Game-models-simulation.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YfI4HEixDYdX"
      },
      "source": [
        "# Proposition 1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-pXF-jHJs6Qr"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import random\n",
        "\n",
        "def compute_x_y(params):\n",
        "    params['x_1'] = 1 / (1 + params['w'] * (1 - params['p_1']))\n",
        "    params['y_1'] = 1 / (1 + params['w'])\n",
        "\n",
        "def compute_lambda(params):\n",
        "    params['lambda^_*'] = ((1 + params['w']) - 1/params['delta']) / params['p_1'] / params['w']\n",
        "\n",
        "def compute_eta(params):\n",
        "    params['eta^*'] = params['C_cyb'] / params['p_1'] / params['beta']"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lWcCZaDRDaMk"
      },
      "source": [
        "## $\\lambda^*$ as a function of $\\delta$ with different values of $p_1$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Vn2exnEk-Ws6"
      },
      "outputs": [],
      "source": [
        "def plot_lambda_vs_delta():\n",
        "    # Define values of p1 and markers for plotting\n",
        "    p1_values = [0.7, 0.8, 0.9]\n",
        "    markers = ['o', 's', '^']  # Circle, square, and triangle markers\n",
        "\n",
        "    # Create a figure and axis for the plot\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.set_title('$\\lambda^*$ as a function of $\\delta$ with different values of $p_1$')\n",
        "\n",
        "    # Initialize parameters with random values within a range\n",
        "    params = {\n",
        "        'w': random.uniform(0.001, 0.999),\n",
        "        'beta': random.uniform(0.001, 0.999),\n",
        "        'C_cyb': random.uniform(0.001, 0.999)\n",
        "    }\n",
        "\n",
        "    for i, p_1 in enumerate(p1_values):\n",
        "        # Set p1 value\n",
        "        params['p_1'] = p_1\n",
        "\n",
        "        # Ensure beta and C_cyb satisfy a condition\n",
        "        while params['beta'] <= params['C_cyb'] / params['p_1']:\n",
        "            params['beta'] = random.uniform(0.001, 0.999)\n",
        "            params['C_cyb'] = random.uniform(0.001, 0.999)\n",
        "\n",
        "        # Set a random p2 value within a range\n",
        "        params['p_2'] = random.uniform(0.001, params['p_1'] - 0.001)\n",
        "\n",
        "        # Compute x and y values based on parameters\n",
        "        compute_x_y(params)\n",
        "\n",
        "        # Generate a range of delta values\n",
        "        delta_range = np.linspace(params['y_1'] + 0.001, params['x_1'] - 0.001, 100)\n",
        "        lambda_values = []\n",
        "\n",
        "        # Calculate lambda values for each delta in the range\n",
        "        for delta in delta_range:\n",
        "            params['delta'] = delta\n",
        "            compute_lambda(params)\n",
        "            lambda_values.append(params['lambda^_*'])\n",
        "\n",
        "        # Plot lambda values with a label and marker\n",
        "        ax.plot(delta_range, lambda_values, label=f\"$p_1$={p_1:.2f}\", marker=markers[i], markevery=10)\n",
        "\n",
        "    # Set labels and legend for the subplot\n",
        "    ax.set_xlabel('Probability that an insider is malicious ($\\delta$)')\n",
        "    ax.set_ylabel('$\\lambda^*$')\n",
        "    ax.legend()\n",
        "\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "# Seed and call the plot function\n",
        "random.seed(0)\n",
        "plot_lambda_vs_delta()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## $\\lambda^*$ as a function of $\\beta$ with different values of $C_{cyb}$"
      ],
      "metadata": {
        "id": "jls5E_jJRjoa"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "iwfKMw1bPNfc"
      },
      "outputs": [],
      "source": [
        "def plot_eta_vs_beta():\n",
        "    # Define the fixed p1 value and markers for plotting\n",
        "    p1_values = 0.7\n",
        "    markers = ['o', 's', '^']  # Circle, square, and triangle markers\n",
        "\n",
        "    # Create a figure and axis for the plot\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.set_title('$\\eta^*$ as a function of $\\\\beta$ with different values of $C_{cyb}$ ($p_1$ = 0.7)')\n",
        "\n",
        "    # Initialize parameters with random values within a range\n",
        "    params = {\n",
        "        'w': random.uniform(0.001, 0.999),\n",
        "        'p_1': p1_values\n",
        "    }\n",
        "\n",
        "    C_cybs = [0.2, 0.3, 0.4]\n",
        "    for i, c_i in enumerate(C_cybs):\n",
        "        # Set C_cyb value\n",
        "        params['C_cyb'] = c_i\n",
        "\n",
        "        # Generate a range of beta values\n",
        "        beta_ranges = np.linspace(params['C_cyb'] / params['p_1'], 0.999, 100)\n",
        "\n",
        "        # Set a random p2 value within a range\n",
        "        params['p_2'] = random.uniform(0.001, params['p_1'] - 0.001)\n",
        "\n",
        "        # Compute x and y values based on parameters\n",
        "        compute_x_y(params)\n",
        "\n",
        "        # Set a random delta value within a range\n",
        "        params[\"delta\"] = random.uniform(0.001, 0.999)\n",
        "\n",
        "        eta_values = []\n",
        "\n",
        "        # Calculate eta values for each beta in the range\n",
        "        for b in beta_ranges:\n",
        "            params[\"beta\"] = b\n",
        "            compute_eta(params)\n",
        "            eta_values.append(params['eta^*'])\n",
        "\n",
        "        # Plot eta values with a label and marker\n",
        "        ax.plot(beta_ranges, eta_values, label=f'$C_{{cyb}}$={c_i:.2f}', marker=markers[i], markevery=10)\n",
        "\n",
        "    ax.set_xlabel('$\\\\beta$')\n",
        "    ax.set_ylabel('$\\eta^*$')\n",
        "    ax.legend()\n",
        "\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "# Seed and call the plot function\n",
        "random.seed(0)\n",
        "plot_eta_vs_beta()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rverIBnvE1ue"
      },
      "source": [
        "## $\\eta^*$ as a function of $C_{cyb}$ with different values of $p_1$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "26d2HL-QFI96"
      },
      "outputs": [],
      "source": [
        "def plot_eta_vs_C_cyb_with_p2():\n",
        "    # Define sample p1 values and markers for plotting\n",
        "    p1_values = [0.2, 0.4, 0.6]\n",
        "    markers = ['o', 's', '^']  # Circle, square, and triangle markers\n",
        "\n",
        "    # Create a figure and axis for the plot\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.set_title('$\\eta^*$ as a function of $C_{cyb}$ with different values of $p_1$')\n",
        "\n",
        "    # Initialize parameters with random values within a range\n",
        "    params = {\n",
        "        'w': random.uniform(0.001, 0.999),\n",
        "        'beta': random.uniform(0.001, 0.999)\n",
        "    }\n",
        "\n",
        "    C_cyb_range = np.linspace(0.001, 0.999, 200)\n",
        "\n",
        "    for i, p_1 in enumerate(p1_values):\n",
        "        # Set p1 value\n",
        "        params['p_1'] = p_1\n",
        "\n",
        "        # Compute x and y values based on parameters\n",
        "        compute_x_y(params)\n",
        "\n",
        "        # Set a random delta value within a range\n",
        "        params['delta'] = random.uniform(params['y_1'] + 0.001, params['x_1'] - 0.001)\n",
        "\n",
        "        eta_values = []\n",
        "\n",
        "        for C_cyb in C_cyb_range:\n",
        "            params['C_cyb'] = C_cyb\n",
        "            if params['beta'] > params['C_cyb'] / params['p_1']:\n",
        "                compute_lambda(params)\n",
        "                compute_eta(params)\n",
        "                eta_values.append(params['eta^*'])\n",
        "            else:\n",
        "                eta_values.append(np.nan)  # Appending NaN for continuity\n",
        "\n",
        "        # Plot eta values with a label and marker\n",
        "        ax.plot(C_cyb_range, eta_values, label=f\"$p_1$={p_1:.2f}\", marker=markers[i], markevery=10)\n",
        "\n",
        "    # Set labels and legend for the subplot\n",
        "    ax.set_xlabel('Cost of cyber attack $(C_{cyb})$')\n",
        "    ax.set_ylabel('$\\eta^*$')\n",
        "    ax.legend()\n",
        "\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "# Seed and call the plot function\n",
        "random.seed(0)\n",
        "params = {}\n",
        "plot_eta_vs_C_cyb_with_p2()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5AkJr1HqEBIa"
      },
      "source": [
        "## Figure 5: $\\lambda^*$ as a function of $\\delta$ with different values of $p_1$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "f_0fIrXaD5tN",
        "outputId": "bc288968-8025-446e-9a54-d8514968e4b4"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "def plot_lambda_vs_delta():\n",
        "    # Define sample p1 values and markers for plotting\n",
        "    p1_values = [0.2, 0.4, 0.6]\n",
        "    markers = ['o', 's', '^']  # Circle, square, and triangle markers\n",
        "\n",
        "    # Create a figure and axis for the plot\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.set_title('$\\lambda^*$ as a function of $\\delta$ with different values of $p_1$')\n",
        "\n",
        "    # Initialize parameters with random values within a range\n",
        "    params = {\n",
        "        'w': random.uniform(0.001, 0.999),\n",
        "        'beta': random.uniform(0.001, 0.999),\n",
        "        'C_cyb': random.uniform(0.001, 0.999)\n",
        "    }\n",
        "\n",
        "    for i, p_1 in enumerate(p1_values):\n",
        "        # Set p1 value\n",
        "        params['p_1'] = p_1\n",
        "\n",
        "        # Ensure beta and C_cyb satisfy a condition\n",
        "        while params['beta'] <= params['C_cyb'] / params['p_1']:\n",
        "            params['beta'] = random.uniform(0.001, 0.999)\n",
        "            params['C_cyb'] = random.uniform(0.001, 0.999)\n",
        "\n",
        "        # Compute x and y values based on parameters\n",
        "        compute_x_y(params)\n",
        "\n",
        "        # Generate a range of delta values\n",
        "        delta_range = np.linspace(params['y_1'] + 0.001, params['x_1'] - 0.001, 100)\n",
        "        lambda_values = []\n",
        "\n",
        "        # Calculate lambda values for each delta in the range\n",
        "        for delta in delta_range:\n",
        "            params['delta'] = delta\n",
        "            compute_lambda(params)\n",
        "            lambda_values.append(params['lambda^_*'])\n",
        "\n",
        "        # Plot lambda values with a label and marker\n",
        "        ax.plot(delta_range, lambda_values, label=f\"$p_1$={p_1:.2f}\", marker=markers[i], markevery=10)\n",
        "\n",
        "    # Set labels and legend for the subplot\n",
        "    ax.set_xlabel('Probability that an insider is malicious ($\\delta$)')\n",
        "    ax.set_ylabel('$\\lambda^*$')\n",
        "    ax.legend()\n",
        "\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "# Seed and call the plot function\n",
        "random.seed(0)\n",
        "plot_lambda_vs_delta()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iIWXb8gGDi2T"
      },
      "source": [
        "##Figure 6: 1-$\\lambda^*$ as a function of $\\delta$ with different values of $p_1$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "8vmmzWHt_1Am",
