AE_onepixel_mnist.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "from model import *\n",
    "\n",
    "# Python Libraries\n",
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "import pickle\n",
    "import numpy as np\n",
    "import os\n",
    "import pandas as pd\n",
    "import matplotlib\n",
    "from keras.datasets import mnist\n",
    "from keras import backend as K\n",
    "\n",
    "# Custom Networks\n",
    "from AE_onepixel_mnist_model import CNNMNIST\n",
    "os.chdir('onepixel')\n",
    "from onepixel.networks.pure_cnn import PureCnn\n",
    "from onepixel.networks.network_in_network import NetworkInNetwork\n",
    "from onepixel.networks.resnet import ResNet\n",
    "from onepixel.networks.densenet import DenseNet\n",
    "from onepixel.networks.wide_resnet import WideResNet\n",
    "from onepixel.networks.capsnet import CapsNet\n",
    "os.chdir('..')\n",
    "\n",
    "from tqdm import tqdm\n",
    "\n",
    "# Helper functions\n",
    "from onepixel.differential_evolution import differential_evolution\n",
    "import onepixel.helper as helper\n",
    "\n",
    "matplotlib.style.use('ggplot')\n",
    "np.random.seed(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this attack, we will use the [Cifar10 dataset](https://www.cs.toronto.edu/~kriz/cifar.html) packaged by Keras. The task of the dataset is to correctly classify a 32x32 pixel image in 1 of 10 categories (e.g., bird, deer, truck).\n",
    "\n",
    "The code below will load the Cifar10 dataset. Keras will need to download the dataset if it is not cached locally already."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n",
    "x_train = np.reshape(x_train, (60000, 28,28,1))\n",
    "x_test = np.reshape(x_test, (10000, 28,28,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class_names = [str(t) for t in range(10)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Image Perturbation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def perturb_image(xs, img):\n",
    "    # If this function is passed just one perturbation vector,\n",
    "    # pack it in a list to keep the computation the same\n",
    "    if xs.ndim < 2:\n",
    "        xs = np.array([xs])\n",
    "    \n",
    "    # Copy the image n == len(xs) times so that we can \n",
    "    # create n new perturbed images\n",
    "    tile = [len(xs)] + [1]*(xs.ndim+1)\n",
    "    imgs = np.tile(img, tile)\n",
    "    \n",
    "    # Make sure to floor the members of xs as int types\n",
    "    xs = xs.astype(int)\n",
    "    \n",
    "    #print(imgs.shape)\n",
    "    \n",
    "    for x,img in zip(xs, imgs):\n",
    "        # Split x into an array of 5-tuples (perturbation pixels)\n",
    "        # i.e., [[x,y,r,g,b], ...]\n",
    "        pixels = np.split(x, len(x) // 5)\n",
    "        for pixel in pixels:\n",
    "            # At each pixel's x,y position, assign its rgb value\n",
    "            x_pos, y_pos, *rgb = pixel\n",
    "            #print(img)\n",
    "            img[x_pos, y_pos] = rgb[0]\n",
    "    \n",
    "    return imgs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can modify the pixels of any image we want.\n",
    "\n",
    "Let's modify our horse image by making pixel (16,16) yellow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f550049d2e8>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(perturb_image(np.array([1,1,255,0,0]), x_train[0]).reshape(28, 28))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict_classes(xs, img, target_class, model, minimize=True):\n",
    "    # Perturb the image with the given pixel(s) x and get the prediction of the model\n",
    "    imgs_perturbed = perturb_image(xs, img)\n",
    "    predictions = model.predict(imgs_perturbed)[:,target_class]\n",
    "    # This function should always be minimized, so return its complement if needed\n",
    "    return predictions if minimize else 1 - predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we can modify a pixel in an image and see how the confidence of the model changes. In almost all cases, the confidence will not change. However, for very special cases it will change drastically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def attack_success(x, img, target_class, model, targeted_attack=False, verbose=False):\n",
    "    # Perturb the image with the given pixel(s) and get the prediction of the model\n",
    "    attack_image = perturb_image(x, x_test[img])\n",
    "\n",
    "    confidence = model.predict(attack_image)[0]\n",
    "    predicted_class = np.argmax(confidence)\n",
    "    \n",
    "    # If the prediction is what we want (misclassification or \n",
    "    # targeted classification), return True\n",
    "    if (verbose):\n",
    "        print('Confidence:', confidence[target_class])\n",
    "    if ((targeted_attack and predicted_class == target_class) or\n",
    "        (not targeted_attack and predicted_class != target_class)):\n",
    "        return True\n",
    "    # NOTE: return None otherwise (not False), due to how Scipy handles its callback function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Attack Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "7rlzqXpqSgrW"
   },
   "outputs": [],
   "source": [
    "def attack(img, model, target=None, pixel_count=1, \n",
    "           maxiter=75, popsize=100, verbose=False, plot = True):\n",
    "    # Change the target class based on whether this is a targeted attack or not\n",
    "    targeted_attack = target is not None\n",
    "    target_class = target if targeted_attack else y_test[img]\n",
    "    \n",
    "    # Define bounds for a flat vector of x,y,r,g,b values\n",
    "    # For more pixels, repeat this layout\n",
    "    bounds = [(0,28), (0,28), (0,256), (0,0), (0,0)] * pixel_count\n",
    "    \n",
    "    # Population multiplier, in terms of the size of the perturbation vector x\n",
    "    popmul = max(1, popsize // len(bounds))\n",
    "    \n",
    "    # Format the predict/callback functions for the differential evolution algorithm\n",
    "    predict_fn = lambda xs: predict_classes(\n",
    "        xs, x_test[img], target_class, model, target is None)\n",
    "    callback_fn = lambda x, convergence: attack_success(\n",
    "        x, img, target_class, model, targeted_attack, verbose)\n",
    "    \n",
    "    # Call Scipy's Implementation of Differential Evolution\n",
    "    attack_result = differential_evolution(\n",
    "        predict_fn, bounds, maxiter=maxiter, popsize=popmul,\n",
    "        recombination=1, atol=-1, callback=callback_fn, polish=False)\n",
    "\n",
    "    # Calculate some useful statistics to return from this function\n",
    "    attack_image = perturb_image(attack_result.x, x_test[img])[0]\n",
    "    prior_probs = model.predict_one(x_test[img])\n",
    "    predicted_probs = model.predict_one(attack_image)\n",
    "    predicted_class = np.argmax(predicted_probs)\n",
    "    actual_class = y_test[img]\n",
    "    success = predicted_class != actual_class\n",
    "    cdiff = prior_probs[actual_class] - predicted_probs[actual_class]\n",
    "    \n",
    "    #print(attack_image.shape)\n",
