machine_learning_but_not_understanding.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "161dd614",
   "metadata": {},
   "source": [
    "# Machine learning, but not understanding\n",
    "\n",
    "CAP 6635 Artifical Intelligence Spring 2021\n",
    "Christian Garbin"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9eb16b8e",
   "metadata": {},
   "source": [
    "In the expression \"machine learning\", are the machines actually learning anything?\n",
    "\n",
    "In the book \"Artifical Intelligence, a guide for thinking humans\" Melanie Mitchell explains that\n",
    "\n",
    "> \"Learning in neural networks simply consists in gradually modifying the weights on connections so that each output’s error gets as close to 0 as possible on all training examples.\"\n",
    "\n",
    "Let's explore what \"learning\" means for machine learning, guided by Mitchell's book. More specifically, we will concentrate on \"deep learning\", a branch of machine learning that has powered most of the recent advances in artificial intelligence.\n",
    "\n",
    "Credit where credit is due: all quoted text comes from Mitchell's excellent book."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b43605d1",
   "metadata": {},
   "source": [
    "## An extremely short explanation of deep learning\n",
    "\n",
    "Deep learning uses layers of \"units\" (also called \"neurons\", but some people, including Mitchell and I, prefer the more generic \"units\" term, to not confuse with actual neurons) to extract patterns from labeled data. The internal layers are called \"hidden layers\". The last layer is called the \"output layer\", or the classification layer.\n",
    "\n",
    "In the following figure (from Mitchell's book, chapter 2), a neural network comprised of several hidden layers (only one shown) was trained to classify handwritten digits. The output layer has ten units, one for each possible digit.\n",
    "\n",
    "![Neural network](pics/neural-network.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e5f8e92",
   "metadata": {},
   "source": [
    "How does a neural network learn? Back to Mitchell’s quote:\n",
    "\n",
    "> \"Learning in neural networks simply consists in gradually modifying the weights on connections so that each output’s error gets as close to 0 as possible on all training examples.\"\n",
    "\n",
    "Going through the sentence pieces:\n",
    "\n",
    "- _training examples_: The labeled examples we present to the network to train it. For example, we present a picture of a square or a triangle and its corresponding label, \"square\" or \"triangle\", respectively.\n",
    "- _output's error_: How far the network's prediction is from the correct label of the example picture.\n",
    "- _weights on connections_: A large-precision decimal number (several digits after the dot) that adjusts the output of a unit in one layer to the input of a unit in the next layer. The weights are where the \"knowledge\" of the neural network is encoded.\n",
    "- _gradually modifying_: This is the neural network learning process. An algorithm carefully modifies the weights on the connections to get closer to the expected output. Repeating the adjustment step over time (many, many times) allows the network to learn from the training examples.\n",
    "\n",
    "## An important consequence of this process\n",
    "\n",
    "> The machine learns what it observes in the data rather than what you (the human) might observe. If there are statistical associations in the training data, even if irrelevant to the task at hand, the machine will happily learn those instead of what you wanted it to learn.\n",
    "\n",
    "Thus, neural networks are not \"learning\" in the sense that we would understand the term. They are not learning higher-level concepts from the samples used to train them. They are extracting patterns from the data presented to them during training (and they assume that the labels are correct). That's all.\n",
    "\n",
    "Or, as Mitchell puts more eloquently:\n",
    "\n",
    "> The phrase “barrier of meaning” perfectly captures an idea that has permeated this book: humans, in some deep and essential way, understand the situations they encounter, whereas no AI system yet possesses such understanding. While state-of-the-art AI systems have nearly equaled (and in some cases surpassed) humans on certain narrowly defined tasks, these systems all lack a grasp of the rich meanings humans bring to bear in perception, language, and reasoning. This lack of understanding is clearly revealed by the un-humanlike errors these systems can make; by their difficulties with abstracting and transferring what they have learned; by their lack of commonsense knowledge; ... The barrier of meaning between AI and human-level intelligence still stands today.\n",
    "\n",
    "Should we be concerned that deep learning is not \"learning\"? We should, if we don't understand what it implies for real-life applications.\n",
    "\n",
    "In the next sections we will explore how neural networks lack the grasp of \"rich meanings we humans bring to bear in perception\", illustrating it with some \"un-humanlike errors these systems can make; by their difficulties with abstracting and transferring what they have learned; by their lack of commonsense knowledge\"."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c45121f7",
   "metadata": {},
   "source": [
    "## Telling squares and triangles apart\n",
    "\n",
    "We will see how a neural network trained to tell squares and triangles apart behaves.\n",
    "\n",
    "For human beings, the pictures below show squares and triangles. Some are small, some are large, some are in a light background, some are in a darker background. But they are all clearly either a square or a triangle in a frame.\n",
    "\n",
    "![Squares and triangles](pics/squares-triangles.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1aa2a24f",
   "metadata": {},
   "source": [
    "In this section we will go through the typical process of training a neural network to classify squares and triangles:\n",
    "\n",
    "1. Get a dataset with labeled pictures of squares and triangles\n",
    "1. Split the dataset into a training set and a test set\n",
    "1. Train the network with the training set\n",
    "1. Validate its accuracy with the test set\n",
    "\n",
    "After we are done with that, we will predict similar images to see how the network handles them."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd2a1b46",
   "metadata": {},
   "source": [
    "First, load some of the frameworks we need and prepare the environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6d8850aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import images\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "# To increase reproducibility (although it's not guaranteed)\n",
    "# Based on https://stackoverflow.com/a/52897216\n",
    "seed_value = 0\n",
    "np.random.seed(seed_value)\n",
    "tf.random.set_seed(seed_value)\n",
    "                   \n",
    "images.create_datasets()             "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e96fe50d",
   "metadata": {},
   "source": [
    "### The \"squares vs. triangles\" training examples"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e977122",
   "metadata": {},
   "source": [
    "Load the square and triangle training examples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f474123d",
   "metadata": {},
   "outputs": [],
   "source": [
    "(train_set, train_label), (test_set, test_label) = images.get_upright_dataset(10)\n",
    "class_names = images.get_class_labels()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b5ac662",
   "metadata": {},
   "source": [
    "This is how some of the training images look like. Each picture is a square or a triangle in different positions. The dataset has hundreds of these pictures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d4e4a533",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x800 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def draw_pictures(pictures, labels, figsize, count, ncols):\n",
    "    plt.figure(figsize=figsize)\n",
    "    for i in range(count):\n",
    "        plt.subplot(count // ncols, ncols, i+1)\n",
    "        plt.xticks([])\n",
    "        plt.yticks([])\n",
    "        plt.imshow(pictures[i], cmap='gray', vmin=0, vmax=255)\n",
    "        if labels is not None:\n",
    "            plt.xlabel(class_names[labels[i]])\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "draw_pictures(train_set, train_label, (8,8), 25, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e51140e",
   "metadata": {},
   "source": [
    "### The \"square vs. triangle\" neural network"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70ddcf58",
   "metadata": {},
   "source": [
    "We will now train a [convolutional neural network](https://cs231n.github.io/convolutional-networks/) (CNN) to classify a picture as a \"square\" or as a \"triangle\", using the training examples. We chose a CNN architecture because it is well suited to image classification.\n",
    "\n",
    "The code is based on the [TensorFlow classification tutorial](https://www.tensorflow.org/tutorials/keras/classification) and the [TensorFlow CNN classification tutorial](https://www.tensorflow.org/tutorials/images/cnn)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2a5eaf34",
   "metadata": {},
   "outputs": [],
   "source": [
