Simple Autoencoder.ipynb

{
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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/stephen/miniconda3/lib/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n",
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import warnings\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.stats as stats\n",
    "import matplotlib.pyplot as graph\n",
    "import seaborn as sns\n",
    "\n",
    "from multiprocessing import cpu_count\n",
    "\n",
    "from rosey.helpers import vec_to_array\n",
    "from rosey.graphing import plot_confusion_matrix\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from sklearn.linear_model import LogisticRegressionCV\n",
    "\n",
    "from xgboost import XGBClassifier\n",
    "\n",
    "import keras\n",
    "import keras.losses as klosses\n",
    "import keras.optimizers as kopt\n",
    "from keras.models import Model\n",
    "from keras.layers import Input, Dense, Dropout\n",
    "from keras.callbacks import EarlyStopping, ModelCheckpoint, ReduceLROnPlateau\n",
    "# %env KERAS_BACKEND=theano\n",
    "# %env THEANO_FLAGS=device=cuda3,floatX=float32,optimizer=fast_run\n",
    "\n",
    "graph.style.use('fivethirtyeight')\n",
    "\n",
    "warnings.simplefilter('ignore')\n",
    "\n",
    "def plot_number(xi, yi=''):\n",
    "    graph.figure(figsize=(1, 1))\n",
    "    graph.title('{}'.format(yi))\n",
    "    graph.imshow(xi.reshape(28, 28), cmap='Greys')\n",
    "    graph.xticks([])\n",
    "    graph.yticks([])\n",
    "    graph.grid(False)\n",
    "    graph.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(42000,) (42000, 784)\n",
      "(37800,)\n",
      "(4200,)\n",
      "(37800, 784)\n",
      "(4200, 784)\n"
     ]
    }
   ],
   "source": [
    "# Load data\n",
    "df = pd.read_csv('data/digit-recognizer/train.csv')\n",
    "\n",
    "y = df.pop('label')\n",
    "x = df.values\n",
    "x = MinMaxScaler().fit_transform(x)\n",
    "print(y.shape, x.shape)\n",
    "\n",
    "y_train, y_test, x_train, x_test = train_test_split(y, x, test_size=0.10)\n",
    "_ = [print(a.shape) for a in (y_train, y_test, x_train, x_test)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "plot_number(x[0, :])\n",
    "plot_number(x[39370, :])\n",
    "plot_number(x[17521, :])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Autoencoder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_1 (InputLayer)         (None, 784)               0         \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 300)               235500    \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 100)               30100     \n",
      "_________________________________________________________________\n",
      "dense_3 (Dense)              (None, 300)               30300     \n",
      "_________________________________________________________________\n",
      "dense_4 (Dense)              (None, 784)               235984    \n",
      "=================================================================\n",
      "Total params: 531,884\n",
      "Trainable params: 531,884\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "None"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From /home/stephen/miniconda3/lib/python3.6/site-packages/keras/backend/tensorflow_backend.py:1340: calling reduce_mean (from tensorflow.python.ops.math_ops) with keep_dims is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "keep_dims is deprecated, use keepdims instead\n"
     ]
    }
   ],
   "source": [
    "# Simple Autoencoder\n",
    "input_layer = Input(shape=(x.shape[1],))\n",
    "\n",
    "encoder_layer = Dense(300, activation='elu')(input_layer)\n",
    "encoder_layer = Dense(100, activation='elu')(encoder_layer)  # Bottleneck\n",
    "\n",
    "decoder_layer = Dense(300, activation='elu')(encoder_layer)\n",
    "output_layer = Dense(x.shape[1], activation='sigmoid')(decoder_layer)\n",
    "\n",
    "# Create models\n",
    "autoencoder = Model(input_layer, output_layer)\n",
    "encoder = Model(input_layer, encoder_layer)\n",
    "\n",
    "display(autoencoder.summary())\n",
    "\n",
    "# Compile\n",
    "autoencoder.compile(\n",
    "    loss=klosses.binary_crossentropy,\n",
    "    optimizer=kopt.RMSprop(),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105f2dd668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105f238198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAACXdJREFUeJzt23fM3XMbBvBPqVWj1Ehr01ohNGbU3iVFG3uXNPYIsRMrQggSUTM2LUXS2BpC7VhVs1qborXVVvOP4/p9+/xex3P89b55/a5/Ts55nvNb9/W97uu+7+/p8fvvv2tQMNt/+wL+19A8kBqaB1JD80Bq6NnuDzNmzPhXqG3v3r17zPq+YUgNzQOpoe2SmRW77LJLl/f77LMPWHrppcE333zTOljP1uF+++038Morr4C+ffuCXr16gW+//RY8+eST4JdfftG7d2+wxBJLgBVXXBHMOeec4JlnngE//fQTmGuuucCee+4JzjnnHHDccceBq6++Giy22GJg6tSp4IcffnDeeee1vdeGITX0aOdUZxXVCRMmgIUXXhjcfffdYOONNwY5xpVXXonClPnnnx8lSuuttx4KY0aPHo0Wc+677z5w0EEHQfX+8MMPR2HhJ598Avr06QPWWGMN8OWXX4JPP/0UzDHHHGD8+PFgtdVWq76/9957V/fZiGo36Ight9xyC0oUdtxxR5R1evDBB4Njjz0WnHLKKeCNN94AW2yxBXjiiSfA999/j6IHM2fOrCK77rrrgnfeeQcMGDAA3H777Shs3HTTTcF8880HttlmGxSWLrTQQmDLLbcE1157LVpsv+SSS6r7bBjSDTrKMr/++iuYffbZwYwZM8D7778PXnvtNTBo0CAUJmy11VbgtttuA2eddRY48cQTwaKLLoqWxlx//fVglVVWAU8//TR4+eWXwYILLoiiQ5MnTwZbb701ePHFF7tc81JLLQVef/31LtcW5rRDw5AaOmLIo48+CtZff320fAPstddeYOzYsSha8cADD6Bkpazvzz//HPTv3x8tT0Br3R966KFg+eWXR8kieT98+HBw+umng5133hl89NFHKGxbc801UTxQGBdGRXPaoWFIDR0xZOWVVwafffYZmD59Othggw3ABx98AM4++2xw4YUXgkUWWQRsu+22XV7jOnPcYcOG2XDDDcENN9wAjjzySDBmzJgu59xjjz3AF198gcKAsC0eaZNNNkFxqLNmm2jbX6FhSA0d+ZDUDVOmTAEvvfQSis9Ye+21URg0cOBAFIWPlsR3hBmJ5korreSpp55CiXgiOmnSpOp/UP1fMl7+nvoo0Y+P2WyzzcD9999fXWN8E40P6RYdachll12GEr3UEz///DN49tlnwU477QTOPPPM1sH/rGn2228/lCimGk40x48fX2WuuOHvvvsOJSvkuzn3csstB1599VUwYsQIlGzy8ccfd/le6rHddtvtb++1YUgNHTHkqquuAvfccw+KFgwZMgTceeedKM411W28QjJEdOGhhx5C1+jFcUbTzj33XHDMMcegOMz4jfPPPx+stdZaXc4Rh5pezTzzzIPC3uhhOzQMqaGjLHPAAQeAueeeGzz88MMoUYrzTLfr3XffRelpxKEeeOCBKFHKep8yZUoVyXTIwrLUTSussAJ47rnnUFg6bNgwFL8RZ5uKNnoWrbn33nsdffTR1X02WaYbdMSQ9CtTX8Shpo5IJrjmmmvA9ttvj8KMdMHS00jH7IorrgAXXHCByy+/HCXiqZ+STdJjWX311cH++++PwsLUUfErwahRo1A6aIMGDap8Eg1DukVHWSZRin+IO4yPSLcrr2+++SaKDqSz1qNHKxizzdaKQ3qyN954Y1WbZK0nQz322GPgoosuQnGqH374IYpe5dxxy+nGp25K1oomtUPDkBo6YkiYkeiljjjiiCNQohNHe9ppp6EofrJPul933HEH2HfffdHSoEQ+jnLVVVdF6dxfd9114NZbb0VhaeqrMCwV9dtvvw2GDh0KXnjhhdYN9+xZHfuv0NEDyYNIURYBi9F6/vnnUQxcbHRsdm4miCCmZB83blz1kJImYwLT+vvxxx/BtGnTUJZCruGmm25CeaA5R5ZvrEESQzs0S6aGjtJuDNQCCyyAIlChfMr80DOFVcQ4tE6zOoxKuu7Tp4+vv/4aJVU/+OCDKCm+3gaIQKf1EKZkoHXSSSehlP9hxtSpU+2www7VfTZptxv8I+t+yCGHoLQGY59jm8OkNJ/vuusulPWcqMV8RSC/+uqrSnijGRl25xiDBw9GEfToVVoSKe6WWWYZsN1224GNNtoIjBw5Epxwwgkef/zx6j4bhnSDjhgybtw4lPSZJ5z1nmwRDUmTJ9oR7cnAOcYsY8fBgwdXx9h9991R2gAZbqUZFcOVLBTtSVM5LYgMrtKcSgtx6NCh1XiUhiHdoiOGZLyQpkuKsxizNHfiUzLKjOaEKTFm2RyTrQzTpk2r/hYtSEGZ9mQiP3PmzC7nDlOiUzGHyy67LIoPCQYOHFjp1J/X0jDk79ARQ2KDY68zJoylTxZK4yUZIsOmuMt6VsqQfMSIEZW1zmdhXVoMYWf8SHQqx473SZkfLcqoI3Z97NixVeaiYUi36KiWybpNuZ5CKtG49NJLUdZ1nGjaeGFQv379UNqAUftevXp56623UIbVqZ9Sg4RVcaapk+I70lwOi6MT0aZs8ol7boeGITV0xJCs/fiRONVoRXQojElmSIswr8lCYUxGoZMmTaqazPPOOy9KnRPGhEFBtnjGh2SDTVgXpsQNZ5getrdDw5Aa/tGWqqzLeIW4yzjPrM9UwdGW9EfCnNQ8cbqTJ0+uao5stkmWSdWbz+vVbpxrsklGoNGpbMEKo7Lhrx0ahtTQEUOiGbNGFBZffHEULUlGyDpNAzh5P63GddZZB7z33ntojSOTwTbffHOoNuGlKZy+Robiec0xc65oStiblmKazxljtEPDkBo6YkjWb7JC/EbW68UXX4ziJrO5Pr3XMCT90gy7E+Xp06dXjen6tu+bb765y3eiCRmKHXXUUSg/UAgDsgH4+OOPR9m0N2HChMpB/xUahtTQUS1T729mS1Uq0PQxw6C4x6z7uMyJEyd2OU60qV+/fk4++eQu30lnLNsfUsNEp6IdubZUuRmKpd6q/wBh5MiRVQ+YppbpFh1pSHDGGWegbF5JdsnWyfywKN2q9EHyc4xEKTXNI488gtZYsj7ryZaL+I3o0mGHHYb/dLLZ+JsuXPogYUNYvOuuu/7tPTYMqeEf1TLxH/EI+TzTskRjySWXRNGIRCcZJFO3eIe+fftWGSpD7ehMqt440fxwIB2xjEvDmFNPPRXFkWYeE/ccV90OHYnq/zMaUe0GzQOpoe2S+beiYUgNzQOpoXkgNTQPpIY/AIj/3kzHQuBZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105f2acfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105f272c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAACYZJREFUeJzt21eMVWUbBeBHxRHr2LCMUsQKii1ixahYYyWKXmgs0ViiiRpbNCYajUa9sN7YgajYCJbEgkZsWBEUK/beC4oKdvRi/rU/ZpvhHK/+P7/7vZnMzJl99tnf+ta71nq/WejPP//UVKmF/9s38L9WzQOpVfNAatU8kFr16e0Xs2fP/lewbWdn50Lzf98gpFbNA6lVr1tm/rrpppvAZ599BtZYYw2w9tprg4UX7n6ugwcPBm+99RaYNGkS2G233cCQIUPADz/8AKZOnVp9Pfnkk8F1110HFltsMfDLL7+AffbZByy77LLglFNOAYMGDQJbbrklWGqppXpcZ/311wdffPEFGD9+vE8++aTXz9ogpFZtIeTDDz8EBx98MPjjjz/Am2++CVZbbTXw6quvgvvvvx/sv//+oKurC/z44489fn7UUUeBY4891tixY8Hee+8N3nnnHTB8+HDw0ksvgXvuuQecf/754KOPPupxr0sssQTYeuutURC0wgorgJ9//nmBn7VBSK0W6s3LzN92x4wZA3bddVfw2muvgREjRoBp06ahcEiQ8uuvv4LlllsOTJ8+HQwbNgystNJK4L333qsQsOSSS6Kgql+/fuCSSy4Bu+yyS4/3PO+881C45cwzz0RB7XrrrQcGDBgAvvnmGzvuuGP1OZu226La4pA80aBp4sSJKE/96aefRlnxb7/9Fmy11VbghhtuABtssAHo379/j+s//vjjNtlkExQ0pRNkpXfaaScUjjnuuOPAnDlzwFNPPQVGjRoFNt54YxS+u+CCC9CNvPkRUq8GIbVqCyHfffcdiiY4++yzwV133QUWWWQRFARMmTIFpQNEt+y5557g7rvvRtElgwYNMnLkSPDiiy+icEKuEX565JFHUJAUZK2yyioo6E2nC9JWXnlldHPIgqpBSK3a6jLZn1npdJHVV18dLL744uDtt98GSy+9NHjllVdQkBVNEDUZZHV0dOjTpxus9957LzjiiCPAZZddBlZccUWw1157oWij5ZdfHkVfPPTQQyhcEq20ww47oFtFh9toukzLaotDlllmGRQdEX+QVfr6669RkBFfEQ3w5JNPgo022ggFMVnNjo6OSpEuuuii4OabbwZnnXUWmDdvHoqCffTRR8EJJ5wAbrvtNnDaaaeBq666Cqyzzjro1jowY8aMHgipV4OQWrWFkDB7HOe4cePA5ptvDj744ANw6KGHQuVLXnjhBRTfEYaPXtl2223BzJkz/f777yjdYo899kBBQjRPlGy6UrpQOtghhxyCop2C1pNOOgkFQb1Vg5BatYWQdIu403DIuuuuC5544glwxRVXoCjReJnnnnsORTNcfvnlKIibMmWKgQMHgi+//BIlD0nWMnv2bPD888+DWbNmoeiTKNIDDzwQpfOl+2yzzTbgq6++WuBnbRBSq7Z0SFg57nbnnXdG0RM//fQTilIdP348SsfI91deeSVKt4p7njBhQoWeaJO5c+eioC1/E7TmdfE2Ua533HEHCmckg4lrnjp1atXRaHRIy2oLIekeRx99dI/XJIWKks3qhVs23HBDFF+SVY02SK4yZMiQimeSeF199dUoHerdd99F4ZDktOGvOO4tttgCfP/99yhu+b777kO3bkkWTIOQltUWQqIsk77HP0TBhumTdG+//fYoDjN8EISdc845KM529OjRXn/99R7Xyt6PP1prrbVQkv+o4nDL4YcfjpLoxwOFm+KN5syZU903DUJaVlsICTKyWvvttx9U6vLTTz8Fq666ao/XJReJyjzyyCNREBJHOm/ePJttthl44403wMcff4yCmNxnuCJ644EHHsDfETN69GgUDolG6tOnTw+1WkdIW8IsJi1kmTdJMDxjxgyUNhorH5KN3L7oootQhkwRXV1dXdVWyFbJQz/jjDNQoobY+BjGTTfdFNx5550o4fPxxx8PXn75ZRRJ0ARE/7Da2jIJdCPIIqsT2mSl0+qCnIwSZs6ciYK0ICZo6Nu3b7Xyt99+Owox//bbb+DSSy8Fp556KkpYFQMZxIR808Yztsi9dHV1VfdPQ6otqy2EZIwQEo3tjzBL2Byii0HLMDvyOgQYI3frrbei26LHhAUZGS+Ej0KWQUReN3ToUJTIISYuyMp1Q7IXX3yxE088sfqcDUJaVFsIieiJjK5H/DF5MXNBTn08kdenW2WfDx8+vJLx6RqR6mnDQWdsffgqAVGihDXXXLPHPWZsmvfu379/9TMahLSstnRIDFf2fGTwdttthyK4YqzSlRL8PvbYYyhmLx3i/fffR7dByzAs3JFwKSLv9NNPRzn4kiF3IsKE0DF7+fvEnwm3Ro4c6Zlnnun1szYIqVVbHJKuEUV6wAEHoKjBBEjpANn/QUw9SEocGG7p7OysZH66R/ils7MTZZwa85bDO4kJomSjiSZPnozSEWP5BwwYUL3vf67fcMiCqi0OyYpnfBC1GP8Re58RQrxOtECUadAYlo9SHTx4cBXgRKskAEo0mAgwHHLLLbegRIXpbDGO4ZyMMeJh0oV6qwYhtWqLQ7LS8ShZrYwHs38nTJiAoh6jKWLN42lyDCJeaPr06W688UaU4VVGlscccwxUAVKukUFVR0cHePbZZ1E62MMPP9zjOvFRw4YNqzoTDYe0rH/kdsPOCXrDGfEJYfisZsLlvn37ooxAs+rhmmuvvbYaDUSbpCPtu+++4KCDDkI5EBNExLukk4WLwjUJmHIPI0aMqPwRDUJaVlsIyaGT+vGkPP3ok2iFdI/6SCB+JQ40qzZ06NAq+A1CMryOqszxhlwzOiXRY7xOuk34K4hK15o4cWLVgWgQ0rLa0iE5ChXmDrNHn+RwS/Z7cpBwSNRiulHGFQmf+/XrV2Wh6QbXX389ioOO487oIt0kHHLNNdegOOwkZ+mE4Y0F+RgahPyt2kLI/CNHiiPN04/7jZuNgo3OiNM899xzUbpRVnfWrFnVoZvPP/8chV/CV3nPJGdRpPn64IMPQqVnMl4NSsNj+ceD3qpBSK3a6jKZbWR/x/1Gb+QATTKJaIB8Hx4I90T5JgmfNGlSde2gMUOvICcznsMOOwxFA6Wz5ffpeOl08VE56j1t2jQXXnhh9TmbLtOi2uKQoCgqMFog48ZkGTlUm2NLGXGGK3KMM//ckyOXc+fOrVRwMtTdd98dxT8lg8lMJfoinJADvzlgE97KAZok/ek+vVVbW+b/uZot06KaB1KrXrfMv7UahNSqeSC1ah5IrZoHUqu/ADsCo/ObvSqKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c1cf4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Before Fitting!\n",
    "for i in range(3):\n",
    "    number = vec_to_array(x_train[i, :]).T\n",
    "\n",
    "    plot_number(number)\n",
    "    plot_number(autoencoder.predict(number))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch Cycle 1\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c15af60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c0fe0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEQAAABVCAYAAADwmUKMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAABCNJREFUeJztnE0ofXkYxz+/m/e3u5IklKKsDPoXSZK81GykWJCaqMmG2dgQC8lGk2xkp4myIZlYUJOykpcNxViwGJKNTJeLhnJncf/nHp5xvczfPec283xWOMc9T98+53ee85yDCQQCKDYetwuINjQQgQYi0EAEGohAAxG4Eogx5hdjzG9uHPstjBt9iDHGC3gCgcCfjh/8DVwJJJpx/ZSxvjbG/GiM+cMYc2WM+dUYk+5GbdGyqH4BqoHvgQbgO+BnNwqJceOgL3AP/BAIBP4CMMZMAj+5UUi0GPK7FcZXzoAMNwqJlkDuxfcBwLhRSLQEEjVoIAINRKCNmUANEWggAg1EELZT9fl8/4vFxev1Put31BCBBiJ4182d1+uNdB2O4vP5wm5TQwQaiEADEWggAg1EoIEINBBBtAyZubq6AuD6+hqAoaEhAJKTkwEYGRkBICkpKaJ1qCGCqDBkc3OT2tpaAG5ubgAwJnjPVVdXB4Df7wfUEMdx1ZCtrS0AGhoauL29BaC+vh6AxsZGADo6OgCIiXGmVDVE4Ioh9/fB51JVVVUAeDwe1tfXASgrK3u2r7WWOIUaInDUEGudGBwcBODh4QGAvr4+Kioqnu17cnICwPLyMgBdXV1A0KZIooYIwj6oejpk/qyJ2eTkJADd3d0AFBYWArCzs0N8fPyLv3N+fg7A0dERAJWVld9cx9OJmQ6Z38CRNeTx8RGAhYUFAFJSUgC7DwlnB0BmZiYAY2NjwOcY8hpqiMARQ+7u7gC7p8jICL4clJiY+O7PKCgoAGB3dxeAoqKizywxhBoicMQQa6YxMTEBQHt7O2Cv9q9dxax1x1pDrHud8fHxiNTqaGOWn58PQEtLCwA1NTUArK2tkZaWBsDc3BwA8/PzACwtLQF2u19SUhLRGvWUETjamEms02F1dZWLi4tnP7NOs5ycHAAGBgYAQoOk9PR//6KzNmYfwJXbf6tRW1xcBGB2dja0rb+/H4DOzk4A8vLyHK1NDRE4asjl5SUAzc3NAKGhUFtbG01NTYDdzjtthoUaInDUkP39fQA2NjYAOD4+BiA7Ozs0+FlZWQHg9PQ0tM1J1BCBK1cZ6+FTbm7uP7aNjo4CUF1dDQS7WCDUyUYaNUTgqCFZWVlA8NFlOFJTUwGYmZkB7CFza2trhKsLooYIHDXE6i2sAdHZ2Rlgm/MUawDd09MD2L1LbGxsRGtUQwSuXGW2t7cB+w52eHiYuLi4F/e1XoPY29sDoLS0NKK1qSECVwyx1oHe3l4ApqenKS4uBuxXqqyHWoeHh4A9XFZDHMbViZmF3+/n4OAAgPLy8mBhXx9ZTE1NAfYcNiEh4ZuPpxOzDxAVhjiNGvIBNBCBBiLQQATvasxe+xu1/xpqiEADEeh/hxCoIQINRKCBCDQQwd/jWyqOdILksgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c0b7278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c0dc160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c098a90>"
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     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c05d390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c169e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1054743080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1054777fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10547217f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Epoch 00064: reducing learning rate to 0.0005000000237487257.\n",
      "\n",
      "Epoch 00095: reducing learning rate to 0.0002500000118743628.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10546f8f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch Cycle 2\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1054737518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
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      "text/plain": [
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      "text/plain": [
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c03b940>"
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c05d860>"
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c0d2dd8>"
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     "metadata": {},
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    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10547a5a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c0799e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1054721cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Epoch 00066: reducing learning rate to 0.0001250000059371814.\n",
      "\n",
      "Epoch 00073: reducing learning rate to 6.25000029685907e-05.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10546f8278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch Cycle 3\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f710fc5c0>"
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f710d5a90>"
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f71097ac8>"
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10547cd5c0>"
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70ffacf8>"
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70fdf048>"
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     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70f94d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70f3f710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70ef8f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70ebb860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Epoch 00010: reducing learning rate to 3.125000148429535e-05.\n",
      "\n",
      "Epoch 00017: reducing learning rate to 1.5625000742147677e-05.\n",
      "\n",
      "Epoch 00024: reducing learning rate to 7.812500371073838e-06.\n",
      "\n",
      "Epoch 00029: reducing learning rate to 3.906250185536919e-06.\n",
      "\n",
      "Epoch 00038: reducing learning rate to 1.9531250927684596e-06.\n",
      "\n",
      "Epoch 00043: reducing learning rate to 1e-06.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105f2c0ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch Cycle 4\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f7111a2b0>"
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      "text/plain": [
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10546c3940>"
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70e75d68>"
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f710dbf98>"
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10547052b0>"
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10547659e8>"
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     "metadata": {},
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     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70f0eef0>"
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     "metadata": {},
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     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70ff5780>"
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     "metadata": {},
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    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105f342f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch Cycle 5\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c0419e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70f30d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
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      "text/plain": [
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      "text/plain": [
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10547653c8>"
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     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105471ba20>"
