Colab_19a_Sudoku.ipynb

{
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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyNdlrnJkLC4pHSVb1egbnHq",
      "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_19a_Sudoku.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install qiskit && pip install pylatexenc && pip install qiskit-aer"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ap492aXiFKYL",
        "outputId": "acd56a6b-0e89-4ede-a6b4-80409c47bcc5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting qiskit\n",
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            "  Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n",
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            "  Preparing metadata (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
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            "Building wheels for collected packages: qiskit\n",
            "  Building wheel for qiskit (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for qiskit: filename=qiskit-0.44.0-py3-none-any.whl size=7620 sha256=60688c3525cbc57b4509ee7b6d738ff59ee4cf57313f036af8ada6d28fc29cc5\n",
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            "Installing collected packages: ply, symengine, rustworkx, pbr, dill, stevedore, qiskit-terra, qiskit\n",
            "Successfully installed dill-0.3.7 pbr-5.11.1 ply-3.11 qiskit-0.44.0 qiskit-terra-0.25.0 rustworkx-0.13.1 stevedore-5.1.0 symengine-0.9.2\n",
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            "\u001b[?25h  Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "Building wheels for collected packages: pylatexenc\n",
            "  Building wheel for pylatexenc (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
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            "Installing collected packages: qiskit-aer\n",
            "Successfully installed qiskit-aer-0.12.2\n"
          ]
        }
      ]
    },
    {
      "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": "6OQHLudUFX3r"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Soluzione classica"
      ],
      "metadata": {
        "id": "cfSLnAwTvZLG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "board = [[None, None], [None, None]]"
      ],
      "metadata": {
        "id": "8pt5BhC2vaMP"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def empty_cell(board):\n",
        "  for i in range(2):\n",
        "    for j in range(2):\n",
        "      print(\"Cell check\")\n",
        "      if board[i][j] == None:\n",
        "        return i, j\n",
        "  return None"
      ],
      "metadata": {
        "id": "YsST-0WEvbnW"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "empty_cell(board)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DHqapaBi_lOQ",
        "outputId": "6197aae6-d3ca-4a13-ae22-787cd70fb877"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Cell check\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0, 0)"
            ]
          },
          "metadata": {},
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def check_board(board):\n",
        "    for i in range(2):\n",
        "        for j in range(2):\n",
        "            cell_value = board[i][j]\n",
        "            if cell_value is not None:\n",
        "                for k in range(2):\n",
        "                    if k != j and board[i][k] == cell_value:\n",
        "                        print(\"Constraint check\")\n",
        "                        return False\n",
        "                    if k != i and board[k][j] == cell_value:\n",
        "                        print(\"Constraint check\")\n",
        "                        return False\n",
        "\n",
        "    return True"
      ],
      "metadata": {
        "id": "drqiq__0_m04"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "check_board(board)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Vw928kReAVZu",
        "outputId": "a8e5e222-7b8c-472d-a18a-d1c7610915f9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 65
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "board = [[1, None], [0, None]]\n",
        "check_board(board)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "61IA6evEAdud",
        "outputId": "f53d9621-abab-4bfd-ab10-927f222db7b0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 66
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "board = [[None, None], [None, None]]"
      ],
      "metadata": {
        "id": "NME7x3W5AqKC"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def solve_sudoku(board):\n",
        "  empty = empty_cell(board)\n",
        "  if not empty:\n",
        "      return True\n",
        "\n",
        "  row, col = empty\n",
        "\n",
        "  for num in range(2):\n",
        "    board[row][col] = num\n",
        "\n",
