6.non-Linear Classification.ipynb

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      "cell_type": "markdown",
      "metadata": {
        "id": "sQy9EvTe1J6q",
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      "source": [
        "### **Preparation**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YgZQmLLx1HWI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import copy\n",
        "import math\n",
        "import csv\n",
        "from collections import deque\n",
        "from google.colab import files"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oDTD9ppr1OAX",
        "colab_type": "text"
      },
      "source": [
        "### **Input Data**\n",
        "load the training data file\n",
        "each row $\\{ (x^{(i)}, y^{(i)}, l^{(i)}) \\}$ of the data consists of a 2-dimensional point $(x, y)$ with its label $l$  \n",
        "$x, y \\in \\mathbb{R}$ and $l \\in \\{0, 1\\}$"
      ]
    },
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          "resources": {
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      },
      "source": [
        "uploaded = files.upload()"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
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          "metadata": {
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        {
          "output_type": "stream",
          "text": [
            "Saving test.txt to test.txt\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MFaPtak-zpwW",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = np.genfromtxt(\"test.txt\", delimiter=',')\n",
        "x = data[:, 0]\n",
        "y = data[:, 1]\n",
        "label = data[:, 2]\n",
        "x_label0 = x[label == 0]\n",
        "x_label1 = x[label == 1]\n",
        "y_label0 = y[label == 0]\n",
        "y_label1 = y[label == 1]\n",
        "\n",
        "train_costs = deque()\n",
        "iters = deque()\n",
        "accuracys = deque()\n",
        "theta_0s = deque()\n",
        "theta_1s = deque()\n",
        "theta_2s = deque()\n",
        "theta_3s = deque()\n",
        "theta_4s = deque()\n",
        "theta_5s = deque()\n",
        "#print(label[57])\n",
        "#print(label[58])\n",
        "#print(type(x))\n",
        "#print(y_label0)\n",
        "#print(type(x_label0))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Cw4DKfx74hAg",
        "colab_type": "text"
      },
      "source": [
        "### **Logistic Regression**\n",
        "1) non-Linear Model\n",
        "<br>\n",
        "$\\ z =  g(x, y; \\theta) = \\theta_0 + \\theta_1x + \\theta_2y + \\theta_3xy + \\theta_4x^2 + \\theta_5y^2  $  \n",
        "$\\sigma(z) = \\frac{1}{1 + \\exp(-z)}$\n",
        "<br>  \n",
        "2) Objective Function\n",
        "<br>\n",
        "$J(\\theta) = \\frac{1}{m} \\sum_{i=1}^m ( - l^{(i)} \\log(\\sigma(g(x^{(i)}, y^{(i)}; \\theta))) - (1 - l^{(i)}) \\log(1 - \\sigma(g(x^{(i)}, y^{(i)}; \\theta)))  )$\n",
        "<br>  \n",
        "3) Gradient Descent\n",
        "<br>\n",
        "$\\theta_{k}^{(t+1)} = \\theta_0^{(t)} - \\alpha \\frac{1}{m} \\sum_{i=1}^{m} (\\sigma(g(x^{(i)}, y^{(i)}; \\theta)) - l^{(i)}) \\frac{\\partial g(x^{(i)}, y^{(i)}; \\theta^{(t)})}{\\partial \\theta_{k}}$, for all $k$  \n",
        "<br>\n",
        "4) HyperParameters Setting\n",
        "<br>\n",
        "$\\ \\theta_0^{(0)} = 10$  \n",
        "$\\ \\theta_1^{(0)} = 10$  \n",
        "$\\ \\theta_2^{(0)} = 10$  \n",
        "$\\ \\theta_3^{(0)} = 1$  \n",
        "$\\ \\theta_4^{(0)} = 1$  \n",
        "$\\ \\theta_5^{(0)} = 1$  \n",
        "$\\ lr = 6*10^{-3}$\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b8ZdZ71zkyiN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def sigmoidFunction(z):\n",
        "  result = 1/(1 + np.exp(-z))\n",