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0fc46b5550>"
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     "metadata": {},
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    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEQAAABVCAYAAADwmUKMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAABDdJREFUeJztnE0odVsYx3+LNx8lp3xTok6GYkAhEwbcuomBgZHelJuBmMiIYqLwJrM7vaZM3DKRW0pJvpKBbklJXB+J18EAyXkH5122s47Duzl771P3+Y2cs9bZ6+nff6/1PGvtTQWDQQSLBK8DiDdEEAMRxEAEMRBBDEQQA08EUUr9pZT6x4ux30N5kYcopXxAQjAY/O764O/giSDxjOe3jP5bKfWHUupAKXWtlPpbKZXtRWzxMqlWAnXA78BvQDnwzYtAvngx6Cs8AF+DweA9gFLqT6DXi0DixSH/ajF+8h+Q60Ug8SLIg/E5CCgvAokXQeIGEcRABDGQxMxAHGIgghiIIAZRM9VAIPC/mFx8Pl9YviMOMRBBDH6puPP5fE7H4SqBQCBqmzjEQAQxEEEMRBADEcTA1S3Eubk5AI6PjyPaDg8PAdjd3QVgenoagMzMTABGRkbC+jc2NgJQVFQU0xjFIQZRy/+XqXus8pDq6moA1tbWbP82PT0dgIGBAQBaWloA8Pv9tq/1Mg+R1P0dXJ1DJiYmAKitrX23b1ZWFgDDw8MAdHR0AJCUlORQdCHEIQauOkSvCHl5eQCcnp4CMDQ0RF9fX1hfpUK3dkpKiosRikMicNUhFxcXAFxeXoZ97/f7SU1NdTOUqIhDDFx1yODgIAAPD+Enl52dnc+rR2trq5shRSAOMXAlU93e3gasTPX+/j6ij55DSkpKgJBrAGpqagAoLy//VAwvkUzVBo465Pr6GoDm5mYAlpaWXu3X3d397JDx8fGwtvz8fAB2dnY+FctLxCE2cHSV2draAt52BsDY2NhzZtrW1gZYrjo6OgKs1WdhYcG5gBGHRODJQ3cNDQ1AyBkAycnJz216Nenp6QGgv78fgOXlZQDW19cBqKysdCQ2RwXJyMgAoKysDLCW34qKCiBcCJP29nbAEkQv1VoYpwSRW8bAlcTs9vYWgP39fcBKvt4q7c/PzwFrq0CTk5MDwMnJyYfjkWXXBjGZQzY3NwEoLi4GrKMDTVpaGgClpaWxGM5RxCEGMXHI3t4eAFNTUwBMTk4CkJDwcb3femTBScQhBjFxSH19PQBdXV0A3N3dAdbxoz5SsIM+snAbcYhBTBySnR16+Uk7RKfkKysrAMzPzwOQmxt64yMxMTHqtc7OzgBYXFx8tV0fWDmFOMQgprVMb2/oJajZ2VnAKt0LCwsBy0H6KFOX+ABXV1cA1NXVAdbKZVJVVRXLkCMQhxg4WsvoyrSpqQmAm5sbAJ6enmxfS9c0GxsbgLW1+BGklrGBqw/M6HxFO+fx8TF6YD+3FAsKCgBYXV0FPucMjTjEBq46RKMPu0dHRwE4ODhgZmYGsLYOtZv0/BNLxCE28MQhXiMOsYEIYiCCGIggBiKIgQhi8Evlv1cbvl4gDjEQQQzkv0MYiEMMRBADEcRABDH4AbaNTbR0z08DAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10547866a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105f25c6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AwyP7E4AtfeRpMrMEMAbYETm+mOLdgVOBhLv/Pi99HvAV4GR3b+/v4ga6wf40NjYO6vzhSHVSSHVSSHVSSHVSqNx1UkqX4HNAg5lNMrNqguCzJi/PGmB5uL0QWJvt4jOzCmARwdhXvoJxLTM7HvgecJa7byv1RkREZHgbsIXl7hkzuwJ4DKgE7nT3F83sOuB5d18D3AHcZWYbCVpWiyNFzAGa3H1TkeLPBc7IS/tnoB54IJy38bq7n7WH9yUiIsNMKV2CuPsjwCN5aV+LbKcJWlHFzl0HzOjj2JFF0uaVck0iIjKyaKULERGJBQUsERGJBQUsERGJBQUsERGJBQUsERGJBQUsERGJBQUsERGJBQUsERGJBQUsERGJBQUsERGJBQUsERGJBQUsERGJBQUsERGJBQUsERGJBQUsERGJBQUsERGJBQUsERGJhZIClpnNN7NXzGyjmV1T5HjSzO4Pjz9jZhPD9KVmtj7y021m08xsVF76O2Z2c3jOHDP7g5llzGxhOW9WRETia8CAZWaVwCrgdGAysMTMJudluxjY6e5HATcBNwC4+z3uPs3dpwHLgNfcfb27786mh8c2A6vDsl4HPgv8dPC3JyIiw0UpLazpwEZ33+TuHcB9wIK8PAuAH4fbDwKnmpnl5VkC3JtfuJk1AIcAvwVw99fc/QWgu+S7EBGRYS9RQp7DgDci+03ACX3lcfeMme0CxgPvRPKcR2GggyCQ3e/uXupFRzU2Nu7NaWU7fzhSnRRSnRRSnRRSnRTakzppaGjo93gpASu/pQSQH1z6zWNmJwCt7r6hSL7FBN2Fe2WgG+xPY2PjoM4fjlQnhVQnhVQnhVQnhcpdJ6UErCbg8Mj+BGBLH3mazCwBjAF2RI4vpnh34FQg4e6/35OLFpGRx91pbm6mu/vAHC1IpVLs2rVrqC/jgNJfnVRUVFBfX0/h6FHfSglYzwENZjYJ+AtB8Dk/L88aYDnwNLAQWJvt4jOzCmARMKdI2UXHtURE8jU3N5NMJqmurh7qSykqmUySSqWG+jIOKP3VSUdHB83NzYwaNark8gacdOHuGeAK4DHgv4F/c/cXzew6MzsrzHYHMN7MNgIrgejU9zlAk7tvKlL8ueQFLDP7uJk1EQS575nZiyXfjYgMW93d3QdssJI9V11dvcet5VJaWLj7I8AjeWlfi2ynCQJMsXPXATP6OHZkkbTnCLodRUREckoKWCIiI92OHTs466ygU2nbtm1UVlYyfvx4ANauXVtSGStWrOCqq64qeSLC1q1b+dznPseWLVvIZDJMmjSJ++67b+9uYBhQwBIRKcFBBx3Ek08+CcA3v/lN6uvr+dznPpc7nk6ncXfcnYqK4qMtt9122x595te//nU++clPcskllwCwYUOxidZ7JpPJkEjE80+/1hIUERmETZs2MXPmTP7+7/+eOXPmsHXrVq688krmzp3LjBkzuOGGG3J558+fzwsvvEAmk+GII47g2muvZfbs2Zx22mm8/fbbBWW/9dZbfPCDH8ztH3vssbntf/mXf2HWrFnMnj2b66+/HoD169dz6qmnMmvWLJYtW5aboTd//nyuv/56Tj/9dL7//e+zbds2LrjgAubOncspp5zCc889t6+qp6ziGWZFZMQb+8O/lLW8dy88bK/Pffnll/n2t7/NLbfcAsC1117LuHHjyGQyfPrTn2bBggUcc8wxvc557733mD17Ntdeey1f/vKXufvuu7nqqqt65bnkkkv4m7/5G6ZOncrcuXNZunQp73//+/nlL3/J448/zhNPPEFNTQ07d+4E4LLLLuPmm29m5syZXHfddfzzP/8zX//613Of98tf/hKACy+8kCuvvJKPf/zjbN68mcWLF/P000/v9f3vLwpYIiKDNGnSJI4//vjc/oMPPshdd91FJpNh69atvPLKKwUBq6amhtNOOw2AadOmFQ0Yn/zkJ1m/fj2PP/44jz/+OHPmzOF3v/sd69atY+nSpdTU1AAwbtw4duzYQTqdZubMmQAsWbKEyy67LFfWOeeck9tet25drxUo3n33Xdra2nLlHagUsEREBqm2tja3/eqrr3L77bfzxBNPMHbsWC699FLS6XTBOVVVVbntyspKMplM0bIPOuggzj33XM4991zOOeccnn76ady94IHbgVa3i16ju7N27drYPSagMSwRkTLavXs39fX1jB49mq1bt/LEE0/sdVm//vWvaWtrA4Iuvc2bNzNhwgROOeUU7r777tyxnTt3Mn78eGpqanjmmWcAuP/++5k9e3bRcufOncu//uu/5vZfeOGFvb7G/UktLBGJpcGMOe1LU6dO5cMf/jAzZ85k4sSJnHBC/lrhpfvDH/7AF7/4RRKJBO7ORRddxNSpU5k6dSobNmzgE5/4BIlEgvnz5/PVr36V22+/nauvvpq2tjaOPPJIVq1aVbTcG2+8kZUrV3LPPffQ1dXFSSedxI033rjX17m/2F4ukj6kdu3aVZaL1mKVhVQnhVQnhYaiTnbt2sWYMWP262fuiXQ6raWZ8gxUJ/39Nx0zZkzBIoPqEhQRkVhQwBIRkVhQwBIRkVhQwBIRkVhQwBIRkVhQwBIRkVhQwBIRKcGZZ55Z8BDwbbfdxtVXX93veYcdFjwv9uabb/KZz3ymz7L/+Mc/9lvObbfdRmtra25/0aJFvPvuu6Vcer8aGxs588wzOfHEE5k+fTpXXnnloMvcV0oKWGY238xeMbONZnZNkeNJM7s/PP6MmU0M05ea2frIT7eZTTOzUXnp75jZzf2VJSIylBYuXMjPfvazXmmrV6/utUZffz7wgQ/wk5/8ZK8//7vf/W5uZQuABx54gLFjx+51eVlf+tKXWLFiBU8++STPPvssl1566aDL7OrqGnQZxQwYsMysElgFnA5MBpaY2eS8bBcDO939KOAm4AYAd7/H3ae5+zRgGfCau693993Z9PDYZmB1f2WJiAylBQsW8Nhjj9He3g7A5s2b2bp1KzNnzqS5uZmFCxcyZ84cZs2axX/8x38UnL958+bcwrRtbW1cdNFFzJo1iwsvvLDXWoMrV67MvZrkG9/4BgC33347W7du5dOf/jSf+tSnAJgyZQrbt28H4NZbb2XmzJnMnDkz986tzZs3M336dD7/+c8zY8YMzj777F4BL2vr1q25ViDAX/3VXwFB0PnqV7/KrFmzmDVrFt/73veAYLmok046iVmzZnH55Zfn6mPKlCnccMMNzJ8/n3//93/nz3/+M0uWLOHkk0/m9NNP509/+tMgaj9QytJM04GN7r4JwMzuAxYAL0XyLACuDbcfBG41M/Pey2gsAe7NL9zMGoBDgN/uQVkiMsLVL59b1vKaf7yu3+MHHXQQH/3oR3n88cc588wzWb16NWeffTZmRiqV4oc//CHve9/72L59O/PmzeOMM84oWKA264477qCmpoannnqKDRs2cPLJJ+eO/cM//APjxo2jq6uLs846iw0bNvC3f/u3rFq1iocffjj3luOs9evX89Of/pTHH38cd2fevHnMnj2bsWPH8uqrr/KDH/yAW265hc9+9rOsWbOG8847r9f5K1as4KyzzmL69Ol84hOfYOnSpYwdO5Yf/ehHbN68md/85jckEgl27txJOp1mxYoVPPTQQxx11FFcdtll3HHHHaxYsQKAVCrFo48+CsBZZ53Ft771LSZPnszzzz/P1VdfzcMPP7yn/1l6KaVL8DDgjch+U5hWNI+7Z4BdwPi8POdRJGARBLL7IwGplLJERPa7c845h9Wrg86gn/3sZ7nuQHfnG9/4BrNmzWLBggW8+eabbNu2rc9ynnrqKc4991wgeCljtlUD8POf/5w5c+Zw0kkn8fLLL/PKK6/0e01PP/00Z555JnV1ddTX1/OpT30q96qSD33oQxx33HFA8AqT119/veD8Cy64gGeeeYYFCxbw5JNPctppp9He3s66deu46KKLcm8nHjduHI2NjRxxxBEcddRRAJx//vk89dRTubLOPvtsAJqbm3n22We55JJLOPHEE/nCF77AW2+91e99lKKUFlax/0XIb+30m8fMTgBa3b3Y+50XE3QX7snn5UTf6bI3Bnv+cKQ6KaQ6KbS/6ySVSpFMJnP79WUuv9grQPLNmzePL3/5yzz77LO0tbVxzDHHkE6nue+++9i+fTuPPfYYVVVVfOxjH8utk+fupNNp2tvb6e7uJp1O093dTWdnZ+4z3Z329nZeeeUVbrnlFh599FHGjh3L5z//eXbv3k06nc6VEz0nnU7T2dlJJpPJpXd1dZHJZGhvb6eqqiqXnv3sYvc5btw4Fi1axKJFizj55JNZv349XV1dva4RoL29Pfe5AB0dHbly3Z3KykrS6TRtbW2MHj26YJJK/me/9957vQL7QOtTlhKwmoDDI/sTgC195GkyswQwBtgROb6Y4t2BU4GEu/9+D8rqZTALcGpR00Kqk0Kqk0JDtfjtvlxctpSyU6kUJ510EitXrmThwoW5c9ra2jj44IMZNWoUv/nNb2hqaiKZTJJKpXJdhslkkoqKClKpFCeeeCIPPfQQ8+bN46WXXuKll14imUzS0dFBXV0dhxxyCO+88w6/+tWvOPnkk0mlUowePZrOzs7cZ2bLnTNnDitWrOCLX/wi7s6jjz7K7bff3uvzIHj/ViKRKLjPxx9/nJNPPpmqqireeust3n33XSZOnMi8efO4++67OeWUU3JdgsceeyxNTU1s2bKFI488ktWrV3PSSSf1us/sz8SJE1mzZg3nnnsu7s6GDRuYMmVKr88ePXo0hx9+OKUqJWA9BzSY2STgLwTB5/y8PGuA5cDTwEJgbbaLz8wqgEXAnCJlFxvX6rMsEZGsgcac9pVzzjmHZcuWceedd+bSsi9YnDt3LlOmTOHoo4/ut4yLL76Yyy+/nFmzZjFlyhQ++tGPAsHEheOOO44ZM2YUvJpk+fLlLFq0iEMPPZRf/OIXufRp06Zx/vnnc+qppwKwbNkypk6dyubNm0u6n7Vr13LNNdfkWq/XXXcdhx56KJ/5zGfYuHEjs2fPJpFIsHz5ci699FJWrVrF8uXL6erq4vjjj+eiiy4qWu73v/99rrrqKr7zne+QyWT467/+64KAtadKer2ImZ0B3AxUAne6+z+a2XXA8+6+xsxSwF3A8QStocWRSRpzgW+5+4wi5W4CznD3lyNpfZaVpdeL7Duqk0Kqk0J6vUghvV6kULlfL1LSCxzd/RHgkby0r0W20wStqGLnrgMKglV47MgiaX2WJSIiI5dWuhARkVhQwBIRkVhQwBIRkVhQwBKRWKioqKCjo2OoL0PKpKOjg4qKPQtBJU26EBEZavX19TQ3NxddD+9A8N577zF69OihvowDSn91UlFRQX39nj3+rYAlIrFgZowaNWqoL6NP27Zt26OHYEeCcteJugRFRCQWFLBERCQWFLBERCQWFLBERCQWFLBERCQWFLBERCQWFLBERCQWFLBERCQWFLBERCQWFLBERCQWFLBERCQWSgpYZjbfzF4xs41mdk2R40kzuz88/oyZTQzTl5rZ+shPt5lNC49Vm9n3zexPZvaymZ0Tpn/IzJ4wsxfMbJ2ZTSjf7YqISFwNGLDMrBJYBZwOTAaWmNnkvGwXAzvd/SjgJuAGAHe/x92nufs0YBnwmruvD8/5CrDN3Y8Oy/11mH4j8BN3Pw64DvjmYG5QRESGh1JaWNOBje6+yd07gPuABXl5FgA/DrcfBE41M8vLswS4N7J/EWEwcvdud38nTJ8MPBFu/6rIZ4mIyAhUyutFDgPeiOw3ASf0lcfdM2a2CxgPvBPJcx5h8DGzsWHa9WY2F3gVuMLd3wL+L3AO8B3gbGCUmY139+3FLq6xsbGEW+jbYM8fjlQnhVQnhVQnhVQnhfakThoaGvo9XkrAym8pAfie5DGzE4BWd98Q+dwJwH+6+0ozW0nQFbgM+DvgVjP7LPAb4C9Apq+LG+gG+9PY2Dio84cj1Ukh1Ukh1Ukh1UmhctdJKQGrCYi+gWsCsKWPPE1mlgDGADsixxfTuztwO9AK/Dzcf4BgHAx33wL8NYCZ1QPnuPuuUm5GRESGr1LGsJ4DGsxskplVEwSfNXl51gDLw+2FwFp3dwAzqwAWEYyY+vTKAAAPwUlEQVR9ARAeexiYGyadCrwU5j84PAfgfwN37uE9iYjIMDRgCysck7oCeAyoBO509xfN7DrgeXdfA9wB3GVmGwlaVosjRcwBmtx9U17RXwrPuRl4G7gwTJ8LfNPMnKBL8PK9vjsRERk2SukSxN0fAR7JS/taZDtN0Ioqdu46YEaR9M0EwSw//UGCmYYiIiI5WulCRERiQQFLRERiQQFLRERiQQFLRERiQQFLRERiQQFLRERiQQFLRERiQQFLRERiQQFLRERiQQFLRERiQQFLRERiQQFLRERiQQFLRERiQQFLRERiQQFLRERiQQFLRERioaSAZWbzzewVM9toZtcUOZ40s/vD48+Y2cQwfamZrY/8dJvZtPBYtZl938z+ZGYvm9k5YfoRZvYrM/ujmb1gZmeU73ZFRCSuBgxYZlYJrAJOByYDS8xscl62i4Gd7n4UcBNwA4C73+Pu09x9GrAMeM3d14fnfAXY5u5Hh+X+Okz/KvBv7n48sBi4bTA3KCIiw0MpLazpwEZ33+TuHcB9wIK8PAuAH4fbDwKnmpnl5VkC3BvZvwj4JoC7d7v7O2G6A6PD7THAllJuREREhrdSAtZhwBuR/aYwrWged88Au4DxeXnOIwxYZjY2TLvezP5gZg+Y2aFh2rXABWbWBDwCfK60WxERkeEsUUKe/JYSBK2gkvOY2QlAq7tviHzuBOA/3X2lma0EbiToNlwC/Mjd/8XMZgJ3mdmx7t5d7OIaGxtLuIW+Dfb84Uh1Ukh1Ukh1Ukh1UmhP6qShoaHf46UErCbg8Mj+BAq76bJ5mswsQdCVtyNyfDG9uwO3A63Az8P9BwjGwQh/zwdw96fNLAUcDGwrdnED3WB/GhsbB3X+cKQ6KaQ6KaQ6KaQ6KVTuOimlS/A5oMHMJplZNUHwWZOXZw2wPNxeCKx1dwcwswpgEcHYFwDhsYeBuWHSqcBL4fbr4T5m9j+BFPD2Ht2