Colab_18_L'algoritmo_di_Grover.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyPuKc1SC5XmClS6PzBRm03r",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/EmmanueleVilla/quantum_computing/blob/main/Colab_18_L'algoritmo_di_Grover.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WIvk5GGw_ylZ",
        "outputId": "2e1712b8-ba91-4934-f9cc-88d861007691"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "  Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n",
            "  Getting requirements to build wheel ... \u001b[?25l\u001b[?25hdone\n",
            "  Installing backend dependencies ... \u001b[?25l\u001b[?25hdone\n",
            "  Preparing metadata (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m6.1/6.1 MB\u001b[0m \u001b[31m42.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m2.0/2.0 MB\u001b[0m \u001b[31m87.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m49.6/49.6 kB\u001b[0m \u001b[31m5.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m115.3/115.3 kB\u001b[0m \u001b[31m14.2 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m49.6/49.6 kB\u001b[0m \u001b[31m4.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m37.5/37.5 MB\u001b[0m \u001b[31m23.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m112.7/112.7 kB\u001b[0m \u001b[31m12.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h  Building wheel for qiskit (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m162.6/162.6 kB\u001b[0m \u001b[31m3.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h  Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Building wheel for pylatexenc (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m12.8/12.8 MB\u001b[0m \u001b[31m27.1 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h"
          ]
        }
      ],
      "source": [
        "!pip install qiskit --quiet && pip install pylatexenc --quiet && pip install qiskit-aer --quiet"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from qiskit import QuantumCircuit, Aer, transpile, execute, assemble, QuantumRegister, ClassicalRegister\n",
        "from qiskit.visualization import plot_histogram, plot_bloch_multivector\n",
        "from qiskit.visualization.state_visualization import array_to_latex\n",
        "from math import gcd\n",
        "from numpy.random import randint\n",
        "import pandas as pd\n",
        "from fractions import Fraction\n",
        "from qiskit.circuit.library import QFT"
      ],
      "metadata": {
        "id": "VWr8P6im_1uC"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def get_state(circuit):\n",
        "  state_vector_simulator = Aer.get_backend(\"statevector_simulator\")\n",
        "  job = execute(circuit, backend=state_vector_simulator)\n",
        "  result = job.result()\n",
        "  return result.get_statevector()"
      ],
      "metadata": {
        "id": "QejzDQ9K_-F5"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "2B5O0uIu__Hh"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Algo di Grover con 2 qubit per ricerca di |11>"
      ],
      "metadata": {
        "id": "eFT-XKTJJy6b"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "qc = QuantumCircuit(2, 2)\n",
        "\n",
        "# Preparazione\n",
        "qc.h(range(2))\n",
        "qc.barrier()\n",
        "\n",
        "# Oracolo\n",
        "qc.cz(0,1)\n",
        "qc.barrier()\n",
        "\n",
        "qc.h(range(2))\n",
        "qc.z(range(2))\n",
        "qc.cz(0,1)\n",
        "qc.h(range(2))\n",
        "qc.barrier()\n",
        "qc.measure([0,1],[0,1])\n",
        "qc.draw(output=\"mpl\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 255
        },
        "id": "-YdLOXUMJ2ZC",
        "outputId": "5d0db7e4-fa70-4f2f-ede1-6151c645e7db"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1039.79x284.278 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "array_to_latex(get_state(qc))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "jT15hVxDKV3i",
        "outputId": "c2f487b8-2692-422c-f782-d93af8d8dc8f"
      },
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.core.display.Latex object>"
            ],
            "text/latex": "$$\n\n\\begin{bmatrix}\n0 & 0 & 0 & 1  \\\\\n \\end{bmatrix}\n$$"
          },
          "metadata": {},
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "simulator = Aer.get_backend(\"aer_simulator\")\n",
        "result = simulator.run(qc).result()\n",
        "counts = result.get_counts()\n",
        "plot_histogram(counts)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 461
        },
        "id": "5pW_rDTTLo8G",
        "outputId": "a0d9dd41-58df-4769-feb9-45061b3ed034"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 700x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Algo di Grover con 3 qubit che cerca |101> e |110>"
      ],
      "metadata": {
        "id": "Keq2I2wmMEM2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def init(qc, n):\n",
        "  qc.h(range(n))\n",
        "  qc.barrier()\n",
        "  return qc"
      ],
      "metadata": {
        "id": "MPenxWscLw2e"
      },
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def oracle(qc):\n",
        "  qc.cz(0,2)\n",
        "  qc.cz(1,2)\n",
        "  qc.barrier()\n",
        "  return qc"
      ],
      "metadata": {
        "id": "RYoC9VFiMPht"
      },
      "execution_count": 36,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def diffuser(qc, n):\n",
        "  # rifaccio inizializzazione\n",
        "  qc.h(range(n))\n",
        "\n",
        "  # inverto l'input\n",
        "  qc.x(range(n))\n",
        "\n",
        "  # controlled not MA con tutti i qubit-1 come controllore\n",
        "  qc.h(n-1)\n",
        "  qc.mct(list(range(n-1)), n-1)\n",
        "  qc.h(n-1)\n",
        "\n",
        "  qc.barrier(range(2))\n",
        "\n",
        "  # inverto l'inversione dell'input\n",
        "  qc.x(range(n))\n",
        "\n",
        "  #inverto l'inizializzazione dell'input\n",
        "  qc.h(range(n))\n",
        "\n",
        "  return qc"
      ],
      "metadata": {
        "id": "nPOBhx41MYXt"
      },
      "execution_count": 40,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "qc = QuantumCircuit(3)\n",
        "qc = init(qc, 3)\n",
        "qc = oracle(qc)\n",
        "qc = diffuser(qc, 3)\n",
        "qc.measure_all()\n",
        "qc.draw(output=\"mpl\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 233
        },
        "id": "N_UXN5S5NVQK",
        "outputId": "fe85968b-09f2-430a-c83f-54d5238edaa7"
      },
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1500.11x367.889 with 1 Axes>"
            ],
            "image/png": 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uueaigqVfTt69YcMG9erVS+Hh4Zo7d6569+6twsLCgNSOwCJcCpIDBw5IUoWXW5SkoqKi0uDo3HCpZBBZTedBE5X4q5srfOwfTw0OcTVAcKWdkHL8OwJYUvHRS/uypA6xga8J5qMP/ofbLYWHS0VFcvTuJYdF93t2dzLNv6OWShRkS7nHpNpNAl8Tqgkb9wD2A7Cahg0b6umnny69PWHCBGVlGT86r6Krwk2ZMkXr169Xt27d1K1bN02aNEnPP//8RdeOwCNcCpLc3FxJUn5+foWPz58/X1lZWapTp45at24d1Fp69eqlzMxMv9ZxhdfSb2bsClgN9WMS1bLzlQHbXkWSEhPlKaz4+x1M48aNq/KyJUelLV26VJs2baryenPmzPGzqurrxicPyOl0yeP1KD6+4vC1pmuWNFCXTnjP0Lpjx/9W6d8vCXBFwWXVMWD3PuiLiJBeeyUg2yrdps8nz7PPS0WFUssW8r7/gZwDL5OjeWAS1aTEJDnO+nE+KoJmQMebdedVxj78Dxv6G+06vD7AFQWXVftgoPtAsHuAFNg+YPf9gD+sOgYC7Td3PCB37brKyMxQfHx8udvVjdd7/knzxo0bVzoFzN///nf961//MvxcFQVLJXMs3XHHHUpJSZEkTZo0SS+88EKlk4MnJiZa9oCNUIiJidGGDRsMrUu4FCQxMTE6ceKEUlJSSi+nWCIjI0OTJ0+WJHXt2jXok3ZnZmYqPT3dr3XCIqODVE3wHM44rKKC0M8EmpdX9ec8c+ZM6Vd/1vP351e9+Uq/Wut1/cxX+6DhdX/KOFTjvi9WHQO274NRkQr0GZreTxbJt2WrnHeMlbPvr1V07+/lefZ5uWbNDMi+8HDGYemMgcMGEXAZjYyP2UPp+5V+mD74S6bsGwLcB4LdA6TA9gHb7wf8YNkxEGBej6f0a3p6ernbNYnD4dDvfve70tvnHsHkr/MFS5K0adMmff7557r66qvVpk0bXX311eUm/C5REl4i9AiXguTKK6/U9u3bNXPmTA0ePFhJSUmSpPXr1+v2228vPVywe/fuQa+lZNZ+f7jCawWhkuBqHtvclL/UREdX/YNHVFRU6Vd/1iuZIM8aHKVfrfW6fhbuOa6is/kKi/BvHHk9hXIVZNa474tVx4Dd+6AvIkJHA7Kl/2wvPV3e2XPkaJ8k58gRcrhcct42Rt635sr7ySK5fjP8op+jeWxzjlyqJk4Xpsnr88rp5+RJeQWn5Q3PoQ9WwIzvSSD7QCh6gBTYPmD3/YA/rDoGAs35nwnMnS6X4uLiyt2ubrxeb6VhTe/evdWuXTtJ0ooVK7Rz505Dz3GhYKnEq6++qquvvlqSdOutt1YaLsXGxnLk0kUwkh2UIFwKkilTpuj999/XoUOH1KlTJ3Xo0EFnzpzR7t27de211yohIUGff/55mfmWgsXIYW0FRdLU+UEoJoh27tqlSBPe0Tt2VH3G0sLCQk2YMEF16tRReHjV/xY4Y8YMI6VVSw++V3zsksvpKp3U3ore/3fxBN3+6NE6XC9uTwlOQUFk1TFg9z6Y6ylSg5UrArItn9crzzPPSV6vXJMfKr3kuHPkCPnWfiPv7Dly/qrPRZ8as3PXTrldfLSpLjZ9LB3b79867fvW1d4/Bu40pFCxah8MVB8IVQ+QAtsH7L4f8IdVx0CgPfHKezqdk6vYmFilpaWVu13d5ObmVnrl8169epX+/5NPPjG0/aoGS5K0bNkyFRQUKDIyssxz/9KuXbvkdrsN1YOLQ6QXJPHx8VqzZo2GDh2qqKgo7d+/Xw0bNtRrr72mJUuWlCa7oQiXUH2Eh4erYcOGfu1IUTNd1v7nY7T8WcfqGAP25P14oXyp2+Uce5scLVuW3u9wueR65CHJ65Hn2ecrnT8BNVPLnv4t73BK8d2DUkq1Ysc+SA/Auew4BqyoZ8+fm/zGjRv9Xt+fYEkqDiW///57SVL79