f-image-interpolation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XRbLC7wcIcK4"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/apssouza22/cnn-for-devs/blob/master/f-image-interpolation.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1oZyY8beAwWo"
   },
   "source": [
    "Image interpolation with Autoencoders\n",
    "======\n",
    "\n",
    "\n",
    "We are going to learn how to work with autoencoders to generate Latent Space/ feature map and from there do some nice things"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "iGWf_LzX6ZoM"
   },
   "source": [
    "Autoencoder Definition\n",
    "-----------------------\n",
    "AutoEncoder is an unsupervised Artificial Neural Network that attempts to encode the data by compressing it into the lower dimensions(dimensionality reduction) and then decoding the data to reconstruct the original input.\n",
    "\n",
    "<img src=\"https://miro.medium.com/max/700/1*AJ_zWZundfZ2-11eZUw5GA.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "QeU9mB0_AwWs"
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import os\n",
    "\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F"
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "Parameter Settings\n",
    "-------------------\n"
   ],
   "metadata": {
    "collapsed": false,
    "id": "8hYScmv6uzoP"
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    ""
   ],
   "metadata": {
    "id": "kt9rwk6M3MJn"
   }
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [],
   "source": [
    "num_classes = 10\n",
    "num_epochs = 30\n",
    "batch_size = 128\n",
    "learning_rate = 0.001\n",
    "use_gpu = True\n",
    "img_size = 64\n"
   ],
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "id": "H81EKwOFuzoP"
   }
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "flbWQTlZAwWu"
   },
   "source": [
    "MNIST Data Loading\n",
    "-------------------\n",
    "\n",
    "MNIST images show digits from 0-9 in 28x28 grayscale images. We normalize and center them around 0, which gives a slight performance boost during training.\n",
    "We create both a training set and a test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "6uK2neSDAwWv",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 431,
     "referenced_widgets": [
      "9b0df9ed02504bebb5e4542bce0873b8",
      "d21783794cbc43dc86a4f13bb915d1f5",
      "4dac8eab4bfe4dd4b90c1bf717df9849",
      "3224cfe2ad004c6c8eb6c1de18feb0ff",
      "4af928d68ad74bc09b76fe05767e0883",
      "5043854612e7423ba9c871097262f657",
      "a7092fb7359e4cbb8fbbcc7642ecac13",
      "873df739019b448790c228de438060ea",
      "c74be2c9e4b84e75a339c8980f1080ac",
      "49bf8feacdeb46c8bda597c9674f5259",
      "9c5df061677648cb8e063d7231eb2172",
      "841658fd789745ce87b10183b2aa4870",
      "9fdce451f0ec49688a5ccffac6e0e681",
      "48f467c3725f47d482f2b0bedee4ca4c",
      "0f2cbd91676544c199e45ef213eb5607",
      "26abe3d18d2045e8afe6337cb7233b76",
      "5a5462dc0fd04d989fd22eb4ba161f3d",
      "d1f2c8a5447d4e3c947a0c4b8940f75c",
      "310d3b0a1c39472fa31b230978bd1108",
      "3f79dd49b2e34e83befeb1e2a06ebe16",
      "24dea4c154894c2388689bf79a2a9ecc",
      "56cf5aaff6474df38696a506dbfb7beb",
      "c491dfe6b06e4c3b9d21723e2ab0d15f",
      "c87dd2f625004723a59ab5dc179171ba",
      "2a47c4a0349944dba4f20ef539b3268f",
      "2f82e7722d33444fba3c683ad867465f",
      "2bf9d03c892342498dc792eee1624f80",
      "fc60f6b4308a40f9ae9ba4024ff7b97f",
      "fa7e3214ac5147f198a35024a3d205f2",
      "b57754f146fa4f11a274ffee1bb84669",
      "ddc79e413a5043bcabd13cfbe4ce742c",
      "420d08e2583a447382b6ad3b4e3e4115",
      "d325c448bcee4d74bc708de3cdfbda62",
      "1c5c1ccf2c094dcd9e31fc46d0a9c276",
      "8451c1e4e64c4e3b9571f440ed007952",
      "cc66190da1f443758a9f51b740f12efa",
      "00f413a57e6b485fb2f14691a2eaba79",
      "8558147d260d4bf2b211096051735a09",
      "6c3ffb76ce33455aac5bb15093499c07",
      "f36b38e905cf460ca914402592effd8a",
      "e3761fbe404240d4bb9ca88ce178e8bc",
      "afab5e70ba514100a01bd8d37a07e8d2",
      "2e06c60ff04e43e69f295655777d9b3b",
      "a8a3d3062fb24ce1a407f0a03ded624e"
     ]
    },
    "outputId": "1cff38ce-4b1e-4fd7-9754-8e5f7435d71c"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz\n",
      "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz to ./data/MNIST/MNIST/raw/train-images-idx3-ubyte.gz\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "  0%|          | 0/9912422 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "9b0df9ed02504bebb5e4542bce0873b8"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Extracting ./data/MNIST/MNIST/raw/train-images-idx3-ubyte.gz to ./data/MNIST/MNIST/raw\n",
      "\n",
      "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz\n",
      "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz to ./data/MNIST/MNIST/raw/train-labels-idx1-ubyte.gz\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "  0%|          | 0/28881 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "841658fd789745ce87b10183b2aa4870"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Extracting ./data/MNIST/MNIST/raw/train-labels-idx1-ubyte.gz to ./data/MNIST/MNIST/raw\n",
      "\n",
      "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz\n",
      "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz to ./data/MNIST/MNIST/raw/t10k-images-idx3-ubyte.gz\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "  0%|          | 0/1648877 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "c491dfe6b06e4c3b9d21723e2ab0d15f"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Extracting ./data/MNIST/MNIST/raw/t10k-images-idx3-ubyte.gz to ./data/MNIST/MNIST/raw\n",
      "\n",
      "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz\n",
      "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz to ./data/MNIST/MNIST/raw/t10k-labels-idx1-ubyte.gz\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "  0%|          | 0/4542 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "1c5c1ccf2c094dcd9e31fc46d0a9c276"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Extracting ./data/MNIST/MNIST/raw/t10k-labels-idx1-ubyte.gz to ./data/MNIST/MNIST/raw\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import torchvision.transforms as transforms\n",
    "from torch.utils.data import DataLoader\n",
    "from torchvision.datasets import MNIST\n",
    "\n",
    "img_transform = transforms.Compose([\n",
    "    transforms.ToTensor(),\n",
    "    transforms.Normalize((0.5,), (0.5,))\n",
    "])\n",
    "\n",
    "train_dataset = MNIST(root='./data/MNIST', download=True, train=True, transform=img_transform)\n",
    "train_dataloader = DataLoader(train_dataset, batch_size=batch_size, shuffle=True)\n",
    "\n",
    "test_dataset = MNIST(root='./data/MNIST', download=True, train=False, transform=img_transform)\n",
    "test_dataloader = DataLoader(test_dataset, batch_size=batch_size, shuffle=True)\n",
    "\n",
    "full_dataset = torch.utils.data.ConcatDataset([train_dataset, test_dataset])\n",
    "full_dataloader = DataLoader(full_dataset, batch_size=batch_size, shuffle=False)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "Autoencoder consists of an Encoder and a Decoder model"
   ],
   "metadata": {
    "collapsed": false,
    "id": "t8MX8KsduzoR"
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "fkY2beRZAwWw",
    "outputId": "f94c52d8-d717-4675-c564-d0b208722630"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Number of parameters: 396171\n"
     ]
    }
   ],
   "source": [
    "# Model responsible for generating our Latent space.\n",
    "#Latent space, Typically it is a 100-dimensional hypersphere with each variable drawn from a Gaussian distribution with a mean of zero and a standard deviation of one\n",
    "class Encoder(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(Encoder, self).__init__()\n",
    "        self.conv1 = nn.Conv2d(in_channels=1, out_channels=img_size, kernel_size=4, stride=2, padding=1) # out: c x 14 x 14\n",
    "        self.conv2 = nn.Conv2d(in_channels=img_size, out_channels=img_size*2, kernel_size=4, stride=2, padding=1) # out: c x 7 x 7\n",
    "        self.fc = nn.Linear(in_features=img_size * 2 * 7 * 7, out_features=num_classes)\n",
    "            \n",
    "    def forward(self, x):\n",
    "        x = F.relu(self.conv1(x))\n",
    "        x = F.relu(self.conv2(x))\n",
    "        x = x.view(x.size(0), -1) # flatten batch of multi-channel feature maps to a batch of feature vectors\n",
    "        x = self.fc(x)\n",
    "        return x\n",
    "\n",
    "# Model responsible for reconstruct the image form our Latent space.\n",
    "class Decoder(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(Decoder, self).__init__()\n",
    "        self.fc = nn.Linear(in_features=num_classes, out_features=img_size*2*7*7)\n",
    "        self.conv2 = nn.ConvTranspose2d(in_channels=img_size * 2, out_channels=img_size, kernel_size=4, stride=2, padding=1)\n",
    "        self.conv1 = nn.ConvTranspose2d(in_channels=img_size, out_channels=1, kernel_size=4, stride=2, padding=1)\n",
    "            \n",
    "    def forward(self, x):\n",
    "        x = self.fc(x)\n",
    "        x = x.view(x.size(0), img_size * 2, 7, 7) # unflatten batch of feature vectors to a batch of multi-channel feature maps\n",
    "        x = F.relu(self.conv2(x))\n",
    "        x = torch.tanh(self.conv1(x)) # last layer before output is tanh, since the images are normalized and 0-centered\n",
    "        return x\n",
    "    \n",
    "class Autoencoder(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(Autoencoder, self).__init__()\n",
    "        self.encoder = Encoder()\n",
    "        self.decoder = Decoder()\n",
    "    \n",
    "    def forward(self, x):\n",
    "        latent = self.encoder(x)\n",
    "        x_recon = self.decoder(latent)\n",
    "        return x_recon\n",
    "    \n",
    "autoencoder = Autoencoder()\n",
    "\n",
    "device = torch.device(\"cuda:0\" if use_gpu and torch.cuda.is_available() else \"cpu\")\n",
    "autoencoder = autoencoder.to(device)\n",
    "\n",
    "#The model’s parameters that need to be trained.\n",
    "num_params = sum(p.numel() for p in autoencoder.parameters() if p.requires_grad)\n",
    "print('Number of parameters: %d' % num_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "oE5kxqxuAwWx"
   },
   "source": [
    "Train Autoencoder\n",
    "--------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ErtOYe8SAwWy",
    "outputId": "1e5398ee-a1a2-4833-b6d7-51c200abe874",
    "scrolled": true
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Training ...\n",
      "Epoch [1 / 30] average reconstruction error: 0.126396\n",
      "Epoch [2 / 30] average reconstruction error: 0.073839\n",
      "Epoch [3 / 30] average reconstruction error: 0.066091\n",
      "Epoch [4 / 30] average reconstruction error: 0.061884\n",
      "Epoch [5 / 30] average reconstruction error: 0.059137\n",
      "Epoch [6 / 30] average reconstruction error: 0.057111\n",
      "Epoch [7 / 30] average reconstruction error: 0.055590\n",
      "Epoch [8 / 30] average reconstruction error: 0.054424\n",
      "Epoch [9 / 30] average reconstruction error: 0.053433\n",
      "Epoch [10 / 30] average reconstruction error: 0.052620\n",
      "Epoch [11 / 30] average reconstruction error: 0.051919\n",
      "Epoch [12 / 30] average reconstruction error: 0.051311\n",
      "Epoch [13 / 30] average reconstruction error: 0.050825\n",
      "Epoch [14 / 30] average reconstruction error: 0.050381\n",
      "Epoch [15 / 30] average reconstruction error: 0.049935\n",
      "Epoch [16 / 30] average reconstruction error: 0.049573\n",
      "Epoch [17 / 30] average reconstruction error: 0.049201\n",
      "Epoch [18 / 30] average reconstruction error: 0.048901\n",
      "Epoch [19 / 30] average reconstruction error: 0.048631\n",
      "Epoch [20 / 30] average reconstruction error: 0.048366\n",
      "Epoch [21 / 30] average reconstruction error: 0.048140\n",
      "Epoch [22 / 30] average reconstruction error: 0.047862\n",
      "Epoch [23 / 30] average reconstruction error: 0.047635\n",
      "Epoch [24 / 30] average reconstruction error: 0.047441\n",
      "Epoch [25 / 30] average reconstruction error: 0.047294\n",
      "Epoch [26 / 30] average reconstruction error: 0.047147\n",
      "Epoch [27 / 30] average reconstruction error: 0.046983\n",
      "Epoch [28 / 30] average reconstruction error: 0.046769\n",
      "Epoch [29 / 30] average reconstruction error: 0.046689\n",
      "Epoch [30 / 30] average reconstruction error: 0.046529\n"
     ]
    }
   ],
   "source": [
    "os.mkdir(\"assets\")\n",
    "\n",
    "ENCODER_MODEL_PATH=\"assets/encoder.pth\"\n",
    "DECODER_MODEL_PATH=\"assets/decoder.pth\"\n",
    "\n",
    "optimizer = torch.optim.Adam(params=autoencoder.parameters(), lr=learning_rate, weight_decay=1e-5)\n",
    "\n",
    "# set to training mode\n",
    "autoencoder.train()\n",
    "\n",
    "train_loss_avg = []\n",
    "\n",
    "print('Training ...')\n",
    "for epoch in range(num_epochs):\n",
    "    train_loss_avg.append(0)\n",
    "    num_batches = 0\n",
    "    \n",
    "    for image_batch, _ in train_dataloader:\n",
    "        image_batch = image_batch.to(device)\n",
    "        image_batch_recon = autoencoder(image_batch)\n",
    "      \n",
    "        # reconstruction error\n",
    "        loss = F.mse_loss(image_batch_recon, image_batch)\n",
    "        \n",
    "        # backpropagation\n",
    "        optimizer.zero_grad()\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        \n",
    "        train_loss_avg[-1] += loss.item()\n",
    "        num_batches += 1\n",
    "    \n",
    "    torch.save(autoencoder.encoder.state_dict(), ENCODER_MODEL_PATH)\n",
    "    torch.save(autoencoder.decoder.state_dict(), DECODER_MODEL_PATH)\n",
    "\n",
    "    train_loss_avg[-1] /= num_batches\n",
    "    print('Epoch [%d / %d] average reconstruction error: %f' % (epoch+1, num_epochs, train_loss_avg[-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "D0dFn3Z3AwWy"
   },
   "source": [
    "Plot Training Curve\n",
    "--------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "LX8glP0EAwWz",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 282
    },
    "outputId": "11e7f3ca-4b80-4491-81a2-41c024076c09"
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": "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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.ion()\n",
    "\n",
    "fig = plt.figure()\n",
    "plt.plot(train_loss_avg)\n",
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('Reconstruction error')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "SzgXndbGAwW0"
   },
   "source": [
    "Evaluate on the Test Set\n",
    "-------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "4fwptU4XAwW0",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "outputId": "ef5e7042-98f0-4263-c659-61e00e877548"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "average reconstruction error: 0.047870\n"
     ]
    }
   ],
   "source": [
    "# set to evaluation mode\n",
    "autoencoder.eval()\n",
    "\n",
    "test_loss_avg, num_batches = 0, 0\n",
    "for image_batch, _ in test_dataloader:\n",
    "    \n",
    "    with torch.no_grad():\n",
    "\n",
    "        image_batch = image_batch.to(device)\n",
    "\n",
    "        # autoencoder reconstruction\n",
    "        image_batch_recon = autoencoder(image_batch)\n",
    "\n",
    "        # reconstruction error\n",
    "        loss = F.mse_loss(image_batch_recon, image_batch)\n",
    "\n",
    "        test_loss_avg += loss.item()\n",
    "        num_batches += 1\n",
    "    \n",
    "test_loss_avg /= num_batches\n",
    "print('average reconstruction error: %f' % (test_loss_avg))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "ZbNtBp8XIcLD"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import torchvision.utils\n",
    "plt.ion()\n",
    "\n",
    "# Util function to display the images\n",
    "def to_img(x):\n",
    "    x = 0.5 * (x + 1)\n",
    "    x = x.clamp(0, 1)\n",
    "    return x\n",
    "\n",
    "def show_image(img):\n",
    "    img = to_img(img)\n",
    "    npimg = img.numpy()\n",
    "    plt.imshow(np.transpose(npimg, (1, 2, 0)))\n",
    "\n",
    "def visualise_output(images, model):\n",
    "    with torch.no_grad():\n",
    "\n",
    "        images = images.to(device)\n",
    "        images = model(images)\n",
    "        images = images.cpu()\n",
    "        images = to_img(images)\n",
    "        np_imagegrid = torchvision.utils.make_grid(images[1:50], 10, 5).numpy()\n",
    "        plt.imshow(np.transpose(np_imagegrid, (1, 2, 0)))\n",
    "        plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "PGOZhBrEAwW1"
   },
   "source": [
    "Visualize Reconstructions\n",
    "--------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "S1u5HgMJAwW1",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 460
    },
    "outputId": "358dcd75-be06-4250-ee6b-80512bdd084c"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Original images\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": "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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Autoencoder reconstruction:\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": "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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "autoencoder.eval()\n",
    "\n",
    "images, labels = iter(test_dataloader).next()\n",
    "\n",
    "# First visualise the original images\n",
    "print('Original images')\n",
    "show_image(torchvision.utils.make_grid(images[1:50],10,5))\n",
    "plt.show()\n",
    "\n",
    "# Reconstruct and visualise the images using the autoencoder\n",
    "print('Autoencoder reconstruction:')\n",
    "visualise_output(images, autoencoder)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "Wgg-LOtFw7WO"
   },
   "outputs": [],
   "source": [
    "# Group all digits in a map ditits[i]=[...]\n",
    "digits = [[] for _ in range(10)]\n",
    "for img_batch, label_batch in test_dataloader:\n",
    "    for i in range(img_batch.size(0)):\n",
    "        digits[label_batch[i]].append(img_batch[i:i+1])\n",
    "\n",
    "    if sum(len(d) for d in digits) >= 1000:\n",
    "        break;\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8v6ACt9AAwW1"
   },
   "source": [
    "Interpolate in Latent Space\n",
    "----------------------------\n",
    "\n",
    "The latent representation of autoencoders have been studied in the context of enabling interpolation between data points by decoding convex combinations of latent vectors\n",
    "\n",
    "<img src=\"https://miro.medium.com/max/480/1*vEZE5VcjUr5RUbt_OWfR_w.gif\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "PRsREYNaAwW1",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 390
    },
    "outputId": "ee19aacd-bb26-4816-ddcf-43f60b63dc4d"
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 1080x432 with 10 Axes>"
      ],
