Single_Systems_Qiskit_Programming_210324.ipynb

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      "name": "python3",
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    "language_info": {
      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/peepeepoopooooo/2022-update-shecodes/blob/main/Single_Systems_Qiskit_Programming_210324.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "91xyTvAurfBY",
        "outputId": "a0e8d654-803f-4a3e-acf0-b2637a4db31f"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.5, 0.5])"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "#Matrix and vector are computed with array\n",
        "from numpy import array\n",
        "\n",
        "\n",
        "ket0 = array([1, 0])\n",
        "ket1 = array([0, 1])\n",
        "\n",
        "ket0 / 2 + ket1 / 2"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "pip install -U qiskit"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GVcGJnWvtJJl",
        "outputId": "809c0ebc-5335-4760-c98a-3287d7012d11"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting qiskit\n",
            "  Downloading qiskit-1.0.2-cp38-abi3-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (5.6 MB)\n",
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            "\u001b[?25hCollecting rustworkx>=0.14.0 (from qiskit)\n",
            "  Downloading rustworkx-0.14.2-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (2.1 MB)\n",
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            "\u001b[?25hRequirement already satisfied: numpy<2,>=1.17 in /usr/local/lib/python3.10/dist-packages (from qiskit) (1.25.2)\n",
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            "Collecting dill>=0.3 (from qiskit)\n",
            "  Downloading dill-0.3.8-py3-none-any.whl (116 kB)\n",
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            "\u001b[?25hRequirement already satisfied: python-dateutil>=2.8.0 in /usr/local/lib/python3.10/dist-packages (from qiskit) (2.8.2)\n",
            "Collecting stevedore>=3.0.0 (from qiskit)\n",
            "  Downloading stevedore-5.2.0-py3-none-any.whl (49 kB)\n",
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            "\u001b[?25hRequirement already satisfied: typing-extensions in /usr/local/lib/python3.10/dist-packages (from qiskit) (4.10.0)\n",
            "Collecting symengine>=0.11 (from qiskit)\n",
            "  Downloading symengine-0.11.0-cp310-cp310-manylinux_2_12_x86_64.manylinux2010_x86_64.whl (39.4 MB)\n",
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            "\u001b[?25hRequirement already satisfied: six>=1.5 in /usr/local/lib/python3.10/dist-packages (from python-dateutil>=2.8.0->qiskit) (1.16.0)\n",
            "Collecting pbr!=2.1.0,>=2.0.0 (from stevedore>=3.0.0->qiskit)\n",
            "  Downloading pbr-6.0.0-py2.py3-none-any.whl (107 kB)\n",
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            "\u001b[?25hRequirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.10/dist-packages (from sympy>=1.3->qiskit) (1.3.0)\n",
            "Installing collected packages: symengine, rustworkx, pbr, dill, stevedore, qiskit\n",
            "Successfully installed dill-0.3.8 pbr-6.0.0 qiskit-1.0.2 rustworkx-0.14.2 stevedore-5.2.0 symengine-0.11.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit.visualization import array_to_latex"
      ],
      "metadata": {
        "id": "-VbudJNCtLGr"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "M1 = array([[1, 1], [0, 0]])\n",
        "M2 = array([[1, 1], [1, 0]])\n",
        "\n",
        "M1 / 2 + M2 / 2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "T-9YrcO2rx0U",
        "outputId": "a61341ef-bead-46a2-e96d-9adcfc115f24"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1. , 1. ],\n",
              "       [0.5, 0. ]])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "array_to_latex(M1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 58
        },
        "id": "IzFojPLmsWHd",
        "outputId": "7301b17e-7e89-4e27-f2dc-caffa363e0a0"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.core.display.Latex object>"
            ],
            "text/latex": "$$\n\n\\begin{bmatrix}\n1 & 1  \\\\\n 0 & 0  \\\\\n \\end{bmatrix}\n$$"
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "array_to_latex(M2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 58
        },
        "id": "yFtGkIGOtSsV",
        "outputId": "e6e79ca8-3feb-4ab4-d275-c7d8b32ef07e"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.core.display.Latex object>"
            ],
            "text/latex": "$$\n\n\\begin{bmatrix}\n1 & 1  \\\\\n 1 & 0  \\\\\n \\end{bmatrix}\n$$"
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from numpy import matmul"
      ],
      "metadata": {
        "id": "BDq9lKSHtUBZ"
      },
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "matmul(M1, ket1)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2CmJ0Z73ts2G",
        "outputId": "42508492-35fe-4382-c1fb-a34eafb79b8f"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 0])"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "matmul(M1, M2)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6NaEG_Bct8xC",
        "outputId": "bf359954-432c-4d63-8dab-21bd8160475b"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[2, 1],\n",
              "       [0, 0]])"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "matmul(M2, M1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "z9_KD-aft_rJ",
        "outputId": "8355f3ed-fc7d-4f33-83c8-e547cc5489e6"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 1],\n",
              "       [1, 1]])"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Aim of Statevector function: #1 define vectors and let us use function like `draw()` on them\n",
        "\n",
        "from qiskit.quantum_info import Statevector\n",
        "from numpy import sqrt\n",
        "\n",
        "u = Statevector([1 / sqrt(2), 1 / sqrt(2)])\n",
        "v = Statevector([(1 + 2.0j) / 3, -2 / 3])\n",
        "w = Statevector([1 / 3, 2 / 3])\n",
        "\n",
        "print(\"State vectors u, v, and w have been defined.\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "M9fC2LxQt_32",
        "outputId": "bd5c21d6-7ca9-4656-8500-16ba6d58f72c"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "State vectors u, v, and w have been defined.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "u.draw('latex')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 40
        },
        "id": "jah9RnA2uVV9",
        "outputId": "bde033ae-26af-4698-fa78-0248b5fb1d40"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.core.display.Latex object>"
            ],
            "text/latex": "$$\\frac{\\sqrt{2}}{2} |0\\rangle+\\frac{\\sqrt{2}}{2} |1\\rangle$$"
          },
          "metadata": {},
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "v.draw('text')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7KczvI-purYq",
