Code of math homework 3.ipynb

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    "colab": {
      "provenance": []
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Question 1"
      ],
      "metadata": {
        "id": "alhnPdXp5x5p"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "B = np.array([[1, 0, 1, 0],\n",
        "              [0, 1, 0, 1]])\n",
        "\n",
        "# Compute the covariance matrix\n",
        "C = np.dot(B, B.T)\n",
        "\n",
        "# Compute the eigenvectors and eigenvalues of the covariance matrix\n",
        "eigenvalues, eigenvectors = np.linalg.eig(C)\n",
        "\n",
        "# Sort the eigenvalues and eigenvectors in descending order\n",
        "sorted_indices = np.argsort(eigenvalues)[::-1]\n",
        "sorted_eigenvalues = eigenvalues[sorted_indices]\n",
        "sorted_eigenvectors = eigenvectors[:, sorted_indices]\n",
        "\n",
        "# Compute the singular values and singular vectors\n",
        "sigma = np.sqrt(sorted_eigenvalues)\n",
        "U = sorted_eigenvectors\n",
        "V = np.dot(np.dot(B.T, U), np.diag(1.0 / sigma))\n",
        "\n",
        "print(\"U:\")\n",
        "print(U)\n",
        "print(\"Sigma:\")\n",
        "print(np.diag(sigma))\n",
        "print(\"V^T:\")\n",
        "print(V.T)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6Kv6d5xC13nI",
        "outputId": "5eed4074-084a-4b7c-83c1-a3e321f1efcc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "U:\n",
            "[[0. 1.]\n",
            " [1. 0.]]\n",
            "Sigma:\n",
            "[[1.41421356 0.        ]\n",
            " [0.         1.41421356]]\n",
            "V^T:\n",
            "[[0.         0.70710678 0.         0.70710678]\n",
            " [0.70710678 0.         0.70710678 0.        ]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Question 2 (a)\n"
      ],
      "metadata": {
        "id": "KuaInemhQgjc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Given data points\n",
        "x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n",
        "y = np.array([1, 11, 31, 60, 101, 146, 207, 279, 356, 445])\n",
        "\n",
        "# Construct the Vandermonde matrix\n",
        "X = np.column_stack([np.ones_like(x), x, x**2])\n",
        "\n",
        "# Perform least squares regression\n",
        "theta = np.linalg.lstsq(X, y, rcond=None)[0]\n",
        "\n",
        "# Generate the fitted curve\n",
        "x_fit = np.linspace(0, 9, 100)\n",
        "y_fit = theta[0] + theta[1] * x_fit + theta[2] * x_fit**2\n",
        "\n",
        "# Plot the data points and the fitted curve\n",
        "plt.scatter(x, y, color='red', label='Data Points')\n",
        "plt.plot(x_fit, y_fit, color='blue', label='Fitted Curve')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.title('Least Squares Regression')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "# Print the estimated parameters\n",
        "print(\"Estimated Parameters:\")\n",
        "print(\"theta0 =\", theta[0])\n",
        "print(\"theta1 =\", theta[1])\n",
        "print(\"theta2 =\", theta[2])\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 541
        },
        "id": "AQuGxBhg56xI",
        "outputId": "219f5b1a-590e-48d0-916e-b48c7aecabdd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Estimated Parameters:\n",
            "theta0 = 1.3727272727271862\n",
            "theta1 = 4.621969696969722\n",
            "theta2 = 4.96590909090909\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Question 2 (b)"
      ],
      "metadata": {
        "id": "8quDb4Y9QnAb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn import svm\n",
        "\n",
        "# Define the positive and negative points\n",
        "positive_points = np.array([[1, 2], [2, 3], [3, 3]])\n",
        "negative_points = np.array([[2, 1], [3, 2]])\n",
        "\n",
        "# Combine positive and negative points\n",
        "X = np.concatenate((positive_points, negative_points))\n",
        "# Assign labels: +1 for positive points, -1 for negative points\n",
        "y = np.concatenate((np.ones(len(positive_points)), -np.ones(len(negative_points))))\n",
        "\n",
        "# Create an SVM classifier\n",
        "clf = svm.SVC(kernel='linear')\n",
        "# Fit the classifier to the data\n",
        "clf.fit(X, y)\n",
        "\n",
        "# Get the coefficients of the separating hyperplane\n",
        "w = clf.coef_[0]\n",
        "# Get the bias term\n",
        "b = clf.intercept_[0]\n",
        "\n",
        "# Calculate the slope of the hyperplane\n",
        "slope = -w[0] / w[1]\n",
        "\n",
        "# Calculate the y-intercept of the hyperplane\n",
        "y_intercept = -b / w[1]\n",
        "\n",
        "# Set up the plot\n",
        "plt.figure()\n",
        "\n",
        "# Plot the positive points\n",
        "plt.scatter(positive_points[:, 0], positive_points[:, 1], color='blue', label='Positive')\n",
        "\n",
        "# Plot the negative points\n",
        "plt.scatter(negative_points[:, 0], negative_points[:, 1], color='red', label='Negative')\n",
        "\n",
        "# Plot the separating hyperplane\n",
        "x_vals = np.linspace(0, 4, 100)  # Adjust the range based on your data\n",
        "y_vals = slope * x_vals + y_intercept\n",
        "plt.plot(x_vals, y_vals, 'k-', label='Separating Hyperplane')\n",
        "\n",
        "# Calculate the margin boundaries\n",
        "margin = 1 / np.linalg.norm(w)\n",
        "upper_margin = y_vals + slope * margin\n",
        "lower_margin = y_vals - slope * margin\n",
        "\n",
        "# Plot the margin boundaries\n",
        "plt.plot(x_vals, upper_margin, 'k--', label='Margin Boundary')\n",
        "plt.plot(x_vals, lower_margin, 'k--')\n",
        "\n",
        "# Plot the support vectors\n",
        "support_vectors = clf.support_vectors_\n",
        "plt.scatter(support_vectors[:, 0], support_vectors[:, 1], color='green', label='Support Vectors')\n",
        "\n",
        "# Set labels and legend\n",
        "plt.xlabel('x1')\n",
        "plt.ylabel('x2')\n",
        "plt.legend()\n",
        "\n",
        "# Show the plot\n",
        "plt.show()\n",
        "\n",
        "# Print the values of w and b\n",
        "print('Optimal values:')\n",
        "print('w:', w)\n",
        "print('b:', b)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 501
        },
        "id": "QZyVHQ6AQqvT",
        "outputId": "727e3bce-cc0d-4254-efa4-fb8635ea604e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Optimal values:\n",
            "w: [-0.6664  1.3328]\n",
            "b: -0.9994666666666664\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "# Define the positive examples (class 1)\n",
        "x1 = np.array([1, 2])\n",
