MNIST.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_train shape: (60000, 28, 28, 1)\n",
      "60000 train samples\n",
      "10000 test samples\n"
     ]
    }
   ],
   "source": [
    "from __future__ import print_function\n",
    "import keras\n",
    "from keras.datasets import mnist\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Dropout, Flatten\n",
    "from keras.layers import Conv2D, MaxPooling2D\n",
    "from keras import backend as K\n",
    "\n",
    "batch_size = 128\n",
    "num_classes = 10\n",
    "epochs = 12\n",
    "\n",
    "# input image dimensions\n",
    "img_rows, img_cols = 28, 28\n",
    "\n",
    "# the data, split between train and test sets\n",
    "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n",
    "\n",
    "if K.image_data_format() == 'channels_first':\n",
    "    x_train = x_train.reshape(x_train.shape[0], 1, img_rows, img_cols)\n",
    "    x_test = x_test.reshape(x_test.shape[0], 1, img_rows, img_cols)\n",
    "    input_shape = (1, img_rows, img_cols)\n",
    "else:\n",
    "    x_train = x_train.reshape(x_train.shape[0], img_rows, img_cols, 1)\n",
    "    x_test = x_test.reshape(x_test.shape[0], img_rows, img_cols, 1)\n",
    "    input_shape = (img_rows, img_cols, 1)\n",
    "\n",
    "x_train = x_train.astype('float32')\n",
    "x_test = x_test.astype('float32')\n",
    "x_train /= 255\n",
    "x_test /= 255\n",
    "print('x_train shape:', x_train.shape)\n",
    "print(x_train.shape[0], 'train samples')\n",
    "print(x_test.shape[0], 'test samples')\n",
    "\n",
    "# convert class vectors to binary class matrices\n",
    "y_train = keras.utils.to_categorical(y_train, num_classes)\n",
    "y_test = keras.utils.to_categorical(y_test, num_classes)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "from_ = np.random.permutation(range(28))\n",
    "to_ = np.random.permutation(range(28))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "def column_transformer(x):\n",
    "    new_x = np.zeros(x.shape)\n",
    "    new_x[:,to_] = x[:,from_]\n",
    "    return new_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "def row_transformer(x):\n",
    "    new_x = np.zeros(x.shape)\n",
    "    new_x[to_,:] = x[from_,:]\n",
    "    return new_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train = np.array([row_transformer(column_transformer(x.reshape(28,28))).reshape(28,28,1) for x in x_train])\n",
    "x_test = np.array([row_transformer(column_transformer(x.reshape(28,28))).reshape(28,28,1) for x in x_test])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/12\n",
      "60000/60000 [==============================] - 57s 949us/step - loss: 0.4553 - acc: 0.8598 - val_loss: 0.1429 - val_acc: 0.9564\n",
      "Epoch 2/12\n",
      "60000/60000 [==============================] - 58s 966us/step - loss: 0.1878 - acc: 0.9427 - val_loss: 0.1039 - val_acc: 0.9665\n",
      "Epoch 3/12\n",
      "60000/60000 [==============================] - 57s 956us/step - loss: 0.1410 - acc: 0.9576 - val_loss: 0.0825 - val_acc: 0.9728\n",
      "Epoch 4/12\n",
      "60000/60000 [==============================] - 57s 943us/step - loss: 0.1120 - acc: 0.9660 - val_loss: 0.0782 - val_acc: 0.9749\n",
      "Epoch 5/12\n",
      "60000/60000 [==============================] - 57s 950us/step - loss: 0.0985 - acc: 0.9699 - val_loss: 0.0720 - val_acc: 0.9770\n",
      "Epoch 6/12\n",
      "60000/60000 [==============================] - 58s 960us/step - loss: 0.0850 - acc: 0.9737 - val_loss: 0.0699 - val_acc: 0.9772\n",
      "Epoch 7/12\n",
      "60000/60000 [==============================] - 57s 945us/step - loss: 0.0761 - acc: 0.9767 - val_loss: 0.0685 - val_acc: 0.9780\n",
      "Epoch 8/12\n",
      "60000/60000 [==============================] - 57s 956us/step - loss: 0.0693 - acc: 0.9784 - val_loss: 0.0663 - val_acc: 0.9790\n",
      "Epoch 9/12\n",
      "60000/60000 [==============================] - 57s 957us/step - loss: 0.0615 - acc: 0.9804 - val_loss: 0.0602 - val_acc: 0.9828\n",
      "Epoch 10/12\n",
      "22400/60000 [==========>...................] - ETA: 34s - loss: 0.0550 - acc: 0.9833"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-69-5bf2edc1b175>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     20\u001b[0m           \u001b[0mepochs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mepochs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     21\u001b[0m           \u001b[0mverbose\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 22\u001b[0;31m           validation_data=(x_test, y_test))\n\u001b[0m\u001b[1;32m     23\u001b[0m \u001b[0mscore\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mevaluate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_test\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_test\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mverbose\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     24\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Test loss:'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscore\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/conda/envs/tensorflow/lib/python3.5/site-packages/keras/models.