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0IAAAF1CAYAAADFvlpIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nO3de5xWZb3///dHDnIOkEBEFEQ8oKZ+NXTnId1mqZWHraVWajsLd2qiHc2yKNPcbbPc5c/vxlTUPG8rKdNUpNSfZkCagqggAgLDSc4nOXh9/7gXea91XTP3+Z61Zr2ej8c8mOsz19xzzT1v1j3XrHVdy5xzAgAAAIA82aG9BwAAAAAAzcZECAAAAEDuMBECAAAAkDtMhAAAAADkDhMhAAAAALnDRAgAAABA7jARAgAAAJA7mZsImdlcM/tInR/zGDNbUEH/z5vZM/UcQyUa8RygPsgn+Uwrskk204psks00I58dO5+ZmwihemZ2mZktNrM1Znarme3YRt/jzOxVM9tgZpPNbPdmjhX5U24+zayrmf1vdGB2ZnZMk4eKnKkgm4eb2eNmtsLMlpnZA2Y2uNnjRX5UkM1RZjbVzFZGb0+Y2ahmjxf5UsnvnUWf873otb0pEy8mQjlhZh+TdLmk4yTtLmkPST9ope8ASb+RdKWk/pKmSrqvOSNFHlWSz8gzkj4naXHjR4c8qzCb/SSNlzQs6rtW0m2NHyXyqMJsLpJ0hgqv6QMkTZR0bxOGiZyq4nVdZjZC0qcktTR8gJHMToTMbLSZPWdmq8ysxcx+aWZdiz7uzOxCM5tlZmvN7CozG2Fmz0Yz0/uL+0efc4WZLY/+0vzZovpOZjYx+ry/SRqR+LwbzOyt6OPTzOyoEmPfxcw2mln/otrB0dfuEo3zSTN7O6rdZWZ9a3zKzpN0i3NuhnNupaSrJH2+lb7/JmmGc+4B59wmSeMkHWhm+9Q4htwgnxUrO5/Ouc3OuZ87556RtK3Gr5s7ZLNilWTzkei4ucY5t0HSLyUdUePXzw2yWbFKsrnKOTfXOeckmQrHzj1r/Pq5Qj4rVsnvndvdKOlbkjbX+LXLltmJkAr/iS9T4S8b/6LCjPPCRJ+PSTpE0uGSvqnCX+o+J2mopP0lnV3Ud+fosYao8MMbb2Z7Rx+7UdImSYMlfSF6KzZF0kEq/KXlbkkPmFm31gbunFsk6TlJpxeVPyPpf51zW1Q4SP1Y0i6S9o3GOy70WGb2meg/ZWtvu0Vd95P0j6JP/YekQWa2U+BhY32dc+slvRHVUR7yqYblE7Uhm2paNo+WNKOMfiggm2psNs1sVfR9/0LSNa31QxD5VOPyaWafkvSOc+6PrX0fDeGcy9SbpLmSPhKoXyrpt0VtJ+mIovY0Sd8qav9U0s+j94+RtFVSz6KP36/CpWGdJG2RtE/Rx66R9EwbY1wp6cAS38cXJT0ZvW+S3pJ0dCt9T5X0QqnnoMTXe0PSCUXtLtFzNCzQ9xZJ1yZq/7+kz7f3zz/tb+Sz8flMfN4CSce09889C29ks+nZ/ICkFZKOau+ffdrfyGbTs9lThV/gP97eP/ssvJHPpvze2VvSrO0fq+brVfvWWRllZntJul7SoZJ6SOqsQuiKLSl6f2OgvXNRe6UrnPnYbp4KM+P3R4/9VuJjxWP5uqTzo/5OUh8VZvlteVDSL6ywkHYvSe9Kejp6vEGSbpB0lArh2EGFkNdiXTSu7ba/v7aMvtv7h/oigHxWrJJ8ogZks2IVZ9PM9pT0iKSxzrmna/z6uUE2K1bVcdM5t97M/q+kZWa2r3NuaY3jyAXyWbFK8jlO0p3Oubk1fs2KZfnSuJskvSpppHOuj6QrVJjhVqufmfUsau+mwuLCZSrM2ocmPiZJiq7L/KakT0vq55zrK2l1qbG4wvWSj0k6U4XTk/e6aBqswszfSTog+t4+19rjmdlnzWxdG2/bxzpD0oFFn3qgpCXOubcDDxvrGz0vI8QlHpUgn2pYPlEbsqnGZdMKO2w+Iekq59ydbX0v8JBNNe24uYMKv8wPKaMvCsinGpbP4yRdYoUd5hZH3/v9Zvattr6nesjyRKi3pDWS1llhEf+X6/CYP7DC1rxHSfqEpAecc9tU2EFtnJn1sMJ2k+clxrFVheB2NrPvyT+b0pq7JZ2rwk4udycec52k1WY2RNI3WnsA59xdzrlebbzNj7reIel8K2yh2VfSdyVNaOVhfytpfzM7Pbrm9HuSXnLOvVrm9wXyKalh+ZSZ7Vh0PXRXM+tmZrW8IOUJ2VRjshl9zScl/dI593/L/F7wHrKphmXzeCssju9kZn1UOLOxUtLMMr8vkE9JDXtdP06FNVQHRW+LJF2gwlqphsryROjrKsxo10q6WbVv77xYhYPCIkl3SfqPol/8L5bUK+ozQfHtUP8k6VFJr6tw6nKT4qcz2zJR0khJi51zxQvKfiDp/6gww39Yhf8QNXHOPSrpJ5ImS5ofjfX72z9uZjMs2rHEObdMhQV1V6vwnBwm6axax5Az5LMCleQz8poKlxkMUeF73KjC9pwojWxWoMJsflGFLWLHFf+FtNYx5AjZrECF2ewr6Z7o67+hwlUeJ7jCzrAoD/msQIW/d77tnFu8/U2FjSlWOucafvy0986KAQAAAEA+ZPmMEAAAAABUhYlQA5nZI60sJLuivccGkE+kFdlEWpFNpBn5rByXxgEAAADInZrOCJnZCWb2mpnNNrPL6zUooB7IJ9KKbCLNyCfSimyi3qo+I2RmnVTYseJ4Fe7uPkXS2c65V9r4HE4/QZLknGvoVseV5pNsoshy59z7G/XgHDtRC46dSDGOnUit1o6dtZwRGi1ptnNujnNus6R7JZ1Sw+MB9UQ+Ua15pbvUhGwizcgnqsWxE5lTy0RoiOL7li9Q4A7FZjbGzKaa2dQavhZQqZL5JJtoJxw7kWYcO5FWHDtRd50b/QWcc+MljZc4RYl0IZtIM/KJtCKbSDPyiUrUckZooaShRe1doxqQBuQTaUU2kWbkE2lFNlF3tUyEpkgaaWbDzayrpLMkTazPsICakU+kFdlEmpFPpBXZRN1VfWmcc26rmV0s6U+SOkm61Tk3o24jA2pAPpFWZBNpRj6RVmQTjdDUG6pyrSa2a/QWsJUimygyzTl3aHsPohj5xHYcO5FiHDuRWo3YPhsAAAAAMomJEAAAAIDcYSIEAAAAIHeYCAEAAADIHSZCAAAAAHKn6u2zUR6z0hv8NHPnPgAAAACcEQIAAACQQ0yEAAAAAOQOEyEAAAAAucNECAAAAEDusFlClXbYwZ9D7rnnnl7tpptuirUXLFjg9fnCF77g1bZt21bD6JBnoQ06BgwY4NU+85nPxNpLlizx+tx///1e7d13361hdIBvxx139GqDBg2KtTdu3Oj1Wb58uVdj8xnUU+i1PlkLHRM5TgLZwBkhAAAAALnDRAgAAABA7jARAgAAAJA7Na0RMrO5ktZK2iZpq3Pu0HoMKqs++clPerWjjjoq1g6t/bnmmmu82muvvVa/geVUXvPZubP/3/riiy/2at/4xjdKPlZo3dDkyZOrGxj+Ka/ZlKQePXp4tQsvvNCrjR07NtYOrf254IILvNqjjz7q1Vg3VJm85rNXr15e7XOf+5xXO/HEE2Pt1atXe32uu+46rzZ9+nSvxlqiyuQ1m5LUp08fr3bcccd5td69e8fab7zxhtcnlMW1a9d6tTzksx6bJRzrnPNXrALpQD6RVmQTaUY+kVZkE3XDpXEAAAAAcqfWiZCT9JiZTTOzMaEOZjbGzKaa2dQavxZQqTbzSTbRjjh2Is04diKtOHairmq9NO5I59xCMxso6XEze9U591RxB+fceEnjJcnMuFAbzdRmPskm2hHHTqQZx06kFcdO1FVNEyHn3MLo36Vm9ltJoyU91fZndQyhxbfvvPOOV0veeC30eSNHjvRqbJZQu7zmM3QDwF122cWrde3ateRjnX322V7tqaf8p5AbAFcmr9mUpP79+3u1j370o15t4MCBJR/r8ssv92ovvviiV2tpaSlzdJDyk8/kzaePOeYYr09y0w5J2m233WLt0PFv77339mpXXnmlV3viiSdi7TwsTq9FXrIp+TeaHjdunNfnzDPPLPl5a9as8fq89NJLXu3OO+/0an/4wx9i7dDvuVlX9aVxZtbTzHpvf1/SRyX521AA7YB8Iq3IJtKMfCKtyCYaoZYzQoMk/Tb6i0pnSXc75/x9S4H2QT6RVmQTaUY+kVZkE3VX9UTIOTdH0oF1HAtQN+QTaUU2kWbkE2lFNtEIbJ8NAAAAIHfqcUPVXAptejBjxgyvtnHjxli7U6dOXp/DDjvMqz388MNlfU0gacuWLV7t1VdfLatf0gEHHODV3v/+93u1xYsXlzk65N2mTZvK6pc83oUWpO+xxx5e7bLLLvNq3/72t0s+FpBcZC5JPXv29GpdunSJtZObLkjSsGHDvNqPfvQjr5Y8Ns+fP7/UMJETyTzuueeeXp8+ffp4te7du8faoQyHaqHX+969e8fav/71r70+W7du9WpZwhkhAAAAALnDRAgAAABA7jARAgAAAJA7rBGqo0WLFnm15I2sQjcT/NCHPuTVOnf2fzTlrOkAQmvJQtlcvXp1rB26Zjh0nfvBBx/s1R555JEKRog8Cx3HQuuG1q9fH2uH1mGEjqennXaaV/vxj38ca69cubLkOJE/3bp182rl3Dw9tEaiV69eXm3//ff3al//+tdj7dAaN9a05VMye6HX6JBkXkL57NGjh1fr16+fV/vP//zPWHv58uVenz/+8Y9eLUs3BuaMEAAAAIDcYSIEAAAAIHeYCAEAAADIHSZCAAAAAHKHzRLqaOHChV5t6dKlsfbAgQO9PqEF6ckbYklsloDyhBb3zpw506vNmTMn1t5rr728PqEcnnTSSV7tT3/6U6ydpYWSaK7Qwt3QDXmTN5rcYQf/73Z77723Vwvd8Hf33XePtdksAZJ/rExu0CFJq1at8mrJY+ebb77p9fnwhz/s1YYOHerVksfT73//+14f8ppPmzdvjrVnzJjh9Rk+fLhXS/4uOm3aNK/PgQce6NVGjx7t1fr27Rtrhzbz+POf/+zV1q1b59XSijNCAAAAAHKHiRAAAACA3GEiBAAAACB3Sk6EzOxWM1tqZtOLav3N7HEzmxX969+FCWgC8om0IptIM/KJtCKbaKZyNkuYIOmXku4oql0uaZJz7lozuzxqf6v+w8uW5MI2yb8DdadOnbw+O+20k1cLLVJfs2ZNDaPrsCaIfJYUWoz+0ksvxdqhTTtCd7LeZ599vFoy12yWIIlsBoU285gyZYpXmzVrVqzdq1cvr8/IkSO9WujYue+++8ba//jHP8oaVwc3QeQzJrQpwcMPP+zVnn766Vh72bJlXp9QNkObJey4446xdp8+fcoaVwc3QWTTex0NHSfnz5/v1SZPnhxrL1++3OvzkY98xKslN5WRpJ133jnW7t27d3iwGVbyjJBz7ilJKxLlUyTdHr1/u6RT6zwuoCzkE2lFNpFm5BNpRTbRTNWuERrknGuJ3l8saVCdxgPUA/lEWpFNpBn5RFqRTTREzfcRcs45M2v1mgIzGyNpTK1fB6hGW/kkm2hPHDuRZhw7kVYcO1FP1U6ElpjZYOdci5kNlrS0tY7OufGSxktSW8HtCLZt2+bVQtcOJ3Xt2tWrhW529dhjj1U3sPwpK595yubGjRu9WvKGlZ/85Ce9PqGbWIaucw/1Q1Duj53lrhFKrpU4/PDDvT6hY24oi8ljbA7XA5UrV8dOM4u1582b5/W57777vFpyzU6PHj28PqF1GSHJtcWrV68u6/NyKHfHzuSx7OWXX/b6hG5mmlxPHjrehW6yunbtWq+WvEH1kiVLvD6h9fFZUu1vLxMlnRe9f56kh+ozHKAuyCfSimwizcgn0opsoiHK2T77HknPSdrbzBaY2fmSrpV0vJnNkvSRqA00HflEWpFNpBn5RFqRTTRTyUvjnHNnt/Kh4+o8FqBi5BNpRTaRZuQTaUU20Uxc2A8AAAAgd2reNQ7vCS1IS26WEOoTusnqkCFD6jcw5F7yxr6SvzC4c2f/cFDuJghsloBybdmyxavNmTPHqyUX6YZu9hdapB5S7sJ15FsoJ+VkZ8CAAV4t9Bqe3JxBkjZs2BBrh47VyKfkDVXnzp3r9Vm/fn3Jz0vetFcKZ3bQIH9H8uRr+wsvvOD1CW1akyX89gIAAAAgd5gIAQAAAMgdJkIAAAAAcoeJEAAAAIDcYbOEBluxYkXJPqEFlP3792/EcJBToQXqyUWWoc0SQtlMLsRsrQaEbN261auFFvz26tUr1t5jjz28PqGNZkJ3OWezBIQkNy9KblzQmi5dusTau+22m9cntBg9tFnSokWLSvZBPiWPlWvWrPH6hF57k6/boc0SPvzhD3u1nj17erWNGzfG2s8++6zXJ+uZ5YwQAAAAgNxhIgQAAAAgd5gIAQAAAMgd1gjVUeg6yXKuOQ7djHLgwIF1GRMglXcdcWiNUEgor9xQFbUI3ZAveTzdaaedvD6hNULlPBYQUu5ax+Sx88ADD/T69O3bt6zHSt7YOus3p0T9JI9b5R7Hkvnca6+9vD6f/OQnvVpoLdGyZcti7RkzZpQcZ9bw2wsAAACA3GEiBAAAACB3mAgBAAAAyJ2SEyEzu9XMlprZ9KLaODNbaGYvRm8nNXaYQBj5RFqRTaQZ+URakU00UzmroydI+qWkOxL1nznnrqv7iDqYF154IdYO3dgyeXM2Sdpzzz29WnIBXNYXqNXJBJHPkkJZWblyZck+oRuqdu3atX4D69gmiGxWLblwN3ST6dAGH++8845XW716df0G1nFMEPmsSvLGk6GbU/bu3durhW4m/OSTT8ba3JxaEtmsSffu3WPtf//3f/f67LPPPmU91l//+tdYO3Tz69DvCVn6/bTkGSHn3FOSVjRhLEDFyCfSimwizcgn0opsoplqWSN0sZm9FJ3C7Fe3EQH1QT6RVmQTaUY+kVZkE3VX7UToJkkjJB0kqUXST1vraGZjzGyqmU2t8msBlSorn2QT7YBjJ9KMYyfSimMnGqKqiZBzbolzbptz7l1JN0sa3Ubf8c65Q51zh1Y7SKAS5eaTbKLZOHYizTh2Iq04dqJRyruVfIKZDXbOtUTN0yRNb6t/noUWliXtsIM/H915550bMZxcIJ++UMaGDBkSa3fr1q2szwstguRu6OUhm2GhDWOOPPLIWDuZVymcz9BmCcm7oyOMfPpC2TzxxBNj7cMOO8zrE9rIY8OGDV7txRdfjLWztMi8mchmWGjzonPPPbfNtuRvRiNJmzZt8moPPPBArL1x40avT9YzW3IiZGb3SDpG0gAzWyDp+5KOMbODJDlJcyVd0MAxAq0in0grsok0I59IK7KJZio5EXLOnR0o39KAsQAVI59IK7KJNCOfSCuyiWaqZdc4AAAAAMgkJkIAAAAAcqeqzRIQFrq7bnLTg9Di3pC+ffuWfPysL1BD84QW7h500EGxdmhRcMjKlSu9GpsloBa9e/f2ameeeWasHVrcGzoGvv76616tnE1rgNBr+MiRI73ad7/73Vi7R48eXp93333Xq73yyitebeHChbE2r+toTadOnbzapz71Ka929dVXx9rdu3f3+oTyOX26v//E008/HWuHNqPJemY5IwQAAAAgd5gIAQAAAMgdJkIAAAAAcoc1Qg2WvKZzy5YtXp/Q2ozQzS1D1y8D5QhdW7zXXnvF2uXmK5ThrF8jjPbVs2dPrzZixIhYO5TP0Nq0N954w6tt3bq1htEhL0JrKQ844ACvFrq5b1LoODl58mSvlrzJKsdSbJdcU96vXz+vzyc+8QmvFjqeJoVu7nvfffd5teSa4NDaoqzjjBAAAACA3GEiBAAAACB3mAgBAAAAyB0mQgAAAAByh80SGmzu3Lmx9qpVq7w+oZuxde3a1aslF3JyE0uUK7QIOLnoMbQIMnQD4OXLl9dvYMidUKZCi8+TC4NDi8g3b97s1R544AGvxrES5ejTp49XO/LII71a8ua+oWzOmjXLq/3iF7/wamQTrUlupLXnnnt6fZKbykj+5kihzWImTJjg1W666Savlod8ckYIAAAAQO4wEQIAAACQO0yEAAAAAOROyYmQmQ01s8lm9oqZzTCzsVG9v5k9bmazon/9Oz0BDUY+kVZkE2lFNpFm5BPNVM5mCVslfc0593cz6y1pmpk9LunzkiY55641s8slXS7pW40bavqFFkzOnz8/1g4tNN955529WmgDhaFDh8bas2fPrnSIHRH5LENogXpyc4TQoshQphcuXOjVzKyG0XVYZDMguZBXkg4//HCvljwGhvIZyuKUKVNqGF1ukE35m8h88IMf9PqMHj3aqyWPi6tXr/b6XH/99V5t6dKllQ4xr3KXz9BxMbmJzMknn+z1GTRokFfbsmVLrD19+nSvz1VXXeXV1q9fX3KcHVHJM0LOuRbn3N+j99dKmilpiKRTJN0edbtd0qmNGiTQGvKJtCKbSCuyiTQjn2imirbPNrNhkg6W9LykQc65luhDiyX509LC54yRNKb6IQLlqTSfZBPNwrETaUU2kWbkE41W9mYJZtZL0oOSLnXOrSn+mCucJ/avoSl8bLxz7lDn3KE1jRRoQzX5JJtoBo6dSCuyiTQjn2iGss4ImVkXFcJ4l3PuN1F5iZkNds61mNlgSVz8GrBhw4ZYe926dWV9Xvfu3b1aci0Ra4QKyGdpyZtTSn6eQut8Qjdie+ONN7xaaC0RyGZI3759vdrpp5/u1ZI3lU5e9y5Jf/zjH73a22+/XcPo8oNs+lm88MILvT577723V0uuV5s6darX5w9/+EPJz0Pr8pbP0O98Z5xxRqx9zjnneH1Cx9NVq1bF2t/85je9PtwY/T3l7Bpnkm6RNNM5V7z6b6Kk86L3z5P0UP2HB7SNfCKtyCbSimwizcgnmqmcM0JHSDpH0stm9mJUu0LStZLuN7PzJc2T9OnGDBFoE/lEWpFNpBXZRJqRTzRNyYmQc+4ZSa3tjXtcfYcDVIZ8Iq3IJtKKbCLNyCeaqezNEgAAAACgo6ho+2y0LbRgPLnYfMcddyzrsUKLKkML14FyDBgwwKslFwGHbroa2twjdMPK5M1ZgdYMHz7cqw0bNsyrJW92Gbpp5QMPPODVOE6iXPvtt1+sfdhhh3l9QovYN2/eHGvffffdXp8VK1bUODp0VKGNifbYYw+vltwcIfQ6Hjrevfzyy7H2888/7/XhNfs9nBECAAAAkDtMhAAAAADkDhMhAAAAALnDRAgAAABA7rBZQoOtXLky1n7yySe9PnvuuadXmzVrllebN29e/QaGXFm8eLFXW7RoUay90047eX2WLvVv3P3666/Xb2DIndAi3XI2mknmVZLmz59f1mMBIf3794+1e/Xq5fUJbSIzd+7cWPvZZ5/1+rAYHa0JbZaw2267ebXBgwfH2p06dfL6rF+/3qvddNNNsfamTZsqHWKucEYIAAAAQO4wEQIAAACQO0yEAAAAAOQOa4QaLHmd+xVXXOH1ue+++7zasmXLyqoB5Vi4cKFXO/PMM2Ptf/u3f/P6JG/MJoXXDQHlevXVV71a6BiYvNnlzTff7PVpaWmp38CQOzNnzoy1k2t/pPB6jm9/+9ux9ptvvun1Ya0aKrFq1SqvtmTJklg7eSNfSfrtb3/r1SZPnhxrs16tbZwRAgAAAJA7TIQAAAAA5A4TIQAAAAC5U3IiZGZDzWyymb1iZjPMbGxUH2dmC83sxejtpMYPF3gP2USakU+kFdlEmpFPNJOVWtBnZoMlDXbO/d3MekuaJulUSZ+WtM45d13ZX8yM1YOQJDnn/BWoFSKb9RVaFBySg0XA05xzh9b6IOSzfKHsJW8euG3bNq9PDrLo4dhZP8mbpXbv3t3rs2XLlpK1POawFRw7qxTK3pAhQ2LtdevWeX1Cm2iFjpVo/dhZctc451yLpJbo/bVmNlPSkLY/C2g8sok0I59IK7KJNCOfaKaK1giZ2TBJB0t6PipdbGYvmdmtZtavlc8ZY2ZTzWxqTSMF2kA2kWbkE2lFNpFm5BONVvLSuH92NOsl6S+SrnbO/cbMBklaLslJukqF05hfKPEYmThFicarx+Ud25HN+uDSuH+qy+Ud25HP0rg0rnwcO+uHS+PqjmNnlbg0rvFaO3aWdUbIzLpIelDSXc6530QPuMQ5t805966kmyWNrtdggXKRTaQZ+URakU2kGflEs5RcI2SFP9XdImmmc+76ovrg6DpOSTpN0vTGDBEII5v1xV8164t8li+Uva1bt7bDSPKBbBa8++67sfb69evbaSQolsd8bty40avNnj27HUaSP+XsGnekpKclvSxp+1HjCklnSzpIhVOUcyVdUBTQ1h6L37QgqW47H5FNNEK9dj4in6g7jp1IMY6dSK3Wjp1lrxGqBwKJ7ep5nXs9kE0Uqet17vVAPrEdx06kGMdOpFZNa4QAAAAAoCMpuUYIqFVyRyjWoiAtQruVkU8AAPKBM0IAAAAAcoeJEAAAAIDcYSIEAAAAIHeYCAEAAADInWZvlrBc0jxJA6L3syirY2+3cQcWn+/eHuMoYXs2JX7G7aFdxt7Kxghpzic/4+ZL07jTnE0pXc9VJbI6bildY09zPtP0PFUqq2NP07hbzWZT7yP0zy9qNjVte82XK6tjz+q420NWn6usjlvK9tibKcvPU1bHntVxt4esPldZHbeU7bE3U5afp6yOPSvj5tI4AAAAALnDRAgAAABA7rTXRGh8O33desjq2LM67vaQ1ecqq+OWsj32Zsry85TVsWd13O0hq89VVsctZXvszZTl5ymrY8/EuNtljRAAAAAAtCcujQMAAACQO0yEAAAAAORO0ydCZnaCmb1mZrPN7PJmf/1KmNmtZrbUzKYX1fqb2eNmNiv6t197jjHEzIaa2WQze8XMZpjZ2Kie+rG3J7LZeGSzeuSz8chndchm45HN6mUln1nNppTtfDZ1ImRmnSTdKOlESaMknW1mo5o5hgpNkHRCona5pEnOuZGSJkXttNkq6WvOuVGSDpd0UfQ8Z2Hs7YJsNg3ZrAL5bBryWSGy2dt8EFUAACAASURBVDRkswoZy+cEZTObUobz2ewzQqMlzXbOzXHObZZ0r6RTmjyGsjnnnpK0IlE+RdLt0fu3Szq1qYMqg3OuxTn39+j9tZJmShqiDIy9HZHNJiCbVSOfTUA+q0I2m4BsVi0z+cxqNqVs57PZE6Ehkt4qai+IalkyyDnXEr2/WNKg9hxMKWY2TNLBkp5XxsbeZGSzychmRchnk5HPspHNJiObFcl6PjP3881aPtksoQausPd4avcfN7Nekh6UdKlzbk3xx9I+dtQm7T9fsplvaf8Zk8/8SvvPl2zmVxZ+vlnMZ7MnQgslDS1q7xrVsmSJmQ2WpOjfpe08niAz66JCGO9yzv0mKmdi7O2EbDYJ2awK+WwS8lkxstkkZLMqWc9nZn6+Wc1nsydCUySNNLPhZtZV0lmSJjZ5DLWaKOm86P3zJD3UjmMJMjOTdIukmc6564s+lPqxtyOy2QRks2rkswnIZ1XIZhOQzaplPZ+Z+PlmOp/Ouaa+STpJ0uuS3pD0nWZ//QrHeo+kFklbVLiu9HxJO6mw88UsSU9I6t/e4wyM+0gVTj++JOnF6O2kLIy9nZ83stn4cZPN6p878tn4cZPP6p43stn4cZPN6p+7TOQzq9mMxp7ZfFr0DQAAAABAbrBZAgAAAIDcYSIEAAAAIHeYCAEAAADIHSZCAAAAAHKHiRAAAACA3GEiBAAAACB3mAgBAAAAyB0mQgAAAAByh4kQAAAAgNxhIgQAAAAgd5gIAQAAAMgdJkIAAAAAcoeJEAAAAIDcYSIEAAAAIHeYCAEAAADIHSZCAAAAAHKHiRAAAACA3GEiBAAAACB3mAgBAAAAyB0mQgAAAAByh4kQAAAAgNxhIgQAAAAgd5gIAQAAAMgdJkIAAAAAcoeJEAAAAIDcYSIEAAAAIHeYCAEAAADIHSZCAAAAAHKHiRAAAACA3GEiBAAAACB3mAgBAAAAyB0mQgAAAAByh4kQAAAAgNxhIgQAAAAgdzI3ETKzuWb2kTo/5jFmtqCC/p83s2fqOYZKNOI5QH2QT/KZVmSTbKYV2SSbaUY+O3Y+MzcRQvXM7DIzW2xma8zsVjPbsY2+Pczs/zOz5Wa22syeauZYkT/l5tPMPmtm64reNpiZM7NDmj1m5EOFx85Pm9lMM1trZq+Y2anNHCvypcJsftHMZkfHzUfNbJdmjhX5Ymb7m9mfot8jXRn9DzKzadFr+jQzO6gZ42QilBNm9jFJl0s6TtLukvaQ9IM2PmW8pP6S9o3+vazRY0R+VZJP59xdzrle298kXShpjqS/N2u8yI9KsmlmQyT9WtJXJfWR9A1Jd5vZwOaMFnlSYTaPkXSNpFNUeE1/U9I9TRko8mqLpPslnV+qo5l1lfSQCsfPfpJul/RQVG+ozE6EzGy0mT1nZqvMrMXMfln8hEV/Ib7QzGZFf5m7ysxGmNmz0V9O7k8+wWZ2RTRznWtmny2q72RmE6PP+5ukEYnPu8HM3oo+Ps3Mjiox9l3MbKOZ9S+qHRx97S7ROJ80s7ej2l1m1rfGp+w8Sbc452Y451ZKukrS51sZ3z6STpY0xjm3zDm3zTk3rcavnyvks2Jl57OVz73DOVfyL04gm1WoJJu7SlrlnHvEFTwsab0S3zfCyGbFKsnmJyQ9EPXdHPU92szIZpnIZ2Wcc685526RNKOM7sdI6izp5865d5xz/y3JJP1rLWMoR2YnQpK2qXCWYoCkf1HhLyIXJvp8TNIhkg6X9E0VznJ8TtJQSftLOruo787RYw1R4eAy3sz2jj52o6RNkgZL+kL0VmyKpINU+CvL3ZIeMLNurQ3cObdI0nOSTi8qf0bS/zrntqjww/+xpF1UOCMzVNK40GOZ2Wei/5Stve0Wdd1P0j+KPvUfkgaZ2U6Bhx0taZ6kH0T/IV42s9MD/dA68qmG5bP48XeXdLSkO9rqhxiyqYZlc6qkmWZ2spl1ssJlce9Ieqm17wkxZFMNPW5a4P39W/ue4CGfqiifldhP0kuJP2i+FNUbyzmXqTdJcyV9JFC/VNJvi9pO0hFF7WmSvlXU/qkKM0+pMBPdKqln0cfvl3SlpE4qnN7bp+hj10h6po0xrpR0YInv44uSnozeN0lvSTq6lb6nSnqh1HNQ4uu9IemEonaX6DkaFuh7RfSxcZK6SvqwpHWS9m3vn3/a38hn4/OZ+LwrJf25vX/uWXgjm83JpgqXgayLnpcNkj7e3j/7tL+Rzaa8rn9E0nJJH5DUXdL/SHpX0tnt/fNP+xv5rC6fRZ+7pyRXos+Vku5N1O6SNK7RP9/MnhEys73M7A8WLRJUISQDEt2WFL2/MdDuVdRe6ZxbX9Sep8LM+P0qnK57K/Gx4rF83QqLY1eb2SpJ7wuMJelBSf9iZoNV+Iv2u5Kejh5vkJnda2YLo+/t12U8XinrVLhmfbvt768N9N2own/CHznnNjvn/iJpsqSP1jiG3CCfFaskn8XOVeFaYpSJbFas7GxaYVeln6jwS872PyL9ypq06DfryGbFys6mc+4JSd+Pxjg3elsrqeydy/KOfDZUMsuK2qV+B6hZZidCkm6S9Kqkkc65PiqcxbC2P6VN/cysZ1F7N0mLJC1TYdY+NPExSZIVrsv8pqRPS+rnnOsraXWpsbjC9byPSTpThdOT97poCqzCfy4n6YDoe/tca49n/g5aybftY50h6cCiTz1Q0hLn3NuBhw1dxsH6i8qQTzUsn9sf+wgVXjT+t63vBR6yqYZl8yBJTznnpjrn3nXOTZH0vAp/jUdpZFONO2465250zo10zg1S4ZfizpKmt/U9IYZ8qqJ8VmKGpA+YWfHX/IDKW19UkyxPhHpLWiNpnRUW93+5Do/5AzPrGoVs+8LCbZJ+I2mcFbaUHqXCtZzF49iqQnA7m9n35M9qW3O3Cn/RPiN6v/gx10labYVdiL7R2gO4xA5agbf5Udc7JJ1vZqOssADuu5ImtPKwT0maL+nbZtY5+oXzWEl/KvP7AvmU1LB8bneepAedcw3/i1EHQzbVsGxOkXTU9jNAZnawpKPEGqFykU01Jptm1s0K2xlb9IvqeEk3RL8cozzkU+XnM8paNxXOjm/PYGvbu/9ZhTVYl5jZjmZ2cVR/sszvq2pZngh9XYUZ7VpJN0u6r8bHW6zCNZaLVLgu8T+cc69GH7tYhdOZi1U4yNxW9Hl/kvSopNdVOHW5SfHTmW2ZKGmkpMXOueIFjz+Q9H9UmOE/rMJ/iJo45x5V4ZKNySpMcuapcJpckmRmMyzascQVFs6dIumkaAw3Szq36PlAaeSzApXkM2p3U+GvYVwWVzmyWYEKj51/UWFt5f+a2VoV/up+jXPusVrHkRNkswIVHje7qfCL7zpJf1Nh4fyVtY4hZ8hnZXZX4XLA7Wd1Nkp6bfsHzewRM7tCklxhJ8NTVZikrVJhc4hTo3pD2XtnxQAAAAAgH7J8RggAAAAAqsJEqIGi036hhWRXtPfYAPKJtCKbSCuyiTQjn5Wr6dI4MztB0g0q7Hn+K+fctfUaGFAr8om0IptIM/KJtCKbqLeqJ0Jm1kmFhVrHq7AP/RQVbsz1Shufw4IkSJKcc7VsOVlSpfkkmyiy3Dn3/kY9OMdO1IJjJ1KMYydSq7VjZy2Xxo2WNNs5Nyfa1eFeFXYaA9KAfKJa80p3qQnZRJqRT1SLYycyp5aJ0BDFt+tbENWANCCfSCuyiTQjn0grsom669zoL2BmYySNafTXASpFNpFm5BNpRTaRZuQTlahlIrRQ0tCi9q5RLcY5N16FOxhzrSaaqWQ+ySbaCcdOpBnHTqQVx07UXS2Xxk2RNNLMhptZV0lnqXDHWiANyCfSimwizcgn0opsou6qPiPknNtqZhdL+pMK2xje6pybUbeRATUgn0grsok0I59IK7KJRqjpPkIVfzFOUSLS6C1gK0U2UWSac+7Q9h5EMfKJ7Th2IsU4diK1GrF9NgAAAABkEhMhAAAAALnDRAgAAABA7jARAgAAAJA7TIQAAAAA5A4TIQAAAAC5w0QIAAAAQO4wEQIAAACQO0yEAAAAAOQOEyEAAAAAucNECAAAAEDuMBECAAAAkDtMhAAAAADkDhMhAAAAALnDRAgAAABA7nSu5ZPNbK6ktZK2SdrqnDu0HoNKIzOLtXv37u312WuvvbzasmXLYu23337b67Nx40av9u6773o151zJceI9eclnMpvdunXz+vTs2dOrrV27NtbesmWL1yeUQ9QuL9mUpB12iP+9rVOnTiX7SNLmzZtjbY5/zZOXfCZzlzyWSuHccVxsPx01m6HsJWuhLHJcrF1NE6HIsc655XV4HKARyCfSimwizcgn0opsom64NA4AAABA7tQ6EXKSHjOzaWY2JtTBzMaY2VQzm1rj1wIq1WY+ySbaEcdOpBnHTqQVx07UldVyfaGZDXHOLTSzgZIel/QV59xTbfTP7MWMrBGqL+ecf0FsnVWSz46UTdYI1Wxao687z9OxkzVC9cWxs35YI1R3HDurxBqhxmvt2FnTGiHn3MLo36Vm9ltJoyW1GsgsGzhwYKx98803e30OOuggr7Zu3bpYe+HChV6fKVOmeLXJkyd7tWnTpsXaK1eu9Prwn+I9HTGfoYPlIYccEmv/6Ec/8vrsvPPOXu3NN9+MtWfNmuX1eeGFF0p+nuRP+OfNm+f12bp1q1fLq46YTSk8CT/nnHNi7VNPPdXrE/rF8umnn461Z86c6fV56623vFooZ8lfeENZ37Rpk1fL6/E06/kMHSd33313r3bJJZfE2rvssovXZ8mSJV7t4YcfjrVff/11r8+aNWu8WuiPAF26dIm1Q6/ryT8KSNK2bdu8Wh5kPZuS1LVrV692yimneLWPf/zjsfbSpUu9PnPmzPFqyd8fFy1a5PV55513vFro/00ys6HchWpZer2v+tI4M+tpZr23vy/po5Km12tgQC3IJ9KKbCLNyCfSimyiEWo5IzRI0m+jGWRnSXc75x6ty6iA2pFPpBXZRJqRT6QV2UTdVT0Rcs7NkXRgHccC1A35RFqRTaQZ+URakU00AttnAwAAAMidmnaNq/iLZWT3jpBjjz021r7tttu8PoMHD/Zq5Sw0S26oIIUX7iY3S7jiiiu8Pq+99ppXC+0G1t6asfNRJbKSzc6d/ZO41113XaydXJwuSb169fJq5WQztKNhaBFkcoHvLbfc4vUJ1ZYvj98TLyWL0xu+81GlspLP0GLz3//+97H2iBEjvD477rijV0tmPbShQmgReShDyYXBf/3rX70+V199tVebPj2+/GDDhg1en2bvIMaxs7TQpgRf/OIXvdoPf/jDWDu02UfomJvc4CCUgXJfd5MZDi1+v/vuu71acpOlBQsWeH1Cm4k0eJMFjp1lSG6+JUm//vWvvdrhhx8ea4dee5NZDNVCx8RyNzNI5njFihVen7///e9eraWlJdZ+3/ve5/X5+c9/7tVefPHFssZVjdaOnZwRAgAAAJA7TIQAAAAA5A4TIQAAAAC5U9MNVfMkec1x6Fri0N3RQzeoSgo9Vu/evb3axz72sVg7dAPXCy64wKs9+mh8d8mUrMNAFcq54VnoZm2ha+ZDeU3q3r17WY/Vt2/fWHvcuHFen9CNNJN5Ta7JkPJ748AsCmUjua4mtB4olNlk1kN5LbfWs2fPWPuEE07w+hxxxBFeLbnuInSz4gcffNCrkdn2Ve5rXHINZGgdQ2gNRjmv6+V+XjKbBx98sNdnv/32K/n11q5d69UuvfRSr3bvvffG2vw+0Hzr16/3aqF14cn1OaG1vqE1bMljYOhnHDoOlyP0f2TXXXctOa7Qcfnkk0/2anvvvXesnbxZeyNwRggAAABA7jARAgAAAJA7TIQAAAAA5A4TIQAAAAC5ww1VyzR06NBYO3QjqEMOOcSrJW8YOXPmTK9PcqG5JI0ePdqr9e/fP9YO/eyeeeYZr3bGGWfE2qEbYjUbNwWsTmjB4XHHHRdrhzbM2H///b1a8ka+8+bN8/qEFkYmFzNK0vvf//5YO7RQOHSDwUmTJsXan/3sZ70+q1at8moNxk0Bq9SjRw+vdsopp7TZlqR9993XqyVvNJk8lkrhxcM777yzVxswYECsnVygLoUXsic3Pfjd737n9RkzZoxXW7NmjVerF46d1Qnd7PfMM8+MtUOvu3vssYdXS+YidKPdZOak8Gt98v9MudlMbjASuqnrfffd59XOP//8WDt0U+IacOwsQ+h1fNSoUV7t+OOPj7VDG2kMHz7cqyXzGbp56uDBg71aKHvJnIWyGMr/brvtFmuHNnUIZe+www6Ltet5g1VuqAoAAAAAESZCAAAAAHKHiRAAAACA3Ck5ETKzW81sqZlNL6r1N7PHzWxW9G+/xg4TCCOfSCuyiTQjn0grsolmKrlZgpkdLWmdpDucc/tHtZ9IWuGcu9bMLpfUzzn3rZJfLIWL1srVu3fvWPvII4/0+oQWfr3xxhux9jvvvOP1GTJkiFdLLmiUpE996lOxdmhh8l/+8hev9pnPfCbWDi0+b/bdpeu14Lde+cxyNvv06RNr9+vnvz6EslnOItnQY4Xucv4f//EfsfbRRx/t9QktsnzwwQdj7a9+9aten9Ai+QbntS4LfvN47Az9jLt16xZrJxffSuHFvMnH6tSpU8nHbq2WXIh83XXXeX2Si3slfwH6xIkTvT4XXXSRV0tuRBJayF4tjp3VCWUzualLORtmSP5i99BC8NCGMSHJBerJDRwk6ayzzvJqH/jAB2Lt0P+Pe++916tdeOGFsXYyqzXi2FmlUPaStVCf0LElmc9QNkK10Otq8rGSm3ZJ0ogRI7zaQw89FGuHNl4K/Q5y7rnnxtoPPPCA16fa42nVmyU4556SlNxm7BRJt0fv3y7p1KpGBdSIfCKtyCbSjHwircgmmsn/M0Z5BjnnWqL3F0sa1FpHMxsjyd9fFGicsvJJNtEOOHYizTh2Iq04dqIhqp0I/ZNzzrV16tE5N17SeCk7pyjRcbSVT7KJ9sSxE2nGsRNpxbET9VTtRGiJmQ12zrWY2WBJS+s5qDRKXic8ffp0r8/bb7/t1ULXvietX7/eqz3//PNe7bTTTou1Q9dzzp4926tt2rSp5Od1MLnK58aNG2Pt5M9bKi+HIaEbQ4ZynrxePbSGLnSt/YwZM2Lt0Bq6DpbXDp3N0M8qmcdQPsv5GYeujw/lM9Rv5cqVsXbo5sGhtZrJsS5atMjrE8p1hnXYfIYyVq+bidbyOMkMP/LII16f5E3RQ0LH+DfffNOrlbPuJKXH3A6bTSn8nFf7c0gek+p5jAq9Rodusp5cCxr6XkI3Yk0eq0P5rLdqt8+eKOm86P3zJD3URl+g2cgn0opsIs3IJ9KKbKIhytk++x5Jz0na28wWmNn5kq6VdLyZzZL0kagNNB35RFqRTaQZ+URakU00U8lL45xzZ7fyoePqPBagYuQTaUU2kWbkE2lFNtFM1V4aBwAAAACZVfOucXmRXCC2ZMkSr8+WLVu8WnKBWPLmVFJ4IdvOO+/s1ZI3Cgx9vdANVUP90HGUsxFCtYsuQ58XupnZIYccEmuHbjAY2mThhRdeiLVDCzGRbfVaeF3L4ySPpwcffLDXJ3SDweRmCXPnzvX6lHPcB1qTzF3yhpKStNdee3m15CLy1atXe30efvhhr1avDSKQT6Ebqn7nO9/xaskbCod+b5g0aZJXS26gVM+bUbeGM0IAAAAAcoeJEAAAAIDcYSIEAAAAIHeYCAEAAADIHTZLKFNyQ4PQAq5q744+aNAgr3baaad5teSiylmzZnl9nn76aa/Wwe58joRGLswObXpw8skne7Wjjjoq1g4tIL///vu92ksvvRRrl7PxA7Bd6Hg6cOBAr/bQQ/F7L/br18/rE9oA55FHHom1Q5vRhDLLZgkICR1Pr702fjucL33pS16f0PF0wYIFsXYy45I0c+bMko9FVtGW/fffP9YOvY6HfodNbjTT0tLi9fnRj37k1ZYvXx5rNyOfnBECAAAAkDtMhAAAAADkDhMhAAAAALnDGqEqVXvdYuja9Msuu8yrJa/LlPy1PnfeeafXZ82aNV6Na4BRjh133NGrnXjiiV7tZz/7mVfr2bNnrP3KK694fULXsCevB27GzdOQTaGbUQ8bNsyrPfroo15t+PDhsfbGjRu9Ps8//7xXu+GGG2Lt0A1VySxCa9WSx0RJuuWWW7zaqaeeGmuHXq9XrFjh1W677