ViIgMOwO2sNw9Y2ZXAI8BlcCd7v6imV0HPO/ua4A7CLruNhK0rBZHipgDNLn7pryivxSeczNBQLowTL8a+Fczu4qgW/Gz2eAnIiIjVyldgrj7IwQTIKJpX4tspwlaUcXOXQfMKJK+mSCY5ae/BMwu5bpERGTk0EoXIiISCwpYIiISCwpYIiISCwpYIiISCwpYIiISCwpYIiISCwpYIiISCwpYIiISCwpYIiISCwpYIiISCwpYIiISCwpYIiISCwpYIiISCwpYIiISCwpYIiISCwpYIiISCyW9wHE4eq+jmz81G4n3MtRVGfVVRk2lYWZDfWkiIlJESQHLzOYD3wEqgR+4+7fyjieBnwAfBbYD57n7a2a2FPhiJOtxwEfcfb2ZVQO3AnOBbuAr7v4zM7sJ+ESYvxY4xN3H7u0N9uXZbR0sXV8D69/quQ+gPgxedYmKXCCrTxj1VRVBelW4HabVRY6PihyvSwTnJioUAEVEymHAgGVmlcAq4DSgCXjOzNaEr7LPuhjY6e5Hmdli4AaCoHUPcE9YzhTgIXdfH57zFWCbux9tZhXAQQDuflXksz8HHD/YmyymudML0hzY3ens7nSCGDp4qUqoS1TkAuGoqux2NNgZdWEQzAa8Udlgmc2fCPJUV6BWoIiMSKW0sKYDG919E4CZ3QcsAKIBawFwbbj9IHCrmZm7R6PCEuDeyP5FwDEA7t4NvFPks5cA/6eEa9xjzZnyBKSBpLsg3dXN9vbylJcwegWyukjrr75X6y8MgpEWYE+LsSd/bULdoCISD6UErMOANyL7TcAJfeVx94yZ7QLG0zsInUcQ2DCzbBff9WY2F3gVuMLdc/1zZvYhYBKwtr+La2xsLOEWCu1+p5Kjaqto7YK2bqO1C9q7D/w/3BmHdzucdzu6ylJeBU5NJdRWOrWVUFuZpPa/XqemAuoSnkuvyx2P/K6A2oQHecO0mkoYjr2ge/s9G85UJ4VUJ4X2pE4aGhr6PV5KwCr25ye/P63fPGZ2AtDq7hsinzsB+E93X2lmK4EbgWWR8xcDD7p7v3+ZB7rBvs+DeQc39jo/0+00dzrNnd20ZJyWsHuwJdMdpgfHmsNjzZ1heqZnO5rekvGCijrQdGO0dEFLV/miTHb8rtdYYNilmd0eFWkV1kXG/LLnRFuMQ90N2tjYuNffs+FKdVJIdVKo3HVSSsBqAg6P7E8AtvSRp8nMEsAYYEfk+GJ6dwduB1qBn4f7DxCMg5F3zuUlXF/ZJCqMsUljbLI8s/3dnbaubBBzdncWBr7d4XZrGOCieXZ3dtMSpmeDYOZAj4AQBPuM81YbwOBbgtFu0LpwnC8a8EZVVVAbpteFwTC7XZc3HliXCNIrh2MzUGSYKyVgPQc0mNkk4C8EgeT8vDxrgOXA08BCYG12/CqcULEImJPN7O5uZg8TzBBcC5xKZEzMzD4MjAvLiy2zYIyoNgHvqxl8ee5ORzc0d3YHLb9Ia3B3tMVXpFXYmvEi+bpJl6dncZ8qdzcoEAS4RO9Zn3V9jAO27UwwkZZeE2CyY4KjwhZhslKTYUT2tQEDVjgmdQXwGMG09jvd/UUzuw543t3XAHcAd5nZRoKW1eJIEXOApuykjYgvhefcDLwNXBg5tgS4L2/SxohnZiQrIVlZyfhUecrs7I50Y2aclze9zrj3T6Al090ruO3ucJojQbAlzB/tQm3udFrj0AQEWjPBtb6dhoFbgdWw6d1+c1QavR5xKDYhJtvVmW0h9nSD9uSPTpRRK1Ckt5Kew3L3R4BH8tK+FtlOE7Siip27DphRJH0zkVZX3rFrS7kuGbyqvG7QylHdNHwwudfldXV7LnhFx/KyLb6WvK7R1rC7c3dkO//8OMTALof3Opz3Osr3SERNZfFWX69ZoYme7s/ssWLPA9ZXVZCsVACUeBuxK13IvlFZYYyuNkZXQ9AgHxx3p70LWjO9W3TNnZHxv0zPOGFzpnDcL78V2BKHCAi0dQVjoO+U1AocWFUFvYJfXdjqq812f0ZbeHnjhPndpC0Z6HanQt2gsh8pYMkBzcxIJSCVqAyeLC+DbvfcLNBsi68l07trNBoYt2zfSWXt6OB4XiBsCQNkx/55rG9QOrthZ7uzs70cY4G18LstuXHA6ASX6NhgMAkm2iqs6HVOfpdpSmOB0g8FLBlxKiz4IzqqqrT8jY3baGjoP1x2dBW26qITX7KBbXdn8W7P6LnZwBgH2RmhgcEHwuxY4KjI0mj5wbC+1yzQ3oGxrqr3TNK6hFGtrtBhQwFLpAyqK4M/jOPK9EhEt3uvrs7duZZfkdmfYYDLPgZRbJbo7k6nKwYxsGcssHwzQqsrKLoUWnR8ry6SHm0lZifKRFuJtQlTV+gQUcASOQBVWPaPKRxahvLcnXQXvR6Kzwa87IPw2SAXnR2a302anR26u72LthisDAPQ0Q072rvZUabl0YCiXaF0JDmkaXuvh+Xzl0SLthpHRY7pTRGlUcASGQHMjJoE1CQqeV8ZymtsbOR/HHVUz0SWyKovLdHAlvfcX0uk1dia6TmnuTM+Y4HQV1doJexM71V52TdF5HdzRleLyQa56ESY/MAY7Rod6hVi9gUFLBHZK73HAgc/IxSCscDo8mfFZntGW4X544G9JtOE44Zx6Art9aaIMq4QUxdZ7Lou0q2ZH+Ty8+Uvj5YNpkP9uiQFLBE5YFRXGgdVlm9GaPaxiOZM7y7O6CMO0RZg9nnAbBfp7uhSatljMZkQk3HY1eHsKuN4YDL6uqS89wTWJYwLjq7jxPfv/XOcA1HAEpFhK/pYxMFlWh0mOyGm14PwGWfj5ibGHPKBSCDs3VXaHJkUE101pjUTjyXSANq7oL2r7/HAkz6QVMASETlQRCfERB26u5uGSbV7VWb2TRFBl2bP+qCtmeIPv+eCX15gzC6g3TJEK8TUV5VnlmxfFLBERIZYz5siYF+MBxY+8xcZD8zfLvK6pOwkk+4BgmB91b4d41LAEhEZhvbFeGD00YjdkZZetmU3eVyJT+PvJQUsEREZULkfjdgb+7bDUUREpEwUsEREJBYUsEREJBYUsEREJBYUsEREJBbMPR7LjETt2rUrfhctIiIlGzNmTMFDXWphiYhILChgiYhILMSyS1BEREYetbBERCQWRmTAMrP5ZvaKmW00s2uG+nqGgpkdbma/MrP/NrMXzezKMP0gM/v/zawx/D1uqK91fzOzSjP7o5n9ItyfZGbPhHVyv5lVD/U17k9mNtbMHjSzl8Pvy8yR/j0xs6vCfzcbzOxeM0uNtO+Jmd1pZtvMbEMkrej3wgK3hH9zXzCzj+zNZ464gGVmlcAq4HRgMrDEzCYP7VUNiQxwtbv/T2AGcHlYD9cAT7h7A/BEuD/SXAn8d2T/BuCmsE52AhcPyVUNne8Aj7r7McBUgroZsd8TMzsM+DzwMXc/lmB59cWMvO/Jj4D5eWl9fS9OBxrCn0uB7+7NB464gAVMBza6+yZ37wDuAxYM8TXtd+7+prv/IdzeTfBH6DCCuvhxmO3HwP8amiscGmY2ATgT+EG4b8ApwINhlhFVJ2Y2GpgD3AHg7h3u/i4j/HtCsHB4jZklgFrgTUbY98TdfwPsyEvu63uxAPiJB34HjDWzD+zpZ47EgHUY8EZkvylMG7HMbCJwPPAMcKi7vwlBUAMOGborGxI3A38PdIf744F33T0T7o+078uRwNvAD8Nu0h+YWR0j+Hvi7n8BbgReJwhUu4DfM7K/J1l9fS/K8nd3JAasYm8YG7FTJc2sHvgZ8AV3f2+or2comdmngG3u/vtocpGsI+n7kgA+AnzX3Y8HWhhB3X/FhOMyC4BJwAeBOoIur3wj6XsykLL8OxqJAasJODyyPwHYMkTXMqTMrIogWN3j7qvD5LeyTfXw97ahur4hMBs4y8xeI+gqPoWgxTU27PqBkfd9aQKa3P2ZcP9BggA2kr8n84A/u/vb7t4JrAZmMbK/J1l9fS/K8nd3JAas54CGcEZPNcFg6Zohvqb9LhybuQP4b3f/duTQGmB5uL0ceGh/X9tQcff/7e4T3H0iwfdirbsvBX4FLAyzjbQ62Qq8YWYfDpNOBV5iBH9PCLoCZ5hZbfjvKFsnI/Z7EtHX92IN8JlwtuAMYFe263BPjMgHh83sDIL/c64E7nT3fxziS9rvzOxE4LfAf9EzXvNlgnGsfwOOIPiHucjd8wdWhz0zmwv8nbt/ysyOJGhxHQT8EbjA3duH8vr2JzObRjAJpRrYBFxI8D+7I/Z7Ymb/H3AewWzbPwJ/QzAmM2K+J2Z2LzAXOBh4C/g/wL9T5HsRBvZbCWYVtgIXuvvze/yZIzFgiYhI/IzELkEREYkhBSwREYkFBSwREYkFBSwREYkFBSwREYkFBSwREYkFBSwREYkFBSwREYmF/wehu6KoGuGPHQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c091a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2h 49min 38s, sys: 2h 20s, total: 4h 49min 59s\n",
      "Wall time: 13min 13s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# Fit model! (n*100) epochs\n",
    "for i in range(5):\n",
    "    print(f'Epoch Cycle {i+1}')\n",
    "    \n",
    "    # Check fit\n",
    "    for i_img in range(5):\n",
    "        number_i = vec_to_array(x_train[i_img, :]).T\n",
    "        \n",
    "        plot_number(number_i, 'in')\n",
    "        plot_number(autoencoder.predict(number_i), 'out')\n",
    "    \n",
    "    # Train\n",
    "    hist = autoencoder.fit(\n",
    "        x_train, x_train,\n",
    "        epochs=100, validation_data=(x_test, x_test), batch_size=4096,\n",
    "        callbacks=[\n",
    "            EarlyStopping(monitor='val_loss', patience=15),\n",
    "            ReduceLROnPlateau(monitor='val_loss', patience=5, factor=0.5, min_lr=1e-6, verbose=1),\n",
    "            # TQDMCallback(),\n",
    "            ModelCheckpoint('data/model.ckp', monitor='val_loss', save_best_only=True)\n",
    "        ],\n",
    "        shuffle=True,\n",
    "        verbose=0\n",
    "    )\n",
    "    \n",
    "    # Summary of performance\n",
    "    graph.plot(hist.history['loss'], label='Train Score')\n",
    "    graph.plot(hist.history['val_loss'], label='Validation Score')\n",
    "    graph.legend()\n",
    "    graph.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c14dda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f407ec5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f4073bba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f407635f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f40737d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f406e2748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# After Fitting!\n",
    "for i in range(3):\n",
    "    number = vec_to_array(x_train[i, :]).T\n",
    "\n",
    "    plot_number(number)\n",
    "    plot_number(autoencoder.predict(number))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAA41JREFUeJztmzssLGEYhp85roVkNaJyKSQuoROFRqMgIaIRUZKIEaIQnUJBpRCFhkQpESFhIy4Rl8pWChISEQoK2USxFSsup5Df7H7nLLvHzowc39NsZndm9tt3n/nn//7NWq+vrygOv/wu4LuhgQg0EIEGIshM9EIkEvkRo20gELBit9UQgQYiSHjJxBIIBNyuw1MikUjC19QQwbcIJBwOY9s2tm1jWRaWZREKhQiFQp7X8i0C+U4kNYa4RTgcBqCnp4etrS0AOjo6ACgrK/OlJjVE4Ish0WgUeDMD4Pj4mJOTEwDKy8v9KOkdNUTgiyHDw8MAbG5uArCzs+O7GQY1ROCpIeauMjs7C8Do6CgADQ0NXpbxIWqIwEq0phrb/n+1l7m/vwegpaUFgMvLSwAuLi4AyMjI+NL5UyW2l9H2/xM8GUNubm4A2NvbA6C/vx/w3oxkUEMEnhhycHAAQFZWFgDj4+NevO0/oYYIPDFkcnIScDrZ/Px8L972n1BDBK4a8vT0BEBxcTEAVVVVKZ/j/PwcgP39fQAWFxcBaG9vB6Cvrw+AzMz0fBQ1RODqTNXMP4wh6+vrADQ3Nyc85vHxEYDBwUEA5ufnAXh+fv7r/qenpwBUVFQkXZfOVFPA1THErIIZkhlDjBlzc3Nxz9fV1QFQVFQEwPLyMgC7u7tAaoZ8hKuB1NTUxG3n5OQk3HdhYQFwLhHD9PQ04Ez3zWK0CSTd6CUjcNWQvLy8uMeVlRXA+bYN0WiUiYkJwBk819bWAGhqagKcRvDq6iru2Pr6+rTWrIYIXDXETNFbW1sBp8mzbRsAy3q74wWDQc7OzgAoLS0FoLGx8a1AMeE6PDyM2y4oKEhrzWqIwJPmbmxsDHB+hOrq6gKgra3tj33NwnNubm7c8w8PD4Bzl6msrATUENfxxJCSkhIAOjs7Aejt7QUcYzY2NhIea8aWkZERAO7u7gDY3t4GIDs7O621qiECTwwx3+LMzAwA1dXVgDOTjZ3BHh0dAY4ZU1NTALy8vADQ3d0dd450o4YIPPmhSnJ7ewvA0NAQAEtLS58es7q6CjhLB19ZENL2PwV8McRg+pZgMPi+eHR9fQ1AbW0tAAMDAwAUFha+FWxZ8jQpo4akgK+G+IUakgIaiEADEWggAg1EoIEINBCBBiLQQAQaiCCpHvqj/6j9b6ghAg1EkLDb/amoIQINRKCBCDQQwW/h4hEQOzs4jAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f4065ff28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10641005f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Representation\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f710a6160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f40688c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f4068cc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_number = vec_to_array(x_test[1013, :]).T\n",
    "\n",
    "plot_number(new_number)\n",
    "\n",
    "sns.heatmap(new_number.reshape((28, 28)), square=True)\n",
    "graph.show()\n",
    "\n",
    "print('Representation')\n",
    "sns.heatmap(encoder.predict(new_number))\n",
    "graph.show()\n",
    "\n",
    "print('')\n",
    "plot_number(autoencoder.predict(new_number))\n",
    "\n",
    "sns.heatmap(autoencoder.predict(new_number).reshape((28, 28)), square=True)\n",
    "graph.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f406b1710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c1bb080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10547d6048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70fc3e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1054749c50>"
      ]
     },
     "metadata": {},
