MNIST Handwritten Digit Clasification.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "toc_visible": true,
      "gpuType": "T4"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "Importing the dependencies"
      ],
      "metadata": {
        "id": "hyQtYQVsDzCL"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "rEWRPWZr8cs0"
      },
      "outputs": [],
      "source": [
        "import numpy as np    # used for handling arrays and numerical operations\n",
        "import matplotlib.pyplot as plt   # used for visualizing data\n",
        "from google.colab.patches import cv2_imshow   # allows displaying images using OpenCV in Colab\n",
        "                                              # OpenCV (Open Source Computer Vision Library) is an open-source library primarily used for computer vision and image processing tasks\n",
        "\n",
        "import seaborn as sns   # is useful for creating a confusion matrix heatmap\n",
        "import cv2    # OpenCV may be used to preprocess or augment the image data\n",
        "from PIL import Image   # helps with loading or transforming the images\n",
        "import tensorflow as tf   # TensorFlow is the deep learning framework that provides the core functionality for building, training, and evaluating neural networks\n",
        "tf.random.set_seed(3)   #  a way to control randomness in TensorFlow, ensuring reproducible and consistent results\n",
        "from tensorflow import keras    # Keras makes it easy to define neural network layers and models\n",
        "from tensorflow.keras.models import Sequential    # The Sequential model is used to define a neural network in a linear way\n",
        "from tensorflow.keras import layers   # The layers module is used to add different types of layers to the model\n",
        "from keras.datasets import mnist\n",
        "from tensorflow.math import confusion_matrix"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Loading the MNIST data from keras.datasets"
      ],
      "metadata": {
        "id": "Yq_LtAWRIH62"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "(X_train,Y_train),(X_test,Y_test) = mnist.load_data()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4LdUG09uFE8s",
        "outputId": "7e2ffaa1-5039-4c42-e86a-fa892b552774"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
            "\u001b[1m11490434/11490434\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m0s\u001b[0m 0us/step\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "type(X_train)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EJ67volsIaK9",
        "outputId": "6affa56d-9e08-4f54-e867-f74c37baa329"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "numpy.ndarray"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# shape of numpy arrays\n",
        "\n",
        "print(X_train.shape,X_test.shape,Y_train.shape,Y_test.shape)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YgscIq9dIfT9",
        "outputId": "717032b3-860b-4a77-aeaf-6ebbe7d02ad9"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(60000, 28, 28) (10000, 28, 28) (60000,) (10000,)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Trainig data = 60,000 images\n",
        "\n",
        "Test data = 10,000 images"
      ],
      "metadata": {
        "id": "X-H8Vz3TI8S3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Image dimesion -> 28 x 28\n",
        "\n",
        "GrayScale Image -> 1 channel"
      ],
      "metadata": {
        "id": "fIyo075rJJWa"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(X_train[10])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KzgMPMlCIhLN",
        "outputId": "d4b2acb0-ffc2-4826-c879-250d3958fa0b"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
            "    0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
            "    0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
            "    0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
            "    0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0  42 118 219 166 118 118   6\n",
            "    0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0 103 242 254 254 254 254 254  66\n",
            "    0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0  18 232 254 254 254 254 254 238\n",
            "   70   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0 104 244 254 224 254 254 254\n",
            "  141   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0 207 254 210 254 254 254\n",
            "   34   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0  84 206 254 254 254 254\n",
            "   41   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0  24 209 254 254 254\n",
            "  171   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0  91 137 253 254 254 254\n",
