04. Learning Rate Decay Methods/01. Time Decay - MXNet.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Time Based Decay - MXNet.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "L3KIZndDdgt4",
        "colab_type": "code",
        "outputId": "f8d713e8-6f5c-4623-b2c0-dfeb49647d32",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 171
        }
      },
      "source": [
        "!pip install mxnet-cu100"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: mxnet-cu100 in /usr/local/lib/python3.6/dist-packages (1.4.1)\n",
            "Requirement already satisfied: requests>=2.20.0 in /usr/local/lib/python3.6/dist-packages (from mxnet-cu100) (2.21.0)\n",
            "Requirement already satisfied: graphviz<0.9.0,>=0.8.1 in /usr/local/lib/python3.6/dist-packages (from mxnet-cu100) (0.8.4)\n",
            "Requirement already satisfied: numpy<1.15.0,>=1.8.2 in /usr/local/lib/python3.6/dist-packages (from mxnet-cu100) (1.14.6)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.6/dist-packages (from requests>=2.20.0->mxnet-cu100) (2019.6.16)\n",
            "Requirement already satisfied: chardet<3.1.0,>=3.0.2 in /usr/local/lib/python3.6/dist-packages (from requests>=2.20.0->mxnet-cu100) (3.0.4)\n",
            "Requirement already satisfied: idna<2.9,>=2.5 in /usr/local/lib/python3.6/dist-packages (from requests>=2.20.0->mxnet-cu100) (2.8)\n",
            "Requirement already satisfied: urllib3<1.25,>=1.21.1 in /usr/local/lib/python3.6/dist-packages (from requests>=2.20.0->mxnet-cu100) (1.24.3)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1YN4PT_Idstj",
        "colab_type": "text"
      },
      "source": [
        "#MXNet (From Scratch)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CLGHa8i6WEaA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import mxnet as mx\n",
        "from mxnet import nd, autograd, gluon\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "mx.random.seed(1)\n",
        "\n",
        "model_ctx = mx.gpu()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "huuK9vLaWEcO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def transform(data, label):\n",
        "    return data.astype('float32')/255.0, label.astype('float32')\n",
        "\n",
        "train_mnist = gluon.data.vision.FashionMNIST(train = True, transform = transform)\n",
        "test_mnist = gluon.data.vision.FashionMNIST(train = False, transform = transform)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sAXcT8nSWEYo",
        "colab_type": "code",
        "outputId": "1e7baa75-2185-41a6-cb2d-811d981e16b2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "image, label = train_mnist[0]\n",
        "print(image.shape, label.shape)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(28, 28, 1) ()\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SIQSLxiFWEXg",
        "colab_type": "code",
        "outputId": "5649f783-c3dd-4349-d1fe-2d4f3f2847fb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "plt.imshow(image.reshape((28, 28)).asnumpy())\n",