bZY+6677vL6bNiwwauRV0jhG0ifffbZXu1//ud/Yu3QOrfQjdBfe+21WPsXv/iF12f27NlerT1u+MsZIQAAAAC5w0QIAAAAQO4wEQIAAACQOyUnQmZ2q5ktNbPpRbVxZrbQzF6M3k5q7DCBMPKJtCKbSDPyibQim2imcjZLmCDpl5LuSNR/5py7ru4j6mC6desWa48dO9brc/7553u1Ll26eLXkwrIpU6bUOLoOYYLIZ1WS2Qxt2vHd737Xq4U2VVi9enWs/fjjj3t95s+f79WSG4B0sI09JohsVq2cY2conz169PBqyQW406dP9/qEFrLPmzevzcfJuAkin1VJZvMrX/mK1+c73/mOV+vVq5dXS25ekNxARgpnM7lZQujzMnw8nSCyWbXka/SXv/xlr88VV1zh1UKbeSUlb5Qq+TeelqT//u//jrVDGyil5Xha8oyQc+4pSf6WJUAKkE+kFdlEmpFPpBXZRDPVskboYjN7KTqFWXoaCTQX+URakU2kGflEWpFN1F21E6GbJI2QdJCkFkk/ba2jmY0xs6lmNrXKrwVUqqx8kk20A46dSDOOnUgrjp1oiKomQs65Jc65bc65dyXdLGl0G33HO+cOdc4dWu0ggUqUm0+yiWbj2Ik049iJtOLYiUYpZ7MEj5kNds61RM3TJPkrT3MouYBSkq666qpY+5JLLvH6dO3a1att2bLFq02cODHWnjVrltcnLYvP2hP59L3vfe/zanfeeWesfdJJ/iY8obtPb9261as9/fTTsfbdd9/t9Vm2bJlXy9tdzslm2MCBA73apEmTYu1Ro0Z5fXbYwf9bXiifU6fG/zD8ve99z+szbdo0r5ZcGJzhxedlIZ++XXfd1as999xzsfaQIUO8Pmbm1ZKbw0jSjBkzYu1rrrnG6zN58mSvtmJFfAlNRz+Wks2wESNGeLW//e1vsXb//v3LeqzQsTO5SdcNN9zg9fnd737n1ZKv96F8puV4WnIiZGb3SDpG0gAzWyDp+5KOMbODJDlJcyVd0MAxAq0in0grsok0I59IK7KJZio5EXLOnR0o+3s5Au2AfCKtyCbSjHwircgmmqmWXeMAAAAAIJOYCAEAAADInao2S8ij5MLH5J17JemOO5I3QZZOPfXUWLtLly5en9AisuTiXsm/U2/oTtKhxZjo2Dp3jv83HjRokNfn8ccf92p77713rB1aeB7KZmjh7tixY2PtBQsWeH3IZj716dMn1v7gBz/o9bn33nu92oABA0o+diifDz30kFf76le/GmsvXLjQ60M+82fw4MGx9hlnnOH1ufrqq71a7969Sz52KJv33HOPV7vyyitj7bfeesvrQzY7vtDmGslNOC677DKvz4UXXujVQht3JYXy+atf/cqr/fSn8V3K33zzTa9P1vPJGSEAAAAAucNECAAAAEDuMBECAAAAkDusESpT8prgj3/8416fY4891qsl12+EhG40ef3113u1lpaWWLuj30ANvtA6ng984AOx9qWXXur1GT58eFmPlRS6ae83v/lNrzZ//vxYOy03SkNzha5N//rXvx5rn3nmmV6fvn37lnzsUKaeffZZrxa6afWiRYtKPj46ttC6nh//+Mexduh1vUePHiUfO5TN0E2lL7roIq+2Zs2ako+PjiW0Hih0DPzhD38Ya59++ulen65du5b8eqE1PN/4xje82o033ujVNm/eXPLxs44zQgAAAAByh4kQAAAAgNxhIgQAAAAgd5gIAQAAAMgdNksICC0+S9547cgjj/T6hG6ymrRhwwavdt5553m1SZMmeTU2R8iX0GYGO+20k1cbOnRorJ28UapU3qYdK1eu9GrHHXecVwstPGdzhPwJHSf3339/rzZs2LBYO7QoOJT1ZKbmzp3r9fnoRz/q1TZu3OjV0LEl8xPK5qhRo7zaiBEjYu3Qxgihhe3JbP7+97/3+oRe13kN7/hCeUnms0uXLl6f/fbbz6sdcsghsXYo16HX3uTmCOeff77X5/bbb/dqecUZIQAAAAC5w0QIAAAAQO6UnAiZ2VAzm2xmr5jZDDMbG9X7m9njZjYr+rdf44cLxJFPpBXZRFqRTaQZ+UQzlXNGaKukrznnRkk6XNJFZjZK0uWSJjnnRkqaFLWBZiOfSCuyibQim0gz8ommKbmC2jnXIqklen+tmc2UNETSKZKOibrdLunPkr7VkFE2UKdOnbzaLrvs4tVOOumkWPvoo4/2+oQWpK9fvz7W/ulPf+r1eeKJJ7xa6E7A8HWkfCYXWQ4aNMjr8+EPf9irnXXWWbF2aFFwaDH62rVrY+3QwvOFCxeGB4uSOlI2JX8zmA996ENeny9/+cte7Zhjjom1+/fv7/UJLTBevHhxrH3ggQd6fdgYoTpZyWYoF6EF4/36xU8MJBeZS9Lll/u/M48ePTrWDi1iDy1Gf+ihh2Lt008/3evDxgjVS2s+k3kM/f6YzGKoFjp2jhs3zqslN0IK/X8I/a6YzOPEiRO9PnhPRWuEzGyYpIMlPS9pUBRWSVosyf+tDWgi8om0IptIK7KJNCOfaLSyt882s16SHpR0qXNuTfHM1DnnzCy4f66ZjZE0ptaBAm2pJp9kE83AsRNpRTaRZuQTzVDWGSEz66JCGO9yzv0mKi8xs8HRxwdLWhr6XOfceOfcoc65Q+sxYCCp2nySTTQax06kFdlEmpFPNEvJM0JWmILfImmmc+76og9NlHSepGujfx8KLbmOngAACpFJREFUfHrqha4JPuGEE7zaF77whVg7eZNASdq8ebNXe/zxx2Pta6+91uvDeqDqdaR8JtfxhK5z/+pXv+rV9t1331i7e/fuXp/QjXzHjh0ba0+bNq2scaI8Wclm6Lrz0HExuWYteUyUpGOPPdarJa+PD61Xe/vtt71a8qbVyTVtqF5as5nMYuhYts8++3i1Aw44INa+8MILvT6htZPJnIfW9Tz22GNe7cwzzyz5eaheGvIZOi4m87jbbrt5fc4991yvlvx98V//9V+9PqGbpSfH8M4773h9QjfuZU1QZcq5NO4ISedIetnMXoxqV6gQxPvN7HxJ8yR9ujFDBNpEPpFWZBNpRTaRZuQTTVPOrnHPSPKnxgXH1Xc4QGXIJ9KKbCKtyCbSjHyimSraNQ4AAAAAOgImQgAAAAByp+ztszuq0KYH55xzTln9kmbOnOnVrr766lh706ZNZY8NHVdoIWbyRpNf+tKXvD6hhcLJBZyhBZU33nijV7v77rtj7dCNA9HxhTYvCN3MN7kAPXQD3j59+ni1ZNZDGyOENlmYM2eOP1h0aMmbkg8cONDrc8EFF3i15A3PBwwY4PUJ3fxy69atsfaECRO8PhdddJFX27Jli1dDx5LMoiTtsssusfbJJ5/s9fn85z/v1ZKv7aHHDm24sWbNmlj70EP9TfBmz57t1VAZzggBAAAAyB0mQgAAAAByh4kQAAAAgNxhIgQAAAAgd3K3WUJyYfDuu+/u9Rk5cqRX69atW6y9fv16r8+jjz7q1V577bVKh4gcCC3c3WOPPWLtfffd1+sTutN6cpODl19+2evzs5/9zKtt3ry55DjR8SQ3L+jatavX5+CDD/Zqxx9/fKzdo0cPr09ow41169bF2l/5yle8Pq+88kp4sOiwQpt09O3bN9Y+8MADvT5HHXWUV0suRg9tRpNceC5Jf/jDH2LtSy65xOvDxgj5FHqtPeKII2Ltj33sY16fZBYl//U+lKmpU6d6tc9+9rOx9vz588ODRU04IwQAAAAgd5gIAQAAAMgdJkIAAAAAcid3a4SSQtcShyRvhDpt2jSvz2233ebVQje3BEI3VBs6dGisHVpHtG3bNq/W0tISa48dO9brs2zZMq/GDVTzKXnMC2Vx+PDhXu1973tfrB1aY7Z27Vqv9l//9V+x9oMPPuj1Cd1MEB1baI1Qz549Y+1Ro0Z5fXr37u3VkvlZsWKF1+exxx7zapdeemmszQ3PsV3o9Te5pjy5rlcK5zp5rHzmmWe8Pl/72te8GmuCmoMzQgAAAAByh4kQAAAAgNxhIgQAAAAgd0pOhMxsqJlNNrNXzGyGmY2N6uPMbKGZvRi9ndT44QLvIZtIM/KJtCKbSDPyiWYqZ7OErZK+5pz7u5n1ljTNzB6PPvYz59x1jRte/SUXiL/wwgtenyuvvNKrzZkzJ9YOLXbbuHFjjaNDhTKbza1bt3q1KVOmxNo/+clPvD7Dhg3zatdff32svXz5cq8PGyO0i0zkM7QBx3PPPefVunTpEmuHFgUnMyxJf/nLX2JtNkZIhVRmM7lZwaxZs7w+kyZN8mpvv/12rP3II494fUI3rAxt7oFUaPd8ho6L8+bNa7MthTfcuOOOO2LtX/3qV16fZIbRPCUnQs65Fkkt0ftrzWympCGNHhhQCtlEmpFPpBXZRJqRTzRTRWuEzGyYpIMlPR+VLjazl8zsVjPr18rnjDGzqWbm/zkGqBOyiTQjn0grsok0I59otLInQmbWS9KDki51zq2RdJOkEZIOUmHm/tPQ5znnxjvnDnXOHVqH8QIesok0I59IK7KJNCOfaIayJkJm1kWFMN7lnPuNJDnnljjntjnn3pV0s6TRjRsmEEY2kWbkE2lFNpFm5BPNYqUWUVvhNuS3S1rhnLu0qD44uo5TZnaZpMOcc2eVeKzUrdgOLfgNPScsNq8v55yV7tW2LGezMPS4ZBZDd7YOLeAM1VCTafX4S2JW8hk6Bnbu7C8fTfYLbXqwZcsWr8axs7468rEzeVzs3r2716dbt25ebcOGDbF2KIccJ5uiwxw7Q6/RydfkIUP8ZUuh1+233nor1g5tlsRxsvFaO3aWs2vcEZLOkfSymb0Y1a6QdLaZHSTJSZor6YI6jBOoBNlEmpFPpBXZRJqRTzRNyTNCdf1inBFCpB5/1awnzgihSF3+qllPnBHCdh352MkZoczrMMdOzgh1PK0dOyvaNQ4AAAAAOoJyLo3r0Li5H9pD6K8/ySzyF0w0QyiLob+ol/N5QC2SmQrdnDJUS34e2UStQhlKviYnz/S0ht8z040zQgAAAAByh4kQAAAAgNxhIgQAAAAgd5gIAQAAAMidZm+WsFzSPEkDovezKKtjT9O4d2/vAQRsz6bUTs9VHRb4pulnXKk0jT3N+az789TEheVp+hlXIk3jTnM2pTo/V01cZJ6mn3Gl0jT2NOez5uepHTflSNPPuBJpGner2WzqfYT++UXNpqZtr/lyZXXsWR13e8jqc5XVcUvZHnszZfl5yurYszru9pDV5yqr45ayPfZmyvLzlNWxZ2XcXBoHAAAAIHeYCAEAAADInfaaCI1vp69bD1kde1bH3R6y+lxlddxStsfeTFl+nrI69qyOuz1k9bnK6rilbI+9mbL8PGV17JkYd7usEQIAAACA9sSlcQAAAAByp+kTITM7wcxeM7PZZnZ5s79+JczsVjNbambTi2r9zexxM5sV/duvPccYYmZDzWyymb1iZjPMbGxUT/3Y2xPZbDyyWT3y2Xjkszpks/HIZvWyks+sZlPKdj6bOhEys06SbpR0oqRRks42s1HNHEOFJkg6IVG7XNIk59xISZOidtpslfQ159woSYdLuih6nrMw9nZBNpuGbFaBfDYN+awQ2WwaslmFjOVzgrKZTSnD+Wz2GaHRkmY75+Y45zZLulfSKU0eQ9mcc09JWpEonyLp9uj92yWd2tRBlcE51+Kc+3v0/lpJMyUNUQbG3o7IZhOQzaqRzyYgn1Uhm01ANquWmXxmNZtStvPZ7InQEElvFbUXRLUsGeSca4neXyxpUHsOphQzGybpYEnPK2NjbzKy2WRksyLks8nIZ9nIZpORzYpkPZ+Z+/lmLZ9sllADV9hyL7Xb7plZL0kPSrrUObem+GNpHztqk/afL9nMt7T/jMlnfqX950s28ysLP98s5rPZE6GFkoYWtXeNalmyxMwGS1L079J2Hk+QmXVRIYx3Oed+E5UzMfZ2QjabhGxWhXw2CfmsGNlsErJZlaznMzM/36zms9kToSmSRprZcDPrKuksSRObPIZaTZR0XvT+eZIeasexBJmZSbpF0kzn3PVFH0r92NsR2WwCslk18tkE5LMqZLMJyGbVsp7PTPx8M51P51xT3ySdJOl1SW9I+k6zv36FY71HUoukLSpcV3q+pJ1U2PlilqQnJPVv73EGxn2kCqcfX5L0YvR2UhbG3s7PG9ls/LjJZvXPHfls/LjJZ3XPG9ls/LjJZvXPXSbymdVsRmPPbD4t+gYAAAAAIDfYLAEAAABA7jARAgAAAJA7TIQAAAAA5A4TIQAAAAC5w0QIAAAAQO4wEQIAAACQO0yEAAAAAOQOEyEAAAAAufP/AERLNLQwpDxyAAAAAElFTkSuQmCC\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "autoencoder.eval()\n",
    "\n",
    "def interpolation(lambda1, model, img1, img2):\n",
    "    with torch.no_grad():\n",
    "        # latent vector of first image\n",
    "        img1 = img1.to(device)\n",
    "        latent_1 = model.encoder(img1)\n",
    "\n",
    "        # latent vector of second image\n",
    "        img2 = img2.to(device)\n",
    "        latent_2 = model.encoder(img2)\n",
    "\n",
    "        # interpolation of the two latent vectors\n",
    "        inter_latent = lambda1 * latent_1 + (1- lambda1) * latent_2\n",
    "\n",
    "        # reconstruct interpolated image\n",
    "        inter_image = model.decoder(inter_latent)\n",
    "        inter_image = inter_image.cpu()\n",
    "    \n",
    "    return inter_image\n",
    "    \n",
    "\n",
    "# interpolation lambdas\n",
    "lambda_range=np.linspace(0,1,10)\n",
    "\n",
    "fig, axs = plt.subplots(2,5, figsize=(15, 6))\n",
    "fig.subplots_adjust(hspace = .5, wspace=.001)\n",
    "axs = axs.ravel()\n",
    "\n",
    "# We start off by taking two images from the dataset, and linearly interpolate between them\n",
    "for ind,l in enumerate(lambda_range):\n",
    "    inter_image = interpolation(float(l), autoencoder, digits[7][0], digits[1][0])\n",
    "    inter_image = to_img(inter_image)\n",
    "    image = inter_image.numpy()\n",
    "   \n",
    "    axs[ind].imshow(image[0,0,:,:], cmap='gray')\n",
    "    axs[ind].set_title('lambda_val='+str(round(l,1)))\n",
    "\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "IAt4HVuZAwW2"
   },
   "source": [
    "Random Latent Vector - generating random images\n",
    "-------------------------------------------------\n",
    "\n",
    "Typically, new images are generated using random points in the latent space. Taken a step further, points in the latent space can be constructed (e.g. all 0s, all 0.5s, or all 1s) and used as input or a query to generate a specific image.\n",
    "\n",
    "We are going to transform our latent space by using simple vector arithmetic to create new points in the latent space that, in turn, can be used to generate images. This is an interesting idea, as it allows for the intuitive and targeted generation of images.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "id": "52NHPksQAwW2",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 323
    },
    "outputId": "d28c6f6b-605c-42b2-9743-fe20c6356bfa"
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ],
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAATgAAAEyCAYAAABu5MwMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nOydd3hc1Zn/P3d60WhURr13WbJlW+7GNu52MMYGU4MTJ9QkwG5InjxJdkl+D2ST/HazsLBhl0CATSChY2yIjQEXXDDuTV1WsWz1Lo00feb+/nDuXclWnRklNj99n4cH39HMOffce8573vOW7yuIosgkJjGJSXwVofh738AkJjGJSUwUJgXcJCYxia8sJgXcJCYxia8sJgXcJCYxia8sJgXcJCYxia8sJgXcJCYxia8sJkzACYKwVhCECkEQqgRB+MlE9TOJSUxiEsNBmIg4OEEQlEAlsAqoB44D94iiWBr0ziYxiUlMYhhMlAY3F6gSRbFGFEUX8BawYYL6msQkJjGJIaGaoHYTgEsDruuBeQO/IAjCQ8BDAGq1epbFYpmgW5nEJCbxVUZTU1O7KIpRQ/1togTcqBBF8SXgJYD4+HjxoYce+nvdyiQmMYnrGE8++WTdcH+bqCNqA5A04Drxr59NYhKTmMTfDBMl4I4DWYIgpAmCoAHuBj6coL4mMYlJTGJITMgRVRRFjyAIjwKfAErgVVEUS8b6+3//93/H5XIF/b6io6N54IEH5Ove3l7++7//G1EUCaY3WRAECgsLWbNmjfxZWVkZ27ZtG/L7gfQtCAK33HIL+fn58md79uzh+PHjfrcrCMKQv1UoFDz88MOEhYXJn73xxhtcunTpqmc41O+ldgVBuOpv0vcFQUChUGA0GnnkkUfk74qiyG9+8xs8Ho9fYxoJ8fHxfOtb35Kvu7q6eOWVV3C73UPe41gw1BiVSiXz5s3jxhtvlD8rKirio48+Glc7Y72nTZs2kZOTI1/v3LmTM2fOjNiev3jssccwmUzy9e9//3va2tqG/O7AMY13jmq1Wn74wx+O+fsTZoMTRXEnsNOf37pcrqsmVzAw1IR1Op1B72eovnw+34QIbQCv13tV3+Md13BC7Ur4fL5B1zabDYfDMa6+xoIrxwSX58VQnweKoeaFzWYL6qYn4cr34vP5xj3XBwr9kXDlu/J4PBOyroa6F7fbPWpf0mbm8/nG/KxHE/hX4u/mZJjE3x8KhQKTyURSUhKiKNLQ0IDNZsPj8QRdqx0vgtG3IAhXCe6/N/9hoP2HhoaSkpJCfX09XV1dQbqr4SEIAkqlEo1Gg0KhwO1243K5AhqHUqnEZDKxYMEC8vLy6Ojo4MyZM9TV1dHX1xdUIXxdCziFQoFWq8VoNKJSqejr60MURVlbmojd/qsAQRAwmUxMnTqVdevWkZ6eTnt7O3V1dXR2dlJfX09JSQlNTU1XaQHXOoxGIxaLhRUrVrB8+XL0er28YGpra9m+fTsnT54ccRH5I9wFQUCr1aJQKHA4HBPy3FQqFd/4xjdYuHAhzz//PEeOHJlQgW00Gpk/fz5z584lNDSU3t5eSktLOXz4MF1dXX6ZC9RqNXPmzOEb3/gGS5YsITo6mo6ODk6dOkVnZyc2m40333yTc+fOBWX9XpcCTqPRkJGRwZo1a1i7di3Jycn09fVRWlpKTU0NTU1NNDU1cezYMXp6egLeceB/J3BISAhhYWHEx8fj8Xioqqqio6PjqpcxkiqtUChQq9XodDqMRiMajUYWzD6fTz72TYSQVigUxMfHs3btWubPn094eDjHjh2jrKyMmJgY5s6dy0033cR7773H9u3bsdvtI7b399aIJCgUCmJiYnjggQdYuXIlubm5hIWFDdLg3G43X//613n11Vd5+umn6evrC1rfs2fPZuPGjbS1tfHWW2/R1NQUlLYHQq1Ws3LlSsLDw1GpJm7pCoJAamoqDz30EOvWrSMkJISysjJ6e3uJjY2lt7eXY8eO4fV6x/3+9Xo9N954I7fccgsGg4Fjx47x4osv0tLSwpYtW9i4cSMzZszgZz/7GUePHg14LNedgNPr9dxwww1861vfkl+2IAjYbDZ8Ph+CIHDjjTcSERHBm2++ydtvv01DQ0NAxmmDwUBubi6rVq0iIyMDt9st22lOnDjBZ599Rnd395hetkKhwGKxkJ+fz+rVq5k1axYRERFER0ej0Wjwer309vZSVFTEtm3bOHr0KHV1deO6/5HuQ6/XU1BQgEKh4MUXX6SyslLWfHU6Hc3Nzdx3331ERkai0+lwOBwjtnctCDhBEEhISOBHP/oR3/jGNwgJCUEQBNxuN319fdjtdtRqNWazmcTERB588EEqKyt5++23g6JpGQwGli9fjlarxeVyodfrZdtSMKHRaAgNDZ3QZ65SqSgsLOSnP/0py5YtQxAETp8+zbZt24iNjSU9PZ2srCzOnTuH3W4f973Y7XbKyspoaWlBoVDw0ksv8Ze//AW9Xk9fXx/h4eFYLBYUiuAEeFxXAk4QBGJiYvjud7/LmjVr0Ol0uN1uOjo6qKmp4ejRoyQkJJCUlIRKpSIqKmqQZ8cfREZGcvvtt7Nhwwa0Wi3bt2/n1KlTiKLIjBkzSE1NJSIiAqvVOkgIDffiFQoFcXFxLFu2jIKCAvR6Pd3d3TgcDhoaGnA4HERGRpKSksLPfvYzysrKeOqppzh79mxQJrbX66W0tJSjR4/S1dU1aBE6nU7i4+Ple3G5XGN2PowGpVKJTqcbtBmNhPEYk3U6HRs2bOD222/HZDLh9XqprKzk+PHjnD9/nubmZiIjI1m/fj3z5s0jKiqKgoICtm7dGrCTSaFQkJmZSVVVFdu2bcPr9eJyuSZEwE2ZMoX09HRcLhcFBQUUFRXR3d0dtPY1Gg033XQT//zP/8y0adMQRZHz58/z4osvcvLkSZYtW8by5cvp7+9nx44d4zb4w2UtuqysjJMnT9LV1cXevXvx+XzceOONbNiwAVEUOXXqFJWVlUEZ03Ul4ADS0tIoKChAp9Nhs9nYs2cPBw4cQKVSkZuby4wZMzCbzbS2ttLe3j6qBjISdDodjz/+ODfddBMHDx5k+/btnDhxgv7+frRaLRERESQlJaFUKq/67XAv3+v10tTUxJ49ezh69ChWqxWr1QpAR0cHHo+HiIgIUlJSuOOOO1i3bh2bN2+mvLw8KN5Kt9tNU1MTbrd70ALU6/Vs3LiRLVu2cOzYMc6ePSsLuECFnNFoZMGCBUydOhWAffv2UVxcPOTxW3puQz3ToSAIApGRkSxZsoSQkBC6uro4ceIEr732GkeOHJGP+4Ig0NLSIh9dVSpVULSE8PBwbrzxRo4ePUpjYyMmkwm9Xo9SqQxqSIsgCHz7298mNjaW/v5+Nm3aRHx8PK+//jrl5eUBt69UKlm1ahVPPvkkU6ZMQaFQ0NDQwNatWzl8+DCCIJCbm0tOTo68MforwBsbG/nwww8RBAGz2UxmZiYPPPAA8fHxFBcX85//+Z90dnYGPCa4zgScWq1mypQphIaG4vV6KSkp4a233kIQBO677z5mzpyJRqOhvb2dQ4cO8cUXX9De3u7XixAEgdWrV3Prrbfy6aef8swzz9DY2IjX60UQBAwGA+Hh4Vy6dInW1tar+hhOIIiiSHt7O19++SWCIODxeK5ykzc1NVFXV0dycjJr1qwhLS0NjUYTFAEniqLsJZXGGRERwaZNm7j11ls5ffo0zz77LJcuXZLHFIhw0+l0rFq1ikWLFsl9eb1ePB4PDQ0N2O12DAYDdrsdr9eLQqEYl2BQKBQkJyej0+mora3l5MmTfPTRRxw/fpzOzk5UKpX8jPv6+uRnbrfbg6JhzZkzh+nTp3PkyBHMZjOxsbEolUpaWlqCGoKUnJzM4sWL8fl81NXVodPp2LJlCzExMfzjP/4j/f39AbU/ZcoUfvjDH5KdnY0gCDQ2NvLcc8/x9ttv09XVRX5+PkuXLkWv19PY2BhQGE1fXx8nTpzgjjvuYPPmzZjNZnJzc2lvb+d73/se586dC2gsA3FdCbiwsDAKCwtlG4vRaOTrX/86M2fOJDo6GpfLxblz53jllVfYv3+/bHvz50WYzWYefvhh6urqeOGFF2hoaJBtfGazmSVLlmCxWNi9eze9vb3jWiyjxcRJrnm1Wk1fXx8tLS1Bs7tIsUdSH+Hh4SxatIisrCxeeukldu3aNaxjYSitdKRjilKpJC4uDqvVyp///Ge8Xi8zZ87E5XLJ9ka3201vb6/suRyvtqjVaklISJAXTWNjIyEhISQlJWG322UNPjExkfvvv5/Q0FDa2tqorq4OOBzBYDDQ3d3Nb3/7W5qbmzEajbKtb6wa6Fig0WjYvHkzFouFHTt28Ktf/Yq8vDwee+wxMjIyyMnJ4fTp037PEb1ezx133MGCBQvQaDT09fXx6quv8vLLL2O32wkJCWHp0qVkZGTIG4Q/70qCKIr09vZisVhYunQpBoMBn8/H008/zalTp/waw3C4rgRcWloaWVlZqNVqFAoF2dnZZGdno1KpcDqdnDx5kt/+9rfs2bMHq9Ua0A6dnp5OUlIS5eXl9PT0yEeaqKgoli5dyqpVq/j444/p6OgIqq1FEATi4uLIyspi+vTpqNVqwsPDMRgM8lE2EKjVakwmEyEhIaSkpDBnzhzS0tLo6uqisbFxTMGZY4UgCFitVs6fP4/H48FisdDc3Ex9fT1VVVVDajjSghnLM1UoFOTk5DB9+nSUSiWRkZFkZWUxdepUmpubOX36NPX19dhsNlatWsWcOXNQqVR0dXVRV1cX0KYREhLCjBkzcDgcVFdX43A46Ovrw+v1YjKZgibgFAoFS5cu5e6776ampoaf/exn1NbW0tXVxfz581m5ciWLFi2iuLjYr0ByQRCYM2cO3/nOd9BoNPh8Po4ePcorr7yCzWbDYDAwY8YM1q1bh0ajwel00t7e7pcH9UoYDAa0Wi1arRaHw8HBgweDbre8bgScFN4QHh6Ox+NBpVKhUqnkXUSaaJWVlWMyYo8EaZfq6+tDpVIxbdo02QA/depUUlNT6e7u5sSJE0HPhFAoFKSmprJ69WpiYmLo6uoiOTmZ3NxcWltbA5pUUgrU1KlTKSgoIC8vj6Sky5wIZrOZNWvWYLVaKS8vH/L5jZRiNRSk96LX6wkPDyc5ORmr1UpjY+Ooz20s4wwLC2Pz5s2kp6cTExNDfHw8BoMBlUqFUqlkw4YNtLW14XA4SEhIICwsDJ/PR1NTE62trcO2O5rdUalUsmzZMvLy8njzzTfp6+uTMxIEQaCzsxONRjPq/Y8FCQkJ/MM//AO5ubn86Ec/oqqqCp/PR09PDz6fj/DwcLKystBoNKMKuCvfnyAIhISEcN999xEWFoYoinR2dvL222/T2dmJIAhER0ezbt06MjMzcblc1NfXc/LkyYDnvRRqpdVqUSqV2Gw2+vr65JCpK8cyUprfSLiuBJzH45HtUNIxS9pJjEYjK1eupKSkhAsXLgR0/BBFkUuXLrFjxw6mT5/O7bffTmxsLGazmebmZi5dukRZWdmwuXaBwOfzUVVVxfnz57Hb7eTm5jJ16lQWLlzI0aNHA7LDSRMnIiKC9PR0GhsbaWpqwuPxEBUVxbx58wgJCeHXv/71mMNeRoLX68XhcNDe3k5PTw99fX1ERUUREhIScPuS0XvRokUkJiYSEhICIB9/dTodISEhWCwWfD6fPE9cLhdVVVUBbRYGg4HCwkKOHTs2KBhaFEX6+/vp6+vDbDYHHAsnCALp6eksWrSIzs5OPv30U3w+nxzzV1hYKNuc/dXeoqKiSE1NlZ9NRUUFp06dwuFwYDQaKSgoYM6cOeh0OqxWKwcOHKCkpCRgTUulUjFlyhTUarXcd0FBAQsXLmTmzJmcPn2ajz/+mLq6Onmd+7OmrzsBJ/1bEARcLhednZ0YDAZMJhOxsbHk5eVhNBoDDuLs6enhrbfekl3Y0kT69NNPiYmJIS0tTbbBBBOiKNLT08Pp06eprKwkNDSUnJwc8vLySE5Oprq6ely5e1eiv7+fvXv3cvLkSWw2G2q1GkEQWLhwIWlpaWi1WsLDw+nr67sq7GWo3XM0T6TH45GN+g6Hg5iYGNmGOtIYRtupQ0JCuPfee8nKysJoNGK326mtreXQoUPExcVRWFhIdHQ0SqVSni+iKNLX10dRUdGoG8VIhAPJycmUl5fz5ZdfDplzbDKZ6OnpGbH9sUCr1bJx40aMRiPHjx+nu7sblUpFbGws3/ve95g6dSqtra1s27ZtTIt/qPFERkai0WjkPNXKykp6enqwWCxs3LiRhx9+mJycHFQqFXa7nerqanp6egJO1br11ltlm56kkRYUFHDLLbcQExPDrbfeygMPPMALL7zAzp076e7u9stEc90IOJ/Px8WLFzl79ixpaWmEhIRQXV3Nxx9/zIwZM1iyZIm8s0lhIoG8BKm/Xbt20draSldXF0VFRTQ1NXHjjTdyzz33YLFYaGxsDOIo/3dhnT9/XtZ0fD4fGo2G+Ph42YMFgxk4xgLJkN/d3U13d7fsaMjIyGDhwoVERETwxz/+kba2tkE7tNTPcAwhY4U0ka+MvxsKo7Wbnp7O+vXrCQkJoa2tjTfffJPt27fT3d1NYmIiBw4cYOXKlUydOpWYmBiUSiU+n4/6+nouXrwYUOiQxWJh37599Pb2Dvkdj8dDc3OzX+1f2dfq1auBy+E90dHRchbKnXfeicFgYPfu3VRUVPht7O/u7qaxsVHWpqZMmcKyZctIS0tj06ZNJCQkoNVq8fl8NDc3U1RUFDARQXh4OKtWrcJoNAKX37VOp2PatGnAZYaVnp4eioqKKC0tpaOjA5vNhtfrHbdt87oRcF6vl+rqav7whz8wffp0cnNz5XCKOXPmyAtCCgkIBqQdrb+/H6vVKi98u92OTqcLerqMZPuREpqNRiNRUVGYzWba2tpwu92yoXegkXesGRSSgJO+r1AoyMrK4sEHH2T58uV88MEH7Nu3T85sGAvGM9FFUaSlpWVMIQ2jtZufn09YWBher5f9+/fz0ksv0dzcTExMDFarlUuXLlFVVUVOTo6sZfb09PDFF1/IAm4kLXI4Ya5Wq6mqqho2/EjSiEdLcRsLvF4v586dIzMzU46LzMjIYN68eYSHh3PmzBlefPFFv+1hoijS1tbGzp07ZYddfn4+P/nJTzCZTBgMBvkIabPZOHv2LLW1tQGtL8l+WVBQMIgVpb6+nh07dtDd3c2ZM2doa2ujpaVFjtf0V6BeNwJOMliXlJTgcDhkRoJly5YxdepUlEol/f39nDp1iqampqCFVTidTrq7uwftILGxscTGxvoVyT0cpPAN6b41Gg2zZ8/mhhtuQKvVUlpaSlNTk2xrkYSh9O+RoFAoZDYIaQzR0dEsX76cNWvWEBcXxwsvvMA777wzYoBloDYznU6H0+n0+zg1EJGRkSiVStnrvGHDBnJycuRjtqRpRUdHo1Ao6Ozs5MiRI5w9e5aurq4Rc3yHS7aXnDQjxdDl5OTIITCBor+/nzfffJO1a9eSkpLCvffei9lsRq/Xc+HCBX7xi19QVlYW0HuxWq3s3LmTzMxMHnnkEXQ6ncwuI80xp9Mp89YFGoCblpbGfffdR2xsrPxZd3c3b7zxBm+99ZbMZjMcxjvW60bASRBFEbfbjUqlIj8/n/z8fAwGA6IoUlJSwqeffiof4YIBSWOTHrparSY6Opr29vag2d+USiVms5mIiAjZtlhQUMDjjz9OUlISe/fu5ZNPPqG+vn5QXN9wdrGBwk9alPHx8RQUFJCamkpOTg7JyclotVrKy8t54oknxuSYGWrhj0XIKxQKwsLC0Gq1tLS0jPWxDAtBEGhvb8fpdGIymZgzZw4zZ85Er9fLWrXX65UDiktLS3n11Vf58ssvsdls9PT0+BXmIKWbGQwGurq6rvp9WFgYSqWSsrKyoAg4n8/HsWPHePvtt7ntttuIirpcV6W0tJSnnnqKzz77LOBsCa/XS0tLC3/4wx+Ii4vjhhtukG2Xoihit9s5ePAgTz/9NKWlpQFFKCgUCqZPn868efPko6bT6eTdd9/l3XffHfbIHwiuOwGnUChobm7G5/Oh0+kAcDgclJWV8dJLL3Hu3LmgJiNL7n+1Wo1arSY+Pp7Y2Fj27Nkzop1lvLmU8+fP57bbbiM0NBS3201mZiZRUVEcPHiQ3/zmN8MeDUai9lGpVGg0GiIjI5k2bRrr1q0jJSWFpqYmDh06xPbt2ykqKgpoMY422SVKK2BcWSWjvcMjR46wZ88epk6dSnh4OEajEbfbLWtXLS0t1NTUcOzYMf70pz9RX18PXN6gHA6HX2P2+XwYDAby8/MRRZHW1lacTqd8dNXpdJw/fz7grIKBaG1t5bnnnqOpqYkZM2bQ3NzMm2++yeHDh4OWCiaKInV1dbz88su0tLSwePFi7HY7LS0tVFZW8sEHH1BeXi5vgP6uL2ku9PX1YTKZ6O7u5t133+XXv/71hHHbXXcCzmaz8frrr6NSqQgNDaWzs5Oqqip27tzJ6dOnJ4Q1V/KMTZkyhfz8fGw2G0eOHBnRzjKeSeDz+QgLCyMtLY3Y2Fi8Xi+1tbW8++677Nq1i4qKinHvmgPtbXa7nYaGBt577z1sNhtFRUV+p7BdiYHH5IFjFgQBlUqFwWCQzQfjcfOPtEFIC/KRRx5h6tSpZGZmYrFYZAEnJdsXFxfLQalSm1fm4I4HUohGamoqiYmJnDt3DpvNhtPppK6ujo6OjqAz5vp8PsrLy/n1r3+NWq3G5XL5nZ0zElwuF6dOnaK5uZm//OUvtLS00N3djd1uDziuVILH42H37t38/Oc/Jysri6qqKv74xz9OKOfgdSfgnE4n+/bto6ioSN4Nuru7J4wOHP6X6tloNKLVaikuLpbDNYIBt9vNsWPHcDqdWCwWent7KS4upra2lv7+fr8nsxSH5nQ6Zc66YE+moWyBCoUCpVKJxWIhNDSUixcvBj0g2ufz0drayt69e9m7d++YfjOStjvWPsvLy+ns7MRkMsljcjgcdHZ2jkkr9MduK8WJTeQclzbC6upqqqurJ6yf1tZW/vCHP0xY+1fiuhNwcFnINTT87aoQ+nw+Ojo62L17NwcPHsTpdAbFSybB4/FQU1NDXV2dTLMTDE1g4IIOhk1oLAVQdDodUVFRhIeHM2/ePOx2OxcvXhx3X8HiA/MXw3lYpWj+SVwfuCYFXHR09IQUx4iMjBx0LXlEx6rVSAtco9EM4pkbyvBuNpsHfabT6YiJiRmTkX48WoYgCOj1+kGfSawWA0MhAj3SSEfOK0NjLBbLoORrnU4n5xdarVY6OjqwWCwyq/Jw9zFQCxxqTHB5XkwEDX1ERMSgaymYVgpPGE6wjzdQWalUDqpIBpfnRXR0tB93PTokG7WE0NDQCevryg0pMjIyqFEGEsabAicE+yzvDyYr209iEpPwF08++eRJURRnD/W3v+85YBKTmMQkJhCTAm4Sk5jEVxbXpA1OIkAMNpRKpcw6AZedB8HgWBsKGo1mkB3J7XYHNQB5IKSUGgmS59QfDEyfGQomk2mQvcXhcMhFeMbyzq70uA6VTytldRgMhkG/nah5oVKp5LxIQGb/DXZfgiDITCcSXC5XUB1WAxHMeTESJNqlgfNC4sabiL5CQ0PH/P1rUsA9//zzE+JkiI6O5rvf/a58bbVaefbZZ4PeD8CsWbO4+eab5evKykree++9Cenr1ltvpaCgQL7+/PPPx11yTTLua7VamQFEwsCF/thjjw0yyu/fv5+SkpJB6UvDOW0kwSWxFYuiKIeuaDQaVCoVPp9PDjH5+te/PkgQvvDCC0Ghbb8SycnJfPvb35avu7u7eeGFF4JaUwEuG+IXLlzIihUr5M/KysrYtm1bUPuRcOeddzJlyhT5et++fZw4cSLoBK0qlYrHHntskOPttddemxA6MY1Gw09/+tMxf/+aFHCTCAz+aB5qtZrU1FSysrK4cOECdXV1gwoYD9dme3s7/f39Y1o0kkCTKk9JkChzBmpzQ7FGBFvgSBhK05gI7cPn803YGMaCYBJRSJBSJwPNUx7YXjDxlRZw0iIJhI3g/xdER0dz//33k5+fzyeffMJf/vIXmpub5ck73DMMJDNAwlAxZxMhYCZxbUGq9bBy5UoSEhJQqVQ0NTXxX//1X5SUlASlj6+MgJOOVwaDgcTERP7lX/6F1NRUduzYwSuvvBJQdLaUa6jVagcxCwdjEUpMHxJhgMfjwel0TmjU+pUwGo2sX7+e5cuXU1dXR01NDW63G4VCITOQDIdAn8FAevCBR1h/axooFAr0ej0RERFyjF5VVdW40uqCETc4EZDeh0TgGayA