    "\n",
    "    # Show the best attempt at a solution (successful or not)\n",
    "    if plot:\n",
    "        helper.plot_image(attack_image.reshape(28, 28), actual_class, class_names, predicted_class)\n",
    "\n",
    "    return [model.name, pixel_count, img, actual_class, predicted_class, success, cdiff, prior_probs, predicted_probs, attack_result.x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_summable_metric(model, image):\n",
    "    \"\"\" Obtaining a metric for how successfull was an attack for a given image \"\"\"\n",
    "    _, _, _, actual_class, predicted_class, _, cdiff, prior_probs, predicted_probs, _ = attack(\n",
    "        image, model, pixel_count=1, verbose=False, plot = False)\n",
    "    return cdiff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "def estimate_random(model, N = 50, do_tqdm = False):\n",
    "    \"\"\" Estimate the mean success of an attack of random samples \"\"\"\n",
    "    \n",
    "    # some random test images\n",
    "    subs = np.random.choice(range(len(x_test)), N)\n",
    "    \n",
    "    # obtaining mean metric over images\n",
    "    tqdm_ = tqdm if do_tqdm else (lambda x : x)\n",
    "    return np.mean([get_summable_metric(model, x) for x in tqdm_(subs)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_p_fail(p_fail):\n",
    "    \"\"\" Compute success of an attack for train dropout probability \"\"\"\n",
    "    cnn = CNNMNIST(epochs = 6, p_fail = p_fail, load_weights = False)\n",
    "    cnn.train()\n",
    "    return estimate_random(cnn, N = 50, do_tqdm = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using 5 repetitions for each of p_fail = [0.0 0.25 0.5 0.75 1.0]\n"
     ]
    }
   ],
   "source": [
    "repetitions = 5\n",
    "pfails = np.linspace(0, 1, 5)\n",
    "print('Using %d repetitions for each of p_fail = [%s]' % (repetitions, ' '.join([str(t) for t in pfails])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EEEIIIUSmSREphBBCCCGEECLTpIgUQgghhBBCCJFp8kykEELkMVprEhMTMU0TpZTVcbLk999/Jykp6b7baa0xDANvb+9cd45CCCGEq5MiUggh8pjExEQ8PT3x8Mh9lwAPDw9sNlumtk1JSSExMZH8+fPncCohhBAib5HhrEIIkceYppkrC8is8vDwwDRNq2MIIYQQbkeKSCGEyGPy0vDOvHSuQgghhLO4/1fRQgghXMqVK1dYtmwZPXr0yNJ+Xbt25euvv6ZAgQI5EyyHRUdHM2vWLEzTpHnz5rRu3TrN+4cOHWLOnDmcPHmSQYMGUbduXft7Y8aM4ejRo1SuXJl33nnH/vpXX33F8ePH0Vrz0EMP0b9/f7y9vdm8eTPz5s3Dz88PgL/97W80b94cgM2bN7N06VIA2rRpQ5MmTXL4zIUQQrgbKSKFEEI41dWrV5k7d266IjIlJeWew2znzZuHh4cHKSkpOZzQ8UzTZMaMGbz33nv4+/szfPhwQkJCKFWqlH2bgIAA+vXrx8qVK9PtHxoaSlJSEuHh4Wle7969Oz4+PgDMmTOHsLAwe3Fav359evXqlWb769evs3jxYsaOHQvAO++8Q0hICL6+vg49XyGEEO5NikgH0WdOcOvQbqha2+ooQgjh0j7++GNOnjzJ008/jaenJ15eXhQuXJiYmBh++uknXnnlFc6dO0dSUhK9evWiS5cuADz55JOsX7+eq1ev0qVLF5544gmioqIICgpi5syZLj2BTkxMDEFBQRQvXhxILfB27tyZpogMDAwEMh6CW716dQ4ePJju9T8LSK01t2/fvm+O6OhoatSoYS8aa9SoQXR0NA0aNMj6SWXB9KjfOXP9HMnJyTl6nNzG01P65K+kT9KTPklP+iRjVUpcpctjhZxyLCkiHUSvWcTVfTsxPvoaVcTP6jhCCOGyRowYwZEjR9iwYQORkZF069aNiIgIypQpA8D48eMpWrQot27d4rnnnuPZZ5+1D8v8U2xsLJMmTWLcuHG89tprrFmzhrZt21pxOpmSkJCAv7+//Wd/f3+OHj3qkLYnT57Mnj17KFWqFN26dbO/vmPHDg4fPsxDDz1E9+7dCQgISJfDz8+PhISEdG2Gh4fb73qOHTuWgICAbGX0zn8VdeMGnp6e2WrH3SilpE/+QvokPemT9KRPMmYYKtv/XmeWFJEOolp3Ru+ORK/6DtWln9VxhBAiU8zvpqFPxzq0TVX6YYwOr2Z6+1q1atkLSICZM2eydu1aAM6dO0dsbGy6IrJ06dJUq1YNSL2bdvr0aQckz5369euHaZrMnDmTyMhImjZtSnBwME899RSenp5s2LCBSZMm8cEHH2S6zRYtWtCiRQv7z5cuXcpWxi6PFSIg4JFst+NuAgICpE/+QvokPemT9KRPMuaIfilRokSmtpPZWR1EBZYgf6uX0D+uR184Y3UcIYTINf4ckgkQGRnJjz/+yMqVKwkPD6datWokJSWl28fLy8v+d5vNxp07d5yS9UH5+fkRHx9v/zk+Pj5dYZwdhmFQv359duzYAUDBggXt39I3b96c48ePZ5gjISHBoTmEEELkDXIn0oF8X+7BrY2rMZfNw/b6cKvjCCHEfWXljqGjFChQgOvXr2f43rVr1yhcuDD58+cnJiaG3bt3Ozldzihfvjznz58nLi4OPz8/IiMjeeONN7LVptaa33//naCgILTWREVF2b9Bvnz5MkWLFgUgKirK/uxlrVq1+Pbbb+39v3fvXjp16pStHEIIIfIeKSIdyCjih2r1EnrFN+hjv6LKV7Y6khBCuBw/Pz/q1KlDs2bN8Pb2TvP8RpMmTZg3bx6NGzemfPny1K7tHpOV2Ww2XnnlFcaMGYNpmjRt2pTSpUuzcOFCypcvT0hICDExMXzyySfcuHGDXbt28f333zNhwgQARo4cydmzZ0lMTKRv37707duXGjVqMGnSJG7evAlA2bJl6d27NwBr164lKioKm82Gr68v/fqlPmbh6+tL27ZtGT489YvOdu3aycysQgghskxprbXVIVzFuXPnsrV/QEAAF8+cxnz3NSheAmPov/L8QtcyZj096ZOMSb+kl1N9cvPmzTRDSHOTrC7xkdG5ZvZ5D/Ff2b0+gvw/nhHpk/SkT9KTPklP+iRj8kxkLqa886Ne6ABHD8G+KKvjCCGEEEIIIYRDSRGZA1SDlhBYAnPpHLTp2pM9CCGEEEIIIURWSBGZA5SHB0abrnDuFDoywuo4QgghhBBCCOEwUkTmlNr14eFH0cu/Qd9OPz29EEIIIYQQQuRGUkTmEKUURtse8J949MZVVscRQgghhBBCCIeQIjIHqUrVoHoIeu1i9PWrVscRQgghhBBCiGyTIjKHGW27Q+It9NrFVkcRQohcqWLFilZHEEIIIcT/kCIyh6mSZVH1m6IjVqHj46yOI4QQQgghhBDZ4mF1gLxAhXZC//IjevkC1CtvWR1HCCEs9fHHH1OiRAl69OgBwPjx47HZbERGRnLlyhVSUlJ4++23adWqlbVBhRBCCJEhuRPpBMqvGKrZ8+jtm9GnY62OI4QQlgoNDWXlypX2n1euXMnLL7/MjBkzWLduHYsWLWL06NForS1MKYQQQoi7kTuRTqKeaYf+cT3m0jnY3hxldRwhhABgetTvxF5OdGibDxf1pndI8bu+X61aNS5dusSFCxeIj4+ncOHCBAYGMmrUKHbs2IFSigsXLnDx4kUCAwMdmk0IIYQQ2SdFpJOoAr6oZ19GL56FPrwXVaWm1ZGEEMIyzz//PKtXryYuLo7Q0FCWLl1KfHw8a9euxdPTkyeffJKkJFljVwghhHBFUkQ6kWr2HDpiJeaSORgjPkEZMppYCGGte90xzEmhoaEMHTqUhIQElixZwsqVKwkICMDT05Nt27Zx5swZS3IJIYQQ4v6kinEi5ZkP9WJnOBmD3rXN6jhCCGGZSpUqcePGDYKCgihevDht2rRh7969NG/enMWLF1OhQgWrIwohhBDiLuROpJOpuk3Q639AL5uHfrwuysPT6khCCGGJjRs32v/u5+eXZrKd/3X06FFnRRJCCCFEJsidSCdThg2jbQ+4eAG9dZ3VcYQQQgghhBAiS6SItEK12lCpOnrVQnTiTavTCCGEEEIIIUSmSRFpAaVU6t3Ia1fQ636wOo4QQgghhBBCZJoUkRZRD1dEhTRAb/gBfeWy1XGEEHmI1trqCE6Tl85VCCGEcBanTawTHR3NrFmzME2T5s2b07p16zTvJycn8+WXX3L8+HEKFizIoEGD7ItML1u2jIiICAzDoGfPntSqVeuebU6aNIlDhw7h4+MDQP/+/SlXrpyzTjXT1Etd0Ht+Rq/6DtX5davjCCHyCMMwSElJwcPDvedWS0lJwZCllIQQQgiHc8pvEKZpMmPGDN577z38/f0ZPnw4ISEhlCpVyr5NREQEBQoUYOLEiWzbto0FCxbw1ltvcebMGSIjI5kwYQKXL1/mww8/5PPPPwe4Z5tdu3albt26zji9B6YCS6AatUJvCUM3D0UFlbQ6khAiD/D29iYxMZGkpCSUUlbHyRIvLy+SkpLuu53WGsMw8Pb2dkIqIYQQIm9xShEZExNjXwsMoH79+uzcuTNNERkVFcXLL78MQN26dZk5cyZaa3bu3En9+vXx9PQkMDCQoKAgYmJiAO7bZm6gnm+PjtyEuWwettffsTqOECIPUEqRP39+q2M8kICAAC5dumR1DCGEECJPc8o4n4SEBPz9/e0/+/v7k5CQcNdtbDYbPj4+XLt2Ld2+fn5+JCQk3LfNb7/9liFDhjB79mySk5Nz6tSyTRUqimrZGnZHoo/9anUcIYQQQgghhLgnt3wgplOnThQpUoSUlBSmTJnC8uXLadeuXbrtwsPDCQ8PB2Ds2LEEBARk67geHh4P1IbZsRfxW8OwrfiGoh9NynXDy+7lQfvEnUmfZEz6JT3pk/Ryc5/cb26AQ4cOMWfOHE6ePMmgQYPSPJIxZswYjh49SuXKlXnnnf+OWvnqq684fvw4Wmseeugh+vfvj7e3N6tWrWLjxo3YbDYKFSrE66+/TrFixQBo3749ZcqUAVLv7A4bNswJZy+EEMKdOKWI9PPzIz4+3v5zfHw8fn5+GW7j7+/PnTt3uHnzJgULFky3b0JCgn3fu7VZtGhRADw9PWnatCkrV67MMFeLFi1o0aKF/efsDpHKzjAr/Vx7kr/5mkubwlA16mQrhyuRoWfpSZ9kTPolPemT9BzRJyVKlHBQmszLzNwAAQEB9OvXL8NrVmhoKElJSfYvPv/UvXt3+yRyc+bMISwsjNatW1OuXDnGjh2Ll5cX69evZ/78+bz11lsA5MuXj3HjxuXg2QohhHB3ThnOWr58ec6fP09cXBwpKSlERkYSEhKSZpvg4GA2b94MwPbt23nsscdQShESEkJkZCTJycnExcVx/vx5KlSocM82L19OXTLjz2cqS5cu7YzTzBbVsCUElsBcOhdt3rE6jhBCCAf637kBPDw87M/x/6/AwEDKli2b4WiU6tWrZ/gc658FpNaa27dv21+vVq0aXl5eAFSsWDHdIyRCCCFEdjjlTqTNZuOVV15hzJgxmKZJ06ZNKV26NAsXLqR8+fKEhITQrFkzvvzySwYOHIivry+DBg0CoHTp0tSrV4/BgwdjGAa9evWyT9meUZsAX3zxBVevXgWgbNmy9OnTxxmnmS3KwwOjTVfMr/8P/fMm1FMt7r+TEEKIXCGj5/iPHj3qkLYnT57Mnj17KFWqFN26dUv3fkREhH1pLEhdUuudd97BZrPx4osv8sQTTzgkhxBCiLzDac9E1q5dm9q1a6d5rX379va/58uXj8GDB2e4b5s2bWjTpk2m2gT44IMPspnWIrXrw8OPopd/g67TEJXPy+pEQgghXFy/fv0wTZOZM2cSGRlJ06ZN7e9t3bqV48ePM2rUKPtrkydPxs/Pj99//53Ro0dTpkwZgoKC0rTp6DkDIHc/z5pTpE/Skz5JT/okPemTjDmzX9xyYp3cSimF0bYH5icj0BGrUH9ra3UkIYQQDpCZuQGywzAM6tevz4oVK+xF5L59+1i2bBmjRo3C09MzTRaA4sWLU7VqVU6cOJGuiHT0nAEgz/hmRPokPemT9KRP0pM+yZgz5w1wyjORIvNUpWpQPQS9djH6xjWr4wghhHCAzMwNkFVaay5cuGD/e1RUlP3iHxsby7Rp03j77bcpXLiwfZ/r16/bl726evUqR44cyXXrKwshhLCe3Il0QUabbpij30SvWYx6uafVcYQQQmRTZuYGiImJ4ZNPPuHGjRvs2rWL77//ngkTJgAwcuRIzp49S2JiIn379qVv377UqFGDSZMmcfPmTSB1DoDevXsDMH/+fBITE+37/7mUx9mzZ5k6dSqGYWCaJq1bt5YiUgghRJYprbW2OoSrOHfuXLb2d+StdXPW5+hftmJ89DXKv5hD2rSCDDdIT/okY9Iv6UmfpJdbl/jI7bJ7fQT5PGdE+iQ96ZP0pE/Skz7JmAxnFajQTgDo5fMtTiKEEEIIkfPMdcu4vnAGcn9DCNcnRaSLUv7FUM2fR2/fjD4Ta3UcIXKMTrzFnS9Gc/vX/VZHEUIIYRH96z704lnc+G4Gev0yq+MIIe5DikgXpp55GfL7YC6Za3UUIXKM/mUL7I/i6sQx6D8m/BBCCJF36MRbmHMmQuBDeNVrgl48G70r0upYQoh7kCLShakCvqhnX4YDu9C/7rM6jhAOp7VGbwmDgoW5c+4UOmyJ1ZGEEEI4mV46F+LjMLq/QeE3P4BHKmHOmICO/c3qaEKIu5Ai0sWpZs+DXwDmkjnyjIBwPydi4NRx1Asd8WrQHL1mEfr37E/gIYQQInfQRw6gN61GNXse9ehjKC8vjP7vQuGimF9+hI6PszqiECIDUkS6OOWZDxXaGU4cRUdtszqOEA6lt4ZBPi/Uk40p2PNN8PTEXPCVfGEihBB5gE5KxJzzBRQLQr3U1f66KlQE442RkJyM+cVo9M0bFqYUQmREishcQNVrAiXLopfNRaekWB1HCIfQN2+gf9mKerIxyqcANr8A1Evd4PBe9C9brY4nhBAih+ll8+DiBYweb6C8vNO8px4qjfH6O/D7WcyswnTmAAAgAElEQVQp/5bff4RwMVJE5gLKsGG07Q4XL6B/XGd1HCEcQu/YAreTUI1a2V9TjVtBuYrohdPRN65bmE4IIURO0r8dREes+mMYa7UMt1FVaqI6vw6H9qC/nSqjVIRwIVJE5hbVguHRauiV36ETb1qdRohs0VqnDmUtUx5VrqL9dWXYMLr2g+vXUidaEEII4XZ0UlLqMFb/QFSbbvfc1mjYEvVMW/TWMPT6H5yUUAhxP1JE5hJKKYx2PeDaFflHVOR+x4/AmROpdx7/QpUpj2r+QuovDMd+tSCcEEKInKR/mA9x5zG6D0w3jDUjqnVXVPBT6CWz0bt/dkJCIcT9SBGZi6iHH039R3T9D+grl62OI8QD01vXgVd+1BONMnxfvdgRigZgzp8sz8EIIYQb0TGH0BtXoJo8i6pcI1P7KMNAvTIIylXEnDEeHXs0h1MKIe5HishcRr3UFVKS0asWWh1FiAeib15HR/2YOqGOt0+G2yhvH4wOr8KZE+iNK52cUAghRE7Qt5MwZ30BfsVQbbtnaV+VzwtjwLtQsAjmpI/Q8RdzKKUQIjOkiMxlVPESqIat0D+uk/X0RK6kf94Mt29nOJQ1jcfrQs0n0Cu+kV8WhBDCDejlCyDuXOowVu/8Wd5fFSqauvTH7STMiaPRt2SOCCGsIkVkLqReaA8enpjLZOIRkbtordFb1kK5iqgy5e+5rVIKo2MfAMxvpzgjnhBCiByij/2K3rAC1fhvqCo1H7gdVaIMRt934MIZzCn/h75zx4EphRCZJUVkLqQKFUW1bA27ItHHj1gdR4jMizkM50+nWdbjXpR/ICq0I+z9Bb1new6HE0IIkRP07STM2Z9DUX9Uux7Zbk9VrZW69MfBPehvp8jSH0JYQIrIXEq1bA0FC2MumSP/eIpcQ28Ng/w+d51QJyOqeSiULIv57VR04q0cTCeEECIn6BXfwoWzfwxjzfhZ+KwyGrZEtWqD3hKG3rDcIW0KITJPishcSnn7oF7oAL8dgP1RVscR4r709avoqG2ouk0yNaX7n5SHB0bX/nD5EnrFNzmYUAghhKPp40fQ639ANWqFqlrLoW2rNt2gdn304lkyWkUIJ5MiMhdTDVtB4EOYS+eiTXkmQLg2/fMmSElGNfpblvdV5SujGrVCb1yJPnU8B9IJIYRwNJ18G3P2F1DUD9Wup8PbV4aB8cpbqUt/TB+PPiFLfwjhLFJE5mLKwwPjpa5w9mTqjJdCuCitdepQ1vKVUaXKPVAbqk13KFAwde1I+dJECCFcnl75LZw/jdF1ACq/Y4ax/pXy8sLo/27qIz5fytIfQjiLFJG5XfBTUK4ievkC9O0kq9MIkbHfDsKFs5meUCcjqoAv6u+9IPY39NZ1DgwnhBDC0XTsUXTYMlSDp1HVaufosVThohgDZekPIZxJishcTimF0a5H6vNim1ZbHUeIDOmtYeBTABXSIFvtqCcbQ5Wa6KXz0FcuOyidEEIIR9LJyZizPoMifqiXX3HKMVXJMhh9h8H505hT/y1LfwiRw6SIdAOqUnWoFoxeswh945rVcYRIQ1+7gt4diarXDJXPK1ttKaUwOvWF5CT0wukOSiiEEMKR9Krv/hjG2h/lU8Bpx1VVH0d17gsHdqO/myaz1wuRg6SIdBNG225w6yZ67WKrowiRho7cCCkp2RrK+r9UUEnUMy+jd/6IPrjHIW0KIYRwDH0yBh22BPVUc1T1YKcf32j0N1TLl9Cb16A3rnD68YXIK6SIdBOq1MOouk3RG1fJQ+XCZWjTTH1+sUJVVIkyDmtXPdMWAktgLvhKngUWQggXoVOSMWd9DoWKpD7DbhHVtjvUrof+fiY6Wpb+ECInSBHpRtSLnQHQyxdYnESIPxzZD3HnUY2zvqzHvSjPfBhdXoeLF9BrFjm0bSFySnR0NG+++SYDBw7khx9+SPf+oUOHGDZsGB06dGD79rS/+I4ZM4YePXowduzYNK9/9dVXDB06lCFDhjB+/HgSExMBSE5O5tNPP2XgwIGMGDGCuLg4+z7Lli1j4MCBvPnmm0RHR+fAmYq8Sq/+Hs6e/GMYq69lOVKX/hgMZStgThuPPhljWRYh3JUUkW5E+RdDNXsevX0T+swJq+MIgd4SBr4FUcH1Hd62qlITVbcJOmwp+vwZh7cvhCOZpsmMGTMYMWIEn376Kdu2bePMmbSf24CAAPr160eDBuknoAoNDWXAgAHpXu/evTvjxo3jk08+ISAggLCwMAAiIiIoUKAAEydO5LnnnmPBgtQvF8+cOUNkZCQTJkzg3XffZcaMGZimmQNnLPIaffIYes0iVL2mqBp1rI6TuvTHgPfAtxDmxI/QCTJKSwhHkiLSzahn20F+H8ylc62OIvI4ffUyOnp76oQ6nvly5Bjq5Z7g5ZW6dqRMoCBcWExMDEFBQRQvXhwPDw/q16/Pzp0702wTGBhI2bJlUUql27969erkz58/3es+Pqlr72mtuX37tv31qKgomjRpAkDdunU5cOAAWmt27txJ/fr18fT0JDAwkKCgIGJi5C6NyB6dkow5+3MoWATV/lWr49ipwkUx3hgJSbcwJ36ITpSlP4RwFCki3YwqUBD1TDvYH4U+st/qOCIP09s2wp07DptQJyOqUNHUZ19+O4D+OSLHjiNEdiUkJODv72//2d/fn4SEBIe0PXnyZPr06cO5c+d45pln0h3PZrPh4+PDtWvX0uXw8/NzWA6Rd+k1i+DMCYyu/VAFrBvGmhFVsizGa8Pg3CnMqZ/I0h9COIiH1QGE46lmz6MjVmMumYMxfFyG32oLkZO0aaJ/XA+VqqOCSuXosVSDlujICPSiWegadVC+hXL0eEK4mn79+mGaJjNnziQyMpKmTZtmu83w8HDCw8MBGDt2LAEBAdlu08PDwyHtuBN36JPk2N9IWLMI78atKNz82Wy3lyN90qQlN5Nucu3rf+O1fD4FXx2cq343cofPiaNJn2TMmf0iRaQbUvm8UC92Qs/+AnZtg2wu8C5Elh3eCxcvoFp3yfFDKcPA6NIP88NB6CVzUN0H5vgxhcgqPz8/4uPj7T/Hx8fj5+fnsPYNw6B+/fqsWLGCpk2b2o/n7+/PnTt3uHnzJgULFkyXIyEhIcMcLVq0oEWLFvafL126lO2MAQEBDmnHneT2PtEpKZgT/gkFCnL7pW6u/TkJboBq+Ru31i4hsVBRjBahjj9GDsntn5OcIH2SMUf0S4kSJTK1nQxndVOqXlMoWRZz2Tx0SorVcUQeY24NA99CqMfrOeV4qlQ51NMvon/agP7toFOOKURWlC9fnvPnzxMXF0dKSgqRkZGEhIRkq02tNRcuXLD/PSoqyn7xDw4OZvPmzQBs376dxx57DKUUISEhREZGkpycTFxcHOfPn6dChQrZyiHyLr12MZyJ/WMYa0Gr49yXatsdatVFfz8DvfcXq+MIkatJEemmlGHDaNMN4s6nDisUwkn0f+IhekfqQtOenk47rnqhI/gHpq4dmZLstOMKkRk2m41XXnmFMWPG8NZbb1GvXj1Kly7NwoULiYqKAlIn3+nbty/bt29n6tSpDB482L7/yJEjmTBhAvv376dv375ER0ejtWbSpEn84x//YMiQIfznP/+hXbt2ADRr1ozr168zcOBAVq1aRefOqUtAlS5dmnr16jF48GDGjBlDr169MAz5VUBknT4Ti179PeqJxqhada2OkynKsGH0HgxlymNO+wR96pjVkYTItZSWKQ3tzp07l639Xe3WutYa85MRcP4MxsdTUN4+Ts/gan3iCty9T8xVC9HLF2CM+RoVmLkhEeCYftF7d2J++SGqTTeMZ9plqy1X4O6flQfhzKE64r+ye30E+TxnJLf2iU5JwfzXULh8CWP0JIc+i+6MPtH/ScD81xAwTYzhn6D8XPvZutz6OclJ0icZc8vhrPdbZPlBFka+X5szZ86ka9euOXNCuYBSCqNtD7h2Bb1+udVxRB6gzTupd76r1MxSAekoqmYdeLwuetV36IsXnH58IYTIC/S6pXDqGEaX13PlZGaqiB/GwPchUZb+EOJBOaWIzMwiy1ldGPl+bR47dowbN2444/RcmnqkEgTXR69fhr562eo4wt0d3AMJFzEa/82yCEaHPqBsmN9MkbUjhRDCwfTZk+iV36HqNETVrm91nAemSj2M8drbcO6kLP0hxANwShGZmUWWs7ow8r3aNE2T+fPn06VLzs8MmRsYrbtC8m30yoVWRxFuztwSBoWKQM0nLcug/AJQrTvBgV2wO9KyHEII4W70nTuYsz4HnwKojn2sjpNtqlpw6nnsj0J/P8PqOELkKk5Z4iOjRZaPHj16123+ujByxYoV7dv978LId2szLCyM4OBgihYtes9cjl4Hy2XXrAkI4GrLF7m1YQVFXu6OR4nSTju0y/aJhdy1T+5ciuPS/ih8XupCwaCgLO/vyH7RL3cn4ZetmN/PwK9hCwyfAg5p19nc9bOSHdInQlhHr1sKJ2Mw+g5DFSxsdRyHMJo8i/n7eXT4cszAEhjNn7c6khC5gtutE5mQkMDPP//MqFGj7ruto9fBcuWHfHWL1rBpLQkzv8DoO8xpx3XlPrGKu/aJuWIhaE1icAOSHuD8HN0vuuNrmP8ayqUZn2Pk0m/M3fWzkh0ysY4Q1tBnT6FXfosKfgoV/JTVcRxKvdwDffE8euF0dEDx1OfrhRD35JThrJlZZPl/t8nMwsh3a/PEiRNcuHCBN954g/79+3P79m0GDpTFx1XhoqinW6N3bUPH/mZ1HOFm9J076J82QNVaqGJZvwuZE9TDj6KaPIPetAZ94uj9dxBCCJEhfecO5uzPwdsH1ek1q+M4nDJsGK8OgdIPY04bJ0t/CJEJTikiM7PIclYXRr5bm7Vr12batGlMmjSJSZMmkS9fPiZOnOiM03R5qlVrKFgYc8kcmXBEONaBXalTvTeybkKdjKjWXaFQYcz5X6FNmTRBCCEehN7wA5w4iurUF1WoiNVxcoTy8sYY+B74+KbO2Ho5/v47CZGHOaWIzMwiy1ldGPlubYq7U94+qOfbw5H9qb/0C+Eg5pYwKOwHNVxrCJDyKYBq3xtOxqA3rbE6jhBC5Dr6/Gn08m+gdn1UiHsNY/0rVcQf44334dYtzC8/RCfesjqSEC5LabklZZfdxZRzw/NLOiUZc2R/yOeFMfIzlGHL0ePlhj5xNnfrEx0fhzn8VdSzL2O0fvAZkXOqX7TWmJ+PgmO/YoyejCrqf999XIW7fVYcQZ6JtEZ2r48gn+eMuHqfaPMO5thhcPE8xj+/RBW694SFjuAKfaL3R2FO/AhqhGD0G57jvyvdjyv0iauRPsmYM6+RTrkTKVyH8vBEvdQNzp5Eb99sdRzhBvSP6wGFatjK6igZUkphdOoLd+5gLpxmdRwhhMg19IYVEPsbqkMfpxSQrkJVD0F1fBX2/oL+fqbVcYRwSVJE5kEquD6UrYBevgCdfNvqOCIX0ykp6J/CoVptlH8xq+PclQp8CPXc32FXJHp/lNVxhBDC5enzZ9A/zIdadVFPNLI6jtMZTZ9DtQhFb1yJGbHK6jhCuBwpIvMgZRgY7XpAwiV0xGqr44jcbN9OuJKA0di1JtTJiGr1EjxUGnPB1+ikJKvjCCGEy9LmHcw5X6Q++tLldZRSVkeyhHq5J9R8Av3ddPS+nVbHEcKlSBGZR6nKNaBabfSaRegb162OI3Ipc2sYFA2AasFWR7kv5eGJ0eV1iI9Dr/7O6jhCCOGydPhKOPYrqmMfVOG8M4z1r5Rhw+j9DyhdDnPqJ+jTsVZHEsJlSBGZhxltu8OtG+i1i62OInIhffECHIpGNXgaZbN20oHMUo9WQ9Vvjl7/A/rsSavjiCzSp46RLOvcCpGj9IWzqcNYaz6BerKx1XEsp7zzYwx4H/L7pC798R9Z+kMIkCIyT1OlHkbVbYLeuBKdcNHqOCKXsU+o0+Bpq6NkiWrXM/WXgfmT0aZpdRyRSfrYr5ifvMfVyWNlnVshcoh9GKunJ0aXfnl2GOtfqaL+GAPfh5vXUwtJWfpDCCki8zr1YmdAp64BJUQm6ZRk9LZwqBGC8guwOk6WqIKFUgvJmMOp5yBcnj6yH/PTkVCwEEXe/lh+sRUih+iI1RBzOHU21iJ+VsdxKarMIxh9hsLpE5jTx6PNO1ZHEsJSUkTmcco/ENXsefTPEegzJ6yOI3KL6B1w9T+5YkKdjKj6zaFiVfSSOehrV6yOI+5B79+F+fk/wT8QY+i/sBULsjqSEG5Jx51DL5sLNeqg6jaxOo5LUjXqoDr0Tl36