        "x2 = np.array([2, 3])\n",
        "x3 = np.array([3, 3])\n",
        "\n",
        "# Define the negative examples (class -1)\n",
        "x4 = np.array([2, 1])\n",
        "x5 = np.array([3, 2])\n",
        "\n",
        "# Combine all examples into one matrix\n",
        "X = np.vstack((x1, x2, x3, x4, x5))\n",
        "\n",
        "# Define the class labels\n",
        "y = np.array([1, 1, 1, -1, -1])\n"
      ],
      "metadata": {
        "id": "p7lbsTpjbFUE"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn import svm\n",
        "\n",
        "# Define the SVM model\n",
        "model = svm.SVC(kernel='linear', C=1000)\n",
        "\n",
        "# Fit the model to the data\n",
        "model.fit(X, y)\n"
      ],
      "metadata": {
        "id": "TIn04XqabH1_",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 75
        },
        "outputId": "8afaefaf-3f65-4337-97da-4fd1c5c4c79c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "SVC(C=1000, kernel='linear')"
            ],
            "text/html": [
              "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>SVC(C=1000, kernel=&#x27;linear&#x27;)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">SVC</label><div class=\"sk-toggleable__content\"><pre>SVC(C=1000, kernel=&#x27;linear&#x27;)</pre></div></div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Get the separating hyperplane\n",
        "w = model.coef_[0]\n",
        "a = -w[0] / w[1]\n",
        "xx = np.linspace(1, 3)\n",
        "yy = a * xx - (model.intercept_[0]) / w[1]\n",
        "\n",
        "# Plot the hyperplane\n",
        "plt.plot(xx, yy, 'k-')\n",
        "\n",
        "# Plot the margins\n",
        "margin = 1 / np.sqrt(np.sum(model.coef_ ** 2))\n",
        "yy_down = yy - np.sqrt(1 + a ** 2) * margin\n",
        "yy_up = yy + np.sqrt(1 + a ** 2) * margin\n",
        "plt.plot(xx, yy_down, 'k--')\n",
        "plt.plot(xx, yy_up, 'k--')\n",
        "\n",
        "# Plot the support vectors\n",
        "plt.scatter(model.support_vectors_[:, 0], model.support_vectors_[:, 1], s=100, facecolors='none', edgecolors='k')\n",
        "\n",
        "# Plot the data points\n",
        "plt.scatter(X[:, 0], X[:, 1], c=y)\n",
        "\n",
        "plt.show()\n"
      ],
      "metadata": {
        "id": "yxdevGJQbLJI",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "outputId": "58f6457b-037e-4d4b-ddef-51224b0d7850"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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Z1dXV6vb169cxcOBATJ8+3WjcxIkT8c0336jb7DpIRGSehBD47rvvoCgKVq9ejbKyMnVfSUkJhBDqisgjRozQKk0yMQ0qWNLT0422ZVmGm5sbDhw4gMcff/yOz/n1bWWJiYlo06bNbQWLra0tPDw8GpIOERG1QFOnTsWGDRvUbV9fX0iShOjoaPj6+mqYGZmyBl0S+rWSkhIAtxcl9/L1118jPDz8tjMyGRkZcHNzQ69evTBv3jxcv379rq9RVVWF0tJSowcREZmesrIyyLKM8vJyNTZmzBg4Ojpizpw52LVrF3JycrBo0SIWK3RPOiGEeJAnGgwGhIaGori4GHv27Lmv52RlZcHf3x+ZmZl49NFH1fitsy6+vr7Izc3FX/7yFzg6OmLfvn13XDnzrbfewuLFi2+L38/y1ERE1LQMBgMyMjIgyzLWrl2LiooKKIqC6OhoAEB5eTl0Ot1dpxJQ61FaWgpnZ+f7+v5+4IJl3rx52LRpE/bs2YPOnTvf13N+97vfYd++fThy5Mg9x/3888/o3r07tm3bhnHjxt22v6qqClVVVep2aWkpvL29WbAQEWno9OnTUBQFsbGxyMvLU+M9e/bE4sWLERERoWF2ZIoaUrA80G3NL730Er799lvs3r37vouVGzduIDExEX//+99/c2y3bt3QoUMH5OTk3LFgsbW15aRcIiITUlBQgF69euHW38DOzs4IDw+HJEkYMWKEOomW6EE1qGARQuDll19GSkoKMjIyGnS9cfXq1aiqqkJkZORvjr1w4QKuX78OT0/PhqRHRETNoK6uDlu3bsXRo0fxpz/9CQDg4eGBcePGwdraGpIkYerUqbCzs9M4UzInDbok9Ic//AEJCQlITU1Fr1691LizszPs7e0BANHR0ejUqROWLFli9NzRo0ejU6dOSExMNIqXl5dj8eLFePrpp+Hh4YHc3Fy89tprKCsrw9GjR+/rTEpDTikREdGDOX78OBRFQVxcHC5dugRLS0tcvHgR7u7uAIDa2lpYWbEfKd2/Jrsk9OmnnwKobwb3S9988w30ej0AIC8vDxYWxjcfnTp1Cnv27MGWLVtue01LS0scOXIEiqKguLgYXl5emDBhAv7xj3/wsg8RkcYKCwuRmJgIWZaxf/9+Ne7q6opZs2ahtrZWjbFYoab0wJNuTQnPsBARNY1PP/0Uf/jDHwDUFySTJ0+GJEkICQnhH5X00Jp80i0REZmfW2e7hwwZgtmzZwMAwsPDIcsywsPDMXv2bLi5uWmcJbVWLFiIiFqxq1evIiEhAbIsIzs7GwDg7++vFizt2rVDZmamhhkS1WPBQkTUCq1fvx4rVqxAWlqaOg/F2toaU6ZMgSRJRuv5EJkCFixERK3QF198gbS0NADAsGHDoNfrER4ejvbt22ucGdGdsWAhIjJj+fn5iI+PR2xsLFJTU9G1a1cAwIsvvoi+fftCkiQ88sgj2iZJdB9YsBARmZnKykqsX78eiqIgPT0dBoMBABAbG4s33ngDADBp0iRMmjRJyzSJGoQFCxGRmbhy5QoWLVqExMREFBcXq/GRI0dCkiTMmDFDu+SIHhILFiKiFqyqqkrth+Lg4IC4uDiUl5fD29sbUVFRkCQJfn5+GmdJ9PBYsBARtTAVFRVISUmBoii4cuUKDh06BJ1OBwcHB7z33nvw9fVFYGDgbV3HiVoyFixERC2AEAJ79+6FLMtISkpCWVmZuu+///2vur7b3LlztUqRqEmxYCEiMnHJycl47bXXkJubq8Z8fX0hSRKio6Ph6+urYXZEzYMFCxGRiSkrK0N1dbXaE8Xe3h65ublwdHTEjBkzIEkSRo0axUs+1KrwXzsRkQkwGAzYsWMHoqOj4eHhgX//+9/qvvHjxyMhIQEFBQX4+uuv8fjjj7NYoVaHZ1iIiDR0+vRpKIqC2NhY5OXlqfGsrCz1v62srBAREaFFekQmgwULEZFGQkNDsWHDBnXb2dkZ4eHhkCQJI0aM0DAzItPDgoWIqBnU1dVh165dCAwMVBcV7NKlCywsLBAcHAxJkhAaGgp7e3uNMyUyTTohhNA6iYdVWloKZ2dnlJSUwMnJSet0iIhUJ06cUC/5XLp0Cbt378bo0aMBABcuXICFhQW8vLw0zpJIGw35/uYZFiKiRlZYWIjExETIsoz9+/ercVdXV5w/f17d7ty5sxbpEbVILFiIiBrR8ePHMXjwYFRXVwOonzA7efJkSJKEkJAQtY0+ETUMCxYioodw5MgR5Obm4qmnngIA9O7dG15eXnBxcYEkSZg1axbc3Nw0zpKo5WPBQkTUQFevXkVCQgJkWUZ2djbat2+PkJAQ2NjYwMLCAvv370eHDh20TpPIrLBgISK6D9XV1UhLS4Msy9i4cSNqa2sBANbW1hgzZgwKCwvh4eEBACxWiJoACxYiovvw97//Hf/85z/V7WHDhkGv1yM8PFxtoU9ETYcFCxHRr+Tn5yM+Ph4BAQF47LHHAAARERFYsWIFIiMjIUkS+vbtq3GWRK0LCxYiIgCVlZVYv349FEVBeno6DAYDwsPD1YKlb9++OH/+PCwtLTXOlKh1YsFCRK2WEAJZWVmQZRmJiYkoLi5W9wUEBCA4ONhoPIsVIu2wYCGiVm3OnDk4fvw4AMDb2xtRUVGIjo5Gr169NM6MiH6JBQsRtQoVFRVISUnBqlWrsHLlSjg4OECn02HevHnIzMyEXq9HYGAgLCwstE6ViO6AawkRkdkSQmDPnj1QFAVJSUkoKysDAMTGxiIyMlLj7IiIawkRUat29epVfPrpp4iJiUFubq4a9/X1RXR0tLr4IBG1HCxYiMjslJeXY9GiRQAAR0dHTJ8+HZIkYfTo0bzkQ9RCNeiTu2TJEgwfPhxt27aFm5sbwsLCcOrUqXs+R5Zl6HQ6o4ednZ3RGCEE3nzzTXh6esLe3h5BQUE4ffp0w4+GiFoVg8GAnTt3qmv23OLr64tXXnkFiqKgoKAAK1aswJgxY1isELVgDTrDsmvXLrz44osYPnw4amtr8Ze//AUTJkzA8ePH4eDgcNfnOTk5GRU2Op3OaP+//vUvfPjhh1AUBb6+vnjjjTcQHByM48eP31bcEBHl5OQgJiYGMTExOHfuHID6VZE/+OADdOzYEQCwfPlyLVMkokbWoIIlPT3daFuWZbi5ueHAgQN4/PHH7/o8nU6nrrHxa0IIvP/++/jb3/6GqVOnAgBiYmLg7u6OdevWITw8vCEpEpEZ27BhA5YtW4a9e/eqMWdnZ8ycOROSJHENHyIz9lDnR0tKSgAArq6u9xxXXl4OHx8feHt7Y+rUqfjpp5/UfWfOnEFBQQGCgoLUmLOzM/z9/bFv3747vl5VVRVKS0uNHkRkfurq6lBdXa1u5+XlYe/evbCwsMDEiRORmJiI/Px8fP755xg5cuRtZ2+J6OHl5eXhn//8J1555RVN83jggsVgMGD+/Pl47LHH0K9fv7uO69WrF1asWIHU1FTExcXBYDBg5MiRuHDhAgCgoKAAAODu7m70PHd3d3Xfry1ZsgTOzs7qw9vb+0EPg4hM0IkTJ/D666/Dx8cHsiyr8fDwcCxduhTnz5/Hpk2bMHPmTNjb22uXKJGZunHjBmJjYxEUFISuXbvib3/7Gz766CNcv35ds5weuA/LvHnzsGnTJuzZswedO3e+7+fV1NSgT58+iIiIwD/+8Q98//33eOyxx3Dp0iV4enqq42bMmAGdTodVq1bd9hpVVVWoqqpSt0tLS+Ht7c0+LEQtWGFhIRITE6EoCrKystT4xIkTsWnTJg0zI2odDAYDvvvuOyiKgtWrV6O8vFzd98QTT0CSJMyYMQNt2rRptJ/Z5H1YXnrpJXz77bfYvXt3g4oVALC2tsbgwYORk5MDAOrclsuXLxsVLJcvX8agQYPu+Bq2trawtbV9kNSJyMQYDAbMnj0bycnJ6uUfS0tLTJ48GZIk4cknn9Q4QyLz9vPPP6uT2M+cOaPGu3XrBkmSEB0dja5du2qX4P/ToIJFCIGXX34ZKSkpyMjIgK+vb4N/YF1dHY4ePYrJkycDqL/90MPDA9u3b1cLlNLSUmRmZmLevHkNfn0iMn1nzpxRf39YWFigpKQE1dXVGDBgAPR6PWbNmnXbZWIiajxlZWVYs2YNZFnG7t271Xjbtm0xY8YMSJKEUaNGmda8MNEA8+bNE87OziIjI0Pk5+erj4qKCnVMVFSUeP3119XtxYsXi82bN4vc3Fxx4MABER4eLuzs7