8GDc13ihUqn4P//n//DNb36T0NBQmRnG4/EQGRnJD3/4w6AEVF/3Ak6tVqPX68nLy+Ob3/wma9euRavVEhoaikql4uabb+bw4cNcuHDBr8BDnU5HSkoKa9eu5aabbiI0NJSKigpee+01jh49GlBitVKpJCkpiU2bNskV2VtbW9m9ezfbtm2jtLR0QmxOV97D3Llz2bhxI06nkw8//JCLFy/KdrLxOBDGioHvQRJoUsUyjUYzyDA+Hmg0GrKzs1mxYgVZWVn4fD7a29vZvn37sHVYrwfo9XpSUlLIysoiKSmJuLg4jEYjdXV1fPbZZ1RUVPxNxqZSqWQ720DGZ6k2yngg0aWbTKZBweNqtZolS5Zw77338rvf/S5gZuTrVsBJFa6WL1/O3LlzWbt2LRkZGdjtdrZt20ZzczO33347ZrOZ0NBQv4Sb0Whk7dq13HLLLcydOxez2YzT6SQiIgK9Xk9/fz/Hjx/3+4hmNpu59957eeSRR4iOjkYQBFJSUigsLGTDhg289tprHDp0iLq6Otra2iZkEicmJvLtb38brVbLhx9+SGlp6aDcR2lsw6UujTfrYmBmhbTzD+Qeg+GPvSP1pVarmTVrFitXrkSpVHLo0CFaW1uJj48nPz+fS5cuDctlFkjEvbTovV4v/f39QX9HYWFhrF27lnvuuYfCwkLMZrNc4c3tdrN06VL+7d/+jaNHj05o0rpSqSQiIoI1a9bg8/nYtWuXTJdEyAcAACAASURBVBnlD/WU1+vl+PHjLFu2TM7u0Gq1chW5FStW8NFHHwXsOb8uBZxCoWDBggXcd999rFy5kvj4eJmx4s033+Q3v/kN/f39LFmyhPj4+DEnQg+EUqlk5cqVPP744yQkJNDS0sLhw4dxOp3MmDGDwsJC5s2bx5kzZ/x2vVssFpYtW0ZUVJR89O3p6UGtVpORkcGPf/xj7rrrLjo6OigrK+O5556jrq7Or76GgsFg4Kc//SmzZ8/m1Vdf5b333sPj8aBUKmUOPMn2Nh7m2yshHfGvXAzS/yVNwN9q8IIgkJ+fz+23305RURFffPGFfLyRKLgjIiKG5HALBAaDgXXr1rFq1SpsNhvvvfceX3zxRdD6UCqVLFmyhB//+MdkZ2dflaYklRS8ePEiZWVlQa8PIglSCRaLhVWrVsnUSdK88Eew+nw+duzYQVpaGmlpaURGRlJYWChr711dXUFxyAQk4ARBuABYAS/gEUVxtiAIEcDbQCpwAbhTFMWgkT0plUrmz5/PCy+8QEZGBjqdDkEQ6O3t5fnnn+eVV16hsbGRzMxMTCYTVqtVLrE2nokXGRnJt7/9bdLT0+U6kSUlJURGRvLII4+QlJQk20L8hUS/A5cXeXl5OXv37sVisZCcnExYWBhxcXHk5uayePFiMjIy+OEPf0hVVZXffUpQqVQ8/PDDrFy5kgMHDrBjxw7a29sxGAy4XC5ZGwn0eCoRbup0uqtqMVzZtsfjwev1DvtMh/tcq9WyaNEilEoln3zyCa2trfh8PjnsJCQkhLCwsFHtieOBWq1mwYIFbNiwgbi4OBwOBwsWLJBrPgRDm9LpdNx2223k5uaiUqlwuVz09PTQ0dGBSqUiLi4OrVYrl98brZDPWKFQKOS8376+PpxOJ6IoygWajx07Nojlxt8+Gxoa2Lt3L8uXLycxMVHeBB0OB6dOnaKlpWXUuMzREAwNbpkoiu0Drn8C7BFF8f8KgvCTv17/ONBOpDP76tWrefLJJ0lOTpYpvl0uF59//jkHDx4kIiKCefPmsWXLFkwmE+fPn/drZ9Pr9XKZwK1bt/LFF19gtVoRBEGmyqmsrAzIyNve3k5zc7NcEu3EiRO8/vrrNDU14Xa70el0GI1G7rrrLh5//HEKCwtZvHgxtbW1AS1UlUrFwoUL2bhxIydOnODVV1+loaEBn8+Hw+GQtbeREs3HAqPRSEJCAna7fcxa9EAeu7EiPj4es9nM559/Lh9DJaLPBQsWEBUVNYiyPRiIi4tj9uzZfPzxxxw+fBiA6dOns2jRInbs2DEsgeN4nmdISAizZs1CqVTicrkoLy9nx44ddHZ2yrbbmJiYQWURA0V4eDjZ2dlotdpBVcOkwtrHjh3j5MmTQWOnWbZsGd/85jeJiIhAoVDIvHQHDx7EZrPJzMI+n8+vTWMijqgbgKV//fcfgc8JgoBLSEjgn/7pn9i0aZNM7S0VZ5Gq2D/22GMIgkBiYiJxcXEoFApqampGLPI7HCSSyNDQUMLDw9HpdNjtduLj48nOzub8+fNUVVUF9KJtNhvnzp3jpptuQqfTERoaitVqpbW1ddCEfe6557j77rtJTU1lxowZfPDBB34fR1QqFXPnzuXRRx8F4JVXXqGsrAylUklcXBw6nY7a2tqAI/mNRiN5eXl4vV6Z+XY87Y3VM6dQKGRvaXV1NQqFArPZTFRUlExQajAYSElJoby8fMhj6pVCZ6CtcLg+w8LC+OSTT6ioqJAdQSaTiRUrVhASEjKsgBvPM5CYP9xuN52dnXzxxRds3bqVtrY2pk+fztq1axFFEavVOiYzyWjCNTIykhtuuAGr1cqhQ4cGbd5msxmtVsuuXbuCdhTOy8tj06ZNWCwW4PKJpra2lt/97necOnVKXgMDa5WMF4EKOBH4VBAEEXhRFMWXgBhRFKWKt81AzFA/FAThIeAh4CpqoSuh0WjYsGED9957LyaTCZ/Ph8vlGhSqkZubi0ajkSewpO5eunTJL09MT08PO3bsICYmhvnz59PZ2UltbS133303JpOJgwcPBlzY1+12s2/fPh588EGSk5OJi4vDYrFQXV096IVKxzbJNhcREeHXJJNsVU888QRZWVn8z//8DydOnECpVDJnzhy5FN0777zDnj17/CbblLRctVpNS0vLoGLdY92FxxomIlErSeE2CQkJ5OTkEBMTg8PhoLy8nJiYGHJzc6moqJDrMQQClUqF2+2mqalJFtxSJa2GhoagpeRFRETQ1tYm1+Pdvn07VVVVCIIgk4m6XC6qq6vHlO41kuAOCQkhKyuLiooKqqurB9m/1Go1a9eu5ezZs9TV1QUc1Gs0Gtm8eTP33nsvqampwOU5XlxczMmTJzl37twgei3Jw+4PAhVwi0RRbBAEIRr4TBCE8oF/FEVR/Kvwuwp/FYYvwWW6pJE6ycrK4rbbbpNjxVwuF319fbhcLrxeL729vZw/f14uKDJ79mz0ej3d3d00NDT4Zax0Op3s3LkTlUrF1772Ne6++258Ph+5ublcuHCBzz//PODi0qIoUllZSVFRkVydfSiPb3Z2NlFRUQiCgNVq9Tt30WKx8P3vf5/p06ezY8cOdu7cidFo5Oabb2bz5s1kZ2fLx+Xa2lpKS0tHfXbDTTybzUZtbS0Oh0M2Vo/GCTeWdq+E1K7NZiMiIoKQkBDMZjMNDQ2UlJTgdDqJi4tj1qxZREVFoVKprhJw412wGo0Gm82G3W4flH3h8Xior68PSm6pIAgyyeqxY8c4evSorFVbLBYWL16MxWKhq6uLI0eOjGmODyfg1Go1eXl5mM1miouLr2pr+vTpiOLlWr2BbA7SkfTXv/41WVlZsvdUFEXa29s5cOAAGRkZFBYW0tDQgMPhwOPxyLF/Ho9n3IIuIAEnimLDX//fKgjCB8BcoEUQhDhRFJsEQYgDxn8+HABBEEhPT8disciOgs7OTo4fPy4bczs6Oujq6mLatGnccMMNZGZmAlBcXMypU6f87ttqtbJr1y7cbjcPPfQQ2dnZiKLI4cOHg1bcpr+/n3PnzrFs2TI0Go1sc5CgVCrJyspCrVbj8Xg4f/68X6XbDAYDP/rRj1i8eDF79uzh97//PV6vl1/96lcsXboUlUpFR0cHoigSFRVFbGwslZWVfm0O4l/prz0eD2q1Wl4U0jE/mKEUoni5Wn1HRwcOh4OGhgY5rEYSQJK2O3/+fEJDQwPKkZSSva8UlGq1msTERICgBWm3tbWxfft2zp8/L7epUCiYOXMmixcvRq1WU1tbO+a846E2F7VaTUpKCjk5OVy8eBGNRjNICJrNZsLCwvjggw8CHldMTAz/9V//RU5OjvyZVJZTpVJx9913o9PpyM3NZePGjXz55Zd8+umntLa2YrVa/bIz+i3gBEEwAgpRFK1//fdq4CngQ2AL8H//+v/t/vYhIT4+npSUFBQKBX19fdTW1lJTU0NTUxPt7e2yO/1rX/sa4eHhCILAl19+yS9/+UtKSkr8FkQ+n4/u7m6qq6vl8A2bzSbb/IIBj8fD/v37mTdvnnz8lnZaKZF5ypQpqFQqnE6nX0csQRDIzc1l/vz5NDY28u6778pxgmvWrKGnp4eysjIaGxuZNm0aSqUSlUolB/qONLGG+1zyiEpam1qtlhmBR3MkSFH6Q30+1GdGoxFBEOQiKQ6HY1AerWSrTUpKwmw2097ePqjv4dod6v4kj73Vah2kvanVakJCQmSn0XAYqwYiCIJMzS9tMoJwuQbs+vXrSUtLw+v18sorr4xZYxwukqCvr4/jx48DlzchjUaD2+3GYDAQExPD8ePHAw44FwSB5cuXy8oHXGY3OX/+PB6Ph5SUFNmDHxkZyZo1a1iyZAnTpk3jpZdeori42K9wrEA0uBjgg7++MBXwhiiKuwRBOA68IwjC/UAdcGcAfVy+yb+Wv3O73dTU1MhhINnZ2TQ1NRETE8Py5csxGo14PB727NnDk08+GZTgR5VKRUZGBrGxsXR2duJ2u8nLyyMrKyso0fE+n48DBw7Q09NDQkIC586dQ6PRDErDMZvNKBQKuru7qamp8SumLyMjA7PZzKVLl3A4HCxcuJDbbrsNu93OhQsXaG1tlY8Mhw8flu0wo20OIwk+6T+1Wi1nK4yl8M1w3tuh+pI2IbVaTWRkJI2NjUMm/0uOoqE00uEE2VDw+Xz09/dfRQXv8/lobm7m0qVLQdHsfT4fNpsNvV6PWq3G5/NhNBq544472LRpEyqVipMnT/Lhhx8G1J/b7aa1tZXW1lY5RU4URZli32azBaVeqVKpZP369YPyw61WKy6Xi9jYWPmE4nK5Bm2G2dnZZGZmUl5ePkoPQ8NvASeKYg0wfYjPO4AVV//C737kKvIulwuVSkVubi7h4eEyt5ter5cF4Pvvv88vf/lLysrKgqJlxcTEsHLlSgRB4I033kClUrFkyRLWrl07YnT8eOB2uzl58iTFxcVkZ2eTmJgoB1NqtVoyMzNRqVS0t7dTVVU17gktxesJgkBaWhoPPPAAUVFRxMXFydXC0tLSaG5u5plnnuHo0aO0t7cPCvQdDqNpJFLaXH9/v2xTGQvGOkafz4fT6USr1aLRaORFMxB6vZ6CggI5vm+s7Y50b1fen1KplCu8jYTxZn7Ex8fLnHtz585ly5YtREdH43A4eOGFF8ZVT3S4vgfSXLndbvkYHh4eTmVlZVAEtsFgICcnR968JIGdkZGB0WiUQ3hcLhetra10d3fT3t7OyZMnqampweFw+HUf10Umg1TRW6vVkpOTg1KpHBRk6/F4aGxs5NVXX+X555+/6gjiLwRBICkpiXnz5lFaWirvltOnT2flypVB5deSnCfR0dGya1yn07Fw4UIyMzMRBIGenh6/KsNLtruamhrZfiN5NLu6uqioqGDHjh0cOnSIjo6OoESQS8e20NBQ1Go1TqdzXO2O57uSV7G+vv6qdyHl2i5ZsoSPPvpo0NFy4O8Hwp8NJD8/H2DUIOzxGMnDwsLYvHkzoaGhNDc3M3/+fFJSUvD5fBw5coSDBw9OGKmkyWSir68vYEeaBK/XS0NDA7m5uWi1WllD0+v1CIKA1+vFbrfz8ccfs3XrVhwOB11dXVRXV9Pf3y9vWn9TJ8PfAoIgUFxcTFdXF5GRkXJiryiKsrfvxIkT/Ou//itlZWVB59vS6/WYTCbS09OZNm2aLGAsFoucIhYse5zP5+PixYssXrwYg8FAZ2cn69evJyYmBq/XKx+//Gm3vLycX/3qV2zYsIHExETcbjcNDQ0cPHiQU6dO+R0+MVy8mmTH6+7u9ouHbKxCRvLA2Ww2Fi1aRFVVFRcuXMDr9RISEkJhYSF33XUX+/fvZ9euXWO244xHyEne76NHj/p9pB8KCQkJrF+/ntDQUFpaWmQ7VXV1Nc899xy1tbVjbms8UKvV5OTk+FVwfDjY7XZ+/vOf09rayooVK0hISJDj23p7e6mrq2Pv3r38+7//O21tbfJzutL++zdzMvwtsX//fqZPn86KFSuIjIykubmZAwcO0NTUJLvRJ4J1QxRFGhsbKS8vJz8/n+985zt0dHSQnJxMc3NzUGwTV0IyUkuCbdq0aej1erq6usa1QK+E3W7n9OnTVFZWotVqcTgc9Pf3B7whDKUNScJNqsLuD8azU9tsNioqKsjMzGTLli1UVFTgdDoJDQ0lMzOT/fv38+mnn9LT0xPUXFS4bJSPjIyUN4lgQRAEUlNTiY6Oxmw2Y7FYUCqVNDU18eyzz7J7926/nE1jgRRu09zc7M+tDwmfz0dxcTH//M//zK5du5g5c6bsVW9sbKSkpISTJ08GvYTANS/gRFGkrKyMX/ziF7z11lvo9Xra2tooLy/HZrNNOB9WVVUV//Ef/8E3vvENsrOziY6O5vTp03z66aeUlJQEncHBarVy/PhxVqxYQX5+PhaLBbfbzfnz5zly5EhA/bnd7qAnZA9kAZHyTkNCQujt7Q1o0xmPgPN6vXz55ZfYbDamTZsma6ilpaV88cUXcmbGcPBX6Gm1WpkoYay2sPF4Ubu6umhubpb50i5cuMC//uu/snXr1gmr76FUKomOjqahoSHo9RvcbjfNzc289957bN26VSZXmEgWlGtewMFle8zFixeD5qEaDxwOB3v27OHYsWMYjUZUKhX9/f2yMXsiKKCl4+SSJUtYsGAB58+f58SJE7S0tPzNxz8aJJOBpLkpFAp6e3sDXoDjIbyUYiMPHDjAkSNH5CR7ye433mc2WqoWIGdNqNVqLl26FHRbmCiKHD16lM2bNxMTE0NHRwctLS20t7dP6KZuMBjwer3j2rzHaxcTxf+lrp9oXBcCTsLfa3F7PB66urrG5bEKBF6vl7KyMsrLy3n55ZcHhSJca9Dr9Wi1Wrxer0yzJMW++QNBGLqilvS34SCK4lXFcsaKoeyIIwk4KT5RCueRUulGG/NAbXc0iKKIzWajuLiY4uLiMf1mNEiOuZHGBZfNJOPJxgiEkGGicU0KuMLCwgkpznFluTGNRsOsWbOC3g9ASkrKoOvw8HC/+xqNMiYyMnLQdXJy8oR51waWvAOYOnUq0dHRMo+c5Or3RxhLwk2lUmE2m69aOLNnzx6ywMlYaYKGW4hXPj+tVsvs2bOvKoQzsB21Wo3BYJA9uMOF1Az8nUKhIDk5+aq+J2oOhoeHD7pOTU2VvedXBjpLnntJIx/4nEcTiEql8iquuvz8/AkpyTmQ/XcsEK6FI098fLz40EMP/b1vYxKTmMR1iCeffPKkKIqzh/rbZGX7SUxiEl9ZTAq4SUxiEl9ZXJM2uJqamiGZC4ZLwFapVCiVSrRaLW63W04QH/h9KTpbYnyAy27rysrKCRlDREQEcXFx8rXVaqWxsfEqyu7hIFWbkhhGJGqoK8elUChISEgYVFW8paWFjo6OYdseLdF8OAiCQEZGxiB7i5RGM1If44VkjB9YlR0IWvrdlTAYDKSlpcnXLpfrqpS4gc9ptEyIkRAREUFsbKx83dPTQ0NDw6i/G80ONvA70meJiYmD7M6NjY0T4igTBEFmvJFQXV09ZJjJePJ+h4JSqRzERjIarkkBt2PHjiGr6QxlxFUoFGi1WnQ6HSaTiZ6eHpxOpyzkBn4vPT2de++9V/5MKhQyEZg1axY333yzfN3Q0MDWrVuvcp4MN3El4RYeHo5CoaCnp0cOnJXGJQn3jRs3kpeXJ//2zJkzY4qqHy8UCgWPPvroIAG3e/fugIk/h4JarSY3N3eQg+X999+fEOdJfHw8Dz74oHxttVp59913g94PXKZsGijgLly4wLZt2yakrzvvvHOQgDtx4gSnT5+ekL4ef/zxQQJOojkKNnQ6HT/+8dgJwq9JAed0OsfF/eTz+bDb7YNy1ob7zt8LPp9vXDFZEvGkVPRjqNALKTRiKALHiXAejbdwTyC4Fpxfk/Afgb4/yaN+5dwerwZ/TQq4sS5QtVothy1IBIsjwd/QEynxPSQkBJPJJEeu9/T0TFjQpUTFLSXhj0ZLNImRMVqozfUAKYxDCpS9FuMiA4UUihQdHY3JZKK+vp7e3l6/x3rNCrjRoNVqiY6OxuVy0dnZOSbh5c/kVigU5OTk8MADD7BmzRosFgtOp5Nz587x/PPP8/nnn48ppWW8gigsLIzU1FTq6+snJJ7o/wcIwuVKbLm5uajVajn1yWq1BlxUR2pf4rqT4rOkjA6n0ymfRIIxDrPZzMyZM5k5cyYOh4OysjJKS0tpa2ubEEEnBT//LYWoWq0mLi6OadOmkZubC8DevXspKioaVIB8PLgmBdxoD1WiWc7MzKS2tnZCMwy0Wi0rV65k8+bNhIWF0dfXR11dHV6vl9mzZ3PmzBlaW1uDqhmYTCaWL1+OUqmcMMaIvxdUKhURERHk5+ejUCgoLS2lpaUl6AtJIkt87LHHWLduHUVFRZw8eZK2tjYqKio4dOjQoJoK44VarSYtLY309HRaW1tlwRkSEsLs2bPRarWUlJT4TfsuQRAEUlJSuPXWW9m8eTMJCQn09vbS1tbGsWPH+OCDDwaV9wsGVCoVhYWFcmnMiTbtKBQK4uPjiY+PR6/X43A4OH36NDqdjvb29quchePBNSngRpp0SqWShIQEpk+fLtM2X7hwYcLuJSYmhvXr1xMeHo7D4eDpp5/m8OHDhIeHk5qaSmRk5CB6l0BhNBpZvHgxCxYsoKyszK80mLFG9Ut2DinpeSJzAyXOtI0bN5KTk0NycjJKpZJ9+/bxu9/9Tq5EHyzEx8fzxBNP8LWvfY2qqiref/99+vv7SU1NJSMjg3PnzvlNoigIAjk5OXz/+99Hp9Px3HPPyTx64eHhbNy4kWnTpvHmm29SU1MTkICLioriO9/5DnfddRehoaFUVFRQWlpKTk4Ot912G3l5eTzzzDN89tlnQdkkJG3xkUceweFw8B//8R9+s+mOtb/k5GTmzZvHxYsXKSoqGlR/wm63jznyYChckwJuJBgMBhYsWEB2djaRkZFXldgbCeMVFlLBm7lz56JUKjlz5gyvvfYaVquVmTNncsstt2AwGPjP//zPoBwjjUYj8+bNIzs7m5aWFvR6/biSzkeDRqMhOTmZ22+/nQULFhAaGorFYkGr1XLkyBFef/11qqurZX61YKXLhYSEcPfdd/Poo49iMBioqamhpaWF/Px8Vq5cyd69e2lqagqagNVqtXzve99j3bp1tLW18YMf/IDi4mISEhLIy8tDpVJhMpn8Lj6j0+m47777WLhwIb/97W/l6l2CIBATE8PUqVNJSkoaF4PxUBCEy2Ue161bh1KpZNu2bTz33HP09fUxdepU7rrrLubNm8edd97JmTNn/CJDvRISg7ZEL97f38+vfvUr2tvbR/+xHwgPDyc9PZ26ujqKi4tlOniJ9TdQxeG6E3BGoxGtVsuZM2dwuVw0NDSMWT0fr4BTKBQyHxtARkYGS5cupa6ujjVr1rB69WpWrFjBoUOHOHDgQEAvIyIighkzZiAIAvv37yc0NJT4+PhR7XtDJXAPda3X6yksLORb3/oWhYWFdHR00NPTg0ajweFw0NjYSFRUFDfeeCP5+fl89NFHbN26VeY4k3IVx/sMo6OjeeaZZ1i0aBEVFRW8//777N69m9DQUP7hH/4BlUo1JO17IAncd911F48++ig6nY533nmHL7/8EqVSidlsJikpiaKiInp6evzWeFJTU1myZAm7du3iww8/lJlT1Go1c+bMIS4ujosXL7Jz586ABJxKpSI9PZ2zZ8/y+uuvc+TIEfr6+hAEgUuXLnH27Fleeukl4uLiSEpKCpo9btWqVXIu8He/+13a29v5wx/+QFdXl7zhSsfWQDYlqbiM0+mkoqJCLgt4ZWW5QHBNCriRJrder8ftdtPb20tzczONjY1jfsj+UFFPmTJFNriq1WpmzpyJzWYjLS2NiIgI+vv75doQI2EkCh61Ws3SpUuJiYlh9+7ddHR0YLFYZLYKf8ckPUetVovJZKK1tZXf//73Mr+c2+0mJCQEm82Gw+GQNdb169ej0+nIzMzk4sWLOJ1OeWcdD0wmEw8++CDz58/nnXfe4bXXXqOiokKmfe/u7ub06dPU1tZeNU5/J3hUVBRr167FYDDQ29vLn/70J3Q6HXPmzOHhhx8mOjqaP/3pT3R2dg6ZSD8WSJXItm7dKpNCCoJAQkICixYtQhRF/vznPwd87NbpdCiVSt555x0OHjx4lc1Q0rQtFguJiYkUFRUFzOGm1Wq59dZb5Wci2ZrLysooKysjPDwcr9dLVVUVbrd7TNELQyEqKorNmzezePFidu3ahUajITY2Fq/Xi8lk4uLFi0OyV38ljqjD0WBLXiuJ67+0tHRcR0N/eKuam5vlCkAvv/wy77zzDv39/axfvx6FQoHT6aSrq2vMdq+hvpeXl8eaNWt4//335ah2g8FwVbCyP5BU/Z6eHtlgO/AersxCaGxs5NSpU6SlpREdHY1Go6GqqmpYr+Nwz1QQBBYvXswdd9zB8ePHefrpp2ltbUUQBBITE/nWt76Fw+HgwIEDQwZ1+wOFQsGtt97KbbfdBlx+f9/97ndpaGhg/vz55OTksG3bNkpLS/1+riqVihtuuIHW1lYqKirkdvR6PevXr2fWrFkcOXKE9957L+AiybNnzyYtLY3S0tIhNzq1Wk1YWBgmkwmdThcwbZEgCNx///1Mn365llR/fz8lJSW0trbS0dFBX18fNptN/k8URTlsZTyIjo7m4YcfZvXq1ezfv5+ioiJsNhuJiYnk5OSQkZHBn//856A42K5JATec1iJxuHd3d8uVhsYDfyaAFIbyzDPP8PLLL9Pb20tKSgohISGI4uWiw2O1Tww1EQwGA5s2bcLr9VJRUYHL5UKv16PX67FarcMK+5HGNJDmRoqjG+n30vcVCgVpaWnk5eXhcDhoaWmht7dXrtcwVloiuGx3u+GGGwgPD+dPf/oT7e3tCIJAZGQkP/jBD5g7dy5PPfUU9fX1QTuOzJo1iyeeeEJedCaTiZtuugmXy4VOp8NqtQ5ZXHs8kIrofPHFF4O89+np6XznO9/B4XDw+uuvB2yzysvL4/7772fKlCnExsai0+k4fvy4XJNXqVSyZs0a0tLS5GLXgRRm1mg03HPPPfzTP/2TrNX39vYSFRXFmjVriIyM5LXXXuPzzz+nv79fro4lrckrMdxaMxgM3HTTTaxZs4YdO3bw5z//mdbWVjweDzqdju9973skJCTw2WeffXUF3HCTz+fz0dLSgkKhkGtfajQanE7nhARwarVaFi9ezOHDh3n//ffp6uqSj6kzZ85EqVTS3d3td0qKlGbW29tLV1cXHo9HLrMn1YZMSkriwoULQaOPlrRfo9GIyWQiMzOTpqYm3G434eHh/OAHP+DixYts27aNS5cu0d/fL28k43nGarUajUaDzWbDYDCQmJiIXq/n5ptvZuXKlRw7dox9+/YFsMdWKAAAIABJREFUxbFgNBpJT0/n9ddfJy4uTg6EdTqd1NbWytWbpDoN/hTukWAymTh9+jT79u3D5/OhUCgwm808/fTTxMTE8Nprr1FcXOwXk7CEkJAQ7rzzTmbOnInRaGT69OkkJCRw6tQpmYI9OTmZxx57DL1ez+eff86ZM2f8tr+lp6fzb//2b9x0001y4Lxerx/E/WexWLDZbJw9e1bW3nw+35j6HGgqSUxMJC0tjeLiYrZv3z6IpTs2NpYFCxZQUVFBc3NzwHmrcI0KuOG0FlEUsVqteL1emXAwLCwMl8sl7zjBiqeSalLm5+fzl7/8hba2NgThcmXxe+65h6SkJHw+n5w3O9Y2r0zg9nq9nDp1ipycHLKzs2VVXa1WY7fbyczMRK/XU1JSEnCsk0qlIicnhwULFlBQUEBqaioWi4XKykp6enqYMmUKarWa/fv3c/78eex2+yDiw5G0xSvR39/PuXPnuPHGG9myZQu33HKLXL+2o6ODP/7xj0GpK6DVavn617/Oz3/+c+Lj4xEEgQsXLrB//35KSkr45JNPmDlzJnfeeScFBQUcOXLkqvc1Hi+8zWajpqaGrKwsnE4nkZGRrF27lvnz51NSUsKBAwcC8qir1WoKCgqIj4+noaFBrs0QFhbGggULuP3223E4HFitViIjI+nr6+Ps2bN+b4CCIPDEE0+wfv16OZfU5/PR2NiIx+Oht7eX7u5uMjIyyMrKIisrSzbbjAdKpZKQkBA0Gg1FRUVUVlYOih/V6XRs2rSJ6OhoPvroo2Hzm78SNriRWDtFUcTpdKJQKHC73eh0OvLy8rDb7fT29tLe3j6s9B8PBEHghhtuIDIykoyMDBISEmhpaeGOO+5g9erVqNVq2tvb+eSTT/wWqlLdgPPnz2OxWMjKyiIsLAyfz8eZM2eoqqoiISGB3NxcWltbaWpq8pu5VqFQkJqaSlZWFna7nbNnz3Lq1Cl6e3upr68nKiqKzs5OqqqqZLuY2+0eZEAeD+W2y+Xi8OHD5OfnM3/+fCwWCzU1NVRXVxMWFkZZWdnYH9QI45wyZQpbtmyRhVtzczNPPfUU7733nuwYMZlMWCwWVCoVH3/8cUCboNPpJCEhgbVr19Le3i7bjfr6+nj//fc5ceKEvAmPdQwD/x0aGkpubi5Op5OzZ8/i8XgoLy9Hp9Nx1113ERERQU9PD4cPHyY2Npbk5OSAAs2lUBDJO2qz2fif//kfOUOnq6sLhULBs88+i8lkwmQyjSlPfODfpZzp7u5uufh2eno6ZrMZq9WKUqlk3bp1bNiwQV5TwQpcviYF3GiLSFKNbTYbPT09dHZ2IggCYWFhhIWF0dPTM2SU+njUW4VCQVJSEkqlkoyMDFatWoVGo+GRRx7BaDTi8/n46KOPqKioGHObQyXLO51OGhoa2L17NwkJCaSlpXHp0iWqqqro7++nq6uLuLg40tLSaGlpGTKxfiwwGo1YLBaKi4tpaWmRKbYVCgUREREIgsAbb7xBfX39sAGw43l+oihy4cIFnn32WRISEjAYDNjtdqZPn/7/2Dvz8Kjqe/+/zuyTycwkk33fCUvCEgJhE0EEBNx3aCtqxeX+bG/b2+3e21tqlee2T20r17YqrqhIQSyyo4AgIBhkDyQkZN/3bZJMMpOZ8/sDz7lJDJDZKHp9P4+PnMnM+Z7lez7n8/0s7zdz5871WVGqQqGQtRi6u7vZunUr77//vrwM1Wg0stLWhx9+yMWLF70as6+vj6amJkwmEwkJCbKc365du1i/fr3b3s1Qj16aW4IgEBwcjCiKhISEEB4eTlhYGBcuXGDt2rXs37+f8ePH88ADD8hq9J4YOafTyV//+leZ2mvr1q3s2LFDji+aTCZ+8pOfkJiYSFlZGS0tLR7fO8kjlGosQ0NDmTx5MqNHj2b58uUEBgby29/+lqNHj/psJXZdGrirpZ1dLpccUHU4HPK/rVYr0dHRJCYmUl9fL8ePpICoO3A6nXzwwQf88Ic/JCYmhn/9139FpVIRGxuLKIrk5eXx+uuvj3h5eqVeVJfLRWtrKx0dHZSUlMicdnApy2m32+X6oOH49K8GyYvp6uqSEzRarRatVoterycuLo6Ojg7KysqGfXN62qjudDqpr6+X46Y6nY6cnBzGjRuHyWTyOhAv1YM98sgjGAwGsrOzZR4y6ZilNqfOzk7eeecdr9qOpITNZ599RmpqKjfddBMWi4Xc3Fx++MMfen0+UghGqjfLzs4mODiYlJQUysvL2bhxI5s3b6akpAS73Y7dbmfhwoUEBgZ6nEEVRZHCwkIefvhhVCoVNptNXu5qNBoWLFjA0qVLZZ3U8vJyr1dH/f391NXVERAQwCOPPMKtt96Kw+HgP/7jP1i/fr1XyZKhuC4N3Egw3IMoiiJms5lRo0ZhNpuprKyUg/dSFnCkEEWRyspKOjs7CQ4OJj4+HoVCgUKhkAsfz5w549MeSqfT+ZW4lFqtxmg00t7ejlar/YrxH+my0eVyYbFYsFgsWK1WoqKi0Gg0lJSUUFVVRUtLy2WXBVcTH7kapKC/w+HA5XKh1+uHVc1yF06nk6amJpqamlAqlUyYMIFbb70Vg8FAVVUVWq2Wn/70p4wbN45XX32V/Px8rx9OyQhFREQQERFBbW0tv/rVr3xS6S+KIm1tbWzfvp0zZ86wbNkyJk+eTFVVFSdOnCA3N5eqqiq5ZlGj0TB+/Hhqa2s5dOjQV+bOSOe7VA0gsZVIL7+srCyeeuop4uPjaWhoYPfu3dTW1np9ntKYUlims7OT1atXs3HjRp8aN7hODZw3DdA6nU4ukO3r65MNkCf7lOIToiiiVCoRBIHe3l62b9/uV/HdgZAMqhS4HsqRNZJJLIoiLS0tlJeXM3r0aLmVqKWlhby8POrr60dcrOmNgZCOtbu72+eiwnApw7l06VIWLFhAdXU1oaGhpKam8vHHH/P222/7THk+JiaGnJwcVCoVO3fu9HmvptRf/fzzzxMSEoJGo5E9bymsEBAQwLhx4wgJCSE1NZX4+HiKi4vd4lEcCo1Gw5gxY8jMzCQiIoL58+fL7CUbNmzwurZvIPR6PZmZmZw5c4Y33niDPXv2+KWp/7o0cJ56RaIoUlNTQ1dXl7xElT6X3k7uwG6388orr/DEE08QEhJCRUUFGzduZNu2bT6t37oSXC4X1dXVdHV1yaUHA+MtV/PgpL85HA5qa2vp7u6mtLQUvV5PW1ubHI8bCbzuC1SpiIyMRKvVEhoa6nU8bChOnz7NhQsXmDBhAvHx8YiiyLZt2/jzn/9MRUWFT8ZQKBRMnDiR8PBwOjo6OHnypFdlJ1eC3W6nrq5u0P1VKpXodDqSk5OZMWMGgiBgsVhITk6msrJykJFw936p1WrGjRvH/fffT0ZGBhaLhdLSUtatW8eGDRt8ztB79uxZPv74Y2pra4elvfcFrksD5yn6+vqor6+Xs0oDCxE9MXA2m43XXnuNv//97yiVShwOxxVZg/2B3t5eueBxpLVVA43ewLhdf38/ra2ttLW1+ayZ2R3o9XrCw8MJDAwkLS2N3Nxcny3xXS4XJSUlcgYuPz+fDRs2cPHiRZ91SsAlo9Hc3ExLSwuVlZVUVVX5nTNt4LFLc6CmpobPP/+c7u5uysvLZbICb85T0rTt6uqiqamJgwcP8uKLL5KXl+dzA9Td3c2xY8e8Puar4apPvCAIbwC3Ao2iKGZ8+ZkF2AAkAuXA/aIotgmXnqrVwGKgB3hYFMWT7h6UNy0nUoZVipcNDJB7MhEl4sJ/FoaLHw704EZCpDn0OoB3TdLeoL6+npKSEtrb22Xj6wuIokhTUxMvvPACL7zwgt/OTxRFtm/fzokTJ7BarbS3t19zZl2n00lbWxt79uxh37599Pf3y0kHb9Db28uhQ4c4f/48zc3NtLa2+o2xWnrh+hsjcWneAv4CvD3gs18C+0RR/J0gCL/8cvsXwCIg7cv/coCXvvy/W9BqtVek6R4pJCMneXO+pB7y5Fgk5XdPMdAzG+iZDsceIhlBl8uFSqWSvyclKmw2m9vHIsUhh441UnR0dPDee++xb98+ioqKrji+py+5a2G47Xa7z5a8nsLpdNLZ2elxhns4uFwu6uvrfSIi5G1frK/2e1UDJ4riQUEQEod8fAcw58t/rwUOcMnA3QG8LV662p8LghAkCEKUKIpuXbElS5Z41X4lPeDSQy3VFRkMhkHf0+v13HXXXR6NcTWEhIQM2o6JieGuu+5y+wEc6rkNndBS8/pASJXwA3tMpe9qNJpBGU13jmO4azh37twRJ1ukfQjCJd60K3mfQw23IAjccccdflnODM3oBgYGcvfdd/tlrLCwsEHb8fHxXs3BKxm46OjoQdtZWVkkJiZ6PNaVIFGKSbj55pv9kjRw10nxNAYXMcBo1QMRX/47Bqga8L3qLz9zy8CNGjXKw8NyD1Ka/VrAZDIxbty4azJWZGTkIGk6fyI1NfWajAOQmZl5TcbRarXXbKzg4GCCg4OvyVixsbFfeRn6C2lpaddknKvBa2X7L701t191giA8LgjCcUEQjl+Lcotv8S2+xf89eGrgGgRBiAL48v9S/rgGiBvwvdgvP/sKRFFcI4pitiiK2b4o+vwW3+JbfIuh8HSJuhVYDvzuy/9vGfD504Ig/J1LyYUOd+NvAHv27PFLhsVoNDJr1ix522azceDAAa/3O1wfYHx8/KAlaX19vd9UxSdMmDAo3pKfn++3IPiNN944KGb1+eef097eftl2uOH6gYeykwwXP1KpVNx8882DvrNnzx6/JBEkpg4JPT09HD582OMymsudl8S3NzAEU1NTw9mzZz088isjKyuLiIgIebugoIDKysqvNMIPPO6hNXdS/FalUskVClJpx0DWnxtuuAGtVitvHzp0iK6uLp+fk0qlYv78+SP//tW+IAjCei4lFEIFQagGVnLJsG0UBOH7QAVw/5df38mlEpFiLpWJPOLOwUv44osv/JKeDg8PH2Tg7HY7x44d83q/w01op9M5yMC1tLT4ZKzhEBMTM8jAVVRU+G2snJycQQYuLy/PZ+07A6FWq7n55psHffbFF1/45cUXExMzyMD19vb6tEZvIARBGGTgmpub/XavEhMTBxm40tJSTpw4MeJaSinzL/3ndDoHqa8NNIZTp04dZODy8vI8FvW5EjQajW8NnCiKSy/zp3nDfFcE/t+IR/8aQ6PRoNVqCQkJwWw2U11dTUdHxzWp7fk6QhAEVCoVgiDITCbuwl8FocPt91qOda0wkprJgd+VeBcjIiLQ6XQ0NjYOEuuRDJy/SkJ8gW9MJ4NU56bX6zEajfT19dHe3u7zJY1SqSQuLo7x48eTlpZGRkYGtbW17N69mxMnTnhdmT2wPOJadxr4C5Kw77Rp02Tqbalv8nLwa3X7l4bW6XTKJUTXaux/Jjw5L5PJxE033URYWBgHDhzg5MmT8n3zxXWSiDADAwNRq9X09/fjcDiwWq1y7603+NobOMmN1mq1REdHs2jRIsaPH09ubi7vvvuuTxviVSoVU6dOZfny5WRnZ9Pd3U1XVxctLS1YrVavipPVajUxMTHEx8cTGhqK0+mkurqa8vJy2trafL5cEoRLAj6S9qrNZvNICHkk39doNEyfPp358+ejVqsJDg6msbFxkKaBP6FWqzGbzURFRXHLLbdgNBpldozy8vJhGaTdvQ4DC8l96cV7yvPmq7HDwsLIzMzEbDZz6NAhn8xDiao/ISGBnJwcJkyYQFhYmExx39nZKbMxD40ZuouvtYFTKBSYTCYCAwNl0eQVK1YQGxtLZ2enzydaYmIiP/nJTwgPD+f8+fOcOHGC7u5uCgoKKCoq8ng8Qbik7r106VISExNlvdeUlBRSU1PZv3+/zxqdJWLQ9PR0MjIymDBhAnq9nrKyMt555x0qKyt9Ms5AuFwuKisrWbNmDeHh4UyaNInw8HC3DdxIl0JS37FKpSImJobx48czceJEpk2bxowZM1CpVFy4cIELFy54nYyRNBksFgtxcXHU1dVRWlrqcQxZWsqbTCaSkpIYM2YMJpOJzs5OioqKKCkpoaOjw28tVAOhUqlwOp0cP34ctVp9Wa97pAZI4iWcOHEiM2bMYNq0aYwfPx6TyURLSwt9fX0olUo0Gg3Z2dno9XrefPPNEXMuDnsOHv/ynwyFQkFsbCyzZs2is7OT3t5eFi9eLFdqf/rppz6bBFK3wBNPPIHRaOTll1/m2LFj9Pf3Ex4eTllZmVfNyFqtlu9973tkZWWxfft29u7dS1tbGxEREcycOZO5c+eyZcsWrxueJZbihx56iAULFhAWFkZgYCAul4uWlhZ6enp49dVXfZ796u/vp6CgAJvNRmxsLLfeeivh4eFusSGPBBqNhuDgYDIzM1mwYAFJSUnyElQQBJKSklAqlVitVo4cOeIVvZDk3UyZMoX09HQcDgejR48mPz+fv//977S0tHh0DlqtlvHjx/PYY49x4403EhISglqtlsk27XY7LS0tvPXWW2zevJmmpiZZBOZqcPc8VSoV7e3t5OfnExIS4pWhgUsdIkuXLmXZsmWEhYXJSnI7duzg4MGD9Pf3M2/ePJYvXy4r3pvNZrq6ur4S9xvxOXh1xP8kCILA2LFj+dnPfkZWVha7d+9GqVSyYMECVCoVR48e5fDhw15Rlg9EeHg4jz/+OFOmTGH9+vXs3buXrq4utFotbW1tw7JVuDOWXq9n6tSp5Ofns2XLFpkNpbu7m6ioKJYsWcKZM2dk0WRPYTKZePzxx3nsscdkbv2+vj76+/uJjY3l+9//PsXFxezevdunHoIU73I6nRgMBsxms08JDKQX0H333cesWbNITEzE6XRSWVnJyZMniYiIQKvV0tvbS21tLatXr+aNN96QOfY8uaYWi4X58+eTkZFBfX09XV1d8jy40v6uRm0VHx/P008/zW233Sa3xQ3UXlUoFISFhbFq1Sr+8z//k7Nnz/KnP/2J3NxcmpubfbaclZbGPT096HQ6DAaDV8kEhULBqFGjmD9/Pjqdjn379vHaa69RVFQkh0akXuebbrqJtLQ02avzZtyvpYFLTEzk17/+NQsWLOD8+fN0dHRwzz33EBgYSE1NDX/84x99Ft/R6XTcfffd3H333WzcuJFNmzbJ6l3D6T54goCAAEwmE7W1tXJNGVxa2klyfqmpqZSVlXmlnjR58mSWLl0qvxXLy8tl/rzU1FRSUlL48Y9/TGFhIcXFxT6L+ymVSrnh32Kx0NzcTHl5+VWPd6QwmUwsX76cpUuXYrVaOX36NFu3buXs2bPodDoefvhhpk+fTn19PZs3b+bNN98cFJt19x4GBASwbNkyJk2aRHl5OXl5ebLRrq+vv+I9utJYKpVK1qXV6XSyIFFubi4dHR0yE3JYWBipqamyzN7f/vY3XnjhBV5//XWfkXrCJQ5BrVZLeHi418wi0rL7woULHDp0iI8//piLFy/S398vL8uNRiPJyckYDAZqa2s5ceLEV5Ty3PZCPT7ifxLCw8P5zW9+w6JFi2hvb2ffvn