        "  return result"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3-gCevCjgKyl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def objectiveFunction(x_data, y_data, class_data, theta_0, theta_1, theta_2, theta_3, theta_4, theta_5):\n",
        "  cost = 0\n",
        "  predictions = deque()\n",
        "  for i in range(0, 118):\n",
        "    estimate = sigmoidFunction(theta_0 + theta_1 * x_data[i] + theta_2 * y_data[i] + theta_3 * x_data[i] * y_data[i] + theta_4 * np.power(x_data[i],2) + theta_5 * np.power(y_data[i],2)) \n",
        "    #print(estimate)\n",
        "    #print(\"Estimate\",estimate)\n",
        "    predictions.append((-class_data[i]*np.log(estimate)) - (1-class_data[i])*np.log(1-estimate))\n",
        "    #print(\"predictions\",predictions)\n",
        "  cost = np.sum(predictions) / 118\n",
        "  #print(\"Cost출력\",cost)\n",
        "  return cost"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NsaVBnlHiAys",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def gradientDescent(x_data, y_data, class_data, theta_0, theta_1, theta_2, theta_3, theta_4, theta_5):\n",
        "  for i in range(0, 118):\n",
        "    lr = 6e-3\n",
        "    estimate = sigmoidFunction(theta_0 + theta_1 * x_data[i] + theta_2 * y_data[i] + theta_3 * x_data[i] * y_data[i] + theta_4 * np.power(x_data[i],2) + theta_5 * np.power(y_data[i],2) ) - class_data[i]\n",
        "    theta_0 -= lr * estimate / 118\n",
        "    theta_1 -= lr * estimate * x_data[i] / 118\n",
        "    theta_2 -= lr * estimate * y_data[i] / 118\n",
        "    theta_3 -= lr * estimate * x_data[i] * y_data[i] / 118\n",
        "    theta_4 -= lr * estimate * np.power(x_data[i],2) / 118\n",
        "    theta_5 -= lr * estimate * np.power(y_data[i],2) / 118\n",
        "  return theta_0, theta_1, theta_2, theta_3, theta_4, theta_5"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nKROWnxQlgsK",
        "colab_type": "code",
        "outputId": "a2047a33-7748-4876-c6d5-32ce88347a1a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        }
      },
      "source": [
        "def main():\n",
        "  theta_0, theta_1, theta_2, theta_3, theta_4, theta_5 = 10, 10, 10, 1, 1, 1  #Initialization\n",
        "  \n",
        "  for iter in range(0, 80000):\n",
        "    theta_0s.append(theta_0)\n",
        "    theta_1s.append(theta_1)\n",
        "    theta_2s.append(theta_2)\n",
        "    theta_3s.append(theta_3)\n",
        "    theta_4s.append(theta_4)\n",
        "    theta_5s.append(theta_5)\n",
        "    \n",
        "    check = 0\n",
        "    for i in range(0, 57):\n",
        "      if theta_0 + theta_1 * x[i] + theta_2 * y[i] + theta_3 * x[i] * y[i] + theta_4 * np.power(x[i],2) + theta_5 * np.power(y[i],2) >= 0:\n",
        "        check += 1\n",
        "    for i in range(58, 118):\n",
        "      if theta_0 + theta_1 * x[i] + theta_2 * y[i] + theta_3 * x[i] * y[i] + theta_4 * np.power(x[i],2) + theta_5 * np.power(y[i],2)  < 0:\n",
        "        check += 1\n",
        "    accuracy = check / 118 * 100\n",
        "    accuracys.append(accuracy)\n",
        "\n",
        "    train_value = objectiveFunction(x, y, label, theta_0, theta_1, theta_2, theta_3, theta_4, theta_5)\n",
        "    #train data 수집\n",
        "    train_costs.append(train_value)\n",
        "    theta_0, theta_1, theta_2, theta_3, theta_4 ,theta_5= gradientDescent(x, y, label, theta_0, theta_1, theta_2, theta_3, theta_4, theta_5)\n",
        "    iters.append(iter)\n",
        "\n",
        "    #print(\"thetas\",theta_0,theta_1,theta_2,theta_3,theta_4)\n",
        "  \n",
        "  print(\"Plotting the Estimated Parameters\")\n",
        "  fig = plt.figure()\n",
        "  graph1 = plt.plot(iters, theta_0s, 'r')\n",
        "  graph2 = plt.plot(iters, theta_1s, 'g', linewidth = 3, linestyle=(0, (5, 2, 1, 2)), dash_capstyle='round')\n",
        "  graph3 = plt.plot(iters, theta_2s, 'b')\n",
