Module4_Lab1.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/nagababumo/iiitfmmlassignments/blob/main/Module4_Lab1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M3xEYaFTrNN8"
      },
      "source": [
        "# FOUNDATIONS OF MODERN MACHINE LEARNING, IIIT Hyderabad\n",
        "# Module 4: Perceptron and Gradient Descent\n",
        "## Lab 1: Perceptron\n",
        "### Module Coordinator: Jashn Arora\n",
        "\n",
        "In this lab, we will be studying the perceptron learning algorithm.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6fxSh2azDWVV"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "from matplotlib import pyplot as plt\n",
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tT5y5bqvEAKn"
      },
      "source": [
        "First we need to define a labeled data set. Let's make a toy dataset."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "CGK5WP6WDZrz"
      },
      "outputs": [],
      "source": [
        "X = np.array([\n",
        "    [-2, 4],\n",
        "    [4, 1],\n",
        "    [1, 6],\n",
        "    [2, 4],\n",
        "    [6, 2]\n",
        "])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uWsK5zfpELdk"
      },
      "source": [
        "Next we need to add a bias term -1 into the data set."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9HhJXqTkDbl_"
      },
      "outputs": [],
      "source": [
        "X = np.array([\n",
        "    [-2, 4, -1],\n",
        "    [4, 1, -1],\n",
        "    [1, 6, -1],\n",
        "    [2, 4, -1],\n",
        "    [6, 2, -1],\n",
        "])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "EeMQDzjjDeyE"
      },
      "outputs": [],
      "source": [
        "y = np.array([-1, -1, 1, 1, 1])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jGaici2BEVZ3"
      },
      "source": [
        "This small toy data set contains two samples labeled with −1 and three samples labeled with +1. This means we have a binary classification problem, as the data set contains two sample classes. Lets plot the dataset to see, that is is linearly seperable"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "czogKw6ADgbt",
        "outputId": "287c17bd-beb1-4776-a296-936d7abb5830"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f7fe334df70>]"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "for d, sample in enumerate(X):\n",
        "    # Plot the negative samples\n",
        "    if d < 2:\n",
        "        plt.scatter(sample[0], sample[1], s=120, marker='_', linewidths=2)\n",
        "    # Plot the positive samples\n",
        "    else:\n",
        "        plt.scatter(sample[0], sample[1], s=120, marker='+', linewidths=2)\n",
        "\n",
        "# Print a possible hyperplane, that is seperating the two classes.\n",
        "plt.plot([-2, 6], [6, 0.5])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lWlVB486EY8e"
      },
      "source": [
        "Finally we can code our Perceptron algorithm using our update rule. To keep it simple, we will linearly loop over the sample set. For larger data sets it makes sence, to randomly pick a sample during each iteration in the for-loop.\n",
        "\n",
        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)\n",
        "\n",
        "The algorithm is shown in the above image."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ltJYDYNIDjLl"
      },
      "outputs": [],
      "source": [
        "def perceptron_algo(X, Y):\n",
        "    w = np.zeros(len(X[0]))\n",
        "    eta = 1\n",
        "    epochs = 10\n",
        "\n",
        "    for epoch in range(epochs):\n",
        "        for i, x in enumerate(X):\n",
        "            if (np.dot(X[i], w) * Y[i]) <= 0:\n",
        "                w = w + eta * X[i] * Y[i]\n",
        "    return w"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "wV0oQoHEDl9e"
      },
      "outputs": [],
      "source": [
        "def perceptron_algo_plot(X, Y):\n",
        "    '''\n",
        "    train perceptron and plot the total loss in each epoch.\n",
        "\n",
        "    :param X: data samples\n",
        "    :param Y: data labels\n",
        "    :return: weight vector as a numpy array\n",
        "    '''\n",
        "    w = np.zeros(len(X[0]))\n",
        "    eta = 1\n",
        "    n = 30\n",
        "    errors = []\n",
        "\n",
        "    for t in range(n):\n",
        "        total_error = 0\n",
        "        for i, x in enumerate(X):\n",
        "            if (np.dot(X[i], w) * Y[i]) <= 0:\n",
        "                total_error += (np.dot(X[i], w) * Y[i])\n",
        "                w = w + eta * X[i] * Y[i]\n",
        "        errors.append(total_error * -1)\n",
        "\n",
        "    plt.plot(errors)\n",
        "    plt.xlabel('Epoch')\n",
        "    plt.ylabel('Total Loss')\n",
        "\n",
        "    return w"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oVRULAv4ry36"
      },
      "source": [
        "Next, we will see the the training error at each epoch."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "EdhdZH5eDtBE",
        "outputId": "97a3760a-4a30-4c5f-cfca-c65d12d388ed"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "w = perceptron_algo_plot(X, y)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "833EECrlsHtT"
      },
      "source": [
        "We now plot the decision boundary and check which samples have been classified as positive and which samples have been classified as negative."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "Rwn0luhQDwWt",
        "outputId": "38d52593-50ba-4339-8c89-31b3fe2f1b69"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.quiver.Quiver at 0x7f7fe2d96220>"
            ]
          },
          "execution_count": 9,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "for d, sample in enumerate(X):\n",
        "    # Plot the negative samples\n",
        "    if d < 2:\n",
        "        plt.scatter(sample[0], sample[1], s=120, marker='_', linewidths=2)\n",
        "    # Plot the positive samples\n",
        "    else:\n",
        "        plt.scatter(sample[0], sample[1], s=120, marker='+', linewidths=2)\n",
        "\n",
        "# Add our test samples\n",
        "\n",
        "plt.scatter(2, 2, s=120, marker='_', linewidths=2, color='yellow')\n",
        "plt.scatter(4, 3, s=120, marker='+', linewidths=2, color='blue')\n",
        "\n",
        "# Print the hyperplane calculated by perceptron_sgd()\n",
        "x2 = [w[0], w[1], -w[1], w[0]]\n",
        "x3 = [w[0], w[1], w[1], -w[0]]\n",
        "\n",
        "x2x3 = np.array([x2, x3])\n",
        "X, Y, U, V = zip(*x2x3)\n",
        "ax = plt.gca()\n",
        "ax.quiver(X, Y, U, V, scale=1, color='blue')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XnMRBEKku2Kq"
      },
      "source": [
        "As you can see, our algorithm has correctly classified all the samples. The decision boundary is shown in blue."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LghXwwPesVSq"
      },
      "source": [
        "# Things to try\n",
        "\n",
        "\n",
        "1.   Try this on a real dataset like the Sonar dataset or the Banknote Dataset and show the error plot.\n",
        "2.   Increase/decrease the learning rate to see how many iterations will be take to coverge. Does it even converge on a huge learning rate?\n",
        "4. Take a toy dataset that is not linearly separable and run the perceptron algorithm on it. What happens? Note your observations. An example is given below.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WmhMHx7zNPt8"
      },
      "outputs": [],
      "source": [
        "from sklearn.datasets import"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FSl65H26Eobw"
      },
      "outputs": [],
      "source": [
        "X = np.array([\n",
        "    [-2, 4, -1],\n",
        "    [4, 1, -1],\n",
