{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a9d0dadb",
   "metadata": {
    "_cell_guid": "b1076dfc-b9ad-4769-8c92-a6c4dae69d19",
    "_uuid": "8f2839f25d086af736a60e9eeb907d3b93b6e0e5",
    "execution": {
     "iopub.execute_input": "2024-11-27T13:06:30.121624Z",
     "iopub.status.busy": "2024-11-27T13:06:30.121250Z",
     "iopub.status.idle": "2024-11-27T13:06:30.970581Z",
     "shell.execute_reply": "2024-11-27T13:06:30.969438Z"
    },
    "papermill": {
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     "exception": false,
     "start_time": "2024-11-27T13:06:30.117404",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/kaggle/input/dynamic-relationship-expansion-dre/pytorch/organized-chaos/2/dynamic-relationship-expansion-dre\n",
      "/kaggle/input/arc-prize-2024/arc-agi_training_solutions.json\n",
      "/kaggle/input/arc-prize-2024/arc-agi_evaluation_solutions.json\n",
      "/kaggle/input/arc-prize-2024/arc-agi_evaluation_challenges.json\n",
      "/kaggle/input/arc-prize-2024/sample_submission.json\n",
      "/kaggle/input/arc-prize-2024/arc-agi_training_challenges.json\n",
      "/kaggle/input/arc-prize-2024/arc-agi_test_challenges.json\n"
     ]
    }
   ],
   "source": [
    "# This Python 3 environment comes with many helpful analytics libraries installed\n",
    "# It is defined by the kaggle/python Docker image: https://github.com/kaggle/docker-python\n",
    "# For example, here's several helpful packages to load\n",
    "\n",
    "import numpy as np # linear algebra\n",
    "import pandas as pd # data processing, CSV file I/O (e.g. pd.read_csv)\n",
    "\n",
    "# Input data files are available in the read-only \"../input/\" directory\n",
    "# For example, running this (by clicking run or pressing Shift+Enter) will list all files under the input directory\n",
    "\n",
    "import os\n",
    "for dirname, _, filenames in os.walk('/kaggle/input'):\n",
    "    for filename in filenames:\n",
    "        print(os.path.join(dirname, filename))\n",
    "\n",
    "# You can write up to 20GB to the current directory (/kaggle/working/) that gets preserved as output when you create a version using \"Save & Run All\" \n",
    "# You can also write temporary files to /kaggle/temp/, but they won't be saved outside of the current session"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9b31f371",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-11-27T13:06:30.980234Z",
     "iopub.status.busy": "2024-11-27T13:06:30.979240Z",
     "iopub.status.idle": "2024-11-27T13:06:32.064405Z",
     "shell.execute_reply": "2024-11-27T13:06:32.063267Z"
    },
    "papermill": {
     "duration": 1.091209,
     "end_time": "2024-11-27T13:06:32.066540",
     "exception": false,
     "start_time": "2024-11-27T13:06:30.975331",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Captured changes for Training Example 0:\n",
      "Scaled Input:\n",
      "[[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]]\n",
      "Scaled Output:\n",
      "[[1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]]\n",
      "Detected Changes:\n",
      "[[0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]]\n",
      "--------------------------------------------------\n",
      "Captured changes for Training Example 1:\n",
      "Scaled Input:\n",
      "[[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]]\n",
