Autoencoder_PyTorch.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/jansoe/ANNet/blob/main/Autoencoder_PyTorch.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "941ca106",
      "metadata": {
        "id": "941ca106"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/jansoe/dl_workshop/blob/main/Autoencoderv2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "28e9bbf3",
      "metadata": {
        "id": "28e9bbf3"
      },
      "outputs": [],
      "source": [
        "import time\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from IPython import display"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "a41a2066",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "a41a2066",
        "outputId": "5929bd49-b739-4f94-b753-384f82de2124"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ],
      "source": [
        "# Importing necessary PyTorch module\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "\n",
        "from torchvision import datasets, transforms\n",
        "\n",
        "# Checking for GPU availability in PyTorch\n",
        "torch.cuda.is_available()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "5310a072",
      "metadata": {
        "id": "5310a072"
      },
      "source": [
        "# Autoencoder\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "e88dca44",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "e88dca44",
        "outputId": "448d65ef-b4fa-4085-e907-1a98ddc5ddc1"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz to /root/.pytorch/MNIST_data/MNIST/raw/train-images-idx3-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 9912422/9912422 [00:00<00:00, 225236399.34it/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting /root/.pytorch/MNIST_data/MNIST/raw/train-images-idx3-ubyte.gz to /root/.pytorch/MNIST_data/MNIST/raw\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz to /root/.pytorch/MNIST_data/MNIST/raw/train-labels-idx1-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 28881/28881 [00:00<00:00, 42593422.58it/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting /root/.pytorch/MNIST_data/MNIST/raw/train-labels-idx1-ubyte.gz to /root/.pytorch/MNIST_data/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz to /root/.pytorch/MNIST_data/MNIST/raw/t10k-images-idx3-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 1648877/1648877 [00:00<00:00, 69798266.08it/s]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting /root/.pytorch/MNIST_data/MNIST/raw/t10k-images-idx3-ubyte.gz to /root/.pytorch/MNIST_data/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz to /root/.pytorch/MNIST_data/MNIST/raw/t10k-labels-idx1-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 4542/4542 [00:00<00:00, 18282657.17it/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting /root/.pytorch/MNIST_data/MNIST/raw/t10k-labels-idx1-ubyte.gz to /root/.pytorch/MNIST_data/MNIST/raw\n",
            "\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\n"
          ]
        }
      ],
      "source": [
        "trainset = datasets.MNIST('~/.pytorch/MNIST_data/', download=True, train=True, transform=transforms.ToTensor())\n",
        "testset = datasets.MNIST('~/.pytorch/MNIST_data/', download=True, train=False, transform=transforms.ToTensor())"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Der MNIST-Datensatz besteht aus 60000 Trainingsbildern (und 10000 Testbildern)"
      ],
      "metadata": {
        "id": "c2-yY1--fQeP"
      },
      "id": "c2-yY1--fQeP"
    },
    {
      "cell_type": "code",
      "source": [
        "trainset"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mIqpsE_-eI4F",
        "outputId": "608081a9-7d2f-4397-e70a-1754e9447a5b"
      },
      "id": "mIqpsE_-eI4F",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Dataset MNIST\n",
              "    Number of datapoints: 60000\n",
              "    Root location: /root/.pytorch/MNIST_data/\n",
              "    Split: Train\n",
              "    StandardTransform\n",
              "Transform: ToTensor()"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "sample_idx = 7\n",
        "\n",
        "\n",
        "type(trainset[sample_idx])\n",
        "\n",
        "img = trainset[sample_idx][0]\n",
        "print(img.shape)\n",
        "\n",
        "label = trainset[sample_idx][1]\n",
        "print(label)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LBka3z9q3cUC",
        "outputId": "95118e51-cba2-4e82-c216-fa2028c6d298"
      },
      "id": "LBka3z9q3cUC",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "torch.Size([1, 28, 28])\n",
            "3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Jeder Datenpunkt besteht aus einem Bild und dem zugehoerigen Label"
      ],
      "metadata": {
        "id": "uytwecl-f_k_"
      },
      "id": "uytwecl-f_k_"
    },
    {
      "cell_type": "code",
      "source": [
        "sample_idx = 7\n",
        "_ = plt.imshow(trainset[sample_idx][0].squeeze(), cmap=plt.cm.gray)\n",
        "_ = plt.title(trainset[sample_idx][1])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 452
        },
        "id": "ihdjyLYveX15",
        "outputId": "1c0f7968-b504-48c5-81c5-2331ff2cb159"
      },
      "id": "ihdjyLYveX15",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "43c3e6c3",
      "metadata": {
        "id": "43c3e6c3"
      },
      "source": [
        "## Encoder\n",
        "\n",
        "The Encoder is similar to a classification network. Only there is no final classification head at the end."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "15538545",
      "metadata": {
        "id": "15538545"
      },
      "outputs": [],
      "source": [
        "class Encoder(nn.Module):\n",
        "    def __init__(self, latent_dim):\n",
        "        super(Encoder, self).__init__()\n",
        "        self.conv1 = nn.Conv2d(in_channels=1, out_channels=32, kernel_size=3, stride=2, padding=1)\n",
        "        self.conv2 = nn.Conv2d(in_channels=32, out_channels=64, kernel_size=3, stride=2, padding=1)\n",
        "        self.flatten = nn.Flatten()\n",
        "        self.fc = nn.Linear(in_features=64 * 7 * 7, out_features=latent_dim)\n",
        "\n",
        "    def forward(self, x):\n",
        "        x = F.relu(self.conv1(x))\n",
        "        x = F.relu(self.conv2(x))\n",
        "        x = self.flatten(x)\n",
        "        x = self.fc(x)\n",
        "        return x"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "encoder = Encoder(latent_dim = 8)"
      ],
      "metadata": {
        "id": "xc6U9RN_hBkq"
      },
      "id": "xc6U9RN_hBkq",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "id": "510d98cd",
      "metadata": {
        "id": "510d98cd"
      },
      "source": [
        "## Decoder"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "e4ec3496",
      "metadata": {
        "id": "e4ec3496"
      },
      "source": [
        "The Decoder is taking an input and reconstructing an image from this"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "48b9121a",
      "metadata": {
        "id": "48b9121a"
      },
      "outputs": [],
      "source": [
        "class Decoder(nn.Module):\n",
        "    def __init__(self, latent_dim):\n",
        "        super(Decoder, self).__init__()\n",
        "        self.fc = nn.Linear(latent_dim, 7 * 7 * 32)\n",
        "        self.conv_transpose1 = nn.ConvTranspose2d(32, 64, kernel_size=3, stride=2, padding=1, output_padding=1)\n",
        "        self.conv_transpose2 = nn.ConvTranspose2d(64, 32, kernel_size=3, stride=2, padding=1, output_padding=1)\n",
        "        self.conv_transpose3 = nn.ConvTranspose2d(32, 1, kernel_size=3, stride=1, padding=1)\n",
        "\n",
        "    def forward(self, x):\n",
        "        x = F.relu(self.fc(x))\n",
        "        x = x.view(-1, 32, 7, 7)  # Reshape to (batch_size, channels, height, width)\n",
        "        x = F.relu(self.conv_transpose1(x))\n",
        "        x = F.relu(self.conv_transpose2(x))\n",
        "        x = torch.sigmoid(self.conv_transpose3(x))\n",
        "        return x"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "decoder = Decoder(latent_dim = 8)"
      ],
      "metadata": {
        "id": "M230xHEphieE"
      },
      "id": "M230xHEphieE",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "id": "e6466ee3",
      "metadata": {
        "id": "e6466ee3"
      },
      "source": [