        "    [1, 6, -1],\n",
        "    [2, 4, -1],\n",
        "    [6, 2, -1],\n",
        "])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Y9xDT1ZhEo9_"
      },
      "outputs": [],
      "source": [
        "y = np.array([-1, -1, 1, -1, -1])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "y1xyTQHYEtAq",
        "outputId": "aac3ec6c-9c9b-4738-a164-26ab4c7b893c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[-2.  3. 15.]\n"
          ]
        },
        {
          "data": {
            "image/png": 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M1tgWvAZ+X42KgWyGYnszYdw5HoAIcCbige4t8EM1ITmANN3ArhBc3v+7Kn2hticwVysqLC0NbPqtQfr8kObVxVoZAB68EmfTnNcDALiSDDs1I/apOcqoxCFpVRMQlLdwjWI2Q2hW4r+XWcYTgbutAb7qoRqABzsP0A3xANgApOkG7lizvQXph8K4swDcEBAbFxV5gNYpA6A9gFVjrQxA3pu+FccA+Jv1nNN6kgaq/bYaA5C0sQ0IzDiuF/3bVIy5vNexMBoLfMP1bQAPdiUQn/KDSWAzn0E2Q6k8gFl9IRUhINuZYDieoFbMoaawuUwbgNVmrQwAEH828F7bQiGXwWYpH3r/br0Ye9O827Jg5jO+q56UpI1tgGvY3JGE02u4nKKxjeH4/1uvb7l/v//gegCdgGQDQ+SWbaZJAret0/pCVQVJYD7tcxIYUKMIehJYQ5eCrh7rZwCqRqza+b2W2yw1b2zjrhcCiiN74JaVFmOPgpwlzaB7twfgtAzFbt1MnQN42TMAr79UQaNiPNAhoLAkMMBTwdJJQdRmcgC2M0lVZsl1/5wEBtSEgNraA1hp1s4ANCqFeEngBWMbd2omrNEk1pfDHS6Tfl5rs2qgY8dvbAO891U/q23UsZ1U4Q0O+VzZKOLKZvGBLgWd5gBOy3W4BiD5Zti1ZkNA6RVBpx7ANAmsohlMh4BWm6UZACIyiehTRPRZInqaiD44c/8/IaLusl5/HqyjL3tin50FPEuS8smks4BnSdMLMDvhDJgmhNMkgu8cD9CoGDDzWVzdLD7QOYCO7aCQzZzRayob2dSNYGHdxWnCQHxSrxUDISAVSWAv7HOpavi/a1aHZXoANoB3CiEeAfAogPcQ0dsAgIhuAthc4mvPpVk1YI0mUl9gIYQXApp/WvcbqCRDJ5OJwL22naoElEnaCzCeCOx3zuobJW1sC3LneICrm25i+epmEa+cqNEXugh6M0qgTMXMJw4BjcYTDEbjM2WgQLqkLUtJ1MwcKoWcKwmtKAdQKmTRqBjaA1hBlmYAhAuf8PPejyCiLICfBvD3lvXaUcSZp9sajGA7k1OVMrPEnQx2vz/EcDxR4wEklIM46toYT8SZRjS+pjSJ4JdPggaghOF4klq2GgCOe0N8w//6u3j89lHqtWTpzpzUmaqRQzfh6bpnn00sT+cCpzAAg2kSWKW+UGswQr2YR72YV2oAfvK3n8P7/vVnlK2nScZScwBElCWiJwHcA/AJIcTjAH4AwL8XQtxd8Nz3EtEtIrp1cHCg7JqaFXeTk5mmdVeiXv9SlT0AuU2OPYU0XcBMUgMwbxxl2m7gyUTg5eMBrrAB2HD/VBEGevZuG/ttG48/fz/1WrJ07fGZBDDghoB6CT0AXwYiRF4iVQjImoaAANcQqPAAlmUAPvPiMZ748rGy9TTJWKoBEEKMhRCPArgK4K1E9HYAfwXAP5V47oeFEDeFEDebzaaya2pU5ZvB9maapcIo5DJoVArSm2ZUY1lctsoFEMVXBJ3X21AquDXkSXsBDro2huMJrm6WAMD3BFQkgm8funLEzx+enyxx1x6d6gJmKkZy8bZgspZREQLqWJyvcL/StWJejQfQdw3ARil/qiQ0LSf9EU76urP4ojmXKiAhxAmAxwC8A8DrAXyRiF4AUCKiL57HNTDTxOniTW6/JbdZ79RMf8TjItLOAg6Sz2awWYrX2AZEN6Lt1pNPBuOTPm/8V1QaAE+P/vbB+dUN9OzxmQogAKh4SeAkuY3ujBJo8PdUVUCDEWrFnF9aXDNzyjqBl+EBHPeH6A21wuhFs8wqoCYRbXi/FwG8G8ATQohdIcQ1IcQ1AH0hxOuXdQ1hbJYKyGZIKi7NmzWHeeaxWzOxJzlNa79lIUNTQ5SWJL0Ae20L2QxhO+Qa0oy55I2eQz+lQg5b5YISA/D8obvx3z7snduoya7toGKebQDk8E0/QfntrBJo8Pd0ISDnVG+BKkVQNgC1Yh5DZ5Ko5HgWIYTfVKa9gItlmR7AZQCPEdFTAP4Ebg7g40t8PSkyGXJ7ASQ2zf22hUalgEIu+p8pjoTCXtsdw5jLqvmnTzIb+G7Lwk7V8NUog7jGLJ0B4JM/AGWloBz66ViOkqE1MsyWazIVI/kYx25IEriQc0M3afSF2oMRqsWAAVCgLwQAJ4MhNkpuCAhQ0w3cH44x9JRKj3Vp6YWyzCqgp4QQbxFCfI0Q4s1CiB8LeUxlWa8fhdsNLJcElgnVXK6ZuN8bSg3ODg5hUUEzgR5QVG/Dbt3EQcdOJCV853iA7XIBpcAM3aubxdTdwENngpeOB3jzFVdg7rzyAD3bQSUkBMRhoSQhGz7lz5aXptUD4mlgjDsVLN3majtjWKOJHwIC1DSDHQdO/cfaA7hQ1q4TGHClj6WSwC25hi3eTO9JhIHSzgKehaUtYklRRLyv3bqJiUg2ZyBYAspc3Szh5eNBqrDNS8d9jCcC73zTDgDg+XOYT+t49fp82g/iD4VJYACm9fqn162mPLG3B7PyEnl0bCfVPAbe7FUbgKAXoUNAF8taGgDZuLnsZh1nmlbaWcCzNCoF6cY2Zr8dPuEMiN/YFuTOcf9U+AdwJSFsJ10vAG/4b39DA/ks+RVBy6Q3dL25sCRwuZB8KljXdpDPkl+tw1TN5L0FAA+ED3gACiaXBbuLN4pu9Zx6D0CHgC6S9TQA3qk5qorDGo1x3B9JeQCyk8EGwzHalqPcAwDkewE61ghd25lrhPxu4Jh5ACHcHgAuAWVUlIJyyOf1lyp47XbZTwgvk7BYPVNJ4QF0rBEqRu6MEKA7FjLdkJnZJDCQTg6CT+obpYLvAag4sQc3fR0CuljW1gA4ExFZ18zhHBnJBlkJhdkpXCrgxjZZA8Ab+7w8RNLh8AddG7YzCQ0BAVOV0CTcPuxhq1zARqmA643yueQAun61TkgIyEhettmxnFMloP6aKXIAHKuvzSSBgXQGYHkhoGHgd+0BXCRrawCA6AaqvQUbZZCamUOpkF0YArrr9QqoDAHF1QPijuV5XshWqYB8lqTLWhne4K9szISAlHgAXVxvlAEANxplvHDUX/qs4XlKoMHbkqimziqBMlUzeXNZJ6ADxKhQBA0agKqpTl/ouOeu0awaOD6nii5NOGtpABoSKpr+Zi1xWiciqfLJfYVNYEyj4sZmZQfDLPJCMhmK1djG+D0AMyGgipHDRimfqhT0+cOebwCuN8oYOhO8suQ5A8sLAc0rLU3euBWM1TMqPAA/BFR09YVqpppu4OP+EFUjh0bF0DmAC2YtDYBM3NyXbJDcrHdqi4ep8OlbZQgoTmMbIGeEkvQChPUAMGlKQXu2g/22fcoAAMsvBZ03DAYAjFwW+SwlCtm0ZwbCMzVvMHyS7uK2ddZY1RVMBWvNGBZV3cAn/SE2ynlslvK6CuiC0QZgDnstG6VCNlQLJozd+uJxivttC1UjF7qpJCVOYxvgxvbrxTzM/NnQBuM2tsUMAZ30sVnKh55ur26UEoeAeKO/wQageT4GoBvSsRukYuSShYBs51SohqmaeQiRrLs4qATKTD2AdCGgqpHzGwZVGYDj/gibpQI2SwWlSeAP/+GX8BO/9Yyy9daBtTQAVSMHI5eJPDXvt6NHQc6yUzNxrxOtfb/Xih4uk5Q4zWAyw2h40H2c2v07ARXQWa543cBJegF4o+eNv1kxUDFySzcA3JVbDUkCA24YKHEIKCKslEQOYlYJNLheGg+gPRihHpiFvVHKK0nanvSH2CgVlK3H/O6z9/Afn95Xtt46sJYGgIjQqEQPVA8bmRjF5bqJ0VjgfsSJ5q6iSWCzNCtync2AXB/Cbs3EYDSOdXq8czzA1Y1S6H1XN4uwRpNEEg680V/bdg0AEeF6o7z0XoBeRBIYcHsB4hoAIQS69rwkcHJF0E5Ic1nWmwmQprT0xNMBYlTpC7keQB6bpQJOBiNl2k73e0Pc10nlWKylAQAWa+jIdgEzOxINVPuKm8AY2c5mQM4D2IlZCiqEwJ3j/pkSUCZNKejzhz1c2SieClm5paDL7QXo2g7MfGauZpPbuBVvcx2MxhhPRGhp6VQQLkFewY/VnzYsaRVBWzMGQF0IaIhNzwMYT4QS2WrANQDdhDOy15X1NgBzNs3JRCycBTzLoslg44nAQffsGEYVyDS2Ae44wsPu4nGUXPoqmwi+3xvCGk3mh4A2kpeC3g5UADHXG2XcOR5IaS8lpWuHV+swZSOH3jDextUJSdYy06lgyUJAuQyhOJPXSXtin2cA0pzYnfEEHcvBhucBAGqay8YT4ecTtBcgjzYAIRz1hnAmItZmvUgO4tAbw7isHMCixjbATXoLsbgKaVeysY2ZVwLKTHsB4pWCCiFw+6B7xgDcaJYhBPDlo+UNnJ83DpKpGPE9gCgDUEujLzRwUCvmz+SramY+dRnoRjAHUMzDmQhfJiPRmt5ndLNUwGbZXVtFKehxfwi2S9oAyLO+BqBi4H5/GKp6mWRqV6NSQIbmh032JMZLJkVWDkJmwhkAXKoZpx6/iKkBCPcA6sU8amYudinoUW+IjuWEegDAdEjMMujZTmS1VsXIxZZv5tN9VG9B8tLSEKNSzCVuBBNCeENmTnsAQLpuYD7tuxLTrgegohIouOmfl1z4KrDQABDRNxJR2fv9O4joQ0T02uVf2nJpVA0IEX5amDcyMYpcNoNm1ZhvAJYgA8HwcJlFoyGnRmj+kHvArXPfKsuPuXz5xD2JzwsBAa53EDcENFsBxFw7h16AzoIQUJIy0KkHECYFkSIENKMEyqTxAKzRBMPx5EwICHDHRCaFT/tcBgqoCQEdBYog7veSCw+uGzIewM8B6BPRIwA+AOBLAP7lUq/qHOBN817IqTmODESQ3Xpx7qaZxKjI0pD1AGJcg0xjG3PneICamQvdhJgrCQbDsArojRkPoGbm0agYS00Ez5NsYCpmDv3hOJYkRVR3cbmQBVEy9c5ZJVCmaiafCXAy8E7qngooAL8klO9LAks/uAbACwH10oeATnkAkhVxGjkD4Ag36/PtAP6ZEOKfA6gu97KWT5SGzl7LHZnYiDm2cbdmzE0C77Ut5LOE7XIh9P40yIaA9tsWCrmM/8WLYrdmLGxsY+6EqIDOcnWzGHsuwO3DHvJZOqMvBLhGYZkeQG+4OATEj5PFHwYTsi4ReXIQyRRGQz2AYj5xd3FQB4hR0V08VRjNo2bmkSE1HkDw1K9zAPLIGIAOEf0IgO8A8FtElAGweAd5lXMpYtPca1toVsJHJkbBDVRh7LcsXKqayMRcUwaZxjbAfV87NUOquW23XpSWhI4qAWWubpbQG45jNf48f9jFa7ZKoaWYy1YFlUkC8+NkiQoBAcnHOLYHztwQ0ETEM1IMh3lCQ0ApDAD3yWyWC8hkCPViXkkSmOP+W+WCNgAxkDEAfxWADeBvCSH2AFwF8NNLvapzoBERN49bAsrs1E20LQf9kC8cb77LgIikuoHj9Dbs1kwcSYy55DkAUfF/IFkpqCsCFz419HqzjMPuUEldehgyZaD8OFnCBsIHqZo5dO1kZaBhISBfETSBUeF/11NVQH7MPk0OYIh8llAuuCWrm6VCZPOkLEddd3bxJclxrxoXKQ8AwM8IIf6IiN4I4FEA/3rRk4jIJKJPEdFniehpIvqgd/tHiOhzRPRnRPTLRHQh3kSxkEXFyIV7AC0Luwk266hpWnE7i+PCvQBRxBlHyZVCi8ZcnvRH6A3HUiEgQL4UdDwReOGoj9fNJIAZzgu8sAQvYOhMYDuTaA8gQdlmx3JQLmTnepZJOndH4wn6w/FcDwBIFrI5CQkB8bWnqgLqjbBRKvhe6IYiQbj7vSG2ygXPA9BJYFlkDMAfAjCI6AqA/xfAdwL4FxLPswG8UwjxCFyj8R4iehuAjwB4E4CvBlAE8D0JrlsJ807Ne20Ll+vRJ9owduc0UAkhXB2gJVQAMYu6gYUQsQbSy04GW1QCyjzM3cCSpaCvnAwwdCZnSkCZG0sUhePqnjDNHqaaIATUtcOVQP01EwyFiewtSBGzD5OYJqLU3cBuF/B0zc1SQUkS+KhnY9s3ANoDkEXGAJAQog/gvwXws0KIvwLgzYueJFy4TCPv/QghxH/w7hMAPgBxE64AACAASURBVAU3pHQhhM0G7tkOOgnHNu7O2TQ7toP+cBy7qigOi0JArcEItjOJ4QHIjbnkE/0iA1Ar5lA1ctIhIL8EdI4BeHirhAxhKZpA3QgpaIbvi1MKOk8IjqkkGAoTtlEzaRRBW4MRiHBGDTetAXCby6aFEBulglIPYLtcUNoH8Ou3XsL/9Ue3la33akPKABDRnwfw1wH8VozngYiyRPQkgHsAPiGEeDxwXx6uN/E7c577XiK6RUS3Dg4OZF4uNmF6QLLNUmFMxymeXpPLKZfpAXBj2yiksQ0Ivi/5HACw2APgE/08ITiGiGKVgs7rAWCMXBZXN0tL8QD8ck2JJHCcZrDOgtJS1wOIt7n6SqBzxkwCCUNAfVcGYrZoQb0HoCYJ7BoAA1tlAx3LwdAJ/x7E5ddv3cG/evxFJWu9GpHZyN8P4EcA/KYQ4mkiugHgMZnFhRBjIcSjcE/5byWioOfwswD+UAjxR3Oe+2EhxE0hxM1msynzcrFpVs8qgqbZrEuFHKpm7symucwmMKYZ0dgGxO9EdmcGZBYKwt05HqBq5EKTkLNc3SzG8gAqRs7v1whjWaJwUcNgmERVQHb4PGAmTQgo1AMoJm8um9UBYtIbgJHfAAa41UCD0TiVgNtkInC/N8R2uYDtirruYsAtE5cVWnwQWWgAhBCfFEJ8G4B/TkQVIcRtIcT74ryIEOIErtF4DwAQ0T8E0ATwwwmuWRmNSgFt67R6YNrNerdm+uMk/TWX2ATGLBpzGVfeQnbM5Z3jPq5sFqVKS69ulqR7AVgELmrd640ynj/oKZMTZjoSOYBkIaBRpFdRNXKwnUms0+s8JVAg4AEkDAGpNgBCCH8WAMNVRmkqi04GI0wEsF0p+H02qprBDjo2OiusMCojBfHVRPQZAE8DeIaIniCir5J4XpOINrzfiwDeDeA5IvoeAP8VgL8mhFDjpyUkbDh83FDJLLt188xA9STaQnFZNBz+bgLPZqdmSiWBF8X/mSsbRXRsR0qfJjgIfh43mmX0hmPlJzQ+1Udt1oVcBkYuE7sKKDoEFP/EHhUCymczKBWyiUJA8wxAmiEuXduBMxFnksBAuhM7V/1wFZB7W3oDMBiO/f/fVfUCZEJAvwDgh4UQrxVCvAauHMQvSjzvMoDHiOgpAH8CNwfwcQA/D2AHwH8ioieJ6B8kvPbUhHXQ7rcs1MwcSoVkYxt3QyQU7rYsbJaixzCmJaqxDXCNUKNSQCEnr//nGrP5BoB7ABaVgDJsKF5akAewnTHuHA8WGgBfFE5xHkAmBAR4iqAxDMAieYlqgtJSNqZhISAguR5QlAfQtkaJuotPAjpADHsAaQwAn/a3y4YfAjpSUAoaPBjKztx+0JDZ5cpCCD/mL4T4AxaHi0II8RSAt4Tcrm4gbkqaFfc0HNw076Yc2rJbN3HgST9zvXec+vukLAoBJSlDdY2ZDSFEaCimPXDQsR1pD+BqoBT0zVfqcx/34lEfQkxLPecRHBD/thvbUtcgQ1ciBMT3y27Wo/EEg9E4dBiMv16CoTBta4QMwW+smiWpImiUARDCDZOF3R/FcUAJlNlU0Fx2P9AFvFV2vwcqQkBBnbB19gBuE9H/TETXvJ8fBbASdVGNqvvhC3YOpt2sd2omxhNxJqy0zPg/4Da2Vec0trnXEH8YzW7dxHA8metOvyRZAspMm8GiE8FfOoguAWUeqhdRyGWUVwL5ZaALvMByQX4mQDeiXp+p+mWbMUJAA7e3YF6uJIkHIIRAa3B6FgCTRg/IVwIN6GGpCAFx2ed2pYCNoqsvpCIEdKANAADgu+EmbD8G4KMAGgD+5jIv6rzYLp89NcuMTIwirBt4r7WcSWCzNCK6gZPIWywacsMloFcWlIAyG6U8SoXswlJQfw7wAgOQyRCub5dx+0BtJVDXclCK6Nhl4ngAUUqgjB8CiuUBhCuBMrVifAPQtR2MJ2KuBwAkO7Fzvf/mzKD5pOsx9wMKo5kMYbOkphcgGPZZWwMghDgWQrxPCPG1QoivE0K8H25e4IGHlTEPuu4G54wnOOjYqUNAwDTpOnQmOOrZSw8BAeGNbQBgjca43xvicsxr2Fkw5lK2C5ghIl8VNIrnD7toVIxIeWlmGQPie8NoHSCmGiMH0I4YBuOvl2AozLxZAME144aAwpRAmTSCcCwFHawCMvNZFPNZ/74k3O8NUTVzfn5ru6JGDuKwY4PIfc+LZFYeVJJOBPvzSq/iAgl20B52h5iIdOWas7OB73UsCBF/tkAS5g26Zz2fxB5AK/zDf+e4j3IhGxoqmIfMYJjnD3tnZgDM43qzjBeP+qGT3ZLSWaAEypRjDIXpLlACDd4XpwqoY4UrgTKuwmi8zTrSAJRSGACWgp5ZN20z2GHXPiXdrkoO4qDrykvs1sz19QBWnaAB4Pr9NOGarVIB+Sz5YRO/BPS8DEDEgJu476tZNUAUEQLyVEBlegCYKxuLu4GfDxkEP4/rjTKciUg0cH4eXTtasoGJEwJapAQavC9WFdAcJVCmVnRnDMTplZgagLOzK3hATJKhMCf9IWpm7oy8d1o5CJaBYLbLhpoQUMc1LPMOVqvA3E8OEX3tvLuwAvMAmEbFwGdePAGgpl4/kyFcqk5LQfn0fB45gGbVbYO3RuNTJadJexvy2QwaFQN7rfDNVWYQzCxXN4toW467cYWcXFuDEQ67w7kSELPcCFQCLcoZyNKznYUJYCBeGWjHXhwC4t4ClSGgmpnHeCLQH44XlrUyYbMAmFQhoP7oVAKY2SznU/YBDPHw1vRzuFUuKKkCOujYaFYNNCoGXnhhebMnLpKoT8T/EXHfc6ov5KLguDkrdgLpO3aD9fPnIQPBNCpc1WSf2pjTyFtcDmlsY+4c93Hz2mas9fxS0OMBapfPbjAvLBCBmyXYC/COWFcyn47lnNpQ5lExcrBGE4zGE+RDhtYEkQkB8f1x9IXaVrS8hK8Iao3kDQB7ACGhPTOfQSGbSWgATncBMxulAu6etGOvxxz1hnj04Q3/71vlAlqDkdT/SxQHHRs3GmW/uGJeOfSDzNxPhBBC1ffpVU2zamAwGqM3HGOvbSOfJWyFfEjjsFsz8eye+4HmMYxx4uRJCTa2BQ3AXttCMZ9FTSKsMctOzcSLR2dDNm1rhLYl3wPABEtBv+Jy7cz9XAEkmwPYKhdQM3NKNYFkk8BBOYiwjS1IW6IMlO+X9QCc8QRde0EVkD8TwMHl+a0Xp/CHwYR4AESEeimfaDD8SX/kN2oFcXMAyU7sQggcz4aAAnpAl6rJDl5CuKXc7AFYI/ffepEBl+F3n9lHfzTGtz3yUOq10qJzAIFNk3sA0o5t3K27oyFZg3+3Zp7LySGssQ1wS1Iv15Ndwzw9IK7kkS0BZa4sGAxz+7CHDAGv2ZZbl4hwo1lR2guwaBwkU40Rs+9YDvJZgrGgEzuOIii/bmQIyJ8KJr9hnwxGyGUIpTnNZUn1gFwl0DAD4J7Yk3QXtweuvETQAKiQg+jYDmxngkbF8PuFVCWCf/6TX8I/+b0vKFkrLdoABAxAnJGJUezWTPSHY3RsB/spO4vjME8PaC9Fc9tu3URrMMJgeFoMK24JKLNdLsDMZ+aWgj5/2MPVzRKMnLxsxg1PFE4VcZLA/PjFa0Y3bDFVU765bJEMhLte/MYt7gKed61JDYA7CyBMX6iAiYhnpBiWfAh6Ftzfcz9FHoA3+2bVmHuwSsrdlnVGLuaiWHsDEJwNvJdwFvAsfv18y0rdWBYH/hIcdk5/8PdSGKGdOc1gsoNgZnF7AeaXgsqIwM1yvVHGKy3rjJFKgu2MMRqL2CGgRciWlsYZCzkVgosKAcXvLZgnA8FsJDAAQ8cNoYR7AKwHlMQATHWAmKkekCIDsEBoMQ6TicC9joWO7cRSkl0Wcw0AEX1t1M95XuQy4f/ce21LqQcAuJvmechAMPns6cY2YPqBS+wBzJlz/PLxAGY+c8r1luXKRhF3Ts6GgIQQeP5AvgSU4YqhF47SewFdiXJNJo52zyIlUKYao27fNwARm3UwCSxLqz8KTQAz9WJ8RVAuG90MWZcrg5LkAbjaR3UIKMwAzM4OSYI7tMkNdS2SWj8PklYBCQDvVHwtF8JmqYBshnD7sIfBaKzUAHxur4NhjDGMKpjtBeAPXJIh98DZxjaGS0CT5BWubhbx1J2TM7cfdGz0huOFInCzBEXhwhLLcejZrhchUzETp25/kRIoUzVz0lVAfghoQSew+9h4IaCwZC1TK+ZjawGxwQhLlk8F4eJv2PcDOkDB9YiAoxQndu78bVYM1It55DKkxAMIHqT2WxZe16ykXjMNa18FlM0QtssF/OnLLQBqGrYueZvtZ15yN7nzCgEBZw3AtLQ1/pB793lzQkAn/djhH+bqZgnH/ZEbaw9stLdjloAy17bVDYjnen0pD8CUDwG1rZFUzwTLS0wmYmExgoy8hJHLwsxnYg2FaQ1GkUa4XnRLVZ3x5ExT1zyOA3o9s/ghoATD4YOzAJhshrBRzKcOAeUy5I/F3K4UlOQAggepV4MHIDvb981E9N8T0d/gn2Vf2HnSrBp49q5btqlCssHMZ7FVLuBJr8HsvEJAgNfX0A0zAMmuoWLkUDFyZ0JAcQbBzMLPm00ELxoEP4+ykcNuzcRtBYlgGdVOJk4IqGs7UmW4VdOVW+4NJYxKxED4IDUz3om9NRiFloAynMiNY1R8GYg5SWD3MQlCQL0hKkbuTNFAWjkI7gJmIzyvyz4udwPfo7uvgkSwzESwfwjgn3o/7wDwUwC+bcnXda5wnS+g7rS+UzN9tczzNACNioHDztBv/VfRiLZTM06dXLq2g5P+KHYJKDOvFPT5wx4KuQweSuCtqJoPzBuvTAiINfg5bBRFx1JfWdS2HBBFTy4D4imCTiYCbSs6CZykG9hXAg3JGdXMHLIZSqQIOisDwaSVgzjwegCY2YNVUvbbFjLkHh4WTds7D2Q8gL8M4F0A9oQQfxPAIwAkW0oeDIL/0ZcSxspn4Zg70XRa13kQbGwDph+4RkRMdxG7dfPUaeXlhCWgjO8BnJz2AG4fdHF9u5yoD+N6s6wmBBQjCZzLZlDMZ9G1ozcuIYTXRCSXAwheRxTtwQgVI7fw3yuOImjHciBEtFeRxAD4swBCPAAiN2STxAOYawAq6T2AUwagapyprkvCXstCs2rgoQ3zjFd9EcgYgIE3u9chohqAewAeXu5lnS/8H71VLsSqP4+CT/3bZSNVO3pcZsdc8gdONlYbxm6teOq0krQE1L/GigEjlzlTCno7hgjcLDcaZRz3R6lkhYHpaV7GAACup7DotD4YjTGeCKku0jiKoIuUQJk4iqB+F3BEZ/NUw1/+3/qkP0Qh5xrMeWsm8QAOu8PQw03aENBh10YzoDDaqLhyEEma1YJwWbjMvO3zQGZXuOUNd/9FAE8A+DSA/7TUqzpn+D9aZbUOr7VbP7/TPxBiANpW4gQws1s3cK/jjrkEpk1gVxIaACI6owrqjCd48agvLQI3i6r5wHyalwnXAF7j1oIQUByvIk5ewVUClTAAxbx0vJ7LNVWHgNwu4PnNZZulQkIPwJ4TAnLXGyfYsCcT4RqW6nTdZtWAMxE4SdAAF4TVBuZ12J83MgNh/gchxIkQ4ucBvBvAd3mhoEiIyCSiTxHRZ4noaSL6oHf7dSJ6nIi+SET/hojSCe8ogDdNlZr9vNZuLd3mG5cwDyBpCSiz64255LK6l08GMHKZUyekuFyZGQxz53gAZyISewDBUtA0dO0xiIDSnJPqLBUjh+6C03VHolqHidO45SqByq0pmwSOmgXgr5dgLORxfxRaAcRslAqxG8GEEF4I6OzncKtcgBDJEstsOIKf79nvVVJ45vhu3Z0xoHKORRJkksC/x78LIV4QQjwVvC0CG8A7hRCPAHgUwHuI6G0A/hGAfyyEeD2AYwB/K9mlq6OxQh5AsLMZSD/iEjjbDXznuB97DsAss93AcUXgZnl4q4RshlIngruWKwUtm4coG9mFSWDezGXCNRwCkk0Cy4SVOAksMxNAxgAkTQJHCSJulvKx+wA6toPRWGA7xAPY8r4HScJAnOxtBoTkmjPfqyT0hw46luMbgIlQ012chqhOYJOItgA0iGiTiLa8n2sArixaWLjwtzHv/XAD2W94t/8KgP8mxfUrga27ynr9Xd8DOL8KIGDa2HbQsf0PXNreBr8XoMUGIP4cgFmubhZx1Bui71XdJO0BYPLZDF6zVVLgAYyk4/8AUDEWyzf7IaAYVUAyMfv2IHoYDFMz8xiNhV/pFsU0BzB/szZy7hjHODH7RR7AZjl+COh+SBcww0YhyVwATvbOJoGBdB6AX5LthYCCt10UUR7A98GN+b8Jbtz/Ce/n3wH4ZzKLE1GWiJ6Emzj+BIAvATgRQvA35g7mGBMiei8R3SKiWwcHBzIvl5irm0U8crWOt93YUrbma7fK+OordXzDjW1la8rAjW0sbgekN0Kzw+FfPh7gyka60NZsL8Dzh13UzFwiaQnmeqOcuhegZ49RNuQLASrG4iqgTozegnIhiwzFyAFIeQDyiqAnEcNggsQVhDuZMwuA2SjlYY0msEbyek5c5rkVkgTmzuBkHoD7OQ8agIYKAxAoyWav+qITwXMNgBDiZ4QQ1wH8XSHE9cDPI0IIKQMghBgLIR4FcBXAW+EaEymEEB8WQtwUQtxsNpuyT0uEmc/i3/3AX1C6WRcLWfw/f+cv4OuvqTMqsvAIO1XDaLYrBnIZwl7LQn/o4Kg3TFwBxPhzAU7YAPRwvVlJFVa63ijjhaNeqkqNju2gEkPzvWLmFoaAuv40sMXrEpGUINxkIrxZAPJhJZmYfXswQiGXOTVRLow4BkAIgZP+KLQElNlM0AzGOanQEJCvBxR/w+ZNPlhdVDVyMHKZVCGb4HjYWa/6opCpAvoFInofEf2G9/MDRBRrKoIQ4gTAY3CHyW8QER+FrgJ4Od4laxbBXYv8gUvbiJbNEC5VDey1rdQ9AAyHkDgP8PyB/CD4eVxvlGGNJqmqK3q2s7CxKkjFyC+Ub45TBQSwIFz0mt2hV68fI7EsUwm0qAuYqZfy0hUxHdvV7I8MASWQg5jqAJ3Ns/FrJWkGO+jYMPOZU/9fRJS6Gzg4HnY6O/xVmgMI8LMAvs77k3//uUVPIqKmVz4KIirCrSB6Fq4h+Mvew74LbkhJoxCuWb6bUgYiyE7drVtOOgdglmbFQCGbwZ3jPgbDMV5pWakNAOvXpMkDdC0ndghoOJ7AduZ7AfENwOKhMLIyEMHHyIaAFoV/ANcDkK0COuktzitsJBCEm0pBnzUs+WwG9WI+WQjIawKb9Uab3mjIpOy1BqiaOZS95r2dmjl33vZ5ETUUPufF6r/eq+Rhfp+IPiux9mUAv0JEWbiG5teEEB8nomcA/CoR/TiAzwD4pRTXrwmBP6h7LQtVM4eSxIDzRezWTHx+v+OHbNImgTMZwkMbJl4+Hvgyzkl7AJgbDVdZ8fZhD9/4+kaiNVyBuhghIH8mwHhuE2HHclAuZJGVrCySGTYvowTK1GKEgBbNAmDqxTz+TNIA3O/PF4JjpiGgeB5AqZCdG67aLhcSeQCH3WFoiXOjYuCl++GT7GSYrch7NfQCRO0MnwLwtQDGRPQ6IcSXAICIbgBYmKkRQjwF4C0ht9+Gmw/QLIlmxcBoLPDcXkepttEffv4Ad477KGTT9QAwXAqaVATu7DUaKOazqaaDuQZA3gMIDoWZl8DuWKNYs2SrZg6HC6pXZIbBMNMksFwI6KGNxZ+ZjRgzAY59HaDoMtDgY2WYJwPBbJULiSShDzo2XhsykrRZNfDpLx/HXo/Za9unvPGduolnXmknXk8FUSEgPq78XQCPEdEfENEfAPh9AB9Y9oVpksPVC8+80lYmRLdbN9EbjvG5vQ6ubBZTz00G3DBS0ACwrHNSiCiVKBxr9sh2AQNy2j2yOkDTNRdLN8QKAcX0AGTWrBfzGIzGGDqLS0s5rBNdBZQsBBQW/mGSykHMCsExzYrhzddI1ry13zo9mGm3Np0dflFEGYAmEf0w3CauX4C78f8+XEmIMyd7zasH/vB2bUeZB8CdzZ/+8nHqElDmykYRh10bz9xtY7dmSilwLiKNKJztTDCeiJghoMWNW7JKoP6apkQIKEZzmZnPopDLSOUApENAJflmME7sRoWACrkMyoUs7sdKAofLQDDbFSO2ARiNJ7jfG4YbgKoBIZKVljrjCQ669pkQ0GA0jiWrrZooA5AFUAFQhRsqIu8n592meZXSCIRnVHkAfHJpW07qBDBzdctd5//74mHq8A9zo1HGS8cDqZPpLNNkbZwQEEtCRxmA+CGgRZvC1AOQMyzuTIDoNZ2xO7dXNgcAyBmAk/4QRIt7CzZKhXgeQDdcBoJx9YBGscqCuXFsngEAkvUCHHZdeYmdmRAQcLGloFGfnrtCiB87tyvRKCP44VUlbxE8uSgzAF4i+bg/Sp0AZq43yhhPBF467scet8en7kQhoCgDYDu4uiWfNK+ZeQwdt7IoKrEMyFcW1WQqi7w1pcpAfQOweMM+7rsNa4uS4JtleUloIQSOeuFKoMxWuYDxRKA1GIXOIQgjOApyFj5YJekF4GTv5cD36HJg2t6f272YM7VMDkDzgFEzcyjk3P9aVSGgoCeRVAV0lmAoKW0JKOOLwiVIBPMpvhyjaiqYBJ5Hx4rbW+ANhYnwAtqWK1khK/NdlVAE5dN31EB4Jo4HwEqgi9iMIQjXG7r5h+gQUPxeAL8JLMQDuJTCAwibzMffzf0L9ACiPj3vOrer0CiFiPwTjKoQkJnP+l/6tCWgzE7NRM47FaoKAaVRBY2j2cPIbNZuCEhtYllWCZSRUQSVEYJj4oWA5E7gcUJAUTpAzLQbOL4BiPQAEhgAvws4cCDj4VMXWQoaJQVx/zwvRKMWDgOpVDjlE4uqEFA2Q3jI8wJUGYCNUgFb5QJuJ6gE4lN8HDE49hbmhYBG4wms0SRmDmBxYrkdM68gMxZyagDkNmsAUqWgrgeweM3NUl7aAzjyJB62F4SAAMQqBZ0qgZ41AMVCFlUjl6gZbK9tIZ+lU1VLRs6dHf6qNACaB5tGxTjzgUvLbt09sV+qqjMqVzaKyGYID8eIkS8iqShcN4EByGQI5UJ2bgioGzNWH3xs1IbdHjjSCWBALgkcxwNg70PWA4jqAmY2SgW0rZHUEBc+1Ucngd374oaAqmZubnNZI6EcxH7LwqWqeaZ8eqdmXmgIKH3dneZVyddcreOkP1RSr8888vAGBsOxdEerDDevbWIshNKxmdcbZXzy8/EVZJMkgfnx80JAcZRAGakQkDWKld+pFXMxPIDFm3Uu62rlyOcA5DwAIdzrWKQKGyUDwSQKAc3pAWCalWQGgAfBzHJ5Zt72eaMNwIryvne9Ae971xuUrvnD736jq+ikkA98y59TuyBcA/AbT9zxunrlP+JJPADAmws8nGMAfCXQ+AZgURL4jTvylSNcWWSNxnNPty1JKWhGRhHUdsboD8fSSWDANRgLDYBEDqCQy6Bq5mLnABoRXe7NqoFn9+J37+63LXzF5dqZ23dqJj770kns9VShQ0CalYMril6ImQjuWg4yhLmDy+dRNWQ8gPg5gKiyzfbAiZ0EDl5PGK3BCKVC1q8gW0S9mPeNxjw4RxDVBczEGTZ/v2fDyGVQKkT/X8XVAzrsLPAAEoSAhBDYa1uh+bjdmomj3jBSTHCZaAOgWTm4pyDugPiu7aBs5GLPJChHiLd1E4SAFg2GF0KgIzkQnpFRBD2R7AJmZDyAYwkhOMb3ACS6gd0egLOKnbO4chAxksAdO1Lnqlk10LGcWINrOraD/nAcOh6Wb7t3QbLQ2gBoVg7WFIrbC9CNOQuAqRi5uUlgDgHFCSsVchkYucxco9IbjjERcjIQjIwekKwMBCNlAHwZiHghoEUsEoJjtsqG9FhIazRGx3YiPQBuPItTCcRJ3jAP4KIng2kDoFk5zHwWVzaKsUXhejGF4JiKOX+CV5IQED9+XuMWb+JxvAoZRdC4BmBDYiiMjBCcv16ZQ0CLPQBZAxAnBOT3ACwIAQUfKwMneS/Xz5ZPc2L4ohLB2gBoVhJXFTRZCCguFSOH3rwkcIIQEBAt3eBLQccJAcl4AJLDYBi5EJDnAURIQTNVI4dchqQ8gKNutBIos10p4Lg3lFLcPIiQgWCaFXfDjmMAokazXq65RkF7ABqNQq43yrh92Isltdux4lUNMRUvCRz2Wh3LQT5LMCQTq/6aEYqgcYbBMDI5gLgeQK04rSyaR5wcABFhQ7IZ7GiBEiizVS7AmYiFPRBAPA9g0byGIBwC4s7fILViDmY+c2GCcNoAaFaSG80yOpYTqwKkF7NslCkbOTgTATtEgZSVQOMmlqsRYaW4SqBA0AOIDgHJNGwx06qdiMRyfwgzv3jI/HTNxXIQ/aEDazTBVkQXMDPVA1p8YpcxALxeXA9gs5QP/TcgogudDKYNgGYlSaIJFLdvgPHr9kNO7HGHwfhrRgybn04Dk9+szXwGuQzN9QBsZ4zBaBw7BAREdwMf90dSp3/GlYOINgCc1JUJAXGnsEwvwEHHBlF0b0E+m8FmKY+DrvyGvT+nBJTZqZk6BKTRqITnA8epBIo7DYyJEoRLHFaKyAGwZxAnB0BEqBXnTxqL0wXMyBiAk/5QKgHMuB5AdAjovt8FvHgsKRsJGU/wsGtjs1RY2JUetxdgrx3eBczs1lfQAyCih4noMSJ6hoieJqIf9G5/lIj+MxE9SUS3iEjPB9Yo58pmEfksSfcC+OMgE4aAgHAPIK4SKCMTAkqSWJ4XAoozYpLZ8ETjFnsA8mvKeAC+DpBECCiOHMSiHgAmtgFoWb72fxi7dRP7LftCRkMu0wNwAHxACPGVAN4G4G8T0VcC+CkAHxRCPArgH3h/12iUks0QXrstDIx3jQAAHW9JREFUPx+4PxxDiPgyEAD83oFwA+DELgEF3DLQ7tAJnWbVtkYo5rOx9ZOiFEF5E49zWmcPICpmL6sDxPBMgKjNUEYHiImjCLpIB4hpVgzpJPDQmeCwO4wMAe3WTAy9UZTnzdIMgBDirhDi097vHQDPArgCQABgUYw6gFeWdQ2a9SZOKag/DCaNBzAnBJSkuaxq5CAEQstL4yqBMq4iaLgBOImpAxR8bHQIKF5iebNcwNCZYBBRWcSdvTJVQGY+i4qRkwoBHSyQgWAaniCczIn9Xmd+CSjD911EGOhccgBEdA3uIPnHAbwfwE8T0UsA/ncAPzLnOe/1QkS3Dg7iKztqNDcaZbxw1JeSF2Y9/yThGs4bhG3WiZPAEdo9bWsUKwHMuIqg4SGgJDmAqpkD0fzegslE4CS2B+C+flQp6FF3iIKnRiqDKwcRbQCEEDiU9QCqBgajMXrDxXIQ/iCYiBAQ33cRieClGwAiqgD4KID3CyHaAL4fwA8JIR4G8EMAfinseUKIDwshbgohbjabzWVfpmYFud4oY+hM8MrJYOFjkwyDYapztHv8vEIKoxIWVmrH1AFiojwAPwQUY91MhlAz53cDdywHE4GYpaWsBzR/wz7yuoBlS2tlDEDXdktLo2YMM3G6gfda7mOkPIDW+esBLdUAEFEe7ub/ESHEx7ybvwsA//7rAHQSWLMU4pSCcvgmTQhoVg+oPxxjPBGJcwBAuCJoXCVQJioHwCGguIYlqhs4ThMYsykxaUxWBoLZLhcW6gHJ9AAwcQzA3ZZ7+IhKAjerBoiAvdbig4pqllkFRHBP988KIT4UuOsVAN/k/f5OAF9Y1jVo1htfFfRgcSI46SwAACgVsiA6e1rvpggr8XPCQjZxlUD9NY0crNEEw5CGtdZghKqRiz3sR8oASMhAMNMQULQHEDUKchYZD2A6C3jxkJ1pN/BiA7DftmDkMpGhtXw2g2bFuJAcwDIHwnwjgO8E8KdE9KR32/8E4HsB/AwR5QBYAN67xGvQrDHNioGKkZPzAFIYACJCpXBWuoFP76kqi0JzAE7CHMDUq9ieKXdsD0aoxwjVMBul/NzTepxZANP12AOYv2Hf79m4vi0/QnSr4hoAIcTcsFHULOBZ4gyH32vb2K2bC8NVbi/A+YeAlmYAhBB/DGDeu/66Zb2uRsMQka8JtIik4yCZsLGQfHpPsllPQ0Bn8wrtQbLegqAi6KwBiKsDNF0zj5ePw0MXSUJAGxJJ4PvdYeQs4Fm2ywUMxxMvIR/+Hg9jhIA2SwVkMyRlAPZb0V3AzE7NxItH/YWPU43uBNasNLKloGk8ACB8KEySYTDMVF7i9EY4GI3hTETiJDAQXrUTdxgMEx0Ckp8FwOSzGVSN3NwQkOVV38QJAfnD4SPyAAddG9kMSSXBsxnCdrkg6QFYUrObL0oPSBsAzUpzvVHGyyeDhROcupaDXCa+aidTCTEAfHpP4lWUCllk6KwHkEQJlIlSBE3qAbABCKuJP+kPkaH417pRnh9W4nr+OEngrcpiOQh3FnABGckcSLNqLMwB8CjIKBkIZrduojUYYSBRWqoSbQA0K82NZhlCAC/ej3aveRhMXNVOphoi38w5gCRVQESEinFWDmI6CyBZIxgQrggaVwmU2Sjm4UxEaE38cX+IejEvvakybjdw+GZ9X2IY/CzbEnIQsk1gTKNi+HmDeRz3Rxg6E2kPADj/ZjBtADQrDZeC3l4gCtexHZQLyVNi5cLZsZBpqoDc5+VDPID4SqDMNAdw+nQthECrn6yyKKobOK4SKLPhyUGEwbLOMjIQzFQPaP6GfdCV0wFiZPSAWONf1gMIPue80AZAs9Jck+wF6FrJOnaZqCRwUsNSDVEETaIEOl0vvLfAGk0wHE8Sh4AAd5rYLK4SaPw1N0v5uVVAvhJojM3azwFEeACHnWEsD4BDQGFaTYzfBSyZBA4+57zQBkCz0tTMPBoVY6EoXG+YbBwkUzFyvpwE0/WkoOPW1jNhiqDTWQAJGta8vMJsCGjaBRz/tM6loyeDs5vrcS+ZB7BZKsztBL6fIAdQLGRRzGf98NEsk4krA9GI4wFUDIzGIlIHyR8FGccD0AZAo1HLDYlKoG5C3X6mYrghoGAytGONUq85m1eYSkEnyyuEdQMn0QFi+DmhlUX9ITZjbNTMRimPtuXAGZ9tWDvqDZHPUmwDGNUMdjIYwZmI2B4AEN0MtteyQARckli3YuRQMXI6BKTRqEamFDSpZg9TMXOYCJxSseykDCu5OYDTG2s7RWkpEK4HxOGWVCGgEANwvz+MVQLKsNcQumbXFZeLm6xvVAo4nGMA4shATNdb3Ay217LQqBjSst07NUMbAI1GNdebZRx2h5Huetd2UEmTBA6ZCZBUCZQJDQENRjBy8jN2ZwlTBJ3OAkjSCRy+WVujMazRJFYX8HTN+c1gssPgZ3E9gPDNeioDEd8DiKoEku0BYC7XizoEpNGo5oaXCH4hwgvoWuk8gDDpho41QiVBqIapmGfzCkmVQJkwDyBNCKhcyCKboTN1+0m6gJnNCDmIuDpAzFbZmJsD4DBOI0EIKMoDWDQLeJaLmA2sDYBm5bnRjK4Emnh17GmSwGEeQNoQUM3MY+hMYDvTsFJSJdDgmvNyAEkMCxGFdgMf9+J3ATNsAMI8AFcJVH6jZrYrBRx5ekCzJAkB1cwcCrnMYg+gLr/mbt3AvY4tNb9CFdoAaFaeh7dKyBDmagLxIJckk7uYSpgBsNNt1r4cRMCrSOsBhIWVWoMRiJK//zADwKf3dCGgsyf2+91hrB4AZqtcgO1M0A9pWDvo2jBymVjvn4jQrMzvBbBGY5z0R7FCQLs1E+OJkBpfqQptADQrj5HL4upmaa4H0LPdTSFVCChks1ZRBeSuEzQAyZRAmVoxPASUpGOXCfUAWAcohhQ0w5VDs6WgtjNGx3YSGwAgvBuYu4BjJ5YjmsH2/RLQovR6HC66e46JYG0ANGuBWwkU3gvAgmsqQkDsTYzGE1ijSaJyTSZMEbSTUAmUqZl59IbjUyWWSXWAmHADkDwHUC5kkc/SmRAQh5W2EuQAGhF6QHFlIJgoD4A38bhJYOB8ewG0AdCsBdcbZTx/0AuNAXc9D0BJCMjbrNMogTL+XOCAImjqJHDxrFdx0ldvAKYhoGR5hY1S4UwSmJO1yTwAVgQ9u2HHbQJjogThph6A/Lo73mPPMxGsDYBmLbjRLKM3HIee2NKMg2T8cI2XA/CVQBWGgNxZAClDQCwIF0gEp/UAwobCHPdHKBWyMHLJylU3S/kzOYBpF3CCJHB5CR5A1cD93jA0acv1/HGqgBplA7kMnWsvgDYAmrWAReG+FCIKxyGgNJu1mc8gmyFfEI5P7WlCQLWZEJDtuJo9SZRA/TX9zt1AXkFBCKhtjU7p4hz3h4nCP0yYIFwSGQhmXg5gNJ7gfn8YqweAaVYKmIipQF2QvbaFciEb6/8/kyFcqp7vaEhtADRrQdSAeD8ElCJcw/LN7E10FISAKn5i2d0I0yiBMlyVFPQAkg6DYerFPITAqZ6Fk34yeWkmTBCOT+9JQkCuN5I5YwDcUZHxSkCZqF6A/baFHQkNoFl26ufbC6ANgGYteKheRCGXCU0E8wabJgQEsHaPa0xUGAA/B+CtNZ0FkK4KyF3TXUsIkXgWABOmB5TWA9gM9QDcqV1JjBWRO8VrdipYkh4AJsoA3G1ZuJzAAOzWTF0FpNGoJpMhXN8O1wTiYSZlI1m8mnENgLtpdRWEgPLZDMx8xj9ZT2cMpzcqHALqDccYT0RqDwDAqTxAWg+Ak8DBpP39nmtUkparusPhT2/W3MiVKAlccTf4UA9AchbwLLt1E/urYACI6GEieoyIniGip4noBwP3/R0ies67/aeWdQ0aTZB5A+I7loNCNpM4YcmUjazfU6AiCew+fzoUJo0SKDM7FjKNEBwTJgiX3gPIYzQ+PWnsKGETGLNdNs6EgHjzllHsnKVRda/lcMarmEwE7nXsWCWgzG7NRG84PiMCuCzSfTqjcQB8QAjxaSKqAniCiD4BYAfAtwN4RAhhE9GlJV6DRuNzvVnG7z67D2c8QS6g0Ni1R6mawJiKOS2HVBECAtzTPm8G7AHUUySBK4UciKbGJI0OEMMzAXit8cQNKyWRgWB8OYje0DeiR71hogQws10u4Iv3TocA2QAk8QBKhRzKhewZD+CwZ8OZCKk5ALPwc/bbVipDL8vSPAAhxF0hxKe93zsAngVwBcD3A/hJIYTt3XdvWdeg0QS53ijDmQjcOR6cur1nj1Of1AG3j4DzCexVJFXt9NcMSDeoSAJnMoSqMVUEnRqAFBU73nN5KEx7MIIQyWQg/DVLZ8NK93vDRE1gTNhMgIOOjaqRQ7GQ7P+pWT07G3i/5f49SQiIn7PXOh85iHPJARDRNQBvAfA4gDcC+ItE9DgRfZKIvn7Oc95LRLeI6NbBwcF5XKZmxbkxpxKoY6WbBsacDgGp8iqmQ2FUJIH5+WxM2io8gJkQkN8FnEAGgvHlIAKVQEddO1UIaKtSwGA0xiAQVjrsJusBYNzZwKdj9lzGmTQJDAB3W4MFj1TD0g0AEVUAfBTA+4UQbbhhpy0AbwPwPwL4NQoR4RBCfFgIcVMIcbPZbC77MjVrgD8gfsYA9GwnVRcwUzHy/madVgmUqRrToTDtAecq0n1tg4qgfMKupwjXmPkMCtlMwADwfIF0OQB3LdcAjMYTtC0ndQgIOF23f9BJ1gXMuN3Ap72KPW/zTpQDqJ/vbOClGgAiysPd/D8ihPiYd/MdAB8TLp8CMAHQWOZ1aDSAGwKombkzpaBd20ldAQQAFSOL3tDBZCJSD4NhqoFh864MRC62aNkswaEw03nAyQ0AEaFeyvuD4U9S6AAxG/5MAM+opOgBYLiDOBgGOkjpATRC9ID22hayGYo1uJ4x81lslPLn1gy2zCogAvBLAJ4VQnwocNe/BfAO7zFvBFAAcLis69BoGCLC9WblTAjIHQeZPuFWMXMQAuiPxqmVQINrdgLNZWni/0w1MBSmNRghlyGUEsbAmaAekK8EmqYMtHjaA/CbwFKc1rdC5CCSykAwzYqB1mB0ambDXsvGpaqBbMJy1d2auRI5gG8E8J0A3klET3o/3wrglwHcIKI/A/CrAL5LhCl0aTRL4IYnChekazuoKPAAygFBODcEpGaz7npeRTulEihTM6elpdwFnNarCBqANLMAmFw2g6qZ8z2ANDIQDCuC8mQwazRGx3JS5wCA06WgcSeBzXKek8GWVgYqhPhjAPM+Vd+xrNfVaKK43ijjNz/zMgbDsV/50bUcNaf1wFCYjqUmr1A1XK+iN3RSK4EytWLulAeQJgHMbBSnYYvj/hDZDKVqWAO4G9jdWNMogTKzekD+KMgUlUXBbuArG1M55zdcqiRec7dm4pm77cTPj4PuBNasFZwIfuHI9QLGE4HBaIyKoeK0HjQAak7rQTmI9mCkJARUM/Po2A7GnleRJgHM1ItTRdDj/ggbCrwKVxFUnQdQMXIoZDM49JLAaWQgGE4gHwbyAHsJu4CZnbqJw66NUWBmw7LQBkCzVsyKwnHVjookcLkwDQG5SWA1ISDAMwCWk0oJlGEvoms5yjyAYGnpSX+YSgaCCc4EuN8bgihdWImI3F4AL1zjG4BK8s3a9wA8b6Jru//3SZrAmMt1E0IA9yIGzqtCGwDNWjFrAFi+WcVpnev+73UsTES6EZOza3btkUIPYKoImnYYDFMvul6FM57guDdKVQHEbJULp5LAm6VC4sRqcE32JnjTTuMBbHvhIzYmewkmgc2y6zeDLT8PoA2AZq0oGzns1kzcPpj1ANTlAFjNUWUI6LA7hO1MFOUApo1brcEoVQkowyf+tuXguD9MdVIPrnnijYG8300nA8FsVwp+FRBv2tspcgBGzi3b5LU4eZs2CRxca5loA6BZO4LzgVWJtgXX2PMNgLrT+isng1N/T8NUEXSEtqXOAwBco3LST6cDxGyWCujYjju0pZdOCI4JegCHXRubpTzy2XTbYLMyHQ3pewApQkD8XO0BaDRL4HqzvNQQkO8BKOouBqYGQI1Rcde4czKAEOmlJYDTBuC4P/SlHNKwGdADOuzZqU7qTFARNG0PABNsBuNKqDQhoM1SHoVc5lyawbQB0KwdNxplHPdHOO4NlYaAjFwW+Sz5Oi4qQ0AvswegIAnMm/Wd+30A6RKrDIeA9loWbGeiJAcw7QYeukJwikJAXduBNRorMwBBQbi9loV6MZ9YXA5wk9VuM5g2ABqNcoKaQGwAVISAeB2VIaBSIYsMAS+fuGuqKgMFgJc8VVSVIaAve+W1qkJAgJv/OOmPEg2DnyXYC3DQtRPNAp7FFYSbegBpTv/Mbs3UHoBGswyClUBdhTkAwPUkOMmoogqIZw2/fMwegBrJCgB40fMAVJWBAsALR+q9Cg7XqcoBAJ4BUOgB9Idj9Gwn8SzgWc5rNrA2AJq14+GtErIZwvOHXaUhIOC0IVERAnLXyftJRhUeQNabCfCSQgPAa7xwqNAD8DbrLx24CXslISBvjRfv92GNJqmUQBn2Ig67NvZaFnZr6dfcrRnYa1lYtkqONgCatSOfzeA1WyU8f9hDz3Zg5jOpK0GY4KbPjWEq11SRA3DXyfuNRiqatoxcFsV8dhoCUpgEZgOg0gN4bq8DIF0PANPw1njlxMJB18ZuvZh6zZ2aCduZnBqzuQy0AdCsJdcbZdw+6KFjq9EBYtiTqBi51E1LDBuAXIZQTDlhbHZNQI0HwOu84uU/VBiVYj6LQi7jj3FMowTK8Bqf23O1dpSEgLw1n7nbhhDpKoAYLgW9u+REsDYAmrXkeqOMF4566CgSgmN4LVXhH3etvL9mWn0dhkNJhVz6sZVM0JBspBgxyRARNkt5vwJKRQioZuaQzxI+p9AD4DX+7OUWAGC3nn5Nnia27ESwNgCateR6owxrNMEX73WVxf+BqQFYhlFRkQBmOJSkoguYYVG5ipFDIeXUMmazVACHwVXkFVyjUsCXvfyHiiqgrXIBGZoagDRdwIzfDaw9AI1GPTwf+PP7nQfAA/AMgIIEMMNrqQr/BNdSEf5heK2NUh45RXmarbJrVLIZUtKvkM0QtsqGn6tQEQK6VNUegEazNK43XQMwngilmzWXWKroAWB4LVUJYHet5RkAFZsqw2upCP8w3FG8XS4goyhP06wamAigkM0oudZCLoNGpbD0UlBtADRryU7V9BOqSwkBveo9AC8EpPK0vhQPYLpZq4IbylTE/xlea6duKMvT7NRMnQTWaJZBJkO45oWBlhKvf7UbgGL+1J8qWI4H4K6p1APw1lJqALxcgorwD3O5vnw5CG0ANGvLjSUYgLKxjBAQJ4EVhoCWkQMosQFQtyYbExUloIxvABSu6XsACg3AecwGXpoBIKKHiegxInqGiJ4moh+cuf8DRCSIqLGsa9Boori+DA/AXEYVEJeBqjcqy0kCqzutczhJaQjIywE0FHoAPFdYpQewWzNx3B/BGo2VrTnLMj0AB8AHhBBfCeBtAP42EX0l4BoHAN8C4MUlvr5GEwkbgGXkAJZTBaQ+Cay0DLS4PA9gKSGgJXgAaeYAzMKaQvfayxsNuTQDIIS4K4T4tPd7B8CzAK54d/9jAH8PwHKFLjSaCLgSaBk5gOWUli6hDFThZu0bAIWb9WZZfQ6Ak8AqPYBlhID80ZBLDAOdSw6AiK4BeAuAx4no2wG8LIT47ILnvJeIbhHRrYODg3O4Ss268dVX6vj+b34d3vGmS8rWfMOlCr7/m1+Hdypc8027VXzfN91Qep1vuuyu+c1vVLfmVz1Ux/e9/Qa+6Y1NZWt+9ZUNvPftaq/zkYfreK/i6/za12zie//idbxd4ZrXtsv4S2/eRSnFbIFF0LLV5oioAuCTAH4CwO8AeAzAtwghWkT0AoCbQojDqDVu3rwpbt26tdTr1Gg0mlWDiJ4QQtycd/9SPQAiygP4KICPCCE+BuB1AK4D+Ky3+V8F8Gki2l3mdWg0Go3mLOoClTOQ2w3xSwCeFUJ8CACEEH8K4FLgMS9AwgPQaDQajXqW6QF8I4DvBPBOInrS+/nWJb6eRqPRaGKwNA9ACPHHACJ7ooUQ15b1+hqNRqOJRncCazQazZqiDYBGo9GsKdoAaDQazZqiDYBGo9GsKUtvBFMBER0A+HLCpzcArFqZ6aq9p1V7P8DqvadVez/A6r2nsPfzWiHE3PbkB8IApIGIbkV1wj2IrNp7WrX3A6zee1q19wOs3ntK8n50CEij0WjWFG0ANBqNZk1ZBwPw4Yu+gCWwau9p1d4PsHrvadXeD7B67yn2+1n5HIBGo9FowlkHD0Cj0Wg0IWgDoNFoNGvKShsAInoPEX2OiL5IRH//oq8nLf9/e3cfIlUVxnH8+2MzkjVSK0R8wSIhqMwkhEJChIL+sig0KbAICqkwghD6J4uCkIqwwkgyDCyT0vKvUEx6oVDRXF+hFxFSVlcRq4XoRX/9cZ+NQXZm2nVt9t55PrDMnTOzl3N4mPvce86950g6LGlvzKxayhVyJK2S1CNpX03ZWEmbJf0Qr2NaWceBqNOepZKOlnUWXEmTJG2VdEDSfkmLo7yUcWrQntLGSdIlkrZL6oo2PRflV0naFse8DyU1XEuzsmMAkjqA74HbgSPADmCB7QMtrdh5qML6CZJuA3qB92xfH2XLgFO2X4pEPcb2klbW87+q056lQK/tl1tZt8GSNB4Yb3uXpEuBncBdwIOUME4N2jOPksYp1lvptN0bC299DSwGngLW214r6S2gy/aKevup8hXATOBH24ds/wmsBea2uE5tz/aXwKlziucCq2N7NcWPsxTqtKfUbHfb3hXbvwEHgQmUNE4N2lNaLvTG2xHxZ2AO8FGUN41RlRPABODnmvdHKHnQKQK8SdJOSY+0ujJDaJzt7tg+BoxrZWWGyOOS9kQXUSm6SvojaQpwE7CNCsTpnPZAieMkqUPSbqAH2Az8BJy2/Xd8pekxr8oJoIpm2Z4B3Ak8Ft0PleKiT7Ls/ZIrKNa/ng50A6+0tjqDI2kUxZreT9r+tfazMsapn/aUOk62z9ieTrG2+kzg2oHuo8oJ4Cgwqeb9xCgrLdtH47UH2EAR9Co4Hv20ff21PS2uz3mxfTx+nGeBlZQwTtGv/DGwxvb6KC5tnPprTxXiBGD7NLAVuAUYLalvpcemx7wqJ4AdwNQYFb8YuA/Y2OI6DZqkzhjAQlIncAewr/F/lcZGYGFsLwQ+bWFdzlvfQTLcTcniFAOM7wAHbb9a81Ep41SvPWWOk6QrJY2O7ZEUN7scpEgE98bXmsaosncBAcRtXa8BHcAq2y+2uEqDJulqirN+KNZyfr+M7ZH0ATCbYura48CzwCfAOmAyxbTf82yXYmC1TntmU3QrGDgMPFrTdz7sSZoFfAXsBc5G8TMU/eali1OD9iygpHGSNI1ikLeD4kR+ne3n4zixFhgLfAc8YPuPuvupcgJIKaVUX5W7gFJKKTWQCSCllNpUJoCUUmpTmQBSSqlNZQJIKaU2lQkgJUDSmZpZIXcP5eyxkqbUzhaa0nBxUfOvpNQWfo/H6lNqG3kFkFIDsQbDsliHYbuka6J8iqTPYyKxLZImR/k4SRtinvYuSbfGrjokrYy52zfF05sptVQmgJQKI8/pAppf89kvtm8A3qB4shzgdWC17WnAGmB5lC8HvrB9IzAD2B/lU4E3bV8HnAbuucDtSampfBI4JUBSr+1R/ZQfBubYPhQTih2zfbmkkxSLjPwV5d22r5B0AphY+/h9TEG82fbUeL8EGGH7hQvfspTqyyuAlJpzne2BqJ2P5Qw5/paGgUwAKTU3v+b129j+hmKGWYD7KSYbA9gCLIJ/F+y47P+qZEoDlWchKRVGxupKfT6z3Xcr6BhJeyjO4hdE2RPAu5KeBk4AD0X5YuBtSQ9TnOkvolhsJKVhJ8cAUmogxgButn2y1XVJaahlF1BKKbWpvAJIKaU2lVcAKaXUpjIBpJRSm8oEkFJKbSoTQEoptalMACml1Kb+AfbDCxda055XAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "print(perceptron_algo_plot(X, y))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JjJYKtxZVqDP"
      },
      "source": [
        "If the training data is not Linearly Separable, the perceptron algorithm will eventually repeat the same set of weights and thereby enter an infinite loop."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TAG_aQNo4ZWU"
      },
      "source": [
        "**1.Try this on a real dataset i.e. banknote  and show the error plot**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 74
        },
        "id": "mvyZ-gYj4nrV",
        "outputId": "d3819b62-8cd8-4905-81c8-f2fba3477c9e"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "\n",
              "     <input type=\"file\" id=\"files-7351a0a0-d060-4dce-a87b-a8b6bbc5bb21\" name=\"files[]\" multiple disabled\n",
              "        style=\"border:none\" />\n",
              "     <output id=\"result-7351a0a0-d060-4dce-a87b-a8b6bbc5bb21\">\n",
              "      Upload widget is only available when the cell has been executed in the\n",
              "      current browser session. Please rerun this cell to enable.\n",
              "      </output>\n",
              "      <script>// Copyright 2017 Google LLC\n",
              "//\n",
              "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
              "// you may not use this file except in compliance with the License.\n",
              "// You may obtain a copy of the License at\n",
              "//\n",
              "//      http://www.apache.org/licenses/LICENSE-2.0\n",
              "//\n",
              "// Unless required by applicable law or agreed to in writing, software\n",
              "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
              "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
              "// See the License for the specific language governing permissions and\n",
              "// limitations under the License.\n",
              "\n",
              "/**\n",
              " * @fileoverview Helpers for google.colab Python module.\n",
              " */\n",
              "(function(scope) {\n",
              "function span(text, styleAttributes = {}) {\n",
              "  const element = document.createElement('span');\n",
              "  element.textContent = text;\n",
              "  for (const key of Object.keys(styleAttributes)) {\n",
              "    element.style[key] = styleAttributes[key];\n",
              "  }\n",
              "  return element;\n",
              "}\n",
              "\n",
              "// Max number of bytes which will be uploaded at a time.\n",
              "const MAX_PAYLOAD_SIZE = 100 * 1024;\n",
              "\n",
              "function _uploadFiles(inputId, outputId) {\n",
              "  const steps = uploadFilesStep(inputId, outputId);\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  // Cache steps on the outputElement to make it available for the next call\n",
              "  // to uploadFilesContinue from Python.\n",
              "  outputElement.steps = steps;\n",
              "\n",
              "  return _uploadFilesContinue(outputId);\n",
              "}\n",
              "\n",
              "// This is roughly an async generator (not supported in the browser yet),\n",
              "// where there are multiple asynchronous steps and the Python side is going\n",
              "// to poll for completion of each step.\n",
              "// This uses a Promise to block the python side on completion of each step,\n",
              "// then passes the result of the previous step as the input to the next step.\n",
              "function _uploadFilesContinue(outputId) {\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  const steps = outputElement.steps;\n",