        "outputId": "c03e436f-de22-4663-9aa5-756996483bab"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[ 0.33333333+0.66666667j,-0.66666667+0.j        ]"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Aim of <Statevector function>: #1 define vectors and let us use function .is_valid()\n",
        "#<is_valid()> check if the Euclidean norm = 1"
      ],
      "metadata": {
        "id": "6TijL1R_usTq"
      },
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "w.is_valid()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "o7DAdg8Xu5_T",
        "outputId": "ed429410-3c8a-4fb4-a4e8-f811564ad895"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "v.is_valid()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1kc_0Bzpu_ay",
        "outputId": "d474812b-da31-41f0-b8cc-8107d7f5b2a8"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "u.is_valid()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KwjAm9QevBlD",
        "outputId": "9c5fd7f6-b43a-40b9-d690-9cccc7357127"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#<function .measure() aim> simulates a standard basis measurement.\n",
        "#It returns the result of that measurement + plus the new quantum state after that measurement.\n",
        "#the measure changes everytime because of the probability\n",
        "v.measure()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AnRFBRRsvDD5",
        "outputId": "c36bb266-2fe0-4ae1-94d0-763b5410a9bb"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "('0',\n",
              " Statevector([0.4472136+0.89442719j, 0.       +0.j        ],\n",
              "             dims=(2,)))"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#they are said to differ by a global phase because one is equal to the other multiplied by a complex number on the unit circle.\n",
        "\n",
        "#<function .sample_counts(n number of count)> results AFTER n number of measurement\n",
        "\n",
        "v.sample_counts(1000)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RIbBe9Omvgse",
        "outputId": "fb2234f3-28f7-40d0-ca72-14f7392b5381"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'0': 592, '1': 408}"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#visualize the <function .sample_counts(n number of count)>\n",
        "from qiskit.visualization import plot_histogram\n",
        "\n",
        "statistics = v.sample_counts(1000)\n",
        "statistics\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CqkUaR8ZxAHF",
        "outputId": "3f357c1e-7bb1-4efc-b0dd-f2212dc6a296"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'0': 534, '1': 466}"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plot_histogram(statistics)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "areeNr4lx8Vj",
        "outputId": "4106fbc5-c1cd-4d28-ca7a-afcdf7eef958"
      },
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 700x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit.quantum_info import Operator"
      ],
      "metadata": {
        "id": "av6Pg91sx-3y"
      },
      "execution_count": 34,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "X = Operator([[0, 1], [1, 0]])\n",
        "Y = Operator([[0, -1.0j], [1.0j, 0]])\n",
        "Z = Operator([[1, 0], [0, -1]])\n",
        "H = Operator([[1 / sqrt(2), 1 / sqrt(2)], [1 / sqrt(2), -1 / sqrt(2)]])\n",
        "S = Operator([[1, 0], [0, 1.0j]])\n",
        "T = Operator([[1, 0], [0, (1 + 1.0j) / sqrt(2)]])\n",
        "\n",
        "v = Statevector([1, 0])"
      ],
      "metadata": {
        "id": "GlnpNdsiy24s"
      },
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# <.evolve(other, qargs=None)>: Evolve a quantum state by the Operator\n",
        "\n",
        "v = v.evolve(H)\n",
        "v = v.evolve(T)\n",
        "v = v.evolve(H)\n",
        "v = v.evolve(T)\n",
        "v = v.evolve(Z)\n",
        "\n",
        "v.draw('latex')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "3hLIMIOdy07d",
        "outputId": "df8f3dd4-ab71-4ce5-82a2-6bd1e004b18a"
      },
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.core.display.Latex object>"
            ],
            "text/latex": "$$(0.3232233047 + 0.9267766953 i) |0\\rangle+(-0.0732233047 - 0.1767766953 i) |1\\rangle$$"
          },
          "metadata": {},
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#QuantumCircuit(number of bits: in both qubit and classical)\n",
        "\n",
        "from qiskit import QuantumCircuit\n",
        "\n",
        "circuit = QuantumCircuit(1)\n",
        "circuit.h(0)\n",
        "circuit.t(0)\n",
        "circuit.h(0)\n",
        "circuit.t(0)\n",
        "circuit.z(0)\n",
        "\n",
        "#the evolution is applied sequentially, from left to right\n",
        "circuit.draw()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 63
        },
        "id": "POg5N9IWzJn9",
        "outputId": "3e148737-32da-4054-f414-419a78592c9e"
      },
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   ┌───┐┌───┐┌───┐┌───┐┌───┐\n",
              "q: ┤ H ├┤ T ├┤ H ├┤ T ├┤ Z ├\n",
              "   └───┘└───┘└───┘└───┘└───┘"
            ],
            "text/html": [
              "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">   ┌───┐┌───┐┌───┐┌───┐┌───┐\n",
              "q: ┤ H ├┤ T ├┤ H ├┤ T ├┤ Z ├\n",
              "   └───┘└───┘└───┘└───┘└───┘</pre>"
            ]
          },
          "metadata": {},
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "ket0 = Statevector([1, 0])\n",
        "v = ket0.evolve(circuit)\n",
        "#== elongated\n",
        "#v = ket0.evolve(QuantumCircuit(1))\n",
        "v.draw(\"latex\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "5AY5HhWvzxQc",
        "outputId": "7743266d-60e5-463d-c569-ca94057e1ac4"
      },
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.core.display.Latex object>"
            ],
            "text/latex": "$$(0.8535533906 + 0.3535533906 i) |0\\rangle+(-0.3535533906 + 0.1464466094 i) |1\\rangle$$"
          },
          "metadata": {},
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# simulate the result of running this experiment (i.e., preparing the state ∣0⟩,\n",
        "#applying the sequence of operations represented by the circuit, and measuring) 4000 times.\n",
        "\n",
        "statistics = v.sample_counts(4000)\n",
        "plot_histogram(statistics)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "PPlVhsoQ0LzS",
        "outputId": "8e2b99d1-61e8-4fdf-8832-cc97ca7f1c67"
      },
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 700x500 with 1 Axes>"
            ],