            "  112   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0  40 214 250 254 254 254 254 254\n",
            "   34   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0  81 247 254 254 254 254 254 254\n",
            "  146   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0 110 246 254 254 254 254 254\n",
            "  171   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0  73  89  89  93 240 254\n",
            "  171   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1 128 254\n",
            "  219  31   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   7 254 254\n",
            "  214  28   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0 138 254 254\n",
            "  116   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0  19 177  90   0   0   0   0   0  25 240 254 254\n",
            "   34   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0 164 254 215  63  36   0  51  89 206 254 254 139\n",
            "    8   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0  57 197 254 254 222 180 241 254 254 253 213  11\n",
            "    0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0 140 105 254 254 254 254 254 254 236   0   0\n",
            "    0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   7 117 117 165 254 254 239  50   0   0\n",
            "    0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
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            "    0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
            "    0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
            "    0   0   0   0   0   0   0   0   0   0]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(X_train[10].shape)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ltyM2txmJjgZ",
        "outputId": "bb83674b-5301-4e73-f59d-074794abab55"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(28, 28)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# displaying the image\n",
        "\n",
        "plt.imshow(X_train[10])\n",
        "plt.show()\n",
        "\n",
        "# corresponding label\n",
        "print(Y_train[10])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "8NqN5NkJJ4Pw",
        "outputId": "4f86c18d-db45-43b5-915c-6455e194179a"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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ODQBIfJ4CVF9fr8rKSu3Zs0dvv/22ent7NW/ePHV3d4f3ue+++/Tmm2/qjTfeUH19vY4dO6Zbb7015oMDABKbpw8h7Ny5M+LrTZs2KTs7W/v379fs2bMVDAb161//Wps3b9Ytt9wiSdq4caOuu+467dmzR9/5zndiNzkAIKF9pfeAgsGgJCkzM1OStH//fvX29qq0tDS8z5QpUzR+/Hg1NDT0+z16enoUCoUiNgBA8os6QH19fVqzZo1uuOEGTZ06VZLU3t6utLQ0jRkzJmLfnJwctbe39/t9ampqFAgEwltBQUG0IwEAEkjUAaqsrNThw4f16qvR/QzJ56qrqxUMBsNba2vrV/p+AIDEENUPoq5evVo7duzQ7t27NW7cuPDjubm5OnPmjDo7OyOugjo6OpSbm9vv9/L7/fL7vf8gHwAgsXm6AnLOafXq1dq6dat27dqlwsLCiOdnzJih1NRU1dbWhh9rbGzU0aNHVVJSEpuJAQBJwdMVUGVlpTZv3qzt27crPT09/L5OIBDQiBEjFAgEdPfdd6uqqkqZmZnKyMjQvffeq5KSEj4BBwCI4ClAL7zwgiRpzpw5EY9v3LhRy5YtkyQ988wzSklJ0eLFi9XT06OysjL98pe/jMmwAIDk4XPOOeshvigUCikQCGiOFmi4L9V6nITTUzHT85rpPz0Y1bGey/+PqNZ59duT3m+w+uu/3hjVsdZPfN3zmsJBuknoOdfnec2G4ISojvU/vzvR85pzncGojoXkc9b1qk7bFQwGlZEx8L+/3AsOAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJrgbNvTxr7zfQVuSRv7J+z+f/3Mvv5ojWofOnPa85sGr+D1cGHzcDRsAMKQRIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACaGWw8Ae9cu/4+o1qWMHOl5zeTRq6I6llejpv09qnUffPu1GE/Sv497uz2vqbrrXs9rhukDz2uAwcIVEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABggpuRImp9p055XnPVf2+IwySxU6ZvWo8wIG4simTDFRAAwAQBAgCYIEAAABMECABgggABAEwQIACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAw4SlANTU1mjlzptLT05Wdna2FCxeqsbExYp85c+bI5/NFbCtXrozp0ACAxOcpQPX19aqsrNSePXv09ttvq7e3V/PmzVN3d3fEfsuXL1dbW1t4W7duXUyHBgAkPk+/EXXnzp0RX2/atEnZ2dnav3+/Zs+eHX585MiRys3Njc2EAICk9JXeAwoGg5KkzMzMiMdffvllZWVlaerUqaqurtapi/zq5p6eHoVCoYgNAJD8PF0BfVFfX5/WrFmjG264QVOnTg0/fscdd2jChAnKz8/XoUOH9PDDD6uxsVFbtmzp9/vU1NToiSeeiHYMAECC8jnnXDQLV61apd/97nd67733NG7cuAH327Vrl+bOnaumpiZNmjTpgud7enrU09MT/joUCqmgoEBztEDDfanRjAYAMHTW9apO2xUMBpWRkTHgflFdAa1evVo7duzQ7t27LxofSSouLpakAQPk9/vl9/ujGQMAkMA8Bcg5p3vvvVdbt25VXV2dCgsLL7nm4MGDkqS8vLyoBgQAJCdPAaqsrNTmzZu1fft2paenq729XZIUCAQ0YsQINTc3a/Pmzfr+97+vsWPH6tChQ7rvvvs0e/ZsTZ8+PS5/AwCAxOTpPSCfz9fv4xs3btSyZcvU2tqqH/3oRzp8+LC6u7tVUFCgRYsW6ZFHHrnonwN+USgUUiAQ4D0gAEhQcXkP6FKtKigoUH19vZdvCQC4THEvOACACQIEADBBgAAAJggQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAEwQIAGCCAAEATBAgAIAJAgQAMEGAAAAmCBAAwAQBAgCYIEAAABMECABgggABAEwQIACAieHWA3yZc06SdFa9kjMeBgDg2Vn1SvrHf88HMuQC1NXVJUl6T28ZTwIA+Cq6uroUCAQGfN7nLpWoQdbX16djx44pPT1dPp8v4rlQKKSCggK1trYqIyPDaEJ7nIfzOA/ncR7O4zycNxTOg3NOXV1dys/PV0rKwO/0DLkroJSUFI0bN+6i+2RkZFzWL7DPcR7O4zycx3k4j/NwnvV5uNiVz+f4EAIAwAQBAgCYSKgA+f1+rV27Vn6/33oUU5yH8zgP53EezuM8nJdI52HIfQgBAHB5SKgrIABA8iBAAAATBAgAYIIAAQBMJEyA1q9fr6uuukpXXHGFiouL9Yc//MF6pEH3+OOPy+fzRWxTpkyxHivudu/erfnz5ys/P18+n0/btm2LeN45p8cee0x5eXkaMWKESktLdeTIEZth4+hS52HZsmUXvD7Ky8ttho2TmpoazZw5U+np6crOztbChQvV2NgYsc/p06dVWVmpsWPHavTo0Vq8eLE6OjqMJo6Pf+Y8zJkz54LXw8qVK40m7l9CBOi1115TVVWV1q5dqw8++EBFRUUqKyvT8ePHrUcbdNdff73a2trC23vvvWc9Utx1d3erqKhI69ev7/f5devW6bnnntOGDRu0d+9ejRo1SmVlZTp9+vQgTxpflzoPklReXh7x+njllVcGccL4q6+vV2Vlpfbs2aO3335bvb29mjdvnrq7u8P73HfffXrzzTf1xhtvqL6+XseOHdOtt95qOHXs/TPnQZKWL18e8XpYt26d0cQDcAlg1qxZrrKyMvz1uXPnXH5+vqupqTGcavCtXbvWFRUVWY9hSpLbunVr+Ou+vj6Xm5vrnnrqqfBjnZ2dzu/3u1deecVgwsHx5fPgnHNLly51CxYsMJnHyvHjx50kV19f75w7/88+NTXVvfHGG+F9/vjHPzpJrqGhwWrMuPvyeXDOue9973vuxz/+sd1Q/4QhfwV05swZ7d+/X6WlpeHHUlJSVFpaqoaGBsPJbBw5ckT5+fmaOHGi7rzzTh09etR6JFMtLS1qb2+PeH0EAgEVFxdflq+Puro6ZWdna/LkyVq1apVOnDhhPVJcBYNBSVJmZqYkaf/+/ert7Y14PUyZMkXjx49P6tfDl8/D515++WVlZWVp6tSpqq6u1qlTpyzGG9CQuxnpl3366ac6d+6ccnJyIh7PycnRRx99ZDSVjeLiYm3atEmTJ09WW1ubnnjiCd100006fPiw0tPTrccz0d7eLkn9vj4+f+5yUV5erltvvVWFhYVqbm7WT37yE1VUVKihoUHDhg2zHi/m+vr6tGbNGt1www2aOnWqpPOvh7S0NI0ZMyZi32R+PfR3HiTpjjvu0IQJE5Sfn69Dhw7p4YcfVmNjo7Zs2WI4baQhHyD8Q0VFRfivp0+fruLiYk2YMEGvv/667r77bsPJMBTcdttt4b+eNm2apk+frkmTJqmurk5z5841nCw+Kisrdfjw4cvifdCLGeg8rFixIvzX06ZNU15enubOnavm5mZNmjRpsMfs15D/I7isrCwNGzbsgk+xdHR0KDc312iqoWHMmDG69tpr1dTUZD2Kmc9fA7w+LjRx4kRlZWUl5etj9erV2rFjh959992IX9+Sm5urM2fOqLOzM2L/ZH09DHQe+lNcXCxJQ+r1MOQDlJaWphkzZqi2tjb8WF9fn2pra1VSUmI4mb2TJ0+qublZeXl51qOYKSwsVG5ubsTrIxQKae/evZf96+OTTz7RiRMnkur14ZzT6tWrtXXrVu3atUuFhYURz8+YMUOpqakRr4fGxkYdPXo0qV4PlzoP/Tl48KAkDa3Xg/WnIP4Zr776qvP7/W7Tpk3uww8/dCtWrHBjxoxx7e3t1qMNqvvvv9/V1dW5lpYW9/vf/96Vlpa6rKwsd/z4cevR4qqrq8sdOHDAHThwwElyTz/9tDtw4ID7y1/+4pxz7uc//7kbM2aM2759uzt06JBbsGCBKywsdJ999pnx5LF1sfPQ1dXlHnjgAdfQ0OBaWlrcO++84771rW+5a665xp0+fdp69JhZtWqVCwQCrq6uzrW1tYW3U6dOhfdZuXKlGz9+vNu1a5fbt2+fKykpcSUlJYZTx96lzkNTU5N78skn3b59+1xLS4vbvn27mzhxops9e7bx5JESIkDOOff888+78ePHu7S0NDdr1iy3Z88e65EG3ZIlS1xeXp5LS0tzX//6192SJUtcU1OT9Vhx9+677zpJF2xLly51zp3/KPajjz7qcnJynN/vd3PnznWNjY22Q8fBxc7DqVOn3Lx589yVV17pUlNT3YQJE9zy5cuT7n/S+vv7l+Q2btwY3uezzz5z99xzj/va177mRo4c6RYtWuTa2trsho6DS52Ho0ePutmzZ7vMzEzn9/vd1Vdf7R588EEXDAZtB/8Sfh0DAMDEkH8PCACQnAgQAMAEAQIAmCBAAAATBAgAYIIAAQBMECAAgAkCBAAwQYAAACYIEADABAECAJggQAAAE/8PHQux+WKWhoUAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Image Lables"
      ],
      "metadata": {
        "id": "i662D_GgKdWw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Unique values\n",
        "\n",
        "print(np.unique(Y_train))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_zFEQjmjKCj1",
        "outputId": "550536c9-d6c7-42a9-8a42-0344b1c37717"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0 1 2 3 4 5 6 7 8 9]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(np.unique(Y_test))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aLCQcZaeKsTZ",
        "outputId": "886d9250-38fa-4fba-b253-1ab3e9ca659e"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0 1 2 3 4 5 6 7 8 9]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can use these labels as such or we can also apply One Hot Encoding"
      ],
      "metadata": {
        "id": "MpDsWQtMK-tK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "All the images have the same dimensions in this dataset, If not, we have to resize all the images to a common dimension"
      ],
      "metadata": {
        "id": "DcLLXAgaLFaj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Scaling the values\n",
        "\n",
        "X_train = X_train/255\n",
        "X_test = X_test/255"
      ],
      "metadata": {
        "id": "axknuNirK6UL"
      },
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(X_train[10])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EixLTB1TLegT",
        "outputId": "3452d67e-068a-4afa-dbfd-233a4f42b542"
      },
      "execution_count": 21,
      "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.         0.16470588\n",
            "  0.4627451  0.85882353 0.65098039 0.4627451  0.4627451  0.02352941\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.40392157 0.94901961\n",
            "  0.99607843 0.99607843 0.99607843 0.99607843 0.99607843 0.25882353\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.07058824 0.90980392\n",
            "  0.99607843 0.99607843 0.99607843 0.99607843 0.99607843 0.93333333\n",
            "  0.2745098  0.         0.         0.         0.         0.\n",
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            " [0.         0.         0.         0.         0.         0.\n",
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            "  0.95686275 0.99607843 0.87843137 0.99607843 0.99607843 0.99607843\n",
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            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
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            "  0.81176471 0.99607843 0.82352941 0.99607843 0.99607843 0.99607843\n",
