VAE.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Variational Auto-Encoder - Vanilla Version\n",
    "\n",
    "## Importing the 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",
    "The model that I have used is a simple fully connected one with one hidden layer in each of the parts( i.e. Encoder and Decoder).\n",
    "\n",
    "<img src=\"Architecture.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, 20)\n",
    "        self.fc2_sig = nn.Linear(400, 20)\n",
    "        self.fc3 = nn.Linear(20, 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": [
    "## Defining the loss function\n",
    "\n",
    "The loss consists of two parts :-\n",
    "1. The cross entropy loss between the original and reconstructed image\n",
    "2. The KL Divergence between Q(z|x) and P(z|X). This loss makes the learned distribution on z to be similar to some assumed distribution(Gaussian in this case). For more on this, read this [tutorial](https://arxiv.org/pdf/1606.05908). Formula is derived on Appendix B of the [paper](https://arxiv.org/pdf/1312.6114)."
   ]
  },
  {
   "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 BCE + 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 = 54789.6172\n",
      "Epoch : 1 , Minibatch : 100 Loss = 2296336.5566\n",
      "Epoch : 1 , Minibatch : 200 Loss = 1641241.8613\n",
      "Epoch : 1 , Minibatch : 300 Loss = 1460765.7021\n",
      "Epoch : 1 , Minibatch : 400 Loss = 1366460.5518\n",
      "Epoch : 1 , Minibatch : 500 Loss = 1306802.2734\n",
      "Epoch 1 : Loss = (9380086.2510) \n",
      "Epoch : 2 , Minibatch : 0 Loss = 11909.7256\n",
      "Epoch : 2 , Minibatch : 100 Loss = 1230171.1699\n",
      "Epoch : 2 , Minibatch : 200 Loss = 1209696.3896\n",
      "Epoch : 2 , Minibatch : 300 Loss = 1185796.5020\n",
      "Epoch : 2 , Minibatch : 400 Loss = 1173013.1475\n",
      "Epoch : 2 , Minibatch : 500 Loss = 1170144.8301\n",
      "Epoch 2 : Loss = (7125041.2344) \n",
      "Epoch : 3 , Minibatch : 0 Loss = 10819.3555\n",
      "Epoch : 3 , Minibatch : 100 Loss = 1149355.5850\n",
      "Epoch : 3 , Minibatch : 200 Loss = 1136657.8994\n",
      "Epoch : 3 , Minibatch : 300 Loss = 1129757.7314\n",
      "Epoch : 3 , Minibatch : 400 Loss = 1127398.5312\n",
      "Epoch : 3 , Minibatch : 500 Loss = 1122224.3330\n",
      "Epoch 3 : Loss = (6785680.2803) \n",
      "Epoch : 4 , Minibatch : 0 Loss = 11511.7969\n",
      "Epoch : 4 , Minibatch : 100 Loss = 1111364.2227\n",
      "Epoch : 4 , Minibatch : 200 Loss = 1108964.0967\n",
      "Epoch : 4 , Minibatch : 300 Loss = 1111118.1553\n",
      "Epoch : 4 , Minibatch : 400 Loss = 1105649.5566\n",
      "Epoch : 4 , Minibatch : 500 Loss = 1101112.1182\n",
      "Epoch 4 : Loss = (6638242.2354) \n",
      "Epoch : 5 , Minibatch : 0 Loss = 10830.5879\n",
      "Epoch : 5 , Minibatch : 100 Loss = 1093098.5352\n",
      "Epoch : 5 , Minibatch : 200 Loss = 1089226.6641\n",
      "Epoch : 5 , Minibatch : 300 Loss = 1094668.0391\n",
      "Epoch : 5 , Minibatch : 400 Loss = 1090882.0518\n",
      "Epoch : 5 , Minibatch : 500 Loss = 1090109.9951\n",
      "Epoch 5 : Loss = (6545630.5469) \n"
     ]
    }
   ],
   "source": [
    "num_epochs = 5\n",
    "print_per = 100\n",
    "model.train()\n",
    "loss_record = []\n",
    "for epoch in range(num_epochs):\n",
    "    train_loss = 0\n",
    "    print_loss = 0\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",
    "        if (epoch == 0):\n",
    "            loss_record.append(loss.item())\n",
    "        train_loss += loss.item()\n",
    "        print_loss += loss.item()\n",
    "        optimizer.step()\n",
    "        \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": "markdown",
   "metadata": {},
   "source": [
    "## Loss record\n",
    "\n",
    "As we can clearly see, the loss is decreasing as we pass more and more number of batches i.e. as we perform more number of iterations. The losses here are only for the first epoch. The fluctuations are due to the use of mini batch gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1156ea390>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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.plot(loss_record)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reconstructing a random image from the training set :-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": [
    "Reconstructing images from the test set :-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": {
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CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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XJf3A3QeG16p870boq5L3rYrwH5fUMez+wmJZS3D348W/JyW9pKHdlFbSd2WS1OLfkxX38//cvc/dL7v7oKSfqsL3rphZ+kVJm919W7G48vdupL6qet+qCP8uSYvNbJGZTZX0HUmvVtDH15hZe/FFjMysXdK31HqzD78qaV1xe52kVyrs5Y+0yszNZTNLq+L3ruVmvHb3pv9IWqWhb/w/kvSPVfRQ0tdtkv6n+Pmw6t4kbdHQx8AvNfTdyHcl3SBph6QDkl6TNKeFevtPDc3m/L6Ggragot5WaOgj/fuSflf8rKr6vUv0Vcn7xhF+QFB84QcERfiBoAg/EBThB4Ii/EBQhB8IivADQRF+IKj/A3GpBcNLcePDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ekfSixj+mdJP9JxZJLX6P1NzP/3P3/e5+zN2PS3paNb52xcrSz0v6hbu/UNxc+2s3WV91vW51hH+jpAvN7Btmdqqk70laX0MfX2FmZxVfxMjMzpL0bXXf6sPrJa0uLq+WtK7GXr6gW1ZuLltZWjW/dl234rW7d/xH0m0a/8b/HUl/W0cPJX1dIOm/i5/tdfcm6VmNvw0c0/h3I/dJ+iNJGyTtkvRvkuZ3UW//ovHVnN/UeNB6a+rtRo2/pX9T0tbi57a6X7ugr1peN/bwA5LiCz8gKcIPJEX4gaQIP5AU4QeSIvxAUoQfSIrwA0n9H5olTbrRAlCuAAAAAElFTkSuQmCC\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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MHmr0daek/y1+3i27N0k7NPY2cFhj3408LelmSXskvS/pvyUtqlBvL0t6R9IBjQWts6TeHtDYW/oDkvYXP+vLfu0SfZXyunGGHxAUX/gBQRF+ICjCDwRF+IGgCD8QFOEHgiL8QFCEHwjq/wHQuMDDt3SEsQAAAABJRU5ErkJggg==\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": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([784])\n"
     ]
    }
   ],
   "source": [
    "image2 = images[1]\n",
    "print(image2.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Original image of some random training example :-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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(images[1].numpy().reshape(28, 28), cmap='gray')\n",
    "plt.show(block=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reconstructed image :-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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": "markdown",
   "metadata": {},
   "source": [
    "# Experiments\n",
    "\n",
    "First we will calculate mu, logvar fomr two images by passing them through the encoder of our network. We will use them later to perform some experiments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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": "markdown",
   "metadata": {},
   "source": [
    "### 1. Sampling epsilon values at regular intervals and reconstructing the images"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the reconstructed images are not actually same, i.e. their values differ but the look very similar. This means that our network tries to maps many z values (following a particular gaussian) to a singe image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([-1.6100e-07, -1.3919e-07, -1.3006e-07, -1.1566e-07, -1.8562e-07,\n",
      "        -1.9818e-07, -5.0689e-08, -6.3592e-08, -1.2538e-07, -1.0813e-07,\n",
      "        -1.3024e-07, -1.3028e-07, -9.6279e-08, -1.3603e-07, -8.6742e-08,\n",
      "        -2.3373e-07, -1.2368e-07, -1.2435e-07, -6.2805e-08, -1.3062e-07,\n",
      "        -1.4138e-07, -9.8231e-08, -1.2456e-07, -1.3576e-07, -1.4953e-07,\n",
      "        -4.7374e-08, -1.9469e-07, -5.9462e-08, -1.4301e-07, -1.1349e-07,\n",
      "        -1.1179e-07, -1.4580e-07, -1.8958e-07, -4.3240e-08, -4.9798e-07,\n",
      "        -2.2435e-07, -7.3589e-08, -3.9425e-08, -1.8130e-08, -3.3894e-08,\n",
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      "        -4.6353e-07, -1.4910e-07, -9.5031e-08, -9.9834e-08, -2.0297e-07,\n",
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      "        -1.8412e-04,  3.1644e-05,  5.4385e-04,  4.1094e-03,  1.3631e-02,\n",
      "         1.0254e-02,  1.7312e-03, -2.1149e-03, -1.0845e-04, -4.1243e-06,\n",
      "        -1.3056e-06, -2.7360e-06, -4.2700e-07, -4.4807e-08, -1.3147e-07,\n",