3odDqSkpLo7+9ny5YtHDlyxKtYgQRBEJg0aRJPPPEESqVSFuMYyYPvzlharVZugh+YRRWESzJ1bW1tsuSep4mMgIAAbrvtNsLCwujr6+PQoUPs2rVLXl5PmzaNxx57jMTERHJycqipqRnx0udqkIL4Go2G8PBw8vPzaW9vv+Jv3InrCIJAXV0dhw4d4vjx4zK1d19fH4sXL+bWW2/FZrOxevVqPvroI69phZKSkpgxYwaFhYWcOXOGlpYWgoKC5Pvj6YtBoVDIguJWq5X6+nref/991q1bR0tLC0qlErVaTUhICMnJycyfP59HHnmEkJAQZs+ezd69ezl//rxPWXcnTpxIaGiozN02HEbyMlIoFJSWltLQ0EB7ezvt7e0yu01AQICsXrd48WLMZjMnTpygoqJikGylJ/haGTiLxcJzzz3HvffeiyiKfPLJJ+zcuZOf/vSn6HQ6zp8/z3vvvecz7y0lJYVXXnmF1NRU1q5dS3l5+YgnrzseSE9PD1arFa1Wi9lslieSVqslMDAQs9lMQkKC24SdA48lIiKCzMxMlEoltbW17Nixgz179sjklw6Hg7lz5zJ27FimT5/OsWPHKC0t9UrAWIJKpUKn05GSkkJmZiZbtmzx2RJYFEU6OzvZuHEjW7ZswWazYbfbUSgUpKen8+///u/09fXxzDPP+MS4CYJAR0cHa9eupbS0VNaysFqtBAQEyILknsDpdFJRUcG5c+dwuVzU1dVRV1cnJ8ycTic2m42Ojg4qKytxOp0sW7aMwMBAxo4dS0pKyhVpqEY6J1UqFYGBgcycOZMJEybwySef0NTUdNl5MJL9OhwOGhoaZB44qRMiMDCQ1NRUwsPDmTx5MrNmzcLlclFYWEhDQ8M3s0xkuAum1+t58sknWbZsGSqVii1btvDb3/6WuLg4Ro8eTX9/P4cOHeLcuXNe3Qjpe1OmTOGvf/0raWlpdHR00NjYiNFoRKlUyint+vp62tra5Lf20LaXkaK9vZ1t27ZhMBiYOHEiTU1NOBwO1Gq1LHlXXV3tcUBcpVIRFBREX18f3d3dskCKRqNBqVTKywRJTDsxMZGoqCiZSdgbDMyc3X333XR1dVFbW3vV83Dn+rlcLqxW6yDdiuzsbJ599lk0Gg2rVq1i+/btbr2crlSeIRmegffcZrNRWlpKUFCQx7yDTqdTbt3SarU4nU7Cw8MZNWqUXBcmcbWZzWbmzJkjK2ppNBpMJpNXnIcKhQKj0ciECROYOHEiUVFR7Nixg1OnTnldkSDVHMJg79zlcqFUKgkPD2fq1KkYjUbq6uooKCigo6PD+5erV7++RpDexvPmzUOtVuNwOKisrCQjI4PFixcTGxsrB7Hj4+OprKz0uEhQrVYzduxYnnvuOTIzM+UHf8mSJcTHx2M0GsnJyUEURT766CPeffddTp8+TU9Pz2Vv4tVgt9v59NNPmT17NllZWVgsFll4JC0tjcDAQKqrqz3m13K5XDQ2NrJr1y7gUu/lTTfdhFar5dChQygUCm688UZiY2PR6XRotdpB3G2eBs2lv0dFRTF16lTCwsLYs2ePxxnGkcJkMvH973+f5ORknnvuOd5//32PtUqH+9twHpIgXBJtlgSPPIH4pTiQJLytVCppbW1Fr9fT19eHw+EgNDSUpKQkcnJyePDBB+W/nTt3jnPnzl0x036leyXFyFJTU5k2bRomk4nz589TWFh4Va/Xne6IgZBeTPX19UyfPn0Q0a308vC2DvC6NHBDT0iqZ9JqtTgcDpRKJbfeeivTp08nMTERg8GAw+Fg1qxZNDc3s23bNkpLS+XszEB67ytBEATi4uL4+c9/zsyZM+X0vEajIT4+npSUFHQ6HQqFgt7eXlJSUoiMjJQDwlJJgrs3RKoTu3jxImPGjMFisciEn7GxsajVagoKCjyOrUjyetu2bcNqtbJkyRIsFgvTp0/HarUyduxYZs+eTVRUlOzR2e121Go1gNvkmAOhVqtJSUlh/PjxKBQK2traPD6PkV7XxMRE0tPTOX36NB988ME1aQuTvNTTp097tQx2OBxcuHCBhoYGtFotRqOR3t5eurq6sNvtjB49mmXLljF37lxZo7ewsJB169ZRUVHh0bkqFAr0ej06nY7W1lY+/fRTkpOTcTgcspfvT+2EgV6n1IGkUqkICAiQDbY0B7+RZSJSpf0XX3yBXq8nMTERvV5PamoqQUFBsrq5JJLc29sr3xB3boogCMTExJCZmYkoXtJF3bJlC6IoyvGj4OBgbDYb5eXlHDx4kLy8PFnxauCSxd3JYLVayc/Px+Fw0NjYSFNTEwEBAVgsFoqKiigtLfVqgvX19VFdXc2uXbuw2+1Mnz6dwMBApk+fzuTJk0lKSiIgIICenh6Ki4vlbK63E1uv1xMREUFbWxulpaVYrVbUarXfdC5UKhWjR48mKCiI9957zy+MFkMhCALp6enExcVd1Vu82gMqlQf19PTIRa/S/NZqtZhMJuLi4uQXX319PX/+85/ZvXu3R+I6SqUSk8mEwWCQO3O6u7tJSUkhPT2d5uZmenp6ZDFyX0gJSFCr1UyZMoWcnBzmzp1Leno67e3t5OXl0dzcjFqtRqFQeJXs+loYuN7eXo4dO8aZM2dkybSpU6fy0EMPERwcjNPp5PTp0/z4xz/m4sWL8nLRXbhcLo4fP85dd92Fw+GgtbUVlUolL40zMjJQqVS0tLTw3nvvsXHjRpqamnxSTuFwOGhqakKj0VBcXExPTw8zZ87EZrOxZcsWWltbvZ5Y/f39NDY2smXLFvLz87nttttYsGABFotFXpY2NjZy+PBhamtrsdlsXp2bQqEgODgYo9FIZWUlBw8exG63ExERQU1NjdfZvoHZZskYTJ06lTlz5tDW1kZXVxdqtfqq43jbLB4QEMCsWbMoKyujpmZY+kO3IQXjpdiX1DERFxdHVFQUWq0Wl8vF0aNH2bFjx6DyoithKF2VWq2WQy8lJSX09/ej1+txOBzU1NTIZUTSy3u4Mdy5ftK9Cg4OZtasWcybN4/Y2FgmTZqERqPhk08+4aWXXqKuro7+/n7ZuH+jDZwoXlLelt7G9fX1dHZ2cuedd6JQKLBarTz77LOcOnXKayNgs9koKSmRt81mM6NGjWLOnDmEhIRw9uxZ3nrrLZ/3uUreksvlwm63Ex0dzfz582lsbOTMmTM+kyqUPISioiIuXrzItGnTSE5OluMfhw8fZv/+/V+pP/IUBoOB+Ph4ioqKaGxsRK1Wk56ejkqloqqqyuNsqlKpJDo6GqPRiMFgwGg0EhkZSWhoqEwDPnfuXPLy8sjPz/eb1GNAQABLliwB4O9///tVu0087ZowGAyMHj2a+++/n3HjxiEIAmVlZfzqV7+itbXVo2OH/9VZlUp49Hq9rMdaXV1NdXXfvVRHAAAgAElEQVT1VRMMIz0nqV88ISGBGTNmMHHiRBITE0lJSZEz4StXrsRqtcr79PYl+LUwcEPhcrnQ6XRERUUhiiLnz5/n2LFjfosRaLVa9Ho9u3bt4o9//OMgRgVfQq1WExoaisFg4J577mH8+PG88sorVFdX+3ysvr4+bDabHOdxuVyUlpby8ssv09jY6BPjJqk0FRUV4XA4UKlUKJVKMjMzSU9PZ+vWrdTW1rqdoROES2LHjz32GFlZWRgMBrmNSKVSkZWVhVqtlgka/UFUIIoiWq2W2bNnk5mZydq1a33mvQ2FwWBg9uzZfOc73yEnJ0deRfz3f/83RUVFXu/f6XTK/bSCIFBYWMjZs2cHtUhdCSN57gwGA7fddhtLliyRs/QhISGIosiZM2d4/fXX2bJli5wJ9xW+lgZOqVQyZswYmXWjvLzcL83HKpVKDua+/vrrbNy4kbKyMr9J01ksFqZOncqECRPIyclh79697N692y+q3wqFgqioKGJiYlCpVFitVtauXUteXp7PMo4Ara2tbN68mbS0NKKjo4mMjCQ6OprOzk50Op1Hx65UKomNjWXRokWMHTsWp9NJT08P7e3t2Gw2uru72bVrF2vWrOHChQs+80Dgf5vh9Xo92dnZTJs2je3bt3sdI70clEolkydP5qmnnmLatGlyy9lrr73Gpk2b3JqLwy0x+/v7aWtrIzAwkN7eXlpaWqirq/Np7FKhUJCRkcEPfvADMjMz5cLvuro61qxZw44dO7h48eKInuFvfCeDBJVKJTcf+4M5FC5N5nPnznHy5Emam5t91pp1ubECAwPJyclh6tSpnDt3jr/+9a8+YxEZbjyFQoFaraarq4sdO3awadMmnxtTl8tFRUUFdXV1BAUF0dLSQklJiay/6enLwmazcfHiRdRqNb29vfT29lJSUkJlZSVnz57l0KFDPolbDoVSqSQhIYHvfOc7xMTEsGnTJk6dOuU38eeAgABuuOEGJk+ejMlkwuFwsHv3bl599VWv27KkBv6Kigq5ztIf2VKVSkVycjLBwcE4HA46Ozv5/PPP+f3vf09BQYFfhdW/lgauv7+fXbt2YTAY5BYqf3g5DoeD4uJin+93OIjiJWX2w4cPU1ZWxqZNm/w6ttPpJDc3l7179yKKIm+99RbV1dV+MeCiKNLX10dDQwMNDQ1e76+/v5/Kykqef/55VCoVDQ0N9Pb2YrVacTgcfitpEAQBs9nMwoULMZlMrFu3jiNHjri1enA3oaFWqzGZTDIZZGFhIa+88orPNDeGJjP8AZfLxcmTJ1mzZg06nY5Dhw5x6tQpn8awL4evpYGDS2Id//M//yMLO38T0NTUxGuvvSZPOn/C6XRy5swZfv3rX+N0Ov3CfuxP2Gw2zp49KxeFeoPhjM5w9YzS8vT06dO8//77fvOuB6K7u5tPPvmEoKAg+vv7OXDggM+IJ32Fqxltp9NJcXExf/nLX/xaTzccrksDN9K3nLt1bv9MjOScRFH0KJboaZmDVDbiDbxpDXJ3vwPP83IdBb6AVMowUFxFWtJ3d3dz8uRJj1YMCoViWPbgK8Fut3PgwAFOnz6NzWbDarV6bNwkOiJfPjMDtTaGfi7Bl/fK3bkuXA8GIjo6Wnz88cfl7ba2Nr8FbM1ms7ztcrmuymrhKbRarcznBZcmqr+KTgMDA9FoNPJ2T0+PX5bsgFxYLcHXzMkSFAoFQUFBgz7z17yQ2pQkuFyuQX2QAx8qyUB4Wu6h0+nQ6/XyZ1J/8Eh+6+6Yw80LqUPGV5CujdlsHjQvOjo6/PICEgSB4ODgQZ8988wzJ0RRzB7u+9elBzf0BPwFiZ/sWkCj0VyzsQICArhWYtoDDYO/cS3nxbUaS6vVDpLb8yeu5bwY6Ej8M+Gpsv23+Bbf4ltc9/jWwH2Lb/EtvrG4Lpeo77777rDUQJfrg5MCwBIbrlTPM/A3kkjInXfeKf+2q6uL9evXj5ibTAo+S9tSj9zQuIykGTFz5kx5H6Wlpezdu9edy/AVYd3LNfLfdNNNpKamytuff/45eXl5Hsdaho4nQalUct999w1alv7jH/+Q+eV8CaVSyaOPPjroWN544w2/xHXCw8MHzYuOjg42bNjg83EAMjMzmT59urxdVFTEgQMH/DLW/PnzSUpKkrdzc3MHMf4O1N+VniEJA+e6lKmWMqADabQktp377rtv0PL3/fff94sspFqt5pFHHhnx969LA1ddXe128Z900YHLZpmGPhxOp5Pa2toR71+r1RIUFCTzWF1JRzQ6OnrQts1mk8kKRwqVSoXBYMDpdA5iSBmKofVE7e3tIz4vdzE0odDc3Oz2eY0Ew7EXe1MYfCUMzcz19/f75ZwAEhISBm17Mi9GiqGJpubm5ivWOkpGzWQyMX78eCIiIjh+/Dj19fVykftwv5Xo9geiqanJLwX4A5MmI8F1uUT11PMY6MX5AwEBAUydOpWUlBSZK+1y8DZTpVAoGDNmDI888gg33HCD16pG3+JbXC37K4qXlK1SUlJ4+OGHiYmJoaenR2aVudxvfVnbJnmSvprr16UH5y6USiV6vZ6QkBD6+vpoamry+ZteFEW5qry0tNSnvFjDITQ0lNtuu4309HTKyspkvrmvA9RqNUFBQYjiJdm5gZTu17osaaCil1Sxfz2URv0zMJLzttvt1NfXs3XrVg4ePDii8IO3z5pEuBkWFkZsbCxBQUHU19dz8eJFr9vRrksD5471llSG4uPjmTx5Mvn5+X6JCanVarKzs2UFJ3/2z5lMJh555BGMRiObNm0iNzfXLbpyT2u0fPHgR0dH8+STTzJlyhS0Wu1XDLPNZiM/P5/c3Fz27NnjMQ375SD110pKZWq1GovFwqhRo7Db7RQXF1NWVjaIPulbz3gwtFotn332mV+eo6EwGAykpqaSkZFBUlISwcHBhIaGyu2K3hQ2w9fUwEkiG4GBgSQkJBAZGUliYiKpqakUFRVdMcbgKaKiopg0aRIfffSR3wpO4VJx5uOPP86SJUt49913OXTokE/ENy4HiUgxPDyc6urqERWdXg4qlYrZs2fz6KOPEhkZOWx1uyiK3HLLLbS2tvL666/z8ssv09DQ4BPyy/DwcG688UYyMzMpKSnh6NGjdHZ2YrFYWLp0KWPGjKG8vJyf//znXLhwwe1rqlarGTNmDPPnz+fIkSNcvHhRXp45HA6vrt21wEjmv6So5Q+KrqHHYjKZuOWWW7j99tuJjo6mra2NyspKRFEkJCQEg8GAQqEYZOC+kZTlEiQm0NTUVKKiomSh5HPnztHW1obD4biitJ+nBs5gMJCVlcX+/fs5efKk35aKwcHBrFixggceeIDc3Fy2bt3qV+OmVCpJTk7mgQceICkpidWrV/sk+zrw306nk5aWFpqbmwkNDcVsNsvkio888gh6vZ63336bgoICjzsiBEEgMTGRlStXcvPNN2O323nnnXf45JNP6OvrIyEhgSlTpsjUUAqFwu1zFASBqVOn8qc//YmJEyciCIJ8vIIgcPToUVatWkVPTw/d3d0UFBT4lMJLoVAwadIkjEYjFy5coL6+3u19jOScY2NjWbhwISUlJX7rhgEICQnhO9/5Do8++ii9vb2cOnWK8vJyxo0bR3JyMgUFBXJM0JvwxtcqyRAZGcmjjz7Ks88+yz333EN4eDhtbW1YrVY6OzspKCigrq7usr/35ALpdDpuv/12lixZ4lfPzWg08uCDD/Ld736Xqqoq3nrrLRobG/3quaWnp7Ns2TJmz55NcHCwLEHnKfr7+9m3bx/r1q2jqamJnp4eampqWLduHc899xxHjx6ltbVV9nqcTieBgYEkJSV5lUQxGAwsX76cW2+9laCgIEpLS9mzZw+NjY2YTCYWL15MdHQ0CoWC3NxcysvLPRonOjqasLAwlEqlzIQrqZDNmTOHXbt28dFHH7Fhwwa+973veaxjOxySk5N5/fXX+fDDD3n++ecZM2aMz/YtQalU8vDDD3PPPff4lexBp9OxZMkSHn74YXp6enjttdd4/fXXaW5ultl9Dx8+TH19vUyr7mni4ap3QBCEN4BbgUZRFDO+/Ow3wApAygP/hyiKO7/8278D3wecwA9FUfzI3YMa7qFWKpWMHTuWm2++mfDwcFpbWwkJCZEZcCdNmkRFRcUVb4wnxiItLY1f/vKXhISEyN5iYWEhjY2NtLa2+oTaW6lUsnDhQp566ikiIiL4+OOPPX4IR4q0tDRWrFjB5MmTUalUNDY2otPpvDJwoijS3NzMSy+9xPjx48nJyQFg1KhRsrKWwWCgp6eHpqYmPvjgA7Zv3y5TxEuKXu4iOTmZuXPnEhAQwJkzZ3jhhRdkT3vWrFncfPPNMq3Syy+/7BFNj/ilelVNTY0sUymJHDkcDoxGIzqdjoCAANLS0rjzzjvZsGGDTwyFIAgsWbKEpKQkAgMDuffee6mrq+N3v/udTyUYk5KSuOGGG2htbfWr9xYTE8PChQtRKBS89dZbbNq0iczMTBYvXozVauXFF18kNzd30LMleXD+ILx8C/gL8PaQz/8siuLzAz8QBGEs8CAwDogG9gqCMEoURa9TmgqFgqqqKl588UVsNhudnZ3yRDWZTIwaNYqurq6rpsHdgUql4t5778VisXDy5Ek6OzuJiorCYrEQFhZGQkIC69atY9euXV55WgkJCfz6178mLi6OmpoawsPDWbRoEeXl5ZSUlNDU1ORWUuNqRspsNnPrrbcSERHBtm3bMJlMhISEkJSUxNGjR70K/IuiSH19PQUFBcydOxedTifH4wRBwG63c/bsWdauXcu2bdvo6OiQM9KeXEOlUkliYiIWi4X6+npWrlzJp59+Sn9/P6mpqaxcuRKLxUJbWxsrV67k9OnTXxlnpONWV1dTVlbGxIkTaWtrY926dezcuZOWlhaioqL4xS9+wQ033IAgCGzcuNFniSiDwUBSUhJOp5O6ujoEQeD+++/niy++YPPmzT5bCgcHB1NYWMjf/vY3v60cpGRdamoqZ86c4cCBA8TGxvLYY48RERHBr3/9aw4ePOizc7qqgRNF8aAgCIkj3N8dwN9FUewDygRBKAamAkfdOajhHlCJ7K+wsHBQx4BCoaCjo4P58+f7nLZcr9cTHR3NqlWrZJEZqRhy3Lhx/Ou//iu33HILR44c8ZiVRK/Xs3LlSkaNGoXT6cRoNDJ//nzuuusuWeT6008/5bnnnqOgoMAjabihCAkJobW1ld/97ncUFRURGBjI7NmzSU1NRafTeZ3ZdDgc5Ofny1J3SqUSURTp7e2lpqaGTz/9lPr6ekwmk1xn5ek5BQUFkZWVhUKh4KWXXuKTTz6Rx/2v//ovkpKS6OvrY+PGjezevdurOdLe3s6HH35IdnY2tbW15ObmcvLkSex2OwqFgsjISFkv4dixYz5b5mVkZBAREcHBgwc5f/48c+bMYdy4cT5vaO/t7eXo0aNUVVW59Tt3vP6AgADGjh1LWFgYFy9eJCEhgRtvvJHk5GR+//vfc+DAAZ+WeHkTJHhaEISHgOPAv4mi2AbEAJ8P+E71l599BYIgPA48DiNjHhjuAZDiOB0dHcTExJCXl+f2SVyuPEIqGn7ppZfIz88f5LJLOhBnzpxhxowZxMbGemTgFAoFRqOR2NhY2VgHBARQWVlJX18fRqORoKAgcnJyeOedd1i7di2vvvqqV6y4UpnL+vXrZeocSZYxMjISs9nsdYuNQqGQWWgHtv8oFAri4uL4l3/5F55++mnKy8vZsGEDa9eupba21qOlvpR0amxsZNu2bbLUXFZWFjNmzEAQBKqqqjh06BCCIBAQEIDNZhtUnDrSB9TlcrFr1y6ioqLo7Ozk/PnzsiDR5MmTSUxMxOVy8eGHH/qsk0TSHxk3bhyVlZXEx8cTFRUlJzJ8ZUSlOsGysrKvvAQGKm/ZbDa5rtETSPvp6ekhKiqK7373u6SlpbF3714OHz7s8/pVTw3cS8CzgPjl//8IPOrODkRRXAOsgUt8cB4eB3BJyTwkJOSqqukjnchS4aEgCJfNJknlFRqNxqPyAMkTdLlcFBQUkJWVhU6n4/z58/z+97+nrq4Oo9FIamoqd955JzfccAPf/e53KSws5MMPP/TYE5EM2lCjbrfbSU5OJjAw0KP9DoRWq+WOO+4YRIQolfYIgiDzoY0bN44f/ehHjBo1in379vHuu++6/eBIQtlOpxOLxUJgYCCpqan827/9m6y6plKpuOGGG4iNjWXv3r2UlJTI2rnueo42m40333xT9q6l8R5++GH0ej1FRUW89tprPuP+k+aJlMnv7u4mJCSEkpISt5NQV5r/CoWC8PBwXC7XV5bWOp2OadOmyXqplZWVlJaW0tfX57YmqiiKVFdXU1VVhdlsJjExkdraWj755BOvi3qHg0cGThRF2YUQBOFVYPuXmzVA3ICvxn75mbv7H/F3BUFg4cKFCILgk+WbtE+dTkdiYiL9/f2cOXNm0N8llaDp06dTWlrqESuu5H329PSwa9cu5s+fT2hoKPX19Zw5c4a6ujoUCgX5+fl0dXURGxtLeHg48fHxaLVajw3c5TxWKa7oiwbpgIAA4uLiBn3W399PR0cHKpVKlvSTCEjvvfdexowZw7Zt29waX/J6W1tbmTZtGq+88grNzc2yVycVGgcFBZGdnY1er+fIkSOo1Wq51c4TD2hgksLpdKJQKMjMzEQQBPbs2eMTKb+B+z927BibNm0iNDQUq9XKd7/7XWpra902old6NiQxnb6+vq+wDvf19ZGXlycrfC1atIi3337bba1ZqbSmurqa1tZWmYa9tbVVzkh7KzY+FB4ZOEEQokRRlDqE7wLOffnvrcB7giD8iUtJhjTgmNdHefnjIDExkRkzZsi6mxqN5rJtVMO9bYb7ntPpxGq1kpqaislkoqCgQL6ZarWa2bNn85vf/IaAgAB++ctfeiye4XK56Onp4ZNPPuHNN9/kwQcfxGAwEBcXhyAI9Pb2yjGd3t5eFAqFHM/yJSSDbbPZfPIWbWlp4YEHHuBXv/oVycnJtLS0sHHjRjo6OigtLaWrq4uZM2fy0EMPMX78eLRaLWFhYcTFxY1YoR3+V5k9PDyclJQUQkNDB/1N0mU9e/Ys27dvZ9++fdTW1spLLF88SJKYjnRfysvLfVrwK4oi586d47e//S1KpZLU1FQWLlzI2bNnferx2O12SkpKiI+PR61Wy3FF+F9q+4CAAGJjY0lPT/f4XHp6erBarQQFBaFSqairq6O9vZ158+ah0+k4d+6c3Nw/NIzgybwfSZnIemAOECoIQjWwEpgjCMJELi1Ry4EnvjyB84IgbATygX7g//kigzocpJv95JNPMnr0aLZv3y7HPaTq56EXxB132uFw0N7ezty5czl37hwXLlxAo9Ewe/ZsfvKTn6DT6Xj++ec5f/78iI3p5WCz2Xj++ec5ffo0P/rRj/jDH/5AcXExZ8+eRafTMWvWLMaNGyezQXir0j50slgsFjIyMr7SwuQpnE4nX3zxBcuWLZM9VWlp2t/fT0REBFOmTGHChAmyNmpfX5/bdYaiKNLR0cH58+dpbm4mKChIpvhxOBzk5uby3nvvsWXLFhoaGvzayzuQOsvXcLlcstFsb2/HarV61C54pWMTRZELFy6QmJhIREQE9fX1GI1GWWdWp9ORmZnJ1KlTsVqtg3p6R6ozIXV86HQ6goOD6evr4/Tp0/T19TFr1iySkpI4e/YsW7dupby8XO5j9uaFPpIs6tJhPn79Ct9fBazy+IiuApVKhVarJTMzkyeeeIJ58+axf/9+1q9fT2lp6Vd44DyFKIrk5eVx22238dhjj9HS0kJQUBA33ngjtbW1/O53v2PPnj0+MQhw6QE5cuQIoaGh/PCHP2TBggXMnz8fg8GAXq+nt7eXjz76iIMHD3olZDz0IVSpVEyaNIm0tDReeukln2aiu7u75VhlUlISoaGhjBs3jlmzZrFo0SLZuDmdTvbs2UNbW5tbb2qp7m7r1q1kZWURFRWF0WhEFEVOnjzJz372M44dO+b35vrGxkaqqqoIDg4mLi6OgIAAnyu0S5BawoYTerkarnYdWlpaOHjwIC6Xi9DQUBITE7FarbS2tpKRkUFqair79+/nxIkTg7xUd66vtGqx2+309/dTXl5OQEAAgYGBpKeno1arZSnLgU6Kp/fwa9WqpdVqycjIYP78+cybN4+IiAj+8Y9/8PLLL8t9gVeCuxepsbGRXbt2sWzZMm644QZMJhOFhYWsWrVKfvP4Ep2dnfzjH/+gvr6en/70p6Snp+NyuWhoaGDPnj2sXr36ip0aI4EUtJbeuomJidx+++0UFBRc1hv1BpGRkTz99NNkZWURExNDbGwsRqNRHt/lclFaWsratWvp6elxe3yn00lTUxPt7e2o1WoEQcBqtbJ+/XrOnDkzov15e87d3d3s3LmT0aNHExQU5DZnmTtwOBy0trbKLWfuYCTnWVVVJcegJQ5Cp9NJVVUVHR0dnDt3zusGeMn7M5lMzJo1S06mGY1GmpqaqKiooKuryycZ1a+VgQsKCmL27NlMnTqVuro6Vq9ezcGDB7FarX6ZyP39/ezdu5djx46hUqlwuVyydNvV9uXpQyPF5M6fP4/FYpEr/6urq33SNSF5cJGRkYwaNYp7771XFs/2tcKYWq1mxYoVPPHEExiNxkFsyHDJuBUXF7Ny5UrOnTvn8bkZDAaio6PlxEFzczMXLlzwmXd9NbhcLnJzc7Hb7UyYMIHw8HCfdhgMRH9/P83NzR7p2I7U4xNFEZvNNqgesqOjA4VCMeyY7nqSjY2NlJWVkZWVxaJFi1Cr1dhsNrZs2cKqVas8LhkaDl8rA9fd3c3nn39OeXk5FRUV5OXl+by4dygkfrlrCZfLRV1dnd+YXpVKJZMmTWLevHnU1dWxYcOGK7KweIOuri5aWlpk+iKXy0VrayvNzc2UlJTw5ptv8vHHH3vVGqRQKOjt7aW/vx9BEKitraWlpeWa8r6Fhoai1WoZM2YMc+fOpaioyC/sw1JtYVNT0zU9PymWOhzc6RMVRZHKykpeeukl5s2bR3x8PJ2dnRw6dEhmzvElvnYG7osvvgB8yyL6fw0ul4vCwkKqq6spLy+ntbXVL9fS4XDw/vvvU1ZWRlpampxkKCwspKCggOLiYp/0PHZ0dPDGG2/Q09ODXq/n8OHDVFRUXLP5oVQqSUpKkj3UhQsX8s477/glDmc2m1GpVB5n7v0Bd9vsent7+eKLLzhx4sQgzQd/3K+vlYETRdGvLAf/V+BwOGSPzd9GoLKyksrKSr+O4XK5+PzzzykoKADAarX6TfV+OAiCQEREBC6Xi97eXpqamlAqlX4ZJywsjKCgIAICAlCpVNf0PH2JK3mEvsR1aeCGitMOfAg9eSAl91nK2g2EtGzyJQRB+ApVjkKh8Cl9ztB9D4RUTDvwWknXQOJCczc7dTmufIkS3NcYbp9SEuFykApfh7v+7ozl7u9FUeSFF15g69atdHZ2UllZKdcwDsXQe+XOvBAEgYKCAp599lmam5tl9mLpGK42lkaj8cl8HyjwJNUiDr0vKpXKL/PialooQyFcD8u86Oho8fHHH5e3/XlMQ2/EN2Gsb+I5fTvW12ecf/ZYzzzzzAlRFLOH++516cFdS478b+JY38Rz+nasr88413qsK+G6ZPT9Ft/iW3wLX+C69OC+qa70tVqKXMuxvgnX75s61jfxnIYb60q4Lg3c888/7xdZvoiICFasWCFvd3R08OKLL/p8HICsrCwWL14sb1+4cIHNmzcPCvB6kzAZuH3HHXcwbtw4+bO8vDyOHTtGe3u7nHW+XCpepVIREBCAwWBAp9OhUCjo7u6WNUQlzjiVSkVwcDB33333IEqlN95446r1egPbr0baiqVWq/n5z38un68oivz1r3/9SpH1lQSGpLINKenidDrl6+F0OuXfJiQk8J3vfEf+bWtrK3/729+ueoyeICcnh/nz58vbeXl5bN261e25MPC6XO7v995776DG+J07d3Lq1CkPjvrqx/KDH/wAk8kkf7ZmzRq/1I9qtVp+9rOfjfj716WBczgcfkkhD1di4q9U9dAHz+l0+q2yfuhYra2tNDQ0jKgIWjJkKpVKbuHq7e2ls7NzUAO5RGAw9HpJrTy+xnBv6a6uLreuoXS/pf5lo9GIy+Wiq6trkFrZ0H36s4Rh6L1yuVxulT5JGUzpheXOWP66V8PBk7GkcxME4bK/dbdM7Lo0cO5CSlUHBgbKJIcdHR3ExcVRWlpKS0vL17ZeaCgGlmtcbpLb7Xa3zlfipXO5XCgUCvn3QwU/JG/OUwzsP/UEvurBHboff7KM+BIqlYrU1FS5+r+iokIm+/w6Q61WExcXR2ZmJhEREdjtdi5cuEBBQcE3U/h5JBAEAYPBwIwZM7jnnnvkJu6goCDgUouVRqNh37597N+/nwMHDvil+PJaQOK5i46OJiQkhL6+Pjo7O+no6Bi2f9TdqnCJrlpqk5Ho2oeyOXjaPaJQKEhKSmLy5MmUl5dTVFREV1fXNSvaFkWRzs5O2trahr02HvGMqVSEhobKtFr+NjIKhYKxY8eyYsUKkpKSZBbcXbt2+YUJ91pAEASMRiMzZ87kgQceICsrC71ej81m4+LFi2zfvp1NmzbR3d3tcVH6dWngrkatHBQUxE033cSDDz5IVlYWFouF/v5+mRQyICAAo9EIXBJYOX78OH19fRgMhquOGxgYSHJyMhkZGZhMJioqKigoKKC5uZnu7u5r8rYXBAGz2SzTDN1+++3ExMQQHBxMa2srZ8+e5fjx4xQXF9PV1eVVkkGtVmM0GmX5O5fLJXuHvjAEcKnAdPny5bK2p1Qc7K6Bc3f8gR6bw+HwWeBbqVRy11138atf/QqtVktnZyc/+clPyM3N9VtvdHx8PD/4wQ+Ii4sjLy+PpqYmmVbfH29yyLEAACAASURBVJDIVQfGcH0JQRAIDQ3lwQcf5IEHHiA0NBRRFOVnLCYmhqysLD766COZ1eQbY+CGo4GRlqGpqak8/fTT3HnnnQAUFxezf/9+du7cybFjx1Cr1cybN4+f/vSnJCQkUF1dTVFR0YgmuFKpZObMmTzzzDNkZGSg1Wrlt/+hQ4dYv349Z8+e5eLFi37zPiSG2pycHDIzM9FqtYSEhOB0OmlsbKS0tJSCggKqq6tpb2+/YpD9SucrXU+dTofdbpeXqBKG+62nk9xsNrNw4UJOnz5NRUWFXxJIAyGRa6anp9PT00NxcbFPH1CVSkV2djZpaWlyZf0777zDH/7wB3bs2EF1dbVPPTqNRsPChQvlB37NmjW4XC60Wq1P2YPh0vxLS0tj3LhxBAUFcfr0aXkZLHn17e3tslflCaTWthUrVvDYY48B8Nlnn3HkyBGSkpKYNGkSJpMJm80md0R46lhclwZuOGg0GsaMGcNTTz3FkiVLaGxsZO3atezcuZPi4mJ5QgmCwJYtW8jOziYzM5NVq1Zx6tSpEd0MhULBmDFjGDVq1CAR5ODgYFnd/tSpU2zbtk3OEFVVVXHy5EmfMH+o1WoSEhJkweSjR49SU1ODy+VCo9HgcDiw2Wy0tbXJ3PWeMBcrlUo5E9rX1zcotia1Dg33QvB0QmdnZxMXF8eRI0ewWq2yx+0tt91wUKvVBAUFYTAYiIyMpLCw8LLGRgpoe8Kr1tzcDCCHPRISEvjDH/7A4sWL2bVrF2+++abPGuJTUlK45ZZbaG5u5t1336Wmpgaz2SzTevsKgiAwbdo0fvGLX5CZmcn58+cxm82UlZURGhpKRkYGZrOZjz/+mE2bNnlMlBAYGMjSpUtZunQpdrudDz74gPXr19Pc3MyTTz6JxWKhqKiI/fv309bWNog92F1clwZuqLWW+MsWL17MvHnz6Orq4tlnn2XHjh2DLrJCoWD69Ok89dRTTJo0ifXr1/PRRx+NmOVX4sGSjIYoitjtdpmiRqlUkp2dzaRJk+RxW1paOHr0KP/93//N2bNnPT5nlUpFVlYW2dnZcoC1tbV1EGXzcMc/nDG72hI/IiICtVpNfX39V7wprVYrN3EPfXg8WQ4JgsCNN96IRqOR+zOzsrJISEjgzTffpLOz0+19Xm6cMWPGAJcybS0tLRw+fPiqwixS8sEdSAbObrcP6m/W6/UsXryYmTNnEhoayqpVq7z29FUqFTk5OYwaNYq3336bqqoq1Go1oaGhPufv0+l03HHHHaSkpPDyyy9z4MABGhoa6O/vJzIykpycHObNm0dLSwubN2/2aAxBEEhJSWHhwoVotVr+8Y9/sGbNGhoaGkhLS2P69Ok4nU527txJbm6uV/E3uE4N3FAEBARw4403MmPGDPr7+8nNzeXAgQODHk5BEJg6dSp//vOfycjI4MCBA7z00ktuTTCn00lBQQFlZWWkp6fLQrhFRUWyMlNqaqq8tJPk3MLCwuju7mblypXU1LgtIgZc8gAeeughSkpKOHXq1Ij1CYa7+QNLCYZ+HhoaisViGVbbQRAEmY12OHJDTyaZUqlk7NixOJ1ObDYbAQEBzJw5k5ycHE6dOsWhQ4e89uI0Gg33338/ixcvZseOHRw/fpzOzs6rxsOkxImn5QxWq1X2hCWPV61WYzKZePDBB3n//fcpKCiQS208Oc+QkBBycnJQKBS0tLSQlJTE9OnTmTBhAps3b2b//v0+iwsnJiYyatQoXn31VdasWTOIYbmxsZEDBw4wduxYSkpKPPYcVSoVkZGRiKLImTNn2L17Nw0NDVgsFr7//e8TGhrKunXr2Lp1q9saHcOO59WvrxHsdrvMmBofH8+JEyew2+3ypJHe3k8++SQRERGsX7+eH/3oR27zcUk8aZs2beK+++4jKipKZhqVRGdycnJISEhg1qxZLFy4kICAADQaDQkJCQQFBXlk4AIDA3n44YdxuVzs3bvXLWWpkULygrOzs/nss88G1YFJUKlUmM1m9Ho9DQ0NX2EQ9uRNKglbW61WiouLZQV4tVot66SOdJ8Dl9HS7/R6PXPmzGHJkiWcOHGC3NxcampqRhzs92SJajQaiY+Px+FwyKpaR48eBWDOnDlERkYSFxfH8uXLWbVqlcfJKUEQGDVqFDk5OTIF00033cS8efMYPXo0iYmJlJSUUFpa6va+h8OoUaOIjY3l6NGjX4mxxcXFERcXx759+9i7d6/HNZ06nU4uc5GE2idOnMh9993HjBkzOH78OG+88Qatra0+OaevhYGT+MvKyspQqVT09fUNirklJSWxevVqUlNTefXVV/nLX/7iMdlga2srW7dupaOjg4ceeoja2loaGxvlt8nWrVsJDQ0lPj5+EGWMVFrh7ptainvMmzdPJof01rgNLPOQxjCbzUyZMoXW1tZhDahU8R8QEEBMTAxwSe1rqJfs7jI1NTUVs9lMe3s7FRUVcklKV1cXgYGBshbmSM55OKqm9PR0FixYQFlZGZ999hk6nY7AwEC3agHdWaJaLBbuuOMOFi1ahFarleeidG2kkIJWqyU1NRWDweBxQF6j0TB9+nQsFgunT5/mxIkT9Pb20tHRwb333kt8fDzTpk2jvLzcJ15cT08PnZ2dg66bIAjMmDGDFStW0NzczObNm6moqPB4PLVajdVq5cSJE9TV1REaGkpOTg5z586lu7ubDz74wCfavBK+FgYOkONhQ98ckZGRfO9732PSpEnk5+ezbds2r2ITDoeDixcv0tjYSGdnJ7W1tdTU1MhLXb1ez2233cbtt98ux1/sdjvl5eUeudRarZalS5cSGxuLVqv1yEgOhbQPySCoVCosFguiKJKfn3/ZySmKIlarlaamJre9msshNjZWjr9J6unh4eGEhIQQExODxWKhvr5+RKGEgbFIURRRKBRYLBZCQkIoLi7G5XIxceJEAgMDyc3N5fz58yPyNEb6sBqNRpYvX87jjz9ObGysnE1UqVTodDrZ0MH/xvYGvozdhdlsZubMmbS3t7Njxw7y8vLk+GJkZCQPPfQQN910E1u2bBlRNvVqL6eCggJ2795NT0+PbPRnzJjBM888Q29vLy+++CJ5eXkee2+CINDX18epU6eorKyUV15jx47FbDZTVVVFdXW1bzPePtvTNYZCoSA7O5sf//jHTJo0icbGRl555RWZ1dVTSDVT7e3tbNmyhb6+Pnm5o9FoeOyxx/jP//xPwsLCEAQBm83Ghx9+yFtvvSVn1tyB2WwmOTkZvV7PpEmTGDNmDCdPnvSqrWtgZlXyLvv7+2loaJDl5obz4JxOpywu4nA4ZI2DgftyF1VVVTQ2NiIIAnPmzGHixIlkZ2djs9mIiYm5am3icJCOx+l0UlhYyCuvvCJrFHR1dZGTk0NERAQGgwGNRkNZWZks+CwZRqlGbmDHxpUgCAJTpkxh2bJlJCcn43Q6qa+v5/Dhw9jtdlmT12w2ExkZKfe/elqnJggCMTExjBkzhuPHj5Obmyt70x0dHeTn59PT00NSUhKBgYE+KRdpb29n7969qNVqsrOzyc7O5t5776W5uZmf//znXnmKUlmSRqNBqVRiNBpJSEggOzubxMREent7KSoqoqWlBaVS+ZW6N09f+telgRt6IgOXEFJgf/78+Tz//POYzWYqKir47W9/y5YtW3xWaCktoyTo9XpWr17N9773PbRaLXBJ5u+9997jD3/4g8dCvIIgsG/fPvR6PSkpKfzoRz9izZo1cqDc02OXJogoXqJ5dzgchIeHo9VqsVqtchZYeuClzKlKpSIhIYGKigqPxh6KgoICNm/e/P/Ze+/ouMqz3fu3pxfNqHerWZIlq7jLli03MO4EAsQ2JAFiCISa5KS8MVmLnI83h5M3IZBDILwJOSEhCd3E2IBt4V5xl2XJlq1q9WaNyqiNpuzvD3vvSLLKjGaGmBxfa3lZ03Z99v3cz12ui2XLlnHvvfeSmJiIRqOhrKyMS5cueaUUJinXt7S04HA4UCqVtLa2ymUNGRkZ5ObmkpGRQWlpKS+99BLV1dUolUq5r9ZdqUKTycRtt91GWloaSqWSixcv8uyzz3Ly5EmUSqX8z2QyMWPGDIKCguTrOREoFAoWL15MWFgYFotlCFuxIAh0d3fT1dXl0UQ43nn29/djs9mYO3cua9euJTk5mfPnz7Np0yavaedVKhXR0dFkZmaSk5PD7NmzSUpKQqvVYjAYKC0tpbW1lczMTNLS0ujp6aGzsxOLxUJvby82m21CGekb0sANhkqlkpc5sbGxJCcnM3/+fDZs2IBOp6Onp4eioiIOHjzot3YZhULB3LlzWbZsmWzcenp6eOGFF3jppZeGyKt5Aqnc4OWXX+bkyZOsWLGCVatW8etf/5odO3bw5ptvyksvT7c7eDBLRcIFBQXodDr5HAYGBuT+UylZExQUhMPhkD0Cb5cLvb29vPXWW3KZj1Rj99577/Hxxx/T2dnptcYm/DOGKMVr6+vrqa2tpa2tjcjISCZNmsSMGTPk8pi2tjb5/N3xskJDQ5k6dSparRa73c6RI0c4duwY3d3dcrxTpVJRUlJCZ2cnZrNZNroT8T6kYuWenh45ZipNRGazmalTpxIWFsbRo0cnPP6GQxJiTk1NJTc3l5qaGl555RWvjZu0ioiJiWH9+vVkZmbK90oKy8TGxnLXXXfxta99jYGBAaxWK319fZw9e5YtW7aMWc84Fm54AxcQEMDKlSvJyspi5syZxMfHExERIScbmpubqaqqIiUlhejoaCorK+nt7ZUzdP39/V4HYBMSEnjqqaeYNGkScNVz2L59O3/5y1+8HlwOhwOr1cr+/ftpbGykpaWFyZMns2bNGsxmM7/61a88jkuM