MRPP/2kjlm6dKlwcXERqamp4siRI2Lq1KnC19dX3Lx5877yKikpEQBESUlJQw6HiJrRlStXxPvvvy8GDx4sdDqdOHfunLrvwIED4tChQ9olR9QK1NXViW3btonIyEjRpk0bAUAAEDqdTgQFBYm4uDhx48aNZs2pId/fDTrD8umnnwKov5b1S9988w30ej2A+tnEv2zOVFRUhOeffx4FBQVo164dhg4diu+//x6PPPKIOua1117DjRs38MILL6C4uBijRo1Ceno6e7AQtXDV1dXYuHEjZFlGWloaamtrAdRfGs7MzESXLl0AAEOGDNEyTSKzdvr0aSiKgpiYGJw/f16N+/n5Qa/XIzIyskXcvMLFD4moSWRlZSEkJATXrl1TY8OGDYMkSYiIiED79u01zI7IvBUXFyMpKQmKouD7779X487OzoiIiIAkSfD399f8kg8XPySiZldQUICLFy9i6NChAIA+ffqgoqICnp6eiIyMhCRJ6Nu3r8ZZEpmvuro6bN26FYqiICUlRb2b1sLCAsHBwdDr9QgNDW2xVy9YsBDRA6usrMSGDRugKArS09PRt29fHD58GED95L0ffvgBffr0gZUVf9UQNZXjx49DURTExcXh0qVLarxv376QJAmRkZFGd+G2VPwtQkQNIoRAVlYWFEXBypUrUVxcrO5zcHBASUkJnJ2dAQD9+/fXKEsi81ZYWIiVK1dCURTs379fjbdv3x6zZs2CJEkYMmSI5pd8GhMLFiJqkPnz5+PDDz9Utzt37ozo6GhER0ejV69eGmZGZN5qamqQnp4ORVGwfv161NTUAKhf+DMkJASSJCEkJAQ2NjYaZ9o0WLAQ0V1VVFQgJSUFAQEB6NatGwBgwoQJ+PLLL/H0009DkiQEBgbC0tJS40yJzNfhw4ehKAri4+Nx5coVNT5o0CC1b9GtVcrNGQsWIjIihMDevXshyzKSkpJQVlaGhQsX4p133gEABAcHo6CggHfkETWhK1euICEhAbIsq/PCAMDNzU2dxD5gwAANM2x+LFiICABw9uxZtT13bm6uGvf19YWXl5e6bWVlxWKFqAlUVVUhLS0Nsixj06ZNat8iGxsbhIaGQpIkBAcHw9raWuNMtcGChYhQU1ODoUOHorCwEADg6OiI6dOnQ5IkjB492qgZJBE1HiEEDhw4AFmWsXLlSvUzCACPPvooJElCeHg4XF1dNczSNLBgIWplDAYDMjIykJaWhuXLl0On08Ha2hoRERE4efIkJEnCtGnT4ODgoHWqRGYrPz8fcXFxkGUZx48fV+NeXl6IiopCdHS0UUd4YqdbolYjJydHbc+dl5cHANizZw8ee+wxAPWFDM+kEDWdyspKpKamQlEUbN68GQaDAQBgZ2eHsLAw6PV6BAUFtapJ7Ox0S0QA6n8ZJCUlQZZl7N27V407Oztj5syZ6NChgxpjsULU+IQQ+OGHH6AoChITE1FSUqLuGzlyJCRJwowZM+Di4qJdki0ECxYiM3bgwAE8//zzAOoLkgkTJkCSJEydOhX29vYaZ0dkvs6fP4/Y2FgoioL//ve/atzb21vtW+Tn56dhhi0PCxYiM3HixAkoioK2bdvir3/9KwBgzJgxCA4OxtixYxEZGWl0tw8RNa6KigokJydDURRs374dt2ZctGnTBk8//TT0ej2eeOIJns18QJzDQtSCFRYWIjExEYqiICsrCwDQoUMHXLx40Wy7XRKZEiEEvvvuOyiKgtWrV6OsrEzdN2bMGOj1ejz99NNo27athlmaLs5hITJzO3bswKeffor169ejuroaAGBpaYnJkydDkiT+BUfUxM6cOaP2Lfr555/VeLdu3SBJEqKiouDr66thhuaHBQtRCyGEUBcy27hxI9asWQMAGDhwICRJwqxZs+Du7q5likRmraysDGvWrIGiKNi1a5cab9u2LWbMmAFJkjBq1CizWnDQlLBgITJhV69excqVKyHLMpYtW4bx48cDAJ599lnU1dVBkiQMGjRI2ySJzJjBYMDOnTuhKArWrl2LiooKAIBOp0NQUBAkScJTTz2FNm3aaJyp+eMcFiITU11djY0bN0KWZaSlpantuWfPno24uDiNsyNqHU6fPq32LTp//rwa9/Pzg16vR2RkJLy9vTXM0DxwDgtRC3Tz5k28/vrriI+Px/Xr19X40KFDIUkSIiIiNMyOyPwVFxerfYv27dunxp2dnREeHg69Xg9/f39e8tEICxYiDd24cUNtgW9nZ4ctW7bg+vXr8PDwQFRUFCRJQt++fTXOksh81dXVYevWrVAUBSkpKaiqqgJQ37coODgYer0eoaGhsLOz0zhTYsFC1MwqKyuxYcMGKIqC77//HhcuXECbNm2g0+mwbNkyWFtbY/z48bCy4seTqKkcP34ciqIgNjYW+fn5arxv377Q6/WYPXs2PD09NcyQfo2/EYmagRACWVlZUBQFK1euRHFxsbovIyMDkydPBgCEhoZqlCGR+bt+/brat2j//v1q3NXVFbNmzYJer8eQIUN4ycdEsWAhamJ79uzB888/j5MnT6qxzp07q5d8evXqpWF2ROatpqYG6enpUBQF69evR01NDQDAysoKkydPhl6vR0hICBsttgAsWIgaWUVFBQoLC9G5c2cAgKenJ06ePAl7e3tMmzYNer0egYGBrWpFVqLmdvjwYSiKgvj4eFy5ckWNDxo0SO1b5ObmpmGG1FAsWIgagRACe/fuhaIoSEpKQmBgINatWwcA6N69O9atW4fAwEDedk/UhK5cuYKEhAQoioLs7Gw17ubmhtmzZ0OSJAwcOFC7BOmhsGAhegjnzp1T23Pn5OSo8RMnTqCmpgbW1tYAgKlTp2qVIpFZq66uRlpaGmRZxsaNG9W+RTY2NpgyZQokScLEiRPVzyK1XCxYiB7Qyy+/jI8//ljddnR0xPTp0yFJEkaPHs31fIiaiBACBw8ehKIoSEhIMOpbNHz4cEiShPDwcLRv317DLKmxsWAhug8GgwG7du3C0KFD1cs6fn5+0Ol0CAwMhF6vx7Rp09SeKkTU+PLz8xEXFwdFUfDTTz+pcS8vL0RGRkKSJDzyyCMaZkhNia35ie4hJydHveRz7tw5fPnll5g7dy4AoKSkBMXFxfDx8dE4SyLzVVlZidTUVCiKgs2bN8NgMACob7QYFhYGvV6PoKAgTmJvodian+ghlJaWIikpCYqiYM+ePWrcyckJJSUl6razszOcnZ21SJHIrAkh8MMPP0BRFKxatcqob9HIkSMhSRJmzJgBFxcXzXKk5seChegXSktL0alTJ5SXlwOob889fvx4SJKEsLAw2Nvba5whkfk6f/48YmNjoSgK/vvf/6pxb29vREdHIzo6Gn5+fhpmSFpq0KzAJUuWYPjw4Wjbti3c3NwQFhaGU6dO3fM5X375JUaPHo127dqhXbt2CAoKQlZWltEYvV4PnU5n9Jg4cWLDj4aogU6ePImvvvpK3XZycsJjjz2GPn36YNmyZTh//jzS09MRERHBYoWoCVRUVCAuLg7jx4+Hj48P/vrXv+K///0v2rRpg6ioKGzbtg1nz57F22+/zWKllWvQGZZdu3bhxRdfxPDhw1FbW4u//OUvmDBhAo4fP37XyYYZGRmIiIjAyJEjYWdnh2XLlmHChAn46aef0KlTJ3XcxIkT8c0336jbtra2D3hIRPdWVFSktufOzMxUC+Rbjd5WrVoFJycntucmaiJCCHz33XdQFAWrV69GWVmZum/MmDGQJAnPPPMM2rZtq2GWZGoaVLCkp6cbbcuyDDc3Nxw4cACPP/74HZ8THx9vtP3VV19h7dq12L59O6Kjo9W4ra0tPDw8GpIO0X2rra3Fli1bIMsyUlNTUV1dDQCwtLTExIkTjX5hcl4KUdM4e/YsYmJioCgKfv75ZzXu6+sLSZIQHR0NX19fDTMkU/ZQc1huTUB0dXW97+dUVFSgpqbmtudkZGTAzc0N7dq1w9ixY/H222/f9R76qqoqdQlwoH7eAdG9JCQkQJIkdXvAgAGQJAmzZ8+Gu7u7hpkRmbeysjKsWbMGiqJg165datzR0REzZsyAJEkYNWoU+xbRb3rg25oNBgNCQ0NRXFxsdCfFb/nDH/6AzZs346effoKdnR0AIDExEW3atIGvry9yc3Pxl7/8BY6Ojti3b98db1V76623sHjx4tvivK2ZAODatWtYuXIl3N3dMWPGDAD1Re2AAQPU2yAHDRqkbZJEZsxgMCAjIwOyLGPt2rWoqKgAAOh0OowdOxZ6vR5PPfUU+xZRg25rfuCCZd68edi0aRP27NmjXvv/LUuXLsW//vUvZGRkYMCAAXcd9/PPP6N79+7Ytm0bxo0bd9v+O51h8fb2ZsHSitXU1GDjxo1QFAXffvstampqMHjwYBw8eFAdI4TgvBSiJnT69GkoioLY2Fjk5eWpcT8/P0iShKioKHh7e2uYIZmaJu/D8tJLL+Hbb7/F7t2777tYWb58OZYuXYpt27bds1gBgG7duqFDhw7Iycm5Y8Fia2vLSbkEAMjOzoYsy4iPj8e1a9fU+JAhQyBJEurq6tSzdCxWiBpfSUkJkpKSIMsyvv/+ezXu7OyM8PBw6PV6+Pv78/NHD61BBYsQAi+//DJSUlKQkZFx35Oj/vWvf+Gf//wnNm/ejGHDhv3m+AsXLuD69evw9PRsSHrUCv3jH/9AcnIyAMDDw0Ntz92vXz+NMyMyX3V1ddi6dSsURcG6detQWVkJoL5vUXBwMPR6PUJDQ9XL/kSNoUEFy4svvoiEhASkpqaibdu2KCgoAFBfSd/qUREdHY1OnTphyZIlAIBly5bhzTffREJCArp27ao+x9HREY6OjigvL8fixYvx9NNPw8PDA7m5uXjttdfQo0cPBAcHN+axUgtWWVmJDRs2QFEUvPvuu2o/hrlz58LKygqSJGHChAmwsmIvRKKmcvz4cSiKgri4OFy6dEmN9+3bF3q9HrNnz+YfmtR0RAMAuOPjm2++UceMGTNGSJKkbvv4+NzxOYsWLRJCCFFRUSEmTJggOnbsKKytrYWPj494/vnnRUFBwX3nVVJSIgCIkpKShhwOmTiDwSB++OEHMW/ePOHi4qL+2/nrX/+qdWpErca1a9fExx9/LIYPH270O9zV1VW89NJL4scffxQGg0HrNKmFasj3Nxc/JJNTXl6Ojz/+GIqi4OTJk2q8c+fOiIqKgl6vZ8dLoiZUU1ODzZs3Q5ZlrF+/HjU1NQAAKysrTJ48GXq9HiEhIbCxsdE4U2rpuPghtTjiF3fwWFlZYenSpSgpKYG9vT2mTZsGvV6PwMBArshK1ISOHDmiTmK/cuWKGh80aBAkScKsWbPg5uamYYbUmrFgIc0IIbB3714oioLDhw+rbfLt7Ozw1ltvoW3btpg+fTrPmhE1oatXryIhIQGyLCM7O1uNd+zYUZ3EPnDgQO0SJPp/WLBQszt37hxiYmIQExODnJwcNZ6VlQV/f38AwPz58zXKjsj8VVdXIy0tDbIsY+PGjaitrQUAWFtbIzQ0FJIkYeLEibC2ttY4U6L/w4KFms2ePXvw5ptvYufOnWrMwcEB06dPhyRJGD58uIbZEZk3IQQOHjwIWZaxcuVKXL9+Xd03bNgw6PV6hIeH33VJFCKtsWChJmMwGHDz5k21/XZVVZVarIwdOxaSJGHatGlwdHTUMk0is5afn4/4+HjIsoyffvpJjXt6eiIqKgqSJOGRRx7RMEOi+8OChRpdbm6uuiLrtGnT8O677wIAAgMDsXz5cjzzzDPw8fHROEsi81VZWYn169dDURSkp6fDYDAAqO8S/tRTT0GSJAQFBbFvEbUovK2ZGkVpaSlWr14NWZaNFsPs2bMnTp06xbbcRE1MCIHMzEwoioLExEQUFxer+wICAqDX6zFjxgy4uLholiPRr/G2ZmpW8+fPxxdffIGbN28CqG/PPX78eOj1ekydOpXFClETunDhAmJjY6EoCk6dOqXGvb291Us+7FtE5oAFCzXYqVOn0LNnT1hYWACoL1Bu3ryJPn36QJIkREZGolOnThpnSWS+KioqkJKSAkVRsG3bNtw6Ud6mTRs8/fTTkCQJgYGB6meUyBzwkhDdl6KiIiQmJkJRFGRmZmLbtm3qStpnz57FlStXMHz4cJ5NIWoiQgjs2bMHiqIgKSkJZWVl6r4xY8ZAkiQ888wzaNu2rYZZEjUMLwlRo6itrcXmzZuhKApSU1NRXV0NALC0tER2drZasHTt2hVdu3bVMFMi83X27Fl1EvvPP/+sxn19fSFJEqKjo+Hr66thhkTNgwUL3dGFCxcwfPhwdXVtAOjfvz/0ej1mzZoFDw8PDbMjMm9lZWVYu3YtZFnGrl271LijoyNmzJgBSZIwatQoXvKhVoUFCwEArl27hiNHjmDs2LEAgE6dOsHJyQm1tbWYPXs2JEnCoEGDeMmHqIkYDAZkZGRAlmWsXbsWFRUVAACdTodx48ZBkiQ89dRTal8jotaGBUsrVlNTg40bN0KWZaSlpcHe3h4FBQWwt7eHTqdDWloaunTpwhVZiZpQTk4OFEVBTEwM8vLy1Lifnx8kSUJUVBS8vb01zJDINLBgaWWEEMjOzoYsy0hISMC1a9fUff3798eFCxfQs2dPAECPHj20SpPIrJWUlCApKQmKomDv3r1q3NnZGeHh4ZAkCSNGjOAZTaJfYMHSynz44YdGCwu6u7urvRr69eunXWJEZq6urg7btm2DoihISUlBZWUlgPq2ABMmTIBer0doaCjs7e01zpTINLFgMWNVVVXYsGEDOnfujBEjRgAAJk+ejD//+c8IDQ2FXq/HhAkT2J6bqAmdOHECiqIgNjYWly5dUuOPPPKI2rfIy8tLwwyJWgZ+U5kZIQT2798PRVGwcuVKFBUV4amnnkJycjKA+lb5V69eZa8GoiZUWFio9i3KyspS466uroiIiIBer8fQoUN5yYeoAViwmImLFy8iLi4OiqLgxIkTarxTp07o37+/0VgWK0SNr7a2Funp6VAUBevXrzfqWzR58mTo9XqEhITA1tZW40yJWiYWLGYiLCwMP/74IwDA3t5eXZF13LhxsLS01Dg7IvN15MgRKIqC+Ph4XL58WY0PHDhQ7Vvk5uamYYZE5oEFSwsjhMD333+PuLg4LFu2TG1lHBUVBTs7O+j1ekyfPp1LFBA1oatXryIhIQGKouDQoUNqvGPHjoiMjIQkSRg4cKCGGRKZH64l1EKcO3dOXZE1JycHAPD1119jzpw5AOoLGV4PJ2o61dXVSEtLg6IoSEtLQ21tLQDA2toaoaGhkCQJEydOhLW1tcaZErUcXEvITFRUVGDNmjVQFAU7duxQ4w4ODnjmmWeM/oJjsULU+IQQOHjwIBRFQUJCAq5fv67uGzZsGPR6PcLDw9G+fXsNsyRqHViwmLDCwkLo9Xp16fjAwEDo9XpMmzYNjo6OGmdHZL7y8/MRHx8PWZbx008/qXFPT0+1b9EjjzyiYYZErQ8LFhORm5uLmJgYXLp0CV9++SUAoHPnzpg7dy68vb0RFRXFFZGJmlBlZSXWr18PWZaxefNmGAwGAICtrS3CwsIgSRLGjx/PvkVEGuEcFg2VlpZi9erVUBQF3333HYD6rpd5eXno1KmTxtkRmT8hBDIzM6EoChITE1FcXKzuCwgIgF6vx4wZM+Di4qJZjkTmjHNYTFxWVhY+/PBDJCcn4+bNmwDqC5WgoCBIksTr4URN7MKFC+ok9lOnTqlxb29vREdHIzo6Gn5+fhpmSES/xoLlHm7cuIErV65ACAE3N7eHmjfyy7t4jhw5gvj4eABAnz591PbcPKtC1HQqKiqQkpICRVGwbds2dW6Yvb09nn76aej1egQGBsLCwkLjTIlMS1lZGa5cuQILCwu4u7ujTZs22iQizEBJSYkAIEpKSh76tQwGg9i1a5eYOXOmsLKyEgAEAGFpaSmeeeYZsWPHDmEwGO7rtQoLC8Wnn34qRowYIT788EM1XlxcLF566SWRmZl5369FRA1nMBjE7t27xXPPPSfatm2rfp4BiMcff1ysWLFClJaWap0mkcmpq6sT6enpIjQ0VFhYWKifG1tbWxEdHS1++OGHRvn+asj3N+ew/MKNGzcwe/ZspKamws/PD7///e8xYMAAAMCxY8fw+eef48SJE5g0aRJWrVp1xxb3tbW12Lp1K2RZRmpqKqqqqgAAw4cPN1pThIiaztmzZxETE4OYmBjk5uaqcV9fX/WST7du3TTMkMh0FRYWYtq0adi1axcGDBiA3/3ud+jduzcMBgMOHDiAzz77DGfPnsWsWbOwYsWKh1puokHf3w9dHpmAxjjDUlVVJcaOHSscHBzE6tWrhcFgEIbaS8JQsV4YKlKFoea8MBgMIjU1VTg5OYlRo0aJmzdvGr3GX/7yF+Hh4WH0V1z//v3F//7v/4r8/PyHPUwiuoeysjIhy7J44oknjD6Djo6O4tlnnxUZGRmirq5O6zSJTFpZWZkYPHiwaN++vdiyZYswGAziwulLYmvsLrE94Ttx7VKhqK2tFYqiCFtbWxEaGipqa2sf+Oc15Pu7QQXLO++8I4YNGyYcHR1Fx44dxdSpU8XJkyd/83lJSUmiV69ewtbWVvTr10+kpaUZ7TcYDOKNN94QHh4ews7OTowbN07897//ve+8GqNgeeutt4SNjY3YtWuXMNQVi7rCl0Rdvp+oy+/5/x5+oq7w98JQd13s27dP2NnZifnz5xu9xtSpUwUA0aFDB/HHP/5RHDx4kJd8iJpQXV2d2LFjh4iOjhYODg5qkaLT6cTYsWOFoiiivLxc6zSJWox58+aJtm3bisOHD4trlwrFn4P/IYJ0z6iPCVYzxNKoD0VFWYVIS0sTlpaW4r333nvgn9dkBUtwcLD45ptvxLFjx0R2draYPHmy6NKlyz1/Iezdu1dYWlqKf/3rX+L48ePib3/7m7C2thZHjx5VxyxdulQ4OzuLdevWicOHD4vQ0FDh6+t72xmMu3nYgqWqqkq4u7uLP/zhD8JgqBJ1V6eKuvzevyhWbj16i8pLE0VKyirRo0cPAcDoOPbt2yfWrVsnqqqqHigPIro/p0+fFm+88Ybw8fExOpvSs2dP8fbbb4tz585pnSJRi1NUVCTatGkj/v73v4vy4nIR1f1FEWw9w6hguVW0/M+YN0RtTa2YPXu26N69+wOfvWy2OSxXr16Fm5sbdu3ahccff/yOY2bOnIkbN27g22+/VWMjRozAoEGD8Nlnn0EIAS8vL7zyyit49dVXAQAlJSVwd3eHLMsIDw//zTwedg5LUlISZs6ciaNHj6Jv99MQJX822i+EQPaxKsQklSEhuQzXCuvUfZGRkYiNjW3wzySihikpKcHq1ashyzL27t2rxp2dnTFz5kxIkoSAgAAuU0H0gD766CMsWLAAeXl52B2bha//Eg9huHuJsDjlNaBjDR577DGkp6cjODi4wT+zId/fD3X/XklJCQDA1dX1rmP27duHoKAgo1hwcDD27dsHADhz5gwKCgqMxjg7O8Pf318d82tVVVUoLS01ejyMffv2wc/PD/369YOoWItf/t9yKqcag8flYdiE8/jwq2JcK6yDu5stXnnlFfTs2RMODg4P9bOJ6O7q6uqwZcsWzJo1Cx4eHnj++eexd+9eWFhYYOLEiUhMTER+fj4+//xzjBw5ksUK0UPYt28fRo4cCU9PT6Sv2KEWK5WiAtfFZaOxFpYW2CzvREBAANzd3e/6fd2YHrgPi8FgwPz58/HYY4+hX79+dx1XUFAAd3d3o5i7uzsKCgrU/bdidxvza0uWLMHixYsfNPXblJWVwdnZuX7DcBmAQd3n7WWFcxdqYWOjQ2iwA6SZTpgQ2A02Xsuxf/9+lJWVNVoeRFTvxIkTUBQFcXFxuHjxohp/5JFH1L5FXl5eGmZIZH5++V14teAq8sU55OMcCnEF1rDFaBECC139H/SGOgOuXyqETqeDi4tLs3wXPnDB8uKLL+LYsWPYs2dPY+ZzXxYuXIgFCxao26WlpfD29n7g13NyckJhYWH9hqUnUHcet4qWNm0skCJ7YkAfW7i2swRgAVh7Aqi/9YsLoBE1jsLCQiQmJkJRFKMWAK6uroiIiIBer8fQoUN5FoWoiTg5OeHkyZOYM2cONpetQS1q1H2OcEI1KmGH+qZxFpYW6OjdAUIIFBYW3rHNR2N7oILlpZdewrfffovdu3ejc+fO9xzr4eGBy5eNTyVdvnwZHh4e6v5bMU9PT6MxgwYNuuNr2traPtR93782atQovPfeezh06BAG9Z4OUf2D0f4nRv6yq58BOvsZOHHiBI4dO4aFCxc2Wh5ErU1tbS3S09OhKArWr1+P6upqAIClpSUmT54MSZLw5JNPNurnnYiM1dTUwNraGqNGjcLKlStx8OBBAIA9HOAJH3jCB/Y64+kPhjoDJj4biN27d+Pq1asYPXp0k+fZoDksQgi89NJLSElJwY4dO+Dr6/ubzwkICMD27duNYlu3bkVAQACA+kZOHh4eRmNKS0uRmZmpjmlqoaGh8PLywn/+8x/AbiJgPRh3/r/GArDqC9hPwaeffoqOHTvi6aefbpYciczJkSNH8Morr6Bz586YMmUK1qxZg+rqagwcOBDvvvsuLl68iPXr1+Ppp59msULUBMrKyrBixQqMGTMGs2fPBlB/E4mDgwOeeOIJbEnfivA+z6GHVb/bihWdhQ5Dxw/A8EmD8Z///Ae9evXC2LFjmz7phtx+NG/ePOHs7CwyMjJEfn6++qioqFDHREVFiddff13d3rt3r7CyshLLly8XJ06cEIsWLbrjbc0uLi4iNTVVHDlyREydOrVZb2sWor7HjKWlpUhPTxeGunJRV/S6qMvvY3RLc13RK8JQVyp27twprK2txRtvvPHAP4+otbly5Yp4//33xeDBg41uRe7YsaOYP3++OHTokNYpEpm1uro6sW3bNhEZGSnatGmjfgbt7OxEWVmZEEKIP/7xj6JNmzYiMzNTFF8tEYuf+bcYbzldvaV5om24+OAPX4iqm1VizZo1QqfTiU8++eSBc2qyPiy//CXzy8c333yjjhkzZoyQJMnoeUlJScLPz0/Y2NiIvn373rVxnLu7u7C1tRXjxo0Tp06duu+8GqNgqampESEhIcLW1lbIsixqamqEoe66MNzcJgw3twpD7VVRW1sr4uPjRZs2bURQUBD7rRD9hqqqKpGcnCymTp1qtDaXtbW1mDZtmkhNTRXV1dVap0lk9j777DPh7e1t9N3t5+cn3nnnHZGXl6eOq6ioEAEBAcLJyUkkJyeLuro6cfXCNbEnJVPs2/CjKLleKqqqqsQnn3wirKysRHh4+EN1kOZaQg+oqqoKzz33HOLj49G5c2c8//zzGDBgAHQ6HY4dO4Yvv/wS586dwzPPPIOYmBjY29s34lEQmQchBA4dOgRZlpGQkIDr16+r+4YNGwZJkhAREYH27dtrmCWReSsuLoatra36PfXee+9hwYIFcHZ2RkREBCRJgr+//x0nsZeVlWHmzJnYtGkTevTogeeffx69e/dGXV0dDh48iK+++goFBQV44YUX8Mknn8DK6oHv3+FaQg/rwIEDYu7cucLe3t7olJlerxdZWVmN8jOIzE1+fr7497//Lfr162f0V5ynp6f405/+JI4dO6Z1ikRmrba2VmzatEnMnDlT2NraGl39uHz5sli1atV9T7UwGAxiz549YtasWcLa2tpoba4//OEPRtM6HgbPsDSS2tpaFBUVQQiBdu3awdrautFem8gcVFZWYsOGDZBlGZs3b0ZdXX0XaFtbW4SFhUGv1yMoKOih/gIjonv76aef1L5F+fn5avzZZ5/FihUrHvr1q6urUVRUBEtLS7i4uDTq57kh39/8LXIPVlZW6Nixo9ZpEJkUIQSysrIgyzISExNRXFys7gsICIAkSZg5cyZcXFw0y5GoNaiqqsKYMWOQmZmpxtq3b49Zs2ZBkiQMGTKkUX6OjY3Nbc1dtcCChYjuy4ULFxAbGwtFUXDq1Ck13rlzZ0RHRyM6Ohq9evXSMEMi81ZTU4MDBw5gxIgRAOrPZDo6OsLKygohISGQJAkhISGwsbHRONOmwYKFiO6qoqICKSkpUBQF27Ztw60ryPb29nj66achSRICAwNhaWmpcaZE5uvw4cNQFAXx8fG4du0aLly4oDZa/eijj9C+fXu4ublpnGXTY8FCREaEENi7dy9kWUZSUpLRGiGPP/44JEnCM88806jzxYjI2JUrV5CQkABZlnH48GE17ubmhpMnT6oFS58+fbRKsdmxYCEiAMDZs2cRExODmJgY5ObmqnFfX1/1kk+3bt00zJCoddi0aRNCQ0NRW1sLoH4OSWhoKCRJQnBwcKu9AYQFC1ErVl5ejrVr10KWZWRkZKhxR0dHTJ8+HZIkYfTo0bCwaNAqHkR0n4QQOHDgACoqKvD4448DqJ+8bmlpiSFDhkCSJISHh8PV1VXjTLXHgoWolTEYDNi1axdkWcbatWtx48YNAIBOp8PYsWMhSRKmTZsGBweH33glInpQ+fn5iIuLgyzLOH78OIYPH66uUu7i4oKff/4ZXl5eGmdpWliwELUSOTk56iWfc+fOqfEePXpAr9cjKioKXbp00TBDIvNWWVmJ1NRUKIqCzZs3w2AwAADs7OzQvXt3VFVVqYt9sli5HQsWIjNWUlKC1atXQ5Zl7N27V407OTkhPDwckiQhICDgju25iahx6fV6rFq1St0eOXIkJEnCjBkz2LfoPrBgITIzdXV12L59OxRFQXJyMiorKwEAFhYWGD9+PPR6PaZOncq1sIia0Pnz5xEbG4tZs2aha9euAIDp06fj+++/Vyex+/n5aZtkC8OChchMnDx5EoqiIDY2FhcvXlTjffr0gV6vR2RkJE8zEzWhiooKJCcnQ1EUbN++HUII1NTUYNGiRQCAsLAwPPXUU5zE/oBYsBC1YEVFRUhMTISiKEbtudu1a6euyDp8+HBe8iFqIkIIfPfdd1AUBatXrzbqW/TEE09g4MCB6jYbLD4cFixELUxtbS02b94MRVGQmpqK6upqAPW/DCdPngxJkvDkk0+qk/eIqOlUVFQgJCQE5eXlAIBu3bpBkiRERUXB19dX4+zMCwsWohbi6NGj6oqsly9fVuMDBw6EJEmYNWuWSSxQRmSuysrKsGbNGuzevRsrVqyATqeDg4MDnnvuOZSXl0OSJIwaNYpnNJuITtxaHKQFa8jy1EQtybVr15CQkABFUXDw4EE13rFjR8yePRuSJGHQoEHaJUhk5gwGA3bu3AlFUbB27VpUVFQAAPbv349hw4ZpnF3L15Dvb55hITIx1dXV2LhxIxRFwbfffqu257a2tsaUKVMgSRImTZrUattzEzWHvLw8fPnll4iJiUFeXp4a9/Pzg16vh7e3t4bZtU4sWIhMgBAChw4dgqIoSEhIwLVr19R9w4YNgyRJiIiIQPv27TXMkqj1OHHiBN5++20AgLOzM8LDw6HX6+Hv789LPhphwUKkoYKCAsTHx0OWZRw7dkyNe3