            "  0.13333333 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",
            "  0.32941176 0.80784314 0.99607843 0.99607843 0.99607843 0.99607843\n",
            "  0.16078431 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.         0.09411765 0.81960784 0.99607843 0.99607843 0.99607843\n",
            "  0.67058824 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",
            "  0.35686275 0.5372549  0.99215686 0.99607843 0.99607843 0.99607843\n",
            "  0.43921569 0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.15686275 0.83921569\n",
            "  0.98039216 0.99607843 0.99607843 0.99607843 0.99607843 0.99607843\n",
            "  0.13333333 0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.31764706 0.96862745\n",
            "  0.99607843 0.99607843 0.99607843 0.99607843 0.99607843 0.99607843\n",
            "  0.57254902 0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.         0.         0.43137255\n",
            "  0.96470588 0.99607843 0.99607843 0.99607843 0.99607843 0.99607843\n",
            "  0.67058824 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",
            "  0.28627451 0.34901961 0.34901961 0.36470588 0.94117647 0.99607843\n",
            "  0.67058824 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.         0.00392157 0.50196078 0.99607843\n",
            "  0.85882353 0.12156863 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.         0.02745098 0.99607843 0.99607843\n",
            "  0.83921569 0.10980392 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.         0.54117647 0.99607843 0.99607843\n",
            "  0.45490196 0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.0745098  0.69411765 0.35294118 0.         0.         0.\n",
            "  0.         0.         0.09803922 0.94117647 0.99607843 0.99607843\n",
            "  0.13333333 0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.64313725 0.99607843 0.84313725 0.24705882 0.14117647 0.\n",
            "  0.2        0.34901961 0.80784314 0.99607843 0.99607843 0.54509804\n",
            "  0.03137255 0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.22352941 0.77254902 0.99607843 0.99607843 0.87058824 0.70588235\n",
            "  0.94509804 0.99607843 0.99607843 0.99215686 0.83529412 0.04313725\n",
            "  0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.         0.        ]\n",
            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.54901961 0.41176471 0.99607843 0.99607843 0.99607843\n",
            "  0.99607843 0.99607843 0.99607843 0.9254902  0.         0.\n",
            "  0.         0.         0.         0.         0.         0.\n",
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            " [0.         0.         0.         0.         0.         0.\n",
            "  0.         0.         0.02745098 0.45882353 0.45882353 0.64705882\n",
            "  0.99607843 0.99607843 0.9372549  0.19607843 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"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Building the Neural Network"
      ],
      "metadata": {
        "id": "v_ULN-28LsVi"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model = keras.Sequential([\n",
        "                          keras.layers.Flatten(input_shape = (28,28)),\n",
        "                          keras.layers.Dense(50, activation = 'relu'),\n",
        "                          keras.layers.Dense(50, activation = 'relu'),\n",
        "                          keras.layers.Dense(10,activation = 'sigmoid')\n",
        "])"
      ],
      "metadata": {
        "id": "Cn9fSuHrLkH_"
      },
      "execution_count": 32,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# compiling the Neural Network\n",
        "\n",
        "model.compile(optimizer ='adam',loss = 'sparse_categorical_crossentropy',metrics =['accuracy'])"
      ],
      "metadata": {
        "id": "hLyMyLRcMuUa"
      },
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# training the neural network\n",
        "\n",
        "model.fit(X_train,Y_train,epochs = 10)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ioSCsJunNRki",
        "outputId": "ac89a877-32b5-4e2a-8be9-b1b163823448"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/10\n",
            "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m5s\u001b[0m 2ms/step - accuracy: 0.8509 - loss: 0.5170\n",
            "Epoch 2/10\n",
            "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m3s\u001b[0m 2ms/step - accuracy: 0.9561 - loss: 0.1489\n",
            "Epoch 3/10\n",
            "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m3s\u001b[0m 2ms/step - accuracy: 0.9680 - loss: 0.1059\n",
