Tutorial_GAN_Hessian_Axes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Tutorial1: Compute Metric Tensor for Generator and Explore the Axes\n",
    "This basically correspond to Figure 1 and our method."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Compute Hessian / Metric Tensor on Image Manifold\n",
    "First load the package and the GAN loaders and wrappers."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "from core import get_full_hessian, hessian_compute, save_imgrid, show_imgrid, plot_spectra\n",
    "from core.GAN_utils import DCGAN_wrapper, loadDCGAN, BigGAN_wrapper, loadBigGAN, upconvGAN"
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "Define the image distance metric using LPIPS. We use squeezenet to save memory."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Setting up [LPIPS] perceptual loss: trunk [squeeze], v[0.1], spatial [off]\n",
      "Loading model from: C:\\Users\\binxu\\.conda\\envs\\tf\\lib\\site-packages\\lpips\\weights\\v0.1\\squeeze.pth\n"
     ]
    }
   ],
   "source": [
    "import lpips\n",
    "ImDist = lpips.LPIPS(net=\"squeeze\", )"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now let's load up our GANs and wrap it using our standard GAN interface."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: pytorch-pretrained-biggan in c:\\users\\binxu\\appdata\\roaming\\python\\python37\\site-packages (0.1.1)\n",
      "Requirement already satisfied: requests in c:\\users\\binxu\\.conda\\envs\\tf\\lib\\site-packages (from pytorch-pretrained-biggan) (2.23.0)\n",
      "Requirement already satisfied: boto3 in c:\\users\\binxu\\.conda\\envs\\tf\\lib\\site-packages\\boto3-1.13.25-py3.7.egg (from pytorch-pretrained-biggan) (1.13.25)\n",
      "Requirement already satisfied: numpy in c:\\users\\binxu\\appdata\\roaming\\python\\python37\\site-packages (from pytorch-pretrained-biggan) (1.19.1)\n",
      "Requirement already satisfied: tqdm in c:\\users\\binxu\\.conda\\envs\\tf\\lib\\site-packages (from pytorch-pretrained-biggan) (4.46.0)\n",
      "Requirement already satisfied: torch>=0.4.1 in c:\\users\\binxu\\.conda\\envs\\tf\\lib\\site-packages (from pytorch-pretrained-biggan) (1.5.0)\n",
      "Requirement already satisfied: chardet<4,>=3.0.2 in c:\\users\\binxu\\.conda\\envs\\tf\\lib\\site-packages (from requests->pytorch-pretrained-biggan) (3.0.4)\n",
      "Requirement already satisfied: idna<3,>=2.5 in c:\\users\\binxu\\.conda\\envs\\tf\\lib\\site-packages (from requests->pytorch-pretrained-biggan) (2.9)\n",
      "Requirement already satisfied: urllib3!=1.25.0,!=1.25.1,<1.26,>=1.21.1 in c:\\users\\binxu\\.conda\\envs\\tf\\lib\\site-packages (from requests->pytorch-pretrained-biggan) (1.25.9)\n",
      "Requirement already satisfied: certifi>=2017.4.17 in c:\\users\\binxu\\.conda\\envs\\tf\\lib\\site-packages (from requests->pytorch-pretrained-biggan) (2020.11.8)\n",
      "Collecting botocore<1.17.0,>=1.16.25\n",
      "  Downloading botocore-1.16.26-py2.py3-none-any.whl (6.2 MB)\n",
      "Requirement already satisfied: jmespath<1.0.0,>=0.7.1 in c:\\users\\binxu\\.conda\\envs\\tf\\lib\\site-packages\\jmespath-0.10.0-py3.7.egg (from boto3->pytorch-pretrained-biggan) (0.10.0)\n",
      "Requirement already satisfied: s3transfer<0.4.0,>=0.3.0 in c:\\users\\binxu\\.conda\\envs\\tf\\lib\\site-packages\\s3transfer-0.3.3-py3.7.egg (from boto3->pytorch-pretrained-biggan) (0.3.3)\n",
      "Requirement already satisfied: future in c:\\users\\binxu\\appdata\\roaming\\python\\python37\\site-packages (from torch>=0.4.1->pytorch-pretrained-biggan) (0.18.2)\n",
      "Requirement already satisfied: docutils<0.16,>=0.10 in c:\\users\\binxu\\appdata\\roaming\\python\\python37\\site-packages (from botocore<1.17.0,>=1.16.25->boto3->pytorch-pretrained-biggan) (0.15.2)\n",
      "Requirement already satisfied: python-dateutil<3.0.0,>=2.1 in c:\\users\\binxu\\.conda\\envs\\tf\\lib\\site-packages (from botocore<1.17.0,>=1.16.25->boto3->pytorch-pretrained-biggan) (2.8.1)\n",
      "Requirement already satisfied: six>=1.5 in c:\\users\\binxu\\appdata\\roaming\\python\\python37\\site-packages (from python-dateutil<3.0.0,>=2.1->botocore<1.17.0,>=1.16.25->boto3->pytorch-pretrained-biggan) (1.15.0)\n",
      "Installing collected packages: botocore\n",
      "  Attempting uninstall: botocore\n",
      "    Found existing installation: botocore 1.17.33\n",
      "    Uninstalling botocore-1.17.33:\n",
      "      Successfully uninstalled botocore-1.17.33\n",
      "Successfully installed botocore-1.16.26\n"
     ]
    }
   ],
   "source": [
    "# If you have not got BigGAN, use the cmd tool to install.\n",
    "!pip install pytorch-pretrained-biggan"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [],
   "source": [
    "BGAN = loadBigGAN()  # Default to be \"biggan-deep-256\"\n",
    "BGAN.cuda().eval()\n",
    "BGAN.requires_grad_(False)\n",
