quantum_computation_refresher_poc.ipynb

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      "machine_shape": "hm",
      "gpuType": "L4",
      "authorship_tag": "ABX9TyPuxzGhOkqFnNDg47uaeAkv",
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
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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/ericyoc/quantum_computation_refresher_poc/blob/main/quantum_computation_refresher_poc.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Quantum Computational Math and Theory Refresher"
      ],
      "metadata": {
        "id": "Sro5mKMMNBPM"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "*   Imaginary Numbers\n",
        "*   Complex Numbers\n",
        "*   Operations (e.g., Addition and Muliplication) on Complex Numbers\n",
        "*   Complex Conjugate\n",
        "*   Complex Numbers on the Number Plane\n",
        "*   Polar Form of Complex Number\n",
        "*   Exponential Form of Complex Number\n",
        "*   Matrix\n",
        "*   Operations (e.g., addition, multiply by scalar, multiplication using dot product) on Matricies\n",
        "*   Identity Matrix\n",
        "*   Inverse Matrix\n",
        "*   Column Vector\n",
        "*   Complex Conjecate of a Matrix\n",
        "*   Transpose Matrix\n",
        "*   Unitary Matrix\n",
        "*   Hermitian Matrix\n",
        "*   Eigenvectors and Eigenvalues\n",
        "*   Single Quibit and Dirac Notation\n",
        "*   Superposition\n",
        "*   Measurement a State of a Quantum Sytem\n",
        "*   Probability Measurment of a Qubit\n",
        "*   Coverting Matrix Notation into Direct Notation\n",
        "*   Bloch Sphere\n",
        "*   Qubit X, Y and Z Gates\n",
        "*   Disgard Global Phase and Keep Relative Phase\n",
        "*   Qubit Hadamard Gate\n",
        "*   Qubit Phase Gates S and T\n",
        "*   Qubit Inverse of Phase Gates S and T\n",
        "*   Multiple Qubits Using Tensor Product\n",
        "*   Multiple Qubits CNOT, Toffoli and Controlled Gates\n",
        "*   Entanglement\n",
        "*   Two Qubit Bell States\n",
        "*   Phase Kickback\n",
        "*   Superdense Coding\n",
        "*   Classical Logical Operations (e.g. NOT, AND, OR, XOR)\n",
        "*   Quantum Circuit Applications\n"
      ],
      "metadata": {
        "id": "GVaferAGZXyy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Imaginary Numbers"
      ],
      "metadata": {
        "id": "EIjtdBGtZSBa"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's say we have $x^2 = 4 $"
      ],
      "metadata": {
        "id": "-S7K0AAhcN9s"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "zUjNRpmlK0r5"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "so we have solutions $x = \\pm 2$"
      ],
      "metadata": {
        "id": "mo6VXuSNcZCt"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Note that the solutions to the $x^2 = 4$ are $x = +2$ and $x = -2$, which represent the positive and negative square roots of 4, respectively. This double-valued nature of the square root function is a fundamental property that arises from the symmetry of the function around the x-axis and the y-axis."
      ],
      "metadata": {
        "id": "WPuqsd3IPJdE"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "KS5QFoaUriBr"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "But now we have $x^2=-4$"
      ],
      "metadata": {
        "id": "hzNS_8qycrQ8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "How can $x^2$ be negative if a number squared is always positive?"
      ],
      "metadata": {
        "id": "JeRTO835an1c"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let us suppose we set i = $\\sqrt{-1}$"
      ],
      "metadata": {
        "id": "W5qjcWtvdFyB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "so we have $x = \\pm \\sqrt{4}$"
      ],
      "metadata": {
        "id": "6osNV_3rdknn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "7O6aCiXDPndd"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$x = \\pm \\sqrt{4} \\sqrt{-1}$"
      ],
      "metadata": {
        "id": "bwCHgtHed4gi"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$x = \\pm 2 \\sqrt{-1}$"
      ],
      "metadata": {
        "id": "uBvEEK2jeEk5"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$x = \\pm 2i$"
      ],
      "metadata": {
        "id": "PzMKlwmFeOoB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this case $x^2 = -4$, the solutions are not real numbers, but instead, they are imaginary numbers, specifically, x = 2i and x = -2i. Imaginary numbers are essential in mathematics and they play a crucial role in solving complex equations and problems.\n"
      ],
      "metadata": {
        "id": "L-yKldz-P5zk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sympy import Symbol, I, latex, sqrt\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def main():\n",
        "    \"\"\"\n",
        "    Main function to demonstrate equation rendering using sympy and Matplotlib.\n",
        "    \"\"\"\n",
        "    # Create symbols\n",
        "    x = Symbol('x')\n",
        "    i = Symbol('i')\n",
        "\n",
        "    # Create the equations\n",
        "    equation1 = latex(i) + ' = \\\\sqrt{-1}'\n",
        "    equation2 = latex(x) + ' = \\\\pm 2' + latex(i)\n",
        "\n",
        "    # Render the equations using Matplotlib\n",
        "    fig, ax = plt.subplots(1, 2, figsize=(12, 3))\n",
        "\n",
        "    ax[0].text(0.5, 0.5, f'${equation1}$', ha='center', va='center', fontsize=20)\n",
        "    ax[0].axis('off')\n",
        "\n",
        "    ax[1].text(0.5, 0.5, f'${equation2}$', ha='center', va='center', fontsize=20)\n",
        "    ax[1].axis('off')\n",
        "\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 307
        },
        "id": "tmHC22IAWxgp",
        "outputId": "c3b67215-21c0-41d2-a2b5-3540efd04f77"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x300 with 2 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Complex Numbers"
      ],
      "metadata": {
        "id": "9gygsWhqecih"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Complex Number = Real Number + Imaginary Number"
      ],
      "metadata": {
        "id": "G72g-7j0eh3Z"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Standard Form for a Complex Number: $a+ib$, where $a, b \\in \\mathbb{R}$"
      ],
      "metadata": {
        "id": "aV75akJpe6Ad"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Examples of Complex Numbers"
      ],
      "metadata": {
        "id": "6qOxxKc8fMWh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "*   $2+3i$\n",
        "*   $-1-i$\n",
        "*   $\\sqrt{2} + i\\sqrt{3}$"
      ],
      "metadata": {
        "id": "O5OVfi4LfRLy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Operations (e.g., Addition and Muliplication) on Complex Numbers"
      ],
      "metadata": {
        "id": "gGOpCuOAmESe"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Complex Number Addition Operation"
      ],
      "metadata": {
        "id": "T-TfZWF4gpkH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sympy import Symbol, I, latex\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def main():\n",
        "    \"\"\"\n",
        "    Main function to demonstrate equation rendering using sympy and Matplotlib.\n",
        "    \"\"\"\n",
        "    # Create symbols\n",
        "    i = Symbol('i')\n",
        "\n",
        "    # Create the complex number addition equations\n",
        "    equation1 = '(2+3' + latex(i) + ')+(4-8' + latex(i) + ') = 6-5' + latex(i)\n",
        "    equation2 = '(1+9' + latex(i) + ') + (-3-8' + latex(i) + ') = (-2+' + latex(i) + ')'\n",
        "\n",
        "    # Render the equations using Matplotlib\n",
        "    fig, ax = plt.subplots(1, 2, figsize=(12, 3))\n",
        "\n",
        "    ax[0].text(0.5, 0.5, f'${equation1}$', ha='center', va='center', fontsize=20)\n",
        "    ax[0].axis('off')\n",
        "\n",
        "    ax[1].text(0.5, 0.5, f'${equation2}$', ha='center', va='center', fontsize=20)\n",
        "    ax[1].axis('off')\n",
        "\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 307
        },
        "id": "pN2XNy7GgEmz",
        "outputId": "2f01b086-6afb-4b41-9669-8ac79ea751a2"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x300 with 2 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Complex Number Multiplication Operation"
      ],
      "metadata": {
        "id": "nM3PeOyxguvt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sympy import Symbol, I, latex\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def main():\n",
        "    \"\"\"\n",
        "    Main function to demonstrate equation rendering using sympy and Matplotlib.\n",
        "    \"\"\"\n",
        "    # Create symbols\n",
        "    i = Symbol('i')\n",
        "\n",
        "    # Create the equation\n",
        "    equation = '(2+3' + latex(i) + ')(4-8' + latex(i) + ') = 32-4' + latex(i)\n",
        "\n",
        "    # Render the equation using Matplotlib\n",
        "    fig, ax = plt.subplots(figsize=(6, 3))\n",
        "\n",
        "    ax.text(0.5, 0.5, f'${equation}$', ha='center', va='center', fontsize=20)\n",
        "    ax.axis('off')\n",
        "\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 307
        },
        "id": "ODp9AOh_gw-X",
        "outputId": "ad1f73cc-68c2-4b02-e5fc-e2001c9bae5d"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x300 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Complex Conjugate"
      ],
      "metadata": {
        "id": "HZL8OcDgozPg"
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Complex Conjugate: $a+ib = (a+ib)^* = a-ib$"
      ],
      "metadata": {
        "id": "h9Cd5XOYo1Tl"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Examples of Complex Conjugate using $^*$ that is, negate the imaginary part"
      ],
      "metadata": {
        "id": "6SDWrulVpBMZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "*   $(-2+3i)^* = -2-3i$\n",
        "*   $(3-i)^* = 3+i$"
      ],
      "metadata": {
        "id": "yCaHBLUDpM6f"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Use Property: $(a+ib)(a-ib) = a^2 -iab + iab -i^2b^2$"
      ],
      "metadata": {
        "id": "DKit3aN_phWg"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Results in $(a+ib)(a-ib) = a^2 + b^2$, that is a real number"
      ],
      "metadata": {
        "id": "W_cVnsz0qayw"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "For example, $(2+3i)(2-3i) = 13 $"
      ],
      "metadata": {
        "id": "ao28uKqmqn6F"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Complex Numbers on the Number Plane"
      ],
      "metadata": {
        "id": "GpOHFSSfrlRq"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Plot the following complex number $-2+3i$"
      ],
      "metadata": {
        "id": "66V5IB5Xr6jK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def plot_complex_plane(number):\n",
        "    \"\"\"\n",
        "    Plot a complex number on a complex plane with a vector arrow from the origin.\n",
        "    \"\"\"\n",
        "    # Extract real and imaginary parts\n",
        "    real_part = number.real\n",
        "    imag_part = number.imag\n",
        "\n",
        "    # Create a figure and axis\n",
        "    fig, ax = plt.subplots(figsize=(8, 8))\n",
        "\n",
        "    # Plot the complex number\n",
        "    ax.plot(real_part, imag_part, 'bo')\n",
        "\n",
        "    # Plot vector arrow from origin to the complex number\n",
        "    ax.arrow(0, 0, real_part, imag_part, head_width=0.1, head_length=0.2, fc='r', ec='r')\n",
        "\n",
        "    # Set labels and title\n",
        "    ax.set_xlabel('Real')\n",
        "    ax.set_ylabel('Imaginary')\n",
        "    ax.set_title('Complex Plane with Vector Arrow')\n",
        "\n",
        "    # Add complex number text\n",
        "    number_text = f\"{real_part} + {imag_part}i\"\n",
        "    ax.text(real_part, imag_part, number_text, fontsize=12, ha='center', va='bottom')\n",
        "\n",
        "    # Draw real and imaginary number lines\n",
        "    ax.axhline(y=0, color='k', linestyle='--')\n",
        "    ax.axvline(x=0, color='k', linestyle='--')\n",
        "\n",
        "    # Set axis limits\n",
        "    ax.set_xlim([-5, 5])\n",
        "    ax.set_ylim([-5, 5])\n",
        "\n",
        "    # Set ticks and labels on both axes\n",
        "    x_ticks = np.arange(-5, 6, 1)\n",
        "    y_ticks = np.arange(-5, 6, 1)\n",
        "    ax.set_xticks(x_ticks)\n",
        "    ax.set_yticks(y_ticks)\n",
        "\n",
        "    # Set equal aspect ratio for proper scaling\n",
        "    ax.set_aspect('equal')\n",
        "\n",
        "    # Display the plot\n",
        "    plt.show()\n",
        "\n",
        "def main():\n",
        "    \"\"\"\n",
        "    Main function to plot a complex number on a complex plane with a vector arrow from the origin.\n",
        "    \"\"\"\n",
        "    # Complex number\n",
        "    number = -2 + 3j\n",
        "\n",
        "    # Plot the complex number\n",
        "    plot_complex_plane(number)\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 718
        },
        "id": "DQnWkPslTbQs",
        "outputId": "61d75565-56c2-4dbc-b15d-6f2ed2e27307"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Calculate magnitude: $|-2 + 3i | = \\sqrt{(-2)^2+(3)^2} = \\sqrt13$"
      ],
      "metadata": {
        "id": "TDd1lItAtAH8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$|a+ib| = \\sqrt{a^2+b^2}$"
      ],
      "metadata": {
        "id": "bAozLbodvGEW"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "For example, magnitude of $|4-3i| = 5 $"
      ],
      "metadata": {
        "id": "VJU3VKrAvReO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Polar Form of a Complex Number"
      ],
      "metadata": {
        "id": "c51FzEN1vmEC"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Use the following: $a + ib = r(\\cos\\theta + i\\sin\\theta)$ where and $a=r\\cos(\\theta)$ and $b=r\\sin(\\theta)$"
      ],
      "metadata": {
        "id": "WA_mc9k5v5id"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Given: $\\tan(\\theta) = b / a $"
      ],
      "metadata": {
        "id": "-jw-9daJw9At"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "therefore, $\\theta = \\arctan(b/a)$ in radians"
      ],
      "metadata": {
        "id": "0WJlEA5rxc6c"
      }
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "Hu1BSgQs64uo"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "and use $r = \\sqrt{a^2+b^2}$"
      ],
      "metadata": {
        "id": "Fe42RTow4mNC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Convert to Polar Form Example: $1+i$"
      ],
      "metadata": {
        "id": "OkA-M5z90C7_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$1+i = \\sqrt2(\\cos(\\pi/4) + isin(\\pi/4))$ where magnitude $|a+ib| = \\sqrt{a^2+b^2}$ or $|1+i| = \\sqrt{1^2+1^2} = \\sqrt{2}$ and $\\theta = \\arctan(b/a)$ or $\\theta = \\arctan(1/1) = \\pi/4\\text{ radians}$ or $45^\\circ$ (degree =  number of radians * 180/π)"
      ],
      "metadata": {
        "id": "jjHCVqFB04pL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def plot_complex_plane(number):\n",
        "    \"\"\"\n",
        "    Plot a complex number on a complex plane with a vector arrow from the origin.\n",
        "    \"\"\"\n",
        "    # Extract real and imaginary parts\n",
        "    real_part = number.real\n",
        "    imag_part = number.imag\n",
        "\n",
        "    # Calculate magnitude and angle\n",
        "    magnitude = np.sqrt(real_part**2 + imag_part**2)\n",
        "    angle = np.arctan2(imag_part, real_part)  # Angle in radians\n",
        "\n",
        "    # Convert angle to degrees for display\n",
        "    angle_deg = np.degrees(angle)\n",
        "\n",
        "    # Calculate rectangular components\n",
        "    r_cos_theta = magnitude * np.cos(angle)\n",
        "    r_sin_theta = magnitude * np.sin(angle)\n",
        "\n",
        "    # Create a figure and axis\n",
        "    fig, ax = plt.subplots(figsize=(8, 8))\n",
        "\n",
        "    # Plot the complex number\n",
        "    ax.plot(real_part, imag_part, 'bo')\n",
        "\n",
        "    # Plot vector arrow from origin to the complex number\n",
        "    ax.arrow(0, 0, real_part, imag_part, head_width=0.1, head_length=0.2, fc='r', ec='r')\n",
        "\n",
        "    # Set labels and title\n",
        "    ax.set_xlabel('Real')\n",
        "    ax.set_ylabel('Imaginary')\n",
        "    ax.set_title('Complex Plane with Vector Arrow')\n",
        "\n",
        "    # Add complex number text\n",
        "    number_text = f\"{real_part} + {imag_part}i\"\n",
        "    ax.text(real_part, imag_part, number_text, fontsize=12, ha='center', va='bottom')\n",
        "\n",
        "    # Add magnitude label\n",
        "    magnitude_label = fr\"$r = {magnitude:.2f}$\"\n",
        "    ax.text(0.05, 0.9, magnitude_label, transform=ax.transAxes, fontsize=12, va='top', bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))\n",
        "\n",
        "    # Add angle label\n",
        "    angle_label = fr\"$\\theta = {angle_deg:.2f}^\\circ$\"\n",
        "    ax.text(0.05, 0.85, angle_label, transform=ax.transAxes, fontsize=12, va='top', bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))\n",
        "\n",
        "    # Add rectangular component labels\n",
        "    r_cos_theta_label = fr\"$r\\cos\\theta = {r_cos_theta:.2f}$\"\n",
        "    r_sin_theta_label = fr\"$r\\sin\\theta = {r_sin_theta:.2f}$\"\n",
        "    ax.text(0.05, 0.8, r_cos_theta_label, transform=ax.transAxes, fontsize=12, va='top', bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))\n",
        "    ax.text(0.05, 0.75, r_sin_theta_label, transform=ax.transAxes, fontsize=12, va='top', bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))\n",
        "\n",
        "    # Draw real and imaginary number lines\n",
        "    ax.axhline(y=0, color='k', linestyle='--')\n",
        "    ax.axvline(x=0, color='k', linestyle='--')\n",
        "\n",
        "    # Set axis limits\n",
        "    ax.set_xlim([-5, 5])\n",
        "    ax.set_ylim([-5, 5])\n",
        "\n",
        "    # Set ticks and labels on both axes\n",
        "    x_ticks = np.arange(-5, 6, 1)\n",
        "    y_ticks = np.arange(-5, 6, 1)\n",
        "    ax.set_xticks(x_ticks)\n",
        "    ax.set_yticks(y_ticks)\n",
        "\n",
        "    # Set equal aspect ratio for proper scaling\n",
        "    ax.set_aspect('equal')\n",
        "\n",
        "    # Display the plot\n",
        "    plt.show()\n",
        "\n",
        "def main():\n",
        "    \"\"\"\n",
        "    Main function to plot a complex number on a complex plane with a vector arrow from the origin.\n",
        "    \"\"\"\n",
        "    # Complex number\n",
        "    number = -2 + 3j\n",
        "\n",
        "    # Plot the complex number\n",
        "    plot_complex_plane(number)\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 718
        },
        "id": "GLm8qfRLwrLR",
        "outputId": "c21cedba-8545-40e0-c7b3-1f6636e2849b"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Exponential Form of Complex Number"
      ],
      "metadata": {
        "id": "0rp9Gh_txo68"
      },
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Exponential form** assists in describing the rotation around a circle and lends itself useful for quantum computing calculations specificly in representing quantum states"
      ],
      "metadata": {
        "id": "nisDaDG0A1I6"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Exponential Form**: $a+ib = re^{i\\theta}$"
      ],
      "metadata": {
        "id": "6w9u7uEHx8l4"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Exponential Form Example $1+i = \\sqrt2e^{i\\pi/4}$ where magnitude $|a+ib| = \\sqrt{a^2+b^2}$ or $|1+i| = \\sqrt{1^2+1^2} = \\sqrt{2}$ and $\\theta = \\arctan(b/a)$ or $\\theta = \\arctan(1/1) = \\pi/4\\text{ radians}$ or $45^\\circ$ (degree =  number of radians * 180/π)"
      ],
      "metadata": {
        "id": "dFVJgVY8yyjT"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Note the following: $\\sqrt2 = 1.41$ and  $\\pi/4\\text{ radians}$ or $45^\\circ$ (degree =  number of radians * 180/π) represented in the next plot."
      ],
      "metadata": {
        "id": "3jHla5yFAQII"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def plot_complex_plane(number):\n",
        "    \"\"\"\n",
        "    Plot a complex number on a complex plane with a vector arrow from the origin.\n",
        "    \"\"\"\n",
        "    # Extract real and imaginary parts\n",
        "    real_part = number.real\n",
        "    imag_part = number.imag\n",
        "\n",
        "    # Calculate magnitude and angle\n",
        "    magnitude = np.abs(number)\n",
        "    angle = np.angle(number)\n",
        "\n",
        "    # Convert angle to degrees for display\n",
        "    angle_deg = np.degrees(angle)\n",
        "\n",
        "    # Calculate rectangular components\n",
        "    r_cos_theta = magnitude * np.cos(angle)\n",
        "    r_sin_theta = magnitude * np.sin(angle)\n",
        "\n",
        "    # Create a figure and axis\n",
        "    fig, ax = plt.subplots(figsize=(8, 8))\n",
        "\n",
        "    # Plot the complex number\n",
        "    ax.plot(real_part, imag_part, 'bo')\n",
        "\n",
        "    # Plot vector arrow from origin to the complex number\n",
        "    ax.arrow(0, 0, real_part, imag_part, head_width=0.1, head_length=0.2, fc='r', ec='r')\n",
        "\n",
        "    # Set labels and title\n",
        "    ax.set_xlabel('Real')\n",
        "    ax.set_ylabel('Imaginary')\n",
        "    ax.set_title('Complex Plane with Vector Arrow')\n",
        "\n",
        "    # Add complex number text\n",
        "    number_text = fr\"${real_part:.2f} + {imag_part:.2f}i$\"\n",
        "    ax.text(real_part, imag_part, number_text, fontsize=12, ha='center', va='bottom')\n",
        "\n",
        "    # Add magnitude label\n",
        "    magnitude_label = fr\"$r = {magnitude:.2f}$\"\n",
        "    ax.text(0.05, 0.9, magnitude_label, transform=ax.transAxes, fontsize=12, va='top', bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))\n",
        "\n",
        "    # Add angle label in degrees\n",
        "    angle_label_deg = fr\"$\\theta = {angle_deg:.2f}^\\circ$\"\n",
        "    ax.text(0.05, 0.85, angle_label_deg, transform=ax.transAxes, fontsize=12, va='top', bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))\n",
        "\n",
        "    # Add rectangular component labels\n",
        "    r_cos_theta_label = fr\"$r\\cos\\theta = {r_cos_theta:.2f}$\"\n",
        "    r_sin_theta_label = fr\"$r\\sin\\theta = {r_sin_theta:.2f}$\"\n",
        "    ax.text(0.05, 0.8, r_cos_theta_label, transform=ax.transAxes, fontsize=12, va='top', bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))\n",
        "    ax.text(0.05, 0.75, r_sin_theta_label, transform=ax.transAxes, fontsize=12, va='top', bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))\n",
        "\n",
        "    # Add exponential form label\n",
        "    exponential_form_label = fr\"$a + ib = {magnitude:.2f}e^{{i\\theta}} \\quad (\\theta = {angle_deg:.2f}^\\circ)$\"\n",
        "    ax.text(0.05, 0.7, exponential_form_label, transform=ax.transAxes, fontsize=12, va='top', bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))\n",
        "\n",
        "    # Draw real and imaginary number lines\n",
        "    ax.axhline(y=0, color='k', linestyle='--')\n",
        "    ax.axvline(x=0, color='k', linestyle='--')\n",
        "\n",
        "    # Set axis limits\n",
        "    ax.set_xlim([-5, 5])\n",
        "    ax.set_ylim([-5, 5])\n",
        "\n",
        "    # Set ticks and labels on both axes\n",
        "    x_ticks = np.arange(-5, 6, 1)\n",
        "    y_ticks = np.arange(-5, 6, 1)\n",
        "    ax.set_xticks(x_ticks)\n",
        "    ax.set_yticks(y_ticks)\n",
        "\n",
        "    # Set equal aspect ratio for proper scaling\n",
        "    ax.set_aspect('equal')\n",
        "\n",
        "    # Display the plot\n",
        "    plt.show()\n",
        "\n",
        "def main():\n",
        "    \"\"\"\n",
        "    Main function to plot a complex number on a complex plane with a vector arrow from the origin.\n",
        "    \"\"\"\n",
        "    # Complex number\n",
        "    number = np.sqrt(2) * np.exp(1j * np.pi/4)\n",
        "\n",
        "    # Plot the complex number\n",
        "    plot_complex_plane(number)\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 718
        },
        "id": "J0w931um_Rw8",
        "outputId": "7193c5f8-8325-48ee-84bd-b4d0aa58cd83"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Matrix"
      ],
      "metadata": {
        "id": "ZThyA67BBrA5"
      },
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Use **m** for rows and **n** for columns then we have **m** x **n** matrix"
      ],
      "metadata": {
        "id": "4FU9S_n-Cm-y"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "2 rows by 2 columns or 2 by 2 matrix or 2 x 2 matrix where m = 2 and n = 2 \\\\\n",
        "$\\begin{bmatrix}\n",
        "1 & -2 \\\\\n",
        "0 & -10\n",
        "\\end{bmatrix}$"
      ],
      "metadata": {
        "id": "gecwxRgtCLoh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Examples of Matricies"
      ],
      "metadata": {
        "id": "Ckh6T7nrCInn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "4 rows by 1 column or 4 by 1 matrix or 4 x 1 matrix where m = 4 and n =1 \\\\\n",
        "$\\begin{bmatrix}\n",
        "1  \\\\\n",
        "2 \\\\\n",
        "-3 \\\\\n",
        "8\n",
        "\\end{bmatrix}$"
      ],
      "metadata": {
        "id": "LA6sD_SQCQ7m"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "2 rows by 3 columns or 2 by 3 matrix or 2 x 3 matrix where m = 2 and n = 3 \\\\\n",
        "$\\begin{bmatrix}\n",
        "5 & -2 & 3 \\\\\n",
        "7 & 2 & 1.5\n",
        "\\end{bmatrix}$"
      ],
      "metadata": {
        "id": "SfUqt77LCY-D"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Operations (e.g., addition, multiply by scalar, multiplication using dot product) on Matricies"
      ],
      "metadata": {
        "id": "8ad3_Qu8DrD-"
      },
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Matricies can be added or subtracted only if both matrices are the same dimensions"
      ],
      "metadata": {
        "id": "FahEa4OkE-u6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sympy import Matrix, pprint\n",
        "\n",
        "def main():\n",
        "    \"\"\"\n",
        "    Main function to demonstrate matrix addition using sympy.\n",
        "    \"\"\"\n",
        "    print(\"\\nMatrix 1 + Matrix 2 = Matrix 3\\n\")\n",
        "    # Create the first matrix\n",
        "    matrix1 = Matrix([[2, -3],\n",
        "                      [7, 0],\n",
        "                      [0, 4]])\n",
        "\n",
        "    # Create the second matrix\n",
        "    matrix2 = Matrix([[4, 12],\n",
        "                      [-2, 7],\n",
        "                      [2, 5]])\n",
        "\n",
        "    # Print the first matrix\n",
        "    print(\"Matrix 1:\")\n",
        "    pprint(matrix1)\n",
        "\n",
        "    # Print the second matrix\n",
        "    print(\"\\nMatrix 2:\")\n",
        "    pprint(matrix2)\n",
        "\n",
        "    # Add the matrices\n",
        "    result = matrix1 + matrix2\n",
        "\n",
        "    # Print the result\n",
        "    print(\"\\nResult: Matrix 3\")\n",
        "    pprint(result)\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "meZbELd5D7C6",
        "outputId": "b9c9d00a-f0ea-40ba-de13-7f47a25e8677"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Matrix 1 + Matrix 2 = Matrix 3\n",
            "\n",
            "Matrix 1:\n",
            "⎡2  -3⎤\n",
            "⎢     ⎥\n",
            "⎢7  0 ⎥\n",
            "⎢     ⎥\n",
            "⎣0  4 ⎦\n",
            "\n",
            "Matrix 2:\n",
            "⎡4   12⎤\n",
            "⎢      ⎥\n",
            "⎢-2  7 ⎥\n",
            "⎢      ⎥\n",
            "⎣2   5 ⎦\n",
            "\n",
            "Result: Matrix 3\n",
            "⎡6  9⎤\n",
            "⎢    ⎥\n",
            "⎢5  7⎥\n",
            "⎢    ⎥\n",
            "⎣2  9⎦\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sympy import Matrix, symbols, pprint\n",
        "\n",
        "def main():\n",
        "    \"\"\"\n",
        "    Main function to demonstrate scalar multiplication of a matrix using sympy.\n",
        "    \"\"\"\n",
        "    # Create a symbolic scalar\n",
        "    k = symbols('k')\n",
        "\n",
        "    # Create the matrix\n",
        "    matrix = Matrix([[-4, 3],\n",
        "                     [7, 0]])\n",
        "\n",
        "    # Print the matrix\n",
        "    print(\"Original Matrix:\")\n",
        "    pprint(matrix)\n",
        "\n",
        "    # Multiply the matrix by the scalar k\n",
        "    result = k * matrix\n",
        "\n",
        "    # Print the result\n",
        "    print(\"\\nResult (k * Matrix):\")\n",
        "    pprint(result)\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RD7qxbyDFsEi",
        "outputId": "31c85b9f-d916-4ad1-c419-ac1a9ac41e23"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Original Matrix:\n",
            "⎡-4  3⎤\n",
            "⎢     ⎥\n",
            "⎣7   0⎦\n",
            "\n",
            "Result (k * Matrix):\n",
            "⎡-4⋅k  3⋅k⎤\n",
            "⎢         ⎥\n",
            "⎣7⋅k    0 ⎦\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Note that the number of columns of the left matrix must be equal to the number of rows of the right matrix to multiply two matricies together as shown in the next output."
      ],
      "metadata": {
        "id": "tACmcltXG2dK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Matix multiplication is not Commutative, $AB \\neq BA$"
      ],
      "metadata": {
        "id": "ugvVoC2HHWDY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sympy import Matrix, pprint\n",
        "\n",
        "def main():\n",
        "    \"\"\"\n",
        "    Main function to demonstrate matrix multiplication using sympy.\n",
        "    \"\"\"\n",
        "    # Create the first matrix\n",
        "    matrix1 = Matrix([[1, 0],\n",
        "                      [2, -1]])\n",
        "\n",
        "    # Create the second matrix\n",
        "    matrix2 = Matrix([[2, 3, 5],\n",
        "                      [5, 2, 0]])\n",
        "\n",
        "    # Print the first matrix\n",
        "    print(\"Matrix 1:\")\n",
        "    pprint(matrix1)\n",
        "\n",
        "    # Print the second matrix\n",
        "    print(\"\\nMatrix 2:\")\n",
        "    pprint(matrix2)\n",
        "\n",
        "    # Multiply the matrices using the dot product\n",
        "    result = matrix1 * matrix2\n",
        "\n",
        "    # Print the result Dot Product\n",
        "    print(\"\\nResult (Matrix 1 * Matrix 2):\")\n",
        "    pprint(result)\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "O8ocg84jGFFP",
        "outputId": "d1ffabcd-fc73-4f4f-abf1-f0761a6ce764"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Matrix 1:\n",
            "⎡1  0 ⎤\n",
            "⎢     ⎥\n",
            "⎣2  -1⎦\n",
            "\n",
            "Matrix 2:\n",
            "⎡2  3  5⎤\n",
            "⎢       ⎥\n",
            "⎣5  2  0⎦\n",
            "\n",
            "Result (Matrix 1 * Matrix 2):\n",
            "⎡2   3  5 ⎤\n",
            "⎢         ⎥\n",
            "⎣-1  4  10⎦\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Special Kind of Matrix Called a Column Vector"
      ],
      "metadata": {
        "id": "fQDDKgmMLcYt"
      },
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "A matrix is called a column vector and useful for representing a state of the quantum computation"
      ],
      "metadata": {
        "id": "6zll2YDoH2Xp"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Column Vector Example: $\\begin{bmatrix}\n",
        "6  \\\\\n",
        "-3 \\\\\n",
        "1 \\\\\n",
        "1\n",
        "\\end{bmatrix}$"
      ],
      "metadata": {
        "id": "75JtvwetIA1E"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Identity Matrix"
      ],
      "metadata": {
        "id": "anZOYinhL-qd"
      },
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "2 x 2 Identity Matrix\n",
        "$\\begin{bmatrix}\n",
        "1 & 0  \\\\\n",
        "0 & 1\n",
        "\\end{bmatrix}$"
      ],
      "metadata": {
        "id": "4vnFDEmKMDLQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "3 x 3 Identity Matrix\n",
        "$\\begin{bmatrix}\n",
        "1 & 0 & 0  \\\\\n",
        "0 & 1 & 0 \\\\\n",
        "0 & 0 & 1\n",
        "\\end{bmatrix}$"
      ],
      "metadata": {
        "id": "B6RAqOI4MIPP"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$IA = A$ where $A$ is a matrix and $I$ is the identity matrix"
      ],
      "metadata": {
        "id": "HtlUa-UHQfuZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$\\begin{bmatrix}\n",
        "1 & 0  \\\\\n",
        "0 & 1\n",
        "\\end{bmatrix}$\n",
        "$\\begin{bmatrix}\n",
        "a  \\\\\n",
        "b  \n",
        "\\end{bmatrix}$\n",
        "=\n",
        "$\\begin{bmatrix}\n",
        "a  \\\\\n",
        "b\n",
        "\\end{bmatrix}$"
      ],
      "metadata": {
        "id": "BrLY25PcQt6D"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Inverse Matrix"
      ],
      "metadata": {
        "id": "RZEHcKbNRRVG"
      },
      "execution_count": 22,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "$A^{-1}A = I$"
      ],
      "metadata": {
        "id": "ZnKYMgWNRUsW"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Note that not all matrices have an inverse"
      ],
      "metadata": {
        "id": "loNBgscvRnqy"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Stated differently, the column vector stays in the same place"
      ],
      "metadata": {
        "id": "SlaBJ-HbSWOe"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Multiplying a matrix with a column vector gives us another column vector and thereby we can use matricies to transform our column vectors"
      ],
      "metadata": {
        "id": "BTEczr-NIFY9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Complex Conjecate of a Matrix"
      ],
      "metadata": {
        "id": "KEfp4MUIT9e1"
      },
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "$A$ = $\\begin{bmatrix}\n",
        "2 + 3i & 0  \\\\\n",
        "5 & 3-i\n",
        "\\end{bmatrix}$\n",
        "$A^{*}$ =\n",
        "$\\begin{bmatrix}\n",
        "2 - 3i & 0  \\\\\n",
        "5 & 3 + i  \n",
        "\\end{bmatrix}$"
      ],
      "metadata": {
        "id": "3_4F8e6mUFGG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Transposing a Matrix"
      ],
      "metadata": {
        "id": "1mMUoS2MLn6v"
      },
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "$\\begin{bmatrix}\n",
        "1 & 2 & 3  \\\\\n",
        "4 & 5 & 6 \\\\\n",
        "7 & 8 & 9\n",
        "\\end{bmatrix}^{T}$\n",
        "=\n",
        "$\\begin{bmatrix}\n",
        "1 & 4 & 7  \\\\\n",
        "2 & 5 & 8 \\\\\n",
        "3 & 6 & 9\n",
        "\\end{bmatrix}$"
      ],
      "metadata": {
        "id": "Nb2YC6khVkKK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Note to find the transpose of a matrix you exchange the rows for the columns"
      ],
      "metadata": {
        "id": "aVigHQZ7WbQu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install sympy\n",
        "from sympy import Matrix, pprint\n",
        "\n",
        "def main():\n",
        "    \"\"\"\n",
        "    Main function to demonstrate matrix visualization using sympy.\n",
        "    \"\"\"\n",
        "    # Create a sample matrix\n",
        "    matrix = Matrix([[1, 2, 3],\n",
        "                     [4, 5, 6],\n",
        "                     [7, 8, 9]])\n",
        "\n",
        "    # Print the matrix\n",
        "    print(\"Matrix:\")\n",
        "    pprint(matrix)\n",
        "\n",
        "    # Transpose the matrix\n",
        "    transposed_matrix = matrix.T\n",
        "\n",
        "    # Print the transposed matrix\n",
        "    print(\"\\nTransposed Matrix:\")\n",
        "    pprint(transposed_matrix)\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hnzR49-4UKka",
        "outputId": "4245ec5a-b648-462c-e17c-5150adfeac17"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: sympy in /usr/local/lib/python3.10/dist-packages (1.12.1)\n",
            "Requirement already satisfied: mpmath<1.4.0,>=1.1.0 in /usr/local/lib/python3.10/dist-packages (from sympy) (1.3.0)\n",
            "Matrix:\n",
            "⎡1  2  3⎤\n",
            "⎢       ⎥\n",
            "⎢4  5  6⎥\n",
            "⎢       ⎥\n",
            "⎣7  8  9⎦\n",
            "\n",
            "Transposed Matrix:\n",
            "⎡1  4  7⎤\n",
            "⎢       ⎥\n",
            "⎢2  5  8⎥\n",
            "⎢       ⎥\n",
            "⎣3  6  9⎦\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "vyFM1XZoYdwt"
      },
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "$(A^{*})^{T} = (A^{T})^{*} = A^{\\dagger}$"
      ],
      "metadata": {
        "id": "4RcXcasFWmNn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "w0B4X6eAYhi1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Unitary Matrix"
      ],
      "metadata": {
        "id": "dSDzn2cdT2aQ"
      },
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "$U^{\\dagger}U = I$ given that $U$ is a unitary matrix"
      ],
      "metadata": {
        "id": "Q23_GpUsXvGJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$\\implies$ Inverse of $U$is $U^{\\dagger}$"
      ],
      "metadata": {
        "id": "bzoSPsiOYAvS"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "When acting on a vector, unitary matricies rotate/flip the vector, keeping the magnitude of the vector the same and we will see this is important in quantum computation."
      ],
      "metadata": {
        "id": "z6FCxCwTYnzw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Hermitian Matrix"
      ],
      "metadata": {
        "id": "3VWcw-KdY5Ej"
      },
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "$H = H^{\\dagger}$ given $H$ is a Hermitian matrix"
      ],
      "metadata": {
        "id": "9HGRMVWzY8wl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Eigenvectors and Eigenvalues"
      ],
      "metadata": {
        "id": "DKEtVLtmZTIZ"
      },
      "execution_count": 28,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "$A\\vec{v} = \\lambda\\vec{v}$ where $\\vec{v}$ is the Eigenvector (vector) and $\\lambda$ is the Eigenvalue (scalar) and $A$ is the matrix"
      ],
      "metadata": {
        "id": "qvXNenbcZ0bR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Example"
      ],
      "metadata": {
        "id": "8R_f9cnMbnxe"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$\\begin{bmatrix}\n",
        "2 & 0 \\\\\n",
        "1 & 2 \\\\\n",
        "\\end{bmatrix}$\n",
        "$\\begin{bmatrix}\n",
        "0  \\\\\n",
        "3  \\\\\n",
        "\\end{bmatrix}$ =\n",
        "$\\begin{bmatrix}\n",
        "0 \\\\\n",
        "6\\\\\n",
        "\\end{bmatrix}$"
      ],
      "metadata": {
        "id": "2oz7_NNXbB9l"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Factor out a scalar, \\\\\n",
        "$\\begin{bmatrix}\n",
        "2 & 0 \\\\\n",
        "1 & 2 \\\\\n",
        "\\end{bmatrix}$\n",
        "$\\begin{bmatrix}\n",
        "0  \\\\\n",
        "3  \\\\\n",
        "\\end{bmatrix}$ =\n",
        "2 $\\begin{bmatrix}\n",
        "0 \\\\\n",
        "3\\\\\n",
        "\\end{bmatrix}$"
      ],
      "metadata": {
        "id": "DXjNB2kSbeua"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "i5DQXbp9dgLg"
      },
      "execution_count": 28,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "_L5VVibndXCp"
      }
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "o1jHkO7MdzFt"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$A\\vec{v} = \\lambda\\vec{v}$ where $\\vec{v}$ is $\\begin{bmatrix}\n",
        "0  \\\\\n",
        "3  \\\\\n",
        "\\end{bmatrix}$ the Eigenvector (vector) and $\\lambda$ is 2 the Eigenvalue (scalar) and $A$ is the matrix"
      ],
      "metadata": {
        "id": "Xr-MNGITcdo-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Single Quibit and Dirac Notation"
      ],
      "metadata": {
        "id": "3NJpLUaJdJNR"
      },
      "execution_count": 29,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Classical Computers use Bits (0's and 1's)"
      ],
      "metadata": {
        "id": "-O52c0wLdSFu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Quantum Computers use Qubits (can be 0 and 1 at the same time)"
      ],
      "metadata": {
        "id": "r8Bgf5BudXhY"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "A qubit can be made from any quantum particle that has 2 distinct states. For example, a photon of light being polarized either horizontally or vertically."
      ],
      "metadata": {
        "id": "_WQHydPfdnUY"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We still use 0's and 1's but written in Dirac notation or bra-ket notation $|0\\rangle = \\begin{pmatrix} 1 \\\\ 0 \\end{pmatrix}, \\quad |1\\rangle = \\begin{pmatrix} 0 \\\\ 1 \\end{pmatrix}$\n"
      ],
      "metadata": {
        "id": "rufYKlnZd62x"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Superposition"
      ],
      "metadata": {
        "id": "3MnLNjcndK78"
      },
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Quantum particle is in two states simultaneously. A Qubit is in superposition if it is both $|0\\rangle$ and $|1\\rangle$ at the same time"
      ],
      "metadata": {
        "id": "t0wdmT4teopQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Back to our previous example, the proton of light is being both horizontally and vertically polarized."
      ],
      "metadata": {
        "id": "L5oMp7AUeyMn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Qubits represented mathematically in the Dirac notation by $|\\psi\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix}$"
      ],
      "metadata": {
        "id": "w_lYOoxaft_S"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$\\alpha$ represents how much the Qubit is in the $|0\\rangle$ state and the $\\beta$ represents how much the Qubit is in the $|1\\rangle$ state"
      ],
      "metadata": {
        "id": "rR1Y0lJHgRAD"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Hense, the following: $|0\\rangle = \\begin{pmatrix} 1 \\\\ 0 \\end{pmatrix}$ means that the Qubit is completely in the $|0\\rangle$ state, and $|1\\rangle = \\begin{pmatrix} 0 \\\\ 1 \\end{pmatrix}$ means that the Qubit is completely in the $|1\\rangle$ state"
      ],
      "metadata": {
        "id": "Vk99PshIg6Dk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Measurement a State of a Quantum Sytem"
      ],
      "metadata": {
        "id": "5_CnC1Rvh7LC"
      },
      "execution_count": 31,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "When we measure a quantum system, it collapses into the measured state"
      ],
      "metadata": {
        "id": "bVKDFr-DiAI-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Back to our previous example...if we have a photon that is in a superposition of both vertically and horizontally polarized, when we measure it we can only measure it as horizontally or vertically polarized, and once it has been measured it will collaps into (becomes) the measured state."
      ],
      "metadata": {
        "id": "XdbE8nYOiObT"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "So in this situation we have a photon in a superposition of both vertically and horizontally polarized and we measure it as horizontally polarized then it become horizontally polarized."
