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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      "--2019-12-06 17:39:41--  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": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "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": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Net(\n",
      "  (conv1): Conv2d(1, 32, kernel_size=(5, 5), stride=(1, 1))\n",
      "  (conv2): Conv2d(32, 48, kernel_size=(5, 5), stride=(2, 2))\n",
      "  (pool2): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n",
      "  (conv3): Conv2d(48, 64, kernel_size=(5, 5), stride=(2, 2))\n",
      "  (pool3): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n",
      "  (bn3): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
      "  (linear1): Linear(in_features=9216, out_features=512, bias=True)\n",
      "  (linear2): Linear(in_features=512, out_features=256, bias=True)\n",
      "  (linear4): Linear(in_features=256, out_features=136, bias=True)\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "## 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",
    "def init_weights(m):\n",
    "    if type(m) == nn.Linear:\n",
    "        torch.nn.init.xavier_normal_(m.weight)\n",
    "    elif type(m)== nn.Conv2d:\n",
    "        torch.nn.init.xavier_uniform_(m.weight)\n",
    "\n",
    "net = Net()\n",
    "net.apply(init_weights)\n",
    "print(net)"
   ]
  },
  {
   "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",
    "                                     Normalize(),\n",
    "                                     RandomCrop(224),\n",
    "                                     ToTensor()])\n",
    "## edit 250, 224\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": [
    "\n",
    "# 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": "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 = 32\n",
    "\n",
    "train_loader = DataLoader(transformed_dataset, \n",
    "                          batch_size=batch_size,\n",
    "                          shuffle=True, \n",
    "                          num_workers=0)"
   ]
  },
  {
   "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": 33,
   "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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": 35,
   "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",
    "        key_pts = (key_pts - 100)/50.0\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",
    "        print(output_pts.shape)\n",
    "        output_pts = output_pts.view(output_pts.size()[0], 68, -1)\n",
    "        \n",
    "        # break after first image is tested\n",
    "        if i == 0:\n",
    "            return images, output_pts, key_pts"
   ]
  },
  {
   "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": 36,
   "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, 136])\n",
      "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": 37,
   "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')"
   ]
  },
  {
   "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": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c52af668>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c5a5d4a8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c588b128>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c58f7198>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6YFOchwFds0sURVzmMhERC9ECy9VlnMBhf2o/VxNXmXKnmBufw0k4qka11+thuzYb9gaZboanPvAUU/YUuXwOx3TAR2Eg13W5cOECYRRiFkwss7+oi/cuggG+6YMBrxx8hf/4o/+RglXAT/qsOqtgQKvcorvSJR2lR86RnpnW/yaWVa/The1y0uHP3HIYRURMpz4wmXzBHefPn2dmZoZUKsWBAwcU29ntdlVmWJKHUrvqez5Wy+LLpS+zFPZdy75oH1ftq0x709ieTUzMz3o/i+mYTI5N0sv0SDgJ1lprdDe7NOoNOp2OIs9s2+bu/3o3+St5WodbfPuj38ZP+gSdgEa9gWEavHzvy9Tytf7Ylg0M3yB2YoiBGMqtMsVEkVQyRT6RZ6o3xVpyjWwlS8JLYGdsVesrgF/nfSSROvz3IAio1WosLy/T7XZVxCgRn84i71R2haLoIAy2s71SfS/W4r777uO+++5jY2ODhYUFarUahUIB27YV1S4RkBBTYRBy3x/eR1SLWP7MMpERsWwu88jiI8RRTM7IkR3rk3iFQkFhok63w6PRoyxYCxRSBY69fIyEnaBQKPT5nK2I3JUcRmSQuZzhK8ZXuHToEtPeNO+++m7qQb2vJNc2bTx7bVEMMDB46PRDjIVjpEtp8vk8cRzz/sr7efJvnyRLFnd/H6RKCaTU4ooIoJWss4gAdEBl4yURqqcTbkkeZVS5nuwKKXMEuOuuu0ilUpw4cYIHHniAs2fPsry8rNLqsvskqgGwGhal5RJGZHB84TinDp1i2psm4SYwMMiX82TcDEE+YL29TtbI4vs+8/V5FmYWiM2YeqGOWTQpFAoUE0Vsy8YqWzTmGhQXi6weX+WyeZmYmHVnnZmjMxTWC0y4E2wmN5WyTPQmqKQqzAQz3Fa6jTAIFX8URRFOwqFklwiCQJ1vymQyFItFVdWnh8ASzQEqqaiz0WI9ZD51l3Uz+AR2iaKIORd+Q+L+SqWC7/scPnyYmZkZTp48ie/7HD16lImJCebm5igUCiwvL7O+sU7baDOdnKbRaKjqMfJQP1CnuFTkc098jm/+9DeJWhFmziSOYh5+7GEKywU+/fc/zav7XiW9lSYMQtwZFwIgARjw3APPERgBc8zxSOMRCoUCZ/7+GcpmmagQcbh2mMvBZaa8KVrVFqViiV/wfoE/iv6IVXOV2WiWD8cfptPp4AQORt5QgBe2c0mTk5NUKhUajQbr6+uMj48zOzsL9LkkOcIhFMLExISi6fWssLjeTqejzin5vq8U8JYk3PREmOwS4T3q9TorKyuUy2VM0+Tll19meXmZubk57r333j4TWSzwtfTXWE+tMxvM8gE+oMCuaZq8/PdexmyaNMwGmSBDx+j0mU8/T2mpRC1T49z0OWIzpjPW6VsAg76S0P/Zpw9Al+IlAqcfMZi2iZtySdkpPlX4FItbizS3mnSCDkmnn5D8SPgRgmRAwSpgZSziZkwQBThJR1XVS1oiDEOy2Sye77HR2aBaq2KafUs2OTlJJpNRlW16nW2lUgEG3Uk6naZcLqv8UCKRoFqtjgTCO1qj72WB/65ESgRardZAfkKyw1tbW3S7Xd72trdx5coVMpkMGxsbnD17lrvuuoswFbJurvdDW2uZIBkMZIXDKCTMhVieRc/tqUhpsbXIQmGBucYcb1l/C2f3nWUqmmLVWlX3ti/Yx7q9ToIEXuxxMDzIRHpCJRqlHMI0TMaSY9RTdcJGqMJQ3/MxAxPXcVUpg5wkAFRtjVyv5/Z48Z4XqRfqpDfS3PbMbVSrVUqlEolEgvHx8QGFkFyWAP4wDBXNL2eHAMVQj0qU7kR2haI0Gg2azSawXS6gk2WdTodOp0MYhnz/938/juNw5MgRdWovmUoyE8ywYq8w7U0TNSPcjKuSiMKrZLNZyuWyOjKRzWaZ/8Q8lbjCL479Im7CpWSX+EL1C1wKLnHQOMinE5/mKleJ2hEnvn6CA2cP0DrU4tsf+TaRHanQ3Ek6/F7we1wuXWY6M837Nt9HLpujWCwSBIGKPsbGxtS4xYpEUaTu6dLaJeoP1MGE7mSXqlulXqurU4/CBenlE6IAiUSCVqvFpUuXXjfH8j7JHt+s7ApFgW1uQAYiLKw+qEajwZve9CYajQZBEJDNZrl69SrZIMtPdH6CNm2iZoRv+QROoHgFvXbDNE1F5smhso32BsHVfh5kI97go8WPYmUt7vvSfWQuZjh44CCXPnqJubNzGJFB/kqeVC9F6GyXQ3SMDpejy0RGxKqzSitqkXATFItFJiYm1M6XMQKq7ldCW8uysD2b1HqK3lSP5HoSs7d9shFQTPSo+ZPSyFGljnqZ5Hcju0JR9CMNsqDDSmJZFouLixw/fpxqtaqA2blz54jjmO/7vu9jtjjL6uqqSqdLOKmDPTmcrte0DhddO46DVbHIXMxgRiblpTLd/V282z2c8w6twy38rI9lbBdXpYIUR+wjXAouMRPNUHJKRFHE1tYWtmmT6qUIUgFBGKizQcMhbxiGBH7AzBMz+Am/ryTXQibJWencyShmVqfz5V+9yEr/+y3HzArNDNsljFJmIGLbtkqOSWeDdDrN7bffzre+9S3q9TpHjx4lnU7z3HPPKRMtOEesSKfVwWk7dHIdTMtUB8wEt8h3BdmAzpEO2UtZ3NtcwkLI+i+t013tUo2rGK6hUgQCLj9V+BQ1r0bQDFgwF3BCB2I4/nvHKS4Vacw1OPm/nRwAr2ItXNclCAPCVAgtsHrWwPkhfVGlfFIvodAZbV2BdBeu1/vCYKj9RrJrFEWk2+3SbDYHzsvI4e5iscjq6ioHDhzAdV3FsbzlLW+hVCphWRYJJ4GX8DDd7bM4khcJ/IB7v3ovhYUCrSMtXvuHr/XDaMPCbtoYeYOY/sQ7SYf1X1on2UviZ33iqO8eqlSp1WuqBka3egkrQb6Z57eM32JxYpFpb5qfXftZiktFzMiksFjAbtp0E92BwiiAmJhvHvgmm7dtktpIsf/P9lMul7Ftm3q9rngS6Zigs9CwXRsrLkzcrpwfktYZUjMj3NNOZVcoyvCBrVEiO2VxcZFisajcCMBtt93Wn9BGnS92vsjFoxcZb4/zrqvvUj7dNE2SQZL8Qh4jMsheyhJXY5pBk7f+7lvJXc7ROtziwj+8QMpLERSuVYKlIuKgvwi9To/uSpeaW6M8Vh5wBaEfcscX76C33mPpM0tEZh+r1LN1arM1lUDsJDtEwXbEocCs7VLJVMCA3mSPKB0xNjam3KQUZRcKBcrlsvpeSXtI4Xen0xlQQgG8Y2Nj6nVJRdxyUc/6+vpARfrw4aQgCNQxS6ncOnHiBLZts2/fPjY2NvpdllrrXIovERsxlWyFqldlPDmujnEEVkB1pkp5pUz9QJ2G1cDZdPqlAteU583/5s3kl/N03txh6TNLKsyNw5gDXzjAsSvHqO6rcuGTF4jNWN2r1bDIzGfIkOHYwjFOHTrFZG+S5nqTJ977BGPmGOaYiREZAzS6Sni6NmPtMSqZCqmNFEW7SC6XU0dna7WasrZS2CWlkvv376dQKFCv11leXqbVaqmD+ALmhU9pt9vq8NktR7jBtlWRnTEMZsXUm6bJ8vIyMzMzHDp0SO2UXq+HYRgcSB5gkUUme5MUrILy71EU4YYuf/VTf0WJEn7W72d8c6ZibtsH2uSWruVv5jP4mz5hLsRu28RBTOFKAROTsdUx3vrFt/L833sey7ao1+uYtWvHI4xYAVDXdbkwf4E77r0DK2GR6qVUyC7/K/dq2bzj8jt4YeEFzC2T3FRO1ePIkdper6cKtaRMQMCq4B79FKIULaVSqYHGOsL/iDvaiewKRZEmOWIq9co0/cCSgLdOp8PCwgJzc3Oqm8Dk5CS1Wo1HGo9Q9aqEjZDACOhaXazYUkch/MCnlqhhuf1d5nouL/78i2S8DH7K58FffxDDNQjtkFpQ465/cxe5KzlCO+xXudFXhNxyjleefoXl1jIZP0Mv2ePOwp3kwhyn5k4RG/0c0YWHLnCycJKZYIYPr36YXrGHYW5HHsIZWbbFUwefonqsSqaS4fDZw9TrdXq9Hul0mlKppCI9ER3g6sdigYEEoC4S7TiOM4AN30h2haJI+wfTNNXkwHb4p7si8b+SB9rY2KDZbHLnnXcyMTFBGIasXu3XdfzF3F+wkd5gojvBe1bfA2g1sddcXBAEkIJOsoNdtzHdfkhqeRZ3f/FuspUsZmRieIZSlMiIuJK/wosXX+Sfrv5Tpp1pVtwVPnfoc2SjLOn1NJ3pDoVOgUah0a+HtVZ58GsPQhH+9mf+duCkIdDPNudqYEJnvIOVt+hUO6poWo6giOhRoj4/etSj4xQBuXINaQ2yU9kViuK6rnItN6KW9VK/Xq9Hp9NhenqabDbL4uKiqmorFAp0rS4b6Q1iI2YzvUndr5P1swPZWmBgwbykR32mTmml1LcaGzkCJwAffMsnESRoHGxw9eNX6bgdfr7583yp+SVOzZ0i5aXopPqm/sSVE3zu85/jn3/0n1PP1iGGYwvHGG+NE7djzIZJlNjumhBFEWbXJF/L0yg1KDaKpKIUG/UNbNtWbbRyuZzqcqADVZ1Y063MG4HVW64epVar0ev1BuL9UaIfpbRtm4WFBWzb5sCBAwCKE8nn8/R6PcYqY2zltpjqTZGKUoRxSL1eZ2xsbCB0lmubpslzP/ccD/77BymsFpRl+ca7vsHWzBZ37L+DKB9x7PeOkb2UZfnoMqd/5jSRFfWV5BqkOjN3hnamzWvTr/X/FsMnnv5EH2Tvr9BL9TBjcyDyMTC47ZnbCJyAA2MHyOayTE5OKiZZ0g9bW1sDHRWGj6LIRtILmYaJNQHRt1zUI4ul9yIZNQidVZTPrKysEIYhc3NzyryKf7735XvJTGQoOSVIbtdoCAGnU/vqlL8Fz/78szzwhw9QvFokSAS854n3sDWzxfz/Pk+ylyR7MYsRG8ycn+H44vHXWZTji8c5tHFIJRqnvWleeOcLnOmewct4mLE5ACpl0WzLppAsYJl9gCyYTAq4ksmk6qgA2wt+PUpf5kufy4FzSzdxUH1XKIrcsOye4e5LIgJqpXJLJnh5eVkdfJLkWq/XY2N9g4logsxkRiUGpXJOfL9+Jll2nu3YPPtzz+IsOfzIV38EA4Px5XEuNy7jZl1CJ8RyLSIn4le++SuEtRAm4bEPPUYpWeLA/gN8+//4Nu+N38sPNn6QuBWDCa1ECyuyCKNQuUlZbInaJCqSYxqyKSRUTqfTqqZk+Ow0bIPVUcqjK4Z+1GUnsisURRrpGYahjoi2Wq3rModS7idHOiqVCo8//jjj4+Nks1larZbiXISWHx8fV81mhJUUfALbjWoEI7mui+/4A9/b7XQ58YcnsFxLuaXiSpH2oTaf+fhnuBhc5LB1mH+U+UdUW/3Iy/M8Ulaq3/Y0alJKlHASjlpgqcyDPhvsOz6NSoN6vU673VYLXiqVyGQyjI2NEcexAvPDNbQyluFOB3riUYC8VM3tRHaFomQyGWUpZLFGmUW96CadTquJkALr8+fPK6QvtaZ+4FP1q2R621ZFJlQ/OTf8PZZlEeZDAifA9myCZEDP7VFY6WOX0AipZfrHQ3sbPeb9eWIj5mJwkd+o/AYbiQ2stEWYCym3y8SZmFq+xkRngvdvvn+gZAAg4SR4+Y6XqRfqFGoFJr4+MTBmaclRLBZVe9J2u61ae8k49MP+sF0IJm5WIp/haOmNZFcoyubmphqMuA3BDTDYxE5P9q2trQ2gfmktHkX9xjSFYoHFhxfpTHS41LrEwwsPq47SOiuq/xuGIVEYke6l+2Y/2LYerutS2V+hfLXMP/n5f8LpudMcXzzOp/+fT2MGZp9r8Q02EhtgQGiFYEA1W+0P1IDNzCYtWqTibRfr+z7NqEk9X+/zL8U6E9kJzOZ2j5N2u83GxgZTU1MkEgnF2EqdiVgfab4s/JLeIFBAsG33D5jdcrme1dV+RZm4HsELw7kfAXaAOpU3DNgExJmmSaVXoTPRARNquRqNoIHVG2z1LWUGIgYGD/3JQ5RXytRmatRmapSXyhixwT3/7R6+cOcXSJQSnJ47TWiFnJ47zS/nf5nQ7CtFbL1xyPmXU3/JhxpZzLg6AAAaCklEQVQfUpYzmUwSV2LSm2k6Ex1SGymCekAcbXdSaDab6jwxbBciyeZaX18f4J30PFCn02F+fv51lvSWC4+HTf/wuRO94k33x0Lz6wmyASDXhuRaEnfaJbOVIW7HeGyfHtRDY7lmqpeivFLGjExKyyWe/eCzPPifHiQ0Qv7VB/4VZ2bP4Kw4HFs8xpm5MxxfPM4/Xv/HfHr907jTLoVmAcd2qGQqpN00vWSPYquInbTZcPqWZjO1SdALcHxH4Qbf8zn0l4eI0zF+3QcLvHD70JZsEkly6vU7upsZDgSE5R5uJDRq3m8ku0JRpHWDuJHhLkN6zYW0HhdrI/Ur+rli1aMtisn8cYYjR45QTBTxkz71oK4sF2yfA5ISTC/tUZ+uU7pawogNHvxPDxIZEZ/6hU/x6tyr/ULrAz6f/PefZGx9jLF2v7Tx0ccfZcvdYio9RS/sUe/V2Vfdx+rYKjkrx5M/8SR/Mv4nVJwK+7x9pOM0rukqt1Kv1/sgNzTIlXJqjOKK5TD6cDgsOSC9S8MwfT/MT91s5hh2iaJI3YUoiuu6qtpcRNLtksiSgbquS7fbVd2vdUvk+37fldz3EK+88oo6UprsJVXrDL3Dte/5/Oh/+1GKq0UAldyrZWqcmz2nyLN90T5eef8r3Pv/3kvpYonqvir/4uF/oTBLTMyZuTOkvBRdp8vxxeNsljbZcraY9CZ53+b7iJxtBrpWr1EP6hQokLATA73kkslkv+DqWoJPwLh8Vs8Ci3Ud3mDymh7h3ZLneoSmltBV/K7UgKZSKdV/VTezekcDQPWmlY5Ikob/gR/4AV44+QLn7jtHLVejUC/wwJkHVJci6C9Axsv03U5sEl/7DyDrZrlz8U5OzZ3i6OZRPlj+II8WH+W3f+63mQvm+ID/AU6nThOafcwSExNZEe1UGww4ffA0kRH13Y6ziWu5OJGjqtqev/N5Wg+1SG2kmH1iFtvaPq4iiyvtQsMwJJ1Ok0qlVGeler1Oq9VSj4LRTw+KUnQ6HfXYGfn7Ta3R977M37tUq1UmJibUCb9qtaoo/VwuN/B4FL36TSq1FCC8toOk/gT6CjA7O9sPT3M1YjOmUWxQ82sEWwET1gS9fI9kKglpqOyrML46Tm2mxgsPvUDbbuM4Dp///c/TyDQodoosHFlg8aOLREbEgr3Anf/hTo49dIzTc6c5tngML+FxfuY8dmTjmz7lXhkDg0q6wpQ71T98bl07QuEEtMotMPsFS3W/TqqXUqceddzleZ7qky9uuFwuq9bvci5odnYW3/dVEXoURWSzWVVrrAP/ncquUBT9vIluCeTUoCiEcAedTkc1kZH36m255JC6mOBOp8PhycPM1+dpFPtJN7tr87EzH+Nw6zBrk2s8+f4nCcyAJ9/3JBOtCe757/fw8H94mMpMhb/50N9Qn60zttTHI4cuHuL44nFOz51mqjXFmy6+CR7qj+Vq/iqe3Qec+VaewAyo5CpM9aZ45MojFK0itrN9xKJb6WKtWIT7Q6yrFm7VhWu9BvUaV3HN8rvMQbVaVeeh5aEOulJVKhUFZKVVl8gtB2Z1JZHDTOKH5Tl4w73dxDcLLyK7TxD+QC1rIsHbH3o7lf9SITOZIW71+ZJDzUOYmExvTGPW+5HWDz/9w0ytTWFc+2/86jiFuMCLH3iRH/nij2DGfUv1+T/4POcPnOfptz5NPVPnzNwZIiuiUq4QGzEYUM/VlcvZSG2QsBLYlq1CXkkzpE+mFbGnH9AfiMauFYeLuxUGOY77D1mQRKfgOylQlyOo+vkfuEVPCkqOplKpqDyMgFQ5ja8fERXQJg9u0k/vD/eADYKACxcu8Mgjj3D27FlWV1dJl9JUoyqLxUVmG7Oc2XeGt//l25mpzCgFkbqT6ky1n+01TbZmthi7OkZlX4W/fdff0rJb7PP2EZUiZWGOLx7Hd3zOT59XwPbUoVPs8/cxmZ0kjvpRXbVW5fzyeZaWlwiDECuyiIkJ4kCdvZY0g2EY1Gq1gdN/kqsR6yGlkolEQlHz6XSabDar2nTJHMEtqiiyu2zbVkoi1kMAnY7kZfIExOqnC4eJtziOWV1dpdls8pM/+ZP81m/9FuVymXQmzVce+AovHHuBaqnKiYUT/OYf/CbEEBkRm9ObPPfjz2GOm9hWf5pe+cVXsFs23WSXRJTgXV99F+WVMq2DLf7B2D9g/2/uZ6w1RmiELB9d5sD8ASr7KzzxoSfImTkMyyAkxPM9nph9gubxJsbdBsYfGP3mf9ewiFADgrMUY3wtqpNWonrLctlM4n5l84irkvpZ3arcjOwKRXFdV7mdbrerzsnqbb1FxLVIKK33h5f/h2syVldXWVpa4v777+eee+7h0qVLZDIZ2rSplqrEZsypuVNsZbfwUh5Pvf0pwkJ/0nPk1GIknASMQYYMVsNSxFxuIYeX9khMJog7Me2Dba787BUWGgs07SZpN00Ub4ezK/UVmrNNMPt9U8ycSdSKBsJcnVfSeSNpGiSJUVEgGasUgInIXOldML+bU4O7QlEEgIlf1bsxi1WIov4jUSRMFgXRywOvl+A7f/48URQxPz/PZz/7WT72sY9hWRYTmQlKrRK1XI18M8+X7/4ybsol2UuSaWTojHfoWl2KdpFsJqtS+6ZpEhdjmgeb5BfytA62iMKIFz/2IkbToJvsgg9xKsbreiqDHRNzaf0Sr37nVYyC0W+uswS0t/kRcaV6rYx+iGu4F668rs+VRDZyv3JdUT5pyaqfUnwj2RWKIgssyiGKIRZDuI58Pj+Q+BP/rJtpncYGMDFpLjQplUosLy9z++2384lPfIIvfvGLNBtNvn/r++kYHWzXppPo4DQcPnT+Q8w2Zvnkxz/J+YnzTLvTfLj34YFwFeD0x09j1k3e+sdv5b7fuI/mwSbf/si3CYNtGj0M+88e8gOfP9v/Z2xMbWCWTOL/O8YqWETNCDthD2AHvaBcxqSnJqQ8Qk9BDNcX60lVOQUp539g+ylpO5VdoSjS4kL30cJMymNoZRfoRcWwDc4kVB7ICUXwz+r/jDuCOwg/GZL71RwvPP8CP3j8Byl9tsSXvvQllpeXyUQZsOFnnv8Z5upzmJhUs1Uu7L+g2pAvXl3kIAfV84fFwjmGQ34xjxmZ5BfyuGsuXna7paksVqVXYTO1CSZEsxFWwcJo97GJLLruOqQeVtyQWEq9UFoPl/XHvul4Rn/olLwmrueWUxR9gYUzkJBXfz7vjeo8h/17HMcUKPCW4C1YWPgnfUqU6P2fPZ575Tnyb8vz7578d/zLX/uXvPTSSyQ7SeYac1j0o49Cp8Cbr76Z12ZeI1/Ls/LaCu1Cu/8A7FSSMBVSsAqkk2m29vejofXJdZbby8SdGC/hkYkz+F7/eYcbmxuYBZNwJoQliFvx65RAH5+MQf6VzSTv05VI2GsB93o+SDafbqXk3M8td/ZYnxwdzestQUeZVF3Ed+tngRpxg/OJ87zFfwvRWyJKqRLdV7oQQvNvmtQu1/jMZz7DV7/6VZ76i6dYLi0zW5vlavkqj933GEcWjzC93O+34gc+tVqNaq3Kq//LqzRLTUqtEm+/+HYu3n+RdC9NJ9kh7sQ8c9szbOW2KNQKHP3WUY4cPsLVq1ex/qhfPml2r1k8a7ATpj4Xw4XTMPi8QnFrokiC2a5XcC2YR+b5ZsX4bkKlv2s5ePBgLIOSwYs/HVWRpovcv0Q8wqPI9WzTpmyW+eDHP8gvfvwXWflfVwheDEjen2T/1/ZTLBZVjulff+Ff8+rfvEqQD/pZYg3stdttGo0GnuPxwg+/ACYQwdE/PdpvZ36tkKhjdDj7vrNgghEbfNL7JM888Qwvv/zyAP6S8Y2K1PRHxejnm+W9w1HgsOLoczNc1SfXF8t96dKlHWnNrrAoOnLXWdVhcLtTnyoTF8cxERF1s8658/0+Kvn/K4/TcbAnbdV2tF6vMzU1xWc/91mefPJJvvzlLysGVPJPxWKx/xzDRr9UsVFq9Gtdqi4eHo1GgyNHjnDX7XfRDJtcNa4yE82Q8BMsLi6qTaCXJuquR5RlVNQ2TLvrm1sH/mI9rjfH+muidDuVXaEouuilAhJljDp2MCx61DDM4hqGwcLCQn/hiTHGtk20lAV2u10cx+Gd73wnnufxzDPPsLq6qo66Qr9uJpPJ8AOv/QBb7hZ+zccv+GQyGQ4fPszc3Bye5/FI8xF8xydv5tmqbqmnn+u7W8cgejW9LPowdhn1sz72UZ5B/4x+zRsp1PVkVyjKsLnUf9YXfqeD098nC7GyssKZM2e48847X1eLKztd+sS9973v5cd//MdZXFzk13/91/E8j3w+T7PZpNFoEIVRv09twuD2226nVCqRTCbVERAAJ+430XnppZcGOj6JRYHB8k1d0fVSzWGmediijOJadNGttT7mm2Vob6565X+QyASapqmegiHhpRQE64BOFz3a0XeOIHxhfF3X5bnnniObzQ5U+g8vgDy30PM8zpw5o5ogv/TSS7z00ku88sorrKysEMcxc3NzTE5Okk6nBwCjbfdbk3e7XTY3N9VrEsnB9sLrrna48EgH8DeK+GRuhKLXx6WDWLnG9c5N3Uh2jUXRd4Qwrno0NGpQ+o4YjoR01yOY5cKFCwMHp/QoQTCEbdtUq1W+/vWv89prrzExMcHRo0eZ2TdDd7XLfGWe+YvzHDp0iAMHDgzwF+JWMpkMcRzz6quvsrGxMXBUQscj+vjlnoet5jB2kfc4jjOA3fRzSTopeD25JSvcYPApoTpGkR0g9L7sSJlwPdchIr/roWIymeTs2bOsr69TLBYHjrFKVFEsFtna2uKP//iPefOb38zhw4e5cOECrUaLu77cb39x/+z9fPsj38b1XAqFAidOnGBpaUmdsRG+47XXXuPll19Wf9Ob9I3CCvq4RYbpef190ldWlEWqAXWWVn//sNySGAVQoHLYxOq8iE4yiUuRidFdko5tRFnkIY2Li4tks1kVIoZhqFxCo9Hg0UcfpdFocPToUer1fiF2yk2Rv9Jv6VVaLpHxMrj0yyLe8Y538O53v5v5+Xnm5+dpt9uk02nOnDkz8NT2YZwwCkfJz7or0cekcyWSHNU3hbw2Cn/oYfZ3Q4nsCowiIgOWbKcuepW9XoIgrw2/V8csIr7vc+XKlYHqN8PoFwrlcjl+//d/n8cff1xZNmXWCxHtI+1+GeVcg2pcpdlsUq/X+e3f/m2efvppTpw4wQ/90A/xzne+kx/7sR+j0+mojkn6d+lj1f82KjQWqylKIa5NP2qik2ujwmw9BP//RXgs1kJ2g4BZ8b06X/BGoifDYBDsfec73+Gnfuqn1PvS6f5jUJ5++mm+8Y1vMDY2pmpi5AFJqVSKzV/e5NzFczTMBr3NHs1mE8/zqFQq/NIv/RJ/+qd/yq/92q+Rz+d5/vnneemll5QV0EV3J7qy6F0V9EWVKnyxFFJULtZETgTqllg9MILXK4ruwm5GdoVF0bOjOsLXiaRhLgAYuVPh9Yuh77TV1dWBRbJtm9dee41vfetb/PRP/zT33HOPerTLwPWMmCDfP38sihQEAffffz+/8iu/wvHjx3nqqafwPI+TJ08qazTKUujXlfsftoo6DtGZV7mm9NWXWh6ZL5nLUfM06rt3vEY39e7/QaL3ChkWPWLQwanur3U3I+5rOJqRyZICbXm92WyyurrKgw8+yLFjxxgfH8d1XXK5nKq4k+LuXq/H1tYW7XZbWcB7772X2dlZHn74YUzT5M///M95/PHHB/qviOiLowNafewyHkneyTELeXCVZIrlNbmmTtTp86BjnuFNeMv1R9HNpu43BafoZnR4cDpYFLkRol9bW6Pb7ZJOpxkbG+O5555jYmKCI0eOsLm5SafT4ZlnnhmozRUlkVYT1WqV+++/n7vvvpujR4/ieR7VapUHH3yQ3/md3+Hy5cvqPnSlHZUZ1u95FJEmXJC8LiBejtTKZ4V/Gv7e4TkeVpqdyq5QFJ38GgVM9Z9HoXzBNiI3UpRGo8HGxgazs7MsLy+TTqfJ5XJUq1WSyaRqSSoRQiqVotvtql63zWaTTCbDe97zHiYnJweeR9xoNHj22WdVLQlsRyuj8NUo8Kr/PGwR9Z/13JdOWOpzpeMR+ez1gP4bya5wPQJYR5FmwzWy4obkc8KxCIC7HsrXpdfrsbS0xPnz53nTm940gAGiKFKn7YSXEMC4ublJJpPhIx/5COVyWR0AD8OQ6elpHnvsMRYXFxWNP4yV9MUbdpsyHvlXdyWjRLcQw9TB9UJv3bLdsjzKKO3Wd5G853q7QK+O0038sIhvX11dHXhIgijg6uoquVxOYYMrV64QhiEbGxuYpskDDzzAbbfdRqvVUhXviUSCI0eO8Nd//dcAigAbZSGuFyJfLzIZBvA6DhEl0OtUhgm7Ud+vf3ansisURa/c0oGnXuqn7zKRYY5ERPfv8rtIIpGg3W6TyWQoFAqqJsQ0+w/dfvbZZ6lUKnz9618nivr96KXx8dTUFHfffbcCmrlcTj2DudPp8Nprr6nvU+WY10QHr/rf5P3D+GFYyYbFMIwBBdexzPDc6FZsWFl2KrtCUcT1wGDTOv0AlA4GdVOtF/Xor8k1hi2QvDeXy6nCbOFr5ufnqVQq6ukV8liX06dP8/zzz/PAAw+oXq+tVksd5bQsi8cff1zdj86F3MjMD7Ox+hiG24YNR3Kw3bpclExOWQ5brevRBzcju0JRdKA1zBaOwi0iursZqLzXFmDYxNq2rRZZQl/pCDA/P08QBJRKJaampiiXy7zyyivKTUmvOVFi13VJJpO4rss3v/nNgZ2tu43h+x61s4ddi1gLHVPoWAoYOAGoz8+wxdAVTmdkb7moZxjwiYzaCcP1GTebBZUnsicSCZUcbLVarK2tUa/XmZmZYWxsjFwup+pPpGo9nU4r5ZAFs22bM2fOcO7cudeFwTe7a/Xx6sVNYjUlNyWiu5tROSXZfEL9yzXE+txyiiImethMj2Ir9YkY3rU7kTAMabVaGIZBsVhkfn5eNeLpdrsqerBtW/WJ832fbDarlEWeQHbs2DFs2+axxx5jeXlZZbZ1C6ADVrnn683BsAsaBU51C6T/fKMNM5zXuVkFhl2iKPD6SYHRA9LxyY0UZHihRLrdLmEYMjHRb89ZrVYxDIOLFy9Sr9fV+SA5+qA/KWttbU2F64ZhkMlkWFpa4vnnnyeZTCpqfRQQ3eniCMk33J5Mp+ihH71JclDHRNfjYvR7+G4wyq7gUXRULhNyvTwPDJYF3ogvGWVthIMZGxuj0WiQTCZZX19naWmJYrHI2NgYyWRSuRcJp6MoUk84l96utm1z9uxZrly5MjIbO7xANyPD+Rp9HkaVUOq8iv4+VWQ+FDXekoTbMEYZTmzpEcTwQG80YH1SRaIoUjzIwsIClUqFc+fOEYYhs7OzWJZFrVYjiiKq1apiXqHfkOfChQvEcUy5XKZUKvGVr3xloMpsWNF3mvEellH0u2ASidb0iGjYbYnIe6RM8pbuZnCzkzmKoLpRWDxsVQ4dOsTm5iaO47CysoLrupTLZfWswsnJSfUELal/lRS/PJS7XC6TTCY5d+7cwHcMf/fNYij9c/Lv9XCZ/p3D36ErjuSHdHc8ijq4kewKi6KbTHh9NdjwxI8y8fpk6Wn34esYhsHhw4eB/k5stVrk83lyuZxiOKMoUr3i9OKjRCLB5uYm586dU65LquBGkWvD0ciwSHird1DSXZgeEuuU/nCBtvBQgm/0OdULyXWqf9RhuhvJrlEUPfU9ylroCz7Kd1/PKglHI6/3ej0KhQLFYpGXXnoJgGKxSLFYVJOu8yF6F0aZ6FOnTlEqlXj++edHAvBhnCDXGXZHujKNcqWmaarnBA67NN0dy3tlfmROxU1Jp81R97dT2RWuRxe94GeUjOJW5O/XM/MSIQknIb3N6vU6qVSKXC5HNptVfEMymVSPPZHssSxmIpFgfX2d8fFxnn76acVP6CTbqPuTn68XEQ3f97BSXW9xdVyn/00aEQ3Xuch33cwBddglijJMOcvC6j5YXht+/yjFGXZXw+Z/bW2NU6dOqYbE+XyeRCKhHmsimWxhPQ3DUI+HNQxDtSz92te+pna1XgSuu9Ab4Qf992EeJI5jFW3piq4rhfyuF4qLFdFdy/AmknHecknBv2sZtUN1Bbx69SrNZpN0Oj3ARejnbvSujLqvl6jh1KlTrKysMD4+fsOdP0qphzGZfMfw/cp79f4mNxofbJ/X1kUURRREMMot7XrEjOt1J9+t6JMpi2NZFuvr66r3ipzgk5BTfxqoPMZEN99CuP3VX/2VKjOQ+x7+bn3x5G86WB3GF3Id+ZwsrH59nUYYJuTEmugKrr8uY7qRm76e7ApFGb7hG2EUGO2C3kjEmsjTyKenpzGMfjJRnt8nlW1iYSR7rfe9lecRfvWrX1XPvNEZWV1BdDAryqArrIxVrykRkX74uvuS6w7XEcPgcdJRY9fd13cju05RZHJGWZNRirEThZIJFWuwf/9+9dQwQDGxyWRyoPZUb85jGIZ6ll8qlVJ0vg4Y5TM6OahbEL2kURZfr8qT7x0+b62PVT6jbyb9MNyouRmOHGVuh89O3Uh2haLoMozg/y6vC/1nC0qJgTxhI4qiAbAqu1UUR3eF4g663e5Iel23HMNMsoi4O3h9MjCKIvVgzVHE2nC5p7xv+CjpsOgKKt99M659V3Rc2pPdL7uCcNuT3S97irInO5I9RdmTHcmeouzJjmRPUfZkR7KnKHuyI9lTlD3Zkewpyp7sSPYUZU92JHuKsic7kj1F2ZMdyZ6i7MmOZE9R9mRHsqcoe7Ij2VOUPdmR7CnKnuxI9hRlT3Yke4qyJzuSPUXZkx3JnqLsyY5kT1H2ZEeypyh7siPZU5Q92ZH8f7Nu06j+YyKxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c53d1198>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c52dcf28>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c5824f28>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c549f588>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c53753c8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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BRQD2uHv4zOBnVPTWH/Dz0f/no5yvnlfvHPVFaTpN7h68mz88/IdkMhlSqRR33nknq6urCuB3Oh2q1aoC6TJmcQ6KFBWvrSRfDQwMqCCj4BeZN9d1iUQiPZl8N6NtoXrENG40GoRCIXK5HMPDw+RyObLZrAKJ/bEJMTnF4WbbNtVqlWq1SqPR4NixYxw4cECBW9u2KRaLfO9732N+fl4FCfsBrkymmKPyr57H6nkegVCAr+/9Ot8a/laXSQzAgBveDf5o7o/oOB0SiQQ1r8ZL1Zd6xl7r1HA8h+fzz/Pgsw/yV85fMbq3619JJBI9CVSAcvAJbpL3F1wiVo4wjI61JNNNJJy8c39k/KfRtpAojUaDK1euUCqVSKVSxGIxBV4nJyd54okniMfjajEl6NXpdJiZmSEWixGJRFSuaDQaJZVKqdhGvV6nUqkoP8WpU6fI5/P88i//MpOTk9i2rZxlgJr8+fl5peP7k4r8fj+VQIW22e4yCIAkwhtwzb7GSn2F3bt2kwvmmAhPcKFxQX1H2AzTdJt4eDiewxX7ClbcYnZ2Vvk6lpaWlP9IVxN65DsajdJsNpVLvt1uK2tM1E5/8pM43m67WI/f76dQKLC4uKiCfpJ9n8vllOqRa2US5ufnOX/+POPj4wBqB0rG2OXLl5mbm8O2bZrNJvF4nF27djE/P8+lS5dUMHH//v0KYAoonJ6e7skvFQ8xrANBq2ThH/HTNtuYmLxp4U1cyFyg5C+RM3K0S23yjTx7BvbwxxN/zPfPfZ/I30b45hu+ycu5lxkLjZEIJ3hp7SWOJY+RbqW5cuOK2gS6uS5SUY9XhUIhMpkM0WiUdDpNPB6n1WqxsrLSA1b7g6CC+W47iZLNZlVKo7yI4BWxanR9qpdInDlzhsXFRUZHR4nFYirRqdVqMT09rTLgJL82Go0SDodZXl7mlVde4cc//jGDg4Mq/rK4uMjMzAyr+VWsNYtmotnjb5AY1NraGotLi7wv9j5CmRB/E/kbnt31bPciA25wg48tf4zWcou703fTbrc575yH96OuuWZfYzI4yffe+z2CdpAfP/tj1pw1Am5AgWlRg/KzHgwUM1rwhkhiMcVhXWXpjjn9GVulbcEox48fp1qt9tTwCKAbGxtj165dPU4nQew+n4+1tTWWlpYIh8McOnRIOeny+TzlcrknEVtiJ3fffTezs7N0Oh1u3LjBl770JVKplMpnDQaCvP/p95NdzrKcXeapX31KOdkEDxVLRV64+wVODZ1iyBja8E4eHk26wbwzhTMYop8M1lUUcLFykXAoTDQU5b+Z/42ze84ybA/zL6v/EgOjx5x23d46pT179ijnWSAQ2FDkJuY50INJxPy+7YKC8XhcRYz1qKa8ZCqVYm5uTqUAiD/D5/OpyWg0GirHVHeGyc8SImg0Gkr6iGQoFovMz8+TyWRIJpNEWhGyy1lMzyS7nCXUCNGMNNVkNxoN6tSpZ+pgwBJLGBh4r3KAMIWnccSx1DFeLL0IgGmYuHTf7Q3ZNzBQGWApuMS50jk8w2MpsIQbcjkwfIBarcba2prKcZH4kjCQAFVYL/gS77REv8XqEWtNrCVdJd2MtgWjSG6JOJBk14jLfffu3SwuLva4ywWQiQkqIE7c47t37+bKlStK9YTDYWKxmArN9+82PddjzVxjKbPEyMoIhmfwCz/4BZ781ScJRUJqXFbLIlKI0Mg0GPeP88jYI8z/xTwDlwYYSYxw9t+c5Y9rf0zTaxK1onzll79C0S5StsuMhkapG3V8lo/O/97hxkdv4Dvh4/hvHueF4gvs8fYwEh9heHgYx3G4dOkSu3fvpl6vq0o/0zSVugaUum6321SrVSqVCvV6XYH8SCSirCCZv1uhbWEeS61wLBZTubPi7paMcXmxUCikwKqUZjSbTZrNJoVCQbnLh4eHSafTKm0wGAwqHd7pdFTGvPhKenJoDfj+z38fDw8Dg+xKlogdUZJMzFfcrvQwDZNgPci9J+/l0OIhYpdjmDWTptddxJpT48LKBYYjw4zHx7FMi/1D+9lr7MU+bYMD9hkb1+4ybigcIpFM4HmeSrmQbPtEIqHev1wuUyqVlKq9evUqlUpFufj1mJVu+YjJr8fRbkbbglGCwSDxeJzLly+rjHzdHEyn0z3iUlIjhVnEWpGaFrludHSURCKh1BGgEoHkej3PQ+4Lh8MYaYPV3au4hsvK8Art6DqgbbfbdIId6pk6Li6v2K/QzrbxJj08w6Oyp8LV+tWed/z1p3+dh/7xIdYqaypy24w0Cf6LIFhQvrfM+fp5XFwuty7jS6wnKckiyzj1YjmRhBLmkL96rbZExEVti8l826UZZLNZcrkcV65cIRaLqRwTmaQ9e/YQjUapVCrqBcUFL0Gyer2ussUAFQfKZrPMzc31JOvIc0WXG55BtBPFdbRaXwOefv/TWGsW9WAXi4iON00Tq2Vhdkxcv0vIDBE1orT+rxb8n/Dw2x7mxdCLG97zTP4Ma84asUaMUqmE3+8n8VcJajdqBBIBjj9/nHPFc+y39tMqtKjYFQVQq9VqT6RbrBrxKYlkFAaR0IekEugbTxx3t0LbglHGx8eJRqNMTEyoiZEyC9d1yeVypNNplXwMqJqYYDBIKpVS9ciSKimfHzp0iKWlJXw+n3LaBYNBBgYGKBaLeI7HRy5/hAP1A1xPXOfRtz+qwgTtTpt2pI3f9BO1o2BDw+zWEDWNJq7PBQNaXovVxiqDtUE6Sx1eHH1x3Qmn0V2Dd7E3vVcVhAk2MwYNLM9a96S6DjPXZzAwlHqsVCo0m02GhoZUZaXgDwHy5XKZaDS6gTnEtSDMJY7JW6kU3BaqR4qzBHSKL