        "    if check_board(board):\n",
        "      break\n",
        "\n",
        "    board[row][col] = None\n",
        "\n",
        "  return solve_sudoku(board)"
      ],
      "metadata": {
        "id": "_3tfScDbBUYu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "solve_sudoku(board)\n",
        "board"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sIZclSn4CA4P",
        "outputId": "c57cc648-aab9-4bed-89da-49c06b824452"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Cell check\n",
            "Cell check\n",
            "Cell check\n",
            "Constraint check\n",
            "Cell check\n",
            "Cell check\n",
            "Cell check\n",
            "Constraint check\n",
            "Cell check\n",
            "Cell check\n",
            "Cell check\n",
            "Cell check\n",
            "Cell check\n",
            "Cell check\n",
            "Cell check\n",
            "Cell check\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[[0, 1], [1, 0]]"
            ]
          },
          "metadata": {},
          "execution_count": 69
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Soluzione con Grover"
      ],
      "metadata": {
        "id": "ax0Z5HswFC-6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Controllo che due qubit siano diversi\n",
        "qc = QuantumCircuit(3)\n",
        "qc.cx(0,2)\n",
        "qc.cx(1,2)\n",
        "qc.draw(output=\"mpl\")\n",
        "\n",
        "# q2 sarà flippato solo se q0 e q1 sono diversi!"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 255
        },
        "id": "MxCgyrXhC2Yl",
        "outputId": "68aec09b-bdad-4a9d-c447-b19a6991a19b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 287.496x284.278 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 73
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "clause_list = [ [0,1],\n",
        "               [0,2],\n",
        "               [1,3],\n",
        "               [2,3] ]"
      ],
      "metadata": {
        "id": "BbKyBkSuGnfK"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Allo stesso modo, controllo ogni clausola\n",
        "var_qubits = QuantumRegister(4, name='v')  # variabili\n",
        "clause_qubits = QuantumRegister(4, name='c')  # controllo clausole\n",
        "\n",
        "qc = QuantumCircuit(var_qubits, clause_qubits)\n",
        "\n",
        "i = 0\n",
        "for clause in clause_list:\n",
        "  qc.cx(clause[0], clause_qubits[i])\n",
        "  qc.cx(clause[1], clause_qubits[i])\n",
        "  i += 1\n",
        "\n",
        "qc.draw(output=\"mpl\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 577
        },
        "id": "Pr7Cj1jUFlsJ",
        "outputId": "bf3b087d-8984-4a46-b67f-c50e521e82ff"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 787.961x702.333 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 75
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Controllo che tutti i qubit \"clausola\" valgano uno con un multi toffoli gate\n",
        "\n",
        "# Allo stesso modo, controllo ogni clausola\n",
        "var_qubits = QuantumRegister(4, name='v')  # variabili\n",
        "clause_qubits = QuantumRegister(4, name='c')  # controllo clausole\n",
        "output_qubit = QuantumRegister(1, name=\"o\") # output totale\n",
        "\n",
        "qc = QuantumCircuit(var_qubits, clause_qubits, output_qubit)\n",
        "\n",
        "i = 0\n",
        "for clause in clause_list:\n",
        "  qc.cx(clause[0], clause_qubits[i])\n",
        "  qc.cx(clause[1], clause_qubits[i])\n",
        "  i += 1\n",
        "\n",
        "qc.mct(clause_qubits, output_qubit)\n",
        "\n",
        "qc.draw(output=\"mpl\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 642
        },
        "id": "jDZUwZlfGPOQ",
        "outputId": "eeced37d-0c3c-4ca7-c03b-b628c7609b97"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 871.572x785.944 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 77
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Controllo che tutti i qubit \"clausola\" valgano uno con un multi toffoli gate\n",
        "\n",
        "# Allo stesso modo, controllo ogni clausola\n",
        "var_qubits = QuantumRegister(4, name='v')  # variabili\n",
        "clause_qubits = QuantumRegister(4, name='c')  # controllo clausole\n",
        "output_qubit = QuantumRegister(1, name=\"o\") # output totale\n",
        "\n",
        "qc = QuantumCircuit(var_qubits, clause_qubits, output_qubit)\n",
        "\n",
        "i = 0\n",
        "for clause in clause_list:\n",
        "  qc.cx(clause[0], clause_qubits[i])\n",
        "  qc.cx(clause[1], clause_qubits[i])\n",
        "  i += 1\n",
        "\n",
        "qc.mct(clause_qubits, output_qubit)\n",
        "\n",
        "# Riapplico le clausole per resettare i clause_qubit\n",
        "i = 0\n",
        "for clause in clause_list:\n",