      "Scaled Output:\n",
      "[[1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]]\n",
      "Detected Changes:\n",
      "[[0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]]\n",
      "--------------------------------------------------\n",
      "Captured changes for Training Example 2:\n",
      "Scaled Input:\n",
      "[[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]]\n",
      "Scaled Output:\n",
      "[[0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]]\n",
      "Detected Changes:\n",
      "[[0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]]\n",
      "--------------------------------------------------\n",
      "Captured changes for Training Example 3:\n",
      "Scaled Input:\n",
      "[[1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]]\n",
      "Scaled Output:\n",
      "[[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]]\n",
      "Detected Changes:\n",
      "[[0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]]\n",
      "--------------------------------------------------\n",
      "Final Cumulative State Change Matrix:\n",
      "[[0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]]\n",
      "==================================================\n",
      "Initial Scaled Test Input:\n",
      "[[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]]\n",
      "Final Predicted Output after applying state changes:\n",
      "[[1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]]\n",
      "Predicted Output:\n",
      "[[1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0]]\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.ndimage import zoom\n",
    "\n",
    "TARGET_SIZE = (30, 30)  # Define the target size for consistent scaling\n",
    "\n",
    "# Function to scale an input to the target size\n",
    "def scale_to_target(matrix):\n",
    "    scaling_factor = (TARGET_SIZE[0] / matrix.shape[0], TARGET_SIZE[1] / matrix.shape[1])\n",
    "    return zoom(matrix, scaling_factor, order=0)\n",
    "\n",
    "# Function to capture cumulative state changes from training data\n",
    "def capture_state_changes(train_inputs, train_outputs):\n",
    "    # Initialize the state change matrix as a neutral matrix (zeros)\n",
    "    state_change_matrix = np.zeros(TARGET_SIZE, dtype=int)\n",
    "    \n",
    "    # Iterate through each pair of scaled training inputs and outputs\n",
    "    for i, (input_matrix, output_matrix) in enumerate(zip(train_inputs, train_outputs)):\n",
    "        # Scale input and output to the target size\n",
    "        scaled_input = scale_to_target(input_matrix)\n",
    "        scaled_output = scale_to_target(output_matrix)\n",
    "        \n",
    "        # Compute the state changes (where input and output differ)\n",
    "        changes = (scaled_output != scaled_input).astype(int)\n",
    "        \n",
    "        # Accumulate these changes into the state change matrix\n",
    "        state_change_matrix += changes\n",
    "        \n",
    "        print(f\"Captured changes for Training Example {i}:\")\n",
    "        print(f\"Scaled Input:\\n{scaled_input}\")\n",
    "        print(f\"Scaled Output:\\n{scaled_output}\")\n",
    "        print(f\"Detected Changes:\\n{changes}\")\n",
    "        print(\"-\" * 50)\n",
    "    \n",
    "    # Since multiple transformations may overlap, apply modulo 2 to only capture the final state\n",
