Mnist_Explanation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "521f19ad-fd27-4474-b40b-71aaf029a201",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/bhui/miniconda3/envs/xy_py38/lib/python3.8/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n",
      "  from .autonotebook import tqdm as notebook_tqdm\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "from models import *\n",
    "import torchvision\n",
    "from torchvision import transforms, datasets\n",
    "from torch.distributions import normal\n",
    "import matplotlib.pyplot as plt\n",
    "import captum\n",
    "from captum.attr import DeepLift, IntegratedGradients, Saliency, NoiseTunnel, GradientShap\n",
    "from captum.attr import visualization as viz\n",
    "import argparse\n",
    "from utils import get_args\n",
    "import matplotlib\n",
    "from models.model import *\n",
    "from models.capsule import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b7d695ef-0e23-48fd-a47d-9698a863fb3b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def add_gaussian_noise(noise_scale, input):\n",
    "    noise = torch.randn_like(input) * noise_scale\n",
    "    return input + noise\n",
    "\n",
    "def predict_with_randomized_smoothing(noise_scale, model, image, num_samples):\n",
    "    # Expand the single image to a batch\n",
    "    image_batch = image.repeat(num_samples, 1, 1, 1)\n",
    "    # Add Gaussian noise\n",
    "    noisy_images = add_gaussian_noise(noise_scale, image_batch)\n",
    "\n",
    "    # Predict using the model\n",
    "    predictions, reconstruction ,primary_caps_output, digit_caps_output, c, b = model(noisy_images)\n",
    "\n",
    "    # Get the predicted classes for each noisy image\n",
    "    _, predicted_classes = predictions.max(1)\n",
    "    #Result\n",
    "    avg_noisy_image = noisy_images.mean(0, keepdim=True)\n",
    "    prediction = torch.bincount(predicted_classes).argmax().item()\n",
    "    # Return the most frequently predicted class\n",
    "    return avg_noisy_image, predictions, predicted_classes, prediction\n",
    "\n",
    "def show_image(input, noise_scale):\n",
    "    fig, axes = plt.subplots(1, len(noise_scale), figsize=(20, 10))\n",
    "    if not isinstance(axes, (list, np.ndarray)):\n",
    "        axes = [axes]\n",
    "    for idx, noise in enumerate(noise_scale):\n",
    "        avg_noisy_image, predictions, predicted_classes, prediction= predict_with_randomized_smoothing(noise, global_model, input, 100)\n",
    "        print(f'Noise: {noise}, Ground Truth: {ground_truth_prediction}, Noised Result: {prediction}')\n",
    "        img = avg_noisy_image.squeeze().cpu().detach().numpy()\n",
    "        img = (img - img.min()) / (img.max() - img.min())\n",
    "        ax = axes[idx]\n",
    "        ax.imshow(img, cmap='gray')\n",
    "        ax.axis('off')\n",
    "        ax.set_title(f'noise_scale:{noise}')\n",
    "    plt.tight_layout()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0d5e6f90-4b3d-49a0-a477-24facade8b2f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Noise: 0, Ground Truth: 7, Noised Result: 7\n",
      "Noise: 0.5, Ground Truth: 7, Noised Result: 7\n",
      "Noise: 1, Ground Truth: 7, Noised Result: 7\n",
      "Noise: 1.5, Ground Truth: 7, Noised Result: 8\n",
      "Noise: 2.0, Ground Truth: 7, Noised Result: 8\n",
      "Noise: 2.5, Ground Truth: 7, Noised Result: 8\n",
      "Noise: 3.0, Ground Truth: 7, Noised Result: 8\n",
      "Noise: 3.5, Ground Truth: 7, Noised Result: 8\n",
      "Noise: 4.0, Ground Truth: 7, Noised Result: 8\n",
      "Noise: 4.5, Ground Truth: 7, Noised Result: 8\n",
      "Noise: 5.0, Ground Truth: 7, Noised Result: 8\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAB8UAAADPCAYAAABsmAAVAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAA9hAAAPYQGoP6dpAACNrElEQVR4nO3dd5iV1dk2/DW99947zNCGjoBIE0QE1ACWvBosSTTRV5OYR01M3sTHmGhMjEZjjaLGXkFFRJCR3jvDDAwDwxSm917v7498YMg+T5k9gwKb83ccOY7nOV3sucu1rrXue1OcLMuyjIiIiIiIiIiIiIiIiIiIiANyPtsHICIiIiIiIiIiIiIiIiIi8m3Rl+IiIiIiIiIiIiIiIiIiIuKw9KW4iIiIiIiIiIiIiIiIiIg4LH0pLiIiIiIiIiIiIiIiIiIiDktfiouIiIiIiIiIiIiIiIiIiMPSl+IiIiIiIiIiIiIiIiIiIuKw9KW4iIiIiIiIiIiIiIiIiIg4LH0pLiIiIiIiIiIiIiIiIiIiDktfiouIiIiIiIiIiIiIiIiIiMO6YL4UnzJlipkyZcrZPozvzIV2vo7oQruHF9r5yqkutPt/oZ2vI7rQ7uGFdr4Xmgvt/l5o53shutDu8YV2vheaC+3+XmjneyG60O7xhXa+F5oL7f5eaOd7IbrQ7vGFdr4Xmgvt/l5o59tXF8yX4nJmvPTSSyYjI8N4enqatLQ089RTT53tQxL5Rn2t2a+++so4OTnB/23evPlbPmoR+z377LNm4cKFJj4+3jg5OZmbbrrpbB+SyDfqT80WFBTQHv32229/ewctAhQVFZkHH3zQjB071gQFBZnQ0FAzZcoUs2rVql5/Rk9Pj/nzn/9skpKSjKenpxk2bJh56623vsWjFuH6W9Pq0XIuaW1tNbfeeqsZMmSICQgIML6+viYzM9M8+eSTprOzs1efoR4t55L+1rR6tJzL1q9ff7Ieq6qqevVr2tvbzX333Weio6ONl5eXGTdunFm5cuW3fKQivWNvTet9tJxrWD0+8sgjvfr152KPdj2rP/079MUXX5ztQzjvPf/88+b222838+fPN7/4xS/MunXrzF133WVaWlrMfffdd7YPz+GoZvvvTNTsXXfdZcaMGXNKlpqa+m0c7gVN9d5/jz76qGlsbDRjx441paWlZ/twHJ5qtv/ORM1ef/31Zvbs2adk48ePPxOHd0FRPffP0qVLzaOPPmquuuoqs2jRItPV1WVee+01M2PGDPPyyy+bm2+++bSf8cADD5hHHnnE/OhHPzJjxowxS5cuNd///veNk5OTue66676Ds3Asqun+ORM1bYx69Jmieu6f1tZWk52dbWbPnm0SExONs7Oz2bhxo/n5z39utmzZYt58883TfoZ69Jmlmu6fM1HTxqhHnymq5zOnp6fH/N//+3+Nj4+PaW5u7vWvu+mmm8z7779vfvazn5m0tDTzyiuvmNmzZ5usrCxz8cUXf4tH7JhU02dOX2vaGL2PPlNUz2fGjBkzzA9+8INTshEjRvTq156TPdoShzR58mRr8uTJZ+zzWlparJCQEOuKK644Jf8//+f/WD4+PlZNTc0Z+1lyYTrXajYrK8syxljvvffeGTsmkRPOdL1blmUVFBRYPT09lmVZlo+Pj7Vo0aIz+vlyYTvXavbo0aOWMcZ67LHHzugxyYXhTNfz/v37rcrKylOytrY2Kz093YqNjT3try8uLrbc3NysO+6442TW09NjTZo0yYqNjbW6urrO2LGKYzrXalo9Wvrj29hzIHfeeadljLFKS0u/cZx6tPTXuVbT6tHSH99mPT/77LNWSEiIdffdd1vGGJu9CLJlyxabem5tbbVSUlKs8ePHfyvHKY7lXKtpvY+W/vg26tkYc8o+2B7nao8+Z//69N///vfGycnJHD582Nx0000mMDDQBAQEmJtvvtm0tLScHNfV1WUeeughk5KSYjw8PExiYqL59a9/bdrb20/5PPT36T/11FNm8ODBxtvb2wQFBZnRo0fb/I7KkpISc8stt5iIiAjj4eFhBg8ebF5++WW7z2f79u3msssuM6GhocbLy8skJSWZW2655ZQxPT095sknnzRDhw41np6eJiwszMyaNcts37795JjFixebadOmmfDwcOPh4WEGDRpknn322V4dQ3t7u/nd735nUlNTjYeHh4mLizP33nuvzbWqqqoyubm5p1znrKwsU11dbX7605+eMvaOO+4wzc3NZtmyZfZeEoejmnXcmm1sbDRdXV29Hn8hUL2fW/VujDEJCQnGycnJ7nO/UKhmHbdmm5ubTUdHR78/53yiej636nnw4MEmNDT0lHEeHh5m9uzZpri42DQ2Nn7jz166dKnp7Ow8Zc/i5ORkfvKTn5ji4mKzadOmXp3D+Uw17Vg1/Z/Uo1XPJ5zNPQeSmJhojDGmrq7uG8epR6umHa2m/5N6tOr5hLNdzzU1NeY3v/mN+d///V8TGBjY6/N///33jYuLi/nxj398MvP09DS33nqr2bRpkykqKur1Z52vVNOOVdP/6UJ8H616Pjfr2Zh//001bW1tdp3/udqjz/m/Pv2aa64xSUlJ5k9/+pPZuXOn+ec//2nCw8PNo48+aowx5oc//KF59dVXzYIFC8w999xjtmzZYv70pz+ZnJwc89FHH9HPffHFF81dd91lFixYYO6++27T1tZm9u7da7Zs2WK+//3vG2OMKS8vNxdddJFxcnIyd955pwkLCzPLly83t956q2loaDA/+9nPenUOFRUVZubMmSYsLMzcf//9JjAw0BQUFJgPP/zwlHG33nqreeWVV8zll19ufvjDH5quri6zbt06s3nzZjN69GhjzL///c3BgwebefPmGVdXV/PJJ5+Yn/70p6anp8fccccd9Bh6enrMvHnzzPr1682Pf/xjk5GRYfbt22f+9re/mUOHDpklS5acHPv000+bBx980GRlZZ1sGrt27TLGmJPHccKoUaOMs7Oz2bVrl7nhhht6dT0cnWrWsWr25ptvNk1NTcbFxcVMmjTJPPbYYzafeSFTvZ8b9S69p5p1rJp98MEHzf/8z/8YJycnM2rUKPPwww+bmTNnntGfcS5TPZ/b9VxWVma8vb2Nt7f3N47btWuX8fHxMRkZGafkY8eOPfnfL5S/+lE17Rg1fYJ6tOr5XKrnjo4O09DQYFpbW8327dvNX/7yF5OQkHDav4pUPfprqmnHqOkT1KNVz+dSPf/2t781kZGR5rbbbjMPPfRQr87fmH/34AEDBhh/f/9T8hM9evfu3SYuLq7Xn3c+U007Rk2fcKG/j1Y9n1v1/Morr5hnnnnGWJZlMjIyzG9+85uT1+ubnLM9+qz9GfXT+N3vfmcZY6xbbrnllPzqq6+2QkJCLMuyrN27d1vGGOuHP/zhKWN++ctfWsYYa/Xq1Sez//6rA6688kpr8ODB33gMt956qxUVFWVVVVWdkl933XVWQECA1dLS0qtz+eijjyxjjLVt2zY6ZvXq1ZYxxrrrrrts/tuJv1rUsiz4My+77DIrOTn5lOy/z/df//qX5ezsbK1bt+6Ucc8995xljLE2bNhwMjtx7bOysk5md9xxh+Xi4gKPPSwszLruuuvouV0oVLNfc4Sa3bBhgzV//nzrpZdespYuXWr96U9/skJCQixPT09r586d3/hrLwSq96+dC/X+3/TXp9tSzX7NEWr22LFj1syZM61nn33W+vjjj60nnnjCio+Pt5ydna1PP/20159zvlI9f+1crGfLsqy8vDzL09PTuvHGG79xnGVZ1hVXXGFzjJZlWc3NzZYxxrr//vtP+xnnO9X01xyhptWjVc8nnEv1/NZbb1nGmJP/Gz16tLV37156XieoR6um/5Mj1LR6tOr5hHOlnvfs2WO5uLhYK1asOGVcb/6q6cGDB1vTpk2zybOzsy1jjPXcc8+d9jPOd6rprzlCTV/o76NVz187V+p5woQJ1hNPPGEtXbrUevbZZ60hQ4ZYxhjrmWeeoed1wrnao8/Zvz79hNtvv/2U/3/SpEmmurraNDQ0mM8++8wYY8wvfvGLU8bcc889xhjzjX89cmBgoCkuLjbbtm2D/92yLPPBBx+YuXPnGsuyTFVV1cn/XXbZZaa+vt7s3LmzV+dw4q/I+PTTT01nZycc88EHHxgnJyfzu9/9zua//edfLerl5XXy/66vrzdVVVVm8uTJ5siRI6a+vp4ew3vvvWcyMjJMenr6Kecybdo0Y8y//6rpE37/+98by7JO+R0hra2txt3dHX62p6enaW1tpT/7QqOadYyanTBhgnn//ffNLbfcYubNm2fuv/9+s3nzZuPk5GR+9atffeOvvZCo3s+NepfeU806Rs3Gx8ebFStWmNtvv93MnTvX3H333WbXrl0mLCzs5P26EKiez816bmlpMQsXLjReXl7mkUceoeNOaG1tNR4eHja5p6fnyf9+oVBNO0ZNq0f/m+r53KrnqVOnmpUrV5r33nvP3H777cbNzc00Nzd/4/kbox79n1TTjlHT6tH/pno+d+r5rrvuMpdffnmf/qYC9eivqaYdo6b1PvrfVM/nTj1v2LDB3H333WbevHnm9ttvNzt27DBDhgwxv/71r0/bY8/VHn3OfykeHx9/yv8fFBRkjDGmtrbWHDt2zDg7O9v81UCRkZEmMDDQHDt2jH7ufffdZ3x9fc3YsWNNWlqaueOOO8yGDRtO/vfKykpTV1dnXnjhBRMWFnbK/26++WZjzL//CoTemDx5spk/f7558MEHTWhoqLnyyivN4sWLT/l7+/Pz8010dLQJDg7+xs/asGGDufTSS42Pj48JDAw0YWFh5te//rUxxnzjBMjLyzPZ2dk25zJgwIBenYuXlxf9d4ba2tpOmZgXOtXsqRypZlNTU82VV15psrKyTHd3t92/3hGp3k91tupdek81eypHqtng4GBz8803m4MHD5ri4uLv/OefDarnU50L9dzd3W2uu+46c+DAAfP++++b6Ojo0/4aLy8vm3/Pyxhz8t/rupD22arpU52vNY2oR6uez3Y9R0REmEsvvdQsWLDAPPvss2bOnDlmxowZpqys7Bt/nXr011TTpzpfaxpRj1Y9n616fuedd8zGjRvNX//6116d839Tj/6aavpU52tNIxfi+2jV86nO9p7jP7m7u5s777zT1NXVmR07dnzj2HO1R5/z/6a4i4sLzC3LOvl//+fvmuitjIwMc/DgQfPpp5+azz//3HzwwQfmmWeeMf/v//0/8+CDD5qenh5jjDE33HCDWbRoEfyMYcOG9epnOTk5mffff99s3rzZfPLJJ2bFihXmlltuMX/961/N5s2bja+vb68+Jz8/30yfPt2kp6ebxx9/3MTFxRl3d3fz2Wefmb/97W8njxnp6ekxQ4cONY8//jj876f7u/ujoqJMd3e3qaioMOHh4Sfzjo4OU11d3eeXI45INfs1R6zZuLg409HRYZqbm23+PYwLker9a2ez3qX3VLNfc8SaPfFza2pqTGxs7Fk5hu+S6vlr50o9/+hHPzKffvqpeeONN07+7uvTiYqKMllZWcayrFPuV2lpqTHGXFD7bNX0187nmmbUo/9N9Xxu7DkWLFhgHnjgAbN06VJz22230XHq0V9TTX/tfK5pRj3631TP3209/8///I9ZuHChcXd3NwUFBcYYY+rq6owxxhQVFZmOjo5v7LNRUVGmpKTEJleP/ppq+vyqaeZCex+tev7aubjn+M89wzc5Z3v0t/F3sp8J7N9aWLx4sWWMsY4ePWr98Y9/tIwx1oEDB04ZU1ZWZhljrHvuuedk9t9/n/5/a29vt6644grLxcXFam1ttbq6uiw/Pz/r+uuvP6PndcIbb7xhGWOsF1980bKsf//7x05OTlZ1dTX9NX/7298sY4x17NixU/Jf//rXJ6/JCf99vrNnz7ZiYmJO+bcI7PHpp59axhhr2bJlp+QbNmywjDHWa6+91qfPdSSqWVuOWLPz58+3PD09re7u7j79ekeherd1Nuv9v+nfFLelmrXliDV7zz33WMYY6/jx4/0/qHOY6tnWuVDPJ/4NsyeeeMKuX/f0009bxhgrOzv7lPzEdVi7dm2/jut8oJq2dT7XNKMerXo+F/YcJ5z49ygfffTRbxynHq2aRs7nmmbUo1XPZ6OejTHf+L/MzMxv/PW//OUvLRcXF6u+vv6U/OGHH7aMMVZhYWGfjut8opq2dT7XNHOhvI9WPds6F/ccTz31lGWMsTZu3PiN487VHn3O//Xp32T27NnGGGOeeOKJU/ITv/PhiiuuoL+2urr6lP/f3d3dDBo0yFiWZTo7O42Li4uZP3+++eCDD8z+/fttfn1lZWWvj7O2tvaU38VijDHDhw83xpiTf33A/PnzjWVZ5sEHH7T59Sd+7YnfIfOfn1VfX28WL1582mO45pprTElJiXnxxRdt/ltra+sp/+5QVVWVyc3NNS0tLSezadOmmeDgYPPss8+e8mufffZZ4+3t/Y3XWr6mmj03axb9enS99uzZYz7++GMzc+ZM4+x8XrfP74Tq/burdzkzVLPnZs3W19eb3NzcU/5KKHS9SkpKzMsvv2yGDRtmoqKi+vSzHInq+but58cee8z85S9/Mb/+9a/N3XffTX8Wqucrr7zSuLm5mWeeeeaU83ruuedMTEyMmTBhwmnP4UKgmj5/alo9+vRUz99dPVdVVdmcgzHG/POf/zTGGDN69OhTjkk9um9U0+dPTatHn57q+bur548++sjmf9dee60xxpjXXnvN/O1vf/vGX79gwQLT3d1tXnjhhZNZe3u7Wbx4sRk3bpz+1r3/n2r6/KlpvY8+PdXzd1fP6HwbGxvNE088YUJDQ82oUaO+8defqz36nP/r079JZmamWbRokXnhhRdMXV2dmTx5stm6dat59dVXzVVXXWWmTp1Kf+3MmTNNZGSkmThxoomIiDA5OTnm6aefNldccYXx8/MzxhjzyCOPmKysLDNu3Djzox/9yAwaNMjU1NSYnTt3mlWrVp32rwc44dVXXzXPPPOMufrqq01KSoppbGw0L774ovH39z85iadOnWpuvPFG8/e//93k5eWZWbNmmZ6eHrNu3TozdepUc+edd5qZM2cad3d3M3fuXHPbbbeZpqYm8+KLL5rw8PCTf+UAc+ONN5p3333X3H777SYrK8tMnDjRdHd3m9zcXPPuu++aFStWnNw4P/300+bBBx80WVlZZsqUKcaYf//9/g899JC54447zMKFC81ll11m1q1bZ15//XXz8MMPn/bfPZB/U82emzWLfv21115rvLy8zIQJE0x4eLg5cOCAeeGFF4y3t7d55JFHenUdL3Sq9++u3o0x5pNPPjF79uwxxhjT2dlp9u7da/7whz8YY4yZN29er/96nwuZavbcrNmPPvrI3HzzzWbx4sXmpptuMsYYc++99578K6Sio6NNQUGBef75501zc7N58skne3UdHZ3q+bur548++sjce++9Ji0tzWRkZJjXX3/9lM+fMWOGiYiIODn2v+s5NjbW/OxnPzOPPfaY6ezsNGPGjDFLliwx69atM2+88Qb9q+MuNKrp86em1aNPT/X83dXz66+/bp577jlz1VVXmeTkZNPY2GhWrFhhVq5caebOnXvKPwugHt13qunzp6bVo09P9fzd1fNVV11l85m7d+82xhhz+eWXm9DQ0JM5+vXjxo0zCxcuNL/61a9MRUWFSU1NNa+++qopKCgwL730Uq+u44VANX3+1LTeR5+e6vm7q+d//OMfZsmSJWbu3LkmPj7elJaWmpdfftkUFhaaf/3rX8bd3f3kzzqvevQZ+hPnZ1xv/qoEy7Kszs5O68EHH7SSkpIsNzc3Ky4uzvrVr35ltbW1nfLr/vuvDnj++eetSy65xAoJCbE8PDyslJQU63/+539s/ih/eXm5dccdd1hxcXGWm5ubFRkZaU2fPt164YUXen0uO3futK6//norPj7e8vDwsMLDw605c+ZY27dvP2VcV1eX9dhjj1np6emWu7u7FRYWZl1++eXWjh07To75+OOPrWHDhlmenp5WYmKi9eijj1ovv/zyaf+qBMuyrI6ODuvRRx+1Bg8ebHl4eFhBQUHWqFGjrAcffPCU8z5x7bOysmzO5YUXXrAGDhxoubu7WykpKdbf/va3M/7XL5yvVLPnb82iX//kk09aY8eOtYKDgy1XV1crKirKuuGGG6y8vLxeX0dHpno/9+p90aJF9K9nWrx4ca+vh6NSzZ6/NXviHv1n9uabb1qXXHKJFRYWZrm6ulqhoaHW1Vdffcq5OTLV87lVzycy9r//HIvq2bIsq7u72/rjH/9oJSQkWO7u7tbgwYOt119/vdfX8XynmnasmlaPVj2fS/W8bds2a+HChSfPwcfHxxo5cqT1+OOPW52dnaf8HPVoTDXtWDWtHq16PpfqGWH3iP361tZW65e//KUVGRlpeXh4WGPGjLE+//zz019AB6GadqyavtDfR6uez616/uKLL6wZM2ZYkZGRlpubmxUYGGjNnDnT+vLLL23O93zq0U6WBf7OHREREREREREREREREREREQegf4RAREREREREREREREREREQc1nn9b4qfCyorK013dzf97+7u7vr3tuWcopqVC4nqXc43qllxJKpncTSqaXEkqmdxNKppcSSqZ3E0qmlxJKrn85v++vR+SkxMNMeOHaP/ffLkyearr7767g5I5DRUs3IhUb3L+UY1K45E9SyORjUtjkT1LI5GNS2ORPUsjkY1LY5E9Xx+058U76c33njDtLa20v8eFBT0HR6NyOmpZuVConqX841qVhyJ6lkcjWpaHInqWRyNalociepZHI1qWhyJ6vn8pj8pLiIiIiIiIiIiIiIiIiIiDsv5bB+AiIiIiIiIiIiIiIiIiIjIt0VfiouIiIiIiIiIiIiIiIiIiMPq9b8p7uTk9G0eh0if9PVv//f09IS5h4eHXZ/j5uYG85aWFpgHBATAvKqqyibz9fWFY9kxNjQ0wJxdI3d3d5izfw/D398f5p2dnTD38/ODeX19PcwZdr7Ozvj39HR0dNhkLi4ucGx3dzfM2bVk58Q+n9UZuyelpaUw740hQ4bAnPXumpoamLNzYby8vGCO7jMby+4xqxV232pra2Hu4+MDc3Z/2H0uKSmxazzrD6x22fmGh4fbZKhnfNOxMOzasB7G+kBBQQHMGxsb7TqeEy666CKYHz9+HOYZGRkwz87OhnlkZCTMm5ubYY7mLJtbrM+zemBzjtUJ67nsnA4dOgTzsLAwu44nMDAQ5uwaszUMzVNvb284lv0bTKjPG8PXNTYvWD2xnrR+/XqY90ZUVBTMR4wYAXM2d1gdsf4RGhoK87q6Opusra0Njk1OTob5tm3bYM6uN6shV1f8OMLq4tixYzBnNc1yVrtsbrO6QNeNnStbB9k5sXUqKSkJ5mwdbGpqgvm+fftgfjqs57J6Y/XM9i7s3rD+iu5BXl4eHDt06FCYs7mF5ooxvG7ZucbFxcGcrefsnrFeX1RUBPOYmBiYl5eXw3z48OE22bJly+DY0aNHw5z1Yra+sN7DrnF7ezvM16xZA/PeYOcSHx8P8+rqapiz/sfW7v3798M8OjraJmPXIz09HeZfffUVzCMiImDOriu7b+waTJo0CeZszT169CjMWe9mtTt+/HiYo70dm6ds78LmI1t7Y2NjYc6wa8PW2dO57LLLYJ6QkABz1odY/2N9aNOmTTBH+3p2rVk/YPVZUVEBc3vf97BnH7aes+Pp6uqCeVpaGszZ8yVbZ3fv3m2TsXPq6emBOVsfr776apivXLkS5qw3sHca+fn5MO+NuXPnwpzVEZvjrH+wPsrOEc0ZVrtsf8HWC1aL7H6y/QVbd9g1O3jwoF2fn5ubC3N7nwPQ3pg967E9OhvPnqfZPWF9g12zxx9/HOan84c//AHmrIZeeuklmLO5P2bMGJiztWbgwIE22ZdffgnHzpgxA+bs/WJlZSXM2XrEPof1Fbav37FjB8ynTZsGc/bcuXHjRpiz+kfPNuy5jfX/OXPmwPyDDz6AOdsvsWvP6uOxxx6DeW/89re/hTnruey94ubNm2HO1lD2bhj1Pzbv2XrO5ldqairMd+3aBXP2brO4uBjm7HmX3U/2LpatAWzujRo1CuZvvPGGTRYSEgLHTp8+Hebs2rD5zq4Ze95ln/Pee+/B/AT9SXEREREREREREREREREREXFY+lJcREREREREREREREREREQclr4UFxERERERERERERERERERh6UvxUVERERERERERERERERExGG5nu0DEDkbAgICYN7S0gLznp4emPv4+MC8vb0d5rW1tTD39PS0yVxcXODYjo4OmDNeXl4wd3Jygjn7ua6uuF20trbCvLq6Gubs2js749+jU1dXZ9fxoHvF7h+7BoGBgTDv7OyEObvf7Np8G8rKymDOrhOri7a2Nph3d3fDnF3Drq4um4xdP1bTbLy7uzvMvb29YR4TEwNzdk6sD/j5+cGc3Wd/f3+Yo2tjjDHR0dEwR9eHHbubmxvM2bVBvccYY0pKSmDO6ik8PBzmfcX6UFxcHMyPHDkC80mTJsE8Ly8P5uzehISE2GSNjY1wbGFhIcyTkpJgXllZCfPIyEiY19TUwBwdozG8P7Gc9YCmpiaYDx48GOYHDhyAOeoZrM9blgXzoKAgmNfX18O8tLQU5r6+vjBnfa0/4uPjYc76DcNqnd1/1kfR+IaGBji2oKAA5mFhYTBn94fNGXb/2XxnfY7lbD/C+iIbz3o02tuxdYrV6Pjx42G+d+9emLN5GhsbC/Pjx4/DvK+Cg4Ptytm9OXjwIMxZDbE1C+1pUlNT4VjW+9j9ZXOLrZPs2FmdDxo0COY7d+6EOdtbsONkawbrDWgdnD59Ohzb3NwMc9bXioqKYM7mOjtXNkf7g12/Xbt2wZxdE7YHYHtFtg6h/squB3vOYZ/NnhkuuugimLPnV7YnZHspNgcyMzNhztYMtkazOYPGDx06FI5lezJWH6wnsfWFzRnWB/oqLS0N5lu2bIE5u9bsuZ31j4yMDJijfT17lmE522+y9Y31CbZ3Ye8i2HrLrjHbM61evRrm8+fPh/n69ethjvYX7Jqx9Yjdp5UrV8KcPaunpKTAfNiwYTDvD3vfUbF9NzsX9tzFnkW2b99uk40dOxaOZdheMTk5GeaHDh2Cub37a9bP2LtNVl9TpkyBeXZ2NszLy8thPnr0aJuMzTu2lrJ9Jvuco0eP2vX57Br01Zo1a2DO1qZf/OIXMGd70ZycHJizvjVgwACbbN++fXAsWyeLi4thzvoN65XoWIzhawB7zmfr6rp162DO5h17bzRmzBiYozpn75fZnP7kk09gPmLECJizZxt2r7KysmDeH7m5uTBPSEiAOZtT7Pnt8OHDMPfw8ID5yJEje/0ZrPdFRUXBfMeOHTBntY7WC2OMCQ0NtStfsWIFzNlelO132Hvt/fv3wxzdE/ZucNOmTTBn7wjYGsvmKasndk6noz8pLiIiIiIiIiIiIiIiIiIiDktfiouIiIiIiIiIiIiIiIiIiMPSl+IiIiIiIiIiIiIiIiIiIuKw9KW4iIiIiIiIiIiIiIiIiIg4LH0pLiIiIiIiIiIiIiIiIiIiDsv1bB+AyNnQ3t4Oc09PT5g3NzfDvKmpCeZ+fn52/VyUs5/p4uICcx8fH5i3trbC3N3dHebsGnR0dMA8MDAQ5vX19TCvqqqCeUhICMzZcVqW1eucHWNtbS3MnZycYO7qilsmO0ams7PTrvG90dDQAPMBAwbAnN0Hdq1YHbG6iIiI6PVYlgcFBcGczY3w8HCYl5WVwZzNme7ubpi7ubnB3N/fH+ZsvrPPYfXo4eFhk7F52tbWZtdnsx7G5uPx48dhHhYWBvO+YufB+kpoaCjMc3Nz7fq5rBbR9YuOjoZjvby8YI7uozG8nsvLy2HO7n1eXh7MGxsbYR4ZGQnzhIQEmFdXV8Pc2Rn//sqkpCSYo17C6pD1Vtbv2Jzz9vaGOepTxvB70h9dXV0wZzUdEBAA8zFjxsCc1Tr7fHQffH194Vi29rHays/PhzlbX1gPZX2LrV9sf8TGX3LJJTA/duwYzFlfRGs6W18KCgrs+plMaWkpzFkPCw4OtuvzT4f1s4qKCpizOcvWjqNHj8Kc1RCqXTbv2VzcuXMnzOvq6mAeFRUFc9b7enp6YM6uGetPBw4cgDlbB1ndpqWlwRytJS0tLXBsRkYGzNlcHDduHMwLCwthzubFmd5zGMPXsoEDB8J8z549MGe9m31+SkoKzNFcPnz4MBzLejebdzU1NTBnx8j2fqym2eezOcPqi+0N7F2TkpOTbTK2z2TXkj0bFBUVwZz1YjY+Pj4e5n3F7gHrE8XFxTBne1G2P2PvQNC+gM0VtocYNGgQzNlzO+v1lZWVMB8+fDjM2TV49dVXYX7FFVfAPC4uDubLli2DOevdqBZZb2DYOsXqg80L9sxj7/NXb2zZsgXmV155JczZfiE9PR3mmzdvhjlbt9Aekq3nrJexeb97926Ys77F5sbYsWNhvnHjRpizvStbA9jxsHVz165dMEdrFXuvw96jsf7P1jXWq1jdsH1NX7HjYj9/06ZNdo1n+/TVq1fDHM3lUaNGwbFr1qyBOesr2dnZME9NTYU5632sF7NnXfa+eP/+/TBn9Tx06FCYs/MaMWKETcaeJWbNmgVzdoxsv3TkyBGYs71+SUkJzPuDrXFsbrJn4rlz58Kc7f0Y9BzIamLkyJEwZ89cMTExMGf7EXZObN1hx8nu55AhQ2D+wAMPwPyee+6BOXtngvouexZjfZ7tsdh6x/oA6xtsb3c6+pPiIiIiIiIiIiIiIiIiIiLisPSluIiIiIiIiIiIiIiIiIiIOCx9KS4iIiIiIiIiIiIiIiIiIg5LX4qLiIiIiIiIiIiIiIiIiIjD0pfiIiIiIiIiIiIiIiIiIiLisFzP9gGInA3+/v4wr6mpsetzPD09Ye7k5ATzuro6mIeGhtpkPT09dv3M2tpamLu4uMC8ubkZ5uznhoeHw7y1tdWu3N3d3a7j8fLygnlXVxfMOzs7bTJ2X318fGDe2NgIc3ZfOzo6YM7ulWVZMO+PkJAQmLe3t8Pc19cX5uwc7T3mI0eO2GR+fn5wrLMz/v1ZbW1tMHdzc4P5nj17YB4ZGQnz4OBgmB8/ftyun1tdXQ1zdo3ZHGB16upqu1R3d3fDsWzesWNh14B9flBQEMzZPewrVivseHft2gXzYcOGwfzo0aMwZ9cJ5S0tLXAsul/GGFNUVARz1lubmppgHhgYCPOKigqYh4WFwZz1ueLiYphHRETYNZ5B1431f9a/WB2w/sXqef/+/TBPS0uDeX+wec/WibKyMrs+h/XLmJgYmKN6ZJ+B1lVjjImLi4N5eXk5zNm5sn2Ht7c3zNn9Z3OP9RO0ThljTEBAAMzZnEHrIzvXgQMHwpztD9kxsj4QFRUF86qqKpj3VWVlJcxZTbA9G9tbsH0629M2NDTYZGzNzs/Ph3lqairMo6OjYZ6QkABztjZs374d5iNGjIA5WzNYnbP1n60B7PpkZGTYZOyasbmemZkJ87y8PJizvf6oUaNgzuqvP9j1KCwshHlycjLM2Tmy5zS2R0U9gY3Nzc2F+ZgxY2DO9psHDx6EOes3rLey4/ziiy9gztZc1rfS09Nhzs4X9Qe2Z2K1iOaFMcbs3r0b5myeJiYmwpytAX116NAhmA8YMADmo0ePhnlBQQHMJ0+eDHO2nj///PM22ZVXXgnHMqtWrYI52yt4eHjAnF0D1ldYrbCfy/oie1Zi6yZb71CvYj1g7NixMGf9iO0D0bsqY/i7FNYz+mP+/PkwZzXH+hy7PykpKTBn9xn1Ffa8wZ7pNm7cCHP2vD1+/HiYs3cg7D6zPdaxY8dgztb0AwcOwJxde5ajvmjv8yWbX2z/Mn36dJivXLkS5pdffrldx3M6bI5kZWXBnO3vWX2ymps9ezbM9+7da5PFx8fDsQsWLIA569FDhgyBOZsvrA7Z+x7WQ6dNmwZz1jNYrbDjfOCBB2D+2muv2WTsufCjjz6COXsmYesCqyf2nrq0tBTm/cHWD3Zsc+fOhfm+fftgztYbVi9ozrB3RZ9//jnM6+vrYc7mBnve/eqrr2DO9ljZ2dkwHzp0KMxXr14N8yuuuALm7Dqw/vfzn//cJmPvKFiPYXupiy66yK5jYe/I2LvK09GfFBcREREREREREREREREREYelL8VFRERERERERERERERERMRh6UtxERERERERERERERERERFxWPpSXEREREREREREREREREREHJa+FBcREREREREREREREREREYflerYPQORsqK+vh7m7uzvMnZycYN7W1gbzlpYWmHt5ecG8qamp15/h5uYGcxcXF5hblmVX7ufnB/PKykqYe3h4wNzX19eu8a2trTBvb2+HeU9PD8zRPWTn2tnZCXMmICDArs9hx8jqqT8CAwNhXlpaatfnsOvNjjkhIQHmdXV1NllERAQcy+Yjq3UmKCgI5mxuFBYWwtzT0xPmXV1dMPfx8YE5q/UjR47APC4uDubo+rCaZj3M1RUv9xUVFTBn4uPjYd7d3W3X55yOszP+PXs7duyA+cSJE2HOzi81NRXmrM4bGxttMtbPWT9g98Db2xvm/v7+MK+pqYF5UlISzKurq2HOejQ7TnZtOjo6YM6ufWRkpE3Gzik2NhbmbL0IDg6GOVtPWU9H/au/2HVl58Kwnp6SkgJzNjfDw8N7/dns3h86dAjmUVFRMGe1UltbC/OwsDCYs3O1d71j+53y8nKYs/pC97C4uBiOjY6OhnlzczPM2Ro7ZMgQmB8/fhzm7Hj6iu0JUa80xpiQkBCYNzQ0wJzVCuofxuAaZXuLWbNmwfzo0aMwZ+fK1inWuy+55BKYs/7H9mNs/Wd7CLZ3OXbsGMzRMwlb79j+Z8OGDTAfOnQozPfv3w9zto6w/V5/oPM2xpgBAwbAnK0rrEZZP2P1FRMTY5Ox652YmAhzdt/Y3EDrgjF8ncrPz4c52/+y+8b2+4MGDYI5W3vGjx8Pc/S8zq47m0dr166FOdt7sWcJ9kzC5mlfsZ/D+g2rCbaes89h6+SIESNsMjbn2LMGW8cyMzNhvnv3bpiza83Ole3f2HxJTk6GeVVVFcxZL2Y9A+3rQ0ND4diioiKYs/vE6oCt7eyZln1Of6xfvx7mrE+wHs2uN5uzl156KcxXrlxpk7EaYvvccePGwZztjdi7x02bNsF80aJFMGfXgPVitrdkfZTVI3tfhXp6WVkZHMvmI3umQ2vpN2H3JCsry67POR32bMX6E7se7N0Pm7Nsf43OOy8vD47Nzs6GOVt32H6ZXQO2H8/IyLDrc/bs2QNzdm2mTZsGc4a9S7z11lttsvfeew+OZesg6xns2OfMmQPzxYsXw/ziiy+GeX/s2rUL5uz5h73XY3vXL774AubsfRGqR/b+i723nzt3bq8/2xi+zu/duxfm7HjYczPr0WlpaTB/9913Yc72rtdddx3MP/zwQ5uM7SPYfWV7NXaubC+Ym5sL8wMHDsD8vvvug/kJ+pPiIiIiIiIiIiIiIiIiIiLisPSluIiIiIiIiIiIiIiIiIiIOCx9KS4iIiIiIiIiIiIiIiIiIg5LX4qLiIiIiIiIiIiIiIiIiIjD0pfiIiIiIiIiIiIiIiIiIiLisFzP9gGInA2WZcG8s7MT5m5ubjB3d3eHeXNzM8ydnfHvQ/H09LTJfH194diuri6Ys2N3dcXT3MXFxa7PCQgIgHlLSwvMvb29Yd7d3Q1zdr4NDQ0wR9fMGHxv2f1ubW2Fub3Xpr29HeYeHh4wb2trg3l/sNpi983LywvmjY2NMGf3k51LcHCwTcaOkWH3h92H8PBwmNfU1MDcx8cH5ux+9vT0wDwyMhLm9fX1MGfXnp0vmjOspllPYn2AzTt2rhUVFTBn9dFX+fn5MEd1ZQzvE+x6HD9+HOYxMTEwR/OI3QOG1QmrZ1YnISEhMGfnWldXB/OkpCSYsx7N6pnNl4SEhF5/TmhoKBzLjp3VM6tbNj4oKAjmrA/2R1hYGMxZ7TJsP8J6Mauvo0eP2mTp6elwbHR0NMwPHz4Mc1Yr/v7+ME9OToY5u5/V1dUwZ+tdXFwczEtKSmDO9gBs34HqhR17aWkpzKuqqmA+dOhQmKP7Zwxf11gd9NWYMWNgztaUnJwcmNt7rSMiImCO1iY2J4qKimDOem5TUxPMKysrYc6uNTsetldkvTUjIwPmbN7V1tbCnK0l6HyHDBkCx9q7v2Jzjs1Rti9i16w/Ojo6YM5qkc1lth8qKyuD+fTp02G+dOlSmyw1NdWuY2HXm2Hzl9UWc+DAAZjb27vZ8UydOhXm+/btgzm6PsOHD4dj2bGzPRPr9fY+67H52FeBgYEwZ3sI9ow2aNAgmK9atQrmM2fOhDnqr2z/w46F7U/Xr18Pc3ZN2Vxne07Wh9hawvacTGJiIszZ+oh+LttH+/n5wTwqKgrmbP/L6pxdS3ufkXqD3Qd2DOy5iL0vYOvQs88+C3O0NrD+f/nll8OcPe+yZ0a2777ssstgztaAgQMHwpz1LfY527dvhzk7fjaH0d5uxowZcOzq1athzsZnZ2fDnK3JbH/BemdfsTnF9v2sHzz99NMw/8lPfgLz5cuXwxz1IbYGs30xezbIy8uDOXsOZznbX7NnqPnz58P8rbfegjnb67B6XrlyJcxRzbHeOnLkSJiza8yemYuLi2HO+iZbN/vjoosugjmb96x/sPd948ePhzm7PwcPHrTJ2PPzsGHDYM56H9sv2Pv8z56X2PPVpEmTYL5kyRKYL1q0CObsGrO+iPaCbH/I3rPu378f5my/wOqG/Vx7v2s4+ev69KtERERERERERERERERERETOA/pSXEREREREREREREREREREHJa+FBcREREREREREREREREREYelL8VFRERERERERERERERERMRh6UtxERERERERERERERERERFxWK5n+wBEzoaenh6Yd3V1wdyyLJh3d3fD3N3dHeYdHR0w9/Lysslqamp6PdYYY1xd8XRmx8g+x83NDeZtbW0wZ9eGnSvLnZycYO7h4QFzdq/Q57Bj9PX1hbmLiwvMq6qqYB4aGgrzpqYmmLP66A92Xdm5s+vHjo3VF8s7OzttsqNHj8KxMTExMC8qKoJ5SkoKzKurq2FeW1sLc1brQUFBMC8sLIQ5m2N1dXV2fT6r9fb2dpgjfn5+MG9oaIA5uwYsZ/XBPr+vWF2xe8/6U1lZGcwHDhwI84MHD8I8JCTEJgsODoZjW1paYM7mYklJCczr6+th7u3tDXOGja+oqIB5c3MzzNm1jI+Ph3l5eTnMUV9k9yM/Px/m0dHRMGdrO+pHxvA+yNbH/mDXw9kZ//5UdgxsDu7evRvmYWFhMEfXytPTE45lvYz16OnTp8OcrYmsbzU2NsKcrSVs7rHPYetmVFQUzEtLS2GO5hg7V9arAgMDYc72I2zdSUhIgDnrV33FjisvLw/mbK6Fh4fDnK0p69atg3lmZqZNxq51QEAAzNk9YPXJ5u6xY8dgbs9abowxl1xyCcxzc3Nhzq4x6wHp6ekwR2sAO3a2d2fQWmoMv2ZJSUkwZ+tmf7Bjq6yshDk7ZlYvqEaN4b176NChNtm+ffvg2DFjxsCc7aXYPGVzg+0LWB9g12bcuHEwLygogDl7vtqwYQPM2V4Craesn7N5zfZSqampMGfztLW1Feb79++HeV+xPSeb96y2Dh06BPNZs2bBfMWKFTCPi4uzyVjPYvXG9ihsv4R+pjHGfPbZZ3Z9jr1zms0LVufsvIqLi3s9nj1DsncdrIey/TL7/G/jnQYzduxYmLPnf3bubK/I9m0REREwR3OM7WlYrbP3fWx/nZaWBnN2H9jnr127FubJyckwZ9fmuuuugzmrF9bT/f39bTL23MTOle1TWM7WkWHDhsGcrad9xd4rsXvP9kOXXXYZzHft2gVz9i4Fvfthezy2HrL9EuuJOTk5MGd1yK4Zq3P2XocdP7v3S5cuhTmbj+idycKFC+HY559/HubsmYRdY3bN2DsTNOf6iz1vs3Nhz6zsPSRbQ7/3ve/BHPUt9o7i+PHjMGfX297neXb/WW2x+7l9+3aYs7UnNjYW5mzPyfoPeiZZvnw5HDtp0iSYjxw5EuZsfbRnD2QMX9tPR39SXEREREREREREREREREREHJa+FBcREREREREREREREREREYelL8VFRERERERERERERERERMRh6UtxERERERERERERERERERFxWK5n+wDOJ+wfr7/iiitgvmDBAphffvnlMHdycoL5kSNHYP6Xv/wF5i+88ALMu7u7YX4hcnbGvx/E19cX5h0dHTDv6emBuasrnlrs8+vq6mCOdHV1wZzVD/uZXl5eMJ82bRrM582bB/Pp06fDnF2z6upqmLN6fvfdd2FuWRbM0XVoaWmBY9mcYPfP09MT5vbWAau//igvL4d5cHAwzFtbW2Hu5uYG87a2Npiz+kJ1GhMTA8fW1tbCPCoqCuastkJDQ2HOanTWrFkwnzx5Msyjo6Nhvm3bNpi/+OKLMF+yZAnMWU2jumM15+Pj0+vPMMaYmpoamLMadXFxgXlTUxPM+2r06NEwr6+vh3lVVRXMvb29Yc7mC6tRNJ6tzewzwsLCYM6udVpaGsxZHY4YMQLmt956K8zLyspg3t7eDvOnnnoK5uvXr4c5m7/ofFk/GjhwIMxZvXl4eMCc1TmbF52dnTDvD9ZD7c3ZfWb1wuYMqseGhgY4ltXEpEmTYM6uX3NzM8wnTJgAc7a+sH13ZGQkzLdv3w7zZcuWwTwrKwvmrI4CAgJsMjavU1JSYH7gwAGYBwUFwZz14sLCQpif6R5dVFQEc7a3ZPut0tJSmKNragzvr2gus/0Py9lehO2vQ0JCYH7NNdfAPCkpCebJyckwZ71+165dMM/Ozob50qVL7crteV5kdciwz/b394c52+uwntEfrG+xveWAAQNgztZW1tPZnEE9ge1PWY9m/Z/NL3a958yZA/MZM2bAPDY2FuYFBQUwZ/vfN998E+ZsP8X2wOiZhD0bsnWE1frmzZthznoVWxvYsfdVZmYmzEtKSmAeHx8Pc3Yehw8fhnlgYCDMGxsbbTI2J/Lz82HO9oRsv8l6609+8hOYDxo0COasF7Ofy9ZHVs/snrB1OzU11SZjfYrti9n+6vjx4zBnPYZd429jH836BDt3dn/Y+xlWj3l5eTAfPHiwTcbe07FezN4Bsnnk7u4O84ULF8Kc7WvYtfzBD34A8+LiYpizZ8CtW7fCfN++fTBH6yD7DNb/2Xsd1sNYzp6F7Hlf2xvsHQXrB+np6TCPiIiAOXt+YDnaj7O6ZXXFPhv1f2N4nWdkZMCcvY9m95Lt39ledO/evTBnz7srV66EOepJ7J329773PZizd+bs/RN7tmEqKirsGt8bbO/H1hu21tv7rMyeZ9B7bbZnY9h3gOydOZunubm5MP/5z38Oc7b+z58/H+aHDh2C+T/+8Q+Y5+TkwJzdQ9T/2HrHeiVbY9n+k91vlveV/qS4iIiIiIiIiIiIiIiIiIg4LH0pLiIiIiIiIiIiIiIiIiIiDktfiouIiIiIiIiIiIiIiIiIiMPSl+IiIiIiIiIiIiIiIiIiIuKw9KW4iIiIiIiIiIiIiIiIiIg4LNezfQDfhdjYWJj/8Ic/hPnChQthnpiYCHMvLy+7jqetrQ3m7e3tME9KSoL5P/7xD5g3NzfD/LXXXuvF0V0YnJycYO7qiqdETU0NzH19fWHe09MDc3aPfXx8bLL6+no4Nj4+HuZXXXUVzK+//nqYR0ZGwtzd3R3mlmXBnJ1TY2MjzKOjo2H+zDPPwJzV8wcffABzNzc3m8zZGf/+H3ZO3t7eMGfn2tnZCfOuri6Ys3PqD39/f5h3d3fDnB0b609BQUEwZ3Xq4uJikzU1NcGxrEfPnTsX5pMnT4Z5cnIyzENDQ2He0dEBc09PT5gfOXIE5oGBgTC///777fr8JUuWwBzVaWtrKxxbVlYGc7ZOsTpgfYD9XHvXwdMpKSmBeXl5OcxZz2X9ht2ziooKmFdVVdlkAwcOhGPZtWN7i5kzZ8Lcw8MD5myO+vn5wfzAgQMwZ+sXW+9+9rOfwZxd+23btsEc1QpaA43hc47VLevd7BiPHTsG84CAAJj3R0tLC8yjoqJgznor+5zg4GCYs3ULXSu2N2K1wnrxuHHjYM7uM6s5dk5s/rJrxvY7d999N8xZn2F7RHQP2dijR4/2+jOMMaa0tBTmbC/IzvXQoUMw76uIiAiYs71fWFgYzNnxsl7M5mZDQ4NNxnri9u3bYX711VfD/Ac/+AHMWd2ycyooKIA52xMcPHgQ5mPHjoX5JZdcAvPc3FyYsxpF/ZL1ULb/ZfW8e/duu8azdZDtdfqD1W5hYSHMWX2x+8/mMvv80aNH22T5+flwLNv/sh7N3mmkp6fDnB0720fv2LED5uw5YMGCBTBnPvzwQ5jv3bsX5mjtYesa+wzWe9i1ZOsRm3fouak/2FrD8okTJ8L8n//8J8wnTJgAc3Ye1dXVNllaWhocO2XKFJizdY+NZ/cgISEB5uxZl/VQNndDQkJgfvnll8P88OHDMN+wYQPMUS2yfTFbe9l9Yv2LrXdsX8fWjP5gfZ/NqZycHJizZ0N2rVJTU2GO9tGsVlhtPfzwwzDPyMiAObsP6P2XMXyOsef2LVu2wBzNX2OMGT9+PMxZTdfV1cEcrb9sT4OeyY0xZtmyZTBnazV7nkpJSYE5q4++2rRpE8yvueYamLP6Z+8d2PMfW8/R+zK2TrJ1j73TY+fE5ta+fftgzs6VXRv2LmLOnDkwZ/OI7XXYsxB6v8DWnfXr18Oc9Wh2DVjviYmJgTl79ugPe2uUraHTpk2DOXuvbc+z8v79++FY9m4hMzMT5oMGDYI56yvsnNizIetb7Ds99u7lnnvugTnb27F9OpoD7JzYexSGPfOz2rXn+4fe0J8UFxERERERERERERERERERh6UvxUVERERERERERERERERExGHpS3EREREREREREREREREREXFY+lJcREREREREREREREREREQclr4UFxERERERERERERERERERh+V6tg+gr2JiYmyy3/zmN3DsddddB/OAgAC7fmZBQQHMa2pqYF5fXw/zRx99FObZ2dkwX7VqFcwHDhwIcxcXF5jL17y8vGDu5uYGc19fX7vGd3V1wdzVFU+5oKAgm+yhhx6CY+fNmwdzdk6sHiorK2HO6ra4uBjmzzzzDMwLCwth/v7778M8NjYW5u7u7jBvb2+HObonPj4+cCxTW1sLcw8PD5h3d3fDnB27t7e3XcfTG21tbTBntevsjH9PFDu2uro6uz4nKirKJrv99tvh2IsuugjmYWFhMO/o6IB5Q0MDzMvLy2FeWloK87feegvmR44cgfnvf/97mI8fPx7mrHY7OzthjuoxLS0NjmX3o6mpCeasP7CcHTvrP33l5OQEc9Yn2L1kddvT0wPziIgImKMePWvWLDiW1XlrayvMGxsbYV5SUgJzNqcPHjwI808//RTm27dvh/nzzz8Pcz8/P5gHBwfDnPVLdK/YXE9KSoI5u6+sN7C+xuqW1Xl/sPvG1lzWz9gcqKiogDlbu0eMGGGTjRw5Eo699NJLYZ6amgpzVutVVVUwZ2slmwOPPfYYzI8fPw7zH/zgBzDPzMyEOXs+YHOspaXFJvP09IRjAwMD7cpZ72bnysazfU1foXM2hvcDtg9j9dnc3AxzVivo/O666y44ltU5m4usHthzYXx8PMzROmIM33Ps3r0b5g888ADM2T4wNDQU5uwaHz58uNefweqN9X927XNycmDO9iKsDvqDrcXsXFhNs2vCngGHDBkCc7SPXrRoERzL5t2UKVNgztZ/tvZt2rQJ5mPGjIH5xx9/DPOioiKYjx49GubsGrM1PSEhAeZZWVk22cSJE+36maynM+xdANt3DBgwwK7PPx12rUeNGgXzsrIymLN7w94jREdHwzwjI8MmS0xMhGPZcyG7dmz/w3q6veskG79mzRqY33rrrTBnawPbW7A9FpqnrG7ZXtLen8nedeTl5cGcrXf9wZ5D2DMdOwa29rFzZPsd1KMnTJgAx7J1m82j9evXw5zNjRUrVsA8Li4O5mzOvP322zC/5557YM7mJHs/jq6ZMXh9TE9Ph2O3bNkCc/bMyNZwe98PhYSEwLyvFi5cCHP2jp+9W2X7p3HjxsGczSO0frK5Mm3aNJiz/TJ7/svPz4f5zJkzYb58+XKYf/bZZzBn7wvY89+dd94Jc7ZPZ/0VrRnsWZo9z7E9PXtePHr0KMwPHToEc7Zf6g+2N2P7X9aftm7dCnO2zrH3BT/60Y9sMnYfWE9MSUmBOesr77zzDszZuy62D2LPJOx9NOuXbE6yXsyePdFc2rBhAxzL1gXWo9mxsDlg77PH6ehPiouIiIiIiIiIiIiIiIiIiMPSl+IiIiIiIiIiIiIiIiIiIuKw9KW4iIiIiIiIiIiIiIiIiIg4LH0pLiIiIiIiIiIiIiIiIiIiDktfiouIiIiIiIiIiIiIiIiIiMNyPdsH0FeBgYE22c033wzHuru7w7yyshLmkydPhnlpaSnM6+vrYX6mPProozB/+eWXYe7v7/9tHo5DaGpqgnlXVxfMPT09Yd7R0QFzNzc3u35uZGSkTTZr1iw41tUVT9u6ujqYX3nllTBn9dzd3W1X7uTkBHN2DZ5++mmYP/LIIzD39fWFeUBAAMz9/PxssvLycjiW3Vdvb2+Y9/T0wNzLywvmra2tdn1Of6CeaIwxVVVVMGfXjx0buq7G8GuF+tD8+fPh2Orqapi3t7fD/Pbbb4c5q8WDBw/CvK2tDebNzc0wj4qKgvnSpUthfvHFF8PcsiyYszmTmJhok+Xk5MCxYWFhMGe1zu5rcXExzH18fGDu4eEB877Ky8uDeUZGhl2fExcXB3O2btfW1sI8ODjYJrv++uvhWDbnampqYP7AAw/AnF1r9vlFRUUwZ2sGq+cXXngB5nfffTfMWQ2xeY32ZGyfxtZYNndZndvbu1nd9Ie9PRrtC4wxprGxEeZBQUEwZ3uDIUOG2GRXX301HOvi4gJzto9gPZrVyrFjx2Du7Ix/7y7rc52dnTBfsmQJzAcNGgTzlpYWmCclJcEc1RF7xmDzsaysDOYhISEwZ3sytrazudRX2dnZMJ8wYQLM9+zZA3N2D9j6z+b+lClTbDI2h9hzEutZd911F8zZPWb52LFjYc76E9v/PvHEEzB/8cUXYf7222/DfPfu3TBPSUmxydg+mj03HThwAOYJCQkwDw0NhTmbFxERETDvj2HDhsH8yJEjMGf3h+39Wd0VFhb24uj+LTMzE+Zsz/Tpp5/C/O9//zvMWZ9g6866detgzvbRzPLly2HOnhvYNWZrxrx582wyVv+sb7CaY88ebH/BrjE7p75izxQNDQ0wZ32I7e8HDhwIc7aeHz161Ca79dZb4Vj2nMT2M4sXL4Y5Wy9iY2NhzvpZbm4uzNkzw2OPPQbzt956C+bsvFg9jxw50iZjdbV//36Ys3pme4stW7bAfNSoUTBnPb0/2HML60PR0dEwZ8+Shw4dgjmrl/DwcJvslltugWOXLVsGc/as9+6778Kcref5+fkwZ9eA9Qc2Z5566imY33bbbTC/6KKLYL527VqYo3u7fv16OJbtoysqKmDOno9ZHbDetnnzZpj3FbvW7Oew50j2/Mfef6WlpcEc7bfYfhP1c2P4uw72HMZ6Lnu3xtapTZs2wRy9vzGGP5Ow58h9+/bBnO3f0PU5fPgwHGvv+0h27GyPOW7cOJhv27YN5v3B+srrr78O84ceegjmrBeza8Xm7KpVq2yy9PR0OJbt2di8Yz26pKQE5uzdAltb4+PjYc72cJ999hnMv//978N8xYoVMGfPNjNmzLDJ2JrM3g8NHToU5uwZht0T9h535syZMD8d/UlxERERERERERERERERERFxWPpSXEREREREREREREREREREHJa+FBcREREREREREREREREREYelL8VFRERERERERERERERERMRh6UtxERERERERERERERERERFxWK5n+wD6Kjs72yZ78MEH4dhdu3bBPDc3F+YFBQV9Pq5vQ1VVlV3j58yZA/Mnn3zyTByOQ+jq6oK5h4cHzDs6Ouz6fH9/f7t+7qFDh2yy5557Do49cOAAzPfs2QPz6upqmDs7498T4+7uDvPu7m67csuyYH78+HGYMzNnzoT5s88+C3N0r1xdcatj94OdE7tmDQ0NMPf09IS5k5MTzPujoqIC5tHR0TBvbm6Gua+vL8x7enpg3t7eDnN0TR5++GE4Ni8vD+YlJSUwZ/ehrq4O5p2dnTBn5xocHAxzVi/s/tfX18N8xowZMF+9ejXMKysrbTIXFxc4NiYmptefYYwx3t7eMA8JCYE5+7lnWkBAAMxZ//Dy8oI56+msJxw+fBjmTU1NNtknn3wCx27cuBHmOTk5MGf1w+qc1SHr3azO7a1nNzc3mEdFRcGc1RaaX+xYysvLYc7WZNYzEhISYM76IFu/+qOsrAzm9t7P1tZWmOfn58M8NDQU5m+99ZZN5ufnB8ey68rmY1tbG8xZX4mNjYU5m6doPhrD1+64uDiYsxq95pprYL53716Yoz7DeiXbF7AeVlpa2uufaQyvpzNd0+PHj4c524uwfsbWf3adWE3s3LnTJmPX9M0334Q5u2dsD8Hq59ixYzBPTk6G+ZEjR2A+cOBAu46npqYG5jfeeCPMv/jiC5ij/sp6KHvGYMfCekliYiLM2V6ArQ39wWqL9UXWb3x8fGDO+iJ7JkD1xfYdqP6N4c+jLS0tMGfXNTw8HOZMcXExzFNTU2HO6oXtO1j/eeyxx2CO7i3rMbW1tTBnWM+Nj4+HOXrmN4bP975iewj2jMNqi9Uze75MSUmBeWRkpE22bNkyOJbNLfbujs1d9jnseWvIkCEwZ/toVkPDhw+HeVFREcy/973vwZzN6y+//NImmzx5MhzLeijra2wvye4ru8bsXPuD9bO5c+fCnK037Jqw+8n2L2hPyN5PsXm0ZMkSmLP3vxMmTID5yJEjYc76E3t/w3I2B1gvXrp0KcxZ/0Hv39lenD2rs/vE9qXs+YitAenp6TDvK7busXc2bA4OGzYM5mxvGRYWBvOjR4/aZG+//TYcW1hYCHP2fIY+2xjec9nzJXsmamxshPl1110H823btsH8pz/9KczZvGB7YLT+s+c2Vp9s383qn/U19l6HPSP1x8GDB2G+aNEimLO1mO2X2ZwZN24czNF7B1ZD7Bnwq6++gjkzZswYmH/88ccwZ3s1tq8JDAyEOasXVhc/+9nPYP7AAw/AHL1/Gjt2LBzLnjH2798Pc3bN2D5i69atMGfvk05Hf1JcREREREREREREREREREQclr4UFxERERERERERERERERERh6UvxUVERERERERERERERERExGHpS3EREREREREREREREREREXFY+lJcREREREREREREREREREQcluvZPoAz6U9/+tPZPoRvRXBwsF3jDx069C0diePw9/e3a3xXVxfMfX19YV5VVQVzT0/PXud//etf4VgvLy+Yd3Z2wtzHxwfm7e3tMHdxcYF5a2srzAMDA2He0tIC84iICJi7u7vDfM+ePTB3c3ODOTpOJycnONbb2xvmlmXBnH0Oq4OmpiaYh4SEwLw/WE23tbXBnN1PVqP19fUwZ+fi6mq7vHz88cdwbENDA8xDQ0Nh3tPTA3NWQ93d3TBn14bdNz8/P5iHh4fDnM3JgwcPwpzVHfq57NgbGxthznpYXV0dzIOCgmDO6uD48eMw7ytUP8YYk5CQAPPCwkKYFxQUwJzVHKshdI+XLl0Kx+bk5MCc9Ql713h2bdg9Zp9fU1MD88zMTJiz+qyoqIA5u5a1tbU2WXl5ORzL1hfWizMyMmDO1iPWv1jP6A/WD9hctnffwdbElJQUmEdHR9tkL7zwAhwbGxsLc9aL2XrE7jO7P+z+s1pkObufrM/t27cP5qz/oc9na2lAQADM7d03lpaWwnzQoEEwZ/Oxr1j/YHtOZ2f8+7BZPbO6Zdepo6PDJvvqq6/gWDbvWV9h6wXLU1NTYe7h4QHzAQMGwJy59tprYc7WO7YvYLWI1pijR4/Csax/sXqLjIyEObuvbJ8eFhYG8/4oKiqCOVqzjDEmJiYG5qwu2Fo8efJkmGdnZ9tkK1asgGNZn8jKyoL5yJEjYc72uWw9Yr07Li4O5qynsxpln8+uMevpaP1lz7v2PjOy8WxfyvoDezboq+HDh8N87969MGd7v5KSEpizPQ2rFfTeobi42K6fyeqcPbcxU6dOhTnrAeycWA2x50K2R/3oo49gzp6t4uPjbbJt27b1eqwxvA6rq6thnpSUBHO27rBr1h+5ubkwZ/tftsZt377drp/L1ic0Bz799FM4lq3/rFbYXo71FXbfbrrpJpi//vrrMB83bhzM2XrH9gCsX7I5s2DBApuM7XPR2mgMr3W2rrF35uwZhh17X7G1Y/DgwTBn/Yn1vylTpsCc7efQvuqTTz6BY9k6cvnll8Oc9QnWV9icZsfO9jR5eXkwR/VmjDErV66EeXNzM8xZnVdWVtpk7P6xz16yZAnMf/rTn8L83nvvhfn//u//wpwdT3+wfQR7HhszZgzM2TMme55n77VRX2Tv0crKymCOni+Nwe9RjOH7U9bT2bEfO3YM5uwasONnz9PsnsyePRvm6J0PuzbsWY9hzzZs3ZkxYwbM165da9fPPUF/UlxERERERERERERERERERByWvhQXERERERERERERERERERGHpS/FRURERERERERERERERETEYelLcRERERERERERERERERERcVj6UlxERERERERERERERERERByW69k+ADm9+Ph4u8Y/9dRT39KROI7m5maY9/T0wDwoKAjmjY2NMPf29rbreCzLsskCAwN7PdYYfuxdXV0wb2lpgbmfn59dP5ddSzc3N5iHhobCvLW1FearVq2CuZOTE8zd3d1tMhcXFzi2u7sb5mw8O0b2OawOOjs7Yd4f7e3tMGf3mdV0bW0tzCMjI+36uTU1NTYZu37+/v4wZ8fOclajERERMGfzl90fLy8vmCcnJ8Oczb0VK1bAvKOjA+ao1qOjo+FYZ2f8e93YsQQHB8OczeuGhgaYJyQkwLyvWP84evSoXZ8THh4Ocx8fH5iz80b1zOqQ9W7WV9i5VlZWwnzgwIEwP3bsGMyzs7Pt+rksZ3uRJUuWwJxdn/r6epuM1aeHhwfM2XrH6tPVFW93WX748GGY90dYWBjM2fU+cuQIzFkdsT5UVVUFc09PT5uMrWV5eXkwZ/Oe9TLWc8ePHw/z/fv3wxwduzF4/TfGmIkTJ8Kc9cs333wT5r6+vjBHdcRqi90Pdu3ZesSuPTsn1tv6it0D9nOSkpJgvmPHDpiz+mf7BbTfYj2UXVN2z9ra2mDO1peQkBCYs55YVFQE84CAAJgfPHgQ5mwe/eMf/4D5RRddBHM07+Li4uBYNifYesT2jGxNZnWWn58P8/5ge1TWc0tKSmDOnk/YubD+iubA2LFj4VjWP1gvRnsaY4xJTEyEOVsT6+rqYM7WdHZtMjIyYM76w+rVq2FeXFwM8wEDBthkbB6NGTMG5hUVFTBn15j1E7ausb1jX7F7xvYK7NqNGzcO5lu2bIG5PXuO6upqOJat5awn7tu3D+YTJkyA+fbt2+36fPZszPbFbI1hfZHVOdvvo96wefNmOJbdj4KCApizufjOO+/A/IYbboA524/3B5rHxhhTWFgIc3v3xaNHj4b58ePHYY56wuTJk+FY9izGaismJgbmI0eOhHlZWRnMWW2xc2V9ju13WB3961//gjnbu+bk5Nhk7J1kSkoKzNkazuYj26uxZ0z2Lqyv2M/ftWsXzC+55BKY79y5E+bs3rO94pdfftnrsWwtZ8/tI0aMgDnbp8+ZMwfm7N6zPQ17lkD1ZowxN954I8zXrFkDc/aeGn0Om6O7d++GObuWbM84b948mLN1h613/cHWRLYesDpizwRsv8V6BdpjpKWlwbFsvrD+wY6F3c+pU6fCnD3PsPGlpaUwZ/3k0ksvhfkjjzwCc9br0fsF9sywdOlSmF988cUwnzRpEszZ8/GhQ4dg3td9tP6kuIiIiIiIiIiIiIiIiIiIOCx9KS4iIiIiIiIiIiIiIiIiIg5LX4qLiIiIiIiIiIiIiIiIiIjD0pfiIiIiIiIiIiIiIiIiIiLisPSluIiIiIiIiIiIiIiIiIiIOCzXs30A8jV3d3eYX3nllTBfsmQJzA8ePHimDslheXp6wrypqQnmdXV1MA8MDLTrcyzLgrmzs+3vT+no6IBju7q6YM50d3fDPCAgAObs2N3c3GDOjtPJyQnmc+bMgfnq1athvmHDBrt+LronnZ2dcKyHhwfM2X1iIiIiYN7S0nJGPr832Gey+19fXw9zdp/b2tpg7uLiAvOqqiqbzNUVLzleXl4wDw0NhTmbA62trTCvrq6GOZsDYWFhMEfnZIwx48ePh/lXX30F86KiIpizekHXh81T1pPYfDx+/Hivf6YxxgQHB8OczbG+Yj+f1a23tzfMWc2x/sHmkZ+fn01WU1MDx7K6LSkpgXlPTw/M2b1kazyr57i4OJjX1tbCfMyYMTBfv349zNvb22GO1jVjjBkwYIBNVlpaekY+m63trDeUl5fDnPXB/mB9q7i4GObsvrE+wT6fXav9+/fbZOjeGGPM7t27YR4eHg5z1g/YfFy7di3M2VwKCQmBub3XEl0DY4xZvnw5zIcMGQJzNPfYfWJrJqs59jlpaWkwZ3XA1q++io+Ph3lBQQHMjx49CnO2RwkKCoI56sXG4OvKPoNda9Zv/P39Yc7WALa++Pj4wJw9/yUlJcGc1WF+fj7M2drDfi6a142NjXAsW5NZvQ0fPhzmrD7Y3oX1kv5gP6u5uRnmycnJMGdzlvVFVkeDBg2yyVj/qKyshDlbz9kxMuwZgO1T2FrM7tu0adNgzno0u2YzZ86EOaov9jP37dsHc7bPZPeVvTtg85rtBfuqoaEB5mwfz+Y469HDhg2DOdtXoWdl9gzCPiM7OxvmF198MczZvUxMTIR5Tk4OzFNTU2HO6p+9F8jLy4P5F198AXO2d0H38KqrroJjWR2y/s+eg1j+Xb53PHz4MMxZX2TjWR86cOAAzFl/Rfsw1pvYMbK9FNtHsPvJ5inbd2zfvh3mrIfeeeedMP/ss89gzq4Z29ejfsL6P7tme/fuhfmll14Kc7bXZ5/P9gJ9xfoHez5n70qvuOIKmG/atAnmbG1Aaxx7rsrNzYX51q1bYc6OkdVDYWEhzHft2gXzgQMHwpztLe+//36YL126FOZsT3vbbbfBHL0zYdedPddce+21MGf7btYD2M9l+7T+YGv36NGjYb5t2zaYs/cRbC1mcxm9T2TzbvDgwTBn+wh236KiomC+ZcsWmI8YMQLm7DuQmJgYmLP30Tt27IA5ez8+duxYmKN3Qey5iT3rsedRtjfKzMyEObuWCxYsgPnp6E+Ki4iIiIiIiIiIiIiIiIiIw9KX4iIiIiIiIiIiIiIiIiIi4rD0pbiIiIiIiIiIiIiIiIiIiDgsfSkuIiIiIiIiIiIiIiIiIiIOS1+Ki4iIiIiIiIiIiIiIiIiIw3I92wcgX7vppptgPmrUKJh/+OGHMLcs60wdksPq7u6Gua+vL8zb29th3tLSYtfP9fDwgHlHR4dN5uqKp6e7uzvMu7q6YN7a2gpzdg3c3Nxgzo6nubkZ5rfeeivMWT0vX74c5uy8WJ3X19fbZH5+fnAsu6/s2nh6esKcHSOrD1Zn/REUFATzhoYGmLP7yc6FjUfX2xhjAgICbLLa2lo4lmHH0tTUBPPq6mqYR0dHw7yqqgrmPj4+ML/hhhtgHhUVBfOsrCyYs/Nicw/dw5CQEDi2p6cH5mwOsJpm95XNd39/f5j3Fetz3t7eMPfy8oI56q3GGNPZ2QlzNjfRPWDHyOZcTEwMzJ2cnOzK2VwsKyuDOavP2bNnwzw8PBzm77//PszZNWbXAeV1dXVwbGRkJMyDg4NhfuDAAZizuhkwYADM2fH0B+tb7H4WFxfDnNVRZWUlzNPS0mAeHx9vk7E+MW3aNJhv2rQJ5rGxsTBva2uD+dChQ2HO+kp+fj7Mr7vuOpizNeDxxx+H+dSpU2FeU1MD88bGRpusvLwcjmVrdVJSEsxZTyopKYE5622hoaEw76u8vDyYV1RUwDwuLg7mrHezuW/P3CwqKoL5xIkT7frsiIgImB89ehTmhw8fhnlqairM7V23WT2/9tprMGd70dzcXJija8+eX9gegs11Z2f8+/HtvTZ79+6FeX+wY77kkktgvmfPHpizPsHmMpuz6FmEXb+DBw/CfPDgwTAvLS2FObvPbF/MapTtc9l9ZufFrqWLiwvM2XmhnK0jbP06fvw4zNHzjjH8mrH9O9u/9BV7JmLnx+Yy63Ps8zMzM2GOnivYz2T70ISEBJize8Pqk+0t2P6K9SG2v2bXeN++fTAfNmwYzNevXw9zdH3YtWH9he09Dx06BHN2X9leh31+f9j7TmvNmjUwHzJkCMxZ3bE1FB0P631s74f2j+yzjbG/dwcGBsKcPRex4ywoKIB5Tk4OzNnaw94joHs1cuRIu34me3fx5Zdfwvzaa6+F+c6dO2HO+kxfsWfQRYsWwZztadmek90DNmfRdU1JSYFjWc9i6wXrxazO//nPf8J8xIgRMGf72R/+8IcwZ3XI3ml88MEHMB8/fjzM0XVgzzVsjm7duhXm7H0qezZgPYnto/pj//79MGe9dcyYMTBndcH2hOwZGt2fLVu2wLFszWK1zp6D2fcLY8eOtevnJiYm2nU87L0ke14aPXq0XePRz2X7BVbrGRkZMGfzl+1f2LXZvXs3zE9Hf1JcREREREREREREREREREQclr4UFxERERERERERERERERERh6UvxUVERERERERERERERERExGHpS3EREREREREREREREREREXFY+lJcREREREREREREREREREQcluvZPgBHlp6eDvPly5fDvKamxq7P7+jogHliYiLMCwoK7Pp8R+bi4gJzJycnmHt4eMC8ubnZrvEtLS0w9/X1tclaW1vt+uz29naYd3V12fU5bW1tMB8+fDjMX331VZjX1dXBvKGhAebs2gwaNAjmrJ7Rdevs7IRjLcuCuaenJ8zd3Nxgzo49KCgI5j09PTDvj+LiYpiHhYXBnJ27v78/zLu7u2HOrpWrq+3ywmqLfUZtbS3M2bFHRETAnM1r1qMfeeQRu46HXbPKykqYp6WlwTwnJwfmwcHBNhm6vsYYU1ZWBvPAwECYs/7AzpXdK7Ye9RU7rtjYWJjv3bsX5qwmQkNDYc76qJeXl00WExMDx1ZXV8O8vr6+159tjDHHjx+HOaoHY4wZMGAAzO+77z6Yu7u7w5zVFqsJb29vmLOaq6qqssnQGmgM7xksZ3OLXXu2htu7H+sNHx8fmLPrHRkZCXN2rViPLiwshHljY6NNVlJSAseyexkeHg5z1g8SEhJgzuYMu89PP/00zNn+gs1rVrvsmrE9AFrTWQ9j+899+/bB3NkZ//5ldk/YvGbrVF9FR0fDvKioCOZsrrHjZT19yJAhMN+zZ49NxnprdnY2zFmdVFRUwJzd40suuQTmbF//29/+1q7xbO/C+h/7HNZ70P7az88PjmX7Mdan2LVsamqCeVRUFMzZs0F/sJpGtWUM77njxo2DOesrrNejPUBAQAAcO3r0aJiXlpbC3N49ZEhICMzZuaampsKc9S1WL6znsvHsWqL6OnbsGBzL7iurD1bT7FmPndOhQ4dg3ldxcXEwZ8/EbI6zvS7bL7CegNZ5VlfsPrLnOXZN2bsONo/Y/nrs2LEwZ89EbD9+4MABmOfm5sKc9Xq0N2L7K/Yz2d6C1c3OnTthPnjwYJh/G+8d2ToxadIkmLP1g507q102l8vLy20y1uPY/Vm1ahXMWY2y3sreu7F+9uijj8KcrRksZ9d4x44dMGe9G10f9mzAnkcnTJgAczZP33jjDZiPGDEC5mf6Xcfnn38Oc/Ysw/a/7D0k639sLzJjxgybjL3LYs8y7H0ku5dbt26FeUZGBszZuvOnP/0J5qyns7UnKysL5j/5yU9g/vLLL8P8qquussnYsbPnHVaHrP7ZusnuN+tV/cGOgWF9ha0f7DmHPeOic2S1xa7rypUrYX7TTTfBfMuWLTBn+2vW0xcuXAhz9uzJ9hHsuZytSeg9nTH4vNh7ILYesZ7E