              "\n",
              "  const next = steps.next(outputElement.lastPromiseValue);\n",
              "  return Promise.resolve(next.value.promise).then((value) => {\n",
              "    // Cache the last promise value to make it available to the next\n",
              "    // step of the generator.\n",
              "    outputElement.lastPromiseValue = value;\n",
              "    return next.value.response;\n",
              "  });\n",
              "}\n",
              "\n",
              "/**\n",
              " * Generator function which is called between each async step of the upload\n",
              " * process.\n",
              " * @param {string} inputId Element ID of the input file picker element.\n",
              " * @param {string} outputId Element ID of the output display.\n",
              " * @return {!Iterable<!Object>} Iterable of next steps.\n",
              " */\n",
              "function* uploadFilesStep(inputId, outputId) {\n",
              "  const inputElement = document.getElementById(inputId);\n",
              "  inputElement.disabled = false;\n",
              "\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  outputElement.innerHTML = '';\n",
              "\n",
              "  const pickedPromise = new Promise((resolve) => {\n",
              "    inputElement.addEventListener('change', (e) => {\n",
              "      resolve(e.target.files);\n",
              "    });\n",
              "  });\n",
              "\n",
              "  const cancel = document.createElement('button');\n",
              "  inputElement.parentElement.appendChild(cancel);\n",
              "  cancel.textContent = 'Cancel upload';\n",
              "  const cancelPromise = new Promise((resolve) => {\n",
              "    cancel.onclick = () => {\n",
              "      resolve(null);\n",
              "    };\n",
              "  });\n",
              "\n",
              "  // Wait for the user to pick the files.\n",
              "  const files = yield {\n",
              "    promise: Promise.race([pickedPromise, cancelPromise]),\n",
              "    response: {\n",
              "      action: 'starting',\n",
              "    }\n",
              "  };\n",
              "\n",
              "  cancel.remove();\n",
              "\n",
              "  // Disable the input element since further picks are not allowed.\n",
              "  inputElement.disabled = true;\n",
              "\n",
              "  if (!files) {\n",
              "    return {\n",
              "      response: {\n",
              "        action: 'complete',\n",
              "      }\n",
              "    };\n",
              "  }\n",
              "\n",
              "  for (const file of files) {\n",
              "    const li = document.createElement('li');\n",
              "    li.append(span(file.name, {fontWeight: 'bold'}));\n",
              "    li.append(span(\n",
              "        `(${file.type || 'n/a'}) - ${file.size} bytes, ` +\n",
              "        `last modified: ${\n",
              "            file.lastModifiedDate ? file.lastModifiedDate.toLocaleDateString() :\n",
              "                                    'n/a'} - `));\n",
              "    const percent = span('0% done');\n",
              "    li.appendChild(percent);\n",
              "\n",
              "    outputElement.appendChild(li);\n",
              "\n",
              "    const fileDataPromise = new Promise((resolve) => {\n",
              "      const reader = new FileReader();\n",
              "      reader.onload = (e) => {\n",
              "        resolve(e.target.result);\n",
              "      };\n",
              "      reader.readAsArrayBuffer(file);\n",
              "    });\n",
              "    // Wait for the data to be ready.\n",
              "    let fileData = yield {\n",
              "      promise: fileDataPromise,\n",
              "      response: {\n",
              "        action: 'continue',\n",
              "      }\n",
              "    };\n",
              "\n",
              "    // Use a chunked sending to avoid message size limits. See b/62115660.\n",
              "    let position = 0;\n",
              "    do {\n",
              "      const length = Math.min(fileData.byteLength - position, MAX_PAYLOAD_SIZE);\n",
              "      const chunk = new Uint8Array(fileData, position, length);\n",
              "      position += length;\n",
              "\n",
              "      const base64 = btoa(String.fromCharCode.apply(null, chunk));\n",
              "      yield {\n",
              "        response: {\n",
              "          action: 'append',\n",
              "          file: file.name,\n",
              "          data: base64,\n",
              "        },\n",
              "      };\n",
              "\n",
              "      let percentDone = fileData.byteLength === 0 ?\n",
              "          100 :\n",
              "          Math.round((position / fileData.byteLength) * 100);\n",
              "      percent.textContent = `${percentDone}% done`;\n",
              "\n",
              "    } while (position < fileData.byteLength);\n",
              "  }\n",
              "\n",
              "  // All done.\n",
              "  yield {\n",
              "    response: {\n",
              "      action: 'complete',\n",
              "    }\n",
              "  };\n",
              "}\n",
              "\n",
              "scope.google = scope.google || {};\n",
              "scope.google.colab = scope.google.colab || {};\n",
              "scope.google.colab._files = {\n",
              "  _uploadFiles,\n",
              "  _uploadFilesContinue,\n",
              "};\n",
              "})(self);\n",
              "</script> "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Saving banknote-authentication_csv.csv to banknote-authentication_csv (1).csv\n"
          ]
        }
      ],
      "source": [
        "from google.colab import files\n",
        "uploaded = files.upload()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "vo5pN7ZaCEs8",
        "outputId": "a18a973f-7638-4cdd-ee50-c58d40b891b7"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-5516b3d3-c25d-477a-9d4a-6040296c3c35\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>V1</th>\n",
              "      <th>V2</th>\n",
              "      <th>V3</th>\n",
              "      <th>V4</th>\n",
              "      <th>Class</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>3.62160</td>\n",
              "      <td>8.6661</td>\n",
              "      <td>-2.8073</td>\n",
              "      <td>-0.44699</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4.54590</td>\n",
              "      <td>8.1674</td>\n",
              "      <td>-2.4586</td>\n",
              "      <td>-1.46210</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3.86600</td>\n",
              "      <td>-2.6383</td>\n",
              "      <td>1.9242</td>\n",
              "      <td>0.10645</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3.45660</td>\n",
              "      <td>9.5228</td>\n",
              "      <td>-4.0112</td>\n",
              "      <td>-3.59440</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.32924</td>\n",
              "      <td>-4.4552</td>\n",
              "      <td>4.5718</td>\n",
              "      <td>-0.98880</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
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              "              title=\"Convert this dataframe to an interactive table.\"\n",
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              "\n",
              "    .colab-df-convert {\n",
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              "\n",