h4ICoqCpIkoW/fvhpmSGTe6urqsHXrViiKgp49e+Lvf/87ACAoKAizZ89GaGgoQkNDYWdnp3GmxDksRM2ssrISGzZsgKIoSE9PR11dHQDA1tYWU6dOhSRJmDBhAqys+PcEUVM5fvy42rcoPz8fAODp6Ym8vDx+9poR57AQmRghBLKysqAoClauXIni4mJ134gRI6DX6zFjxgy0a9dOuySJWoGYmBh8/PHH2L9/vxpzdXVVJ7GzV4rpYsFC1IQuXryI2NhYKIqCkydPqvHOnTurl3x69eqlYYZE5q2mpgaWlpZqd9kff/wR+/fvh5WVFSZPngy9Xo+QkBDY2NhonCn9FhYsRI2soqIC69atg6Io2Lp1K25ddbW3t8e0adOg1+sRGBjIv+SImtDhw4ehKAri4+ORlJSEMWPGAABeeOEFdO/eHREREXBzc9M4S2oIFixEjUAIgb1790JRFCQlJaG0tFTdN3r0aOj1ejzzzDOcY0XUhK5cuaL2LcrOzlbjq1evVguWfv36oV+/fhplSA+DBQvRQzh37hxiYmIQExODnJwcNd61a1dIkoTo6Gh069ZNwwyJzF9RURH0ej02btyo9i2ysbFR+xZNnDhR4wypMbBgIWqg8vJyrF27FoqiYOfOnWrc0dER06dPhyRJGD16NFdkJWoiQghcunQJnTp1AgC4uLjg2LFjqK2txfDhwyFJEsLDw9m3yMywYCG6DwaDAbt27YKiKFizZg1u3LgBANDpdBg7diwkScK0adPg4OCgcaZE5is/Px9xcXFQFAWXLl1Cfn4+bG1todPp8Pnnn8PLywuPPPKI1mlSE2HBQnQPOTk56iWfc+fOqfEePXpAr9cjKioKXbp00TBDIvNWWVmJ1NRUKIqCzZs3w2AwAADs7OyQnZ0Nf39/APWN3si8sWAh+pWSkhKsXr0asixj7969atzJyQnh4eGQJAkBAQFsz03UxFJSUjBnzhyjvkUjR46EJEmYMWMGXFxcNMuNmh8LFiLUt+fevn07ZFlGSkoKKisrAQAWFhYYP348JElCWFgY7O3tNc6UyHydP38elZWV6NmzJwCgd+/eKC4uhre3N6KjoxEdHQ0/Pz+NsyStNHhW4O7duzFlyhR4eXlBp9Nh3bp19xyv1+uh0+lue/xyfZS33nrrtv29e/du8MEQNdTJkyexcOFC+Pj4IDg4GCtXrkRlZSX69OmDZcuW4fz580hPT0dERASLFaImUFFRgbi4OIwfPx4+Pj7429/+pu7r06cP9u3bh7Nnz+Ltt99msdLKNfgMy40bNzBw4EDMmTMH06ZN+83xH3zwAZYuXapu19bWYuDAgZg+fbrRuL59+2Lbtm3/lxjXcqAmUlRUhMTERCiKgszMTDXerl07REREQK/XY9iwYbzkQ9REhBD47rvvoCgKVq9ejbKyMnVfSUkJhBDq52/EiBFapUkmpsFVwaRJkzBp0qT7Hu/s7AxnZ2d1e926dSgqKsKzzz5rnIiVFTw8PBqaDtF9qa2txebNm6EoClJTU1FdXQ0AsLS0xMSJE6HX6zFlyhTY2tpqnCmR+Zs6dSo2bNigbvv6+qp9i3x9fTXMjExZs5/G+PrrrxEUFAQfHx+j+OnTp+Hl5QU7OzsEBARgyZIld737oqqqClVVVer2L7uKEv3S0aNH1fbcBQUFarx///7Q6/WYPXs23N3dNcyQyLyVlZVh7dq1eOaZZ+Do6AgAGDNmDHbu3IkZM2ZAkiSMGjWKfYvoNzVrwXLp0iVs2rQJCQkJRnF/f3/IsoxevXohPz8fixcvxujRo3Hs2DG0bdv2ttdZsmQJFi9e3FxpUwtz7do1rFy5ErIs4+DBg2q8Q4cO6oqsgwYN4iUfoiZiMBiQkZEBWZaxdu1aVFRUwMLCAtHR0QCA3/3ud/j973/PvkXUIM1asCiKAhcXF4SFhRnFf3mJacCAAfD394ePjw+SkpLw3HPP3fY6CxcuxIIFC9Tt0tJSeHt7N1neZPqqq6uxadMmyLKMtLQ01NTUAACsra3x5JNPQpIkTJo0iSuyEjWhnJwcKIqCmJgY5OXlqfGePXvC2tpa3b51poWoIZqtYBFCYMWKFYiKivrNLw0XFxf4+fkZrc3yS7a2tpxrQBBCIDs7W73kc+3aNXXfkCFDIEkSZs2ahQ4dOmiYJVHrUFBQAD8/P3V1cmdnZ7Vv0YgRI3hGkx5asxUsu3btQk5Ozh3PmPxaeXk5cnNzERUV1QyZUUtz+fJlxMfHQ1EUHDlyRI17eHggMjISkiRxNVaiJlRXV4etW7fi6NGj+NOf/gSg/vM3btw4WFtbQ5IkhIaGshUANaoGFyzl5eVGZz7OnDmD7OxsuLq6okuXLli4cCEuXryImJgYo+d9/fXX8Pf3v+MXyauvvoopU6bAx8cHly5dwqJFi2BpaYmIiIgHOCQyR1VVVdiwYQNkWUZ6ejrq6uoA1J9tmzp1KiRJwoQJE3g7PFETOn78OBRFQVxcHC5dugRLS0tER0erE9c3bdrEzyA1mQb/y/rxxx8RGBiobt+aSyJJEmRZRn5+vtG1S6D+vvq1a9figw8+uONrXrhwAREREbh+/To6duyIUaNG4YcffkDHjh0bmh6ZESEE9u/fD1mWkZiYiKKiInXfiBEjoNfrMWPGDLRr107DLInMW2FhIRITEyHLMvbv36/GXV1dMWvWLNTW1qoxFivUlHTi1gXHFqy0tBTOzs4oKSmBk5OT1unQQ7p48SJiY2OhKApOnjypxjt37oyoqChIkoRevXppmCFR6/Hpp5/iD3/4A4D6gmTy5MmQJAkhISGcS0gPrSHf3yyHySRUVFRg3bp1UBQFW7duVSfu2dvbY9q0adDr9QgMDISlpaXGmRKZryNHjkBRFAwZMgSzZ88GAISHh0OWZYSHh2P27Nlwc3PTOEtqrViwkGaEENi7dy8URUFSUpJRA8DRo0dDkiRMnz6dZ82ImtDVq1eRkJAAWZaRnZ0NoL431q2CpV27dkZLWBBphQULNbtz584hJiYGMTExRhO4u3btqq7I2r17dw0zJDJ/69evx4oVK5CWlqbOQ7G2tsaUKVMgSZLRej5EpoAFCzWL8vJyrF27FoqiYOfOnWrcwcEB06dPhyRJePzxx9mem6iZfPHFF0hLSwMADBs2DHq9HuHh4Wjfvr3GmRHdGQsWajIGgwG7d++GLMtYs2YNbty4oe4bO3YsJEnCtGnT2PWSqAnl5+cjPj4esbGxSE1NRdeuXQEAL774Ivr27QtJkvDII49omyTRfWDBQo0uNzdXveRz9uxZNd69e3d1RdZfL35JRI2nsrIS69evh6IoSE9Ph8FgAADExsbijTfeAFC/JMovl0UhMnUsWKhRlJaWYvXq1ZBlGXv27FHjTk5OmDlzJiRJwsiRI3lNnKgJXblyBYsWLUJiYiKKi4vV+MiRIyFJEmbMmKFdckQPiQULPbC6ujrs2LEDiqIgOTkZN2/eBABYWFhg/PjxkCQJYWFhbM9N1ISqqqrUfigODg6Ii4tDeXk5vL291b5Ffn5+GmdJ9PBYsFCDnTp1CoqiIDY2FhcuXFDjffr0gSRJiIyMRKdOnTTMkMi8VVRUICUlBYqi4MqVKzh06BB0Oh0cHBzw3nvvwdfXF4GBgZzETmaFBQvdl6KiIiQmJkJRFKOeDO3atUNERAQkScLw4cN5yYeoidzqWyTLMpKSklBWVqbu++9//6t2f547d65WKRI1KRYsdFe1tbXYvHkzFEVBamoqqqurAQCWlpaYNGkSJEnClClT2J6bqIklJyfjtddeQ25urhrz9fVVJ7H7+vpqmB1R82DBQrc5duwYZFlGfHw8CgoK1Hj//v2h1+sxe/ZsdXVWImp8ZWVlqK6uVnui2NvbIzc3F46OjpgxYwYkScKoUaN4yYdaFRYsBAC4du0aVq5cCVmWcfDgQTXeoUMHzJ49G5IkYdCgQbzkQ9REDAYDMjIyIMsy1q5di5dffhlLly4FAIwfPx4JCQkIDQ2Fg4ODxpkSaYMFSytWU1ODjRs3QlEUfPvtt6ipqQFQ3577ySefhCRJmDRpEmxsbDTOlMh8nT59Wp3EnpeXp8azsrLU/7ayskJERIQW6RGZDBYsrVB2djZkWUZCQgKuXr2qxocOHQpJkhAREYEOHTpomCFR6xAaGooNGzao287OzggPD4ckSRgxYoSGmRGZHhYsrcTly5cRHx8PRVFw5MgRNe7u7q72aujXr5+GGRKZt7q6OuzatQuBgYHqpdUuXbrAwsICwcHBkCQJoaGh7FtEdBc6IYTQOomHVVpaCmdnZ5SUlMDJyUnrdExGVVUVNmzYAEVRsGnTJtTV1QEAbGxsEBYWBkmSMGHCBFhZsW4laionTpxQL/lcunQJu3fvxujRowEAFy5cgIWFBby8vDTOkkgbDfn+5jeVmRFCYP/+/VAUBStXrkRRUZG6z9/fH3q9HjNnzkS7du00zJLIvBUWFiIxMRGyLGP//v1q3NXVFefPn1e3O3furEV6RC0SCxYzcfHiRcTFxUGWZZw8eVKNd+rUCdHR0YiOjkbv3r01zJCodTh+/DgGDx5s1Ldo8uTJ0Ov1CAkJYd8iogfEgqUFu3nzJtatWwdZlrFt2zZ1RVZ7e3s89dRTkCQJ48aNg6WlpcaZEpmvI0eOIDc3F0899RQAoHfv3vDy8oKzszP0ej1mzZoFNzc3jbMkavlYsLQwQgh8//33anvu0tJSdd+oUaOg1+sxffp0zuUhakJXr15FQkICZFlGdnY22rdvj5CQENjY2MDCwgL79+/nnXZEjYwFSwtx7tw5xMbGQlEU5OTkqHEfHx+1PXf37t01zJDIvFVXVyMtLQ2yLGPjxo2ora0FUN+3aMyYMSgsLISHhwcAsFghagIsWExYeXk5kpOTIcsydu7cqcYdHBzwzDPPQJIkjBkzhu25iZrB3//+d/zzn/9Ut4cNGwa9Xo/w8HC1hT4RNR0WLCbGYDBg9+7dkGUZa9aswY0bN9R9gYGB0Ov1mDZtGhwdHTXMksi85efnIz4+HgEBAXjssccAABEREVixYgUiIyMhSRL69u2rcZZErQsLFhORm5uLmJgYxMTE4OzZs2q8e/fu0Ov1iIqKgo+Pj3YJEpm5yspKrF+/HoqiID09HQaDAeHh4WrB0rdvX5w/f56T2Ik0woJFQ6WlpVi9ejVkWcaePXvUuJOTE2bOnAlJkjBy5EguOEjURIQQyMrKgizLSExMRHFxsbovICAAwcHBRuNZrBBphwVLM6urq8OOHTugKAqSk5Nx8+ZNAICFhQXGjx8PSZIQFhbG9txEzWTOnDk4fvw4AMDb2xtRUVGIjo5Gr169NM6MiH6JBUszOXXqlNqe+8KFC2q8T58+kCQJkZGR6NSpk4YZEpm3iooKpKSkYNWqVVi5ciUcHByg0+kwb948ZGZmQq/XIzAwkJPYiUwU1xJqQkVFRVi1ahUURcEPP/ygxtu1a4eIiAhIkoThw4fzkg9RExFCYM+ePVAUBUlJSSgrKwMAxMbGIjIyUuPsiIhrCWmotrYWW7ZsgaIoSE1NRVVVFYD6a98TJ05UV2Rle26ipnP16lV8+umniImJQW5urhr39fVFdHS0uvggEbUcLFgaybFjx6AoCuLi4lBQUKDG+/fvr7bnvtVUioiaVnl5ORYtWgQAcHR0xPTp0yFJEkaPHs1LPkQtVIM/ubt378aUKVPg5eUFnU6HdevW3XN8RkYGdDrdbY9ffqkDwCeffIKuXbvCzs4O/v7+yMrKamhqze7atWv46KOPMGzYMPTv3x/Lly9HQUEBOnTogD/+8Y84ePAgDh8+jAULFrBYIWoCBoMBO3fuhCRJmDVrlhr39fXFK6+8AkVRUFBQgBUrVrDJIlEL1+AzLDdu3MDAgQMxZ84cTJs27b6fd+rUKaPrU79cDGzVqlVYsGABPvvsM/j7++P9999HcHAwTp06ZXKLhtXU1GDTpk2QZRnffvstampqAABWVlZ48sknodfrMWnSJNjY2GicKZH5ysnJUfsWnTt3DkD9Z/CDDz5Ax44dAQDLly/XMkUiamQNLlgmTZqESZMmNfgHubm5wcXF5Y773n33XTz//PN49tlnAQCfffYZ0tLSsGLFCrz++usN/llNITs7G7IsIyEhAVevXlXjQ4YMgV6vR0REBNcPIWpiGzZswLJly7B371415uzsrPYt4meQyHw12xyWQYMGoaqqCv369cNbb72ldo+srq7GgQMHsHDhQnWshYUFgoKCsG/fvju+VlVVlTqZFYDRisWNqbi4GN988w1kWcaRI0fUuLu7u9qeu3///k3ys4movm9RXV2desYyLy8Pe/fuhYWFBSZMmAC9Xo/Q0FD2LSJqBZq8YPH09MRnn32GYcOGoaqqCl999RWeeOIJZGZmYsiQIbh27Rrq6urg7u5u9Dx3d3ecPHnyjq+5ZMkSLF68uKlTR0VFBV599VUYDAbY2Nhg6tSp0Ov1mDBhAqysOF+ZqKmcOHFCncT+5ptv4oUXXgAAhIeHo7y8HFFRUfDy8tI4SyJqTk3+rdurVy+jjpEjR45Ebm4u3nvvPcTGxj7Qay5cuBALFixQt0tLS+Ht7f3Quf6al5cX/ud//gc9evTAzJkz0a5du0b/GURUr7CwEImJiVAUxWjSfUpKilqwtG/fHn/+85+1SpGINKTJaYJHH31UXTunQ4cOsLS0xOXLl43GXL58+a531tja2jZbHxNO3CNqWgaDAbNnz0ZycjKqq6sB1Pctmjx5MiRJwpNPPqlxhkRkCjS5xy87Oxuenp4AABsbGwwdOhTbt29X9xsMBmzfvh0BAQFapEdETezMmTPqf1tYWKCkpATV1dUYMGAA3n33XVy8eBHr16/H008/zSaLRATgAc6wlJeXIycnR90+c+YMsrOz4erqii5dumDhwoW4ePEiYmJiAADvv/8+fH190bdvX1RWVuKrr77Cjh07sGXLFvU1FixYAEmSMGzYMDz66KN4//33cePGDfWuISJq+a5evYqEhAQoioLs7GycPXsWXbp0AQC8/fbbeOeddzBo0CBtkyQik9XgguXHH39EYGCgun1rLokkSZBlGfn5+cjLy1P3V1dX45VXXsHFixfRpk0bDBgwANu2bTN6jZkzZ+Lq1at48803UVBQgEGDBiE9Pf22ibhE1LJUV1dj48aNkGUZaWlpqK2tBQBYW1sjMzNTLViGDBmiZZpE1AJw8UMiahJZWVkICQnBtWvX1NiwYcMgSRIiIiLQvn17DbMjIlPAxQ+JqNkVFBTg4sWLGDp0KACgT58+qKiogKenp9q3qG/fvhpnSUQtFQsWInpglZWV2LBhAxRFQXp6Ovr27YvDhw8DANq2bYsffvgBffr0Yd8iInpo/C1CRA0ihEBWVhYURcHKlStRXFys7nNwcEBJSQmcnZ0BgJ2giajRsGAhogaZP38+PvzwQ3W7c+fOiI6ORnR0tFGTSCKixsS11onorioqKpCQkICff/5ZjU2YMAH29vaIjIzE1q1bcfbsWfzzn/9ksUJETYpnWIjIiBACe/fuhSzLSEpKQllZGRYuXIh33nkHABAcHIyCggLekUdEzYoFCxEBAM6ePYuYmBjExMQgNzdXjfv6+hotNGhlZcVihYiaHQsWIkJNTQ2GDh2KwsJCAICjoyOmT58OSZIwevRoWFjw6jERaYsFC1ErYzAYkJGRgbS0NCxfvhw6nQ7W1taIiIjAyZMnIUkSpk2bBgcHB61TJSJSsdMtUSuRk5MDRVEQExOjLp+xZ88ePPbYYwDqCxmeSSGi5sROt0QEoP6XQVJSEmRZxt69e9W4s7MzZs6ciQ4dOqgxFitEZMpYsBCZsQMHDuD5558HUF+QTJgwAZIkYerUqbC3t9c4OyKi+8eChchMnDx5EoqiwNHREX/9618BAGPGjEFwcDDGjh2LyMhIo7t9iIhaEs5hIWrBioqKkJiYCFmWkZWVBQDo0KEDLl68CBsbG42zIyK6N85hITJzO3bswGeffYbU1FRUV1cDACwtLTF58mRIksT5KERkdliwELUQQgjodDoAwMaNG7F69WoAwIABA6DX6zFr1iy4u7trmSIRUZNhwUJkwq5evYqVK1dClmUsW7YM48ePBwA8++yzqKurgyRJGDRokLZJEhE1A85hITIx1dXV2LhxI2RZRlpaGmprawEAs2fPRlxcnMbZERE1Hs5hIWqBbt68iddffx0JCQm4du2aGh86dCgkSUJERISG2RERaYsFC5GGbty4obbAt7Ozw5YtW3Dt2jV4eHggMjISkiShX79+GmdJRKQ9FixEzayyshIbNmyAoij4/vvvceHCBbRp0wY6nQ7Lli2DtbU1xo8fDysrfjyJiG7hb0SiZiCEQFZWFhRFwcqVK1FcXKzuy8jIwOTJkwEAoaGhGmVIRGTaWLAQNbE9e/bg+eefx8mTJ9VY586dERUVBUmS0KtXLw2zIyJqGViwEDWyiooKFBYWonPnzgAAT09PnDx5Evb29pg2bRr0ej0CAwNhaWmpcaZERC0HCxaiRiCEwN69e6EoCpKSkhAYGIh169YBALp3745169YhMDCQt90TET0gFixED+HcuXOIiYlBTEwMcnJy1PiJEydQU1MDa2trAMDUqVO1SpGIyCywYCF6QC+//DI+/vhjddvR0RHTp0+HJEkYPXo01/MhImpELFiI7oPBYMCuXbswdOhQ9bKOn58fdDodAgMDodfrMW3aNLWnChERNS625ie6h9zcXCiKgpiYGJw7dw5ffvkl5s6dCwAoKSlBcXExfHx8NM6SiKhlYmt+oodQWlqKpKQkKIqCPXv2qHEnJyeUlJSo287OznB2dtYiRSKiVocFC9EvlJaWolOnTigvLwcAWFhYYPz48ZAkCWFhYbC3t9c4QyKi1qnBswJ3796NKVOmwMvLCzqdTr11826Sk5Mxfvx4dOzYEU5OTggICMDmzZuNxrz11lvQ6XRGj969ezc0NaIGO3nyJL766it128nJCY899hj69OmDpUuXIi8vD+np6YiIiGCxQkSkoQafYblx4wYGDhyIOXPmYNq0ab85fvfu3Rg/fjzeeecduLi44JtvvsGUKVOQmZmJwYMHq+P69u2Lbdu2/V9iXEeFmkhRURESExOhKAoyMzOh0+kwceJEtdHbqlWr4OTkBJ1Op3GmRER0S4OrgkmTJmHSpEn3Pf7999832n7nnXeQmpqKDRs2GBUsVlZW8PDwaGg6RPeltrYWW7ZsgSzLSE1NRXV1NQDA0tISkyZNQllZmTqW81KIiExPs5/GMBgMKCsrg6urq1H89OnT8PLygp2dHQICArBkyRJ06dLljq9RVVWFqqoqdbu0tLRJc6aWLyEhAZIkqdsDBgyAXq/HrFmz4O7urmFmRER0P5q9YFm+fDnKy8sxY8YMNebv7w9ZltGrVy/k5+dj8eLFGD16NI4dO4a2bdve9hpLlizB4sWLmzNtakGuXbuGhIQEeHh4qP/OwsLC4OPjg6eeegqSJGHQoEHaJklERA3yUH1YdDodUlJSEBYWdl/jExIS8PzzzyM1NRVBQUF3HXert8W7776L55577rb9dzrD4u3tzT4srVh1dTU2bdoEWZaRlpaGmpoaDB48GAcPHlTHCCE4L4WIyISYZB+WxMREzJ07F6tXr75nsQIALi4u8PPzM1qb5ZdsbW1ha2vbFGlSC5OdnQ1ZlhEfH49r166p8SFDhkCSJNTV1amrIrNYISJquZqlYFm5ciXmzJmDxMREhISE/Ob48vJy5ObmIioqqhmyo5bsH//4B5KTkwEAHh4eiIyMhCRJ6Nevn8aZERFRY2pwwVJeXm505uPMmTPIzs6Gq6srunTpgoULF+LixYuIiYkB8H+THT/44AP4+/ujoKAAAGBvb6/ejfHqq69iypQp8PHxwaVLl7Bo0SJYWloiIiKiMY6RzEBlZSU2bNgARVHw7rvvws/PDwAwd+5cWFlZQZIkTJgwgbfDExGZK9FAO3fuFABue0iSJIQQQpIkMWbMGHX8mDFj7jleCCFmzpwpPD09hY2NjejUqZOYOXOmyMnJue+cSkpKBABRUlLS0MMhE2YwGMQPP/wg5s2bJ1xcXNR/O3/961+1To2IiBpBQ76/ufghmZzy8nJ8/PHHUBQFJ0+eVOOdO3dGVFQU9Hq9eoaFiIhaLpOcdEt0L+IXd/BYWVlh6dKlKCkpgb29PaZNmwa9Xo/AwEB1Ai0REbUuLFhIM0II7N27F4qi4PDhw2qbfDs7O7z11lto27Ytpk+fzrNmRETEgoWa37lz5xATE4OYmBijCdxZWVnw9/cHAMyfP1+j7IiIyBSxYKFms2fPHrz55pvYuXOnGnNwcMD06dMhSRKGDx+uYXZERGTKWLBQkzEYDLh58yYcHBwA1HcovlWsjB07FpIkYdq0aXB0dNQyTSIiagEstE6AzE9ubi7efPNNdOvWDW+88YYaDwwMxPLly3H27Fls374d0dHRLFaIiOi+8LZmahQlJSVYvXo1FEXBnj171HjPnj1x6tQptsUnIqLb8LZmalbz58/HF198gZs3bwIALCwsMH78eEiShLCwMBYrRET00FiwUIOdOnUKPXv2hIVF/RVFCwsL3Lx5E71794Zer0dkZCQ6deqkcZZERGROeEmI7ktRURFWrVoFWZaRmZmJbdu2Ydy4cQCAs2fP4sqVKxg+fDjPphAR0X3jJSFqFLW1tdiyZQsURUFqaiqqqqoAAJaWlsjOzlYLlq5du6Jr164aZkpEROaOBQvd0YULFzB8+HB1dW0A6N+/P/R6PWbNmgUPDw8NsyMiotaGBQsBAK5du4YjR45g7NixAIBOnTrByckJtbW1mDVrFiRJwuDBg3nJh4iINMGCpRWrqanBxo0boSgKvv32W9jb26OgoAD29vbQ6XRIS0tDly5dYGNjo3WqRETUyrFgaWWEEMjOzoaiKEhISMDVq1fVff3798eFCxfQs2dPAECPHj20SpOIiMgIC5ZW5sMPPzRaWNDd3R1RUVGQJAn9+vXTLjEiIqJ7YGt+M1ZVVYU1a9bghx9+UGOTJ0+Gra0tpk+fjrS0NFy4cAH//ve/WawQEZFJ4xkWMyOEwP79+6EoClauXImioiI89dRTSE5OBlDfKv/q1ato27atxpkSERHdPxYsZuLixYuIi4uDoig4ceKEGu/UqRP69+9vNJbFChERtTQsWMxEWFgYfvzxRwCAvb09nnrqKUiShHHjxsHS0lLj7IiIiB4OC5YWRgiBffv2ITY2FsuWLVNbGUdFRcHOzg56vR7Tp0/nEgVERGRWuJZQC5GXl4eYmBjExMTg9OnTAICvv/4ac+bMAVBfyLCpGxERtSRcS8hMVFRUYM2aNVAUBTt37sSt2tLBwQHPPPMMBg4cqI5lsUJEROaMBYsJKywshF6vVwuVwMBA6PV6TJs2DY6OjhpnR0RE1HxYsJiI3NxcxMTEID8/H1988QUAoHPnzpg7dy68vb0RFRXFFZGJiKjV4hwWDZWWlmL16tVQFAXfffcdAMDCwgJ5eXno1KmTxtkRERE1Lc5hMXFZWVn48MMPkZycjJs3bwKoL1SCgoIgSRLat2+vcYZERESmhQVLM/nlXTxHjhxBfHw8AKBPnz6QJAmRkZE8q0JERHQXLFiaUFFREVatWgVFUTBr1iy8/PLLAIDp06fj8OHDiIqKwvDhw3mHDxER0W/gHJZGVltbi61bt0KWZaSmpqKqqgoAMHz4cGRlZWmaGxERkSnhHBaN/PWvf8WKFStQUFCgxvr37w+9Xo9Zs2ZpmBlRy1RbU4tD24+i6HIJOnRyxcDAvlxqgqiVsmjoE3bv3o0pU6bAy8sLOp0O69at+83nZGRkYMiQIbC1tUWPHj0gy/JtYz755BN07doVdnZ28Pf3bxFnI0pKSoy2f/rpJxQUFKBDhw744x//iIMHD+Lw4cNYsGABPDw8NMqSqGXaFrcbEd6/x18mv4N/P/sJ/jzhH5jtMw/fJWdqnRoRaaDBBcuNGzcwcOBAfPLJJ/c1/syZMwgJCUFgYCCys7Mxf/58zJ07F5s3b1bHrFq1CgsWLMCiRYtw8OBBDBw4EMHBwbhy5UpD02tyNTU1SE1NxbRp0+Dm5oacnBx13+uvv45169bh4sWLeP/99zF48GDOTyF6ANvidmNZ9EcovmL8R8H1/CL8ffpy7F1n+n/QEFHjeqg5LDqdDikpKQgLC7vrmD//+c9IS0vDsWPH1Fh4eDiKi4uRnp4OAPD398fw4cPx8ccfAwAMBgO8vb3x8ssv4/XXX//NPJp6DosQAtnZ2VAUBfHx8bh27Zq676OPPsJLL73U6D+TqLWqralFeOffoeRq6Z0H6ACPrm5QTn8EC4sG/81FRCbEpOaw7Nu3D0FBQUax4OBgzJ8/HwBQXV2NAwcOYOHCher+Wz1J9u3bd8fXrKqqUiezAvUH3FROnTqF6dOn4+jRo2rM3d0dkZGRkCQJ/fv3b7KfTdQaHdp+9O7FCgAIoODMFZz44TT6juzVfIkRkaaavGApKCiAu7u7Uczd3R2lpaW4efMmioqKUFdXd8cxJ0+evONrLlmyBIsXL26ynH/J29sb586dg42NDaZOnQq9Xo8JEybAyorzlYmaQmFBcaOOIyLz0CK/dRcuXIgFCxao26WlpfD29m6Sn9WmTRukpqZiwIABcHV1bZKfQUT/p73X/X3OOnTi55GoNWnygsXDwwOXL182il2+fBlOTk6wt7eHpaUlLC0t7zjmbnfW2NrawtbWtsly/rUnnnii2X4WUWs3eGw/tPNwQdFdzqDodDp49fBA70d7NG9iRKSpJp+xFhAQgO3btxvFtm7dioCAAACAjY0Nhg4dajTGYDBg+/bt6hgiaj0srSzx0odzAB3qH7+g0+kAHfDiB8/yDjyiVqbBBUt5eTmys7ORnZ0NoP625ezsbOTl5QGov1wTHR2tjv/973+Pn3/+Ga+99hpOnjyJ//znP0hKSsL//M//qGMWLFiAL7/8Eoqi4MSJE5g3bx5u3LiBZ5999iEPj4haosefCcCiNa/CrUtHo7hnd3f889uFGD5xsEaZEZFWGnxJ6Mcff0RgYKC6fWsuiSRJkGUZ+fn5avECAL6+vkhLS8P//M//4IMPPkDnzp3x1VdfITg4WB0zc+ZMXL16FW+++SYKCgowaNAgpKen3zYRl4haj1FP+WPk1OE4vu+/KCooRvtOrujj35NnVohaKa4lRERERJpoyPc3uy4RERGRyWPBQkRERCaPBQsRERGZPBYsREREZPJYsBAREZHJY8FCREREJo8FCxEREZk8FixERERk8liwEBERkclr8tWam8OtZr2lpaUaZ0JERET369b39v003TeLgqWsrAwA4O3trXEmRERE1FBlZWVwdna+5xizWEvIYDDg0qVLaNu2baMvjFZaWgpvb2+cP3/eLNcpMvfjA8z/GHl8LZ+5H6O5Hx9g/sfYVMcnhEBZWRm8vLxgYXHvWSpmcYbFwsICnTt3btKf4eTkZJb/CG8x9+MDzP