+gl7F5qUlARz1utPR39SXEREREREREREREREREREHJa+FBcREREREREREREREREREYelL8VFRERERERERERERERERMRh6UtxERERERERERERERERERFxWPpSXEREREREREREREREREREHJaTZVlWrwY6OX3bx+Jw0tPTYb57926Yu7u7n5Gf29TUBPMdO3bA/JFHHrHJVqxYcUaO5dvWy/K14enpCfOAgACYd3Z22vX57e3tdv1cpLW1FeZsLnZ0dMDcw8MD5t3d3TB3c3OD+aBBg2D+6aef2vU57Hi6urpg3tLSAvOdO3fC/O9//7tN9tVXX8Gx3t7eMHd1dYU5qzd2v9k1Zjk7195ITU2FOTsXdgyNjY0wd3bGv4fKy8ur159v7zrS3NwM84iICJiXlZXB3N/fH+bBwcEwX716NczZNSssLIQ5uyesR7OafvLJJ22ytWvXwrHsnFh/YL3Nz88P5mydOn78OMzZPTydcePGwZz1CVYTrA+x42VqampssoSEBDiW9W5fX1+YFxQUwDwpKcmuz2fry7PPPgtzFxcXmPf09MCcCQsLg3lpaSnMH3/8cZts7969cCy736yvtbW1wZz1L7bmHz161K68N6ZNmwbz+vp6mLPeyvqHj48PzI8cOQLzyZMn22R79uyBY4cPHw5z1j9YL2b3LTc3F+YjRoyAOdq3GsOvWWBgIMxra2thPnDgQJiz/c4rr7xik+Xn58OxQUFBMM/JyYH5lClTYM76BpsDrD9s2rQJ5qczatQomLN9FZuD1dXVMGfHy/aiqL9u2LABjmVziK1XrE8MGDAA5uxc2Rx98803YZ6Xlwfz8PBwmB8+fBjmbM2oq6uD+apVq2yyQ4cOwbEMu5asH7G6mThxIsx37dplV94bbM1l+wtWo2yvGBcXB/N9+/bBHPVLtu9gaxM79oaGBpiz/TLbM7F97i233AJztr9gez52XuxZks3tjz76yCbbsmWLXZ/NapSdE6uPoqIimLN9OquP05kzZw7M2bMYW/fYswnrf2wfga4He9Zg6yTbc7B9KNuLsJ7I9sXPP/88zPfv3w/zYcOGwZytz6wm2PMlqmf2LqKqqsqufPr06XaNZ/d7yJAhMH/vvfdg3husr7C5w/aW7BzZnpCtreiZOzMzE459/fXX7ToW1p8mTJgAc9bT2bW5//77Yc76Fut/lZWVMGf7fdZP1qxZY5Ox/QLrG+Xl5TBna3tISAjM2d6LPccvWbIE5qdz5513wpydt73YO73ExESYo/pn9zctLQ3mbH1h33+wNZvtXdg+atGiRTC/6KKLYM56Mdu7btu2DeZs3qF9wYcffgjHsmNcuXIlzGfPng1z1ovZ++WYmBiYL168GOa9wfocWz8+/vhjmM+YMQPmBw4cgHl0dDTMUR9lPZp9BnuuYO8Y2f6C7WvY3mvkyJEwj42NhTl79mDrGutzKSkpMM/OzrbJ2DrFnhnGjh0Lc/Zee968eTBney/2DPPEE0/A/AT9SXEREREREREREREREREREXFY+lJcREREREREREREREREREQclr4UFxERERERERERERERERERh6UvxUVERERERERERERERERExGHpS3EREREREREREREREREREXFYrmf7ABxZbm4uzJ9++mmY/+IXv7Dr8zs6OmB+9OhRmE+ePBnm4eHhNtngwYPtOpbzjWVZMG9oaIC5v78/zDs7O2Hu6oqnlouLSy+O7t88PDzs+mzGx8cH5qx+PD09YX7w4EGYv/nmmzC/5ZZbYN7T0wPz1tZWmB86dAjmU6dOhXlgYKBNtm3bNjiW1QHL7T12Nt7d3R3m/eHk5ARzVqPsmFmNOjvj30PV1NQEczRn2tvb4diAgAC7jqWmpgbmwcHBMD927BjM6+vrYf7iiy/C/KabboI5mzMFBQUwLy0thfmwYcNg/sgjj9hkl19+ORzL5jWrD9ZP2Dmxz09KSoJ5X5WUlMA8IiIC5hUVFTDv7u6GOZubKSkpMPf29rbJamtr4Vh2jcrKymAeHx8Pc3Zv2FwsLCyE+ZIlS2C+cOFCmLN5mpCQAPN9+/bBnNXEHXfcYZPdfPPNcCzrlexasmvj5eUF88bGRpgPHDgQ5v3B7s+AAQNgzo6NjWf7l5iYGJi/8847NtmUKVPg2N27d8O8q6sL5mgdNob3odTUVJiz9WX58uUwv/7662HOrj27z2zPMHr0aJijufrzn/8cjmVrb2RkJMzXrVsH85CQEJiz/er+/fth3lesh/r5+cGcredhYWEwZ3O8uLgY5qiPstpnc4vtLViPZutLc3MzzNk9e+qpp2B+0UUXwbylpQXmW7ZsgTnbG6Wnp8N8wYIFNtn9998Px4aGhsLc3n0xq5vs7GyYs2vQH2wOsvUjPz8f5mztY32IzQF0f9asWQPHoj2KMbzWk5OTYc7mHdvvsPnI9t3Dhw+HOesPbC+6ceNGmLOePm3aNJuMPet9+umnMGfvUb788kuYx8bGwpxde7aP7aucnByYjxo1CubHjx+36/Pt3Uej/dyyZcvgWHatWT3k5eXBnD3nsWNke44PPvgA5hMmTIA5e3fB5jqbvxkZGTBH73Z+85vfwLGJiYkwZ+sje29QXl4Oczan2fzqD/ZMwO5/UFAQzNlz/nXXXWfX8WRmZtpke/bsgWOvvPJKmLN5b+973ujoaLvyrVu3wpztC1gtHjhwAObjxo2DOevRaJ/14IMPwrFsn7t3716Yz5gxA+ZsD8fWfPYOoq/YtWNzdsOGDTAfP348zNl1qq6uhjnaV7H7xepq586dMGfvo9k1ZfvotrY2mLP1jl1Lti+urKyE+bXXXgvzjz/+GOZXXXWVTcb2Cuy+sn0RW6vZuzP27FpVVQXz/vjss89gHhcXB/MhQ4bAnJ0Le1ZYu3YtzNF7DbYvWLlyJczZ+LS0NJizZ8kxY8bAnD3nsD0We/fC3rGwfRPbC7JrP3HiRJvs8OHDcCx79mDz1M3NDebsmYddY7aHOx39SXEREREREREREREREREREXFY+lJcREREREREREREREREREQclr4UFxERERERERERERERERERh6UvxUVERERERERERERERERExGHpS3EREREREREREREREREREXFYrmf7AByZi4sLzIcNGwbzvXv3wvy+++6DeXl5OcyjoqJgfu+998J806ZNMHdkfn5+MGf3rKmpCebu7u4w7+zshLmHhwfMe3p6en0sHR0dMG9paYG5qyue5ixnx+7m5gbztLQ0mLN6/sMf/gDz0tJSmKempsL8rrvugvm6detsMmdn/Pt/mpubYc7Ge3l5wTwgIADm7F6x/Nvg5OQEc3bMlZWVMGfn3traCnN/f3+bjNU0+5msFr29vWFeVFQE8+DgYJizmk5MTIT5gQMHYP7MM8/AvLa2FuaxsbEwX7BgAcxLSkpsMh8fHzi2qqrKrp/JehvL2f1uaGiAeV+xdayrqwvm9p63vbWIamvIkCFwLDtG1m9Q/zfGmGPHjsE8Ojoa5jExMTAfPnw4zNke4oEHHoA5m0dsXbvllltgvmPHDpsM9QtjjGlsbIQ5u69sPFvvwsLCYM7uSX+wfQdb+2pqamDOzpH1LdYr0NrKapddD7aOsM9hfSIyMhLmrEZHjBgB8yNHjsD8jTfegHldXR3MWf+54oorYI7mNjungoICmAcGBsI8NDQU5mxNZp/D6qOvWL9hPTQiIgLm+fn5MG9ra4M5q2e0H2d7iLi4OJgz7NqtXbsW5t3d3TDPy8uD+cUXXwxztt4uXboU5oWFhTAPCQmBOdsftre39yozxpjq6mqYs547efJkmLNnBrZWs97dH6xv1dfXw3zQoEEwZ+dyzTXXwLy4uBjmGzdutMnYMxF7t7Bv3z6Ys9pi61R4eDjMWV2w8ez5h72jYNd+4MCBMGfPb6ge2Xxh8/fo0aMwZ/2E9Z/169fDfNKkSTDvq3HjxsGc7UXZ+mxZFszR87YxfF+Ant3YMbK1n713Yc8s6enpMGd7BTb++9//Psyzs7Nhzt6t5eTkwJzt09n1QT+X7VvYnoPVLVt72Z6D9YBvAzs2hvW5X/ziFzBn7xFYH3r33XdtMjaPN2zYAPNLLrkE5uw5h70DOXjwIMxZL2Z7MvZM8sknn8C8oqIC5mj9MsaYUaNGwRz1jcGDB8OxZWVlMGfvUdgay/aTCQkJMM/NzYV5X7F3t+yasneuvr6+dn0O2z+h9Xnbtm1wbFJSEszZ82JycjLMDx06BHP2jo71aDZf0DsHY/iz9LJly2A+Y8YMmLN3NWhNYnORvS9k14Ct1Sxna8O3sY/OzMyEOdv3TJw4EeZbt26FObtvbE1HzxAZGRlw7KxZs2DO9iPsGYod465du2DO3mGytWTnzp0wZ+8L2HMa2wtOmzYN5ocPH7bJ0DtqY/gxsp7O9pnHjx+HOeuF7Hn6dPQnxUVERERERERERERERERExGHpS3EREREREREREREREREREXFY+lJcREREREREREREREREREQclr4UFxERERERERERERERERERh6UvxUVERERERERERERERERExGG5nu0DcGQPPfQQzC+99FKY/+pXv4L5ihUr7Pq5u3fvhvny5cvt+hxH1tHRAXN/f3+Ye3l5wby5uRnmwcHBMG9paen153d1dcGxra2tMPfz84O5szP+vS/t7e0wd3Jygvk999wD80mTJsH8iSeegPnGjRthzs43Ozsb5llZWTBH19jFxQWO7e7uhrm7uzvM2THaey3d3Nxg3h8NDQ0wZzXK6oXVemBgIMzZOaI6ZT+TcXXFSxQ7p5CQEJizObBo0SKYDx48GOZvvfUWzD///HOYx8XFwXz//v0w/+STT2Du6+trk9XU1PR6rDHG1NbWwtyyLJgzaWlpMM/NzbXrc07H29sb5qzOIyIiYN7Y2AhzVosVFRUwDwoKssnYOsJ6Vnh4OMxZX2HnyvrT7bffDvP09HSYv/vuuzAvKCiAOTtfNu8eeeQRmB88eNAmY+eUnJwM88rKSpj7+PjAnO2L2BrA5lF/hIaGwry4uBjmSUlJMN+zZw/MWb+Mj4+HOZoDeXl5cGxkZCTMWY329PTAfNSoUTBn/WnBggUwZ9dm2bJlMD98+DDM2Vxla8Dq1athPmDAAJuM1ZCnpyfMExISYM7uN1tf2Nxg+6C+2rZtG8zHjh0L8/LycpizXp+RkQFzds/KyspsMra+tbW1wZytI6x/sLoNCAiA+eOPPw7zzMxMmP/5z3+GOZunYWFhMEc91xhj3n//fZijdX7o0KFw7IEDB2DObNiwAebDhg2DOXvmYfvu/mB9hc1Z1ufGjBkDc7b3Y/UyYcIEm2zv3r1w7Pr162HO1la2nrN+w/rTNddcA3PWQ/ft2wfz0tJSmLP9flNTE8xZf0Cfw3o06z1sb8TeHbD7yuY7u1d9xfa5x44dgzk77+PHj9s1nt2boqIim4w9U6A11Ri+52BzlK2HMTExMJ88eTLMWV2xOY3WI2OM2bFjB8yrq6thvnPnTpije+Lh4QHHsrWfXTO2J2X3mz0DsHWqP9CzmDHGdHZ2wpzN8XfeeQfmrM+xvSh69mV78Tlz5sCcvedlfYV9Prs/F198McyHDBli1/GsWbMG5gMHDoT5oUOHYL527VqYo/0Le35NTEyE+euvvw7z0aNHw5ztEdm7rblz58K8r9h7AfbOzd5nU1bPbL6UlJTYZNdeey0cy95ps+8b2L1k96Cqqgrm7B37iBEjYM72uehcjeE9hu2x2PEXFhbaZDNmzIBj6+rqYM7qdtOmTTCfPn06zPPz82HO3pH1B9tDsj7BniFYraekpNj1OWidYz10+/btvf4MY/izIdq7G8P3kOw7FrYfeeWVV2C+detWmI8fPx7mrKezdyno+YM9T1922WUw37VrF8zZno/1KvbMyN7T/PSnP4X5CfqT4iIiIiIiIiIiIiIiIiIi4rD0pbiIiIiIiIiIiIiIiIiIiDgsfSkuIiIiIiIiIiIiIiIiIiIOS1+Ki4iIiIiIiIiIiIiIiIiIw8L/yrzYJTAwEOaTJ0+G+bvvvgvzxx577EwdkpyGi4sLzGtqamDu4eEBcycnJ5i3tbXBvLu7G+bt7e02WU9PDxzr7e0Ncy8vL7uOhV0Df39/mLN6Xr58OcwfffRRmLu64rbj7u5u1/iuri6YW5Zlk3V2dsKx7Fqy8eizjTEmICAA5qye2DXuDzc3N5iz/sTqi9VFQ0MDzP38/GCO7s/hw4fhWHaMnp6eMPf19YV5Y2MjzENDQ2E+evRomH/11Vcwf+mll2DOjrO2thbmrG+w+kL3NiwsDI5tbW2167PZ/GLndOzYMZgHBwfDvK+qq6thzq5dXV0dzNncZCIjI2He3Nxsk7Frza4dOxZ27fLy8mAeExMD88zMTJjv27cP5m+99RbM2XxhPaCiogLmTHp6uk1WUFAAx+bm5sKc9amxY8fC3NkZ/x5Qto6UlZXBvD9Yj2Y1x64361tNTU0wLyoqgrmPj49NxtYFdoys1tn9ycnJgXlQUBDMZ82aBfO3334b5u+99x7M2X1GtWgMr5eBAwfCHPV69jPZNdu/fz/My8vLYc56ZHx8PMzR/e4PtrdkvTg6OhrmhYWFMF+9ejXMY2NjYY72W2x9W79+PczZPpd9zrRp02C+Z88emKO9vjHGbNmyxa7xbP1vaWmBOVq/jDFmzJgxMD969KhNxp6D2Geza8bWF9YDmG9jH71582aYs3Nn58L2xWzus2uI1j82v1lvtXc9T0hIgHlISAjMp0+fDvODBw/CfOnSpTBPSUmB+bp162DOrhmD6ovtXdg1Y8+prBbZHpE9q9TX18O8r1ifYzXEnlnZ+s+exdgaUFpaapOxtRaNNYb3FVY/bH1h9cPOie3HFy9eDHO2t0hKSoJ5R0cHzNPS0mC+detWm+ySSy6BY9k1YKZMmQJzNqerqqpgzvaT/cFq65prroH5p59+CnO2t2Q9obKyEuZo3zZgwAA4ltU06xOXXnopzFkPZb2Y1RZ7J7NmzRqYs/0C2+9MnToV5rt27YJ5XFycTcbmHVuT2fMR63msp7N3quwdSF9FRETAnO3v2XMFq092PdjaMGrUKJuMPYezdxfsHQXb57LnKta32PhNmzbBnL27GzFiBMzZsw3LWa9HzzCsn7O9O5vr7D01qye232PvXvojOTkZ5mz9mDNnDszz8/Nhzubs9773PZiHh4fbZMXFxXDsxRdfDPMNGzbAnO2X0c80hr+nY/sadn/Y+wK2FrN9NHvOfvjhh2GenZ1tk7FnN9Yfhg4dCnO2/2R7u2XLltn1+aejPykuIiIiIiIiIiIiIiIiIiIOS1+Ki4iIiIiIiIiIiIiIiIiIw9KX4iIiIiIiIiIiIiIiIiIi4rD0pbiIiIiIiIiIiIiIiIiIiDgsfSkuIiIiIiIiIiIiIiIiIiIOy/VsH4Aj+M1vfgPz2NhYmP/4xz+GeU9Pzxk7JvlmHR0dMHdxcYG5ZVkwd3Nzg3lXVxfMvby8YN7a2mqTNTc3w7G+vr4wt/fY2fgHHngA5tHR0TC/6667YN7d3Q3ztrY2mPv7+8Pc2Rn/3h1XV9y+0L318/ODYzs7O+36bKahoQHm7Nirq6vt+vze8PHxgTmrl7KyMpjX19fDnNU6q2l0TSIiIuBYDw8PmLNaYfOL1dzPf/5zmA8bNgzmv/vd72DOarSkpATmgYGBMGfny+4h6gWs5thnsPWFzYGqqiqYs3WN3au+YvXG6tnemhg8eDDM2XWtqKiwyVDfNsaY8PBwmLOezvpESEgIzKdOnQpzdo+fe+45mLN7z2qoqakJ5mwtiYuLgznqPZGRkXBsS0sLzNncOnLkCMwZdk88PT3t+pzeYHOkrq4O5qwuWE3X1NTAnN0HtA5lZGTAsQcOHIA56wdsHkVFRcH86quvhjnbd+Tk5MA8MTER5mydQvPaGGMOHz5s1/Gge8J6KPsMdm3CwsJgXllZCXO2ru3cuRPmfcX6BDs/NtdYPaekpMCc7Z/Q57N5PGDAAJizemD1w9b+W265BeaDBg2C+R133GHX8bBnmJEjR8KcPQewno72wBs3boRj2XpUWloKc9Zj1qxZA/OYmBiYt7e3w7w/hgwZAvOAgACYs33K8uXLYe7t7Q1z9owyfPhwm4ytF6x/sHWH7VNYT2f3gfWBjz76COZsvrNnErZ+sfNiewa0NrB1xMnJCeZs38GeGdma3NjYCHP2jNFX7Nqx82PYvWHzYtWqVTC/9NJLbbLy8nI4ll0j1tPZObF6vuSSS+z6/FdeeQXmc+fOhfnevXthXlRUBHO2d9m6dSvM0b6A1fPAgQNhvmLFCpiz+832HOwasDWjP1jfZ8fM9iNsf8bqjq2ho0ePtsny8vLgWDZfWA/dsmULzNmzATvGSZMmwfwf//gHzFkfcnd3h/nEiRNhztYAtpYUFxfbZOzZHq2Nxhizbt06mLP5xeqAXWO2Z+qrzZs3w3zOnDkwX79+vV2fz67fZZddBnP0rMf2OWxPz95xTZs2DebsvSN7H83m0euvvw7zpKQkmI8dOxbmS5YsgXlycjLMUd0ag68b2xezdyDp6ekw//zzz2HOem58fDzMMzMzYd4fbE6xdej48eMwZ8/hbL/F1m60LrIe9MUXX8CcPTOyPvHOO+/A/Pbbb7fr85988kmYs2cJ9l5y3rx5MGfXcseOHTBHfbS2ttauz2DvKsePHw/zTZs2wXzEiBEwz83Nhfnp6E+Ki4iIiIiIiIiIiIiIiIiIw9KX4iIiIiIiIiIiIiIiIiIi4rD0pbiIiIiIiIiIiIiIiIiIiDgsfSkuIiIiIiIiIiIiIiIiIiIOS1+Ki4iIiIiIiIiIiIiIiIiIw3I92wdwPhk1ahTMb7zxRpj//ve/h3l2dvaZOiTpIxcXF5i3tLTA3NvbG+aenp4w7+7uhnltbS3MPTw8bDJ/f384tqenB+b19fUwZzIyMmA+bdo0mP/973+HeUlJCcydnJxgHhAQAPPGxka7PsfZGf+eHh8fH5