      ],
      "metadata": {
        "id": "-h_HX66MiiTL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Probability Measurment of a Qubit"
      ],
      "metadata": {
        "id": "f1RFuh-Oi71l"
      },
      "execution_count": 32,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "When we measure a qubit we only measure a 0 or a 1 whereby when we are measuing a qubit it collapses it's superposition due to the laws of quatum mechanics"
      ],
      "metadata": {
        "id": "oQaRPXIXjAed"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "If we were to measure the qubit $|\\psi\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix}$ we would not meausre $\\alpha$ or $\\beta$, we still only measure a 0 or a 1"
      ],
      "metadata": {
        "id": "WsEFDWK6jEih"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Probability of measuring $|\\psi\\rangle$ as 0 i: $|\\alpha|^2$ given $|\\psi\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix}$"
      ],
      "metadata": {
        "id": "Ud7EG5GRjdiP"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Probability of measuring $|\\psi\\rangle$ as 1 i: $|\\beta|^2$ given $|\\psi\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix}$"
      ],
      "metadata": {
        "id": "olgp5381j1fN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "For example, let's say we have $|\\psi\\rangle = \\begin{pmatrix} \\sqrt3/2 \\\\ 1/2 \\end{pmatrix}$"
      ],
      "metadata": {
        "id": "JxBF4tCgka_F"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We will have the probability of measuring $|\\psi\\rangle$ as 0 i: $|\\sqrt3/2|^2 = 3/4$"
      ],
      "metadata": {
        "id": "3BLlyAOxkHLz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Likewise, we wil have the probability of measuring $|\\psi\\rangle$ as 1 i: $|1/2|^2 = 1/4$"
      ],
      "metadata": {
        "id": "d1a9j6X2kWNS"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Given $|0\\rangle = \\begin{pmatrix} 1 \\\\ 0 \\end{pmatrix}$ means that the Qubit is completely in the $|0\\rangle$ state, and $|1\\rangle = \\begin{pmatrix} 0 \\\\ 1 \\end{pmatrix}$ means that the Qubit is completely in the $|1\\rangle$ state"
      ],
      "metadata": {
        "id": "KKlZjG6DlGPu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "therefore, we have the probability of measuring a 0 is 1 for $|0\\rangle = \\begin{pmatrix} 1 \\\\ 0 \\end{pmatrix}$ and we have the probabililty of measuring 1 is 1 for $|1\\rangle = \\begin{pmatrix} 0 \\\\ 1 \\end{pmatrix}$"
      ],
      "metadata": {
        "id": "5ZvgscjHlPhQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Likewise, we have a valid Quibit state in the previous example since we have $|\\alpha|^2 + |\\beta|^2 = 1$"
      ],
      "metadata": {
        "id": "MBzaRnnfl2rV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Coverting Matrix Notation into Direct Notation"
      ],
      "metadata": {
        "id": "sqv-qy3Pnpkx"
      },
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Dirac notation by $|\\psi\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix}$"
      ],
      "metadata": {
        "id": "4FVL4cVhnuQD"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "into the sum of two matrices $|\\psi\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix}$ $= \\begin{pmatrix} \\alpha \\\\ 0 \\end{pmatrix}$ + $\\begin{pmatrix} 0 \\\\ \\beta \\end{pmatrix}$"
      ],
      "metadata": {
        "id": "pL0CbUxanyqK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "factor out $\\alpha$ and $\\beta$ and sum of two matrices $|\\psi\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix}$ $= \\alpha \\begin{pmatrix} 1\\\\ 0 \\end{pmatrix}$ + $\\beta \\begin{pmatrix} 0 \\\\ 1 \\end{pmatrix}$"
      ],
      "metadata": {
        "id": "nHDWEARdoNLo"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "given that we have the probability of measuring a 0 is 1 for $|0\\rangle = \\begin{pmatrix} 1 \\\\ 0 \\end{pmatrix}$ and we have the probabililty of measuring 1 is 1 for $|1\\rangle = \\begin{pmatrix} 0 \\\\ 1 \\end{pmatrix}$"
      ],
      "metadata": {
        "id": "FDc2x-bNov-P"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "we now have $|\\psi\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix}$ $= \\alpha|0\\rangle + \\beta|1\\rangle$ where $|x\\rangle$ are called Ket Vectors and represent a quantum state"
      ],
      "metadata": {
        "id": "Bkm0iRVxo7RC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Write a quantum computing state by converting the following: $|\\psi\\rangle = \\begin{pmatrix} 1/2 \\\\ {2\\sqrt3}/4 \\end{pmatrix}$ $= 1/2|0\\rangle + {2\\sqrt3}/4|1\\rangle$"
      ],
      "metadata": {
        "id": "ZqIvS1mXqFl6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Bloch Sphere"
      ],
      "metadata": {
        "id": "sX6XvvEPrJu9"
      },
      "execution_count": 34,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can represent a qubit $|\\psi\\rangle$ as a point on the surface of the **Bloch Sphere**"
      ],
      "metadata": {
        "id": "T4dKqYoIrN_Z"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Create a Bloch Sphere for $|\\psi\\rangle = 1/2|0\\rangle + {2\\sqrt3}/4|1\\rangle$"
      ],
      "metadata": {
        "id": "GYkm6Nlorspk"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 536
        },
        "id": "cAArvJbKSpD3",
        "outputId": "04a4a241-c6f9-43e3-ae13-523411034b7c"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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jX/7Lf4mVlRUAwLfefBNf/spXoKkqPr98Gf/tBz+A5Tj4v//Tf8Lf//t/H+fPnhV+C/zIn3vuOciyDMu28dZbb8EPQ9imicnJSVx4+WXkCwUQSUIuIUoEmNtjCwkIE6ZLyeiGRAgkTYurNXgkhh1DO5Kw41q1XH/u6+D5PlzXxUS5jHqjgcWlJTxcWsJWpYJTp09jbXUVtxQF2Xwe0zMzmJqdRZaJI1NBY4ovGlJykCIFg2vbqG1twazV4DjO9qo0itBoNEAIQdYwMDkxgSxbNe8GbUkBg/hP60TG/2Yr4iYHRJ7zT2xPkSQomUxsPsS8AgghojQwn8tBkWVQAD/8kz/B6soKCID/19/8m/jOr/+62M6p06fx9Nmz+L1/9a/g+z5++Cd/gmfPnQNp8VHQNA1nz57Fp59+ip++9Rb+8ne+g6dfew0TLEpQbzSEmFFVlG0iEEVxeSWv5khUYygsHaPKMiSm5yCJc2++cPHxhNxPYQBorDwSAOYOHMCxo0extraGDz74ANeuXsWp06dhAKhWKqhWq1i4cwfZXA6lchmT09MwDEP8pEix35GSgxRPLCilcF0X9UoFjUoFjm03TSgScwP0fB/5fB6qoqBcLAqB39D7xbbQkLKJMDmNcdfEnumEhBZBZmZBrc9zEGY0ZJlmXE1BCMIwRKVaRTaTgaaq+P/9z/8JQgjm5ubwl/7SX9qxuzOnTuErr7+O999/H1euXMGt27dx8sQJMZFTAAsLC9A0LRYgbm7itS9/WWgwPFZaWG80oCoKctmsIDMSEn0WmDhT6ZKWEe6O7P3ic2PXUmFeCrtRW2uqikPz8yj/+T+PX/7yl7hx9SpeevllZDIZeKyfRaNeR71axeKDBygUiyhNTKA8MYFCoYBMJpMKGlPsW6TkIMUTB8/zUK/VUK9U4Jhmk++AoijQVBW6psEPAtRNM/b1VxSUCoWugz0vV/SDQITIA/Y49P04JQHEk1nCmIibGvGVc/L/vPuhzIiKeG2b42gXPufkAwnVfhRFmCiVYFoWPN+HZdv47PPPhcnQ17/+9bar7iAI8PLLL+P9996D7/v44IMPcPLkSQBAo9HAh5cuYW19HRcuXMClS5dQr9dx/fp1zM/Px86JTGAJ1rFRN4yYCDBS0PdKP0EEIlbFkYwiUHZ9iSwLx0nxGfe3hybksll84xvfwK9+9Stc/OADXLhwAYcOHYoNq1gqImDpk9rWFpZ0HYVyGZOTk5hgRCHtB5FivyG9Y1M8EQjDELZto7q1BbteR+C6Qv2uaZr4kdmkazK3PRpFUFUVWcOA7ThNkz4PiXMCIKyBE26EIiqQKMFL9jYQkxWfyHmVAnuPQCJ8LwyQWmyGFUURlQuaqkLTtG3/Af6bERRZllEsFOC6LhqWhYWFBWRzOfieh6fPnhX+AsnJ1PU8zM/Pi5D+jRs3xO/Lly8jk8ngjTfewOTkJP7sZz/D4tISPvz4Y0xPT8fHqyjIZzIgrIQz2+/Kml+HRJSAH5vEjoUfE4kvTHz8URR/DvyaJrYjjKK462QPYqKpKl5//XVcunQJ77//PizLwpkzZ6BrGnLZLIIwhO/78DwPtuOgsraG6vo6lnM5lCYnMTk5iXK5jEza/yHFPkFKDlJ8YcFtjE3TRKNahWfbiHwfhJA4N8y6/fEJ1AsCVGs1bGxuwrJthGEIWVGg8VUfm/glbNsecxKgSFK86mc/CsuNy6xNMQ/rA2juhUApKCuti5jYkSvyk6WM/DE/L2C7cRK3NQ6DALZlCdMgWZbjKAgrsRTWy4mJUNM0TKiqECEqqopcoQDf96FoGqKI4u1fABcvAfmCj298XUJ5YgK1ahUPHzzAT996C9WtLZw4eRInTp5EGIao1mp45plnsLi0hKtXruA3vvMd6EwICcRpGu4LobeSgxbNhPhfy2P+H4kQROKp5ueaSBS7hlEUNTebYgh5aoJ/Ti3HwAnEK6+8glw2i88//xyWaeKFF1+EJElQWXVKNpOJSZfnwWLWz41aDesrKyiUSihPTGBqagqFHlGoFCkeNVJykOILB9/3Yz/+eh22ZSFwnDgCoCjIFQrCuTAIAtQbDVi2DdO24TkOXN8XoWpD1+Mugyw0z4VxMgvz83C4+H+iSRIHF8f16zXW1G+g3fMJrULyN09puL4P3/OEG6MfBPA8DxGAIIowOzcHPZPBytqaiDDouo71tTXYto1SsQhN01Ct11Gr6fgX/zwL1yUAfGTzEd59l0BV/gaAf4l6owHXcXDhS19CLpuF73kxYZIkPP/88/ijP/oj3LxxA2ajgfzsrDgHVZbhsjJCtNogj8mTjRACmRG5TsZIPHIT8uNIRhgSQtDz584hl8vh4sWLMC0Lr732WpOdsyRJyBgGMoaBUhDAtm00TBPry8uobGxgbWUFxXIZExMTmJyc7FpemiLFo0JKDlJ8IRBFESzLgs2a9fiWhcDzQAAxUBNCYNk21jY2YNk2XNeNJw22ggvDMJ4wFQXlUglGJtNkZTwoKOLV/EDTXY/JsZPeoBVRFMHzvPiHhbtVJvZTFAW2ZcG0LGG4pBoGCoUCVF2PSwgpxff+tQdV8xGEWUhS3CzK91U4zhkY2b8IVf0lnnn2WdErQWVaDU3TMD05iamJCayureGjjz7Cr3372+LYFEWB63kIEqWKu4HEe1T081pWsdHz9TwNk0xH8KckCUefegqGYeDdd9/Fz3/2M3zlq1/dThkkqi0URUGhUEA+n4+1LqaJeqWCaqWCzfV1LBcKKJVKmJycRKlUGuzEU6QYI1JykGJfIwxD0VAnYC2QoyCApmko5HIIadwMaXNrKy5PxHauXlNVaMw9MIwiFAsFyLKMQj4/EgFZP57/rRDVC12siFvBOy0mywolWW4qq+Nh8dWlJZH/9jwPPnMZlABkMxnk8nmYpomr1wJkcz6MDJArKpCIC99XoapZhKECgtdByLsIgkBcR05aAtZ18uVXXsGPfvQjXLp0CW+++aYQDvIW1lEUIaPrbc+Tp2H4ZwU0ayAo0HS+7Zo9dYIkSQDvCjkEuG5jemYGX/v61/H222/j7V/+Em9+85sxiUycj9BuECK8JybLZZimiSqrdKhubmJzfR35YhGHDh1CLpdLfRNSPHKk5CDFvkQQBGg0GrBtO7Y1bjQgI879+wDq9TpWbFtMitxLX2aTZjaTQSaTgaqqsG0bpmUBgCAIu0XIJp+k4BBomdxaHnNL4uTr+0WT+LFln/HDONzPOz5OTkwI8aPv+3A9L+6amM1CohSrSyF0jUJRXCi6hSB0oMgUllmE6+Zgm3l4bhQbLbEKjVacO38e77zzDh4uLmJtY2PbaplSmLYtjqtXJIS3p+YdF5N/c/Igc1dJTpIS13uHuJPbKgfBwNe5FcViEV/5ylfw05/8BJ9+9hmef/bZuPNmcruJclVOFAqFAgqFAhzHQZVpEizLguM4mJiYwPT0NDKZTEoSUjwypOQgxb5CEASo1+uw2eRi1WqwarXYs8DzREdEiRAokgRJlpHRdeiMEOhsgkpuz2IivhxLIwyM1om/DwU8afN4VNMAjz4I0SNrCEWjCEYmA0VVUa3VRFkhpRT5TAaVjQ006nVMTU8jk/XhuyYI1aHKKgpZFVFEEWkqKCUgkolMdgJeGEKPIjHxJ3H82DGETAuxtLiIM6dPixC9pqqxURFiT4J258C1AVxT0QmcLPBJv5VANGkGsE2kFGbCBAzXwpqjXC7j2eeewyeffIIDs7OYTegr2pacJoiCYRgxwfJ9rG9uYmNlBQHTKRSLRRSLRWSz2ZQkpNhzpOQgxb6A7/siUgDEVr+bKyvwbBuSokBigjNF06DrOgzDQCaTgaFp8UquDShzPqQAVEXZQRzaooUItEOvtsxtj6WPEHerYRLvRMh7MNAwRJiohGiXKzd0PXZEZMSAIC5rLJVKuLOwAJ81b3rjdQXv/qoI05SgqSE8TwaRfOiaD0W3oZBFKIYBVZJgNRpwXRe5bBa5XA5Zdh0//ewz2KYJRVHw/LPPbndvRJyL9zwP2WRXx9bryM5FdFlMdKjkvRH4dejkNMnPOxlpSD6OgO3qE+yM6PSL06dOYWV1FR988AH+/J/7c9DYNUjeC0lxIy+/BNufrmk4ODuLhmWhvrWFwHVFaaRhGMjn8ylJSLGnSMlBiscanueh0WjAcRwAgGVZqGxtwW00oCkKNF2HrqrIZDKx8HAAVzrTthGw1Wu+xesfQF9EoBWd/P17vq/TxAbmUZBoR+wzn4V+KyCSgkrHthH4PkqlUhzZYKvtAwcOQCIEqqZhY20NIAQHDyi4dfMMpHwdhBDUqkXoug1V0wDyf+LY0Snkczk4joOIUjQaDdRqNUiShFw2iw8+/FCo+7lYj3sRcBFoxK5/2+MmBGAiytYz5eWaNEEWeD+GZJtrbrwUdCBsvDqEN8pSVFUc20CEgRC8cuECfvTjH+ODixfx1a9+dcdLWsWN3IGTb1eSJBTzeRiahlq9jkalgjAMkc1mRcQsn8+nmoQUe4KUHKR4LBEEAarVKlzXFb0NuOhQAZDRtLhUrFSKJ5529fFd4Lqu6J/AmwEBuw/tDxo1EA6GSIjX2G/hsNghpw/EEyiRZfFbIgRSotySl+MB8eTjs1JNLriMogi2ZeHYsWNQWLvp9z/4ABMTE/hr/8vTWFyk+MlPCTY3CQCC2ZkIK2v/H2iai6NHX0Ihn8fM1BRMViViOw6iKILJjJVm5+fx7PPPwzRNYXpEEQsmQUgc6eDmRl2uU+tzgjQlykcpYrKRTCFwotAu8hCFIQilCKIIEavs4NepHVlIHkc7zYhhGHjlwgX88u23cevWLeEe2Qn8XqHsc+Q+GpqmoVwuo2GasGs1yJKEKIqQzWZRq9XQaDRSkpBi7EjJQYrHCpStQBuNhiAItm1DohQkCGCwtsSFYjH2INh+Y9/7CMNQCBAzhgGttdZ+l8ffC8nmSfxxQKmICHDHxXbv490feUli0omxn+OKEm6CjuPAdhwQQnD8xAnomoatzU1c+uAD/ON//I9x4sQJHDtu4ZVXAdux8cu3f4TV1VXcubsCGhl45tlnBXkr5HIo5HIx2XBd3Lp9G45lQVMUHH3qKSyvroJIErKGgXwuF5tPIU7tSEDXvhAdr2O7/7GJnEcoJEaYqCxDa3ONoiiC43nwPQ9+ECBkVRReC1lQVTW+5owstNOMAIhbPJ86hU8/+wzT09Molko9CSdBs78FT32UCgVYloXa5ibyxaLYv6qqqNVqsG0b5XK5yWMhRYpRISUHKR4beJ6HSqUCx3GwtbUF27ahKQrUKAKhFMVyGcVCYTt3OwgSK3ST9VNQFAVZ1oVvVEiSg9YOikkk+zB4ntfUnphDSpABlRkttVYg9DqWJhtnQkRDo2q1KpTzqizD0HUcPXIE62traDQauHL1Ko6fOIEgCLD14R8iWPg5zgcR3vk4AAFw4sQJnD1zBg3ThO/7qDcayOdykBl5u37tGpYWF3Hy1CkcmpuLq0qYhbVp2yINkM1kUMjldpaOErIdwmeVCP1MssJGOZkS4nbK2C5/5GWVkiRBV1WoLPoQUYqQfS5JsuC6Llz+uXCywD6b1jTEc889h/X1dbz3/vv41ptvQmbnRntERzh4RIEgLi9VFAWWaaJRqyFXKKDEjJN838fa2hry+TwK7HuRIsWokJKDFI8cURShVqthc3MTW1tbcQhaVWFIEhQAxYkJFPN5AP2tzJPg/vl8RWlZVlxjTymK7XQGQ4AiFrWJ9EDrIE3iDoiiKVMQCMtjYFujILNwtph0WK5d2PkO4HvA99v0Dkpj215ZBmXkKGMY8IIAb//iFzhx4kRcdri6iv/8n/4TlpeX8fLxEtR7F5GJXMgE+K3ngO+9r+O3fuu3oGoaCpIkojy1RgOFfB6yJOGjS5cQRRFeeO45TE9OAgBsx4Fl27BtG77vw3EcVNgKPZfNopDPI5/NCs1Iaxno9ml0nmRF6WKn65K4Jk33BpuQJUIgsdU5EH82ydROE1lgjaqSZEFlZOFLX/oSfvKTn+DTTz/Fiy+91LT/XucgzpO9TpFl5HK5uA9GrRaThHweE9PTUDVNCHVLpVLaLjrFyJCSgxSPFLZtY3FxERsbG7BtG7oso8iMiYrFInK5nFg59ksMmgb/+AEAZqvMvA/yudzuve05GUjqBthE09SVkU0orZAVBSrrvaCw32LVy+r1W8+hHTqVTfKJ0nPdWAtAt7tP5vP5OI1QqeCXb78NRVHw7W9/G199/XX83u/9HpYWF/HLt9/GaS+DGSMEAQUFQVEH/vff/qt46uhRQTAK+TwapokwDFGv1+G6Lhbu3YMky3j5wgWhzudOlZiYgOt5kFZWYDsOFEmC57pYdRxsyDLKxeKODpid/Bt29EDo/Gm1BxN7thI6CpbySJhlAQmy4PsxWWACyHZk4fz58/jk009xYHYWc4cO7SynHOAYJaZFkCQpjr7U6zDrdeQKBRQnJmBkMtjc3EQmk0FxBG3FU6RIyUGKRwLf93Hv3j2srq7C8zwoUYSCrqOQz6NYKMAwjO2SPfQgBokJNZnHTyKKIjRMExQQHRiHQutqnP2P+yzwVXG7402K3BRZBmFWvqKNMdt2P4QA2E4bdPJT8NjxhAlS4DoOPNeFrmlYWlnBu+++i1KxiK9+9atxh8FcDv/8n/9z/OmPfoQHl9/BZKYCiTaLIafqn4CQ3xATs8wsghuNBoIwxMUPP4xbXBeLOH7s2Pa5JEL6uqZholxGIQigqioC30edEYyNrS1sVSooMZLQmnJoJQrCJZGtxqPW1/RAu88qmYpJmigNQhampqYwMz2N9y9exBuZTGxPzfUB7T6zLvc4LzkFpcjlcrDZ59io1+HZNoxsFlomE9+Hriv8EVKkGBYpOUix57h37x7u37+P0PNAoghZTcPk1BQmJybEAMjRNHkmkaz5T2oQOkyUNuuySAiJoxF9gLKQM0nsr/V5Pwjgspp0AKKjIiEkJgKJn3ZGPHwf208MkDpoR1SwLbjkokaJkLi3BOKOiABwZ2EBly5dwvzcHL70pS81rTQNXcdvfOc7uImrcNYrkFvIgbt8FfbSFRhz58R1kSQJxUIBDdPE1cuXkc3l8NKFCzuOV1y7KIIsywiCQEQfSuUy6vU66o0GfN/HVq2GrUoFhUIBE6whVMdrAYiJXMJ22WA/efiOZaStVSRs+8mUQC+y8PS5c3jv3Xfx2eef49lnn401Dqyh147IVY+KG4KYiNEgQJYZdlmWBcfzQJh3Rb1SQZZ11bQsCxP8O5UixYBIyUGKPYNt27h+/TqqW1uA78PQNEzPzmJyYkK45CXD76JBTjJPmyAC/QqwuII+AlDoYzWVJBrt8t5BEMBlufLkxCIzYR+RpPh8kpMhm1B2hK/7nMDYi3uGph3HgWnbIqJgMD//ZI8Cy7Jw6dIlnDxxAi+8+GLTdvjK3nx4Gc76nfi8sLN51NaH38f83D9prjJgJOH69euQZBnnzp2DZdvI8oZEyWNONJCKEvn+UrGIQqEAi/Ue8HwfpmmiXq8jl81iokdePXmN+b5ol0m371RVYpvJzysCSyvx02ohCwVKce7sWXz0ySewLQuZbDZuDmbbolFVsm14a8qkNXLBIwi8SRgoFToOICZ2TqOB6uYmiuUyfN/H1NRU2vkxxcBIyUGKPcHq6ipu3ryJwLYhA5g5cAAHZ2fFBCEiBAzcTCipuG+qUhhAme24LkApZJYL7oiWSSS5B5FX9rwdrnd8JchXaEFLJ8Zu1RV9EYNk2qQDuLeAH8TVBJqiIJvLNdXo83MzGw089+yzOH3mTFv/ABCCzY/+CAB2RA04RPTg4Fl+IgCATz75BI1GA+VSCSdOnBAGSfkWUkawbS0ctng4SEwTkc/nYdk2avW6KLs0TROGYWCiXEauA9HjFQtJ/4jWz5Y/GsbNsulY0RJVaNEvSITgxIkTuH79OpYWF/Hc88/HHSmDAL7vw/d9SJIETdOa7iF2Is2kjJ2DRAggSQijuLcFpVSIPXlDMVVVUa9UYLK22gcOHtzuGpkiRR9IyUGKscLzPNy9excrS0ugngdDVXH0yBHkWfUBAOFit/0n3V5pt9SUD4ooimCzbozZ1hVnB/1A8jh4vXurCREfzLnXQPI9kixvVyN0m/y7rFqbyvF6EAjP80T7ZQDI5XJtex2srq2BRhFKpRLOnDnTcXvO8hU0Vu8ARIGM9uQAYNGDv/RP4uNl/7t8+TKy2Syee+45lFiawXNd2ITsmJxkWd5eGXdANpNBNpOB63moVquwmKZjaWUFqqpiolxuqnAAmlfyTUhGXVhUKgjDrj0w+gFpISG8CoIfhSxJOHP6ND759FM8c/48ioUCwjCMm10xsuk4DhzHgcpcP7VkNCF57JwgsCZalFIYhoGIUniuC8uyQLJZaJqGXDYLy3HwYGEBZq2Gw8eOpW2hU/SNlBykGBs2Nzdx9+5dNCoVkCjCZLGI+fn52H6Xg1KhBQDQMY8+LFzXjVdziCf0frwBkmmDJFRFEWLGbpEAAgBs8O61r3b/410keyGicTtq1/NiDwNFQT6XE3bDBBBdCm/cuoXV1VUhyOxY7kcIti59HyEkUApIoQ8KipBGAGXHxDZuL30Oa/FzGHPnxXv/zt/5O/g7v/3bYjLLIvaVsBwHRJKgG4ZwQySSBEpI3ByKX7sO10zXNMzOzMD3fdTqddRNE1EUYXV9vW2Fg4gedABFTBxl5tiIATQK3UBaJnF+HY4dP46r167h+o0beOHFFyHLctwZ1DBEV0yf6RT8IIDF/Bc01gujZScAYnIVhCFAaZy6YaJY07JizYuqIpvJwHYcbG5swLQsHH3qKRyYm9v1eab44iMlBylGjiAI8ODBA6ytrsKp16EpCmYPHMDUxERsm8tB4857onSP/Tvs0yymF3i4lSJegXYbEMVKznV3+N/rrJnTIKWPkiQ1eRm0Pb6WY22tPODhalC63YqYPeezltX8WA3WbIqwyVZsn1I8ePgQH3/4IWZmZnD9+vX2x8Le4yxfhbl4DVQuxOeBuPeBhDi/DiCRbyHY/PAPMc/IQdNkzB7rmoYoDEVKACzsLUyNoqhJ5JckVK2fFwGgahqmJidRKpXi/gONRtsKB1lRukYkaKJRk0g7sHtwUC+NTkgev6aqOHXqFK5cvYqzTz8NnUVRCCGCcIZRBC+RunJcF47rQlEU6G1IKSEEMksvAECGVSt4vo+GaaKQz8dGXwnx4q1r11CrVnHq6ad3X8qb4guNlBykGCkqlQoePnwoOsuV8nlMT02hWCjsEFuFbEVPxkAM+CoqYivxdh0XoygSEYKkQyEhRAzGO5z70L+IUJblOJ/e7rUJX31+DURJXsu++Pnwyd6ybbiOAxAiHAnbHScArK+t4f3338fRp57CufPncWB2FtMzM21fSwhB5cPvg5KYwMk06PlZuMtXYC9dRmbufMfrkslkhGbDbDQgsfJEQkgcPWCdJdGSZmidpJtKCiUJpVIJpWIxbviUqHDYrFRQZCWxWofPPWyjNdghPh0RSeA4efIkrl+/jlu3b+OZZ54RpI9DlqS4k6hhxM6Zrgsv4ZVh2XZTOguINQ3iTCQJuVwOlJlS1RsNFAsFyLIsqiNM08Ty4iLqtRqePn8e+UJhpOeY4osDQkdFk1M80QiCAIuLi9ja3IRVrYJQiqmJCZRKpbb11iHL9bYq5ZtSDAOitaVxpVqFz8q+uMKdUhqHcV13h45AVVXoug61RUeQPL5Bj4yfE9v5tniNV2K0KZHshCAIYJqmaC5kMFOhTterVqvhrbfewuTkJF5//fWuK0VKKdyVa1j+4T+HK2XgEx0qdaFHsQo+ogEi2n4/+sFzQnvQbfumacLzfRBCYidFWUatVkMYhsjn823FolGfZJGyFEu1XofveQijCL7vI5fPo1QoxN06CUHIDKqEO2If1z5JSnaLTz/7DLdv3cKv/cW/CJWXtyYiQq3gBNb1vKZIlCzL0HU9rkKgtElYmRSnSoQIW2sgvhcbLCWjKApOnjmDA3NzIzm3FF8spJGDFLtGrVbDgwcP4FsWXMtClrkbFvP5OMecAGUTotxu8h0y59vkR8De77qumAR0XYfv+/DYIJuEwnQEei89Qpd8OH++3QRCEDf/2UF6+Gv7rFZwHCcuVyNx18VcNtu18sKybfzi7beRy+XwlS9/uXsImV336mf/AwAQgUcOuqdFONzlK/A2FqBNHev4Gu4vETUaCHjYOxFN6nRlpR7agdbtc4OgWq0WewA4DkzLijt4FovimiUjMq2Cwk7/b/U4GAanTp3CzZs3cefWLZx5+ummEkVg53WQJEk4S3Jtguf7CMMQlmXBtu3YXIs1ZeLvyedyqNXrsfcBiyBIrHV3IZ+PfTCCANevXEGjWsWREyfScscUTUjJQYqhEUURHj58iM31dSAIQIMA5VJJOO01EQM+2HaqN2fbG4QcNJECoGmitW07VnXLMmr1elPagOsINF1vLvVr3XaXY9kRRegygUkAIMuIWAdCIJG/74EwCOJ+ECxaoGkastlsV4W95/v45S9+AYkQvPHGG2LS6HguLNoSNNbiSAdhIesOZYzt4NfXupIDIJ7A87kc6vU6QtaGm59Ft5LCduZD3cAnU9txUK3XYZsmbNtG3TSRz+UwUSo1pWE4UWiNEHBbbIJt/Qe/J4YlCRnDwLGnnsLNmzdx8tSpHQZFQkjZJqKkshLFKIrgsehXGIYx8fV9EMdBJpMRka9CPo96o4GIRQty2SxkWRbkoc70GisrK7BtG/NHjmByenqIs0rxRUSqSEkxFBqNBq5du4bN1VXAdZHVdUEMDMPYNqqh28ZFXdXjg0QN+GqLT+wt7/M9D7bjCKc9Tgx0TUMhn0e5VEImk2lLDCjb3o5jaTn2ficG/i4JcU5ZCAz7WA27joNavS4iIPlcLu4J0eU6RVGEX73zDhzHwRtvvNGzEU+S5BTP/nlEbL1AQCH1SWGU0hwy88/29VpJkpBnzZnCIBCCUdqFHIAd46Alh4ZhYHpyEjOzs3GkRZJgWxYeLi2hVq/3fD8nJLxkMIoiRFwfgZhU8dcMgtNnzsDzfSwsLLTZKW12v2yzbUmSYOg6SsUiioVCLJYFSxk0GqLPhSRJIn0TRREsy9omWYQgl82CSBKCIECjXseDhQUs3LgBz3V37DPFk4dUc5BiIERRhKWlJayvrYH6PhQA01NT8H0fURRBVVUhPiSJVReNoq6r66jHhNmkJ+gySfieh5W1NbieB01VRV7e6JSbT6wEkdzHLrHDhCeBiNIdeoem51nImL9GYSWKvdTllFK89/77WF5cxNe+/nVMTU0NfNz15Tuort6FIgF5Q4GzdguNy38qNAfEKGLqS/+reL2sZWHMnYOkZprOu9c1DMIQtVoNrusiiiKUy+UmJ8Vu50jQX/+EkK2w+efOW4F7QYAgiqCrKibL5V13MqTYTn+0ujN2wvvvv4+V1VX8hb/wF3qTYkLaW4gnELFITDJtxok6pRT1RgOUfT+zuZyoyghYVAHMLyFjGJBlGfNHj6LMummmeDKRphVS9I0oinD79m1YtRrgeSjm85icnESj0YhrxmUZ+Xx+xwApJt5u2+4QphWpgx4DqO95sGwbDisFA4BioYBcLtfxvUky0ot0DAIRfejwPC9Bo1HUZA8NxIZGVsLQKJvNtjU02rlTik8+/RQPHz7EV7785b6IgSjlS+xfKswiq8cTZjaTAZE1NC7/6fbzSgaFU2903Ga/0R+F5b49Vt9vW1Zf5KDp3upwT0V8ld8SjTIMAwcOHEC9Xke1XkfAzJQK+TzKExNQhiztS5Y/0gTJbXXGTF6ZM08/LXqMHD16tPsO+Hl0ES/yVIGu67Adp0mfoOs6ctks6kwQqvl+rL0gcf+PjGHAtm04jgOZuTXev3MH1a0tHHrqqY6VMCm+2Eg/9RR9IQgC3LlzB1a1CimKMDs7i3w+H+ePWdi7WChsh84T4CZEndCuCkCsQPskBQFbZfOOg9x+N7mPHfsbUZSgaR+9hItAU1pEBoTxkm3bsfESIVAUReSI+8H1mzdx6+ZNvPzSS5ifn+/7mFuvL7+OO4x3BkQ/aSJVVZHP5eAya2THdfsjQtg2eGI7E/sMacJts03unpdA5nM5bFYqsC0Lpm3Dsu24S2TSuXNINPVeSJasEiLyuMViEXPz87h67RqOHDnSH6lKkjlOQlp9D2QZ+VxOlD6GYQjHcSCxXhY0DGHZNoqJihxD10GZr4Jp25AkCYqioFapwLZtHDt5EkZqvfzEIdUcpOiJIAhw59YtOIwYzB08iHw+LyYzTgzaWQlHPYgBf10TWP17t34Cge+jVqvFOXnmJaDpOoxMJhbtZTJxOgM7FeAk8TMK0MRqricxQJv6fVaGxzsmGoYhcsX94P79+/js009x7uxZHD9xYqBjTyJZ/7/b1WK/EQRd16Gz0LeduAZ97YP98HLRIAybtAvdelrIioKZ6WnMzM5CZ1bF61tbWFxe3lHRshuIviBAXHLIf6IIp06dQqNWw/r6+mAbTUYmWv7mUBQljpwxa+koioQZlc+0HklkMhlRydFIRK5818Xtq1dRq9WGOPsU+xkpOUjRFUEQ4NaNG3BrNYARA8MwQKMItm2LJjntyqD6rQ+P+OTahQyI42GkoFqrwWf5ZMMwUC6VhEpbUdUmJ8bW9MFYogVDbjcIgriagtWdF0ulWCjW5+S6srqKDy5exLFjx3D+/PkBDnznyp4LN+VEx8RxQ1SOsPvHZCLSXqCA6I0QhWFXN8RuyBgGDh44gHKhAFWWEfg+FpeXsbG5ueumTAIJ/U0Sk1NTyGSzePDwYSx0HFL+1VpFkYSmaSgWCsgYBiTWeMyyLFSqVbgtwsNcNivSXUnyEEYR7t64gY3V1aGOL8X+REoOUnQEJwZBvQ5KqSAGoLEtMUG8AmsXCm7tstgJlBGCXpNhO1Kg6zpKpRJyzOSFt1DWWkr3yC4m747Hje30xKDb5ZNO4Puo1+uIwhCyJKGYz4uGO5IkiR4LnaaMSqWCd3/1KxyYncVLL700kGaCtnltkBBA7hX4566pakwQCIHJ1PbtQGnsrBkEQWwKlPAJGNY8S5IklMplzB04IKoaGqaJh0tLaDQaQ22zLfh9ntBNzM/NYWlxUaQJkhURA1GFZFXQjt3GBJprcFRVRRAEWGP9Fvj9SAhBhokzW7uPAsDDe/eweP/+cOeeYt8hJQcp2sLzPNy6fj0mBoTg0Nxck8ugy1YWnURkverAkyvubiVqfhCgniAFSJCCfCL0HjFHPIrYf79p0hjs1HuCJgb3oUAIXNdFvV4HBaCoKgqFQnPfCfY6Ll5sbcZkmSZ+8fbbKBQKeO211wZa6XdyehSRg0dADgiJuzYqigJKqRC58lLCMIrghyFCljpod/yCILTk4fuFqqqYmZnB9PR03JyKUqxtbmJpZWVHE67dgB8nBTA3Pw/btlGpVptewyt8BFnoM6ogIhRtSoclSUI2k8HM1JTwS6g3GqjV63FJKaVQVTUmh5TGrc7RLFzdWF3FnRs3drTZTvHFQ0oOUuyA53m4ff06/EYDlBDMHzwoOikSQIQcFb7aa0G36oR2Sv52wzcPt1erVbgJUlBuIQXimBkxkNlkOmqxIT92ilhXsJtt27Ydt1gmRHgv9JzcGTng+eO333kHqqLgq1/96sAr/U7HHnBysEsxIkdSi9HxWJi+hIPnyIMwjK2QWYSARlFfeg6CeFDbzeeTzWYxd+BA7KgoSfB9Hw+Xl7GxtTW6VANiUjwzPQ1V07C0tNT1tX1HFdi9SVgkod3rVFXF1OQkctksgiAQosVavQ7X80Qk0GU9R1rNy+q1Gm5eu7YjLZHii4WUHKRoguM4WLh2DYFlAYwYcCdBiZDY651HDdr0TOCiq3bgim0ATau75KuDIEC9XkelWhViR2740o4UcHieJ6IGj1MKoXU79UYjJlesrrxbqWUnfPbpp7BNE1/96ldFmoe2/HQ8hg7Ph2EoJr7dVipwtMuzdzqeKIrgBwEopfF9RQgC3xer16H2TUhXotoNkiRholzG3NwcMroepxoaDTxcWoJpWUMdU9v9yDLmDh7E4uJi3+9JRhXChN6i9XPlRKndc7zTaJ7df5x0WpYlUoZN0QNsf08JANe2cevKFZh9mEml2J9IyUEKAcuycO/6dXi2DSJJODw/D13XmwZ4iw2MqqbFjWNaEGGnYl8MKu0mQbYqSZICrhZPkoJuq2PeTAmUQh+TP/xuyUZEabwyc12AUuRyub7q+lvx8OFD3Lp1Cy+88AKKxSI7OCImQ9KGdHFXvHa+BhzJqMGwuftOSJIWXhHBqwt4dUTENSqE9Y5gLbYd2+5qGNUNBLuPgqiqigMHDmBqagoaS3msrq9jeXUV3ohC64fm51Gv12Hb9sDCSkJIM1FoQ4R4GqP1c81mMuI5XdeRYdecfza248BxHOHQKXxL2HvCMMTt69dRq1QGP+kUjz1ScpACQBwxuH/zJjzHgSTLcSqBieP4oBIEgci9tpvYKKWiFTH/m7aIsFoRhiHqptlECpLpg66kgP34vi/q6kclpqMYgbaAIYgi1LiQEkCBWd4OCss0cfHiRRw6fBjHjh3r+LpWE6rk5CCsgPmEDVYKyK4hjxo0RSJAgYgCFPFj7iuw43UQ206W7HESEDJjotZ0Az/eZMRJZStb3mY4HFbJD+zUcgyBXC6Hubk5lAoFqJIEz3WxuLSErRGkGg4cPAhZlrG0uBgPyEOSM/75iuucfA4QKQcOWZZhcBLmutCYu6mu60J3YloWtiqVjtEoSinu3bkD2zSHOuYUjy9ScpAClmVh4cYN+I4DWVEwd/AgtDZdCnmOUdP1HZOwsEhO/N0rrOy4LqrVKvwWUlDoI1LADW4IIGrj1RFEDZrCp0NOSEkETFAZsIqEfKHQtZtix+OKIrz/wQdQFWXgyoTtjVAh/iSJ/4GVBALxhLFjIqAEFAQRjRBF25M+ZUI58cOFc8kfoKeeQpThtfw/k8mI47F2Mfl0UvEPCkmSMDExgQMHDyJjGFAIQbVex+Ly8g7fgEGgKApmZmawuLTUpJVpV1HSL5JRmlbywgWLQJxekGVZVCBx0WIxn0chlwMQa2SqieZlrUcVhSEWbt0S3+MUXwyk5OAJh2VZ8RfbtiHLMg4dPCjK6VrBw7utpYLANjEQgsNu0YIoQq1ej/vKUwpFVfsiBcntJ8sffV7CuEtykMypjiKw7vq+8DBQmSnNsGHuK1euYH19Ha++9trQ59ltcuTh/VGJEXfuvPPexWTYmjMnRGgyAt+HM+QEzEneoI2bOkHXNBw4cACTk5PQmep/eWUFWy0VB4Ngfn4eGxsbIjLH3RQHSfF00/rwyE0r8SWEiCggt7IG4vugUCggn8sBhMD3PNQbjR1VG3wBEPg+Fm7d6liCmmL/ISUHTzAsy8KtGzcQcmIwPw+lAzGglIrypVatAUVcSkhbCUGbwYpHC3hDnFwmE4dqe7UV7lCa6AdBPLER0lYD0Q9E+gOjIQVAnKZp1OuImO9CIZ9vUuUPgrW1NVy9cgXPnD+PqV00w+kUGo4Sq8txmB/18iAQz7U5PlmWkWWmUBbLfw+K5Ap8lGqKfD6PgwcOIJ/NQpVlVGo1LK+uIhgizTA3NwdQiuXl5R3P9RP54C6RvZCMJvD7XVHVWFtECCzbbrpPDF1HnglEKaUwLaup9wffNwiBbZp4cOdOv6ec4jFHSg6eUDQaDdy6cQPUdaEqCg7Pz3ddtfOoAZGkHe6DURjGdsdoCcUnBuUwilBPRgsUBaViUYighLK8BTxk3Wly4SsZTVWHGvhFpGMEKQQOk5UqAmxwZcRgmOPzXBfvv/8+pmdncebMmV0dV6dryCcV7r+/5+BphQ6fga7r0FhbYn7/DLT5ln31U0XRL2RFwfT0NCYmJqASAs91sbS0NHCUwzAMTExOdq1a6Bb5GKjlObajCQEzksoYBgirWEimSGTmOso7PAJxiWO90dhOMzBRMSEElUoFSw8e9H0cKR5fpOTgCYTnebhz6xYiz4OmaXHEoMeqO+B5/cQKP+J5/+Rg22aAcjxP+BUkowXJkrnW1WVTv4Iugx4XIw6Vx0/sexTgpYp8YshkMk2ligPTD0px8dIlhGGIV155ZejIQ7ypznsfe0oB/UUOuh1jNpOBJMugrNxuBAfUkZAOg0KhgAMHDkDVNESUYml1FdUB+xEcOnQIq6urXSMAnfpFDCuKJKw8mVKKDBPJOqyNNrBd1hpGUUx0czkQSYqFxB3SDOsrK9hYWxvqeFI8PkjJwROGKIpw9+5dUM+DoSg4PDfX16TgJ1IKwm4VvfPY9Xo9drtrEy1oResk2iscHYYhgiCI/Q0GJAejJga8VNHzPIBS5PN5ZHbZye7WrVtYXFzEK6+8sqtt9TIjSvZUeBTohzwRSRJEy2PtiEcBSZJGRhB0XcfBmRnkMxmokoTNSgWra2t9T9zz8/MIwxCrffQwEJqePrwt+oVwR0RMEEApZFmOo0mUIgxDqKqKItMGtUsz8O/T4v37qKfNmvY1UnLwhGFlZQVurQaJUhyYmekrjMxbClPEq0tu5dttJdsaLci2iRZ02lcvUsDBVy2qqvYtNhu16BCIPQKS9s6FQqG9aHCAAbxSqeDTTz/FqZMncfDgwV0fY7dz5VqScdsmd/pMhSCxxySqKIoovTNNs2/9AS/j6wQ++Y0CMqs8KJVKUCUJtuNgcXm5L/vlfD6PYrHY0y2RgyAmTaMiNwDEfeu6Lnzmm8AXD7z3hiRJyOdyHdMMAABKcf/2bdgjNIxKsbdIycEThEajgc3lZdAwxPTUFLQ+a+2DIACYgEnTNEEK2q2IOkULsh2iBRy89HGQnDdfpbernui0j1HDZ+ZNYRhCluXYcneIFEcSYRDg/ffeQ6FYxLPPPTeiI+2yvxE7I3ZCp09/kFy5oeui+6ZlWX1/pr32QSRppPdHqVTC7OwsNEVBFIZYXFlBvY8mTnNzc1haWup7wue+EhIhIyE4qqJAYumWgDlWyuza+InJnzdp6pZm4CZJI0kDpdhzpOTgCUEQBFhaWAANQ+Sy2W13vS7gAxQFgDZCxNbBaJhoAQ9585V8a4OhTuB2u1GfeoNRGRol4fk+6rWaKFUs7aJUMYmPPv4YlmXh1Vdf3bVAsFfIOUw09dkLMWJHl0z0jhzw9+dyOUiyjDAMYdt2vzvu+ZJRlTpyGKwddMYwIBOC9c1NrG1sdE0zzM3NwfN9VPpwHeQdKvlRS5K0a3dL7pYIQprKKsF8LJL3C4D2aYZExUMQBLh59SqsUXa3TLEnSMnBE4KlhQWErguZxM1euqFVCMhz0U3lS4nHu4kWJE1fOPoZ4JIK+265ctEXge6uWVIr/CCISxURR1MKhUJPwWA/q8H79+9jYWEBL7z0EgqFwkiOtatug6cUxmCb3C/4det33StJEnKsvNFxnL5sjPs9t1FfAZ5mKLImTqZpdrVeniiXITHVfy906hux289RU1WhMeDRg+R2uQMjx440g+uKNINEYnvnG1evjrb9dYqxIyUHX3BQSrHx4AGcRgN+GOLA7GzH1W0yH58cEFrV5DTxeGhtQWJfreARhG7g+eZe9sqd9rEb8D4QnBjk+2ye1IscmKaJS5cu4eiRI3jqyJERHW13cJI17pQCR6fPGxgs7aOqKgxem78Le+WdBzP6bp68idP09DQ0RYmjeB0aOEmyjEI+35MccJfKVvAI3G4qWyRJgs4cUl3W0AzYNjziEz5v1sXLKDulGXjDtltXrqCRNmraN0jJwRcYURTB2trC1vo6XN/HZLks2H0SSctgYLtmWnj0t5YYsvDiUNGCljRCJ/SqRQ/7IAfosY9hEIQhauycNVXtmxiA0q6h7SiK8O6770LXdbz44otD++s37RK9CQnXG4yi/0C/aL1e/ZQytoORyUBVFFDEfSe6VjsMdoBjiaJks1kcOHAABpt4V9fX27aBnpic7EoOuLdINxCmQxj2LHjvD4+1bd65g+1SUGGixVJ87dIMkiQhjCLcunoV9V04SabYO6Tk4AuKKIoQNBpYW1pCEIbQNQ0TExNNr0kOxnyyFj0REoNjMhcdRZFwORwqWjDAgNVt9SOU0y37bPJH6HM//SJghChiGoN8Pt/3JNJr2rt8+TIq1Sq+9OqrUHYpaEyi1/E9qjLG1nuP/XMggkAIQTaXE/a9bhfjoWHiCqPox9AKVVUxOzuLQi4HVZJQr9djV8VEmqFUKqFWq3VtdtQvuhmMdYMsy3GqSZJE2WjyXuKP+DXi+ocoikAI2ZFmaDQasTtjEODWtWuopQThsUdKDr6AiKIIoWlic20tZv6UYnZmpuk1NLGSTQ7OncoIuVlKrV5HfcBoATBciJ+gvUiOsnxoRGkTIRmUfAyCMIqE+FBRlNgOeYDVZTcHxpWVFVy/dg3PnD+PiV3YI+9AjwmBX0dg/GWMSbTeY00kcIhJLJe0Vx5RG2UOaYhj6rlNScLU1BQmJyehKAoC329q3lQulxExItqKdo2UeoFgOPKXjB50c2BMkigeSQCwwzTJtix4QRCnGK5dQzVt9fxYY+9GhBR7Ak4MzFoN9XodXhhidmpKKPqTX3KR6+VphB4r9YZpIpvJQFYUZAwjtlztRQoYCRl2wuYEITkg8r71EiHbYklu4TrkfrohojQuV2Q138P0Seg0vXiuiw/efx+zs7M4c/r0ro9V6EKiCNH2P7cjKonVeRAEcY8LxE6THhO4JbUlthfAkTKIECKKKCToMC2r+R7in2+bVFSSCIh7hf/m90aLoc+gn6Gm6/CDAJ7romFZKBYKOzQrQ98XfOXN+neMEvl8HqqmxQ2XfB/Lq6sol0ool0oghKBaqTRVFYWsE+awGDR9I8oaowhBEHT1qWiNTgiHRUVBMZ+HaVkIggCu6yKMImR0HbevX8fx06dRbolopng8kJKDLxCiKELYaMB3HGxubsIPAhTzeeTzefGa1oG6VV/QDpZtw06UJ5UKhZ65fmB0K3lOECjrKpdsL8z3M8reCElwYsBbLhcLheFK/jrUoX/y6aeIKMUrr7zSdvLhgi/xm+WbRbMrphxvLVlsmgBa9Q7sb491OpRluWMtuhuECKAgZKtDAkW07m46PbQIWhOPgWZyRABEiAkMv++SSnZFUeI+D4ywcv8LIklxp8I2JXvZTAZBECAMQziOIzoNjgqEEETYBcnoAF3TcPDAAWxsbsK2LFRqNbiui4xhoFKtgstSo10SAyBx7CwK2NP7gcQ9FeqmKRql9XhDk5gZiAkNry5xXRe268J1HBDEkQVOEEYaMUsxEqTk4AsCTgwi3xetXxVFweTkpBAAtoICXRsCUUphmiYc140HbFmGYRj9E4MO+x0GBAAkCWB5SyDWG3Q6t1GA90oIggCSJKEwLDEAmogBn+jX1tZwd2EBzz3/PMIogmlZTRN+MlrSbpLl5y4G4wQJECtwPsHyx0ktie9DlmXoqhqXryUiAHyfVJWgRjbkKERIARkudMPYPp9kpCGh90geE49YtL6GT1Jgq86QGe/0gyRR4ERCkiTYrguPfV6qqsakgl+/HqLQ7juMWyj3M6kOCkmSMDM9jVqthkqlAtd1oWYy2NzaAtDcNXMU4GmGfhpYyayfBU34KXTbLsCIFE9RYtu/wjAMSLKMer0Ox3Hifg6GgTs3boCeOoXJqaldnFWKUSMlB18AcPEhggC1eh2O6yKkFHOzs51V/5R2fo5ts95oiP7uxVIJtm0L46FOpYa7TSN0AycIAUsrKIoyfmLAzr+Qz/dtcMSrObgAK2Rh2WS+mEYRPvzoIxSKRUxOTcVe9mgz4QMi5SMlf7PJUEqsrPlrgeb0USfUCYGsKMhlsyK/3IpIUaDCQ0RDSBGFDB+ZNhUvw4CTICAujwvCELlMBpKiiAmJR0Ui/pib8FAar+RbJs0wCOD7PnzXFWJFIcpDPClKsix+Szyl0SckPvGNoZqhWCxC13Wsr6+jkMvhwcOHqFaryOVyI98XAOGE2I0iBGEIhfVT8Xy/b/dPnmZIXiUu5M1ks7H+gAkdM4aBhZs3QaMIUy3aqBSPDik52OeIoghBvQ6EYVxFUKnADQJMT05C0zSxMuPoR18QhqEIpYMQFPJ5qKoqypo8z4PRZjIZJzFo2k8UAVE0ttp8CsBMEKNChzRKxGq9wzCMJ/4gQNAh/BsGgdBFgBDcv38fjUYDX/nyl6Fpmljhtk74vVI+nY6/n3cII6k9LGNsArtX+HnLjPD1moB4VIXrKpJEIscqAPh9qijKdrg7irAjLiFJkAmJCQNrMiT6h7T7jhAi6vbHQRB0XcfBAwdQq9WwcPcuFldWcGBmBsURGWK1gi8Qwg7n4/t+3GyNUvieh8gw+oqetdMhAPEYoWsaaBTFBlYJgnD39m1QSjE9OzuKU0uxS6TkYB8jSQzCKMLmxgb8MEQ+k0GpVBLRAQ5Kadc0AhCL1GqsXE9iOXZFURCyckjLttuSg3FWCiQRsgZQEu8gNwatgWmacH0foFSUK3qeJ6IAISMFbffNfRwIgSLLYpUKbIfAHcfBnTt3cPrUKczPz4/8+Pu5Jsm0xThbNXeDuDeTWok+3iexyRwdjlvXNFhMNMn1NhH73IIgQBSGCLlXQBgiJARhFMVkMBmxYZ/djmgD0z/QMREEIkk4cvgwPvnkEzi2ja1qFZRSlPqwPB8W7bpTBmxc4RqQMIri7/4gkaM2OgQAUFQVOgDHtuGxqFnGMHCPEYSZAwd2eUYpdouUHOxTJIkBAGxtbcHxPBAS2yNz0RdHP8TAdV3UTRNgJYIF1iuAf7E1Rg6SqYVxeQq0A0VzkyA+oHWykR0EfNJvNBqwLAtREMDIZDpavvIIDLdvlhNEoJ0VcZiIJnz66adQVRXnzp3b1THvBlHC32DUPQWGwSiPQNc0uIzMua6LbDYb1+1TCjURAeKiziiKEIUhAvab/4+EIWgYxtGG5DUiBDJP8bD7UGGPd0MW+L0cRRH0TAaGriMKAsiShEqthohSTJRKQ2+/G8RKH9sTuZ/oeqoqCkzbhut50JkzZb/bjR80pxkI2y6lFI7jiLRaxjBw/84dRFGEA3Nzozq9FEMgJQf7EFEYxhoDNsD7vh+3sI0izB84sF2znhCF9XIctB0HpmkCiL+0hXxehA/5YKHIclyXzQZdvoLYK2IAbJsf8dVua2Sk322FQYCA/fis9tp1XTis1jyTyQjy0RoFkFsiAoNgeXkZDx48wJdefXXX3Rvbod9rwKMGe9FsqRsEieVaiVFskxBkDQN1JqbVNK1tWogL82RJAhQFyVgYrwoJE+RBaEaiCCEhQBSB+n6T1bisKJBlWXxX+r2+yYoUfmylchmO46BULKLKSpOjKMLUGEv/uCCVUgqPpdU4OZAcRzQ867cTarvtEkBEXjRNAwXgOo6ogskYBh7evQtQigPjiKyl6AspOdhnEOLDhKVppVpFGEXIZjLIZrMAtgcbHgLtBG5xyidFQ9eRS1gCt5bI6araRA72khgALK1Am82Pmurk2+X7owgBayLDy914tIGyQd7zvDhHLcvI5fPxarNDFGCoc2Cfx8cffYTZmRkcOnx419vcDVrLQR8ZCImbYrVJMewGqqqKCIJl27E3BfonHxIhkBRlxwDZLtoQJsSm1Pdjt0Z2P0qSJIgCJw6t91OnaoRyuYx79+6hVCyCEIJKtQrTskCjCJMTE2MjdgQQDZcIIFpkq6oK13URDEEO+Ha5DkHCdmRT1zQgiuB4XjNBuHcPAFKC8IiQkoN9htA0BTGgiG1jbctCEEU4WC6L11FK4zBnl21RVsPPVwjZbHZnfXjLQMZTC2EYxgShg8p9FEi6OHLwSoV2jn6cJPhBgMD3EYQhfN/fHnj5ag/xillRVSiyLHzhNVVFNpsdLKfaJwghuH7tGkzTxFe++tWx5KoHmVZF5OBRkwO0RH9GuF0jk4Hv+wiDAJ7nQdW0XW+zU7SBAqKLYRgEMRmNIlCWpuDfsWR0gZPPTiiVy7CvXYPrecLYabNSgeU4iDY3MT05ORaCQCmFZdsxMUikEBRFget5u3eh5CLbBCHSmaGa3RpBuH8fmVwOxTGlU1J0RkoO9hFC2wZlgwxXpNfqdQRRhKxhbE9qtLfL3I6KhFyubTlbciXOCUc2m4XFGqporJZ81GhHDHg5G5AwQGJhTh4VCMJQEIBkmFaWZaiKAoX98Pe7rhsbABECI3kNR4xGo4GrV6/izNNPj6wV8w4MsOp+XNIKOzBCganMPlPLtmE7Tl/+HMOCkwZJ0wBGQmgUbUcWwhAB1zN4Hjxsfwa8j4FIRTBSXy6XAUJQq1YxMzMTi2MlKTZMcl2sbWxgZmpq5J+hw9IHkiQhyyZtmtBrcF3GsPvlEZzWSI6W0CAkCcLdmzfx9HPPQRsBuUvRP1JysE8Q+T5C2waw/YXyfR9moxFHDXgekpcTtikj4khWJBBWkaB2GDiTBjdceWwYBjy2gmhYFooJB8ZRgFc+tCJkq7KQmTNx5XnSfZALL9VkKLeNox4AeEyrAUKg6/rIXfWS+Oijj2BkMjh79uzY9jEI9rpVc1eMURCpa5q4Vx3HGRv5A3aW7hFJgipJ4rtFmcmTz6JaALZLYcMQXmI7PLKgyDK2trYww+r/c9ksCIDNzU24nofV9XXMTk+PjCAErCQaiF0nuehYRA9kGQHiMWRXkzUfT5I+C5IUfz6ENIkUAWDh5k2cOX9++P2lGBgpOdgHiKIIARMLchBCdkYNEhN4Ry9/z0O90YhD87KMYj7fsemOUC6zcH1SaZzL5VCt1eB7XqxgHhGr33HcTBjl+T7q9Tosy4pX/4nSK5kRAZHbbTfhUdrkCOcHARr1OijiFUuOaTXGgYcPH2J5ZQVf/cpXxpbjT7bC7gUeUeE54McBo9YcJLebzWRQazTgeh5kRelIhEe1P2CnMJR3LZQkCbqui3RE0iuD62JoFCGgFAHi79n6xgbmGw0oqgqVpb4kScL6+jp838fK2hoOzMzsmiBQSoWNtqZpQjCbrDhQFCVO1+2WHCTuuyZSRSl0tl9OEPiVXHrwAHOPWKvzJCElB/sAoWmKUDkQf5l8z2uOGvRhQOQ4DhodKhI6gmxb6SahyDIymQxsy4JpWbFV7S4nGn5+ERMI+r4P3/d3VCpomiZsnBXWVrYnSGx/SxGXaDVYZ0ld05p6T4waQRjiw48/xvzBg5gbc2lWv1c/aX702JADXhkzhm0rigJd1+E4DmzbhlIojE1I20rMk10K2+2Tm14lK1eCMBS6hWw2i4ZlxcSB9Y2QCIGiqpiYmMBWpYKANW2anZ7eVerEcV2EYQgiSW1dMHn5ocNEibtB0kKbV1NRJhDmPR0ANKUYlh4+RK5QSPUHe4THLOGYohWhbSPyPPGl4YN5U9RA13cSg5aVS8M0BTHQdb2vBkLdBjUgzgdy73WzJbIxKPwggGVZqNZq2KpUYFoWPFYmJrGwfy6bRbFQQLFQQCaTgaqqg3VHZAORZduIKIWmKGMlBgBw9coVeJ6H5194Yaz7GSQ0L3Ldj5HegBO3cZhaAfG9KhGCKAyF6c64wCMyIcvNDwpFlsX9ns/nETDTMVmSREml53nwgwCGrgtx8Mra2tCTdphMJ3RxQVSZeyTlRmBDouluTRAEAPE9wIi7YRhCh2DZNu7evClcFVOMF2nk4DFG5PsIbHvH6s73POFrcICJlnZMDby0j1I0WEgVQFO5YzfwgbrblEMA5HM5VOt1eAOmFyhizYTPSgjDpM0zq0bQVRWqpom8eIUJu4aOUFCKhmkK17dCoRDXW4/ARKkd6vU6bty4gbNnz47NH19ggOPnhkyPQ6WCANnufzAOSIQgw0ytLNuGoqojJ0c8DcdD5BIhCPsQB3eDYRhwmVeDpmnbugVWkSMpCorFIrYqFdTZuR2cnY1bq/fbC4RSmLYNUApVVbumC7jnh8+OY2RpskSEki+EuNUywFIMrJvj3Vu3cPoRGog9KUjJwWOKKIrgm2ZTlzyOGvOOzxoGMplM1+ZJtXpdrCYKuVzcUa8H+jXSAeKQrWEYcGwbDdOMQ6QdQpu8pMtnGgIkBlIQAk1RoLJcZ7uBm7KSw4GiBQnYjhO3ngWaUioiTwyIbnKjwKUPP0Qul8OZ06dHtMXRgK/4HqfIATB+My1d0+CoKnzWqnpUOhNOCnb0W+CprF0QT8MwRCWOkvAbUFUVNJOJG00FAQghwj59cXkZE6WSSL1pqtrRr4P7nIRsG/2IclVmhBaEITQ6XBOqnteEE/aWFINt21hdWUG+UEj1B2NGSg4eU4SmGXec6xA18KMIsxMTHQfUMAhQZSSCEBJXJPRhXDLMQJbNZBCGIXzPQ61eb6p+CMIwJgRt6qMJIWJFxI1WuiFiorthhFe+58G2LFAA+XYdFln0Rea5z11GEu7fv4/19XV87Y03IMtyk33yo8ZjWcbIPvtRtiZut49MJoOA+R7w+24Y8MhaUuTa7v7tJFDsF4augyAuuW3VExBAlOZmDAP5XA7LKytwPA8blUpMEDQtTqMw0q6yxlZ8ZW5aVtxTghDkmNCxFxRVBXGc+PvMXQ9HpV1JCp8TQsVWgnDn1q1UfzBmpOTgMURo24h8v+0XLhk1yHaIAoRhKIhBr4qEJJKCx3ZOg53AV+L1RgO+56FSqUDTdVEPnYQsy1A1bXs10+c+okTof9C0QhhFaDBiYBhGT5V1UttB2QQwyB5938cnn3yCI4cPY2Z2dmx5dI5Btk4p3Y4cPEZpBR4hG6dAklfoGLoOm+WwiwOKE1tTB+OGbhigrLSvV2pKVVXMz81hfWMDruuiwSp7ZGb0RT0PPtMvKbK87YIoSchns33becuSBEgSwFwiFda1ceSfXCJ6ADQTBMu2cePKFTz38sup/8GY8BgtHVIAzM/AcdoOkkmtwWQHf/UwilCt1+O8vSyjVCz2RwzYF5HvNxpi8NNUFQ6LHmxsbAjhEC+/KpdKKJVKQsg4yGAixJGSNFhdPKUwGw1EUQRFVZEb0MuAkLjJjjTAxPX5558jCAI89/zzA+1rGAwq4hPXkZDHKnKQLJcb9z50Ju6jUQSX2YZ3gkgZsFLEpLFW3/vdBenhFuVOnyJKWZYxPTUVk2BVRcM0Y31NLhdPopKEKIpQbzRQazTQsKzYvGmAe4HrDgghIhqYbMLWD3peQ0KANv4kOltYALFt/O3r1wfYa4pB8PiMDina+hkkwaMGGcNoW2oUMTtkyuqpy6VSX196HhYcJgQahCFMy4orDEwTOmulzLs5FgoFFAoFGIYBKdHhcdChkiZsjweBaVkiJ5vP5YabfLjPA5tQJT5otdnWVqWCW7dv4/wzzwjDnbGuMgfcNk9vPE5RgyaM8VoRroqXJKHVsR1nR8onSQi4K+duP0N+7wy6HZU5kPYiMUnIsoyZ6WlkGAnaYIZJmUwGhXw+Tk/wkkFW7VCr11FnwuV+jlFVFBDEVUYcfTeZQv/pI/6ZJWGwagpKKZaXl/Hw/v2+tpViMKRphccIoWl27BHPowZhFOFAm6gBRayO53XKxWKxbzY/6KqGIs6Bui31zkSSYGgayqUSTMtCEASoNxooFgpQFGW7AmKICZqrvgdJKSS7LPbl6TAAkl0uaSIN89FHH6FcLOLUyZMj21ePAxkscvCYihHHGTFotx9V06D4PgLPg23bImQ/7pSBxEp/+wUhBEYmI+7jQd43PTUVWy07Dja2toTlcRCGMHQdmXIZEiFwWVkkFz7aCS1QJwdNRVFiAsV6nQjiRUjPFEM7a/SOryVxA6woUTbJhZMN5pK6cPs2CsViqj8YMR6zEeLJRWBZHXUGAFCr1RBFEYw2UQMKoN5oCIFQMZ/vaBnc/Mb2g2CnwcsPAjRMU0QJgiAQ5U/5fB7lUinuZsjKBBVFAShFrV6Pe8N3ID79gEcO+q1UCIIAlmmCAshks1DG0B4ZgBBQSZKEBw8eYGNzEy+89NKeTHbDTGTh4yhGxPgrFbZ3tF0ua+i6ILqO6w6VMhh498lj6BOGYQxMDuLdEExNTsZljQAWl5dRqVZBEDdZ01llUD6XQ6lQgK7rIJKEkFK4rot6vY5avQ7XdXdcF1mWxT3UKjTuReAHvcJ8PCKJY5BlWYyDtm3jxtWrqf/BiPF4jRBPKMIuOgOAKe1tG0EYttUamKYZT77A9qTM0PFr2oG9cxtejohS2I6DSrWKWq0WDxRsBZLJZFAul1EoFKBpWtPxE0LEsVBKUWs0+s6btgPvnNhP5IBGERqmGRsdaVrbFMyoQSnFlcuXcXh+HjPT07FGAWhKP4xj4hl0Un0cxYitGEvHSn5f07itd0QpZEkS9+0gYfvdYlBBraHrQ393CCGYKJfjVBji1CSAHS2XJdbXoFgoIM/INO80adk2qqxddJII8NLKdsZLhJC4HXoLKDovPrqcRExEWght0uK5Uqmk+oMRI00rPGKEYRiXLXYYMAgguie2ixpYti3sRfP5PLQe4kMRAuwxQPmsUU2SjVNKY194Xe9L2UwIQT6fh9lowAsCWLYN3/eRy+UGDmtH/UYOuNFRGEKS5VhnsAe4e/cu6qaJ1778ZfG/VrIk8qcs3UN7hF97YsCUAvCYljG2gpfH7WITFG3EmowYANukipsMhay9d7+K/d1iEIMkwzCwvrEx1H5834fF0iZRFCFg+gIjk4HRQeXPfRS4L4nnecLS3PN9Qar4d9gPArST+QrXywRaFx/9IimYTpLsjGEIJ8rlpSUUSiUcOnJkiD2kaMVjPEI8GYgsq+sAH9HY7jcIQ0yUy03POa4Lm3VqzLEwYSuSE1SvAZdGEWzbFlECTgxkSUI2m8XkxATy+XzfAyjv5lYoFIQrox8E8bZZ6+l+IVo195jUWo2O9qJ3QBRFuHL1Kg4fOoRSr7wn2XaCS1ZAJMPNfUcYBiUGdNvn/7FyR2yDfj81TgIisPNjVQUdXS9b7geJkNhLQJKGCt0PDVYB0w8Mwxg4skERh9tNywKlFIosY+7gQeRzOciEYGNjo6fVsiRJMJjVej6Xg8IIQxCGsG07boVt23AZeWh/mi0LkWGjZ4SIhUFSpJg0bgrCEAu3bqFWqQy3jxRNSMnBI0RgWaCdvqBsIrdtW9QSJ93LXCZQBBCvArqEzgm6RwxoFMEyTWxubYlVNxCXDRWLRZTK5bikaoDVpmD67O+MrsdllZIUV1U0GjBtu++JMFmC1wnC6IhSZHO5PQud311YgGVZODdkS1n+ufA0hCANLSVwtGUVPCi4qEuSpF03yRo5Wo+n5W9ePcB1FlHL38nrMSgh1Fm5YBiGe5q37rfEUdf1OJ3X53bDMGyyTDd0HTlWpTA5MRG7K0YRVtfX+64aUBQFOVaOnGFjASUEURTBcRxUarXYTKndebJz5Q6kwyL5TiJJ4jNv0h84Dq5fubLrxlApUnLwyBCGIaIueUQ+OViWhZDSJmLAhYFAPHD0qt3v5GCWJAW244Ai/qJls1lMlMtiQBkUncoVFea7kDQzqdbrfbkHcuvkTuHwVqOjUbWQ7gURNTh8GMVCYTQbTUYTsD2J8BJK0YOARxrY63iqotuxAo9fSqFpgk+ILEOmDQgTHUlFumCEaIoejLkp0zDgzYf6aRjlsY6jYRhCkiTkcznhlQDE3++pqSkoioIwDLG2sTGQKyUvfywWCijk89B0HZTSuNOpZcVGaF2igrv67FpJYOI+TrpdVms1PFhY2M2eUiAlB48MlKUD2oGHmLlJSxiGotQqCIJYVMSqBHo29GETanKibkcKJOakWGKe7MP2L2g6h3b/Z34D+VxOrNaq1apY5bQ/BSomvrYr3l0aHe0Gt+/cgW3bOL/HjWAIsB1aTfyvLQlkv8NE5KD1efEz4MqudWJPTvDJaork5N7u+dZjReJc9iI1pCe7Nj5m0QPeddXtQg64FbJl26CIfQgKHci9qiiYnpyETAg8z8NWtTrUsSuyjHw2Gy8iZBmIIgRB0JEk0CjatcamdVxKjgeZTEb4H9y7e1ekXFMMh5QcPAKEQYCwwwCUzD07jBhwJXEYRag1GgCl210Fe+2MpxIY2bAsawcpKLAyxFGIsfoVkvGUhSzLoIhbStcbjbZRBB4+Jm0GB2BERkdDIAxDXLt6FU899dTYWz8nQSnFIHpvfjUidg1b0y0k+bMjGsEn/KhpQqcJcR9/ffKn9XiRIBH90o+9IAUcvC04IbFV8V7ZIwO9DZJ0wwAo7TjZeb4vJmOCWKSXy+W6Xj9N0zA5OQkZcbVTtVYb6th5ikrTNBQLBeiqGpMEZo5WbzTgM5tmrkEaJZLbTOoPPN9Pqxd2iZQcPAJEHcoWW2ugbdtGRKkQ89VqNVFG2BcxYNuLoggWExrabGWRJAWj8iYfVGGuyDJKzD0RiL/QFVYylcxN8hVHO2IgjI4oRSGX29OQ+e1bt+C4Ls6ePbtn+wSaDZgGAQ8f91MpkkxpbK/YSOIZ7J1x0QjR7Yh1XYfE7IW7hcbHhU4iUcMw4nLLlsgBNxmzLAtRFEGWJOTzeei63tf+spkMSqUSFElCtVaDaVmDHzPL/YeJ8uZioQBNUUAZSWg0GqjWak1Wy0PfOe2Epi3+B3w8WVpcxNbm5rB7euKRkoM9Ruj7iPoMW3Jvg2wmg3q9HreETbgf9kLEIgVblQqcPkjBbtZKHdXhPUAIQS6TQSnhz+C4LiqVShzdoBQh227rOe+Z0VEbBEGAa9eu4fixY71TOyPGsJ9T1CGt8Dig3d3cWrY2CnTbHtceSI8gegB0NkiSZRmapolqijAMYZqmEA8TQmAYBvKFwsAi3EKhIEqLNzY34QyYUuH3Ek0YSEmShGyCJIQJksBdDdvZIvcD2i562FL5oWuasIi+fvXqnn+OXxQ8fqPEFxyhbe+MGrSpJOApBYD1XGhxP+wGQQqq1TgHSWlMCnI5TJTLOwxQdgv+1dtNyFBRFJSYyEmWJFDEHg6VWg0uS4EkB4VHYXSUxK1bt+D7Pp5++uk93S8whIkM0KQUfxzJQSeMPLXQY3u6roOwLoaPJHrQ4fh01knStm0Rqifs/8VCQbR2HgblUgmGrvdd4th0vAkn1lZhI0+HFnK52H+FUgS+L0jCsO252031rSmLDIu21KtV3EvFiUNh/4wSXwCEngckPMI52g2Atm3HoTps25MWW9wPW8En1K1qFZbjCC/1Qi4XRwpYTrWT2HAYht1asrhbaKqKUrGIbDYbC8QYCWg0Gtv+6o/I6Igj8H1cu3YNx44fFymfrhjhymVoE5nEQPxYk4OWa7WXugO+P4OlFx5F9ADY2eGQMo0R9xQA4u9JoVAQk+BuQAjZLnEMw4FKHAEI98LW91DE0SqebigUCvHCJEESLG7DPgi6HBu/Ejx6AUJwj5UapxgMj/Eo8cVCFEUI2wiKOoUSbcuC7Tii3XI+nxelOq2giOt7N7e2YtMTTgp4+qDPHOSgGLbDYi8QQpDR9e2aakrj2m0mWqxb1p4bHSVx48YNRGG451oDYHi9wePaU2Gv0ZevgKYJ7cGgZl0jAQuTUxr3OKjVaqKSRGZkOJvNjvSzFCWOqjpwiSPXHbS+PoqiprEtSRJUThKCAKZpxk3l2iycOuyw41PJdIWiKDCYR8TCnTup98GAeLJHij0EZY2H+oHHnA9d14WeyXR0PwTiqEK1WoXFwnSyLIsmSFx93YpO5VPDrJLGOS1z9XG+VBKpENu2sb6+Dsu2oen6nvcI8DwP12/cwPGTJ7saT40Lw65kH2e9QTdwA6893SerXOCtkvd6/9yquNFoxAJiVsIrM73QMN4j/WDYEkee5kySg25NwfiqvpUkNOr1vqM1nUhea/pR13UosozV5WVsbGyk+oMBsL9Gin2KKIoQttqf8lB8m5u8WqvBdhzoui5MTFpBEZfwVWo1BGEISoiIFHQiBUm0XYEOsALfdV+AASATgkwmg1wuh8D3RVtrvqpyPW+koftuuHHjBiIAZ86c6fs97RrQDIuhxYjcTW6fkYNWl8hdo8/7RNe0uL0ypXvmexCGISzLQq1ejyuVogiQJBiZzNgIQSuGKXGUJElURQHxPRr2cZ2bSAK71q7rCtFiN/TaepP+IJNBGARYXlxEbciSzScRaeOlPUDUZvLqZGUcBAEqlQqCKML0xERbQx8/CGIXNOYaqGoa8tnswH753IJ00EqDvSQGYp+EIAwCaIYBTdehaxp830cQhghMExbLFfMV3zjgeh5u3LyJUydOxMY0ewy+GhuqjJFFDnZrbvUoMI6qhX72qes67DCE67o7uo6OCpRS+Ky5UXJClCQJumFAZV1NiSQNJUQdBtlMBmGphGqthmqtJqyTO4F/33hPi3DA8USWJORyOai+H5cxs1SDpmmijHM34OmMzbU1zBw4gGw2u2cNtvYzUnKwB6CtzmaUduxxUKtWEQQBJEnC7PR00/MRpbAsS5Q0Efal0jVtVzXnBP2vSAWR2MM8Pxc2ea4LXddFOJJSCsd14bouoiiK1dyOA1VVYfTZOXIQXL92DQBw+vTpAU9gdBPbsFddRA4e84ZLj1PQV1dVuLKMMAjgeV7f/gH9QHQ5bGlapKoqNF1v0hdRGreXHlbdPwwKhUJcfmia2NjchMwqD9ohSQ52c4yaqkIpFOLureyaB0GATIfISS/SKBEi7ntVUeBLEiqbmzAMA5OTk0Mf55OClByMGaHrImK1yADidEKH1RvvdEajCKVisekL4fk+GqYpVg+6riObyey6u57w6e9jAhtFyeIw4M6OsiQ1tYsmhCBjGMjoumgx7QcBfN+H7/uQZRm6pvWVZukFx3Fw69YtnD59euBJYhDy1Q272YawTt6nxkXc3XH3G+u/vp5XLlhBAGdE0YOATXqe72/bX0sSNFXtHvVKTHR7hXKphIB9rza2tnBgZqbtJJ0UJHIzpGEhSRJy2Sw834fNKq5M04TKypU7NiJrA4rm756u61hbXUVpYgKe543M/O2LipQcjBG8QiF5Q3caXHzPg+t5cB0HiqaJ8ryIUpimCc/zhF9BntcNjwiEkNiOt0tEYFyVCf3Adl2EYSiaQu0AIaIHfcjCwK7nxTlc1lZW03XoqirMUQbF9evXIUnS4FGDxwDJngmPe+SgLUatOxgAmqrCURSEQQDXdYcSoUZRFK+E2X3MIcuyILvdzo8QAkWW4e9hzwe+38mJCaytr8Pzfayur+Pg7OyOyZ8fOQVE+fRu96upKhRZhuO68DwPPo8iGMZ2RHBAIyVZlkE8Dxvr69B1HdMtkdkUzUjJwRhBW7QGnQSIfGVMWfc5Qgjy+Xzclpn/n1IYhoFsNjuWgZL76tM2BOFREoMgDOGyEtB+zp0TiEwmE5MtNiC7LP3ABx7Rxa2Pa2nbNm7fuoWnz54dKlUxkqjBLvQGyVx1P/cOZe8J2xgB8XC4LMuxDe6oNAx9CGhHojsYcBs8OmU2GkJ70M/kx02UPEZSExsU998gIsNW74O9Ai9xXFtfhx8EWNvYwMzU1PY1oFREdXiEZ1QgkhSTAUWJ3VLZOKmqKgzDEA3luu6RHRe/d3RNw/rqKianpuA4ziOpONovSMnBmBBFEaLWCoUOsFgvAdfzoCgKKOIwtud5seUxMzIap4gm6TDW7sv2KIgBZWZHEQBFVQdyduQhYUPXEfg+XDZQU3adXc8DAcvxalrX1dvVa9cgKwpOnTo1mhMbEskVmsd6SvDeEkEQxIKwKEIYhnFLcPaYr1ojlrsOowhRGG7/TryWP+Youw9wTDRZorBtC3/yx3+8fUySBFmSICkKZP5YlmPyIEmQZVn8j/8tsf/JsizeD8RCW0PX4fl+/NkZhoh0jIwcDGHbqyoKZEVBwO6hThNKGIbwWEoraqnZ5xbIqqo2kYvv/z//D/7wBz/A2bNn8U/+yT/pfNiSBMLI4V6TBF7iuLq2JkocpyYmAMRkIBktGJUuQrguMgOofC4X3+ueFwuRgwCGYfQ9JvD7R5Ll2AlydRU6u8dStEdKDsYE6rpNq71O1Qme68aGPuw513UhyzJcNpFlMxlkMpkmzcI4xYCCILAB9FFUJnA4rhuLM8E60w153oqqilbOQRDA8314vi9MbrihEicgydyyZVm4c+cOnjl/fvhysn4+M0qFbsJxHLiOA9fzxGPTsmLxJXseaM6p8tAzIWR7MpZlKKzMjCKeoFRFgappkAhpmqSlxCSe/B9WM/A/fBcAAQWFpun40pe/vJNUMDFaxEhKGIbxxBGGog1yKynhOWreoEdMqGwCJ2BGNoYB3TCgMf2IYRjif4auQzcM6Lo+tjJN3rvATFQu8MkwSGhcmiZGQqAoSpzuUpTdh9qZpXi7qoWf/fzn+D//4A9QKBTwb//tvx1LZJGXOG5ubMBsNKAwzwV+zq3ljKMAAQSZ5Z+BqqpCl2XbNnzfR4ZFEXpujxEEXdexvraGyZkZ2LaNzB62eN9PSMnBGBBFESJWoSD8BNqlE8JQtGFVFQVrjQZM28bM9LTosNY0IY1JkNS6IuPH2ySk3GMErOYblELPZEa2auREIYvtgd3z/XiFzQZ507LiSVRVcfnyZWiqihMnTgy1S94RU6zy2WNeZcHJgMPEV8kJnwswDV2HpuuYKJe3J0Y2SepsclS6aAks24brONB0vWtJWjuY3kOsJv6WZRmH5ueHuRRd4fk+zEZDrBRdfo04WXJdUXfPiROAJiLBr5UgDi0EgkeShmnQpakqHFkW94csSQiCYAch4PeNMgJCkARBfC9xA7Pk9+GlF18EkSTU63Vcv359bP0+kiWOW5VKUwUDF7qOo6JCShAi7hDJU4ZBEKBumsj0E0Vg94ksScIYiX+PHtU49zgjJQdjAG1NJ3S48XhrYkmSYJkmPNeFRAjK5fJOz3Q+GOzRTSyiHY8IlmXFnvKqGnfJay0HHQEURYGiKLFJClvdcu8EPwhQq9excPcuTp8+DcdxxOvbRRB4+9x6rYZ6vY5arRY3mGk04LEmORzJCT+fz2N6erp5RcweK4oiJgI+MQyDQVo1P1KwfHwhnweKxR1PU5bfBmJi7XoeHJ5eaSETZqOBjY0NuOwz5dunYQhV01AsFlFgjb4KhQIKxSKyyQgdQ0QpwiBAEIYIWf19FEXI5fOx5oKJYXmUYFzfmSQhaK0wKhQKOHXqFG5cv45Lly6NtRlYvlCA47rwwxCblYoQKHayUB4FCAAkCAJPGXItQsSiCFEUdfcfSXw2mqZhc2MD07OzsCxrzzur7gek5GDEiKJouyVzl/Ir13Xh85UHpXBZamGiXI4bhiQxZmKwY01OaVNrVEppbP28R2TBcV0xoOeyWRFdGefeZVlGhqVwuOju1s2bUBQFc3NzQqfgsVC/bduwLQuWaaLWaMShftYUibu+Tc/M4PiJEzAyGbFq5c2vBsIuy/iaQr/7GQm9AJHl+Lr2ERIOw7ApPVNjBG5zcxN3795tIk/5QgH5fB65bBYGux8y2SxkRgQkRQENAkiEIJfLCQI3bkiS1EQOJDSL/y5cuCDIwd/8m39zLMfAyVm5XI7HrzAU+gOhOeCp1BFfEx7NTEZMZFlGLpsVFQ3c76RXMyqeetNUFeurq2MVeu9npORgxKBsUhOq/zY3XMTSCQGrdZZUFTSKoBlG+8Fur30FWvZHCAFlK4Nxgxs9RYiJQVO4fI+ug0Ria+bFxUVMTkxg4c6deEJhrXLjQ2GWzpkMZmdmkM/nUSqXUSwWd+RAg34bynTAbq+6IAePcRlj3+c4hOZGlmXkcjnkcjmUJyYwn0iLhGGIRr2Oaq2GWq0Gk3UAXVtdFVoUsM86Xyggn81C03VEUbS3EwohO6pOktGEl19+Gf/lP/9nLC8vY2lpCXNzcyPdPaVU5P4lScLExATW19Zg2zZMlq4SUS5KIY+joqpFD8X/x8kAX1REURR7wHQiw+z9mqqiVq0iDEOYpol8Pj/yY97PSMnBiEETtchtBw7mW+C6LkLfRyabhappUFQVju8/GmOOPhud9GuWtBuYphnnnWV5h5J4HMNwo9HA1tYWGvU66o2GSAdwsdzGxgYKxSKKxSLm5+eRLxSQy+WgaRqiKEIQBE2DFS+ZlCQJaiIFQXjodY9BRaXBY26A1Ee5rCi3HWrz8XUIggB+ECAMAiGaBIAi+4yBmEzIigLKfDJM0xSpouWlJViOI6zLjUwGhXx+O01RKGCCtT8eJdqVMhJJAmXEc+7gQczNzWFpaQmXLl3Cr//6r49kv7ysNVnNBACGYSBfKKDeaKBSrTY3hhvnGNGh2kTXdUiyDNuyECJO2Waz2fapNB4VjSLIkoRGvR73eRhxp8v9jpQcjBBRFMVf1i4Kf9u20Wg0EAQBcqypUsYwUKlUAEqbRTV7rDOId9l5ZcYrLsaVZvBYqRgoRT6bbSrdGwWiKMLW1hY2NzawsbGBjc1NuEzLoBsGCvk8pqam8NRTT+H69esoT0zgy6+91nN1GIYhgiAQE0/ElPs8FRExnwpC4s56TeV97HEniIqXIa81b9X8qMjJwNil3wHXZ/CqiJBVQYRsgkMUNYXjCQCZkTj+2SSvUy6fx8zMTNM+zEYDG5UKbMuC73mo1+tYW1/HnTt3hDakVCphenoak5OTmJqaam/eNQCUreuYW3kHEf3zguQRNFcvvHzhAn74J3+CiyMiB9zUqBOKxWJMhn0fW5VK7Bw65sVDq/5A/J+JQaVcDpZtI2LRgGwn62VAEPhGvY58oYBGoyEIYoqUHIwUNKmgbgPf97G1tYXA90WXQV3XRWkXgJ2Rg70gBoyN0z73N440A3eCpEDnLnQDXgvX87aJwMYGtra2RFvryYkJHD9+HJOTk5iYnISeIGVLy8uwbRuvfulLfU3KfFLhtsphGMYNodjqlFvlUkoFiWg+rfZlhbIs71ixDQo+uH9h8qn8XmWRHVEayYkAJwHt3goAsgyNkzRGCAa9NplMBoUgQC6bRSGfb3KdbDQaWF9fx+bmJpaXl3Hz5k2AxK3Hp6amMDU1hcnJSZRKpb7JWhRF0G//CTTfQe3TH6L8/HfEcxIhiBhhuvDyy/jhn/wJbt68iXq9jkKhMNB5JZFMI3SCJEmYKJexurYGlwl5M3vgG0DAUp9txh+uQ7BYq2vTNNs3Wkq830u8NpfL7U8X0TEgJQcjBOV+6R10Butrawh8H6qqopwIPfq+HzdXaVm17FnEgBODATDqNINl28KXfYcgk++zxzbq9To2NjawubmJ9fV1NBoNAEDGMDA5PY1nDx3C1NRUPDB3uba3bt3CRLmMqSGbswiywIhemJi4kkZDQRgK98swCLBDmcAiNVwVz1Xh/G/CHnebZITY7nEf8Ph9xHLWlPsm8MeJ377vd3Xi49ek1ZyJMFHfbstiJVmGrqpwmEA1WSefz+eRz+dx7NgxAIDneYKcbmxu4uHDh6BRBFlRMDk5ibX19fi0u6zQa5/+ECQMQAFUPvoBis/9etP9S0jcd+HU6dMoFIuo12r48KOP8PWvfW3gc+uURugETddRLBZRrdVgNhqiIdq4IQEI0X5M4P0ZLNtGGASwLEuUsgqwcVpixMq1bRjZLBqNBkql0tiPfz8gJQcjgkgptKlDDoIAGxsb8JgD4vTsbFPXNZ+51wl2u9fpBDpcp8WmNMMuBgTf9+EytX8+l9vxhW832IRhiK1KJSYD6+vY2NyMUxIASuUyZmZnce7sWUxNT3ckG+1QbzSwvLyMCxcujHS1zSf21ogIZUZBQRtDIXAToV4bbyEP/DEhBK7jIAhDKIyMcIEdz9+Pqw0xsJ0OSt4fUcvkz7UAjuvCtm3IsixEn722z42clBbTp26WzqNqe6wxJ0feb6HTddQ0DXNzc0IgKFJbm5tYZ4QhCkOsra/jxz/6ESZZdIGnIiilqH78A+Z/QUCDndED/nnTKMKLL76In//sZ7h08eJQ5GCYUsRisRh/fo4TRyz2oiyQT+z8eFu9Wli0pmMlA/+82Ptcx4GRzYqyxqENz75ASK/AiEBdt+0E67suqrUaHNuGrCiYnp5uIgZAbBtLk+QAeGx0Bv2gSSQ2oBaBUoqGZYEiFhW1XhsOz/NQr9VQrVZFioBHWyYnJ3HixAlMTU9jcmKi4zb6wc1bt6DrOg4fPjz0NgYBISQOb7chDWEQwGcaFpFLZ7/56o4yEsHDwK3RB8u2RXqjNZ2ROIimyS3p6Om4PhwpD4oAASgIyaDeaDQTADb588fD0MSQEQVBXJIkR5IgAeIxgNH2dRgCXKPAbc+71tcnIEmSmPxPnz6NpcVFfP7ZZygUCihPTGBtbQ23b98GSFzLf4TeRcH3WCg9pghtoweIQ+2vXLiAn//sZ/jss8/gB0Ff34VktGBYTJTLqNVq8Jkp0dQeCKuT6QXK7rvWJne8cshxHFHJkEvomfj91qjVMH3gAHzfR71exwSzh36SkZKDEYGXMCZvTsdxYJsmbNuGoigolctt2/36QYAIcWnNuO2R22IE+gFRZiTLMUHoE5bjIAxDSITsEG1tVSpYWlrCvXv3UKnVQChFNpvF9NQUjhw9Gudui8WRqfC9IMDCnTs4ffr0Iw/Dc9LQq/yQk4YkeUiuyiVWOSErigir7/isW0LtyWeDkCIkCighCAmFBLkzyWh3Hkh8JxJpEhHhYJO86vtQWP+BQo+Ssl5Cub2CrmkImHlWv+SgFfzaGIaBl156CUBMhBcXF7Fw5w7qn/8KDRqCgIivlSI5KHz0R5h66TebtiMBePbZZ6FqGlzXxWeffYaXXnyx474ptu+f3UaQVFVFoVBApVJBvdFAgVX0jBsSIQjpduOndqOYzuyuueNqwzSRa4kmBqyCBYhF4/l8fqy9bPYDUnIwAkRhKFIKHI5lwWbubYqqIpvNIt9BsRz4fuxzsNdljGPIDQo1cR+phiAI4Ng2QCmybEJYXVvD4uIilhYXYdo2NFXFxOQkDh0+jLm5OZTHqCa+u7CAKIpwfEir5FGjn0+HV0B0Atc1FAqFplBpMvdOk6v95P8oBdEVmJGFKAwhhREkmkWOp34S6QnwvxNKegB9Tzo0iuDvQUXFKO94VdMgs7SNz7REo4Cmabh//z7+/f/1f7H/cGtiAKAoG8D/nvs+LtcnMDc/j/n5eeG5oOs6njp6FDdv3sTNmzfbkgMe4eG6jVGllrIsLE8BbFYqmJ2e3pMKmaS9cieorHmTacX3cp1VMvDjkyQJ9UoF0wcPwrZt1Ot1TA6pOfqiICUHIwD1vKaBkXfMC4IAkqJAU9XY077Nl5CL1YCYfe951AAYD0nooUfg6QQ/CFCrVnH71i0sLS/D931kMxkcnJvD/Pw8pqamRG+AdlGXUSGiFDdv3cLhw4dHrrgeuqPgLj+XJAFonQD61Rv4sgSFeqA0BBBBQjBQd8yB0U+1zG42j9ERBEIINF1HyHo/jHKl2et+kWiA3ObH+GRjA5988glKpRLm5+cxMTmJOwsLAICzbWyUxxl1IQBKhQIapokwDFGt1zGxF+I+no4ipCtJ4H0ZTMsCjSKYlhVrnFhqYmtrC0eOHxe9TjzPezS+M48JUnIwAiSNjwKmjuXCK431Hu8kcOGVChIheyuC2QNFMdBej2DbNu7eu4eHDx5gk/k7lMtlnDp1CnNzcyiVSjty4OM+5pWVFZiNBl555ZWRb3tY9XacYR4eUYKY7QuPgwEw7CQ/6jtI0zTYLHoQhuHI0lFnjBX8v7/V/L+oRZ4/Uf0I5//G3xPRtus3bmBhYQGB70PTdUzPzDR5ZER095Ua3UAQV3IUi0XU6nU0Gg1k9qAtskhp9kF6eCVDg/XIsGxb9NSImFtmJpOBZVmo1+uYmpoa67E/zkjJwS4RMTEhIQRREIjOcmEYQlNVKLLcdSXKy7KUR5FSSOaCxzxo1Gs1LC4u4sHiIjY3NxEBKBeLeOb8eRw5cqRr4xPx5R/bEcZCxPLExNDli90wTORgFK2yRdSA5fcfZ/Cr0+9RDh2NGTEkSepY1jgslpeXYX7+Q/SiGTRwYF/7Uxx+/js4fPgwoijCv/7X/xqSJGF2dhbvvPMOFFnGwYMHcXBuDrMHDuxKrNsvDMOIm1TZNrYqFRxgzZnGCZ7m6uee4G6I9VotTm26blzFAGBjbQ2nnn4almXFLrYjJHz7DSk52CV41CCKojicxm5OHgXI5HJdQ6UBIweZvSIHe1QmSaMIm5ubQj/QME3IbKA6dOgQ8sUictksiv0YtXByMKbJoFavY2V5eSxRg2ExijPlxlpftKgBgLET2kGg6broELnb9r8LCwv46MOLeLG17qRDGMldvdn097WrVwEAv/Gd7+Dpp5/Gw6UlLC0tYeHePciShNmZGczNz2Nubm70K/rEeRdLJbisBTpvzjRuEEJAomhHb5h2kCUJmUwGtm3D9by4EZOmoVapgFIKTdPgeZ4QJz6JSMnBLhExhatlmgijKG44QghCJjBUerBO3n1wrHncXhjRIEujCMsrK1haXMTi0hI814Wu65ibm8NzL7yA2dlZRGGIWq2GiFLkslkhjurqxMb1C2PKld66dQu6YeDQuMoXh7i+ZMiSwCSi/ZRSGOIaDWorPS5yydt40yAYqKyxFZ999hlu3LiBEydO4egz/57lEWK8/fYvmioaOCR9O+J27do11Op1gBA8/8ILyGazKE1M4Pz587BME0tLS1hcXMSHH36IDz/8EJMTE5ibm8ORI0eQHYE3QdLuXJZllEslrG9sxN1LdX3XFtJ9HYMs9zVOcF8ZbnNuO07sQyLL2NzYQC6fFx1YU3KQYmBEvg+wXuJ8ktdZvop37esKSuMyxlaPg3Ghw+C42yHTtiwsLCxgYWEBtm2jUCjgqaeewvz8PCYnJppWFI1GI7ZITugwkmY57QZ7Lhgax9DuBQEWFhZw+syZrj0OdoUhVrkjiRzsh4ZLDAM7dCJOlwxyXcd5FXZb1lir1XDjxg08//zzOHny5I7nvUhCPlNoIgMcnPR88P77oJTi3NmzyOXz2+ZmALK5HE6eOoWTp07Bc12sLC/j4dISrl69is8vX8bBAwdw7PhxHJyb2/39wvZpsH4l9UYDlVotXiyNOa1BwCyle90X7HluXx8EgRAobqytYWp6GtVqFZ7nIQiCJ9IU6ck74xGCeh4814XrOKCIrVMdxwHAamt7fMkoENfWUjpWJX68s9FOrTSKsLK6ijt37mB5aQmSJOHo0aM4dvw4yuVy2/f4nidIVFKH0UoIWkmCcDQbw8rvLmuWc+L48ZFvezfYTbMlDkEO9kPkgGGQMx5UlDhOjcKwZY3cM8LzPHz5y1/u2Gq53QTVWpJ48cMPAcTtmwEAhEBmPgBJaLqOI089hSNPPYUwCHD/wQPcuXMHv3rnHRjZLI4fO4Zjx44Nrp9oc78WC4XYpZClF2bGLPAjfRCD1mczhgHLshAygSI2NmDbNnRdh8ucO3fTp2K/IiUHQ4IGAXzbhm3boICoMw6CAISQOJ/XY0LzPA8U8eC9X0QvjuOIKIFpmiiXSnjhhRdw5MgRKD0GRIuRKMMw2pr7iBp5JiwS7nsJtfUoEVGKm7dv48iRI+NVVA84yY+CGADb6u3HXYzYhAGOdeCKhTHqFIYpa2w0GlhgZYelUqkjMQDi9KMQE7LvRpRwI3344AFWV1YAJMgBAEgSSBh2vE6youAYIwOVSgULt2/j+vXruHL1KuYOHsTx48cxe+DAQNGE5L4Ia860trYG13XRaDTGGqZPuiR2IoOt/+dRXpMRBMd18WBhAUdPnEjJQYrB4VsWTNNERCkMTYOu66jX6wDiqEFXa1d2c/KUwthDVrsdECnF6soK7ty5g0UWJTh8+DC+9Oqrsc1oHwOH63kIfF9YmvZC0vFMSlikjhLLKytoNBp4dcxCRPIIUgrA/owcDAIy4GQ/boo0SFnjxsYGfvWrX4mJrBeZ8H0fkiw3d51MfO8uXbwIADh86BBmDxxoeq8kSaJ1dzeUy2W8+PLLePa55/Dg/n3cWVjA22+/jVwuJwhEVxLdIcKnaRqKhQKq9XqcXjAMaONOL3TQKQnL8Rbwhm+maSIIAiwvL+PgoUNiwTdKk6v9gpQcDIHQ89CoVBCyiT2TzcL3/eaoQTewL7XPNAvaOFet/QyeHSybXcfB3bt3sXDnDhqmiUKxiOeffx5HjhyBOkh1BaXbERbmdd4vREMhQuIGRCNc/d26dQsTExNjd0J7VJr6/SRIHLSUcah9jLm6IVnW6Hpex4ZfDx48wMWLFzE5OYmnnnoKH3/8cdft8hbgCmvh3Q4fXLoEAHj5woWdT5KdzeC6QVFVHDtxAseOH0dlawu379zB1atXceXKFczPzeH48eOYmZ3daawFdPxu5vN52KwJUmVrC9NTU2O5L4WzJyEglCJC8z3V7f6SZRmZbBa2ZcH1PNy+eRPHTp6MbfBtOyUHKbqDUor6xgaCIIgdt/L5uEEN1xroenPUoMtkFrCeCntRe9wVyS85pVhbX8fC7dt4sLgIAuDw4cO48OqrO8SF/cLxPIRBAEmShgrf81UAYbX/tOV4hwEvX3z11VeHev8gGDSsPwqPA97VEdgf5GDYz3EgvwNJAsIdjbFHCl7W6PLa+ZbP/vr16/j8889x9OhRvPzyy/jBD37Qdju87wGlFB7T6XRK21UqFdy5fRtAS0ohAd6DYCAQgvLkJF6enMTzzz+Pe/fu4c7CAn7+9tvI53I4fuwYnnrqKej8O93lPieShMlyGSvr63FzI9NEaQyheu53wI9Haoke9EpNqoqCyDDgui421tcxNTsLVVVh2zaKY7RufxyRkoMBYdVqCFwXhBDk8nkQQpqjBgMIC3lefWx6gz4GA/4Kz3Vx9949LNy+HTdOKRTw7LPP4qmjRweLErQ5Bse2QSlFdsga8GSJVPJvYHiicOvmTWi6jvlDhwY+nkExyIpV2E3vVoy4jwyQkhj0WAfSHeyBL4KiKFBUFdT3m8oaKaX46KOPsLCwgHPnzuHs2bMth0abBIaiNwViLxSgc+rh888+QyaTQaFQaFvpEG9osOjBjvNSVZw4eRInTpzA5uYmbt++jc8vX8bnly/j0Pw8jp84IRZKna6zoqooFYtxcybmRDiO9ELynhCLCXZM/Zy/rmmIogi+7+P+wgJOnD6NkFWiPEl2yik5GABRFMGp1YQAkU/qjm0DaBM16GN7u22X3BF9DgKbm5u4ceMGHjx8CEopDh86hBdffhnTU1MjOS6H5WBlWR66IoNIksgftnrBtCUKPSZY1/excPcuzjz99PjKF3eBJ1KMuAcT915dCV3TEASBKGsMggDvvfceVldXceHCBRw9ehQAq1aKIgRhKNpwtztOXuHTSZv0+htv4PU33uh5XENFD1pBCCanpjA5NYUXXngB9+7dw+3bt3H/5z9HPpfD/Pw8jh49ik7xwXwuFzel8zzUajVMjyGl13qGTaWNfZ4//9ws08TW1hYmJiZg23ZKDlK0R6NSAaJIuGkB8Rc3CMPeWoMuk9WjGMC3KhVcuXwZi8vLyBgGzp87h6eOHRvpzU+jCLbjAJQiw/zLh0GyiiFi17/t67bf0JUo3F1YQEQpjh87NtTxDIqBjHpGtM9wn4kR24ns+sIAGpS90n6oqgpZkhAEAWq1Gt5//31YloU33ngD09PTImXA701RqtsBvNyxVzVQT+wyetAKVdNi74STJ7G+vo6bt27hxs2buLOwgLNnzuD4iRNto6LFUgnO2hps245dJUdcxt0umtSvKFNsg0WBbcfByuIiSqUSHMdBsVjcP4R7l0jJQZ8IwxCeaQJAXP/LbpCmqEGnm6bD/+m4TGq6fPlr9TquXLmCBw8eIJ/P40uvvoqDBw8OFPHoF7bjIIoiKIqya9LBGzj1O7B1IgpRFOHW7ds4cvjw2BvCDIVRuVVyvcE+GcjE5zpEWuFxAyEEmqahUq3ik48/BpEkfOOb30Q+l9vREfHcuXP4XwDMzMx03B6PHIxCmyRJUuytMsr7ghBMz8wgn8+jevw47t29i08//xw3btzA2bNncezYsabxRdO0uDLAtlGr10dODjoRxkG7UaqqGltAex62trYwNTUFz/PG70nzmCAlB32iXq0CUQRFlgWD7ztqAMQ3bKIuea9hWhauXLmCe3fvwshk8PLLL+Po0aOQCEEwBpFWFEWxOdQuowYcvLRxKCvi7Y1gbW0NjUYDr7z66sj8BEaJ1rTJsNivfRWGOfeB/Q7GDEoptjY3ceniReiZDL76la90rFw4d+4czp0713V7QRCAonNaYVBIkjRyzxAg1rnouo7nnnsO586dw5XLl/HhRx/h+o0bOHfuHI4cOSK+b8VCAZZtw/M80RlxZOhwbn05J7bA0DRYloXq1hbK5bIwR3oSkJKDPhAEARzThIo4asAHsL6iBkm02L2KrnmjnKBawui2bePq1atYWFiAqut47oUXcOzYMSitFRUjhu04wsNhFKkKvgLe7ZD24MEDFAuFto1gxvJ5DIBRVCkktwVgLBGhcUAc7xDvfeQdGikVojdKKe7cuYOPP/4YMzMzePrpp3cdvQmCAASjEy6TMS1URAmhJCGXy+GVV1/F02fP4vLly/jggw9w7do1nDt3DocPH4aiqsJamUcPxklkRUphwFJoRVUhKwps5mujqupjuagYB1Jy0AdqtRokGvc/UBQFEaUiatCzPC+Z7265KYWidtRfCkLgeB6uX72KW7dvQ5ZlnHvmGZw8caJtI6hRr7zCKILLKxRG1Wylh+tZPwiYVeyZM2c67KL5C8/V47uOevT5ulF/BsD+ixwMNWGN0fmwHWgbgs/3/+mnn+LmzZs4deoUnn76aZi2Dc/3d5XC8oMgjlaOakJi3iGjjh7wiovkURYKBbz22muobG3h8ytX8P577+Ha9et45tw5TM/OwrIs+GEIy7LG5pwo9B0YInpAKQxdh2lZqFaryGQycFn3zS86UnLQA57nwTFNGCw8zm+rvqMGyec6kISRcVBWE33jxg3cuBm3cj1z5gxOnz7dPV854sHVtqzYv0HTRmYcwq/xbga0paUlhEGAI0eO9LfPeMdN/xvnqmEUnRg5hOZgn5CD3ZogjfNzaUsGWhCGIS5evIiHDx9uN09i5l8Ba+wzbFogCIKRe6EM6i7ZDyjz1mh3z5UnJvD6V7+KjY0NfH75Mn75zjuYnJzEsePHoSgKao0GstnsaO7X5LlRijCKmu+rQUSs7HxURYHDoge2bafkIEUiaqBpkBnb9j1PRA265p96iKxG2TUvCEPcuHEDN69fRxCGOHXqFE6fPg19j0tvgjCE57oApSPNI4qBfxdtm+89eICJqSnkdtGeVvi2g0VcRpiKGCUxGJvYdVzYxXUkQH8dGvuZEBIEjUeOesHzPLzzzjuoVqvNzZMIgappiFjjoWHJgb+L93YEMwgaZfQg6jHeAcDU1BS+/sYbWFlbw5XLl3Hp4kWUy2UcnJ9HLptFaQRGQ8lIaNIzgmOQ8+b3o67rqNXrMPN51Go1lMvlL3xqISUHXWDbNjzHgU4pDDbRUaDZDbHfqEHr/xOlTLsJF4ZhGNubXrmCIAhw7PhxnD1zZiBmO8q0Ao8aaLo+0gFNwu6O03FdLC8u4vkXXxzJ8QiTmk6VKC2TXT958VGtfqNEfnW/RA52u4od9N7Y8VkMGbVp1Ov45TvvIAwCfP1rX0O5RcuiKQpc1o2UDmkCNq6WwdxieCTf/cT17HmOhODA7CwOzMxgaXkZn332Ga5dvYrFpSW8+Nxzu7Yz559tp+qmgc+XfY8MXcfWxgay2Sxs2x5dyvQxRUoOOoBSinq9DjkIYGQykFkp3aiiBkkMM2BEUYSFu3dx9coV2I6Do0eP4vy5c8Ot1kcUYgxY2c+oowYAYjEnhk8rPHj4EJQQHN4DR0Rg52dK0HzsvdpU7waPWlg5DIb2OeBvQ/tBn19XSmPnwUHL2bphY2MD77zzDgzDwNfefLNti2NFUSBLEvwwjNMDQ6TZfM8bj6//CH0PktvoO1pFCObm5jB38CA+v3oV9+7exVs/+xkOzc3h3PnzKA5pr8z9UNo1WAIYsZekjs/vADs3TdPQqFTQqNextbWVkoMnFZZlIfA8aIQI7/CBogZA94GO0qEb41SrVXzw/vuoVqs4fPgwzp4/j8IuQuWjgsWaKxm6PnJLaInZAPf9hW7B/Xv3cODAgUfncMYG4h1gK7coIZra7aQesjLGx9H9sSN2MUEJEVxyFZwQx4mV5AiJwYP793Hx0iVMTU3hy6+91tmgiBCoihL7pAzZ2W+cvv6j0h6I8P2QgtKTx4+jVCxiZW0Ni4uLWPzRj/D000/j7NmzA4+PtOV3210CTbbKvY6PaymymQzW1taQLxRw8ODB8VnfPwZIyUEHmKYJJQyRzWTAb82BowbdMGS04Nq1a7h69SryhQK++eabmCiXB97OjkPZ9Rbia8PNWtqtoHYLvhoZxOWMo2Ga2NjYwCt70GRpYDD/huRnkCzro60RiMQE2DOlsY/IQes5Jb9ByQm+3ft41KA1v9x6dUaVOrt27RouX74smif1InOapsF1XQS+j4jSgXUgpmVh9uDB3RxyZxACmezeVllUKgxJbA3DgGEYmJ2dxaFDh7C+uoqr169jaWkJr7zyCkqlUv/Hgv4Mj/qOmiTKPjOGgVqjgVqlgkqlgqmpqb6Pa78hJQdtEARBHDVgph5AfMPZg/ga9HieDxL9hpNr1So++OADVKrVZkb9KOu7E7AcJ44aGAakMbBpztCHWf3dv38fsixjngvFHgF6fsYdUg473sXNoIC2fTkID51TKsjBDmFdYsU0jtRD03Gxx6TD//nrxeqe7myz22sFKB6PuaSRUooPP/wQd+/ebds8qRNkWYYsy6IEehCRcBiGcF139Gm6JEagPaCsImA391OhUIDjuvBcF8dPnsT8/DwuXryIn/z0pzj79NOxZ0QfhLffMYIAO+619i9MfB8JQUbXUW80YJpmSg6eNLiuC4nGBj78tvCDYHRRA0A0EeKq4U6IogjXr1/HlStXUMjn8c1vfhMTXPT0mBAD1/MQ+H78xRlTiY9ECMBziRjMO+DevXs4dOjQow0BjkGM2Pb17BrxFSHQviQz+Xen1VM82QKUxvlbGoXx44Tgq90kzkP8iR00hfvR8pi2EKNhp5duosTdflMC38e7772HtbU1vPLKK32Xw3KoqoogDAcmB3xBMtb8NhPcDROV4+CRg91Ux+iahkwmA9uyUKvVMDs9jTe/+U1cvXoVV65exeLiYs8oAsVgCwipX+1BgniqioIGK2n8ImP/xB33EJ7ngVDalEf0PA9AHCLsWaEwwBdE6pSLRhwteOutt3D5889x5vRpfPNb39omBnxfjxqslltEDcYUyk5GIwYRlW1tbaFWrw88mI8cXT6r3YRj225vwKgAYfdg60/8JECIBCIRgEjNq6jW7bT536DYzfvHJcC0bRt/9rOfYWtrC2+88cZQ9xIfN3yWWugXFpuAxpGqa0KXcagf8JTObj+DYj4fXydmq0wkCefOn8c3v/ENRFGEn/z0p7h69WrbMYBSGuttxjwuapqGIAxhmqZIpX4RkZKDFlBK4bouSBSJXuO8SgEAtG6CooSorJ/9CLRRrl+9ehU//slPEIYhvvnmmzj/zDM7BWYjihzsWOkNAMfzEAYBpDFGDTj4+Q9CDu7fvw9D17s2ttkLdB2uRhwBEv4Z+0Vz8BhXV1QqFbz105/G38NvfAPT09NDbUeSJCiyDEmSxFjSD2zLAsUekAPs0hNjBJEDII6w5HM5SISgVq+Le7k8MYE3v/UtnDl9GpevXMFbb72FarW6vXtgp9lRHyAYXJsjyzIUSUKjXodlWQPucf9gn4wee4cgCBAFAWRCIDNy4Pt+3PhElsX/2mKAqEFrpQLPl9ZqNREtOH36NN5sjRZwjDqlMMyXmlI4zCZ5FM2VekEakBxElOL+/fs4fPjwI5949jIBtN9KGXfTV6EJIz7f5eVl/PxnP0Mmm8U3vvEN5IcsrePg0QNvAHJgWdbYdDw7sIvoQTTCey6fz0Nm3SOtROheSkQRwjDET3/6U1y9dk2UqO5mzz2/ny2pL1lVYZnmF5ocpJqDFgi9gaqKm83zfVBKoXTLFQ5jZpTIM1NKcf3GDXz2+efI53KxtqCTGchjojXwfB9hGEKS5T3pVCZJUiwi6pMcrK6uwnYcHDl6dLwHtkuMsmlQUty3byIHHLucWEYZnbl9+zY++eQTzM3N4ZVXXhmJXkVlY0oQRQijqK9SU8u2xx6RS2JY34NRVsjIshy3f67VUK/X44qxxHZ5FOHq1av4/PPPce/+/ViLMKwvAvrQHrSM75qqwrIsWJY1VuvuR4mUHLSApxTURJVCkNAbdMSAN0dytVSr13Hxgw+wtbWF06dP49zZs90HozGosruJuTpBeD700mGMCINGDh7cv49CPj+Scs9xYpSDS9LCdr+Qg5FFDtBlcuv3+lKKTz/7TDRPeu7ZZ0cWkSCEQFVVRJ4H3/Mg9zHp25Y13kqFFgx7H/LmRqMaBXL5PEzWlKneaOywVZYkCefPn8eBgwfxwfvv46c/+QnOnjuHM6dPD5Xa6Fm50LJNTVHQiCLUazV4nveFbOO8P0aPPQKlFJ7nQQaEWQlPKciEdJ6wh2HabPWwuLiIH//oR/A9D9/4xjfw3LPPxp0TO21zAF3DQBjwCxUEAQIWUTH26IshMyOkfshBEAR48PAhDj9qISJDp6s76lbDfPWzL9cxI5iEd7NyDcMQ7773Hm7duoUXXngBzz333MhTFZqmgUgSvD6FbJZl7bkT3zCTK6++GhUhlQhBoVAAoRT1RgNBEOx4TRRFKJdK+Na3voWTJ0/i8uef46233kK9VhtunwMcuyzLkGRZkIMvIlJykIDneaBhCIkQEfLjH7w6Yme9hmni4qVLuHvvHmZnZ/HG17627SneKff3mKQTgDjCwnso7Ek+FABhpKmfkqulpSUEvv/oqxR6YBQK7ySGdd18lNiLu7oXCXNdFz//+c+xurKCL7/2Gk6cODGW41AVBRLiia3dhNcKy7aR2WNyMIxfRD9NlwZFLpuFqqqQCEG9Xm/eXxQ1pc+eeeYZfP0b30AQBPjRj36EhYWFgfc3iN8BF5g26nURQf2iYf+MIHsA13UhRZGIGkSAWB13JQeDOp6ZJj744AMQxKRjZXkZ/+N//A/82Vtv4drVq6hUq+1r+ccYuh9kyzSKROfFvYoaAHH0BqQ/C+V7Dx6gPDWF/GNgK90No54YReSgFzlIDP7tjoFrF+IOjxQh1zIkbQo6vHfHttC+zFGYOfFjfkT3d6Nex5/92Z/Btix87etfx8FxmmWRuFOj1Ef0wPU8hMyldU8xaEqK30tjyL2XikUQxCZrPiNTSV1NEpMTE3jzzTdx9NgxXPrwQ1y+cmXgyFzX701iW5wc2LYN0zRH2rPjcUGqOUiAixFFSsHz4lAZczhriwGFiFubm/jlO+9AlmU89+yzkBQFBw8cwPLyMlZWVoQ1q5HJxJ3LDh7EzMzMyPu578AAqwXX8xAxk6ixNITpAB6hiCjtakPruC6Wlpfx/HPP7dmxDYuOtsB9DLS8H0PydUmTqJ4DYw+CkES8C9L2tf3cNe2GTtryO/mYJP4eZLrh2pnW93Q6xvX1dfzqV79CJpPB1772tT0pGdQUBZ7r9uzUaDMl/F5HDgA2SbIeHb0gVvE9DN2GAbdVth0HtVoNk5OTXSdiWZbx0osvIpfN4rPPP4dlmnj55ZdHE0lrGesVRQEhBLVqFZ7nDdQJdz8gJQcMURTBd13olDaVMAI9hIgDYHlpCe+++y5K5TK+/NprWFldhed50DQNx48fx/HjxxGGITY2NrCyvIzllRXcvXsXIAQTExOYm5vDwYMH41zcSI5oCFAKx3H2VGvAQdiKhpcudUpnPHj4EIiiPevA2DcIafJpb+dv0e5xx8212YYoKdtHaYV2pLQdYWiHVjIgDKX6sAN+cP8+Prh4ETMzM/j/s/fnUXJk93kg+t1Yc629sqqAqsJWWBpbN7oBNNDslZIoWQstURTJ86TxyHNsyR4fyZZI6fhIb55sv5HGT6ZEja3FmpHtsWXJEkVTlijTFCl2N5cG0Gzs+9KoAqqwZNZelVvs9/0R90ZFZuUSmRlZVUDX16cPgFwiImO597u/3/f7fi8eP169eVLIkCTJdSS0rJqdGtfMAKkKglYuhG3iVQ5uq6xpGrRiMdB4vHvPHkSiUZw/dw6apuHFF18MtJAhAKgguM9pOcrs6kVBgCgIWFpagq7rm+TgaYVt2+4qTBQhEuKlFIAaxkcNRA0mxsdx8cIFDG3diqNHj3qGKCAEtmV5kQlRFJFKpZBKpXAIbgoincng0aNHuH7tGq5evYpYNIqBgQEMDA4i1d/fll7v1eCVLwoClHVQ6ApsReM4DlCFHExNTmJgcHDDKIi9yYsPOL4wbHmzII6mVePcAOkJKq1qxZehUvSh/N+U18ET4r1+88YN3Lh+Hdu2b8eRI0fWthSNVS3YjlOzU2OxUAAhZN3uY4EEa8gURl+FWlAVBRFFQZ6F8OuSA0YOR0ZGEIlE8O6ZM/jmt76FD508iUgAoiWgcqSrhNiDiRIFAfls1uuE+jRhkxz4IPgme55S8DdNaQqU4vr167h58yZ27tqFw4cPewM3V99bto1qt3s8HseuHTuwc8cO2JaFmdlZpDMZpNNpTNy7B0EQ0NfXh0FGFpKJRHPHGRC6rgNwhYjrUdtL6ngdrHcHRorKKQEKrErdNBoyD4IwzWjWCl4qIaxjLjvP3A6ak4QLFy9i8t49PLN/P/bt3eutCP2eI+2GLMt1OzV6lQob/Fpatu2NlWGDP0/xRAL5YhFFXUfSsmoviHzXr7+/H6+++ipOnT6Nt99+Gy+9/DI6gvghVIselHzEjc49rYLETXJQBV6VQgtRA+o4bkXC/fs4fOgQxsbGSgZAHhavxzr5rS5KEgYHBzE4MAB66BBy+bybfkincfXaNVy+cgXxRAIDAwMYHBhAX1+fWxYZAALYxFLjN9m27ZImShFdp9VMPQvlqakpiIKAoXa1uGWoRgKA6pNcM14SjeKJs05GuD4HfDurIgnU7Yh45t13MTc3h2PHjq2UubL9l5ACdm0p8TWCCpCqCApJkup2aixq2rroDTzwNF6dSZK/H8TUqRFQ37YVRYEiy9AtC0VNa2gR1NHZiddeew2n3nkH33j7bZw8ebKuDXbF6EHZc82fMdu2USgUVqrNnhJskgMfBMcBBAEOAJspY6uGsOoQA4sNRLMzMzh+/DhGhodXfUZkaYUgJU3l+yYAkokEkmNjGBsbg2VZmJ6ZQSadxuOHDzF+9y4EQUB/KuURinidgYYIQs1Vk6broFjb8sVyCDW8DijcDoxbtm4NJdXihawbJAFVUR45aMMK9Yl0Rwy5DK7SVgqFAk6dOoWipuHlD32ofo8EnoKoRAhIWefIJklDvU6NhUIB8XWutiFA3YWQw1KyYd5zfmLAEYvFYCwtIV8o1CQHla5FNBrFq6+9hjNnzuDb3/42jh09iq0VxuTy7ZRf55LGY76qjlyT3gobGZvkgIFS6qYVUJZSEITKD36NB0YrFnHq1Cnk83m8/PLLVQciUZLcvF6NyEHVCYRPNOxPSZKwZWgIW4aGQAEsLy8jnckgk07j8qVLuEQpkokEBgYHMTg0hN7eXq+lbxDw8sX1ECL6UcslcXFxEdls1jWvaRB8Iqh0TdsVog+9jNFf4rXBQ9F+tCWt4MPC/Dy+/c47kCQJb4TQI6EWGSAsHB3k2iqKAo1VLVRKLRQKhaYbPYUGnwi4IpjvCK/qahW8PLZSuXIsFsNyNgvbcaBpWsMCQFmW8fKHPoSz587h3ffew6FiEbt37676eaFMkFkpDeiRg1yuoWN5ErBJDjh8N6NRzy65BjHILi/jnXfeAQC89vrrNfNbvFeAVY0ccDfEaoNmGUHwXoZbH9zZ0YG9u3fDsCxMZzJIZzKYevAA77//PiRJQqq/HwODgxgYHESMlVRVIyO6Ybh+8KK4puWL5eAizkrkYHJyEqqqIpVKBdqWUx4RaPOE6hfEAQjd1Mo/gD+RgsQQt8nv5cePH+M73/kOEokETp482XZxH/WJTv0VI5WeK14r7zgOzDILXoe6Tc3WNa3AUMsUyf8ctpxWYKSr2hgkCAKi0Sjy+TzyrCFVoyCCgGNHjyIWjeLKlSsoFIs4fOhQZWJaYVxddUyMEGU3ycFTDHaTU0q9MD+fBCuFFSthdnYWp0+dQjQWw4deeqluCZIkiq64rgo58ERsteAvi6vyUCmShOGtWzG8dSsogKWlJaSZVuHihQugcPNyA6kU+lMp9Pb0rCqF07jp0TqX64hMPOawgcRfwvbo0SNs2bKl4oNeyTd9vUV7oTds8YkR1/u3NYJ2dZG8+/77uHT5MrZs2YLnn3++LYK5qign2pzElz2nsizDtCyYllVCDjRNAwXW3gCpElgapdLowqOeYegNglRGJOJxFAoFaLoOq5IwMYhfCyE4cPAgYrEYLl2+DK1YDNZcq8L9yaOvhXy+7rE/adgkBwyEkQPTsiAzsVDVG77Cav7Rw4f4znvvoa+3N3BNrSiKbiljWO5aAR4MAqCrsxNdnZ3Yt3cvdNPENEs/3L9/Hzdv3oQsy0gNDLjlkgMDEEURtmWBCMK6lwcSFjkAU57za7S8vIxsPo/DTIhYfhY22lTZjk5ufBX3JBGDEoR03NRxcPnyZdy5cwe7d+/GwYMH19/Bjv82XxkrBMFNLWjaqtQCN0Ba674K1UCqdC3kY1crKQUKl2QEuW9lWXaFiaaJfKGwqiFTI6LfHTt3IhKJ4L333sO3v/1tvPTSSyXjNgFA64ypnFDouu551jwt2CQHHOwmt0wTsiTVTimUYX5+Ht957z1sGRrCC0ePBmbRgiiCEOLZgtbbTzugyjJGhocxMjwMCmCWGzCl0zh/7hwAINnRgc7OTgwNDaGrs3NdJx/PCMlxXCMkpgl5nE5DIAR9fX1r4tXfFBpwJGwGT2KlAhBu5MCyLJx97z08evQIzz37LHbu2rUmpYkNg006/H4WBAGWZUFVFFBKkS8UQLF+BkjlIKg88TotRA78+oJGrn08Hoe+uOhVLbRyvw9t2YJXXnkF77zzDt47exYnTpwoSckJhNQsYyc8GgRgaXER/QFTmk8CNskBh+PAodSrUqjaS6HsJtaKRZw5fRrd3d0NEQMAXkjM9a93SnOUDR5+yfE1ORgSAN09Peju7sa+Z56Brut4/PgxJqem8GBqCvfv34eqKK6ocXAQqVRqTSMJfotWClerwd0sM+k0+vv7vX9vSPjvnXZWKjxpkYOQRJSapuH06dPILi/j5MmTKwP1Bj8fkiTBtG1YluUZruVyOaiKsjJGrOcBAm5qoYImyXEct1KhwcgBxYr9d6OIRCIQmZBb07SWoyvdPT04fuwYTp05gxvXr+PAgQMlx1l64KVRYwqXGDmUbpKDpxH8BufCQEmSAin5bdvGmdOnIQgCXnzxxYbZsygI3kBu2TZk/v1WJ44WJiH/AMDFfclkEqIowjJNV6uQyWBqagqEEHR3dbmlkkND6GxDVIEfCwU8hzJRFEGYUyPg2lzPzMw0VaWwluCCxCDhymbwRFonIxxBIhcCO5Ti1ddeQ1dXFxxmzlPPzGa9IUsSdF0viSAuLS6io6OjpPrEr69ZDxBCSl0CeaVCA2WM/NiDphEqQRAExGIxZHM5FIrFUFIvqcFBHDhwAFevXkVnR4fngbHqWa1wzDy6kH/KRImb5ADwGozwXgo1jY8Ab3V+4fx5LC4v4/XXX2+6vI87/lm2XV0A2QrKc531Pu7fP6XQWfliNBqF0tmJ3r4+HDh4EMViERnWLOr2nTu4fuMGIpGIq1NIpZAaGGg6/+YRgvJjZr9FLDOPmpmehk0pBtpsfBQGPN9/Wtk2uRU8idbJgK+Uscnvz0xP48y77yIWjeKll15aUfjzc90GIhYmeAMfatuwbRuiKGJpeRmD/vvZXz7pq4RY019VVtboaaVYj4F68HsXtLqIiMViyOXz0E0ThmmuWNy3cJ13j41haXER586fRyKZRFdXl3esNVNT7LfknzJR4iY5AADHge04sC0LgiCsTin4bwx2I9y5cweTk5M4fvw4ujo7m961xEWJfNVQr3yxzfDvVTcMV/Qniqsm+mg0iu07dmD7jh1wbBtz8/NuZ0kmbCSEoLe313Nr7AgQVahW31wOkVV5cHKQTqeRjMeRaLN1dFioVC8dBp5E62SgNc3B5L17OH/hAvr7+3G8TAjMiW6Qe2pdQQgkSYLtODAtC5RS5PJ5dJSJ7fyfp2Vj0lpFFfxljdz8qJ7Kv5UUQjXIsoyIqqKoacgXClDYGNzSHgjBkSNHkM3lcPr0abzxxhuIRCJ1RY5cj1FkjbKeFmySAwDUtgHHgUDIiirXd8N7Kw82eGUyGVy5cgV79+3DcB2XrXrwW3B6aMfg3kSqgTsiqnXKFwVRRH9/P/r7+3Ho0CHk83lkmK/CzZs3ce3aNURZsyiuVZAkacWBrsFBgxtTOY4Dx7aRTqexZaN1YKyGNq5ivVXZE5RW8F/7RsgBpRQ3b97EjRs3sH3bNhx57jmQ8kmKi/6wAXL2dSDLMgzThGWaKLBKhc6giw5/VIGQ6o2DwoCvrNFmQsJqKQUuOHRaSCHUQiwedzs1ahqcZDIUIa4oSThx4gTefustvHvmDF5+5RWvqqySp4zNUleEiaS9fhhPATbJAeBGDjgDZqrhVT0J2A2Ry+XwnXffxdDQEPY/80zLuxYlCYTtE1ijQazGBMUfYYsNVISQitautRCPx7Fz507s3LkTjm27zaJYCmJiYgKENYsaYNbOyUSiIUJEBMHzpV9YWEChWMTgwEBDx7heIEDzTbzqgQsSnyByUCkqV/crto1z589jcmoKB/bvx569eyvbW/PPh3CY7QZPLZiWhaXFRYBSJJtxcqTUJQasVLId54B3a/QqFSpEDijzIgHaF8mKRiIQJQmmZaFQLCIRj4fyO6PRKE6cOIFvfutbuHjxIp5//vmVqgV/xZHPE4f7r+Sy2U1y8LTAcRyA5fokWQaFqz0o0RCwG8I0TZw6fRqRSARHjx4N5aYX2QNsM1HkmqHWCpYQL2oQUZSWJhsiCEgNDKA/lcIhx0GuUHC1Cuk0rl2/jqtXriAWj2NwcBADAwNuxUEA5bMoCLAIwaN0GqIgoLe3t+ljfFrwpKYVOIIct2kYOPPuu5ifm8Px48drR+78A/oGPyeCIEASBDiCgMXFRcTj8dZMm7jewvdvgpWKn5ZACAgTIzqUrtIb2CGnEGohFo16wsREiH0ount6cOS553Du/Hl0dXVh165d7hu+cZPbRnMtBgVcUeITslCphw88OeBKZtuyIIoiKCtnLM8LUwDfee896JqGN954IzQLYVEU3QeNK6vXEtXEiqyPAihtulSxRFToE3Im4nEkdu3Crl27YNu21ywqnU67zaJEEf19fS5ZGBys2nhGEkUYpolMJoPUwMDGLmH0g5C2XGe/yc+TJEhspFIhn8vh1OnTMDQNL7/8MnoD9B0QCIH9hJwPXtK4tLyMjhZ0TBXBiQLzVmg1N+9vfiaIohuxIGTN9R3xeBzZXA6WZUEP2YRodNs2LC0t4dLly0gmk+jv7y85b1wn5kWZn7KKhSdkRG0jmKjGtu2Vjn+UwrQsKHzCoRRXr15FJp3Gh15+OVThG08r2Ja1fiucMpLAowayLDfc3ZDyQchf8lQFoihiaHDQba9MKbLZLNJMq3D5yhXQS5eQ4C2oh4bQ19fnRTFESYJlWVhYWMCRI0ca/MHrB756C71SwRc1eJIiB0EbRS3Mz+P06dOQJAmvvfFG4GfwyTkTgCTLgGEgl8thx/bt7dmJX8zYgpCRl39zMd5aRgv8EEUR0UgEhWIRhXw+dIfCg4cOYXl5Gd/5znfw+uuvI+ZbrFhsESmJIiy2uHuabJQ/8OSAskoFwA2BK7IMXddhmaZHDu5PTuLO7ds4fPgwBkI2uRC5S6Jtr3/okzF/XdPgUFpXiMjhCQvZn3xbje472dGBZEcHdu/eDdM0MTszg3Q6jYePHuHu3bsQRRH9AwMYTKXQ19+P+bk5OJRi4EkK47UpzN2O5kVrAa+Mscb5ePTwIc6+9x46u7pw4sSJwPcl23BrB7iGkEQRtmnC0HXE16Lyxpd24Oc/6PRuM/JP6zgIrgUSiYRLDjQNiUr9FloAIQTHjx/HW2+9hVOnT+P1115zxdSUwnIcUMeBpKqeR45hGE+NjfIHnhxwvQHgTtSyJEHXNM+QZH5xEWfPncO2bdtW8k4hgufrbMta5ZK4HrBs280jEgKFaTCqDa8eKQgQJWgUsixjaMsWDG3ZAlCKpWwWmceP3WZRly6BOg4ESYIsy8hms4ioaigtY9sNivZoAp7ESgWgdhkjpRR3797F5cuXMbx1K1544YUnJ33UDAhBgZXDrbWorTyaUHW6Z5/zhHgbgHwpigJFlmFYlmepHCZkRcHJkyfx9ttv47333sOJEye838+tr4GVc5jPZqE8BRqop/hJCwjmbwC4zF1iWgLHsmA7Ds6dO4fuzk4cOXKkLYO6JEkQiGsJrBkGouvc9dAwDIAQyKq6sprwDeDeIFImdmorCPFaUO/ZuxemYSAzPY13v/MdUMfBt7/9bSi8WRSrgIhsEE/6tUI9rwDKSkb90R1/KWmlslJKKTTThiFE4Tg2LMGBTdxGQXxfxP2L9yf/Oz+KkjRHpZRHlUgTdRxcuXwZ74+PY++ePdh/4MATlS5pFoVCAWKt3i7tRlk0wRMw8nvGcUCJa11MsHEqY2KxGMxsFoVCIXRyALj9ZY4eO4bTp07h4cOHnt6F+9T4kc1m0b1JDp5slNsm8xC/JMuwLAv37t/H4sICXnvjjVBaklaDrCjQTBOarm8MckBpSfmi39XPExyt40AtKwrisRhs28Zzzz2HaDSKxYUFt1nUhQsA3BrxwcFBDA4MoLunZ8MMYq2cN0rdTpTlfzqOgyKr95YkacU2GBVcJhuEbtowiQpHsGFTCoIVctAK+ERvsfteZpblRBDg2DYuXrqE6elpPHv4MHbu3Nk0MXjSCEUul0MikXAFyuscSeSEkoCNlYz8AfDusTBD+K0gFothOZuFxZ6FdoyjQ0NDGBwcxLXr13HyxAlQSiGp6kpklT1r3KfiScfGuLLrBUYKuOaAlw5JzJDk1s2b2LJ1K3q7u9t3DGwiLhQK0DUNCFul3ABM0/SMTXhKga8keOe0EqXzOpaIpTMZyJKEzq4uKLKMwcFBr1lUJpNxPRXGx3Hr1i0osuzaOg8OYiCVaixnHTYqqLkrTfo2y2c6vtdqTfQWi3SJvvryaihZ7fO/+6MAvvdsSYREdVDHBnEcEJjuqtYfccBKFMK7X3x/rwT+W2z2+2zHgWGaMDQNl65cQbFYxOFDh9Db14el5WUA7iqVsH4k3LDM/yd/v2xHNc/FRkN2eRnJeByCILii6PWMIPivJQMX1PKeCpIobggfCUEQEItGkcvnUSgU2rbIOnjwIP7ma1/Dg0ePMDQ05PqtsGean4fCU1Kx8MEmB2zVxSc+Hh2QJQmPHz1CvlDASydPttXVjgJQWAjfMIy27CMoDNN0HREZMfCXIfpXYCUK53UiCOl0GqlUyi1V87lLqqqK0dFRjI6OwnEcN6KQySCdTmPq7FkAQE93t+vUODCA7u7utq8uKTOMsRwHpmHANM3Ak34leBMiq67hURFBFBGLRFzLV//18oXzG/6tigjVKcKhFohDIVK9qXy4/17y/2ZN0yAQ1z7YNE2cvXABoBTHjh1DIh53zxHbhuM4bhqwzr74OfGTHG6ctaEjCZRieXkZ/WNjbr8V01xbcsDJAPt7tfdNy3JTR+w8W21yQGwEhBCv34Kmaa6RXRuiGp2dndgyPIx74+PYsmVLadqMnTNd10Pf73rgg00OsGJbLAqCN8lRABMTExgcHERsDVTDKiMHpmF4jVfWA4ZhuKsBWXYjBHVqlv0DwlquHnRdx/zcHJ57/nkA8FYx5QOUIAjo6e1FT28v9u/fD03TXE+FTAZ3WLMoVVW9/g+pVApKCy2o/STAtm3377Zd4kHAw8Xl58s/2Pon/UqvVQJ3q2um/HQt4O97779KgihCkiRkczlcvHAB8VgMJ196CVGfZoSnsxz+p//vjGhwosU/z59rh3uIsPd4hEEURe/PjUIacvk8bNtGV1cXCCGu6G0tyDc7N0GrDvi5FSQJRBQhotRnY70gyzIURYFumsgXCuis1puiSfAxZtfYGB6n03g4NYV9PpfcsFJ5GwUbbxRZSzjOit7AN6CO370L0zSxY8cOGLq+0uUtZPBbSBQEd+VkWdB0HfF1sN80LcsbjJoxeFpVL93GQS2TToMCGBocdNXdbFKup2SPRCLYtn07tm3fDse2Mb+wgPTjx0hnMpicnAQhBD09PV4PiGotqIOQgHIQFgqXfBNRkEk/KNa7nKxpUIpHjx/j9s2bSKVSOHb8+Kr7jxACIoqod4ZWkQjmV2JZFmyWdnH4tbNL4w8bgTRks1lQAF1dXbBYS3LLtttH9hokBRxcwC1Lkpcm46ZI60Wy+C+IRaMwDAN6G6KwAvuNEVXF4OAg7rz/Pnbt2gXRd79yovo04INNDrDCeHkZnGEYuHXrFnbs2IGoqkLXdSiq2h5Bou+hVBQFRV2HvsbkgIcQPeMjRSkJQTfKgj2S0MZBIjM9je6uLkQiEbdzJBOVNlLmJogi+vr60NfXh4OHDqFQKLhahXQat27dwvXr1xFRVaRSKfSnUq6okZBAJEAUBHdFzCYYPtl4AkK/sDMkePfxRhFeBgClFLdu38b4+DhGRkZw9IUXWhLgrSIRlEKWJC+FA5Yrdxips9m13CikYXFxEYosIxqNosgiHm0Jj7P0QDOTOe8n4FDqHRfhqT0eHVoPosr2GYlEgKUlmIbRlnOnsRb2u8fG8OjhQ9y+cwf79+9f9bn1jACHhQ88OeAsmF/IW7dvw6EU+555xjUkMU0UQ/bt9uB7kBRFgQiEogQPAk4KHKZGNnmVgr/lbRPkwPsu309ZKVSr0QTqOHiUTmPXjh0AXLW0ZVmlXS2bQCwWw7Zt27B161YYhoHZmRlMz8xgZnYW9yYnIRCCzq4u9Pb0oLevD/F4HJIoViQBVY+d/VmzjrxZcG3IE0IOHNY8aWpqCmNjY9i7Z0/bjt0vvOSTe0l0opw0sG6fNUmDIHjXXZKkkrRks8hms0gmkyBw72udTXBhwKs68IsLmzheL6Xg02jxksYSjRLvbrtG4OMUv7aURQ/CJAeWZcE0TVDHQWdHB8bGxnD37l3sZGMRAM8Xhtp2SWffJxEfaHLgz01KoohisYi7d+9iz9gYIqoKW5ZhMhaqy3LD3Qnr7Lzkn6qiQBDFtosSS3oewL2R/ZOr7PuNXJTYyirJX+Pu90jgrzWK+YUFmLqOgcFBACukzm5iIOJhW8s0PbU/R0dXFzq6urB7zx7omoaF+XnMzs3h3sQE7t69i3gs5pZKDg6ir78/0CDESUE7YipPkkOiaRg4feYMFubncfjw4RJb7DBBffdeTTRDGhwHhuMApsk24aaMREly/VIq1L/Xw9LSEvp4/bwkec9m0yWNZWmDMAgpJyvl93v5QoL6ohLtzsGX71tVFJimGXoUlqcqZFmGKIrYs2ePWxF1+zZ2coM8thiyHOeJn1yf9ONvCRZ7sAUWJrx54wZEUcTu3bsBuFoANRqFVixC0zQoTKgXBmhZ+E1RVS+n1Q77zVpiGV6lIJf9Pp4LD+vhrkgU3IMKPJCm02moioLuri4ApQ6T9cDDtDwPXSk9IDD9hyxJ7oqQkY9BRkZsy8LM7KwnbByfmIBACPr6+zHItAqJKq12aYiDdPl2/cY1Gxn5XA6nTp2Coet4+eWXoajqSkg6bPgJUzPh7hqkweLEkhFryvQN3FmVACtEgf1Z6zfajoNsNutNMvw+dBwHpmkGF8pWKD8ME7yHQHkKr5o2h79XtQKiDVAjEeTzeTfl6DihEE+TaUAcx4EajbpGcZKEPXv34vr169iyZUup8dqTqgHy4QNNDviEIggCsrkcJu7dw6FDhzyXRACIqCoMXYdt29ANo7SVcysou3kEQiDLMnTGeMMiB+WRgkrgVQoV99mmHGLVSoc6RCGdTmNgcHClAZMvclA+ENiMBHhkoMLv4GFhTgbqDSSiJHkRg8PU7cKWZl0lr169istXriARj3u+Cv19fd5A6t97qxEZP0o6Mm7gtMLC3BxOnT4NWVHw+htvIJ5IYHlpCUD7SU2oqRxWeilJEqCqXoTBsixYtg2b3WsWF/my0jY/URAlqeQ3czFip49YSrLs3bv1yEGlCpiwwfUG1Kc34ODVNpXGmYoOqyEflx8q001RSmGYZstjNmWaLIdSr4U93+eunTtx9+5djI+PY/+BAyv+HS2mOTcCPtDkwPKlFK5cuYJoJIIdO3eWfIYQgkgk4tXPKorStpa4sqJA0DRouo5kldVnIyi3y60ELswiAJSQ2lA3iqBEoVgsYmFxEWNjY95rXPFvs4gLAG9QrkQGJP9qLgAZqHfciWQSY8kkxnbvhmVZmJmeRjqTwaPHj3F3fByCIGAglcLAwAD6+/sRi8dLa6NDAP+VG7lV88MHD3Du7Fl0dXXhxMmT3mTX1nRIWX69beFtX4SBT0M2s2XnhMFhlVF+7YIkCG50QZKwtLgIUIqkzwRNliRocCuJVpFm37O9VmtUi40TRBAqCrSJILi59irwHBdDvk/LhZWEECiqCkfToOt6y+TAMAw3TeJbQHEyJIointm3D5evXMHotm1eGmOTHDzh4JGDXC6Hqakpt7FLhZteUVVImgbLtqFrWkkNdjOo9jCrigIBrZtoeINGgMFQZykFSZYr5jW5iGmtwtW1iEImkwHoShdGh63WdF1HQdPc8GuZ7TNvpsXJQDt/hyRJXrMoSl1Dm0w6jcz0NC5dugTLttHR0eERhZ7e3lCqYDaCpXU1UErx/p07uHL1KkaGh/HCCy94lUH+dMhGjng0A1EQICqKdz/ye5WntmzHgeU4sJhwbmZuDtFoFLZluWI/n8iVEwupwnlbS/AWxXIVfQ0JMN74dQhhpCyrEe2IqkLTtJZLGh3Hgc4qFKIVzMUopRjdtg23338fE+PjSLGuvU+D18EHmhxYzOnr8aNHiEQiGB0ddd8oY+kEQDQWQzabdaMHrZY2VrlxFFUFEQRXA9CECInfkLwCIQhMduNXjRqEvMptBOVEIZPJoLOrCw6lyOZyrnLYV6bmOA5kWS7RC6znsXd2dqKzsxN79u6FoesrTo1TU7h16xZEUUSKNYoaGBhomnT6DX42Eqjj4NKlSxifmKjcPMn/HLTh2Etsf9f53AiCUEJceYieezBkl5YQTySgs3JmIgjuJMzy9aZhQFjnviueGLGKCp87UgaZFksiOW1IXYZV0sjJhcA0Bn54fiWEYNvoKG7dvg3LMCBFo54p2ZOMDyw54IY/hBDMzs6iv7+/RDBXDlmWIcsyzDaWNiqyDFEQQChtuEOjX4QUdBjkan0C1KzEWOuypHI4lMLQdUzPzKA/lUI+n/feEwQB8VjM1Q7Icls6soUBSVGwdetWbN26FZRSLCws4DEzYLpw4QIopejs7HQNmIaG0NPdHXg17V33DbT6tiwL3/nOd5DJZHDkyBHs8JV7cbR78i4JYW+wlRxhGiNZluE4DpaWljC2e7dnhubwlIRpQjMMGJLkpSDWA5RVbFDUbrbEU3yNbrvZKEK1b4RR0mjbNkzmoxKvQNz9Iu/u7m6AUszPz2PL1q1PhRHSB5scwA0bLSwuYgcvRamBaDQK0zRhGAYsVW3uQa3zAMiq2lCHxiCCw2ow6qQUOEqaLa0RbKbSNgwDpmVBZ10HOzs6XAEhKy3ljU9MFrLl+cf1XimuQtlE2NXdjc7OTuzbtw+GYWB6ehrpdBr37t3D7du3ISsKBlIppJi1c6TGveA0SArbDa1YxKlTp5DL5/HSyZNe2Wk56rWZbgWrcttspbrh7gsAC4uLMC0L/f39iEajiLCoAq+pB6XQNM1NNQgCJEYq1jIyxhcR3BSqKpo4Hn8UoWFtSI3PtlrSqJUJScv3RXxjbyQSgRqJYHZ2dpMcPOng5GBxcREAvFxRNRC4bFRVFOiGgWKx2JRosLyEsRyqLKNASKAOjfU639WDV6UQQIi4FgOrzRoT6cx3wI9sNgtQipHh4VWNfwQWgjVZPldRlFVCzI02KfjDr4qiYHh4GMPDw15UIcNSEOfPnQMAdHd3exUQ3V1dJQP0RoocLC8u4tTp0wCA1199FR2s5LQS2lp+WbZNPrFthPiBn9ATQjA3OwtRENzVJ0qjCtFoFBRAQdNcS2jiNmgzDMP9nCRBUpQSW+52oJq/QTmaLhtlcBwHgigGjlTWIhK8pNFooqSRp3scx0GsTrqPk/Oe7m5Mz8y4r22SgycX/Kaam5tDPJGoewPwsH0kEvFWs1ozStg6D40aibi6gzpCmma6+fnBS6+CVikQQWhLaNZyHJi6DoOXffkgSRIUWYasKJiamkIikajaEVCSJK/uXFGUlUGKoeRcEbLmq+yg14r3d+jp6cEzrAV1moka746P4+bNm1AUxdMppFIpbyBdb83BdCaDM+++i0Q8vqp5UiW0M3JQEW0qy62HcjKwcjju32fn5tDV1VXx+hFC3MZslEKORCAKAizThMlKCg3m4krAmm6xxlthn9Nq/gaVIBDSdK8P3vAtSAShnr6BlzTa1PWgCGpiR1mkhsIl7rVIBREEUOaX09vbi4cPHkArFjerFZ50ELjkoF7UgH8WhEAQRUSiURSLRRQLBVdoFGIJIJ/YuOlGuR1vK2kEP0zD8PKHQhWBkR9hloLZjgND16Gz3+iHJElQGSHwiz7nZ2fR29tbdZuSLAO6XtVutnywXGuyQNFc2F9VVWzbtg3btm2D4zhes6jM9LTXLKqjsxM9PT3YumWL1+FzrXHv3j1cuHABAwMDOHbsWKDmXWtNDtpazuhDPTJQ/tm52VmMbttWdXuiKAKCAMeyEInHIcsyItR1dzVNExZrAc6JAuBWFMiK0lQTtVXHyBvUUVpVjOhHGFeTL35qRRHqXUl/SaOmaYHIAaUUhWLREzl7ItIqxNJvSd3T2wsKYGZmZrNa4UkGpRS6riOfz6O/vz/Qd/hNH4lE4DBTpEIuB6GjI9BDE+R2EQXBFT5aFjRNQ9wnfGw1WuCHzpT+a9kv3mLRFoMREwCej7zCBrJKVSCWbWNxaQnDvJqkAni402JudfUmnKpkgSuuQ5y4uK/9qv2X167XgSAI6OvtRV9vLw7C9X3IZDJ48OAB7t+/j/HxcUQjES/9kEql2u5dQSnF9WvXcOv2bezYsQPPPfts4PTGWnkccIS6H3btSlwvA5CBcuTzeei6Xpv4iiIISmvnic+IiUYiq4gCd2vkVRJKHV1RLViWBQFwm1oF2AbX/IRRptiqELrRkkZN07x0QjwWCxSN48cYVVV0JJOYmZ3djBw8yaBMWQoA/f7IQY0B2x/GisZi7kNomsjlckgmk/XLGwM+LIqioMjMkOLxeOh9wm3HgcVCkUEnD0IIHDQ+wFJKXddH5hPBIUkSVFYHXu8BXFxYgO046KsxgIrMDIk3yalWi10N5QN5uS98+WAXBmkgLdZ5R6NRbN++Hd09Pa6TnmFgdnYW6XQa9+/fhyAI6Onp8VIQHR0doa7SHdvGuXPnMPXgAQ4dPIix3bsb2v66pBWaBCd43GOAlK0ky9NYQTE3NwdKKXp7eqp+xu8CWqnE2U8UEI3CYip7k+XaNbZyVtjz1mi3QJ5SaOSZCjtKU8kXIcj2Gylp1HQdpml6OoOS81SFpPgjB0QQ0J9K4fHjx5uagycZlFIszs+jo6OjNNxU4wH3iwkJIYjHYsjlcrBsG/l8HolEIpS8r6IoEAlxzTcAIGRrVJOxaJF1FQwKoYEH3mbmITqzHQXcB0lRFEQarPSYn5+HKAh1BaAy86K3LKthclAN1VaClJFIf5Sh/DMln20jKKWuoK2/H4ODgzh48CDy+bzbgjqTwY0bN3D16lVEYzEMMF+FVCrVUlmcoes4c+YMFhcW8OLx49g6PNzUcQNtIgdNlsX5r2d5BIoCoaeg5ubmkOzoqBn+J4RA9N/bdaJ9kihCikYRiUQ8ga9j256QkUfqgmoTuPlRkOio/5jDBCcbjZKOoCWNhmnC0HU4joNIJLL6c1XSChQo0fz09/fj7t27ruPlE44PLDlwLAvzi4vYMjQU+DvlAhgiCIjH48jmcrAsC4V8HnFmj7sKDdzQKjND4i1bw3DR88NLKTQqpgwg6DJZGSbPfQKsgZWiQI1EmiJPc/Pz6OntDdT3ACG2ua2FSqShpAGS7+9rQQ7YgXivxeNx7Ny5Ezt37oRt215EITM9jXv37rkpir4+11dhcBCJRCLwgJ7P5fDOqVMwDQMvv/IKempEdOocuPtnOzoyVkkreBM+pR7Z9+tBSp7vNYhozM3N1UwpcEiiCIu43f6CJop4zl1RVViWBUPXvV4NFnNiVFS1ZsqBd6EE0FDEgaC+YLAZ8GdMaGDb9UoaLZbCdViatWI0tcozTADwGAERBPT39YEAmHrwAM8+/3zAI9yY+MCSg4WFBeia5rVIbRaCKCKRSCC7vOyqhovFijdgvRJGP3h3RB4SDLPtqEMpLOZvoDQReq/0Cyil0A3Dzdf5wmmyJEGNRKC0oJ4OItjy7w/AmpCDSiivqy+ZcCpNVkzVTXyfafQ8lTRdqvJdURRdHQKznc7l8y5RSKdx7do1XLlyBXHWLGpwcBD9/f3eREDkUgJpEwlvv/02FEXB66+/jngLplOhag7YZE8odZsQ+cPPKJ2ovPfaqXkIAN0wsLy87HWBrQWRuSUG6T5aCTzt4Ni2u0pm5j5eykGWXefXMgLA/Q142q4RtMs8zZuQA46pKuuNU6mk0bZtFAoFN20iihWrz2rdH5RSbyEgEAIiSejq7saDBw8a/FUbDx9YcvDgwQMQoOFVTyWxmyiKiMfjyDFxkUDI6jKugMSAfyoSjcKwLOTz+VDJARcD8s5wDaHsN1i27aUO/AJDRVXd1EGDuc1KyBcK0DQt0HXipjAOa3rT8O9rEwgYOSwHXe1TUV5F4X3f96efRPgn2KDEIhGPY2zXLozt2gXbtjE9M+O2oE6nMT4+DkEU0d/X52oV+kYgxDrh5OcAAI+sHiSTSZw4caLxyFMZeLqpZjTJN+kDKLnP/GJA4osCQBAAv3iv7M+NgnmmNwhyb0uiCAHBBbfVIIgiIqIIVVXd1bRhrBAG0/S8XCS2QOFkpJkUVLvOd3kX0nqROZXpmqyykkbHcVAoFr2JvarRWA0S4jiOtxDg1ySVSuHho0dr4g3TTmyM0XMd8PDRI/R2dTVU6lNrAJYVBTFKUSgUUNQ0COwhaxQ8bBaLxVDI5dyyGkpDq2E3ealTM1UKTIXMowSmbxUjCgIiLIQZZr39/NwcKFBTsLVyeK4wy2EmShuFHDQdWi2bECuRCIdVsBBBKElpgEd5/CmHCuJKQRQxyFwYn332WWSzWaQzGUxnMrhy5QouOg66uj+CpDyOuSKFuvU5vPzSS6u0Kl5FRoVQ/Sp3Qjbh8+obijJSVG3S9++P7wsVJqEak8ValTMGwdzcHNRIpKp3hx+CIICIIojjwHaclok3IcQTKFq27aYcWGlxoViEoGmQFcVzUW3mWWrXxCgKgkcsuVCxlgCwUkkjL1mkjuP2zolGmzpej+D6ohH9/f24Oz6OTCaDwSruoE8CNsbouQ5YXFjAjv7+xtltDRapqqqXCijk826zDlkONDlQrLBQwC3BEUQR1LahaVpdk6ag4D0lmhHs6bqOQrFYErZXeOqgTSVz8/PzSCQSgUsuJUmCyUxiWlvXhogGSxYb27RP1McJA98nfBNnucrbF3nwH1mctaAeGR3DH/0hxTvv2Ih0TuPoCxoikgNxZgZnzpzB4MAABoaGvAiZ4Nuet5/yffsneUpXhKrl56bapB8UNc71RiMHvb29gX+nJIqwmXNfGFE5/3alWAzUcaCbJkwmIi4Wi8gXChAlqaSkuhHUm7ibQXmK1mEVHLVSGCoraeSusEVuVERpzZJFL1JX7VgYufDfw91dXaCUYnp6epMcPImgTQ7Y9UQ20WgUjuPAMAy3giFAiSMFY6B+kZsglKQWwiAHtuN4D2ojYULTNFEoFLzGKwRuHk9VVUhttuwNKtji8PsdbATUu89KVtjNgF1P4o8UlCvsKx9Yxc8QAEtLwG/+BjA+TgBIMGa24Ou3uvBdBx/iwI6DWFpawsVLl0AvXUJHMonBoSEMDAygt6enZi39qtU/0wZU8nwoec785YMBsFEm/1qwbBvz8/PYf+BA4O+IoriiO2gxpVMJhEX/VEWBxUq0CQA4DnL5PCK89LiBZz5sSuz47nc/6rkqRiMRLC0twTCMlbGMexnU+D31fqnD7k2xTKD85CYTVvCBJQd8QGrmItbLJcViMa/sKJfLIZFIVCUI5RGD8u3kcznkCwX0hpBa4CVJQRu2WJblRgp45QEhiEYiiKyRcZJlWVhYWsK27dsDf4evqBzbrugwuaFQYRCpppyvFn2wywfDFu+Rhw+Az34WmJ0t248l4gEe4vu3/QC6urpgGoanVbjPmkVJkoSBVAoDzFehVrMooLRhVLlos5rwles3/DqCqpqNDYzFxUXYjtMQ8RUrmCG1A4QQyIoCSVEQ8Y11GiuFVBiBWI98uj+lUI5apY6iKEKWJBjFIvL5PBRFQbTcy6ASBKGqxwGwEjlYVRL+BGsNOD6w5ABg4akGL2IQ4RchBIl4HNlsFrZtI5fNVowgULir+WrbizD1sBlSasGrV64TNXBY3tHf30FVVcSiUc+4Zy1aOM8vLAQWbHEIguClFqwNQA5KQutl4VCKKpNgpQ1VC3tWC803gevXgP/z/wQKhbI35Byw7y+RwI6Vl3wtqEEpFhcXkc5kkEmncf78eQBAV1eX56vQ3dOz2ieiiWPnJKKSDsP7DL83feebk66NIhCbm5uDKAjoqtNczQ9RFEEEATbzLWjEo6RROLbt7kOS0JFIwLZtaLoO23E8l9OIqq6pwypQv+qrFkEghLhli4SgI5kMxQuFE5Wwy803Aj7Q5MATUDX8xfolNEQQkEgksJzNwnYcZLNZxONx74bkqYRag1XYqYV6egPqOK4zo6Z5r8mKglgkUiJIWqsWzvNzc5AlCR0Ndr+UJMmr5W5GFNoKyidrSumKiVWFe6aVJjV+tDrpfftbwB/8QYnI30V8Gjj5rzCUEjG4PFBt5+jq7kZXd7fbglrXXQOm6WlMTEzg1u3bUGTZaz89MDCwIgQmpC3dJCud72ZTie3A3NzcKsJUD4S47ZIJIbDbTA4MXqXALJM56TaY26lDKQosh1/RNMh3zGHpPKqlFMpRcp2Z6FXTNFBKvZbuQUgNdXdaM7rsHdMmOXj60MygWk93wCGIIpLJJPLMRTGXyyEajUJR1cAPC08ttFq1QFG97SrvM1EoFr0BVZIkxGKx6lGGgDXGrWB+fh7d3d0NXyNZkqABTdeEB4avEqC8IZb/z5pnqcXz6FUdNDvpUeCLfw78+RcrvNf9PvDSbwLqMj666+8hfSETaJOKqmJkdBQjo6OglGJhft4zYDrL6r+7urrQ3d2Nvr4+dHV0hDdp1zrfbB+VSPmq9E4by9C4d8eOHTvqf7gMnhmSbQc2Q2oGJvdC8QmNCSGu5bksQzcM6LoOy3GQKxQgiaJLEioQlrDIQa2UwiqwyBSFWw5tWxYIa5InsHLnetqJetO9v9fNendEbQc2yUGT3ws6eAjM9jdfKLiNnpibYjQaDTQg8qoFU9dbSi3wlIIgCCUrDk4KPAtQQUAsFqvLrNut+qaUYnZuDjt37mz4u54okbW1bXWQLy/DWzVA1Qlz1kKrQ0pJCL1BWBbwB/838M47Fd7c+h5w9PcA0cCe3j043HcYaXyt4X0QQtDT24ue3l7sP3AAuq4jk07j0ePHmJyawsTEBC5fuuQaMA0NIdXf31yZ7coO65ItoULka9U3ykSS/P0wpoBcLgfdMBrSG3Bwy+N2Cm5tptehlFZcHBBC3JSCLLs+JyyFl8vnveqldoTZGzGSA9yUbaFQ8ESDyWTStXNnwuy6wsp6egPfsfjHw5ZFxhsEH3hy0Awazl0S4qlii4UCdOYkGI/F6oajiCAgGo3CbDG1YJZFDfwVCN5+WAVCkN/mufu1iTHncjnout6UNa8gCBBF0XWDtKyG29Z6wjffv5smQm2OrjTrMpjPAf/6XwPXr1d4c+y/A4f+BCDutj914FOhXWdVVTG6bRuGhoaQy+eRy+WwvLyMNCMLBK4x2SDrLNkZZlSBI+AkU8m4KoyBf25uDgRAdwDvjnLwigWnRTOkWjBZUzZJlmsr+dnYpLAyQdOyYFgWjFyupLIhjGN0amizqv0G3nqZEOL1vZFEEQYbF1rpLQKUphAFQVgZS3kp7hMeTfhAkgP/RW36AjbIYincgVEQBBTyeZiGgaxtI55I1BXNxaJR5LPZllILXG9AACxnsyUVCJFIBNFIpOFzEcSdrFnMLSwAlKK7u7up70uSBNu2A5ED/yDLxZYVHQ2bQN3JpMXz561oGzjemRngs/8KePSo9HVCKITn/gj2jq94rx0ZOoLdfXuwsLDQ0nGWg5/znp4ejIyM4MCBAygWCl6zqJu3buHa9euIsBbUQwMD6B8YaHlAD+XYS/7R+AQ9OzeHjo6OpgRxgiC44XW2um/H+eAphaDHJwoC4rEYLCactmx7dWUDgqViqyHoWMNTpDqzh5YlCZFo1Ov1IEoSwNpZ16qlaURv0M5xcD2x/k/aOqDihWxQrBTkZvd7uPO/y7KMREcH8rkcbNtGdnnZFSrWCKVGIhEIktRSasE0TRSLRVi27eUF/RUITaHMpjZMzM/OoqOzs2lzJUkUoaNGnwVKq0cGwiIGXJFfa3uElDRpamofCE4Oxu8Cv/EbwPJy6euKCuz/gbdwEV/xvUrwif2fbPLIasOpEPGIxmLYvmMHtu/YAce2MTc352kV7t+/D0LISrOogQG3S2d5vXuAfYeaEitPUfiJJioTw9nZWaT6+5vepSiKMC2rLeTA9jVaajTiJokiEvG413yNVzaYhuE2XWuzaI+bGxmmCYdSRBRlVSRUlmWPwNQCJxO1UM3++0mPGHBskoMWt1P3RqAUdpmfAm8/nM/nYZom8rkcItEoIlUm/VZTC7pheGWVkUikYgVCU2CTajsehvn5efQ0EXbl8Jsh8fyiVwa3Viy/lchUQDRCDs6dBX73dwFfhSoAoKsL+Lv/aB7/+uZ/LJldXxl9GcOdjbdiDgLvuKtMGIIooj+VQn8qhUMACqxZVDqTwY3r13H16lXEolEMDA66zaL6+tz7eb1XcGVkofz50DQN+VwOvfv2Nb0LURQhkPaYIRkspSC20CxNluWSygabUuQLBciy3JQ/QpDn1XEc5AsFN93iOK5uqozc+Mu464mVSYDIME8jrCI9630PhoQPJDnw4DehaYPfAQCv697qXbt5sEKxCF3TUGT5sVgsVtkQyZdaaASapmFhacldZbDqibBqkwkhrsVzyJ4HhmlicXERO3ftanob3OiJlzSuRzg6MAlpoWKhUrvmSvjK/wD+6I+xamk9PAx85jPA5yf+FDZdWU2JgoSPPfOjTR1TEDQa8YjF49i5axd2smZRs7OzXrOoiYkJCISgv78f/f39GBwcrNktck1XdmVkYXZ2Fg6Avr6+pvULPA3ZDlGiZRhwAERbtEPnlQ2yJEHTNOisZbJlWYhFow1FEepZMHOzNv6ZRI1UrcS6W9Y9dwH8FDg5kMqI1Gbk4AlGaCHkGjcQr6mthxhz6Srm8zB0HbZtIxGPg5Td3P7UQkHTEKvjPmczJm2aptehsLurK3zTkjY8CAsLC6BAU5EDf4pAkiTYjgNznchB0HSBQMhqp8OAqFdK5TjAH/1n4KtfXf3ewYPAz/4sMG3cx6mp0pKFj+z8HvTFW2tnXgutmDf5W1AfPnwYuXwemXQaj9NpXLl6FZcvX0Y8kXC7Sg4Ooq+3t3SyWMeV3eN0Gp3JJCLR6EpUgZXWBT0T3AyJWlaoZkiWZXmLmbCeF179JBkGsvm8awqXyyESiYQyFhmGAa1YhE0pRFFErEafBID9LvZc1lo0OI5Ts5TR8Vl/C4JQck89HXGDDzA5oIBnfdnsxaz53QYGIFVRIAkCcvk8bMvCci6HRDxeajzkTy3kcjXJgW6ayOfzJTqHiCi2xc2MUAoH4ZbuzM/NQZFlJGqs/vyoVk0gSxIMw4BpmojWIVPtQNA7oOnBpKyUqhy6BvzO7wAXLqz+6muvAX/37wKiBHz+wp+WvBeVo/jo3r/d7FEFQqB2zUHAInCJsTHsGhsrsXV+9PAh7r7/PkRJQn9fn5eCiIbYAr0hUIpMJoPRkRF26GWdM9lr9ZT5hBCIggA7ZDMkvxAx7NWvoijoIAR51vCoqGmwLMtd9NTqx1Hl2ebGRrppglIKWZYDiaq9igUmVq5WqknqjN888sAjlP5PO7a9JinFduMDSQ4EQUBXd7e7Qm1QiFiOSjn3usY3FSBKkqdDsC0L2WwW0WgUqqp6x1cvtUDh5mY1llSWRBHRWAzZ5WX3AWrH6pkQt248xNXY3Pw8enp7qz5c5UZD1SDLshtCtCyXCG5QF7NWvDa8bZSdq8VFV3h4b2L1937sx4CPftTd8Y2ZG7icuVzy/g+M/SASajBi1jT4sYd8TURJwtDQEIaGhgBKsZzNuqLGTAaXL1/GpYsXkezoQG9fHwYHBtDb29tWp0E/FhcXoRWLGKjQqc8vYvT/uxpRECUJxLJCM0OilLbWzj0ARElCPBZzV/u6DtOyYOVyiMZiVcemSikFx3G87rCUUrdZVAPaC1GSINh29dRCgDSfZyjH7x3fNZpfWIAoSU90R0bgA0oORFHEli1bMHHjBjTmEd4MKukOWuk7IPiEioZhoFgowDAMxGIxiJJUM7VgWZYbeWD7jkQiiEWjXj92QRDaNjmGbYg0Pz+/yvyoGTGhIAiQRNEd+Cxr7X3ggx5rkKqGetv3fffBA7dUcW6u9POiBPz0TwMnT67s90+u/knJZzojnfi+3d/b0HE0A890q52rK0LQ0dGBjo4O7NmzB6ZpYnp6Gul0Gg+mpvD+nTuQJAkp1ixqcGCgqig4DKTTaUiyjN466TLCxbPez1gdYZBCbsJk2fZKSqFNZImPl6qqQpIkz6CoUChAURRE6nis+MsUKft3vJaLaxXIkgRd113XxEpjV53n1q83WCXqJgTTmQy6urqaMrnaSPhAkgMAGB0dxdXz5zGTyWBkdLSpwbkcHjHg22lywozH45BkGRpjx9nlZaiqikg0uiq1QAEUmaARcAfbRCLhMXHOcNsSNeBgg1cYw7xuGNANA8mOjlCqC2RZhmVZME1zzclBYLC8c6PwygF937121W2eVB5ciseBn/s5YK9PJP/eo7MYX7hb8rkf2fcjUKX2p2A4fQ6TGgSJJPFmUc899xwWFhc9UePFCxdAKUVnZ6dbKjk4iJ46LagbRTqdRiqVamibq4gCy28LguCZIYUBi0UbZVluXzicTcSEEIiiiEQiAU3TYJgmDMPwxIpcH+JPKZimCY31dHAcx/UvqNNuuRpEnyiRUuqeY9+CzqG0pt7Ab3bEnSCJ71mcnZvDoSNHNtMKTyq6uroAWcb0zIxLDpq8kJx5lte0t7qS5h7mxWIRhq67ndBYjkwEUGC5u1yh4BEAVZYRi8dLVmM89NZuQV5YqYVsNgvHcRCPx0OpgpAlCUVC3Hxqm8ouq6ERwtSS9oX9pm99E/iDfwc4ZfNFKgV85heAoaGV1xzHxp9d/3zp5xIDeH37600eRXCUdGRcr1QPIejq6kJXVxf2smZR09PTSGcyuMdaUMuyjBTrKjkwMAC1Bd2KrmmYm5/HC88/39IxewJU1gzJDmoFXAM8pUDRuLdBIyBYITeAe99Go1FIkuRVa+XyeUSZWJE3mNI0zTs+wE2vtnKckiSVrP4dx/HGr0b0BpXGVEPXkcvnm+qbsdHwgSUHoihiYHAQ6Uym5UnD76kdJgghiMViUBXFy7GBUuiGAdOykJmZ8Uw+4uxzJceF6s2WQkerhkhM2Li4uAgCBBYj1oMkSW74lQ0Ga1W1wC2Yg6KZ1MyKdTLBF/4M+Iu/WP2ZXWPAp38eSHaUvv6N+9/E4+zjktc+sf/HIArtPz/+fhChkrUGzl/5+VZUFcMjIxgeGQF1HLcFNdMqnDt3DgDQ3d3tVUl0d3c3RGymp6cBAAMDVTpbNgjCbIkJ3JWu2AI59/quAG1vcV7pPpdlGaIoehbMRdbtURRF6LoOSgio40Bl2oJW7xmZjQklHij+kuCAegP/ueLfmJ6ZgShJTfWE2Wj4QJODrVu34saFCygUi4g3qWDmt2k7jXW4WNHvh1Bg+oKtW7YgmUxWbHRic8tkQlo3PKqDZla+lUhVLpdDLB4PtXGLLMtwKIVhmhvCfjcsuFoK4PNfJPjWN1e/f/w48A/+ASCXZVMMS8cXb5a2YdzetQPHtx5v49GugF/vMGMGjYqAa00vRBDQ3dOD7p4ePLN/P3RNQyaTQTqdxt27d3Hz5k0oioIBFlFIpVJ1BXGPHz9GV2dnS9GHcgiiCGKarvGPJLkTfAV9Qj14QsR2phQYBEJQaQnBSx4Nw0Aul0Ne1z1CoCgKoslkaA6L3ETKgTvR83RjEOMjntYAKmszpqenMcjG5CcdT89I2SC4KPE7p05hZmYG8W3bmtrOWta0qpEIDMuCqqrI53JeOZBlWRAr5NNNtiJoq97Ah/LcXVWwgbxSCWQ2mw39wVJkGYZpuv0k2ig486PR+yLIwFSOXN7Bf/x/gDt3Vr/3/T8AfOqTAKkwnn717lexWFwoee2TBz8JUunDbQAfXMNMKbSzS6gaiWB02zaMbtsG6jiY5y2oMxlMTU6CEILu7m7PV6Grs7MkTUkdB5lMJvTVpEAIwFILgE+4CF/1QwBxnZdSWGdNjuM4sLhIEGwiptTrSRMmJEmCbZol5CBIBNnviljpmGbn5nDy5ZdDPdb1wgeaHKiqimgigelMBtubJAcca5HPzudysC3L1UsAyOXzyGazIIRAVxTEfWIeYA1TCgzl9b7l4O/xbo6Vztby8jKGtmwJ9bh4ftIfRmw3Gu6X0ODENjMN/NZv8R4Jfnc24Cd/Evjwd1X+Xt7I4Uu3/6rktQOpAziYOtjQ/luCP4S7XmhWYyQI6O3rQ29fHw4cPOg2i5qeRiadxu3bt3H9+nWokQgGmFYhlUpheXkZhmmGXtomsoqFSqLE8mqHaiWRvAEbYfX/7Ua1s24Yhic4pISgI5GA4zhe2+VYE1UJtSBJEnRWCuodm49gVjvOVSWM/Ltwx2PdMJ6KlALwAScHADA4NIQHjx/jGBpXTlOs1CG3szMXpRT5fN67MePxuGfZqem6GzI3DJiGgWgs5pqBYO3EiL4DrXjsvL0zRzUSZbPeEWFHDvjA5zC3xHJtRjvQ8J1AiGtnGGDSev994Dd/EzBNiogKUMf9jqICP/szwLPPVf/ul259CQUzX/LaJw98qtGjbQmhGSD50MyzFwahj8Zi2L59O7Zv377SLCqTQSadxiSLKkQiEYhspRnmIoL7M9R0YuWVRIKwkvrznSseNVDbKEQsh9+7wLZtryEcpdTr8MjPFddaFQoFRKLRphuxlUOSZRCu4yoDEQT3WayAqiWMcFMKsixj+/btoRzjeuMDTw62bt2Kc5OTWF5aQmdnZ8Pbqfigh0gSKKXIsQ6OhBCPGEiShKWlJUiO41YwCAIM03S9EXQdqqp6lqxrRg6YwMyf/3WAuupfjmwuB0ppW/J1iq+kcS3IQVMIMGm89x7we78LmCYQjXEzKIKubuAznwa2ba/+3fniPL46Xuqj/OLwi9jRvbbK6lask8MCQbhllEBZs6hDh1DI55HJZHD16lXYjoM333wTUd4samAA/alUS8+myM6f7TiBTL5WGSzZNgy+gFhDcsDtonVdh8F6OYBS11JZlr30JCEEsWgURVatwMu1wyAIXqk3jxz4ogbUcTyBph8OqwwBKusNZmZmsG3HjoYMmTYyPrDkgNfaDg4OomgYyGQyDZEDf9SAb8+7uZrIH1eC4zjI5XLefvwNRfi/rYUF5HI5DG/dCsMwUCgUYNk2CktLsEwTsVhsbQdhpiyulTqohmw2CwBtIQdew5U1Kmls5urXtuMG/sdXgD/2NU8ixP3L0FaCf/KPgXqtKL5447/CtE3v3wIR8WP7f6yJI20NbSEHzTxvZZ74YSMWj2NoaAjnL1zAC88/j0g06naWfPwY9yYmIAiC24KakYV4ItHQOSGCAJGtwm3HgRQwXcZ/sclV98wsbC3ANQ75fN4T9ymyXGKj7NctEUI863NOELhQsRXwcdRmqUZRFEuePaHCGF5umVzyu+A6I77w4ostHddGwgeWHADuRRZFEd19fZiensaePXsa+n75DRKmKMp2HOSyWW8iS1SoSEgkk1haXnYfmkLBsyEtsKoGQ9cBwPMdb3cEgZtAUTQ38GezWVed3IZVjCRJEAiBRSksy2prPTeApiadavePYwP/6Q+Br/9N2edBsWs38Hd/kqAer320/BDfvF9a0vDG9tcxkFh7i1c++IdJDkInYyEhk8kAcNOXiqIglUq5zaKyWVerkMng2tWruHL5MuLxuGfA1NffH6isUBBFgE1wjUI3DBBgTczBKKsW0llzOctxILJIqF8wXema8AiCRgh0Zr1MWaShWfDKDOo4sCrokCppD+wKJYwcS4uLcBznqdEbAJvkAAAwMjKCybt3YTtOoBK68qhByXshkAPeuYwyJ7REIlFRRCcKAuLxOLLLy1haXkY0FgNhOTvTMGDZNgRBcMN3ug5ZURCNRMKfGNkKgLC0ggCUaAyCIpfNItnRUf+DTULmXRpNs+3koCnHyAqrFU0Dfue3gYsXV3/8xRMUH/0oEIvW39Pnr/1ZaV2/qOJHnvmRRo8wFHiljOvtIBdShK8WHqfT6OnuXjUBJ5JJJJJJ7GItqGeYAVM6ncb4+DhEUURffz8GGVmIxeMVty8wLUGj5MBiHR0ppR4Zr2TT3Cocx3EdEJk2yoF73aOsRNE/hlJWnVCNNEZYYyWNWygzgtAsyZQkyetaiyoNmPznwjM/qkAO0tPTiMRiGB4ebupYNiI2yQGAnTt34s7Vq7g3MYFdu3bV/V61sDQhbhOiZiZGDpv1SKDUbUEaj8drqus7kkm3rLFYhGEYK4MQIUjEYohGo7BtG4ZheKJFSZJcklD2cDYEpivgZj+VwmyNbnlpebmpNs1BISsKdGbT2nb43DKDovzTiwvAZz8L3L+/+rOf/CTw6qsUDq2/An9//n2ce3y25LXvG/s+dEa6Gjq+sBB6KWOTz1u7IweObWM6k8Hu3btrfk4URQwODWFwaMjVGPmbRV25gkuXLiGZTCI1MIChwcGSZlFCjYqFWuBRRVVRvOsQpqDadhwYZZoCQRAQVRQoioJKLe2DjEWqqoIIgjveMTFlkG6MlSBJEgzL8iIC5fBHD2xGpIDVkQPLcTAxPo6DR4603URqLbFJDgB0dnZi19gYbty4gW3bttUNv7crZ21ZFnK5nHtskoREPF53P7IsIxqNwrJtLC0tob+/H8DKYKEoCkSm1C9qGnTmjZDN5SCKIiKRSOOuY5RWDLtxEEIgslVCUDiOg2w2i20tlpTWgsx1ByFYztZC0/eHb3CemnKJwXxZ8ySJNU86cRJYXgpQEkgp/uTqfyl5KaEk8IN7fqDx4wsJoWsO1iAC0Azm5+dhWlbFLozVQAhBsqMDyY4O7N6zB5ZpYnpmBul0Gg8fPHBbUIui1yyqr7cXIMTzOggCx7ZhsBJGpUbunggCKGs/HBSWbbukgE3clFJIggCFRSw907iy7zVCTHikQysWXQMnShGNRhu+nyRJgkApzBrEilcu1NIbjI+PQ9M0fPd3f3dD+9/o2CQHcFnh8RMn8NW//EvcvnMH+595pup3HNQZ1JocqAzTRCHvlphJktSQfXBHMomipiGfy6G7q8v9XWzlytMkAks3xKJRaJoGTdNg2zby+TwKxSKikYjbFa3WhMmrEIL8PpbPC/rAFgoF2I7TVmcxQghkUQRlqYUNpypm987VK27zJE0rfTseB37+54E9e91/16vJBoBLmUu4NXur5LWP7v3biMrNOYKGgbBLGZulBe0WpT5Op6GqalNVUBySLGPLli3YsmULKKXILi+76YfHj3Hx4kWAUiQSCXR1dWF4dBR9PT0gdVavXGsgimJNguy3uQ5iKcxt3cHSAxLzkqlkwlZ+5hvVaymyDIEQFAoF1+yNaa4auacEQjxr5mrg7/ESxvKFo26auHnzJnbv2fPEd2EsxyY5gHvhk93d2LVrF27fvo1dO3ZUtTkNMuE1Gq60LcsjBrIsI14lv1gNaiQClZXqLWez6GAdDQkhq1g/b3YSjUSg6TqKmub1Ry8Wi4ioqqscLhtguNgw6IDaqPdDOysV/JBlGSYvaWwTOWhlDfuNbwD//t9XaJ40APzCLwD+RWh5adqq46AO/vRaaXOl3mgvvnvn+q1wqOOE33RpA0YNALcL4+DAQGgkhBCCjs5OdHR2ui2oDQPT09OYevAAD9Np3Lt/H5IsuwZMAwMYGBxcNY5RSmGylseBSnr9xKACSTCZyNBi19WhFLIsI6YotSsgQjgnkiQhFou5XgjML6FhG/wgZmWEVDU/un3rFhzbxvOtNNTaoNgkB3BD2pQQ7N27F/fu3cONmzfx3HPPrfp83agB4NX6897o9UApRa4FYsCRSCah6TqWs1nEYjFQ1OnLzsxZIqoK3TTd9tC2jaKuQ9M0KKqKaCTipSS42LARNLIayGazkEUR0TbbG8uyDMIavLQrPdRcnwngC18AvvhF4pUocuze7UYMEtV4U5XfcGrqFKaWJkte+9H9H4csrmFNexn8DW5CO/cbkBwU8nlkl5fxzL599T/cJGRFwdbhYXR0dWE3C+XPzc66zaLOnwfgdp8dGBjA4MAAunt6vO6kAiGNexvwUm0ApmG4lQesOok6DhRVhaooTfVFaVbvIEkS4rGYZxKnM4+XIOALoHr7tizLvV9RqjcoFIt4/+5d7N69G53MtfZpwgeaHHB/bG5uoagq9u7di6vXrmFsbKwktM8fgLoDGgvnCwHtc/NMfCiwyoNmwe1FLcNwzZEkKVhOnRCoigJVUdySSE2DxcqFipoGVVEQiUSa6s/QqMdBoo2VChz+nGHbShobHOgsC/j93wdOn+Hkc+X7x19kzZPKD9PvOFlpm7aJL1z/Qslrwx3D+NDIhxo6trARujtiozbVa4R0Og0AngaonZAEAaYgoCOZRH9/P/Y98wwMXUcmk0Emk8HE+Dhu3boFRZbR29eH7u5ubPH37w4IWqHyAHDdFRVVbf6atkjuRFFEJBpFsViEpusQRTF42XbAlAnfjx/Xb9yAJEnYu2dPS2WVGxUfaHIAwFsZ27YNSRCwa2wMd+/exbXr1/Hi8dIudQ0ZlARYNfPGSQAQb7FFMSEEyWQS1sIClrNZdHd3N8zgZVl2w+6MJBisZMjwVzg02LktaPXGcjaLZEhtmutBluW2ljQ2MtTlcm6PhJtMFkAI9caqH/xB4BOfqNw8yX9vVboeX5/4OmYLsyWvfeLgJ9ekr0QthO5xsEHFiOlMBj29vWvSzMirWPDlzhVVxcjoKEZGR0EdBwvz83j4+DEymQwepdO4du0aunt63FLJgQG3X0uVa+I4jlftxN1PCVxSoDKr9kZBfH827tCwGn4H1EKxiESdKi/vGHzi6kooaUzlGyuWsllMTk7i0KFDkNh5eNqwSQ5E0a11tW1ILE++f/9+nD13DrvHxrzSurCHH9M0oTPFWVgtiuOJBJaXlz0v8mbaUPNeDMlEAnYk4lY46Lqbp8/lIAoCFFaOFDSaUK+skQutBlKpho+3GSiyvCKeWkdkpoF/9a8AtsgEAJa+ofjJnwTe+HD175YMaGWDumYW8Rc3/6LktT29e3Fk4LnWD7pFeJGDdSYpQPj2yRy2ZWE6k8EzNYTNYUIQBBBWhVMJRBDQ09cHNRrFtpER2I6DxaUlTGcyuHPnDm7cuAGVt6AeHMRAKgVJFD1tDl/AOKz3gcqef2/7DaRRS44L4bnJAm5Jo2PbbrMmpj+oRkL9adJae+fpR0EQSqIRV69eRTQaxY7t2wFKN8nB0wi/KJGwkPPIyAju3LmDq1ev4pVXX/UYZkNgOapKrJR3GgNchh+WI6DIDJOWslnk8nkMBp1sfbnEku2xqoloNAqN1Szbto0iq3YQ+EChqlX1DdwUqRY75x7ra9UDXZZlgFLYLGK0HrXJ778P/MZvANlc6euRKPCP/hFw+HDt79c6n//9zpeRNbIlr33q4KdCEYG1irDLGDdezMBtwGPbduhdGKvB007VKMlzbBuWacKhFB0dHejq6sL2bdvg8BbUrAKCN4vq7OxEb28vunt6vH4ucVWtGK6nTRADAF5FU1gghCAWiyGXz8O2bWiaVlHD5Ne91INpGACYVomVNc7OzSGdTuPo0aNuA6ZNcvB0gj9YlmV5iV0iCDhw8CBOnTqFzOPHGGDmJA0L8lB58CpwkyNJQixkAV4ikYBECHKGAcM064uOAuRsRVH0yiBN03RDjKYJy7ZhaxqKmgZRkrzcY3kUpFbLWIBVKtD2NFyqBlmWQQ0DumGEfg3qnc933wX+7b8FzLLARU838JnPAMPD9bdRrVJhSVvCl+98ueS154eex+7e2kY8a4XQPQ42YEphamoKHcyrYC3grYIphWPbqyqNALd8EXDve3/URiAEXZ2diMViGB0ZQbFYxOzcHOZmZzF+7x7s99+HGolgiEUUUvWaRbF0apCr6+/OGBYEQUA0EkGBmSSJkrRq8cWrqARezVXlHrJZFAJYWVBQAFeuXHFLR7kbIhN3P234wJMDHh4zDMMtJIf7sA0ODKC/vx9Xr11DanCwucGswo1XKBRWOiw2EfavB0EQoKgqZNNEllUuVAQTTtayKy0HIcRLKVBKPZJg6DosFn4sFIuQJMlVLrOBiIDVFFfZbjabBQShZd1FI1BV1QubIuwKiSqDDaXAf/8y8Cd/svq9baPApz/tNk+iNHiVR/mV+4ub/w2Gra+8Twh+bP8ngh5528Eng7DSCq26+oXZDwVwUwqPHz/Gnr17Q9tmPfCyYW6GtKoMmbkV+ssXLcuCZZowWDTB/SBFhIXK9+zeDRCCubk5ZNJppDMZ3JuYACGkpFnUKkLPiUGAdEG7WtzLsgzVtt0+DMUipGp+DpxQVdmO4SdUbPx6+OgR5hcW8KEPfcjVXzylUQNgkxx4TNpxHJi2DRHwJs6DBw7grbffxuT9+xgN6txX9lD4BXlc3Aegri1ys3AcB7F4HEVNc+t/K0UPfGZGza7gCCFQVdVtDR2Lrdgzm6aXpyzAPb+KotQU/mWzWfd8rGHYW2FubbZtw7KsUJtSVdJY2A7wn/4j8PU3V3/+2cPAz/wM4I0xQfKwFVbg07kM3pwo3cEro69guHPj+L3zCSGUa70BowaPHz+GZdsYWWOPfVEUIVhWxZU4H3MAlxQUi0W3fBsrbp6KLEOS5VXpwVR/P1L9/Th06BDyhQLS6TSmMxlcv34dV69cQSwW85pF9fubRVHqtV5eD6iq6j7bto18oVAyvgQxD3Mo9TRJPPLgOA6uXb2KVCqFVH+/m2agdOOZqYWEDzw54JNckVlxeo8Gpeju6cHw1q24du0atg4PB8tN1whRFZnOINLGDok2b4GqqnAALC4vuxarvuOjtHHf/1oQBMH1TIhE3D4OvPuaZbmRBdN066pFETIjCv5JbTmbRccaphQ4ZFkGBbxqjNBQdn41Dfg3/wa4dHn1Rz/8BvA//yQgNsgTK4Xnv3DjC7DpSt5ZEiT86DM/2tiG2wxvsgiDGIcgZgs7cjA1NYXurq6qjZLaBS5KLCcHNrNKN3Udkiy7v5Xdn7IkQZblwPd+PBbDrp07sWvnTrdZ1OysRxYmJiZABAGp/n4MMAOmRDzuXueyY1oLSkcIQTQW81rea5qGWDRaMZVR6fqbzF6ad+4FgPv37iGby+EYq2LjaeNaFtRPMj7w5ACARw50XUdEUUoG9v0HDuCrX/0qzp07h2PHjjW+0maDT54bHUlSW/NT1HFAKUWyowP5XA65fL7EUpmyY2oXRFFEVBQRjURgWxZ0lnawbRs6pa51qyBAYREFSZKQXVrC1pGRth1TNaiK4pGXaEiGSOXalIUF1jxpcvVnP/Up4Ae+f/XlIAEmK+8T7Mv3F+/h9NTpks98ZNdH0BPbWJauofscbCAYuo50JoMDBw6s+b55FNKxbc+PgFdEaZoGUAqFKe6VBghBNYii6JVBAkAul0OapR+uXL2Ky5cvI55IYHBwEAMDA+jv6/OOkU+q7b4DBJa6zefzrlZKFEuqLKpFbrmLJLBSvri0tITLV65gdHQUXcwOmz+Dm5GDpxj84hqWBaooJTmzRDyOY0eP4jvvvYdkMtlUeRIP4xFC2r6i4Kw4EY+7tqbMNbGrBX/3ZiFKEmJMdGlZlttqVdfh2DZ0x3H/zio32qG/qAfeCMamtC2GSJOTrHnSQtl+JdfY6MUXq3yxiXztn14ttUmOylH80J6PNnrIbQXP0QLhkIMwVvxhTlCPHj8GpRTDW7eGuNXgMBnR9Zfo6roOQRAQi8UCNXJrFolEAmNjYxgbG4NlWZiZnUUmncbDhw9x9/33IfBmUQMDGEil3HGQ5fHbSRJ4c7mipnkGSZUiwP5GbJZte1osWZKgaRpOnz6NRDy+4pzre0Y3ycFTDFEUPfMfy7IgSxIIW2VTAMPDw8hms7h+7RqSyWRDPbsty/JYaCKRaHuzF66uJYKAZDIJ3TCwuLiIZDzult2sEyRJQoIRBU/IaBhu2ZHjAIRgYXHRTT2wlU27Ui9+KIoCyrQSYZKDy5eBf/1vVjdPSiSAT/+8a4lcC/XC3f60wo2Z67gyXZqz+MHdP4iEunYCz0Co4c3wNODB1BT6ensRabMFOOBOZhZrN2xZFixGtk3LgiTLkCXJ9SRQVVfsW6PmP2xIkoShwUEMDQ7iObhpQ55+uHTpEhzHQUdHhxtR6O9HT29vWyNJiqLAYtoiTdM8J9pqvT38QkTHcXD6zBnYjoNXTp6EKIqgAPzfVNfgeq8HNskBg6qqLvO2ba+1L3xNYvY98wxyuRzOvvce4rEYupk5Uj0Ui0Vv+2tRT++wvuMiGxCWlpZg2zYWlpZKtQfrBIEQz4kxHo26LaoJQSQadcOhPiEQIQSSJEFmRKEdZEFVFE8o2kzb10p46y3gP/wHwCmb2wcH3VLFwYH622ikP8OfXC0tf+iMdOJ7x7434LfXDo6P0LR6nnkjsJZJRkiTklYsIjM9jSNHjoSyvXJQRgb4JGf7PA24uFgQRSiCgEQ8DlmWUSwUIDAr4fU0nepIJtGRTGLP7t0wLQsZ5qkwNTWFmzdvQpQkDLCowuDgYFvSrhFVRY6VX3MBskdIWMWCAHjeJ4BLDs6ePYulxUW88uqrnmeCRyrY/RzZjBw83VBVFblczhWi8Ivtq9klAJ5//nnk8nmcOnUKH/7whxGtEwq3GKsnrA42bPFTJXg1xixk19XVhdmZGSwvL6OjoyM0w6WmwcquHDaw27YNAa4qmlLqlUSallWSO3W/ukIWZFkOhWzxQcICYJlmS3a3lAL/5b9QfOmvVr+3dw/wcz/nRg4CoV5qgb13OXMZ4wvjJW99bN+PQpU2XnlVmGWMnrveBsHDhw8hEIKtW7aEsj3qON5EtooMsKgmJ8wSJwCiCMM03XGGPTuU0vV/5n2QJQnDW7di69atAKWYX1jAo0ePMD09jQsXLnhj1kAqhcHBQXT39LQcVaCUuv0WWHRY9wmQCS+xdhxAELworyRJuH37Nh4+eIDjL76I7u5u/wZL0iGbpYxPORRFAWF1wp5rXpmZhyiKOHniBN56+22cOnUKr73+es3VLI8aKIribc9BG21bmRjRr8WNRqNQIxHYxSLm5+c9AdFGga5pkH3GSf5SKj4wmuzPErJQLLo5QZaCkCWpabKgKApsTYPeAjkwTbd50jvvEKCsq+KJE8BP/1SF5kktgFIKx7HxV3e+VPL6QGIAr21/NbwdhYkwDZA2WE+Fqakp9KdSTd8/lOlebB8h4BMXZWWHnARI7F4vD4sT7srqODBs2/UXKbP93SjgC5ienh50dHRg3759MEwT05kM0uk07t27h1u3b0ORZVenwP5vJr8viCKo4yCiqt7io6R8mTvE+qKW0zMzuHH9Op7Zvx9bygifZ6AEV1e1Ec9vGHg6f1UT4CWNGrMZFUWxottXJBLByZMn8c1vfAPvvfceTpw4UXGw8z/gqi8SUc9KuBVQx4HDfMD96Onuhs58DwqFQnVjpDUC8TmTabpeta88HwgjcM8ZHzhNJrqijuOlBAjccJ8sSV7ONegKVZFlzx6aNpGbzWaBz30OuHNntQr7b38U+PjHG49ee5bdVb5IKcW5x+eRyU+XvP6J/Z+AKGzMx9oJkxyEBG5x3sox5XM5zM/P44WjRwN/x38/e5EBn86JUgqJTeycFFTLkXMILF1jUwpT10Ep3TjOfVXIHD/3PMIxPDyM4eFhOJRicXHRNWBKpzH14AEAoLury62AGBxEd1dX3etGKfVKKQVBWBU94Ok73pmXUopsLoeLFy5geGQEe/bsWbVNgfkbAE+vGBHYJAclUFUVWqEA07LAL3mlW6+rsxPHjh/H6VOncPXqVRw6dGjVZ1ZFDXzba9d6h6+uxbIlqiTLSCSTWFpexvzCAiKRyLo3vuHmULqmBQrL8ZSCxEpBKaVu2JURBcuyQG0bmm2DMLLABwOuWaj2myVJgkgIHEJgmmZJuVM9ZDJu86RMhr/C1fjA//K/AK+/HnhTFX9ztXvFsE28NfEm/HfTju4dOL71eJVvrD/CTCuESbBbpSoPHjyAIAgYqtEGmVLWy4MLCFnJof99gZFbkRGCSjbItcDJg2kYLhFjkbUNgSrXq9rkLhCCnu5u9HR345lnnoGmaZienkY6k8Hdu3dx4+ZNt1kU0ymkBgYqpk+4VTJHefTAT74N04Sm67hw4QI6Ozvx/PPPVzw+/4Jxw5CvNmCTHPjAWaBlWSU3c6Vym6HBQRw6dAhXrlxBMpnE9u3bvfcqRg04WPQgSBvjRuCwlQhQefDt7OxEPp+HYRjrVtroB48eaLre1APGy4xkSUIUK2FZHlWwLcsdjDUNOgu3ghkxiWzg5X8nhEBRVVjFIgzDCEwObt92Iwa58uZJEeAf/yxQgTM2+iOrDqrfuv9NZI1sCXn45IFPbugqgND7KoQF30qwGUxNTWFwaAiSJHnlmvz+4+3guSMhAC9CIBDiEQGuGWgFvL+CputQZPmJW9XW0mRFIhGMjo5idHQUDqVYmJ9HOp1GZnoak1NTIAB6e3s9stDR0VFxe+XRAx5tMW0bpmni8uXLEAUBJ06cqDiOlt+7yiY5+GBAkiSIsgzKJhhJkrwHrhLGdu9GNpfD+fPnEY/H0d/fDwCu6QhWRw3aBT7w8LBYJQGPIAjo7OjA/MIClpaW1r20EXAHR61YRCKEngpcf8BXSrzUy/SHbVk1BDFNbxLl6QgC1h2SETrv2lfBu+8Cv1+peVIPxS/+AhCGp1O1KFPOyOHrnk2y+4lDqUM4kDpYfWP8Hm5yYubOev4mP/7IRnn6rdJxh+ZxEFalAkOz0TzHcbC4sIDl5WXs2rULWebGBx8R8J8fQRBcQspIbatkoBwCIS4xtm1AUZ4IcsBJOwHzGmD6gFoQCEFvby96e3tx4MABFItFZDIZZDIZ3Lp9G9euX0ckEvFMmvpTqZIIij96wMuoDV3HtWvXUMjl8Nprr1U8d7Ts/gc20wofKKiqCoNZKfuFJpWiBwTAs88+i1w2izNnzuCNN96AqigwmWK46o1DqrdzbhQOXemqyMO21QhJMplELp+HpusborSREALdMNpSCiQIgtckCljJ8Xr/M/JAHQfUtkFZSsFmBiiqokAUBM80RfSiDAL++38H/vRPV+9z2zbgn/wTwC9sbglViOmXbn0JuqVDggiHOnAIxScOfrLqZkom7lbuObYS4/dt+f1bb8v8/lxVysi1FbR+h1BvP2sYffDfOzwSwO+Tifv3IUgSEh0dsFhVDQhx7xdBgCAIEJnnQD3NQKsg7B6mjvNETVqcnAmsF0OjVV3RaBTbt2/H9u3b4VCKudlZPGa+Cvfv3wdhZMLfLEry+dqAELx/9y5mZ2dx7OjRqt00BSYq92Mtm8WtNTbJQRkikQg0QXAfdF7XWuNmFQUBL544gbfffhunT53CUSZKqhc14ENbK/SgJFSJAIIvQkpKG5OJxLoOIrwPw1qUAvk1C344juPlgkEp8oUCbNMEFUWYrJyMrxgcm+Kv/krAmXdFPFBBgQAApKBJREFURCMibEeEbYtwbAGHnxXwMz8DiGG2aKiwgpovzOGv3/8KIjQKBwAlFCeHT2J757bqed3wDqkl8N8jiOLq56mcaFBfS13AM57hYr1aYs1GwScntwLEWU0Cyp4zfnygFOl0GgOpFKLRqEcmeYfEtQYnBgCqinzXEkEnef/n+N+bbecsEIL+/n6kUilQSlEoFFxfhXQaN2/cwLWrVxGLRtE/MOCmVgnB3Pw8Hjx8iL179mCoRikqN8bj96ooiujs6mr4GJ8UbJKDMiiKAiqKsA3DDXPx8HON9IKqKHjppZfw5ptv4vyFCzh8+HD9SbfF6IFd63s1BqZoNIpINAq7UMDCwgIGBweb2n8YMAwDAtZX1COw1R33TgBcwpBMJktWjIWCgz/+Yxu3bzsQiANBtiARlzQcP07xQz8kwTAIqAFvlSgwTwevpW5AeKtzVq/uv5r/9foXYVHLzZUCEIiAj+//eLgnpQ3wl9gGSSt4KQvffe743lvdkILUJQ3cH4AyQsiNlCyWb3Zsu6QMmO+fm4oJLBrACcDy0hIK+Tyef+65dRem8TJfAC15dYSJwGNb2ec4QWjWF8Y/rsZiMezYsQM7duyA4ziYZc2i0pkMJu/dgyBJoHB9Vnbu3Fl9m35hI5sLkp2d6y7sbic2yUEZBEGArKpwDAOWT7leLy+ZTCRw5MgRnD13DufPncPLr7xSv2SwyVpthw+CZQgq+Oru6oJWLKKgaW4703UqbdQ0DRQuYWm1nCwMiKIIWZJgMCe1iKpClmUsLAC/9TlgcopCEByIou3+L9n4wR908KGTFii1oBm+XLhvIHEnceJqGwhxPR0YYfCTh5JwewVS+iD7EN+c+qb7OjNwfWX0VQzGN5Z3RUX479kWr3OlCcMrRXMcN6LC/m5TCmrbsPlrFb5rUwqHiXl5lQtPBfC/VyI0Dx4+RCQS8bRG6wndV6EjsolsvZ+noKA1yhzDhCAIbrvlVAqHKMW1a9dwd3wcRBCwbdu2mpUdlcb/oC65Tyo2yUEFqKrqdvKyrMDKdYdSJJNJHDt6FFeuXMGbb72Fl06eRE+dG6jR8JkXVq30XsCHiZc2Li8vY2FhAdF1Km3UdR2gFBFV9XqjrzcURXGVy0wLwZsnLSwAAIHjiHAcN130Uz8FHDtW5sFgWSU105Qr1uFOToRSmHwwrDB4EzYh+aMOfND/wtU/KxmhZEHB3963sZorVYO/G2Mjk5Z3Dtmf3KTM/7rjn/R92+ZaixLRpCBAANM9sPPM3URFUQx8fJRSTD144DZZWufVI3Uc6Ixo8/bB60oOGlz0eOH6VZtpPHIQ5DsOpbh08SImJibQl0qhu7sbqqpWPV/cWKr8ee3ZAHb07cQmOaiASCSCnCC4grWyh6ySMBFg5Y9wRX8ffuMNnDp9Gt/4xjdw7Nixuo2aGlFLO7Zdd+UVZFDo7OxEoVCAvo6ljbyqIxKJuGrlDbDakWUZKBZh2TYuXnTwO78jrGqe1JEEfu7ngbEx999czyBKEmQ+cfk+7/hIAs9r+1/jExzYKtdhJIJfZ8dxMLk8iTuP30cnOkEJRQIJHBs8BsEUkc3lSs4bJxQ8/O5XhHvvl70HYOU7/s/UAA/jewJFrITu/ZEC7jxnGAYEUUSRtRBe9V3fNkGpe458Az2f7G3/pM/2RwjxJnZ/SscfmeFEgP8u71mm1NOWBI1qzM7OQtO0hpqwtQu6rgMAJEGAIMswGEF9YkLeNciEd60CkITyiplKME0T7777LmZmZnDgwAE47NpLtaIGZV4JPNoZVoOt4eFhPHz4EG+88QbefPPNmp+9evUqnnvuOdi2jc9+9rP49Kc/HcoxVMImOagAWZZBRBGUqdf9PtwAKt7InBzIkgQ1EsGrr7yCc+fP491330Uul8O+vXurDjyEuIZA9W5suwJ7LQFPK9TZDuCuRDs6OrAwP79upY2apkGW5ZU+7xsgeiCKIhRJwre/beDPvmBA00pzyYODwC/8ApDqX6GJfOBw2IRWDoEQoEqrWD/8q2NOIqhtw3IcfOXuX8MBdUV5jtuS+XDqOU8w1xIqDM5+kgAA2WwWALxGWf6J3/ucb/XuH0wJIdBNE4amQZRlzyq7Jij1ws18wucrewnwJnviIwCNEstVomAfqaKA12a9EqamphpqwNYuOLYNjZEDNRJxWzSjNaFzS2gmVRpEg8IqGWpvprppGAAU8nm8c+oUipqGkydPQpZlzM7OQlKUmk6Z5fcBAUIVIr744ov44he/iPPnz9eN+Pz8z/88bNvGrl278DM/8zOhHUMlbJKDKlCjURi6vqqkEagcPeAGRHyCFSUJx44dQyKRwNWrV5HL5XDkyJHKEwQhEKqE1jjqTgBNTKrJRAK5XA6apmFhcRF9fX0Nb6MV6GUGSARoa++JIHAc4K/+SsE3v21BkkwA7vFRypon/TwQj9NVYrkwUI1EnHt0HlcWL/k+J+Bvbftb6Ep0IMbtnrnYjh+XbwXvj2SUlCHy7/CJ2Peb+EDMv2cxEuLY9kp+3j+I8VU3n2CZdwSPYli2DVGWocgyFFUtiWaURC98UQ0BK2kWP1omQ1XgkYUKKRDKiJ9btWLj4YMH2LFjx7pUJfih67qnY5ElyW03zISs64JmnokgUYE6JY71JtW5uTmcOXMGoiTh9ddegyhJyOVyEGUZEru//AtBjmrbDJMUnjhxAl/84hextLSE27dvY+/evRU/96UvfQlf+9rXAAC//uu/3pCTazPYJAdVoKoqNEGAYZpeq06g8sRFAbcUDii5uQgh2L9/PxLJJM6dPYt8Po+TJ09WvKg1b3y0aSVAfKWN2SySyeSaljbqul6yP0La23ui7vEYbvOk73xHRjJJQWADxIZjCXjpQ67GYK19oxzq4PNXS00VuqM9eHH4RUiC6JashT1B+cP9jECYtg1CCGLxuOc+BwRLPwAACgWIgoBIJNKSsr9dxKAa/PciFyVmpqdhmCZGwnC6agGObUNnXQT5OeXHuNbnCUDTAutgm6697XKbZD8mp6Zw/tw5dHV14cSJEx4xcBynpGdFOTnwd7gtP5bO0MxMXHLAcfbs2YrkwDRNfOYznwEAvPrqq/jYxz4W2v6r4QlJSq09IpEIIIpwWJlTLViW5eU9K0UGRkdG8Morr2BpeRlvvvmmF6ItQY1Blq/UaqJKBUM98NyZKAhYcFV3awYtYF+FtcDyMvB//BrFmTOAbRMYpgwQAlXV8cM/Avyv/2t9YtCOYfH01ClMZadKXvvRZz4OSWij8yavrODle75oBv+7P58fCD4DpGZRruUIDQ0e0/jEBLq7u9HR2elOxutEZjVNgwB4zZmAlYjNehxR20k9uy8r7afaa9dv3MDZ997D8PAwXnnlFSiq6mpe4BIpiVUoAW50yw+BNd8rR7KjI9ROjEePHvW2995771X8zG//9m/j9u3bIITgc5/7XGj7roVNclAFgiAglkiAYkU4x1Ge27J8UQN/ja0ffX19eOP11yEIAt566y1MT0+v+kylIaquzoChZI8NDnbdXV0QBcErbVwraJq2yh2xYg17G0EpxaPHwP/2v1Hcuk0BOCCEwjAUiCLFpz6h42M/GnDQC3lwtGwTX7j+hZIJdSQ5gpPDJ1c+tM5h7aDwqhVaEMnxFEXYaGSb+UIB0+m0VxPPw9kC1nYwtS0LhmnCAUqeIf78rHlaoZVr08g9TFd3na2mE3jv7FncvHED+/fvd5soCQJMw4BtWSBwx2sKrPibcFGqb1+V0BVi1ABwF2iHDx8GUJkczM3N4V/8i38BAPg7f+fv4Pnnnw91/9WwSQ5qIJFMAqLodVHzw387WuUphSo3eyKRwGuvvYbu7m58+9vfxsS9e6UfKIseNBUabGKy4KWNkiBgfn5+zUKSmqZVDDHXExa1Cm4yRCnFjZsUv/IrDmZmacmpUyQZf/cnJbxw1O1yFwRhV1p8feLrmC3Mltxrnzj4yZWH9gkhBoCvI+MGPOZGVrz3JiYgsdbCJdvAihZJQPt1M5qmgcAVQEu+aOW6pBVajZ40+N1yfUH5b9U1Dd/85jfx6OFDHD9+HHuYGJw6jrfQUyMRV0NCqdvngo05diU9Tdm+u9ogQuWphYsXL3rHwPErv/IrWFxcRDwex6/92q+Fvu9q2CQHNSCKIhRmEMTLhTj4BObXG8gBQk0Kc1Pcvn07zp89iyuXL5ewfC7QajSEyj/b7ATV2dkJSZJgWRaWl5eb2kYjsG0bhmFU1DgQtG8S4Sp0h1K8c4riX/5LIJ8v/UxPD/D/+RVg/0EVIARaQHIQZuSgaBbx3279BQCAr8n29O7Dc4PPrZ8SvUn4+zG0u79AMwhKRm3HwcS9e9g2Olqz8sR7Fv3/h3hv8K6vFKvdRfn5XdN7pMXf1nCViY+MlGtelpeX8dbbbyOXz+PVV17Blq1bvfd01spaFASoiuJW+vhSZ0B9cqCqKpLJZEPHGwScHBQKBVy7ds17/fr16/j93/99AMAv/uIvYksNe+ewsfGe1A2GKLsRDMNwQ/w+ELjEgK8YvAGjzsMiCAKee+45HH72Wdy+cwdn3n3Xiz7AV0a1luCljZIgYHFpySM87YLBJtyaAsgQBlQK1s6alQi6PvkEf/kXwO/+LlD+M7dvB/75PweGhwGVhRspMzgKsq+w8OX3v4ycvqJNoQA+deBTJZ/ZeGvwyvDfy62kFdqZ0w5yLh89fAhd17G9hs1u9R2El3rwVr8VykJ56mWt0gphRMuauqosfeK/tzKZDN5++22IkoQ3Xn+9ZIXv2DYMtsCLRCLedwkjCx45qFMVEaYQ0Q+/KNGfWvj0pz8Ny7IwPDzsCRLXCpvkoA6i0ShERQEo9W4uP8wqVQr1QAjB2NgYTp48iUwmg2+8/TYWFxdX3m9wEA1qnVwLyUTC82WfmZ1tejtBoOt6xZUPB69tbwY86uJ3KuSwbeDf/Tvgz76w+ntHngP+378M8BJmIggeedEqXPt2YUlbxP+48+WS114YOordvWNrdgxhIqyowboo8H0Yn5hAX18fkk124gsj9WCZJhy2IKlErLnRU7mBVLsQxj6aOQ8O6zkiCAIcSnHz5k2888476O3txWuvvopomSU8t2qXJAmSLLt+IrbtNvSSpFWRg2robhM52L17t+eme/bsWQDAl7/8ZXzlK18BAPzar/1afTv+kLFJDgIgGo8DcCc0v8kNIcS7mZpVrw4NDeG1116D7Th48+tfx5XLl2ExwUxDCGMgIG5rU0kQUNQ0LC4ttb7NKtCYS16opZPUbe7jWeqWvV0suFbI3/jG6q9+z3cDP/dzgFrGVXh3O9M0KxoctQP/7eZ/g26tkBFCBHzK15I5DCK4lghLb9DW31tn20vLy5idncXOHTtC2R2/k3gDraDQNA0O3PuyUhTG7465XiXBjaKZ4+ST+dzcHL7+9a/j+vXr2LNnD06eOLHK7ZDbmhMAUbYY8dIHcJ0l3XbsxHMtrYZ2ml69+OKLANzIgWVZnvvh0aNH8RM/8RNt2281bJKDAIgkEl6bWaMs/2yxVr+tlLZ0dXXhwx/+MJ45cAA3b9/G1772NWQymabKpFodPhVFQWdXFyRRxMLCwiqtRVjwWydXQ9Aaem5QY7NmO5UwNwf8i/8vcPVq2T4A/PiPA//T3wFIhaeBt3kmQMXIUdmB1D3WepjOZfDmvbdKXnt19BVs7dha5RsbH35ToScVE+PjUCOR0HO+3rlh/9e6h0zD8Ca1Wi2ZSYWQe+gI8Vo2TPoIgaHruHjxoptGEAR8+MMfxv4DB1b3uaDUG2sUVXXLEwFYrApM8GlHRFEEYbb5lZBIJtva8ZKnFq5cuYLf+q3fws2bNwEAn/vc59ZlIbBpghQARJKgKgqKxaJbm68opRerhRA4hyiKbj/xwUFcuHAB3/r2t7Ft2zYcOnQokBMWD6WHcRN1dHR4XRtnZmexZWgodJ92XddLrJOrod4KiIsLa5VA3rsH/MZvAL6sDQBAll3/gqNHax9rJBJBLp+HZhhQWR+ISqjWXa4R/Nn1L8BxVkKbkiDjY/vLDE8asMneCHBCSCu0exVc6z4zLQv3JycxtmtX2wSV/kgCAKya1in1UlsRVa353AisuVTbzhg7V+tx/1FK8ejRI1y8eBGWaeLw4cPYuWtX1c/rjFAJhJQQKocRAP95FAC3QdoalTCWg5MDwzDwS7/0SwCAj3/843j55Zfbut9q2CQHASAIAiKJhJu3chyYvlbOYcJxHCQSCbz88suYmprC5cuXkX78GAcPHcK20dE1LV3r7e2F/vgxTMvCwsICekPuQKZpWuCUgt9XnTfHKVHA1zgvFy8Cv/3bQPmivyMJfPrTwM7q44oHWZa9kKNpWVCqRYlanMDuLd7DmQenS177yK7vQU/UPferJrAnZCXupRU2YKWChxrXbmpqCrZlYXtIKYWah8H+5FUOnCQYhuGZoSk1mgQBa+B1EDIxCPrUFAsFXLx4EY/SaQwODOC5555b0RZUqO6ijuNFPtVIpITY2bbtish9rxFRdEVJVdDuPhovvvii94ybpglVVfHrv/7rbd1nLWySg4AQJMm1VNY06LpeQg54js//70Y7DJY3qhkdHUVqYABXrlzB2bNnMTk5iSNHjiDRpBiqUYiShN6eHszNzWFpeRnRWAyxkLqQAe7DGaT0E4Dn+Ob1AQg4Cf/N3wD/6T+uHnyGhtzmSf39wY6VsFWHpmkwNA1KtWvQYuTgT6+V2iRH5Rg+unelJTNpgBRtJPBJqunjXQtxXZVrRynF+Pg4BoaGSmzU1wJcvAigZJKrG20D2nfO2uAIWa/M03EcTExM4OrVqxAlCcePHcOWrVtXRW/Lj0vTdVBK3ZL0ssWc7TigfkdbP5mqcJ+Kohhqs6VK6OzsxL59+3Djxg0AwM/+7M+6/TvWCRuYym8sEFl2rX4J8eqMS1DOXBscCCuJ3SKqimNHj+KVV15BvlDA1/7mb3Dr5s2KK4J2DASxeByxeBySKGJ2djbU8sag5MnrTkippy6u+x0H+OM/Bv5jBWLwzD7gn/1KcGLAoaqu54FpWatKWn0H29hGfbg2fQ1XM1dKXvuhvT+EuOIjIk+IwKwcrboj0jUgQdX2ML+wgKWlJexax0G6qGmgzBmwltbAQ7tcRtslcqxxrEtLS/jGN76BCxcuYHhkBN/z3d+NrcPDq8aOcmMk7qMCoCKps20bhJ1TSt1up7WOo90pBY5UKgUA6O/vxy//8i+vyT6rYTNyEBCiLMNmDNTQdRQ1DclEosTHnP+dM/egDyil1Os6VgkDqRS+57u/GzeuXcO1a9cwNTWF5194wSt98SPs1WR3dzcMXYem65idn8cAu3lbhuPUzd86vn4RvG9FPZGVYQD/9veA986ufu9DLwF/7+8BUu2obEWIzIPdtCzohoFYBSGlf6XXEChdFTXoinTje3d9b+WPN7OPdQRtsVrB/4y1C9W2P373LuKxGFIDA20+gsqwbRsGK8OLxWJe7wSHNcKqBP5qmOeMwl3hr1WsyrZt3Lx5E7dv30YsFsNrr72G3hpdY8vPBe+foMhyRcMqx3HggPUKEYS6XVbXojX3e++9h2+wUqp//s//OTo7O9u+z1rYJAcNgMgyIqoKQ9dhmeaqmth6ncOqoV67UQCQRBGHDh3C8MgIzp0/j7fffBM7x8Zw8MABt27XfwwhQhAE9PT0YHp6GvlCAVnWvbFVOJSWKIX9aCR14MfyMvCbvwncvbv6vR/5YeBHPtbagkpVVZiWBUPXEa0gTGx20+8+fA8TC+Mlr33smR+BIpatEvnB83PzBKQVNro7IkclAqIbBh4+fIhn9u9fj0MCBVAoFgFCXJtkbsoFNz9ejySEGWlqdmxrBtPT07hw4QIKhQL27tuHvXv3Bo4yEjDDOla6WK0aikcOPGLgQ/meREFAb6Ohxibwi7/4iwCAgwcP4qd+6qfavr962CQHDUCIRCDoOiRZhmWaXrtUYPXAEnSS5mHzQJ8nbovlN15/HePj47h2/ToePXqEI88+W5NVtwo1EkGyowNLS0uYnZtDJBLxmpU0i4qEiPkUVFNCe6YnFaIHjx4Bn/1XwEyZd5MguNGCV15p6XABwKuu4J06/cKwZodN27HxheufL3ltMDGE17a/VvU7/kjVRkcY7ohrUa9f6Vzev38fFMC2bdvavv9KMHTdMzyqFBqncDsHtt0NcY2IgW4YuHrlCu7du4fe3l6cOHkSHclkYH8Rrsnx90+oREg9AyRCApWgp4aGWh7v6uEP/uAP8PbbbwNwOzDWsudeK2ySgwYgiiIcRUFEVZEzzYoeAJ5Pe8AbulHhIiEEgiBg19gYhrZswaVLl3DqzBkMDQ5i544dbbuJuzo7oWsairqO6dlZDA0MtKQ+dxzHCzPzwd9hpKDW2SBww9P+AePmTeC3PgfkyxpKRqPAP/nHwP4DTR9m6b6ZMLHIRakhnOtv3P8G0rl0yWs/duDHIJDKg8PGXXtXRstRg7Vy+quQw54YH8fWrVvbUplUDw5rEsSJQbXzRwGAt2nmabiwI0rtPv+UYnJyEpevXIFj23j++ecxum2bN9k3Mj5qmlbSP6ESbNsGb3JXbxIWCMHWkZGGfk4QFAoFPHr0CNlsFn/5l3+JX/3VXwUA/PRP/zRee636wmAtsUkOGoQYiUAyDIiS5LVNLZ8kguZIKaVun/smH+ZYLIaTJ07g4cOHuHjhAjLpNLbv3Ilnnnkm/AGNuSc+fvwYhq5jaWmpJStR/tCXhJ3LPlPUgLffcssQv+u7gWSCH8rKSubUO8D/9X+vrkDq6wN+4TPAlpC9g3jFimVZsG07cD+NSjAsHX9+44slr+3s2YXjW47V/N6TGDko7wEQGGu0ai0/l9PT08jn83ihnglGm1DUNIBNXkqAkl8KeONIqPdFG88/BTAzPY3rN24gMz2NrVu24PCzz3qpAILGxKimacIwDAiEeP0TKsFyHIBVMZQfTzl6+vtrGrU1iz/6oz9alTo4fvw4Pve5z4W+r2axSQ4ahCBJgCQhoqrIWxYMw6i6Wg/EepsgBtwi1WHEYuvwMLq6unDt2jVMjI/j3r172LlzJ3bv3h3qjS3JMrp7ejA/P4+FxUVEo9Gmt+8w9l5rVfi7vwOcv+D+/e23gV/5Z0B3l/tvgQj48//m4AsVeiTs2A58+jNAO/Q8giBAlmUYhuEKE3m4t4nr+JW7f41FbbHktU8e+FT9bT1BmgOn1TLGNUL5XTg+Po6Ojo6Kot92w7QsWKYJSumqHgF1wSoVhBAqC9plwUwBpB8/xs1btzA/N4fOzk68dPIkBgYHV/aNxlJ1jm2jWCwCcJ0Qyy2U/TB1HUQQIFZLKXCSRQiG2xA1AIDz588DcBcb27dvxyc+8Qn8wi/8wpqXy9bCJjloAnI0CmqabqiPGVaUs2uBENRu4dF6LtXfalZRVezevRs7du5EOp3G+N27uHv3LrZv3469e/Y0PshUQSKRgFYsIlcsYmZ2Flu3bGk4vUApheU4NfN9E/dWiAHgagl+8zeAX/5lQJKAf/fvXcJQPuccOQL8o38EhNmyoRyqqsIwDBiG4YZ80fi1zBlZfOn2X5W8dmjgMPb3P1P7i2V+GhsdngFSkznUtarM8J/LQrGIdDqNw88+u0Z7XwGl1Jvk1Eik+gRWC77JrZWVP0/zhQWHUjx6+BA3b97E4tIS+np78dKHPoRUKlVSHkwbJL+UUhSKRc/ToF65p24YgONU/Rzfa0dXFxJtaM8MAL/3e7+H3/u932vLtsPCJjloAoIsg4giVFVFFljVb4GDEFIzbdDqwOdn9jx/L0kSDhw4gD179mD87l3cef993B0fx/Zt27Bnz55QKg16enthPH4M3TQxNz+P/oBiSN4DAax0s1Zp29/8zerXxieAf/NvANMCrl1zowcOXVFrf+QjwE/8OCr2SAgTsiyvpJUMI1jteRn+8taXoJmlIolPHvhEsC9v8FW4H62WMfLue2uJe/fugYgiRtq0aqwFTdfdsmZBQKRJhltSXl2m6wm+EVLXnCgobMfB1OQkbt+6heVcDqlUCq+++ir62LhRfmyCb9ETBJqmeRbJcVbuWe33UsdxozKErNYMlbmPDg8PN3AUTx82yUGTEKNRKJYFIgiwbRuariNRxvIJADDxXMWwaggPn+etwOuf2TZlWcbeffswNjaGe/fu4fbt27h/7x6GR0awZ88edLXg9iUIArp7ejA7M4NsLodoJFLXudFPDMCOs5rIKpcDTp+qvJ2Ll3z/IACoCAIHP/4TwPdWtgVoC1RFQcG2oet6w+RgrjiHr939WslrJ4Zfwrau7Q1tZ6OH6gHAbtEAaa1/oUMpJiYmMDoy0lIztWZgsTJZSqnroxHW9WVphsCNmELSGVi2jfv37uH2nTvI5/MYGhrCC0ePrvYMKIuGNbJnk0XwACDCiAGwWrTsfZ51VxUEYZUuy//peCyG7pAt4580bJKDJiGpKqx8HrFYDNlsFvl8HtFotFR4VcPmNqxcHuEMn4cQbdtbeQCuDfKusTHs2LEDk5OTuHX7Nt78+tcxODSEffv2NZ1TjUajSCSTWF5extz8PFRVram9KB+Yapk+fetbgF45GLMKkQjwD/8h8MILDR1+y+CNuGzbhmVZDYXNv3j9v8JyTO/fgiDix/Z/PPjOnyDNAWVK0Y3ekZEf3ePHj6FpWmitmYOCYkWEKMtyzZx5I9v0/71aGbAfhC9mWtivaVmYGB/HnTt3oOk6tm7dipMnT6Kjo6PKga4caSOjom1ZKykYVS2xY6+2HY2d41XEgDmwAm5VWjsqFJ40bJKDFiBFo4hqGvL5PEzTRLFYRCIe994nPvZaLk4MNZdalmOs5BMgiCK279iBbdu24cGDB7h56xbeeustpFIp7Nu3z00NBBjA//yLX8QX//zP8cy+ffilX/olr9fE7NwchnyCIsAlABSViZBTJa3gOJVTCpUQiwH/9J8CO3fWH/TCBhEEKKoKnblHxgJqOh4uP8C3Jr9d8tp3bf8upBIhOU9uIDjs+gPNaw7WCpQ9N3fu3EFvby861tidztB1T6QbbVVEzATL5eARRuqL4K36TAvEwDAM3L17F++//z5My8K20VHs3rOnflQRq8fHeqCO4+oMAMiStEoYXWnMEQhx9QaUror22T4SG4tG0ReWE+wTjE1y0AIEtlqORiIoFApeQyZ/Lsu73SvUUYd6LFiJUDiOU3UwJoKAkdFRjIyM4NGjR7h58ya++c1voqe3F/v27nUn+KAPKStvzKTT0DQNi4uLXrrCSyNUQbW0wrXrQDoTbPcWW3wTtE9ZXQsRVYWuaTBN03VkCxA6//y1z4PSFSKjSip+eN/fbmi//rK1jQx/w6VmUiBBzW/CwuzcHObm5nDy5Mk13S/3NADce6pVJ0mezqz6frM6hCrQNA3vM22T7TjYuWMHdo+NBRdBU9qwzqBYLLrjnCBUVPiXjweEuD1xTNMEBVZFDiweNZAkDA0Pb+wOomuETXLQAgRBgByPQ8pmISsKbNtGoVCA1NGxsipm+btVubSwBz5WE81zakE+v2XrVmzZsgWZ6WncunkTp0+dQmdnJ/bu24fhrVsDTUCKoqCrqwsLi4teeaOsKHVd26oJEv/maxU+XAWG6VYw/LN/5voaNGoo1Sp4tzfDNFGs0m/Bjztzd3D+8fmS1/7W7u9HR6TBVSpf3W1wgtBqw6W1bjR16+ZNdHZ2YrAsAtZuFJlFssCiUaGg3rljhK0Vd8V8oYA7t29jYmICgihi586dGBsbC9yK3TtUNBZJ1TUNJmsCF6thEOURBDYucG2CKEmr9CS2ZbkRBVXFwNBQQ8f/tGKTHLQIkZUbqYoC07JAHQfFYhHxsj7jfBinVdIMYUAQBK+8MjAIwcDAAAYGBjA3O4ubt27hO+++i+vJJPbs2YPR0dG6g3uyowNFTUO+UEBmehqDAwN1ncccrNZizM4B589X/nw1LC4Bn/0s8Ku/SiBK9RszhY1IJALDMGAaBhxFqX6uKMWfXPsvJS8l1CS+f+z71+Ao1wdOi5UKa4mF+Xlkpqdx/FhtA6qwYZomLMtyRYi+lGRL4JGBQB9tPIqQzeVw+9Yt3J+chCRJ2LtvH3bt3Am5WeO1BvZtWRY05kwbrVPq6RdrUwCaYQCEQC3TcziUwmY6ra3Dw2suRN2o2DwLLUIQBKjxeIkZksGsdWVZLglv1a1eaBFEEEp0Do2it68PH+rrw+LCAm7euoVzZ8/i6pUr2Do8jG3btqGnhiNiT3c3dF2HYZqYmZ3FQCq16jfeuHEDv/prvwYA+Ikf//FV77/1JuA0cegPHrqeCMePNa52bhWSJEGWZTiG4WoPqpiYXExfxO3Z2yWv/fDeH0ZUbt70ZKNPuZ4B0gbXGwBu1CCRSGDL1pAtNWuAUup1D1QjkdB0GV5UKcA44H2izucNw8CDhw8xef8+5lh/lQMHDmDHjh0tT6Y0oOUzdRwUC275ryLLdaMs5Qsx3t2ynMTwJk2iKGJknfpobERskoMQEOnowPL8PAD3xrNME4ViER2S5LkZlqBN4VJ/r4JWcvBd3d04ceIEstksJu/fx+TkJMbHx5FIJDAzO7v6C5RCkCT09fUhk8m47Z3n5mr6H/B8IYdlAV//elOHC8DtowC4BKlmp7o2gEcPdE1DJBJZtVJ2qLOqJXNfvB/ftePDLe13o5cyetbJTRznWupHlpeX8SidxuHDh9f0nGqsbFFowdOgFVCe6+cW5mUEwbZtpDMZTE5OIv34MRxKkUqlcPTYMdf8rAUyUxI5DUIMKEWhUPDKECMBnAQpVp4R27Jg2barNyg715ZtwwEwODCwLn00Nio2yUEIkGQZUiQCS9MgiiJs24Zj29A0bZVYxnsM2tAghXsd+IVgrQyyyWQSBw4exIEDBzAzO4vJyUmcPXsWtm1jYWHBa0wjKYqXr+vt7cXs3Bzy+TxkWUZXBdU3JQ7+qPgn+Gjuo9gPtx3u174GZHONH6MsAd/3fcBB1lyJwPXxX0sxm2eKxIRl5dGDdybfwYPlByWvfXz/xyGJrZWrbWxqsKI5aEZgF7hTaQi4eesWYtEoRtewfM2yLOhsJRtLJMLXj7B0Zi34LZb9Y8Xc3Bwmp6bwYGoKumGgu6sLBw4exPDwcCh27NRx3GhSA8+oruuwbBsErgdBkHtDYClWyr4PQqCIIqSycnPevnn7GpevbnRskoOQoMTjsDQNlmkiGo2ikM9D03XIigJJFEtqhwkhXulUmAOgwEoZ+b44c255FUYI+vv70d/fj4mJCdy4fh0gBOcvXsS5CxcwNDiI0ZERDA4NIR6Pw7IsLC4tYWFpCZIklZR3AsDi81nknTz+YOrf4UeOfhSSIOErfx3sUCSRwrJvA7iOf/gPXsOx4z1Qy8l+SCYujSBaJXpg2ib+643SBhAjnaN4afil1nf6hEQOmhEkrhUxyOfzePjgAQ4eOtRylUBQcE8Dwlz6ws5xBzl35WLEXC6HqakpTE5OIpfLQVVVbNu+HdtGR5Gs5k/QBCivUvKF/OvB9HXAjUajgSIWxN24R5C4TkEuixpQSuHYNjq6utC5xuWrGx2b5CAkRONxFBYWYNk2YpIESZbd9EKhgGSlOt8qtcitgA9uXuSAvU5DnCz5pNfZ0YHv+97vxYMHDzA1OYnTZ85AURQMDw9jdHQUiXgcuWwWs7OzkETRW3GYCRPFrRooBQxq4LPnPod/euwXQB0TwOqVtECAHTuA/fvd//fsIfjlX/6/kM5ksJyNQFX+1urzADeUba9x9ECSJFimCd0XMfr6+N9grjBX8tlPHvhEOJMfr1ffgCSBMotsoIVqhTXArVu3ICsKtm/fvmapDEPXvaZp7ej4x1Ht1xC4xM306Qjm5+chSRK2bNmCI88/j76+vracj1WC6Tr3bklDJUUJJHr0Fka+13TDAAVWiRF51cPWkZENfZ+uBzbJQUhQFAVEUeBoGhzbdrs2svp3TdfdQaD8YQt5hSswt8Ryvb4ArHqtFVC4fukRVcXYrl0Y27UL2VwOk5OTmJycxMT4OKKxGPr6+tDZ2YnpmRnPIGn++GLJtv763lfxongMBw8Cp069AtMSkEwQnDwJHDoE7Nvnmh358fwLL+DLX/4yzp09i+//W6vJAYBQSrUaRSQSQd62oRsG1EgEmqXhL279Zcln9vXtw7MDITX0IaSmj/x6wl810igRWqvfUywWcf/+few/cACiKMJiE0U74XkaUFpi9xs2/E3Zyvf/+NEjV0eQTgMAUqkUjh07hqGhodIqo5C9QypGMWtsv7yhUlAiVU4MTNP0DKa4poBbzduWhVg87vV52MQKNslBSCCEQInFoBsGTNNEJBKBGo1CKxahaZqbl+Yr+zYeA4jb7Kk8ZRGWSRDFipuYH8lEAgf278f+/fsxOzvrhSgnJycRi8eRmZ7G2dw52ElnZUMMv3339/Av3/jf8ff/vgBKCeqNl88fOYIvf/nLuHPnDnK5XFUHNoLgSugwoMgyiqzXhqHr+PL4XyFnZEs+86mDAVoyN4D1MH8KAi+XzSpoGvjimukN7ty5A1GSsHP79rbvC3Bv+Xyh4HmStE38xomBL3Q/NzeHqclJPHjwAIZporurC4cOHcLw8HBVXwICJvANg2BXuU9r3bn+hkqxaLTuPcHFnd7vZq97egNZ9qIDPPVq2Ta2DAw07M3wQcAmOQgRqqpCl2W3U5+qQlEUmIYB27ZRLBQQTyTcBw4VSohCmMT8TnS240DyrQJ4eROt0SUyCJw63ycA+vv60N/Xh8PPPotHDx+67mkT4/hr+6ugAiMtvpMwj3ncUyaxm+wOdGh79u5FMpFANpfDhYsX8crLL1c9FoEJRNckh82sb/OFAmaWZ/E/7vyPkrePbjmKXT1jLe+mrWZaIaFZvUGzboqNQtd1TExMYPfu3ZBkeU3KXzUWVQQhge22mwalyBcKmJqawhTTEcSiUezYuROjIyPBu7OyCbdlglDtPq3yeklDpYA6A6E8EsvGVJ2Vi3pkjBED0zShRqPo7eur2hfmg4xNchAiYrEYcrkcbGbTqSgKotEocrmcq07W9colS2UliK1AEEVYjlPxofNWAk1OKE6FiEE5/vdf/VXcuHmz5DVVUZB8oQOx/igsamKZ5kCpA8L+A4B/+a3/H/6fX/4PAIBXXnkF/+Cnf7rqPkRBwHNHjuBb3/oWzp87V5UcAGtfvaAoCoqahrcm3gR8p4sQAT8WtCXzU4BmDZDWiuq8f/cuAGDnrl1rsj+TdVx0KEWiTekE27IwNzeHTCaDx48fY2lpCaIkYeuWLXjhhRfQ09vbnM6pxdLoWuNapS2uaqgUYOKuuHW2GDJME5TSEr0BpRSGaWLX3r2Ix+Mbvix4PbBJDkKEIAhIJBJYtiwUWSpBEEWoqgpN1730QsUbka+YWpzEeGSiFtNv5kFvJXStGwYwvYyeoQ44lgMHFFmaBXUczylRKK7cikFWKbt378a3vvUtvP/++4GOYc3C74Rg2V7GucdnoSICA+7q59Vtr2JLckvo++LC1rb9NlYDz69J0P00GzlYC3Jgmibu3r2LHTt2rDTgaeO94TgOCvk8ALd3QhgdF9mGsbi0hOnpaUxPT2N2dhaObUOJRNDd1YXR0VFs37EDkiiuT+qJrdxrTrxlx+UwC3oKQGJjZ6BdoTJBME3TTVMJgnve2f5M00RfKoVEIlG3MdQHFZvkIGTE43Hk83nYjuNGCiIRKKoKg4liCiy90DYjJJ5Tq0UOgMbERj7leT381E/9lFd2VI7Pnv0susVOODaFAQM6MbwH+qdH/j6cH7KRz+ehyDK+/vWvI5VKob+/H319favKvW6y6MTevXvrHhMnXW0dHn3E7i/v/IVr1gIBMhRABD72zMfat2tUn1Sp48Bh18/x/52fD5bSor5/e173vpx1LpcDhVvyxgd7z4mPERTi+3uxWHTr0glxhbKC4Np7E+L9WQmO47Tdv+Hu+Dhs28busZUUT7tWjhRAgbn6CQ2I6ipvjCKfz2NmehqZ6WnMzMzAMAyIooj+vj4cOHAAqVTKFcYWCiCEhEYM+PWtl1ZcOVQayMrd/65ju8+/QykEUUQsgJ8BN3Kqdsxcb6AqSolJnCBJGNyyBclkcjNqUAWb5CBkEEKQTCaxaNtel0ZBEBCLxZDNZmGaJgxdr756aDF6wMlBkAEhqNVwI/nGVH9/1fd+dPZH8Yfjf4geoQM2tTFPF2DBwvdt+wg+fsydPIua5q6CZmZwf3ISt27fhiAI6O3tRaq/HwMDA+jo6MClS5cAAC+88EKg4yKEQICrxWjLYMDO98TCBM48PAMFEUSICpVG8PqOV9ET7Ql9X4B7bSzbhs36ethMjOoRAV9IuCQyxc+BjzR5pa98H/zzfgLgPwwAhJML9m++gjNME9RxYJkmij6PD29fjCSUEwfCxHrtGrAty8L7d+5g27ZtgVz2WgUX1VFKXXOsBn+XrmmYmZ3FTCaDzPQ0CmzS7+npwc6dO5FKpdDd3V0SoTEMY2Uyp823YK6EINUxq+612h92vVnKiEGQ1EstYgC495rnb+BbXJiWhVFm+9x27ccTjE1y0AZ4OgPHgW4YboMQFiIrahoKhQI6kknUlOU3KVD0t22u+Tm4/gek1oqa1m673Cj61D4UHhSRGImji3bAdmwUhSI+c/TnvM9EIxFsGx3FttFRUEqRzeUwMz2N6ZkZ3Lp1C9euXcP8wgLy+TwkUcSusbHAWg1CSNv1B9wm2YSOCFQkpBi+d+f3tbxdh5m12LaNoqa5zZ4sC7IkuWkk9jnqn4h995DIJ2D/RAyUrPq9ahesrBSB0pRMIpFAZ0fHiuUu35e7Qy8CwfO8kUjEi1I5juNW0rDPOsy21vuN/HVKIQkCBEmCKAgQRRGiKIZSh37v3j0YhoG9e/aseq9aaLpZmJbl+fnH4/FAojrLsjA3O4uZmRlkMhksLS0BlCLZ2YmhoSGkeCStRmqCUuo+2wj39wD1FxS8YiBwtIITA581clBNhlAnMmGZJgzmb8Atkyml6OzuRiweR0dHx2bUoAY2yUEbQAhBR0cH5ufnods2VNZHgHvwW6aJXD6PRDXFsG9V1yhB8CyUA0YOaqUX+GAdKs4C+aE8ElISHU4CP7Hz/+XuqMK4SQhBRzKJjmQSu3btgkMpFhYW8J//83+G4zjo6u3FN7/xDcRiMaQGBjDA0hD1QrdBIyaN4tr0NVybvgoAoIRCpzo+sv0jEGhjHvT+aIDtOHBs27OOBdyVoWXbbsgYKxO/QAgEtuoWA4TwmwHfZr3jV9jkVUns5bAUB6W0NNLhOG7rXFaKZ1kWbKwQH8JWlZIgQJQkCIw4BP19juPg9u3bGBkZafuKkVKKYqEAykLaVSdzx8HCwgKmZ2Ywnclgdm4O1HGgRqMYSKUwtns3Un19DUU5KKWA40BokwK/VvVCQ8SAEcR8oeD1WknE44GIAWHfr4VcoQBKKRRFgcIiB4SlE2RZbqsB1dOATXLQJkQiESiK4lrqWhaiigJCCOLxOJaXl6EbBsRCAdFqg1STFQyiKAKENGToIpDVnRy5w13ovJoC9CKQP5pDSkzhSO8RTM/MYGBgoK6yXSAEvT09uDcxAUIIvucjH8HzR464gqyZGUyw1zs7OjAwMID+VAo93d0loia+Og7bHIlSB3969U9KXotHYzg5cgK2ZcEwTW/CLIdDKSzLgsXa9/qJALCyKidsMlRlGTKzpY6w+m+/RmC94XVjrEJMBEZmgBVPTE/zgBXyYLNIiW3bsFmu23EcmI4Dw7K83ytKEiRJgsQiDNWel/v370PTtKo6lbDudQrXlpkCq817HAfZbBYzs7OYzmQwMzsL0zQhSRL6e3tx+PBh9Pf3I5FINEXqKI/2hVD5VGMnFccMvv+gsB2neWIQZNu5HEAI4myMpQC2DA15qd/NqEFtbJKDNiKZTGJubg46pV70gPcaWF5edvOHLKJQEaRxi2W+YuSDqxgglAmUEYR2EQOOSeCHfuCHEFmKQCQEumFgrk4XR++rU1NeZ8hjR4+iv78fg8x9UdM0zMzMYHpmBlNTU7h1+zYIIYhGo+jq7ERHZ6f7Z0cHkiw0HhbeffgdTCxOlLz2w8/8CJLRJDRNg6ZpHjnwyAD73/YROX5Eoih6IXVBFCGJYsnAaVpWW3PzrcDm3RgbSQP4ctScPPhFqDy6wMkCjzLwdIth2yiySYsTBUmSvPufUoo7t29jCxOhtRM60xkYpgnHspBOp7G8tITFhQUsZ7OeyVNPTw92j42hn+kGWr2W3kKizD69XfBHEBqtBqJs8ubEIB4wlcCjfjV/GyHI5/Ou2ZRvfO3q7UU0HoeiKJtRgwDYJAdthKqqrjGSrkMHwAODiqoiGouhUCwin8tBJGRVQxAPDQoUuULZYKHpoOQAYASBCdnajYPdB/H+/F309fVhZnbW1RDIMrrrND85d+4cAGBkZAT9ZeLHSCSCkZERjIyMgFLXBGZxcRFLS0tYWlrC5P37uMXqpwVRREcyiU5GGjrZ/8241tmOjc9f/3zJa0PJIby27VWAuqTF1HVkAS9cXi7+45OZJMuriEAg+MSH6w3qixwERb1UDxcqlt/Ptm17JAuWBQesPa9lwdE0iIwsZNJp5PJ5HDt+vPEfVAe8mmNpaQkLCwtYmJ9HNpfzbJIFQXDvsa4ujG7bhs6ODnR1d4fecEkQBFCWpqFoXwUGR4nmpEFikMvnYfqIQSPtn+sRA8e2kSsUAC4CBaBEIujp7QUAdITYSOppxiY5aDOSySR0XYdmWVAjEQhs4IxEo7BsG4ZhIJvLISkIobl0SZIEg4Wo1QYnO8pC7u2eYmRZhmkYiMVi6OrsxOLSEhaXlrxweTWcP38eAPDC88/X3D4hBIl4HIl4HMNbt3qvG6aJpcVFLC8vu50jFxYwef++16QpGo2is7MTXaxLW0dHB5KJRM2J7u17byOTTcM/bH1i/yfgOBSmYUA3DNfnwjC8wYqvcHnDplZNcTYCKeDg9tqNRA6apaOcMKiq6moYmD6DR2S4OPL2nTvo6e2FJMvQDcP1IGninJmm6ZLNxUUsLS9795LNjMfUSATxeBxbt2xBT28vOjs7m04RNAKCFVLmtcpeg33y/QXdFycGNhtjAhODevvg5cqUuk6UlgVCiFchMrR1KwghXrp3E/WxSQ7aDO6SWCwWUXQcxNlNzP3CqePAtCzkslkkk8nKwiX+UASsMZYkCYSQknB1YPhL3xr/dk3sf+YZ/NEf/iEA4P7kpCe86+zshGVZbmXC7Kxb+llBgDW/sPD/b+/Ng+W67vvO792X3t6+4j3sIAACxEqRlESKFGXLlkVJ1GqNUxNV5JEqdmJLrkomVUpcFacmVTOeycSOPRNZiiLHSo2tjTapLZbKIsV9AR5IAgQoAg8bQWJ5a293v2f+uOecd7tfd7/ufg1wOx/WK+L1675bd9/zPb/z+31/OHfuHICk+VI36JrG208DyaAUxzHK5TKWlpdRpDf98+fPo+o43GExVyigP7U0USgUoOk6vNDDA6ceALtVykTG9r4d2J7dgVKxCEJFgETrrVVVhd2mHeya1H0W3ix9FuLU8kA7EPTGxEliSwqqCqTEwuzsLCqOg927d/PGR061ClXXodP8jfqBhxCCcqWSDP5UuC4vL8OhngWSLKOQzyPf14epqSkUCgWeJClJ0g0RBOnzTvtD8JLS691lkC57Kk3yD+ohcYwyq0qQJNhtVnAku2otDNKfnzJdUjAtC7IsY2R0FAqN0lzvJaW3E0Ic3AByuWTd2fd9mLYNhapaSZaRyWRQKpcRRRHK5TJy+Xwy42r0ZUjXnbdAVVVIqUzwtlU9Vm7SvXBrbAVT74HvQ7Us9Pf3I4oiVB0HV69excjIyCqBcPToURBC0N/fj809apYjIRnEcrlccuPYsIH/zfM8HmEo0ijD+fPnuYFQxrZxWj2NorMMHTp0YkCGgg9u+jUuzDRNg2bbMC0Lvutyt7a3Myxy0K44uF7VI+xz/8orr2B6wwZMTk7CDwIEvo8QyfJDsVqF5/sIwxCVchmlUgnFYhHLy8sr0QDLQl8+j6kNG1Do60Mhn08G/9T5edQBlQBJYt0NjOSsMo6ix309j4B7KLR5nyDp5EMkLe7b3lfrA6kRBr7nJeWLkoSMZcGwLBQGBhBFESzLEj0UOkCIgxuAqqrIZDIol8soOQ7yhgGZJiURGv4ulcuI6Aw2m802zhVos4JBkiQoqsrXXtv9QqxS/9dRILBjCoIAFlX4LP/AcRxcuXYNI4ODyKRuIkdpvsGB/ft7W56HxoOTYRg1UQYgucmV6Prya9cu4dS5U8jEOfhRgBgE/cjj3NGzeN14DaZpImPbsCwLpmkm9da0MVehUOARnk5p+Y506Y/RKwjNlAc6ixxcj+NwXRcvvfQSgiBAJpPBSy+9lEQNHAfVajUxKKKVERKAII6RzWRQyOcxMTGBvr4+5Pv61lyaC8MwEQaE8M/yjaA+YsBgHhTXS6Cw6hi+/TXuE0wYRFQYZKhdcTvRhlZn0MixsUQdPA1qUz06MZF0dpRlkWvQIUIc3CByuRyCIIDneSh5HnKaBhnUiEhRkM1mUS6VEIYhqtUq7EwGiiStvtG3WcGgqCqkDsQBARqX97EbQY9FAosc+EHAH5NlGcNDQ5ifn0elWsXV+XkMI5mJ+b6P8+fPw7IsHD58uKfHAnQQkpeSnvC5XA6nX5/lmfmxFCEgAe7fdz8GlAE4tFW34ziYm5+H4zhJ453UpjRFgUXFg2WaMC0r+Tf73bZh6npnkYY2LGuvJ+l23m2Lgw6PN6SNedj1Zf92HQcVx4FTrXILbzZQnjp1CpZlwbZtmKaJQqEA27Jg0tmkqqqJ90JqCU/V9TXzJuI45vbImq7f0PXsRrlBLKp1PbpbMkvkRu9WM++DemFgZzKQZRlhG03cZCQeF83OIq4TwlEUJUmgADKWhb6BAZ702d/f31FytkCIgxuGJEno7+/H3NxcEsL0fWRUlWerK4qSRBcqFfi+D5mumTWNILAZWpMbgEqd86I2voSu5+H3f//3USwWMTw8jD/+4z+u2S9zUfSDAI888giApLfByVOnsGvnzs4vBsAbUAW0LSuDWSUDSFofz82BEIJcNos///M/72pf7bCmIRTtleF6HgghWKwu4omLT8CFCx8eAhLg3VPvwYGtzRMlWde8arWKMIpAqNuh4zgolcu4eu0aHNflLoLMpdC0bVimyQcziZb52ZYFwzRrXARZeaOSche8UTNZdp0ANF1LJsCqcsQw7WeQ+mFCmQ38VSoEwjBccX8kJDG0sSzYloVCPo+x0VGYpomLFy9ieXkZ99xzT00EqhkBTeL1qPtkRL+niqbB0PWGIttxHH4sN6o8Tmrl05H6/PZSHMSEQGkiDJLdNvA8aCAMFEVpS7zKa+Q9NdpCmfoaaJoGK5tFob8fAFAoFNpu4CRYQYiDG4gsyxgYGEgEQhzDC0MYqspnk6qmwbKs5IboeZAVJenNoCirvyRr5R1QM6SAZmy3erZhGPjIRz6Cb33rW7h27RoeffRR3H333bX7IgT/z5//OeYXFgAAkxMTXQsDIJllgRDesz0NEwiSLKNcLmNuYQGEkMRy+jrSSCCw2YhHbVgRx5AVBX9/8e+xSBb48xRFwad2f7Ll9hVVRf/AAHRdB4lj5AuFVTNTQkhS3UAHQz47pv9fXl5GxXFqk00liUd2WLUJ+3xIhEBKeSY0+lGpl0Laprj+b6yF7sWLF3H5yhVu5cwGdpIycvJpnwdCPQhCKgTCMEREDZ64dXdqpsvNnrBy82dLMpZlYXh4mP/OhJJpmslnvY7FpSXMzMxg//79bQkDNsCrmgZV0xDR3ii+7ye5MJVK8n00DOhU2Hqel5RMEoJcJtNV9UM3tGpOVZMz1ENaCQO2Px7mp8dRcRxelcCFAdZeRmrp8NpEwJM45sZTpmliaHgYCm3e1M77L1iNEAc3GFVV0dfXh4WFBbhxDNCyKoZhGCBxzAcDWZKg0RunXL/M0CKCoCgKZElCRI1jGt1AOYTg3nvvxY9//GPMz8/jwQcfxJ133lkTPfjWX/1VUkYYx7hl3z7ccccd67sO1Ds/vayQRpZlDLEIQrmM+cVFkDhGYQ0fhPXCrmJA15E93+eOiqqqwrQsXHYu47FXH6153Qc2/QqGMiNrbl+jg08QBHAcZ1XZpiRJMA0DpmGgr6+v4TbK5TJc34dJowZ8Jp4asEP2O7VgrncbjMKwxlQo8Dz+2jj1HP7aIEBMCF45fTpxJKwzaFIUJVnKkuXELlhVoes6FxhKnQBhIoR5OjR6XKHRr04hAF588UXkcjls6jJxlQ0spmEkLqe+z/MYPNeFoqoIPI+Xy92IkDWLGLS6JnxZoVfRIpbn1MZTWb4JQdKJkgnBTEoY8Oc1QW4y+HNR0OS1FWqVLMsy+gcGkMlmoev6db9fvJ0R4uANwDRN5PN5FItFuGEIOQx5qQ2QeCBEcQzf91GpVpGjN82IEMiomxW0mCGoqoqIzthaiYOIDnz3338/vv71r+PatWv4xSOP4J73vx8A8OMf/Qh//9OfAgA+fN99+OxnP9uTdW2dDpKtGBochCxJKJVKWFheBgHQdx2/8DENhXqex6s3NFWFmcnw9cvvPPcdpNtVmaqJ+3d9rO19WJaVzLBpGLtjMxwpcX7TVLVhslyvSgPTzC8s4Gc/+xnuft/7mooWICkjC4MAtm2vuf7OowY9PVLg9ddfx9zcHN59xx3rnkHLigLTshIzM9pRNY5jLC8tgQCwLeuG5BmkfQxa0cvIQafvjSRJgCyjUi5zC/B6YQA0TkQkbNmiyed2rc9ziUYNLNPE+OQkFEXpievkO5m3d03Vm5hsNgvLsgBVRdlxENflBti2DU1VuftazMKxpEGnRPYFqHucfSlb+R2kX3HXXXdxK+IHH3oIURTh6aefxv/310nPgDvuuAOf/c3f5Ptc7/Cj6zp8mjjWioGBgSS7X5a5cVGvIYTAcRwsLS8jCAIQSYKm68jTsjU2gP9y/mXMXJ6pee2Htn0IObN9waKw5SJJQpWG67s65mZ/uA43xHZD5h25I9ImYb0kJgTHjx/H8PAwRulnuRdIsgzTMJDLZnk5KjvDMh0MryedNDOSsH7B1U1CYxzHqFYqCKgDqG3bbUVUSBw3Fgb0HrPWmTuOg5guWW3ctAmqqmJgYEAkIK4TIQ7eQPr6+pLEPE1DuVKp+XKwJk2KonCTHj5zoOYuNV+mBpUNzNylVROmdIaxJEn4xCeTdfO5uTl885vfxFe/+lUQQrB71y584QtfqNmHtE6BoOs6gjaNmvpofbkqy1guFrHQQ4HgBwGKxSIcWtomyzIKuRxy9bMeQvDXdc2VckYOv7791zveJ+uyxzz4u6LZgEETGm80rMsi0J474vWY083OzqJULmPvnj293zghqDpOkjxs2+gbGICsKIgJQaVUQtVxem49LtH9tn+IPShj7MJMKwrDRCSFIRRJgm3bDSNi9dtt2uK5g2Ng4iyTy2FgaIjfVwXrQ4iDNxDWfEU1TcRIOrnV/J12KpNlOekylhIQrPSupnyoPu+AmiGxLnf1NAo/3/6ud2F6ehoA8PDDDyMIAkxNTeFLX/5ywy/7em5Cuq6vuayQpq+vjyfxFYtFzC0srP2iFkTUs6BcLiOgA2omk0Eul+OiQMbKNTr6+lG8Mv9KzTY+tvNjMDWr41JPWZZ5R0We8d4ua1xzqc1y117D14TbnHX2eukjCEOcOnkSG6enUWix9NEt6UqJTCaTVEfkckmCoqIkrdhLpcSEpwfn1o3jJb8/dJlzwE2NOvhe+76fTG7imJdlN1sqS58NEwZ1B9DRspjvecn7EgTYvGXLSkRWsG6EOHiDYWtjimki9H1uz8qQ6ZdNopUH1bq/A6iNIqQiCJIkQdE0kDWiBzVIEu655x7+a6FQwL/4F/+i9ReuywiC1uayQpq+QiG5XnRtc25+vuP9EjoDXF5eTjrnEQJD11HI51ev4dP1fRLH+M5L36n503BmGPduvpc/r1NMw0jqxmmFQi95I9ZaWdSAWQi3glUm9JJTp04hjGPcfPPNPd0ukJT7ekHAnTHZ4CfJMmzbRjaT4RVCjusmuRfd2JdT2s0xqGddfRXY97jdJSSaoOnQJkes46zSIocmfU5y2jyJ3rc6FUMlGq0o9PdjYmJCGB31ECEO3gTouo6+wUFIug7X81YNmIqicEtWv4GAqIkipL9sWPE7aHdN9MqVK/j+97/Pf/c8r62EuW5uRrqmdXUDzefzGBgYgCzLqFQquHrtWtvh3DAMk0RQ10VE/SXyuRxsOotvxmMXH8OrxVdrHvvkrk9CkdeR0ytJsGhtvNNBSJof5RtodtQIkhIHa9Jj8VKpVnH69Gns2L69534Dge9zcx3LNJMy3DpUVUU2m4Vtmvz7WC2XO44Ksdr+riMPNHrT6dXtNr/Ao9fFME1ucNT68BocH71e3ZhhLS0vIyIE23fsaJkoK+gcIQ7eJNi2jWx/P2QA1UpllUBgHghAMoup1OUoMKI4Tm7SrG67hRlS/etLpRL+j//9f0epVEKWWpy6rouHHnqovZPo8Aajaxp3suuUXC6HwYEBKLIMx3VxbW5uzcHV8zwUSyUE9FpkbRu5ZlbVKYIowPdPfb/msenCNO6YWl85JwDuYwFJ4gNQu7SsO1/fYXVFJ90Ye+24efz4cRiGgR3bt3f1+mZHE4YhKjRp1ND11mY6kgTdMFDI5WBoGqAoCMIQlUql4bLeqmMgpHkpX5t02q6ZRQo62WMUhiuREUmCRV0n0/ts6EVQH9WQEvv4bs6XxDGuXbsGxDH6+/uxbfv2G2r29U5AXM03EYX+fuiZDCBJqFBnuDSGYcC2bQDJOl8lnaRIYUmCEVXoGoscUDOkNOkvped5+D//+I9x9do1mKaJf/Wv/hUO0c6HP/vZz9qvEOhAINiZDDzP6yjvIE02m8XA4CAUum5/rUkEgRCCSqWSNH4hiaNeLpdruwTtp7M/xXx1HumV/M/s+QwkqQdfH1onLyF5D9qK8DSpTln9tBsrEXhIu42bdC+lwfzCAi5duoTdu3a1DGm3otGViqIo6fCHJLnXajMiIckyLNtGln5XY0LWXmbogTAA6OQA7UVvOhERjCAIkvyCKOI5UY2+R80EItsfXzbp4nzjKMLS0lJy/5NlHDh0qPNyYMGaCHHwJkKSJAyOj8MwDEgAnGp1VYTAMAy+xBDQNsf1ZZBA8uWLqFOeTC1L0zcngpUwcBzH+NM//VPMnj0LWZbxe//8n2Pjxo34xCc+kewnCPC3DzzQ6cms+RS2PlgqlTrbdopsJoOhoSGoNIJQv8QQxTGKpRI830cUx7BMkyd5tkM1qOLBlx9MfpEACRJ2De/CLSO31DxvPcMwc+WT2owetLuvGy4OOogc9GpJhAB44cUXkc/nMb1x47q2U/M7TQCWkLiNZmy748iYqmnIZ7NQ6fWoVCoNI2WsumC9wiCmS4uEVty0ohth4LouqpXKSn5BNttcjNVtm1c20f/HDZ7TDqx77eLSEiRFwaZNm7Ah1UlV0DuEOHiToagqCkNDsOhsMmARgtSNQ6ONf2TqjsdaPtfDbjiyLINIEqL66AH9cn7jG9/ACy+8AAD4/Oc/j723JAPf1NQUb3L08COP4OrVq+2dRDq82OJpuWwWEoDiOsQBkCzJDA0PQ5VleK6LK1euICYEfhBgeXk56WNA99fpevQPXv4Byn555QEJ+M2bf3PVjY2scyBmS0ZBEHQdSamHhZhvFLyMca368h6KlkuXLmFxYQF79+5dnxhKD8w00hTT2Xw3woDBEop1TYNEP59VGsFKdtWbiAGQ6mshyy3FQaceBjEVSiy/QDeMNfML0lvnwoeQrpIsGUEYolqpoFguJwZUmQwOXocmbIIEIQ7ehGi2Dcu2YWezYP0RynURAkVRkvVy2g2tVCqtamLEUDUNIKR21kJvRg98//u8mdLH778fd911V81r77//fu6Z/r3vfrezE6E3oWa3PVVVkclmUSoWO9tuA2zLwsjICBRZhh8EuHDhApaXl5MbvCwjl8t1XPu85C7hJ2d+UvPY4YnD2Da4bbUp0Dpv7gr17Zdotnsr2J7X2mMvzHDaJU7luaxZqbCOASJNFMc4/uKLGB0dxcjI2tbVbUEIKtUqQtZeOJNZvxUxrfu3TROgHQmZJ0AvIgaMOIoAmmTb/FCkjrwYoihChbpeAkiagK2RvAusdkGMmXlblyLL9zw4NPISeB50w8COHTtE34TriBAHb0JkRYFGbVlZCDwMApTrIgSyoiSDHnVSrKRa1abRaevZMIoQ+D5iQhBGER555BF8ny4X3HXXXbj/4x9f9dqpqSnceuutAICnnnoKFy9e7Ph8Wt1ICoUCij0QB0BiSz0yMoIwCFCpVHBtfh6yJHER1SkPnHwAfrQiuGRJxmdu/kzqd2l1ktU6sEwTkJJ+GF6Pogc3amkhnYzYap+99DaYnZ1F1XGwd+/enm3TcRxuzGVnMk27S3aDTh0WmbCsrrPcsZ5W+QZsGaGT5YSA3nNill+QzTa0624G289633PXdeG4btKzwXGgmybyuRx27tq1ru0KWiPEwZsU1baTBjSalqztKQqiOEa5VKq5oUiyzJuMEEJQrVYbljqyNW3WBfH555/HX3zta4jiGLfs3YvPf/7zTY/l4x//OGQ64/jud77T9HktYXXMdQ/ncrmeiQMgGaTYkguzW+7Govhy+TJ+fu7nNY+9b+P7MJ4br3ms5ka8zpugJMtJ1jfWKG1kN9117a23rNWqmdGrhkCu6+LUyZPYvHkzcj3o1kmQVAH5QQAQUuNl0EsUKuhVVU36EFQqbbVVb4eY+p00MhZKd7psh3R+gbJWfkEKnsuUEs6rzNrahBACp1qF73mQkEQPVFWFLMvYtXt3EhEVXDdEiuebFFmWYfb1wVlc5DcUlvFcLpeThi+0rIpbLdOkPNfzEBMC27a5ejcMg7egtWwb+/fvx7f+6q/4l7nVTXtychJ/+d/+W0/Oi89e6I0jn89z57n13oyrtMJDVRRMTU2hWCzC831cm5uDn8+jv4M66O+c+A5isnJD0xQN9++6f/X5IBWq7cEs3TQM3tzHcZxkvbvBPgG0JUbaXYJYL+n17lb0InJAAMwcO5YMEj2aPfppLwPLun72u3Sgztp28n1G4tGQabMPQStY5CDdGpktW7QbLWCfO7aMoBkGrLoyxUawd5XE8YrL4jogcYwqjeIoAGRVRUCbK23ctAkbN29e1/YFayMiB29iFE2DwWZFNDyuaVqSSV2t8gQhhmlZyFBB4Pt+TT8GVVX54OvTNsRAMnjI1AEwvkGe/OnbDKtYWG/0oOo4SeiRkCRfw7YxOjqaOLZJEorLy7hy9Wpbs7TZxVk8fenpmsc+uPWDGLAGmr6mZ+F7SYJN11HXU+ZZu8nrv7TAlxXWGuB6IA4uXbqE1197Dfv272/tO9AmYRjCqVYhATDX8jLoFjZAp0zKMradVDLQ0uVuZteMRpUKvGywzfd/VX6BZa1pDgZqXsTKEhs9t9N+E3EUoVytIgzDZJJk2yiXy4AkoVAoYP+BAx1tT9AdQhy8ydEsCzqLAEgSspkMv3lVHQdV2secodNSR1lKLJNLpRK/cRuGAUhSQ6tetn0uEq63+x7dXy8qFhzHges4IHEMi7bXTXYhYXBwMLFbVhR4rovLly+vabz0Nyf+pub3jJ7BfTvua3066F3yn6qq0A0Dsiyj2shh7024rNBWw6UeiBTP93Hs2DGMT0xgcnJy3dtjDYMgSUlr7uvhy08I0KC5kCTLyGQyXCCU2zRLakQ6ctNNBKI+vyCTzbYWSfRcWto1swqFLhIgoyhKcqpsG061iiiKoKoqbn/Pe4SnwQ1CiIO3AHo2C5UlAtGZpW3bvAKhWueFoGoasrkcFNqwieUp6DTvIArDhm2cWYgcWFknvN4iQdW0dVUsuK4Lx3ESDwPLgtGgVDGXy2F4eBiqqiKKIly+cgWVBj0qAOD4leM4cfVEzWP37bgPGX3trOheNjyyTJP3XWhavfAmsU/mM0e0XlboxWfphRdeAIljHNi/f93biuMYZfo5UBSFG4z1nBZhdiYQFCYQuowgsHwDRVE66o8AICmvrMsvaNU4iSARBawMsykdVmIEQYBKuYyYEOiqiqxtJ5UdlQogy9h/8GBP8ksE7SHEwVsASZJgFAqQFYV/2QzDSBoyIWk5nI4QALWJTzEhSefBIICu6zWJic32xyC0BIl33LsOFAoFlEqljgcPz/eTmvEWwoBhmiZGR0cTgylJwrW5OSwuLdU8JyYx/vpEbUvmAXsAv7r1V9s6nrS4Wi+SLPN8A9fz1p3Vfj2XFtjnTmpRqUCwfnFw+fJlXLx4EXtvuaXle90OrHYfhEBmwqDX16jN7TGnQYU+v1KtdhwV4pUKHUQNoihCpVzmuRaariPTxL+AvX98+YAlG7bYPiEkcWpdA9bAqUrPW9M0ni+1uLgISFKSZ7BpU9vnJlg/Qhy8RZBlGSYVCAxN15HN5SBLUmKGVCrBSS0zsPIjXdN4qSPLJG6nrWyNecl1FAn5fB7FYjFJimxz21EUcTMZwzTbMjdSVRWjo6NJaaMkoVgs4sqVK3xwe+bSMzi3dK7mNR/f+XHoSvvlWwBdXujBNVI1DZquQ5YkVNLLCzfY+XAt4jaXFNZz1EEYYmZmBiMjI9i4DidEALyqhx13xrZbz4C7ocOkPBZBYOWxnfTZkGSZe6C0ZZtMt88rnyQpyS9IJTCnnlwTGeJ/71HVCYsMeJ4HgmTSk6GVWqViEWEUoa+vT+QZvAEIcfAWQtE0GHUtSVVVRT6f56WMruclXyo605ToMoRJ1w+DMOTCoFWyG09mqrsJ1IiEHpGuWGC5CGtRdRxEUQRFUdr2vAeS8xoYGMAAbdrkeh4uX76MilvFd07UlmlO5CZw5/Sd7Z9IKgFMluWeNBeyLYvf/NmA0VVXxuu4BNFOMuJ6r8Xx48cRhCEOrHOQYBGDiBoGZTOZlVB8L6hPPOwAWVFgW1Yi3tuIFhGA5zJE9Du5Vr4Bq3ZiyczMBjmdX8A6JLLvOtBd5KnV4ghbLqvQPAdZlpG1bZ4A6XkeSuUyDNPEftE74Q1BiIO3GJphQM9kagZnNutgiYgRdUxkyYqSJPEMfobToLFTI/gtod4umOYk9EIosHXEcqm0sp8WzoqsJBNA1+HgbDaLkZERaDQP4efHH0axUpsU+endn4Yid19e1kkkpNU22A3Tcd2kMVMX59upZW4ntFPGuJ6rcG1uDmfPnsXNN9+8rryAtDAghCCTqt3vhdiVgI7X2etRNQ2GpkFSFFSp8U/DfbH3kg7gTT0OKDEtDWSDMWhzqEy6KykhPKeg0X46pZkTJhMorPOsrutJhJPmVcVxjMXFRaiahpt278bg4GDH+xasHyEO3oIY2SzUBrNlTdeRo1EEgLYoLhZ5aRJr2qSratKQaHm5rZbJLNGuWUYyISRZ8+xSKORyuaRioS4psdH+QrqcQAiBaZrrqg03DANjY2OQVRlHXz+CQQyggD4AwLaBbTg0caij7TUaenvRRlbT9WR5QZZRrVb5jfq6V5S0yVrigABdi6QwDHHkyBEMDg5iy5YtXR7hijBgx5pLJd31RBj00AbZNM1kmaNBMipBIhjTTocxa7DWpKcCq0QI6Hdd03XkmHEaUvkEQBL5aHyCHZ1Dw5bN1EOBvQ+yJCGbzcK27ZolqVKxiIgQTG7ciM3Cz+ANQ4iDtyhmPg+5QahNpols2WwWMuu7UC4n3R3jGJquo9DXB0PXEVGF3lGNdZObhISVcCSvcmjzZqmqKjKZTGOvA1ZiSbfl0GNVFKXjJkqNUBQFzy0/i7nwGmRJRhZZDGEYn9796Z7NtOUuw8xpbMsCaKMtJui62WKv5QQThkAbHgdd8NLJk3BcFwcPHux6G6z1MhtEs5lM162dG8GFQQ+TUVlEzPc8bufMhUHdZ4l93+pzPlhZYJV+9yVFQSabhWVZibdJKsGwEaSZUGiD+k6xrD8Mi/jpqsqt39P7YMsJI2Nj2LJli1hOeAMR4uAtCktQbHhDojXb+VyOryX6vo8ibc6kKAoGBgdhmiaCIIDnuijRaoa1YHtb0zGNhTvbLIfM04qFpvuVZbiuiyAIko5sPSo7K7lF/Oj0j7CIRSxgAbIkYUfhJuSDQltRlXZZr22wJMuwqVOdT9tPdzrQX49GTOmGS72IkqSZX1jA6dOncfPu3chms11tgw2Q5HoIg+sYwVFVFYauQ1YUOI6TCIPUPtNEYcirLtjxeJ6XNHdiUUPT5NGSdISv1fdYbrG015KUUCJxDKdaRZV1uaSTF5tOXurPY3FxEX1DQ5jcsAEDA81NxwTXHyEO3sIoqgqrr6+pQGAzkGyqe2O5UkGlUoGmqrBphzUC6kpGIwxrRRE6dV4jhCTrvC0GNFax0GIj8KgttLXO5YQ0f/fLB+GESei2ggqu4ireu+ndiKMIr1+5ktRYt0mr68EH5nUMJLph8B4Zrut21d2w13kHa1UqdFvdEsUxjh45gv6+Pmzbtq2rY2MRA5Z3w5IPe0KbibPrwTJNXt7oeV7T/TFnU1mWEYUhKpUKXMfhvgWZXI43TOrESrnbT2oURYjjmC9n+FSgsNwCTddXidQ4jjE3Pw8rm+2ZwZVgfQhx8BZH1XWYfX0tb8AaDeGZqShCqVSCoihQFAWGrvMQPftbKx+ENO0a/7CeCiSOeX5Cmnw+jyq1TG0EEwaKoqy7xp0xV5nDz2Z/VvPYrVO3Ys/mPTANAzKAubk5LCwursvalsGSAtczpLBysyiKGjpdrglbW+4Ra1UqdBsxOXXqFMrlMg4eOtSVoOHOh4Twkt5mx9jVzL9HbaebQgdxk3bq9IOg6XFGNDGYdW6tL09kBkvt7LMXxHGMarXKS41lmjCdocfSUBjMzUE3TYxPTmLTpk08b0rwxiHEwdsATddh9PU1v8nRQcmybeRyOSiKgpgQBGEIz3Hg+z4Mw1j5G03eaieKkN5+u7D8hDjVzyGXy4GAViw0wPd9xFEEg846WGb4evjuye8ijFfEiCqr+OTuT0FRFIyMjiKfz0ORZZRKJVy9dg1BD7rntUzubANZlmFnMjx6EHU4SEmS1NOa/jWTEbsYcJaWlvDyyy9j565dvPdGJ0RhiFK5zI8r28TYpxv4+3YdowbcyhyJIRDzPggaCOeYEAS+j0q5DI8uubHyRGZ41tY+kx2v+9h9z0OpUuHHypKgjSaNrOI4xtzCAhRNw/iGDdi8efP1c6oUdIQQB28TdNOEWSi0FAggBCqNIlimCVVRAElCpVJBqVzmrooWLZ1jUYR2Z6jd3mBIHHM76IWFhVUzmJDaPROAd6IE1lc7f3H5Ah6/8HjNY/duuRfDmaFk25KE/v5+7ofg+z5eu3SpZQ+ItjPW1ykQDF2HoiiQ6HvXDfUla6TBT4yVhj6sZJW/jg5gURSBSBL3CiBsnZr9v8P3KCYER2ZmkM/nsWPHjo7PKwxDlCuVRAQpSlPHv465gRUiNfuQpBVX07ocmJhaozNnQYUuI3Zzzus9K7acUab5HbKiIJvN8iXARttnJYuyLGNiagqbN2/uOrdE0HuEOHgboVsWzHy++Wyf5QqAJijlcrBsG4QQFJeXsby83DCKUK1UkqYsa81S2aCX2le7aJqGoaEhvH75ck0iI0uuigiBaRirQpLdJtn9zYlvIx1gt1QTH9vx0VXPY34IuqZBArCwsIDLV640Td7s5FikLrPBWbhZQpIF7rZInKwxtAEQpfM/WNJo6jnpHz6wpz43NduNY4TMTpcNRvWDqCQlbnpthrZ/+ctfYnlpCYcOHep4gGPe/ATJMgdz2luTVgN+B2v0XbPGPgxdB+j7FkYRCBLr8GKplDTmQlL+mKVdW9ulF2fFRQFNaCaEQDdNnt/R6ryWlpYQSxImqTDoJkokuH6IOpG3GbptI45jeKVSc+MbOogrsoyB/n5uRezSlseu58GgyUOsz30QBCgWizVdD5vC1tVZxnKbs62x8XGcOHEicUyjfSRIHCfh8yiCRuuyG91uagauNfbz8twpHLt8rOaxD23/DeTMxjcn5odQLBZRLBbheR4uvf46+gsF5HK5mgGI5Va0hSS15VHf6HWKoiR9IpB0pdQ0DQorT0NyPWLUXfu6wX69RKlKhZbWyXUz4WZ/L5ZKOHnqFLZv346+vr6OjiUIAh5FUWnEoN1BvZXk7XWZYoMdtDZOosJL1zR4vg/HcQCA5+YQktiHd7x0QgjIOs4poqI0TIlkWVH4ktdaS1eLS0sIowiTGzdi46ZNKBQKXR+L4PogIgdvQ8xsFkYul8wIWz2Rlp/19fXxUCQhidua4zi8tJA1cGKe9OVyuaO17nZv0uPj44jjGNfm5vhjHrV6VjWNH18Ur+3M2HSPhOCvj9e2ZC4YBfz69l9f8xwKhQLGxsZgGQYUAEvLy7hy9WpNyWPH4Vkq4DrOA5CkxBiJluWVKxWEcYyIRgKita5PDwY7FklS2014a34wIACOPPccbMvCrp07O3q57/tcGGia1pEwALA6cpAuxevoSNqH5RWgvpoj9W++jEOrDnzfx9LSEgLmFaDrSbmjJK3tB1Afpery/UpHCpgw0OhEIkOTZdf6LC9T87WJqSlMT0+jv7+/q2MRXF+EOHibYmazMDIZbqvaClVVYRgGNE2DqqqwMxnIdEnBcRyUy2VomsZzEYIgQKlY5JGGdlnrhp2jN5grly/zxwIqDoxU9rKUunHXeymsiizU7fPI60fxysIrNY99bOfHYKrtVUBomobRsTH001yEIAhw+fJlLC4tIY7jrgfdTkrMUi+CoaqIaLKaS2eV7e5vvdnprO13IzOuTnnhhRewXCzi1ltvTUrd2szf8DwvcY2UpJpufuuCDdrXg3SkoIEo4G6F9Pc4juHQtuSsCkGSpCRiRXOGVFVdO2rQrWcBJWwiCnK5HE8gJMCawqBYKsFxHExOT2NqehpDQ0PrOCrB9USIg7cxVj4P3bYblg5yaPTAouuzrDQtn8utEgme50HTdR5FYMIhaiOLn3sjoLlIkCQJY2NjeP3yZX6DZFGCljMjeuOrz1UAapMWIxLh2ye+XfPSkcwI7tl8z5rHX08ul8P4+Dhs6jZXLBbx+pUrvKFNp7RVxUAHlDiKQKIIMSGQVDVp7UyXg8I2jKzS+1wPTZ0ROxQer168iNkzZ7Bv3z4MDAzw906mZW/NjtLzPLiOAwmAvg5hwAbqbhsmtbmTle2zqFs6x4MdB4V950qlEu9YqGkaLNqBVJFlhGGYRNVafDfWGx9ioqCSEgV6ShTIioIoiiDJckthQAhBmSYsTkxPY3LDBoyMjKzz6ATXEyEO3ubYfX0wLCsxJmly45Po7MOiHeFY22dD11eJBN/zEl90OiCEYYhSqdR+FIGJhCZrrePj43yGEsdxkvkste++x/0UsGLty27+j51/FK+WLtU8/1O7PwVV7m7mq6oqhoeHMTg4CFVREIUhLl+9ioWFha59EZoKhDhGFEXcGTGdAKjrepKsKUkoV6urrGub76xH4qD+vWEh8zYolUo4OjODDVNT2LxpU+NjlFb7Q3h0Nh0jaUa2HmEg0WWR65VbIAG8e2JaCDTM4I8iVJko8P2aKoR8Pg9N0/hnOgxDkDhuKQ66lTphGKJSLjcUBRYVBezcmLlXq+9/1XFQLBYxMTWFiclJjI+Pd3lkghuFSEh8B2BRDwTfcYAmzVlkJBUMvu8jCAK4rstvuIauQ9c0+PTx9OATEwKJRhE834dpGG3XV0sA71zIbitDQ0NQFQVXrlzBxulpAOvz7GfH4YU+vvvS90BigohEgARs7tuM2yZv6y6knyKTycA0TSwsLqJSLqNcqaDqOBgYGEh6InR6zPS4mTVxRK1/0wNXfbc807IQRhFPLs1ms2sOdOspy2O5KcDq96fdJYEwCPDUU0/Btu2kFfNa7wGdeXuuyzuKmqbZUcvu+nNomQzY3UZrklJZRchan684iuB6HncTBJLratLlPmAlCTGKIh41kGR5RRzU7bsbwjCE57o1ZmS6rsMwDC4IGJIkrXw2WwmDahVLy8uYmJrC+Pi4cD98iyDEwTsASZK4QAg9DxGdjdfcsGjGuW3bPCPfMAx+40+LhCAI4FCRIEsSwjBETAg0QlClN7lORAKrbmAh0pHRUVy+fBmTk5PJYz2wvP3p2Z9iwVmAJAGKlGzvMzd/hrs2skhG+mg7EQyKomB4aAiWZWF+fh5RFOHa1avIZDLo7+vryM+fzSqZv0Cr40h75GdsG6VyOelc6Tjtmcl0GUpnS0lyfbkam0Gude0IwdGZGbiOg3vuuaetBjuEEFSq1STXQZJgGkbXzbfY0a1bGDQQGPz8U+9NMxqJAlVVYRrGqmuSbpYUhCEQx1A1bSWBch3CoBNRICPlk5HKlahHolHIpeVljE9OYmxsDBs2bOjyCAU3GiEO3iHIsgy7vx+V+XlEQZAIBFmuKXeUsJKc6LouqtUqcrkcv/mxGa2u69BSIkEFDeHT5EeFiQTXhUFFQidlVmNjYzh27Bj8VFh1PVSDCh489WDNY7uHb8Yto7esShCrucmxDO+UaFhLMNi2DU3TsLS0lHTEq1bhuC4G+vuRyWTWPNaYEBBay8721yiywZMyU4MSKyWr0O53qqLUmEY1pMvBkdsmN1pSaIPTZ87g0quv4rbbbkM2l2trf5VqlffnyGQy0DVt1Vp9u3Ajpw5fy74H9Z8T9jc2gK+13SiK4Lku/NRg3EwUMGRZhiLLiEji/UEIga5p3S+F0KUJ1/N4cinQXBQAVBjQ/UVR1DKnwXVdLCwuYmR8HKNjY5ienu55cy7B9UOIg3cQsiwjMzjIBQJbA2UiAbQMybIseL6fzCZ8n1sWp2kkEthAFoYhAio+WIvhdkQCG/DGx8YwQwiuXr2aVAWsMxv+oZd/gEpQ6yT4mT2fWRU5AVYPNGx2xB9NCQakBu20wFJkGYMDA8hmMphfWEAQhpibn0elWkV/fz+0BufDjYrqchWYIKsfatIVG2k0VYVpmom4c10oqrrmssyqwa4N1tOmeX5+HsePH8e27dsx0UaIOQgCVKrVpEyO+vQr6TVv+rnrSiTUv4b9nooG1Iuz+r2w8D6LfrWikSjQqCBvJ3oiKwqCMEQYhpAVpauoWhSGCIIg6deQ+ry1FAWpXB5gRSQBdGkRKXEUx/B9H/Pz8xgaG8Po+Dg2bdokhMFbDCEO3mHUCwQguWHJisJzAGRCYFsWKtUqXMdJ3AFbVBjoug5d1+H7PnzfrxEJVcfhJX8sKmEYRssbRSaTQT6fx9zcHPr6+9eVD7DoLuJ/nPkfNY+9a/Jd2Nq/pfY8Vk4IQOubfE04lQms1LIEWwrQDQPj4+NYXlpCsVSC6zh43XXR39eXRGT4Bkl7FR9YuTm3CoubpomQDiCVSgW5bLZ1A6QuZtAxHdxqxEEbywmu6+KZp5/GwMAA9uzZ03onhMBxXXielyTNUtfDRufCxG0cRas+L/XlremwP08MJKT2eanr0fTzl1oOW+v6hWEIz/Nq+iPoqgqjww6jCu28GEdR0pyoze8GiWP4QYAgCGqiBMxgSaftoethFRb1Z5cWsVLq/6wqoVgsYnB0FGPj49iyZYsQBm9BhDh4B8IEglsswqczMhaulWnComEYPDnRqVu/5hnedTdEJhJiOnPwfB+qqiKi66pwXbieB13TYNKSrGY3jYnxcczOzkLasWPNcqyYEPzNib/GM68+g419G/GxnR/Dpr5NAIDvn3wAfrTSG0KWZHzq5k833VYnImHlqdKqASbtu5AvFGBaVhJF8H3MLyygUqlgcGAguT5tVDbU3IBTx9dsUGL5B3Eco+o4LZc0Op5xE5LYJqNOHDT4TNTv59lnngEB8K53vWvNXIpKpcJD14Zp8oqMZkigbYvjmGfQSyzMT39nyxBsO3FqYG9bgqauPUHrpSYWtg/XKQrSg3RIhWQ7xkdhGPLvcRpV02DQsuRGAqMmYlX39/TnlXl7MJG8tLAAPwgwTj0MRMTgrYsQB+9QZFmG3dcHVdfhFIs8vMijCJLUMjlx1Uyrbtts8GdLE2z5wfP9xLjGcWDoOmzbhmlZq9aux8bG8PLLL6NcLiPfaE06NUt99rVn8cNf/hAAcK16Dc+99hzumLodd03fjUfOPVzzsvdtuhvj2bE1r0+9SGg0e2r+YmnVgKPrOsZGR1EqFrFMr+nF115DxrK4A+XKyyW+He7TUJ9zQP/f7JgkWUbGtlEslxODJNdtmbzXydJC2ja55sa/hsg4ceIE5ubmcOedd7Y8ljAMeTMhCYCdyUBjJljsfUjP2lNRAObQx8p22ec6fWT1CZRtkRLEbVViNBIFmlbzPVoTSYKMlL0zFfFhFEFRlIbLU0DzZQNFVaFpWhIJbDJg8yUzNP48pKNmrMQUSMzK5hcXYZompqemMDY+jtHRUSEM3sIIcfAOR7dtKLqO6uIioiBYiSIQApn699ckJ6ZoZ6alqmpimmRZyQ2L9mpwqUBwHAe6rsOybWSzWS4SBgcHoaoqFubmMD7WYDBP3eAvLp1f9ecnLz6Fpy4+XdNcSVd0fHzX/e1dmPpzZIMR6ICzxgy2WfZ2vlCAZdu4NjeHkFpRlysVZOlSikJ7SgCoESSEzYallb4VBKmZb2qNnB2ZrCiwTTPpm+E4/L1oRCexgxrbZL6B1ksKr7/2Gn75y19iz549GBoebvo8z/NQdV3IoAInk4Eiy3xdO72/dB4IkMr7YAKhjaWadioruHfGGqKAEMIFcHqZSNc0mE3W8hvsjFcDAKuXRFhzI1WWa7a31rKBpmmtc3caJL02IqbJsrKUdOSUJAnlchnFYhEDw8MYHh3Fhg0bRBOltwFCHAigqGqyzFAqwace9UwkGKYJj86AWHJiI3iotsnNNp2bYNs2fN/nmfweXYIoFYuwbRu5XA6apmFwaAhzCwtNzZsYPglBQCCjNnGvfq5/7+Z70W/2d3Zx6s8DSMLnaDFYrLGGrygKRoaH4TgOlotF+J7H3eOyuRzy2WxD7wAGX7qIY17umN5fes+arkMLQ/hBgFK5zLvl8XMBzT6PY4Am1dW/h3xfdD8BbZ8tMSFDZ5Ck7hgkkjT3KZdKePbZZzE+Po5t27Y1vG6EEFQdByHNWVE0jbtPpo+1XSR6nXmUoxEthEFa4LXMP6H5Iix0n84J0XQdZpO1/Ib7bDFjZ/jU30CjJYzdLhvU7Bfgn+lW8PeannMcRVhaXkYYhpiYnsbQ8DA2btzYVmKl4M2PeBcFAOgyQ6EA1TDgLC0lzoSyDFCB4DhOy+TEdCgcQMsbb/2yQ7VaRaVS4QNYqVyGaZro7+vDa6+9Bs91k5KtJoRRCFliAzadYTcYTh678CgG7UHcu/kD0JTuP/qr8hLqIgmtbsVsQAcAy7JgWRaqlQqWi0UEvo9yqYRKuYxcNptEUpoMLPx6szXfFtEMmzpkRmEIhxokpd9DKf1epaIW/JhRO5ONowgghEd5WL6KVH8N6Oz96aefhmEYOHToUMPPDjNuiuk5sM9GW5DWxj8sga/RtWlUdcC9BNbYbVoQpMWrLCUNsYw2y3c7TbYNg4C3bi6WSh0vG9Qjt7h29XARSghfRrBsG+PU9XB0dLSjcxG8uRHiQFCDbppQh4ZQocsMsiwnzok0elAqlZDL5da+qbV501NVFfl8HrlcDq7rolQqwaEOeAptLHPh/Hls376dd2asJ4hrEw6BRCQQCZDIynGU/DK+9cK38JPTP8E/3v+PcWDsQFvH2PQU+U7XiCRQmJ1zPXYmk/gTVCpYXl5GEIZYLhZRopUG+QbVBuw6sBt2TeLdqgOVkMlkUCwWEdFGPt04NzJYQhwTLnKTfRNCMDMzg0q5jLvvuYc7/aUJwhBVGq2ClBg5NXpeo223M9MGkkGzVTUIEwXppZlGxFEEPwwR+H7N+ygh6Xugs5n6GvBkvzbzHVh0wnVdVKpV+L6fVG2gg2WD9P7p7J+0KwwkCRGNWABAqVxGsVTC4PAwhkdGMD09nThyCt5WCHEgWIVMlxm8UglepQJVkpDJZlEqleD7fhKezmY7bjPcyqZYkiQ+kw6CAKVSCVEYwrYsvPraa8gXCjxUaloWdNpBEgDCOGywPVp3LsVJECN5FAAwV53Df3jy/8a/u+ePeFXDeuCVBCwDvsm5rtVvIZPJwLJtVKtVFGm/+2KxmCRl0kgCEwl8YEw18WGPNxp0ZFlGNpNBuVyG73lQVXV1NKaNwSqOY96QRU5FDhqJwfPnz+PChQs4fOgQCoXCqr97ngfHcZIcAVqm2G6y3qpI1VrPp/X3aZotiaSJ4xhhEMCnpaFpdFWFquvQVHVNscz9RICVSEOL1zCL5DAIEFJzMcdxkmREukTHDZPavQap5S7SzmtYFQIVVnEcY3FhAVEcY3J6GiMjI5iamhLLCG9TxLsqaIgsy7AKBSh0mUEHEoFQLCYCIRVBaFcisFr0tQYhTdOSvgS2jVKphJOnTqHqOLBoOLNSrSaDm6pCN01EfgwZMmKsHnwlyPzeGZOYPiaBkBhnF8/2RBzUI0uJFXU6ebGd1tnstdlMBrZtJ8sNy8uIoghLxSJK5TJyuRyymUzNrJnEMTfh4WH2BgO2SktIWYKpnMmsvrGv8f7EdLlJVpREHDRZPpqfn8exY8ewefNmTG/cWPM3Qgiq1SpfJ2+n1fJ6+1/IkpSINqA2G79JxCMIQ4S+X2NWBIB/7ppFsVZti+47/X41Oo+YViGEQZDYkTcQkkEQQFUU5Pv62pupp69ZJ2JKSjmG0h/P8zA/Pw87m8XE+DgmJiZEV8W3OUIcCFrClhmqS0swCQGhs8/A9+FUqzBMEw888AD+9oEHsGv3bvzrr3yl9QbTs6Y1BkvDMDA1NYXz589jcX4eU/v2walW+Swu8P3EBdCTMYB+BAgQIESAECGCVQmJfMkBMSzVxp6RvfxvX/3qV/Hoo49iaGgI//E//seOr1M9fJZG8zbWSqqsR5YkZLNZ2JkMyqVSEkmJYywtL6NUKiXZ4KxKAXV5DmyZoYFAME0TYRwj9P0kATKbrXXZa1GiCiQzWjXluthoOWNpaQlPPP44BgcHccstt6x6PbNBBo0WmS0snpkoWG97aSCp3kgnKNYfdzq5L/0XRZah6Tp0VW07uZBVlbQ66igMudthfVQCWKn0UVUVvu9DURQYup50T20Fy53o9JpRUSCRFcdDEscolUpYLhYxPDqKIRotEMsIb3+EOBCsiayqyA4NwS0WQUolsAY4juvyMHdM10XZwPJf/st/wc8ffhgHDxzAH/zBH6zeaN2NudGAJEkSDMPAxk2bcPLkSdxyyy0YHBpCFIbwggCe6yLwfYRxBBMWTJhUFoSIECFERH9LHmFsyG3A79z6uxjODK2UJ7YYvK9eu4Y/+PKXAQD/27//97xbZCvYdiUAEVbPFpl5zFrIkoR8Po9sLrciEqIIi4uL8IIAtmUha9uQ66tIGszov/+97+GBBx7Azl278Pu///vcQTFdQgqkhE0D2Nq9SisV6mf0pVIJjz32GLK5HO64/faaZQLP85LPTLIT5BpFLupYryhId6/kFRT0d3Y+fhAg8P3ViYU0j6DjpY4mxHGMgEYGwtQaPt8n7bCoahpUFpmhr2OiRafLGM2otzlu88BrRAGwUpa5sLCAGMDUxo28TFEsI7wzEO+yoG3MfB6qrgOLi4gJgUOrDNJEUQRZlrH/4EH8/OGHceLECQRBsGaSGRsw6gclVdMwMTGBM2fO4JXTp7Fv3z4oqgpbVWFbVlLtoFRQQhEqNKhQYMCADKlGKBAQhAjwno3vxaf2fgqmlmTD89KzuqTCtFgZGR7G1NQULl68iKNHjrQlDtLGPI1CxHwZAFhdw9+AtEgo0SWG2HWTJMMowsDAADJ1XRjZ7K/RenvGtlGmDoTMZyHwfZw7dw5nZmdx5vRpzJ49i7lr1wAA+b4+3P2+9614HDRYZ69Wq/jDP/xDXLt2Db/yK7+SdAwErUZwHERhmJQpqioytt0wLL/e5QMglY9RV+IpIYkeMCtjx3WbJhYq9d0mmxxnowZY6ecwIRBQy+P641QVJREDLXpgBFQYSDSCUZ94yJb2uCho9/o1EAWMarWKhYUF2NksRmib5eEW/hSCtx9CHAg6QjVN5IeHIcsyYtpUCQAPTbOa+F07d0KWZbiuixMnTmD//v1rb7zBDVajN83pDRtw5uxZ7Nq5s6bToKqqcOBgGUWoUKFBhw4VMhQoUKBBgwkDhmriQzs/hJuGb4JbceHLPp+hKYqCL37hC/jiF77At1t/szx48GAiDmZmcP/997d9vZrN4NLbZ4mdzdbAUffcQqGAXDaLK1evolgsIgwCLMzPo1gsopDP11hdsyhAfW6IRBMUmcVypVLBf/pP/wknT55MjqVJZCOdxJfG8zw89thjmJ6exrVr1/DCCy+AEALX85LeCPRYTNOE0cAGeb3LB+kIAU/OTG07ZAl+1K8jTok2jZYAai16iKzaT4N/x3GclIym9lWPoqrQ6FLBWgKEHTtr6azSY6zZf0rMtk0LUeC4LhaXlhD4PoZHRzE8Oorp6en22n8L3lYIcSDoGEVVkRseBmQZi3NzAJJM+/RM0NB17NmzBzMzM3j22Wexb//+jo1sgKRcTlVVTE5N4ez581wgpPGiRKCE9D8HgAoVOnRo0LBraBfu234fTMmAQ933VE1LwrV1+1JopztFUbiNNAAcPHQIf/u3f4vZ2VksLC5ioL+/5XFzv/k2+ibw1yQvBLCy1NHsmsmKgnw+D0PX+YAXBgHm5+extLyMDHOcTM9GpVqnP0mWkc1mUaYCQdd1ftzZbBZbtmzBL195BZ7r1uybXR+2Hd/38dhjjyEMAnzsox/FkSNHMD8/jzNnzmB4eBgSIVA1DZZlrZoddysK0tcKdRGC9IydiYKa10oSVFmGqutrJxZKtY6FjLQQiKnvQKPogUSXJ1juQKd2wr7vJ8mKYQjTNBMBU3d8bdNCFHieh2KxmCT7KgompqYwuWEDxsfHxTLCOxTxrgu6QpZlFIaHoagqD2nqmoaYED4TPnDgAGZmZnDs+ef5ckMn1Q1AcqPXNQ2BrmPDhg04ffo0dmzbVhNaXagurnpdiBCyIuM39/4m3rPhvUnmOc2Oj6kRkR8EyRotIXzQiqKoRjDIsgxFlpPs7OFhLCwuYmZmBve+//0rx4jGiWed1LKvei1qZ6bNBh5JlpHL5zGk61imZY8RNcgpFoswTBPZTAYWNRWSJYlnz7Pyukwmg3Klgv379+P222/H9m3bMEYtq3//S19aJQ4UReEJhVEU4Yknn4RTreLOu+5CLpfDli1bsLCwgBMvvYS7774btm0nHQQbnGMng9uqpSf6fzZ4MiHQyNOAiUxVUXgSZcMkUZbMx3+lUQcmBOI4qflvcoyyLHOBqWpaVy2t03gsakCFRSeli5w2RIHreSBxDE3TsHPPHmzatKnheyZ45yDEgWBdZPv7sUg7O8YAyrTcTkIiDgBgYWEBF86fx8aNG3kpV9oHHwC+9OUvJ0153vtefPGLX8Ts7Cx+9OMf45cvv4xSqYTx8XFMTU9D0zScO38e27Zu5WusfuytHFAI4BxgXjWhlGV883vfxN+Yf41cPo+RkRHcvGcP9u7di1xdtvX3vvc9vPjiiygUCvi93/u9moE5jmMgDLH/wAE899xzOHH8OG5717ug0NCwQgeEVUjtu8+1Q/36Ns+TiGPIioL+/n4U+vpQpVbMvu/Dc114rguJHh9PZmMZ6UgGzmwmg1tvvRVAslTDO282gJlTRVGEJ596CstLS7jzzjthWRZKpRL27N2LX/ziFzjx4ov4yH33rfgh1OUTtHNtGkUIeNieuj42MpZSmRigPzXvJ8CFYvq6RnGc9CjwfYQ0MtCsP4OEJFGXvffspxdVFWz7IT031/NgW1bD5ZhWryetRIHvo7i8nAg/WvraPzCAw7ffLioRBACEOBD0AMf38ciTT+Ifb9qUlKqVy8hks+jv68OmTZtw7tw5HD16FBtpvTvLcicAN4ZJ88gjj+Ab3/hGzU3/6tWrWF5eRgyg6jjYsnUrN+PZkN+A04unITmA9JgMlAAXK7PdSrWKSrWKy5cv44UXXsDShz6E/+mzn4XPrGhp2JnNDNlAzyIM7Ia8c9cuPPfcczg7O4tqtbpqZqXUDRbMga4Xw0WjtW5+nKnnsRLIbDYLPwhQKZdRrVb5bHp0fBzZbBalcjnpXaAoSR+C1BJDGIaoOs5qF0W6X40uyTz33HOYu3YNd9xxB3TDQJWKxJt378aPfvhDnFpaQqlYRKGvr6MoQVoEEQAxTeiL6FJB/YxfQnLtuRhoMUgTICktjSJETACEIUIqDJodT1oAKLSSoFdCgADJZ7kuIddx3cSwikY7jBYln6mD5ZUZaEMUQJJgmSYmpqaw8+abxRKCgCM+CYKecHV+HidOn4Ysy9wSN5PJ4MD+/Th37hxmjh1blcjHkhcJwNdvz50/jyeffBL5fB4f+chHsGXrVgRBgGPHjuGJxx9HFAQ48uyzePqWW3DH7bdDAvCVO7+C//zcf8ZLP3gJ5WIZhBC8573vxbsOH0b/wABkWcbS0hJmZ2dx9OhRvn9d0wCa4BVGEUqlEkzThK7rDUPT27Zsga7r8H0fr7zyCm6++eaapYMoTBdMrhjbsIGEzSwlWU7C+2yZpctBhpvrMOMj9gd6PLqmQafRBNdxeO29rChYWlrC0tISLMtKnBlNE6qqJi6KlQqCIIDzy1/ikOuiBMAOQ4xcvgztxAngwgWcO3sWfrmMA7/+6zBMk/cvME0Tu3fvRjabxdLSEo4eO4Z77r577SiBtNKCOUyV+zVay2fXsiYykPo7WwpgIjSmXUbjlCjwfB+NYMtILCokN4sK9QD+3q0cOP9bSJtlOY4DK5OB2SJqwPNbWuSoeL6ftF+njpTMkTSXy2F8chLTW7b0TOwI3h4IcSDoGRXHwcSWLXj93Dn4vg9JlrH/wAE88P3v48yZM1haWkJfX1/LbZw7dw6Dg4P4o3/379BXKKzM2m+6CTfv3o2/+Iu/QGxZ+Pa3v43bqTgwFB3/9NDv4H/5f38bkiThQ7/xG/itz352pXuhlHjJHzhwAJ/4xCdQKZcb7juiDnUsM5t52kd0HTuUJGzbtg0vvfQSTp06hZtvvpkPXDKdhXEIQYyV6AOAVZ3zGBIdkIBkcKr/aSYguF1zXXZ+/QxdJoSf06VLlzAwMACVlvQ51SqcajUpD7VtZOhP5YUX4P/lX+JTUQQLQNXzUD1xAtrMDKRqFRsVBcOZDKJbb4VEra1NKjAA4OCBA3j44Ycxc/Qo7rn77lXHzq5LTKM17Id5ZdSfJ4sIMIHFnCHDMORtjNk21qr6YBEplnSqUjHArvf1YtU72OIYWZWHRitqGpUCp0UB+70eJgpcx+Fi0rQs9BUKUFUV45OTGJ+aWs9pCd6mCHEg6Cl2JoPRjRtx5cIFeJ6H4eFh9A8OYpEm8t3z/vevWa73j37rt5DP5RDFMb+hSZKEvXv34vDhw3jqqadQLpdx5MgRHD50CABQoYl4ALCTVjOwW6VUt79sNtveejcblFKh1j179uDZZ5/F8RdfxKc//emVWWl9Tb2UdOdjHgbp/fFlFTqQkThGuEZVA7sGiiwnkQc6iEV0hhxFEZg9dX0yI+/HgGRg9D0PExMTcD0P1XI58SCIIpSKxSSJ0TCgVyqJba5pQopjxEy8RBGqpgnfspK17EolSTisC3nvP3AAjz76KF6mOSOKLCflg1G0almAe0ukTJVkFl1hiaJUCPDQO1tPb3K9ZBahSQkshf4/amDe1GtqlgpS59gOIS0Rdl03cZA0zZVjTZcvttimRy3OXbrUI6dEgUaTGqe3bMGg8C4QNEGIA0HPyWazkDdtwtVXX4XvODh48CB+8YtfYObYMdxzzz0t1+GzmQwO0gGfhZnTCXjvfve78eyzz8I0TTzx5JNcHGSzWaiqijAM8fhjj2H/vn01rn9se+l/k9T/68vhmnHgwAF8/etfx9z8PF577TXcdNNNNdnyLNJACEFEjW8aZcVLACRFWWmXXFeKR/9RkzVfb6hECElMqFKigG8//TuLakgS8rkcdNPknRBN24ZpWag6DqqVCqIgQCUMUQkCRMPDkMMQlmEAUYSIEAR0BhvLMtQogoYkB6RcrSYhe5I06hkdHcXkhg0IwxDPP/88Nm/Zwk2hGOmBm/8/tZ7PuljWiABaDdNs4E8/1gzSpHfBeklfbyn1Htb8rQ0834frulBVFYZhcP+FmCYXtnyt56FULsOtVrkfBRcFmpYsYygKtmzfjvwaUTzBOxshDgTXBdu2MbV1K65cuoRdNJHvzOnT8INgVTfA9O1u48aNqwZ1/rw4xvTGjQhoKdnC/DzmFxcx2N8PTVVx+2234bHHH8czzzyD2dlZ3Hbbbdi1axe2b9++yj0QSEUWgBp/gfTfagQEEhGyY8cOnDp1CkeOHsVNN90EWZah6zrS6YlsKUJVVXhBAEL7KxAaNicA73bXDcwJjw2iMYscpEVGzQuSgYWF/st1zpYgBKZhIFAUeK4LJ4oQmyZ8VcXc0BAcTYPieciXy1CiCKbnQYljOHEMlMur7JolABs3bcIrp0/jzJkzuGnnzpqIAK+EICu9HFjkQ04N8uncDJ6zsY4ZPxMc3W5h1esaRTC6LF8FkghJmXY/NUyT951oFiWJ45h3t3Q8DwhDEHptLctCIZfjUR1CCKxMBpu3boUpTI0EayDEgeC6oSgKxqemcEhR8LWvfx2mYWDm2DEcPnSo1ssfNDExjpHL51tuk3nOs5nfM888gw984APQFAX/8+c+h4rjYOboUczNzeGHP/whfvjDH0KSZWzatAm3vetdeP/73786C58fiLTKh2GV4Qwh2LZtG06+9BJeeeWVpAVv/fNAKxdUFZquQ6tLfotT58uc+uoT59LLDg0Ple1HlhHRwUhRFB4FYYMJ764nSUDKZ0Kmtf6kTkzIigI7k4Gl63AqFZBsFq5lIZIkRJaFKgDT8wBFgeG6MABY1ApZVlUodPavyDJ27dyJZ556CjMzM/it3/otnpeRFgLsXG5UMlw71SONBEDTAb/F0kYnsK0vLy8nbaxlGdlcbpVVMpAIAsd14ToO9ydgxyjR6oO0KAAhgCxjfMMGjE1MiMRDQVsIcSC4rkiShInJScA0ceb8ebz00kvYsX07MplMTQSBZfGnZ59Nb+SEoFwuY+vWrXCqVczMzODQwYMwdR1f/tKXcGZ2Fs88/TROnjqFC+fPI45jnJ2dxdnZWfzoRz/Cl7/8ZWzftq2z86D7BYCXX34Zkiyvym1g/2ZeDnxQrhtcZCDp1rhG8huLMLB2z1w00Nkv4jjJh6ClmHLq+vGoCJ3ZMmMqx3EQBAEyrO0z9TNga/CsdNDTNGiOg7zrwimVULJtRIRAiWMoYQidNlCKkZTc6YYBS9OgGwYvuduxYwd86tq4uLCAkZGRN3xgYsmInQqA60F9VKpSqaBULiMiBH3U/ZIRRVESHaCCgAkq5nFhmSZsy4JpWbXXmBBY2Sw2bdkiogWCjhDiQHBD+I3f+A38zu/8Dogs4xOf/CQqlQoCXYdt2zU36uLycsvtRHGMcqWCOI5hWxZuuukmvHTyJG+OBEKwZfNmbN68GbIkwfE8nDp5Eo8++iiee/ZZFItF/Mmf/An+r//wH2Cs0QyqEculEk6fOQMAOHzwIIDVA01aSEhIZvRRFNUmJqYS69L/Z9UVbBYoEQKZmvisSkCjf/NdF6ZpwrSsmkGuJp9CSmyAq9UqwjBEJpPh22ARkyAM4ToOwiiCRAj0IIDp+zCCAH3Ly5B8H76mIVRVRIoCKY7h07VwZrbE3CYNw8BLL70ETVWRy+UwOjZWmwPB9ouVyAsPnaevSeoY68+dCyEqwnjHxQbPZVeu6ZLCdRIANbvAiljjSYX0b34QYHFpCVEUIZPJIJPJJOWkjpP4Hfg+9/WQCYGiqrAsC5Ztw6C21/XIsozRyUmMTUxc93MTvP24fnU7AkGKD3/4w4jjGDPHjuHq8jIMatLDugoyLpw/33R2RwCcv3ABIS0JnNywATft2IHRkREce/55lFIlimywMXUd+/ftwz//Z/8M937gA4jiGAuLi/jlyy93dR4zMzMgcYxCPo+tbUQfJKz4EdTnADT6P2n0NzTJTKeJeMBKOWPDnIO6gaPGpVKSEAYBSsUiyqUSz5S/cOYM+opFGHSWCgAZx0G+XE5Eg+fB9n2MGwbGRkdRKBRgGAYU2gHScRycPn0aY+PjuPW22zA3P49SuZyUc6YTLlmSHWlQ759OEmX/bvAYX0pJv77uuRJom+wbIALSkFS1Au+1UXcMURxjfn5+pRoDwJWrV3Hl8mWUSiUEVBioTGiNjmJiYgL9/f2N/Q8IgZ3L4aa9e4UwEHSNEAeCG8Lk5CQO0pn2T3/6U4xt2IDc4CAkWUaxVOLtfcuVCmZSRkVpJAC/ePhhPrO8ec8eGIaBffv3Q1UUHD16tGEnPMaePXsAJIPE0vLySmJgB+dx9MgRAEnVQrsBcjk1iPcaVtLYzOaXkbZCZv0kfFruVq5Wkxm1JMFzHBw9cgSRqkImBBFd81ZoNEENQ2TL5eRvAMqWBUVV0dfXh7GxMd7a1zJNnDt7FrIkYcuWLXCqVSwuLuK111/Hpddfx/zCAiq0ZfSNgC/FXO/9pP4fEwLQpSCg8RJZGEV4/coVLC4tYXFpCSF1tQx9H5IkQdc09BUKGJ+YwPj4OPr6+laVjaaRZRmTGzfipt27YdJ+GgJBN4hlBcEN48Mf/jCOHj2Khx56CH/4h3+I0fFxLFkWSouL0FQ1Md+pVvGt//7fsX37dhQKhZrXnzx1Cj//+c8BAJs2b8bWzZsBAP2FAqamp/HMM89gcHAQO2+6qaEN7IsvvgggmTWPDA/XlLMxK92WteNBgOPHjwMADtASynZgs/R0ImWv4H4Hqe3y0Hw6k56el0yz/kulEl/qUGQZumFgbm4OR48cQV9fH275lV8BDh/G33zjG3CCALqu4x/9038KILlp5AhBxbIQbtmCMrVi1g0jWf+2bZw4cQKXLl2CYZrYd8stiGhEwvc8RGGYlEtSL4W00yHriaBQ459euRPGdcmXvYJXt9D1/5rHUvsOggBB2vmRmjdVqlVub53L5aAqCl8isht0sWxFNp/H1KZNyfKSQLBOhDgQ3DDuu+8+/NEf/RGOHDmCy5cvY2xsDAMDA9B1HS+ePo28aWLXjh24+Oqr+Nf/5t/gI/fdhy1btyIMQxw7dgw/+clPEMUxFFnG5z73Ob5dSZJgGgaeP3YML586hX379mHb9u0YGhoCAMzNzeHpp57CU08/DUmSsHF6Glu3bq05NjagxqzUra5kTgJw/Phx+L4Pnbaj7gS2vMCa4fQCVt+P1JJFfTIaL8mkA1cun4eqqryHhGEY0DUNr5w+jRPHj2NqehqHDh5MzIf27sXLto3l5WXIqop/9O53J9ui55MFUK1U4AcBqtUqYloqCQBHjh4FQRKtyedy/JCiKErc/1wXnuchCILED4KW5K0cOhUzspy4GKaEA/vR2myBHKVD+usgnSCbXsqQsCIugyBAwAQAFQPcoIrCckGq1Spcx4FECIYGBzE0OLg6obANZFnGxPQ0hkdH13V+AkEaIQ4EN4xDhw5hfHwcr7/+On7wgx/gt3/7twEk3gHzCws4Vyrh5n378PFPfhI/ePBB/M23vw3P82oGU1VR8MUvfhHb6gd3SUKpVEIcRXjyySfxxBNPwKEDUPo5E+Pj+NKXvlTjONdo0Kgv8wOAZ595BmEUYf/u3dA1rbOmSnQpRJHlxA1xLYFAVroipqsfVm2W+gEw6+D6mSahfQTYdWCih7VRJnGMozMzuHDhAkbHxuBUq3js8cf5a/0g4APZLx59tGbb+265BYVCATIrq3McxFEE0zTx/LFjkCUJhw8frkksVBSFWzQDtEW27/NBtKbbYhQBJDGTisIQ7J2sMVJi7ZEVZaX5UirqQJD0KWD9FtqFRXhqEgjpeaRn/+kf7teAFSHB3jvWbpkJGt/3QQiBruvIZrPo6+/vuCRSkiQMDg1hbHISWjtNmQSCDhDiQHDDkCQJH/7wh/G1r30NDz30EBcHQHLDvXbtGoqVCn71vvswOjGBX/z853j90iUsLy/D0HXs3LUL9334w5icnFy17R07duArX/kKnnv2Wbx4/DggSdCrVVQrFSiKgumNG3Hr4cO48847a33qyYqNbs3sMjUYE/q3mZkZ3oqarZXXtJ6uKyOsOffUvxVZrn19IyOduplmKzEhSxLv46AoCljzIj8Ikh4XKSHkOA4814VhGPA9D0899RQWFhdx+PBhnDt3Dl/72tf4OZumCYs2VSqXSvjaX/xF6rIRfOUrX0GhUIBlmlBkGZVqFX4Q4MyZM6hUKpBlGQf27199TqlzURQFVpMwOCGEh9/TgiGg3TRj6hURxHGSpEqvY7pCg+ViRHUdNuv3w64zSR1jK48JgpWErbQoUFUVqqZBYz4XmpYIlZTddblS4cdo2Tby+XxHwkCSZQwMDWF0YqK9To0CQRcIcSC4oTBx8LOf/QwuLcFjsFr+kZER3HnPPTj4rnehsrwMn85IdVWF0STJipnu7Nq5E6fPnMGxY8ewd+9e9PX3Q9M0ZGy7Zbj2i1/4Ar74hS+sPJAawCQAp0+fRrFUgizLOHjw4KptpcvTkhelRANS4oGKAFVRVvIE6oVBh8iKAtAyRN/3awQBK6Vk1zmghkzlUgmPP/EEwiDAnXfeicHBQZw7dy45HPo6jeZtBA2SPNNiCAB0XYcky6iUyzhx4gSyuRwmxseRTS0p8HNlyyBrRE8kSeKDayPSkYZ0CJ8LijBsmMlP0sIvLQ6BmmqGZu8J7whJRYBKRcBa7Y6DMExaYlPRZlgWcplM23