    "train_set, train_label = images.prepare_set(train_set, train_label)\n",
    "test_set, test_label = images.prepare_set(test_set, test_label)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4fe51d78",
   "metadata": {},
   "outputs": [],
   "source": [
    "INPUT_SHAPE = (images.CANVAS_SIZE, images.CANVAS_SIZE, 1)\n",
    "NUM_CLASSES = len(class_names)\n",
    "\n",
    "def get_model():\n",
    "    \"\"\"Return a compiled model, ready to be trained.\"\"\"\n",
    "    model = tf.keras.Sequential([\n",
    "        tf.keras.layers.Conv2D(64, (3, 3), activation='relu',\n",
    "                               input_shape=INPUT_SHAPE),\n",
    "        tf.keras.layers.MaxPooling2D((2, 2)),\n",
    "        tf.keras.layers.Conv2D(128, (3, 3), activation='relu'),\n",
    "        tf.keras.layers.Flatten(),\n",
    "        tf.keras.layers.Dense(32, activation='relu'),\n",
    "        tf.keras.layers.Dense(NUM_CLASSES, activation='softmax'),\n",
    "    ])\n",
    "    \n",
    "    model.compile(optimizer='adam',\n",
    "              loss=tf.keras.losses.SparseCategoricalCrossentropy(),\n",
    "              metrics=['accuracy'])\n",
    "    \n",
    "    return model\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "29dc5640",
   "metadata": {},
   "outputs": [],
   "source": [
    "callback = tf.keras.callbacks.EarlyStopping(\n",
    "    monitor='val_loss',\n",
    "    patience=2, verbose=1,\n",
    "    restore_best_weights=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "70825cc9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/5\n",
      "10/10 [==============================] - 2s 167ms/step - loss: 1.3369 - accuracy: 0.5098 - val_loss: 0.7072 - val_accuracy: 0.5075\n",
      "Epoch 2/5\n",
      "10/10 [==============================] - 2s 148ms/step - loss: 0.6836 - accuracy: 0.5749 - val_loss: 0.6310 - val_accuracy: 0.4925\n",
      "Epoch 3/5\n",
      "10/10 [==============================] - 1s 133ms/step - loss: 0.5642 - accuracy: 0.6824 - val_loss: 0.4645 - val_accuracy: 0.8209\n",
      "Epoch 4/5\n",
      "10/10 [==============================] - 1s 130ms/step - loss: 0.3293 - accuracy: 0.9072 - val_loss: 0.2488 - val_accuracy: 0.8955\n",
      "Epoch 5/5\n",
      "10/10 [==============================] - 1s 133ms/step - loss: 0.1002 - accuracy: 0.9902 - val_loss: 0.0573 - val_accuracy: 0.9851\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.src.callbacks.History at 0x29a35bb10>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BATCH_SIZE = 64\n",
    "EPOCHS = 5\n",
    "\n",
    "model = get_model()\n",
    "model.fit(train_set, train_label, batch_size=BATCH_SIZE, epochs=EPOCHS,\n",
    "          validation_data=(test_set, test_label), callbacks=[callback])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "200d6801",
   "metadata": {},
   "source": [
    "### How does the neural network perform?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0395e346",
   "metadata": {},
   "source": [
    "Before we started the training process, we set aside 10% of the pictures to use later. They are pictures that the neural network was not trained on. This is the _test set_. We use the test set to measure the performance of the neural network.\n",
    "\n",
    "A traditional measure of performance is \"accuracy\". It measures the percentage of pictures in the test set that were correctly classified.\n",
    "\n",
    "First, we ask the neural network to predict what the pictures are (more details on how that happens [here](https://github.com/fau-masters-collected-works-cgarbin/decision-threshold-effect-on-accuracy))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2779d62b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3/3 [==============================] - 0s 13ms/step\n"
     ]
    }
   ],
   "source": [
    "pred_prob = model.predict(test_set)\n",
    "pred_label = np.argmax(pred_prob, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42348052",
   "metadata": {},
   "source": [
    "Now we compare with the actual labels and calculate the accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e813f241",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Out of 67 pictures, 66 were classified correctly\n",
      "Accuracy = 98.5%\n"
     ]
    }
   ],
   "source": [
    "pred_correct = pred_label == test_label.flatten()\n",
    "num_labels = len(test_label)\n",
    "print('Out of {} pictures, {} were classified correctly'.format\n",
    "     (num_labels, sum(pred_correct)))\n",
    "print('Accuracy = {:.1%}'.format(sum(pred_correct) / num_labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4164542a",
   "metadata": {},
   "source": [
    "This is a pretty good accuracy for a relatively small neural network that can be trained quickly.\n",
    "\n",
    "Let's visualize where the neural network made the mistakes. The picture below shows the mistakes with a red border. All other pictures were classified correctly. Below each picture is the neural network's classification."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b7f34b1f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 67 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "for i in range(num_labels):\n",
    "    ax = plt.subplot(7, 10, i+1)\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    plt.grid(False)\n",
    "    if pred_label[i] != test_label[i][0]:\n",
    "        ax.patch.set_color('red')\n",
    "        ax.patch.set_linewidth(5)\n",
    "    plt.imshow(test_set[i], cmap='gray', vmin=0.0, vmax=1.0)\n",
    "    plt.xlabel(class_names[pred_label[i]])\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00622326",
   "metadata": {},
   "source": [
    "Despite the good accuracy, does the neural network understand the concept of what it is learning?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ff16d34",
   "metadata": {},
   "source": [
    "### When are squares not squares?\n",
    "\n",
    "When they are larger. At least for this neural network.\n",
    "\n",
    "In this section we will use the neural network we just trained to classify a set of squares. But there is a twist to these squares: they are larger than the ones we used in the training set.\n",
    "\n",
    "This is how some of them look like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "03d82598",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "large_squares = images.get_square_large_dataset()\n",
    "draw_pictures(large_squares, None, (8,8), 25, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c52adb00",
   "metadata": {},
   "source": [
    "Using the neural network, we classify the large squares."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7583a37b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3/3 [==============================] - 0s 20ms/step\n"
     ]
    }
   ],
   "source": [
    "large_squares, _ = images.prepare_set(large_squares)\n",
    "pred_prob = model.predict(large_squares)\n",
    "pred_label = np.argmax(pred_prob, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcb9bfc2",
   "metadata": {},
   "source": [
    "This is the accuracy of the classification."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c5d8f795",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Out of 77 pictures, 34 were classified correctly\n",
      "Accuracy = 44.2%\n"
     ]
    }
   ],
   "source": [
    "pred_correct = pred_label == images.LABEL_SQUARE\n",
    "num_labels = len(pred_label)\n",
    "print('Out of {} pictures, {} were classified correctly'.format\n",
    "     (num_labels, sum(pred_correct)))\n",
    "print('Accuracy = {:.1%}'.format(sum(pred_correct) / num_labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01d5c93e",
   "metadata": {},
   "source": [
    "That's significantly worse than the accuracy on upright squares.\n",
    "\n",
    "Below are all the squares in this set and how the neural network classified them. The ones with the red border were incorrectly classified as triangles (there are many of them)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "aa3ce598",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x1200 with 77 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,12))\n",
    "for i in range(77):\n",
    "    ax = plt.subplot(11, 8, i+1)\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    plt.grid(False)\n",
    "    if pred_label[i] != images.LABEL_SQUARE:\n",
    "        ax.patch.set_color('red')\n",
    "        ax.patch.set_linewidth(5)\n",
    "    plt.imshow(large_squares[i], cmap='gray', vmin=0.0, vmax=1.0)\n",
    "    plt.xlabel(class_names[pred_label[i]])\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9070689",
   "metadata": {},
   "source": [
    "### Why does this experiment matter?\n",
    "\n",
    "The simplest and fastest way to improve this neural network is to increase the size of the training and test sets. In this case, we should add larger squares to the training set and retrain the neural network. It will very likely perform better.\n",
    "\n",
    "But this does not address the fundamental problem: ***the neural network does not understand the concept of \"square\".***\n",
    "\n",
    "Quoting Mitchell again (emphasis added):\n",
    "\n",