ustbXVrmNh94kdC7p/xhjT3NwM88DAQJj3R0dHB8zLyspg7ubmBnN2bO7u7jCvqqqCeWhoqE3W1tYGx7J7yWqdzY2hQ4fCfPDgwTB/5plnYF5ZWQlzVqPh4eEwb29vhzm79k1NTTBH9zYsLMyuz2A9jF1jdk/YsbPP6Ss2Ny3LgnlCQgLM6+rqYH4m1mE2V9i8Z8fO1osBAwbAfM6cOTB/6aWXYF5RUQHzrq4umLN7z+ZvUlISzNm1R+uvvcdYU1MDc9YD2JxmewHUv/qLrSustyYnJ8M8JycH5sOGDYM5O3dXV9tHgOPHj8OxbK/D7jHDrvesWbNg/vzzz8OcXQO0/htjTHx8PMzLy8thnpKSAvOCggKYp6am2mTsugcHB8OcnZOfnx/M2bxbuXIlzNm62Vdsr8h66/Dhw2HOrgfrCQy6Bw0NDXAsuzdsfWP7XHYNpk6dCvM333wT5oyXlxfM0bkaY0xhYSHMWU8vKiqCOVrbfvzjH8Ox69evhznra/v37+/1z/ymnO11+oP1A7ZGs34zbtw4mLN90vbt22EeFBRkkx07dgyOZWvfli1bYJ6ZmQnz0tJSmLMevWTJEpizc2XPDOhcjeHrJhvP5OXl2WRoDTSGHyN7lmTnyvYRbF6zOuurkSNHwjwrKwvm6enpMGc1wfroxRdfDPMjR47YZOz5ie1/v/zyS5izvSK7NwsXLoT5D37wA5hPnjwZ5uxaRkZGwvyiiy6COatztoah+mf7YlZXQ4YMgXlaWhrMo6KiYM7W/IiICJj3B7uuH3zwAczZfWbvTHbu3Alztp5FR0fbZJMmTYJjv/jiC5iPHj0a5gxb/+fPnw/zxYsXw5ztc319fWHO5l5sbCzMWX9lcxL9XPbugmHPKmwfwY6RrbMDBw6063hOh80RtuccM2YMzNmzGNsTsnfAaI1jay17ZmHj2Rxi72/YO9cVK1bAnO3HWM9dt24dzNGcNoa/d2PvRlAfZf1r3759MGfrGuvR7HMSExNh3tnZCfP+YO/v3n77bZgPGjQI5mw/wmqd9SG092PvZ9mzEusf7H6yY2H7iM2bN8OcvU9kawDrf3v27IE5O1/2vQbaS8TFxcGxxcXFMJ8+fTrMd+3aBfOrrroK5mz/ae+zwQn6k+IiIiIiIiIiIiIiIiIiIuKw9KW4iIiIiIiIiIiIiIiIiIg4LH0pLiIiIiIiIiIiIiIiIiIiDktfiouIiIiIiIiIiIiIiIiIiMPSl+IiIiIiIiIiIiIiIiIiIuKwXM/2AZxP7rrrLph3dHTA/O233/42D0f6wcPDA+aurnhKdHd3w7y5uRnmzs7495v4+vrC3MnJySbr7OyEY93c3GDe09MDc+bGG2+EuYuLC8w/+eQTmPv4+MDc3d0d5my++Pn52XU8bW1tMGf3Cmlvb7crDwgIgDm7V6zO2DXoD3YM3t7edo0vLS2FeXh4OMzZfWtoaLDJurq64FgmJCQE5mze3XDDDXZ9zhdffAFz1gcYVotMbW0tzNkc9vLy6vVns/vN5gU7Fna/y8vL7fq5fVVUVATzxsZGmMfHx8O8tbUV5ikpKTA/dOgQzKOiomwyNofYz2TrQlNTE8yvvPJKmKP1whhjtm/fDnNWn+z4a2pqYM76X3V1NcyDg4NhnpOTY5ONHz8ejmXHXlxcDHPWG1h9sjlXVVUF8/5g93nSpEkwX7VqFcxZP8vNzbVrPDqeESNGwLHr1q2D+ejRo2HO5um8efNgfuTIEZgvXboU5qy22NzbvXs3zENDQ2HO1uhZs2bBPCsryyZDPcMYYw4fPgzzwMBAmLNzKisrg/nUqVNhnpeXB/O+Yj2a7XPXrl0L8+joaLs+h61l6HiOHj0Kx2ZkZMCc7dnYGszuWX19PczZPGKCgoJgXlFRAXM219m6HRsb2+tjYcfOrvGoUaNgzo49JiYG5qxuKysrYd4fbN6z/pGcnAxzNvdZT8/MzIQ5WivZntveZ0O29xs6dCjMCwoKYI6O0RhjWlpaYM5qlN1nNpeGDRsGc7YPQsczcOBAOHblypUwnz17NszZ3uill16COXv+PtP7DvY8x+5BXV0dzNn+mu0Vhw8fDnP0bM3qmd1HtndnvZLtr9j6yd5dsB7A1iN2jbdt2wZz9nzMetKYMWNsMlaHbA/B9tesDpi4uDiYs31gf+zatQvmrC7Y8xJ7Vpg7dy7M2Rqan59vk+3YsQOOZde7pKQE5mx+/eY3v7Hr81mPRvtWY/i+mNUoqxd73/l4enraZGyesvWfrb1s/ULvqozh/eTgwYMw7yt27dg7mJ07d8Lc3veT7D0Xuvdsr8D2v4mJiTBne0X2roP10M8++wzmkydPhvmHH34Ic3acbC+1YcMGmLPrgI5/06ZNcCx7j8Jy9qzO9pKsF7P3Uv3BnivY+wK272G9m+1p2RxHx3Ps2DE4ll3XZcuWwZzNo9/+9rcwZ/viV199FeasD/zzn/+E+cyZM2E+YMAAmLN+8uabb8J8ypQpNhnr0QsXLoT5559/DvOxY8fCfPny5TBn/eTOO++E+enoT4qLiIiIiIiIiIiIiIiIiIjD0pfiIiIiIiIiIiIiIiIiIiLisPSluIiIiIiIiIiIiIiIiIiIOCx9KS4iIiIiIiIiIiIiIiIiIg5LX4qLiIiIiIiIiIiIiIiIiIjDcj3bB3A+mTZtGsyff/55mNfW1n6bhyP94OyMfz+Ik5MTzN3c3GBeV1cHcy8vL7s+p6mpySbz8fGBYxl2Tt3d3TCfMmUKzF966SWYV1dX2/VzGVdX3HY6Ojpg3tnZCXN2jdvb220yf39/OLaqqgrmQUFBMG9uboa5h4cHzNm17+rqgnl/9PT0wLympgbm4eHhMI+IiIC5ZVkwZ9cE1YW3tzcc6+LiAvPW1laYs/szevRomH/11VcwZ8fO5nVbWxvM2Vxlte7p6Qlz1n/QPWT3iR07O8bAwMBe/0xj+Dx1d3eHeV8dOXIE5oMHD4Y5qyFWK5WVlf0+ntjYWDiW9URWD6wfxMfHw3zt2rUwb2hogHliYiLMi4qKYH748GGYR0ZGwpxd+5aWFpjHxcXZZLt374ZjWV2xOmR9EK0LxhgTEBAAczZH+wOdtzH8frJ1hdULu97sXFCd5ufnw7HBwcEwZ2soO5bJkyfDnO072BpQUlIC85CQEJizPrd3716YjxgxAub79++HObpXbO+SlJQEczYf2b7R19cX5mydYnOmr9C+1RhjCgsLYc72YWFhYTBn51FeXg7z9PR0m4zdx+PHj8OcYevFr371K5izexkVFQXzxsZGmLNrzNZ5Nl/s3UejHsP2s+zZmM0t1ktYPQ8dOhTmbI/SH2xusuvN1qecnByYs2vF+i7ad7N9wZIlS2DO9gVs7bvssstgzmo6Ozsb5qzfJCcnw5z1h+joaJgfOHAA5ux80Rqwfft2OJb1jdzcXJizHjZjxgyYs3WT3ZO+2rRpE8zZNRo3bhzMWc9la9OuXbt6cXT/xs6ZfTbbz7A5eumll8J8/fr1MGfzi/Xo0NBQmK9atQrmrJ5ZL2E/NysryyZj94/1XHaN/fz8YM7mNHs/9G0YNmwYzNma/vbbb8OcvS/YsGEDzNk1Qc+kBw8ehGOvvvpqmLP+z/atMTExMGfvo9mcSUtLgznbw7FaZ8+2c+fOhXlBQQHM0flu27YNjt23bx/MBw0a1OvPNsaY4uJimLN3B2d6H83ezbB7wPoEe0dXUVEB83feeQfmkyZNssnYMbI5wX4mU19fD/OlS5fCnJ0r2xOyZwmGzS/2boeNR7XF9phTp06162eyNZaNZ8+u7D1of7DnJdaH2P1ne0V27uz5H/Vj9q6IrdsZGRkwZz2UvRdj76Mvv/xymLNrlpqaCnM2Nw4dOgRz1hcfeughmL/xxhs2WWZmJhzL3gOx97isb7A5w3rhli1bYH7bbbfB/AT9SXEREREREREREREREREREXFY+lJcREREREREREREREREREQclr4UFxERERERERERERERERERh6UvxUVERERERERERERERERExGHpS3EREREREREREREREREREXFYrmf7AM4nGzZsgPmf//zn7/hIpL+cnJxg3tnZCXPLsmDu5uZmV97c3AxzDw8Pm6y9vR2O9fb2hnlrayvM2Tnt27cP5i+88ALM0TF+0+ezvKurC+aMi4sLzNk9QePZWHd3d5iza+nsjH8fEaunjo4OmHt5ecG8P/z9/WHO6sjVFbd/di7sc/z8/GCO6rSmpgaOZfOC3beenh6Ysx792GOPwZwdD6vRiIgImLO5weqotLQU5sHBwTBHdcqOnc07X19fmLNaZPVUX18Pc3YN+mrcuHEwZ3XI5iY73rS0NLs+JyQkxCarqKiAY6uqqmCekJAAc3YvN27cCPOPP/4Y5vHx8TBvamqCeVtbG8xZnYeFhcGczZeDBw/CPC4uziaLjo6GY1mPZmssOyc251i/Ky8vh3l/FBUVwTwgIADmAwcOhDmrl7q6Oph3d3fDPDw83CaLioqCY9n1Y/eH9SHWo9etWwdzNt9ZjbL7xo5zwIABMGfXjNUXwvr//v37YY56jDF8HWTzsbCwEOb27r1Oh9Xh0KFDYR4aGgpz1idYT0hMTIT5pk2bbLKRI0fCscnJyTAvKSmBOepZxvBr/e6778K8srIS5mxPw65xSkoKzFn9s/Nle9Ta2lqYI7m5uTBnaymbQ4GBgTDfu3cvzNm97Q+2Vv7yl7+EeXZ2NszLyspgzq63j48PzFFPZ9ePzQu2l9u8eTPMDx8+DPMPP/wQ5mzvN2HCBJiztXvLli0wZ32LrZusj6Kfy/ZkrP+z8ex56ujRozBnpk6datf402HPZ2z9ZPtl1j/y8vJgPmjQIJij/lRcXAzHsjqPjIyEeX5+Psw/++wzmO/atQvm7HmUYdeGrQ2sbo8cOQJz1uvRvGPnxHoAmyvsZ7JzYtd+/PjxMO8Pts9ltT548GCYs77C5n5sbCzM0dxnayKr6ZiYmF5/tjHG7N69G+YNDQ0wZ+sR25OxdxGenp4wZ1auXAnzpKQkmKPjzMjIgGPZ/WtpaYE524+wdwHsGlRXV8O8r9hzHnuGYuszq0/Wb9ieY8eOHTYZm0NsLrJ1j11rtu58+eWXMB8xYgTMWa+/9tprYc6e0Q4dOgRztsdifRHNazbnXn75ZZhfddVVMGefw/ZR7B6yudgfQUFBMP/kk09gPn36dJh//vnnMGfPCmz/jtY51ufZdyxsT8PuPZunrNd/8MEHMGc9/corr4Q5e8fC9k3sOYDtg9CzMHu3xe4Hw5472TVj72/YNTsd/UlxERERERERERERERERERFxWPpSXEREREREREREREREREREHJa+FBcREREREREREREREREREYelL8VFRERERERERERERERERMRh6UtxERERERERERERERERERFxWE6WZVm9Gujk9G0fi4jdelm+Ntzd3WHu4+MDc1dXV5i7ubnBvKmpCeYeHh4wr62ttcl8fX3h2O7ubpizc2ptbYV5Z2cnzNm5sh7g6elp13h7c3Yt2XgvLy+brL29HY51dsa/L4hdS3bNWB00Nzfb9XPZ+N4YN24czKurq2HO7rOfnx/M8/LyYB4XFwdzVNPsOrm4uMCczW92f+rq6mDO9PT0wJzNmfDwcJjX19fb9TmsD7DPb2lpscm8vb3h2K6uLpg3NjbCnM0jVuusR6L7bYwxDQ0NMD+dgQMHwtzf3x/m7HqwmmDzYsiQITDfuXOnTRYVFWXXsbB6CwkJgXlgYCDM2Vxk84jdG3b87NowbA2IiIiAeXZ2tk0WGRkJx6LaN4ZfSza3wsLCYM56CTpGY4w5fPgwzHtj8ODBMGf3ga1baI0zxphdu3bBnF3bgIAAm4z1MnaPWf8/fvw4zFlPZJ/P7hu7D6zfpKWlwZz1E9YX2dqNrtuBAwfg2MTERJh3dHTAnNU6O3bWTyorK2G+YcMGmJ/O7NmzYV5TUwNzVs9sjo8YMQLm7N6sW7fOJktKSoJjWW8tLS2FeXR0NMzLy8thnpKSAvO2tjaYM/n5+TBn6/zkyZNhzvZ1RUVFMN+3b59NxvZjY8eOhXlWVhbMU1NTYc7qk117tp9cunQpzHsjMzMT5uy5ix0DmwPsXNj+DK1nrB+w2mU9lD1bhYaG2jWe9TNW62xOsv7Hfu6WLVtgPmXKFJhv3LjRJps1axYce/ToUZiz/QK7J2x+sXWT7TuOHTsG89OZOHEizNkegq2Tmzdvhjnrc+w6oXkxfPhwOJbtIVhdsXUkKCgI5oWFhTBPTk6G+fLly2E+bdo0mLMezXoD2weyPcfevXttMvbeiO3F2TVj15j1wfj4eJizfdqmTZtg3hvjx4+H+aRJk2DO1mj2vM2eGauqqnr9Oeyebdu2za5jYf1g1KhRMD9y5AjM2fshtqazvRr7fFbrFRUVMGd7x88++8wmY/OL1SK7f2hPY4wx6enpMLf3Pe7nn38O89P54x//CPOcnByYs/eEbPzdd98N848//hjm6B0Pe4fAni137NgB84SEBJgPGjQI5rt374Y5m1/smcje9WvMmDEwZ3sjtl9A72qCg4PhWNa73377bZjfe++9MGdzNCMjA+Zbt26F+SeffALz3rj66qthzp7pWP9bsmQJzNmcLSkpgTmqF/aOkb2jYPmwYcNgzvbjrBZZbaH3NMbw53Z2jdm1YWsD2xug/Qt7f8Ou8Zo1a2DOniUOHToEc3bN2HugDz/8EOYn6E+Ki4iIiIiIiIiIiIiIiIiIw9KX4iIiIiIiIiIiIiIiIiIi4rD0pbiIiIiIiIiIiIiIiIiIiDgsfSkuIiIiIiIiIiIiIiIiIiIOS1+Ki4iIiIiIiIiIiIiIiIiIw3KyLMs62wchIiIiIiIiIiIiIiIiIiLybdCfFBcREREREREREREREREREYelL8VFRERERERERERERERERMRh6UtxERERERERERERERERERFxWPpSXEREREREREREREREREREHJa+FBcREREREREREREREREREYelL8VFRERERERERERERERERMRh6UtxERERERERERERERERERFxWPpSXEREREREREREREREREREHJa+FBcREREREREREREREREREYf1/wHAPXhFJ6NdUAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 2000x1000 with 11 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "args = get_args.get_arg()\n",
    "data_dir = './data/mnist'\n",
    "sigma = 0.5\n",
    "apply_transform = transforms.Compose([transforms.ToTensor(), transforms.Normalize((0.5,), (0.5,))])\n",
    "train_dataset = datasets.MNIST(data_dir, train=True, download=True, transform=apply_transform)\n",
    "test_dataset = datasets.MNIST(data_dir, train=False, download=True, transform=apply_transform)\n",
    "train_loader = torch.utils.data.DataLoader(train_dataset, batch_size=128,\n",
    "                                          shuffle=True, num_workers=2)\n",
    "test_loader = torch.utils.data.DataLoader(test_dataset, batch_size=128,\n",
    "                                         shuffle=False, num_workers=2)\n",
    "device = 'cuda'\n",
    "global_model = CapsNet(device=device)\n",
    "global_model.load_state_dict(torch.load(f'./checkpoints/Capsule/mnist/common/checkpoint_mnist_epoch30.pth'))\n",
    "# global_model.load_state_dict(torch.load(f'./checkpoints/Capsule/mnist/common/best_model_mnist.pth'))\n",
    "global_model.to(device)\n",
    "dataiter = iter(test_loader)\n",
    "images, labels = next(dataiter)\n",
    "images, labels = images.to(device), labels.to(device)\n",
    "classes = ('0', '1', '2', '3', '4', '5', '6', '7', '8', '9')\n",
    "ind = 41\n",
    "input = images[ind].unsqueeze(0)\n",
    "input.requires_grad = True\n",
    "global_model.eval()\n",
    "ground_truth_predictions, reconstruction, primary_caps_output, digit_caps_output, c, b= global_model(input)\n",
    "_, predicted_classes = ground_truth_predictions.max(1)\n",
    "ground_truth_prediction = torch.bincount(predicted_classes).argmax().item()\n",
    "noise_scale = [0, 0.5, 1, 1.5, 2.0, 2.5, 3.0 ,3.5, 4.0, 4.5, 5.0]\n",