            "Epoch 4/10\n",
            "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m3s\u001b[0m 2ms/step - accuracy: 0.9750 - loss: 0.0832\n",
            "Epoch 5/10\n",
            "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m4s\u001b[0m 2ms/step - accuracy: 0.9798 - loss: 0.0671\n",
            "Epoch 6/10\n",
            "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m4s\u001b[0m 2ms/step - accuracy: 0.9831 - loss: 0.0560\n",
            "Epoch 7/10\n",
            "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m3s\u001b[0m 2ms/step - accuracy: 0.9858 - loss: 0.0477\n",
            "Epoch 8/10\n",
            "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m6s\u001b[0m 2ms/step - accuracy: 0.9881 - loss: 0.0399\n",
            "Epoch 9/10\n",
            "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m4s\u001b[0m 2ms/step - accuracy: 0.9895 - loss: 0.0347\n",
            "Epoch 10/10\n",
            "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m3s\u001b[0m 2ms/step - accuracy: 0.9911 - loss: 0.0303\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.src.callbacks.history.History at 0x79b1bf6d5a20>"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Trainig data accuracy = 99.11%"
      ],
      "metadata": {
        "id": "r9gwrzS2PORr"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Accuracy on Test data:**"
      ],
      "metadata": {
        "id": "HQDHaSxGPT0C"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "loss,accuracy = model.evaluate(X_test,Y_test)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hhXhAxgqNhSr",
        "outputId": "e68f04b1-b049-4b83-ff27-5854f9f7d072"
      },
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[1m313/313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m1s\u001b[0m 3ms/step - accuracy: 0.9623 - loss: 0.1495\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "accuracy"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tmVqn1Z-PfTU",
        "outputId": "c157a9c7-32ba-4ce9-f408-881636704f03"
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9653000235557556"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Test data accuracy = 96.53%"
      ],
      "metadata": {
        "id": "mweX4KcCPkF9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(X_test.shape)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1_6EOIblPhUq",
        "outputId": "88cc539c-edca-4d37-92f2-41a46c12d6ff"
      },
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(10000, 28, 28)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.imshow(X_test[11])\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "UnKPdIkAPz2w",
        "outputId": "24ade13d-a4d3-4f35-9395-81d590140253"
      },
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(Y_test[11])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0n6s2UT-P6BS",
        "outputId": "e88a5b72-e53d-4cbf-9e90-fd31e564f0ce"
      },
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "6\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "Y_pred = model.predict(X_test)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KYf06MyyQDJI",
        "outputId": "ff5f51ad-2449-4832-be5a-3b9ac208df37"
      },
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[1m313/313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m1s\u001b[0m 2ms/step\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "Y_pred.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "M1fmGaHeQHuD",
        "outputId": "17078e0a-903a-49b9-dd4c-ba014b2bc035"
      },
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10000, 10)"
            ]
          },
          "metadata": {},
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(Y_pred[11])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YIXelEqSQKxm",
        "outputId": "a1ebd13b-5743-455e-8cf8-6aa8f77c61c8"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[7.8674972e-01 2.2942196e-03 5.0526885e-03 4.6600822e-02 1.1002130e-02\n",
            " 1.5536110e-01 9.9999964e-01 3.3906612e-03 9.8943019e-01 9.8084631e-05]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "model.predict() gives the prediction probability of each class for that data point"
      ],
      "metadata": {
        "id": "Q3evOzubQX8c"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# converting prediction probability to class label\n",
        "\n",
        "label_11 = np.argmax(Y_pred[11])"
      ],
      "metadata": {
        "id": "wyX98d1nQPsh"
      },
      "execution_count": 46,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(label_11)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VjoSi19WQvfF",
        "outputId": "7483f0e5-8467-40ba-e904-51ddffb98095"
      },