        "outputId": "694df18d-c169-4c07-c465-f4b5d89d2005"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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169fTsGHDZ4aNs/J5T+/nOr33I7O/t3Lqs3vu3DkePnyY7A+Khw8fMm3aNNq1a/fMLHmRNdJjJ1I0d+5cHj9+nPTg7bZt27hz5w5gGnJwdHTMtmslJCQwZswYWrZs+cxfwZ6enjmW2HXq1IlVq1bh6OiIp6cnvr6+7Nu3DxcXl6RjIiMjKVWqFD169KB27doULlyYffv2cerUqWR/mWe2/Yzq3bs3n3zyCV27dmXUqFFER0ezYMECKleunOkHtKdOncqePXt4+eWXefvtt6lWrRr379/nl19+4ejRo0kFSOvXrw/A//73P3r37o2lpSVeXl4ptjllyhT27t3LSy+9xLvvvouFhQWLFi0iLi6Ob775JlNx5sZ1unbtyscff8z777/P7du3cXJyYvXq1Zw9e5ZffvklXb0VzZo148svv+T27dvJErjmzZuzaNEiypYt+8yQVEoycr8zYtKkSezatYtmzZrx7rvvkpiYyJw5c6hevXqyxCI7fPXVVxw4cIBGjRoxdOhQPD09CQsLw8/Pj3379qVrYlR2tPFfqd3b1AoiW1pa0q1bN9atW0dUVBTTp09/5pisfN4z8rlOz/3Iyu+t7P5MPXjwgIcPH1KrVi06derEiBEjiImJYd68eRgMBpYtW5bhNsVz5Po8XJEnlClTJsUinuTAUjgzZsxQLSws1HPnzj2zz9vbW1UURY2MjMzWa6qqqj569EgdPHiwWrRoUbVw4cJqu3bt1AsXLqhlypRRBw0apKqqqsbFxakfffSRWrt27aRinbVr11bnz5+fLe2nJq1SAnv27FFr1KihWllZqVWqVFFXr16dZrmT/y49lVK5hZs3b6oDBw5UixUrllS0dsSIEUkFip/64osv1JIlS6o6nS5dBYrbtWunFi5cWLWzs1NbtmypHjt2LNMxpiY918lIaYbjx4+rTZs2VW1sbFQHBwe1Q4cOz7SXloiICFWv16v29vbJSmQ8XSZvwIABz5yT2veb0v3Ojnt26NAhtX79+qqVlVW6CxSrasbLnaiqqj548EAdMWKE6uHhoVpaWqpubm5q69at1R9++CHpmOctk5aVNjJyb9Oyd+9eFVAVRVFv3779zP70ft5Tiye9n+v03I+s/N5S1ez9TD29bydPnlTfeuutpMLRvXr1Um/dupXqee+88446ceLEdMUrklNU1UyetBVCCCFEvjJr1iw+/PBDoqKisLa2Tvd5w4YNw83NTWbGZoI8YyeEEEKIHHH27FnKly+f7qQuMTGR2NhYDAZDsvci/SSxE0IIIUSOOHfuXFKFg/SYMmUKtra2LFmyhC+//BJbW1tWrVqVgxHmPzIUK4QQQohsp6oq9vb2jBw5kq+++krrcAoMSeyEEEIIIfIJGYoVQgghhMgnJLETQgghhMgnJLETQgghhMgnZOUJTAsr37t3D3t7+xxZn1EIIYQQIrNUVSUyMpISJUqg06XdJyeJHXDv3r1sWZRcCCGEECKn3L59+7lLEkpih2mxeTDdsOxYnFwIIYQQIrtERETg4eGRlK+kRRI7SBp+dXBwkMROCCGEEGYpPY+LyeQJIYQQQoh8QhI7IYQQQoh8QhI7IYQQQoh8Qp6xE0IIIfIxg8FAQkKC1mGINFhaWqLX67OlLUnshBBCiHxIVVWCgoJ4/Pix1qGIdHBycsLNzS3L9XQlsRNCCCHyoadJnaurK3Z2dlKA30ypqkp0dDTBwcEAuLu7Z6k9SeyEEEKIfMZgMCQldS4uLlqHI57D1tYWgODgYFxdXbM0LCuTJ4QQQoh85ukzdXZ2dhpHItLr6c8qq89Dml1id/jwYby8vChRogSKorB58+bnnnPw4EHq1auHtbU1FStWZMWKFTkepxBCCGHuZPg178iun5XZJXZRUVHUrl2befPmpev469ev07FjR1q2bIm/vz9jxozhrbfeYvfu3TkcqRBCCCGEeTG7Z+w6dOhAhw4d0n38woULKVeuHN999x0A1apV4+jRo8ycOZN27drlVJjp8/g2RIemvt/OBZw8ci8eIYQQQuRrZpfYZZSvry9t2rRJtq1du3aMGTNGm4Ceenwb5taHxDgAfG2s+cqlCGNDH9E41rQNC2sYeVqSOyGEEEJkC7Mbis2ooKAgihcvnmxb8eLFiYiIICYmJsVz4uLiiIiISPbKdtGhSUmdCsx2duKalRWznZ1Qnx6TGJd2j54QQgihMYNRxfdqKFv87+J7NRSDUX3+SXnMvHnzKFu2LDY2NjRq1IiTJ0+m+9yvvvoKRVFS7FDKSruZlecTu8yYNm0ajo6OSS8Pj5ztMTtma0OAtTUAAdbWHLO1ydHrCSGEENlh17n7vPT1fvosPs7odf70WXycl77ez65z97UOLdusX78eb29vJk6ciJ+fH7Vr16Zdu3ZJdeXScurUKRYtWkStWrWytd2syPOJnZubGw8ePEi27cGDBzg4OCTVhfmvcePGER4envS6fft2tsdlUE1/0ajAdGcn+PtrRVWZU8Qxqdfu6XFCCCGEOdl17j7DV/txPzw22fag8FiGr/bL0eQuKCgIRVGYPXs2devWxcbGhurVq3P06NFsv9aMGTMYOnQogwcPxtPTk4ULF2JnZ8eyZcvSPO/Jkyf069ePxYsXU6RIkWxrN6vyfGLXuHFjfHx8km3bu3cvjRs3TvUca2trHBwckr2yW8Bd0/DuMVsbrlhZwd/TmFVFSdZr9/Q4IYQQIiepqkp0fGK6XpGxCUzcGkBKXQ9Pt32+9TyRsQnPbUvNRAeGv78/AMuWLWPWrFn4+/tTunRp+vXrh9FoTPPcqVOnUrhw4TRft27dAiA+Pp7Tp08ne1Zfp9PRpk0bfH1907zOiBEj6Nix4zPP+We13awyu8kTT5484cqVK0lfX79+HX9/f5ydnSldujTjxo3j7t27/PjjjwAMGzaMuXPn8vHHHzNkyBD279/Pzz//zPbt27X6FgAIi45HBeYUcUSnqhj/XZ9GVZniUoQdd+4TFh2vWYxCCCEKjpgEA54TsqcUmAoERcRS8/M9zz32/OR22FllLN04c+YMlpaWbNmyhbJlywIwZcoUGjRowN27dxk1ahQHDx6kdevWbNiwIdm5w4YN4/XXX0+z/RIlSgAQEhKCwWBI8Vn9CxcupHr+unXr8PPz49SpUynuz2y72cHsErs//viDli1bJn3t7e0NwKBBg1ixYgX3799PyrQBypUrx/bt23n//feZPXs2pUqVYsmSJZqXOnG2s0r2bF0yisIdS0vmOznQzM4q94MTQgghzJi/vz/dunVLSuqAZKNro0ePZsiQIaxcufKZc52dnXF2ds6x2G7fvs3o0aPZu3cvNjbm98y82SV2LVq0SLPbNqVVJVq0aMGff/6Zg1FlnGcJe/oXcURRVdRUqkkvdHKkjs2tFPcJIYQQ2cnWUs/5yenr9Dh5PYw3lqfcG/VvKwa/QMNyaSdRtpYZX/fU39+fQYMGJdvm6+tL0aJFKVmyJB4eHhw8eDDFc6dOncrUqVPTbP/8+fOULl2aokWLotfrU3xW383NLcVzT58+TXBwMPXq1UvaZjAYOHz4MHPnziUuLi5T7WYXs0vs8gujrRP3LSxSTeoAUBTGnJnNYrea1HGtk2uxCSGEKHgURUn3kGizSsVwd7QhKDw2xefsFMDN0YZmlYqh12XvsmUxMTFcvnwZg8GQtM1oNDJr1iwGDRqETpf29ICMDMVaWVlRv359fHx86NKlS9K1fHx8GDlyZIrntm7dmrNnzybbNnjwYKpWrconn3yCXq9Hr9dnuN3sIoldDrFyKc/6Dqs5GHCGX/3u8jj6n0V9m+rO0tXiMDOcnfGzhXf3vcvSdkup5lJNw4iFEEIIE71OYaKXJ8NX+6FAsuTuaRo30csz25M6gLNnz6IoCqtXr6ZVq1Y4OTkxYcIEHj9+zGefffbc8zM6FOvt7c2gQYNo0KABDRs2ZNasWURFRTF48GAA5s6dy6ZNm5Imatrb21OjRo1kbRQqVAgXF5dk25/Xbk6RxC4HubnXo7d7PXq2Ujl5PYzgyFg2/HGHFVdeoLtzFAsenGC4Rxn8iOSdve+wvP1yKjhV0DpsIYQQgvY13FnQvx6Ttp1PVvLEzdGGiV6etK/hniPX9ff3p2rVqnz88cd0796d8PBw2rVrx6FDh3Bycsr26/Xq1YuHDx8yYcIEgoKCqFOnDrt27Uqa+BASEsLVq1ezvd2coqiZmYecz0RERODo6Eh4eHiOlD75t0sPImk78zBFlXCOO40nJjaUoRVrEJAYTjHbYqxsvxIPB1liTAghRObFxsZy/fp1ypUrl+UH/A3GfzonXO1taFjOOUd66p4aMWIEjx49Ys2aNWked/DgQebOnfvMrNi8Kq2fWUbylDxfxy6vqVzcnjbVihOiOvKj60fYqyoLrwZQ0c6dhzEPeWvPWwRFBWkdphBCCAGYhmUbV3Chc52SNK7gkqNJHZh67FJayeHf2rRpQ8+ePdmxYwelSpXK8dpweYkkdhp4t6VpuHXaldI8qT0EJ6ORxbduULpwSe5F3WPonqGExIRoHKUQQgiRu1RV5ezZs89N7Pbt28fDhw+Jjo7mzp07aS5KUNBIYqeBeqWL8GJ5ZxIMKt/rBkCxahSNfMCSWDvcC7lzI+IGb+99m8exj7UOVQghhMg1iqIQERHBq6++qnUoeZYkdhp5t0VFAFb9EUz4qwtAb437ZR+WuL1CMdtiXH50mbf3vk1EvCw5JoQQQoj0kcROI80qFaVGSQdiEgwsvWwHr0wGoPTB6SxpMA5nG2cCwwIZvm84UQlRGkcrhBBCiLxAEjuNKIrCiL977VYcu8GTOm9CxVcgMZbyuybyQ8s5OFg58NfDvxjpM5KYxBiNIxZCCCGEuZPETkPtqrtRvlghImITWXPyFnSZD4WKQXAAVf5YzQ+v/EBhy8L88eAPxhwYQ5whTuuQhRBCCGHGJLHTkE6nMPxl0wzZxUeuE2vtAl0WmHaeXET1sDvMbzMfWwtbjt07xgcHPyDBkJBGi0IIIYQoyCSx01iXuiUp6WTLw8g4Npy+A5VegRffNe3cPJy6tu7MbTUXa701h+4c4qPDH5FglOROCCGEEM+SxE5jlnodQ5uVA2DR4askGozQ5nMoXhOiQ2HTMBoWb8D3Lb/HSmeFzy0fxh0ZR6IxUdvAhRBCCGF2JLEzA71eKI1LIStuh8Ww7a97YGENPZaChS1cOwC+c2hSsgkzW87EQmfB7hu7+ez3zzAYDVqHLoQQQggzIomdGbC10jPkJVOv3fwDVzEaVShWBTp8ZTrAZzLcPU3zUs357uXvsFAs2H5tO5/7fo5RNWoYuRBCCCHMiSR2ZmJA4zLYW1twOfgJewMfmDbWGwSencGYCBvehLhIWpVuxdfNv0av6Nl8ZTOTfSdLcieEEEIIQBI7s+FgY8nAJmUAmHfgCqqqgqKA12xw9IBH12H7hwC0LduWqS9NRafo+PXyr0w9MdV0vBBCCJFdHt+Ge/6pvx7f1jC47DVv3jzKli2LjY0NjRo14uTJk8895+7du/Tv3x8XFxdsbW2pWbMmf/zxR5bbzSqLHL+CSLchTcux9Oh1/roTzpHLITSvXAxsi0C3xbDiVfhrHVRoBbV78Wr5VzGoBv539H+sv7genaJjXMNxKIqi9bchhBAir3t8G+bWh8Q06qdaWMPI0+DkkXtx5YD169fj7e3NwoULadSoEbNmzaJdu3ZcvHgRV1fXFM959OgRTZs2pWXLluzcuZNixYpx+fJlihQpkqV2s4P02JkRl8LW9GlYGoC5B678s6NMY3h5rOn9dm8IvQqAVwUvJjedjILC2gtr+ebUN9JzJ4QQIuuiQ9NO6sC0Pzo0Ry4fFBSEoijMnj2bunXrYmNjQ/Xq1Tl69Gi2X2vGjBkMHTqUwYMH4+npycKFC7Gzs2PZsmWpnvP111/j4eHB8uXLadiwIeXKlaNt27ZUqFAhS+1mB0nszMzbzctjqVc4eT2MUzfC/tnR/EMo8xLEP4ENg5M+cF0qdmFi44kArA5czXd/fCfJnRBCiGepKsRHpe+V3mUsE2Oe31Ym/k/y9/cHYNmyZcyaNQt/f39Kly5Nv379MBrTfq586tSpFC5cOM3XrVu3AIiPj+f06dO0adMm6XydTkebNm3w9fVN9Rpbt26lQYMG9OzZE1dXV+rWrcvixYuT9me23ewgQ7Fmxt3Rlh71S7H25G3m7r/CyiENTTt0euj2AyxsCvfPwL5J0H4qAN0rd8egGvji+BesPL8SnU7H+/Xel2FZIYQQ/0iIhqklsrfNZe2ff8yn98CqUIaaPXPmDJaWlmzZsoWyZcsCMGXKFBo0aMDdu3cZNWoUBw8epHXr1mzYsCHZucOGDeP1119Ps/0SJUz3ISQkBIPBQPHixZPtL168OBcuXEj1/GvXrrFgwQK8vb359NNPOXXqFKNGjcLKyopBgwZlut3sIImdGRr2cgXWn7rNoUsPOXsnnJqlHE07HEtC5/mwrg8cnwflX4bK7QB4vcrrGFQDU09MZfm55SgojKk3RpI7IYQQeY6/vz/dunVLSuoAHBwckt6PHj2aIUOGsHLlymfOdXZ2xtnZOUfjMxqNNGjQgKlTTR0sdevW5dy5cyxcuJBBgwbl6LWfRxI7M1TGpRCv1S7BZv97zD1wmUUDGvyzs+qr0GgYnFgIm4fDsKPgYPrLo0/VPqiqyrST01h2bhkKCqPrjZbkTgghBFjamXrP0iPor/T1xg3ZBW61nn/dDPL3938mQfL19aVo0aKULFkSDw8PDh48mOK5U6dOTUq4UnP+/HlKly5N0aJF0ev1PHjwINn+Bw8e4Obmlur57u7ueHp6JttWrVo1fv31V4BMt5sd5Bk7M/Vuy4oA7A54wKUHkcl3vjIZ3P5ecmzj2/CvFSj6VuvL2IamiRZLzy3l+z+/l2fuhBBCmEpoWRVK38vCNn1tWtg+v60Mdi7ExMRw+fJlDIZ//m8zGo3MmjWLQYMGodOlnboMGzYMf3//NF9Ph2KtrKyoX78+Pj4+ya7l4+ND48aNU71G06ZNuXjxYrJtly5dokyZMllqNztIYmemKhe3p311U1Y/798zZOHvJcdWgGUhuHEEDn+bbHe/av2SkrslZ5dIcieEECLPOHv2LIqisHr1anx9fQkMDKRXr148fvyYzz777LnnOzs7U7FixTRfFhb/DFh6e3uzePFiVq5cSWBgIMOHDycqKorBgwcDMHfuXFq3bp3sGu+//z7Hjx9n6tSpXLlyhTVr1vDDDz8wYsSIdLebUySxM2MjW5l67baduceNkKjkO4tWhE4zTO8PfQ03kk8Bl+ROCCFEptm5mDoR0mJhbToum/n7+1O1alU+/fRTunfvToMGDTAYDBw6dAgnJ6dsv16vXr2YPn06EyZMoE6dOvj7+7Nr166kiQ8hISFcvXo12TkvvPACmzZtYu3atdSoUYMvvviCWbNm0a9fv3S3m1MUVf63JyIiAkdHR8LDw5M9nGkO3lh+koMXH9KrgQdf90jhOYZNw+HMGrB3h2G/Q6HkH7LV51fz9amvAXizxpvyzJ0QQhQAsbGxXL9+nXLlymFjY5O5Rh7fTrtOnZ1LjhQnHjFiBI8ePWLNmjVpHnfw4EHmzp37zKzYvCqtn1lG8hTpsTNz7/3da7fxzzvcfZxCXaFXvwWXShB53zSZ4j/1ffp79k/2zN1Mv5nScyeEEOL5nDygRJ3UXzm04oS/vz+1aqU9IaNNmzb07NmTHTt2UKpUqRyvDZeXSGJn5uqXcaZxeRcSDCqLDl199gDrwtBzBeit4fJuUxmU/+hXrR/jGo4DYPm55cw4PUOSOyGEEGZHVVXOnj373MRu3759PHz4kOjoaO7cuZPjExLyEkns8oCnvXbrTt0mOCL22QPcakD7aab3+z6HO388c0jfan35tNGnAKwIWMH0P6ZLcieEEMKsKIpCREQEr776qtah5FmS2OUBjSu4UK+0E/GJRhYfuZbyQQ2GgGcXMCbCL4Mh5tEzh/Sp2ofxL44H4MfzP8raskIIIUQ+I4ldHqAoCu+1rgTA6uO3CIuKT+kgeO17KFIWwm/BlpEprs/3epXXmdB4gqmtwNVMPTEVo5r2untCCCGEyBskscsjWlQuRs2SjsQkGFh85Cq+V0PZ4n8X36uhGIx/J3A2jtBjOegs4cJvcGJRim31rNyTSU0moaCw7uI6vjj+hSR3QgghRD4giV0eoShKUl27hQev0WfxcUav86fP4uO89PV+dp27bzqwZD1oO8X0fs9ncNcvxfa6VerGF02/QEFhw6UNfH7scwz/WsFCCCGEEHmPJHZ5iMFg6pn77wBrUHgsw1f7/ZPcNXoHqnYCYwL88gbEPE6xvc4VOzOt2TR0io5NVzYx/vfxktwJIYQQeZgkdnmEwajyxfbzKe57muhN2nbeNCyrKNB5HjiVhsc3Yet7KT5vB9CxfEe+bvY1ekXPtmvbGHd0HInGxBz6LoQQQgiRkySxyyNOXg/jfngKpU7+pgL3w2M5eT3MtMHWyVTfTrGAwK2wdwLc83/29fg27cu159uXv8VCsWDn9Z18fPhjEgwJOfwdCSGEECK7WTz/EGEOgiNTT+pSPa6QKyiYsr5j35te/2VhDSNP80qZV5jZcibeB73Ze3MvCYYEvmvxHVZ6q2yJXwghhBA5T3rs8ghX+/St9ZfsuOhQU127tCTGJa0F2MKjBd+3+h5rvTUH7xxk1P5RxCamL6EUQgghhPYkscsjGpZzxt3RBiWV/Qrg7mhDw3LOWbrOSyVfYl7redha2PL7vd8Z4TOC6IToLLUphBBCiNwhiV0eodcpTPTyBEg1uZvo5Ylel9re9Gvk3ogFbRZgZ2HHyaCTDN83nCfxT7LcrhBCCGGO5s2bR9myZbGxsaFRo0acPHky1WMNBgPjx4+nXLly2NraUqFCBb744otnVnLKSJvZSRK7PKR9DXcW9K+Hm2PyYVmdArN716F9Dfdsu1b94vX5oe0P2Fva4xfsx9A9QwmPC8+29oUQQuQdvvd86by5M773fLUOJdutX78eb29vJk6ciJ+fH7Vr16Zdu3YEBwenePzXX3/NggULmDt3LoGBgXz99dd88803zJkzJ9NtZidJ7PKY9jXcOfpJK9YOfZHvetbCpZAlRhXCY7J/FmvtYrVZ0m4JTtZOnAs9x5DdQwiNCc3XH3AhhBDJqarKbL/ZXAu/xmy/2bmyxnhQUBCKojB79mzq1q2LjY0N1atX5+jRo9l+rRkzZjB06FAGDx6Mp6cnCxcuxM7OjmXLlqV4/LFjx+jcuTMdO3akbNmy9OjRg7Zt2ybrkctom9lJErs8SK9TaFzBhe71PRjTpjIA8w9eJS4x+4sLe7p4srzdcoraFuXSo0u8sesNvvvju1z9gAshhMg6VVWJTojO8OvArQMEhAYAEBAawIFbBzJ0fmb+n/D39wdg2bJlzJo1C39/f0qXLk2/fv0wGtNeAnPq1KkULlw4zdetW7cAiI+P5/Tp07Rp0ybpfJ1OR5s2bfD1TbnzokmTJvj4+HDp0iUAzpw5w9GjR+nQoUOm28xOUu4kj+vZwIO5B65wPzyWDafv0K9RmWy/RsUiFVnRfgVv7XmLGxE3krYHhAZw7N4xmpZsmu3XFEIIkb1iEmNotKZRltsZfXB0ho4/0fcEdpZ2GTrnzJkzWFpasmXLFsqWLQvAlClTaNCgAXfv3mXUqFEcPHiQ1q1bs2HDhmTnDhs2jNdffz3N9kuUKAFASEgIBoOB4sWLJ9tfvHhxLly4kOK5Y8eOJSIigqpVq6LX6zEYDHz55Zf069cv021mJ+mxy+NsLPUMe7kCAPMPXCU+8V9/ydi5mOrUPU/oleceUsahDMvbLcdSZ5m0TYeOOX/OkV47IYQQ2crf359u3bolJXUADg4OSe9Hjx7Njz/+mOK5zs7OVKxYMc2XhUXm+7V+/vlnfvrpJ9asWYOfnx8rV65k+vTprFy5MtNtZifpscsH+jQszfyDV7n7OIaNfnfo3bC0aYeTB4w8nVSn7hkHv4JLO2HXWCjTFBzSnnxxM+ImCcZ/nuUzYpReOyGEyCNsLWw50fdEuo9XVZXBuwdz8dFFjOo/nQY6RUeVIlVY3m45ivL8Sgy2FrYZjtXf359BgwYl2+br60vRokUpWbIkHh4eHDx4MMVzp06dytSpU9Ns//z585QuXZqiRYui1+t58OBBsv0PHjzAzc0txXM/+ugjxo4dS+/evQGoWbMmN2/eZNq0aQwaNChTbWYn6bHLB2ws9bzTvDwA8w5eIcHwr147Jw8oUSflV49lULwGRD2EDUPAkHoxY1VVmfPnHHTKs/9kvjn1jfTaCSGEmVMUBTtLu3S//B/6ExgWmCypAzCqRgLDAvF/6J+udtKT/P1bTEwMly9fxmD457lxo9HIrFmzGDRoEDpd2qnLsGHD8Pf3T/P1dCjWysqK+vXr4+Pjk+xaPj4+NG7cOMX2o6Ojn4lBr9cnPfuXmTazkyR2+US/RmUoWtiK22ExbPrzbvpOsrKD138EK3u4dQz2T0710GP3jhEQGvDMBxzgWvg1VgSsyGTkQgghzM3TP+aVVCqnKig59ijO2bNnURSF1atX4+vrS2BgIL169eLx48d89tlnzz0/o0Ox3t7eLF68mJUrVxIYGMjw4cOJiopi8ODBAMydO5fWrVsnHe/l5cWXX37J9u3buXHjBps2bWLGjBl07do13W3mJBmKzSdsrfS83bw8U3dcYN6BK3SrWxILfTrydpcK0Hku/DIIfp8NHo2gasdkh/z7A66S8od45umZVHCsQHOP5tnx7QghhNBQgjGBoKigVH/nq6gERQWRYEzI9jXF/f39qVq1Kh9//DHdu3cnPDycdu3acejQIZycnLL1WgC9evXi4cOHTJgwgaCgIOrUqcOuXbuSJj+EhIRw9erVpOPnzJnD+PHjeffddwkODqZEiRK88847TJgwId1t5iRFlTE0IiIicHR0JDw8PNnDmXlNdHwizb4+QGhUPNN71qZH/VLpP3nXODg+H6wd4Z2D4Fw+aVe8IZ62G9oSGpvKs3p/0yt6vmn+DW3Lts3kdyCEECI7xMbGcv36dcqVK4eNTfrWGv+voKggwmLDUt3vbOOMW6Hsf2ZsxIgRPHr0iDVr1qR53MGDB5k7d+4zs2LzqrR+ZhnJU6THLh+xs7JgaPPyfLXzAnP3X6ZLnRLp67UDeGUy3D0Nt0/A+oHw1l6wND3waqW3Yl2ndal+wBONiSz+azEH7xzko8MfEZUQRddKXVM8VgghRN7gVsgtRxK35/H398fLyyvNY9q0acOZM2eIioqiVKlS/PLLL7ny/FpeIM/Y5TMDXiyDcyErboRGs8X/XvpP1FtCzxVgVxQenIUdHybb7VbIDU8XzxRftYrVYlbLWXSv1B2jamTCsQmsOr8qe78xIYQQ+Z6qqpw9e5ZatWqledy+fft4+PAh0dHR3LlzR5K6f5HELp8pZG3BW83KATD3wBUSDWlX6E7GoQT0WAqKDv5cDX4p1whKiV6nZ2LjiQzyNE1P/+bUNyzwXyCzZYUQQqSboihERETw6quvah1KniWJXT40sHFZithZcj0kiq1nMtBrB1C+BbT8n+n99g/hnn+6T1UUhQ8afMDIOiMBmH9mPt+c+ibFmbRCCCGEyH6S2OVDha1Nz9oBzN2fwV47gJe8oXIHMMTBzwMgOvWHZ/9LURTeqf0OYxuOBWB14Gom/D6BRGPqNfKEEEIIkT0kscunnvbaXctMr51OB10XQpGy8PgWbHoHnrPo8n/1q9aPL1/6Er2iZ8vVLXxw8APiDHEZi0MIIYQQGWKWid28efMoW7YsNjY2NGrUiJMnT6Z5/KxZs6hSpQq2trZ4eHjw/vvvExsbm0vRmqcs99rZOsHrq8DCBi7vgcPfZjiG1yq8xswWM7HSWbH/9n7e3fcuUQlRGW5HCCGEEOljdond+vXr8fb2ZuLEifj5+VG7dm3atWtHcHBwisevWbOGsWPHMnHiRAIDA1m6dCnr16/n008/zeXIzc+/e+22/ZXBXjsA91rQaabp/cFpcHlfhptoWbolC19ZSCHLQpwMOslbu9/iUeyjjMcihBAiw4wZHG0R2smun5XZFShu1KgRL7zwAnPnzgVM36iHhwfvvfceY8eOfeb4kSNHEhgYmGxNtg8++IATJ05w9OjRdF0zvxQoTsn8g1f4ZtdFyhctxJ73m6e/rt2//fY+/LEMbJzgnUOmIdoMCggJYNi+YTyOe0x5x/IsemWRJvWRhBCiIDAajVy+fBm9Xk+xYsWwsrLK8JqtIneoqkp8fDwPHz7EYDBQqVKlZ9aizbMFiuPj4zl9+jTjxo1L2qbT6WjTpg2+vr4pntOkSRNWr17NyZMnadiwIdeuXWPHjh0MGDAgt8I2awMbl2Xx4WtJz9p1q5eB1Sieav8V3D9jKmD880AYsjupeHF6VS9anZXtV/L23re5Fn6NgTsHsuiVRZRzLJfxeIQQQqRJp9NRrlw57t+/z717mRixEbnOzs6O0qVLP5PUZZRZJXYhISEYDIZn1lIrXrw4Fy5cSPGcvn37EhISwksvvYSqqiQmJjJs2LA