    "    state_change_matrix %= 2  # Ensures we're left with 0 or 1 states\n",
    "    \n",
    "    print(\"Final Cumulative State Change Matrix:\")\n",
    "    print(state_change_matrix)\n",
    "    print(\"=\" * 50)\n",
    "    \n",
    "    return state_change_matrix\n",
    "\n",
    "# Function to apply the cumulative state change matrix to a test input\n",
    "def apply_state_changes(test_input, state_change_matrix):\n",
    "    # Scale test input to the target size\n",
    "    scaled_test_input = scale_to_target(test_input)\n",
    "    \n",
    "    print(\"Initial Scaled Test Input:\")\n",
    "    print(scaled_test_input)\n",
    "    \n",
    "    # Apply the cumulative state change matrix\n",
    "    final_output = (scaled_test_input + state_change_matrix) % 2  # Flip based on state changes\n",
    "    \n",
    "    print(\"Final Predicted Output after applying state changes:\")\n",
    "    print(final_output)\n",
    "    \n",
    "    return final_output\n",
    "\n",
    "# Sample task data for testing\n",
    "train_inputs = [\n",
    "    np.array([[1, 1], [0, 0]]),\n",
    "    np.array([[1, 1, 0], [0, 1, 1], [1, 0, 1]]),\n",
    "    np.array([[0, 1], [1, 0]]),\n",
    "    np.array([[1, 0, 0], [0, 1, 1]])\n",
    "]\n",
    "\n",
    "train_outputs = [\n",
    "    np.array([[1, 0, 0, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0]]),\n",
    "    np.array([[1, 0, 1], [0, 0, 0], [1, 0, 1]]),\n",
    "    np.array([[0, 1, 0], [1, 0, 1], [0, 1, 0]]),\n",
    "    np.array([[1, 1, 1, 1], [0, 0, 1, 1], [1, 1, 0, 0]])\n",
    "]\n",
    "\n",
    "test_input = np.array([[1, 1], [0, 1]])\n",
    "\n",
    "# Capture state changes from training data\n",
    "state_change_matrix = capture_state_changes(train_inputs, train_outputs)\n",
    "\n",
    "# Apply state changes to the test input\n",
    "predicted_output = apply_state_changes(test_input, state_change_matrix)\n",
    "\n",
    "# Display the final predicted output\n",
    "print(\"Predicted Output:\")\n",
    "print(predicted_output)\n",
    "\n",
    "# Visualize the transformation sequence\n",
    "fig, axes = plt.subplots(1, 3, figsize=(15, 5))\n",
    "axes[0].imshow(test_input, cmap='viridis')\n",
    "axes[0].set_title(\"Test Input\")\n",
    "\n",
    "axes[1].imshow(state_change_matrix, cmap='viridis')\n",
    "axes[1].set_title(\"Cumulative State Changes\")\n",
    "\n",
    "axes[2].imshow(predicted_output, cmap='viridis')\n",
    "axes[2].set_title(\"Predicted Output\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f75a4a23",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-11-27T13:06:32.075519Z",
     "iopub.status.busy": "2024-11-27T13:06:32.074983Z",
     "iopub.status.idle": "2024-11-27T13:06:32.583378Z",
     "shell.execute_reply": "2024-11-27T13:06:32.582191Z"
    },
    "papermill": {
     "duration": 0.515397,
     "end_time": "2024-11-27T13:06:32.585520",
     "exception": false,
     "start_time": "2024-11-27T13:06:32.070123",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Captured changes for Training Example 0:\n",
      "Scaled Input:\n",
      "[[0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 1 1 1 1 1 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 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]]\n",
      "Scaled Output:\n",