0WYIZlMkkwme6Kdkq8qDijxYEr+iVTPJRIJFV3Wq+NkZ0Y7UQ7UD2Bhsbeyl4Sb6NmVfp+fX/qHX+L+L97P/V+8n5//5s/juR7+tp/Qcgg82GvtJWWliH4uSrQaJdAO9JjAQqfzp3nvP7wXDJQVJt7VpeoSZ1fP4uJyzblGuVMGoFgsKiYRNSm5MRL0FOAKXd+SHhwV6SluBQGzYilulbYFo8ik6Qskloxt2wSDQRXX6DfpJLKql2q4jkt7uY2BQTKZVJlkgkP0BOuKVeFq5CoODrPxWSzTwsQk1OgyQbwTZ2B+AOPVP5nFDBE7gt/nZ8/39jBQG+C6c51HrjyCc8nh1z7+a9hBe6NEeZVxLtcv867vv4tUOqXCBj6/j0+c/QSu54IHg/VBjPo6jhCVKnhMUkEleClzIhJJ8ldeKzFJTOrbDqMACqDB+i6Ql9V7fci/0uVAalhEstSrdd72d28jPZ9mbe8aL/zrFzh8+DAvv/yyYjhhPtM0cQyHP93/pwwHhvlXV/8VH/r2h+j4O/hsH4VcgdMPnaa0u8TAXDcPJj+Sp+B2s92DA0GKkW7C9VRziqlfmFJ4Bo9N1Q9A3akzU5vhyMARPM/jeuE6U5Wp7vUuvH3p7fgCXW+y1P+0223S6bSSqtVqlXq9riSnnvIA64X3/RFiwXd66ctWaFtIlKeeekrlUdi2rUL/ekWdIHf9M9lJ+mdeySO9kMb0TBKzCUKtkMr40k1gUXOO42D5u8670bVRTM/Eb/sxMUnPpzHXTLxX/+SH8jz2i4/huF3Xd9gLYzkWeBAyQxz7+DFCxqsL81NSPWKBGMdHjq97elt+dju7wYXkWpJsJKtUpPiLpNh9eXmZq1evcv36dcUkwihi/chG0130/bknoo62StuCUT7/+c/z+7//+4r79YwsyckAlEqCrvjU/SkSDS16RSp7K7iGS3lPGSe+XoQuKY8CkqWCrlFr8OuXfh3T6zKF7bdxcVkdWqW50GRgfgATk8H8IJRRmWxVp4pjOWBAw21wduEsX7nrKxyMHOxKFPkLxPwxTExODJ/g2r+5ptRqrV7j1NQpyuUuJjEMQzkfDcMgHo+ze/duxsfHSafTSiIAqo+MLLokYUnGW39Gm8ytpHnedrGeaDTKiy++yFe/+lUeeOABlYik+wr0F+0Pm4tTrdPp0O60OftbZynNlHDiDlkvq5x0MkF654JAIEDUjjJaGVVu+HKsDBYMLQ/xwLceoO1v4+v4WMosgQee6+E5HqlaivBKmMZQAz9+Pn7t4xwIHuCzhz5LZDBCpBMhmO3mlexO7u5aRqFBbNumXC5Tq9f48A8/zNniWbwBDwwox8vUq3VSVkrlkoiPBFBJ3cCGPBmZAz27fjMcIvN52zGKtK04efIk73rXu6jX68RisR7LBlCOIv0lJVNeShQAXFwCwwEWFhYYzAz2+A2kEEyfpIpVYT42z57Kni5gLWbAWI/Z+No+vv3+b3PPM/fwoW9/iPmBeWzbZqw6xivXXuEzhz7D3Ae6hVxXWld4+OrDfH3868RjXXM8HAjTaXdIB9Oqi0CtXmNqZaob3xGx40KqkiLh6zYFEoym4zBYB+WSfScbANb7u+nz1b+55LNbUT3bglFk0FLpFo/HVc+1crlMPB7vSU7W+4PouEawR6PRIJFIcPXqVWXhiGSC3o6LkUiERq2BY3Sf6eGxkl3BsAyGFrpR4ZWRFerBOsP5YUzPZFdhFyYmBgZHmkf41Muf4nM3PsfF0YtgwCu1V3jiuSe4O3o34VyYilNhIDCAh8d8aZ6oEeUPL/0hU9UpIr4I9U6d8GqYvc/tJeVLsXpklYHUAOPj4ywuLrK8vEy5XCaZTKqNIlWH8u5ra2sqAi+Atr9OuX++b4W2BaM0Go2eDgUiScSJJknVuitbLCDxv4iZbBgG5XJZRVtrtZryOcj9bbvNgDGAlbS6MaZ2TKke13D5wX0/oBVuMVQbomJU8AyPmlVjZXCFodUhlmJL7KqsF3jvb+3nv37pv/Lv/rd/x8XcRcJ2mE/e+CSTs5O4IZcLIxfYZ+7DMA2mO9PsC+xjxp7BxaXeqfPhzod57uRzJBNJlY0nnRtSqRSFQkF1OBBXfCQSUTEwsQwl81/fVJuRAv63m0SRTgJAjyjtr1nRgWx/Io6edS4RY8uyqNfrimkCga4j7NdO/hq5Uo6lzBI/+uCPOPirB2l9oUXocoiVkRUqVoX3PPkesstZHL+DZVtdk7ntYym9xF9M/gX//uS/J0KEOnVMwyTkhfjTL/0p05lpfud3fwfHcnhp9KUu8+Ey7UxjuN2fr9nXuGPgDqZKU9ydvpv0XBqn4yhnWbFYZG5ujrGxMQKBAMlkUgU8YR1b6dafzInkp8g86Wq3P9PttsMokn0WDAZJp9OqZkciprDe2E7SEvXuAbCeLijdBSTlIJ/PMzQ0pMBg2kyTK+WwPIuR/Aj7Uvu4+8TdhL4YImJHWM2vEvm/I2RXuvkoht11tAXaXR/PcGEYf9PPHxz9A/ZZ+8jbeT798qe7eMaDvWt7uWP2Dl4afYnJ2UkwYSo3xdHVo1iHLM6vnedE5gRf/PkvUrSLpHwpvvzlL1Mul2k2m6oWeX5+npdfflm55MPhcE9FgDTr0SsGXNdVhfR6CoWevS+f35axHpEGYu62Wi2VwaYDMdk5YlrqGVq6WpKYjzjXpMtBoVDAiTsspBfYVdjF4uAiBbfAuXPnyGQyHDlyhLv23EWxWKT6fJXYtW7+CpoEb4+3OfGOE5w5e4ZIOkJkJcJyaZnsSpbVzCorH1nhP//Rf6YcKZOqpfBMj3K4TKqZwvmag/9tfnLJHJ7nkfVlVWcEwRti7VUqFaanp1W5ilQVyvuLQ1LMXP1fPSlJfpZ0DB3c3pYFYLBefqDb+MI4uvqR/9d9CjrybzQa3aKsVx1qEiiMRCLU63X+7m1/R6AeoB1tE7ge4NRPTjGWGiPwGwEOHznML/7SLzK9b5rz3z7P8f9yvGeM4USY33zPb/Liiy+ysLDAnXfeyaljp7CXbcy0ybGhY7T2tRi4NkB9vFv3O3B1AG/Sw5/xM+AfUI4yURHHjh3j8OHDTE9P97Rcr9VqDAwMKCtHXPIidST3RM+tlTgOrGO5fjUtf2+7AjAhKRcVQAuoLszywnqcQkow5IVFEknVfyQSUeWp0v7KtrtxGCNtUFwqcnHqIp9Y/QQTzgSzT8/yw0/9kGPHj+G3/Bz/y+Mbxuieccn/Yp6Pjn+UL+/9MmdOn2Hyjkniu+KYhkmtnaLHAAAXWklEQVTmsxnCC2HscZvCJwqEwiG8jkdkd4RINKICgXocZmRkhN/+7d/mySef5IUXXlCRZan+m5iYAODxxx/n9OnTShIcPHiQffv2KUkspKeB9qeVytzpLTq2QtvCMyuDlzIF4X5d9fR7GV8rqNXfhUAvD9XNSunQGGwGmXAm8NF14Z8/eZ75G/O4H3Gh/hoDdiD8cpjf/cff5aHnH+Lbj32b559/nnArTHohjeEaBK4GiDkxguEgkdw6kwj2kvFLjVAul+OBBx5QHST9fj/JZJK3ve1tHDhwgHe+852MjY319EG5evUqo6Oj7NmzR6UNiGUEG932MndCt51EkQBVf3wCUBJB3zES99F1sZ691el0WF1dVVFWCR4KYE4kEszNzZHP58GCi9ZFjjpHueS7xBM/eQKA37j8Gzcdt+EZHLYPE7bDXLhwgVdefoWx0Bjj9XFwYfDPBrH+i0W1VgV6a6dh3QqR8MPY2BgPPfQQ09PTZLNZdu/eDXSb8gQCAU6cOMHf/u3fqvhOu93mmWee4Z577unpuCDz2a9eBOMBPQy1FdoWjKIH94REavRLFL2bQH8mufSKF6AnCTr6cSmSkJ3P5xUW+GTskwz5h8g7eUzb5ORLJ3nvvvcSn4lj7DcwIybui33SKwTYsJJZoWSXyPgyFDoFPuv/LF/gC1hYOC84rFxcIT2eVkBTcISesilWifTDP378OD6fj0wm09Pu68iRIz0dLuXdxZUvz9psbvQN1e+p3dIa3dLVP0MSbyLQoz9lZ/SXP4o60cGsLo3K5bKyfiSTy27ZDFlD4HWBoOoVH/CRd/Nd7GIYzC/M89U3fJXmviZMg2d5WMf7stabgAGxeIzP1D/Dny3/GY+UHqHoFbnkv4SDwyX/JT7/5c/zve99j/Pnz6v0R9npgiFk4WZmZpS0kARuKUaPRqMcPHiQkZGRns6V0WhUtToHelQubDwAShjsViwe2CYSRQepjUaDTCbT4ygSAKjvQj1zSxhJ3y2O46gukbZtEwwE+eCPPkh2JUtlb4Xnxp5jfn5emZydTodYJEaSJDPtGS785ALBG0HwwH3RJfT3IdKDaVY/skrzbLMbFXYgdi3GIecQFhYTnQlSRopPxj5JykhRD9RxL7tcvHRRZaadOHGCw4cPc/ToURX5fvzxxxkbG2NyclL1xU0mkz311q7bPQntU5/6FF/72te4evWqajokpRtSyiGuA7GGNsN0egvVrdC2YBTdcdb/uQDQ/mJrXaL0H2Kk/z90i6ai7agq6opfjzN4YLCn173hGTxceJjD9mEuWBf4dP3TXA5d5mDrIK0DLay2hX/Yz9F/PEprqcX1D1+neqqKeafJtSvXGFsbw8DgY9WP8UjiEdasNbyO15NVJ203nnnmGZLJpGL4O++8Ux3sEIvFVPpAfxOcWq3GO97xDt7xjnfw6KOP8id/8iccO3ZM9dPtd8lvZga/Hvc9bBNG0T2uPy3tsd+d3+/ml2tgXRVJp8fcHTka4w0iVyPU9tUIjYRIJBJUq12gmfASHLJflQzOBHEvzn/I/gcODBzgd5Z+h9AHQyzcvUDyO90mNxNPTFCdrbLirPDY//EY//b7/xYLiyPOEVJGitX2as945GdZPGkUDLB//36lUkQ69r+7aa4fTVOr1XjXu96lMu9rtRqhUGhDo0JYB/n9c3SrGGVbMIpwvRyvopdNStqivgP6HUryDFg/bMnzPEZGRrjrrrtIJBJYlsXKH6xQm69hDVq82Xkz/oCfb33rW91S02CDS81LHOkc4ZLvEkWviFW3mKnOkF5NY2DQOt3ixf0v4jZc4m+Oc/AfDpKqpHASDi8HXuaQfUjd278Qune5340+OjqqpIjgs/5OBpLAJcVdq6urHD9+nFarxY9//GNWVlZUvZIkMIkPRS8zkUCqXLNV2haMoksGeRFB8oDCLrKD9AZ8eijdNE0VN4L1s3ssqxslLlOmmWmqjgbHjx9X5mbbafNI/BEi7QgVq4JpdNVewS2wkFwgV851A3yV7iJXflLBXrYJDYQwTIP/tOs/YVZMykZ50wx8nXSmMU1TlcGK40zqdASbue76eYHPPvss58+fZ2FhgVwux/Hjx3njG9+o2pmLF7o/iXwzxr0VqbItGEVIXk6KyXVLSMpGpbGelB6I6aurINM0icfjPR2txVMrCT+G0c3Q37NnD4uLi2oHV7xXi8w6Xab1B/w8/cDTPPTcQ3jnX+UAA+JviuOlPPIreYrFInbHxrZsLNPCbd98ASRHREIM+o4X5tGxSa1W45VXXuFzn/sctVqN5eVlBgYGaLVavPvd7+Z973sfAwMDPPnkkz24RAey/WrwVmhbMIroZWl4J8etSq1Ou91WRVPCLHqsR0CsAF/T7PZVabVaXL16lUuXLlGtVsnlchw+fJiBgYGuinLhPT/3Hh47+RjLK8sq4izkut2TtE7cc4LMv86w8o6VboDQhNG/GqVerzMzM8PKyop6j630bhUmEYaQ5CvJrdGZZXFxkUcffZSvfvWrQLfVqlh1juPw+OOPc/z4ce644w4mJiZ461vfyp//+Z9TKpUUwN8sUnwrFg9sEz+KqJtIJNLTZFdU0Orqqiq6ltwVPfgltUCi36PRKLt37+5JO6hWq8zNzalz9aprVUb/ZJR3f+ndfHzx4/jM9RwPHUMcOnSI8f3jlD5WUlHk6JvWq/F+9KMfkc/nNwQqN9vF/STSU6LBcq+oG8mtffLJJ1leXlZH/urPFA+z4JATJ07wvve9j5GRkZ7yF51kM91Ka65twShi4mazWVVlL+ak3sBPB6qblSLIZIsvQroSpVIptavC4TC5XI6R8AixazFM12Tv2l5GE6MKA8lzHMdh3759hFoh2mdelRQWeLbH5X9xmeXfWMZzPUKhUE/rLiHLsEi6yU0xiwQGBwcHSSaTm0rIQCDA3NwcCwsLCqfohzk1m02FwfQeuPfddx9vectb1Hf1JyzdqtqBbcIo7XabRCLBoUOH6HQ6yquqN/vVQWy/t1EmTrK75OAlQKUNykJKL/rgcBD7sI1nelT3VcndkSMUCqkj3Xy+bmvyt7zlLST3JQneEwQfRE5EqJ+pQwfq/72OVbHU+X2wfiiB4Rl8uvZpvlj9Ip+ufhrD62WiZrNJMBjk8OHDarHF2pPKSdu2mZqaUifKC/aQ6K/rurzxjW9UMSHJW8lkMrzzne9k7969G1z5er7wrdC2wCjQzXKTJOr+VMf+41hgo8NIb9klLb6kO2IgEFCZ96rswzIpfbJEc7HJmrXG/qv7efYn3R5s4qndvXs3IyMjWJbFrq/vIuklacfazHxghtpzNUL3hLhRvaFO0/K8bhlH0k3iuR5H3aP48DHhTJDwEl2LCJRpGo1GyeVyG5oXS/F9vV5nfn6+RwKIipHKwXvvvbcnJ1jyctLpNLlcjosXL/bc+3qkCWwTRjEMQ3V/XF5e7smq13W+zhwC/PQz9/TcE0nukVIO6Ipg6ZdiGAaYEB+LEydONBblzJkzXLp0SfVLu+eee1S+i2EaeHEP0zUZ+doIvoqPeqjOS//rS2p3e47Hp9Y+xYQzwQXzAhfNi0y4E1y0LiomkXFAt2Hyvffe29NkWcCtSNIXXnihx28kKaDRaJTf+73f48iRIwpv9Me/hoaGNmAlCT7qkeSt0LZgFOh6J3UPLayXG4gq6Q+ZAyqtANb9McVikXq9rnqwimrQ/Rd6yYfUPU9MTHD9+nVarRaZTIYTJ04ob6kwpM/nIxqL4kZcrKqlgKjnecScmMptOeoe5cPRD3cb61iVHpwiC37HHXf0nPQu79RsNnu8s3IEjagfv9/PwYMHOXjwoIomiwEA69JWqg/1TfZ6vLKwTTAKQCKRUEnVermB67oqmXqziKfuJ5CJKpVKKuBnWZZKONZPrBCKRCKqbdc999yjjpK988472b9/v/Jw6ucMijQrl8uUy+X1k0