61fPvtt7Jy5UrZsWOHtGrVymzz5z//WXr27Cl//OMfTUsgAACAjRwX7K4nLi5OEhISzOlXt/DwcGnTpo1s3brVBDu919Ov7lCndPvQ0FDTwnffffdl+thJSUnm5nbu3Dlzn5ycbG5KH6NAgQKSmpoqaWlpnm3dy1NSUkz4dNNlui6r5e7HdSItY26UKSzs50NMt8/O8oIFC5q61f/vpqfkdfuslmf1fOTV8xRoZXI6Jz9PTqRlD5Rjz8bXE2WiTKkOfy8PqGCnoU5pC116+rt7nd5XrFjRa71WbtmyZT3bZGbatGkyadKka5avXr1aihUrZn6uUaOGNG/eXPbs2SPx8fGeberXry8NGjSQ7du3y8mTJz3LmzVrJjVr1jSngs+fP+9Z3q5dO7OP+thOpf0Wc1qm9Adg586dTV/IFStWeD2+tqBevnxZ1q9f7/U8RUZGyqlTp0xAdytZsqTcddddcvToUdm9e7dneYUKFaR9+/ZmXw8cOOBZnhfPUyCXyemc+Tw5961Ryxgox56NryfKRJm2+qFMmzdvluwKcaWPhg6jiXfp0qXSp08f8/uWLVukQ4cOcuzYMTN4wu2BBx4w27777rvy8ssvy8KFC70qUumTqsFt2LBh2W6xq169unkSdRBGXn17qDfemeHu8Es9gvIbkY1lunncKnGqI9MjHfk8OfV1qeKm9QyYY8/G1xNlokypfiiTDgotV66cJCYmejJJVpz7tTQTlStXNvfHjx/3Cnb6u6Za9zYnTpzw+jutKK0U999npnDhwuaWkT6RektPK1pvGbkPhuwuz/i4TuIuX26VyZflehDrLbvLs3o+8vp5CuQyOUkgPE9Ooh8YgXzs2fh6okyUKdRB7+XOfgfLoHbt2iacrV271qtlTfvOaVOr0vuzZ89KbGysZ5t169aZZKx98QAAAGzluK/zOt/coUOHvAZM6Hlr7SOn56ZHjRolU6dOlXr16pmgN378eDPS1X26tmHDhtKjRw8ZOnSomRJFm15HjBhhBlYwIhYAANjMccFu586dpkOj25gxY8x9VFSUREdHyzPPPGPmutN56bRl7o477jDTmxQpUsTzN++8844Jc126dDFNo/369TNz3wEAANjMccGuU6dOXh0HM+tfMnnyZHPLirbuLV68OI/2EAAAwJkCqo8dAAAAskawAwAAsATBDgAAwBIEOwAAAEsQ7AAAACxBsAMAALAEwQ4AAMASBDsAAABLEOwAAAAsQbADAACwBMEOAADAEgQ7AAAASxDsAAAALEGwAwAAsATBDgAAwBIEOwAAAEsQ7AAAACxBsAMAALAEwQ4AAMASBDsAAABLEOwAAAAsQbADAACwBMEOVnvxxRclJCTE69agQQPP+scff1zq1q0rRYsWlQoVKkjv3r1l//79ft1nAAByimAH6916663y448/em6bNm3yrGvZsqUsWLBAvv32W1m1apW4XC7p1q2bpKam+nWfAQDIibAc/RUQQMLCwqRy5cqZrnvsscc8P9eqVUumTp0qt912mxw5csS05AEAEEhosYP1Dh48KFWrVpU6derIwIEDJT4+PtPtLl68aFrvateuLdWrV8/3/QQA4EYR7GC1Nm3aSHR0tKxcuVLmzZsncXFxcuedd8r58+c928ydO1dKlChhbp988omsWbNGChUq5Nf9BgAgJwh2sFpERITcf//90rRpU+nevbusWLFCzp49K++9955nG23F+/LLL2XDhg1yyy23yAMPPCBXrlzx634DAJAT9LFDUCldurQJb4cOHfIsCw8PN7d69epJ27ZtpUyZMrJ06VJ58MEH/bqvAAD4ihY7BJULFy7I4cOHpUqVKpmu11GxektKSsr3fQMA4EYR7GC1p59+2pxi1VGuW7Zskfvuu08KFChgWuO+++47mTZtmsTGxpoBFbpeT9vqnHY9e/b0964DAOAzTsXCat9//70JcT/99JOZgPiOO+6