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    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70e21390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f71098a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c0ae828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f710747b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f407a7588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEQAAABVCAYAAADwmUKMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAABbNJREFUeJztm11oVEcUx3/HD4zRGjEkNSCaogkoCNEkoNhKY4wUIpEKoSFarNXkoS30xaeKoAbfRIgILX2JNX4gUmkRBKFYRRsDMYhGDMaQGiT0IwHdgkkaIdOH3fHunu7Gu+69rrbzg7DZuzPnHs7+78yZM7NijMHhMS3bDrxuuIAoXEAULiAKFxCFC4jCBUQRSEBE5LiI/BSErTTvu11EAk2knEIUgQfEqkVEmkVkUET+EpEfRaQgrs1+EekXkUYRGRCR8Vifd3QbZftdETEiUiwi7wPtsesm9nc8U//DUkglUAXUAh8AZcBh1aYI+Az4CHgPeAv4QUTE5z06gC/ibBUBX2bmNszI1EAKJoBPjDF/A4jI1/zb2dxYm/5Ym4+B+0A18MLxyBgzISKR2P+/B+V4WArptcGIMQS8rdoM22AAGGP6gBFgRUg++SKsgEyo9wbw8yjEt5lM0mdmJk75IZuzTIGILLVvRKQUyAd6Y5f+BApFZHpcn9XKxkSs73QCIpsBGQXaRKRcRCqA74AevPHjZ6LjTIuILBWReuBzZePX2GudiBSIyNxMncpmQH4DvgW+B34BxoAPTaxiZYy5DzQBDcBd4FPgq3gDxpguoBX4BvgDOJapU5KNipmI7Ae2G2OWvfKbvwCXqSpcQBRZeWReZ1JmqpFI5H8Rqby8vIRcxz0yChcQha/FXV5eXth+vFIikUjKz5xCFC4gChcQhQuIwgVEEUoJcXR0FIDDh6Nl1AcPHgBw6tSppO2NMTQ0NACwfPlyAHJzcwFoamoCXt1M5xSiSLmWiU/d/X47T58+BaCurg6AK1euZOgeLFiwAIAzZ84AsGHDBgCmTXv57zI+D3Gp+wsIVCG3bt0CoKKiAoDCwkIArl+/DkB+fn7Kvh0dHQCcPXsWgNOnTwMwOTmZ0O7cuXMAbN261ZdPyXAKSYNAFdLX1wdATU0NAEVFRQB0dnam7ZidmdasWQPAkydPAJgzZw4A9+7dA2DRokVp23YKSYNA85DS0lIAbt++DcDNmzdf2lZJSQkA165dA2D9+vUAPH78GIAjR44kvAaFU4gilEx1/vz5AGzcuDFjWytWRLd6V61aBcDly5cBGBwcBKJZLoD/QwNT4xSiCHSWCRM7HtlZx/o9NDQEwMKFC33bcrNMGoR1YCZwbPY7e/ZswFtRP3r0CEhPIVPhFKJ4YxSSigsXLgBQWVkZiD2nEMUbr5Cgxg5LKAGxU+LVq1cTrnd1dQHe4q+srMy3ze7ubgDGx8cTrmdSBkiGe2QUgSpkeHgYgD179gBw8uRJwCsDPnv2DIC9e/cCMG/ePABycnI4evQoALW1tQDMmjUrwbbtYwtGtkxpi1BB4RSiCFQhdoywyiguLgbgzp07gFeEPnToEADHjnln5Orr6wFYtix67OzAgQMALF68GPDGEMvMmdEjq5kUm5PhFKIIVCFWGZbNmzcDXtnPvtoNLLs5VVNTw9jYGAD9/dHT3tu2bZvyXjt37gzI60ScQhShJmbl5eVJr9vnf+3atUC0LHjp0iUAdu3aBcDIyMiUtu1M1tsbPQl+8OBBAHbs2AFAa2vrS/nsFKIItEDU2NgIeJtNdsGVzjaE3f6srq723Qc8Zdh8Zu7c1MfeXYEoDQIdQ3bv3g14Cunp6QG8gvCSJUtS9rU5ysWLF5N+3tzcDEBBQUHC9dWro78Y2bJlC5B5sdkpRBGoQqqqqgDYt28fAC0tLQCcP38eSJ07nDhx4vlhGltMthlqe3s7AOvWrQOC225IhVOIIpRtCLsitduRDx8+9N1306ZNALS1tQHBF4DAzTJpEUqmalegN27cALzNJTvbaHJycp4fqlm5cmXUsRnZqW46hShC/RpsNWtgYCDM2wSKU4jCBUThAqJwAVG4gChcQBS+pt2pfqP2X8MpROEConA/dVc4hShcQBQuIAoXEMU/ZiGx6zg1y3cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f406ce438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f5009a3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f406865f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f71043a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f40739550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f40758d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70e9cc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f247dbc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70ecf6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70efd828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Test set fits!\n",
    "for i in range(10):\n",
    "    number = vec_to_array(x_test[i, :]).T\n",
    "\n",
    "    plot_number(number, 'Input')\n",
    "    plot_number(autoencoder.predict(number), 'Output')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predicting Numbers\n",
    "\n",
    "I'm going to use the representations as the features for predicting which number is being represented."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(37800, 100) (4200, 100)\n"
     ]
    }
   ],
   "source": [
    "# L stands for latent representation\n",
    "l_train, l_test = [encoder.predict(data) for data in (x_train, x_test)]\n",
    "\n",
    "print(l_train.shape, l_test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 5.21 s, sys: 1.44 s, total: 6.65 s\n",
      "Wall time: 57.9 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "logit = LogisticRegressionCV(Cs=25, cv=2, penalty='l2', n_jobs=-1, multi_class='multinomial')\n",
    "logit.fit(l_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 7h 3min 36s, sys: 212 ms, total: 7h 3min 36s\n",
      "Wall time: 9min\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "gbm = XGBClassifier(n_estimators=4000, n_jobs=cpu_count())\n",
    "gbm.fit(l_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raw = 0.9130952380952381\n",
      "XGB = 0.9642857142857143\n"
     ]
    }
   ],
   "source": [
    "# Scores\n",
    "print(f'Raw = {logit.score(l_test, y_test)}')\n",
    "print(f'XGB = {gbm.score(l_test, y_test)}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c14d940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70e817b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10547d6978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f406ce9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f406b6f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105f2dd978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f5007ff28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f406c8198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f40794cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0fc467cf28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f4074af28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70ef8a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0fc4667eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0fc4669fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c1c0e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f247b9048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70f42e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70f324e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c706e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c68dcf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70edf1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c6f4588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c0c6438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10546c3e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f50068eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAATMAAAAwCAYAAAB9u51EAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAB1VJREFUeJzt3X2MVFcZx/Hvw/KqtJalC7JQ+yItKlWgRWvfQUIjxdhImwaqViXEYGqiTYzFvlilia7xD/6xsVRYm5pKa6x9waQRbAu1L1BxW9puWoHCapddStlZdpbuwrKzj3+cu3fXmTszu3tLjJPfJ5nszHPPvXN2ZvbZc+4594y5OyIi/+9G/a8rICLyQVAyE5GKoGQmIhVByUxEKoKSmYhUBCUzEakISmYickqYWb2ZHTazNwbFfmlmb5nZa2b2mJmdUWTfJjN73cxeNbNdQ3k+JTMROVUeAL6YF9sKXOjunwH2AD8qsf9Cd5/r7vOH8mRKZiJySrj7c0AmL7bF3XujhzuAGR/U840utfGZqTc6wDjri2NXZ14KtZjy2Ti2xroB+N7J6jj2lcxzADw16Yo4tqT9eQDWT1kYx25Y1ApA3fapcewdPw7Aw607C+r01drPx/ev6p0AwNLzmuPYpqbw2qxcdCiOrXh6LABbDu0uON7d0xbE93/auq1ge8dtlwPw3ub2OFazNLSMF/72cBxrOLKvYN/f1ITf82u718axzA0rAZj+4t449sr0iwAwG7gaY27zKwXHa6gN5T7+zYlxbOevcwBUjz8ex/6ROx2A83tPxLE5S0L9Jz/0ZhxrmjcLgH1Nk+PYy+PHAXB767MFz7+9+tL4fv/nAOCP1VcDcM0PPhTH6n4VPhOzeiyOzZsQ6rAuN1Bu3bJQx3c298axXC78j/1Fbmwc2xR9FjbUDHx2rrssvO81Twy8lkn6P2831Z0dx759x5v/dVyA/pqWuyZm3dRwvFvfHXiNOn4cYnduGPg9MpwEYMHJCXHsglx4n14fMz6OtUdNirsGvebvLp4JwLS/vh3HHj8j/C11jaqKY8vbtgFwz7SB16X/OI9G7wvA9ZntANxSe2Ucu7flb/H93p6DA2/UMPW0NDrA2NrZwz3GSuCRItsc2GLhj2K9u99f7mAlk5mISDmePRLu1A59HzO7A+gFHipS5HJ3bzGzKcBWM3sraukVpW6miKTi2cN49nBB3MzqgV3AzEGx6mhA4E7gdCBxAABYbGZ7gReA/cDnytVDyUxEUvFsG55tS9r0APCNvNh6oAb4GGEwYE3+TmY2A/gJcAmwAFgCNJWrh7qZIpLO0SPFtnwHWASMM7Nm4G7gOuA9QiIbTRgAuM3MaoEN7n4tcD2h1fZsVOY1YEy5aqhlJiLpdBwNtzzuvoLQPWx09xnuvhHocvfp0ZSLC4nGW9y9JUpkEBLXOnef4+6zgc3A9HLVUMtMRFLx9sJEllLSqGjZhReVzEQkFe/IJsbNbBbwGHCumb0KnAccN7Np7t5qZtOATjPrAA5Eu/0J2Es4V9ZvBrCtXD2UzEQklb72Y4lxd/+nmV0L/Bm4GDgIPEEYFKiLfr4AnObuX+rfz8yqgZ+Z2aQodA2lrxQAdM5MRFLKtXWTa+suiJvZJuAlYBZwCOgEbmdg2sVi4PdR2flmtgHA3TPAPcDfo9vaKFaSWmYikkpvpi8xHg0AAPGcswZ3byOMcPbHFwCXAhuBFjOb7e6N7l4P1A+nHmqZiUgq3ZnRdGeS20XR6hdvADcDqxKKNAB/AD4MfAJ4aqT1UDITkVS6OsfS1Tm2VJE64Bl3n5uw7QrgHOB8YAUw1czOHEk91M0UkVTef79kIgNYBmwqsm058KC7u5n1ERpYZSfIJlEyE5FUjvaMK1fky4TpGWPc/X4zWw3g7vcBFwFXmtkaoBvYTZgg2zrceiiZiUgqWSuZRi5LWP3ivkHb/wX83N2fBzCzpxnCBNkkSmYikkp7VfKpdzM7C3jQzD4K9AH/JlzeNHgpnxxh3bI90eMZQMtI6qEBABFJ5WhVuCUYA9zl7p8EvkCY1Z9/ucCLwDFgHrAa2O/uw+5iglpmIpJS+6iSvcJ7zQxCrjkAHMg7Z7YD6AL2RT+/NdJ6KJmJSCod5BLj7r4fmANgZucQupc73X1rXtHTgGZC97LwUoIhUjITkVSy0XcdFGNmE4FHge+7e343swE4292PRddxPk6YczZsSmYiksrRvp6i28xsKWGGfzdwQUKRE4RBgouBNmCCmZ3p7kVXfCxGAwAikkq27wTZvhMFcTOrAh4mfANTLbDCzD6VV+xWoN3dZwJPApMISW3Y1DITkVQ6ckVPc60CJgLzgZcJa///0Mx2QDwAcDMw3sx2E1pvpfusJSiZiUgq2d6iyawN2OjuqwDM7OvAJXmTZvuAq9y9OSrzNjAZGHY3U8lMRFLpPNlVbNNQlr8e0RLZSXTOTIZs8LeYi/TL9nSR7UlMaM3AWYMeJ83uj8uY2WjgI0DZhRiTmPuIkqCISElRctpDWIzxIGHV2JvcvXFQmVuAT7v7ajNbDixz9xtH8nzqZorIKeHuvWb2XeAvQBVQ7+6NZrYW2OXuTxJWmP2dme0jtMiWj/T51DITkYqgc2YiUhGUzESkIiiZiUhFUDITkYqgZCYiFUHJTEQqgpKZiFQEJTMRqQj/AbZ0UnFPYLNxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f5003ccc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c04ffd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0fc46557b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f406aff60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