        "  graph4 = plt.plot(iters, theta_3s)\n",
        "  graph5 = plt.plot(iters, theta_4s)\n",
        "  graph6 = plt.plot(iters, theta_5s)\n",
        "  plt.xlabel('iterations')\n",
        "  plt.ylabel('value')\n",
        "  plt.show()\n",
        "  \n",
        "\"\"\"\n",
        "  print(\"Plotting the Training Error\")\n",
        "  plt.plot(iters, train_costs, 'b')\n",
        "  plt.xlabel('iteration')\n",
        "  plt.ylabel('Traing Error')\n",
        "  plt.show()\n",
        "\n",
        "  print(\"Plotting the Training Accuracy\")\n",
        "  plt.plot(iters, accuracys, 'r')\n",
        "  plt.xlabel('iteration')\n",
        "  plt.ylabel('Training Accuracy')\n",
        "  plt.show()\n",
        "\n",
        "  print(\"Final Training Accuracy : \",accuracys[-1],\"%\")\n",
        "\n",
        "  print(theta_0, theta_1, theta_2)\n",
        "\n",
        "  print(\"Plotting the Obtained Classifer\")\n",
        "  points = np.arange(30,100,0.5)\n",
        "  xs,ys = np.meshgrid(points, points)\n",
        "  z = theta_0 + theta_1 * xs + theta_2 * ys\n",
        "  z = sigmoidFunction(z)\n",
        "\n",
        "  fig = plt.figure()\n",
        "  plt.xlim([30,100])\n",
        "  plt.ylim([30,100])\n",
        "  graph4 = plt.imshow(z, cmap=plt.cm.bwr)\n",
        "  graph5 = plt.scatter(x_label0, y_label0, alpha=0.3, c='b')\n",
        "  graph6 = plt.scatter(x_label1, y_label1, alpha=0.3, c='r')\n",
        "  plt.show()\n",
        "\"\"\"\n",
        "if __name__ == \"__main__\":\n",
        "  main()"
      ],
      "execution_count": 88,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Plotting the Estimated Parameters\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FvYhujX-JNLK",
        "colab_type": "text"
      },
      "source": [
        "### **1. Plot the training data**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T8fDzM1DJH53",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "75a2ab43-ec1a-42c0-e517-dcc650f756cc"
      },
      "source": [
        "print(\"Plotting the training data\")\n",
        "plt.figure()\n",
        "plt.scatter(x_label0, y_label0, alpha=0.3, c='b')\n",
        "plt.scatter(x_label1, y_label1, alpha=0.3, c='r')\n",
        "plt.show()"
      ],
      "execution_count": 89,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Plotting the training data\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B7tMlhmkJZit",
        "colab_type": "text"
      },
      "source": [
        "### **2. Define High dimensional Function**\n",
        "$\\ g(x, y; \\theta) = \\theta_0 + \\theta_1x + \\theta_2y + \\theta_3xy + \\theta_4x^2 + \\theta_5y^2  $  "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D4-SO5AfK4Qe",
        "colab_type": "text"
      },
      "source": [
        "### **3. Plotting the Training Error**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Xpmo7Xr-LKzC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "outputId": "055f30b0-e5ec-4eb2-b072-9f788522e73d"
      },
      "source": [
        "print(\"Plotting the Training Error\")\n",
        "plt.plot(iters, train_costs, 'b')\n",
        "plt.xlabel('iteration')\n",
        "plt.ylabel('Traing Error')\n",
        "plt.show()"
      ],
      "execution_count": 90,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Plotting the Training Error\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oX0DzAdQLpGD",
        "colab_type": "text"
      },
      "source": [
        "### **4. Plotting the Training Accuracy**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_tI6dv4cLmDQ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "outputId": "369537d1-80f7-40c9-adfb-a6b5dfc53a35"
      },
      "source": [
        "print(\"Plotting the Training Accuracy\")\n",
        "plt.plot(iters, accuracys, 'r')\n",
        "plt.xlabel('iteration')\n",
