MNIST Digit Prediction Using ANN.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "MNIST Digit Prediction using ANN.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "eHhS5A2YIJDZ"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "import tensorflow as tf\n",
        "from tensorflow import keras\n",
        "from tensorflow.keras import Sequential\n",
        "from tensorflow.keras.layers import Dense, Flatten"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7KeSQjMUIMoz"
      },
      "source": [
        "(X_train, y_train), (X_test, y_test) = keras.datasets.mnist.load_data()"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0tSVuoX0IW_t",
        "outputId": "850ae19d-fe3b-4bea-f070-27668c2a5db4"
      },
      "source": [
        "print(len(X_train))\n",
        "print(len(X_test))"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "60000\n",
            "10000\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lMlsOelUIfJv",
        "outputId": "0078d534-5676-4661-bb66-50a1ffaa2cae"
      },
      "source": [
        "X_train[0].shape"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "i87olxy6IikQ",
        "outputId": "cbddcd94-430e-4afd-8b66-c5f2146ac789"
      },
      "source": [
        "X_train[0]"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bcp_JZRyIsqh"
      },
      "source": [
        "# Function to Visualize Data from Matrix\n",
        "\n",
        "def show_digit(mat):\n",
        "    return plt.matshow(mat)"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "iM-zYnLiI5CQ",
        "outputId": "0b2cd120-fcf9-4794-a14a-94fe7df43cbd"
      },
      "source": [
        "for i in X_train[:5]:\n",
        "    print(show_digit(i), end = '')"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "AxesImage(43.2,25.92;223.2x223.2)AxesImage(43.2,25.92;223.2x223.2)AxesImage(43.2,25.92;223.2x223.2)AxesImage(43.2,25.92;223.2x223.2)AxesImage(43.2,25.92;223.2x223.2)"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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J5Y+kBdCWxnN14DRJX5T0lO0nqm3rJK20vUxDlw13SLpoUiYEMKnGc3Xgx5JGur5YfhN+AFMCKwaB5CgBIDlKAEiOEgCSowSA5CgBIDlKAEiOEgCSowSA5CgBIDlKAEiOEgCSowSA5CgBIDlKAEhuzM8daOrO7NckvTRs03xJu1s2wMFjvsa083ztPJvU/PmOiogPjxS0tAR+Zed2T0R01TbAGJivMe08XzvPJrV2Pp4OAMlRAkBydZfAhpr3Pxbma0w7z9fOs0ktnK/W1wQA1K/uMwEANaMEgOQoASA5SgBIjhIAkvsfsRZSmOVUgvYAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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7JV0eEXsl3SrpOEmz1XemcMMgv2+h7dW2V+/XviaMDKCZhlQCtrvUVwB3RcR9khQROyPiQET0SrpN0ikD/d6IWBwR3RHR3aVxzZobQJMM5d0BS7pd0qaIuLHf9un9nna+pA3NHw9Aqw3l3YFPSrpQ0nrb62rbrpY03/ZsSSFpi6RLWjIhgJYayrsDj0sa6OeQH27+OADajRWDQHKUAJAcJQAkRwkAyVECQHKUAJAcJQAkRwkAyVECQHKUAJAcJQAkRwkAyVECQHKUAJAcJQAk54ho387s/5K0td+mIyS92rYBho/5GtPJ83XybFLz5/uNiPjgQEFbS+BXdm6vjojuygaog/ka08nzdfJsUnvn43IASI4SAJKrugQWV7z/epivMZ08XyfPJrVxvkpfEwBQvarPBABUjBIAkqMEgOQoASA5SgBI7n8B0YsyoP44dJIAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
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            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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T6CSuJwA0o3Q9AUYCQHKEAJAcIQAkRwgAyRECQHKEAJAcIQAkV+s8AduvS9o8YtFsSTtqa+DA0V97erm/Xu5N6nx/R0fEr4xWqDUEfmHl9kBE9DfWQAv0155e7q+Xe5Pq7Y/dASA5QgBIrukQWNbw+luhv/b0cn+93JtUY3+NHhMA0LymRwIAGkYIAMkRAkByhACQHCEAJPe/ts8M0CxpZSwAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-i5exLggJCgP",
        "outputId": "9ddbc3ea-375b-49b6-8fb8-a97936829778"
      },
      "source": [
        "# Verifying if y_train has correct labels for X_train\n",
        "for i in y_train[:5]:\n",
        "    print(i, end = ' ')"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "5 0 4 1 9 "
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rz1Cgb7XKjZk"
      },
      "source": [
        "# Every value in a matrix has a value upto 256 (0-255)\n",
        "# Thus, we can normalize each matrix (each image), to normalize the values\n",
        "# This will help in getting better predictions"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kMpX9oPuK2Au"
      },
      "source": [
        "# Normalize\n",
        "\n",
        "X_train = X_train/255.0\n",
        "X_test = X_test/255.0"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AqKpJYTLK95M",
        "outputId": "2db79b06-397d-47d5-86f2-dc7cc59e0e6b"
      },
      "source": [
        "print(X_train[0])\n",
        "print('*'*100)\n",
        "print(X_test[0])"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.01176471 0.07058824 0.07058824 0.07058824 0.49411765 0.53333333\n",
            "  0.68627451 0.10196078 0.65098039 1.         0.96862745 0.49803922\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.11764706 0.14117647 0.36862745 0.60392157\n",
            "  0.66666667 0.99215686 0.99215686 0.99215686 0.99215686 0.99215686\n",
            "  0.88235294 0.6745098  0.99215686 0.94901961 0.76470588 0.25098039\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.19215686 0.93333333 0.99215686 0.99215686 0.99215686\n",
            "  0.99215686 0.99215686 0.99215686 0.99215686 0.99215686 0.98431373\n",
            "  0.36470588 0.32156863 0.32156863 0.21960784 0.15294118 0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.07058824 0.85882353 0.99215686 0.99215686 0.99215686\n",
            "  0.99215686 0.99215686 0.77647059 0.71372549 0.96862745 0.94509804\n",
            "  0.         0.         0.         0.         0.         0.\n",
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            " [0.         0.         0.         0.         0.         0.\n",
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            "  0.99215686 0.80392157 0.04313725 0.         0.16862745 0.60392157\n",
            "  0.         0.         0.         0.         0.         0.\n",
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            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.05490196 0.00392157 0.60392157\n",
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            "  0.99215686 0.74509804 0.00784314 0.         0.         0.\n",
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            " [0.         0.         0.         0.         0.         0.\n",
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            "  0.74509804 0.99215686 0.2745098  0.         0.         0.\n",
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            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.1372549  0.94509804 0.88235294 0.62745098 0.42352941 0.00392157\n",
            "  0.         0.         0.         0.         0.         0.\n",
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            " [0.         0.         0.         0.         0.         0.\n",
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            "  0.09803922 0.         0.         0.         0.         0.\n",
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            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.17647059 0.72941176 0.99215686 0.99215686\n",
            "  0.58823529 0.10588235 0.         0.         0.         0.\n",
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            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.0627451  0.36470588 0.98823529\n",