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      "        -1.9267e-06, -8.4560e-06, -1.7922e-05,  3.4790e-04,  1.1853e-03,\n",
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      "        -8.3941e-04, -3.1696e-04, -2.7356e-04,  1.0703e-03,  1.4346e-02,\n",
      "         4.2412e-03,  1.3358e-03, -6.8905e-03, -8.8666e-04, -6.9175e-06,\n",
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      "        -4.1144e-03, -6.3697e-04, -4.2389e-04, -7.0380e-04,  4.2644e-03,\n",
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      "        -5.8768e-03, -6.8240e-04, -9.2991e-05, -2.5606e-05,  2.8773e-03,\n",
      "         1.5804e-02,  3.1644e-04, -4.9567e-03, -1.2433e-02, -1.3679e-04,\n",
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      "        -8.6924e-06, -5.1955e-04, -7.9314e-03, -2.8694e-04,  5.8115e-04,\n",
      "         3.1630e-03, -1.4227e-04,  4.2677e-05,  1.4628e-04,  3.1604e-03,\n",
      "         2.2949e-02,  1.2394e-03, -1.6499e-03, -2.7017e-02, -1.4240e-03,\n",
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      "        -3.8779e-03,  6.0791e-04,  6.3968e-04,  3.4639e-03,  5.7736e-03,\n",
      "         4.4536e-03,  7.4722e-03,  2.1983e-02,  6.0873e-03,  2.6733e-04,\n",
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      "         2.4319e-05,  1.0383e-04,  9.2506e-04,  3.2879e-03,  7.2559e-03,\n",
      "         5.0794e-03,  1.2345e-03,  2.2054e-05, -8.8462e-03, -1.8938e-03,\n",
      "        -2.9492e-05,  8.5987e-06,  3.2228e-06,  5.5000e-07,  7.4008e-08,\n",
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      "        -2.1003e-03, -3.5477e-03, -2.2329e-05,  8.1352e-06,  3.3933e-06,\n",
      "         1.0801e-06,  3.5874e-07,  8.9396e-08,  1.6518e-07,  3.3904e-09,\n",
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      "         3.1878e-03,  3.8350e-04, -1.1323e-03, -1.2509e-02, -9.5108e-04,\n",
      "        -3.7052e-06,  2.0101e-06,  6.8490e-07,  2.8893e-07,  1.0903e-07,\n",
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      "         7.0385e-07,  2.5199e-06,  7.7505e-06, -2.6864e-06,  6.5692e-04,\n",
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      "        -5.0397e-05, -1.3903e-06, -1.0105e-07, -8.2508e-09, -3.1872e-10,\n",
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      "        -1.6482e-07, -2.6384e-07, -1.4606e-08, -8.7142e-09, -7.8626e-09,\n",
      "        -5.0048e-09,  3.0082e-07,  5.0160e-06,  6.0821e-05,  1.4794e-03,\n",
      "         1.2714e-02,  2.8122e-03,  2.4754e-04, -1.8731e-02, -4.0253e-03,\n",
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      "        -1.2020e-07, -7.9785e-08,  6.6061e-07,  2.9380e-05,  1.2214e-03,\n",
      "         2.0073e-02,  3.8887e-03,  1.1638e-03, -9.6804e-03, -8.1386e-03,\n",
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      "        -1.3925e-07, -1.8454e-07, -2.9247e-07, -3.9297e-07, -3.5687e-08,\n",
      "         2.2467e-06,  8.9652e-05,  2.7231e-03,  1.8228e-02,  4.5697e-03,\n",
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      "        -6.3923e-09, -2.4550e-08, -6.7871e-08, -7.9704e-08,  3.5521e-06,\n",
      "         1.3601e-04,  1.0114e-03,  1.9071e-04, -3.1843e-03, -1.1050e-03,\n",
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      "        -2.2825e-07, -7.4879e-08, -1.7749e-07, -7.5508e-08, -9.5529e-08,\n",
      "        -1.2796e-07, -9.6637e-08, -2.0772e-08, -5.2415e-09, -2.0603e-09,\n",
      "        -1.8963e-09, -8.8365e-09, -3.8895e-08, -6.0447e-07, -7.1822e-06,\n",
      "        -3.4080e-05, -1.2931e-05, -1.2306e-06, -3.3336e-07, -7.9200e-08,\n",
      "        -1.1670e-07, -2.7159e-07, -1.0427e-07, -2.0796e-08, -2.7861e-08,\n",
      "        -1.2742e-07, -2.8325e-07, -1.1679e-07, -2.4300e-07, -6.9967e-08,\n",
      "        -1.1394e-07, -6.6400e-08, -5.8954e-08, -1.7115e-07, -1.4095e-07,\n",
      "        -9.3084e-08, -1.2478e-07, -4.8572e-08, -7.6195e-08, -1.5749e-07,\n",
      "        -1.2070e-07, -6.8384e-07, -7.9125e-07, -1.2263e-06, -6.5750e-07,\n",
      "        -2.0530e-07, -2.5056e-08, -2.7750e-08, -4.6856e-08, -1.1141e-07,\n",
      "        -2.0327e-07, -7.7735e-08, -1.4574e-07, -2.4899e-07, -9.3156e-08,\n",
      "        -7.9402e-08, -1.8019e-07, -1.3077e-07, -2.6220e-07])\n"
     ]
    }
   ],
   "source": [
    "print(recon_images1[0] - recon_images1[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\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 = 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": "markdown",
   "metadata": {},
   "source": [
    "### 2. Changing just one dimension of the latent variable and reconstructing the images\n",
    "\n",
    "This doesn't affect the constructed images a lot since we have 19 more dimensions which point to the same digit so changing one dimension doesn't create a visual effect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "with torch.no_grad():\n",
    "    recon_images1 = []\n",
    "    eps_val = torch.randn_like(mu1)\n",
    "    for ctr in range(0, 100, 5):\n",
    "        eps_val[7] = ctr * 0.05 * std1[7] + mu1[7]\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": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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t6enpTjLnnntu1X4/+tGPOslMTExU7Xf++ecXM+9///ur1jrggAOKmZqzP/fcc1X71fw61/zaRETknKtywGired1ZunRp1Vr6Rb8ARNS95tRkInRLRMRll11WtVZNt7zwwgvFjG4BWqVf6vtl/fr1xUxtvxx44IHFTE2/PPvss1X76ZduuSMfAAAAAAAaZpAPAAAAAAANM8gHAAAAAICGGeQDAAAAAEDDDPIBAAAAAKBhBvkAAAAAANAwg3wAAAAAAGiYQT4AAAAAADTMIB8AAAAAABo2NugDjKLp6eli5qmnnqpaa+fOncXMwQcfXMx86lOfqtrvox/9aDGzbdu2YubZZ5+t2u+XfumXipnXvva1VWvVPO8PP/xwMfP00093tl/OuWotgBo1rztPPvlk1Vpd9cuf/MmfVO1X0y/bt28vZnbs2FG1n34BqNPitYtu2euhhx4qZnQL0Kphvnb52Mc+VszUzMZa7RfXLu1yRz4AAAAAADSsOMhPKV2bUtqRUtq6z2OfTCk9nVLaMvPf23p7TAAWG/0CQNd0CwC9oF+AFtTckX9dRLx1lsevzjmfPvPf/+v2WACMgOtCvwDQretCtwDQvetCvwADVhzk55zvjIjn+3AWAEaIfgGga7oFgF7QL0ALFvIe+VemlO6f+edFy+cKpZQ2pJQ2p5Q2L2AvAEaHfgGga7oFgF7QL0DfzHeQ/4WIWBMRp0fEtoj4s7mCOedrcs7rcs7r5rkXAKNDvwDQNd0CQC/oF6Cv5jXIzzk/k3Pek3Oejoi/joizuz0WAKNIvwDQNd0CQC/oF6Df5jXITymt2ue7l0TE1rmyAFBLvwDQNd0CQC/oF6DfxkqBlNKXIuKciDgipfRURHwiIs5JKZ0eETkiHouID/XwjIvOnj17ipnPfOYzVWtNTEwUM+9617uKmUMPPbRqv9WrVxczy5fP+bZwP1PzHERErFixophJKVWt9fzz5c+l+fznP1/MbNu2rWq/2v+NMKr0S/f0S8TJJ59ctZ9+gcVJt3Sv5jXnT//0T6vWGhsrXn7Gr//6rxczumWvz33uc8WMboFu6JfuDXO/HHXUUcXMYYcdVsy02i9XX311MaNfBqP4Oz3n/O5ZHv5iD84CwAjRLwB0TbcA0Av6BWjBfD/sFgAAAAAA6AODfAAAAAAAaJhBPgAAAAAANMwgHwAAAAAAGmaQDwAAAAAADTPIBwAAAACAhhnkAwAAAABAwwzyAQAAAACgYSnn3L/NUurfZiNiYmKimDnzzDOLmTe/+c1V+x188MHFzLJly4qZ9773vVX7rVy5spjZvXt31Vp/9Ed/VMz8+Z//eTHz0ksvVe1HvZxzGvQZGG76pXv97peDDjqomDn00EOLmUH0yx//8R8XM5///OeLGf3SPf3CQuiW7tV0yxlnnFHMvOlNb6ra75BDDilmaq5d3ve+91Xtp1tGxn0553WDPgTDS790b3x8vJipuXbRL3vpl8GouXZxRz4AAAAAADTMIB8AAAAAABpmkA8AAAAAAA0zyAcAAAAAgIYZ5AMAAAAAQMMM8gEAAAAAoGEG+QAAAAAA0DCDfAAAAAAAaFjKOfdvs5T6txmvypIldX+nMz4+Xsy84Q1vKGZuu+22qv2OOOKIYubRRx+tWuu8884rZp566qlipp9/ZkZFzjkN+gwMN/3SrpTq/nhPTEwUM/qFV0u/sBC6pV1ddsupp55azHz1q1+t2q+mW773ve9VrXXuuecWM7plYO7LOa8b9CEYXvqlXaPQLzXXLk8++WQxo1+6V3Pt4o58AAAAAABomEE+AAAAAAA0zCAfAAAAAAAaZpAPAAAAAAANM8gHAAAAAICGGeQDAAAAAEDDDPIBAAAAAKBhBvkAAAAAANCwsUEfgDZMT09X5aampoqZs846q5hZvnx51X415/riF79YtdYzzzxTzOScq9YCoE7t62pNv5x55pnFTJf9cu2111atpV8A+muYu8W1C0C7hrlf/uZv/qZqre3btxcz+qVd7sgHAAAAAICGGeQDAAAAAEDDDPIBAAAAAKBhBvkAAAAAANAwg3wAAAAAAGiYQT4AAAAAADTMIB8AAAAAABpmkA8AAAAAAA0zyAcAAAAAgIaNDfoADJeDDjqomPngBz9YzCxZUvd3SD/84Q+LmS996UtVa+3atasqB0D/tdgvN954Y9Va+gWgTTXdsmHDhmJGtwCwrxavXW644YaqtfTLcHNHPgAAAAAANKw4yE8pHZNS+o+U0kMppQdTSh+ZeXxFSun2lNJ3Z75d3vvjArBY6BcAuqZbAOgF/QK0oOaO/KmI+P2c8ykR8T8i4sMppVMi4uMRcUfOeW1E3DHzfQCopV8A6JpuAaAX9AswcMVBfs55W875GzNfvxgRD0fE6oi4KCKun4ldHxEX9+qQACw++gWArukWAHpBvwAteFUfdptSOj4izoiITRGxMue8beaHtkfEyjl+zoaIKH+CEAAjS78A0DXdAkAv6BdgUKo/7DaldEhE/ENE/F7O+Sf7/ljOOUdEnu3n5ZyvyTmvyzmvW9BJAViU9AsAXdMtAPSCfgEGqWqQn1Iaj70vVDfknP9x5uFnUkqrZn58VUTs6M0RAVis9AsAXdMtAPSCfgEGrTjITymliPhiRDycc/7sPj90a0RcOvP1pRHxle6PB8BipV8A6JpuAaAX9AvQgpr3yH9zRLwvIh5IKW2ZeeyqiPh0RNySUroiIh6PiHf15oj0w95OKlu/fn0x8/M///PFzNTUVNV+t99+ezGzffv2qrWA5uiXEVDbL+edd14x8/rXv76Yqe2Xf/u3fytm9AsMJd0yAmq75dxzzy1muuyWO+64o5jRLTC09As/c8455xQzp5xySjFT2y///u//Xsxs27atmGH4FQf5OeevR8Rc/0+pPNUFgFnoFwC6plsA6AX9ArSg+sNuAQAAAACA/jPIBwAAAACAhhnkAwAAAABAwwzyAQAAAACgYQb5AAAAAADQMIN8AAAAAABomEE+AAAAAAA0zCAfAAAAAAAaNjboA9CGsbG63wof