0h2Lj4uKIi/vnQf6IiIjs+QbM0NNn7b7ZdZHvfS7zWu0MrEbxlIU19FwJP7xsSvC2f2haXzaDf/2VdyrPqg6reHvv29yIuMGgnYNY0GYB1YtWz1g8QgghnsvKyorSpUuTmJiIwWDQOhyRBr1ej4WFRbb0qppVYpcZBw8eZOrUqcyfP59GjRpx5coVRo8ezRdffMH48eNTPGfatGlMmjQplyPVzqDGZVly5Do3QqPZ7H8vY2vIPuXkAT2Wwaqu4L8aStWHBkMy3Ix7YXdWdljJu/veJSA0gCG7hzC71WxedH8x4zEJIYRIk6IoWFpaYmlpqXUoIpeY1eSJokWLotfrefDgQbLtDx48wM0t5eexxo8fz4ABA3jrrbeoWbMmXbt2ZerUqUybNi3VBxHHjRtHeHh40uv27dvZ/r2Yk0LWFrz99wzZOfsvZ3yG7FPlW0DrCab3Oz6G26cy1YyzjTNL2y2lkXsjohOjeXffu+y9uTdzMQkhhBAiiVkldlZWVtSvXz/ZRAij0YiPj0+q68BFR0c/Mx6t1+sBUl3OytraGgcHh2Sv/O7pGrI3Q6PZ+OfdzDfUdAxU8wJjgul5uycpz1Z+nkKWhZjfej6vlHmFBGMCHx76kF8u/ZL5uIQQQghhXokdgLe3N4sXL2blypUEBgYyfPhwoqKiGDx4MAADBw5MNrnCy8uLBQsWsG7dOq5fv87evXsZP348Xl5eSQmeMPXaDXv5n167hMz22ikKdJ4PRStD5D34ZTAYMreqhJXeim+bf0uPyj0wqkYm+05m4ZmFsr6sEEIIkUlm94xdr169ePjwIRMmTCAoKIg6deqwa9eupAkVt27dStZD99lnn6EoCp999hl3796lWLFieHl58eWXX2r1LZit/i+W4YfD17gdFsNGvzv0eqF05hqycYBeP8HiVnDzKOydAO2nZqopvU7PhBcn4GLjwqK/FjHPfx6hMaGMbTgWvU4ScyGEECIjzK6OnRbycx27/1py5BpTtgdS0smWAx+2wMoiC522gdtgfX/T++5LoWaPLMW2JnANX538ChWVtmXaMq3ZNKz0VllqUwghhMjrMpKnmN1QrMhZ/RqVoZi9NXcfx/DL6SxOGqnmBS95m95vGQlB57LUXN9qffmm+TdY6CzYc3MP7+57lyfxT7IWoxBCCFGASGJXwNha6Xm3RQUA5u2/QlxiFmsbtfoMKrSGxBhY3w+iw7LUXPty7Znfej52FnacCDrBkN1DCIkJyVqMQgghRAEhiV0B1KdhaYo7WHMvPJafT2Wx106nh+5LwKkMPLoBG4eCMWvJYuMSjVnWfhnONs4EhgXSf0d/bkbczFqcQgghRAEgiV0BZGOpZ2TLigDM3X+FQ5eC2eJ/F9+roRiMmXjk0s4Zev8EFrZwZR/sn5LlGKu7VGdVh1V42Htw98ldBuwYwLmQrA31CiGEEPmdTJ6gYE2eeCou0cCLU314FJ2QbLu7ow0TvTxpX8M9442e3QC/vml633MlVO+S5ThDYkIY4TOC86HnsbWwZUaLGbxU8qUstyuEEELkFTJ5QjzXgQvBzyR1AEHhsQxf7ceuc/cz3mjNHtB4pOn95nchODCLUUJR26Isa7eMJiWaEJMYw3s+77H16tYstyuEEELkR5LYFUAGo8qkbedT3Pe0+3bStvOZG5ZtMwnKNYeEKFjXF2IeZT7QvxWyLMTcVnPpWL4jiWoi/zv6P5acXSKFjIUQQoj/kMSuADp5PYz74bGp7leB++GxnLyeiRmuegvosQIcS0PYNfj1rSxPpgCw1Fsy9aWpDK5hWoFktt9svjzxJYZsaFsIIYTILySxK4CCI1NP6jJz3DMKuUDv1f+aTPFF5tr5D52iw7u+N2MbjkVBYf3F9Xgf9CY2MZNxCiGEEPmMJHYFkKu9TbYelyL32tB5run90ZlwbmPm2/qPftX6Mf3l6VjprNh/ez9D9wzlcezjbGtfCCGEyKvMbq1YkfMalnPG3dGGoPBYUnpKTQHcHG1oWM45axeq2QPun4Fj38Pm4aAawaViysfauYCTR7qbblu2Lc42zow6MAr/h/4M2DmABW0WUMq+VNZiFkIIIfIwKXdCwSx3suvcfYav9gN4JrlTgAX962Wu5Ml/GQ2wohPcOpb2cRbWMPJ0hpI7gCuPrjDcZzhBUUE42zgzv/V8qhetnoWAhRBCCPMi5U7Ec7Wv4c6C/vVwc3x2uLVdjeLZk9SBaWWKFuOef1xiHESHZrj5ikUq8tOrP1GlSBXCYsMYvHswh+8czkSgQgghRN4niV0B1r6GO0c/acXaoS8yu3cdPnilMgCHL4UQ+iQu+y5kk7O9oK52rqxov4LG7o1Nte72v8cvl37J0WsKIYQQ5kgSuwJOr1NoXMGFznVKMrJVRWqVciQ63sDCQ1e1Di1DClsVZl6bebxW4TWMqpHJvpP53u97qXUnhBCiQJHETiRRFIX3/+61+9H3Jg8i8lYZEUudJVOaTuGdWu8AsPjsYsYdHUe8IV7jyIQQQojcIYmdSKZF5WLUL1OEuEQj8w9c0TqcDFMUhZF1RzK5yWT0ip7t17YzbN8wwuPCtQ5NCCGEyHGS2IlkFEXhg7amXrs1J29x51G0xhFlTtdKXZnfej6FLAtxKugUA3cO5O6Tu1qHJYQQQuQoSezEM5pUKErTii4kGFTm7s97vXZPNSnZhJXtV+Jq58q18Gv0296PgJAArcMSQgghcowkdiJF3q9UAeCX03e4HhKVtcbsXEx16tKiszAdl82qOFfhp1d/onKRyoTGhjJ492AO3DqQ7dcRQgghzIEkdiJF9csUoVVVVwxGlVn7LmWtMScPU/Hhtw89+2o6xnSMMRGCA7Mcd0rcCrmxsv1KmpZoSkxiDKMPjGb1+dUA+N7zpfPmzvje882RawshhBC5SVaeoGCuPJEe5+6G02nOURQFdo1uThU3++y/iKrCb2Pg9AqwdoC39kGxKtl/HSDBmMDUE1PZcGkDAH2q9OGvkL8ICA2gukt11nZci6IoOXJtIYQQIrNk5QmRLWqUdOTVmm6oKny352LOXERRoMO3ULoJxEXA2t4QHZYjl7LUWTLhxQl41/cGYO3FtQSEmp65CwgN4Ni95yx7JoQQQpg5SexEmrxfqYxOgT3nH3Dm9uOcuYiFFfRaBY6lIewabBgMhsQcuZSiKAyuMZhvm3+Lwj+9czpFx5w/50hBYyGEEHmaJHYiTRVd7elStyQA03Oq1w6gUFHoswYsC8G1g7D705y7FmBvZY/KP0mcUTVKr50QQog8TxI78VxjWlfGQqdw5HIIJ66F5tyF3GpCt0Wm9ycXwR/Lc+Qyqqoy58856JRn//lPPTFVeu2EEELkWZLYiecq7WJH74YegKnXLkcTn2pe0Ooz0/sdH8L1I9l+iWP3jhEQGoBRNT6z71bkLaYcn5Lt1xRCCCFygyR2Il3ea1UJawsdp2484uClhzl7sWYfQo3uphIoPw80PXeXTZ721v37+br/+vnSz0zxnUKiMWee8xNCCCFyiiR2Il2KO9gwqElZAKbvvojRmIO9dooCnedBiXoQEwZrekNs9qz1mmBMICgqKNnzdSlZf2k9I31GEhkfmS3XFUIIIXKD1LFD6tilV1hUPM2/OcCTuETm96vHqzXdc/aCEfdhcSuIvAcVX4G+60Gnz3KzQVFBhMWmXlIlMCSQr059RawhlgqOFZjbei6l7Etl+bpCCCFEZmQkT5HEDknsMmLm3kvM9rlMhWKF2D2mORb6HO70vfcnLOsAiTHw4ghoPzVnr/e3gNAARvmMIjgmGGcbZ2a3nE0d1zq5cm0hhBDi36RAscgxbzUrRxE7S64+jGLTn3dz/oIl6kLXBab3x+eZVqjIBdVdqrOm4xqqOVcjLDaMIbuH8Nu133Ll2kIIIURmSWInMsTexpJ3W1QEYNa+y8QlGnL+otW7Qou/69pt/wCuH875awLFCxVnRfsVtC7dmgRjAuOOjON7v+9TnE0rhBBCmANJ7ESGDWhchuIO1tx9HMPaE7dy56Ivf/zPTNn1AyD0aq5c1s7SjhktZvBmjTcBWHx2MR8c/IDohOhcub4QQgiREZLYiQyzsdQzqnUlAOYeuEJUXC6UBXk6U7ZkA4h9DGt6QcyjnL8upuXGxtQfw5cvfYmlzpJ9t/bxxq43CIoKypXrCyGEEOkliZ3IlNcbeFDGxY6QJ/Es//167lzU0hZ6rwGHUhB6GX55AwwJuXNt4LUKr7G03VKcbZwJDAuk7/a+nAs5l2vXF0IIIZ5HEjuRKZZ6Hd6vVAZg0aFrPIqKz50L2xeHvuv+WVN2x0eQixO767rWZU3HNVR0qsjDmIe8sesNdl7fmWvXF0IIIdIiiZ3INK9aJajqZk9kXCILD+XOM2+AaU3ZHksBBU4vhxMLc+/aQMnCJVnVYRXNSzUnzhDHx4c/Zs6fc2RShRBCCM1JYicyTadT+Lh9FQBWHLtBUHhs7l28Sgdo+/earrs/hUu7c+/aQGGrwnzf8nsGVx8MwA9//YD3QW+ZVCGEEEJTktiJLGlZxZUGZYoQl2jk+/2Xc/fijUdAvUGgGmHDEAg6m6uX1+v0eDfwZkrTKVjqLPG55cOAnQO49+RersYhhBBCPCWJncgSRVH4uH1VANafus31kKjcvDh0/A7KvQzxT0wzZSNzf6Zq54qdWdZuGc42zlx6dIk+2/vg98Av1+MQQgghJLETWdawnDMtqhTDYFSZvvsCvldD2eJ/F9+roRiMOTyxQW8Jr6+EopUh4q4puYvPxeTyb3Vc67Cu4zqqOlclLDaMN/e8ya+Xfs31OIQQQhRsslYsslZsdgi4F07H748+s93d0YaJXp60r+GeswGEXYPFrSEmDKp2gtdXgS73/26JTohm/O/j2XNzDwB9q/bloxc+wkJnkeuxCCGEyB9krViR626HpTxpICg8luGr/dh17n7OBuBc3lTjTm8FF36DfRNz9nqpsLO0Y/rL0xlZZyQAay6sYdi+YYTHhWsSjxBCiIJFEjuRZQajyqRt51Pc97Q7eNK28zk/LFumsWl1CoBj38PpFTl7vVQoisI7td9hVotZ2FrYcuL+Cfps78OVR1c0iUcIIUTBIYmdyLKT18O4n0apExW4Hx7LyethOR9MrdehxTjT+9+84er+nL9mKlqXac3qV1dTsnBJbkfept+Ofvjc8tEsHiGEEPmfJHYiy4Ij01e/Lr3HZdnLn0CtXqAa4OdB8CDl3sTcULlIZdZ2XEtDt4ZEJ0Yz5sAYFpxZIMWMhRBC5AhJ7ESWudrbZOtxWaYo8NocKN0E4iJgzesQ+SB3rp2CIjZFWPjKQvpW7QvAfP/5fHDwAylmLIQQIttJYieyrGE5Z9wdbVBS2a9gmh3bsJxz7gVlYQ29fwLnChB+G9ZqUwblKUudJeMajWNyk8lY6izZd2sf/Xb043bkbc1iEkIIkf9IYieyTK9TmOjlCZBqcjfRyxO9LrW9OcTOGfr9ArbOcO9P+HUoGA25G8N/dK3UlWXtllHUtihXHl+h92+9OXb3mKYxCSGEyD8ksRPZon0Ndxb0r4eb47PDrV3rlcz5OnapcakAfdaC3houbodN78A9/5Rfj3On9+xpMeNaRWsRER/BcJ/hLD+3HCkpKYQQIqukQDFSoDg7GYwqJ6+HERwZy/l7ESw6fA1HW0sOf9wSR1tL7QI7+QPs+CjtYyysYeRpcPLIlZDiDfFMOT6FTVc2AdChbAc+b/I5dpZ2uXJ9IYQQeYMUKBaa0esUGldwoXOdknzcviqVXAsTHpPAwkNXtQ2sVMPnH5MYB9GhOR/L36z0VkxqMon/NfofFooFO2/sZODOgdyJvJNrMQghhMhfJLETOUavU/i4fVUAlv9+naA0at0VVIqi0Ltqb5a0W4KzjTMXH12k9/beHLsnz90JIYTIOEnsRI5qU82VBmWKEJtgZLbPJa3DMVv1i9dnfaf11HCpQXhcOMP3DWfZuWXy3J0QQogMkcRO5ChFUfikg6nXbv2p21wJfqJxRObLrZAbKzqsoGvFrhhVIzNPz+TDQx9KvTshhBDpJomdyHEvlHWmTbXiGFX4dvcFrcMxa9Z6ayY1mcT4F8djobNgz8099NvRj5sRN7UOTQghRB4giZ3IFZ+0r4JOgd0BDzh985HW4Zg1RVF4vcrrLG+3PKneXZ/f+nDo9iGtQxNCCGHmzDKxmzdvHmXLlsXGxoZGjRpx8uTJNI9//PgxI0aMwN3dHWtraypXrsyOHTtyKVqRHpWK29OjfikAvt55QZ4dS4c6rnX4udPP1HWtS2RCJCP3j2Tun3MxaFxkWQghhPkyu8Ru/fr1eHt7M3HiRPz8/Khduzbt2rUjODg4xePj4+N55ZVXuHHjBhs2bODixYssXryYkiVL5nLk4nnef6Uy1hY6Tt4Iwycw5Z9njrFzMdWpe54r+3I+lgwoZleMpW2X0qdqHwAW/bWIkftHEh4XrnFkQgghzJHZFShu1KgRL7zwAnPnzgXAaDTi4eHBe++9x9ixY585fuHChXz77bdcuHABS8vMFcCVAsW556udF1h46CqVXAuza0zz3F1m7PHt1OvU+a2EP5aBooPea6BKh9yLK522Xd3GJN9JxBniKFm4JLNbzqaKcxWtwxJCCJHD8myB4vj4eE6fPk2bNm2Stul0Otq0aYOvr2+K52zdupXGjRszYsQIihcvTo0aNZg6dSoGgwxXmaPhLSrgaGvJ5eAn/Ho6lwvxOnlAiTopvzrOgHoDQTXChiFw53TuxpYOXhW8WP3qakoWLsndJ3fpt6MfW69uTdrve8+Xzps743sv5c+KEEKI/M+sEruQkBAMBgPFixdPtr148eIEBQWleM61a9fYsGEDBoOBHTt2MH78eL777jumTJmS6nXi4uKIiIhI9hK5w9HWkpEtKwIwY+8lYuLNJAFXFFNyV/EVSIiGNa9DqMarZaSgqnNV1ndaT9OSTYkzxPG/o/9jyvEpxCXGMdtvNtfCrzHbb7Y8wyiEEAWUWSV2mWE0GnF1deWHH36gfv369OrVi//9738sXLgw1XOmTZuGo6Nj0svDI3fWBhUmAxqXoaSTLUERsSz7/brW4fxDbwk9V4B7bYgOgZ96QFSI1lE9w9Hakfmt5zO89nAUFNZfXE+PbT0ICA0AICA0QFauEEKIAsqsEruiRYui1+t58OBBsu0PHjzAzc0txXPc3d2pXLkyer0+aVu1atUICgoiPj4+xXPGjRtHeHh40uv27dvZ902I57Kx1PNB28oALDx4lbColH9OmrAuDH1/AafSEHYN1vSCePMrEKxTdLxb513mtZ6HvaU9NyJuJNs358850msnhBAFkFkldlZWVtSvXx8fH5+kbUajER8fHxo3bpziOU2bNuXKlSsYjcakbZcuXcLd3R0rK6sUz7G2tsbBwSHZS+SuLnVKUs3dgci4RObuv6J1OMnZF4f+G8G2CNz9w/TMnSFR66hS1KxUMz5p+EmybUbVKL12QghRQJlVYgfg7e3N4sWLWblyJYGBgQwfPpyoqCgGDx4MwMCBAxk3blzS8cOHDycsLIzRo0dz6dIltm/fztSpUxkxYoRW34JIB51O4dNXTUuNrTp+g1uhZtYrVrQS9FkHFjZwaSds9wYz7AFTVZW1F9aiU579KM/ymyW9dkIIUcCYXWLXq1cvpk+fzoQJE6hTpw7+/v7s2rUraULFrVu3uH//ftLxHh4e7N69m1OnTlGrVi1GjRrF6NGjUyyNIsxLs0rFaFapKAkGlel7LmodzrNKvwjdl5hKoPithMPfah3RM47dO0ZAaABG1fjMvgthF1h7Ya0GUQkhhNCK2dWx04LUsdNOwL1wOs05iqrC1pFNqVXKSeuQnnVqCWz/wPT+tblQb4C28fxNVVX6bO/D+dDzqKT8MVZQGP/ieHpU7oGi5GLNQCGEENkmz9axEwVP9RKOdK1jWiVk6o5A8xw6fOEtaPZ3YrdtNFzarW08f0swJhAUFZRqUgegojL5+GQ++/0zohPMbLhbCCFEtpMeO6THTmt3HkXT6rtDxCcaWTqoAa2rFX/+SblNVWHLCPD/CSxs4Y3foFQDraMiKCqIsNiwFPepqsqem3tYEbACo2qkolNFZrSYQTnHcrkcpRBCiKzISJ4iiR2S2JmDaTsCWXT4GpVcC7NzdDMs9GbYmWxIgLV94MpesHWGN/eYJlmYuVNBp/jo0EeExoZiZ2HHpCaTaF+uvdZhCSGESCcZihV5zrstK+JkZ1pqbENuLzWWXk8LGJeoBzFhsLobRKa8Ioo5ecHtBX7x+oUGxRsQnRjNR4c/YuqJqcQbzKh+oBBCiGwhiZ0wC/9daiw63jzrxmFdGPr9As7l4fEtWN0DYsO1juq5itkVY3HbxbxV8y0A1l5Yy8CdA7kTaaZJtBBCiEyRxE6YjQGNy+DhbEtwZByLD5vRUmP/VaioqYBxIVd4cBbW9YOEWK2jei4LnQWj641mXut5OFg5EBAawOu/vc7+W/u1Dk0IIUQ2kcROmA1rCz0ftzMVLV50+CrBkWacLDmXg/4bwMoebhyBTW+D0aB1VOnSvFRzNnhtoFaxWkTGRzL6wGimn5pOgjFB69CEEEJkkSR2wqx0quVObQ8nouMNzNp3Wetw0uZeG3r/BHorOL8Fdn5slqtTpMS9sDsr2q1ggKepJt/K8ysZvGsw95/cf86ZQgghzFmGE7sjR44A8Pvvv2d7MEIoisL/Xq0GwNoTt9jwx222+N/F92ooBqMZJk3lX4auiwDFVMjYDFenSI2l3pKPX/iYWS1mYW9pz5mHZ+j5W08O3T6kdWhCCCEyKcOJ3c6dO/H19WX79u05EY8QNCznTO1SjqjAhxv+YvQ6f/osPs5LX+9n1zkz7FGq0Q06fGN6f+BL+GOZtvFkUOsyrVnvtZ7qLtUJjwtn5P6RzPhjhgzNCiFEHpShxG7SpEkkJibSqlUrDAYDkydPzqm4RAG269x9ztx5dqZpUHgsw1f7mWdy1+htaP6R6f32D+D8Vm3jySAPew9+7PAj/av1B2B5wHIZmhVCiDwowwWKFy9eTHh4OE5OTrz11ls5FVeukgLF5sNgVHnp6/3cD0954oQCuDnacPSTVuh1Zrb2qarCb2Pg9ArTc3f9f4VyzbWOKsP23dzHhN8nEJkQiaO1I1OaTqGFRwutwxJCiAIrRwsUJyYm8uGHH2Iw5I0ZgCJvOXk9LNWkDkAF7ofHcvJ6ystoaUpRoOMMqNoJDPGwti/cP6N1VBnWpkybZEOz7+1/j29OfUOCQYZmhRDC3GU4sRs+fDgA77zzTrYHI0R6S5yYbSkUnR66L4WyzSA+ElZ3h9CrWkeVYR72HqzqsCppaHbV+VUM3DmQ25G3NY5MCCFEWqTciTArrvY22XqcJixtoPcacKsFUQ9hVdc8sfTYf1nqLfmk4Sd83/J7HKwcOBd6jte3vc7uG7u1Dk0IIUQqJLETZqVhOWfcHW1I6+k5d0cbGpZzzrWYMsXGwfSMXZFy8PgmrOoGMY+0jipTWpZuyQavDdQpVocnCU/48NCHfOH7BbGJZtprKoQQBZgkdsKs6HUKE708AVJN7iZ6eZrfxImUFHaFgZuhsBsEB8CaXhAfrXVUmeJe2J1l7ZfxZo03UVD4+dLP9Nneh6uP894wsxBC5GeS2Amz076GOwv618PN8dnhVgWoUKxw7geVWUXKwoCNYOMIt0/AzwMhj05CsNRZMqb+GBa+shBnG2euPL5C7996s/HyRjI4uV4IIUQOyXC5k7QYDAYuXLjAuXPnkl6bNm3KruZzjJQ7MU8Go8rJ62EER8biam/DsqPX2BsYTMsqxVg+uKHW4WXMrRPwY2dIjIEKraHVeNMs2v+ycwEnj9yPL4NCYkL49Min+N73BaBD2Q6Mbzweeyt7jSMTQoj8JyN5SqYTu2vXrnH27NlkSdzly5dJSEjAysqKatWqUbNmTVauXJmpbyI3SWKXN1wPieKVGYdINKqsfrMRL1UqqnVIGeO/BjYPT/sYC2sYeTpPJHdG1cjyc8uZ8+ccDKqBkoVL8k3zb6hVrJbWoQkhRL6S44ld//79Wbt2LYqiYGdnR1RUFB07dmTAgAHUrFmTSpUqodfrM/0N5DZJ7PKOSdsCWP77Daq62bN9VLO88azdU/f84YeXn3/c24egRJ2cjibbnHl4hk8Of8LdJ3exUCwYWXckg2sMRqfIkx5CCJEdcrRAMcCGDRv4/vvvefLkCffu3WPkyJHs2bOHU6dOUaZMmTyV1Im8ZXTrSjjYWHAhKJINp6WmmjmoXaw2P3v9TLuy7UhUE5nlN4t39r7Dw+iHWocmhBAFTqYSu/fff5+BAwdiY2ND4cKFmT17Nr///jsHDhygevXq7Nq1K7vjFAIAJzsrRrWuBMD0PZeIikvUOCIB4GDlwLfNv2VSk0nYWthy/P5xemzrweE7h7UOTQghCpRMJXbTpk3D3j75Q9L169fn5MmTjB49ml69etG3b18ePpS/2EX2G9i4LGVc7HgYGceiQ1Juw1woikK3St1Y13EdlYtUJiw2jBE+I/j65NfEGeK0Dk8IIQqEbH0IRlEURo8ezfnz54mLi6Nq1arZ2bwQAFhZ6BjXwfRv64cj17j3OEbjiMS/lXcqz5qOa+hXrR8AqwNX0297P649vqZxZEIIkf/lyNPNJUuW5Ndff+XHH3/MieaFoF11NxqWcyY2wcj03Re1Dkf8h7XemrENxzKv9TycbZy5+OgivX7rxc8Xf5aad0IIkYNydNpax44dc7J5UYApisL4jqYVKjb+eZcztx9rG1B2Cs0/w8vNSzVng9cGmpRoQqwhli+Of8H7B9/ncexjrUMTQoh8SeoRiDyrZilHutUrCcAXv503/54gOxdTnbrn2fFRvkruitkVY0GbBXzY4EMsdBb43PKh+9buHL9/XOvQhBAi38nWlScuXbpE+fLlsbCwyK4mc4XUscu7gsJjaTH9ALEJRub1rUfHWu5ah5S2x7chOjTlfXGRsP0DCLkIjqVhyE5wLJW78eWwwNBAPjnyCdfDr6Og8Eb1N3iv7ntY6i21Dk0IIcxWrqw8kRK9Xk9gYCCVK1fOriZzhSR2edvMvZeY7XOZUkVs2ef9MjaWebiO4pOHsLw9hF4Bl0oweCcULqZ1VNkqJjGGb099yy+XfgGgmnM1vm7+NeUcy2kcmRBCmKccL1CcGrMfChP50jsvl8fNwYY7j2JY/vsNrcPJmsLFYMBmcPSA0MuwqivEPNI6qmxla2HLhMYTmNVyFk7WTgSGBfL6tteTTazwvedL582d8b3nq3G0QgiRt8gzdiLPs7Oy4KN2VQCYd+AKDyPzeM00Jw8YuAUKucKDs/BTT4h7onVU2a516db8+tqvvOj+YtLEilH7RxEaE8psv9lcC7/GbL/Z8gejEEJkgCR2Il/oWrcktUo58iQukRl780H5E5cKMHAz2BaBO6dgXR9IiNU6qmznaufKolcW8VGDj7DUWXLwzkG8NnkREBoAQEBoAMfuHdM4SiGEyDsksRP5gk6nML6TqfzJ+lO3OX8vQuOIskHx6tD/V7Cyh+uH4eeBkBivdVTZTqfoGFh9IGs7rqWCYwUiEyKT7Zvz5xzptRNCiHSSxE7kGy+UdaZjTXeMKkzZngfKn6RHyfrQdz1Y2MLl3bBxKBgNWkeVI6o4V2F0vdHJthlVo/TaCSFEBkhiJ/KVsR2qYmWh49jVUPYFBmsdTvYo2xR6rwadJZzfDFvfA6NR66iynaqqLPprETrl2V9LE49NJNGQqEFUQgiRt0hiJ/IVD2c73nrJVDbjy+3niU/MJwlQxTbQYxkoevD/CXZ+BPmhR/Jfjt07RkBoAEb12Z/Zg+gH9NzWkzuRdzSITAgh8o5sTew++eQTXFxcsrNJITLs3ZYVKWZvzY3QaFYeu6F1ONnH8zXosgBQ4NQS2Dsh3yR3qqoy5885KCipHnMl/ArdtnRj0+VN+WOYXQghckC2JnbTpk2TxE5orrD1P+VPvve5TOiTPF7+5N9q94JOM03vj30Ph77WNp5skmBMICgqCJXUEzYLxYIYQwwTjk1gzIExhMWG5WKEQgiRN2TryhN5law8kf8YjSpec48ScC+Cvo1KM7VrTa1Dyl6+82H3ONP7VyZD09FpH58HBEUFpZmsOVk5sePGDub5zyPRmIizjTOTm0zmZY+XczFKIYTIfZotKZZXSWKXP524FkqvH46jU2D7qGZUc89nP9vD02H/F6b3Hb6FRm9rG08uuRB2gXFHxnHl8RUAulfqzkcvfEQhy0IaRyaEEDlDsyXFhDAnjcq7