CAPTCHA.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## CAPTCHA image recognition\n",
    "### By Ali Shannon\n",
    "\n",
    "The data is obtained from [Kaggle](https://www.kaggle.com/fournierp/captcha-version-2-images) which provides labeled datasets for ML practice.\n",
    "The goal here is to use computer vision provided by torchvision from pytorch to read and attempt to recognize lettersin in CAPTCHA images.\n",
    "The only downside is that labels are not uniformly distributed so some discrepancies may occur. A larger dataset with more variations may prove helpful.\n",
    "\n",
    "Each CAPTCHA image has exactly 5 characters and they could be letters or numbers, the labels are inferred from the training data.\n",
    "If a new character is introduced, this model will not perform well since it does not have it in the dictionary of characters as explained by the encoder. For encoding I am using the scikit-learn `OneHotEncoder` class which replaces the matrix of characters into a more sparse matrix of zeros and ones."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from glob import glob\n",
    "from PIL import Image\n",
    "import numpy as np\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import OneHotEncoder\n",
    "from torchvision import transforms\n",
    "from torch.utils.data import DataLoader, TensorDataset\n",
    "from torch import nn, optim\n",
    "from torch.nn import functional as F\n",
    "import torch\n",
    "\n",
    "DEVICE = 'cuda' if torch.cuda.is_available() else 'cpu'\n",
    "PATH = 'samples/*.png'"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Import all images and labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "pics = {}\n",
    "for image_file in glob(PATH):\n",
    "    #label = image_file.split('/')[-1].split('.')[0] # linux version\n",
    "    label = image_file.split('\\\\')[-1].split('.')[0]\n",
    "    with Image.open(image_file) as pic:\n",
    "        pics[label] = np.asarray(pic)\n",
    "\n",
    "\n",
    "# The data needs to be array-like for train_test_split\n",
    "x = list(map(transforms.ToTensor(), pics.values()))\n",
    "y = list(map(list, pics.keys()))"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Set up the encoder to create ones and zeros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "encoder = OneHotEncoder().fit(y)\n",
    "y_encoded = encoder.transform(y).toarray()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": "<Figure size 432x288 with 1 Axes>"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "distribution_of_chars = np.sum(y_encoded, axis=0)\n",
    "plt.bar(np.arange(len(distribution_of_chars)), distribution_of_chars)\n",
    "plt.title('Rough distribution of all characters\\nin trainin')\n",
    "plt.xlabel('Characters')\n",
    "plt.ylabel('Count')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Split into train and test sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train, x_test, y_train, y_test = train_test_split(\n",
    "    x, y_encoded, test_size=0.33, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Tensorize all of them to prep for neural network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train = torch.stack(x_train)\n",
    "x_test = torch.stack(x_test)\n",
    "y_train = torch.tensor(y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Define the CNN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "class CNN(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.feats = nn.Sequential(\n",