u0rDb1gHsKlIEpOTtbixYuVnZ2t7OxsrVu3ThMnTlRubq72798vp9Opzp07m10mQujgwYO65557dPCg8Tl5UDPEN5RG9K768tdfIrVpGrx6qgvGgP34Dh6Ud+47ciR3kPOmG8s97khoJedtY+T7/gd5P1lkQoUIlkatpTb9qr58x2skd8Pg1VNd2K0P0gPwS3YbA1bVoUOH0v9v2bLFr3X9DZZKbN68WVLxFdZLpp1B9cGx4ybYtm2bfD6fkpKSKjzP+OOPP5YkpaamlrmdkJBw3kMAq6P4jpfr/nfP/1eoCz1uJdnZ2fryyy917733ml0KQqB/khQeJi3cIJ0prHiZiDBpeA+pf2JoazOLHceA3fugo2VLhS/59LzLuG4ZJdcto0JUEUKpdV/JFSHtWSN5PRUvExYpJV8lNbPB0ZuS/fogPYD9wC/ZbQxYVVZWlg4ePCin01k6SXtV3HbbbYaCJal4UvfDhw9XekV2mItwyQQlh/NVdkrczTffXOHtsWPHWuISnICd9GkjdWshbdwvrdsrHcj6+bGbekm920hRHBUOwKIcDqlVL6l5Zyljm5SRKmX/JMlXfBpc8mCpWQfJRR8EgBpl+HBjk/Dv2LFDp0+fVv369f0KliTp8ccf1+OPP27oeRF8hEsmuFC4xPnmgLVEhkv9Eov/lUxo7pB0qU3+Sg8A4VHFczC17Cmt+ZtUkCNFREvNu5hdGQAglDZs2KDBgwfrhhtu0LRp08wuBwFEuGSCC4VLAAAAAABY0YYNGwxd0RzVG+GSCVauXGl2CTBJs2bNNHXqVDVr1szsUgBTMAYA2B19EHbHGACsiXAJCKHGjRtr3LhxZpcBmIYxAMDu6IOwO8YAYE1OswsA7OTUqVNavny5Tp06ZXYpgCkYAwDsjj4Iu2MMANZEuASEUFpamh588EGlpaWZXQpgCsYAALujD8LuGAOANREuAQAAAAAAwDDCJQAAAAAAABhGuAQAAAAAAADDCJeAEIqKilJycrKioqLMLgUwBWMAgN3RB2F3jAHAmsLMLgCwk7Zt22rhwoVmlwGYhjEAwO7og7A7xgBgTRy5BAAAAAAAAMMIl4AQSk1NVdeuXZWammp2KYApGAMA7I4+CLtjDADWRLgEhJDP51NhYaF8Pp/ZpQCmYAwAsDv6IOyOMQBYE+ESAAAAAAAADGNCb1QowiXNHGV2Ff6JcJldAQArsXsfjHa6dOKKwYHbYAhEO9kRAIFk9z5g9/0AEB0drZycnIBt75nXPtDp3DzVdUdr8m9Hl7sdCNHR0QHZDvxHuIQKORxSJO8OADZm9z7ocDjkdtn4GwDA9n3A7vsBwOFwyO12B2x7EZFRiij0KCIySm63u9xt1Gy0SyCE2rZtq0WLFqlFixZmlwKYgjEAwO7og7A7xgBgTYRLQAhFRUUpMTHR7DIA0zAGANgdfRB2xxgArIkJvYEQSk9P17Rp05Senm52KYApGAMA7I4+CLtjDADWRLgEhNDJkye1YMECnTx50uxSAFMwBgDYHX0QdscYAKyJcAkAAAAAAACGES4BAAAAAADAMMIlAAAAAAAAGEa4BIRQ48aNddddd6lx48ZmlwKYgjEAwO7og7A7xgBgTWFmFwDYicPhUEREhBwOh9mlAKZgDACwog4dOvi17MCBA4NYDVC98VkAsCaOXAJC6OjRo3rllVd09OhRs0sBTMEYAADA3vgsAFgT4RIAAAAAAAAMI1wCAAAAAACAYYRLAAAAAAAAMIxwCQihevXqadiwYapXr57ZpQCmYAwAAGBvfBYArImrxQEhFB8fr6efftrsMgDTMAYAALA3PgsA1sSRS0AIFRQU6MCBAyooKDC7FMAUjAEAAOyNzwKANREuASG0e/duXXPNNdq9e7fZpQCmYAwAAGBvfBYArInT4lAhn0866zG7Cv9EuCSHw+wqAFiF3fugz+dTnrdmfQOinS45ArgjqGnvAfaDgVXTfv5S4N8Ddu8DvAcA+Hw+5eXlmV2GX6KjowP6eaiqCJdQobMeaep8s6vwz8xRUiTvaAABYvc+mOf1qMHKFYHZWIicuGKw3K7A7Qhq2nuA/WBg1bSfvxT494Dd+wDvAQB5eXmqXbu22WX4JScnR263O+TPy2lxAAAAAAAAMIxwCQAAAAAAAIZx0CQQQp06ddL27dvNLgMwDWMAAAB747MAYE0cuQQAAAAAAADDCJeAENq3b59Gjx6tffv2mV0KYArGAGBvPl/xv5L/A7AfPgsA1sRpcUAI5eXlacuWLTXucpZAoDAGAHspyJV++lE6lSllH5Fyj0v6T6h0Nlda97ZUN0aqGys1S5LCIk0tF0AI8FkAsCbCJQAAAATUyXTpUIr00y7J5618ueyfiv+lb5V2rpRikqUWPaTajUNXKwAAuHiESwAAAAiIogJp55fS4R/8X9dTWBwyHf5eSviV1Lqv5HQFvkYAABB4hEsAAAC4aCfTpO+XSAXZF7cdn0/a9610dLfU5XrJ3TAw9QEAgOBhQm8ghOLi4jRz5kzFxcWZXQpgCsYAYE1Z+6SUjy8+WDpXTpa0YV7xaXMArIPPAoA1ES4BIVS/fn1df/31ql+/vtmlAKZgDADWc+KQtPVTyVsU+G0X5kspH/1nInAAlsBnAcA4h8Oh+Ph4s8uoEKfFASF0/PhxLVu2TNdee60aNuQ4f9gPYwCwlsIz0veLgxMslT5HvvTDEqn3rczBBFgBnwVgN+Hh4erZs2fpvxYtWigyMlKFhYX66aeftHHjRm3cuFHfffedcnNzK92Ow+HQ3/72N91www264oortG3bthC+igsjXAJCKCMjQzNmzFD37t3ZmcKWGAOAtexcKZ2t/HNwhfrcJkW4i9f77t2qrZN9RNr/ndSmr/81Aqhe+CwAu2jRooUmTpyou+66S82aNat0udGjR0uScnJy9O677+rVV1/V999/X2aZkmBp4sSJkqR//vOfSkxMVF5eXvBegJ84LS5EsrKyNGXKFLVr105RUVFq0aKF7r//fuXm5mrChAlyOBx6+eWXzS4z4NJSv9Jfb3No45JZlS7z19sc+nTWdSGsCmY4WyTtOiL5/nPbd96lrcfnkw6fKPv6fXb7JtgUfVDyzJ6jwquGyLv8n+Ue8/l8KnpkqgqHXi/fvv2hLy4ErPoeOH5Qykj1f70ItxRVp/irP/b9W8o76f/zmc2qP39/0AN4DwB2UqtWLT333HPat2+fpk2bdt5g6Vy1a9fW3Xffra1bt+rjjz9W06ZNJZUPljwejx588MFqFSxJHLkUEps3b9a1116rzMxMud1udezYUYcPH9aLL76oPXv26Pjx4okEunfvbm6hQBAcz5HW7JTW7ZHyzpZ9bM4a6dL2Utum5tQWCkUeacM+6etdUtov5gx5eqnUP1H6VVspnFM9YGHO28fI++06eV57Q46ePeRo0rj0Me/CT+Tb+r2c48fJ0TrBvCLht0MpoX0+n1dK3ywlXh7a58XFowcAsIu+fftqzpw5SkpKKr2vsLBQn376qVauXKmNGzdqx44dys/PV3h4uNq0aaOePXtqwIABGjVqlOrUqSNJuummmzRw4EDde++9+q//+q8ywdKtt96qDz/80JTXdz4cuRRkWVlZGjZsmDIzM/Xwww8rIyNDKSkpyszM1MyZM7VkyRKtX79eDodDXbt2NbtcIKD2HJGeWSp9ub18sCRJmw9KL62QvqhepwsHzJlC6bUvpQ/WlQ+WJCnjpPTxeumVL6TcgpCXB4SMIzxcYZMfls6ckee5F0rv9x1Kk3fO23J0aC/nzTeZVyD8dua0dHRP6J/38A+SpzD0z4uLQw8AYAc33HCDvvzyy9Jg6cyZM/rzn/+sli1b6uabb9b//d//6bvvvtPp06dVWFiovLw8/fDDD5o7d67uuusuxcXFadKkSTp69KgkqXHjxpo/f36NCJYkwqWgu++++5SWlqZJkyZp1qxZpUmkJE2ZMkXdunVTUVGREhISVLduXRMrRSi43W71799fbref5wLUQGnHpde/kvKr8EvA4s3S6h+DXVFoFXmk2auLTwW8kP1Z0htfFZ86aHV2GgMoy5HYTs7RI+XbmCLvkmXyeTzyPD1L8vnkmvywHC4O36tJMrfLlPObC89IWXtD/7y4ePQAlOCzAKzouuuu00cffaTIyEhJ0jfffKPu3btr+vTpyszMrNI2srOz9corr6hjx47lAiSv11utgyWJ0+KCavv27Zo/f74aN26sJ598ssJlevbsqS1btqhbt26l93388ceaN2+eNmzYoKNHj6ply5a66aab9Ic//EG1a9cOVfkBVXQ2T/nZWWaXYbqEhAS9+eabZpcREp+