9F2n00l9fT0KhQKtVivHDwcHyU0mE0ajkUuXLsm0RN4uUUVRpLa2lkOHDrF8+XIcDgc7duzg1Vdf9ThTNlZLmpSdnT17Ng0NDZjNZvR6Pbm5ufT29rJr1y7OnDlDU1MTHR0dQzz98c5LStJEREQgiiIWi4UtW7bI2VHpwTOZTGRkZBASEgJcZT+Z6PhwuVzykjo2Npbo6GgGBgYIDAzk9ttv55577sFgMLBv3z6fGTi46sVJz9eZM2fkTKc3kO5RTEwMSUlJBAYGykkgo9GI2WzGbDbL5SNtbW1yvG5gYEAOlYDnY/CGNnCCIDBjxgy+9rWvkZWVJdccDc4QhoeHc++997JmzRosFgv5+fk0NTURFRWFzWZj165dVFRUTDimZTAY2LBhAytWrJDbcurr63nnnXfkuIsvYLfbaWlpIT8/n4iICCZNmsTkyZOJioqivr7eawMnQVJ+kqrDpe9qNBqCgoJob28fddk40cSD3W6noaEBhUJBU1MTr7zyyoTKAMY7L4fDQV5eHkqlEoPBwOnTp9mzZw+1tbXU1taOKtg93gQoiiLt7e1cvnyZ7OxsnE4nYWFhREdH09vbS39/P0ajkQcffJBvfOMbmEwmOabU3d09IS/Y5XJx9OhRHn74YaZOncrtt9/O+fPnueWWW7jjjjsICQlhz549HDhwwKdtgyaTibVr18ryjr5qBVMoFGRnZ8s91ZJXp9VqZa4+m83G+fPn+fjjj6mvr6e9vZ2Kigo5/PNvE4OToNfr2bhxIwsWLECn0yGKohwnkDjMDAYDAQEBcpA8IyODzs5Ouru7KS8vp7y8nLq6ugnH5mbNmsVTTz0lN+87HA527dpFfn6+T7M9Wq2WSZMmkZycTFxcHAaDgYaGBr/UxEmJFAkajYbw8HBsNhtXrlwZUoIj/S+VnkwECoWCnJwcTCYT7777LkVFRX45p/r6ep577jk0Gg1Op1Pmj3PHgI2HpqYmjhw5wqJFiwgODubFF1/EarXS0dFBR0cHYWFhTJkyRe5fLioq4v333/fK+BQXF7Nlyxa++tWv8sQTT8hFxA6Hg/379/Pzn/+c5uZmn15Ls9mMVqulqamJwsJCn21br9eTkpIiyx1KMV+LxUJnZyeVlZX89a9/5dChQ1gsFjl0ICWBxurmGQs3tIEzm820tbVx+fJl2cpfvnyZ4uJimpubiYuLIywsDJPJhMFgQKlU0tHRQV1dHWfOnOHMmTPU1NTIgWRP3VutVst//ud/Eh0dLb/X0NDAH//4R58uCwRBIDQ0lMWLF7Ns2TKmTJlCV1cXmzdvpqGhYULxG08gLbsk1obB7w/enicK5oOh1WqZOXMmdXV1fPbZZ36j93E6nROqoXLnnAYGBsjPzyc+Pp7Vq1fLhd2JiYmy8Xc6nXIB6/PPP09tba1XBqKnp4c//vGPNDU1MXfuXIKDg7Hb7Xz++ee8/fbbExobY0GpVJKcnExISAjNzc1etR4OR39/P4cOHZKb9h0OB/X19Xz++edcuHCB5uZmt+shPcENbeBaW1v5zW9+w6effiqfeF1dHdXV1del/PV6vVw0OrgJefAF8/TiKRQKEhIS5AfA4XBw9OhRn8QlhsNqtXLmzBmUSiVFRUUUFRWxc+fOCdU3eVpLJ2VZx4I3A8/pdHL48GF27NjB559/PuFkkK8HvwR3DJwoilRVVfHiiy9y+PBhZs2aRWJiIgkJCXIyoKysjIsXL5Kfn09VVZXXGX1RFKmpqeH3v/89f/7znxEEAbvdPqQ/2ZcIDQ1l1apVREREcOrUqXH7eD1Bb28vb7zxBps3b8bpdNLf3+835u7BuKENnNPplOMno0Fi1LDb7T5r3B68/8LCQiZNmoRCoaC0tJSXX355wiwKo0EUrzIQHzp0iBMnTqBUKunr65vw8sZTA+cOCYE3vGM2m42//OUvbhnSseAv7jN3r5PL5aK1tZXt27eze/dumWBVrVZjs9loa2uT9Sx8ZYCkMh9/k4MKgkB2djbLly9Hq9Wyd+9en+/TbrfT1tbm022Oh3ENnCAIccBfgUhABF4XRfFlQRBCgPeAROAysF4UxXbh6ih8GVgD9ALfEkXxjH8O378YGBjg6aef5tVXX8Vut1NZWUlTU5PfSC+luixvoVKphiRivMHgOJw3hau+WNL7y8B5ul0pUdPf3+8XYRV/YazzlOKGL7zwAg0NDZw4ceJLQ+U+Ftzx4BzAD0VRPCMIggk4LQjCLuBbwB5RFP9LEIRNwCbgJ8BqIPXav3nAf1/7323Exsb6RaAlNDR0yGulUklMTMyI3x3sAV26dEl+PzIy0q19SdTpEgwGA3FxcUN0DiaC4YNUEAQMBsOQ9yIjI0lJSZFJLD3NwA6OuUl1XJLmhZRJlhAREeEXwzNSgWxSUtKohbnunuPw5npBEIbEWKV9jzQupPP0xjsLDAwc8lrq/fUHuYJerx/yXlBQ0HX7Gn7vDhw4gCiKBAUFXXesY+1reD+vRMnla0hsN+5CmEAAeyvw6rV/S0VRbBQEIRrYL4pimiAIf7j29zvXvn9J+t5o24yJiREfffRRj47jJm7iJm4C4LnnnjstiuKckT7zKO8vCEIiMBM4DkQOMlpNXF3CAsQCg4Nmddfeu4mbuImb+ELhtoETBCEA+BD4viiKQ6L54lU30CNXUBCERwVBOCUIwilfUTvfxE3cxE0MhltZVEEQ1Fw1bm+JoviPa283C4IQPWiJ2nLt/XogbtDPJ117bwhEUXwdeB2uLlEHf2axWPySBpcIHSW4XC6sVqvbzLXj8aFJ8StBENBqtUNiIFJ/nT8QEBAg95fC1fopTzK9g89pvOseFBQ0JN7S2dnplwyfIAhyy5OE/v7+ITxvYxV/Dj6nkbLK0n2S4ouDqcedTqdHlFuexOb0ev2QmKnNZvNpOcZgmEymITErqevCE+69scbG4PEeGBg4JLbpLynFkcbFWHAniyoAfwJKRFF8adBH24AHgf+69v/WQe8/JQjCu1xNLnSOFX8bCX/4wx/8kmSIjIzksccek1/39PTw5ptv0t3dPYSeZbQBIDU7Sw+MFMCXmtWl36nVanJycliyZIn827KyMjZv3uzzcwK46667mDZtmvz64MGDnDhxwu3fDzfaYz0ATz/99JAB9t577/lEcGc4VCoVP/3pT4cYjxMnTnDhwgV5UpLas0YzcNJvjUajrLcpfaZQKGRjM3nyZBYsWCD/tqOjg1dffdXtYx18jOMZu9zcXFauXCm/vnjxIh999JHb+/IE69evl3UqAA4dOsTJkyflcTtWKZFEXiAlmaTrPbyrQJrMn3jiCbnbB+Dtt9/2S4ZZo9HwzDPPuP19dzy4POB+oEgQhLPX3vspVw3b+4IgPAxUA+uvfbadqyUi5VwtE9no9tFcg78KOodv1+Vy0d3d7XZtltQAPTgTJ1WxSy1BoijK+gNfFigUCjQajdzCdaMqpdfX12OxWNyqMxs84QwMDKDRaOTyDul9yaMJDw/3+tgkY+GvsesLOBwOt9uelEolGo1mSJ/oSGUjoij6rfDYFxjXwImieBgYbV22bITvi8CTXh7XF4aJPsxKpRKdTie75q2trXJDsK8H+mAKcl/XJgnCVSGayZMn09nZyZUrV+js7PS7dulE0NHRMaEiWpfLRV9f33U05na7ne7ubq8ayjUajawtK7Fe+LLQ94uG5JElJiYSGRlJX18f1dXVYy6jPTlXybM2GAwkJydjsVhoamrym2D2DdnJ4K+CzpHgicGQPB2pWTgoKIjo6GhMJpPM8Aq+8UA1Gg1RUVEsXryY+fPnY7PZ+OCDDzh+/LhPjZzBYGD16tXMmjWLS5cu0draisPhID8/3ydMEpKKvcTwIWkmqNVqQkNDycrKwmQyUVZWxqlTp2htbR212Hmi2gZ2u33EB0jyWCdyntL9mT17NsHBwZw9e5awsDAMBgMnTpzwi+ar1LOs0WgICQlhYGCA5uZmrFarW2PCnYnXYDAwd+5csrOzsdvtnDt3bty4nacGLiQkhP/xP/4H3/zmNxEEgcOHD/PKK69QXFxMb2+vT1cQN6SBuxEhCIL8cEpB/K6uLoxGIzabzW1mWHf2o9FoyMjIYO3atdx9992EhISwefNmn3dRCIJAamoq8+bNo6KigvPnzxMTE0NbW5vXS2xBuKpePm/ePJKSkoiNjWXVqlUkJCSgUqloaWmhqKiIM2fOEBMTw5o1azh+/Dgffvghp06dGnGb/prlPd2u0WgkIyODnJwcIiIiqKioIDMzk2XLlnH58mWOHDniFw8uKSmJ/Px8IiMj0el0tLe38+yzz/K3v/3NJyERvV7PrFmzyM7OxmKxUF5eTlVVlc8ErOGftFYqlYqBgQE6OztpaWkhKiqKjo4OrFYrDQ0NPhvnXzoDJ8W/husO+HtJIBHwDY5FqFQqOjo66Ovrk2fR8YK3Y21fo9EwadIkWTehra2Ns2fPUlBQwJtvvunzXtvQ0FAeeOABAgMDKSoqorGxkaamJq9UkyQEBwezYcMGHn/8cSIiItDpdDgcDmpra9m/fz8HDx7kwIEDtLW1ERYWxs9+9jPuvPNO6uvrOX369IR424bD3XY1T+6VSqUiJyeH1atXA1BUVERZWRm33XYbCQkJ7N+/3+eCzHDVE163bh0xMTHo9XqcTieVlZXs2bPH7Yz5WOepUqlITk4mNTWVoqIizp07R3d39xBCT1/BarXy6aefcuXKFcrLyzl9+rRMCxYSEiKTF/gCXzoDp9FoiI+PZ2BgQFZ+FwTBLd6viUJKKAyXU1MqlfT09FyXhZU+9wQajYaZM2eyevVqysvLOXHiBHv37mXPnj3U1dX5dBaFqw/M3XffzYoVKygoKMDhcKDRaKisrPTaG1AoFKSnp3PPPfeQlJQke2yvvvoq+fn5lJWV0dXVJV+vpqYmZsyYQUJCAiEhIdjt9glrGUiQRF/cORd375UgCEyaNImNGzcyadIkPvvsMwoLC+nq6mLq1Kn09vZSWlrql7KZkJAQvvrVr8q8iKdOneLnP/85dXV1Ptm+TqcjKSmJlpYWCgsLZYPjzn3wdKxLAusmkwlRFGltbZVV16QwkMPh8Eny4ktl4BQKBVOmTOGZZ54hKytLlvWz2Wy89dZbnDx50udsBVJJyPBZTJKE84VhFQSBxMREHn30UaZOncrFixdlcs+mpia/lMyEh4ezfv16AgICsFqtZGVlUVNTw8WLF73etl6vZ8OGDUyfPh2VSiXTlP/2t78dsRZw6tSppKWlDaHpHq+2zR24myhx9yFSq9XMmDFDNgRHjhyhpqaGkJAQoqOjOXToEOfOnfPLamLdunVkZGQgCAJNTU28/PLL7NmzRx4b3vbJSnyKxcXFsk6GvxJbcLXWNTAwkGeffZb8/HxefPFFmpqaMJlMMvlqdXW1157cl8rABQUF8d3vfpevfOUr8kwmGaC1a9fy/PPP89JLL/lsgCkUCkwm04iBT6fTOeZM7ckxxMbG8v3vf5/Vq1ejUCj4xje+QV9fH83NzbS0tIy/AQ8hCALLly8nPT1dbshfsGDBdV7oRBEbG8sdd9yBXq9HFK9K+Z06dWpEARaNRsOmTZsICAigqamJ8+fPe71/aULytaExGo0EBQVRU1PD+fPnaWxsJDAwkNzcXNra2ti9e7dfinbDw8O58847MZlMcrJp165dhIWFERUVRVNTk1fxWSm+bLfbsdlscl0nTLzKYDw4nU4KCgrQ6/U89NBDNDc3s2fPHtLT05k1axZOp5P33nuPU6dOeWVgb0gDJwUgh8NoNMrkiVeuXKG1tZXAwECWLVtGaGgokZGRPovHSdXZksSc9B6Mn40azlgxGhQKBZGRkWzatIkHHnhAptrOycnBarVSWlpKR0eH11qvw5GcnCxrB/z2t7/l7NmzPPLII3R2dvrs2kn6B1Jd3Zw5cygoKKCgoAC73Y7L5UKtVrNw4ULmzJmDIAjU1NRQWFg46naVSuW4CQEpdODJMtFdKnaHw0FnZyeNjY20tbUREhJCTk4O3/72tyktLR3z2CcKhULBvffey6JFi4Cr3RxqtZonn3xSluDbu3cvIlF4NwAAIABJREFUL7300oSXxwqFguDgYIKCgoiMjMRut9Pb2yvz941X9jLRqoeKigp27NjBI488wuOPP87q1asJCQkhPDycpqYmDh486HVFxQ1p4KQiQ6loVjIwra2tvPzyy9hsNtrb2+ns7ESv17Nw4UJ+8YtfEBQUhNFo9ElLVFBQEBqNBovFIqtOScutsSB5lKM9NINbuZKTk2WhEqmtS6lUEhISwpo1a5g9ezY9PT3U1tb6zDNQKBQsXLiQmTNn8uGHH/L6668TFBREV1cXdrvdJwbOYrFw/vx5UlJS5NoziV4+ODhYloCUMsUJCQnYbDb27t1Lff11XX0yhlPyjPYdlUrl0dLK3YdI8ui1Wi1BQUEsWLCAVatWERcXx/79+0cN9kv33F2JwsFITU1l48aNcitZYGAgjzzyyBD6+A0bNhAbG8sPfvADSkpKPJ7kpZKd0NBQcnNz6ejokONjKpUKi8UiL8d96RUPDv3ExsYSGhpKW1sber2ekJAQgoKCRqQH8wQ3pIEbrNU52EW22WxyfEpCT08Pu3fv5nvf+x5JSUnExMQM4W+bCDQaDQkJCdTV1Q0xVoP/HolnTfpsLA9PEATMZjPz589n2bJlrFmzBqPRKA9+l8uFxWKhp6eHyMhIHn/8cS5dusT27dvdLmcYaxBIvHQWi4VXXnmFzs5OTCYTer2eKVOmjOo9e4Kenh62bt1KVlYWgYGBdHV1yTqk8+fPR6PRkJiYyJIlS0hPT0epVHLkyJFx2ZLdGdzS0lQyKu48kO4q2+v1etLS0pg3bx6JiYmYzWaSkpLo7++nuLhYJgSVjKt0vFqtFqfTKSfE3MWcOXN49dVXmTFjxpD3hxt6o9FIXl4eYWFhgOdxOI1Gg0KhkBNmHR0dcoJGqVQydepU0tPT+eCDDygpKblukp+I0VOr1bzwwgvccccd9Pb2IggCn332GUeOHOHee+8lNjaWqVOnXucoeLqvG9LASZztwzHayTmdTrZu3coPfvADkpKSvDJwWq2WRYsWDclYPffcczQ3N8ulHCEhIfT19dHe3j5i5nQsAyctzZxOJxqNhpKSEpnLPzY2lv7+fk6dOsX06dO57777iIuL429/+xu//e1veeWVV4aoXnkK6SHVarWUl5fLZSeSLuWKFSvYvXs3paWldHZ2TrjuzOFwUFVVRVVVFUFBQZw9e5bPP/+c0NBQsrOzaWlpITs7m+nTp2MymTh69Cj33XffuAkipVJ5Xd/vcAyeFN31uj15aFpaWrBarQwMDMhelEaj4aGHHiItLQ2VSoXRaKSkpIS6ujo6Ozvp6emhpqaG5uZmt/cTGBjIM888Q05OjnyM58+fp6+vj4yMDHQ6nWzoRFGkrKxsQoI7cPV+lZWVcf78edrb26+b4NRqNfPnz+f2228nMDCQY8eODbmmE1lGPvnkk2zcuJH6+noefvhhqqqq5KqIqqoqfvGLXzB79mzUarVXE+4NaeA8DSoKgsDUqVMJDAz0qq9QoVAQFhZGcnIywcHBxMfHc+DAAbnGTXpgDAYD/f39I3oI0sM31jm0t7dz+PBhioqKcDgcQ5bBRqOR0NBQUlJS5MZ+o9HIunXrKC0t5R//+Me4y9WxHn5JgX3mzJl8+9vf5siRI9x+++0sWrQIpVLJK6+8wrZt29i8eTOlpaUTMnKieFVjQiri1ev1pKamEhwcjFqtpr+/nyVLlhAeHk53dzevvfaaW9lvrVYr12a5exzSdfV2aSWKV5XH3n33Xa5cucLkyZOZO3eu3J2Rnp5OUlISOp1O9sLr6+s5fvw4R48elZd37h6HzWZj//79BAQEyOGDZ599FrVazeuvv87MmTMxGo0A1NbW8stf/nLciX00Q+RyuWRDPFK8zWazcfLkSWJjY4mPj6ewsHBIGMjjZaNKxaxZs1CpVJw+fZqjR48OyZbW1dXR0dHBlStX/t8qExkNERER5ObmotfrCQ0NnbAegSiKWK1WDh48SHFxMYIgcObMGdmFliDFB4fDXXpwSURkeG2blHEcGBjAaDTK+xFFkZ6eHi5cuOC14I0U9A8NDeXpp5/mgQceIDw8XJZyCw4OlpMrE4VEN3TlyhVuu+02AgMDiY+Pp7GxkV27dhEXF0dgYCCCIHDs2DFOnz7tllcaHh6O1Wp1m/IHhlL6jPYbd891YGCA1tZW9u3bh8vlYsWKFRgMBmw2G8XFxdTV1ckTVllZGS0tLTQ1Nckixp6Myf7+fv74xz/yj3/8g97eXuLj44mPj+frX/+6rC8K0NbWxve+9z2PQhjDISV9xrqmg4/d28B/VFQUISEhWCwWfve73133HKjVahwOByUlJV6XqNyQBs4Tq61QKEhKSpKLA4ODg9FqtRMqVhVFka6uLnl2Gnwckvej0+kICwujrq7uuovvqwCsKIokJSXJzdtwdWlUVlbmddq+u7ubv//977KCUlRUFHA1brZlyxa2bNlCSUkJtbW1Ey5Yla7VpEmTSEtLo6+vjyNHjvDOO++gVCp57LHH0Ol0tLW1sWXLFhoaGtzetj/KFjy5by6Xi46ODlQqFSkpKXKx99///ncOHDggt/H19PTI3uNEj1sStdm4cSNPPvkkBoOBxGs6rHBVyOcb3/gGu3bt8mrsiaIo88b19/ePeN8zMjKYN28eH3/88XX1hZ7uu7e3l/r6evr7+7lw4cKQ3ysUCsLDwzEajbS2tnp9vycmVX4DweVyce7cObZu3UpjYyMzZswgNtY7hvTRlhJS/KepqclvJIVw1cN76aWXOHTokDzYGhsbZbYSb+Byubh48SKPP/44f/rTn2hvb6etrY333nuP559/nh07dlBeXu51b21ERIRc6CvV8y1YsID//b//N/PmzWNgYIAtW7bw/vvvu12Q29nZ6Zf6Nk+9BKnAG/6ZUHnvvfcoLy+noaEBi8WCzWaTyywGe0ieHntWVhY/+tGPyMrKYvLkySgUCqxWK4cOHWL+/PkeGbexEl8hISGkpqYSEhIi1ysqlUqMRiM5OTl873vfo7S0lDNnznidhGpvb6epqYmsrCx+/OMfExUVhVarxWQykZWVxcaNG4mKipJDN97ghvTgPMXAwACfffYZM2bMICMjg8TERCorK68buBN1raXYm06nw2w2c/nyZb9ypomiKNeMzZkzB4PBQHR0NAEBAT4xcqIo0tjYyJ/+9CdZ6Wvr1q3U1dX5hCZJoVCQlZXFjBkzcDgcBAQE8LWvfY34+Hh0Oh09PT189NFH/OxnP/Oob3M0TjJ3Eg9jwdNxERYWxl133UVfXx87duzgl7/8Jd3d3T43vFqtlvXr15OUlCTXFFZVVfHaa6/xxhtveFzlP9p5Sh5cbm4uTqeToqIiurq6CA4OZtq0acTExPDee++xe/fuEceHp+ctiiI7duzgwQcf5Hvf+x55eXns3LmTzMxMbrvtNnQ6Hfn5+T6RLvy3MHBOp5MrV67gcrkIDg5mzZo1FBUV0dLS4jPqooCAANkwjGcEBrPJThTd3d0cPHiQjIwMsrOzKSwsHLETYKJwuVyUl5fzhz/8AZVKRVFRkU9bwqTldWBgIGazWX7v2LFjbNu2jb/+9a8ed2mMFnbw9iEYTPfuDlJTUwkNDeX06dO8/fbbfqFGApg0aRKPPvoooihy4cIFPvnkE/bt28fevXsnNMGOldm3WCxUVFSQmppKVlYWHR0d2O12SktL2bZt25gMHxMZ6wUFBfz6179m1apVZGdn89RTT9HT08OlS5c4duwYH3zwwZiC7+7i38LASUH4vr4+FAoFs2bNIjY21quSCglSA7DUxuKuh+Otgevr62PXrl1UVVURERFBWVkZFovFp32BVquVnTt3DqFf9wVcLhcnT57kL3/5C/PmzaOyspLi4mJKS0uprKykoqJiQsbUl8coQalUEhAQ4NFvLly4wH/8x3/Q399PTU2N32icnE4nW7ZsoaysjD179lBcXOw3puj29nb279/P8ePHUSgUct2ev0gsbDYbr732Gtu2bSM6Olru7e7q6qKxsXHC3H/D8W9h4OBqfObgwYOYzWZOnz4txxDGM3DjZVylpcFwNtjxtulNFlKC3W6npKTE561ag+GPwSuKIjU1NTz33HNDmCG8Zbr1tZCwVJYzXCB5PFgsFiwWi0+PZSTU1tby/e9/f0jMz18QRVE2aF8UXC4XNTU11NTU+G0fN6SBm4j309fXx+bNm9m3bx/9/f1uqT1JRZpjxbVEUfQomyjF6/yh6v1lgiiK9PX1+dTjMJvNcnZS2oenkMIHEi1PUFCQxwbui4LT6fSpEpsvQxwSJEfii2Th9gQ3pIHLycnxeGk5/EIPVwAChqj+wNXYS15eHn19fT6hPIKr3ptarSYhIWHI51Kfnz8gtehIGFxK4GsMltcDyM7Ovu5cfYHhxy8IAvPmzePKlSvyknAiS9bBymhS5m6wlCRcpXvy170afq3Cw8P9tq/h8nrJycmo1Wqfee3SZKFWq4fIEwJMnz7dL5UGnq6MBH8ERz1FTEyM+Oijj/6rD+MmbuImvoR47rnnTouiOGekz770dXA3cRM3cROj4aaBu4mbuIl/W9yQMbiioqIJxQnGo22WKIEkDAwM+C1DGRoayqRJk+TXHR0dVFdX+2Vf8fHxBAcHy6/r6+u5cuWKx9sZfP1GupaCIJCenj4k3lJWVuZzvQi4GivLzs4e8t6FCxdGLcmQYrDSMYuiKLO2SGNJOhcpdiTxxul0OiZPnixvS6Ll8gfCw8OJiYmRX7e3t/sti5iYmDgkvlhXV+dzSn/4J9nF4MTapUuXvO6bHglKpZKsrCy3v39DGrhPPvlkQunq8QxcZGTkEAPX19fHRx99NLGDHAdz5swZYuDq6+v9tq+77rpriIErKiri+PHjHm1jcEP6WC09Tz311JDg9b59+2hsbJzYgY8BlUpFVlbWkHv68ccfj/nQSHxsCoWCwMBAMjMzKS0tpa2tTS6DkKBQKGTB5piYmCEGrru722/3Kjc3d4iBq6mp8du+1q9fP8TAnT17ltOnT/t8P5KmyGADt2fPHlpbW32+L41G8+U3cBNN/4/3uy8yofKvTN54um9BEIiJiSE7O5uCgoJRO0D+1Qmp8bx6u90u17ZNmTKFRx55hK6uLo4ePcrnn3/O5cuXZSMniqLcL+rPtrsbCf66f//qcTEWbkgD52lNzUR4+D2BRGw4fGnjC1mz4ftRq9Vy65A/K8kHIzw8nHvvvZfo6Giv2ZD/1RBFUdYtsNvtaLVambh0+Pek5e6N/ICOBIVCQUBAAGFhYcTFxREZGSlrjLa0tPhlaehP+Lo2bzBuSAPnCSSWWpVK5REZorvQarWEhITI2w0MDGT+/PkMDAywY8cOr0V+JaOp0+lISUlh4cKFZGVl0dvby7Fjxzh06JBHTLCeQqvVcssttxAZGcnbb7/tc959X8Lde+twODhy5Aj19fVD9HNHmwC9PV9p0vPXxDcYWq2WadOm8fTTT7Nq1Sp5Cdre3s6rr77Kn//8ZxoaGiZUH6jT6QgICCA4OJjg4GCcTic2m43e3l66u7tRKBR0dXX5pI1KopuKj49Hq9VisVg4d+6cTwub4Utu4KTg8OTJk+nr6+PAgQM+N3BBQUGyVFxfXx+CIJCWlkZkZCTHjh3ziYHT6XQsWLCAb33rWyxdulSmRJ83bx5Op5NPPvnEb/2OZrOZ3NxcCgsLuXDhgk+Xa1IRqFqtxmg0YjAY0Ov1mEwmgoKCqK+vp7y83CcMJsNhs9koLS0d4h1MlG1kPGi1WpYsWUJqaioDAwMcOHCAsrIyn49Fqdj52WefZcGCBXIXjsPhwOVy0d3dLauZuQvJG4yPjyc9PZ2YmBhSUlJITEzkzJkztLS00NvbS19fH4mJiZw6dYqjR4961aEiCAJJSUk899xzLFmyBIPBQFVVFb/85S95//33fboS+9IZOEEQCAgIYMqUKcydO5eFCxeSmJhIRUUFp0+f9trgDIfdbqetrU3udhgYGMBsNtPW1ub1bCO1ik2fPp2nn36avLw8zGYzSqVSFhm+5ZZbOHz4sF8CtnA126vX6ykuLvaZoVEoFERERJCXl8e8efOIiYkhMDAQvV4vMxVrtVpqa2v54IMP+Oijj0bVtxiMidDyTOR3niIiIoInnniCrKwsBgYGmDt3Li+//DJFRUU+3Y9Go+HRRx8lLy8PhUJBWVkZH374IWFhYTQ1NbF9+3aPugcUCgV6vZ7bb7+dmTNnUltby5kzZzh8+DBOp5OmpibsdjtqtZqoqChSU1PJyMigtLSU+vr66+Q03YUgCLL4kcFgwOFwoNfrycvLY8eOHRPWlhgJN6SBG21AKhQK4uPjefLJJ5k/fz7h4eGYzWaMRiNqtZqAgIAxDdxE+uUkDjLpZgYEBJCbm8tHH33kteq2pLC1bt06lixZgtFolD0OacmwdOlStm7dyoEDB3weY1QoFOTl5dHc3ExZWZlPDIGUsHjmmWdYu3YtQUFBcnbN4XDQ19eHw+FArVYTHR1NSEgIzc3No3KNeXMcUuuedN9Hk0X0po9Sr9ezbt065s2bh8FgQBRFbr31VgoKCiguLvaZcRUEgdtvv52VK1eiUCjYt28fv/zlL2lubiY3N5f6+npqa2s98hpVKhURERHceuutVFRU8MEHH9DS0jKiFy9RsYeGhhIWFkZLS8uEl+KieFWO0Ol0yt6hNCkGBQX9+xu4kaBQKEhOTuaHP/whq1evxuFwyB6UIAhUVlaOOnt5E8SUZpuuri5cLhcJCQmEhIRQW1vrk0bylJQUFixYINPFSING4p8zGo1kZWVx5MgRvxi4zMxMzp8/75PYh3StlixZwuLFi9HpdNTV1VFRUUFrayt1dXUUFRXR3t5OVFQUmzZtIjY2lsTERFmu0Bdel8RQK+klSISYbW1tI15Db/YVFxdHYmIiVVVVlJeXM2XKFOLj4+XSFF8hOTmZn/zkJwQHB2O1WsnPz6e5uZn09HSZL87TCUKhUDB58mR0Oh3Hjx+/zrhJscWgoCBWrFjB2rVrZd1S8M5DTk1NZdKkSRgMBgICArDb7SQnJ5OZmUlNTY3PQiXjGjhBEOKAvwKRgAi8Loriy4Ig/H/AI4C0dvqpKIrbr/3mGeBhwAl8VxTFfE8OaiSx14CAAPLy8pg1axY2m43Tp0/T0tJCQkICU6ZMobe3F71ef50H54k+5kiQNBhaW1vRarU88cQTNDc3+0TFXBAEwsLCsNvtXLlyhba2NpqamoiPjyclJUVeHo9EzTMei607MJvNzJo1i+3bt084XiTdK2lZHRQUhFKpJD8/n9bWVk6cOEFBQYE8GUiUSdHR0XzrW9/CbDbL5R2+yqap1WrS09NRKBRUVVXhcrmIi4tDEASam5uv24c3TM8DAwPs3buXd955h/r6en784x/T39/P559/7vV5SNDpdDz22GNyXWB3dzcpKSmkpaWRkZHBp59+Kk/Anh6/UqmkpKSE6upqeeWgVqvR6/VERESQnJzMzJkzWblyJTExMZw8eRKr1erVZCsRHVy6dEmWQJR0SJ588kmqq6t95v2648E5gB+KonhGEAQTcFoQhF3XPvuNKIq/HvxlQRAygHuBTCAG2C0IwhRRFCdkkqVZRFK6bmtro76+nsuXL+NyudBoNOh0OmbPns3tt9/OW2+9NaSy3lsjoNVq0Wq1KJVK5s+fz8qVK9m9e7dPyikkIk2n04lKpZI1VyMiIlAoFPT29tLc3ExjY6NcquLLuNJXvvIVent7qayslA2Mt4ZOEpjZt2+fHLsc6VjDwsJISEiQxXR8QcUO/4wrtbW10d7eTk9PDwkJCSxbtozGxkY2b97ss0ydxPB85coVHA4H8+fPJywsjNdee436+nqf7EOlUrF69Wq++tWvotVqZZLNtLQ0pk2bhkqloqCgwC0jPfz6OhwOOjo6aGtrQ6fTERgYSEREBMuXL0ev1+NyuTAajSQkJKBQKLDZbHKIwZt7JYoiO3fupLCwkOjoaDQaDUajkcWLF8uaxOXl5T5ZIY1r4ERRbAQar/1tFQShBBhL1eVO4F1RFG1AlSAI5cBcYEJT2uAWHGkppVarCQ8PJzw8HFEU6e3tJTIykq9//etUVVWxb98+n7m4kuJ3YGAgGzduRBRFt5hV3fUKJAFos9ksez8ajUbWL50yZQqPPfYYaWlpvPfee7L8nLfGIC8vj29/+9ts27YNgLlz55KZmcmRI0coLS31ePtSS5Tdbpe9idEml4CAAP7jP/6DkJAQDh8+THl5uU+yxAqFAoPBgN1up7y8XJ4AJa3ZqVOnUlVVxf79+8fdlrvepHSe6enpfPe73+XQoUNs377dZ+GEtLQ0fvSjHxEfH09vby+nTp1i8+bNpKWlkZ6ejsFgICUlhdjYWDo7O8c9p+HH3tvbS2NjI0FBQXR3d8uB/wsXLlBYWIjD4cBoNDJt2jQ2bNjgtXGT9tvS0kJLS4u8ElIoFOzevZvf//73LF68mA8++MAn7XIexeAEQUgEZgLHgTzgKUEQHgBOcdXLa+eq8Ts26Gd1jGAQBUF4FHgUuI6PazAkwsnu7m4qKiqora2V+bz6+/vRarWkpaVx5513smzZMtatW0dRUZFPascGZ3vmz59PZmYmBw8e5He/+53X24arS6mQkBCZFl2tVg/htJPiE0lJSaxatYrVq1fzq1/9iqKiInp6ekYNmrtzXvfffz+pqalcunSJsLAwMjMzWbduHYsWLeIHP/iB24HewR7l8GORJiaFQoHJZEKj0aBQKHj44YdZsWIFVVVVvPXWW257O2NNGpKnL7EvS/20DoeD8+fP8+6777J+/XomT57MwYMHx/RU3Z2cpCTR7Nmz+e53vysrbPkqnpmVlcULL7xATk4Oly9f5r//+785ceIEtbW1nDx5kuTkZJYsWUJSUhLx8fFcuHDBo32Iokh9fb087trb22Xve/AkKggCVquVrKwsOdngbQnM8LHidDppa2vj5MmTPPLII6SkpHyxBk4QhADgQ+D7oih2CYLw38DPuRqX+znwIvCQu9sTRfF14HW4ygc3xvdwOp10d3fjcDjQarUIgkBnZ6f8gJeVldHd3U1ubi6JiYmEh4fT2trqExLLxMRE7r//fhITE+np6eHNN98cd6Z0d9tGo5H09HRZNk0QBPkB7e7ulktTgoKCCAwMZOnSpcTExPDiiy+yc+fO60or3IVKpSIgIABBEEhJSaGlpYXdu3cTFhbGjBkziIqK8jqTpVKpZC87OTmZuXPnotPp0Ol0LFy4EIvFwieffEJBQYHb92k0wzOYnn64oXW5XPJEGBAQ4FaVv7thDaVSSVpaGvfddx86nY7/+3//LxUVFW6dy3iIioritddeIzc3l9bWVp599lm2bNki77enp4fq6mqUSqXMnuwpXC4XVqtVzqCPJhUpiiJRUVFkZ2eTn59/nQH3FZuvKIq0trbKxca+gFsGThAENVeN21uiKP7j2sE0D/r8j8An117WA3GDfj7p2nsThtRWI6lb6fV6bDabzPcviT87nU7ZsEmfTVSP8tp5ERsbS05ODoGBgbS1taFWq30SK5LOqaOjQz7Gvr4+Ll68SEdHB+fOnePcuXN0dHQQHR3NqlWrmDdvHtHR0cyaNYtjx45NKLAM/+TCb21tJTIyko6ODlpaWqiqqmL69Olexz6USiUxMTEsX76cmTNnkpycLDPnKhQK+vr6OHToEDt37hy11Ga8Ojjp88HJieFhCUnqMTQ0lJCQED7++GNOnjzpkwJcqRzm/vvv55ZbbuH1119n165d4//QDeh0Oh555BFmzJhBZ2cnb7/9NkeOHJGPWwprhIWFoVAoqK2tpbS0dNztjjRupVKNsZ4RjUbDN7/5TTQaDYWFhV6V87iz9JcmeV/AnSyqAPwJKBFF8aVB70dfi88B3AUUX/t7G/C2IAgvcTXJkAqc8PZApbYRk8lEZGQkNpsNs9mMy+UiNTWVRx55BL1ez6VLl+QUvS9iBSdPnqSoqIiFCxcSGRnJnDlz5JnUW0gxlcrKSqKioujv76euro6ysjJ27NhBYWEh/f39ctvM5MmTiYmJYerUqcTHx9PQ0DCh2JXT6eTw4cMyHZHVakWpVBIbG4vVavV6ea/T6UhLSyMzMxOj0YjFYqGjowNBEHA6nXR0dNDY2Cj3jIqiOGQiGu2+De4Hluoe1Wo1nZ2dQx46SR09NzeX2bNnU1ZWxv79+2lubvbdg6NSkZmZyfTp09FqtVitVp8ExQVBYNGiRdx7772oVCq2b9/OX/7yFywWiyyQJAgC06dPJzs7G5fLRXV19YRpkMZ7TpRKJQ899BCLFi3iN7/5DYWFhddNEJ7UFkrZ/5EmGSkk5Il63Xhwx4PLA+4HigRBOHvtvZ8C9wmCMIOrS9TLwHcARFE8LwjC+8AFrmZgn/Q0gzraBR8YGKCtrY3ExETmzp1LSEgIYWFh3HHHHSQnJ3Pp0iUKCwuxWq0Tjk8NP46LFy/y4YcfMm3aNKKiooaInkzkHAbDbrdTWFjI1q1byc3NJSAggMWLF5Oenk5SUhKFhYU0NTWRkJBAVlYWkZGRGAwGkpOTSU5O5uTJkxM+t+LiYsrLyykuLiY4OJi8vDzmz5/PG2+84VWztiAIaLVa2cuur6+XA9VWq1Uu6MzOzqavr4/i4mLq6+tpamqit7eX/v7+Ua/v4KJdvV7P4sWLSUhIkCmbbDYbSqWSiIgI5s6dS1ZWFqdOnWLHjh1jxsU8XWIpFApSUlJYtWoVvb29XL58mcDAQAwGg9c6BFqtlvnz5xMbG8vAwACXL19GpVIRGBjIwMAAKpWKGTNm8Oyzz5KcnExzc7NPWvkG01JJ0Ov1bNiwgYceeogdO3bwj3/8w+39jDX+JSKE4UZOrVazfPly+vv7vS6il+BOFvUwMNII2D7Gb54HnvfiuEbbLhaLBZvNxtq1a4nlePPSAAAgAElEQVSJiSEiIoKoqCiqq6t59913OXLkCP39/T7rA5TEbxsbG4mIiKCkpMRnBZyiKGK1Wvn4449ZsWIFM2fOJCQkhNTUVKZMmcKdd96Jy+WSZz2pjMNqtWKxWHA6nUMeek/Q2NjItm3byMjI4L777iMyMpLi4mIOHz7sE89Xr9cTFhaGSqWitbUVm81GTU0NJpNJlurLzMwkKCiI06dPy7q2Y0Ga+QVBoL+/H4vFQl5eHg8++CAqlQqLxUJnZydKpZLGxkZ+97vfuUUe4On5KhQK4uLi0Ov15Ofn09DQwJUrVwgPD/eJ0Iq03DYYDDz88MPcdttt1NfX09LSQkREBPPmzSM0NJSOjg7+/ve/s2fPHq/vmRTLczqdKBQKEhISuPPOO1m5ciU7d+7kV7/6lU8y3UqlksmTJ+NyuWT6KlEUUSqVZGZmMnPmTM6fP+8zctgvTSeDhP7+fpklQqlUcuXKFY4fP86ePXvYv38/HR0dPu89rK6upqysjGnTppGenu6W3qonqKmp4Uc/+hFr166V41bBwcGoVP+8PZIxbGxs5JNPPuH48eNy7dhEztdut3Py5EkcDgdKpZKTJ09y+PBhn8ycUmDf6XQSGhpKQ0ODbIwBWlpasNlsVFZWcvnyZZnmxxNqKLvdzqVLlzCZTJjNZhQKBZ2dnTQ2NlJTU0NbW5tfed76+vqoqKiguLiYuro6Fi5cSHp6On/961+9StA4HA7Onj1LSUkJU6dOxWQyMWPGDGbOnCnfa6fTSWlpKX/+85/5wx/+4PbSeKxlo8FgkLPemZmZPPTQQyQnJ/PWW2/x/vvv+8yjkoTZFy5cyPnz56moqKClpYWpU6eybt06BEHgwIED1NXV+WR/XzoDJ1n+rVu3EhISQkNDA2VlZaP20PkC7e3tHD16lOXLl5OTk4PBYPAprYvL5ZK9xO3bt5OUlERkZCQmk4mUlBQSEhJkQ1BXV8fZs2dpaWnx2kvt7u7m+PHjnDt3jr6+Pp/Ep6Tq/sLCQux2OyEhIVgsFllBXhAEurq6aGlpoaamhq6uLnm5Mrg0YSyjLT3kzc3N5Ofny7G9L4q40ul0Ul5ejtlsxmAwcOutt7Jx40bZ6Obn5094knU4HOzfv5/29naWLFnCV77yFSIiIhBFkfb2diorKzlw4ADHjx+npKTEJ/3QQUFBrFq1irlz5xIZGUlYWBiVlZVs2rSJs2fP+lTbdmBggKqqKr71rW+xZs0aWTs3ODgYvV7Pnj17+OCDD3zGafelM3CiKNLd3c3hw4flwlJ3B/ZEB53T6eStt97izJkzhIaG+oXeRxRFurq66Orq4tKlS3LngsQzJhXSSnWBvlqC+1rN3OVyYbPZaGhokLPORqNRNkoDAwNyz+3wJY+nS0kpE/1FQxRFmpqa+Pzzz1m2bBkrV67EYDDIHQEKhcIrY2u1Wjly5AgnTpzgt7/9rawRK937sbjtPIHEZhMfH8/ixYuZNm0aDoeDX/ziFxw6dMgnvG/D4XK5OH36NP/rf/0vHnzwQaZPn47BYKCwsJC//e1v7N27V64s8AW+dAYO/lmB/UXCZrNx9uzZ8b/oAwwuefAXS7E/IYqibDilmkUpfuhvduIvClI8eNu2bRw7dozg4GDa29tpbW31iSc5+Br6C9IEUVJSwqZNm2RCS3+POZvNxoEDBzhw4IBf9wM3qIHzVeHgF7Xdf/W+/pUY7zwlY+2LRvrhave+gOQlTxQ2m43a2lpqa2t9eFT+wfB+ZmnS8bYswx/3ZTR4+lzdkAbu7rvv9stMr9Pphrw2GAxs2LDB5244cF0ldlxcHOvXr/f5foAhKk0As2bNIjEx0ef7kVhdBmP58uVuxWg8NXDSwzj49/fcc4/P42xS7dVgmEwmv92rwYpkcFXaz1/7GqzqBjB79mySk5PljDz4hrRBSlIMxqpVq/wSypESIe5C8MfD7SliYmLERx999F99GDdxEzfxJcRzzz13WhTFOSN9dlPZ/iZu4ib+bXHTwN3ETdzEvy1uyBicL/m0BsNsNrN06VL5dV9fH7t37x6xiXusfsjRMDh4m5CQwLRp0+TPGhoaOHXq1JjHNzwAPBYGf2/mzJlD4i3FxcVUVlaO+fuJQBAEbr31VoxGo/zeoUOHfCL0M/weKJVKVq9ePeR+bN++/boYnCdBZyn2NPzeBgcHs2jRIvl1T08