            "  0.99215686 0.73333333 0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
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            "  0.         0.         0.         0.         0.         0.97647059\n",
            "  0.99215686 0.97647059 0.25098039 0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.18039216 0.50980392 0.71764706 0.99215686\n",
            "  0.99215686 0.81176471 0.00784314 0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.15294118 0.58039216 0.89803922 0.99215686 0.99215686 0.99215686\n",
            "  0.98039216 0.71372549 0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.09411765 0.44705882\n",
            "  0.86666667 0.99215686 0.99215686 0.99215686 0.99215686 0.78823529\n",
            "  0.30588235 0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.09019608 0.25882353 0.83529412 0.99215686\n",
            "  0.99215686 0.99215686 0.99215686 0.77647059 0.31764706 0.00784314\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.07058824 0.67058824 0.85882353 0.99215686 0.99215686 0.99215686\n",
            "  0.99215686 0.76470588 0.31372549 0.03529412 0.         0.\n",
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            "****************************************************************************************************\n",
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            " [0.         0.         0.         0.         0.         0.\n",
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            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.4745098  0.99607843\n",
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            " [0.         0.         0.         0.         0.         0.\n",
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            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VXKz9OhoLMGa"
      },
      "source": [
        "# Flattening each (28,28) image --> (784,1) (A flatbed of the matrix values of each image)\n",
        "# This will be given as input with input neurons = 784"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "40toyKjILpFt",
        "outputId": "1f50d08e-ef11-423f-bfee-a62fafba0bd5"
      },
      "source": [
        "# Current Shape\n",
        "X_train.shape"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p47WL_xTVUTt"
      },
      "source": [
        "### Model 1: Manual Flattening to flatten the Input Image"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0fvabtaTLw-w"
      },
      "source": [
        "# Manual Flattening\n",
        "\n",
        "X_train_flattened = X_train.reshape(len(X_train), 28*28)\n",
        "X_test_flattened = X_test.reshape(len(X_test), 28*28)"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hbbYx3gNL2fT",
        "outputId": "b55933aa-9c9f-41a8-c9c1-9d5a12471255"
      },
      "source": [
        "# New shape\n",
        "X_train_flattened.shape"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 784)"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "m84C3EEVL3hh",
        "outputId": "5440e418-ccd9-4f6b-c993-af5b36e0a4ac"
      },
      "source": [
        "X_train_flattened[0].shape"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(784,)"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eLd-bzkRL-Nf"
      },
      "source": [
        "# Building the Model\n",
        "\n",
        "model = Sequential([\n",
        "                Dense(10, input_shape=(784,), activation='sigmoid')          # 10 Neurons in Output Layer and 784 Neurons in Input Layer\n",
        "                                                                             # No Hidden Layer\n",
        "                                                                             # Sigmoids are often used as Output Layer\n",
        "])"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "y2SYMumxMH6K"
      },
      "source": [
        "# Compiling the Model\n",
        "model.compile(optimizer='adam',\n",
        "              loss='sparse_categorical_crossentropy',                        # Sparse Categorical Cross Entropy is used when we have discrete classes in Y                                                  \n",
        "              metrics=['accuracy'])                                          # Categorical Cross Entropy is used when we have one hot encoded values in Y"
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "R_TmGUyLYsBA",
        "outputId": "9f113ad6-46ce-4915-944f-32e51f3e9a0a"
      },
      "source": [
        "model.summary()"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model: \"sequential\"\n",
            "_________________________________________________________________\n",
            " Layer (type)                Output Shape              Param #   \n",
            "=================================================================\n",
            " dense (Dense)               (None, 10)                7850      \n",
            "                                                                 \n",
            "=================================================================\n",
            "Total params: 7,850\n",
            "Trainable params: 7,850\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "M7-y13L_MIkC",
        "outputId": "5732d140-aab2-4e35-cf33-86f3d5b96730"
      },
      "source": [
        "# Fitting the Model with Training Data\n",
        "\n",
        "model.fit(X_train_flattened, y_train, epochs = 10)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.4721 - accuracy: 0.8745\n",
            "Epoch 2/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.3041 - accuracy: 0.9150\n",
            "Epoch 3/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.2834 - accuracy: 0.9208\n",
            "Epoch 4/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.2733 - accuracy: 0.9233\n",
            "Epoch 5/10\n",
            "1875/1875 [==============================] - 3s 1ms/step - loss: 0.2666 - accuracy: 0.9254\n",
            "Epoch 6/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.2615 - accuracy: 0.9273\n",
            "Epoch 7/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.2585 - accuracy: 0.9283\n",
            "Epoch 8/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.2552 - accuracy: 0.9298\n",
            "Epoch 9/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.2530 - accuracy: 0.9297\n",
            "Epoch 10/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.2509 - accuracy: 0.9304\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7f85c106ca90>"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pMUwMfZzNWzd",
        "outputId": "231c7dc5-c566-4cc7-b256-03ae5fa8ce84"
      },
      "source": [
        "# Evaluating Model Performance\n",
        "model.evaluate(X_test_flattened, y_test)"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "313/313 [==============================] - 1s 1ms/step - loss: 0.2651 - accuracy: 0.9259\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.26512137055397034, 0.9258999824523926]"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cj3kpPLRNiS4"
      },
      "source": [
        "y_pred = model.predict(X_test_flattened)"
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4vHJHM-6NfD8",
        "outputId": "7ee60d3b-6ae4-459f-c7dd-b160874d70a5"