JJU/mbwtn5Q/+bfmH0KzD03vd34Ep1dqG08uqepclXWd1jHQcyAKCr9e/pXuW7tz+sFprUMTQgjN5Vhid/v2bYYMGZJTzQuRLk/Ln/heC2Xn2SB8r4ayxf8uvldDMRjzQaLX6jNoPNL0fttoOLNe23hyibXemo9e+Iil7ZZSolAJ7j65y+Bdg5nxxwziDfmviLMQQqRXjg3Fnjlzhnr16mEwmH8xVRmKzd+m777I3ANX0Ctg+Ne/dndHGyZ6edK+hrt2wWUHVYUdH5pmyio6U1mU6l21jirXPIl/wtenvmbzlc0AVHSqyLRm06jqXFXbwIQQIptkJE+xyOxFtm7dmub+a9euZbZpIbJVRdfCQPKkDiAoPJbhq/1Y0L9e3k7uFMX0jF1iLPy5Gn59C/RWULWj1pHlisJWhfmi6Re09GjJJN9JXHl8hT7b+zC89nCG1BiChS7Tv+aEECLPyXSPnU6nQ1GUNJ9bUhRFeuyEpgxGlZe+3s/98NgU9yuAm6MNRz9phV6Xeg21PMFogM3D4a/1plUq+qyFSq9oHVWuCo0J5YvjX+BzyweAmkVrMuWlKZR3LK9xZEIIkXm5MnnC3d2djRs3YjQaU3z5+flltmkhss3J62GpJnUAKnA/PJaT1/NBTTSdHjrPB88uYEyAdf3g6gGto8pVLrYuzGwxk6kvTcXe0p6zIWd5fdvrrDq/KsUVLYQQIr/JdGJXv359Tp9OfRba83rzhMgNwZGpJ3WZOc7s6S2g+xKo0hEMcbC2D9w4qnVUuUpRFLwqeLGx80YauzcmzhDHN6e+4c3db8qSZEKIfC/Tid1HH31EkyZNUt1fsWJFDhwoWL0Fwvy42ttk63F5gt4Sei6HSm0hMQZ+eh1u+modVa5zK+TGolcW8Vmjz7C1sOWPB3/QbWs3fr74s/zRKYTIt6RAMfKMXX729Bm7oPDYFBerylfP2P1XQiys7Q3XDoBVYRiwGTxe0DoqTdyOuM1nv3+GX7DpEZHG7o2Z3HQyboXcNI5MCCGeTwoUC/E3vU5hopcnQKrLy0/08sx/SR2ApQ30XgNlm0H8E1jdDe4WzCK+Hg4eLG+/nI8afIS13hrf+7503dKVTZc3Se+dECJfkcRO5Hvta7izoH893ByfHW5tW7143i518jxWdtB3PZRpCnERsKor3PPXOipN6BQdA6sP5BevX6hVrBZPEp4w4dgERu4fyYOoB1qHJ4QQ2UKGYpGh2ILCYFQ5eT2M4MhYboVG893eS1jpdezzfpnSLnZah5ez4iJhdXe4fQKsHaDjDChaKeVj7VzAySN348tlBqOBFQErmOc/jwRjAvZW9oxtOBav8l4oSj7svRVC5GkZyVMksUMSu4JIVVUGLD3J0SshvOJZnMUDG2gdUs6LjYDlr8KDs2kfZ2ENI0/n++QO4MqjK3z2+2cEhAYA0KJUCyY0nkAxu2IaRyaEEP+QZ+yEeA5FUZKerdt7/gFHLj/UOqScZ+MAHb56/nGJcRAdmvPxmIGKRSqy+tXVjK43GgudBQfvHKTLli5su7pNnr0TQuRJktiJAqtScXsGNi4DwKRt50kwFIACtlaFtY7A7FjoLHir5lv83OlnPF08iYiP4NOjn/Le/vcIjg7WOjwhhMgQSexEgTamTWWcC1lxJfgJP/re1DocoaFKRSqx+tXVjKo7CkudJYfuHKLLli5subJFeu+EEHmGJHaiQHO0teSjdlUAmLXvEiFP4jSOSGjJUmfJ0FpD+bnTz9RwqUFkfCSf/f4Z7/q8S1BUkNbhCSHEc5llYjdv3jzKli2LjY0NjRo14uTJk+k6b926dSiKQpcuXXI2QJGvvN7AgxolHYiMTWT67otahyPMQMUiFVn16irG1BuDpc6So3eP0nVLVzZc2iC9d0IIs2Z2id369evx9vZm4sSJ+Pn5Ubt2bdq1a0dwcNrPuty4cYMPP/yQZs2a5VKkIr/Q6xQ+96oOwPo/bvPXncfaBiTMgoXOgjdrvskGrw1Jde8m+U5i6N6hsuasEMJsmV1iN2PGDIYOHcrgwYPx9PRk4cKF2NnZsWzZslTPMRgM9OvXj0mTJlG+fPlcjFbkFw3KOtO1bklUFSZuDcBoLOC9Mo9vax2B2SjvVJ4f2//Ihw0+xFpvzYn7J+i2tRs/Bf6EUS0AE26EEHmKWSV28fHxnD59mjZt2iRt0+l0tGnTBl/f1Bcxnzx5Mq6urrz55pu5EabIp8Z2qEohKz1/3nrMpj/vah1OzrBzMdWpe57fxkDI5RwPJ6/Q6/QMqj6IX1/7lfrF6xOTGMNXJ7/ijV1vcD38utbhCSFEEgutA/i3kJAQDAYDxYsXT7a9ePHiXLhwIcVzjh49ytKlS/H390/3deLi4oiL++ch+YiIiEzFK/KX4g42vNe6El/tvMC0nRdoW7049jaWWoeVvZw8TMWHU6tTFxsO2z+A0MuwoiO8sT31FSoKoDIOZVjWbhnrL65n5umZ/Bn8Jz229mB4neG8Uf0NLHRm9StVCFEAmVWPXUZFRkYyYMAAFi9eTNGiRdN93rRp03B0dEx6eXjk/wr7In0GNy1LuaKFCHkSx/c++bTHyskDStRJ+VX+ZRiyG1yrw5MHpuTuoUwo+TedoqNP1T5s7ryZpiWaEm+MZ7bfbPpu78uFsJT/ABVCiNxiVold0aJF0ev1PHiQfEHuBw8e4Obm9szxV69e5caNG3h5eWFhYYGFhQU//vgjW7duxcLCgqtXr6Z4nXHjxhEeHp70un1bnicSJtYWeiZ4eQKw/PcbXAmO1DgiDRRygUHboHiNv5O7ThAsCct/lShcggVtFjCl6RQcrBwIDAukz299+N7ve+IMphEB33u+dN7cGd97qT9KIoQQ2cmsEjsrKyvq16+Pj49P0jaj0YiPjw+NGzd+5viqVaty9uxZ/P39k16vvfYaLVu2xN/fP9WeOGtraxwcHJK9hHiqZRVX2lRzJdGo8vnW8wWzvMXT5M6tJkQFw8pO8OC81lGZHUVR6FyxM1u6bKFN6TYkqoksPruYHlt7cDroNLP9ZnMt/Bqz/WYXzH9HQohcZ1aJHYC3tzeLFy9m5cqVBAYGMnz4cKKiohg8eDAAAwcOZNy4cQDY2NhQo0aNZC8nJyfs7e2pUaMGVlZWWn4rIg8b38kTKwsdR6+EsDuggBamtXOGgVvBrRZEPYSVXvAgQOuozFJR26LMbDmTGS1mUNS2KDcibvDG7jcICDXdr4DQAI7dO6ZxlEKIgsDsErtevXoxffp0JkyYQJ06dfD392fXrl1JEypu3brF/fv3NY5S5HdlXArxTnNT6ZwvfgskJt6gcUQasXOGgVvAvQ5Eh5iGZYPOah2V2XqlzCts7ryZLhW6JNuuoDDnzznSayeEyHGKKr9piIiIwNHRkfDwcBmWFUli4g20mXGIu49jGNW6Et6vVNY6JO3EPIJV3eCeH9gWgQGbTZMtRIp+v/s7w/YNe2b7182/5tVyr2oQkRAiL8tInmJ2PXZCmAtbKz2fdawGwMJDV7kVGq1xRBqyLQIDN0PJBqYk78fX4K6f1lGZJVVVmfPnHHTKs79exx0Zx6bLm6TnTgiRYySxEyIN7Wu48VLFosQnGpn8WwGfPGDjCAM2gUcjU727HzvD7VNaR2V2jt07RkBoQIqrUhhVIxOOTWDo3qHcjpDZ+EKI7CeJnRBpUBSFz1/zxEKnsC/wAQcupL1mcb5n4wD9f4XSTSAuAlZ1hVvHtY7KbDztrVNQUj1GQUlalmzZuWUkGBNyMUIhRH4niZ0Qz1HR1Z4hL5UDYNK2AOISC+hEiqes7aH/BijbDOIjTc/e3TiqdVRmIcGYQFBUECqpD7U6WTvxQvEXiDXEMvP0TPr81odzIedyMUohRH4mkyeQyRPi+SJjE2j93SGCI+P4sG1lRraSZbaIj4Z1feHaAbCwhb7roHwLraPSXFBUEGGxYanud7ZxprhdcbZe3cq3f3xLeFw4OkVH36p9ea/ue9hZ2uVitEKIvCAjeYokdkhiJ9Jn8593GbPeHxtLHT4ftKCkk63WIWkvIRbW94cre0FvDb1/gkqvaB1VnhEaE8q3f3zL9mvbAXAr5Mb/Gv2PFh4ttA1MCGFWJLHLIEnsRHqoqkqvH45z8noY7asXZ1CTcgRHxuJqb0PDcs7odak/V5WvJcbBL4Ph4nbQW0HPlVBVSnpkxO93f+eL419w98ldwFQPb2zDsbjauWocmRDCHEhil0GS2In0uhAUwauzj2D8z6fG3dGGiV6etK/hrk1gWjMkwK9vwvktoLOA7kuheheto8pTYhJjWHhmISsDVmJQDRS2LMzoeqPpWbknep1e6/CEEBqSOnZC5JAbIVHPJHUAQeGxDF/tx65zBXRVFL0ldF8GNXuCMRE2DIa/ftY6qjzF1sKW9+u/z/pO66lZtCZPEp7w5YkvGbhzIBfDLmodnhAij5DEToh0MhhVJm1LuZbd01xv0rbzGFLK/AoCvQV0XQR1+4NqhI1vg9+PWkeV51RxrsKqDqv4tNGnFLIsxF8hf9Hrt15898d3RCcU4CLZQoh0kcROiHQ6eT2M++Gxqe5XgfvhsZy8nvqMyHxPpwevOdDgTUCFre/BycVaR5Xn6HV6+lTtw5bOW3ilzCsYVAMrAlbQZUsXDt0+pHV4QggzJomdEOkUHJl6UpeZ4/ItnQ46fgcvjjB9veND+P17bWPKo4oXKs6MFjOY13oeJQqV4H7UfUbuH8n7B94nKCpI6/CEEGZIEjsh0snV3iZbj8vXFAXafQnNPjR9vXc8HPwaZK5WpjQv1ZxNnTcxuMZg9Iqefbf20XlzZ1adX0WiMVHr8IQQZkQSOyHSqWE5Z9wdbVJdLErBNDu2YTnn3AzLfCkKtB4PrT4zfX1wKuybKMldJtlZ2uFd35ufvX6mTrE6RCdG882pb+izvQ9/PfxL6/CEEGZCEjsh0kmvU5jo5QmQYnKnAhO9PAtuPbvUNP8I2k01vf99Nuz8GIxGbWPKwyoXqczKDiv5vPHnOFg5cCHsAv139OcL3y8IjwvXOjwhhMYksRMiA9rXcGdB/3q4OT473GqpV6hewlGDqPKAxiOg00xAgZM/mCZVGAv4mrtZoFN0dK/cna1dtvJahddQUfn50s+8tvk1tl3dhpQnFaLgkgLFSIFikXEGo8rJ62F/rzxhzex9lzl+PYw21YqzZFADrcMzX2fWwebhpnIo5Vuahml1Fs8eZ+cCTh65H18edSroFFOOT+Fa+DUAGhRvwGcvfkYFpwoaRyaEyA6y8kQGSWInsuryg0g6zD5ColFl6aAGtK5WXOuQzNeppbDdO+1jLKxh5GlJ7jIgwZDAyvMrWXRmEbGGWCwUCwZVH8Tbtd7GztJO6/CEEFkgK08IkcsqFbfnzWblAJi4NYCYeBlmTFXJ+s8/JjEOokNzPpZ8xFJvyVs132Jzl8208GhBoprI0nNL6bKlCz63fGR4VogCQhI7IbLJqFaVKOFow51HMcw/eEXrcEQBVbJwSea0msP3Lb9Pqn035sAYRviM4Hbkba3DE0LkMEnshMgmhawtmPD3rNlFh65x7eETjSMSBVnL0i3Z3GUzQ2sOxUJnwZG7R+iyuQsL/BcQZ4jTOjwhRA6RxE6IbNSuuhstqhQj3mBkwpYAGf4SmrK1sGVUvVFsfG0jL7q/SLwxnvln5tNlcxcO3zmsdXhCiBwgiZ0Q2UhRFCa9Vh0rCx1Hr4Sw/ex9rUMSgnKO5fjhlR/4tvm3uNq6cufJHUb4jOC9/e9xJ/KO1uEJIbKRJHZCZLMyLoUY0aIiAJO3nScyNkHjiPKosOtaR5CvKIpC+3Lt2dp1K4OrD8ZCseDg7YN02dKFhWcWyvCsEPmEJHZC5IB3Xi5PWRc7giPjmLn3stbh5E1bR8KdP7SOIt8pZFkI7wbebHhtAw3dGhJniGOe/zy6bukqw7NC5AOS2AmRA2ws9UzuXAOAFceuE3BPlnpKYudiqlOXJgXin8DK1+DaoVwJq6Cp4FSBJW2X8E3zb3C1deV25G1G+IxgpM9ImT0rRB4mBYqRAsUi54xY48f2v+5Tt7QTvw5rgk7WkTV5fDvtOnUWtrDzI7h+CPTW0HM5VO2Ye/EVMFEJUSw6s4hV51eRqCZipbNiSM0hDKkxBFsLW63DE6LAk5UnMkgSO5FTHkTE0vq7QzyJS2Rq15r0bVRa65DyjsQ42DAELvwGih46z4M6fbSOKl+7Fn6NaSemcfz+cQBKFCrBRy98ROvSrTl+/zhfnfyKsQ3H0rhEY40jFaJgkcQugySxEzlp2dHrTP7tPI62lvh88DJFCz9vGFIkMSTCtlHg/5Pp6/Zfw4vDtI0pn1NVlb039/LtH98SFBUEQCO3RoTGhnLl8RWqu1Rnbce1KIr0PguRW2RJMSHMyMDGZfB0dyA8JoGpOwK1Didv0VvAa3PhxXdNX+/6BA5MA/l7NMcoikLbsm3Z2mUr79R6ByudFSeCTnDlsWk1lYDQAI7dO6ZxlEKI1EhiJ0QOs9Dr+LJrDRQFNvrd5fg1WQM1Q3Q6aDcVWnxq+vrQV7DzEzAatY0rn7O1sGVk3ZFs6rwJe0v7ZPu+OP4FBqOshyyEOZLETohcULd0Efo2ND1f99nmc8QnSlKSIYoCLT6BDt+avj65CDYPA4PUCMxptyNvE5kQmWzb3Sd36bqlK+dCzmkUlRAiNZLYCZFLPm5XlaKFrbgS/ITFR65pHU7e1Oht6LYEdBbw13pY1w/io7WOKt9SVZU5f85Bpzz7X8X1iOv02d6H8b+PJyQmRIPohBApkcROiFziaGfJZx09Afje5zK3QiUhyZRaPaH3GrCwgcu7YXU3iHmsdVT50rF7xwgIDcCopt7DvPnKZjpt6sSKcytIkB5UITQniZ0QuahznRI0qeBCXKKRCVvPIZPSM6lyOxiwGawd4ZYvrOgIkQ+0jipfedpbp5Dy7FcFhXKO5fB09iQqIYrvTn9H162yeoUQWpPETohcpCgKX3SpgZVex8GLD9l5LkjrkPKuMo1h8A4oXBwenINlbSFMhrizS4IxgaCoIFRS/uNDRSUiLoKVHVYyuclkXGxcuBlxkxE+Ixi+bzjXw2WtXyG0IHXskDp2IvfN3HuJ2T6XcbW3xueDl7G3sdQ6pLwr7Dqs6gKPbkAhV+j/K7jX0jqqfCEoKoiw2LBU9zvbOONWyA2AJ/FP+OGvH1gVuIpEYyIWigV9qvVhWO1hOFjJ71UhskIKFGeQJHYit8UmGOgw+wjXQ6J4o0lZPn+tutYh5W2RD2B1d3hwFqwdoM9aKPuS1lEVSDfCb/DtH98mDckWsS7CyLoj6V6pO3qdXuPohMibJLHLIEnshBaOXg6h/9ITKAr8OqwJcYlGgiNjcbW3oWE5Z/SyrmzGxIbD2j5w83fT+rI9lkI1L62jKrB+v/s735z6hmvhpuHxKkWq8EnDT3jB7QWNIxMi75HELoMksRNaGbPuTzb738NCp5Bo/Oej6O5ow0QvT9rXcNcwujwoIQY2vAkXt4Oig06zoP4graMqsBKMCfx88Wfm+c8jMt5UC6916dZ8UP8DPBw8NI5OiLxDlhQTIo9oUrEoQLKkDiAoPJbhq/3Yde6+FmHlXZa28PqPULc/qEbTOrOHv5UlyDRiqbOkX7V+bO+6nV5VeqFX9Pjc8qHzls7MOD2DJ/FPtA5RiHxHEjshNGIwqszceynFfU/TkEnbzmMwSlKSIU/Xl33J2/T1/imw82NZgkxDRWyK8NmLn7HBawON3RuTYExg+bnldNzUkQ2XNsjyZEJkI0nshNDIyeth3A+PTXW/CtwPj+Xk9dRnJYpUKAq0mQjtvzJ9ffIH+HUIJMZpG1cBV7FIRRa9soh5redR1qEsYbFhTPKdxOu/vc7x+8e1Dk+IfEESOyE0EhyZelKXmeNECl4cDt2Xgs4SAjbBTz0gNkLrqAo0RVFoXqo5G1/byCcvfIKDlQOXHl1i6J6hvOfzntS/EyKLJLETQiOu9jbZepxIRc0e0O9nsCoM1w/LKhVmwlJvSX/P/uzotoN+1fphoVhw8M5Bum3pxlcnv+Jx7GOtQxQiT5LETgiNNCznjLujTSoLNoGCaXZsw3LOuRlW/lShFbzxGxQqBkF/wdJXIPSq1lEJwNHakbENx7Kx80ZeLvUyiWoiPwX+xKubXuXHgB9l/VkhMkjKnSDlToR2dp27z/DVfgApLty0sH89KXmSncKuwapu8Og62LlA57lgXyL14+1cwEnKcuQm33u+TP9jOpcemSYWlbYvjXd9b1qVboWiSG1HUTBJHbsMksROaGnXuftM2nb+mYkUpZxsOfhRCyz00rGerZ4Ew0894b7/84+1sIaRpyW5y2UGo4EtV7fwvd/3hMaGAlDPtR4fvfARNYrW0Dg6IXKfJHYZJImd0JrBqHLyehjBkbFYW+j45Ne/CI9J5NNXq/J28wpah5f/xEXCqq5w59Tzj337EJSok+MhiWdFJUSx7NwyVgasJM5gmtH8arlXGV1vNCUKp9HTKkQ+IwWKhchj9DqFxhVc6FynJO1ruPO/Vz0BmLn3MrfDojWOLh+ytod207SOQjxHIctCvFf3PX7r+hte5U3Lw+24vgOvTV7MPD0zaTULIcQ/JLETwgz1bFCKRuWciUkwMH7LOaRjPQfoLbWOQKSTWyE3pjabyvpO63nB7QXijfEsO7eMjhs7siZwDQlGmWAhxFOS2AlhhhRFYWq3mljpdRy8+JBtf8nSYkJ4uniytO1S5rSaQ1mHsjyKe8S0k9PouqUrPjd95A8gIZDETgizVaFYYUa2qgjA5G0BhEdLr4QQiqLQwqMFGztv5LNGn+Fs48zNiJuMOTiGN3a9wV8P/9I6RCE0JYmdEGZs2MsVqORamJAn8UzbGah1OEKYDUudJb2q9mJ71+0MrTkUa701fsF+9NvRjw8OfsCtiFtahyiEJiSxE8KMWVnomNatJgDrTt3m+LVQjSMqgB5e0DoCkYbCVoUZVW8Uv3X9jc4VOqOgsOfmHjpv6cxXJ7/iUewjrUMUIldJYieEmWtQ1pl+jUoD8OnGs8QmGDSOKJ+wczHVqXuebWPg0p4cD0dkjVshN6a8NIVfvH6hacmmJBr/XsFi46ssObuEmMSYpGN97/nSeXNnfO/5ahixEDlD6tghdeyE+YuITaDNd4cIjozjvVYV+aBtFa1Dyh8e34boVHpB46Ng/xdwyxcUPXSaAfXfyNXwROb53vNlxukZXAgz9bi62rkyos4IXiv/Gv139icgNIDqLtVZ23GtrGghzJ4UKM4gSexEXrDr3H2GrfbDQqewfVQzqrjZax1S/mdIgG2jwf8n09fNPoRWn4EkAnmCUTWy/dp25v45l3tR9wBwL+TO/ah/ZpkvbLOQpiWbahWiEOmS5wsUz5s3j7Jly2JjY0OjRo04efJkqscuXryYZs2aUaRIEYoUKUKbNm3SPF6IvKp9DXfaehYn0ajyya9/YTAW+L/Jcp7eEjrPg5fHmr4+Mh02DYPEeG3jEumiU3R4VfBia9etfNjgQ+wt7ZMldTp0zPlzjpRJEfmK2SV269evx9vbm4kTJ+Ln50ft2rVp164dwcHBKR5/8OBB+vTpw4EDB/D19cXDw4O2bdty9+7dXI5ciJw3uXMN7K0t8L/9mFW+N7QOp2BQFGg5Dl6baxqS/Wsd/NQdYh5rHZlIJ2u9NYOqD+LzJp8n227ESEBoABsvb9QmMCFygNkNxTZq1IgXXniBuXPnAmA0GvHw8OC9995j7Nixzz3fYDBQpEgR5s6dy8CBA9N1TRmKFXnJquM3Gb/5HIWs9OzxfpmSTrZah1RwXNkHPw+C+CdQrBr0+wWcPLSOSqSDqqr02d6HwLBAjKrxmf3dK3Xn3Trv4mrnqkF0QqQtzw7FxsfHc/r0adq0aZO0TafT0aZNG3x90zd7KTo6moSEBJydnVM9Ji4ujoiIiGQvIfKKfg1L06BMEaLiDXy26awMI+Wmim1g8E6wd4eHgbCkDdw/o3VUIh2O3TtGQGhAikkdwK+Xf6Xjxo7M9ptNRLz8nyDyLrNK7EJCQjAYDBQvXjzZ9uLFixMUFJSuNj755BNKlCiRLDn8r2nTpuHo6Jj08vCQv7hF3qHTKXzV3bTc2AFZbiz3udeCt/aBqyc8CYJlHaQciplTVZU5f85BIeVJLwoKtha2xBpiWXJ2CR1+7cCKcyuITYzN5UiFyDqzSuyy6quvvmLdunVs2rQJGxubVI8bN24c4eHhSa/bt2/nYpRCZF1FV3tGtDQtNzZpawCPouRh/lzlWAqG7ILyLSAhCtb2glNLtI5KpCLBmEBQVBAqKfduq6jYWdjx3cvfUcGxAhHxEXx3+js6berExssbSTQm5nLEQmSeWT1jFx8fj52dHRs2bKBLly5J2wcNGsTjx4/ZsmVLqudOnz6dKVOmsG/fPho0aJCh68ozdiIvik800mnOES49eEK3eiWZ8XodrUMqeAwJpgLG/qtNXzd5D9pMBl2++ps5XwiKCiIsNizV/c42zrgVcsNgNLDt2jbm+c8jKMo0UlTOsRyj6o6idenWUvNOaCJP17Fr1KgRDRs2ZM6cOYBp8kTp0qUZOXJkqpMnvvnmG7788kt2797Niy++mOFrSmIn8iq/W4/ovuAYqgo/DmlI88rFtA6p4FFVUxmU/VNMX1d7Dbr9AJYyqSUvizPEse7COhafXUx4XDgANVxqMLr+aF50z/j/M0JkRZ6dPAHg7e3N4sWLWblyJYGBgQwfPpyoqCgGDx4MwMCBAxk3blzS8V9//TXjx49n2bJllC1blqCgIIKCgnjy5IlW34IQuaZe6SIMalwWgE83nSU6XoaMcp2iQPOPoNti0FtB4FZY0QmePNQ6MpEFT0uk7Oy2k3dqvYOthS3nQs8xdM9Qhu4ZyrmQc1qHKESKzC6x69WrF9OnT2fChAnUqVMHf39/du3alTSh4tatW9y//8/D4gsWLCA+Pp4ePXrg7u6e9Jo+fbpW34IQueqjdlUo6WTLnUcxTN99SetwCq5ar8OAzWBbBO7+AUtaw8OLWkclssjeyp6RdUeyo9sO+lXrh4XOguP3j9Nnex/GHBjD1cdXtQ5RiGTMbihWCzIUK/K6gxeDeWP5KRQFNg5vQt3SRbQOqeAKuQI/9YBH18HaEXqtgvIvax2VyCZ3n9xlvv98tl3dhoqKTtHRqXwnhtceTin7UlqHJ/KpPP2MnRYksRP5gfd6fzb+eZfKroUZ38mTsOh4XO1taFjOGb1OHvjOVVEhsK4v3D4BOgvwmg11+2sdlchGVx5dYZ7/PPbd2geAhc6CHpV68HattylmJ8+6iuwliV0GSWIn8oNHUfE0++YAT+KSP2fn7mjDRC9P2tdw1yiyAiohFra8C+d+NX39kje0Gi8zZvOZcyHn+N7ve3zvm4ro2+ht6FOtD0OqD8HJxknb4ES+kacnTwghMufE9dBnkjqAoPBYhq/2Y9c5KWScqyxtoNsS08QKgKMzYMNgSIjRNi6RrWoUrcEPbX9gadul1C5Wm1hDLMvPLafDxg4sOLOAJ/EykU/kLumxQ3rsRN5nMKq89PV+7oenXClfAdwcbTj6SSsZltWC/xrYOgqMCVCyAfRZC4VlTdL8RlVVDt85zJw/53DxkWnijJO1E0NqDKF31d7YWkgJHJE50mMnRAFz8npYqkkdgArcD4/l5PXUC7SKHFSnLwzc/M+M2cWt4cF5raMS2UxRFF72eJmfvX7m2+bfUtahLI/jHjPj9Axe3fgqawLXEG+QVWJEzpLEToh8IDgyfWtapvc4kQPKvgRv+YBzBQi/BUvbwuV9WkclcoBO0dG+XHs2dd7EF02/oGThkoTEhDDt5LSkZcoSjAlahynyKRmKRYZiRd7nezWUPouPP/e4tUNfpHEFl1yISKQqOgzWD4CbR0HRwctjoXK71I+3cwEnj9yLT2S7BEMCGy9v5Ie/fiA4JhiA0valGVZ7GK+WexW9Tq9xhMLcyazYDJLETuR1T5+xCwqPTWWZc9PsWHnGzkwkxsNv7/+zxmxaLKxh5GlJ7vKB2MRY1l9cz7Jzy5LWrS3vWJ5367zLK2VeQafIIJpImTxjJ0QBo9cpTPTyBEwTJVIyqnVFSerMhYUVdJ4LDd9+/rGJcRAdmvMxiRxnY2GTtEzZ6HqjcbBy4Fr4NT489CE9t/XE55YP0tciskoSOyHyifY13FnQvx5ujjbJtlvqTcnc3vPB8p+GOVEUqNNP6yiEBuws7Xir5lvs6r6L4bWHU9iyMJceXWLMgTH0+q0Xh+8cls+qyDQZikWGYkX+YjCqnLweRnBkLK72NjjZWfLa3KMkGFRm9apDl7oltQ5RPHXPH35Ix3Jjbx+CEnVyOhqhkfC4cFYGrGR14GpiEk11DmsVrcW7dd6lSYkmKIr0tBd0MhQrRAGm1yk0ruBC5zolaVzBhWruDoxqVQmAz7cF8DAyTuMIhRD/5mjtyKh6o9jVfReDqw/GRm/DXyF/MWzfMAbuHIjvPV/pwRPpJomdEAXAsBYV8HR34HF0Ap9vDdA6HCFECpxtnPFu4M3O7jsZ4DkAa701/g/9eXvv27yx6w1O3j+pdYgiD5DETogCwFKv45setdDrFLafvc/Os7K8WJ6SEK11BCIXFbUtyscvfMzObjvpV60fVjor/IL9eHPPmwzeNZhTQaeSjvW950vnzZ3xveerYcTCnEhiJ0QBUaOkI8NfrgDA+C3neBQlFfDzjM0j4NFNraMQuayYXTHGNhzLjm476FO1D5Y6S/548AdDdg9hyO4hnLx/ktl+s7kWfo3ZfrNluFYAktgJUaC817oiFV0LE/IknknbZEhWc3Yupjp1z/PoGixuBTelV6YgKl6oOJ82+pQd3XbQq0ovLHWWnAo6xZt73iQg1PQ5DggN4Ni9YxpHKsyBzIpFZsWKguXPW4/ovuAYRhWWDGxAG8/iWodUsD2+nXadOkMCbPeGoL9AZwles6Bu/1wLT5ifoKggFv+1mJ8v/Zxse1mHsmztslVm0eZDMitWCJGquqWL8Faz8gB8uuks4dGyZqWmnDxMpUxSe3m8AEN2gWdnMCbAlhGw+39gNGgYtNCSWyE3WpVu9cz2GxE36L61Oyfvn5Rh2QJMEjshCiDvVypTvmghgiPj+GL7ea3DEc9jVQh6rDCtKwvgOxfW9ILYcE3DEtpQVZU5f85JcQmyy48v8+aeN3lj1xscv39cErwCSBI7IQogG0s93/SohaLAhtN3OHAxWOuQxPPodNByHPRcARa2cGUvLG4NoVe1jkzksmP3jhEQGoBRNaa4X6/o8Qv2Y+ieoQzcOZDf7/4uCV4BIomdEAVUg7LOvNGkLACfbjxLRKwMyeYJ1buahmYdSkLoZVjcEq7u1zoqkUue9tYpqawKraBQ0akifav2TaqDN2zfMPrv6C9LlRUQktgJUYB91K4KZVzsuB8ey9TtgVqHI9KrRB0YegBKNTQNx67uDscXgPynne8lGBMIigpCJeWftYpKSEwIHzT4gJ3dTIWOn65kMcJnBL2398bnlk+qvX0i75NZscisWFGwHb8WSu8fjgPw45CGNK9cTOOIRLolxsG2MXBmjenrOv2h04z0lVAReVZQVBBhsWGp7ne2ccatkFvS1yExIawMWMn6i+uT1qKtVKQSb9d6m1dKv4Jep8/xmEXWZCRPkcQOSeyEmLjlHCt9b1LSyZZdY5phb2OpdUgivVQVjs+HPZ+BajT14vVaDfZSxkYk9yj2EavOr2LNhTVEJUQBUN6xPG/VfIsO5TpgobPQOEKRGknsMkgSO1HQRccn0n7WEW6FRdOnYWmmdaupdUgio674wIbBpqFZ+xLQ+ycoWU/rqIQZCo8L56fAn1gduJrI+EgAPOw9eKvmW3iV98JSL3/YmRtJ7DJIEjshwPdqKH0Wm4ZkV7/ZiJcqFdU4IpFhoVdhbR8IuQgWNuD1PdTupXVUwkxFxkey/uJ6fgz4kUdxjwBwL+TOkBpD6FqpK9Z6GdI3F5LYZZAkdkKYyJBsPhAbARuHwqVdpq+bvAdtJoE8RyVSEZ0QzS+XfmFFwApCYkIAKGpblDeqv0HPyj2xs7TTOEIhiV0GSWInhIkMyeYTRiMcmAJHvjN9XaEV9FgGtkW0jUuYtThDHJsub2LpuaUERQUB4GjtSP9q/elbrS8OVvL/o1YkscsgSeyE+IfMks1Hzm00LUGWEA1FykGfteBaTeuohJlLMCTw27XfWHJ2CbcibwFQyLIQvav0ZoDnAFxsXTSOsOCRxC6DJLETIrnPtwaw4tgNSjjasH10My7cjyQ4MhZXexsalnNGr5NFxvOMoLOwti+E3wKrwtB1IVTz0joqkQcYjAb23NzDD3/9wJXHVwCw1lvTvVJ3BtcYnKykishZkthlkCR2QiQXHZ9Ih9lHuBkaja2lnpiEfxacd3e0YaKXJ+1ruGsYociQqFD4ZRDcOGL6+uVPTOvO6qRGvXg+o2rk4O2DLP5rMedCzwFgobPAq7wXb9Z8kzIOZbQNsACQxC6DJLET4llzfC7z3d5Lz2x/2le3oH89Se7yEkMC7BkPJxaYvq7cAbotAhtHbeMSeYaqqhy/f5wlZ5dwMugkYFrCrG3ZtrxZ402qucgwf06RxC6DJLETIjmDUeWlr/dzPzw2xf0K4OZow9FPWsmwbF7jvxa2jQZDHLhUgt5roFhlraMSeYx/sD9Lzi7h0J1DSdualmzK0JpDqV+8voaR5U+S2GWQJHZCJPfvmnZpWTv0RRpXkAep85y7frC+P0TcBSt7aDcV3GulfrydCzh55F58Is+4GHaRpeeWsvvG7qT1Z+u61uXNGm/SvFRzFEX+8MsOkthlkCR2QiS3xf8uo9f5P/e42b3r0LlOyZwPSGS/J8Hwyxtw8/fnH2thDSNPS3InUnU74jbLApax5coWEowJgGk92jdrvEm7su1kubIsykieIk/OCiGe4Wpvk63HCTNU2BUGboHq3Z5/bGIcRIfmfEwiz/Jw8GBi44ns6r6LN6q/gZ2FHZcfXWbskbF02tSJ9RfWE5uY8qMdIntJYieEeEbDcs64O9qQ2iCKgml2bMNyzrkZlshuekv+396dhzV1rWsAf0MgAREZZVARFBVBERwKRWy1grNWa20dEau1DtiqOFRtFa3H6rXH43S0Hj0qUm2pWmurUofai/UohSraKjiA4qVVwAllkjHr/sElt5EpAUJCfH/Pw/O4V9Ze+daXne2XvXd2EDBb11GQAbFvYo95Pebh5KiTmOUzC9Zya9zNvYu/xf0NA74ZgB2/70B2UbauwzRoLOyIqAKpkQThwzwBoNLiTgAIH+bJL04QUaUs5ZaY5j0NJ0adwCLfRWhh3gKPCx5j06VN6HegH9ZdWIfMvEyVdWLvxWL44eGIvRero6gNAws7IqrUwM5O+HxCNzhaVjzdai6TorsLj9YRUfXMjM0w3mM8jo48itWvrEY7q3bIL8lHRGIEBh4aiGXnluH209sQQmBjwkbcfnobGxM2gpf/1x6/PAF+eYKoOqUKgfjUx7ifUwCbJjKsir6G6xk56OfpgO3B3fmtt8bu3mVge++a+713Bmjho+1oyMAJIXD27lnsvLITCfcTlO1d7Lrg94e/K5e3BW1DQMsAXYSol/jlCSKqN1IjCfzdbDHcpyVe6dAc60f7wEQqwamkTHx76a6uw6OG8rDizaqJNCWRSPBqq1exZ9AefDHoC7zm/BoAqBR1Ekiw+dJmHrWrJRZ2RKQRD6dmmBNUdkPb8O8Tkf70mY4jogZxeCZwaa+uoyAD4mPvg019NyHcP1ylXUAg8VEi/n7h7yguLdZRdI0XCzsi0ti0V9vCx9kKOQUlWHjwd36ybsya2Jbdp646EiNAUQx8FwocmVN2+xOieiCEwMGbB2EkqViORCZFYsDBAdh1dRdyinJ0EF3jxGvswGvsiGrj1oNcDNl0FgXFCqwc0RnBL/OHwButJ39Uf586M2vg96+B//4UgABadgfejgQsWzVYiGSYzt09h+k/Tq+xn7mJOUa1H4UJnhPgaO7YAJHpF/7yhIZY2BHVzu5zqVhxJAlmJlIcn/MKXGzNdR0SaVPyj8A3U4CCJ2VH+kbtAtr20XVU1EgJITD22FgkPUqCQMVSRAIJnMydYCo1xe3s2wAAY4kxBrUZhJBOIXC3cW/okHWGX54gogYR4u8K/7a2eFZcinn7f0Op4oX/nGjY2gcB084Ajl3KjvB98QZw9h8Ajw9QLRQripGRl1FpUQeUXWtXWFqIr4d9jS2BW9DDoQdKRAmO3D6CUUdGYdqpaTh/7zwvBXkOj9iBR+yI6uLPrHwM3HAWuYUlWDSoI6b3dtN1SKRtxc+AY/OAy/vKlt2HAG98Dpha6jYuanQy8jLwuOBxlY/bmNqonHq9+vAqIhIjcOp/TkEhFAAAd2t3hHQKwcA2A2FiZKL1mHWBp2I1xMKOqG72X/gDCw/+DpnUCN+/H4COjnwfGTwhgIsRwA8LgdIiwKYtMHov4NBJ15HRC+DPnD+x99peHEo+hGclZd/Md2jigPEe4zGqwyhYyCx0HGH9YmGnIRZ2RHUjhMDUyAv48dp9eDg1w3ehAZAZ80qPF8Ldi8D+EODpH4CxGTBsA+A9RtdR0QviaeFTHLh5APuu7cPDZw8BAE2Mm2Bk+5GY4DkBLZu21HGE9YOFnYZY2BHV3YOcQgzY8DMe5xUh9DU3LBjQUdchUUPJewQcehe49VPZco/JwMA1Nd9GhaieFJUW4djtY4hMikTKkxQAgJHECP1c+iHEMwRezb10HGHdsLDTEAs7ovrxw5V0zNiXACMJcGB6T3R3sdZ1SNRQFKXAmbXAmf8CIIAWXYG39gDWvA0ONRwhBM7fO4+IxAj8kv6Lsr2rfVdM9JyI15xfg9RIqsMIa4eFnYZY2BHVn7CvL+PQpbtwtW2C6NmvoInMWNchUUNK/rHs6N2zLMDUChi5A+jQX9dR0QvoxuMbiEyKRHRqNEoUJQCAVk1bYYLnBLzR7g00MWmi4wjVx8JOQyzsiOrP02fFGLThZ9x7WoDxfq2x6o3GfQqEauFJWtl1d/f+70feX10A9FkMNMIjJdT43c+/j6jrUfj6xtfILsoGAFiYWGBUh1EY5zGuUdzwmIWdhljYEdWvcykPMf7fcQCA3e+8hNfc7XUcETW4kkLgxBLg13+XLbfpDby5E2jaXLdx0QsrvzgfR24dQWRSJNJy0gAAUokU/V36I9gzWK+vw2NhpyEWdkT1b8WRROw+dwfNLeQ4OedVWJvLdB0S6cLvB4Ajs4HiPMDCCRi1G3Dx13VU9AJTCAV+/vNnfJH0BeIz4pXtPs19EOwZjL6t+8LYSL8uIWFhpyEWdkT1r6C4FEM2ncWtB3kY4uWEf47rColEouuwSBce3AC+DgYe3gAkUiAoHOj5AcDtgXTs+uPr+CLpC5Xr8FqYt8A4j3EY2X6k3twPj4WdhljYEWnHlT+f4o2t51CiEFg/2htvdOWPxr+wCnOBo3OBK/vLlt0HAyO2Amb85jTp3oP8B4i6EYUDNw4gqzALQNn98Ea0G4HxHuPRullrncbHwk5DLOyItGfT6WT849RNWJga4/icV9HSykzXIZGuCAFc2AUcX1T2axVWLsDbe8pujUKkBwpKCnDs9jHsvbZXeT88CSTo3ao3xnuOh5+jn07OPGhSp+jlreG3bNkCV1dXmJqaws/PD/Hx8dX2P3DgADp27AhTU1N4eXkhOjq6gSIloprM7OOGrq2tkFNQgvn7f4NC8cJ/lnxxSSTAS1OAKSfLiron/wPs7A/E7ygr+oh0zNTYFG92eBOHXj+Ef/X7F15t9SoEBGL+jMHUk1Mx8vuR+ObmNygoKdB1qFXSu8Lu66+/RlhYGMLDw5GQkABvb28MGDAA9+/fr7T/+fPnMXbsWEyZMgWXLl3CiBEjMGLECFy9erWBIyeiyhhLjbD+bR+YmUgRe/sRdp1L1XVIpGstugLTfgY6Di07chc9Hzg4GSjI1nVkRAAAiUSCni16YkvgFhwZcQRj3MfAzNgMKU9SsDx2Ofod7IeNCRuRkZeh61Ar0LtTsX5+fnjppZfwz3/+EwCgUCjg7OyM999/H4sWLarQf/To0cjLy8PRo0eVbS+//DJ8fHywbds2tZ6Tp2KJtO/LuDQs+fYKpvRqg6VDPXUdDukDIYBftgKnlgGKEsDGDRi9F3Dg9kH6J7soG98mf4svr32Je3n3AADGEmMEuQRhgucEeDf31t5zN9ZTsUVFRbh48SKCgoKUbUZGRggKCkJsbGyl68TGxqr0B4ABAwZU2R8ACgsLkZ2drfJHRNo11tcZh0MDWNTR/5NIAP9Q4J3jQLNWQG4mIOVtcUg/NZM1Q0inEESPjMaGPhvQw6EHSkQJjt85jmmnpiG/OF/XIQIA9OpGLQ8fPkRpaSkcHBxU2h0cHHD9+vVK18nIyKi0f0ZG1YdHV69ejRUrVtQ9YCJSm0QigY+zla7DIH3k/BIw/SyQmQjYtdN1NETVkhpJEegSiECXQFx/fB37ru2Dtam13vxEmV4Vdg1l8eLFCAsLUy5nZ2fD2dlZhxEREb3gmtgAbV7RdRREGulo0xErA1bqOgwVelXY2dnZQSqVIjMzU6U9MzMTjo6V/5abo6OjRv0BQC6XQy6X1z1gIiIiIj2iV9fYyWQydO/eHadPn1a2KRQKnD59Gv7+lf8Ejb+/v0p/ADh16lSV/YmIiIgMlV4dsQOAsLAwhISEoEePHvD19cWGDRuQl5eHd955BwAwceJEtGzZEqtXrwYAzJ49G71798a6deswZMgQREVF4cKFC9i+fbsup0FERETU4PSusBs9ejQePHiAZcuWISMjAz4+Pjh+/LjyCxJpaWkwMvr/A409e/bEl19+iY8//hhLlixB+/btcfjwYXTu3FlXUyAiIiLSCb27j50u8D52REREpK8a7X3siIiIiKj2WNgRERERGQgWdkREREQGgoUdERERkYFgYUdERERkIFjYERERERkIFnZEREREBoKFHREREZGBYGFHREREZCD07ifFdKH8xzeys7N1HAkRERGRqvL6RJ0fC2NhByAnJwcA4OzsrONIiIiIiCqXk5MDS0vLavvwt2IBKBQK3Lt3DxYWFpBIJLoOB9nZ2XB2dsYff/zB366tJeaw7pjDumMO64b5qzvmsO70IYdCCOTk5KBFixYwMqr+KjoesQNgZGSEVq1a6TqMCpo1a8Y3Yh0xh3XHHNYdc1g3zF/dMYd1p+sc1nSkrhy/PEFERERkIFjYERERERkIFnZ6SC6XIzw8HHK5XNehNFrMYd0xh3XHHNYN81d3zGHdNbYc8ssTRERERAaCR+yIiIiIDAQLOyIiIiIDwcKOiIiIyECwsGsAW7ZsgaurK0xNTeHn54f4+Pgq+0ZEREAikaj8mZqaqvSZNGlShT4DBw7U9jR0SpMcAsCTJ08QGhoKJycnyOVydOjQAdHR0XUas7Gr7xwuX768wnbYsWNHbU9DpzTJYZ8+fSrkRyKRYMiQIco+QggsW7YMTk5OMDMzQ1BQEJKTkxtiKjpT3znk/rDm9/KGDRvg7u4OMzMzODs7Y+7cuSgoKKjTmI1dfedQr/aHgrQqKipKyGQysWvXLpGYmCimTp0qrKysRGZmZqX9d+/eLZo1aybS09OVfxkZGSp9QkJCxMCBA1X6PH78uCGmoxOa5rCwsFD06NFDDB48WPznP/8RqampIiYmRly+fLnWYzZ22shheHi46NSpk8p2+ODBg4aaUoPTNIePHj1Syc3Vq1eFVCoVu3fvVvZZs2aNsLS0FIcPHxa//fabeP3110WbNm3Es2fPGmhWDUsbOeT+sPoc7tu3T8jlcrFv3z6RmpoqTpw4IZycnMTcuXNrPWZjp40c6tP+kIWdlvn6+orQ0FDlcmlpqWjRooVYvXp1pf13794tLC0tqx0zJCREDB8+vB6j1G+a5vDzzz8Xbdu2FUVFRfU2ZmOnjRyGh4cLb2/v+g5Vb9V1m1m/fr2wsLAQubm5QgghFAqFcHR0FJ999pmyz5MnT4RcLhdfffVV/QavJ+o7h0Jwf1hTDkNDQ0Xfvn1V2sLCwkRAQECtx2zstJFDfdof8lSsFhUVFeHixYsICgpSthkZGSEoKAixsbFVrpebmwsXFxc4Oztj+PDhSExMrNAnJiYG9vb2cHd3x4wZM/Do0SOtzEHXapPD77//Hv7+/ggNDYWDgwM6d+6MTz/9FKWlpbUeszHTRg7LJScno0WLFmjbti3Gjx+PtLQ0rc5FV+pjm9m5cyfGjBkDc3NzAEBqaioyMjJUxrS0tISfnx+3wyo8n8Ny3B9WncOePXvi4sWLylONt2/fRnR0NAYPHlzrMRszbeSwnL7sD/lbsVr08OFDlJaWwsHBQaXdwcEB169fr3Qdd3d37Nq1C126dMHTp0/x97//HT179kRiYqLy92wHDhyIkSNHok2bNrh16xaWLFmCQYMGITY2FlKpVOvzaki1yeHt27fx008/Yfz48YiOjkZKSgpmzpyJ4uJihIeH12rMxkwbOQQAPz8/REREwN3dHenp6VixYgVeeeUVXL16FRYWFlqfV0Oq6zYTHx+Pq1evYufOncq2jIwM5RjPj1n+mCHRRg4B7g+B6nM4btw4PHz4EL169YIQAiUlJZg+fTqWLFlS6zEbM23kENCv/SELOz3j7+8Pf39/5XLPnj3h4eGBf/3rX1i5ciUAYMyYMcrHvby80KVLF7i5uSEmJgaBgYENHrO+USgUsLe3x/bt2yGVStG9e3fcvXsXn332mbIooeqpk8NBgwYp+3fp0gV+fn5wcXHB/v37MWXKFF2Frpd27twJLy8v+Pr66jqURquqHHJ/WL2YmBh8+umn2Lp1K/z8/JCSkoLZs2dj5cqVWLp0qa7DaxTUyaE+7Q9Z2GmRnZ0dpFIpMjMzVdozMzPh6Oio1hgmJibo2rUrUlJSquzTtm1b2NnZISUlxeB2ZLXJoZOTE0xMTFQ+rXt4eCAjIwNFRUX18ro0JtrIoUwmq7COlZUVOnToUO222ljVZZvJy8tDVFQUPvnkE5X28vUyMzPh5OSkMqaPj0/9BK5HtJHDynB/qGrp0qUIDg7Gu+++C6Cs+M3Ly8N7772Hjz76iPvD/1OXHBoZVbyqTZf7Q15jp0UymQzdu3fH6dOnlW0KhQKnT59WOSpXndLSUly5ckVlx/+8P//8E48ePaq2T2NVmxwGBAQgJSUFCoVC2Xbz5k04OTlBJpPVy+vSmGgjh5XJzc3FrVu3uB0+58CBAygsLMSECRNU2tu0aQNHR0eVMbOzsxEXF8ft8DlV5bAy3B+qys/Pr1B4lH9gE0Jwf4i657AyOt0f6va7G4YvKipKyOVyERERIZKSksR7770nrKyslLcwCQ4OFosWLVL2X7FihThx4oS4deuWuHjxohgzZowwNTUViYmJQgghcnJyxPz580VsbKxITU0VP/74o+jWrZto3769KCgo0MkctU3THKalpQkLCwsxa9YscePGDXH06FFhb28v/va3v6k9pqHRRg7nzZsnYmJiRGpqqjh37pwICgoSdnZ24v79+w0+v4agaQ7L9erVS4wePbrSMdesWSOsrKzEd999J37//XcxfPhwg7/dSX3mkPvDmnMYHh4uLCwsxFdffSVu374tTp48Kdzc3MTbb7+t9piGRhs51Kf9IQu7BrB582bRunVrIZPJhK+vr/jll1+Uj/Xu3VuEhIQol+fMmaPs6+DgIAYPHiwSEhKUj+fn54v+/fuL5s2bCxMTE+Hi4iKmTp1qsG/AcprkUAghzp8/L/z8/IRcLhdt27YVq1atEiUlJWqPaYjqO4ejR48WTk5OQiaTiZYtW4rRo0eLlJSUhpqOTmiaw+vXrwsA4uTJk5WOp1AoxNKlS4WDg4OQy+UiMDBQ3LhxQ5tT0Ln6zCH3hzXnsLi4WCxfvly4ubkJU1NT4ezsLGbOnCmysrLUHtMQ1XcO9Wl/KBGiiuOIRERERNSo8Bo7IiIiIgPBwo6IiIjIQLCwIyIiIjIQLOyIiIiIDAQLOyIiIiIDwcKOiIiIyECwsCMiIiIyECzsiIiIiAwECzsiIiIiA8HCjoiIiMhAsLAj0oE+ffpgzpw5Wh/j+T41LWtTQz6XttT3HGrzGjbkc+tCXbZRfZnTo0ePYG9vjzt37qi9zpgxY7Bu3TrtBUUvDGNdB0CkzyZNmoQ9e/YAAExMTNC6dWtMnDgRS5YsgbGx/r99Dh06BBMTE7Uf79OnD3x8fLBhw4Y6PW99jdPQY9ekpnzqerzG8tya0CROfZnTqlWrMHz4cLi6uirbMjIyEBYWhp9++gmPHz+GnZ0dwsLCMH/+fADAxx9/jFdffRXvvvsuLC0tdRQ5GQL9/5+JSMcGDhyI3bt3o7CwENHR0QgNDYWJiQkWL15coW9RURFkMpkOoqycjY1NnR4nVfWdr4bIf1XbZGN57TWJUx/mlJ+fj507d+LEiRMq7dOmTUNxcTF+/PFHWFtbIzMzE0+ePFE+3rlzZ7i5uWHv3r0IDQ1t4KjJkPBULFEN5HI5HB0d4eLighkzZiAoKAjff/89gLKjR7NmzcKcOXNgZ2eHAQMGAAAKCwvxwQcfwN7eHqampujVqxd+/fVXlXFLSkowa9YsWFpaws7ODkuXLoUQQvn48ePH0atXL1hZWcHW1hZDhw7FrVu3NBqjplNTf3180qRJOHPmDDZu3AiJRAKJRIJPPvkEtra2KCwsVFlvxIgRCA4OrnTMysYpPyWlUCiwcOFC2NjYwNHREcuXL1dZt6Y5Vze2JuOUz/2DDz6oNp7q8qXuGAcPHoSXlxfMzMxga2uLoKAg5OXlVTpeXl4eJk6ciKZNm8LJyanSU3MKhQKrV69GmzZtYGZmBm9vbxw8eFAlpsq2yZrmUl2cVa3//vvvY86cObC2toaDgwN27NiBvLw8vPPOO7CwsEC7du3www8/KNdR53WpKU6FQoG1a9eiXbt2kMvlaN26NVatWlVp35reh66urhWO/Pr4+Ki8hprmJTo6GnK5HC+//LJKe2FhIVJTUxEbG4uioiJ069YNffv2VekzbNgwREVFVZsPopqwsCPSkJmZGYqKipTLe/bsgUwmw7lz57Bt2zYAwMKFC/HNN99gz549SEhIQLt27TBgwAA8fvxYZT1jY2PEx8dj48aN+Mc//oF///vfysfz8vIQFhaGCxcu4PTp0zAyMsIbb7wBhUKh9hia2LhxI/z9/TF16lSkp6cjPT0d8+bNQ2lpqbKQBYD79+/j2LFjmDx5strjODs7K+M1NzdHXFwc1q5di08++QSnTp1Se87Vjf1X6uROnXjUUd0Y6enpGDt2LCZPnoxr164hJiYGI0eOVCm+/2rBggU4c+YMvvvuO5w8eRIxMTFISEhQ6bN69WpERkZi27ZtSExMxNy5czFhwgScOXNGJabnt8nqaBrnX5/Hzs4O8fHxeP/99zFjxgy89dZb6NmzJxISEtC/f38EBwcjPz8fgPqvS3UWL16MNWvWYOnSpUhKSsKXX34JBweHSvuq8z6s77ycPXsW3bt3V2krKSnBwIEDERUVhX79+mHLli14/fXXkZubq9LP19cX8fHxFT5IEWlEEFGVQkJCxPDhw4UQQigUCnHq1Ckhl8vF/PnzhRBC9O7dW3Tt2lVlndzcXGFiYiL27dunbCsqKhItWrQQa9euVa7n4eEhFAqFss+HH34oPDw8qozlwYMHAoC4cuWK2mP07t1bzJ49u9bLQggxY8YMMWjQIOXyunXrRNu2bVWe93mVjdO7d2/Rq1cvlbaXXnpJfPjhh1WO8/ycqxq7JlWNo2k8leWrujEuXrwoAIg7d+7UOF5OTo6QyWRi//79yscfPXokzMzMlH0KCgpEkyZNxPnz51XGmTJlihg7dqxyzOe3yZqeu6Y4q1r/r3MvKSkR5ubmIjg4WNmWnp4uAIjY2NhKx1Dn9f3rcnZ2tpDL5WLHjh01zkmd96GLi4tYv369yhje3t4iPDxcCFG7vAwfPlxMnjxZpW3mzJni4MGDKm0uLi7KOMr99ttvGj8f0fN4xI6oBkePHkXTpk1hamqKQYMGYfTo0Sqnap7/dH7r1i0UFxcjICBA2WZiYgJfX19cu3ZN2fbyyy9DIpEol/39/ZGcnIzS0lIAQHJyMsaOHYu2bduiWbNmygux09LS1B6jPkydOhUnT57E3bt3AQARERGYNGmSyvOqq0uXLirLTk5OuH//vnJZnTmrQ91xaopHHdWN4e3tjcDAQHh5eeGtt97Cjh07kJWVVek4t27dQlFREfz8/JRtNjY2cHd3Vy6npKQgPz8f/fr1Q9OmTZV/kZGRKqc0n98ma6JJnFXNXSqVwtbWFl5eXsq28iNp5fmo6+t77do1FBYWIjAwsMa+6r4Pq1ObvDx79gympqbK5cuXL2Pv3r14/fXXVfpZWloiPT1dpc3MzAwAlEc4iWqDhR1RDV577TVcvnwZycnJePbsmfLUW7m//rs+DRs2DI8fP8aOHTsQFxeHuLg4AFA5DdwQunbtCm9vb0RGRuLixYtITEzEpEmTajXW899YlEgkKqfh6mvO6o5TUzzqqG4MqVSKU6dO4YcffoCnpyc2b94Md3d3pKamavQc5cpP3R07dgyXL19W/iUlJalcZ6fpNlnbOCub+1/byov/8nzU9fUtL3zqi5GRUYXTqsXFxcp/1yYvdnZ2KsXfN998gw4dOqjkJS8vDzdv3kSnTp1U1i0/Rdy8efM6zYtebCzsiGpgbm6Odu3aoXXr1mrd4sTNzU15fVO54uJi/Prrr/D09FS2lf+nVu6XX35B+/btIZVK8ejRI9y4cQMff/wxAgMD4eHhUemRgurGqA2ZTFbp0b53330XERER2L17N4KCgiq9rk2dcaqj7pxrGlvdcRqKRCJBQEAAVqxYgUuXLkEmk+Hbb7+t0M/NzQ0mJiYqr2lWVhZu3rypXPb09IRcLkdaWhratWun8lfTa1JfcdZWfbwu7du3h5mZGU6fPl1jX3Xeh82bN1c5apadnV2haNM0L127dkVSUpJyOSsrq8KXLbZv3w4AGDlypEr71atX0apVK9jZ2dU4P6Kq8HYnRPXM3NwcM2bMwIIFC2BjY4PWrVtj7dq1yM/Px5QpU5T90tLSEBYWhmnTpiEhIQGbN29WfgvS2toatra22L59O5ycnJCWloZFixZVeK7qxqgNV1dXxMXF4c6dO2jatClsbGxgZGSEcePGYf78+dixYwciIyNrNU5N1J1zVTFqOk5DiIuLw+nTp9G/f3/Y29sjLi4ODx48gIeHR4W+TZs2xZQpU7BgwQLY2trC3t4eH330kcrcLCwsMH/+fMydOxcKhQK9evXC06dPce7cOTRr1gwhISFaj7O26uN1MTU1xYcffoiFCxdCJpMhICAADx48QGJiosp7C1Dvfdi3b19ERERg2LBhsLKywrJly1Q+FNUmLwMGDMDixYuRlZUFa2tr+Pn5YcuWLVi/fj2GDh2K48ePY/Hixdi6dSusra1V1j179iz69++vUU6InsfCjkgL1qxZA4VCgeDgYOTk5KBHjx44ceKEyo584sSJePbsGXx9fSGVSjF79my89957AMpOEUVFReGDDz5A586d4e7ujk2bNqFPnz4qz1PdGLUxf/58hISEwNPTE8+ePUNqaipcXV1haWmJN998E8eOHcOIESNqNU5N1J1zVTFqOk5DaNasGX7++Wds2LAB2dnZcHFxwbp16zBo0KBK+3/22WfIzc3FsGHDYGFhgXnz5uHp06cqfVauXInmzZtj9erVuH37NqysrNCtWzcsWbKkweKsjfp6XZYuXQpjY2MsW7YM9+7dg5OTE6ZPn15p35reh4sXL0ZqaiqGDh0KS0tLrFy5UmVbrU1evLy80K1bN+zfvx/Tpk3DhAkTkJaWhk2bNiE8PBxeXl44dOgQBg8erLJeQUEBDh8+jOPHj2uUD6LnScTzFxgQEVUiMDAQnTp1wqZNm3QdCpFeO3bsGBYsWICrV6+qHHGtzueff45vv/0WJ0+e1HJ0ZOh4xI6IqpWVlYWYmBjExMRg69atug6HSO8NGTIEycnJuHv3rtrXPpqYmGDz5s1ajoxeBDxiR0TVcnV1RVZWFpYuXar8XUsiItJPLOyIiIiIDARvd0JERERkIFjYERERERkIFnZEREREBoKFHREREZGBYGFHREREZCBY2BEREREZCBZ2RERERAaChR0RERGRgWBhR0RERGQgWNgRERERGQgWdkREREQG4n8BWyVGIBmHEFMAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "def plot_one_minus_lambda_vs_delta():\n",