f40680128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f40791cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c77d240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f406eadd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f4070d780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f7111ef60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70e77160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f71079eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f71096f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK0AAABVCAYAAAA7bmQ3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAACkxJREFUeJztnX+MVcUVxz9fkCKCLIVqsPzQUhSrNP4ArBAELS3ExoBSUw3UFiuCgtXY+APbBTYkLdKkC2loSgoaLEJt/1BjSwEp6bZBKSZlMYK6FFtg+SFaWXdZ+VVh+sfc67vv7dv37nu7LHv3nU9yk907M2fOnTn33DNzZ+6Tcw7DSBKdzrUChlEoZrRG4jCjNRKHGa2ROMxojcRhRmskjpIwWklVklacaz2SgqQ9kspzpF8myUka3ZZ6hcQyWkm9JS2U9LakY5LqJG2X9FNJA862kq3AZOBHxRaWdF1g+IclnZS0T9JSSb1aIHOppNOSHi6ibLmkPcXW3QrUApcAW4sVIOkxSW9JapDUKKla0vfjlD0vhvABwGbgU6ACeBM4AXwZmAQ8BjxSrPJtgXPuSAtFnARWAtVAHTAE+BXQD7ijUGGSLgC+C/wMmAH8soX6tSnOudPA+y0Uswd4AngPOANMBJ6RVO+cezmfAjkP4I/AIaBnM+mK/F0FrMhILwf2ZJy7G9iON/49QCXQPZI+GngNOBocbwITIuk/Bv6NN6YPgQ1AtxzXkKZXPvlxDvyNWldImUjZe4FtQFfgCDAqS55hwHqgAWgE3gC+BkwDXMZREZTZA5RnyFkBVEX+/2bQHkeAeuBvwA0ZZZrIyUi/LKh3dLF90ozcamBxvnw5Pa2k3sC3gLnOuYZseVyB74ElTQMWAw/jDac/sBS4CLhHUmfgFbxnmxYUGwocC8pPBuYAU/HG1hu4uYD6c8qPKWMAcCfw17hlMpgJrHTOnZT0At7bvh6RfzXw90DPr+ONazg+nPs9cCX++kcERRoLqLsH/inxJtAFeBRYL+ly59xHxVxMK/RJJ2A8/gk2P2+BPJZ/A/6OuiPj/Ov4hmoEdhbiafF38QMZecYE9Xw+OBxwczM6PQrsAroUcAd/plc++XnkvA4cD8q/QoGeJJBxDXAKuCjSxseAXpE8q/Cd36kZGU2eXnE9bZYynfAhz9RiPW0xfRKU+2pgQ58G7To9Trl8AzE1c/4u4FrgN0D3PDJSwqSLgEuByiD4bpTUCKwLsgx2ztUFDb1B0jpJcyQNiYj5A95D7JW0UtI9ki6Mq0MM+bm4C7ge+DZwObAsbr0RZgJ/ds59GOjzBvAffIwbMgzY5Jw7U4T8nEj6kqRVknZLasCHH2X4fimWYvukBm9HI/DjpUpJt+YrlM9o/4UPkq+KnnTO1TrnduPjoihnaGroXbLU90igbHhcgzeCtwL59+M7biMwFtghaWaQdgD/ePwB8AEwF6gpZBYjl/w85Wqdc+84514M6v+epCvj1iupO/4ROlHSp+EBfAUfIqRVF1duhHztD/AnYCAwG7gR3/4fAJ8roj6g+D5xzp1yzu12zlU75xYBvyNGeJDTaJ0fda8DfiipLIb+HwBfzDh3fUTeYfx0yZBA2czjRCTvDudcpXPuVuAZIp3qnDvpnFvvnHsC/4i5ALg9hn7Ra2tWfkzCtutaQJm7gdP4mzR6094EXC3pxiDfP4FvBLFeNk4BnbOcz9b+14V/SOqDd0BPO+c2OOfexg+GLy7gGrLSGn2Cb9O87Zl3yguYhR8wVUuqwI/6G/FB8234Tgj5C/BrSd/Bj47vxHfIx5E8P8FPbXwMvAz8D+9pbnXOzZQ0GLgfP2tRi++EmwJ5SLovuLg3ArnjgAuBt2NcC/nkN1NmelDXTnwnDwUW4Ue7b8WpN2Am8JJzrkkZSa/hb5x/AD/Hz4GulvQLfMx5PbDfObcFH070lTQS/zQ85pw7hm//WZJeAvYCD+Af++ETsQ4/sr9f0ntAn6Cu4wVcQxOK6RNJlcBL+D7ojh/wT8NPg+UmZsD8BXwnvYO/wOOBQouByyL5ugBL8Hf8x/hR6gKaTnndDmzBD0Aa8DfCvCDtEuBFYD9++uQgsBwoC9In4wdEdUH5HcB9efSvIjUQyym/mfL34g20IaizBnga6JOR77Pppywyrg3Ss06t4R/Xn0Su8wa8EX6Cn5bbSjA1FbTzGrwxRqe8LsQP4uqCPqig6ZTXWFJz7TX4+Hx3VG8KH4gV0ycv4G+sk8B/8Y5xShx7VCDAaCGSBuE7/ybn3GvnWp+OTEmsPWgjbgN+awZ79jFPayQO87RG4ogze9BhqK+v7/CPlbKysuZeCHUYzNMaicOM1kgcJRUeRCkri/OCLxnU19efaxXaFPO0RuIwozUShxmtkTjMaI3EYUZrJA4zWiNxmNEaiaNk52nbglOnTgHw4IMPAvDss88CMGnSJADGjh2bln/y5MkADBjgd6l06mQ+JRvWKkbiKKmlidEFM2frjdjx437nyvPPP8+cOXMAqKurS8sTtrmUfW3LvHnzAJg7dy4AnTtn2w6WIvpGzBbMGEY7xDxtCzlw4AAAS5YsAWDNmjUAHDp0qEnePn36AHDxxX7zaxiz7t+/P9QvLf+uXbsAGDx4cE4dzNMaRjvHZg+KJPSwo0f7T7Tu3bu3SZ5hw4YBsGjRIgCuusp/86Rv374AnD7td99Pnz4dgOeee+4satxxME9rJA7ztEUSxrCZHjaMW2fMmEFFRQUAXbqkf5nozBn/ia7KykqgqYedMmUKAP37929dpTsI5mmNxGGetkhmz54NwPvv+w9iX3qp/+jgQw89BKTi1ihHjvivEy1fvhyAp556Ki196NChAKxY4X8e4vzzz29ttTsE5mmNxGHztG3ARx/5D2yHMe7SpUuB1BuxcePGAbBw4UIAhg8fXpB8m6c1jHaOxbQt5N133wWgtrYWgGXLlqWdh1Qse/jwYQDOO883e7i24MknnwSga9dCPnVbupinNRKHxbRFEq7c6tevHwAnTpzIlT2NHj16ANDQkPUHgwqm1GJaCw+KpLq6GijMWI3WwcIDI3FYeNBCtm71Pw+7Y8eOJmlTp04F4NVXXwVS22zCgdjOnTsBuOKKK4qqe9WqVQBMnDjxs3OlEB6YpzUSh3naNiQctB08eBBIbWDct29fi+SW2kDMPK2ROGz2ICbhEyl8URBOWxXyQmDBggVAatG3URzmaY3EYZ42JlVVVUBqccstt9wCpJYZDho0KK+M1atXp/0/cODAVtSwdDBPayQO87QxmTVrVtr/4RaacDt4Lo4ePQqk5nS7desGwNq1a1tTxZLBPK2ROMzTxmTChAkA1NTUAPD4448DqVmEXIRvwsJPJoVlOtKPlbQl5mmNxGGeNibhxsWQ+fPnAzBixAgAevbsmZbe0NDAypUrAdi8eXNaWqHbaYx0zNMaicPWHsQkXLDdq1evtPPhlpnw80ghFRUVbNmyJe3cyJEjAdi0aRPQelvEbe2BYbRzzNPGJGyncJvN+PHjAdi2bVvesqNGjQJg48aNQGqetrUwT2sY7RzztEXS2NgIwJgxYwDYvn17kzzl5eVA6vNHre1hQ8zTGkY7xzxtB8A8rWG0c8xojcRhRmskDjNaI3GU7IKZzN/sMpKDeVojcZjRGomjpOZpjY6BeVojcZjRGonDjNZIHGa0RuL4P4hlwFSKmhu8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f7111bf60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c0c6828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f406b6128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10641e87f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1054714dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f5003f048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK0AAABVCAYAAAA7bmQ3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAChtJREFUeJztnXlsFdcVh79jcKEsNjVBNAiKQYkoNFVQ0kJYwpooSoVKoVWaKiR1iqjZGtaisISaIkANNIBICKVUQo2gtH80JUYsChG0EjiAQkyhgFtaTCEBCvUGNk6Juf3jzvgtfsu8Bdvjdz5pJHuWc+/ce+Z3zz0zb0aMMSiKn8hq6QooSqKo0yq+Q51W8R3qtIrvUKdVfIc6reI7MsJpReSwiGxr6Xr4BREpF5FlMbbni4gRkZHNWS8XT04rInkiskZEzopInYhUikipiKwSkT73u5JpYDIwPx2GRKSniFxzOq13CnbeFJEGEXkliWOXiUh5smWngcvAg8CxdBgTkR867XnQy/5xndZxyo+B54A1wBPAUGAx0B1YmHx1mwdjTIUxpiZVOyKSBewAjqdopxMwBVgN/DjVejU3xpgGY8w1Y8zdVG2JyCCsX/0lkQrEXIBi4CqQE2W7BP19GNgWtn0ZUB627nmgFKgHyoE3gM5B20cCR4BbznIKeCZo+xLgX8BnwA3gAPDFGOcQUq949mPY+RmwDxgLGKB3vGOi2HkZOAl0ACqA4RH2eRzYD9QAt7EXylCgwCk7eClyjikHloXZ2QYcDvr/aac9KoBq4M/AkLBjmtgJ257vlDsy2T5xjukEnAF+AGwHDnppv/aRHNlFRPKAbwGvRVMqk+B9YBEpANYDr2AdpzfwJtADeFFE2gHvOSdR4Bz2CFDnHD8ZeBV4AetsecCYBMqPaT/GcWOBacBjwCCv5UWhENhujPlMRHZh1fZoUFlfwyrPe8A4rHN9Azsy/h74Kvb8v+kccjuBsrsAb2HbLhuYB+wXkYeNMf9N5mRS6JO3gGPGmN+JyDOeC4xzJQzBXlGTwtYfxTbUbeBviSgt9iqeHrbPKKecLzmLAcZEqdM84O9AdgLK1livePajHN8T+AR42vl/DEkqLfAo8D+gR1Ab1wHdgvZ5B9v5WVFsNBm9vCpthGOygErghWSVNsk+eQk4hzPCkoDSxotpJcr67wODga1A5zg2AsZEegB9gTdE5La7YIdcgIeMMZVOQx8QkX0i8qqIDAgy8wesQlwSke0i8qKIdPVaBw/2I7ED+K0x5n2v5cSgENhrjLnh1Oc4cBEb47o8DnxgjLmXhvJCEJF+IvKOiFwQkRps+JGL7ZdkSahPnPZeDzxvjKlNtLB4TvsP4B5hw6Ex5rIx5gI2LgrmHk0dPTtCeXOwTu8ujwIPA6cd+9OwHfc+MBo4IyKFzrZPsMPjj4D/AK8BZYlkMWLZj8J44Kci8rmIfA584KwvF5FfeS1XRDpjh9Bvu7YcewNpOiFL5vG7eO0PsAf4CjALO6kejG3HLyRRHpBUnwzDhhAfBbXBS8A45/8R8QqMJ+N7gGtAbrxhCtgF7Avbpzhsn38D6xIcUrcAH0XZ1gGoAn7iJTxI1L6z/ZGw5WWsU40HeiVwHlOxF/rXw+yNABqAJzyGB4uAyxHWfwi8HbburzjhATbbY4Bng7b3xjp7UbLhQaJ9AnSL0KZ/AkqcvzvFaseYEzGHmdgJ08ciUoSd9d8GBgATnMZ2OQi8LSLPYWfH3wOedE7AZSnwGxGpcip6F6s0zxpjCkXkIeyEpxibD+zl2DgJICJTsYp93LE7HugKnPVwLsSzHwljzJkwGw84f5YZYz71Uq5DIfCuMeZ0hHodwarth8Dr2BzoDhH5JTbmfAy4YowpwYYTXxaRYdjRsM4YU4dt/5ki8i5wCZiOHfbdEbESO7OfJiL/xDrx68CdBM6hCYn2iTGmilCfwPGHLuFtHRGPCvEA8Ats4HzHWc5i45L8oP2ygQ3YIaIKOzv8OU1TXt/BXlV12JiqFFjubHsQ+CNwBZs++RT4NY7SY28UHMV2QB02ZTI1Tv0PE5iIxbTvsT3GEGEiRlD6KcIxg53tEVNr2OG6Nug8h2CdsBabljuGk5py2nkn1hmDU15dsSpd6fRBEU1TXqOxKl4PlAHfBS6QgtIm0ycRbG7H40RMnAOUFBGR/tjOf9IYc6Sl69OWyYhnD5qJCdgMgzrsfUaVVvEdqrSK7/CSPWgzVFdXt/lhJTc3N9oNoTaDKq3iO9RpFd+RUeFBMLm5uS1dhbRRXV3d0lVoVlRpFd+hTqv4DnVaxXeo0yq+Q51W8R3qtIrvUKdVfEfG5mnvF27OtKGhgby8vJRsNTTY5+tXr14NwPLlywHI9IecVGkV35FRjyYGPzCT7jtiZ8/aX5aMGjUKgJqaGmbNmgXAmjVrAOjYsWNCNquq7C9SwhX73r3QH+kG3xHTB2YUpRWiMW2ayM62v9SurKwEbNy5ceNGAObOnQtA377eXi3gKum8efNC1i9c2Opfm9YsqNIqvkNj2jQzYcIEAPbu3du47uLFi4B3pS0uLgZg4sSJIetv3LgBQPfu3UPWa0yrKK0cjWlTxI0/V6xYAcDRo40vP2xUxC5duniyVVdnX9y4efPmkPUzZ84EICcnJ7XKthFUaRXfoUqbIO4c4OrVqwAUFRUBsG1b6CcdcnJyKCkpAZrGoNFYsmQJAAcOHACgX79+AGzYsAGA9u21u0CVVvEheul6xFXYY8fstzGGDx8ecb8pU+xrZletWkWfPt7ePnrz5k0A9uzZE7J+9uzZgCpsOKq0iu/QPG0cysrKgEB2YNeuXSHb27VrBwRyq2PHjgWgQ4cOnus1aJB9Z/X58+cBGDhwIACnT9s3gmZlxdYWzdMqSitHg6Uo3Lp1C4DJkycDcO7cOSCgevPn22/pLV26FEjsDpub2125ciUQUFg3dt20aVNIWUoo6rRRWLRoERBwVhE76rqprYKCgqRtnzhxAgiEHC5bt24FYNy4cUnbzgT0UlZ8hyptFLZs2QIEFHb06NFAcgrrPq546tQpIPDzmXCuXLkCQHl5OQD5+fkJl5UJqNIqvkNTXlHo3Nl+0+/OndAPvwwYYL+T5z7EEgs3DeY+ROM+EBMPN102ffp0ANavXx9zf015KUorR2PaKLhpqLVr1wKBrIF7s2HOnDlJ2+7WrRsAI0bE/jBhfX190mW0ZVRpFd+hMa1Hrl+/DsChQ4cAOHky6gceARuP7t69G4AFCxaEbFu8eDFgH6pJBxrTKkorR5X2PlFfX0/Xrvbr8e7rjdzbszNmzADSd5tWlVZRWjmaPUgztbW1AOzcubNRYXv16gXApEmTAH0QJlW09RTfoUqbZkpLSwEoLCxsXOe+uMNVXCU1VGkV36FKmybcPK77w8asrCyeeuopAPr3799i9WqLqNIqvkOVNk2sW7cOgEuXLgEwbNgw9u/f35JVarOo0iq+Q++Ipcjdu3cB6NmzJxB45XxJSQlDhw5NSxnx0DtiitLK0Zg2RdzX1ldUVLRwTTIHVVrFd6jTKr5DnVbxHeq0iu/I2IlYcJpI8ReqtIrvUKdVfEdG3RFT2gaqtIrvUKdVfIc6reI71GkV3/F/r22zBTp3rYcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c044f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70f88470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0fc46daf28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1054774160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c1d9cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1054795198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0fc4664f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0fc4671ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f710a8c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAATMAAAAuCAYAAABEZ/6vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAABqVJREFUeJzt3W2MXFUdx/Hvv7stbW3BXdbSboUSoDVUBaVEwEZcAhQCjRhDcAtoY2xMCYgSEiu+KKZGRfCFxje8kFVKRBSIQlCiTZSnKKUPtEoVKQL2YbduuzM7M9BlZx/+vjh37kx37szO7hWLk98nmcyd/zn33DO7M/+c+3DumLsjIvL/bsbx7oCIyH+DkpmINAUlMxFpCkpmItIUlMxEpCkomYlIU1AyE5F3hJn1mFm/mb1UEWs3sy1mtjd6bqux7tqozl4zW9vQ9updZ3b3khsd4JLRt+LYRYdfACD/7Svi2Hn3/BWAy+aeEcfu7X0OgLsWXhLH7jj0RwD+suTcOPbeU4YAOPGyhXGsu6cAwJOHXqzq01Dvs/Hy2hW3h3ZnjMaxgaOzAWif83Yce2X4xNDuwFNV7W1c1BUvf7c/9HlkrNzeI+2fBGDb7PI6V75dBOAWeuPYnsy/qtq+M2r7yxeW69ncFgBO/tnf49iGzrCNx4Zei2MvZ/dXtffi4vMAOK1rKI4d2RbaGxuzOPbF/AgAD3aW1/1Jf/j7bup7Ko5l150DwI5H58WxBfOOAnDO/l1V2/9GZ1e8/J3ecjs/7Qj/48GWct3dLcMAtFLu1+b+8NnZvnh5HDv9+6HNG259Lo59hPkA3H5jMY6ddM+fAPh928o4lrdWAK7NPF3V10qlz+pnf9Qfx/YVM0Dy/20yp87vAGB/4Ugce6LtEwB8fPVAHNv6RDsAf57dGsfOjt7Svpnlv8ullgfg/L4dcax70QUAPNS3NY7d2hm2sXFl+X10PPwPAL5X8T3bEH3PlrefFsf+ltl3TD8BVmfL36XR4sFyh6ZopH+vA8xcsPSYNszsYuBNYLO7fyiK3Q1k3P0uM/s60ObuGyas1w5sB84HHNgBrHD3bL1+aGQmIqmM5w4znjtcFXf3Z4DMhPA1wP3R8v3ApxOavALY4u6ZKIFtAa6crB+tk1UQEanHK0aoDTjF3fsA3L3PzBYk1FkMVO6aHIhidSmZiUgqnp9SMmtE0i7vpPMutZspIunkjoRHY/5tZosAouf+hDoHgFMrXr8fKg5Q16BkJiLp5LLhMYGZfQD4LXCmme0yszxwECidnVwL7DSzXFS+y8w2Ar8DVplZW3S2c1UUq0vJTERS8WwWzyaeaPwm0EY4nNVB2FW8DbjczPYClwMPAs8C64Dt7r7J3TPAt4Bt0aMUq0vHzEQkFc8VkuPua0rLZrYKuNPddwOXVsS7orrbCQmttG4P0DOVfmhkJiKp+GABH0xOaBW6gZ/XKLvIzHab2ZNm9sHp9kMjMxFJZWzgrbrlZjYL+BRwR0LxTmCJu79pZlcBvwaWTqcfSmYikspoZrRmmZm9ES3OAn5DuKq/UgH4YZTIjgLvMbMOd5/y9R7azRSRVIYHZjA8UDeV7AS+4u4TExnA9YSR2FLgB8DJwEBCvUlpZCYiqQzlZ9UrNqAL+EIcMFsP4O73AjcBS4BdwBBwCFgI9E21HxqZiUgqhcIJFAon1CoeB94A/mBmX4KQxKJEBjAIrHH3c939QuBVGpi6lEQjMxFJpTBcd2S20t17ozmYW8zs5WgCesm0pi4l0chMRFLJ+0zyPjOxzN17o+d+4FfAxyZUmdbUpSQamYlIKtmWlsS4mS0Dfgy8jzDamkM4RlbpdWCzmW0A5gJzS3fVmCqNzEQklcGWY2/MWaGNcDC/SNidnA/sM7P1pZMAwPOE+ZrzgWGS72/WEI3MRCSV7IzkQ1zuvhVYVnptZo8BiysO/pe85O6r0/ZDIzMRSSVn4+RsvG4dMzsd+CiwNaFY05lE5PjLUXsGAICZzQMeBb7q7vkJxZrOJCLvDoNerFlmZlcDvyRcELssocow4QTACsKV/3M0nUlEjov8eJH8eHVCM7MW4CHgF0AnsMbMlk+odhuQdfezgMcJJw00nUlE/vdyY0O1itYB8wiTy18gXKLxNTN7HuLpTJ8HZpvZbsLobWS6/VAyE5FUCrWT2QBwn7uvAzCzzwEXTDibOQ5c7O4Hojr/JEw2n/JuppKZiKSSG6l5P7NGpippOpOIvDsUikMUiomjs0amKsV1zKwVOInqHw5uiLlPKwmKiNQVJadXCPf8P0j4cZLr3X1PRZ2bgQ+7+3oz6wY+4+7XTWd72s0UkXeEu4+a2S2En4lrAXrcfY+ZbSL8EtPjwH3AA2b2KmFE1j3d7WlkJiJNQcfMRKQpKJmJSFNQMhORpqBkJiJNQclMRJqCkpmINAUlMxFpCkpmItIU/gPNaSJeNpOZFwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f710dfe10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK0AAABVCAYAAAA7bmQ3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAACC1JREFUeJztnW2MFVcZx39/XhQL242sBdfoggSyIipYlFYDqVGM1lTTRVM2KU3Qhq5WrS8xhioVYqLVJqIfakyUJhsJRv0gphoKEQk1obWbsK3pyqaACN0KCMiywFKQZR8/nFkY7+59v3dvz93nl0xy5+U888w5/3nmnGfmzsjMcJyYmFRrBxynWFy0TnS4aJ3ocNE60eGidaLDRetEx4QQraS9krbU2o9YkHRU0oYc6+dKMknLx9OvEQoSraSZkh6VdEDSJUn9kl6Q9D1Jb6u2kxVgFfD1UgtLapa0TdLfJQ1J2l2uQ5Iel3RN0kMllN0g6Wi5PpRBH9AMPFeqAUltkp6SdDI5AdYUWjavaBNRPg/cAzwK3A7cBjwMNAHfKM3t8cPMzprZ+TJMvB44C2wGKiHYm4A1wPeBB8q1N96Y2TUzO2lmV8swMwPoAr5QigM5J+APwAng5izrlfq9F9iSsX4DcDRjWTvwAnAZOEoQw/TU+uXAPuBCMv0N+Fhq/beAI8AV4DSwC3hDjmP4P7/y2c9TH53A7kK2zWHjs0A3N06GD46xzVJgJ3AeuJg08G3AWsAypk1JmaPAhgw7W4C9qfmPJvVxFhgAngaWZZQZZSdj/dxkv8tLbZMMewasKbT+pmSXc+gWAJ8AHskWqazI+8CS1gI/Bh4iCOetwOPALcB9kiYDTxLEsTYp9i7gUlJ+FbAeuJcgtpnAh4rYf07740QH0GlmVyT9mhBtn0n5uAj4S+Lnhwnieh/hyvgb4B2E439/UuRiEfueAfyUUHdTga8BOyUtMLP/lHIw5bZJseQULTCfUFG96YWSngHek8weM7NFRexzE/CwmW1N5o9I+hLwdKp/90bgSTM7lMwfSpWfA5wEdiaXp5cJUbtQbs5jv6pIWgzcCnwyWdQJ7JX0VTM7lyxbDxwG7jWz4UwfJV0ErpnZyWL3b2bbM/x5APg08HFgW7H2Esptk6LI16dVluWrgSXAz4Hphe5M0i2EA9ws6eLIBDyVbDLfzPoJl7RdSUd9vaTWlJnfEiLEMUmdku6T1FCoDwXYrzYdwA4zO5340wX8k9DHHWEp8OeUYCuGpLdL2irpsKTzhO5HI6FdSqWsNimWfKI9BAwD70wvNLM+MztM6BelGWa00KeOsb+vEEQ/Mi0GFgAvJvbXERruT8AdQI+kjmTdvwiXx88Bp4BHgJeKyWLksl9NJE0nXEI/lWQhhiQNAQsZPSAr5fG7fPUP8EegBfgiYVC9hFCPrythf0Bl2qQYcorWzM4SouCXJTUWYO8U8JaMZbem7P2bkC5pNbPDY0yXU9v2mNlmM7sTeIJUo5rZFTPbaWbfBN4N3ATcXYB/6WPLar+KtAPXCCdp+qRdASySdHuy3X5gpaRs7fNfYPIYy8eq//eO/JDURAhAPzCzXWZ2gDAYnlXa4dygEm1SKPn6tAAPEgZMz0vaROirXARagbsIjTDCbuBnku4hjI4/Q2iQc6ltvg08Iekc8HvgKiHS3GlmHZLmA+sIWYs+QiOsSOwh6X7CydaV2P0I0AAcKOSA89nPUW5J8nMmMGNk3syK6bt1ANvN7MUx7O8jnDh/BR4j5EC3SfoR0E84+V8xs2cJ3Yk3S/oA4Wp4ycwuEer/QUnbgWPA5wmX/ZErYj9hZL9O0j8IKcvHgFeLOIZRlNImySC/JbWoJanTs2b2cs4dFpiSeBPwQ8KA7NVkOkDIAsxNbTcV+AnhjD9HGKV+l9Epr7uBZwkj9vOEE+E7ybpm4HfAK4T0yXHgF0Bjsn4VYaTdn5TvAe7P4/9ekpRXPvt50jKjpjG22ZSl/JJk/ZipNcLlejB1nMsIIhwkpOWeI0lNJfX8K4IY0ymvBmBrUjenCIPezJTXHYQR/mXgJcIg7HDab4pMeZXYJmuz1GlnPj2qyIyVkwVJ8wiNv8LM9tXan3pmQjx7ME7cBfzSBVt9PNI60eGR1omOQrIHdcPAwEDdX1YaGxuz3RCqGzzSOtHhonWiY0J1D9I0NhZygy8OBgYGau3CuOKR1okOF60THS5aJzpctE50uGid6Jiw2YNqcebMGQBaW1tZvHgxAHv27KmlS3WHR1onOjzSVpiuri4A+vv7ker+jmpN8EjrRIdH2gqzY8cOIPwjZHBwEIChoSEApkzx6q4EHmmd6PBTv0pIut6/PX78OAAtLS25ijgF4pHWiQ4XrRMdLlonOly0VcL/MFo9XLROdHj2oEpIYunSpQA0NzfX2Jv6wiOtEx0eaavI/v37AThx4gTgedpK4ZHWiQ6PtOPAwYMHAY+0lcIjrRMdHmkrzOzZs0ct2707fHps5cqV4+1OXeKirTCrV68GYOPGjdeX9faGjwON3HDwh8PLw7sHTnRMqPfTpt+aWK3XIl24cAGAhQsXXn8kcYSrV8NXOSdPHusbH6WTfi2SvzXRcV6DuGgrTENDAw0NDcyaVfZXjpwsuGid6HDRVommpqZau1C3uGid6HDRVomOjtGf2u3u7qa7O+eHIZ0CcNE60eGiHUd6e3uv3x1zSsdF60SH3xGrEqdPnx718My8efMA6OnpAWDatGkV2ZffEXOc1zj+lFeVaGpqYtmyZcCN138eOXIEgL6+PgAWLFhQG+cixyOtEx0eaavEpEmTaG9vB25EWqcyeKR1osNFW0Xa2tpoa2urtRt1h4vWiQ7v01aROXPmADA8PFxjT+oLj7ROdLhonehw0TrR4aJ1osNF60SHi9aJjgmb8ko/zufEhUdaJzpctE50TKh/Ljj1gUdaJzpctE50uGid6HDROtHxPxK4nwqDnYx6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f71049f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c6ff7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c0dcba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70e53cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105f2d2f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105f379e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10546ffeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1054716cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f40690e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f710be080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f50095f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f5006b0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70ed0c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70eb47f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f4078df28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f4070cef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c6c7e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c6b5c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70fd8ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10547e9908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c1a6ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70f6ee80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f40762e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c195940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105471dcc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70f8a748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK0AAABVCAYAAAA7bmQ3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAACg1JREFUeJztnX9sVlcZxz8PAuN3sQPDEF0x4EAmJbJVWKEDjDGSadwmm2YQQOggmw4wxkxlgqAuzDEWnGEIEmAbTP8A4yYU0YBi2VbklyBmwEY3hoINPwql0AE9/vHc2/ft2/fHfS8vLbd9PslN23vu+XHPee73POfc03PFOYdhRIl2LV0Aw8gWM1ojcpjRGpHDjNaIHGa0RuQwozUiR5swWhHZLiIrW7ocUUFEKkVkbprwAhFxIjKqOcvlE8hoRSRfRJ4WkUMiUisiZ0Vkn4j8TEQ+caMLmQMeAL57PQmIyHQROeDd//siMl9EQj/0IvKCiFwTkSdCxJ0rIpVh884Bx4HbgLfCJiAivURkuYgcF5FLIlIhImOCxM1Y6Z5R7gUeAp4GRgCfB34A3Ap8L2zBmwvn3Bnn3Pmw8UWkFPgl8CxwJ/BtYCawMGR6XYCJwM+BR8OWq6Vwzl1zzp10zl0JE19EBNgIDAceBoYCfwLKROTOIAVIewCvAf8FeqQIl7jftwMrE8LnApUJ574B7AMuA5XAc0DXuPBRQDlwwTv2A1+KC/8h8C5QB1QBW4DOae6hUbkypZ8k/t+BFxPOzQEuxpc76AFMBfYAtwBngHuSXDMcKAPOAzVABSoWUwCXcMz34lQCcxPSWQlsj/v7i159nAGqgb8CRQlxmqSTEF7g5TsqTJsAA7z4IxLO7wfWZKq/9knsuAERyQfGA0+lUiqX5XtgEZkCLAGeQA2nH/AC0BuYJCIfAf4ArEYbCFTdar34DwBPAo94N5kPjMki/7Tpp6AT+oDFcwnoAtyFNnw2zABWO+fqRORVVG13xpVxCPA3r5zjUOO6C+0ZfwsMQu//bi9KTRZ5dwN+hdZdB/ThKxORgc6501neh1/ebNukk/czWZ2WZMwwgyIUoU/E/Qnnd6IVVQP8KxulRZ/imQnXlHj5fNQ7HDAmRZnmAIeBDlkoW0O5MqWfIv5CVJmKAQEGA2976XwzS5UtBD4EesfVcS3QM+6al9DGb5cijSa9V1ClTRKnHXAWeCSs0mbbJkB7VJX/CHzM+3sKUA/UZYqfyaeVFOcfBoYBvwa6ZkgjlphIb+B24DkRqfEPYLN3yQDn3FmvoreIyGYReVJE7ohL5neoQrwnIqtFZJKIdA9ahgDpJ+OnXr7bgCvADuBlL+xa0Lw9ZgCbnHNVXnkqgGOoj+szHPiLc64+y7QzIiL9ReQlETkqIudR9yMPbZewZNUmzrmrwP2owZ5CFfdR4BUC1Gcmoz2CWv9nEjI97pw7iqpPPPU0NfQOSfKbhRq9fxQCA4EDXvqlaMNtBe4FDorIDC/sBNo9fgv4H/AU8HY2sxjp0k9xfZ1zbibqDhSgI+fdXvA7QfMVka5oF/pVEbnqH6hyJw7Iwiy/y1T/AK8DnwQeRwfVw9B67BgiPyBcmzjn9jvn7gZ6AB93zt2D+viZ6zOAlL8OnATyMnVTwKvA5oRrXku45n3g2Sy71BeB3SnCbgHOAd8J4h5km36aOC+jXVzSLjxFnGnog/5Z1I/2j2JUYUa4YO7B94HjSc6/CSxLOPdPPPcAne1xwJfjwvuhxj4/rHsQpk2SxLkV9d1/kunatAMxj8fQAdNeEZmPjvprgDuA+2gs538GlonIQ+jo+OvAaO8GfH4E/EZEzgG/R7vbwV5FzhCRAUApauzHgb5eGnsARGQaqtgVXrpfALoDhwLcC5nSTxOnGHjDy2sa6iJ9xWXXhc8ANjrnDiTJoxxV2zeBZ9A50FdEZDHqc34O+MA59wbqTvQRkZFob1jrnKtF6/8xEdkIvIdOy91OrEc8i47sS0XkHdRQnkEHQKEJ0yYi8qB37buoLf0COOH9TE/Ap6AXsAj4t3eDl7wCLQEK4q7rADyPdhHn0FHqAppOeX0NNYBa1KfaB/zYC7sN2AB8gE6f/AdYgaf06IuCnWgD1AIHgWkZyr+d2EAsbfop4n8a+Ac6xVWD+rYlSa5rmH5KEjbMC086tYZ21xfj7rMINcKL6LTcW3hTU149r0ONMX7Kqzuq0me9NphP0ymve1EVv4wOJh8EjnIdShuyTR5HH6wP0SnVZUCvIPYoXgLGdSIin0Ibf7Rzrryly9OaaRNrD5qJ+4C1ZrA3HlNaI3KY0hqRI8jsQauhurq61XcreXl5qV4ItRpMaY3IYUZrRI425R7Ek5eX19JFyBnV1dUtXYRmxZTWiBxmtEbkMKM1IocZrRE5zGiNyGFGa0QOM1ojcrTZedrm5OrVqwBMmTIFgHXr1gEwc+ZMAJYuXQpA+/bWHEEwpTUiR5tamhi/YKY53ohVVVUBMHv2bADWr18PgG6wEqOmRrct6Ny5c