            "image/png": 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JBEMAAADYEAwBAAAgiWAIAAAAG4IhAAAAJBEMAQAAYEMwBAAAgCQPDIYnTpzQokWLlJCQoIiICPn4+Khly5YaNmyYvv7668u+/+DBgwoICJDBYNBjjz1W6bwVK1aoa9eu8vf3V2hoqAYPHqxdu3ZVOn/nzp0aOHCgQkJC5O/vr27dumn16tU16hEAAMATeVwwfPPNNzVp0iQdPHhQCQkJmjx5snr27KlPP/1UPXr00EcffVTpey0Wix566KHLfsacOXP0wAMP6Oeff9Zjjz2mESNGaMuWLerRo4e2bdvmND89PV1xcXHaunWr7rvvPj322GPKy8vTyJEjtXDhwitpFwAAwGMYrFar1d1FXOyTTz5R06ZN1bt3b4fxr776Sv369VNAQIBOnjwpX19fp/cuXLhQL7zwgl577TVNmjRJEydO1DvvvOMwJycnR9dff72ioqKUlZWl4OBgSVJ2dra6deumqKgo7d27V0bjhcxcWlqqmJgYHT9+XDt27FBsbKwkyWw2q2vXrjp8+LAOHDigyMjIaveYn5+v4OBgmc1mBQUFufLXU20TFtXJboEaW/KMuysAgKuTK7nD444Y3nvvvU6hUJLuuOMOxcfH68yZM/ruu++ctu/bt0/Tp0/XlClT7OGtIikpKSotLdW0adPsoVCSYmNjNXr0aP3www/aunWrfTwtLU0//fSTxowZ47Df4OBgTZ06VcXFxVq2bFnNmgUAAPAgXu4uwBXe3t6SJC8vx7LLyso0btw4RUdHa/r06dq+fXul+8jIyJAkJSQkOG1LTEzU0qVLtXnzZvXq1ata8yVp8+bNVdZdVFSkoqIi++v8/HxJUklJiUpKSiRJRqNRJpNJZWVlslgs9rnl46Wlpbr44K7JZJLRaKx0HPA05f/Wy5V/j0tLSx3Gvb29ZbFYVFZWZh8zGAzy8vKqdLyy701tfZ+qWzs90RM90ZMn9uSKBhMMjx49qi+//FKtWrVSp06dHLbNmzdPu3bt0o4dO+Tj41PlfnJychQQEKCWLVs6bYuOjrbPuXj+xdsu1rJlSwUEBDjMr8i8efM0a9Ysp/HU1FQ1btxYkhQREaHOnTtrz549Onr0qH1Ox44dFRMTo6ysLJ06dco+Hhsbq8jISG3ZskVnz561j3fv3l3Nmzevsh7AHdatW+fweuDAgTp37pzS09PtY15eXho0aJBOnz6tzMxM+3hgYKD69u2rY8eOKTs72z7erFkz9ejRQzk5Odq/f799vLa/T6mpqQ4/yOPj4+Xn50dP9ERP9NQgegoLC1N1edwaw4qUlJSof//+2rJli5YvX64HH3zQvm337t267bbb9Oyzz2ru3LmSLhzli4+Pr3CNoY+Pj5o3b67jx487fU5OTo46dOigIUOG6NNPP5V04Ujhxo0blZOTo2uvvdbpPa1bt1ZBQYHMZnOl9Vd0xDA8PFynT5+2n+uv7d9eWGMIT/PXJzhiSE/0RE/05I6eCgsLq73G0OOPGJZfabxlyxZNmDDBIRQWFxdr3LhxuvbaazVjxgw3Vlk1X1/fCi+W8fb2tp8eL2cymWQymZzmXnr6/HLjgKe59N96VeNGo7HC0x+VjVf2vamt75MrtVc2Tk/0JNFTZTW6Ok5PrvdUXR6dKiwWix5++GGtXLlSDzzwgNPRv3nz5um7777T9u3bKwxeFSlPzBUpX/t38UUp5X+u6j2hoaHV+mwAAABP5rFXKVgsFo0fP17Lli3T6NGjtXTpUqfE/O2338pisahbt24yGAz2/+Lj4yVJ7777rgwGg+6++277e6Kjo1VQUKC8vDynz6xoPWFF6w7L5eXlqaCgoML1hwAAAA2NRx4xLA+Fy5cv18iRI/W3v/2twsOid955p6655hqn8ZMnT2rdunWKiYlRXFycOnfubN/Wu3dvZWZmKjU1VWPHjnV434YNG+xzLp4/b948paamatSoUZedDwAA0FB53MUn5aePly1bphEjRmjlypUur6Or6uKTAwcO6IYbbnDpBtcdO3bUiRMnKr3B9f79+9W2bdtq18cNrnE14gbXAOAeruQOjzti+NJLL2nZsmUKCAhQhw4d9PLLLzvNufvuu6u8iXVVOnTooJkzZ2r69Om6+eabNWzYMJ09e1arVq2SJC1ZssThlLWXl5eSk5OVmJioXr16adSoUQoMDNSaNWt05MgRLViwwKVQCAAA4Kk8LhgePnxYklRQUKA5c+ZUOKdt27Y1DoaSNG3aNLVt21aLFi3S22+/LR8fH91xxx2aPXu2unTp4jQ/Pj5eW7du1YwZM/TRRx+ppKREnTp10iuvvKKRI0fWuA4AAABP4nGnkq8GnErG1YhTyQDgHg36WckAAABwD4IhAAAAJBEMAQAAYEMwBAAAgCSCIQAAAGwIhgAAAJBEMAQAAIANwRAAAACSCIYAAACwIRgCAABAEsEQAAAANgRDAAAASCIYAgAAwIZgCAAAAEkEQwAAANgQDAEAACCJYAgAAAAbgiEAAAAkEQwBAABgQzAEAACAJIIhAAAAbGocDLds2aKjR49WOefYsWPasmVLTT8CAAAA9ajGwTA+Pl5Lly6tcs7y5csVHx9f048AAABAPapxMLRarZedY7FYZDAYavoRAAAAqEd1usYwJydHwcHBdfkRAAAAqCVerkx++OGHHV7/93//tw4fPuw0r6yszL6+8K677rqiAgEAAFA/XAqGF68pNBgMys7OVnZ2doVzDQaDbrvtNr3xxhtXUh8AAADqiUvB8NChQ5IurC+MiorSM888o6efftppnslkUmhoqPz9/WunSgAAANQ5l4JhZGSk/c8pKSnq3LmzwxgAAAAaLpeC4cXGjRtXm3UAAADAzWocDMtlZWVp586d+t///V+VlZU5bTcYDHrxxRev9GMAAABQx2ocDH/99Vfdfffd2rZtW5X3NCQYAgAANAw1DoZJSUnaunWr+vTpo3HjxqlNmzby8rriA5AAAABwkxonubVr16pr167atGkTTzcBAAD4Hajxk0/OnTunXr16EQoBAAB+J2ocDGNjYyt86gkAAAAaphoHwxkzZuizzz7Tjh07arMeAAAAuEmN1xjm5eVp0KBB6t27t+6//3516dJFQUFBFc4dO3ZsjQsEAABA/TBYq7rXTBWMRqMMBoPDrWouXW9otVplMBgqvL/h1Sw/P1/BwcEym82VhukrNWFRnewWqLElz7i7AgC4OrmSO2p8xDAlJaWmbwUAAIAH4pF4AAAAkHQFF58AAADg96XGRwyPHj1a7bkRERE1/RgAAADUkxoHw7Zt21br5tYGg0GlpaU1/RgAAADUkxoHw7Fjx1YYDM1ms3bv3q1Dhw6pd+/eatu27ZXUBwAAgHpS42C4dOnSSrdZrVYtXLhQr776qt57772afgQAAADqUZ1cfGIwGPTss8/qhhtu0HPPPVcXHwEAAIBaVqdXJd96661KS0ury48AAABALanTYPjTTz9x4QkAAEADUeM1hpWxWCw6ceKEli5dqk8//VT9+vWr7Y8AAABAHahxMCx/VnJlrFarQkNDtXDhwpp+BAAAAOpRjYNhr169KgyGRqNRoaGhuu222zR+/Hg1b978igoEAABA/ahxMMzIyKjFMgAAAOBuPCsZAAAAkmrp4pNt27YpOztb+fn5CgoKUmxsrOLi4mpj1wAAAKgnVxQMt2/frvHjx+vHH3+UdOGCk/J1h9HR0UpJSVH37t2vvEoAAADUuRoHw