    "            nn.Conv2d(4, 24, kernel_size=2, stride=2),\n",
    "            nn.AvgPool2d(kernel_size=2),\n",
    "            nn.Dropout(0.2),\n",
    "            nn.Conv2d(24, 48, kernel_size=2),\n",
    "            nn.MaxPool2d(kernel_size=2),\n",
    "            nn.Dropout(0.2),\n",
    "        )\n",
    "        self.fc = nn.Linear(5760, 95)\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = self.feats(x)\n",
    "        x = x.flatten(1)\n",
    "        x = self.fc(F.relu(x))\n",
    "        return F.softmax(x, -1)\n",
    "\n",
    "model = CNN()\n",
    "model.double().to(DEVICE)\n",
    "\n",
    "error = nn.BCELoss()\n",
    "opt = optim.Adam(model.parameters())"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Define the train function and start training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": "Epoch: 100 \t loss: 0.10280555339796826\nEpoch: 200 \t loss: 0.09527726726109494\nEpoch: 300 \t loss: 0.0932475486697658\nEpoch: 400 \t loss: 0.0918443012334607\nEpoch: 500 \t loss: 0.09139890883700973\nEpoch: 600 \t loss: 0.09084757545282005\nEpoch: 700 \t loss: 0.0905401900598109\nEpoch: 800 \t loss: 0.09017886497628548\nEpoch: 900 \t loss: 0.08985160414548853\nEpoch: 1000 \t loss: 0.08942246852779413\n"
    },
    {
     "data": {
      "image/png": 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      "text/plain": "<Figure size 432x288 with 1 Axes>"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_t = y_train.to(DEVICE)\n",
    "x_t = x_train.double().to(DEVICE)\n",
    "\n",
    "def train(x, y, num_epochs=1000):\n",
    "    losses = []\n",
    "    model.train()\n",
    "    for epoch in range(1, 1 + num_epochs):\n",
    "        opt.zero_grad()\n",
    "        out = model(x.double().to(DEVICE))\n",
    "        loss = error(out, y_t)\n",
    "        loss.backward()\n",
    "        opt.step()\n",
    "        losses.append(loss.item())\n",
    "        if epoch % int(0.1 * num_epochs) == 0:\n",
    "            print(f'Epoch: {epoch} \\t loss: {loss.item()}')\n",
    "    return losses\n",
    "\n",
    "losses = train(x_t, y_t)\n",
    "plt.plot(losses)\n",
    "plt.title('BCE loss per epoch')\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Loss')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Run model on test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "with torch.no_grad():\n",
    "    out = model(x_test.double().to(DEVICE)).cpu().detach().numpy()\n",
    "\n",
    "# Decode the ones and zeros matrix\n",
    "res = encoder.inverse_transform(out)\n",
    "true = encoder.inverse_transform(y_test)\n",
    "\n",
    "test_images = list(map(transforms.ToPILImage(), x_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Sample and show results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JXC11JHQuFA0NDQ0/hU4nq6FxBpB1qWyMrPx0oWTh4eFeDFR1RKohabSHnzhxQr7P9+hUCwkJ8fquw+EQhq6itVE65yqq5FTtnsvIlZb0FRISIvPMhGZBQUHCsj0jjCorK70igjoCWoFraJwBnkrY4XCIU46fWSwWLydYWVmZ/MhpcrFarW7hhWyD7fB8m80mJoT9+/cDANavXy9ZBaOiogAA6enpp42IOBvTSHNCKpvbbmtk8mV2aWkbvt73dZ7dbneLFAKcRTZ4rYYNGwYA6Nu3LwCXWa2joU0oGhoaGn4KzcA1NM6AiooKAC7HoRqjrYbOkZWTncXExLiZTgBn+FlxcTEA4MCBAwCAPXv2oKCgAICTtfOz3NxcaZv9Ep2FAZ4vCAwMdIu3B5zzHhMTAwCYOXMmAGepQMDp4PRlumpvaAauoaGh4afQDFxD4wygE5O2bXXzzLFjxwAAhw4dwqFDhwBAwtGys7Ol6PORI0cAOAseE+pmHM+NLiEhIWJvTUpKAuBkfZSF7yUnJzfbVuxp+21qamqxLVnNE9Kc753JLn6675zOQXyqcTX3O57