    "G = BigGAN_wrapper(BGAN)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Compute the Hessian and it's eigen-decomposition at a randomly sampled vector. To see results faster, we compute top eigen pairs using Lanzcos iteration. Uncomment lines to explore more random samples. ([ImageNet 1000 class](https://gist.github.com/yrevar/942d3a0ac09ec9e5eb3a))"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\binxu\\.conda\\envs\\tf\\lib\\site-packages\\torch\\tensor.py:746: UserWarning: The .grad attribute of a Tensor that is not a leaf Tensor is being accessed. Its .grad attribute won't be populated during autograd.backward(). If you indeed want the gradient for a non-leaf Tensor, use .retain_grad() on the non-leaf Tensor. If you access the non-leaf Tensor by mistake, make sure you access the leaf Tensor instead. See github.com/pytorch/pytorch/pull/30531 for more informations.\n",
      "  warnings.warn(\"The .grad attribute of a Tensor that is not a leaf Tensor is being accessed. Its .grad \"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hessian computed with BackwardIter in 15.56 sec\n"
     ]
    }
   ],
   "source": [
    "feat = G.sample_vector(device=\"cuda\", class_id=145) # class King Penguin\n",
    "# feat = G.sample_vector(device=\"cuda\", class_id=17) # class Jay\n",
    "# feat = G.sample_vector(device=\"cuda\") # sample a random class\n",
    "eva_FI, evc_FI, H_FI = hessian_compute(G, feat, ImDist, hessian_method=\"BackwardIter\", cutoff=20)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Transforms encoded in the eigen directions\n",
    "Next, visualize the transformations that these eigen directions encodes. We shall see the top eigen vectors"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [=================================================================>]  Step: 812ms | Tot: 53s922ms | ploting row of page: 75 of 75\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b 76/75 \n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 360x216 with 1 Axes>",
      "image/png": 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AUQ8qUmPmEtj9AUT1g7Dk5s/tYrRW/uvJJ5/k6NGjaDQakpOTG5T+Ajhz5gzZ2dlMnDjxon1tKf8F8NBDD5GcnMzYsWMBuPHGG/njH//Ygnela2G1O9l1toxVWQWcK1G8QiEE1w2J47ohcfi0gypNo1RXwfq/Q/Ex5fnR7yFlQqurYl7WmSpL9p/nm925hBn0DEkIYXB8CAPigttcdrzTKcyCVX8GpDKUnv5XJY6xhXSHrAhV/qtjcThdHDpfydZTJew5V47d6fLsiwv1477xPdtdtPUiqgpg3fNQlac8jx4AVz+hJDV4yRWZqXIgVylMX2aysf5oEeuPFqHVCPrFBjE4PoQhCaHEBPt2f+8xegAMvhkOfAEVObD7fzDq/s7uVbugyn+1P1JKTheb2HqqlO2nS6iyOurtD/LzYVK/aGYOjkPv08FTASUnYd3foFoRyqpOHMWWpKEMFy7aQhrisjaI941LZX9OBQdyKziSX4nDKXG6JIfPV3L4fCULdmQTHezL4PhQBseH0C82qOM/4LYi7QZFY7HoKJxYBbFDIGl0Z/eqzVHlv9qPwkorW0+XsuVkCYWV1nr7dFoNw5NDGdszkgFxQR07PK4hdxf88C9w2qiQTtbF9uYHVz6WE6cxOq1c17P1lUgua4MYHezHNQP9uGZgDNUOJ0fyqtifW8GBnHJKjEo6UWFlNasrC1idVYBOq2FAXLAyvE4IITKw5cPOTkOjhaseg6W/UtL7tr8BEb2VioEqKo1QZbWz80wZW06VcLLQWG+fEDAwLpgxvSIYnhTWuVNNx1fBjrfJldWscRnZGRKJEyO4ndcjJUeYlTqr1aO9y9og1sXXR8vQxFCGJoYiZRJ5FVa391jOsQIjLpfE7nSxP6ec/TnlgDJHMiQ+lMEJIfSJDuycX8WWYIiE0Q/BD/8Emwk2vwJT/6TqKarUw+ZwsS+nnC0nSziQW4HLVX8dITE8gKt6RTAqNbzT1Gg8SInc+wlHDi9gtauKI9ggPFVRfwJ6hvRkStIUhkQNUQvVXypCCHqE+tMj1J8Zg2Kx2JwczqvwDK9r9Nryyq3kleez/FA+fnot43pFMi0tpmt7jkmjofc1yrC56IhS0Gqw90IFKpcvJwqNbDhWxK6zZVjtznr7wg16xvSMYEyvCOJDu0ZAtcNuZef6p1mTt5nz0g4aH4joi9AHMjR6KFOTppIaktqmr3lFGsQL8ddrGZEczojkcKSUZJda2J9bzoGcCk4WGZESrDYnq7MKWHOkkJEpYUxPiyWlo1fXvGX4ncrKc2WukuscO1gJx1G5IrHYnHyxK5v1R4vqtfvrtYxMCWdMzwj6xgR2mcVFs93MD2dXs37PG1RY3MraPr7oowYyNnkykxMnE+kf2S6vrRrECxBCkBQRQFJEANcN6YGx2sHB3Ao2nSjm8HmlpOT206VsP11K/7ggZqTFMSg+uMt8mQAl5Gbc47D8d0pZgk2vwLUvtCgsoSsxc+ZMPvnkE0JDQxs95umnn+att94iKkop6/rXv/6VmTNn1jvm7Nmz3HjjjTidTux2O48++igPPfQQoGSh5OXleeIQe/fuzZdfeiec8cEHH/Dcc88B8Pvf/5677roLUOIad+7ciU6nY9SoUbzxxhteZce0JQdzK3h/8xnK3BJcWo1gaGIoY3qGMzg+tEstIpZYSlibvZbN59ZhKzwEDmVhJ9gvlInDHmR8SiYGXfs6IZd1HGJbc67EzPJD+Ww7XVovjaxm6D06NbxrzTMeXQa73lMeJ42Bcf/XZGpfZ8e8tYann36awMBAnnjiiUaPsdlsSCnx9fXFaDQyaNAgNm/eTI8ePZg0aRIvvfTSRbnMdWkoda+0tJSMjAx27tyJEIIRI0awa9cuwsLCWLp0Kddeey2gpBNOmDCBhx9+uEX3damfidnmYMGObH6oo1LdPy6Iu69KJSqoa035nKk4w+pzq9lbuBdpN0HJCXDaiRU6rokeyYjJz6DTt60hbCwOsV3/e4UQM4QQR4UQJ4QQTzZx3EghhNNdy7nLkhQRwP0TevLCTYOZlhaDr055+86XW3j3h9P8+qv9fH8gD7PN0cyVOoi+0yHerQZzbiucXNO5/WmG1sh/eYNer8fXVzEG1dXVuFyuZs5onq4o/7Uvu5w/LDzkMYa+Og0/HpvME9P6dRljKKVkf9F+/t+u/8dLO19iT+EepLUCio7Sz6Xlp9oonup/N2MyX2xzY9gUXg2ZhRD+QJKU8qi3FxZCaIH/AJkoJUl3CCEWSSkPN3DcCyjFqLoFEYG+zBuZxOyhPVh3tIhVWQVUmO1UmO18uSuHJfvzmNA3ksyBsYQbOnGVTghl1fn7X4OlTPEWo/op2SzN8OWxL8mpavt/4ISgBG7ue/HvXlvIf7366qv873//IyMjg3/84x+EhYVd9DrZ2dnMmjWLEydO8OKLL9KjRw/Pvu4u/9VQRbuBPYK566qULrUQeKT0CAtPLKz3/dJYShlRXsRUTTQJQg/Dfgz9Z3V4Kd5mDaIQYjbwEqAHUoUQ6cAzUso5zZw6CjghpTzlvs5nwFzg8AXHPQp8BYxsWdc7nwC9DzMHx5E5MIZtp0pZdiiPvHIrVruTFYcKWJVVyOjUcKanxXZs0ntd/IJh7COw5jlFKmzTK4rIbDMV/HKqcjhRfqKDOtl6+a+HH36YP/zhDwgh+MMf/sAvf/lL3n333YteJzExkf3793P+/Hmuv/56br75ZmJiYoDuLf+151wZH245S4VFiZDw02uZP7Jr1S45V3mOb09+y9HSWr/K38efcdKXiRV5hGnClZXksY9A8thO6aM3HuLTKMZtHYCUcq8QIsWL8+KB7DrPc4B6qRNCiHjgBmAKTRhEIcQDwAMASUlJXrx0x6LTahjfJ5JxvSM4kFvBsoP5HM2vwuWSbDlZwpaTJaT1CGb6oFgGxnXCAkzsIKXG8+GFUH4W9n4MGfc0eUpCUPNe5KXQ2HVbK/9VY9QA7r//fq67rumshR49epCWlsbGjRubrJ/S1eW/jNUOPtl2lm2nSj1tgxNCuHNsSueOTupQZC5iyakl7CrY5WnTa/VkJk5hUsFp/M/8AMIH9AaY8GuIblypqL3xxiA6pJQVl/BP3NAJF36j/wX8RkrpbOr6Uso3gTdBWVRpaUc6CiEEQxJCGZIQyuliE8sO5rPrbClSwqHzlRw6X0lieABz03uQnhjasYZx8C1QcFCZsD62DOKG1M4vNkBDw9r2pLXyX3l5ecTFxQHwzTffMGjQoIteIycnh4iICPz9/SkrK2PTpk0XqWa3lM6U/9p1tpQPt5z15Br767XcPiqJsb0iuoRXWGWr4vvT3/ND7g+4pDJfqxVaxieMZ0aPCQTteEfRMgQlqWDS7yAkvhN77J1BPCiEuB3QCiH6AI8Bm704LwdIrPM