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, x, y, batch_size, epochs, verbose, callbacks, validation_split, validation_data, shuffle, class_weight, sample_weight, initial_epoch, steps_per_epoch, validation_steps, **kwargs)\u001b[0m\n\u001b[1;32m    961\u001b[0m                               \u001b[0minitial_epoch\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0minitial_epoch\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    962\u001b[0m                               \u001b[0msteps_per_epoch\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msteps_per_epoch\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 963\u001b[0;31m                               validation_steps=validation_steps)\n\u001b[0m\u001b[1;32m    964\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    965\u001b[0m     def evaluate(self, x=None, y=None,\n",
      "\u001b[0;32m/opt/conda/envs/tensorflow/lib/python3.5/site-packages/keras/engine/training.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, x, y, batch_size, epochs, verbose, callbacks, validation_split, validation_data, shuffle, class_weight, sample_weight, initial_epoch, steps_per_epoch, validation_steps, **kwargs)\u001b[0m\n\u001b[1;32m   1703\u001b[0m                               \u001b[0minitial_epoch\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0minitial_epoch\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1704\u001b[0m                               \u001b[0msteps_per_epoch\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msteps_per_epoch\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1705\u001b[0;31m                               validation_steps=validation_steps)\n\u001b[0m\u001b[1;32m   1706\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1707\u001b[0m     def evaluate(self, x=None, y=None,\n",
      "\u001b[0;32m/opt/conda/envs/tensorflow/lib/python3.5/site-packages/keras/engine/training.py\u001b[0m in \u001b[0;36m_fit_loop\u001b[0;34m(self, f, ins, out_labels, batch_size, epochs, verbose, callbacks, val_f, val_ins, shuffle, callback_metrics, initial_epoch, steps_per_epoch, validation_steps)\u001b[0m\n\u001b[1;32m   1233\u001b[0m                         \u001b[0mins_batch\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mins_batch\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtoarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1234\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1235\u001b[0;31m                     \u001b[0mouts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mins_batch\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1236\u001b[0m                     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mouts\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1237\u001b[0m                         \u001b[0mouts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mouts\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/conda/envs/tensorflow/lib/python3.5/site-packages/keras/backend/tensorflow_backend.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, inputs)\u001b[0m\n\u001b[1;32m   2476\u001b[0m         \u001b[0msession\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_session\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2477\u001b[0m         updated = session.run(fetches=fetches, feed_dict=feed_dict,\n\u001b[0;32m-> 2478\u001b[0;31m                               **self.session_kwargs)\n\u001b[0m\u001b[1;32m   2479\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mupdated\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moutputs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2480\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/conda/envs/tensorflow/lib/python3.5/site-packages/tensorflow/python/client/session.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, fetches, feed_dict, options, run_metadata)\u001b[0m\n\u001b[1;32m    887\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    888\u001b[0m       result = self._run(None, fetches, feed_dict, options_ptr,\n\u001b[0;32m--> 889\u001b[0;31m                          run_metadata_ptr)\n\u001b[0m\u001b[1;32m    890\u001b[0m       \u001b[0;32mif\u001b[0m \u001b[0mrun_metadata\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    891\u001b[0m         \u001b[0mproto_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtf_session\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTF_GetBuffer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrun_metadata_ptr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/conda/envs/tensorflow/lib/python3.5/site-packages/tensorflow/python/client/session.py\u001b[0m in \u001b[0;36m_run\u001b[0;34m(self, handle, fetches, feed_dict, options, run_metadata)\u001b[0m\n\u001b[1;32m   