        "plt.title(label)\n",
        "plt.show()\n"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oF-WKS-xX73T",
        "colab_type": "text"
      },
      "source": [
        "##Creating data loader for training and testing"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IVmMwE94WEWY",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "batch_size = 64\n",
        "training_data = gluon.data.DataLoader(train_mnist, batch_size = batch_size, shuffle = True)\n",
        "testing_data = gluon.data.DataLoader(test_mnist, batch_size = batch_size, shuffle = False)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5HUXvMyHYKoM",
        "colab_type": "text"
      },
      "source": [
        "##Building the model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u7Vdh54QWESq",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "weight_scale = .01\n",
        "\n",
        "#  Allocate parameters for the first hidden layer\n",
        "W1 = nd.random_normal(shape = (784, 256), scale=weight_scale, ctx=model_ctx)\n",
        "b1 = nd.random_normal(shape = 256, scale=weight_scale, ctx=model_ctx)\n",
        "\n",
        "#  Allocate parameters for the second hidden layer\n",
        "W2 = nd.random_normal(shape = (256, 128), scale=weight_scale, ctx=model_ctx)\n",
        "b2 = nd.random_normal(shape = 128, scale=weight_scale, ctx=model_ctx)\n",
        "\n",
        "#  Allocate parameters for the output layer\n",
        "W3 = nd.random_normal(shape=(128, 10), scale=weight_scale, ctx=model_ctx)\n",
        "b3 = nd.random_normal(shape=10, scale=weight_scale, ctx=model_ctx)\n",
        "\n",
        "params = [W1, b1, W2, b2, W3, b3]\n",
        "\n",
        "for param in params:\n",
        "    param.attach_grad()\n",
        "    \n",
        "def neuralnetworks(inputs):\n",
        "    layer1 = nd.relu(nd.dot(inputs, W1) + b1)\n",
        "    layer2 = nd.relu(nd.dot(layer1, W2) + b2)\n",
        "    return nd.softmax(nd.dot(layer2, W3) + b3)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HW4Jzb46EyyD",
        "colab_type": "text"
      },
      "source": [
        "##Defining our objective function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "avO1uf5fItMV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def categoricalcrossentropy(predictions, labels):\n",
        "    return -nd.sum(labels * nd.log(predictions))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3qr1NTDkE7Kh",
        "colab_type": "text"
      },
      "source": [
        "##Defining our parameters optimizer"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hvFKa4WuI9c-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def sgd(params, lr):\n",
        "    for param in params:\n",
        "        param[:] = param - lr * param.grad"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lbHoiGM3ZrQY",
        "colab_type": "text"
      },
      "source": [
