Handwriting Recognition.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model\n",
    "Multi layer CNN in Keras to classify\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/devops2/anaconda3/lib/python3.6/site-packages/tensorflow/python/framework/dtypes.py:516: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_qint8 = np.dtype([(\"qint8\", np.int8, 1)])\n",
      "/home/devops2/anaconda3/lib/python3.6/site-packages/tensorflow/python/framework/dtypes.py:517: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_quint8 = np.dtype([(\"quint8\", np.uint8, 1)])\n",
      "/home/devops2/anaconda3/lib/python3.6/site-packages/tensorflow/python/framework/dtypes.py:518: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_qint16 = np.dtype([(\"qint16\", np.int16, 1)])\n",
      "/home/devops2/anaconda3/lib/python3.6/site-packages/tensorflow/python/framework/dtypes.py:519: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_quint16 = np.dtype([(\"quint16\", np.uint16, 1)])\n",
      "/home/devops2/anaconda3/lib/python3.6/site-packages/tensorflow/python/framework/dtypes.py:520: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_qint32 = np.dtype([(\"qint32\", np.int32, 1)])\n",
      "/home/devops2/anaconda3/lib/python3.6/site-packages/tensorflow/python/framework/dtypes.py:525: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  np_resource = np.dtype([(\"resource\", np.ubyte, 1)])\n",
      "/home/devops2/anaconda3/lib/python3.6/site-packages/h5py/__init__.py:34: 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",
      "/home/devops2/anaconda3/lib/python3.6/site-packages/tensorboard/compat/tensorflow_stub/dtypes.py:541: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_qint8 = np.dtype([(\"qint8\", np.int8, 1)])\n",
      "/home/devops2/anaconda3/lib/python3.6/site-packages/tensorboard/compat/tensorflow_stub/dtypes.py:542: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_quint8 = np.dtype([(\"quint8\", np.uint8, 1)])\n",
      "/home/devops2/anaconda3/lib/python3.6/site-packages/tensorboard/compat/tensorflow_stub/dtypes.py:543: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_qint16 = np.dtype([(\"qint16\", np.int16, 1)])\n",
      "/home/devops2/anaconda3/lib/python3.6/site-packages/tensorboard/compat/tensorflow_stub/dtypes.py:544: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_quint16 = np.dtype([(\"quint16\", np.uint16, 1)])\n",
      "/home/devops2/anaconda3/lib/python3.6/site-packages/tensorboard/compat/tensorflow_stub/dtypes.py:545: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_qint32 = np.dtype([(\"qint32\", np.int32, 1)])\n",
      "/home/devops2/anaconda3/lib/python3.6/site-packages/tensorboard/compat/tensorflow_stub/dtypes.py:550: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  np_resource = np.dtype([(\"resource\", np.ubyte, 1)])\n",
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "# Importing * the libraries\n",
    "from __future__ import division\n",
    "import numpy as np\n",
    "import os,glob\n",
    "from PIL import Image\n",
    "from random import *\n",
    "import tensorflow as tf\n",
    "from tensorflow.keras.utils import to_categorical\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "from sklearn.model_selection import train_test_split\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.image as mpimg\n",
    "%matplotlib inline\n",
    "\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Dropout, Flatten, Lambda, ELU, Activation, BatchNormalization\n",
    "from keras.layers.convolutional import Convolution2D, Cropping2D, ZeroPadding2D, MaxPooling2D\n",
    "from keras.optimizers import SGD, Adam, RMSprop"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Model is built on handwriting from 50 different writers\n",
    "so the class will be 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "file = 'forms_for_parsing.txt'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "config = tf.ConfigProto()\n",
    "# config.gpu_options.allow_growth = True\n",
    "config.gpu_options.per_process_gpu_memory_fraction = 0.9\n",
    "session = tf.Session(config=config)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create sentance writer mapping\n",
    "# dictionary with form and writer mapping\n",
    "d = {}\n",
    "with open(file) as f:\n",
    "    for line in f:\n",
    "        key = line.split(' ')[0]\n",
    "        writer = line.split(' ')[1]\n",
    "        d[key] = writer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create array of file names and corresponding target writer names\n",
    "tmp = []\n",
    "target_list = []\n",
    "path_to_files = os.path.join('data_subset', '*')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'data_subset/*'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path_to_files"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for filename in sorted(glob.glob(path_to_files)):\n",
    "    tmp.append(filename)\n",
    "    image_name = filename.split('/')[-1]\n",
    "    file, ext = os.path.splitext(image_name)\n",
    "    parts = file.split('-')\n",
    "    form = parts[0] + '-' + parts[1]\n",
    "    for key in d:\n",
    "        if key == form:\n",