kSAV+hCWLNkk9EyR3ZNBKCqmUA9LOqu1HJBUHTN/tlQYkXXjZmsxOY+CX6IOSc8wt8v57nTxvvCnnnr3y/bhTzol3ytGiel5SN9Cs9B445Ud/C7TTmVKz9uY9v1FW+vkbRQ/gPSDZ+7MArCkpKUkffvihwsKK45W5c+dqwoQJ8ng8hrZ37NgxnTx5ssx9Tqez2s2x9EuES0E0b948eb1ejRkzptJQqFatWpJUJlyaNWuWWrZsqSeeeELx8fHavHmz/vSnP2nVqlVavXq1nM6ad8DZtwum69sF080uw3Qej0f5+fmqVauWXBb+C13mKWl3FY7YOVeRpzhcGZQcnJpCbe1O/9f5emfxHEwOR+DrqS7sMgYqQh+UHGFhCpv8kIp+/4C8i5fI0bmTnDfeYHZZIWOl98BpE8OlbD/3L9WFlX7+RtEDeA9I9v4sAOtxOp166623Sn+vf//993XHHXfIZ/DKPb+cvNvr9Zb+/v/aa6+pU6dO5YKn6oJwKYhWrlwpSRo0aFCly6SlpUkqGy599tlnatKkSentgQMHqkmTJhozZoy+/vprXXbZZUGqOHg6D5qoxF/dXOFj/3hqcIirMc+OHTs0YsQIffzxx+rUqZPZ5QTNdwZPWbBKuHTktHTgmP/rZZ6SDh2XWjYKfE3VhV3GQEXog//hdkvh4VJRkRy9e8lRA/9gYpRV3gNFZ6WCbPOeP8dAf60OrPLzv2j0gAofs9N7wM6fBWA9kyZNUr9+/SRJu3bt0p133hmwYKlkjqWxY8dqyJAhat68uZ577jmNHz8+YPUHEuFSEB04cECS1KpVqwofLyoq0tq1ayWVDZfODZZK9OrVS5KUnp7udx29evWq8nmeJVzhtfSbGbv8fq7K1I9JVMvOVwZsexVJSkyUpzA/qM9RkXHjxlV52YyMDEnS0qVLtWnTpiqvN2fOHD+rMlef0S+r5SU3+L3egcMnFR/fOfAFhVjTdgN02V0fGFp3xK136vC25QGuKLisOgbs3gd9ERHSa68EZFul2/T55Hn2eamoUGrZQt73P5Bz4GVyNI8NyPaTEpPkOFvB1QMMqmnvgVDtB+tFN9FfJ1Y+fvvcJkWcZyqVSPfPXwf8tvLlzuZK371b/v5TJ3IUH9+hitUaV9N+/lLg3wOB7gPB7gFSYPsA74Gqs+pngUD7zR0PyF27rjIyMxQfH1/uttXVxNfv9XorfSwsLExTpkwpXW78+PHKzzc2/ioLlj788EOtXbtWP/zwg+rXr6///u//1mOPPXbeXCAxMdHw2U4xMTHasGGDoXUJl4IoNzdXkip9g82fP19ZWVmqU6eOWrdufd5tffnll5Kk5GT/D+vIzMz0O5QKi4z2+3nMdjjjsIoKQn8eqj/nvp45c6b0qz/rGQkVzZSXl2toPa/XW+Nea0Wc9Y8aXvfYsawa9z2w6hiwfR+MilR4YLZUyvvJIvm2bJXzjrFy9v21iu79vTzPPi/XrJlyBOB80MMZh6Uzgbv0Yk17D4RqP5hb+/xXaohwS1F1zruIJMnhrNpyvxSqfUVN+/lLQXgPBLgPBLsHSIHtA7wHqs6qnwUCzfufOXi8Ho/S09PL3bY6q73+66+/XnFxcZKkRYsW6euvvza0nfMFS1Lxe/+FF17Q448/LpfLpYkTJ2r69MpPsS0JcEONcCmIYmJidOLECaWkpKhv375lHsvIyNDkyZMlSV27dj3vDjU9PV2PPfaYrrnmGnXv3t1QHf5yhdfyex2zNY9tbspfaqKjq/7BIyoqqvSrP+uVNK0a4+xJQ6udOZ1Z815rBaLDiv9i6vP5qvxhuWTZWq6CGvc9sOoYsHsf9EVEyHhMWsH20tPlnT1HjvZJco4cIYfLJedtY+R9a668nyyS6zfDL/o5msc2D/iRSzVJqPaDkeHnH7tnL/D3hUh3cbDk80oF51m2su0UevJD0hNq2s9fCvx7IJB9IBQ9QApsH+A9UHVW/SwQaM7/zDHldLkUFxdX7rbV1cTX7/V6Kw1rSsIgSXrlFWNHeV4oWCrxxhtvaNq0aQoLC9Ndd92lxx9/vNLT72JjYy/qyCWjCJeC6Morr9T27ds1c+ZMDR48WElJxZeBWr9+vW6//XZlZRVfLeJ8gVFOTo6GDx+uiIgIzZ4921AdRg5rKyiSps439HSm2blrlyJNeEfv2LGjystu27ZNs2fP1pAhQ/w6x3zGjBlGSjPNkVPSk4v9X2/cdR01Z3Ja4AsywQufS/uzqv5XWIfDodj60vffLqtxE3pbdQzYvQ/meorUYOWKgGzL5/XK88xzktcr1+SHSi857hw5Qr6138g7e46cv+pz0afG7Ny1U25X4HYENe09EMr94NevSWcqmXepolPZzjXgt8VHLBXkFm/HX206NiudszKYatrPXwr8eyBQfSBUPUAKbB/gPVB1Vv0sEGhPvPKeTufkKjYmVmlpaeVuW11NfP25ubkVXpzL6XSqf//+kornUf7Xv/7l97arGixJ0uHDh/XPf/5TQ4YMUWxsrNq2bavdu3dXuN1du3bJ7T7P+elBYp8Z9EwwZcoUNWrUSIcOHVKnTp3UpUsXJSYmqk+fPmrTpo2uuOIKSWXnWzpXfn6+hg0bpn379umf//ynYmMDdz46zJGUlKS1a9eWBo1W1ayelNjMv3XCXVKfNsGpxwwDDPyIB1j8SnGSfcYAyvJ+vFC+1O1yjr1NjpYtS+93uFxyPfKQ5PXI8+zzhifAROjVMf6HzYt/bj/3LzAfPQDn4rMArCApKak0dFq3bp3f/cufYKnEt99+W/r/nj17Gqg6uAiXgig+Pl5r1qzR0KFDFRUVpf3796thw4Z67bXXtGTJEu3cWXyt8orCpcLCQo0YMUIbNmzQsmXL1LFjx1CXjyAIDw9Xw4YNFR4e6JlMqp/f9JSi/HiZN/SQoiODV0+oXdJK6uBHHtymidSnbfDqqS7sNAZQzHfwoLxz35EjuYOcN91Y7nFHQis5bxsj3/c/yPvJIhMqhBH1TAyXzHxu+I8egF/iswCs4JJLLin9/8aNG/1a10iwJJU9I+nc568uOC0uyJKTk7V4cfnzg3JycrR//345nU517lz26lher1djxozRv/71Ly1dulR9+vQJVbkBF9/xct3/7vlT3As9biUHDx7UU089pUcffVQtz/nLnRU1byD9dpD0xldS3gWmPhjeQ+pvsT9euZzSuEult9ZIP15gTr22TaUJlxUfvWV1dhoDJezeBx0tWyp8yafnXcZ1yyi5bhkVoopCz4rvgZhkaffXkkJcdniU1KiGHeVqxZ+/P+gBvAd+yY6fBWA9DRs2LP3/wYMHq7ye0WBJkg4dOlTh81cXhEsm2bZtm3w+n5KSkspNZHfvvffqo48+0qOPPqro6Ogyh7+1bdtWTZo0CXW5CJDs7Gx9+eWXuvfee80uJSRaN5GmDJW+3il9u1vKOefiLS6n1L2ldGl7KaGxeTUGU1S4NPFyKWV/8ffgwLGyj8c3KD59rldrKcwGwZJkvzEAWFVUXalJW+loxdM9BE3zLlIAp9UCYAI+C8AKFi5cqB9++EG1atXS1q1bq7xe69atNXLkSEn+BUuStH//fg0ZMkRnzpyplnNUsXs2yffffy+p4lPili1bJkl66qmn9NRTT5V57K233tK4ceOCXh8QKPWjpeu6S9d0kQ4ek/LPShFhUkx9qU6U2dUFn8sp9W5T/C/zlHTiP1c/qh8txdSz/hxLAKyrZc/QhksOlxRf8TSVAACEVEZGRqVXkTufvXv3avDgwVq2bJnuvffeKgdLUvHZTyVZQXVEuGSS84VL+/fvD3E1QPCFuaQ2Tc2uwlwx9Yr/AYAVNGghxXaWMn4IzfO16SfVqh+a5wIAIFg2bNigNm3aKDu7ksuu1lBM6G2S84VLAAAANUHS5VJk+Ss0n9fZXOlMdvHXqqobI7Xq7d/zAABQXVktWJI4csk0K1euNLsEmKBZs2aaOnWqmjXjOsqwJ8YAYC3hUVKXYVLKR5K3qGrrfPeuf88RES11Hio5+ZMoYAl8FgCsiXAJCKHGjRszZxZsjTEAWE/9OKnbDdKWT6oeMFVVRLTU42YpukFgtwvAPHwWAKyJvwEBIXTq1CktX75cp06dMrsUwBSMAcCaGiVIPUYWX0UuUGo3lXrdItXmIrmApfBZALAmwiUghNLS0vTggw9Wy0tHAqHAGACsq35z6dfjpLiLnE7S4SyevLvPGI5YAqyIzwKANXFaHAAAAAIiLEJKHiw17ywd2iQd+VHyeaq2ritCiu0ktbhEcjcMbp0AACCwCJcAAAAQUPVii/8lXS79tFM6faT4X+6xn8MmZ1jxKW91m0l1Y6