      "[[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 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 1 1 1 1 1 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 1 1 1 1 1 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 1 1 1 1 1 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 1 1 1 1 1 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 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 1 1 1 1 1 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 1 1 1 1 1 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 1 1 1 1 1 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 1 1 1 1 1 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 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]]\n",
      "Detected Changes:\n",
      "[[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 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 1 1 1 1 1 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 1 1 1 1 1 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 1 1 1 1 1 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 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]]\n",
      "--------------------------------------------------\n",
      "Captured changes for Training Example 1:\n",
      "Scaled Input:\n",
      "[[0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 1 1 1 1 1 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 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1]]\n",
      "Scaled Output:\n",
      "[[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]]\n",
      "Detected Changes:\n",
      "[[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1]]\n",
      "--------------------------------------------------\n",
      "Final Cumulative State Change Matrix with Colors:\n",
      "[[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 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 0 0 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 0 0 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 0 0 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 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]]\n",
      "==================================================\n",
      "Initial Scaled Test Input:\n",
      "[[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1]\n",
      " [1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 0 0 0 0 0 0 0 0 0 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 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]]\n",
      "Final Predicted Output after applying state changes with colors:\n",
      "[[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]]\n",
      "Predicted Output:\n",
      "[[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1 1 1 1]\n",
      " [1 1 1 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 0 0 0 0 0 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]\n",
      " [1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]]\n"
     ]
    },
    {
     "data": {
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XXIfs7Gynf6datGihrl272h+HhIQU+p2w2WyqUuXSR9C8vDydOHHCfrpeUes1YsQIhwsiF8y/YJ7btm3TiRMnNGrUKPn4/O8kg2HDhqlWrVoO81q+fLmaN2+uZs2aOfxMCk41uvKzxYcffqj8/HynfgYAXC8uLk4hISGKiIjQ0KFDVaNGDaWmpuo3v/mNw3SPPfaYw+OS7n+sXbtW58+f19ixYx1O8xs/fvw1a9u5c6fS09M1fvz4Qkf0Xj6v4lREjZJ0+vRpSVf/bFHw3JX7QWVh4MCBDu9Xx44d1alTJ33yySdlviy4F04nhGXt379fWVlZDtcOuVzBhXFvvfVW3X333Zo6dapeeeUVde/eXQMHDtT9999fLnejKtjBKVDwAfnkyZMKDAy0j7/hhhsKvbZJkyY6e/asjh8/rtDQ0DKvDUDlVLDtKfjAWR6u3PYFBQXJz89PderUKTT+xIkTZbbclStXatq0adq1a5fDNYtK8kG/OEOGDNGKFSu0efNm3XLLLTp48KC2b9+u2bNn26fZv3+/jDFFbssl2U/VuJoOHTrogw8+0Pnz5/XVV18pNTVVr7zyiu655x7t2rVLLVq0uOrrf/31VyUnJ2v+/Pn6+eefHUK3rKysay5///79kv53LZgrXd6zinve2d+pK39PpEt98vLrtOTn52vOnDl6/fXXlZ6e7vDFzuWn+hQ3z8v7rnTpVFDp0nXfLufj41PodMn9+/fru+++s18f5UoFny2GDBmiv/zlLxo5cqSeeuop9erVS3fddZfuueceewAHwLrmzp2rJk2ayMfHR/Xq1VPTpk0L/e36+Pg4nG4slXz/o2C7c2WPCAkJKRSeX6ng1EZnLy9SkTVK/wuoTp8+Xezp8yUJukqruH2pZcuWlfmy4F4IsWBZ+fn5qlu3rhYtWlTk8wUfQL28vPT+++8rLS1NH330kVavXq2HHnpIf/rTn5SWlqYaNWqUaV3F3eXq8p2LkipuJ4wjtQA4IzAwUOHh4YUueFqc0mx7itr2lWR7eD3buX//+9+688471a1bN73++usKCwtT1apVNX/+fC1evPiary/OHXfcoWrVqmnZsmW65ZZbtGzZMlWpUsV+gXTpUg/y8vLSp59+WuR6OtNbfH191aFDB3Xo0EFNmjTRiBEjtHz5ck2ePPmqrxs7dqzmz5+v8ePHKzY2VkFBQfLy8tLQoUNLdHRQwTTvvPNOkV+cXH7UUlGaNWumXbt26fz58yW+NXxJfideeOEFPfPMM3rooYf0/PPPq3bt2qpSpYrGjx9f5HqVZd/Nz89X69atNWvWrCKfj4iIkHTpKLhNmzZp/fr1+vjjj7Vq1SotXbpUPXv21D//+U+X3PESQMl17Nix0I06rnT5UaEFSrr/4UoVVWPz5s21YsUKff3118Ve5/Lrr7+WJPuXMhW9b+Pl5VVkL2BfyrMRYsGyoqOjtXbtWnXu3NnhlIri3Hzzzbr55ps1ffp0LV68WMOGDdOSJUs0cuTI6/rGvrQKvgG/3L59+1StWjV7c6lVq5ZOnTpVaLqCb04u54p1AOA++vfvrzfffFObN29WbGzsVact+Ab2yu1PUdue63U9y/r73/8uPz8/rV692uHI2vnz5xea1pltZPXq1dW/f38tX75cs2bN0tKlS9W1a1eHC4pHR0fLGKOoqCg1adKkxPO+loKdql9++eWatb///vtKSEhwuOPjuXPnCv0si3t9wQXi69at69QFdwvccccd2rx5s/7+978Xe0v60nj//ffVo0cPvf322w7jT506VejIvpKIjIyUdOmi8j169LCPv3jxog4dOuRw8d7o6Gh99dVX6tWr1zV/Z6pUqaJevXqpV69emjVrll544QX93//9n9avX1+qnycA6yvp/kfBdmf//v0Od7w9fvx4oTsEFrUMSdqzZ89VtyVX27aXd43Spc8VycnJWrhwYZEhVl5enhYvXqxatWqpc+fOkpzr+dfaBhe3L3X5Eba1atUq8hIGVy6P/SjPwvHQsKx7771XeXl5ev755ws9d/HiRfvG8eTJk4US+Hbt2kmS/dSTgruNFBUYlZfNmzc7XNsjIyNDH374oXr37m3/Bjc6OlpZWVn2bzGkSzs2qampheZXvXr1Cq0fgHt54oknVL16dY0cOVLHjh0r9PzBgwftt+4ODAxUnTp1tGnTJodpXn/99TKvq+DD+uXLysvL05tvvnnN13p7e8vLy8vhG9VDhw7Z7yB3OWe3kUOGDNGRI0f0l7/8RV999ZWGDBni8Pxdd90lb29vTZ06tVCPMcZc85TJ9evXF/ntcMG1PJo2bXrN2r29vQvN47XXXiv0DXP16tUlFe5x8fHxCgwM1AsvvFDkNSOPHz9+1XV49NFHFRYWpt///vfat29foeczMzM1bdq0q86jKEWt1/Lly/Xzzz87PS/pUjAYHByst956SxcvXrSPX7RoUaEdtXvvvVc///yz3nrrrULz+fXXX5WTkyNJ+u9//1vo+Ss/WwDwPCXd/4iLi1PVqlX12muvOWzPLj8tvTg33XSToqKiNHv27ELb7cvnVdy2vSJqlKRbbrlFcXFxmj9/vlauXFno+f/7v//Tvn379MQTT9jDtMjISHl7e5fo80Vx61dgxYoVDn3hyy+/1JYtW9S3b1/7uOjoaH3//fcO/eyrr74qdCdZV+wLovxwJBYs69Zbb9Ujjzyi5ORk7dq1S71791bVqlW1f/9+LV++XHPmzNE999yjv/3tb3r99dc1aNAgRUdH6/Tp03rrrbcUGBiofv36Sbp0WkCLFi20dOlSNWnSRLVr11arVq1KfS56SbRq1Urx8fEaN26cbDabfeM9depU+zRDhw7Vk08+qUGDBmncuHH2W583adKk0MVtY2JitHbtWs2aNUvh4eGKiopSp06dyq1+AO4lOjpaixcv1pAhQ9S8eXM9+OCDatWqlc6fP68vvvhCy5cv1/Dhw+3Tjxw5UjNmzNDIkSPVvn17bdq0qcig4nq1bNlSN998s5KSkvTf//5XtWvX1pIlSxzChuLcfvvtmjVrlvr06aP7779fmZmZmjt3rho3buwQ/kvObyP79eungIAATZo0Sd7e3rr77rsdno+Ojta0adOUlJSkQ4cOaeDAgQoICFB6erpSU1M1evRoTZo0qdj5jx07VmfPntWgQYPUrFkz+/uwdOlSNWzYUCNGjLhm7f3799c777yjoKAgtWjRQps3b9batWsLXTeqXbt28vb21syZM5WVlSWbzaaePXuqbt26SklJ0W9/+1vddNNNGjp0qEJCQnT48GF9/PHH6ty5s/785z8Xuw61atVSamqq+vXrp3bt2umBBx6w37Bkx44deu+996551F9R+vfvr+eee04jRozQLbfcot27d2vRokUORwo4w9fXV1OmTNHYsWPVs2dP3XvvvTp06JAWLFig6Ohoh2/gf/vb32rZsmV69NFHtX79enXu3Fl5eXn6/vvvtWzZMq1evVrt27fXc889p02bNun2229XZGSkMjMz9frrr6t+/frq0qVLqeoEYH0l3f8ICQnRpEmTlJycrP79+6tfv37auXOnPv3002seUVqlShWlpKTojjvuULt27TRixAiFhYXp+++/1zfffKPVq1dLkn17O27cOMXHx8vb21tDhw6tkBoLLFy4UL169dKAAQN0//33q2vXrsrNzdUHH3ygDRs2aMiQIfrDH/5gnz4oKEiDBw/Wa6+9Ji8vL0VHR2vlypX263Rdrrj1K9C4cWN16dJFjz32mHJzczV79mwFBwfriSeesE/z0EMPadasWYqPj9fDDz+szMxMzZs3Ty1btnS42Lwr9gVRjir4bohAsYq7zeqbb75pYmJijL+/vwkICDCtW7c2TzzxhDly5IgxxpgdO3aY++67zzRo0MDYbDZTt25d079/f7Nt2zaH+XzxxRcmJibG+Pr6XvMWqwW3h12+fLl9XMFt5q+83XZRt4+XZBITE827775rbrjhBmOz2cyNN95Y6Hazxly6DXurVq2Mr6+vadq0qXn33Xfty7rc999/b7p162b8/f1LdFtcAJXTvn37zKhRo0zDhg2Nr6+vCQgIMJ07dzavvfaaOXfunH26s2fPmocfftgEBQWZgIAAc++995rMzMxC28fitn0JCQmmevXqhZZ/6623mpYtWzqMO3jwoImLizM2m83Uq1fPPP3002bNmjWFbsN95S2xjTHm7bfftm9HmzVrZubPn+/UNrKobXSBYcOGGUkmLi6u2J/n3//+d9OlSxdTvXp1U716ddOsWTOTmJho9u7dW+xrjDHm008/NQ899JBp1qyZqVGjhvH19TWNGzc2Y8eONceOHStR7SdPnjQjRowwderUMTVq1DDx8fHm+++/N5GRkYV6wFtvvWUaNWpkvL29C/1c169fb+Lj401QUJDx8/Mz0dHRZvjw4YX6ZHGOHDliJkyYYJo0aWL8/PxMtWrVTExMjJk+fbrJysqyTxcZGWluv/32Qq+/8hbo586dM7///e9NWFiY8ff3N507dzabN28uNF1RvdiYom/Vbowxr776qomMjDQ2m8107NjRfP755yYmJsb06dPHYbrz58+bmTNnmpYtWxqbzWZq1aplYmJizNSpU+3rs27dOjNgwAATHh5ufH19TXh4uLnvvvvMvn37SvQzA+AaBdv8rVu3XnW64npYgWvtfxhjTF5enpk6dap9W9a9e3ezZ8+eQtvogm3ZlfsBn332mbnttttMQECAqV69umnTpo157bXX7M9fvHjRjB071oSEhBgvL69Cfa8sa7ya06dPmylTppiWLVval9W5c2ezYMECk5+fX2j648ePm7vvvttUq1bN1KpVyzzyyCNmz549hbbbxa1fwTb+pZdeMn/6059MRESEsdlspmvXruarr74qtLx3333XNGrUyPj6+pp27dqZ1atXF/l5wpl9QViblzGluComgKvy8vJSYmLiVb/hBgAA5Sc/P18hISG66667ijx9EAB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      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.ndimage import zoom\n",
    "\n",
    "TARGET_SIZE = (30, 30)  # Define the target size for consistent scaling\n",
    "\n",
    "# Function to scale an input to the target size\n",
    "def scale_to_target(matrix):\n",
    "    scaling_factor = (TARGET_SIZE[0] / matrix.shape[0], TARGET_SIZE[1] / matrix.shape[1])\n",
    "    return zoom(matrix, scaling_factor, order=0)\n",
    "\n",
    "# Function to capture cumulative state changes with color tracking\n",
    "def capture_state_changes(train_inputs, train_outputs):\n",
    "    # Initialize the state change matrix as a neutral matrix (zeros)\n",
    "    state_change_matrix = np.zeros(TARGET_SIZE, dtype=int)\n",
    "    \n",
    "    # Iterate through each pair of scaled training inputs and outputs\n",
    "    for i, (input_matrix, output_matrix) in enumerate(zip(train_inputs, train_outputs)):\n",
    "        # Scale input and output to the target size\n",
    "        scaled_input = scale_to_target(input_matrix)\n",
    "        scaled_output = scale_to_target(output_matrix)\n",
    "        \n",
    "        # Compute where there are changes and update the state change matrix with output values\n",
    "        changes = (scaled_output != scaled_input)\n",
    "        state_change_matrix = np.where(changes, scaled_output, state_change_matrix)\n",
    "        \n",
    "        print(f\"Captured changes for Training Example {i}:\")\n",
    "        print(f\"Scaled Input:\\n{scaled_input}\")\n",
    "        print(f\"Scaled Output:\\n{scaled_output}\")\n",
    "        print(f\"Detected Changes:\\n{changes.astype(int)}\")  # Display as binary changes\n",
    "        print(\"-\" * 50)\n",
    "    \n",
    "    print(\"Final Cumulative State Change Matrix with Colors:\")\n",
    "    print(state_change_matrix)\n",
    "    print(\"=\" * 50)\n",
    "    \n",
    "    return state_change_matrix\n",
    "\n",
    "# Function to apply the cumulative state change matrix to a test input\n",
    "def apply_state_changes(test_input, state_change_matrix):\n",