    "            target_list.append(str(d[form]))\n",
    "\n",
    "img_files = np.asarray(tmp)\n",
    "img_targets = np.asarray(target_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gMMjx48fRNI327dsrY+rkyry2bduyZMkSsrOzmTFjBrGxsTzxxBPq2i/tXMrM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\nGBgYnAeGMWVgYGBgYGBgcB78P6pwTvRPwSiWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f84c003dc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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27duH2WzG6/XKGZSvv/46derUwev1YrfbadeuHT6fT8Yv3X777fTo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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f84ac4f0748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JZJImVr2T1BvlpEmTyn1gN5vNcsuDYDBIVFQUffr0ITY2FoAGDRqgaRqLFi3i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\nUQH8P5BhWB9bduJMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f84ac4b27b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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IKrZrsHk+FIt6NvCa7373u2hvb8eRI0fwwgsvoKenR/aM+DhJ7tMejwcHDx5E\nTU0Npk6dimnTpkGv18NisSAQCMi1nxfOq5uvpKREy8jIQEdHh9DT06ZNw4kTJ+ByucSCoKDneXRX\nXnkllixZguzsbNhsNrjdbrS0tOD48eN48MEHY2IFbDYbpkyZgn379onSxQEOh8MoKCjAD37wA8yb\nNw8ZGRkwm81Dlg8gC/BRR24AZx4jww2LFHxtbS3uvfde7N27Nyb9Ozc3F4888ghGjx6N9vZ2dHR0\n4ODBgwAgdDkXuMPhwMKFC1FcXIxoNIoRI0ZI4UVuYqq7lP1Cdu6joLr5VAHOuABN0/D0009j3bp1\n6OzsFJpYp+svwUCXgsVikYxDp9OJxx9/HGPGjBHhxA2fliqQcPOdK2666Sbs2bNH5ibnPftbDdBW\njRPVRaxp/Ykdb7/9NtLS0mCxWOQkAbJeLL+wbds2/PKXvxQrkRv1nDlz8O1vfxvJyclSz4qKAN0Y\n3GDoQuOm1tvbi127duGhhx6SGlc9PT1nGAxAP+tEy1plNamskM0mW8OMwOTkZOTl5eGnP/0pnE4n\nkpKSYLVaJavQZDLJ2mxoaMD//M//wO12o729HTabDZMmTcJ9992HjIyMmEPGgTOP9BnMkudm7HK5\ncOzYMbz11lvYuXMnLBYLbrjhBixYsAAOhwMmk0ncN6rCpiq96meRSERYvJ07d+K5557D6dOn0dfX\nJ7KOWdNpaWlITk4W1xtjNkOhEDweD1wuV0yQv1rfju+jts9kMknZmmXLlmHs2LFnzM/ly5djx44d\nUlk/FAohJycH3//+97Fz505UVlais7NTYvZUBZ7zlvGfZrMZbrdb3Dc02Ox2Ozo7OwddHwyiDwQC\nOHToEOx2O8aMGQOTyYQdO3bgv//7v9HW1iZzhv/iZZ/KOKljS8bqsssuw89+9jOMGDEiRulqb2/H\n/fffjxMnTiAUCslZsQxPoduKhkR8AhZ/tlgssFqt+N3vfofMzEwkJSXh2LFjuP/+++VEDxrZBQUF\nuPfeezFr1ixYrVbZz/gOXq8XXq8X+/btQ2trK3bt2oXTp0+jp6dHsnzD4TBSU1PxyiuvIDU1NcZw\nOJsyFR8fRqOuu7sbe/bswYQJE5Cfny/yQV0vlFEej0cMqqNHj+LgwYPYt28famtr0dDQEDMvo9Eo\nbDabtPfee+/FLbfcIvIgXpH8LPB36eajlUChZjKZcMMNN8Dn8+G1117Dzp075VpaFcFgEBs2bEBT\nUxOKi4sxcuRI7N+/HydPnhRalhRlUlISZsyYgZtvvhk2mw1btmyRDYaWl8vlwuuvv45x48YhNTX1\nI9s8FI04FCVP65GTjALB5/OSnhzkAAAgAElEQVTB5XLFTD6gn5VKT09HamoqsrOzAQAXXXSRWOqq\nlRoKhZCamiqTSQ3G5b1UBo19/nGhWkq8fzAYhNfrxUsvvSRuGi4c+u15BE5fXx/MZnNM1WvVGmPm\nWIKZ+viYM2cOjh8/jq6uLlFcAMTQ5OxfBnwzWJ0HjasZtZwfVHQIn8+H6upqrFixQgpvGo1GZGZm\n4uKLL8aNN96ItLQ0YVjUkwsYoxdfx4rueZvNhtTUVFG42DZurMnJyTJnuCHr9XpYrVZh3BhzEl/8\nl24ct9uNtrY27Ny5E+Xl5cjMzIyJCYlGo+js7ER1dTXWrFmDU6dOyfNo4WuaFqNIxW+y7DcaW+xT\ntlHTNOzZswd/+ctfUFdXB6/XC6vVih07dqC0tBRlZWVnnMagxvuoiN+w6urq8L//+79oaWkBEJt9\nOH78eFx++eUoKysD0B/H1NTUJCwRx1Jli9mflGFczwaDAdOnT8fMmTMRDodxzTXXICMjIyYYWMWJ\nEyfQ09MjfREKhdDW1obf//73qK6ujolDVWUl54/KSA7l8lQzpePR09ODtWvXoqmpCYcOHYLP58Pl\nl1+O0tJSPP3002hvbz8jY5QKHPtDnU+qm1b9bMeOHTh06BDS0tIkFsztdmPXrl3Yv3+/tJ/3SklJ\nwbJly0TZ37dvnyR00FvDec11EwqFJEYtEomgpqYG9fX1MfF4JpMJHR0d+POf/4zk5GSMGTMGRqNR\n9g+v14uTJ0+itrYWzz77LPr6+iROkWygzWaD0WiUo6fiPSBDQd0DWXLlyJEj8Hg8qKurw5YtW1BX\nV4dbb70VVqtVmM5QKCQu0lAohJSUFElKmzp1KsrLy3H11Vfjww8/xG9/+1scOnRI1iTb7Pf74XK5\nsGbNGixevBgpKSmfu0F+3p+uvnBSUhKGDx+OlJQUZGZmor6+Hp2dnTJZuDl4PB7s2bMHH3zwgfiF\nNU1DT0+PsCCRSAQVFRW4+eabMXr0aFx//fU4ceIE6urqxPplodCDBw/iyJEjKC4uPueilvHK01CK\nlOrqUhUnBoPG3yu+CjUtLzJzZAsoZNVMHmDg4GV14nMxngujNhhUyhqAbMjNzc3o7e2VRe/3+2Gz\n2VBaWopLL70UW7ZsQXV1tbyXXq+H3W4XZYs4l2ypBAZHfn6+CBXOmUAgEHOGJP9nnAQNArJZXIM+\nn08SMTjX6Apoa2vDm2++iY6ODhnvaDSKCy64AFdeeSXS09MRCAREKFL5YeadaoFyDjJDye/3Izc3\nV9xPamwiNw9udgw2zsjIQEFBAfbu3SvV/WnZ043BZ/f19Yly8NRTT2H+/Pm48sorkZ2djeTkZLGK\nN2/ejOeffx5NTU3SPt7zxIkTOHnyJIYNG3aGCx6IPX2A6wUYUHaAfrm1atUq1NTUwOVyScDz7t27\nkZycLK5PbjJ0cxLxbDfhcrmwfv16dHR0yN/IQCcnJ+O73/0uhg8fLnGOOp0OxcXFWLlypWxKDFoO\nh8NIT0/Hrbfeivfeew979+4VmcN2+f1+TJ8+HQUFBZIFONTGxWO71PUeDodRXV0tSj3ZMSrRVKQt\nFgvMZjP8fr+8P8eKcUxmsxkjRowYcn2cOnUKb7zxBnp6eiR+c/Xq1UhKSkJDQ8MZIQt6ff8ZpxMn\nTsTRo0djjJO0tDTU1tZKW9QYNLfbLfMG6I+z2rVrF9auXSvzIhwOIyUlBdnZ2Zg/fz5uvPFGSaa4\n5JJL4Pf7cezYMfzlL3+RBA2uT44p28oQGR7HxDVLJfDEiRN44oknsGjRIkyfPl28PwcOHMCWLVvQ\n2toqfcj35j7KzHAaXz6fT8JqzsWtTddmTU0NnnjiCfh8PvT29sJqtaKlpUWMCypPnZ2dsNlsMW5w\nhrOQQTYYDCgvL8e//du/4f3338fu3buxYcMGmM1mKRWkaRpOnDiBbdu24YILLkBOTs6Q7TwfOO8x\nUw6HA16vF3q9HsnJycjJyUFSUhIyMzPx6quv4tChQ3j00Udx4sQJqYOiHqtCHzqz13p6elBUVISy\nsjL8+7//uxxXYTabcdlll+EPf/iDLEagfwDcbjeefvppjB07VjJNhkL8hvBRAdScIGTWuEDy8vIw\nZswYtLW1nbGgdTodkpOTZUMkxa2+O5/NDQuIZc3UdvEebM8nAa1XKq0ulwvr1q2Te3NBOp1OXHfd\ndSguLsaIESPw+OOPS4BwWloa8vLypIL7UGcink9X8xcd48aNw+WXXy7pxBSsV111FRYsWID29nY8\n8sgj6O7ulkBYYMCFS8YhHA7jK1/5CubPn49Zs2Zh6tSpImA7Ojrwq1/9SqxnNVvpO9/5DlJSUqDT\n9cfsARClTT0Pk1DjUFTGhS4oo9EocTxkQlTL+b777sPFF18swpZKot/vx4YNG1BbW4uamho0NDQI\nK0WG1GAwoK6uDi+//DJWr16NpUuX4qabbsKHH36I119/HVu2bJHsMibAMND35MmTWLNmDSZMmACz\n2SwnNahKE9vIz8js9Pb2Yv/+/XjmmWewfft2eS+GMXg8HlRWVsp7cmOkLFBdGkwlpxypra3Fk08+\nia1bt0pdPQC4+OKLcd111wkLp2Z0ce3ddtttePHFF4Uh47wIhUK44oorUFhYiBMnTqCvr0/eSdM0\nHD16FH6/H8nJybLJDoU777wT999/f0x/Uhlg/5lMJowaNQpz5szBwoULkZGRgaSkJGFTVYZk+/bt\neO6559Dd3Y1f/epXyM7ORlFR0ZDPX7duHZqbm2POOO3q6oop3xGNRlFeXo7Zs2ejvLwcZWVlsrnT\nnU3jYf/+/Th16hS2bt2KdevWYezYsbj00ktx2WWXoaSkBCaTCW63Gxs2bMBvfvMbeDwe6e+kpCT8\n7ne/Q1FRkbjt6LJKT09HJBJBSUkJZs+ejePHj+N3v/sdTp8+HXOKR3d3N7Kzs2E2mzFs2DCMHTsW\n1dXVknQSiUQkKeTAgQM4cOCAuMHVfuf6pIKpZhMynMbhcIhMARAz1qq3Ahgo56Np/Wff/uEPf8DR\no0fFdWg2m8W9SEOLylJeXp4oV3Tj63Q6iSFUFTi6aa+//npomoadO3fGxOB6PB6REQ8++CBKS0uH\nnBt/a5x3ZooDpcY5Af0uKqPRiOLiYkyfPh2tra3iV1d9+qTqo9H++ijTpk3DggULMGPGjBj3YXJy\nMubOnYs333xTLBI1hqOlpQWNjY3wer1ISkoasr3xm78aDzUYFc+JwUmsThhaXirTpKa1qsGlpHD7\n+vpkITIgk4HGqsCLt2LVNO9PAtUVxP5WWUNarz09PThw4ACKioqQmZmJkpIS7N+/X6htTdMk7iTe\nfThUHycwNMxmMxYsWIA9e/bg+PHj8vmxY8ewaNEiTJw4EbfffjveeOMN1NTUiHtWVeA5/5qamvDK\nK69g06ZNuP322zFq1ChkZGTg0KFDwiRw3ILBIEaOHCnKvcpMqD+rjCswwNzQ7auykllZWbDZbLjs\nssvQ1NSE6upq7Ny5U2rPce5w/jOzjGtkyZIl8Pv9OHXqFH7+85/D5XLB6/UCGGCZGJNhsViwceNG\nFBcX45VXXsGxY8diFHzVdUT2hjFFmtafMcmil+q1apYYMMBQrFy5UqrCUybx73TTkX3wer1y2gGN\nGPYdY+DC4TAOHDiADRs2oLKyUtpB1vdrX/saxo8fH/PuNDoZ5F1eXi6nJQSDQWRmZkoZCrPZjFGj\nRmH48OE4evRoTMxbNBpFa2urtElVIOOhhk6oGY2q/NU0Dffcc48o8E6nUwK5mdhAxTsjIwPjxo1D\ne3s7LrzwwkHZeRXqsUk6nQ4+ny9mzDgX77nnHowfPx4Oh0M+I2ukhk9Mnz5dFK7x48fjggsukPII\nZFoY50qlORKJwG63Y968eSgsLERqaqoY11x7XDdk5JxOpzBD0Wj/kU9k4jgPpkyZgu9973tYtWoV\nXn31Vdjtdng8Hvk7mV0GofOdOc9TU1MlGauvrw9Go1Fc6mazGaNHjxZjnXviUOPM/S0YDGL79u1o\nbm4WQ40Gt6YNlNRR50R8iAfJB44PlT31GpvNhjvuuEPWAUNJGMdJRfKfRpmigGQAMmsg0VUQiUSE\n6Th9+rQIVqZtUxjTDWAymXD33XcjPz9fJjeFlsPhwOjRozFp0iSpDq4GvTErTaXP4zEYxXkujA8n\nE4VHMBhEKBTC6dOnxXoFBtxpFCL8jP8z20jN9lNjpHidKqj4GQXDJ1FU1HgrWgq0jOKVyHA4jO3b\nt8NkMmHx4sWYNGkS9u3bB5vNJmcSst/VytjxG3IC5wabzYbc3FyUlJSgrq5OxqilpQX79u3DggUL\nMH/+fEyYMAHvvfce3nvvPRw7dkz6nvPCbDZL+nlvby/+8z//EyNHjkROTg56enrQ1dUlCj+FM8ef\na0h1BamBnyp1z2s4byjY6SIcMWIEJk2ahOLiYmRkZODAgQOyzlX6PxqNivuI7cnKykIgEEBqaiq+\n8Y1vYOvWrVLvjOuHrJPf70dTU5MEmqv1iOiypLFGI4KZqDT0AIgxp6ag63Q6WePt7e147LHH0N7e\nLqwgMHDEFI3DSKS/TExqaqq4OwHIfQHIWqer7bXXXsPmzZslO4yKxYwZMzBp0iQpKcD+571YINnh\ncKC0tBR79+6F1+sVlogyxuFwYO7cuTh27JhsaDykXd3YySAMhuTkZAAQxVd1MXNMbTab1Aijksw2\nkClU3WqlpaUYP348nE6nKJdDYfLkyVi7dq3MF9XlrBrBEyZMgN1uF1lKpo7slOqadjqdGD16NIqK\niqBpmiiwTGZ4//33JT6X756UlISrrrpKYnnUEwbU+zNO7+TJk3C73eJ2dzgcCIfDyMjIEPmekpKC\n8vJymEwmvPXWW/J8gu/JdphMJtjtdjgcDgSDQSxbtgxOpxPNzc1YuXKlKD9cbxUVFcIQcr5yHg4W\n66tpGjweD44cOSJGC93uVNC4ZuLd/iqby35W9x0aVJzDBoMBJSUl+N73vof3338fjz32mBgplEf7\n9+/HjTfeOOTc+FvjvO5mFOaciAxEozDhwho+fDjuvPNOaJqGbdu2iTXEeiNOpxPp6emoqKjAhAkT\nxMequhG8Xi+cTicuuugibNiwQf6mpoZu374dN9xww5Dt/biKSLzyxYXC9E1aQVzQFHis70OhBUA+\nj3czxhdVU5+pPttut0uMwscFFR/VitLpdDFp5oRer0djYyPWrFmDwsJCOBwOlJSUoLe3FzNnzsTk\nyZNlUbAtvOdgfZbA2UFlhJXtOW96enrw1ltvobS0VAoNZmVlIT8/H4888ogoxWoWEDcruhPcbrfM\nO9U65MZEVwitdz6fhgOv5YahKlOqe4ACMj09HWPGjEFmZqYEwHLTZzsZW8XnAoiJsWGdqjlz5mDU\nqFEYNWoUnnnmGQADm0tSUhK8Xq/Euqhp/kajEZMnT8b7778vcoFyioqmxWKRvlDP81RjCru6uuBy\nufDOO++gu7s7hi3mz9wUqLT19fUhIyND+pv9RCWA8V8Min/77bdl86SSdNFFF+G2224Tg5TuQfa7\nKk+Sk5Mxbtw4jBgxQpQWm80mCS1OpxOzZ8/GE088IW0mc3b8+HG5nxpPGY/09HRhgthfPT09MUpE\nfn4+UlNT4XA4ROapcZ6qYq5urByvsxmy48aNk7ZTMSEzS+UQ6Hdh0Q3JMaEnQXW1cq8ig0mXrDqv\n33jjjZjkDYPBgKKiIonh4b3UsjBUqtk/hw8fFjewzWZDKBRCWlpazFmbTLYYOXIkRo4cierqajEs\nqFBQuQD6y1dcc801yMzMhN/vR0VFBQCgqqoqJlyD2ZNqEU/OcRoP6p7FeREKhSRble8UX/YhJSVF\nFEpVoQUGFKn4cgYcK44h+9Rut6OwsBBWqxW//e1v4fF4RPkDgKNHjw45L84HzqsypQbAcWNWN2sK\n3JSUFIwaNQoPP/wwTp8+jba2NjQ3N8PlciEnJweXXXaZdK4aoK0GTnLSL168GI8++qj4itX4q7fe\negutra3Iysr62O8Sr8gM9hknDheq0+mM+Zy1p2pqaqRuCzMV6F9XFzKtDk70QCAwZNkDuhU/iaLC\nuj7cbA0GA1JSUrBw4UI899xzEmSqZo24XC78/Oc/F8XpoYcewoQJE+B0OkVokE3k5ns2VjCBoWEy\nmXDdddfhxRdflGBMAKivr8ePf/xjPPzwwxg2bBjsdjtmzpwp5UQ4N9X1wrg+VelWLWiuTwpfu90u\n81etwca5SWWP8Smqq4nf4Yb505/+VIyq1tZW7N27Nya7ymQyIS8vTxhnbkhsl1oKgMHlo0ePhsFg\nwEsvvYT29nYxSNSjbKgwzp49G7fccgtMJhO2bt0qjJF6f5fLBZvNhkAgAJfLJcVAdTodvF4vGhsb\n8cEHH+Cxxx4TVxjfkXGQp0+flg2IsSvRaBQrV67EHXfcAb2+/3gfHu7OvqPl7fF48OKLL8Lj8cRs\nyhMmTMBdd92FrKysmFIo6pgwRod/y8zMxPz58xGNRrFs2TIpiMyju0pLSzF8+HA0NTXFsN51dXUy\nL86WTVdYWIjhw4ejvb1d3Gzs+0gkghEjRuDHP/6xKAlkvDg36LXgBk+5SSWTLMdQoRlMaCIz4na7\nY9hEq9WKiooKkZtURDj/aZyospzFZ9X9RqcbSNSoqakRxSsSiSA9PR3f/OY3kZOTE5N1RwVKncvh\ncBgvvfQSKisrZbyNRqPECdHQJglBReTuu+/Gww8/jLa2NplPNAauv/56LF26FCNHjpTnUrEMBAKS\ndOX3+2XcGRdIZpZxx2r/qMaS3+9HV1cXXn75ZTQ3N8fIA87daDSKiooKiWXkc2k4sA/UvYDyiXON\ncgjoZ+X5PkuWLMGaNWuECdPr9aivr/8o0fk3xXlNqaJ1y45LTk6OyVpQrR0W3Bs3bhxmzpyJK6+8\nEsuXL8e8efNE4KquAACyGKk0sf5Nbm5uTJYNhR0tyo8LlbJUfwdiK+Cq1iEpUX6PizYUCqG5uVne\nXXWLcMLR0gQQU5NmMEVKbYf6+8cFFTEuHlq2s2fPlnaRESSLwEUWCATw7LPPYvPmzbLQaIXQMuQC\n4BgmcG6g8LFYLJg1a5aMLwV5d3c3VqxYgUOHDqGjo0OCU7nGuD5U40V149CFwTmnKlM7duyAz+eT\n4F7el79z0+D8VhkMfsbswnjFbu3atTh27JgEl+v1ekyZMiUmq4juecZ9qHFZZH+j0SjmzJkjbi8A\nUkIhGAzC4XBIDNbSpUuRlZUlrinejzFTwWAQO3fulKNa1CzIzs5ObNmyBb/4xS/w+9//XuKrmLGY\nmpqKhQsX4pprrpHvqVlUdA+dPn1asirpMuVYMGC4t7cXDQ0NZ8iE0tJSYZa4TtkflBME3XgWiwVl\nZWWoqKhAcXGx1OCikmez2VBYWChjyw28ra0tZt4M5aLX6XQoLCyMkeuUj0ajEbNnz8bo0aNjUvLj\nwxbUOFIyUqqyczZ5EZ/kYrPZJJxE0zSkp6dj8eLFEr+qyiHuH2TIVKVKZeqoBAWDQXz44YfyLM6f\n8ePHIzs7W/qLz7BarTHMEdvJrHQqa5mZmbjkkkvEkKDSQcXYbDZj4sSJWLZsmbgQ2T6TyYRly5ah\npKREvD6ccyy1wGxXwmTqP5Zs4sSJEnbD8Vdd/arbnW70rq4uGR+6utneaDSKadOmxezzapgH93G1\nL6g88TqVzePnTqcTM2bMgMPhiFlbn7dxfl6ZKW7QRqNRsnnUkvwUkHp9f0o92Q81jVLN9lGvYRwI\nrRoqW0ajEeXl5Th16lRMlVtOsO3bt2POnDmDtle1WAhat1TW2G62T13I8W4OXq9eZzAYJH2Ui4Lx\nYVy0g8UJqL/Hu/o+jXLCe3GDJP0L9C+AK6+8Er29vdi9e7cE03LRsf+B/oDo5uZmvPfee7j//vuR\nn58vCyJ+M0/g3GE2m9HT0yPxL4yh4d88Hg8OHTqEvr4+OdiWLBTHifOJLEswGITT6cSYMWMwbdo0\nbNu2DYcOHQIwIMRCoRC6u7vR2dmJ7OzsmLFj4Uxu8ozB4PpRNxCV/eHPHo8HW7duFTeG2WxGTk6O\nGE78x5pmvLdaC4nrzGQyISUlRZJRAIi1zbo7VqsVJSUlGDdunFjASUlJsslwowkEAli1ahVyc3PF\nfcQjT3bt2oXHH38cHR0dwroCA+60G264AZdeeikaGxvx8ssvo6WlRRRHtr2mpgavvPIKbr/9dkn3\nV1lbbl4ulwsffvihbDCUE2VlZcIUkv1Rg3utVqvUhONnlKfz5s2TtZ2UlCTr2O124/jx4zEbcEpK\nCi677LKYdT5U3BLHguPLcINoNIqioiIsWLBAMiPj46k43zgH+Dy+L6/5qMKM7LdoNIrU1FSkp6dL\nDOD06dMxffr0GIWe/UKlQFUYyCYyc44GLPuVrJSKioqKmFgesmjxMpLv3tfXJ/uDTqfD1VdfjYkT\nJ8q5fewX9eBjs9mMiooKZGdno7m5OUYZoetLjYejW5drgOuazLBOp5MK8ZFIBElJSWK0qOPEZ5A9\n9Xg8MclO9D7pdDpkZWUhIyND3Lhcq+xvjlV8KAufwT7jvKKRYzAYUFZWhnHjxmH//v1nsIufF86r\nMpWUlITU1FT09fUhFAoJJU9rQD2Ql9QjBQEnOSc3O5vuME58DpaaVXHLLbcgEAhg/fr18jxa2K+8\n8gruv//+QdurKnd83lB++3hXh0q7cxKRslXR29uLjRs34stf/jLy8vKkb2ilDnb+ECffYJMQGFAC\n1TilcwHT6dva2rB9+3aMGTMGDocDxcXF0vfl5eUYNWqUZFDV1dUJ1coA4UgkIofWHjhwALfddhtK\nS0tRXl6O6667Dg6HA3a7XQRTIhD93GEwGJCdnY1IJIIvfelLKCoqwnPPPSfHxuj1erjdbhw9ehQf\nfPBBTJwChafZbMayZctw1113CeOSnJwsP48ZMwa//OUv0dLSIkoMXb9f//rXMWvWLCxZsgRlZWXi\njmM1cZWdUeOtuIZZ6Rzod0uuW7cOu3fvjin0unDhQixevBilpaXCDqhxFOo8o+uC68ViseDIkSM4\nePCgbBCqu/EHP/gBLrroImRlZUmJFgAYM2YMOjs7RRHkhl1bW4sf/vCHYrFT4fN4PLJxRKP92Vdl\nZWVYtGiRKCqRSASpqan49a9/jZ///OfYtWuX9KVer0dfXx9efvllmM1mOXSYxhSNtr6+PmzcuBFH\njhyRzZB/GzVqlLC+fD8qVCqDAgy4XmjZUw5zcw8EAlL8kTFGzABbvnw5rrvuOlGUA4FAzNmHKsLh\nMCZOnIgjR44IS0nFYtasWeL6V5lP9iFdOMCAAkz2Ww1m5jsNhdLSUlRXVyMSiSAzMxPNzc3CzM2b\nN08qihOMk2PmGY13lbVS557qAmfQtcPhkMObT548KS47ujppcHD8VTfsHXfcEVOiID09XeYzMJCU\nQAOba6qnpwcej0eU097e3hh3nBr0n5qaKor8uHHjpC1Go1HGk5lxJpMpxrDhPsbvq56X3NxceL1e\nCXJn6EpBQQEeeOCBmGQFGh1qwgWhEiqcr+wjGjeUKzTyx40bh5qaGgkjUPWHzwPnPWaqs7NTFk1R\nUZFMDpUx4kRS2R+VJlQZHwoTWmYcDNbpAPoz+3iAIzBQXT0a7U9/HgrqBqRSvvzbYDFSKm1JQZKU\nlITk5GRMmTIFmzdvjrkP0J/O++6772LixIlinZAZ4sKOj81S/x+s3aqQjQ/wGwrRaH8K9DvvvINH\nHnkEubm5GDNmDH7xi1+IK4ALPD8/H/fddx+ef/55VFVVifXJ1Fy6WplJxXT7lJQUzJkzJ8bi+bwt\nii8aOA5paWmYNGkSbrrpJmzfvj3GYoy35tnfTPQoKiqKOTaC8VChUAilpaWYNWuWnI3JOCWbzYae\nnh68++67aGxsxM9+9jPYbDZRanidKvA5xrTGeRLAyZMn8fTTT6O2tlau9/v9cDgcuOmmm5CdnS0b\nDDCQPaQyYIQqD0KhEN544w20trbGlFFgVlZFRQWysrIkvZ6K07x583Dw4EE5iF11W1KWsH5avMBP\nTk7Gd77zHUyYMAHp6eliJLDtxcXF+MpXvoKqqirZ6KgchMNhvP3227j77rtj4sHUuBEqrNwgVYYE\nGMgUpFzj+ufmRxZGZSc5j/icjo4ObNu2DZWVlUhOTpZ3njp1KpYsWYLU1FRRbPhvMOh0OmFGqETT\nMCaLRqVXLZWh9re6qavuW27uKrMTD4PBgIyMDDlKrLa2VvYT1Y2tZnOqbVD7J17mqgHsQL8hP2zY\nMGkTZe3evXtxzTXXIC0tTeYwx4jrkJ4Ii8UiZ0CqSoM6/vRUcPzYL11dXbLPMIyCMthisUgg+2CK\nWXxsnaZpMUf80M2sKoWcr+FwGD09PWhubkZTU9MZeyQAOJ1OOJ1OkUF076uMNZXDeJZK7Xv2AceF\na5rH1fh8PjF0Pm9l6rzHTNGyYNyCGpCsBjbSspOGKhsuKVFOUl7L06c5uBxg0vRM11UP1xw+fPiQ\n7VVdi/EUpBqzoUIdfGCg1kpKSgqWLl16BoWv0/UHVm7cuDEm1oH9E+86VH33Q4GCTo1bOBfU1tbi\nmWeewaOPPipHUGzduhVr167FgQMH0N7eHmO5FxUV4Vvf+haWLVsmNWPUOAkAwg7S0nz11VdRWVmJ\nU6dOSRvPJhwTiAXXjN1ul42rvLwceXl5AGIPNOaGSsWcBkppaSkuvvhiidNg7ApZJafTiQULFiA3\nN1fGOjc3VyzPYDCI6upq/PGPf8TKlSuxa9cudHR0wO12i1BXs2Z5Kn1zczNWrVqFxx57DL/61a9w\n4sQJUQ6A/viWadOmYcSIEeJ6UueyahioQcpkfDVNQ1dXFw4fPixsCzcFk8mEiRMniotSVeYBYMaM\nGZgyZYqEHXB90pXN+lXcpGnojBgxArfeeivmzJmDYcOGSSFSygjWUCorKxMlUDXEwuH+g3dbWlqE\nLef96RYaN26cBKcDkOajEWkAAB6bSURBVOw+HhTM+6qxp/yMShb7mf3I38l+bd26FWvWrEFraysy\nMjLgdDqRlpaG2267DSNGjJD4G7X/B4Ner0dBQYEoq4xNstvtGDZsmCiE8cYy5QXlOeek+jcaCWeD\npmkYNWrUGd+nop6SkiLynPOdSgp/Vr0RqvyMVyyA/uxB7ms+nw9GY/9BxQ0NDTJXVHZQfRdg4Kw/\n9gX3Qv6dMahqXBfbxcOBebIHADGK6L6je623tzemJAcNE86bUCiExsZGie1iH1EpVtepx+PB+vXr\n8eyzz2LXrl0yv9iHzKCkzOe8UN8bGFDm1Viq+LEEBsJi1MSQvr4+OQFA0zQZ188T58RM6XS6kwA8\nACIAwpqmTdPpdOkAVgEoAnASwPWapnWf7T7RaH/ac19fH0aOHImsrCz4fD4RYGr2GSe70oZBlQo1\ncBPAGVo5y+QXFBQgNTVVjgCgUPnqV7961vZSeFC4UbsGYoMhVfaIND03O5/PJ4VE4+OrOGEmTpwo\n96TloW4kVN7YDxQQQ2XsUYn5OFi5ciVeeeUVqYBMN8Zjjz2GjIwMXHnllbjuuuvkLCWTyYTs7Gxc\nc801mDNnDrq7u1FfX49QKISenh45HodCJRgMoqOjQ6rPP/zww5IencDHRygUgtVqRVZWFu6//368\n/vrr2LVrVwyDQkHFDXratGn4xje+gaysLHGVAbFz2WKxYOTIkZgzZw5ef/11cQGRbaRrYN26dbBY\nLHj77bdx8cUXo7CwEJdccglMJpNkUzU1NaGlpQXhcBg7duzAxo0bY6xobtCTJ0/GhRdeiGnTpolb\nh5uMKiRVNpiCle6nSCSC9vZ2OdCXMkTTNGRlZWHp0qVITU2Ve5IFAYDc3Fx8/etfh9FoxLp162KM\nHRptdF3rdDpMmjQJixcvxsiRIzFq1ChhIKjIqq4iKq3AQKYeYz2pPG3atCnmmB41XKGgoADFxcUy\nBmTiXnjhBRQVFcFut8fICCq9ajiEyWSSPqKLy+/3o6WlBXv37sUf//hHUcz0er0Etk+cOFHi7tTM\n4rMxU2Q8OVcY9kDlEBgwOrnhs2+ZzKKGSnAenwvLbrfbkZOTIxl4KvtktVrFCAEQU/eLrjr1Pbiv\nxMe4cgwjkQi6urqE9aPCYbPZ0NnZCZfLJSdycC6x0CT7R3Wjsz/oadE0TepNcb1zzra3t6O2tlZc\n3JShdrsdmZmZ8hyyhFxPdOWTaeP33G43tmzZgq997WtnJB9pmiZJGADQ3NyMP/3pT6IwMdaQ4xOJ\n9B8vw7FVXfPq/s4+oCxQ9/h4g0J143PeqrFaoVDocz9ORjeYRnjGRf3K1DRN0zqUz34JoEvTtP/Q\n6XT3A0jTNO2HZ7vPqFGjtIsuukgOMhw+fPgZ2RfxikG8i0tFvJ9UjRGiQDIYDHLY7qFDh3DFFVfI\nZCopKcHatWsxbNiwQe/PwF5S6vHtGCzoTbU+dLr+SrNUrnw+H26//XZs2LBBJoum9QcMXnHFFXj8\n8ceFeVDvS6qUwlLd+M4GVZCeC/Lz89HY2CgTnAKTi4JWz/Tp01FWVoaFCxciPT1dLCG/349gMIiW\nlhasWLECOTk52L17N3p7e4UVZL+ZTP1HSixfvhwzZszA6NGjz6mN/+xgwUZuNFTwPR6PbEZPPvkk\nKisrcfz4cQQCATm1vaysDD/60Y/E9TxYyQ0qMIFAQOI/brjhBpl36nET3BBV143T6RRljsqe2m5g\nYD5aLBakp6fj5ptvxs033xxD98fLBdUAGWwdUlF/4YUX8MILL0gcjE6nw4wZM3DfffdhxIgREpcS\n77IJhULCxt5+++1ob28Xw8xisSAtLQ2zZs1CSkoKKioqMGXKFNl8+T8VU8Y6cpMmw7V+/Xo88cQT\nwpyxXhcrzRcVFWH27Nm44oorkJeXJ33X3t6OBx98EIcPH0ZycrLIEr2+v0L4VVddheXLlyM5OVmM\nPRpCfDeyBezDrq4u/OAHP0BDQ4PEYRmNRjgcDjmWgzGuZG7U2Ea/3y+lXlS0tbVh5cqVeOqppyQm\njYrR//t//w/z58+XsjgcY1XhIVSjM95dTQV1MLhcLlRVVeFnP/uZKJ9UhrOysvDDH/4QFRUVolTT\nM6DOOXVPZI0rdR6yT1lnacGCBXKSBtcj4+WeeuopYVrJcqlJApw3qutNDbRXs8LJ9HZ3d2P58uVo\na2tDJBKRaunLli3DkiVLUFxcDGCA9VKZNr2+vy7gokWLhAWkkmSz2fD6669LFXsSAX19fWhqasJL\nL72ExsZG1NbWxswv7pNU0skIjxs3DitWrBBWk23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0aZJv36VWA2hXDuH7yS1hiZdw0aoW\no5u1dRkIaCyRxoI1Nzfz+uuvc+DAAY4dO0ZTU1MHq6oqI42NjX5Br4qSiwLH1dWminh2djalpaWs\nXr2aadOm+ThDdR3q5+u1W39TtYpCe0eRMCHi8uXLnDx5ki1btni39cqVK2ltTRYE1vpm8XjcL1BU\n8dVK+KE3qLGxkWeffZYPPvjAX/u1Obe64LSyerhg0pCAcJGiypQqhEOHDmXhwoU+yF57/oWLpRs3\nbvSpm++WYqb+VJgy1b/RBrNh48zQRQL4Nhpnz57lpZde4vDhw9TX1/ssIzUjh/EHGhSanZ3tT8hY\nLOYz+XJycry7xDAM43ZBywKE1t6zZ89y5swZqqqq2LVrF/X19X4/wF9jw9g4Hdd6YHoNLSgo4IEH\nHmD58uXk5+d7C5YmOYSxf6pI6fVbrchqJQubOGuBWM1w1IWwVvAPOxqESSthRrYupPV7X7lyhY8/\n/pgdO3ZQU1Pjy6voe4Tt4dTqqYtuVdjDSu9qrVZL6XPPPcekSZN8w279TtevX/clW36oMqXW8Z07\nd7J9+3amTp3Kq6++CsDQoUN/9NIIxp8Z6u7QlNNQKVJ3Sk5ODllZWWRnZ/P0009z5swZjh49yocf\nfsiBAwd8E009OYEOliotBlhSUuLbLaTq5jUMw+gPhJYTDUpPJBLEYjHGjBlDcXExdXV17N27l8rK\nSl9NXK95YUFKrR+mlqjCwkJWrlxJUVEROTk53hqlipMGuXcmjN9T12hbW5u3bIZtXFpbW5k4cSLQ\nnlgUul3D2Eu9D1y7ds27bXXebW3JgtyzZs1i3bp17Nq1i2PHjnVQmFROWtBTFStdcOs9R2M4hw8f\nzuzZs1mwYAG5ubnMmDGDWCzWoY+gZhb21lJ648YNamtref7557l69Srjx4/3RbFvFVOmDI8e3FqE\nUwkDfdUsPXz4cEaPHk1WVhYTJ05k8eLFlJeX8+WXX/LNN994JezChQv+RCkrK6O4uJhx48ZRXFzs\ngyb7uqeSYRjGDyHM7Atj+tSaU1payrRp0ygvL+ejjz7i1KlTnDt3joaGBjIyMjh//jzTpk0jFotR\nU1NDZmYmpaWlvj2RZleGNeX0WT9blSctpBlaqTRbUccAr9iowjVixAjvlVBlLcwYVfQ7hq7eMO7R\nOUc8Hueee+5h6tSp7N+/n927d9PQ0EAsFqO2tpZhw4b5uC4tVxKPx8nLyyMWi5Gfn+/7+s2cOZOy\nsjJfNyzs1Rl+dmjZ+qGcP3+eyspKvv32W0SETz/9lKtXr6akTJmbzzAMwzCMAcumTZsYNGgQ27Zt\n89nnq1evZvPmzcycOdPcfIZhGIZhGD1RW1vLvn37vBVQRNizZw933nnnLb+H1QYwDMMwDGPA8uij\nj7JkyRJvldISHgcPHrzl9zDLlGEYhmEYA5bly5dz7733smrVKk6cOMGyZctYu3YtZWVl5OfftFMe\nYMqUYRiGYRgDGM1ifOqpp3jvvfeoqKhg/vz5KWUIpjUAXUQageNp+8Dbnzygvq8ncRth8kodk1lq\nmLxSw+SVGiav1EiHvO50zt20TUe6LVPHbyUq3kgiIodMXreOySt1TGapYfJKDZNXapi8UqM/ycsC\n0A3DMAzDMHqBKVOGYRiGYRi9IN3K1I40f97tjskrNUxeqWMySw2TV2qYvFLD5JUa/UZeaQ1ANwzD\nMAzD+HPD3HyGYRiGYRi9IG3KlIgsF5HjInJSRJ5O1+f2Z0Tk30TknIgcDcZGisheEfkyev5JNC4i\nsi2S3xERmd13M+8bROQOEXlPRKpFpEpEfh6Nm8y6QERiIvKxiByO5PX30fhEETkYyes1ERkWjWdE\n2yejv0/oy/n3FSIyWEQqReSdaNvk1Q0iclpEvhCRz0XkUDRm52M3iEiuiPxORI5F17EFJq+uEZHi\n6LjSx2UR+UV/lVdalCkRGQxsB1YA04E1IjI9HZ/dz/l3YHmnsaeBfc65KcC+aBuSspsSPR4Hfp2m\nOfYnWoGnnHMlwHzgZ9FxZDLrmmvAEudcGVAOLBeR+cA/Ab+M5HUReCza/zHgonNuMvDLaL+ByM+B\n6mDb5NUzf+mcKw9S1O187J6twH8756YBZSSPM5NXFzjnjkfHVTkwB7gKvEF/lZdz7kd/AAuAPwTb\nm4HN6fjs/v4AJgBHg+3jQEH0uoBkbS6AfwHWdLXfQH0AvweWmsxuSVaZwGfAPJJF7oZE4/7cBP4A\nLIheD4n2k76ee5rlNI7kBXoJ8A4gJq8e5XUayOs0Zudj17KKA6c6HyMmr1uS3TLgf/uzvNLl5hsL\nfBNsn4nGjO8z2jn3LUD0rI2BTIYBkUtlFnAQk1m3RC6rz4FzwF6gBrjknGuNdgll4uUV/f2PwKj0\nzrjP+RXwd0BbtD0Kk1dPOGCPiHwqIo9HY3Y+dk0RcB54JXIjvywiIzB53Qp/A/xn9LpfyitdypR0\nMWZphKlhMowQkSxgF/AL59zlnnbtYmxAycw5d8MlzeTjgLuBkq52i54HtLxE5EHgnHPu03C4i11N\nXu0sdM7NJuli+ZmILOph34EuryHAbODXzrlZwBXaXVRdMdDlBUAUo/gw8F8327WLsbTJK13K1Bng\njmB7HFCXps++3TgrIgUA0fO5aNxkCIjIUJKK1KvOudejYZPZTXDOXQL+h2SsWa6IaCupUCZeXtHf\nc4CG9M60T1kIPCwip4HfkHT1/QqTV7c45+qi53Mk41nuxs7H7jgDnHHOHYy2f0dSuTJ59cwK4DPn\n3Nlou1/KK13K1CfAlCgrZhhJk91bafrs2423gPXR6/Uk44J0fF2UsTAf+KOaOgcKIiLAvwLVzrl/\nDv5kMusCEUmISG70ejjwVyQDXt8Dfhrt1lleKsefAvtdFHwwEHDObXbOjXPOTSB5jdrvnPtbTF5d\nIiIjRCRbX5OMazmKnY9d4pz7DvhGRIqjofuA/8PkdTPW0O7ig/4qrzQGkD0AnCAZs/FMXwWy9acH\nyQPkW6CFpFb9GMmYi33Al9HzyGhfIZkRWQN8Aczt6/n3gbzuIWm2PQJ8Hj0eMJl1K6+ZQGUkr6PA\ns9F4EfAxcJKk6TwjGo9F2yejvxf19XfoQ9n9BfCOyatHGRUBh6NHlV7X7XzsUWblwKHonHwT+InJ\nq0d5ZQIXgJxgrF/KyyqgG4ZhGIZh9AKrgG4YhmEYhtELTJkyDMMwDMPoBaZMGYZhGIZh9AJTpgzD\nMAzDMHqBKVOGYRiGYRi9wJQpwzAMwzCMXmDKlGEYhmEYRi8wZcowDMMwDKMX/D/gz2FlvB+CzQAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f84ac475630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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bKd2YAZyxWdFnIqP+17/+FWvXruXn2Ww2fPXVVxg1ahSPBR0RUpMKPC4FyK4V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\npszMzMwKcDFlZmZmVsAvvle5iOxmgYQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f84ac4362e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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O+++/T25uLrFYjOrVq9O0aVN69erFZ599xoMPPkhGRsbvLtDfS2ZmJkVFRSpQ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f84ac3f70f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualizing data\n",
    "for filename in img_files[:6]:\n",
    "    img = mpimg.imread(filename)\n",
    "    plt.figure(figsize=(10,10))\n",
    "    plt.imshow(img, cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "encoder = LabelEncoder()\n",
    "encoder.fit(img_targets)\n",
    "encoded_Y = encoder.transform(img_targets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array(['data_subset/a01-000u-s00-00.png',\n",
       "        'data_subset/a01-000u-s00-01.png',\n",
       "        'data_subset/a01-000u-s00-02.png',\n",
       "        'data_subset/a01-000u-s00-03.png',\n",
       "        'data_subset/a01-000u-s01-00.png'], dtype='<U35'),\n",