WmicXhFAAAqHkIlwAAABAUEdFSfPey93m9kkPFp78BAABrIFwCQigqKkrJycmKiooyuxTAFIwBAE5CJcDW+CwAWBPhEhBCbdu21cKFC80uAzANYwAAAHvjswBgTfztCAAAAAAAAIYRLgEhlJqaqq5duyo1NdXsUgBTMAYAALA3PgsA1kS4BISQz+dTYWGhfD6f2aUApmAMAABgb3wWAKyJOZdQoQiXNHOU2VX4J8JldgUArMTufTDa6dKJKwYHboMhEO0M7I6gpr0H2A8GVk37+UuBfw/YvQ/wHgAQHR2tnJycgG3vmdc+0OncPNV1R2vyb0eXux0I0dHRAdmOvwiXUCGHQ4rk3QHAxuzeBx0Oh9wuG38DxHvA7vj50wd4DwBwOBxyu90B215EZJQiCj2KiIyS2+0ud7sm47Q4AAAAAAAAGEYWD4RQ27ZttWjRIrVo0cLsUgBTMAYAALA3PgsA1kS4BIRQVFSUEhMTzS4DMA1jAAAAe+OzAGBNnBYHhFB6erqmTZum9PR0s0sBTMEYAADA3vgsAFgT4RIQQidPntSCBQt08uRJs0sBTMEYAADA3vgsAFgT4RIAAAAAAAAMI1wCAAAAAACAYYRLAAAAAAAAMIyrxQEXqUOHDlVetl69epo+fbr69eun2NjYIFYFhA5jAAAAe+OzAADCJSCEYmNj9fjjj5tdBmAaxgAAAPbGZwHAmjgtDgAAAAAAAIYRLgEAAAAAAMAwwiUAAAAAAAAYRrgEAAAAAAAAwwiXAAAAAAAAYBjhEgAAAAAAAAwjXAIAAAAAAIBhhEsAAAAAAAAwjHAJAAAAAAAAhhEuAQAAAAAAwDDCJQAAAAAAABhGuARJ0jvvvKOePXuqQYMGqlWrlpKTk/Xcc8/J5/OZXRoAAAAAoAJLly5V9+7dFRkZqYSEBD333HNmlxRSq1ev1vDhw9WqVSs5HA7NmDHD7JJC6plnnlHfvn3VoEED1a9fXwMGDNDy5ctNqSXMlGdFtdO0aVM99thjat++vSIjI7VmzRrdc889crlcuv/++80uDwAAAABwjg0bNmj48OF65JFHNG/ePK1bt0533323oqOjdffdd5tdXkjk5OSoY8eOuvXWW/XAAw+YXU7IrVy5UuPHj1fv3r0VHR2tN998U9ddd51WrVql/v37h7QWwiVIkq6++uoyt9u0aaNPPvlEX331FeESAAAAAFQzzz33nHr37q0nn3xSkpScnKxt27bpqaeesk24NGTIEA0ZMkSSNHXqVJOrCb1ly5aVuf30009r+fLlWrhwYcjDJU6LQzk+n0/fffed1q5dq0GDBpldDgAAAADgF9auXatrrrmmzH3XXHONDhw4oLS0NJOqgpm8Xq9Onz4tt9sd8ufmyCWUOnXqlOLi4nT27Fl5vV5Nnz5d9913n9llAQAAAECNcfxUtrKOnyp3f5HHU/p15760crfP1bpFjMLDzv/rekZGhmJiYsrcV3I7IyND8fHxhl/DxfB4vNpz8HC5+/15/Y3q11WjBnWDX2yQHD6SpZy8M+Xur+r3IDzMpdYtYv1+3ieeeEInT57UxIkTDVZuHOESStWpU0ebN29WXl6evvnmG/3hD39Q8+bNNWHCBLNLAwAAAIAaITzMpfmfrVRufvlwQZLy8s9o9odLK73dpX0bJSbEBb3OYHG5nNqculspP+ys8PELvf6oyAg9OH5E0OsMpvyCs3rrw6Wq7PJYF/oeDLuyn9/h0quvvqonnnhCixYtMiVY5LQ4lHI6nWrXrp26du2qu+++W1OmTNEf//hHs8sCAAAAgBqjjjtaN15zmbF1a0frhqsHyOFwXHDZ2NhYZWZmlrnvyJEjpY+Z6for+6l+3dqG1r3hqgGqZ3Dd6qJty+bq37uLoXUTE+LUt0cnv9aZNWuWJk+erEWLFunKK6809LwXi3AJlfJ6vTpzpuK0HQAAAABQsU5JCerZJcnv9UZcO1DuWlFVWrZ///76/PPPy9y3fPlytWrVyrRT4kpERUZo5NDLdeGIrKyuHdqoW3LboNQUaldf1lvNGjfwa52oyAiNGHK5nFUIF0v87//+r/70pz9p6dKlpgVLEuES/mP69On64osvtHfvXv3444964403NHPmTI0dO9bs0gAAAACgxhn2X/3UoF6dKi//60s6qn2bFlVe/sEHH9R3332nP/7xj9qxY4fmzp2rl156SY8++qiRcgOuTcvmurRP1yovX7d2tG64qmpHbZXIycnR5s2btXnzZp09e1aZmZnavHmzdu/ebaTkgAoPC9Oo6wbJ5ax67PKbqwaoXp2qT8b9wAMP6JlnntE777yj9u3bKzMzU5mZmTp1qvycX8Hm8Pl8lZ0GCBt58MEH9dlnnyk9PV1RUVFq06aNxo8fr7vvvlsul8vs8gAAAACgxtl7KENvvP9ZpXPvlGjcoJ7uG3ejIiLC/dr+kiVL9D//8z/asWOHYmJidP/99+uhhx4yXnCAFRYV6eW5/9CRrBMXXHb8zdcqyY9wTZK++uqrCq9wPnDgQH311Vd+bStYvvp2s5av+u6Cy3VLbqtbrv8vv7ZdWRA3duxYzZkzx69tXSzCJQAAAAAAgmTpl99q9XdbK33c6XDo7tuGq2XzpiGsKnQO/3RMr8z9hzxeb6XL9O3RUcMHDwhhVaHj9Xr12vuf6UD6kUqXqVvbrQfG36ToKp4SWR1xWhz8kpd/RmkZR80uAwAAAABqhKsu7a2YJg0rfXxQ30ssGyxJUvOmjTT40l6VPt64YT1de/mvQ1hRaDmdTo28btB5j0q7ecjAGh0sSYRL8NOa9d/r5bf/oSUrvzW7FAAAAACo9sLCXMVz77jK//odH9NEV/TrYUJVoXVZn65KiI8pd7/T4dCo6wYpIjzMhKpCp1H9urruir4VPtavZycltjZ3AvZAsEy45HA4Ss83/Oyzz3TppZeqbt26aty4sUaMGKE9e/aULrt48WINHDhQ9evXV926dTV8+HDt2rWr0m0XFBTor3/9q/r166f69esrKipK7du31+TJk5WVlVXhOuvWrdPUqVPVu3dvxcTEKDIyUnFxcRo5cqTWr19f6XMtXbpUQ4YMUdOmTRUeHq5GjRopOTlZ48eP19q1aw1+dwIjN/+Mvtn4gyRV2BgAAAAAAOXFNm2kqy7tXea+sDCXRlYSOlmN0+nUyKGXlzt654p+PdQi1rpHbZ2rd9f2Sm7Xssx9TRrW0zUDf2VSRYFlmTmXSoKll19+WZMmTVLz5s3VrFkz7dixQ/n5+YqLi9OmTZv03nvv6cEHH1RsbKxiYmJKH4+JidHWrVvVpEmTMts9cuSIrr32Wm3atElOp1MtWrRQ3bp1tXPnThUUFKhly5b68ssv1aZNmzLrtWvXTnv27FHDhg0VGxuriIgIHTx4UMeOHVNYWJg++OAD3XTTTWXWefXVV3XvvfdKkho1aqRWrVopPz9fhw4dUk5Ojn7729/qb3/7WxC/i+f3+er1+vLfmxTbtJHuG3ejX7P4AwAAAICdeb1evT5vsfanZUqShl3ZT/17dja5qtBav3WHFixbLUmKj22i340ZbotwrUR2bp5emP2xcvPOyOl06J7bblB8bJMLr1gDWO6nOGXKFM2dO1fp6elKSUlRWlqaevfurfT0dI0fP17/8z//o7lz5+rw4cNKSUnRoUOH1LNnT2VmZurZZ58tsy2fz6dRo0Zp06ZNGjp0qPbs2aP9+/dr69atysrK0vjx43Xw4EHddttt5er43//9X+3atUvHjh3TDz/8oJSUFP30009auHChoqKidOeddyonJ6d0+aKiIk2bNk1Scch05MgRbdy4UampqTp9+rRWrVqlq6++OrjfvPM496ilK/v3JFgCAAAAAD+UzL0TGRGuxIQ49e3RyeySQq5Xl/ZKbtdK4WEujRpqj6O2zlXHHa0br75MUvFRW1YJliQLHrn0+9//Xi+++GKZx5YvX65rr7220seXLVumIUOGqGvXrtqyZUvp/UuXLtXQoUPVuXNnrV+/XlFRZSfY8ng86tOnj1JSUvT111+rf//+Var1scce04wZMzRv3jyNHj1akpSZmanY2Fg1aNBAx48f9+/FX8BLcxcqOyf/orZRcPasCs4Wyul0qnZ0rQBVBgAAAAD2UlhYJJfLKafTXsFKCa/XJ4/Ho3CLz7N0PmfPFio8PKzaHbRRp3Yt/X7sjYbWtdxP88477yx3X48ePar0+N69e8vcv2DBAknS2LFjywVLkuRyuXT99dcrJSVFX331VblwadeuXfrggw+0ZcsWHTt2TIWFhZKkn376SZK0efPm0nCpSZMmioqK0smTJ7VixQoNHjy4yq/5QrJz8nU6Jzcg2/J6vQHbFgA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          },