Pe/fuHfFeDI5fSZC6AAC5X3Skfk1BEJg8eTKZmZny+7W1tRQUFLh9Dp4gJyeH6Oho+XVhYaFfZCEFQeC2226TqcwB9u3b53MJQLjaA7xmzRr3v+/zI/ABzp4965f6poiIiCEGbmBggDNnzvh8P3D1pg82cO3t7X4byAkJCUMMnD8fmry8vCEGrqSkhMbGxjF+MTFITLaDUVBQ4Jdi3piYmCEGrr+/36NxoVKpUKvVsi7qWP20Go1miIGzWCx+u1epqalDDFxNTY3fxvuSJUuGGLiSkhK/KMFpNJovv4G7kSAIV3VLTSaTLAwj/ZMGsb8TNVqtFpfL5RM21f8XoFQqZYbkgYEBrly54peMngRRFAkODkahUPiEDNJf+H9x7Nw0cKNAEAQUCgVRUVEsXbqUBQsW4HA4OHHiBHV1dTJFjd1u95mewEiIjIxk7ty5dHV1cezYMb8+qBPBSEvEwfVWvqCt8hSRkZE8+eST3H333dTU1PDCCy+wf/9+vxawarVauZfWV+c7mPNutBY2qY7P5XKhVCpRKpUMDAyM6EHeKLWZUgdFcHCwLFjtS4KMwfhSG7jBZIcKhQKlUolOp8NsNmM2m+nq6pKZLDzZplKpRKVSMWnSJDZs2MDy5csxm82UlZXJmglmsxmbzUZXV5fP1KCGIzo6mscff5yvfe1rHD582Ct6pOGQekPDwsIIDg6mr6+PlpYWOjo6fEK9YzAYCAoKQqfT0dXVJXO2+dvYSSSlubm5TJo0idDQUJYuXcqxY8d8wvQxEmJjY5k9ezYFBQU+M6JarZbs7GxycnJwOBxUV1fLfbsS+WtISIjMs2cymQgPD8dms3H8+HEaGhq8PgbJYGq1WkwmE4Ig0NTU5FWYQLo/99xzD3PnzpX5AaX+8srKSp+OkRvSwI0300gzQEREBGFhYUyZMoWpU6fKzBghISHExcXR2trKhx9+yKFDh0YtRh0e2Fer1ZjNZjIzM1m1ahWzZ8+mra2Ns2fPsmfPHk6dOkV/f/+Q3kp/PLRarZaVK1fywAMPEBwcTEFBgc8akIODg1m1ahWrVq0iKSkJs9lMX18fra2tFBQU8MYbb3gdjI6KimLdunVkZGTQ19fH9u3bOXfuHPX19T47j9HQ0dFBeXk56enp6PV6EhISMJlMfjFwRqORtWvXYjQa2bdvn08MnFarJS8vj5/+9KdkZGRQX1/PBx98wIULF2hubqa/vx+r1SpLCBqNRnJycsjLy6O0tHTUmJ6791OtVhMREUFWVhbJyckEBARgMpkoLCxk586dXl1HrVbLnXfeyY9//GOZRACukr9+9atf5bXXXmPLli1fKOHlvxTSUlGtVhMYGEh0dDSZmZmsWLGCKVOmEBkZSVBQEBqNhtbWVpqbmwkODiYoKIienh5sNhtVVVVUVFS4ZTgl/dUNGzYQHh7OZ599xq5du7h8+bKsCyF5jr6mTRqM2NhY1q1bR3R0NE1NTezevdsnLrxKpWLhwoX8+Mc/JjU1FY1GIy8jXS6X7Pn86le/oqysbNx9jvTQSFlEk8lERkYGoigSEhJCe3s7hw8f5tNPP/VLAFo6nitXrrBr1y5MJhPLly8nPDwcs9ns82RIQEAACxYsIDk5mc2bN/skmywIAlFRUXz9619nzpw5dHZ28v777/Pmm2/S0dEhx2FFUaS6ulrOzKakpDB58mTeeecdamtrJzQ5abVapkyZwt13383SpUuJi4uTPXCJf/DkyZNeNeEHBASQkZEhd3R0d3czMDCAXq9n3rx5pKWlsXLlSp5//nkqKyu9HvM3rIGTvDStVsvUqVNZtmwZt9xyC2lpaQQHB6PRaICrKf2WlhYAOjs75ViEIAj09PTQ2NiI1Wod9YYML09ITEzknnvuISMjg82bN8t00YMNmfQbieHD19DpdHznO99h2bJlKJVKqqqqfPLwALLGbF9fHxcuXKClpYWenh70ej1paWnExsZyyy23UFBQQENDw4RS/aIoUltby+9//3uOHDmCyWRi8eLFzJgxgxkzZpCYmMhrr70m3zdfQ6VS0dvbK2sX6PV61Gr1qN+fSGwqIiKCb37zm6xfvx6r1cqf//xnr1lEJGi1WhITE1EqlRw4cIA333yT1tbW68awy+UiNjaWBx54gJUrV3LgwAF27NgxIS9Sq9WydOlSvv/97zNr1iz6+vqwWCzy2JdWQEajEa1WK1NceWroOjs7uXDhAlarFa1Wy+nTpykpKSE8PJwFCxYQHR3Nhg0bMJlM/M//+T+5cOGCVyuJG9LASSekVquZPXs2TzzxBIsXL8ZkMiGKokxsWFpayqlTpzh//jxhYWFMmjSJxYsXk5iYiMPhoKKigrNnz8oGbrwLJXk3ixYtwmazUVxcLLOWSHG5pKQkVCoVNTU1PiMBHAxBEHjooYd4+umn0Wg01NXV8ac//clnBs5ut3Ps2DHa29tpamqSWVUDAwP5wQ9+wP3333/d8UxkgA0MDFBdXU1dXR1KpZKysjJuueUWVq9ezbe//W0GBgb4r//6r1EniIkGxBUKhSy1mJCQACAbudHg6fmZzWY2btzIo48+SmhoKO3t7dxxxx3s3buXixcv0tXVNeGHUrwmPiSVmtTX12Oz2a67D0qlktzcXL7xjW+watUqTp48yf/5P/9nzHEy2jVVq9UsXryYxx57jNTUVIqLi+VVS3BwMAkJCfT397Nz507ZC5bq/TyF3W7n6NGjnDhxQmawttvtfPrpp1RXV3P33XcTHR3NvHnzuPXWW6mpqZGXxBO5pjekgQNkGuNp06bJjeMWi4Xjx4+zdetWKioqZBpnhULBvHnzWLp0KWlpaRgMBqqrq9mzZw/FxcVux3ykwK7RaJRnzLCwMKKjo8nIyCA2NpbMzEzMZjOXLl3io48+4vjx4z6NKT344IP87Gc/Q6fT0dfXxzvvvOMTzn0JTqdTvnbSTK9SqZg8eTIzZ85Ep9NhtVqpqamR6Y7AOy49p9Mpk3SGh4eTnp7OsmXL+P3vf4/FYvHJeUmQYrCpqakYDAZ6e3uxWq0+ox3SarU8/vjjPPTQQ5jNZpxOJ0qlkkWLFjF//nx2797NJ598Ql1d3YT3abFYuHjxIvPmzWPhwoVs2rSJxsZG8vPzqa6uxul0kpuby6ZNmzAajbz00kvs3LmTqqoqj42OIAikp6fzk5/8hOjoaN577z327dtHVVUVcXFxREdHo9PpqKqqoqqqiu7u7hHlGT3BxYsXeeONN9i4cSPx8fEkJSVx+vRp9u3bh1qtZv369eh0OvLy8jh48CDV1dXyfj3FDWvg4J+cW/39/djtdsrKynj//ffZv3+/rASl0+lITk7m4YcfZtGiReh0Ourr6/nkk0/46KOPPMr6SOSS/f39NDU1ySImWq2WkJAQkpKSmDRpEgkJCcyZM4ecnBx++MMfcurUKa+XJpKa0g9/+EPCw8Nllt/8/Hy6urq82vZI0Ol0BAQEYDabyc7O5vHHH2fmzJnYbDY+++wzTpw44dMEisPhoLGxkTNnzrB48WJUKhWpqamjyvhNdL8qlYr29naOHTvGwMCArMHqC8omlUrFfffdx3e+8x20Wi1FRUV0dXXR29tLX18fOTk5LFu2jPj4eLZt28aJEyfkzLEn++7t7eXVV18lLi6O5ORk7rzzToKCgvjmN79JaWkpVquVyZMno1QqeeGFF9izZ8+EJ1mj0cjXv/51Zs6cSWVlJefOnaOpqYm4uDiWLFnC1KlTCQ0NxeFwYDKZfFLn19/fz9Gj/397Zx4c1XWm/d/pVS219n3fhQAhJBBgbDA4kMgIExyMsceOQyY4HjsflWQymTiZmXK+uJI4E/uLiWucOGHsGTAQDDY2e7EYi1Xsi0ACCW1oATVoV2vv7vv9ob43QkhCS0tqqH6qutR9b6vPe8899z3nvNtzgrS0NMXj7enpSW5uLkajUeGwTU1NZfbs2QpH8EOn4CwWC/n5+QrRS0VFBaGhoSQlJdHa2srkyZOZO3euQlHn5uZGTU0NJ0+eZPPmzZhMpiHZI7q6uvjyyy8BKCoqoqioiKqqKioqKsjJyVGIMf7jP/6DWbNmkZSUxLe//W1KS0v7tJEMFiqVitTUVN544w0mTpyoFDssLy9XVqiOcmbIIRyzZs0iKyuLBQsW4O/vrxiTN27cyJtvvjkqaTZWq5XLly9z48YNIiIiCAwMdGhslkqlwmKxUFlZiclkIicnhylTphATE0NISAh5eXnD/m2DwcCMGTN4+eWX8ff3Z8+ePfzmN7+hpqaGzs5OAgMDWbBgAcHBwYSHhyslv86fP6/YqgbrGZQdCK+99ho+Pj6EhobyrW99i+TkZKZMmUJYWBgVFRX87ne/4+DBg8PyOMrOO39/fyIiImhvb0en0/GNb3yDRYsWERwcDHTb+WQmrzlz5nDnzp0RE5/rdDpCQkJwc3MjLCyMgIAAfHx8SE5OprOzE09PTzQajRInJ9vWH6otKqB4QA8cOIBGo8HT05NnnnmGhQsXUlNTQ0ZGBiEhIYqXVV46WywWDAYDHh4emM3mQW/v2tvbOXLkCCaTCbPZrNg/eqK0tJSdO3cSGBjI5MmTmT9/Plu2bKG+vn5YmQZqtZp58+bxi1/8gscffxz4exlxi8VCdHQ04eHhlJWVUVpa6pCtlpubG6mpqcybN4/IyEjUajWtra0cOXKEtWvXjoptEf7u4TSZTISFheHt7Y1OpxsxaUpPyBOaHDIUHx8PcE8du6FApVIRERHBihUrSExMxGq1Ul1dTX19PfX19XR1ddHW1sZXX33F/PnzmTp1KhMmTKC4uJibN2/S0tIy5FW4vHupq6ujrKyMq1evMmnSJNasWYO7uzvl5eXKCnE4kBVcZ2cne/fuxWg0EhERQUxMjPIM5eTkUFxcTGRkJFlZWcyZM0chHB/JCnvSpEm8/PLLfOtb38Lf318Jt5Lvr9VqVRxFp06dor6+ftirRqdWcFarFbPZzJkzZ/D19SU5ORk/Pz8lqDEgIACr1UpdXR06nQ61Wo3FYiE4OJi0tDQAysrKqKmpGVQHWSwWbt++TXt7u0Jk0hudnZ1UVVUpLnuVSoWfn59i7xmKrUylUhEVFcUbb7zBnDlzlDYtFgs6nY60tDReeeUV/Pz8+OKLL/jss8+oqKgY0WpOkiTa29sxmUzU19fj4eGBh4cHjY2NnDt3DpPJNGrBuEIIAgMDCQsLw9/fn/DwcIKCgrh586ayjZNDTIayspMfVvn6oHviWLx4MUFBQco1yeOjr/+/Hzw9PYmMjFTGWVpaGs888wwnT56ksrKSiIgInn76aebOnUtMTAy1tbW0trYSEBCAWq0e0YrYZrPR1NREWloaCQkJCCEwmUwj+k05jlMO3dHpdMTFxdHW1kZAQADV1dXs27ePiooKQkJCmDdvHmlpaUycOJGSkpJhT7TBwcF8//vf57nnnsNoNFJbW8vOnTspKSlh8uTJTJgwQXmuL168SGVl5YiyQ5xawcHfKehKS0sBaGpqIiAggAkTJlBdXU1RURGlpaXMnDmTqKgoVCqVEn8lh4kM9mGRtxENDQ14enoq1U/Ly8sVFvYZM2awatUqJWH6xo0b1NfX3xOGMJg23d3dWbRoEYmJiUr7cpgLoGxT8/Pzyc3NVZbqI4EQgq6uLo4ePUp7ezuTJ09WbDzD8YwNtm/VajXBwcEsXryYjIwMtFot8fHxpKWl4efnp5Cp1NTUKNymg23fy8uLwMBALBYLDQ0NaDQapk2bxne+8x0MBoOSSdG7ZPdgYbPZKC8v58iRI8TFxREZGcnUqVOJjo4mLy9PSemLi4vDYDAoq7mioiI6OzuHPPH1hYCAAFatWoXRaMRisWA0GgcMfekLPa9bdhJ0dnZiMpk4ePAgMTExiuf5/PnzilPBYrHQ2tqKn58fISEhQ66qK0OO2cvMzMTb25uKigr++te/8vHHH9Pa2qo4TvR6PS0tLWzbtm3AEK/BwOkVnNVqpaWlBa1Wi6+vL+Hh4YSFhdHV1cW1a9coLi4mPj5eYX2Xtw2tra3K9nQoNiyZiMNoNPKTn/wEX19fNm3aRGVlJSkpKfzrv/4rUVFRCCEoLy8nOzubxsbGITNdycHClZWVbN++nbi4ODIyMjAYDFgsFhobG/n000/5y1/+wp07d/pkAh8K5FWO3BcVFRXU1tbS2dnJ8uXLFVaooaZT9aXg5Lbkvzqdjrlz5zJv3jwyMzPx8/OjqqoKDw8PHn30UaKiomhoaODy5cuKLXCwitNoNLJs2TJmzJihsMwbjUYWLVrE5MmTMZvN7N69mytXroxo5VtTU8N7773HunXrWLRoET/96U+Ji4vjiSeeUGTV6/VKJZJNmzZRUFBAZ2cnbW1tI8pw0Gg0rF69mri4OMVZEhYWNqJttwyZk6G6uhroXqnq9XqKi4uVECkPDw8iIiKoqamhsLBw2NtiOf0xKCgIq9XK+++/zwcffEBra6uirCMiIlCr1RQXF5Ofnz/izBCnV3DyUtpgMDBx4kSFDLezs5OIiAgeffRRvLy80Ol0dHR0cOvWLa5evUpxcTFlZWUKUzcMfrUhSRKtra00NTUxZcoUfvzjH2MwGAgODiYkJAQhBLW1tezYsYNt27Yp29qhKAa5DTlTYuLEibz33nukpaWh0+m4efMmn376KVVVVSPeMsq5ih4eHnR2diqr0QkTJrBy5UpCQkI4c+YMOTk5I7bxqVQqwsLClBQfm81GYGAg//iP/8ikSZPQ6XRKmMCJEycwm82YzWZlZTmQgu3ruF6vJy4ujhkzZlBdXU1ISAiJiYlMnDgRIQQ5OTl89NFHChXdSPqyq6uLmpoaNm3axPXr13n++eeZMGGCUi7JaDRy6tQp1qxZo6S6aTSaEd+/9PR0vv71r6NSqejq6kKtVlNVVeVQZjmr1UpHRwc+Pj74+/srCwMPDw+++c1vEhERwZdffklhYeGwJ1qVSqUECXd0dHD69GmsViu+vr5kZGTw05/+lIiICOrq6tiwYcOI2pLh9AoOur0ubm5uBAUFERMTg4eHx12kJBaLhZaWFs6dO8dHH31Efn4+LS0tiuF/OJ3U0NDA/v37mT17NomJibi5uaHT6bBYLFRXV/P555+zfv16KioqlDaGOpB7khU3NDQo4QzNzc2sXbuWK1euOMQeptVqSUlJYfLkyZhMJlpaWpg+fTpLliwhNTWVvLw8fve731FYWDii9uRc3oSEBJ599llSUlJwc3PD19eXgIAAxWG0d+9eTp8+fc+k0HMCGizTlfwQhoWFERkZqaTb2Ww2Tpw4wZo1a7h586ZDK4lYrVZOnjzJ+fPniYqKQq/Xo9fr0Wq1d3nUexaCGG6IipubG1/72teIiYmhs7MTd3d3WlpaFOO7oyBPuN7e3kRFRREfH09ISAjTpk3jlVdeoaWlhd27d2MymYbdhsVioba2lvr6etzc3FixYgWzZs0iJiaGhQsXEhsbS3t7O+vXr2fr1q0OUeAPhIKTIUmSYliV7QeVlZUcPXqU8+fPc+HChXsCVHs6C4YywGRPWV5eHl1dXXh7e2O1WsnOzmbXrl3k5eVRW1vrsPANPz8/goODaW9vZ/fu3ezYscMhaWByWMjUqVN54YUXgO6VSHx8PH5+fuTn5/Pzn/+cnJycYdmJele9tdlsXL9+nR07diixinfu3KGwsJCSkhLKysr6tav0PDbYfpUntrS0NCVI22w2s3XrVj788EMuX758X+U2XKXe2dlJUVGRYpPqPcnJ3kjZeTIcJCYmsmTJEjQajUIqffLkSfbs2ePwogU2m00JeXnppZcIDQ0lISEBT09PNm7cyL59+0a0wpeDzK9du8acOXN46aWXlIgHefHw+eefs2bNGmXLPFI8EAqupaWF3NxcvLy8yM7OVtJhampqqKmpoampqd8aWMOFzWajrKyMd955B41Go3jFZFb2+z0UQ31oSkpKePfddwkODmbfvn3U1dU5ZPUm5/R6eXkRFhaGr6+v4kndtWsX//Zv/8aNGzdGrExlWeUVrpx1Ipf3GepKeihBsdu3b+f48eNK7FZlZaUSID4WtegGGncjifhXq9WK88Rms9Hc3Exubi4/+9nPHF5WCLonvsuXLzNr1izmzp2LTqejrKyMjRs38vnnnzskXbCoqIjNmzcTGxtLZGQkWq0Ws9lMZWUlb731lsMD2x8IBdfV1UV+fj7l5eVKiZixYElvbGwccVDjYFFXV8fmzZsd/rty7u7hw4cJDw/H19eXhoYGDh06xP79+0cc89b7IZNtpm1tbYOObxtp+7Idr6ysbNTbG0vYbDZyc3PZtGkTaWlpbN++nRMnToxKEDZ0K+q8vDz+8pe/UFFRwe3btzl8+DBlZWUOK1/U2dnJ9u3bMZlMTJ8+XSnlf/Xq1RF7TPvCA6HgoLvzx0rZPEyQt/Lnzp3jypUrCCFG7NVzYWwgB0avXbtW+Tza7bW2tnLp0iXFgykHzzsSTU1N7N+/n/379zv0d/uCUyo4ZymtPBI40zXIoS+jQeQje6hh+JVH7ve7PX9/NOBM96ovOLoE+v3Q0/n1oOO+zPZCCDfgCKCnWyF+KknSL4UQscBmwB84B7wkSVKnEEIPrAemA7XAc5IklQ3URm9m+9FYqsLfS+nIkOvBjwZkz68MOZ1nNNC73ll7e7vDqmf0htFovEv5tLS0jMrDIIe29MRoFB2AbltXT6awh3VctLW1jcokB/eOC9mM5Gj0NS4GYrYfzAquA/iaJElmIdTGDhoAABzUSURBVIQWOCaE2Av8BHhXkqTNQogPgFXAn+1/6yVJShBCPA/8J/DcUC6i9wWMFlQqFV5eXmPSllarHXLk+XDh5uZ210M0muipGEYbY3WvHtZxYTAYBqyL50g4IgjZEbgvs73UDXk609pfEvA14FP78XXA0/b3S+2fsZ9fIJx9D+CCCy48lLivggMQQqiFEBeB28ABoBhokCRJtlRXAuH29+FABYD9fCPd29jev/mKEOKsEOKsIyOyXXDBBRdkDMrJIEmSFUgTQvgAnwPJI21YkqS/An+Fbhtcz3Nr164dFVuBv78/zz33991yc3MzGzZsGHLuZU8uSrnyRc8gTyEEkydPVsofQXec24EDB+6xSwzU9mCM9iqVigULFigJ+wBHjx7l8uXLg76moeDFF1/E29tb+bx169ZRIZBRq9W88sord1UUXr9+PW1tbSOKLesNOa9z6dKlyrHGxkY++eSTe2yL8r3vif5kkfNwZS+k/L9Tp05l9uzZyvcKCgqUGoR9oaddayjXLYQgMzOTuLg45Vh2djb5+fmD+v+ebcttytfR85jc1ksvvXTXtvSTTz6htrZ20G31lr13GzL0ej2rVq0a9G8NyYsqSVKDEOIrYDbgI4TQ2FdpEUCV/WtVQCRQKYTQAN50OxsGDTm53NHoPThtNtuwiE80Gg2hoaHodDqqq6v7DCiNioq663NbW5vDorN7o3dEu9lsHjXWqt4PfX19/ai01VeqVlVV1aiMi942MDmLpT9lIudUyrmhNptt0OEUvR0l7e3tA/afnP4mF/McSthG79i15ubmId0rOUNDVqwDtdt74q6trR2VcSGTTQ0W992iCiEC7Ss3hBAG4OvAVeArYLn9ayuB7fb3O+yfsZ8/JI1FOPkYwmg08uKLL/JP//RPeHl5jUm0/EAY7/bHCmN1nQM9zLLCiYqKYsaMGUybNo3o6OhRcxTIk+n06dOJiooadI7uSKFSqRSaTpnAe7hlksYTg+mtUGCdEEJNt0LcIknSLiFEPrBZCPFr4ALwof37HwIfCyGKgDrg+VGQ+x6o1Wo8PT2Jjo6mtbWVqqoqZTvjaFitVm7cuMHFixf7JU1x5BZKq9UqXtHRCstwYXCQlZ+npyepqalKOlNdXd2wCzsMBJVKRVJSEpmZmZw+fZqampoRk77cD/K2PT09nebmZiorK5Wq2UVFRQ7LahgL3FfBSZKUC6T3cbwEmNnH8XbgWYdINwDkGUYulTNt2jSioqIIDAyksbGRvXv38sEHHzg8rUW2tx08eJDm5uZRiyuSc0j9/f1ZtGgRqampZGdns2fPHpeCGyKEEOj1etzd3dFoNDQ1NSn3Ta70OxTICk7OELl165ZS1cTRWSLu7u7Mnj1buf8986AdGVjdE25ubsydOxcvLy+OHTtGa2srU6dORQhBUVGRw9vrCbVarZCRd3Z23jNhDDUgwykzGQYDf39/Vq1axQsvvKDUaJMkCa1Wq7z/7LPPMJvNDh0Evr6+eHl5jbh0+ECQV23e3t6kpqayfPlygoOD2bBhg8MCeOU2YmNjaWho4Pbt2w5/WOSVZ08njFqtVlYD8rZHrlFXX19/T3WSoUIIgVqtxt3dHaPRSEBAADNnzmTatGlIUjfn6O7du8nLy6O9vV2pjTdUdHV1cezYMQoLC5UabXI5c0emN6nVamw2G+fOnePMmTN32Vtlx4Wj79v06dOZN28ee/bsobS0FLVaTWNjo8I050jIk4+Pjw+RkZGkpKQwadIkbt26xf79+ykoKLhrEdFXhstAeCAVnE6n4/nnn2f16tX4+flhNps5efIkubm5hISEMGvWLCXp25HQarUsWLCAS5cujZpyU6lUuLm5KaWhDAYDYWFhXLlyhby8PIcMZpVKRXBwMPPnz+ett97i7NmzvP766w6tUOHm5saiRYtYsWIFgYGBCvtUZGQkRqORxMRExVAvSRL5+fk8/fTTVFRUDEsGmYUpNDSUwMBApRZdU1MTnp6eXLhwASEEEyZMUIz2kr1E/HDuZUtLy13cpxaLBY1GQ3R0NGazmerqaodsV5uamjh58iReXl73ZFcIIYiMjKS1tZWamhqHVLhxd3dn1apVNDc3KzX7AgICFBKmweJ+E5QQAh8fH6ZMmcK0adNISkqivb2djo4OEhISlOrW77//Po2NjXd5coeCB1LBxcXF8YMf/ICAgAA6Ojq4ePEif/rTnzh//jyTJ08mPDwcvV7vcHtIVlYW3/zmN8nOznbo78qQi0N2dXXR0NCAWq0mISEBo9HIJ5980m8BwKGudvz8/Fi5ciWvvvoqkZGRBAcH09XVxa9//WuuXr3qkH4LCAjgueeeY+nSpeh0uj5l7Lmqk/kZKisrBwy96A0560Au6KlSqbh+/TqnTp2ivLxcCVXQaDQkJSVhtVopKSmhoaHhLg/oUCFz9faWLzo6mokTJ5KdnU1ubu6Qf7cvhIWFERMTQ3Z29l3VX7RaLc8++yxBQUFs2LCBK1eujPjeZWRkEB8fz5o1a6ipqUGn0/HYY49RWVk5JHPMQIpIr9czc+ZMMjMzefLJJ9HpdHz11VccPXpUoQ0MCgqio6PjntXwQ6/g1Gq1wj8phKCjo4Py8nLq6+tRqVQkJiYSHR2tLKcdtSJ54okn+OUvf0lXV9eo5ETqdDoiIyORJInKykosFgsBAQEkJiZSUlLCiRMn+v3foVyjWq3miSee4OWXXyY8PFxpOysrC4A//OEPXLhwYcR2pI6ODpqbm+8qhAnd5XIqKio4duwYsbGxpKSk4O/vT2dn54ChGXC3ghNCYDAYmDRpEgsWLAC6iVKuXbuGyWSiq6vrrt8yGAzExMRQVlbGzZs37xobw6343Hu71t7ezoULF3jsscdYvHgxeXl5I17py9coc440NDQoE4D88C9btoyWlhbKyspGNDY1Gg3z58+no6ODU6dOYbPZFA9ubm6uQyY+nU7H/PnzWb16NVFRUZSWlrJr1y4OHz7MrVu38PDwUMoonT179p483YdewXl6epKZmYmHhwc2m41bt25RWlqqbLumTp2Kj48Ply9fdljN+pCQEF577TViYmLIysoaNtFuf/YSjUbD9OnTcXd3V7gu1Wo1KSkpBAUF8c477/TrrR0qAgICWLp0KVFRUQoto7xdS09PZ9q0aRQWFg6a+7K/1WNraysnTpxg6tSp+Pn58d5779Hc3ExOTg4NDQ34+Pjwzjvv4Obmhs1m4/Dhw4PagssBtD4+PixevJjMzEy6urr47//+b86ePdvnpKbVannkkUeIjY1l48aNI/auG41Gmpub75kEJEmitraWL7/8kmeffRa9Xj/iMahWqzGbzeTm5lJbW3uXkrFYLGzZsoWMjAyCgoJwd3cfkYKLjIwkPT2dyspKamtr0Wq1CqH6UMdfX+NCq9Uyffp0nnnmGQoLC3njjTcoLy/HbDYrW/3AwEDi4+PJzs4eMVEQPGAKTqVS8eijj5KSkoIQgtu3b7Nr1y4OHjxIXV0dgYGB+Pv7K0TGjrCTeXt78/rrr/PUU0+xbds2rly5opC3DLRk749tqveDJYTgscce45//+Z95++23FaeIp6cnGRkZHDp0iJycHIeVL09OTiYzMxMhBI2NjdTX16PT6RT7VVZWFjt37hxx7b2WlhY2b95MQUEB8fHxbNu2TdkSJiYmsnr1ahYsWIAkSZw8eZLvf//7gyq+KWeR+Pn5KVH6x44dU7g6e/evRqMhNTWVJUuWcPjw4RFXSpYpAmUay96QJEkhIdLpdCNWcJ6envj7+3P06NE+J9aamhqOHTumrP6HC5VKxdy5c0lNTWXDhg2oVCoSEhJYvnx5n9vxoUKj0RAWFkZaWho5OTns2rXrnkBgnU7HokWL8PHx4ciRIw6pau2UCq6/VYHBYGDRokUEBATQ0NDAhg0bWLt2reKm12q11NXVYbPZmDhxInq9/r6laAbyQgkhWLhwIa+99hrHjx/nj3/8I1qtloyMDLy8vDhx4sR9t1U90df3DAYDjzzyCGfPnuXixYtIkqQQQgcEBLBlyxaHbYnVajVTpkzBy8tLYTaCbmUk88nGx8czffp0bt26NajrGug77e3tnDlzhvz8fLy9vUlOTiYkJIQf/OAHzJw5k/r6er744gveeuutQROoyFszmfG9ubmZixcvKobo3mPHx8eH9PR0qqurOX78+IgfVJk9q78tvBCC8PBwDAaDQ8wj3t7e2Gy2fsnL3d3dSUhIoKGh4b4cDQPZat3d3UlKSgLg2rVrBAUFsWDBAtLT0zl48KBiRx3uNcnez9OnTys20N7nFyxYwLe//W2++OIL8vLyHDKpO6WC6w/JycmkpaWhVqvZt28ff/7zn7l586bSESUlJZw/f56nnnqK4ODgQbmU5ZvW183T6XS8+uqr1NXVKQQmMkPSihUrmDt3Lr/97W/7TPcazEBQq9UEBQVhMBi4du0aOp0Oq9VKaGgoEydO5MiRIxQWFg6yd+4PeXtnsVhQq9UK2fPZs2e5ceMGCQkJTJs2jaysLI4fPz7ibbGsjHQ6HT/84Q9ZsmQJvr6++Pv7U1VVxc9+9jMOHTo06JxF2SkhM4+dPn0avV7PjRs36OjouMcMoNfrCQ4ORqfTkZ2dPei0vIHMCXJ5qP4ePh8fH1JSUigvLx9xnTd50j5z5gzl5eX3nNfr9TzzzDPEx8ezdu3aEZWf9/DwwMfHh9raWgICAsjMzGThwoV4enri7u5OcnIyly5dorW1dVhKzmaz0dTUpHAW9/6NqVOn8pOf/IS2trZ+V6vDwQOj4GQ7SnJyMh0dHezbt+8u5Qbdhu2eJMmDmQEGcj+7ubkxYcIEWlpakCQJd3d3mpubOXPmDMnJySxbtoykpCSFJu5+7fT+juw9nD17NkuXLuUf/uEfOHPmjPLAygPKUZCkbn4G2VOl0Wioqqpi/fr1nDp1Cg8PD95++23mzp1LVlYWW7ZsGXHcnexZXLZsGfHx8dhsNq5cucJ3v/tdLl++PKxZWlZypaWlaDSauwJC5aBdjUaD0WjEz8+PtrY2hd5xpNfi5+eHr6+vEp/W85zBYGDevHkkJCSwZcuWEbenVquJjY3F09Ozz7Zefvllvve977F3716OHj06ovZksqDq6mqSkpKIjIxk0qRJaLVakpOTmTdvHnV1dZSWlg6bdEmj0eDu7o6np6eS+aFSqQgPD+dHP/oRKSkpbN26FbPZrLCj9WYqeygCfftTNiEhIYonqaioqM+ZVg62rK2tHfF2pKuri+zsbCIjIwkNDWXq1KkcO3aMhoYGcnNzyczMVLg4hzOrWa1WioqK2LBhA9/97ndxd3dHp9NhMpkoKChQglaHiv4GgRxvduLECR555BFaW1tZt24dBw4cUDye//M//8Mf/vAHHnnkEfbt2zfshGkhBG5ubmRkZPD2228TExODJHXX/N+0adOwQhp69rFMbNPbsyq/1Go1bW1tGAwGjEajQ1YEKpWKwMBAJk6cSH5+Prdv31ZWw6GhoSxZsoTHHnuMnJwcCgoKBh3qMlB7kyZNwmg0KnyoWq2WpKQkfvjDHzJ37ly2b9/Or3/96xGTB7W0tHDs2DE6OjpISUnBx8eHrq4uzGYzJpNJsYcNNwDbZrOhVquZN28eM2fOVEiJdDodc+bMUTh7CwoKiI2NBeD69esjvm9OqeD6glqtxmAwoFKpqK6upqSk5B7trtPpmDBhAt7e3nz11VeD2iIMpJja2tp49913WbZsGWazmZaWFmw2G1qtlsTERMLDw+8JRxgK5JzWjz/+mI0bNypbarVaTXh4OC+++CK7d+/m4sWLDqHcs1qtnD17lh/96Ec8/fTT3Lx5k88++0wZRJIkkZubS0FBAQEBAfj7+w8qgLQ3tFot/v7+pKens3r1amJiYjh37hw1NTXo9foRPSi90Xt2lx1LXV1d6PV6IiIi6OjoGLRXWP7N/r4bEhLC8uXL6ezsZNu2bTQ1NSnpdI8//jiFhYUcOHDAIRR7ktRN7+jv74+np6eifP7lX/6FqKgotm7dyu9///tBK7eBrr+jo4MLFy7Q3NxMUFAQ8fHx1NXVcfDgQf72t79RUlJCR0fHsO1iNpuN9vZ23NzcCAsLIyIiAqvVSnh4OEajkZs3b7J7926OHDlCS0uLEqf4UDoZ+oLFYsFsNmOxWJR8v94Xn5SUxMKFC9Hr9Zw6dWrEnSNJEgUFBXzyySeoVCrq6urQ6XTEx8fzxBNPYDQaKS8vd4gxueeW2mKx0N7eTkxMDEuWLOHGjRvDrq3VG5IkUVRUxB//+EeAe1a5ZrOZ5uZm4uLi8Pe/p07poBAVFcWKFSuIi4vDZDLx+9//nuzsbGpra3nyySd59NFH8fHxoaamZsTXI0NOlZJLCqnVahITE5kxYwbbtm1zCEmy1Wrl/PnzVFVVMXv2bIqKimhubiYtLY0nn3yS/Px81q1bR1lZWZ/pWn3Vk7tfe1VVVcycOZNnn30WX19fpk6dipeXF++88w47duxwGJ+DnDkjj+fo6GhycnLYtGkT165dc1hWxu7du6mrqyM9PR2bzUZSUhJCCPbs2cOhQ4cclgEi44FRcF1dXYqBMjo6mu9973t8+OGHSvrK5MmT+dWvfkV6ejoVFRUcOnTIIYqntbWVvLw8Jb1Htr1cuXKFy5cvc+3atRG30Rdu377Np59+yvz58wkMDHQYEbSM/rbvBoOBuLg4fH19h1W/X6VSkZWVxQsvvEB1dTX/+7//y969e2lublZIflNTU3n11Vf57W9/67DB3Ht7Gh0dzdKlS8nPz+f06dMDhgwNRencuHGDN998k4ULF5KYmEhoaCjJyclUVlaybt06SktLHZbGJ0kSdXV1xMXFKfGEt2/f5je/+Q07d+50OFmNJEkYjUaioqK4c+cO27Zto6ioyGH3SPYGHz9+nIaGBgIDAykqKsJkMnHq1CmH543DA6bgiouLqaqqIiEhgddff53vfOc71NbW4uXlRUREBG5ubphMJt58802HkgDLlQ2g+2EoKCjg3XffVbYQowGLxcLp06dJTEwkIyOD8vLyPh0OQ10V3A/BwcH4+/vj5uZGQEAAarV6SMZrjUbDlClTCA4OxsPDg7S0NPLy8tBoNEqKXXJyMk899RTvv//+oMND7ger1YrNZsPDw4OgoCAWLVqE0WjkT3/6k8P5dK9evUpdXR1RUVGEhoayb98+CgsL7+tsGmjr2xdsNhtFRUVcunSJgIAAbt++zS9/+Uuqq6tHhddWnhjkFdWBAwcczs4me1Nv3Lih2NOvXr06aOX20GYy2Gw2jh8/zn/913+xePFiYmNjCQkJISgoiObmZgoKCigsLGTjxo0cP3581GjzZA/eWLC2NzQ0UFpaysqVK2lqamLXrl19zqaOUnByCaq6ujp8fHzw8fFBq9UO+WE6efIkU6ZMISEhgZUrV7JgwQI0Gg1qtZqoqCi6urpoaWnB29t7SApuoOuUA3CnT59Oeno6Qgg2bdrksK19T0iSRHV1NSaTSfk8WigqKuLVV1/FarWOOlm31Wrl+vXrrF27lvPnzzsse6YvSJKEr6+vUhF7tPDAKDjoLo+9fv16du7cSVJSEnFxcajVampqaigsLKSqqmrYcTrOCKvVyuXLlzl58iQeHh5KSERvOOp6NRoNtbW1FBcXk5CQoCiloaCzs5M9e/ZgNpt57LHHmD59OgkJCahUKlpbW7l+/TonTpxg165dVFRUOERu6I4JmzJlCrGxsRQXF3P27Nl+PZmOwliMM0mSxqzApCRJVFVVDalqyHDa6OzsxGQycenSJdra2pQwrNHAA6XgoHvrdufOHe7cucPx48fHW5xRR3l5OR9++OGolH/qDUmSqKmp4cCBAxw9epQDBw4Ma3Y1mUx88cUXHDp0iLCwMCUro6GhgZs3b1JSUkJtbe2QB/VAgdsWi4W8vDzy8/Opr6+nsbFx2P01WnXWXOiGJHXX5ZPt16O5MnVKBafX6x1qV5LRF2GFHLYwXPS0gck2FrmYZE9oNBoMBsM9oS2DgRwGoNFo0Gg0dz18suOjd1tDJeeQ/0/2dMlea7lAZc/r7QmtVttvW01NTTQ3N3P9+nU0Go1iJ5Mk6b5FJvviHvD09KS1tbXfbbrsgZMkSemr+1UnEULcQ14thMDd3b1PT/1wITs/9Hr9XcflY45Wpn3FUA50r0baVu9x4ebmdt/rkv9vKEUsh0poLpxhlgoLC5NeeeWV8RbDBRdceADxq1/96pwkSRl9nRta/V8XXHDBhQcILgXnggsuPLRwKTgXXHDhoYVT2OCEEHeAFsBxuTuORwDOLR84v4zOLh84v4zOLh+MvYzRkiQF9nXCKRQcgBDibH+GQmeAs8sHzi+js8sHzi+js8sHziWja4vqggsuPLRwKTgXXHDhoYUzKbi/jrcA94GzywfOL6OzywfOL6OzywdOJKPT2OBccMEFFxwNZ1rBueCCCy44FC4F54ILLjy0GHcFJ4R4UghRIIQoEkL8fLzlkSGEKBNCXBZCXBRCnLUf8xNCHBBCXLf/9R1DeT4SQtwWQlzpcaxPeUQ33rP3aa4QYto4yvh/hRBV9n68KITI6nHuF3YZC4QQmWMgX6QQ4ishRL4QIk8I8SP7cafpxwFkdIp+FEK4CSFOCyEu2eX7lf14rBDilF2OT4QQOvtxvf1zkf18zGjKdw/kChjj8QLUQDEQB+iAS8Ck8ZSph2xlQECvY78Hfm5//3PgP8dQnseBacCV+8kDZAF7AQE8ApwaRxn/L/DTPr47yX6/9UCsfRyoR1m+UGCa/b0nUGiXw2n6cQAZnaIf7X1htL/XAqfsfbMFeN5+/APgNfv7HwAf2N8/D3wyFmNRfo33Cm4mUCRJUokkSZ3AZmDpOMs0EJYC6+zv1wFPj1XDkiQdAXqXWO1PnqXAeqkbJwEfIUToOMnYH5YCmyVJ6pAkqRQoons8jBokSbolSdJ5+/tm4CoQjhP14wAy9ocx7Ud7X5jtH7X2lwR8DfjUfrx3H8p9+ymwQIxGLbR+MN4KLhzoWda1koFv5lhCAvYLIc4JIeRaTsGSJN2yv68GgsdHNAX9yeNs/bravsX7qMe2flxltG+V0ulegThlP/aSEZykH4UQaiHEReA2cIDuVWODJEly5cqeMijy2c83AsOjaxsGxlvBOTPmSJI0DVgE/B8hxOM9T0rda26nibFxNnl64M9APJAG3AL+3/iKA0III/AZ8GNJkpp6nnOWfuxDRqfpR0mSrJIkpQERdK8Wk8dLlvthvBVcFRDZ43OE/di4Q5KkKvvf28DndN9Ik7xFsf+9PX4SwgDyOE2/SpJksj8QNmAtf98+jYuMQggt3YpjoyRJ2+yHnaof+5LR2frRLlMD8BUwm+7tu1yGuacMinz2896A45mA+sF4K7gzQKLdA6Oj2wi5Y5xlQgjhIYTwlN8D3wCu0C3bSvvXVgLbx0dCBf3JswP4jt0L+AjQ2GMLNqboZbP6Ft39CN0yPm/3ssUCicDpUZZFAB8CVyVJ+kOPU07Tj/3J6Cz9KIQIFEL42N8bgK/TbSf8Clhu/1rvPpT7djlwyL5KHhuMpUejH69MFt2eomLg38dbHrtMcXR7pi4BebJcdNsOvgSuAwcBvzGU6W90b0266LZxrOpPHro9Xe/b+/QykDGOMn5slyGX7sEe2uP7/26XsQBYNAbyzaF7+5kLXLS/spypHweQ0Sn6EUgFLtjluAK8YT8eR7diLQK2Anr7cTf75yL7+bixGIvyy5Wq5YILLjy0GO8tqgsuuODCqMGl4FxwwYWHFi4F54ILLjy0cCk4F1xw4aGFS8G54IILDy1cCs4FF1x4aOFScC644MJDi/8PeCEM5m5hN4YAAAAASUVORK5CYII=\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "autoencoder.eval()\n",
    "\n",
    "with torch.no_grad():\n",
    "    # approx. fit a multivariate Normal distribution (with diagonal cov.) to the latent vectors of a random part of the test set\n",
    "    images, labels = iter(test_dataloader).next()\n",
    "    images = images.to(device)\n",
    "    latent = autoencoder.encoder(images)\n",
    "    latent = latent.cpu()\n",
    "\n",
    "    # Finding the mean and standard deviation from our latent space\n",
    "    mean = latent.mean(dim=0)\n",