1118\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mfinal_fetches\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mfinal_targets\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mhandle\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mfeed_dict_tensor\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1119\u001b[0m       results = self._do_run(handle, final_targets, final_fetches,\n\u001b[0;32m-> 1120\u001b[0;31m                              feed_dict_tensor, options, run_metadata)\n\u001b[0m\u001b[1;32m   1121\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1122\u001b[0m       \u001b[0mresults\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/conda/envs/tensorflow/lib/python3.5/site-packages/tensorflow/python/client/session.py\u001b[0m in \u001b[0;36m_do_run\u001b[0;34m(self, handle, target_list, fetch_list, feed_dict, options, run_metadata)\u001b[0m\n\u001b[1;32m   1315\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mhandle\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1316\u001b[0m       return self._do_call(_run_fn, self._session, feeds, fetches, targets,\n\u001b[0;32m-> 1317\u001b[0;31m                            options, run_metadata)\n\u001b[0m\u001b[1;32m   1318\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1319\u001b[0m       \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_do_call\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_prun_fn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_session\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhandle\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfeeds\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfetches\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/conda/envs/tensorflow/lib/python3.5/site-packages/tensorflow/python/client/session.py\u001b[0m in \u001b[0;36m_do_call\u001b[0;34m(self, fn, *args)\u001b[0m\n\u001b[1;32m   1321\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0m_do_call\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1322\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1323\u001b[0;31m       \u001b[0;32mreturn\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1324\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0merrors\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mOpError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1325\u001b[0m       \u001b[0mmessage\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcompat\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_text\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0me\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmessage\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/conda/envs/tensorflow/lib/python3.5/site-packages/tensorflow/python/client/session.py\u001b[0m in \u001b[0;36m_run_fn\u001b[0;34m(session, feed_dict, fetch_list, target_list, options, run_metadata)\u001b[0m\n\u001b[1;32m   1300\u001b[0m           return tf_session.TF_Run(session, options,\n\u001b[1;32m   1301\u001b[0m                                    \u001b[0mfeed_dict\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfetch_list\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtarget_list\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1302\u001b[0;31m                                    status, run_metadata)\n\u001b[0m\u001b[1;32m   1303\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1304\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_prun_fn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msession\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhandle\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfeed_dict\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfetch_list\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "\n",
    "model = Sequential()\n",
    "model.add(Conv2D(32, kernel_size=(3, 3),\n",
    "                 activation='relu',\n",
    "                 input_shape=input_shape))\n",
    "model.add(Conv2D(64, (3, 3), activation='relu'))\n",
    "model.add(MaxPooling2D(pool_size=(2, 2)))\n",
    "model.add(Dropout(0.25))\n",
    "model.add(Flatten())\n",
    "model.add(Dense(128, activation='relu'))\n",
    "model.add(Dropout(0.5))\n",
    "model.add(Dense(num_classes, activation='softmax'))\n",
    "\n",
    "model.compile(loss=keras.losses.categorical_crossentropy,\n",
    "              optimizer=keras.optimizers.Adadelta(),\n",
    "              metrics=['accuracy'])\n",
    "\n",
    "model.fit(x_train, y_train,\n",
    "          batch_size=batch_size,\n",
    "          epochs=epochs,\n",
    "          verbose=1,\n",
    "          validation_data=(x_test, y_test))\n",
    "score = model.evaluate(x_test, y_test, verbose=0)\n",
    "print('Test loss:', score[0])\n",
    "print('Test accuracy:', score[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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