          "metadata": {},
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "simulator = Aer.get_backend(\"aer_simulator\")\n",
        "result = simulator.run(qc).result()\n",
        "counts = result.get_counts()\n",
        "plot_histogram(counts)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "KKS-s5OaNjJq",
        "outputId": "0fd53f2c-fc5a-4653-b250-e320655c4d42"
      },
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 700x500 with 1 Axes>"
            ],
            "image/png": 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IkAcAAGAgQh4AAICBCHkAAAAGIuQBAAAYiJAHAABgIEIeAACAgQh5AAAABiLkAQAAGIiQBwAAYCBCHgAAgIEIeQAAAAYi5AEAABiIkAcAAGAgQh4AAICBCHkAAAAGIuQBAAAYiJAHAABgIEIeAACAgQh5AAAABiLkAQAAGIiQBwAAYCBCHgAAgIEIeQAAAAYi5AEAABiIkAcAAGAgQh4AAICBCHkAAAAGIuQBAAAYqMwhb/PmzTpx4sR1+5w8eVKbN28u60cAAACgjMoc8qKiorR48eLr9vnkk08UFRVV1o8AAABAGZU55Dkcjhv2sdvtslgsZf0IAAAAlFGlzslLSkpSQEBAZX4EAAAAiuBRms5PPvmky+tVq1bp2LFjhfrl5+c75+P169evXAUCAACg9EoV8q6dg2exWLR3717t3bu3yL4Wi0WdOnXS22+/XZ76AAAAUAalCnm//vqrpKvz8Zo3b65nn31Wf/7znwv1s9lsqlu3rurUqVMxVQIAAKBUShXymjRp4vzvRYsWKSIiwqUNAAAA1UOpQt61RowYUZF1AAAAoAKVOeQV2Llzp3bt2qWMjAzl5+cX2m6xWDR16tTyfgwAAABKocwhLz09XQ8//LC2bt163WfmEfIAAACqXplD3uTJk7Vlyxb17NlTI0aMUKNGjeThUe6BQV2+fFkvv/yy/vd//1dHjhxRenq6AgMD1aJFC40ePVpDhw6Vp6eny3uysrI0bdo0rVy5UikpKWrQoIEeffRRxcXFydfXt9Bn2O12/fOf/9SCBQt05MgR+fr6qnfv3poxY4aaN29e7mMAAABwN4ujJEtXFCEkJES33Xabtm3bVqGrWqSmpiosLEz33HOPWrZsqdDQUJ07d05r1qzR8ePHFR0drTVr1shqvfoc5wsXLqh79+7au3evoqOjFRERoR9//FEJCQnq1KmTNm/erFq1arl8xpgxY7Rw4ULdcccdio2NVXJyslasWCFfX19t375d4eHhJa43KytLAQEByszMlL+/f4X9PfzemHcqbddAqX34rLsrAFxxjUR1UtnXyJJmjzIPvV26dEk9evSo8GXLgoKClJmZKS8vL5f2vLw89enTRwkJCVqzZo1iY2MlSW+88Yb27t2rF198UX//+9+d/V966SXNnj1bb7/9tqZMmeJs37hxoxYuXKgePXro22+/dX7O448/rv79+2vChAlat25dhR4TAABAVSvzsmbt27cvcrWL8rJarYUCniR5eHho4MCBkqQjR45Iuvq8voULF8rX17fQvL+pU6fK19dXCxcudGn/8MMPJUmvv/66y+f069dPPXv2VEJCgk6cOFGhxwQAAFDVyjySFxcXpwEDBmj79u3q3LlzRdZUJLvdrrVr10qS7rzzTklX18ZNTk5WTExMoQcv16lTR926ddO6det08uRJhYWFSZISExOd234vJiZGiYmJ2rRpk4YNG1ZkHTk5OcrJyXG+zsrKkiTl5uYqNzdX0tWgarPZlJ+fL7vd7uxb0J6Xl+dys4rNZpPVai22/ep+XechAu5U8G+9QMF83Ly8PJd2T09P2e12lzvvLRaLPDw8im0v7ryp2PPpxrVzTDXrmKSK/VUJKI+qOJ9KoswhLyUlRbGxsYqMjNQTTzyhDh06FPu78PDhw0u9/ytXrmjmzJlyOBxKS0vThg0bdPDgQY0aNUr333+/pKshT1Kxc+jCw8O1bt06JSUlKSwsTBcuXNDp06d15513ymazFdn/2v0WZdasWZo+fXqh9oSEBNWuXVuS1LhxY0VERGjfvn0uo4K33367WrVqpZ07d+rs2bPO9vbt26tJkybavHmzsrOzne1dunRRvXr1lJCQICm22JqAqhYfH+/yun///rp06ZI2btzobPPw8FBsbKxSU1O1bds2Z7ufn5969eqlkydPuiyLGBoaqq5duyopKUmHDh1ytlfG+XTtBTIqKko+Pj4cUw0/Jqny5kQDpVXZ59Pu3btLVEeZb7ywWq2yWCwu38B+Pz/P4XDIYrEU+fy8Gzl//rz8/Pxc9v38889r1qxZzm9un376qZ544gm98sor+tvf/lZoH6+88opmzpypf/3rXxo4cKCSk5N16623qlu3btqyZUuh/t9++62io6M1adIkzZ07t8i6ihrJCwsLU2pqqjPkVsY32mf+yUgeqo/54xnJ45iq1zE9PZeRPFQfH0yq3PMpPT1dwcHBlXfjxaJFi8r61hLx9fWVw+GQ3W5XcnKyvvnmG7388svatm2b4uPjK/VO1uvx9vaWt7d3oXZPT89Cj3ax2WxFjhgW96iZ4tp/v1/A3Yr7N1lUu9Vqdd4NX5L24s6byj6fOKaafUxAdeKu86lQvxL1KkJVLWtmtVrVqFEjjRs3TiEhIRo8eLBmzJih2bNnKyAgQJKUmZlZ5HsL5ssV9CttfwAAgJqqzHfXukN0dLSkqzdPSDeeQ/f7OXt16tRRgwYN9Ouvvxb5E/KN5vgBAADUFGUeySvNY0YaN25c1o9xkZycLOk/w/Xh4eFq2LChtm7dqgsXLrjcYXvhwgVt3bpVzZo1c95ZK0mRkZFatmyZtm7dqh49erjsv+D5eL9vBwAAqGnKPJLXtGlTNWvW7IZ/SrtM2L///W9dvHixUPvFixc1efJkSVfvppKuTlgcPXq0zp8/r9dff92l/+uvv67z589rzJgxLu1PP/20pKvP0bty5Yqzfc2aNUpMTFR0dLSaNGlSqpoBAACqmzKP5A0fPrzI1S4yMzP1008/6ddff1VkZKSaNm1aqv2uWLFCb731lrp3766mTZvK399fv/32m9asWaO0tDTdd999eu6555z9//KXv+irr77S7Nmz9eOPP6pDhw7as2ePc1mzZ5991mX/UVFRGj16tBYuXKgOHTooNjZWp0+f1vLlyxUUFKT33nuvLH8dAAAA1UqZQ97ixYuL3eZwOPTmm2/qjTfe0EcffVSq/T7wwANKTk7WDz/8oG3btun8+fMKCAhQu3bt9Mc//lFPPvmky10lderU0aZNmzRt2jStXLlSGzduVIMGDfT8888rLi5OPj4+hT7jgw8+UNu2bbVgwQLNnTtXvr6+GjhwoGbMmKEWLVqUql4AAIDqqMzPySuJqKgoBQUFaeXKlZX1EW5X0kWCy4vFt1GdVPbi20BpcY1EdVLZ18iSZo9Kvbv27rvv1nfffVeZHwEAAIAiVGrIO3r0aInXVwMAAEDFKfOcvOLY7Xb99ttvWrx4sb766ivnOrMAAACoOmUOeQVr1xbH4XCobt26evPNN8v6EQAAACijMoe8Hj16FBnyrFar6tatq06dOmnUqFGqV69euQoEAABA6ZU55BUsLQYAAIDqp0atXQsAAICSqZAbL7Zu3aq9e/cqKytL/v7+at++vbp161YRuwYAAEAZlCvk/fDDDxo1apSOHDki6erNFgXz9MLDw7Vo0SJ16dKl/FUCAACgVMoc8g4cOKDo6GhdvHhRffr0UVRUlBo0aKCUlBRt3LhRCQkJiomJ0fbt29WmTZuKrBkAAAA3UOaQ99e//lVXrlxRfHy8+vbt67LtxRdf1Nq1azVgwAD99a9/1bJly8pdKAAAAEquzDdeJCYmatCgQYUCXoG+fftq0KBB2rhxY5mLAwAAQNmUOeRlZmaqWbNm1+3TrFkzZWZmlvUjAAAAUEZlDnkNGzbU9u3br9tnx44