8AbiwFFoG8Jn7w4sEZgohHFLKhV5cv0uTGmng4Um9KKyKZ9XhQjYeL8LmcJFdaubVNSdIjTRww/D4jvMYtT5Kat/3v1bCGbb+F679OwSEt/9re0Fr5b9+/etfs3fvXoQQpKSkNOiRZWVl8ctf/hIhBFJKnnjiCQYPHuzZ313kvyqtdj7eeo6dZ2q9wvTEUH48NrnzM0sAq8PKmnNrWHVuFTanzdM+ImYE1yXPIOr8Xlj+VG3d8fCeMPHX4H/xnG9H02zYjRAiAHgKqFEeXQ48J6W0Nn4WCCF8gGPAVCAX2AHcLqU81Mjx7wNLpJRNBn9110L1xmoHa44UsuJQPhZbbZZA39ggbhwWT5+YNpT/b4ozm5SUPlDqsEz+vSe1rzuE3VzJ8l9SSnacKePjbWcxur1Cg68Pt49OYnRqeKd7hQ6Xg025m/j+zPcYbbV50f3C+3F9r7kklucp0zXGgtqTegxXYmZ1fh3a10uW/5JSmlEM4lMteUEppUMI8QiKAdUC70opDwkhHnLvb1jB8zIl0NeHOUN7cM2AaJYfymfl4QKq7S6O5Vfxt++PkBYfwg3D4ttfWy5lnDJMOb0eCg5B1iJIu759X7MNuVLlvyosdj7aepbdZ8s8bcOTw/jR6GRCAjo22PtCpJTsKtjFklNLKLbUxj0mBiUyt/dc+ru0sPWtWjFXgMBoGHq7Eh/bBYb3NXjjIa4EbpFSlrufhwGfSSmnN3liO9ESD9ElXewp3MPw6OGd/ut5IZVWO8sO5LPmSGE90c3hyWHMTe9BQlg7rkrbrbDsN1CVr6zqzX4FDBHdwkO80sjKysJqiOW9TWcwVSteYaCfDz8ak0xGclinf6+PlB7h2xPfkl1Vu34a6R/J7F6zGe7fA7H/MyUGtgZ9IAy6CfpMa7W6dWtojUBsZI0xBJBSlgkhops4vsuwIWcDXx77kvUh67l9wO3EGmI7u0segv103DoykcyBMSw5kMfGY0U4XZLdZ8vYc66MUanhzE2PJya4HYYSOj8Y81NY+Uclte/A5zCmZRkUKh2D0yV5ff1JHE7FcclICeeOMUkE+3WuV5hdmc3CkwvrhdAE6gOZmTqTqyIG43N4ERz/p/L9AuWHt9+1im5nBwZatxRvDKJLCJEkpTwHIIRI5uLV4i6HS7rYlLsJgFMVp3h+2/NMS5nGtJRp6DSd+2WqS5hBz4/HJDMjLZbF+86z+WQxUsK2U6VsP13GuN4RzB7ao+0Da6P6KYXvc3bCqfXQv/Ximipti5QSY7UDh1MiBNx/dU9G9+xcfctiSzGLTy6+KITmmqRrmNJjPH6n1sGWXyianDWkjIch8yEwquM73EK8GTLPQAl5We9umgA8IKXslMySlgyZq53VLDm5hHXZ65BuGx5riOX2/rfTM7RnO/by0smvsLJwby47TteuIGo1gon9opg1OK5tVxErcuC7JwAJ8RlkRV+nDpm7EJUWO/sPHuK9Q3auGRjDbaM6Lwa3ylbFsjPL+CHnB5xSWRTUCA3j48czI2U6wXkHYN+nYKqdQyR6IAz7EUT06qReN05jQ2avxB2EEJHAGJTYwi1SyuJmTmk3LmWV+WzlWT7J+oRcY21K1dXxVzOn9xz8fbqG9tuFZJeaWbgnl73Z5Z42nVbDlAFKLYtA3zaaf9n6OpxaC0DWkKcYMGhI21xXpVXYnS7Ol1vIPnWcxWc1/HluWqcoVtucNtZkr2HlmZVUO6s97cNjhjO752yiqgphz0dQeqr2pOB4GHaHsoLcxebua2ituIMvUApUAAOFEBPasnPtTXJwMr8a+Svm9JrjGS5vzN3Ic1ufY3/R/k7uXcMkhgfw6NQ+PDVrAAN7KOVz7E4Xyw/m85sv9/Pt3tyLRD4vicG3gNY9hWAzKYW/uxgzZ86kvLy8yWP27dvH2LFjGTx4MLNnz6aysrLB486dO8e0adMYMGAAAwcO5MyZM4CShdKvXz/S09NJT09vMnvlQj744AP69OlDnz59+OCDDzztr776Kr1790YI4RGn8AYpJSVGm+ejuHtcSocbQ6fLyabcTfx5y59ZcnKJxxj2DevLr0b+insTpxG14z1Y/UytMfQLgZH3w8wXlaD/LmoMm8KbIfMLwDzgEFCzHCq9yGVuF1obh1hkLuLTI59yrKw2BCA9Op1b+t5CiG9IW3SxXTiaX8XXu3M4UafuRUiAjpuGJ3BVazMT9nwMWYvI6vszBgwZ0aUnvRtj5MiRvPTSS0ycOJF3332X06dP8+yzz1503KRJk3jqqafIzMzEaDSi0WgICAhoF/mvPXv2EBYWxqRJk9i5cyeRkd6JmlZZ7Z6aP0U5pxiZPriZM9oOKSUHig+w6OQi8k35nvYegT2Y23suAwMSEAc+V5ST3NknaPUwYLay6brmiOtCWrPKfD3QT0pZ3dyB3YGogCgeHfYoW/O28s3xbzA7zOwt3MvR0qNc3/t6rupxVaeHMjREv9ggnry2PwdzK/lqdw7ZpWYqzHbe/eE0Kw8XMH9UIv1jL7EQ48C5SskBAHMp6AI65df9o48+4pVXXsFmszF69Ghee+01tFotKSkpHoPy7LPP8vHHH5OYmEhkZCQjRozgiSee4OjRo0yYoAxcMjMzmT59+kUG8fDhwzgcDjIzMwEIDGy9YG5d+a+a1162bBm33XYbw4YNa/H1HE4XpXXEXAP0HecZnqo4xcLjCzlVUTv8DfUNZXav2YyMHoHm1FpY+w9lJAGAgF6TlVFGF8l4ai3eGMRTgA64LAwiKDnHY3uMJS0yjS+Pfcnugt1YHBY+PfIpO/J3cFv/24gxxDR/oQ5GCMHghBAGxQez5WQJX+7OocJsJ7vUzIvLjjIsKZRbMxKJbmmojm+gEpxtBpw2sBkp+/Z77NltL/+lS0wg7NZbL2pvrfzXoEGDWLRoEXPnzuWLL74gOzv7otc4duwYoaGh3HjjjZw+fZprrrmGv/3tb2i1itFpL/kvb5FSUmKqHSpHBOoxdsAPU4GpgEUnF7GvaJ+nzd/HnxkpM5iQMAFd2RlY+Yf684RxQ5UFk9CuJ7bSGrwxiGZgrxBiNXWMopTysXbrVQcRrA/m3kH3Mip2FJ8d+Yzy6nJOlJ/g+e3PMyN1BtckXYOPputVWRBCcFXvSIYnh7H8UD7fH8jH7nSx51w5+3MqmNI/mtlDe2BoycJL32th33blsbkUe3Y21ce7j/zXu+++y2OPPcYzzzzDnDlz0OsvXo13OBxs3LiRPXv2kJSUxLx583j//fe57777gPaT//IWk83pSes0+PoQoG/f715FdQVLTy9l8/nNnvvw0fgwMWEi01OmE+B0wM536wsLGyJhxD3ddo6wObx5xxe5t8uWQZGD+P2Y37P41GI2ZG/A4XKw5OQSduXv4vYBt7d5Za+2wk+nZW56PBP6RPH1nlw2nyjG6ZKsPFzA5pMlzBnag0n9orwra+Cjh5p6FS4HuthIGhYsah26xPaR/+rfvz8rVqwAFE/wu+++u+iYhIQEhg0bRs+eSsjV9ddfz9atWz0GsSFaK//lLU6Xi1L3vKFGI9pVusvqsLLq3CrWnFvjEV8QCEbFjWJWz1mE60Ph5GoljKZmeKzxUaZWBs5VavZcpniTy/xBc8dcDvj5+HFL31vIiMngk6xPyDPlkWfK4587/8mExAnM7jkbP5+OTUD3ljCDnvvGpzK1fzQLdmZzLL/Ko5685mgh8zISGZIQ0rzn4uOrTJA7bYRdOxFCE0HTMXNYrZX/KiwsJDo6GpfLxXPPPecpHlWXkSNHUlZWRlFREVFRUaxZs6bJRRRvaEr+qyWUmGy43AY/wqBHq2n7H6PGxBcGRgxkbu+5xAfGQ/Fx2PniBcPjdEU/M6jrZHq1F94oZvcBngcGAh6LIKXsmpHNrSQ1JJXfjPoNq86u4vvT3+OUTtZnr2df4T7uTLuTvmF9O7uLjZISaeDX0/ux+1w5X+7KprCymoIKK6+sPs7AHsHcmpHYtHK3EMrkeFU+SCdYyyGgYzIjWiv/9emnn/Kf//wHUGS2ary6umi1Wl566SWmTp2KlJIRI0Z4DCq0vfzXK6+8wt///nfy8/MZMmQIM2fO5O23377oGqZqB+ZqZagcoNe2+UKKS7rYVbCL7059V098ISk4ibm95tIvvB9YK2HbG1fU8LghvAm7+QH4E/D/gNnAPe7z/tT+3buYjpT/KjAV8OmRTz1S+kIIbuh9A5MTJ3fJlei62J0uVmcVsmT/ec+8lBAwvnckNwxLaFAhJSsriwH9+0PleUUzUQgISerUJPwLudzkv5wuyflyC06XRCMEPUL96k1xtEZwQ0rJvqJ9LDm1pF4IjUd8IXo4QsorcnjcmrAbfynlaiGEkFKeBZ4WQmxEMZKXNTGGGB4f/jg/5P7AV8e/wuFy8PXxr8muyua2/reh13a+GGdj6LQaZgyKZVzvCBbtO8/aI0VIKdl4vJjtZ0qZOTiOaQNjL67LW+MlVp5XgrStZWDoOjmol5v8V6nJhtOlOCXhBl2blLGVUnKk9AiLTy3mXOU5T3uQPogZKTMYFz9OWSwsPg473oGy07UnX0HD44bwxiBahRAa4Lhb3zAX6BZqN22BEIKrE64mOTiZN/e/SXl1OTvyd5BnyuP+wfcT4d+5yfbNEeSn447RyUzuF80XO3PYn1NOtd3FN7tzWX+0iDvGJJOeGFr/JJ0/6APAZgZrFfiGNFuUqqP45JNPOrsLbYbF5vBIevnrtS2LCmiEU+WnWHRyUb0CYQE+AVyTfA0TEyfiq/UFawXs/dSTsglckcPjhvBmyDwSyAJCgWeBYODvUspt7d67BuhMxewqWxXvHnyX42XHAQjQBXDvoHvpH955RXFayqHzFSzYkU1umcXTdvOIBGYMiuXIkSO1wzNHtSL+AErmyhXqMbQXLpck1z1UFgLiQ/0b9A69HTJnV2Wz5OQSDpXUCtLrtXqmJE1hSuIUAnQB4HJdkcPjhrhkcQchxC1Syi+aa+soOruEgNPlZOGJhazNVn5dBYLre1/PlKQpXX5esQanS7LxeBFf7Mzx5ENP7BdFRoiZgQMH1h5oLKytexEc3+Ey75czJcZqT3GocIOeYP+GJemaM4j5pny+O/Udewr3eNp8ND5MSJhAZnImQXp3aQprJax/QSkyVsMVPDxuzRzib4ELjV9DbVcEWo2Wm/reRFJwEp9kfYLdZeebE99