        "  qc.cx(clause[0], clause_qubits[i])\n",
        "  qc.cx(clause[1], clause_qubits[i])\n",
        "  i += 1\n",
        "\n",
        "qc.draw(output=\"mpl\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 642
        },
        "id": "C22YyD1PGzjv",
        "outputId": "b8513671-7688-4889-ef21-45273c8eae24"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1540.46x785.944 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 78
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def oracolo(qc):\n",
        "  i = 0\n",
        "  for clause in clause_list:\n",
        "    qc.cx(clause[0], clause_qubits[i])\n",
        "    qc.cx(clause[1], clause_qubits[i])\n",
        "    i += 1\n",
        "\n",
        "  qc.mct(clause_qubits, output_qubit)\n",
        "\n",
        "  # Riapplico le clausole per resettare i clause_qubit\n",
        "  i = 0\n",
        "  for clause in clause_list:\n",
        "    qc.cx(clause[0], clause_qubits[i])\n",
        "    qc.cx(clause[1], clause_qubits[i])\n",
        "    i += 1\n",
        "\n",
        "  return qc"
      ],
      "metadata": {
        "id": "0HjpelkINWpC"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def diffusore(qc, nqubits):\n",
        "\n",
        "    # Metto s in sovrapposizione H\n",
        "    for qubit in range(nqubits):\n",
        "        qc.h(qubit)\n",
        "\n",
        "    # Inverto s\n",
        "    for qubit in range(nqubits):\n",
        "        qc.x(qubit)\n",
        "\n",
        "    qc.barrier()\n",
        "\n",
        "    # Multi-controlled Z\n",
        "    qc.h(nqubits-1)\n",
        "    qc.mct(list(range(nqubits-1)), nqubits-1)\n",
        "    qc.h(nqubits-1)\n",
        "\n",
        "    qc.barrier()\n",
        "\n",
        "    # Inverto s\n",
        "    for qubit in range(nqubits):\n",
        "        qc.x(qubit)\n",
        "\n",
        "    # inverto H\n",
        "    for qubit in range(nqubits):\n",
        "        qc.h(qubit)\n",
        "\n",
        "    return qc"
      ],
      "metadata": {
        "id": "gz7pqPUNNokt"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "## Algoritmo completo!\n",
        "\n",
        "# Inizializzo il circuito\n",
        "var_qubits = QuantumRegister(4, name='v')\n",
        "clause_qubits = QuantumRegister(4, name='c')\n",
        "output_qubit = QuantumRegister(1, name='out')\n",
        "cbits = ClassicalRegister(4, name='cbits')\n",
        "qc = QuantumCircuit(var_qubits, clause_qubits, output_qubit, cbits)\n",
        "\n",
        "# Metto 'out0' nello stato -\n",
        "qc.initialize([1, -1]/np.sqrt(2), output_qubit)\n",
        "\n",
        "# Metto i qubit di variabile nello stato H\n",
        "qc.h(var_qubits)\n",
        "qc.barrier()\n",
        "\n",
        "## Prima iterazione\n",
        "\n",
        "# Applico l'oracolo\n",
        "\n",
        "qc = oracolo(qc)\n",
        "\n",
        "qc.barrier()\n",
        "\n",
        "# Applico il diffuser\n",
        "\n",
        "qc = diffusore(qc, 4)\n",
        "\n",
        "qc.barrier()\n",
        "\n",
        "## Seconda iterazione\n",
        "\n",
        "# Applico l'oracolo\n",
        "\n",
        "qc = oracolo(qc)\n",
        "\n",
        "qc.barrier()\n",
        "\n",
        "# Applico il diffuser\n",
        "qc = diffusore(qc, 4)\n",
        "\n",
        "qc.barrier()\n",
        "\n",
        "# Misuro\n",
        "qc.measure(var_qubits, cbits)\n",
        "\n",
        "qc.draw(output=\"mpl\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "RoTUhXUzMfiv",
        "outputId": "adc10afb-b54f-46b7-d39b-824e13ea56cc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 2242.6x2709 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {},
          "execution_count": 88
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Simulate and plot results\n",
        "simulator = Aer.get_backend('qasm_simulator')\n",
        "transpiled_qc = transpile(qc, simulator)\n",
        "result = simulator.run(transpiled_qc).result()\n",
        "plot_histogram(result.get_counts())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 484
        },
        "id": "QLu-rZPTOE4L",
        "outputId": "b62c729d-ea57-46a2-caa6-d318554ae638"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 700x500 with 1 Axes>"
            ],