        "plt.ylabel('Training Accuracy')\n",
        "plt.show()"
      ],
      "execution_count": 91,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Plotting the Training Accuracy\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zaf0tCc4L6q2",
        "colab_type": "text"
      },
      "source": [
        "### **5. Final Training Accuracy**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DVRpopvuL-G3",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "0e48d60f-408a-4f2d-8b40-3b248aeed61e"
      },
      "source": [
        "print(\"Final Training Accuracy : \",accuracys[-1],\"%\")"
      ],
      "execution_count": 92,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Final Training Accuracy :  81.35593220338984 %\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w9rPVPoMMGJH",
        "colab_type": "text"
      },
      "source": [
        "### **6. Plotting the Optimal Classifer superimposed on the Training Data**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6Qda9OL1AlZV",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "7dd67b55-e363-434c-c594-372c4c243667"
      },
      "source": [
        "theta_0 = theta_0s[-1]\n",
        "theta_1 = theta_1s[-1]\n",
        "theta_2 = theta_2s[-1]\n",
        "theta_3 = theta_3s[-1]\n",
        "theta_4 = theta_4s[-1]\n",
        "theta_5 = theta_5s[-1]\n",
        "\n",
        "Xmesh, Ymesh = np.meshgrid(np.linspace(-1.0, 1.0, 300), np.linspace(-1.0, 1.0, 300))\n",
        "\n",
        "Z= theta_0 + theta_1 * Xmesh + theta_2 * Ymesh + theta_3 * Xmesh*Ymesh + theta_4 * Xmesh**2 + theta_5 * Ymesh**2\n",
        "fig = plt.figure()\n",
        "levels = [0]\n",
        "grpah7 = plt.contour(Xmesh, Ymesh, Z, levels, colors = 'green')\n",
        "graph8 = plt.scatter(x_label0, y_label0, alpha=0.3, c='b')\n",
        "graph9 = plt.scatter(x_label1, y_label1, alpha=0.3, c='r')\n",
        "plt.show()"
      ],
      "execution_count": 99,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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QRUYqtjZ9mj8v/iMZzTNYettS2sa3NaVsj4z+rKyyLrgAtm6FBQtg7lzH59atVWslqyreF/wXNXz2+hH1eeSiR9g2fhsvXP4CK/eupOc7PRk4dSArf/jE/q4wk/AFr59V6NVHLcbqvVfL5lcppXhg3gO8suwVRncezaSrJxEaHHp25hravR6fu1VZZXXvDt98c3be6pa9sHJCm7f9F9VRy2evE1aHB3s9yB1pd/D68tf550//5PzC2YyMvZinw2+iRXij38v0kivMSteNL3j9rEIvOucBrPY7KqW4Z+49vJH5BuPTx/NSv5fO3eTER0e70K2b47g2w0kC1eELpjx7fmE+z0++lVcOfEUJpYxLuJLHGt1A3AnllaE8Vr/CgTBqSW9M40Ws7Fkrpfi/b/+PNzLf4M89/8wLl79Q8dwAX1kMpqLKmjOndl01my9HYTZnt/0pdOuW4tbjx0TE8PdB/+buzy7g8dPf8ur+r3jvwAL+FjmAO4c9T2j1RZiK1a+w1da7ndExAh/nXz//ixeXvMi4buMqVwLg27N1fCFA62UsC3SmpND42jFMaj6eX+MfpWtUS8Yfn0HnL69iwZYFpsjuKla/wgG6KgqgLQL7U4WJP2P9DB6a/xA3dLiBVwe8WvVy0b68DVUgd9VcxNLesmFZncc1fKOeZNbGWTzwzQP0/aAv17e/npf6vURKPfc39KnOk+WJVzjAjMgzaIvAzlTRzVu5dyWjZ46mV5NeTBkypfqNz31htEtlBHJXzUXK95YjDuTSas1MGnxq7jIYIsLgtoNZd9c6nrrkKb7c9CXt3mjHK0tfoaS0pFZlumrN+PIrbHd0sNjOVBK9yg9XdN39BEUlRawYu4LE6MTKy3AmkIOn3sbiund+VSIO5JK47AuOBcUQVD+anh2tGxiw9fBWxs0Zx9zsuXRN6sqkQZPo0qhm24vUJEirX2H30MFiX6SC8WyqTh3u3Ph3thdt54c//uC6EoDAtXu9jQe273L2njXcmMmxoBjyS+uR3gZLBwakxqYye+Rs/rf+f9w7917SJqYx4cIJPHbxYy6vclqTYZv6FbYG7RqyMxUESaft/ZZphZk8ecmTLq8bFLDYZZVQD8xUcvaeFeXmEVQ/mvR0iI83Mlg4MEBEGNZhGOvHrWdU51E8u/hZuk7s6vL6RXosgPfRisDOlHOK5h3O5Z7975GecD4TLpzgbem8T1UNvZ3WC/DQiK2y5Rkuvi6Bnh0LflcC4JGWNS4yjncHv8uckXM4XHiY9EnpPPn9k9XGDrTv3/toRWARpnRGywVJH8r/H0elmHeGfuDWRuV+QXUNvZ3WC6ioy7t9O+TkWGOteLllHdB6AGvvXMvwjsP526K/ceHkC8k5VPleU3osgPfRisACTO2MGt28zKvOZ8rhhdzf436vbE5uO6pr6O00b6J8w7x1K/z0EyQnV/2C1LY3YYOWNTYylg+v/ZBp101j48GNdPlPFz5c/WGVIntrsTmNVgSWYHZnVCnFQ/MfIiEqgUcvftRcYX2V6hp6OzmeyzfMu3ZB796Qmlr5C+Jub8ImLesNHW9g9R2r6dKoC6NmjuLmz2/mePFxr8iiqRxTFIGI9BeRjSKSLSLnOK9F5GYRyRORlcbfbU7nxojIZuNvjBnyeBuzO6MLty3k+23f89eL/0q98HrVX2AVdgm+QvUNvd0cz84Nc8uW0KzZ2efLvyB2cm25SZP6TVg4ZiGPXfwY7696n/RJ6Ww4sMHjctjp9bUbbisCEQkG3gAGAO2BESLSvoKs05VSXYy/Sca1ccATQDrQHXjC2L7SpzG7M/r4t88SF9KY4JVjvfcC2yn4CtU39DZwj1SKKy+InVxbJhASFMJTfZ5i3k3z2Hd8H93+243PfvvMY/e32+trN8ywCLoD2UqpLUqpYmAaMNjFa/sB3yqlDimlDgPfAv1NkMmrmNkZnbdqJT/t+Y4r6t9HSqMI773AduuhutLQ28Q9cg6uvCB2cm25i1NX/PLVBfxy9Ww6JHTguk+u49EFj1KqSi0XwW6vr90wY0JZMrDT6TgXRw+/PNeJyMU4Nrq/Xym1s5Jrk02QyauYuWT9v354gzCJZFDy7WdeYPDCoqHuLNZu1XRQX51d5MoL4i/rK1Uwma7JgkwWDfyIu1c9x99//Dur96/mo2s/stTtGch7DbiCp2YWfwl8rJQqEpE/Ae8Bl9akABEZC4wFaNq0qfkSmowZbdTx4uMsPjyNi2KHEx0ScybdpRfY7Ma3tit+eWBWrU9S3QviCxvguEIlq+GF/7KaiUMm0qVRF8Z/PZ7ek3vz1YivaBbTrIrCao8vr7noCcxwDe0CmjgdpxhpZ1BKHVRKFRmHk4Curl7rVMZEpVSaUiotIUB+vS82fkGRKqBn5M1npVf7AlvhEK2tv0vb5LXHrq6tmlBFrENEGNd9HF/f9DU7j+wkfVI6WbutWUPMbmMH7IYZiiATaC0iqSISBgwHZjlnEJEkp8NBwG/G93nAFSISawSJrzDSNDiWmU6MakzDwgtr9gJb0fjWNvjqZ0FPTQ1xIdbRt0Vflty6hMjQSDKmZDBn85za36+SoUF2HjtgB9x2DSmlSkTkbhwNeDAwWSm1TkSeArKUUrOAe0VkEFACHAJuNq49JCJP41AmAE8ppQ65K5M/UFRSxDc53zDqvFFc0yWoZh4CqxyitfF3aZs8sHEx1tEuoR1Lbl3CVVOvYtDHg5g8eDKjO4+u2b2qcUP6akjJE5gSI1BKzQHmlEt73On7I8AjlVw7GZhshhz+xJLcJRw/dZwBrQfU/AW2U+PrL0FPTe2oQayjUXQjvh/zPddMv4Yxn4/h0MlD3NfjPtfv5SvbsdoQvQy1Tfl+2/cIQkazWjSYdmp8/SXoqak9NejJ1A2vy+yRsxn52Ujun3c/BcUF/PXiv7p2Hz00qNZoRWBTluYupVNiJ+pH1K/5xXZrfH3JJtc7n3id8JBwpg+dzi1f3MJjCx+jqKSIp/o8VfVWrGAvS9jH0IrAhiil+GXPLwxsM7D2hfhS42sX9FBX2xASFMKUIVMICw7jmcXPAPD0pU9XfZGdLGEfQysCG3LgxAHyTuRxXuJ53hYlsNA+ZlsRJEFMvHoigvDM4mcICw7jsYzHKr/AbpawD6EVgQ3ZdHATAG0atPGyJAGG9jHbjiAJ4j9X/4fi0mIe//5x6obXrTqArC3hWqEVgQ3ZcWQHAM1jmntXkEBD+5htSZAE8c6gdzhefJz7591PbEQsY7rYc6FiXw0x6f0IbMiegj0AJEUnVZPTT/HWesF6+qltCQkK4aNrP+Ky1Mu4ddatfJ39tbdFOgdfXuFUKwIbcujkIYIkiJiImOoz+xve/G/S009tTXhIODNvmEmnxE4M/WQov+751dsinYUvr6aiXUN2IzeXY+tXEk0Y8vnnvmNbmoW3A7bax2xr6obXZc7IOaRPSmfgxwNZfttykuvZY8FiXw4xaYvAThi94eJThYQHh/uWbWkWem0iTTUk1U3iq5FfcbToKEOmD+HkqZPeFgnw7S0ktCKoAK9taWf0hlVYKAL2tS2trCBf/m/SeIzzEs9j6rVTWbF7BWO/GotSytsi+XSISSuCcng14GP0hkMlmGJV4kizW2/Y6gry5f8mjUe5+g9X8+QlT/Lh6g95I/MNb4vj0yEmHSMoR21c1KYNGTN6w3WCIjheamzfYLfesNU+fD0pSFMDHr34UTJ3Z/LAvAfontyd7sndvSqPr4aYtEVQjpq6qE3tIBu94diSEE6pEo7n77dfb9gTPnx/2JBF4xGCJIgpQ6bQuG5jbphxA0cKj3hbJJ9EK4Jy1NRFbeqQMaM3nBAZD8C+0GL72Zbah69xF5NjTHGRcXx83cfsPLKTu+bcZSfRfAatCMpRUxe16R3klBRSLhkEQG7PDvZSAqB9+Br3sCjG1LNJT57IeIKpa6Yybe00O4nmE5iiCESkv4hsFJFsEZlQwfkHRGS9iKwWkQUi0szp3GkRWWn8zSp/raepacDHig5yakwqAFsOb6l9IVbhyxExjfexcNbVIxc9QnpyOuPmjGNvwV47iWZ73A4Wi0gw8AZwOZALZIrILKXUeqdsvwJpSqkTInIn8Dxwg3HupFKqi7tymElNAj5WrHybGptKaFAoGw5sqH0hVuKrETGN97Fw1lXZ0tVd3u7C3XPuZsawGXYRzfaYYRF0B7KVUluUUsXANGCwcwal1EKl1AnjcCngN62IFR3kkKAQ2sa3ZfW+1eYJqtHYAYtjTG3j2/JExhN8+tunfLHhCzuJZmvMGD6aDOx0Os4F0qvIfysw1+k4QkSycGxs/5xS6vOKLhKRscBYgKZNm7olsNlY0UE+P+l85mXPQylV/c5M7uKrSyZqfA8PbB7zYK8Hmbp2Kvd+fS99W/SlTlgdu4hmWzwaLBaRm4A04AWn5GZKqTRgJPCKiLSs6Fql1ESlVJpSKi0hAFR0enI6+47vY1v+tppdWNNhD4EcIdN4Hg/EmEKDQ3nzyjfZcWQHz/34nJ1Esy1mWAS7gCZOxylG2lmISF/gUSBDKVVUlq6U2mV8bhGR74HzgRwT5PJpLmx6IQCLdywmNTbVtYtqs9Witxd50wQeHogxXdTsIkZ0HMG/lvyL27veTtP6rnkRAjX8ZYZFkAm0FpFUEQkDhgNnjf4RkfOB/wCDlFL7ndJjRSTc+B4P9Aacg8wBS8eGHYmPimf+lvmuX1SbYQ96kTeNn/Jc3+dQSvHYwiq2t9QAJigCpVQJcDcwD/gN+EQptU5EnhKRQUa2F4Bo4H/lhom2A7JEZBWwEEeMQCsCHDMmL29xOfNy5lGqSl27qDaNeiBHyDR+TdP6Tbk3/V4+WPUBa/ev9bY4tsaUGIFSao5Sqo1SqqVS6lkj7XGl1Czje1+lVKJSqovxN8hI/1kp1Ukp1dn4fMcMefyFq1pfxf7j+1mWu8y1C2rTqNtxgligTu/UmM7DvR8mOiyaJxc96W1RbI2eWWxjrmpzFaFBoXz626euXVCbRt1uETIdvNaY2BFoENWA8enjmbF+BuvztLOhMrQisDExETH0a9WP6eumu+Yeqm2jbqdF3gJ5eqfGko7A+B7jiQqN4vmfnjdRUP9CKwKbc2OnG8k9msvCrQtdu8BOjXpt0MHrwMaCjkB8VDy3nn8rU9dMZc+xPSYK6z9oRWBzBv9hMDERMUz6dZK3RfEMOngd2FjUEbg3/V5KSkv4z4r/uFWOv6IVgc2JDI1k9Hmj+XT9p+wrCIBFT+wYvNZ4Dos6Aq3iWtGvVT8m/TKJktISt8ryR7Qi8AHu6nYXp0pPBUZvxm7Ba41nsbAjMPaCsew6tot52fNMENS/EDts+lxT0tLSVFZWlrfF8ChXTb2KzF2ZbL9vO5Ghkd4WR6OxDovWvjp1+hSNX2rMZamXMW1o7fYs8BZmVYmIrDCW9DkLvWexj/BQr4e45L1LeHflu9zVzb1dmDQaW2PROg+hwaFc3/56pqycwvHi4y4vRucu7jbitVk5pqZo15CPcHGzi+nVpBf/+PEfFJUUVX+BRqM5h2EdhnGy5CRzs+dWn9kEzBgN64kR1VoR+Agiwt8y/kbu0Vz++8t/vS2ORuOTXNj0QuIi45i10TObIZrRiHtiRLVWBD5E3xZ9uaT5JTy16CmOFR3ztjgajc8REhRC/1b9+Tr7a9fX8HIDMxpxT4yo1orAhxAR/tn3n+SdyOOfP/3T2+JoND7J5S0uJ+9EnkcWojOjEffEiGqtCDyAmWuodU/uzo2dbuRfP/+LrYe3midkZegF4DR+xiXNLwFg0bZFlt/LjEbcEyOq9fBRi3GO+Dtvf+fOD5l7NJe2r7fl0tRLmTXCQl+nu8LrLTA1NkQpRZOXm5DRPIOPrv3I8vvZ6d9ADx/1ElZsAJZSL4UnMp7gofkP8fmGzxnSdog5wpbHHeE9MeZN43ns1KrVEhEhrXEaWbut6UxWVEXXXGPJrUzDFNeQiPQXkY0iki0iEyo4Hy4i043zy0SkudO5R4z0jSLSzwx57IQpEf8K3DP39biP8xLPY9ycceQX5psq8xncEV6vIup/+NES4V0adWHzwc2cOHXC1HJ9tYrcVgQiEgy8AQwA2gMjRKR9uWy3Am1BI5EAACAASURBVIeVUq2Al4F/Gte2x7G1ZQegP/CmUZ7f4HawqJI3K3TPPt4Z9A77CvbxwLwHTJcbcE94vYqo/+FHyr19QnsUis0HN5tarq9WkRkWQXcgWym1RSlVDEwDBpfLMxh4z/g+A7hMRMRIn6aUKlJKbQWyjfL8BreDRVW8WWmN03i498O8u/Jdvtjwhb2Er40S0YFpe+NHyr11XGsAsg9lm1qur1aRGYogGdjpdJxrpFWYx9jj+AjQwMVrfRq3I/7VvFlPXPIEXRp14bYvbzN/rXV3hK+pEvFVmzqQ8KMlwpvWbwrAjiM7TC3XV6vIZ4LFIjIWGAvQtGlTL0tTM9xaOqXszSoL1MJZb1ZYcBhTr51K14ldGTVzFPNumkdwkInetdoKX6ZEMjMdSiQhATIyKi/Liqi6xly6dXMoZzh7FFlGhum3sjomHRcZR1hwGHsL9ppXKB6tIlMxwyLYBTRxOk4x0irMIyIhQH3goIvXAqCUmqiUSlNKpSXYXb2aiQs963YJ7XhtwGss2LqAZ354xovClqMmu6X5qk0dSHhoiXBPGIciQoPIBhw8edC8QvHdVdTNsAgygdYikoqjER8OjCyXZxYwBlgCDAW+U0opEZkFTBWRl4DGQGtguQky+Q8u9qxvOf8WFm1fxJOLniQ9JZ3+rfp7SeBaUo3lo7EJFq0M6oynjMO64XUpKC6oPmMN8UAVmY7bikApVSIidwPzgGBgslJqnYg8BWQppWYB7wAfiEg2cAiHssDI9wmwHigBximlTrsrk7/wu3mcQkJCCt2urPwFExHeHvg2q/atYuSnI8m8PZOWcS09K3AFuGzi+6pNrTGdvDyHJeBMdLSjH2QmESERFJYUmluoj2LKPAKl1BylVBulVEul1LNG2uOGEkApVaiUul4p1Uop1V0ptcXp2meN6/6glPLM2rA+QG3M46jQKGbeMBMR4eqPr+ZI4RHPCVwBNXoGX7WpNabjqYBrkAR5ZOE5X8BngsW+hBmBrtqaxy1iWzDj+hlc8eEV3DDjBr4a+RUhQd75mWv8DL5oU2tMx1PG4anTp1z+3/CDCdVVohedMxmzAl3uxE77pPbhraveYl7OPMbNHoe31pPS8V9NbfCUcXji1AmiQqOqzRcII5u1RWAyZgW63I2d3nbBbWw5vIV//PgPkusl83jG467f3CR0/FdTWzxhHOYX5hMTEVNtvkAY2awtApMxqxdsxvK1z176LKM7j+aJ75/grcy3aiaACXhiHXWNpjYUlRRxuPAwiXUSq80bCJatVgQmY1agywzzWESYdPUkrm5zNePmjOPD1R/WTAg30fFfjV3JPerw66TUq/5l9NXZwjVBu4ZMxsxAlxnmcWhwKNOHTueqqVcx5vMxhAeH07P+9R4LfOn4r8YtLIrSlq0x5MoQ60AY2awtApOxYy84MjSSWSNm0TOlJyM+HcHfPpnh14EvjZ9gYZR2Xd46ANrGt602rx3/p81GWwQWYMdecHRYNHNvnEv3Vwfw7rHhxDb4kIuDhvtl4EvjJ1gYpV25dyVJ0Uk0rNPQpfx2/J82E60IAoi64XW5s+5cJsrVvLTtRopKT3B5/C2WzNr0e/x9YLkdsHCK8dLcpXRL1qMWytCuoQCjSWJdHkicQ+d6l/Pajlv5fN9Lfhf4spxAGFhuByyK0u45tofNhzZzYZML3SrHn9AWQYDhCHxFcW/CF/w3aBSTd/2ZHZF7eWfEc5jaL7Bjj9ksmQJhYLkrWP0buxOlrUK2b3K+AaBvi77myerjaIsgwCgLfNWvE86oiI/p1+BO5p98gUcyR1FUUmTOTezYYzZTpkAYWF4dnviNaxulrUa2Lzd9SVJ0El0adTFPVh9HWwQByO+Br2D+pN7guR+b8Jfv/kLu0Vw+G/YZDaIauHcDO/aYzZRJT5n23G9cmyhtFbIVNIxhbvZcxnQeg2O33NpjR6O3tmiLwIvYYYteEeGRix5h6rVTWZa7jB7v9GDDgQ3uFVqTHrOnKsHMXryeMm1vq6gK2Wb+NpMTp04wouMIt25hR6PXHbQi8BJ2e5FGdBrBd2O+42jRUdInpTN70+zaF+ZqkM+TlWBm4NGOA8s93auw83TbKmSb9OskWsa25MKm7gWKnY2OoCDHZ0yMI90X0YrAS9jxRerVpJdjQ5vYllz98dU888MztVuv3dUesycrwexefE224bQab/Qq7GwVVSLb6pbR/LD9B8Z2Heu2W8jOBlFtcEsRiEiciHwrIpuNz9gK8nQRkSUisk5EVovIDU7npojIVhFZafwFTPTGri9S0/pN+fGWHxnZaSSPLXyMIdOGcPjk4ZoV4mqP2ZOVYMdevFl4o1fhifqsrZVTiWz/yvmAqNAobrvgNrdFs7NBVBvcDRZPABYopZ4TkQnG8cPl8pwARiulNotIY2CFiMxTSuUb5/9PKTXDTTm8Tk0DR3aON0aFRvHBNR+QnpzOA/MeoN0rXbml7nS6JXdzPSDmSpDP05Xgr9NDPbW3Y3msrM8yKycmxvFsBQWOY1eVTTnZcg7lMHXNVO7pfg9xkXFui+dv6w+56xoaDLxnfH8PGFI+g1Jqk1Jqs/F9N7AfsEFzZx61scxta1kbvTD5738ZsSaFCfIpJaWneeFQbz7d/TKff67M8zi4Wwl2iLbbAX/rnoLpVs4T3z9BWHAYD/V+yBTx/M3AdFcRJCql9hjf9wJVLu4tIt2BMCDHKflZw2X0soiEV3HtWBHJEpGsPG/7T8pRm3fWli9SOY22de0Jrs7ZyX8Sv6JrvSv56MAD/PfklXz7s0k9TXcqwW7Rdm9i216FG5joNszclclHaz7ivh73kVQ3ySQB7RUmcpdqXUMiMh9oVMGpR50PlFJKRCrdE1FEkoAPgDFKnYlAPoJDgYQBE3G4lZ6q6Hql1EQjD2lpad7Ze7ESamuZ285TUW789cFT9YiPhSZbsvlLj5nMPfAWk3P/zPiNnYjb8F8Gtx3s/j1rWwl2nKvgLcoUamam46VLSHD4KHy5HkxyG54uPc3dc+8msU4iEy6cYLKQ/kO1ikApVek8bBHZJyJJSqk9RkO/v5J89YDZwKNKqaVOZZdZE0Ui8i7wYI2ktwl29vdDDeIX5TRa/fpQUBhN7JF9iAhXJtxFqlzC2/tvZMj0Idzc5WZe6fcK9SPqe+5hKpEV8Ixf3K7YrlfhJiY54d/MfJPlu5bz4TUfUi+8XvUXBCjuuoZmAWOM72OAL8pnEJEwYCbwfvmgsKE8EMdYriHAWjfl8Qp2tsxr5EEp52tu3RqKDxaQH5pw5rnqnGjP/OHLePSiR3l/1ft0eLMDczfP9dwDVSIrYC/tq3EPE3yn2YeymbBgAv1b9Wdkp5EWCuv7iFK197KISAPgE6ApsB0YppQ6JCJpwB1KqdtE5CbgXWCd06U3K6VWish3OALHAqw0rin3330uaWlpKisrq9ZyW4Fdp5vPnOlo/J2tlaNHHf9X11xTLrPzSA2jF3Z4Wz5LGw5mp0o557mW71rOH7/4I+vz1nPTeTfxcr+XiY+K98yDVSAr+fk2CLRo7EDx6WIunHwhmw9tZs2da1zakjIQEJEVSqm0c9LdUQTewo6KwK5MnOiwBIKcbL/SUkcna+zYCi6ooUYrKini2cXP8o8f/0H98Pq8eMWLjO482u0JOy5hV+2r8Trj547n1eWvMuP6GVzX/jpvi2MbtCIIUGpkEbjB2v1rGfvlWJbkLiGjWQZvXvUm7RPam3cDjcZFPlj1AaM/H8349PG80v8Vb4tjKypTBHqJCT/HU/GLjg078uMtPzJx4ERW71tN57c78+A3D3K06Ki5N9JoqmDx9sXc9uVt9Gnehxcuf8Hb4vgMWhH4OZ6crxAkQdze9XY23bOJmzvfzEtLXqLNa21455d3OF162vwbajROrN2/lkHTBpEak8qMYTMIDQ71tkg+g3YNaSwja3cW478ez887f6ZzYmdevOJFLmtxmSll6/CAxplNBzeRMSWDIAnip1t+onlMc1PK9bf3TLuGNB4nrXEaP/7xRz6+7mPyC/Pp+0FfBnw0gNX7VrtVrp5UrHFm44GN9HmvD6dLTzN/1HxTlUCgvGdaEWgsRUQY3nE4G+7ewPN9n2dp7lK6vN2Fmz67iexD2bUq045LeGu8wy97fuGidy+ipLSE78Z8R7uEdqaVHUjvmVYEGo8QERLB//X+P7bcu4WHez/MZ799RtvX23LbrNvYlr+tRmVVtgzN8Y0mL0KnF7WzNfOy55ExJYPI0EgW/3ExHRt2NLV8uy4VbwVaEWgqxKo2MDYyln/0/Qdbxm/hrm538cHqD2j9Wmtun3U7Ww5vcamMiiYVn96eS8ctJtrxdvELaGV0Dkop3lj+BldNvYqWsS35+ZafadOgjen3CaTJ61oR2BxvtAOeaAMbRTfi1QGvknNvDnd0vYMPVn9Am9faMGrmKNbur3qlkYqGxEaszaRJRxPteDv4BeyijCoQy1u66eSpk9wy6xbunns3V7a+ksV/XExyvWRL7mXnpWPMRisCG+OtdsCTbWBKvRReu/I1to7fyvj08cz8bSad3urEwKkD+WH7D1Q0qq2iIbE9W+bRoJmJdrwd/AJ2UEbl8KZuWp+3nvRJ6UxZOYXHLn6Mz4d/Tt3wupbdz5ZLxVuEuzuUaSzEWyste2Nhz6S6SbzY70X+ctFfeCPzDV5b/hoZUzJIa5zG/T3uZ2j7oYQFh53Jf85imzNNXgLWDkvK2nCFVW+8k6WqlDcz3+Shbx8iOiyaOSPnMKD1AGtuVg5/W9S1MrRFYGO81Sn1pm+0QVQDHs94nO33beetq97iWNExbvzsRpq/0pynFz3N3oK9Z+Uvc1N8uLEbKxflc3CrSXa8HfwCNnRSe/qdzDmUQ9/3+3LP3HvIaJ7B6jtXe0wJBBJaEdgYb7UDdmgDo0KjuCPtDtaPW8+ckXM4L/E8Hv/+cZq83IRh/xvGwq0L2blTnXFT1G2XwpaOg1m2NorDG0yw4+3gF7DDD1EOT72TRSVF/H3x3+n4VkdW7FnBxIETmTNyDo2iK9ojS+MuemaxjfHmSst2nFG56eAm3s56mykrp3C48DBJYa25uO6tDGg8mrhQxxaEViyo51Vs9kNY/U4qpfhy05c8+M2DbD60mevaXce/+//bsoBwoKFXH/VRbNYO2IKTp07yv/X/4+nZ/yX71I8EEcwF9fpzWYOb6Vp3IIfzIipeYltjCla9k0tzlzJh/gQWbV9E2/i2vNLvFfq16ud+wZozVKYIdLDY5gRKsKomRIZGMrrzaOpuGU12/kaWFb3LwkMfkLV1NlFB9ekVcz2tt47k4mYXExwU7G1x/Q6z38nlu5bz5KInmbN5Dg3rNOT1Aa8ztutYvWicB3F3h7I4YDrQHNiGY4eywxXkOw2sMQ53KKUGGempwDSgAbACGKWUKq7uvoFkEWgqx9lNEVnnNMvzFrDw4IesK53J8VMFJEUnMbT9UK5vfz29m/YmSHRIzC4opZi/ZT7P//w887fMJy4yjj/3/DP3pt9LdFh09QVoaoUlriEReR44pJR6TkQmALFKqYcryFeglDrn1xWRT4DPlFLTRORtYJVS6q3q7qsVgaaMitwUcYkn+GrTV0xfN505m+dQWFJIo+hGDP7DYK5pew2XNL+E8JBw7woZoGbe8eLjfLTmI15b/hpr96+lUXQj7u9xP3em3WnpnACNA6sUwUbgEqXUHmMj+u+VUn+oIN85isDYsD4PaKSUKhGRnsDflFLVOgW1ItC4yrGiY8zePJtPf/uUuZvncvzUcaLDounXsh8D2wykf6v+1o5ECdS9lZ2Un4qPZ0VqOJN3z+ajNR9xtOgonRM7c1+P+xjRcYRnlXI1+LvOtkoR5CulYozvAhwuOy6XrwTH5vQlwHNKqc9FJB5YqpRqZeRpAsxVSlW4cpSIjAXGAjRt2rTr9u3bay23JjApLClkwZYFzNo4i682f8XuY7sBOL/R+fRr2Y/LW15Orya9iAiJMO+mntor1JNU11oaym9LnWKmFa/go4Pfs754FxHB4QztcD13dL2DXk161W5fawtb6kDQ2bVWBCIyH6ioy/Qo8J5zwy8ih5VSsRWUkayU2iUiLYDvgMuAI9RAETijLQKNuyilWLVvFXM2z2Fezjx+3vkzJaUlRIRE0LtJb/o070NG8wy6Ne7mXo914kTH7OAgp/hEaaljboIvDm2qorVUycmsy1vHrJn/4LPDS1hRtBWA3nXacVNUD4Y3vJSYoTdZcm8zWmp/1NnlqfWoIaVU3yoK3SciSU6uof2VlLHL+NwiIt8D5wOfAjEiEqKUKgFSgF0uPY1G4yYiQpdGXejSqAt/uegvHCs6xqLti1iwZQHfbfuOvy78KwDhweF0S+5G7ya96ZnSk/SU9Jq5kuywVIWZlFtjIj8qiIUFm/lm5m3MPb2B7Ucclnp6VBueT76Z62N60zw88XflZ+K93V3forxxsXEjtCu3nYGXV/TwGO4OH50FjAGeMz6/KJ9BRGKBE0qpIsMd1Bt4XimlRGQhMBTHyKEKr9doPEHd8LoMbDOQgW0GAnDwxEEW71jM4u2L+XHnj7y05CVOlZ4CoGn9pqQ1TqNrUlcuSLqALo26VK4cunVz9GLh7F5sRoYnHqt6auhq2bM3m5+jDvBT7kYWHVvLrye3oFBESziXtunHIxc+wtVbQmh8KsJ85Wfi2kvOxkViokO8LVscvf/UVHPF9gXcjRE0AD4BmgLbcQwfPSQiacAdSqnbRKQX8B+gFMeSFq8opd4xrm+BQwnEAb8CNymliqq7r3YNaTzNyVMn+WXPLyzbtYzlu5aTtTuLnMM5Z843rNOQTg070SGhAx0adqBtfFv+0OAPNKzTENm1y54RyGrcPNuPbGfNvjWs2reKFXtWsGL3CnYe3QlAhISRXqcNl0R35NLgVvSI7UTYdcOqLdet5zbRd1NRUVu3wtq1Dh2tYwQ+gFYEGncxI+aYX5jPyr0rWbV3Fav2rWLt/rWsz1vP8VPHz+SpF16PVnGtaBnbktSYVOrTnOO7mxJUkEKrhslc2qMBTZrUImhaC8o/c88DMygO3cX28JNsK9pPTtEesgt2sPH0Pjac3kdB8e+LCrWOa01a4zS61WlNzw3HuSC+E2F1YypvLa0I6pqoYCoL3WzYAG3a2E9nm4VWBBqNgZUxx1JVyo4jO9h4YCMbD25k08FN5BzOIedQDtvyt51xL5URQhiJdRqRVL8hCVEJxEfFExcZR0xEDPXC61EvvB7RYdFEhkQSGRpJeHA4ocGhBEswQRKEiFCqSjldeppTpacoPl1MYUkhJ06doKC4gGNFxzhSdIQdeYdZk32QwuA8CtQ+Dhbv4WjJPpT8/v8vCE1C4/mDxNO2S186JHSgU2InOjXsdPYY/2oaeUuHYJpUeCAEhitCKwKNxsBbjcCnn5Wy59heTobv4EDxTg6e2sW+gj0UyF4iGuwn73geB47t4/CJQxwtPWHqvSOD6hId1ICYsATqhzQkNrQRSblHSS6tS0bnpjQPa0jzsETCC066VRG+MgTTV+Q0G73WkEZj4K39Xg4eCKJJYmOCghpDnR4AlMYbI0lv5PfWqVEMp+tEcuzoAY7l76fg0t6ciKtHYUkhRaeLOHX6FKfVaUpVKUopgiSI4KBgQoJCCA8OJzwknDqhdYgOi6ZueF3qhddj8qSQc1whYZG51FnwBRd2joEwcwLZ3tpMqaaUrTKememo/4QEx2PbSUZPohWBJuDw1ojOau/r1IoGAzGxScQE14HN+XBNH9PvfSAihdI+gyHKvNbQhpuqVYpe0PF3tCLQeBVvTOn31ojOau9rYSta6b0Hm9sa+tu0iUBBL8eo8Rre2gjdW5uPVXtfC7f/8tQz23BTNY0LaItA4zW86U/2llugyvtabKp44pm179030YpA4zV8yZ/sEfykFdW+d99DKwKN19D+5ArQrajGC+gYgcZraH+yRmMPtCLQeA1vBW01Gs3ZaNeQxqtoT4hG4320RaDRaDQBjlYEGo1GE+Bo15BGo/Ea/r5ZvK/glkUgInEi8q2IbDY+K9qvuI+IrHT6KxSRIca5KSKy1elcF3fk0Wg0voO3ZpZrzsVdi2ACsEAp9ZyITDCOH3bOoJRaCHQBh+IAsoFvnLL8n1JqhptyaDReRfdsa46vrFQaCLgbIxgMvGd8fw8YUk3+ocBcpZS5i61rNF7E2z3b3FzHHgsTJzo+faVHnZfnmEnuTHS0I13jWdxVBIlKqT3G971AYlWZgeHAx+XSnhWR1SLysoiEV3ahiIwVkSwRycrTb4rGRjj3bIOCHJ8xMY50q/G2EnIHC9fY09SQahWBiMwXkbUV/A12zqccW51Vut2ZiCQBnYB5TsmPAG2Bbjg2sH+4gkvLyp+olEpTSqUl6DdFYyO82bP1phJyFz2z3D5UGyNQSvWt7JyI7BORJKXUHqOh319FUcOAmUqpM5u2OlkTRSLyLvCgi3JrNLbBm2sm+fLCfX6yxp5f4G6weBYwBnjO+PyiirwjcFgAZ3BSIoIjvrDWTXk0Go/jrY1uwPcX7tMzy+2BuzGC54DLRWQz0Nc4RkTSRGRSWSYRaQ40ARaVu/4jEVkDrAHigWfclEej8TjeXDNJu1c0ZiAO175vkZaWprKysrwthkZjC/TQVY2riMgKpVRa+XQ9s1ij8XG0e0XjLnqtIY1GowlwtCLQaDSaAEcrAo1GowlwtCLQaDSaAEcrAo1GowlwtCLQaDSaAEcrAo1GowlwtCLQaDSaAEcrAo1GowlwtCLQaDSaAEcrAo1GowlwtCLQaDSaAEcrAo1GowlwtCLQaDSaAEcrAo1Gowlw3FIEInK9iKwTkVIROWezA6d8/UVko4hki8gEp/RUEVlmpE8XkTB35NFoNBpNzXHXIlgLXAv8UFkGEQkG3gAGAO2BESLS3jj9T+BlpVQr4DBwq5vyaDQajaaGuKUIlFK/KaU2VpOtO5CtlNqilCoGpgGDjQ3rLwVmGPnew7GBvUaj0Wg8iCe2qkwGdjod5wLpQAMgXylV4pSeXFkhIjIWGGscFonIWgtkdZd44IC3hagEu8pmV7nAvrLZVS6wr2x2lQs8K1uzihKrVQQiMh9oVMGpR5VSX7grlasopSYCEw2ZsiragNnb2FUusK9sdpUL7CubXeUC+8pmV7nAHrJVqwiUUn3dvMcuoInTcYqRdhCIEZEQwyooS9doNBqNB/HE8NFMoLUxQigMGA7MUkopYCEw1Mg3BvCYhaHRaDQaB+4OH71GRHKBnsBsEZlnpDcWkTkARm//bmAe8BvwiVJqnVHEw8ADIpKNI2bwjou3nuiO3BZiV7nAvrLZVS6wr2x2lQvsK5td5QIbyCaOjrlGo9FoAhU9s1ij0WgCHK0INBqNJsCxrSKw6/IVIhInIt+KyGbjM7aCPH1EZKXTX6GIDDHOTRGRrU7nupghl6uyGflOO91/llO6N+usi4gsMX7z1SJyg9M5U+ussnfG6Xy48fzZRn00dzr3iJG+UUT6uSNHLWV7QETWG3W0QESaOZ2r8Hf1kFw3i0ie0/1vczo3xvjtN4vIGDPlclG2l53k2iQi+U7nrKyzySKyXyqZ8yQOXjXkXi0iFzids7TOzkEpZcs/oB3wB+B7IK2SPMFADtACCANWAe2Nc58Aw43vbwN3miTX88AE4/sE4J/V5I8DDgFRxvEUYKhFdeaSbEBBJeleqzOgDdDa+N4Y2APEmF1nVb0zTnnuAt42vg8Hphvf2xv5w4FUo5xgE38/V2Tr4/Qu3VkmW1W/q4fkuhl4vYJr44Atxmes8T3Wk7KVy38PMNnqOjPKvhi4AFhbyfkrgbmAAD2AZZ6os4r+bGsRKPsuXzHYKM/VcocCc5VSJ0y6f1XUVLYzeLvOlFKblFKbje+7gf1Agkn3d6bCd6YKeWcAlxn1MxiYppQqUkptBbKN8jwmm1JqodO7tBTH/BurcaXOKqMf8K1S6pBS6jDwLdDfi7KNAD428f6VopT6AUcnsDIGA+8rB0txzKtKwvo6OwfbKgIXqWj5imRquHxFDUlUSu0xvu8FEqvJP5xzX7xnDVPwZREJN0mumsgWISJZIrK0zGWFjepMRLrj6N3lOCWbVWeVvTMV5jHq4wiO+nHlWneoafm34uhRllHR7+pJua4zfqMZIlI2idQ2dWa40VKB75ySraozV6hMdqvr7Bw8sdZQpYhNlq8oT1VyOR8opZSIVDr+1tDunXDMoSjjERyNYRiO8cMPA095WLZmSqldItIC+E5E1uBo7GqNyXX2ATBGKVVqJLtVZ/6IiNwEpAEZTsnn/K5KqZyKSzCdL4GPlVJFIvInHBbVpR66t6sMB2YopU47pXmzzmyDVxWBsunyFVXJJSL7RCRJKbXHaLT2V1HUMGCmUuqUU9llPeMiEXkXeNBVucySTSm1y/jcIiLfA+cDn+LlOhOResBsHB2BpU5lu1Vn5ajsnakoT66IhAD1cbxTrlzrDi6VLyJ9cSjYDKVUUVl6Jb+rGY1atXIppQ46HU7CERcqu/aSctd+b4JMLsvmxHBgnHOChXXmCpXJbnWdnYOvu4a8sXzFLKM8V8o9xx9pNIRlPvkhOPZ0MItqZROR2DLXiojEA72B9d6uM+P3m4nDZzqj3Dkz66zCd6YKeYcC3xn1MwsYLo5RRalAa2C5G7LUWDYROR/4DzBIKbXfKb3C39WDciU5HQ7CsYoAOKzhKwz5YoErONtCtlw2Q762OAKvS5zSrKwzV5gFjDZGD/UAjhidHqvr7FysjES78wdcg8M3VgTsA+YZ6Y2BOU75rgQ24dDijzqlt8DxT5oN/A8IN0muBsACYDMwH4gz0tOASU75muPQ7EHlrv8OWIOjMfsQiDaxzqqVDehl3H+V8XmrHeoMuAk4Bax0+utiRZ1V9M7gcDUNMr5HGM+fbdRHScxPRwAAAJ1JREFUC6drHzWu2wgMsOC9r062+cb/Q1kdzarud/WQXP8A1hn3Xwi0dbr2FqMus4E/errOjOO/Ac+Vu87qOvsYx+i3UzjasluBO4A7jPOCY9OuHOP+aU7XWlpn5f/0EhMajUYT4Pi6a0ij0Wg0bqIVgUaj0QQ4WhFoNBpNgKMVgUaj0QQ4WhFoNBpNgKMVgUaj0QQ4WhFoNBpNgPP/ZsgVnRd+gCAAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}