KNMheti3TocMG8QMksUTbLG+qQpe3YyMiIeqaeHiDJScLkstCGYZBOpzl27BgPPvigAu2yufTeMXJaqj5+vfvBrZrH20Ki7Nu3j6GhIdXHXlSDMIlkqG/2crrqCYVCqgHe7Owsd955p1pUWM+Yg/W4i2S4A4yNjXHPPffQbDa5//77FT7x+/3dWmAMGvMNfEM+5d+QbHgA13N5OPIwCS9B0StiGq+9GENDQwwNDREKhVRpiVgvEqz84Q9/yMLCglJHg4ODfOhDH+JXfuVXgPVmQqZpqt51Aqrz+Tyrq6s9+S4ChvXcnq3StpAoklYgXQ3FNIXugq6trakka1Eh8ld2Sr/LWuIiEp4PBAJkMpmeQndRdfIsMcs/8IEPqGPelIfUMLn83stcuPMCV/+XqzQbTVZXV3vEuM/nw/Jbm0oRnVy3e0JYJpNRvh9ZUL1jo2AOy7LYvXs3b3/727nvvvt68nVENepxnXa7vZ7B9yrpbUaF+W87jCIue3Hby8KLLpczhmFjExhdSvR3PZBr5Eg3qU8W01n+X+Ijksx07Ngx4vG4ir34fD7cgkvtuRp0oPZcjdalFmfOnFFeVj3etBVKJBKqRFTP2BPzOhAIMDAwoKThgw8+yOTkpMrOl8/7GcDn85HP55menlZGgVRRyne8HtoWjJLJZBRD9E+4Ljmko1A/yaTpoFZKGcTVLf4JXY/LzpJ65XK5zNGjRzlw4AChUEgF64LBIFbEInJvhPp/rxM4EeA//vV/ZH5+vsc93o+VXossy+Lnfu7nSCQShEIhlWikSxN57gc/+EHuvvtuJicnew7i1BPPLcvq8VwLtpGW8XqEXcdDt11/FOleqO8OAY39BU39idX69bC+w1qtFrOzs+p8YEmy1nev7EDp/eY4Dvv37wdQsSf5Hs/zGPnaCLlncjz/0PNcevmSOmdYZ4yt7NhAIKDOEtRVjm5duW73iN/77ruPiYmJHhUL9HiQ9ZYXwhSFQqHn/7Y6tteibcEoegM+XefL5Ok7QACfTIzcJ/+vm5TT09OsrKwQi8U21L7ofhopCh8ZGVEt1n2+3nMBTdPEH/BzduYsf/OVv1G4qV8Fynh1JpAFlp9TqZTCSzKufobzPI9du3aRyWQ2mLMC+EUdi7SV8QQCAdbW1jaAV11i35Ylpf0LKC+ht3CQydIBmO6Mg14U3+l0WF5eplgscscdd7Bnzx6lp/UGvdI9QI400Y/WFfUjQPc73/kOX/jCF3j55Zc3pF3qY9JJZyRZpMOHD5NIJJTV1X+GoG6lNRoNVXccj8cxDIPV1VVarRaHDx9Wc6I3GtK/V2cUfWy3UtMD20Si6Aus681+3apT/+LIjhU8Iz3goNuCUzLZdXIcR0kGaaUu+bdikppmtya6XC7zjW98g7m5ORXt3ioJQ4g0OXToUE8Gmv5dIhV1MC7WmESWQ6EQ09PTypWvz40unQTzyHP7mfi2qz3WWzjA5rpUlzT9J4rKz/K73nFI+sSXSiV18JOYkHrMRQ5f6AfSIpmeeuopFaCTLDRdmv00koUX1/uhQ4dU1YDeWl1XFXr4QsZbKBQYGRlRKRVyYpqc5NovWQXXbDbOWz00YVswikykeCGlwBx6uV4/q1gwxk8DasIwpVKJkydPYlkWIyMjatL0fvqicnRT2+/3c+rUKb7+9a/zgx/8QLXybDabG5x3Mh65V198/T2OHj1KKpVSak2ulfiSSCrbthkYGGDPnj0MDw9TrVY5d+4cp0+fJh6PE41GeeWVV3jLW97SA+gFtKdSKRYWFmg2mxskc/+YtkLbhlF0K0YX681mk0aj8bpC47C+iJKtLr+Lp1faSujNkMVbu7y8zDe+8Q1Onjypird0bLLZeygvrfavzny5XE6Vuur36WpC9yPJqenxeJzJyUkajQbnzp1T7TL0kAJsLPjazCJ7PT6VbcMowAYmWVtbY3p6mmKxuEHtyH39zrZ+cl1XoX3xVErOrZig4kaX73cch6mpKf76r/+axx9/XD1LHF39vpJ+5tAxhq5GJGlK0gLkWnHqiaUl90uClrjpq9Uqk5OTDA8P8+ijj7K4uMiNGzd6DsMC1M/6nL2WOt8qbSswqx8VW6lUmJmZUUe6CfX7TW6ma6UHfqfToVarUSwWN1gX+g4ThvrOd77DD37wg57v61c1OuDcLIl5M0YWc7jfrNa7XPZLIV19SJK4nIEo0rY/277fJ9M/nltNYNoWEkV2kbjWHcehUChw48YN1tbWeq7VmUavUZHfoXen6BhmdnaWfD7PwMAAnU5HHd7oeZ5avHa7zZNPPsmjjz5KsVjs6bQAqASq/oL6/u+V75T3EsmlM4L8q/evk+/QJZGUroh6EstH5kpI78ubyWQ2MIKAd/m+W7Lctnzlz5Dk5SUZ2nW7gUABj7DenK5fzOth8812utxrmqZy0wt4FMaS3bi4uMg3v/lNvva1r6nr+qVZv/+hH19sZsqbZrdEJJfLMTIysmG8svuldENMabkXUIlMcs2BAweYmZmhXC6rblKwzmzJZFK9t+40lPHLBtkqbQtGEd0swTzLstQBT/J/r0V6YjX0FpMJCTP5fN30gH6MIfGRv//7v+exxx6jWCz2AMSfRpvp+X5mFvUiZnW/J1oqCySGI2MS0hdY3lnOL9KjzyJ9xKPcX4iuq6NbpW2henScIS8rea7C+XraQf/O1Xeofo1utsquKpVKdDoddYaPPGNhYYHvfve7dDodkslkTy/5fmb4aV2L9HHIvdJ9W0pjhWn0RdQDgjrY7ifP85QKE+kr2fj9DCXP0Md7q5JEaFswiuS+6swgJRywDrxkgnUTVSZDxyfigBLfhIhswzCoVCrk83nS6TShUIhSqUSxWORLX/qSCvLJmDYDrLJbX4tkYXRJJwcg9EtH3cGme0/1KHl/m3K5VhoFindWJLGoVJlP8U3JtUKC0ba8Rlu+8mdIwhjiqZRJkKQd6O3ApHsxoRew6vdtBi6lG7ZUIC4vL/Pd736Xq1evKjCtWyX6c4Vhb8msNHsTqvo/k+dJXqz+rrolJaUcwhRSwlKpdM8dTKVSPfMj90lWvm56C7PfdhluOtrXzbzNUHk/9tALmjYzV2XiJFvNsixmZ2fxPI9arcapU6d4/vnne7oA9DPJrTimYGOTmv779STyfjUlG0ZfbD2DTxr6LS0t0Wq1WFhYoFarqVZkQA+w3qzfndBt181gcXFRLawk8eTzeWUByGRBb6BQB7DSzK/fnyHdr4WhpPGv4zicP3+e7373uyokb5rmhtxcXceLStiKjteb6olalITnwcFB5bwzDKMn70V2v6RyCjhfWFggHo+rfOBnn31WNTGUwKbgFkk7EAmqq2XdwrqVVINtwShPPfUUgNphYiaXy2XV7kImvtFo9Oh5mVRhDGEukU46Q7VaLRYXFymXy1QqFS5fvtxzTGy/s2wz1fXT6LXArzD7wsICTz/9NFNTUz27XgfVYv7q2EraYIiqNE2T6elpms0mL730EleuXOH8+fNAN1dlcHCQc+fOsbq6qpKudUtLLCPp+7YVMl6vufRPST6fb9NBbIYF9ELyrWAFub7fL/E/Qjd7xs0Y7Fbv13/XwbzOzMJsevdJXeVspp4BOp3OlhJTth2j3ApQfD3Uv0g/6+/7WZAO3nVfzVY20Cbm+5YYZVuonv8v6Wa7/VYtmlu9Z7Pv7KetPq9PMmzp3te7MbaFRDFNc8uD2Aw77NDrp61KlG1hHt8K7TDJPw9tC9XTb47ebs///wNtC0b5WS/eDnP8j9O2YJR/StoMc/UHym5Gt1rKsB3pnxp7/k/HKDdb5P8ZmGAr9E/9ntvC6tmh7U+3ndWzQ/88tMMoO7Ql2mGUHdoS7TDKDm2Jdhhlh7ZEO4yyQ1uiHUbZoS3RDqPs0JZoh1F2aEu0wyg7tCXaYZQd2hLtMMoObYl2GGWHtkQ7jLJDW6IdRtmhLdEOo+zQlmiHUXZoS7TDKDu0JdphlB3aEu0wyg5tiXYYZYe2RDuMskNboh1G2aEt0f8LZ0h/VS8bywcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c53a34a8>"
      ]
     },
     "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",
    "\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",
    "        # 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": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "## TODO: Define the loss and optimization\n",
    "import torch.optim as optim\n",
    "\n",
    "criterion = nn.SmoothL1Loss()\n",
    "\n",
    "optimizer = optim.Adam(net.parameters(), lr = 0.001)\n",
    "\n",
    "\n",
    "#net = net.cuda()\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": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_net(n_epochs):\n",
    "\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",
    "            key_pts = data['keypoints']\n",
    "            \n",
    "            key_pts = (key_pts - 100)/50.0\n",
    "\n",
    "            # flatten pts\n",
    "            key_pts = key_pts.view(key_pts.size(0), -1)\n",
    "            \n",
    "            \n",
    "\n",
    "            # convert variables to floats for regression loss\n",
    "            key_pts = key_pts.type(torch.FloatTensor)\n",
    "            images = images.type(torch.FloatTensor)\n",
    "\n",
    "            # forward pass to get outputs\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",
    "            # print loss statistics\n",
    "            running_loss += loss.item()\n",
    "            if batch_i % 10 == 9:    # print every 10 batches\n",
    "                print('Epoch: {}, Batch: {}, Avg. Loss: {}'.format(epoch + 1, batch_i+1, running_loss/(10)))\n",
    "                running_loss = 0.0\n",
    "            #if epoch % 10 == 0:\n",
    "                #torch.save(net.state_dict(), './epochc-{}.pth'.format(epoch))\n",
    "\n",
    "    print('Finished Training')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "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: 0.05801323726773262\n",
      "Epoch: 1, Batch: 20, Avg. Loss: 0.06304833367466926\n",
      "Epoch: 1, Batch: 30, Avg. Loss: 0.057142515853047374\n",
      "Epoch: 1, Batch: 40, Avg. Loss: 0.05991389118134975\n",
      "Epoch: 1, Batch: 50, Avg. Loss: 0.056588397547602656\n",
      "Epoch: 1, Batch: 60, Avg. Loss: 0.048722635582089426\n",
      "Epoch: 1, Batch: 70, Avg. Loss: 0.06852307841181755\n",
      "Epoch: 1, Batch: 80, Avg. Loss: 0.051193592697381975\n",
      "Epoch: 1, Batch: 90, Avg. Loss: 0.05183498188853264\n",
      "Epoch: 1, Batch: 100, Avg. Loss: 0.047851669043302535\n",
      "Finished Training\n"
     ]
    }
   ],
   "source": [
    "# train your network\n",
    "n_epochs = 10 # 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",
    "    train_net(n_epochs)"
   ]
  },
  {
   "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": 44,
   "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, 136])\n",
      "torch.Size([32, 1, 224, 224])\n",
      "torch.Size([32, 68, 2])\n",
      "torch.Size([32, 68, 2])\n"
     ]
    }
   ],
   "source": [
    "# test the model on a batch of test \n",
    "import torch\n",
    "from models import Net\n",
    "\n",
    "\n",