    "> The phrase “barrier of meaning” perfectly captures an idea that has permeated this book: humans, in some deep and essential way, understand the situations they encounter, whereas no AI system yet possesses such understanding. While state-of-the-art AI systems have nearly equaled (and in some cases surpassed) humans on certain narrowly defined tasks, ***these systems all lack a grasp of the rich meanings humans bring to bear in perception, language, and reasoning. This lack of understanding is clearly revealed by the un-humanlike errors these systems can make; by their difficulties with abstracting and transferring what they have learned; by their lack of commonsense knowledge;*** ... The barrier of meaning between AI and human-level intelligence still stands today.\n",
    "\n",
    "Even if we collect lots and lots and lots of example, we are confronted with ***the long-tail problem***:\n",
    "\n",
    "> the vast range of possible unexpected situations an AI system could be faced with.\n",
    "\n",
    "For example, let's say we trained our autonomous driving system to recognize a school zone by the warning sign painted on the road ([source](https://virtualdriveoftexas.com/texas-school-zones/)):\n",
    "\n",
    "![](pics/school-spelled-right.png)\n",
    "\n",
    "Then, one day our autonomous driving system comes across these real-life examples (image sources: [1](https://www.anyvan.com/blog/whats-going-on/back-to-shcool-for-some/), [2](https://www.wibw.com/content/news/School-misspelled-at-Florida-crosswalk-508798331.html?ref=331)):\n",
    "\n",
    "| ![](pics/school-spelled-wrong-1.png) | ![](pics/school-spelled-wrong-2.png) |\n",
    "\n",
    "Any (well, most) human beings would still identify them as warning signs for school zones (presumably, the human would chuckle, then - hopefully - slow down).\n",
    "\n",
    "Would the autonomous driving system identify them correctly? The honest answer is \"we don't know\". It depends on how it was trained. Was it given these examples in the training set? In enough quantities to identify the pattern? Did the test set have examples? Were they classified correctly?\n",
    "\n",
    "But no matter how comprehensive we make the training and test sets and how methodically we inspect the classification results, we are faced with the fundamental problem: ***the neural network does not understand the concept of \"school zone warning\"***.\n",
    "\n",
    "The autonomous driving system lacks common sense.\n",
    "\n",
    "> ...humans also have a fundamental competence lacking in all current AI systems: common sense. We have vast background knowledge of the world, both its physical and its social aspects.\n",
    "\n",
    "The neural network may be _learning_, but it is definitely not _understanding_."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2742a519",
   "metadata": {},
   "source": [
    "## Not understanding \"squares\" - part 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e54d34b8",
   "metadata": {},
   "source": [
    "In the first section we changed the shape of an object. In this section we will not change the object. We will change the environment instead.\n",
    "\n",
    "We will train a neural network to classify squares and triangles again. This time they are in different environments, represented by different background colors. The squares are in a lighter background and the triangles are on a dark(er) background (we can think of the background as \"twilight\" and \"night\").\n",
    "\n",
    "The picture below shows how they look like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e39c5818",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(train_set, train_label), (test_set, test_label) = images.get_color_dataset(10)\n",
    "class_names = images.get_class_labels()\n",
    "\n",
    "draw_pictures(train_set, train_label, (8,8), 25, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19f36657",
   "metadata": {},
   "source": [
    "Following the same steps we used in the first section, we will train a neural network to classify the squares and triangles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "db512df6",
   "metadata": {},
   "outputs": [],
   "source": [
    "train_set, train_label = images.prepare_set(train_set, train_label)\n",
    "test_set, test_label = images.prepare_set(test_set, test_label)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "9562c39e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/5\n",
      "10/10 [==============================] - 2s 147ms/step - loss: 0.7370 - accuracy: 0.5212 - val_loss: 0.6325 - val_accuracy: 0.5075\n",
      "Epoch 2/5\n",
      "10/10 [==============================] - 1s 129ms/step - loss: 0.4810 - accuracy: 0.7932 - val_loss: 0.1361 - val_accuracy: 1.0000\n",
      "Epoch 3/5\n",
      "10/10 [==============================] - 1s 142ms/step - loss: 0.0327 - accuracy: 1.0000 - val_loss: 1.7382e-04 - val_accuracy: 1.0000\n",
      "Epoch 4/5\n",
      "10/10 [==============================] - 1s 133ms/step - loss: 4.0138e-05 - accuracy: 1.0000 - val_loss: 1.4341e-06 - val_accuracy: 1.0000\n",
      "Epoch 5/5\n",
      "10/10 [==============================] - 1s 137ms/step - loss: 6.4672e-07 - accuracy: 1.0000 - val_loss: 2.4731e-07 - val_accuracy: 1.0000\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.src.callbacks.History at 0x2db217f50>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model2 = get_model()\n",
    "model2.fit(train_set, train_label, batch_size=BATCH_SIZE, epochs=EPOCHS,\n",
    "           validation_data=(test_set, test_label), callbacks=[callback])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "061d9c4d",
   "metadata": {},
   "source": [
    "Now we calculate how accurate the neural network is using the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "2f1e2048",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3/3 [==============================] - 0s 13ms/step\n"
     ]
    }
   ],
   "source": [
    "pred_prob = model2.predict(test_set)\n",
    "pred_label = np.argmax(pred_prob, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e7346c05",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Out of 67 pictures, 67 were classified correctly\n",
      "Accuracy = 100.0%\n"
     ]
    }
   ],
   "source": [
    "pred_correct = pred_label == test_label.flatten()\n",
    "num_labels = len(test_label)\n",
    "print('Out of {} pictures, {} were classified correctly'.format\n",
    "     (num_labels, sum(pred_correct)))\n",
    "print('Accuracy = {:.1%}'.format(sum(pred_correct) / num_labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c42ee0e",
   "metadata": {},
   "source": [
    "A perfect score. All squares and triangles in the test set were classified correctly.\n",
    "\n",
    "So far, so good, but..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb137e7b",
   "metadata": {},
   "source": [
    "### In the dark, all squares are triangles\n",
    "\n",
    "What happens if the squares are now in the same environment as the triangles (all squares are in the \"night\" environment)?\n",
    "\n",
    "This is how the squares look like in the darker environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "994684c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dark_squares = images.get_square_dark_gray_dataset()\n",
    "draw_pictures(dark_squares, None, (8,8), 25, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc39ef1e",
   "metadata": {},
   "source": [
    "When we ask the neural network to classify these squares, this is what we get."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "24f2a7bb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11/11 [==============================] - 0s 21ms/step\n"
     ]
    }
   ],
   "source": [
    "dark_squares, _ = images.prepare_set(dark_squares)\n",
    "\n",
    "pred_prob = model2.predict(dark_squares)\n",
    "pred_label = np.argmax(pred_prob, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4896eff9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Out of 67 pictures, 0 were classified correctly\n",
      "Accuracy = 0.0%\n"
     ]
    }
   ],
   "source": [
    "pred_correct = pred_label == images.LABEL_SQUARE\n",
    "num_labels = len(test_label)\n",
    "print('Out of {} pictures, {} were classified correctly'.format\n",
    "     (num_labels, sum(pred_correct)))\n",
    "print('Accuracy = {:.1%}'.format(sum(pred_correct) / num_labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f9fa711",
   "metadata": {},
   "source": [
    "The performance is now abysmal. All squares are misclassified as triangles.\n",
    "\n",