wtuosdwy4QxmSdHG0GsGkftH0igrk5dXHKTPZWH+0iH5DfHG5JJqakA//MLAZlblESyn4xF3Rw6m2wmp3eoyhr05DkF/Lh8ollhKWnl7K9rztHmk7jdBwVY+rmJEyg1C/0DovWKHU5S53zyeqw+NGafSTEEJcC8wE4oUQr9TZFQw4vLm4W0vxZZSaKm9LKf92wf65KMNwl/ua/yel/KFFd9BJjIwdSawhlrf2v0WptZTdBbvJN+XzwJAHiPT3Lom/s0kMD+D3swbw8urjnCsxY3e6yKu0EhPkqwzftDrwDVb+oewWZdO3Y2mDKwCXlBQblYQvISAy0LdFI4uK6gqWn1nOptxNHl1CgSAjNoOZqTOJCrhgAcxaAaufhQp3KmPKeBj1wBU1PG4JTS1pnQd2AlZgV51tEdBsPRUhhBb4D3AtSgzjbUKIgRccthoYKqVMB+4FLg7S6sIkBiXy65G/9sQmnjee5+/b/87hksOd3DPvCQ3Q85sZ/RnqXlixO1zkVVipdrilxfzDQLi/JpaSTpEH80b+64svviAtLQ2NRkPdKZWPP/7YI+mVnp6ORqNh7969F52/evVqhg8fTnp6OuPHj+fECWVo+f777xMVFVXvGocPe/f5nj59mtGjR9OnTx/mzZuHzWaj3GzH7nDx9G+fYPKooYwYls7u3bubvZbJbmLhiYU8vflpNuRs8BjD9Oh0fjf6d9yVdlcjxvCZWmOYOgHG/Ew1hk3gzRyiTkppdz8OAxKllM2KCAohxgJP1xSjEkL8FkBK2WAYv/v4d6WUTc4gd/YcYkM4XU4WnVzE6nOrAeUXe3av2WQmZ3abeUWXS7J7/0EiE5R4eyEgKshXyae1lCkqOKBUS/PtoJKpLSArKwuNRsODDz7YqIzXgQMHmDt3LqdOnbpoX9++ffn2228ZMGAAr732Gtu3b+f999/n/fffZ+fOnbz66quNvvb777/PmTNnePrpp+u133rrrdx4443Mnz+fhx56iLRBg5k9/27WrlzOh++8zqoVy9i+fTuPP/4427Y1vEaZlZVFUVARi04uwuqorfw7IGIA1/W8juTg5AbPw1KuGMNKt9BE6kQY/ZCn5OyVTmsEYlcKIYKFEOHAPuA9IcQ/vTgvHqgrOZLjbruwYzcIIY4A36F4iQ11/gEhxE4hxM6ioiIvXrpj0Wq03NDnBu5OuxudRodEsujkIt45+E49leGujEYjMPj6eHJopYTCymoqLXYl7KZG5MJSWquD18Z89NFHjBo1ivT0dB588EGcTsULSklJ8QisPvvss/Tv35/MzExuu+02XnrpJQAGDBhAv379mrz+p59+ym233dbgPiGER1S2oqKCHj16tOpepJSsWbPGIzT74zvv5KuvFwKwctkS7rn7LjQaDWPGjKG8vJy8vLwGr2N1WPn86OceY9gztCePD3+cn6X/rAljWFbfGPacpBQRU41hs3gzmxsipawUQvwEeE9K+SchhDcy0w25Rhe5o1LKb4Bv3CrczwLXNHDMmyh1XcjIyOh6ks5uMmIziAuM4639b1FsKWZv4V7PvGJ0QPcI3Qz21+GjEexcm425VPkn1Pto8BNORE3hIJ3pkoddwZF+pF190e9iq+W/vGHBggV8++23De57++23mTlzJv7+/gQHB7N169Z65/3wQ+3U9pYtWzwpfo1RUlJCaGgoPj4+7vuOIS9PMVAlhfmkptQasxrJsLi4uHrXMNqMmB3Ke27QGbgz7U4Ghg9setRhLoU1zyqB9QA9J8PoB9XFEy/xxiD6CCHigFtpWbH6HCCxzvMElHnJBpFSbhBC9BJCRHZmzZbWEh8Yz69G/or3D71PVkkW+aZ8XtzxInel3cWgyEGd3T2vCPD1QWNyYCy0eKYMtRqBXjqUVC9RCT5+bfpP1lr5r+bYtm0bAQEBDBrU8Gfw//7f/2Pp0qWMHj2aF198kV/84heevON58+ZdNGQuKSlh6tSpgKKabbPZWLhwIQAffvghsbG1oSw2h5MqiwMhBHofDT4NCDdcaOTMdjOlVmWawt/Hn0eGPUJiUOJF59U/qVTxDKvc3mavKcoCimoMvcYbg/gMsBz4QUq5QwjREzjuxXk7gD5CiFSU7Jb5wO11DxBC9AZOSimlEGI4oAdKWnIDXRGDzsDDQx9myaklrDizAovDwhv73mBWz1lMT5neLeYVw6IDEEJgqnZ4VFj06PDDqrj+Pj6XJBcfHNlwLGNr5b+a47PPPmt0uFxUVMS+ffsYPXo0oBjAGTNmNHm9iIgIz+JMQ3OIUkrKy8ux2+0Umxzkn88lOiaOiEA9CQkJ9QRsc3Jy6g3RLQ5LPRGGh4c+7KUx/LMizAHQ+xoY+RPVGLYQb+S/vqBOzKGU8hRwkxfnOdypfstRwm7elVIeEkI85N7/uvs6dwoh7IAFmCdb863vQmiEhjm95pAYlMiHhz/E5rSx5NQSzlWd444Bd2DQde26JTXDWqdLUlRV7QngjnAWYdA6lVjF0KTaucVW0lr5r6ZwuVx88cUXbNiwocH9YWFhVFRUcOzYMfr27cvKlStbXY5VCMHkyZP58JMFTJl1A18t+Jg5c+bg66Nlzpw5vPrqq8yfP59t27YREhLiGS5bHVaKzbXGMEgf1HzJXNUYthlNxSH+Wkr5dyHEv2l47q9ZxWwp5VJg6QVtr9d5/ALwQot63M0YFj2MmIAY3tz/JsWWYvYX7edMxRnm95/PkKiuX/JTqxHEBPtSYrJhtDqo1ASjdRTj66NBa2k74YfWyn998803PProoxQVFTFr1izS09NZvlwpHb5hwwYSEhI8wrAX4uPjw1tvvcVNN92ERqMhLCyMd99917P/wjnE1157jauuuqrZe3ruL88zb/58nnn6TwwaMpSfPfwAoIQRLV26lN69exMQEMB7770HKHXEiyxFnkDrSP9ITBpTo9cHwFSiGENjgfK8TyZk3Kcaw0uk0bAbIcRsKeViIcRdDe3vLOHYrhh24w1mu5kPD3/IgeIDnraRsSO5ue/NXcZbbCpNTEpJpcVOmdlOqLMEvbSi02rQhSfXljHtALqT/FdBpdUjvRYb4tdkKVGb00ahuRCXewU/wj8Cg87QdOrehcaw73QlA0U1hs3S4tQ9KeVi998rQjG7vQnQBfDAkAfYnr+dL499icVhYUf+Do6UHmFev3mkR6d3dhebRAhBSIAeH62G8qpg9HYrdocLe0UR/mFxHTYv2l3kv2wOl8cYBvr5NGkM7U57PWMY5hfW/I+kqdhtDAuV531nwIi7VWPYSpoaMi+mgaFyDZ1Vl7k7I4RgdNxo+of355Mjn3Co+BBVtirePvA2I2JGcEvfWwjUt740Znti8PVBqwnCUmbE12mGaiOllVWEBQeh6YB/xu4i/1VptXseh/g17kE7XA4KLbXGMNQ3tFaQoTGMRYoxNLljcvtdC8PvUo1hG9BUpOZLwD+A0ygLHm+5NyNwsP27dvkS4hvCQ0Me4s6BdxLgo+QG7yrYxXPbnmNv4d7O7ZwX+Om0BIZGebxCrbXMU1hdRSkYVVfnUHehCK/nOCeF5kKcLsWTDPYNJti3mdraxiJY/XQdYzhTNYZtSFND5vUAQohnpZQT6uxaLIRoeLlOxWuEUKqc9Qvvx2dHPuNA8QGMNiNvH3ibYdHDuLXfrc17Cu2AlNKr4a9O74s2MBSbqRy9qxqz1Yi1maHhlUKV1eGJ3wxpRNarxhg6XIrhDNQHEqIPqXfMRfP7xkK3Z+hehe4/C4b9WDWGbYg3uTxR7thDANxxhV1HU76bE+IbwgNDHuCutLsUEU9gT+Eentv6HLsLmk/6b0v8/PwoKSnxOt5PExCG3kcLAgzOSkpNtlbFCl4OuKSk0i3tpffR4NuAd+iSLoosRdhdyrDaoDMQ5htW74dISklJSQl+fu64zaoCWFXXGF6nGsN2wBtxhxkoaXM1GfEpwANSyhXt27WG6a6rzN5QUV3B50c/Z1/RPk9benQ68/rN6xBv0W63k5OTg9Vqbf7gGmwmnNUmnC6JRWPA18//ivYSrXanZ7gc6OeDr0/990JKSZW9yuMZ6jV6DHoDooFMVz8/PxISEtBZ3XGGZnfOwoA5kH67agxbwSUrZrtP9gVqdPKPSCk7TbHgcjaIoPzD7C7czYKjCzC7c4cDdAHM6zdPqZLW1f4JbCacCx/hyLl8CkQki3v8H3+9KR3/Ni6l2R2QUvKHbw+SV24lzKDnbzcOrlcWwOFy8NaBtzhUrMj8p0Wkcf+Q+5WCT41hLoWVf6j1DAfOhaG3qcawlbRG7QYpZbWUcp976x7yLd0UIQQjYkbw+zG/94TimO1m3jv4Hu8cfIdKW2XndvBC9Aa0aXPpEepHuKOQ2Io9LN7faMr6Zc2B3AryyhXv+poBMfWMoUu6+PDwhx5j2Du0Nz8Z/JOmjWG1Edb+tY4xvF41hu2MqgfURQnWB/OTwT/h3kH3emLS9hbu5bmtz7Ezf2fXmqvrO4PQ8EgMvlrGGFez5tB58itaMOy+TFhxSAmQ9tVpmNC3VjVdSsmnRz5lV8EuAJKDk3lo6EPomgpod9hgw99rxV37ZMLQ+aoxrIPLasX4wyYKXvg7Vi9Fe5uj61QgV2mQ4THD6RPWh8+Pfs6ewj2Y7WbeP/Q+uwp2Ma/fvPq1MzoLnR8i7UbiK9/GXFBKX/NuFuwI5/Fr+nR2zzqMcyVmsvIU731CnyhFWBfFGH59/Gu2nN8CQJwhjp+m/xQ/nyYKdrmcsOllKDqqPE8cDSPuVY0hyvtpO3UK06ZNmHftRlYrA1bjpk34DbxQkL/lNGsQhTJpdQfQU0r5jBAiCYiVUm5v9aureEWQPoj7Bt/HnsI9LDi6AKPNyIHiAxwrO8bc3nO5Ov7qzp9b7H0NAVmLCTPaGGVay/+y0zmQE83ghJDmz70MWHFYEVYQAqYOiPG0f3/6e0+Fxkj/SB4Z9kjTWShSwva3INc9Tx6TBlc9esWLuzqrqjBt3Ypp0yYc+QX19mlDQ9G1UtC3Bm88xNdQikBNQZECqwK+Aka2SQ9UvGZY9DD6hPbhy2NfsrNgJ9XOaj4/+jk78ndwW//b6BHYNl+KS0Krg0E3EVf1OhWWSgZZdvDZjkAGxKU1WG/4cqLcbGP7aUW7cERyOFFBinjuptxNLD2taJuE+oby6LBHCfFt5gdi/4LaAvJhKXD1Ex2aK96VkC4X1sNZmDZtwrJ/P7gV1AHQavEfMgTDVVfhlzYQ0UY/GN4YxNFSyuFCiD0AUsoyIYS+TV5dpcUE6gO5e9DdjIwbyYIjCyi1lnK64jR/2/43MpMzmZEyo+m5qfYkdSK6w98SY7YxsnI975eNYM2RQqalXd51f1dnFeJ0KXO609IU77DaWc2ik4sA5TN7dNijRPhHNH2ho9/DoW+Ux4HRMOnJK7LKoaO4GNPmzZi2bMVZVlZvn09MDIbx4zCMHo02uJmsnkvAG4Nod1fQkwBCiCgUj1GlE0mLSOOpMU+x9NRS1pxbg0u6WH5mObsLdzO/33z6hTddX6Rd0PrA4FuIrPo3JcYqhlq2smifP2N6RRDcRD5vd8Zqd7LumJJG1zs6kF5RSi76ptxNmOyKdNctfW8hxhDT6DUAOLsZdrl1VHyDYfJTSsXDKwRps2HZtw/jpk1UHzlab5/Q6wnIGIFh3Dj0PXu26/SQNwbxFeAbIFoI8RfgZuD37dYjFa/x1fpyQ58byIjJ4JMjn5BdlU2RuYh/7/k3Y+LGcEOfGzpeWix5HJrDC+lhPc3w0o0c8B/Jwj253Dk2pWP70UFsPlmM2R2IXeMd2p12TwXG6IBohkUPa/oiefthy38AqdSqmfxbCLq8veoabDk5mDZtxrxtGy6zud4+fWoqhquuIiBjBJpmati0Fd4oZn8shNgFTEUpHHW9lDKr3Xum4jWJwYk8kfEE63PWs+TUEmxOG1vztnKw5CA39bmJjJiMjlt00Whg8K0EV/yDKL2JYebNbDjmz6S+0SRFXF7DP5dLsvKwMsEfGejLsETFo9uat5WK6goApqVMQyOamN8qOQkbXwKXQ1Efn/ArCG9GIbubI6XEsmcvVcuXYzt7tt4+jcFAwJjRBF51Fbr4i4uRtTferDKHA4XAp3XaPLWaVboGWo2WKUlTGBo1lAVHF3C45DBGm5EPDn3A9vztzOs3j0j/yOYv1BYkjkKE9yLefpzhhZvZFzCWT3ec49fT+3X+angbsjennMJKJewjc2AMGo3A4XKw8uxKAML9wsmIubg+tIfKPFj3N3BUAwLGPgKxgzug552H9cgRKr5ZWN8QCoHfgP4Yxo3Df8gQhK7zple8WZrZDRQBx1CKSxUBp4UQu4UQTdaAFELMEEIcFUKcEEI82cD+O4QQ+93bZiHE0Eu5CZVaIvwjeHjow9yddrdHWzGrJIu/bP0Lq8+u9khNtStCwJBb8dNpiTPACNNGjuVXsfNsWfPndiOWH1JCbfz1Wsb3UX5sdhbs9FTLy0zObDwTxVIGa/8C1e7MoxF3Q/LY9u5yp2E7c4bCl1+m6F8ve4yhxmAgeNZM4p57lqjHHiNgxIhONYbg3RziMuAbKeVyACHENGAG8DlKSM7ohk5yL8T8B8hEKUm6QwixSEpZN6T8NDDRvXJ9LYqIRIPXU/EeIQQZsRkMiBjAwhML2XJ+C3aXnW9OfMOOgh3c3v92koKT2rcTcekQ2ZdY11FG5G9jb8BYPt+RzdCEUPSN6AN2J04VGTlRYARgYt8o/HRaXNLFijOK5kmIbwhj4sY0fLLNBGufr9U0TLsR+jVd5a+7Yi8ooGLRIiy7apWbhK8vQddMJeiaazpsbtBbvPlmZtQYQwC3ys0EKeVWoKlq5aOAE1LKU1JKG/AZMLfuAVLKzVLKGrdhK0rtZpU2wqAzcMeAO3hs+GNEByg1jnOqcnhxx4t8dewrqp3tmJYuBAy9Da1GEB+sJcO8gVKTjWVur6q7s8I9d6jRCE8g9t7CvRSaFUn/qUlTGw5/cthgw0tQ7h4y9poCQ27tkD53JI6yMko/+pj8Pz9Tawx9tAROnkzcs88QMnt2lzOG4J2HWCqE+A2KQQOYB5S5PcCmwm/igew6z3No2vu7D/i+oR1CiAeABwCSktrZs7kM6RvWl9+O+i3Lzy5n5ZmVOKWTtdlr2Vu0lzsG3EH/8P7NX+RSiBkIsYOJyNvPSNNudjvHsXS/hvG9Iwk3dN9Q1mJjNTvPKL/jo1LCCTfokVKy7MwyQPkhGhc/7uITXS7Y8m8odA+S4jMuu3KhTqOJquXLMa5bh7S7lxmEIGDUKEJmX4dPZAfNY18i3niIt6N4bguBb4Ekd5sWaOqnraFPuUFFAiHEZBSD+JuG9ksp35RSZkgpM6KiVG3aS0Gn1XFdz+t4ctST9AxRVjHLrGX8Z89/WJe9rv1eeMh8hBAkhuoZZVqH3enii53ZzZ/XhVmTVegR16gJtTlYfJDzRkXlZ3LSZHy1FwyepISd70C2O+M1qh+Mexw0l4dMmqu6msrvvyf/j3+gauVKjzH0GzKYmKeeIuKeu7u8MQTvwm6KgUcb2X2iiVNzgMQ6zxOAi3ShhBBDgLeBa6WUJc31pyU4jUZcZjO66Oi2vGy3Ji4wjp+P+DkbczfyzfFvsLvsfHnsSwrNhdzU5ya0bf0PGtkb4jMIzN3JWONBdjmuZvtpmNI/mj4xHV8iobVYbE7WH1fm/vrFBpEcYUBKyfIzyqySv48/E+InXHziwa/gxCrlcUgiTPg1+HRfL7kG6XBg2rSJiu++w1VZ5WnX9+pJ6A034Nu7dyf2ruV4E3YTBfwaSAM8Eh1SyinNnLoD6OMuOZALzEfxLOteOwn4GvixlPJYy7rePKYtW6j46mt08fH4DxuGf3o6uvgel1Xox6UghGBCwgSSg5N5c/+bVFRXsCFnA8WWYu4ZdA/+Pm08tzPkVsjdRXyIL1dVrGVp0C18vO0cf7xuIBpN9/osNh4vwuouLzrdnZJ4tOwoZyrPADAhYYKnFISH4yvhwBfKY0MkTP4d+Hbt6orNIaXEvGMHlYsX4ygq9rTr4uMJuX4ufoMGdcv/M2/mED8GFgDXAQ8Bd6GE3jSJlNIhhHgEWI4yvH5XSnlICPGQe//rwB+BCOA195vnaEjF9lKx7N0LgD03F3tuLpVLluATFYV/ejr+w4ahT03plh9aW5EcnMwTGU/wxv43yKnK4XDJYf6x8x88PPTh5vNuW0JYMiSPRX92M1fpjrHNUUB2aQybThZzdZ/uMwXidElWZSmLKTEhfgxxK/nUeId6rZ7JiZPrn3RuG+x4R3msD1RS8gLCO6zPbY2UEuuhw1QsXIg9J8fTro2MIGT2HAJGjezW/1Pe1FTZJaUcIYTYL6Uc4m5bL6Wc2CE9vICWlBCw5+Zi3rsXy9592LMvnrfShoTgnz4U/2HD8O3dG+FzZcpDVjuree/gexwsVqrLBuoDeXDIg6SGpLbdi1SehyW/wOlysaIykS8D5hPk58Nfbxzs0Q7s6uw4U8rr604C8KOxyUzuF82p8lP8c9c/AWVl+YY+N9SeUHBIUbx2OUCrh6l/UqYQuiFSSqqPHqVi8WJsJ0952jVBQQTPvJbAq6/uVv8/jZUQ8Ercwf03TwgxC2UesFuEx+ji4wmJjydk1iwcRUVu47gX26nTICXOigqM6zdgXL8BTUAA/kOH4J+ejt+AAQh995/f8RZfrS8PDHmAb45/w9rstRhtRl7e/TI/HvhjRsQ0GXvvPcE9oOdEtKfWMUZ/ig32HApJYMm+PG4dmdj8+Z2MlJLlB5WQIYOvD1f1UjzompVlH40PU5LqzCIVHYX1LyjGUGjh6l90W2NYffw4FYsWU338uKdN+PsRnJlJ4NSpaHybir7rXnhjEJ8TQoQAvwT+DQQDP2/XXrUDPlFRBGdmEpyZibO8HMv+/Vj27sV69Bg4nbjMZkxbtmLashXh64tfWhoBw9LxS0tDE3B55eA2hEZouKnvTcQYYlhwdAEOl4P3Dr5HobmQGSkz2mYYNOhmOPMDoQGSWcaNvMdtrMwqYELfKGJDmlCQ7gKcLDJyulhRr5ncPwpfHy3nKs9xuEQJoRkbN7ZW67DkJKx7vk5K3k+hRzMCD12Q6lOnqVi8iOqsI542odcTOHkyQZmZaAM7WDikA/BmlXmJ+2EFMLmpY7sL2tBQAidMIHDCBFwmE5YDBxXjeOgQ0m5HVldj2b0by+7d4KPFr19/Zd5x8CC0oaGd3f12ZXz8eCL9I3nnwDtYHBa+O/UdheZCbh9wOzpNK9OqAqOg12TE8ZUM159lhf0MuboUFuzI7vLlBpa766VoNYIp/ZRQmxVnlawUjdBwTfI1yoGlp2HNc2C3KM9HPwAp4zu8v63Bdu4cFYsXYz1w0NMmdDoCJ04gaNq0dtEh7Cp4s8qcihJ2k1L3eCnlnPbrVsehMRgwjBmNYcxoXNXVWA8dxrJvH9YD+3GZLeBwYj10COuhQ5QBusRE/Ael4TdoEPrU1DZT6u1K9A/vzy8zfsl/9/2XEksJO/J3UGIp4f4h97e+PnTajXBqHQF6uJlNvCyT2Z9TzoGcii5bbqCw0sqec0og9pieEYQE6Mgz5rG3cC8Ao2JHKYtQ5efcxtAtYzXyJ0omSjfBlpNL5ZLFWPbW1gXHR0vg+KsJnjH9sncGwLsh80LgHWAxl7kwrMbXl4DhwwgYPgzpcFB97BjmPXuw7NvnibGyZ2djz86m8vtlaAwG/AYOxG/QIPzSBqIN7N6hFHWJNcTyRMYTvLX/LU5VnOJUxSn+sfMfPDT0IWINrdDqCwiHPtPhyBIGaHPpbT/NCdGTT3ec67LlBlZmFVCz9lgTiF3jHQoEmcmZUJELq58Fm5LfzIi7lUp53QB7Xh4VS5bUyzdGq8Vw1ViCr70Wn/DuuyreUrxZZd4mpewyggudUaheulzYzpxRPMWDB7GdPXfxQUKgT0nBb1Aa/oMGoUtK6tbhBzXYnXY+OfIJO/J3AErg8X2D72tdup+1EhY9Ao5qzshYnrXdAUIwb2Rilys3YKp28MQX+7A5XKT1COYX0/pRZC7imS3PIJGMiBnBPcnXwqqnFQUbgPQ7YGDXH0DZCwqpXLoU8/bteCy+RoNhzGiCZ87sFpkll0pjq8zeGMTbgT7ACsCjBiCl3N3oSe1IZxjEC3FWVGA9fBjLwYNYDx9GWi6uQawJDsI/TRla+w0Y0K0XZmrydL879R2gBHbP6zeP8fGtmBvb/zkc/AqXlLwub2SXoxf+ei1/vXFwlyo3sPRAHl/tUuLtfp7Zl0HxIXyc9bGnrOhvBz1I/Jb/gtmdZDX4Fhh8c2d11yscxcVULl2Kaes2Jb8alHzjkSMJnjULXczln9nVmrCbwcCPUaru1QyZpfv5FYk2JATD2LEYxo5VhtanTmE9