            "image/png": 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EREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaxJBHREREpEEMeUREREQaZHUh7+HDhxgzZgyaN28Of39/ODo6omzZsmjatCmWLl0KvV6f7WcSExMxZswYBAYGwsHBARUrVsR///tfJCcn51jDYDBg/vz5qFWrFpycnODj44NXX30VFy5cKOz2iIiIiIpEvkNeVFQUrly58th1YmJiEBUV9VTPm5ycjC+++AKKoqBTp04YM2YMunfvjtjYWAwYMACdO3eGwWBQ109JSUGLFi3wySefIDg4GKNHj0a1atUwZ84ctGrVCg8fPsxWY/DgwRgxYgREBCNGjECHDh3w888/o0GDBoiOjn6q8RIRERFZI9v8/mBYWBimTp2KKVOm5LrOt99+iylTpiAjIyPPz+vp6YmEhATY29ubLE9PT0fbtm2xdetWbNq0CZ06dQIAfPTRRzh27BjGjx+PmTNnquu//fbbmDVrFj755BNMmDBBXb5r1y4sXrwYzZs3x7Zt29Q6//nPf/DCCy9g+PDh2LJlS57HS0RERGSN8n0kT0SeuI7BYICiKE83IJ0uW8ADAFtbW3Tv3h0AcO7cOXUMixcvhqurKyZPnmyy/uTJk+Hq6orFixebLP/6668BAO+9955JnY4dO6Jly5bYunXrE49QEhEREVm7Qj0nLzo6Gh4eHmZ5LoPBgM2bNwMAatasqT7/tWvX0LRpU7i4uJis7+LigqZNm+LChQuIiYlRl+/evVt9LKv27dsDAPbs2WOWMRMRERFZylN9XTtgwACT/16/fj0uXbqUbb2MjAz1fLyOHTvma2BpaWmYMWMGRAR37tzBjh07cPr0afTv3x+tW7cGAPX8uaCgoByfIygoCFu2bEF0dDQCAgKQkpKCuLg41KxZEzY2Njmun/l5c5KamorU1FT1vxMTEwEAer1evShEp9PBxsYGGRkZJucPGpenp6ebHAm1sbGBTqfLdXnWi01sbR/ttvT09Dwtt7Ozg8FgMPnaXFEU2Nra5ro8t7GzJ/ZU1D0BdigIYw/W1FNx2U8FOKMHwKNtb209aXE/saeS2VNePNVv8LJly0wGduzYMRw7dizHdRVFQYMGDfDJJ588TQlVWloapk+fbvJ848aNw4cffqguS0hIAIBcjxa6u7ubrPe06+fkww8/NBmX0datW+Hs7AwAqFChAurUqYPjx4+bfPVbrVo1BAcH49ChQ7h165a6PDQ0FIGBgYiKikJSUpK6vHHjxvD19cXWrVtNdmhYWBicnJwQGRlpMoYXXngBDx48wK5du9Rltra26NSpE27fvo0DBw6oy93c3NCqVSvExMSY7EMfHx80adIE0dHROHPmjLqcPbEnS/UEdENBGMdqTT0Vl/0EtMp9w+ZBZGSk1fWkxf3EnkpeT0eOHEFeKJKXk+v+v8uXLwN4dC5c5cqVMWrUKIwcOTLbejY2NihdunS2r1Dzw2Aw4Nq1a9iwYQMmTpyIZ599FpGRkXB3d8cPP/yA3r17Y9KkSXj//fez/eykSZMwY8YM/Pzzz+jevTuuXbuGcuXKoWnTpti7d2+29bdt24Z27dphxIgR+PTTT3McT05H8gICAnD79m01JJbUTxXsiT0VRk9DPy/YkbyFw3gkL789DVlQsCN5C4fxSB57Yk+F0VN8fDy8vLyQkJCgZo+cPNVvcGBgoPr/ly5dijp16pgsKww6nQ7ly5fHkCFD4O3tjfDwcHzwwQeYNWuWekQutyNvxq9Sjes97fo5cXBwgIODQ7bldnZ2sLMzfTOysbHJ8Wth4wsjr8uzPm9+lut0Ouh02U/BzG15bmNnT+zpaZebq6f8yjoma+qpOOyngshcx5p60uJ+Yk/sKSf5/pgWERGR3x/Nt3bt2gF4dPEE8ORz6LKes+fi4gI/Pz9cvHgRGRkZ2Tbck87xIyIiIiouCnYsHsChQ4dw+PBh3Lt3L8f74SmKku32Jvl17do1AP9LzUFBQfD398e+ffuQkpJi8vVwSkoK9u3bh0qVKiEgIEBd3qJFC6xatQr79u1D8+bNTZ7feH+8rMuJiIiIipt8h7z4+Hi8+OKL2Ldv32Pvmfe0Ie+ff/5BxYoV1YsYjO7fv48xY8YAeHSyo/G5X3/9dbz77rt47733TG6G/N577yE5ORkTJ040eZ433ngDq1atwuTJk01uhrxp0ybs3r0b7dq1K/SvoImIiIgKW75D3pgxY7B37160bNkSERERKF++fJ6/I36cNWvW4OOPP0azZs1QsWJFuLu7IzY2Fps2bcKdO3fw/PPPY/To0er6b731Fn755RfMmjULf/31F+rWrYujR49i69ataNCgAUaNGmXy/GFhYXj99dexePFi1K1bF506dUJcXBxWr14NT09PzJ8/v8A9EBEREVlavlPZxo0b0bBhQ+zYseOpZ7V4nM6dO+PatWvYv38/Dhw4gOTkZHh4eCAkJASvvPIKBgwYYBImXVxcsGfPHkybNg0//fQTdu3aBT8/P4wdOxZTp06Fk5NTthqLFi1CrVq18NVXX+HTTz+Fq6srunfvjg8++ABVqlQxWy9ERERElvJUt1DJzMXFBcOGDcNHH31k7jEVK4mJifDw8HjiZcxElD+D5hXs578eZY5RlEzc9kTWKa/ZI9/Xy4eGhuY42wURERERWV6+Q97UqVPx66+/4uDBg+YcDxERERGZQb7Pybt+/To6deqEFi1aoHfv3qhbt26uhwz79u2b7wESERER0dPLd8jr168fFEWBiGDZsmVYtmxZtgswRASKojDkERERERWxfIe8pUuXmnMcRERERGRGxWpaMyIiIiLKG/PORk1EREREViHfR/KuXLmS53UrVKiQ3zJERERElA/5DnkVK1bM00wXiqIgPT09v2WIiIiIKB/yHfL69u2bY8hLSEjA33//jYsXL6JFixaoWLFiQcZHRERERPmQ75C3bNmyXB8TEcydOxcfffQRvvnmm/yWICIiIqJ8KpQLLxRFwbhx4/Dss8/iv//9b2GUICIiIqLHKNSra+vXr4+dO3cWZgkiIiIiykGhhrzz58/zogsiIiIiC8j3OXm5MRgMiI2NxbJly/DLL7+gdevW5i5BRERERE+Q75Cn0+keewsVEUHp0qUxd+7c/JYgIiIionzKd8hr3rx5jiFPp9OhdOnSaNCgAfr37w9fX98CDZCIiIiInl6+Q97u3bvNOAwiIiIiMifOXUtERESkQWa58GLfvn04duwYEhMT4e7ujtDQUDRt2tQcT01ERERE+VCgkLd//370798f586dA/DoYgvjeXpBQUFYunQpGjduXPBREhEREdFTyXfIO3XqFNq1a4f79++jbdu2CAsLg5+fH65fv45du3Zh69ataN++PQ4ePIgaNWqYc8xERERE9AT5Dnnvvvsu0tLSEBkZiQ4dOpg8Nn78eGzevBldu3bFu+++i1WrVhV4oERERESUd/m+8GL37t3o0aNHtoBn1KFDB/To0QO7du3K9+CIiIiIKH/yHfISEhJQqVKlx65TqVIlJCQk5LcEEREREeVTvkOev78/Dh48+Nh1/vjjD/j7++e3BBERERHlU75DXteuXbF7925MnjwZDx8+NHns4cOHmDp1Knbt2oVu3boVeJBERERE9HTyfeHF5MmTsXHjRsyYMQOLFi1Cw4YNUaZMGdy4cQOHDx/GrVu3ULlyZUyePNmc4yUiIiKiPMh3yPPy8sLBgwfx1ltvYdWqVYiMjFQfc3R0RP/+/TFr1ix4enqaZaBERERElHcFuhmyt7c3lixZgkWLFuH06dPqjBfBwcGws7Mz1xiJiIiI6Ck9dcj74IMPkJKSgunTp6tBzs7ODrVq1VLXSUtLw6RJk+Dm5oa3337bfKMlIiIiojx5qgsvtm/fjilTpsDLy+uxR+rs7e3h5eWFSZMm8T55RERERBbwVCHv22+/RenSpTF8+PAnrjts2DB4enpi6dKl+R4cEREREeXPU4W8/fv3o02bNnBwcHjiug4ODmjTpg327duX78ERERERUf48Vci7du0aKleunOf1K1WqhLi4uKceFBEREREVzFOFPJ1OB71en+f19Xo9dLp832+ZiIiIiPLpqRKYv78/Tp48mef1T548iXLlyj31oIiIiIioYJ4q5D3//PPYuXMnLl269MR1L126hJ07d6J58+b5HRsRERER5dNThbxhw4ZBr9ejR48euH37dq7r3blzBz179kR6ejqGDBlS4EESERER0dN5qpsh161bF6NGjcK8efNQo0YN/N///R/CwsJQvnx5AEBsbCx27NiBr776Crdu3cKYMWNQt27dQhk4EREREeXuqWe8mDt3LhwdHTF79mx88MEH+OCDD0weFxHY2NhgwoQJeP/99802UCIiIiLKu6cOeYqiYMaMGRg4cCCWLl2K/fv34/r16wCAsmXLomnTpujXrx+qVKli9sESERERUd48dcgzqlKlCo/UEREREVkp3sSOiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIOsMuStWLECgwcPRv369eHg4ABFUbBs2bIc1502bRoURcn136VLl3L8uS1btqBFixZwc3ODu7s7wsLCsGPHjsJrioiIiKgI2Vp6ADl55513cPnyZXh7e8PPzw+XL19+4s9ERESgYsWK2ZaXKlUq27IVK1agT58+8PHxQb9+/QAAq1evRtu2bbFmzRr06NGjgB0QERERWZZVhrzFixcjKCgIgYGBmDlzJiZMmPDEn+nXrx9atmz5xPXu3r2LN998E97e3jh69CjKly8PABg/fjzq1KmDIUOGoH379nBzcytoG0REREQWY5Vf17Zp0waBgYGF8txr167FvXv38Oabb6oBDwDKly+P4cOH4/bt21i3bl2h1CYiIiIqKlYZ8vIjKioKs2bNwuzZs7F+/XokJyfnuN7u3bsBAO3atcv2WPv27QEAe/bsKbRxEhERERUFq/y6Nj+mTp1q8t+lSpXCp59+ir59+5osj46OBgAEBQVlew7jMuM6OUlNTUVqaqr634mJiQAAvV4PvV4PANDpdLCxsUFGRgYMBoO6rnF5eno6RERdbmNjA51Ol+ty4/Ma2do+2m3p6el5Wm5nZweDwYCMjAx1maIosLW1zXV5bmNnT+ypqHsC7FAQxh6sqafisp8K+hah1+utrict7if2VDJ7yotiH/Jq166NJUuWoGXLlvDz88P169exceNGTJkyBf369UOpUqXQtWtXdf2EhAQAgIeHR7bncnd3N1knJx9++CGmT5+ebfnWrVvh7OwMAKhQoQLq1KmD48eP48qVK+o61apVQ3BwMA4dOoRbt26py0NDQxEYGIioqCgkJSWpyxs3bgxfX19s3brVZIeGhYXByckJkZGRJmN44YUX8ODBA+zatUtdZmtri06dOuH27ds4cOCAutzNzQ2tWrVCTEwMjh07pi738fFBkyZNEB0djTNnzqjL2RN7slRPQDcUhHGs1tRTcdlPQKvcN2weREZGWl1PWtxP7Knk9XTkyBHkhSKZY6wVMl54sXTpUvVK2LzYsWMH2rZti5o1a+L48ePq8qpVqyI6Ohp6vV5N4UZ6vR729vYICQnB33//nePz5nQkLyAgALdv31ZDYkn9VMGe2FNh9DT084IdyVs4jEfy8tvTkAUFOw6wcBiP5LEn9lQYPcXHx8PLywsJCQlq9shJsT+Sl5vWrVujSpUqOHHiBBITE9WNYDyCl5CQAC8vL5OfMX71mtNRPiMHBwc4ODhkW25nZwc7O9M3IxsbG9jY2GRbN2u4fNLyrM+bn+U6nQ46XfZTMHNbntvY2RN7etrl5uopv7KOyZp6Kg77qSAy17GmnrS4n9gTe8qJZi68yIm3tzcA4P79++qyx51397jz9YiIiIiKE82GvJSUFJw6dQouLi5q2AOAFi1aAHh0Dl1WW7ZsMVmHiIiIqLgq1iEvKSkJZ8+ezbb8wYMHGDRoEJKSkhAeHm5yWDM8PBweHh6YP38+rl69qi6/evUqFixYAG9vb3Tv3r1Ixk9ERERUWKzynLzFixdj7969AIATJ06oy4z3uGvWrBlef/113LlzB8HBwWjQoAGqV6+OsmXL4saNG9i+fTuuXr2KWrVqYfbs2SbPXbp0aSxYsAB9+vRB3bp10atXLwCPpjW7c+cOVq9ezdkuiIiIqNizypC3d+9eLF++3GTZvn37sG/fPvW/X3/9dXh6emLo0KE4dOgQIiMjcffuXTg5OaF69eoYMWIEhg8fDicnp2zP/9prr8Hb2xszZszA0qVLoSgK6tWrh3feeQdt2rQp9P6IiIiICpvV30LF2iUmJsLDw+OJlzETUf4Mmlewn/96lDlGUTJx2xNZp7xmj2J9Th4RERER5Ywhj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIiINIghj4iIiEiDGPKIiIqRihUrQlGUbP+GDRtm6aERkZVhyCPKh2nTpmV7kw0ODrb0sKgIWHrfHz58GHFxceq/bdu2AQB69uxZZGMoySy9/y1dn4oXhjyNmDlzJhRFwahRoyw9FIuwRP/PPvusyZvt3r17i6w2WZYl972Pjw/Kli2r/tu4cSOqVKmCFi1aFNkYSjpL/+5buj49UhzedxnyNODw4cNYtGgRQkJCirTuF198gZCQELi7u8Pd3R2NGzfGpk2binQMgOX6t7W1NXmz9fb2LrLalt72lq5vaZbc95mlpaVhxYoVGDBgABRFscgYipo1vPYsvf8tVd8atr21sNT7ztNiyCvmkpOT0bt3b3z99dcoXbp0kdYuX748Zs6ciSNHjuDPP/9Eq1at0K1bN5w6darIxmDJ/qOjo+Hv74/KlSujd+/euHLlSpHVtvS2t3R9S7Pkvs9s/fr1uHfvHvr162eR+pZgDa89S+9/S9W39Lb/8MMP0aBBA7i5ucHX1xcvvvgizpw5UyS1M7Pk+87TUkRELD2I4iwxMREeHh5ISEiAu7t7kdePiIiAp6cnPvnkE7Rs2RKhoaGYN29ekY/DyNPTE7Nnz8bAgQOLpJ6l+t+0aROSk5NRrVo1xMXFYfr06YiNjcXJkyfh5uZW6PVzUtTbvqjqD5pXsJ//epQ5RvE/1rTv27dvD3t7e2zYsKFQnt/atn1uivK1b+n9b+n6WRXltu/QoQNeeeUVNGjQAOnp6Zg4cSJOnjyJf/75By4uLoVe38ga3nfzmj1si3BMZGarVq3C0aNHcfjwYUsPBRkZGVi7di1SUlLQuHHjIqlpyf47duyo/v+QkBA899xzCAwMxJo1a4o8ZFli21tT/aJmLfv+8uXL2L59O37++eciq2ltLPHas/T+t3R9I0ts+82bN5v897Jly+Dr64sjR46gefPmRTIGa3rfzQuGvGIqJiYGI0eOxLZt2+Do6GixcZw4cQKNGzfGw4cP4erqinXr1qFGjRqFXtda+jcqVaoUqlatinPnzhVZTUtte2upby0sse8BYOnSpfD19UWnTp2KtK41sKbXnqX2v6XqW9O2T0hIAPDoaGJRsLb3nbzgOXnF1JEjR3Dz5k3UrVsXtra2sLW1xZ49e/DZZ5/B1tYWGRkZRTKOatWq4dixY/jjjz8wZMgQRERE4J9//in0utbSv1FycjLOnz8PPz+/IqtpqW1vLfWthSX2vcFgwNKlSxEREQFb25L3Wd2aXnuW2P+WrG8t295gMGDUqFFo2rQpatasWSQ1re19Jy94Tl4BWeqcvKSkJFy+fNlkWf/+/REcHIzx48cX2Ys+qzZt2qBKlSpYtGhRodaxdP/jxo1Dly5dEBgYiGvXrmHq1Kk4duwY/vnnH/j4+BRq7dwU1bYv6vrWdl6YNez7rVu3on379jhz5gyqVq1aaHWsbdvnpihf+5be/5aun5Wl/u4MGTIEmzZtwt69e1G+fPkiqWnp953MeE6exrm5uWV7Qbm4uMDLy8tiAQ949OkqNTW10OtYuv+rV6/i1VdfxZ07d+Dj44NmzZrh4MGDFgt4QNFte2utX1SsYd+3a9cO/Hz+P0X52rP0/rd0/aws8Xs/fPhwbNy4EVFRUUUW8ADLv+/kB0Me5duECRPQsWNHVKhQAUlJSfjhhx+we/dubNmyxdJDK3SrVq2yaH1Lb3tL17ckS+/7ks7Srz1L739L1rf0thcRvPnmm1i3bh12796NSpUqFUnd4qxEh7zDhw9j6tSp2L9/P/R6PWrVqoUxY8YgPDzc0kPLl927dxdpvZs3b6Jv376Ii4uDh4cHQkJCsGXLFrRt27ZIx2FU1P1bkqW3vaXrlyTF5SvTosLXnuVYetsPGzYMP/zwA3755Re4ubnh+vXrAAAPDw84OTkVyRiysvb3nRJ7Tt6uXbvQvn17ODo64pVXXoGbmxt++uknXL58GXPmzMHYsWPz9DyWvk8ekdaV9JBjyf5L+rYn65LbrC5Lly4tUTcEB3hO3mOlp6dj0KBB0Ol0iIqKQmhoKABgypQpaNiwISZOnIgePXogMDDQsgPNpKT/sbV0/wWpX9y3fUln6dceWY6l972l61ubojwmpZVtXyJD3s6dO3H+/Hn0799fDXjAo0O+EydORL9+/bB8+XJMmTLFcoO0Mlp5wRdHlt72lq5PJRdfe5bF7V/8lciQZ/wOvV27dtkea9++PQBgz549Of5samqqyZVExpsxxsfHQ6/XAwB0Oh1sbGyQkZEBg8Ggrmtcnp6ebvKJxMbGBjqdLtfler0eaQ/t8tntI/fuGUzu4aMoCmxtbWEw5Lw869gLWv/OnUfbJnNPmRnv9ZWenp7j8rSHBZt8PTERue6PvOyngvRv7N0ot17t7Oxy3B9pDwv2a3rnjp6vPZTM1x5g+vrja4+vveLy2rO1tcWbC/Nf++NBxfu196T9FB8fDyAPRzelBOrRo4cAkD///DPHx11dXSUgICDHx6ZOnSoA+I//+I//+I//+I//LPovJibmsXmnRF540a5dO2zbtg3R0dF45plnsj1erlw5JCcnq0fpMst6JM9gMCA+Ph5eXl65nhRa2BITExEQEICYmBiLXPxRkuuX5N5Zv2TXL8m9sz5fe5asDwAigqSkJPj7+0Ony33yshL5dW1BODg4wMHBwWRZqVKlLDOYLNzd3S16hW9Jrl+Se2f9kl2/JPfO+nztWbK+h4fHE9cpkXPXGjdMTkfqgP9dmkxERERUXJXIkBcUFAQAiI6OzvbY9evXkZycrK5DREREVByVyJDXokULAI8m+c7KOD2LcZ3iwMHBAVOnTs32NTLra7s267M+X/usXxLrl+Ten1aJvPAiPT0d1apVQ2xsLA4ePKjeKy8hIQENGzbEpUuXcObMGVSsWNGi4yQiIiLKrxIZ8gDzTWtGREREZI1KbMgDgEOHDmHq1KnYv38/9Ho9atWqhTFjxqBXr16WHhoRERFRgZTokEdERESkVSXywgsiIiIirWPIIyIiItIghjwiIiIiDWLIIyIiItIghjyNMV5HUxKvp8ncc0nrvyT3DmTvvyRuAyKirBjyNEZRFJP/BUrOm37mnjP/f4PBYInhFKmS2Hvm17WiKEhLS1P/v3EbZGRkWGRsRS3zfi4pv++ZZe5fy6/53JTE/nN6nZeU3p8Gb6GiAenp6Thz5gy2bt0KFxcX2NnZwdfXF6GhoShXrpylh1foHjx4gP3792P79u2ws7ODoiioVKkSnn/+eVSpUsXSwytUJbl34NEsNT///DP27duHjIwMGAwG1KhRA506dULNmjXV9UTEJPyaW2E/f17o9XrY2dmp/208oqnTlYzP8omJiXB3d1f/m/2XjP7T0tJw7949+Pr6miw3GAya7z0vGPKKuYsXL2Lu3LlYuHChyXInJycEBQUhLCwMXbp0QaNGjeDs7GwVb0bmdPr0abz//vv44YcfAADOzs64f/8+AMDDwwOtW7fGK6+8gnbt2pn8ATQHvV4PGxubp/5DYq59YMneAcv3f+zYMUyZMgUbN24EAHh7e+P27dvq43Xq1MGgQYMQHh4OT0/PAtfLKjExEba2tnB2dn6qnzPn7+CFCxcQGRmJU6dOwd7eHi4uLqhZsybCwsLg5+dnlhrWSkTw999/4/vvv8fFixeh1+vh5uaGBg0a4MUXX0RgYKDJulr6uweU7P7T09Oxd+9efPnll4iLi0NCQgJcXV3RvHlzvPzyy6hXr566bkn4gPdYQsVajx49xNbWVoYMGSLLli2TFStWyOeffy69evWS0qVLi6Io4u/vL5MmTZKbN2+avf6cOXNkx44d8vDhQ7M/d1507dpVHBwcZPLkyRIZGSm///67bNiwQYYPHy5lypQRRVFEURTp3bu3HDt2zKy1J0+eLIsXL5azZ8/K/fv38/QzBoPBbPUt2buI5fvv0KGDuLi4yNy5c+XQoUMSExMjf/31l7z33ntSv359tf8mTZrIb7/9Zra6RiNGjJB33nlHduzYIbGxsaLX65/4MxkZGWarv2rVKqlQoYIoiiI6nU5cXV3Vnv38/GTAgAGyfft2SU1NFRHzbnsRkfv37+frOc01jkWLFomfn58oiiKenp7i7e2t9q8oirRu3VrWrl0rDx48MEu9rOLi4tRt+zTYf8H7/+ijj9R+q1Wrpv4eGP/VqlVLvvzyS0lOTi5wrZz8+++/kpSUZLLMYDA8sTdz/w7mBUNeMXbx4kWxsbGRcePG5fjiiY2NlS+++EIaNGggiqJIq1atJDo62qz1jb9UNWrUkKlTp8rx48dzXNf45hYbGys///yznDlzpsD1L126JDqdTiZOnJjrOhs3bpR27dqJra2thIaGyp9//lngusbaxt4DAwNl0KBB8uuvv8rVq1clLS3NZF1j75cuXZLPPvtM9u7da5b6lurdWN8a+p86dWqu6xw4cEBeeeUVsbOzk4oVK8qWLVtExDx/aDP37+XlJZ07d5bPPvtMDh48KLdv3zZZ11gvOjpaxo8fL+vXry9w/StXroi3t7cEBQVJZGSk7NmzR44ePSrr1q2TPn36iLOzs/rmP2HCBLl3716Ba2YWGxsrERER8vPPP8vly5fz9GaflxCcV5cvX5ZSpUpJaGioHDhwQP7991+Jj4+XAwcOyFtvvSXVqlVT988rr7wiZ8+eNVttEZGrV69Kx44d5ZNPPpF9+/bJzZs3c31dGZfnJxDlpiT3f+nSJXF1dZVmzZrJqVOn5M6dOyIicvLkSfnkk0+kffv2YmtrK4qiSKNGjWTPnj1mqWsUExMjdevWlZEjR8qaNWvk7Nmzkp6ebrKOsWfj/xZW0M4LhrxibMGCBeLk5KQepcjtl+jMmTMydOhQURRFBgwYkO0FmV+fffaZKIoidevWNTly9Pzzz8vChQvlypUr6rrGF/unn34qiqLITz/9VOD6ixYtEkdHR1m3bp2IiBouDAaDSY9JSUkyZ84cURRFOnbsaJZPdwsXLlSDc8OGDcXe3l79BDlx4kSJioqSW7dumRy5WbBggSiKIitXrixwfUv2LmL5/pcsWSIODg6yevVqEflf/xkZGdle3z/99JPY2dlJnTp1zHY0e9GiRaIoirz00kvSs2dP9fVfoUIF6dOnj3z77bdy4sQJSUxMVH/miy++EEVRZPny5QWuP3nyZPH19ZWNGzfm+HhaWposXbpU6tSpIzqdTl5++WWzHsmfNGmSKIoiNjY2EhwcLGPHjpUdO3bIjRs3cn3D27Jli8yYMUNiY2MLXH/KlCni6+srmzdvznWd3377TVq2bCmKokjLli3l/PnzBa5rNHnyZFEURezs7MTf319eeeUV+eabb+TYsWPZArWx/59//lkGDRok586dK3D9ktz/tGnTxNvbW7Zt2yYiOR8d37t3r/Ts2VMURZGQkBA5evSoyVgKYurUqaIoijg4OIiLi4s0a9ZM/Tbl6tWrJusa63333XfStm3bXA+CFCaGvGLM+Eaza9cuEXn8C/jBgwcyaNAgURTFLEfRRESGDh0qOp1ODh06JKdPn5b3339fWrZsqR5FcHZ2lpdfflnWrFkjSUlJkp6eLq+88oooimKWsPHjjz+Koijyyy+/PHHdjIwM9Y3pjz/+KHDt0aNHi6IocvDgQbl27ZosWbJE+vXrJ0FBQeofgJYtW8qcOXPkxIkTcv36dfWPTnHvXcTy/e/YsUMURZHFixfnuk56err6O/Hxxx+LoiiyadOmAtcWEXnrrbdEURTZv3+/JCcny6ZNm2T69OnSsmVLcXNzE1tbW6lZs6aMGDFCNm7cKCdOnJCXX37ZbP23bt1aateurQYm41GyrCH34sWL0qdPH1EURebOnVvgukYtWrQQJycn6dWrlzz77LPqG36TJk1k5syZcvjwYbl37546locPH0q3bt3EycnJLEc1OnXqJNWrV5eYmBgREbVO1v71er362h8zZkyB6xq1bdtWnJ2dZfTo0dK+fXspVaqUGniHDh0qP/74o5w9e1bd1+np6fLSSy+Jvb19nk9teJyS3H/Pnj2lcuXKcunSJfW5RR71njXwff3116IoivTo0aNANTPr1KmTuLi4yEcffSSvv/66+lWxj4+PdOnSRebMmSN79+41OaLfs2dP0el0kpKSYrZx5BVDXjH2999/i7Ozszz//PPq17BZj+SI/O8ox9q1a8XGxkaWLVtW4NoJCQnSqVMnURTFJFympKTI9u3bZdy4cVKnTh316J6/v7/06NFDXFxcpFOnTgWuLyJy/vx58fT0lOrVq8v+/fvV5Znf3EX+9wa4efNmsbGxkc8//7xAdRMTE+XFF18URVFMzkV8+PCh/PnnnzJv3jzp3r27lC1bVv3KrHXr1mJvb1/sexexjv7j4uKkQoUKUrZsWVm/fn2uwcHY/549e8Te3l5mz55d4NopKSkyYMAAcXBwMDlqodfr5dy5c/LTTz/J6NGjpU6dOmJvby/Ozs5St25dURRFOnfuXOD6aWlpMmjQIHF1dc1TYEpOTpbQ0FCpXbu2JCQkFLj+tWvXJCQkREJCQkRE5NixY/L5559LeHi4lC9fXhRFEXd3d+nSpYt8+eWXEhMTIzt37pSyZctK+/btC1xf5FHItrGxyXbkJDPjG77BYJBWrVpJtWrVzHIU8fr161K3bl0JCgoSkUdB+pdffpG33npLGjRoII6OjuLg4CDPPfecTJw4UX7//XdZv369+Pr6SocOHQpcX6Rk9z9jxgxRFEWOHDmS6zrp6enq736PHj0kMDBQTp8+XeDaN27ckIYNG0pAQICIiMTHx8uff/4pCxculK5du4qXl5coiiKVKlWS3r17y4oVK2T58uXi4+MjHTt2LHD9/GDIK8bu378vb7zxhvq10V9//WXyeEZGhskb/rJly8TW1lY9zF0QaWlpMn/+fOnTp4/Ex8eLwWDI9inqxo0bsmbNGunfv79UqVJFDXzmOgk+IyNDpk+fLoqiSNOmTeXXX381eTzrkc3ly5eLra2tem5WQequWLFCIiIi1K/AsvZ+9+5d2bFjh0ybNk1at26tnhQfGRlZoNqZx2CJ3o21Ld2/iMjixYtFURSpXLmyzJ8/X27cuJHrusuXLxcbGxuzHMkzGAyyYcMGGTt2rNy6dUtdlllKSor8/fffsmTJEhk4cKD6da65+v/uu+9EURTp06ePekQj6we8zL+TgwcPFi8vL7McxT9y5Ig4ODjIiy++aLI8MTFRoqKi5IMPPpC2bduqF36VK1dOGjZsKIqiyIYNGwpcX+TRV5GKokjbtm3lyJEjOZ6Ckrn/MWPGiLu7u5w8ebLAtf/55x8pX768dO/e3WT5gwcP5OTJk/Ldd9/JoEGDpGrVqmJjYyOlS5eW6tWrs38z9f/777+LTqeT0NBQ2bZtW45HBjNfBDF58mRxdnZWv7ItiPPnz0toaKi8/PLLJsvT09MlLi5O9uzZI++//740a9ZMnJycxN7eXv3gY659/7QY8oq5tLQ0GTFihBqgOnbsKCtXrjQ5F0jk0aevFi1aiK+vr1nrp6amZnuDy+kciUOHDklQUJCUKlXKrPVFRGbPnq1+gqpdu7bMnz9frl27JiKiHh4/f/68PPfcc+Ln52f2+pnl1Pvx48elZs2a4uHhYfZ61tS7SNH3v2rVKvUNJCgoSCZOnCj79++Xq1evyrVr1yQ1NVWOHDkitWvXVj99F6acTpk4e/as1KtXz6z937p1S9q0aSOKokh4ePhjL6q5e/eu9OvXT8qWLWuW2ikpKTJt2jT58ssvRa/X53hV4fXr1+XXX3+Vt99+W73SuXTp0mapL/Lo785rr70miqJIs2bN5Mcff8z1a/B79+5Jv379xMfHxyy1Hzx4IPPnz5cVK1aoR4uy9n/v3j05ePCgLFq0SLp168b+zdz/22+/rX7Amzt3rpw+fTrHo9oJCQkSEREhXl5eZqmbmpoqP/zwg6xfvz7XC4kePnwoFy5ckC1btsjQoUPF3t7erL0/LYa8Ysz4hnrjxg2ZN2+eVK5cWQ17Li4u0rZtW5kwYYKEh4eLv7+/uLi4yMcff1xk4zMYDOrFILt37xY3NzcZOHCgWZ9f5NERhJUrV0rr1q1NLqNv2LChvPbaa9K8eXNxdnYWDw8Ps3xdKSJ5unjF+DX5jh07xNnZ2ay9G/d9QkKC/PDDD9KqVasi611Esl1B+7h1CqN/475PS0uTHTt2yIABA0wu/qlWrZo0b95cgoODRVEUKVOmjHzzzTdmq5+X/W98E9i6das4ODiYtX+RR6/7gQMHqj23bNlSVqxYIbdv35aHDx9KfHy8iDy64MPd3V2GDBli1vo5ySnkL1myRBRFkcGDB5u93vTp09VbadStW1dmzZolf/75p1y8eFFiYmLkwYMHMnPmTHF1dZVhw4aZvX5WOYX8lStXik6nkzfeeMPs9Upy/8uWLVOvIg4KCpIRI0bIjz/+KPv27ZPTp0/LtWvX5K233hIXFxcZOXKkWWvn1bp168Te3l4GDRpkkfoiDHnFVm4XWaxfv15efPFF8fb2FhsbG/UiiPr168vq1avNduJnbvf7ym1cY8eOFUVR5PDhw2apn5s9e/bIyJEjpX79+uo5W7a2tvLCCy/I1q1b8xROzG3atGmiKIocOnTILM+X2zbeuXOnvPnmm4Xee271c3tNmLv/3Bw5ckRmzpwpPXr0kMaNG0vVqlXFx8dH+vfvL4cOHbLIPapERObOnSs2NjZm7d8YIGNiYuTjjz+W2rVrq2HPzs5OmjZtKp07d5ZnnnlGPdpjjqs6RR7t/yfdDiXz0b2JEyea/Xff+Fq7d++erFy5Urp16yZubm6iKIrY2tpK9erVpXbt2moA6tixo1y4cMEstXM6NSWndYz9Gy/SMWf/xt/l+Ph4+f7774u8/9yO4GVep7D6Nz5venq67N69W0aOHCnBwcFiY2MjNjY2UqZMGSldurT63terVy+TOz0UtPbT/B0pqve9x+GMF8VYbGwsypUrhwcPHkCv15vMapCcnIyjR48CAMqVKwdXV1eUKVOmUOqnpaUhPT091zv/iwh+++03/Pjjj1i2bJlZx2B8fskyfc/Dhw8RHR0NJycnlC5dGo6OjnBxcTF77byIiorC5s2bMWPGDLM9Z3R0NHx9fXHv3j04Ojqa7Nv79+8jOjoaLi4uhda7sX5SUhKcnJzg5eWV67qF0X9mWacvSktLw40bN1CqVCnY2dnBwcHBonek/+uvv7Bv3z4MHz680GqkpqZi8+bN2LBhA/7++28kJiYiKSkJ9vb26N27N4YMGYLy5csXWn0g52mk4uLi8Oqrr+LKlSu4cOFCodXW6/U4ePAgdu7ciRMnTuDOnTuIi4tDqVKl0KtXLwwYMAAeHh6FVj83t27dwhtvvIF///0Xp0+fLrQ6aWlp2LdvH3bv3o1Tp05ZpP+c9n9R9J+RkYGTJ0/i8OHDOH36NOLi4nD+/HlUqFABL7zwAl577TXY2toWSu3HuXv3LsaOHYs///wTx48fL/L6Rgx5xYyIYOPGjfjmm29w4sQJJCcnIyQkBCEhIahTpw5q1aqFZ555ptACzePq161bF3Xq1EGVKlXg4OBQqNO9ZGRkQKfTZXv+jIwMKIpSqHMW5la7sKWmpmLt2rVYuHAh/vrrL+h0OgQFBeGZZ55B3bp10ahRI9SpUwelS5cu8vr16tVD06ZNERoaWihTqBmJCDIyMmBjY5Nt+xsMBiiKkm25OV+Hj6tfVG7evIlbt27By8sLCQkJ8Pb2NgnZd+/exbVr19RQ5+7ubtaxZq6fnJwMb29vlCpVKsd1ja8ZR0dH9OjRw2xjMMrpA15KSgqSk5NRpkwZpKamwsHBwex180qv12PHjh2wtbVFmzZtCvx8GRkZiI6Oxt27dyEiMBgMqFy5Mvz9/dV1kpKSkJycDD8/P7P3n7m+UeXKlXM9gGDu/rPK+rudlpYGnU4HW1tb9ffUUjIyMvDXX39BRNCgQQOLjYMhr5iZMmUK5syZA2dnZwQEBECv1yMtLQ0xMTEQEdSuXRs9evRAnz59ULZsWYvV79u3r8kvvrl+4WJiYhAQEKD+t8FggIjk+NzmDplPUzuz9PR0s3ySHDt2LD799FMEBgYiKCgIdnZ2uHfvHk6ePImEhAQEBASgc+fO6N+/P+rXr1/gevmtP2DAAJO5I82178+fP48qVaqo/20wGGAwGIrsU7ql68fFxWHSpEnYtm0bYmNj4ebmhkqVKiE4OBgNGzZEkyZNEBISoh5RN/fr/3H1GzVqhGbNmqFWrVqFEqqMvTxum2cN+cafMcd2yEv9wnbmzBlMmDABkZGRSEtLg4ODA0qXLo3AwEA0atQI7dq1Q7NmzeDm5gYg5yNrhVW/SZMm6NChA5o0aWKRb0yy9mrOfV/sFf43wmQuFy9eFGdnZ3nhhRfk33//FZFHV9kdPXpU1q5dK2+++aZUrVpVFEWR0NBQ9XYN5pov0xrqK4oi7du3l2XLlmWbPio9Pd3k3lAi5ptKx5K1RUQuXLggjo6O0rNnT/W2JYmJiXLlyhX5448/ZPbs2dKkSRN1Ci/jrArmOg/N0vXPnTsniqJI9erVZfbs2RIXF2fyeHp6unoxhLFmcnKyXL9+3SzTaVm6flxcnDRq1Eg9v6pnz57Sq1cvadSokXru0bPPPivTp083y73QClLfeHW3SN7OX8uLhIQEuXz5ssmyzNu8sFm6fmxsrNSqVUt0Op1ERETI2LFjZfz48dK5c2fx8PBQr14dMGCAHDx40KL1M99w/WnPYctJfHy87N6922Lzo1u6fkEx5BUj7777rnh6esr27dtFJPtckAkJCbJ//34ZNWqUKIoiZcuWzXbvvOJc33gTTOM/b29viYiIkN9++y3bWIwB68svv5TWrVsX+P5glqwtIvLBBx+Ip6en7NixQ0SyX92p1+vlwoULMm/ePPHx8RFFUR475VFxqz9r1iyT7Z/5atKsF5Rk3v4NGzY0y/2xLF1/ypQp4uHhIfPmzVOX3b17V2JiYiQqKkreeecdqVGjhuh0OmncuLE6P7C5Qral648ZM0YU5dGUiUuWLMl2AZler88WJuPi4uTGjRtmGYOl67/zzjtSunRpkxleUlNTJS0tTa5cuSKLFi2Spk2bik6nkxo1aqjT3Zlr+1uy/rhx49Srh997773H3uvPWO/s2bNy7Ngxs1xsZun6BcWQV4z07dtX/Pz85Pr16yKSfRLkzFatWiUeHh7SqFEjzdTv3LmzuLm5yeLFiyUiIkI9gqAoijzzzDMybty4bFcwvvTSS2aZSsqStUUeTSFXqlQpdRqjx/3x3Lp1q/j5+Um1atXM9unT0vVffvllcXJykh9++EGmTJkiNWrUMLma9JVXXlEDqJE5t7+l69eoUUM6d+6sHkXNuv0fPnwof//9txpGgoODH3tz6OJWv1atWtlCdvfu3bPdWD3zbZV69+4t7du3N8uRVEvXr127tnTo0EHdpjn9/t26dUvmz58vnp6e4ubmJv/880+B61pD/dDQUNHpdOLp6alu+7CwMFm0aFGOM34kJyfLq6++Ko0aNTJLyLJ0/YJiyCtGjBPNr127Vl2W9dNj5l++/v37i7e3t1mmc7F0/Zs3b0rDhg2lXLly6rIHDx7I999/n+3+eA0aNJDPPvtM1qxZI35+ftKlS5diW9vom2++EUVR5PPPPze5hUBuYWvChAni6upqlqNIlq5/69YtadKkicnNfFNTU2XTpk0ycOBA8fPzU7e/j4+PvP3227JixQqzbX9L179+/bpUr15d2rZt+8R19Xq9fPbZZ6IoiowfP77Ata2h/vnz58XHx0datGghUVFRMmTIEHW+UOPXhEOHDjV5rf31119SunRpadGiRbGvf/v2balfv36ePjDr9XpZtWqVWe9LaMn6Fy9eFH9/f2nUqJEcO3ZM3nvvPWnevLk4OjqKoiji5uYm4eHhsm7dOrlz546IPLrxvqenp4SFhRX7+ubAkFeMREVFiaurqwQHB2e7707mc1+M/ztjxgxxcXEx2/25LFn/ypUr8vzzz6tzn2Y93+3atWsyZ84ck0/cxl/Egk6jZsnaRidOnJBy5cqJp6dntulxMk9nZdz2H3/8sTg6OprMa1tc61+/fl06dOggbdu2Fb1en+3T8a1bt+Tbb7+Vrl27iouLi0noNsf2t2R94+9Vjx49xN3dXT3fKac5qjOrVauWtGrVSpKSkop1fZFHR4YVRZGxY8eqy+7duyerV6+Wnj17queEKYoiVapUkZkzZ8r48eNFURT1a8PiWt/4IWrQoEGiKI+mxjJ+uHrcEcKmTZtKgwYN1OBRXOvv3LlTdDqdjBgxQl2WlJQkW7ZskdGjR0tISIi67cuVKyejRo2SwYMHm23fW7q+OTDkFRPGX7avv/5abGxsRFEUeeONN2T79u3ZpjATeTSv7auvvmq26VwsXT8tLU127twp+/fvN7nAIfMFD0ZnzpyRYcOGiaIo4unpWaxrG2uJiGzatEmdB7F9+/ayZs0adVaDzJKTkyU8PNzs+95S9UVEoqOj5eTJk9m2f9YjiVeuXJF3331XnJ2dzTqVkKXrf/XVV+o5YVnPCcrIyDAZS0JCgrzwwgtSs2ZNTdTfv3+/BAQEyFdffSUi2c8Fvnz5ssyfP19atmxpErDNtf0tXV9EJDIyUhRFkapVq2abf9p4AYhx+9+7d09efPFFqVq1arGvf+zYMQkKCpLPPvtMrZVZXFycrFy5UiIiIqRSpUpm3/aWrm8ODHnFTHJysnzxxRfi6+sriqKIr6+vdOvWTWbMmCHbt2+X+Ph4+eOPP2Tw4MFib29v8ulTC/UfN9OGXq9XfwkPHTokzs7OZp1Kx5K1RR69ufz4448mnx5r164tw4YNk59++kn+/fdf+fnnn6VXr15iY2Mjb7/9tqbq58YYuIzb/8CBA4Wy/S1df+bMmaLT6URRFImIiJAtW7aYzNdpfJPdvn27lCtXzuxTKVmqflpampw6dUo9F9hYK6cjiWfPnlXndDXXNF6Wrm/0/fffq1P3hYWFyerVq03O9zRu/99++038/f3Nvv8tVT8xMTHbh8mc/hbHxsbK8OHDRVEUGTp0qFlqW0P9gmLIKyayHjFITk6WefPmSePGjcXW1lZ909XpdGJvby+Kokj//v1zPDG0ONbPfHuKvNy2wPjL9riJ24tD7dysW7dOOnXqlG3bK4oi9vb2Mnr0aJM3Ja3VfxzjkdTC3P5FWd/4u3f37l2ZO3eu+gHL1tZWnnvuORkzZoxs2LBBoqKiZO7cuVKpUiXx9vaW48ePa6J+XsaX+fdy+vTpRbr/i6r+w4cP5fvvv5d69eqpv3NlypSR8PBw+frrr+Xbb7+Vt956S7y8vMTf3/+xV4EWx/o5ybrtp0yZYtF9X9T184I3Qy7mbt++jbNnz+LgwYP4/fffkZGRgapVq6J69eoYOHCg5uvnJDExEYMHD8auXbtw/fp1zdSW/3+H+8w3Fr5+/Tp27dqFffv2wc7ODv7+/ggODkaXLl3MWtsa6udFSkoKhg0bhsjISNy8eVMT9SXLDV0fPnyI5cuX49tvv8WBAweyrV+jRg1MmDABvXv31kR9441uH3dTbeMYz549iy5duiA9PR3nz5/XRP2cam3YsAFfffUVtm7divT0dJPHGzdujHfeeQcdO3bUZP3cXLhwAS+++CKSkpJw8eLFIq1tDfVzw5BXDNy8eRMnTpzA2bNnkZycjIYNGyI4OBje3t7Z/uhkncYm6x9oLdX38vJS7zyf9Q9wamoqbt68aTJDRXGrDTzdXeuzjsMc27441c8sMTHRLNOrWbr+k1y5cgXbt2/HyZMnUbZsWfj6+qJZs2Z45plnCr22NdTP6syZM3jxxRfRpUsXfPTRR5qqLzlM4ZaQkIDdu3fjwoUL8Pf3h6urKxo0aABfX1+z1raG+k9y8eJFDB48GC1atMCkSZNKXP3cMORZuU2bNuH999/P9onZ09MTrVu3Rq9evdClSxfY2dmpj5lzOhtrrt+mTRu1fmFMM2TJ2jnJbbtmnkvXXFOoFaf6maWnp0NRlEKZs9IS9Tdv3oyTJ0/i2LFjKFOmDOrXr49nnnkGAQEB8PLyMvm9KwzWVN/X1xcNGjTAM888g8DAQHh5ecHGxibHDxPmeh1aun5uRw+LYo5uS9fP73SI5ppG0dL1zabovhmmp3XlyhWpXLmylClTRsaPHy+bN2+WhQsXyqBBg6Rhw4bqbTqeffZZ+f7779Vbe5jrLufFpX7NmjVN6ptjGiVL1hZ5dNuOMWPGyObNm+Xu3bsmj5ljqiDWt+76d+/elbfeeks99y3zVZteXl7StWtXWbp0abZbVJhrXMWlftZ9Y65pxixdP6f7j+b0tyXz8ifd1qS41M9r7azMNY2kpeubG0OeFZs0aZKULl1afvrpp2yPxcTEyOrVq6V3797qH59Zs2axvgZqi/zvBN5KlSpJp06dZPbs2XLo0KFsM0gYb18hIrJr1y7ZtGkT62ug/kcffSTOzs7SvXt32bVrl5w5c0ZWrVol06dPl86dO6tTx9WtW1fWrVtnlpqsbz31Fy5cKOHh4bJx48Zs9xrMyMgw24dJa6xfknsvDAx5Vuy5556Tli1byq1bt0RETG7TkdnOnTulTp064uDgIN988w3rF/PaIo+m0rG3t5dGjRqpVytXrFhRevfuLYsXL5Z///3XZP2UlBTp2rWr6HQ6k9tasH7xrB8YGCidOnWS27dvZ3ssNjZWNm7cKG+88YZ6lOnrr78ucE3Wt576FStWVG+q/txzz8nkyZPlwIED2Y6UGo+cpaSkyCeffCI7d+4s9vVLcu+FgSHPSiUlJUmbNm0kODhYnQw78yeIrIeQjx49KqVLl5auXbuqj7N+8ast8uir4ooVK0q9evUkLS1NDhw4IJMnT5batWuLoihiY2MjISEhMnz4cFmzZo0kJCTIoUOHpGzZsmaZRov1LVv/33//FVdXV5k4caK6LKcjCKmpqfLbb79J5cqVxdPT02yzm7C+ZeufPHlSFEWR+vXrS9u2bdVvC1xdXaV9+/by6aefZvuQ8fvvv4uiKNK0adNiXb8k915YGPKsmHFqnJyOEGUOEsY/Pt26dZOqVavKpUuXWL8Y1/7jjz/E09NTIiIiRETUmTVu3LghmzZtkv/7v/+TwMBAURRFnJ2dpXnz5uoculmnHGP94lf/n3/+kfLly0uvXr1E5NERg6wfMjK/BtevX2/WUwZY37L1V65cKYqiyMcffywij2bRmTVrloSGhqqhw8/PT1599VX59ttvJT4+XubOnSuKYp6ptCxZvyT3XlgY8qzY1atX1flQ33zzTTly5Ei2r4KMh4wTEhKkZ8+eUqFCBdYv5rWjo6PlpZdeku+//z7Hx9PS0uTSpUvy3XffSXh4uHh6eoqimG8qHda3bH2RR6cLuLm5SWRkZLbHjAHDGDzu3LkjlSpVkh49erC+BuovWrRIFEXJsfahQ4dk9OjREhAQoIaOqlWrStmyZcXDw6PY1y/JvRcWhjwrt27dOnVOvPr168t7770nu3btkkuXLpmEjhUrVoiPj48MHjyY9TVQ+969ezmeD5SZ8U3myy+/FEUx71Q6rG+Z+sYA8ccff0i5cuVEURQZNWqU/PHHH9k+ZBgvAtm/f7/4+/ubTKLO+sW3/oEDB2T06NFy7ty5bOMyevDggWzcuFEiIiLEw8NDFEWR4cOHF+v6Jbn3wsSQZ4Wyvqju3Lkj48aNkwoVKoiiPJovtlWrVvLaa6/JG2+8IX369BEHBwcJDg6W06dPs34xrZ1TfZH/fV2Ym//+97+iKIocOXKE9Yt5/cw1ly1bJn5+fqIoj25TNHr0aFm7dq2cOnVKHc/Vq1fl1VdfFVtbW9bXUP2kpKRcb8mR9TVqnEbvr7/+0kT9ktx7YWDIs1LGF1NMTIz6B+XEiRPy4YcfSvv27dXQoSiKeHp6SqtWrcw6V2BJrm8tvcfFxWULF+np6SZ/aGJiYiQkJES8vb1ZXyP1M7t586ZMmTJFgoODRafTiaurq1SrVk3q1asnbdu2lYCAAHF0dJQhQ4awvgbr58b4Gjx37pzUq1dPnnnmmRJTvyT3nh+c8cLKpKenY9++fViyZAnOnj0LRVHg7OyMBg0aIDw8HHXq1IGIICYmBg8ePMCFCxcQHByMgIAA2NraFngqqZJc39p61+l0cHJyQu3atfHyyy+jSZMm2X7m9u3b+O677+Dv749evXrluzbrW75+ZpJpnuAHDx4gOjoahw8fxr59+/DHH3/g9OnT8PHxQUBAAF5//XW89tprcHFxYX2N1M+rjRs3omvXrvjvf/+LWbNmlaj6Jbn3p2KJZEm5mz17tri7u4uiKBIUFCTBwcHqUSPj1waff/653Lhxg/U1VDsv9atXry4ff/yxxMXFmfxcamqqWW7QyfqWrf8kGRkZkpKSInq9Xm7fvm3Wo8esb13183obpuvXr8uyZcuyzTxSnOuX5N4LA0OeFblw4YK4uLjI888/LxcuXJCrV6+KXq+XmJgYWbhwoYSFhalvOK1atZLDhw+zvgZqP2391q1bm/X8H9a3fP379+/L6dOn5f79+9key8jIMHnjyfomZI6AyfrWW/9JzDGVmiXrl+TeiwJDnhWZPHmy+Pr6yvbt29VlWf+gHD9+XPr27SuOjo5SrVo1+fPPP1m/mNcuaH1zzBfK+pat/+GHH0r9+vVlxowZsnPnTomNjc32BpL1/mw3b94021ylrG/99bPSSv2S3HtRYMizIi+99JJUrlxZLl++LCL/uw+bwWDI9qKbN2+eKIoi/fr1Y/1iXpv1Wd94uw5bW1vx8vKSLl26yPz58+XQoUM53solOTlZxo0bJ/379zfLkSTWL771zXE0yZL1S3LvRYEhz4q89957oiiKnDp1Ktd1Mn+SfPnll6VChQpy/vx51i/GtVm/ZNc/c+aMuLq6SpMmTWTBggXSrVs38fX1FUVRJDAwUCIiIuS7776TkydPyt27d0VE5ODBg+Lh4SHdunVjfdYvtvVLcu9FhSHPiuzdu1cURZHQ0FDZsWNHjvfqyXxkYeLEieLs7Cx///036xfj2qxfsutv2LBBbG1tZdq0aSIicunSJdmyZYtMmzZNmjdvLq6urmJrayshISEyatQo2bx5s3pvPnNMpcT6rG+p+iW596LCkGdF0tPTZezYseqVfAsWLJDr16/nuG58fLz07dtXfHx8WL+Y12b9kl1/7dq1oiiKrF692mR5WlqaREdHy48//igjR46U2rVri729vbi4uIizs7PZplFjfda3VP2S3HtRYcizQl9++aVUqVJFFEWRcuXKyfDhw+W3336T48ePy6lTpyQ2NlbefvttcXR0lDFjxrC+RmqzfsmsbzAY5J9//pELFy6o/51VcnKyHD16VFauXCnt2rUTRXk0pzLrs35xrl+Sey8qDHlWyGAwyNmzZ+W///2vyWTIZcqUkfLly4uNjY0oiiL/+c9/JCYmhvU1Upv1WT+n8WT15ptviqIocvToUdZnfc3WL8m9mxNnvLByKSkpOHToEH799Vdcu3YNN2/ehLu7O8LDw/Hyyy/D0dGR9TVYm/VZPzODwQCdTodLly6hW7duuHv3Lq5cucL6rK/5+iW5d3OwtfQA6PFcXFwQFhaGsLAw6PV62NnZsX4JqM36rJ+ZTqcDAMTGxkKv12Po0KGsz/olon5J7t0ceCSPiKiYEBFcvXoVnp6eFpkrlfVZ31L1S3LvBcGQR0RERKRBOksPgIiIiIjMjyGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg0iCGPiIiISIMY8oiIiIg06P8BLhuJeacpNzgAAAAASUVORK5CYII=\n"
          },
          "metadata": {},
          "execution_count": 90
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Configurazioni valide\n",
        "\n",
        "colonna 0  | colonna 1\n",
        "---|---\n",
        "0       | 1\n",
        "1       | 0\n",
        "\n",
        "e\n",
        "\n",
        "colonna 0  | colonna 1\n",
        "---|---\n",
        "1       | 0\n",
        "0       | 1"
      ],
      "metadata": {
        "id": "lwrnEIi77zhc"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "wDvDp2En77k8"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}