        "    # Define sample p1 values and markers for plotting\n",
        "    p1_values = [0.4, 0.6, 0.8]\n",
        "    markers = ['o', 's', '^']  # Circle, square, and triangle markers\n",
        "\n",
        "    # Create a figure and axis for the plot\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.set_title('$1-\\lambda^*$ as a function of $\\delta$ with different values of $p_1$')\n",
        "\n",
        "    # Initialize parameters with random values within a range\n",
        "    params = {\n",
        "        'w': random.uniform(0.001, 0.999),\n",
        "        'beta': random.uniform(0.001, 0.999),\n",
        "        'C_cyb': random.uniform(0.001, 0.999)\n",
        "    }\n",
        "\n",
        "    for i, p_1 in enumerate(p1_values):\n",
        "        # Set p1 value\n",
        "        params['p_1'] = p_1\n",
        "\n",
        "        # Ensure beta and C_cyb satisfy a condition\n",
        "        while params['beta'] <= params['C_cyb'] / params['p_1']:\n",
        "            params['beta'] = random.uniform(0.001, 0.999)\n",
        "            params['C_cyb'] = random.uniform(0.001, 0.999)\n",
        "\n",
        "        # Compute x and y values based on parameters\n",
        "        compute_x_y(params)\n",
        "\n",
        "        # Generate a range of delta values\n",
        "        delta_range = np.linspace(params['y_1'] + 0.001, params['x_1'] - 0.001, 100)\n",
        "        one_minus_lambda_values = []\n",
        "\n",
        "        # Calculate 1 - lambda values for each delta in the range\n",
        "        for delta in delta_range:\n",
        "            params['delta'] = delta\n",
        "            compute_lambda(params)\n",
        "            one_minus_lambda_values.append(1 - params['lambda^_*'])\n",
        "\n",
        "        # Plot 1 - lambda values with a label and marker\n",
        "        ax.plot(delta_range, one_minus_lambda_values, label=f\"$p_1$={p_1:.2f}\", marker=markers[i], markevery=10)\n",
        "\n",
        "    # Set labels and legend for the subplot\n",
        "    ax.set_xlabel('Probability that an insider is malicious ($\\delta$)')\n",
        "    ax.set_ylabel('$1-\\lambda^*$')\n",
        "    ax.legend()\n",
        "\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "# Seed and call the plot function\n",
        "random.seed(0)\n",
        "params = {}\n",
        "plot_one_minus_lambda_vs_delta()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3man_ibsDndg"
      },
      "source": [
        "##Figure 7: $\\eta^*$ as a function of $C_{cyb}$ with different values of $p_1$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "_mTp_oBp6eug",
        "outputId": "863cb8e5-7755-43ee-cc00-a9a52734c928"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "def plot_eta_vs_C_cyb():\n",
        "    # Define sample p1 values and markers for plotting\n",
        "    p1_values = [0.4, 0.6, 0.8]\n",
        "    markers = ['o', 's', '^']  # Circle, square, and triangle markers\n",
        "\n",
        "    # Create a figure and axis for the plot\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.set_title('$\\eta^*$ as a function of $C_{cyb}$ with different values of $p_1$')\n",
        "\n",
        "    # Initialize parameters with random values within a range\n",
        "    params = {\n",
        "        'w': random.uniform(0.001, 0.999),\n",
        "        'beta': random.uniform(0.001, 0.999)\n",
        "    }\n",
        "\n",
        "    C_cyb_range = np.linspace(0.001, 0.999, 200)\n",
        "\n",
        "    for i, p_1 in enumerate(p1_values):\n",
        "        # Set p1 value\n",
        "        params['p_1'] = p_1\n",
        "\n",
        "        # Set a random p2 value within a range\n",
        "        params['p_2'] = random.uniform(0.001, params['p_1'] - 0.001)\n",
        "\n",
        "        # Compute x and y values based on parameters\n",
        "        compute_x_y(params)\n",
        "        # Set a random delta value within a range\n",
        "        params['delta'] = random.uniform(params['y_1'] + 0.001, params['x_1'] - 0.001)\n",
        "\n",
        "        eta_values = []\n",
        "\n",
        "        for C_cyb in C_cyb_range:\n",
        "            params['C_cyb'] = C_cyb\n",
        "            if params['beta'] > params['C_cyb'] / params['p_1']:\n",
        "                compute_lambda(params)\n",
        "                compute_eta(params)\n",
        "                eta_values.append(params['eta^*'])\n",
        "            else:\n",
        "                eta_values.append(np.nan)  # Appending NaN so the lengths match\n",
        "\n",
        "        # Plot eta values with a label and marker\n",
        "        ax.plot(C_cyb_range, eta_values, label=f\"$p_1$={p_1:.2f}\", marker=markers[i], markevery=10)\n",
        "\n",
        "    # Set labels and legend for the subplot\n",
        "    ax.set_xlabel('Cost of cyber attack $(C_{cyb})$')\n",
        "    ax.set_ylabel('$\\eta^*$')\n",
        "    ax.legend()\n",
        "\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "# Seed and call the plot function\n",
        "random.seed(0)\n",
        "params = {}\n",
        "plot_eta_vs_C_cyb()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PtbzxLpqDv09"
      },
      "source": [
        "##Figure 8: 1-$\\eta^*$ as a function of $C_{cyb}$ with different values of $p_2$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "y6MLHd_XBdY6",
        "outputId": "5134f1de-a333-4b4d-e630-81b3100a9161"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "def plot_one_minus_eta_vs_C_cyb():\n",
        "    # Define sample p1 values and markers for plotting\n",
        "    p1_values = [0.3, 0.5, 0.7]\n",
        "    markers = ['o', 's', '^']  # Circle, square, and triangle markers\n",
        "\n",
        "    # Create a figure and axis for the plot\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.set_title('$1-\\eta^*$ as a function of $C_{cyb}$ with different values of $p_1$')\n",
        "\n",
        "    # Initialize parameters with random values within a range\n",
        "    params = {\n",
        "        'w': random.uniform(0.001, 0.999),\n",
        "        'beta': random.uniform(0.001, 0.999)\n",
        "    }\n",
        "\n",
        "    C_cyb_range = np.linspace(0.001, 0.999, 100)\n",
        "\n",
        "    for i, p_1 in enumerate(p1_values):\n",
        "        # Set p1 value\n",
        "        params['p_1'] = p_1\n",
        "\n",
        "        # Compute x and y values based on parameters\n",
        "        compute_x_y(params)\n",
        "\n",
        "        # Set a random delta value within a range\n",
        "        params['delta'] = random.uniform(params['y_1'] + 0.001, params['x_1'] - 0.001)\n",
        "\n",
        "        one_minus_eta_values = []\n",
        "\n",
        "        for C_cyb in C_cyb_range:\n",
        "            params['C_cyb'] = C_cyb\n",
        "            if params['beta'] > params['C_cyb'] / params['p_1']:\n",
        "                compute_lambda(params)\n",
        "                compute_eta(params)\n",
        "                one_minus_eta_values.append(1 - params['eta^*'])\n",
        "            else:\n",
        "                one_minus_eta_values.append(np.nan)  # Appending NaN for continuity\n",
        "\n",
        "        # Plot 1 - eta values with a label and marker\n",
        "        ax.plot(C_cyb_range, one_minus_eta_values, label=f\"$p_1$={p_1:.2f}\", marker=markers[i], markevery=10)\n",
        "\n",
        "    # Set labels and legend for the subplot\n",
        "    ax.set_xlabel('Cost of cyber attack $(C_{cyb})$')\n",
        "    ax.set_ylabel('$1-\\eta^*$')\n",
        "    ax.legend()\n",
        "\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "# Seed and call the plot function\n",
        "random.seed(0)\n",
        "params = {}\n",
        "plot_one_minus_eta_vs_C_cyb()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AGiS483iJxgA"
      },
      "source": [
        "# Proposition 2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1EAoo8igC7B_"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import random\n",
        "\n",
        "\n",
        "def compute_x_y(params):\n",
        "    params['x^*'] = 1 / (1 + params['w'] * (1 - 2*params['p_1']))\n",
        "    params['y^*'] = 1 / (1 + params['w'] * (1 - 2*params['p_2']))\n",
        "\n",
        "def compute_lambda(params):\n",
        "    numerator = 1 + params['w'] * (1 - 2 * params['p_2']) - 1 / params['delta']\n",
        "    denominator = 2 * params['w'] * (params['p_1'] - params['p_2'])\n",
        "    params['lambda_1^_*'] = numerator / denominator\n",
        "\n",
        "def compute_eta(params):\n",
        "    params['eta_1^*'] = params['C_cyb'] / (2*params['beta']*(params['p_1']-params['p_2']))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "684aHBjmMD6j"
      },
      "source": [
        "## $\\lambda_1^*$ as a function of $\\delta$ with different values of $p_1$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XI72COZvLVV3"
      },
      "outputs": [],
      "source": [
        "def plot_lambda_vs_delta():\n",
        "    p1_values = [0.3, 0.4, 0.5]\n",
        "    markers = ['o', 's', '^']  # Circle, square, and triangle markers\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.set_title(r'$\\lambda^*_1$ as a function of $\\delta$ with different values of $p_1$')\n",
        "    params['w'] = random.uniform(0.001, 0.999)\n",
        "    params['beta'] = random.uniform(0.001, 0.999)\n",
        "    params['C_cyb'] = random.uniform(0.001, 0.999)\n",
        "\n",
        "    for i, p_1 in enumerate(p1_values):\n",
        "        params['p_1'] = p_1\n",
        "        params['p_2'] = random.uniform(0.001, params['p_1']-0.001)\n",
        "        while params['beta']<=params['C_cyb']/2/(params['p_1']-params['p_2']):\n",
        "              params['beta'] = random.uniform(0.001, 0.999)\n",
        "              params['C_cyb'] = random.uniform(0.001, 0.999)\n",
        "\n",
        "        compute_x_y(params)\n",
        "        delta_range = np.linspace(params['y^*'] + 0.001, params['x^*'] - 0.001, 150)\n",
        "        lambda_values = []\n",
        "\n",
        "        for delta in delta_range:\n",
        "            params['delta'] = delta\n",
        "            compute_lambda(params)\n",