vqfPPOa6trZVrzpJ9kZGRAJyrMtrKOxKdXoG3Z86L1qKtvPnnCq2Rz9cOPV+xzFxG8gfgcDi8zAt1dXXymp9ZLBavXYoRERHi9aeCVJ15fE+Ne25u8if1L79//PhxAE5TB9um2WLnzp0AnM4tblDj+d99951Ei9CZqEaPMIqhoaFBFN4FF1wg4xkwYAAAICEhAYBzxya3cffr10/O55zShBMXFycOSzW+nK+5czMiIkLMLeXl5fKeGrmituE5Z75enw7n6vfYGeXj/RkYGNimuqm10CYUDQ0NDT9Fp2fgGh0DLh3J1hobG4X9qTsSVcce4FyWeyZwioiIEKZOE4LdbhdGSMZ68uRJaY95JhwOh5gkyGa6desm7aism98l6z1+/LiYLug4PHjwIA4ePAjAtRNy8+bNwnLj4+PdzlfHwfNtNhtSU1MBOM0aAJCRkSHpPsmi+/Xrh549e7rNq9lsFrbOpXqfPn2E5ZPRV1ZWigNNnXfPVVBtba3MPftXdxSqsnPOuNvzXKVD1Wg/aAauoaGh4afQDFzDJ8j6yGpDQkKE9ak7Esl21bA22pNpMzYMQ9gmbb1hYWHyXbZ78uRJ+S7bCwsLk9AtOgw3bdokqYtZVGT37t3IyckB4GKgtbW1XjvoVJsx7ZmpqalITk6WcQLA7bffLmP4+eefAbhWBddcc42w7OrqagDAqFGj3FKTcqyUOSUlRdonK+bqJjs7G7169QLgSrkcHBzslYNFXbVwxdC9e3d5zfGEhITIa7LtvLw8GSPzqXSGMDiNs4NW4Bo+4Zljuq6uzi0+FnDfVcjza2pqREnTY+9wOMRMwu8eOXJEdhV+8sknAJyOQ5oDqPCOHz+OPXv2AHA9VIKCgryS6VutVnnY0KyRlpYmpo5u3boBAGJjY8WsccUVVwBwKrz8/HwAwA8//ADA9bBITU2VXXhU7nv37sWuXbsAAJdeeikAYPbs2Rg9ejQAl2IMCwvD4MGDAbgU8/HjxyW3NOcsMTFR4sApu9VqlQcBTSmlpaXo2rWr2zw6HA75Dp2YJ06cEHMKx2M2m5GYmAgAEhkTGxsLDf+GNqFoaGho+Ck0A9fwCS7B1VweZHrqjjUyYTrIrFarLP3Zxr59+7B+/XoATvMH4AzX4+d0etbX1wsrpfPRZDIJY05LS5P3yJ7JrFNSUoR1qqGKlJ9/rVarmBxef/11AMD7778v7N5zlXHRRRdJu/wsJydH+uW4/vjHP0rlqWuvvRYA8M477+Cxxx4DAFx++eXSBserFm9gUQe1hBfnm3McGBiIoqIiAC7TyMaNG2W8HNfChQsxYsQIAC4T02233SbXhfNIhq/hv9AMXENDQ8NPoRm4hk94hhGqu9LUHYSeBQs2bNiAL774Ql4D7mXE1Mx5tJWTCZrNZmGO9957LwAnc/WsIRkcHCz2XkLdoMO/JpNJWDP7raurk9e0vdfX18tGG9rl6Uzdvn27bLhhaGGfPn3Eebl9+3YAwNatW/HrX/8agJONA86CJ59//jkAyCriwgsvlM01lHPXrl1iK8/OzgbgzHpHW/m7774LALjyyiuF5XM+KysrsXTpUgCu1cgvv/wijty33noLgNPOTpk5d55ZETX8D5qBa2hoaPgpNAPX8AluKFGrcJM5MoveDz/8gG+//RaAMzIDcDJDNd8H4GTWZPKMRunfvz+uvPJKAMB1110HwBnxwVA9lTmTMVMWtRI77boOh0MYupqvQ92IBDiLLFBmMtLq6mphvp546KGHMGjQIADA3XffDcDJmNk/N/7k5eWJfZrsePjw4fjoo48AuGzblZWVwry/++47AMC0adPwpz/9CYDL9r97924JLSTr3rlzJ+bPn+827h49esg4mIvF4XBg8+bNMqeAM6rGs2CBDiP0f2gFruETVCQ7duwAAKxdu1ZC0hiDrYJOwrq6OlFgVG4DBgzAr371KwDAkCFDADh3DaoVaQCnoi8pKXFrt0uXLl65UAIDA33WhvSMSXc4HCIXQwAbGxslfI5OPzVumu2xz2XLlkkY49SpUwE4FeDf/vY3AMD48eMBAG+//bYo5JEjRwJwPuA4fwxFLCkpwRtvvAEAGDNmDACnyeORRx4BAEyZMgUA8MILL2DcuHEAXAUd2JYKOilVREZGivx8mEZFRYmpigpcw/+hTSgaGhoafop2Z+CtrVnXUtjtdmFaaqY4hmtx2clQraamJnmPYWMqmySTq6qq8sr1UV1d7bU8bWhokCWq6iwiC+J7aj4KXxnmVLOBynLZB2WlqaCoqEjGRCdYXV2dV+VyNQSQbFsN9du2bZvbuNU+VDCcjU7AoUOHCttk6FxNTY0wQjou7Xa7MGaVJXL+OD/qXKjhd55OVsMwpA+VYZKN03FXWVkp41R3OLIPynfXXXcBcJYsYxuffvopAODiiy/GLbfcAgD45ptvAADz5s3DAw88AMDF4j///HP85S9/AQD853/+JwCn+WnVqlUyXsrOFcArr7wi41+yZInbXFutVrmnPB3AgHveEzpU6Xjt37+/rGC4qYj3SUvQ2bODdnb5TtVWa/vSDFxDQ0PDT3He2sCjoqKEedMJFhcXJzbDPn36AIBsoVaT1ZPVqOyYLCw0NFRYPL9rsViEvZNdHT58WOy+l1xyCQAn4+P2cpVZe+brANwL6PJ/vibrrampEYbFp3ZcXJzYe5kbJDY2VmRlnustW7YgKysLgIuBk6GZzWZpg8wQcDHLG264Qf5yKzkLDKjVuslwAwIChAHzs4aGBlkhcD6tVqtcKzpMLRaLMEt12z5ZuzpPnvmu1XnheCIjI70KDQOuVc3FF18MwOVY3bZtm7zmaqewsFAY7o8//gjAyXRnzJgh3wGcm5Xo+OR1v/LKKzFp0iQAwKJFiwA4WT79Cpxvh8Mh8022XV5eLnPGebrkkktkvNzKP2TIEFkRcfv80aNHpe0ePXoAcF+ZavgnzlsFXltbK0tpNfaYsbJUWvxhv/XWW/KD6t27NwBnOlC2QQfSiRMn5Ed0+PBh6ctXZXAugakURo8eLT8oRmAYhuFlIrBYLPJaBfvgEthkMomZiD/ikydPiuJmtMWKFSsk/wUTTKnwrK/ocDhkDhiXPXz4cIll7tKli/RPRUqFGxISIg8VKkXGUQMuZXT8+HG32GzAafrg9VArvHvWKqypqZHzCLXghFqb0tMEtmLFCqxcuRKA60HIvCeAezpXwJmHhJExdDoePHhQZBo+fDgA533BByDPi4mJkYcOr4kaV878J9HR0aJcadaoqakRJzBzocTGxsrDk2PMzMyUSBPmSbFarV61OB0Oh8wPnbca/o8zmlCSkpKwdu1a7N69Gzt37hRPfJcuXbBy5Urs378fK1eulBtfQ0NDQ6N9cEYG3tjYiMceewxZWVkIDw/H1q1bsWrVKkyePBlr1qzB888/j2nTpmH69OmYPn16e8jcLNTV1cnSnCykoqLCKzUpmenixYuFQTG5/q5du4S1qKk9uQQlgxs0aJCwNDKzmpoa6YNLaqYlBVwM02azifmBZp3+/fvLa/YVGRkprIpsrqCgQBjw1q1bpS+agLhENplMPpP3kwkyzjkzMxOAM+SN7JgPZrPZLPPDv6qzRTW5cLw0L0RHR4u5guaI8PBwGTdXOXa73c2xCDiZsyeLDggIcAsVpHxsR3VweppVhg8fLnHs//jHP+S7KnsFXDsnIyIi5Dr/8ssvAJwOW64yaDrr2rWrrG54/okTJ2Q8zK74+eefi3w0rW3cuFHmmXL26NEDEydOdPtur169kJ6eDsDl+O3Zs6fcF7xmao1MthccHCyy8PfQ0aX+NM4eZ2TgRUVFYiutrq7Gnj17kJiYiPHjx2PBggUAgAULFuCmm246t5JqaGhoaLihRTbwlJQUDBw4ED/88APi4+Nl51lRUZE4eDxx3333yeYENSTtXMNms4kdkzZru90udkcmt3/xxRcBuNvJuTlj4MCBch6ZT2BgoDAZsrXS0lKxV5LdFBcXC2NbsWIFAGd4HpmjypLJlLlh5Msvv/TaUGIymbxC4lQZ1F11nvbh4OBgKaR7zTXXAAAGDx4sDNhzV2N9fb3Yucm2a2pqxJ6rskUyZbK5qKgomePly5cDcLdjs5xZcnKyOAK52iguLhaZCDUk0FeolRpu6VkAQb3feN7cuXMlPwnHUVhYKLlDPFc0o0ePlvmmLbqsrEx8D5wfu93uxaLT0tJkvLQ7BwcHS+FkOoB/+OEHcXLS+Thq1CiMHTsWgMsRabFYvMIIa2pq3ByfgNMpzHlT86aT+esdmOcPmq3Aw8LCsGTJEjz88MMtSkM5Z84c2QpMhdpe4A+aS8rQ0FDx9vMHypjgxsZGcdwxSuDiiy+WnYFUALW1taKMuFSOiIhAWVkZAJfZYs2aNfjggw8AuMw1ahyvL6g7CVXFTfAHqiptz/PCwsLE0TVq1CgAToeppwklMDBQFDIfXhxrQUGBKDSaFhISEkSRqA8SjocKqKysTByaVIYBAQGi6KjUIyMjRclwXPv37xelxoeKWr2eY2hoaBBlyoeVYRiirDiPauw725g8ebJct3nz5gFw+nMoM/9ybl566SX07dsXgHvkEl/TKd7Y2CjmFD789uzZIw92PtQmTJiAf/7znwAgK9vIyEi5f66++moAzhqbnul2CwoKxFRH+ex2u1dUSW1trTx0OGdqYi/OhRqFo+GfaFYcuNVqxZIlS/D+++/LZobi4mKxoSYkJLh58jU0NDQ0zj2axcDnzp2LPXv2iNMHAJYuXYpJkybh+eefx6RJk2RZ2llQXV0ty0wyM4fDIYz7ww8/BOAeQvfb3/4WgGupfOzYMVltkFVFRUUJk2G7ERERsrp4//33AUBSqqpobGyUdtiu6mhTocaJe4LL97CwMNn1SB9Ejx49hNmSnZeVlUl/fNDm5uZKWTDm2uAY1ORTdATHxcWJs5O5PtLS0oQJkvXm5eUJs+M80lGsnqfuDuUYd+3aJY5AMsj4+HhZXXDuIiIihHnTwRcbG+sWMw84mb9aEg4AXnvtNYmJJ+x2u8hMRk32azabRX46Zfv37y+JpmgmS09Pl+tC02JsbKysPPj7uOCCC7yYdWZmJr7//ns3mSorK+U+43WMjo4WMw0/q62tFae2GlfP73gWqgBcK0fKpuG/OKMCHzZsGO6++27s2LFDlnwzZ87E7NmzsXjxYtx77704cuQIbr311nMurIaGhoaGC2dU4Js2bTpluBGdUJ0RVqtVmCiZRkFBAV544QUA3hnZLrroItnJRmZot9u9wgOPHz8urJNOsp07d+J///d/ATiz1wHum0jUHXVsT3X+eZbx8nxN0EZPx+vAgQMlnE21hZNlc9dpfn6+bEQi6y4tLRWbqWeB4NDQULFf89r/8ssvcj6ZXnh4uNjIyXoPHDggTJmlu1QGzjnr2rWr1w7UkpISuVZksTk5OcLK1cyCtLmreVfILD1XICquuOIKWUEwT0ltba20vXHjRgCuDU+HDx+W603WX1xcLOdzVXLixAmRiWy+qalJxta/f38ZF9/j+TExMcMvK/0AACAASURBVBLeylVjfX29mChVXwLnkveRzWbzygujbtRhe2ohaK46fW0W0/AvdPqdmK1NTqPmpeYPOTc3V5Spp9K69dZbvRRpQ0OD7IxT4435A6Wjb/ny5VizZo18h/2rFWQAp4OMTjI1QsJTWZvNZonqUfu//fbbAbhMCTU1NfI5f9h2u13MN+vWrQPg3EbtmUpU3bnoCdX5R9kCAwOl+gwdjRs3bpToHKaJ9bWVXp0DKujw8HAxZ3311VcAnIrRU8mYTCavB3FoaKg8AC+88EIAzjh+1smk6cZisch7X3/9tYyHZg8q6fDwcFGwfMBRkZvNZrmOVIbbt2+Xe4URRvfcc4+cx2tXX18vc0nnZF1dncTJc0W7a9cuca4zFn/IkCFelXPq6+ulD8oeEhIisvDe6tKli1tOdMD5gOEDjlDjxYlzlcCpNWjLpE/t1VdrE2e1FjqZlYaGhoafotMz8NZCDdnjUvHkyZNesbBkSMnJyfKemvxfdWYBTvZHZsTEUKtXr/ZZZ5CMkY6kgIAAYadq1RrKQLY4YcIEMQ3wCX706FGvdKl2u136pYMtKytLqrHQlKIyfM+VB+Bi9Go8MZk9ZVdTrpLt19fXSx4O1THnufIwmUxeuWJycnK8UupWVlaKWUGNdafMapECykJmraasve222wA4mThDI+nsTE1NlcIUXEmsX79eKvKo5iF1rIB76tYtW7a4yTZkyBCRiXORmJgo73FF8e2338r1Y9ihavIgK+/SpYvIrlYV8jTLhYeHC7NmuGNcXJxXSGVgYKDc12oNUg3/hr6CGhoaGn6K85aBG4bhVYextLTUy95MJpOYmOhVU7GpqUlek5FZrVbJafLZZ58BcGU2VL+rMk6y2aqqKmFiZEOZmZnCGGmHDQgIEBbH85OSkoS9qysKhpDR3r1p0yZhdoTFYpH+GP6WlpYmm1G4QYc7BHft2iWhhXSSqkUUWHuxuLgYGRkZAFwsOiYmRnYfMixRzbhI1NXVyfUhi4+IiBCZaM/9+eefZf7Ynjq3zFsTHR0ttuWBAwcCcF4zroJog54+fbrMgRpuyBUPMxWy/9TUVOmDq4KQkBCvTWkLFy6UMEL6Krp37+6VaXLHjh0yRjqlv//+exkjK8yvW7dOmDk/s1gsMmdsNy0tTeaD9vOLLrpIdrRyZ6dawEP1JWj4N85bBd7Y2Oi1c7GwsNArdSqX8ZGRkV5xt126dJGbncvZAwcOiJNww4YNAJwRFdxJxx+TmkCKS9Z+/frh+uuvB+Ba5gOuJTKVRlBQkDx0qLTVmF3Kd/LkSVFaNAFUV1fL5/xrsVgkJQCTSV177bXynuc296SkJFFuasw026NZwWazycOCn/Xp00dkobMQgJcjsKqqShTe0KFDAThjvhnVQufk/Pnz5eHDWOmCggKvSIro6Gh52LDAcr9+/bzymj/88MMSxcO5nTx5srTDyB3KVFFRIYWE2YZqVmFcdn5+vuy25A7YwMBAufc4Tzk5OTIHfHCq8eo0rakmJDUnuyfsdrt8zjnOysrCb37zGwCuVMbqfgPG9vuKdNLwL2gTioaGhoaf4rxl4CaTyasOZEFBgRfrYB6J4OBg+Yxst6ysTJxVH3/8MQCX8wpwmVV8JTeqqqoSpyTTgl5++eVuYXzsl0xQzYXC12S2YWFhXrldSkpKxJyjpjLguLkauOiiiySJ1bXXXgvA6dQjcyPrUwsI0Gyg7uBTnY2Ac9XC8DeuUJKTk2VsvgoHqE5ULvPpTOzXr5/0cdlllwFwTzFL5vr22297MeuSkhK3vCicB8ZLs3bl0aNHxYRCBlxYWChmnCeffBKAu+mIpg6uUD777DOsXbsWgLujmvLRDHLppZcKA+ZngwYNkvEwzttqtXqxbIvFIt9RK+dwxaia0Xi9aco7evSorGBYOCQ+Pt5rhanh/9BXUkNDQ8NPcd4ycNWu6Lm7j58DLhZ26NAhceowz/nq1auFiRGqI4l2TYvFIgyUGDt2rNRIZB8VFRUik8q2PUP7fJUHa2pqciu3BTiZIxmwGh7pGbIXEREhDlKybHWTCTe+ECUlJV5ZE9X8KITNZhO7PTf5xMXFiY2V8kZHR4vdmOzcZrPJTk0WNoiNjZXvcKPKwIEDZYwssqA6qImKigphtFwhbNq0SVI8cHPNVVdd5VaDk3NH+ch2uVkrLS1Nri39Ab1795Y55gaupqYmCeMjm163bp2s8BiqOWnSJCkoQTu3w+GQMXLeCwoKZK54vYuKitzy1RBqqTl+xpUiVxs33XST3POe4bUa/ovzVoGrMbP8oagVUmiO4A9i/vz52LRpEwDXDkvAO+90UFCQWww34PzBcGmrJrhSt99TDsY5qxEQnmk9GxsbvaqmqHUOOYbq6mqR1fPHqb4XExMjioR91dbWuuWUBlxL8H379olzlErOV9Ktbt26yXhochk6dKjEJbP/yMhItwRPgNPxy/6pUI8cOSJmJypLtSAzx3rxxRe7VTcCnKYFPpw4xm3btkm6B5pkysrKZEyqTJ7XhXLu3btXtrnzvUsvvVSuCx22JSUl2LdvHwCXucThcMi9x/qkv/rVr+Ra0ATXp08fMa3xvty1a5cQBNU5yaRYvM6sy+o5F5wzXpeJEyeKiYmERucF939oE4qGhoaGn+K8ZeC1tbVubBNwsmPPeGSGun333XdebQQHB8t31ThnhgXyb0NDg1cq0/r6ercajoCTzaqMljJ57va0WCxecqqsnIzVYrGICcMXmyKby8vLE3bIqj85OTliHuLuP7K2xsZG+S5lV9k3zRyxsbFiHqKDz2w2C7PkaqS+vt4rgZPNZpPQS8af79ixQxyGNDnU19eLg5Z/J0+ejCeeeAKA69o2NDS41SgFnCsJmkS4QgoPDxdWTEZdWloqrJjXgjKlpqbKKo2OwYaGBgk3ZPrZtLQ02eHJsRYVFUmcPpn6oEGDxGSl7tD1vC+GDRsm9wNXHqGhoXI9eO/961//8sozo94XXGWojnGOUd01rOGf0AxcQ0NDw0/R7gz8dNm62jJzV1NTk4SQzZw5E4CTcagbJAAXQwkJCfEK5QoMDMS9994LwGm7BJybbf7whz8A8G1vJuvMzc0Vxxgz9tXW1spGFXWHnqed3WQy+az5qKYpBdyzzqmg7Z9McOvWrbKzUs3n4ekUJYNV855wXGpmRo6hd+/ewkrJROPi4oRlk0GqG3qY7a9bt27CGBnCFxgYKNeH/YaGhsp15LWy2Wwyz2TOZWVlsrGKtvBrrrkGS5YsAQA89dRTch4333AuAgIChA1zztTryb7UnbC0i3Mz1FtvvSVj5DxWVlYKK+fKIjIyUlYSXElFRUW5lUPjeby2tI8nJSXJPUfZIyMjxUFL56jdbhd2TQdsfHy8bHCis9dzU1tz0NrsoGdqq61++20pX3v21dq5OG9NKN26dRMHD5f0ajIrz2gQu90uKVG5W/Gqq64SZUVUVlZ6RXn4QmlpqTgCqWTi4+Plx0uZzGazLJ954ZqammQprZpm+B3+iGNiYkRJqgm4fCWs8qxjGh0d7WV2oakgIiJCzmdkRUpKiuwe5XiCgoLE1EE5s7OzJeaaD78XX3xRlB/Ps9lssn2dSjspKUkeBLw+akwzH4T79+8XJURTRkxMjDxkGRkyfvx4PPfcc27nhYeHy4OAD6S4uDiJAqHypxyFhYVeueO7du0q5iY+IADXrky1CDJNVnyAnDx50i0tA+BeFJv3QHl5ucwBlXFoaKiQAjp7Kyoq5AFMOevr6+WBwHnPz8+XB6tqatHwb2gTioaGhoaf4rxl4IWFhcKIHnjgAQDOXBoM6SMbYd6KG264QRL/kN0FBgYK02JoWHp6urSr7pDzZL3FxcVYtWoVAFdCoRE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QXFyM4uJiWK1WWK1W2O12KdlF0AMFcOrDqTdvCpSXl6O8vFz6xax1YWFhInN1dbW8HA5Hk+0ONDQ0mh7nbT7w3NxcMfrRcHn//fdj06ZNAICTJ0+6fT85ORnJyckAnEFKgDNHM1UoqrcHjYKnc9M7FwgJCQEA/P777yIzczzTIygsLExk1sZLDY3zG+c1A9fQ0NA4n3HeMvCgoCAUFBQAcPpLA07j35133gkAeOqppwC43O8cDgc+/fRTAC4f8QEDBvh0zOex5vID/+mnnwA4/drZj8jISADOvqql0AB3tY+Ghsb5A83ANTQ0NFopzltq5nA4hHnTrS4gIACDBg0C4IrA/Pnnn+U3SUlJAICrrroKANC7d2+vdg3DEOZNvXhTGTLJrBm8U11dja5duwIAoqKiADiDfOhSSFZOG4CGhsb5hRa/gDc0z4PVahUVCnOHqB4lDz30EADXAu7v7y8LJEPvBw4cKMZBRnXm5ubKOfz8/AD4XsDVhZ4wm81yjL/NyclBRESE/AZwLrh8OFCmsLAweSB9++23AJxGTS7g7Ku/v7/4f/NYUFCQqF9KS0sBOA20jOikioULfVBQkPjC8zuhoaES0RoTEyNjQYMp+1BeXi7jERQUBMDpo87+UI7g4GBpj/0ym81evuueXkDA2amu7Ha7qM3y8vLkONVmHG8+9P38/OR8/CwkJER+y3517NgRmZmZAFxquYY82NVx4numQsjKypIC0ZSltLRU5reaYoHy8/oEBweLPPzrcDi8UjEArnnoa9wbM+/KmdCU+UkagqYci9qgVSgaGhoarRQtnoE3FJWVlcLsyHYLCwuFrbAAL3OYf/XVV25MBwAeffRRrFy5EgBw6tQpAE4myqcqVRlqWlcyV5XRqIxHfa/KBrjYsdVqFRfIoqIiAE5GSDbMY+3bt5fzqOcjqyKzrqqqErl85VMh02rbtq38nsxNzadClcyhQ4fk/EzHy4jQoKAgHDlyBIBLJXX55Ze7yczx5DXgZypboUwqi20M43FOTo6MPdVOdrtdsr0FBwcDcCY3A4CMjAzZmTCDZVFRkbBsfv/333+X9jxT/NYHKuv1TJoWEBAgx/hXdWvlfD916pS8p0wnT54UeSif3W73GkvDMLzkbi6jvcaZoRm4hoaGRivFecvAHQ6HMGoyB4fDIYyXx2655RYAwIYNG4QBM2Dm6NGjmD17NgBIzc+8vDxhXdQxx8XFCSMic62srPRiUDabTZgbYbVa5TfUa9rtdmHIZH9+fn44duyY23mvvPJKYdmq7tQzLa7NZnPTj/J7ZNQ8F5lcYWGh107CMAw5Rt12aWmp9JFtFBYWYv/+/QCcuWcA4MiRI8LU4+LiADgNxNQZczzPxPBUJtjQYhUdOnQQ/TDbKC0tlZ0J+8sdRVhYGHbt2gUAeO+99wAAgwcPxuDBgwG4bCKXXHKJpFPOzs4G4Nrt1Afso8VikXlB+Pn5eenobTabfI9zOyQkROZ+SkoKAHcbD7+n6vfrItPZjLvGucF5u4BbLBavG9Xf31/ec9verVs3AMA999wj/tUsOmG327Fs2TIArvSzs2bNkps8Pj4egHOh5+LGBVotBqEajzxvwJqaGvkeF1R/f39R2fDmbNOmDfbt2+fWn969e7sl2QKchizPm0zdZqsPBILyUSZ/f3+vBTwnJwcHDx6U8wLA3r17ZWGmYXPFihVYvny52/lXrVolxlaeq7CwEP/5z39knHkuz/zrdS0cUlecOnXKy3CnGueo/qEaLT4+XtQQPXr0AACcOHEC7777LgCXx9KmTZtkwaahkXOsIbBYLG7Eg8f4IFavj6fBu7S0VMaZyebMZjO2bt0KAOKJdeONN3o97GszVAJnN+4a5wZahaKhoaHRSnFeM3CCrMXPz88rPwhZy/jx4zFmzBgArvJFs2fPRnp6OgDghx9+AABMmzYNTzzxBACn6xjgVAtQhcD2VLbCLXVycjL27t0LwMWgAgICxLDXt29fAE7Wp34OOFUUzNVCJCYmelXf8eW+WFpaKmoKNdUst//8jKzNarVKrhi6yyUlJUkqXrLp4OBgJCYmAnDtPFasWIEJEyYAAF599VUATkMgU/sSgYGB0h5VVkwgxvfslyfz89XHusJisUh/uePZvn27qHs4BhybVatWCRvnZ2PHjhVDLq/PuHHjZA5QxUVWWx+obFstLAI4x4LHeN78/HzZBX333XcAnFWwuIOjnPn5+ejSpQsA4A9/+AMA533BcVbHXZ1LKs5m3DXODTQD19DQ0GilOG8ZeE1NjVckphq4QJc5Mq327dt7sZEnn3wSzzzzDACIwe3333/H008/DQB48cUXATjZMXXKZKybN28WF0RmDwTglSExKChIgoR69eoFwJmDhUYysqbMzEzs3LkTgIuxduzY0asMnMViEfauBgaxT6phjL+h7L/99hsApw3gq6++AuAy5p04ccItbwzgNOr1798fgIsx33bbbfj6668BQIyugCsQiu1NmDABCQkJbnL6gi/XwrNBZGQkDhw4AMB1TcPDw0WX/dlnnwEAPv74YwBOoyevxYcffgjAyXR5XTZs2AAAeOmll7B48WIAkH41xI1QtZeoBmTA97XdunWr7OpWrFghx1RDJeDcGd52220AgO+//x4AcP311/uUwZdroUbLhGbgGhoaGq0U5y0DV4NrVEs7GQ5ZBRlKSUmJF5u96KKL8NprrwEApkyZAsCpz2btzwcffBAA8Nhjj8mxX375BYDTfUsNlgGczIbeLERFRYXoK6krP3TokMjMgBKz2SweEvR+oQ5Xhap3VYOFGHSkloMja6bXDdnn119/LbYCNbMhZeLuoUuXLtLe0aNH5RjL1Kmh6nTRJCZOnIi1a9cCACZPnizte+p9Vfan5qBpaP6Zxx57TIpvU7f9zDPPiN2D9hKea+LEiXj88ccBAC+//DIAIDU1VTxtmHZh69atmDt3LgDInGlISTs1CIgyqMFfvKa0KXz00UfSj927dwNw7ob4Pe54bDabzCW6eappF9Rxry11wdmMu8a5wXm7gBuG4VVwwc/PTxYfqk7atWsHwLkoeW5Pa2pqxGD3ySefAADuvfdeUQ3QwPm3v/1NbpjTFVFQbwyei+odwLVY7tmzR9wX6cIWEBAgsvNYSEiILDjqgufpkx4cHCwPDqqOTCaT5CLhuTZv3gzAudj6MlbxgcQIyrCwMDm/qhrigsIFIz8/3yvF7ezZs0UWqroAeOXrqKmpkcVF/dvQheTpp5/GqlWrAABLly4F4FT10IDMftPlbs2aNeJeyod4//79cc899wCALO5PPvkk3n//fQDAunXrAAAjRoyot3x8qDocDrmmavQlrykfmCtXrpQ5pLpeepIRwzDE9ZEPotrG3fO3jTHuGucGWoWioaGh0UrR5Az8dNm6GtNFSY1Q4zaxqqpKGA6NamSQZrPZK3LSYrHIMWbbmzNnjmybaTSqqakR5q0ya7ZDVUf//v3le4zaS0lJ8cnGuR1+8803AbgyKgIutU92drYYFtkvm80m51UjHDkG7G9ZWZmcgwycjExlWczSR9c4wGWkO3DgADp37gzAtXvYvHmzuFceP35cfsO26cK2f/9+/Otf/wLgCnhRc32ouWXU6wE4dwiUi7/18/MTNQ37bRiG9Jfyjx07VnYLdGPs0qULevbs6db3q6++GoAz0IsulTRsVlVViQGQu5Yvv/wSl112GQBIv0aNGiVjwAjUyspKuVacC3a7XeTjZ+3atZO+qdeOboGvvPIKAKcRnOoxVdXiOadqamrkPeejr92iOlc83Qmrq6sbNQPfubj3W7p8tbXV0HNpBq6hoaHRSnHe6sDPBmS1xcXFYohjJroePXrgwgsvBODKy6265pHljBo1Cvfffz8AV2j1wYMHhWGSuYWGhkoQCeHn5yfMkfr2/Px80dePHj1a5OROQs3BQvnJ4GpqarzcF7ds2SLyqzlQAPeAETUohQEjLPq8fv16MajSwLp582Zcd911AFy5Q6xWq5yXRaUHDx4sOwmOidlsFuZImSorK4WRqCH3at8Ap26fdg3KWVxcLC52NBAvW7YMX375JQDXDiEtLU3G+/bbbwcAXHPNNdKHhx9+GIBrF7F9+3ZJwUAW/8033whT5a7krrvuwvPPPw8AIkeXLl28ik6bTCbZUXD+FBUVyXvKVlNTIwz8xx9/BOCeO55QdeAq1J2JxvkBvYAr4A3DZE12u92rmo3qi8u/ERERclNyEfnhhx9k0WTxiAsvvFBuRkZfAvBawNUtFNUCVVVVUs9z6NChAJxqC3XhBpyLJc/BG7aoqEj6wQVn48aN4g/sieDgYC+vET8/PzHo8oG0Zs0aWSjo2VBWVoYrr7xSZOZfjhULZFx66aWiRuKC0qFDB3lQqtt4qhXUiESqlLiQHzp0SKJCKUtmZqaktKXaYPz48W4pennee++9FwBw7bXXAnCpsC688EJRofDvpEmTRI325z//GYAzJoAPwEsuuUTkoM++Oo98JQrzTDSlqonot/7zzz9Lf1SDNs/LaxYQECBzgDCZTF4JuzRaP86oQomJicGGDRuwZ88e7N69Wxaj8PBwrFmzBvv27cOaNWsalHlNQ0NDQ6PhOCMDr66uxqOPPort27cjODgYv/32G9auXYs777wT69evx9y5czF9+nTMmDEDM2bMaAqZzznIhiwWixgviezsbGFVI0eOBOBkbcyVohaAWLJkCQAXI7zmmmvwxz/+EYBLHaCm9CTDVI2ZdN3r2LGjbO/5udlsFjZJlhoWFiZqF2YINJlMwtzWrFkDwMkwydiocuFDOCAgQFwkqTaoqKiQ9hjBmJCQ4FXcok2bNuKjTFVGXl6eyHzRRReJTHSFGzVqlIw3x0U1zPEYVS2qgVpNp8vfkH2mpKSIux//XnzxxbJLYprYfv36SWQlWTZ3ComJieLuyB3Itm3bZHfDSMzbb79dVEaMqP3jH/+Ib775BoBrrpSVlcn8UQsreBa1MJlM0g/K+cEHH4iLJl1J+/fvj7S0NACuecZx47jwf8pMlq9VKa0fZ2TgmZmZ2L59OwCXTjE6Ohpjx47FokWLAACLFi3CDTfccG4l1dDQ0NBwQ7104HFxcejfvz+2bNmC9u3bCxPLzMwU3aUnpkyZIvpF6v5aKshMaFyqqakRhqdm6rv88ssBuPIq22w2MezR0Pjyyy9Le9Q779q1S9wC6XJ25MgRr3OQaaoYMGCA6H3JjmNiYuQcZHMOh0MMm9QxOxwOMZpu3LgRgNNgSWZLpsz+UOeqQnWV5HWnoY+yAE72y3P4AufJyZMnJb85c42UlpYKOyUTDQkJkX4zYlXNacMdgs1mE7l5jgkTJkjQCtvYtWuXMH9i9erVsmtQZQGc+mzmPycrP3r0qOigaQjdsmWL7GDIkrt37y59nDRpEgDnzoJ94znU3PFq4Y0tW7YAcBXeLioqkt9wJzNw4EDpB/O1l5eXe0VxAq6dFufK6YLONFoH6ryABwUFYdmyZXjkkUfqlah+/vz5mD9/PgCXl0NLhae3Q3V1tdyo/CwwMNCrqk9hYaF876abbgIADBs2TLasTKq/atUq2Q7TAwRwPThU1Qnb5uJ62WWXydafxi2TySQPRaoU8vPzxeeY6pLff/9dzstFPTQ0VDxI+JeeFQcOHBCZVOMbPSCuuOIK+R234fSjTktLw44dOwC4h89zLOgNEhERIeoK7vCysrLkAch+d+zYUQyQnHehoaFiBKbaICIiQvzTqXZ67bXXZOHmQnv06FFpjx42nTt3FpWE50Pg22+/lcWd475u3Tp5gFDFlpubKw809qdPnz4yVmyDDyjAdY2rqqpkoeX32rdvLxGgNHK3bdtWrjMfJuPGjZM0AKoBVH2gc8zUzwHXPNdovaiTH7jVasWyZcvw4Ycf4osvvgDgZFCc9FFRUcI6NDQ0NDSaBnVi4AsWLMDevXsl+gsAli9fjsmTJ2Pu3LmYPHmypB9tzeCWkkzFarV6Jb9SWTmNZu3atZPf0gVRzcVy1113AQBuuOEGSYJE+0FOTo6oUNRESmSs9DmPjo4WVkUVSXl5uVf1dsMwZNvO9LOrVq1yi6QEnNt7RkXSgEc2yxwpKiwWi7BTGs4LOIMAACAASURBVORCQ0Pl/GS1e/fulfFhv6xWqxiGuSu48cYbxdhH2Q8fPuzmjgg4mTvZJhnwgAEDhFF3794dgHvkKwsbxMXFSZIxMvoJEyZIXhsiMzNTDIFUoTCaNDMzU5JuUY7y8nKv8nZ2u112D5deeqn0gS6X3AF169ZNWDsZsFoJnkU7TCaT+I5zpxIRESGqN6q7EhMTpR2qSHwx8Pbt28vn3AUxV41G68UZF/BBgwZh0qRJ2Llzp2wNZ86cieeffx6ffPIJ7rnnHhw5ckRUBxoaGhoaTYMzLuCbNm2qNTZ/2LBhjS5Qc4L9pJ5RjQxUs7Wp1b8Bp26WrJiGNn9/f2FGzAT4zTffCMOiPtczUAhw6pPJ5hjV2KdPH5GF0aFms1lYFZk/ALE5MKPe3r17RWbqbvv06SPue2RiZMdZWVlexXNtNptXetzg4GA5RiYaGBgo48gdSHV1tYwF+52VlSW6euYY2bVrl/RDzUvD3Yiqz2aBYfYnNDRUrgf18e3btxcDMr//1ltvyXmpO1Z3J9Q30x6Rn58v3yMTLigokOvGXUFubq60w3OFh4fLvCAj7tChg+xMOC9UHThZd3JyslsqWI43y/4xV8vBgwfdKtQTntGZkZGRMgc4RzUDb/1o8ZGYDU1OYzab5aZRfaU98x9zYamqqvKZi9rTI8RkMskxGoNMJpPcRPQZLikpkWg+hj3/9NNPslXn4ma1WmWxpirjiiuuEOMXt+Bms1nOoSau4nuqPTZt2iQ5yfnXbrfLgjxkyBAATg8Sek3wxmdblZWV4t3BhUr1GeZCWV5e7uW5U11d7eVfrMrOc23cuFHUAVwgs7OzRS3Fa1FUVORlNLZareJ3z+jUiIgIaZu+9jNmzJCoVdpuBg8e7KVWycvLk9/yHHzQFhcXe82voqIiUWGkpKQAcKYUpp84HxB9+/Z1i/YEnAZvPohUH22qZPjA+eWXX0Qm9n/gwIGivuI83rNnj1w3qpOKioq8IjFtNpvX3A8MDJTx5oOzsLBQPlcjeYGmN3o2ZtKnpjpXQxNnNRQ6mZWGhoZGK0WLZ+ANRXFxsTAIMi21OjvVJGqlGjIjNRqOUFm55+cWi0WYKl3o1q9fL4mbGBmp+t2SrfXt21d8eXksMjJS5CQbUlPhkgEbhiG+v/S9/u6778TYyO8VFxdL7Uq6unXr1s1LraLmyPAswODv7y/qErXGqGfVI7Wii686nGoUKceHKg/DMOR6EGpEIs+xZcsWN5UE4GSfLMpAI92UKVNEFhonN27cKPJQFVVZWSnHTqcmouyhoaEynnRd7N27t7ge0khZXV0tKhTOD39/f6/kYfv375e8NPRRr6iokH5TXTJ06FBh5dz9paWliQGZfVDdN1UDJ9U0/Dw7O9tn/h9PozphtVq173gLg2bgGhoaGq0U5y0DDwwMFPZFprN+/XphSWSnNAJGRUWJUclXcQS1LiA/VwsMMA/GRx99BMCpNySzVZk6WS914WpmPcrStm1bN3dEwMn+yIrJoHJzc0VXS333rl27vDIJJiYmSnkv6tbVlLVqnUz1f8DdRkDQBlBTUyMyqfU3PX+rlgfjOWJiYuS6UE/dp08fMQTys61bt3oFUzkcDmGTrL8ZGhoqbJy7oEGDBom7Ifu/d+9eiWKk3WDdunVir/BEdXW1XGf2tby8XNrlrikhIUF030RxcbFbrhbPcaScTBQHOIOuAOf8ZHQrd019+vSRseA4V1RUyHuyc7PZ7FWO7dSpUzJmZOwJCQkyBvx+aWmp2HHU3DOU/VzrdDXqh/N2AVcNZzSS/ec//3HLrQzAzduCNwINeMHBwbKQcpENCgoS9QYX3NjYWImaU6NUVb9cwtPrZP/+/RKaTkPW1VdfLUYy+iObTCbxQ+ZN/vPPP4vPM/2MS0tLZdGgkfLqq68WgyGPlZaWeqU1VVVIqt87x4uLEFVSgYGBsm1nW6qhy1MdAbgWivbt2+NPf/oTAEga2Ntuu00eopTlH//4h4wPF/fjx4/LNeJ4h4SEyLhQ5q5du3qpeO677z4JUafHyYkTJ2TM6BtPj5PU1FS5jqpBm+NOmTp16iReHZwzUVFRos5R0yrwc6qQkpKS5IFAgjFkyBCJNuWCWllZ6eXzDbgeRJTFZDJ5JUjLy8uTecjreOTIEfke26uurvbKV055y8rK9ALewqBVKBoaGhqtFOctA1cNbGqekNpQVVUljJ3MkezJE55GP3VrSSZTWVkpjEdNOOWZBrWqqkpYJJnhzp07JWKT1V0iIyNlC0+5Dh8+LMyNn/n7+4s7Irf0w4cPlzwnZMoVFRVeOwT2y9/f30vOiooK+S3d8MrLy73c0Nq0aYOLL74YgDPtqifYn44dO+Kqq64C4IosjY2NlZ0R2efgwYPFb5m7jOPHj3sZWXNzcyWdA/vtcDjkfDT2hoSESEUejrGfn5/sqsjsucto06aNV21KwDVHqAYpLi6WXQMNpna7XcaWBlOqutRj+/fvl7FlX6OioiTDJ2WxWCxec7pTp06yW+AxdadAxp6dnY1169YBcCVDczgcGDt2LABXSt+wsDBph2PMa2uz2XwmWtNoPmgGrqGhodFKcd4ycMBbzx0SEiJsyjPiTzWMEapLnHpMjcoEnMyI7NWTGfqSA3DpF9UiBtwBlJWVSUQeAzsCAgKE7apGUU+dZHl5ueiCyZTXr18vwUJkmKGhoaJv5TGeU62zqLZP+Zn3pqysTPpLljhq1CjRBdMwV1VVJePN/CdhYWGis2UqXqvV6nVdRo4cKSkc1IhJz+uyadMmCWThOCUnJ4thk4a77777TnYttAdERESIUZvsnXpnpk8GXLaUU6dOeaWE3bp1q0RgMslbQECAlFdjlsGioiKxlxBFRUWya6JLpVp7lXNFdUHk+Fx44YUSpOQrSyh3UIWFhbIj4t/27dtLqlxmqYyPj5dzcF5w/paXl7f4lND/13DeLuBWq1W2tPQPnjt3rtxwnlvb/Px8WUD5WUFBgZdXhHqMi5fNZjutz6zqecBFg1vw6upqr20pbzp+DjgXJR5Xox4JLrieIdSA8wakIdBXsVs16ZT6G7WPKnypljgmGzZsEBlU/2/2l8WPc3Nz5eHE74WHh8sCrqqOOD7sb/fu3UUNwN/m5OSI6oaL66+//iqRrFyMfvjhB/G1pkotPz8f48aNAwDJ9c4Q+by8PFmY6Wu/du1ar4jRmpoaUafw2MqVK/HAAw+4yblx40aRnWMWEBAgHic07Hbq1EnGnu1ZrVZ5KLPSz/fff++VnqE2UGXGdjt37iwLMmMHaDQHXCSH87e6ulov4C0MWoWioaGh0Upx3jLwyspKYQ5kxwMGDHDL9wG42I3D4XAzLAJOxuGZM8VsNnsxazUXOplZTk6OsE4yntzcXGGvPH9GRoZszVmwQWXWqv+5muCJx1T5PX97OpjNZmHZlEVVl9BYpo6X57msVquMC3ctntVuACfD9IxUDQoKkrGiSsFisUjbjD5MSEgQwx4Z8+DBg4W9UzUSHh4u15lqk8rKSmG5S5cuBQCsWLFCrhcNlwMHDsTDDz8MwKX+oGtefHy87OSoZsnLy5MqOeoug26gZLOJiYle/t9+fn7ik/7+++8DcBpvKSf/njp1CitWrADg8nVPT0+XfvNalZWVebFidWzVHZSvHDW8Luyv2WyW33iqa1QDp0bLgGbgGhoaGq0UTc7AT5etqzGDBFR9LhlUdXW1sAo1qo8gG1GztRFqDg8yHn5fTcup6qLV/CA8F8+nZvtjUMjjjz8un3kG/FxwwQViiGShBn9/f6/cIarcas1Fz5wXvn5HqBkXCYvF4sXu/f393YpQqH8BeBXDUKFeH7X4APW0HJPvvvvOqyo984YALtvEqVO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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for s in np.random.choice(len(x_test) - 1, size=5):\n",
    "    plt.tit(f'True: {true[s]}\\nPred: {res[s]}')\n",
    "    plt.imshow(test_images[s])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Write a scoring algorithm for multilabel classifier\n",
    "I chose to go with giving it partial credit for getting some characters correct even though it wouldn't pass a CAPTCHA test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": "Accuracy score: 79.3%\n"
    }
   ],
   "source": [
    "def multi_label_score(true, res):\n",
    "    score = []\n",
    "    for x, y in zip(true, res):\n",
    "        if all(x == y):\n",
    "            score.append(1)\n",
    "        elif any(x == y):\n",
    "            score.append(sum(x == y) / len(x))\n",
    "        else:\n",
    "            score.append(0)\n",
    "    return sum(score) / len(score) * 100\n",
    "\n",
    "print(f'Accuracy score: {multi_label_score(true, res):.4g}%')"
   ]
  },
  {
   "cell_type": "markdown",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "This is pretty good for a back of the napkin code that tries to cheat CAPTCHA"
   ]
  }
 ]
}