kFsiyjX4gCwQ1CiAPBDeUDH/gATNNEtVrFP/zDP+BDH/rQquewdrKWZSGfz6NcLqO4uIjAcRCUSlBUFaZpJp7zDfaxdetWXL1yBadefhm3Hj4MWZJQLpeRyWa5GVCnHKFVClu3bkV+DRfH9MBXvzTBcwNIYkzUqO9Cu7Cwv+M4qFar0HU9EU80F0HTNGi6vmrQCoIADz/yCAzDwN333MM9D+666y7cddddyaBPKzpACHL5PBTaxbHRubIrqqkq8vk8Tp48CQnAvn37EAYBr0RJTryupLNBNKFdFNqlMT1MsioBkuqGyZYWgNoB/0YaMvm+j0q1CkIIgjCEZVnQqGlUKwghkBUFg0NDGJ2chK7rLZ8vEPQKIQ4ENxTbtvFnf/ZnuHjxYlulVrquY2BgAPl8HpVKBUtzc/AdB+VyGYosJwl1hlEz6EtI8ht++rOf4eTJkzx5sFQqwaY35U45SssrD9ByzG6QCOFioN4MKU5Z4DJzoLQlLoPlEPCZMWj9PpKZpWWa0HW94WyUDZaLy8soFAq47bbbGg82bH2e5j20mtnWD6+XL1/GuXPnkMlksGvXLpQrFWi0HbRUnzyYHpzrEikbUf8oX9dPCbH00hBPHiSka1G4XgghyVIOzZ3xaeUHAN5GuyE0T6F/YACjk5MiUiC44QhxILjhfP7zn+/4NaqqolAoIJfLoVKpYHFuDl65jCpNOtQNIxkU6QBkGAbuuOMOPP744zh69Cj27dsHXddRLpehM2fGNgeMa9euYWl5GbZl8S6QXZF28WMPIVnnlmkeArddBvggyZL2fN/nz2HHrqgq7FQSnmVZDashXnvtNcyeOYOYEOSyWbz3Pe9ZPViz48HKTFtbI1Rez5GjR0EIQS6Xw+SGDXBdF0EYYrlYhGWaySDXTAikxBEL8cf0Oc1aLHNfASoKGlaC3GDjI0YQBKjSJbGQ5khomoYojpHL5Zp+/mRFSUTBxETTZTSB4HojxIHgLYUsy8jlcshms3AcBwvXrsEpleC4LhzHgUKzwlVVRSGfxz333IPHH38czz77LA4fPgzTNPlgZdv2qg6RjRgeHsZffPWrPTl+iToI1jwGJEsBqsrD4XEcw6cRgvpSOI02dFJpoltElxdYy2hJkngkwq1Wcez55/Haa69B0/UkQ94wGq/5p8osfTrTVVS1tnKjLlGTiQnGiRMnYBgGbr311mTpR1VRdRyE1NfA8zxYtp10WKy/OGnnw9T2k92u5AXUExPalbLB37gZ0Q2EEIKq48CnFSJs/ypNFs3ncqujMXQpqDAwgDEhCgRvAoQ4ELwlYeV49saNcBwHy/PzKBeLiHwfke/zEjwZwK233ornjx3DU089hQMHDmBgYABBGKJSLsOnUYQbFnZOlcWxVstRHCfZ9LTeP6QzTQkrpYcsf6BRbb9CWxvHhPA20YQQnJ2dxfETJ6ApCm6//XYAwHM0dyI5lLp8CJrNH8Uxt/Jl22IVG/WCon7Y/V//5b+sOVdFUZDNZOD5PlzHSbL1S6WkHbFpdl6+hxVBEtGS0GbtjBud4/WGeT6wjpqyLAMs2iPLyGYykGh3TIAmfuo6+oeGMDA0JESB4E2DEAeCdXP33XcDADZt2tT1NlimfDdYlgVrw4bESMdxUF5eRqVUgu+6iGg4et++fTj50ks4cvQotm3disnJyaQczvMQ+H7SJfI6JXsROmjHzCiH1sXHUbSq7wF9wUqtfptmP4qqIqZRhgq1oF5YXMTmzZuxZ8+epsmb7PjSSxWsokHTtJ4k7TGTKk3T4FSrCIIAnusiCALYlrVmlv+q4wXNn2D5Genyw5QxEX/eDSAmBFV6bqz5lCzL3F9C0zTeCZMlGeb7+jAwOIh8X98NOUaBoBMkcqOltUBwgwg8D+WlJVTLZQTUaOeVV17B7NmzmJiYwPZt2+C6bjJLlyQYug7TsqCmQ771fgOoK09MPYf9PS0EIlqLXw9vLkXtjGWa+KdQUyNZUWoy+eMoapgjwGAVCxcuXMC5c+eQy+Vw4MABDA4O8uecPHkSJ196CUPDw0lVQuq80jeBYrGIOIpgZTK8bTDB2v0bWJngWnKifnatN+jO2YxObJDT/RTIGhGGbmE9KqqOw3NFLNNMlnp8H3EcJ3bIpplU4WQy6B8cRP/gYMeiSCC4kQhxIHjbE8cxvGoVbrkM33UxOzuLY8eOYXBwELt370YYhvB8P1nvJyQpMUslN9aQdips4lrY6PG0AJCp+FBkGWi3IRNbimgSbbj02mt4fmYGnu9j965d2L5jR1vWwvVEUYRSsQhIEgqFQs1a/5rioANiQuCyNs9IjJxMy+JipNHzO71VRVG0usKB1LWFRip3giaMNnyPU4miTEz5ngfX8xIBEsdQNQ2macJzXfg0MmTbNmwqCAaGhmC1qlAQCN5ECHEgeEcRBgHcchnnZ2fxxOOPw7Qs3HH77VBVFZVKJQkLIxlYNE2Does8KQ/AKv+CRl8fmc7+mRBg/Q/SkFRZY8fQtf+YzlpfeOEFXLxwAX39/bhp505MjI21jDK0wqVWyJquc/8DoPfigBGGIaqOg4jaD2vUw0JV1XU1S2LvYa9hkQLPdXlUQpYkGDT5slypJEtGhGBsfBxjExPI9/V1JdQEgjcSIQ4E71guXbyIHz34IGRCsH//foyPjyOOY7ium3jfI0nS03UdpmnyGX8v4KV33azpE4L5+XnMzs7i1Vdfhaqq3A0yjiLkstla46EOYEsKdl0ORifigKS9Gtp8vud5SdkfIUAcQ1YU6IYBQ9O6EjoxjQL1CkIIAt+HS0UBIUmfDMM0oWta0r/CdaFoGvL9/di8eTOslLgSCN5qCHEgeEdTLpfxwPe/j9cvXsTQwABu2r4dGzduBIDrLhI6jR4EnofzFy/i7OwsyqUS7EwGmzdvxsaNG2HoOsrVKgLfT/wEush6b7akAHQXOWjmTZD+OyMGEIdhstRAEyJZGF83DBgNnB6bbhe9ixq0EgWaqsLzPHi+D8u20TcwgHx/PwYGBnrWalogeKMQ4kAgAHDp0iU88dhjmD19Gnnbxvbt27Ft61aoqtpQJOjUZ2C9xFHUOnpACObm53H27FlcevVVEEIwMTGBzZs3Y3h4uGbwdanXg6ZpyGYyNUsZhDkwUuqTEAHg6tWrmD17Fq+++irOzs7izOwsyuUyAOA97343vpDuPdGE//zVr+Kxxx7DoUOH8OUvfSl1GoTvk/80a4REfRvSoXsSx1BUta1oQi+iBjFt8OR5HsI4TuyuqShQFIW3m87m8ygMDiKbzSKTycDqouWyQPBmRKTLCgQAJicn8anPfAYLCwt46qmncOT553Hi5Els3bQJ27dvRy6XS9z+ggBBGML3fciyzIVCt9EEOd2AKUWjKMHu3bsxvXEjzCZWumxmHTVIWmSD6Xe/+11873vfw5/86Z9ieGio5jn/9t/+W0iyjGq5DL9BH4V2OHTwIB599FG8+MIL8IOgxiehfshsNohK1BbbMAyEYQifzs7jOIZbrcJB82gC8z/oZoDm3SypT4aEJBFSkSQYtg1FluG4buIAWSigMDiITCaDbDYr7I0FbzuEOBAIUgwMDOBDH/oQ7r77bjz77LN47pln8MszZ7Bxeho7tm1DoVCAHwQIfJ+vlbuuC5XOanVNa+xd0ALegCmOMbewsCpKsG/fvlVRgkYoisLdEaMoWhXaZkFCWVFWVVP4vs/dG/0gwODAAMYnJ3H8hRfYi1e2wfIJUlbQbPDfu3cvVBpuP3H8OPbv39+8qqMNmNulZVk10YTA9+G7bhJN0HWotBokTvsetEkURfA9Lyk9ZOdJqw8MXYdE32dJklAYGEBhYAC2bSObzXbVp0MgeCsgxIFA0ADbtvG+970P7373u/H888/jySefxOy5c5gYGUGhUICdycAwDGh0cJIkCdVKBY4kQWPLDk3WyH3fR7lUQrlcRqlUQqlYxDL9ncRxW1GCRkjU0TCgs1/Lsvjf1qrxd10X99x9N6anp7Fjxw4UCgVcu3YNX/6DP2Abr6nYqB/q2bYNw8Cem2/GsWPHcOToUezfv5+XDq5nBbNlNMF1k2ZRrHpAlrlYkGUZiqpCpg6F/HqwpQvPQxgE3F0SALfgjqIIQbUK3TAwODqKbD6PbDaLbDYrcgoEb3uEOBAIWqBpGg4fPoyDBw/i5ZdfxosvvIBX5+dRmp1FFATJ4EPtjTO0zbRpWTANAxnbhqKqcKlBUblUwnK5jJDmLwCJu2Mum8XIyAg2bdqEvr4+DA4Odr1urev6KnHAEgObDc6sf8O9996LfD6/7rK7AwcP4tixY5g5ehTkn/wTHmVodQydUB9NCMIweS/ISlfGIG1+xPZPIyNRFCW+FlQQSJIE0zRhZ7MwWVdL6nWhUqGXyWQSm21Rkih4hyDEgUDQBrIsY9euXdi1axeAZNBxXReLi4tYWlri/1+Ym8OrV6+iUi4DUQRFlqFrGvLZLLK5HDZv3Ih8oYA8nYWm3RjXU9fP0GiyXhzHCIMACo1etNqu67oAkll/Lwa/gwcP4r/+1/+KpaUlzJ45g61bt/ZMGKTh0QRd54ZHMetTEUUIwzDJEaHLQCFLJjUMZG2bC4JcLscFh6IoUBSl5t8iSiB4JyLEgUDQBZIkJT0dLAsTExOr/h5FEebn5+H7PhRFge95CFwXnuMkkQO6jh2rKlTaw0CirYrX02JYkiRoqpoY9fg+7DXK/4IgQBiGiX10j5Lq+vv6sHXLFpw5cwZHjx7F1q1b+bExi+VetlGOmW0zc5GkzasCKo7683lYmQw0w4BCe1bYVBywwV9UGAgEtQhxIBBcBxRFwcjICABaKx8ESQ2/5yVlcJ4Hr1pFxXFAKhWoisKbLEm0rwIfruhA2u4AZhgGb/e8ltcAawyk63pPQ+YHDh7EmTNncOToUXzqU5/ij3M75k4FQvq5TEQhcVgMqcAJaVdLw7KQzedh5XIwTZPnKhhUHAgEgrUR4kAguM5IksRLHoEkqsBEgud5Saa868J3HHi0IZGsKJAlCQoLb1MLZpbcJ9XuYOXfhEBVVV61EARB026TLOTO1tx7yaFDh/Dd73wHr168iKvXrmFkeHjlcOkPWJVG6tjTJY9p6cAMo6IoQsSWDMIQJIqg6TpM20Yhk4FJIwJMDPSqs6RA8E5DiAOB4AajKErSkIc24UlHFYIgSGbCvp9EF1wX1UoFkiTxzHtFUZJIgywnGfis42BqXV/TNLiui2q1ClVRkufRwTim3SIr1SoIkJTrsRk9azK0BukGRHwwp6F9AmDDhg0YGh7GlStXcOTIEfzar/1aQ+OlRssozOGw5odGBSRZThIHM5mkdJQmEOq6zgWBSBoUCNaPEAcCwRuMpmnQNA25XI5n0LNZve/7WF5YQHlhIRnYaXIdEwQybe4kSRIUSYLEIg70sSiKUCyXkctmuQCQZRnVSgUaTcIzDIO3NAbAB2vmlwAAYdp1kK3t0+PnQ3tdiePBgwfxk5/8BEePHMEHP/jBmufFhCROhnU/URQlFQUNSi8108TY5CRs6i/AfoQYEAh6jxAHAsGbCOZVwEr1AGBoaCip7WfRhCBA4HkIwzDx+49jREGQDK60tC+OIoRRBKdaBQB4rsuXF/r7+3k+gmGavJyvZrmCCgkuKNLRhFT74rSoILRbJHt8/759+PnPf45z589jbm4OpmHw45VkOelYqWlQNQ0azblQVBUSjZDomgZN15PumDQqIJYIBIIbgxAHAsFbACYYQJciAPCcAjbjbvTjui6WFhaSPIcoQhBFCAlBDEAzDPhUJLCBPU71MiiXy+jr6wNohGJpaSnZMYsg0AoL9gO69MH+Pb15M/wwRNlx8NrVqzhw8CAUWp3BqgRYa+v6H5Y3IRAI3hiEOBAI3qLItM6/GWyJYnBwEKVSKbEJJgQnT5/G2PQ0JqemuDCo/wGA+NIlvPDyy5BlGdPbtmFsagqQ5SSKkBICNQIB4P9+4okn8Mq5c5BlGXfefTcKhUKNGBAIBG9ehDgQCN6msCWKvr6+JAJAOX/+PPr7+zFU13gpDTN5unz5MgDACwJMbNiwSgC0mt3//d//PRYXF/HBD34Qo6OjvTkpgUBwQxDiQCAQrIJVR7CEREJLJDvhoYceAgB85CMf6fnxCQSC64tI8xUIBD1nZmYGFy5cACDEgUDwVkSIA4FA0HP+7u/+DgBw4MABbNiw4Q0+GoFA0CliWUEgEAAAHnvsMZw+fZr/Pjc3x/99+vRpfPOb36x5/uc+97mm23rwwQcBAB/96Ed7eowCgeDGIMSBQCAAAHz961/HX/7lXzb82+OPP47HH3+85rFm4uDixYuYmZkBIJYUBIK3KkIcCATvIO6++24AqKle6DUsajA1NYUDBw5ct/0IBILrh0R63WRdIBC8o/nVX/1V/PSnP8Xv/u7v4s/+7M/e6MMRCARdIBISBQJBzygWi3j44YcBiCUFgeCtjBAHAoGgZ/z4xz9GEATI5/N8CUMgELz1EDkHAoGgZ/zDP/wDCoUCPvrRj/JGTwKB4K2HyDkQCAQCgUBQg1hWEAgEAoFAUIMQBwKBQCAQCGoQ4kAgEAgEAkENQhwIBAKBQCCoQYgDgUAgEAgENQhxIBAIBAKBoAYhDgQCgUAgENQgxIFAIBAIBIIahDgQCAQCgUBQgxAHAoFAIBAIahDiQCAQCAQCQQ1CHAgEAoFAIKhBiAOBQCAQCAQ1CHEgEAgEAoGgBiEOBAKBQCAQ1CDEgUAgEAgEghqEOBAIBAKBQFCDEAcCgUAgEAhqEOJAIBAIBAJBDUIcCAQCgUAgqEGIA4FAIBAIBDUIcSAQCAQCgaAGIQ4EAoFAIBDUIMSBQCAQCASCGoQ4EAgEAoFAUIMQBwKBQCAQCGoQ4kAgEAgEAkENQhwIBAKBQCCoQYgDgUAgEAgENQhxIBAIBAKBoAYhDgQCgUAgENQgxIFAIBAIBIIahDgQCAQCgUBQgxAHAoFAIBAIahDiQCAQCAQCQQ1CHAgEAoFAIKhBiAOBQCAQCAQ1CHEgEAgEAoGgBiEOBAKBQCAQ1CDEgUAgEAgEghqEOBAIBAKBQFCDEAcCgUAgEAhqEOJAIBAIBAJBDUIcCAQCgUAgqEGIA4FAIBAIBDUIcSAQCAQCgaAGIQ4EAoFAIBDUIMSBQCAQCASCGoQ4EAgEAoFAUIMQBwKBQCAQCGr4/wEC0qdR7mUKhgAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "#!pip install qutip\n",
        "from qutip import Bloch, basis\n",
        "import numpy as np\n",
        "\n",
        "def create_bloch_sphere(state):\n",
        "    \"\"\"\n",
        "    Create a Bloch sphere and customize it with points, vectors, and annotations.\n",
        "    \"\"\"\n",
        "    # Create a Bloch sphere\n",
        "    bloch = Bloch()\n",
        "\n",
        "    # Add points to the Bloch sphere\n",
        "    bloch.add_points([0, 0, 1])  # |0⟩ state\n",
        "    bloch.add_points([0, 0, -1])  # |1⟩ state\n",
        "    bloch.add_points([1, 0, 0])  # |+⟩ state\n",
        "    bloch.add_points([-1, 0, 0])  # |-⟩ state\n",
        "\n",
        "    # Add the quantum state to the Bloch sphere\n",
        "    bloch.add_states(state)\n",
        "\n",
        "    # Add vectors to the Bloch sphere\n",
        "    bloch.add_vectors([0, 0, 1])  # |0⟩ to |1⟩ vector\n",
        "    bloch.add_vectors([1, 0, 0])  # |+⟩ to |-⟩ vector\n",
        "\n",
        "    # Add annotations to the Bloch sphere\n",
        "    bloch.add_annotation(basis(2, 0), \"|0⟩\")\n",
        "    bloch.add_annotation(basis(2, 1), \"|1⟩\")\n",
        "    bloch.add_annotation((basis(2, 0) + basis(2, 1)).unit(), \"|+⟩\")\n",
        "    bloch.add_annotation((basis(2, 0) - basis(2, 1)).unit(), \"|-⟩\")\n",
        "    bloch.add_annotation(state, \"|\\psi⟩\")\n",
        "\n",
        "    return bloch\n",
        "\n",
        "def plot_bloch_sphere(bloch):\n",
        "    \"\"\"\n",
        "    Plot the Bloch sphere.\n",
        "    \"\"\"\n",
        "    bloch.show()\n",
        "\n",
        "def main():\n",
        "    \"\"\"\n",
        "    Main function to create and plot the Bloch sphere for the given quantum state.\n",
        "    \"\"\"\n",
        "    # Define the quantum state |ψ⟩ = 1/2|0⟩ + √3/2|1⟩\n",
        "    state = 0.5 * basis(2, 0) + np.sqrt(3)/2 * basis(2, 1)\n",
        "\n",
        "    bloch = create_bloch_sphere(state)\n",
        "    plot_bloch_sphere(bloch)\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Qubit X, Y and Z Gates"
      ],
      "metadata": {
        "id": "YRb1bnTGtjQY"
      },
      "execution_count": 36,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Qubit X-gate flips the qubit $\\pi$ radians around the x-axis on the **Bloch Sphere.**"
      ],
      "metadata": {
        "id": "__zGRZgOt_Of"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install qutip\n",
        "from qutip import Bloch, basis, sigmax\n",
        "\n",
        "def create_bloch_sphere(initial_state, final_state):\n",
        "    \"\"\"\n",
        "    Create a Bloch sphere and customize it with initial and final states.\n",
        "    \"\"\"\n",
        "    # Create a Bloch sphere\n",
        "    bloch = Bloch()\n",
        "\n",
        "    # Add the initial state to the Bloch sphere\n",
        "    bloch.add_states(initial_state)\n",
        "\n",
        "    # Add the final state to the Bloch sphere\n",
        "    bloch.add_states(final_state)\n",
        "\n",
        "    # Add vectors to the Bloch sphere\n",
        "    bloch.add_vectors([1, 0, 0])  # |+⟩ to |-⟩ vector\n",
        "\n",
        "    # Add annotations to the Bloch sphere\n",
        "    bloch.add_annotation(basis(2, 0), r\"$|0\\rangle$\", fontsize=12)\n",
        "    bloch.add_annotation(basis(2, 1), r\"$|1\\rangle$\", fontsize=12)\n",
        "    bloch.add_annotation((basis(2, 0) + basis(2, 1)).unit(), r\"$|+\\rangle$\", fontsize=12)\n",
        "    bloch.add_annotation((basis(2, 0) - basis(2, 1)).unit(), r\"$|-\\rangle$\", fontsize=12)\n",
        "    bloch.add_annotation(initial_state, r\"$|\\psi_0\\rangle$\", fontsize=12)\n",
        "    bloch.add_annotation(final_state, r\"$|\\psi_1\\rangle$\", fontsize=12)\n",
        "\n",
        "    return bloch\n",
        "\n",
        "def plot_bloch_sphere(bloch):\n",
        "    \"\"\"\n",
        "    Plot the Bloch sphere.\n",
        "    \"\"\"\n",
        "    bloch.show()\n",
        "\n",
        "def main():\n",
        "    \"\"\"\n",
        "    Main function to create and plot the Bloch sphere demonstrating the X gate.\n",
        "    \"\"\"\n",
        "    # Define the initial state of the qubit\n",
        "    initial_state = (basis(2, 0) + basis(2, 1)).unit()  # |+⟩\n",
        "\n",
        "    # Apply the X gate to the initial state\n",
        "    x_gate = sigmax()\n",
        "    final_state = x_gate * initial_state\n",
        "\n",
        "    bloch = create_bloch_sphere(initial_state, final_state)\n",
        "    plot_bloch_sphere(bloch)\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 536
        },
        "id": "u2Nmi3jUuBsU",
        "outputId": "b7a62b42-3938-4e26-ef7e-1c189d0b26b0"
      },
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Qubit Y-gate flips the qubit  π  radians around the y-axis on the Bloch Sphere."
      ],
      "metadata": {
        "id": "L47wQF42ufpG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install qutip\n",
        "from qutip import Bloch, basis, sigmay\n",
        "\n",
        "def create_bloch_sphere(initial_state, final_state):\n",
        "    \"\"\"\n",
        "    Create a Bloch sphere and customize it with initial and final states.\n",
        "    \"\"\"\n",
        "    # Create a Bloch sphere\n",
        "    bloch = Bloch()\n",
        "\n",
        "    # Add the initial state to the Bloch sphere\n",
        "    bloch.add_states(initial_state)\n",
        "\n",
        "    # Add the final state to the Bloch sphere\n",
        "    bloch.add_states(final_state)\n",
        "\n",
        "    # Add vectors to the Bloch sphere\n",
        "    bloch.add_vectors([0, 1, 0])  # |+i⟩ to |-i⟩ vector\n",
        "\n",
        "    # Add annotations to the Bloch sphere\n",
        "    bloch.add_annotation(basis(2, 0), r\"$|0\\rangle$\", fontsize=12)\n",
        "    bloch.add_annotation(basis(2, 1), r\"$|1\\rangle$\", fontsize=12)\n",
        "    bloch.add_annotation((basis(2, 0) + 1j * basis(2, 1)).unit(), r\"$|\\chi_+\\rangle$\", fontsize=12)\n",
        "    bloch.add_annotation((basis(2, 0) - 1j * basis(2, 1)).unit(), r\"$|\\chi_-\\rangle$\", fontsize=12)\n",
        "    bloch.add_annotation(initial_state, r\"$|\\psi_0\\rangle$\", fontsize=12)\n",
        "    bloch.add_annotation(final_state, r\"$|\\psi_1\\rangle$\", fontsize=12)\n",
        "\n",
        "    return bloch\n",
        "\n",
        "def plot_bloch_sphere(bloch):\n",
        "    \"\"\"\n",
        "    Plot the Bloch sphere.\n",
        "    \"\"\"\n",
        "    bloch.show()\n",
        "\n",
        "def main():\n",
        "    \"\"\"\n",
        "    Main function to create and plot the Bloch sphere demonstrating the Y gate.\n",
        "    \"\"\"\n",
        "    # Define the initial state of the qubit\n",
        "    initial_state = (basis(2, 0) + 1j * basis(2, 1)).unit()  # |+i⟩\n",
        "\n",
        "    # Apply the Y gate to the initial state\n",
        "    y_gate = sigmay()\n",
        "    final_state = y_gate * initial_state\n",
        "\n",
        "    bloch = create_bloch_sphere(initial_state, final_state)\n",
        "    plot_bloch_sphere(bloch)\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 536
        },
        "id": "ZnPNUkUcuint",
        "outputId": "d2128c36-8bb6-497e-85a4-3c6b3b014598"
      },
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Qubit Z-gate flips the qubit π radians around the z-axis on the Bloch Sphere."
      ],
      "metadata": {
        "id": "qgJbVD2FvSmw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install qutip\n",
        "from qutip import Bloch, basis, sigmaz\n",
        "\n",
        "def create_bloch_sphere(initial_state, final_state):\n",
        "    \"\"\"\n",
        "    Create a Bloch sphere and customize it with initial and final states.\n",
        "    \"\"\"\n",
        "    # Create a Bloch sphere\n",
        "    bloch = Bloch()\n",
        "\n",
        "    # Add the initial state to the Bloch sphere\n",
        "    bloch.add_states(initial_state)\n",
        "\n",
        "    # Add the final state to the Bloch sphere\n",
        "    bloch.add_states(final_state)\n",
        "\n",
        "    # Add vectors to the Bloch sphere\n",
        "    bloch.add_vectors([0, 0, 1])  # |0⟩ to |1⟩ vector\n",
        "\n",
        "    # Add annotations to the Bloch sphere\n",
        "    bloch.add_annotation(basis(2, 0), r\"$|0\\rangle$\", fontsize=12)\n",
        "    bloch.add_annotation(basis(2, 1), r\"$|1\\rangle$\", fontsize=12)\n",
        "    bloch.add_annotation(initial_state, r\"$|\\psi_0\\rangle$\", fontsize=12)\n",
        "    bloch.add_annotation(final_state, r\"$|\\psi_1\\rangle$\", fontsize=12)\n",
        "\n",
        "    return bloch\n",
        "\n",
        "def plot_bloch_sphere(bloch):\n",
        "    \"\"\"\n",
        "    Plot the Bloch sphere.\n",
        "    \"\"\"\n",
        "    bloch.show()\n",
        "\n",
        "def main():\n",
        "    \"\"\"\n",
        "    Main function to create and plot the Bloch sphere demonstrating the Z gate.\n",
        "    \"\"\"\n",
        "    # Define the initial state of the qubit\n",
        "    initial_state = basis(2, 0)  # |0⟩\n",
        "\n",
        "    # Apply the Z gate to the initial state\n",
        "    z_gate = sigmaz()\n",
        "    final_state = z_gate * initial_state\n",
        "\n",
        "    bloch = create_bloch_sphere(initial_state, final_state)\n",
        "    plot_bloch_sphere(bloch)\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 536
        },
        "id": "-XyDh_rEvlIw",
        "outputId": "0e3dd4bb-d65f-4326-fc55-a7a70b3c0fe5"
      },
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**X, Y, Z gates are their own inverses** when we apply the same gate twice, that is the qubit will end up in the original state or rotate around $2\\pi$ radians since a single X, Y, Z gates only rotates around the spcified axis $\\pi$ radians."
      ],
      "metadata": {
        "id": "-KfxRC1xxU1o"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Note that X, Y, Z gates are also referred to as Pauli gates.  The Pauli gates, being linked to the foundational concepts of quantum mechanics, are named in honor of Wolfgang Pauli, whose work significantly contributed to the development of quantum theory."
      ],
      "metadata": {
        "id": "sDXKlpRu3WW4"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "X, Y, Z gates represented as matrices \\\\\n",
        "$X = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix}$\n",
        "$Y = \\begin{pmatrix} 0 & -i \\\\ i & 0 \\end{pmatrix}$\n",
        "$Z = \\begin{pmatrix} 1 & 0 \\\\ 0 & -1 \\end{pmatrix}$"
      ],
      "metadata": {
        "id": "B2ayN1VayJLU"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Inverse Example: Applying X gate to an arbitrary qubit $|\\psi\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix}$ \\\\\n",
        "$X|\\psi\\rangle = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix}$ $ \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix}$ = $\\begin{pmatrix} \\beta \\\\ \\alpha \\end{pmatrix}$\n"
      ],
      "metadata": {
        "id": "nCgMfFpazEbB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "that results in an $X$ gate to $|0\\rangle$ gives $|1\\rangle$ is shown by $|\\psi\\rangle =$\n",
        "$X|0\\rangle = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix}$ $ \\begin{pmatrix} 1 \\\\ 0 \\end{pmatrix}$ = $\\begin{pmatrix} 1 \\\\ 0\\end{pmatrix}$ = $|1\\rangle$"
      ],
      "metadata": {
        "id": "_KUoMHpk0cDE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Disgard Global Phase and Keep Relative Phase"
      ],
      "metadata": {
        "id": "OZx3HFR6qh0p"
      },
      "execution_count": 40,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can represent the phase by using complex numbers. So representing i as a complex number and in the **Exponential Form** and we have $i = -1 = e^{i\\pi}$ to mathmatically demostrate rotation around a circle by changing the value of $\\phi$ in $e^{i\\phi}$ where in this case $\\phi = \\pi$"
      ],
      "metadata": {
        "id": "SMB445LAqp0G"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Global phase can be shown by multiplying both $|0\\rangle$ and  $|1\\rangle$ by $e^{i\\pi}$, we rotate around the z-axis (on the Bloch Sphere) by $\\phi$ radians. \\\\\n",
        "Represented by $|\\psi\\rangle =$ $e^{i\\pi}\\alpha|0\\rangle + e^{i\\pi}\\beta|1\\rangle$\n",
        "However, we can discard Global phase and use only relative phase."
      ],
      "metadata": {
        "id": "yFY-9TL3vSwL"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Relative phase can be shown by multiplying the $|1\\rangle$ by $e^{i\\pi}$, we rotate around the z-axis (on the Bloch Sphere) by $\\phi$ radians. \\\\\n",
        "Represented by $|\\psi\\rangle =$ $\\alpha|0\\rangle + e^{i\\pi}\\beta|1\\rangle$"
      ],
      "metadata": {
        "id": "irC-u-zYuDQM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Qubit Hadamard Gate"
      ],
      "metadata": {
        "id": "Y8_0RaVCoj1g"
      },
      "execution_count": 41,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The **Hadamard Gate** is it's own inverse"
      ],
      "metadata": {
        "id": "3HnzOKhwqPIU"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Arguably the **Hadmard Gate** is most important gate in quantum computing."
      ],
      "metadata": {
        "id": "HANOni2kwV0K"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "On the equator of the **Bloch Spher**e we have four states $|+\\rangle$, $|i\\rangle$, $|-\\rangle$, $|-i\\rangle$ and represent shorthand for commonly used states in quantum computation. All these states have the even chance of beining measured aa 0 or 1 but each have a different **Relative Phase.**"
      ],
      "metadata": {
        "id": "UflN39NBw13o"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's define each state"
      ],
      "metadata": {
        "id": "SzlhZgvayPIm"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$|+\\rangle$ $= 1\\sqrt2|0\\rangle$ $+ 1\\sqrt2|1\\rangle$"
      ],
      "metadata": {
        "id": "1W2UPmwbzo1k"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$|i\\rangle$ $= 1\\sqrt2|0\\rangle$ $- 1\\sqrt2|1\\rangle$"
      ],
      "metadata": {
        "id": "wksVDzZLzQUh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$|-\\rangle$ $= 1\\sqrt2|0\\rangle$ $+ i\\sqrt2|1\\rangle$"
      ],
      "metadata": {
        "id": "zvwDH2mCzD7H"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$|-i\\rangle$ $= 1\\sqrt2|0\\rangle$ $- i\\sqrt2|1\\rangle$"
      ],
      "metadata": {
        "id": "5AdIsXEuzd8W"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$H = 1/ \\sqrt2$\n",
        "$\\begin{bmatrix}\n",
        "1 & 1 \\\\\n",
        "1 & -1\n",
        "\\end{bmatrix}$"
      ],
      "metadata": {
        "id": "4bLn9XiNomLm"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$|0\\rangle \\overset{H}{\\rightarrow}|+\\rangle$ \\\\\n",
        "$|1\\rangle \\overset{H}{\\rightarrow}|-\\rangle$"
      ],
      "metadata": {
        "id": "BHHEsiLFpJqY"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$|+\\rangle \\overset{H}{\\rightarrow}|0\\rangle$ \\\\\n",
        "$|-\\rangle \\overset{H}{\\rightarrow}|1\\rangle$"
      ],
      "metadata": {
        "id": "ChxeYpJSqHEE"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In Direc Notation $H(\\alpha|0\\rangle + e^{i\\phi}\\beta|1\\rangle)$ $= \\alpha H|0 \\rangle$ $ + e^{i\\phi}\\beta|1\\rangle$ $= \\alpha |+ \\rangle$ $ + e^{i\\phi}\\beta|-\\rangle$"
      ],
      "metadata": {
        "id": "b01caRls0MU9"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "thus, we have $H(\\alpha|0\\rangle + e^{i\\phi}\\beta|1\\rangle)$ $= (\\alpha + e^{i\\phi} \\beta / \\sqrt2 ) |0 \\rangle + (\\alpha - e^{i\\phi}\\beta / \\sqrt2)|1\\rangle$"
      ],
      "metadata": {
        "id": "DYoLLvQ13z2e"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Using Cirq (Google) to create a Hadmard Gate"
      ],
      "metadata": {
        "id": "rAB0y-DqLfmT"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the code snippet:\n",
        "\n",
        "We import the cirq module, which provides the necessary functions and classes for working with quantum circuits.\n",
        "\n",
        "We define a single qubit using cirq.NamedQubit('q') and assign it to the variable qubit.\n",
        "\n",
        "We create a quantum circuit using cirq.Circuit and pass in two operations:\n",
        "\n",
        "cirq.H(qubit): This applies the Hadamard gate (H) to the qubit q.\n",
        "\n",
        "cirq.measure(qubit, key='m'): This measures the state of the qubit q and stores the measurement result in the key 'm'.\n",
        "\n",
        "Finally, we use circuit.to_text_diagram() to print a text-based diagram of the quantum circuit.\n",
        "\n",
        "In the diagram, the H represents the Hadamard gate, and M('m') represents the measurement operation with the key 'm'."
      ],
      "metadata": {
        "id": "vkEDJRu4Lra1"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The Hadamard gate is a widely used gate in quantum computing. When applied to a qubit in the state |0⟩ or |1⟩, it creates an equal superposition of the |0⟩ and |1⟩ states. The Hadamard gate is an important operation in various quantum algorithms and quantum circuit transformations."
      ],
      "metadata": {
        "id": "6NoHiI68L6Qo"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install cirq\n",
        "import cirq\n",
        "\n",
        "# Define a qubit\n",
        "qubit = cirq.NamedQubit('q')\n",
        "\n",
        "# Create a quantum circuit\n",
        "circuit = cirq.Circuit(\n",
        "    cirq.H(qubit),  # Apply Hadamard gate\n",
        "    cirq.measure(qubit, key='m')  # Measure the qubit\n",
        ")\n",
        "\n",
        "# Draw the circuit\n",
        "print(circuit.to_text_diagram())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "D2SWXWr_LXWe",
        "outputId": "5af9116f-6f74-4928-8b97-183093b944a4"
      },
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "q: ───H───M('m')───\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Qubit Phase Gates S and T"
      ],
      "metadata": {
        "id": "v4LwoK7f4feV"
      },
      "execution_count": 43,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "$S = \\begin{pmatrix} 1 & 0 \\\\ 0 & e^{i\\pi/2} \\end{pmatrix}$ \\\\\n",
        "$|0\\rangle \\overset{S}{\\rightarrow}|0\\rangle$ \\\\\n",
        "$|1\\rangle \\overset{S}{\\rightarrow}e^{i\\pi/2}|1\\rangle$ \\\\\n",
        "Add a relative phase of $e^{i\\pi/2}$ \\\\\n",
        "We have $\\alpha|0\\rangle + \\beta|1\\rangle$ $\\overset{S}{\\rightarrow} \\alpha +  e^{i\\pi/2}\\beta|1\\rangle$"
      ],
      "metadata": {
        "id": "mSBxiNy84saH"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Using Cirq (Google) to create a S Gate"
      ],
      "metadata": {
        "id": "oZya1hqFMfnf"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the code snippet:\n",
        "\n",
        "We import the cirq module, which provides the necessary functions and classes for working with quantum circuits.\n",
        "\n",
        "We define a single qubit using cirq.NamedQubit('q') and assign it to the variable qubit.\n",
        "\n",
        "We create a quantum circuit using cirq.Circuit and pass in two operations:\n",
        "\n",
        "cirq.S(qubit): This applies the S gate (also known as the phase gate or √Z gate) to the qubit q.\n",
        "\n",
        "cirq.measure(qubit, key='m'): This measures the state of the qubit q and stores the measurement result in the key 'm'.\n",
        "\n",
        "Finally, we use circuit.to_text_diagram() to print a text-based diagram of the quantum circuit.\n",
        "\n",
        "In the diagram, the S represents the S gate, and M('m') represents the measurement operation with the key 'm'."