        "            lambda_values.append(params['lambda_1^_*'])\n",
        "\n",
        "        ax.plot(delta_range, lambda_values, label=f\"$p_1$={p_1:.2f}\", marker=markers[i], markevery=10)\n",
        "    # Set labels and legend for the subplot\n",
        "    ax.set_xlabel('Probability that an insider is malicious ($\\delta$)')\n",
        "    ax.set_ylabel(r'$\\lambda^*_1$')\n",
        "\n",
        "    ax.legend()\n",
        "\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "# Seed and call the plot function\n",
        "random.seed(0)\n",
        "params = {}\n",
        "plot_lambda_vs_delta()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## $\\lambda_1^*$ as a function of $p_1$ with different values of $\\delta$"
      ],
      "metadata": {
        "id": "ZLtgGgS_Ssoe"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Yu0QvpWVPNff"
      },
      "outputs": [],
      "source": [
        "def plot_lambda_vs_p1():\n",
        "    # Define delta values and markers for plotting\n",
        "    delta_values = [0.6, 0.7, 0.8]\n",
        "    markers = ['o', 's', '^']  # Circle, square, and triangle markers\n",
        "\n",
        "    # Create a figure and axis for the plot\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.set_title('$\\lambda^*_1$ as a function of $p1$ with different values of $\\delta$')\n",
        "\n",
        "    p1_start = 0.5\n",
        "    p1_values = np.linspace(p1_start, 0.999, 100)\n",
        "\n",
        "    # Initialize parameters with random values within a range\n",
        "    params = {\n",
        "        'w': 0.9,\n",
        "        'C_cyb': random.uniform(0.001, 0.999),\n",
        "        'p_2': 0.001\n",
        "    }\n",
        "\n",
        "    for i, delta_ in enumerate(delta_values):\n",
        "        lambda_values = []\n",
        "        params['delta'] = delta_\n",
        "\n",
        "        for p_1 in p1_values:\n",
        "            params['p_1'] = p_1\n",
        "\n",
        "            # Set beta within a range based on conditions\n",
        "            params['beta'] = random.uniform(params['C_cyb'] / 2 / (params['p_1'] - params['p_2']), 0.999)\n",
        "\n",
        "            compute_x_y(params)\n",
        "\n",
        "            if not (params['y^*'] < params['delta'] < params['x^*']):\n",
        "                print(\"WARN\")\n",
        "\n",
        "            compute_lambda(params)\n",
        "            lambda_values.append(params['lambda_1^_*'])\n",
        "\n",
        "        ax.plot(p1_values, lambda_values, label=f\"$\\\\delta$={delta_:.2f}\", marker=markers[i], markevery=10)\n",
        "\n",
        "    # Set labels and legend for the subplot\n",
        "    ax.set_xlabel('Probability that the malicious insider with proper authentication is detected ($p_1$)')\n",
        "    ax.set_ylabel('$\\lambda^*_1$')\n",
        "    ax.legend()\n",
        "\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "# Seed and call the plot function\n",
        "random.seed(0)\n",
        "params = {}\n",
        "plot_lambda_vs_p1()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## $\\lambda_1^*$ as a function of $\\delta$ with different values of $p_1$"
      ],
      "metadata": {
        "id": "wyHTiB9e916j"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qiDUkh-oPNfg"
      },
      "outputs": [],
      "source": [
        "def plot_lambda_vs_delta():\n",
        "    p1_values = [0.3, 0.4, 0.5]\n",
        "    markers = ['o', 's', '^']  # Circle, square, and triangle markers\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.set_title('$\\lambda^*_1$ as a function of $\\delta$ with different values of $p_1$')\n",
        "\n",
        "    params['w'] = random.uniform(0.001, 0.999)\n",
        "    params['beta'] = random.uniform(0.001, 0.999)\n",
        "    params['C_cyb'] = random.uniform(0.001, 0.999)\n",
        "\n",
        "    for i, p_1 in enumerate(p1_values):\n",
        "        params['p_1'] = p_1\n",
        "        params['p_2'] = random.uniform(0.001, params['p_1']-0.001)\n",
        "        while params['beta']<=params['C_cyb']/2/(params['p_1']-params['p_2']):\n",
        "              params['beta'] = random.uniform(0.001, 0.999)\n",
        "              params['C_cyb'] = random.uniform(0.001, 0.999)\n",
        "\n",
        "        compute_x_y(params)\n",
        "        delta_range = np.linspace(params['y^*'] + 0.001, params['x^*'] - 0.001, 150)\n",
        "        lambda_values = []\n",
        "\n",
        "        for delta in delta_range:\n",
        "            params['delta'] = delta\n",
        "            compute_lambda(params)\n",
        "            lambda_values.append(params['lambda_1^_*'])\n",
        "\n",
        "        ax.plot(delta_range, lambda_values, label=f\"$p_1$={p_1:.2f}\", marker=markers[i], markevery=10)\n",
        "\n",
        "    # Set labels and legend for the subplot\n",
        "    ax.set_xlabel('Probability that an insider is malicious ($\\delta$)')\n",
        "    ax.set_ylabel('$\\lambda^*_1$')\n",
        "    ax.legend()\n",
        "\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "# Seed and call the plot function\n",
        "random.seed(0)\n",
        "params = {}\n",
        "plot_lambda_vs_delta()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sSKHWCimPIJn"
      },
      "source": [
        "## $\\lambda_1^*$ as a function of $\\delta$ with different values of $p_2$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uBkq9RouMKMW"
      },
      "outputs": [],
      "source": [
        "def plot_lambda_vs_delta():\n",
        "    # Define p2 values and markers for plotting\n",
        "    p2_values = [0.2, 0.4, 0.6]\n",
        "    markers = ['o', 's', '^']  # Circle, square, and triangle markers\n",
        "\n",
        "    # Create a figure and axis for the plot\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.set_title('$\\lambda^*_1$ as a function of $\\delta$ with different values of $p_2$')\n",
        "\n",
        "    # Initialize parameters with random values within a range\n",
        "    params = {\n",
        "        'w': random.uniform(0.001, 0.999),\n",
        "        'beta': random.uniform(0.001, 0.999),\n",
        "        'C_cyb': random.uniform(0.001, 0.999),\n",
        "        'p_1': 0.8\n",
        "    }\n",
        "\n",
        "    for i, p_2 in enumerate(p2_values):\n",
        "        params['p_2'] = p_2\n",
        "\n",
        "        # Ensure beta and C_cyb satisfy a condition\n",
        "        while params['beta'] <= params['C_cyb'] / 2 / (params['p_1'] - params['p_2']):\n",
        "            params['beta'] = random.uniform(0.001, 0.999)\n",
        "            params['C_cyb'] = random.uniform(0.001, 0.999)\n",
        "\n",
        "        compute_x_y(params)\n",
        "\n",
        "        delta_range = np.linspace(params['y^*'] + 0.001, params['x^*'] - 0.001, 100)\n",
        "        lambda_values = []\n",
        "\n",
        "        for delta in delta_range:\n",
        "            params['delta'] = delta\n",
        "            compute_lambda(params)\n",
        "            lambda_values.append(params['lambda_1^_*'])\n",
        "\n",
        "        ax.plot(delta_range, lambda_values, label=f\"$p_2$={p_2:.2f}\", marker=markers[i], markevery=10)\n",
        "\n",
        "    # Set labels and legend for the subplot\n",
        "    ax.set_xlabel('Probability that an insider is malicious ($\\delta$)')\n",
        "    ax.set_ylabel('$\\lambda^*_1$')\n",
        "    ax.legend()\n",
        "\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "# Seed and call the plot function\n",
        "random.seed(0)\n",
        "params = {}\n",
        "plot_lambda_vs_delta()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "186zlNjvPzXt"
      },
      "source": [
        "## 1-$\\lambda_1^*$ as a function of $\\delta$ with different values of $p_2$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uw8vjYmeOz_q"
      },
      "outputs": [],
      "source": [
        "\n",
        "def plot_one_minus_lambda_vs_delta():\n",
        "    # Define p2 values and markers for plotting\n",
        "    p2_values = [0.2, 0.4, 0.6]\n",
        "    markers = ['o', 's', '^']  # Circle, square, and triangle markers\n",
        "\n",
        "    # Create a figure and axis for the plot\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.set_title('$1-\\lambda^*_1$ as a function of $\\delta$ with different values of $p_2$')\n",
        "\n",
        "    # Initialize parameters with random values within a range\n",
        "    params = {\n",
        "        'w': random.uniform(0.001, 0.999),\n",
        "        'beta': random.uniform(0.001, 0.999),\n",
        "        'C_cyb': random.uniform(0.001, 0.999),\n",
        "        'p_1': 0.8\n",
        "    }\n",
        "\n",
        "    for i, p_2 in enumerate(p2_values):\n",
        "        params['p_2'] = p_2\n",
        "\n",
        "        # Ensure beta and C_cyb satisfy a condition\n",
        "        while params['beta'] <= params['C_cyb'] / params['p_1']:\n",
        "            params['beta'] = random.uniform(0.001, 0.999)\n",
        "            params['C_cyb'] = random.uniform(0.001, 0.999)\n",
        "\n",
        "        compute_x_y(params)\n",
        "\n",
        "        delta_range = np.linspace(params['y^*'] + 0.001, params['x^*'] - 0.001, 100)\n",
        "        one_minus_lambda_values = []\n",
        "\n",
        "        for delta in delta_range:\n",
        "            params['delta'] = delta\n",
        "            compute_lambda(params)\n",
        "            one_minus_lambda_values.append(1 - params['lambda_1^_*'])\n",
        "\n",
        "        ax.plot(delta_range, one_minus_lambda_values, label=f\"$p_2$={p_2:.2f}\", marker=markers[i], markevery=10)\n",
        "\n",
        "    # Set labels and legend for the subplot\n",
        "    ax.set_xlabel('Probability that an insider is malicious ($\\delta$)')\n",
        "    ax.set_ylabel('$1-\\lambda^*_1$')\n",
        "    ax.legend()\n",
        "\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "# Seed and call the plot function\n",
        "random.seed(0)\n",
        "params = {}\n",
        "plot_one_minus_lambda_vs_delta()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LfofnHs9QbFa"
      },
      "source": [
        "## $\\eta_1^*$ as a function of $C_{cyb}$ with different values of $p_1$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uVwySlRJPMsb"
      },
      "outputs": [],
      "source": [
        "def plot_eta_vs_C_cyb():\n",
        "    # Define p1 values and markers for plotting\n",
        "    p1_values = [0.3, 0.4, 0.5]\n",
        "    markers = ['o', 's', '^']  # Circle, square, and triangle markers\n",
        "\n",
        "    # Create a figure and axis for the plot\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.set_title('$\\eta^*_1$ as a function of $C_{cyb}$ with different values of $p_1$')\n",
        "\n",
        "    # Initialize parameters with random values within a range\n",
        "    params = {\n",
        "        'w': random.uniform(0.001, 0.999),\n",
        "        'beta': random.uniform(0.001, 0.999)\n",
        "    }\n",
        "\n",
        "    C_cyb_range = np.linspace(0.001, 0.15, 150)\n",
        "\n",
        "    for i, p_1 in enumerate(p1_values):\n",
        "        params['p_1'] = p_1\n",
        "        params['p_2'] = random.uniform(0.001, params['p_1'] - 0.001)\n",
        "        compute_x_y(params)\n",
        "        params['delta'] = random.uniform(params['y^*'] + 0.001, params['x^*'] - 0.001)\n",
        "        eta_values = []\n",
        "\n",
        "        for C_cyb in C_cyb_range:\n",
        "            params['C_cyb'] = C_cyb\n",
        "            if params['beta'] > params['C_cyb'] / params['p_1']:\n",
        "                compute_lambda(params)\n",
        "                compute_eta(params)\n",
        "                eta_values.append(params['eta_1^*'])\n",
        "            else:\n",
        "                eta_values.append(np.nan)  # Appending NaN so the lengths match\n",
        "\n",