       " array(['000', '000', '000', '000', '000'], dtype='<U3'),\n",
       " array([0, 0, 0, 0, 0]))"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "img_files[:5], img_targets[:5], encoded_Y[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  0,  0, ..., 47, 47, 47])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "encoded_Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['000', '000', '000', ..., '635', '635', '635'], dtype='<U3')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "img_targets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_files, rem_files, train_targets, rem_targets = train_test_split(img_files, encoded_Y, train_size=0.66, random_state=50, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "validation_files, test_files, validation_targets, test_targets = train_test_split(\n",
    "rem_files, rem_targets, train_size=0.5, random_state=22, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((3233,), (833,), (833,))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_files.shape, validation_files.shape, test_files.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Input to the model\n",
    "* random patches cropped from each sequence. \n",
    "* resized each sentance so that new height is 113px and new width\n",
    "* distorting the shape of image by changing the aspect ratio\n",
    "* adjusted image, patches of 113*113 are randomly cropped"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Generator function for generating random crops from each sequence\n",
    "# # Now create generates for randomly cropping 113*113 patches from these images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "batch_size = 20\n",
    "num_classes = 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def generate_file_data(samples, target_files, batch_size=batch_size, factor=0.1):\n",
    "    num_samples = len(samples)\n",
    "    from sklearn.utils import shuffle\n",
    "    while 1: # loop forever so the generator never terminates\n",
    "        for offset in range(0, num_samples, batch_size):\n",
    "            batch_samples = samples[offset:offset+batch_size]\n",
    "            batch_targets = target_files[offset:offset+batch_size]\n",
    "            \n",
    "            images = []\n",
    "            targets = []\n",
    "            for i in range(len(batch_samples)):\n",
    "                batch_sample = batch_samples[i]\n",
    "                batch_target = batch_targets[i]\n",
    "                im = Image.open(batch_sample)\n",
    "                cur_width = im.size[0]\n",
    "                cur_height = im.size[1]\n",
    "                \n",
    "                height_fac = 113 / cur_height\n",
    "                \n",
    "                new_width = int(cur_width * height_fac)\n",
    "                size = new_width, 113\n",
    "                \n",
    "                imresize = im.resize((size), Image.ANTIALIAS)\n",
    "                now_width = imresize.size[0]\n",
    "                now_height = imresize.size[1]\n",
    "                \n",
    "                #generate crops of size 113*113 from this resized image and keep random 10% of crops\n",
    "                \n",
    "                avail_x_points = list(range(0, now_width - 113))\n",
    "                \n",
    "                #pick random x%\n",
    "                pick_num = int(len(avail_x_points) * factor)\n",
    "                \n",
    "                #now pick\n",
    "                random_startx = sample(avail_x_points, pick_num)\n",
    "                \n",
    "                for start in random_startx:\n",
    "                    imcrop = imresize.crop((start, 0, start+113, 113))\n",
    "                    images.append(np.asarray(imcrop))\n",
    "                    targets.append(batch_target)\n",
    "                \n",
    "                #trim image to only see section with road\n",
    "                \n",
    "                X_train = np.array(images)\n",
    "                y_train = np.array(targets)\n",
    "                \n",
    "                #reshape X_train for feeding in later\n",
    "                X_train = X_train.reshape(X_train.shape[0], 113, 113, 1)\n",
    "                # convert to float and normalize\n",
    "                X_train = X_train.astype('float32')\n",
    "                X_train /= 255\n",
    "                \n",
    "                #one hot encode y\n",
    "                y_train = to_categorical(y_train, num_classes)\n",
    "                \n",
    "                yield shuffle(X_train, y_train)\n",
    "                    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# geneartiing data from training and validation\n",
    "\n",
    "train_generator = generate_file_data(train_files, train_targets, batch_size=batch_size, factor=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "validation_generator = generate_file_data(validation_files, validation_targets, batch_size=batch_size, factor=0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Building a neural network in Keras\n",
    "\n",
    "###### Type of popular neural network\n",