    "model = Net()\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",
    "        key_pts = (key_pts - 100)/50.0\n",
    "        \n",
    "        \n",
    "        ## TODO: load the best saved model parameters (by your path name)\n",
    "        ## You'll need to un-comment the line below and add the correct name for *your* saved model\n",
    "        # net.load_state_dict(torch.load('saved_models/keypoints_model_1.pt'))\n",
    "        state_dict = 'saved_models/keypoints_model_1.pt' # i saved the model first then i ran the test!\n",
    "        \n",
    "        model.load_state_dict(torch.load(state_dict, map_location='cpu'), strict = False)\n",
    "        \n",
    "        model.eval()\n",
    "        \n",
    "        output_pts = model(images)\n",
    "\n",
    "        # forward pass to get net output\n",
    "        \n",
    "        # reshape to batch_size x 68 x 2 pts\n",
    "        print(output_pts.shape)\n",
    "        output_pts = output_pts.view(output_pts.size()[0], 68, -1)\n",
    "        \n",
    "        # break after first image is tested\n",
    "        if i == 0:\n",
    "            return images, output_pts, key_pts\n",
    "        \n",
    "# get a sample of test data again\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": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c59e9c50>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c5ab7ba8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c57b8550>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c59c44a8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c57d8860>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c5129358>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c537bc50>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c592d4a8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c57a8630>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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gsrqF48g50WgUt9vN9va24qxifuvX1BV4nWN6vd5bFpfOzcREF+dgIBDouvbdaF8ARZKTwuEwoVBIKZG9UVforKJ6vU6j0aDRaCgzNpfLkc1msSyLer2uzpcVLlFZGTyXy8X8/LyKTMvvykToVpWsYD0uczeS39DvW7e2hDvJee12G6/XSywWU36bfuCTa8t96IFIOV93Luq6nn5cf65BaF8ApVAodCXTBAIBdaz34WCPA9XrdarVKsVikUqlokxPPaFIJgO6rZVgMMjZs2fVyu0VLbrDSz7TPcg69WPh/dINxAGmT7RwLJnIoaEh0um0OibhAp0r9QII9mI7gPIZ6cq3LhJFhN930eN8Pk+hUGB3d5dkMqkcSbLagS7WLemIhUKBcrlMsVikXC53Oa9EJ5CVLLJcdI+zZ89y5MiRLhDIMbfbrVi77lir1+sKTPqA34lkouR8EQPiINPPEf/KyMgImUxGPYvOGeT3xZckCrP4l8Sj3GudSRzK5/PdUzBQaF8AReIi4vYWp1Gv+SYrslqtKk5SrVYVN9IHRU8KktUj1oPkcIg/Qya7d5XroJDvCmfTOUY/sOhcQ7eaPB6Psj7kOnrqpHiWc7mcctCJl1d0OAGV3IOkGHg8HgWWXutMRK7cx33JUXppaGiIRCKh4hGSauByudjZ2aFer5NKpUilUmSzWaDb8oC9wdBXrYDm6NGjPPjgg12+FyE5R1c0xYIQy6NXwZXrD5KYJIDTJ0tf+c1mk2g0SjAYJJPJ0Gg0GBoaUpzU7/fz4osvqiSura0tyuUy8XhcJX8bhsHu7i61Wo1gMEg6nVYA2tnZwefzUavVFNcahPYNUISdSnxCsswdx+H8+fNqQDOZDPV6nVKp1CVqekkHjS6jTdMkGAx2sXSdY+iRWj3VUti7XFvnAAKSuym6ArhepVTXi0QfCYVC3Lhxg1qtptIf/X4/oVAIy7IwDEMBQKzEmzdvApDL5bhw4QKxWIxoNEqhUODYsWOcO3cOn8/HxMQEKysrxOPxgednXwBFzLx2u821a9dYWlrqclKJFSNWi6xoCeLp19EBopvGuhUQiUS60gLku70xoH6pCfq1hfRrQH9RJNeQ6+rf07mXvBfPcCKRUK7/4eFhBSbJdYnH4yoddHd3F8MwVGabRJVDoZDiVJZlkU6nOXr06P2XZqCTrF6R56ZpqgcWjiBueHGDC0fo1VOERGzJcdFP9MkWbiGWhh4MlMmRyRadSo/rGIbRZZn1chc990QHiijcOleSNErR0UKhkHL1y2eO4yiRNDQ0pGJkjUZDVQ3oCqx4mmWR1Ot1ksnkwPOyL0pKZVLFTyHyXwZN2L8c71Uke5VRoV6OYpomfr+f4eFhJbZ6f1+8vSIidAW01xGom+F6ioDOge7EiXpJjomlVSwWyWazFAoF1tfXqdVqXcFQ4Yq2batIsKRtFotF6vW64jCAEtnBYBC3262y6wahfcFRTLNTlZdOp2/xfOrA0PM64NYkZN1c1Z1a8l3oaP8SHRauIdcSPwwGuKIujgaPggH5Zp5oMYrL7+oCmG65yG8KidIrx2UBiKUln+sg61VqDx06BKA4hXynXq8rF8Hu7q7yZt+8eRPLshgZGSGVSjE6OkqpVKJSqTA9Pa0SzvXUg0FpXwBF0gOr1aoyS3Vx0ku6IinxC31S5Bw9G04ywoaHhzl//jyzs7OMj4+r79atOlc2rxBwAvx267dZaa9w3NtJ7r6Uv8T82jwff/XjpP+/NHFvXIm+O92jXFv8M71Bwd56IgGOZVlUKpUusTcxMQF0HGtvf/vbVTKWVP4BvPe971V5KoFAgFqtprLYSqUS73znOzFNU+kwvZH5O9G+AEpvQjFwW3ECt3om+5mmouyKjnP48GFValEoFCiVSoyPj3d+q+3wK5lf4XrjOtPmNOv2Oo7pcK1+DSxwTIeLUxd52nyapQtLzIXm+PjZj9N22ncd7F7F1u/3YzdtyEHD0+gqF5W0Regsgnw+rxK/pRrR7XZz7tw5JZ5kQSUSiS7vr4hqyecRN4NeH9RqtXjyyScHmqN9AZRgMMj09LRynvWSLl76mcJSESekV9oFg0Hm5+d54IEH2NzcpFgscvz4cbLZLMVisZMtZlS53riOg8Oqs8rpjdMsTSxxZu0M6ZE0O4EdTm2cYmlyCRubxdIii6lFZpwZzIQJfTi4ssAcsEs2rjEXhd0C0aEo/mf9+C75qJ2tUftXNYyyQT6Ux2f7FAcRZdnn8ylxq2fc6RUIhmGwurqqjgu3c7vdql5aACivdUfjILQvgOLz+fD5fCpJR6dBfBS3UxAty+Lo0aMkk0ksy+LYsWPk83mVhlAoFDrWQ2yI+Z15FpILzKXn+MhffARfxUcj2OCL3/lFinaRifwEHsfDxemLBBoBnll+hvnVeX7hxV8g/VNpPL5OgE3ETKvVomk1Gf6lYUobJT76vo+yMLnA3M4cn7z0SX7yB3+SS9OXOHn5JO6Gm4XDC0yb0/xr81+rMRES0Akn0PNi5L9+PqDc9L1dE+6k/N+J9gVQdFHSL+Cl57n2o14FWH/vOA47OzvcvHmTd7/73cTjceLxuIqnVKtVyMFzn3qOQqBArBrjD/7ZH+D2ummGmlQLVYpWkUK1wNN/9jQtT4t/+4F/i2M6XJq+hJWyqKfqNEeaKtnIsiyy2Sy1VI1PPP4JLk5fxDEdMODy6GUuHL/ApelL2C6bpbElDAxs02alvcKOs0N7t016J93lARa/ySABvX6B0NuN26C0L4Byp4fRfQzQ39F1p2s2Gg18Ph/T09McPny4Y424TIywQagWolAocGnjEiOREaaL02wPb1ML1GjaTTY3Nzk3ew5r1CKQ6RSze11ewoUw5ViZ+bV5nKhDjhz+cifxWhKpdnZ2WC+sc/HwN0DSBpft4vjWcf7u1N8xWh8lFUxxcvsk3oZXcapP+T7FaHSU+SvzhIIhVcfTm1CuOxf7gUY4SW+ylU73AhTjXk7+X0Vve9vb1E30PrTu0ewdGL2Wpx8ZRqfNxdzcHGfOnMHv95Mv5Pkd+3d4I/cGx33H+eUzv4zLdPHySy+TuZbBlXTRclp8cfiLrLvWv3EhwAFv2ktjpIE/4+fMjTMcc44RGAtQq9eIRqOqRLVWq7GyskIun+O1B16jPFQmsBvgzItnaDgNkskkwyPDFJoFhgPDnPCeYOqvpvjAj3wA22Vjtk1+wvgJZkdnqVarvP766/zZn/2ZKuDql6fT+9y9i6gfpzYMg1wud/90XLp8+fJA5/X6HO4mY8UDefToUY4cOcK5c+e4vHaZC6MXcHC4Zl2jaBeZDE8yMjpC3ep4K0t2ic3mZgcg7c6fr+nDGrXAgPpIndeGX+NG6Qb/dPefKgdYOpOm4WngbXopForUa3VOv3KabD2LU3Koe+rggnHfOP4RP83NJqurq9gTNqc4xfzaPJcOX+Ko9ygRO0I8Hse2bR544AFefvll1tfXbxupvhOnvV1W3n2no9yOI9yJ+sVf+h1/8MEHmZqa6ngx7Tbf/fnv5vWnXufS4UucCJ4g7o7TaDRUMnI8Gudtn3wbf/HIX3TEhtHRLVrunns0oRgpUkwVOXbsGCOjI/xm9TfZcG2QrCR57PJjNBoNtlPbeF1emv+kyeLUInNrc1zkIpcSlxj2D/NE5AmcusNX/tlXmFma4bRxmtHIKL4JH1/+8pf56le/yrFjx/oWut/J+/utlhT7Aih3ot4HvpdVEI/HmZmZUQXtfsvP6PYoz/3uc+TCOZxf2RNlKts+D+7Lbp5beI7d4C4//76fZ3FqkTNrZwBYmF7A3/BT89Y4u3aWKWOKhx56iIa7wdbSFm2jTTaQxQgZDLWHyJzOsDSxpJTZhekFDAwcl8NOeIf/EfofjDXHeF/tfTAEh+KHGJ8Z57DrMNakRSKR6Phe7sE5Nug43Xcc5V7odmy0l6QrQSQS4fLly0xPTxOZjuCccWAB6kfreGKerk5N8XgcAwPruIXvqg8zYvLcf3uOYrBIvBIHA7KhLO6EGztn4xv3kf2PWaampiitlji5cZKliSXOrp1l1jdL2k5zfeI6jstRIizQ6KR5Vv2d+ItjOmx7t3HaDsdPHOdz4c+xnllnfnWej33tY1x66yU8Xo/yMt/NArwd9Ruz+87quRPdC+p7aXJyknA4zNraGh6Ph7m5OQKfDvBv/ue/4ap9lbnVOX5z4jcJh8N4PB6VTpl5NsPujV2WUku86y/eRXIzie21cTfdRKYi1H+hjq/sY/jkMGOuMbK5LM+mn+XK5BXmNub4T1/5T6R/Ok0oFOKNv3+Dy6OXFUexvBZt2kr/MR2TWe8sZyfOslPZYa2wpkzveqrOzD+ZoeztVBPqbv5euhvn7TeO9125Rq/nVRxLEtjTo8hAV4aYREjlc31AIpEIzWaTkydPqp4qNaPGVfsqDg5L1SVyjRyTgUkikYhKCAIIT4cZaY/w+r98nYAVwAk7uCouzISJ57qHxx57jEQiwfr6OoVmgcvVDhguT1ymFq1x8+ZNHn3sUX7tfb/GV//2q/zx9h9zZewKZ9bPQJuOg82Z5l+E/gXjkfFOEyArxmHjMGvOGvNr84SnwphJk2a2O/u/N1+3H5fVc1t6x7jfuN+N9gVQxsbGlKkrPcfcbjder1f1dRPxIPELv9+v+oNIiqK48sUFHg6HMU2Tt73tbVQqFXK7OcwfNTn78FkuTXeU2VC7k+vi9/sJBoMqmz8QCDA2NkY+n8cO2jgth5JRIlAPMDk1STQaVVl2PtuH3/BTdaoEGgFGL42S+J4EKysrvOc97+HhRx8msZxgd2eXSryCWTL5tsq3MRYZYygwRCwWw+fzUa1W+WHvD1NulWm5W2w/s00inWBza7MrVwW642J347q3sxD7mcy3o30BlA9/+MMq/yMcDvP888/zvd/7vcBe+F/6fbzyyiucOXOGRx55RNXy1Ot1VePrdrsJBoPYtk2hUFDlH4VCgbAdhovw3IWOMlv8uU72vgQQpbZHEpij0SjT09PKKpP8Ddu2Va6uZVnsVHaot+sd09lbJ3M2w/FHjnNj+Qa/9mu/psIToViIYDRI0V9kxD3C+Nh4V6+TWr2G7bN5/Mzj/OWlvySTyTA0NMTm5qbioP3ycvWyV/lcf98vx/deaV8ARUAi2W160q9ebtFud0pPxU2ud5EUziK1vAI6WYGJRIKKt4J92sZYNLBmLOqBTl2QYRiqUY3L5SISiSgxJx2d6vU6uVyOpaUlksmk6od26NAh3G43J/0nuWpd5bTvNDwDhWKBqakpxsfHuXjxokp8jkajRCIRQqEQsVhMZfbXrTq/Xvp1bjo3Ofuls3zijz5B6eslUs90Esj7iQndTd8rYno5iB40FbpvlVmJjOrRTVlFXq9XVdNVKhUVLe0tEO/NQ5V8XK/Xizvupv3JNv/u5X/HNfsax/LH+Cn/TynXezAYVKkJ0g+lUqmoclWpZX7HO95BPB5Xlki9XudDyQ9h/DeDoy8dxZq12P6pbc6fP084HOaJJ57oKrCXsk7hloZhkK1nuencxMHhUuJSx9Jaj7OV26JSqahgY7/nhD2u0o/jyPF+4z0o7QugeL3ernYPAgYpAJNjEnaH7u5GutIrHEfkea1WY2Njg1arRSqVotwuc82+hmM4XG9ep9wu42l6VC6rVCBKW7BsNsvW1hbXrl3j4sWLfMd3fAe7u7ucO3eOcDhMMpnk6rWr/Hn0z9l69xbzJ+b55O99kvp2nUAgwOc//3lCoRDJZJJ4PK5yV+W3oNMW1CpZTNqTbLg2mEvPEa/FqR+rs5xfVoVo+nND/2pEHSy6SOp1avaKq7vRvgAK7GWrCecQjiCJNjJAXq+3q5hJOgL0K8zSB01aWoXcIc7snGFxeJHTmdPEpmPq90VpNoxOgXqr1WJjY4PV1VUuX76sREk2m+Xzn/88R44c4fHHH2d5Z5mN5AZts82l6UtcPXyVy6nLhMIdRfnGjRuK+4kYkwbGjUZD9YR9n/0+zLDJ2OwYG89tUHaXuf78dQUoXazooOjlMjoIxJzurVa4F4sH9hFQhGM0Gg2OHTtGsVhUOkOvYpZKpZibm1MZYXo9jl6grg+OJCWfPnqa//Lz/4VCoEC0FmUOpK50AAAZJklEQVTp1BLRRFSJOdF1yuUyhUKBK1eucOnSJU6fPs1TTz2lUgx/7Md+DI/Xw1pujXAkzGxqlhtjNzi6fZTPnvksD7sfZm5ujmg0yhe/+EVlzVUqFTXxEhm2bZtGo0EimSAyGmGSSVxJF4uvLqp2XNL/5E5cQK8KkPfyX2/4JxmA90L7Aij6w0tpqW3bDA0NUS6XVdabPKAkFEterJ43q3OlRqPR1Win2WzSCDaoHq0SXY7y9AeeZiG/wMn6SZ4Ze6ZLnMk+N+VymePHj/PEE08ov0woFKJWr/HxnY9zgxsw3bn3gBXg+qHrXJ+4zpZ3i8cDj3PkyBHcbjcrKysEAoGuVuPSzdIwDFp2i9+o/AY76zud/NxXPs7NB25SKpW60h77ufJ7c4b1ZG75XBaNXux2L7QvgDI0NMTu7m5XmYQUW0sEWB8MvayzVqt1pU/KawEH7CVaO46D7dh87Qe+xuLFRRbGFnBwuFK/QskpEXPFMAxD3UOz2WRiYoIHHniA8fFx1ZXRNE3sks3N1s1Owcs3cF7z1dTr643rbBW2GI+Mc/ToUWWqC0jq9brSGzweD2WnTMqT6oivqUsUP1dkx9fpetnbGqw36KeLIXmt1yYBXf3n9CL8QWlfAOXXf/3XVY8U6Pgm3G63ysGQ/vey2svlMtvb27RaLQUumcByuYzf71ebBghgvF4vzWaTz372s3jdXkb9oxx97Cg3nZuc8J8gYkSUr0LYsuyuNTw8fEspxlhrjPnVed488qb63I+/408Bzq6c5dRnT7Hz0zvMz89z5coVJRb0hGroiEW7ZBMiRHWoyvzaPDknx1ZtC8PcExN65pplWYTDYeVkvJ1I0jmMPEOz2SQSidx/5vH6eidBSLyqYg4aRqe0UnqKQEfplN24pHpOlF4xH6XKrrddVbVaxW26eTbzLLOpWfKfybP2H9dIBpJqpYuF0W63VZsu2GtE47QdCq0C4USYX3rpl/iw+WGWJpc4tnMMv+VnYXqBkxsn+dnP/Szeqhc72ynOkl4usKc7CAAqlQp2y+at599Kw9VgqDbE75z9HfxNP8Vi8Zastng8ztjYWFdHKJ3T6Hk78lpEUbvdVknXvXm2d6J9ARTpXCAiRTZYkiLqeDyuOixJyYIoigsLCwAKMOLUklZfsJdQbNs2UTvKbHUWFy6G1oYolou0/e0uiwFQnaUbjQbVepUdZ4cT8RN8ZPEjLJYXOWwc5p+//5+z2F4EA66OX+08jAGL04u8/+n3czpzmg+GP0jQFWRsbIzl5eWuzkfCIev1Oi63i4njE0wZU1TcFVzuzjl/+qd/qvrbioncaDT4ru/6LgKBQJdi2i9Ptjd/xeVykclk+K3f+q37T/SMjIwoa0DKFNrtNlNTU0CnpkU2fdK7CpRKJaVgygSEw2HV4jyTyaiVVa1WO6LJLLMeX2cqP0VmPEPdXyfgBJSjT9i0xI/yxTwf2v4Qdep4214aNMCAm/ZNfiP3G5Cgk0KgZcMB2C6bhbEFmt6mcqpJU0HdvG82m5TKJf5y9C/JBXLMr87z01/4aV76gZdwufvvqeP1elWdTr9SFuEuuh4i3EhvQiiW2CC0L4AiGyHU63WVZGQYBjdu3FAms1g28qDr6+tKxuotudrtttpZVICntzE3DIOfi/wc0XCU4WPD/GDjByn6igy5hrp610KHEy1lllQcp0GDQDaAFbc4tXGKy5OX9wAiJO8dGLfG2d7ZJhaNETEjXSa4ANKyLOquOruBXeWH8ZQ9NHYaODFHufh18ZPP59nZ2VEFbLCnxEtwUdwG8huBQECJqlQqdU8bT8I+AcrW1pZqACPZ49LKQSwbPcXA4/Gwvb2tVo5uBhqGccvGlLLHjt5nNdvO8sFzH+S5mee4dPgSxwPHeXbyWdAWsOM4jDCCDx9W2yJUD/FHn/4jNuObHEkf4fue+T4q/m8UegtY2hCsB/nF3/1FPvPez/BR/0ehCseMY/xI4EcU0AU0rVYLK2sRdAepJWvMr83TCDYou8v4bJ/qQC0k+oiIRQGC6GCjo6MUCgXVlVqsOGkgqF+nVCoNPEf7Aigf/OAH1eYAsifP9vY23/3d3002m1U7XsHe3oAf+MAHmJqaYn19nWazqcBi2zajo6MqTgN7JR/FYpFMJsP8/DzOrkPiY4lOfY1pc9W6Sq6RI+7u6EUiGqampvi9zO9R+uUSRzJH+ND//SEuHb7EyfWT1L31PQ6i/a/6q/z4D/84bbOtzOVle5lDv3eI3A/laDkttddOJpNhe3ubk6mTzJ2aI1wJ89dP/TV2qxMgla7cwg3EvC2VSmoDK+HAYsmImNYtIhkbXexJueogtC+AMjQ0pDa3Fj1EIsixWAyXy9W1YWKhUFArS+Ss43S6PUsDX9ldQxRG6HSfFDO6FW3hHfWqzPcZ7wwBO0Czvdd6Qywg91E3M5UZcsGcAtbl6csEGgGqZseS0TkKQNvV7tJZ5tfmmVyYpFAqYPv3/DSVaoU3HnyDUrzEprXJd9a/E5fh6mr3IRxERK34loTbSPxIxKa4DaR8VPcNyVjput4gtC+AIg+om8TilBI/gHQzFHe9pBTIBtCS+yptwmWAZRVK+2/pDO1yu1j5f1f4ocIPkfVnGfINqSIrXYwZhkHLaZH97Szt1TbH7eNcq1/j1MYpFicW+3IU2mDaJvNr8/zs534Ws20yVBmierhKxVOhaXUmyLIsiq0i5ViZttkm7UtTNzvKtTT3E+pt6yWiRt9HSPfcis4mTYkESC6XSxWp3Xd+FLlh27aV0iUdDg1jryW4HqKXyvxKpdJlcobDYRU51ou4RSmUgbRtGweHdrRNxI5QqVZoeVsk/UmVSadbFG1XG2vC4pntZ4j9Yoyh0hBP/6unuTR9CV/TR81bI2gFVXb+z3zuZ0iWkzh+B1fDRflwmTf+nzeoFquKI9TrdbxpL2c9nYy7+bV5PNseCt6C8glJz109CDoyMkIwGFRiRm9xapqmysfR23IIYES5j8Vi919rLlkpep2K/qC9bFMq5uS7OvXWushA6YEy3QklvVE+bX2atfoaM8UZPjj0QZX6oHtDAdqxNv4xP0bF4JO/+0kKwQLRapR8MI8r6sIu2iQrSdpGm8sfvkzzUBMn71DxVLAalkp9EEsm5+T493/870kYCYwhg7/7P/8ODFTDvxdeeKHrWVyuzmabJ06cIB6P31KHbJomgUBAbUXT28VaUkxlQQ5K+wIookcIqxQ2Kqy01z8gu1zJYMuK0WW57skFuoCl+11s2yZTy7DGGo7hcNO+SezTMTZ+eIMECZW8rbaH83pIfyRNO9dm9DdHGVoegjYMV4Zp19pUp6tQg+pMldZUxzNsBS2cxt4+g1L/XHSKXF++zs+Ffo5R3yieEQ/Ri52d2yORiNolRM+Tdbk6u8ivr6+rtvB6krXf72dzc1Pds+gvom+Zpsn169dVp8lBaV8ABfb0FJ1zALdMuOTGitkr5wgXktiOvorkeuJCbzQabG1tsb6+zsbGBpndDKPfNUo6kObM2hmee+w5LhYuMlOZ4Sf4Cbyeveit2+3GMR2aiSabP7mJk3WY+u0pgstBasdqbP7EJu6qGytgYdqm8v+IMt5qtXB73PxR8I9YD6/jfacXzx96yBVy+Iv+rsWg73ou+oVwiUKhoFIpZes46eUmIRB5VgkDhMNh3G43xWLxnmuD9g1QhMS5JjkawjEERLI/TT6fV/1UJKXANDsN8mT3dPGw1ut1XnrpJTY3N9na2lKlG5K7Ypom37v9vTz52pMEVgO8/+n34xgOy/YyuUaOpJkk28gy7B9W92nbNqbbpJ1ss/mTm7jKLuzINzolJAzMhkm7tWdxVWtVduu7xD1xXBEXG84GbaNNa6LFz/Az/GfnPyvu1Ru7kueXP8m/lYZ/vZtey5Y2eotUUfR1T62eu3M32hdA6Q15y+AKy9QVU91cFOtHH4xGo6F2F3/55Zd58803VV6JzoH0XnHSoLj8o2VqxRpzq3NcHrnMqZ1TNGnyy8Yvs9JeYdYzy4eHP4xjO6oqQO7RdJm4rL0kKwG6ZVmsb6zz+ejnSQ+nOeIc4Uf9P8pkfpJN9ybza/M8Vn6MId8QRVexS+HuNV9FPBuGofJ3T506pfq0yW+KuJHEcX2chavp0eRBaF8ARXJeBSziL4G9wQG6zFxZLXovWBFHzz//PIuLi2xvb3eZgXoGmCiperFZy2kR8AX41d/61U5TnVqMv/rgX7ESX8ExHG40bnBl/QrBdlBNpnR61HfhkMlstppkqhnStTTpsTRto80aa4z/7jjveeQ9vP1v386p9VMsmosUzVstELHe5LX8b7Va3Lhxg3K5zPLyMpOTk8zMzKhNN2UcZIMq0QEFHKJM33c5szqyZfL6OYpkImKxmNovULyyFy5cYG1tjdXVVXZ2dpSnF7r3Fe7NAJMNCQDK5TK+hI/G8QZD14aozFSIDEU41DxEypVifnWeR//6Uf7qyb+i0exst5YcTtJsNQkSxDT2QGc7Nn/g+QO2fFtMHpnkiHOENToVgJOXJ3HPufnqO77Kf1/877x24zUMcy96LeCQ+9aVVfm82Wyys7PD9vY2Fy5cYGpqimAwSCwWIxaLMTExocDbFYAslcjlcl3hkkFoXwBF175lcMTyEV+KTKrkiliWxYsvvsjKygpLS0tdPgNZ0ZJjqvtZBIgySHq78CtXrnDy5En8H/HjZB3qgTqRWoT/sPsfmHluhmSpY/YWVgqkrBRO2+HK/3GFgrdArBjjwTcexOPuJFH7h/1sHet0N9g0Nvno0EeZ+vQUk5cnSSVSFMwCbo+b0FQI46bRxe30RCXYc7bJMXEwio7i8Xg6fVZsW7n05f/p06c5ceIEjzzyCNFolFAoRD6f59q1a30bK96O9gVQoHu1iNkrdr9o/OVymYsXL7K9vc0bb7yhtozrzeDSX4v+omfp9wu5u1wuKpUKN2/eJJlM4oq5cDnf2Nc4ZOFOuGlX2mQPZan5aqRWUth+m3wkDyYUogV2a7sk/Z39hsbD45zePs3SyBJz6Tm8AS+b/9cmr1x6hfXyOj7TpywiwzBUVp4+FnpcRk88Eo4iY6Qr5aLXlMtlTNPk9ddf5/z583z9619nYmKCEydOqBjTveTN7hugyECIMgZ7SUSpVIrr16+zvLzMysoKlmV1RZR7E3D6Od3kenpuqXxPlOB2u7PT6fr6OlNTU6o0pFQu8fL7X2bYPYwVsAie63SSdjkufNs+mqNNzq6d5ccXf5wvvOsLJJIJRtwj/Opv/CrFQJF4Lc5rP/UaK7kV1gprqrpAT43QTXn9nu/0PEJ6PrFQl1e53WZtbY21tTXOnz+vvN76Tmt3o30BFPGCymqQ3JQXX3yRV199lY2NDaB76zcB1t0azPRmrunxH+FcUi46OTmJaZqsr6+rNqOyy0WpWiITyNDMNYnH46oB8PQL0zy98jTJShLHcJgKTeGKuHDH3dSO1hi6OUR+Ks8bq29QKBZUO3LgFr1JVrg4GXUPsl5q0UuDZKqJ+BVLzDTNe8pJ2RdAEfHi8Xi4du0amUyGc+fOqd2+ZKB0q6gXADrdbmXqbFy3eKTBr57fUi6X2djYYGJiglAopBKoZNMB2R7FdmxKrhIJI8FWYouqr8qIfwSP18PCDy3Qzre5kb1BPpVXFhLQZfJDd+sK3SLrtXp6Sa7RCxZd/OpiVudO9103gzfffJNsNksmk+HatWuq+Fz8Ab3xGqFeawlu3bNHjukgEVJmbLNJNpvl6NGjikO1220ymQw+n49EItG1QaXeCdp2bP7rsf/KydGTtCItgnZwr2V5q8F2ZZv1jXVVBK+XxwoXFWW1N64Et27K3S818nYcpR9Ybieu70b7Aih/8id/0rUNm1gsvQEvIR0U0K0Iy0TqbFsnXc5L1r/L5WJ1dZUzZ87g8/m6uNXGxga5XE7lt/h8PqLRqOrSpMIJkab6zDAMUqkUq6urVCoVgsGgqssRLgYd3SiTyXSlYPaKl95WF73AkWfpt2jktc45vtn2F/sCKHogr9dL2xsD6jf5wC2rcZDXejF7sVjEsizVzQAgEAioXVANo1MALxxmdHSU3d1dPB6PcqcHg0EVHU6n0+qzXn+F3EOr1VLpiFJDfTfq9/z9OO29ONMGoX0BFB31AhZZfXpm191czvoA9YKjn0gSa0OsgJWVFebm5tR3JVNd0hFlPyEJtMlWKeFwmEwmo8AWi8UIhUIqNVG/JwGhlGmIGXs76j12Jw57r3TfeWbvZs/3stZ+gBEZrOeZ9A5qL6eSvBbxo6yurjI1NUU8HldxJPFx6LupSwcCcZOLmSm1RKFQiFAo1JUk1Y9EtOriplec9tLtdLBeutfo8N1oXwBFZ7l6kE8UPz04puenCOkrVbnQ7e59+npJztGdb/l8nlQqpYCiX7/VaqkUTdM0mZub4/r167TbbXK5HG63m0gkQjKZJJFIdFUF6p5hIT0bX87rJyL76SO91+oHxNuJp9uNx91oXwDlTtTP8dRL/QZT/t9OFMn39M+bzSY3b95kbm6uk6ao7Tjucrnw+/20Wi3S6TR/8zd/o8xmsVoABRjdJ9JPgezNStMdgHeifmPQ73v9RNQg37sd7Xug6HS7ldBvlfQqxrdTaOV9b5MbPTMMOgMvbvZUKqX0FymJkL4p29vbOE5nE24JWPbm3+rK+b2A5B+T9vfd9dDtOEovBxFX/SAg0UsaZGPuSqXS5RHVfzeVSrG2tsbIyAhDQ0PE43FisU7XJjHx19bWKBQKQH9RKc8iVQW997sfaV/dmVg6veKmn/gQEmD0OsLg1t3UdYVRTzcQnwp0tnwV60aCdqLDlEol3njjDZV/YlkW5XJZla56vV6GhoYIBoO8+uqrqjUp9N8H0ev1qqSpXnd+733fSd+62/He5/9maF8ARV+1/RRT+Rz2tH6VWdZHsdXpTpaP/h29x0ipVFK/Lec3Gg3VHdLn8+H3+1Umu6RoSrwmGAxSq9VYWlrqW7aphw70wJye7ngnGgQYd/rON0P7AijQ7T/R38tr4Ba53vtaJ/1473n9VqmIHrFw5DNJHfR4POzu7lKr1bq4g3Alff9kAYxsUde7a7tO/RbIP5TkWnfTf+47P8o3Q70iR0gXVb1OPP27+n/oXuVSu6sfcxyH5eVllRXfa6aK5SN9XCzLolAoUK/XCYVCHDlyBK/X21Xv2xt7uZcSz3ul23HSgb//rbyZb5aEzeuTrIud2+VhyGe3+7z3+KAsW7yv9Xpd7Uno8XjY2tqi3W5TLBZvKUrrFVGWZQGo/BYpddX1qG+1m733+e/2dy+0L4CiD7pQ7wT36iv68X5AElGi9yK5Ewk3EZKoLnTyZbLZrEq31HuciJiR4jXhKHreq0TGdceYz+e7pQBrEN/Ht5LuO9EjwTi9DgX2xMHtgl5yTFdsdbGjR2r7DYruI4G9vJhqtUqtViORSKga36WlJeX/kNiPrgALFxLAycYN8vmVK1cIBAKMj4+r1MVcLketVuty5ffLS9Hpbolat6M7Pf8gtC84il5qqTujegesn5dWF1t3S/LppX4WkcfjIRaL8d73vlf1xs9ms2SzWcLhsGr9pSvGjuMoLiIgkUw28ZGI2Q3w4IMP8swzzzA6OtrV2PBOfiJ9LG53/FslZvrRvuAoQJcLHG7dJaJXDPUzg+WzQZOG9ewwXZxMTU3x1FNP8fd///cMDw+zubnJ2NgYU1NTqjOU4zhKDxGgAMrH4vF4VKa8YRgqXQE65SYPP/wwhw4dUv1c9Hze3nvsJ2Z1GoQz/EPF2r4BSm+CjtDdosC9yq/+981SKpXi05/+ND6fj0wmQzAYJBwOq3JXXbcQp1wvGYahlOB4PM76+nqneWA+z5e+9CVKpRLnzp1T8aLeBsq946KL2m/GjP6Hmt77RvToDf1gzxcgLnC9IrA35UD0EykiF1E1iOMK9lab4zgEg0EymQwXL15kfHycVqtFMplUvVgkI06vDOy9nmmaqmOj4zgEAgFcLpfy4EajUV577bXO7mLfSPDuLdYCutIURN/ROc+dxMogfpR7oX0BFMkjkXYU+ooVwOhKqt7qUy8Yk8H+ZtP9fD4fkUgEj8dDqVRibW1N+UzK5TLlclnpHuJHESVc/wPUa8uyCIVCzM7OEo1GuXDhgiqkl4j08PDwbWNCcCsHvRsI/leY3fsCKDoQ9JC9HOs9RwZLN33lr9f7Kq8HIamw8/l8pFIpzp07p1i/aXbadkp1noBS/y/UW9VnGAbhcJjjx4/jOI7qqKB3q9TDBf9Qup0e0+9vUNoXQJHVKeLidsG8fqy2l9PcLgFoEJIBdrvd7O7ukkqlKBaLuFwu1Wpd35QBuvfr08WicCK9PjoajRKNRtne3mZpaYlGo8Ho6CiGYXQV4w9yn98KXexeyPjf9UMHdH/TvuAoB7T/6QAoBzQQHQDlgAaiA6Ac0EB0AJQDGogOgHJAA9EBUA5oIDoAygENRAdAOaCB6AAoBzQQHQDlgAaiA6Ac0EB0AJQDGogOgHJAA9EBUA5oIDoAygENRAdAOaCB6AAoBzQQHQDlgAaiA6Ac0EB0AJQDGogOgHJAA9EBUA5oIPr/AXBAdBuKvsvzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00c543c710>"
      ]
     },
     "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",
    "# test the model on a batch of test images\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": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "## TODO: change the name to something uniqe for each new model\n",
    "\n",
    "\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(model.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 chosed Adam optimization function and SmoothL1 loss function.\n",
    "I knew i should choose either MSE or SmoothL1 or any regression loss function as it's a regression not a classification problem, so at first I chose MSE but it didn't give a good results, it didnt converge even I when I trained the model with many epochs, I read online that MSE is good with normally distributed inputs which is not the case here, I also read that it's sensitive to the outliers as it squares errors and make them larger. so I went with SmoothL1Loss and the loss was quickly below 1 and converged so quickly with good results in testing!\n",
    "\n",
    "for the optimization function: I went first with RMSprop with a momentum of 0.9 and Adam, Adam worked better and converged faster.\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 started with a big model with 5 convolution layer and 5 Maxpooling layers and 4 Batch normalization after the pooling, so it was conv-pool-BatchNormalization. and after that I put 5 layers with tanh activation functions as I believed it'd be better because we need the output to be in the range [-1, 1]. but it didn't work well and it was so slow \n",
    "\n",
    "I replaced the tanh with relu in all layers except the last layer which was with tanh layer to have the [-1, 1] output. so I decided to get rid off the tanh and replace it with a linear activation function in the output layer, it seemed to work but the model was so slow in training and It produced a large saved model in size. so again I modified the model couple of times and reduced it to only 3 conv. layers with only pooling and bathnormalization after the second and the third layers, (I thought the input was already normalized, so no big need for the normalization after the first conv. layer), for the linear layers I reduced them to 4 layers with a smaller number of neurons to avoid the large model size and the data overfitting. It worked nicely and the model converged with no overfitting."
   ]
  },
  {
   "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**: By experiment, I trained on a GPU to save time, the training in the workspace was slow and not very good whe you try to attempy many times, so on the GPU environment I was free to train for more epochs and stop it when I see the loss value converging (or falling in a local minima) in the final version of the model it converged after 10 epochs but I continued training to 30 epochs anyway.\n",
    "\n",
    "for  the batch size: I tried couple of things from 32 to 128 and it worked nicely in both 32 and 128, but I went with 128 to avoid noisy loss results."
   ]
  },
  {
   "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": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.04556986  0.02656803  0.02240152  0.05583742 -0.03814065]\n",
      " [-0.07810125  0.02533447 -0.00922998  0.03196966  0.01861695]\n",
      " [ 0.03756156  0.0802031   0.00109466  0.08582655 -0.01198297]\n",
      " [-0.08171423  0.05720215 -0.04376685 -0.05608023  0.06039109]\n",
      " [-0.04055027 -0.02043107  0.03052038  0.05268964  0.00729574]]\n",
      "(5, 5)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fa0aae98940>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa0ab035860>"
      ]
     },
     "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.conv1.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": 51,
   "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 0x7f00c51ccac8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "##TODO: load in and display any image from the transformed test dataset\n",
    "\n",
    "## TODO: Using cv's filter2D function,\n",
    "## apply a specific set of filter weights (like the one displayed above) to the test image\n",
    "\n",
    "import cv2\n",
    "from random import randrange\n",
    "\n",
    "\n",
    "weights1 = model.conv1.weight.data\n",
    "\n",
    "f1 = weights1.numpy()\n",
    "\n",
    "\n",
    "it = iter(test_loader)\n",
    "batch = it.next()['image']\n",
    "\n",
    "index = randrange(32)\n",
    "\n",
    "kernel = np.squeeze(f1[25, :])\n",
    "\n",
    "img = np.squeeze(batch[index].numpy())\n",
    "dst = cv2.filter2D(img, -1, kernel)\n",
    "\n",
    "plt.subplot(121), plt.imshow(img, cmap='gray')\n",
    "plt.subplot(122), plt.imshow(dst, cmap='gray')\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**: I think it detects the edge well, so it's probably a high pass filter."
   ]
  },
  {
   "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
}