    "    # Scale test input to the target size\n",
    "    scaled_test_input = scale_to_target(test_input)\n",
    "    print(\"Initial Scaled Test Input:\")\n",
    "    print(scaled_test_input)\n",
    "    \n",
    "    # Apply the cumulative state change matrix\n",
    "    final_output = np.where(state_change_matrix != 0, state_change_matrix, scaled_test_input)\n",
    "    \n",
    "    print(\"Final Predicted Output after applying state changes with colors:\")\n",
    "    print(final_output)\n",
    "    \n",
    "    return final_output\n",
    "\n",
    "# Replace these arrays with the ARC data examples\n",
    "train_inputs = [\n",
    "    np.array([\n",
    "        [0, 0, 0, 0, 0, 0, 0],\n",
    "        [0, 1, 0, 0, 0, 0, 0],\n",
    "        [0, 1, 1, 0, 0, 0, 0],\n",
    "        [0, 0, 0, 0, 1, 1, 0],\n",
    "        [0, 0, 0, 0, 0, 1, 0],\n",
    "        [0, 0, 0, 0, 0, 0, 0],\n",
    "        [0, 0, 0, 0, 0, 0, 0]\n",
    "    ]),\n",
    "    np.array([\n",
    "        [0, 0, 0, 0, 0, 0, 0],\n",
    "        [0, 1, 2, 0, 0, 0, 0],\n",
    "        [0, 1, 1, 0, 0, 0, 0],\n",
    "        [0, 0, 0, 0, 1, 1, 0],\n",
    "        [0, 0, 0, 0, 2, 1, 0],\n",
    "        [0, 0, 0, 0, 0, 0, 0],\n",
    "        [0, 0, 0, 0, 0, 0, 1]\n",
    "    ])\n",
    "]\n",
    "\n",
    "train_outputs = [\n",
    "    np.array([\n",
    "        [0, 0, 0, 0, 1, 1, 0],\n",
    "        [0, 0, 0, 0, 0, 1, 0],\n",
    "        [0, 0, 1, 0, 0, 0, 0],\n",
    "        [0, 0, 1, 1, 0, 0, 0],\n",
    "        [0, 0, 0, 0, 0, 0, 0],\n",
    "        [0, 0, 0, 0, 1, 0, 0],\n",
    "        [0, 0, 0, 1, 1, 0, 0]\n",
    "    ]),\n",
    "    np.array([\n",
    "        [0, 0, 0, 0, 1, 1, 0],\n",
    "        [0, 0, 0, 0, 2, 1, 0],\n",
    "        [0, 0, 1, 2, 0, 0, 0],\n",
    "        [0, 0, 1, 1, 0, 0, 0],\n",
    "        [0, 0, 0, 0, 0, 0, 0],\n",
    "        [0, 0, 0, 2, 1, 0, 0],\n",
    "        [0, 0, 0, 1, 1, 0, 0]\n",
    "    ])\n",
    "]\n",
    "\n",
    "test_input = np.array([\n",
    "    [0, 0, 0, 0, 0, 1, 1],\n",
    "    [1, 1, 0, 0, 0, 0, 1],\n",
    "    [1, 0, 0, 0, 0, 0, 0],\n",
    "    [0, 0, 0, 1, 0, 0, 0],\n",
    "    [0, 0, 0, 1, 1, 0, 0],\n",
    "    [0, 1, 0, 0, 0, 0, 0],\n",
    "    [1, 1, 0, 0, 0, 0, 0]\n",
    "])\n",
    "\n",
    "# Capture state changes from training data\n",
    "state_change_matrix = capture_state_changes(train_inputs, train_outputs)\n",
    "\n",
    "# Apply state changes to the test input\n",
    "predicted_output = apply_state_changes(test_input, state_change_matrix)\n",
    "\n",
    "# Display the final predicted output\n",
    "print(\"Predicted Output:\")\n",
    "print(predicted_output)\n",
    "\n",
    "# Visualize the transformation sequence\n",
    "fig, axes = plt.subplots(1, 3, figsize=(15, 5))\n",
    "axes[0].imshow(test_input, cmap='viridis')\n",
    "axes[0].set_title(\"Test Input\")\n",
    "\n",
    "axes[1].imshow(state_change_matrix, cmap='viridis')\n",
    "axes[1].set_title(\"Cumulative State Changes\")\n",
    "\n",
    "axes[2].imshow(predicted_output, cmap='viridis')\n",
    "axes[2].set_title(\"Predicted Output\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c18c00c",
   "metadata": {},
   "source": [
    "# All I needed to do was subtract the test input from the output... "
   ]
  }
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