    "* Sigmoid or Logistic\n",
    "* Tanh — Hyperbolic tangent\n",
    "* ReLu -Rectified linear units"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From /home/devops2/anaconda3/lib/python3.6/site-packages/keras/backend/tensorflow_backend.py:4070: The name tf.nn.max_pool is deprecated. Please use tf.nn.max_pool2d instead.\n",
      "\n",
      "Model: \"sequential_1\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "zero_padding2d_1 (ZeroPaddin (None, 115, 115, 1)       0         \n",
      "_________________________________________________________________\n",
      "lambda_1 (Lambda)            (None, 56, 56, 1)         0         \n",
      "_________________________________________________________________\n",
      "conv1 (Conv2D)               (None, 28, 28, 32)        832       \n",
      "_________________________________________________________________\n",
      "activation_1 (Activation)    (None, 28, 28, 32)        0         \n",
      "_________________________________________________________________\n",
      "pool1 (MaxPooling2D)         (None, 14, 14, 32)        0         \n",
      "_________________________________________________________________\n",
      "conv2 (Conv2D)               (None, 14, 14, 64)        18496     \n",
      "_________________________________________________________________\n",
      "activation_2 (Activation)    (None, 14, 14, 64)        0         \n",
      "_________________________________________________________________\n",
      "pool2 (MaxPooling2D)         (None, 7, 7, 64)          0         \n",
      "_________________________________________________________________\n",
      "conv3 (Conv2D)               (None, 7, 7, 128)         73856     \n",
      "_________________________________________________________________\n",
      "activation_3 (Activation)    (None, 7, 7, 128)         0         \n",
      "_________________________________________________________________\n",
      "pool3 (MaxPooling2D)         (None, 3, 3, 128)         0         \n",
      "_________________________________________________________________\n",
      "flatten_1 (Flatten)          (None, 1152)              0         \n",
      "_________________________________________________________________\n",
      "dropout_1 (Dropout)          (None, 1152)              0         \n",
      "_________________________________________________________________\n",
      "dense1 (Dense)               (None, 512)               590336    \n",
      "_________________________________________________________________\n",
      "activation_4 (Activation)    (None, 512)               0         \n",
      "_________________________________________________________________\n",
      "dropout_2 (Dropout)          (None, 512)               0         \n",
      "_________________________________________________________________\n",
      "dense2 (Dense)               (None, 256)               131328    \n",
      "_________________________________________________________________\n",
      "activation_5 (Activation)    (None, 256)               0         \n",
      "_________________________________________________________________\n",
      "dropout_3 (Dropout)          (None, 256)               0         \n",
      "_________________________________________________________________\n",
      "output (Dense)               (None, 50)                12850     \n",
      "_________________________________________________________________\n",
      "activation_6 (Activation)    (None, 50)                0         \n",
      "=================================================================\n",
      "Total params: 827,698\n",
      "Trainable params: 827,698\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "# function to resize image to 56*56\n",
    "\n",
    "def resize_image(image):\n",
    "    return tf.image.resize(image,[56, 56])\n",
    "\n",
    "# Function to resize image to 64*64\n",
    "\n",
    "row, col, ch = 113, 113, 1\n",
    "\n",
    "model = Sequential()\n",
    "model.add(ZeroPadding2D((1,1), input_shape=(row, col, ch)))\n",
    "\n",
    "# Resize data withing the neural network\n",
    "model.add(Lambda(resize_image)) # resize images to allow for easy computation\n",
    "\n",
    "#Using CNN model - Building the model suggested in paper\n",
    "\n",
    "#LAYER 1 \n",
    "model.add(Convolution2D(filters=32, kernel_size=(5,5), strides=(2,2), padding='same', name='conv1')) #96\n",
    "model.add(Activation('relu'))\n",
    "model.add(MaxPooling2D(pool_size=(2,2), strides=(2,2), name='pool1'))\n",
    "\n",
    "#LAYER 2\n",
    "model.add(Convolution2D(filters= 64, kernel_size=(3,3), strides=(1,1), padding='same', name='conv2')) #256\n",
    "model.add(Activation('relu'))\n",
    "model.add(MaxPooling2D(pool_size=(2,2), strides=(2,2), name='pool2'))\n",
    "\n",
    "#Layer 3\n",
    "model.add(Convolution2D(filters= 128, kernel_size =(3,3), strides= (1,1), padding='same', name='conv3'))  #256\n",
    "model.add(Activation('relu'))\n",
    "model.add(MaxPooling2D(pool_size=(2,2),strides=(2,2), name='pool3'))\n",
    "\n",
