2. Define the Network Architecture.ipynb

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    "## Define the Convolutional Neural Network\n",
    "\n",
    "After you've looked at the data you're working with and, in this case, know the shapes of the images and of the keypoints, you are ready to define a convolutional neural network that can *learn* from this data.\n",
    "\n",
    "In this notebook and in `models.py`, you will:\n",
    "1. Define a CNN with images as input and keypoints as output\n",
    "2. Construct the transformed FaceKeypointsDataset, just as before\n",
    "3. Train the CNN on the training data, tracking loss\n",
    "4. See how the trained model performs on test data\n",
    "5. If necessary, modify the CNN structure and model hyperparameters, so that it performs *well* **\\***\n",
    "\n",
    "**\\*** What does *well* mean?\n",
    "\n",
    "\"Well\" means that the model's loss decreases during training **and**, when applied to test image data, the model produces keypoints that closely match the true keypoints of each face. And you'll see examples of this later in the notebook.\n",
    "\n",
    "---\n"
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    "## CNN Architecture\n",
    "\n",
    "Recall that CNN's are defined by a few types of layers:\n",
    "* Convolutional layers\n",
    "* Maxpooling layers\n",
    "* Fully-connected layers\n",
    "\n",
    "You are required to use the above layers and encouraged to add multiple convolutional layers and things like dropout layers that may prevent overfitting. You are also encouraged to look at literature on keypoint detection, such as [this paper](https://arxiv.org/pdf/1710.00977.pdf), to help you determine the structure of your network.\n",
    "\n",
    "\n",
    "### TODO: Define your model in the provided file `models.py` file\n",
    "\n",
    "This file is mostly empty but contains the expected name and some TODO's for creating your model.\n",
    "\n",
    "---"
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    "## PyTorch Neural Nets\n",
    "\n",
    "To define a neural network in PyTorch, you define the layers of a model in the function `__init__` and define the feedforward behavior of a network that employs those initialized layers in the function `forward`, which takes in an input image tensor, `x`. The structure of this Net class is shown below and left for you to fill in.\n",
    "\n",
    "Note: During training, PyTorch will be able to perform backpropagation by keeping track of the network's feedforward behavior and using autograd to calculate the update to the weights in the network.\n",
    "\n",
    "#### Define the Layers in ` __init__`\n",
    "As a reminder, a conv/pool layer may be defined like this (in `__init__`):\n",
    "```\n",
    "# 1 input image channel (for grayscale images), 32 output channels/feature maps, 3x3 square convolution kernel\n",
    "self.conv1 = nn.Conv2d(1, 32, 3)\n",
    "\n",
    "# maxpool that uses a square window of kernel_size=2, stride=2\n",
    "self.pool = nn.MaxPool2d(2, 2)      \n",
    "```\n",
    "\n",
    "#### Refer to Layers in `forward`\n",
    "Then referred to in the `forward` function like this, in which the conv1 layer has a ReLu activation applied to it before maxpooling is applied:\n",
    "```\n",
    "x = self.pool(F.relu(self.conv1(x)))\n",
    "```\n",
    "\n",
    "Best practice is to place any layers whose weights will change during the training process in `__init__` and refer to them in the `forward` function; any layers or functions that always behave in the same way, such as a pre-defined activation function, should appear *only* in the `forward` function."
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    "#### Why models.py\n",
    "\n",
    "You are tasked with defining the network in the `models.py` file so that any models you define can be saved and loaded by name in different notebooks in this project directory. For example, by defining a CNN class called `Net` in `models.py`, you can then create that same architecture in this and other notebooks by simply importing the class and instantiating a model:\n",
    "```\n",
    "    from models import Net\n",
    "    net = Net()\n",
    "```"
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      "--2021-03-17 17:43:30--  https://s3.amazonaws.com/video.udacity-data.com/topher/2018/May/5aea1b91_train-test-data/train-test-data.zip\n",
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    }
   ],
   "source": [
    "# load the data if you need to; if you have already loaded the data, you may comment this cell out\n",
    "# -- DO NOT CHANGE THIS CELL -- #\n",
    "!mkdir /data\n",
    "!wget -P /data/ https://s3.amazonaws.com/video.udacity-data.com/topher/2018/May/5aea1b91_train-test-data/train-test-data.zip\n",
    "!unzip -n /data/train-test-data.zip -d /data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">**Note:** Workspaces automatically close connections after 30 minutes of inactivity (including inactivity while training!). Use the code snippet below to keep your workspace alive during training. (The active_session context manager is imported below.)\n",
    "</div>\n",
    "```\n",
    "from workspace_utils import active_session\n",
    "\n",
    "with active_session():\n",
    "    train_model(num_epochs)\n",
    "```\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import the usual resources\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# import utilities to keep workspaces alive during model training\n",
    "from workspace_utils import active_session\n",
    "\n",
    "# watch for any changes in model.py, if it changes, re-load it automatically\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "## TODO: Define the Net in models.py\n",
    "\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "\n",
    "## TODO: Once you've define the network, you can instantiate it\n",
    "# one example conv layer has been provided for you\n",
    "from models import Net\n",
    "\n",
    "net = Net()\n",
    "#print(net)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Transform the dataset \n",
    "\n",
    "To prepare for training, create a transformed dataset of images and keypoints.\n",
    "\n",
    "### TODO: Define a data transform\n",
    "\n",
    "In PyTorch, a convolutional neural network expects a torch image of a consistent size as input. For efficient training, and so your model's loss does not blow up during training, it is also suggested that you normalize the input images and keypoints. The necessary transforms have been defined in `data_load.py` and you **do not** need to modify these; take a look at this file (you'll see the same transforms that were defined and applied in Notebook 1).\n",
    "\n",
    "To define the data transform below, use a [composition](http://pytorch.org/tutorials/beginner/data_loading_tutorial.html#compose-transforms) of:\n",
    "1. Rescaling and/or cropping the data, such that you are left with a square image (the suggested size is 224x224px)\n",
    "2. Normalizing the images and keypoints; turning each RGB image into a grayscale image with a color range of [0, 1] and transforming the given keypoints into a range of [-1, 1]\n",
    "3. Turning these images and keypoints into Tensors\n",
    "\n",
    "These transformations have been defined in `data_load.py`, but it's up to you to call them and create a `data_transform` below. **This transform will be applied to the training data and, later, the test data**. It will change how you go about displaying these images and keypoints, but these steps are essential for efficient training.\n",
    "\n",
    "As a note, should you want to perform data augmentation (which is optional in this project), and randomly rotate or shift these images, a square image size will be useful; rotating a 224x224 image by 90 degrees will result in the same shape of output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from torch.utils.data import Dataset, DataLoader\n",
    "from torchvision import transforms, utils\n",
    "\n",
    "# the dataset we created in Notebook 1 is copied in the helper file `data_load.py`\n",
    "from data_load import FacialKeypointsDataset\n",
    "# the transforms we defined in Notebook 1 are in the helper file `data_load.py`\n",
    "from data_load import Rescale, RandomCrop, Normalize, ToTensor\n",
    "\n",
    "\n",
    "## TODO: define the data_transform using transforms.Compose([all tx's, . , .])\n",
    "# order matters! i.e. rescaling should come before a smaller crop\n",
    "data_transform = transforms.Compose([Rescale(250),\n",
    "                                     RandomCrop(224),\n",
    "                                     Normalize(),\n",
    "                                     ToTensor()])\n",
    "\n",
    "# testing that you've defined a transform\n",
    "assert(data_transform is not None), 'Define a data_transform'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of images:  3462\n",
      "0 torch.Size([1, 224, 224]) torch.Size([68, 2])\n",
      "1 torch.Size([1, 224, 224]) torch.Size([68, 2])\n",
      "2 torch.Size([1, 224, 224]) torch.Size([68, 2])\n",
      "3 torch.Size([1, 224, 224]) torch.Size([68, 2])\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
    }
   ],
   "source": [
    "# create the transformed dataset\n",
    "transformed_dataset = FacialKeypointsDataset(csv_file='/data/training_frames_keypoints.csv',\n",
    "                                             root_dir='/data/training/',\n",
    "                                             transform=data_transform)\n",
    "\n",
    "\n",
    "print('Number of images: ', len(transformed_dataset))\n",
    "\n",
    "# iterate through the transformed dataset and print some stats about the first few samples\n",
    "for i in range(4):\n",
    "    sample = transformed_dataset[i]\n",
    "    print(i, sample['image'].size(), sample['keypoints'].size())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "use_cuda = torch.cuda.is_available()\n",
    "device = torch.device(\"cuda:0\" if use_cuda else \"cpu\")\n",
    "torch.backends.cudnn.benchmark = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Batching and loading data\n",
    "\n",
    "Next, having defined the transformed dataset, we can use PyTorch's DataLoader class to load the training data in batches of whatever size as well as to shuffle the data for training the model. You can read more about the parameters of the DataLoader, in [this documentation](http://pytorch.org/docs/master/data.html).\n",
    "\n",
    "#### Batch size\n",
    "Decide on a good batch size for training your model. Try both small and large batch sizes and note how the loss decreases as the model trains. Too large a batch size may cause your model to crash and/or run out of memory while training.\n",
    "\n",
    "**Note for Windows users**: Please change the `num_workers` to 0 or you may face some issues with your DataLoader failing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load training data in batches\n",
    "batch_size = 40\n",
    "\n",
    "train_loader = DataLoader(transformed_dataset, \n",
    "                          batch_size=batch_size,\n",
    "                          shuffle=True, \n",
    "                          num_workers=0)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Before training\n",
    "\n",
    "Take a look at how this model performs before it trains. You should see that the keypoints it predicts start off in one spot and don't match the keypoints on a face at all! It's interesting to visualize this behavior so that you can compare it to the model after training and see how the model has improved.\n",
    "\n",
    "#### Load in the test dataset\n",
    "\n",