+9jHipmDDjqomNm5c2fVfrfddlsxs3v37qq1AOi/VvvlX/7lX4oZ/QLQptpu+ehHP1rM/NzP/VwxMzk5WbWfbgEYbuPj41W5mmsX/UIvuCMfAAAAAAAaZpAPAAAAAAANM8gHAAAAAICGGeQDAAAAAEDDDPIBAAAAAKBhBvkAAAAAANAwg3wAAAAAAGiYQT4AAAAAADRsbNAHoA1HHnlkVe71r399J/s999xzVbmNGzcWMznnhR4HgB5ZuXJlVa7f/bJp06ZiRr8AtKm2W0499dRiJqVUzLh2ARgNr3vd66pyXfXLD3/4w6r99Asvc0c+AAAAAAA0zCAfAAAAAAAaZpAPAAAAAAANM8gHAAAAAICGGeQDAAAAAEDDDPIBAAAAAKBhBvkAAAAAANAwg3wAAAAAAGjY2KAPQBvWrFlTlcs5FzO7d+8uZrZu3Vq131NPPdXJmQAYjNp+qVHTLw8++GDVWk8++WQxo18A2nT88cdX5bq6dnnooYeq9tMtAMPthBNOqMp11S+11y5PPPFEJ2di+LkjHwAAAAAAGmaQDwAAAAAADTPIBwAAAACAhhnkAwAAAABAwwzyAQAAAACgYQb5AAAAAADQMIN8AAAAAABomEE+AAAAAAA0zCAfAAAAAAAalnLO/dsspf5txqsyPj5elVu7dm0x8yu/8ivFzI033li1349//OOqHMMt55wGfQaGm35pV22/rFmzppg599xzixn9wr70CwuhW9qlWxiw+3LO6wZ9CIaXfmlXl/2yfv36YuaGG26o2u+FF16oyjHcaq5d3JEPAAAAAAANKw7yU0rHpJT+I6X0UErpwZTSR2Ye/2RK6emU0paZ/97W++MCsFjoFwC6plsA6AX9ArRgrCIzFRG/n3P+RkppWUTcl1K6febHrs45f6Z3xwNgEdMvAHRNtwDQC/oFGLjiID/nvC0its18/WJK6eGIWN3rgwGwuOkXALqmWwDoBf0CtOBVvUd+Sun4iDgjIjbNPHRlSun+lNK1KaXlc/ycDSmlzSmlzQs6KQCLln4BoGu6BYBe0C/AoFQP8lNKh0TEP0TE7+WcfxIRX4iINRFxeuz9W8k/m+3n5ZyvyTmv86nuAMxGvwDQNd0CQC/oF2CQqgb5KaXx2PtCdUPO+R8jInLOz+Sc9+ScpyPiryPi7N4dE4DFSL8A0DXdAkAv6Bdg0IqD/JRSiogvRsTDOefP7vP4qn1il0TE1u6PB8BipV8A6JpuAaAX9AvQgpRz3n8gpbdExF0R8UBETM88fFVEvDv2/tOhHBGPRcSHZj78Y39r7X8zYCTlnNOgz0D/6Reg1/TL6NEtQB/c5+1RRo9+AXqt5tqlOMjvkhcrYDYGLSyUfgFmo19YCN0CzMEgnwXRL8Bsaq5dqj/sFgAAAAAA6D+DfAAAAAAAaJhBPgAAAAAANMwgHwAAAAAAGmaQDwAAAAAADTPIBwAAAACAhhnkAwAAAABAwwzyAQAAAACgYQb5AAAAAADQMIN8AAAAAABomEE+AAAAAAA0zCAfAAAAAAAaZpAPAAAAAAANM8gHAAAAAICGGeQDAAAAAEDDDPIBAAAAAKBhBvkAAAAAANCwsT7v91xEPP6Kx46YeXzYDOu5I5x9UJx9dsf1aF1Gyyv7xZ+3wXD2wXD22ekXFmoxXbtEOPsgDOu5I5x9f/QLC+XapQ3OPhjOPruqbkk55x7tXyeltDnnvG6gh5iHYT13hLMPirND/wzz71lnHwxnH4xhPjujaZh/zzp7/w3ruSOcHfppmH/POvtgOPtgtHB2b60DAAAAAAANM8gHAAAAAICGtTDIv2bQB5inYT13hLMPirND/wzz71lnHwxnH4xhPjujaZh/zzp7/w3ruSOcHfppmH/POvtgOPtgDPzsA3+PfAAAAAAAYG4t3JEPAAAAAADMwSAfAAAAAAAaNrBBfkrprSmlR1JKj6aUPj6oc8xHSumxlNIDKaUtKaXNgz7P/qSUrk0p7Ugpbd3nsRUppdtTSt+d+Xb5IM84lznO/smU0tMzz/2WlNLbBnnGuaSUjkkp/UdK6aGU0oMppY/MPN70c7+fcw/F8w4R+qVf9Ev/DWu3ROgXhp9u6Q/dMhjD2i+6hcVAv/SHfum/Ye2WiLb7ZSDvkZ9SWhoR34mICyLiqYi4NyLenXN+qO+HmYeU0mMRsS7n/Nygz1KSUvqfEfHTiPg/Oec3zDz2vyPi+Zzzp2eKYnnO+X8N8pyzmePsn4yIn+acPzPIs5WklFZFxKqc8zdSSssi4r6IuDgi3h8NP/f7Ofe7Ygied9Av/aNf+m9YuyVCvzDcdEv/6JbBGNZ+0S0MO/3SP/ql/4a1WyLa7pdB3ZF/dkQ8mnP+fs55V0TcFBEXDegsi1rO+c6IeP4VD18UEdfPfH197P3N2Jw5zj4Ucs7bcs7fmPn6xYh4OCJWR+PP/X7ODcNCv/SJfum/Ye2WCP3C0NMtfaJbBmNY+0W3sAjolz7RL/03rN0S0Xa/DGqQvzointzn+09FI09IpRwR/5pSui+ltGHQh5mHlTnnbTNfb4+IlYM8zDxcmVK6f+afFzX3T3BeKaV0fEScERGbYoie+1ecO2LInndGln4ZrKF5jZvD0LzODWu3ROgXhpJuGayheo2bxVC9xg1rv+gWhpR+GayheY2bw9C8zg1rt0S01y8+7HZ+3pJzPjMifjUiPjzzz1yGUt773kr9f3+l+ftCRKyJiNMjYltE/Nlgj7N/KaVDIuIfIuL3cs4/2ffHWn7uZzn3UD3vMMT0y+AMzevcsHZLhH6BAdEtgzNUr3HD2i+6BQZGvwzO0LzODWu3RLTZL4Ma5D8dEcfs8/2jZx4bCjnnp2e+3RERX469/xxqmDwz835PL7/v044Bn6dazvmZnPOenPN0RPx1NPzcp5TGY+8f+Btyzv8483Dzz/1s5x6m552Rp18Gq/nXuLkMy+vcsHZLhH5hqOmWwRqK17jZDNNr3LD2i25hyOmXwWr+NW4uw/I6N6zdEtFuvwxqkH9vRKxNKZ2QUpqIiN+IiFsHdJZXJaV08MwHHURK6eCIuDAitu7/ZzXn1oi4dOYFGbkqAAAgAElEQVTrSyPiKwM8y6vy8h/2GZdEo899SilFxBcj4uGc82f3+aGmn/u5zj0szzuEfhm0pl/j9mcYXueGtVsi9AtDT7cMVvOvcXMZlte4Ye0X3cIioF8Gq+nXuP0Zhte5Ye2WiLb7Je39Vwz9l1J6W0R8LiKWRsS1OedPDeQgr1JK6cTY+zeNERFjEXFjy2dPKX0pIs6JiCMi4pmI+ERE/N+IuCUijo2IxyPiXTnn5j44Y46znxN7/wlLjojHIuJD+7y3VjNSSm+JiLsi4oGImJ55+KrY+55azT73+zn3u2MInneI0C/9ol/6b1i7JUK/MPx0S3/olsEY1n7RLSwG+qU/9Ev/DWu3RLTdLwMb5AMAAAAAAGU+7BYAAAAAABpmkA8AAAAAAA0zyAcAAAAAgIYZ5AMAAAAAQMMM8gEAAAAAoGEG+QAAAAAA0DCDfAAAAAAAaJhBPgAAAAAANMwgHwAAAAAAGmaQDwAAAAAADTPIBwAAAACAhhnkAwAAAABAwwzyAQAAAACgYQb5AAAAAADQMIN8AAAAAABomEE+AAAAAAA0zCAfAAAAAAAaZpAPAAAAAAANM8gHAAAAAICGGeQDAAAAAEDDDPIBAAAAAKBhBvkAAAAAANAwg3wAAAAAAGiYQT4AAAAAADTMIB8AAAAAABpmkA8AAAAAAA0zyAcAAAAAgIYZ5AMAAAAAQMMM8gEAAAAAoGEG+QAAAAAA0DCDfAAAAAAAaJhBPgAAAAAANMwgHwAAAAAAGmaQDwAAAAAADTPIBwAAAACAhhnkAwAAAABAw8b6uVlKKfdzP2A45JzToM/AcNMvwGz0CwuhW4A5PJdzfu2gD8Hw0i/AbGquXRZ0R35K6a0ppUdSSo+mlD6+kLUA4GX6BYCu6RagI48P+gC0Rb8A/TLvQX5KaWlE/EVE/GpEnBIR704pndLVwQAYTfoFgK7pFgB6Qb8A/bSQO/LPjohHc87fzznvioibIuKibo4FwAjTLwB0TbcA0Av6BeibhQzyV0fEk/t8/6mZx/6blNKGlNLmlNLmBewFwOjQLwB0TbcA0Av6Beibnn/Ybc75moi4JsIHegDQHf0CQNd0CwC9oF+ALizkjvynI+KYfb5/9MxjALAQ+gWArukWAHpBvwB9s5BB/r0RsTaldEJKaSIifiMibu3mWACMMP0CQNd0CwC9oF+Avpn3W+vknKdSSldGxFcjYmlEXJtzfrCzkwEwkvQLAF3TLQD0gn4B+inl3L+35vI+YMBscs5p0GdguOkXYDb6hYXQLcAc7ss5rxv0IRhe+gWYTc21y0LeWgcAAAAAAOgxg3wAAAAAAGiYQT4AAAAAADTMIB8AAAAAABpmkA8AAAAAAA0zyAcAAAAAgIYZ5AMAAAAAQMMM8gEAAAAAoGEG+QAAAAAA0DCDfAAAAAAAaJhBPgAAAAAANMwgHwAAAAAAGmaQDwAAAAAADTPIBwAAAACAhhnkAwAAAABAwwzyAQAAAACgYQb5AAAAAADQMIN8AAAAAABomEE+AAAAAAA0zCAfAAAAAAAaZpAPAAAAAAANM8gHAAAAAICGGeQDAAAAAEDDDPIBAAAAAKBhBvkAAAAAANAwg3wAAAAAAGiYQT4AAAAAADTMIB8AAAAAABpmkA8AAAAAAA0zyAcAAAAAgIYZ5AMAAAAAQMMM8gEAAAAAoGEG+QAAAAAA0DCDfAAAAAAAaJhBPgAAAAAANMwgHwAAAAAAGjY26APQhomJiarcgQceWMxMTk4WM7t27araL+dclauRUipmxsbKfyROPPHEqv3OO++8Yuahhx6qWuvuu+8uZmqfU4B+0i971fTLCSecULXf+vXrixn9AixmumWvmm457rjjqva74IILihndAix2BxxwQGc5/bJXTb88/PDDVWvV9EvN8z7M3JEPAAAAAAANW9Ad+SmlxyLixYjYExFTOed1XRwKgNGmXwDoBf0CQNd0C9AvXby1zrk55+c6WAcA9qVfAOgF/QJA13QL0HPeWgcAAAAAABq20EF+joh/TSndl1LaMFsgpbQhpbQ5pbR5gXsBMDr0CwC9sN9+0S0AzINrF6AvFvrWOm/JOT+dUnpdRNyeUvp2zvnOfQM552si4pqIiJRSdx+zDMBipl8A6IX99otuAWAeXLsAfbGgO/Jzzk/PfLsjIr4cEWd3cSgARpt+AaAX9AsAXdMtQL/Me5CfUjo4pbTs5a8j4sKI2NrVwQAYTfoFgF7QLwB0TbcA/bSQt9ZZGRFfTim9vM6NOefbOjkV1Wae//1atmxZMfPmN7+5ar9DDz20mPnP//zPYub555+v2m/Pnj3FTM1zEBExPj5ezBx//PHFzOc+97mq/VavXl3M3HTTTVVrff3rX6/KwSKhXxrQYr987WtfK2aee+65qv2mp6eLmdp+GRsr/9+pE044oZi5+uqrq/Y7+uiji5mbb765ai39wojRLwPW7255zWteU8zUXLu02i011y613XLMMccUM7fcckvVWrqFEaNbGqBfuu2X4447rpjpsl/+/u//vmqtu+66qyq3mM17kJ9z/n5EnNbhWQBAvwDQE/oFgK7pFqCfFvQe+QAAAAAAQG8Z5AMAAAAAQMMM8gEAAAAAoGEG+QAAAAAA0DCDfAAAAAAAaJhBPgAAAAAANMwgHwAAAAAAGmaQDwAAAAAADRsb9AFYmAMOOKCY+a3f+q1i5rLLLqva74EHHihmNm3aVMxMT09X7ZdzrsrVGB8fL2bOOOOMTjIREbt27SpmHnnkkaq19uzZU5UD6EpNv/z2b/92MfP+97+/ar+u+qW2N7rsl4mJiWLm9NNPL2Zq+2X37t3FjH4BWtRVt3R57bJx48ZiZhDdUnPtctpppxUzZ555ZtV+XXZL7bUeQFdq+uV3fud3ipkur130y15TU1PFjH6p5458AAAAAABomEE+AAAAAAA0zCAfAAAAAAAaZpAPAAAAAAANM8gHAAAAAICGGeQDAAAAAEDDDPIBAAAAAKBhBvkAAAAAANCwsUEfgIU56aSTipkrr7yymDnssMOq9tuyZUsx89JLL1Wt1ZUlS+r+Purwww8vZt773vcWM8uWLava78c//nExs2nTpqq1APqtpl8+/OEPFzP6Za/3vOc9xcyhhx5atV9Nv2zcuLFqLYB+6ura5TWveU3Vft/85jeLmWHulve9733FTO21y09+8pNiprZbcs5VOYCu9PvaZZj7ZcWKFcVMTb/UXrvU9Mvdd99dtZZ+cUc+AAAAAAA0zSAfAAAAAAAaZpAPAAAAAAANM8gHAAAAAICGGeQDAAAAAEDDDPIBAAAAAKBhBvkAAAAAANAwg3wAAAAAAGiYQT4AAAAAADRsbNAHYHZLltT9HcsVV1xRzBx55JHFzOTkZNV+P/jBD4qZn/70p8XM9PR01X41xsfHq3LHH398MfPGN76xmBkbq/tj88QTTxQz27Ztq1oLoCu1/fKBD3ygmOmyX77//e8XM632y3HHHVfMnHbaacWMfgGGVW23fPCDHyxmVq5cWcx02S0vvvhiMdNlt9S+1nfVLbVd9uSTTxYz//Vf/1W1FkBXavtlw4YNxUzNtcvOnTur9hvmfjn22GOLGf3SLnfkAwAAAABAwwzyAQAAAACgYQb5AAAAAADQMIN8AAAAAABomEE+AAAAAAA0zCAfAAAAAAAaZpAPAAAAAAANM8gHAAAAAICGjQ36AMzu4IMPrspdfPHFxcz4+Hgxs3Pnzqr9br311mJmcnKymMk5V+2XUuokExGxbt26YmbFihXFzO7du6v2u+qqq4qZqampqrUAulLbLxdddFEx02W//NM//VMna7XaL4cffngxo1+AYTXM3dLqtctZZ51VzOgWYLHrsl/Gxsoj0NrX+2Hul5prlyOOOKKYqe2XP/zDPyxm9Es9d+QDAAAAAEDDioP8lNK1KaUdKaWt+zy2IqV0e0rpuzPfLu/tMQFYbPQLAL2gXwDomm4BWlBzR/51EfHWVzz28Yi4I+e8NiLumPk+ALwa14V+AaB714V+AaBb14VuAQasOMjPOd8ZEc+/4uGLIuL6ma+vj4jyG7UDwD70CwC9oF8A6JpuAVow3w+7XZlz3jbz9faIWDlXMKW0ISI2zHMfAEaLfgGgF6r6RbcA8Cq4dgH6ar6D/J/JOeeU0pwfs5xzviYiromI2F8OAPalXwDohf31i24BYD5cuwD9UPMe+bN5JqW0KiJi5tsd3R0JgBGmXwDoBf0CQNd0C9BX8x3k3xoRl858fWlEfKWb4wAw4vQLAL2gXwDomm4B+qr41joppS9FxDkRcURK6amI+EREfDoibkkpXRERj0fEu3p5yFF0xhlnVOWOOuqoYibn8r/a2rp1a9V+999/fzEzNTVVtVaNmrOPj49XrXXJJZd0stYjjzxStd/GjRurcjCq9MtgnHnmmVW5Fvtlz549VWvVqDn72FjdOxBefHH5c81q1vrOd75Ttd+mTZuqcjCq9Ev/nXXWWVW5VatWFTM1r88PPPBA1X4tdkvttcuv/dqvFTM13fLoo49W7efaBfZPtwzGunXrqnJHHnlkMaNf9nr7299ezHTZL3fffXdVjjrFX5mc87vn+KH1HZ8FgBGiXwDoBf0CQNd0C9CC+b61DgAAAAAA0AcG+QAAAAAA0DCDfAAAAAAAaJhBPgAAAAAANMwgHwAAAAAAGmaQDwAAAAAADTPIBwAAAACAhhnkAwAAAABAw8YGfQBmd8EFF1Tlli5dWsxMTk4WM1/4wheq9tu5c2dVrp+OOeaYqtyxxx5bzExNTRUzt9xyS9V+Nc87QL9deOGFVTn9UtcbERHHH398MbNnz55i5u/+7u+q9mvxuQJGm26pV3vt0lW33HzzzVX7tfhcAeiXekcffXRVrqZfpqeni5na2ViLz9Uwc0c+AAAAAAA0zCAfAAAAAAAaZpAPAAAAAAANM8gHAAAAAICGGeQDAAAAAEDDDPIBAAAAAKBhBvkAAAAAANAwg3wAAAAAAGjY2KAPMIqWLl1azJx88slVa+Wci5nJycli5p577ulsvy6Nj48XM+94xzuq1jrssMOKmZrnasuWLVX79fu5Aqjpl7Vr11atpV/63y/f/OY3q/bTL0A/9btbdu7cWczce++9ne3XJd0CUE+/1Kvpl3e+851Va9X0S81z9Y1vfKNqP/3SLXfkAwAAAABAwwzyAQAAAACgYQb5AAAAAADQMIN8AAAAAABomEE+AAAAAAA0zCAfAAAAAAAaZpAPAAAAAAANM8gHAAAAAICGjQ36AKNoyZLy35/UZCIipqenO8mcd955Vfu98MILxcyPfvSjYmZiYqJqv/Xr1xczl19+edVaBx54YDGzffv2YubZZ5+t2q/m17Dm1yYiIudclQNGm36JGB8fr9rv/PPPL2b0C0D/u6XmdanmNTyi/91Sc+1yxRVXVK2lW4DFruZ1J6VUtZZ+6X+/7Nixo2o//dItd+QDAAAAAEDDDPIBAAAAAKBhBvkAAADw/9m7+1hLy/JewPfN7FEMHzojX1O+BZqIINCO5FRQaRXrMWmtqVppIjRpBVttNGkUYxP1j2qpqYJNT00wWkBpT2zUU9uoPYTS6lE0AqWCfIhVEKbzER1aMJWBmf2cP2bpmUP2nudh9rvW+6y9ryshs2fte97nzpo968f6zZq1AQA6psgHAAAAAICOKfIBAAAAAKBjinwAAAAAAOiYIh8AAAAAADqmyAcAAAAAgI4p8gEAAAAAoGMLYy+wFi0uLlZnHnzwwaZrPfbYY9WZQw45pDrz/ve/v+m8d7zjHdWZbdu2VWd27NjRdN65555bnTnyyCObrtVyv999993VmS1btgx2Ximl6VoALeY5Xy6//PLqzNatW6szQ+bLUUcd1XStPXv2VGda8uWhhx5qOk++ALPU8pjz/e9/v+laQ2XL+973vqbz3v72t1dnWp67bN++vek82QLQbsjnLrt27arOyJe9WvLlrrvuqs7oxsbhFfkAAAAAANCxapGfmR/PzB2Zeec+t703M7dk5u2T/1453TUBWG3kCwBDky0ATIN8AXrQ8or8ayLiFUvcfmUp5ezJf58fdi0A1oBrQr4AMKxrQrYAMLxrQr4AI6sW+aWUL0XEzhnsAsAaIl8AGJpsAWAa5AvQg5W8R/5bMvObk39etGG5ocy8NDNvycxbVnAWAGuHfAFgaLIFgGmQL8DMHGiR/5GIOCUizo6IrRHxweUGSylXl1I2l1I2H+BZAKwd8gWAockWAKZBvgAzdUBFfilleyllTyllMSI+GhHnDrsWAGuRfAFgaLIFgGmQL8CsHVCRn5mb9vnpqyPizuVmAaCVfAFgaLIFgGmQL8CsLdQGMvOvI+KCiDgiMx+KiPdExAWZeXZElIi4PyIum+KOq86ePXuqMx/4wAearrVu3brqzG/8xm9UZw4//PCm837mZ36mOvOsZz2rOnPaaac1nbdx48bqTGY2XWvnzvr3pbnyyiurM1u3bm06r+X3GdYy+TK8lsedP/mTP2m6Vstj6+tf//rqTGu+bNq0qTrzzGc+szozRr788Ic/rM605Mu2bduazpMvsDzZMjzZEnHqqac2ndfjcxfZAsOQL8Nredy54oorBjtvyHxp6cbmOV+uuuqq6ox8GUe1yC+lXLTEzR+bwi4ArCHyBYChyRYApkG+AD040G92CwAAAAAAzIAiHwAAAAAAOqbIBwAAAACAjinyAQAAAACgY4p8AAAAAADomCIfAAAAAAA6psgHAAAAAICOKfIBAAAAAKBjWUqZ3WGZsztsjVi/fn115pxzzqnOnHfeeU3nHXLIIdWZww47rDrzhje8oem8Y445pjrzxBNPNF3r3e9+d3Xmz/7sz6ozP/7xj5vOo10pJcfegfkmX4Y3VL688IUvbDrv0EMPrc7IF54q+cJKyJbhtWTLWWedVZ05//zzm86TLbJlSm4tpWweewnml3wZ3lD50tqNDZUvF198cdN5Q+bLe97znurMhz/84eqMfBley3MXr8gHAAAAAICOKfIBAAAAAKBjinwAAAAAAOiYIh8AAAAAADqmyAcAAAAAgI4p8gEAAAAAoGOKfAAAAAAA6JgiHwAAAAAAOpallNkdljm7w3hKMrNp7mlPe1p15nnPe1515h/+4R+azjviiCOqM9/97nebrvWLv/iL1ZkHH3ywOjPLPzNrRSml7QsQliFf+jVkvjz3uc+tztxwww1N58mXtUG+sBKypV+t2bJ+/frqzOmnn16dkS08ya2llM1jL8H8ki/9mud8+d73vtd0rQsuuKA6I1/G0fLcxSvyAQAAAACgY4p8AAAAAADomCIfAAAAAAA6psgHAAAAAICOKfIBAAAAAKBjinwAAAAAAOiYIh8AAAAAADqmyAcAAAAAgI4tjL0AfSilNM3t3r27OnPOOedUZzZs2NB03uLiYnXmL//yL5uutW3btupM6/0AQJt5zpdrrrmm6VryBWC2Wh9T9+zZU52RLQD8hHzZS770yyvyAQAAAACgY4p8AAAAAADomCIfAAAAAAA6psgHAAAAAICOKfIBAAAAAKBjinwAAAAAAOiYIh8AAAAAADqmyAcAAAAAgI4p8gEAAAAAoGMLYy/AfHnGM55Rnbn00kurMwcd1PZ3SDt37qzOfPKTn2y61uOPP940B8DsteTLm970purMkPnyiU98oula8gWgTy3Zctlll1VnZAsA++oxX6677rqma8mX+eYV+QAAAAAA0LFqkZ+Zx2fmTZl5V2Z+KzPfOrl9Y2bekJn3TX7cMP11AVgt5AsAQ5MtAEyDfAF60PKK/N0R8QellNMj4r9FxJsz8/SIeGdE3FhKOS0ibpz8HABayRcAhiZbAJgG+QKMrlrkl1K2llJum3z8aETcHRHHRsSrIuLaydi1EfFr01oSgNVHvgAwNNkCwDTIF6AHT+mb3WbmSRFxTkR8PSKOLqVsnXxqW0QcvcyvuTQi6t/9FIA1S74AMDTZAsA0yBdgLM3f7DYzD42IT0fE20opj+z7uVJKiYiy1K8rpVxdStlcStm8ok0BWJXkCwBDky0ATIN8AcbUVORn5vrY+0B1fSnlM5Obt2fmpsnnN0XEjumsCMBqJV8AGJpsAWAa5AswtmqRn5kZER+LiLtLKR/a51Ofi4hLJh9fEhF/O/x6AKxW8gWAockWAKZBvgA9aHmP/PMi4g0RcUdm3j657V0RcUVEfCozfzsiHoiI101nRXrykpe8pDpz+umnV2d2797ddN6NN95Yndm6dWt1BuiSfOGnXvSiF1VnhsyXf/zHf6zObNu2relaQFdkCz/Vki3Pe97zqjOt2XLTTTdVZ2QLzC35wk+df/751Rn5wjRUi/xSyv+JiFzm0y8ddh0A1gr5AsDQZAsA0yBfgB40f7NbAAAAAABg9hT5AAAAAADQMUU+AAAAAAB0TJEPAAAAAAAdU+QDAAAAAEDHFPkAAAAAANAxRT4AAAAAAHRMkQ8AAAAAAB1bGHsB+rCw0PalcPnll1dnnvGMZ1Rndu3a1XTeF7/4xerME0880XQtAGavNV/e+c53VmeGzJcvfOEL1ZnHH3+86VoAzFavz10+//nPV2dkC0C/es0X3Rg/4RX5AAAAAADQMUU+AAAAAAB0TJEPAAAAAAAdU+QDAAAAAEDHFPkAAAAAANAxRT4AAAAAAHRMkQ8AAAAAAB1T5AMAAAAAQMcWxl6APhx11FFNc8973vOqM5lZnfnhD3/YdN7NN99cnSmlNF0LgNk78sgjm+bOOOOM6ox8ASCiPVvOPPPM6kxLtuzcubPpvK9//evVGdkC0K8jjjiiaW7W+fK1r32tOrO4uNh0LeabV+QDAAAAAEDHFPkAAAAAANAxRT4AAAAAAHRMkQ8AAAAAAB1T5AMAAAAAQMcU+QAAAAAA0DFFPgAAAAAAdEyRDwAAAAAAHVsYewH6cPLJJw92rSeeeKI6c9dddzVd68EHH6zOlFKargXA7M06X+6+++6ma8kXgPl14oknDnatIbPlgQceqM7IFoB+zTpf7rnnnqZr3X///dUZ+bI2eEU+AAAAAAB0TJEPAAAAAAAdU+QDAAAAAEDHFPkAAAAAANAxRT4AAAAAAHRMkQ8AAAAAAB1T5AMAAAAAQMcU+QAAAAAA0DFFPgAAAAAAdCxLKbM7LHN2h/GUrF+/vmnulFNOqc689KUvrc5cf/31Tef9x3/8R9Mc862UkmPvwHyTL/2SL4xJvrASsqVfCwsLTXOnnnpqdeZlL3tZdeaTn/xk03myZc24tZSyeewlmF/ypV+zzpfW5y4PP/xw0xzzreW5i1fkAwAAAABAx6pFfmYen5k3ZeZdmfmtzHzr5Pb3ZuaWzLx98t8rp78uAKuFfAFgaLIFgGmQL0APWv7NyO6I+INSym2ZeVhE3JqZN0w+d2Up5U+ntx4Aq5h8AWBosgWAaZAvwOiqRX4pZWtEbJ18/Ghm3h0Rx057MQBWN/kCwNBkCwDTIF+AHjyl98jPzJMi4pyI+Prkprdk5jcz8+OZuWGZX3NpZt6SmbesaFMAVi35AsDQZAsA0yBfgLE0F/mZeWhEfDoi3lZKeSQiPhIRp0TE2bH3byU/uNSvK6VcXUrZ7Lu6A7AU+QLA0GQLANMgX4AxNRX5mbk+9j5QXV9K+UxERClleyllTyllMSI+GhHnTm9NAFYj+QLA0GQLANMgX4CxVYv8zMyI+FhE3F1K+dA+t2/aZ+zVEXHn8OsBsFrJFwCGJlsAmAb5AvQgSyn7H8g8PyK+HBF3RMTi5OZ3RcRFsfefDpWIuD8iLpt884/9XWv/hwFrUiklx96B2ZMvwLTJl7VHtgAzcKu3R1l75AswbS3PXapF/pA8WAFLUbSwUvIFWIp8YSVkC7AMRT4rIl+ApbQ8d2n+ZrcAAAAAAMDsKfIBAAAAAKBjinwAAAAAAOiYIh8AAAAAADqmyAcAAAAAgI4p8gEAAAAAoGOKfAAAAAAA6JgiHwAAAAAAOqbIBwAAAACAjinyAQAAAACgY4p8AAAAAADomCIfAAAAAAA6psgHAAAAAICOKfIBAAAAAKBjinwAAAAAAOiYIh8AAAAAADqmyAcAAAAAgI4tzPi8H0TEA0+67YjJ7fNmXveOsPtY7L60E6d0XdaWJ+eLP2/jsPs47L40+cJKrabnLhF2H8O87h1h9/2RL6yU5y59sPs47L60pmzJUsqUzm+TmbeUUjaPusQBmNe9I+w+FrvD7Mzz16zdx2H3cczz7qxN8/w1a/fZm9e9I+wOszTPX7N2H4fdx9HD7t5aBwAAAAAAOqbIBwAAAACAjvVQ5F899gIHaF73jrD7WOwOszPPX7N2H4fdxzHPu7M2zfPXrN1nb173jrA7zNI8f83afRx2H8fou4/+HvkAAAAAAMDyenhFPgAAAAAAsAxFPgAAAAAAdGy0Ij8zX5GZ92bmdzLznWPtcSAy8/7MvCMzb8/MW8beZ38y8+OZuSMz79znto2ZeUNm3jf5ccOYOy5nmd3fm5lbJvf97Zn5yjF3XE5mHp+ZN2XmXZn5rcx86+T2ru/7/ew9F/c7RMiXWZEvszev2RIhX5h/smU2ZMs45jVfZAurgXyZDfkye/OaLRF958so75Gfmesi4tsRcWFEPBQR34iIi0opd818mQOQmfdHxOZSyg/G3qUmM18cET+KiOtKKWdMbvtAROwspVwxCYoNpZTLx9xzKcvs/t6I+FEp5U/H3K0mMzdFxKZSym2ZeVhE3BoRvxYRvxUd3/f72ft1MQf3O8iX2ZEvszev2RIhX5hvsmV2ZMs45jVfZAvzTr7MjnyZvXnNloi+82WsV+SfGxHfKaV8t5TyeET8z4h41Ui7rGqllC9FxM4n3fyqiLh28vG1sfeLsTvL7D4XSilbSym3TT5+NCLujohjo/P7fj97w7yQLzMiX2ZvXrMlQr4w92TLjMiWcZwCOVYAACAASURBVMxrvsgWVgH5MiPyZfbmNVsi+s6XsYr8YyPiwX1+/lB0coc0KhHxvzPz1sy8dOxlDsDRpZStk4+3RcTRYy5zAN6Smd+c/POi7v4JzpNl5kkRcU5EfD3m6L5/0t4Rc3a/s2bJl3HNzWPcMubmcW5esyVCvjCXZMu45uoxbglz9Rg3r/kiW5hT8mVcc/MYt4y5eZyb12yJ6C9ffLPbA3N+KeXnIuK/R8SbJ//MZS6Vve+tNPv3VzpwH4mIUyLi7IjYGhEfHHed/cvMQyPi0xHxtlLKI/t+ruf7fom95+p+hzkmX8YzN49z85otEfIFRiJbxjNXj3Hzmi+yBUYjX8YzN49z85otEX3my1hF/paIOH6fnx83uW0ulFK2TH7cERGfjb3/HGqebJ+839NP3vdpx8j7NCulbC+l7CmlLEbER6Pj+z4z18feP/DXl1I+M7m5+/t+qb3n6X5nzZMv4+r+MW458/I4N6/ZEiFfmGuyZVxz8Ri3lHl6jJvXfJEtzDn5Mq7uH+OWMy+Pc/OaLRH95stYRf43IuK0zDw5M58WEa+PiM+NtMtTkpmHTL7RQWTmIRHx8oi4c/+/qjufi4hLJh9fEhF/O+IuT8lP/rBPvDo6ve8zMyPiYxFxdynlQ/t8quv7frm95+V+h5AvY+v6MW5/5uFxbl6zJUK+MPdky7i6f4xbzrw8xs1rvsgWVgH5Mq6uH+P2Zx4e5+Y1WyL6zpfc+68YZi8zXxkRV0XEuoj4eCnlfaMs8hRl5nNi7980RkQsRMRf9bx7Zv51RFwQEUdExPaIeE9E/K+I+FREnBARD0TE60op3X3jjGV2vyD2/hOWEhH3R8Rl+7y3Vjcy8/yI+HJE3BERi5Ob3xV731Or2/t+P3tfFHNwv0OEfJkV+TJ785otEfKF+SdbZkO2jGNe80W2sBrIl9mQL7M3r9kS0Xe+jFbkAwAAAAAAdb7ZLQAAAAAAdEyRDwAAAAAAHVPkAwAAAABAxxT5AAAAAADQMUU+AAAAAAB0TJEPAAAAAAAdU+QDAAAAAEDHFPkAAAAAANAxRT4AAAAAAHRMkQ8AAAAAAB1T5AMAAAAAQMcU+QAAAAAA0DFFPgAAAAAAdEyRDwAAAAAAHVPkAwAAAABAxxT5AAAAAADQMUU+AAAAAAB0TJEPAAAAAAAdU+QDAAAAAEDHFPkAAAAAANAxRT4AAAAAAHRMkQ8AAAAAAB1T5AMAAAAAQMcU+QAAAAAA0DFFPgAAAAAAdEyRDwAAAAAAHVPkAwAAAABAxxT5AAAAAADQMUU+AAAAAAB0TJEPAAAAAAAdU+QDAAAAAEDHFPkAAAAAANAxRT4AAAAAAHRMkQ8AAAAAAB1T5AMAAAAAQMcU+QAAAAAA0LGFWR6WmWWW5wHzoZSSY+/AfJMvwFLkCyshW4Bl/KCUcuTYSzC/5AuwlJbnLit6RX5mviIz783M72TmO1dyLQD4CfkCwNBkCzCQB8ZegL7IF2BWDrjIz8x1EfE/IuK/R8TpEXFRZp4+1GIArE3yBYChyRYApkG+ALO0klfknxsR3ymlfLeU8nhE/M+IeNUwawGwhskXAIYmWwCYBvkCzMxKivxjI+LBfX7+0OS2/09mXpqZt2TmLSs4C4C1Q74AMDTZAsA0yBdgZqb+zW5LKVdHxNURvqEHAMORLwAMTbYAMA3yBRjCSl6RvyUijt/n58dNbgOAlZAvAAxNtgAwDfIFmJmVFPnfiIjTMvPkzHxaRLw+Ij43zFoArGHyBYChyRYApkG+ADNzwG+tU0rZnZlviYh/iIh1EfHxUsq3BtsMgDVJvgAwNNkCwDTIF2CWspTZvTWX9wEDllJKybF3YL7JF2Ap8oWVkC3AMm4tpWweewnml3wBltLy3GUlb60DAAAAAABMmSIfAAAAAAA6psgHAAAAAICOKfIBAAAAAKBjinwAAAAAAOiYIh8AAAAAADqmyAcAAAAAgI4p8gEAAAAAoGOKfAAAAAAA6JgiHwAAAAAAOqbIBwAAAACAjinyAQAAAACgY4p8AAAAAADomCIfAAAAAAA6psgHAAAAAICOKfIBAAAAAKBjinwAAAAAAOiYIh8AAAAAADqmyAcAAAAAgI4p8gEAAAAAoGOKfAAAAAAA6JgiHwAAAAAAOqbIBwAAAACAjinyAQAAAACgY4p8AAAAAADomCIfAAAAAAA6psgHAAAAAICOKfIBAAAAAKBjinwAAAAAAOiYIh8AAAAAADqmyAcAAAAAgI4p8gEAAAAAoGOKfAAAAAAA6JgiHwAAAAAAOqbIBwAAAACAjinyAQAAAACgYwtjL0Afnv70pw82t2vXrurM448/3nReKaVpbigLC/U/EieddFLTtV72spdVZ+65556ma918883VmZb7HWDWWvPl4IMPrs489thj1Zl5zpcTTzyx6VoXXnhhdUa+AKuZbNlryGxpee5y7733Nl1LtgDzSr7s1ZIvJ5xwQtO1Wp67yJd2XpEPAAAAAAAdW9Er8jPz/oh4NCL2RMTuUsrmIZYCYG2TLwBMg3wBYGiyBZiVId5a5xdLKT8Y4DoAsC/5AsA0yBcAhiZbgKnz1joAAAAAANCxlRb5JSL+d2bempmXLjWQmZdm5i2ZecsKzwJg7ZAvAEzDfvNFtgBwADx3AWZipW+tc34pZUtmHhURN2TmPaWUL+07UEq5OiKujojIzNl+m2UA5pV8AWAa9psvsgWAA+C5CzATK3pFfilly+THHRHx2Yg4d4ilAFjb5AsA0yBfABiabAFm5YCL/Mw8JDMP+8nHEfHyiLhzqMUAWJvkCwDTIF8AGJpsAWZpJW+tc3REfDYzf3KdvyqlfHGQrWg2uf/367DDDqvOvOhFL2o67/DDD6/O3HTTTdWZH/yg7Zu5Ly4uVmda7oOIiIWF+pf78ccfX5258sorm8478cQTqzOf/vSnm6715S9/uWkOVgn50oGh8uXFL35x03kt15Ive7Xky2c+85mma8kX1hj5MrKWx9WW5xutz11We7Ycd9xx1ZnWbDnppJOqM5/97GebriVbWGNkSweGypfW5y4t17rxxhurM2Pky7p166ozLc9dPvShDzWdd/LJJ1dn5Eu7Ay7ySynfjYizBtwFAOQLAFMhXwAYmmwBZmlF75EPAAAAAABMlyIfAAAAAAA6psgHAAAAAICOKfIBAAAAAKBjinwAAAAAAOiYIh8AAAAAADqmyAcAAAAAgI4p8gEAAAAAoGMLYy/Ayjz96U+vzrz5zW+uzvzWb/1W03l33HFHdebmm2+uzpRSms5rnWuxfv366sxZZ51Vndm8eXPTebt3767O3HvvvU3XWlxcbJoDGMrBBx9cnZEve7Xky5lnnlmdkS/AateSLW95y1uqM5dccknTefOcLQsL9afqQ2bLnj17qjP33HNP07VkCzBrLfny+7//+9WZiy++uOm8lnz5yle+Up3p9bnLGWecUZ15wQte0HReS758+9vfbrqWfPGKfAAAAAAA6JoiHwAAAAAAOqbIBwAAAACAjinyAQAAAACgY4p8AAAAAADomCIfAAAAAAA6psgHAAAAAICOKfIBAAAAAKBjC2MvwMqceuqp1Znf+73fq84861nPajrvtttuq878+Mc/brrWUA46qO3vozZu3FidecMb3lCdOfzww5vOe+SRR6ozN998c9O1SilNcwBDOe2006ozQ+bLv/zLv1Rnes2XDRs2VGcuvvji6ox8AVa7lmx505veVJ0Z8rnLf/3XfzVdayhDPndpyZZnPvOZTec9+uij1RnZAvTqZ3/2Z6szv/u7v1udaf3/8XnOl6GeuwyZL1/5yleariVfvCIfAAAAAAC6psgHAAAAAICOKfIBAAAAAKBjinwAAAAAAOiYIh8AAAAAADqmyAcAAAAAgI4p8gEAAAAAoGOKfAAAAAAA6JgiHwAAAAAAOrYw9gIs7aCD2v6O5bLLLqvOHHPMMdWZxx57rOm87373u9WZRx99tDqzuLjYdF6LhYW2L+MTTjihOnPOOedUZ9avX9903kMPPVSd2bJlS9O1AIbSmi9vfOMbqzND5st9991XnZEve7XkS8sMwFB6fe7Ski0/+tGPqjNjZMvxxx9fnfm5n/u56oxsAebZkPly1FFHVWfWQr4cd9xx1ZlZ54turJ1X5AMAAAAAQMcU+QAAAAAA0DFFPgAAAAAAdEyRDwAAAAAAHVPkAwAAAABAxxT5AAAAAADQMUU+AAAAAAB0TJEPAAAAAAAdWxh7AZZ2yCGHNM396q/+anVmYaH+21xKaTrv7/7u76ozu3btGuy8zBxkJiLi53/+56szRxxxRHXmiSeeaDrvXe96V3Vm9+7dTdcCGMqhhx7aNPeqV72qOjNkvvz93/99dWae8+XZz352daY1X/7wD/+wOiNfgFlqzZZf+ZVfqc7Ilr1kC0C/+aIbGzZfWq+FV+QDAAAAAEDXqkV+Zn48M3dk5p373LYxM2/IzPsmP26Y7poArDbyBYBpkC8ADE22AD1oeUX+NRHxiifd9s6IuLGUclpE3Dj5OQA8FdeEfAFgeNeEfAFgWNeEbAFGVi3ySylfioidT7r5VRFx7eTjayPi1wbeC4BVTr4AMA3yBYChyRagBwf6zW6PLqVsnXy8LSKOXm4wMy+NiEsP8BwA1hb5AsA0NOWLbAHgKfDcBZipAy3yf6qUUjJz2W+zXEq5OiKujojY3xwA7Eu+ADAN+8sX2QLAgfDcBZiFlvfIX8r2zNwUETH5ccdwKwGwhskXAKZBvgAwNNkCzNSBFvmfi4hLJh9fEhF/O8w6AKxx8gWAaZAvAAxNtgAzVX1rncz864i4ICKOyMyHIuI9EXFFRHwqM387Ih6IiNdNc8m1aPPmzU1zxxxzTHWmlPq/2rrjjjuazvvmN79ZndmzZ0/TtVq07L5+/fqma/36r/96dWZhof5uU9/5zneazrv55pub5mCtki/jeMELXtA0N+t8aZmbdb60ZEJEW7487WlPq87827/9W9N5X/3qV5vmYK2SL7N37rnnNs157tKeLa95zWuqM0Nmy1e+8pWmOVirZMs4WvPl6KOX/fYEP9XyGP2v//qvTefN83OX1772tdUZ+dKv6u9yKeWiZT710oF3AWANkS8ATIN8AWBosgXowYG+tQ4AAAAAADADinwAAAAAAOiYIh8AAAAAADqmyAcAAAAAgI4p8gEAAAAAoGOKfAAAAAAA6JgiHwAAAAAAOqbIBwAAAACAji2MvQBL++Vf/uWmuXXr1lVndu3aVZ35i7/4i6bzHnvssaa5WTruuOOa5k4++eTqzOLiYnXmU5/6VNN5Pd5XAK35ctBB9b/rX+35cuyxxzbNPec5z6nOyBdgNZt1tvz5n/9503kt15q11mzx3AUg4hWveEXT3Kyfu8xzvgz13OVv/uZvms6TL8PyinwAAAAAAOiYIh8AAAAAADqmyAcAAAAAgI4p8gEAAAAAoGOKfAAAAAAA6JgiHwAAAAAAOqbIBwAAAACAjinyAQAAAACgYwtjL7AWrVu3rjpz2mmnNV2rlFKdeeyxx6oz3/jGNwY7b0jr16+vzrzmNa9putaznvWs6kzLfXXbbbc1nTfr+wqgJV9OOeWUpmvJl4jXve51TdeSL8Bq1mO23HrrrYOdN6SWbHnta1/bdK0NGzZUZ2QLMM+GzJcW8mWvofKl1/tqtfOKfAAAAAAA6JgiHwAAAAAAOqbIBwAAAACAjinyAQAAAACgY4p8AAAAAADomCIfAAAAAAA6psgHAAAAAICOKfIBAAAAAKBjC2MvsBYddFD9708ys+lai4uL1ZlSSnXmwgsvbDrvP//zP6szDz/8cHVm/fr1Tee99KUvrc78zu/8TtO1Dj744OrMtm3bqjM7duxoOq/l97nl9y+i7fcQoOVxp2UmYvb58sgjj1Rndu7cWZ2Z53zZvn1703nyBZilHrPl5S9/edN5s86WX/qlX6rOvPGNb2y6lmwBVrsh82XPnj3VGfmyl3yZb16RDwAAAAAAHVPkAwAAAABAxxT5AAAAAADQMUU+AAAAAAB0TJEPAAAAAAAdU+QDAAAAAEDHFPkAAAAAANAxRT4AAAAAAHRMkQ8AAAAAAB1bGHuBtWhxcbE68/3vf7/pWrt27arOHHLIIdWZ973vfU3nveMd76jObN26tTqzY8eOpvNe8IIXVGeOOuqopmvt2bOnOnPXXXdVZ7Zs2dJ0Xsvvcyml6VoALVZ7vmzbtq06s3379qbz5AtAm5bHnAceeKDpWi3Zcuihh1Zn/uiP/qjpvLe//e3VGdmyl2wBZq3HfJn1c5eWmQj5wv/jFfkAAAAAANCxapGfmR/PzB2Zeec+t703M7dk5u2T/1453TUBWG3kCwBDky0ATIN8AXrQ8or8ayLiFUvcfmUp5ezJf58fdi0A1oBrQr4AMKxrQrYAMLxrQr4AI6sW+aWUL0XEzhnsAsAaIl8AGJpsAWAa5AvQg5W8R/5bMvObk39etGG5ocy8NDNvycxbVnAWAGuHfAFgaLIFgGmQL8DMHGiR/5GIOCUizo6IrRHxweUGSylXl1I2l1I2H+BZAKwd8gWAockWAKZBvgAzdUBFfilleyllTyllMSI+GhHnDrsWAGuRfAFgaLIFgGmQL8CsHVCRn5mb9vnpqyPizuVmAaCVfAFgaLIFgGmQL8CsLdQGMvOvI+KCiDgiMx+KiPdExAWZeXZElIi4PyIum+KOq86ePXuqM1dccUXTtUop1ZmLLrqoOnP44Yc3nbdp06bqTMu1Tj311KbzNm7cWJ3JzKZr7dxZ/740V111VXVm27ZtTee1/D7DWiZfhtfyuPPHf/zHTddaXFyszvSYL6ecckrTefIFVifZMjzZIlsA+TINLY8773//+5uutXv37urMb/7mb1ZnWvPlmGOOqc4cdthh1ZnnPOc5TefNOl+uvPLK6ox8GUe1yC+lLPV/Uh+bwi4ArCHyBYChyRYApkG+AD040G92CwAAAAAAzIAiHwAAAAAAOqbIBwAAAACAjinyAQAAAACgY4p8AAAAAADomCIfAAAAAAA6psgHAAAAAICOKfIBAAAAAKBjWUqZ3WGZsztsjVi/fn115qyzzqrOnHfeeU3nHXroodWZww47rDpz8cUXN513zDHHVGd2797ddK13v/vd1ZkPf/jD1Zkf//jHTefRrpSSY+/AfJMvw2vJl+c///nVmdZ8ackO+cJTJV9YCdkyvFlnyyGHHFKdOfzww6szl1xySdN5smXNuLWUsnnsJZhf8mV4Lfly5plnVmeG7MbmOV+uuuqq6sxjjz3WdB7tWp67eEU+AAAAAAB0TJEPAAAAAAAdU+QDAAAAAEDHFPkAAAAAANAxRT4AAAAAAHRMkQ8AAAAAAB1T5AMAAAAAQMcU+QAAAAAA0LEspczusMzZHcZTkplNc+vXr6/OnH766dWZG264oem8I444ojrzve99r+laF1xwQXXmwQcfrM7M8s/MWlFKafsChGXIl34NmS/Pfe5zqzOt+XLkkUdWZ+TL/JMvrIRs6dc8Z8v999/fdK2XvOQl1RnZMppbSymbx16C+SVf+iVf9pIv42h57uIV+QAAAAAA0DFFPgAAAAAAdEyRDwAAAAAAHVPkAwAAAABAxxT5AAAAAADQMUU+AAAAAAB0TJEPAAAAAAAdU+QDAAAAAEDHFsZegD6UUprm9uzZU505++yzqzMbNmxoOm9xcbE6c+211zZda9u2bdWZ1vsBgDZD5ss555xTndm4cWPTeS35ct111zVdS74AzNasn7vIFoC1Ych8Oeuss6ozQ+bLJz7xiaZryZf55hX5AAAAAADQMUU+AAAAAAB0TJEPAAAAAAAdU+QDAAAAAEDHFPkAAAAAANAxRT4AAAAAAHRMkQ8AAAAAAB1T5AMAAAAAQMcU+QAAAAAA0LGFsRdgvhx88MHVmcsuu6w6c9BBbX+H9PDDD1dnrr322qZrPf74401zAMxej/ly3XXXNV1LvgD0qcds8dwFYP615Mub3vSm6syQ+XLNNdc0XeuJJ55omqNPXpEPAAAAAAAdqxb5mXl8Zt6UmXdl5rcy862T2zdm5g2Zed/kxw3TXxeA1UK+ADA02QLANMgXoActr8jfHRF/UEo5PSL+W0S8OTNPj4h3RsSNpZTTIuLGyc8BoJV8AWBosgWAaZAvwOiqRX4pZWsp5bbJx49GxN0RcWxEvCoifvIGf9dGxK9Na0kAVh/5AsDQZAsA0yBfgB48pW92m5knRcQ5EfH1iDi6lLJ18qltEXH0Mr/m0oi49MBXBGC1ky8ADE22ADAN8gUYS/M3u83MQyPi0xHxtlLKI/t+rpRSIqIs9etKKVeXUjaXUjavaFMAViX5AsDQZAsA0yBfgDE1FfmZuT72PlBdX0r5zOTm7Zm5afL5TRGxYzorArBayRcAhiZbAJgG+QKMrVrkZ2ZGxMci4u5Syof2+dTnIuKSyceXRMTfDr8eAKuVfAFgaLIFgGmQL0APWt4j/7yIeENE3JGZt09ue1dEXBERn8rM346IByLiddNZkZ6cf/751ZkzzjijOrN79+6m82666abqzLZt25quBXRHvvBT5513XnVmyHz5p3/6p+rMv//7vzddC+iKbOGnXvjCF1ZnzjzzzOqMbAFCvrCPX/iFX6jODJkv//zP/1ydac2Xve8AxbyqFvmllP8TEbnMp1867DoArBXyBYChyRYApkG+AD1o/ma3AAAAAADA7CnyAQAAAACgY4p8AAAAAADomCIfAAAAAAA6psgHAAAAAICOKfIBAAAAAKBjinwAAAAAAOiYIh8AAAAAADq2MPYC9GFhoe1L4fLLL6/OPOMZz6jO7Nq1q+m8L37xi9WZJ554oulaAMzerPPl8ccfbzrvC1/4QnVGvgD0ad26dU1zs84Wz10A5pt8oXdekQ8AAAAAAB1T5AMAAAAAQMcU+QAAAAAA0DFFPgAAAAAAdEyRDwAAAAAAHVPkAwAAAABAxxT5AAAAAADQMUU+AAAAAAB0bGHsBejDs5/97Ka55z//+YOct3Pnzqa5m2++uTqzuLi40nUAmJLWfDnrrLMGOe+HP/xh09zXvva16ox8AehTr9niuQvAfNu4cWPT3Nlnnz3Iea358tWvfrU6I1/WBq/IBwAAAACAjinyAQAAAACgY4p8AAAAAADomCIfAAAAAAA6psgHAAAAAICOKfIBAAAAAKBjinwAAAAAAOiYIh8AAAAAADq2MPYC9OHEE08c7Fq7d++uztxzzz1N17r//vurM6WUpmsBMHvHH3/8YNdqyZd777236VryBWB+nXDCCU1zmVmdacmWb3/7203nyRaA+daaLy1a8uW+++5rupZ84Se8Ih8AAAAAADqmyAcAAAAAgI4p8gEAAAAAoGOKfAAAAAAA6JgiHwAAAAAAOqbIBwAAAACAjinyAQAAAACgY4p8AAAAAADomCIfAAAAAAA6lqWU2R2WObvDeEoWFhaa5k455ZTqzIUXXliduf7665vOe/jhh5vmmG+llBx7B+abfOnXkPny8pe/vDrzyU9+suk8+bI2yBdWQrb0S7YwsltLKZvHXoL5JV/6Net8ae3Gdu7c2TTHfGt57uIV+QAAAAAA0LFqkZ+Zx2fmTZl5V2Z+KzPfOrn9vZm5JTNvn/z3yumvC8BqIV8AGJpsAWAa5AvQg5Z/M7I7Iv6glHJbZh4WEbdm5g2Tz11ZSvnT6a0HwComXwAYmmwBYBrkCzC6apFfStkaEVsnHz+amXdHxLHTXgyA1U2+ADA02QLANMgXoAdP6T3yM/OkiDgnIr4+uektmfnNzPx4Zm5Y5tdcmpm3ZOYtK9oUgFVLvgAwNNkCwDTIF2AszUV+Zh4aEZ+OiLeVUh6JiI9ExCkRcXbs/VvJDy7160opV5dSNvuu7gAsRb4AMDTZAsA0yBdgTE1Ffmauj70PVNeXUj4TEVFK2V5K2VNKWYyIj0bEudNbE4DVSL4AMDTZAsA0yBdgbNUiPzMzIj4WEXeXUj60z+2b9hl7dUTcOfx6AKxW8gWAockWAKZBvgA9yFLK/gcyz4+IL0fEHRGxOLn5XRFxUez9p0MlIu6PiMsm3/xjf9fa/2HAmlRKybF3YPbkCzBt8mXtkS3ADNzq7VHWHvkCTFvLc5dqkT8kD1bAUhQtrJR8AZYiX1gJ2QIsQ5HPisgXYCktz12av9ktAAAAAAAwe4p8AAAAAADomCIfAAAAAAA6psgHAAAAAICOKfIBAAAAAKBjinwAAAAAAOiYIh8AAAAAADqmyAcAAAAAgI4p8gEAAAAAoGOKfAAAAAAA6JgiHwAAAAAAOqbIBwAAAACAjinyAQAAAACgY4p8AAAAAADomCIfAAAAAAA6psgHAAAAAICOKfIBAAAAAKBjCzM+7wcR8cCTbjticvu8mde9I+w+Frsv7cQpXZe15cn54s/bOOw+DrsvTb6wUqvpuUuE3ccwr3tH2H1/5Asr5blLH+w+DrsvrSlbspQypfPbZOYtpZTNoy5xAOZ17wi7j8XuMDvz/DVr93HYfRzzvDtr0zx/zdp99uZ17wi7wyzN89es3cdh93H0sLu31gEAAAAAgI4p8gEAAAAAoGM9FPlXj73AAZrXvSPsPha7w+zM89es3cdh93HM8+6sTfP8NWv32ZvXvSPsDrM0z1+zdh+H3ccx+u6jv0c+AAAAAACwvB5ekQ8AAAAAACxDkQ8AAAAAAB0brcjPzFdk5r2Z+Z3MfOdYexyIzLw/M+/IzNsz85ax99mfzPx4Zu7IzDv3uW1jZt6QmfdNftww5o7LWWb392bmlsl9f3tmvnLMHZeTmcdn5k2ZeVdmfisz3zq5vev7fj97z8X9DhHyZVbky+zNa7ZEyBfmn2yZDdkyjnnNF9nCaiBfZkO+zN68ZktE3/kyynvkZ+a6iPh2RFwYEQ9FxDci4qJSyl0zX+YAZOb9L/HjYQAAIABJREFUEbG5lPKDsXepycwXR8SPIuK6UsoZk9s+EBE7SylXTIJiQynl8jH3XMoyu783In5USvnTMXerycxNEbGplHJbZh4W/5e9uw/Sq6zvBv77sRuIJQHCGEIg9KkgL1ItoDFgZRTbygDtDPYPbW0rONOZgEqrbWda29raP2qn81TBP2o7Q0cKj9p2tK2avviCtCOgtmPi2IIvvApCBsIw1BGVJCS5nj+yOCmzm3Oxe+77XGf385lhsnvvL+e65mRzvtzf3HvuiB0R8bqIeHM0fO4Ps+83xAjOO8iX6ZEv0zfWbImQL4ybbJke2TKMseaLbGHs5Mv0yJfpG2u2RLSdL0O9In9LRNxbSrm/lLI3Iv4uIi4faC/LWinl1oh44lkPXx4RN819fFMc/GZszgJ7H4VSyiOllK/MffxkRHwjIk6Oxs/9YfYNYyFfpkS+TN9YsyVCvjB6smVKZMswxpovsoVlQL5MiXyZvrFmS0Tb+TJUkX9yRDx0yOcPRyMnpFKJiM9m5o7M3Dr0ZhZhQynlkbmPH42IDUNuZhGuycz/nvvxouZ+BOfZMvPHIuK8iPjPGNG5f9a+I0Z23lmx5MuwRnONW8BornNjzZYI+cIoyZZhjeoaN49RXePGmi+yhZGSL8MazTVuAaO5zo01WyLayxdvdrs4F5ZSXhoRl0bE2+Z+zGWUysF7K03//kqL95cRcVpEnBsRj0TE+4bdzuFl5pqI+IeIeEcp5buHfq3lcz/Pvkd13mHE5MtwRnOdG2u2RMgXGIhsGc6ornFjzRfZAoORL8MZzXVurNkS0Wa+DFXk74yIUw75fNPcY6NQStk59+tjEfHxOPjjUGOya+5+T8/c9+mxgfdTrZSyq5Syv5RyICL+Kho+95m5Kg7+hf9IKeUf5x5u/tzPt+8xnXdWPPkyrOavcQsZy3VurNkSIV8YNdkyrFFc4+YzpmvcWPNFtjBy8mVYzV/jFjKW69xYsyWi3XwZqsj/ckScnpkvyMwjI+IXI2LbQHt5TjLz6Lk3OojMPDoiLo6IOw//u5qzLSKunPv4yoj45IB7eU6e+cs+5+ej0XOfmRkRH4yIb5RSrj3kS02f+4X2PZbzDiFfhtb0Ne5wxnCdG2u2RMgXRk+2DKv5a9xCxnKNG2u+yBaWAfkyrKavcYczhuvcWLMlou18yYM/xTB9mXlZRLw/ImYi4oZSynsG2chzlJmnxsF/aYyImI2Iv2l575n5txFxUUQ8PyJ2RcS7I+ITEfHRiPjRiHgwIt5QSmnujTMW2PtFcfBHWEpEPBARVx1yb61mZOaFEXFbRNwREQfmHv69OHhPrWbP/WH2/cYYwXmHCPkyLfJl+saaLRHyhfGTLdMhW4Yx1nyRLSwH8mU65Mv0jTVbItrOl8GKfAAAAAAAoJs3uwUAAAAAgIYp8gEAAAAAoGGKfAAAAAAAaJgiHwAAAAAAGqbIBwAAAACAhinyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhinwAAAAAAGiYIh8AAAAAABqmyAcAAAAAgIYp8gEAAAAAoGGKfAAAAAAAaJgiHwAAAAAAGqbIBwAAAACAhinyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhinwAAAAAAGiYIh8AAAAAABqmyAcAAAAAgIYp8gEAAAAAoGGKfAAAAAAAaJgiHwAAAAAAGqbIBwAAAACAhinyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhinwAAAAAAGjY7DQXy8wyzfWAcSil5NB7YNzkCzAf+cJSyBZgAY+XUtYPvQnGS74A86l57uIV+QAAAAB1Hhx6AwCsTEsq8jPzksy8KzPvzcx39rUpAFY2+QJA32QLAJMgX4BpWXSRn5kzEfGBiLg0Is6OiDdm5tl9bQyAlUm+ANA32QLAJMgXYJqW8or8LRFxbynl/lLK3oj4u4i4vJ9tAbCCyRcA+iZbAJgE+QJMzVKK/JMj4qFDPn947rH/JTO3Zub2zNy+hLUAWDnkCwB9ky0ATIJ8AaZmdtILlFKuj4jrI7wzNwD9kS8A9E22ADAJ8gXow1Jekb8zIk455PNNc48BwFLIFwD6JlsAmAT5AkzNUor8L0fE6Zn5gsw8MiJ+MSK29bMtAFYw+QJA32QLAJMgX4CpWfStdUop+zLzmoj4TETMRMQNpZSv9bYzAFYk+QJA32QLAJMgX4BpylKmd2su9wED5lNKyaH3wLjJF2A+8oWlkC3AAnaUUjYPvQnGS74A86l57rKUW+sAAAAAAAATpsgHAAAAAICGKfIBAAAAAKBhinwAAAAAAGiYIh8AAAAAABqmyAcAAAAAgIYp8gEAAAAAoGGKfAAAAAAAaJgiHwAAAAAAGqbIBwAAAACAhinyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhinwAAAAAAGiYIh8AAAAAABqmyAcAAAAAgIYp8gEAAAAAoGGKfAAAAAAAaJgiHwAAAAAAGqbIBwAAAACAhinyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhinwAAAAAAGiYIh8AAAAAABqmyAcAAAAAgIYp8gEAAAAAoGGKfAAAAAAAaJgiHwAAAAAAGqbIBwAAAACAhinyAQAAAACgYYp8AAAAAABo2OzQG6ANRx11VNXc6tWrO2d2797dObN3796q9UopVXN9mZ3t/iuxadOmqmNdfPHFnTP33HNP1bG++MUvds7s2bOn6lgA0yRfDpIvAP2RLQf1mS2vfe1rO2fuvffeqmPJFmCs5MtBMzMznTN9PneRL/W8Ih8AAAAAABq2pFfkZ+YDEfFkROyPiH2llM19bAqAlU2+ADAJ8gWAvskWYFr6uLXOa0opj/dwHAA4lHwBYBLkCwB9ky3AxLm1DgAAAAAANGypRX6JiM9m5o7M3DrfQGZuzcztmbl9iWsBsHLIFwAm4bD5IlsAWATPXYCpWOqtdS4spezMzBMi4ubM/GYp5dZDB0op10fE9RERmTndt1kGYKzkCwCTcNh8kS0ALILnLsBULOkV+aWUnXO/PhYRH4+ILX1sCoCVTb4AMAnyBYC+yRZgWhZd5Gfm0Zm59pmPI+LiiLizr40BsDLJFwAmQb4A0DfZAkzTUm6tsyEiPp6Zzxznb0opn+5lV1SbO/+Hdcwxx3TOvOpVr6par+ZYt9xyS+fM44/XvZn7gQMHquZqzM52f7tv2rSpc+baa6+tWu/UU0/tnPnEJz5Rdaxbb721ewiWD/nSgL7y5dWvfnXVejXH+tznPtc502q+nHTSSZ0z1113XdV6Nfmybdu2qmPJF1YY+TKwvrLloosuqlpv7dq1nTPLPVtqn7ucdtppnTOyBeYlWxow7XypOdbNN9/cOdNqvmzcuLFzpjZfXvjCF3bO/PM//3PVseTLEor8Usr9EXFOj3sBAPkCwETIFwD6JluAaVrSPfIBAAAAAIDJUuQDAAAAAEDDFPkAAAAAANAwRT4AAAAAADRMkQ8AAAAAAA1T5AMAAAAAQMMU+QAAAAAA0DBFPgAAAAAANGx26A2wNKtXr+6c+bVf+7XOmSuvvLJqvTvuuKNz5gtf+ELnTCmlar3auRqrVq3qnPnxH//xzpktW7ZUrbd///7OmbvvvrvqWAcOHKiaA+hLTb78+q//eufMFVdcUbVeTb7cfvvtnTOt5suLX/zizpnafKnJBPkCtKgmW97+9rd3zqyEbJmd7X6q/qIXvahz5vzzz69aryYP7rnnnt6OBdCnmnx5xzve0Tnzpje9qWq9mny57bbbOmdazZezzz67c6b2uUsNz13qeUU+AAAAAAA0TJEPAAAAAAANU+QDAAAAAEDDFPkAAAAAANAwRT4AAAAAADRMkQ8AAAAAAA1T5AMAAAAAQMMU+QAAAAAA0LDZoTfA0pxxxhmdM295y1s6Z4455piq9Xbs2NE584Mf/KDqWH2ZmZmpmlu3bl3nzBVXXNE5c+yxx1at9+STT3bO3H777VXHKqVUzQH05cwzz+ycufrqqztnVkK+HHfccZ0zNflSe66+//3vd8584QtfqDqWfAGmqa9sWbt2bdV627dv75xpNVtqnru8+c1v7pyRLcBKUJMvV111VefMtPOlz+vlEUfUvVa7r+cuNceJqDsPurF6XpEPAAAAAAANU+QDAAAAAEDDFPkAAAAAANAwRT4AAAAAADRMkQ8AAAAAAA1T5AMAAAAAQMMU+QAAAAAA0DBFPgAAAAAANEyRDwAAAAAADZsdegPM74gj6v6N5eqrr+6cOeGEEzpndu/eXbXePffc0znzve99r3PmwIEDVevVmJ2t+zbetGlT58zLXvayzplVq1ZVrbdz585eZgD6NDMzUzUnX/rNl82bN3fOHHnkkVXr3X333Z0zDz30UNWxAPpQmy1vectbOmfWr1/fObMSsuXkk0/unOkzW2rO1be//e2qYwH0pTZf3vrWt3bO9JkvNf8//uSTT3bOlFKq1qtR21WddNJJnTNbtmzpnJEvw/CKfAAAAAAAaJgiHwAAAAAAGqbIBwAAAACAhinyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhs0NvgPmtWbOmau7nfu7nOmdmZ7v/mEspVev90z/9U+fMnj17elsvM3uZiYg477zzOmfWr1/fOfP0009Xrff7v//7vR0LoC9HH3101dzP/uzPds70mS+f/OQnO2emnS+1XvrSl3bO1OTLvn37qtZ717ve1TkjX4Bpqn3uctlll3XOyJaDarLlhBNO6JypzRbPXYAW1ebLtJ+7bNu2rXNm7969va0nX3iGV+QDAAAAAEDDOov8zLwhMx/LzDsPeez4zLw5M++Z+3XdZLcJwHIjXwCYBPkCQN9kC9CCmlfk3xgRlzzrsXdGxC2llNMj4pa5zwHgubgx5AsA/bsx5AsA/boxZAswsM4iv5Rya0Q88ayHL4+Im+Y+vikiXtfzvgBY5uQLAJMgXwDom2wBWrDYN7vdUEp5ZO7jRyNiw0KDmbk1IrYuch0AVhb5AsAkVOWLbAHgOfDcBZiqxRb5P1RKKZm54Nssl1Kuj4jrIyIONwcAh5IvAEzC4fJFtgCwGJ67ANNQc4/8+ezKzI0REXO/PtbflgBYweQLAJMgXwDom2wBpmqxRf62iLhy7uMrI+KT/WwHgBVOvgAwCfIFgL7JFmCqOm+tk5l/GxEXRcTzM/PhiHh3RPxpRHw0M381Ih6MiDdMcpMr0fnnn181t2HDgrdg+6FSun9q67/+67+q1rvjjjs6Z/bv3191rBo1e5+Zmak61hve0P1teuSRR3bO3H///VXr3X777VVzsFLJl2FccMEFVXPTzpevfe1rnTPTzpfZ2bo7EL7+9a/vnJEvMD3yZfpky0GyBZYv2TKMV7ziFVVz69ev75yRLwf9wi/8QudMTb5861vfqlpPvvSr80+5lPLGBb700z3vBYAVRL4AMAnyBYC+yRagBYu9tQ4AAAAAADAFinwAAAAAAGiYIh8AAAAAABqmyAcAAAAAgIYp8gEAAAAAoGGKfAAAAAAAaJgiHwAAAAAAGqbIBwAAAACAhs0OvQHmd8kll1TNHXFE97/F7Nmzp3PmL/7iL6rWqznWtJ188slVc6eddlrnzIEDBzpnPvrRj1att3v37qo5gGmadr584AMfqFpvzPnywhe+sHOmJl8+9rGPVa331FNPVc0BTMull15aNSdbIk466aSqOdkCMP18+fM///Oq9eSLfBmKV+QDAAAAAEDDFPkAAAAAANAwRT4AAAAAADRMkQ8AAAAAAA1T5AMAAAAAQMMU+QAAAAAA0DBFPgAAAAAANEyRDwAAAAAADZsdegMr0czMTOfMaaed1tt6u3fv7pzZsWNH1bFKKUvdznOyatWqzpnXv/71Vcdat25d58yYzxVAi/myffv2qmNN+5o5O9v9v0B95suePXs6Z1o9V8DKVpMtp556am/ryZaDjj/++M4Z2QKMWYv50mrf02K+fPnLX65aT770yyvyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhinwAAAAAAGiYIh8AAAAAABqmyAcAAAAAgIbNDr2BlWhmZqZzJjOrjrV///7OmVJK58zFF19ctd53v/vdzpknnniic2bVqlVV6/3UT/1U58zWrVurjrV69erOmUcffbRzZteuXVXrHXFE97+THThwoOpYNX+GAC3myyWXXFK13t///d93zvSZL695zWs6Z+QLQJvZcumll1at97GPfaxzZtrZctVVV1UdS7YAy11NvtSquT7Jl4P6ypeamQj50jevyAcAAAAAgIYp8gEAAAAAoGGKfAAAAAAAaJgiHwAAAAAAGqbIBwAAAACAhinyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGzQ69gZVo//79nTMPPvhg1bH27NnTObNmzZrOmfe85z1V6/32b/9258yjjz7ay0xExMtf/vLOmRNOOKHqWDXn/etf/3rnzM6dO6vWO3DgQOdMKaXqWAA15EvErl27qtbbvHlz58y08+Xhhx+uWk++ANNUc4174IEHqo7VV7b88R//cdV6037uIlsA6vWZL7t37+6cGXO+1HRj69evrzqWbmzcvCIfAAAAAAAa1lnkZ+YNmflYZt55yGN/lJk7M/Orc/9dNtltArDcyBcA+iZbAJgE+QK0oOYV+TdGxCXzPH5dKeXcuf/+td9tAbAC3BjyBYB+3RiyBYD+3RjyBRhYZ5FfSrk1Ip6Ywl4AWEHkCwB9ky0ATIJ8AVqwlHvkX5OZ/z3340XrFhrKzK2ZuT0zty9hLQBWDvkCQN9kCwCTIF+AqVlskf+XEXFaRJwbEY9ExPsWGiylXF9K2VxK2bzItQBYOeQLAH2TLQBMgnwBpmpRRX4pZVcpZX8p5UBE/FVEbOl3WwCsRPIFgL7JFgAmQb4A07aoIj8zNx7y6c9HxJ0LzQJALfkCQN9kCwCTIF+AaZvtGsjMv42IiyLi+Zn5cES8OyIuysxzI6JExAMRcdUE97js7N+/v3PmT/7kT6qOtW/fvs6ZX/qlX+qcOeaYY6rWO/HEEztn1q5d2zlz6qmnVq13/PHHd85kZtWxnnii+31prrvuus6ZRx99tGq9mj9nWMnkS/9qrjvvec97qo61d+/ezplf/uVf7pw59thjq9aTLxG7du2qWk++wMJkS//GnC0bNmzonFmzZk3nzAte8IKq9WQLLF/ypX/LPV9qnru0mi/XXntt54x8GUZnkV9KeeM8D39wAnsBYAWRLwD0TbYAMAnyBWjBYt/sFgAAAAAAmAJFPgAAAAAANEyRDwAAAAAADVPkAwAAAABAwxT5AAAAAADQMEU+AAAAAAA0TJEPAAAAAAANU+QDAAAAAEDDspQyvcUyp7fYCrFq1arOmZe85CWdMz/5kz9Ztd7atWt7mXnzm99ctd6JJ57YObNv376qY/3hH/5h58z73//+zpndu3dXrUe9UkoOvQfGTb70b3Z2tnPmxS9+cefMhRdeWLWefJEvkyBfWArZ0r++suWVr3xl1XrHHHNM50yr2fLud7+7c+a6667rnJEtE7GjlLJ56E0wXvKlfy3my5o1azpnavNl48aNnTPyZfxqnrt4RT4AAAAAADRMkQ8AAAAAAA1T5AMAAAAAQMMU+QAAAAAA0DBFPgAAAAAANEyRDwAAAAAADVPkAwAAAABAwxT5AAAAAADQsCylTG+xzOktxnOSmVVzq1at6pw566yzOmc+97nPVa23fv36zpkHHnig6livfvWrO2ceeuihzplp/p1ZKUopdd+AsAD50q4x58uDDz5YdayafPn2t7/dOSNf+idfWArZ0q4+s+WMM87onPm3f/u3qvVky4qxo5SyeehNMF7ypV1jzpeaTIiIeNWrXtXLseRL/2qeu3hFPgAAAAAANEyRDwAAAAAADVPkAwAAAABAwxT5AAAAAADQMEU+AAAAAAA0TJEPAAAAAAANU+QDAAAAAEDDFPkAAAAAANCw2aE3QBtKKVVz+/fv75w599xzO2eOP/74qvUOHDjQOfPhD3+46liPPvpo50zteQCgTu11dd++fZ0z55xzTudMn/nyoQ99qOpYjzzySOeMfAHoT5/Zct5553XO9JktH/nIR6qOJVsApq/PfKnpxtatW1e1nm6MZ3hFPgAAAAAANEyRDwAAAAAADVPkAwAAAABAwxT5AAAAAADQMEU+AAAAAAA0TJEPAAAAAAANU+QDAAAAAEDDFPkAAAAAANAwRT4AAAAAADRsdugNMC5HHXVU58zVV1/dOXPEEXX/hvSd73ync+bGG2+sOtbTTz9dNQfA9K1evbpzRr4A8Fy0mC033HBD1bFkC0C7avLlqquu6pyZmZmpWq8mX/76r/+66lh79+6tmqNNXpEPAAAAAAAN6yzyM/OUzPz3zPx6Zn4tM98+9/jxmXlzZt4z9+u6yW8XgOVCvgDQN9kCwCTIF6AFNa/I3xcRv1VKOTsiLoiIt2Xm2RHxzoi4pZRyekTcMvc5ANSSLwD0TbYAMAnyBRhcZ5FfSnmklPKVuY+fjIhvRMTJEXF5RNw0N3ZTRLxuUpsEYPmRLwD0TbYAMAnyBWjBc3qz28z8sYg4LyL+MyI2lFIemfvSoxGxYYHfszUiti5+iwAsd/IFgL7JFgAmQb4AQ6l+s9vMXBMR/xAR7yilfPfQr5VSSkSU+X5fKeX6UsrmUsrmJe0UgGVJvgDQN9kCwCTIF2BIVUV+Zq6Kgxeqj5RS/nHu4V2ZuXHu6xsj4rHJbBGA5Uq+ANA32QLAJMgXYGidRX5mZkR8MCK+UUq59pAvbYuIK+c+vjIiPtn/9gBYruQLAH2TLQBMgnwBWlBzj/xXRsSbIuKOzPzq3GO/FxF/GhEfzcxfjYgHI+INk9kiLTn//PM7Z17ykpd0zuzbt69qvc9//vOdMzt37qw61sGfcgMaIl/4oZp8+Ymf+InOGfkCK55s4Ye2bNnSOdPnc5dbb721c0a2wGjJF37o5S9/eefMOeec0zlTmy+33XZb58zDDz9cdSz5Mm6dRX4p5faIyAW+/NP9bgeAlUK+ANA32QLAJMgXoAXVb3YLAAAAAABMnyIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhinwAAAAAAGiYIh8AAAAAABqmyAcAAAAAgIYp8gEAAAAAoGGzQ2+ANszMzFTN/e7v/m7nzPOe97zOmb1791at96lPfapz5umnn646FgDTV5svv/M7v9M502e+fPrTn+6ckS8AbeozW37kR36kc0a2AKwM8oXWeUU+AAAAAAA0TJEPAAAAAAANU+QDAAAAAEDDFPkAAAAAANAwRT4AAAAAADRMkQ8AAAAAAA1T5AMAAAAAQMMU+QAAAAAA0LDZoTdAG44//viqufPOO6+X9f7nf/6nau4//uM/OmcOHDiw1O0AMCHr1q2rmnvpS1/ay3ryBWD5q82Wl73sZb2sV5stX/rSlzpnZAtAu4477riquc2bN/ey3ne+852qOfnCM7wiHwAAAAAAGqbIBwAAAACAhinyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhinwAAAAAAGjY7NAboA2nnHJKb8fat29f58zdd99ddaz777+/c6aUUnUsAKZv06ZNVXOZ2TkjXwCImH623HPPPVXryRaAcWs1X+67777OGfmyMnhFPgAAAAAANEyRDwAAAAAADVPkAwAAAABAwxT5AAAAAADQMEU+AAAAAAA0TJEPAAAAAAANU+QDAAAAAEDDFPkAAAAAANAwRT4AAAAAADQsSynTWyxzeovxnMzOzlbNnXrqqZ0zl1xySefMhz/84ar1nnjiiao5xq2UkkPvgXGTL+2SLwxJvrAUsqVdsoWB7SilbB56E4yXfGlXn/ly6aWXds586EMfqlpPvqwMNc9dOl+Rn5mnZOa/Z+bXM/Nrmfn2ucf/KDN3ZuZX5/67rI9NA7AyyBcA+iZbAJgE+QK0oOafmvZFxG+VUr6SmWsjYkdm3jz3tetKKe+d3PYAWMbkCwB9ky0ATIJ8AQbXWeSXUh6JiEfmPn4yM78RESdPemMALG/yBYC+yRYAJkG+AC14Tm92m5k/FhHnRcR/zj10TWb+d2bekJnrFvg9WzNze2ZuX9JOAVi25AsAfZMtAEyCfAGGUl3kZ+aaiPiHiHhHKeW7EfGXEXFaRJwbB/9V8n3z/b5SyvWllM3eDAaA+cgXAPomWwCYBPkCDKmqyM/MVXHwQvWRUso/RkSUUnaVUvaXUg5ExF9FxJbJbROA5Ui+ANA32QLAJMgXYGidRX5mZkR8MCK+UUq59pDHNx4y9vMRcWf/2wNguZIvAPRNtgAwCfIFaEHnm91GxCsj4k0RcUdmfnXusd+LiDdm5rkRUSLigYi4aiI7BGC5ki8A9E22ADAJ8gUYXJZSprdY5vQWA0ajlJJD74Fxky/AfOQLSyFbgAXscJ9zlkK+APOpee5S/Wa3AAAAAADA9CnyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhinwAAAAAAGiYIh8AAAAAABqmyAcAAAAAgIYp8gEAAAAAoGGKfAAAAAAAaJgiHwAAAAAAGqbIBwAAAACAhinyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhs1Ne7/GIePBZjz1/7vGxGeu+I+x9KPY+v/8zoeOysjw7X/x9G4a9D8Pe5ydfWKrl9Nwlwt6HMNZ9R9j6Qj4jAAAgAElEQVT74cgXlspzlzbY+zDsfX5V2ZKllAmtXyczt5dSNg+6iUUY674j7H0o9g7TM+bvWXsfhr0PY8x7Z2Ua8/esvU/fWPcdYe8wTWP+nrX3Ydj7MFrYu1vrAAAAAABAwxT5AAAAAADQsBaK/OuH3sAijXXfEfY+FHuH6Rnz96y9D8PehzHmvbMyjfl71t6nb6z7jrB3mKYxf8/a+zDsfRiD733we+QDAAAAAAALa+EV+QAAAAAAwAIU+QAAAAAA0LDBivzMvCQz78rMezPznUPtYzEy84HMvCMzv5qZ24fez+Fk5g2Z+Vhm3nnIY8dn5s2Zec/cr+uG3ONCFtj7H2Xmzrlz/9XMvGzIPS4kM0/JzH/PzK9n5tcy8+1zjzd97g+z71Gcd4iQL9MiX6ZvrNkSIV8YP9kyHbJlGGPNF9nCciBfpkO+TN9YsyWi7XwZ5B75mTkTEXdHxGsj4uGI+HJEvLGU8vWpb2YRMvOBiNhcSnl86L10ycxXRcT3IuL/lVJePPfY/42IJ0opfzoXFOtKKb8z5D7ns8De/ygivldKee+Qe+uSmRsjYmMp5SuZuTYidkTE6yLizdHwuT/Mvt8QIzjvIF+mR75M31izJUK+MG6yZXpkyzDGmi+yhbGTL9MjX6ZvrNkS0Xa+DPWK/C0RcW8p5f5Syt6I+LuIuHygvSxrpZRbI+KJZz18eUTcNPfxTXHwm7E5C+x9FEopj5RSvjL38ZMR8Y2IODkaP/eH2TeMhXyZEvkyfWPNlgj5wujJlimRLcMYa77IFpYB+TIl8mX6xpotEW3ny1BF/skR8dAhnz8cjZyQSiUiPpuZOzJz69CbWYQNpZRH5j5+NCI2DLmZRbgmM/977seLmvsRnGfLzB+LiPMi4j9jROf+WfuOGNl5Z8WSL8MazTVuAaO5zo01WyLkC6MkW4Y1qmvcPEZ1jRtrvsgWRkq+DGs017gFjOY6N9ZsiWgvX7zZ7eJcWEp5aURcGhFvm/sxl1EqB++tNP37Ky3eX0bEaRFxbkQ8EhHvG3Y7h5eZayLiHyLiHaWU7x76tZbP/Tz7HtV5hxGTL8MZzXVurNkSIV9gILJlOKO6xo01X2QLDEa+DGc017mxZktEm/kyVJG/MyJOOeTzTXOPjUIpZefcr49FxMfj4I9Djcmuufs9PXPfp8cG3k+1UsquUsr+UsqBiPiraPjcZ+aqOPgX/iOllH+ce7j5cz/fvsd03lnx5Muwmr/GLWQs17mxZkuEfGHUZMuwRnGNm8+YrnFjzRfZwsjJl2E1f41byFiuc2PNloh282WoIv/LEXF6Zr4gM4+MiF+MiG0D7eU5ycyj597oIDLz6Ii4OCLuPPzvas62iLhy7uMrI+KTA+7lOXnmL/ucn49Gz31mZkR8MCK+UUq59pAvNX3uF9r3WM47hHwZWtPXuMMZw3VurNkSIV8YPdkyrOavcQsZyzVurPkiW1gG5Muwmr7GHc4YrnNjzZaItvMlD/4Uw/Rl5mUR8f6ImImIG0op7xlkI89RZp4aB/+lMSJiNiL+puW9Z+bfRsRFEfH8iNgVEe+OiE9ExEcj4kcj4sGIeEMppbk3zlhg7xfFwR9hKRHxQERcdci9tZqRmRdGxG0RcUdEHJh7+Pfi4D21mj33h9n3G2ME5x0i5Mu0yJfpG2u2RMgXxk+2TIdsGcZY80W2sBzIl+mQL9M31myJaDtfBivyAQAAAACAbt7sFgAAAAAAGqbIBwAAAACAhinyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhinwAAAAAAGiYIh8AAAAAABqmyAcAAAAAgIYp8gEAAAAAoGGKfAAAAAAAaJgiHwAAAAAAGqbIBwAAAACAhinyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhinwAAAAAAGiYIh8AAAAAABqmyAcAAAAAgIYp8gEAAAAAoGGKfAAAAAAAaJgiHwAAAAAAGqbIBwAAAACAhinyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhinwAAAAAAGiYIh8AAAAAABqmyAcAAAAAgIYp8gEAAAAAoGGz01wsM8s01wPGoZSSQ++BcZMvwHzkC0shW4AFPF5KWT/0Jhgv+QLMp+a5i1fkAwAAANR5cOgNALAyLanIz8xLMvOuzLw3M9/Z16YAWNnkCwB9ky0ATIJ8AaZl0UV+Zs5ExAci4tKIODsi3piZZ/e1MQBWJvkCQN9kCwCTIF+AaVrKK/K3RMS9pZT7Syl7I+LvIuLyfrYFwAomXwDom2wBYBLkCzA1SynyT46Ihw75/OG5x/6XzNyamdszc/sS1gJg5ZAvAPRNtgAwCfIFmJrZSS9QSrk+Iq6P8M7cAPRHvgDQN9kCwCTIF6APS3lF/s6IOOWQzzfNPQYASyFfAOibbAFgEuQLMDVLKfK/HBGnZ+YLMvPIiPjFiNjWz7YAWMHkCwB9ky0ATIJ8AaZm0bfWKaXsy8xrIuIzETETETeUUr7W284AWJHkCwB9ky0ATIJ8AaYpS5nerbncBwyYTyklh94D4yZfgPnIF5ZCtgAL2FFK2Tz0Jhgv+QLMp+a5y1JurQMAAAAAAEyYIh8AAAAAABqmyAcAAAAAgIYp8gEAAAAAoGGKfAAAAAAAaJgiHwAAAAAAGqbIBwAAAACAhinyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhinwAAAAAAGiYIh8AAAAAABqmyAcAAAAAgIYp8gEAAAAAoGGKfAAAAAAAaJgiHwAAAAAAGqbIBwAAAACAhinyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhinwAAAAAAGiYIh8AAAAAABqmyAcAAAAAgIYp8gEAAAAAoGGKfAAAAAAAaJgiHwAAAAAAGqbIBwAAAACAhinyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhs0NvgDYcddRRVXPPe97zOmeeeuqpzpm9e/dWrVdKqZrry8zMTOfMpk2bqo712te+tnPmvvvuqzrWF7/4xc6ZPXv2VB0LYJrky0E1+XLyySdXHasmX+6///6qY33pS1/qnNm9e3fVsQCmRbYcJFsA+rV69ere5pZ7vpx00klVx/qZn/mZzpkHHnig6ljyxSvyAQAAAACgaUt6RX5mPhART0bE/ojYV0rZ3MemAFjZ5AsAkyBfAOibbAGmpY9b67ymlPJ4D8cBgEPJFwAmQb4A0DfZAkycW+sAAAAAAEDDllrkl4j4bGbuyMyt8w1k5tbM3J6Z25e4FgArh3wBYBIOmy+yBYBF8NwFmIql3lrnwlLKzsw8ISJuzsxvllJuPXSglHJ9RFwfEZGZ032bZQDGSr4AMAmHzRfZAsAieO4CTMWSXpFfStk59+tjEfHxiNjSx6YAWNnkCwCTIF8A6JtsAaZl0UV+Zh6dmWuf+TgiLo6IO/vaGAArk3wBYBLkCwB9ky3ANC3l1jobIuLjmfnMcf6mlPLpXnZFtbnzf1jHHHNM58xrXvOaqvVqjvXZz362c+bxx+vezP3AgQNVczVmZ7u/3U888cTOmfe9731V651++umdM//yL/9Sdazbbrutag6WCfnSgJp8OfbYYztnavNl7dq1nTOt5svMzEznzMaNGztnavPljDPO6Jz513/916pjyRdWGPkysGlnS81zl8985jOdM7XZsn///s6ZmnMQUZctNc9d3vve91atd+aZZ3bOfOpTn6o6lmxhhZEtDZAv/ebLhg0bOmf+7M/+rGq9s846q3Om5lxFyJeIJRT5pZT7I+KcHvcCAPIFgImQLwD0TbYA07Ske+QDAAAAAACTpcgHAAAAAICGKfIBAAAAAKBhinwAAAAAAGiYIh8AAAAAABqmyAcAAAAAgIYp8gEAAAAAoGGKfAAAAAAAaNjs0BtgaVavXt058xu/8RudM29605uq1rvjjjs6Z2699dbOmVJK1Xq1czVmZ7u/3c8+++zOmfPPP7+P7URExN133101t3///t7WBKjRV778yq/8StV6Y86XVatWdc6cddZZnTMXXHBBH9uJCPkCtKnF5y6f//znO2f6zIzaY/WVLa94xSuq1qtx1113Vc3JFmDaavLlN3/zNztn+nzu0mq+1HRjNfnyyle+smq9Gp671POKfAAAAAAAaJgiHwAAAAAAGqbIBwAAAACAhinyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhs0NvgKU588wzO2euuuqqzpk1a9ZUrbd79+7OmR/84AedM6WUqvVqHHFE3b9HHXfccZ0zV1xxRS/Hiag7D7fffnvVsfo8XwA1XvSiF3XObN26tXOmz3z5/ve/3zkzRL4ce+yxnTNXXnll50yf+XLbbbdVHUu+ANM07Wx56qmnOmfGnC3Tfu4iW4BW9ZUvRx99dNV6y/25i3xpl1fkAwAAAABAwxT5AAAAAADQMEU+AAAAAAA0TJEPAAAAAAANU+QDAAAAAEDDFPkAAAAAANAwRT4AAAAAADRMkQ8AAAAAAA1T5AMAAAAAQMNmh94A85uZmamae9vb3tY58/znP79zZvfu3VXr3X333Z0zTz75ZOdMKaVqvRqzs3XfxieddFLnzJYtWzpnjjzyyKr17r333s6ZBx98sOpYAH2pzZe3vvWtnTPTzpfvfe97nTOt5sv555/fOSNfgLHq87nL+vXrO2eeeuqpqvXuuuuuzpkxZ8sFF1zQOVObLffdd1/njGwBpq02X6655prOmZrnLnv27Kla75vf/GbnjHw5qCZfvvWtb1UdC6/IBwAAAACApinyAQAAAACgYYp8AAAAAABomCIfAAAAAAAapsgHAAAAAICGKfIBAAAAAKBhinwAAAAAAGiYIh8AAAAAABo2O/QGmN+aNWuq5i677LLOmdnZ7j/mUkrVetu2beuc2bt3b2/rZWYvMxER5513XufMhg0bOmf27dtXtd673vWuzpmnn3666lgAfZEvB8kXgP7UZsull17aOTMzM9M5sxKy5dxzz+2cOfHEEztnZAswZmvXrq2a6ytf9u/fX7XemPPlnHPO6ZzZuHFj50xtvvzBH/xB54x8qecV+QAAAAAA0LDOIj8zb8jMxzLzzkMeOz4zb87Me+Z+XTfZbQKw3MgXACZBvgDQN9kCtKDmFfk3RsQlz3rsnRFxSynl9Ii4Ze5zAHgubgz5AkD/bgz5AkC/bgzZAgyss8gvpdwaEU886+HLI+KmuY9viojX9bwvAJY5+QLAJMgXAPomW4AWLPbNbjeUUh6Z+/jRiFjwHdwyc2tEbF3kOgCsLPIFgEmoyhfZAsBz4LkLMFWLLfJ/qJRSMnPBt1kupVwfEddHRBxuDgAOJV8A/n979xtrV13mC/x5OKeKIqlUKlSu94IESHCUqgVvAA3J5N4Amji+8A8qwTgJKphoMooT3+ALTczNKDdqYiJC9CoyAXVGX1z1GlDRxOi0iMqfzIBDQWr/BAjoRNva9ndfdDNpyDldv7Zrr/Vb53w+SdNz1n7O+j0sdtc3+zlrr808HC5fZAsAR8NrF2AINffIX8rOzNwQETH7e1d/LQGwiskXAOZBvgDQN9kCDOpoB/nfiYirZl9fFRHf7qcdAFY5+QLAPMgXAPomW4BBdd5aJzNvjYhLIuLkzHwsIq6PiE9FxG2Z+bcR8UhEvHWeTa5GF154YVXd+vXrO2tK6X7X1q9+9auq9e67777Omv3791ftq0ZN7wsLC1X7etvb3tZZ85znPKez5uGHH65a76677qqqg9VKvoyjNl9OPvnkzhr5cpB8gbbIl+FdfPHFVXVeuwyfLVu3bq1a78c//nFVHaxWsmUctfnitUt9vrz97W/vrOkzX370ox9V1VGnc5BfSrlimYf+uudeAFhF5AsA8yBfAOibbAFacLS31gEAAAAAAAZgkA8AAAAAAA0zyAcAAAAAgIYZ5AMAAAAAQMMM8gEAAAAAoGEG+QAAAAAA0DCDfAAAAAAAaJhBPgAAAAAANGxx7AZY2mWXXVZVd9xx3b+L2bNnT2fN5z//+ar1avY1tA0bNlTVnXXWWZ01Bw4c6Ky5/fbbq9b785//XFUHMKTLL7+8qq6vfPnc5z5Xtd6U8+Xss8/urJEvwEp26aWXVtUNnS179+6tqhtSbbacc845nTU12XLbbbdVrSdbgBYN/drls5/9bNV6LebLqaeeWlXXV7584xvfqFpPvvTLFfkAAAAAANAwg3wAAAAAAGiYQT4AAAAAADTMIB8AAAAAABpmkA8AAAAAAA0zyAcAAAAAgIYZ5AMAAAAAQMMM8gEAAAAAoGGLYzewGi0sLHTWnHHGGb2tt3v37s6aLVu2VO2rlHKs7RyRxcXup+hb3vKWqn2tW7eus2bPnj2dNZs3b65ab+hjBVCTLy972ct6W68mX+6+++6qfckX+QK0qSZbzjzzzKp91Zy/ZMtBsgVY6fqcjfWVL7/85S97W69PfebLi170os6amnz5xS9+UbWefOmXK/IBAAAAAKBhBvkAAAAAANAwg3wAAAAAAGiYQT4AAAAAADTMIB8AAAAAABpmkA8AAAAAAA0zyAcAAAAAgIYZ5AMAAAAAQMMWx25gNVpYWOhtXwcOHOhlP5dddllV3e23395Z8+STT3bWrFmzpmq9Sy65pLPmmmuuqdrX8ccf31mzY8eOzprt27dXrXfccd2/J6v9/1dKqaoDVjf5Il+eIV+AvsgW2fIM2QL0Sb70my/XXntt1b7ky7S5Ih8AAAAAABpmkA8AAAAAAA0zyAcAAAAAgIYZ5AMAAAAAQMMM8gEAAAAAoGEG+QAAAAAA0DCDfAAAAAAAaJhBPgAAAAAANMwgHwAAAAAAGrY4dgOr0f79+ztrHn300ap97d69u7PmhBNO6Kz5xCc+UbXedddd11mzY8eOXmoiIs4///zOmvXr11ftq+a433///Z0127Ztq1rvwIEDnTWllKp9AdSoOc9t3bq1al8t5svOnTs7a7Zv3161nnwBqNNntuzZs6ezpiZbPvnJT1atJ1tkC9CumvPcww8/XLWvFvNl165dnTW///3vq9aTLzzDFfkAAAAAANCwzkF+Zt6cmbsy895Dtn08M7dl5j2zP5fPt00AVhr5AkDfZAsA8yBfgBbUXJH/5Yi4dIntN5RSNs7+/N9+2wJgFfhyyBcA+vXlkC0A9O/LIV+AkXUO8kspd0XEkwP0AsAqIl8A6JtsAWAe5AvQgmO5R/4HMvPXs7cXnbRcUWZenZmbM3PzMawFwOohXwDom2wBYB7kCzCYox3kfyEizoyIjRGxPSI+vVxhKeWLpZRNpZRNR7kWAKuHfAGgb7IFgHmQL8CgjmqQX0rZWUrZX0o5EBE3RsQF/bYFwGokXwDom2wBYB7kCzC0oxrkZ+aGQ759c0Tcu1wtANSSLwD0TbYAMA/yBRhallIOX5B5a0RcEhEnR8TOiLh+9v3GiCgRsTUi3ltK2d65WObhF+M/nXrqqVV1H/7whztr3vWud3XWrF27tmq9hYWFzpo//elPnTX79u2rWm/dunWdNZlZta/HH3+8s6bmWN1xxx1V69X+NxJRSqn7n8iKIl/Gccopp1TVfeQjH+mskS8HyZd2yZfVR7aMozZbal67XHnllZ01qyFbnnjiic6ad77znZ01smUutrg9yuojX8YhXw4aOl/e8Y53dNbceeedVevJl3o1r10WK3ZyxRKbbzqqjgBgRr4A0DfZAsA8yBegBUf7YbcAAAAAAMAADPIBAAAAAKBhBvkAAAAAANAwg3wAAAAAAGiYQT4AAAAAADTMIB8AAAAAABpmkA8AAAAAAA0zyAcAAAAAgIZlKWW4xTKHW2yVWFxc7Kx5+ctf3llz4YUXVq23du3azpoTTzyxs+bd73531XobNmzorNm3b1/Vvq6//vrOmhtuuKGzZvfu3VXrUa+UkmP3wLTJl/7JF/myEsgXjoVs6V9Ntpx77rmdNRdddFHVejXZcsIJJ3TWvOc976laT7asGltKKZvGboLpki/9ky/yZSWoee3iinwAAAAAAGiYQT4AAAAAADTMIB8AAAAAABpmkA8AAAAAAA0zyAcAAAAAgIYZ5AMAAAAAQMMM8gEAAAAAoGEG+QAAAAAA0LAspQy3WOZwi3FEMrOqbs2aNZ01Z599dmfNnXfeWbXe+vXrO2seffTRqn29/vWv72VfQ/6bWS1KKXVPQFiGfGlXbb4sLi521pxzzjmdNa3myyOPPFK1L/olXzgWsqVdQ2fLHXfcUbXei1/84s6a3/3ud1X7et3rXtdZI1tGs6WUsmnsJpgu+dKuPvOlz9mYfFkdal67uCIfAAAAAAAaZpAPAAAAAAANM8gHAAAAAICGGeQDAAAAAEDDDPIBAAAAAKBhBvkAAAAAANAwg3wAAAAAAGiYQT4AAAAAADRscewGaEMppapu3759nTXnnXdeZ81JJ51UtV5NX7fcckvVvnbs2NHLegDUqz2v7t+/v7Nm6Hz5+te/XrWvmnwBoD99ZssrXvGKzpp169ZVrSdbAKatz3x55Stf2VnTZ77ceuutVfuSL9PminwAAAAAAGiYQT4AAAAAADTMIB8AAAAAABpmkA8AAAAAAA0zyAcAAAAAgIYZ5AMAAAAAQMMM8gEAAAAAoGEG+QAAAAAA0DCDfAAAAAAAaNji2A0wLccff3xnzfve977OmoWFhar1nnrqqc6am2++uWpfe/furaoDYHjPfe5zO2v6zJenn366s+amm26q2pd8AWhTTbZcc801nTV9ZsuXvvSlqn3JFoB21eTL+9///s6aPvPlxhtvrNqXfJm2zivyM/OlmfnDzLw/M+/LzA/Otq/LzB9k5oOzv0+af7sArBTyBYC+yRYA5kG+AC2oubXOvoj4u1LKuRHx3yPi2sw8NyL+PiLuKKWcFRF3zL4HgFryBYC+yRYA5kG+AKPrHOSXUraXUu6eff3HiHggIk6LiDdFxFdmZV+JiL+ZV5MArDzyBYC+yRYA5kG+AC04og+7zczTI+JVEfHziDillLJ99tCOiDil184AWDXkCwB9ky0AzIN8AcZS/WG3mfmCiPhmRHyolPKHzPzPx0opJTPLMj93dURcfayNArAyyRcA+iZbAJgH+QKMqeqK/MxcEwdPVLeUUr4127wzMzfMHt8QEbuW+tlSyhdLKZtKKZv6aBiAlUO+ANA32QLAPMgXYGydg/w8+OvFmyLigVLKZw556DsRcdXs66si4tv9twfASiVfAOibbAFgHuQL0IKaW+tcFBFXRsRvMvOe2baPRcSnIuK2zPzbiHgkIt46nxYBWKHkCwB9ky0AzIN8AUbXOcgvpfw0InKZh/+633Zo3aZN3e8CO++88zpr9u/fX7XeT37yk86axx57rGpfpSx5qzpgJPKFQ73mNa/prJEvQBfZwqGGzpaf/vSnnTXbtm2r2pdsgbbIFw716le/urNm48aNnTXyhSNVdY98AAAAAABgHAb5AAAAAADQMIN8AAAAAABomEE+AAAAAAA0zCAfAAAAAAAaZpAPAAAAAAANM8gHAAAAAICGGeQDAAAAAEDDDPIBAAAAAKBhi2M3QBsWFhaq6j760Y921jz/+c/vrNm7d2/Vet/73vc6a/7yl79U7QuA4bWaL9/97nc7a+QLQJuOO67uerSabHne857XWVObBzWvXWpzCoDh1ebLdddd11nTZ758//vf76yRL6uDK/IBAAAAAKBhBvkAAAAAANAwg3wAAAAAAGiYQT4AAAAAADTMIB8AAAAAABpmkA8AAAAAAA0zyAcAAAAAgIYZ5AMAAAAAQMMWx26ANrzwhS+sqtu0aVMv6z311FNVdT/72c86aw4cOHCs7QAwJ2vXrq2qu+CCC3pZT74ArHy1r13OP//8zprM7Kx5+umnq9aTLQDTVvva5bWvfW1njXxhHlyRDwAAAAAADTPIBwAAAACAhhnkAwAAAABAwwzyAQAAAACgYQb5AAAAAADQMIN8AAAAAABomEE+AAAAAAA0zCAfAAAAAAAatjh2A7ThtNNOq6rLzM6affv2ddY89NBDVev99re/7awppVTtC4DhveQlL6mqky8A1KrNluOO675urc9sqamTLQDtajVfHnzwwc4a+bI6uCIfAAAAAAAaZpAPAAAAAAANM8gHAAAAAICGGeQDAAAAAEDDDPIBAAAAAKBhBvkAAAAAANAwg3wAAAAAAGiYQT4AAAAAADTMIB8AAAAAABqWpZThFsscbjGOyOLiYlXd6aef3lnzhje8obPma1/7WtV6TzzxRFUd01ZKybF7YNrkS7sWFhaq6s4444zOmje+8Y2dNV/96ler1pMvq4N84VjIlnbJFka2pZSyaewmmC750i75wphqXrt0XpGfmS/NzB9m5v2ZeV9mfnC2/eOZuS0z75n9ubyPpgFYHeQLAH2TLQDMg3wBWlBzGfa+iPi7UsrdmXliRGzJzB/MHruhlPIP82sPgBVMvgDQN9kCwDzIF2B0nYP8Usr2iNg++/qPmflARJw278YAWNnkCwB9ky0AzIN8AVpwRB92m5mnR8SrIuLns00fyMxfZ+bNmXnSMj9zdWZuzszNx9QpACuWfAGgb7IFgHmQL8BYqgf5mfmCiPhmRHyolPKHiPhCRJwZERvj4G8lP73Uz5VSvlhK2eTDYABYinwBoG+yBYB5kC/AmKoG+Zm5Jg6eqG4ppXwrIqKUsrOUsr+UciAiboyIC+bXJgArkXwBoG+yBYB5kC/A2DoH+ZmZEXFTRDxQSvnMIds3HFL25oi4t//2AFip5AsAfZMtAMyDfAFa0PlhtxFxUURcGRG/yVccAdUAAAZmSURBVMx7Zts+FhFXZObGiCgRsTUi3juXDgFYqeQLAH2TLQDMg3wBRpellOEWyxxuMWAySik5dg9Mm3wBliJfOBayBVjGFvc551jIF2ApNa9dqj/sFgAAAAAAGJ5BPgAAAAAANMwgHwAAAAAAGmaQDwAAAAAADTPIBwAAAACAhhnkAwAAAABAwwzyAQAAAACgYQb5AAAAAADQMIN8AAAAAABomEE+AAAAAAA0zCAfAAAAAAAaZpAPAAAAAAANM8gHAAAAAICGGeQDAAAAAEDDDPIBAAAAAKBhBvkAAAAAANAwg3wAAAAAAGiYQT4AAAAAADRsceD1Ho+IR5617eTZ9qmZat8Reh+L3pf23+a0X1aXZ+eLf2/j0Ps49L40+cKxWkmvXSL0Poap9h2h98ORLxwrr13aoPdx6H1pVdmSpZQ5rV8nMzeXUjaN2sRRmGrfEXofi95hOFN+zup9HHofx5R7Z3Wa8nNW78Obat8ReochTfk5q/dx6H0cLfTu1joAAAAAANAwg3wAAAAAAGhYC4P8L47dwFGaat8Reh+L3mE4U37O6n0ceh/HlHtndZryc1bvw5tq3xF6hyFN+Tmr93HofRyj9z76PfIBAAAAAIDltXBFPgAAAAAAsAyDfAAAAAAAaNhog/zMvDQz/zUzH8rMvx+rj6ORmVsz8zeZeU9mbh67n8PJzJszc1dm3nvItnWZ+YPMfHD290lj9ricZXr/eGZumx37ezLz8jF7XE5mvjQzf5iZ92fmfZn5wdn2po/9YfqexHGHCPkyFPkyvKlmS4R8YfpkyzBkyzimmi+yhZVAvgxDvgxvqtkS0Xa+jHKP/MxciIh/i4j/ERGPRcS/RMQVpZT7B2/mKGTm1ojYVEp5fOxeumTm6yPiPyLi/5RS/mq27X9FxJOllE/NguKkUspHx+xzKcv0/vGI+I9Syj+M2VuXzNwQERtKKXdn5okRsSUi/iYi3h0NH/vD9P3WmMBxB/kyHPkyvKlmS4R8Ydpky3Bkyzimmi+yhamTL8ORL8ObarZEtJ0vY12Rf0FEPFRK+fdSyt6I+MeIeNNIvaxopZS7IuLJZ21+U0R8Zfb1V+Lgk7E5y/Q+CaWU7aWUu2df/zEiHoiI06LxY3+YvmEq5MtA5MvwppotEfKFyZMtA5Et45hqvsgWVgD5MhD5MrypZktE2/ky1iD/tIj43SHfPxaNHJBKJSL+X2Zuycyrx27mKJxSStk++3pHRJwyZjNH4QOZ+evZ24uaewvOs2Xm6RHxqoj4eUzo2D+r74iJHXdWLfkyrsmc45YxmfPcVLMlQr4wSbJlXJM6xy1hUue4qeaLbGGi5Mu4JnOOW8ZkznNTzZaI9vLFh90enYtLKa+OiMsi4trZ21wmqRy8t9Lw91c6el+IiDMjYmNEbI+IT4/bzuFl5gsi4psR8aFSyh8OfazlY79E35M67jBh8mU8kznPTTVbIuQLjES2jGdS57ip5otsgdHIl/FM5jw31WyJaDNfxhrkb4uIlx7y/X+ZbZuEUsq22d+7IuKf4uDboaZk5+x+T8/c92nXyP1UK6XsLKXsL6UciIgbo+Fjn5lr4uA/+FtKKd+abW7+2C/V95SOO6uefBlX8+e45UzlPDfVbImQL0yabBnXJM5xS5nSOW6q+SJbmDj5Mq7mz3HLmcp5bqrZEtFuvow1yP+XiDgrM8/IzOdExNsj4jsj9XJEMvOE2QcdRGaeEBH/MyLuPfxPNec7EXHV7OurIuLbI/ZyRJ75xz7z5mj02GdmRsRNEfFAKeUzhzzU9LFfru+pHHcI+TK2ps9xhzOF89xUsyVCvjB5smVczZ/jljOVc9xU80W2sALIl3E1fY47nCmc56aaLRFt50sefBfD8DLz8oj43xGxEBE3l1I+OUojRygzXxYHf9MYEbEYEV9vuffMvDUiLomIkyNiZ0RcHxH/HBG3RcR/jYhHIuKtpZTmPjhjmd4viYNvYSkRsTUi3nvIvbWakZkXR8RPIuI3EXFgtvljcfCeWs0e+8P0fUVM4LhDhHwZinwZ3lSzJUK+MH2yZRiyZRxTzRfZwkogX4YhX4Y31WyJaDtfRhvkAwAAAAAA3XzYLQAAAAAANMwgHwAAAAAAGmaQDwAAAAAADTPIBwAAAACAhhnkAwAAAABAwwzyAQAAAACgYQb5AAAAAADQsP8PEGtntTmOwGsAAAAASUVORK5CYII=\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 = 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": "markdown",
   "metadata": {},
   "source": [
    "### 3. Transitioning from one digit image to another digit image in the latent space and reconstructing images at regular intervals\n",
    "\n",
    "It is important to note that we have used the same value of epsilon to construct z from the images. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\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()"
   ]
  }
 ],
 "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
}