import java.util.*;

public class Solution 
{
    public static void main (String[] args)
    {
        //************ALL DOCUMENTED TEST CASES**********
        //Ascending
        //float[] nums = new float[]{0f,2f,3f,4f,6f,8f,9f};   //Test case 1    PASS             
        //float[] nums = new float[]{-1f};   //Test case 2             PASS             
        //float[] nums = new float[]{0f};   //Test case 3       PASS                    
        //float[] nums = new float[]{0,1f,2,4f,5,7f};   //Test case 4    PASS            
        
        //Descending
        //float[] nums = float int[]{9f,8f,6f,4f,3f,2f,0f};    PASS            
        //float[] nums = new float[]{-1f};                PASS             
        //float[] nums = new float[]{0f};          PASS                    
        //float[] nums = new float[]{7f,5f,4f,2f,1f,0f};      PASS 
        
        //For some reason, no test cases above went through junction 8. All others are valid.
        //So these were new devised cases.....
        //float[] nums = new float[]{0f,1f,2f,4f,5f,7f,8f,10f,14f};   //Test case 4    PASS            
        //float[] nums = new float[]{0f,2f,4f,5f,7f,8f,10f,14f,17f,19f,23f,24f,25f,26f,35f,42f,43f,44f};  PASS     
        //float[] nums = new float[]{5f,4f,3f,4f,5f,7f,6f,10f,14f,17f,19f,23f,24f,25f,26f,35f,42f,47f,60f,61f};  PASS
        //float[] nums = new float[]{7f,6f,9f,3f,5f,8f};
        
        //Merging both ascending and descending code
        //float[] nums = new float[]{5f,4f,3f,4f,5f,6f,8f,8f};   PASS
        //float[] nums = new float[]{5f,4f,3f,4f,5f,7f,6f,5f,10f,14f,17f,19f,23f,24f,25f,26f,35f,34f,33f,47f};  PASS
        
        //float[] nums = new float[]{5f,6f,7f,6f,5f,9f,10f,11f,44f,45f,46f,47f,46f,45f,44f,43f,25f,24f,24f,23f,23f,22f};  //using ascending, descending and non-changing....PASS
        
        //float[] nums = new float[]{5f,9f,13f,2f,3f,4f,3f,1f,2f,3f,4f,5f,6f,22f,66f,65f,65f,64f,63f,90f,89f,60f}; //using standalone numbers in between and also ascending/descending...PASS
        //float[] nums = new float[]{1.5f,1.9f,  1.13f,  1.2f, 1.3f, 1.4f, 1.5f, 1.3f,  1.1f,  1.2f};
        
        //float[] nums = new float[]{1.5f,1.9f,  1.13f,  1.2f, 1.1f, 1.4f, 1.5f, 1.3f,  1.1f,  1.2f};
        
        //float[] nums = new float[]{2.0f,4.0f,2.0f,1.2f,1.3f,1.4f,1.3f,1.1f,1.2f,1.3f,1.4f,1.5f,1.6f,1.22f,1.66f,1.65f,1.65f,1.64f,1.63f,1.90f,1.89f,1.60f}; 
        
        //repeat numbers
        //float[] nums = new float[]{2,2,2,4,4,1,1,9,9};  PASS
        
        
        float[] nums = {
        //4.9f, 4.8f, 4.7f, 4.6f, 4.7f, 4.8f, 4.9f, 5.0f, 48.5f, 91.7f  //in test documentation,  used to test the transition 4.6
        //4.9f, 4.8f, 4.7f, 4.5f, 4.6f, 4.7f, 4.9f, 5.0f, 48.5f, 91.7f  //in test documentation , used to test 4.5f standalone merging upwards into ascending
        //0.9f, 0.8f, 0.7f, 0.6f, 0.7f, 0.8f, 0.9f, 5.0f   //test case in documentation where I resolved end of range with standalone....
        //86.0f,77.7f, 77.8f, 77.9f, 78.0f, 78.1f,78.0f, 77.9f, 77.8f, 77.7f, 25.3f, 72.8f, 42.5f   //this will be section of the ChatGPT data in order to ensure I can resolve issues quicker
        //25.3f, 72.8f,42.5f, 74.5f, 74.4f, 74.3f, 74.2f, 74.1f, 74.2f, 74.3f, 74.4f,74.5f   //this will be section of the ChatGPT data in order to ensure I can resolve issues quicker
        //47.3f, 47.2f, 47.3f, 47.4f,47.5f  //issues encountered at end of the chatGPT array. it did not merge last two items.
        