++//14JCQn67bffdOeddyo+Pl6tWrVSXl6e0tPTlZqaqsTERO3YsUPXX399bdYMAACAOlDjYPjSSy+puLhY69at04ABAxy2Pf/88/riiy80ZMgQvfTSS1q1atUVFwoAAIC6VeOLTzIyMjR8+HCnUFhuwIABGj58uNLT02tcHAAAAOpPjYOh2WxWu3btqpzTrl07mc3mmn4EAAAA6lGNg2FYWJh27NhR5Zyvv/5aYWFhNf0IAAAA1KMaB8MhQ4YoIyNDL774os6fP++w7fz585oxY4bS09M1dOjQKy4SAAAAdc9gtVqtNXnjL7/8ottvv12HDh1S06ZN1bVrV7Vo0UL/8z//o507d+rUqVOKiopSVlaWmjRpUtt1N2j5+fkKDg6W2WxWUFBQnXzGhEV1slugxpY84+4KAODq5EruqPFVyU2bNtWOHTv0n//5n1q1apXWrVtn39aoUSONHz9er7zyCqEQAACggbiiG1xfc801ev/99/Xuu+9q37599iefxMTEyNvbu7ZqBAAAQD1wORjOmTNHhYWFmjVrlj38eXt7q1OnTvY5xcXFmjZtmgIDA/XCCy/UXrUAAACoMy5dfPLll1/qz3/+s5o2bVrlEUEfHx81bdpU06ZN4z6GAAAADYRLwXD58uUKDQ3Vk08+edm5TzzxhJo0aaKUlJQaFwcAAID641Iw3L59u/r37y9fX9/LzvX19VX//v21bds2l4v64IMPNHHiRN16663y9fWVwWDQ0qVLq3zPoUOHNGHCBEVGRsrX11ctWrRQfHy8/v73v1c4f8WKFeratav8/f0VGhqqwYMHa9euXZXuf+fOnRo4cKBCQkLk7++vbt26afXq1S73BgAA4KlcWmOYm5urqKioas9v166dPv30U5eLmj59uo4cOaJrrrlGrVq10pEjR6qcv3HjRt19992SpD/84Q+KiorSmTNntGfPHn355ZcaMWKEw/w5c+Zo+vTpioyM1GOPPaazZ89q1apV6tGjhzZt2qS4uDiH+enp6UpMTFSjRo00atQoBQYGas2aNRo5cqSOHTumyZMnu9wjAACAp3EpGBqNRpWUlFR7fklJiYxG1++hnZycrOjoaEVGRmr+/PmaMmVKpXOPHj2q4cOHq3Xr1vryyy8VERHhsL20tNThdU5OjmbOnKkOHTooKytLwcHBkqTHH39c3bp104QJE7R371573aWlpZowYYKMRqO2bNmi2NhYSdKf//xnde3aVVOnTtXw4cMVGRnpcp8AAACexKXUFhYWpr1791Z7/t69e9W6dWuXi+rfv3+1g9bcuXOVn5+vd955xykUSpKXl2P2TUlJUWlpqaZNm2YPhZIUGxur0aNH64cfftDWrVvt42lpafrpp580ZswYeyiUpODgYE2dOlXFxcVatmyZix0CAAB4HpeOGN5xxx364IMPdPjwYbVt27bKuYcPH1ZaWprGjh17JfVVyWq16u9//7uaNm2qvn376l//+pc2b94si8Wi2NhY9e3b1+mIZUZGhiQpISHBaX+JiYlaunSpNm/erF69elVrviRt3ry5yjqLiopUVFRkf52fny/pwhHV8iOwRqNRJpNJZWVlslgs9rnl46Wlpbr4ITUmk0lGo7HSccDTXHq2ofyXtkuP6nt7e8tisaisrMw+ZjAY5OXlVel4Zd+b2vo+Vbd2eqIneqInT+zJFS4FwyeeeEIpKSkaPny4vvjiC11zzTUVzvvll180YsQIlZaW6k9/+pNLBbni0KFD+vXXX3Xrrbdq4sSJWrx4scP2zp0767PPPlObNm3sYzk5OQoICFDLli2d9hcdHW2fc/H8i7ddrGXLlgoICHCYX5F58+Zp1qxZTuOpqalq3LixJCkiIkKdO3fWnj17dPToUfucjh07KiYmRllZWTp16pR9PDY2VpGRkdqyZYvOnj1rH+/evbuaN29eZT2AO1z8dCRJGjhwoM6dO+dwSysvLy8NGjRIp0+fVmZmpn08MDBQffv21bFjx5SdnW0fb9asmXr06KGcnBzt37/fPl7b36fU1FSHH+Tx8fHy8/OjJ3qiJ3pqED2FhYWpulx+VnJSUpIWLVqka665Ro899pji4+PtwevEiRPatGmTFi9erFOnTikpKUkLFixwZfdOytcYpqSk6KGHHnLYtmPHDnXv3l0mk0l+fn568803NXToUJnNZs2dO1dLlizR7bffrh07dtjf4+Pjo+bNm+v48eNOn5WTk6MOHTpoyJAh9otmEhIStHHjRuXk5Ojaa691ek/r1q1VUFAgs9lcaQ8VHTEMDw/X6dOn7c8srO3fXnhWMjzNX5/giCE90RM90ZM7eiosLKy7ZyUvXLhQjRo10muvvaY5c+Zozpw5DtutVqtMJpOmTJmil19+2dXdu6S88bKyMs2ePdseHENDQ7V48WLt2bNHX3/9tbZu3aqePXvWaS1V8fX1rfAWP97e3k43CjeZTDKZTE5zL10reblxwNNUdlP8isaNRmOFpz8qG6/se1Nb3ydXaq9snJ7oSaKnymp0dZyeXO+pulxOFQaDQXPnztUjjzyilJQUbd++XXl5eZIunFqNi4vTQw89pPbt29e4qOq6+OKRIUOGOG3/wx/+oK+//lrffPONPRiWJ+aKlK/9u3i/5X+u6j2hoaE1awAAAMCD1PhwU/v27ev8iGB1aig/bBoSEuK0vXzs3Llz9rHo6GhlZmYqLy/PaZ1hResJL153eMsttzjMz8vLU0FBgbp27Vob7QAAALhVg758tVGjRurRo4ck6d///rfT9vKxi6+g7t27t6QLF35casOGDQ5zajIfAACgoWrQwVCS/arnmTNnOlzgsW/fPi1dulSBgYEaMGCAfXz8+PHy8vLSnDlzHE4PZ2dn68MPP9R1113nsB6xX79+ioqK0sqVKx2uCiq/wMXHx6dOb8kDAABQXzzyyoXk5GT7Taa/++47+1j5PQV79uypRx99VJI0atQoffLJJ/r444918803KzExUWazWWvWrNH58+e1fPlyhzWAHTp00MyZMzV9+nTdfPPNGjZsmP2ReJK0ZMkSh0WeXl5eSk5OVmJionr16uXwSLwjR45owYIFl72nIwAAQEPg8u1q6sNDDz1U5dNExo0bp6VLl9pfl5aW6s0339R7772nH3/8Ub6+vurWrZumTp1a6WneFStWaNGiRfr+++/l4+OjuLg4zZ49W126dKlwflZWlmbMmKHt27erpKREnTp1UlJSkkaOHOlyf/n5+dW+bLymuF0NPM2SZ9xdAQBcnVzJHR4ZDH/vCIa4GhEMAcA9XMkdDX6NIQAAAGoHwRAAAACSCIYAAACwIRgCAABAEsEQAAAANgRDAAAASCIYAgAAwIZgCAAAAEkEQwAAANgQDAEAACCJYAgAAAAbgiEAAAAkEQwBAABgQzAEAACAJIIhAAAAbAiGAAAAkEQwBAAAgA3BEAAAAJIIhgAAALAhGAIAAEASwRAAAAA