handwritten_digit_recognition_GPU.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "handwritten_digit_recognition_GPU.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "metadata": {
        "id": "MHvuWIUHdIpt",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Handwritten Digit Recognition\n",
        "- Author = Amitrajit Bose\n",
        "- Dataset = MNIST\n",
        "- [Medium Article Link](https://medium.com/@amitrajit_bose/handwritten-digit-mnist-pytorch-977b5338e627)\n",
        "- Frameworks = PyTorch\n"
      ]
    },
    {
      "metadata": {
        "id": "oGjRmijsaXJ3",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Necessary Imports"
      ]
    },
    {
      "metadata": {
        "id": "TOyGrPT5ASDc",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# Import necessary packages\n",
        "%matplotlib inline\n",
        "%config InlineBackend.figure_format = 'retina'\n",
        "\n",
        "import numpy as np\n",
        "import torch\n",
        "import torchvision\n",
        "import matplotlib.pyplot as plt\n",
        "from time import time"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "XPuuTDEfAfDy",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import os\n",
        "from google.colab import drive"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "uLdtrS4zaeEs",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Download The Dataset & Define The Transforms"
      ]
    },
    {
      "metadata": {
        "id": "sZD2NGz2Ak6w",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "### Run this cell\n",
        "\n",
        "from torchvision import datasets, transforms\n",
        "\n",
        "# Define a transform to normalize the data\n",
        "transform = transforms.Compose([transforms.ToTensor(),\n",
        "                              transforms.Normalize((0.5,), (0.5,)),\n",
        "                              ])\n",
        "\n",
        "# Download and load the training data\n",
        "trainset = datasets.MNIST('drive/My Drive/mnist/MNIST_data/', download=True, train=True, transform=transform)\n",
        "valset = datasets.MNIST('drive/My Drive/mnist/MNIST_data/', download=True, train=False, transform=transform)\n",
        "trainloader = torch.utils.data.DataLoader(trainset, batch_size=64, shuffle=True)\n",
        "valloader = torch.utils.data.DataLoader(valset, batch_size=64, shuffle=True)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "GcAfrn2falkK",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Exploring The Data"
      ]
    },
    {
      "metadata": {
        "id": "xOjlOyjcCezX",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "c68b40b1-cf61-461f-c3c8-39f865d35209"
      },
      "cell_type": "code",
      "source": [
        "dataiter = iter(trainloader)\n",
        "images, labels = dataiter.next()\n",
        "print(type(images))\n",
        "print(images.shape)\n",
        "print(labels.shape)"
      ],
      "execution_count": 76,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "<class 'torch.Tensor'>\n",
            "torch.Size([64, 1, 28, 28])\n",
            "torch.Size([64])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "EuBvOWmGDHOq",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "1ef33d49-4947-47cc-91f1-1895b8544559"
      },
      "cell_type": "code",
      "source": [
        "plt.imshow(images[0].numpy().squeeze(), cmap='gray_r');"
      ],
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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v6Yc+ALACw/iZ/fj81weorE0y/+f0Q2utV5ZSfjbJWUl+P8kBSe5KL+D/rNZ6wxBqAYCp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\nSUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 249,
              "height": 248
            }
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "F9CppCcqDLtB",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "d6bd6bd1-3d7b-47ae-f734-4d3bf24c975d"
      },
      "cell_type": "code",
      "source": [
        "figure = plt.figure()\n",
        "num_of_images = 60\n",
        "for index in range(1, num_of_images + 1):\n",
        "    plt.subplot(6, 10, index)\n",
        "    plt.axis('off')\n",
        "    plt.imshow(images[index].numpy().squeeze(), cmap='gray_r')"
      ],
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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NAdh1112B8LpIw0qCVgK0QnLuuecCIQq1yiqrACGKE49+Z0d71FZdUTE1jVGDMc2PNphn\nl8RLK5VcUznM7EjhxhtvDIRjSxppA1q/fv2AsFFNpdtUai7X5ujqCgBcf/31QCiBt+SSSxZwxMmq\nSwMgSXNkXI2Abr755mqv1/9WbePzofOOMWPGADBv3rzI9autthoARxxxBADNmzfP+zEKSWWA1fBK\nJUBV9jb+fqlshkL48ccfAdh3332BUNwjyQ3CjpCbmZmZmSUo/eG6MvXVV18BIU9SVKZMrZDTSLlv\nihAOGDAAKJ/mAqXyxBNPAFWjEJKd55kdLU+73XbbLfJVJbTeeustIJSk0vxcffXVVe5DZaxUMrMU\nbecLRfnciqR8+eWXQCj1qf0CalaRqzRhdlnIww8/HIBLL70UgJNOOgkIjS5mz54NhNWJSvDxxx/n\nvC5NewZyUTk7vS6WXXZZIKyMqLGWmrboeaLGQM8991zmvqZNmxa5L5UePeyww4r3B5RYbbnj2c1/\n0ljmUNT0RucIcXvuuScALVu2rPN9qoW8jg8zZ86s9nbag1CfUs7F8Ndff0V+1opgrpKwOi5odaEh\nx4kZM2YA4TWl0qpJrj46Qm5mZmZmliBHyItE1VXi1Cgo6dythlCEXDmOynlrbCZNmlTt5fqkneZV\nkHy0bt068lUU/a6OcurTFBnXipCic6qaor9TkfH6UHT02GOPBcJrTMcR5ZZ37dq13o9RbqprFCWq\nupBmHTt2jPys4+Upp5wCwJQpUwBYd911AbjrrrsAWH311YGQ0wrQs2dPIKw6nXPOOUBlRMhrawCk\n11va9ygpin3NNddUe72i13Vtgpbd1EerKrnOO3T80Epcuartda/XgXLO69OAUA3a9BoS7eNZfvnl\n877PQnGE3MzMzMwsQY6QZ4nvald+k3KEF1544Zy/q8oSF198MVC1bbhkt5dPK9UdV1UE5UY2FqoB\nrXrBcTvssAPQeFcO1ApdNbMlu059+/btSzqmQlCuuL6qikoxo9Z6jan9uuqVp9mcOXMAeO211yKX\nK8pXKRTpVnt7VVlR7vBZZ50FhMhovO60VtogRNUVIf/kk0+AUC1DPSFyUS30IUOGAKFGfj55yoWm\nyHhtVVXSXFEl24svvgiECK3ouDh06FCg9r1Yioxnryzkiox36tQJgCuuuAKApk2b5jvsknrssceA\n0H8iTuNXZZT6UFUsrdDp/KW2lZpScITczMzMzCxBjpADHTp0AMLO3vfffx8IkWBVS1DnQdWRVU4Y\nhJymU089FcjdmVPRkDRSNQ3lzCo609iqq5x++ulAqLsdd8ABB5RyOGVDOa/KA1S9elEt7bRSvru+\n6vWgyijxnMR86FijnGDVE1ZueSHr7yZN8xWvQNW7d+8khlM0qhGuqjwN0b17dwC22WYbIEQSb7nl\nFiDkBq+33npAmFtdr/cdXb/ooos2eEz1Vdd645USGY+Lnxvk6nyslXmtrKiPweTJk4Fo59dc3T73\n228/IETKy526HOtYsOCCCzb4Pn/55RcgdOCcOHEiEHpdaPUoydUicYTczMzMzCxBjpATPhkpeqAI\nudx///0AbL311gAstdRSQKi6AKFOcPyT6gorrADAhAkTCj3skotHeiohn7WQ2rRpA1RWJYx8qCtt\nduQmW312xJcTPd+nTp0KhLxu5X6qMoq6bNZWdUWRLgh1x3XsueSSS4DQ5VP7EhRB0mOnkWok61i5\n/vrrA6GCguV28MEHA6HCk7oNqqujOpsqqjp9+nQAFl98cSDkrWuVNwm1rfao3niaa43nQ3spVFN7\ngQUWAMIqxwsvvFDn+9KK2ogRI4DyX5XUMVJde1VfX7niWm2tz3uqVvJV0Us5/MoZV2S8nFYPHCE3\nMzMzM0uQI+RZxowZA4RPbdkRLMgd+cum6LkiFgcddBAAK6+8csHGWS40P8ccc0zCIymN8ePHA6HC\ngaj6jjqwKXe0sVHnReVYq5qAIj7ZVSPSTFFrRfq0418RckWl1HVOkWDVH9bPqtIC0K1bNyDsQVEE\nXMccVYBShZc0euONN4Cq1YlatGgBNL69KPWx1VZbAdClSxcAnnnmGSB3xSe9FuPvbUnSSlk8h7xS\n6o3nMmvWrBqv1/FEr/VceeGSXedec6e9AlqtLXfaGzF48GAA+vXrB4T9evE9EqpcpGOnKjbpuKgu\nuNnXifLSr7rqKqA8csbjHCE3MzMzM0tQk3jt7ZQryB+jOp/qnKYod1x27pE+9ffq1QsIEYwiqPlj\nc1RB/7maF+V6KhfrzjvvLOTD5Ktk8/HKK68A4X/9/fffA7DzzjsDobZvwhJ7fohWEvr37w+Enf4D\nBgwoxsPVpmTzobq2qr8ej4irLr0i7KreBCH3M06rDJ07dwZCvekG7FNI7PmhHgyPPvpo5HIdP/r0\n6VPIh6urxF8v9aH8YkWTH3roISBETRX9O/HEEyM/10HR50ORcdV9VnS3TKuqFGw+PvvsMwCGDx8O\nhPOL7L1oECLk6hgZr7mt6mbZ/T9KuLqUz3xAns+RW2+9FQj79rTy8+GHH+b5sKFztKLrxx9/PFCY\nyi0x+c5JTo6Qm5mZmZklyBHy9EllRKeIPB9Rno8oz0dUYvOhOsC33347EFaaFA1TJZAS8/MjyvMR\n5fmIKmqEPG7u3LlAiG4/+OCDkevVQ2bzzTcHwuojhONNrtXHAnKE3MzMzMysEjhCnj7+xB7l+Yjy\nfER5PqI8H1GejyjPR5TnI6qkEfKUcITczMzMzKwS+ITczMzMzCxBPiE3MzMzM0uQT8jNzMzMzBLk\nE3IzMzMzswRVWpUVMzMzM7NUcYTczMzMzCxBPiE3MzMzM0uQT8jNzMzMzBLkE3IzMzMzswT5hNzM\nzMzMLEE+ITczMzMzS5BPyM3MzMzMEuQTcjMzMzOzBPmE3MzMzMwsQT4hNzMzMzNLkE/IzczMzMwS\n5BNyMzMzM7ME+YTczMzMzCxBPiE3MzMzM0uQT8jNzMzMzBLkE3IzMzMzswT5hNzMzMzMLEHzJz2A\nAvs76QGUQJM8buv5iPJ8RHk+ojwfUZ6PKM9HlOcjyvNRleckD46Qm5mZmZklyCfkZmZmZmYJ8gm5\nmZmZmVmCfEJuZmZmZpagStvUaVYw7733HgCtW7eOXH7//fcDsNNOOxV9DL///jsAf/31FwALLbRQ\n0R/TzMzMSssRcjMzMzOzBDlCnuXuu+8G4Oyzzwbgtddei1z/73//G4A2bdrU+T7XX399AHbccUcA\nFlxwQQCaNClYpZxUOOSQQwCYNGkSAK+88goASyyxRGJjykXR6EGDBlV7/UUXXQSUJkK+7777AvD6\n668D8MILLwCOlKfZiSeeCMCIESMyl/399/+qg/Xr1w+ACy+8sPQDs0RoFey2224D4J577gHCSlxN\nVl99dQCOPfZYAI4++uhiDNHK3K+//grAvffeC8Bjjz0GwJgxY+r0+6eddhoAQ4YMKcLorK4cITcz\nMzMzS5Aj5ISIqCITs2bNAqpGsW+55ZYGP5YiGeeccw4Aiy22WIPvs5w9/PDDQJi7Tp06AbDwwgsn\nNqbazJs3DwjRhiRMnToVgIceegiAjTfeGIB//MOfodNq+PDhQIiMzzfffJnr/vzzz8h177//PhCO\nQbfffnvJxmnF9fPPPwPwwAMPAGG18LzzzovcLvu1rpWyVq1aAbDddtsBcOihhwJw0kknAdCsWTMA\nDjjggKKMvRh+/PFHAIYOHQrAP//5TyD8jXVxzDHHADBu3DgAnn/+eSDMVyX59NNPgejzZfLkyQDM\nmDEjctu6rsTreWPJ8ru7mZmZmVmCHCEnRKNKEYW67LLLAHjuueeA8Ek+O1pWCfQpXrnjijo3b94c\nCLn05ahp06YA9OjRA0gmOjllyhQAvv/+ewDWWmstABZYYIGSj6Wh5syZA8BSSy2VuUzff/7555Gv\nd955JxBWkBThGTVqFAAHH3xwCUZcWPob9FX54oqKV3eZ5kG/c8cddwDOMa+radOmAbDooosCsMYa\nayQ5nAjlecfzexXN1f+4Q4cOmesUNY474YQTADjooIOAsMckTRHyq666CoBhw4YBYVUwnwj5jTfe\nCMBPP/0EhPefSoqQf/vtt0DYN6C/Feq/J2233XYDwnOuXOn9b5999gFCzvszzzwDwAorrADAaqut\nlsDoCscRcjMzMzOzBDlCDiy99NJAyNNVlKGYXnrpJSDkr1dahPzrr78G4MMPP4xcvuqqqyYxnLwo\nWqnoynrrrQfA9OnTSzaG66+/vmSPVSzKje3WrRsALVu2zFy34oorAvDuu+8Coea7xKPKZ555JpCu\nCLlyxvU36DWuKHh1OeS5bhPPMa+ECPlbb70FwK677grA/vvvn7lOlWjqSpVK9tprLwAeeeQRADbZ\nZBMAHn300QaNtZBGjx4NhFUfzYOi+Pm8F7Rv3x5IV9UlrZZefPHFQIiMa/UvV3Wrxuqrr74C4F//\n+hcQ9iDofAXCe5T2HmmOddzQSpGeL7179wagZ8+eQPmvvGqVdeDAgUB4Del9Y/HFFwfCCjyE176i\n63Gam5tuuilyuebku+++A+CKK66IPEYxOUJuZmZmZpYgR8gJlU7OP/98IESfVId8zz33BOqXn6Sd\n4++880611ysHaquttsr7vsuZ8gJlzTXXBMIcl7P55//fy+K4444DQgTH6kbVihTNVq6jIoEQIh6V\nSPnf6msQzw+vSw55bT9vuummANx1110ArLTSSsX4Uwrql19+AWDixIkA7L333kDYs6FVk/pQ3rFq\ndysiqNzqchKPgOeK4NXFb7/9BoSV1jT47LPPgBDtlLPOOgsI0du6OOyww4BwjOncuTMAG220UYPH\nWS7U/+Q///kPALvvvjsAt956a87f0d4j1SdfdtlliznEolHfEh331PtD52xaVdP7yQcffJD53fru\n/VJEvEWLFgD88ccf9bqf+nCE3MzMzMwsQY6QZ9FO9lw72utD+V8DBgyo9vquXbsW7LHKifIjZb/9\n9gPKu7pK3BtvvFHt5Q2JaNXm2WefBWD27NlFe4xiUURYO+EVvauLJZdcEgi5kE899VRhB1dCe+yx\nBxAioXXJIVc+qKpmKCKunHFVZdLvaJ+LHkvPm3I2cuRIINTMXmSRRYCQ312fqObMmTOBUFVEx5cL\nLrgACNHESnXfffcBIYc+DVRBSZZZZhkg9OioC/3ftUIk22+/PVBZe7LefvvtvH+nFPnOpaBqOToe\n6nWdq2pS9kpRfNVI1fQef/xxIKyE6/0qLn7cLgVHyM3MzMzMEuQIeYEoh+nll18GQuRC3djilCdX\nCZ/klWN16qmnZi5TxEYRq1yfQstZrk6d2u1eDD/88AMQdsnLuuuuW7THbKghQ4YAIXqRKzKevfK0\nzjrrAKFzq65T7qMi5fHblzP1FKgt/7tv375AiIZDqAgQ16dPHyBEa+L3qch5OVP0XhHytddeG4DT\nTz8dqF9kXPd54IEHAqFGs+YrTdV4GiLeYVF5+eVI+f1jx46NXH7UUUcB0QoZtVEeuiphSDnVmy8W\n9SSoKYe8scrubhvvaq0Kb+Vc6c0RcjMzMzOzBDlCXg+K4inCA3DzzTcDVT+x56JoQH07bJWT//73\nvwBcdNFFVa5TjeGGVFAw2HHHHZMeQhVaBVKN8PhzeeWVVwZCd9qaqieoSsI222wDhAiwqDNbOVJk\nXNWYassZV4SrLvKpZV5utA/g+OOPB8IqoqppKP89H6rBrC6Xuk+txJ1yyin1H3CK/Pjjj0BYgVUV\nq44dOyY2ptp88cUXQLS6EOTXkVNat24NhOohum/1iqjPc6tc6X1VNfb1GjjyyCMzt4lXNatUqtSk\nY6hWW+LPKQgrL6orngaOkJuZmZmZJcgR8jy8+uqrABxyyCEAvPjii/W+rxtuuAGALbbYAoB99923\nQWNLkualOpVe5aAxi0fG9VVVFPQ6qakGriIeqierigK6L70+unTpUsCRF5YqPWgXfzxnXDXCVZ88\nH6qmUpda5uVCFTDUbXPGjBlAqBndv3//et+3egJMnjw5crmiiJVUf7omer9QN9zzzjsPCJVr0kSv\neUX3Vf2iJloRid82vvekEvTq1QsIvUq0KqJVIgivrUr7+7/88svIz6ozr/rqWilZbrnlAPjmm28y\nt1XNclWwUq+CfPYqlJoj5GZmZmZmCXKEPA9ff/010LDIeNzcuXMLdl+lpuoq1XWyVN6oPp2mUTz6\nsvzyywPF3aUdz51OE62GqOa0zIv+AAAgAElEQVR+fJd7dRTtUXdPadWqFRByIxdYYIGCjbPQVCs8\nV363IuO5KqnUJL76kIYc8ksuuQQIK2fK4VRO58ILL1zv+546dSoQjpvt2rUDwgpLpVP1peyut1De\n1VVkhx12AKB9+/YAzJo1CwidKK+99logrLxpdaw62p+y9NJLA/DJJ58UfsBlRsdV1e1XlBhCx+9K\ni5BPmDAh8rOOodpTpBWxpZZaCgj7+yD0QlH1N82NKjStssoqxRp2vTlCbmZmZmaWIEfIrd6UO/vm\nm29WuU41qcs5slmbk08+GQgRP9W+Vc5jMWrepqnqzsUXXwyEqIRqidclMq7KJLnq02vOVT2inNWW\n312fyLheW4qu53qM2267rb7DLhjlziui+fHHHwOw0EILAXD22WcDDaslf/vttwPheSPKnW5I1D1N\nttxySyDk6WtvRYsWLRIbU12tsMIKADz88MNAqKik9w9V5VFtfd1eqx/Z1TI22GCDoo+33Gy66aZA\n6DS5+eabZ65TxFi3KedqO3WhqjnafyKKeud6783uUNqvXz8g9D3QCk2HDh0AeOmllwBYffXVCzXs\nBnOE3MzMzMwsQT4hNzMzMzNLkFNWikTLt9qIoWWmCy+8MKkhFZwaw0j20nw5bjZLg6+++qray1XO\nqZyWprfddtu8bq9N0RBK4v3222+R2wwZMgSAnXfeuYGjK51ibLhUyk6u+9Rm6fqkwxTawIEDAXjn\nnXcilyt16aabbgJgypQpQGjaoo1Y1fn999+B0AAkntqk0olpep40hDazqsyhqLRbmlID1STuiSee\nAELzOKUEqtSdnk96fqmhFIRN32oophQubXjUfSn1a+LEiQAstthiBf97Sm2zzTYDon+L5kHHDTUq\nTCuVw9VzYfvttwegbdu2ed9Xjx49gLDJXMdMvdfceOONDRtsATlCbmZmZmaWIEfI86CNEvrUfeut\nt2auU/mtvn37AqG0kzY2PfjggyUbZ7EpSqOSRIp0ZUf/67KxL60UfWkIlaxS6a8PPvgAgBNOOKHG\nx1xrrbUa/Nilpvbmu+yyS+YybUoTRXzV4CINtMGwkBsudZ/6quh7/DE0l2o6lCSNRc1aVILtjTfe\nAOCyyy6L3P7SSy8FwoZdlREdOnRo5jYqLasGOJqH1VZbDahfu/WkqVShSn2qdJ82ncVf24oSQti8\nquOGoszHHntsEUdcXC1btgTCJk5R5Pz888+PXK+W8RCOl6LnRzzaqdK1KnWnSGslyP7f6/mhufrx\nxx8BWHTRRUs/sALQuFU+WZtW63NeoeeGNpXvtttuQGjOuNdeewHlcUyp3LMmMzMzM7MUaJLmRiTV\nqPaPUVRJke0NN9wQKE7Zurhx48YB4VOYciNFTRAGDRpU17vMpy5eUf65++23HxByQzt16gQUtmFS\nHoo2H2o2ofJb0rVrV6Bq++44lYMDePfddwF47LHHIr9b232I5lZzXYPEnx+K7GkFReWnsqNailqo\nsYOihssuu2yhh1O0+VAutEoTxvO7VaqvLlFsRcT33HNPIDx3cuWQx48jeSj680P7HT766KPI5Zon\ntbnPjgBD9HissmfZrbAh7FtR7nQBFH0+dGxXxFd/t1ZPRS3SDznkECC6R2fkyJFAiBAqJzrffRx1\nkPjxI05lESdNmpS5TH+/2qHnctBBBwGhXF49lN18iMr2QdUGfDqOFCGXPN+6vGV3gqn3Gr3etLKv\n96l6KFitYkfIzczMzMwS1Cgi5Np5fNJJJwEhCnfggQcCIf+qELQzXC2/9Qk1V95xmiLkyvvt3r07\nAJ9++ikQdsGrAUiJFW0+VBVELXc//PBDAJZYYgkgND965JFHgJATqZzp2bNnZ+5LEfJcmjdvDoQd\n4IrOK19/2LBhQKhOotzIaiQe0bn77rsB2H333aMPlnWsUaRfES61wC6Cos2H/j5FfhX1/+uvv+r0\n+9lNblQ5IZ4zHv9ZzUCUE1sPiT8/lAusCgqKVKkKAlT9+0W5pWrapeNnAxR9PpRbr1UN5bCee+65\nQIiEa+Wgpj0qxxxzDFA1L7+AEn9+1IVWjF5++WUgNCVT1aYnn3wSCKuZDWi4Vrbz8ccff2S+1961\n8ePHA6FBjlZktRJZAKmPkGve9B707bffAqEJUT0q8ThCbmZmZmZWCRpFlZV49Fn5iWr9LbVFyhW1\nrK5iiqKh2uWt6E8uiroed9xxNd6uHCjqoDqwiowrmnvKKackM7AiU/UYRaVU+/i7774DGlYRRJ/C\n1RZaj6E2voq6Kgqrxz7qqKOAGiPkiVFkPF4zWrLzHBXJKWJkvOgUdYvXIR8+fDgQVjPi4vni1d1H\nrrrjyktPs0UWWSTyVTWlsyPkTZs2BcIxp02bNpHL01h/fPnllwfC3hvlkCt3VfOh13g2zVEBVgQq\ngl4XnTt3BkIddr1XaW4bEBkve9nvAausskrkuu+//x6o/TykMdK8dejQAYCxY8cCoZZ7krXqHSE3\nMzMzM0tQ+YXZikBRR+WbiXKJFCnX7lt9clJEXPV0dftc3RTrQpFx7RivqVtd0lTzVjvV77333sj1\nik4oslOpVAtVOeUPP/wwANOnT6/x9/S/hrCaoGiYIjqKfKWZcmC1JyPefVOvp+yVpXJ+3teVnv/q\nJqmotvaq6H+dKx88O3qXq5a5fm5AznjZ0kqT6pZnUz3+U089taRjKqYddtgBCNFb7TVQBaUzzjgj\n5+++9957QFiJLUI1olTTe7z23GiFMV59JEk6/1C1N+W9V1Jt9EKZN28eEPabFGMlVcdvRcjLgSPk\nZmZmZmYJahQRclUByVW7VpHv1157LfK1kOKR8TTkzir/7JZbbolc3rNnTwCOPvroko8pCaqScM45\n5wBw+umnAyHnLJdmzZplvk8yL61YVE1Geb7qDieKTikyXglR8WzKEVckPFf+d20/13SbBtTGLVuK\n/j/++ONAiJRr1QjCMaYSqF698v8VGdWeC63MyqabbgpAt27dMpepypIq0ijaqi6nqkldwGoaqaJ5\nUYRcNfBzVetJgqqT6fmujrXK/1a/Ao1ZNea7dOkS+aqIbnYvgtdffz3yWOr+mv0cShOde+i8Sc93\n7SUphGnTphXsvgrFEXIzMzMzswQ1igh5jx49gJALPGLEiKI/5qGHHgrAlltuCYSqAPHubGm09957\nAyFvr7FQBE9fixn1LoeITi6ff/45AFtvvTUQOnBqzEsuuSQQKqlUWmQ87j//+Q8QIqHqspkrHzz+\nc/ZlWlWoxJxx0YqkunBqj4G6GUOoy14JRo8eDUD79u0BGDx4MBB6EyhCqlzioUOHAuF1BKH+uvY7\nqSKYnkO6j8YaIT/iiCOAsIqpPG2tjq+11lrJDCyLjg/XXHMNEPbaaKVRX+Xpp58Gwh4tvd+oSlz2\n8SN+7FUflLTu71puueUA2HHHHQFYf/31gfB/bUiHWh1rVdVJvR3K4X3KEXIzMzMzswQ1ik6dmSv/\n/29VTuvUqVOBkNOVq/uZcrsOOOCAyOXZP6+44oqR61TrsgiRzpJ1DlMHq3//+98ATJ48GQgRwOwI\nToLKtpNaQoo2H8qZ16qP8vr0ulKN6FtvvRUom1rRJXt+TJkyBYBx48YBYSWuLjnkt912GxCq8eiY\nUwR+vUQlNh9aBdlggw2A6J6TXPSaU9+Ctm3bAqHr58orr9zQYaXy+aFos1YZnnrqKQDatWsHwKxZ\ns+p71wWbDx0nVTlE1NfjhhtuAEKOuFYea7s/CNFzdctWlaIiSKRTp57vem9Rrwedm2QfS3NRVTSt\nUKk6mPaybLHFFvUdnjt1mpmZmZlVgkYVIa8QqYxgFJHnI6rg86GccXWVVY1fUZ6iutTusssueQyh\n6Pz8iPJ8RHk+olI9H+qCOmDAACCs6mkVvB5SPR9FkEiEXO6//34gdDlWtbp11lkHgE6dOuX8nTff\nfBOAX375BQh7CydOnNjQYTlCbmZmZmZWCRwhTx9/Yo/yfEQVfD60s11VAuLuueceAHr37p3HQ5eM\nnx9Rno8oz0eU5yPK8xGVaIRcVMGrf//+QOimXhPtferTpw8A++yzD1CQammOkJuZmZmZVQJHyNPH\nn9ijPB9Rno8oz0eU5yPK8xHl+YjyfESVRYS8zDhCbmZmZmZWCXxCbmZmZmaWIJ+Qm5mZmZklqNJy\nyM3MzMzMUsURcjMzMzOzBPmE3MzMzMwsQT4hNzMzMzNLkE/IzczMzMwS5BNyMzMzM7ME+YTczMzM\nzCxBPiE3MzMzM0uQT8jNzMzMzBLkE3IzMzMzswT5hNzMzMzMLEE+ITczMzMzS5BPyM3MzMzMEuQT\ncjMzMzOzBPmE3MzMzMwsQT4hNzMzMzNLkE/IzczMzMwS5BNyMzMzM7MEzZ/0AArs76QHUAJN8rit\n5yPK8xHl+YjyfER5PqI8H1GejyjPR1Wekzw4Qm5mZmZmliCfkJuZmZmZJcgn5GZmZmZmCfIJuZmZ\nmZlZgnxCbmZmZmaWIJ+Qm5mZmZklyCfkZmZmZmYJqrQ65GZmqfXll18CcN111wHwyiuvAHD77bdH\nbtesWTMAxo8fD8BWW21VqiGamVkROEJuZmZmZpagJn//XVGNlCrqj8kh8c5hf/75JwDPPvts5PK2\nbdtmvl9xxRWL8dDVSXw+ykzZzscLL7yQ+f6TTz4BYLnllgNg8uTJACy44IIAnHjiiYV62LKdj2yP\nPfYYAKeddhoAL730UuT6xRdfHIB//ON/MZRvv/0WgPXWWw8IkfQ6SGw+Zs6cCUCHDh0il7dr1w6A\n2bNn5/zd7t27A3D33XcDYT4KoGyfH/ofA2y99dZA+PvbtGlTrIdNbD6ee+45ADbffHMAjjrqKAAu\nu+wyIDz3S6xsnx8JKYtOnXPmzAHgiiuuAODtt98GYMKECZnb9OrVC4ARI0YAcPPNNwPwyy+/AHDw\nwQcDsMIKKwDQtGnT+g7HnTrNzMzMzCqBc8itih9++AEI0bp77703cv1ff/0FhCinLLnkkpnvlePa\nqVMnAAYNGgTAuuuuW4QRWzl6//33Aejfvz8A48aNy1zXvn17IEQl/vvf/wJw3nnnlXKIifjtt98A\nGDBgQOYy5Yx///33ALRo0QIIr8HtttsOgDfeeAOA3r17AzB9+vQSjLgwHnroIQCaNIkGlN58880q\nt43fZtKkSQD07dsXgEceeaQYQywrw4YNy3w/bdq0BEdSGmuvvTYABxxwAACjR48Gwuvl/PPPz9x2\nqaWWKvHorBwoyn3IIYcA8OuvvwLQp08fAHr06JG5raLlDzzwQLX3pedT165dAbjyyisBWGeddQo9\n7DpzhNzMzMzMLEGOkNeDojNTp07NXKacz/vvvz9y25VXXhmAp59+Gihq7l+DvfzyywCcfPLJADz5\n5JPV3k7RK+WMt27dOvIV4KmnngJg4sSJQKgGsf322wOhasSiiy5aoNGXj59++gkIKwkQIlzvvfce\nAM8//zwAn332GQBPPPEEEObn+uuvB2DhhRcuwYiLY8yYMUDIe73qqqsy1+23334AXHTRRUDIH95j\njz1KOcSS+uCDDwDo1q0bAO+++27mOr12zjzzTAB22mknANZYY43IfXz11VdFHmXhacw6BsRpPpo3\nb565TMeYKVOmAPDpp58CIde+MbjvvvuSHkJJLbHEEkA49m2zzTZAOFa8+uqrmdvq+NkYaWU6+/xD\n5x065or2CA4ePBgIx5e0ufXWWwE4/PDDgfDeettttwFhRV6Rcgj7THbffXcgrMBsttlmQFiB0XFJ\ncxPPCCglR8jNzMzMzBLkKit1oCjvqaeeCsCMGTOAaERYObHa2at5VV5Sly5dABg5cmRDh1O0Xd/6\n5BiPPihfT58+lb+10UYb1XqfinYcccQRQMgH3GeffQC48cYbgao5o3ko2nz8/vvvQKgNrWi2qgGI\nqs3odrpekfL6UBREucR5KJuqAFtssQUQdrErygGh4oZeF8obveSSSwo9jMTnQ9ErPee1R+Piiy/O\n3Oawww4DQqQnF1WcOO644wDYc889gejc1qLk86EqB/HKOcOHDwdCNY0FFligyu/+61//AqquPGav\nPjVQ4s+POO0j2HbbbTOXKRqqahKtWrUq1sOX3Xw888wzQFg1ArjjjjuA6BwVSdnMh1YTL730UgA+\n/vjj2gf0/+chyy+/PACvv/46EN3vlaeSVln58ccfAdhkk00AmDVrFhCi2NpL89ZbbwHQs2fPzO9q\ntUDnNbmoh4Pet/V+Xpfzm//nKitmZmZmZpXAOeQ10CfQXXfdFYD1118fCJ+8dtlll8xtF1tssWrv\nQ59I05AbO2rUKCBEgkWfTmuL3lXnwAMPBOCdd94BYMiQIQCMHTsWgFNOOQVIdmez6NP4brvtBsBH\nH30EhBWRQlK+pOpuf/HFFwV/jHKhPPjsusqqAasVgNNPP730AysRRW8UGd9ggw0AOPLIIzO3qa0G\nriqRDB06FID55//foVtVjMpZdu4vhP99TZFx1QrWngvRCmQlU+7rd999l7lM9eaLGBkvW6qCsemm\nm2YuU/5vCSLkJafnvqqDHH300QB88803QFi5zT5mKN8+HtU9++yzAfj888+B8B6v991yp8pcioyr\nRr2qTsnqq68O1NzLIBedz+k1pupGd911Vz1G3DCOkJuZmZmZJcgR8hrok6miUcoHV4SrJopuvPji\ni0DIw87+lF9uFKUuZLRaedTxvGvR/JRDhFwRTO0ZqCt9OtcKgv4WXQ4hj1pVd3QbRTCuvfbayH3o\nOZdmimIo/1f7BSB07Rw4cCAAyyyzTIlHVzrKj1e1Gf3t2d04lUufizpxavVqlVVWAeCEE04o7GCL\nQBHf448/Hgi54zXRionq07ds2RIIEb7GRvsxGrPs6Gdtr5c00Xug9pSoGlN2Z2MI3a+16pxdc1ur\n2HFaSdBqv6LvaRGPePfr1w9oUFfNKrTqpGo+qm6kY63y70vBEXIzMzMzswSlPwxXBNrBr/q52ulf\nl8i4KA9JdXQrsd52XVx++eVAqLNdzpZddlkgROcmT54MhO6iq622GhDydldaaSUg5EHn86ld+erx\naPyxxx4LVEbEWPOiCJC+Qqi3ftZZZ5V+YCW29NJLA2H3vvZRZNfUzhXxU75odg13SFcutVaBtG8i\nl7lz52a+v+WWW4BQfUmVWkoZrSonOjY1RnPmzAGie5tUuz7NdDz85z//CYSuk/GKY1ppVJUVVXSr\nC1UhKUB1t5LScU8R/o4dOwKwww47FO0xdWzRCsVrr70WubwUHCE3MzMzM0uQI+TVUMULRUjzydPU\nrmB9slMusGp3NxaqjpCdN5xNOfWdO3cu2Zhqo/+VIpjFdMYZZwChkouq9GjfQiVQtZpBgwYB8P77\n72euU+e4f/yj8cQE9PxSxLguFFVXp1/tQcjnPpJWW2Rc1KsAQlWIjTfeGICdd9658AMrU+pn8PXX\nXyc8kvJw2mmnATDffPNlLtt7772TGk6D/fHHH0DYP6PIuGqG6/WiHgPx1bF86Dmk+05L3xmdNyhL\nQV3Bq6vIVEkaz7uhmZmZmVkZcoS8GsoFVg6sOleqU1h1UT11GFR0VZUF9Om2b9++RRxx+VEO/Rtv\nvFHt9WeeeSZQHtVVSknRkDvvvDNyuXKIVY2lEij38+eff65yXXaNZatKkS11B5Zzzz0XqIw9BqIV\nyOycekXCtMdA9fobg2nTpgFhlQBg6623Tmo4idFqs76qOycUtspGqanr6qOPPgqEnHFFxlX/WrXF\nG+L222+PPIb2QZW7e+65J/Jzds+XSuYIuZmZmZlZghwhr4Y+qXbv3h2ACy64AAifNlUTdvz48Znf\nUcRPOVqKZDWGyPi8efMAuOGGGzKXXXfdddXeVnlxqknc2Jx88skAfPLJJ0BYbdGKQiXR60U5sdkU\n+dXqU3Z+aGOmudKxR/XHVX1nn332SWZgRaCKCXoOZNO+A1XjaUzi9acBmjdvnsBIkqFI+DHHHAOE\nqmfZvSy22morIOxFShOdG8SpX0MhKshkV7QCWHvttYFQMa7cffjhh0BYCczeX1LJHCE3MzMzM0uQ\nT8jNzMzMzBLklJUaqHThrrvuCoTW12+//TYQLb2kdqvajFTMAvblQq3m99prLwAeeOCBnLfdfPPN\ngYaVcEqzmTNnAlU3c+64444AdOjQoeRjKhalME2YMAEIKV7Z5e/0elE5Py1Bp4maOz3zzDMAbLTR\nRkDDmrgopUmpKvpZKRxppuOFnusqjSrZDTjWW289IGxuTWNqQn1pU19jpQ2I+++/PwBt2rQBYNSo\nUZnb3HvvvUA4fqyyyiolHGHDqNStHHjggUBhmx0NHTo08rOaCTVr1qxgj1EMb775JhDmSBtbS9FY\nUc8lFfNYffXVi/6YcY6Qm5mZmZklyBHyGiy00EJAaD+rr/Lpp59mvldUQ+V50vSJPV8q3afIp8p0\nVUefbLXaoM0m2tQoai/eo0cPIGx2rJTGMcOHDwdC+2c1iVFziEry8MMPAzBr1iwgbM7SRkUIEXKt\nOqUhQq7NZeeffz4AY8eOBUJpz5YtWwLQqlWryO9pI9UGG2wAwJZbbgmE5wCE44dWmfr16weE58fC\nCy9cyD8lEb/99hsQXgPxFuHZrdF79uwJwEorrQSETeLZz6FK165du8z38edUJVNDMX2VfffdN/O9\n3lcURX/iiSdKM7gC0ObN6dOnA7DtttsW/DHmzp0b+Tkt5YW1eVllo9dff/2iP+bNN98MhEaQKjGq\nJmylVBlnO2ZmZmZmKeUIeQNkt4X/5ptvgMpu8fzkk08CoWThjBkzav0d5dkqh602+mS81lprAWGl\nQfl1aWot//3332e+nzhxYuQ6RQA7duxY0jGVwjvvvAOEKJb2U2RHHA4//HAgrK78/vvvQHm3RlYe\n9+DBg4GQa6jLFZVSww+toE2ZMiVyP507dwaizV60gtS6dWsgNMQp95zPfGgVTLma2SuMAP/5z38y\n31999dVAKH/Wp08fIOzB2G677Yo72DKQ/V7SmBoj5aIVa4A111wTqLrSmgZ6TyvGKvpPP/0EwC+/\n/AKEMsxdu3Yt+GMVg/bfLLbYYiV7zCuvvBIIK6ADBgwo2WPHOUJuZmZmZpYgR8gbILv4vnJg05AL\nW1eK8J500klAyOPUp+76UE5Yrtbf8aiBdjqnsUFIdvMjRQOVEx9viV6JNt54Y6D6XDztFbjmmmsA\neP/994HybO2s6iCq8qDVG0Vr4/mZur0iwaqYcu211wLhuBFv3gGhClEpI0SlphWCuJ122inzvaJV\nF198MRDmVHsOGkOEvJJWRwohe8+F9mWMGTMGgM8//xyA5ZZbrvQDKyNqxqZKcEsuuSTQsMpPlWr2\n7NkAfPDBBwCccMIJAHTp0iWxMTlCbmZmZmaWIEfI60HRTtUfBjjssMOSGk7BqS6qKmEoPz6XVVdd\nFQiRQwhVIuK54/rEXsk5kWrxHK85DqEKT64oYSVRBEL7CLJrySoCPN988wEh77ocWyT3798fCK97\n1UDOVblAf5v2CWh1RzW1L7nkkpyPdcoppwChusimm27aoLGnybhx4zLfjxw5MsGRJEN7EF5//XWg\nNBUm0koVjb777jsgVPBprL788kug6h6rM844A6j7Hq5yo4pdhVxR1nNGq7R67mjVJUmOkJuZmZmZ\nJcgR8no499xzgVAZAuCQQw5JajgFpzxN5W3GKc9bkb9hw4YB0U6MjZHyXhXd0453CLnjysevZIrG\nqEKGcqezc+q110IdGBVFL0f6fypqnV0fuiZfffUVEI4NiqyLKqlAeO1oVUqVWRpDhFz1x2+44YbM\nZdmvHQgR0SFDhpRsXKU2depUAP744w+gPPdTlIvXXnsNCDnjen40Vookx1cK0v4cUufOQlJ1PHUK\n1nFZe56S5Ai5mZmZmVmCHCGvhxdeeAGAvn37Zi6rpM6cqsOpig8dOnQAoFOnTgCcfPLJQGVXgqgP\n7fhX569sWlXZZJNNSjqmJCj3VXWDq6smItpL8NBDDwHhuVWODj30UCB0k8tFkXHlwysCs/zyywMw\nadIkANZee+3M76hr5XHHHQc0rJJRuVOnX3VXPO2004BQjQbCfOjYc8cddwBhDiuR9pyovn1jj/rW\nRBFyrTxqL0pjMmfOnMz3Z555ZuQ6rSSltS+KKupopUxdTddbb72870s12bUCp+7H6iCtPhnlwBFy\nMzMzM7MEOUKeh7vuugsIeU3VVdGoBIpY6avVTDmft9xyS+Ry5UcD7L777iUdU5IU4dtrr70AuOmm\nmwDYYostMrdRRR5VLklDFQBFdnPRytmll14KhONF27ZtgVCVSfNTnUqO9GkV5JxzzgHCfFVH+w1U\ndaamOasU6nC77bbbArWvxDQ2inQCzJw5E4CDDz44qeEkRvMwdOjQzGXKh1YedNqrvt12221AWG1V\n34GxY8cC4Xiw4oorAiGirnmA0AfioosuAkKvi2OPPRaAESNGFO8PqCdHyM3MzMzMEuQIeR5uvfVW\nIET+WrduneBorFyoWsaTTz4ZuXz48OGZ79u0aVPSMZWDs88+G4B58+YBcPjhh2euUy6gcoVPPPHE\n0g6uHhRRURSqV69eQNhroci4VtB69+4NhOdBY4jyZlPVEOXFv/TSS0BYUZJWrVoB8O9//ztzmZ47\nlbxiIOoy+e677wLheWVR2XsMvv32W6BxRsgV8VW1EICmTZsCocdB9upsGqmSlXpADB48GKjaoXfN\nNdcEwl6kGTNmZK7TPhxV4tGK/6BBg4o17AZzhNzMzMzMLEFNKmw3f1H+GEX4VCv46quvBkJHyxJr\nksdtK+qfm0Ni86GOnFtvvTUQcvv23HNPIOROQ8hxK4Gye378+eefQIgkQ6iaoW6WquxTBGU3Hwkr\n2Xw8++yzAHTt2vV/D/z/qyHdu3cHwv+8Y8eOACy++OINebj6Svz58fbbbwOhZrQiwfWpKFEAic9H\nLoqWAowaNQqAjz76CD12DsAAACAASURBVIBFFlmkWA9bNvOh85Cll14aiO5p6dOnDxCOq0WUz3xA\nA+dE7x36f0+YMAEIddfjsrvbaqVJ1a6KuEKZ75zk5Ai5mZmZmVmCHCGvA+1mvu6664CQp9SsWbNi\nPFxtyuYTe5lIbD6uv/56AA466KDI5Q8++CCQWH1TPz+iPB9Rno8oz0eU5yOqbOZDNcXHjx8PwGab\nbZa57vHHHwdC74ciKmmEPCUcITczMzMzqwSuslIHqg6gDk8JRcatzKnLZI8ePRIeiZmZVZK5c+cC\noT59dhWvEkTGrQQcITczMzMzS5BzyNOnbHLayoTnI8rzEeX5iPJ8RHk+ojwfUZ6PKOeQV+UccjMz\nMzOzSlBpEXIzMzMzs1RxhNzMzMzMLEE+ITczMzMzS5BPyM3MzMzMEuQTcjMzMzOzBPmE3MzMzMws\nQT4hNzMzMzNLkE/IzczMzMwS5BNyMzMzM7ME+YTczMzMzCxBPiE3MzMzM0uQT8jNzMzMzBLkE3Iz\nMzMzswT5hNzMzMzMLEE+ITczMzMzS5BPyM3MzMzMEuQTcjMzMzOzBPmE3MzMzMwsQfMnPYAC+zvp\nAZRAkzxu6/mI8nxEeT6iPB9Rno8oz0eU5yPK81GV5yQPjpCbmZmZmSXIJ+RmZmZmZgnyCbmZmZmZ\nWYJ8Qm5mZmZmlqBK29RpZmZmlmqvvPIKAHPmzAFg3rx5AIwePRqAtddeO3Pb9u3bA9C2bVsAOnbs\nCMByyy1XmsFaQThCbmZmZmaWoCZ//11RVWkq6o/JwWWYojwfUZ6PKM9HlOcjqmzm488//wTg5JNP\nBuDZZ5/NXDd16lQAunXrBsCVV14JwDrrrFPoYZTNfJSJks3Hzz//DMDBBx8MwD333APAr7/+mvd9\nHXDAAQBcf/31DRlSdVz2sCqXPTQzMzMzqwSOkNfB119/DcCaa64JQI8ePQC46aabivFwtXEEI8rz\nEVW28/HTTz9lvt9zzz0BmDBhAgALLLAAAM899xwAG220UaEetmznIyGJzYfea7755hsAjjrqKABu\nv/32Wn/31FNPBeCUU04BYMkllyzUsBJ/fvz+++8A7LfffgDcdtttAPTs2TNzG/29d955JxBeL3ff\nfTcQ3pMKIPH5KDNFn4/p06cDcPTRRwNhZaR58+YA7LHHHgDstNNOQMgL1/lI9u+ce+65QDiOrr76\n6gAMHDgQgN13370+Q8zmCHlVjpCbmZmZmVUCR8jr4IorrgDgmGOOAUI0YuLEicV4uNo4ghHl+Ygq\nu/n45ZdfgGh0Zvz48dXedtNNNwXgkUceAWCxxRZr6MOXzXwouqmo5l133ZXztiuvvDIAffr0AWD4\n8OGFGkZi8/HZZ58B0LJly3rfx6KLLgrApEmTAOjcuXNDh5X480PR//PPPx+AI444AoCrrrqqym23\n2morAJ588kkgzMfMmTMBaNWqVUOHk/h8yLvvvguEv1XzA7D55psDRcmRjiv6fOh40LdvXyD8bTrv\nWH/99fO+z2HDhgEwYsQIIFRo0fNkpZVWqs9QoRFFyH/77TcAPv74YwAWWWQRoNrKNY6Qm5mZmZlV\nAtchrwNFdmSbbbZJaCTp8frrrwMwbtw4AGbMmBG5/vHHHwfghx9+AEIk8MQTTwQKmkPcYBrjjTfe\nCMBjjz0G5I7y1mSTTTYBYMqUKTXeTpUWhg4dCsD886fvpaqccf3Nis4ArLjiikCoLPHpp58C8Pzz\nzwNhfrp3716awRbBBx98AMBuu+0GVP2fa14gRMQVudI8XHLJJZGf9TWNRo0a1eD7+PHHH4GwYlCX\n/PNypSoa+h+vu+66AFx66aU5f2eFFVYAYKmllgLC/iZFWU866aTiDLaE3nrrLQC23HJLIEQos1fz\n33nnnch1yrtX3nUa/PHHH0B4XbRo0QII740LLbRQve+7f//+QFjN79q1KwDbbrstAM888wwASy+9\ndL0fI+10LFGd9xdeeAGAt99+Gwjv77NnzwbC6pOee8XgCLmZmZmZWYLSF3YrIeUQvfbaa5HL9am8\nOvrU9cUXXwAwd+5cIHTdilOkUDvt9957bwDmm2+++g675N577z0AevXqlbns1VdfrfF3WrduDUCX\nLl0A+Pbbb4GQQ6zoUfZ9JuW0004DYMyYMUCoF9ukSf6pY/oUXtvvqvqIIuXLLrts3o+VtH322QcI\nkfHsKL8qBtx8882R31lwwQWB0HkujXJFxpUjqtUgXV8TvR50H/o5jZFyVdZRxYe4jTfeOPO9InrX\nXXcdECqziKJWaaQ9FZoH1ZkeOXIkECqoVEevF0XpNttsMyAcm7TPSa+jNNE8nHHGGUB4n1VkMnvl\n4IILLgDg0UcfBeDaa68FwvEyDfQ8+Pzzz4Hwnt+QyHjceuutB4SV50GDBgEhx1zzWIneeOMNAF58\n8UWg6mq95l8ZEFqBib83q1LNcccdV+QRO0JuZmZmZpYoR8hr8MADDwBw7733AmG385lnngnAE088\nkbmtcvhUeUU7xHNRjnSHDh2AkDuqqPzCCy/c4PEXmz5xqrOYotwAbdu2BUIkVPmyingrGqBokD6d\nHnrooUD4RF8OEfLLL78cCBHOL7/8smD3rRqzyids1qwZECovpDEyrpq4ev1IdoRLVTKUny/KG9XK\nURopjzceGVeVlXzod1R5QfepKLxyz9NAq2I777wzEPYNKBp+1llnZW6rqNXo0aOrva+11167WMMs\nOr0OtHJ04IEHAtEVgtosscQSkZ+1ivvRRx8B0KZNmwaPs9SuvvpqIFQfWn755YGQU73qqqtmbvvJ\nJ58Aod52GqlCjvYF6Dmv1fKaVkrypRrn5513HhAq+FRKhFzR8OzKVfrblLVQ26q0zlFWW201IKw2\n6byvkCsXuThCbmZmZmaWIEfIq6Gd64pSyldffQWET1LV5TFql7duo7wj5XKJPu2X4lNXoSiPU5+y\nL7zwwsj16qIHMHjwYKD2v0859rq9ciQLUF+44Lp161bw+4x/aldVkX333bfgj1UqF110ERAiPYpU\nZK/6xKPnstdeexV5dMWjyh/x+uL1iYyLIuCaU9VyX2WVVYCGRd9LTXsIND/K4dSqUDY9D7777rtq\n7yu7i2VaaO/J2LFjI5drj0o++4Y0L1plqATxvVp6L82OjEvTpk1LMqZS0Pvm/vvvD4RVdq0uF8Iy\nyywDhNeNKoio2opWqdJGe2m0ypS9cqSupXqN6P1HWQmqOKP64uXAEXIzMzMzswQ5Ql4NfWp88803\ngfCpUnmviuz07t078zvKBd56662BdOb+5qL5UO6nVhA6deoEhG5g2TmQuaI98Z306kamOVXEWFH4\nSqUoWTx3vF+/fomNqaFUdzxep1X/2+ya0YqeK9dVlQa22267oo+zWPQ6kDvuuKPB96m9FKpVHado\nsyLm77//foMfs9h0bNBz/q+//gJCHijkrvWrihuqVJMmyttVJPiQQw4BQm59Y6d9RPp6wAEH5Lxt\nvDJGmm2xxRYATJ06FShN9F/vs2msxgNhX4FWCCX7OKka7GniCLmZmZmZWYIcIc+ivLzjjz8eCJ2z\nbrrpJiB8KtcnWEWlAP7xj8r7bKPcK+WyqYqKIjoPPfQQEPLTqqOOnco3v++++4CqdYVFufeKGlQa\nRTS1t0ARHq0YqK5wGilHb8cddwRCvdfs6hmi+vN6Xmj1SZUV0kiVT6S2OuPZt1cupKo1xfPQ45Rb\nrmPVhx9+mN9gy8iQIUMAOPvss3PeRntRdPxIY+darRRJu3btgPr1nFA9aVlyySWB8sqHzZfqPSt6\nq9XU6qhPRX16QZSrYq6qa0VS77s6X0lbp051y1a+vc5FHn74YSC8ptKq8s4izczMzMxSJH1hhiLQ\np0fV01YNcXX90m5vfW0slPOryPj2228PhBWDeGQ8uxupbqMOavF603FabVDUvdIoT/axxx4Dwpxq\nJUD1t9NMURflPV922WVAyC3Ppp3uWhHR1zRT1DreqTOutuh3TZQzecIJJwChc2cajRo1CgjdOKuj\nCJ66fMarVaXJ/fffH/lZe3LqQ/ubRFUy0rzCFKfnx5FHHgnAUkstlbkuV/Udq57eb5588kkg7N9Q\nv5Byp/4Lhx9+OBBqtKvnQ9oj4+IIuZmZmZlZghwhJ3RyUv6mogyKYHz//fdA6ApWXcRPnQUrIdIn\n6pwmynPdcMMNq729uqdByIuM5/jpk+3ee+8NhFxIdS1TLmQlUNdVCLm+WjFQhEK1Usux7np9aeVE\nXVerqxCimv6VJJ5D3pBIeJwi4qp1Xgl0PI3PWzb1gtCqSxpp79GcOXOAUFlIe5TqI15dpBKOH6o6\noxrZen7ssMMOANxwww2Z22YfWy1/aVvtHzBgABD2Fag6zLRp04BQhzy7g686bqr6W8uWLUsz2AZw\nhNzMzMzMLEE+ITczMzMzS5BTVgjLH1rSUOrF5ptvnvd9qQzPs88+C4RUljRSCb7Zs2cDYWOIvmrJ\nVRsqJkyYkPldLTuqpJlKOh1xxBFA1bJdlUgtkCGk/6i1r5bg0rwprzYqUddYqBGQ2tvXJruphdI2\ntHkpfptKSlXJh1LbKsk666wDhLS1fPz8888AfPnll5HLV1pppYYPLGFKo1CzOJW2e/HFFwFYa621\nMreNp0KqeV+a6X97+eWXA6HAwTbbbAOEDZizZs0CoH379pnf1TEnV/nlt956K/Lz6aefXqhhl4TO\nRSZPngyE1JUxY8bU+rtKk33hhRcA2GCDDYoxxIJwhNzMzMzMLEFNKqH1bJYG/THvvfceEErTLbbY\nYpHr4z9//PHHme+1AUWf2NTo5ZxzzmnIkKqTTyeEBs2HGgPlKjGlqLfKUamdLcAee+wBhEiO5kHz\nUkAlm4+6UvtybSaBsLFLUZ/rr7++WA9fNvOhDbrVPX+0+WbmzJnFHAIkMB+KdmsTtNTUKEhlP/W7\nKqGo51IBlc3zY/To0UBYRatuc+dee+0FhDKqRWjAVvT50P9QjW8UIX/55Zfzvi+t3q677rpAOL4+\n/fTTAHTr1q0+Q8xWNs8PUYnHYcOGZS6LHz81D0VodFO0+XjnnXcA6N+/PwCPPPIIEIpI5EMrr717\n9wZg4MCBQFjF3mWXXSKPoYh5Pcoe5tuJ6f/au88AqaozjON/rKixRA120aiIsYA1NlRQsKBGwRIV\nexAJYkFAwQYRwQIqKqKiBgsaC6LGBjbsRrEbxRglmKgIiiUSiDUfzLPn3ruzy87uzJyZ2ef3ZZeZ\n2Zkzh5k7d97znvct6GtEmQdqhFbfRk3Ngd4bWhXQ8aaACtadyhFyMzMzM7OInEOe0Lp1ayA0CMqH\n8t8UIVd0uZLp2/XCynNNnz4dCFFxCBELlWtTAf9qptbYZ511FhCi4hBKaaoUYDVTG+P6mkEl80Gr\njaLb+lmX22+/veb3bHT4mWeeKfzAyozK3ClPPhn1HDFiBAC33HILEBpr6d+VZLHFfvqY1V6lptAq\npI6vSy65JACrr756k++7XLVp06bWZcohV351JZXL1Xt99913B0K0umXLlkCIcmv/hEoCZ+lzF8L+\nLa0k6dii4+wrr7wCwP777w9URgnAXHbcccd6r1dTRwh7D6Rz587FGFJBOUJuZmZmZhaRI+QFUq0t\n3+ujfEZVDEnu/FeOsBrfLLXUUiUeXemNHDkSgJtuuqnWdWoDXU2No7Lmz58PhFboimp26tQJgMce\ne6zmttOmTSvx6MqHcstzVWMZNWoUsPDoejVRdDPZ/Kdjx44A7LzzzgDcddddQKiUkNyfUe5UEUIN\n6BpDkfE+ffqkLtecVUoL9ELbd999gdCIrhLoOKjIuFY5JkyYAIR874XZc889a34/4YQTgNB4TveV\nXWlTsxxF46vFhx9+CMDhhx9ec5lWrBVVr4RjhiPkZmZmZmYROULeBGqFDCEqqty2ffbZJ8qYSkER\nn9GjRwNwzz33AKFSBIS24c0hMq42zskqAJCuQa/KCtVs9uzZANx5552py3PlKyajO82F8jpzRcaV\nR13JLeILac6cOUBYZcm+xxQxr0SqN63jqCKkWWoLDiH3V/syOnToAMCJJ55YtHGWm1zVR5KfOZVC\nx0NVDFK1srZt2zb6PlVre+uttwZg7NixqetVfefVV18FwvHmpJNOAsJKVGxaTdV7ItnLIxetmHXp\n0gVI71vSvgpVlqmEVQFHyM3MzMzMInKEvAmUHw3w7bffAiGnTT+riSI6Rx99NAC33norEGri3n//\n/TW3rYbOcQ2lCirz5s0DwnOfMmVKzW3WXXfd0g+sxLLd80T5jEmqMNCcZCPjyTzxZMWV5ipZr/74\n448HQjRZklHjSqHjgaKU6jaoyF32s+Kzzz4DQrdjCJE/5cOqIs3CKmBVk+TKW13HmkqgaG6vXr0A\nuPrqqwHYY489gLAfTdVlstV59Dn83Xff1VymlaOLLroodZuBAwcC4VxFFX/Uc0U9RMqF6qkr913j\n1OV6/+vcQznzkuzCqU7RSy+9dBFHXFiOkJuZmZmZReQIeR6Uw3bJJZcAoeYnwMorrwzA0KFDSz+w\nIlP+ZjYy3qpVKyB8K29OUXEItV8VxdO3eHV63XDDDeMMLJLk+yGXZH3/rl27Fns4ZSPbobOIXTjL\ngiK8qizUvXt3oHY96bfeeguAK6+8EgjdjiFdTzhJvSIqifJ71XVUEXLl7ypqqePGzTffDKSrVmk/\nysknnww0r6oqyX4Ooq7Z7du3L/VwCkav+3bt2gEhir3pppsCYd/RFltsAYSa4qpildzDljVo0CAA\nhg8fnvP6cn0fKZ9er/26VpbVYV6rBzrGXHjhhTW3qcTzEUfIzczMzMwicoS8AZS/17dvXyBEAhUV\nh9Chs5K/sWepo5giOZMmTQJCzrTqbisnrrl4+umngRDx0v4B5Qg3t8i4aCWlLslIsaKC1Ux54ao4\nJHrfVCsdNxStuuyyywBYZ511gJDnqZzgZCS4LsoDzc5lJVFlIUV3tQpQ12qRqnAAXHrppUCIBDYH\nWmlRbnXSVlttBVRmlZUs5ZKrQ6d6NCiXXCsn9a1A6j72228/oDK6Uuai6jDal6bXgH6+//77AGy/\n/fZAqD5ULZ2fHSE3MzMzM4uo+sNUTaAdvb179wbghRdeAEJkXN9coboi49q9ffnllwMhMq6IzbBh\nwwDo0aNHhNHFpwi5qqpox3+lRiWKbcyYMQDstttukUdSGnXVGz/llFOA2jnl1UbHQj1frQioZrB+\nNoTyaQcMGACEfSuVSNFcdWh8++23gRD5VE696idr/iDUHW9OVIv+tddeq3WdcqSriSrm7L333qmf\nzYk6rqrzaHPjCLmZmZmZWUQttFu1SjTpySxYsAAIO5PPP/98IOQEqyuaIl/LLbdcUx6usfIpwJrX\nfHz//fdAyI1WpE87/FVPuly6ev1f0eYja/z48UD49q7qKj179gRCPdnISjYfWcp9VLc45Qy//vrr\nQMidLbGSz4ciocqlVlUV1dZN1h+PoOTzMWrUKCBEueuywQYb1PzerVs3AHbYYQegqNHCaO+XMhV9\nPrRn64ADDgDCSrSqkQA8+uijQEnqaEefjzKTbwF4z0keHCE3MzMzM4vIEfLKU7Rv7P369QNCnXVF\nxh9//HEgHcEqIyWLYHTq1AmAqVOnpi5XJFTzFZkjOmklnw/tKSizyLj49ZHm+UiLPh+qGDJu3Dgg\nrFAnj7uq9FUC0eejzDhCXpsj5GZmZmZm1cAR8spTtG/s6oqlSgY33XQTULvDXpkpWQRj8ODBQNhb\noAjOMccc89NAWhTsi3JTOKKT5vlI83ykeT7SPB9pno80R8hrc4TczMzMzKwaOEJeefyNPc3zkeb5\nSPN8pHk+0jwfaZ6PNM9HmiPktTlCbmZmZmZWDaotQm5mZmZmVlEcITczMzMzi8gn5GZmZmZmEfmE\n3MzMzMwsIp+Qm5mZmZlF5BNyMzMzM7OIfEJuZmZmZhaRT8jNzMzMzCLyCbmZmZmZWUQ+ITczMzMz\ni8gn5GZmZmZmEfmE3MzMzMwsIp+Qm5mZmZlF5BNyMzMzM7OIfEJuZmZmZhaRT8jNzMzMzCLyCbmZ\nmZmZWUQ+ITczMzMzi2ix2AMosB9jD6AEWuRxW89HmucjzfOR5vlI83ykeT7SPB9pno/aPCd5cITc\nzMzMzCwin5CbmZmZmUXkE3IzMzMzs4iqLYfczCrYnDlzAOjRowcAiyzyU8zgnnvuAWCJJZaIMzAz\nM7MicoTczMzMzCwiR8jNLLoffvgBgIceegiAKVOmANCpUyfAkXEzM6tujpCbmZmZmUXkCHkTDB8+\nvOb3P/zhDwD897//BWCPPfYA4O9//zsAxxxzDADdu3cHoE2bNiUbZwx33HEHAAcddBAAXbp0AWDy\n5MnRxhTTZZddBsDtt98OwDnnnANA586do42pnOj1csQRR6QuX3PNNWMMxyyazz77DAifIQDTpk2r\n92/atm0LwNNPPw3ASiutVKTRmVmxOEJuZmZmZhaRI+R5+OabbwC45pprADjjjDNqrmvRokXqZzYS\nrNt+9dVXAIwYMaK4gy2hjz/+GEhHN1966SUgzMe8efMA+OKLLwBYYYUVSjnE6BQZf/bZZ4GwctLc\nI+RvvfUWAKeffnrq8lVXXRWAnj17lnxMVlj/+Mc/ALj11ltTlz/88MNA/e+BLbfcEggrbNVswIAB\nAIwcORIIx87s77m88847AHz++eeAI+TV6NRTTwXgqaeeAuDFF1+suW6NNdYAoH///kA4bi6zzDKl\nHGLRKBvhyy+/zHn9X/7yFwAOO+ywmssOOeQQAH72s58VeXSF4wi5mZmZmVlELX788cfYYyikoj6Z\nwYMHA3D++ef/9GCJuVtYBEMWX3xxADbZZBMgRJLz0LAH+klR52Pu3LlAyHVcWJ4jwP777w/AxIkT\nCzWMspmP+mjPgCLjY8aMAaB3796FfqiKmI/vvvsOgB133BEIEY7FFvtp0U4rTKqy0gQVMR8lVPL5\nGDZsGBD2TTTogf9/bF1yySVTP08++WQANt98cwB+85vfNHV4ZfP6WG655QD497//DcAqq6xSc93y\nyy8PhOPngw8+CMAbb7yRuo+//e1vAKy//vqNHUbZzIfMnj0bgNdee63mMvUl0GfQggULAHjiiSeA\nEB3V5+zxxx/f2IePPh/HHXccAOPHjwfCsTP1wP9/v+g8pGvXrkBYlSpglDif+YAmzok+F3bbbTcA\nvv766wb/rT5ztZKg91cR5DsndXKE3MzMzMwsIkfI66FIRa9evYBQI1l50Mm5U0TilltuAcK3seee\new4IVVZEkXLlDSqK1ADRv7HLXnvtBYR5yYciXsrHP/zwwxs7jLKZj/pk9xgol3zbbbct+EPlcduS\nzse3335b8/tJJ50EwNixY4Hwfhg3bhwARx55ZKEetmznIxcdc1S1SceaP/3pT0CIEPXp0wcIuZV5\nRH9KNh+K4nbr1g0Ie3Aa9MCZiF+Wjh8DBw4EwvF17bXXzneYZfP6mDRpEhAioFoFgNoR7+yxV3ty\nFEVea621GjuM6PPx8ssvA3DxxRcD4Vg5c+bM2gNYyOtEvv/++8YOJ9p83HfffUB4/yy66KJAiJhr\nfwWEebjqqquAEFnW3rVzzz23UMMqaYRcK6VaCdOqkV4b8q9//QuAs846q+YyHUtnzZqV+tsicITc\nzMzMzKwauMpKPZSPpuhUlvKaAK688koANthgg9RtVlttNSB0HtR9KVp4xRVXAHlFyKNRLp+ey/PP\nP9/o+1K99hNPPBEI316rqZqCopu5bLjhhiUcSVx6rV900UU1lykyLvvssw8ABx54YOkGFtlHH31U\n83uPHj2AEAWcMWNG6rbKrVckUHsQ1NegY8eOxR1sHhQZVzWIuiLjSy+9NBDe87vvvnvNdYr46Vij\nCJj2qej4ocifOrlqn08lUn54LvPnzwfg/vvvB8Leo5///OdAWJltQmS8bGhfif6P69OqVSugdoRc\nn7v77bdfgUdXOsp714rJscceC8Do0aPr/ButLihCrpr2lUrHhMceewwI/6/rrrtuztt/8MEHNb9n\no+iVwBFyMzMzM7OIHCHPQfVx9Y1UFKVSFGbIkCELvS/ldqo6QF3R9nKmyLiimMn6p02luqKKmFZT\nhDxXbr3qwi6ySPV/F1ZkPJsvnqRqCH/84x+BkBtcjVSLX3mOinYCvPvuu0CopqHIkKolXHfddUDI\nEV5qqaWAECEtJ9pz8+GHH9Z7O+W3ZmvQ57qvTz/9FIBtttkGqJ1PrAhxJUfI66PVWnU+lhNOOAFI\nry5UOtVQ1wrSRhttBOT+vD3ggANKNq5S06rXhAkTGvw3jz/+eOrf119/PRCqVVXqfG2//fb1Xj9n\nzhwg5N1Xquo/KzAzMzMzK2OOkCcognX22WcD4VuXKOexIZHxaqAOe8pTfeWVVxp9X3vvvTcQInz/\n/Oc/U9erruxpp50GwAUXXNDoxyoX06dPr3WZ8iMVCa1m+r/MFRnXaosiONUYGdfx5K677gJC5RTV\nol9nnXVqbnvDDTcAsOuuuwJhJUUR8ldffTV134MGDQKgffv2xRh6k6jiSV2VHXQcbdeuXcEeU8dq\nHaOSFUoqVfIYqO6doo6EqrJTTVRRQ8cNrQpUanS3sQ499FAAbr75ZqD+CkJ6/WvlSHswlIevz9dq\nnUPVW1cd/krlCLmZmZmZWUSOkBN2sPft2xcIO5RVG1mVU84888wIo4tHVRIaExlXvr1yQFVhQ5E+\nRf4+//zz1N/pm74qM6h6QiVRVEKVd5IK0HmybKlr3tChQ4FQY17/h4rqAYwYMQKAli1blnKIJfHJ\nJ58AsOeeewLh/bPssssCoVZwcr+Eqga89dZbQOh+++abb6buW6t3Wn0oR4qQa1+AKqSIjg2qQqRj\nQK58+AceeAAIq5K5alFD7Q6elUirh4piKm8ewl4b0XupgB0Yy4aOI4ryVlmvlAZTFTd1nFSnW9Uf\nT0bMDz74YCDUhT9VUgAAIABJREFU3lbVmV122QVoUp+PspatxpSkSlSqxFMJHCE3MzMzM4vIEXJC\nNYzx48enLl9vvfWA2lGqQtp3332Ldt9Ndffdd9d7/VFHHQXAL3/5SwAuvPDCmutUV/nyyy9P/Y06\nUyoHVp32RP8Hp5xyCgCbbrppI0Ye1w8//ACkI1yy6qqrlno4RacVgd/97ndA6DgoqgWsfPFq9eST\nTwIhWqvjhqolKBd09dVXB9L1uRUJVofSbP1g1d/V+6qcV44UuTv66KOB2rnkX331FRCeiyqnJGvz\nKzqoKJfqbmfpGK37qmSquqM9BvV1n1Rlms022wwIr6lqoEpk2e7GzY1W6FWVScfX3/72t0C687E6\n+Kr6kqrvaLWqbdu2JRhx6ajz6qhRo4Dw3tlkk01qbqN5qqTXjyPkZmZmZmYROUJO7vwjCHmchTB5\n8uSclys6VA6Up9i7d2+g7gj5GmusAYQum6r0oM5iEPJlmyPl3udSTZ0otfdCKyXq0CiqMX7ZZZct\n9L5ef/11IOyWz9LKgvYerL/++vkPuMhUL1j7JJS/qS5zWXqfQci3Vk5kNqozceJEoHYn4HJ2xBFH\nACGvVdHuZGQP4IUXXkj9BLjxxhuBuqNbih4qalgNHSr79+8PwH/+859a1ykCqDxzvV/69OkD1F6V\nqkQ6nmRpPtQPI6mS8oMbS6s/Tz/9NBD25uSiXPHkanU10vEyu5cmudeiX79+qevUCVdVfMqRI+Rm\nZmZmZhE16wi58psVfVJ0Svmair40hWp5Kzdaj6Eos3K9yoHGWlc3UXUdVRQzWwN55ZVXXuhjKL9a\nOW/VSB0Kq7U6gPL3FIG4/fbbgRC17NmzJxDeX7lqjCvqpTxrRS1mzZpV72OPHj0agHfeeSf1mDFN\nmzYNCPOgHOrzzjsPCPXoFfVVXfL6auYuuuiiQMi//vWvf13oYRed9pYoz3OrrbYCwnxdeumljb7v\nnXfeGai9B6WSaV/AsGHDal2nvQWquCHav1ENFPXMUoUu/UzSseb8888HYIUVVijS6OLRXiTVEq+P\nqppVK52b1FV/P9nfRL0dRNXzdGxVb5Ry4gi5mZmZmVlEPiE3MzMzM4uoWaesqDWxloS0gei6664D\n4Fe/+lWTH0MlrGbMmJF6jEUWqbzvQiq/pPbvjaGSZ2ojnqVNrpW4WUeb1bS5MbkhTc+nEv/fRelG\nauqjBjey/fbbA2HTkRrCKM0kmQqludImnAULFgAhrUGpKNocrI3Xeh/ddtttQHmUu7v44ouB0OhG\nPzUfdVEaAoRNezoWbbHFFkAob1cNtMlXP9XER5s/k+pK91JpRB2jm4tf/OIXQJgzbRx+++23gfBe\nW3PNNSOMLh4da95//30gpHWo/F810ObvbDrf1ltvXfP7iy++CITCCn/+858BWGWVVUoxxJJRmp8+\nB0QpffU9X83JHXfcAThlxczMzMzMMpplhFybrLLlpdRcoXXr1k1+jA8++ACAAQMGpC5ffvnlgfpL\nF8VSVzRO7ZnXWWedJj+GWoNnaaOFomWV+M1e5d3uvPPOWtdpw1I5N3RZGEXhtFIiiloqAqEyh2ee\neSYQ5iUXtY8fPHgwEFZf9Dd77bVX6vZqr37QQQc18lkUnjYvtmzZEggb7fR/reZWKknWrVs3IF0e\nU6sqKmuYLSFZTbQhVxvy6mvckb1Oq5bNLRKszYonnXQSEJouzZw5EwgrK5U8L1qBy66OLLbYT6cp\nWpkDOPXUU4GwAVar3Wqw1b179+IOtoSmTp0KhPeCzk8U6YVQVrlv375AKBaRvE01+P3vfw/ULh+s\n13195ZZ1PF5mmWWKNLqmc4TczMzMzCyiZhkhf+SRR4CQ6yn61tWU3HFFxlXGTY0cpHPnzkBhmw4V\nyueff57zcpVobErUQfOg/FFRrvApp5wChG/AlWju3Ll1XrfnnnuWcCTF8d5776X+rYiwVnu+++47\nAIYOHQqEKLdulywjqvfaDjvsAIQVEuWAXn/99QA899xzQIiMq7yZbl8OFKXLtrTWazvZzjnpySef\nrPl9zpw5QGheseKKKxZnsBEpiquc2G+++SbmcCrSZpttlvq3VlyrIWdar301nFNEWOVDFRVP0iqc\nmm/99a9/BaojQj5v3jwgHFdFzzm5kn/ccccB8PzzzwNhtVLZAG3bti3uYEtEpZUbUmJZtNdJx2Xt\n1ylHjpCbmZmZmUXULCPkWWpxnashQ0Mpz0uR3mxkXJEMfftvbtQUJVm4H2DIkCEADBo0qNRDKjhV\nAqlWaqwgyu3ceOONgdAA6NhjjwVChSG1BM9VdeTee+8FQhQs2T49STnV5dwgp65IeJaOM8l9JLvu\nuitQe89JNVDL88MOOwyAJ554otH39eijjwLwxhtvACE/v7lQ8ynRCpP2cVQyrcQq73n+/PkAHHro\noQ2+D+3VOfvssws8utLTClqyHTzU/5rv06cPAHfffTcQmm9pX08l72FqLJ2bVQJHyM3MzMzMImqW\nEfJsDVvtYG/o7ltFeY866qiay1QxIZvvpVzyM844Awh1lqud8kNVkeOKK65IXa984lx5gZVKNYEl\nWyGk0imCJV9//TUQKj506tQJCBHR5ZZbDgiR4JEjR9b8rVYTlCcpei8q0qMVp2rIqVZ0U3nwyYoY\nl1xyCQDrrbde6QdWJIpMKWdcNYSbQvsSVLe+nL3yyitAqB+tWuKN+QxQhaPsZ5cq/FSTpuR/V8Lr\nopi23HJLINQo17F3v/32A8pz71qxqfeJqLJXOXKE3MzMzMwsomYZIVdXL1HeqqqvZCOB+oalWqeq\npa16ulC7Xq4iwqoqoioRlUgRHuX77rPPPkDYtaz6scm8+VGjRgG1a3Irl14dxaopp015rfLRRx9F\nGklxqH52trOidvTrZz6yeytUX7yh+diVQO8f5dar/8Gtt95ac5tqer6iqk2FiIxXElXa0oqRcoDb\nt28PwJgxYwDYbrvt6r0f5VBD2FugSjXKxx8+fHihhm1lRpVEVK1Jq4T1rYqocpyqzejzNZ+qJNXm\n5ZdfTv27Xbt2kUaycI6Qm5mZmZlF1Cwj5MptVT6iIplNyS1S3tu+++6b+qkIYCVQRCdb6UIRHuWh\naaVAtaKTKwV1Ub69IqGKFlWzV199teb3d999FwidGCvR0ksvDYTInaqnKDdatbRFezJ23333Wvel\n6hDqPFhOdcULRe8b1aBXzr2imnvvvXecgZWIuuapRnYy4ttYWp1bf/31m3xfxaJOrdnqGDoeKI9X\n3YjVXTG7h+mhhx6q+V0rjR07dgRg4MCBQOii3Fy9+eabQDi+dujQIeZwCkp54Dpf0etK+25yRb1V\nrUrnNHqtVdveNc2FOjyrr8W2225bcxvtU8r2mylnjpCbmZmZmUXU4scff4w9hkJq0JNRrm/Xrl0B\n+PjjjwH4/vvv6/075Ykr8pOsW65OWSXIiW6x8JvUyOs/V1GGnXbaCYBPPvkknz9P0bd31Q1Wndwi\nzE/R5iNf55xzDgDnnnturetuu+02IHyTL6KymY8yEW0+1FFPEXEdN9RNb6ONNirkwzVUyedDK486\nFjTogf//uaRj7mqrrQaEGuYFrEZT8PlQpS3l8WplcebMmQ17kMxzh7C3Yvz48UDoflsEFXX8WGut\ntYAQEdYxuIB1yKPPx9ixY4FQcWrttdcG4Nprr625zYwZMwA4/fTTgfDZPW7cOCDsXymAfOYDijQn\n2pej44JWnpMrATqfmTZtGhBW5SdPngxAq1atCjWcfOekTo6Qm5mZmZlF1Cwj5Fmq1an8q2w3SUUn\nttlmGwD69evX6AEWQNG/sT/77LNAyFdUNZWFSe5eVlWAfLqsNVL0CIYol17zps6VECIYJVA281Em\nSj4f06dPB8LxQntVlNPYuXPnQjxMY5V8PlRDW8+7IVVX9Lmk/QfKoW5or4g8FH0+VBtbUdtkPf5c\nlBebfJ2oy60qbhRR9OOH+hjo+KmOwJMmTaq5zT333APAxIkTgZBv/cADDwCw0korFWo40edDTjvt\nNCB030x+LmdXVbT6r0pOBdxrUBYRcq1CvfTSSwAcfPDBQP2rUFq51splATlCbmZmZmZWDRwhrzxl\n8429THg+0jwfaSWfj/vuuw8IFUG0YqIIuSJ+kUR7fShaN2LECCDkWOei1UqtRhZxb47fL2nR5kO5\nvapKpFxp7b1Q/48k5edfddVVQOiGWkBl9/oYMmQIkO7aussuuwAhh1qdsCOvKEGJ5kSrkslVJa3M\nqYqRjjtlMCd1coTczMzMzCwiR8grT9l9Y4/M85Hm+Ugr+Xyoko7ynlVxaPTo0UBJ9lXUx6+PNM9H\nWrT5mDt3LhDeL9nu18kO2meccQYAvXr1KuQQcvHrI60sI+SROUJuZmZmZlYNmmWnTjOzYlE/A+V1\nqhZwOXeXNIttxRVXBOCHH36IPBKzOBwhNzMzMzOLyDnklcc5bWmejzTPR5rnI83zkeb5SPN8pHk+\n0pxDXptzyM3MzMzMqkG1RcjNzMzMzCqKI+RmZmZmZhH5hNzMzMzMLCKfkJuZmZmZReQTcjMzMzOz\niHxCbmZmZmYWkU/IzczMzMwi8gm5mZmZmVlEPiE3MzMzM4vIJ+RmZmZmZhH5hNzMzMzMLCKfkJuZ\nmZmZReQTcjMzMzOziHxCbmZmZmYWkU/IzczMzMwi8gm5mZmZmVlEPiE3MzMzM4vIJ+RmZmZmZhEt\nFnsABfZj7AGUQIs8buv5SPN8pHk+0jwfaZ6PNM9HmucjzfNRm+ckD46Qm5mZmZlF5BNyMzMzM7OI\nfEJuZmZmZhZRteWQm5mZVZUZM2YAcMcddwDQosVPaasDBgyINiYzKyxHyM3MzMzMInKE3KL67rvv\nAOjSpQsAq6++OgA333xztDGZmZWTCRMmAHDWWWcBcNhhh8UcjkX00UcfAXDVVVfVXHbTTTcB8I9/\n/AOA4cOHA3DaaacBsMgijr1WAv8vmZmZmZlF5Ai5RfHtt98C8NBDDwHw+OOPA3DZZZdFG1MxKapx\n8sknA3DnnXcCIQf0ggsuiDMws0iuvfZaAP7whz8A8M9//rPmuiOOOAKAM844A4A2bdqUeHTx7bLL\nLjW//+UvfwHguuuuA+CAAw6IMaQm0f/vf/7zn5zX6/XQoUMHADbccMM676t169YAtGzZspBDLEs/\n/PADEKLgU6dOBeCGG26odVvtLdD7ZvHFFwegf//+xR6mFYAj5GZmZmZmETlCbiX1/fffA/Dggw8C\n8Jvf/AaA5ZZbDoBdd901zsCKQKsAECL/EydOBEIko7lTtOzhhx8GQrR0jTXWAGDatGkAzJo1C4B7\n770XgL333ruk48zH3/72NwCuvPJKoPaqz48//tS8rn379jWXKSL8s5/9DICePXsWfZylNm7cOADO\nPfdcAP71r38BYT6SbrzxRgBuueUWAE444QQALrnkkqKPMzZVUnn++edrLvvvf/8LwNprrw2E42Ul\n0Opnt27dAPjiiy/qvf3IkSMXep/bbrstAAMHDkz9e7XVVmv0OMvN119/DcDVV18N1F9RZ+mll079\nW8fVa665BoAePXoAsOqqqxZ8nJXiww8/BOD6668HwmeL6Ji7xRZbAGE/Wyk5Qm5mZmZmFlGLXNGJ\nClbvk/n3v/8NwI477gjA66+/DoRvnkOHDgVgqaWWKtoACyCf0GpR/3MVtVEERNFfCBELRToV7Xni\niSeAkAenSE/v3r0BOP/88/MdRtnMR5aiuhDmIUu5fQXMIS+b+XjjjTeAEOlJeuCBBwB49NFHgZAj\nq+NRXSsIa665JgAzZ85s6DBKNh99+/YF4LbbbgPgs88+y/0g9TzHxRb7adFSkax77rkHSEfTm6jk\nr48//elPQKgMopzYfLRt2xaAt99+uxBDSiqb98vcuXMB2G233QB45ZVXaq7r2LEjEOayVatWxRpG\nwedDEd7f//73P/3R/1//eq3XJbnCuDB6f0yePBko6PyU/PXx5ZdfArDddtsBMH369NT1SyyxBAB9\n+vSpuezggw9O3ea3v/0tEKqu6Fxnk002aerw8l3ajXaCqRU5Rca1/0L/rovm6P777wdgrbXWWthD\nFWy52xFyMzMzM7OImlWEfPbs2QBsttlmqX+Ldm4rYq6IzvLLL1/YUTZN2UR0FAFuSt7eIYccAoRc\n0UYom/nISkZ4VBXhvvvuS93mtddeAwoSuZDo83HXXXcBcMwxxwBhZSp5rKkrAl5JEXKtEA0ZMgQI\nqxy/+MUvgFAZ5PDDDwegXbt2QFgdSr4WNEdaVZBVVlkFgP322y/1GMsuu2w+Q00q+etDPQU0D41R\nzRFy5VR36tQJCJHxnXbaqeY2ek+ttNJKxRhCUtHmQ91G9bn761//ut7bT5o0KXV7VeRK/r5gwYLU\n3+h18uabbwKw6KKL5jPEXEr2+tBK4nHHHQeE1RDZeOONgbAHQ8eEXBRd18pjtUbI1cfkxRdfBKB7\n9+4113388cdA/vu1dHvV/NfPel5LjpCbmZmZmVWDZhUhl6+++gqAzp07A+HbVdYGG2wAwA477ADA\n9ttvD4Td4iuuuGIThtpo0SM6cs455wChMkZDKLdcOZFnnnkmUHuXeB7KZj6y5s2bV/O7agq//PLL\nQIh2PPvss0CorlEA0edD+YyqtV7zYPVEyBUV0utAneXWX399IEQ7ttpqKyCvKisFnw9VUVH+v3IN\n9fwU+d5rr70a/MDKN7/77rtT9618Us2XVh2036URlQBK/vp47rnnANhzzz2B8JzyodXKInTwjfZ+\nqS9nHEIVGqh7D0oRRD9+NIRqcOv9kN2X8M033wChDncTlGw+9N7X+YXos+LPf/4zAOuss06d96GV\nAVUrmzNnDlB9EXLlxmtfQnL1pOaB/388XmGFFQA48MADgXAOcumll6Zur+NSsh8CwHvvvQfAuuuu\nW9dwHCE3MzMzM6sGzbIOuSp76BuSdt0q+vLII48A8O6776Z+jh8/Hgh1hRWtgxDB0Y7ybARQ39bU\nQUv5pJVItcQfe+yx1OWqnwshGpaliIV2ilezZI7wSy+9lLpOHTsLGBkvG3qtZ1ffkjl4Z599NhDy\n8yqJotmKjItWQZK5vw2l3OBjjz0WCCsDo0ePBkK1FdXQ1TFKebnlTPmsf/3rX4Gwt0LH0YbUFq8n\nOlWxFPFUZFzzpMpDzaELZWMp0qtjSmMq95QbfWYeeeSRQKhMplrr9UXGtRp70UUXASEyrv1v1fZa\n0r6dXJFxUT1x5ZUPHjw4df1BBx2U+reO61qxUmRcKxbZFaxicITczMzMzCyiZhkhF0UkRJUwnn76\naSBUW9FOZVGukSLm2d/rM3/+fCDU7K7ESLGiEltvvTUQ5kvPDULViJVXXhlYeM3ZapSMimdXTDR3\n1URVRz7//HOg9nNWVBwqMzIu/fr1A2qvAGRXjJpi5513Tv1Uh0blFVdiRFB50Ir6jx07tsF/q8if\n5lwrCZUYOVc9ZHUfFe05KPM+GCWnFRXVGIfQ2TZbq1z7uiqxE/KSSy4JwB//+EcgdNusq59BkrpO\n3nTTTanLVblHK26VSjnj6uytXHnR+cVVV11Vc5lqsde1Py27Oq2KLdk65QurBlRIjpCbmZmZmUXU\n/MKWDaBOntr1rBxyURewZKcs5f0tjPJOtcNeHfkqib5JZvO3FLVIUq1U7fpWBQ7Vam5utGJQjbnj\nzzzzDFB3pLiSo+IQdt+rbrSicMnIf6Gp29wnn3xSsscsFkU4Tz/9dKB2Den6aPXlvPPOA0JdbnV8\nrS+/ttyoQoiev7pM9uzZM9qYypGiolOmTAGgV69eC/0bdcmthhVZRXbrivBqFRrC3rUs9W2oVNoj\n06VLFyDkdYuen3LKVXWnMa688kqg9nEpj4peTeYIuZmZmZlZRJX/NbKI1CVPP7MUnYEQLVaOU10U\nyankXc/K41Q991z0zVWrDPo5ZswYIOSElvLbZ6kpEpaknd+VmPu6MOogl6Ua45VOVQ9Uh1yK2clX\nlUm0KqUKUb/85S+L9pjFokifKi3lEyHPUsdOVWq5+OKLmzi64tPrR91YlTOsylt1fc7k49NPPwXC\nao5WZPv27QuUV9dpVQbRa1yfEVoV0qpIMhK8MOqJoZ4hTehvUfaS5x/Zrp7Kex42bFhJx1Roei1k\nI+OiXihNiYyL9vVllXJPhyPkZmZmZmYROULeBMolBTjxxBMb9DcnnXQSELpHVSJFuJS3pXq6yQ5j\nqg6hvFE97+nTpwMwfPhwoDoj5MpFUy1YCLm/1VhdRaZOnQrUrnCgCgAfffRRzWWN6DAZXfL9Xmgv\nvPACALNnzwZC/qwiwJpT1V9Wp9tK0qFDBwCuueaa1E+toKiSTNKsWbMA6N27NxDmR1RVohIi5H//\n+9+B8DrSKoeqezWGVitVGeKQQw4BQuUrUZ56ORxvZ86cCYTXcCFr6T/11FNA2Aemijabb755wR4j\nNq1M11e/X5Wgll122ZKMqdDUE+baa6/Neb3272VriTeGVlXUzVS0il3K1UhHyM3MzMzMInKEvAmU\nEwjhW39dNthgAwAOPfTQoo6plH73u9+lfuainfEPPvggEDoOKgf0rbfeAuBXv/pV0cZZasqlTtap\nVkS4ELlu5UYdSRXFzUbIX375ZQDatGlTc1nXrl1Tl6mudDlXy1DubzGoc2u250E1Un1g/WwI5XGq\nVncluuCCCwp2X6q/feeddwJ1f66o/vTGG29csMduKh0PGhoZP+qoo4CwSpKLOtiq2oi6Kvbv3x+A\nSZMmAWEPRiVSLr0+b7WqlqSO4XV1yi532p+jFXVVoxOtqui91Jg9Auo0PnToUKD23ietrmi1pZQc\nITczMzMzi8gn5GZmZmZmETllpQkeeeSRBt9WmxSaa0OcZHoPhKXDakpVUct4LYklUzf0/17OKRmN\nlW2cVRe1goaw1C5qF63W8OVIS5lXXHFF6vInn3wSCGknjaH0pmSaU0P+3VwsscQSsYfQZNrIvu++\n+zb5vo488kgAbr311npvp2ZtpSizqmP8tttuW+/t1CxOxwClLaoMZLZMqko1ZlPhklROVrdRC3U1\nKVN6wqhRoxryVMqSGqtlj50QPl8GDRoEVF7jufnz5wNhg6U+S/X/qdeAyiY3JlVFG5/12lCTMT2G\nPpsHDx6c930XiiPkZmZmZmYROULeCCrzp5Jk9VELX337rwT6tipNKYyvzUdqVHDvvfcCoXRTNW3q\n1Lf3zz77rNZ13bt3L/VwSkabjE499dRG38fHH38MwEsvvQTAlltu2fSBFdg+++wDhLFpc5o2Kh9+\n+OFAKOe3sPeNmrdAKIVXVxSwrg2z1U7lHzW3WauuumoJRxOPXitqPPfmm2/We/sRI0YAMGDAgOIO\nLGGllVZq0O30GtYxsRDHRn3Ojh07Fgjl8tRQS587lRghV8Q2V6M5OfDAA4HK/RzV8f+WW27Jeb2e\n30YbbZT3fU+ZMgWAgQMHArXLG6633noAXHjhhUDcDbGOkJuZmZmZReQIeSM899xzQMOiVWoRv9lm\nmxV1TIWgRjbKAVR0QSUL8/n2rXzho48+GggRCllzzTXzvs9ypYY32SYGO+20U83vamRQjdR84vHH\nHwdC5FiU36mfEEpNXX755UBok73//vsD8MEHHxRxxI2jiLdKmGaf54QJEwBo2bIlEEp31XX7U045\npeZ3lfvSSpqi8M8880zhnkAF0mqDImiiyLjazleCXXfdFYBtttkGCKX5FAFVjrmonCjA2Wefnfqb\nuigyrtWqRRddtKnDbjC9zsuRmjJVEn3uqtGcVpVFn6EAu+22W+kGVgQ9evTIebn2G2gOFia5T6lL\nly5AKA+p8xm9J9Rk7e677wagdevW+Q674BwhNzMzMzOLyBHyRtAO4IbYaqutijiSwvryyy8BeP/9\n91OXqxnHjTfeCIQdz+3atUvd7uuvv675XTvlb7/99tRt1Op22LBhhRp2dOPHjwfSOcGQblP985//\nvJRDimLnnXdO/ayPKgZMnjwZCDmxlZAjreijIpjz5s1LXa8mJVoV0v6J+++/HwiVUpLPVVFTzYve\nc4ss0jxjJrNmzQLgxRdfzHm9osn5NBeKTZUhtAqi/TVqcqKKIJKMhn/zzTc571OvIVURUc54KSPj\nDaW9SVo11ueIVpKaQits2s+iaKgcf/zxTX6MYtPKu5qDaVUk+bmalKxIdcghhwBh5UgNoQ4++GAg\ntH/X59Dmm28OhD1czz77bOq+dX2p9vLUlXWw9dZbA2GPgKiSmY4PavyUrHynFUndZ6tWrYDwGinH\nc5DmebQ3MzMzMysTjpA3gnKO6tO2bdvUz0o2c+ZMIEQ+Va9T36JPOOEEIJ1Dna2Pu/baawPhW2k5\n5xs2lHLHx40bB9SuEd2QSHFzpUhwtlpEmzZtYgwnL4oaqSLAxRdfDMDUqVNTt/v000+BEBnPat++\nfc3vd911FwCrrbZaQccag1YMlButlt+q077GGmsAoSqH9q4k83y1kpatS696y6oJX4kUEVekWNE9\nRUbro/0JqiverVs3ILyfypn20ajngF7/TYmQv/fee0CoX61+H1nl3P9Bxw1VccquuDWEVgj0Wa2f\njz76KBBeN4svvjgQVmsWLFgAhNVxfaZnV2uKbcMNNwTCXhrRqnz2/0/vlYZUutPnsN5v5Zy14Ai5\nmZmZmVlELaqs81tJnozqVs6YMaPWdeqQdfXVVwMht6uA8kmyzWs+9G1Z+auqmiGqvqLawMrzrI++\n2WrHeBFWDIo2H3VR7qeiUvrmLcpVy1aGKJGSz0dDKVIKoQJNtibsyJEjgXQFkiYq2Xz069fvpwf8\nf86iOngmq+0k/62a0vWpq/649mYccMAB+Q6z6POhWs/9+/fPeb2OCXvssQcQVhzrO54oh1RzrChz\nAUR7v+j9MHHixNTlPXv2BNJ5szrWqDJEIbp91qFo89GxY0cgRISz0X7ttdDP+mgFVitsc+fOzXk7\nvca0z2c9gTGXAAAFNElEQVSVVVbJZ8hQxPnQvoAVVlgBCJ+/Wbr+qKOOSl3eoUOHmt+feuopIHTx\nzLfjsXLsVaVH+f055LvJp0FzotWzhkS866MVAIDOnTsD4TOliNkKBdv45Ai5mZmZmVlEjpA3gCLC\nxxxzDBAix7kqQihila0uUkBFj+ioc5ryWhtq9913r/m9U6dOQPhWr6hxEZQ8wqWOX3V1fdOOcVXO\nKLGSzYdqvqoz6VprrZXzdk888QQAu+yyS81l2feOapkrl7GAokVA9VzqiTYtlHI6sysJt912G1Ce\nEfLVV18dKMwKkarMKN9YnVwLqOxWlJQXrjxfqDs3ugiKNh/vvPMOEGpm5xvFbQgdR1S/esiQIUCo\nMtIIRZsP5b1rjKJV9kGDBgEhxz75eqiLKtlornWcyNL7qWvXrgAss8wyQIOqXBUlQq7PTK18qfqW\ncuProlrs2tdz2mmn1VynFf0ScITczMzMzKwauMpKA6iecLaKQi6qDlDJbrjhBiB0llON29mzZwMh\nj3OJJZYAQs558htpMper2ignLRtN0LfzZEfKaqbqIaoFfeSRRwKh/rqiM9o5n5wv/b7yyisDtfNo\nq0FTIuNyxBFHALXzsVVFoRwp4terV6+8/i75+lCeuWoxZ/Nnq1m+K5OVQpU0tMI8ZswYINTC1uXa\no9MQirZrdU57TzbddNMCjLi4shFcRcCnTJmS8/qGUDdhRcCTlZzK2XbbbQeE/SSqovLwww8DMG3a\nNCCcX6neuvLCtSpX6RwhNzMzMzOLyDnkDfDFF18Aoa6wamjnyrdqQvWDhiq7nMfISj4fqgKgb+2q\nc6rIRrarWImVbD6UO66cV+30rysPMXms0fvjvPPOA4pal76i3y9aXVDdbc25IoCvvvpqvndZsvkY\nPXo0kK6uAzB9+nQAJkyYkLpc0XAIq3IlUNGvjyKINh+qKa4ujA2hjpRF7Gjr10daUXLIK5xzyM3M\nzMzMqoEj5I2g6hmKkCY5Ql5yno+0ks+HIqDKHX7ggQeAEN3VDvhkbqy6NCrnsYiq4vXRunVrIKy+\nPPTQQ0CjVhaqYj4KyPOR5vlI83ykOUJemyPkZmZmZmbVwBHyRrjvvvuA3N3SHCEvOc9HmucjzfOR\n5vlI83ykeT7SPB9pjpDX5gi5mZmZmVk1cIS88vgbe5rnI83zkeb5SPN8pHk+0jwfaZ6PNEfIa3OE\n3MzMzMysGviE3MzMzMwsIp+Qm5mZmZlFVG055GZmZmZmFcURcjMzMzOziHxCbmZmZmYWkU/IzczM\nzMwi8gm5mZmZmVlEPiE3MzMzM4vIJ+RmZmZmZhH5hNzMzMzMLCKfkJuZmZmZReQTcjMzMzOziHxC\nbmZmZmYWkU/IzczMzMwi8gm5mZmZmVlEPiE3MzMzM4vIJ+RmZmZmZhH5hNzMzMzMLCKfkJuZmZmZ\nReQTcjMzMzOziHxCbmZmZmYWkU/IzczMzMwi8gm5mZmZmVlEPiE3MzMzM4vIJ+RmZmZmZhH5hNzM\nzMzMLCKfkJuZmZmZReQTcjMzMzOziHxCbmZmZmYWkU/IzczMzMwi8gm5mZmZmVlEPiE3MzMzM4vI\nJ+RmZmZmZhH5hNzMzMzMLCKfkJuZmZmZReQTcjMzMzOziHxCbmZmZmYWkU/IzczMzMwi8gm5mZmZ\nmVlEPiE3MzMzM4vIJ+RmZmZmZhH5hNzMzMzMLCKfkJuZmZmZReQTcjMzMzOziHxCbmZmZmYWkU/I\nzczMzMwi8gm5mZmZmVlEPiE3MzMzM4vIJ+RmZmZmZhH9D7G4+Rfni5YbAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 60 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 370,