        //47.4f, 47.3f,47.4f   //realised at end of the documentation, that this is failing...
        //47.3f, 47.4f,47.3f   // NEED TO FIX THIS ALSO, resolved as part of the above one...
        //47.4f, 47.3f,47.5f  //NEED TO FIX THIS ALSO
        //47.3f, 47.4f,47.5f  //late fixes in code   -  FAIL   (this is straight forward ascending)  -  FAIL************
        //47.3f, 47.2f,47.3f,47.4f  //late fixes in code 
        //47.4f,47.3f,47.2f,47.4f  //late fixes in code
        //47.3f,47.2f,47.3f,47.4f,47.5f  //late fixes in code
        //47.3f,47.2f,47.3f //late fixes in code
         //47.2f,47.3f,47.2f //late fixes in code
        //47.2f,47.3f,47.2f,47.1f //late fixes in code
        
        //this is first chatGPT extract
        //30032025/SummaryRange/5/4/ChatGPTgeneratedNumbers.txt
        //4.9f, 4.8f, 4.7f, 4.6f, 4.7f, 4.8f, 4.9f, 5.0f, 48.5f, 91.7f, 82.9f, 57.6f, 57.5f, 57.4f, 57.3f, 57.2f, 57.3f, 57.4f, 57.5f, 57.6f, 26.1f, 25.4f, 21.2f, 83.5f, 56.3f, 56.2f, 56.1f, 56.0f, 55.9f, 55.8f, 55.7f, 55.6f, 13.9f, 35.7f, 54.8f, 54.7f, 54.6f, 54.5f, 54.6f, 54.7f, 54.8f, 54.9f, 49.9f,  9.6f, 86.0f, 77.7f, 77.8f, 77.9f, 78.0f, 78.1f, 78.0f, 77.9f, 77.8f, 77.7f, 25.3f, 72.8f, 42.5f, 74.5f, 74.4f, 74.3f, 74.2f, 74.1f, 74.2f, 74.3f, 74.4f, 74.5f, 90.6f, 30.0f, 66.5f, 11.2f, 64.2f, 64.3f, 64.4f, 64.5f, 64.6f, 64.5f, 64.4f, 64.3f, 64.2f, 18.8f, 49.3f, 60.3f, 51.1f, 52.5f, 52.4f, 52.3f, 52.2f, 52.1f, 52.0f, 51.9f, 51.8f,  1.8f, 70.5f, 69.2f, 79.8f, 86.7f, 86.6f, 86.5f, 86.4f, 86.3f, 86.4f, 86.5f, 86.6f, 86.7f, 17.9f, 80.8f, 23.9f, 89.6f, 36.0f, 35.9f, 35.8f, 35.7f, 35.6f, 35.7f, 35.8f, 35.9f, 36.0f, 95.8f, 28.9f, 71.6f,  5.3f, 60.0f, 60.1f, 60.2f, 60.3f, 60.4f, 60.3f, 60.2f, 60.1f, 60.0f, 45.2f, 16.2f, 