              "    .colab-df-convert:hover {\n",
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              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
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              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-5516b3d3-c25d-477a-9d4a-6040296c3c35 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-5516b3d3-c25d-477a-9d4a-6040296c3c35');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "        V1      V2      V3       V4  Class\n",
              "0  3.62160  8.6661 -2.8073 -0.44699      1\n",
              "1  4.54590  8.1674 -2.4586 -1.46210      1\n",
              "2  3.86600 -2.6383  1.9242  0.10645      1\n",
              "3  3.45660  9.5228 -4.0112 -3.59440      1\n",
              "4  0.32924 -4.4552  4.5718 -0.98880      1"
            ]
          },
          "execution_count": 39,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import pandas as pd\n",
        "df=pd.read_csv(\"banknote-authentication_csv.csv\")\n",
        "df.head()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bubGoKI1DpuH"
      },
      "outputs": [],
      "source": [
        "X=df.drop([\"Class\"],axis=1)[:5].to_numpy()\n",
        "y=df[\"Class\"][:5].apply(lambda x: 1 if x==1 else -1)\n",
        "y=y.to_numpy()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "d2ELz-_eERx4",
        "outputId": "528eefca-9397-42fe-983e-cd186b2cac58"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[ 7.81684  1.5726   3.6887  -1.32934]\n"
          ]
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "print(perceptron_algo_plot(X, y))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S6RNxxKuGUxA"
      },
      "source": [
        "It seems data is overfitting and easily converged"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-ybrv-rPGXEX"
      },
      "source": [
        "**2.Increase/decrease the learning rate to see how many iterations will be take to converge. Does it even converge on a huge learning rate?**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "M-n7UE43GnH3",
        "outputId": "d2535fbf-f220-4655-9c81-9ae1b73e08f7"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Learning Rate 1000\n",
            "[ 7.81684  1.5726   3.6887  -1.32934]\n"
          ]
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Learning Rate 100\n",
            "[ 7.81684  1.5726   3.6887  -1.32934]\n"
          ]
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Learning Rate 10\n",
            "[ 7.81684  1.5726   3.6887  -1.32934]\n"
          ]
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Learning Rate 1\n",
            "[ 7.81684  1.5726   3.6887  -1.32934]\n"
          ]
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Learning Rate 0.1\n",
            "[ 7.81684  1.5726   3.6887  -1.32934]\n"
          ]
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Learning Rate 0.01\n",
            "[ 7.81684  1.5726   3.6887  -1.32934]\n"
          ]
        },
        {
          "data": {
            "image/png": 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SClV8ALRbI7RGwklgScUpPgBsCympVMUHALgiqKQyGQDUC8I5BCSpMAYA1YJwtoWUVBoDgHoIyDMASYUxAHAOQFKZDAAMAEllMgCo7gZ2CEhSaQwAZiaBp9m2zbaQksphAACTMwvCeSWQpIIYAFRnAABPbbIvsKRy9CUAIuL1EfHfEfFARFzSjxq67VgRdEufK5GkhbPgARARo8BngTcALwTOjogXLnQd3TrtUQA2OBEsqSCtPnzmycADmfkgQERcDZwG3NeHWgDotMcAeOdX7uTgJaP9KkOSdnPlipez9NkHN/K7+xEARwP/1/X8YeC3d/2hiDgfOB9g6dKljRZ0wtGHcNbyY9ngEJCkRWZJq7mBmn4EQE8ycyWwEmD58uWNXp958JIWHznjJU1+hCQtOv2YBH4EOLbr+TH1NknSAupHAPwIOD4ijouIJcCbgRv7UIckFW3Bh4Ayc2tEvBP4N2AU+GJm3rvQdUhS6foyB5CZ3wK+1Y/PliRVvBNYkgplAEhSoQwASSqUASBJhYrMxb8GfkSsB36+j28/Anj8AJazGAzbPrk/i9+w7dOw7Q/Mvk/Pycypud4wEAGwPyJidWYu73cdB9Kw7ZP7s/gN2z4N2/7Avu2TQ0CSVCgDQJIKVUIArOx3AQ0Ytn1yfxa/YdunYdsf2Id9Gvo5AEnS7Eo4A5AkzcIAkKRCDXUALLbm8/srIh6KiB9HxF0Rsbrf9eyLiPhiRKyLiJ90bTs8Im6KiJ/W/x7Wzxr3xhz784GIeKQ+TndFxBv7WePeiIhjI+KWiLgvIu6NiAvq7YN8jObap4E8ThExHhG3R8Td9f58sN5+XETcVn/fXVMvtz//7xrWOYC6+fz/AK+jajv5I+DszOxb7+H9FREPAcszc2BvYImIVwEbgasy84R620eBJzLz0jqoD8vMi/tZZ6/m2J8PABsz8x/6Wdu+iIijgKMy846ImATWAKcDb2Nwj9Fc+3QmA3icIiKAiczcGBFjwA+AC4CLgOsy8+qI+Dxwd2ZePt/vGuYzgO3N5zNzMzDTfF59lJnfB57YZfNpwKr68Sqq/zkHwhz7M7Ayc21m3lE/3gDcT9XHe5CP0Vz7NJCysrF+Olb/l8CpwNfq7T0do2EOgNmazw/sQa8l8J2IWBMR5/e7mAPoyMxcWz9+FDiyn8UcIO+MiHvqIaKBGS7pFhHLgJcCtzEkx2iXfYIBPU4RMRoRdwHrgJuAnwFPZubW+kd6+r4b5gAYRq/MzJcBbwD+sh5+GCpZjUkO+rjk5cDzgJOAtcDH+lvO3ouIDvB14MLM/FX3a4N6jGbZp4E9Tpk5nZknUfVUPxl4wb78nmEOgKFrPp+Zj9T/rgOupzrww+Cxepx2Zrx2XZ/r2S+Z+Vj9P+g24AsM2HGqx5W/Dnw5M6+rNw/0MZptnwb9OAFk5pPALcApwKERMdPlsafvu2EOgKFqPh8RE/UEFhExAfw+8JP53zUwbgRW1I9XADf0sZb9NvNFWfsjBug41ROMVwL3Z+bHu14a2GM01z4N6nGKiKmIOLR+fBDVhS73UwXBGfWP9XSMhvYqIID6sq5PsqP5/N/1uaR9FhHPpfqrH6pezl8ZxP2JiK8Cr6ZauvYx4P3AvwLXAkuplv0+MzMHYmJ1jv15NdWwQgIPAW/vGj9f1CLilcC/Az8GttWb30c1Zj6ox2iufTqbATxOEfESqkneUao/4q/NzA/V3xFXA4cDdwLnZOameX/XMAeAJGluwzwEJEmahwEgSYUyACSpUAaAJBXKAJCkQhkAEhAR012rQt51IFePjYhl3auFSotFa88/IhXh1/Wt9VIxPAOQ5lH3YPho3Yfh9oh4fr19WUR8t15I7OaIWFpvPzIirq/Xar87In63/lWjEfGFev3279R3cEp9ZQBIlYN2GQI6q+u1X2bmi4HPUN1ZDvBpYFVmvgT4MvCpevungO9l5onAy4B76+3HA5/NzBcBTwJ/0vD+SHvkncASEBEbM7Mzy/aHgFMz88F6QbFHM/PZEfE4VZORLfX2tZl5RESsB47pvgW/XoL4psw8vn5+MTCWmR9ufs+kuXkGIO1ZzvF4b3SvyTKN829aBAwAac/O6vr3h/Xj/6BaYRbgLVSLjQHcDLwDtjfteNZCFSntLf8KkSoH1R2WZnw7M2cuBT0sIu6h+iv+7Hrbu4B/ioi/BtYD59bbLwBWRsR5VH/pv4Oq2Yi06DgHIM2jngNYnpmP97sW6UBzCEiSCuUZgCQVyjMASSqUASBJhTIAJKlQBoAkFcoAkKRC/T924to0W+JY1gAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Learning Rate 0.001\n",
            "[ 7.81684  1.5726   3.6887  -1.32934]\n"
          ]
        },
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAEGCAYAAABsLkJ6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAUy0lEQVR4nO3dfYxldX3H8fd35s7egbmDgEwIBdZFpTWKgmalpRqjWBu1jdCWgkTMSmkwtioE24ImjQ+xCdr6gE/IWqxLqwJRKESNlSBoTS24y5MCbUWCLWRhlyC6C7IPs9/+cc7s3t2dmb37cObOvb/3KyF777lz535PTrifOb/fOb9vZCaSpPKM9LsASVJ/GACSVCgDQJIKZQBIUqEMAEkqVKvfBfTiiCOOyGXLlvW7DEkaKGvWrHk8M6fmen0gAmDZsmWsXr2632VI0kCJiJ/P97pDQJJUKANAkgplAEhSoQwASSqUASBJhTIAJKlQBoAkFWqoA+D6Ox/mX/5z3stgJalYQx0A37h7LV+57X/7XYYkLUpDHQCd8RYbN23tdxmStCgNdwC0WzxlAEjSrIY+ADYYAJI0q6EPgM1bt7F567Z+lyJJi85QB8BEu1rs1GEgSdrdUAdAZ7wKACeCJWl3Qx0Ak20DQJLm0ngARMRoRNwZEd+onx8XEbdFxAMRcU1ELGnqsycMAEma00KcAVwA3N/1/CPAJzLz+cAvgPOa+mCHgCRpbo0GQEQcA/wB8I/18wBOBb5W/8gq4PSmPr8zcwbwjAEgSbtq+gzgk8DfADPXYT4beDIzZ76RHwaOnu2NEXF+RKyOiNXr16/fpw/veBWQJM2psQCIiD8E1mXmmn15f2auzMzlmbl8amrOpvbzcghIkubWavB3vwJ4U0S8ERgHDgEuAw6NiFZ9FnAM8EhTBUwsqXZvg0NAkrSbxs4AMvO9mXlMZi4D3gx8NzPfAtwCnFH/2ArghqZqGB0JDl4y6hCQJM2iH/cBXAxcFBEPUM0JXNnkh020XRFUkmbT5BDQdpl5K3Br/fhB4OSF+FyobgYzACRpd0N9JzB4BiBJcxn6AOi0W94HIEmzGP4AsCuYJM1q+APAISBJmlURAeBloJK0u6EPgJlJ4MzsdymStKgMfQBMjrfYMp1ssi2kJO1k6APABeEkaXZDHwA2hZGk2Q19AHQMAEmaVTkB4M1gkrST4Q+AuifAU5sNAEnqNvwB0LYngCTNppgAcA5AknY2/AEw7mWgkjSboQ+Ag8dGASeBJWlXQx8AIyNRLwg33e9SJGlRGfoAgJkVQbf0uwxJWlSKCICJ9qiTwJK0iyICoDM+5hCQJO2ijABoj7LxGYeAJKlbIQHQ4inPACRpJ4UEwJhzAJK0i0ICYJQNDgFJ0k7KCIDxFk9tnrYtpCR1KSIAJtotprclz2yxLaQkzSgiACZdEE6SdlNEANgWUpJ2V0QA2BheknZXRgCM2xRGknZVRgA4BCRJuykqABwCkqQdigqADQaAJG1XRgDYFlKSdlNEABw0NspI2BZSkroVEQARwUS75SSwJHUpIgCguhvYAJCkHYoJgIl2yyEgSerSWABExHhE3B4Rd0fEvRHxwXr7cRFxW0Q8EBHXRMSSpmroVq0IagBI0owmzwA2Aadm5onAScDrI+J3gI8An8jM5wO/AM5rsIbtOu2WdwJLUpfGAiArG+unY/V/CZwKfK3evgo4vakaunWcA5CknTQ6BxARoxFxF7AOuAn4GfBkZs58Ez8MHD3He8+PiNURsXr9+vX7XUvVF9gAkKQZjQZAZk5n5knAMcDJwAv24r0rM3N5Zi6fmpra71qcBJaknS3IVUCZ+SRwC3AKcGhEtOqXjgEeWYgaJsdbbNy81baQklRr8iqgqYg4tH58EPA64H6qIDij/rEVwA1N1dCt026RCU9vnl6Ij5OkRa+15x/ZZ0cBqyJilCpors3Mb0TEfcDVEfFh4E7gygZr2K67K9jMY0kqWWPfhJl5D/DSWbY/SDUfsKAmx3cEwJEL/eGStAiVcyfwkjoAnAiWJKCgAHBJaEnaWTkBYFMYSdpJcQHgGYAkVcoJgHEbw0tSt3ICYGYIyElgSQIKCoB2a4TWSDgEJEm1YgLAtpCStLNiAgBcElqSuhUVAJPjrggqSTOKCgCHgCRph6ICwKYwkrRDcQHgncCSVNljAETEKyJion58TkR8PCKe03xpB55nAJK0Qy9nAJcDT0fEicB7qPr6XtVoVQ3pOAksSdv1EgBbs+qjeBrwmcz8LDDZbFnNmGi3eGrzNNu22RZSknoJgA0R8V7gHOCbETECjDVbVjMmZxaE2+xZgCT1EgBnAZuA8zLzUapG7n/faFUN6W4LKUml66Ul