        "        ax.plot(C_cyb_range, eta_values, label=f\"$p_1$={p_1:.2f}\", marker=markers[i], markevery=10)\n",
        "\n",
        "    # Set labels and legend for the subplot\n",
        "    ax.set_xlabel('Cost of cyber attack $(C_{cyb})$')\n",
        "    ax.set_ylabel('$\\eta^*_1$')\n",
        "    ax.legend()\n",
        "\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "# Seed and call the plot function\n",
        "random.seed(0)\n",
        "params = {}\n",
        "plot_eta_vs_C_cyb()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## $\\eta_1^*$ as a function of $\\beta$ with different values of $C_{{cyb}}$"
      ],
      "metadata": {
        "id": "L1JWzWSfUn2P"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7iiZr3f7PNfg"
      },
      "outputs": [],
      "source": [
        "\n",
        "def plot_eta_vs_beta_v2():\n",
        "    # Define C_cyb values and markers for plotting\n",
        "    C_cybs = [0.1, 0.14, 0.18]\n",
        "    markers = ['o', 's', '^']  # Circle, square, and triangle markers\n",
        "\n",
        "    # Create a figure and axis for the plot\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.set_title('$\\eta^*_1$ as a function of $\\\\beta$ with different values of $C_{cyb}$')\n",
        "\n",
        "    # Initialize parameters with specific values and random values within a range\n",
        "    params = {\n",
        "        'p_2': 0.4,\n",
        "        'p_1': 0.6,\n",
        "        'w': random.uniform(0.001, 0.999)\n",
        "    }\n",
        "\n",
        "    for i, Ccyb in enumerate(C_cybs):\n",
        "        eta_values = []\n",
        "        params['C_cyb'] = Ccyb\n",
        "\n",
        "        # Generate beta values within a specific range\n",
        "        beta_ranges = np.linspace(params['C_cyb'] / 2 / (params['p_1'] - params['p_2']), 0.999, 150)\n",
        "\n",
        "        for b in beta_ranges:\n",
        "            params['beta'] = b\n",
        "            compute_x_y(params)\n",
        "            params['delta'] = random.uniform(params['y^*'] + 0.001, params['x^*'] - 0.001)\n",
        "            compute_eta(params)\n",
        "            eta_values.append(params['eta_1^*'])\n",
        "\n",
        "        ax.plot(beta_ranges, eta_values, label=f\"$C_{{cyb}}$={Ccyb:.2f}\", marker=markers[i], markevery=10)\n",
        "\n",
        "    # Set labels and legend for the subplot\n",
        "    ax.set_xlabel('$\\\\beta$')\n",
        "    ax.set_ylabel('$\\eta^*_1$')\n",
        "    ax.legend()\n",
        "\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "# Seed and call the plot function\n",
        "random.seed(0)\n",
        "params = {}\n",
        "plot_eta_vs_beta_v2()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OwdG2aF0Qvqj"
      },
      "source": [
        "## $\\eta_1^*$ as a function of $C_{cyb}$ with different values of $p_2$"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 1-$\\eta_1^*$ as a function of $\\beta$ with different values of $C_{{cyb}}$"
      ],
      "metadata": {
        "id": "_5FkKIgjgfCd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "def plot_eta_vs_beta_v2():\n",
        "    # Define C_cyb values and markers for plotting\n",
        "    C_cybs = [0.1, 0.14, 0.18]\n",
        "    markers = ['o', 's', '^']  # Circle, square, and triangle markers\n",
        "\n",
        "    # Create a figure and axis for the plot\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.set_title('1-$\\eta^*_1$ as a function of $\\\\beta$ with different values of $C_{cyb}$')\n",
        "\n",
        "    # Initialize parameters with specific values and random values within a range\n",
        "    params = {\n",
        "        'p_2': 0.4,\n",
        "        'p_1': 0.6,\n",
        "        'w': random.uniform(0.001, 0.999)\n",
        "    }\n",
        "\n",
        "    for i, Ccyb in enumerate(C_cybs):\n",
        "        eta_values = []\n",
        "        params['C_cyb'] = Ccyb\n",
        "\n",
        "        # Generate beta values within a specific range\n",
        "        beta_ranges = np.linspace(params['C_cyb'] / 2 / (params['p_1'] - params['p_2']), 0.999, 150)\n",
        "\n",
        "        for b in beta_ranges:\n",
        "            params['beta'] = b\n",
        "            compute_x_y(params)\n",
        "            params['delta'] = random.uniform(params['y^*'] + 0.001, params['x^*'] - 0.001)\n",
        "            compute_eta(params)\n",
        "            eta_values.append(1 - params['eta_1^*'])\n",
        "\n",
        "        ax.plot(beta_ranges, eta_values, label=f\"$C_{{cyb}}$={Ccyb:.2f}\", marker=markers[i], markevery=10)\n",
        "\n",
        "    # Set labels and legend for the subplot\n",
        "    ax.set_xlabel('$\\\\beta$')\n",
        "    ax.set_ylabel('1-$\\eta^*_1$')\n",
        "    ax.legend()\n",
        "\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "# Seed and call the plot function\n",
        "random.seed(0)\n",
        "params = {}\n",
        "plot_eta_vs_beta_v2()"
      ],
      "metadata": {
        "id": "miq7fcHGgeLS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "W6HsVxhSP37A"
      },
      "outputs": [],
      "source": [
        "def plot_eta_vs_C_cyb_with_p2():\n",
        "    # Define p2 values and markers for plotting\n",
        "    p2_values = [0.1, 0.12, 0.14]\n",
        "    markers = ['o', 's', '^']  # Circle, square, and triangle markers\n",
        "\n",
        "    # Create a figure and axis for the plot\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.set_title('$\\eta^*_1$ as a function of $C_{cyb}$ with different values of $p_2$')\n",
        "\n",
        "    # Initialize parameters with specific values and random values within a range\n",
        "    params = {\n",
        "        'w': random.uniform(0.001, 0.999),\n",
        "        'beta': random.uniform(0.001, 0.999)\n",
        "    }\n",
        "\n",
        "    C_cyb_range = np.linspace(0.001, 0.999, 200)\n",
        "\n",
        "    for i, p_2 in enumerate(p2_values):\n",
        "        params['p_2'] = p_2\n",
        "        params['p_1'] = random.uniform(params['p_2'] + 0.001, 0.999)\n",
        "        compute_x_y(params)\n",
        "        params['delta'] = random.uniform(params['y^*'] + 0.001, params['x^*'] - 0.001)\n",
        "        eta_values = []\n",
        "\n",
        "        for C_cyb in C_cyb_range:\n",
        "            params['C_cyb'] = C_cyb\n",
        "            if params['beta'] > params['C_cyb'] / params['p_1']:\n",
        "                compute_lambda(params)\n",
        "                compute_eta(params)\n",
        "                eta_values.append(params['eta_1^*'])\n",
        "            else:\n",
        "                eta_values.append(np.nan)  # Appending NaN for continuity\n",
        "\n",
        "        ax.plot(C_cyb_range, eta_values, label=f\"$p_2$={p_2:.2f}\", marker=markers[i], markevery=10)\n",
        "\n",
        "    # Set labels and legend for the subplot\n",
        "    ax.set_xlabel('Cost of cyber attack $(C_{cyb})$')\n",
        "    ax.set_ylabel('$\\eta^*_1$')\n",
        "    ax.legend()\n",
        "\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "# Seed and call the plot function\n",
        "random.seed(0)\n",
        "params = {}\n",
        "plot_eta_vs_C_cyb_with_p2()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vvPH8O0_QzDv"
      },
      "source": [
        "## 1-$\\eta_1^*$ as a function of $C_{cyb}$ with different values of $p_2$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-7TEpPHJQplT"
      },
      "outputs": [],
      "source": [
        "\n",
        "def plot_one_minus_eta_vs_C_cyb():\n",
        "    # Define p2 values and markers for plotting\n",
        "    p2_values = [0.1, 0.12, 0.14]\n",
        "    markers = ['o', 's', '^']  # Circle, square, and triangle markers\n",
        "\n",
        "    # Create a figure and axis for the plot\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.set_title('$1-\\eta^*_1$ as a function of $C_{cyb}$ with different values of $p_2$')\n",
        "\n",
        "    # Initialize parameters with specific values and random values within a range\n",
        "    params = {\n",
        "        'w': random.uniform(0.001, 0.999),\n",
        "        'beta': random.uniform(0.001, 0.999)\n",
        "    }\n",
        "\n",
        "    C_cyb_range = np.linspace(0.001, 0.999, 150)\n",
        "\n",
        "    for i, p_2 in enumerate(p2_values):\n",
        "        params['p_2'] = p_2\n",
        "        params['p_1'] = random.uniform(params['p_2'] + 0.001, 0.999)\n",
        "        compute_x_y(params)\n",
        "        params['delta'] = random.uniform(params['y^*'] + 0.001, params['x^*'] - 0.001)\n",
        "        one_minus_eta_values = []\n",
        "\n",
        "        for C_cyb in C_cyb_range:\n",
        "            params['C_cyb'] = C_cyb\n",
        "            if params['beta'] > params['C_cyb'] / params['p_1']:\n",
        "                compute_lambda(params)\n",
        "                compute_eta(params)\n",
        "                one_minus_eta_values.append(1 - params['eta_1^*'])\n",
        "            else:\n",
        "                one_minus_eta_values.append(np.nan)  # Appending NaN for continuity\n",
        "\n",
        "        ax.plot(C_cyb_range, one_minus_eta_values, label=f\"$p_2$={p_2:.2f}\", marker=markers[i], markevery=10)\n",
        "\n",
        "    # Set labels and legend for the subplot\n",
        "    ax.set_xlabel('Cost of cyber attack $(C_{cyb})$')\n",
        "    ax.set_ylabel('$1-\\eta^*_1$')\n",
        "    ax.legend()\n",
        "\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "# Seed and call the plot function\n",
        "random.seed(0)\n",
        "params = {}\n",
        "plot_one_minus_eta_vs_C_cyb()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Proposition 3 and 4"
      ],
      "metadata": {
        "id": "WmrzOv4DYeE-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import random\n",
        "def determine_solution(params):\n",
        "    k1 = params['beta'] * (2 * params['p_1'] - 1); params['k1']=k1\n",
        "    k2 = 2 * params['beta'] * (params['p_1'] - params['p_2']);params['k2']=k2\n",
        "    k3 = params['beta'] * (1 - 2 * params['p_2']);params['k3']=k3\n",
        "    params['x^*'] = 1 / (1 + params['w'] * (1 - 2 * params['p_1']))\n",
        "\n",
        "    if params['p_2'] < 0.5:\n",
        "        if params['delta'] < params['x^*']:\n",
        "            if params['C_cyb'] > k1: return 'B'\n",
        "            else: return 'A'\n",
        "        else:\n",
        "            if params['C_cyb'] < k1: return 'No equilibria'\n",
        "            else: return 'C'\n",
        "    elif params['p_2'] > 0.5:\n",
        "        if params['delta'] < params['x^*']:\n",
        "            if params['C_cyb'] < k2: return 'D'\n",
        "            else: return 'E'\n",
        "        else: return \"No equilibria\"\n",
        "    return 'Unknown'  # Default, in case some combinations don't fall into the defined categories"
      ],
      "metadata": {
        "id": "V6FemzN9YVir"
      },
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "params={}\n",
        "# please define all the parameters\n",
        "params['beta']=float(input())\n",
        "params['p_1']=float(input())\n",
        "params['p_2']=float(input())\n",
        "params['w']=float(input())\n",
        "params['C_cyb']=float(input())\n",
        "params['delta']=float(input())\n",
        "determine_solution(params)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 142
        },
        "id": "rC3ouwFfZl-r",
        "outputId": "b4fe9194-b93b-4eee-aff3-22ccf3c31c03"
      },
      "execution_count": 15,
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "0.5\n",
            "0.55\n",
            "0.49\n",
            "0.68\n",
            "0\n",
            "0.8\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'A'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "toc_visible": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8.13"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}