qHiP9vNKdqKrssqzao1Gg2+vXvilpeE/ZDA+cXHdynsUQnBt6rVE+UfxUdZHOFwOPjvyGYXmQq7vfX3TitCN0X8WHFuGxmbiVt1mdtl7YrE5WXYwn1szukYYjsPp8gRix4f5k9YjmDJrGdvzlHzkwSG9iN/6Rq0xTLuhSxtDR1mZYgg3b6lXwc5/xHBCrrsOXVxcJ/aua+CNQbwBpSazrb070x0RPj749e2LX9++cOMNOEpLPUNra9YRpM0GLhfVx48r8VwLF+ITG0PAiBH4DxverVIJM2IzCPcP5839b2K0GVlzbg1F5iLuHnT3xWIGzaE3wIA5sO9TIh0FTAk4yRpLbzYcK2LO0B746Tpf9GD7mVIqzEoY7rSBsQghWHVuFU7pBKeNGTmHwewWeO1/HQyZ14m9bRxnVRWVy5ZhXL8eHHUM4dAhBM+ejT6hW4QVdwjeDJkXAI9KKQs7pktN0xWGzN4ibTaqT55UhtYHDuIovPgt7I7GscRSwn/3/Zd8kxKonBCUwINDHiTMr4VV4uxWWPQoVFdSRBi/rb4bKbSeLJDORErJnxcfJrvUTLC/jr/fPASL08ifNv0Ju8NM/7I8HnG4c777zlAWUbrYZ+cym6lavZqqVauR1bXal36DBhEy+zr0ycmd2LvOpTVziOuAIShiDXXnEDtl1rg7GcQLsRcUYtm7F8vu3RcV14Fa4xgwfDg+Pbq2cTTbzbx78F2OlCpBu5H+kTw+/PGWG8UjS2H3B0gpeds+ja0MJS7Uj2fndq44QFZeJS8tV8phXj8sntlDe7DwxEJWnV4Gxcd43BVEH+EHva/pcpqGLpsN49p1VC1fXq+SnW/fvoTMnYNvr16d2LuuQWsMYoM5y1LK9W3UtxbRnQ1iXRxFRZh378Gye1eDq9bdwTg6XU4+P/Y5m3I3AZdoFB02WPJ/YC4hxxbAM/IBnMLHs4DRWby86jj7c8rRaTW8eMsQNFobf9j4O2wFB+nlcPJzbQykToQxD3cZY1gjxVW5dCnOikpPuz45mZDr5+Lbv3+X/B51Bpe8qNJZhu9yxycqiuDp0wiePk0xjrt2Y9mz22McHfkFVH63lMrvlnZZ46jVaJnfbz4+Gh/WZ6+n2FLMy7tf5v+G/x+hfqHeXcRHrwRr73iLWB8TQ0272e07ilVZBZ1mEPMqLOzPKQdgXO8Igvx0fHdsCbbCQ2A3M10bBcnjYPRDXcIYSpcL8/YdVCxZjLO4VlLUJy6WkDlz8E9P7zLfma5OowZRCFFFwwrXApBSyss3f6eD8YmKInjGdIJnTPfeOI4ciS6282P2hBDc3OdmpJQeTcV/7f5Xy4xiz0mQ9S0+xkJmiK3sk8M5kFNBfoW1U3Kcv9uf53mcOTAWi6Wc9XveAJuJJKFnQOJEGPszpQZ1JyKlxLJ3LxWLFuHIq61Vo42MIOS62YoU12WYSdWeNDtk7mpcLkNmb7AXFmLZvQfz7l3Yz10sX+bbty+BkyYqtWw7WXpJSskXx75gQ84GAKICovi/4f9XK3jQHCfXwrbXsdqdvG6axIGA0UzuH82PxnTsxH9+hZXfLzyAlDA8OYyfXZ3Iiu8fZVHZAQDuj7maodf8FbSd935LKak+coSKhd/Wm4vWhoQQPPNaDOPGdfr3oavTmjhElU5CFx2Nzu05NmQcq48do/rYMSUu8uqrCRw/rtPyTYUQ3NL3FqSUbMzdSJG5iJd3v8zjwx/3ziimXA2HvsbPWEgmWzgsR7D5ZDE3Do/vUL3ERftykVIZCc8dHIlt/QusKVMUbeIMcQyZ+lynGsPqU6eoWPgt1cdqBeY1AQEETZ9O4ORJaK4g2br2QPUQuyH2ggJMGzdi2rxZEaCoQaPBPz2dwIkT8e3bp1PmjaSUfH70czbmbgQgOiDae6Po9hIrLXberZ7CgYDR3Doy0SPV396cL7fwx28PIiWMTg7mAbGQdTnr+dJVBr5B3D3+GTLiG6m13M7YcnKpWPQt1v0HPG2e+sZTp3brTKjOQPUQLyN0MTGE3nwzwXPmYN6xA+P69YrX6HJ5ZMt84mIJnDgRw+jRHVr/VgjBrf1uxYWLTbmbKDQXeu8pplwNB78iiEKuNm7isBzB6qwCMgfEdEjtlW/3nkdK0OBkvn0h9qJdrHJVgj6QqIQxDO8xqt37cCH2ggIqlyzBvHOXJ99Y6HwwTJhA8IwZaIO6X6GutsbpdCFdEp82COZvV4MohJgBvIxSU+VtKeXfLtjfH3gPGA48JaV8qT37c7mh0esJHDcOw1VXYTt9BuOG9Vh27ULaHTjy8in/bAEV3yzEMGY0gRMmoIuP75B+CSGY328+gMcovrL7FR4b/ljTRlHrA4NuRGx7g2R/CwMtuzggRrMnu5wRyS2Mb2wh2aVmdp4pBeC2gF0EF+9mkzRRrveDiN5kps64tBTFS8RRUkLld98pqZ91hReuuorgWTPxCWvf96MrY7M6KMs3U5ZnojTPREWhhX6jY+k5rPX1edrNILoL2f8HyEQpSbpDCLFISnm4zmGlwGPA9e3VjysBIQS+PVPx7ZmK8+abMW3ajHHDepwlpcjqak+ZBN8+vQmcOFEJw2jnSfcaoyilZPP5zRSYC/j3nn/z2PDHCNY3EaCQMgEOfk2Yq5AxhRs57D+CVVkF7W4QF+1TctBDnKVcZfsBp5Cs9HFCRG/CAiIZFdsx3qGjrIyqZcswbtpUm2YnBAEZIwi+7jp0MTEd0o+ugpQSc6WtngE0ll4splKaZ+zaBhEYBZyQUp4CEEJ8BswFPAbRnQ5Y6K7VotIGaAMDCZ4+jaDMa7AeOoRx/Qashw6BlFQfP0H18RNoQ4IxjB+PYfz4dvU0hBDc1v82JJIt57eQb8r3eIqNGkW3l6jd9gZJfhYGWHZzMH8U50rMJEW0zzzZuRIzu88q0l136Nbhp3Gx3WWmOCQWND5kJmfio2nfHxBnVRVVy5djXL/BU+QdwD89neDrrkOf0DHefWfjckkqiy2U5ZkoyzdTmmei2mRv+GAhCI7wIyzOQFRi20wdtOenHA/UjRXJAS5JV1EI8QDwAEBSUlLre3YFIDQa/AcPxn/wYOyFhZg2/qAswphMOCsqlbjG75fhPyyd4Bkz0Ce2j8KMEILb+yvluOsaxceHP964+nbKBDj4FZGOQkYVrifLfzirsgq4d3wbVgGsw7d7cwFItR1lkN9xpNSwIjAQ9IEE64MZGze2XV4XwGUyUbVqFVVr1tbPN05LU/KNU1La7bW7Ag6bk7KCWu+vvMCM096wDrXWR0NoTABhcQbC4wyExgag07etCEh7GsSGZsEvaUlbSvkm8CYoq8zenld4tpLibCOhsQGExQbgH3hlhiTooqMJvelGQmZfh3nXLozr1ivxay4Xll27sezajd/AgQRNn94uq9M1RlFKyda8reSb8j0LLQ0aRa0PDLoJ/bY36KE3McCym22nR3NzRkKbayWeKTaxN7scrbRzi1iFr4+WHRon+QGK5zw1aSo6bdvrM7osFqrWrMG4enW9SAHfPn2UfOPe3bNCX1NIKbFU2SkvMFGapxjByhJr7RzpBfgG6AiLCyAsVjGAwZF+aNpZUb09DWIOUNftSEApYdphFJyu5NyhEnCXiPAz6NzG0UBYbADBUf5ou6BkfXsh9HqPjqPtzBmq1q7DvGMHuFxYDx/Gevgw+tRUgmdMx2/IkDY1jEII7hhwBxLJtrxt9YbPDRpFt5cYVe1gZMl6DvuPYN1RRRqsLfl2r/KVzLD8QGqgiQop+SLQH7Q6DDoD4xPatkCUy2bDuG4dVctX4DKZPO361FTFEPbrd9mk2bmcLiqKLMr8X74yBG50+AsEhvm5vT/FCwwI1nf4e9GeBnEH0MddpCoXmA/c3o6vdxFOhwuhEUiX8gtkNdnJP1lB/skKAIRGEBKteI9hblfcz9B11JrbE31KChH33E3InNlUrVyJadNmpN2O7fRpiv/7Oj5xsQRPn05ARkabLcDUGEWAbXnbyDPlKQstwx4jUH9BPRqtD6TdiGH7G0RpjAy07GLdET9mDopts7orJ4uM7M8pJ9hZxnS2otP68JbejtlPmd+c129ey3UeG0Ha7Rh/+IGqZcvqCS/oEhMJmTMbv0Gdq+7TFlRbHIrhy1MMYEWRBZej4eGvRqshJMrfM/wNiwtA79f5UYDtGpgthJgJ/Asl7OZdKeVfhBAPAUgpXxdCxAI7UWo9uwAjMFBKWdnIJVscmO10KL9S5flmygqa/5XyC9IrxtHtSXaEm94VcFZVYVyzBuP69fWGcNrwcIKuuQbD+HFtlgXhki4+OvwR2/MV5ekegT0aNopOByx5nNLC8xyu0PFBxC+4d0IfxrqLxLeWf648xqHcCmZXfMzMsFy2aEx8ER4NvoGMjB3JXWl3tfo1pMOBaes2Kr/7DmdZmafdJy6WkNmz8R82rFsaQiklVaVWyvLNlOebKc03YS6vbvR4X4PO8z/VFUZnlyz/1dVobaZK3XkMxZU3U1ls8XiRF6Lxcf+SxQYQEh1ASJR/p7jyHYXLYsG4cSPG1avreTKawECCpkwmcOJENIbWFyh3SRcfHv7QU7wqPjCex4Y/hkF3wbVPrMa17Q0On69kpWE2xqTJ/H7WgFa//ycKq3h+6RGSq49xr+MzfEJ1vODrwB6WRLhfOE+OepIA3aWvakspsezZS8U33+AoKvK0+0RFETxrVrcTXnA6XJQXKKu+NYsfjmpnwwfXWf2tMYL+Qbou9T+jGsQmcNpdlBcpv3Rlbk/SZnY0eryPXktwlD8hUf6ERPoTHOVPYKgvogOyKToKabNh2raNqhUr6/1DC19fAidcTdDUqa3Om/bKKLq9xPzzOZww+fJBxC/4zaxB9I5uXcnXl5Yf5dj5Un5c+m9GRNn4t7aM7KjeCK2ex4c/Tu+wS1/UsOfnU7ZgAdVZRzxt2rAwgmfOxDB2TLcQXrBXOynNMymrv+dNlBeaG3UafHy1nimnsFgDoTH+bZI10p6oBrEF1ASDKsNsZT6ksrjx1TAArU5DcIQ/IdGKgQyJ9Ccw3K9DUs7aE+lOB6xcvgJ7dp0oKh8thtFjCJo2rVVV2lzSxf8O/Y+dBcpn2jOkJ48Oe7T+yu6JVdi3vMHhvErWBM7Bb+AMHp506arPR/Or+PuyI2SY1jGHjewOqWZ5UDAExpCZnMnc3nMv7V6qq6n8bilVa1Z7gqo1