    "The test dataset is one that this model has *not* seen before, meaning it has not trained with these images. We'll load in this test data and before and after training, see how your model performs on this set!\n",
    "\n",
    "To visualize this test data, we have to go through some un-transformation steps to turn our images into python images from tensors and to turn our keypoints back into a recognizable range. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load in the test data, using the dataset class\n",
    "# AND apply the data_transform you defined above\n",
    "\n",
    "# create the test dataset\n",
    "test_dataset = FacialKeypointsDataset(csv_file='/data/test_frames_keypoints.csv',\n",
    "                                             root_dir='/data/test/',\n",
    "                                             transform=data_transform)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load test data in batches\n",
    "batch_size = 32\n",
    "\n",
    "test_loader = DataLoader(test_dataset, \n",
    "                          batch_size=batch_size,\n",
    "                          shuffle=True, \n",
    "                          num_workers=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Apply the model on a test sample\n",
    "\n",
    "To test the model on a test sample of data, you have to follow these steps:\n",
    "1. Extract the image and ground truth keypoints from a sample\n",
    "2. Wrap the image in a Variable, so that the net can process it as input and track how it changes as the image moves through the network.\n",
    "3. Make sure the image is a FloatTensor, which the model expects.\n",
    "4. Forward pass the image through the net to get the predicted, output keypoints.\n",
    "\n",
    "This function test how the network performs on the first batch of test data. It returns the images, the transformed images, the predicted keypoints (produced by the model), and the ground truth keypoints."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# test the model on a batch of test images\n",
    "\n",
    "def net_sample_output():\n",
    "    \n",
    "    # iterate through the test dataset\n",
    "    for i, sample in enumerate(test_loader):\n",
    "        \n",
    "        # get sample data: images and ground truth keypoints\n",
    "        images = sample['image']\n",
    "        key_pts = sample['keypoints']\n",
    "\n",
    "        # convert images to FloatTensors\n",
    "        images = images.type(torch.FloatTensor)\n",
    "        \n",
    "        key_pts = key_pts.type(torch.FloatTensor)\n",
    "\n",
    "\n",
    "        # forward pass to get net output\n",
    "        output_pts = net(images)\n",
    "        \n",
    "        # reshape to batch_size x 68 x 2 pts\n",
    "        output_pts = output_pts.view(output_pts.size()[0], 68, -1)\n",
    "        \n",
    "        \n",
    "        \n",
    "        # break after first image is tested\n",
    "        if i == 0:\n",
    "            return images, output_pts, key_pts\n",
    "            "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Debugging tips\n",
    "\n",
    "If you get a size or dimension error here, make sure that your network outputs the expected number of keypoints! Or if you get a Tensor type error, look into changing the above code that casts the data into float types: `images = images.type(torch.FloatTensor)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([32, 1, 224, 224])\n",
      "torch.Size([32, 68, 2])\n",
      "torch.Size([32, 68, 2])\n"
     ]
    }
   ],
   "source": [
    "# call the above function\n",
    "# returns: test images, test predicted keypoints, test ground truth keypoints\n",
    "test_images, test_outputs, gt_pts = net_sample_output()\n",
    "\n",
    "# print out the dimensions of the data to see if they make sense\n",
    "print(test_images.data.size())\n",
    "print(test_outputs.data.size())\n",
    "print(gt_pts.size())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize the predicted keypoints\n",
    "\n",
    "Once we've had the model produce some predicted output keypoints, we can visualize these points in a way that's similar to how we've displayed this data before, only this time, we have to \"un-transform\" the image/keypoint data to display it.\n",
    "\n",
    "Note that I've defined a *new* function, `show_all_keypoints` that displays a grayscale image, its predicted keypoints and its ground truth keypoints (if provided)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_all_keypoints(image, predicted_key_pts, gt_pts=None):\n",
    "    \"\"\"Show image with predicted keypoints\"\"\"\n",
    "    # image is grayscale\n",
    "    plt.imshow(image, cmap='gray')\n",
    "    plt.scatter(predicted_key_pts[:, 0], predicted_key_pts[:, 1], s=20, marker='.', c='m')\n",
    "    # plot ground truth points as green pts\n",
    "    if gt_pts is not None:\n",
    "        plt.scatter(gt_pts[:, 0], gt_pts[:, 1], s=20, marker='.', c='g')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Un-transformation\n",
    "\n",
    "Next, you'll see a helper function. `visualize_output` that takes in a batch of images, predicted keypoints, and ground truth keypoints and displays a set of those images and their true/predicted keypoints.\n",
    "\n",
    "This function's main role is to take batches of image and keypoint data (the input and output of your CNN), and transform them into numpy images and un-normalized keypoints (x, y) for normal display. The un-transformation process turns keypoints and images into numpy arrays from Tensors *and* it undoes the keypoint normalization done in the Normalize() transform; it's assumed that you applied these transformations when you loaded your test data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c73e1e10>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QKKS03ZXMgjzudrtVYlEcatEc8jpJJwjo3iqLsSWAEgwG8fl8pNNppUl8Ph+dnZ2KoHK73XR2djI4OEgul1PcgyS2pJzA6XTS0dGB0+kkk8ko89TT00Nvb6+68aJpRD23rz752+VyKb/A7XarTLcwqGbfRyIcWakS9kuOSt5LmFtzbYrUzBiGgcfjUddDWN1AIEBHR4ciJiX6Ed9IiD8Bomiat0q2BFBefPFFdF2nWCxSqVRIpVJMTk6SSCRIpVLKJ5mYmGBhYYG1tTXle4hmyOVyysbH43EA1tfXKZfLNJtN5ubmiMfj5HI5SqUSwAYfRKTdeZW8kdPppKurC4fDoQDi8XiUzySmSDSBFBBJyYSYrHA4vCF3JCG0+EV+v199/vLysvJBDMNgbW1N+Wblchmn06nOW16Tz+eVWXsrgbIlnFmn02mI31CtVlU4KYXDEjWIY2eOTkTdy4qs1+uK2zBnjSW0lWPMallMhbyH2bfo6enB6XQSiUTYuXOnMhdyE4QQrNVqpNNplX+x2WwEAgFcLpeqPXE6nYTDYQUwc/RljkYEAMlkUhVfzc7Oqmo6Od5qtdJsNjc44oVCQTHX6XT6dU3P2yopeOTIEQKBANlslrNnz+J2u9m9ezdDQ0Osra3xi1/8AqvVSiQSUaziwsICxWKRXbt2sXPnTpaXl7l48SKVSoVDhw7R19fH3Nwcy8vLG/JCjUZDRRQul0uZnHw+/xr6W55zOBz4fL4NZQwOh0OFtS6Xi1KppHwDKZUUs9PZ2bkhy+xwODZkeIV+F99D8lvlcpl8Pk8qlSKTySjuBC4z0e3MsxCKZib6rZAtAZQdO3YQCoVYW1tjbm6Ojo4OxsbGOHr0KNPT00xMTOB0OhkbG+Pw4cOqsLlQKHDDDTdw4MABpqenyeVyZLNZDh8+zJ49ezb4PVLMk06nFfUu/o1c2Ewm85ralfasr9xw0XZm0yGJSHM0JXU1UoPS/lq5mTabTTml1WqVarVKNpulUCioZKlQ+3Iucp4CNgG8RDxvhCd5PdkSQJEaCSlQkpUlF6lareJ2uzeYBkDxGWa+wO12qxA1n8+rC+v1ejfQ8qJhgA0pd7nB4pRKZhg2choS/spxYkbEbAl4rFarouUlIhJNIBXz4muJU1ooFCiVSuTzecrlsiL02kN38evkfeS4K+V+flXZEj5KIBAwxLmTVL40dhWLRXK5nHIKPR4PuVyOfD6Pw+FQkYRQ841Gg46ODjwej2IzJUoRYk54DmFHxVzIqhRAeDweent72bFjB52dnarizOl0KhMiN6k9Oy2AMdP+AkDJ0wjoBTRCBgpIxBmv1WrKqTdX/UuUJRyMiDwnbK/58Xbu5G3lo9jtdlX2KL5CtVpVK1kuRqFQUI6b9PpIhld4BWlTkHYNKfzxeDy4XC4ajQbZbFa9h3mVm+lus30Xh7Fer2+g3s3pAQGAaCGzo2yOzoSeF3CIE3slJ1vOQ7SVHC+8ipgYSUKKJhb/SD7jrZAtAZQbbriBUChENBrl5MmTqu5zeHiY1dVVXnzxRYLBIHv37mVoaIiVlRVefvllyuWyIsLS6bTKJr/zne+kr6+Pl19+mYsXLwJwxx13MDAwwNTUFE8//TSVSkXR4ZKNNdemAKroSG62aAepcwWUtjCLWUu3s7wStYgGM5sd0U5mTqXRaFAulzeYIDM5J4vCHA3JectieStkSwBlbGwMv99Po9FQVPnhw4cZHx9nbm6Oqakp+vr6uPvuuxkbG+PUqVNks1mWl5e57rrriEQizM7Oksvl8Hg8HDlyhL6+PuLxOEtLS/T29nL33XfT29tLV1cXZ86cIZvN0tHRgdfrVQVOQpcDaiWn02mCwSDBYFDlb8zaq1QqKYpfKt7EtAk1b/ZDzKRce5egmQqQGyy+llT2SXuI2ZmVGhVAcULiHJuB8kYo+3bZEkCZmJjA7Xar9gan08nKygo2m42ZmRlVH3v69Gmy2SynTp0iGo1SKpWIx+MYRqv1U8yW9MZcuHCBYrFINpvl3LlzxGIxpqamlONssVgoFouqrUPUvvzouk65WMZRdNCoN2g2mtgLdgiC1+tVr69Wq6oeRrSO+BHi84jGEhMmpQ5mDgjY4KiLHyMAM2sbc9JSXiPPeTwe3G63Or+3QraEM9vZ2WlYLBZyuZzqcQmFQng8HorFIrFYDLvdTjAYxOPxqL7dWq2mfA+JFHRdp6OjA5vNpsgqu93O/v37sdvtpNNpZmdnVZ2GuUHcbHp0XcdoGPyt5W8Za4yRCCew2qx0rHaQ7k8z+aFJtKCGp+Gh7q1Tq9dUq6Y59yJmy2KxoKFBGmqeVuG0JWeh4qpQb9TV54pJqVQqiomNRqNEo1GVJhByTc63vWDc7/fT1dUFwNzc3DW5lLeVMxsKhXA4HAQCAVZWVpQTJ5FFOp2mWq2+puUTLrdGmhuzhScR7kJunEQs4uh1dXURCAQUoKTWVZhdd8nNSHmEha4FBhODZL1ZtKZGaCnELX97Cw1HA72qkxnMcPq/nsbn821Y3eKTGA0DPauz97t7CSwFSPenMTAIrYRI9iV59gPPAuAoOdA8mjJdXq+XWq2G1+t9TX+zaBUxMeaIplqtks/nN7Sntpd6vlHZEkA5duwYfr+fpaUlotEoXq+Xffv2cfToUaLRqMoeX3/99ezYsYPp6WkmJyep1WqMj48zMjLCzMwMExMTlMtljh07RjgcZm5uTpm1O++8k507dxKPx/n+979PLpfj6NGjvPOd72R+fp7nn3+eWCxGJBLB6/WysrTC5zKf44Nf+SAFZwHd0NHQGL80ztcf+joWw4Kl3NISgaUAtqKNeDGuqt/Eh9DQOPpPR/HOe9EMDQ2N4HKrX1o3dDpWO/A3/Bz5tyOEVkKs967z09/86YaaW2GCpRPSzAeZm+rNIXmpVHqND/S291GCwSA9PT0q0SUFQoFAQCW5wuGw4jSazSbLy8tUq1X6+/sZGBigUqmowTT9/f309PSwurqq0viDg4Ps3LmTZrOJy+XC5/Nx8OBBDh48iM/nU76QOKVBLYi7w03BWQANmjRBg4kdE5w5eIYDEwcw7AZ6TSe/I4+jx8GAdUCtfIlS9LSOd8GLbugYGDT1Jun+NGgQXA6S6m+N6AithNCbOp3RTlxlF41mg6JR3FBYJWKuwIPLptLn86nal3g8viGX9KvKlgDKM888o/IUkgWenJxkbm6OXC5HMplUK2Rqaor19XVWV1ep1WqcPHmSWCzG8vIyi4uL6LrO888/r3pvS6US0WiUZ555hnPnzrG4uMjq6ioul4uzZ88Crfks586do1KpsLS01MpCp9IUy0XcZTdFZxEMwAC9ofPFe79I/z393KffR0+9h7qnTrPYVBVowsRaLBYs3RZKwyXcs24KOwvM/t4sJWeJSrmCtWCl4qrQqDVI9iXpWOlgrXuNYz86RjgWJtoV5ZF3PbJBg7QzrxKeS1N/T0+PysC/VaExbBFn1uVyGeJ3mHuKzTNJxO+Q0FJqMiRkNQxDsZOSdBPnEtgwMSCbzao2y0AgQCaTUTkhIasMw8BoGNirdnI7c9hiNgJDAVY/uNqafGeAhsZAY4CP1T+GhqZGTTSNJvlmHg8eNF0jX88TKAaoOCtoFo2KtYLH8Chfo1wuUywU0TIazXqT93/n/eiGTlNr8v37vk+8FlcLon04kABT5snIObzyyiuqcOta8rZyZjs6OlRxcyKRwOv1smfPHg4fPkwmk+EnP/kJ1WqVoaEhAoGAigLcbjfXX389Bw8e5MKFC7z00kusr6+zY8cOurq6WFpaIplMKlpfLqrwGh6PRw2dkbKBvr4+/H4/lVKFYrTIwscWqPfVsVQtxGyx1g00fhkdaQbL+jJzF+YIdARa0wrqHh4KPUTUHqWz1ImGxpprjW6tmztm7+DJ/idJuBL0Vnv5SPQjFAIFArYAukWn7C5jtVhZ71unc7WTRG8CguCv+Ont7SWfz5PNZjc0lfl8PsLhMENDQ1gsFvx+v2qcN9fw/qqyJYAiMb8k0GTm2P79+4nH47z44osARCIRurq6VAN3R0cHQ0ND7N69m1qtxtTUFPV6nX379qlBN4VCAavVyvDwsOq9TSaTaFprMF4oFKLZbJLL5ejo6GDPnj04HU7uefIevHUvH+n9COhQdpRBo2WCfvlba2jsWd7Dp/6/TxHviqOhYSvZ+Osv/TWGZrDmbNX/okHMEWPywiRru9YwNIOYNcZ/6P/Bed95QsUQvzn3mxhBg7qzzpO//iTuihsj0PKBADUyI5fLYbPYCGgBmt1NIuEIO4Z2qHpcaVsVWv+tki0xPlTK+0RVyo2LxWKsra0pIk2OkU7+UqnEysoKs7OzrKysqGo2uWhmFlTMmuRTpC0ik8mo1LyEj66Ki0gmQmehkwOLB6AJrqoLraGhN/UWWIDR5VG+8Q/fIOvO0rPWQ0+ih858JwcutV7jSDhwJpzQhJHFEf7qpb9idHkUvaEzujzKVP8UTUuTlDvFrz3xaxy3HufbPd/mh6EfUnaXaRqXi6ikyNtpd/IX1b+g88OdxH8nztkbz9JoNlQW3Vzs9VZmkbeERjFzJ9JPG4vFeOGFF1QlfSqVIh6Pb8i2yvSgn//85+q4ZrPJT3/6U6VNKpWKSg6Kb1MqlbDZbMTjcWX3hfXMZrNoaNxkvYnR+iif/s6n+Zf3/Qu7uncx/vw4f3TfH7U0CnA+cp4v/P4XuDBwgdH4KA/89AF2XNzBH//oj/n2e75NfD5OLB7D7rPzzTPf5Csf/wpTA1OMrI7wN//wN3z5419mMjLJ+OI4FixM901jaAZxZ5xSvoTVuJzDEd+k19lLv9HP2chZmpYm+VCexclF7Da7GtIj82PeSv9zSwBFogQhzIR5bK8i13Udv99PtVolk8koDSBknHAG0ropj0uJoGShAVWlLsXSknwTYu5PXX+Kq+aiECxwXe46bAM2Jt85SWe5k4Q7cRksg+cxdIOzfWf55Ec/yVBliPtq97GnsYdIZ4Tvub5HypviD2/6Qxb6FmhamlwYuMAXfv8LWJtWNDQqegVf0cfI6ggXBi7QU+3B1XRhsVs2EG2aplH1VEkVU4wvjnNm6AzhSpg9/Xtwuy5PcJD5um9l4dKWiHrGx8cNt9tNIpEgFothsVgYGBhQU4JOnDiB3W5neHiYoaEhUqkUFy9eJJ1O093dTVdXl6K6K5UKo6OjiuVdW1ujXq8zMjKiEoAyZXJgYIBdu3axvr7OxYsXVYFUwBfAWrQy/evT1PvrhHIhfrfxu7icLhpGg4edD7OqrxKpR2jqTVb0FZpa66ZYGhb+/rt/z/n3n6fmrPG3lr/F0AwwwJPyUAi1eBmaLcKtaWmiGRq/Pfnb2Nw2NJ9GwBrAoluUiSyXy8zNzZFMJmk2m4S7wuzt2UvGk6E30EutWlNhcqPR4D/+4z+4dOnShhqVq8nbKupxu92EQiGy2SwWi4VAIMCOHTs4dOgQqVSKmZkZDMNgaGiIsbExNWFRepR37txJNBrl1VdfJRaLceTIESKRCJOTk/ziF79A13VGR0cJBoOsrKwQjUbxeDyMjo6yf/9+ZmZmiMfjFItF+nv7+fz85/E1fHykr+XIpv1paoUaHt1DrVLjQ9kPUbaUCVgDhMNhynqZb+W+xUJjgfHFcXbM7GChsoBm0einn2XLMgB+nx9P3UPcGgcNrIaVmlEjYkTYvW83jXpD+VXikwGqvSMYDGKxWOjr68PpclIttZrgbFabIirFjzMXoL8VsiWAsry8TCKRUJnYXC7H6uqqGi4jvEc0GlVtlAKqeDyuxngmk0my2SyXLl1SvyUtPz8/j8PhIJvNqqqx5eVlDMNQYbTD4UDLagxlh9DRGV8cZ2Jogo5CB9aqFZvL1updrtZwO9wYTQNd0/Hg4ROWT9DzUA8753eSHkhTdVex2+z8ZuU3+Tv336lI5/7S/TxkfQhDM6jrdT5R/QT99v5W/km/DBKzNhB2GQADLDkL3/Z9m2hnlMHmIB/n4zjsDjVwB97YsOHNyJYASiKRUN69RDPT09PEYjHVXKVpmiqyNjdyV6tV5ufnVblAo9HgxIkTKrUvVLpMF5LkoaZpXLhwgaWlJdWXU61WmcpPcc5yjrHGGB9/F4qCAAAf