VAE_without_cross_entropy_loss.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Variational Auto-Encoder without the Cross Entropy Loss\n",
    "\n",
    "## Importing required packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch.autograd import Variable\n",
    "import numpy as np\n",
    "import torch.nn.functional as F\n",
    "import torchvision\n",
    "from torchvision import transforms\n",
    "import torch.optim as optim\n",
    "from torch import nn\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Defining the model\n",
    "\n",
    "Model is same as that in [this notebook](https://github.com/ac-alpha/VAEs-using-Pytorch/blob/master/VAE_two_latent_variables.ipynb)\n",
    "\n",
    "<img src=\"Architecture_2_latent.png\" width=\"800\" />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class VAE(nn.Module):\n",
    "  \n",
    "    def __init__(self):\n",
    "        super(VAE, self).__init__()\n",
    "        \n",
    "        self.fc1 = nn.Linear(28*28, 400)\n",
    "        self.fc2_mu = nn.Linear(400, 2)\n",
    "        self.fc2_sig = nn.Linear(400, 2)\n",
    "        self.fc3 = nn.Linear(2, 400)\n",
    "        self.fc4 = nn.Linear(400, 784)\n",
    "  \n",
    "    def encode(self,x):\n",
    "        a1 = F.relu(self.fc1(x))\n",
    "        a_mu = self.fc2_mu(a1)\n",
    "        a_logvar = self.fc2_sig(a1)\n",
    "        return a_mu, a_logvar\n",
    "  \n",
    "    def decode(self,z):\n",
    "        a3 = F.relu(self.fc3(z))\n",
    "        return torch.sigmoid(self.fc4(a3))\n",
    "  \n",
    "    def reparameterize(self, mu, logvar):\n",
    "        std = torch.exp(0.5*logvar)\n",
    "        eps = torch.randn_like(std)\n",
    "        return eps.mul(std).add_(mu)\n",
    "  \n",
    "    def forward(self,x):\n",
    "        mu, logvar = self.encode(x.view(-1, 784))\n",
    "        z = self.reparameterize(mu, logvar)\n",
    "        return self.decode(z), mu, logvar\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Getting the Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_dataset = torchvision.datasets.MNIST(root='./data',train=True, transform=transforms.ToTensor(), download=True)\n",
    "test_dataset = torchvision.datasets.MNIST(root='./data',train=False, transform=transforms.ToTensor(),download = True)\n",
    "\n",
    "train_loader = torch.utils.data.DataLoader(dataset=train_dataset, batch_size=100, shuffle=True)\n",
    "test_loader = torch.utils.data.DataLoader(dataset=test_dataset,  batch_size=100, shuffle=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Instantiating the model and optimizer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = VAE()\n",
    "optimizer = optim.Adam(model.parameters(), lr=1e-3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loss function\n",
    "\n",
    "Note that here we are not using the KL Divergence loss which tries to make the learned distribution similar to a known distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss_function(recon_x, x, mu, logvar):\n",
    "    BCE = F.binary_cross_entropy(recon_x, x.view(-1, 784), reduction='sum')\n",
    "\n",
    "    KLD = -0.5 * torch.sum(1 + logvar - mu.pow(2) - logvar.exp())\n",
    "\n",
    "    return KLD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch : 1 , Minibatch : 0 Loss = 1.1156\n",
      "Epoch : 1 , Minibatch : 100 Loss = 27.0651\n",
      "Epoch : 1 , Minibatch : 200 Loss = 0.9784\n",
      "Epoch : 1 , Minibatch : 300 Loss = 0.5960\n",
      "Epoch : 1 , Minibatch : 400 Loss = 0.4124\n",
      "Epoch : 1 , Minibatch : 500 Loss = 0.3025\n",
      "Epoch 1 : Loss = (30.6950) \n",
      "Epoch : 2 , Minibatch : 0 Loss = 0.0017\n",
      "Epoch : 2 , Minibatch : 100 Loss = 0.1640\n",
      "Epoch : 2 , Minibatch : 200 Loss = 0.1372\n",
      "Epoch : 2 , Minibatch : 300 Loss = 0.0974\n",
      "Epoch : 2 , Minibatch : 400 Loss = 0.0760\n",
      "Epoch : 2 , Minibatch : 500 Loss = 0.0606\n",
      "Epoch 2 : Loss = (0.5840) \n",
      "Epoch : 3 , Minibatch : 0 Loss = 0.0003\n",
      "Epoch : 3 , Minibatch : 100 Loss = 0.0336\n",
      "Epoch : 3 , Minibatch : 200 Loss = 0.0281\n",
      "Epoch : 3 , Minibatch : 300 Loss = 0.0235\n",
      "Epoch : 3 , Minibatch : 400 Loss = 0.0204\n",
      "Epoch : 3 , Minibatch : 500 Loss = 0.0158\n",
      "Epoch 3 : Loss = (0.1360) \n",
      "Epoch : 4 , Minibatch : 0 Loss = 0.0002\n",
      "Epoch : 4 , Minibatch : 100 Loss = 0.0119\n",
      "Epoch : 4 , Minibatch : 200 Loss = 0.0100\n",
      "Epoch : 4 , Minibatch : 300 Loss = 0.0090\n",
      "Epoch : 4 , Minibatch : 400 Loss = 0.0087\n",
      "Epoch : 4 , Minibatch : 500 Loss = 0.0074\n",
      "Epoch 4 : Loss = (0.0546) \n",
      "Epoch : 5 , Minibatch : 0 Loss = 0.0001\n",
      "Epoch : 5 , Minibatch : 100 Loss = 0.0070\n",
      "Epoch : 5 , Minibatch : 200 Loss = 0.0082\n",
      "Epoch : 5 , Minibatch : 300 Loss = 0.0051\n",
      "Epoch : 5 , Minibatch : 400 Loss = 0.0041\n",
      "Epoch : 5 , Minibatch : 500 Loss = 0.0043\n",
      "Epoch 5 : Loss = (0.0333) \n"
     ]
    }
   ],
   "source": [
    "num_epochs = 5\n",
    "print_per = 100\n",
    "model.train()\n",
    "for epoch in range(num_epochs):\n",
    "    train_loss = 0\n",
    "    print_loss = 0\n",
    "    loss_record = []\n",
    "    for i, (images, _) in enumerate(train_loader):\n",
    "        images = images.reshape(-1, 28*28)\n",
    "        optimizer.zero_grad()\n",
    "        recon_batch, mu, logvar = model(images)\n",
    "        loss = loss_function(recon_batch, images, mu, logvar)\n",
    "        loss.backward()\n",
    "        train_loss += loss.item()\n",
    "        print_loss += loss.item()\n",
    "        optimizer.step()\n",
    "        if (i%print_per == 0):\n",