        "## Autoencoder\n",
        "\n",
        "Combining Encoder-Autoencoder\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "a8c7ee30",
      "metadata": {
        "id": "a8c7ee30"
      },
      "outputs": [],
      "source": [
        "class Autoencoder(nn.Module):\n",
        "    def __init__(self, encoder, decoder):\n",
        "        super(Autoencoder, self).__init__()\n",
        "        self.encoder = encoder\n",
        "        self.decoder = decoder\n",
        "\n",
        "    def forward(self, x):\n",
        "        encoded = self.encoder(x)\n",
        "        decoded = self.decoder(encoded)\n",
        "        return decoded"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "autoencoder = Autoencoder(encoder, decoder)"
      ],
      "metadata": {
        "id": "mAcv9o_EkSnl"
      },
      "id": "mAcv9o_EkSnl",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "0ca2979e",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0ca2979e",
        "outputId": "41544a26-f95c-4953-8e67-0dbc3a1de5b9"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Autoencoder(\n",
              "  (encoder): Encoder(\n",
              "    (conv1): Conv2d(1, 32, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1))\n",
              "    (conv2): Conv2d(32, 64, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1))\n",
              "    (flatten): Flatten(start_dim=1, end_dim=-1)\n",
              "    (fc): Linear(in_features=3136, out_features=8, bias=True)\n",
              "  )\n",
              "  (decoder): Decoder(\n",
              "    (fc): Linear(in_features=8, out_features=1568, bias=True)\n",
              "    (conv_transpose1): ConvTranspose2d(32, 64, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), output_padding=(1, 1))\n",
              "    (conv_transpose2): ConvTranspose2d(64, 32, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), output_padding=(1, 1))\n",
              "    (conv_transpose3): ConvTranspose2d(32, 1, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n",
              "  )\n",
              ")"
            ]
          },
          "metadata": {},
          "execution_count": 106
        }
      ],
      "source": [
        "autoencoder"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "e5106baa",
      "metadata": {
        "id": "e5106baa"
      },
      "source": [
        "initial model predictions"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "f411fed1",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 229
        },
        "id": "f411fed1",
        "outputId": "e05f392a-87b9-4839-cc69-3e95c2ec6ce3"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 2000x400 with 20 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAABiEAAAE/CAYAAAAg+mBzAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAACHqUlEQVR4nO3dd7xV1bnu8Rexi71iwS5gQUDUYAFBRAQr2LARTawxMbbkXI/HaDT2xIoxamzBjoAUURRBwAYq9o6IGkRRiNgr9797z3jex+wV3HOB+vv+N97P2Iu515pzjDHnYo+nydy5c+cGAAAAAAAAAABAI1tofh8AAAAAAAAAAAD4ceJLCAAAAAAAAAAAUAm+hAAAAAAAAAAAAJXgSwgAAAAAAAAAAFAJvoQAAAAAAAAAAACV4EsIAAAAAAAAAABQCb6EAAAAAAAAAAAAleBLCAAAAAAAAAAAUAm+hAAAAAAAAAAAAJXgSwgAAAAAAAAAAFAJvoQAAAAAAAAAAACV4EsIAAAAAAAAAABQCb6EAAAAAAAAAAAAleBLCAAAAAAAAAAAUAm+hAAAAAAAAAAAAJXgSwgAAAAAAAAAAFAJvoQAAAAAAAAAAACV4EsIAAAAAAAAAABQCb6EAAAAAAAAAAAAleBLCAAAAAAAAAAAUAm+hAAAAAAAAAAAAJXgSwgAAAAAAAAAAFCJhef3AQA/VhdeeGGqffbZZ6n2zDPPFO2BAwfW9PpHH3100e7YsWPqc/DBB9f0WgAAAAAAAABQBf4SAgAAAAAAAAAAVIIvIQAAAAAAAAAAQCX4EgIAAAAAAAAAAFSCLyEAAAAAAAAAAEAlmsydO3fu/D4I4Iduv/32S7U77rijrsewwQYbpNr999+fai1atKjH4eAn4JVXXkm1li1bptqll16aar/+9a8rOSYsuD755JOiffLJJ6c+V155Zap16NChaLuxde211/6eRwcAAADgp2r27Nmp9uabb87Ta7l7k4suuqhob7rppqnPRhttlGqbb775PB0DsCDiLyEAAAAAAAAAAEAl+BICAAAAAAAAAABUgi8hAAAAAAAAAABAJfgSAgAAAAAAAAAAVGLh+X0AwA+RBlF/nxDqVq1aFe0ePXqkPq+//nqqDR06tGi/9tprqc+AAQNS7ZRTTvlPDxGwJk+enGoLLZS/215jjTXqcThYwE2fPr1oX3311alP06ZNU+3xxx8v2sOGDUt9jj322O95dPihefLJJ1Otd+/eqfbGG2/U4Wj+vVGjRhXt1q1bpz5rrbVWvQ4HPxBurNt9991T7bLLLku1o48+umi7sRULnvfeey/V9t1331TbZpttUu2II44o2uuss06jHVdj+vDDD1Nt3LhxRdvdCy2yyCKVHROAH7/hw4cXbTfHjh07NtVeffXVefr3WrZsmWq6Jv3iiy9qeq1vv/12no4BWBDxlxAAAAAAAAAAAKASfAkBAAAAAAAAAAAqwZcQAAAAAAAAAACgEmRCAA3Q/cgjIgYPHtzgz2266aappjkOERErrbRS0W7WrFnq8+WXX6ba1ltvXbSffvrp1OeDDz5o8DiBefXUU0+lmjt/3T7t+HGbOXNmqvXr128+HAl+rO69995Uq3Vv3XrTuf/aa69NfW699dZ6HQ4WULpmO+aYY2r6uV//+tep9otf/KJoL7HEEvN+YKjM7Nmzi/Ymm2yS+rgMhVVXXTXVFsQMCHfs7du3T7X333+/aLt7rw033LDxDgz/sTlz5qTaf/3XfxXt559/PvW5//77U418D3wfU6ZMKdr9+/dPfa666qpU++yzz4r23LlzG/fAxMsvv1zp6wM/VPwlBAAAAAAAAAAAqARfQgAAAAAAAAAAgErwJQQAAAAAAAAAAKgEX0IAAAAAAAAAAIBKLLDB1AMHDky1q6++OtVWX331or344ounPgceeGCqrbbaaqm2wQYb/CeHiJ+Id955J9U0yMiFULvQzObNm8/TMVx44YWp9uKLLzb4c7vuuus8/XuA8+yzzxbtyy67LPU55JBD6nU4WEBceumlqTZkyJBUmzRpUqP8e+PHj081Fy63+eabp1qnTp0a5RhQX19//XWq3X333fPhSOZNhw4divZf/vKX1OeTTz5JtaWWWqqyY8KCZ9y4cUX77bffrunn+vbtm2rufgjzl4YvR0Tsu+++RVvDySMifvWrX6WaW38tiM4666xUmzp1aqppiCwh1PPXgAEDUu3UU09NtTfffLPB13KB1iuuuOK8HRgQeW68+OKL58+B/C+tWrVKNfd8CD8er732Wqq5eX7w4MFFe+zYsanPQgvlvw046qijUm2bbbYp2j/UuZK/hAAAAAAAAAAAAJXgSwgAAAAAAAAAAFAJvoQAAAAAAAAAAACV4EsIAAAAAAAAAABQiSZzXZrjAmDddddNtTfeeKPRXn+ZZZZJtY033rjRXr+xrLXWWqn2u9/9LtU09BDVmjZtWtFeeumlU58VVlih0f49F7CqIcHO6NGjU61Lly6Nckz46Rk4cGDR3meffVIfF7bUuXPnqg4JCwAXptW0adNGe/1vvvlmnl67RYsWqXb77bcX7S222GLeDwx1c99996Vajx49Uu33v/99qp199tmVHNN/QoOoTz755NRnxowZqbbyyitXdkyYv7744otU22677Yr2448/XtNruZD2XXbZZd4ODJUZNWpUqrlxTL377ruptqCODc8991zR3myzzVKfvfbaK9VuuOGGou3uq1ANDfmNiGjXrl2qucDVJk2aNPj6+++/f6pdfvnlRbsx75mxYNLzx4VJ6xwY4cfIRx55pGj37Nkz9WnWrFmqffzxx0V75513Tn1cmPTWW2+danqNLLHEEqnPUkstlWr4YXDP2fr371+0Bw0alPrMnDmzsmOKiFhkkUWKdsuWLVMfdx1dcsklRXvRRRdt3AP7D/GXEAAAAAAAAAAAoBJ8CQEAAAAAAAAAACrBlxAAAAAAAAAAAKASC8/vA/gu11xzTao9/fTTqaY5Di+88ELqM3ny5FRz+5Y/+uijRdvtJ/3mm2+mWi10/66IiJVWWinV3nnnnX97TBE+J4JMiPpae+21K3vtCy64INVeeeWVBn/O7VfoasC8Ov/884v2Ouusk/owFv24uX1XXbSU5jh8HzpXuj1WNacnImLq1KmptuWWWxbtb7/99nseHaqge7G6PaU32GCDVDvllFMqO6bvY+jQofP7ELCAeeaZZ1KtlgwIdz9B/sOC57333ku1O++8s8Gfu/baa1Pth5L/EBGx0047NfhzvXv3TjUyIOafCy+8MNU++OCDRnv9W2+9NdVGjhxZtE899dTU59e//nWqze99zFGbTz75JNV0bHDP9YYMGVLT63fs2LFou2d97h5Vn+OtueaaqY/LucOPh1t7adZDRMRtt92Wah9++GGDr+/Oqe23375ou3PTPf9zuYWPPfZY0XZjtcsJ03zZo446KvWpJ64yAAAAAAAAAABQCb6EAAAAAAAAAAAAleBLCAAAAAAAAAAAUAm+hAAAAAAAAAAAAJVYYIOpd9xxx5pqqkePHjW9/uzZs1NNQ21cwOqkSZNqen212GKLpVrLli1TrVWrVkV71qxZqc/6668/T8eABdPw4cOL9mmnnZb6fPHFF6m26qqrFu1zzz039VlyySW/59Hhp+qNN95INR3/3BjmQoPxw/Xggw8W7Zdeein1adKkSao1bdp0nv49F5TVvXv3or3sssumPg888ECq/elPf2rw3/vrX/+aakcffXSDP4dq6Wf36aefpj4DBgxItWbNmlV2TLVy6za9jtw1g5+WwYMHz9PP6XiIBdOJJ56Yam7Mat++fdHeZ599KjumxjZhwoRUmzFjRtE+9NBDU5+DDjqosmNCw6ZNm1a0r7vuupp+ToNNI/K96H333VfTa2nAqwvHPvDAA1NttdVWq+n1UT9ffvllqh1wwAGppkHUp5xySurTrVu3eToGF/TrtGjRYp5eHz9cRx55ZNF2a6+ZM2fW9Fp6fm622Wapz9lnn51qiy++eIOv/cgjj6Sau0fVOfWpp55Kfdw4ecwxxxTtPn36pD4rr7xyQ4fZaPhLCAAAAAAAAAAAUAm+hAAAAAAAAAAAAJXgSwgAAAAAAAAAAFAJvoQAAAAAAAAAAACVWGCDqau2/PLLp1rXrl0b/LlawrFrdeedd6aaBma3adMm9dl///0b7Rgw/z3++ONF24VQO/vtt1/R7ty5c6MdE6BBqk49A4xQPRdGrvPN+++/P8+vr4Fwe++9d+rzhz/8IdWWXHLJBl977bXXTrW//e1vqabH/7vf/S71+fzzz1Pt2GOPLdqLLLJIg8eE2gwcODDV7r777qK9wQYbpD5bbrllZcf0fZx11lmppkHUO+ywQ+qz3HLLVXREWBCNGzeuwT6LLbZYqrnzCwseFz7vamussUbRXnTRRSs7plp99tlnqebCNvv3759q+jtee+21jXdgaBQaZDpnzpzUp1OnTqnm7gt0vXTzzTenPuecc06qvfbaa0VbA80jIvbYY49UGzlyZKqtsMIKqYbqfPzxx0XbjQ3Dhg1LNb1nPPnkk1OfWtb7QIS/Vzv//PNT7eqrry7ac+fOTX1WWWWVVDv66KNTTc/ZpZZaqsHjrNUHH3yQal9//XWqnXHGGUV75513Tn3c/fyChr+EAAAAAAAAAAAAleBLCAAAAAAAAAAAUAm+hAAAAAAAAAAAAJXgSwgAAAAAAAAAAFCJn2wwdb299957qXbMMcekmoalnHbaaakPAUw/XHvuuWeq3XvvvQ3+XL9+/VKNcEJU6Zlnnmmwjwv1xQ/XV199lWrzGkTtQg1vu+22or3SSivN02s7Lpj6lFNOSbUTTjihaH/yySepjzuvd99996K9/vrr/6eHiO9wxx13pJp+Li4gbkHgwt9cMOfCC5fL7VNPPTX1Iez8x+vhhx9OtYceeqjBn3MhnW3btm2MQ8ICYvjw4UW7e/fuqY8LrW/MMXHs2LH/th0R8eijj9b0Wvvss08jHBGq9MUXXxRtF5h+/PHH1/Raiy++eNE+7LDDUp+BAwem2pQpU4q2C4t149+CENz+UzdkyJCife6556Y+bk0+fvz4or3ssss26nHhp8XNUxdccEGq6diyxhprpD6DBg1Kta222mreD0588803Rfutt95KfQ455JBU69WrV6rNnj17no7h4IMPLtpuXVFP/CUEAAAAAAAAAACoBF9CAAAAAAAAAACASvAlBAAAAAAAAAAAqASZEHXSv3//VHM5Ebo/V8uWLas6JFTsnXfeSTW3L7DuzbnyyiunPm7/6GbNmn2PowP+v0ceeSTVrrvuulRr165d0d5pp50qOyb8cGy55Zap5s6fxsyAqIXmOERE3HTTTUV74sSJ9TocRMSHH36YarXsNe4ytBYEV111VarNnDkz1TbeeOOi3bVr18qOCQueSZMmzdPPLajnPRp23HHHpdoDDzyQatOnTy/aDz74YOrj9su/6667vsfR/fvXdxkBjstGOvvssxvlmFCdW265pcE+I0aMSDWXa1iLxx9/fJ5+7mc/+1mqce87/7lnGUrvFyMi1lxzzSoOBz9RX3/9dao1bdq0wZ9z+WuPPfZYqrksm5deeqnB119iiSVS7cUXX/y37Qh/jzxjxowG/z1n1VVXTTV9lji/c+j4SwgAAAAAAAAAAFAJvoQAAAAAAAAAAACV4EsIAAAAAAAAAABQCb6EAAAAAAAAAAAAlSCYugITJkxItXPPPbemn9WgsU033bRRjgn117t