1klEQVR/6OP8xchfMNwxTGZvhq7O1iRFOUcA3aKTrWU5+P8cJLgYJNWT4vh9x2lWm1htVsLuMIPGIMvaMjutO9nXuY8d5R1cMi4xYAzQrXdj0S3K2dZ1XRVXi48hRGCj3uCOR+/AWrDyjS99o8XjWJZxBp3YKi2SMJlMqma4t1K2BFD279+P2+0ml8sxPz+PpmlqvGWpVGJubo56va4mNEofjVSJASoMNgyDUCiEz+dTdbRWq5VwOEwgENjwGcFgkKGhIdLpNIuLizSbTTo6Ovjn7n+mGq9y7q5zlPvKTKxNMBAdANiQcLM77Pyvwv9irjbHgdsP8OBDDxKKhXDX3NR9rf4it9vNp0ufZjWzSi1TY8mxxAcdH6TuqBOyhXC4HCpCERCbSzjFfBiGga1gozvejWZoHLh0gDM7zrDLugvyUKgWSCQSTExMqHKDt8rswBYBytjYGJ2dnUSjUZWHGRsb48Ybb2RtbU01XY+OjrJ3715VgJRIJBgcHCQcDpNIJFSIfN1116mp16dOnaLZbKqqt5WVFdLpNBaLRbG6iUSCJ554gkqlwv79+xkbHWPkX0b4fN/nwQKVcAVryarqc8UH8Lg8zNXnaGpNJocmSbqTaEENI2Bgt9oVSeZ2uwn4A5TDrTmvMuCvvQZWHFcRc/QHUHVXiXfH6Yp38bnnPsf0zmlC1pCqJ56bm2NhYeE1LSdvhWwJoEirZyKRUA1VMidFkoTCn8gYLHH62mtKAdXmYW6ZkMJtofRlqLB8DqB6aWJTMe5evLsVgkbO4M/6ceMmk8lgs9lYW1tjYGCALncXw+VhZuuzjMZGCRVDJAOt7j6L1aJMhoxhlxSCnK+EsKIZJbVgHt5jrp0FePTOR/npwE+JuqJEiPCh9Q9Rr9V59dVXOXv2rDLJ7QXiv6psifC4u7vbkFyPdPF5vV56enqo1WrMz89jtVqVOUqlUsRiMRXOmvt/xXzIiFHhW7q6utQwvWQySSAQUHkdqb+VubVul5svL3+ZkeYIf/iJP2S+f55wOczd8bupVqo4HA527tyJz+fDarWycHGB//LN/4IVK02tyY8/8WPSeppmo8mQb4gdR3agW3RF9gnPYd7GxVzeaG7/ECBpmka5VKaUL/HD63+IoRnohs6Hlz5MZiXD2bNnX5M03AxQ3lbhcTqd3lBrKvPLxFYDavyW0PzmnTPEsRSKPpVKqahI3iMajarEI6DS8DLZwLxtSa1W44/tf4zD5iDZlwQd1lxrpCopaumaGoJTr9X5h4v/wLnwOZ78r0/y9Ye+TqYnQ9PXxBl3cvMTN9OT6KGwq8DKl1doGI0NHYICkvZJT3C5VUO1mtYb3P3E3fQmeznbc5aLgxcJ5AJcOHWBleWVDQ3y/zdkSwBleHgYn89HKpVidXUVt9vNyMgIO3fuZG1tjZdeekmVNUodrWgeKdSRSZAOh4Pe3l6CwSCpVIpUKoWmaRw7dozh4WEWFxc5fvw4jUaD/fv3s2fPng1tInv27GHnzp0szC8w/+o8hXiBak+VUCFEbC6Gy9kqesrkMiwVlpgMT2JYDCYjk6TdaQKxADd86wa6Ul3otKriPHMe4hfiaJ2ayupKL5DMmG0f7COAkoWjZTT6kn1YDAvf/H+/yed3f54aNfJ6XtX+yjUwl0y+VbIlgCLlflarFU1rzZnv6elheHgYp9PJ6dOnVQWX3+9XCT4pJJZ2TbnYsoVcPp9XBN7Ro0fVZgRnz56lVqvR1dXF2NgYTqeTCxcuqPmtPq+Pj5/6OH3rfcx+e5an7nuKSrrCYm0RV8iF3Wnnm+5vUtNrrQRhA/Yt7iNQDPDAxx9Q+ZuvP/R1NE1jrWeNtcYavrJPJfcMw9iwm5m5CQ0u+yeSmihbyywHl+lL9/Fqx6vUjBq9vb34/X5eeOEFVd0mCc4raZe3fc2shLsypE7KCKLRKPF4fEPrpRBmApRisYjL5VIDgiWvI+2jctFkd6/V1VVVr1EoFFSdruSF4vE4lqyFvvU+LFgYzg/zfPJ58vW82rAgZsSo7aqpfA8anOs7x8vBl5mMTNKwNJiMTLK4Z5HFuxdZzC9SzVYpV8oEg0H1HaWrEC6vfnOhtNxsMbWP7H+E565/jmQwiWfdw+j8KDfecKNKZzgcDoLBoNpyzwy8X1W2hDPrcDjUfBRzW6asNqlUk+p0iQLM81HEXxGVbZ5PD+Dz+VSfi3ArkoxsNpuqIMjtdmOz2vhq9qvsa+7jnOUcXxv4GgUKlJPlVsuFDoXPFjDsv7x2v6xP2bOyh4v9rc7EseUx3tV4F566h5KjRLVW3VDlL9V65lIAc7O5REG1Wo1KucK9z9yLu+bmI1/8SCs/1NR4/8z7ueudd5HNZvnzP/9zVaAlZRvtI1Lf9r3Hss1JoVBQq1Zmy5fLZbVhosvlwu12qy5/86YDsnqk29DsyxiGoXa/qFarLC4uqtA5FAqp0FnA6fV6+W/Gf8OSt1CwF2je3aTSXUFf0nE/4qZurTP87WE+VP8Q3/i9b1B0tmprZ3tnQWvV1f73h/87FUuFvlwfy8Fl/vn6fwYNRRqKryKgl8jH7F+IJrEX7QykB9ANnQOLB5gYmiCQDeBsOvH7/fT39xMIBFhbWyObzdLV1YWmaYqpfitkSwBl//79+Hw+8vk8J06cQNM0BgcH2bVrF2tra0xMTKgWjuHhYaanpzl//rwKmR0OB2tra0pTDA8P09PTw/T0NPV6HZ/Px2233cbw8DDz8/M89thjOBwO9u/fz/79+1VNS7PZZPfu3fT397O0tMT09DSDPYNMd0+DDs2BJoWPFDD6DWaY4Zvlb/LwXz/Mswef5faJ23ng9x9gamCK8cVxNDT6s/3o6PSke0hkEvTme8l2Z1X/T3tzPKC0iPyUy2VyRo4zvWcYj47zhX/9At96x7fw6l4CgwE6OztVX7bwUNVqlUAgQCAQUNv/mgut34wV2RJAkT13pHFchtfIQD3Z5Mjn8ynCDdigxiXkFNUqZJqUPPb399Pd3a0mOfp8PiKRCP39/QD09PRgGAZ79+6ls7OTWq3G4sIif7LwJzx46UEmhybxFr1k+jLKNyk4C7z/z94POnzt3q9BE3bFdtGkyW9/6bcZXxznLx/6Sz7wlQ9QdpbxlD1856+/w9+97+/UQB64zHfI+Ao590qlQrFU5NThUzz1zqfoSHdw44Ub8Vv8eL1edu7cqfY4vuWWW5ibmyMWi6ncmWxzFw6HVdVgIpFQubE3IlsCKFNTU2oPQLm5i4uLGwbKaJrG3Nyc2iZW2k/NTK7Y9mg0yvr6OplMRs0yO3nyJOfPn1dZ5mq1ysWLFxV5t7CwgM/nY3p6mmg0ytLSEnpOJ5KO8OBDD7LmWeNb7/oWz449Sz7YGmiMQauYVGppLTDXN9d6ToMzkTP82cE/o+xs1dsWnAUSXQn6a/1YbJfnzZoJNzG1ok3KWplsIIuhGyRDSTSfhkdvbdMSDofx+/1ql6++vj6SyaTyb9bX19H11lj3UCikto3buXMn2WxWDUXcjGwJoCwuLm5o1pbVJUN2xdmUUaLm8Q/tqfVGo8H6+vqGwb/ZbJZnn31WTReQm3HixAm8Xu+GqCuRSOB0OlvqulLlnOUco81R/vS+P2UmMkOgFGid9JVcQFPhNQY4a07+x8T/4N577qVkL+Epe+hd76XQVcBn+Da0k8iEBLMTWy6W+dTZT1HaUeJM5AyhYgh7zU7d0ho8HIlE1HgL6fmRER6AmtGfz+dVQ5imafT09NDV1cXevXs3fY+2BFDe85734Pf7SSaTvPLKK8r3GB4eJpFIMDU1RaPRUHY3l8upvXs6Ozvxer0kk0mVixkdHWVgYIDl5WVmZmaoVqvceOON9PX1EYvFOHnyJIZhMDIywq5du0gkEpw/fx6LxUJPTw87duxgfX2dCxcu8L9D/5uhgSFmIjMYukHanaaz2sm6fX0DKHRDx1a1UXH8so5Eg4qtQsFd4F//8l95+FMPE06H+f7vfB+HxaFGasnikN8C4kqlgqfmYWd+Jw8+9CBJT5In73mSaqjla3R0dDA6OqpY3aWlJdbX11VJqXkEmPwvUaJstWfuPnw92RJAGRsbY2RkhFgsxtzcHG63m0OHDnH06FGWlpaIx+NUKhV6enrUIN9isai2aQ0Gg8zPz6tK+gMHDjAyMoLb7WZtbQ3DMDh27JiaoyIbP+3bt48bb7yR6elp1tfXgdZQn7GxMWZmZlor3tD4yImPsDq02koQ5v3cnr2dn3T+hHXnOs6Kk7K9zNjiGBoaZyNncVadVOwVxhfHCRQCJPuT+B1+St0lXDXXhtpg8wSFRqNBpVqhZqthxw4uWA4uM5AeoOauUbKXsOmtxrgjR44o5rZarRKPxxWNb2Zn2xOEAizRYJuVLQGUZDKpKuKFN8lms6oYSUZvxWIxstmsygPpus7a2hrlcplEIqGc4WQyyfLyskoc1mo1zp8/TywWY3V1VVHd6+vrTE5Oqtkq0us8MTHB+vo6gUAAUjCUGeLBhx4k4U7wyd/7JI8MPkJ/s5/fyf4O3/V/F3Q4P3QeAwNDN6jaq/yfv/s/+G1+Hr3/UQiB3WZXpk9ACaiJBI1Gg6bR5NSRU2R8GYL5ILdM38Jjdz5GwAhQdVcVbfCud72Lm2++GbvdTqlUYn19nenpabWnj3nshtkHkmJ10SRvJPrZEkB56aWXOHfuHOVymVQqha7rnDt3bsN8VRk+I0ymJANLpZLKHouNnpiYUJOqZZW98MIL2Gw25Rzrus7FixfVvsOBQMv3kMG/sl9xrVrjvPU8o/VRpvVp8t150GBVXyXsDTPIIEvGEhEtgqEZLBlLDOqDXPrtS63kYNOpeB65WeaxXubvU9bLZL0txzXjyVCz1fBYPJRtZdyu1viO4eFhbrjhBjXlUnYfSSQSCjhweUauMNoib3as6JYASiKRYH19XaG/Wq2SSCTUHjzSWiEX1szMyugq8yAc2WSpUCgoWj+ZTOJyuZQzJ7NfZQCfjEeXzxIHuV6v80W+SNgR5iv5r3Dw0kEmhyYZMAYIWoPc37ifsl7GQ+v9pK+4br/cPmJON0iTlmJmNR0jZVAySnSWWw1nkivqrnXTdF2eAxMIBHjve99LV1eXMinShru+vr6hztbcDAaXtYdonDfKpWwJoNx66610dHQQjUZ58cUXcTqdHDp0iJtvvpn5+XkeffRR5aSOjY2xtLTExMQElUqF4eFhuru7WV1dVSWO73vf+xgaGuLcuXPMz89Tr9fVptmyF7LsDio1LAI+c67FXApQqVYYN8b5m4f+hjX3Gk98+AkywUyrjdRmI1vLXp5l60Z17knILqF/MplUILRYLNzx0h3sXdrLkn+Jfzzyj3zxh1/EW/NScVX40ft+pPYYjEQi3HDDDQwPD6ss+draGslkkhMnTlAqldRmmMCG1ICZtn8zIIEtApShoSHC4TBwuRmso6ODrq4uisWi2n5E5tGbR4t2dnYSiUQAlPaJxWLE43G1kbSEibJbmHmQnlw0ySOJVmtvPkuRYpJJ9rGPP/1wK1TuLnTzG5nf2DBlyW63U6lU1ChyCbtz2Rz1tTrr1XUazZY/MnFogh+O/5DxxXG+9tDXcFacfO/Y9wjbwlTdVZxWpwp/ZZaLvK98XrVaZWFhYQOo4TJQzIN32ssY3kjCcEsARdorJNZvNptEo1HOnDnDysoK+XxebfA0Pz/P+vq6ihoKhVZRcT6fV1rjwoULqv5UIiHzDFczAESFmy8yXE7zm38/wAP4PX5Sg6lWMZN7jUPfPcSPD/8Yj89DtVDFq3uxWqxqHm2pXCKWi3HfE/cxlB1iwbvAP133T5SsJVLBFIbeqmWZ7Jmk5Cjhd/ipe+rYLDY1+DgSiXD06FG8Xi+AqtRvNFp7MEoU1z7Xrf37tP//tgPKM888o+aqSdbz+PHjnD59WlW8Z7NZlpaWGBwcVJnfYDCohuiY9wsUEJlNCVxeXe0jreR3ewLNvPOnpmkYGKSLaayLVoyIwfjiOGPLYxw/eJyf7f4ZUWsUT9LDdU9fR8PbwGKz8MrhVyhECix7l3nwoQfZkd+Bp+6hUC7gSXrId+QJZAI8duAxgt4ggUCAZrO1Z9HQ0BCHDx/m4MGDqu7G3AWQSCR4/PHHVZmE+fu0l0NeSYO8Ead2SwDl4MGD9Pb2srS0xKlTp9RGTv39/WQyGWKxmNqPr6+vD6vVSqlUUolA8fSF2TQP522/OObywnbNYpb2nmd14dFo/mOTr7q+yk2Fm5iyTGHdaSVuj2NgUOwo8vm5z5M20vzP0f9JPpQHvUXnJ91JcpYca/U1qpUqu57ZhdVvpcvdhdfnVbP9oZX/uvnmmxkfHycQCGwoJhfHfXV1lYmJiQ37B16rTrb98bddeHzXXXexZ88eFdZqmsbevXs5dOgQ8XicZ599Fl1vbX8ijKJkRM3EkYSCEhGZQWLWHO2PtQNKNM6VLqQc99XSVwlZQ5SdZe4t3cuIc4Tp8jTjl8bpzHcSIoRz3Ykz7qTcXcaesPPg0INU3VUsmkWVR3id3larqWlT7cHBQaVJ2vdBlEKscrnMq6++SjQaVb6R2RG/GgjMz73tTI8MFZatYWV2rM1mU3vUyA6c5iG9QkvL/+Zw0Ox3tDtvVwKLgEPe60oq3HyRG0aDpJHEaTixWW38Sf+fkK1nGfnuCOiQ6ksxeGCQyjMVChSwlC3E9TjOihO/w08wGMTtduN0OjfMor3tttu46aab6Onp2VD9JvSARFG5XI4nn3xS5XbaHVXzubd/1zcjWwIozz77LA6HQ2V86/U6Fy9eVE6q9PZIJ52ZCzB79Ob/r3bBzBfdzL2Yw2G5cVd6nfytquNlNDqtKQSrX15Fz+rUvDVuXL0Rj9fDiRMnaNIqgJY63u7ubjVmtFwu4/f7OXbsGHfccQeBQGDDBk5msJtD4/n5+Q3nIyH+lb6z+Zq8bcPj8+fPb2hXkClI0WgUm82mZpu0q9X2Gy2PiVzrgph9FZH2yOdar5XzMW9O4HA4cLqd4IZCqrWZ9dGjR6lWq5w7d45MJqMG8olmgNbIsfe85z0cPnyYQCCw4bu2i9zoyclJ1YnQfm7t/pWZvn9bm54777yTUChELBbj+PHjOJ1O9u3bRzgc5tSpU8rLF1NzJTCYzdBmQj/zCm03V9cqH2wHlrRdyEiwQCCgakOkBvdzn/sctVqNhYUF/u3f/o2lpSUuXbrE+vo6R44c4fOf/zyDg4MbEoTtfIiIxWLh1Vdf5ZFHHlHa9Wp+19XO+82YoC0BlGPHjqmo58KFC3i9Xo4dO0aj0eDll1++qtN5LeJoMxfD/PrNEFDtobTsF9jZ2Uk4HKazs5NQKEQw2ApzpUZENpHas2cPf/AHf0AymeRnP/sZFouFd7zjHYowNDeomTWe2WeSctGlpSV1TcwAu9pCMn+3t61GWV1dVeGeTK+Ox+PMzMwocq09bS7S/mXNPsu1pP15s+NrPsbsj5htvMyi7evrY3R0lEgkoqIwybmYzZNwO7JzSKlU4uabbyYSiagZuo1GQyUQ289JzMfU1BSPPPKIqk67GsBFy8lz5vID0b5vRLYEUJ5++mlsNhuZTEYl9F544QVisZiqln+jDti1jr9aBCRytcfMJk3+DgaDhEIhtcEBXC6QNqcERJ577jm+853vsLS0xMzMDPfeey8333zz5RkobWG5aAzRYi+99BJzc3NXJcvM52kG2pul7kW2BFAWFhaw2+3KuSuVSmocl5oi/Qa/4LWOvdZz7eFw+3PmSjGbzaZ2WZdicHOXnpmPqVarXLp0iUcffZRYLKbaKx5//HH8fj/j4+No2uVt5syfLdqhVqvx4osvqmy5mTm+2neU9zKf9+tdgyvJlgDK/fffz+7du5mfn+cHP/gBuVxOqW+50Ne6KLBx5bWv+vbjzH+bm8baeQizI9mecJPP2rNnjypclkSlmCBzZPPcc8/x8MMPs76+js/nIxgM4vP5qNfrfOtb32LHjh38xm/8BqOjo6p+WIYKy0KZm5vj5Zdffo2zfS2KQID3ZvwSs2wJoAwNDTEwMECpVFJ7FZuJtDcqV9I+V3LwrkZpX8lstfMo8lvqSmDjNm3m46empnj00UeZn5+np6dHcSGy+VQ0GmVubo5oNMoDDzxAOBzGZmvNixOwlMtlXnnlFVUXLMlTs1xpYVyLPngjsiWAMj8/T6lU4uLFi4ppvJr3vhl5PU7lajf9WtLOQwgYhKCrVCp0dHRsIPQky/vTn/5U1cVIHksGGUrOqlQqkUgk2LNnD7/1W79FOBxWiwVa5vjUqVPKjLWH9iJXAo+cU/tr3sg13RJAefjhh9UUJRlT/npm483IlYi6dgCJWWnnL9rNmbxOhhibb5CwqqVSiTNnznDp0iUOHz7MmTNn1I4hMqojHo9TKpVwuVz09PSwvLzM3//93/Pud7+bW2+9VZmZU6dO8eKLL26YWWfes0fkSmPNX09Dbka2BFDcbjder1dtAP1mq7BEzKbH7FfI3+YL3M5Umm18+3vK+4oP4XK51C7s5hsm5y/z5w4dOoTT6VQbdodCIcrlstozMBAIcOzYMa677jp27drFxYsXOX78OP39/QwPD1Ov15mZmSGRSGwIdzdrTszndy1n/VqyJYAyMjKCxWJRGzNd6Yu3m6JryRsh2zYr7ZrHbBYkLJY5J9JOUigUGBwcpLu7m0uXLim+BFoTnyR6GRkZ4d3vfjfXX3+92homFArx85//nHK5zNDQEK+++qqaEmUetfpm5I1+d9giQHE6ncpem7O3b9aevlmu4FrSrmWkC0Bm1jocDuWX1Ot1EokEHo+Hnp4eFhcXmZqaIh6Pq80ul5eXKRQK+Hw+7rrrLvbv36+q+BwOB8PDwwSDQSYnJ5mYmOAXv/jFhv2N3+zsE7Ov8kYmHWwJoFy4cAFN01RILKv1SibgP0vMXISMwjIXEckqbTQaanSH7JBaLpdZWFhQVWjSWmIYBgMDA9x88810dHQAbGgz7ezsxGq1Mjk5qboUrpQdf7PytvNRotHoBoSLJrkSzX6t/0Wu5ASb30vqOq52vPm928dSyGtljJiscjNQAHp7e1WhtTSZAWqPRCmwqtfr+P1+tUWdaFQZsVWtVllZWVGfs1lteSWfyfz329KZvf/++xkaGmJhYYEf/OAHavrRlZxSkWs5Y+1Au9Lqu9pFMqt24UXkb2m/EG0gYyvM+x+KJpFmrIsXL3L69GmcTifj4+Oqg6BWq+F0OkkkEkSjUfr6+hSNr2mtjkAZ9S7DCeX9zeb49SJDuQ7XKvXcjGwJoLz//e9nbGyMiYkJnn76aVU9f6XQ72o5mvYLeCXn81rSfow5TyL7/EiST8oORXs4HA51k0WrFItFlpeXOX36NMvLywSDQQVuaTwDVJgsPxaLRfk7UmUfjUYVd2P2K14vFSHXxFwi+WZlSwBlamoKu93O8vLya8oZzXIlal3ErF43wyVcTUOZ6XBzt7/T6VQaxZyZFXDY7XY1fqJer3PixAm+973vcfr0abUjvGEYqs+o2WxSLBbVfs7hcFiNaBdWVsaayhiPzTqf5sX0q1INIlsCKI899hjHjx8nFouRTqfVimvPtcBri6TlYrQzkGbQmI8BlDMqr29PoMn/4seYt8zVdV0Nr3G5XGSzWcWqSl4ll8vx+OOP88ILLwAtrSETtO12O/l8nlAoRLFYVO2ukiUXZ7ZYLKqebDkvc/OX+XzNHE+7SZaF90Z9knbZElMhDx48aEilmDm/YdYu7c3WIu1gkuPMVDuw4bVmKtsMCvk8c9IPUMyppmnqfQSAHo+Hzs5OXC6XqoYvFApqMkOtVsNqbTWECaVvHh4sM14AXC6XanEFyGazZDIZ4HKx1NXoArMPcqVKwKs5/q+88sqm7NGWAIrb7TaADTfZbAbkOTOPIBdOLpAUB8koUblY5lZRuZlS5Cx9NNI0XiwW1fMyIt0cJZjPRQbWSDefmAvZmEpeK4/L68SESagsjq8kCgE1AzeVSim/pL1h7Wq0vPmYKx3Xbs7r9frbByiBQMAwbyUvX8as7sUpkxvXbDY5ePAgt99+u6K877zzTkZHR3n44YcZHBzkHe94B88//zxer5euri5+8pOfcM899/Dcc8/xoQ99SK3wZ599Fk3TuPfee5mdneXkyZPcfvvt6iLHYjE8Hg8//vGPede73sXCwgKPP/44uq7znve8h2PHjjEzM8PPfvYzxbI2Gg3+/d//HYAPfvCDiu5/+eWXOXDgAI899hi33XYbZ8+eZf/+/fT395NKpfjxj39MMpmku7ube+65h6eeeooXX3xRheMiV/O5hB2Wx67m/IuUSqVNAWVL+Chi22XXikAgQCqVUrT3jh07uOmmmzh58qQaCWqxWHjve9/LZz7zGVZWVvjd3/1dfv3Xf51bb72Vl156iaNHj/LpT3+atbU1QqEQ9913H7FYjE996lOcPn2aD3/4w1QqFS5evMjExAQf+9jH0HWdX/u1X+Ov/uqvuOWWWxgbG+PMmTMcP36c+++/n0AgwAc+8AE+85nPKEf3ox/9KHfeeSdPPvkkExMTfPazn+Xw4cN4vV40TeOFF17gE5/4BAsLCyQSCbLZLA888ADT09N86Utf4o/+6I/41Kc+pfqm7XY7Dz/8MMeOHeOzn/0spVKJs2fPvmZOncypNU9i0HV9wzQD0ajmx81+2hshNLeERtmWrS9bhyPfli0t20DZlk3JNlC2ZVOyDZRt2ZRsA2VbNiXbQNmWTck2ULZlU7INlG3ZlGwDZVs2JdtA2ZZNyTZQtmVTsg2UbdmUbANlWzYl20DZlk3JNlC2ZVOyDZRt2ZRsA2VbNiXbQNmWTck2ULZlU7INlG3ZlGwDZVs2JdtA2ZZNyTZQtmVT8v8D3PQqAHu5218AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c6d83fd0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c6d52780>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c6d16860>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c6cd8c18>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c6c9b9b0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c6c55a90>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c6c19b70>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c6bdbc50>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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cPXqUzc1NeYfats3KyopMlpVKJXRd30FiXdm4wvXR6/iaT9tvgwaX25f5zeXfZC44x+9kfwfLtHao80GSS1wkYR7EOQjNkM1mZUmlWqQ0GGWJm6BYLEp/Rpga4T9pmiYz3K1W61k0vdBAL6UMnelRL4QaaYgLMzIygqZp1Ot1WSYgip+h30ZRr9cxTXMH99LzejRo4OMzNz7HQf0gmq9h+RY8czN6eFx1rpLfzLPd3JbOpvoYPE5RFqkCIRQKySQi9MNy8X7TNOXr4UYtjjBnapeAKOAWvpnI9ahmT6zRS5U1FjIUGuVmalMsvLDtgUCATCYjiatgMEipVJJ8iUjZa5rG2NgYjuMQDAYxAgaf0T/Dmr7GNNO8J/gePvxfPkw330VLaZSDZR569UOcmznHsc1jPNx5mPmZeQ5bh/m9+O9hpI0dGkSIrAHxPerUCQfCdJodIuEIvuczEZygMFng+tJ1UqmU7AuKRqPk83mp5YQGAWSUJlpLxHO7mRj1eP6vMD2DxTWws+xR+B4AExMTFItFarUamUyGSqUiw9zt7W06nQ7JZJKZmRlqtRqhUIi6V2ctsIaneaz4K2yvb3Pn0p3ono5X90iR4sGrD1IMF0GDf/Hef0FP77HYWST8O2HCE2E2/59NNEOTmgMN8s087WKbT/U+xZK/RKgTwgk4HFs8xu9/4fdJb6SZOzzHH3p/SKVSoX2gTSrdB0w4HCafz8vUgmhEE3+L8gffv1G9J7TQbsm/QXM4SL69WK0zFEBRKepB9lGtGhPEWKvVwrZtGeVA389ptVpYQYvEZIKgHcTt9On8GDGyXpZ1bZ2Tyyc5/chpcqM5xnJj5EZzoMFYbgwv5uHhcXLlJPMz85xcPkm6loYG9Io93Gg/3+Pj8+HCh7nWu8aIM0LBLODrPk2r2fd3DlyGCrzvl9/H/PQ8R9aO8KH/9iGuF67zt3f8LYSR+SfhS4mLLNIDgvcR5ybCZFHKoIbQKukmfn6vNcxQAEWtpRCi5l/E84I3EbZcUNymafYZ0FaTpfuWODNyhjPeGd6qv1UmEn+18Kuc+tQpRmoj+JrPnz3wZ6BBN9ovM4y6UYLjfc11X+s+Xtt6La9//PWgQ+tICy/u0e30K862W9tc617D0zy2rW1OrJ7g4uRFQp0QbavN0c2jbMQ3mJ+ep2f0WMguUAvXmGvM8Zv/+zdZTazyJ0f/RDaZCU0hOg8TiQSdTkdWuInWjsFE4GAOCHZW5n8vSw2GAigqtwA3FkLcReJOmpycpFarSUa0Wq1KfqRYLGImTBrpBr7ms6qvosd0TL/PjtZ6NfSkjl/32cxs4sZc7FGbeCRO2kzjbDrUvTo+Pl7cw+yanH37WUYCI/gJH9x+YVGz2SS/ledA/ACb1ibjnXF+93/9LmbdxE/4PPnmJwmNhci9PUemmWErusXBrYPEGjEADN9gqjJFrBfDsR1pcsTNUq/XGRsbIxqNomnajhZUQQ6KrgCVsVXXTdUy4vkXfY1e9Cd8D2SwVwVunJxYEKEZOp2OzMeIWo16vd5PrgVTpBopytEyE70JIn6/IEk0ZZ39lbOUl8pcyV/hiZknKEVLANyycQv/8a/+I91Il79749+R9JK0Q208PPQRXYK2UqnIEoJ/1v5ntI02ESI8/pOPY7dsOpEOFhZWr+9n/Hjxx/m88XkWJxb52Xf/LH/46T/kSPMIy9Fl2qE2RtvYoU0FYysSlqKwarB/SZgecQMNFlPfjO95MTIUQFFrKVS+QjizjuPIND/c6FVW7Xs8HiedSnPf0n0cPHkQv+kT0kLoYV0yo7FEDG/Wo1VsUYqU4Jm1uzRxiV947y9wauUU/+5z/45gOwgJWPmVFRLxBB4euUaunw1eb+GG3H5y0Y/0Sxs6Lm7Lpek0SRtpSolSX0t2oBgq4ms+1UyVPz75x9Qv1TFHTcb8MZkLEmG4uMj1ep3R0VHK5fKOdRJpANEbrTq4z2VifmA0iuqMCfVp2zbpdJpAIMDGxgahUGiH/a3ValLbBINBpqam+vmQoEWr2eIN/98bSK4maR1pkf/tvLxLI5EIdzTv4OnW0+TDeQkW3/A5O3uW//TT/4nL2cucXDnJh//gw7jHXd77tvdyuX2ZW5q38NDfPsT2gW0+/6bPE6IfvZz++mkOLxzGNVzMnsl6Yh3LtMjkM3zjHd/g4uRFIqUIVs/Cjbr0nN6OczEMQ2oH13UpFApkMn2GuFqtyn4fUaapMrbq2u1Wk/K9kqEAymBexfd92cCl6zr1el2aHvEatR1TlBc6HYe/H/978naer73+azz48IOEF8IE20H0kRuM6PiBcf5V9V/xV7m/4uroVTztxgJfyl7CMzzmp+ephCv4az6X25fx8Lh84DLlcJkP/PgHOJs9y7g7TsAP8Mlf+mQfWA9/GIO+DwKgofHHf/rHXMle4S9m/4K23iYajcr+ZdMwiffiVP2qZHhFOFwqlYjH49LZ9X1fJheTySSjo6PU63UWFhYoFovPWr8fyKhH9c534wUEtQ03vHq1bTQWi6FpGjWvxra9ja/5zM/MU4qWiGajkLxhu0VlmmEYvN1+O7Vyjb+p/Q2XRy9zfPs4ABdHL3Ji7QTJZhL3uMtR+yhX2lf6/9fh3Mw5fM1nw9x45gTg7PRZFjOLpJtpUo0UOjo+PoZvcGztGCOHRlhjTZoap+XwruV3MVub5UrwCu9Pvp+ef6NHp1qtks1m5aQFMbLjwIEDHDt2jEgkIimBSqWya4nGD1zUs1tpQa1WY3FxUd5JgtVU619FE1cymaTVahHTY0z706yyyqQ/yfZvb+MedPG58fmmaZJIJEgkEn1+Itvjfe77aNaaxA/3B+gUc0Xit8fZeGiDQCbAe2vv5Wr5KqmJFOu/ts60Ps2yv0ysGqMeruMFPHzN553vficAp5ZP8eCnH8QzPALdAFujWzSsBnpHpxfqEagH0Koas7VZDAyOOkeJe3GKFAkEAriuS6PRoNFoyNJPkQQ8dOgQExMT2LZNpVKRa/B/BYUvRD1h3/dlIZCoNRHddaJmQ6hrwzBk6v1fBv4l241tgt0ggVi/0g1tZ6W/cG7hxlSEZCrZv0PbLVJjqX5uJajh4fGh/IdY6CxwfPM4D33iIR469BCPvPkRGp0Gn4l/Rvo54ue5mXP8z3f+T0LREH7ZZ7O9iZ7XufDDF6gla9g5G/fzLguhBY60jrAQWqBu1jG8G7W+gkcRs10E6+w4jizcPn/+PMvLyziO86yKvMHfX6wMBVBulv0UjKTjOHS7XTnRCG5U5KfTabkgInO7Wd3knv9+D6nVFK0jLdZ/a12+B26YIbWI2vM8Wq0WhmGQSCTk8RScAgudBTw8Lo1eohKqkLqW4lTiFOVUmWwry5qxJrUWPmTJMjIxQsfp0Ig0wIGyW6aWrIEO7bE2junwgbEPkI1mKVPGbtuSVBPnLIb2RCIRtre3KRaLrKyssLKyQqvV4tKlSzI6vFlh+g9UzSzcfCSXuJgCLOJii4yqbdty3lokGuFjjY9xPXKdr7/+6zz48IOEFvp3dS94ozV1sCBZ+EOCzBNA8jyPpJlkNjDLdfc6t+RuIdnsR1L6iE68F+fd+rspd8r8pf+XfZOnTfJu6907qucdx0Fratg5m/ZYm3A+jN7QCQfCVPUq+DsjH0EXtFotWf8rHufPnwdu3ESqYy/O6aWQoQEK7NQsakpfhH1irIUoXRQtD6L0sE6d69HreJrH/Mw8xWiR4GiQVrCF3r1BnKkVa+JiDiblANDg/dffz1J3iUl/kv/wd/+hDzINglYQk37bSNSP8l7vvTS1JhG/72QK0yEq4gBG/2G0X9jUi/Du8rs51jnGYnmRjx35mASEMKVq3S3c0AwibSHIOXXSw25lm98rGQqgiBMfpJ7FCQuKWyycuLiiVqNarXL27FnskM3sP59lyVsiS5YL77gACTBbZj+v80zuRIBF7eP1PI9MJiP7gMLhMA0aXGpewsNjQ9uAEmieRmghhNWy6MV7O+7gUC+0ozxSHHur3WL+rnnq6TrmpskdX76DY51jGBgcbh4m2o1SMSo7WkuEVnFdl0gkIgEhQKf6c4PRzXfTLi8EQEMBFNg5InO3+k+hYlVSTji3ruvKIuef7P0k+Vae8eg4TbNJuBymk+jIxBogs86iYSwajdLpdLh8+TLtdptUKsXU1FR/ckFwjsvOZaaYQktqeHWP9uE2XvxGXauYXyJAIv4WvTl1r049XQcd3HGXarTKleAV5pw5FkOL1AI1fG8n/yE0ifBb1G7AF2teXsj7hwIou9Wk7laFr5YYAHI4jcggi2Rh0AuCD3f/v3eTXEtSnioz/6vzBKz+6aoTkES43XbaXNu+RnGlyMHZgziOQygcoqW1wH8GXL7X10y9Ll7PQ9d0ObxH3O3CERXmp91uY7om8XK8H/Fs25hdkz/I/AEhJwQpsLW+IysApib21PYT8X9x0wgwfT9kKIAyKLvZWmFu6vW6LIcUfoWYQ6LpWr+IyFhitjfLJ9Y+ge7pJFeTUIZ2vC3BKBJr0WgUK2jx6dqnWTi8QHY2y6H1Q1xev0yxXWT55DLosG6sU+6UyXgZoktRlpaWCFgBtJSGpmvSfxK+SaVSoVgq0tJbHD58mNu4jfJ2mcvfvkxH65DSU5RDZaJmdIdPI5xtESIL8yg0omjAF+mLm2ni59IaL3uNshf6WYBDbf+sVCoEAgHqXp0lfwlP81jSl1g+sszBhYOUs2U6kQ6ar0nSTZ1VW+vVZAi8aqzyyOQjbOh91jXUDtGyW6DBO9/1Tm5buo1//+i/Z/bPZomtx2gcarDwngU0Q5Ndgp1Oh47b4dHJR8mH8mS9LL/Q+gWmIlNc9a/ynoX3cLB+kIXQAh+NfxS350rnXR1sKBKiYoauqnlVf0as3XPJizVXQwGUQXAMUtDquCrhW4RCNxxHIXpbZ6Q5QiFcYLI3yaU3X2K5vYyf8DEDpnSYRQGz53l0e138gM9h8zCL7iIzgRmWWJKf6VgOmq/h6/1jOj99Hq/lESvF0NCIXIvgl3060Q6tVktqgbJbJh/K42s+68Y6PbuHbdq0t9ocbBzEwOBI6wjRXpSCVwDYkc9Sz7/T6cjzHVyj70aw/UBS+EKeyyu3LEvOGel2uzSbTeLxOOVymVAoxD1X7uFVP/UqKgsVQtEQruUSaofQUhoBsw+QQqFArVGjbJZ5PPw4W4Etsl6Wd3XeRcpO8ef6n7PsL4MPJ1dOAnB29izQ/ztTyqCh4eNTnaxSpoxf7/Meokreq3lkEhny4TyT3iQRIjz55JO4EZeV+ArTlWmuR6/TMBt4rRthufC72u229KUajYYc8KfO+f9+ylAARZWb5S1U7SKKjUWmVTh1nu/x1UNf5XPLn2M6MM3bum/jjj+/g8RqgsbBBlfedQVP86jWq3wi+Ql6gWfuUA1WtVXOnz/Pd275DsVIkQPeAd5ivIXZiVnG/2ac0H8PgQWZUgYv6IED1WyVb7z1G/idGx2EnU5fs/iez23fuo3r29c5ED3A162vc+3aNQ4dOsSnkp+iW+jiRlz03s6xYCKKEr6IWnejahuVC3qp8zwwJEBRi3ZuxgEITgH6vTu6rlMulyWFbds2ruVSipXw8VnRVnDqDonVBLqnE70exWyauFEXb8Sjp/X6uRkf8GDMGSM7neXxyOOgwZa+xZ94f9J3Gn/O4+TySf7tV/8tVtgivhGnmq3ytZ//GvQDEVzXlW0k3W4Xp+NwZe0K20vblOwSsVi/FDJoBWkVWrSCLXgGp8IUCoJOzHoRTW/CNKslo4PO7EstQwEUVW7mxQuaWt3jRvxfzFkLeAGStSSVeIUj1hGMoEE5Wya5lqQ2U6MeqBMkyKHwIayWRcfvoLs6tzx2C4cyh7CP2jcSfAA6ElDnZs/xa9O/xqmVUzz48IPE1+Jolb6/07L7OSJR49vzenzl0FconSqhrWmMPTaGZVqYhskvPfVLZEtZrkWu8fG5j6MHdDkWQ7SXikyx0JqqL6ZW+d1s7V4KGTqg3EyEhhGz3AA5rbHb7ZJMJsnlcrz6yquZPDrJa0+/lm9+85t85+3fwaga9OI9jK6B6fVLFn7b+W2+vfxtjIqBdotGKphiZXmFcX2czdjmDW0oOkG9AAAYWklEQVSjiGd4nJ0+y5npM9y6fit3/6+7yWxlKIwX+Mef/Ed8r7+nT1Nr9utxdfCnfCJjEfSmznhwnGw5i4HBocYhYl6MptaftCD2ARKDdwRvorLTKl0PLy0wBmUoWkoH4//BxKCIekQSMJvNkkwmZWKs0WjISQCGbnD5W5f782HLJap+lVaoBWVwOzfo71gkxq2jt/J/bvk/fPbQZ/nMxGf40skvMVoc5fjqcfSezpHNI5xaOoXe0wm3w9DrV62971fex8+97+dIbiXRfZ3MRoYH/vQB7v/C/QSMAKlgCmvTAg/i5ThhP0wsFsMYMViOLdOjJx1ZkdQU0Zyo7hOjzoWIHNCgif5+yVBplEGAqDkM0VJq27bc9s3zPDkHRZ0EWa/XmT8/z6OTj7JpbHJ8+zgf+eRHqE3VuPTrl2RJYUtrsRHYAA06dEDvh7/H1o71b6EscK0PjiNbR3jzE2/m/b/4ftCgYTeYPzHPK+ZfgYaGjs7Y1hhRN8p2e5vxr40ze2IWo22gxZ5pZAsYPHTwIWzHxo24oLFj1onIMw1W5ov81PfTeR2UoQLKc4kICUWRkrirBEBEqUGlUiEcDvPk2SfZ/JHNfh3J2CWqoSrJ1SRaVcML9ets08E0453xGyWNPtyyfgsXsxfxNI9r3Wsw9YzJmT3Luelz/TZU3SPSjjBTmtlxjJ7mUdfrXL54mVuP34ppmJTdftgetILUVmo0W01cy8XW+ucQjUbl4B8xHFloF3G+aifhc9WavFQlBjAkQFHvHHHyYsFgZ61Ko9GgXC7TaDQYGRmRs+wFIVUulzl06BBPn32ag/cc5FrvGrfkbiHRSlDOlmkFWxi9fsQQjUb5xdov8iAP4ms++PCazdeA3y+yPrZ2DMM3uDB1gZ7ewzd8tJ7Gh/7bhzi1eYpAJyBrY7tal3/zjn/DhfELRCIRHth8AF3T+2NKTYuf/vJPM1OdYTG8yH+95b/S6/Vko325XJaN9sCOrkBB6xcKhR1J0d3qYfeiaVSi7vlopqEBiiqDi6BqE5HXEeRTNNrPu1QqFbn45XKZkB3ijaU34od9WrR49DceBRNChLAaFt1oF03XSJtpZruzLPvLjLRG+B8n/geFUIGQE+JC9gK3rdzGXz74l7z/Z9/P+enznFw5yR3Ld+BrPqXxEqmtFNtj23zhvi9wceIiaNAcaeIWXAJOgFarRdgJM1OdkWUFKS3Fprsph+3UajVpXgadWKFNRPJRrMeLNUHP971DARR4brUpQCIWrFwuY1kWruty+PBhQqGQnFPS7XbZ3t4mGAyS385z19138QHvA+SsHJO9SR789IOMrI5QP1Rn8T2LhEIh3tV7F02auEGXDzgfwNd8mna/4Xx+Zh6ABx9+kEq4QrKRxNd8ChMFvvjAF4m4EaqBKmWnTLKWpBQtkW6mCfaCXF+5zuHDh1lfW+eqfZW59hyL4UW6sS5G2ZDN6GoBknqTCC2qgkYA54UC5YW+byiAoia7xO9q8Y/gEgZ3Cdvc3CSVSvFDP/RDrK6uyoRhu92WPUE1r0bOyuFpHuvGOhT7xUfRa1GslkVgtM+Kjhn93TqObRzjcvsylmbh4JD1szz99qe5/W9uJ7mepDxd5qkff4rt3jY9r0fez/PFzBcpRopES1F+5IkfIR1Ms5Jf4cStJ7DbNuus87EjH6OT6xCaDBH349Trdba3tyV5qJZACrAIv2SQhFTX6fslQwGUm2kTsVAqQMRGS9B3YBcXFzl9+rScV29ZlvRldF1Ha2jM6DMseUuMu+P0Yj28pkd9tt5PFiobSBmGwe9O/y5Fp4jRNii0ChhtA++Ax9O/+jSUoapXabVbdDt94q/u1SlG+m2jtWQNXdPZ3NhkZnqGn/jST5DZzLASX+H3Ir+Hg8OB3gGZoyoWi3viR15KJ3WvMjRA+W6hn7iLIpEIqVQK6I8ALxaLLC0tkUgkZHgp9u8TxUBv197OSmmFYC/I37/p7xkPjeOMOEx0JvAdHz/t91nYZ5zFmBbDDbikrBSO78iMcM3oT6LuuB3aRhvTM9HbOqPtUbbtbSKlCJ1iB6thcTBxkMxmBsM3mK5MEzSCeLYnux7VxnKxBuI8h1GGAiiwEyxC1BJIoX7VbenFnbiwsCCzq6ISrlqtsrW1xdTUFKZpMhoelRtEfjLySTa9TW69dCsf+eRHaMw0uPjOi/1CJCX6EhX0YtxFrVaj43b44vgXydk5RpojvH759byl+hbK+TJnvnaGX1/9dQ43D3N97TpXzCscdY9yNXiVTrhDKNhv1hLbuKiV9+o6vJQa5IUCcSiAsptGGfxdDBRWbbrQIJqmUalUCAaDOwqQxZC9Wq0m57NWe1U2rU18zb/Brywnqa5U0dM6dtvGi3sy51Or1XA6DmW3jN7Taettcnau79CGC1gpi6AVhBLEejEONQ+h+zqz9Vl+/9bfJz2SZrG0SDqQJhKJUK1Wd2yGMKwaZFCGBihw815ZYce73S5bW1sUi0UJGpEwExOYBP8iUv5CA4lkYsJMMNYeI2fnOLp5lEQzwXp6nUtbl3jDF97AsZVjbI9t88gDj6AbOq12i8emHiOfzJNpZnjd0utkcdS4O07aShPvxZnfnsdP+FyPXOdg/SBX7avUzP5GCFbQkrW56qBh4cCKWtibrckwyFDs1yN2KYWbD7IbbEfYrXxSfW+v1+PkyZPcf//9NBqNHQMDa/Ua1W4VGkARttwtzpw6Qzle5uTKST748Af55Bs+Sctu4QZdHj31KL7mo3kaD8w/gO3ZRMYiTKemufsv+gXcy7Fl/vPMf6ZarZLUktSMGolkQo4yD4fDBAIB8vk81WpVJjNfalMzKIN+4Mtuvx4huzm06nOD46jUhVaLf+AGqymaxKDfBhEJRzA7Jm3a5Ft5fNOnmCji6z7z0/PMH5hn293G8A1oQ7KapBKtcGrlFG/9ylv50k98ienRaaJulORaEt3Tma5O0y108S0fL+HRKXXkPjyiEEnUlwxOdxyGm/W7ydABZVBTiN/VyUKD2ka8b7B5TPgB4iGyzWI0qRhHbjgGqXqqPyajGOVPR/6UQDkgOxLvfepefvnMLzNSH8HXfY6NHcOMm+BDdbpKfCXOWmINJ+SQSWXkpk7CRwJ27MyuDjd+ucjQAUWI6uCqgBksKt4tShK/i+owMc5KFcuy5LQAgNdeey35Vh6n6NDSWvL74/E4wViQXrSH3/SpTvedXkGOnf2Vs7S32my0NjiycQTHccjlcjLUVtlV8ZwK/O93ucALlaECynMRTWq5pGqGxOt20zLiMwc/VyXYhJkyAyYjwRGctIM20i8LCAaDkuD7x7f+IyPGCMaIgRWwboxdNzTcqEsi2J9te+HCBVmdppKFuwEbnrtS7btpnBeSFBTve1nmega5C/EcPNv7H2QwB/0XQXkL9a76JoOfKcJpMTxPvFd0HKpRimEYBOzAjkJoldvxfZ9UKsU999zDiRMnuHDhgtyZvdFoyGPebTzFc5GMQnarun8xEZHQdnuVoQCKkJvVWtwst3GzaGiwg050BarqX/gp6vYn4m+xZYv47sFdtwYvtACK+Jx0Os0P//APc+jQIRYXF1laWpItGOL4BNheLn7KUABlUJPcLFSGvbVKCudVVLVrmvasPl11MwbxP3X2vjAb4jnxnt2mLQjzohYaBYNBxsfHyWQyTE1NkcvlWFtbY3t7W07fFmUFe12jf0oZCqCosltRzs0KdW72/kFORY181Jm2akOVCiZ1Jom617KqlURxkQoy8R4BHLEL6ujoqKwzWVxc5NKlS5w7d27HvHtVXmiW+CWl/odB9YXDYR9291WEqHkfYXLEhRN+BiDnzrbbbX7mZ36GW2+9VUY+g5sMqO8TfIsKEgGeQTZVBYtIGKrHJEwU3NgsUmWMu90uy8vLbG5usrKywoULF3ZMkxJdgmJ3DXGeIsRXfaTdaIFBoO0WNYr/OY6zJyQOJVCeS1SgiNeKRRWqv9fr8cpXvpL7779fFiWrW9CKC62Sd5qmyU0pVcCqQFHNnzBr4jNuBhRhxgQohSkUFWuu63Lp0iWuX79OrVbDNE1WVlbY3NzcEcWJhKeQm63TblHfDwxQQqGQBIqQmzmvakisiui2M02T3/qt32JmZkZu/ihE+BzqnsLqnH1xUdVoRgBlcGMHcSxqnkb4MyrgRU+x0AoiuanOOslms0xNTbG9vc0HP/hBDhw4wOXLl7l48aIsshY3gvgcMUZMaBQBgt0c5O8FUIbKR9kLb6DeIUJ7mKaJ67pMT0/z8z//89xyyy0Ui0U5502USApmVmVGB6cH7PY9KmhVsKoaR9U6uznkQkRzvdBwvt+f+eK6Luvr69RqNXRd58SJE0xPT9Nut7l+/TobGxty/AX0ASjyV/V6nVarJb93L5rn+cpQAUWVm90V4neV3XQch3e84x3cd999Uq2HQiHZ/iAcT5X70DRt52A/dnILqhOsLr4wOwKgkUhEmhrV8R28QMI/UY9f1UqPPPIIX/va13Bdl9HRUe644w4AefzlcplSqcS5c+fI5XLEYjEymQy+77OwsMDSUn9Uh9r/czN5IeAZWqDsJuoQYkCSXA888ABvfOMbsSxLtmQKrbCbLwHsuKg3m1w0qB3g2ZMrhV+k7n6+G0ssgCd8E1ED3Ov1WF1d5ctf/rLsSZqenqbRaMjGdtM0yWazHD58mLm5OenPiFm08XhcAk518HeT3SiHvcjLBiiqQyjaNJLJJD/1Uz/FAw88IHcpFVvHCp9FjUjUGly1VEENbdWfg06h0CrCdxGmR5g4lW9R36Pe5eqxiMfFixcpFAp0u10OHz4s9+kRGkvU2Ipyhbm5ObkJeLFYlNMyB7eduxlgbmYWn0teNkCB/l149OhRkskkk5OT/MZv/Aa1Wk02UqlZ4sGpByI8FhGEINrU7WMHHT21+l0AS2SdxUM4lLuZRti5dZsawUAfCBsbG1y8eBFd15mcnOS2226j3W4TDofZ2tqi1+sxNjZGq9UikUjs2AFtbGyM8fFxbrvtNk6dOsXFixdZX1/n3Llz8ga5mfzAahSAsbExZmdnOX36NLfffjvb29uYpimdOvVCq+PCYecsfHVDy8HhNOK1KljET2GuBFEn7l6V1lc/Z5DvGUwZuK7LwsKCBEY0GqXVasnuQXHs1WqVsbExPM+T+zrHYjFCoVB/PGm9Tjwe5+DBg9xxxx04jsOVK1d2NI2psptJ/W4yFEAZ7OFRR2UKLZBIJDh58iSvfvWruffee2Uko4aD4sLV63VZFhkOh3fc3eJ16oVXnx9ka8XrBn9XF3qQ9BOfJUTNJdm2LV/31FNPsbCwgGVZkuoXkslkWF5eJplMEg6HabfbHDhwQO64Loqzfd+nVqvheR6FQoGJiQnuuOMOAoEATz/9tCwRFeemcj7PhxoZCqCod7AanYyNjXHixAnm5ubY2NggkUgwOzvb32hS4RXEBRSdhLre381crWxTIww1NBbbu6ghpbgAg9pDfJf4vEHNoW7CoPo/6hA/ERp/5zvf4Utf+hKVSoU777yTWCxGu93ubwNTLDI+Ps7Y2JjMWTWb/Tkqo6OjcteRXq/H1tYWlmVJf0aYxx/90R9ldnaWz33uc/J8BNn3XM7uzWQogCLEdV0sy5I+yGtf+1qOHDnC1atX5YRp4YOoFwVuMLaqKRDgUbWOeE5Q4appUTWL6qPAzrHhg5GD6ryKhzg+FWiqc/3UU0/JsaciFyTGeomZsvF4XEZtQsuqc1REn7Vt23IWrdoKMjc3JzfqVCc4vRAZCqCIu3FkZITTp0/zute9jomJCVZXV6nVahSLRarVKrFYTF5QsQGSChpVw6gRjvp/8X3igg22TKgs525hrniPmn9RP2OQwld/9/1+zmlhYYGFhQV0XSebzVIqlchkMoTDYRzHkaPbHcchFovhuq5MPaysrMiqPNd1CYfDdDodqYXq9Tq2bZPL5RgfHyebzbKysiJvMPWcno8MBVDuv/9+Tp06xejoKLquyzslk8mgaRrFYpHt7W1832d6epput0s0Gt2RCBSqWaXMhTOnmgwhYuGFDyPuuN3mpcFObbGbxhHfowJG1S4CxPPz8zzyyCN4nsfo6CiZTIZer0ehUCAajRKNRimXy6RSKdkWGwwG+zukPtPAFg6HpVMrtr0bHx8nFouxtrbG+Pg4uVwOgFe96lVks1m+/OUvy/JPcT7PR4YCKG95y1sIBAIsLCxgGAbxeFyaId/3ZdFPoVCQDuogK+q6LqVSSW6arWZX1QurVrwBOzZFEnedEDVhqGquQY3z3RZdANb3fZ588kny+TzxeJypqalnXbxIJCJBkUqlKJfL0s8R0ZHYnNKyLAqFAuFwf/SXANby8jKxWEyG7zMzMzsc8hdifoYCKJubm4RCIalyRU5mbW2NRCKBbdtyt3QxdCYcDpNIJHak8VXNISroByMddaEG/RLxc5A4U82O+rpBQm7Q4VVfaxgGa2trrK6u4rous7OzjI2NkcvlZNN9rVaTvdVCy4mxpOl0GoB4PM7m5qbcC1p8r1oI5bqufE5EWiJSeiFmB4YEKGKYr+u6JBIJcrkcvu+ztbW1Y7+8YrHIxsYGmqZRrVYplUqSOFPDWnHnqy2ncKOmVg2XxevVKEcASJ3l+nyobzUXJSKyzc1NvvjFL1Kv10mlUrKfeWxsrN8A/8wwnUqlQjqdJh6Ps7y8TCgUkhtoz8zMsL6+TigUIpPJUC6X5X7Oa2trBAIBQqGQBMb6+jrJZJJKpcKrXvUq/uEf/mHXYu69yFAAxTRNarUajUZDOnz1ep1MJgMgnVehcsVmlOJiCjuuElmDPMGgVlC1hWpiVI2k+iiDTqt4/W65IPV7ABqNBt/+9rdZWFjAtm2SySSJRALP8+S+gd1uV06DzOfz0ryKAm8xPr1SqUhaPxAI9DegajQwjP5gnnw+z9TUFK7ryj5tTdNIpVJyZ7Hn65/AkIwPbTab5HI5aYfFRk2VSoVms0k4HCadTtPtdqnX65KJFQ6o4zj9bU+KRUqlEo1Gg2azuSOCgWdnhAdlkF/QdV3S/CLEVaMoVXZ7TtM0wuEwjz32GF/5yleo1+vceuutzMzMYNu2nFLd6/UYHx8nGo1KDbq8vEw6ncYwDMm+CudVRESapkmQiI23E4kEzWYTx3EYHR1lc3NTdiceOXJEAu/5mp+hAIraSqHr/dHlzWZT2tl0Oi3JM7GQgmQKBoPy5IVZUQuTblaHIkChJghVP0etut+N5n+u6Ec4vpZlUalUOHPmDJ7XHy6YTvenGogalF6vR7vdJhaLkUqlyOVy2LZNOBymVCqhadqOjHgmk5G5Ktu2qVarVKtVqU1F1JjP5+Wxiq3m5ubmJCn3fEm3oQBKt9slk8lg27bs0RUhsPBBxMk1Gg15sYVXLx4iOhhcABUcgyZpMKczqHV2o+tvtsgqQyvA89RTT8kBhbfddpvs8xEkmWBSRWGS2J7XNE3K5TL1el1mhtvtNrlcTq6V2GXEdV1yuRzxeBzLsiThtrW1xdjYmNTSmUyG8fFx2ZO9W6/QzWQogKJpmgSIyOb6vo9t24yMjEg1q2ka29vb1Gq1ZzGfwWBQ7iuo+iuDdSKq5hkMcQdfo5qo3aIF9bPFazStn6lut9s8+uijfPWrXyUUCnH77bfLdIHYESSZTJJKpaQJqlQqciBQpdLfjDKXy0nN2m63MQxDmhvxeb7vE41GpfYMBoNSqyaTSdrtthy7evz4ccLhMJqmSeJuLzIUQBEXvVgsEovFSCaTRKNRuZuWGG0uFqnX60liTWgL9SLbti29f9V87Haxd7PVu2kY8bz4uZtPIr7HNE0uXbrEt771LSqVCtPT00Sj0f7GDs/cDACpVEoOI85msxIMomRCrXVJJBJS83Y6HcmZiPIJkTisVqtSq4yPj7OysiIZX9ERmc1mn3fz2VAApdlsEolE+g3hz+QmxFjNer1OMpmU6lbQ0GpuB25Q58L5HGysGtQgg1X1g+ZJrSMRny8+ezdnWITogUCAer3OE088QalUIpFIEAwG6fV6HDhwQBKJuq5Lul2YEV3XWVtbo9FoSM0aj8clwCYmJiiVStLfqlQqeJ5HKpWSvwOynNIwDEqlkmzGF9njdDr9vCOfoajC35fhl6HQKPsy/LIPlH3Zk+wDZV/2JPtA2Zc9yT5Q9mVPsg+UfdmT7ANlX/Yk+0DZlz3JPlD2ZU+yD5R92ZPsA2Vf9iT7QNmXPck+UPZlT7IPlH3Zk+wDZV/2JPtA2Zc9yT5Q9mVPsg+UfdmT7ANlX/Yk+0DZlz3JPlD2ZU+yD5R92ZPsA2Vf9iT/P3F++2cwXwmIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c6b22d30>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualize the output\n",
    "# by default this shows a batch of 10 images\n",
    "def visualize_output(test_images, test_outputs, gt_pts=None, batch_size=10):\n",
    "\n",
    "    for i in range(batch_size):\n",
    "        plt.figure(figsize=(20,10))\n",
    "        ax = plt.subplot(1, batch_size, i+1)\n",
    "\n",
    "        # un-transform the image data\n",
    "        image = test_images[i].data   # get the image from it's Variable wrapper\n",
    "        image = image.numpy()   # convert to numpy array from a Tensor\n",
    "        image = np.transpose(image, (1, 2, 0))   # transpose to go from torch to numpy image\n",
    "\n",
    "        # un-transform the predicted key_pts data\n",
    "        predicted_key_pts = test_outputs[i].data\n",
    "        predicted_key_pts = predicted_key_pts.numpy()\n",
    "        # undo normalization of keypoints  \n",
    "        predicted_key_pts = predicted_key_pts*50.0+100\n",
    "        \n",
    "        # plot ground truth points for comparison, if they exist\n",
    "        ground_truth_pts = None\n",
    "        if gt_pts is not None:\n",
    "            ground_truth_pts = gt_pts[i]         \n",
    "            ground_truth_pts = ground_truth_pts*50.0+100\n",
    "        \n",
    "        # call show_all_keypoints\n",
    "        show_all_keypoints(np.squeeze(image), predicted_key_pts, ground_truth_pts)\n",
    "            \n",
    "        plt.axis('off')\n",
    "\n",
    "    plt.show()\n",
    "    \n",
    "# call it\n",
    "visualize_output(test_images, test_outputs, gt_pts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training\n",
    "\n",
    "#### Loss function\n",
    "Training a network to predict keypoints is different than training a network to predict a class; instead of outputting a distribution of classes and using cross entropy loss, you may want to choose a loss function that is suited for regression, which directly compares a predicted value and target value. Read about the various kinds of loss functions (like MSE or L1/SmoothL1 loss) in [this documentation](http://pytorch.org/docs/master/_modules/torch/nn/modules/loss.html).\n",
    "\n",
    "### TODO: Define the loss and optimization\n",
    "\n",
    "Next, you'll define how the model will train by deciding on the loss function and optimizer.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "net.cuda()\n",
    "\n",
    "## TODO: Define the loss and optimization\n",
    "import torch.optim as optim\n",
    "\n",
    "#criterion = nn.modules.MSELoss()\n",
    "#criterion = nn.modules.L1Loss()\n",
    "criterion = nn.modules.SmoothL1Loss()\n",
    "\n",
    "\n",
    "optimizer = optim.Adam(net.parameters(), lr=0.001)\n",
    "#optimizer = optim.SGD(net.parameters(),lr=0.001)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training and Initial Observation\n",
    "\n",
    "Now, you'll train on your batched training data from `train_loader` for a number of epochs. \n",
    "\n",
    "To quickly observe how your model is training and decide on whether or not you should modify it's structure or hyperparameters, you're encouraged to start off with just one or two epochs at first. As you train, note how your the model's loss behaves over time: does it decrease quickly at first and then slow down? Does it take a while to decrease in the first place? What happens if you change the batch size of your training data or modify your loss function? etc. \n",
    "\n",
    "Use these initial observations to make changes to your model and decide on the best architecture before you train for many epochs and create a final model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_net(n_epochs):\n",
    "    \n",
    "    loss_over_time = []\n",
    "    # prepare the net for training\n",
    "    net.train()\n",
    "\n",
    "    for epoch in range(n_epochs):  # loop over the dataset multiple times\n",
    "        \n",
    "        running_loss = 0.0\n",
    "\n",
    "        # train on batches of data, assumes you already have train_loader\n",
    "        for batch_i, data in enumerate(train_loader):\n",
    "            # get the input images and their corresponding labels\n",
    "            images = data['image']\n",
    "            \n",
    "            key_pts = data['keypoints']\n",
    "            \n",
    "            # flatten pts\n",
    "            key_pts = key_pts.view(key_pts.size(0), -1)\n",
    "\n",
    "            # convert variables to floats for regression loss\n",
    "            key_pts = key_pts.type(torch.cuda.FloatTensor)\n",
    "            images = images.type(torch.cuda.FloatTensor)\n",
    "            \n",
    "            \n",
    "            #key_pts.to(device)\n",
    "\n",
    "            # forward pass to get outputs\n",
    "        \n",
    "            output_pts = net(images)\n",
    "\n",
    "            # calculate the loss between predicted and target keypoints\n",
    "            loss = criterion(output_pts, key_pts)\n",
    "\n",
    "            # zero the parameter (weight) gradients\n",
    "            optimizer.zero_grad()\n",
    "            \n",
    "            # backward pass to calculate the weight gradients\n",
    "            loss.backward()\n",
    "\n",
    "            # update the weights\n",
    "            optimizer.step()\n",
    "            \n",
    "\n",
    "            # print loss statistics\n",
    "            running_loss += loss.item()\n",
    "            \n",
    "            if batch_i % 10 == 9:    # print every 10 batches\n",
    "                avg_loss = running_loss/10\n",
    "                # record and print the avg loss over the 1000 batches\n",
    "                loss_over_time.append(avg_loss)\n",
    "                print('Epoch: {}, Batch: {}, Avg. Loss: {}'.format(epoch + 1, batch_i+1, running_loss/10))\n",
    "                running_loss = 0.0\n",
    "            \n",
    "    print('Finished Training')\n",
    "    return loss_over_time\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1, Batch: 10, Avg. Loss: 0.04702361524105072\n",
      "Epoch: 1, Batch: 20, Avg. Loss: 0.05608122833073139\n",
      "Epoch: 1, Batch: 30, Avg. Loss: 0.06127690374851227\n",
      "Epoch: 1, Batch: 40, Avg. Loss: 0.041282277554273605\n",
      "Epoch: 1, Batch: 50, Avg. Loss: 0.04633979294449091\n",
      "Epoch: 1, Batch: 60, Avg. Loss: 0.041800412349402905\n",
      "Epoch: 1, Batch: 70, Avg. Loss: 0.04050051905214787\n",
      "Epoch: 1, Batch: 80, Avg. Loss: 0.03990806043148041\n",
      "Epoch: 2, Batch: 10, Avg. Loss: 0.048314320109784606\n",
      "Epoch: 2, Batch: 20, Avg. Loss: 0.04155727755278349\n",
      "Epoch: 2, Batch: 30, Avg. Loss: 0.03680910412222147\n",
      "Epoch: 2, Batch: 40, Avg. Loss: 0.044032881036400795\n",
      "Epoch: 2, Batch: 50, Avg. Loss: 0.04357215724885464\n",
      "Epoch: 2, Batch: 60, Avg. Loss: 0.03927287328988314\n",
      "Epoch: 2, Batch: 70, Avg. Loss: 0.03497628383338451\n",
      "Epoch: 2, Batch: 80, Avg. Loss: 0.034526838921010494\n",
      "Epoch: 3, Batch: 10, Avg. Loss: 0.04180300571024418\n",
      "Epoch: 3, Batch: 20, Avg. Loss: 0.034822501428425315\n",
      "Epoch: 3, Batch: 30, Avg. Loss: 0.03555800560861826\n",
      "Epoch: 3, Batch: 40, Avg. Loss: 0.039561483263969424\n",
      "Epoch: 3, Batch: 50, Avg. Loss: 0.036351115256547925\n",
      "Epoch: 3, Batch: 60, Avg. Loss: 0.03487373050302267\n",
      "Epoch: 3, Batch: 70, Avg. Loss: 0.033568673953413966\n",
      "Epoch: 3, Batch: 80, Avg. Loss: 0.040065270848572254\n",
      "Epoch: 4, Batch: 10, Avg. Loss: 0.030979400500655174\n",
      "Epoch: 4, Batch: 20, Avg. Loss: 0.03399317134171724\n",
      "Epoch: 4, Batch: 30, Avg. Loss: 0.030939933471381666\n",
      "Epoch: 4, Batch: 40, Avg. Loss: 0.04464379940181971\n",
      "Epoch: 4, Batch: 50, Avg. Loss: 0.03666882254183292\n",
      "Epoch: 4, Batch: 60, Avg. Loss: 0.028460476920008658\n",
      "Epoch: 4, Batch: 70, Avg. Loss: 0.028057989478111268\n",
      "Epoch: 4, Batch: 80, Avg. Loss: 0.033309452794492246\n",
      "Epoch: 5, Batch: 10, Avg. Loss: 0.029687671549618246\n",
      "Epoch: 5, Batch: 20, Avg. Loss: 0.03040791805833578\n",
      "Epoch: 5, Batch: 30, Avg. Loss: 0.038993358798325065\n",
      "Epoch: 5, Batch: 40, Avg. Loss: 0.034279124811291695\n",
      "Epoch: 5, Batch: 50, Avg. Loss: 0.031466510333120826\n",
      "Epoch: 5, Batch: 60, Avg. Loss: 0.033452346734702584\n",
      "Epoch: 5, Batch: 70, Avg. Loss: 0.031373835355043414\n",
      "Epoch: 5, Batch: 80, Avg. Loss: 0.03209426775574684\n",
      "Epoch: 6, Batch: 10, Avg. Loss: 0.03433948811143637\n",
      "Epoch: 6, Batch: 20, Avg. Loss: 0.041580405458807944\n",
      "Epoch: 6, Batch: 30, Avg. Loss: 0.03781421985477209\n",
      "Epoch: 6, Batch: 40, Avg. Loss: 0.030548289231956006\n",
      "Epoch: 6, Batch: 50, Avg. Loss: 0.03069525267928839\n",
      "Epoch: 6, Batch: 60, Avg. Loss: 0.033314119279384616\n",
      "Epoch: 6, Batch: 70, Avg. Loss: 0.0313282435759902\n",
      "Epoch: 6, Batch: 80, Avg. Loss: 0.02795834019780159\n",
      "Epoch: 7, Batch: 10, Avg. Loss: 0.03616993892937899\n",
      "Epoch: 7, Batch: 20, Avg. Loss: 0.03084715027362108\n",
      "Epoch: 7, Batch: 30, Avg. Loss: 0.02893493454903364\n",
      "Epoch: 7, Batch: 40, Avg. Loss: 0.028482494689524174\n",
      "Epoch: 7, Batch: 50, Avg. Loss: 0.029232474416494368\n",
      "Epoch: 7, Batch: 60, Avg. Loss: 0.032165095768868925\n",
      "Epoch: 7, Batch: 70, Avg. Loss: 0.031658392027020456\n",
      "Epoch: 7, Batch: 80, Avg. Loss: 0.026272764522582294\n",
      "Epoch: 8, Batch: 10, Avg. Loss: 0.03377690371125937\n",
      "Epoch: 8, Batch: 20, Avg. Loss: 0.03170678522437811\n",