        "##Defining our accuracy function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-3osTW97ZuHR",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def accuracy(predictions, labels):\n",
        "    return nd.mean(predictions.argmax(1) == labels.argmax(1))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6GHgqNdMK7y_",
        "colab_type": "text"
      },
      "source": [
        "##Defining Time Based Learning Rate Decay "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eRG13WS5OSAQ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def time_based_decay(current_lr, decay, epoch):\n",
        "    return current_lr * (1. / (1. + decay * epoch))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lr2eiTs8OTHd",
        "colab_type": "text"
      },
      "source": [
        "##Doing a quick visualization for different decay values"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CJ7dmGxrLNRB",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "11f3622a-f0ae-43d0-83bf-ea758bbe8185"
      },
      "source": [
        "decay1 = 0.001\n",
        "decay2 = 0.01\n",
        "decay3 = 0.1\n",
        "\n",
        "epochs = 50\n",
        "\n",
        "lr = 0.01\n",
        "lrs1 = []\n",
        "for epoch in range(epochs):\n",
        "    lr = time_based_decay(lr, decay1, epoch)\n",
        "    lrs1.append(lr)\n",
        "\n",
        "lr = 0.01\n",
        "lrs2 = []\n",
        "for epoch in range(epochs):\n",
        "    lr = time_based_decay(lr, decay2, epoch)\n",
        "    lrs2.append(lr)\n",
        "\n",
        "lr = 0.01\n",
        "lrs3 = []\n",
        "for epoch in range(epochs):\n",
        "    lr = time_based_decay(lr, decay3, epoch)\n",
        "    lrs3.append(lr)\n",
        "\n",
        "plt.plot(list(range(epochs)), lrs1, label = 'Decay = 0.001')\n",
        "plt.plot(list(range(epochs)), lrs2, label = 'Decay = 0.01')\n",
        "plt.plot(list(range(epochs)), lrs3, label = 'Decay = 0.1')\n",
        "plt.title('Learning rate for 100 epochs')\n",
        "plt.xlabel('Epochs')\n",
        "plt.ylabel('Learning rate')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Lp8XTfiO38rlYjAcVM9Nh8XP2vZaT83K38HA7ow9lZNco1u9Lpee7qxj61a8k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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UlkEn5XxFPkd",
        "colab_type": "text"
      },
      "source": [
        "##Training the  model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kVao6lbWCizF",
        "colab_type": "code",
        "outputId": "1cb9137e-35bc-4709-e9a2-64e55e6d5a1e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 185
        }
      },
      "source": [
        "epochs = 10\n",
        "num_batches = 60000//batch_size\n",
        "learning_rate = .001\n",
        "decay = 0.001\n",
        "losses = []\n",
        "accs = []\n",
        "\n",
        "for epoch in range(epochs):\n",
        "    cumulative_loss = 0\n",
        "    cumulative_acc = 0\n",
        "    \n",
        "    # \n",
        "    learning_rate = time_based_decay(learning_rate, decay, epoch)\n",
        "    \n",
        "    for features, labels in training_data:\n",
        "        features = features.as_in_context(model_ctx).reshape((-1, 784))\n",
        "        labels = labels.as_in_context(model_ctx).one_hot(10)\n",
        "        with autograd.record():\n",
        "            output = neuralnetworks(features)\n",
        "            loss = categoricalcrossentropy(output, labels)\n",
        "        loss.backward()\n",
        "        \n",
        "        sgd(params, learning_rate)\n",
        "        \n",
        "        cumulative_loss += loss\n",
        "        acc = accuracy(output, labels)\n",
        "        cumulative_acc += acc\n",
        "        losses.append(loss.asscalar())\n",
        "        accs.append(acc.asscalar())\n",
        "    print(f'Epoch: {epoch} | Loss: {cumulative_loss.asscalar()/num_batches:.5f} | Accuracy: {cumulative_acc.asscalar()/num_batches:.5f} | Learning Rate: {learning_rate:.10f}')"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch: 0 | Loss: 78.17708 | Accuracy: 0.54054 | Learning Rate: 0.0010000000\n",
            "Epoch: 1 | Loss: 38.15196 | Accuracy: 0.78785 | Learning Rate: 0.0009990010\n",
            "Epoch: 2 | Loss: 31.17092 | Accuracy: 0.82619 | Learning Rate: 0.0009970070\n",
            "Epoch: 3 | Loss: 27.51733 | Accuracy: 0.84497 | Learning Rate: 0.0009940249\n",
            "Epoch: 4 | Loss: 25.36990 | Accuracy: 0.85701 | Learning Rate: 0.0009900647\n",
            "Epoch: 5 | Loss: 23.77352 | Accuracy: 0.86668 | Learning Rate: 0.0009851390\n",
            "Epoch: 6 | Loss: 22.53241 | Accuracy: 0.87250 | Learning Rate: 0.0009792634\n",
            "Epoch: 7 | Loss: 21.48579 | Accuracy: 0.88005 | Learning Rate: 0.0009724562\n",
            "Epoch: 8 | Loss: 20.75956 | Accuracy: 0.88185 | Learning Rate: 0.0009647383\n",
            "Epoch: 9 | Loss: 19.98225 | Accuracy: 0.88756 | Learning Rate: 0.0009561331\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JJOc7DOepwEE",
        "colab_type": "text"
      },
      "source": [
        "##Lets see test accuracy"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dvvQC3oQYu5A",
        "colab_type": "code",
        "outputId": "199c7460-0524-428f-fd99-90632dc3c2fc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "acc = 0.0\n",
        "batches = 0\n",
        "for features, labels in testing_data:\n",
        "    features = features.as_in_context(model_ctx).reshape((-1, 784))\n",
        "    labels = labels.as_in_context(model_ctx).one_hot(10)\n",
        "    predictions = neuralnetworks(features)\n",
        "    acc += accuracy(predictions, labels)\n",
        "    batches += 1\n",
        "print(f'Test Accuracy: {acc.asscalar()/batches}')"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Test Accuracy: 0.8789808917197452\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hIBgjWVBYu3t",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def plot(losses = losses, accs = accs, model = neuralnetworks, samples = 5):\n",