5AbgssycjojfBF4AfLXZspphUxhJ2qGXM4DvA+2IOBr4DvBW4EtNFtWUSVcElaTtegmAyMyngT8GPpeZfwqc0GxZzXAISJJ26CkAIuIU4C3AN/fifYuOXcEkaYdevsgvBN4LXJ+Z90bEc4Fbmi2rGTaFkaQd9jgJnJnfA74XEZ2I6GTmg8C7my/twHMSWJJ26GUpiBdHxJ3AvcB9EbEmIl7UfGkH3kR7FHAOQJKgtyGgK4CLMvM5mbmUajmILzRbVjParVGWjI6wcdN0v0uRpL7rJQAmMnP7mH9m3gpMNFZRwzrjLTZu2tLvMiSp73q5EezBiPhb4J/r5+cADzZXUrMm2qMuCCdJ9HYG8GfAFHAd8HXgCODcJotqUqc95hCQJNHbVUC/YJerfiLiGqo1ggZOpz3qEJAkse83dJ1yQKtYQFVTGM8AJGkg7+jdH53xMS8DlSTmGQKKiJfN9RID2g8AqiEg7wSWpPnnAD42z2v/daALWSj2BZakypwBkJmvWchCFspEu8Wvt0yzdXobrdHiRsAkabvivgG3rwi62YlgSWUrLgAmx+0JIElQYABsbwrjRLCkwu3LVUAAZOYd870eEccCVwFHAgmszMzLIuJw4BpgGfAQcGZ9s9mC6NgVTJKAfb8KKIFT9/C7twLvycw7ImISWBMRNwFvA27OzEsj4hLgEuDivah5vxgAklRp7CqgzFwLrK0fb4iI+4GjgdOAV9c/tgq4lYUMAJvCSBLQ22qgRMQJwAuB8ZltmXlVrx8SEcuAlwK3AUfW4QDwKNUQ0WzvOR84H2Dp0qW9ftQedZwDkCSgt45g7wc+Xf/3GuCjwJt6/YCI6FCtInphZv6q+7XMTKrhpN1k5srMXJ6Zy6empnr9uD3a3hfYMwBJhevlKqAzgNcCj2bmucCJwLN6+eURMUb15f/lzLyu3vxYRBxVv34UsG6vq94PM1cBOQQkqXS9BMCvM3MbsDUiDqH6wj52T2+KiACuBO7PzI93vXQjsKJ+vAK4Ye9K3j9joyO0WyNOAksqXi9zAKsj4lCqPsBrgI3AD3t43yuAtwI/joi76m3vAy4Fro2I84CfA2fuddX7aXK8ZQBIKl4vDWH+on74+Yj4NnBIZt7Tw/t+QLVy6Gxe23uJB16n3XISWFLxepkEvnnmcWY+lJn3dG8bRBOuCCpJ894JPA4cDBwREYex46/5Q6iu5x9YnXbLq4AkFW++IaC3AxcCvwF0L/vwK+AzTRbVtE67xdpfPtPvMiSpr+a7E/gy4LKIeFdmfnoBa2pcZ7zFU+s9A5BUtl6uAroiIt4NvKp+fitwRWZuaayqhjkJLEm9BcDnqHoAf65+/lbgcuDPmyqqaZ22l4FK0nyTwK3M3Aq8PDNP7HrpuxFxd/OlNafTbrFp6zY2b93GklZxLREkCZj/MtDb63+nI+J5Mxsj4rnAQPdTdDkISZp/CGjmss+/Am6JiAfr58uAc5ssqmmdrraQh00s6XM1ktQf8wXAVERcVD++AhitH09TLe18S5OFNcmmMJI0fwCMAh12X86hBUw2VtEC6DgEJEnzBsDazPzQglWygGaGgLwbWFLJ5psEnmsht4FnVzBJmj8A+rpiZ5McApKkeQIgM59YyEIW0oSTwJLUU0ewoeNVQJJUaACMjgQHLxl1DkBS0YoMAKibwmw2ACSVq9gAmGy32OAZgKSCFRsAE64IKqlwxQZAx77AkgpXbgCMOwQkqWzlBoCTwJIKV3QAeBmopJIVGwBOAksqXbEBMDneYst0smnrQDc3k6R9VmwAuCKopNIVGwA7+gJ7BiCpTMUGwMwZwIZNW/pciST1R/EB4BCQpFKVGwB1W0jvBZBUqnIDYGYIyDMASYUqPgCcBJZUqnIDYHymK5iTwJLKVGwAHDw2CjgJLKlcxQbAyEhU6wE5BCSpUMUGAMBEe9QhIEnFaiwAIuKLEbEuIn7Ste3wiLgpIn5a/3tYU5/fi6opjGcAksrU5BnAl4DX77LtEuDmzDweuLl+3jed8TE2uCKopEI1FgCZ+X3giV02nwasqh+vAk5v6vN70WmP2hZSUrEWeg7gyMxcWz9+FDhyrh+MiPMjYnVErF6/fn0jxdgURlLJ+jYJnJkJ5Dyvr8zM5Zm5fGpqqpEabAojqWQLHQCPRcRRAPW/6xb483cyaQBIKthCB8CNwIr68QrghgX+/J10xqsAqE5GJKksTV4G+lXgh8BvRcTDEXEecCnwuoj4KfB79fO+mWi3mN6WbNq6rZ9lSFJftJr6xZl59hwvvbapz9xbk10rgo7XS0NIUikKvxN4ZkE45wEklafoANixJLQBIKk8ZQfAuE1hJJWr7ADwDEBSwQwAnAOQVCYDAFwQTlKRyg6AcYeAJJWr6AA4aGyUkbAtpKQyFR0AEeGCcJKKVXQAgAvCSSpX8QEwYU8ASYUqPgA64y2e2mwASCqPAdBueSewpCIZAO2Wl4FKKpIB4CSwpEIVHwBeBiqpVMUHwKRtISUVqvgAmGi3yISnN0/3uxRJWlDFB4BLQksqVfEBMDnuiqCSylR8AEws8QxAUpmKD4CZJaFdDkJSaQwAm8JIKpQB4CSwpEIZAOP2BZZUJgPAxvCSClV8ALRbI7RGwklgScUpPgBsCympVMUHALgiqKQyGQDUC8I5BCSpMAYA1YJwtoWUVBoDgHoIyDMASYUxAHAOQFKZDAAMAEllMgCo7gZ2CEhSaQwAZiaBp9m2zbaQksphAACTMwvCeSWQpIIYAFRnAABPbbIvsKRy9CUAIuL1EfHfEfFARFzSjxq67VgRdEufK5GkhbPgARARo8BngTcALwTOjogXLnQd3TrtUQA2OBEsqSCtPnzmycADmfkgQERcDZwG3NeHWgDotMcAeOdX7uTgJaP9KkOSdnPlipez9NkHN/K7+xEARwP/1/X8YeC3d/2hiDgfOB9g6dKljRZ0wtGHcNbyY9ngEJCkRWZJq7mBmn4EQE8ycyWwEmD58uWNXp958JIWHznjJU1+hCQtOv2YBH4EOLbr+TH1NknSAupHAPwIOD4ijouIJcCbgRv7UIckFW3Bh4Ayc2tEvBP4N2AU+GJm3rvQdUhS6foyB5CZ3wK+1Y/PliRVvBNYkgplAEhSoQwASSqUASBJhYrMxb8GfkSsB36+j28/Anj8AJazGAzbPrk/i9+w7dOw7Q/Mvk/Pycypud4wEAGwPyJidWYu73cdB9Kw7ZP7s/gN2z4N2/7Avu2TQ0CSVCgDQJIKVUIArOx3AQ0Ytn1yfxa/YdunYdsf2Id9Gvo5AEnS7Eo4A5AkzcIAkKRCDXUALLbm8/srIh6KiB9HxF0Rsbrf9eyLiPhiRKyLiJ90bTs8Im6KiJ/W/x7Wzxr3xhz784GIeKQ+TndFxBv7WePeiIhjI+KWiLgvIu6NiAvq7YN8jObap4E8ThExHhG3R8Td9f58sN5+XETcVn/fXVMvtz//7xrWOYC6+fz/AK+jajv5I+DszOxb7+H9FREPAcszc2BvYImIVwEbgasy84R620eBJzLz0jqoD8vMi/tZZ6/m2J8PABsz8x/6Wdu+iIijgKMy846ImATWAKcDb2Nwj9Fc+3QmA3icIiKAiczcGBFjwA+AC4CLgOsy8+qI+Dxwd2ZePt/vGuYzgO3N5zNzMzDTfF59lJnfB57YZfNpwKr68Sqq/zkHwhz7M7Ayc21m3lE/3gDcT9XHe5CP0Vz7NJCysrF+Olb/l8CpwNfq7T0do2EOgNmazw/sQa8l8J2IWBMR5/e7mAPoyMxcWz9+FDiyn8UcIO+MiHvqIaKBGS7pFhHLgJcCtzEkx2iXfYIBPU4RMRoRdwHrgJuAnwFPZubW+kd6+r4b5gAYRq/MzJcBbwD+sh5+GCpZjUkO+rjk5cDzgJOAtcDH+lvO3ouIDvB14MLM/FX3a4N6jGbZp4E9Tpk5nZknUfVUPxl4wb78nmEOgKFrPp+Zj9T/rgOupzrww+Cxepx2Zrx2XZ/r2S+Z+Vj9P+g24AsM2HGqx5W/Dnw5M6+rNw/0MZptnwb9OAFk5pPALcApwKERMdPlsafvu2EOgKFqPh8RE/UEFhExAfw+8JP53zUwbgRW1I9XADf0sZb9NvNFWfsjBug41ROMVwL3Z+bHu14a2GM01z4N6nGKiKmIOLR+fBDVhS73UwXBGfWP9XSMhvYqIID6sq5PsqP5/N/1uaR9FhHPpfqrH6pezl8ZxP2JiK8Cr6ZauvYx4P3AvwLXAkuplv0+MzMHYmJ1jv15NdWwQgIPAW/vGj9f1CLilcC/Az8GttWb30c1Zj6ox2iufTqbATxOEfESqkneUao/4q/NzA/V3xFXA4cDdwLnZOameX/XMAeAJGluwzwEJEmahwEgSYUyACSpUAaAJBXKAJCkQhkAEhAR012rQt51IFePjYhl3auFSotFa88/IhXh1/Wt9VIxPAOQ5lH3YPho3Yfh9oh4fr19WUR8t15I7OaIWFpvPzIirq/Xar87In63/lWjEfGFev3279R3cEp9ZQBIlYN2GQI6q+u1X2bmi4HPUN1ZDvBpYFVmvgT4MvCpevungO9l5onAy4B76+3HA5/NzBcBTwJ/0vD+SHvkncASEBEbM7Mzy/aHgFMz88F6QbFHM/PZEfE4VZORLfX2tZl5RESsB47pvgW/XoL4psw8vn5+MTCWmR9ufs+kuXkGIO1ZzvF4b3SvyTKN829aBAwAac/O6vr3h/Xj/6BaYRbgLVSLjQHcDLwDtjfteNZCFSntLf8KkSoH1R2WZnw7M2cuBT0sIu6h+iv+7Hrbu4B/ioi/BtYD59bbLwBWRsR5VH/pv4Oq2Yi06DgHIM2jngNYnpmP97sW6UBzCEiSCuUZgCQVyjMASSqUASBJhTIAJKlQBoAkFcoAkKRC/T924to0W+JY1gAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "\n",
        "lr_rates = [1000, 100, 10, 1, 0.1, 0.01, 0.001]\n",
        "for lr in lr_rates:\n",
        "  print(f\"Learning Rate {lr}\")\n",
        "  print(perceptron_algo_plot(X, y))\n",
        "  plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QrEc-GNJG86j"
      },
      "source": [
        "**It seems that the model converge on all the possible rages of learning rates for given dataset**"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **3.Take a toy dataset that is not linearly separable and run the perceptron algorithm on it. What happens? Note your observations. An example is given below.**"
      ],
      "metadata": {
        "id": "ug5oUbINT9Ru"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "here im taken non linear separable datasets from sklearn library that are moon and circles datasets. performed perceptron algorithm. from both graphs , we conclude that \n",
        "\n",
        "1.that model is does not converge at anypoint\n",
        "\n",
        "2.that the perceptron algorithm will eventually repeat the same set of weights.\n",
        "\n",
        "3. and entered into an infinte loop and still oscillating\n",
        "  this all are done because of multiple classes,which are not separable by a single line"
      ],
      "metadata": {
        "id": "LXhgkG5TXw2y"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "first we will try on moon dataset , with noise of 0.7"
      ],
      "metadata": {
        "id": "f7G9G5ftW6kE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "from sklearn.datasets import make_moons\n",
        "\n",
        "# generate 2d classification dataset\n",
        "v, b = make_moons(n_samples=100, noise=0.7)"
      ],
      "metadata": {
        "id": "iiTG7mtdUGiC"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "perceptron_algo(v, b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SdutTTjbWdVQ",
        "outputId": "fb774099-ee58-4376-ccdd-c3446ee519a4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1.65167734, -0.31939487])"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "w = perceptron_algo_plot(v,b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "3LHfWShXVZJu",
        "outputId": "df5f2f19-91e3-4533-a3ab-d61b2911b7cd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "lets try it also on circle dataset"
      ],
      "metadata": {
        "id": "q_2Sb9uhXX3e"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.datasets import make_circles\n",
        "# generate 2d classification dataset\n",
        "X, y = make_circles(n_samples=100, noise=0.05)"
      ],
      "metadata": {
        "id": "3FQYFTPPV45_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "w = perceptron_algo_plot(X, y)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "X-baIz0DV42b",
        "outputId": "27190ee6-add8-4ce3-f550-b42b89ae8900"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}