Y9Esq+MIYSkpIgXq2ZfB2wdz6Vyro4hcwty6DvyKwWOPWx3lgSilMLr0g8Rb6EWyBpir0rsjMSeNgYdKYwz5WO6MCJFDtGlizv4CbDKM9X6MZs+jmr+ADl+BuWmN1XGEsIwUkQJVoCDqmXawPwp95IDVcYSL03Hn4PBeVKNWKCN3TKiTEVWiDKrVS+ifN6F/3Wd1HPEX5vZNmFP+DeUqYPzjI1TBQlZHEsJt6U1r4OghVPveqKL+Vsdxeervr0CNOuhvp6L377I6jhCWkCJSAKCaPw9F/DGXzJZJK8Q96a3rwGZDPdXC6ijZpp77OxQLwlzwFTo52eo44g/m1jD0zM/g0WoYg/6J8ilgdSQh3JaOO49eOgeqBaPqN7M6Tq6gDBvGq0OgVFnMKf+WpT9EniRFpABA5fNCvdgJYn+D3ZFWxxEuSicno7dtTJ363Q2GFqp8XhidXoMLZ9HrllgdRwDmhuXoeZOhWjDGwPdR3vmtjiSE29KmiTlnIthsGF37yzDWLFDe+TEGjpSlP0SeJUWksFP1m0GJMphL56FTUqyOI1yQ3vMzXL+K0Sh3TqiTEVUtGBXSAL16UepQXWEJrTXmqoXo72dAcH2MfsNR+bysjiWEW9Nb1sJvB1B/75XrZtp2BWmX/vgInZRodSQhnEaKSGGnDBtGm+4Qdw7903qr4wgXpLeug2JBUKWm1VEcSrXvBZ6emAu+luHcFtBao5fNRS9fgKrXFOPVoSgPT6tjCeHW9MUL6CVz4LHH3eLxBKuoMo9gvDoUTsfK0h8iT/GwOoBwMTVCUpc+WPkdum5TGUom7PSFM3BkP6pNN5ThXt8/qSL+qNZdUidJ+GUr6snGVkfKM7RpohdOR0esQjX+G6pTX7f7fP0pOjqaWbNmYZomzZs3p3Xr1mneP3ToEHPmzOHkyZMMGjSIunXr2t8bM2YMR48epXLlyrzzzjv217/44guOHTuGh4cH5cuXp0+fPnh4eLBixQp+/PFHAEzT5MyZM8yYMQNfX1/69++Pt7c3hmFgs9kYO3asczpAuAz7MFalMLoNkGGs2aRq1kG174X+bhp68WzU33tZHUmIHCdFpEhDKYXRtgfm2LfRG5ajXuhgdSThIv47oU5zq6PkCNXkGXRkBPr7GejqwSgfX6sjuT1t3kHPnYTeFo5q2RrVrqfb/jJrmiYzZszgvffew9/fn+HDhxMSEkKpUqXs2wQEBNCvXz9WrlyZbv/Q0FCSkpIIDw9P83qDBg0YOHAgAJ9//jkRERG0bNmS0NBQQkNDAYiKimL16tX4+v73M/3BBx9QqJDMeJtX6a3rUr8U7DYA5VfM6jhuwWj+Aubv59AblmMGPoTR5FmrIwmRo9zz616RLap8ZahdH71uGfrqf6yOI1yATr6NjoxA1aqLKlTU6jg5QhmpE0tw7Sp62Tyr47g9nZKCnj4htYB8oYNbF5AAMTExBAUFUbx4cTw8PKhfvz47d+5Ms01gYCBly5bNsB+qV69O/vzpR4bUrl0bpRRKKSpUqEB8fPrJPbZt28ZTTz3luJMRuZq+9Dt68WyoWgvV4Gmr47gV1b43VA9JHdVyQJb+EO5NikiRIeOlLpCchF71ndVRhAvQu7bBjWuoxu4zoU5GVNnyqGbPobeEoY8fsTqO29LJtzG/Hove+SOqXQ+M0E5uXUACJCQk4O//3/X3/P39SUhIcFj7KSkp/Pjjj9SqVSvN60lJSURHR6cZGgupw2OHDRuW7s6mcG9aa8y5XwLIMNYcoGw2jD5DoMQfS3+cOWF1JCFyjAxnFRlSQaVQDVuit65DtwhFBZawOpKwkN6yDgJLQKXqVkfJcap1Z/SuSMx5kzHem4Cy2ayO5FZ0UhLm5DFwKBrVqS9GUxny5QjTp0+nSpUqVKlSJc3ru3btolKlSmmGsn744Yf4+flx5coVPvroI0qUKEHVqlXT7BceHm4vMMeOHUtAQPZn7vTw8HBIO+7E2X1yc/0PXDu8l4J938anUtX772ABd/ic3PngUxKG9YZJYyj6f9OwZXPmW3foE0eTPsmYM/tFikhxV+qFjuifN6GXzUe99rbVcYRF9NlTEHModbihm0548r+Utw9Gx1cxvxqL3rgS1bL1/XcSmaJv3cScOBpifkX1fBOjfu55vnbNmjU0aNDggZ8j9PPzSzPUND4+Hj8/x6y1umjRIq5evUqfPn3Svbdt2zYaNGiQLgtA4cKFqVOnDjExMemKyBYtWtCixX9n7Lx06VK2cwYEBDikHXfizD7R8XGYMydC5RrcqP0UN130v4V7fE4M6Pcu5r/f4dLowRhDP0Z5eT9wa+7RJ44lfZIxR/RLiRKZu3Hk/r8RigemChdFtWyNjvoJHXvU6jjCIvrHdeDhgcpFv/Bn2+P1Up9rWfENOv6i1Wncgr5xDXPC+3D8COrVIbmqgAQ4cOAA/fv3Z+zYsURGRpKcnJyl/cuXL8/58+eJi4sjJSWFyMhIQkJCsp1r48aN7N27l0GDBmH85UuemzdvcujQoTTHSUxM5NatW/a/79u3jzJlymQ7h3Bt/x3GqjG6D5RhrE6gypbHeHUInDqGOWOCLP0h3I5t1KhRo6wO4SquXbuWrf19fHy4efOmg9K4iLIV0D9tQJ+JRdVrluULj1v2STblpj7Rt5PQMz9F1XwSo17THD2WK/WLUgpVvjJ602r07+cwnmhkSQ5X6pPs0FcvY45/D86fxnh9OEbteg/cliP6pGDBglne56mnnuLpp58mOTmZ8PBwvvnmGy5cuICPjw/Fit1/dkvDMAgKCmLixImEhYXRsGFD6taty8KFC0lMTKREiRLExMQwYsQIYmNjiY6OZsuWLbRq1QqAkSNHsn79es6dO8eGDRsoVaoUQUFBjBgxApvNxtatW9mwYQNXr16131Xctm0bQJo7kfHx8YwZM4YNGzYQHh7Ok08+SdOm9/9/O7vXR3Cfz7MjOatP9E8bIHwFqkNvjKqP5/jxssOdPicqqBTkLwDhK+B2EuqxB+t7d+oTR5E+yZgzr5FKy8radufOncvW/u56a93cuAr93VSMNz5AVQ/O0r7u2ifZkZv6xIzciJ71OcaQj1GVquXosVyxX8ywJeglczD6j0DVqnv/HRzMFfskq3TCJcxP34eESxj930VVrXX/ne7BmUN17uXkyZN8+eWXnDp1ioCAAJo3b86zzz6Lt/eDD1lzZdm9PoJ7fJ4dzRl9ouMvYo4aAGUrYAz+0OUfS3C3z4nWGv3tFPSmNagu/TAeYII6d+sTR5A+yZgMZxUuRTVuBcWCMJfMluEYeYzeug6CSsGjj1kdxRKqxYtQsizmt1PRibesjpPr6IsXMP/9Dly5jDHon9kuIF3B/v37mTx5MqNGjaJw4cIMGDCAAQMGEBsby8cff2x1PCHS0FpjzvsS9B/DWF28gHRHSilU+1ehWjD6m6/RB3ZbHUkIh5B/TcR9KQ9P1Etd4exJ9PYtVscRTqLPxMKxX1GNWuXZ52eUhwdGl36QcAm98lur4+Qq+vwZzH8Ph8RbqXc/KrrmTJCZNXfuXPr27cusWbMoUaIE48eP57333qNhw4ZUqVKFN998k9jYWKtjCpGGjtwIB/eg2nZHFQuyOk6epWw2jNeGQokymFP+D332pNWRhMg2KSJFpqjgp1Kfj1y+AJ182+o4wgn0lnXg4Ymq38zqKJZSFaqkLncTvgJ9WoqEzNBnYjHHDQfzDsaQMahyFa2OlG3JyckMGTKECRMm0Lp163Qzq3p4eDB27FiL0gmRnk64hF44Ax6thmr8jNVx8jzl7YMx8H3wyo/5xWj0lctWRxIiW6SIFJmiDAOjbXdIuIjetNrqOCKH6aRE9I7NqJAGqAJZn4TE3ai23aFAQcz5k9GmaXUcl6Zjf8Mc9y54eGIM/ReqVDmrIznESy+9RFBQ2js5169fJyEhwf5zyZIlnR1LiAxprTHnT4Y7yTKM1YUov2IYA9+D61cxv/wInZRkdSQhHpj8qyIyTVWpCdVqo1cvQt+4bnUckYP0L1vh1s3U52EFqkBB1MuvwPEjqc+Jigzp3w6kLuNRwBfj7X+hgtynqBo3blyaghEgISGBTz75xKJEQtyd/jkC9keh2nRHBT5kdRzxP1TZChiv/gNOxmDOnCBfTIpcS4pIkSVGm+5w6wZ67WKro4gcpLeugxJloHwVq6O4DFW3CVSugV46V4YhZUAf3IP5+SgoGpBaQAYUtzqSQ507dy7deoplypTh7NmzFiUSImP6cjz6u+lQsSqq6XNWxxEZULXqpn4xuftn9NI5VscR4oFIESmyRJV+GPVkE/TGlegEWYTdHelTx+DEUVSjv+XZCXUyopTC6NwXkpPQ38+0Oo5L0dHbMb/8EIqXxBj6MaqIv9WRHK5QoUJcuHAhzWsXLlx4oDUnhcgpqbOxTvpjGOsbMozVhakWoagmz6DXLcOUES4iF5J/XUSWqRc7ARq94huro4gcoLesg3z5UPWaWB3F5aigUqi/tUP/sgV9aI/VcVyCuWML5ldjofQjGP8YgypY2OpIOaJp06aMHz+eXbt2cebMGaKiohg/fjzNmuXtiaeEa9HbN6cOY32pK6p49tdDFTlHKYXq0Cf1MaEFX8k1ReQ6UkSKLFMBxVFNn0NHbpJpqjRPjNsAACAASURBVN2MTryJ3rEFFdIQ5eNrdRyXpJ5tB4ElMBd8nednKjZ/2oCeMQEqVMUYPBpVwH0/M61bt6Zhw4bMmzeP4cOHM3/+fBo2bEjr1q2tjiYEAPo/CejvpkKFKqhmz1sdR2SCstkw+rwND5XG/FqW/hC5ixSR4oGoZ18G7/yYS+daHUU4kP5lKyTdQjWSCXXuRnnmSx3WGncevSbvPhtsblyFnjMRHnsc440PUN4+VkfKUYZhEBoaymeffca8efP47LPPCA0NxZDhgsIF2GdjTf5zGKvN6kgik1R+H4yBIyGfF+bED9FX5Zl7kTvI1U88EOVbCPVMW9i3E/3bAavjCAfQWqO3hEGpcvBIJavjuDRVtRbqicbosMXoC2esjuN05trFqXc8Hq+L0e9dlJeX1ZGcIiUlhVOnTnHgwIE0f4Swmv5lK+z9BdW6s1vNipxXKP9iGAPeg2v/wfxyjCz9IXIFj8xu+P/s3Xt8zvX/x/HH+3NdO5phm1lySJvzea1oKaeRb0oLlU4IyRfV+FZf5Nt58pOQdHSKUk5RpNDIcSkKhcIomtPYGHbePu/fH5eWtWHY9rmuXa/77eZmu/b5vD/P6+3y2fW6Pu/P+/3ll1/SpEkTrrvuOvbs2cPEiRMxDIOnnnqKevXqlWZG4aRUx7vQq5dhLvwQY+TrMgmLq/sjAQ7uRz04SP4ti0Hd3w+9Ywvmx+9i/OdVt+gzrTX68znor+ajWrVFPRqDsrnHFY/ffvuNCRMmkJOTQ0ZGBj4+PmRmZhIYGMiUKVOsjifcmE49if70A7i+Piqqm9VxxBVS19XFGPA05ruvYc6YiPH4szIxknBqxX51Llu2jODgYAA+/fRT7rzzTnr06MGHH35YWtmEk1OeXo5Jdn7fAz99Z3UccZX0uuXg5e1YykJckvKvgureB3b/4pjMopzTWqPnT3cUkLd2RvVznwISYNasWXTr1o2ZM2fi4+PDzJkz6dGjB507d7Y6mnBjjmGs70JWJkbfp2QYq4tTLVujevaFn+LRiz+yOo4QF1XsK5Hp6en4+vqSkZHBH3/8wf/+9z8Mw2D27OLdE7dt2zZmzpyJaZp07Nix0GQEOTk5TJkyhf3791OxYkViYmLyi9bFixezevVqDMPg0UcfpUWLFhdt891332X//v1orbnmmmsYMmQI3t7exX2q4jKomzugV36OuWg2RvObUPZiv6SEE9Hpaegf1jmuLvmU73vbSpK6tTM6fhV6wQx0swhUhfK53IM289Afv4tevxLV8S7U/QPc4srr+Q4fPswdd9xR4LHo6GiGDBlCt25y9UdYQ29eD9s2oXr2RV1Tw+o4ogSoTtGOe+6Xf4ZZNQRD5igQTqrYVyIDAwPZvXs3GzdupGHDhhiGQXp6erEmFTBNk+nTpzNq1CgmTpzIxo0bSUwseB/R6tWrqVChAm+99RZdu3Zlzpw5ACQmJhIfH8+ECRN47rnnmD59OqZpXrTNPn368PrrrzN+/HiCgoJYvnz55fSJuAzKZsPo0QeSDqM3fGN1HHGF9PdrITtLJtS5TMowMB4ZDGln0J+VzwWjdV4eesYkRwF5x31uWUAC+R+iAlSuXJnExETOnj1LZmamxcmEu9KnT6I/fR/q1EN1utvqOKKEKKVQDzwOjVueW/pjm9WRhChSsYvIhx9+mAkTJrB48WJ69uwJwE8//URYWNgl901ISCAkJIRq1apht9uJjIxk8+bNBbbZsmUL7dq1A6B169bs2LEDrTWbN28mMjISDw8PgoODCQkJISEh4aJt+vo6rqRorcnOdu8p+MtEsxshrBF66afozAyr04jLpLV2DGWtFYq6rq7VcVyOqlEHFXU3ev1KdMIuq+OUKJ2Tg/n+/zmWfbnnEYx7HnbLAhKgVatWbN3qWMetffv2vPTSS4wYMYLWrVtbnEy4I6015pz3IDMT41EZxlreKJsN4/H/5i/9kfvn71ZHEqKQYo89DA8P5/333y/wWOvWrYv1CzQlJYXAwMD87wMDA9m7d+8Ft7HZbPj6+nLmzBlSUlKoW/fvN7YBAQGkpKTkt3OhNt955x22bt1KjRo16N27d3GfprgCSimMnn0xxz6LjvsCdWcvqyOJy7F/NyT+gXpksNVJXJbq9gB6ywbHJDujJ5aLYd06Owvz3ddgx0+oXo9hdLzL6kiW6tu3b/7X3bp1o169emRkZNC8eXPrQgm3pbdshJ++Q3Xvg7qmptVxRClwLP3xP8wxT3NqzLPo5yejPDysjiVEvmK/00lMTMTPz4/KlSuTmZnJkiVLUErRrVs37E74hmnw4MGYpsmMGTOIj4+nffv2hbaJi4sjLi4OgLFjxxIUFHRVx7Tb7VfdhssKasOp1u3IXvE5AdEPYlQOANy8Ty7A2fok9dM1ZHn7EvSvezB8KliWw9n65XJlPv40qa/9F9/4b6jQ/ZESadOqPjEz0jj15ouYO7fiP2QkPlHOU0Ba0SemafLUU08xYcIEPM69iWvQoEGZZhDiL/pMKvqT9+C6uqjO0ZfeQbgsFRiM0W8YeZNeQK35SoYtC6dS7OrvzTffZNiwYVSuXJnZs2dz5MgRPDw8+OCDD3jiiScuum9AQADJycn53ycnJxMQEFDkNoGBgeTl5ZGenk7FihUL7ZuSkpK/76XaNAyDyMhIlixZUmQRGRUVRVRUVP73J06cKEZPXFhQUNBVt+HKdNf70D+s48TsdzEefByQPimKM/WJTj+LuSEO1boDKWkZkGbdcGRn6pcrcn1DaNGas/Omk96wJapqyFU3aUWf6LSzmJNfgj/2ovoPJ63FzaQ50b9LSfRJ9erVL2t7wzAwDIOcnJz8IlIIq+hP3ofMdMdsrG40Q7K7Uo1b4tn8RrKXzUff0hHl62d1JCGAy7gnMikpierVq6O15ocffmDYsGEMHz6c7du3X3Lf0NBQjhw5QlJSErm5ucTHxxMREVFgmxtuuIE1a9YAsGnTJho3boxSioiICOLj48nJySEpKYkjR44QFhZ2wTa11hw9ehRw3DOwZcuWy37DIK6MCqmBatMZvW45OumI1XFEMejv1kB2NqqtTKhTEowHHgNlYH76AVprq+NcNn0mFfON5+DgPox/j8Bo1dbqSE7jjjvuYOLEiezatYujR49y7Nix/D9ClBX940b0lg2oO3uhrq1ldRxRRvx6n5vAbfkiq6MIka/YVyI9PT3JyMggMTGRoKAg/P39ycvLIycn55L72mw2+vXrR2xsLKZp0r59e2rWrMm8efMIDQ0lIiKCDh06MGXKFJ544gn8/PyIiYkBoGbNmtx8880MHz4cwzDo379//oywRbVpmiZvv/026enpANSuXZsBAwZcSd+IK6Du6oXe9C36849RA5+xOo64CK01eu3XjiFRtUKtjlMuqICqqG4PohfMcKydekOk1ZGKTZ9KxpzwPCQfwxgyGtUk3OpITmXGjBkA/Pzzz4V+Nm/evLKOI9yQPnPaMZlO7TBUlx5WxxFlyOP6+qhWbdGrlqDbd0VVCbz0TkKUsmIXkbfccgsvv/wyGRkZdOnSBYDff/89fy3HSwkPDyc8vOCbkvvvvz//a09PT4YPH17kvt27d6d79+7FatMwDF555ZViZRIlT1UOQHW6G71sPrpTNLjwPW7lXsKvcORPVJ+LD0cXl0d1vAu96VvMuR9gNGrhEutu6hPHMCf8D06nYjz1IqpeE6sjOR0pFIXV9KfvQ3oaxvBXZBirG1J3P+S4Er3kE/m9LZxCsYez9u3bl169ejFgwID8IlIpRZ8+fUotnHBN6vbu4OeP+dmHLjmkz13odcvBxxd1461WRylXlM2G8fBgSD2J/mKO1XEuSR89hPn6SEg7g/GfV6SAFMIJ6Z/i0ZvXo+68H1XjOqvjCAuoqiGodnegN65CHz5odRwhin8lEqB58+acOHGCPXv2EBAQQGioDIEThSkfX9Sd96PnTiV76/dQ69JriYqypc+eRm/ZiLq1E8rL2+o45Y66vj6qbRf06mXomzugajvnuVIfOuC4Aqk1xtNjUDXrWB3JaT3//PMXXCPzpZdeKuM0wp3os6cxP34Xal0vw1jdnLrjPvTGOMxFs7ENHW11HOHmil1Enjx5kkmTJrF37178/Pw4c+YM9erV46mnnio0K6oQqm0X9KqlnJ39NnrEOJRdZjR0Jvq7byE3B3VbF6ujlFvqnkfQWzdhfvQ2xqjXnW4xcH0gAXPiC+DhgTH8VdQ1NayO5NQ6dOhQ4PtTp07x7bffcuutxb+Sv23bNmbOnIlpmnTs2JHo6ILLM+zatYtZs2Zx4MABYmJiCqzDHBsby969e2nQoAEjRozIf3zy5Mns27cPu91OaGgoAwcOxG63s3PnTsaNG5d/y0mrVq3o2bNnsXII56I/nQrpZzGGv1wu1qAVV05V9Efd3h39+cfovbtQdRtZHUm4sWIPZ506dSq1a9dmxowZfPDBB8ycOZPrrruOqVOnlmY+4aKU3QPj3n7kHtiH/uR9GdbqRLTWjqGsoQ1kWFQpUr5+qPv6w4EE9JqvrY5TgE7YhfnGaPD2wXh2rBSQxdCuXbsCf6Kjoxk5cmSRE+0UxTRNpk+fzqhRo5g4cSIbN24kMTGxwDZBQUEMHjyYNm3aFNq/W7duDB06tNDjbdq0YdKkSYwfP57s7GxWr16d/7OGDRvy+uuv8/rrr+cXkMXJIZyH3roJ/cNaVNf7UTVkpIAAFXU3VA7AXDhT3lsJSxW7iNy9eze9e/fG29sx9M3b25uHH36YPXv2lFo44dpUy9ZU6NEbvX4levUyq+OIv+zZCUcPoW6TZT1Km7rxVmjUEr34I/Sp5EvvUAb0r9sdVyD9qzgKyBJYz9JdBQQEcODAgWJtm5CQQEhICNWqVcNutxMZGcnmzZsLbBMcHEzt2rWLHDbbtGlTfHx8Cj0eHh6OUgqlFGFhYQXWT77SHMI56LQzmB+/AzXroP7V0+o4wkkoLy9Utwdh/27YusnqOMKNFbuIrFChQqFPKw8fPoyvr/PPPCisU+HBgdCiFXreNPTOrVbHEZybUMe3Aiqi8NUOUbKUUhgPPQ65uei506yOg96+GXPyy1A1BOPZMagAmT25uFavXl3gz/Lly3nttdeoV69esfZPSUkhMPDvafkDAwNJSUkpsXy5ubmsX7+eFi1a5D+2Z88ennnmGcaMGcOff/5ZJjlEydFzpzkmvOr7lAxjFQWoyI4QUgNz8Wx0Xp7VcYSbKvZZqVu3brzyyit06NCBqlWrcvz4cdasWVNgmQ4h/kkZBkb/YZhj/4v5/jjHvWEhMnTOKvpMKvqneFTbf6E8vayO4xZUcHVU1/vQX8xB//IjqukNluTQWzZgTnsDal6PEfMiqkJFS3K4qvXr1xf43svLi/r169O1a1eLEhU0bdo0GjZsSMOGDQGoU6cO77zzDt7e3vz000+8/vrrTJ48udjtxcXFERcXB8DYsWMJKoHlmux2e4m0U55cqE+yNm/g1KZvqXBfP/zCb7IgmXXkdVJYUX2S2XcoqWNHUGHbd/je7n73NcvrpGhl2S/FLiKjoqIICQlhw4YNHDx4kCpVqvDkk0+ya9eu0swnygHl7YsxdDRm7H8wp8RijHwdVcHP6lhuScevgtxcGcpaxtTt3dHfr8X85D2MF6egvMq2gDfjV6E/fAtCG2A8+bxLrF3pbF544YWr2j8gIKDAUNPk5OQSm5RuwYIFnD59moEDB+Y/dv4oofDwcKZPn87p06eLnSMqKoqoqKj870+cOHHVOYOCgkqknfKkqD7RaWcx3x4L19Ymo31XMt2sz+R1UliRr5PrG0JYQ858OpW0JhFuN9O6vE6KVhL9Ur169WJtV+zhrABNmjRh0KBBjBw5kkGDBtGgQQMWLVp0RQGFe1FB1TD+PRJOHMP8YJwMv7CANk30uhVQtxGqei2r47gV5eGB8fC/4cQx9LKyXbTe/PYr9Mw3oWEzxxVIKSCvyNq1awvd//jHH3+wbt26Yu0fGhrKkSNHSEpKIjc3l/j4eCIiIq4616pVq9i+fTsxMTEYxt+/0k+dOpU/6UZCQgKmaVKxYsVSyyFKjp43Dc6cwng0RmY2FxeklMLo0dexJvE3X1gdR7ghGWQvyoyq1xj10CD07CnoBTNQvR6zOpJ72f0LJB1B3fWA1UnckqrfFHVzB/TKxehW7VDXln4hb65YjF44E5rfhPH4sygPz1I/Znk1b948xo0bV+CxoKAgxo0bx2233XbJ/W02G/369SM2NhbTNGnfvj01a9Zk3rx5hIaGEhERQUJCAuPHjyctLY0ff/yR+fPnM2HCBMCxTuWhQ4fIzMxk0KBBDBo0iBYtWjB16lSqVq3Kc889B/y9lMemTZtYuXIlNpsNT09PYmJiUEpdMIdwDvrnzejvVqO63ue068sK56HCGkKL1ugVi9Btu6AqVrI6knAjUkSKMmXc2hnz8J/ouC8wq9fCkGGVZUavXQ5+FVE3RFodxW2pex9F/7wZ8+N3MJ4ZgzIuazBIsWmt0Us/RS+di7rxVlS/YTIxx1XKyMgoNJGcr68vaWlpxW4jPDyc8PDwAo+dP69AWFgY7733XpH7vvzyy0U+Pnfu3CIf79KlC126FL0ObFE5hPV0+lnMj96Ga2ujusp8E6J4jO69MV8cil42Xz6cF2Xqku8qduzYccGf5ebmlmgY4R5Uz77oo3+iP3kPXe1aVP0mVkcq9/Tpk+htm1Ad7pSrURZSFSuhevRxXI2PX4Vq06nEj6G1Ri/8EL1yMeqWjqjeQ1GGrcSP425q1KjBpk2biIz8+0OYH374gRo1ZKIwUTL0/Olw+hTGkOdQHjKMVRSPuqYGqk0n9Jqv0R3vkmWbRJm5ZBH57rvvXvTnMjOSuFzKZsN47BnM157BfO81jFFvyEmvlOmNqyAvTybUcQLqlih0/GpHodf8phIdfqRNE/3p++g1X6Pad0X1eqzUrna6m4ceeojXXnuN+Ph4QkJCOHr0KL/88gsjR460OpooB/QvP6I3rkLdcS/qurpWxxEuRt3VC73pW/Tij1ADn7E6jnATlywi33777bLIIdyM8q3gmLF1zNOYU17FGDFOJvwoJdo00etXQv2msryKE1CGgfHwYMxXnkIv/BD16FMl0q7Oy0PPmoz+7ltUlx6o7r2LXLReXJkGDRrwxhtvsGHDBk6cOEFYWBh9+/aVD1LFVdPpaZizp8A1NVF39rI6jnBBqnIgKioa/dV89O33oGqHWR1JuAH5iFpYRlWrjvH4s3A0EXPaG2hTZmwtFb9uh+NH5SqkE1HX1kJ1jkbHr0LvvvAtA8Wlc3PQU8c7Csi7H5ICshTk5ORQuXJloqOjGTBgANHR0VSuXJmcnByrowkXpxfOhNSTGI8+JcNYxRVTXbqDX0XMz2blz8wsRGmSIlJYSjVq4bgR/OfN6MUfWx2nXDLXLQc/f1TLm62OIs6juvaCoGqYH7+DvopCROdkY77zGvrHjaj7+mPceb8UkKXg1VdfZf/+/QUe279/P7GxsRYlEuVB1rbv0etXom6/B1WnntVxhAtTPr6OCZl+3Q47t1odR7gBKSKF5VS7O1Btu6CXf4b53bdWxylX9Klk2Pa9Y4IV+YTbqSgvL4wHB8HRRPTKxVfUhs7MwJz8Muz4EfXIYIxOd5dwSvGXgwcPUrduwXvVwsLCCq0dKURx6Yx0Tr89FkJqoLrJ0kvi6qm2/3J8OPnZLLRpWh1HlHNSRArLKaVQvQZC/abo2W+h9/1mdaRyQ2+IA9OUoaxOSjW9AXXDLehl89FJRy5rX52ehjnpBdi9A9UvBuO2opdzECXD19eX1NTUAo+lpqbi5eVlUSLhyrTW6PnTMVOOY/R9UmbNFiVCeXigoh+GxN/RP6y1Oo4o56SIFE5B2e0Yg/4LVYIw3xmDTjludSSXp808x4Q6DZujgqtbHUdcgOo1AGw2zDnvFfs+Fn3mNOYbo+GPBIzHn8Vo3b6UU4pWrVrx5ptvcvDgQbKysjh48CBTpkyhdevWVkcTLkZrjf78Y/SGb/C952FUaAOrI4lyRN14K9QKRX8+B52TbXUcUY5JESmchvLzxxg6GrKzMN+ORWdlWh3Jte3cCinHMdrKFSpnpioHoqIfgV1b0Vs2XHJ7nXoSc/woOPInxpBRqBsiL7mPuHq9evXi2muvZdSoUfTu3ZvnnnuOa6+9ll69ZDZNUXz5BeRXC1C33Y7fgwOtjiTKGWUYGD36QHISes3XVscR5ZgUkcKpqOq1MAY+A3/+jjlzkozpvwrm2uXgXxmat7I6irgE1f5fUDsMPW8aOv3sBbfTyccxx42A5CSMJ59HNY0ow5TuzdPTkwEDBvDRRx8xdepUXn31Vex2O089VTJLtIjy758FpHro37KOqygVqlELaNTScavERX6nCHE15OwlnI5qGoHq0Rd+jEd/Oc/qOC5Jp5yAn7egbolC2S+5HKywmDJsGI8MhtOpF5ylWCcddhSQZ05jDHsZ1aBZGacUp0+f5uuvvyY2NpZnn32W/fv307dvX6tjCRfgKCDnOArIWztLASlKndGjN6SdQS//zOooopySd5fCKanO0XDoAHrpp+jqNVERbayO5FL0hm8Ajbq1s9VRRDGp2mGoDl3Rq79ER3YoMN2/PnwQc8LzkJeL8fSrqFqhFiZ1L7m5uWzZsoU1a9awfft2QkJCuOWWW0hKSmLYsGFUqlTJ6ojCyf1dQM53FJAPD5YCUpQ6VSsU1aotOm4puv2dqCqBVkcS5YycxYRTUkqhHhkCoQ0cw1oP7LM6ksvQeXmOIrJRC1TVEKvjiMug7n4IKlXB/OhtdF4eAPrgPszXRwFgPDNGCsgy9thjjzF16lSqV69ObGwsEydOpGfPnnjIkjmiGKSAFFZS0Q+DNtFLPrE6iiiH5EwmnJby8MAYPBL8/B0T7ZxKsTqSa9jxI5w8IUs+uCDl44vR6zH483f06i/J/u0XzPGjwdML49kxqOq1rI7odmrXrk1aWhoJCQns27ePs2fl/iJRPFpr9BdSQArrqKBqqHZ3oDeuQh8+aHUcUc7I2Uw4NeVfBWPIaEg741j6Q6arviRz7XKoFADNbrQ6irgS4ZHQNAL9xRxOvRQDFf0xnh0ry7RY5MUXX+Stt96iWbNmLF26lIEDBzJ27FiysrLIO3e1WIh/yi8gl0kBKayl7rgPvL0xF822OoooZ+SMJpyeqnU9Rv9h8Pse9Oy3i72WnjvSyUmw40fUrZ1kQh0XpZTCePBx0BqjagjGM6+hAqtaHcutVa1alZ49ezJ58mSef/55qlSpglKKZ555ho8/LnoiJOG+pIAUzkRV9Ed16QHbf0Dv3WV1HFGOyFlNuAQVHom6+yH0pm/RKxZZHcdp6fUrAYVqIxPquDIVVA3j5bcJHDcNVTnA6jjiPA0aNODxxx/ngw8+4NFHH+XgQRkiJv6mtUYv+UQKSOFUVMduUDkAc+FM+SBelBg5swmXobreh7rxVvSi2ejtP1gdx+no3Fz0hjhoEi5XrsoBFRiM8vaxOoa4AE9PT9q0acOoUaOsjiKcRH4B+eU8VJtOUkAKp6G8vFDdHoT9u2HrJqvjiHJCzm7CZSilUH2ehFqhmFPfQB86YHUk5/LzZkhNwWgrE+oIIURZKlRAPjJECkjhVFRkR7imJubi2fmzfwtxNeQMJ1yK8vLCGPIcePtgvvUK+kyq1ZGchrluOVQJgiY3WB1FCCHchqOA