6h84t+I2YIZw7gJMSfqBlFVVcWkSZMA2Lp1KwB9+/YFoLZWN7Npa2sGcoUprRE5TGlzjD9TMHv27AaF7devHwB79+4FYPLkyQBs2rQJgIqKCgCGDx8OQLdu3ZqvwBHElNaIHKa0OeL0ad1wcNasWYDOFAwePBiAHTt2ANC1q257VllZCeD//z9jx44FYO5c3Xx7wYIFzVPoiGJKa0QOU9rr5Px53ba3qKgIgGPHjgEwYMAAdu3aBUCXLl0A2LdvHwCHDuluQYnztRcuXLjxBW4FmNIakcOUNiRXrujnBvy3Xb6f2r9/fwDKy8sbFNZn9+7dpKNjx9C7bbYpTGmNyGFrD7LEn4ctLS0FYO3atUDTudj8/PwmcX2ftWfPnknT9tcqJIubDlt7YBg3OebTZsmlS7r/8Jo1awDo0EF3h9+yZQuQXiUXLVoExOZnfbZt25YxrhHDjDYgdXV1AEycqN/z6NRJvyo0b948AAYNGpQy7pEjRwBYsWJFo7hz5swBYNSoFvlaZ2Qx98CIHDYQC8iqVasAmD59OgDDhg0DYM+elJ9q4Nw5/dTEuHHjgNjLhZEjRwIxt+B6p7psIGYYNznm0wYkcRFLcXFx0uv8lwyrVq1iyZIlQGzRt4+v2vYyIRymtEbkMJ82IH369AHg1KlTQNPFLj5+fSYLHz16NABlZWVA+H9kTMR8WsO4yTGfNiC+H+pvsHHixAkgtuxw4MCBQGxBd2FhIVOnTm2UxuLFi4HcKWxbxZTWiBymtAEZP348AIcPHwZii1/8GQDfR752TT8VvHDhwoa4Q4YMAWDo0KHNU9hWjimtETlMabPEXzfg/0zEnz3YsGFDw7kJEyYANi+bK0xpjchhSptjDh482OgnQElJSUsVp1ViSmtEDlPaHLN8+XJA34gVFhYCsVVdRm4wpTUihyltjjh58iTQWGn9/0ywWYPcYkprRA5T2hxx+fLlRn/36NEj5Zpb4/owpTUihyltjigoKACgvr6+ZQvSBjClNSKHGa0ROcxojchhRmtEjjY7ELNveEUXU1ojcpjRGpGjTe17YLQOTGmNyGFGa0QOM1ojcpjRGpHj/wKUgVGS9CvWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105f238eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105f276908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0fc46ddf60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f500a24a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105476ce80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f71104748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70f20cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1054783240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f710a4da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAS0AAAAsCAYAAAAwyO7/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAABqBJREFUeJzt3WuMnFUdx/Hvfy8tbZUt7gqtFkqXFtNaS4u2kIiFJiRyE2KymgImFK2mia+0EokvCAFLSHxjpQRCSI3FxHhJMLUBjATX1ht2oXQtLalttcv2spfu7M4s2+3u7Px9cZ49O87M7lCfoJnk90kmO/M7Z+bMzE7+e55nzvOsuTsiIrWi7v/9BERELoaKlojUFBUtEakpKloiUlNUtESkpqhoiUhNaZip8dHF9zvA3YXhmK3r6QBg4IFPxmxgf/myiWWHDwNwdPmKqexIyE5/bmnMdhxfBMDd+fdiNm/OGADXdXXGrJAszXj5sptittW6APjl/Pkx259tBuBL7Vti1nbrkwC82vf3mI1P5AF4+vINMftm7+8BaKirj9nJG1sBmLvqQzHr/8MFADp6L4/ZvefaATCmDB/YFZ5719sx8yPhOTQ9/NJUv46dAOQeeiJmH2s/DkCdTf1dOf35JQB0vdUUs0IhjNjUNBqzfD7c565zvTG7Z961AGw/vTdmT10RXvv9d/bHrGdveJ9XHJ96zpPvfeeVq2O2uvtgvL63eR0Ae2ZdErMlyXO47wfXxOzg1vDaf9c4J2bffrAAwKHnLsTssqYRAP6cbYnZ5r7wuzn12anPznBfGO8TRw/FbPL9v665NWYbGxcDsGn5uzHreGshAF/I7ItZffJ7zxcmirLwOiYKhZi93boKgE/9c+rzdH1zeF77OnfG7OztXwdg9qX5mM1qCY9nc6c+Y2v3DAJwMtcTs0evuBmAbX1/ilnP1rUA1N20PmZXffkpAL7XtDZmD50N79UjC2+J2eNn2gH424LPTI17tiNez4+dKv7oXpTx/hMO0NjSWvYYZjYfeB5YCTjwVXf/S1G7AduBO4ARYJO7vznTeDMWLRGRagpDyR/HltZKzduBV9y9zcxmAXNL2m8HliWXG4Bnkp/TUtESkVQ8118xN7NLgfXAJgB3HwPGSrrdA+zysMr9r2Y238wWuvuZ6cbTPi0RScUHe/HB3kpNrUAf8GMzO2Bmz5vZvJI+HwfeLbrdnWTTUtESkXSyA+FSrgG4HnjG3dcA7wEPl/SptC9txmMLtXkoIukMnpuupTu5dJjZAeA8kCnpMxd4ycxOJLcXAKdnGk4zLRFJxYeG8KGh8tz9LGHT7/vAEaAFOFzS7QChkK0BtgBdM+3PAs20RCQlH8rO1Pw48CvCvq15wBNmtgXA3Z8FOoFbgWOEJQ8PVhtPRUtEUvGBGYvWN4ANwIeB77h7Bni2pM9HCUXtKNBDFdo8FJFUJjIjTGRGynIzuwvodfc3Zrj7b4Cr3X0V8Crwk2rjaaYlIqnk+8ena1oPbDazzSTfEprZT939K0V9hoFdZvZp4BywvNp4mmmJSCpjmTrGMhVLyXeBj7j7LOA2QoHaUdLnW0DG3ZcCf6R88WkZzbREJJXzQ40V82SV++SByw2ESZKb2WNAh7vvJuzzwswOEr5FrDcz8xnOA6+iJSKpDOdmT9tmZvXAG8BS4Gl3fx14vajLCHCbu3cn/Y8DzUDlY4PQ5qGIpJQbnU1utHLhcvcJd18NLALWmdnKki5aES8i/1uDXnnz0Mx2ApPfIK40s3bCvq1DSfstwLXAa2Y2AvwaaAIqHhM0STMtEUllsL6ewfr6Sk0vAm0AZjaHsIj0nZI+7wCvJbOxyeuaaYnIBydTsV4BcBL4GXANsB/4hbvvmdwRD2QJh/k0m9kxwgxrY7XxVLREJJWhusoTI3fvNLM7gT3uvrIofwTi5uENhIOq/0FYMX+i0mMVU9ESkVSGrFC9U2VvAovdfdjM7iDs01pW7U7apyUiqWTIkyE/XfPNwDIzO2Zm/3EuLXfPAuNm9nPgR8BVZram2ngqWiKSStbHyXr5oTzJGq3HgH8BK4B7zWxFUfsC4GuERaX3ATnKTxJYRpuHIpLKYOHCdE0vE07qVwecICwq3WZmv01OS9MGPAmcAVYDXwRerLYiXjMtEUklWxglWxit1PQc8IK7N7r7IsI+q1NJwcLddxBmYRvc/UZ33wcMEVbET0szLRFJJZsvPy1N4v2sdr/oFfGaaYlIKrnxEXLjFQtXN3Bl0e1FlJ//PfYxswa0Il5EPmi5sfPkxs5XatpP+OZwSfKPWjcCu0v67AYeSK638T5WxFuVdhGR/1qy/uqHQD2w0923FZ+axswuAV4g/GOLAWBjtQWmKloiUlO0eSgiNUVFS0RqioqWiNQUFS0RqSkqWiJSU1S0RKSmqGiJSE1R0RKRmvJvqp0sIyPgzFwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f710d9c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70f22d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70f540b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK0AAABVCAYAAAA7bmQ3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAACg1JREFUeJztnX2MVcUZh58fiAjULhVoSguULwOtEhGRQlU0LW1DMVbFVIJA16qFWFExxpAW27UJRUm6KkrAViOptlBi0NCmStoGuilSTdqVgCh0bZGVL/lYdrusLhWmf8w57Nm7995z7t0P9uy+T3LCcmfmnTkz7/mdmfd8yTmHYaSJHue6AYZRKOa0RuowpzVShzmtkTrMaY3UYU5rpI5u4bSStkh69ly3Iy1I2itpSZ704ZKcpKs7sl0hiZxW0kWSlknaJalBUo2ktyQtlTS0vRvZBtwMPFBsYUmXB45/WFKjpH2SnpbUvxU2n5Z0WtK9RZRdImlvsXW3AdXAYOCNYg1IelDSDkl1kuolVUr6XpKy5yUwPhT4G/AJUAZsBz4GRgHfAR4E7iu28R2Bc+54K000AmuASqAGGAOsBL4A3FSoMUl9gTnAz4EfACta2b4OxTl3GjjUSjN7gYeA94AzwA3Ac5JqnXOvxDUg7wb8HjgIfDpHuiJ/bwGezUhfAuzN+G0W8Bbe+fcC5UC/SPrVwFbgv8G2HfhWJP1HwL/xznQE2AT0ybMPzdoVZz/Jhj9QawopEyl7O/BPoDdwHPhqljxXAK8BdUA98CbwFaAUcBlbWVBmL7Akw86zwJbI/78R9MdxoBb4KzApo0wLOxnpw4N6ry52THLYrQQej8uXV2klXQR8G3jYOVeXLY8r8DqwpFLgceBevOMMAZ4GBgFzJfUENuKVrTQodinQEJS/GVgM3IZ3touA6wqoP6/9hDaGArcAm5OWyWA+sMY51yhpHV5tX4/YvwSoCNr5NbxzTcRP534HjMXv/5VBkfoC6v4U/iyxHegFLAJek3Sxc+5YMTvTBmPSA/gm/gz209gCMZ4/CX9E3ZTx++v4jqoH3i5EafFH8YKMPFODej4TbA64LkebFgF7gF4FHMFn2xVnP8bO68BHQfmNFKgkgY3LgFPAoEgfNwD9I3lewA9+jxw2Wpy9kiptljI98FOe24pV2mLGJCg3LvChT4J+vTNJubiFmHL8fiswHvgl0C/GRpMxaRDwRaA8mHzXS6oHXg2yjHbO1QQdvUnSq5IWSxoTMbMerxDvS1ojaa6kC5O2IYH9fNwKTABmAhcDq5PWG2E+8Efn3JGgPW8C/8HPcUOuAP7inDtThP28SBoh6QVJVZLq8NOPEvy4FEuxY7Ib70dX4tdL5ZKmxxWKc9p/4SfJX47+6Jyrds5V4edFUc7Q0tF7ZanvvqCx4XYZ3gl2BPbvwg/cn4BrgZ2S5gdp+/Gnx+8DHwIPA7sLiWLksx9Trto5945zbkNQ/zxJY5PWK6kf/hR6g6RPwg34En6K0Ky6pHYjxPU/wB+AYcAPgcn4/v8QOL+I+oDix8Q5d8o5V+Wcq3TOPQasJcH0IK/TOr/qfhVYKKkkQfs/BD6f8duEiL3D+HDJmKCxmdvHkbw7nXPlzrnpwHNEBtU51+ice8059xD+FNMXuDFB+6L7ltN+QsK+611AmVnAafxBGj1orwEukTQ5yPcPYFow18vGKaBnlt+z9f/l4R+SBuAF6FHn3Cbn3C78YvizBexDVtpiTPB9GtufsSEv4G78gqlSUhl+1V+PnzRfjx+EkD8DqyR9F786vgU/ICcieX6MD22cAF4B/odXmunOufmSRgN34aMW1fhBuCawh6Q7gp17M7D7deBCYFeCfSHOfo4ydwZ1vY0f5EuBx/Cr3R1J6g2YD7zsnGtRRtJW/IHzd2A5Pgb6G0m/wM85JwAfOOe24acTn5M0BX82bHDONeD7/25JLwPvAwvwp/3wjFiDX9nfJek9YEBQ10cF7EMLihkTSeXAy/gx6Idf8Jfiw2D5SThhHogfpHfwO/hR0KDHgeGRfL2AJ/BH/An8KvVntAx53Qhswy9A6vAHwk+CtMHABuADfPjkAPAroCRIvxm/IKoJyu8E7ohp/xaaFmJ57ecofzveQeuCOncDjwIDMvKdDT9lsTE+SM8aWsOfrk9G9nMS3glP4sNybxCEpoJ+/i3eGaMhrwvxi7iaYAzKaBnyupamWPtu/Py8KtpuCl+IFTMm6/AHViNwFC+Ms5P4owIDRiuRNBI/+Nc457ae6/Z0ZbrFvQcdxPXAr81h2x9TWiN1mNIaqSNJ9KDLUFtb2+VPKyUlJbkuCHUZTGmN1GFOa6SObjU9iFJSkuQCXzqora09103oUExpjdRhTmukDnNaI3WY0xqpw5zWSB3mtEbqMKc1Uke3jdMWSmNjIwBnzjR/bOvFF18EoK6u5cPK+/btA+Cpp54CCO8jRWp+pTWMGa9cuRKAmTNnAtC7dyEPRXQfTGmN1NGtbk2M3jCT9IrYkSNHAJg6dSoAe/bsaYeWNWfoUP884NKlSwGYNWsWAD17ZnssrPkVMbthxjA6ITanjaG8vBzoGIUNqa6uBmDevHlA0xx49uzZHdaGzowprZE6TGljeOAB/4bQfv38i3TefffdrPkWL14MwHnnJe/SMCIxYcKEvPni0rsbprRG6jCljWHQoEEALFmS88XYRXPq1Km86Y888ggAo0ePbvO604wprZE6TGk7kIqKCgCOH/dvKTp92r9RatGiRQAcPHgQgLKyMgBGjhwJ5I7PdldMaY3UYUrbRoRXFjPvTYhy//33A7B9+3YA+vf33xk5evRoMxs9epiW5MN6x0gdprRtRKiw55+f+93Effv2BeCZZ54BYNq0aUDTFa/Mu7+M7JjSGqnDlLaNaGiI/zjO8OHDAZgzx39e4YILLmjPJnVZzGnbiLVr18bm2bXLvxg7DHUZxWHTAyN12E3gbURNTQ0AAwcOzJln82b/rbyrrroKaLuLBnYTuGF0ckxp24iwH8MbuGfMmHF2Dhsydqz/5NiGDRsAGDMm6Tf38mNKaxidHFPadqKiooL169cDsGrVqmZp4Q3lpaWlAKxYsaJVdZnSGkYnx5S2HQn7NnwMffz48QAcPny4Wb577rkHgCeffLKoekxpDaOTY0rbgUycOBGAysrKZr+PGDECgKqqqqLsmtIaRifH7j2IYdu2bQAMGzYMaHrQMd8tiJkcO3YMgJMnT2ZND5XWSIYprZE6TGlj2LhxIwDLly8HYMGCBQAsXLgQaHq8O1TRMAZbVVXFunXrgKZXeIYPNIb06dMHgJdeeqnd2t8VMaU1UocpbYGsXr262b9TpkwB4MCBAwAMGTIEgK1bt+a0MW7cOKBJxbvSh/g6AlNaI3VYnDaG8PHu8AVzzz//fMH1jho1CoBly5YBMH36dKDpQcfWYnFaw+jkmNImJHxEfP/+/QBMnjwZgEOHDmXNP3fu3LMvkBs8eDBQWGy3EExpDaOTY9GDhISvKgo/4hEqrtHxmNIaqcOc1kgd5rRG6jCnNVJHt12IRcNERrowpTVShzmtkTq61RUxo2tgSmukDnNaI3WY0xqpw5zWSB3/B4hboezzSgJ3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10640e90b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f247c9ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105c719908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f105f28d278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70efbdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70f1be48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0fc46f8c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10547172b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for pos in range(50):\n",
    "    number = x_test[pos, :]\n",
    "    latent = vec_to_array(l_test[pos, :]).T\n",
    "    label = y_test.values[pos]\n",
    "    \n",
    "    plot_number(number, f'Guess is {gbm.predict(latent)[0]}, Actual is {label}')\n",
    "    \n",
    "    graph.figure(figsize=(5, .5))\n",
    "    sns.heatmap(latent)\n",
    "    graph.xticks([])\n",
    "    graph.yticks([])\n",
    "    graph.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f70efdb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph.figure(figsize=(12, 12))\n",
    "plot_confusion_matrix(y_test, gbm.predict(l_test))\n",
    "graph.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}