    "model.add(Flatten()) #=> Return copy of original array, If you modify any value of this array value of original array is not affected\n",
    "model.add(Dropout(0.5)) #=> Dropout is easily implemented by randomly selecting nodes to be dropped-out with a given probability (e.g. 20%) each weight update cycle.\n",
    "\n",
    "model.add(Dense(512, name='dense1'))\n",
    "#add (BatchNormalization)\n",
    "model.add(Activation('relu'))\n",
    "model.add(Dropout(0.5))\n",
    "\n",
    "model.add(Dense(256, name='dense2'))\n",
    "model.add(Activation('relu'))\n",
    "model.add(Dropout(0.5))\n",
    "\n",
    "model.add(Dense(num_classes, name='output'))\n",
    "model.add(Activation('softmax')) #=> softmax since output is withing 50 classes\n",
    "\n",
    "model.compile(loss='categorical_crossentropy', optimizer=Adam(), metrics=['accuracy'])\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " #### Train the model\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/devops2/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:13: UserWarning: The semantics of the Keras 2 argument `steps_per_epoch` is not the same as the Keras 1 argument `samples_per_epoch`. `steps_per_epoch` is the number of batches to draw from the generator at each epoch. Basically steps_per_epoch = samples_per_epoch/batch_size. Similarly `nb_val_samples`->`validation_steps` and `val_samples`->`steps` arguments have changed. Update your method calls accordingly.\n",
      "  del sys.path[0]\n",
      "/home/devops2/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:13: UserWarning: Update your `fit_generator` call to the Keras 2 API: `fit_generator(<generator..., validation_data=<generator..., verbose=1, callbacks=[<keras.ca..., steps_per_epoch=3268, epochs=8, validation_steps=1)`\n",
      "  del sys.path[0]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From /home/devops2/anaconda3/lib/python3.6/site-packages/keras/backend/tensorflow_backend.py:422: The name tf.global_variables is deprecated. Please use tf.compat.v1.global_variables instead.\n",
      "\n",
      "Epoch 1/8\n",
      "1146/3268 [=========>....................] - ETA: 29:52 - loss: 3.5494 - accuracy: 0.2155"
     ]
    }
   ],
   "source": [
    "nb_epoch = 8\n",
    "samples_per_epoch = 3268\n",
    "nb_val_samples = 1\n",
    "\n",
    "# save every model using keras checkpoint\n",
    "from keras.callbacks import ModelCheckpoint\n",
    "filepath = 'checkpoint/check-{epoch:02d}-{val_loss:.4f}.hdf5'\n",
    "checkpoint = ModelCheckpoint(filepath=filepath, verbose=1, save_best_only=False)\n",
    "callbacks_list = [checkpoint]\n",
    "\n",
    "# Model fit generator\n",
    "history_object = model.fit_generator(train_generator, samples_per_epoch=samples_per_epoch, validation_data=\n",
    "                                    validation_generator, nb_val_samples=nb_val_samples, nb_epoch=nb_epoch, verbose=1, callbacks=callbacks_list)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Test model performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "images = []\n",
    "for filename in test_files[:50]:\n",
    "    im = Image.open(filename)\n",
    "    cur_width = im.size[0]\n",
    "    cur_height = im.size[1]\n",
    "\n",
    "    # print(cur_width, cur_height)\n",
    "    height_fac = 113 / cur_height\n",
    "\n",
    "    new_width = int(cur_width * height_fac)\n",
    "    size = new_width, 113\n",
    "\n",
    "    imresize = im.resize((size), Image.ANTIALIAS)  # Resize so height = 113 while keeping aspect ratio\n",
    "    now_width = imresize.size[0]\n",
    "    now_height = imresize.size[1]\n",
    "    # Generate crops of size 113x113 from this resized image and keep random 10% of crops\n",
    "\n",
    "    avail_x_points = list(range(0, now_width - 113 ))# total x start points are from 0 to width -113\n",
    "\n",
    "    # Pick random x%\n",
    "    factor = 0.1\n",
    "    pick_num = int(len(avail_x_points)*factor)\n",
    "    \n",
    "    random_startx = sample(avail_x_points,  pick_num)\n",
    "\n",
    "    for start in random_startx:\n",
    "        imcrop = imresize.crop((start, 0, start+113, 113))\n",
    "        images.append(np.asarray(imcrop))\n",
    "        \n",
    "    X_test = np.array(images)\n",
    "    \n",
    "    X_test = X_test.reshape(X_test.shape[0], 113, 113, 1)\n",
    "    #convert to float and normalize\n",
    "    X_test = X_test.astype('float32')\n",
    "    X_test /= 255\n",
    "    shuffle(X_test)\n",
    "\n",
    "print(X_test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "predictions = model.predict(X_test, verbose=1)\n",
    "predictions.shape\n",
    "predicted_writer = []\n",
    "for pred in predictions:\n",
    "    predicted_writer.append(np.argmax(pred))\n",
    "print(len(predicted_writer))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "writer_number = 18\n",
    "total_images = 10\n",
    "counter = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for i in range(len(predicted_writer)):\n",
    "    if predicted_writer[i] == writer_number:\n",
    "        print('xx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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