        "    plt.plot(losses, 'r')\n",
        "    plt.title('Loss during Training')\n",
        "    plt.xlabel('Epoch')\n",
        "    plt.ylabel('Loss')\n",
        "    plt.show()\n",
        "    \n",
        "    plt.plot(accs, 'g')\n",
        "    plt.title('Accuracy during Training')\n",
        "    plt.xlabel('Epoch')\n",
        "    plt.ylabel('Accuracy')\n",
        "    plt.show()\n",
        "    \n",
        "    for i, batch in enumerate(test_mnist):\n",
        "        features = batch[0].as_in_context(model_ctx).reshape((1, 784))\n",
        "        labels = batch[1]\n",
        "        predictions = model(features).argmax(1).asscalar()\n",
        "        plt.imshow(features.reshape((28, 28)).asnumpy())\n",
        "        plt.title(f'Predicted Class: {predictions}, Target Class: {labels}')\n",
        "        plt.show()\n",
        "        if i == samples:\n",
        "            break"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mkorWu1EYu2b",
        "colab_type": "code",
        "outputId": "d0e27a37-5137-4e7e-a026-40a7a4f0dfb5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "plot(samples = 10)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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PUez1q64Kv/99YfkvfxnOAiF00txnn8J1Mn7yk8piOfPM0ssnTw5VS3GZdqOe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\nREoQIiKS6P8BNg/ek5FHBIsAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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kzJ/kO67VKlbzf4GsXanowICyws4U4vDW3LdiFzI0q9GMbbu3sXHnxqjlnu39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\nUjDGGONnScEYY4yfJQVjjDF+/w+8SUM/ErfQ0AAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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L8YQQY89oLD7yp+6+eRSOI4RoAGoTEKLk1CoCDtxmZg+Y2bLBdjCzZWa20sxW9hC/2woh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\nAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3IblqgbZdifLu3vL258cvWhldduc350TT+w6K92HftT7etr0SKW9PfS5PnAEWLy5P6tge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\nQUAkcwoCIplTEBDJ3P8HjZ4t/tV48JEAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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xBspPsttfrPhK/JxdfU98TgKA/A6mTOuV9jgLrdU+btom3m6lOU5N7jjOAYyb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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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33P17Y+LVKOibMTlqH9gT17veg+OR29gS22ni5x6Id2GgdU8qJl1+/oGE34MpeyTWDlX0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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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o9wD4S4iaQBAkTphAECROmEAQJE6YQBAkTphAECROmEAQJE6YQBAkTt/PJ9ANqidOKNQe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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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trwMLgFutGHfdBtzk7t8bF6+akH3zI28ybfGAtrfE34Ja9saLoWXggFaaHpF53JzsR5AY