50.6f, 34.1f, 68.4f, 68.3f, 68.2f, 68.1f, 68.0f, 67.9f, 67.8f, 67.7f, 67.6f, 89.9f, 27.1f, 14.4f, 98.9f, 63.8f, 63.9f, 64.0f, 64.1f, 64.2f, 64.1f, 64.0f, 63.9f, 63.8f, 54.8f, 22.6f, 41.1f, 91.4f, 47.9f, 47.8f, 47.7f, 47.6f, 47.5f, 47.6f, 47.7f, 47.8f, 47.9f, 58.5f, 70.8f, 11.3f, 58.6f, 58.7f, 58.8f, 58.9f, 59.0f, 58.9f, 58.8f, 58.7f, 58.6f, 35.3f, 76.8f, 44.2f, 96.7f, 52.0f, 51.9f, 51.8f, 51.7f, 51.6f, 51.5f, 51.4f, 51.3f, 51.2f, 20.3f, 93.8f, 37.8f, 61.8f, 30.6f, 30.7f, 30.8f, 30.9f, 31.0f, 30.9f, 30.8f, 30.7f, 30.6f, 12.1f, 84.4f,  2.9f, 63.2f, 69.7f, 69.6f, 69.5f, 69.4f, 69.3f, 69.4f, 69.5f, 69.6f, 69.7f, 55.4f, 81.6f, 32.4f,  6.0f, 79.8f, 79.9f, 80.0f, 80.1f, 80.2f, 80.1f, 80.0f, 79.9f, 79.8f, 88.2f, 21.3f, 45.1f, 90.3f, 42.3f, 42.2f, 42.1f, 42.0f, 41.9f, 41.8f, 41.7f, 41.6f, 41.5f, 62.9f, 97.6f, 53.1f, 24.7f, 66.0f, 65.9f, 65.8f, 65.7f, 65.6f, 65.7f, 65.8f, 65.9f, 66.0f, 49.6f, 83.5f, 38.6f, 10.4f, 77.6f, 77.5f, 77.4f, 77.3f, 77.2f, 77.3f, 77.4f, 77.5f, 77.6f,  3.1f, 60.6f, 88.0f, 92.6f, 74.6f, 74.7f, 74.8f, 74.9f, 75.0f, 74.9f, 74.8f, 74.7f, 74.6f, 31.4f, 13.4f, 55.7f, 64.5f, 50.2f, 50.1f, 50.0f, 49.9f, 49.8f, 49.9f, 50.0f, 50.1f, 50.2f, 58.0f, 67.8f, 41.3f, 96.8f, 72.3f, 72.2f, 72.1f, 72.0f, 71.9f, 71.8f, 71.7f, 71.6f, 71.5f, 29.7f, 81.9f, 18.0f, 46.4f, 34.3f, 34.4f, 34.5f, 34.6f, 34.7f, 34.6f, 34.5f, 34.4f, 34.3f, 85.7f, 14.3f, 26.5f, 56.9f, 61.6f, 61.5f, 61.4f, 61.3f, 61.2f, 61.1f, 61.0f, 60.9f, 60.8f, 43.6f, 89.0f,  7.1f, 75.2f, 39.2f, 39.1f, 39.0f, 38.9f, 38.8f, 38.9f, 39.0f, 39.1f, 39.2f, 94.9f, 23.7f, 48.2f, 87.2f, 52.8f, 52.9f, 53.0f, 53.1f, 53.2f, 53.1f, 53.0f, 52.9f, 52.8f, 12.8f, 97.0f, 20.7f, 68.9f, 73.1f, 73.0f, 72.9f, 72.8f, 72.7f, 72.6f, 72.5f, 72.4f, 72.3f, 54.6f, 15.5f, 40.1f, 30.8f, 