    "            print(\"Epoch : {} , Minibatch : {} Loss = {:.4f}\".format(epoch+1, i, print_loss))\n",
    "            loss_record.append(print_loss)\n",
    "            print_loss = 0\n",
    "    print(\"Epoch {} : Loss = ({:.4f}) \".format(epoch+1, train_loss))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(784,)\n",
      "torch.Size([784])\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(model(images)[0].data[0].numpy().shape)\n",
    "image1 = images[8]\n",
    "print(image1.shape)\n",
    "plt.imshow(model(images)[0].data[8].numpy().reshape(28, 28), cmap='gray')\n",
    "plt.show(block=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_loss = 0\n",
    "print_per = 10\n",
    "with torch.no_grad():\n",
    "    for i, (images, _) in enumerate(test_loader):\n",
    "        images = images.reshape(-1, 28*28)\n",
    "        recon_batch, mu, logvar = model(images)\n",
    "        test_loss += loss_function(recon_batch, images, mu, logvar).item()\n",
    "        if (i%print_per == 0):\n",
    "            plt.imshow(model(images)[0].data[0].numpy().reshape(28, 28), cmap='gray')\n",
    "            plt.show(block=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([784])\n"
     ]
    }
   ],
   "source": [
    "image2 = images[1]\n",
    "print(image2.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(model(images)[0].data[1].numpy().reshape(28, 28), cmap='gray')\n",
    "plt.show(block=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RfiCo/wJoRYsGzyE3jwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(images[1].numpy().reshape(28, 28), cmap='gray')\n",
    "plt.show(block=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Experiments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "with torch.no_grad():\n",
    "    mu1, logvar1 = model.encode(image1)\n",
    "    std1 = torch.exp(0.5*logvar1)\n",
    "    mu2, logvar2 = model.encode(image2)\n",
    "    std2 = torch.exp(0.5*logvar2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "with torch.no_grad():\n",
    "    recon_images1 = []\n",
    "    for ctr in range(0, 100, 5):\n",
    "        eps_val = torch.full_like(mu1, fill_value = ctr * 0.01 )\n",
    "        z_val1 = eps_val.mul(std1).add_(mu1)\n",
    "        recon_image1 = model.decode(z_val1)\n",
    "        recon_images1.append(recon_image1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 2016x2016 with 20 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure(figsize=(28, 28))\n",
    "columns = 4\n",
    "rows = 5\n",
    "for i in range(1, columns*rows +1):\n",
    "    img = recon_images1[i-1].detach().numpy().reshape(28, 28)\n",
    "    fig.add_subplot(rows, columns, i)\n",
    "    plt.imshow(img, cmap=\"gray\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "eps_any = torch.randn_like(mu1)\n",
    "z1 = eps_any.mul(std1).add_(mu1)\n",
    "z2 = eps_any.mul(std2).add_(mu2)\n",
    "all_recons = []\n",
    "for i in range(20):\n",
    "    z_bet = z1 + torch.full_like(mu1, fill_value = 0.05*i).mul(z2 - z1)\n",
    "    recon_image = model.decode(z_bet)\n",
    "    all_recons.append(recon_image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AAAAANJhFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANFjKOXftsLFjx+YTTjihbWaXXXapmvWa17ymmLnnnnuqZi1ZsqSYOeOMM4qZESNGVJ132223FTNLly6tmvWlL32pmLnxxhuLmSuuuKLqvO23376YmTRpUjFz9NFHV5130EEHFTNf+MIXqmY98cQTxcyZZ55ZzNx7771V582bN6+YWbZsWdWsFStWFDPnnXdeMTN27Niq884555xi5pOf/GTVrCFDhrS9/eMf/3g88sgjqWoYbIJ+adEv+qWXftEv9J1uadEtuqWXbml5+9vfflfOeXLVQNgI/dKiX/RLL/1S/9jFM/IBAAAAAKDBiov8lNJ3UkqLU0r3veRtY1NKN6aUHun5dcf+vUwAtjT6BYD+oF8A6DTdAjRBzTPyvxsRb3nZ2y6IiJtyzvtExE09fwaAV+K7oV8A6Lzvhn4BoLO+G7oFGGDFRX7OeWZEvPxFqd4REZf1/P6yiHhnh68LgC2cfgGgP+gXADpNtwBNsLmvkT8+57yg5/cLI2L8poIppXNTSrNTSrNXr169mccBsJXQLwD0h6p+0S0AvAIeuwBd1ecfdptzzhGR29x+cc55cs55cu1PrgYA/QJAf2jXL7oFgM3hsQvQDZu7yF+UUpoQEdHz6+LOXRIAWzH9AkB/0C8AdJpuAbpqcxf510bEmT2/PzMiftaZywFgK6dfAOgP+gWATtMtQFcNLQVSSj+IiGMjYqeU0pMR8Z8R8bmI+HFK6eyIeCIiTqs5bOTIkTF58uS2mQMPPLBmVDz99NPFzCGHHFI1a9asWcXM4sXlf1itvfaFCxcWM+PGjaua9etf/7qY+dznPlfMTJ06teq8bbYp/9vPyJEji5nx4zf50nF/5Zxzzilmxo4dWzVrzZo1xczdd99dzNR8/CIiPv7xjxczV155ZdWsxx57rJh5/PHHi5lLLrmk6rxRo0YVM9dee23VrCVLlrS9vebvMlsm/dKiX1r0i37ppV/oq071i25p0S26pZduYWvmsUuLfmnRL/qlV7cfuxQX+Tnn0zdx0/FVJwDARugXAPqDfgGg03QL0AR9/mG3AAAAAABA/7HIBwAAAACABrPIBwAAAACABrPIBwAAAACABrPIBwAAAACABrPIBwAAAACABrPIBwAAAACABrPIBwAAAACABhvazcPGjBkTxx9/fNvMQw89VDXrscceK2bmzZtXNeuQQw4pZu67775iZuTIkVXnveENbyhmZs6cWTXr7//+74uZc889t5i59tprq84766yzipnp06cXM0uXLq06r+Y+Pf/886tm/dd//Vcxc9BBBxUzQ4YMqTrv0UcfLWYOPfTQqlk15s+fX8z867/+a9Wse+65p5i58MILq2adcsopbW8fNmxY1RxoR7+06Bf90ku/6Bf6Tre06Bbd0ku3QGfolxb9ol966Zf6xy6ekQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA02tJuHPf300/Gtb32rbWaPPfaomrV69epi5t/+7d+qZl166aXFzPz584uZBx98sOq80aNHFzPvfve7q2Z9//vfL2ZWrlxZzEycOLHqvG233baYueWWW4qZKVOmVJ03bNiwYuaUU06pmjV27Nhi5tprry1mJk+eXHVezrmY+e1vf1s1a+eddy5m5s2bV8w89dRTVeftv//+xcy4ceOqZu22225tb6/5GEOJfmnRL/qll37RL/SdbmnRLbqll26BztAvLfpFv/TSL/WPXTwjHwAAAAAAGswiHwAAAAAAGswiHwAAAAAAGswiHwAAAAAAGswiHwAAAAAAGswiHwAAAAAAGswiHwAAAAAAGswiHwAAAAAAGizlnLt22A477JCPPfbYtplttqn7t4UddtihmDnllFOqZi1YsKCYWb58eTFz8cUXV5131VVXFTM///nPq2btvPPOxczee+9dzNxzzz1V51133XXFzLbbblvMHHTQQVXnbdiwoZh55plnqmadd955xcyQIUOKmYsuuqjqvJprP+aYY6pmvfrVry5mfvaznxUzEydOrDqv5u9hzd+JiIjFixe3vX3GjBmxePHiVDUMNkG/tOgX/dJLv+gX+k63tOgW3dJLt7R885vfvCvnPLlqIGyEfmnRL/qll36pf+ziGfkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgQ7t52NixY+PUU09tm7nrrruqZv3oRz8qZk455ZSqWa961auKmXnz5hUz//RP/1R13jbblP/95Nlnn62a9b3vfa+Y+epXv1rMjBo1quq8yy+/vJj51a9+VcxMmDCh6rwZM2YUM4888kjVrO9+97vFTM3HZuedd646b9WqVcXMAQccUDXrjjvuKGbuvPPOYmafffapOu/mm2/u2KxHH3207e0vvvhi1RxoR7+06Bf90ku/6Bf6Tre06Bbd0ku3QGfolxb9ol966Zf6xy6ekQ8AAAAAAA1WXOSnlL6TUlqcUrrvJW/7TEppfkrpTz3/ndy/lwnAlka/ANBpugWA/qBfgCaoeUb+dyPiLRt5+//mnA/p+e+Xnb0sALYC3w39AkBnfTd0CwCd993QL8AAKy7yc84zI2JpF64FgK2IfgGg03QLAP1BvwBN0JfXyD8vpTSn59uLdtxUKKV0bkppdkpp9rJly/pwHABbCf0CQKfpFgD6g34BumZzF/nfjIi9IuKQiFgQEf+9qWDO+eKc8+Sc8+QxY8Zs5nEAbCX0CwCdplsA6A/6BeiqzVrk55wX5ZzX55w3RMS3I+Kwzl4WAFsj/QJAp+kWAPqDfgG6bbMW+SmlCS/547si4r5NZQGgln4BoNN0CwD9Qb8A3ZZyzu0DKf0gIo6NiJ0iYlFE/GfPnw+JiBwRj0fE1JzzgtJhEyZMyO9///vbZnbccZMvKfZXjjzyyGLmYx/7WNWsnXfeuZh561vfWszst99+Vefde++9xczvfve7qllvfvObi5mxY8cWMzfeeGPVeaNHjy5m5s+fX8zsscceVefV3Kc150VELFq0qJiZO3duMXPUUUdVnfe+972vmLn88surZtV8ztTYaaedqnKHH354MXPIIYdUzVqxYkXb29///vfHgw8+mKqGsUXRLy36pUW/6Jde+oW+0C0tuqVFt+iWXp3qloiII4888q6c8+SqgWwx9EuLfmnRL/qlV7cfuwwtBXLOp2/kzdNL7wcA7egXADpNtwDQH/QL0ASb+8NuAQAAAACALrDIBwAAAACABrPIBwAAAACABrPIBwAAAACABrPIBwAAAACABrPIBwAAAACABrPIBwAAAACABrPIBwAAAACABhvazcNGjBgRe+65Z9vMXnvtVTXrN7/5TTHznve8p2rWfffdV8x8+ctfLmYWLVpUdd60adOKmeOOO65q1jXXXFPM7LTTTsXMfvvtV3VejbPOOquYOeecc6pmHXroocVM7bXvtttuxcwb3vCGYmbu3LlV5y1fvryYOeCAA6pmlf7eRESsW7eumPnLX/5Sdd6TTz5ZzOyyyy5Vs0r318qVK6vmQDv6pUW/6Jde+kW/0He6pUW36JZeugU6Q7+06Bf90ku/1D928Yx8AAAAAABoMIt8AAAAAABoMIt8AAAAAABoMIt8AAAAAABoMIt8AAAAAABoMIt8AAAAAABoMIt8AAAAAABoMIt8AAAAAABosKHdPGzNmjXx5JNPts2cc845VbN++MMfFjMrV66smvXVr361mNl7772LmbPOOqvqvMcff7yYedvb3lY168UXXyxmaq5rxYoVVed9+9vfLmZOPvnkYub//u//qs775S9/Wcxsu+22VbOWLl1azEyZMqWYWbJkSdV5//u//1vMnHDCCVWzJkyYUMw89thjxcw229T9290BBxxQzEyfPr1qVulz6/nnn6+aA+3olxb9ol966Rf9Qt/plhbdolt66RboDP3Sol/0Sy/9Uv/YxTPyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwVLOuWuHjRo1Kv/d3/1d28ynPvWpqlm33357MTN27NiqWa9+9auLmYcffriYGT16dNV548ePL2Z+85vfVM3addddi5mDDz64mFm1alXVeWeccUYxc8899xQzjz/+eNV5EyZMKGYeeOCBqln7779/MfPNb36zmDnmmGOqzluyZEkx8+ijj1bNOvLII4uZuXPnFjOLFi2qOu+f//mfi5k///nPVbNOPPHEtrefdtppcd9996WqYbAJ+qVFv+iXXvpFv9B3uqVFt+iWXrqlZf/9978r5zy5aiBshH5p0S/6pZd+qX/s4hn5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYEO7ediIESPida97XdvMpEmTqmb98Ic/LGbGjh1bNWufffYpZiZPnlzM/OAHP6g676CDDipm9t9//6pZw4YNK2Z+85vfFDNf/vKXq8675JJLipkHHnigmPnLX/5Sdd5uu+1WzOy5555Vs6644opi5k9/+lMx8+53v7vqvMWLFxczhx9+eNWs2bNnFzMnnnhiMfOZz3ym6ry1a9cWM5/4xCeqZs2YMaPt7c8++2zVHGhHv7ToF/3SS7/oF/pOt7ToFt3SS7dAZ+iXFv2iX3rpl/rHLp6RDwAAAAAADVZc5KeUJqaUbkkpPZBSuj+l9JGet49NKd2YUnqk59cd+/9yAdhS6BcAOk23ANAf9AvQBDXPyF8XEZ/IOU+KiCMi4kMppUkRcUFE3JRz3icibur5MwD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w7YNjKF8726ah/Dnr2gfeUL3uCNcOA2kof8669sHh2gfHoF/7oL9HPgAAAAAAsHlNeEU+AAAAAACwGRb5AAAAAADQYIO2yE8pvSWl9KeU0iMppU8P1nVsiZTSgpTS/Sml36eU5g729XSSUvp2SmlpSmneS24bm1K6KaX0cO+Puw7mNW7OZq798ymlRb2P/e9TSicO5jVuTkppn5TSrSmlB1JKf0gpfaT39kY/9h2ue0g87hChXwaKfhl4Q7VbIvQLQ59uGRi6ZXAM1X7RLWwN9MvA0C8Db6h2S0Sz+2VQ3iM/pbR9RDwUEdMi4omIuDsiTss5PzDgF7MFUkoLImJyzvnpwb6WkpTS1IhYHRFX5pwP6b1tRkQszzl/obcods05f2owr3NTNnPtn4+I1TnnfxvMaytJKfVERE/O+XcppTERcU9EvDMizowGP/YdrvvUGAKPO+iXgaNfBt5Q7ZYI/cLQplsGjm4ZHEO1X3QLQ51+GTj6ZeAN1W6JaHa/DNYr8l8fEY/knOfnnDdExDUR8Y5BupatWs55dkQs/4ub3xERV/T+/IpofTI2zmaufUjIOS/OOf+u9+erIuLBiNg7Gv7Yd7huGCr0ywDRLwNvqHZLhH5hyNMtA0S3DI6h2i+6ha2Afhkg+mXgDdVuiWh2vwzWIn/viFj4kl8/EQ15QCrliPhlSumelNI5g30xW2CPnPPi3p8/FRF7DObFbIHzUkr39f7zosb9E5y/lFJ6VUQcERFzYgg99n9x3RFD7HFnm6VfBteQ+Rq3GUPm69xQ7ZYI/cKQpFsG15D6GrcJQ+pr3FDtF93CEKVfBteQ+Rq3GUPm69xQ7ZaI5vWLb3a7Zd6Qc/7riHhrRHyw95+5DEm59d5KA//+Slvu4ojYPyImRcTiiPjy4F5OZymlHSPi2oj4aM555Uvva/Jjv4nrHlKPOwxh+mXwDJmvc0O1WyL0CwwS3TJ4htTXuKHaL7oFBo1+GTxD5uvcUO2WiGb2y2At8hdFxD4v+fUre28bEnLOi3p/XBoR10Xrn0MNJUt63++p/b5PSwf5eqrlnJfknF/IOb8YEd+KBj/2KaXh0foDf3XO+Ye9Nzf+sd/UdQ+lx51tnn4ZXI3/Grc5Q+Xr3FDtlgj9wpCmWwbXkPgatylD6WvcUO0X3cIQp18GV+O/xm3OUPk6N1S7JaK5/TJYi/y7I+LAlNJfpZR2iIj3RMQNg3QtL0tKaXTvNzqIlNLoiHhTRMzr/FGNc0NEnNH78zMi4keDeC0vS/sPe693RUMf+5RSioiZEfFgzvnfX3JXox/7zV33UHncIfTLYGv017hOhsLXuaHaLRH6hSFPtwyuxn+N25yh8jVuqPaLbmEroF8GV6O/xnUyFL7ODdVuiWh2v6TWv2IYeCmlEyPiqxGxfUR8O+f8/w3KhbxMKaX9ovU3jRERwyLiv5p87Sml70bEcRGxW0QsiYh/jojrI+L7EfH/IuKxiDg159y4b5yxmWs/Llr/hCVHxIKIOPcl763VGCmlN0TEryPi/oh4sffmz0brPbUa+9h3uO7TYgg87hChXwaKfhl4Q7VbIvQLQ59uGRi6ZXAM1X7RLWwN9MvA0C8Db6h2S0Sz+2XQFvkAAAAAAECZb3YLAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANNmwgD9t5553zHnvs0THz/PPPV8165plnipkNGzZUzRo3blwx88ILLxQzGzdurDpv2LDywz5ixIiqWTWP15gxY7oyJyLixRdf7Nqsbp23bt26qlnbbVf+e6vtt9++mNlhhx2qzqt5HGquKSIi51zM1DwOteftsssuxcxOO+1UNeu5557reP9TTz0VzzzzTKoaBpuhX1r0Sz390qJfYPN0S4tuqadbWrbmbomI+NOf/vR0znl81UDYBP3Sol/q6ZeWrblfap+7DOgif4899oj//M//7Jh58sknq2Zdf/31xczChQurZp155pnFTM0Xx+XLl1edV/OJcOCBB1bNqnm8jj/++GJm0aJFVeetWbOmmFm6dGnVrBpr164tZv7whz9UzRo1alQxU/MHcN99960676mnnipmXvGKV1TNqvnC9+CDDxYzO+64Y9V573rXu4qZE044oWrWnXfe2fH+c845p2oOdKJfWvRLPf3Sol9g83RLi26pp1tatuZuiYg49thjH6saBpuhX1r0Sz390rI190vtc5c+vbVOSuktKaU/pZQeSSl9ui+zAKBNvwDQbboFgP6gX4CBssWL/JTS9hHxnxHx1oiYEBGnpZQmdOvCANg26RcAuk23ANAf9AswkPryivzXR8QjOef5OecNEXFNRLyjO5cFwDZMvwDQbboFgP6gX4AB05dF/t4R8dI32nqi97b/JaV0Tkppbkpp7rPPPtuH4wDYRugXALpNtwDQH/QLMGD69B75NXLOl+ScJ+ecJ++88879fRwA2wj9AkC36RYA+oN+AbqhL4v8RRGxz0t+/cre2wCgL/QLAN2mWwDoD/oFGDB9WeTfHREHppT+KqW0Q0S8JyJu6M5lAbAN0y8AdJtuAaA/6BdgwAzb0g/MOW9MKZ0XEb+IiO0j4ts55z90+pjnnnsu7rzzzo5zf/Ob31Sd/+pXv7qYee1rX1s1q8aee+5ZzJx++ulVs/77v/+7mPnc5z5XNevcc88tZq644opiZtddd606b9y4ccXM3XffXczU/t7cdNNNxcyyZcuqZv3Lv/xLMXPfffcVMzX/+yIijjnmmGJmv/32q5r12GOPFTPPP/98MbPDDjtUnTdjxoxi5uabb66atWrVqo731/7+se3QL/+XfmnRLy36pUW/8HLolv9Lt7Tolhbd0lLqFvhL+uX/0i8t+qVFv7R067nLFi/yIyJyzj+LiJ/1ZQYA/CX9AkC36RYA+oN+AQZKv3+zWwAAAAAAYMtZ5AMAAAAAQINZ5AMAAAAAQINZ5AMAAAAAQINZ5AMAAAAAQINZ5AMAAAAAQINZ5AMAAAAAQINZ5AMAAAAAQIMNG8jDtttuuxg1alTHzEknnVQ164477ihmVq1aVTVr6tSpxcx9991XzPzgBz+oOm/mzJnFzIknnlg165e//GUx88c//rGYqXkMIiJe+cpXFjNvfvObi5ma646IOPfcc4uZRYsWVc1atmxZMfO3f/u3xczChQurzqt5TP/jP/6jatb+++9fzPT09BQzjz32WNV5f/VXf1XMHH744VWzHn744Y73Dx8+vGoOdKJfWvSLfmnTL/qFvtMtLbpFt7TpFugO/dKiX/RLm36pf+7iFfkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgKec8YIfttdde+dxzzy1lqmZ97WtfK2YmTZpUNWvEiBHFzKhRo4qZCRMmVJ33u9/9rpg5/fTTq2bNnTu3mJk6dWox8+KLL1add