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\nArw4k5MrAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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KRHx7QryaBLYfnde7nSfkB5j33V0fF1Z+SD592/JvQbsOzfv2y0s+m7Wf+/NX1tqOnb0x\nm3b97tlZ+4I/2ZW1r9o5L2t/1rtX1dqGIx+LX3TW1qz9xre9MGvfcnx954+9s/N5R757BTsX5a9Z\nEf0EIuI3wLMm0BdjTAdwiNCYwrEIGFM4FgFjCsciYEzhWASMKZxihhL37MzbtSevh3vn1ttmNgyf\nGs6POmXWuvyQ2pN/+Pqsfe4h9cOBf/HA07Npn/GUh7P2W+46OWs/45m/ztq/8Z3n1tpOPfuX2bQ3\nfqk+LcDRDz+atffPX1Rr2zM/f+sfsiYf1t1xZD7E2H344Vn70Pr1WftU4pqAMYVjETCmcCwCxhSO\nRcCYwrEIGFM4FgFjCsciYEzhHDT9BLoX18eEAfbmR7xyyCMNS3A/t35I7uzl+YGjG9+cX+f6iAX5\n4b67t2c6KQBPml/fUWHLjpnZtJcs+WHWftltx+fTH/HPWfvdxx1Va3toa34a+IXn1Q9DBtj9yoZp\nw79ef023nZTvm9H74/zzsWn4+PCxi/M7uJ+AMWa6YBEwpnAsAsYUjkXAmMKxCBhTOBYBYwrHImBM\n4Rw0/QS2viAfzx6akY8p9z+WP/6O3fVLbD/lsvyY+gfvPTFrH16wKWvfvPWQrP21J91Va/vZl56W\nTfs3816UtS/54WDW/t4nX5C185tZtaYjz16dTbpjYEbW/m+OzvdR+E8nv67WFt35+6Erf9qNbD+2\n/rwBZq1o7/gTiWsCxhSORcCYwrEIGFM4FgFjCsciYEzhWASMKRyLgDGFc9D0E+jenY/79u7IzxM/\nkA/rsndT/TLXF5yWD/r+5NGnZu2/2JDv47DkR/mx75/+2kW1tr7Z+XJZ86Mjs/befDcD+m/NL6ow\nZ1V9wP3R+/L9J/o35s/740vqzxugJ3P44cV7s2l3H5rvmxEH0eOz8VQkXS5pnaR7W7YtlHSTpF+l\n//nZIYwx05bx6NkXgHNHbXs/cHNEnATcnL4bYw5AGkUgIr4PjJ7/6nzgivT5CuA1E+yXMWaK2N82\ngcURMdLxew1QO6GapEuBSwH6yb9nGWOmnrabNyIigNrWp4hYHhHLImJZL/kBIcaYqWd/RWCtpCUA\n6f+6iXPJGDOV7K8IXA9ckj5fAlw3Me4YY6YaVbX5zA7SV4FzgMOAtcCHgGuBq4BjgAeBCyMiP3k+\nMFcL4yy9uE2XO4POeEatbc+h9X0IAFY/L9/0MnNNvg/DnoYA7IzMdARdQ/nr270nf+yugXz6wZl5\n33PH3zsvn7Zvaz7vPQ3pF925o9bW+2h+DofYvCVrH2qwd4rb42a2xsZ8wYyisWEwIi6uMR2Yv2Zj\nzBM4iPo9GWP2B4uAMYVjETCmcCwCxhSORcCYwjlohhJPNnHHPbW2/ln5cch7L35K1t63OR9i7M6P\neqVrsD6UNtybjxYN51dkpys/mrfx+NkQYz4CyFB+lDIDs/P2nvXbam2DKx/KJy4I1wSMKRyLgDGF\nYxEwpnAsAsYUjkXAmMKxCBhTOBYBYwrH/QRG6GoImA/XB8zjycdlk8bu/LGjIeum6a01nDPm0+b6\nGDQeG5pj/ZnJpJqGKQ/XrwYPjMO3noaCzdF0P0RD5g1D9KcTrgkYUzgWAWMKxyJgTOFYBIwpHIuA\nMYVjETCmcCwCxhSO+wmM0BT3zdC1fVfW3r96XtY+ODN//N76mbMrMn0BoqGfwFBffgc1hLubYv3Z\nYzcU+eCsfZo5+/fpauMZdxD1A2jCNQFjCsciYEzhWASMKRyLgDGFYxEwpnAsAsYUjkXAmMJxP4ER\n2on7bsgvc62BI7L2dsfND81oM57eBk1zHUR3vW89OxvKvME83HD35vI2j9NYE5B0uaR1ku5t2fZh\nSask3Z3+zptcN40xk8V4Xge+AJw7xvZPRsSp6e+GiXXLGDNVNIpARHwf2DgFvhhjOkA7DYNvl/TT\n9LqwoG4nSZdKWiFpxQB72sjOGDMZ7K8IfBY4ETgVWA18vG7HiFgeEcsiYlkvmVknjTEdYb9EICLW\nRsRQRAwD/wCcObFuGWOmiv0SAUlLWr6+Fri3bl9jzPSmsZ+ApK8C5wCHSXoE+BBwjqRTqSK5K4G3\nTKKP056hTQ39BBri3b3b23Qg14+gMZbecOz65Raq9F35WHzu+E1zHfRuzxfcnoX59F3b6ud52P/Z\nIw4+GkUgIi4eY/PnJ8EXY0wHcLdhYwrHImBM4VgEjCkci4AxhWMRMKZwPJR4BDXEqzJDjbtmzcom\n3XNoPiA1Y0Nei9UUpsuE4ZqG27a79HgTGqy3NQ2h7tvatGx6wzNst7upjwfXBIwpHIuAMYVjETCm\ncCwCxhSORcCYwrEIGFM4FgFjCsf9BCYAdefH42pgcqe+boz1t5O2yfWmfgSZ9MM9DcOQGx5RXU3d\nANpZmrwgXErGFI5FwJjCsQgYUzgWAWMKxyJgTOFYBIwpHIuAMYXjfgITQDQsa940rXfTuPqugf1P\n33Tspn4ATdOCdzVOSZ4zNqRtmg69gaFFtavjwapH2zv4QYRrAsYUjkXAmMKxCBhTOBYBYwrHImBM\n4VgEjCkci4AxhTOepcmXAl8EFlNFdpdHxKclLQS+DhxHtTz5hRGRX6P7IKVr3tz8Dg1rk3fvzgfj\nh3vzh8/1BejZmU/bOF9Am4+Jrr2ZrNtc86Apfdfe+kUPGro3FMV4LvEg8J6IOBl4DvA2SScD7wdu\njoiTgJvTd2PMAUajCETE6oi4K33eBtwPHAWcD1yRdrsCeM1kOWmMmTz2qbIn6TjgNOB2YHFErE6m\nNVSvC8aYA4xxi4Ck2cDVwLsiYmurLarO82O+wUm6VNIKSSsG8Npwxkw3xiUCknqpBODKiLgmbV4r\naUmyLwHWjZU2IpZHxLKIWNbLjInw2RgzgTSKgCQBnwfuj4hPtJiuBy5Jny8Brpt494wxk814hhI/\nH3gDcI+ku9O2y4CPAVdJ+nfAg8CFk+PiFKEGPYz6oNLQ4fOzSfs254/dnQmjAeydl7crN9S4IQQ4\n3DRct93Z0nPLpjeEPpuGUDfZc8vJm8dpFIGIuI36W+HFE+uOMWaqcY9BYwrHImBM4VgEjCkci4Ax\nhWMRMKZwLALGFI6nHJ8IevJaOtyXj1cPNM3r3RDu7s0MF27qB9AUq28YBd3IcOYOy9kANNywdHnT\nuR3SNN+6AdcEjCkei4AxhWMRMKZwLALGFI5FwJjCsQgYUzgWAWMKx/0ERoim+a/rGe5rCFg39APo\n2Z1P3t0wK9tgfybrNpf3bnfa75y9q35G8HHZB2fm7UMz6ztB+On3OC4LYwrHImBM4VgEjCkci4Ax\nhWMRMKZwLALGFI5FwJjCcT+BEdqYo37nEQ0rKzUMyh/uyfcjGGoYFp/rC6A21+COhsdEk285mtYN\naMq7sf/EIfUF0+h2QWsWuCZgTOFYBIwpHIuAMYVjETCmcCwCxhSORcCYwrEIGFM4jf0EJC0Fvggs\nphpdvjwiPi3pw8CbgfVp18si4obJcnQ6M9ifj/NrqGH+/AYpHm4Ianft3f9jN80H0BTLr120fiT/\nTB+GaLj7htuYqwBguM/PuPEwns5Cg8B7IuIuSXOAOyXdlGyfjIi/njz3jDGTTaMIRMRqYHX6vE3S\n/cBRk+2YMWZq2Kf6kqTjgNOA29Omt0v6qaTLJS2oSXOppBWSVgzQ0M/TGDPljFsEJM0GrgbeFRFb\ngc8CJwKnUtUUPj5WuohYHhHLImJZLw197I0xU864REBSL5UAXBkR1wBExNqIGIqIYeAfgDMnz01j\nzGTRKAKSBHweuD8iPtGyfUnLbq8F7p1494wxk814ogPPB94A3CPp7rTtMuBiSadShQ1XAm+ZFA8P\nADY/Oa+lQzPyw1J7G0KIA7MbhrV21ds12BDDa2ISR9R2NQxz7tme971pWfXBmZMYIlRTbPTAGYo8\nnujAbYwdDS6yT4AxBxvuTWFM4VgEjCkci4AxhWMRMKZwLALGFI5FwJjC8ZTjE8DR38uvLb53fr6Y\ne7flA+ZNU5JH1/73BdBwPp6tofbi3dFd71vTUF8N5vPeOze/7vq8u9fX2hpnYu9qWNN9uM253KcR\nrgkYUzgWAWMKxyJgTOFYBIwpHIuAMYVjETCmcCwCxhSOYgrHPUtaDzzYsukwYMOUObBvTFffpqtf\nYN/2l4n07diIOHxfEkypCPxe5tKKiFjWMQcyTFffpqtfYN/2l0775tcBYwrHImBM4XRaBJZ3OP8c\n09W36eoX2Lf9paO+dbRNwBjTeTpdEzDGdBiLgDGF0xERkHSupF9IekDS+zvhQx2SVkq6R9LdklZ0\n2JfLJa2TdG/LtoWSbpL0q/R/zDUgO+TbhyWtSmV3t6TzOuTbUknfk/QzSfdJemfa3tGyy/jV0XKb\n8jYBSd3AL4GXAo8AdwAXR8TPptSRGiStBJZFRMc7lkh6IbAd+GJEPD1t+ytgY0R8LAnogoh43zTx\n7cPA9k4vV59Wx1oSEXdJmgPcCbwGeCMdLLuMXxfSwXLrRE3gTOCBiPhNROwFvgac3wE/pj0R8X1g\n46jN5wNXpM9XUN1EU06Nb9OCiFgdEXelz9uA+4Gj6HDZZfzqKJ0QgaOAh1u+P8I0KIgWArhR0p2S\nLu20M2OwOCJWp89rgMWddGYMGpern0okHQecBtzONCq7UX5BB8vNDYO/z9kR8WzgFcDbUrV3WhLV\nu9x0ivGOa7n6qULSbKrVtN8VEVtbbZ0suzH86mi5dUIEVgFLW74fnbZNCyJiVfq/DvgG02/J9bUj\nK0Kn/+s67M/vmE7L1UvqpfqhXRkR16TNHS+7sfzqdLl1QgTuAE6SdLykPuAi4PoO+PF7SJqVGmyQ\nNAt4GdNvyfXrgUvS50uA6zroyxOYLsvVSxLweeD+iPhEi6mjZVfnV6fLrSM9BlMI5FNAN3B5RHx0\nyp0YA0knUD39oZqO/Sud9E3SV4FzqIaargU+BFwLXAUcQzUs+8KImPIGuhrfzqGq0v5uufqWd/Cp\n9O1s4AfAPcBw2nwZ1ft3x8ou49fFdLDc3G3YmMJxw6AxhWMRMKZwLALGFI5FwJjCsQgYUzgWAWMK\nxyJgTOH8f64Tuwcuc1XlAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Fy/OWwTRdvZnVkn3R7nD3e8PTFd93PZWr0vutEklgCXCsmU03szrgI8ADFSjH\nO5hZQ7hgg5k1ABcw+KZcfwCYHx7PB+6vYFkOMFimqzczA24GVrr7dQWhiu67vHJVer9VpMdgaAK5\nHqgGbnH3r5S9ED0wsxlkv/6Qzdj8/UqWzczuBM4ju9V0E3AN8CPgbuBIstuyL3P3sl+gyynbeWRV\n2remqy84By9n2eYATwLLga55368mO/+u2L6LlOtyKrjf1G1YJHG6MCiSOCUBkcQpCYgkTklAJHFK\nAiKJUxIQSZySgEji/j+z1tGa2Ik53QAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "59YfC3nthjfA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q0bTWSV-hjeE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "twG_qVM8hjc6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}