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "6\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# converting prediction probability to class label for all data points\n",
        "\n",
        "Y_pred_labels = [np.argmax(i) for i in Y_pred]\n",
        "print(Y_pred_labels)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VqQs89_wQxLk",
        "outputId": "82b48364-c074-4344-ee1d-812848d9fa36"
      },
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[7, 2, 1, 0, 4, 1, 4, 9, 5, 9, 0, 6, 9, 0, 1, 5, 9, 7, 3, 4, 9, 6, 6, 5, 4, 0, 7, 4, 0, 1, 3, 1, 3, 4, 7, 2, 7, 1, 2, 1, 1, 7, 4, 2, 3, 5, 1, 2, 4, 4, 6, 3, 5, 5, 6, 0, 4, 1, 9, 5, 7, 8, 5, 3, 7, 4, 6, 4, 3, 0, 7, 0, 3, 9, 1, 7, 3, 2, 9, 7, 7, 6, 2, 7, 8, 4, 7, 3, 6, 1, 3, 6, 9, 3, 1, 4, 1, 7, 6, 9, 6, 0, 5, 4, 5, 9, 2, 1, 9, 4, 8, 7, 3, 9, 7, 4, 4, 4, 9, 2, 5, 4, 7, 6, 7, 9, 0, 5, 8, 5, 6, 6, 5, 7, 8, 1, 0, 1, 6, 4, 6, 7, 3, 1, 7, 1, 8, 2, 0, 4, 9, 9, 5, 5, 1, 5, 6, 0, 3, 4, 4, 6, 5, 4, 6, 5, 4, 5, 1, 4, 4, 7, 2, 3, 2, 7, 1, 8, 1, 8, 1, 8, 5, 0, 8, 9, 2, 5, 0, 1, 1, 1, 0, 9, 0, 3, 1, 6, 4, 2, 3, 6, 1, 1, 1, 3, 9, 5, 2, 9, 4, 5, 9, 3, 9, 0, 3, 6, 5, 5, 7, 2, 2, 7, 1, 2, 8, 4, 1, 7, 3, 3, 8, 8, 7, 9, 2, 2, 4, 1, 5, 9, 8, 7, 2, 3, 0, 2, 4, 2, 4, 1, 9, 5, 7, 7, 2, 8, 2, 6, 8, 5, 7, 7, 9, 1, 8, 1, 8, 0, 3, 0, 1, 9, 9, 4, 1, 8, 2, 1, 2, 9, 7, 5, 9, 2, 6, 4, 1, 5, 8, 2, 9, 2, 0, 4, 0, 0, 2, 8, 4, 7, 1, 2, 4, 0, 2, 7, 4, 3, 3, 0, 0, 3, 1, 9, 6, 5, 2, 5, 9, 7, 9, 3, 0, 4, 2, 0, 7, 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2, 2, 0, 8, 9, 9, 0, 2, 5, 1, 9, 7, 8, 1, 0, 4, 1, 7, 9, 9, 4, 2, 6, 8, 1, 3, 7, 5, 4, 4, 1, 8, 1, 3, 8, 1, 2, 5, 8, 0, 6, 2, 1, 1, 7, 1, 5, 3, 4, 6, 9, 5, 0, 9, 2, 2, 4, 8, 2, 1, 7, 2, 4, 9, 4, 4, 0, 3, 9, 2, 2, 3, 3, 8, 3, 5, 7, 5, 5, 8, 1, 2, 4, 4, 6, 4, 9, 5, 1, 0, 6, 9, 5, 9, 5, 9, 7, 3, 8, 0, 3, 7, 1, 3, 6, 7, 8, 5, 9, 7, 9, 6, 5, 6, 3, 7, 4, 6, 5, 3, 5, 4, 7, 8, 7, 8, 0, 7, 6, 8, 8, 7, 3, 3, 1, 9, 5, 2, 7, 3, 5, 1, 1, 2, 1, 4, 7, 4, 7, 5, 4, 5, 4, 0, 8, 3, 6, 9, 6, 0, 2, 7, 4, 4, 4, 4, 6, 6, 4, 7, 9, 3, 4, 5, 5, 8, 7, 3, 7, 2, 7, 0, 2, 6, 1, 1, 6, 6, 9, 2, 8, 7, 2, 0, 1, 5, 0, 9, 1, 9, 0, 6, 0, 8, 6, 8, 1, 8, 0, 3, 3, 7, 2, 3, 6, 2, 1, 6, 1, 1, 3, 7, 9, 0, 8, 0, 5, 4, 0, 2, 8, 2, 2, 9, 8, 4, 0, 4, 5, 8, 5, 1, 2, 1, 3, 1, 7, 9, 5, 7, 2, 0, 5, 8, 8, 6, 2, 5, 4, 1, 9, 2, 1, 5, 8, 7, 0, 2, 4, 4, 3, 6, 8, 8, 2, 4, 0, 4, 0, 4, 4, 7, 9, 3, 4, 1, 5, 9, 7, 3, 5, 8, 8, 0, 9, 3, 3, 6, 6, 0, 1, 6, 0, 3, 7, 4, 4, 1, 2, 9, 1, 4, 6, 9, 9, 3, 9, 8, 4, 4, 3, 1, 3, 1, 0, 8, 7, 9, 4, 8, 8, 7, 9, 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0, 1, 2, 3, 2, 7, 7, 8, 5, 2, 5, 7, 6, 9, 1, 4, 1, 6, 4, 2, 4, 3, 5, 4, 3, 9, 5, 0, 1, 5, 3, 8, 9, 1, 9, 7, 9, 5, 5, 2, 7, 4, 6, 0, 1, 1, 1, 0, 4, 4, 7, 6, 3, 0, 0, 4, 3, 0, 6, 1, 9, 6, 1, 3, 8, 1, 2, 5, 6, 2, 4, 3, 6, 0, 1, 9, 7, 6, 6, 8, 9, 2, 9, 5, 8, 3, 1, 0, 0, 7, 6, 6, 2, 1, 6, 9, 3, 1, 3, 6, 9, 0, 6, 0, 0, 0, 6, 3, 5, 9, 3, 4, 5, 5, 8, 5, 3, 0, 4, 0, 2, 9, 6, 8, 2, 3, 1, 2, 1, 1, 5, 6, 9, 8, 0, 6, 6, 5, 5, 3, 8, 6, 2, 1, 4, 5, 4, 3, 7, 8, 9, 0, 9, 3, 5, 1, 1, 0, 4, 4, 7, 0, 1, 7, 0, 1, 6, 1, 4, 5, 6, 6, 5, 7, 8, 4, 4, 7, 2, 5, 3, 7, 0, 7, 7, 9, 6, 4, 2, 8, 5, 7, 8, 3, 9, 5, 8, 9, 9, 8, 6, 2, 8, 4, 2, 3, 6, 1, 1, 8, 9, 3, 4, 0, 7, 9, 6, 7, 1, 4, 1, 3, 4, 9, 3, 1, 4, 7, 7, 4, 7, 2, 9, 3, 0, 8, 0, 8, 4, 0, 4, 4, 1, 5, 2, 8, 3, 4, 9, 5, 2, 8, 1, 5, 3, 3, 9, 4, 2, 5, 6, 2, 5, 9, 3, 5, 9, 2, 1, 9, 8, 3, 0, 6, 9, 8, 4, 0, 4, 7, 2, 9, 0, 1, 0, 3, 1, 6, 5, 8, 1, 5, 3, 3, 0, 3, 5, 5, 9, 2, 8, 7, 0, 4, 9, 1, 9, 7, 7, 5, 5, 2, 0, 9, 1, 8, 6, 2, 3, 9, 6, 2, 1, 9, 1, 3, 5, 5, 0, 3, 9, 3, 3, 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2, 4, 5, 7, 2, 6, 4, 9, 4, 9, 4, 1, 2, 2, 5, 8, 1, 3, 2, 9, 4, 3, 8, 2, 2, 1, 2, 8, 6, 5, 1, 6, 7, 2, 1, 3, 9, 3, 8, 7, 5, 7, 0, 7, 4, 8, 8, 5, 0, 6, 6, 3, 7, 6, 9, 9, 4, 8, 4, 1, 6, 6, 6, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 7, 4, 0, 4, 0, 1, 7, 9, 5, 1, 4, 2, 8, 9, 4, 3, 7, 8, 2, 4, 4, 3, 3, 6, 9, 9, 5, 8, 6, 7, 0, 6, 8, 2, 6, 3, 9, 3, 2, 9, 6, 1, 7, 4, 8, 8, 9, 0, 3, 3, 9, 0, 5, 2, 9, 4, 1, 0, 3, 7, 5, 8, 7, 7, 8, 2, 9, 7, 1, 2, 6, 4, 2, 5, 2, 3, 6, 6, 5, 0, 0, 2, 8, 1, 6, 1, 0, 4, 3, 1, 6, 1, 9, 0, 1, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 4, 0, 0, 7, 2, 4, 3, 8, 6, 6, 3, 2, 6, 3, 3, 6, 1, 4, 7, 8, 0, 3, 1, 9, 0, 1, 9, 1, 2, 7, 0, 1, 3, 8, 2, 9, 2, 7, 6, 5, 5, 9, 9, 8, 2, 9, 1, 3, 2, 3, 4, 3, 1, 9, 0, 9, 3, 6, 8, 7, 0, 1, 0, 5, 8, 2, 7, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 7, 4, 8, 1, 5, 6, 5, 7, 2, 8, 6, 3, 3, 8, 6, 5, 4, 0, 9, 1, 7, 2, 9, 1, 5, 1, 3, 2, 2, 3, 0, 6, 4, 3, 7, 6, 9, 0, 4, 8, 1, 4, 0, 6, 1, 2, 6, 9, 2, 2, 3, 5, 5, 1, 0, 7, 7, 9, 6, 2, 9, 4, 7, 0, 2, 3, 4, 0, 0, 8, 8, 8, 5, 1, 3, 7, 4, 9, 8, 8, 9, 0, 9, 8, 9, 0, 2, 6, 5, 6, 7, 4, 7, 5, 4, 1, 3, 5, 3, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 6, 0, 1, 2, 4, 5, 6, 7, 8, 1, 7, 2, 4, 1, 4, 1, 4, 9, 