Qbdu2mZ+Tk5Pl888/l9mzZ8uZM2ekUqVK0rFjRxPwKlas6O9dBwDAZwQ7WG3JkiVZrtMpUHQwBQAAtuBULAAAgCUIdgAAAJYg2AEAAFiCYAcAAGAJBk8goNR67mNxqiPTI/29CwCAIEeLHQAAgCUIdgAAAJYg2AEAAFiCYAcAAGAJgh0AAIAlCHYAAACWINgBAABYgmAHAABgCYIdAACAJQh2AAAAliDYAQAAWIJgBwAAYAmCHQAAgCUIdgCAfDVt2jRp3bq1lCxZUipWrCh9+vSRAwcOeG3z+OOPS926daVo0aJSoUIF6d27t+zfv99v+wwECoIdACBfbdiwQYYPHy7btm2TNWvWSHJysnTr1k0uXrzo2aZly5ayYMEC+fbbb2XVqlXicrnMNqmpqX7dd8Dpwvy9AwCA4LJy5Uqv36Ojo03LXWxsrHTs2NEse+yxxzzra9WqJVOnTpXbbrtNjhw5YlryAGSOFjsAgF8lJiaa+7Jly2a6XlvytPWudu3aUr169XzeOyCwEOwAAH6TlpYmo0aNkg4dOkjjxo291s2dO1dKlChhbp988ok5bVuoUCG/7SsQCAh2AAC/0b52e/fulSVLllyzbuDAgfLll1+aPnm33HKLPPDAA3LlyhW/7CcQKOhjBwDwixEjRkhMTIxs3LhRqlWrds368PBwc6tXr560bdtWypQpI0uXLpUHH3zQL/sLBAKCHQAgX+kI15EjR5qQ9tlnn5m+c9n5G70lJSXlyz4CgYpTsQCAfD/9+vbbb8vixYvNXHYJCQnmdvnyZbP+u+++M3Pd6SjZ+Ph42bJli9x///1mTruePXtKsNKWzV69eknVqlUlJCREli1b5rV+8ODBZnn6W48ePfy2v/APgh0AIF/NmzfPjITt1KmTVKlSxXN79913zfoiRYrI559/bkLczTffLAMGDDABUAOeTosSrHR0sE75MmfOnCy30SD3448/em7//Oc/83Uf4X+cigUA5Cs9pXo92iK1YsWKfNufQBEREWFu11O4cGGpXLlyvu0TnIcWOwAALKF9FrVVs379+jJs2DD56aef/L1LyGcEOwAALKCnYRctWiRr166VV155xUwToy18wXwZto2/0C/xgw8+MJeqK1eunFm/e/duCXQEOwAALPDrX/9a7r33XmnSpIn06dPHTCWzY8cO04oXrC7+Qr9EXX/HHXeYIGwL+tgBAG5Yrec+Fic6Mj1SglWdOnWkfPnycujQIenSpYsEo4hf6Jc4aNAgc6/XILYFLXYAAFjo+++/N33sdMQxggctdgAABIALFy6Y1je3uLg40yesbNmy5jZp0iTp16+fGRV7+PBheeaZZ8x0Md27d/frfiN/EewAAAgAO3fulM6dO3t+HzNmjLmPiooycwPu2bNHFi5cKGfPnjWDBXRQwJQpU8wUKAgeBDsAAAKATuh8vTkAV61ala/7A2eijx0AAIAlaLEDAABB1y+xRo0acvr0aXM94mPHjpn1Bw4cMPfaTzFQr+BBsAMAwA+YIsa//RKjo6Nl+fLl8sgjj3jNBagmTpwoL774ogQigh0AAAjKfomDBw82N5vQxw4AAMASBDsAAABLcCoWAAAEBPol/jJa7AAAACxBsAMAALAEwQ4AAMASBDsAAABLEOwAAAAsYXWwmzNnjtSqVUuKFCkibdq0ke3bt/t7lwAAAPKMtcHu3XffNZcO0cuC7Nq1S2677Tbp3r27nDhxwt+7BgAAkCesDXavvfaaDB061FwDrlGjRvLGG29IsWLF5B//+Ie/dw0AACBPWDlB8dWrVyU2Nlaef/55z7LQ0FDp2rWrbN26NdO/SUpKMje3xMREc3/69GlJTk72PEaBAgUkNTVV0tLSvB5bl6ekpHhdk06X6bqsluvjpiVdEic6c+ZMjsuUXljYz4eYbp+d5QULFjR1q3XsFhISYrbX5U6tr/THjK9lymx5VsdYTo49J9fZuXPncvX1lFvHntOPs9x6PeXmsefUOrveMebvY8/JdZbX7+U5PfacWmdnz57N0/dyzSLqete99XBZ6IcfftCSu7Zs2eK1fOzYsa7bb78907+ZOHGi+Rtu3Lhx48aNGzdx4O3o0aO/mIGsbLHLCW3d0z55bpqkNSGXK1fOJG+n029Y1atXl6NHj0qpUqX8vTsBgTrzDfXlO+rMd9SZ76gz++vM5XLJ+fPnpWrVqr+4rZXBrnz58qb58vjx417L9ffKlStn+jeFCxc2t/RKly4tgUYP0EA4SJ2EOvMN9eU76sx31JnvqDPfBVKdhYeHB+/giUKFCknLli1l7dq1Xi1w+nu7du38um8AAAB5xcoWO6WnVaOioqRVq1Zy++23y+zZs+XixYtmlCwAAICNrA12AwYMkJMnT8qECRMkISFBmjVrJitXrpRKlSqJjfQ0ss7Zl/F0MrJGnfmG+vIddeY76sx31JnvCltcZyE6gsLfOwEAAIAbZ2UfOwAAgGBEsAMAALAEwQ4AAMASBDsAAABLEOwAAAAsQbCzEAOdkR84zgDAeQh2FgqEa9si8HGcIa/pFYOQ8zrjy1dwYh47SyQnJ8s333wjH3/8sbnuXfPmzaVWrVpmQuawsDDzYg8NJcdnJjU11YQU6ueXXbp0SbZt2ybvv/++lC1bVho2bCg333yz3HLLLeZ3ZI5jDPnp6tWr5tKaCE4EO0s8/fTT8s9//lMqVqwoZ86ckfj4eKldu7Y89NBD8uSTT0qFChX8vYuOs2fPHmnatOk1H8D64UtrVOZ++9vfypo1a8yXhp9++skcZ5UrV5aOHTvK7373O2nRooW/d9FRvvjiC2nTpo3XspSUFHOMEfKyduzYMfN+pvVXr149ufXWW82XCP25RIkSpiWK16i3Q4cOyZ///Gf58ssvTT3VrVtXGjdubC6pqa9RZE0bPvR4suaY0mCHwLZv3z5XyZIlXR9//LHr2LFjrtTUVNeRI0dcEyZMcN10002u8PBw11tvveXv3XSUgwcPusLCwlwdOnQw9fT1119fs83Vq1ddX3zxhSspKckv++jE46xEiRKuTZs2uS5dumSWnT592vX666+7br31VldoaKhrxowZ5vhLS0tzBbv9+/e7QkJCzGtwyJAhrm3btnmt1zrSY2v58uWuhIQEv+2n08TFxblat27tqlu3rqt///6u+vXru8qUKeNq0qSJ69lnn3WdPHnS37voOIcPH3Y1bNjQdfvtt7uefPJJV5cuXUx9tWjRwjV48GDX9u3b/b2LjnP8+HHz2ktJSfFaru9fGT8HAg3BzgJTp051dezY0fN7+gP1woULrqeeesq8yE+cOOGnPXSeF1980VWjRg3XE0884Wrfvr358OjevbvrL3/5i+uHH34w2xw9etR8MOs9XK6ZM2e67rjjDs/vGQPvq6++6qpdu7bru+++88PeOc+UKVNM4NUvDlpv+gXrlltucY0fP96EF/Xjjz+aYyw+Pt7fu+sYjz/+uCsyMtLrdaf1NXHiRFeFChVcVapUca1atcqv++g0+j7Wq1cv15kzZzzL9H1s7ty5rubNm7tKlSrlevvtt/26j04zfPhw89orX768KyoqyrV58+Zrvnjpcafva1euXHEFEk7FWuCDDz6QF154QVatWiU1atTwnO7R5mXtZ3Hw4EHp37+/DBs2TJ544gl/764j6Clq7X84duxY+eGHH8wpH73t27dPkpKSTB/Fixcvyv/93/+ZZRBZu3atORX71ltvyR133OE5zrR/Z9GiReX48ePSp08fuffee+X555+XYKenprV/6/jx480x9dVXX8m6detk9erV8p///Md0AyhWrJg5/jjG/qdDhw7Sr18/GTNmjDm29PSY1qPS97S+ffuaZUuXLuWU7H/16NFD2rdvLxMmTDDdSVSBAgU86/W9X48x7UahnwnUmUjbtm3NsabdSt59913Td/imm24ynw1Dhw6VOnXqyKRJk8z7nZ7mDiR08rDAr371K3MfEREh//73v82HiL4RujvPan8LRZ8e8YSRyMhIE+yqVq0qrVu3lhEjRsgf//hHmTFjhvzmN78xoe7DDz+U0aNH+3t3HUM/OHSgxIABA+TNN9+Uy5cvm+NMQ53S+tRl4eHhEuz0w/Wee+6RBg0amP6t1apVM8fc5MmTzcCTv/3tb6YuP/30U/n973/v7911lK5du5r+dfo+VrBgQXOMacDTY0vfw7TP8N69e2XHjh0ElP/q3r27REdHy3fffWcCnd50AIXWodIv9N9//7358kqdifkyVb16ddNvc+TIkfLJJ5+Yunn44Ydl2bJl5rXZsmVLmTlzpvlsCDS02FnU2Vi/4X777bfmQ0TDSufOnaVmzZqmQ+3ChQtNK0Hx4sX9vauOox8a+gGS3pIlS8w3twsXLphWFfxMP1y1dVjf/LRedGCAttCVLl1a5s+fb1r1tJWT48xbZqPSY2JiTN1xjHnbuXOn9OrVy7yPTZw40QTk9PT40tbO06dPU2//pYFOWznPnTtnWu2ioqK81mtrnZ6FOHv2LHUmP4/u1/cqHWyYfnCTvk518KG2rs+aNcsEvvPnz3u+vAYKgp1FTpw4IStWrDCtABriDhw4IKdOnZJOnTqZU2gaVJD5h2zG0Yp6ilZbBD777DO/7KOT603f6DZt2mRuWkf6Qax1py0tQ4YMMS1Twe6//Zev20qup3m2bNliulDAm576evbZZ82xVa5cOXPKrGfPnuY9TVvztLXlX//6l79301H0dfncc8+ZL6X6erz77rvNKVpt3dT3sSZNmpjTirhWZqf0Bw0aZD5HN27cKIGGYBfgtF9TXFycFC5c2Hyr0H4B+mFy+PBh861EW07Kly/PHGOZ1JmeqtbDX/tY6IeHmy7T07Da30JbPpF5GNZTPSdPnjTH3ZUrV8wpWFrqfpadeSP1w1ZP0+pUHriWdofQVhXtl6hfIL7++mvzOtUvD9pdQl+38D7e9HWo9aRhROstNjbWfCYMHDjQ9E2sUqWKv3c1IKY3uXz5svTu3dv0Tbzvvvsk0BDsApj2c1qwYIHs2rXL9EOpX7++6TPQpUsXc4onfVhB5nXWqFEj0w9KWwS0pUlP/yBr+nah/ce0Dw99dXKn5Q7/o2cc9FSYHmPaKqdzsOmXBf2SqsectkrpF1VcX/r5OBMTE+n3moPuOdpa3K5dOwlEBLsApZPD6qCI4cOHmxE82rdC3xT1G66OgtWJKf/0pz+ZSYoZOfbLdaanfvRUhfar0DrTUxnukXjBTD9kddJh7b/zyCOPeLUupb+agrtvZ8mSJSWYXa++0rcSaH1p64n2TcTPpxG1g7+O2tTXntaNBjr9ctqtWze5//77PV+6uIrOz7SetJ+h9hND9qQES535dbIV5Nif/vQnV5s2bTJdt27dOjPBZ6NGjbzmNQp21FnO6kznemratKm510lQdRLi9BPq6nxjzZo1M5OkBjvqK+dzcepcmxs3bjS/64Thb7zxhmvgwIGmLu+//37X2bNn/b2bjjJr1ixX6dKlXSNGjDD1dvHixWu2SUxMdK1YsSIgJ9n1Z53FxMQE9MT0fO0JUDqKU0fT7d+/3/yufSu0z5PS0bCLFi0y3070GzB+Rp3l7LJr2rr50UcfmcESOkBCR1nrNDE6KEc7ausUOzpSUfvyBDvqK2d09KH2nbvzzjvN73rG4fHHHzevyVdffdVMRTF48GB/76aj6CAS7UqidaPHlk7P8eKLL5rBEu657N555x0zSCfjqP9g9c9s1tmUKVMC+lq7BLsApacm9HSEfmhoQClSpIg5EPU0hdJ+Y3oaQ0f14GfUmW90Diw9laid1HXia53HTk9V65uihhO9/qTOAaVz/ekIxmBHfeW8P5PWm044rN0llH7BcvcT01Oxc+bMMd0l9AMYYgYt6XuXdu7fvn27qRft5K9z2