              "height": 248
            }
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "lGyau0mOaP2m",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Defining The Neural Network"
      ]
    },
    {
      "metadata": {
        "id": "n-NR96UtFSkB",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "![](https://raw.githubusercontent.com/dmlc/web-data/master/mxnet/image/mlp_mnist.png)"
      ]
    },
    {
      "metadata": {
        "id": "3WJXInzQGcAy",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 153
        },
        "outputId": "662e4399-1448-4688-88b6-c2e60ae456a8"
      },
      "cell_type": "code",
      "source": [
        "from torch import nn\n",
        "\n",
        "# Layer details for the neural network\n",
        "input_size = 784\n",
        "hidden_sizes = [128, 64]\n",
        "output_size = 10\n",
        "\n",
        "# Build a feed-forward network\n",
        "model = nn.Sequential(nn.Linear(input_size, hidden_sizes[0]),\n",
        "                      nn.ReLU(),\n",
        "                      nn.Linear(hidden_sizes[0], hidden_sizes[1]),\n",
        "                      nn.ReLU(),\n",
        "                      nn.Linear(hidden_sizes[1], output_size),\n",
        "                      nn.LogSoftmax(dim=1))\n",
        "print(model)"
      ],
      "execution_count": 79,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Sequential(\n",
            "  (0): Linear(in_features=784, out_features=128, bias=True)\n",
            "  (1): ReLU()\n",
            "  (2): Linear(in_features=128, out_features=64, bias=True)\n",
            "  (3): ReLU()\n",
            "  (4): Linear(in_features=64, out_features=10, bias=True)\n",
            "  (5): LogSoftmax()\n",
            ")\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "XyXEUFICQeqF",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 170
        },
        "outputId": "687ca786-145f-443a-8e72-33feb1cbc721"
      },
      "cell_type": "code",
      "source": [
        "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
        "print(device)\n",
        "model.to(device)"
      ],
      "execution_count": 80,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "cuda\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Sequential(\n",
              "  (0): Linear(in_features=784, out_features=128, bias=True)\n",
              "  (1): ReLU()\n",
              "  (2): Linear(in_features=128, out_features=64, bias=True)\n",
              "  (3): ReLU()\n",
              "  (4): Linear(in_features=64, out_features=10, bias=True)\n",
              "  (5): LogSoftmax()\n",
              ")"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 80
        }
      ]
    },
    {
      "metadata": {
        "id": "oxSLypv2LOD-",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "criterion = nn.NLLLoss()\n",
        "images, labels = next(iter(trainloader))\n",
        "images = images.view(images.shape[0], -1)\n",
        "\n",
        "logps = model(images.cuda())\n",
        "loss = criterion(logps, labels.cuda())"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "Pj4I2lLgLVWw",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 289
        },
        "outputId": "dd42b7e7-0461-4d4d-a541-2c57946447d4"
      },
      "cell_type": "code",
      "source": [
        "print('Before backward pass: \\n', model[0].weight.grad)\n",
        "\n",
        "loss.backward()\n",
        "\n",
        "print('After backward pass: \\n', model[0].weight.grad)"
      ],
      "execution_count": 82,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Before backward pass: \n",
            " None\n",
            "After backward pass: \n",
            " tensor([[-2.3965e-03, -2.3965e-03, -2.3965e-03,  ..., -2.3965e-03,\n",
            "         -2.3965e-03, -2.3965e-03],\n",
            "        [ 4.3686e-05,  4.3686e-05,  4.3686e-05,  ...,  4.3686e-05,\n",
            "          4.3686e-05,  4.3686e-05],\n",
            "        [ 1.0837e-03,  1.0837e-03,  1.0837e-03,  ...,  1.0837e-03,\n",
            "          1.0837e-03,  1.0837e-03],\n",
            "        ...,\n",
            "        [ 0.0000e+00,  0.0000e+00,  0.0000e+00,  ...,  0.0000e+00,\n",
            "          0.0000e+00,  0.0000e+00],\n",
            "        [-2.6536e-03, -2.6536e-03, -2.6536e-03,  ..., -2.6536e-03,\n",
            "         -2.6536e-03, -2.6536e-03],\n",
            "        [-8.4573e-05, -8.4573e-05, -8.4573e-05,  ..., -8.4573e-05,\n",
            "         -8.4573e-05, -8.4573e-05]], device='cuda:0')\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "F0ZVHVbvI_yt",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "from torch import optim\n",
        "\n",
        "# Optimizers require the parameters to optimize and a learning rate\n",
        "optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.5)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "dS9JqXhhLdkr",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 306
        },
        "outputId": "0538fd2f-07a8-4cec-9efc-f6e64f749794"
      },
      "cell_type": "code",
      "source": [
        "print('Initial weights - ', model[0].weight)\n",
        "\n",
        "images, labels = next(iter(trainloader))\n",
        "images.resize_(64, 784)\n",
        "\n",
        "# Clear the gradients, do this because gradients are accumulated\n",
        "optimizer.zero_grad()\n",
        "\n",
        "# Forward pass, then backward pass, then update weights\n",
        "output = model(images.cuda())\n",
        "loss = criterion(output, labels.cuda())\n",
        "loss.backward()\n",
        "print('Gradient -', model[0].weight.grad)"
      ],
      "execution_count": 84,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Initial weights -  Parameter containing:\n",
            "tensor([[-0.0114,  0.0183, -0.0115,  ..., -0.0267, -0.0321, -0.0175],\n",
            "        [-0.0098,  0.0242, -0.0102,  ..., -0.0347,  0.0079, -0.0282],\n",
            "        [-0.0196, -0.0178,  0.0274,  ...,  0.0317, -0.0261,  0.0053],\n",
            "        ...,\n",
            "        [-0.0065,  0.0330, -0.0105,  ..., -0.0171,  0.0187,  0.0168],\n",
            "        [ 0.0201, -0.0256,  0.0337,  ..., -0.0301,  0.0309, -0.0120],\n",
            "        [-0.0166, -0.0180,  0.0195,  ..., -0.0128, -0.0186, -0.0229]],\n",
            "       device='cuda:0', requires_grad=True)\n",
            "Gradient - tensor([[ 0.0014,  0.0014,  0.0014,  ...,  0.0014,  0.0014,  0.0014],\n",
            "        [-0.0002, -0.0002, -0.0002,  ..., -0.0002, -0.0002, -0.0002],\n",
            "        [ 0.0013,  0.0013,  0.0013,  ...,  0.0013,  0.0013,  0.0013],\n",
            "        ...,\n",
            "        [ 0.0000,  0.0000,  0.0000,  ...,  0.0000,  0.0000,  0.0000],\n",