      },
      "source": [
        "y_pred[0]                            # Gives probability for each class for the given input image"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([3.7021041e-03, 2.1899988e-08, 1.4558345e-02, 9.7607893e-01,\n",
              "       1.1482239e-03, 1.3208205e-01, 3.9989654e-08, 9.9985600e-01,\n",
              "       8.8031083e-02, 6.4242482e-01], dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RIyQOiJ9N45z",
        "outputId": "be552756-4570-46e4-888f-007a00b3d00b"
      },
      "source": [
        "np.argmax(y_pred[0])                 # This gives the index for which the probability for the given input is maximum, \n",
        "                                     # Thus gives the Class Name or Digit"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "7"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 294
        },
        "id": "bd5vsld1Nvpf",
        "outputId": "28790544-e92c-4065-f439-e3d95112bc68"
      },
      "source": [
        "# Verifying if given input is same as output\n",
        "show_digit(X_test[0])"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f85bd6b8710>"
            ]
          },
          "metadata": {},
          "execution_count": 24
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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LId/VeNhqNOUAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IxJ6Z5puPhBU"
      },
      "source": [
        "# To find the Confusion Matrix, we want an array with predicted discrete classes\n",
        "# Currently, we have y_pred in form of array of probabilities"
      ],
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Vsn_3wrDPTzu"
      },
      "source": [
        "y_pred_labels = [np.argmax(i) for i in y_pred]"
      ],
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VmVid9DLPyL2",
        "outputId": "81d7534e-5802-4d89-86e2-b0393fc8e4d9"
      },
      "source": [
        "# Comparing with Y true and Y predicted\n",
        "print('Predicted:', str(y_pred_labels[:5]))\n",
        "print('Actuals: ', str(y_test[:5]))"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Predicted: [7, 2, 1, 0, 4]\n",
            "Actuals:  [7 2 1 0 4]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B_nlwSzHmHWV"
      },
      "source": [
        "#Labels for Confusion Matrix\n",
        "labels = [str(i) for i in range(0,10)]"
      ],
      "execution_count": 49,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9GyB73OyQAzl"
      },
      "source": [
        "# Confiusion Matrix\n",
        "\n",
        "cm = tf.math.confusion_matrix(y_test, y_pred_labels, num_classes = 10)"
      ],
      "execution_count": 28,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 388
        },
        "id": "626hZvg9QSXD",
        "outputId": "fe42e5aa-b98d-4dde-935f-60cdc550edb1"
      },
      "source": [
        "plt.figure(figsize = (10,6))\n",
        "sns.heatmap(cm, fmt = 'g', annot = True, xticklabels = labels, yticklabels = labels)\n",
        "plt.xlabel('Predicted')\n",
        "plt.ylabel('Actuals')\n",
        "plt.show()"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1jTePfLEVgJj"
      },
      "source": [
        "### Model 2: Using Flatten() from TensorFlow to flatten the Input Image"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "urEkar2OQeUd"
      },
      "source": [
        "# Using Flatten() Layer and Building the Model"
      ],
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "spEJExUuRHn2"
      },
      "source": [
        "model2 = Sequential([\n",
        "    Flatten(input_shape = (28,28)),\n",
        "    Dense(10, activation = 'sigmoid')\n",
        "]\n",
        ")"
      ],
      "execution_count": 31,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rLuhE02JSyrj"
      },
      "source": [
        "model2.compile(\n",
        "    optimizer = 'adam',\n",
        "    loss = 'sparse_categorical_crossentropy',\n",
        "    metrics = ['accuracy']\n",
        ")"
      ],
      "execution_count": 32,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ap1mo8d_Yu_U",
        "outputId": "bca7cd83-e679-411b-c2a2-62ef65aedf77"
      },
      "source": [
        "model2.summary()"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model: \"sequential_1\"\n",
            "_________________________________________________________________\n",
            " Layer (type)                Output Shape              Param #   \n",
            "=================================================================\n",
            " flatten (Flatten)           (None, 784)               0         \n",
            "                                                                 \n",
            " dense_1 (Dense)             (None, 10)                7850      \n",
            "                                                                 \n",
            "=================================================================\n",
            "Total params: 7,850\n",
            "Trainable params: 7,850\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NzXp2q0-THyc",
        "outputId": "b9cbbc8a-e0c4-41a2-adbe-b198d38f6ef4"
      },
      "source": [
        "model2.fit(X_train, y_train, epochs = 10)"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.4665 - accuracy: 0.8788\n",
            "Epoch 2/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.3030 - accuracy: 0.9147\n",
            "Epoch 3/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.2830 - accuracy: 0.9207\n",
            "Epoch 4/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.2731 - accuracy: 0.9238\n",
            "Epoch 5/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.2670 - accuracy: 0.9255\n",
            "Epoch 6/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.2621 - accuracy: 0.9269\n",
            "Epoch 7/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.2585 - accuracy: 0.9277\n",
            "Epoch 8/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.2553 - accuracy: 0.9295\n",
            "Epoch 9/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.2529 - accuracy: 0.9299\n",
            "Epoch 10/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.2507 - accuracy: 0.9304\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7f85bebdce10>"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AvfiULbuTSuS",
        "outputId": "080da40e-1ca4-4281-d002-ebd88e53c03c"
      },
      "source": [
        "model2.evaluate(X_test, y_test)"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "313/313 [==============================] - 1s 1ms/step - loss: 0.2647 - accuracy: 0.9258\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.26473626494407654, 0.9258000254631042]"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IXmMbj3QWmS_"
      },
      "source": [
        "y_pred_2 = model2.predict(X_test)\n",
        "y_pred_2_labels = [np.argmax(i) for i in y_pred_2]"
      ],
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 388
        },
        "id": "Dpp3NNeYWpA2",
        "outputId": "c93cd843-6120-4445-eea3-27e8856450f7"
      },
      "source": [
        "cm2 = tf.math.confusion_matrix(y_test, y_pred_2_labels)\n",
        "\n",
        "plt.figure(figsize = (10,6))\n",