6, 8, 4, 5, 3, 7, 8, 9, 3, 3, 5, 6, 7, 0, 6, 1, 6, 8, 7, 0, 1, 5, 0, 8, 6, 0, 1, 5, 8, 4, 2, 3, 9, 7, 6, 9, 1, 9, 0, 6, 7, 1, 2, 3, 9, 2, 4, 5, 5, 3, 7, 5, 3, 1, 8, 2, 2, 3, 0, 2, 9, 4, 9, 7, 0, 7, 7, 4, 9, 9, 2, 5, 9, 8, 3, 8, 6, 7, 6, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 7, 2, 6, 5, 5, 3, 7, 8, 6, 6, 6, 6, 4, 3, 8, 8, 3, 0, 1, 9, 0, 5, 4, 1, 9, 1, 2, 7, 0, 1, 3, 8, 2, 9, 2, 7, 4, 2, 6, 5, 5, 9, 9, 1, 1, 5, 7, 6, 8, 2, 9, 4, 3, 1, 9, 0, 9, 3, 6, 8, 7, 0, 1, 0, 5, 8, 2, 7, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 1, 2, 1, 3, 9, 9, 8, 5, 3, 7, 0, 7, 7, 5, 7, 9, 9, 4, 7, 0, 3, 4, 1, 5, 8, 1, 4, 8, 4, 1, 8, 6, 6, 4, 6, 0, 5, 5, 3, 3, 5, 7, 2, 5, 9, 6, 9, 2, 6, 2, 1, 2, 0, 8, 3, 8, 3, 0, 8, 7, 4, 9, 5, 0, 9, 7, 0, 0, 4, 6, 0, 9, 1, 6, 2, 7, 6, 8, 3, 5, 2, 1, 8, 3, 8, 6, 1, 0, 2, 1, 4, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 7, 6, 4, 7, 6, 2, 3, 4, 8, 7, 8, 6, 9, 8, 3, 2, 2, 8, 4, 8, 5, 6, 5, 0, 2, 0, 1, 1, 2, 9, 6, 8, 2, 1, 0, 6, 5, 2, 9, 7, 6, 3, 9, 3, 7, 1, 8, 3, 8, 1, 9, 5, 5, 0, 1, 1, 9, 8, 2, 6, 0, 4, 5, 0, 3, 1, 8, 6, 7, 5, 9, 9, 3, 0, 3, 1, 4, 4, 0, 4, 9, 0, 1, 2, 3, 5, 6, 7, 8, 0, 1, 2, 3, 5, 6, 7, 8, 9, 0, 1, 2, 3, 5, 6, 7, 8, 9, 9, 7, 0, 9, 0, 1, 5, 8, 8, 0, 9, 3, 2, 7, 8, 4, 6, 1, 0, 4, 9, 4, 4, 0, 5, 0, 1, 6, 9, 3, 2, 9, 1, 6, 0, 1, 1, 8, 7, 7, 6, 3, 6, 0, 7, 2, 4, 1, 7, 0, 6, 7, 1, 2, 5, 8, 1, 8, 2, 8, 7, 6, 8, 7, 1, 6, 2, 9, 3, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 6, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 5, 7, 0, 3, 1, 6, 8, 4, 1, 5, 6, 4, 2, 7, 8, 1, 3, 4, 3, 4, 7, 2, 0, 5, 0, 1, 8, 2, 3, 2, 3, 5, 5, 7, 8, 4, 9, 9, 7, 1, 1, 9, 0, 7, 8, 3, 4, 8, 6, 3, 8, 9, 9, 6, 2, 8, 0, 1, 0, 6, 2, 3, 8, 9, 0, 7, 2, 3, 4, 5, 5, 2, 8, 5, 4, 6, 6, 6, 7, 9, 1, 8, 6, 1, 5, 3, 4, 7, 9, 4, 0, 0, 9, 1, 2, 3, 4, 8, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 9, 0, 1, 3, 1, 5, 1, 8, 4, 9, 8, 4, 6, 8, 0, 1, 1, 9, 2, 6, 6, 8, 7, 4, 2, 9, 7, 0, 2, 1, 0, 3, 6, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 6, 5, 9, 7, 0, 2, 3, 4, 3, 8, 5, 1, 5, 2, 3, 0, 1, 2, 1, 3, 2, 6, 5, 3, 0, 7, 2, 7, 4, 6, 4, 0, 5, 9, 9, 8, 9, 5, 3, 1, 7, 4, 7, 6, 5, 4, 0, 0, 6, 6, 2, 0, 6, 3, 7, 9, 4, 4, 3, 9, 2, 8, 9, 6, 0, 9, 5, 3, 8, 8, 7, 1, 4, 0, 4, 8, 5, 2, 3, 9, 0, 1, 9, 1, 5, 1, 7, 4, 8, 6, 2, 1, 6, 8, 8, 0, 1, 2, 9, 4, 7, 8, 9, 0, 1, 2, 3, 9, 6, 7, 8, 9, 0, 1, 7, 3, 4, 7, 8, 9, 1, 4, 5, 3, 3, 9, 9, 5, 4, 9, 0, 8, 4, 6, 7, 2, 7, 7, 1, 6, 4, 1, 3, 6, 2, 9, 8, 2, 3, 8, 9, 5, 8, 8, 7, 1, 7, 1, 1, 0, 3, 4, 2, 4, 4, 7, 4, 2, 7, 4, 2, 9, 2, 7, 9, 2, 1, 6, 6, 5, 3, 4, 8, 5, 9, 6, 9, 0, 6, 3, 0, 8, 1, 6, 0, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 7, 8, 9, 0, 1, 2, 3, 4, 7, 2, 5, 1, 6, 4, 3, 9, 9, 0, 9, 7, 1, 6, 4, 3, 6, 2, 2, 9, 8, 6, 5, 7, 0, 0, 1, 7, 4, 3, 2, 4, 1, 9, 7, 6, 4, 7, 7, 7, 9, 8, 4, 3, 6, 2, 6, 3, 5, 8, 0, 5, 4, 7, 1, 3, 1, 7, 9, 6, 2, 0, 9, 1, 7, 3, 3, 9, 1, 6, 4, 3, 9, 8, 2, 1, 8, 6, 4, 1, 5, 5, 6, 5, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 6, 9, 7, 0, 2, 3, 4, 3, 8, 5, 1, 3, 0, 1, 2, 1, 3, 2, 9, 7, 2, 6, 4, 0, 5, 9, 9, 8, 9, 5, 3, 8, 7, 4, 7, 0, 0, 6, 6, 6, 3, 7, 9, 2, 8, 8, 8, 7, 1, 4, 0, 4, 8, 5, 2, 3, 9, 0, 1, 9, 1, 5, 1, 7, 6, 1, 2, 1, 6, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 5, 6, 7, 8, 1, 0, 4, 5, 6, 6, 3, 4, 4, 2, 8, 1, 0, 6, 4, 9, 7, 2, 9, 2, 0, 9, 3, 3, 9, 1, 5, 2, 3, 1, 6, 7, 3, 7, 8, 4, 0, 2, 4, 0, 2, 4, 7, 8, 0, 7, 0, 6, 9, 3, 2, 4, 8, 6, 0, 5, 7, 5, 1, 0, 8, 1, 6, 7, 2, 9, 7, 9, 5, 6, 5, 2, 6, 2, 8, 1, 7, 5, 5, 7, 3, 5, 0, 1, 1, 3, 8, 4, 9, 4, 5, 1, 8, 6, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 3, 5, 3, 2, 9, 3, 2, 1, 4, 5, 5, 2, 3, 2, 1, 3, 9, 7, 2, 1, 2, 8, 9, 1, 8, 8, 7, 8, 1, 0, 0, 6, 7, 7, 8, 7, 5, 0, 6, 1, 5, 7, 4, 6, 1, 2, 5, 0, 7, 9, 9, 0, 3, 4, 4, 8, 4, 1, 8, 6, 5, 9, 0, 0, 0, 3, 7, 1, 6, 4, 6, 0, 4, 5, 4, 1, 3, 8, 6, 3, 9, 9, 5, 9, 3, 7, 8, 5, 6, 4, 7, 6, 2, 2, 0, 9, 4, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 6, 4, 2, 6, 4, 7, 5, 5, 4, 7, 2, 9, 3, 9, 3, 8, 2, 0, 9, 5, 6, 0, 1, 0, 6, 5, 3, 5, 3, 8, 0, 0, 3, 4, 1, 6, 3, 0, 8, 3, 0, 6, 2, 7, 8, 1, 7, 1, 3, 8, 5, 4, 2, 0, 9, 7, 6, 7, 4, 1, 6, 2, 6, 7, 1, 9, 8, 0, 6, 9, 4, 9, 9, 6, 2, 3, 9, 1, 9, 2, 2, 5, 3, 7, 8, 0, 1, 2, 3, 4, 7, 8, 9, 0, 1, 2, 3, 4, 7, 8, 9, 0, 1, 7, 8, 9, 8, 9, 2, 6, 1, 3, 5, 4, 8, 2, 6, 4, 3, 4, 5, 9, 2, 0, 3, 9, 4, 9, 7, 3, 8, 7, 4, 4, 9, 8, 5, 8, 2, 6, 6, 2, 3, 1, 3, 2, 7, 3, 1, 9, 0, 1, 1, 3, 5, 0, 7, 8, 1, 5, 1, 4, 6, 0, 0, 4, 9, 1, 6, 6, 9, 0, 7, 6, 1, 1, 0, 1, 2, 3, 4, 2, 2, 3, 4, 5, 6, 2, 0, 1, 2, 2, 8, 6, 3, 9, 2, 1, 9, 3, 9, 6, 1, 7, 2, 4, 4, 5, 7, 0, 0, 1, 6, 6, 8, 2, 7, 7, 2, 4, 2, 1, 6, 1, 0, 6, 9, 8, 3, 9, 6, 3, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 8, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 6, 8, 9, 9, 0, 1, 2, 4, 4, 3, 7, 4, 4, 4, 0, 3, 8, 7, 5, 8, 