datiwYVk/AgAAAGVU5pA3YMAAJSYmaurUqbp8+bLLtsuXLysuLk4bN27UQw89VO4iAQAAUDplvvFi6tSpWr16tWbOnKkPPvhA99xzj2655RadOXNGu3bt0tmzZ9W8eXNNnTq1IusFAABACZQ55AUHB2v79u36y1/+omXLlik+Pt65rVatWho1apRmz56toKCgCikUAAAAJVeuhyGHhITo448/1gcffKCDBw86V7xo1aqVPD09K6pGAAAAlFKpQ96MGTN04cIFTZ8+3RnkPD091bZtW2efK1eu6JVXXpGfn59eeumliqsWAAAAJVKqGy/Wr1+v1157TcHBwdcdqfPy8lJwcLBeeeUVnpMHAADgBqUKeZ988onq1q2rCRMm3LDv+PHjFRQUpEWLFpW5OAAAAJRNqULeDz/8oN69e8vb2/uGfb29vdW7d29t3bq1zMUBAACgbEoV8pKTk9W8efMS92/WrJlOnz5d6qIAAABQPqUKeVarVbm5uSXun5ubK6u1zM9bBgAAQBmVKoE1bNhQ+/fvL3H//fv369Zbby11UQAAACifUoW8++67T999952OHTt2w77Hjh3Td999px49epS1NgAAAJRRqULe+PHjlZubq0GDBik1NbXYfmlpaXr00UeVl5encePGlbtIAAAAlE6pHobcoUMHPfvss3rnnXfUpk0bjR07VlFRUWrUqJEk6bffftOGDRu0YMECnT17VpMnT1aHDh0qpXAAAAAUr9QrXrz55puqVauW5syZoxkzZmjGjBku2x0Oh2w2m6ZMmaK//e1vFVYoAAAASq7UIc9isWjmzJl66qmntGjRIv3www9KSUmRJNWvX1/dunXTyJEj1aJFiwovFgAAACVT6pBXoEWLFozUAQAAVFM8xA4AAMBAhDwAAAADEfIAAAAMRMgDAAAwECEPAADAQIQ8AAAAAxHyAAAADETIAwAAMBAhDwAAwECEPAAAAAMR8gAAAAxEyAMAADAQIQ8AAMBAhDwAAAADEfIAAAAMRMgDAAAwECEPAADAQIQ8AAAAAxHyAAAADETIAwAAMBAhDwAAwECEPAAAAAMR8gAAAAxEyAMAADAQIQ8AAMBAhDwAAAADEfIAAAAMRMgDAAAwECEPAADAQIQ8AAAAAxHyAAAADETIAwAAMBAhDwAAwECEPAAAAAMR8gAAAAxEyAMAADAQIQ8AAMBAhDwAAAADEfIAAAAMRMgDAAAwECEPAADAQIQ8AAAAAxHyAAAADETIAwAAMBAhDwAAwECEPAAAAAMR8gAAAAxEyAMAADAQIQ8AAMBAhDwAAAADEfIAAAAMRMgDAAAwECEPAADAQIQ8AAAAAxHyAAAADFQtQ97SpUv1pz/9SXfffbe8vb1lsVi0ePHiIvtOmzZNFoul2D/Hjh0r8n3r1q1TZGSk/Pz85O/vr6ioKG3YsKHyDgoAAKAKebi7gKK8+uqrOn78uEJCQtSgQQMdP378hu8ZMWKEmjZtWqg9MDCwUNvSpUs1bNgwhYaGauTIkZKk5cuXq0+fPlqxYoUGDRpUziMAAABwr2oZ8hYuXKjw8HA1adJEf//73zVlypQbvmfkyJHq2bPnDfudO3dOEydOVEhIiPbs2aNGjRpJkl588UVFRERo3LhxiomJkZ+fX3kPAwAAwG2q5c+1vXv3VpMmTSpl359//rkyMjI0ceJEZ8CTpEaNGmnChAlKTU3Vl19+WSmfDQAAUFWq5UheWWzevFk7duyQ1WpVeHi4evfuLV9f30L9EhMTJUnR0dGFtsXExGjatGnatGmThg8fXuTn5OTkKCcnx/k6KytLkpSbm6vc3FxJktVqlc1mU35+vux2u7NvQXteXp4cDoez3WazyWq1Ftt+db+eJf/LACpZwb/1Ah4eVy8leXl5Lu2enp6y2+3Kz893tlksFnl4eBTbXtx5U7Hn041r55hq1jFJFgHVRVWcTyVhTMiLi4tzeR0YGKi5c+cWCmtJSUmSpPDw8EL7KGgr6FOUWbNmafr06YXaExISVLt2bUlS48aNFRERoX379unEiRPOPrfffrtatWqlnTt36uzZs8729u3bq0mTJtq8ebOys7Od7V26dFG9evWUkJAgKbbYmoCqFh8f7/K6f//+unTpkjZu3Ohs8/DwUGxsrFJTU7Vt2zZnu5+fn3r16qWTJ09q7969zvbQ0FB17dpVSUlJOnTokLO9Ms6nay+QUVFR8vHx4Zhq+DFJ/gKqi8o+n3bv3l2iOiyOa79CVUMFc/IWLVrkvEniWl9++aUyMjLUs2dPNWjQQCkpKVq9erVee+01ZWRkaNWqVRowYICzf8uWLZWUlKTc3NxrvgFelZubKy8vL7Vr104//fRTkfUUNZIXFham1NRU+ftfvchUxjfaZ/7JSB6qj/njGcnjmKrXMT09l5E8VB8fTKrc8yk9PV3BwcHKzMx0Zo+i1PiRvIEDB7q8btq0qSZMmKDWrVurT58+evXVV11CXnl5e3vL29u7ULunp6c8PV2DmM1mk81mK9T39+HyRu2/3y/gbsX9myyq3Wq1ymotPP23uPbizpvKPp84ppp9TEB14q7zqdDnlahXDXT//ferRYsW+vnnn53z5iQpICBAkpSZmVnoPQX9CvoAAADUVMaGPEkKCQmRJF28eNHZdr15d9ebrwcAAFCTGBvyLly4oAMHDqhOnTrOsCdJkZGRkvT/b2ZwtW7dOpc+AAAANVWNDnnZ2dk6fPhwofZLly5pzJgxys7O1uDBg11+ux48eLACAgL03nvv6dSpU872U6dOad68eQoJCSk0zw8AAKCmqZY3XixcuFBbtmyRJP3888/OtoJn3HXv3l2jR49WWlqaWrVqpU6dOql169aqX7++zpw5o/Xr1+vUqVNq27at5syZ47LvunXrat68eRo2bJg6dOigIUOGSLq6rFlaWpqWL1/OahcAAKDGq5Yhb8uWLVqyZIlL29atW7V161bn69GjRysoKEjPPPOMdu7cqfj4eJ07d04+Pj5q3bq1Jk2apAkTJsjHx6fQ/ocOHaqQkBDNnDlTixYtksViUceOHfXqq6+qd+/elX58AAAAla3aPyevusvKylJAQMANn1VTXmPeqbRdA6X24bPurgBwxTUS1UllXyNLmj1q9Jw8AAAAFI2QBwAAYCBCHgAAgIEIeQAAAAYi5AEAABiIkAcAAGAgQh4AAICBCHkAAAAGIuQBAAAYiJAHAABgIEIeAACAgQh5AAAABiLkAQAAGIiQBwAAYCBCHgAAgIEIeQAAAAYi5AEAABiIkAcAAGAgQh4AAICBCHkAAAAGIuQBAAAYiJAHAABgIEIeAACAgQh5AAAABiLkAQAAGIiQBwAAYCBCHgAAgIEIeQAAAAYi5AEAABiIkAcAAGAgQh4AAICBCHkAAAAGIuQBAAAYiJAHAABgIEIeAACAgQh5AAAABiLkAQAAGIiQBwAAYCBCHgAAgIEIeQAAAAYi5AEAABiIkAcAAGAgQh4AAICBCHkAAAAGIuQBAAAYiJAHAABgIEIeAACAgQh5AAAABiLkAQAAGIiQBwAAYCBCHgAAgIEIeQAAAAYi5AEAABiIkAcAAGAgQh4AAICBCHkAAAAGIuQBAAAYiJAHAABgIEIeAACAgQh5AAAABiLkAQAAGIiQBwAAYCBCHgAAgIEIeQAAAAYi5AEAABiIkAcAAGAgQh4AAICBCHkAAAAGIuQBAAAYiJAHAABgIEIeAACAgQh5AAAABiLkAQAAGIiQBwAAYCBCHgAAgIEIeQAAAAYi5AEAABiIkAcAAGAgQh4AAICBCHkAAAAGIuQBAAAYiJAHAABgIEIeAACAgQh5AAAABiLkAQAAGOimDnm7du1S//79FRgYqDp16qhz585asWKFu8sCAAAoNw93F+AuGzduVExMjGrVqqU//vGP8vPz08qVKzVkyBCdPHlSzz//vLtLBAAAKLObciQvLy9PY8aMkdVq1ebNm7VgwQK9+eab+umnn9SyZUu9/PLLOn78uLvLBAAAKLObMuR99913Onr0qB5//HG1b9/e2R4QEKCXX35ZV65c0ZIlS9xXIAAAQDndlCEvMTFRkhQdHV1oW0xMjCRp06ZNVVkSAABAhbop5+QlJSVJksLDwwttq1+/vnx9fZ19fi8nJ0c5OTnO15mZmZKk9PR05ebmSpKsVqtsNpvy8/Nlt9udfQva8/Ly5HA4nO02m01Wq7XY9tzcXF257FmOIwYqVlparstrD4+rl5K8vDyXdk9PT9ntduXn5zvbLBaLPDw8im0v7rypyPOpJLVzTDXrmK5ctgioLjIyKvd8Sk9PlySXc6coN2XIKwhmAQEBRW739/d39