        "sns.heatmap(cm2, fmt = 'g', annot = True, xticklabels = labels, yticklabels = labels)\n",
        "plt.xlabel('Predicted')\n",
        "plt.ylabel('Actuals')\n",
        "plt.show()"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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rcthY9scfZvyEMKOjWMUV27KjeXfEp1R8KJjKj9Tn+V4D2LBhKy/0edXoWLlyprZ8PDGZuvVq4eVVBICWLRo7/IBul9z3XPgQlb2ug1MWaAuc/8t6Bfxqp/fMUUZGBq+9PoKI5XNwM5mYNn0e+wzs7Xh75KdEx+7iwoVLtOrSiwF9e+Nb7AE+GTeRcxcuMuDtkTxW5SHCxn0EQEi3F7hy9Ro309NZv/lXwsZ9RDn/srwyZAQ309PJzMikfp2adO/UzrD/U7lyZZk6ZTxubiZMJhM//riU5RFrDctjjUYN69C7V3d27d5HTHTWF9V7733KipXrDU6WPUdry9aYNfMbmjVtgJ9fSY4diWHUB2P4Ydpco2O5FGdry1HRsSxcuJyoqFWkp6ezM24vk7+fbXSsHDnjvpcrB++FsYWyx6BUpdQU4Aet9ZZ7PDZHa/1cbq9h9gh07NNv/uJ6ymajI+SZV0AToyMIIZyEMjpAHjnVH5A7pKclF+hHfX3hxzZ9VF5d/+uwTcMuPTha62yvMGVNcSOEEEIIYQuZqkEIIYQorFz4EJUUOEIIIURhJQWOEEIIIVyOg19t3hZS4AghhBCFlQv34BSaqRqEEEIIUXhID44QQghRWLlwD44UOEIIIURh5eBXI7aFFDhCCCFEYeXCPTgyBkcIIYQQLkd6cIQQQojCSk4TL3gOO7lFNnwCmxodIc8u//BvoyPkWYm+042OkCcZmRlGRygUlHK2bwzn4+NexOgIeXI57brREZyDCx+ictgCRwghhBB2JgWOEEIIIVyOC59FJYOMhRBCCOFypAdHCCGEKKR0pgwyFkIIIYSrkTE4QgghhHA5LjwGRwocIYQQorBy4UNUMshYCCGEEC5HenCEEEKIwkrG4AghhBDC5UiBI4QQQgiX48JzUckYHCGEEEK4nEJV4Bw6uI3YHWuJiV7Ntt8ijI5zT2GTxpB0PI7YHWtvrytRojgREXPYu3czERFzKF7c18CEWWZHHqTbxJV0nbiSWdsOArB633G6TlxJzQ/mszfl3O1tf0tI5Z+T19D9u1X8c/Iaoo6eNCo2AEFB5Vi1ai6xsevYsWMtAwdmTTpaooQvy5fPZs+eX1i+fLZDfM7Zee3Vl4iLW09s7DpmzvwGT09PoyPlyFn3vU8+GcHuXRvZHrOGBfO/x9e3mIEJ/+5emf9v5Ftsj1lDdNQqli+fTblyZQ1MeG8mk4lfti5h7oIwAL757jPi9mxg069L2PTrEp6s9rjBCe8tKCiAtasXsGvnBnbGrWfwoL5GR7JdZqZtiwMrVAUOQOs2zxJcJ4T6DToYHeWeZsxcQMfQXnetG/r2QDas30rVqk3YsH4rQ98eaFC6LIdPXWThjiPM6tea+a+EsPlQConnLlO5tC9fPNuQWhVK37V9CW9PJvyjMT/+py0fdq7Lu4uiDEqeJT09g2HDRlOzZiuaNu3Mf/7zLx57rApvvTWQDRu28uSTzdiwYStvvTXA0JzZCQjwZ+DAf1O/fgdq1myFm5sbPXt0NjpWrpxx31u3bhM1araidnAbDh06wrChgwxKd2/3yjz2i++oHdyGOnXbEhGxjnfffd2gdNn7z4A+HDxw+K5174/4jKYNO9G0YSf27N5vULKcpaen8/bQUTxVvQWNGofSv38fHn+8itGxbJOpbVscWKErcBzdli2RnD9/4a51oaEhzJy1AICZsxbQqVNbI6LdduTMJaoFlsLL3YzZZKJ2hdKs25/MQ6WLUdHv779wHytXgjJFvQB4uHQxbtzMIC09o6Bj35aaeoq4uD0AXLlylfj4wwQG+hMa2oZZs34EYNasH+nUKcSwjLkxm814eRXBzc0Nby8vUk6kGh3J6d1r31u7dhMZGVltNTJyB4GB5YyIlq17Zb58+crt2z7eXmgHG2MREOBPSLvmzJg+3+goeZaaeorYu747DhEY4G9wKhvpTNsWB2a3Akcp9ZhSqpVS6oG/rG9nr/fMjdaaFRHhRG5bQb++zxsVI8/KlPEjNfUUkLWDlSnjZ2ieyqV92ZF4mgvXbnD9ZjpbDqVy8tI1q567dn8Sj5crjofZzc4prVOhQhA1alQlKirW4T7n7KSkpDJu3HccSYjieGIsly5dYu3aTUbHypGz7nt36tOnJ6tWbTA6hlU+GDWUhMNR/POfzzBq1Bij49zl4/+NYOSIz8j8y6//Ee8PYcu2ZXz06bt4eHgYlM56FSoEUaP6k0RGxRodxTbSg5M3SqlXgcXAYGCPUurO/vOPc3jey0qpGKVUTGbm1XzP1bzFM9St146Oob3o378PjRvXy/f3KAhG/yJ7qHQxXmz0GP1nb2Lg7E086l8ck0nl+rzDpy4yYd0uRjwdXAApc+fj4014+CTeemvUXb96b3GwH763FS/uS2hoW6o8Up8HK9TC28eb557ranSsHDn7vvfOsMGkp2cwJ3yh0VGs8v7I//Fw5bqEh//MgP4vGh3ntrbtWnDm9Fl2xu29a/0HI8dQt1YILZt2pUQJX14b8rJBCa3j4+PN/HmTGfLWyHt+dwjHYK8enJeA2lrrLkBz4D2l1GuWx7L9S6i1DtNaB2utg00mn3wPlZKS1Y1/+vRZFi1eQZ06NfL9Pezh1Kkz+PuXAcDfvwynT581OBE8U/Mhwl9qw9Q+LSlaxJ0KJYvmuP3JS9cYMn8rH3auR/mSD+S4bUEwm83MnTuJuXN/ZvHilcC9PuczRkbMVqtWTTh2LJEzZ86Rnp7OokUraFDfMYrG7DjrvgfQu/ezdOjQmn+94Fjjb6wRPvdnnnmmvdExbqtXvzbtOrRi596NTJk2nibNGjDp+7GcPHkagLS0NGbP+onatZ8yOGn2zGYzC+ZNJjz8ZxYtWmF0HJvpzEybFkdmrwLHpLW+AqC1PkZWkdNeKfUFORQ49uTt7cUDD/jcvt2mdTP27j1gRJQ8W7psDb17PQtA717PsnTpaoMTwbmrfwBw4uJV1scn077ag9lue+mPNAaHb+a1Vk9R80HHOOwzadLnxMcf5ssvv7+9btmyNfTq1R2AXr26s3TpGqPi5eh4YjJ169XCy6sIAC1bNCY+/pDBqbLnzPteSEhz3nqzP127vcj1638YHccqlStXun07NLQtBw4kGJjmbh/83xiefLQx1as2p2+f19n8y2+80u9Nypb988SEpzu2Zv8+x23Pk8PGsj/+MOMnhBkdJX+48CEqe13o76RSqobWOg5Aa31FKdURmApUs9N75qhs2dL8uGAKAG5mN+bOXcTq1RuNiJKjmTO+pmnTBvj5leRIQjQffDiWzz//mjlzvqPPi/8gMTGJ557rb3RM3pz/Kxevp2F2UwxvX4tiRTxYH5/EpytiOX/tBoPDN/No2eJM7NWMeVGHSTx3hUmb9jFp0z4AvuvVlJI+RQzJ3rBhHZ5/vhu7d+8nMjLrF9j77/+PMWO+ZfbsifTp05PExGSef974z/leoqJjWbhwOVFRq0hPT2dn3F4mfz/b6FjZcuZ9b+jQQXh6eLAiIhyAyKgdDBo03OCkf7pX5vbtWvLIIw+RmalJTExioAPlzU7Y1C/w8yuJUordu/Yz5LX3jI50T40a1qF3r+7s2r2PmOisH5rvvfcpK1auNziZDRx8oLAtlD3GcyilgoB0rfXfTu1QSjXSWm/N7TXcPQIduzT8C6UM6ZiyycWpjnNs3lol+k43OkKeZGQad7ZYYeKM+5+z8XE35gfJ/bqcdt3oCPclPS25QBvz1dG9bPpb6zNilsPufHbpwdFaJ+XwWK7FjRBCCCEKgIMfZrKFzEUlhBBCFFYOPlDYFnKhPyGEEKKwsvMgY6XUG0qpvUqpPUqpcKVUEaVUJaVUpFLqsFJqnlLKw7Ktp+X+YcvjFW35r0mBI4QQQhRWdrySsVIqEHgVCNZaPwm4Af8APgPGaa0rA+eBW5N69QXOW9aPs2x336TAEUIIIYS9mAEvpZQZ8AZOAC2BHy2PTwe6WG53ttzH8ngrZcMZBFLgCCGEEIWVHQ9Raa2TgTFAIlmFzUVgO3BBa51u2SwJCLTcDgSOW56bbtm+1P3+16TAEUIIIQopW69kfOcUS5bl9jwbSqkSZPXKVAICAB+gwOajlLOohBBCiMLKxtPEtdZhQHaXdW4NHNVanwZQSi0EGgHFlVJmSy9NEJBs2T4ZKA8kWQ5p+QL3PTeR9OAIIYQQhZV9z6JKBOorpbwtY2laAfuADUB3yzYvkDU5N8ASy30sj6/XNlyNWAocIYQQQuQ7rXUkWYOFdwC7yao5woBhwBCl1GGyxthMsTxlClDKsn4I8I4t7y+HqIQQQojCys5zUWmtRwIj/7L6CFD3Htv+ATybX+/tsAWOs1082h5zetlb8b7TjI6QZxdmvGR0hDwp2muS0RHyzNPsbnSEPLuRftPoCHlicsK5s66npxkdIU+c7xM2iEzVIIQQQghXo124wJExOEIIIYRwOdKDI4QQQhRWLtyDIwWOEEIIUVi58GziUuAIIYQQhZX04AghhBDC5bhwgSODjIUQQgjhcqQHRwghhCiknPEabtaSAkcIIYQorFz4EJUUOEIIIURhJQWOEEIIIVyNXMnYBQQFBbB29QJ27dzAzrj1DB7U1+hIVmkb0py9ezYRv28LQ98eaHSce5o0aQzHE2PZsX3tXesH9O/Drp0biN2xlo8/+q9B6f40+7d4un21jK5fLmPWr/EAfLFyB10mLOXZr5fzxpxfuHQ9a76d5PNXqDdqLj2+iaDHNxGMXhJpZPS/cfR2ERhYjogV4cRsX0N0zGoGDHgRgOkzvua3bRH8ti2Cffu38Nu2CIOT3puzfF+ETRpD0vE4Ynf8ue998skIdu/ayPaYNSyY/z2+vsUMTHi3SZM+JzFxB9u3r7m9rlq1x9m48WdiYlbz009TKVr0AQMT5uyRRx4mJnr17eXsmXheHdzP6FgiG8pRBxiZPQLzNZi/fxnK+ZchNm4PDzzgQ1TkSrp1/zf79x/Kz7fJVyaTif17N9Ouwz9JSjrBtt8i6NV7QL5ldjPlT33buHE9rly5ytQp46lVuzUAzZo14J1hg+ncpQ9paWmULl2K06fP2vxe9zvZ5uGTFxg2fwuzXmmHu5uJgTM28G6nuiSdv0LdSmUxu5kYvyoWgNfb1iT5/BVenbWRnwZ3tCmvPSbbtHe7yI/JNv39S+PvX4a4uL088IAPW7Yu5R89XyY+/vDtbT755F0uXrrMp598afP75fdkm/b+vsivyTZv7Xs/TB1PzVpZ+17r1k3ZsGErGRkZt39Y/Pfdj21+L5Oy/fuiceO6XLlyjSlTxlG7dhsAtmxZyvDho9m8OZIXXuhBxYrlGTVqrM3vlZGZYfNr5MRkMvH7se00atyRxMTkfHvdm2nJBTpP6MUXWtn0t9Z3+jqHnde00PTgpKaeIjZuDwBXrlwlPv4QgQH+BqfKWd06NUlIOMbRo4ncvHmT+fMX0ym0rdGx/mbLlkjOn79w17qXX+rN52O+JS0tq0ckP4obWxw5fZFqQX54eZgxu5moXbEM6/Yl0rByOcxuWbvBU+X9OHnpmqE5reEM7SI19TRxcXuBrP3twIEEAv6yv3Xt9jQL5i8xIl6unOX74l773tq1m8jIyPrjHhm5g8DAckZEu6ctW6L+lrdKlUps3pzVQ7pu3Wa6dOlgRLQ8a9myMUeO/J6vxY0hMm1cHJjdChylVF2lVB3L7SeUUkOUUg7RcitUCKJG9SeJjIo1OkqOAgL9OZ6Ucvt+UvKJv/2RcFRVqjxEo0Z12bxpCWvWLKB27eqG5qlcpjg7fj/FhWs3uJ6WzpZDKZy8eHcxs2hHAo2rBNy+n3z+Cj2/iaDvlDXsOHaqoCNny9naxYMPBlG9+hNER8fdXteoUV1OnTpDQsIx44JZyVm+L+6lT5+erFq1wegYOdq37yChoSEAdO36NEFBjlOQ5aRnj87Mm7fI6Bg205napsWR2WWQsVJqJNAeMCul1gD1gA3AO0qpmlrrj+zxvtbw8fFm/rzJDHlrJJcvXzEqhsszm82ULFGcJk07ERxcgzmzv+XRxxoZluehMr682OQJ+k9fj5e7G4/6l8Bk+rNndfLGPbiZFB2qVwSgdFEvVr71DMW9PdmXfJY35mzip2yZOUwAACAASURBVMEdeaCI7YdvChMfH2/mhE9k6NAP7trfnu3RyWF7b+7kzN8X7wwbTHp6BnPCFxodJUevvPI2X3wxiuHDX2P58jWkpeXv4UZ7cHd3p2PHEN4d8YnRUUQO7HUWVXegBuAJpAJBWutLSqkxQCRwzwJHKfUy8DKAcvPFZPLJ11Bms5kF8yYTHv4zixatyNfXtoeU5FTKB/3ZoxAUWI6UlFQDE1kvOfkEixZnfcYxMXFkZmr8/Epy5sw5wzI9U7syz9SuDMCXa+IoW8wbgMU7Eth8MJlJfVqhLGMjPMxueJjdAHgisBRBJR/g97OXqBpYypjwd3CWdmE2m5kz5zvmzV3EksWrbq93c3Ojc6e2NGocamC63Dnb98Wdevd+lg4dWtO2XU+jo+Tq4MEEOnbsBUDlypVo166lwYly165dC2Jjd3Pq1Bmjo9jOwXthbGGvQ1TpWusMrfU1IEFrfQlAa32dHI7aaa3DtNbBWuvg/C5uACaHjWV//GHGTwjL99e2h+iYOCpXrkTFiuVxd3enR4/OLF222uhYVlmyZBXNmjUEoErlSrh7uBta3ACcu/IHACcuXGX9vuO0f6oiWw+lMH3LPsY/3wwvjz/r/XNX/yDDMstu0rnLJJ69TFAJxzi7w1naxcSJn3HgwGG++mrKXetbtmzMgYNHSEl2vKLsTs72fXFLSEhz3nqzP127vcj1638YHSdXpUtn/WhQSjF8+Kt8//0sgxPlrmfPLi5xeApw6TE49urBSVNKeVsKnNq3ViqlfDHoI2nUsA69e3Vn1+59xERn/TF4771PWbFyvRFxrJKRkcFrr48gYvkc3Ewmpk2fx759B42O9TczZnxN0yb18fMrScLhKD4cPZZp0+cRFjaGHdvXkpaWRr9+bxgdkzfnbuLitRuYTSaGd6xDMS8PPl0WTVp6Jv+ZltUOnipfihGd6rHj2Cm+XbcLs5sJk4IRneri6+1p8P8gizO0iwYNgnnu+W7s2b3/9qng/zfyf6xatZHu3UNZsMCxD085y/fFzBlf07RpA/z8SnIkIZoPPhzL0KGD8PTwYEVEOACRUTsYNGi4wUmzzJjxFU2aNMDPrwSHD0cyevQX+Pj48J///AuARYtWMn36fINT5szb24vWrZoyYMAwo6PkC0cfR2MLu5wmrpTy1FrfuMd6P6Cc1np3bq+R36eJi7/Lr9PEC9L9niZuFHucJm5v+XGaeEHL79PE7S2/ThMvSPlxmnhBsvdp4vZS0KeJn+/W3Ka/tSV+2uiwjdkuPTj3Km4s688ALnDQUgghhBCOTKZqEEIIIQopVz5EJQWOEEIIUVg5+EBhW0iBI4QQQhRSWgocIYQQQrgcFy5wnGtYvBBCCCGEFaQHRwghhCik5BCVEEIIIVyPFDhCCCGEcDWu3IMjY3CEEEII4XKkB0cIIYQopFy5B0cKHCGEEKKQkgJHuKTMTOdr2c42eeXlmS8bHSHPivYOMzpCnjnsbH/ZyLTDJMf251zfFx5OOGmsIbSz7T3WkwJHCCGEKKRcuQdHBhkLIYQQwuVID44QQghRSOlMOUQlhBBCCBfjyoeopMARQgghCiktg4yFEEII4WpcuQdHBhkLIYQQwuVID44QQghRSMkgYyGEEEK4HKe85qSVpMARQgghCilX7sGRMThCCCGEcDmFpsAJCgpg7eoF7Nq5gZ1x6xk8qK/RkXI1OWwsKUk7iYtdZ3QUq/n6FmPu3DB27/6FXbs2Ur9ebaMj5ciR28Xs3+Lp9vVyun61nFm/xgPwxapYuny5jGe/ieCN8E1cup4GwIVrN+g3dS0NRs/nk2XRRsa+p7Yhzdm7ZxPx+7Yw9O2BRsexymuvvkRc3HpiY9cxc+Y3eHp6Gh0pVyaTieioVSz+ebrRUe4pbNIYko7HEbtj7e11JUoUJyJiDnv3biYiYg7Fi/samPDvAgPLEbEinJjta4iOWc2AAS8C8NRTT7Bh48/8ti2CzVuWUDu4usFJ74/OVDYtjqzQFDjp6em8PXQUT1VvQaPGofTv34fHH69idKwczZgxn6c7Pm90jDwZ98UHrF61gWrVmlG7dhv2xx8yOlKOHLVdHD55gYXbE5j1clvmD2jP5oPJJJ69TP2H/flxYAcWDOxAhVJFmbp5LwCeZjcGtnqKIW1rGpz870wmE19O+IiOob2oVr0FPXt2cYjPOCcBAf4MHPhv6tfvQM2arXBzc6Nnj85Gx8rVq4P7Ee/A+9yMmQvoGNrrrnVD3x7IhvVbqVq1CRvWb3W4AjgjI53/Dh9NcO02tGj+DC+/0pvHHqvM6NHv8MnHE2hQvwOjP/yC0aOHGx31vmht2+LICk2Bk5p6iti4PQBcuXKV+PhDBAb4G5wqZ5u3RHLu/AWjY1itWLGiNG5cj6k/hANw8+ZNLl68ZHCqnDlquzhy+hLVgkrh5WHG7GaidsUyrNt3nIaVy2F2y9ptnwry4+SlawB4eZipWaEMHmY3I2PfU906NUlIOMbRo4ncvHmT+fMX0ym0rdGxcmU2m/HyKoKbmxveXl6knEg1OlKOAgPL0aF9K6ZODTc6Sra2bInk/F++00JDQ5g5awEAM2ctoFMnx2obqamniYvL+iFx5cpVDhxIICDAH62haNEHAChWrBipJ04aGfO+SQ9OPlBKzSio98pNhQpB1Kj+JJFRsUZHcSmVKj3ImTNnmfL9OKKjVjHpu8/x9vYyOpbVHKldVC7ry47fT3Ph2g2up6Wz5WDK7WLmlkU7EmhcJcCghNYLCPTneFLK7ftJyScIcIAiMicpKamMG/cdRxKiOJ4Yy6VLl1i7dpPRsXL0xdhRvDN8NJmZznXltjJl/EhNPQVk/eAoU8bP4ETZe/DBIKpXf4Lo6DiGDh3FRx8P58DBX/n4k//y/vv/MzrefdFa2bQ4MrsUOEqpJX9ZlgJdb93P4XkvK6VilFIxmZlX7RENHx9v5s+bzJC3RnL58hW7vEdhZXZzo2bNakyaNIM6ddty9eo1hg4dZHQsqzhau3iotC8vNn6C/tPXM3DmBh4tVwKT+vPLZPIve3BzM9HhqYrGhXRhxYv7EhraliqP1OfBCrXw9vHmuee6Gh0rW093aM2pU2fYEbvb6Cg20w563MPHx5s54RMZOvQDLl++Qr+XejFs6Ic8+khDhg39kIkTPzM6oviLPBU4SqkSSqmnrNg0CLgEfAGMtSyX77h9T1rrMK11sNY62GTyyUs0q5jNZhbMm0x4+M8sWrQi31+/sEtKPkFS0gmiorN6QH5auJyaNaoZnCp3jtounqn9MOH92zO1bxuKFvGggl9RABbHHmHzgWQ+7tYQpRz7FxRASnIq5YP+7GkKCixHSopjH+5p1aoJx44lcubMOdLT01m0aAUN6gcbHStbDRsGE9oxhMMHtzF71re0aNGI6dO+NDqWVU6dOoO/fxkA/P3LcPr0WYMT/Z3ZbGbOnO+YN3cRSxavAuD557uxePFKABYuXO7Eg4xtW6yhlCqulPpRKRWvlNqvlGqglCqplFqjlDpk+beEZVullPpSKXVYKbVLKVXrfv9vuRY4SqmNSqliSqmSwA5gslLqi1yeFgxsB94FLmqtNwLXtda/aK1/ud+wtpocNpb98YcZPyHMqAgu7eTJ0yQlpfDIIw8D0LJlY/bvP2hwqtw5ars4d+UPAE5cuMr6/Um0r1aRrYdSmL5lH+Ofb4aXh3Ncxio6Jo7KlStRsWJ53N3d6dGjM0uXrTY6Vo6OJyZTt14tvLyKANCyRWOHHrz77ohPqfhQMJUfqc/zvQawYcNWXujzqtGxrLJ02Rp693oWgN69nmXpUsdrGxMnfsaBA4f56qspt9edOHGKJk3qA9C8eUMSEo4ZlM42mVrZtFhpArBSa/0YUB3YD7wDrNNaVwHWWe4DtAeqWJaXgYn3+3+z5hvSV2t9SSnVD5ihtR6plNqV0xO01pnAOKXUAsu/J618L7tp1LAOvXt1Z9fufcREZ+1A7733KStWrjcyVo5mzfyGZk0b4OdXkmNHYhj1wRh+mDbX6Fg5ev2N95gx/Ss8PNw5cjSRfv2GGB0pR47cLt6cu5mL129gNpkY/nQwxbw8+HR5DGnpmfxnela+p4L8GNGpLgDtv1jM1Rs3uZmRyYb4JCb+qyUPlzH+lNuMjAxee30EEcvn4GYyMW36PPbtc+zCNyo6loULlxMVtYr09HR2xu1l8vezjY7l9GbO+Jqmlu+0IwnRfPDhWD7//GvmzPmOPi/+g8TEJJ57rr/RMe/SoEEwzz3fjT279/PbtggA/m/k/xg08B0+HzMSs5uZP27cYNAgZz2Lyr69wEopX6Ap0Cfr/XQakKaU6gw0t2w2HdgIDAM6k1VraGCbpfennNb6RJ7fO7fjnUqp3UCIJcC7WutopdQurbU1h6puvcbTQCOt9X+tfY7ZI9AxD8S6EMc/uPF3ztYoLs982egIeVa0t2P1ZFnD2dqys7Vj4K4xYM7A3c05ejj/6uq1YwX6Qcc/0sGm5vj4oRWvkNXTckuY1vr2l4hSqgYQBuwjq/dmO/AakKy1Lm7ZRgHntdbFlVLLgE+11lssj60DhmmtY/KazZoW8AGwCthiKW4eAvLUV6u1Xg4sz2s4IYQQQjguSzGT068iM1ALGKy1jlRKTeDPw1G3XkMrpfK97s+1wNFaLwAW3HH/CNAtv4MIIYQQomAVwElrSUCS1jrScv9Hsgqck7cOPSmlygGnLI8nA+XveH6QZV2eZVvgKKW+IoeeVK21c4xgE0IIIcQ92ftifVrrVKXUcaXUo1rrA0Arsg5X7QNeAD61/LvY8pQlwCCl1FygHlknKuV5/A3k3IOT5+NdQgghhHAeeTgTyhaDgdlKKQ/gCPAiWWdxz1dK9QV+B3pYto0AOgCHgWuWbe9LtgWO1toxZ2sTQgghhNPQWseRdfmYv2p1j201kC8TkuU6BkcpVZqsU7eeAIrcEaJlfgQQQgghhDEcfboFW1hzJePZZF2UpxIwCjgGRNsxkxBCCCEKQGGfTbyU1noKcNNyJeJ/A9J7I4QQQji5ArqSsSGsuQ7OTcu/JywX7EsBStovkhBCCCEKgisforKmwBltudTym8BXQDHgDbumEkIIIYSwgTUX+ltmuXkRaGHfOEIIIYQoKI4+jsYW1pxF9QP3uOCfZSyO3Thbp5kzthFnzFzE7GF0hDwp5oTzOl14ra7REfKs5JdOdt6DE/5Vcba5nW6k38x9I+Hw42hsYU2LXXbH7SLAM2SNwxFCCCGEEyvUY3C01j/deV8pFQ5ssVsiIYQQQhQIV+7BseY08b+qApTJ7yBCCCGEEPnFmjE4l7l7uEYqWVc2FkIIIYQTc77RYNaz5hBV0YIIIoQQQoiCVagPUSml1lmzTgghhBDORWtl0+LIsu3BUUoVAbwBP6VUCf48c7sYEFgA2YQQQggh7ktOh6heAV4HAoDt/FngXAK+tnMuIYQQQthZptEB7CjbAkdrPQGYoJQarLX+qgAzCSGEEKIAaKe7rK71rDlNPFMpVfzWHaVUCaXUADtmEkIIIUQByNS2LY7MmgLnJa31hVt3tNbngZfsF0kIIYQQBSETZdPiyKwpcNyUUrf/F0opN8C5JgQSQgghRKFiTYGzEpinlGqllGoFhAMr7BvLPl579SXi4tYTG7uOmTO/wdPT0+hIOQoKCmDt6gXs2rmBnXHrGTyor9GRcjU5bCwpSTuJi3XcKwl4enqwcdMiftsWQXTMKt4d8fpdj38+ZiSpp/YYlM46jtiWVekAvN744vbi8+Fs3Bt3xBRQEa9Bn2atf/VzTOWrZD3By4ciLwzDa8g4vAb/D1PZBw3NHzZpDEnH44jdsfb2uk8+GcHuXRvZHrOGBfO/x9e3mIEJc/bIIw8TE7369nL2TDyvDu5ndKy7BAaWI2JFODHb1xAds5oBA14E4KmnnmDDxp/5bVsEm7csoXZwdYOT3punpye/bV3G9pg17Ixbz8j33zQ6ks00yqbFkVlT4AwD1gP/sSy7AS97hrKHgAB/Bg78N/Xrd6BmzVa4ubnRs0dno2PlKD09nbeHjuKp6i1o1DiU/v378PjjVYyOlaMZM+bzdMfnjY6Roxs30ni6/XM0qN+BBvWfpnWbZtSpUwOAmrWqUby4r8EJc+aobVmfTuH6uCFZy/i30DdvkL4nEo+nXyBtzXyujxtC2upwPJ/+FwAeLbuTkXKU61+8wR9zJ+DR2dgCfsbMBXQM7XXXunXrNlGjZitqB7fh0KEjDBs6yKB0uTt4MIHgOiEE1wmhbr12XLt2nUWLHeu3aEZGOv8dPprg2m1o0fwZXn6lN489VpnRo9/hk48n0KB+B0Z/+AWjRw83Ouo93bhxg9YhPagd3IbawSG0DWlOvbq1jI5lk0wbF0eWa4Gjtc4EIoFjQF2gJbDfvrHsw2w24+VVBDc3N7y9vEg5kWp0pBylpp4iNi6rJ+HKlavExx8iMMDf4FQ527wlknPnL+S+ocGuXr0GgLu7GXd3MxowmUx89NFwRoz4xNhwVnD0tuxWpRr6bCr6wmnQGlUk6zeRKuJN5qVzAJjKBpFxeDcA+nQyppJlUA8YV1xu2RLJ+b+03bVrN5GRkQFAZOQOAgPLGREtz1q2bMyRI7+TmJhsdJS7pKaeJi5uL5D1nXbgQAIBAf5oDUWLPgBAsWLFSD1x0siYObrzu8Ps7o7WDj7SNheu3IOT04X+HgH+aVnOAPMAtNYt8vomSqnGZBVHe7TWq+8vqm1SUlIZN+47jiREcf36H6xd+wtr124yIsp9qVAhiBrVnyQyKtboKC7BZDKx5delPPRQBcImzSQmOo4BA/qwfPlaTqaeNjpejpyhLZurNyE9djMAN5ZMxavf+3h07ANKcf3rrF/nmSnHMD9Zn7Sj+zGVr4IqXhrlWwp95aKBybPXp09PFixYanQMq/Ts0Zl58xYZHSNHDz4YRPXqTxAdHcfQoaNYvGQGH3/yX0wmEy1bdDM6XrZMJhNRkSup/HBFJn43jaho+U52VDn14MST1VvTUWvd2HItnAxrXlQpFXXH7ZfIujBgUWCkUuqdHJ73slIqRikVk5l51ar/gLWKF/clNLQtVR6pz4MVauHt481zz3XN1/ewFx8fb+bPm8yQt0Zy+fIVo+O4hMzMTBrWf5pHqzQgOLg6jRrVpUvXDnw3cbrR0XLl8G3ZzYy5ah3Sd/0KgHuDttxYOpVrH71E2pKpePYYCEDahoUoLx+83vgC90YdyEw5AtoxO73fGTaY9PQM5oQvNDpKrtzd3enYMYQff1pmdJRs+fh4Myd8IkOHfsDly1fo91Ivhg39kEcfaciwoR8yceJnRkfMVmZmJsF1QqhQKZg6wTWpWvVRoyPZpLAeouoKnAA2KKUmWwYYW9sf5X7H7ZeBNlrrUUAIkO0ADa11mNY6WGsdbDL5WPlW1mnVqgnHjiVy5sw50tPTWbRoBQ3qB+fre9iD2WxmwbzJhIf/zKJFjnU83RVcvHiZTZt+o2mz+jz8cEV27dnI3v2b8fb2YufuDUbHuydHb8tuj9UiI/nI7Z4Y99otyNi9DYD0Xb/idmuQ8Y3r3Jj/NdfHDeHG3AkoH18yzzreoYnevZ+lQ4fW/OsFxx1/c6d27VoQG7ubU6fOGB3lnsxmM3PmfMe8uYtYsngVAM8/343Fi1cCsHDhcocdZHynixcvsfGXrbQNaW50FJsUygJHa71Ia/0P4DFgA1nTNpRRSk1USoXk9rqWCwKWApTW+rTlNa8C6fmUPU+OJyZTt14tvLyKANCyRWPi4w8ZESVPJoeNZX/8YcZPCDM6isvw8yuJr29RAIoU8aRlyybExu7h4Up1qfp4E6o+3oRr165TvVqej8YWCEdvy+YajW8fngLQl87j9lBVANwqVyPzzImsB4p4g1vWUXJz3TZkHN0LN64XeN6chIQ05603+9O124tcv/6H0XGs0rNnF4c+PDVx4mccOHCYr76acnvdiROnaNKkPgDNmzckIeGYQelylvXdkXUmXZEiRWjdqikHDiQYnMo2hXIMzi2WomQOMMcy6eazZJ1ZldNYGl/+nL9KK6XKaa1PKKUewPpeoHwVFR3LwoXLiYpaRXp6Ojvj9jL5+9lGRLFao4Z16N2rO7t27yMmOuvjfu+9T1mxcr3BybI3a+Y3NGvaAD+/khw7EsOoD8bww7S5Rse6S1n/MoRNHoObyQ2TSbFw4XJWrnDcz/SvHLotu3tirlKDGz99d3vVHz9+i2fnvmAyQfpNbvz4LQCmsuUp0vNV0JrMk8f5Y4GxU9zNnPE1TS1t90hCNB98OJahQwfh6eHBiohwACKjdjBokGOe4QPg7e1F61ZNGTBgmNFR7qlBg2Cee74be3bv57dtEQD838j/MWjgO3w+ZiRmNzN/3LjhsJ9xuXJlmTplPG5uJkwmEz/+uJTlEWtzf6IDy3TsGsUmqiBHgCulvIGyWuujuW3r7hHoVEPTnSqsEytidq5rTN5ITzM6Qp6df62u0RHyrOSX0UZHyBNnPPPGw+ye+0YO5Eb6TaMj3Jf0tOQCLTmW+v/TpsYYmhrusCVSrj04+UlrfQ3ItbgRQgghhP05+nQLtijQAkcIIYQQjsP5+hKtJwWOEEIIUUg5+plQtpACRwghhCikMpXrHqKyZi4qIYQQQginIj04QgghRCElY3CEEEII4XJkDI4QQgghXI4rX+hPxuAIIYQQwuVID44QQghRSMmF/oQQQgjhcmSQsQGUk52b74xzy5ic7DMG+MPJ5nZyvk8YSn0VY3SEPLs45QWjI+RJ0X9PMzpCnjnr3E4iZ648BsdhCxwhhBBC2Jcrn0Ulg4yFEEII4XKkB0cIIYQopJxvcIX1pMARQgghCikZgyOEEEIIl+PKY3CkwBFCCCEKKVcucGSQsRBCCCFcjvTgCCGEEIWUljE4QgghhHA1cohKCCGEEC4n08bFGkopN6VUrFJqmeV+JaVUpFLqsFJqnlLKw7Le03L/sOXxirb836TAEUIIIYQ9vQbsv+P+Z8A4rXVl4DzQ17K+L3Desn6cZbv75tIFTtikMSQdjyN2x9rb60qUKE5ExBz27t1MRMQcihf3NTBhzjw9Pflt6zK2x6xhZ9x6Rr7/ptGRcjVoUF9id6wlLnYdgwf3zf0JBpscNpaUpJ3Exa4zOorVHnnkYWKiV99ezp6J59XB/YyOdZdJk8ZwPDGWHdvX3rV+QP8+7Nq5gdgda/n4o/8alO5usyMP0e271XSduJpZkYcAuHg9jVdmbSL0m5W8MmsTl65nzYF2+Y+bvDp3Kz0mraHrxNUsijtmYPK7BQUFsHb1Anbt3MDOuPUMHuTY+5+z5b2lbUhz9u7ZRPy+LQx9e6DRcWymbVxyo5QKAp4GvrfcV0BL4EfLJtOBLpbbnS33sTzeStkwMaVLFzgzZi6gY2ivu9YNfXsgG9ZvpWrVJmxYv9WhG+iNGzdoHdKD2sFtqB0cQtuQ5tSrW8voWNmq+sSj9P33P2nYqCO1g0Po0KE1Dz9c0ehYOZoxYz5Pd3ze6Bh5cvBgAsF1QgiuE0Ldeu24du06ixavMDrWXWbOXEBop953rWvWrAGhoSEE12lLzVqtGTd+kkHp/nT41EUWxh5lVt+WzH+lNZsPnSDx3BWmbo2nXqUyLB3YjnqVyjB1azwA82IO85BfUea/0obv/9WML9bs5GaGY4xiSE9P5+2ho3iqegsaNQ6lf/8+PP54FaNjZcvZ8gKYTCa+nPARHUN7Ua16C3r27OLwmXOTqWxbrDAeGMqfR7RKARe01umW+0lAoOV2IHAcwPL4Rcv298WlC5wtWyI5f/7CXetCQ0OYOWsBADNnLaBTp7ZGRLPa1avXAHB3N2N2d3foWcsfe6wyUVFxXL/+BxkZGWzetI0uXdobHStHm7dEcu4vbcSZtGzZmCNHficxMdnoKHe517738ku9+XzMt6SlZfWGnD591ohodzly5jLVAkvi5W7GbDJR+0E/1sUns/FACqFPVQAg9KkKbDiQAoBCcTUtHa0119PS8fXywM3kGKehpKaeIjZuDwBXrlwlPv4QgQH+BqfKnrPlBahbpyYJCcc4ejSRmzdvMn/+YjqFOvbfkNzYOgZHKfWyUirmjuXlW6+tlOoInNJaby/A/9JtdilwlFL1lFLFLLe9lFKjlFJLlVKfKaUMPSZUpowfqamngKwdrEwZPyPj5MpkMhETvZoTybtYt24TUdGxRkfK1t59B2jcuC4lSxbHy6sI7dq1JCgowOhYLq1nj87Mm7fI6BhWqVLlIRo1qsvmTUtYs2YBtWtXNzoSlUsXY0fiGS5cu8H1m+lsOZzKyUvXOHv1BqWLegHg90ARzl69AcA/6jzM0TOXaTN+Od0nrebttjUw3X8Put1UqBBEjepPEhnluN8Xd3KWvAGB/hxPSrl9Pyn5BAEOXpTlxtYCR2sdprUOvmMJu+PlGwGdlFLHgLlkHZqaABRXSt06izsIuPULLRkoD2B53Be4719C9urBmQpcs9yeQFbIzyzrfrDTe94XR+4RAcjMzCS4TggVKgVTJ7gmVas+anSkbMXHH+bzMd8SsXwOy5bOYueuvWRkZBgdy2W5u7vTsWMIP/60zOgoVjGbzZQsUZwmTTsxfPhHzJn9rdGReKh0MV5s+Cj9Z29m4JwtPOpf/G8Fi1KKW6t+TTjJo/6+rHn9aea93IZPV8Zy5cZNA5Jnz8fHm/nzJjPkrZFcvnzF6Di5cra8wnpa6+Fa6yCtdUXgH8B6rfXzwAagu2WzF4DFlttLLPexPL5e2/BH2l4FjumO42vBWuvXtdZbtNajgIeye9KdXV2ZGVftEuzUqTP4+5cBwN+/jEN0k1vj4sVLbPxlK21DmhsdJUfTps2lfoMOtGrdnQvnL3Lo0BGjI7msdu1aEBu7m1OnzhgdxSrJySdujxWKiYkjM1Pj51fS4FTwTM1KIvcTIAAAIABJREFUhL/UmqkvNKdoEXcqlCpKKR9PTl++DsDpy9cp6e0JwOKdx2j1WCBKKR4s+QCBxX04euaykfHvYjabWTBvMuHhP7NokWONy7oXZ8ubkpxK+Tt6pYMCy5GSkmpgItvZe5BxNoYBQ5RSh8kaYzPFsn4KUMqyfgjwzv2/hf0KnD1KqRctt3cqpYIBlFKPANn+3Lmzq8vk5mOXYEuXraF3r2cB6N3rWZYuXW2X98kPfn4l8fUtBkCRIkVo3aopBw4kGJwqZ6VLZ40HK18+gC5d2jN3rnMcPnFGPXt2cZrDUwBLlqyiWbOGAFSpXAl3D3fOnDlncCo4d/UPAE5cvMb6+BTaP1meZo8GsHTX7wAs3fU7zR/N+qNWztebyKNZh7jPXvmDY2cvE1TCPt9V92Ny2Fj2xx9m/ISw3Dd2AM6WNzomjsqVK1GxYnnc3d3p0aMzS5c57t8QaxTAIGMAtNYbtdYdLbePaK3raq0ra62f1VrfsKz/w3K/suVxm34h2+tKxv2ACUqpEcAZ4Del1HGyRkcX2PmsM2d8TdOmDfDzK8mRhGg++HAsn3/+NXPmfEefF/9BYmISzz3Xv6Di5Fm5cmWZOmU8bm4mTCYTP/64lOURa3N/ooHmzQ2jVKkS3LyZzquvvcvFi5eMjpSjWTO/oZmljRw7EsOoD8bww7S5RsfKlbe3F61bNWXAgGFGR7mnGTO+pmmT+vj5lSThcBQfjh7LtOnzCAsbw47ta0lLS6NfvzeMjgnAmwt+4+L1NMwmE8Pb16BYEQ/+3fBRhv60jZ/jjhHg683/utUH4KUmj/P+kmi6f7caDbzesholLL07RmvUsA69e3Vn1+59xERn/dF9771PWbFyvcHJ7s3Z8gJkZGTw2usjiFg+BzeTiWnT57Fv30GjY9nEMc4BtA9lzzEoloHGlcgqpJK01ietfa6HZ5BjD475i0wHH8tzL444ODI3zvY5O98nnDWw3dlc+P5fRkfIk6L/nmZ0BOGg0tP+v737jo+qTPs//rlmJoSEFpASQhNFQBQl1FAEpShVWFRQhF0LoiwoNtBdd/URfVYFFNfVpYgiPaAiiFQpPoA/IEEIJSQIBIQkhCIdgWSS+/fHDBgklWRyplxvXvNicjJzzjfnNXPmmvu+z7lTSvSw8U6dgUU6qP7tl5lee5jz6FxUxpgzwDZPbkMppZRS6o90sk2llFIqQGUVZaiwl9MCRymllApQ/jwGRwscpZRSKkD5b/uNn0/VoJRSSqnApC04SimlVIDSLiqllFJK+Z3CXKzP12iBo5RSSgUoPYtKKaWUUn7Hf8sbHWSslFJKKT+kLThKKaVUgNJBxhbQOYc8zya+14BnTKbVEfxeZpbvHfJ8bW6nswu9c5LUvJTr/Z7VEQotyO61H3FeQ8fgKKWUUj5Ei5uC8d/yRgscpZRSKmD5XnttwfleH4VSSimlVD60BUcppZQKUDoGRymllFJ+x3/LGy1wlFJKqYClY3CUUkoppXyItuAopZRSAcr4cSeVFjhKKaVUgPLnLiotcJRSSqkApWdRKaWUUsrv+G95o4OMlVJKKeWHAqbA+XTy+6QmbyNu6yqroxRKhQrliY6ezI4d/8f27T8Q1aqZ1ZGuUrNmdZYvj2br1lVs2bKSYcOeAKBv3x5s2bKS3347QNOmd1icMm/evo9zMuK5p4iLW83WrauYMeMTgoODrY6UJ198/913793E71xL4q71jBo5zOo4V8z6v2088O4c+r47m5k/bANgwtIYurzxBf3GRNNvTDTrdh0AIMOZyeuzV/Hge3PoNyaa2D0pFia/Ws2aEaxc8SXbt61hW9xqnh3+pNWRclSzZnWWLYtmy5aV/PTT9wwb9vhVvx8x4ikuXPiFG26oaFHCosnCFOnmzQKmwJk+fR49ej5qdYxCG//BaFYsX0Pjxh1o1qwLCYl7rI50Faczk1deeZvIyE60b9+bZ575Mw0b3kJ8/G769x/C+vWbrI6YL2/fx38UERHOsGFPEBXVncjITtjtdvr36211rDz52vvPZrPx0b//l569BtL4znvo378Pt956i9Wx2Hv4V+Zv2MXMFx9k3siHWbfrAAePnQJgYIc7mTfqYeaNepi7Gt0IwNcbdgHw1SuPMHHo/Xyw8EeysrzjQ8npdDJy1Jvccec9tG3Xi6FDH/OKffxHTmcmr776Nk2bdqZDhz48/bTrGAeu4qdTp7s4eDDZ4pTXL6uIN28WMAXOuvWbOHHylNUxCqV8+XK0a9eKz6fOASAjI4PTp89YnOpqaWlHiYvbCcC5c+dJTNxLjRrh7N69lz17kixOlz9f2Mc5cTgchISUxm63ExoSQurhNKsj5cnX3n8tW0Syb98B9u8/SEZGBvPmLeT+XvdZHYukIydpXKcaIaWCcNhtNLs5glXbc3+fJR05QctbagJQqVwo5UJKEX/oaEnFzVNa2lG2XnXs2EONiHCLU10rp2NcREQ1AMaMeZ3XXnsHY7yjaLwepoj/vJlHChwReU5Eanli3YGkbt3aHD/+K59NGU9szHImTRxLaGiI1bFyVadOTZo0uY2YmK1WRykwX9vHAKmpaYwfP5GkfTEcOriVM2fOsHLlWqtj+ZWIGuEcSk698nNyymEivODDt154JbYkpXLq/EUupGewftcvHDl1DoDodTt46L1o3pi9ijO/XQSgfkRlfti5H2dmFim/nmHXoWNXHu9N6tSpSZM7b2eTlx87atd2HeNiY+Po2bMLqalp7NiRYHWsItEWnMJ7C9gkIutE5K8iUqUgTxKRISKyWUQ2Z2Wd91A03+Gw24mMbMykSdNp0fI+zp//jVGjhlsdK0dlyoQyZ84kXn75Tc6e9b4DaG58aR9fFhZWgV697uOW+lHUrtOU0DKhDBjQ1+pYqgTcFF6Jxzs1ZeiEbxk2cRENalTGJkK/drfz3T8HMndkfypXKMP7C34EoE+rW6kWVpYB789j7DfruLNuODYRi/+Kq5UpE8q8uZ/y4stvePWxw3WMm8jIkaNxOp2MGjWM0aM/sDqWyoOnCpwkoCauQqcZsEtElonIX0SkXG5PMsZMNsY0N8Y0t9nKeCia70hOOUxy8mFiYl3far6ev5jIJo0tTnUth8NBdPQkoqO/YeHCZVbHKRRf2cfZdep0FwcOHOT48RM4nU4WLFhK66jmVsfyK6kpadSqGXHl55o1qpOa6h3dgH+KasScl/vx+XN9KRcaTJ2qYdxQLhS7zYbNJvSNasTOg65uKIfdxsg/tWPeqIf5cHAPzl5Ip07VMIv/gt85HA6+nPspc+Z8w4IFS62OkyuHw8GcOROZO3cBCxcu46ab6lCnTi1iYpaSmLieGjWqs2HDYqpVK9B3ea+iXVSFZ4wxWcaYFcaYJ4EI4L9AV1zFjyqAI0eOkZycSv36NwPQsWM7EhJ+tjjVtSZNGkti4l4++miK1VEKzVf2cXaHDqbQslVTQkJKA9DxnnYkevnAaF8TuzmOevXqcuONtQgKCqJfv94s+m6F1bEAOHH2NwAOnzzL6u1JdGtan2Onf2/xXr0jiXrVKwFwIT2DC5cyANiw+xAOm3BzeKWSD52LTye/T0LiXj7892Sro+Rp4sQx7N79+zEuPn43deo0o2HDdjRs2I6UlMO0bt2DI0eOWZy08Py5i8pTF/q7qg3UGJMBfAt8KyKhHtpmnmbO+IQO7VtTuXIlDiRt5s3R45j6RbQVUQrl+Rf+yfRp/6FUqSCS9h9k8OAXrY50lTZtWvDoow+wY0cCmza5voG9/voYgoNL8cEHo6lSpRLffDOV7dt30avXIIvT5szb9/EfxcRuZf78xcTELMfpdLItLp5Pp8yyOlaefO39l5mZyYjn/8GSxbOx22x8MW0uu3Z5R+H70tRlnD5/EYfdxt8ebE/50GBem7mW3SnHEYSISuX4R7+7AThx9gJ/nbgImwhVw8rw9sDO1obPpm2bFgwa+CDbd+xic6yrePznP99l6bLVFie7Wps2za8c4zZuXALAG2+MZfnyNRYnKx5ZPjxAOj/iidHfIlLfGFOko4GjVA2f2uve1atdMHab3eoIhZaZlWl1BL/nU288H3V24StWRyi0cr3fszpCoQTZffNC/Rcu/FKiHyeD6vQt0lt+xi/zvfbjzyOvgKIWN0oppZTyPH/+QuObJa5SSimliszbr0ZcFFrgKKWUUgHK28+EKgotcJRSSqkA5e1nQhVFwEzVoJRSSqnAoS04SimlVIDSMThKKaWU8js6BkcppZRSfsefx+BogaOUUkoFKE9c7Ndb6CBjpZRSSvkdbcFRSimlApQOMraA105ukQsRX0vsm/M6OXxsfhlnptPqCIVW2lHK6giFlp6ZYXWEQqnQZ4zVEQrtzNheVkcolAojF1kdwSfoGByllFJK+R1/PotKx+AopZRSyu9oC45SSikVoPx5DI624CillFIByhhTpFt+RKSWiKwRkV0iEi8iI9zLK4nI9yKyx/1/RfdyEZGPRGSviGwXkabX+7dpgaOUUkoFqKwi3grACbxkjGkERAHDRKQR8CqwyhhzC7DK/TNAN+AW920IMOF6/zYtcJRSSqkAZYr4L9/1G3PYGLPFff8skADUAHoD09wPmwb0cd/vDUw3LhuBMBGpfj1/mxY4SimllLouIjJERDZnuw3J47E3ApHAJqCaMeaw+1dpQDX3/RrAoWxPS3YvKzQdZKyUUkoFqKIOMjbGTAYm5/c4ESkLfA08b4w5k/3accYYIyLFPtpZCxyllFIqQJXEXFQiEoSruJlljJnvXnxERKobYw67u6COupenALWyPb2me1mhaReVUkopFaCyMEW65UdcTTWfAQnGmA+y/epb4C/u+38BFmZb/mf32VRRwOlsXVmFoi04SimllPKUtsAgYIeIxLmX/R14F5gnIk8CvwD93L9bAnQH9gK/AY9f74YDqsDZ8/NGzp07R2ZmFk6nk6jW3a2OlK/hw5/kySceQUT47PPZ/Oc/n1kdKU8VKpRn0qRx3HZbA4wxDHnqJTZu+snqWFepWbM6U6aMp2rVyhhj+Pzz2XzyyVQAhg59jKefHkRmZhbLlq3mtdfesThtzkY89xSPP/EIxhh27kxk8OAXuXTpktWxrggOLsXy7+cRXKoUDoedBQuW8r9vf8gnE96laeQdiAh79+7n6SEvc/78b1bHBWDypHF0796ZY8eOE9m0MwAVK4Yxa9Z/qVOnFr/8cogBA4Zy6tRpi5P+LqfM77zzD3r26Ex6egZJSb8w+KkXOX36jKU5HZGdcNzWFowh69dU0r+fBplOglr3xn5LUzBZOLevxbltDQBBHfphv/F2cKZzacU0zLFD+Wyh5Pji50hePD1VgzFmPblPL9kph8cbYFhxbDvguqg6d3mI5i3u9YkX5W2NGvDkE4/Qpm1PmjW/l+7dO3PzzTdaHStP4z8YzYrla2jcuAPNmnUhIXGP1ZGu4XRm8uqrb9O0aWc6dOjD00//mYYNb6F9+9b07NmFli270axZFz78MN9xc5aIiAhn2LAniIrqTmRkJ+x2O/379bY61lUuXUqnR7cBtI7qTuuoHnTu0oEWLZrw6qi3aR3VnahW3Th0KIWnn/mz1VGvmD7jS3r2GnjVslEjh7Fm9Y/cdttdrFn9I6NGFstxt9jklHnVqrU0iexEs+Zd2LMniVdGDbconYuUCcNx5z1cnPMOF2e9BWLDXr8F9katkXIVuTj9f7g4402cP28GwHbj7djCqnJx2uukr5pFqY4DLM2fE1/6HMlPljFFunmzgCtwfEnDhvWIiYnjwoWLZGZmsm7tRvr06WZ1rFyVL1+Odu1a8fnUOQBkZGRY/s0xJ2lpR4mL2wnAuXPnSUzcS0RENYYMGci4cf8lPT0dgGPHfrUyZp4cDgchIaWx2+2EhoSQejjN6kjXuNwyExTkICjIgQHOnj135fchIaVLZIBjQa1fv4mTJ09dtaxXr3uZMfNLAGbM/JL777/Pimi5yinzypVryczMBGDTpi3UqHFdlxApXjYbOIJAbEhQEOb8KRyNO5CxaTFcbkG4cBYA+0134EzYCEBW2n4kOARCy1sU3P+ZIt68WUAVOMYYli6Zw6aNSxn85KNWx8lX/K7dtGvXkkqVwggJKU3Xrh2pWTPC6li5qlu3NseP/8pnU8YTG7OcSRPHEhoaYnWsPNWuXZMmTW4jNjaOevXq0rZtS9auXcCKFXNp1uwOq+PlKDU1jfHjJ5K0L4ZDB7dy5swZVq5ca3Wsa9hsNv7fxsXs/2Uzq1etZ3Osq/t9wqQxJO2PpX79m5k4YVo+a7FW1aqVSUtzndyRlnaUqlUrW5yocB57rD/Ll6+xNIM5fwrnlpWEPPEvQga/h7l0kayDCdgqVMZevznBD/+N4N7DkbCqANjKhmHOnfz9+edOYSsbZlX8a/ja50h+PD3I2EoeKXBEpJSI/FlEOrt/HiAiH4vIMPfpYpa4+54/0bJVV3r2GsjQoY/Rrl0rq6IUSGLiXsaO+y9LFs/mu0Uz2bY9/so3M2/ksNuJjGzMpEnTadHyPs6f/41RFjeP56VMmVDmzJnIyJGjOXv2HA6Hg0qVwmjfvg9///u/mDnzv1ZHzFFYWAV69bqPW+pHUbtOU0LLhDJgQF+rY10jKyuLNlE9aHBLa5o3v5NGjeoDMPTpUdS7uRW7d+/lgQd7WpyycLypxSk/r77yLE5nJrPnzM//wZ4UHIr9pju48MU/uPDZKxBUCnuDlmB3gDODS9Hv4Ny5nlKdB1mbs4B87XMkkHmqBWcq0AMYISIzgIdwXbmwBTAltydlvyJiVtb5Yg+Vmupqxj927FcWLFxKixZNin0bxe2LL6KJat2dTp0f5NTJ0+zZk2R1pFwlpxwmOfkwMbFbAfh6/mIimzS2OFXOHA4Hc+ZMZO7cBSxcuAyAlJTDLFjgur958zaysrKoXLmSlTFz1KnTXRw4cJDjx0/gdDpZsGApraOaWx0rV6dPn2Xt2g107tLhyrKsrCy++vI7evfpamGy/B09epzwcFfLQnh4Va/utsxu0KCH6N69M3/+i/VfMOy1GmLO/AoXzkFWFpl7t2KLuBlz7hSZ+1zHisx9cdgq1wQg69wppGzFK8+XsmFknTuV47qt4IufI3nRFpzCa2yM6Q/8CbgXeNAYMwPX6V6RuT3JGDPZGNPcGNPcZitTrIFCQ0MoW7bMlftdOncgPn53sW7DE6pUuQGAWrUi6NOnG9HRCyxOlLsjR46RnJxK/fo3A9CxYzsSEn62OFXOJk4cw+7de/noo9/r7UWLVtChQ2sA6tWrS6lSQRw/fsKqiLk6dDCFlq2aEhJSGoCO97Qj0csGc1euXIkKFcoBULp0MB073sWePUncdFOdK4/p3qMzP+/23oIdYNF33zNo4EMADBr4EIsWrbA4Uf7uvfduXn5pKH0feJwLFy5aHQdz9gS28LquMTi4C54Th8lMisNWswEAthr1yTp1BIDMpO04bo1yLQ+vi7l0EX7zjrF8vvo5khdPzyZuJU+dJm4TkVJAGSAUqACcAIIBS7qoqlWrwldfuk6xtjvsREcvYMWKH6yIUihzoydzww0Vychw8tyI17xy0G52z7/wT6ZP+w+lSgWRtP8ggwe/aHWka7Rp05xHH32AHTsS2LhxCQBvvDGWadPmMWnSWDZvXkF6egaDB79kcdKcxcRuZf78xcTELMfpdLItLp5Pp8yyOtZVqoVXZfKn47Db7Nhswvz5i1m2dDUrVs6jfLmyiAg7diTw/Ih/Wh31ihnTP6Z9+9ZUrlyJpH2xjH7rfcaO/ZjZsyfy2OMPc/BgMgMGDLU65lVyyjxq1HCCS5Vi6RLXYP9NMVsYPvxvlmXMOnKAzL1bKP3Ia5CVSdaxQzh3rgd7EMFdnyAoshMm4xLpK2e4Hn9gJ1k33k7pv7wFznTXKeVewlc/R/Li7a0wRSGeqMBE5AXgWcAOvI9rdtAkXFOlf2WMeTO/dQSVquFTez37vBq+wtur75w47L516SZnptPqCIUW7ChldYRCS8/MsDqC3zs1xrfGS1UYucjqCNclIz2lRD9MWkS0L9IHQWzqWq/98PPIp4UxZryIzHXfTxWR6UBn4FNjTIwntqmUUkopdZnHvg4bY1Kz3T8FfOWpbSmllFKq8HyxJb+gfKu9XymllFLFxp/H4GiBo5RSSgUof27BCagrGSullFIqMGgLjlJKKRWgtItKKaWUUn7HaIGjlFJKKX+T5cdjcLTAUUoppQKUP7fg6CBjpZRSSvkdbcFRSimlApR2USmllFLK7/hzF5XXFji+NnmlL14syfcSQ2ZWptURCqWUI8jqCIV2yZludYRC87XXcrAPvi58bfLKM1OfsDqCT9AWHKWUUkr5HX9uwdFBxkoppZTyO9qCo5RSSgUo7aJSSimllN/x5y4qLXCUUkqpAGVMltURPEbH4CillFLK72gLjlJKKRWgdDZxpZRSSvkdX7yGW0FpgaOUUkoFKG3BUUoppZTf8ecWHB1krJRSSim/49cFzuRJ40g+FMfWLSuvLKtYMYwlS2YTH7+OJUtmExZWwcKEeatf/2Y2x664cvv1eCLPPTvY6lh5+nTy+6QmbyNu6yqroxTY8OFPsnXLSuK2ruLZZ5+0Ok6OatSozpKlc9j80/fEbl7BX//6OAB33NGINT98w4aNS1i3/luaNb/T4qQ5G/HcU8TFrWbr1lXMmPEJwcHBVkfK13333k38zrUk7lrPqJHDrI5zjdxeE9Omf8yGjUvYsHEJuxLWs2HjEouT5sybj2+zNv3MAxOW0XfCMmZu/BmAFbsO0XfCMiJHzyM+9cSVx27Yl8Yjn37PgxOX88in3xOz/4hVsa9LljFFunkz8dbmqVLBNYscrF27Vpw7d56pn39IZNPOALzzr9c4ceIUY8d9wsiXh1GxYgX+/tq/ipzX0/vRZrPxy4GfaNuuJwcPphTLOj2R+K7L+3zqv2kS2anY128r5klYb2vUgJkzP6FN256kp2fw3XczGT78b+zbd6BY1h9kL55e4PDwKoSHVyUuLp6yZcuw/sdFPNx/CGPGvM7HH3/OihU/cN99d/P8C8/QrevDRdpWujOjWDJfFhERzg9rvuGOO+/h4sWLzJ49kWVLVzN9xrxi20Zxv5ZtNhsJ8evo2v0RkpMPs3HDEgYO+isJCXuKZf3FMdlmbq+JxMS9Vx7zzjuvcfrMWd5956Mib6+4XxfZeeL4dr2Tbe49eppXvt7AzMGdCbLbGDZrLa/1aIYz02ATeGvxT7zY5U5ui6gEQOLhk1QqW5qq5ULYe/Q0Q2et5fsXel137pBH3yrRmabDw24t0tsn7VSC186M7dctOOvXb+LkyVNXLevV615mzPwSgBkzv+T++++zIlqhdezYjqSkX4rtze8p69Zv4sQf9rk3a9iwHjExcVy4cJHMzEzWrd1Inz7drI51jbS0Y8TFxQNw7tx5du/eR0REOMZAuXJlAShfvjxph73z26PD4SAkpDR2u53QkBBSD6dZHSlPLVtEsm/fAfbvP0hGRgbz5i3k/l7edazI7TWRXd8HevDlvG+tiFco3nR8Szp+hsY1biAkyIHDZqNZnSqsSkjhpirlubFy+Wse37B6RaqWCwHg5irluZSRSbozs6RjXzdjTJFu3sxjg4xF5CagL1ALyAR+BmYbY854apsFUbVqZdLSjgKQlnaUqlUrWxmnwPr3683cuQusjuF34nftZvToV6hUKYwLFy7StWtHftqy3epYeapduyZ33tmI2Ng4Ro16k4XfTudf7/wdm81Gx3sesDreNVJT0xg/fiJJ+2K4cOEiK1f+HytXrrU6Vp4iaoRzKDn1ys/JKYdp2SLSwkR5y/6auKxt25YcPXq82FojPcmbjm/1qlTg49U7OPXbJYKD7Kzfk0ajiIoFeu7KhGRurR5GKYfdwymLjz+fReWRFhwReQ6YCJQGWgDBuAqdjSJydx7PGyIim0Vkc1bmeU9Eu4a3V6AAQUFB9Ox5L199/Z3VUfxOYuJexo77L0sWz+a7RTPZtj2ezEzv/fZVpkwos+dMYNSo0Zw9e47BTw3klVFv0aB+G14Z9RYTJrxndcRrhIVVoFev+7ilfhS16zQltEwoAwb0tTqW3/jja+Kyh/rd7xOtN952fLupSnkeb9uQobPWMmzWWhqEh2Gz5d8Ls/foaf69ajv/6NG8BFKqgvBUF9VTQDdjzNtAZ+A2Y8xrQFdgfG5PMsZMNsY0N8Y0t9nLeCTY0aPHCQ+vCkB4eFWOHfvVI9spTl273sPWrTs4evS41VH80hdfRBPVujudOj/IqZOn2bMnyepIOXI4HMyePZG50Qv4duFyAB599AEWLlwGwPz5i71ykHGnTndx4MBBjh8/gdPpZMGCpbSO8u4PgdSUNGrVjLjyc80a1UlN9b5utZxeEwB2u53e99/nNUVDXrzx+PanyJuY81QXPn+sI+VKB1GnUrk8H3/kzG+8OO9H3urdilqVypZQyuLhz11UnhyDc7n7KxgoC2CMOQgUfXRdESz67nsGDXwIgEEDH2LRohVWximQ/v37eE3zrT+qUuUGAGrViqBPn25ER3vnvp4w4T12797Lf/7z2ZVlhw8f5a67ogC4++42XtkdcehgCi1bNSUkpDQAHe9pR2Ji8QzW9ZTYzXHUq1eXG2+sRVBQEP369WbRd953rMjpNQGuMS27f04iNcX7irI/8sbj24nzFwE4fPo8qxNT6Na4dq6PPXMxnWfnrGNEpzuIrO0bQx6y07OoCrtSkRHAk8Am4C7gPWPMVBGpAnxtjGmf3zqK4yyqGdM/pn371lSuXIkjR44z+q33+fbbZcyePZFatWpw8GAyAwYMvWYg8vXwVCUbGhpC0r5Y6jdozZkzZ4t13Z5IPHPGJ3TIts/fHD2OqV9EF9v6i/ssKoDVq77mhhsqkpHhZOSoN1mz5sdiW3fDCGMGAAAJXUlEQVRxnUXVunVzVq76ip07Eq4cVP7njTGcOXOOsePewGF3cPHSJZ5//h/Ebd1ZpG154myZ119/iYceuh+n08m2uHiGPP0y6enpxbZ+T7yWu3XtyPvvv4ndZuOLaXN5592in4l0WXGcRZXba2L58h+YNGkcMbFb+WzKrCJv5zJPvC48eXy73rOoAB6fuprTF9Jx2IWXujSh1U3VWJ2YzLtLt3Lyt0uUKx1Eg2phTBjYgU/X7uKzHxOona2VZ+LA9lQqU/q6tl3SZ1FVLFuvSG+fk+f2eu1ZVB47TVxEbgNuBXYaYxIL+/ziKHBKkrc31eXE9xJ7psDxpOIqcEqSJ08H9hRfey0XR4FT0nztdVGUAsdKWuAUH48dfY0x8UC8p9avlFJKqaLx57OofO/rpVJKKaWKhS/2PhSUFjhKKaVUgPL2gcJFoQWOUkopFaCMH3dR+fVUDUoppZQKTNqCo5RSSgUo7aJSSimllN/RQcZKKaWU8js6BkcppZRSfsfTc1GJSFcR2S0ie0Xk1RL4k67QAkcppZRSxU5E7MAnQDegEfCIiDQqqe1rF5VSSikVoDw8BqclsNcYkwQgItFAb2CXJzd6mbbgKKWUUgHKFPGWjxrAoWw/J7uXlQivbcFJv5TssQm8RGSIMWayp9Zf3HwtL/heZl/LC5q5JPhaXtDMJcHX8ubFmZ5SpM9aERkCDMm2aLK37JtAbcEZkv9DvIqv5QXfy+xreUEzlwRfywuauST4Wl6PMcZMNsY0z3bLXtykALWy/VzTvaxEBGqBo5RSSinPigVuEZG6IlIKeBj4tqQ27rVdVEoppZTyXcYYp4gMB5YDduBzY0x8SW0/UAscr+gfLARfywu+l9nX8oJmLgm+lhc0c0nwtbyWMcYsAZZYsW3x58s0K6WUUiow6RgcpZRSSvmdgCpwrLxk9PUQkc9F5KiI7LQ6S0GISC0RWSMiu0QkXkRGWJ0pPyJSWkRiRGSbO/ObVmcqCBGxi8hWEfnO6iwFISIHRGSHiMSJyGar8xSEiISJyFcikigiCSLS2upMeRGRBu79e/l2RkSetzpXXkTkBff7bqeIzBGR0lZnyo+IjHDnjff2/RvoAqaLyn3J6J+BLrguNhQLPGKMKZErKl4PEWkPnAOmG2NutzpPfkSkOlDdGLNFRMoBPwF9vHwfC1DGGHNORIKA9cAIY8xGi6PlSUReBJoD5Y0xPa3Okx8ROQA0N8YctzpLQYnINGCdMWaK+wyQUGPMKatzFYT7eJcCtDLG/GJ1npyISA1c77dGxpgLIjIPWGKM+cLaZLkTkduBaFxX6E0HlgHPGGP2WhpM5SiQWnCuXDLaGJOO60Xa2+JMeTLGrAVOWJ2joIwxh40xW9z3zwIJlOBVK6+HcTnn/jHIffPqql9EagI9gClWZ/FXIlIBaA98BmCMSfeV4satE7DPW4ubbBxAiIg4gFAg1eI8+bkV2GSM+c0Y4wT+D+hrcSaVi0AqcCy9ZHSgEZEbgUhgk7VJ8ufu7okDjgLfG2O8PfOHwCggy+oghWCAFSLyk/vKp96uLnAMmOruCpwiImWsDlUIDwNzrA6RF2NMCjAOOAgcBk4bY1ZYmypfO4G7ROQGEQkFunP1heyUFwmkAkeVEBEpC3wNPG+MOWN1nvwYYzKNMU1wXWWzpbsZ2iuJSE/gqDHmJ6uzFFI7Y0xTXLMKD3N3v3ozB9AUmGCMiQTOA14/bg/A3Z12P/Cl1VnyIiIVcbWi1wUigDIiMtDaVHkzxiQA7wErcHVPxQGZloZSuQqkAsfSS0YHCvc4lq+BWcaY+VbnKQx3F8QaoKvVWfLQFrjfPaYlGugoIjOtjZQ/97d1jDFHgW9wdRl7s2QgOVtr3le4Ch5f0A3YYow5YnWQfHQG9htjjhljMoD5QBuLM+XLGPOZMaaZMaY9cBLX2E7lhQKpwLH0ktGBwD1g9zMgwRjzgdV5CkJEqohImPt+CK5B6InWpsqdMeZvxpiaxpgbcb2GVxtjvPpbr4iUcQ86x93Ncy+upn6vZYxJAw6JSAP3ok6A1w6W/4NH8PLuKbeDQJSIhLqPHZ1wjdvzaiJS1f1/bVzjb2Zbm0jlJmCuZGz1JaOvh4jMAe4GKotIMvCGMeYza1PlqS0wCNjhHtMC8Hf3lSy9VXVgmvusExswzxjjE6de+5BqwDeuzzAcwGxjzDJrIxXIs8As9xeiJOBxi/Pky11AdgGetjpLfowxm0TkK2AL4AS24htXCP5aRG4AMoBhPjb4PKAEzGniSimllAocgdRFpZRSSqkAoQWOUkoppfyOFjhKKaWU8jta4CillFLK72iBo5RSSim/owWOUj5KRDLds0bvFJEv3ZeOv951fSEiD7rvTxGRRnk89m4RKfQF2dwzile+3oxKKVUYWuAo5bsuGGOauGeaTweeyf5L9wSGhWaMGZzPDPB34wNXnFVKBTYtcJTyD+uAeu7WlXUi8i2wyz2R6FgRiRWR7SLyNLiuOi0iH4vIbhFZCVS9vCIR+UFEmrvvdxWRLSKyTURWuSdRfQZ4wd16dJf7atBfu7cRKyJt3c+9QURWiEi8iEwBpGR3iVIqkAXMlYyV8lfulppuuCb/A9ecSbcbY/a7Z+4+bYxpISLBwI8isgLXTO8NgEa4rjS8C/j8D+utAnwKtHevq5Ix5oSITATOGWPGuR83GxhvjFnvvnz9cuBW4A1gvTFmtIj0AJ706I5QSqlstMBRyneFZJsSYx2uecDaADHGmP3u5fcCd1weXwNUAG4B2gNzjDGZQKqIrM5h/VHA2svrMsacyCVHZ6CReyoGgPLuGeXb45qrB2PMYhE5eZ1/p1JKFZoWOEr5rgvGmCbZF7iLjPPZFwHPGmOW/+Fx3Ysxhw2IMsZczCGLUkpZQsfgKOXflgNDRSQIQETquydkXAv0d4/RqQ7ck8NzNwLtRaSu+7mV3MvPAuWyPW4FrokpcT/uctG1FhjgXtYNqFhsf5VSSuVDCxyl/NsUXONrtojITmASrpbbb4A97t9NBzb88YnGmGPAEGC+iGwD5rp/tQj40+VBxsBzQHP3IOZd/H4215u4CqR4XF1VBz30Nyql1DV0NnGllFJK+R1twVFKKaWU39ECRymllFJ+RwscpZRSSvkdLXCUUkop5Xe0wFFKKaWU39ECRymllFJ+RwscpZRSSvkdLXCUUkop5Xf+P4CmhpnSL3acAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 720x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WNUV5XZNVvG6"
      },
      "source": [
        "### Model 3: Adding Hidden Layer with Flatten() Layer"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AQ8YNR-AUJ80"
      },
      "source": [
        "# Adding a Hidden Layer"
      ],
      "execution_count": 37,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cWC0sbQfUOkS"
      },
      "source": [
        "model3 = Sequential([\n",
        "                     Flatten(input_shape = (28,28)),\n",
        "                     Dense(16, activation = 'relu'),\n",
        "                     Dense(10, activation = 'sigmoid')\n",
        "])"
      ],
      "execution_count": 38,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vRrfbFmzUdpl"
      },
      "source": [
        "model3.compile(\n",
        "    optimizer = 'adam',\n",
        "    loss = 'sparse_categorical_crossentropy',\n",
        "    metrics = ['accuracy']\n",
        ")"
      ],
      "execution_count": 39,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dU9HkinzYxxm",
        "outputId": "6b905b31-f723-4d2f-e186-2d14a7b63917"
      },
      "source": [
        "model3.summary()"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model: \"sequential_2\"\n",
            "_________________________________________________________________\n",
            " Layer (type)                Output Shape              Param #   \n",
            "=================================================================\n",
            " flatten_1 (Flatten)         (None, 784)               0         \n",
            "                                                                 \n",
            " dense_2 (Dense)             (None, 16)                12560     \n",
            "                                                                 \n",
            " dense_3 (Dense)             (None, 10)                170       \n",
            "                                                                 \n",
            "=================================================================\n",
            "Total params: 12,730\n",
            "Trainable params: 12,730\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ACfDpQJhUoV2",
        "outputId": "7a5e88ec-4959-4fab-f187-6cf10473145b"
      },
      "source": [
        "model3.fit(X_train, y_train, epochs = 10)"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.4327 - accuracy: 0.8780\n",
            "Epoch 2/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.2449 - accuracy: 0.9309\n",
            "Epoch 3/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.2069 - accuracy: 0.9405\n",
            "Epoch 4/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.1854 - accuracy: 0.9463\n",
            "Epoch 5/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.1720 - accuracy: 0.9497\n",
            "Epoch 6/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.1629 - accuracy: 0.9515\n",
            "Epoch 7/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.1552 - accuracy: 0.9548\n",
            "Epoch 8/10\n",
            "1875/1875 [==============================] - 4s 2ms/step - loss: 0.1490 - accuracy: 0.9557\n",
            "Epoch 9/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.1451 - accuracy: 0.9568\n",
            "Epoch 10/10\n",
            "1875/1875 [==============================] - 3s 2ms/step - loss: 0.1403 - accuracy: 0.9585\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7f85be8776d0>"
            ]
          },
          "metadata": {},
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hHtH_hJ4UteG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "03fbfa83-8118-4092-82a8-bbbacc99d45e"
      },
      "source": [
        "model3.evaluate(X_test, y_test)"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "313/313 [==============================] - 1s 1ms/step - loss: 0.1716 - accuracy: 0.9484\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.1716499626636505, 0.9484000205993652]"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1XfYqBJHWMAc"
      },
      "source": [
        "y_pred_3 = model3.predict(X_test)\n",
        "y_pred_3_labels = [np.argmax(i) for i in y_pred_3]"
      ],
      "execution_count": 42,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 388
        },
        "id": "jOTzfc3kWHD2",
        "outputId": "af6e6350-50ca-442e-cb41-137f0b842414"
      },
      "source": [
        "cm3 = tf.math.confusion_matrix(y_test, y_pred_3_labels)\n",
        "\n",
        "plt.figure(figsize = (10,6))\n",
        "sns.heatmap(cm3, fmt = 'g', annot = True, xticklabels = labels, yticklabels = labels)\n",
        "plt.xlabel('Predicted')\n",
        "plt.ylabel('Actuals')\n",
        "plt.show()"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eq_yNmF_Wio8"
      },
      "source": [
        ""
      ],
      "execution_count": 43,
      "outputs": []
    }
  ]
}