/NRRQN4SJQWkcErKZsPo3huOHjq3lrQQV0fOcsLlqCqBGENGQepJzPfGonNzrI5kOX38KOza5vgE3GazOo4QQriFvwvIuY4CsvdQKSCF82p+E4Q1RC/9FJ2VaXUa4eLkTCdckqpTD9X3SdizE/3J+25/o/jfE+p0sjqKEEK4DSkghStRSmH06AupJ9HffGF1HOHi5GwnXJbRqi3qjnvR61eiV39pdRzL6Nwc9MY4aBaBCgiyOo4QQrgFc8kn5wrIjlJACpehwhpCy9boFYvkliBxVWQhOeHS1N0PoQ8fRM+bjg6pgWrc0upIZW/b93D6lEyoI4ST27ZtGzNnzsQ0TTp27Eh0dHSBn+/atYtZs2Zx4MABYmJiaN26df7PYmNj2bt3Lw0aNGDEiBH5j0+ePJl9+/Zht9sJDQ1l4MCB2O121q9fzxdffIHWGh8fHwYMGMB1110HwJAhQ/D29sYwDGw2G2PHji2T51+emEs+QS/9q4B8QgpI4VKMe3pjbh/quI/3gYFWxxEuSs56wqUpw8DoPxyurYX5/jj00USrI5U5c90KCAwGdyyghXARpmkyffp0Ro0axcSJE9m4cSOJiQXPV0FBQQwePJg2bdoU2r9bt24MHTq00ONt2rRh0qRJjB8/nuzsbFavXg1AcHAwL774Im+88QY9evTggw8+KLDfCy+8wOuvvy4F5BWQAlK4OnVNDVSbTui1y9FJR6yOI1yUnPmEy1PePhhDR4PdjjklFp121upIZUYnHYZftzsWtTZkQh0hnFVCQgIhISFUq1YNu91OZGQkmzdvLrBNcHAwtWvXRilVaP+mTZvi41N43dDw8HDH8kdKERYWRnJyMgD169fHz88PgLp16+Y/Lq6OFJCivFB3PQA2G/rzj62OIlxUmQ1nvdQwnpycHKZMmcL+/fupWLEiMTExBAcHA7B48WJWr16NYRg8+uijtGjR4qJtXmh4jyi/VGAwxr9HYr4xGvODcRhPvuAWs5TqdSvAZkPdEmV1FCHERaSkpBAYGJj/fWBgIHv37i2x9nNzc1m/fj19+/Yt9LPVq1fTsmXBkQqxsbEAdOrUiagoOX8UhxSQojxRlQNQUXejv5qP7hyNuq6u1ZGEiymTyuqvYTyjR48mMDCQkSNHEhERQY0aNfK3Wb16NRUqVOCtt95i48aNzJkzh2HDhpGYmEh8fDwTJkzg5MmTvPLKK7z55psAczOhBAAAIABJREFUF2yzTZs2PPHEEwC8+eabrF69ms6dO5fFUxUWUnUboR4ahJ49Bb1gBqrXY1ZHKlU6Jwe9cRU0vwlVOcDqOEIIC02bNo2GDRvSsGHDAo/v2LGDb7/9lpdffjn/sVdeeYWAgABSU1N59dVXqV69Oo0aNSqwX1xcHHFxcQCMHTuWoKCrn7TLbreXSDtWODtvOmlL5+Ld4Q78h4wqsQLSlfuktEifFFZafWI+9BgnNqzEvuQTKr80uchREM5KXidFK8t+KZMi8vxhPED+MJ7zi8gtW7Zw7733AtC6dWtmzJiB1prNmzcTGRmJh4cHwcHBhISEkJCQAHDBNsPDw/PbPX94jyj/jFs7Yx7+Ex33BWb1mhi3ld/JZvTW7+Ds6XL9HIUoLwICAgr8LkpOTiYgoGQ+/FmwYAGnT59m4MCCE2QcOHCA999/n5EjR1KxYsUCWQAqVarEjTfeSEJCQqEiMioqqsAVyhMnTlx1zqCgoBJpp6yZSz5FL/0UFdmR7PsfIzklpcTadtU+KU3SJ4WVap/ccS/Zc6dyYu03qCbhl97eScjrpGgl0S/Vq1cv1nZlMhajqGE8Kf84CZ+/jc1mw9fXlzNnzhTaNyAggJSUlGK1+dfwnr+Gvwr3oHr2hSbhjvUjd++wOk6p0etWQNUQaNjc6ihCiEsIDQ3lyJEjJCUlkZubS3x8PBEREVfd7qpVq9i+fTsxMTEY510dO3HiBOPHj2fo0KEF3hBkZmaSkZGR//XPP/9MrVq1rjpHeWUunZtfQKo+Q+Xec1HuqNu6QFA1zM9moU3T6jjChZTrGwUvNLznLyU9XEcurRdmVZ+YI8aS8t/HMN//P6qMm4Y95Noyz3AhJdEnuYcOkLz7F/weHkSFc/cOuzr5/1OY9ElhrtonNpuNfv36ERsbi2matG/fnpo1azJv3jxCQ0OJiIggISGB8ePHk5aWxo8//sj8+fOZMGECAM8//zyHDh0iMzOTQYMGMWjQIFq0aMHUqVOpWrUqzz33HACtWrWiZ8+eLFy4kLNnzzJt2rT8448dO5bU1FTGjx8PQF5eHm3atJEPWi/AXDoXveQT1M0dpIAU5Zby8EBFP4ye9gb6h7Wo1u2tjiRcRJkUkcUZxvPXNoGBgeTl5ZGenk7FihUL7ZuSkpK/78XavNDwnvOV9HAdubRemJV9ov89Ej3maZJf+Q/GiHEoH19LcvxTSfSJ+cVcsNlIb3kzGeXkNSf/fwqTPimsLIfqlLTw8PACt1sA3H///flfh4WF8d577xW57/n3NJ5v7ty5RT7+V6H5T9WqVeP1118vbmS3VaCA7PuEFJCiXFM33ope+Tn68znoG25BeXhaHUm4gDIZzlqcYTw33HADa9asAWDTpk00btwYpRQRERHEx8eTk5NDUlISR44cISws7KJtXmh4j3Avqlp1jEH/haOJmNPeQJt5VkcqETonGx2/GtWiNcq/itVxhBCiXDG//KuAbC8FpHALyjAwevSB5CT0t19ZHUe4iDK5ElmcYTwdOnRgypQpPPHEE/j5+RETEwNAzZo1ufnmmxk+fDiGYdC/f//8wrCoNoELDu8R7kc1bI7qNRD9yXvoxR+jevSxOtJV0z9uhLQzqLYyoY4QQpQk88u56C/+KiCflAJSuA3VqAU0aon+agG6TRTK18/qSMLJldk9kZcaxuPp6cnw4cOL3Ld79+507969WG3ChYf3CPdktL8D89Af6OWfYVavhXGza4/312tXQHB1aNDM6ihCCFFuSAEp3J3Row/mKzHo5Z+hurv+h+7uRmdnlenxZKyncAuq10Co3xQ9+y30vt+sjnPF9KGDkLALddvtLrWekxBCODPzy3mOArK1FJDCfala16NatUXHLUWnyP34rkT/sRdz1ECyd/xUZseUIlK4BWW3O+6PrBKE+c4YdMpxqyNdEb1+BdjtqMiOVkcRQohywVFAznEUkI9KASncm4p+GLSJXvqp1VFEMemjhzDffAnsHtiq1yyz40oRKdyG8vPHGDoasrMw345FZ2VaHemy6Ows9HerUeGRqIr+VscRQgiXJwWkEAWpoGqodl3RG1ehDx+0Oo64BH0yGXPSC6AUxrCXsQVULbNjSxEp3IqqXgtj4DPw5++YMya51MK6essGSE9zLAwshBDiqpjL5ksBKUQRVNd7wdsbc9Fsq6OIi9BpZxwFZNoZjKdeRFUr2+WrpIgUbkc1jUD17As/xaO/dJ1JmPS6FRBSA+o1tjqKEEK4NHPZfPTnH6Nat5MCUoh/UH7+qC49YPsP6D07rY4jiqCzsjDfegWSDmMMeQ5VO7TMM0gRKdyS6hSNiuyIXjrXcYXPyenEP2DfbzKhjhBCXKWCBeRTUkAKUQTVsRtUDsT87EO01lbHEefRubmY7/8f7N+D8djTKItm65ciUrglpRTq4cEQ2gBz5iT0gX1WR7oovW452D1QkR2sjiKEEC5LCkghikd5eaG6PQD7d8PW76yOI87RpomeNRl+2YJ6+N+o8EjLskgRKdyW8vDAGDwS/PwdE+2cSrE6UpF0ViZ60xpURBtUhYpWxxFCCJeUX0C2aisFpBDFoCI7wjU1MRd9hM7LszqO29NaoxfMcLwnjH4Y47bbLc0jRaRwa8q/CsaQ0ZB2xrH0R0621ZEK0T+sg4x0VFtrTxZCCOGqChSQ/WKkgBSiGJTNhtG9Nxw7hN7wjdVx3J5e/hk6bgmq412oO+61Oo4UkUKoWtdj9B8Gv+9Bz57idGP/9boVUL0WhDa0OooQQrgc86sFUkAKcaWa3wRhjdBLP3W5pdHKE3P9SvSi2Y7z2H39nWJ+DCkihQDH2ot3P4TetAa9fJHVcfLpg/vgj72o27o4xQlDCCFcifnVAvTij1A3SQEpxJVQSmH06AOpJ9HffGF1HLekf/oO/dE70OQGVN+nUIZzlG/OkUIIJ6C63oe68Vb04tnobd9bHQcAvXYFeHqibm5ndRQhhHApBQrI/lJACnGlVFhDaNkavWIR+kyq1XHcit79C+bU8VCnLsag/6Lsdqsj5ZMiUohzlFKovk9CrVDMaRMcy2pYSGemo79fi4q4FeXrZ2kWIYRwJebXC+UKpBAlyOjeG7Kz0F/OszqK29AH92FOeRWqhmA8+TzKy9vqSAVIESnEeZSnF8aQ58DbB3PKq5Z+4qZ/WAdZGSiLZ98SQghXYn690HHv0F8FpE0KSCGulgqpgWrTCb12OTrpiNVxyj2ddBhz0ovg64cR85JTzs4vRaQQ/6CqBGIMGQWnT2G+Nxadm2NJDr12BdS4Dq6vb8nxhRDC1fxdQN4mBaQQJUzd9QDYbOjPP7Y6SrmmT6VgTnwBtMYY9hIqIMjqSEWSIlKIIqg69VB9noA9O9GfvF/mM7bqP/bCwX2otjKhjhBCFIf59WfnFZDDpIAUooSpygGoTnejN693vE8RJU6nn8V880U4k4rx5AuokBpWR7ogKSKFuACjVVvUHfei169Er/6yTI+t1y4HL29Uq3ZlelwhhHBFjgJylhSQQpQydXt38PPH/GyW0y2J5up0dpbjHsgjiRiDR6Hq1LU60kVJESnERai7H4IWrdDzpqN3bi2TY+r0NPQP6xxvhnx8y+SYQgjhqvILyBtvlQJSiFKmfHxRd94Pv/0MZfS+yB3ovDzMD16HhF9R/YejGrWwOtIlSREpxEUow8DoPxyurYX5/jj00cRSP6b+fi1kZ8mEOkIIcQnm8vMKyP7DpYAUogyotl0gqJrjaqRpWh3H5Wmt0bOnwPYfUA8+jnFjG6sjFYsUkUJcgvL2wRg6Gux2zLdeRaedLbVjaa3R65ZDrVDUdc49jEEIIaxkLv8M/ZkUkEKUNWX3QEU/DIm/Oz74FldFf/YhOn4V6q4HMNrdYXWcYpMiUohiUIHBGP8eCclJmO//Hzovr3QOtH83JP6BaitXIYUQ4kKkgBTCWurGW6F2GPrzj9E52VbHcVnmikXoFYtR7e9A3dXL6jiXxW51ACFcharbCPXwv9Gz3kLPn456YGCJH0OvWwFePqibbivxtoUQ1tq2bRszZ87ENE06duxIdHR0gZ/v2rWLWbNmceDAAWJiYmjdunX+z2JjY9m7dy8NGjRgxIgR+Y9PnjyZffv2YbfbCQ0NZeDAgdjtdrTWzJw5k61bt+Ll5cXgwYO5/vrrAVizZg2LFi0CoHv37rRr1670n3wJMlcskgJSCIspw8Do0Qdzwv/Q336F6hx96Z1EAebGVeiFHzrOZb0Gutxs/HIlUojLYLTphIq6G736S8x1y0u0bZ1+Fr1lPapVW5S3TKgjRHlimibTp09n1KhRTJw4kY0bN5KYWPAe66CgIAYPHkybNoXvh+nWrRtDhw4t9HibNm2YNGkS48ePJzs7m9WrVwOwdetWjh49yuTJkxk4cCDTpk0D4OzZsyxcuJAxY8YwZswYFi5cyNmzpTdEv6SZKxb9/aZLCkghLKUaNofGLdFfLUCnu855xBno7T+gZ78FjVo41rQ1XK8kc73EQlhM9ewLTcId60fu3lFi7erv1kB2tgxlFaIcSkhIICQkhGrVqmG324mMjGTz5s0FtgkODqZ27dpFfhrdtGlTfHx8Cj0eHh6OUgqlFGFhYSQnJwOwZcsWbrvtNpRS1KtXj7S0NE6ePMm2bdto1qwZfn5++Pn50axZM7Zt21Y6T7qE5ReQEW2kgBTCSRjd+0D6WfTyz6yO4jL0np2Y74+D2mEY/x6JsntYHemKSBEpxGVSNhvGY89A1Wsw33sNffzoVbeZP6FOnXqoWqElkFII4UxSUlIIDAzM/z4wMJCUlJQSaz83N5f169fTokWL/OMFBQUVOt4/cwQEBJRojtJirlj8dwE54D9SQArhJFSt61Gt2qLjlqJTTlgdx+npxN8da0EGVsV44nmUd+EPB12F3BMpxBVQvhUwho7GHPM05pRXMUaMu7o1HRN+hcMHUX2eKLmQQgi3MW3aNBo2bEjDhg1LpL24uDji4uIAGDt2bIGC9ErZ7fYraift8084u3AmXrd0pNKwF1C28vPW5Ur7pDyTPinM2fsk79EnOLFlI54rF1Fp6KgyOaaz90lRco8e4uTklzF8KxDw8lvYqoaU+DHKsl/Kz5lYiDKmqlXHGPRfzEkvYE57A2PIKJRxZZ+O63XLwcfXMduZEKLcCQgIyB9qCpCcnExAQECJtL1gwQJOnz7NwIF/T/YVEBDAiRN/XxX463gBAQHs2rUr//GUlBQaNWpUqM2oqCiioqLyvz+/rSsVFBR02e2YKxejF8xE3XALOY8MJfnkqavO4UyupE/KO+mTwpy+TwwPVLs7yFy1lOxbu6CurVXqh3T6PvkHffok5tj/QnY2xrOvcVLZoRTyl0S/VK9evVjbyXBWIa6Catgc1Wsg/LwZveijK2pDnz2N3rIR1bodysu7hBMKIZxBaGgoR44cISkpidzcXOLj44mIiLjqdletWsX27duJiYnBOG9ihoiICNatW4fWmj179uDr60uVKlVo0aIF27dv5+zZs5w9e5bt27fnD4F1NucXkOqxp2UIqxBOTHW9F7x9MBfPtjqK09HpaZiTXoTUkxhP/A9VvfSL7LIgVyKFuEpG+zswDx9Ar1iEWb0WRmSHy9pff/ct5OagbutSSgmFEFaz2Wz069eP2NhYTNOkffv21KxZk3nz5hEaGkpERAQJCQmMHz+etLQ0fvzxR+bPn8+ECRMAeP755zl06BCZmZkMGjSIQYMG0aJFC6ZOnUrVqlV57rnnAGjVqhU9e/akZcuW/PTTTzz55JN4enoyePBgAPz8/OjRowcjR44EoGfPnvj5+VnTKRchBaQQrkX5+aP+1QO9aDZ6z05UvcZWR3IKOicb8+1YOHwQY+hoVGgDqyOVGKW11laHcBaHDx++qv1d7dJ6WXCXPtG5uZiTXoB9v2I8PeaiJ4nz+0Rrjfn8YKhQEduIcWUV1ym5y2