2BEMAAABIIhgCAADAhmAIAAAASQRDAAAA2BAMAQAAIIlgCAAAABuCIQAAACQRDAEAAGBDMAQAAIAkgiEAAABsCIYAAACQRDAEAACADcEQAAAAkgiGAAAAsCEYAgAAQBLBEAAAADYEQwAAAEgiGAIAAMCGYAgAAABJBEMAAADYEAwBAAAgiWAIAAAAG4IhAAAAJBEMAQAAYEMwBAAAgCSCIQAAAGwIhgAAAJBEMAQAAIANwRAAAACSCIYAAACwIRgCAABAEsEQAAAANgRDAAAASCIYAgAAwIZgCAAAAEkEQwAAANgQDAEAACCJYAgAAAAbgiEAAAAkEQwBAABgQzAEAACAJIIhAAAAbAiGAAAAkEQwBAAAgA3BEAAAAJIIhgAAALAhGAIAAEDS7yQYWq1WffLJJ4qPj1erVq3UuHFjdezYURMnTtTBgwed5ufn5yspKUmRkZHy9fVV27Zt9dxzz6mgoKDC/VssFr355pvq1KmT/Pz81KxZM40ePbrCfQMAADRUv4tg+Oyzz2rYsGHav3+/7r77bv3Hf/yH2rVrpyVLlig2NlZ79+61zy0sLFTv3r31xhtvKCYmRpMmTVLHjh21YMEC9e3bV+fPn3fa/8SJE/XUU0/JarXqqaee0oABA/TJJ5/otttuU05OTn22CgAAUGe83F3AlcrLy9OiRYsUGRmp3bt3Kzg42L7tjTfeUFJSkl5//XW9//77kqRXX31V2dnZev755zV//nz73BdeeEGvvPKK3njjDU2ZMsU+np6eruTkZPXq1UsbN26Uj4+PJGnMmDEaOHCgnnzySW3YsKGeugUAAKg7Df6I4eHDh2WxWBQXF+cQCiVp8ODBkqRTp05JunDKOTk5WQEBAXrxxRcd5r744osKCAhQcnKyw/iSJUskSbNnz7aHQkm666671KdPH6Wmpuro0aO13hcAAEB9a/BHDKOjo+Xj46Nt27YpPz9fQUFB9m1r166VJPXr10+SlJOTo9zcXCUmJsrf399hP/7+/oqLi9OGDRt07NgxhYeHS5IyMjLs2y6VmJiojIwMbd68WQ8++GClNRYVFamoqMj+Oj8/X5JUUlKikpISSZLRaJTJZFJZWZksFot9bvl4aWmprFarfdxkMsloNFY6Dnia8n/r5by8Lvz4KS0tdRj39vaWxWJRWVmZfcxgMMjLy6vS8cq+N7X1fapu7fRET/RET57YkysafDBs2rSp5s+fr8mTJysmJkZDhw5VUFCQdu/erbS0ND3++ON68sknJcm+HjA6OrrCfUVHR2vDhg3KyclReHi4CgsLdfLkSd14440ymUwVzr94v5WZN2+eZs2a5TSempqqxo0bS5IiIiLUuXNn7dmzx+EIZMeOHRUTE6OsrCz7kU9Jio2NVWRkpLZs2aKzZ8/ax7t3767mzZtXWQ/gDuvWrXN4PXDgQJ07d07p6en2MS8vLw0aNEinT59WZmamfTwwMFB9+/bVsWPHlJ2dbR9v1qyZevTooZycHO3fv98+Xtvfp9TUVIcf5PHx8fLz86MneqInemoQPYWFham6DNaLo28Dtnr1aj366KMO/4P17NlT8+fPtx/tW7lype6//35NmzZNL7/8stM+pk2bprlz5+qTTz7RPffco9zcXLVu3VpxcXHaunWr0/yNGzcqISFBTz31lP7yl79UWltFRwzDw8N1+vRp+xHO2v7tZcKiavylAfXor09wxJCe6Ime6MkdPRUWFio4OFhms9nhzGpFGvwRQ0l66aWX9PLLL+ull17SAw88oJCQEGVnZ2vSpEnq06eP1qxZoyFDhritPl9fX/n6+jqNe3t7y9vb22HMZDJVeHSy/B9TdccBT3Ppv/Wqxo1GY4WnPyobr+x7U1vfJ1dqr2ycnuhJoqfKanR1nJ5c76m6GvxitC+//FIzZszQk08+qRdeeEFt2rRRQECAevbsqc8//1ze3t6aPHmyJNkvTjGbzRXuq3ztX/k8V+cDANDQnThxQg888ICaNm0qPz8/derUSd98842kC2uFn3/+eXXq1En+/v4KCwvT2LFjlZub67CPtm3bymAwOPx38Z1A4Lka/OGm9evXS7pwPv9SLVu2VExMjL799lsVFBRcdk3gpWsQ/f391apVKx06dEhlZWVOCfxyaxYBAGhIzpw5o7i4OMXHx2v9+vVq1qyZcnJyFBoaKkn67bfftGvXLr344ou6+eabdebMGT399NMaMmSIPTyWe+mllzRhwgT768DAwHrtBTXT4INhcXGxJDksEr3YqVOnZDQa5e3trejoaIWFhWnbtm0qLCx0uDK5sLBQ27ZtU7t27exXJEtS7969tWrVKm3btk29evVy2Hf5/QsvHQcAoCF65ZVXFB4erpSUFPtYu3bt7H8ODg7Wxo0bHd7z1ltvqWvXrjp69KgiIiLs44GBgWrZsmXdF41a1eBPJZdfWPL66687nfJ95513dPz4cXXv3l2+vr4yGAx69NFHVVBQoNmzZzvMnT17tgoKChx+u5GkP/7xj5Iu3OewPIRKF45UZmRkKCEhQZGRkXXRGgAA9eqzzz7TrbfeqhEjRqh58+bq3Lmz/X6+lTGbzTIYDAoJCXEYnz9/vpo2barOnTvrtddec7rgAp6pwV+VXFZWpr59+2rLli1q3ry5hgwZopCQEO3atUtpaWny8/NTRkaGunbtKunCkcG4uDjt3r1bCQkJ6tKli3bt2qXU1FTddttt2rx5s/z8/Bw+Y8KECUpOTtYNN9ygQYMG6eTJk/roo48UEBCgzMxMdejQwaWa8/Pzq311UE1xVTI8zZJn3F0BgMtp1KiRJCkpKUkjRozQzp079fTTT+udd97RuHHjnOafP39ecXFxiomJ0YoVK+zjr7/+urp06aImTZpo+/btmjJlisaPH6/XX3+93nrB/3MldzT4YChduB3MG2+8odWrV2v//v0qLi5WixYtFB8fr6lTp+q6665zmG82mzVz5kytWbNGeXl5atWqlUaMGKEZM2ZUuAbCYrHorbfe0uLFi/Xjjz8qICBA/fv315w5c9S+fXuX6yUY4mpEMAQ8n4+Pj2699VZt377dPvbUU09p586dDvfYky5ciDJs2DAdP35cGRkZVf7/s/fff18TJ05UQUFBhXfpQN266oJhQ0MwxNWIYAh4vsjISN15550Oj4d9++239fLLL+vEiRP2sZKSEt133306ePCg0tLS1LRp0yr3+/333+vGG2/Uvn371LFjxzqrHxVzJXc0+ItPAABA7YiLi3N4moYkHThwwGEtfXkozMnJUXp6+mVDoSRlZ2fLaDTyZK4GgGAIAAAkSZMmTVKPHj00d+5c3XfffcrKytLixYu1ePFiSRdC4fDhw7Vr1y6tXbtWZWVlysvLkyQ1adJEPj4+yszM1Ndff634+HgFBgYqMzNTkyZN0gMPPGC/7Q08F6eS3YBTybgacSoZaBjWrl2rKVOmKCcnR+3atVNSUpL9jh2HDx92uH3NxdLT09WnTx/t2rVLjz/+uPbt26eioiK1a9dODz74oJKSklhf6CasMfRwBENcjQiGAOAeruSOBn8fQwAAANQOgiEAAAAkEQwBAABgQzAEAACAJG5XAwC4CnGBHjyJJ12cxxFDAAAASCIYAgAAwIZgCAAAAEkEQwAAANgQDAEAACCJYAgAAAAbgiEAAAAkEQwBAABgQzAEAACAJIIhAAAAbAiGAAAAkEQwBAAAgA3BEAAAAJIIhgAAALAhGAIAAEASwRAAAAA2BEMAAABIIhgCAADAhmAIAAAASQRDAAAA2BAMAQAAIIlgCAAAABuCIQAAACQRDAEAAGBDMAQAAIAkgiEAAABsCIYAAACQRDAEAACADcEQAAAAkgiGAAAAsCEYAgAAQBLBEAAAADYEQwAAAEgiGAIAAMCGYAgAAABJBEMAAADYEAwBAAAgiWAIAAAAG4IhAAAAJBEMAQAAYEMwBAAAgCSCIQAAAGwIhgAAAJBEMAQAAIANwRAAAACSCIYAAACwIRgCAABAEsEQAAAANgRDAAAASCIYAgAAwIZgCAAAAEkEQwAAANgQDAEAACCJYAgAAAAbgiEAAAAkEQwBAABgQzAEAACAJIIhAAAAbAiGLti5c6cGDhyokJAQ+fv7q1u3blq9erW7ywIAAKgVXu4uoKFIT09XYmKiGjVqpFGjRikwMFBr1qzRyJEjdezYMU2ePNndJQIAAFwRjhhWQ2lpqSZMmCCj0agtW7Zo8eLFWrhwoXbv3q0OHTpo6tSpOnLkiLvLBAAAuCIEw2pIS0vTTz/9pDFjxig2NtY+HhwcrKlTp6q4uFjLli1zX4EAAAC1gGBYDRkZGZKkhIQEp22JiYmSpM2bN9dnSQAAALWONYbVkJOTI0mKjo522tayZUsFBATY51SkqKhIRUVF9tdms1mS9Ouvv6qkpESSZDQaZTKZVFZWJovFYp9bPl5aWiqr1WofN5lMMhqNlY4Xn69hs0Ad+eWXEofXXl4XfvyUlpY6jHt7e8tisaisrMw+ZjAY5OXlVel4Zd+b2vo+lX9PL1c7PTWcnorPGwR4ivx81en3qbCwUJIcvjeVIRhWQ3mQCw4OrnB7UFCQfU5F5s2bp1mzZjmNt2vXrnYKBBqA5VPcXQEAeKb6+vl49uzZSrNMOYJhPZgyZYqSkpLsry0Wi3799Vc1bdpUBgO/tXqq/Px8hYeH69ixYwoKCnJ3OQDgUfgZ2XBYrVadPXtWYWFhl51LMKyG8nRd2VHB/Px8hYaGVvp+X19f+fr6OoyFhITUWn2oW0FBQfzQA4BK8DOyYbjckcJyXHxSDeVrCytaR5iXl6eCgoIK1x8CAAA0JATDaujdu7ckKTU11Wnbhg0bHOYAAAA0VATDaujXr5+ioqK0cuVKZWdn28fNZrPmzp0rHx8fjR071n0Fok74+vpqxowZTssAAAD8jPy9Mlirc+0yKn0k3pEjR7RgwQIeiQcAABo8gqELsrKyNGPGDG3fvl0lJSXq1KmTkpKSNHLkSHeXBgAAcMUIhgAAAJDEGkMAAADYEAwBAAAgiWAIAAAAG4IhAAAAJBEMAUkXniN58f8FAOBqRDAEJBkMBlmtVhkMBuXl5clisbi7JAAA6p2XuwsA3K20tFTbtm3T+++/rwMHDshoNMrPz0+xsbG699571aNHD3eXCABAveA+hrjqLViwQLNnz9bZs2fVvn17eXl5af/+/fbtMTEx+uMf/6hRo0apZcuWbqwUANyr/MwKfr8IhriqHTp0SJ06dVKXLl20bNky+fj4qEWLFsrLy9Nnn32mjz/+WBkZGZKkvn376tVXX1WXLl3cWzQA1JNz587p6NGjioiIkJ+fn7vLQT0gGOKq9uc//1nvvvuuVq5cqX79+kly/o34u+++04IFC7R69WpFRkZqxYoVuuWWW9xVMgDUm/nz52vNmjW699571a1bN3Xs2FEtWrSQyWSq9D2nT59WSEiIvLxYrdYQEQxxVRs2bJiys7OVnp6uiIgIlZaWysvLS1arVRaLxeGH31/+8hdNmjRJ48aNU0pKihurBoD60aZNG+Xm5spkMik4OFg9evRQQkKCbr/9dkVFRalp06YO8wsLCzVz5kz98ssvSk5OltHINa4NDXEeV7XOnTvrH//4hwoKCiTJ/huuwWCwh8LyI4hPP/20vvrqK6WlpengwYOKiopyW90AUNcOHDggs9ms7t27a8yYMdq4caMyMzO1du1aRUREqE+fPurfv786d+6s1q1bKyQkRHv37tWSJUvUp08fQmEDRTDEVS0+Pl6SdP/992vhwoXq2bOnfHx8nOaVlZXJZDKpY8eOWr9+vT1IAsDv1YEDB3T+/HklJCToiSee0ODBg7V//35lZmYqLS1Na9as0YoVK3T99derb9++GjBggDZt2qT8/HxNmDDB3eWjhjiVjKtaWVmZnn/+eb3++uuKiYnRE088oeHDh6tFixZOc8+cOaNnnnlG69ev188//+yGagGg/nz88ce67777tGrVKt1333328ZKSEh05ckS7d+/WV199pYyMDP3www/y9vaW1WqVr6+vfv31VzdWjitBMAQkvfvuu3rttdd08OBBhYWF6Z577tFdd92l8PBwmUwmhYSE6M0339SiRYv0+OOPa+HChe4uGQDqlNVq1b59+9SoUSO1a9euwlvVFBYW6sCBA9q/f79SUlK0ceNGPfnkk/qv//ovN1WNK0UwBHThB+CPP/6oJUuWaNWqVTp+/LgkqXnz5vL29tbJkydlsVg0evRovfLKK2rTpo2bKwYA96koJD711FN666239K9//UudO3d2U2W4UgRD4BKFhYXKysrSZ599ptzcXP38888KCgrSfffdp2HDhqlRo0buLhEAPILFYpHRaNThw4c1dOhQnTlzRkePHnV3WbgCXHwCXMLf31/x8fGKj49XSUmJvL293V0SAHik8iuPT5w4oZKSEj3++ONurghXiiOGAADgilitVh0/flxNmjSRv7+/u8vBFSAYAgAAQJLE3ScBAAAgiWAIAAAAG4IhAAAAJBEMAQAAYEMwBAAAgCSCIQAAAGwIhgAAAJBEMAQAAIANwRAAAACSpP8DmramdsqCOisAAAAASUVORK5CYII=\n"
          },
          "metadata": {},
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#**CONGRATULATIONS !! you've done it! 210324 18h48pm  🎉 🎉 🎉 🎉 🎉 🎉**"
      ],
      "metadata": {
        "id": "obs0dgrH1oFF"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "Ar9OBDF31TjP"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}