            "        [-0.0012, -0.0012, -0.0012,  ..., -0.0012, -0.0012, -0.0012],\n",
            "        [ 0.0050,  0.0050,  0.0050,  ...,  0.0050,  0.0050,  0.0050]],\n",
            "       device='cuda:0')\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "wy0KOQ95LgYN",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 170
        },
        "outputId": "de026080-d851-4215-fd6a-a36dac6b0ab5"
      },
      "cell_type": "code",
      "source": [
        "# Take an update step and few the new weights\n",
        "optimizer.step()\n",
        "print('Updated weights - ', model[0].weight)"
      ],
      "execution_count": 85,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Updated weights -  Parameter containing:\n",
            "tensor([[-0.0114,  0.0183, -0.0115,  ..., -0.0267, -0.0321, -0.0175],\n",
            "        [-0.0098,  0.0242, -0.0102,  ..., -0.0347,  0.0079, -0.0282],\n",
            "        [-0.0196, -0.0178,  0.0274,  ...,  0.0317, -0.0261,  0.0053],\n",
            "        ...,\n",
            "        [-0.0065,  0.0330, -0.0105,  ..., -0.0171,  0.0187,  0.0168],\n",
            "        [ 0.0201, -0.0256,  0.0338,  ..., -0.0301,  0.0309, -0.0120],\n",
            "        [-0.0166, -0.0181,  0.0194,  ..., -0.0128, -0.0187, -0.0229]],\n",
            "       device='cuda:0', requires_grad=True)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "wstRGu4FaJBe",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Core Training Of Neural Network"
      ]
    },
    {
      "metadata": {
        "id": "XCsoAdjdLjPb",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 306
        },
        "outputId": "14fb7709-94a1-4f79-8de4-ddf6f7e94e46"
      },
      "cell_type": "code",
      "source": [
        "optimizer = optim.SGD(model.parameters(), lr=0.003, momentum=0.9)\n",
        "time0 = time()\n",
        "epochs = 15\n",
        "for e in range(epochs):\n",
        "    running_loss = 0\n",
        "    for images, labels in trainloader:\n",
        "        # Flatten MNIST images into a 784 long vector\n",
        "        images = images.view(images.shape[0], -1)\n",
        "    \n",
        "        # Training pass\n",
        "        optimizer.zero_grad()\n",
        "        \n",
        "        output = model(images.cuda())\n",
        "        loss = criterion(output, labels.cuda())\n",
        "        \n",
        "        #This is where the model learns by backpropagating\n",
        "        loss.backward()\n",
        "        \n",
        "        #And optimizes its weights here\n",
        "        optimizer.step()\n",
        "        \n",
        "        running_loss += loss.item()\n",
        "    else:\n",
        "        print(\"Epoch {} - Training loss: {}\".format(e, running_loss/len(trainloader)))\n",
        "print(\"\\nTraining Time (in minutes) =\",(time()-time0)/60)\n"
      ],
      "execution_count": 86,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch 0 - Training loss: 0.6485169944621479\n",
            "Epoch 1 - Training loss: 0.28772426600744727\n",
            "Epoch 2 - Training loss: 0.22218721673321495\n",
            "Epoch 3 - Training loss: 0.17751274647504917\n",
            "Epoch 4 - Training loss: 0.14714437284306295\n",
            "Epoch 5 - Training loss: 0.12703789881408722\n",
            "Epoch 6 - Training loss: 0.11110581199465784\n",
            "Epoch 7 - Training loss: 0.09855154845347283\n",
            "Epoch 8 - Training loss: 0.08801297230649986\n",
            "Epoch 9 - Training loss: 0.08139357314323947\n",
            "Epoch 10 - Training loss: 0.07304080039945873\n",
            "Epoch 11 - Training loss: 0.06733504345596854\n",
            "Epoch 12 - Training loss: 0.061133228770610115\n",
            "Epoch 13 - Training loss: 0.0577682187713222\n",
            "Epoch 14 - Training loss: 0.0530630665571133\n",
            "\n",
            "Training Time (in minutes) = 2.5549638867378235\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "75j9X1b6ME5K",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def view_classify(img, ps):\n",
        "    ''' Function for viewing an image and it's predicted classes.\n",
        "    '''\n",
        "    ps = ps.cpu().data.numpy().squeeze()\n",
        "\n",
        "    fig, (ax1, ax2) = plt.subplots(figsize=(6,9), ncols=2)\n",
        "    ax1.imshow(img.resize_(1, 28, 28).numpy().squeeze())\n",
        "    ax1.axis('off')\n",
        "    ax2.barh(np.arange(10), ps)\n",
        "    ax2.set_aspect(0.1)\n",
        "    ax2.set_yticks(np.arange(10))\n",
        "    ax2.set_yticklabels(np.arange(10))\n",
        "    ax2.set_title('Class Probability')\n",
        "    ax2.set_xlim(0, 1.1)\n",
        "    plt.tight_layout()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "Ie9Fffl_Mqp6",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 261
        },
        "outputId": "f343c543-4b80-4b77-da25-5f9ebb1e2e05"
      },
      "cell_type": "code",
      "source": [
        "images, labels = next(iter(valloader))\n",
        "\n",
        "img = images[0].view(1, 784)\n",
        "# Turn off gradients to speed up this part\n",
        "with torch.no_grad():\n",
        "    logps = model(img.cuda())\n",
        "\n",
        "# Output of the network are log-probabilities, need to take exponential for probabilities\n",
        "ps = torch.exp(logps)\n",
        "probab = list(ps.cpu().numpy()[0])\n",
        "print(\"Predicted Digit =\", probab.index(max(probab)))\n",
        "view_classify(img.view(1, 28, 28), ps)"
      ],
      "execution_count": 90,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Predicted Digit = 8\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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1SZ6Y5Jtz/iTJQaP/ftlEqgNgkMxEATDNTk3ymQWOnZHus6JentlQBQCXS4gC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\nRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x648 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 424,
              "height": 227
            }
          }
        }
      ]
    },
    {
      "metadata": {
        "colab_type": "text",
        "id": "wAEvDtiaM6RQ"
      },
      "cell_type": "markdown",
      "source": [
        "### Model Evaluation"
      ]
    },
    {
      "metadata": {
        "id": "5sBPmaBONPkT",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "b2e7b282-8b3b-411f-9d7f-e6f7c2c4faef"
      },
      "cell_type": "code",
      "source": [
        "correct_count, all_count = 0, 0\n",
        "for images,labels in valloader:\n",
        "  for i in range(len(labels)):\n",
        "    img = images[i].view(1, 784)\n",
        "    # Turn off gradients to speed up this part\n",
        "    with torch.no_grad():\n",
        "        logps = model(img.cuda())\n",
        "\n",
        "    # Output of the network are log-probabilities, need to take exponential for probabilities\n",
        "    ps = torch.exp(logps)\n",
        "    probab = list(ps.cpu().numpy()[0])\n",
        "    pred_label = probab.index(max(probab))\n",
        "    true_label = labels.numpy()[i]\n",
        "    if(true_label == pred_label):\n",
        "      correct_count += 1\n",
        "    all_count += 1\n",
        "\n",
        "print(\"Number Of Images Tested =\", all_count)\n",
        "print(\"\\nModel Accuracy =\", (correct_count/all_count))"
      ],
      "execution_count": 89,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Number Of Images Tested = 10000\n",
            "\n",
            "Model Accuracy = 0.9716\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}