63.5f, 63.4f, 63.3f, 63.2f, 63.1f, 63.0f, 62.9f, 62.8f, 62.7f, 49.2f,  5.9f, 91.5f, 84.7f, 51.0f, 50.9f, 50.8f, 50.7f, 50.6f, 50.7f, 50.8f, 50.9f, 51.0f, 78.7f, 36.4f, 59.9f, 95.3f, 44.9f, 44.8f, 44.7f, 44.6f, 44.5f, 44.4f, 44.3f, 44.2f, 44.1f, 83.6f, 25.9f, 32.1f, 11.1f, 67.5f, 67.4f, 67.3f, 67.2f, 67.1f, 67.2f, 67.3f, 67.4f, 67.5f, 52.7f, 98.0f, 19.5f, 60.7f, 28.1f, 28.0f, 27.9f, 27.8f, 27.7f, 27.8f, 27.9f, 28.0f, 28.1f, 70.7f, 54.5f, 13.5f, 77.1f, 41.2f, 41.1f, 41.0f, 40.9f, 40.8f, 40.7f, 40.6f, 40.5f, 40.4f, 59.4f, 90.0f,  6.7f, 85.4f, 69.5f, 69.6f, 69.7f, 69.8f, 69.9f, 70.0f, 70.1f, 70.2f, 70.3f, 38.0f, 12.4f, 95.2f, 57.1f, 50.4f, 50.3f, 50.2f, 50.1f, 50.0f, 49.9f, 49.8f, 49.7f, 49.6f, 61.7f, 27.6f, 43.1f, 83.8f, 73.4f, 73.5f, 73.6f, 73.7f, 73.8f, 73.7f, 73.6f, 73.5f, 73.4f, 16.3f, 97.2f, 21.5f, 66.2f, 47.1f, 47.2f, 47.3f, 47.4f, 47.5f, 47.4f, 47.3f, 47.2f, 47.1f, 33.5f, 76.3f, 42.9f,  4.3f, 62.4f, 62.3f, 62.2f, 62.1f, 62.0f, 61.9f, 61.8f, 61.7f, 61.6f, 82.4f, 24.4f, 58.4f,  9.7f, 90.4f, 90.3f, 90.2f, 90.1f, 90.0f, 89.9f, 89.8f, 89.7f, 89.6f, 34.9f, 14.7f, 30.2f, 96.2f, 52.4f, 52.3f, 52.2f, 52.1f, 52.0f, 51.9f, 51.8f, 51.7f, 51.6f, 71.8f, 59.2f, 10.6f, 84.2f, 63.7f, 63.8f, 63.9f, 64.0f, 64.1f, 64.0f, 63.9f, 63.8f, 63.7f, 46.6f, 18.2f, 45.4f, 82.0f, 78.6f, 78.5f, 78.4f, 78.3f, 78.2f, 78.3f, 78.4f, 78.5f, 78.6f, 95.4f, 32.6f, 23.3f, 68.8f, 41.8f, 41.7f, 41.6f, 41.5f, 41.4f, 41.3f, 41.2f, 41.1f, 41.0f, 58.9f, 27.4f, 56.1f, 88.7f, 50.8f, 50.9f, 51.0f, 51.1f, 51.2f, 51.1f, 51.0f, 50.9f, 50.8f, 12.9f, 72.1f, 33.3f, 67.9f, 74.9f, 74.8f, 74.7f, 74.6f, 74.5f, 74.6f, 74.7f, 74.8f, 74.9f, 49.0f, 21.9f, 61.2f, 93.6f, 55.3f, 55.2f, 55.1f, 55.0f, 55.1f, 55.2f, 55.3f, 55.4f, 55.5f, 43.4f, 61.0f, 47.3f, 47.4f
        