2, 1, 7, 5, 3, 8, 5, 2, 5, 1, 1, 6, 2, 1, 3, 8, 6, 4, 2, 6, 2, 5, 5, 0, 2, 8, 0, 6, 8, 1, 7, 9, 1, 9, 2, 6, 7, 6, 6, 8, 7, 4, 9, 2, 1, 3, 3, 0, 5, 5, 8, 0, 3, 7, 9, 7, 0, 2, 7, 9, 1, 7, 8, 0, 3, 5, 3, 6, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 9, 4, 7, 8, 9, 6, 4, 2, 6, 4, 7, 8, 9, 2, 9, 3, 9, 3, 0, 0, 1, 0, 4, 2, 6, 3, 5, 3, 0, 3, 4, 1, 5, 3, 0, 8, 3, 0, 6, 1, 7, 8, 0, 9, 2, 6, 7, 1, 9, 6, 9, 4, 9, 9, 6, 7, 1, 2, 5, 3, 7, 8, 0, 1, 2, 4, 5, 6, 7, 8, 9, 0, 1, 3, 4, 5, 6, 7, 8, 0, 1, 3, 4, 7, 8, 9, 7, 5, 5, 1, 9, 9, 7, 1, 0, 0, 5, 9, 7, 1, 7, 2, 2, 3, 6, 8, 3, 2, 0, 0, 6, 1, 7, 5, 8, 6, 2, 9, 4, 8, 8, 7, 1, 0, 8, 7, 7, 5, 8, 5, 3, 4, 6, 1, 1, 5, 5, 0, 7, 2, 3, 6, 4, 1, 2, 4, 1, 5, 4, 2, 0, 4, 8, 6, 1, 9, 0, 2, 5, 6, 9, 3, 6, 3, 6, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 5, 6, 7, 8, 1, 0, 9, 5, 7, 5, 1, 8, 6, 9, 0, 4, 1, 9, 3, 8, 4, 4, 7, 0, 1, 9, 2, 8, 7, 8, 3, 5, 9, 6, 0, 6, 5, 5, 3, 3, 3, 9, 8, 1, 1, 0, 6, 1, 0, 0, 6, 2, 1, 1, 3, 2, 7, 7, 8, 8, 7, 8, 4, 6, 0, 2, 0, 7, 0, 3, 6, 8, 7, 1, 3, 9, 9, 3, 7, 2, 4, 9, 4, 3, 6, 2, 2, 5, 3, 2, 5, 5, 9, 4, 1, 7, 2, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 8, 6, 7, 8, 4, 1, 0, 1, 2, 7, 5, 3, 4, 4, 0, 0, 6, 9, 6, 6, 5, 9, 2, 3, 4, 4, 9, 1, 4, 0, 7, 9, 5, 7, 2, 3, 1, 4, 4, 0, 9, 9, 6, 1, 8, 3, 3, 7, 3, 9, 8, 8, 4, 7, 7, 6, 2, 1, 9, 8, 7, 8, 8, 7, 2, 2, 3, 9, 3, 3, 5, 5, 0, 7, 4, 5, 6, 5, 1, 4, 1, 1, 2, 8, 2, 6, 1, 5, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 8, 0, 6, 0, 8, 2, 3, 7, 9, 4, 7, 1, 9, 1, 7, 1, 4, 0, 0, 1, 7, 5, 7, 1, 3, 3, 3, 1, 6, 9, 7, 1, 3, 0, 7, 6, 0, 8, 9, 4, 3, 5, 4, 8, 1, 5, 9, 0, 6, 3, 3, 8, 1, 4, 7, 5, 2, 0, 0, 1, 7, 8, 9, 6, 8, 8, 2, 3, 6, 1, 2, 9, 5, 2, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 6, 6, 7, 8, 9, 7, 4, 6, 1, 4, 0, 9, 9, 8, 7, 8, 2, 7, 5, 8, 6, 3, 9, 0, 0, 5, 8, 6, 0, 3, 8, 1, 0, 3, 0, 4, 7, 4, 9, 0, 9, 6, 7, 1, 7, 1, 6, 6, 0, 6, 0, 8, 7, 6, 4, 9, 9, 5, 3, 7, 4, 3, 0, 4, 6, 6, 1, 1, 3, 2, 1, 9, 0, 1, 2, 3, 4, 7, 8, 4, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 7, 8, 9, 0, 8, 3, 9, 5, 5, 3, 6, 8, 4, 1, 7, 1, 3, 3, 5, 6, 9, 1, 1, 1, 2, 1, 8, 0, 7, 7, 5, 8, 2, 9, 8, 6, 7, 3, 4, 6, 8, 7, 0, 4, 8, 7, 7, 5, 4, 3, 4, 2, 8, 1, 5, 1, 0, 2, 3, 3, 5, 7, 0, 6, 8, 6, 3, 9, 9, 8, 2, 7, 7, 1, 0, 1, 7, 8, 9, 0, 1, 0, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 9, 8, 9, 7, 8, 6, 4, 1, 9, 3, 8, 4, 4, 9, 0, 1, 9, 2, 8, 7, 8, 2, 6, 0, 6, 5, 3, 3, 5, 9, 1, 4, 0, 6, 1, 0, 0, 6, 2, 1, 1, 7, 7, 8, 4, 6, 0, 7, 0, 3, 6, 8, 7, 1, 5, 2, 4, 9, 4, 3, 6, 4, 1, 9, 2, 6, 6, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Y_test => True labels\n",
        "\n",
        "Y_pred_labels => Predicted labels"
      ],
      "metadata": {
        "id": "tTDbgI6PRLdq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Confusion Matrix**"
      ],
      "metadata": {
        "id": "t3pzlqq9RSvD"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "conf_mat = confusion_matrix(Y_test,Y_pred_labels)"
      ],
      "metadata": {
        "id": "0s27QWTYRGqB"
      },
      "execution_count": 49,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(conf_mat)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PqBfY18mReCl",
        "outputId": "d8e1915d-0834-4f9d-bf21-75a1679a0a48"
      },
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tf.Tensor(\n",
            "[[ 942    0    4    0    3    2    7    0    2   20]\n",
            " [   0 1113    0    7    0    1    5    2    7    0]\n",
            " [   7    2  978   10    5    0    7   12    9    2]\n",
            " [   0    0    3  980    1    8    0    3    4   11]\n",
            " [   0    0    4    0  956    0   11    1    0   10]\n",
            " [   4    1    0   12    5  840   16    2    8    4]\n",
            " [   2    1    0    1    6    0  945    0    1    2]\n",
            " [   1    0    7    5    1    0    0  989    3   22]\n",
            " [   4    0    3   11    4    2    3    3  936    8]\n",
            " [   2    2    0    3   12    6    0    3    7  974]], shape=(10, 10), dtype=int32)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(15,7))\n",
        "sns.heatmap(conf_mat, annot=True, fmt='d', cmap='Blues')\n",
        "plt.ylabel('True Labels')\n",
        "plt.xlabel('Predicted Labels')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 627
        },
        "id": "_vYRNzVsRg41",
        "outputId": "8f566efe-fc21-4c84-cd0a-d63cd12157ff"
      },
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 47.7222222222222, 'Predicted Labels')"
            ]
          },
          "metadata": {},
          "execution_count": 51
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x700 with 2 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "_ghTRbwuRtYl"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}