vlckifFFaWQ3XE36729yMU/9/OXPk5esEMRwE54D8oe/n9vFv+jxcmfVKYq/SJzsrCHD0IAoIcc0WU4rqHrtAnOi8P873/g22bUAP+g9GqbakfU4azCuFilN2OMei/UCUI850x6JTjxdtxz044egh1myzrIYQQ7lRAClHeKC8vVLcHYP9u2Pqd1XEspbVGz3nXUUD2eqxMCsiyJkWkECVE+fljDB0N2VmYb8eiszIvuY9etxx8K6AiCi8uLoQQ7uSvApIbIqWAFMJFqciOcE1NzEUfoXNzrY5jGb34I/T6laiu92F0vMvqOKVCikghSpCqXgtj4DPw5++YMyahTfOC2+ozp9E/xaNu7oDy9CrDlEII4VzMb77ILyCNAU9LASmEi1I2G0b33nDsEHpjnNVxLGF+8wX664Wo27qg7n7I6jilRopIIUqYahqB6tkXfopHfzn3gtvp+FWQmytDWYUQbs385gv0/OlSQApRXjS/CcIaoZd+WqxRWeWJuelbx/ksPBL10OOlel+o1aSIFKIUqE7RqMiO6KVzMTdvKPRzbZqOoax1G5WbqZ6FEOJy5ReQ4VJAClFeKKUwevaF1JPobz63Ok6Z0b9sQX84GRo0wxjwnyteO9xVSBEpRClQSqEeHgyhDdAfTkIfSCi4we5fIOmILOshhHBbBQrIx6SAFKI8UaENoGVr9PLF6DOpVscpdTrhV8z3xsK112EMHoXy8LA6UqmTIlKIUqI8PDAGjwS/SphTYtGnUvJ/ptcuB7+KqBsiLUwohBDWMOOkgBSivDO694acLPSX86yOUqr0oQOYb70MlYMwnnoB5eNrdaQyUWZn7W3btjFz5kxM06Rjx45ER0cX+HlOTg5Tpkxh//79VKxYkZiYGIKDgwFYvHgxq1evxjAMHn30UVq0aHHRNpcvX86yZcs4duwY06ZNw9/fv6yephAFKP8qGENHY459FvOdMRhPx5J3KgW9bROqw50oD0+rIwohRJky475Az5sO4TdLASlEOaZCaqDadEavXY7ueBcq+BqrI5U4nZzkWCfcwwtj2Eso/8pWRyozZXIl0jRNpk+fzqhRo5g4cSIbN24kMTGxwDarV6+mQoUKvPXWW3Tt2pU5c+YAkJiYSHx8PBMmTOC5555j+vTpmKZ50Tbr16/P//73P6pWrVoWT0+Ii1I160C/4fyedIalc77kjYXfsdf3GplQRwjhdgoWkM9IASlEOafu6gU2G/rzj62OUuL0mVTMiS9AdpajgAyqZnWkMlUmZ++EhARCQkKoVs3RuZGRkWzevJkaNWrkb7NlyxbuvfdeAFq3bs2MGTPQWrN582YiIyPx8PAgODiYkJAQEhIc95ddqM06deqUxdMS4oLyTM3vJ7PYmZTOjqR0diUFcvbGYQDYz+TyxQ1PctNueNArkzpVvC1OK4QQpS996TwpIIVwM6pyAKrT3ehl89Gdo1HX1bU6UonQmemYb74EJ49jDHsZdW1tqyOVuTI5g6ekpBAYGJj/fWBgIHv37r3gNjabDV9fX86cOUNKSgp16/79ggsICCAlJSW/nYu1eSlxcXHExTnWsBk7dixBQUGX98T+wW63X3Ub5Y279EmuqdmTdJath1LZlpjK9sOnScvOA6BGJW/a1a1Ki+r+hH49Hc/vviHuvudZkJRBzFd/0KFuEP1b1+K6APcYQ38h7vJauRzSJ4VJn7gmM24JZ+ZNg5atpYAUws2o27uj1y7H/GwWxvBXXH7ZC52Tg/nOa/Dnfowhz6HCGlkdyRJufRaPiooiKioq//sTJ05cVXtBQUFX3UZ5U177JCdPk5CSwc5jGexISufX4xlk5poAXOvvSZtaFWlSzZfGwT4E+v49Q5d+sC/+7Ttwd81QorJNvvgthSW/pbAm4QS31fanV7MgrqnonvdJltfXytWQPimsJPqkevXqJZRGFIc+8id6/nS8WrUlp+9TUkAK4WaUjy/qzl7ouR/Azq3QJNzqSFdMm3mY09+AX7ej+g1DNbvR6kiWKZMzeUBAAMnJyfnfJycnExAQUOQ2gYGB5OXlkZ6eTsWKFQvtm5KSkr/vpdoUoqTk5JnsSc5k5zHH8NTfjmeQlacBqFXJk/Z1/M8Vjb5U8bnwfyvl4YlXeGvUiRP4edl4qHlV7qpfhcW/pvDl7pOsO3CaDtdX4v4mQQT7lf/poYUQ5Z+6piZGzItUimxP8qlTVscRQlhAtb0dvWqJ42pkoxYow/UWiNBao+e8Dz/Go+7rj3Fze6sjWapMisjQ0FCOHDlCUlISAQEBxMfH8+STTxbY5oYbbmDNmjXUq1ePTZs20bhxY5RSREREMHnyZO68805OnjzJkSNHCAsLQ2t9yTaFuFJZuSa7T2Scu6cxgz0nMsg+VzReV9mLqLDKNAn2oXGwL5W8r+6/kb+3nT4tg+nWIICFO5NZvvcUa35PpVNoZe5tEljgSqYQQrgi1ailXIEUwo0puwcq+mH01PHo79eiXLAA00s+Ra9bjvpXD4xOd1sdx3Jlcka32Wz069eP2NhYTNOkffv21KxZk3nz5hEaGkpERAQdOnRgypQpPPHEE/j5+RETEwNAzZo1ufnmmxk+fDiGYdC/f3+Mc59eFNUmwFdffcWSJUs4deoUzzzzDC1btmTQoEFl8VSFi8rMNfnt+Lmi8Vg6e5IzyTU1Crg+wIsudSvTJNiXRsG+VPSylUqGKj52HouoRnTDABbsSGZlwilW7U+lS93K9GgcSOWrLFaFEEIIIayiItqgV36O/vxjdMQtLrXMmbnqS/SXc1G3RKHu6W11HKegtNba6hDO4vDhw1e1v9y/VJiz9kl6Th6/Hc9gxzHHlcaE5AzyNBgKQgO8aRzsS5NgXxoG++DnWbJFY3H75NjZbOb+ksya31PxtCm61qvCPY0CS62ItZqzvlasJH1SmNwTaY2r/f0I8nouivRJYdInhZWnPtG/bsec8D/Uvf0wOkdfeocLKMs+Mb9fi572BrRojTHovyib874PK8vfkXJpQ7iFtOw8fs0vGtPZl5KJqcGmICzQh+iGATSp5kuDqj74ejjHyaGanydP3XwNPRoHMO/nZBbtSuHrvafo1qAK3RoEUKGEi1shhBBCiNKkGjaHxi3RXy1At4lC+fpZHemi9I6f0DMnQb0mGAOfduoCsqxJESnKpbNZeew8nn5uIpwMfj/pKBrtBtQL9KFHo8D8otHb7tw3d9fw9+I/barTs0kgn/58nLm/JPPl7pPc0yiQrvWq4OPh3PmFEEIIIf5i9OiL+UoMevlnqO59rI5zQXr/bsx3X4NrajmW8nCh4bdlQYpIUS6czsxlZ5JjuY2dSen8cTILDXgYivpB3tzXJJDGwb7UD/LBy8mLxgupXdmLEbfVYF9KJp9sP85H246z5NcUejQOpEvdyi77vIQQQgjhPlTNOqhWbdFxS9HtuqICnG/tX33kT8zJL0OlKhgxL6J8K1gdyelIEVlC5v58gl9TDlPBpqnsbaOyt53KPnYq/fX1ub/ljX7JOJWRe27m1HR2HsvgQGoWAJ42RYOqPjzQLIgmwb7UDfLG01a++jw0wJv/ta/J7hMZzNl+nBk/JfH5ryn0bBxI57BKeJSz5yuEEEKI8kXd/RB6ywb0kk9QfZ1rdQWdchxz4gtgt2MMexlVqYrVkZySFJElxNOu0Bp+P5lFamYuaTlmkdv52A0q+xQsLCt7/6PYPFd8+tgNlFJl/EycU0pGruN+xmOOK42Jp7MB8LYrGlT15dbrKtKkmi9hAT542Nyjz+oH+fByx1rsOJbOnO3H+WDLMRbvSub+pkG0v74SdsM9+kEIIYQQrkUFVUO17+q4GtkpGnVtLasjAaDPnnYUkJnpGM+8hqoaYnUkpyVFZAnp3iiQgbf9PSNSdp5JamYepzJzOZVx7u/MXE799VhmHn+mZrMjKYMzWXlFtulpUwUKy/OLzr++rnSuIK3gUb4KzuNpOfnLbexMSufwmRwAfD0MGlb1oeP1lWhczZfQAG+3L5aaVPNlTKdabDvqKCanfH+UhTuTeaBZELfW9sfm5v0jhCh5WmsyMzMxTbPYv3uOHTtGVlZWKScrWVprDMPA29u7XP2OFcIZqDvuRW+Iw1w8G9vQ0VbHQWdmOIawJic5hrDWrGN1JKcmRWQp8bQZVK1gULXCpReKzzU1qZm5fxedmXmcyihYdB47m8PuE46C0yxiURa7oQoNnf27+Cz4mJ+XDcPJfhkeO5vNzqQMfjlXNB476ygaK3gaNKrqy+11K9MkuAJ1qnhJUVQEpRQtr6lAixBfthxKY87Px5kYf4QFO5J5sFkQN9eq6HT/5kII15WZmYmHhwd2e/HfRtjtdmwuOLNhbm4umZmZ+Pj4WB1FiHJF+fmj/tUDvWg2es9OVL3GlmXRuTmY746FAwkY/x6JqtfEsiyuQopIJ2A3FIG+HgT6XrrgzDM1Z7L/KjIdBebfxafjqufJjNz8YbV5RRScNgX+/yw2zx9Se95VT38vW4kXbVprjp7NyV9uY+exdI6n5wJQ0ctG42Af7qpfhcbBvtSuLEXj5VBKcWMNP264tgKb/jzDJz+fYNyGw1xX2YsHmwdx07V+8mm6EOKqmaZ5WQWkK7Pb7S53BVUIV6E63oVevQzzsw8xRoyz5D2KNk30jEmwayuq75OoFq3KPIMrco/fAOWIzVD5Q1ovxdSas9nmueLyH1c6M3NJPfd1YmoWpzLzyCniEqcC/L0KDp39Z/H5V9Hp72Uv8n5ErTWHzmSz81hGftGYnOEoGit52WhczZd7gn1pHOxDrcpecsWsBBhKEVnLn1Y1KrL+wGnm/nKCMWsPUTfQmwebBdHymgpSTApRxrZt28bMmTMxTZOOHTsSHV1woe1du3Yxa9YsDhw4QExMDK1bt87/WWxsLHv37qVBgwaMGDEi//Hly5ezbNkyjh07xrRp0/D39wdgyZIlrF+/HnAUfImJiUyfPh0/Pz+B+N1yAAAZd0lEQVSGDBmCt7c3hmFgs9kYO3bsZT8Xdzt/uNvzFaKsKE8vVLcH0LOnwNbvIDyyTI+vtUbPnYrevB7Vow/GLVFlenxXJkVkOWYohb+XDX8vG7UqeV10W6016TnmefdsOq5qpmadf09nHntOZHAqM5fM3CIucQJ+nkZ+gVnJ246n53G2JZ7iZKbjvs8q3jaaVPOlcbAvTar5UsPfU345lyKboWhXpxK31vbn299TmffLCV76NpGGVX14qHkQTavJlNVClAXTNJk+fTqjR48mMDCQkSNHEhERQY0aNfK3CQoKYvDgwSxdurTQ/t26dSMrK4u4uLgCj9evX5/w8HBeeumlQtt369YNgC1btrBs2TL8/P5e1PuFF17ILzhdVWpqKosXL6Zv376Xtd8jjzzClClTqFSpUukEE0JcFhXZEf3NF5iLPsJodhOqDEc56GXz0N8uQ3W+B6NLjzI7bnkgRaQAHJ+yVvC0UcHTxrX+l15MNTPXLDCk9vx7OVOzHH//fjILVDbNQirkF47VK3pI0WgBm6GICq1M2+sqEbfvFPN3JDM67k+aVfPlweZBNKzqa3VEIcq1hIQEQkJCqFatGgCRkZFs3ry5QBEZHBwMFH3Vq2nTpuzcubPQ43XqXHrih40bN3LLLbdcaXSndfr0aWbPnl2oiMzNzb3oUNuPPvqolJMJIS6HstkwevTBnPIqesM3qHb/KpPjmmu+Rn/xCermDqgefcrkmOWJFJHiinjbDUIqehJS8eLbBQX9PWOtsJ6HTfGvelXocH0lViScYuHOZEasPMgN1SvwYLOqhAV6Wx1RiHIpJSWFwMDA/O8DAwPZu3dvqR83KyuLbdu20b9//wKPx8bGAtCpUyeiogoP34qLi8u/6jl27FiCggouBn7s2LEruieyJO+jfO211zhw4ACdO3fGw8MDLy8vKlWqREJCAt999x19+vTh8OHDZGVlMWDAAHr37g1AREQEK1asIC0tjQcffJCbbrqJLVu2EBISwqxZs4qcQMfLy6tQH5QEu91eKu26MumTwtyhT3SHf3Fy1dL/b+/+o6Oq7/yPP+9MYhKSEDIZICQEgfCjhZgGDAdl4xpMRA5BpCpUXWyp7Cq7LMp2TQHbFSrgjxIUC/HQ46L1iH4XXVGJQr9dCKhLCiIphxYKJYIoEoyZgZBAfs3cu39EInECDDDJDcnrcU4OM3c+93Pf8yYn73nP/YX//bW48u7CEXXhL7evNCd124qpen0V12T+HT1+trBd9362pfb8XekcGRORSxIR5mDS91yMG9SDDQdOsG6fh3///WfckBLDvde56R+vZlKkM9i1axdDhw5tcSjrokWLcLlcVFVVsXjxYpKSkhg2bFiL9XJzc1s0l9/9MrC+vr75Sqvmf72I9cXhi8ZiGAaW1fqpEAFjUwbguOefLjhm/vz57N+/nz/84Q+UlJTw4x//mOLiYvr164fP56OgoID4+Hhqa2vJy8tj/PjxuFwuLMvC7/fj9/s5dOgQK1eu5Ne//jUPPfQQ69ev5667Ag9pq6+vb5MvRPVFayDlJFBXyYl1xz9gPv1zKte+hGPiPRcceyU5sfbtbrqVR+r38U2fg+fkycuapyMKxe9KUlJSUOPURIp0YZFhDu4cnsD4IT1Yv/8E7/7Vy44vPiPr2ljuSXfTt/uFz6UVkeC4XC48Hk/zc4/Hg8vlavPtbtu2jaysrIBYAOLi4hg1ahRlZWUBTeTVKCMjg379vr1h+UsvvcTGjRsBOHbsGIcPHw7IeUpKCmlpTZfyT09P54svvmi/gEWkBSP1ezDyRqzfv4319+MxuvcI+Taszw5ivvAUJCbj+NdfYkToc87lUhMpInQLd3LPdW7yhsTzzl+9vHfAy7bPq8ke0J0fpblJjL34ebIicn6pqamUl5dTUVGBy+WipKSEhx9+uE23eebMGfbt28fs2bObl9XV1WFZFlFRUdTV1bFnzx7uvvvuK9rOxfYYnhUWFobP57uibV1It27fHv5WUlLCRx99RFFREVFRUdx9992t3qYj4pwPkE6nk7q6ujaLT0QuzvHD+zF378B6/w2Mex8M6dzW8aOYz/8KYmJxzFmIER1z8ZXkvNREikiz2Agn92f0ZNL34lm3z8uGv53gg8OnyE3twZS0BHpGX/xepiISyOl08sADD7BkyRJM02Ts2LGkpKSwdu1aUlNTyczMpKysjIKCAk6fPs2uXbt44403ePbZZwF4/PHH+fLLL6mrq2PmzJnMnDmTjIwMNmzYwPr16zl58iT5+fmMGDGCmTNnAvDxxx/zgx/8gMjIbw9Pr6qqoqCgAAC/309WVhYZGRntn5AQiI6OpqamptXXqquriYuLIyoqirKyMkpLS9s5OhG5HEZiX4yscVgf/B4r53aMXn1CMq91woP53AIwDBz/9gRGj4SLryQXpCZSRALERYbx05G9uOP7Lv77L5X8/7IqNh+q4rbBPbh7eAKuKP3pELlUI0eOZOTIkS2W/ehHP2p+PGjQIFatWtXquk888USryydMmMCECRNafS07O5vs7OwWy3r37s3SpUsvIeqOy+VyMWrUKG655RYiIyNbXEwiOzubV199lZtvvpnU1NSAvItIx2Xcfg/W9i1Y76zBeDD/iuezTldjLl8AZ2pwPPokRu/gzvmTC9MnQRE5L1dUGA+OSuSHwxJ44y+VbPzbCf6n7CQThsRz5zAXcZH6EyIi9iksLGx1eUREBGvWrGn1tR07dgBNTWhxcXHz8rN7cEXEXkYPF8a4yVjvrcUaNxmj/+DLnsuqr8NcsQgqjuF4ZCHGtamhC7SLc9gdgIh0fD2jw5k1ug8v3D6Qv+sXy/r9Xh589xBrdn9NTb3f7vBERESkEzHG/RBiumO+9UrQV3X+Lsvnw1z1DBz6G45/ehTje+khjrJrUxMpIkHrE3sNc8YksSJvAJnJ0by518OD737K2j9XcqZRzaSIiIhcOSOqG8bEe2D/Hth76ec0W6aJ9cpv4C+7MKb9M8bIMW0QZdemJlJELlnfuAjys5J5fkJ/0np34/U9lTz4zqes2+uhzmfaHZ6IiIhc5Yybb4OeiU17I83gP1tYloX15ktY27diTJ6G4+9va8Mouy41kSJy2frHR/LYzX0pGH8tQ9xRvLL7ax5691OK9ntp8KuZFBERkctjhIVjTJ4GRz/D2vFB0OtZG/8ba9N6jJzbMSZMacMIuzY1kSJyxQYnRPH42BSeHtePfnER/OeuCma+e4iNfztBo//yzmUQERGRrs3IzIJrB2G9swarseGi482P/oD19qsYo2/GmDoDwzDaIcquSU2kiITM93t2Y1FuPxblpNArJpxVO7/iX4oOsenTk/hNNZMiIiISPMPhwHHXT8D7NdaWDRcca5X+EevVFyDteozpj2A41Oa0JWVXREIuPTGap27tx4Kxfeke4WTF9uP863uH+OBwlZpJEbHF4MGXf5sAEbGP8f0fwPARWBvexDpT0+oY68CfMV8sgIFDcMycixGmW5C1NTWRItImDMNgZFIMBeOv5bGbk7nG6eDZknLmbDhMyeenMC/zkt0iIiLStTjumg5narA2vhXwmvX5p5grF0PPRByz/wMjIrL9A+yC1KaLSJsyDIPRfWMZlRxDyefV/L89lTzz0TEGxkdwX3pPMpOjdc6CiFyyJ598kqSkJKZPnw7AsmXLcDqdlJSUUFVVhc/n4+c//zm33aYrM4pc7YyUARijs7E2F2GNzQO3GwCr4hjm8oXQLQbHnF9hRMfaG2gXoiZSRNqFwzDIurY7N6bE8uFnp/ivP1ey+IOjDEmI5N50N6O6xXG6wU+40yDMYeBQYylyVfjPT77i8Im6i44zDCPom4YPiI/kHzN7X3DMpEmTWLBgQXMTWVRUxGuvvcaMGTOIjY3F6/Vy++23M27cOH1RJdIJGHfch/XJR1jrX4dHn8A66cV8bgFYFo5/+xWGy213iF2KmkgRaVdOh8HYgXHc1L87xYeqeOPPlfxqy1HYcrTlOAPCnQbhjqamsqm5dDQ9P7v8O68H87jVf1s8drRYfnYbZ5c5DTr9B1LLsvCZ4DOtIH/A57+Esd9d5rfwWec8vsDY9GQPszIT7E6RdABpaWlUVlZy/PhxPB4PcXFx9OrVi4ULF7Jjxw4Mw+D48eN8/fXX9OrVy+5wReQKGe7eGGPzsDYV0fDXuzELn4LqUzgeXYyR2Nfu8LocNZEiYoswh8G4QT0YO6A727+owR8eSdWpGhr9Fo2mic+ERr9J4zfNQ9Pybx+f/bfGZ7Zc9k0jcu7YUJ59aUCrTeZ5m9LzNrSO8za3Zx/HnIATVacu3JSdbbqsYBq5izSG36zflndlcRpN//dhZ9+rcc7j5p+mMRFhBtEOR4vXUt3RbRecXJaL7TE8KywsDJ/PF9JtT5w4kffff5+KigomTZrEunXr8Hg8bNy4kfDwcEaPHk19fX1Ityki9jEmTMH6302c+I9ZgIHj4ccx+uuiWXZQEykitgp3Oripf3fcbjeVlZUhn9+ympqiFo3od5rMpqb1/I3qd5vUFg1rK+s1mhb1Posa0zxnW2bAHKFo1s5tui78A1FhTXtzL9zABTvf2XWDHPvNvFe6F7etfk/k6jRp0iTy8/Pxer289dZbFBUV4Xa7CQ8PZ9u2bRw9evTik4jIVcOI6Y4xcSrWW69g/OO/YwzLsDukLktNpIh0aoZhEPbN3q/IDvYXz7QCG9SzTWej38IVH0/NqZPn3XPXFQ6tFbmQoUOHcvr0aRITE+nduzd33nknP/nJT8jJySE9PZ1BgwbZHaKIhJhx62TcE6fgbQjtkQ1yaTrYRyoRka7DYRhc4zS4xtn66253NJVGbfsGJXKV2bx5c/Njl8tFUVFRq+MOHjzYXiGJSBsyDANH9x6go1JspftEioiIiIiISNDURIqIiIiIiEjQ1ESKiIiIiIhI0NrtnMjdu3fz8ssvY5omOTk5TJ48ucXrjY2NrFy5kkOHDhEbG8ucOXOa7+v09ttvU1xcjMPh4Kc//SkZGRkXnLOiooLly5dTXV3NwIEDmT17NmFhOv1TREQkFCyrDe8D0wF1tfcrInIx7bIn0jRNVq9ezWOPPcZzzz3X6mW3i4uLiY6OZsWKFeTl5fHaa68BcPToUUpKSnj22Wf5xS9+werVqzFN84Jzrlmzhry8PFasWEF0dDTFxcXt8TZFRES6BIfDEfJ7PnZUPp8Ph0MHbomInKtdds+VlZU1X34bYMyYMezcuZO+ffs2j/nkk0+YMmUKADfccAMvvfQSlmWxc+dOxowZQ3h4OL169SIxMZGysjKAVudMTk5m7969PPLIIwBkZ2fz5ptvMm7cuPZ4qyIiIp1eZGQkdXV11NfXB32bmYiICOrr69s4stCyLAuHw0FkZKTdoYiIdCjt0kR6vV4SEhKanyckJARcavvcMU6nk27dulFdXY3X62Xw4MHN41wuF16vt3me785ZXV1Nt27dcDqdAeNFRETkyhmGQVRU1CWt43a7qdQl+UVEOoUufaLgpk2b2LRpEwBPP/00brf7iuYLCwu74jk6G+UkkHLSOuUlkHISSDkRERGxX7s0kS6XC4/H0/zc4/HgcrlaHZOQkIDf7+fMmTPExsYGrOv1epvXbW3O2NhYzpw5g9/vx+l0thj/Xbm5ueTm5jY/v9JvSPUtayDlJJBy0jrlJZByEigUOUlKSgpRNCIiIl1Tu5wpnpqaSnl5ORUVFfh8PkpKSsjMzGwx5vrrr2fr1q0AbN++neHDh2MYBpmZmZSUlNDY2EhFRQXl5eUMGjTovHMahsHw4cPZvn07AFu3bg3YloiIiIiIiFwew2qn61aXlpbyyiuvYJomY8eO5c4772Tt2rWkpqaSmZlJQ0MDK1eu5PDhw8TExDBnzpzmi+asW7eOLVu24HA4mD59OiNGjDjvnABfffUVy5cvp6amhgEDBjB79mzCw8Pb422KiIiIiIh0bpaEzNy5c+0OocNRTgIpJ61TXgIpJ4GUk6uX/u8CKSeBlJNAykkg5aR17ZkX3fhIREREREREgqYmUkRERERERILmXLhw4UK7g+hMBg4caHcIHY5yEkg5aZ3yEkg5CaScXL30fxdIOQmknARSTgIpJ61rr7y024V1RERERERE5Oqnw1lFREREREQkaGF2B9BZ7N69m5dffhnTNMnJyWHy5Ml2h2SrF154gdLSUuLi4li2bJnd4XQIlZWVFBYWcvLkSQzDIDc3lwkTJtgdlq0aGhpYsGABPp8Pv9/PDTfcwNSpU+0Oq0MwTZN58+bhcrmYN2+e3eF0CLNmzSIyMhKHw4HT6eTpp5+2OyQJgupjINXIQKqRgVQjz081siU76qOayBAwTZPVq1fzy1/+koSEBObPn09mZiZ9+/a1OzTbZGdnM378eAoLC+0OpcNwOp3cf//9DBw4kNraWubNm0d6enqX/j0JDw9nwYIFREZG4vP5ePzxx8nIyGDIkCF2h2a7DRs2kJycTG1trd2hdCgLFiyge/fudochQVJ9bJ1qZCDVyECqkeenGhmoveujDmcNgbKyMhITE+nduzdhYWGMGTOGnTt32h2WrYYNG0ZMTIzdYXQo8fHxzSc7R0VFkZycjNfrtTkqexmGQWRkJAB+vx+/349hGDZHZT+Px0NpaSk5OTl2hyJyRVQfW6caGUg1MpBqZOtUIzsG7YkMAa/XS0JCQvPzhIQEDh48aGNE0tFVVFRw+PBhBg0aZHcotjNNk7lz53L8+HFuu+02Bg8ebHdItvvd737HtGnT9A1rK5YsWQLArbfeSm5urs3RyMWoPsrlUI38lmpkINXI1rV3fVQTKdLO6urqWLZsGdOnT6dbt252h2M7h8PB0qVLOX36NAUFBXz++ef069fP7rBss2vXLuLi4hg4cCB79+61O5wOZdGiRbhcLqqqqli8eDFJSUkMGzbM7rBEJIRUI1tSjWxJNbJ1dtRHNZEh4HK58Hg8zc89Hg8ul8vGiKSj8vl8LFu2jJtuuonRo0fbHU6HEh0dzfDhw9m9e3eXLpAHDhzgk08+4U9/+hMNDQ3U1tbym9/8hocfftju0Gx39u9qXFwco0aNoqysTE1kB6f6KJdCNfL8VCObqEa2zo76qHMiQyA1NZXy8nIqKirw+XyUlJSQmZlpd1jSwViWxapVq0hOTmbixIl2h9MhnDp1itOnTwNNV6Hbs2cPycnJNkdlr/vuu49Vq1ZRWFjInDlzSEtL6/LFEZr2Tpw9dKmuro49e/Z06Q9SVwvVRwmWamQg1chAqpGB7KqP2hMZAk6nkwceeIAlS5ZgmiZjx44lJSXF7rBstXz5cvbt20d1dTUzZ85k6tSp3HLLLXaHZasDBw7w4Ycf0q9fP/Lz8wG49957GTlypM2R2efEiRMUFhZimiaWZXHjjTdy/fXX2x2WdEBVVVUUFBQATReYyMrKIiMjw+ao5GJUH1unGhlINTKQaqQEw676aFiWZbX5VkRERERERKRT0OGsIiIiIiIiEjQ1kSIiIiIiIhI0NZEiIiIiIiISNDWRIiIiIiIiEjQ1kSIiIiIiIhI0NZEiEpSpU6dy/Phxu8MQERHpUFQfpSvSfSJFrlKzZs3i5MmTOBzffheUnZ3NjBkzbIxKRETEXqqPIm1PTaTIVWzu3Lmkp6fbHYaIiEiHovoo0rbURIp0Mlu3bmXz5s3079+fDz/8kPj4eGbMmMF1110HgNfr5cUXX2T//v3ExMRwxx13kJubC4Bpmrzzzjts2bKFqqoq+vTpQ35+Pm63G4A9e/bw5JNPcurUKbKyspgxYwaGYdj2XkVERIKl+igSOmoiRTqhgwcPMnr0aFavXs3HH39MQUEBhYWFxMTE8Pzzz5OSksJvf/tbjh07xqJFi0hMTCQtLY333nuPbdu2MX/+fPr06cORI0eIiIhonre0tJSnnnqK2tpa5s6dS2ZmJhkZGTa+UxERkeCpPoqEhppIkavY0qVLcTqdzc+nTZtGWFgYcXFx5OXlYRgGY8aMoaioiNLSUoYNG8b+/fuZN28e11xzDf379ycnJ4cPPviAtLQ0Nm/ezLRp00hKSgKgf//+LbY3efJkoqOjiY6OZvjw4Xz22WcqkiIi0uGoPoq0LTWRIlex/Pz8gHM+tm7disvlanEYTc+ePfF6vZw4cYKYmBiioqKaX3O73Xz66acAeDweevfufd7t9ejRo/lxREQEdXV1oXorIiIiIaP6KNK2dIsPkU7I6/ViWVbz88rKSlwuF/Hx8dTU1FBbWxvwGkBCQgJfffVVu8crIiLSHlQfRUJDTaRIJ1RVVcXGjRvx+Xz88Y9/5Msvv2TEiBG43W6GDh3K66+/TkNDA0eOHGHLli3cdNNNAOTk5LB27VrKy8uxLIsjR45QXV1t87sREREJDdVHkdDQ4awiV7FnnnmmxX2w0tPTGTVqFIMHD6a8vJwZM2bQo0cPfvaznxEbGwvAI488wosvvshDDz1ETEwMU6ZMaT7kZ+LEiTQ2NrJ48WKqq6tJTk7m0UcfteW9iYiIXC7VR5G2ZVjn7tMXkave2UuYL1q0yO5QREREOgzVR5HQ0eGsIiIiIiIiEjQ1kSIiIiIiIhI0Hc4qIiIiIiIiQdOeSBEREREREQmamkgREREREREJmppIERERERERCZqaSBEREREREQmamkgREREREREJmppIERERERERCdr/AdXJATpOwLYvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5/5 [20:03<00:00, 234.73s/it]\n"
     ]
    }
   ],
   "source": [
    "results = [[compute_p_fail(p) for _ in range(repetitions)] for p in tqdm(pfails)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "    \n",
    "# means/stds for values\n",
    "means = np.mean(results, axis = 1)\n",
    "stds  = np.std (results, axis = 1)\n",
    "    \n",
    "plt.plot(pfails, means, label = 'Attack cdiff')\n",
    "plt.fill_between(pfails, means - stds, means + stds, alpha = 0.5)\n",
    "    \n",
    "plt.xlabel('Train input dropout')\n",
    "plt.ylabel('Attack success')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}