8YeXwtn7kfo7kfH2D+x9gUx/dbZ1Zu4aRbIiIiMnksWIiIiMjksWD5Dba2tli0aBFsbW21TqVJmPvxAeZ/jDy+ls/cj9Hcjw8w/2M0heMzi0m3REREZN54hoWIiIhMHgsWIiIiMnksWIiIiMjksWAhIiIik9eqCpbdu3djypQp8PLygk6nw7p1637zORkZGRgyZAhsbW3Ro0cPyLJ825hPPvkEXbt2hZ2dHfz9/ZGVldX4yd+nhh5jcnIyxo8fj44dO8LJyQkBAQHYvHmz0Zi33noLOp3O6NG7d+8mPIq7a+jxZWRk3Ja7TqdDQUGB0ThTeQ8benx6vf6Ox9e3b191jCm9f0uWLMHw4cPRtm1buLm5ISwsDKdOnfrN561evRq9e/eGnZ0d+vfvj40bNxrtF0LgzTffhKenJ+zt7REUFITTp0831WHc04Mc45dffonRo0ejXbt2aNeuHYKCgm77N3in93rixIlNeSh39CDHJ8vybbnb2dkZjTGV9/BBju+JJ5644+cwJCREHWMq7x8AfPrppxgwYIDaBC4gIACbNm2653NM4TPYqgqWGzduYODAgfjkk0/ua/yZM2cQEhKCwMBAZGdnY/78+Zg7d67RF/qqVauwYMECLFq0CAcPHsTAgQMRHByMK1euNNVh3FNDj3H37t0YP348Nm7ciAMHDiAwMBBTpkzBoUOHjMb17dsX+fn56mPPnj1Nkf5vaujx3XLq1Cmj/N3c3NR9pvQeNvT4PvjgA6PjOn/+PFxdXTF9+nSjcaby/u3atQsvvvgifvjhB2zduhU1NTWYMGECbty4cdfnfP/994iIiMBzzz2HQ4cOISwsDGFhYTh27Jg65l//+hc+/PBDfPbZZ8jMzISDgwOCg4NRWVnZHIdl5EGOMSMjAxEREdi5cyf27dsHb29vTJgwARcvXjQaN3HiRKP3ceXKlU19OLd5kOMD6juk/jL3c+fOGe03lffwQY4vOTnZ6NiOHTsGS0vL2z6HpvD+AUDnzp2xdOlSHDhwAD/++CPGjh2LqVOn4qeffrrjeJP5DIpWCoBISUm555jXXntN9O3b1yg2c+ZMERwcrG4/+uij4sUXX1S36+rqhJeXl1iyZEmj5vsg7ucY7+SRRx4RixcvVrcXLVokBg4c2HiJNZL7Ob6dO3cKAKKoqOiuY0z1PXyQ9y8lJUXodDpx9uxZNWaq758QQly5ckUAELt27brrmBkzZoiQkBCjmL+/v/jd734nhBDCYDAIDw8P8e9//1vdX1xcLGxtbcXKlSubJvEGuJ9j/LXa2lrRtm1boSiKGpMkSUydOrUJMnw493N833zzjXB2dr7rflN+Dx/k/XvvvfdE27ZtRXl5uRoz1ffvlnbt2omvvvrqjvtM5TPYqs6wNNS+ffsQFBRkFAsODsa+ffsAANXV1Thw4IDRGAsLCwQFBaljWhqDwYCysjK4uroaxU+fPg0vLy9069YNs2fPRl5enkYZPphBgwbB09MT48ePx969e9W4ub2HX3/9NYKCguDj42MUN9X3r6SkBABu+/f2S7/1OTxz5gwKCgqMxjg7O8Pf398k3sP7OcZfq6ioQE1NzW3PycjIgJubG3r16oV58+bh+vXrjZrrg7jf4ysvL4ePjw+8vb1v+2velN/DB3n/vv76a4SHh8PBwcEoborvX11dHRITE3Hjxg0EBATccYypfAZZsNxDQUEB3N3djWLu7u4oLS3FzZs3ce3aNdTV1d1xzK/nSLQUy5cvR3l5OWbMmKHG/P39Icsy0tPT8emnn+LMmTMYPXo0ysrKNMz0/nh6euKzzz7D2rVrsXbtWnh7e+OJJ57AwYMHAcCs3sNLly5h06ZNmDt3rlHcVN8/g8GA+fPn47HHHkO/fv3uOu5un8Nb78+t/zXF9/B+j/HX/vznP8PLy8voC2DixImIiYnB9u3bsWzZMuzatQuTJk1CXV1dU6R+X+73+Hr16oUVK1YgNTUVcXFxMBgMGDlyJC5cuADAdN/DB3n/srKycOzYsds+h6b2/h09ehSOjo6wtbXF73//e6SkpOCRRx6541hT+QyaxWrN1DgSEhKwePFipKamGs3xmDRpkvrfAwYMgL+/P3x8fJCUlITnnntOi1TvW69evdCrVy91e+TIkcjNzcV7772H2NhYDTNrfIqiwMXFBWFhYUZxU33/XnzxRRw7dkyz+TTN4UGOcenSpUhMTERGRobRxNTw8HD1v/v3748BAwage/fuyMjIwLhx4xo17/t1v8cXEBBg9Nf7yJEj0adPH3z++ef4xz/+0dRpPrAHef++/vpr9O/fH48++qhR3NTev169eiE7OxslJSVYs2YNJEnCrl277lq0mAKeYbkHDw8PXL582Sh2+fJlODk5wd7eHh06dIClpeUdx3h4eDRnqg8tMTERc+fORVJS0m2n/n7NxcUFfn5+yMnJaabsGtejjz6q5m4u76EQAitWrEBUVBRsbGzuOdYU3r+XXnoJ3377LXbu3InOnTvfc+zdPoe33p9b/2tq72FDjvGW5cuXY+nSpdiyZQsGDBhwz7HdunVDhw4dNHsfH+T4brG2tsbgwYPV3E3xPXyQ47tx4wYSExPv6w8Brd8/Gxsb9OjRA0OHDsWSJUswcOBAfPDBB3ccayqfQRYs9xAQEIDt27cbxbZu3ar+pWBjY4OhQ4cajTEYDNi+fftdrwWaopUrV+LZZ5/FypUrjW7Du5vy8nLk5ubC09OzGbJrfNnZ2Wru5vIe7tq1Czk5Off1i1LL908IgZdeegkpKSnYsWMHfH19f/M5v/U59PX1hYeHh9GY0tJSZGZmavIePsgxAvV3WfzjH/9Aeno6hg0b9pvjL1y4gOvXrzf7+/igx/dLdXV1OHr0qJq7Kb2HD3N8q1evRlVVFSIjI39zrFbv390YDAZUVVXdcZ/JfAYbbfpuC1BWViYOHTokDh06JACId999Vxw6dEicO3dOCCHE66+/LqKiotTxP//8s2jTpo3405/+JE6cOCE++eQTYWlpKdLT09UxiYmJwtbWVsiyLI4fPy5eeOEF4eLiIgoKCpr9+IRo+DHGx8cLKysr8cknn4j8/Hz1UVxcrI555ZVXREZGhjhz5ozYu3evCAoKEh06dBBXrlwx+eN77733xLp168Tp06fF0aNHxR//+EdhYWEhtm3bpo4xpfewocd3S2RkpPD397/ja5rS+zdv3jzh7OwsMjIyjP69VVRUqGOioqLE66+/rm7v3btXWFlZieXLl4sTJ06IRYsWCWtra3H06FF1zNKlS4WLi4tITU0VR44cEVOnThW+vr7i5s2bzXp8QjzYMS5dulTY2NiINWvWGD2nrKxMCFH/7+LVV18V+/btE2fOnBHbtm0TQ4YMET179hSVlZUmf3yLFy8WmzdvFrm5ueLAgQMiPDxc2NnZiZ9++kkdYyrv4YMc3y2jRo0SM2fOvC1uSu+fEPW/R3bt2iXOnDkjjhw5Il5//XWh0+nEli1bhBCm+xlsVQXLrVtcf/2QJEkIUX/b2ZgxY257zqBBg4SNjY3o1q2b+Oabb2573Y8++kh06dJF2NjYiEcffVT88MMPTX8wd9HQYxwzZsw9xwtRfyu3p6ensLGxEZ06dRIzZ84UOTk5zXtg/09Dj2/ZsmWie/fuws7OTri6uoonnnhC7Nix47bXNZX38EH+jRYXFwt7e3vxxRdf3PE1Ten9u9OxATD6XI0ZM8bo358QQiQlJQk/Pz9hY2Mj+vbtK9LS0oz2GwwG8cYbbwh3d3dha2srxo0bJ06dOtUMR3S7BzlGHx+fOz5n0aJFQgghKioqxIQJE0THjh2FtbW18PHxEc8//7wmRfWDHN/8+fPVz5e7u7uYPHmyOHjwoNHrmsp7+KD/Rk+ePCkAqF/6v2RK758QQsyZM0f4+PgIGxsb0bFjRzFu3DijvE31M6gTQohGOllDRERE1CQ4h4WIiIhMHgsWIiIiMnksWIiIiMjksWAhIiIik8eChYiIiEweCxYiIiIyeSxYiIiIyOSxYCEiIiKTx4KFiIiITB4LFiIiIjJ5LFiIiIjI5LFgISIiIpP3/wMe7LlYqfjBzgAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from cvxopt import matrix, solvers\n",
        "\n",
        "# Define the positive examples (class 1)\n",
        "x1 = np.array([1, 2])\n",
        "x2 = np.array([2, 3])\n",
        "x3 = np.array([3, 3])\n",
        "\n",
        "# Define the negative examples (class -1)\n",
        "x4 = np.array([2, 1])\n",
        "x5 = np.array([3, 2])\n",
        "\n",
        "# Combine all examples into one matrix\n",
        "X = np.vstack((x1, x2, x3, x4, x5))\n",
        "\n",
        "# Define the class labels\n",
        "y = np.array([1, 1, 1, -1, -1])\n",
        "\n",
        "X = X.astype(float)\n",
        "y = y.astype(float)\n",
        "\n",
        "# Define the number of samples\n",
        "n_samples = X.shape[0]\n",
        "\n",
        "# Define the Hessian Q = y_i y_j x_i^T x_j\n",
        "Q = np.outer(y, y) * np.dot(X, X.T)\n",
        "\n",
        "Q = Q.astype(float)\n",
        "\n",
        "# Convert to cvxopt matrices\n",
        "P = matrix(Q)\n",
        "q = matrix(-np.ones(n_samples))\n",
        "\n",
        "# Define the constraints Gw <= h\n",
        "# Constraints are y_i*w^T*x_i >= 1 for all points\n",
        "G = matrix(np.diag(-np.ones(n_samples)))\n",
        "h = matrix(np.zeros(n_samples))\n",
        "\n",
        "# Define the constraints Aw = b\n",
        "# Constraint is sum(y_i * a_i) = 0\n",
        "A = matrix(y, (1, n_samples))\n",
        "b = matrix(0.0)\n",
        "\n",
        "# Solve the quadratic programming problem\n",
        "solution = solvers.qp(P, q, G, h, A, b)\n",
        "\n",
        "# Extract the Lagrange multipliers\n",
        "multipliers = np.ravel(solution['x'])\n",
        "\n",
        "# Extract the support vectors and their labels\n",
        "sv_idx = multipliers > 1e-5\n",
        "support_vectors = X[sv_idx]\n",
        "support_multipliers = multipliers[sv_idx]\n",
        "support_labels = y[sv_idx]\n",
        "\n",
        "# Compute the weight vector w\n",
        "w = np.sum(support_multipliers * support_labels * support_vectors.T, axis=1)\n",
        "\n",
        "# Compute the intercept b\n",
        "b = np.mean(support_labels - np.dot(support_vectors, w))\n",
        "\n",
        "print(\"Weights:\", w)\n",
        "print(\"Intercept:\", b)\n"
      ],
      "metadata": {
        "id": "pKz3AJGObNGP",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3712def3-81a9-40a3-edbc-962f6b46d8ac"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "     pcost       dcost       gap    pres   dres\n",
            " 0: -1.3804e+00 -3.5127e+00  2e+00  1e-16  2e+00\n",