    "    std = (latent - mean).pow(2).mean(dim=0).sqrt()\n",
    "\n",
    "    # sample latent vectors from the normal distribution\n",
    "    latent = torch.randn(latent.shape[0], latent.shape[1])*std + mean\n",
    "\n",
    "    # reconstruct images from the latent vectors\n",
    "    latent = latent.to(device)\n",
    "    img_recon = autoencoder.decoder(latent)\n",
    "    img_recon = img_recon.cpu()\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(5, 5))\n",
    "    show_image(torchvision.utils.make_grid(img_recon[:100],10,5))\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "source": [
    " latent = torch.randn(128, num_classes)*std + mean\n",
    " latent"
   ],
   "metadata": {
    "id": "Roanl84aSJDu",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "outputId": "7483bded-11a7-45db-987c-71772fb8d473"
   },
   "execution_count": 13,
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "tensor([[ 9.0840e-02, -4.5237e-01,  2.2183e+00,  ..., -1.3740e+00,\n",
       "         -6.4963e-02, -2.8003e-03],\n",
       "        [ 3.2632e+00,  1.1726e+00,  2.4515e-01,  ..., -1.8426e-01,\n",
       "          1.6845e+00,  1.5643e+00],\n",
       "        [ 8.4475e-01, -1.2661e+00, -1.6921e+00,  ...,  1.7783e+00,\n",
       "         -9.0094e-02, -8.6120e-01],\n",
       "        ...,\n",
       "        [ 1.6846e+00, -1.4430e+00, -6.4717e-01,  ...,  1.6274e+00,\n",
       "          1.8105e+00,  9.6155e-01],\n",
       "        [ 1.9199e+00,  7.4258e-01, -7.1180e-01,  ...,  5.1276e-01,\n",
       "         -1.8358e+00, -1.2301e+00],\n",
       "        [ 3.4816e-01, -4.6150e-01,  2.8393e-01,  ...,  2.8381e+00,\n",
       "          2.9283e+00, -2.4696e+00]])"
      ]
     },
     "metadata": {},
     "execution_count": 13
    }
   ]
  },
  {
   "cell_type": "code",
   "source": [
    ""
   ],
   "metadata": {
    "id": "p-KtxeuuSJ1o"
   },
   "execution_count": 13,
   "outputs": []
  }
 ],
 "metadata": {
  "accelerator": "GPU",
  "colab": {
   "name": "autoencoder.ipynb",
   "provenance": []
  },
  "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": "3.7.6"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "9b0df9ed02504bebb5e4542bce0873b8": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "HBoxModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "HBoxModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "HBoxView",
      "box_style": "",
      "children": [
       "IPY_MODEL_d21783794cbc43dc86a4f13bb915d1f5",
       "IPY_MODEL_4dac8eab4bfe4dd4b90c1bf717df9849",
       "IPY_MODEL_3224cfe2ad004c6c8eb6c1de18feb0ff"
      ],
      "layout": "IPY_MODEL_4af928d68ad74bc09b76fe05767e0883"
     }
    },
    "d21783794cbc43dc86a4f13bb915d1f5": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "HTMLModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "HTMLModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "HTMLView",
      "description": "",
      "description_tooltip": null,
      "layout": "IPY_MODEL_5043854612e7423ba9c871097262f657",
      "placeholder": "​",
      "style": "IPY_MODEL_a7092fb7359e4cbb8fbbcc7642ecac13",
      "value": ""
     }
    },
    "4dac8eab4bfe4dd4b90c1bf717df9849": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "FloatProgressModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "FloatProgressModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "ProgressView",
      "bar_style": "success",
      "description": "",
      "description_tooltip": null,
      "layout": "IPY_MODEL_873df739019b448790c228de438060ea",
      "max": 9912422,
      "min": 0,
      "orientation": "horizontal",
      "style": "IPY_MODEL_c74be2c9e4b84e75a339c8980f1080ac",
      "value": 9912422
     }
    },
    "3224cfe2ad004c6c8eb6c1de18feb0ff": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "HTMLModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "HTMLModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "HTMLView",
      "description": "",
      "description_tooltip": null,
      "layout": "IPY_MODEL_49bf8feacdeb46c8bda597c9674f5259",
      "placeholder": "​",
      "style": "IPY_MODEL_9c5df061677648cb8e063d7231eb2172",
      "value": " 9913344/? [00:00&lt;00:00, 24201104.47it/s]"
     }
    },
    "4af928d68ad74bc09b76fe05767e0883": {
     "model_module": "@jupyter-widgets/base",
     "model_name": "LayoutModel",
     "model_module_version": "1.2.0",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "5043854612e7423ba9c871097262f657": {
     "model_module": "@jupyter-widgets/base",
     "model_name": "LayoutModel",
     "model_module_version": "1.2.0",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "a7092fb7359e4cbb8fbbcc7642ecac13": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "DescriptionStyleModel",
     "model_module_version": "1.5.0",
     "state": {
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "DescriptionStyleModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "StyleView",
      "description_width": ""
     }
    },
    "873df739019b448790c228de438060ea": {
     "model_module": "@jupyter-widgets/base",
     "model_name": "LayoutModel",
     "model_module_version": "1.2.0",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "c74be2c9e4b84e75a339c8980f1080ac": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "ProgressStyleModel",
     "model_module_version": "1.5.0",
     "state": {
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "ProgressStyleModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "StyleView",
      "bar_color": null,
      "description_width": ""
     }
    },
    "49bf8feacdeb46c8bda597c9674f5259": {
     "model_module": "@jupyter-widgets/base",
     "model_name": "LayoutModel",
     "model_module_version": "1.2.0",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "9c5df061677648cb8e063d7231eb2172": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "DescriptionStyleModel",
     "model_module_version": "1.5.0",
     "state": {
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "DescriptionStyleModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "StyleView",
      "description_width": ""
     }
    },
    "841658fd789745ce87b10183b2aa4870": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "HBoxModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "HBoxModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "HBoxView",
      "box_style": "",
      "children": [
       "IPY_MODEL_9fdce451f0ec49688a5ccffac6e0e681",
       "IPY_MODEL_48f467c3725f47d482f2b0bedee4ca4c",
       "IPY_MODEL_0f2cbd91676544c199e45ef213eb5607"
      ],
      "layout": "IPY_MODEL_26abe3d18d2045e8afe6337cb7233b76"
     }
    },
    "9fdce451f0ec49688a5ccffac6e0e681": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "HTMLModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "HTMLModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "HTMLView",
      "description": "",
      "description_tooltip": null,
      "layout": "IPY_MODEL_5a5462dc0fd04d989fd22eb4ba161f3d",
      "placeholder": "​",
      "style": "IPY_MODEL_d1f2c8a5447d4e3c947a0c4b8940f75c",
      "value": ""
     }
    },
    "48f467c3725f47d482f2b0bedee4ca4c": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "FloatProgressModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "FloatProgressModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "ProgressView",
      "bar_style": "success",
      "description": "",
      "description_tooltip": null,
      "layout": "IPY_MODEL_310d3b0a1c39472fa31b230978bd1108",
      "max": 28881,
      "min": 0,
      "orientation": "horizontal",
      "style": "IPY_MODEL_3f79dd49b2e34e83befeb1e2a06ebe16",
      "value": 28881
     }
    },
    "0f2cbd91676544c199e45ef213eb5607": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "HTMLModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "HTMLModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "HTMLView",
      "description": "",
      "description_tooltip": null,
      "layout": "IPY_MODEL_24dea4c154894c2388689bf79a2a9ecc",
      "placeholder": "​",
      "style": "IPY_MODEL_56cf5aaff6474df38696a506dbfb7beb",
      "value": " 29696/? [00:00&lt;00:00, 300326.36it/s]"
     }
    },
    "26abe3d18d2045e8afe6337cb7233b76": {
     "model_module": "@jupyter-widgets/base",
     "model_name": "LayoutModel",
     "model_module_version": "1.2.0",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "5a5462dc0fd04d989fd22eb4ba161f3d": {
     "model_module": "@jupyter-widgets/base",
     "model_name": "LayoutModel",
     "model_module_version": "1.2.0",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "d1f2c8a5447d4e3c947a0c4b8940f75c": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "DescriptionStyleModel",
     "model_module_version": "1.5.0",
     "state": {
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "DescriptionStyleModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "StyleView",
      "description_width": ""
     }
    },
    "310d3b0a1c39472fa31b230978bd1108": {
     "model_module": "@jupyter-widgets/base",
     "model_name": "LayoutModel",
     "model_module_version": "1.2.0",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "3f79dd49b2e34e83befeb1e2a06ebe16": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "ProgressStyleModel",
     "model_module_version": "1.5.0",
     "state": {
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "ProgressStyleModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "StyleView",
      "bar_color": null,
      "description_width": ""
     }
    },
    "24dea4c154894c2388689bf79a2a9ecc": {
     "model_module": "@jupyter-widgets/base",
     "model_name": "LayoutModel",
     "model_module_version": "1.2.0",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "56cf5aaff6474df38696a506dbfb7beb": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "DescriptionStyleModel",
     "model_module_version": "1.5.0",
     "state": {
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "DescriptionStyleModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "StyleView",
      "description_width": ""
     }
    },
    "c491dfe6b06e4c3b9d21723e2ab0d15f": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "HBoxModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "HBoxModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "HBoxView",
      "box_style": "",
      "children": [
       "IPY_MODEL_c87dd2f625004723a59ab5dc179171ba",
       "IPY_MODEL_2a47c4a0349944dba4f20ef539b3268f",
       "IPY_MODEL_2f82e7722d33444fba3c683ad867465f"
      ],
      "layout": "IPY_MODEL_2bf9d03c892342498dc792eee1624f80"
     }
    },
    "c87dd2f625004723a59ab5dc179171ba": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "HTMLModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "HTMLModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "HTMLView",
      "description": "",
      "description_tooltip": null,
      "layout": "IPY_MODEL_fc60f6b4308a40f9ae9ba4024ff7b97f",
      "placeholder": "​",
      "style": "IPY_MODEL_fa7e3214ac5147f198a35024a3d205f2",
      "value": ""
     }
    },
    "2a47c4a0349944dba4f20ef539b3268f": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "FloatProgressModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "FloatProgressModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "ProgressView",
      "bar_style": "success",
      "description": "",
      "description_tooltip": null,
      "layout": "IPY_MODEL_b57754f146fa4f11a274ffee1bb84669",
      "max": 1648877,
      "min": 0,
      "orientation": "horizontal",
      "style": "IPY_MODEL_ddc79e413a5043bcabd13cfbe4ce742c",
      "value": 1648877
     }
    },
    "2f82e7722d33444fba3c683ad867465f": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "HTMLModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "HTMLModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "HTMLView",
      "description": "",
      "description_tooltip": null,
      "layout": "IPY_MODEL_420d08e2583a447382b6ad3b4e3e4115",
      "placeholder": "​",
      "style": "IPY_MODEL_d325c448bcee4d74bc708de3cdfbda62",
      "value": " 1649664/? [00:00&lt;00:00, 1903108.93it/s]"
     }
    },
    "2bf9d03c892342498dc792eee1624f80": {
     "model_module": "@jupyter-widgets/base",
     "model_name": "LayoutModel",
     "model_module_version": "1.2.0",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "fc60f6b4308a40f9ae9ba4024ff7b97f": {
     "model_module": "@jupyter-widgets/base",
     "model_name": "LayoutModel",
     "model_module_version": "1.2.0",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "fa7e3214ac5147f198a35024a3d205f2": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "DescriptionStyleModel",
     "model_module_version": "1.5.0",
     "state": {
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "DescriptionStyleModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "StyleView",
      "description_width": ""
     }
    },
    "b57754f146fa4f11a274ffee1bb84669": {
     "model_module": "@jupyter-widgets/base",
     "model_name": "LayoutModel",
     "model_module_version": "1.2.0",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "ddc79e413a5043bcabd13cfbe4ce742c": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "ProgressStyleModel",
     "model_module_version": "1.5.0",
     "state": {
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "ProgressStyleModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "StyleView",
      "bar_color": null,
      "description_width": ""
     }
    },
    "420d08e2583a447382b6ad3b4e3e4115": {
     "model_module": "@jupyter-widgets/base",
     "model_name": "LayoutModel",
     "model_module_version": "1.2.0",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "d325c448bcee4d74bc708de3cdfbda62": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "DescriptionStyleModel",
     "model_module_version": "1.5.0",
     "state": {
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "DescriptionStyleModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "StyleView",
      "description_width": ""
     }
    },
    "1c5c1ccf2c094dcd9e31fc46d0a9c276": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "HBoxModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "HBoxModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "HBoxView",
      "box_style": "",
      "children": [
       "IPY_MODEL_8451c1e4e64c4e3b9571f440ed007952",
       "IPY_MODEL_cc66190da1f443758a9f51b740f12efa",
       "IPY_MODEL_00f413a57e6b485fb2f14691a2eaba79"
      ],
      "layout": "IPY_MODEL_8558147d260d4bf2b211096051735a09"
     }
    },
    "8451c1e4e64c4e3b9571f440ed007952": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "HTMLModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "HTMLModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "HTMLView",
      "description": "",
      "description_tooltip": null,
      "layout": "IPY_MODEL_6c3ffb76ce33455aac5bb15093499c07",
      "placeholder": "​",
      "style": "IPY_MODEL_f36b38e905cf460ca914402592effd8a",
      "value": ""
     }
    },
    "cc66190da1f443758a9f51b740f12efa": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "FloatProgressModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "FloatProgressModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "ProgressView",
      "bar_style": "success",
      "description": "",
      "description_tooltip": null,
      "layout": "IPY_MODEL_e3761fbe404240d4bb9ca88ce178e8bc",
      "max": 4542,
      "min": 0,
      "orientation": "horizontal",
      "style": "IPY_MODEL_afab5e70ba514100a01bd8d37a07e8d2",
      "value": 4542
     }
    },
    "00f413a57e6b485fb2f14691a2eaba79": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "HTMLModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "HTMLModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "HTMLView",
      "description": "",
      "description_tooltip": null,
      "layout": "IPY_MODEL_2e06c60ff04e43e69f295655777d9b3b",
      "placeholder": "​",
      "style": "IPY_MODEL_a8a3d3062fb24ce1a407f0a03ded624e",
      "value": " 5120/? [00:00&lt;00:00, 9892.77it/s]"
     }
    },
    "8558147d260d4bf2b211096051735a09": {
     "model_module": "@jupyter-widgets/base",
     "model_name": "LayoutModel",
     "model_module_version": "1.2.0",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "6c3ffb76ce33455aac5bb15093499c07": {
     "model_module": "@jupyter-widgets/base",
     "model_name": "LayoutModel",
     "model_module_version": "1.2.0",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "f36b38e905cf460ca914402592effd8a": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "DescriptionStyleModel",
     "model_module_version": "1.5.0",
     "state": {
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "DescriptionStyleModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "StyleView",
      "description_width": ""
     }
    },
    "e3761fbe404240d4bb9ca88ce178e8bc": {
     "model_module": "@jupyter-widgets/base",
     "model_name": "LayoutModel",
     "model_module_version": "1.2.0",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "afab5e70ba514100a01bd8d37a07e8d2": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "ProgressStyleModel",
     "model_module_version": "1.5.0",
     "state": {
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "ProgressStyleModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "StyleView",
      "bar_color": null,
      "description_width": ""
     }
    },
    "2e06c60ff04e43e69f295655777d9b3b": {
     "model_module": "@jupyter-widgets/base",
     "model_name": "LayoutModel",
     "model_module_version": "1.2.0",
     "state": {
      "_model_module": "@jupyter-widgets/base",
      "_model_module_version": "1.2.0",
      "_model_name": "LayoutModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "LayoutView",
      "align_content": null,
      "align_items": null,
      "align_self": null,
      "border": null,
      "bottom": null,
      "display": null,
      "flex": null,
      "flex_flow": null,
      "grid_area": null,
      "grid_auto_columns": null,
      "grid_auto_flow": null,
      "grid_auto_rows": null,
      "grid_column": null,
      "grid_gap": null,
      "grid_row": null,
      "grid_template_areas": null,
      "grid_template_columns": null,
      "grid_template_rows": null,
      "height": null,
      "justify_content": null,
      "justify_items": null,
      "left": null,
      "margin": null,
      "max_height": null,
      "max_width": null,
      "min_height": null,
      "min_width": null,
      "object_fit": null,
      "object_position": null,
      "order": null,
      "overflow": null,
      "overflow_x": null,
      "overflow_y": null,
      "padding": null,
      "right": null,
      "top": null,
      "visibility": null,
      "width": null
     }
    },
    "a8a3d3062fb24ce1a407f0a03ded624e": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "DescriptionStyleModel",
     "model_module_version": "1.5.0",
     "state": {
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "DescriptionStyleModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "StyleView",
      "description_width": ""
     }
    }
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}