      ],
      "metadata": {
        "id": "PMbS5-r_MOO7"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The S gate is a single-qubit gate in quantum computing. It applies a phase shift of π/2 (90 degrees) to the |1⟩ state of the qubit, leaving the |0⟩ state unchanged."
      ],
      "metadata": {
        "id": "eOtTB71PMWHS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install cirq\n",
        "import cirq\n",
        "\n",
        "# Define a qubit\n",
        "qubit = cirq.NamedQubit('q')\n",
        "\n",
        "# Create a quantum circuit\n",
        "circuit = cirq.Circuit(\n",
        "    cirq.S(qubit),  # Apply S gate\n",
        "    cirq.measure(qubit, key='m')  # Measure the qubit\n",
        ")\n",
        "\n",
        "# Draw the circuit\n",
        "print(circuit.to_text_diagram())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "b1vL-IwlMCXp",
        "outputId": "7f90773f-f98b-44c7-aa13-2ef75b7b55dd"
      },
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "q: ───S───M('m')───\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "$T = \\begin{pmatrix} 1 & 0 \\\\ 0 & e^{i\\pi/4} \\end{pmatrix}$ \\\\\n",
        "$|0\\rangle \\overset{T}{\\rightarrow}|0\\rangle$ \\\\\n",
        "$|1\\rangle \\overset{T}{\\rightarrow}e^{i\\pi/4}|1\\rangle$ \\\\\n",
        "Add a relative phase of $e^{i\\pi/4}$ \\\\\n",
        "We have $\\alpha|0\\rangle + \\beta|1\\rangle$ $\\overset{T}{\\rightarrow} \\alpha +  e^{i\\pi/4}\\beta|1\\rangle$"
      ],
      "metadata": {
        "id": "zifVA45G9gHH"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Using Cirq (Google) to create a T Gate"
      ],
      "metadata": {
        "id": "rGrjb9cHMljL"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the code snippet:\n",
        "\n",
        "We import the cirq module, which provides the necessary functions and classes for working with quantum circuits.\n",
        "\n",
        "We define a single qubit using cirq.NamedQubit('q') and assign it to the variable qubit.\n",
        "\n",
        "We create a quantum circuit using cirq.Circuit and pass in two operations:\n",
        "\n",
        "cirq.T(qubit): This applies the T gate (also known as the π/8 gate or √√S gate) to the qubit q.\n",
        "\n",
        "cirq.measure(qubit, key='m'): This measures the state of the qubit q and stores the measurement result in the key 'm'.\n",
        "\n",
        "Finally, we use circuit.to_text_diagram() to print a text-based diagram of the quantum circuit.\n",
        "\n",
        "In the diagram, the T represents the T gate, and M('m') represents the measurement operation with the key 'm'."
      ],
      "metadata": {
        "id": "ssZm_ztAMwAn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The T gate is a single-qubit gate in quantum computing. It applies a phase shift of π/4 (45 degrees) to the |1⟩ state of the qubit, leaving the |0⟩ state unchanged."
      ],
      "metadata": {
        "id": "UdVksTIAM64F"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install cirq\n",
        "import cirq\n",
        "\n",
        "# Define a qubit\n",
        "qubit = cirq.NamedQubit('q')\n",
        "\n",
        "# Create a quantum circuit\n",
        "circuit = cirq.Circuit(\n",
        "    cirq.T(qubit),  # Apply T gate\n",
        "    cirq.measure(qubit, key='m')  # Measure the qubit\n",
        ")\n",
        "\n",
        "# Draw the circuit\n",
        "print(circuit.to_text_diagram())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JkVYOhU0MqJb",
        "outputId": "eb87416a-11c1-404f-ad3f-29dbf2d8391f"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "q: ───T───M('m')───\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Qubit Inverse of Phase Gates S and T"
      ],
      "metadata": {
        "id": "3rpb36Oy9qI3"
      },
      "execution_count": 46,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let see how we get the inverse phase gates $S^{\\dagger}$ and $T^{\\dagger}$ \\\\\n",
        "Now, add a relative phase of $e^{i-(\\pi/2)}$ \\\\\n",
        "$S^{\\dagger} = \\begin{pmatrix} 1 & 0 \\\\ 0 & e^{i-(\\pi/2)} \\end{pmatrix}$ \\\\\n",
        "and add a relative phase of $e^{i-(\\pi/4)}$ \\\\\n",
        "$T^{\\dagger} = \\begin{pmatrix} 1 & 0 \\\\ 0 & e^{i-(\\pi/4)} \\end{pmatrix}$ \\\\\n"
      ],
      "metadata": {
        "id": "3klBHfmj-WcO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Using Cirq (Google) to create a Inverse S Gate"
      ],
      "metadata": {
        "id": "TzOPFT5UNNhO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the code snippet:\n",
        "\n",
        "We import the cirq module, which provides the necessary functions and classes for working with quantum circuits.\n",
        "\n",
        "We define a single qubit using cirq.NamedQubit('q') and assign it to the variable qubit.\n",
        "\n",
        "We create a quantum circuit using cirq.Circuit and pass in two operations:\n",
        "\n",
        "cirq.inverse(cirq.S)(qubit): This applies the inverse of the S gate (or inverse phase gate) to the qubit q. The cirq.inverse() function is used to obtain the inverse of a given gate, and cirq.S is the S gate.\n",
        "\n",
        "cirq.measure(qubit, key='m'): This measures the state of the qubit q and stores the measurement result in the key 'm'.\n",
        "\n",
        "Finally, we use circuit.to_text_diagram() to print a text-based diagram of the quantum circuit.\n",
        "\n",
        "In the diagram, the S† represents the inverse S gate (or inverse phase gate), and M('m') represents the measurement operation with the key 'm'."
      ],
      "metadata": {
        "id": "VNQ7qsVANcMg"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The inverse S gate, denoted as S†, is the inverse operation of the S gate. It applies a phase shift of -π/2 (-90 degrees) to the |1⟩ state of the qubit, leaving the |0⟩ state unchanged. The inverse S gate is represented by the following matrix:"
      ],
      "metadata": {
        "id": "i2KcZx5uNidr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install cirq\n",
        "import cirq\n",
        "\n",
        "# Define a qubit\n",
        "qubit = cirq.NamedQubit('q')\n",
        "\n",
        "# Create a quantum circuit\n",
        "circuit = cirq.Circuit(\n",
        "    cirq.inverse(cirq.S)(qubit),  # Apply inverse S gate\n",
        "    cirq.measure(qubit, key='m')  # Measure the qubit\n",
        ")\n",
        "\n",
        "# Draw the circuit\n",
        "print(circuit.to_text_diagram())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yYReJqPhNTbW",
        "outputId": "9cc01686-1eeb-42ca-e920-8f049fbb03fb"
      },
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "q: ───S^-1───M('m')───\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Using Cirq (Google) to create a Inverse T Gate"
      ],
      "metadata": {
        "id": "aSh0ybAONoP3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the code snippet:\n",
        "\n",
        "We import the cirq module, which provides the necessary functions and classes for working with quantum circuits.\n",
        "\n",
        "We define a single qubit using cirq.NamedQubit('q') and assign it to the variable qubit.\n",
        "\n",
        "We create a quantum circuit using cirq.Circuit and pass in two operations:\n",
        "\n",
        "cirq.inverse(cirq.T)(qubit): This applies the inverse of the T gate (or inverse π/8 gate) to the qubit q. The cirq.inverse() function is used to obtain the inverse of a given gate, and cirq.T is the T gate.\n",
        "\n",
        "cirq.measure(qubit, key='m'): This measures the state of the qubit q and stores the measurement result in the key 'm'.\n",
        "\n",
        "Finally, we use circuit.to_text_diagram() to print a text-based diagram of the quantum circuit.\n",
        "\n",
        "In the diagram, the T† represents the inverse T gate (or inverse π/8 gate), and M('m') represents the measurement operation with the key 'm'."
      ],
      "metadata": {
        "id": "u1tCk-jZN0zv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The inverse T gate, denoted as T†, is the inverse operation of the T gate. It applies a phase shift of -π/4 (-45 degrees) to the |1⟩ state of the qubit, leaving the |0⟩ state unchanged."
      ],
      "metadata": {
        "id": "vxoP1aFWN68c"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install cirq\n",
        "import cirq\n",
        "\n",
        "# Define a qubit\n",
        "qubit = cirq.NamedQubit('q')\n",
        "\n",
        "# Create a quantum circuit\n",
        "circuit = cirq.Circuit(\n",
        "    cirq.inverse(cirq.T)(qubit),  # Apply inverse T gate\n",
        "    cirq.measure(qubit, key='m')  # Measure the qubit\n",
        ")\n",
        "\n",
        "# Draw the circuit\n",
        "print(circuit.to_text_diagram())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c7ub-hpkNsZ0",
        "outputId": "919eaf87-a230-4755-e5d5-281ace1c3ae0"
      },
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "q: ───T^-1───M('m')───\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Multiple Qubits Using Tensor Product"
      ],
      "metadata": {
        "id": "2o-BRg6j_1iU"
      },
      "execution_count": 49,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Two quibits in zero state can be representatd by using the Tensor Product symbol $ \\otimes$, so we have the following: $|0\\rangle \\otimes |0\\rangle $"
      ],
      "metadata": {
        "id": "k3GyQa_-AHNC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "This can be shortend into $|0\\rangle \\otimes |0\\rangle = |00\\rangle $"
      ],
      "metadata": {
        "id": "ptEs1D0kArAY"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Represent two qubits in superposition, we have $(\\alpha|0\\rangle + \\beta|1\\rangle)$ $\\otimes$ $(\\gamma|0\\rangle + \\delta|1\\rangle)$"
      ],
      "metadata": {
        "id": "BhyhWpdTA1sr"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "can be shown with two quibits we have four states $(\\alpha|0\\rangle + \\beta|1\\rangle)$ $\\otimes$ $(\\gamma|0\\rangle + \\delta|1\\rangle)$ $= \\alpha\\gamma|00\\rangle + \\alpha\\delta|01\\rangle + \\beta\\gamma|10\\rangle + \\beta\\delta|11\\rangle$"
      ],
      "metadata": {
        "id": "p9Mj7XzlBKE9"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Probability of measuring $|00\\rangle$ is $|\\alpha\\gamma|^2$"
      ],
      "metadata": {
        "id": "YItJ6KP1DJSy"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Probability of measuring $|01\\rangle$ is $|\\alpha\\delta|^2$"
      ],
      "metadata": {
        "id": "oS-jRNs3Dodq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Probability of measuring $|10\\rangle$ is $|\\beta\\gamma|^2$"
      ],
      "metadata": {
        "id": "x8uKkuDfDrky"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Probability of measuring $|11\\rangle$ is $|\\beta\\delta|^2$"
      ],
      "metadata": {
        "id": "skABwttSDv-V"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Also, we can use shorthand notation"
      ],
      "metadata": {
        "id": "WG5kq13vDzK4"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Having any number (or n) of 0's can be represented as $|0000...0\\rangle = |0\\rangle^{\\otimes n}$"
      ],
      "metadata": {
        "id": "Km3WAvnGD-uM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "For example, $|1\\rangle^{\\otimes 5} = |11111\\rangle$"
      ],
      "metadata": {
        "id": "mW8tZio5EQRo"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Using Cirq (Google) to display a quantum circuit with two qubits and demonstrate the tensor product operation."
      ],
      "metadata": {
        "id": "lry4C8epONYN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the code snippet:\n",
        "\n",
        "We import the cirq module, which provides the necessary functions and classes for working with quantum circuits.\n",
        "\n",
        "We define two qubits using cirq.NamedQubit('q1') and cirq.NamedQubit('q2').\n",
        "We create an initial quantum circuit with the following operations:\n",
        "\n",
        "cirq.H(qubit1): Apply the Hadamard gate to qubit1.\n",
        "cirq.X(qubit2): Apply the X gate to qubit2.\n",
        "cirq.measure(qubit1, key='m1'): Measure the state of qubit1 and store the result in the key 'm1'.\n",
        "cirq.measure(qubit2, key='m2'): Measure the state of qubit2 and store the result in the key 'm2'.\n",
        "\n",
        "We print the initial circuit using circuit.to_text_diagram().\n",
        "\n",
        "We create a new tensor circuit using the tensor product operation:\n",
        "\n",
        "cirq.ops.H.on(qubit1): Apply the Hadamard gate to qubit1.\n",
        "cirq.ops.X.on(qubit2): Apply the X gate to qubit2.\n",
        "cirq.ops.CNOT(qubit1, qubit2): Apply the CNOT (Controlled-NOT) gate to qubit1 and qubit2, where qubit1 is the control qubit, and qubit2 is the target qubit.\n",
        "\n",
        "We print the tensor circuit using tensor_circuit.to_text_diagram().\n",
        "\n",
        "In the tensor circuit diagram, the @ symbol represents the control qubit of the CNOT gate, and the vertical line represents the control operation on the target qubit."
      ],
      "metadata": {
        "id": "L-f7fAIKOfMW"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The tensor product operation allows us to combine the operations on individual qubits to create a joint operation on multiple qubits.\n",
        "\n",
        "In this example, the tensor circuit applies the Hadamard gate to qubit1, the X gate to qubit2, and then applies the CNOT gate, which is the tensor product of the Hadamard and X gates."
      ],
      "metadata": {
        "id": "vUVFL64tOoZV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Note that we will discuss the CNOT gate in the section called \"Multiple Qubits CNOT, Toffoli and Controlled Gates\"."
      ],
      "metadata": {
        "id": "3BNPgitqO1IZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install cirq\n",
        "import cirq\n",
        "\n",
        "# Define two qubits\n",
        "qubit1 = cirq.NamedQubit('q1')\n",
        "qubit2 = cirq.NamedQubit('q2')\n",
        "\n",
        "# Create a quantum circuit\n",
        "circuit = cirq.Circuit(\n",
        "    cirq.H(qubit1),  # Apply Hadamard gate to qubit1\n",
        "    cirq.X(qubit2),  # Apply X gate to qubit2\n",
        "    cirq.measure(qubit1, key='m1'),  # Measure qubit1\n",
        "    cirq.measure(qubit2, key='m2')  # Measure qubit2\n",
        ")\n",
        "\n",
        "# Draw the circuit\n",
        "print('Initial circuit:')\n",
        "print(circuit.to_text_diagram())\n",
        "\n",
        "# Apply tensor product operation\n",
        "tensor_circuit = cirq.Circuit(\n",
        "    cirq.ops.H.on(qubit1),\n",
        "    cirq.ops.X.on(qubit2),\n",
        "    cirq.ops.CNOT(qubit1, qubit2)  # Tensor product of H ⊗ X and CNOT gate\n",
        ")\n",
        "\n",
        "# Draw the tensor circuit\n",
        "print('\\nTensor circuit:')\n",
        "print(tensor_circuit.to_text_diagram())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xLv8DrPMOWy9",
        "outputId": "8b411d23-a094-4b45-d904-bb08f694e9b4"
      },
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Initial circuit:\n",
            "q1: ───H───M('m1')───\n",
            "\n",
            "q2: ───X───M('m2')───\n",
            "\n",
            "Tensor circuit:\n",
            "q1: ───H───@───\n",
            "           │\n",
            "q2: ───X───X───\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Multiple Qubits CNOT, Toffoli and Controlled Gates"
      ],
      "metadata": {
        "id": "aQBU8TyPHL1r"
      },
      "execution_count": 51,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "CNOT Gate also called Controlled-X Gate"
      ],
      "metadata": {
        "id": "rUcwfITmHmew"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The CNOT gate applies an X gate to the target qubit if the control qubit is a 1"
      ],
      "metadata": {
        "id": "C_RKaOryISKV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Using CNOT gates enable us to create controlled versions of our single qubit gates."
      ],
      "metadata": {
        "id": "Gqsrq_KwKTAh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We also can have different controled gates such as Controled Y = CY thus we have CY, CZ, CS, CT, CH..."
      ],
      "metadata": {
        "id": "OndOJadtKe-U"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Using Cirq (Google) to create a CNOT Gate"
      ],
      "metadata": {
        "id": "YUtK1LtZH80_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The CNOT (Controlled-NOT) gate applies an X gate (NOT operation) to the target qubit if the control qubit is in the state |1⟩."
      ],
      "metadata": {
        "id": "EfwYVUqKIlhO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The line cirq.X(control_qubit) applies the X gate to the control qubit, which puts it in the state |1⟩.\n",
        "\n",
        "Then, the line cirq.CNOT(control_qubit, target_qubit) applies the CNOT gate, where control_qubit is the control qubit, and target_qubit is the target qubit.\n",
        "\n",
        "Since the control qubit is in the state |1⟩ (due to the previous X gate), the CNOT gate will apply an X gate (NOT operation) to the target qubit."
      ],
      "metadata": {
        "id": "h1h60UBRI0u8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install cirq\n",
        "import cirq\n",
        "\n",
        "# Define qubits\n",
        "control_qubit = cirq.NamedQubit('control')\n",
        "target_qubit = cirq.NamedQubit('target')\n",
        "\n",
        "# Create a quantum circuit\n",
        "circuit = cirq.Circuit(\n",
        "    cirq.X(control_qubit),  # Apply X gate to control qubit\n",
        "    cirq.CNOT(control_qubit, target_qubit),  # Apply CNOT gate\n",
        "    cirq.measure(control_qubit, key='m1'),  # Measure control qubit\n",
        "    cirq.measure(target_qubit, key='m2')  # Measure target qubit\n",
        ")\n",
        "\n",
        "# Draw the circuit\n",
        "print(circuit.to_text_diagram())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "33QTX7CfH3Fb",
        "outputId": "187507fd-cff4-4de4-8925-a9a50268f58a"
      },
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "control: ───X───@───M('m1')───\n",
            "                │\n",
            "target: ────────X───M('m2')───\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Toffoli Gate also called a Controlled-Controlled-X Gate"
      ],
      "metadata": {
        "id": "ll6GSJ4KJVJl"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Same as teh CNOT Gate but the Toffoli Gate has two control quibits"
      ],
      "metadata": {
        "id": "QIhbJVsyJaR-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Using Cirq (Google) to create a Toffoli Gate"
      ],
      "metadata": {
        "id": "DuqNVQdvJmRk"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this code snippet:\n",
        "\n",
        "We define three qubits: control_qubit_1, control_qubit_2, and target_qubit.\n",
        "We apply an X gate to both control_qubit_1 and control_qubit_2, putting them in the state |1⟩.\n",
        "\n",
        "We apply the cirq.CCX gate, which is the Toffoli gate (Controlled-Controlled-X gate). This gate takes two control qubits (control_qubit_1 and control_qubit_2) and one target qubit (target_qubit). If both control qubits are in the state |1⟩, it applies an X gate to the target qubit.\n",
        "\n",
        "Finally, we measure all three qubits, storing their respective measurement results in the keys 'm1', 'm2', and 'm3'."
      ],
      "metadata": {
        "id": "G1lsfc3EJ5Ce"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install cirq\n",
        "import cirq\n",
        "\n",
        "# Define qubits\n",
        "control_qubit_1 = cirq.NamedQubit('control_1')\n",
        "control_qubit_2 = cirq.NamedQubit('control_2')\n",
        "target_qubit = cirq.NamedQubit('target')\n",
        "\n",
        "# Create a quantum circuit\n",
        "circuit = cirq.Circuit(\n",
        "    cirq.X(control_qubit_1),  # Apply X gate to the first control qubit\n",
        "    cirq.X(control_qubit_2),  # Apply X gate to the second control qubit\n",
        "    cirq.CCX(control_qubit_1, control_qubit_2, target_qubit),  # Apply Toffoli gate\n",
        "    cirq.measure(control_qubit_1, key='m1'),  # Measure the first control qubit\n",
        "    cirq.measure(control_qubit_2, key='m2'),  # Measure the second control qubit\n",
        "    cirq.measure(target_qubit, key='m3')  # Measure the target qubit\n",
        ")\n",
        "\n",
        "# Draw the circuit\n",
        "print(circuit.to_text_diagram())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0rZdY2SwJH-J",
        "outputId": "d08fd86b-3767-4978-98a2-da65333d401f"
      },
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "control_1: ───X───@───M('m1')───\n",
            "                  │\n",
            "control_2: ───X───@───M('m2')───\n",
            "                  │\n",
            "target: ──────────X───M('m3')───\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Entanglement"
      ],
      "metadata": {
        "id": "46SSSYvlPfkJ"
      },
      "execution_count": 54,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "A state is entangled if it cannot be factored into the tensor product of individual qubits."
      ],
      "metadata": {
        "id": "dUXM21oHP4_f"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "That is, by measuring one of the qubits, we know the state of the other qubit."
      ],
      "metadata": {
        "id": "nhxijbsKQxfz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Said differently, with two qubits, each qubit depends on the other to determine their states."
      ],
      "metadata": {
        "id": "ZZU5RNVaRA3F"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Maximially Entangled States - Qubits are maximally entangled if by measuring one of the qubits we can determine with certainty if the other qubits will be measured as 0 or 1."
      ],
      "metadata": {
        "id": "jZlt4XtsRYir"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "For example, the following is maximally entangled $|\\psi\\rangle = 1/\\sqrt2(|00\\rangle + |11\\rangle)$"
      ],
      "metadata": {
        "id": "jhrTHW4ARzAR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Two Qubit Bell States"
      ],
      "metadata": {
        "id": "waeV5TpPSdtJ"
      },
      "execution_count": 55,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "$|\\Phi^{+} \\rangle = 1/\\sqrt2(|00\\rangle + |11\\rangle)$ \\\\\n",
        "$|\\Phi^{-} \\rangle = 1/\\sqrt2(|00\\rangle - |11\\rangle)$ \\\\\n",
        "$|\\Psi^{+} \\rangle = 1/\\sqrt2(|01\\rangle + |10\\rangle)$ \\\\\n",
        "$|\\Psi^{-} \\rangle = 1/\\sqrt2(|01\\rangle - |10\\rangle)$"
      ],
      "metadata": {
        "id": "Jx5TYOVsSoBD"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Partially Entangled States - Qubits are partially entangled if by measuring one of the qubits, the amplitudes of the other qubits are affected."
      ],
      "metadata": {
        "id": "o981i6uMShHT"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "That is, partially entanged means that a qubit can affect the probabilities or phase of the other qubits."
      ],
      "metadata": {
        "id": "W6KiCi66Y6YQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Phase Kickback"
      ],
      "metadata": {
        "id": "Q3bF1WccZej4"
      },
      "execution_count": 56,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Phase kickback is used in some quantum algorithms when we have a state $|v\\rangle$ that is an eigenvector of a gate $U$, by applying a $controlled-U$ gate with $|v\\rangle$ as the target, we can \"kick' the phase onto the control qubit."
      ],
      "metadata": {
        "id": "zmETsjtAZ38z"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Superdense Coding"
      ],
      "metadata": {
        "id": "q4pir_bRadQN"
      },
      "execution_count": 57,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Quantum protocol that allows us to send two bits of classical information (00, 01, 10 or 11) using 1 qubit."
      ],
      "metadata": {
        "id": "ILnoBTA1aoZd"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "For example, we have Alice $⇒$ Bob where Alice wants to send two classical bits to Bob. Alice takes the left qubit and Bob takes the right qubit in the following $|\\psi \\rangle = 1/\\sqrt2(|00\\rangle + |11\\rangle)$"
      ],
      "metadata": {
        "id": "tbP1K5jQay-4"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Alice wants to send 00: Does nothing, Qubits: $|\\psi \\rangle = 1/\\sqrt2(|00\\rangle + |11\\rangle)$"
      ],
      "metadata": {
        "id": "wBhUUHDMbl6f"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Alice wants to send 01: Applies X to her quibit, Qubits: $|\\psi \\rangle = 1/\\sqrt2(|10\\rangle + |01\\rangle)$"
      ],
      "metadata": {
        "id": "rtz-xC39bmDA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Alice wants to send 10: Applies Z to her quibit, Qubits: $|\\psi \\rangle = 1/\\sqrt2(|00\\rangle - |11\\rangle)$"
      ],
      "metadata": {
        "id": "zCRBuDimbmPZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Alice wants to send 11: Applies X, Z to her quibit, Qubits: $|\\psi \\rangle = 1/\\sqrt2(|10\\rangle - |01\\rangle)$"
      ],
      "metadata": {
        "id": "rXaxwGqXbmaw"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Then Alice sends her qubit to Bob so he now has both."
      ],
      "metadata": {
        "id": "_TGEhLdccVXb"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Bob will apply CNOT to each of qubits sent from Alice \\\\\n",
        "$|\\psi \\rangle = 1/\\sqrt2(|00\\rangle + |11\\rangle)$ $\\overset{\\text{CNOT}}{\\rightarrow}$ $1/\\sqrt2(|00\\rangle + |10\\rangle)$ $\\overset{\\text{H}}{\\rightarrow}$ $H|+\\rangle|0\\rangle = |00\\rangle $ \\\\\n",
        "$|\\psi \\rangle = 1/\\sqrt2(|10\\rangle + |01\\rangle)$ $\\overset{\\text{CNOT}}{\\rightarrow}$ $1/\\sqrt2(|11\\rangle + |01\\rangle)$  $\\overset{\\text{H}}{\\rightarrow}$ $H|+\\rangle|1\\rangle = |01\\rangle $ \\\\\n",
        "$|\\psi \\rangle = 1/\\sqrt2(|00\\rangle - |11\\rangle)$ $\\overset{\\text{CNOT}}{\\rightarrow}$ $1/\\sqrt2(|00\\rangle - |10\\rangle)$  $\\overset{\\text{H}}{\\rightarrow}$ $H|-\\rangle|0\\rangle = |10\\rangle $ \\\\\n",
        "$|\\psi \\rangle = 1/\\sqrt2(|10\\rangle - |01\\rangle)$ $\\overset{\\text{CNOT}}{\\rightarrow}$ $1/\\sqrt2(|11\\rangle - |01\\rangle)$  $\\overset{\\text{H}}{\\rightarrow}$ $H|-\\rangle|1\\rangle = |11\\rangle $"
      ],
      "metadata": {
        "id": "J0Bq80wrcyNU"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The reason this works since there are two entangled qubits in the entire system."
      ],
      "metadata": {
        "id": "EJlA4mlof0Kw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## Classical Logical Operations (e.g. NOT, AND, OR, XOR)"
      ],
      "metadata": {
        "id": "GAjw3FSXgI1q"
      },
      "execution_count": 58,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install prettytable\n",
        "from prettytable import PrettyTable\n",
        "\n",
        "# Create a new PrettyTable instance\n",
        "table = PrettyTable()\n",
        "\n",
        "# Add columns to the table\n",
        "table.field_names = [\"Input\", \"Output\"]\n",
        "\n",
        "# Add rows to the table\n",
        "table.add_row([\"0\", \"1\"])\n",
        "table.add_row([\"1\", \"0\"])\n",
        "\n",
        "# Print the truth table\n",
        "print(\"Truth Table for NOT Operation\")\n",
        "print(table)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7yGXlouBhW83",
        "outputId": "6a758d52-571a-44e9-cfaa-7fdeaccaf20a"
      },
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Truth Table for NOT Operation\n",
            "+-------+--------+\n",
            "| Input | Output |\n",
            "+-------+--------+\n",
            "|   0   |   1    |\n",
            "|   1   |   0    |\n",
            "+-------+--------+\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install prettytable\n",
        "from prettytable import PrettyTable\n",
        "\n",
        "# Create a new PrettyTable instance\n",
        "table = PrettyTable()\n",
        "\n",
        "# Add columns to the table\n",
        "table.field_names = [\"Input 1\", \"Input 2\", \"Output\"]\n",
        "\n",
        "# Add rows to the table\n",
        "table.add_row([\"0\", \"0\", \"0\"])\n",
        "table.add_row([\"0\", \"1\", \"0\"])\n",
        "table.add_row([\"1\", \"0\", \"0\"])\n",
        "table.add_row([\"1\", \"1\", \"1\"])\n",
        "\n",
        "# Print the truth table\n",
        "print(\"Truth Table for AND Operation\")\n",
        "print(table)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0Y2pAu0shh6V",
        "outputId": "5be22d80-0b5f-4583-b662-7fe1d9fe7277"
      },
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Truth Table for AND Operation\n",
            "+---------+---------+--------+\n",
            "| Input 1 | Input 2 | Output |\n",
            "+---------+---------+--------+\n",
            "|    0    |    0    |   0    |\n",
            "|    0    |    1    |   0    |\n",
            "|    1    |    0    |   0    |\n",
            "|    1    |    1    |   1    |\n",
            "+---------+---------+--------+\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install prettytable\n",
        "from prettytable import PrettyTable\n",
        "\n",
        "# Create a new PrettyTable instance\n",
        "table = PrettyTable()\n",
        "\n",
        "# Add columns to the table\n",
        "table.field_names = [\"Input 1\", \"Input 2\", \"Output\"]\n",
        "\n",
        "# Add rows to the table\n",
        "table.add_row([\"0\", \"0\", \"0\"])\n",
        "table.add_row([\"0\", \"1\", \"1\"])\n",
        "table.add_row([\"1\", \"0\", \"1\"])\n",
        "table.add_row([\"1\", \"1\", \"1\"])\n",
        "\n",
        "# Print the truth table\n",
        "print(\"Truth Table for OR Operation\")\n",
        "print(table)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lYOR9TWLhiFj",
        "outputId": "ceb712e8-62d8-43b4-af26-cb5bc4479b76"
      },
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Truth Table for OR Operation\n",
            "+---------+---------+--------+\n",
            "| Input 1 | Input 2 | Output |\n",
            "+---------+---------+--------+\n",
            "|    0    |    0    |   0    |\n",
            "|    0    |    1    |   1    |\n",
            "|    1    |    0    |   1    |\n",
            "|    1    |    1    |   1    |\n",
            "+---------+---------+--------+\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install prettytable\n",
        "from prettytable import PrettyTable\n",
        "\n",
        "# Create a new PrettyTable instance\n",
        "table = PrettyTable()\n",
        "\n",
        "# Add columns to the table\n",
        "table.field_names = [\"Input 1\", \"Input 2\", \"Output\"]\n",
        "\n",
        "# Add rows to the table\n",
        "table.add_row([\"0\", \"0\", \"0\"])\n",
        "table.add_row([\"0\", \"1\", \"1\"])\n",
        "table.add_row([\"1\", \"0\", \"1\"])\n",
        "table.add_row([\"1\", \"1\", \"0\"])\n",
        "\n",
        "# Print the truth table\n",
        "print(\"Truth Table for XOR Operation\")\n",
        "print(table)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dmiP0tSUhid5",
        "outputId": "0e8156c3-a251-473a-b68b-b87768b64503"
      },
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Truth Table for XOR Operation\n",
            "+---------+---------+--------+\n",
            "| Input 1 | Input 2 | Output |\n",
            "+---------+---------+--------+\n",
            "|    0    |    0    |   0    |\n",
            "|    0    |    1    |   1    |\n",
            "|    1    |    0    |   1    |\n",
            "|    1    |    1    |   0    |\n",
            "+---------+---------+--------+\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Note: A function f is **reversible** if given f(x) we can find **x**."
      ],
      "metadata": {
        "id": "fuFmx4vYiaKM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Using XOR denoted by $\\oplus$ operation makes a classical operation reversible."
      ],
      "metadata": {
        "id": "IwtGvH4EiqZe"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In quantum computation, all operations we apply (besides measurement) must be reversible."
      ],
      "metadata": {
        "id": "5qh513SLkniE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from prettytable import PrettyTable\n",
        "\n",
        "# Truth table for OR operation (A, B)\n",
        "table = PrettyTable()\n",
        "table.field_names = ['A', 'B', 'Output (A OR B)']\n",
        "\n",
        "# Add rows to the table\n",
        "table.add_row(['0', '0', '0'])\n",
        "table.add_row(['0', '1', '1'])\n",
        "table.add_row(['1', '0', '1'])\n",
        "table.add_row(['1', '1', '1'])\n",
        "\n",
        "# Print the truth table\n",
        "print(\"Truth Table for OR Operation (A, B)\")\n",
        "print(table)\n",
        "\n",
        "# Reversible OR Gate with inputs A, B, C and output C XOR (A OR B)\n",
        "table = PrettyTable()\n",
        "table.field_names = ['A', 'B', 'C', 'Output (C XOR (A OR B))']\n",
        "\n",
        "# Add rows to the table\n",
        "table.add_row(['0', '0', '0', '0'])\n",
        "table.add_row(['0', '0', '1', '1'])\n",
        "table.add_row(['0', '1', '0', '1'])\n",
        "table.add_row(['0', '1', '1', '0'])\n",
        "table.add_row(['1', '0', '0', '1'])\n",
        "table.add_row(['1', '0', '1', '0'])\n",
        "table.add_row(['1', '1', '0', '1'])\n",
        "table.add_row(['1', '1', '1', '0'])\n",
        "\n",
        "# Print the reversible OR gate truth table\n",
        "print(\"\\nReversible OR Gate with Inputs A, B, C and Output C XOR (A OR B)\")\n",
        "print(table)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cEXhSIJ2jZtU",
        "outputId": "ebb7716e-2848-413c-8888-470f8bb47822"
      },
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Truth Table for OR Operation (A, B)\n",
            "+---+---+-----------------+\n",
            "| A | B | Output (A OR B) |\n",
            "+---+---+-----------------+\n",
            "| 0 | 0 |        0        |\n",
            "| 0 | 1 |        1        |\n",
            "| 1 | 0 |        1        |\n",
            "| 1 | 1 |        1        |\n",
            "+---+---+-----------------+\n",
            "\n",
            "Reversible OR Gate with Inputs A, B, C and Output C XOR (A OR B)\n",
            "+---+---+---+-------------------------+\n",
            "| A | B | C | Output (C XOR (A OR B)) |\n",
            "+---+---+---+-------------------------+\n",
            "| 0 | 0 | 0 |            0            |\n",
            "| 0 | 0 | 1 |            1            |\n",
            "| 0 | 1 | 0 |            1            |\n",
            "| 0 | 1 | 1 |            0            |\n",
            "| 1 | 0 | 0 |            1            |\n",
            "| 1 | 0 | 1 |            0            |\n",
            "| 1 | 1 | 0 |            1            |\n",
            "| 1 | 1 | 1 |            0            |\n",
            "+---+---+---+-------------------------+\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Comparison of Quantum Gates"
      ],
      "metadata": {
        "id": "WVYWTAYEnRne"
      },
      "execution_count": 64,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Using Cirq (Google) to demonstration comparison of various quantum gates"
      ],
      "metadata": {
        "id": "KYKmrYZXn36y"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install prettytable\n",
        "from prettytable import PrettyTable\n",
        "\n",
        "# Create a new PrettyTable instance\n",
        "table = PrettyTable()\n",
        "\n",
        "# Define the column names\n",
        "table.field_names = [\"Gate\", \"Type\", \"Definition\", \"Usage\", \"Importance\"]\n",
        "\n",
        "# Add rows for each gate\n",
        "table.add_row([\"X\", \"Pauli Gate\", \"Flips the state of the qubit\", \"Bit-flip operations, quantum error correction\", \"Forms a basis for quantum operations\"])\n",
        "table.add_row([\"Y\", \"Pauli Gate\", \"Introduces a phase shift of π/2\", \"Quantum error correction, quantum algorithms\", \"Forms a basis for quantum operations\"])\n",
        "table.add_row([\"Z\", \"Pauli Gate\", \"Introduces a phase shift of π\", \"Quantum error correction, quantum algorithms\", \"Forms a basis for quantum operations\"])\n",
        "table.add_row([\"S\", \"Phase Gate\", \"Introduces a phase shift of π/2\", \"Quantum error correction, fault-tolerant quantum computing\", \"Used in combination with other gates\"])\n",
        "table.add_row([\"T\", \"π/8 Gate\", \"Introduces a phase shift of π/4\", \"Quantum error correction, fault-tolerant quantum computing\", \"Universal gate set with H and CNOT\"])\n",
        "table.add_row([\"H\", \"Hadamard Gate\", \"Creates an equal superposition of |0⟩ and |1⟩\", \"Quantum algorithms, quantum error correction\", \"Universal gate set with T and CNOT\"])\n",
        "table.add_row([\"CNOT\", \"Controlled Gate\", \"Flips the target qubit if control is |1⟩\", \"Entanglement, quantum algorithms, quantum error correction\", \"Universal gate set with H and T\"])\n",
        "table.add_row([\"Toffoli\", \"Controlled Gate\", \"Flips the target qubit if both controls are |1⟩\", \"Universal reversible gate, quantum error correction\", \"Used in classical and quantum computing\"])\n",
        "table.add_row([\"Controlled Gates\", \"Controlled Gate\", \"Applies an operation to the target qubit(s) based on the control qubit(s)\", \"Quantum algorithms, quantum error correction\", \"Enables conditional operations\"])\n",
        "table.add_row([\"Pauli Gates\", \"Pauli Gate\", \"Consists of the I, X, Y, and Z gates\", \"Quantum error correction, quantum algorithms\", \"Forms a basis for quantum operations\"])\n",
        "\n",
        "# Print the table\n",
        "print(table)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7Mk78M95neQP",
        "outputId": "e4f68e4b-3e3d-4753-8b06-45c0aacc0d53"
      },
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "+------------------+-----------------+---------------------------------------------------------------------------+------------------------------------------------------------+-----------------------------------------+\n",
            "|       Gate       |       Type      |                                 Definition                                |                           Usage                            |                Importance               |\n",
            "+------------------+-----------------+---------------------------------------------------------------------------+------------------------------------------------------------+-----------------------------------------+\n",
            "|        X         |    Pauli Gate   |                        Flips the state of the qubit                       |       Bit-flip operations, quantum error correction        |   Forms a basis for quantum operations  |\n",
            "|        Y         |    Pauli Gate   |                      Introduces a phase shift of π/2                      |        Quantum error correction, quantum algorithms        |   Forms a basis for quantum operations  |\n",
            "|        Z         |    Pauli Gate   |                       Introduces a phase shift of π                       |        Quantum error correction, quantum algorithms        |   Forms a basis for quantum operations  |\n",
            "|        S         |    Phase Gate   |                      Introduces a phase shift of π/2                      | Quantum error correction, fault-tolerant quantum computing |   Used in combination with other gates  |\n",
            "|        T         |     π/8 Gate    |                      Introduces a phase shift of π/4                      | Quantum error correction, fault-tolerant quantum computing |    Universal gate set with H and CNOT   |\n",
            "|        H         |  Hadamard Gate  |               Creates an equal superposition of |0⟩ and |1⟩               |        Quantum algorithms, quantum error correction        |    Universal gate set with T and CNOT   |\n",
            "|       CNOT       | Controlled Gate |                  Flips the target qubit if control is |1⟩                 | Entanglement, quantum algorithms, quantum error correction |     Universal gate set with H and T     |\n",
            "|     Toffoli      | Controlled Gate |              Flips the target qubit if both controls are |1⟩              |    Universal reversible gate, quantum error correction     | Used in classical and quantum computing |\n",
            "| Controlled Gates | Controlled Gate | Applies an operation to the target qubit(s) based on the control qubit(s) |        Quantum algorithms, quantum error correction        |      Enables conditional operations     |\n",
            "|   Pauli Gates    |    Pauli Gate   |                    Consists of the I, X, Y, and Z gates                   |        Quantum error correction, quantum algorithms        |   Forms a basis for quantum operations  |\n",
            "+------------------+-----------------+---------------------------------------------------------------------------+------------------------------------------------------------+-----------------------------------------+\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## Quantum Circuit Application"
      ],
      "metadata": {
        "id": "C7M_7lmZE32m"
      },
      "execution_count": 66,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Using Cirq (Google) to demonstrate the integration of a quantum circuit with a classical neural network for digit classification using the MNIST dataset."
      ],
      "metadata": {
        "id": "TFfNpzGjEyJG"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The code snippet demonstrates the integration of a quantum circuit with a classical neural network for digit classification using the MNIST dataset. The code starts by loading the MNIST dataset and preprocessing the images by normalizing and downscaling them to 4x4 pixels. It then creates a quantum circuit for each training image, where the pixel values are encoded into the quantum states of the qubits. The quantum circuit applies a series of quantum operations, including Hadamard gates and controlled-Z gates, to introduce quantum effects. The qubits are then measured, and the measurement outcomes are processed to obtain a quantum feature vector. These quantum feature vectors are used as input to a classical neural network model, which is trained to classify the digits. The code also demonstrates the prediction of a single test image using the trained model. Finally, the predicted digit and the corresponding quantum circuit diagram are printed. It's important to note that the downscaling of images to 4x4 pixels may significantly impact the classification accuracy, and this example serves as a proof of concept for integrating quantum circuits with classical models for digit classification."
      ],
      "metadata": {
        "id": "Sj4_Sxrz02D0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install cirq tensorflow scikit-image\n",
        "\n",
        "import cirq\n",
        "import tensorflow as tf\n",
        "from tensorflow.keras.datasets import mnist\n",
        "import numpy as np\n",
        "from skimage.transform import resize\n",
        "from concurrent.futures import ThreadPoolExecutor\n",
        "\n",
        "def resize_image(image):\n",
        "    return resize(image, (4, 4), anti_aliasing=True)\n",
        "\n",
        "def create_cirq_circuit(image):\n",
        "    flat_image = image.flatten()\n",
        "    num_qubits = len(flat_image)\n",
        "    qubits = [cirq.GridQubit(0, i) for i in range(num_qubits)]\n",
        "    circuit = cirq.Circuit()\n",
        "\n",
        "    for i in range(num_qubits):\n",
        "        if flat_image[i] > 0:\n",
        "            circuit.append(cirq.X(qubits[i]))\n",
        "\n",
        "    circuit.append(cirq.H.on_each(qubits))\n",
        "    for i in range(0, num_qubits - 1, 2):\n",
        "        circuit.append(cirq.CZ(qubits[i], qubits[i + 1]))\n",
        "\n",
        "    circuit.append(cirq.measure(*qubits, key='result'))\n",
        "    return circuit, num_qubits\n",
        "\n",
        "def process_quantum_output(output, num_qubits):\n",
        "    counts = output.histogram(key='result')\n",
        "    quantum_output = np.zeros(2 ** num_qubits)\n",
        "    for key, value in counts.items():\n",
        "        quantum_output[key] = value\n",
        "    quantum_output /= np.sum(quantum_output)\n",
        "    return quantum_output\n",
        "\n",
        "def create_model(num_qubits):\n",
        "    with tf.device('/GPU:0'):\n",
        "        model = tf.keras.Sequential([\n",
        "            tf.keras.layers.Dense(128, activation='relu', input_shape=(2 ** num_qubits,)),\n",
        "            tf.keras.layers.Dense(10, activation='softmax')\n",
        "        ])\n",
        "\n",
        "        model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=0.001),\n",
        "                      loss=tf.keras.losses.SparseCategoricalCrossentropy(),\n",
        "                      metrics=['accuracy'])\n",
        "    return model\n",
        "\n",
        "def train_and_predict():\n",
        "    (train_data, train_labels), (test_data, test_labels) = mnist.load_data()\n",
        "    train_data = train_data / 255.0\n",
        "    test_data = test_data / 255.0\n",
        "\n",
        "    # Use a smaller subset of the dataset for initial testing\n",
        "    train_data = train_data[:1000]\n",
        "    train_labels = train_labels[:1000]\n",
        "    test_data = test_data[:100]\n",
        "    test_labels = test_labels[:100]\n",
        "\n",
        "    # Parallelize image resizing\n",
        "    with ThreadPoolExecutor() as executor:\n",
        "        train_data = list(executor.map(resize_image, train_data))\n",
        "        test_data = list(executor.map(resize_image, test_data))\n",
        "\n",
        "    train_circuits = []\n",
        "    train_quantum_outputs = []\n",
        "    simulator = cirq.Simulator()\n",
        "\n",
        "    for image in train_data:\n",
        "        circuit, num_qubits = create_cirq_circuit(image)\n",
        "        train_circuits.append(circuit)\n",
        "        result = simulator.run(circuit)\n",
        "        quantum_output = process_quantum_output(result, num_qubits)\n",
        "        train_quantum_outputs.append(quantum_output)\n",
        "\n",
        "    model = create_model(num_qubits)\n",
        "    train_quantum_outputs = np.array(train_quantum_outputs)\n",
        "    model.fit(train_quantum_outputs, train_labels, epochs=10, batch_size=32, verbose=1)\n",
        "\n",
        "    test_image = test_data[0]\n",
        "    test_circuit, _ = create_cirq_circuit(test_image)\n",
        "    test_result = simulator.run(test_circuit)\n",
        "    test_quantum_output = process_quantum_output(test_result, num_qubits)\n",
        "    predicted_digit = model.predict(test_quantum_output[np.newaxis, ...])\n",
        "    predicted_digit = np.argmax(predicted_digit)\n",
        "\n",
        "    return predicted_digit, test_circuit\n",
        "\n",
        "def main():\n",
        "    predicted_digit, test_circuit = train_and_predict()\n",
        "    print(f\"Predicted digit: {predicted_digit}\")\n",
        "    print(\"Test Circuit Diagram:\")\n",
        "    print(test_circuit)\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "q-erRqq5zMJU",
        "outputId": "26486e27-6bd7-4153-e877-4129094ae038"
      },
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/10\n",
            "32/32 [==============================] - 1s 6ms/step - loss: 2.3026 - accuracy: 0.0940\n",
            "Epoch 2/10\n",
            "32/32 [==============================] - 0s 6ms/step - loss: 2.2721 - accuracy: 0.3560\n",
            "Epoch 3/10\n",
            "32/32 [==============================] - 0s 6ms/step - loss: 2.2052 - accuracy: 0.5370\n",
            "Epoch 4/10\n",
            "32/32 [==============================] - 0s 6ms/step - loss: 2.0556 - accuracy: 0.9530\n",
            "Epoch 5/10\n",
            "32/32 [==============================] - 0s 6ms/step - loss: 1.8240 - accuracy: 0.9970\n",
            "Epoch 6/10\n",
            "32/32 [==============================] - 0s 6ms/step - loss: 1.5279 - accuracy: 0.9970\n",
            "Epoch 7/10\n",
            "32/32 [==============================] - 0s 6ms/step - loss: 1.1932 - accuracy: 0.9970\n",
            "Epoch 8/10\n",
            "32/32 [==============================] - 0s 6ms/step - loss: 0.8687 - accuracy: 0.9970\n",
            "Epoch 9/10\n",
            "32/32 [==============================] - 0s 6ms/step - loss: 0.5985 - accuracy: 0.9950\n",
            "Epoch 10/10\n",
            "32/32 [==============================] - 0s 6ms/step - loss: 0.4048 - accuracy: 0.9960\n",
            "1/1 [==============================] - 0s 47ms/step\n",
            "Predicted digit: 7\n",
            "Test Circuit Diagram:\n",
            "(0, 0): ────X───H───@───M('result')───\n",
            "                    │   │\n",
            "(0, 1): ────X───H───@───M─────────────\n",
            "                        │\n",
            "(0, 2): ────X───H───@───M─────────────\n",
            "                    │   │\n",
            "(0, 3): ────X───H───@───M─────────────\n",
            "                        │\n",
            "(0, 4): ────X───H───@───M─────────────\n",
            "                    │   │\n",
            "(0, 5): ────X───H───@───M─────────────\n",
            "                        │\n",
            "(0, 6): ────X───H───@───M─────────────\n",
            "                    │   │\n",
            "(0, 7): ────X───H───@───M─────────────\n",
            "                        │\n",
            "(0, 8): ────X───H───@───M─────────────\n",
            "                    │   │\n",
            "(0, 9): ────X───H───@───M─────────────\n",
            "                        │\n",
            "(0, 10): ───X───H───@───M─────────────\n",
            "                    │   │\n",
            "(0, 11): ───X───H───@───M─────────────\n",
            "                        │\n",
            "(0, 12): ───X───H───@───M─────────────\n",
            "                    │   │\n",
            "(0, 13): ───X───H───@───M─────────────\n",
            "                        │\n",
            "(0, 14): ───X───H───@───M─────────────\n",
            "                    │   │\n",
            "(0, 15): ───X───H───@───M─────────────\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Using Cirq (Google) to another demonstration of an Shor's algorithm, a quantum algorithm for factoring a composite number N into its prime factors."
      ],
      "metadata": {
        "id": "mCEHJFPF1OTB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The code snippet implements Shor's algorithm, a quantum algorithm for factoring a composite number N into its prime factors. The algorithm starts by choosing a random integer a coprime to N. It then creates a quantum circuit using Cirq, a Python library for quantum computing. The circuit consists of initialization of qubits, controlled operations based on the chosen value of a, and the quantum Fourier transform (QFT). The circuit is run on a simulator to obtain measurement results. From these results, the code estimates the period r, which is a key component of Shor's algorithm. If the estimated r is even, the code calculates the greatest common divisors (GCDs) of a^(r/2) ± 1 and N. If either of these GCDs is a non-trivial factor of N, the code prints the factors found. Finally, the code prints the quantum circuit diagram to visualize the circuit used in the algorithm. The success of finding the correct factors depends on the accuracy of the estimated period r, which is determined probabilistically by the quantum algorithm."
      ],
      "metadata": {
        "id": "a5EW4dQ0xyuF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#!pip install cirq\n",
        "\n",
        "import cirq\n",
        "import math\n",
        "import numpy as np\n",
        "\n",
        "def create_circuit(N, a):\n",
        "    n = int(math.ceil(math.log2(N)))\n",
        "    qubits = [cirq.GridQubit(0, i) for i in range(n)]\n",
        "    circuit = cirq.Circuit()\n",
        "\n",
        "    # Initialize the qubits in superposition\n",
        "    circuit.append([cirq.H(qubit) for qubit in qubits])\n",
        "\n",
        "    # Oracle for the modular exponentiation\n",
        "    for i in range(n):\n",
        "        circuit.append(cirq.X(qubits[i]).controlled_by(*qubits[i+1:])**(a**(2**i) % N))\n",
        "\n",
        "    # Apply the Quantum Fourier Transform (QFT)\n",
        "    circuit.append(qft(qubits))\n",
        "\n",
        "    # Measure the qubits\n",
        "    circuit.append(cirq.measure(*qubits, key='result'))\n",
        "\n",
        "    return circuit\n",
        "\n",
        "def qft(qubits):\n",
        "    circuit = cirq.Circuit()\n",
        "    n = len(qubits)\n",
        "    for i in range(n):\n",
        "        for j in range(i):\n",
        "            circuit.append(cirq.CZ(qubits[i], qubits[j])**(1 / 2**(i-j)))\n",
        "        circuit.append(cirq.H(qubits[i]))\n",
        "    return circuit\n",
        "\n",
        "def run_circuit(circuit, repetitions=1024):\n",
        "    simulator = cirq.Simulator()\n",
        "    result = simulator.run(circuit, repetitions=repetitions)\n",
        "    return result\n",
        "\n",
        "def estimate_r(result, num_qubits):\n",
        "    measurements = result.measurements['result']\n",
        "    counts = {}\n",
        "    for measurement in measurements:\n",
        "        decimal = int(''.join(str(bit) for bit in measurement), 2)\n",
        "        counts[decimal] = counts.get(decimal, 0) + 1\n",
        "\n",
        "    # Find the most frequent measurement outcome\n",
        "    r_estimate = max(counts, key=counts.get)\n",
        "\n",
        "    return r_estimate\n",
        "\n",
        "def calculate_gcds(a, r, N):\n",
        "    if r % 2 == 0:\n",
        "        gcd_1 = math.gcd(pow(a, r // 2, N) - 1, N)\n",
        "        gcd_2 = math.gcd(pow(a, r // 2, N) + 1, N)\n",
        "        return gcd_1, gcd_2\n",
        "    else:\n",
        "        return None, None\n",
        "\n",
        "def main():\n",
        "    # Define the parameters\n",
        "    N = 15  # N = p * q\n",
        "    p = 3\n",
        "    q = 5\n",
        "    a = 7  # Choose a such that gcd(a, N) = 1\n",
        "\n",
        "    # Create the quantum circuit\n",
        "    circuit = create_circuit(N, a)\n",
        "\n",
        "    # Run the circuit on a simulator\n",
        "    result = run_circuit(circuit)\n",
        "\n",
        "    # Estimate r\n",
        "    num_qubits = int(math.ceil(math.log2(N)))\n",
        "    r_estimate = estimate_r(result, num_qubits)\n",
        "    print(f'\\nEstimated value of r: {r_estimate}')\n",
        "\n",
        "    # Calculate the GCDs\n",
        "    gcd_1, gcd_2 = calculate_gcds(a, r_estimate, N)\n",
        "\n",
        "    if gcd_1 is not None and gcd_2 is not None:\n",
        "        print(f'\\ngcd({a}^({r_estimate // 2}) - 1, {N}) = {gcd_1}')\n",
        "        print(f'gcd({a}^({r_estimate // 2}) + 1, {N}) = {gcd_2}')\n",
        "\n",
        "        if gcd_1 != 1 and gcd_1 != N:\n",
        "            print(f'\\nFactors found: {gcd_1} and {N // gcd_1}')\n",
        "        elif gcd_2 != 1 and gcd_2 != N:\n",
        "            print(f'\\nFactors found: {gcd_2} and {N // gcd_2}')\n",
        "        else:\n",
        "            print('\\nNo non-trivial factors found.')\n",
        "    else:\n",
        "        print('\\nNo factors found. The estimated period r is odd.')\n",
        "\n",
        "    # Print the circuit diagram\n",
        "    print('\\nQuantum Circuit:')\n",
        "    print(circuit)\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4VQ6gB9lrWwc",
        "outputId": "96d5d583-c3ff-49af-c573-158583ef5411"
      },
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Estimated value of r: 0\n",
            "\n",
            "gcd(7^(0) - 1, 15) = 15\n",
            "gcd(7^(0) + 1, 15) = 1\n",
            "\n",
            "No non-trivial factors found.\n",
            "\n",
            "Quantum Circuit:\n",
            "                                             ┌───────┐   ┌────────────┐   ┌───────┐\n",
            "(0, 0): ───H───X─────────────────H───@─────────@───────────────@──────────────────────────────────M('result')───\n",
            "               │                     │         │               │                                  │\n",
            "(0, 1): ───H───@───X^0───────────────@^0.5────H┼──────────@────┼────────────@─────────────────────M─────────────\n",
            "               │   │                           │          │    │            │                     │\n",
            "(0, 2): ───H───@───@─────X─────────────────────@^0.25─────@^0.5┼───────────H┼─────────@───────────M─────────────\n",
            "               │   │     │                                     │            │         │           │\n",
            "(0, 3): ───H───@───@─────@───X─────────────────────────────────@^(1/8)──────@^0.25────@^0.5───H───M─────────────\n",
            "                                             └───────┘   └────────────┘   └───────┘\n"
          ]
        }
      ]
    }
  ]
}