8cddxQzNZ9T8+fPrzpvhx12KGY++MEPVs36h3/4h2LmzDPPLGYeeOCBqvM2bNhQzBx99NFVs+67775i5uyzzy5m/ud//qfqvMsuu6yYGTlyZNWsffbZp+P9V155ZTz11FOpahhshn5p0S/6pU2/6Bf6Tre06Bbd0qZbWr70pS/dk3OeXDUQNkG/tOgX/dKmX+qfu3hFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANNiwgTwspRTbb799x8zs2bOrZp199tnFzFFHHVU169/+7d+KmWOPPbaYSSlVnbd8+fJi5q677qqaVWP9+vXFzEMPPVQ1qyb3zDPPFDMHH3xw1XkLFiwoZpYtW1Y164ILLihmvvrVrxYzb3vb26rO22WXXYqZBx54oGrW/Pnzi5lvfvObXbmmiIgvfvGLxczHP/7xqlmlz4cXXnihag50ol9a9It+adMv+oW+0y0tukW3tOkW6A790qJf9Eubfql/7uIV+QAAAAAA0GAW+QAAAAAA0GAW+QAAAAAA0GAW+QAAAAAA0GAW+QAAAAAA0GAW+QAAAAAA0GAW+QAAAAAA0GAW+QAAAAAA0GDDBvKwVatWxS233NIxs3bt2qpZe+65ZzEzc+bMqlnHH398MXPdddd15ZoiItavX1/M7LjjjlWzli1bVszMmjWrmHnxxRerznvjG99YzFx99dXFzKtf/eqq8yZPnlzMXHrppVWznn766WJm9erVxUzOueq8OXPmFDNvfvObq2Y9//zzxczSpUuLmbvuuqvqvGnTphUztb+H++67b8f7f/7zn1fNgU70S4t+0S9t+kW/0He6pUW36JY23QLdoV9a9It+adMv9c9dvCIfAAAAAAAarE+vyE8pLYiIVRHxQkRszDmX/4oIAAr0CwD9Qb8A0G26BRgo3Xhrnb/NOZf/XQYAvDz6BYD+oF8A6DbdAvQ7b60DAAAAAAAN1tdFfo6IX6aU7kkpnbOpQErpnJTS3JTS3A0bNvTxOAC2EfoFgP7QsV90CwBbwHMXYED09a113pBzXpRS2j0ibkop/THnPPulgZzzJRFxSUTETjvtVPctjQHY1ukXAPpDx37RLQBsAc9dgAHRp1fk55wX9f64NCKui4jXd+OiANi26RcA+oN+AaDbdAswULZ4kZ9SGp1SGtP+eUS8KSLmdevCANg26RcA+oN+AaDbdAswkPry1jp7RMR1KaX2nP/KOf+80weMHj06Xv/6zn8x+YY3vKHq8DvuuKOYOeqoo6pmLV68uJg54ogjipnex6Jozpw5xcyyZcuqZk2YMKGYeeihh4qZmv99ERG33357MbNkyZJipua6IyLGjRtXzPz5z3+umjV79uxipua6Pv3pT1edd9VVVxUza9eurZp1yimnFDO77bZbMXP99ddXnVfz+3zooYdWzZo1a1bH+1euXFk1h22KfvkL+qVFv7Tolxb9whZ4Wf2iW1p0i25p0y2wSZ67/AX90qJfWvRLS7eeu2zxIj/nPD8iDt/SjweATdEvAPQH/QJAt+kWYCD16T3yAQAAAACA/mWRDwAAAAAADWaRDwAAAAAADWaRDwAAAAAADWaRDwAAAAAADWaRDwAAAAAADWaRDwAAAAAADWaRDwAAAAAADTZsIA8bMWJEHHDAAR0zf/jDH6pmvfKVryxm3vve91bNOvvss4uZQw45pJhJKVWdN2PGjGJmzpw5VbM2bNhQzPT09BQzr33ta6vOq7F69epi5r777quaVXPtN910U9WsXXbZpZhZuXJlMXPkkUdWnff0008XM88++2zVrB133LGY+e1vf1vMPPnkk1Xn1Xxe/fznP6+atf3221floC/0S4t+0S9t+gX6Tre06Bbd0qZboDv0S4t+0S9t+qWeV+QDAAAAAECDWeQDAAAAAECDWeQDAAAAAECDWeQDAAAAAECDWeQDAAAAAECDWeQDAAAAAECDWeQDAAAAAECDWeQDAAAAAECDDRvIw3LO8cILL3TM/OlPf6qatXr16mLmySefrJp10EEHFTM/+MEPipmzzz676rxPf/rTxcxRRx1VNWvu3LnFzP3331/M7LvvvlXnLV68uJg544wzipnrrruu6rwf/vCHxcx5551XNevnP/95MTN8+PBipvbzatq0acXMtddeWzXrl7/8ZTFzwgknFDO1n6Nf//rXi5k1a9ZUzTr44IM73n/fffdVzYFO9EuLfqnvl5qvvx/60IeqZukX/cLWSbe06Bbd0qZbWn7yk59UzYLN0S8t+kW/tOmX+ucuXpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANZpEPAAAAAAANNmwgD1u1alXcfPPNHTMPPfRQ1awPfOADxcz48eOrZm3YsKGYefTRR4uZ3/72t1Xnfe1rXytmbr311qpZ69atK2Y+9alPFTM33nhj1Xnnn39+MbNkyZJi5qCDDqo6b/To0cXMsGF1n8YnnHBCMTNy5MhiZvr06VXn/f3f/30x8973vrdq1n777VfMfOMb3yhmXvWqV1Wdt/vuuxcztX++xowZ0/H+HXbYoWoOdKJfWvSLfmnTL/qFvtMtLbpFt7TpFugO/dKiX/RLm36pf+7iFfkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgKec8YIeNHTs2v/GNb+yY2XPPPatmvepVrypm7r333qpZy5YtK2ZOP/30YmbEiBFV591xxx3FzPLly6tmffWrXy1mbrrppmLmqquuqjpv5513LmYmTJhQzLzhDW+oOu+www4rZr70pS9VzXrssceKmTPOOKOYuf/++6vOW7hwYTGzcuXKqlmrV68uZs4777xiZuzYsVXnTZ8+vZj5xCc+UTVr++2373j/xz72sXj44YdT1TDYDP3Sol/0S5t+0S/0nW5p0S26pU23tLz97W+/J+c8uWogbIJ+adEv+qVNv9Q/d/GKfAAAAAAAaLDiIj+l9O2U0tKU0ryX3DY2pXRTSunh3h937d/LBGBro18A6A/6BYBu0y1AE9S8Iv/yiHjLX9z26Yi4Oed8YETc3PtrAHg5Lg/9AkD3XR76BYDuujx0CzDIiov8nPPsiPjLN6V6R0Rc0fvzKyLinV2+LgC2cvoFgP6gXwDoNt0CNMGWvkf+Hjnnxb0/fyoi9thcMKV0Tkppbkpp7vr167fwOAC2EfoFgP5Q1S+6BYCXwXMXYED1+Zvd5pxzROQO91+Sc56cc55c+52rAUC/ANAfOvWLbgFgS3juAgyELV3kL0kp9URE9P64tHuXBMA2TL8A0B/0CwDdpluAAbWli/wbIuKM3p+fERE/6s7lALCN0y8A9Af9AkC36RZgQA0rBVJK342I4yJit5TSExHxzxHxhYj4fkrp7Ih4LCJOrTls1KhRMXny5I6ZQw89tGZU/PnPfy5mJk2aVDVrzpw5xczSpeW/WK299qeeeqqYGTduXNWsX/3qV8XMF77whWLm3HPPrTpvu+3Kf/czatSoYmaPPTb71nH/y/Tp04uZsWPHVs3asGFDMfO73/2umKn5/YuI+NjHPlbMXH311VWzHn300WJmwYIFxcyll15add7o0aOLmRtuuKFq1rJlyzreX/Nnma2TfmnRLy36Rb+06Rf6qlv9oltadItuadMtbMs8d2nRLy36Rb+0DfRzl+IiP+d82mbuOqHqBADYBP0CQH/QLwB0m24BmqDP3+wWAAAAAADoPxb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYMMG8rCddtopTjjhhI6ZP/3pT1WzHn300WJm4cKFVbMmTZpUzMybN6+YGTVqVNV5r3vd64qZ2bNnV83667/+62LmnHPOKWZuuOGGqvPOPPPMYmbmzJnFzPLly6vOq3lMP/7xj1fN+td//ddi5rDDDitmtt9++6rzHnnkkWLmiCOOqJpVY9GiRcXMhz70oapZ9957bzHzuc99rmrWSSed1PH+4cOHV82BTvRLi37RL236Rb/Qd7qlRbfoljbdAt2hX1r0i35p0y/1z128Ih8AAAAAABrMIh8AAAAAABrMIh8AAAAAABrMIh8AAAAAABrMIh8AAAAAABrMIh8AAAAAABrMIh8AAAAAABrMIh8AAAAAABps2EAe9uc//zm+8Y1vdMzsu+++VbPWr19fzHzyk5+smnXZZZcVM4sWLSpmHnzwwarzxowZU8ycfPLJVbOuueaaYmb16tXFzD777FN13siRI4uZW2+9tZiZOnVq1XnDhw8vZk466aSqWWPHji1mbrjhhmJm8uTJVeflnIuZX//611Wzxo8fX8wsXLiwmHnyySerzps4cWIxM27cuKpZe++9d8f7a36PoUS/tOgX/dKmX/QLfadbWnSLbmnTLdAd+qVFv+iXNv1S/9zFK/IBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBUs55wA7bZZdd8nHHHdcxs912dX+3sMsuuxQzJ510UtWsxYsXFzOrVq0qZi655JKq86699tpi5sc//nHVrPHjxxczBxxwQDFz7733Vp134403FjMjR44sZg477LCq81588cVi5umnn66add555xUz22+/fTHzzW9+s+q8mms/9thjq2btvvvuxcyPfvSjYmafffapOq/mz2HNn4mIiKVLl3a8f9asWbF06dJUNQw2Q7+06Bf90qZf9At9p1tadItuadMtLRdffPE9OefJVQNhE/RLi37RL236pf65i1fkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAgw0byMPGjh0bp5xySsfMPffcUzXre9/7XjFz0kknVc16xSteUcwsXLiwmHn3u99ddd5225X//mTFihVVs77zne8UMxdddFExM3r06KrzrrzyymLmF7/4RTHT09NTdd6sWbOKmYcffrhq1uWXX17M1PzejB8/vuq8tWvXFjOHHHJI1ay77rqrmLn77ruLmQMPPLDqvFtuuaVrsx555JGO969bt65qDnSiX1r0i35p0y/6hb7TLS26Rbe06RboDv3Sol/0S5t+qX/u4hX5AAAAAADQYMVFfkrp2ymlpSmleS+57fMppUUppd/3/ndi/14mAFsb/QJAt+kWAPqDfgGaoOYV+ZdHxFs2cftXcs6Tev/7WXcvC4BtwOWhXwDorstDtwDQfZeHfgEGWXGRn3OeHRHLB+BaANiG6BcAuk23ANAf9AvQBH15j/zzUkr39f7zol03F0opnZNSmptSmrty5co+HAfANkK/ANBtugWA/qBfgAGzpYv8iyNi/4iYFBGLI+LLmwvmnC/JOU/OOU/eaaedtvA4ALYR+gWAbtMtAPQH/QIMqC1a5Oecl+ScX8g5vxgR34qI13f3sgDYFukXALpNtwDQH/QLMNC2aJGfUup5yS/fFRHzNpcFgFr6BYBu0y0A9Af9Agy0lHPuHEjpuxFxXETsFhFLIuKfe389KSJyRCyIiHNzzotLh/X09OSzzjqrY2bXXTf7lmL/y5QpU4qZ888/v2rW+PHji5m3vvWtxczBBx9cdd79999fzPzmN7+pmvWmN72pmBk7dmwxc9NNN1WdN2bMmGJm0aJFxcy+++5bdV7NY1pzXkTEkiVLipn58+cXM0cffXTVee9///uLmSuvvLJqVs3nTI3ddtutKnfkkUcWM5MmTaqatXr16o73n3XWWfHggw+mqmFsVfRLi1L7uzYAACAASURBVH5p0S/6pU2/0Be6pUW3tOgW3dLWrW6JiJgyZco9OefJVQPZauiXFv3Sol/0S9tAP3cZVgrknE/bxM0zSx8HAJ3oFwC6TbcA0B/0C9AEW/rNbgEAAAAAgAFgkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA02bCAPGzFiROy3334dM/vvv3/VrNtuu62Yec973lM1a968ecXMhRdeWMwsWbKk6rwZM2YUM8cff3zVrOuvv76Y2W233YqZgw8+uOq8GmeeeWYxM3369KpZRxxxRDFTe+177713MfO6172umJk/f37VeatWrSpmDjnkkKpZpT83EREbN24sZh5//PGq85544oliZs8996yaVXq81qxZUzUHOtEvLfpFv7TpF/1C3+mWFt2iW9p0C3SHfmnRL/qlTb/UP3fxinwAAAAAAGgwi3wAAAAAAGgwi3wAAAAAAGgwi3wAAAAAAGgwi3wAAAAAAGgwi3wAAAAAAGgwi3wAAAAAAGgwi3wAAAAAAGiwYQN52IYNG+KJJ57omJk+fXrVrGuuuaaYWbNmTdWsiy66qJg54IADipkzzzyz6rwFCxYUM29729uqZq1bt66Yqbmu1atXV533rW99q5g58cQTi5mf/vSnVef97Gc/K2ZGjhxZNWv58uXFzNSpU4uZZcuWVZ33la98pZiZNm1a1ay99tqrmJk/f34xs912dX93d8ghhxQzM2fOrJpV+tx69tlnq+ZAJ/qlRb/olzb9ol/oO93Solt0S5tuge7QLy36Rb+06Zf65y5ekQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA2Wcs4Ddtjo0aPza17zmo6ZT33qU1Wz7rzzzmJm7NixVbN23333Yuahhx4qZsaMGVN13h577FHM3HbbbVWz9tprr2Lm8MMPL2bWrl1bdd7pp59ezNx7773FzIIFC6rO6+npKWYeeOCBqlkTJ04sZi6++OJi5thjj606b9myZcXMI488UjVrypQpxcz8+fOLmSVLllSd9773va+Y+eMf/1g1a9q0aR3vP/XUU2PevHmpahhshn5p0S/6pU2/6Bf6Tre06Bbd0qZbWiZOnHhPznly1UDYBP3Sol/0S5t+qX/u4hX5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYMMG8rARI0bEQQcd1DEzYcKEqlnXXHNNMTN27NiqWQceeGAxM3ny5GLmu9/9btV5hx12WDEzceLEqlnDhw8vZm677bZi5sILL6w679JLLy1mHnjggWLm8ccfrzpv7733Lmb222+/qllXXXVVMfP73/++mDn55JOrzlu6dGkxc+SRR1bNmjt3bjEzbdq0Yubzn/981XnPP/98MXPBBRdUzZo1a1bH+1esWFE1BzrRLy36Rb+06Rf9Qt/plhbdolvadAt0h35p0S/6pU2/1D938Yp8AAAAAABosOIiP6W0T0rp1pTSAymlP6SUPtJ7+9iU0k0ppYd7f9y1/y8XgK2FfgGg23QLAP1BvwBNUPOK/I0RcUHOeUJEHBURH0wpTYiIT0fEzTnnAyPi5t5fA0At/QJAt+kWAPqDfgEGXXGRn3NenHP+Xe/PV0XEgxGxd0S8IyKu6I1dERHv7K+LBGDro18A6DbdAkB/0C9AE7ys98hPKb0qIo6IiDkRsUfOeXHvXU9FxB6b+ZhzUkpzU0pz169f34dLBWBrpV8A6DbdAkB/0C/AYKle5KeUdoyIayPioznnlS+9L+ecIyJv6uNyzpfknCfnnCePGDGiTxcLwNZHvwDQbboFgP6gX4DBVLXITykNj9YXqqtzzj/svXlJSqmn9/6eiFjaP5cIwNZKvwDQbboFgP6gX4DBVlzkp5RSRMyMiAdzzv/+krtuiIgzen9+RkT8qPuXB8DWSr8A0G26BYD+oF+AJkitf/nTIZDSGyLi1xFxf0S82HvzZ6P1XmDfj4j/FxGPRcSpOeflnWbtvPPO+Zhjjul43qGHHlp14RMmTChmfvWrX1XNGjVqVDFz5JFHFjN77bVX1Xnjxo0rZq677rqqWaecckoxs3HjxmJmzpw5VeetWLGimHnqqaeKmbvuuqvqvI9+9KPFzE477VQ1q6enp5i57LLLipmjjjqq6rwddtihmJk9e3bVrB/9qPz/BT7zmc8UM88991zVeTXXfuutt1bNmjp1asf7L7zwwli4cGGqGsZWRb+06JcW/aJf2v5/9u492O6qvB//syCBmBCEhAgB8sMS0HIRgkYQVKBEiiVekDpMARmwTKC1ikVFHWWsbec3g1HrrUWIBATEa/ACVkQUJEVKJFgIAeQyEQghJJIASciVsL5/7HNmqE32WuTss/fnJK/XDEM4+51nLXZOznv2k5Nz9AsDoVtadEuLbtEt/TrVLRERF1xwwV0558lVA9lq6JcW/dKiX/RLv26/dhlWCuScb4uIzQ2aUvr5ALAp+gWATtMtAAwG/QI0QfU3uwUAAAAAALrPIh8AAAAAABrMIh8AAAAAABrMIh8AAAAAABrMIh8AAAAAABrMIh8AAAAAABrMIh8AAAAAABrMIh8AAAAAABpsWDcPGz16dLz1rW9tm3nmmWeqZt1www3FzBFHHFE1a9dddy1mHn/88WLmlFNOqTpv1qxZxczRRx9dNWvGjBnFzLBh5V/mk08+ueq8yy67rJj5wAc+UMzU/jrfc889xczOO+9cNWvfffctZhYuXFjMTJw4seq86dOnFzPTpk2rmvXxj3+8mPnWt75VNatGza9zzftVRMTYsWPbPj58+PCqOdCOfmnRL/qln37RLwycbmnRLbqln26BztAvLfpFv/TTL/WvXXxGPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANNiwbh62cuXKuPXWW9tm5syZUzXrjDPOKGbWrl1bNeuqq64qZk444YRi5qc//WnVecOGlZ/2G2+8sWrWpEmTipnZs2cXMyNGjKg67/nnny9man4NTz311KrzFixYUMyMHz++Y7OOPfbYYuaoo46qOu+ggw4qZmqf91GjRhUzF154YTFzxx13VJ33mc98ppiZMGFC1azVq1e3fXz9+vVVc6Ad/dKiX/RLP/2iXxg43dKiW3RLP90CnaFfWvSLfumnX+pfu/iMfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaLBh3Txst912i2nTprXNvOMd76iatWDBgmJm3bp1VbN22WWXYmbDhg3FzAsvvFB13g9/+MNiZvjw4VWzpkyZUswcdthhxcwpp5xSdd5FF11UlSuZPn16VW7EiBHFzEknnVQ164knnihmJk6cWMzMnz+/6rzDDz+8Y7Nq/h8vv/zyYubWW2+tOu/Tn/50MbPDDjtUzbrmmmvaPr569eqqOdCOfmnRL/rl5c7SL7B5uqVFt+iWlztra+4W6AT90qJf9MvLnbU190vtaxefkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA1mkQ8AAAAAAA02rJuHbdy4MVasWNE2c+WVV1bNOvvss4uZefPmVc362Mc+Vsxcdtllxcwee+xRdd55551XzCxbtqxq1tKlS4uZF154oZgZP3581XmXXnppMfO5z32umKn9tbn44ouLmW9/+9tVs84888xi5nvf+14xc+qpp1add+SRRxYzw4bV/Ra89tpri5kJEyYUM1/84herznviiSeKmUsuuaRq1lFHHdX28VtvvbVqDrTT1H654IILiplvfOMbxYx+adEvLfqlRb8w2HRLi27RLf10C3TGUO6XGTNmFDP6pUW/tOiXlk69dil+Rn5KaUJK6ZaU0v0ppftSSh/ue/tnU0qLUkp39/1zYtWJABD6BYDO0y0ADAb9AjRBzR95vBARH805/y6lNDoi7kop3dT32Jdyzl8YvOsBsBXTLwB0mm4BYDDoF6Dniov8nPPiiFjc9+OVKaUHImKvwb4YAFs3/QJAp+kWAAaDfgGa4GV9s9uU0qsj4rCImNP3pg+mlOallC5PKe26mZ9zTkppbkpp7qpVqwZ0WQC2TvoFgE7TLQAMBv0C9Er1Ij+ltFNEXBsR/5hzXhERX4+IiRExKVp/KrnJ7xSQc56Rc56cc5680047deDKAGxN9AsAnaZbABgM+gXopapFfkppeLQ+UF2Tc/5hRETOeUnOeWPO+cWI+EZEHD541wRga6RfAOg03QLAYNAvQK8VF/kppRQRMyPigZzzv73k7eNfEntPRMzv/PUA2FrpFwA6TbcAMBj0C9AExW92GxFvjogzIuLelNLdfW/7VEScmlKaFBE5Ih6NiHMH5YYAbK30CwCdplsAGAz6Bei5lHPu2mHjxo3LJ510UtvMu971rqpZb37zm4uZpUuXVs26/fbbi5l169YVMxs3bqw678gjjyxmrrjiiqpZI0eOLGb222+/Yqb2/eDcc8udNH369GJm//33rzqv5pvATJw4sWrW4sWLi5lbbrmlmFm7dm3VeRMmTChmZs2aVTVr6tSpxcyKFSuKmQ0bNlSdVzNr5syZVbNOO+20to/Pnj07nn322VQ1DDZDv7ToF/3ST7/oFwZOt7ToFt3ST7e0XH/99XflnCdXDYRN0C8t+kW/9NMv9a9dqr/ZLQAAAAAA0H0W+QAAAAAA0GAW+QAAAAAA0GAW+QAAAAAA0GAW+QAAAAAA0GAW+QAAAAAA0GAW+QAAAAAA0GAW+QAAAAAA0GAW+QAAAAAA0GDDunnYmjVr4oEHHmib+dSnPlU16/vf/34xM3PmzKpZ559/fjFz8803FzNTpkypOq/mXqtWraqatXr16mJm7733LmZuuOGGqvOOPfbYYmbNmjXFzMaNG6vOe+aZZ4qZD3/4w1Wz3v72txczNc/VnnvuWXXe8uXLi5np06dXzbr44ouLmfPOO6+Yef7556vOe+ihh4qZmt+DERGHHnpo28fnzp1bNQfa0S8t+kW/9NMv+oWB0y0tukW39NMtLddff33VLNgc/dKiX/RLP/1S/9rFZ+QDAAAAAECDWeQDAAAAAECDWeQDAAAAAECDWeQDAAAAAECDWeQDAAAAAECDWeQDAAAAAECDWeQDAAAAAECDWeQDAAAAAECDpZxz9w5L6Y8R8difvHm3iHi6a5fonKF67wh37xV337R9cs7jBmk224hN9Ivfb73h7r3h7pumXxiQrey1S4S798JQvXeEu7ejXxgQr10aw917w903rapburrI3+QFUpqbc57c00tsgaF67wh37xV3h+4Zyu+z7t4b7t4bQ/nubJuG8vusu3ffUL13hLtDNw3l91l37w13740m3N2X1gEAAAAAgAazyAcAAAAAgAZrwiJ/Rq8vsIWG6r0j3L1X3B26Zyi/z7p7b7h7bwzlu7NtGsrvs+7efUP13hHuDt00lN9n3b033L03en73nn+NfAAAAAAAYPOa8Bn5AAAAAADAZljkAwAAAABAg/VskZ9SentK6cGU0iMppU/26h5bIqX0aErp3pTS3Smlub2+TzsppctTSktTSvNf8rYxKaWbUkoP9/17117ecXM2c/fPppQW9T33d6eUTuzlHTcnpTQhpXRLSun+lNJ9KaUP97290c99m3sPiecdIvRLt+iX7huq3RKhXxj6dEt36JbeGKr9olvYGuiX7tAv3TdUuyWi2f3Sk6+Rn1LaPiIeiojjI+KJiLgzIk7NOd/f9ctsgZTSoxExOef8dK/vUpJSOjoiVkXEVTnng/veNj0iluecL+oril1zzp/o5T03ZTN3/2xErMo5f6GXdytJKY2PiPE559+llEZHxF0RcVJEnBUNfu7b3PuUGALPO+iX7tEv3TdUuyVCvzC06Zbu0S29MVT7Rbcw1OmX7tEv3TdUuyWi2f3Sq8/IPzwiHsk5L8g5r4+I70bEu3t0l61aznl2RCz/kze/OyKu7PvxldF6Z2yczdx9SMg5L845/67vxysj4oGI2Csa/ty3uTcMFfqlS/RL9w3VbonQLwx5uqVLdEtvDNV+0S1sBfRLl+iX7huq3RLR7H7p1SJ/r4hY+JL/fiIa8oRUyhHxi5TSXSmlc3p9mS2we855cd+Pn4qI3Xt5mS3wwZTSvL6/XtS4v4Lzp1JKr46IwyJiTgyh5/5P7h0xxJ53tln6pbeGzMe4zRgyH+eGardE6BeGJN3SW0PqY9wmDKmPcUO1X3QLQ5R+6a0h8zFuM4bMx7mh2i0RzesX3+x2y7wl5/z6iPiriPiHvr/mMiTl1tdW6v7XV9pyX4+IiRExKSIWR8QXe3ud9lJKO0XEtRHxjznnFS99rMnP/SbuPaSedxjC9EvvDJmPc0O1WyL0C/SIbumdIfUxbqj2i26BntEvvTNkPs4N1W6JaGa/9GqRvygiJrzkv/fue9uQkHNe1PfvpRHxo2j9daihZEnf13vq/7pPS3t8n2o55yU554055xcj4hvR4Oc+pTQ8Wr/hr8k5/7DvzY1/7jd176H0vLPN0y+91fiPcZszVD7ODdVuidAvDGm6pbeGxMe4TRlKH+OGar/oFoY4/dJbjf8YtzlD5ePcUO2WiOb2S68W+XdGxP4ppT9LKe0QEX8TEdf16C4vS0ppVN83OoiU0qiI+MuImN/+ZzXOdRFxZt+Pz4yIn/TwLi9L/2/2Pu+Jhj73KaUUETMj4oGc87+95KFGP/ebu/dQed4h9EuvNfpjXDtD4ePcUO2WCP3CkKdbeqvxH+M2Z6h8jBuq/aJb2Arol95q9Me4dobCx7mh2i0Rze6X1PpbDN2XUjoxIr4cEdtHxOU55/+/Jxd5mVJK+0brTxojIoZFxLebfPeU0nci4tiI2C0ilkTEP0XEjyPi+xHx/0XEYxFxSs65cd84YzN3PzZaf4UlR8SjEXHuS762VmOklN4SEf8VEfdGxIt9b/5UtL6mVmOf+zb3PjWGwPMOEfqlW/RL9w3VbonQLwx9uqU7dEtvDNV+0S1sDfRLd+iX7huq3RLR7H7p2SIfAAAAAAAo881uAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwSzyAQAAAACgwYZ187BXvvKVeffdd2+b2bBhQ9WsZ599tphZv3591ayxY8cWMxs3bixmXnjhharzhg0rP+077rhj1aya52v06NEdmRMR8eKLL3ZsVqfOW7t2bdWs7bYr/7nV9ttvX8zssMMOVefVPA81d4qIyDkXMzXPQ+15u+yySzGz8847V816/vnn2z7+1FNPxbPPPpuqhsFm6JcW/VJPv7ToF9g83dKiW+rplpatuVsiIh588MGnc87jqgbCJuiXFv1ST7+0bM39UvvapauL/N133z3+4z/+o23mySefrJr14x//uJhZuHBh1ayzzjqrmKn54Lh8+fKq82reEfbff/+qWTXP13HHHVfMLFq0qOq81atXFzNLly6tmlVjzZo1xcx9991XNWvkyJHFTM1vwH322afqvKeeeqqYecUrXlE1q+YD3wMPPFDM7LTTTlXnvec97ylmpkyZUjXrjjvuaPv4OeecUzUH2tEvLfqlnn5p0S+webqlRbfU0y0tW3O3REQcc8wxj1UNg83QLy36pZ5+adma+6X2tcuAvrROSuntKaUHU0qPpJQ+OZBZANBPvwDQaboFgMGgX4Bu2eJFfkpp+4j4j4j4q4g4MCJOTSkd2KmLAbBt0i8AdJpuAWAw6BegmwbyGfmHR8QjOecFOef1EfHdiHh3Z64FwDZMvwDQaboFgMGgX4CuGcgif6+IeOkX2nqi723/S0rpnJTS3JTS3Oeee24AxwGwjdAvAHSabgFgMOgXoGsG9DXya+ScZ+ScJ+ecJ7/yla8c7OMA2EboFwA6TbcAMBj0C9AJA1nkL4qICS/577373gYAA6FfAOg03QLAYNAvQNcMZJF/Z0Tsn1L6s5TSDhHxNxFxXWeuBcA2TL8A0Gm6BYDBoF+Arhm2pT8x5/xCSumDEXFjRGwfEZfnnO9r93Oef/75uOOOO9rO/c1vflN1/mtf+9pi5g1veEPVrBp77LFHMXP66adXzfrv//7vYubCCy+smnXuuecWM1deeWUxs+uuu1adN3bs2GLmzjvvLGZqf21uuummYmbZsmVVs/75n/+5mJk3b14xU/P/FxHx5je/uZjZd999q2Y99thjxcyGDRuKmR122KHqvOnTpxczv/rVr6pmrVy5su3jtb9+bDv0y/+lX1r0S4t+adEvvBy65f/SLS26pUW3tJS6Bf6Ufvm/9EuLfmnRLy2deu2yxYv8iIic888i4mcDmQEAf0q/ANBpugWAwaBfgG4Z9G92CwAAAAAAbDmLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaLBh3Txsu+22i5EjR7bNTJ06tWrWbbfdVsysXLmyatbRRx9dzMybN6+Y+cEPflB13syZM4uZE088sWrWL37xi2Lm97//fTFT8xxEROy9997FzAknnFDM1Nw7IuLcc88tZhYtWlQ1a9myZcXMX/zFXxQzCxcurDqv5jn993//96pZEydOLGbGjx9fzDz22GNV5/3Zn/1ZMXPooYdWzXr44YfbPj58+PCqOdCOfmnRL/qln37RLwycbmnRLbqln26BztAvLfpFv/TTL/WvXXxGPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANJhFPgAAAAAANFjKOXftsD333DOfe+65pUzVrK9+9avFzKRJk6pm7bjjjsXMyJEji5kDDzyw6rzf/e53xczpp59eNWvu3LnFzNFHH13MvPjii1Xn3XbbbcVMzfvUggULqs7bYYcdipl/+Id/qJr193//98XMWWedVczcf//9VeetX7++mDnqqKOqZs2bN6+YOfvss4uZ//mf/6k674orrihmRowYUTVrwoQJbR+/6qqr4qmnnkpVw2Az9EuLftEv/fSLfmHgdEtLTbe8733vq5p15513FjO6pUW3NLNbIiI+//nP35Vznlw1EDZBv7ToF/3ST7/Uv3bxGfkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgFvkAAAAAANBgw7p5WEoptt9++7aZ2bNnV806++yzi5k3velNVbO+8IUvFDPHHHNMMZNSqjpv+fLlxcxvf/vbqlk11q1bV8w89NBDVbNqcs8++2wxc8ABB1Sd9+ijjxYzy5Ytq5r10Y9+tJj58pe/XMy8853vrDpvl112KWbuv//+qlkLFiwoZi699NKO3Cki4nOf+1wx87GPfaxqVun9YePGjVVzoB390qJf9Es//aJfGDjd0lLTLXPmzKmaVUO3tOiWZnYLdIJ+adEv+qWffql/7eIz8gEAAAAAoMEs8gEAAAAAoMEs8gEAAAAAoMEs8gEAAAAAoMEs8gEAAAAAoMEs8gEAAAAAoMEs8gEAAAAAoMEs8gEAAAAAoMGGdfOwlStXxs0339w2s2bNmqpZe+yxRzEzc+bMqlnHHXdcMfOjH/2oI3eKiFi3bl0xs9NOO1XNWrZsWTEza9asYubFF1+sOu9tb3tbMXPNNdcUM6997Wurzps8eXIxc9lll1XNevrpp4uZVatWFTM556rz5syZU8yccMIJVbM2bNhQzCxdurSY+e1vf1t13vHHH1/M1P4a7rPPPm0f//nPf141B9rRLy36Rb/00y/6hYHTLS26Rbf00y3QGfqlRb/ol376pf61i8/IBwAAAACABhvQZ+SnlB6NiJURsTEiXsg5l/+ICAAK9AsAg0G/ANBpugXolk58aZ2/yDmX/14GALw8+gWAwaBfAOg03QIMOl9aBwAAAAAAGmygi/wcEb9IKd2VUjpnU4GU0jkppbkppbnr168f4HEAbCP0CwCDoW2/6BYAtoDXLkBXDPRL67wl57wopfSqiLgppfT7nPPslwZyzjMiYkZExM4771z3LY0B2NbpFwAGQ9t+0S0AbAGvXYCuGNBn5OecF/X9e2lE/CgiDu/EpQDYtukXAAaDfgGg03QL0C1bvMhPKY1KKY3u/3FE/GVEzO/UxQDYNukXAAaDfgGg03QL0E0D+dI6u0fEj1JK/XO+nXP+ebufMGrUqDj88PZ/MPmWt7yl6vDbbrutmHnTm95UNWvx4sXFzGGHHVbM9D0XRXPmzClmB4uBzAAAIABJREFUli1bVjXrwAMPLGYeeuihYqbm/y8i4tZbby1mlixZUszU3DsiYuzYscXMH//4x6pZs2fPLmZq7vXJT36y6ryrr766mFmzZk3VrPe+973FzG677VbM/PjHP646r+bX+XWve13VrFmzZrV9fMWKFVVz2Kbolz+hX1r0S4t+adEvbIGX1S+6pUW36JZ+ugU2yWuXP6FfWvRLi35p6dRrly1e5OecF0TEoVv68wFgU/QLAINBvwDQaboF6KYBfY18AAAAAABgcFnkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAgw3r5mE77rhj7Lfffm0z9913X9Wsvffeu5g57bTTqmadffbZxczBBx9czKSUqs6bPn16MTNnzpyqWevXry9mxo8fX8y84Q1vqDqvxqpVq4qZefPmVc2quftNN91UNWuXXXYpZlasWFHMHHHEEVXnPf3008XMc889VzVrp512KmZuv/32YubJJ5+sOq/m/ernP/951aztt9++KgcDoV9a9It+6adfYOB0S4tu0S39dAt0hn5p0S/6pZ9+qecz8gEAAAAAoMEs8gEAAAAAoMEs8gEAAAAAoMEs8gEAAAAAoMEs8gEAAAAAoMEs8gEAAAAAoMEs8gEAAAAAoMEs8gEAAAAAoMGGdfOwnHNs3LixbebBBx+smrVq1api5sknn6ya9ZrXvKaY+cEPflDMnH322VXnffKTnyxm3vSmN1XNmjt3bjFz7733FjP77LNP1XmLFy8uZs4888xi5kc/+lHVeddee20x86EPfahq1s9//vNiZvjw4cVM7fvV8ccfX8zU/P9FRPziF78oZqZMmVLM1L6PXnzxxcXM6tWrq2YdcMABbR+fN29e1RxoR7+06Bf90k+/6BcGTre06Bbd0k+3tPz0pz+tmgWbo19a9It+6adf6l+7+Ix8AAAAAABoMIt8AAAAAABoMIt8AAAAAABoMIt8AAAAAABoMIt8AAAAAABoMIt8AAAAAABoMIt8AAAAAABoMIt8AAAAAABoMIt8AAAAAABosGHdPGzlypXxq1/9qm3moYceqpr1gQ98oJgZN25c1az169cXM3/4wx+Kmdtvv73qvK9+9avFzC233FI1a+3atcXMJz7xiWLmhhtuqDrv/PPPL2aWLFlSzLzmNa+pOm/UqFHFzLBhde/GU6ZMKWZGjBhRzEybNq3qvL/7u78rZk477bSqWfvuu28xc8kllxQzr371q6vOe9WrXlXM1P7+Gj16dNvHd9hhh6o50I5+adEv+qWfftEvDJxuadEtuqWfboHO0C8t+kW/9NMv9a9dfEY+AAAAAAA0mEU+AAAAAAA0mEU+AAAAAAA0mEU+AAAAAAA0mEU+AAAAAAA0mEU+AAAAAAA0mEU+AAAAAAA0mEU+AAAAAAA0WMo5d+2wMWPG5Le97W1tM3vssUfVrFe/+tXFzD333FM1a9myZcXM6aefXszsuOOOVefddtttxczy5curZn35y18uZm666aZi5uqrr64675WvfGUxc+CBBxYzb3nLW6rOO+SQQ4qZz3/+81WzHnvssWLmzDPPLGbuvffeqvMWLlxYzKxYsaJq1qpVq4qZD37wg8XMmDFjqs6bNm1aMXPBBRdUzdp+++3bPv6Rj3wkHn744VQ1DDZDv7ToF/3ST7/oFwZOt7ToFt3ST7e0vOtd77or5zy5aiBsgn5p0S/6pZ9+qX/t4jPyAQAAAACgwYqL/JTS5SmlpSml+S9525iU0k0ppYf7/r3r4F4TgK2NfgFgMOgXADpNtwBNUPMZ+d+MiLf/yds+GRG/yjnvHxG/6vtvAHg5vhn6BYDO+2boFwA665uhW4AeKy7yc86zI+JPvyjVuyPiyr4fXxkRJ3X4XgBs5fQLAINBvwDQaboFaIIt/Rr5u+ecF/f9+KmI2H1zwZTSOSmluSmluevWrdvC4wDYRugXAAZDVb/oFgBeBq9dgK4a8De7zTnniMhtHp+Rc56cc55c+52rAUC/ADAY2vWLbgFgS3jtAnTDli7yl6SUxkdE9P17aeeuBMA2TL8AMBj0CwCdpluArtrSRf51EXFm34/PjIifdOY6AGzj9AsAg0G/ANBpugXoqmGlQErpOxFxbETsllJ6IiL+KSIuiojvp5TOjojHIuKUmsNGjhwZkydPbpt53eteVzMq/vjHPxYzkyZNqpo1Z86cYmbp0vIfrNbe/amnnipmxo4dWzXrl7/8ZTFz0UUXFTPnnntu1XnbbVf+s5+RI0cWM7vvvtkvHfe/TJs2rZgZM2ZM1az169cXM7/73e+KmZpfv4iIj3zkI8XMNddcUzXrD3/4QzHz6KOPFjOXXXZZ1XmjRo0qZq677rqqWcuWLWv7eM3vZbZO+qVFv7ToF/3ST78wUJ3qF93Solt0Sz/dwrbMa5cW/dKiX/RLv26/diku8nPOp27moSlVJwDAJugXAAaDfgGg03QL0AQD/ma3AAAAAADA4LHIBwAAAACABrPIBwAAAACABrPIBwAAAACABrPIBwAAAACABrPIBwAAAACABrPIBwAAAACABrPIBwAAAACABhvWzcN23nnnmDJlStvMgw8+WDXrD3/4QzGzcOHCqlmTJk0qZubPn1/MjBw5suq8N77xjcXM7Nmzq2a9/vWvL2bOOeecYua6666rOu+ss84qZmbOnFnMLF++vOq8muf0Yx/7WNWsf/mXfylmDjnkkGJm++23rzrvkUceKWYOO+ywqlk1Fi1aVMx86EMfqpp1zz33FDMXXnhh1aypU6e2fXz48OFVc6Ad/dKiX/RLP/2iXxg43dKiW3RLP90CnaFfWvSLfumnX+pfu/iMfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaLBh3Tzsj3/8Y1xyySVtM/vss0/VrHXr1hUzH//4x6tmXXHFFcXMokWLipkHHnig6rzRo0cXMyeffHLVrO9+97vFzKpVq4qZCRMmVJ03YsSIYuaWW24pZo4++uiq84YPH17MTJ06tWrWmDFjipnrrruumJk8eXLVeTnnYua//uu/qmaNGzeumFm4cGEx8+STT1add9BBBxUzY8eOrZq11157tX285tcYSvRLi37RL/30i35h4HRLi27RLf10C3SGfmnRL/qln36pf+3iM/IBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBUs65a4ftsssu+dhjj22b2W67uj9b2GWXXYqZqVOnVs1avHhxMbNy5cpiZsaMGVXnXXvttcXM9ddfXzVr3Lhxxcx+++1XzNxzzz1V591www3FzIgRI4qZQw45pOq8F198sZh5+umnq2Z98IMfLGa23377YubSSy+tOq/m7sccc0zVrFe96lXFzE9+8pNiZsKECVXn1fw+rPk9ERGxdOnSto/PmjUrli5dmqqGwWbolxb9ol/66Rf9wsDplhbdolv66ZaWr3/963flnCdXDYRN0C8t+kW/9NMv9a9dfEY+AAAAAAA0mEU+AAAAAAA0mEU+AAAAAAA0mEU+AAAAAAA0mEU+AAAAAAA0mEU+AAAAAAA0mEU+AAAAAAA0mEU+AAAAAAA0mEU+AAAAAAA02LBuHjZmzJh473vf2zZz1113Vc363ve+V8xMnTq1atYrXvGKYmbhwoXFzF//9V9XnbfdduU/P3nmmWeqZn3rW98qZr72ta8VM6NGjao676qrripmbrzxxmJm/PjxVefNmjWrmHn44YerZn3zm98sZmp+bcaNG1d13po1a4qZgw8+uGrWb3/722LmzjvvLGb233//qvNuvvnmjs165JFH2j6+du3aqjnQjn5p0S/6pZ9+0S8MnG5p0S26pZ9ugc7QLy36Rb/00y/1r118Rj4AAAAAADRYcZGfUro8pbQ0pTT/JW/7bEppUUrp7r5/ThzcawKwtdEvAHSabgFgMOgXoAlqPiP/mxHx9k28/Us550l9//yss9cCYBvwzdAvAHTWN0O3ANB53wz9AvRYcZGfc54dEcu7cBcAtiH6BYBO0y0ADAb9AjTBQL5G/gdTSvP6/nrRrpsLpZTOSSnNTSnNXbFixQCOA2AboV8A6DTdAsBg0C9A12zpIv/rETExIiZFxOKI+OLmgjnnGTnnyTnnyTvvvPMWHgfANkK/ANBpugWAwaBfgK7aokV+znlJznljzvnFiPhGRBze2WsBsC3SLwB0mm4BYDDoF6DbtmiRn1Ia/5L/fE9EzN9cFgBq6RcAOk23ADAY9AvQbSnn3D6Q0nci4tiI2C0ilkTEP/X996SIyBHxaEScm3NeXDps/Pjx+f3vf3/bzK67bvZLiv0vRx55ZDFz/vnnV80aN25cMfNXf/VXxcwBBxxQdd69995bzPzmN7+pmvWXf/mXxcyYMWOKmZtuuqnqvNGjRxczixYtKmb22WefqvNqntOa8yIilixZUswsWLCgmDnqqKOqzjvjjDOKmauuuqpqVs37TI3ddtutKnfEEUcUM5MmTaqatWrVqraPv//9748HHnggVQ1jq6JfWvRLi37RL/30CwOhW1p0S4tu0S39OtUtERFHHnnkXTnnyVUD2Wrolxb90qJf9Eu/br92GVYK5JxP3cSbZ5Z+HgC0o18A6DTdAsBg0C9AE2zpN7sFAAAAAAC6wCIfAAAAAAAazCIfAAAAAAAazCIfAAAAAAAazCIfAAAAAAAazCIfAAAAAAAazCIfAAAAAAAazCIfAAAAAAAabFg3D9txxx1j3333bZuZOHFi1axf//rXxczf/M3fVM2aP39+MfOVr3ylmFmyZEnVedOnTy9mjjvuuKpZP/7xj4uZ3XbbrZg54IADqs6rcdZZZxUz06ZNq5p12GGHFTO1d99rr72KmTe+8Y3FzIIFC6rOW7lyZTFz8MEHV80q/b6JiHjhhReKmccff7zqvCeeeKKY2WOPPapmlZ6v1atXV82BdvRLi37RL/30i35h4HRLi27RLf10C3SGfmnRL/qln36pf+3iM/IBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBhnXzsPXr18cTTzzRNjNt2rSqWd/97neLmdWrV1fN+trXvlbM7LfffsXMWWedVXXeo48+Wsy8853vrJq1du3aYqbmXqtWrao67xvf+EYxc+KJJxYz//mf/1l13s9+9rNiZsSIEVWzli9fXswcffTRxcyyZcuqzvvSl75UzBx//PFVs/bcc89iZsGCBcXMdtvV/dndwQcfXMzMnDmzalbpfeu5556rmgPt6JcW/aJf+ukX/cLA6ZYW3aJb+ukW6Az90qJf9Es//VL/2sVn5AMAAAAAQINZ5AMAAAAAQINZ5AMAAAAAQINZ5AMAAAAAQINZ5AMAAAAAQINZ5AMAAAAAQINZ5AMAAAAAQINZ5AMAAAAAQIOlnHPXDhs1alT+8z//87aZT3ziE1Wz7rjjjmJmzJgxVbNe9apXFTMPPfRQMTN69Oiq83bfffdi5te//nXVrD333LOYOfTQQ4uZNWvWVJ13+umnFzP33HNPMfPoo49WnTd+/Phi5v7776+addBBBxUzX//614uZY445puq8ZcuWFTOPPPJI1awjjzyymFmwYEExs2TJkqrz3ve+9xUzv//976tmHX/88W0fP+WUU2L+/Pmpahhshn5p0S/6pZ9+0S8MnG5p0S26pZ9uaTnooIPuyjlPrhoIm6BfWvSLfumnX+pfu/iMfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaLBh3Txsxx13jNe85jVtMwceeGDVrO9+97vFzJgxY6pm7b///sXM5MmTi5nvfOc7VecdcsghxcxBBx1UNWv48OHFzK9//eti5itf+UrVeZdddlkxc//99xczjz/+eNV5e+21VzGz7777Vs26+uqri5m77767mDn55JOrzlu6dGkxc8QRR1TNmjt3bjFz/PHHFzOf/exnq87bsGFDMfPRj360atasWbPaPv7MM89UzYF29EuLftEv/fSLfmHgdEuLbtEt/XQLdIZ+adEv+qWffql/7VL8jPyU0oSU0i0ppftTSvellD7c9/YxKaWbUkoP9/1716oTASD0CwCdp1sAGAz6BWiCmi+t80JEfDTnfGBEvCki/iGldGBEfDIifpVz3j8iftX33wBQS78A0Gm6BYDBoF+Anisu8nPOi3POv+v78cqIeCAi9oqId0fElX2xKyPipMG6JABbH/0CQKfpFgAGg34BmuBlfbPblNKrI+KwiJgTEbvnnBf3PfRUROze0ZsBsM3QLwB0mm4BYDDoF6BXqhf5KaWdIuLaiPjHnPOKlz6Wc84RkTfz885JKc1NKc1dt27dgC4LwNZHvwDQaboFgMGgX4Beqlrkp5SGR+sD1TU55x/2vXlJSml83+PjI2KT34Y45zwj5zw55zx5xx137MSdAdhK6BcAOk23ADAY9AvQa8VFfkopRcTMiHgg5/xvL3nouog4s+/HZ0bETzp/PQC2VvoFgE7TLQAMBv0CNMGwisybI+KMiLg3pXR339s+FREXRcT3U0pnR8RjEXHK4FwRgK2UfgGg03QLAINBvwA9V1zk55xvi4i0mYenvJzDNm7cGM8991zbzNVXX101693vfncx88tf/rJq1sKFC4uZI444opiZMqXu6Rg7dmwxc+edd1bNmjp1ajFz3HHHFTNXXnllMRMRsXLlymJm+PDhxcyyZcuqzjvjjDOKmZ133rlq1gknnFDMvOIVryhmNmzYUHXegQceWMzMnj27ataNN95YzLz+9a8vZv72b/+26rwddtihmPnXf/3XqllHH31028e32+5lfc9ttiL6pUW/tOgX/dJPvzAQuqVFt7ToFt3Sr1PdwrZLv7Tolxb9ol/6dfu1i1c4AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYBb5AAAAAADQYMO6edjo0aPjrW99a9vMM888UzXrhhtuKGaOOOKIqlm77rprMfP4448XM6ecckrVeT/4wQ+KmaOPPrpq1owZM4qZYcPKv8wnn3xy1XmXXXZZMfOBD3ygmKn9db7nnnuKmZ133rlq1r777lvMLFy4sJiZOHFi1XnTp08vZqZNm1Y16+Mf/3gx861vfatqVo2aX+ea96uIiLFjx7Z9fPjw4VVzoB390qJf9Es//aJfGDjd0qJbdEs/3QKdoV9a9It+6adf6l+7+Ix8AAAAAABoMIt8AAAAAABoMIt8AAAAAABoMIt8AAAAAABoMIt8AAAAAABoMIt8AAAAAABoMIt8AAAAAABoMIt8AAAAAABosGHdPGzlypVx6623ts3MmTOnatYZZ5xRzKxdu7Zq1lVXXVXMnHDCCcXMT3/606rzhg8fXszceOONVbMmTZpUzMyePbuYGTFiRNV5zz//fDFT82t46qmnVp23YMGCYmb8+PEdm3XssccWM0cddVTVeQcddFAxU/u8jxo1qpi58MILi5k77rij6rzPfOYzxcyECROqZq1evbrt4+vXr6+aA+3olxb9ol/66Rf9wsDplhbdolv66RboDP3Sol/0Sz/9Uv/axWfkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAg1nkAwAAAABAgw3r5mG77bZbTJs2rW3mHe94R9WsBQsWFDPr1q2rmrXLLrsUMxs2bChmXnjhharzfvjDHxYzw4cPr5o1ZcqUYuawww4rZk455ZSq8y666KKqXMn06dOrciNGjChmTjrppKpZTzzxRDEzceLEYmb+/PlV5x1++OEdm1Xz/3j55ZcXM7feemvVeZ/+9KeLmR122KFq1jXXXNP28dWrV1fNgXb0S4t+0S8vd5Z+gc3TLS26Rbe83Flbc7dAJ+iXFv2iX17urK25X2pfu/iMfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaDCLfAAAAAAAaLBh3Txs48aNsWLFiraZK6+8smrW2WefXczMmzevatYFF1xQzMyYMaOY2WOPParOO++884qZZcuWVc1aunRpMfPCCy8UM+PHj68679JLLy1mPve5zxUztb82F198cTHz7W9/u2rWmWeeWcx873vfK2ZOPfXUqvOOPPLIYmbYsLrfgtdee20xM2HChGLmi1/8YtV5TzzxRDFzySWXVM066qij2j5+6623Vs2BdvRLi37RL/30i35h4HRLi27RLf10C3SGfmnRL/qln36pf+1S/Iz8lNKElNItKaX7U0r3pZQ+3Pf2z6aUFqWU7u7758SqEwEg9AsAnadbABgM+gVogpo/8nghIj6ac/5dSml0RNyVUrqp77Ev5Zy/MHjXA2Arpl8A6DTdAsBg0C9AzxUX+TnnxRGxuO/HK1NKD0TEXoN9MQC2bvoFgE7TLQAMBv0CNMHL+ma3KaVXR8RhETGn700fTCnNSyldnlLadTM/55yU0tyU0txVq1YN6LIAbJ30CwCdplsAGAz6BeiV6kV+SmmniLg2Iv4x57wiIr4eERMjYlK0/lRyk98pIOc8I+c8Oec8eaeddurAlQHYmugXADpNtwAwGPQL0EtVi/yU0vBofaC6Juf8w4iInPOSnPPGnPOLEfGNiDh88K4JwNZIvwDQaboFgMGgX4BeKy7yU0opImZGxAM55397ydvHvyT2noiY3/nrAbC10i8AdJpuAWAw6BegCYrf7DYi3hwRZ0TEvSmlu/ve9qmIODWlNCkickQ8GhHnDsoNAdha6RcAOk23ADAY9AvQcynn3LXDxo0bl0866aS2mXe9611Vs9785jcXM0uXLq2adfvttxcz69atK2Y2btxYdd6RRx5ZzFxxxRVVs0aOHFnM7LfffsVM7fvBueeWO2n69OnFzP777191Xs03gZk4cWLVrMWLFxczt9xySzGzdu3aqvMmTJhQzMyaNatq1tSpU4uZFStWFDMbNmyoOq9m1syZM6tmnXbaaW0fnz17djz77LOpahhshn5p0S/6pZ9+0S8MnG5p0S26pZ9uabn++uvvyjlPrhoIm6BfWvSLfumnX+pfu1R/s1sAAAAAAKD7LPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBLPIBAAAAAKDBhnXzsDVr1sQDDzzQNvOpT32qatb3v//9YmbmzJlVs84///xi5uabby5mpkyZUnVezb1WrVpVNWv16tXFzN57713M3HDDDVXnHXvsscXMmjVripmNGzdWnffMM88UMx/+8IerZr397W8vZmqeqz333LPqvOXLlxcz06dPr5p18cUXFzPnnXdeMfP8889XnffQQw8VMzW/ByMiDj300LaPz507t2oOtKNfWvSLfumnX/QLA6dbWnSLbumnW1quv/76qlmwOfqlRb/ol376pf61i8/IBwAAAACABrPIBwAAAACABrPIBwAAAACABrPIBwAAAACABrPIBwAAAACABrPIBwAAAACABrPIBwAAAACABrPIBwAAAACABks55+4dltIfI+KxP3nzbhHxdNcu0TlD9d4R7t4r7r5p++Scxw3SbLYRm+gXv996w917w903Tb8wIFvZa5cId++FoXrvCHdvR78wIF67NIa794a7b1pVt3R1kb/JC6Q0N+c8uaeX2AJD9d4R7t4r7g7dM5TfZ929N9y9N4by3dk2DeX3WXfvvqF67wh3h24ayu+z7t4b7t4bTbi7L60DAAAAAAANZpEPAAAAAAAN1oRF/oxeX2ALDdV7R7h7r7g7dM9Qfp91995w994Yyndn2zSU32fdvfuG6r0j3B26aSi/z7p7b7h7b/T87j3/GvkAAAAAAMDmNeEz8gEAAAAAgM2wyAcAAAAAgAbr2SI/pfT2lNKDKaVHUkqf7NU9tkRK6dGU0r0ppbtTSnN7fZ92UkqXp5SWppTmv+RtY1JKN6WUHu779669vOPmbObun00pLep77u9OKZ3YyztuTkppQkrplpTS/Sml+/5fe3cPImcVBWD4PURtooUghBAVf7CzUBGrIGkUtIk2wVSx0kJBO8FGG0FExc5CFCL4g+BfSkutJCSFigERiZiwbpAUmkowx2K+wLDMzGanuPeezfs0mZ0lcLhkzwtf9vsmIl6Y3h/67FfMXeLcJbAvrdiX9qq2BeyL6rMtbdiWPqr2xbZoN7AvbdiX9qq2BcbuS5dn5EfEHuAX4BHgHHASOJqZPzcfZg0RcRZ4MDP/6j3LdiLiYeAS8GFm3ju99wZwMTNfn0Jxc2a+1HPORZbM/ipwKTPf7DnbdiJiP7A/M09HxE3AKeAJ4GkGPvsVcx+hwLlL9qUd+9Je1baAfVFttqUd29JH1b7YFlVnX9qxL+1VbQuM3Zdev5H/EPBrZv6Wmf8CnwKHO82yq2Xmt8DFLW8fBo5Pr48z+8c4nCWzl5CZG5l5enr9D3AGOMDgZ79ibqkK+9KIfWmvalvAvqg829KIbemjal9si3YB+9KIfWmvaltg7L70upB/APhj7utzDHIgVymBbyLiVEQ803uYNezLzI3p9Z/Avp7DrOH5iPgc3wEBAAACiUlEQVRhur1ouFtwtoqIO4D7ge8pdPZb5oZi565rln3pq8yOW6LMnqvaFrAvKsm29FVqxy1QasdV7YttUVH2pa8yO26JMnuualtgvL74YbfrOZiZDwCPAc9Nt7mUlLNnK7V/vtL63gXuBu4DNoC3+o6zWkTcCHwOvJiZf89/b+SzXzB3qXOXCrMv/ZTZc1XbAvZF6sS29FNqx1Xti22RurEv/ZTZc1XbAmP2pdeF/PPAbXNf3zq9V0Jmnp/+vAB8yex2qEo2p+c9XXnu04XO81y1zNzMzP8y8zLwHgOffURcz+wH/qPM/GJ6e/izXzR3pXPXNc++9DX8jlumyp6r2hawLyrNtvRVYsctUmnHVe2LbVFx9qWv4XfcMlX2XNW2wLh96XUh/yRwT0TcGRE3AE8BJzrNsiMRsXf6oAMiYi/wKPDT6r81nBPAsen1MeDrjrPsyJUf9smTDHr2ERHA+8CZzHx77ltDn/2yuaucu4R96W3oHbdKhT1XtS1gX1Sebelr+B23TJUdV7UvtkW7gH3pa+gdt0qFPVe1LTB2X2J2F0N7EfE48A6wB/ggM1/rMsgORcRdzP6nEeA64OORZ4+IT4BDwC3AJvAK8BXwGXA78DtwJDOH++CMJbMfYnYLSwJngWfnnq01jIg4CHwH/Ahcnt5+mdkztYY9+xVzH6XAuUtgX1qxL+1VbQvYF9VnW9qwLX1U7Ytt0W5gX9qwL+1VbQuM3ZduF/IlSZIkSZIkSdL2/LBbSZIkSZIkSZIG5oV8SZIkSZIkSZIG5oV8SZIkSZIkSZIG5oV8SZIkSZIkSZIG5oV8SZIkSZIkSZIG5oV8SZIkSZIkSZIG5oV8SZIkSZIkSZIG9j/oBcTpWGp1/wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 2016x2016 with 20 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure(figsize=(28, 28))\n",
    "columns = 4\n",
    "rows = 5\n",
    "for i in range(1, columns*rows +1):\n",
    "    img = all_recons[i-1].detach().numpy().reshape(28, 28)\n",
    "    fig.add_subplot(rows, columns, i)\n",
    "    plt.imshow(img, cmap=\"gray\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8. Here in the scatter plot we see that the points belonging to all the digits are mixed up at random but they are very close to each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_dataset = torchvision.datasets.MNIST(root='./data',train=False, transform=transforms.ToTensor(),download = True)\n",
    "test_loader = torch.utils.data.DataLoader(dataset=test_dataset,  batch_size=2000, shuffle=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_set, y_set = next(iter(test_loader))\n",
    "x_set = x_set.reshape(-1, 28*28)\n",
    "z_set = model.encode(x_set)[0].detach().numpy()\n",
    "color = y_set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(z_set[:, 0], z_set[:, 1], c=color, cmap = \"viridis\")\n",
    "plt.colorbar()\n",
    "plt.grid()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}