vm9WbNmafr06YXamzVrVnEFAtXcJ1PcXQEAVF9VdY3Mzs4uNstIN2nIK48pU6Zo8uTJztd2u13p6ekKDg6WxcI3yeosKytLYWFhOnnypPz9/d1dDgBUK1wjaw6Hw6Hs7Gw1bNjwuv1uypBXkHqLG63LyspS3bp1i9zm7e0tb29vl7bAwMAKrQ+Vy9/fnwsYABSDa2TNcL0RvAI35Y0XBXPxipp3l5KSovPnzxc5Xw8AAKCmuClDXmRkpCQpISGh0LZ169a59AEAAKiJbsqQd//996t58+b69NNPtXfvXmd7ZmamZs6cKS8vLw0fPtx9BaJSeHt7Ky4urtDP7QAArpEmsjhudP+toYpb1uz48eP6xz/+wbJmAACgRrtpQ54k7dy5U3Fxcfrhhx+Um5urtm3bavLkyRoyZIi7SwMAACiXmzrkAQAAmOqmnJMHAABgOkIeAACAgQh5AAAABiLkAQAAGIiQBwAAYCBCHgAAgIEIeQAAQJLEU9XMQsgDAACSJIvFUqiN4Fdzebi7AAAA4F75+flKSkrSuXPnJF0Ndi1atNAtt9xSZPBDzUDIg9EcDocsFovsdrvsdrs8PPgnDwDXOnTokKZMmaL4+HhduXJF3t7eqlu3rpo2baouXbqob9++6tq1q+rUqePuUlFKLGsGo2VlZSkjI0ONGzd2tuXn50uSbDabu8oCgGohOTlZffv21YEDBzRs2DCFhITIw8NDBw4c0Pfff6+srCwFBgZq4MCB+tOf/qR77rnH3SWjFBjWgNGmT5+ut99+W927d9eoUaM0ZMgQ1a5d27k9Ly9PVqtVVut/pqempKTIarUqNDSUnykAGO3999/XqVOntGDBAj311FOSpCtXrshisSglJUVr1qzRJ598osWLF2v79u164403FBsb6/yVBNUbI3kwWrt27bR//36XtocfflijR49W//79nW0FF6zs7GyNGzdOqampWr16NT/vAjBa+/bt1aBBAy1ZskT16tUrMrylpqZq2bJliouLU25urnbs2KHWrVu7qWKUBnfXwli//PKLUlJS1KNHD23atEljx45VWFiYVq1apQceeEBBQUEaP368fvzxR+dF7ejRo4qPj9fly5cJeACMlpaWJk9PT2VkZKhevXqSir67NiQkRGPHjtX8+fN1/vx5zZ07t6pLRRkR8mCso0ePKjU1VXfffbfuu+8+zZ8/X/v27dOyZcs0aNAg2e12vf/+++rYsaNuu+02zZ49W8uWLVNGRoZeeOEFd5cPAJXG4XAoODhYERER2rFjh1avXq38/Hw5HA7l5eUV6u/h4aEhQ4aoa9eu2rNnj9LT091QNUqLkAdj+fr6qlGjRrr99tslXZ1/FxAQoMGDB2vFihXat2+f3n33XUVGRuqXX37RlClT9MYbbygwMFCxsbFurh4AKk/BiN3AgQMlSc8//7w2bNggi8Xi/BUjPz/fGfwkKTMzU6GhocrMzFRQUJB7CkepEPJgrLvvvltr167VgAEDJF39JupwOJx31zZu3FgTJkzQxo0bdejQIT3xxBOSpMcff9xtNQNAVerXr5+WLl2qzMxM9e3bV7169dKKFSt04cIF2Ww2l6cQbN26VTt37lRkZKQbK0ZpMOkIxvL09FSbNm1c2iwWi/Oi5XA4ZLfbZbPZFB4ervDwcEnSqFGjqrxWAHCXRx55RJL01ltvKTExUYmJiapXr54iIyPVp08feXt7a//+/froo4/k7e2tP//5z26uGCXF3bUwlt1ul9VqVX5+frHPxCu4k+zw4cN68MEHlZeXp6NHj1ZxpQDgfg6HQ998840WLFighISEQnPzunTpoldffVX9+vVzU4UoLUbyYKyCZ99d76HHBfNSHA6HrFar8xstANwsHA6H8xo4YMAADRgwQJmZmUpMTNQvv/yihg0bytfXV506dXLehYuagZE8GGnt2rXav3+/9u7dq3r16qlTp0667bbb1KRJEwUHB8tmsxX5PKi8vDwenQLAeMX9wpGfny+LxeLygHjUXIQ8GCUjI0OzZs3SnDlzZLPZnDdZSFJQUJC6deumgQMH6uGHH1ZgYKBz2/V+0gUAUxRMYylw7Sjeta5tL7hhjS/ANQ8hD0aZM2eOpk2bppiYGE2aNEkNGzbUjz/+qEOHDmnXrl3asWOHUlNTFRERoalTp+rhhx92d8kAUGXef/99JSYmavjw4YqMjJSvr69zm91ulyRG8QxCyINRmjZtqjvvvFNLlixRcHCwy7bk5GT9+OOP+vrrr/Xxxx8rPz9fCxYs0OjRo91ULQBUrWbNmun48ePy9vbWXXfdpejoaPXv31/33nuvy/SVgqkrFy9e1IIFC3TXXXcpKirKjZWjLAh5MMbBgwfVqVMnTZo0STNmzJBU9DfTK1euaP369Zo4caIyMjK0evVqdenSxS01A0BVOXDggNq2bauOHTuqbt26Wr9+vSSpTp066tatm/r376/o6Gi1atXK+Z4tW7aoR48e6tq1q7Zs2eKu0lFG/MAOYzgcDgUGBjofgZKXlyer1eoMeAXfZ7y8vNS/f3/l5uZq4MCB+v777wl5AIz3888/S7r6wPfnnntOhw8f1qpVq/TZZ58pISFBCQkJql+/vnr27Kl+/frpgQce0M6dOyVJU6ZMcWfpKCNG8mCUzp0769///reWL19e6FlOBXfTFkw8Tk9P1913362OHTvq888/d1PFAFA1FixYoLFjx+p//ud/Cl0fd+3apc8++0xffPGFTp06JUkKDw9XVlaWLl26pIyMDDdUjPJidiWMUPBd5d1335W/v79iY2P13HPPaefOnbp8+bKk/zwTLzc3V5J06NAh5eTkqGHDhu4pGgCqiMPhULt27fTss8+qZcuWLu2S1KlTJ7311ls6fPiwvvnmGw0fPlxnzpzRmTNnNGzYMHeVjXJiJA9Gyc/P19KlSzVlyhSlpKSoTZs2io6OVteuXdWmTRu1atVKVqtVv/32m1544QV9/vnn2rFjhzp06ODu0gGg0p0/f15eXl7y8vIqtO33zw6dMGGC5s+frz179qh9+/ZVWCUqCiEPRjp79qzmzZunFStW6PDhw6pdu7ZuvfVW+fr6KigoSAcPHtTZs2c1atQozZ8/393lAkC1UBD0jh49qiFDhigzM1NJSUnuLgtlRMiDURwOh+x2u2w2my5duqSkpCTt2rVLW7du1Y4dO3Tw4EGFhoYqLCxMo0eP1tChQ1WnTh13lw0A1crq1as1YMAAvfDCC5o9e7a7y0EZEfJgPLvdrsuXL8vLy0uZmZlKSUnRHXfc4e6yAKDKFbWcY1HOnDmjtWvX6sEHH1RQUFAVVIbKQMhDjXbp0iWdOHFCjRs3lo+Pj8s2u90ui8XivKD9/uL2++V9AMA017tG3gjLPdZ8/B8ONdrcuXM1dOhQvfPOO9q4caOSk5Od69VarVZZLBbnGowFAe/s2bPOZ+gBgMmud40sTsE1koBX8zGShxqtUaNGSk5Ols1mU0BAgLp27aro6Gjde++9at68eaGlzS5cuKBp06YpLS1NCxcuJOgBMFp5rpEffvghQa+GY8UL1FiHDx9WZmamunTposcff1zffvuttm3bptWrV6tx48bq2bOnevfurYiICN16660KDAzU/v379eGHH6pnz54EPABGK+81koBX8xHyUGMdPnxYly9fVnR0tMaPH68HHnhAhw4d0rZt2/Tdd99p5cqV+u///m+1adNGvXr1Ut++fbVhwwZlZWVpzJgx7i4fACoV10jwcy1qrC+++EKDBw/WsmXLNHjwYGd7bm6ujh8/rp9++knff/+9EhMT9X//93/y9PSUw+GQt7e30tPT3Vg5AFQ+rpEg5KHGcjgcOnjwoGrVqqVmzZoV+WiACxcu6PDhwzp06JAWLVqkb7/9VhMmTNC7777rpqoBoGpwjQQhD0Yq6mI2adIkzZs3T7t371ZERISbKgMA9+MaeXMg5MFoBc/CO3bsmB566CGdO3dOJ06ccHdZAFAtcI00G7cXwmgFd9D+9ttvys3N1TPPPOPmigCg+uAaaTZG8nBTcDgcOnXqlIKCglirFgB+h2ukmQh5AAAABuLnWgAAAAMR8gAAAAxEyAMAADAQIQ8AAMBAhDwAAAADEfIAAAAMRMgDAAAwECEPAADAQP8PGglDdO1vgJUAAAAASUVORK5CYII=\n"
          },
          "metadata": {},
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "lW-c-AADNw6R"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}