    "To confirm, we can visualize the predictions. The wrong predictions have a red frame around them (all of them are wrong in this case)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "ee4b1a9f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NkUM/5NIQOfQzKaovUa4YjIi/R0RHRFQmdZzpq4iI3ohYEp4jNRINldPQ6PRTTj/VaaichqrTUDkNjU4/5fRTnYbKaWh0+kmT2lDSEuXvEXHDBAw1GxyNiOvrPcQUpKF0GhpOP+n0MzINpdPQyDSUTkPD6SedfkamoXQaGk4/Y1PWUNISpePKP9esWRONjUmfMuv09/fHvn37rl4rhtJQOQ2NTj/l9FOdhsppqDoNldPQ6PRTTj/VaaichkannzSpDSVdwX8+5KexsdFFL+HhUSPTUDoNDaefdPoZmYbSaWhkGkqnoeH0k04/I9NQOg0Np5+xKWvI08UAAAAAEliiAAAAACTwWB4AAABgWujv708+O2fOnKhUJvZJXpYoAAAAwJR36dKl2Lt3b/L5L37xi7FkyZIJncESBQAAAJg2/v3f/730ESavv/76pHxvSxQAAABg2pgzZ040NFS/xetEP43nn9xYFgAAACCBJQoAAABAAksUAAAAgARZ90QpimLMLy9U9rwlAAAAgKkoa4ny8ccfxx//+Mfk88uXL4+urq6cbwkAAABQF9mvztPQ0BBf//rXS8/94Q9/yP1WAAAAAHUzIS9x7Ck6AAAAwEw3IUsUAAAAgFo4dOhQ6Znz589Pyve2RAEAgCngvffei0uXLiWdbWxsjBtuuGGSJwKYWiqVSnzhC19IOjt//vzo6OiY8BksUQAAYAo4duxYVCqVaG5urnqur68vLl26ZIkCzDqNjY3JS5RJm6Gu3x0AALjq+uuvj0WLFlU9c/LkyXj77bdrNBEAn+aOsAAAAAAJLFEAAAAAEliiAAAAACTIvifK4OBg/OlPfyo919fXl/utAAAAAOoma4nS0tISX/ziF5PPt7e353w7AAAAgLrJWqI0NjbGkiVLJmoWAAAAgCnLPVEAAAAAEmTfEwUAAJgYg4OD0d/fX3oGgPqwRAEAgCniL3/5S/zlL38pPdfS0lKDaQD4LEsUAACYAm677bZ6jwBACUsUAACYAhoa3K4QYKqzRAEAAJhFent7429/+1vy+ZtvvtlTyOAKSxQAAIBZ5OLFi3H69OlYsmRJ6dmjR4/GTTfdVIOpYHqwRAEAAJhl5s6dG//7f//v0nPvv/9+DaaB6cMTLwEAAAASeCQKJCiKYkznK5XKJE0CAABAvViiQII333wzjh8/nnS2oaEhvvGNb0zyRAAAANSaJQokWrRoUelNtS5cuBB//vOfazQRAAAAtWSJAonmzJkTTU1NVc8MDAzUaBpgturv74//+q//Sj5/ww03RFdX1yROBAAwe1iiAMA0UhRFfPTRR3HTTTeV3n/pvffei76+vhpNBgAw81miAMA0dP3110dDQ/UX2Ttx4kSNpgEAmB0sUQAAAGaZwcHBOHfuXOm5sb5KJcx0ligAAACzTH9/f7z22mul58qeOgqzjSUKAADALNLV1RXf+MY36j0GTEvVn0wNAAAAQERYogAAAAAk8XQeSHTq1Kl44403qp4ZGBio0TQAAADUmiUKJPjc5z4XjY3l/3NpbGyMJUuW1GAi6qG3tzc++uij5PNLliwpfQlaAABg+rBEgQSLFi2KRYsW1XsM6uz06dPxt7/9Ldra2krPnj17NhYtWmSJwqQ5e/Zs6RmPjgMAmFiWKABj0NHREStXrqx6pr+/P/bs2VObgZiVGhsb49ChQ0lnLfIAACaOJQoATCNz586Nr3/96/UeAwBgVvLXUwAAAAAJPBIFAGAS9Pb2Jj/tKiLi3/7t36K9vX0SJwIAclmiAABMgoGBgejv749/+Zd/KT37xhtvxODgYA2mAgByWKIAAEySSqUSXV1dSecAgKnPPVEAAAAAEliiAAAAACTwdB6AMXLfAgAAmJ0sUQDG4MyZM/G73/2u3mMAAAB1YIkCkOj666+PxYsXJ59vbPSvWAAAmEn8CR8gUUNDQzQ0uJUUAADMVv5rAAAAACCBR6IAAEySoiji2LFjpefcsBoApgdLFACASdDY2Bjz5s2L999/v/Rsa2urpwsCwDRgiQIAMAna29ujp6en3mMAABPIX3kAAAAAJLBEAQAAAEhgiQIAAACQwBIFAAAAIIElCgAAAEACSxQAAACABJYoAAAAAAkaUw4VV/7Z398/iaNMb/+8NkXJudlKQ+U0NDr9lNNPdRoqp6HqNFROQ6PTTzn9VKehchoanX7SpDZUKYpi9DPNzRF9ffFeRNwwcbPNaEcj4vqIiKamiIsX6zzNFKChMdPQp+hnzPTzGRoaMw19hobGTEOfop8x089naGjMNPQp+hmXsoaSHomy5MoX6oiIygQON5MUEdEbl68Vw2monIZGp59y+qlOQ+U0VJ2GymlodPopp5/qNFROQ6PTT5rUhpKWKA1xZRNDVZ31HmAK01AaDY1MP2n0MzoNpdHQ6DSURkMj008a/YxOQ2k0NDL9pEtpqPoSpalpYiaZjVy7y1yH8XPtXIMcrt1lrsP4uXaXuQ7j59q5Bjlcu8tch/Fz7VyDXKNcv+r3RAEAAAAgIrzEMQAAAECSui9Rtm7dGitXrqz5992xY0csWLCg5t+XiachcuiHXBoil4bIoR9yaYhcs62hCV2iVCqVqr+2bt067HMeeuiheOmllyZyDKYxDZFDP+TSELk0RA79kEtD5NJQuaRX50l17Nixq79/7rnnYsuWLXHkyJGr72tvb7/6+6IoYmBgINrb24e8n9lNQ+TQD7k0RC4NkUM/5NIQuTRUbkIfibJo0aKrvzo7O6NSqVx9+80334yOjo7YvXt33HbbbdHc3Bx79uwZ9tCf/fv3x9133x1dXV3R2dkZd9xxR7z22mtDvk+lUomnn3467r333mhtbY3u7u7YtWvXkDO7du2K7u7uaGlpiTvvvDOeffbZqFQqcebMmVHnf+GFF2LVqlXR0tISN910U2zbti36+/sn8hJRQkPk0A+5NEQuDZFDP+TSELk0VK7m90R5+OGH4/HHH4833ngjVqxYMezjvb29sX79+tizZ0/s27cvuru7Y+3atdHb2zvk3LZt2+K+++6LgwcPxtq1a+P++++PU6dORUTEO++8E+vWrYt77rknDhw4EBs2bIhNmzZVnevVV1+NBx54IB588ME4fPhwPPXUU7Fjx47Yvn37xP3wTAgNkUM/5NIQuTREDv2QS0PkmvUNFZPkmWeeKTo7O6++/fLLLxcRUTz//PNDzj3yyCPFrbfeOurXGRgYKDo6OooXX3zx6vsioti8efPVt8+dO1dERLF79+6iKIpi48aNxfLly4d8nU2bNhURUZw+fXrE+e66667iscceG/I5O3fuLBYvXpzy4zIJNEQO/ZBLQ+TSEDn0Qy4NkUtDI5vQe6Kk6Onpqfrx48ePx+bNm+OVV16JEydOxMDAQJw/fz7efffdIec+vfFqa2uL+fPnx4kTJyIi4siRI7F69eoh52+//faq3/fAgQOxd+/eIVuqgYGBuHDhQpw/fz5aW1uTfj4mn4bIoR9yaYhcGiKHfsilIXLN9oZqvkRpa2ur+vH169fHhx9+GE888UQsW7Ysmpub46tf/Wr09fUNOTd37twhb1cqlRgcHBz3XOfOnYtt27bFt7/97WEfa2lpGffXZeJpiBz6IZeGyKUhcuiHXBoi12xvqOZLlDJ79+6NJ598MtauXRsREUePHo2TJ0+O6Wvccsst8Zvf/GbI+/bv31/1c1atWhVHjhyJm2++eWwDM+VoiBz6IZeGyKUhcuiHXBoi10xvaMotUbq7u2Pnzp3R09MTZ8+ejR/+8Icxb968MX2NDRs2xE9+8pPYuHFjfPe7343XX389duzYERGXt1sj2bJlS3zrW9+KpUuXxrp166KhoSEOHDgQhw4dikcffTT3x6KGNEQO/ZBLQ+TSEDn0Qy4NkWumN1TzV+cp84tf/CJOnz4dq1atiu985zvx/e9/PxYuXDimr3HjjTfGL3/5y/jVr34VK1asiJ/97GdX7+Tb3Nw84ud885vfjF//+tfx29/+NlavXh1r1qyJn/70p7Fs2bLsn4na0hA59EMuDZFLQ+TQD7k0RK6Z3lDlyp1xZ7zt27fHz3/+8zh69Gi9R2Ga0hA59EMuDZFLQ+TQD7k0RK6p0tCUezrPRHnyySdj9erVce2118bevXvjxz/+cXzve9+r91hMIxoih37IpSFyaYgc+iGXhsg1VRuasUuUt956Kx599NE4depULF26NH7wgx/Ej370o3qPxTSiIXLoh1waIpeGyKEfcmmIXFO1oVnzdB4AAACAHFPuxrIAAAAAU5ElCgAAAEACSxQAAACABJYoAAAAAAksUQAAAAASWKIAAAAAJLBEAQAAAEhgiQIAAACQwBIFAAAAIIElCgAAAECCxqof7eiI6Our0SgzTFNTRG9vvaeoPw2Nn4b0k0M/l2lo/DR0mYbGT0P6yaGfyzQ0fhrST65RGqq+ROnrc9HJoyFy6IdcGiKXhsihH3JpiBz6mRTVlyhXDEbE3yOiIyIqkzrO9FVERG9ELAnPkRqJhsppaHT6Kaef6jRUTkPVaaichkann3L6qU5D5TQ0Ov2kSW0oaYny94i4YQKGmg2ORsT19R5iCtJQOg0Np590+hmZhtJpaGQaSqeh4fSTTj8j01A6DQ2nn7EpayhpidJx5Z9r1qyJxsakT5l1+vv7Y9++fVevFUNpqJyGRqefcvqpTkPlNFSdhsppaHT6Kaef6jRUTkOj00+a1IaSruA/H/LT2Njoopfw8KiRaSidhobTTzr9jExD6TQ0Mg2l09Bw+kmnn5FpKJ2GhtPP2JQ15OliAAAAAAmsoQAAYIa4cOFCnD17Nvl8V1dXNDT4e1WAVJYoAAAwQ5w+fTr+8pe/xLx580rPnj9/Pr72ta9FU1NTDSYDmBksUQAAYAZpa2uLnp6eqmeKooj/+I//qNFEADOHx+4BAAAAJLBEAQAAAEjg6TwAANPEsWPH4r333ks+/5WvfMXLWQIREXHw4MG4ePFi0tnW1tb48pe/PMkTwfTk/1UBAKaJS5cuRVEUsXTp0qrniqKII0eO1GgqYDr4+OOPY+HChdHW1lb13EcffRS9vb01mgqmH0sUAIBppKmpKRYtWlT1TH9/vyUKMExnZ2d0dXVVPVMUhSUKVOGeKAAAAAAJPBIFAAAAGJdLly4ln61UKtP+Xl3Te3oAAGCYoijqPQIwS/zhD3+I/v7+pLMLFiyIlStXTu5Ak8wSBQAAZpBz587F7373u3qPAcwiK1eujPnz51c98+6778aZM2dqM9AkskQBAIAZ4rrrrovPfe5zyefnzp07idMAs0VDQ0M0NFS/5WrZx6cLSxQAAJghGhsbp/39BgCmspmxCgIAAACYZNbUAADTyKVLl+LkyZNVz7ipKDCSc+fOlZ75+OOPazAJTF+WKHDFpUuXku8qHRExb968SZwGAIZrbGyMgYGBePvtt0vPtrS01GAiYLpoaWmJDz74IOlsW1vbJE8D05clClzxt7/9Ld57772oVCqlZ4uiiG984xsz5uZIAEwPS5YsiSVLltR7DGAa+spXvlLvEWBGsESBT7nuuuviy1/+ctUzly5dir1799ZoIgAAAKYKf40On5LyKBQAAABmJ49EAQAAAMbtzTffjDlz5lQ909fXNyPuK2mJAgAAAIzL//7f/zv5VeGampomeZrJZ4kCAAAAjMvixYvrPUJNWaIAMGsNDg7Gxx9/nHx+3rx50djo/zoBAGYrfxIEYNY6f/58/OlPfyp9Dm9ExMDAQCxfvjy6urpqMBkAAFORJQoAs1pDQ0P8n//zf0rP/ed//mcNpgEAYCrzEscAAAAACTwSBT7lww8/jD/84Q9Vz6TeeRoAAICZxRIFrli0aFF0dnYmn69UKpM4DQAAAFONJQpc0d7eHu3t7fUeAwAAgCnKPVEAAAAAEliiAAAAACSwRAEAAABIYIkCAAAAkMCNZQGY1QYHB+P3v/996bm+vr4aTAMAwFRmiQLArNXS0hIrV65MPt/W1jZ5wwAAMOVZogAwazU2NsaCBQvqPQYAANOEJQrAp1y4cCHOnj2bfL6rqysaGtxeCgAAZgNLFIBPOX36dPzlL3+JefPmlZ49f/58fO1rX4umpqYaTAYAANRbzZYog4ODMTg4mHS2oaHB3+wCddPW1hY9PT1VzxRFEf/xH/9Ro4kAAICpoGZLlD/84Q9x8eLFpLPt7e2l/wEDAAAAUEs1fTrPl7/85fjc5z5X9cwHH3wQH3zwQY0mAgAAAEhT0yVKpVKJxsbq33LOnDk1mgYAAAAgnRuPAAAAACSwRAEAAABIYIkCAAAAkMASBQAAACBBTW8sCzBdFEVR7xEAAIApxhIF4DPOnTsXv/vd7+o9BgAAMMVYogB8ynXXXRef+9znks/PnTt3EqcBAACmkpouUf72t7/F3//+96pnLl68GJVKpUYTAQzV2NgYjY32ywAAwHA1+y+FG264Ifr7+5PONjU1TfI0AAAAAGNTsyXK9ddfX6tvBQAAADDhvMQxAAAAQAJLFAAAAIAEligAAAAACSxRAAAAABJYogAAAAAksEQBAAAASGCJAgAAAJDAEgUAAAAggSUKAAAAQAJLFAAAAIAEligAAAAACSxRAAAAABJYogAAAAAksEQBAAAASGCJAgAAAJDAEgUAAAAgQWPKoeLKP/v7+ydxlOntn9emKDk3W2monIZGp59y+qlOQ+U0VJ2GymlodPopp5/qNFROQ6PTT5rUhipFUYx+prk5oq8v3ouIGyZuthntaERcHxHR1BRx8WKdp5kCNDRmGvoU/YyZfj5DQ2Omoc/Q0Jhp6FP0M2b6+QwNjZmGPkU/41LWUNIjUZZc+UIdEVGZwOFmkiIieuPytWI4DZXT0Oj0U04/1WmonIaq01A5DY1OP+X0U52GymlodPpJk9pQ0hKlIa5sYqiqs94DTGEaSqOhkeknjX5Gp6E0GhqdhtJoaGT6SaOf0WkojYZGpp90KQ1VX6I0NU3MJLORa3eZ6zB+rp1rkMO1u8x1GD/X7jLXYfxcO9cgh2t3meswfq6da5BrlOtX/Z4oAAAAAESElzgGAAAASFL3JcrWrVtj5cqVNf++O3bsiAULFtT8+zLxNEQO/ZBLQ+TSEDn0Qy4NkWu2NTShS5RKpVL119atW4d9zkMPPRQvvfTSRI7BNKYhcuiHXBoil4bIoR9yaYhcGiqX9Oo8qY4dO3b1988991xs2bIljhw5cvV97e3tV39fFEUMDAxEe3v7kPczu2mIHPohl4bIpSFy6IdcGiKXhspN6CNRFi1adPVXZ2dnVCqVq2+/+eab0dHREbt3747bbrstmpubY8+ePcMe+rN///64++67o6urKzo7O+OOO+6I1157bcj3qVQq8fTTT8e9994bra2t0d3dHbt27RpyZteuXdHd3R0tLS1x5513xrPPPhuVSiXOnDkz6vwvvPBCrFq1KlpaWuKmm26Kbdu2RX9//0ReIkpoiBz6IZeGyKUhcuiHXBoil4bK1fyeKA8//HA8/vjj8cYbb8SKFSuGfby3tzfWr18fe/bsiX379kV3d3esXbs2ent7h5zbtm1b3HfffXHw4MFYu3Zt3H///XHq1KmIiHjnnXdi3bp1cc8998SBAwdiw4YNsWnTpqpzvfrqq/HAAw/Egw8+GIcPH46nnnoqduzYEdu3b5+4H54JoSFy6IdcGiKXhsihH3JpiFyzvqFikjzzzDNFZ2fn1bdffvnlIiKK559/fsi5Rx55pLj11ltH/ToDAwNFR0dH8eKLL159X0QUmzdvvvr2uXPniogodu/eXRRFUWzcuLFYvnz5kK+zadOmIiKK06dPjzjfXXfdVTz22GNDPmfnzp3F4sWLU35cJoGGyKEfcmmIXBoih37IpSFyaWhkE3pPlBQ9PT1VP378+PHYvHlzvPLKK3HixIkYGBiI8+fPx7vvvjvk3Kc3Xm1tbTF//vw4ceJEREQcOXIkVq9ePeT87bffXvX7HjhwIPbu3TtkSzUwMBAXLlyI8+fPR2tra9LPx+TTEDn0Qy4NkUtD5NAPuTRErtneUM2XKG1tbVU/vn79+vjwww/jiSeeiGXLlkVzc3N89atfjb6+viHn5s6dO+TtSqUSg4OD457r3LlzsW3btvj2t7897GMtLS3j/rpMPA2RQz/k0hC5NEQO/ZBLQ+Sa7Q3VfIlSZu/evfHkk0/G2rVrIyLi6NGjcfLkyTF9jVtuuSV+85vfDHnf/v37q37OqlWr4siRI3HzzTePbWCmHA2RQz/k0hC5NEQO/ZBLQ+Sa6Q1NuSVKd3d37Ny5M3p6euLs2bPxwx/+MObNmzemr7Fhw4b4yU9+Ehs3bozvfve78frrr8eOHTsi4vJ2ayRbtmyJb33rW7F06dJYt25dNDQ0xIEDB+LQoUPx6KOP5v5Y1JCGyKEfcmmIXBoih37IpSFyzfSGav7qPGV+8YtfxOnTp2PVqlXxne98J77//e/HwoULx/Q1brzxxvjlL38Zv/rVr2LFihXxs5/97OqdfJubm0f8nG9+85vx61//On7729/G6tWrY82aNfHTn/40li1blv0zUVsaIod+yKUhcmmIHPohl4bINdMbqly5M+6Mt3379vj5z38eR48erfcoTFMaIod+yKUhcmmIHPohl4bINVUamnJP55koTz75ZKxevTquvfba2Lt3b/z4xz+O733ve/Uei2lEQ+TQD7k0RC4NkUM/5NIQuaZqQzN2ifLWW2/Fo48+GqdOnYqlS5fGD37wg/jRj35U77GYRjREDv2QS0Pk0hA59EMuDZFrqjY0a57OAwAAAJBjyt1YFgAAAGAqskQBAAAASGCJAgAAAJDAEgUAAAAggSUKAAAAQAJLFAAAAIAEligAAAAACSxRAAAAABJYogAAAAAksEQBAAAASNBY9aMdHRF9fTUaZYZpaoro7a33FPWnofHTkH5y6OcyDY2fhi7T0PhpSD859HOZhsZPQ/rJNUpD1ZcofX0uOnk0RA79kEtD5NIQOfRDLg2RQz+TovoS5YrBiPh7RHRERGVSx5m+iojojYgl4TlSI9FQOQ2NTj/l9FOdhsppqDoNldPQ6PRTTj/VaaichkannzSpDSUtUf4eETdMwFCzwdGIuL7eQ0xBGkqnoeH0k04/I9NQOg2NTEPpNDScftLpZ2QaSqeh4fQzNmUNJS1ROq78c82aNdHYmPQps05/f3/s27fv6rViKA2V09Do9FNOP9VpqJyGqtNQOQ2NTj/l9FOdhsppaHT6SZPaUNIV/OdDfhobG130Eh4eNTINpdPQcPpJp5+RaSidhkamoXQaGk4/6fQzMg2l09Bw+hmbsoZcQQAAIMng4GCcPHky+XxHR0fMmzdvEicCqC1LFAAAIMnAwEAcPnw4WltbS89euHAhbr75ZksUYEaZckuUoihiYGAg+byHIwEAQG319PREQ0P110D505/+VKNpAGpnym0gPvjggzhy5Ejy+a997WvR1NQ0iRMBAAAATMElSkREW1tbfOUrXyk9t2fPnhpMAwAAADBFlyiVSqX0aTpFUdRoGgAAAICI6k9kBAAAACAiLFEAAAAAkliiAAAAACSwRAEAAABIMCVvLAsAAExtXugBmI0sUQAAgDF59dVXS88URRGLFy+uwTQAtWOJAgAAJGlsbIw1a9aM6TwwPRw4cCDOnz+fdLalpSW+8pWvTPJEU9OU/LfaJ598EgcPHqz3GAAAwKdUKpVoaWmp9xjAJOjr64uFCxdGZ2dn1XO9vb1x/PjxGk019Uy5JUpHR0fccMMNSWfnz58fDQ3ujQsAAAC52traoqurq/ScJcoU0t7eHu3t7fUeAwAAAGAID+MAAAAASGCJAgAAAJDAEgUAAAAggSUKAAAAQAJLFAAAAIAEligAAAAACabcSxwDAAAAtffRRx9FURRVz5w7d65G00xNligAAAAwy7W2tkZvb2/09vaWnm1ra6vBRFOTJQoAAADMcl/+8pfrPcK04J4oAAAAAAk8EoW6On/+fPzxj39MPr98+fK45pprJnEiAAAAGJklCnU1ODgYERE9PT2lZ19//fWr5wEAAKDWLFGYElpbW0vPVCqVGkwCANPf4OBgHD58OPn8woULY+HChZM4EQDMDJYoAAAzzODgYJw8eTKuv/760r+E+Mc//hHt7e01mgwApjdLFACAGeoLX/hCNDZW/+Pexx9/XKNpAGD68+o8AAAAAAksUQAAAAASWKIAAAAAJLBEAQAAAEjgxrIAMIFOnjwZR48eTT6/fPnymDt37iROBADARLFEoe6Kooi333679Fx/f38NpgHIc+nSpfjkk0/ihhtuqHquKIr461//GkVR1GgyAAByWaJQV42NjdHV1RUXL14sPXvNNddES0tLDaYCyNPU1JS8RAEAYPqwRKGuWlpa4stf/nK9xwCAGemTTz6JSqVS9czAwECNpgGA6c8SBSBRURRj+o+Nxkb/igXqp6GhIf785z8nnf3c5z43ydMAwMzgT/gAiY4ePTqmp198/etft0gB6qKxsTG+8Y1v1HsMAJhx/OkeYAwWLFgQy5cvr3pmcHAwfv/739doIgAAoFYsUQDGqOzRJV5JCgAAZqaGeg8AAAAAMB1YogAAAAAk8HQeAJhgAwMDcebMmXqPAQDABLNEAYAJVKlU4tKlS3Ho0KHSs169CYDJUhTFmO7T1tjYGJVKZRIngpnBn94AYAItWrQoFi1aVO8xAJjlPvroo3j99deTz69atSrmz58/eQPBDGGJAgAAMAM1NjbG1772tdJzv//972swDcwMligAAAAzVEOD1xKBiWSJAjAG586di4MHD1Y9UxRFjaYBAABqyRIFINH8+fPj+uuvTzrb2dnpb34AAGCGsUQBSLRgwYJYsGBBvccAAADqxF+TAgAAACSwRAEAAABIYIkCAAAAkMASBQAAACCBG8sCAADMQAMDA/GnP/2p9Fx/f38NpoGZwRIFAABghmltbY3u7u6ks4sXL46WlpZJnghmBksUAACAGaapqSmWLFlS7zFgxnFPFAAAAIAEligAAAAACSxRAAAAABJYogAAAAAksEQBAAAASGCJAgAAAJDAEgUAAAAggSUKAAAAQAJLFAAAAIAEjSmHiiv/7O/vn8RRprd/Xpui5NxspaFyGhqdfsrppzoNldNQdRoqp6HR6aecfqrTUDkNjU4/aVIbqhRFMfqZ5uaIvr54LyJumLjZZrSjEXF9RERTU8TFi3WeZgrQ0Jhp6FP0M2b6+QwNjZmGPkNDY6ahT9HPmOnnMzQ0Zhr6FP2MS1lDSY9EWXLlC3VERGUCh5tJiojojcvXiuE0VE5Do9NPOf1Up6FyGqpOQ+U0NDr9lNNPdRoqp6HR6SdNakNJS5SGuLKJoarOeg8whWkojYZGpp80+hmdhtJoaHQaSqOhkeknjX5Gp6E0GhqZftKlNFR9idLUNDGTzEau3WWuw/i5dq5BDtfuMtdh/Fy7y1yH8XPtXIMcrt1lrsP4uXauQa5Rrl/1e6IAAAAAEBFe4hgAAAAgiSUKAAAAQIK6L1G2bt0aK1eurPn33bFjRyxYsKDm35eJpyFy6IdcGiKXhsihH3JpiFyzraEJXaJUKpWqv7Zu3Trscx566KF46aWXJnIMpjENkUM/5NIQuTREDv2QS0Pk0lC5pJc4TnXs2LGrv3/uuediy5YtceTIkavva29vv/r7oihiYGAg2tvbh7yf2U1D5NAPuTRELg2RQz/k0hC5NFRuQh+JsmjRoqu/Ojs7o1KpXH37zTffjI6Ojti9e3fcdttt0dzcHHv27Bn20J/9+/fH3XffHV1dXdHZ2Rl33HFHvPbaa0O+T6VSiaeffjruvffeaG1tje7u7ti1a9eQM7t27Yru7u5oaWmJO++8M5599tmoVCpx5syZUed/4YUXYtWqVdHS0hI33XRTbNu2Lfr7+yfyElFCQ+TQD7k0RC4NkUM/5NIQuTRUrub3RHn44Yfj8ccfjzfeeCNWrFgx7OO9vb2xfv362LNnT+zbty+6u7tj7dq10dvbO+Tctm3b4r777ouDBw/G2rVr4/77749Tp05FRMQ777wT69ati3vuuScOHDgQGzZsiE2bNlWd69VXX40HHnggHnzwwTh8+HA89dRTsWPHjti+ffvE/fBMCA2RQz/k0hC5NEQO/ZBLQ+Sa9Q0Vk+SZZ54pOjs7r7798ssvFxFRPP/880POPfLII8Wtt9466tcZGBgoOjo6ihdffPHq+yKi2Lx589W3z507V0REsXv37qIoimLjxo3F8uXLh3ydTZs2FRFRnD59esT57rrrruKxxx4b8jk7d+4sFi9enPLjMgk0RA79kEtD5NIQOfRDLg2RS0Mjm9B7oqTo6emp+vHjx4/H5s2b45VXXokTJ07EwMBAnD9/Pt59990h5z698Wpra4v58+fHiRMnIiLiyJEjsXr16iHnb7/99qrf98CBA7F3794hW6qBgYG4cOFCnD9/PlpbW5N+PiafhsihH3JpiFwaIod+yKUhcs32hmq+RGlra6v68fXr18eHH34YTzzxRCxbtiyam5vjq1/9avT19Q05N3fu3CFvVyqVGBwcHPdc586di23btsW3v/3tYR9raWkZ99dl4mmIHPohl4bIpSFy6IdcGiLXbG+o5kuUMnv37o0nn3wy1q5dGxERR48ejZMnT47pa9xyyy3xm9/8Zsj79u/fX/VzVq1aFUeOHImbb755bAMz5WiIHPohl4bIpSFy6IdcGiLXTG9oyi1Ruru7Y+fOndHT0xNnz56NH/7whzFv3rwxfY0NGzbET37yk9i4cWN897vfjddffz127NgREZe3WyPZsmVLfOtb34qlS5fGunXroqGhIQ4cOBCHDh2KRx99NPfHooY0RA79kEtD5NIQOfRDLg2Ra6Y3VPNX5ynzi1/8Ik6fPh2rVq2K73znO/H9738/Fi5cOKavceONN8Yvf/nL+NWvfhUrVqyIn/3sZ1fv5Nvc3Dzi53zzm9+MX//61/Hb3/42Vq9eHWvWrImf/vSnsWzZsuyfidrSEDn0Qy4NkUtD5NAPuTRErpneUOXKnXFnvO3bt8fPf/7zOHr0aL1HYZrSEDn0Qy4NkUtD5NAPuTRErqnS0JR7Os9EefLJJ2P16tVx7bXXxt69e+PHP/5xfO9736v3WEwjGiKHfsilIXJpiBz6IZeGyDVVG5qxS5S33norHn300Th16lQsXbo0fvCDH8SPfvSjeo/FNKIhcuiHXBoil4bIoR9yaYhcU7WhWfN0HgAAAIAcU+7GsgAAAABTkSUKAAAAQAJLFAAAAIAEligAAAAACSxRAAAAABJYogAAAAAksEQBAAAASGCJAgAAAJDAEgUAAAAggSUKAAAAQILGqh/t6Ijo66vRKDNMU1NEb2+9p6g/DY2fhvSTQz+XaWj8NHSZhsZPQ/rJoZ/LNDR+GtJPrlEaqr5E6etz0cmjIXLoh1waIpeGyKEfcmmIHPqZFNWXKFcMRsTfI6IjIiqTOs70VUREb0QsCc+RGomGymlodPopp5/qNFROQ9VpqJyGRqefcvqpTkPlNDQ6/aRJbShpifL3iLhhAoaaDY5GxPX1HmIK0lA6DQ2nn3T6GZmG0mloZBpKp6Hh9JNOPyPTUDoNDaefsSlrKGmJ0nHln2vWrInGxqRPmXX6+/tj3759V68VQ2monIZGp59y+qluujf07rvvxpkzZ5LONjQ0xPLly8f8PTRU3XRvqBY0NDr9lNNPdRoqp6HR6SdNakNJV/CfD/lpbGx00Ut4eNTINJROQ8PpJ51+RjbdG7p48WJERFx33XVVz126dCmOHj2a9TNqaGTTvaFa0tBw+kmnn5FpKJ2GhtPP2JQ15AoCwDTQ0dERN9xQ/cG4n3zySRw9erRGEwEAzD7uuQMAAACQwBIFAAAAIIElCgAAAEACSxQAAACABJYoAAAAAAksUQAAAAASWKIAAAAAJGis9wAAQLmLFy/GmTNnqp65dOlSbYYBAJilLFEAYIqbM2dOfPjhh6VLlIiIuXPnTv5AAACzlCUKAExxX/ziF+OLX/xivccAAJj13BMFAAAAIIElCgAAAEACSxQAAACABJYoAAAAAAksUQAAAAASWKIAAAAAJLBEAQAAAEhgiQIAAACQoLHeAwAAzBR//vOf4+OPP04629LSEj09PZM8EQAwkSxRAAAmSH9/f3z+85+Pa6+9tuq5jz76KN5///0aTQUATBRLFACACTRv3ryYP39+1TN9fX01mgaYTf7nf/4n+d8vc+fOjRtvvHGSJ4KZxz1RAAAAZoB//OMf8fHHH8fg4GDVX+fPn4/jx4/Xe1yYljwSBQAAprFz585FURRJZxsbG2PevHmTPBH1tHjx4li0aFHVMydPnoy33367RhPBzGKJAgAA09jrr78eg4ODUalUqp4bHByMzs7OWLlyZW0GA5iBLFEAAGCaW7lyZem9eN599904depUjSYCmJncEwUAAAAggSUKAAAAQAJLFAAAAIAE7okCADCBPvzww+jr66t65vz58zWaBgCYSJYowKxz6dKlOHfuXPL5jo6OaGz0r0ug3Pz58+OTTz5Junln2U1AAYCpx38VALPORx99FIcOHYqmpqbSs319fXH77bdbogBJbrnllnqPAMxy/f39ceHChdIzwPj4rwJgVmppaYk1a9aUnvvd735Xg2kAAPJVKpV4++234+233y49O2/evBpMBDOPJQoAAMAMcNttt9V7BJjxLFEAAGCaO3jwYDQ0VH/hzYGBgejo6KjRRNRDpVKp9wgw41miAADANLZ8+fLks+7xBUwFRVHEgQMHoiiKpPPXXXddXH/99ZM8VRr/FgUAgGlswYIF9R4BYMzOnDkTy5YtK13uHj9+PD755JMaTVVu1i1RBgcH4+TJk8nnOzo63HQJAAAAJtjnP//50lfMPHfuXI2mSTPrligDAwNx+PDhaG1tLT174cKFuPnmmy1RAAAAgNm3RPmnnp6e0ptv/elPf6rRNAAAAMBUV32LAAAAAEBEzOJHogCz24ULF+LVV18tPTc4OFiDaQAAgOnAEgWYdRYsWBA9PT3J51taWiZxGgAAYLqwRAFmncbGxmhvb6/3GAAAwDRjicK08cEHH0R/f3/S2aampli4cOEkTwQAAMBsYonCtPHOO+/EnDlzorGxeraXLl2KOXPmWKIAAABMYWfPnk3677uyM7U0dSaBBDfddFN0dXVVPXPs2LF4//33azQRAAAAYzV37tx48803k862tbVN8jTpZvUSpSiKeo8AAAAAs0qlUol///d/r/cY4zJrlygpL21aFEUsXry4BtMAAAAAU92sW6I0NjbGmjVrxnQeAAAAYNZtCCqVSrS0tNR7DAAAAGCaaaj3AAAAAADTgSUKAAAAQAJLFAAAAIAEs+6eKEx/g4ODVT/upasBAACYDJYoTCuHDh1KOtfe3j7JkwAAADDbWKIwbaxevTr5USaVSmWSpwEAAGC2sURh2mhslCsAAAD148ayAAAAAAksUQAAAAASWKIAAAAAJLBEAQAAAEhgiQIAAACQwBIFAAAAIIElCgAAAEACSxQAAACABJYoAAAAAAksUQAAAAASWKIAAAAAJGhMOVRc+Wd/f/8kjjK9/fPaFCXnZisNldPQ6PRTTj/VaaichqrTUDkNjU4/5fRTnYbKaWh0+kmT2lClKIrRzzQ3R/T1xXsRccPEzTajHY2I6yMimpoiLl6s8zRTgIbGTEOfop8x089naGjMNPQZGhozDX2KfsZMP5+hoTHT0KfoZ1zKGkp6JMqSK1+oIyIqEzjcTFJERG9cvlYMp6FyGhqdfsrppzoNldNQdRoqp6HR6aecfqrTUDkNjU4/aVIbSlqiNMSVTQxVddZ7gClMQ2k0NDL9pNHP6DSURkOj01AaDY1MP2n0MzoNpdHQyPSTLqWh6kuUpqaJmWQ2cu0ucx3Gz7VzDXK4dpe5DuPn2l3mOoyfa+ca5HDtLnMdxs+1cw1yjXL9qt8TBQAAAICI8BLHAAAAAEksUQAAAAAS1H2JsnXr1li5cmXNv++OHTtiwYIFNf++TDwNkUM/5NIQuTREDv2QS0Pkmm0NTegSpVKpVP21devWYZ/z0EMPxUsvvTSRYzCNaYgc+iGXhsilIXLoh1waIpeGyiW9xHGqY8eOXf39c889F1u2bIkjR45cfV97e/vV3xdFEQMDA9He3j7k/cxuGiKHfsilIXJpiBz6IZeGyKWhchP6SJRFixZd/dXZ2RmVSuXq22+++WZ0dHTE7t2747bbbovm5ubYs2fPsIf+7N+/P+6+++7o6uqKzs7OuOOOO+K1114b8n0qlUo8/fTTce+990Zra2t0d3fHrl27hpzZtWtXdHd3R0tLS9x5553x7LPPRqVSiTNnzow6/wsvvBCrVq2KlpaWuOmmm2Lbtm3R398/kZeIEhoih37IpSFyaYgc+iGXhsiloXI1vyfKww8/HI8//ni88cYbsWLFimEf7+3tjfXr18eePXti37590d3dHWvXro3e3t4h57Zt2xb33XdfHDx4MNauXRv3339/nDp1KiIi3nnnnVi3bl3cc889ceDAgdiwYUNs2rSp6lyvvvpqPPDAA/Hggw/G4cOH46mnnoodO3bE9u3bJ+6HZ0JoiBz6IZeGyKUhcuiHXBoi16xvqJgkzzzzTNHZ2Xn17ZdffrmIiOL5558fcu6RRx4pbr311lG/zsDAQNHR0VG8+OKLV98XEcXmzZuvvn3u3LkiIordu3cXRVEUGzduLJYvXz7k62zatKmIiOL06dMjznfXXXcVjz322JDP2blzZ7F48eKUH5dJoCFy6IdcGiKXhsihH3JpiFwaGtmE3hMlRU9PT9WPHz9+PDZv3hyvvPJKnDhxIgYGBuL8+fPx7rvvDjn36Y1XW1tbzJ8/P06cOBEREUeOHInVq1cPOX/77bdX/b4HDhyIvXv3DtlSDQwMxIULF+L8+fPR2tqa9PMx+TREDv2QS0Pk0hA59EMuDZFrtjdU8yVKW1tb1Y+vX78+Pvzww3jiiSdi2bJl0dzcHF/96lejr69vyLm5c+cOebtSqcTg4OC45zp37lxs27Ytvv3tbw/7WEtLy7i/LhNPQ+TQD7k0RC4NkUM/5NIQuWZ7QzVfopTZu3dvPPnkk7F27dqIiDh69GicPHlyTF/jlltuid/85jdD3rd///6qn7Nq1ao4cuRI3HzzzWMbmClHQ+TQD7k0RC4NkUM/5NIQuWZ6Q1NuidLd3R07d+6Mnp6eOHv2bPzwhz+MefPmjelrbNiwIX7yk5/Exo0b47vf/W68/vrrsWPHjoi4vN0ayZYtW+Jb3/pWLF26NNatWxcNDQ1x4MCBOHToUDz66KO5PxY1pCFy6IdcGiKXhsihH3JpiFwzvaGavzpPmV/84hdx+vTpWLVqVXznO9+J73//+7Fw4cIxfY0bb7wxfvnLX8avfvWrWLFiRfzsZz+7eiff5ubmET/nm9/8Zvz617+O3/72t7F69epYs2ZN/PSnP41ly5Zl/0zUlobIoR9yaYhcGiKHfsilIXLN9IYqV+6MO+Nt3749fv7zn8fRo0frPQrTlIbIoR9yaYhcGiKHfsilIXJNlYam3NN5JsqTTz4Zq1evjmuvvTb27t0bP/7xj+N73/tevcdiGtEQOfRDLg2RS0Pk0A+5NESuqdrQjF2ivPXWW/Hoo4/GqVOnYunSpfGDH/wgfvSjH9V7LKYRDZFDP+TSELk0RA79kEtD5JqqDc2ap/MAAAAA5JhyN5YFAAAAmIosUQAAAAASWKIAAAAAJLBEAQAAAEhgiQIAAACQwBIFAAAAIIElCgAAAEACSxQAAACABJYoAAAAAAksUQAAAAASNFb9aEdHRF9fjUaZYZqaInp76z1F/Wlo/DSknxz6uUxD46ehyzQ0fhrSTw79XKah8dOQfnKN0lD1JUpfn4tOHg2RQz/k0hC5NEQO/ZBLQ+TQz6SovkS5YjAi/h4RHRFRmdRxpq8iInojYkl4jtRINFROQ6PTTzn9VKehchqqTkPlNDQ6/ZTTT3UaKqeh0eknTWpDSUuUv0fEDRMw1GxwNCKur/cQU5CG0mloOP2k08/INJROQyPTUDoNDaefdPoZmYbSaWg4/YxNWUNJS5SOK/9cs2ZNNDYmfcqs09/fH/v27bt6rRhKQ+U0NDr9lNNPdRoqp6HqNFROQ6PTTzn9VKehchoanX7SpDaUdAX/+ZCfxsZGF72Eh0eNTEPpNDScftLpZ2QaSqehkWkonYaG0086/YxMQ+k0NJx+xqasIU8XAwAAAEhgiQIAAACQwGN5mNX6+/uTzzY0NERDg70jAFBfRVHEwMBA8vk5c+ZEpeJJDgATwRKFWasoitizZ0/y+c9//vPR3d09iRMBAJT78MMP49ChQ8nnb7/99mhtbZ3EiQBmD0sUZr3/7//7/2Lu3LlVz/zlL3+p0TQAAOWam5tj9erVped+//vf12AagNnDEoVZb86cOaV3qfYQWABgKqlUKl5lA6AO3OABAAAAIIH1NQDANNHb2xsfffRR8vklS5a4KToATCBLFACAaeL06dPxt7/9Ldra2krPnj17NhYtWmSJAgATyBIFAGAa6ejoiJUrV1Y909/fP6ZXoAMA0virCQAAAIAEligAAAAACTydBwAAYIbp7e2NQ4cOJZ//t3/7t2hvb5/EiWBmsERh1jt8+HDpTffOnTsX1113XY0mAgCorq+vLw4ePFh6bnBwsAbTMBUNDAxEf39//Mu//Evp2TfeeEMrkMgShVntC1/4QtK5+fPn28wDAFNCa2trLF26NOns/PnzY+7cuZM8EVNVpVKJrq6upHNAGksUZq1KpZK8RAEAmCpaW1v9GQagTtxYFgAAACCBR6IAAEwz7l0AAPVhiQIAMI2cOXMmfve739V7DACYlSxRAACmieuvvz4WL16cfL6x0R/1AGAi+X9WAIBpoqGhIRoa3NIOAOrF/wsDAAAAJPBIFAAAgBmoKIo4duxY6Tk3q4Z0ligAAAAzTGNjY8ybNy/ef//90rOtra2eKgiJLFEAAABmmPb29ujp6an3GDDjWDcCAAAAJLBEAQAAAEhgiQIAAACQwBIFAAAAIIElCgAAAEACSxQAAACABJYoAAAAAAksUQAAAAASWKIAAAAAJLBEAQAAAEhgiQIAAACQwBIFAAAAIIElCgAAAEACSxQAAACABJYoAAAAAAksUQAAAAASWKIAAAAAJGis1Tc6ePBgXLx4Melsa2trfPnLX57kiQAAAADS1WyJ8vHHH8fChQujra2t6rmPPvooent7azQVAAAAQJqaLVEiIjo7O6Orq6vqmaIoLFEAAACAKcc9UQAAAAAS1PSRKADTzaVLl5LPViqVaGz0r1UAAKaf/v7+KIoi+fzcuXMncZqpy5/2Aar4z//8zxgcHEw6u3DhwvjXf/3XSZ4IAAAm3p///Of4+OOPk862tLTEmjVrJnmiqckSBaBET09PtLa2Vj3z17/+Nfr6+mo0EQAATLxbbrkl/tf/+l9Vz3z44Yfx3//93zWaaOqxRAEo0dDQEA0NbiE1U/y///f/4uzZs0ln586dGz09PZM8EQDA1FCpVEr/3FupVGo0zdRkiQLArNLX1xfXXHNNXHvttVXPffLJJ/G3v/2tRlMBADAdWKIAMOu0trZGV1dX1TNnzpypzTAAAEwbNV2inDt3rvRM6o1sAAAAAGqpZkuUlpaW+OCDD5LOtrW1TfI0AAAAAGNTsyXKV77ylVp9KwAAAIAJ5+UmAAAAABJYogAAAAAk8Oo8ACX+3//7f9HQUH3nfPHixViwYEFtBgIAgEnwP//zP/H+++9XPdPf31+jaaYmSxSAKm6++ebks/PmzZvESQAAYPIsW7YseUFS9heMM5klCkAVS5YsqfcITIKzZ8/GsWPHqp755JNPajQNAED9LVy4sN4jTAuWKADMKq2trdHb21v6UNWIiPb29hpMBADAdGGJAsCscsstt9R7BAAApqnZ+0QmAAAAgDGwRAEAAABIYIkCAAAAkMASBQAAACCBJQoAAABAAksUAAAAgASWKAAAAAAJGlMOFVf+2d/fP4mjTG//vDZFybnZSkPlNDQ6/ZTTT3UaKqeh6jRUTkOj0085/VSnoXIaGp