BgPBs2YROH4cogsLL1hNdkrPK95f6XkTVaWNf98DQn0JjzV4VoADw3y7lPfnDWoucwsQQmAI8cUQ4kt8PyX8wulwUVVipaLI4t7MVJVYPb+aTrvLvZJWu3Ko8dEQHOFHSJS/x6MMCu9ec5JCoyEgIwP/ESOwHjpM1fLlVB8/Dg4npk2bMG3ejP/wYZccy6gRGn488Mc4pZM9hXs4VXGK9w69x08G/6Q2VS51ErpD3xBWYWWkeT3/O5NBqSmRcMOlGZhv9+YS5CxjtHk9xhgNK7R2MESTEJTArJ4tzxGQUmLZtYvyL7/CWV6uNAqB4erxhMyZizaw9VMMbYmUElO5jdI8o8cIWiobqSHnHv6G96hZ/Li8Fx5Vg+glNUGhoTG180oup4uq0moqisxUug1lZYnVs7Lmcs+7lBfU1rUQGoEh1JegcD9li/AjMMwPQ4i+Sw+5hRD4D0rDf1Aa1adOUbV8OZZ9+0HK2ljGIYMJvvZafFNbFkCt1Wi5M+1OTHYTx8qOsb9oP18c/YJb+92qeB5aH0i7gciy/1JqqmCAeSdrjsRz84iWV4vLyqvkaH4VM6u+J8QA/6MMGdITH62Ouwbe1eKMFPv585Qt+Jzqo0c9bfrUVMLmz+syRZxcLkllkUUZAucrHqDN0vCUkEarfM/D4wII7xHYLsHPXRl1yNzGuFwSY6mVimKLYiQLLVSWWBqNvq9B46MhMNTXYyCDIhSD2dUmo+tiP3+eyuUrPLGMNfgNHEDwzJktDi422838a/e/OG9UYgOv63UdM1JmKDudDlj8OMfPnCbfEcRXPZ7ghVuH4+vj/T+rlJK/LTuC7dwebqj4gD2xDnb4+0F4Kjf1uYnJSZO9vpbLYqHyu++oWrvOU+NYExhIyA3XY7jqqk79zBx2J+UFFk/2R1m+qdHvn4+v1hP4HN7DQEj0lRGbq84hdiLSJTFVVLuNo5WqUmWzVjVf6lqr0xAU7kdgHY8yKNwP3wCfLmMoHUVFVC5fgWnrlnp1f3379iV41kx8+/b1uq/l1nJe2vkS5dXlAPxo4I8YE+fWIDy+ivL1/+FMiZk1wXMZMfUWJvb1PqH/0PkKXl5+mNtLXsUeWMS3BhPEpNEvajCPpD/iVR+llJi3bafim69rV+GFIHDiREJmX9cmK/Atpdri8Bi/0jwTlUWNR034GnQe4xceZyAowq/LfI86EtUgdkHsNidGt3E0llYrhrLESrW58TjJGvT+PoTFBhAaY3CHBHX+yp6jrIyq5SswbfoBaa8dkul79ST42pn4pQ306p8v35TPP3f+E7PDjBCCh4Y+RFpEGjgduBY/xpETpykhmFW9fsvT1w/12pD9dWkWYWe+Z5hlGV9HmbGE9iAgNJXfjf6dV/VfbDm5lC/4jOrjJ+rdW9j8+e2WC34hNQt+nhXgPDOmsovVX2rwZH+4DWBXHnF0JKpB7EbYrA6qSmoMpZWq0mqqSizYG4v7AmXyO9KPsJgAQt3Br50VL+ksL6dq1SqMGzYibbVesD45meCZ13qVFniy/CT/3vNvHC4HencoTHJwMhxfRcHqf5NXYWVN8PVMn3s7aT2aV+M+kFPB28u386OSf7EmvJLsAB+IHsi9g+9jeMzwJs91mc1ULF6Ccf16z9SAJjiI0BtvJGD06HZ9j6WUVJVYKTlv8niBjSUWCI2ozf7ooYTA+PqrywQNoRrEbo6Ukmqzw+NFlhcqcZOWJobden8fRR0ktnO8SGdVFVWrV2Nctx5prfVidPHxBM+8Fv/hw5s0JnsL9/LOgXeQSAL1gfxyxC+J8g3DvvARsk6epkITyp6hT/NY5oAm+yGl5Lnvshhw4m3MYjfbQqsRUX0ZmTylyWwUKSXmrVsp//obXFVVSqNGQ+DkSYTMmtUusv1SSoxl1ZTkGt2bCbu14QUQrU7jmf8Li+se8X9dBdUgXqZYTXbKC2qT55vKH/VkEMR2rBfpNJowrl2Lce2aemmBSr70DAJGZiC0Df8jb8jZwOdHPwcg0j+SX2b8kqCz28he8TIlRhtrgq/nR3fcQ3Rw4+VK92aXs3Dp90yofIcvwqvQBkcQ1mMEvx3120azUWzZ2ZR99hm2k6c8bb59+hA6b16bahPWDIFLco0U5xgpzTU1OmWiD/BR5v/cBjA40r/bx7l2FqpBvEJwOV1UFls9AeXNeZE6Px9CovwJjfYnJCaA0OiAdoszc5nNGNevp2rV6npKLz5RUQTNmI5h9OgGszgWnVzEijMrAEgKTuLxoT/DufDnHDt9liptKDnjnue2sT0bfE0pJc8u2s+44y+w3HAKU6AWTcwgHhv5BH3C+lx0vNNoonLxIowbNnoCk7UhIYTefBP+GRlt8uNhqbJRnKsYv+KcKqzGRgygvw8R8YFEJAQS0SMQQ+jlmzLa0agG8Qqm1os0U15gorywCS8SZSUyNNqfkGjFQIZE+7epEomruhrjhg1UrVyJq7LK066NCFfS2y4wjFJKPjz8oUcMIi0ijfsDUjn7/b+psjrYEHYjP7n7vgbLle46W8a2Je8iHQvZG2TDNzyRqWl3cEOfG+odJ51OjBs3UrloMS6zO25UqyVoymSCZ81C49e4B9ocShaI4gGW5JowVzQsgqDz1RIeH0ik2wh2xwyQ7oJqEFU81HiR5QVmygvNVBRaMJZXN5maGBDiS0i0v8dAhkS1fr5K2mwYf9hE1YoVtRkeuAUQrrtOGUq7BRAcLgdv7H+DrJIsAMbGjmLGnvVk5+ZQpQ3FOv0fZA6uH6gtpeTvX29iwJln+SqoFIPBQGKvTJ4Y9Wt0mlov2HrsGOULPseem+tp8x3Qn7Bbb0UXF9fi+3I5XZTmmSk8U0nRuSqMjawCa3VaIuINihcYH0hw5JUZAtMZqAZRpUnsNieVRRaPgSwvaHqojRAEhfkqCkDR/oTFKjFtlzKnJe12TFu3Urn0+wYksubgPywdIQRWh5WXd79MdpWSUz3DL55eWzdQ7XCxM+ZW7r3z3nqvv/NMKce+fZYt+s1YfcEQl8avr36OHoGKyKyjrIyKr75SSny60UaEE3bLLfgN9S6cp4Zqi4PCs5UUna2i6FwVDtvFEQFaHw1hcYoBjEwIJDhKnQPsLFSDqNJiqi0OKmoMpPtvUzGSWp2m3qp2WKwBnW8LMkncHmPlsu/rDaUVEdU5+A1Ko9JWyT93/ZMSSwlIF5k5+SQXmKjUhhF0878ZlqIEartckv8sWIi5+CUO+9owhEZx85gnmJI0BWmzUbVqFZXfL/MUdBI6HcHXziDommu8EmGQUlJZbKXwbCWFZyopL7Rc7GELQVhsAFGJQUTEBxIa49+t8tgvZ1SDqNJqpJRYTfZ6BrK8sGldvMAwX8VAxgUQFmPwamGgUZn9nj0JmTuHysQw/rHzH5jsJqSxiGtOFZFq03Es5XZunaeE0Ww7UcCh7x5irV82fnofBg+8gUdG/orq/fsp+/JLnMUlnusGZIwg5Kabmq1A6LS7KM41UnimksKzlQ0uhuh8tUQlBROdEkRUUlCXUIFWuRjVIKq0CzXKKWUFtdLxDdXNrUHn51NPOTk0OgCtrmGvqaYQU9WqVUhL7TV9+/WjavIw/lP+LTaHFVv2fq4v0RNINKl3v0l8eBDv/u+fbLcuoFojiYzpzW+H/gnXt8vraRTq4uMJnXcrfn37NtpfS5WNgjOVFJ6toiTX2OBiVGC4H9HJihEMizWow+BugGoQVToMm9XhWdUuy2+6tKTQCIIj/d1GMgBDqB+GUH29BRun0UTVqpUY16ytl/lSmRrFJ8m5FPtWIgvOMr8qGHu/ewntNZLF6+7lrI8Fg8afh5hNxN5ztSIMAQGEzJ2DYfz4evGPDrsTY2k1xnIlM6jonJGqktq4ybp9jkwIdBvBYAKCu67OoUrDdIpBFELMAF5GqanytpTybxfsF+79MwEzcLeUcndT11QNYvfD5VLSz2qCx8vym9Dfc+Nr0GEI9SUw1BeDe/PzsePYtAbLDxs8udKl1jJ2RVWxp0cJLj/JbEsShw2B7JH76ZntYkpuLD39UpSLCoHh6qvxy5yJxabFWFaNsczq+dtYPGBNf6KTg4hOCSYyIVDNCOnmdLhBFEJogWNAJkpJ0h3AbVLKw3WOmQk8imIQRwMvSymbLGavGsTLA6vJXq88ZUUTEvX1EAJ/P4lPwVk0547iL02YLOcprTxGTmQZ5/voqXa6GHTATqQpnMTYMdiEAXtUMq5eg7E4dE3nhNd5nZAof2JSlKFwcKS/GhJzGdEZitmjgBNSylPuDnwGzAUO1zlmLvA/qVjlrUKIUCFEnJQyrx37pdIF8DPoiOsVQlwvRZjB6XBhLKvGVO7eKpShq6m8uv6ijZRYLEBwMq6+cRQVFuKkDKtuFAHVFfTbVwFS4PQJwRQdxkldALq4WDShoQgTQH1jWKNDaQjzJSjMj8AwXwLD/QgI0V8RuoAq9WlPgxgP1CnCQQ6KF9jcMfGAahCvMLTu6oYhUf712qWU2KxOxUiW1TeU5goNmoQEXFFRaAoKcBTacaAEXOu0evxi4/GJjkJoNOj8fBRjF+ZLYI3hC+vaArwqHU97GsSGvmUXjom8OQYhxAPAAwBJSUmt75lKt0EIga+/D77+irBBXaRLYjHa3V5lT4pPnOPAqqUApE2fQ2TveAJDFY9PlcFS8Yb2/JbkAHVVMxOA85dwDFLKN4E3QZlDbNtuqnRXhEYQEKwnIFhPVFIQKUMiybixaW1DFZWmaM9Jkh1AHyFEqhBCD8wHFl1wzCLgTqEwBqhQ5w9VVFQ6i3bzEKWUDiHEI8BylLCbd6WUh4QQD7n3vw4sRVlhPoESdnNPe/VHRUVFpTnadWJFSrkUxejVbXu9zmMJ/Kw9+6CioqLiLWpcgYqKioob1SCqqKiouOl2ucxCiCLgbAtPiwSK26E7XR31vq8s1Pv2nmQp5UVFvbudQbwUhBA7G0rTudxR7/vKQr3v1qMOmVVUVFTcqAZRRUVFxc2VYhDf7OwOdBLqfV9ZqPfdSq6IOUQVFRUVb7hSPEQVFRWVZrksDKIQIlwIsVIIcdz9t8FqQUKIM0KIA0KIvUKInS09vyviTd+FEIlCiLVCiCwhxCEhxON19j0thMh1vyd73aK9XRIhxAwhxFEhxAkhxJMN7BdCiFfc+/cLIYZ7e25Xx4t7v8N9z/uFEJuFEEPr7Gvwe98d8OK+JwkhKup8f//o7bkNIqXs9hvwd+BJ9+MngRcaOe4MEHmp53fFzZu+A3HAcPfjIBQl84Hu508DT3T2fXhxn1rgJNAT0AP7au6hzjEzge9RZOXGANu8Pbcrb17e+1VAmPvxtTX37n7e4Pe+q29e3vckYMmlnNvQdll4iCjK2x+4H38AXN/B53cmzfZdSpkn3bVqpJRVQBaKEG93wqPALqW0ATUK7HXxKLBLKbcCoUKIOC/P7co0238p5WYpZZn76VYUKb3uTms+t0s693IxiDHSLRvm/hvdyHESWCGE2OUWnW3p+V2RFvVdCJECDAO21Wl+xD3UercLTxc0pq7uzTHenNuVaWn/70PxlGto7Hvf1fH2vscKIfYJIb4XQqS18Nx6dBsZYSHEKiC2gV1PteAy46SU54UQ0cBKIcQRKeWGtulh+9FG944QIhD4Cvg/KWWlu/m/wLMo/zTPAv8A7r303rYbrVFg90qZvQvjdf+FEJNRDOL4Os3d8nuPd/e9GyUNz+ie/14I9PHy3IvoNgZRSnlNY/uEEAU1xancQ6TCRq5x3v23UAjxDYpbvQHw6vzOoi3uXQihQzGGH0spv65z7YI6x7wFLGm7nrcprVFg13txblfGK2V5IcQQ4G3gWillSU17E9/7rk6z913nhx0p5VIhxGtCiEhvzm2Iy2XIvAi4y/34LuDbCw8QQhiEEEE1j4FpwEFvz+/CeHPvAngHyJJS/vOCfXF1nt5A7XvS1WiNArs353Zlmu2/ECIJ+Br4sZTyWJ32pr73XR1v7jvW/f1GCDEKxaaVeHNug3T2SlIbrUZFAKuB4+6/4e72HsBS9+OeKCtN+4BDwFPNnd8dNi/vfTzKcGE/sNe9zXTv+xA44N63CIjr7Htq4l5noqyQn6z5/ICHgIfcjwXwH/f+A0BGU+d2p82Le38bKKvz+e50tzf6ve8Omxf3/Yj7vvahLCZd1ZrPXM1UUVFRUXFzuQyZVVRUVFqNahBVVFRU3KgGUUVFRcWNahBVVFRU3KgGUUVFRcWNahBVmkUIYWyg7RdCiMPulL/VQojkRs7d3MLXel8IcXMzx9wthOjRkutecH56V1b1Uek8VIOocqnsQYnzGwJ8iaK6cxFSyqva4bXvRomzvFTSUWLUVFTqoRpElUtCSrlWSml2P21UXaXGu3Tr1q0TQnwphDgihPi4JsOgMYQQfxRC7BBCHBRCvOnOQLkZyAA+duvf+QshRggh1rvFC5bXZN+4X+8FIcR2IcQxIcTV7qyFZ4B57vPnXfCaae7j97q93z5CiBR3nz9wt30phAhorI/u9t5CiFVu0YHdQohe7vZfuY/fL4T486W+/yrtRGdHoqtb198AYzP7XwV+39S5KLp1FSiGUwNsAcY3cPz7wM3ux+F12j8EZrsfr8OdhQLogM1AlPv5PODdOsf9w/14JrDK/fhu4NVG+vtv4A73Yz3gD6SgZPqMc7e/i1tDsok+bgNucD/2AwJQ0ubeRMmo0aDkjU/o7M9X3Wo31UNUaRVCiB+heGwvenH4dilljpTShZJeltLM8ZOFENuEEAeAKUBaA8f0AwahqLjsBX5PfW+1RshilxevB4qh/p0Q4jcoKioWd3u2lHKT+/FH1KrJXNRHd+5wvJTyGwAppVUq3vQ097YHRaWlP4oyi0oXoduo3ah0PYQQ16BIkE2UUlZ7cUrdY5w08f0TQvgBr6F4gtlCiKdRPK2LDgUOSSnHNvOaTb5eDVLKT4QQ24BZwHIhxE+AU1wsHSWb6GNjUwECeF5K+UZz/VDpHFQPUeWSEEIMA94A5kgp20Murcb4FQtFx7HuynMVSikEgKNAlBBirLtfOlErEtoYdc+vhxCiJ3BKSvkKitjFEPeupJrXAG4Dfmisj1KRpMoRQlzvvqave85xOXCv+1iEEPFC0ShU6SKoBlHFGwKEEDl1tl+gDJEDgS/cCxBtKqclpSwH3kJRrVmIIudUw/vA6+4hshbFEL0ghNiHMhRvbmV7LTCwoUUVlDnIg+5r9wf+527PAu4SQuwHwoH/NtPHHwOPuY/fDMRKKVcAnwBb3EPsL2nEMKt0DqrajYpKMwil7MISKeWgzu6LSvuieogqKioqblQPUUVFRcWN6iGqqKiouFENooqKioob1SCqqKiouFENooqKioob1SCqqKiouFENooqKioqb/w8sn8OXRoTaqQAAAABJRU5ErkJggg==\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from core.hessian_axis_visualize import vis_eigen_action, vis_eigen_explore, vis_distance_curve\n",
    "refvect = feat.cpu().numpy()\n",
    "mtg, codes_all,  = vis_eigen_explore(refvect, evc_FI, eva_FI, G, eiglist=[1,2,4,8, 16], transpose=False,\n",
    "      maxdist=0.5, scaling=None, rown=7, sphere=False,\n",
    "      save=False, namestr=\"demo\")\n",
    "distmat, ticks, fig = vis_distance_curve(refvect, evc_FI, eva_FI, G, ImDist, eiglist=[1,2,4,8,16],\n",
    "                   maxdist=0.5, rown=5, sphere=False, distrown=15, namestr=\"demo\")"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Spectrum of Hessian\n",
    "Let's see how fast these eigenvalues decay along the spectrum."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(eva_FI[::-1])\n",
    "plt.title(\"Top hessian Spectrum\")\n",
    "plt.ylabel(\"Eigenvalue\")\n",
    "plt.xlabel(\"Rank\")\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 720x360 with 2 Axes>",
      "image/png": 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\n"
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 720x360 with 2 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_spectra([eva_FI], titstr=\"BigGAN Top Spectrum\", save=False)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Let's compute the full rank Hessian and spectrum, and see its structure. Here the full Hessian is computed by 2nd order backpropagation. It takes ~ 90 sec for full Hessian of BigGAN, on GTX 1060."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [================================================================>]  Step: 392ms | Tot: 1m33s | full hessian columns: 255 of 256\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b 256/256 \n",
      "Hessian computed with BP in 94.50 sec\n"
     ]
    }
   ],
   "source": [
    "eva_BP, evc_BP, H_BP = hessian_compute(G, feat, ImDist, hessian_method=\"BP\") # ~ 91 sec\n",
    "# Un comment following lines to try other methods and see the speed\n",
    "# eva_BI_h, evc_BI_h, H_BI_h = hessian_compute(G, feat, ImDist, hessian_method=\"BackwardIter\", cutoff=None)\n",
    "# eva_FI_h, evc_FI_h, H_FI_h = hessian_compute(G, feat, ImDist, hessian_method=\"ForwardIter\", cutoff=None, EPS=1E-4) # ~ 88 sec"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation similarity of the Full Hessian matrix and the rank 20 approximation: 0.9974\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 720x360 with 2 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_spectra([eva_BP], titstr=\"BigGAN full\", save=False)\n",
    "cc = np.corrcoef(H_BP.flatten(), H_FI.flatten())[0, 1]\n",
    "print(\"Correlation similarity of the Full Hessian matrix and the rank 20 approximation: %.4f\"%cc)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "We shall see that the full Hessian is quite correlated with the low rank approximation we computed above.\n"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}