            " 1: -1.8245e+00 -2.1119e+00  3e-01  3e-16  4e-01\n",
            " 2: -2.3247e+00 -2.6229e+00  3e-01  5e-16  9e-02\n",
            " 3: -2.4982e+00 -2.5070e+00  9e-03  4e-16  2e-03\n",
            " 4: -2.5000e+00 -2.5001e+00  9e-05  5e-16  2e-05\n",
            " 5: -2.5000e+00 -2.5000e+00  9e-07  2e-16  2e-07\n",
            " 6: -2.5000e+00 -2.5000e+00  9e-09  5e-16  2e-09\n",
            "Optimal solution found.\n",
            "Weights: [-1.  2.]\n",
            "Intercept: -2.0000000082288234\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# Define the weights and intercept from the SVM calculation\n",
        "w = np.array([-1., 2.])\n",
        "b = -2.000000008228825\n",
        "\n",
        "# Get the separating hyperplane\n",
        "a = -w[0] / w[1]\n",
        "xx = np.linspace(1, 3)\n",
        "yy = a * xx - b / w[1]\n",
        "\n",
        "# Plot the hyperplane\n",
        "plt.plot(xx, yy, 'k-')\n",
        "\n",
        "# Plot the margins\n",
        "margin = 1 / np.sqrt(np.sum(w ** 2))\n",
        "yy_down = yy - np.sqrt(1 + a ** 2) * margin\n",
        "yy_up = yy + np.sqrt(1 + a ** 2) * margin\n",
        "plt.plot(xx, yy_down, 'k--')\n",
        "plt.plot(xx, yy_up, 'k--')\n",
        "\n",
        "# Plot the support vectors (you need to identify these manually)\n",
        "# For the purpose of this demonstration, let's assume x2 and x4 are support vectors\n",
        "support_vectors = np.vstack((x2, x4))\n",
        "plt.scatter(support_vectors[:, 0], support_vectors[:, 1], s=100, facecolors='none', edgecolors='k')\n",
        "\n",
        "# Plot the data points\n",
        "plt.scatter(X[:, 0], X[:, 1], c=y)\n",
        "\n",
        "plt.show()\n"
      ],
      "metadata": {
        "id": "SK8Xs-ixbO0i",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "outputId": "b940257c-c209-49d6-d1d5-bee03728d6c1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Question 5 (a) and (b)"
      ],
      "metadata": {
        "id": "7cuax-nLrqa6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "def max_pooling_2d(input_matrix, pool_size=(1, 2), stride=1):\n",
        "    rows, cols = input_matrix.shape\n",
        "    pool_rows, pool_cols = pool_size\n",
        "\n",
        "    output_rows = int((rows - pool_rows) / stride) + 1\n",
        "    output_cols = int((cols - pool_cols) / stride) + 1\n",
        "\n",
        "    output_matrix = np.zeros((output_rows, output_cols))\n",
        "\n",
        "    for i in range(output_rows):\n",
        "        for j in range(output_cols):\n",
        "            start_i = i * stride\n",
        "            end_i = start_i + pool_rows\n",
        "            start_j = j * stride\n",
        "            end_j = start_j + pool_cols\n",
        "\n",
        "            output_matrix[i, j] = np.max(input_matrix[start_i:end_i, start_j:end_j])\n",
        "\n",
        "    return output_matrix\n",
        "# Input X1, X2 or X3\n",
        "X = np.array([[5, 0, 3, 5, 1],\n",
        "              [2, 8, 8, 7, 4],\n",
        "              [3, 3, 3, 3, 3],\n",
        "              [7, 7, 2, 9, 8]])\n",
        "\n",
        "# Input K1, K2 or K3\n",
        "K = np.array([[7, 0, 6],\n",
        "              [1, 1, 1],\n",
        "              [9, 3, 0]])\n",
        "\n",
        "rows_X, cols_X = X.shape\n",
        "rows_K, cols_K = K.shape\n",
        "\n",
        "rows_out = rows_X - rows_K + 1\n",
        "cols_out = cols_X - cols_K + 1\n",
        "\n",
        "output = np.zeros((rows_out, cols_out))\n",
        "\n",
        "for i in range(rows_out):\n",
        "    for j in range(cols_out):\n",
        "        output[i, j] = np.sum(X[i:i+rows_K, j:j+cols_K] * K)\n",
        "\n",
        "print(\"Convolution Result Matrix:\")\n",
        "print(output)\n",
        "# Example usage:\n",
        "input_matrix = np.array(output)\n",
        "\n",
        "output_matrix = max_pooling_2d(input_matrix, pool_size=(2, 2), stride=1)\n",
        "\n",
        "print(\"Maxpooling result:\")\n",
        "print(output_matrix)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "t_VeMbrtjE9u",
        "outputId": "76b098a6-2abf-435a-99e6-56676955d419"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Output Matrix:\n",
            "[[107.  89.  82.]\n",
            " [155. 176. 134.]]\n",
            "Output Matrix:\n",
            "[[176. 176.]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from sklearn.decomposition import PCA\n",
        "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n",
        "X = np.array([[-1, -1, 0, 2, 0],\n",
        "              [-2, 0, 0, 1, 1]])\n",
        "pca = PCA(n_components=1)\n",
        "X_pca = pca.fit_transform(X.T).T\n",
        "lda = LinearDiscriminantAnalysis(n_components=1)\n",
        "X_lda = lda.fit_transform(X.T, [0, 0, 0, 1, 1]).T\n",
        "print(\"PCA Result:\")\n",
        "print(X_pca)\n",
        "print(\"LDA Result:\")\n",
        "print(X_lda)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uXytWu3VVFDQ",
        "outputId": "67427e67-17ce-4fee-df13-485df63f63c8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "PCA Result:\n",
            "[[ 2.12132034  0.70710678 -0.         -2.12132034 -0.70710678]]\n",
            "LDA Result:\n",
            "[[-2.01246118e+00 -6.70820393e-01 -7.44760246e-17  2.01246118e+00\n",
            "   6.70820393e-01]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "X = np.array([[2, 0],\n",
        "              [1, 1]])\n",
        "\n",
        "# Calculate the covariance matrix\n",
        "covariance_matrix = np.cov(X)\n",
        "\n",
        "print(\"Covariance Matrix:\")\n",
        "print(covariance_matrix)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MoirQJS5WxeA",
        "outputId": "7e0ef59d-3cf2-4e5b-86c0-4dbdf14bc22f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Covariance Matrix:\n",
            "[[2. 0.]\n",
            " [0. 0.]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "matrix = np.array([[0.917, 0.917],\n",
        "                   [1.834, 1.834]])\n",
        "\n",
        "# Calculate eigenvalues and eigenvectors\n",
        "eigenvalues, eigenvectors = np.linalg.eig(matrix)\n",
        "\n",
        "print(\"Eigenvalues:\")\n",
        "print(eigenvalues)\n",
        "print(\"Eigenvectors:\")\n",
        "print(eigenvectors)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c2Nf_wC0YNMI",
        "outputId": "4130246d-b72c-4e52-ce79-e2bc04c40ac4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Eigenvalues:\n",
            "[0.    2.751]\n",
            "Eigenvectors:\n",
            "[[-0.70710678 -0.4472136 ]\n",
            " [ 0.70710678 -0.89442719]]\n"
          ]
        }
      ]
    }
  ]
}