371R7//33G/y5Aw88MNVc+BvQWEaPHp1qs2fPTrUePXoU7cUXX7yyY8KC4Ztvvmmwjwv0WhC4MM9vv/22wT7ud/7DH/5QtAcMGPA9j+6n6Ysvvki1t99+O9X69u1bj8P53qZMmVJTP9ZyP221BrMut9xyRfuoo46q4GhQD1tssUWqPfvss6n21FNPFe177rkn9Tn//PNTbZVVVkm1fv36/QdH+P8dfPDBRbtNmzY1/dw222yTatyvLPh0fnUh55MmTUo1F8qq5/TgwYNTH3c/oWOd63PVVVelmp6rEREbb7xxqqE6LrBXjRw5MtXOOOOMor377runPi7QGnB23HHHVOvSpUuq3XfffUV72rRpqc9vfvObeTqGhRfOj9JdYHYtag2hXmih8m8I3PPGSy+9NNWaN28+T8dVFf4SAgAAAAAAAAAAVIIvIQAAAAAAAAAAQCX4EgIAAAAAAAAAAFSCLyEAAAAAAAAAAEAlmsx1qYz4Xk455ZRUO+ecc1KtW7duqXb33XcX7UUWWaTxDgyVGTp0aKrtu+++qfbll1+m2g477NDgazVr1mzeDw5owD777JNqLnhs0KBBRXuvvfaq7JhQfyeeeGKquXAr9dVXX1VxON/bZZddlmonnHBC0XYh1E2bNk01DWQkfHPefPbZZ6m23XbbpZoGu40ZMyb1WWGFFRrvwGrw3nvvpdpqq61W08/qdXTsscc2yjFhwTRhwoSi3blz59Tn22+/TbV11lmnaE+dOrVRjwtwXn/99aLt5re2bdum2qhRo1Jt5ZVXbrTjQjVmzZpVtN3n/eGHH6aae2TUpEmTBv+9nXbaKdX69+9ftHfdddfU55VXXkm1I444ItWuvPLKBo8BjUc/81rOAcettY866qhU23rrrVPtrbfeKtobbLBB6rPJJps0eAzPP/98qnXs2DHV1lxzzQZfCwumf/3rX0X73HPPTX0eeuihVFtxxRVTrUWLFkX7iy++SH2efvrpVHvssccaOsyaHX300UX77LPPTn2WW265Rvv3qsJfQgAAAAAAAAAAgErwJQQAAAAAAAAAAKgEX0IAAAAAAAAAAIBKLDy/D+DHQPc4vueee1KfxRZbLNXOOOOMVCMD4ofhgw8+KNpuPzaX/+DoPqvkP6BqM2bMKNrjx49PfVq1apVqZED8uA0fPnx+H0JNZs6cmWovvPBCqrlxuRYrrbRSqjE3N44lllgi1dxevppJ06tXr9RH8z2+j+eeey7VpkyZUrSnTZuW+tS6F/JCC/F/fn5KdI3o8h8ct3c6ULU//vGPRduNa+eff36qkf/ww6R5SnfccUfqs/fee6daLTkRv/nNb1Kf8847L9UWX3zxot27d+/Ux+Vp3nvvvammczWZXdU66aSTivaf//zneXodl8mmWSHfVavSKquskmqa3xkRceutt9bhaPB9aT6Cy4RoTIccckiq1ZIJscwyy6TaX/7yl1T7+c9/XrRdtsoPAXdFAAAAAAAAAACgEnwJAQAAAAAAAAAAKsGXEAAAAAAAAAAAoBJ8CQEAAAAAAAAAACpBMHUjuOCCC4r25MmTU59ddtkl1bbZZpvKjgnV0hCmiRMn1vRze+65Z6ppIBxQteuvv75ov/vuu6mPG7OABcGf/vSnVJvX4Lp11lkn1W644YZUa9GixTy9Php2+umnp5qGXbrQ9P3337/RjsEFrGo46/vvvz/Pr3/ooYfO88/ih0eD1R0NS4yIOPzwwys4GuD/cyHEOue5gMwVV1yxsmPC/NWtW7dUc2PYzTffnGo6jrl7Wg2hdv7nf/4n1V588cVUu+uuu1JN/023hkPj0WDffffdN/U58MADU+2rr74q2m+//Xbq48Kq6+29995LNTdubrrppkX71FNPreyYsGA6//zzU21eA8v/+te/ptoBBxwwT6/1Q8BfQgAAAAAAAAAAgErwJQQAAAAAAAAAAKgEX0IAAAAAAAAAAIBK8CUEAAAAAAAAAACoBMHU/yEXjnjmmWcW7WWXXTb1cYFL+OH6y1/+Mk8/58JTmzVr9n0PB/iPTJs2rcE+yy+/fB2OBGhYz549i/ZLL73UaK+98cYbp9r222/faK+PhrVu3TrVbr/99qI9efLk1GfKlCmNdgx77713g3369euXagMGDKjp9ZdYYon/+Jjww+DCNV2Aq1prrbVSbcstt2yUYwK+y8iRIxvs06tXr1Rr3759FYeDBZQLq3a1xuLmyP322y/VXDD1mDFjivasWbNSnxVWWOF7HB3+t6ZNmxZtN2+98sorDb7O6NGjU03DqyMiTj/99FSbOHFig6/fmObOnZtqTzzxRF2PAfPfNddcU7TPOuus1Medw0pDzSMi+vTpM+8H9gPEX0IAAAAAAAAAAIBK8CUEAAAAAAAAAACoBF9CAAAAAAAAAACASvAlBAAAAAAAAAAAqATB1P/GBx98kGq/+c1vUu3rr78u2hqiGRHRsWPHxjsw/GC5c2qRRRZplNd2gejutV1gzocfftjg68+ePTvVLrroohqPrqShVhER5513XtFecskl5+m10bBhw4Y12GfXXXetw5FgQeKC17755psGf66WoMuIiMMPP7xoT58+fZ6Oq0mTJjX9XC2GDx/eaK+F6rRr166mWpXWW2+9ef7ZZ599tmhvttlm3/dwsIB4+OGHU+3bb79t8Of22GOPKg4H+LfcfL3UUksV7ZNOOqlehwN8p3333TfVhg4dmmq33npr0b788stTn9NOO63xDgyNYscdd6yp31NPPZVqGkztnncceuihqab3Ie45xs0331zTceHHzYWfn3jiiUX7o48+qum1ll566aL917/+NfVZbLHF/oOj++HjLyEAAAAAAAAAAEAl+BICAAAAAAAAAABUgi8hAAAAAAAAAABAJciE+F907+sePXqkPlOnTk21DTbYoGifeeaZjXtg+NFo06ZNZa/t9s5s3rx5qr377ruppvtpzg+rrrpq0T711FPn05H8uIwfPz7V3DkAHH300an2u9/9rsGf69WrV6q53Jd56ROR5+Zaf8456qij5vln8dPmMlNczSED4sfLZX2plVdeOdWOO+64Kg4H+H+uvPLKVJsxY0aq6fq7ffv2lR0TUKuFFsr/V9atSYcMGVK0Tz/99NRn//33T7WNNtpono8N9dO9e/dUO+WUU4q2y7u86qqrUu3VV18t2mPHjp3n41pjjTXm+Wex4HP5mXPmzGnw5zRjKSJn2Wy33XbzfmA/EvwlBAAAAAAAAAAAqARfQgAAAAAAAAAAgErwJQQAAAAAAAAAAKgEX0IAAAAAAAAAAIBKEEz9v0yZMqVoP/744zX93F/+8peivf766zfaMWHB1LNnz6KtoVjzw+23395or7XIIoukmgsIU7vvvnuqdejQoaZ/k5CeagwePDjVvv7666Ldrl271Kdz586VHRMWTL179061888/v2i///779Tqc77TSSiulWuvWrVPt6quvTrXmzZtXckz48WvSpElNNfy0jBo1qsE+a621Vqotu+yyVRwO8P+4YGo3Zuk9jfPRRx+l2uzZs1OtRYsWNR4d8J9r27Ztqp155plF+6STTkp9/s//+T+pNmDAgKK9xBJLfL+DQyXc+n6//fYr2rfddltNrzVmzJgG+yy8cH482qtXr1Q777zzavo3seBz85ve/9bqoIMOSrUddthhnl7rx4y/hAAAAAAAAAAAAJXgSwgAAAAAAAAAAFAJvoQAAAAAAAAAAACV4EsIAAAAAAAAAABQiZ9sMPW0adNSrXv37g3+3IUXXphqu+66a6McE344Bg0aVLRdeM2XX345T6/9wgsvpNqtt946T6/1i1/8ItXWXnvtBn+uT58+qeaCobBg+fTTT1Nt5MiRDf7cPvvsk2pNmzZtlGPCD4cbGzTsbciQIanPxRdfXNERef/93/+dascee2xdjwE/PZ9//nlN/Qi3/PH66quvUu21115r8OfcObHIIos0yjEB35cGsWpgb0TERRddlGqbbrppqt1www2Nd2BADQ455JCi/be//S310fv2iIhXX321aLdp06ZxDwyNws2fet/hgoWfeOKJVHv33XeL9jrrrJP66PkUEXH66af/+4PED8bHH3+cau4ZVy3P8TbffPNUq/c98Q8VfwkBAAAAAAAAAAAqwZcQAAAAAAAAAACgEnwJAQAAAAAAAAAAKtFk7ty5c+f3QcwPp5xySqqdc845Df7cpEmTUq1Dhw6NckwA8H24/ao7deqUaquuumrRvvnmm1OfJZdcsvEODD9q99xzT6pdddVVqTZs2LCivdtuu6U+Rx55ZKrpMmXjjTdOfVq0aNHgcQLfx2qrrZZqbsw97bTTUu24446r5JhQX998802qHX744al23XXXFe1+/fqlPtdff32jHRfgtG3bNtWeeeaZVNM5tkmTJqnPL3/5y1T7n//5n1Rba621/oMjBBrfm2++mWou86xv375F290L4YfrH//4R6o98sgjRdtlPayyyipVHRIWAEOHDk21PfbYY55ea/To0anWtWvXeXqtnxr+EgIAAAAAAAAAAFSCLyEAAAAAAAAAAEAl+BICAAAAAAAAAABUgi8hAAAAAAAAAABAJX4SwdTjx49PtV69eqXaRx991OBrEUwNAADw0+KC1I8//vhUI5Tup2X69Ompduqppxbt9u3bpz7HHntsZccERPj73z/84Q+p1qlTp6J99NFHpz7LL798qi266KLf4+iA+unevXuqPfzww0V74sSJqc/GG29c2TEBqL/NN9881Z555pmafvZ3v/td0T7vvPMa5Zh+ivhLCAAAAAAAAAAAUAm+hAAAAAAAAAAAAJXgSwgAAAAAAAAAAFAJvoQAAAAAAAAAAACV+EkEU59zzjmpdsoppzT4cxtssEGqDRs2LNVatWo1bwcGAAAAAACARjdnzpxU04DaSy65JPXZfffdKzsmAPW31lprpdrbb7+daqusskqqPfXUU0W7efPmjXZcPzX8JQQAAAAAAAAAAKgEX0IAAAAAAAAAAIBK8CUEAAAAAAAAAACoBF9CAAAAAAAAAACASiw8vw9gQdK2bduiPXr06NRnhRVWqNPRAAAAAAAAYF4ss8wyqTZ16tT5cCQA5qcTTjihptr//M//pBpB1I2Hv4QAAAAAAAAAAACV4EsIAAAAAAAAAABQCb6EAAAAAAAAAAAAlWgyd+7cufP7IAAAAAAAAAAAwI8PfwkBAAAAAAAAAAAqwZcQAAAAAAAAAACgEnwJAQAAAAAAAAAAKsGXEAAAAAAAAAAAoBJ8CQEAAAAAAAAAACrBlxAAAAAAAAAAAKASfAkBAAAAAAAAAAAqwZcQAAAAAAAAAACgEnwJAQAAAAAAAAAAKsGXEAAAAAAAAAAAoBJ8CQEAAAAAAAAAACrBlxAAAAAAAAAAAKASfAkBAAAAAAAAAAAqwZcQAAAAAAAAAACgEnwJAQAAAAAAAAAAKsGXEAAAAAAAAAAAoBJ8CQEAAAAAAAAAACrBlxAAAAAAAAAAAKASfAkBAAAAAAAAAAAqwZcQAAAAAAAAAACgEnwJAQAAAAAAAAAAKsGXEAAAAAAAAAAAoBJ8CQEAAAAAAAAAACrBlxAAAAAAAAAAAKASfAkBAAAAAAAAAAAqwZcQAAAAAAAAAACgEnwJAQAAAAAAAAAAKsGXEAAAAAAAAAAAoBJ8CQEAAAAAAAAAACrBlxAAAAAAAAAAAKASfAkBAAAAAAAAAAAqwZcQAAAAAAAAAACgEnwJAQAAAAAAAAAAKsGXEAAAAAAAAAAAoBJ8CQEAAAAAAAAAACrBlxAAAAAAAAAAAKASfAkBAAAAAAAAAAAqwZcQAAAAAAAAAACgEnwJAQAAAAAAAAAAKsGXEAAAAAAAAAAAoBJ8CQEAAAAAAAAAACqxcK0dzz///FR7//33i/bqq6+e+owbNy7VOnXqlA9k4fJQPvjgg9TnzTffTLUWLVoU7aWXXjr1+fzzz1NtkUUWSbVFF120aE+bNi31adasWaotu+yyRbtdu3apz1NPPZVqTz/9dKqtttpqRXvxxRdPfb788stUa9u2bdF+/vnnU59lllkm1T7++ONU++yzz4r2Yostlvr88Y9/TLUqXHDBBan2yiuvFO0NNtgg9Zk4cWKquc9lzTXXLNqjRo1KfX72s5+l2ksvvZQPtoHXjvCf+SabbFK03TnsPqcmTZoU7ZVWWin1cdfM3LlzU+2LL74o2t98802DfSIiOnfuXLQfffTR1Md9Pi+++GKq6b/prtsbbrgh1RrbWWedlWqzZ88u2m3atEl9Bg4cmGo77rhjqn377bf/9rUjIlZYYYVUe/fdd/PBCvfZfvTRR6m24oorFu2FFsrfR7vxQvutt956qY875x566KFUW3XVVYv2V199lfosscQSqabn3JgxYxp87YiIOXPmpNqnn35atN3YesUVV6RaFS699NJU03F84403Tn3uvffeVNt0001Tbd111y3azz77bOqz3HLLNXSY9hxr2rRpqs2aNSvVtthii6I9ZcqU1MfNN3ouus/X/T5uzNLPWK+FCH+ttWrVqmi/8cYbqc8666yTau531LFtqaWWSn0uvvjiVKvC2WefnWp6LbrxaPjw4amm71FEPu/cHOg+T/3s3DHoWiXCzxu6rnLnhTvv9PXXWmut1EfHkAh//uh87cZJt4bWa1nXPxH+HHZrhvfee69ou9/53HPPTbXG5taPOk+5sW7IkCGp1rVr11TTMcq9F27O037u/XFrI/f6unZ3Y6Qbb/U82XDDDVOft99+O9UeeOCBVNPzyV0v7hi22267oj169OjUZ4011kg1t5bR68O9f5dffnmqVcGd2/qeLL/88qnPI488kmrrr79+quma391DurFH7yHdeee4z1PvH/71r3+lPnq/HZHvf931N3PmzFR7+eWXU03vk93ay60vdaxz9wm13h9pzf3Obu5rbGeccUaq6edW63pG57GIfL66z8g9t9Dr0F2Xn3zySarp+BQRsfLKKzf4Wl9//XWDx7DRRhulPm4udeeTXlfuvse9D+3bty/ar7/+eurjztW33nor1XROce9VPc65CH8fq9wzgwcffDDVNttss1TTNev06dNTH/ecTT8XfYYX4e8F3Tim99JujnVr61rW367mzju9Rtw14+ZYnSteffXV1Mdd7+4Y9H1w71891nUREeecc06q6RpglVVWSX3cMwJ3P6FrXXcdunOlZcuWRdvd67txy9H52T2vdmPNkksuWbTdePfcc8/VVNN7TT0Hvoued24t6T4ffd4fkecx/f0iIs4888x/ezz8JQQAAAAAAAAAAKgEX0IAAAAAAAAAAIBK8CUEAAAAAAAAAACoRM2ZEG4faN0Hy+0J161bt1SbNGlSquleu27/Rs09iMj7UX744Yepzw477JBqTzzxRKrpXrtuf163n6fuxXXdddelPm7vr969e6eaZg288MILqY97H3QvVrcvstuXzu3TqPvBunyJenH7kOk+g25P5o4dO6aa26tv6NChRXvvvfdOfdzegJrx4c7XrbbaKtWaN2+eamPHji3abj8/3Qc/Iu8T585Xt5+w27f8rrvuKtpun7guXbqkmmZo6N6gEf7z0f35IvJ+8cOGDUt95hc9d9y+5nvuuWequXFGr033ubn3cfz48UV77bXXTn169uyZam5Pet2PXPcKj/Cfm74Pbj9Gl2NzyCGHpNr999/f4M+5fadHjBhRtN2+o24/Rnf963Xl9iCuFzd36bzo9obU8TrC72Grv5vLunHj2PXXX1+03T6yRx11VKq5fBi9blzmh9sDWPf4dHt3uuwZd43o3ulTp05Nfdx8rft26x7aEf68c/v1ay6WyyKqF/deas3teerWdm6s0blSM5Ai/B6kOi+6fdLdPO/OO92r1J1jbj9TfR9cJoHLOHNrzjvvvLNou9/Z5UjpvvJuT2D3Wm5c3GabbYq2+7zqweUx6PjsxuLddtst1dz6VF/L5Ym481DnFpd5pO9hhF8v6Tnm8hLctad7Zrvxye2Lf+CBB6aarhncPYBbf9xzzz1F280L7np094m6bnRz2Pyk93Quq8XNsZMnT041/TzdfOByZV577bWi7fY233bbbVPtmWeeSTUdH9w9q6PjxU033ZT6uFw9dz08+eSTRdvtv+3WEXq/V+v+6m7tqJkWteT4VcHdY+s9pbu+3Pg0Y8aMVNM1uNtj393D6rnj1owu087tXa/njp7PEX5u07FO7wki/Dnn1me1fL6aTxWR16Tueqn1OtZ52OWl1IubW3TN6tZBLmPpn//8Z6rpZ+zW2q1bt041HRvca7ssAHd/pPO62xfffZ46Xrjz1eXq6TOKCL/eVG5t6e65lTt2N/fr8wKXC1Mv7p5OPzs9ByL8c02Xz6JjhntvO3TokGp6P+HmHzfHujxfvR9y848bq3Xc0vVmhF/L9+rVK9U0k9A9r3H5VjoGuLW44+47dtppp6I9L8+K+UsIAAAAAAAAAABQCb6EAAAAAAAAAAAAleBLCAAAAAAAAAAAUImaMyHcPl+zZs0q2rvvvnvqo3uLRkSsttpqqaZ7qrp96TSzISLvmeb203J77H/88ceppntI6t5jEX5PuEGDBhVt3Ts6wu9b5jI0xowZU7TbtGmT+ri98XSPMrfXrzt2d6y6Z6vLZaiXzTbbLNX0PXKfk9t/0u2zqvvhuj0p3X6axxxzTNEeOHBg6uP25dPshYi8f53b283tH6h7DLt9Dd0eiW6fVb22XHaF27dc9010e9DpHuwRtV1Hbs/1enB7JOt77fYW1X3rI/z1pfsmu4wO3cs5IuLggw8u2m7/vccffzzV3Lmjv6Pbk9a9/zpOu8/bXS9uH2jdw9VlFDz77LOppvuzunHU7V/oMlr0vXGvVS/unNJcFLdnpdvT0f0eet65vX3dftiaXaTzfoTfv/2dd95JNZ2f3d6gbj/9++67r2i7vWzdPO/2NHb7aCs3p+h74+ZFd1xuT+N77723wX+vXtw1rPOUy0py86lb5+ge3m6N9thjj6Wa7n3r8mHc++b2Qtb1q9vP3u3BrRkQbh3s9n12c6zOD27cd9eW7j3txkS3v637fPScdeNkPbj9tPVYaukT4T8TXd+7/YbdukTPc/deu/sQN9atuuqqqaZcbofu9evWEG5udus/Pdb27dunPm4vdd3j2M0Lbq97vYeKyGOiGyPrxb1vmrvXvXv31Mft7+w+F31P3P78bt2mc7jLBHP3rG7dpuO5mxfd648cObJou/PX3U+4PBTdy9vtr+4yUvR6cK/txoUmTZqkmp77bkyuB3ee6DXuPkc3T7r98/XccetB/fci8nzq7jtdJqXLfdEx2K0p3Fin44qbE12eiFt76RjsciPcGKnrbrcudte/+310PeLm83px7+UNN9xQtN1e8+58dfk3+hzPPavRMSUiYssttyza7nx1axf3Xup849aRm2++earpnFfrOnLixImppu+Ny8hxY7eub9345N4HlzGnP+sy3OrFZVZoNqbLk9Psswg/juh44D5f9xxE52L3HNp9Bu55ho7Nbsxwz7j0Ptad+24t715fz2H3c45mkrq5wa0P3Pus9z615Jwo/hICAAAAAAAAAABUgi8hAAAAAAAAAABAJfgSAgAAAAAAAAAAVIIvIQAAAAAAAAAAQCVqDqZ2IS0amqwh0RE+gMSFbKy99tpF24WXuXBTDT3U14nwQXIuBPX2228v2i5gxgU+77vvvkVbw0QjfMjU2LFjU61Lly5F24V3uRA85QKH3Pu34YYbppqGfK2//voN/ntVefjhh1NNQyVd2JwLz3rwwQdTbY899ijaLgTLhdXoZ9y5c+fUx4W16rkSkUPcXJidCzY66KCDirYLgXJhNS60VkOP3bnpgnw0HGevvfZKfVxwZKtWrVJNQ8rcNVMPLgxKg+Pc5+G4EHkNF3aB1u691vPXBd66ADX3Whrc1KdPn9THBU/quOmuKfd5uzFrt912K9qTJk1Kfdz7p4GJbpx24cMuNFeDTjUkvp4mTJiQahoQ7z5LNye591sD4T777LPUx411Gg6prxPh52v3uYwePbpo77777qmPu7aOPPLIon3PPfekPi400839hx12WNF257C7JnV8OuCAA1KfQYMGpZoLatPfUcPW68n9rhqq5uZFd465cEsND3TXtAsc1nPfrVWefvrpVHNru/Hjxxft9dZbL/VxYZd6fg4cODD1cSFuLnx21113LdpuHewCVh955JGi7cZqXUNE+GBZnftXWGGF1Kceaplj3bnk7kPc+bvddtsVbXd+ufXFuHHjirYL23RjnXsfn3zyyaKt812EX6dutdVWRdsFaLs171tvvZVqev/11FNPpT7uvWnZsmXR3mGHHVIft751IY56DzM/51h3fen45OYRt3Zw85Su3d09sfucdJ2+5pprpj4ulHj11VdPNR0vXECm+8x1rLv//vtTH3fe1TIGu2N375/e2/Xs2TP1qTVIU8NZXZ960JD3iDzf63OMCL92cc8D2rZtW7RdmOvUqVNTTc9zdz/h1pbunrKWe1j3PvTo0aNojxo1KvVxAdNuvtPnUe6cc/OO3sO69YO7n3Dzh44vrVu3Tn3qRderERFdu3Yt2m48fPbZZ1PNXfd6PbnQb7cG0fHP3U+49ZO7n9CxwIXWu9fScGc3Tru1hnuG1rt376KtYb0Rfv2socRureF+zt1fayBwrSHFVXDr6E033bRou3WPO2Z3r6BrE70/jfDXvt6HuevXnQfunLr77ruLtnv+515L7wFcgLZbQ7nxrlOnTkXbzRcuoFznGndduedIbgzQZ0Tu+XtD+EsIAAAAAAAAAABQCb6EAAAAAAAAAAAAleBLCAAAAAAAAAAAUAm+hAAAAAAAAAAAAJWoOZh63XXXTTUNBHEBVcsss0yqaZBSRA5A+uijj1Kfr776KtU0+McFfbgAkvvuuy/VNDTYhXO4UKyhQ4cW7UMPPTT1ueKKK1LNBVvqcblQaBf+ocFTM2fOTH009DrCh3KuscYaRdu9p/XiQos0FMYFptx6662pdsQRR6TatGnTivbkyZNrOi4NN3XBVS4QyYUW7bPPPkXbBf65mp6LLsTNhV+6MDsNtd5xxx1Tn0cffTTV9t5776LtxoBddtkl1fQzjIho37590XYhZb/85S9TrbG54KdFFlmkaLsg2RdeeCHVtt9++1TTQOAnnngi9XHh4RpEruduhA+FcmPwnnvuWbRduNOsWbNSTT83DQCNyMGIET6MUoPTXJidhpVG5LHNBTl179491dy5qYFZt99+e+rz85//PNWq4MI/NYDZXYNunnLBuxrG9vDDD6c+bo7VuX/EiBENvnaEP3/0Gnehsi4E9LLLLivaLjxwnXXWSTUXRHj11VcX7Z122in1cdfDBhtsULSHDBmS+rjP0I35Gro8duzY1Kde3Hygc74G30X4AFcNwo3IgZRurtTxNSIHprk1mwtXd++3hge668gdg44HLhTaBRW7wPUBAwYU7T322CP1cWHfGnqs4e4RPlzOhZHqWOk+i3rQANqIPNa7ecuF77nfXUMB3eft3uv999+/aLv30IXDuvB5nWPda7lzR+d1Nz658cLNxRpo6AKP3XpHw0NdcK47rkmTJqWa3u+5tXm/fv1SrQouKFXvNd06zs1JHTt2TDWd89y63Z0rGrbp1oQuRNaNdTvvvHPRdteMO+/0fkXvSyL82OMC14cNG1a0N99889THre30/XOfhZv7NQQ+It/313pv19jc9aX3rC7U193Du/WFvtaYMWNSH3e/ovfWLsjYHYM7d7bddtui7e5N3GtpCLIGt0ZEPPTQQ6nmgmB1TNxkk01SH7eu07Ft4sSJqY8LDXbvg87V7l7IPYeoghuzn3rqqaLt7p1cgLgb6/S91IDvCB8+r88p3Nz8+eefp5rOSe61JkyYkPq4gGC93txzJjdfu7Fn3LhxRXvjjTdOfdx9ub737tmiey33Puhn7cbDetH7pIj8Xrp1p5sX3e+v44hbj7lAbw1Sd2OB9onwc5A+H3P3Qm580PsJXSNG+PFHn1NE5LFlww03TH3cdaS/9yeffJL66BoiImL8+PGppp+Pm3sawl9CAAAAAAAAAACASvAlBAAAAAAAAAAAqARfQgAAAAAAAAAAgErwJQQAAAAAAAAAAKhEzcHUgwcPTjUNHDv88MNTHw0eioh47LHHUk3DTFz4sgvaWX755Yu2C9lwQS4bbbRRqj3wwANF2wXjubAuDTtzQTsu0MaF1WyxxRZFu02bNqmPCwDSUG33vmswYoQPaltppZWKtoam1ZMLVtbjc++tC5LTzzci4oMPPijaGkwY4QNmrrnmmqLtwnhcuLMLW9bXciFuxx9/fKpdcsklRduFxrmwTRfao9eDC7RxIXgaONyuXbvUx40dLiBRQ4HcuV8PLvRRA8fc+OSC9lz47zfffFO0XWC8C6nSQCYXuKVhfBERCy2Uv2vWAEkXALXaaqs1+FpuDFtrrbVSzYWA6nXsxiI31mk4nwuYcqHB7jPT0MBOnTqlPvXiwtp1fnMBce66dOeGBnO7MLYpU6ak2ocffli0XQCWC8d246bOzy4wcf311081Ddp2wbbu33PBeFtttVXRdmHcLpxPg6/d9e7GDjcG6zzvPtd6cSFxutZygcwudNGFf+rc4kLqXZClBsa6ccx9Tq6fzv3uHHbh6jpuffrpp6mPO/fd/Klh1e4adTUNxXQBoi40bu7cuammwZ8umLIeXICdnnN6zUf4cF4X5KfXpganRvj3UUMO3VqpRYsWqfb111+nmoZkujnWrRt17erGtVatWqWaC4/X0HkXQu+CFzXw0wXnuvsJd13p+Oc+i3pxwaU6rv/yl79MfTTQNcLfx+pY58Jx//nPf6aafuZuXnTnmFuj6e+4xhprpD49evRINV0LubWAW9u5NZquLdzay61bNFzdnftubafrpIh8H+Xev3pw146OY7vssktNP+fmGl0LuXuwf/3rX6mm86s7L9376uY2vc9xa3l3XDq/Pvfcc6mPm5fd9ajhre4ZgKNjsL4vEX5+dfOA3ie6e/l6cdevnit77bVX6uPeWzfH6vXkQsXd2KD3a24N17x581TTZzUReV3n1gz6nDIiBze7e0i3fvrss89STT/jWbNmpT7uXkGvEbcWe+KJJ1LN3dN07dq1aLsg43oZMWJEqq277rpF2z1H1WcSEX6OaN26ddFedtllUx93Tum16YKw3X2Iu871uNxzF3cfq5+dG3Pd2s49+9b3wYVqu99nv/32K9ruHHPP7Nz7pWPsvDyz4y8hAAAAAAAAAABAJfgSAgAAAAAAAAAAVIIvIQAAAAAAAAAAQCVqzoRw+/I1bdq0aLv938aNG5dqbq813V9O9++KyHtau2Nw+7G5/ZbdXuaafbDoooumPrXsF+/2eHf79bv9k3XfWPe+u99Ra+69ctzejdOnTy/abq+2enF7kOp+bHq8EXlv0YiIe+65J9X0M3/88cdTH7dntu5xp3sJR/i96tw+lbpnrts72O2hrK/l9kl3e8a690vzT1wmgdvvV/u5/eXcPnH6/kXkfVJdtko9uHNOc2XcHqtuH1+3F6Tu/ej223R7g+t+l+4Y3L63brzQ39HtNat7BEfkfafdOeH2JnR7O86ZM6dou72L3fun7417bXfsbm9HzZxx4/sJJ5yQalVw+z7qnshuv1rNGInwY5aeP25/U5fB07t376L9yiuvpD5uznNjgY6TLm/I7Umrc7Hbq1j3eY3w56eeL27vTvf6uoe8u27deOv2Bdf3we1VftJJJ6VaFdyYoXOX2xPZ7Wfq8hj083T74LvMGN2PX8eLiIiddtop1WpZr7jf2a1f9fxx55M7drcnre6b7eZFXc9G5HPF/Xsud8Sdd7pPtJtjjzzyyFRrbC4TSn8vt09zrRkW+v67OUKzbiLyGsRlgLj7FzcX63jr5liXYafZT2496NZ6blzW89zNge619Np78cUXUx+3lq1lve5ysuo11rnrUn/XBx98MPVx94vO66+/XrR13+aI2nJl3L7fbrxwY7B+nu4+1l33eq/pzjs3D7j1peYGuDHfZQtoPpPLRXBjncuc0M/CrSvqweXY6BrW3Xe6+wmXUaPXuDtX3bj5/PPP/9vXifBrI/fcQud99+9NnTo11XTN69bAbk3h1vf6ebv7b/dzOufWcr8fkTPtIvIYrMdUT+731/POjQPufHXPN3TvevfMyc2xelzunNacngg/B+n54vLd3BiizzvctebGYJcTq7+3Oy/c6+szBfcef/vtt6nm1nW6dnLvVb2490ivMbdW0fEown+emnPg5imXiavntVtruwwXtw7V8cDNge4Zmp777t+7//77U83dl2sOhXstl6mka1WXCebWSW4M1LWqu+dvCH8JAQAAAAAAAAAAKsGXEAAAAAAAAAAAoBJ8CQEAAAAAAAAAACrBlxAAAAAAAAAAAKASNQdTu6BoDTJyQY0uqMyFeGjY1FVXXZX6HHrooan23HPPFe127dqlPi6AxIWxaXDxYYcdlvq4cEQNC73++utTny233DLVXGCYHtd9992X+my00UappqEuLuTVfYYu1FTDi7baaqvUp15cQO8ee+xRtG+//fbUx4VsuVBJfZ/69++f+vzqV79KtQEDBhTtrl27pj6jRo1KtQ4dOqTahRdeWLRdAIwLcdOgHRfgVetnroHDLlzJhc9efPHFRbtnz56pj7tmXOCQ/o4HHnhg6lMP7th+9rOfFW0XHuQCmdx5qMHNbtw85ZRTUk3D7TfbbLPUxwVZufP+6quvLtoaPhzhzx09dhfm6oKiXNCRBlu6UCN3vWhAsDvv3RipIUoReW5wQbf14sJaNdDMBWe7UEYXkLzDDjsU7Ysuuij1OfHEE1Nt+PDhRdvN6S4IzQVIaiCZhrdG+PBAHes01C3CB3PpuBaRw1ndeOhCQG+99daivfXWW6c+tdJA2r59+87za31f7lzRdYgLWXM/58Ll9Bq+7bbbUp9jjjkm1XS80/M3ImL69Omptuqqq6aa/pv9+vVLfVyYpp7Dw4YNS33ceOfeLz1f3NrGjeka7Ov6uPfdndd6HW277bapTz24eapt27ZF2411Sy+9dKq531Ov8XvvvTf1Oe6441LtoYceKtrufsKFSbv55tprry3affr0SX1ceKjOsS5QV9+rCH9Po8GdLlTW/Y4aqOrmWHcefvDBB6mmc6xbK9eLuy/SoHEX9uzGFBc0rq/v7k3cfaUGPrv31p3nbp0+cuTIot2rV6/Ux4Wra0Ds4MGDUx8XiurWdhpyrffpET6sWsdzdy/kAmPd/ZGO3e3bt0996sGt63QcdgHG7np2n7fOW0OGDEl93Dmg/6Z7f9z17MaLm266qWivvvrqqc/CC+fHTXpd1To+uWtPxzo3ZmmYckS+/3Jh3C6s2d3b6TMdvW+sJ3ed6Ofi3kd33+f66X2lC/DdZpttUk3nM/d8ya3v3X3slClTirY779w6S8+Vzz77LPXRNUSED/LW43LXrRsj9dpyx+5C5t3YrXNDp06dUp96cc9B9Pgee+yx1Mf9/i7MXs9Pne8i/FpLn9m4ZwtujnVrhgcffLBo6zPJiBwWHpFDoW+55ZbUx10z7j5Wnw24sVPDqyPyMxs33rl7cDeefPrpp0V7Xu4n+EsIAAAAAAAAAABQCb6EAAAAAAAAAAAAleBLCAAAAAAAAAAAUAm+hAAAAAAAAAAAAJVoMtelnBiXXHJJqj3++ONFe5111kl9NFwwwocCakiLC3qbMGFCqmnQkIZrReQQmoiIESNGpJqGi7iwTQ0WiciBS+59ePfdd1PNvb7+3i7USsPzInI4qQv22WuvvVLNhcFq8MszzzyT+mgwc1XuuOOOVLv88suL9vHHH5/6XHHFFanmgidbt25dtF3I6yOPPJJqGpim4ZER/rxzAWoa4ube7x49eqSahva40DIXsrfFFluk2nXXXVe0XQioCy7T0Cf9bCIijj322AZ/LiIHOt19992pz80335xqjc0F9j788MNFu3nz5qmPC99z54AGD7lzzl2XGo7mwrQ++uijVHPhlxoC5YJUXZCcjq8aohnhg71nzZqVahq25EKN3O+o4aTuvXLhly7EVsOxn3322dTn73//e6pV4dJLL001/d1c4Nidd96ZajqmROT3zQVzPfnkk6mmY50LoHNjipunNCjLXTM6JkfkwDANAIzw4YEu8HH55Zcv2u69cq+v4XJDhw5NfVxAmf57ETlc7oEHHkh9brjhhlSrwp///OdU0/BAF9Tt5kU3R2h4mQskdcHBOge5IEg3PrhzWMcDN19r0FtEPqfcsbux0wXvaQCcC2V3r6XrMff7ufPuww8/TLU5c+YU7RdeeCH1qccce+GFF6aaru/dvOjGC7fu0fHIvZZ7H3UN4s4v9766wGwNttQQzQgfMqnnuQuA12vqu45L510XeujCZ3Xd4uZFNxe5uUHfG3ffc9VVV6VaFS644IJU0/Ng8803T300iDIiYpdddkk1vT90ofVurG/ZsmWqKReI7s6pLbfcsmi7gMzZs2enmgY5uyBYF06pa+OIPE669bK7R9V7NHf/4taJ7rV0/ereK73vqYIb63R+2HTTTVMfF0jvgo51jHLPTjSUNSLP1e7Zhhsb3Lmjx+/GIhf6qudmly5dUh/3Wm7e0n4uUNbNA0qDqiMiunXrlmruutJ1ozvn3D1yFdy/o9eqm1tmzpyZau6Zlj7LcM+qnn/++VTToHF3vzht2rRUc3OlzrHu59w9qs6xa621Vurz5ptvppobg3XO22yzzVIfF0yt422toezufdB1i1vbXHnllalWBTfHahiymxfd/aIbF/Uac2Hz9913X6q5+Uy5UHb3Wvo8zn12bu2o54ELP3fPcNyYpOsvd/0NHjw41fS+yj1vdPcm7tzXtZ0b7xpa2/GXEAAAAAAAAAAAoBJ8CQEAAAAAAAAAACrBlxAAAAAAAAAAAKASedPv7+AyDXSvcbcPt+OyHXr27Fm0X3vttdTH7d2s+9e5TAi3Z6zbY1/3m3X7rrq9r9XYsWNTTfdgj4jYddddU033GXR7C7t9iXX/MbfXmNvr1+23+Pvf/75ou/2x68Xtu6jvpduHdquttko1t+el7r/m9u/u2LFjqumelO68cPsTuj3+xowZU7S33nrr1Med+7o3p9tDtJY8gIiIn//850Xb7fft9qXT98blCIwaNSrV3P7bBx98cNF2e9bXg9t7XPcdbNu2berj3mu3D6ruM/7qq6+mPm4PyaZNmxbtJZZYIvVxe3y6PWJ1H8Blllkm9XH7AuqewG58csewzz77pJrus+z2Q3fnieaJuH0c3b7L3377bappnoz79+rFjbP6u7nxaaeddko1t++27gHs3g/32elnrnvbR/ix1e3F+uijjxZtd+xuL1+dp/R1vuvfc3Osvlat2Qb6b7rryo35blzWXCz3ntaL2+dbzzP33rr3yI1lugepjmMRfq9r3efbjXduz1i3BtTP2J1j7jPQfXtvuumm1MfNBbqGiogYN25c0Xb7Wru1ne7j7PZ+1Xy2CP8+697W7j2tBzcv6vnkPluX6+XGzYUWKv9/le5JHOHHel2/uDHS7UHsPjcdL9wc6z5Lve9wn62b81zmm86x7pxz90d6P6FZPhF+r2SXy3PSSScVbbdOqhc31q266qpF2+0b78Yn915qHoPbI9ntr65reXd9uKwkdw5rVlwt69mIvObU+5IIvz7Yb7/9Uk3XH08//XTqo1lTEfk5g1vvuLnfvV96Pbixox7cHu563btzwuXmuX259fdyOVjuc9N+7p7D7W/vnhnoee7GJzfO6LXm7hXduNm7d+9U0/w0l13hMkaUex/cGtHNndttt13RrjFytRLuGZquWd044PaId89Y9FmG+3zdNa6fgZtjXS6PG7v1mZ0bu925r9eWrs0ifE6Ee26o84BbA7vfR3OWdB6K8O+7mz91fnb3JvXixi19Huk+J/e81eWTdO7cuWi7+yv3++vazuVUumwvd4+qWSeayRHhn1/pXOzmMvfstm/fvqk2Y8aMon3XXXelPttvv32qaR6eW0O4LBddU0dE9OnTp2jPy7Ni/hICAAAAAAAAAABUgi8hAAAAAAAAAABAJfgSAgAAAAAAAAAAVIIvIQAAAAAAAAAAQCVqDqbecMMNU02Df84+++zUR0NEIiIOPPDAVNNgGPfvuSAwDb5xIW4uHMiFx2hYigsqdMEbGo7jQplcqIcGL0bkUCQNOovIYcoREZtssknRHjRoUOrjQtJc6Iq+NyNGjEh9fvvb36ZaFVzI1gcffNBgHxdq6MLR9P3W0JYIH8qur+/OTRdm5wKuNJDHBSK560E/F9fHnSsusPL6668v2i5Y0wWuDxs2rGifcMIJqc/999+fai7wTIPFBg4cmPq4168HDVsaMmRI6tOpU6dUc6GAGvrjQi1dEOz7779ftN3n6IIhNZzS/awLFXNheePHj2+wjwZuRfhr7/PPPy/aLjDdBdPrsbogLPe+u4Cye++9t2i7c/WXv/xlqlXB/R4aSN+/f//Ux82xPXv2TDWdG11o3JJLLplqOrfcdtttqY+bR958881U0/PanT9uHNPxaOONN059XDjYe++9l2pPPvlk0XbrER0PI/L71bx589RnwoQJqdamTZtU07l48ODBqc9pp52WalVwv4eGBboxpGPHjqm2zTbbpJqGr7nPya2rNPDZfSZubefmPA2YdmHSLpDy5ptvLtruvXLXjFt/6et36dIl9XGBcF27di3aLsDvgQceSDV3bU2fPr1ou8/1xBNPTLXG5s4B/dwGDBiQ+rigefd+6BrWhf25oFoNXXWfrRun3RpZX9/dF6y33nqppkHkLsRx8uTJqab3IY4LZHdBs3o9ujWwW3+4dcs999xTtN0ce9hhh+WDrYBbY+hnrGvaCD9euHNRPzv3fmjod0QOKn7ooYdSHzdG6r1QRB67df6OiFhuueVSTdff7t9zYbwu9F1DQDXENsKP01tttVXRfuyxx1KfadOmpZpbQ2u/0aNHpz7HH398qjU2txbVsGUXBuzC4N29oa45XHCtW+vp3OnuYV0wrgsI1s/bzT3uHkPDVN14685VF0ar77M7J9y4qc953DrArWV1bR6R59eJEyemPvXifn+9h7z22mtTnz333DPV3D2G3tNNmjQp9XHzro7Bbj5wXIC1hjm7Z3bu+tNnGe7cdHR8d6+v4eQR/rmPjvnu3t1df269869//atov/HGG6lPvbjPXI/vqquuSn322muvVHOB3vrZtW7dOvWZOnVqquk6yr237n6ilnBwN7669ZE+X9RzICI/V4/w575yzxvdua/PLt1169a4Ljhd72NdwHtDcyx/CQEAAAAAAAAAACrBlxAAAAAAAAAAAKASfAkBAAAAAAAAAAAqwZcQAAAAAAAAAACgEjUHU2toVUQO+uzbt2/q48J7brzxxlTTn3XhHC48RgOKXPioCzft0aNHqmnojAu/dEFZGsaoISwRPtDLhRbpcd1xxx2pz7bbbptqeuwu4MmFC7kgFg3Jqlcwq/PPf/4z1fR4XOCfC3jUUN2IiN69exftL7/8MvVx57AGsLRq1Sr1cYFtW2+9darpeeaCsVwg7RZbbFG0XTjl6aefnmru+jvqqKOK9pgxY1Kf3XffPdX0HK4loDHCh7Jr+JcLeKoHd2warOeCiJo1a5ZqLsy7Q4cORfubb75JfT755JNU0/dHw+0ifLiVCyjTwCL3c3fffXeq6e/tgrr0XIrwQYsamOheywXcaVDdjBkzUh8XjuWubQ3zdKFs9fLiiy+mmgatHXDAAamPCwp04dE6/rux3wVS3XrrrUXbBVS5gFt3/Woop7vW3HnXp0+fou2CHDXUMsKH3mkAmjs3e/XqlWoacu1e2wUzaxhgRP6sDz744NSnXjSwPCJiyy23LNou3HT55ZdPtVrChN055oLkXn/99aLtwmFdAJ8ee0QOUXTrSxfyuv322zfYR+fhCL/W0EC44cOHpz5urNZQOvc7u/WshmRG5PGue/fuqU89uOu+ZcuWRdutu1xYrgbNR0S0b9++aLtzztX0nHNzrIacR+Rjj8ifm1vX3XvvvQ2+lgvUdXOsex/atGlTtF1woAtbX3rppYt2re+DW0doGOwee+yR+tTLK6+8kmq6VnBrAHePMXTo0FTr1KlT0Z45c2bq4847PS4XRu7Ccd3Y4+47lAsx33DDDYu2u5d2614XbKljsAv7dms7/R3d9e7m2Dlz5qSahtO74NN6cJ/bzjvvXLTdGs7dT7h1lp4DLsTUrUFmzZpVtN2a2YWyunB7DSj9/PPPUx+3XtJQWXe/r2N5hF8v6Pk7cuTI1MedcwstVP5fXHd9uvBb957qddWxY8fUp17c/K+h0O6e3s0Hbl2n16H7uQ8//DDV9D1yYevvvvtuqrk1qJ7D7nx1Y7c+c3HPCN15p2NKRH5P3drPHYOub5599tnUx91rffXVV6mmz7v0mOrJ3ccutthiRXv//fdPfWp9fqL3AW4t7963Rx99tGi78+6jjz5KNZ3TI/L7rb9fhA8j1/HAXaMurNrd73bt2rVou2fFLqxary03x6688sqppmvCiBy0PS9zLH8JAQAAAAAAAAAAKsGXEAAAAAAAAAAAoBJ8CQEAAAAAAAAAACrBlxAAAAAAAAAAAKASTea6dErjb3/7W6ppWLULA3HhPRqoERFx3333FW0XrOKC1/S1XPioC61y4X4aFuXCalxoiAbHufAuF2h95JFHppqGnbn3yoWUaKCKhrdG5ACmiIiFF87Z5Bo46YI7b7nlllSrggtE0tDeTz/9NPXR8yki4je/+U2q3XPPPUXbhZu6z07Dq1yIkQuxdMFi//Vf/1W0Bw0alPq4QNqTTjqpaLvgJhceuNlmm6WaBtkef/zxqc/ZZ5+danrs7r1yoUxu2NGwShfqV4/z7pxzzkk1HVdcUKMbnw499NBU08A0FwDorjkNXnNjkTvn3FjXs2fPou1CoV3I0A033NDgMbggvh122CHVNJTTBQ66IEkd61xArgsK1RCziPx+uflKf+equBB5HdtcmJaGqUb491uDAd187eYWPfc1WD0iYokllkg1F7q6yy67FG03x7pjv+aaa4q2C85yoWI77bRTqt11111Fu1+/fqmPmz90LHXnnZtjXfC8BpK5827w4MGpVoWLL7441fS6a9WqVeqj4WwREbvttluq6dzirs1Ro0alWrdu3Yq2C6B3r+XCCTXoVQPSI/y6TediF77oPrsdd9wx1fTzdAG9LnBT58GmTZumPu5adgGl+t64efjqq69Otcbm1hIaZuquLw05joj4+c9/nmp6/br3x63FNtpoo6LtQlh1/Rnhw4B1rJs4cWLq464XXfO6MFV3nrgQ1DFjxhRtF1TogiQ1UNStUVyIuptjNXTXhTHeeOONqVaFv/71r6mmofUuFNpd4xpaH5EDmHXNFuEDKzVc2AX7uuvBzZ86Vrs1oQazRkSMGDGiaLtrxgWzunWi3hO7NYNbl+q47MJK3T2Nq/3rX/8q2u5+4tprr021xnbllVemmoaDuuN34eEukF7XRm4ec/cmes/q1ikuaN7db+s5565xDZSNyPPrKquskvq45zfbbrttqun61o11bn2rc7r7LNxc6ubh9957r2i7kOsrrrgi1apw0UUXpZqukd1Y594j98xAn/+5e0EX0qzPKdx75ELSXWi5hju7c9jNXRpS7MZD/Swj/Hiu46Zb++lYFJHnlK+//jr1cfd7bjzXezR33brzoQqXXXZZqul6xZ13L7zwQqp17tw51XQd5dZoDzzwQKrp84XFF1889XHXvnumpWOLu/dcb731Uu3xxx8v2u7ZmD4Hi/DPRvSZjRsT3Ryr9wBujnVrDbfu1evP3RNef/31qfa/8ZcQAAAAAAAAAACgEnwJAQAAAAAAAAAAKsGXEAAAAAAAAAAAoBI5EOA7fPXVV6mme326PbDcfl3XXXddg/+e20t9/fXXTzXdj23XXXdNfZZccslUc3u6P/XUU0Vb97uK8Hsd6r/pcgzcXmPLLrtsquk+sm5fOrfPV5cuXYq22+vX7Qvp9iTbeuuti7b7XOvF7Xmq+0gefvjhqY9mFUREXHXVVamme7m5Pejc/uNTpkwp2i+//HLq4/Za23vvvVPttNNOK9pu30G3H+Lvfve7on3rrbemPm4/RLc36sEHH1y03bni8jJ0H8N27dqlPu6acbkB+vour6Qe3L+re/ntvvvuqU/fvn1T7dJLL0013UvU7Unv9izXfRVdbs6iiy6aano9R0SMGzeuwZ9zexdrRo3LknB7uLqMGt0T3f3OSy+9dKrp3qNuXpg0aVJNr7XddtsVbbdPZL0stthiqaafk9tD3I1PAwcOTDXdh7h3796pj9uXVMc6N5e5ObZXr16ppvtRuv1g3d6Tet7pfrQRfk9at27RMXjatGmpj9vD9bjjjivabu9Ol+XiPld9712WRL24/cf1M9c9yyN8XpXb/1r3sHVZWG7fe90jtk2bNqmPO19ryRJw61I3Bnbq1Klo6xrxu37O7W2t+3lPmDAh9XFz5b777lu03dzp5mt3DDpvufO8Htw4q5+3W4v16dMn1S6//PJU0z2RXaaW28dX19YuA8RxeQw6drv5x40XmoXi9tV22Qtu/2j9vN14645Lrw+XveLyOdznqvsnz8851u2nrevhTTfdNPVx+Qh///vfG/z3DjnkkFRza3J9L12+m+P2QNe1quacRPjrXtdCmpcX4ed+9/voOuW1115LfdxYp2sGd6/iMkzcWKfXpDv368HlmmmGjI7xEf6ac5kmteQTuvW3Pr9xWRKzZ89ONffcQtfbbj53463mcGqGTYRfP7k5fs899yzaLr/EvZbmD7jjdOOGey2919JsnXpyuQCaQ7DSSiulPptvvnmqjR07NtX0PtaNWe5c0fwCd7/txjV3Dms+icsrcfkDuse+u0bdszc3x+oY7+493f2Rzovu/te91lJLLZVqmkPhxs16cXOE3mO4c9OdP+4+Vp9tumw191xTn1W4exqX/eKybHQ8cPkwer8dke9hNDspwp/7LiNF3wd3HbnsMH3O5t4rXUNE+NzH1q1bF213j9YQ/hICAAAAAAAAAABUgi8hAAAAAAAAAABAJfgSAgAAAAAAAAAAVIIvIQAAAAAAAAAAQCVqTn51IYx77bVX0XbhioMHD041F16hgbYuLPLiiy9OtSOOOKJou2AjDdyK8EG/GszkwohcWLUGbbuwHxds5n7H/v37F20XxuMC+zTMWAO7IyL222+/VHOf2WOPPVa0Z8yYkfr07Nkz1argQhj1/HHBQyeffHKqHXbYYan24IMPFm0XtqcBXhE58NQFZbnAFxeWdcYZZxRtF2asxxmRw81cKLv7fVxQ3QMPPFC0XZDc/vvvn2oavuOuPxfO50K9NLzIhWG5Y2hs7ro88MADi7YLwvvv//7vVHNBwhoKOHHixNTHvY8ayunGJxcS6EIsNRTr+eefT31c6KuGZLpQVhfk5M57DeV04V0uVFuDI++6667UZ5dddkk1F3isIdq1vlYV3FinAcYucOySSy5JtcMPPzzV9Lx24ZQuKEtDE11YoQs31RC8iPzZuQAs9zkNHz68aGsQW4S/HlwA2t1331203Vi08cYbp5qeGy7o8uc//3mquQDOZ599tmi7OVZDG6uiQYEReXzQoOqIiJEjR6baPvvsk2oa2vbMM8+kPi7kVecNF0bu3iMXtK2hdy7cz50ret65taQ7X13I4GWXXVa03drOBXpqQKIbq3V+ivDXnwbDu5DXgw46KNUamxvrdH3qxpQzzzwz1dxYoHOXG2fcWKfhpm7t50LN3f3ElltuWbQ19DrChwned999RdsFOXfo0CHVNNg7IodjL7PMMg0eZ0QOxXX3EzvttFOqufNe5xk9poiIHj16pFoV3Jit6yoXSDpgwIBUc5/BeuutV7TdtXrLLbekmoZrukBSd9/nzjudu1zQpYZaRuTP2AUV631PhJ/frr766qLtznMX5q5jsJt3NGw9wgfS6j2Mm2PdPXFjc+G8OmbpOjQi4pprrkk1F2Ctobp6/x7h13r6zMC91+5ZhruGdAxxgajuGdKTTz5ZtF04rVtvvvPOO6mmQepuHdCpU6dU07WACynebLPNUs1dC3o9unDaenHzhj7vccen93gROcw2Is+N7h5Pw4Aj8nXv7rfdnOTGMaXjb4R/9qbrOjfWOS6c98477yza7rmPWyPq9efWxRqgHeHfBx2D9f4iwj//qoJb5+h1587Nm266KdXat2+fajpGuCB5XWtHRPz6178u2u7ZmN73fNfr67joPt/mzZun2tChQ4u2OzfXXHPNVHNj57Bhw4q2CwR3axQNV3f3Ve65lVsL6/pmXu5j+UsIAAAAAAAAAABQCb6EAAAAAAAAAAAAleBLCAAAAAAAAAAAUAm+hAAAAAAAAAAAAJWoOZjahRd++OGHRdsFjnXp0iXVXGiKhtC50MPTTjst1f72t78V7VatWqU+LtRDjz0i/44urMYFSGm4iAsI0XDGCB88paFbLpzXhSPee++9RXvzzTdPfVxIuIaUROSQr2+//Tb1qRcXgqVhPVdddVXqc84556SaC4nT4NtHH3009XEhSRomvMEGG6Q+LvTRBcX85S9/Kdq9evVKfVyAuH4uQ4YMSX1cGJG7/jQsyoW8uhCd119/vWi7UJ1//OMfqebGBQ1kdKFM9eACSjWU57bbbkt9XMidOwc0WMmFZh555JGppgFYLVq0SH1ciNvKK6+carW81y54TcdNFzDqwuXcdaUhUBoYHOFDUjX4yoUI33jjjanWvXv3VNMwNXed1YubN/T91QD5CB+I7q5fDVS97rrrUp8zzjgj1W6//fai7cLPXaiamz/1M3bhpm6O1bC3Rx55JPVx4+Zzzz2XajrWuSBHFwKq14wLFnbvn3stDYt3oez14s55DQt0oWQHHHBAqrnzTs8DFwh8yimnpJpew25ccUFoOidF5CA8F0Cnn0lExCqrrFK0n3rqqdSnZ8+eqebmBw2Zd6GN7ly5//77i7YLydQ1RISfjzQ4U8MR60WDoyNyeKoL8N1rr71S7aWXXko1PVfc+PSrX/0q1XSsc+sZN8e661fvh7bYYouafk7PQxfy2rp161Rz45iOdRrIGeGvY71ncueJO8fduk6P33329eLGuqeffrpou0B3F4bsApl1nHHrHre2GzhwYNF2n687Lhcsq2P1+uuvn/q4e7oVV1yxaLuwTRfK7tb3Ohe78Eu994rIc8Omm26a+rj7WLcG1HVEs2bNUp96cEGyGuDu7k1/8YtfpJoLj9b3yI11buzRIOdag8hdCLiuF9z98DLLLJNqyy+/fNF2c7Abg90aQsNv3Xi49tprp5peoy7c2F3H7rrSz8cde724QF29t3VzWZs2bVLt7bffTjV9dvTQQw+lPnvssUeqaaCueybijt2Nt7oGd/Opux50nHbnyt57751q7l5dzxc3Trtgb11LuiBjveeI8OtNHT/m53nn6HU9ZsyY1Kdbt26p9tprr6Xae++9V7RdkPqFF16YarqedM8+XSi9ux9ddNFFi7YbM3Q9G5HvYz///PPUx91rufFuxx13LNru+nPPijUc270Puh6J8HP/3Llzi7YbTxrCX0IAAAAAAAAAAIBK8CUEAAAAAAAAAACoBF9CAAAAAAAAAACASjSZq5s6fQeX0aD7O6+zzjqpz4QJE1Lt2GOPTTXd19/tBen2+j388MOL9vXXX5/6OG5fw65duxZt3fc/ImdXROR9iRdeOEdtLLXUUqnm9mnUfd9/+9vfpj79+/dPtaOPPrpoX3bZZamPyzZw+4/p/ppuH7zLL7881apw7rnnpto777xTtN3ea26vVLcHsO6P5vZk1r0zIyKOOOKIou32Y3vhhRdqqvXp06dou33iHN0f/ve//33q4/YadTkbuifiySefnPq4fekOOeSQou3O11133TXV3D6p+jm6PIWbb7451RqbXoMRES+//HLRduecnpcRfk9M/R1cn0GDBqXaUUcdVbTduaR7s0ZEzJw5M9V0P163t7ruERwRMWnSpKK90UYbpT6Oy+q54447irbLf3DnnPY766yzUh+9piL8+9WyZcui7fYPveKKK1KtCm4PdD3v3F6p7vc67rjjUk3HsR122CH10WyhiIj999+/aLvsDt3jOCJnd0RE9OvXr2i7zAY3x+r45PY8dftCL7HEEqmm17c7V9yYf+KJJxbtSy65JPVx+/Uvtthiqab7U7s8HzcGVMGt7XQ+c3s1uz163X7ntexB6rJl9tlnn6L997//PfVxWTaTJ09ONd3T3b23br9o3b/erZfcXtduT2zNCHB5Te64NNvB5Y64a9llAeke3KNGjUp96jHe6TkRkffmd3OsyxzZbbfdUu2GG24o2nouReT8h4j8mbj51O0b7NZU2267bdF2+xu7sU4zu9x+w25Pf3fPpLkNffv2TX3c/sza789//nPqU2sGj86x7v1z9ytVcJkYuu+2y41wGYI6L0bk+8/27dunPm5dq++3W4O6uczlNtSyV7R7Lc1EdPch7t7Wzbt6b+LmBZfbpfcT7j7TvafuuHSecVl45513Xqo1tmuvvTbVdCxwe2m7ucZl4mhmkMsqcPfwet/hzhOXA6hr0oic7eXWpG4dpPcd7jmJq62++uqppvcmBx98cOrjxjpdQ7jz0uWXuGwb/R3dGunss89OtSq4Z2F6PO53cOt2d83p8ziXKeLmPH0v3Zzh8ltc1oI+s3P5AC5rT8cL9zzC3Wu5ffF17eryH1yWi+b+uHsAl13mci80u+zBBx9MfVxuWBVcbqHmgLi1tstIc88Ebr311qKtuVcR/tmtru3c2tetL3XN7P5Nl4es+Q8R+fpzc6z792rJ9NFrIcI/P9G18E033ZT6uDndPUfS/BiXmdfQ/QR/CQEAAAAAAAAAACrBlxAAAAAAAAAAAKASfAkBAAAAAAAAAAAqwZcQAAAAAAAAAACgEjnN6Tu44A0Nc+nWrVvq44JvTj311FTTgAsXdKlBLhERf/jDH4q2hqBF+OC6t99+O9U0HNuFC2roV0QO6Fl22WVTHxeu9NZbb6XaAQccULRdwIwLx9FQMRdS9+ijj6baoosummoafuXCWuvFBeZq4JgLA3Uh5iNGjEg1DeueOnVq6qMBgxE5zNMF9Lrz1Z2LV155ZdHeeeedUx8XxKWfuQsWc4Gf7hz+6quvirYLBHfBU0888UTR1qD4CB9W89JLL6Wahn27YOR60BDciBzkt/fee6c+LpDJhZzpefHqq6+mPjoeRuQgIhdq6YJaXaCQhnJ279499WnevHmqaVCdGyNdGJkLo9T3wQXeuXFTx7E999wz9XHhyS48VN8vd47XiwsP3GSTTYq2C2B0x3zdddel2nbbbVe0x44dm/p06NAh1TSUtF27dqnPOuusk2ouzE5DxF1guRsjdZx2gZwuSO7TTz9NNR3/NJg0woeT6jzYpUuX1McFe7u1jL4P7pqpF7e20/OulgDdCH/e6fzsQlHdeuWiiy4q2m6sceedWwPq3NKjR4/Ux73+nDlzirZbL7maC7jbddddi/bgwYNTHxfG/M9//rNou/nbzf1uzfDb3/62aLu5rh7culbPi3333Tf1cUF7GkIdkedPFzC9+eabp5oGl7qAzE6dOqWaC838xz/+UbTd57baaqul2nvvvVe03Xnp1qku8FjHVzcPuzlWr20XQu0C7V3Ap4ZrtmjRIvWpF12vRuQgSPc5ubny4osvTjUNXXVjvwt91HtPd4/n5hs35+l87UItdT6NyPcKLtjejd3uPlbHOvf+uftkPffdvZ07h1347A477FC0XVhyPbigX51P3Zji5tehQ4emmr5Hel8Y4c8BXSO7tZib9916u3///kV7++23T33cfKTrLL23j/Bzoruu9PjdHKPzeUSeX13A69NPP51q7lrQa9QFjteLW1Pqmtxdu7r2i/DXjoYL6zOEiIg111wz1fR5gLuncWs4t9b705/+VLTddeSezeh54NZrbnxq0qRJqq233npF2z3vcO+N1tz9Uq3P3vr27Vu03fteLy5gWoOz3efrQpp1XInI97FuDnTjiN6buOdLbp3jrhF9ZufGNjcG6jnlzie35nTPRnSd4vq48fvbb78t2u45pbve3bHqNfnOO++kPg3hLyEAAAAAAAAAAEAl+BICAAAAAAAAAABUgi8hAAAAAAAAAABAJfgSAgAAAAAAAAAAVKLmYOoPP/ww1TS41AV4zJ07N9U0JDAi4rbbbivaLvTHhfxooKqGbkT4ADUXoLH77rsX7Y8//jj1efLJJ1NNgwlXWmml1Oe5555LNRfGqCFJLkx6jz32SDUNb5o+fXrqs+GGG6aaC0nT8DYXtFMvHTt2TLVrrrmmaGtQTYQPKnPhMRpw5cJk7rrrrlSrJXjNnQePPPJIqmkQtQulc0Ex66+/ftF2YYXu+ps1a1aq6fnpgsxcGNjzzz9ftJdccsnUx70PLghZ3xt3zRxzzDGp1thciJSOBS5Y2wWUuvNp/PjxRdsFIbqQIb1WXTivOy4X0q7h887bb7+dahpMrUGCERHvvvtuqrlwsMmTJxdt9/65UE49x9x54sY6PfaIiClTpjT4WvXirhMNjnWBki7Qy4VuaUBinz59Up9TTjkl1TSI0IXdu3DT+++/P9U0LNIFqLnPQMdud426cFgXbKnvqQtgd9eMhtvOmDEj9XGBaO7c1zBsF0peL8stt1yqaRCjW1dp2FxEnssi8nrCzenDhg1Lta222qpouwBDN/6419J/010fbm2nY4abO1dYYYVUcyGfd9xxR9F277sLhdSgUTe+us+iloBdF2hdD+580jlW1xYRPrRvp512SjUde9w87D5LDembOXNm6uPCIt1YoCGHLtjPha4utthiRdut5d1xufWtXh/u3HGBnzqeT5gwIfXR8O8Iv/7TOVbb9fTFF1+kmoZFurX24osvnmoHHXRQqo0aNapou7Ff7/EiItq1a1e09RyI8NeDm6e23Xbbou2umUmTJqWaBlG768OdrxpQG5E/Y/dsQH/niHyNuDndhW126NAh1XQNrevNenHjvF6Hbu5xIe/bbLNNquma36153L2hriXdv+eew9x+++2ppuHz7l5x4sSJqabngDtP3Gu50HS9X3HXuls/L7PMMkX7xRdfTH3cOeeenei1/eqrr6Y+9eLuJ3Rd557rud/LjfV6H+DeW/dcRNdLbpxx6zoX1K7ztbvHc2HkOj65EGp3/ugzl4i8rnP3NO6a1ONq2rRp6uOeY7kAa71n0nucenKfp94Xffrpp6mPm6f0fjEiP490551b5+g85d5b93zOPWfRz8CNk24c0TWuO5/cue+eZ+hc7MZ4N8fqvbO7n3c/59ZAOm+537kh/CUEAAAAAAAAAACoBF9CAAAAAAAAAACASvAlBAAAAAAAAAAAqARfQgAAAAAAAAAAgErUHEz9wQcfpJqGc9x4442pjwuN+8c//pFqGmjoQoxckKYGN7vAIheWtvfee6faLbfcUrSPPvro1OfMM89MtX333bdou2BEFybjQos0rNoFc7mgHQ0n1XCyiIiHH3441Vq0aJFqN910U9E+9thjU596cSFueq6430tDLSN84Gm3bt2KtguhdqGGf/vb34q2C6Bzn50Li9Rz3Z3DLjRM1RKO+F3HpcFTLgTPhehoMI2+nxE+/NIFUz/wwANF2wWw14MLItLwxsGDB6c+7prTANqIiB49ehRt917vsssuqabniQsjdYFMLtxJj8uN0/p5ROTAIhcy6UK4NFw1Igewv/POO6mPC7nSYCUXRuY+Qw0xi8gh9507d0596sVd4xpy5sLZXLCyC2Hcfffdi/bFF1+c+riwzdGjRxdtF3jn5iT3Wjr3a6BhhD92/Td13o+I6Nu3b6q5fuutt17Rvv7661Mfdy3rdepC093n44KYdZ458sgjU596ccGPGtboricXpHfnnXemWs+ePYu2G1e23nrrVNP5zIUHujm9S5cuqTZ8+PCi7eb0ESNGpNq6665btN256d6H2267LdV0bXfvvfemPu5aHjNmTNHWcTPCz/1u7NTP56ijjkp96sEdm4Zy62cW4YNZNQw4ImLXXXct2i4wz82xulZxIZMuyM8dl57nekwRfh2h9wouqNCNPY4GsL/22mupjwuJ1JBXHTMjcshihA80vPXWW4u2W5vXixvrVltttaKtwZcRPjDeBfTqWP/KK6+kPm5u0XHMre3cHOvWWnoOu3vdv//976mmY52bO11ApruPbdmyZdHWNUSEX4/pHOvOO7fmdMGgOp7369cv9akHF/6r6xk3r7gwYHdu6uem126EnzP0vXbzq3vuo/N5RL4PdEHh48ePTzVd87pzqVWrVqnmxmC9b3b/3uqrr55qeu3peBBRe0i73qNtscUWqU+9uLFu4YXLR37u2dgbb7yRam7+1GcLQ4cOTX1caPD06dOLthtT3OfrPrtnnnmmaLv7X3dfqfP1zJkzUx8XxOvOKZ3zpk2blvq482f27NlFW8ObI3w4dpMmTVJNrz+3vp2f9LwbN25c6uOee7l+tZx3bqzXsdNd524eceOw/pvu2XT//v1TTZ9dTpgwIfVxc557RqTPbt09gDtXagmUd/ORG/dHjhxZtOflmR1/CQEAAAAAAAAAACrBlxAAAAAAAAAAAKASfAkBAAAAAAAAAAAq0WTu3Llza+l41llnpZruL+r2xa91T0zd73KhhfL3I25/9T333LNo697tEREvv/xyqmn+Q0TEqaeeWrR1v6sIvxfr3XffXbTdXrOPP/54qnXq1CnVhgwZUrTdnr1uL0LdF3fs2LGpz5VXXplqN9xwQ6odfPDBRVv3TY/w+7BV4aKLLko13Uvvo48+Sn2aNWuWam3btk218847r2i7vX0feeSRVNP3yO2n6fZR1L37IvJ54PboXWGFFVJt6tSpRdvtx6a/X4TfY1OHAZfZcNlll6Wa7knr9g53/577zHSfVLf365///OdUa2ynn356qumejrrXsusTkfcBj4h44YUXGnwtd57ouelyZlyGio4pERH7779/0XZ72bv9EfXYdY/DCJ+Js9tuu6XapEmTirbLpXB7vute1Pfff3/qc/LJJ6ea25dYM1rce+UyjKqg809EHgt0r/4Iv4erO+/0nNp4441TH7fPtZ4rbk9v3Zs1ImLAgAGpdtxxxxVtN5e5vWx1n2u3htBzM8JfI3qsLjfHnSvLLbdc0XZ7Zv/6179ONbdnva5b3P73brytwimnnJJqOj67tZ3bt3exxRZLNX3f3L69bi9oPT9dboSbR9xerCeeeGLRdmOGy8fSPZ5d5tFLL72Uai4/Sddkel1F+PdU93V1mRr77bdfqrn1subCuAyPO+64I9Ua2xlnnJFqunez2xff5RDo/vMReQ9d99m6dZ3mibhx9K233ko1N29oVtzTTz+d+rjrRe9XXI6Yyy9xGTx6zrl1nVun6l7ULivthBNOSLUHH3ww1XQvYXd+1WuOdeedrplq3YPe7VGu+TAuD0DX7RH53sTdZ7rzzq21fvGLXxRtdy/osk50rOvatWvq49ZjLpdC/80DDjgg9XF7tetn4eZOt7Zz14Pu0+1yetxzgMZ29tlnp5rmNmiuQ4Tfp96t/zQP0q2fNEctIs9R7h7Trc/cPuY6brrsiqWWWirVNJ/Q7TuumUgRft/0119/vWjrGivCj8E61rlnNZrjF+HXm7p/vHsfrrjiilSrwmmnnZZqem64ffjd3vIur07vTdwe+y5/Uu8r3Z777ry75557Uk3nWJd55DK7dJxxY5h7dumuU50bXB5KLRkmbl3n7tHcGkjX54899ljqc+2116ZaFf74xz+mmuZaLbLIIqnP119/nWruc9FzSvMmIvycp88g1l577dTHfeZubXfSSScVbfd+u3NF5yl3X+XmRTf+DBo0qGi7+1iXxan3Wm4N4Z6BuQw7ve9w55ibd/83/hICAAAAAAAAAABUgi8hAAAAAAAAAABAJfgSAgAAAAAAAAAAVIIvIQAAAAAAAAAAQCVyosd3mD59eqppaJsLiHMhSS7AVUOLNMgkorZgQg2wjPABJPvss0+qadCkC9ldY401Uq1z585Fe/LkyamPCztz4UoaPuvCj5ZccslU0+CvLbbYIvVxgY3uPdUwk44dO6Y+9eLCuTS0vF+/fqmPC7p0IYwahqwhVRE+aFw/Oxca58KxNRgyIocpuWvGBdWttdZaRdv9fhoKGuFDMzVEx4XVuBArDaZxAccuLNmFk+p4or9fvWjAWUQOEHKhfS6cyAWgbrjhhkXbBU25z1uDv9zY4MZWNy7rZ6LB5BF+rNPa3Xffnfq4MCl3XekY5cK4XSCahuC5sdWdvy4E6oMPPijam2++eepTLy5ATYOVF1100dTHBXO5c0rHTf3dI3zg89JLL120XWjc4osvnmqHHHJIqs2ePfvftiP8fKOhiS7wb9VVV021Wt5TN2a54LTtttuuaDdv3jz1GTlyZKq5UFw9r901Wi/uPdJr051jGkwY4ccf7eeuaRfAp+s2F8Cu52ZERN++fVNNw2Dd2s7NixqaOHjw4NTHhby6uVLXEe59d++fHtcRRxyR+lx//fWppmG3EXlN4kKP68F9ljovdurUKfVxoaguDFmvJxcQ7O4LdBxz44wbW/XYI3LAoI6/EbWtxdyY4tbtblzW69j9Pu461gB2N4a542rdunWq6b3c/Bzr3Hmg14lb97iAVRf6qOORC9tcZ511Uk3v6dwa1AX7uqBxXdt9++23qY/7HXv37l20XbinO3Y37+o6wr1/bqzT89qdTzfeeGOq6X1zRA5j/tnPfpb61IO7n9Prya0l3Lnq1tH6DMSdJ8svv3yqaUCwu09z8757HzV41x2D+zn9fVwQuR5nhJ9fdR6eNm1a6uPeUx2D3b2Xm2NqeU/duqZe3BpW5yn33ro1lXv+p/ej7lnNKquskmp6X++CeN0xHHjggammn7Gby1xQtI4rbl3h1gduzNf5zN1Lu7lf54Y99tgj9XniiSdSzQWA633h/Hxm5+7p9B599dVXT31caLx7TqRrNDcmurXvnDlzirZbC7n7WPf8b8qUKUXb3U+4a0ufFbt7T3e+uuPStZ0b79z4vcMOOzR4nO5ZYrt27VJN15xuPdsQ/hICAAAAAAAAAABUgi8hAAAAAAAAAABAJfgSAgAAAAAAAAAAVIIvIQAAAAAAAAAAQCVqDqZ2YT0aiKThfxG1hXdF5JBMF5zlQoV23nnnou3CtFzokwvx0MBKx4XSaeCJC6m77777Us0FzGhYlwt5dSEoGurqgr1dUKgLcL799tuLtoaC1pML9NFAqLvuuiv1eeaZZ1LNhTC+9NJLRfvtt99OfV5++eVU0+AtF8jizrtJkyalmoYcP/DAA6mPu440fNcFx7jQHhds/vDDDxftnj17pj4ulO70008v2jomRERccMEFqTZ+/PhU02BnF3S12267pVpj04DsiIjFFlusaLvrxgUru1AjPTddyLU7pzXkywVAuSA0F1ip4VkuHMyFmutxaXBrRL6mInzIl15XGvwb4a9/DRHTYPeIiL333jvVHn/88VTTcdnNc/XiguSee+65ou0CQjWAMcJfqxqm5eYyF/Kt574Lf3P/ngtq13BCPaYIPzdPnjy5aLsAcTfHunNKx1cN6oqIWGaZZVJtwIABRduFfrnxyf2ON998c9F211q91BKQ7IIgXZDllltumWo61ruAeA0rjMjnp/tM3LzoQlD1unbBeO68e/TRR4u2mxv0Go2IWHHFFVNN14nu93HB8DpODho0KPU54YQTUs0F/V177bVF21239eDmKT0P3XXj1mJuXadzQpcuXVKf2267LdX0/XjhhRdSHzeXORo8qeGtEf4c0HWduy9xx+U+Sz03XehhkyZNUk3Xg+7fq3WO1QDIeQkvbCwuRFnvK12Qs5tjXfiujokaMh4R8c0336Sajk/uPNd5OMKPdfr+unW0jkURES+++OK/PaaIiIkTJ6aam7v09VdaaaXUx703egzuvPvlL3+Zam6sGDp0aNF2zx3qwQV/LrvsskXb3Xe6+3z3O+g6xN2vu/NX7w1diLD799y5qeO5+9xcyKzeM7lzzv177v3SAHC3lnXzzowZM4r28OHDU5/dd9891dy1p0Gzn3/+eepTL259r2OdBhpH5Gswwq+jdX3vnlW5UHZds7m1n/s595nrMzR3jumzxYiIRx55pGhvsskmqc8rr7ySaltttVWq6f11s2bNUh+3btT15uDBg1OfQw89NNV0TeqOtdY1ShXcc039PN2149Yhbt7Q58zuWbEby/Secdy4camPC5t36zb3bE+55y76XNY9s3PPsPv27Ztqeq67sc2NPzqHv/XWW6mPuyd2v4+uVd371xD+EgIAAAAAAAAAAFSCLyEAAAAAAAAAAEAl+BICAAAAAAAAAABUouZMCLfPme5Z6PaZ7NixY6q5vaJ130S3l5Xb83TEiBFF2+1l5fb+cnuD6l67+++/f+rj9gvU/dfcvlgtW7ZMNbeH9bHHHlu0L7zwwtTnxBNPTDXdJ71t27apj+6DF+H35dxzzz2LtttPsl7cvqu6T6XuFx4R0b1791Rze0vqPsQuN+PBBx9MNd1n1e1B5/Zac3vyXnHFFUX7oIMOSn3cPrW6x53r4/bnGz16dKrtu+++RfuWW25JfX71q1+l2n777Ve0XW6Ly39we3/qXpTbb7996lMPbj9v3a9Q90yOiNhjjz1Sbfr06amm56/L7XDjhY5PLrfD7bXo9vDX/cLdXuQ6pkTkvS3dOaf73Ub4nJM+ffoU7VGjRqU+vXr1SjXdA3K99dar6d9z+9r36NGjaLu9SOvFfU46T+le/RF+rHeZIjovub2D3b6relw77bRT6uPOFTdfn3POOUXb7WXvxgv9HXW/9Qi/r+uNN96Yajq/uT32Dz/88FTTvbbd7+dyYdxaQ7M9XI5Uvbh9V/W6dnOny79w84a+vltPuH1X9Vx0e//rfs4Rfh9r3au+c+fOqc/999+fajouuv293V6pQ4YMSbXf/OY3RVuztyL8fuf6O7p1qRvv3JpdMztq2du2Cm6O1XPO3Se4Oc+NWfo5uXsTt4eufiYu08mNwe6c1iwEl5fy0EMPpVrr1q2Lthvr3Lr4nnvuSTVdn+k++RERe+21V6rpXOmudXe9uKwV/Vm3RqkXl1+ga1Z3fO6zc3tz6xzr9vV3n53em2299dapj8shc/eaOhe7cdOttfQ+1r1Xbi5za2G9j9IMpIiIgw8+ONU0S8DdA7hcCjfWbbPNNkXb7X9fDy73RXNBXL6SHn+Ez1xZc801i7Ybi9ycqOOYWwe4+dVlCj7xxBNF282vbo7S+xx3zrn7CZcBouf5vffem/q4uVMz7HR9GOE/H3fvo9ejm+fqxY0NmrHn5lh3z+XyCnS8cGOdewaiuZHuGnc5Ze4+WTOP3PjkzmFd173++uupj3t24s5hXZO4807n4YicVeHed/e80d13aB6Hu2bqxWXl6RrZXTtuznP3grU8K3bnj57Dmicc4XPU3LM9fXarzzIi/FpL15xubefWUO5+XseyO+64I/WpJctGcxoj8to1Iq9LIyK6detWtN3v0xD+EgIAAAAAAAAAAFSCLyEAAAAAAAAAAEAl+BICAAAAAAAAAABUgi8hAAAAAAAAAABAJZrMnTt3bi0dzz///FTTQBAX5OICB10w17PPPlu0NbgxIuKdd95JNQ2YcX3cr6ghuBE52HLq1Kmpjwuz0/BZ18eFAWuwcETEbbfdVrSPPvro1EcDbSJy0IsL8XHBIvq+R+RAIw0Li4i4/vrrU60K5557bqpNmzataLdp0yb1ef7551PNBbDceeedRdsFhLrgQ+23yCKLpD4ulMoFi3Xp0qVoX3XVVamPC/rS886FwGtgWIR/H66++uqi7QK8XDipBt+4sD4NdI3w552GtbkwySuvvDLVGtuf//znVNMwHxdQ+vHHH6eaOwf03HRjnbvmNMBLw7LdcUb40C0NcRsxYkTq4wKPNeTLhee5c84FbWvYkgsBdYFwOm66a8r9e25u0DnMhWqdddZZqVaFP/zhD6k2e/bsot2+ffvUx4V3aeB2RMS1115btDt06JD6aEhfRH6/3XvrzjEXILnDDjsUbQ34isjh5xE5iNDNne7YO3XqlGp///vfi3a/fv1Sn1deeSXVttpqq6LtQsxcaNwbb7yRajp+uPevXnPs6aefnmoa4qnhlxH+Ot9iiy1STc9PFx6oc1lEfi9d0KIbH9zYqdeDO3YXCKfBhy600oULu5DPSZMmFe0DDjgg9XHhszqHuDHKBUy7c0rPOzenX3HFFanW2C644IJUe++994q2C1esNehX59gNNtgg9XHXr67F3Hvtzjm3RtSxxwVWaqBkRJ7DddyJ8GOre61BgwYVbRd+6X4ffa0nn3wy9dH7pQgfGKthhe49Pfvss1OtCuecc06q6brTrdncfawLrNT7yrXWWiv1effdd1NtvfXWK9ruPXL3o+61dG501/hGG22UajpeuPPJBVZqQG1ExNixY4u2C2Z114wGTLuQZX2vIvzvqGHMet8YEXHZZZelWmNz57Ze4+6ZgXtG4eZhXV+4uceNm/pcxI23GigbkYPcI/Jn4uZXfVYTkc+nVq1apT5ufHJz9bhx44q2BgZH+GtIr1F3H7fGGmukmptfdexw16cbg6rwu9/9LtV0zFphhRVSHze3uGcsen6613Lvt97vuvPu008/TTX33Ktdu3ZF283p7l5dP5euXbumPs8880yquZB5XSO6e2Jd20TkcVMDuyP8XOTOOx0n9b4xIuKvf/1rqlXhoosuSjW993bXkxvD3Rz04IMPFm33/MQFout44N4j93OvvfZaqulY5tbt7nm4vg/uunJjp5sfRo4cWbTdvcnMmTNTTen6J8K/p+6807W3C4Fv6LzjLyEAAAAAAAAAAEAl+BICAAAAAAAAAABUgi8hAAAAAAAAAABAJfgSAgAAAAAAAAAAVCKnX32HhRbK31e44A3lwmo0qCwih2Rq0HKEDzScNWtW0W7atGnq44JvXDCKhiIttthiqY8LrNRwEReq48I2XRCNBlG7wFgNz4vIIY4PPPBA6uMCXF2gsoaDuVC/etFjici//+TJk1MfFxrnAq40SNOdmy7kdV6DUl1QnQZpdu/ePfVxoTAaHuoC4lz4jgsZPPTQQ4u2hnxF+FAmDSlz19XAgQNTzYVjuzD1+eGzzz5LNb3GXeCYO3fcGKljlAvoc0FZGhLnrg13Drj3VceoLbfcMvVxv48Ggbn3yo3TLsxOr+Phw4enPhrGHZHPexfK6sJpV1555VTTgDsX4FcvLgxKw8ddWFq3bt1SzV3jGqblwi87d+6cajpHuM9yySWXTLWOHTummob+rbvuuqmPC1fX89oFdLtjcEF1Rx55ZNEeM2ZM6uOOS88f9/5paFqED/LWc1YD0uvJjdk6ZrhgPbeucuGBrVu3Ltru83XzogZRu2NwoYNt27ZNNQ3rdGsaF6qmYXZuvHPheRqMHBHxi1/8omi7OdaN31pz57Rb27n3VIMO3TqpHtz7qGtkNxa7OckF1S6++OJF282xbh2t49Nyyy1X07/35ZdfpprSuTPC/446trnXdtesC5Hdcccdi/awYcNSH7fW0FBfFwTr5lgXHq/rxvm5znNrJh3H3fvt1r7uHlXHOhdy695LXRO6n3Pvrbt/W3/99f/ta0f4IE0972r5/SIipk+fnmoHHXRQ0XZzrLtn0rFu0qRJqY97Lbe20/nJrUvrwb2PGgzuwk/d3Oaew+h75q4vd+5omK07T9wc4o5B1zO1hprr/bcbb3Usj/Ah4xrM6p6BbLjhhqmmawN37Y0ePTrVXIi2cu9pvbgwWw0jd/Owu59yz7R0jezWde490jncrX3due/mPF1vuvWMe31dk7s+7tx3z5B23XXXou0Clt1zUL2O9F4vwo9/7rh0rHPzXL24+yKd89yzVbdunzNnTqrpHKThyBERa665ZqrpGtDdL+q4/F399DNw548LhdZr0q3ZNtlkk1Rzr9+7d++i7ebFTp06pZquD8aPH5/6vPnmm6nmxn2dU/XZTC34SwgAAAAAAAAAAFAJvoQAAAAAAAAAAACV4EsIAAAAAAAAAABQCb6EAAAAAAAAAAAAlag5mLqWwIknnngi1VxglAtr1SBNFwTmwmpqCTlzQWMu5FCP4Z133kl9XKDhhAkTirYLI9JAwO+iIV9bbbVV6uMC4bTmAu9c6KELYdKQLBf8Ui/us9NwIBe+7EJ+3HmnAZLuPHehYRqA5EJhNPAqIuKxxx5LNQ2idqFb7vPUUBgXMOOCUt15MHXq1KKtgYYRPoDu7rvvLtouaMeFUD/33HOppiF7Lhy2Htz5rr+XC6h3Qa0u+EvHSTemuM9bx5UXX3wx9XGvpSHqEfkccEGqLlxOzycXeOd88803qaZzgwYtRfhxWq8hF9rk5h0XFKXzhwvMqhd37Wig2axZs1Ifd91ryGtExOTJk4u2C7V057ByIa/uWp04cWKqaVCdG6fd56T9XOigW3+4sU7DvV0ou5tT+vfvX7RdiKILA3z99ddTTdcWLgywXtxYo2Gabi3kxkkXSqdrk1pDXjUA3YWl1XKeR+Rry617OnTokGr62bn3ygVnuvdG1xEumNXNK3q9uWD4ddZZJ9Xcseoat5brvQou7E/XenqdRvj31Y2JGtRda5i0jjPuGFzQ/FtvvZVqOia6z9aNFzrHuuvFjd0utFs/3z59+qQ+bo7V0HT3Xrl7GvdaGoDrxvx60WOJyGPPG2+8kfq4dY47F/Uzdud5LcflAlDdOezWDDoPvvvuu6mPC4zVcdp95i5g1Z2LOla70FG3jtDx1v1+bqxzn6t+Fm6crgcNeY/Ia1b3HMPdi7prR+8X3XjhPku9f3T3ubWuo/XzduuFWu47HQ1TjvC/o4YUb7311qmPux/Te1G3znD3VW6NqHOR++zrxQVF63vpAupd8LE7F3WcdNeXO191vHDH4J57Pf3006mm3PrTzbE6X+u5E+HHd1fT43fhxu6ZnV4jbk2q12hExIwZM1JNj39+PrNzn7l+Lu6zdOePm/OeffbZou1+Vw3CjshjoJtj3fXqxjJdM7h1j3ve+NJLLxVt91zEzbEuGF5r2223XerjniVqcLp75uHeBzee6Pjtnn03hL+EAAAAAAAAAAAAleBLCAAAAAAAAAAAUAm+hAAAAAAAAAAAAJWoORPC7Uml+2C5PULd3lxuX3zdP9Xt7eb2ytK9X7t165b66B5iEX7/LN2vS/f9j/B7x+m/OXjw4NTH7Yfo9ifUfdiHDh2a+iy0UP7uSI/V7W/s9i1z+7fp/n+15llUwe0/qXuYrbnmmqmP2+t49OjRqabvt9tH2b3+pEmTinbnzp1TH7efcNeuXVNN9xR0+1y7PbN32GGHon3ttdemPh07dkw1t8em7nM8ZMiQ1Kddu3apptfpYYcdlvq4PfXcfti6/6sbA+rBXeN6nbhxzR2vy+TQPSrdNehqej65DAW3H3qXLl1STffedfuAuj0A9fwdOXJk6uPOE3f+6j6rw4cPT31atGiRas2aNSvaLnPE5WW4cUzf5/m1b3CEnw/mzJlTtF12gDtmnRcjItZYY42i7fajdK+vmSIuL0b3EI+I2GeffRp8LbeHpDuGHj16FG03x7qxzr2nW2yxRdG+8847Ux93fes+2i5Lwu1vu+GGG6aavvd6TteTnmMR+bpwe5u7fYJdtoxew+68c3uu617Neg5E+LWk66drQLcPqsta0D1phw0blvq0b98+1dx7qnvEPvzww6mPWyfqfuedOnVKfXSf14jaMtRqzfRpbC7HQWvuGnRjncvE0XWdm5vdHKt7N++6666pj5tb3Geie2a738edJ9tvv33RdnOsW9+7bCQds0aMGJH6uOPSPYFdPpTb57qWewW3n3u9uPtYvb7cNeGuJZdr5tYryo31ml+g50CEP++22WabVNPPxWXTuTG4devWRfv+++9Pfdy54s47zW1w6wN3Hug9vltLuj3Ra8msnF9jXS05Qm7/cDc+udwG/VmXDeP2ltd7AHdP5vZNd5+J7g3uznH3Gel8p/fVET6Dp5a1q7v3cmtLXQtoRmOEf3bifkfd139+ZkK4LBgdn9dff/3Ux52vLs/IPRdRbr9+HcfcWOee2bl1lp7Dbpz+6KOPUk2vh6eeeir1cXkoLvtJx82HHnoo9XHjps47el8S4fOJ3O+oY/D8vI9177c+23FjsXuP3H2sXsPuc3Lre32+67JCXEaNe76geUZu3eOeI7Vp06Zou/sXd6/lnp/omsytE915oO+fu47duO+ev+u6el7mWP4SAgAAAAAAAAAAVIIvIQAAAAAAAAAAQCX4EgIAAAAAAAAAAFSCLyEAAAAAAAAAAEAlmsx1KbUAAAAAAAAAAADfE38JAQAAAAAAAAAAKsGXEAAAAAAAAAAAoBJ8CQEAAAAAAAAAACrBlxAAAAAAAAAAAKASfAkBAAAAAAAAAAAqwZcQAAAAAAAAAACgEnwJAQAAAAAAAAAAKsGXEAAAAAAAAAAAoBJ8CQEAAAAAAAAAACrxfwF+F4rqH1tKXAAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "n_plot = 10\n",
        "\n",
        "fig, ax = plt.subplots(2, n_plot, figsize=(20, 4))\n",
        "for i in range(n_plot):\n",
        "\n",
        "    # display original\n",
        "    orig_img = testset[i][0]\n",
        "    ax[0, i].imshow(orig_img.squeeze(), cmap='gray_r', vmin=0, vmax=1)\n",
        "    ax[0, i].axis('off')\n",
        "\n",
        "    # display autoencoded\n",
        "    with torch.no_grad():\n",
        "        autoencoded_img = autoencoder(orig_img[None])\n",
        "    ax[1, i].imshow(autoencoded_img.squeeze(), cmap='gray_r', vmin=0, vmax=1)\n",
        "    ax[1, i].axis('off')"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "9279a260",
      "metadata": {
        "id": "9279a260"
      },
      "source": [
        "### Training\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "66841b49",
      "metadata": {
        "id": "66841b49"
      },
      "outputs": [],
      "source": [
        "loss_fn = nn.BCELoss()\n",
        "\n",
        "optimizer = torch.optim.Adam(autoencoder.parameters(), lr=1e-3)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "train_loader = torch.utils.data.DataLoader(\n",
        "    dataset=trainset,       # The dataset object to load data from\n",
        "    batch_size=256,        # Number of samples per batch\n",
        "    shuffle=True,           # Shuffle the dataset at every epoch\n",