1+0qQ2VCmKYvQzzc0RfX3xXkTcMHGzzWhHI+L6iIimpoiLF+s8zRSgoTHT0KfoZ8z08xkaGjMNfYaGxkxDn6KfMdPPZ2hozDT0KfoZl7KGkh6JsuTKF+qIiMoEDjeTFBHRG5evFcNpqJyGRqefcvqpTkPlNFSdhsppaHT6Kaef6jRUTkOj00+a1IaSligNcWUTQ1Wd9R5gCtNQGg2NTD9p9DM6DaXR0Og0lEZDI9NPGv2MTkNpNDQy/aRLaaj6EqWpaWImmY1cu8tch/Fz7VyDHK7dZa7D+Ll2l7kO4+fauQY5XLvLXIfxc+1cg1yjXL/q90QBAAAAICK8xDEAAABAkrovUbZu3RorV66s+ffdsWNHLFiwoObfl4mnIXLoh1waIpeGyKEfcmmIXLOtoQldolQqlaq/tm7dOuxzHnrooXjppZcmcgymMQ2RQz/k0hC5NEQO/ZBLQ+TSULmkV+dJdezYsau/f+6552LLli1x5MiRq+9rb2+/+vuiKGJgYCDa29uHvJ/ZTUPk0A+5NEQuDZFDP+TSELk0VG5CH4myaNGiq786OzujUqlcffvNN9+Mjo6O2L17d9x2223R3Nwce/bsGfbQn/3798fdd98dXV1d0dnZGXfccUe89tprQ75PpVKJp59+Ou69995obW2N7u7u2LVr15Azu3btiu7u7mhpaYk777wznn322ahUKnHmzJlR53/hhRdi1apV0dLSEjfddFNs27Yt+vv7J/ISUUJD5NAPuTRELg2RQz/k0hC5NFSu5vdEefjhh+Pxxx+PN954I1asWDHs4729vbF+/frYs2dP7Nu3L7q7u2Pt2rXR29s75Ny2bdvivvvui4MHD8batWvj/vvvj1OnTkVExDvvvBPr1q2Le+65Jw4cOBAbNmyITZs2VZ3r1VdfjQceeCAefPDBOHz4cDz11FOxY8eO2L59+8T98EwIDZFDP+TSELk0RA79kEtD5Jr1DRWT5Jlnnik6Ozuvvv3yyy8XEVE8//zzQ8498sgjxa233jrq1xkYGCg6OjqKF1988er7IqLYvHnz1bfPnTtXRESxe/fuoiiKYuPGjcXy5cuHfJ1NmzYVEVGcPn16xPnuuuuu4rHHHhvyOTt37iwWL16c8uMyCTREDv2QS0Pk0hA59EMuDZFLQyOb0HuipOjp6an68ePHj8fmzZvjlVdeiRMnTsTAwECcP38+3n333SHnPr3xamtri/nz58eJEyciIuLIkSOxevXqIedvv/32qt/3wIEDsXfv3iFbqoGBgbhw4UKcP38+Wltbk34+Jp+GyKEfcmmIXBoih37IpSFyzfaGar5EaWtrq/rx9evXx4cffhhPPPFELFu2LJqbm+OrX/1q9PX1DTk3d+7cIW9XKpUYHBwc91znzp2Lbdu2xbe//e1hH2tpaRn312XiaYgc+iGXhsilIXLoh1waItdsb6jmS5Qye/fujSeffDLWrl0bERFHjx6NkydPjulr3HLLLfGb3/xmyPv2799f9XNWrVoVR44ciZtvvnlsAzPlaIgc+iGXhsilIXLoh1waItdMb2jKLVG6u7tj586d0dPTE2fPno0f/vCHMW/evDF9jQ0bNsRPfvKT2LhxY3z3u9+N119/PXbs2BERl7dbI9myZUt861vfiqVLl8a6deuioaEhDhw4EIcOHYpHH30098eihjREDv2QS0Pk0hA59EMuDZFrpjdU81fnKfOLX/wiTp8+HatWrYrvfOc78f3vfz8WLlw4pq9x4403xi9/+cv41a9+FStWrIif/exnV+/k29zcPOLnfPOb34xf//rX8dvf/jZWr14da9asiZ/+9KexbNmy7J+J2tIQOfRDLg2RS0Pk0A+5NESumd5Q5cqdcWe87du3x89//vM4evRovUdhmtIQOfRDLg2RS0Pk0A+5NESuqdLQlHs6z0R58sknY/Xq1XHttdfG3r1748c//nF873vfq/dYTCMaIod+yKUhcmmIHPohl4bINVUbmrFLlLfeeiseffTROHXqVCxdujR+8IMfxI9+9KN6j8U0oiFy6IdcGiKXhsihH3JpiFxTtaFZ83QeAAAAgBxT7sayAAAAAFORJQoAAABAAksUAAAAgASWKAAAAAAJLFEAAAAAEliiAAAAACSwRAEAAABIYIkCAAAAkMASBQAAACCBJQoAAABAgsaqH+3oiOjrq9EoM0xTU0Rvb72nqD8NjZ+G9JNDP5dpaPw0dJmGxk9D+smhn8s0NH4a0k+uURqqvkTp63PRyaMhcuiHXBoil4bIoR9yaYgc+pkU1ZcoVwxGxN8joiMiKpM6zvRVRERvRCwJz5EaiYbKaWh0+imnn+o0VE5D1WmonIZGp59y+qlOQ+U0NDr9pEltKGmJ8veIuGEChpoNjkbE9fUeYgrSUDoNDaefdPoZmYbSaWhkGkqnoeH0k04/I9NQOg0Np5+xKWsoaYnSceWfa9asicbGpE+Zdfr7+2Pfvn1XrxVDaaichkann3L6qU5D5TRUnYbKaWh0+imnn+o0VE5Do9NPmtSGkq7gPx/y09jY6KKX8PCokWkonYaG0086/YxMQ+k0NDINpdPQcPpJp5+RaSidhobTz9iUNeTpYgAAAAAJrKEAJlhRFPGPf/wj+Xxra2u0t7dP4kQAAMBEsEQBmGADAwNx+PDhmDdvXlQq1R8QeOHChVi6dKklCgAATAOWKACT5Lbbbit93unBgwdrNA0AAJDLPVEAAAAAEliiAAAAACSwRAEAAABIYIkCAAAAkMASBQAAACCBJQoAAABAAksUAAAAgASN9R4AYCYriqLeIwAAABPEEgVgkuzdu7f0TFEUMX/+/BpMAwAA5LJEAZhgc+bMiTVr1iSfb2z0r2IAAJgO/MkdYIJVKpVoaWmp9xgAAMAEc2NZAAAAgASWKAAAAAAJPJ0HAACASdPX1xcDAwNJZz0tmqnOEgUAAIBJ89///d9x/PjxqFQqSefvuOOOSZ4Ixs8SBQAAgEm1ZMmS+OIXv1j1zCeffBL/9//+3xpNBOPjnigAAABMqtRHocBUZ4kCAAAAkMDTeQAAYIZ66623oiiKpLMdHR2xePHiSZ4IYHrzSBQAAJihjh07Fn19fTE4OFj115kzZ+L06dP1HhdgyvNIFAAAmMFuuummaG1trXrm7bffjr6+vhpNBDB9eSQKAAAAQAJLFAAAAIAEligAAAAACdwTBQAAgEl1/PjxOHXqVNUzqa8kBfVkiQJj1N/fH2+++Wby+SVLlsQ111wziRMBAMDU9fnPfz66urrqPQZMCEsUGKOiKOLkyZNxww03lJ49fvy4BQoAALPa/Pnz6z0CTBhLFBinG2+8MRoaqt9W6MyZM7UZBgAAYBo5ffp08tnm5ubSl2qvFUsUAACYwfr6+kr/4mdwcLBG0wBcfnT/gQMHYu7cuVGpVKqe7e/vj8WLF0d3d3eNpqvOEgUAAGaw119/PencwoULJ3cQgM9YvXp1NDU1VT3zxhtv1GiaNJYoAAAwQ/2f//N/6j0CwIxiiQIAADNU2cPkARgbSxQAgBo7c+ZMvPPOO8nn/+Vf/iVaWlomcSIAIIUlCgBAjfX398fHH38cy5YtKz3717/+1U0/AWCKsEQBgCmmKIr4xz/+kXy+tbU12tvbJ3EiJkNjY2PccMMNpefG8ogVAGByWaLAOJ0/f770jL85BMZjYGAgDh8+HPPmzSu9n8GFCxdi6dKlligAADVgiQLj0NDQEK+99lrSWTd0A8brtttui8bG6v9XffDgwRpNAwCAJQqM0dy5c+Mb3/hGvccAAACgxixRAAAAgJrbt29f6SP3BwcHY8mSJTWaqNyUWKL8+c9/jv7+/qSz8+fPj1tuuWWSJwIAAAAmQ6VSiZ6enuTzZU9vrqUpMcnHH38c119/fbS0tFQ99+GHH8Ynn3xSo6kAAACAyTBdb4o/JZYoERHXXHNNzJ8/v+qZvr6+OHXqVI0mAgAAAPj/mzJLFACA2WRwcDDOnDlTeq4oiskfBgBIYokCAFBjDQ0NMTg4GIcOHSo9O2fOnNKb7gEAtWGJAgBTmEchzEzXXHNNfP3rX6/3GADAGFmiAMAUtXfv3tIzRVGU3lMMAICJYYkCAFPMnDlzYs2aNcnnp9LL/gEAzGT+1AUAU0ylUomWlpZ6jwEAwGc01HsAAAAAgOlgyjwS5aOPPoq+vr6qZ86fP1+jaQAAAACGmhJLlJaWlnj//feTznZ2dk7yNAAAAADDTYklSk9PT71HAAAAAKjKPVEAAAAAEliiAAAAACSwRAEAAABIYIkCAAAAkMASBQAAACCBJQoAAABAAksUAAAAgASWKAAAAAAJLFEAAAAAEliiAAAAACSwRAEAAABIYIkCAAAAkMASBQAAACCBJQoAAABAgsaUQ8WVf/b390/iKNPbP69NUXJuttJQOQ2NTj/l9FOdhsppqDoNldPQ6PRTTj/VaaichkannzSpDVWKohj9THNzRF9fvBcRN0zcbDPa0Yi4PiKiqSni4sU6TzMFaGjMNPQp+hkz/XyGhsZMQ5+hoTHT0KfoZ8z08xkaGjMNfYp+xqWsoaRHoiy58oU6IqIygcPNJEVE9Mbla8VwGiqnodHpp5x+qtNQOQ1Vp6FyGhqdfsrppzoNldPQ6PSTJrWhpCVKQ1zZxFBVZ70HmMI0lEZDI9NPGv2MTkNpNDQ6DaXR0Mj0k0Y/o9NQGg2NTD/pUhqqvkRpapqYSWYj1+4y12H8XDvXIIdrd5nrMH6u3WWuw/i5dq5BDtfuMtdh/Fw71yDXKNev+j1RAAAAAIgIL3EMAAAAkKTuS5StW7fGypUra/59d+zYEQsWLKj592XiaYgc+iGXhsilIXLoh1waItdsa2hClyiVSqXqr61btw77nIceeiheeumliRyDaUxD5NAPuTRELg2RQz/k0hC5NFQu6dV5Uh07duzq75977rnYsmVLHDly5Or72tvbr/6+KIoYGBiI9vb2Ie9ndtMQOfRDLg2RS0Pk0A+5NEQuDZWb0EeiLFq06Oqvzs7OqFQqV99+8803o6OjI3bv3h233XZbNDc3x549e4Y99Gf//v1x9913R1dXV3R2dsYdd9wRr7322pDvU6lU4umnn4577703Wltbo7u7O3bt2jXkzK5du6K7uztaWlrizjvvjGeffTYqlUqcOXNm1PlfeOGFWLVqVbS0tMRNN90U27Zti/7+/om8RJTQEDn0Qy4NkUtD5NAPuTRELg2Vq/k9UR5++OF4/PHH44033ogVK1YM+3hvb2+sX78+9uzZE/v27Yvu7u5Yu3Zt9Pb2Djm3bdu2uO++++LgwYOxdu3auP/+++PUqVMREfHOO+/EunXr4p577okDBw7Ehg0bYtOmTVXnevXVV+OBBx6IBx98MA4fPhxPPfVU7NixI7Zv3z5xPzwTQkPk0A+5NEQuDZFDP+TSELlmfUPFJHnmmWeKzs7Oq2+//PLLRUQUzz///JBzjzzySHHrrbeO+nUGBgaKjo6O4sUXX7z6vogoNm/efPXtc+fOFRFR7N69uyiKoti4cWOxfPnyIV9n06ZNRUQUp0+fHnG+u+66q3jssceGfM7OnTuLxYsXp/y4TAINkUM/5NIQuTREDv2QS0Pk0tDIJvSeKCl6enqqfvz48eOxefPmeOWVV+LEiRMxMDAQ58+fj3fffXfIuU9vvNra2mL+/Plx4sSJiIg4cuRIrF69esj522+/ver3PXDgQOzdu3fIlmpgYCAuXLgQ58+fj9bW1qSfj8mnIXLoh1waIpeGyKEfcmmIXLO9oZovUdra2qp+fP369fHhhx/GE088EcuWLYvm5ub46le/Gn19fUPOzZ07d8jblUolBgcHxz3XuXPnYtu2bfHtb3972MdaWlrG/XWZeBoih37IpSFyaYgc+iGXhsg12xuq+RKlzN69e+PJJ5+MtWvXRkTE0aNH4+TJk2P6Grfcckv85je/GfK+/fv3V/2cVatWxZEjR+Lmm28e28BMORoih37IpSFyaYgc+iGXhsg10xuackuU7u7u2LlzZ/T09MTZs2fjhz/8YcybN29MX2PDhg3xk5/8JDZu3Bjf/e534/XXX48dO3ZExOXt1ki2bNkS3/rWt2Lp0qWxbt26aGhoiAMHDsShQ4fi0Ucfzf2xqCENkUM/5NIQuTREDv2QS0PkmukN1fzVecr84he/iNOnT8eqVaviO9/5Tnz/+9+PhQsXjulr3HjjjfHLX/4yfvWrX8WKFSviZz/72dU7+TY3N4/4Od/85jfj17/+dfz2t7+N1atXx5o1a+KnP/1pLFu2LPtnorY0RA79kEtD5NIQOfRDLg2Ra6Y3VLlyZ9wZb/v27fHzn/88jh49Wu9RmKY0RA79kEtD5NIQOfRDLg2Ra6o0NOWezjNRnnzyyVi9enVce+21sXfv3vjxj38c3/ve9+o9FtOIhsihH3JpiFwaIod+yKUhck3VhmbsEuWtt96KRx99NE6dOhVLly6NH/zgB/GjH/2o3mMxjWiIHPohl4bIpSFy6IdcGiLXVG1o1jydBwAAACDHlLuxLAAAAMBUZIkCAAAAkMASBQAAACCBJQoAAABAAksUAAAAgASWKAAAAAAJLFEAAAAAEliiAAAAACSwRAEAAABIYIkCAAAAkKCx6kc7OiL6+mo0ygzT1BTR21vvKepPQ+OnIf3k0M9lGho/DV2mofHTkH5y6OcyDY2fhvSTa5SGqi9R+vpcdPJoiBz6IZeGyKUhcuiHXBoih34mRfUlyhWDEfH3iOiIiMqkjjN9FRHRGxFLwnOkRqKhchoanX7K6ac6DZXTUHUaKqeh0emnnH6q01A5DY1OP2lSG0paovw9Im6YgKFmg6MRcX29h5iCNJROQ8PpJ51+RqahdBoamYbSaWg4/aTTz8g0lE5Dw+lnbMoaSlqidFz555o1a6KxMelTZp3+/v7Yt2/f1WvFUBoqp6HR6aecfqrTUDkNVaehchoanX7K6ac6DZXT0Oj0kya1oaQr+M+H/DQ2NrroJTw8amQaSqeh4fSTTj8j01A6DY1MQ+k0NJx+0ulnZBpKp6Hh9DM2ZQ15uhgAAABAAksUAAAAgASWKAAAAAAJLFEAAAAAEliiAAAAACSwRAEAAABIYIkCAAAAkMASBQAAACCBJQoAAABAAksUAAAAgASWKAAAAAAJLFEAAAAAEjTWewAAAGBy/OEPf4jBwcGks11dXdHd3T3JEwFMb5YoAAAwQ128eDFuvvnmaGpqqnrugw8+iEuXLtVoKoDpyxIFAABmsAULFkRra2vVM2fOnIm+vr4aTUSOY8eOxYULF5LOzpkzJ5YuXTrJE8HsYokCAAAwTfzzUUPz5s2reu7SpUtx/vx5SxSYYJYoAAAA08jixYvjhhtuqHrmzJkzcejQoRpNBLOHV+cBAAAASGCJAgAAAJDA03kAqvj973+f/NKQ1113Xdxyyy2TPBEAAFAvligAVfT398eXvvSlaGlpqXruvffei4GBgRpNBQAA1IMlCkCJ9vb20peGbGpq8tKQAAAww1miAADADHbixIlobm6ueub8+fPR2Og/DQDK1OzflOfOnYuiKJLOzpkzp/RvfQEAgOra29vj5MmTyWcBqK5mS5T/+q//ikuXLkWlUql6riiKaG1tjZ6enhpNBgAAM9OqVavqPQKTYGBgIPr7+6ueSb0xPjA2NX3M3r/+679GV1dX1TPHjh2L999/v0YTAQAATC//8z//E//zP/9Tem7u3LmTPwzMMp74yKxy9OjReOedd5LPf+1rX/P8YAAApoxbb7213iPArOa/DplViqKI9vb2+NKXvlT13ODgYPzxj3+s0VQAAJCmoaGh3iPArGaJwqzT0NBQeuPisueYAgAAMPtYogCUOHbsWOlzint7e0tfPhIAAJjeLFEAqliwYEH09vaWnqtUKl6aHQCAWe3ChQvxySefJJ/v7Oycdk9Rs0QBqGLFihX1HgEAAKaF06dPx1/+8pekV4bq6+uLr33ta9HU1FSDySaOJQoAAAAwIdra2qKnp6fqmaIo4j/+4z9qNNHEml6PmwEAAACok5o+EuXNN98sfb7TwMBAzJs3r0YTAQAAAKSp2RLly1/+cgwODiadnTNnziRPAwAAADA2NVuizJ8/v1bfCqr65JNP4u233656piiKGk0DAADAdOHGsswqra2tMX/+/Lh48WLp2euuu27avdwWAAAAk8cShVmlq6srurq66j0GAAAA05AlCgDAOBVFEQMDA8nn58yZE5VKZRInAgAmkyUKAMA4ffzxx/HHP/4x+fzy5cs9IhIApjFLFACADA0NDfG1r32t9Nz+/ftrMA0A1Ne5c+fi1VdfrfcYk8YSBQAgU2OjP1IBQFdXV3R0dCSfnzt37iROMzn8Pz4AAACQbe7cudNyMTIWligAkOnYsWPJNxdtaWlxTwwAgGnKEgUAMv33f/93NDc3x5w5c6qeu3jxYsybN88SBQBgmrJEAYAJcMstt8T8+fOrnnn33Xfj1KlTNZoIAICJ1lDvAQAAAACmA0sUAAAAgASWKAAAAAAJ3BMFACDD4OBgHDx4sPTcpUuXajANADCZLFEAAMapubk5vvCFLySdnT9/frS1tU3uQADApLJEAQAYp7lz5yYvUQCA6c89UQAAAAASeCQKAEyAwcHBGBwcLD0DAMD0ZYkCABPg9ddfTzq3YMGCSZ0DAIDJY4kCAJnWrFkTRVEkna1UKpM8DQAAk8USBQAyNTb6v1MAgNnAjWUBAAAAEliiAAAAACSwRAEAAABIYIkCAAAAkMASBQAAACCBJQoAAABAAksUAAAAgASWKAAAAAAJLFEAAAAAEliiAAAAACSwRAEAAABI0JhyqLjyz/7+/kkcZXr757UpSs7NVhoqp6HR6aecfqrTUDkNVaehchoanX7K6ac6DZXT0Oj0kya1oUpRFKOfaW6O6OuL9yLihombbUY7GhHXR0Q0NUVcvFjnaaYADY2Zhj5FP2Omn8/Q0Jhp6DM0NGYa+hT9jJl+PkNDY6ahT9HPuJQ1lPRIlCVXvlBHRFQmcLiZpIiI3rh8rRhOQ+U0NDr9lNNPdRoqp6HqNFROQ6PTTzn9VKehchoanX7SpDaUtERpiCubGKrqrPcAU5iG0mhoZPpJo5/RaSiNhkanoTQaGpl+0uhndBpKo6GR6SddSkPVlyhNTRMzyWzk2l3mOoyfa+ca5HDtLnMdxs+1u8x1GD/XzjXI4dpd5jqMn2vnGuQa5fpVvycKAAAAABHhJY4BAAAAkliiAAAAACSo+xJl69atsXLlypp/3x07dsSCBQtq/n2ZeBoih37IpSFyaYgc+iGXhsg12xqa0CVKpVKp+mvr1q3DPuehhx6Kl156aSLHYBrTEDn0Qy4NkUtD5NAPuTRELg2VS3qJ41THjh27+vvnnnsutmzZEkeOHLn6vvb29qu/L4oiBgYGor29fcj7md00RA79kEtD5NIQOfRDLg2RS0PlJvSRKIsWLbr6q7OzMyqVytW333zzzejo6Ijdu3fHbbfdFs3NzbFnz55hD/3Zv39/3H333dHV1RWdnZ1xxx13xGuvvTbk+1QqlXj66afj3