    "show_image(input, noise_scale)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9be5150e-f5c3-4e6b-b1ae-a033bd7cedde",
   "metadata": {},
   "outputs": [],
   "source": [
    "label_list = list()\n",
    "for i, label in enumerate(labels):\n",
    "    label_list.append(f'{i}: {classes[label]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1883822f-460c-470b-ac16-8fc5fa3ab35e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def forward_logits_only(input_data):\n",
    "    return global_model(input_data)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "695d182f-65a5-4a8d-a5f5-bd8687eeec8b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-------------------\n",
      "Original Image\n",
      "Predicted: 7  Probability: 0.20104677975177765\n"
     ]
    }
   ],
   "source": [
    "saliency = Saliency(forward_logits_only)\n",
    "ig = IntegratedGradients(forward_logits_only)\n",
    "dl = DeepLift(forward_logits_only)\n",
    "nt = NoiseTunnel(ig)\n",
    "print('-------------------')\n",
    "print('Original Image')\n",
    "print('Predicted:', classes[predicted_classes],\n",
    "      ' Probability:', torch.max(F.softmax(ground_truth_predictions, 1)).item())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "059510e4-162d-468c-87f9-ca930de9c1e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def visualization(noise_scale, model, input):\n",
    "    avg_noisy_image, predictions, predicted_classes, prediction= predict_with_randomized_smoothing(noise_scale, model, input, 100)\n",
    "    global_model.zero_grad()\n",
    "    tensor_attributions = ig.attribute(input, \n",
    "                                   target=labels[ind], \n",
    "                                   baselines=avg_noisy_image * 0, \n",
    "                                   n_steps=1000, \n",
    "                                   return_convergence_delta=True)\n",
    "    attr_ig, delta = tensor_attributions\n",
    "    tensor_28x28 = attr_ig.squeeze().cpu().detach().reshape(28, 28)\n",
    "    attr_ig = np.transpose(tensor_28x28.detach().numpy(), (1, 0))\n",
    "    print('-------------------')\n",
    "    print('Smoothing Image')\n",
    "    print('Predicted:', classes[prediction], ' Probability:', torch.max(F.softmax(predictions, 1)).item())\n",
    "    attr_ig = attr_ig[:, :, np.newaxis]\n",
    "    avg_noisy_np = avg_noisy_image.squeeze().unsqueeze(-1).cpu().detach().numpy()\n",
    "    _, axis = viz.visualize_image_attr(attr_ig, avg_noisy_np, method=\"masked_image\", sign=\"positive\",\n",
    "                              show_colorbar=True, title=\"Overlayed Integrated Gradients\", use_pyplot=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7867c1dd-8730-4286-9c85-8c4f7449804e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-------------------\n",
      "Smoothing Image\n",
      "Predicted: 7  Probability: 0.201076477766037\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 600x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualization(noise_scale=0.001, model=global_model, input=input)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0d17175c-d196-4014-84c1-98a20e032f99",
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_capsule(model, device, test_loader):\n",
    "    model.eval()\n",
    "    correct, total = 0, 0\n",
    "    for images, labels in test_loader:\n",
    "        # Add channels = 1\n",
    "        images = images.to(device)\n",
    "        # Categogrical encoding\n",
    "        labels = torch.eye(10).index_select(dim=0, index=labels).to(device)\n",
    "        logits, reconstructions, primary_caps_output, digit_caps_output, c, b = model(images)\n",
    "        pred_labels = torch.argmax(logits, dim=1)\n",
    "        correct += torch.sum(pred_labels == torch.argmax(labels, dim=1)).item()\n",
    "        total += len(labels)\n",
    "\n",
    "    print('Accuracy: {}'.format(correct / total))\n",
    "test_capsule(global_model, device, test_loader)\n",
    "test_capsule(global_model, device, train_loader)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "eea789a0-4abf-4bc8-b385-fcecea5febfe",
   "metadata": {},
   "outputs": [],
   "source": [
    "def visual_images(model, index):\n",
    "    input = images[index].unsqueeze(0)\n",
    "    label = labels[index]\n",
    "    input.requires_grad = True\n",
    "    global_model.eval()\n",
    "    ground_truth_predictions, reconstruction, primary_caps_output, digit_caps_output, c, b = global_model(input)\n",
    "    reconstruction_min = reconstruction.min()\n",
    "    reconstruction_max = reconstruction.max()\n",
    "    normalized_reconstruction = (reconstruction - reconstruction_min) / (reconstruction_max - reconstruction_min)\n",
    "    _, predicted_class_index = torch.max(ground_truth_predictions, 1)\n",
    "    is_correct = (predicted_class_index == labels[index]).item()\n",
    "    original_image = images[index].view(28, 28).cpu().detach().numpy()\n",
    "    reconstructed_image = reconstruction.view(28, 28).cpu().detach().numpy()\n",
    "    normalized_reconstruction_image = normalized_reconstruction.view(28, 28).cpu().detach().numpy()\n",
    "    actual_class = classes[labels[index].item()]\n",
    "    fig, axes = plt.subplots(nrows=1, ncols=3, figsize=(10, 4))\n",
    "    axes[0].imshow(original_image, cmap='gray')\n",
    "    axes[0].set_title(\"Original Image - \" + actual_class)\n",
    "    axes[0].axis('off')  \n",
    "    axes[1].imshow(reconstructed_image, cmap='gray')\n",
    "    axes[1].set_title(\"Reconstructed Image\" + (\" - Correct\" if is_correct else \" - Incorrect\"))\n",
    "    axes[1].axis('off')  \n",
    "    axes[2].imshow(normalized_reconstruction_image, cmap='gray')\n",
    "    axes[2].set_title(\"Normalized Reconstructed Image\" )\n",
    "    axes[2].axis('off')  \n",
    "    return reconstruction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "3cfe85f2-3c77-4980-b179-4b671dd32878",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "reconstruction1 = visual_images(global_model, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "9e15fd3f-f49a-4835-8740-e1153609678a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "reconstruction2 = visual_images(global_model, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "c4ed8f36-8158-41f9-bcbf-dcc7b27ae6e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "reconstruction3 = visual_images(global_model, 7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "b2645392-e4b9-4b11-9b5c-18bbcc9d0eca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "reconstruction4 = visual_images(global_model, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "b334dd2f-b1df-4945-bb68-a6f0b834eb29",
   "metadata": {},
   "outputs": [],
   "source": [
    "def visual_images2(model, index):\n",
    "    input = images[index].unsqueeze(0)\n",
    "    label = labels[index]\n",
    "    input.requires_grad = True\n",
    "    model.eval()\n",
    "    ground_truth_predictions, reconstruction , primary_caps_output, digit_caps_output ,c , b= model(input)\n",
    "    _, predicted_class_index = torch.max(ground_truth_predictions, 1)\n",
    "    print('--------------------')\n",
    "    print(f'The size of primary caps is {primary_caps_output.size()}')\n",
    "    print(f'The size of digit caps is {digit_caps_output.size()}')\n",
    "    print('--------------------')\n",
    "    print('Primary Caps: ', primary_caps_output)\n",
    "    print('Digit Caps: ', digit_caps_output)\n",
    "    print('--------------------')\n",
    "    print(f'The size of c is {c.size()}')\n",
    "    print(f'The size of b is {b.size()}')\n",
    "    print('c: ', c)\n",
    "    print('b: ', b)\n",
    "    return primary_caps_output, digit_caps_output, c, b, reconstruction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "773e5865-00bb-4bee-a250-63590106d625",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def visualize_digit_caps_output(digit_caps_output):\n",
    "    caps_sizes = np.linalg.norm(digit_caps_output.squeeze().cpu().detach().numpy(), axis=1)\n",
    "    plt.bar(range(len(caps_sizes)), caps_sizes)\n",
    "    plt.xlabel('Capsule')\n",
    "    plt.ylabel('Size')\n",
    "    plt.title('Sizes of Digit Capsules')\n",
    "    plt.show()\n",
    "visualize_digit_caps_output(digit_caps_output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "d4c992e7-e624-45f9-a107-fdbfd8aa6645",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([], device='cuda:0', dtype=torch.int64)\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def visualize_top_n_primary_caps_for_digit_caps(c, digit_caps_index, top_n):\n",
    "    threshold = 0.2\n",
    "    coupling_coeffs = c[0, digit_caps_index].squeeze()\n",
    "    indices = torch.where(coupling_coeffs > threshold)[0]\n",
    "    print(indices)\n",
    "    top_n_indices = coupling_coeffs.topk(top_n).indices\n",
    "    plt.figure(figsize=(10, 2))\n",
    "    plt.bar(range(top_n), coupling_coeffs[top_n_indices].cpu().detach().numpy())\n",