      "Epoch: 8, Batch: 30, Avg. Loss: 0.027490041591227053\n",
      "Epoch: 8, Batch: 40, Avg. Loss: 0.0369372421875596\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 20, Batch: 40, Avg. Loss: 0.023297969345003368\n",
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      "Epoch: 28, Batch: 30, Avg. Loss: 0.024257592484354974\n",
      "Epoch: 28, Batch: 40, Avg. Loss: 0.020261577703058718\n",
      "Epoch: 28, Batch: 50, Avg. Loss: 0.020561234559863806\n",
      "Epoch: 28, Batch: 60, Avg. Loss: 0.023603531438857316\n",
      "Epoch: 28, Batch: 70, Avg. Loss: 0.022278539557009935\n",
      "Epoch: 28, Batch: 80, Avg. Loss: 0.01956823915243149\n",
      "Epoch: 29, Batch: 10, Avg. Loss: 0.017053075972944497\n",
      "Epoch: 29, Batch: 20, Avg. Loss: 0.024568153917789458\n",
      "Epoch: 29, Batch: 30, Avg. Loss: 0.026478416472673415\n",
      "Epoch: 29, Batch: 40, Avg. Loss: 0.02290510945022106\n",
      "Epoch: 29, Batch: 50, Avg. Loss: 0.02025635614991188\n",
      "Epoch: 29, Batch: 60, Avg. Loss: 0.01992513332515955\n",
      "Epoch: 29, Batch: 70, Avg. Loss: 0.024998316261917352\n",
      "Epoch: 29, Batch: 80, Avg. Loss: 0.019309793040156363\n",
      "Epoch: 30, Batch: 10, Avg. Loss: 0.01629736889153719\n",
      "Epoch: 30, Batch: 20, Avg. Loss: 0.021219238825142383\n",
      "Epoch: 30, Batch: 30, Avg. Loss: 0.02293840777128935\n",
      "Epoch: 30, Batch: 40, Avg. Loss: 0.021831158269196748\n",
      "Epoch: 30, Batch: 50, Avg. Loss: 0.02273551532998681\n",
      "Epoch: 30, Batch: 60, Avg. Loss: 0.021049862541258336\n",
      "Epoch: 30, Batch: 70, Avg. Loss: 0.021132806222885846\n",
      "Epoch: 30, Batch: 80, Avg. Loss: 0.021107431221753358\n",
      "Epoch: 31, Batch: 10, Avg. Loss: 0.019971851166337727\n",
      "Epoch: 31, Batch: 20, Avg. Loss: 0.019650337938219308\n",
      "Epoch: 31, Batch: 30, Avg. Loss: 0.01838089684024453\n",
      "Epoch: 31, Batch: 40, Avg. Loss: 0.023436635546386243\n",
      "Epoch: 31, Batch: 50, Avg. Loss: 0.02010208023712039\n",
      "Epoch: 31, Batch: 60, Avg. Loss: 0.02172792125493288\n",
      "Epoch: 31, Batch: 70, Avg. Loss: 0.0174323252402246\n",
      "Epoch: 31, Batch: 80, Avg. Loss: 0.018921379651874303\n",
      "Epoch: 32, Batch: 10, Avg. Loss: 0.017541377060115337\n",
      "Epoch: 32, Batch: 20, Avg. Loss: 0.018748696055263282\n",
      "Epoch: 32, Batch: 30, Avg. Loss: 0.017636749148368835\n",
      "Epoch: 32, Batch: 40, Avg. Loss: 0.020140817761421202\n",
      "Epoch: 32, Batch: 50, Avg. Loss: 0.020985555090010165\n",
      "Epoch: 32, Batch: 60, Avg. Loss: 0.02060921983793378\n",
      "Epoch: 32, Batch: 70, Avg. Loss: 0.02543697040528059\n",
      "Epoch: 32, Batch: 80, Avg. Loss: 0.018728269543498755\n",
      "Epoch: 33, Batch: 10, Avg. Loss: 0.017670567892491818\n",
      "Epoch: 33, Batch: 20, Avg. Loss: 0.017041636537760495\n",
      "Epoch: 33, Batch: 30, Avg. Loss: 0.01819210248067975\n",
      "Epoch: 33, Batch: 40, Avg. Loss: 0.020063360407948493\n",
      "Epoch: 33, Batch: 50, Avg. Loss: 0.018506996519863605\n",
      "Epoch: 33, Batch: 60, Avg. Loss: 0.017822727840393782\n",
      "Epoch: 33, Batch: 70, Avg. Loss: 0.022991100326180458\n",
      "Epoch: 33, Batch: 80, Avg. Loss: 0.020791866444051267\n",
      "Epoch: 34, Batch: 10, Avg. Loss: 0.020215182658284904\n",
      "Epoch: 34, Batch: 20, Avg. Loss: 0.02052378300577402\n",
      "Epoch: 34, Batch: 30, Avg. Loss: 0.017187430616468193\n",
      "Epoch: 34, Batch: 40, Avg. Loss: 0.02478138292208314\n",
      "Epoch: 34, Batch: 50, Avg. Loss: 0.019487860053777693\n",
      "Epoch: 34, Batch: 60, Avg. Loss: 0.021887903939932583\n",
      "Epoch: 34, Batch: 70, Avg. Loss: 0.025754505209624766\n",
      "Epoch: 34, Batch: 80, Avg. Loss: 0.01771497130393982\n",
      "Epoch: 35, Batch: 10, Avg. Loss: 0.018153314758092166\n",
      "Epoch: 35, Batch: 20, Avg. Loss: 0.017818421591073275\n",
      "Epoch: 35, Batch: 30, Avg. Loss: 0.01942049991339445\n",
      "Epoch: 35, Batch: 40, Avg. Loss: 0.020540270395576953\n",
      "Epoch: 35, Batch: 50, Avg. Loss: 0.016556476429104804\n",
      "Epoch: 35, Batch: 60, Avg. Loss: 0.01558539541438222\n",
      "Epoch: 35, Batch: 70, Avg. Loss: 0.02022551540285349\n",
      "Epoch: 35, Batch: 80, Avg. Loss: 0.021052521374076604\n",
      "Epoch: 36, Batch: 10, Avg. Loss: 0.021352357883006334\n",
      "Epoch: 36, Batch: 20, Avg. Loss: 0.01876529725268483\n",
      "Epoch: 36, Batch: 30, Avg. Loss: 0.016403834242373704\n",
      "Epoch: 36, Batch: 40, Avg. Loss: 0.020617284160107375\n",
      "Epoch: 36, Batch: 50, Avg. Loss: 0.02135718036442995\n",
      "Epoch: 36, Batch: 60, Avg. Loss: 0.01764364568516612\n",
      "Epoch: 36, Batch: 70, Avg. Loss: 0.018155330885201694\n",
      "Epoch: 36, Batch: 80, Avg. Loss: 0.01897614961490035\n",
      "Epoch: 37, Batch: 10, Avg. Loss: 0.018756070639938116\n",
      "Epoch: 37, Batch: 20, Avg. Loss: 0.01989352870732546\n",
      "Epoch: 37, Batch: 30, Avg. Loss: 0.016026079561561345\n",
      "Epoch: 37, Batch: 40, Avg. Loss: 0.01923829847946763\n",
      "Epoch: 37, Batch: 50, Avg. Loss: 0.025898053776472807\n",
      "Epoch: 37, Batch: 60, Avg. Loss: 0.019165273755788803\n",
      "Epoch: 37, Batch: 70, Avg. Loss: 0.015895459335297346\n",
      "Epoch: 37, Batch: 80, Avg. Loss: 0.015881365910172463\n",
      "Epoch: 38, Batch: 10, Avg. Loss: 0.018683868274092675\n",
      "Epoch: 38, Batch: 20, Avg. Loss: 0.014368188567459583\n",
      "Epoch: 38, Batch: 30, Avg. Loss: 0.020238660182803868\n",
      "Epoch: 38, Batch: 40, Avg. Loss: 0.01461745472624898\n",
      "Epoch: 38, Batch: 50, Avg. Loss: 0.016611106041818858\n",
      "Epoch: 38, Batch: 60, Avg. Loss: 0.018164356518536807\n",
      "Epoch: 38, Batch: 70, Avg. Loss: 0.01758043738082051\n",
      "Epoch: 38, Batch: 80, Avg. Loss: 0.014790661726146936\n",
      "Epoch: 39, Batch: 10, Avg. Loss: 0.015583113953471183\n",
      "Epoch: 39, Batch: 20, Avg. Loss: 0.01660054363310337\n",
      "Epoch: 39, Batch: 30, Avg. Loss: 0.021457985602319242\n",
      "Epoch: 39, Batch: 40, Avg. Loss: 0.0231976879760623\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 39, Batch: 50, Avg. Loss: 0.019920764677226543\n",
      "Epoch: 39, Batch: 60, Avg. Loss: 0.025385365169495345\n",
      "Epoch: 39, Batch: 70, Avg. Loss: 0.018385207373648883\n",
      "Epoch: 39, Batch: 80, Avg. Loss: 0.01990005047991872\n",
      "Epoch: 40, Batch: 10, Avg. Loss: 0.02061985582113266\n",
      "Epoch: 40, Batch: 20, Avg. Loss: 0.013936930056661367\n",
      "Epoch: 40, Batch: 30, Avg. Loss: 0.015046548005193472\n",
      "Epoch: 40, Batch: 40, Avg. Loss: 0.016492578946053982\n",
      "Epoch: 40, Batch: 50, Avg. Loss: 0.01866449126973748\n",
      "Epoch: 40, Batch: 60, Avg. Loss: 0.017877279501408338\n",
      "Epoch: 40, Batch: 70, Avg. Loss: 0.015853506047278643\n",
      "Epoch: 40, Batch: 80, Avg. Loss: 0.01582360137254\n",
      "Finished Training\n"
     ]
    }
   ],
   "source": [
    "#net.cuda()\n",
    "# train your network\n",
    "n_epochs = 40 # start small, and increase when you've decided on your model structure and hyperparams\n",
    "\n",
    "# this is a Workspaces-specific context manager to keep the connection\n",
    "# alive while training your model, not part of pytorch\n",
    "with active_session():\n",
    "    training_loss = train_net(n_epochs)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 0.8)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2d02686390>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(training_loss)\n",
    "plt.xlabel('batches')\n",
    "plt.ylabel('loss')\n",
    "plt.ylim(0, 0.8) # consistent scaleplt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test data\n",
    "\n",
    "See how your model performs on previously unseen, test data. We've already loaded and transformed this data, similar to the training data. Next, run your trained model on these images to see what kind of keypoints are produced. You should be able to see if your model is fitting each new face it sees, if the points are distributed randomly, or if the points have actually overfitted the training data and do not generalize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([30, 1, 224, 224])\n",
      "torch.Size([30, 68, 2])\n",
      "torch.Size([30, 68, 2])\n"
     ]
    }
   ],
   "source": [
    "# get a sample of test data again\n",
    "net.cpu()\n",
    "test_images, test_outputs, gt_pts = net_sample_output()\n",
    "\n",
    "print(test_images.data.size())\n",
    "print(test_outputs.data.size())\n",
    "print(gt_pts.size())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2d0248acc0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2d001043c8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2d003fb080>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2d001db748>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2d02528518>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2d0264fb38>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2d026d16d8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2d1a4c0f60>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NJvF4nO985zucPXuWVCrF4uIiDz30EKVSiU6nw/Xr19F1XfFbJJISysMgctLdCF13wr6Ievr5I/fyM+hYYgIMwyCbzTI9PU2z2QS6iS7hoUYiEZUWDwaDTE9PKz9neHiYw4cPk0gklIYSYRRKo1xcMV1SV5IKcSQSUZwVKRwKTVLKCg899BCJRIJms6k0ggibpmnMz88zMjKiCEuNRoNwOKxokXKuzWZT/fZnYCUJJ4LU/7NX7BuNshv81eR7OVYgEFDV4Hq9ztGjR9XiplIpms0m09PTHD9+nFu3bhEOhxkdHaVWqxGLxZicnCSXy/V8rgiKP/JwHEdFHiI8cnHkNUIFME1TEY1M06RQKFAsFnnqqadYWFigUCgoZp3neSQSCUzTZGVlBU3TqNfrVCoVAMrlMnCbSN5oNNR3sCxLUTb9GuV+fBPBvhCUO+F+HV3JJwgHNplMUqvVqNVqQFcrSOgrjx3Hod1uE41GcV1X7XARAD/8giCP/ZpMnFromiFN07BtW0VM2WxWMfPr9TpjY2NAl2kntEm/uTp27Bjb29u0Wi06nQ6tVotIJIJt2yo0DoVCrxAMqU29GiGBB0BQ7gfi+Uvk89hjj7Gzs4OmaWQyGXRdJ5FIEI1GMQyDQ4cOqbxJq9UiGo2qymu/ipbQttlsqtyI+C/+to9gMNiTbxHfRtLrnueRTqcZHx9nYWGBRCLB2NgYq6uryqRI3iYWiwHdCx+PxymXy4r3KwW/eDyukm9+4RiUeX/g2zX6e1TupR7h9yPC4TCapqmopt1uk8vlaDab1Go1EokEiUSC8fFxlbe4du0ai4uLjI2NMTw8TCKRIBgMqlwKoMr4Yu8lHJXvKX02/bxU8XvEF5K/NU1jYmKCeDzO9evXFeWyXq9TKpVIp9OqFlQul1U/kFAT5HNN0+wxd+IP7YZ7NeewT5zZ1xJyoQAViVSrVQBFSZS8SjqdxnEcLMsil8uRyWSYmpoim80qhxG6kYOfaiC7WBxXfxlffBa/Uy3aRH4Lb1aipUQiwUMPPaS6DGOxGPl8nkajoUjcol1Ea8h3ExMnmkOExe/sv1qzA/tMo9wPRJP4F8OfdZS+l06no3InQhfwL2Q2m2V2dpZEIkEsFuvpJBQydSKRUI+FRSaCKVGGn7ciPFpAObySf/Fzb6XKnEwmAXryNc1mUxGoJKqSaMufvpeWjn5tMoiD8sCbntciQeTnjJqmqQRFOuuGh4cVYVoulOzWbDardr20acgFNwyDRCKhTIafqikXyn8sMVFikuQ56SuORqOEQiFM08SyLEzTVO2m+XweTdOwLAvLslQdqdFoKPa+vFd8JL+GGiQUg3JVPzKmZy8n0i9c/SbAsizV5B0KhZiamlIXXcyJ7Hy5KBKZyPH6F140iQiIv5VThEH6c0Tj+F8TjUaJRqM9x5S21Ww2SyQSIZ1Oq+8h2WXRIIN6jiXKi0Qiu/og/bmne0ly7iuNcj/w+yR+kyN5FMl5yC7UdA0r1BUIDw8n4igeiSTO4DbLrl9r9BfTOp1Oz/v8dRaB38TJ95GcilAI5PjShrG5udkTYQmlUbSMYRhKGOVzJTraLRn5ampq+0JQ/LujPwt6N/gXqp/FJeo4EAh0Vfpwnr9J/w2rrVVmt2aJt+Oc2znHPxn+J/zpk3/K4sYiQTOoNFKn01FZUtEwstidTkc9b1mWEhYxcfLdRCP5d7k8lnBc8h+maSrikZgjoOf4jUZDfX4qlVKMuXA4rLRJf87ntSiR7AtB8aM/9u/fwYMEyO9Qymv8GiAWi+G6LrHhGKv6Ki4u8+Y8mqXheA7fu/U9fvbvf5alzhInQyf5V7P/irbWJtfKYQ/bVKwKuXaO0Giop7ldPlsujHye+CnQG4r6zZl09/U/FgadaBvXdZU/ImZPjlOv15WpNQxDJRb9kO/aLzz3in0jKCIQ/jAPXhna+UNWgT8b6vcfgsEgqVRK+SGTmUlmgjPc6NzgZPQkVsfipn2TSXuSRRZxcbnSusInn/0k80PznC6chihcyl9irjDHZ5//LJ3PdjCCBtvb2ziOQywWU58hF1guqmR+JTMrED9IenBEK4ipi8fjyodqNpu0Wi3gdl7Jr33l3KWu5Neiu8Hf67RX7AtBuZdpQYPe0/+cX7uIiRgaGiI/lOfXsr9GsVqkvlGnUW9w9u/PMrM0w0c/8FHmx+c5sXqCa5PXcHSHi1MX0dDU35W/rmAsGxhBg06wQ6PZUBdR/I5AMEBTazISG8FxHEq3SoxMjKBVNbaj26T1NHpZR4t0BbpUKlGv15V5EKf25MmTii8LKA0TiURotVrKARbBSaVSpFKpHqqBYFDV+F79lX0hKK8Fduss9PM1wuEwZtukvd2mtF3C3XY5vnScaqzKF/7dFzg/e56H5x/mmfc/w/WJ65wunMYO2syPzzNXmCM2FkP/jE5oPkT0oSjexz3aVlv5CI1mg0/Mf4LL9cucTpxGW9C4mLvI6dXTaJ7GxemLnNk+w+f+zecIPBxA/4JOoPaD8Nbp1oGkhuN5HrlcjkajoaiRUi+S7K6cm/gnYnZarZYSFNEsg6KdexGWB0pQditu+f0Yv1YB1EK2222VyJI+3nK7zC//4i9zffI64U6YVqhFajuFq7t4mkchXmDupTl+bP3HOBw4zLn/+Ryv+8zr0FwN44pBPphnob7A2toajUaDG8UbXMxcxNM8LlQvoOd0HMPh4uRtzXQhd4FypEz25SztD7ZprDdITCa49bFb1Lwa8VDX7Liuq7gyMthHzku0iYTNUq4wDINMJgOg/BvxT8Rs+SOwHxlBGWSS/MWu/sxof7VUaiqRSAQPDytoESeuopqG1mB+ah5P92jpLdCgOlTtfu4P/u6EO7SrbebdefIzedrH20RuRNDOaATyAQK1ACsrK2xublIulckFc5TiJVKVFGP1Ma6PX+fUyil0T+fioYs8tPkQ6Vaa2lSN33jDb3Bx+iKnC6exFi3mmWc2MstHUx8FUE1e0hLSbDZVI7oUGEUQRHNIolD8GL/z3+8M/0jkUe7WFNavOQT9AhWNRsGDK49f4Zmbz3AicoKfHvrpbuIrFuV65zrFUBHd1XE0h0Q5wejIKAv2AmPmGDcevcFOYodMOcMb9Tey9L8vMZmYRJvWyIa6c9aE57Jxa4Njy8cYjY4SKAfQPZ03xN5AKpMiTZoT3gnSgTT/6X/9T7TzbS5mLnb9n+mLaI6Ga7jMt+fZieyQCCfI5/NkMhlu3ryp6k1yzkL4tm2bZDKJrusqRyNOtVAl4f6avvzYd4KylyhHbDX02ll/rkMWJRFL8N6V9/Lx1Me7YXF7nkfe8Aitre5sksdrj3Nh8QJfSXyFVX2VkfwI2KC5GtmtLFcmr+DpHtV0lYf+8iH4GPx66de5uHiRhzMP88nDn2R0dJRLly6RG8rx7JFnKSfLxEtxMn+b4crKFWLEOHnyJI7pEHWjZNIZkkaS4dgwG+EN5gpzaHR9mJnQDJlARs1tyWazJJNJNjc3FZ1AWHNSIJQUPtyOjKR1pN1uvyoKpLoO9/3O/87oT6bBnacfSuIpakV5rPQYc4W5rjOZOkM+mmcjvAF0fZhsOsuq282vLNqL4IFruFyduMrJlZNcm7zGXGGOw/OHmS/Oc9G5iOM5nCufYzW1iuEaPHbkMZiCvyv9HQDNoSbB9wRpx9romzpLuSXWA+vkqjkePf8oVwpXmCvO8eaJN/Pur76b7HqWtZNrNJ5poBu3KQviqKKBF/UIhUOMjIzQbrcV+VsiHYmGhKoZj8dVnevVdjrse0EZ1JPiH0M1qNAldtx1XeqBOkuJJT77559l48wGx/6vY2pykhw3E8ww2ZpkVV/lzPIZPDwuTXdzJ7/3F79HNVZlaGcINDjxGyc4/eHTXBy+yNn0WQKtAJOfm+TkzZNYJy1mf36WeXOew8HD3EzcBKA50qRJEzTYTm2zPLvM9ZHrbNW3eOvyW3n5F14m3AwTGY+Q1JM9RGnHcXA9l8q7KtjjNs2NJofnDxM3uu0j4XCYQqGgkoxSihBNI+G0JCBljeDe6Af7XlB2w24nKQuiBEyDPzr2R3zwPR+kHWkTWYuo9gtJkuXzeT7V+BSb9U1O/8VpwvNhyrEyuUYOdMiX82h0nUBP89CaWjeKcR3cskv8ZhzN1QhdC/G7Y7/LqrdK7PdivP8974cBX/NG/gae5lGOlznzxBlykZyq8QDYlk2n1MHUuvWg5GgSe8wGHawRi8BGgFPTp5iYmOCll15SBVCpb0nTWSwWU5SJZrPZk8p/IMnV99K1NqjZuh/9NMCO3cEKWWohy+WymmYQjUbJ5XK0222Ga8OYv23S3mmT+EwC5qFxtAEexBfjEIEdY4eL0xdxcLhUvYRzyME6YRG6FsI55ZA+lCa0HiIyH+HhpYe5OH2RucIcruZyeeoyc4W5Ho119s1n8TKeYtM1603yv5UnPB+meqjKfzv737CrNoFiAHvcJt/KM5GeALoTnsrlsloTMbdC4xRGXTweVyWC+3Vo94Wg/DCgwmfdoPWGFr9a/VVObZ3iV2K/wo6xg2maRCIRlc00DIN8Pg90/Yv679XZLmyz7WwTi8Y4PnwcO2aTrWY5s3qGC5ULnIqfIhfOUfo/S0Q2IyTmEgRDQcJHw5hzJp//889TjpbJNrK4utvVUvUcruZSjpeJT8Xh3TCUH1JjRBsrDcLzYTRXI7mcxJlwaDVbTP6XSbSExjvf9k5SkynC4TA7Ozs9kyHh9gYSLSOTtUOhkKo6P7Cdgv35En9eZLeU/l6yi57nEdAC3Ji4gWM4XM5fprhaxLRMVVEWElE4HFaz56VdouSVCIVDHDpyiOmZ7oyS4FiQPzv6ZxSrRbSmRmWnQu63c4TmQ2hnNLw/8AhHw8S/GMfasDA+ZuCd9wg8HGDIHcK74KGd1pj4nQmCo8Eeuma5XKaiVUgcSxBbiFEaL7Ha6M6Zs0yLyfwkoWCI8fFxQqEQX/7yl3s4u34tKxokFAqpxjJd12m328qHu5dC4b4QFD/uJu17UZv+Y1QaFU7cOsG10Wuc2jxF4mRCEbCFgSbtDuI8isq2LIuf/MmfJJvNYhgGi0uLlDtlxqPjpIwUVa8KFQhdC6G5Gt4FD6NmYKQMjIBBaDSE+6cuzraDl/HQ0LC3bIy8QTgaVuM4pJDY6XTw8LjxyzdoFVuU3BLe/9ctFMbiMQ7PHQYNpR1qtZrKk/QPzhEqg3QV+CcxSJR0L9h3gvJqw7hBgvaO9Dt42nma4cPDmJap+mGkP0bmufkZZFtbWzz11FNsbm52C3eNOr96/lc5Xz7Po0OP8qmZT3Wr0sNB7IdsAlcCOA85mFETw+wy6Gzb7o4sT3TUdzFyt/k2wjkplUpKo1iWhe3a6EM6Gbs7ZSEWjzH/xnn+JvE3TLqT/Lr361y7dq1nbq1fSPw82U6ng+d5ivopmtrPkdkL9p2g3K2SvFsmdrfX2I7Nl+JfokCBw53DfMD4AGEvfDv09DV0i5Capolpmty4cYOVlZVuA3jQ5Hz5PI7n8NL2S1yLXCMTyJBMJmn+ZhPrhoVxzCDUDOF6rmq1EPhpEJZlqYZ0mSkrbDzbsvFKHkbOwDO6UxG0hEYpUcLFZVVfpVgtsra2pqZn96+D0BVkHfycYeG23OukrX0hKH4t4udu+E92Nwz6v38RAqkAN7mJi8uSs0Q72CbqRNUubDQayr7LLpOx5BcuXODSpUucPHmS4eFhZiOzXGtdYyY0Q1Lr9tesrawx88czpK6nsE5YdD7dUccQaqKcl+u6qnFMwthms0mj0eg6oy4c/5PjJBYT1I/UufD+C8RiMUaSIxwxjrDoLHI8dBwaXdKS3zcZNI4LbnN1/OQlaU574IqCr9VUoEGIEeMQhyi4BeaW53j82ce5+cxNPLyeMoBfUCTElBsUrK6ucuLkCXYmd/DCHuVymd/6t7+FoRu886l3Mnd9TuVRtgvbhMe6+RB/t588FpNXr9fVxCTZEHpVJ7GYQHM1EosJwu3umHSAp48/zdLmEkEryHPPPdfzPqBnGmQ/C1DGZQCK4CSO7V6xLwTlhwnLtPhg64PM/sksQ7UhPN0j3Apjxs0eRrtAqIyVSoV8Ps/Y+Bip8RQ7zg63QrdAg83w2p5eAAAWO0lEQVTIJsdnjlMqlHh5+WVmp2eZXZ7FmrHoxDt06l2fRBJ6AvFLRGDg9t0uNE2DLNQO10guJWkcbdAMNQnRza46tkPMi3Fz5SaVSkVViP3FUYkSB+Wl5LMlxS+Fw71iXwjKD3MyZSAQoBVsERwK4jU8aodqdBIdPNfrWSh/BCRUwkazwfcf/j7rwfXuaxwDR3OY8qZ442NvZPXoKl9Nf5Vn3/Qsc8tzfPofP002k6VaryphkDyHPwkGqPC1h7StwaV/cYlQKwQZ8JqeKg5alkUmk6FQKKhUvV9b+fMn/X6enJNoTAmb/UJ813W8/0vww4H/JP31ifuF4zi0zBbP/fxzZJoZ3KRLsN1dYLlYMidFIh/oLnDbaLMeWFdpeMdw0NDQHI3/GPmPFMYLeFr3Ql+cvkjjrxrktnMExgKUdkpqSqM/NPWbH4Ft2zgdB8qgB3WsuIXdsrFdm1AmpCIWgUxu0nW9Z/ZJf0ZaHvub4izLUvRKKRnsBftCUAZVhl8rhMIh/kPwP3BLu8WhyCF+3vl5XNNVO9zv7InDKWp9KDzEhDXBmrGmhMXTPFb0FTRPw9M98MBwDeYKc2SbWfgQhE6F0D92u11E2kiFbS95E3V/nY7DoS8cIn4zTvVQlfO/eB49qPNF54sUygVO26f55OFP0qg31Hn5HdT+gt9uPp8/Ieef9bYX7AtB+WGiE+pQDBa71EatwNH/5ygLP7ugOKryI/NjAYKhIE2aDAeG+aXgL9FKtBiJj/DHq3/MMsucKpzC0R2uTl5lrjDHJ7/0SYYaQwBoaBiXDZJukjbtHsfSr1H8eQyn5KjCYnI5iVbVqKarFCjg4nK5fpmaU2NtZU0JXzgcpl6vq8kNfm0iwtIfEfpZ/P5eob1gXwhKf1P1awmtqZEupallaswV5pien2a5towds9V9+qSyWq/X8fD4r4f+K+uBdaaYQvM0CrUCJ+wT/M6Z38H5bYdPP/ZpLk9e5qG1h/jcFz9HwAvg4eFGXHRLp3OiQzvS5YtIGAu32zT8Uw0cx8EO21SmK6QKKSpTFdqRNsFOkAm62uywfphLz1/i3MvnVN+PlB+EE9y/fv4oqF/DSCJONN1esO8EBXrvSdzv6Iq6vFNI7S986brOzLdn+HD1wxy+cZjKZAU7aRPQAmrMuWVZlMtlLl+9TDlZZvXoKmiw7C13D6jBleYVrq5eZftntrlgX8DVXK5MX2H19CqJxQTBdJDnf+F5UqSIjEdINLtE7v7IQvwg+REtc+H9Fwg0AjRDP+DF6gEeeeERjthHiHkxXrJfUuftuq6aCydRlAhGf0+yf33lvdL39MCGx4Ps6yD12f+eu8EwDJ5/2/OsPL1CJ9HpETbV/+N0OP/0eRzDAQ9wIboTpZXtmiM8+MzNz1DL1gh1QnQCHWZvzfKv3/WvWdaXmVue4+N//nGe/8DzDDeH0Q1d+Tt+srdfSCQ7rHka4XYYM2ri2q4aY262TeJGvCc5JpooHA6rEef906F2S0L2r9UDncIX+CcA3Am7hdb9i7K6vop2QiPlpAg1Q3Ti3QKcpmndu4NOBHE8307UIJlL0tJa6qlargYaWKGuyi7kCjS1Juhwfvo8v/k//SZXtCuM74zzIfNDBINBcrmc0oySlYXb81Ic2+Hxf/84qUKKnYkdvvUz36JltljaWlIOtL9rUrKwnU5H5UIkzPb7KoPWQgTjfm7Vsm8FRXC32s4gdr6EjLIwHbvD16e/TiPW4FTxFL//b3+f6lSV59/7PKFwtwyfNtJE7AhtbqvjDTbQHR1Xd7sXzf/RGjTDTaLtKK1Ii4gV4fL0ZdBgLbLGxL+boPiLxZ4JBv5EG/xg1ls9SKqQQnd1smtZ7G2bvx7/a7aGt0jX0rz+8utxnduN5/65cDI+Q+5TuBuJ2u/k+v9/LxplX81H8Y+48vNRxLaKDfb7IKJq5Xk/l1ZUfcNrUM/V8TSPqyNXqUarZFYymLdMRUh2XZePaR/jQ96HmPAmukKhgUvfYrqguzp4EDNjtENt0MAM9ZbuM9sZ3vDpN2B4hppcAKjBgCqvEbfYmdjB1Vw2RzdZtBbZimzh6R6VZKXbb8TtkFYgRUQZuS4TEOS1sjaSSPSvj+BeUhH7SlCAHiEBXiEocPedILkFNYKz7hLeCKOjc+LWCdKtNNtj29QDdZWplKLciDvCL+m/xIQ7ge7oPFx4mLnlOXBhqDTEH/7ZH3KqcArN1ThWPMaZwhkMx+BM4QxnCmfQXZ2zS2cZagyht3WCxaA6vlSl/ZMKTMvkm+/6Jl/+377M377lb3HqDulaGs3VSNfShDqhHk3gz8CKdpHb2fYP/emHvN//s1fsK9Pjd/oGnUQ/h2K3KrMMm5Fyuuu4TH11imc+9gyb1iZ//wt/TyPYUPQCP6tfooYPBj5I3a6TDWSpZqv8yv/9KxxdOMrC4QWuHOr2+lyevsxffv4v0TyNXCOHq7tc+JcXmPuLOQCciMNOakcJhZgewzC6obHt4G67VJwKO40dvGh3I7zu0uuwghahTnfwT/8ayIYRqqMMJhTuiT9tL+jvPX7gm9T7tUZ/DWYvkCnOEg3Ytk0qlUJv6qTTaRZuLuDiktASBGtBvJCHFrjtPGcyGQzDIOflCE2GGK2NcmzhGJqrMXNzhrnlOS4eusjc6hy5eg7tB16n7uk8/NsP05xpMv/0PPV8nYAZUGMw/IW5Rr3Bm//6zeSLeZYzy/za+3+NUqJEpprhzTfeTNAJYmMP9NHkOTlWIpEgmUyqGy7033zSj/vxT2CfCcqgZnNJVctz/Sfo7ySURJKkx4GeIXiBQADbsXn28LPcCt/i5NpJ/vDP/pDKZIWX3/eyIvakUim1c1utFpF8hM7JDsGrQTRX4/Nf/Dw7iR2ytSw6ejd6+kE7h4ZG7GYMM2biaZ7SapI/0fXumDBrw2KoOITu6SQ6CUqJUreFI1nGDJiE3FAP/UF+95OjxXeJRCJYlqWG68j/BkU491Mm2Xc+iqCfW+G30/58gZijdrutbjYt7xMH0rZtNSGgpbfYCG/gaR7zY/NUY1Wya1mC9W7hTi6C+DnBYJCO3WHjX26w9Sdb2KdsNF0jPZ3GOeXg6R5etNvv40a6UxDqR+q0wi3FZPOP2pK7lS5XlymkCjiaQyfeYcwaAxdCGyG2lraA3nlwft+t3ykVcyZNX8Lc86/jIDzweRR/ROOvWUio6d9RjuOoVHZPAq3T6dEqcqyoE2WKKVa8FY6vH8fVXLbGt6gH68TMbtm9Xq+rqY0yq8TxHIxhg/qn6kStaJcra9lUVitYEQu7ZFPxKhh1g6pRxW7YSosoonOzRWWpwkZng5bR4j+/7T8zFZvCjJmc/f5Z6ufqJPUkt7hFcb2oRoq5rsvExASxWEzN7Jd1kM0gDfnSGbibrwK3fZQH1pmFV04F8juB8uOHLGT/D9y257Kgkkt4H++j4lT4q9G/4t3/x7sZt8f5mfrPkOgkaCaaaucGg0E1El1Y+bqu44U9jEZXCNvRdjfLGjFpV9sQhk67ozSI/G632jz9X55mtDTKM+9/hvmpeQpWgZ8q/RS6pnPt6jVibgyrY6lmMDlXy7IoFArqDu2SP/FvBsnWxuPxe6rh7BX7QlD6KX3iiAr52A+Z+y5C5C+0ybH8v0U45C4buq7jOi4aGuuBdTzNYz24zpn/9wwzN2coT5Y594vnFHFZGrNqtRqpVArDMHpYav4RoCIYrVZLzbe1LIutrS3cbZfx7XEq8Qo3JrotpcVQkU6wQ+FKgZ2dHeLxOHBbo4rZlQnWcmcQud2dvxgoghWLxVQl3F8+GLQ2D6xG8TyPSqWiohUZEAy9eQN/Uq2/PiSmqt9Gl0pdIpHMl095Kaa8KQoUyO5kObxwmHKsTHoljVk0udW+pfqBJQwVVpnfvElhzXEcNjc3abfb3WlO5TLlchnbsok7ccwhk7WhNSZKE5y4dYIr41cYt8dJ6AleeukldataIRn1c3REKOQOZsViUd1JIxQKMTw8TCaTUbfVFS26G5XggQyPRSP4h/OKNy+L5hcUvwby5xUk6dTDwv9BfqHVatFoNNSNIwHe67yXJk0q1Qof/cBHuT5+nePrx3mi+QRhJ0ytWiNhJ+gkOrhRl6gXJWAE1DgscVLFYd3e3mZra4tyudwdS6EH+PDND/NH/8sfceHQBRZft8g/3/rnvD3ydt5UfhMJPcFSYUmdw51aT2RuW7PZVELj/3tlZYXt7W1SqRRHjx4ll8uxsbExcL0f2GkGIgSy4P6KaL8zJs/Dba9dXtPf2yLHlgtx6dIlHnvsMWWODN0g0onQzrW5lrzWTfFPXCX9XJokSd738vsYK43xkX/xEa6mrzLWGeOntro+hWiaer1Oo9mgbJWp3aphNk0iZoRIIsKQMUTWy3Jx+iKu7rIR3qCSqhB1osSJY7ZNLl++3DPO038Ocl4yvlzOx7IsRTXwm+Z6vU6r1aJer6t7JgI9/T/3i30hKKqvhduToP28T3/k459s7S92+VP+cLvO4bfz3/zmNzly5AixWEzdo1jXdVJGiglngjV9jXgpTmWtgtu57VPMj813fZnAOt859x1C7RBxO862s029WefWP7tFe7hNfDvOF/78CxytH2U9t87f/fjfYS1a3SE+hy4y7o0T82JdBl2zyXe/+12KxWLvmA5e2Vft1wCS1VWTGn6QYJOQWXwmGQ4oPcaZTEbNro3FYkor7hX7QlDE3MBtDdBPWvJrCHFmgR4B8WsfETh5HI1GKZfLrK+vMz093cNJCRgB3mu9l6uFq9y6eYsKFWpGjeuR68w0Zji2eoz5qXkimxFqazU+VvwYs+Ys8+F5fvfY79IeboPenYKQ8TIYnsFEaYJ8MM9zP/0c79DewVvMtxB2wzh0neBCocD6+rryt+Sc/LmTQcw/cabFXPcPchbIe2UykwikpmnqnszZbHbP12hfCIrfhPgd093aJft7bfuP4T+WkHugGzGdP3+e8fFxbNvuiRo81+PI8BHixLl27RqdToffP/z7JJwE2nMaR0JHCHVCpINpZs1ZDAxmzVmORY5RrpappquMmCN04h3chsvW2BahkRDBUBBHdwg7XUZauVlmZWWFS5cuqdvWyq1doNdv6I9WRAOKwzvIr+mvX/nT+X4mXKVSUcnJvWBfCMpu6C9kAa9ohezXMNA7Q1X8HbHpm5ubKqEmGU0xX57nqZHlpVKJYDiIiYlu6UTs7hy1mlFjIbbAseYxlpJLxCfi/NO1f4pX9khoCZ5957NkvAyNUIOQEVLlA8Ha2hqVSoX19XXVyO7/vn6ahV+r+H+LwPhHhPqjQOHiiDnvH3EhZveBG3vh1yL+IqD/edk9ckH9Fd9++HeZ/8YEuq6zvb3Nyy+/zNzcHOl0WrVTyLHkptmO41Cv11VorPggGvzBkT9gLDIGWRhODavchXx/M2QS0kM9N1BwHIfFxUXW1tbUWE9/aC9mZBCrz78W/UICvRvDz0Xxbx5/73E/CWov2BeCshv8J+83Nf4yu2C3Kqn/YshuXV5eZmVlhYmJCebm5sjlcsBtiuDQ0BCJRIJisUipVOrp5pOMbXI6qUhDsptlGDCgbnipaRoXL15kdXWVZrNJJBJhc3OTQCDQow1347r2Q8Jk0R5+B3hQf5Rfa7yajsx9KSj9zmr/DoLe6EYe+zmj/shBkk/SStlqtUgmk6ytrdFsNhkeHiaXy5HP59F1Xd3ONpFIqF4fuD0jTVoxRUtJ5OHv5ovH4xSLRTXVWjoS6/U65XKZbDbbkyfaawQipkzMqV+TDXqtH/eiQfqx7wSlP9Mqj3cjDg9a6EGvk2MZhkGlUiGZTBIKhahWq1SrVVZWVshms+RyOXK5HIFAgNHRUXVDarnpkhxX7soF9NxkUnp5NjY2lBYJBoPqvoRyA0z/SC3/9+vHoAqvmDR/fqV/w/jP99UIiED7YTaI7xX5fN6DV7aW9oe+uwmAH4POx98+Ko/lJo/+Y/a3lSYSCYaGuh2A/uZv0TrBYJBEIqHqQTs7O+qOo57nEQ6HFQ/Gdbu30P3e975HOBx+hekYRAHt9zMEshb9a+IPr+XxIKKS/5jz8/N7UmX7QqP4GfN3wr0kiPzod4xd11U7Ox6P99wgSf52XZd6vU673VZtm/7bzArzXeo7/kKhmCE5L3lOSgd+QpFEcf2bwr8ug6I//5rcKSW/m+92r9gXgjJIbfbjfil88l6/TZcMpmmaqmILtx0/iUikXC/hZLlc7vkuYhbFtAgnREJPf+ZY13VqtdorLtRuF87PbuuH37kehDut0f1wUWCfCIo/59GPvZibO8HPWJMdLLeb9Q+6EXMjaXLXdZVTq2maGl8hDqgIgtRRJAzuzyjLa5LJJCsrKypqkc/0j6ToP2dx4v1V8t1cBX9k5885CQZNO3ggaQb+sHc3wRi0SP3hr7x/t13nz3LKBRHOqWgEP5UQbucg/LvcfzEHRVvyP+HhAlSrVaWtRNP4TYv4QfLdJBm3W4F0EPoH6fiflzXaq6n3Y18Iip8D23+S/seDTu5O3FBZ9EHPy0XKZrN4nqduLevXYCK8/QLhf14ugP97inkTTSPDjuUeyYM0iP9vEZC9mOS74dVqZMG+ERTZsZJ27s+D+C/ObscQ9N9Foh/+/pqFhQUeeeQR1XUnJXz/9xA6pt9xlCjK74OIOdI0jXg8rjK6gUCAGzduKP7tIOqEvK9/M+zGU/nvjX0hKAK/rRcMyhXs9l6/8yjP9S+yqF1RwRLZpNNpxWKTgqHwY+CVTVPSHC4tGH5hCYfDPaWBarVKo9EglUqp1/vh1x79eZX+rPRezE//sV8L7CtBgdsn5h/t6Z9RttvrB2G33egXxlgsxvz8PEePHiWbzarsqpiUSqXSw82F20Ijvotommg02sN+k+9348YNdR/AQfNd+53fOyXh+kN9eOU9o++UcJRzu9fZePtWUPwO16AS/J1wL6pacirb29tq5ohoBED1AwkDzx9RiJMpAiNC4v9fPB5XFEzRYnc677thkDbxa9HdsrB70cp3wr4TFOg1Gf4K8V4E4F7tued1B/Btbm6SSCS6s1J8Gkf+dl1XTY/072oRFH/JX/wf0SJiynb7boPMzl4hmra/8Cnop1/Icw9kHsUPf2q6fwcOCv0GEXfuFin54TiOyqlUKhXlQ/TzNcQH6lfzokH8N04SxzwQCKhR5/3mxQ//br+boA/SCOIEiz83iGfyan2VfScoYqM9z1OV2/5S+d00zL1qFXEabdum3W5TrVYVXVDmmfQXJeW3n5MbDAZ7PtswDK5evdpzbnfyDe5FY4pWE3MokWO/kOzm/EricK/Yd4ICtxdfuvOEHiACNCixdr+Qiy/8EMdx1M0a/RlYwSBV7nd0+9FoNHqE616jlkGQepRwZzVN61mfQdpj0PP3omX2RfX4APsf+3aawQH2Fw4E5QB7woGgHGBPOBCUA+wJB4JygD3hQFAOsCccCMoB9oQDQTnAnnAgKAfYEw4E5QB7woGgHGBPOBCUA+wJB4JygD3hQFAOsCccCMoB9oQDQTnAnnAgKAfYEw4E5QB7woGgHGBPOBCUA+wJB4JygD3hQFAOsCccCMoB9oT/H8s9jL2K0VYhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2d02641668>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2d0252e0f0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## TODO: visualize your test output\n",
    "# you can use the same function as before, by un-commenting the line below:\n",
    "\n",
    "visualize_output(test_images, test_outputs, gt_pts)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once you've found a good model (or two), save your model so you can load it and use it later!\n",
    "\n",
    "Save your models but please **delete any checkpoints and saved models before you submit your project** otherwise your workspace may be too large to submit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "## TODO: change the name to something uniqe for each new model\n",
    "model_dir = 'saved_models/'\n",
    "model_name = 'keypoints_model_1.pt'\n",
    "\n",
    "# after training, save your model parameters in the dir 'saved_models'\n",