nvvjdbW1uju7o5du3YNObNr167o7u6OlpaWuPPOO+PZZ5+NSqUSZ86cGXX+F154IVatWhUtLS1x0003xbZt26K/v38iLxElNEQO/ZBLQ+TSEDn0Qy4NkUtD5Wp+T5SHH344Hn/88XjjjTdixYoVwz7e29sb69evjz179sS+ffuiu7s71q5dG729vUPObdu2Le677744ePBgrF27Nu6///44depURES88847sW7durjnnnviwIEDsWHDhti0aVPVuV599dV44IEH4sEHH4zDhw/HU089FTt27Ijt27dP3A/PhNAQOfRDLg2RS0Pk0A+5NESuWd9QMUmeeeaZorOz8+rbL7/8chERxfPPPz/k3COPPFLceuuto36dgYGBoqOjo3jxxRevvi8iis2bN199+9y5c0VEFLt37y6Koig2btxYLF++fMjX2bRpUxERxenTp0ec76677ioee+yxIZ+zc+fOYvHixSk/LpNAQ+TQD7k0RC4NkUM/5NIQuTQ0sgm9J0qKnp6eqh8/fvx4bN68OV555ZU4ceJEDAwMxPnz5+Pdd98dcu7TG6+2traYP39+nDhxIiIijhw5EqtXrx5y/vbbb6/6fQ8cOBB79+4dsqUaGBiICxcuxPnz56O1tTXp52PyaYgc+iGXhsilIXLoh1waItdsb6jmS5S2traqH1+/fn18+OGH8cQTT8SyZcuiubk5vvrVr0ZfX9+Qc3Pnzh3ydqVSicHBwXHPde7cudi2bVt8+9vfHvaxlpaWcX9dJp6GyKEfcmmIXBoih37IpSFyzfaGar5EKbN379548sknY+3atRERcfTo0Th58uSYvsYtt9wSv/nNb4a8b//+/VU/Z9WqVXHkyJG4+eabxzYwU46GyKEfcmmIXBoih37IpSFyzfSGptwSpbu7O3bu3Bk9PT1x9uzZ+OEPfxjz5s0b09fYsGFD/OQnP4mNGzfGd7/73Xj99ddjx44dEXF5uzWSLVu2xLe+9a1YunRprFu3LhoaGuLAgQNx6NChePTRR3N/LGpIQ+TQD7k0RC4NkUM/5NIQuWZ6QzV/dZ4yv/jFL+L06dOxatWq+M53vhPf//73Y+HChWP6GjfeeGP88pe/jF/96lexYsWK+NnPfnb1Tr7Nzc0jfs43v/nN+PWvfx2//e1vY/Xq1bFmzZr46U9/GsuWLcv+magtDZFDP+TSELk0RA79kEtD5JrpDVWu3Bl3xtu+fXv8/Oc/j6NHj9Z7FKYpDZFDP+TSELk0RA79kEtD5JoqDU25p/NMlCeffDJWr14d1157bezduzd+/OMfx/e+9716j8U0oiFy6IdcGiKXhsihH3JpiFxTtaEZu0R566234tFHH41Tp07F0qVL4wc/+EH86Ec/qvdYTCMaIod+yKUhcmmIHPohl4bINVUbmjVP5wEAAADIMeVuLAsAAAAwFVmiAAAAACSwRAEAAABIYIkCAAAAkMASBQAAACCBJQoAAABAAksUAAAAgASWKAAAAAAJLFEAAAAAEliiAAAAACRorPrRjo6Ivr4ajTLDNDVF9PbWe4r609D4aUg/OfRzmYbGT0OXaWj8NKSfHPq5TEPjpyH95BqloepLlL4+F508GiKHfsilIXJpiBz6IZeGyKGfSVF9iXLFYET8PSI6IqIyqeNMX0VE9EbEkvAcqZFoqJyGRqefcvqpTkPlNFSdhsppaHT6Kaef6jRUTkOj00+a1IaSlih/j4gbJmCo2eBoRFxf7yGmIA2l09Bw+kmnn5FpKJ2GRqahdBoaTj/p9DMyDaXT0HD6GZuyhpKWKB1X/rlmzZpobEz6lFmnv78/9u3bd/VaMZSGymlodPopp5/qNFROQ9VpqJyGRqefcvqpTkPlNDQ6/aRJbSjpCv7zIT+NjY0uegkPjxqZhtJpaDj9pNPPyDSUTkMj01A6DQ2nn3T6GZmG0mloOP2MTVlDni4GAAAAkMASBQAAACCBJQoAAABAAksUAAAAgASWKAAAAAAJ3JoXADL9+c9/jv7+/qSz8+fPj1tuuWWSJwIAYDJYogBApo8//jiuv/76aGlpqXruww8/jE8++aRGUwEAMNGyliiXLl2K48ePJ5/v6uoq/QMmAExH11xzTcyfP7/qmb6+vjh16lSNJgIAYKJlLVEuXrwYb7/9dukfGiMient7o6WlxRIFAAAAmJayn87T0NAQq1atKj33n//5n7nfCgAAZqVLly4ln61UKtHY6Fn7wNTS398fRVEkn587d+4kTjN+/u0KAABT3B//+Me4ePFi0tn29vbo6emZ5IkAxubvf/97/PWvf00+//Wvf31KLoSn3kQAAMAwy5cvj2uuuabqmePHj8f7779fo4kAxmbBggWxYsWKqmcGBwdjz549NZpo7CxRAABgmmhoaKj3CABZyv49Njg4WKNJxse/hQEAAAASWKIAAAAAJPB0HgCYAB999FH09fVVPXP+/PkaTQMAwGSwRAGATC0tLck3cuzs7JzkaQAAmCwTskSZ6jd+AYDJ5KVEAQBmh+wlyuDgYPzud7+biFkAAAAApqysJUpbW1v8+7//e/L5OXPm5Hw7gGRnz56NgwcPJp+/9dZbo6OjYxInAgAAprusJUqlUom5c+dO1CwAE2ZwcDCKoohbb7219OyBAweiKIoaTAUA4/ff//3f8be//a3qmUuXLkVjo9seAlNTb29v/OlPf6r3GFn8G5Yp65NPPomjR48mn1+6dGm0tLRM4kRMN5VKJebPn590DgCmshtvvDH5PoT+khOYiq655prkJe/ixYujoaFhkicaH0sUpqyLFy/GsWPH4n/9r/9Vevb48eOxaNEiSxQAYEZatGhRvUcAyNLe3h7t7e31HiObJQpT2pw5c+JLX/pS6bmTJ0/WYBoAAABms6n5+BgAAACAKcYSBQAAACCBJQoAAABAAksUAAAAgASWKAAAAAAJvDoPMGMNDg7Gu+++m3QOAACgjCUKMCM1NjbG/Pnz49SpU6Vn58+fH42N/nUIADDZBgcH46OPPko+P2/evGhpaZnEiWBs/FcDU96FCxfqPQLTUHt7e6xcubLeYwAA8CkDAwNx4MCBaGpqKj176dKl6O7ujiVLltRgMkhjicKU1t/fH/v27av3GAAw5RVFMabzlUplkiYBKLdmzZpoaKh+i84//elPNZoG0lmiMGUtWLAg7rjjjuTz/jAIwGz217/+NY4ePZp8/hvf+Ebpf8AAAENZojClWYwAQJqiKOLaa6+NW265peq5vr6++OMf/1ijqQBgZrFEAQCYIebMmVN6nwF/QQEA4+cxnAAAAAAJLFEAAAAAEliiAAAAACSwRAEAAABIYIkCAAAAkMCr8wAAAFBTe/fuLT0zMDAQixcvrsE0kM4SBQAAgJpobGyMnp6e5PPNzc2TOA2MnSUKAMAMcfbs2XjjjTeqnhkcHKzRNADDVSqVaG9vr/cYMG6WKAAAM0BnZ2cURZF09vOf/3xUKpVJnggAZh5LFACAGeC6666L6667rt5jAMCM5tV5AAAAABJYogAAAAAksEQBAAAASGCJAgAAAJDAEgUAAAAggSUKAAAAQAJLFAAAAIAEligAAAAACSxRAAAAABJYogAAAAAksEQBAAAASGCJAgAAAJDAEgUAAAAggSUKAAAAQAJLFAAAAIAEligAAAAACSxRAAAAABJYogAAAAAksEQBAAAASGCJAgAAAJDAEgUAAAAggSUKAAAAQAJLFAAAAIAEjSmHiiv/7O/vn8RRprd/Xpui5NxspaFyGhqdfsrppzoNldNQdRoqp6HR6aecfqrTUDkNjU4/aVIbqhRFMfqZ5uaIvr54LyJumLjZZrSjEXF9RERTU8TFi3WeZgrQ0Jhp6FP0M2b6+QwNjZmGPkNDY6ahT9HPmOnnMzQ0Zhr6FP2MS1lDSY9EWXLlC3VERGUCh5tJiojojcvXiuE0VE5Do9NPOf1Up6FyGqpOQ+U0NDr9lNNPdRoqp6HR6SdNakNJS5SGuLKJoarOeg8whWkojYZGpp80+hmdhtJoaHQaSqOhkeknjX5Gp6E0GhqZftKlNFR9idLUNDGTzEau3WWuw/i5dq5BDtfuMtdh/Fy7y1yH8XPtXIMcrt1lrsP4uXauQa5Rrl/1e6IAAAAAEBFe4hgAAAAgiSUKAAAAQIK6L1G2bt0aK1eurPn33bFjRyxYsKDm35eJpyFy6IdcGiKXhsihH3JpiFyzraEJXaJUKpWqv7Zu3Trscx566KF46aWXJnIMpjENkUM/5NIQuTREDv2QS0Pk0lC5pJc4TnXs2LGrv3/uuediy5YtceTIkavva29vv/r7oihiYGAg2tvbh7yf2U1D5NAPuTRELg2RQz/k0hC5NFRuQh+JsmjRoqu/Ojs7o1KpXH37zTffjI6Ojti9e3fcdttt0dzcHHv27Bn20J/9+/fH3XffHV1dXdHZ2Rl33HFHvPbaa0O+T6VSiaeffjruvffeaG1tje7u7ti1a9eQM7t27Yru7u5oaWmJO++8M5599tmoVCpx5syZUed/4YUXYtWqVdHS0hI33XRTbNu2Lfr7+yfyElFCQ+TQD7k0RC4NkUM/5NIQuTRUrub3RHn44Yfj8ccfjzfeeCNWrFgx7OO9vb2xfv362LNnT+zbty+6u7tj7dq10dvbO+Tctm3b4r777ouDBw/G2rVr4/77749Tp05FRMQ777wT69ati3vuuScOHDgQGzZsiE2bNlWd69VXX40HHnggHnzwwTh8+HA89dRTsWPHjti+ffvE/fBMCA2RQz/k0hC5NEQO/ZBLQ+Sa9Q0Vk+SZZ54pOjs7r7798ssvFxFRPP/880POPfLII8Wtt9466tcZGBgoOjo6ihdffPHq+yKi2Lx589W3z507V0REsXv37qIoimLjxo3F8uXLh3ydTZs2FRFRnD59esT57rrrruKxxx4b8jk7d+4sFi9enPLjMgk0RA79kEtD5NIQOfRDLg2RS0Mjm9B7oqTo6emp+vHjx4/H5s2b45VXXokTJ07EwMBAnD9/Pt59990h5z698Wpra4v58+fHiRMnIiLiyJEjsXr16iHnb7/99qrf98CBA7F3794hW6qBgYG4cOFCnD9/PlpbW5N+PiafhsihH3JpiFwaIod+yKUhcs32hmq+RGlra6v68fXr18eHH34YTzzxRCxbtiyam5v/f+3dX2zV9f348ddpC6cUWjohiEZhODp2YZB04GrmsizLYkK82AzxxjgvvODGuAs1aDQoCZglJprdoEtmxsLVEmM2ZzQxWbY42PiGzIhjOiKbf7qJMgSkXYHa9vwuYPzs2p7Pu32350/7eCQE2r57ePWTZwRf9HxO3HLLLTE8PDzu3KJFi8a9XSqVYmxsbMZzDQ4Oxq5du+KOO+6Y8LH29vYZPy6zT0Pk0A+5NEQuDZFDP+TSELkWekM1X6IUOXjwYOzduze2bt0aERH9/f1x6tSpaT3Ghg0b4pVXXhn3vsOHD1f9nN7e3jh27FisX79+egPTcDREDv2QS0Pk0hA59EMuDZFrvjfUcEuUnp6e2L9/f2zevDnOnTsXDz30UCxZsmRaj7F9+/Z4+umnY8eOHXHvvffGm2++Gfv27YuIS9utyezcuTNuv/32WLNmTWzbti1aWlriyJEjcfTo0di9e3ful0UNaYgc+iGXhsilIXLoh1waItd8b6jmr85T5Pnnn48zZ85Eb29v3H333XH//ffHqlWrpvUY69atixdeeCFefPHF2LhxYzz77LNX7uRbLpcn/ZzbbrstXn755Xjttddiy5Yt0dfXF88880ysXbs2+2uitjREDv2QS0Pk0hA59EMuDZFrvjdUunxn3Hlvz5498dxzz0V/f3+9R6FJaYgc+iGXhsilIXLoh1waIlejNNRwT+eZLXv37o0tW7bEihUr4uDBg/HUU0/FfffdV++xaCIaIod+yKUhcmmIHPohl4bI1agNzdslyrvvvhu7d++O06dPx5o1a+KBBx6IRx55pN5j0UQ0RA79kEtD5NIQOfRDLg2Rq1EbWjBP5wEAAADI0XA3lgUAAABoRJYoAAAAAAksUQAAAAASWKIAAAAAJLBEAQAAAEhgiQIAAACQwBIFAAAAIIElCgAAAEACSxQAAACABJYoAAAAAAnaqn60szNieLhGo8wzixdHDAzUe4r609DMaUg/OfRziYZmTkOXaGjmNKSfHPq5REMzpyH95JqioepLlOFhF508GiKHfsilIXJpiBz6IZeGyKGfOVF9iXLZWER8FBGdEVGa03GaVyUiBiLi2vAcqcloqJiGpqafYvqpTkPFNFSdhoppaGr6Kaaf6jRUTENT00+a1IaSligfRcT1szDUQtAfEdfVe4gGpKF0GppIP+n0MzkNpdPQ5DSUTkMT6SedfianoXQamkg/01PUUNISpfPyz319fdHWlvQpC87IyEgcOnToyrVivGZo6KOPPopTp04lnS2VSnHjjTdGqTR7u1wNTa0Z+qk3/VSnoWIaqk5DxTQ0Nf0U0091GiqmoanpJ01qQ0lX8L//m9jW1uaiF/DtUZNrhoaGh4djbGwsrr766qrnRkdH4/3334/W1tZoaZn9bxbU0ETN0E+j0M/kNJROQ5PTUDoNTaSfdPqZnIbSaWgi/UxPUUOuIHxBR0dHXH999W92+/zzz+P999+vzUAAAAA0DPfcAQAAAEhgiQIAAACQwBIFAAAAIIElCgAAAEACSxQAAACABJYoAAAAAAksUQAAAAAStNV7AGgkn3/+eZw9e7bqmZGRkdoMAwAAQEOxRIHLWltbY2BgII4ePVp4dtGiRVEqlWowFQAAAI3CEgUuW7duXaxbt67eYwAAANCg3BMFAAAAIIHvRAEAgBr561//GufOnUs6u2jRoti8efMcTwTAdFiiAABAjQwPD8dVV10VK1asqHru/Pnz8cEHH9RoKgBSWaIAAEANdXR0xMqVK6ueKXq1QKiV999/PyqVStLZpUuXxqpVq+Z4IqgvSxQAAAAm9eGHH0ZXV1e0trZWPfef//wnurq6LFGY9yxRAAAAmNJXv/rV6OjoqHrm+PHjMTw8XKOJoH68Og8AAABAAksUAAAAgASWKAAAAAAJLFEAAAAAEliiAAAAACTw6jwAAFBD586dixMnTlQ9c/78+RpNA8B0WKIAAECNdHR0xMDAQPzrX/8qPLts2bIaTATAdFiiAABAjWzYsKHeI8C0jY6OxsjISNUzlUqlRtNAfVmiAAAAMKU///nPSedWrVo1x5NA/VmiAAAAMKlbb7213iPQAP7v//4vLl68mHR22bJl0dvbO8cT1Y8lCgAAAJNqafGCrkSMjY3F+vXro7u7u+q5kydPxqlTp2ozVJ1YogBAHVQqlXj77beTn0O+YsWKuOaaa+Z4KgCAyS1evDg6OjqqnimXyzWapn4sUQCgTv7973/HtddeG62trVXPffrppwviLyUAAI3OEgUA6ujLX/5yLF68uOqZ4eHhGk0DAEA1nuAGAAAAkMASBQAAACCBJQoAAABAAksUAAAAgASWKAAAAAAJvDoPAAAAUNXHH38cZ8+erXpmaGioNsPUkSUKAAAAMKUVK1bE559/HhcvXqx6rrW1Nb70pS/VaKr6sEQBgDoaGhqK4eHhqmdGRkairc0f2QBAfXz1q1+t9wgNoyH+RjYyMpJ8tqWlJVpa3MoFgObX2toab731VtLZa6+9do6nAQCgSEMsUQ4dOpS8SOnu7o5NmzbN7UAAMMdKpVJ861vfqvcYAABMQ0MsUSIiNm3aFMuWLat65p///GfhjWwAAAAA5kLDLFFaWloKn+/taTwAQCM5f/58HD16NPl8T09PdHd3z91AAMCcapglCgBAsxkdHY2hoaHYsGFD4dnjx49P6z5wAEDjsUQBmtbnn38en3zySfL5lStXRnt7+xxOBCxEpVIpVq9eXXjuvffeq8E0AMBcskQBmtbFixfj+PHj0dXVVXh2YGAg2tvbLVEAAIAZs0QBmlpLS0v09vYWnvvTn/5Ug2kAAID5zJ1aAQAAABJYogAAAAAksEQBAAAASNAw90Q5fvx4tLVVH+f8+fNRLpdrNBEAAADA/9cQS5Q1a9bE2NhY4bmuri6vrAEAAADURcMsUQAAmlGlUolTp04Vnkv5ByMAoLE1xBIFAKAZtba2RrlcjuPHjyedLXrqMgDQ2PxJDjQ9/7oL1MuSJUuir6+v3mMAADViiQI0tbGxsXj99dfrPQYAALAAWKIATWvp0qXxzW9+M/l8a2vrHE4DAADMd5YoQNMqlUqxaNGieo8BAAAsEC31HgAAAACgGViiAAAAACSwRAEAAABIYIkCAAAAkMASBQAAACCBJQoAAABAAksUAAAAgASWKAAAAAAJLFEAAAAAEliiAAAAACSwRAEAAABI0JZyqHL555GRkTkcpbn999pUCs4tVBoqpqGp6aeYfqrTUDENVaehYhqamn6K6ac6DRXT0NT0kya1oVKlUpn6TLkcMTwc/4yI62dvtnmtPyKui4hYvDji4sU6T9MANDRtGvoC/Uybfv6HhqZNQ/9DQ9OmoS/Qz7Tp539oaNo09AX6mZGihpK+E+Xayw/UGRGlWRxuPqlExEBculZMpKFiGpqaforppzoNFdNQdRoqpqGp6aeYfqrTUDENTU0/aVIbSlqitMTlTQxVLa/3AA1MQ2k0NDn9pNHP1DSURkNT01AaDU1OP2n0MzUNpdHQ5PSTLqWh6kuUxYtnZ5KFyLW7xHWYOdfONcjh2l3iOsyca3eJ6zBzrp1rkMO1u8R1mDnXzjXINcX1q35PFAAAAAAiwkscAwAAACSp+xLliSeeiE2bNtX89923b190d3fX/Pdl9mmIHPohl4bIpSFy6IdcGiLXQmtoVpcopVKp6o8nnnhiwuc8+OCD8dvf/nY2x6CJaYgc+iGXhsilIXLoh1waIpeGiiW9Ok+qEydOXPn1L3/5y9i5c2ccO3bsyvuWLVt25deVSiVGR0dj2bJl497PwqYhcuiHXBoil4bIoR9yaYhcGio2q9+Jsnr16is/li9fHqVS6crbf/vb36KzszNeffXV+PrXvx7lcjkOHDgw4Vt/Dh8+HN/73vdi5cqVsXz58vj2t78db7zxxrjfp1Qqxc9+9rP4wQ9+EB0dHdHT0xMvvfTSuDMvvfRS9PT0RHt7e3znO9+JX/ziF1EqleLs2bNTzv/rX/86ent7o729PW644YbYtWtXjIyMzOYlooCGyKEfcmmIXBoih37IpSFyaahYze+J8vDDD8ePf/zjeOedd2Ljxo0TPj4wMBD33HNPHDhwIA4dOhQ9PT2xdevWGBgYGHdu165dceedd8Zbb70VW7dujbvuuitOnz4dERHvvfdebNu2Lb7//e/HkSNHYvv27fHoo49WnesPf/hD/PCHP4wf/ehH8fbbb8dPf/rT2LdvX+zZs2f2vnhmhYbIoR9yaYhcGiKHfsilIXIt+IYqc+TnP/95Zfny5Vfe/t3vfleJiMqvfvWrcecef/zxyk033TTl44yOjlY6Ozsrv/nNb668LyIqjz322JW3BwcHKxFRefXVVyuVSqWyY8eOyo033jjucR599NFKRFTOnDkz6Xzf/e53K08++eS4z9m/f3/lmmuuSflymQMaIod+yKUhcmmIHPohl4bIpaHJzeo9UVJs3ry56sc/+eSTeOyxx+L3v/99nDx5MkZHR2NoaCg+/PDDcee+uPFaunRpdHV1xcmTJyMi4tixY7Fly5Zx52+++eaqv++RI0fi4MGD47ZUo6OjceHChRgaGoqOjo6kr4+5pyFy6IdcGiKXhsihH3JpiFwLvaGaL1GWLl1a9eP33HNPfPrpp/GTn/wk1q5dG+VyOW655ZYYHh4ed27RokXj3i6VSjE2NjbjuQYHB2PXrl1xxx13TPhYe3v7jB+X2achcuiHXBoil4bIoR9yaYhcC72hmi9Rihw8eDD27t0bW7dujYiI/v7+OHXq1LQeY8OGDfHKK6+Me9/hw4erfk5vb28cO3Ys1q9fP72BaTgaIod+yKUhcmmIHPohl4bINd8barglSk9PT+zfvz82b94c586di4ceeiiWLFkyrcfYvn17PP3007Fjx4649957480334x9+/ZFxKXt1mR27twZt99+e6xZsya2bdsWLS0tceTIkTh69Gjs3r0798uihjREDv2QS0Pk0hA59EMuDZFrvjdU81fnKfL888/HmTNnore3N+6+++64//77Y9WqVdN6jHXr1sULL7wQL774YmzcuDGeffbZK3fyLZfLk37ObbfdFi+//HK89tprsWXLlujr64tnnnkm1q5dm/01UVsaIod+yKUhcmmIHPohl4bINd8bKl2+M+68t2fPnnjuueeiv7+/3qPQpDREDv2QS0Pk0hA59EMuDZGrURpquKfzzJa9e/fGli1bYsWKFXHw4MF46qmn4r777qv3WDQRDZFDP+TSELk0RA79kEtD5GrUhubtEuXdd9+N3bt3x+nTp2PNmjXxwAMPxCOPPFLvsWgiGiKHfsilIXJpiBz6IZeGyNWoDS2Yp/MAAAAA5Gi4G8sCAAAANCJLFAAAAIAEligAAAAACSxRAAAAABJYogAAAAAksEQBAAAASGCJAgAAAJDAEgUAAAAggSUKAAAAQAJLFAAAAIAEbVU/2tkZMTxco1HmmcWLIwYG6j1F/Wlo5jSknxz6uURDM6ehSzQ0cxrSTw79XKKhmdOQfnJN0VD1JcrwsItOHg2RQz/k0hC5NEQO/ZBLQ+TQz5yovkS5bCwiPoqIzogozek4zasSEQMRcW14jtRkNFRMQ1PTTzH9VKehYhqqTkPFNDQ1/RTTT3UaKqahqeknTWpDSUuUjyLi+lkYaiHoj4jr6j1EA9JQOg1NpJ90+pmchtJpaHIaSqehifSTTj+T01A6DU2kn+kpaihpidJ5+ee+vr5oa0v6lAVnZGQkDh06dOVaMZ6Gimloavoppp/qNFRMQ9VpqJiGpqafYvqpTkPFNDQ1/aRJbSjpCv73W37a2tpc9AK+PWpyGkqnoYn0k04/k9NQOg1NTkPpNDSRftLpZ3IaSqehifQzPUUNeboYAAAAQAJLFAAAAIAEligAAAAACSxRAAAAABJYogAAAAAkcGteoGmdP38+jh49mny+p6cnuru7524gAABgXrNEAZrW6OhoDA0NxYYNGwrPHj9+PEZGRmowFQAAMF9ZogBNrVQqxerVqwvPvffeezWYBgAAFpYTJ07E6Oho0tn29vZYuXLlHE80tyxRAAAAgBn5+9//HuVyOVpbW6ueu3jxYixZssQSBQAAAFi4NmzYEF1dXVXPfPjhh3H69OkaTTR3vDoPAAAAQAJLFAAAAIAEligAAAAACSxRAAAAABJYogAAAAAk8Oo8QFOrVCpx6tSpwnNjY2M1mAYAAJjPLFGAptXa2hrlcjmOHz+edLatzX/yAACAmfN/FEDTWrJkSfT19dV7DAAAWNDGxsYKv/N7vnxnuCUKAAAAMGNvvvlm0rnu7u45naMWLFEAWFD+8pe/xGeffZZ0dtGiRfGNb3xjjicCAGhefX19UalUks6WSqU5nmbuWaIAsKCMjIzE1VdfHVdffXXVc4ODg/GPf/yjRlMBADSnhXbfwYX11QJARLS3t0dXV1fVM/PlebsAzC/9/f1x/vz5pLOtra3xla98ZY4ngoWlpd4DAAAAkObUqVMxMDBw5UaeU/24cOFCnDhxot7jwrzTVN+JMjw8HBcvXkw+v2zZsnnxnCsAAID/WrVqVVx//fVVz5w9ezaOHj1ao4lg4WiqJcrHH38c//jHP6K1tbXw7OjoaNx6660L7vlZAAAAwNxoug1Dd3d3bNq0qeqZkZGROHDgQG0GAgAAABYE90QBAAAASGCJAgAAAJCg6Z7OA0XOnDkT//rXv5LPf+1rX3PvHAAAAAr5P0fmnQsXLsRnn30Wq1evLjzb398fY2NjNZgKaCRnzpyJSqVS9cyFCxdqNA0AAM3CEoV5qVwux1e+8pWqZyqVSvT399doIqBRdHZ2xuDgYJw+fbrwbHd399wPBABA07BEAWBBWb9+fb1HAIAsIyMjhd8xOTIyUqNpYGGxRAEAAGgSpVIpPvjgg/jggw8Kzy5atKgGE8HCYokCAADQJG666aZ6jwALWtMtUT777LP44x//WPVM0c0CAQAAmlGpVKr3CLCgNdUSZdWqVdHV1ZV8vrW1dQ6nAQCA+WdsbCyOHDmSfP6aa65JelVEgPmgqZYo7e3t0d7eXu8xAABg3hobG4vPPvssvvzlLxf+o+SJEye8JDywoDTVEgUAYD64cOFCnDt3Lvn8VVddFW1t/tpGbV133XWF3Z05c6ZG0wA0Bn8aMy+NjY3F4OBgvccAgEkNDg7GO++8E0uWLCk8OzQ0FDfffLMlCgA0AH8aM++USqW4cOFCvPHGG4VnW1paajARAExULpfj5ptvLjz3+uuv12AaACCFJQrzzurVq93cDAAAgFnnn+EBAAAAEliiAAAAACSwRAEAAABIYIkCAAAAkMCNZQEAgAkGBgaiVCpVPTMyMlKjaQAagyUKAAAwTltbW/z1r39NOrty5co5ngagcViiAADUSaVSqfcIMEFbW1vceuut9R4DoCFZogAA1MGFCxfi9ddfLzxn0QIAjcMSBQCgxrq7u6Ovry/5fLlcnsNpAIBUligAADXW1tYWbW3+GgYAzcZLHAMAAAAksEQBAAAASGCJAgAAAJDAEgUAAAAggSUKAAAAQAJLFAAAAIAEligAAAAACSxRAAAAABJYogAAAAAksEQBAAAASGCJAgAAAJDAEgUAAAAggSUKAAAAQAJLFAAAAIAEligAAAAACSxRAAAAABJYogAAAAAksEQBAAAASNCWcqhy+eeRkZE5HKW5/ffaVArOLVQaKqahqemnmH6q01AxDVWnoWIampp+iumnOg0V09DU9JMmtaFSpVKZ+ky5HDE8HP+MiOtnb7Z5rT8irouIWLw44uLFOk/TADQ0bRr6Av1Mm37+h4amTUP/Q0PTpqEv0M+06ed/aGjaNPQF+pmRooaSvhPl2ssP1BkRpVkcbj6pRMRAXLpWTKShYhqamn6K6ac6DRXTUHUaKqahqemnmH6q01AxDU1NP2lSG0paorTE5U0MVS2v9wANTENpNDQ5/aTRz9Q0lEZDU9NQGg1NTj9p9DM1DaXR0OT0ky6loepLlMWLZ2eShci1u8R1mDnXzjXI4dpd4jrMnGt3ieswc66da5DDtbvEdZg51841yDXF9at+TxQAAAAAIsJLHAMAAAAksUQBAAAASFD3JcoTTzwRmzZtqvnvu2/fvuju7q7578vs0xA59EMuDZFLQ+TQD7k0RK6F1tCsLlFKpVLVH0888cSEz3nwwQfjt7/97WyOQRPTEDn0Qy4NkUtD5NAPuTRELg0VS3qJ41QnTpy48utf/vKXsXPnzjh27NiV9y1btuzKryuVSoyOjsayZcvGvZ+FTUPk0A+5NEQuDZFDP+TSELk0VGxWvxNl9erVV34sX748SqXSlbf/9re/RWdnZ7z66qvx9a9/Pcrlchw4cGDCt/4cPnw4vve978XKlStj+fLl8e1vfzveeOONcb9PqVSKn/3sZ/GDH/wgOjo6oqenJ1566aVxZ1566aXo6emJ9vb2+M53vhO/+MUvolQqxdmzZ6ec/9e//nX09vZGe3t73HDDDbFr164YGRmZzUtEAQ2RQz/k0hC5NEQO/ZBLQ+TSULGa3xPl4Ycfjh//+MfxzjvvxMaNGyd8fGBgIO655544cOBAHDp0KHp6emLr1q0xMDAw7tyuXbvizjvvjLfeeiu2bt0ad911V5w+fToiIt57773Ytm1bfP/7348jR47E9u3b49FHH6061x/+8If44Q9/GD/60Y/i7bffjp/+9Kexb9++2LNnz+x98cwKDZFDP+TSELk0RA79kEtD5FrwDVXmyM9//vPK8uXLr7z9u9/9rhIRlV/96lfjzj3++OOVm266acrHGR0drXR2dlZ+85vfXHlfRFQee+yxK28PDg5WIqLy6quvViqVSmXHjh2VG2+8cdzjPProo5WIqJw5c2bS+b773e9WnnzyyXGfs3///so111yT8uUyBzREDv2QS0Pk0hA59EMuDZFLQ5Ob1XuipNi8eXPVj3/yySfx2GOPxe9///s4efJkjI6OxtDQUHz44Yfjzn1x47V06dLo6uqKkydPRkTEsWPHYsuWLePO33zzzVV/3yNHjsTBgwfHbalGR0fjwoULMTQ0FB0dHUlfH3NPQ+TQD7k0RC4NkUM/5NIQuRZ6QzVfoixdurTqx++555749NNP4yc/+UmsXbs2yuVy3HLLLTE8PDzu3KJFi8a9XSqVYmxsbMZzDQ4Oxq5du+KOO+6Y8LH29vYZPy6zT0Pk0A+5NEQuDZFDP+TSELkWekM1X6IUOXjwYOzduze2bt0aERH9/f1x6tSpaT3Ghg0b4pVXXhn3vsOHD1f9nN7e3jh27FisX79+egPTcDREDv2QS0Pk0hA59EMuDZFrvjfUcEuUnp6e2L9/f2zevDnOnTsXDz30UCxZsmRaj7F9+/Z4+umnY8eOHXHvvffGm2++Gfv27YuIS9utyezcuTNuv/32WLNmTWzbti1aWlriyJEjcfTo0di9e3ful0UNaYgc+iGXhsilIXLoh1waItd8b6jmr85T5Pnnn48zZ85Eb29v3H333XH//ffHqlWrpvUY69atixdeeCFefPHF2LhxYzz77LNX7uRbLpcn/ZzbbrstXn755Xjttddiy5Yt0dfXF88880ysXbs2+2uitjREDv2QS0Pk0hA59EMuDZFrvjdUunxn3Hlvz5498dxzz0V/f3+9R6FJaYgc+iGXhsilIXLoh1waIlejNNRwT+eZLXv37o0tW7bEihUr4uDBg/HUU0/FfffdV++xaCIaIod+yKUhcmmIHPohl4bI1agNzdslyrvvvhu7d++O06dPx5o1a+KBBx6IRx55pN5j0UQ0RA79kEtD5NIQOfRDLg2Rq1EbWjBP5wEAAADI0XA3lgUAAABoRJYoAAAAAAksUQAAAAASWKIAAAAAJLBEAQAAAEhgiQIAAACQwBIFAAAAIIElCgAAAECC/wf5XwZjbCniAwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1200x1200 with 88 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,12))\n",
    "for i in range(88):\n",
    "    ax = plt.subplot(11, 8, i+1)\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    plt.grid(False)\n",
    "    if pred_label[i] != images.LABEL_SQUARE:\n",
    "        ax.patch.set_color('red')\n",
    "        ax.patch.set_linewidth(5)\n",
    "    plt.imshow(dark_squares[i], cmap='gray', vmin=0.0, vmax=1.0)\n",
    "    plt.xlabel(class_names[pred_label[i]])\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16537b9e",
   "metadata": {},
   "source": [
    "### Why does this experiment matter?\n",
    "\n",
    "The neural network we just trained fails in the same way the first neural network failed. This neural network...\n",
    "\n",
    "> (...) lack(s) a grasp of the rich meanings humans bring to bear in perception, language, and reasoning. This lack of understanding is clearly revealed by the un-humanlike errors these systems can make; by their difficulties with abstracting and transferring what they have learned; by their lack of commonsense knowledge;\n",
    "\n",
    "In this case, the neural network is very likely learning not from the shape, but from the background (a case of [spurious correlation](https://arxiv.org/pdf/1907.02893.pdf)). It is assuming that a darker background means \"triangle\" because it doesn't really understand the concept of what makes a triangle a triangle.\n",
    "\n",
    "Sometimes this leads to some funny examples, like the neural network that \"learned\" to classify land vs. water birds based on the background. The duck on the right was misclassified as a land bird, simply because it was not in its usual water environment ([source](https://arxiv.org/abs/2005.04345)).\n",
    "\n",
    "![](pics/land-and-waterbirds.png)\n",
    "\n",
    "Other times the mistakes are more consequential, for example, when neural networks misclassify X-rays based on markings left by radiologists in the images. Instead of learning actual attributes of a disease, the neural network \"learned\" from the marks left behind in the images ([source](https://storage.googleapis.com/cloud-ai-whitepapers/AI%20Explainability%20Whitepaper.pdf)). Images without such marks may be classified as \"healthy\". The consequences can be catastrophic.\n",
    "\n",
    "![](pics/x-ray-pen-marks.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83b43913",
   "metadata": {},
   "source": [
    "## Should we be concerned that deep \"learning\" is not \"understanding\"?\n",
    "\n",
    "Mitchell asks the following question in her book:\n",
    "\n",
    "> but the question remains: Will the fact that these systems lack humanlike understanding inevitably render them fragile, unreliable, and vulnerable to attacks? And how should this factor into our decisions about applying AI systems in the real world?\n",
    "\n",
    "Until we achieve humanlike understanding, we should be concerned that neural networks do not generalize well.\n",
    "\n",
    "Does it mean we need to stop using neural networks until then? No.\n",
    "\n",
    "> I think the most worrisome aspect of AI systems in the short term is that we will give them too much autonomy without being fully aware of their limitations and vulnerabilities.\n",
    "\n",
    "Deep learning has successfully improved our lives. It's \"just\" a matter of understanding its limitations, applying it judiciously, for the tasks that it's well suited.\n",
    "\n",
    "To do that we need to educate the general public and, more importantly, the technical community. Too often we hype the next \"AI has achieved humanlike performance in (some task here)\", when in fact we should say \"under these specific circumstances, for this specific application, AI has performed well\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a1bf720a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
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