    "    plt.xlabel('Primary Capsule Index')\n",
    "    plt.ylabel('Coupling Coefficient')\n",
    "    plt.title(f'Top {top_n} Primary Capsules for Digit Capsule {digit_caps_index}')\n",
    "    plt.show()\n",
    "visualize_top_n_primary_caps_for_digit_caps(c, 2, top_n=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "66900718-c47f-47c9-80c3-e058d9b79ff0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 1152, 8])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "primary_caps_output.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "aa9f73a4-27bb-4954-a8b6-fd65d27395bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "#-----Select-----\n",
    "def modify_primary_caps_output(primary_caps_output, indices):\n",
    "    modified_output = torch.zeros_like(primary_caps_output)\n",
    "    for index in indices:\n",
    "        modified_output[:, index, :] = primary_caps_output[:, index, :]\n",
    "    return modified_output\n",
    "#-----Reconstruction-----\n",
    "def reconstruct_image_with_selected_capsules(model, primary_caps_output, indices):\n",
    "    modified_primary_caps_output= modify_primary_caps_output(primary_caps_output, indices)\n",
    "    digit_caps_output, c, b = model.digit_caps(modified_primary_caps_output)\n",
    "    logits = torch.norm(digit_caps_output, dim=-1)\n",
    "    pred = torch.eye(10).to(model.device).index_select(dim=0, index=torch.argmax(logits, dim=1))\n",
    "    batch_size = digit_caps_output.shape[0]\n",
    "    reconstruction = model.decoder((digit_caps_output * pred.unsqueeze(2)).contiguous().view(batch_size, -1))\n",
    "    image_size=(28, 28)\n",
    "    image = reconstruction.view(*image_size).cpu().detach().numpy()\n",
    "    plt.imshow(image, cmap='gray')\n",
    "    plt.axis('off')\n",
    "    plt.title(f'Capsule {indices}')\n",
    "    plt.show()\n",
    "    return reconstruction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "489044c1-6206-4b7a-974b-98fe3967bef8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAGbCAYAAAAr/4yjAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAA9hAAAPYQGoP6dpAAASuElEQVR4nO3cfZBVdf3A8c/CyuOyIQELODy0EhASLjlhpgEFE2OBhklS44CAupPJ2D82oz2hSZmNIlijksKkZc0gMQLVCMzQH6F/VDQ9MBkIogWxQMTDSsiynN8fxGd+2yLsXZEVeb1mdoa9ez7nnruz3Peee89+y4qiKAIAIqJdWx8AAO8cogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIosB5qaysLObOnXtG9rVt27YoKyvLj2efffaM7PdMqKmpyeOaNGlSWx8O5wBRoCRbtmyJ2traqK6ujk6dOkVlZWVceeWVsWDBgvjPf/7T1ofXpm699dZ4+umnY/To0c2+tmHDhrjmmmuiR48e0aVLlxgxYkQsXLjwTfe1b9++6N2790kjs3Hjxpg6dWpUV1dHly5domfPnjFmzJhYuXJls/18+9vfjqeffjp69uz51h8g54Xytj4Azh2/+MUvYurUqdGxY8eYPn16jBgxIo4cORK/+c1v4s4774yNGzfGokWL2vow28wVV1wRN954Y7PbV69eHZMnT45Ro0bF17/+9aioqIgtW7bEP/7xjzfd1ze+8Y04dOjQSb/26quvxsGDB2PGjBnRr1+/OHToUCxbtiyuueaaePzxx+PWW2/NbT/1qU9FRMTXvva1t/joOG8U0AJbt24tKioqimHDhhU7duxo9vXNmzcXDz/8cBscWetERPHNb37zjOzrlVdeKSKiWLJkSbOv7d+/v6iqqiqmTJlSNDY2tmh/f/7zn4vy8vLi3nvvLSKiWLp06Wlnjh49Wlx66aXF0KFDT/r1gQMHFp/+9KdbdP+c37x8RIs88MADUV9fH08++WT07du32dcHDx4cd9xxR36+ZMmS+MQnPhG9e/eOjh07xvDhw+PRRx9tNjdo0KCYNGlSrF69OmpqaqJTp04xfPjw+PnPf95ku4aGhrjnnnvi/e9/f3Tq1Cne+973xlVXXRVr1qzJbcaNGxfjxo1rdh833XRTDBo06LSPcfv27TFr1qyoqqqKjh07xiWXXBKLFy8+7dypPPPMM1FXVxfz5s2Ldu3axeuvvx7Hjh075cwdd9wRU6ZMiY997GMtvp/27dtH//79Y9++fW/peEEUaJGVK1dGdXV1fPSjH23R9o8++mgMHDgw7r777njwwQejf//+cdttt8UPfvCDZttu3rw5brjhhrj66qvjO9/5TpSXl8fUqVObPOHPnTs37rnnnvj4xz8e3//+9+OrX/1qDBgwIDZs2HBGHl9dXV185CMfibVr18btt98eCxYsiMGDB8fs2bPj4YcfbvV+165dG5WVlbF9+/YYOnRoVFRURGVlZXzxi1+Mw4cPN9t+6dKl8cILL8QDDzxw2n2//vrrsWfPntiyZUvMnz8/fvWrX8X48eNbfawQEV4+4vT2799fRERx7bXXtnjm0KFDzW6bOHFiUV1d3eS2gQMHFhFRLFu2rMn99e3btxg1alTedumll5725Y+xY8cWY8eObXb7jBkzioEDBza5Lf7n5aPZs2cXffv2Lfbs2dNku2nTphXvec97Tvp4TjjVy0cjR44sunTpUnTp0qWYM2dOsWzZsmLOnDlFRBTTpk1rsu2hQ4eKAQMGFHfddVdRFEWxbt26U758VFtbW0REERFFu3btiuuvv77Yu3fvSbf18hEt5UyB0zpw4EBERHTr1q3FM507d85/79+/P/bs2RNjx46NrVu3xv79+5ts269fv5gyZUp+XllZGdOnT48//OEPsXPnzoiI6N69e2zcuDE2b978Vh7KSRVFEcuWLYvJkydHURSxZ8+e/Jg4cWLs37+/1Wck9fX1cejQoZg+fXosXLgwrrvuuli4cGHU1tbGz372syaP5/7774+Ghoa4++67W7TvL3/5y7FmzZr40Y9+FFdffXU0NjbGkSNHWnWccIIocFqVlZUREXHw4MEWz6xfvz4mTJgQXbt2je7du0evXr3yye5/ozB48OAoKytrctuQIUMi4vjfAERE3HvvvbFv374YMmRIfPCDH4w777wz/vSnP7X2ITWxe/fu2LdvXyxatCh69erV5GPmzJkREbFr165W7ftEHD//+c83uf0LX/hCRES8+OKLEXH8cX7ve9+LefPmRUVFRYv2PWzYsJgwYUJMnz49Vq1aFfX19Rk2aC2XpHJalZWV0a9fv/jLX/7Sou23bNkS48ePj2HDhsVDDz0U/fv3jw4dOsQvf/nLmD9//mnfaD2ZMWPGxJYtW+K5556L1atXxxNPPBHz58+Pxx57LG6++eaIOP4HaSd7QmxsbDzlvk8cz4033hgzZsw46TYjR44s+Zgjjp8Fbdy4Maqqqprc3rt374iI+Pe//x0Rxy9Bveiii2LcuHEZwhNnSbt3745t27bFgAEDol27N/897vrrr4/a2trYtGlTDB06tFXHC6JAi0yaNCkWLVoUL774YlxxxRWn3HblypXxxhtvxIoVK2LAgAF5+7p16066/csvvxxFUTQ5W9i0aVNERJOrhnr06BEzZ86MmTNnRn19fYwZMybmzp2bUbjwwgtj69atzfb/6quvnvJ4e/XqFd26dYvGxsaYMGHCKbct1WWXXRZr1qzJN5pP2LFjR953RMRrr70WL7/8clRXVzfbx2233RYRxwPSvXv3N72vE388+L9nYlAKLx/RIl/5yleia9eucfPNN0ddXV2zr2/ZsiUWLFgQEccvj4yIJr+179+/P5YsWXLSfe/YsSOWL1+enx84cCCeeuqpqKmpiT59+kRExL/+9a8mMxUVFTF48OB444038raLL744Xnrppdi9e3fe9sc//jHWr19/ysfWvn37+OxnPxvLli076dnQ/99fqT73uc9FRMSTTz7Z5PYnnngiysvL8xLa++67L5YvX97k41vf+lZEHP/eL1++PLp27RoRJ38pq6GhIZ566qno3LlzDB8+vNXHC84UaJGLL744nnnmmbjhhhviAx/4QJO/aH7hhRdi6dKlcdNNN0VExCc/+cno0KFDTJ48OWpra6O+vj5++MMfRu/eveOf//xns30PGTIkZs+eHb/97W+jqqoqFi9eHHV1dU0iMnz48Bg3blxcdtll0aNHj/jd734Xzz77bNx+++25zaxZs+Khhx6KiRMnxuzZs2PXrl3x2GOPxSWXXJJvlr+Z+++/P9atWxeXX3553HLLLTF8+PDYu3dvbNiwIdauXRt79+5t1fdt1KhRMWvWrFi8eHEcPXo0xo4dG7/+9a9j6dKlcdddd0W/fv0iIuKqq65qNnvirODDH/5wfOYzn8nba2tr48CBAzFmzJi46KKLYufOnfGTn/wkXnrppXjwwQdb/J4EnFRbXvrEuWfTpk3FLbfcUgwaNKjo0KFD0a1bt+LKK68sHnnkkeLw4cO53YoVK4qRI0cWnTp1KgYNGlR897vfLRYvXlxERPHKK6/kdiculXz++eeLkSNHFh07diyGDRvW7DLM++67rxg9enTRvXv3onPnzsWwYcOKefPmFUeOHGmy3Y9//OOiurq66NChQ1FTU1M8//zzLboktSiKoq6urvjSl75U9O/fv7jggguKPn36FOPHjy8WLVp0yu/JqS5JLYqiOHLkSDF37txi4MCBxQUXXFAMHjy4mD9//in3WRRvfknqT3/602LChAlFVVVVUV5eXlx44YXFhAkTiueee+5N9+WSVFqqrChcqkDbGTRoUIwYMSJWrVrV1ofSatu2bYv3ve998cgjj8S0adOisrIyOnTo0NaHFRHHF9Y7evRofOhDH4qRI0ee099nzg7vKcAZMmfOnOjVq1esWLGirQ8ljRs3Lnr16hV///vf2/pQOEd4TwHeoj59+jRZkqO1l6++HR5//PH8+5ITVzrBqYgCvEWdOnU645eynimXX355Wx8C5xjvKQCQvKcAQBIFAFKL31P43wXLADi3tOTdAmcKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAUnlbHwC8U7Rv377kmeuuu67kmVWrVpU8ExFx+PDhkmeKomjVfXH+cqYAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYBkQTze8dq1K/13l759+5Y806dPn5JnBgwYUPLM6NGjS56JiPjb3/5W8kxdXV3JMxbRO785UwAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAFJZ0cIlEcvKyt7uY+FdrjWrnUZEXHvttSXP/PWvfy15pr6+vuSZXbt2lTzTWq35P9jQ0FDyzLFjx0qe4dzQkqd7ZwoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEgWxOOs6dixY6vmLOrWeq1ZhND37t3LgngAlEQUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSBfFolbP589DCH1FOYsCAASXPvPbaa2/DkfBOYEE8AEoiCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIAqbytD4Bzk0Xqzr6ampqSZzZv3nzmD4R3NWcKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAKitauNxlWVnZ230scF7o169fq+Z2795d8kznzp1Lnjlw4EDJM5wbWvJ070wBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgDJgnjwX+3alf47UkVFRckzR48eLXkmonX/B2tqakqeWb9+fckznBssiAdASUQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACBZEI93vNb87JWXl5c8U1VVVfLMwYMHS545mwvivf766yXPtPApgXOQBfEAKIkoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgCk0lcNg1Y6m4sqHjt2rOSZw4cPlzzT2NhY8kxDQ0PJMxERlZWVJc/U19e36r44fzlTACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAsiAeZ01RFK2aGzt2bMkzv//970ue6dmzZ8kz27dvL3mmtQsD7t69+6zdF+cvZwoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEAqK1q4dKXVFnm3Ky8vfdHg1sx079695JmIiJ07d7ZqDk5oydO9MwUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACQL4sFb0KlTp5JnGhoaWnVfjY2NrZqDEyyIB0BJRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIJW39QHAuezIkSMlz7RwDUpoE84UAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQLIgH/1VWVnZW7seCeLyTOVMAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAECyIB7vSq1Z3K5fv34lz+zYsaPkGXgnc6YAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgCksqIoihZt2IpVJ+FMaM3PXrt2pf++08L/Ck0cO3as5BloKy35GXemAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAZEE8gPOEBfEAKIkoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAFJ5SzcsiuLtPA4A3gGcKQCQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQ/g/nsMm6R/DzEwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "reconstruction_new = reconstruct_image_with_selected_capsules(global_model, primary_caps_output, [0])\n",
    "reconstruction_new = reconstruct_image_with_selected_capsules(global_model, primary_caps_output, [123])\n",
    "reconstruction_new = reconstruct_image_with_selected_capsules(global_model, primary_caps_output, [116])\n",
    "reconstruction_new = reconstruct_image_with_selected_capsules(global_model, primary_caps_output, [643])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "c5da2162-dfb3-4226-995d-b80e1cca004d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "reconstruction_new = reconstruct_image_with_selected_capsules(global_model, primary_caps_output, [989])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ee1af080-4efc-4919-8c99-2a9ebcbb3358",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}