    "torch.save(net.state_dict(), model_dir+model_name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After you've trained a well-performing model, answer the following questions so that we have some insight into your training and architecture selection process. Answering all questions is required to pass this project."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1: What optimization and loss functions did you choose and why?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer**: I used L1Smooth as loss function since it is a regression task and it handles outliers with large values better than MSE. Further I used the Adam Optimizer since it is an adaptive learning rate algorithm and the default hyperparamters already worked quite well and the loss dropped much faster than with SGD. Also it was proposed in the NaimishNet paper.   \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 2: What kind of network architecture did you start with and how did it change as you tried different architectures? Did you decide to add more convolutional layers or any layers to avoid overfitting the data?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer**:  I startet with the network architecture as it was described in the NaimishNet paper. I added an additional conv layer and also some batch normalization layers. I used only dropout layers with a 0.2 propability. Also I changed the activation functions to selu."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 3: How did you decide on the number of epochs and batch_size to train your model?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer**: Increasing the batch size led to a better loss so 40-50 was a good value. The loss still dropped after 10 epochs so i decided to let it run for 50 epochs. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature Visualization\n",
    "\n",
    "Sometimes, neural networks are thought of as a black box, given some input, they learn to produce some output. CNN's are actually learning to recognize a variety of spatial patterns and you can visualize what each convolutional layer has been trained to recognize by looking at the weights that make up each convolutional kernel and applying those one at a time to a sample image. This technique is called feature visualization and it's useful for understanding the inner workings of a CNN."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the cell below, you can see how to extract a single filter (by index) from your first convolutional layer. The filter should appear as a grayscale grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Net(\n",
       "  (conv_1): Conv2d(1, 32, kernel_size=(5, 5), stride=(1, 1))\n",
       "  (conv_2): Conv2d(32, 64, kernel_size=(3, 3), stride=(1, 1))\n",
       "  (conv_3): Conv2d(64, 128, kernel_size=(3, 3), stride=(1, 1))\n",
       "  (conv_4): Conv2d(128, 256, kernel_size=(3, 3), stride=(1, 1))\n",
       "  (conv_5): Conv2d(256, 512, kernel_size=(1, 1), stride=(1, 1))\n",
       "  (conv1_bn): BatchNorm2d(32, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "  (conv2_bn): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "  (conv3_bn): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "  (conv4_bn): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "  (conv5_bn): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "  (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n",
       "  (dropout): Dropout(p=0.2)\n",
       "  (dense_1): Linear(in_features=18432, out_features=1000, bias=True)\n",
       "  (dense_2): Linear(in_features=1000, out_features=1000, bias=True)\n",
       "  (dense_3): Linear(in_features=1000, out_features=136, bias=True)\n",
       ")"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "from models import Net\n",
    "\n",
    "net = Net()\n",
    "net.load_state_dict(torch.load('saved_models/keypoints_model_1.pt'))\n",
    "\n",
    "net.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.11123786  0.10643028  0.0055051  -0.20681031 -0.07370002]\n",
      " [ 0.03202429 -0.15141626 -0.21944816 -0.0748659  -0.03933848]\n",
      " [-0.18000433 -0.17345938 -0.25568163 -0.13837044 -0.11900678]\n",
      " [-0.09777482 -0.13340716  0.07318709 -0.19223122  0.12311244]\n",
      " [ 0.16333964 -0.05948487  0.02374522  0.07879235  0.0075032 ]]\n",
      "(5, 5)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f61e41c26d8>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPgAAAD8CAYAAABaQGkdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvpW3flQAACbRJREFUeJzt3U+IlYUexvHnuTpp2Y0KXYQj1xYRV4JbMUjgTgLtDwVtMqgWBW5uYBCEbYoWbaNNG+nfhcoIahHRRYT+SNC/qSzyToJEt9RwvERMUhnWcxczC+k6nvc47zvvnN/9fmBgjh5eH2S+855zZniPkwhATX/qewCA7hA4UBiBA4UROFAYgQOFEThQGIEDhRE4UBiBA4Ut7+KgK1asyKpVq7o4dOvWrl3b94ShnDhxou8JQzly5EjfExq75JJL+p7Q2MzMjH7++WcPul8nga9atUpbtmzp4tCte+yxx/qeMJR9+/b1PWEoDz/8cN8TGrvtttv6ntDY7t27G92Ph+hAYQQOFEbgQGEEDhRG4EBhBA4URuBAYQQOFEbgQGEEDhRG4EBhBA4URuBAYQQOFEbgQGEEDhTWKHDbW20ftH3I9s6uRwFox8DAbS+T9KSkGyRtkHSH7Q1dDwOwcE3O4BslHUryVZJfJb0k6dZuZwFoQ5PA10r69rTbh+f+DMAS1yTwM1258X/eVNz2dtuTtidPnjy58GUAFqxJ4IclrTvt9riko3+8U5JdSSaSTKxYsaKtfQAWoEngH0m6wvblts+TtE3Sa93OAtCGgddFT3LK9n2S9khaJumZJAc6XwZgwRq98UGSNyS90fEWAC3jN9mAwggcKIzAgcIIHCiMwIHCCBwojMCBwggcKIzAgcIIHCiMwIHCCBwojMCBwggcKIzAgcIIHCiMwIHCGl3RZViXXnqpbr/99i4O3bp77rmn7wlDmZqa6nvCULZt29b3hMZWr17d94TGli9vli5ncKAwAgcKI3CgMAIHCiNwoDACBwojcKAwAgcKI3CgMAIHCiNwoDACBwojcKAwAgcKI3CgMAIHCiNwoLCBgdt+xva07S8WYxCA9jQ5gz8naWvHOwB0YGDgSfZJ+n4RtgBoGc/BgcJaC9z2dtuTtidnZmbaOiyABWgt8CS7kkwkmbjooovaOiyABeAhOlBYkx+T7Zb0nqQrbR+2fW/3swC0YeDbIyS5YzGGAGgfD9GBwggcKIzAgcIIHCiMwIHCCBwojMCBwggcKIzAgcIIHCiMwIHCCBwojMCBwggcKIzAgcIIHChs4AUfzsXRo0f1yCOPdHHo1i1f3sl/QWemp6f7njCUgwcP9j2hsSNHjvQ9obGffvqp0f04gwOFEThQGIEDhRE4UBiBA4UROFAYgQOFEThQGIEDhRE4UBiBA4UROFAYgQOFEThQGIEDhRE4UBiBA4UNDNz2Ottv2Z6yfcD2jsUYBmDhmlyv6JSkB5J8YvvPkj62vTfJvzreBmCBBp7Bk3yX5JO5z3+UNCVpbdfDACzcUM/Bba+XdI2kD7oYA6BdjS8pavtCSa9Iuj/JzBn+fruk7ZI0NjbW2kAA567RGdz2mGbjfiHJq2e6T5JdSSaSTIzapYiBqpq8im5JT0uaSvJ495MAtKXJGXyTpLskbba9f+7jxo53AWjBwMfSSd6V5EXYAqBl/CYbUBiBA4UROFAYgQOFEThQGIEDhRE4UBiBA4UROFAYgQOFEThQGIEDhRE4UBiBA4UROFAYgQOFEThQWCdXR7zgggt07bXXdnHo1h07dqzvCUN5//33+54wlLvvvrvvCY298847fU9obMuWLY3uxxkcKIzAgcIIHCiMwIHCCBwojMCBwggcKIzAgcIIHCiMwIHCCBwojMCBwggcKIzAgcIIHCiMwIHCCBwobGDgtlfa/tD2Z7YP2H50MYYBWLgml2w6KWlzkhO2xyS9a/ufSUbr2kHA/6GBgSeJpBNzN8fmPtLlKADtaPQc3PYy2/slTUvam+SDbmcBaEOjwJP8luRqSeOSNtq+6o/3sb3d9qTtyV9++aXtnQDOwVCvoif5QdLbkrae4e92JZlIMrFy5cqW5gFYiCavoq+xffHc5+dLul7Sl10PA7BwTV5Fv0zSP2wv0+w3hJeTvN7tLABtaPIq+ueSrlmELQBaxm+yAYUROFAYgQOFEThQGIEDhRE4UBiBA4UROFAYgQOFEThQGIEDhRE4UBiBA4UROFAYgQOFEThQWJMrugxt/fr1evbZZ7s4dOt27tzZ94ShfPPNN31PGMqLL77Y94TG9uzZ0/eExmZmZhrdjzM4UBiBA4UROFAYgQOFEThQGIEDhRE4UBiBA4UROFAYgQOFEThQGIEDhRE4UBiBA4UROFAYgQOFEThQWOPAbS+z/ant17scBKA9w5zBd0ia6moIgPY1Ctz2uKSbJD3V7RwAbWp6Bn9C0oOSfu9wC4CWDQzc9s2SppN8POB+221P2p48fvx4awMBnLsmZ/BNkm6x/bWklyRttv38H++UZFeSiSQTa9asaXkmgHMxMPAkDyUZT7Je0jZJbya5s/NlABaMn4MDhQ31ziZJ3pb0didLALSOMzhQGIEDhRE4UBiBA4UROFAYgQOFEThQGIEDhRE4UBiBA4UROFAYgQOFEThQGIEDhRE4UBiBA4UROFCYk7R/UPu4pH+3fNjVkv7T8jG7NEp7R2mrNFp7u9r6lyQDr27aSeBdsD2ZZKLvHU2N0t5R2iqN1t6+t/IQHSiMwIHCRinwXX0PGNIo7R2lrdJo7e1168g8BwcwvFE6gwMY0kgEbnur7YO2D9ne2fees7H9jO1p21/0vWUQ2+tsv2V7yvYB2zv63jQf2yttf2j7s7mtj/a9qQnby2x/avv1Pv79JR+47WWSnpR0g6QNku6wvaHfVWf1nKStfY9o6JSkB5L8VdJ1kv6+hP9vT0ranORvkq6WtNX2dT1vamKHpKm+/vElH7ikjZIOJfkqya+afYfTW3veNK8k+yR93/eOJpJ8l+STuc9/1OwX4tp+V51ZZp2Yuzk297GkX0CyPS7pJklP9bVhFAJfK+nb024f1hL9IhxlttdLukbSB/0umd/cw939kqYl7U2yZLfOeULSg5J+72vAKATuM/zZkv7OPWpsXyjpFUn3J5npe898kvyW5GpJ45I22r6q703zsX2zpOkkH/e5YxQCPyxp3Wm3xyUd7WlLObbHNBv3C0le7XtPE0l+0Oy73C7l1zo2SbrF9teafVq52fbziz1iFAL/SNIVti+3fZ6kbZJe63lTCbYt6WlJU0ke73vP2dheY/viuc/Pl3S9pC/7XTW/JA8lGU+yXrNfs28muXOxdyz5wJOcknSfpD2afRHo5SQH+l01P9u7Jb0n6Urbh23f2/ems9gk6S7Nnl32z33c2PeoeVwm6S3bn2v2m/7eJL386GmU8JtsQGFL/gwO4NwROFAYgQOFEThQGIEDhRE4UBiBA4UROFDYfwEo4wntuZCR1gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61e4271518>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get the weights in the first conv layer, \"conv1\"\n",
    "# if necessary, change this to reflect the name of your first conv layer\n",
    "weights1 = net.conv_1.weight.data\n",
    "\n",
    "w = weights1.numpy()\n",
    "\n",
    "filter_index = 0\n",
    "\n",
    "print(w[filter_index][0])\n",
    "print(w[filter_index][0].shape)\n",
    "\n",
    "# display the filter weights\n",
    "plt.imshow(w[filter_index][0], cmap='gray')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature maps\n",
    "\n",
    "Each CNN has at least one convolutional layer that is composed of stacked filters (also known as convolutional kernels). As a CNN trains, it learns what weights to include in it's convolutional kernels and when these kernels are applied to some input image, they produce a set of **feature maps**. So, feature maps are just sets of filtered images; they are the images produced by applying a convolutional kernel to an input image. These maps show us the features that the different layers of the neural network learn to extract. For example, you might imagine a convolutional kernel that detects the vertical edges of a face or another one that detects the corners of eyes. You can see what kind of features each of these kernels detects by applying them to an image. One such example is shown below; from the way it brings out the lines in an the image, you might characterize this as an edge detection filter.\n",
    "\n",
    "<img src='images/feature_map_ex.png' width=50% height=50%/>\n",
    "\n",
    "\n",
    "Next, choose a test image and filter it with one of the convolutional kernels in your trained CNN; look at the filtered output to get an idea what that particular kernel detects.\n",
    "\n",
    "### TODO: Filter an image to see the effect of a convolutional kernel\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[-0.22897477,  0.02605487,  0.14255652, -0.12292922, -0.2000438 ],\n",
       "        [ 0.15222955, -0.16696355, -0.16444109,  0.16017896,  0.08106515],\n",
       "        [-0.1303602 ,  0.04918216, -0.17598966,  0.20360373, -0.0204873 ],\n",
       "        [ 0.07762628, -0.07734349,  0.04743836,  0.15432268,  0.20453088],\n",
       "        [-0.02872146,  0.13434139,  0.04217802, -0.01097109, -0.05942493]]], dtype=float32)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/workspace/data_load.py:39: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
      "  key_pts = self.key_pts_frame.iloc[idx, 1:].as_matrix()\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c6b944a8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import cv2\n",
    "##TODO: load in and display any image from the transformed test dataset\n",
    "img = test_dataset[42]\n",
    "img = img['image'].numpy().reshape(224,224)\n",
    "#plt.imshow(img, cmap='gray')\n",
    "## TODO: Using cv's filter2D function,\n",
    "img_filter_applied = cv2.filter2D(img, -1, w[1][0])\n",
    "## apply a specific set of filter weights (like the one displayed above) to the test image\n",
    "plt.subplot(121),plt.imshow(img, cmap='gray'), plt.title('Original')\n",
    "plt.subplot(122),plt.imshow(img_filter_applied, cmap='gray'), plt.title('Convolved')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 4: Choose one filter from your trained CNN and apply it to a test image; what purpose do you think it plays? What kind of feature do you think it detects?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer**: This filter detects sharp edges from left(dark) to right(bright) areas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Moving on!\n",
    "\n",
    "Now that you've defined and trained your model (and saved the best model), you are ready to move on to the last notebook, which combines a face detector with your saved model to create a facial keypoint detection system that can predict the keypoints on *any* face in an image!"
   ]
  }
 ],
 "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}