TVr1szMbfrGG2/I3Llzr7lWcbA6GUx15u8mQ/jOfS3Of//7365q1aqZy8UMHTrUtWvXLrNerxe7ePFic11P96WLgh11ljN6KR33JdYyu4ainubRU47ff/+9n/bQWaivnNm6davr5ptvdo0bN8516tSpa9br6evixYtTb/+l71evvfbaNZdW08tJ6ilGvT6sXsKOSyIGZ50xeCLAWwh0WpMNGzaY6Tn01I92zNZpOvRbsA5x15nu8T/Ume9+/PFH8003s1HWespCRxnrBKn4GfXlG/0I0hY6rZc//OEPpqXugQcekAcffNBMsL57925Zvny5mcZDRyrif1NyKJ1uKLMBck8//bSZ8kRnAEBw1RnBLsDohMN6XTvtd6IfHDo/XZkyZcy0ADqzuE4LoB8aenkxHQHKaFjq7EbqTC+zpnOtlSpVyvQT02l0dFoYfWPUU9h///vfzfKMVwcINtRX7tArI+ipscWLF5tAp9N0aJcJHWms1x/W63vil2lXEz29qCOzOe0ffHVGsAswjz76qLnciYaQEiVKmD4p2vdEr32n3261o6x2DsX/UGc3Vmc6hYnWmU7RcfToURN+9fJ1gTrHU16gvnLegpLxck36kaTLdaCTttLpazbg+zzlcZ1lts17771nWj0DeRBAbrkcZHVGsAsg+lTpm5zOvaYdPd3LNKR8/vnnpjVA5+jRS+3oqDJQZ7lZZ3oKW+tMJ3nWSU/1TZCrJlBfN+L3v/+9mRxcRyfq4BK9gk5mcwNqCzvzcWa/zrTlkzkSg7jO/NzHDz7Yu3evq3Hjxq4dO3Zkuv7SpUtmzqeJEyfm+745FXXmO+rMN9RXzrzzzjumo3rBggVdtWvXdo0ePdrMJ6lz/rnnXdM5xXr37u3as2ePv3fX0XV2/PhxV3JystnmwoULrl69epm5AOEKyjpjupMAovNe6YzZ+u1Dr3WasbFVm5qjoqIkJibGb/voNNSZ76gz31BfOaOd1PVqEzqvpM5hp9Od6OUQe/bsKTNnzpQvv/zSTBPz8ccfm6vCIOs60y4A2r9T60xbhnVeQM5ABG+dEewCiH5ATJ061VwKa9CgQaaDsY7Ac4/00RGf27ZtM9eMxc+oM99RZ76hvnyno2A1EOupL71/4YUXTCjWAROtWrWS6dOnS8eOHc0kxVqnoM5yIiVY68zfTYbwnZ6W0EvsFClSxFW+fHlXnz59XE888YRpZtbLYn311Vf+3kXHoc58R535hvryjV66b//+/eZnvXyTzjOZ3ttvv21Ooe3evdtPe+g81JnvzgRhnTF4IoCdOHHCnN5ZtmyZaTXQZuT+/ftLw4YN/b1rjkWd+Y468w31lXM6JYx+JBUoUMAMOnnqqafMdETIGnXmuzTL64xgZ9GBqpffQfZRZ76jznxDfeXca6+9ZiYrHjt2rL93JWBQZ76zsc4IdgAAx9ErwWiLCsE4+6gz39lYZwQ7AAAAS9gTUQEAAIIcwQ4AAMASBDsAAABLEOwAAAAsQbADAACwBMEOAADAEgQ7AAAASxDsAAAALEGwAwAAEDv8P2j32oNT7SGKAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results5 = noisy_qasm_simulator.run(qc4_transpiled, shots=1000).result()\n",
    "plot_histogram(results5.get_counts())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1fc56204-0108-4a89-8317-ef67a42b4834",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "jupytext": {
   "formats": "ipynb,md"
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}