        "    num_workers=4           # Number of subprocesses to use for data loading (optional, depends on your system)\n",
        ")\n",
        "\n",
        "\n",
        "test_loader = torch.utils.data.DataLoader(\n",
        "    dataset=testset,\n",
        "    batch_size=256,\n",
        "    shuffle=False,\n",
        "    num_workers=4\n",
        ")"
      ],
      "metadata": {
        "id": "Pz_zfG_C8N05"
      },
      "id": "Pz_zfG_C8N05",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "num_epochs = 40\n",
        "\n",
        "for epoch in range(num_epochs):\n",
        "\n",
        "    # Training phase\n",
        "    autoencoder.train()\n",
        "    train_loss = 0.0\n",
        "    for data in train_loader:\n",
        "        inputs, targets = data\n",
        "        optimizer.zero_grad()\n",
        "        outputs = autoencoder(inputs)\n",
        "        loss = loss_fn(outputs, inputs)\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "        train_loss += loss.item()\n",
        "\n",
        "    # Validation phase\n",
        "    autoencoder.eval()\n",
        "    val_loss = 0.0\n",
        "    with torch.no_grad():\n",
        "        for data in test_loader:\n",
        "            inputs, targets = data\n",
        "            outputs = autoencoder(inputs)\n",
        "            loss = loss_fn(outputs, inputs)\n",
        "            val_loss += loss.item()\n",
        "\n",
        "    # Logging the losses\n",
        "    print(f'Epoch {epoch+1}/{num_epochs} \\t Training Loss: {train_loss/len(train_loader)} \\t Validation Loss: {val_loss/len(test_loader)}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MO7MqULOufMM",
        "outputId": "b4b7a24a-8fdf-4e97-e114-8753889f8048"
      },
      "id": "MO7MqULOufMM",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/40 \t Training Loss: 0.20999598877227052 \t Validation Loss: 0.1454343345016241\n",
            "Epoch 2/40 \t Training Loss: 0.13941595427533413 \t Validation Loss: 0.1333814537152648\n",
            "Epoch 3/40 \t Training Loss: 0.13208055654738812 \t Validation Loss: 0.12941980585455895\n",
            "Epoch 4/40 \t Training Loss: 0.12851335200223518 \t Validation Loss: 0.1256643423810601\n",
            "Epoch 5/40 \t Training Loss: 0.1260002261463632 \t Validation Loss: 0.12407862860709429\n",
            "Epoch 6/40 \t Training Loss: 0.12433465627279687 \t Validation Loss: 0.12290417142212391\n",
            "Epoch 7/40 \t Training Loss: 0.12284544357594024 \t Validation Loss: 0.1222331641241908\n",
            "Epoch 8/40 \t Training Loss: 0.12189266868728273 \t Validation Loss: 0.120450334623456\n",
            "Epoch 9/40 \t Training Loss: 0.12082460842868115 \t Validation Loss: 0.11979458145797253\n",
            "Epoch 10/40 \t Training Loss: 0.11994796785268377 \t Validation Loss: 0.11980451885610818\n",
            "Epoch 11/40 \t Training Loss: 0.11944882219776194 \t Validation Loss: 0.11840823292732239\n",
            "Epoch 12/40 \t Training Loss: 0.11863197858663316 \t Validation Loss: 0.11800538506358862\n",
            "Epoch 13/40 \t Training Loss: 0.11820297862621064 \t Validation Loss: 0.1178604057058692\n",
            "Epoch 14/40 \t Training Loss: 0.11747801665295945 \t Validation Loss: 0.11748937778174877\n",
            "Epoch 15/40 \t Training Loss: 0.11714540028825719 \t Validation Loss: 0.11649640910327434\n",
            "Epoch 16/40 \t Training Loss: 0.11662479505894031 \t Validation Loss: 0.1161330034956336\n",
            "Epoch 17/40 \t Training Loss: 0.1162088118969126 \t Validation Loss: 0.1160913772881031\n",
            "Epoch 18/40 \t Training Loss: 0.11583554969823107 \t Validation Loss: 0.11536661814898252\n",
            "Epoch 19/40 \t Training Loss: 0.11552319082807987 \t Validation Loss: 0.11511445883661509\n",
            "Epoch 20/40 \t Training Loss: 0.1151230220147904 \t Validation Loss: 0.11503906641155481\n",
            "Epoch 21/40 \t Training Loss: 0.11476151819558854 \t Validation Loss: 0.11562303770333529\n",
            "Epoch 22/40 \t Training Loss: 0.11468523452256588 \t Validation Loss: 0.11472866982221604\n",
            "Epoch 23/40 \t Training Loss: 0.11429141965952326 \t Validation Loss: 0.1148607850074768\n",
            "Epoch 24/40 \t Training Loss: 0.11413492366988608 \t Validation Loss: 0.11394498739391565\n",
            "Epoch 25/40 \t Training Loss: 0.11380479110682264 \t Validation Loss: 0.11400097217410803\n",
            "Epoch 26/40 \t Training Loss: 0.11355627505703175 \t Validation Loss: 0.11369167882949113\n",
            "Epoch 27/40 \t Training Loss: 0.11333422942998561 \t Validation Loss: 0.1134447354823351\n",
            "Epoch 28/40 \t Training Loss: 0.11310866918969661 \t Validation Loss: 0.11308349203318357\n",
            "Epoch 29/40 \t Training Loss: 0.11296475945000953 \t Validation Loss: 0.11308509185910225\n",
            "Epoch 30/40 \t Training Loss: 0.11278220462672253 \t Validation Loss: 0.1135673301294446\n",
            "Epoch 31/40 \t Training Loss: 0.11257936491611156 \t Validation Loss: 0.11306852102279663\n",
            "Epoch 32/40 \t Training Loss: 0.11242087083928129 \t Validation Loss: 0.11264919564127922\n",
            "Epoch 33/40 \t Training Loss: 0.11228007036954799 \t Validation Loss: 0.11275661941617728\n",
            "Epoch 34/40 \t Training Loss: 0.11207681704074779 \t Validation Loss: 0.11229431889951229\n",
            "Epoch 35/40 \t Training Loss: 0.11205190337718801 \t Validation Loss: 0.11261147614568472\n",
            "Epoch 36/40 \t Training Loss: 0.11181022550197357 \t Validation Loss: 0.11225395686924458\n",
            "Epoch 37/40 \t Training Loss: 0.1115641362172492 \t Validation Loss: 0.11220308933407068\n",
            "Epoch 38/40 \t Training Loss: 0.11152934593723175 \t Validation Loss: 0.1119412638247013\n",
            "Epoch 39/40 \t Training Loss: 0.11146207572297848 \t Validation Loss: 0.11202531475573778\n",
            "Epoch 40/40 \t Training Loss: 0.11124467012730051 \t Validation Loss: 0.11204470992088318\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "1eb6237d",
      "metadata": {
        "id": "1eb6237d"
      },
      "source": [
        "ouput after the training"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n_plot = 10\n",
        "\n",
        "fig, ax = plt.subplots(3, n_plot, figsize=(20, 4))\n",
        "for i in range(n_plot):\n",
        "\n",
        "    # display original\n",
        "    orig_img = testset[i][0]\n",
        "    ax[0, i].imshow(orig_img.squeeze(), cmap='gray_r')\n",
        "    ax[0, i].axis('off')\n",
        "\n",
        "    with torch.no_grad():\n",
        "        encoded_img = encoder(orig_img[None])\n",
        "    ax[1, i].imshow(encoded_img, cmap='gray_r')\n",
        "    ax[1, i].set_yticks([])\n",
        "\n",
        "    # display decoded\n",
        "    with torch.no_grad():\n",
        "        autoencoded_img = decoder(encoded_img[None])\n",
        "    ax[2, i].imshow(autoencoded_img.squeeze(), cmap='gray_r')\n",
        "    ax[2, i].axis('off')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 235
        },
        "id": "j5tmf07qAIKJ",
        "outputId": "aa6b333e-6a64-4ffe-bf07-aafd30753931"
      },
      "id": "j5tmf07qAIKJ",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 2000x400 with 30 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Aufgaben\n",
        "1. Dimension des latenten Raumes\n",
        "  - Verlgleichen Sie die Resultate für unterschiedlich große latente Räumen\n",
        "    - Wieviele Dimensionen muss der latente Raum mindestens haben?\n",
        "\n",
        "2. Rechnen im latenten Raum\n",
        "  - Berechnen Sie die latente Darstellung für 2 Testbilder (encoded images)\n",
        "  -  Erstellen Sie ein gewichtetes Mittel der beiden Embeddings  $\\alpha \\vec{e_1} + (1-\\alpha) \\vec{e_2}$ für verschiedene Werte von $\\alpha$ zwischen 0 und 1\n",
        "  - Dekodieren Sie nun wieder den gemittelten Code\n",
        "  - Bonus: Wie sieht das Ergebniss aus, wenn man dieses gewichtete Mittel direkt im Pixelraum ausführt?"
      ],
      "metadata": {
        "id": "jywU9Pfsbiwe"
      },
      "id": "jywU9Pfsbiwe"
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "machine_shape": "hm",
      "gpuType": "T4",
      "include_colab_link": true
    },
    "language_info": {
      "name": "python"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 5
}