        //small extract taken from second chatGPT extract    
        //40.1f, 40.1f, 35.1f, 35.2f, 35.3f, 35.2f, 35.1f, 85.6f, 85.5f, 85.4f, 85.3f, 85.2f,19.6f, 19.7f, 19.8f, 19.9f, 20.0f, 19.9f, 19.8f, 63.5f    
   
        //this is second chatGPT extract   30032025/SummaryRange/5/4/ChatGPTgeneratedNumbersBetterDataSet.txt     
        //75.0f, 75.0f, 95.6f, 95.7f, 95.8f, 95.9f, 96.0f, 96.1f, 40.1f, 40.1f    //************************FAIL
        
        //this is second chatGPT extract
        //30032025/SummaryRange/5/4/ChatGPTgeneratedNumbersBetterDataSet.txt
        //75.0f, 75.0f, 95.6f, 95.7f, 95.8f, 95.9f, 96.0f, 96.1f, 40.1f, 40.1f,35.1f, 35.2f, 35.3f, 35.2f, 35.1f, 85.6f, 85.5f, 85.4f, 85.3f, 85.2f, 19.6f, 19.7f, 19.8f, 19.9f, 20.0f, 19.9f, 19.8f, 63.5f, 14.9f, 14.9f, 48.6f, 48.5f, 48.4f, 48.3f, 48.2f, 48.3f, 48.4f, 48.5f, 48.6f, 65.2f, 82.1f, 82.2f, 82.3f, 82.4f, 82.5f, 82.4f, 82.3f, 82.2f, 82.1f, 28.9f, 28.8f, 28.7f, 28.6f, 28.5f, 28.4f, 28.3f, 28.2f, 28.1f, 28.0f, 39.0f, 33.6f, 33.7f, 33.8f, 33.9f, 34.0f, 34.1f, 34.2f, 34.3f, 75.9f, 75.9f, 54.3f, 54.2f, 54.1f, 54.0f, 53.9f, 54.0f, 54.1f, 54.2f, 54.3f, 11.5f, 91.4f, 91.5f, 91.6f, 91.7f, 91.8f, 91.7f, 91.6f, 91.5f, 91.4f, 66.8f, 66.9f, 67.0f, 67.1f, 67.2f, 67.3f,  7.7f,  7.7f, 49.6f, 49.6f, 49.6f, 57.7f, 57.8f, 57.9f, 58.0f, 58.1f, 58.0f, 57.9f, 57.8f, 57.7f, 24.2f, 70.5f, 70.4f, 70.3f, 70.2f, 70.1f, 70.0f, 69.9f, 69.8f, 69.7f, 92.2f, 31.3f, 31.4f, 31.5f, 31.6f, 31.7f, 31.8f, 31.7f, 31.6f, 31.5f, 31.4f, 13.3f, 13.3f, 86.4f, 86.3f, 86.2f, 86.1f, 86.0f, 85.9f, 85.8f, 85.7f, 45.0f, 45.1f, 45.2f, 45.3f, 45.4f, 45.5f, 45.4f, 45.3f, 45.2f, 45.1f, 22.2f, 22.2f, 22.2f, 99.0f, 98.9f, 98.8f, 98.7f, 98.6f, 98.5f, 98.6f, 98.7f, 98.8f, 98.9f, 99.0f, 12.8f, 12.9f, 13.0f, 13.1f, 13.2f, 13.3f, 13.4f, 13.5f, 13.6f, 13.7f, 55.4f, 55.5f, 55.6f, 55.7f, 55.8f, 55.9f, 55.8f, 55.7f, 55.6f, 55.5f, 40.2f, 40.2f, 40.2f, 83.0f, 82.9f, 82.8f, 82.7f, 82.6f, 82.5f, 82.4f, 82.5f, 82.6f, 82.7f, 82.8f,30.8f, 30.9f, 31.0f, 31.1f, 31.2f, 31.1f, 31.0f, 30.9f, 30.8f, 18.5f,62.9f, 63.0f, 63.1f, 63.2f, 63.3f, 63.4f, 63.3f, 63.2f, 63.1f, 63.0f,41.2f, 41.1f, 41.0f, 40.9f, 40.8f, 40.7f, 40.6f, 40.5f, 40.4f, 40.3f,18.7f, 18.8f, 18.9f, 18.8f, 18.7f, 60.7f, 60.6f, 60.5f, 60.4f, 60.3f,60.4f, 60.5f, 60.6f, 60.7f, 71.3f, 71.4f, 71.5f, 71.6f, 71.7f, 71.6f,71.5f, 71.4f, 71.3f, 55.1f
       
       //***THESE ARE EXTRACTS FROM CHATGPT second extract.... *****
        //Trying to understand why failing after changes in code.. It now passes
        //75.9f, 75.9f, 54.3f, 54.2f, 54.1f, 54.0f, 53.9f, 54.0f, 54.1f, 54.2f, 54.3f, 11.5f  //(RESOLVED)
        //I am not sure where (53.9->54.0) has arisen from..
       //I will quickly investigate
       //[33.9->34.3, 75.9, 54.3->53.9, (53.9->54.0), 53.9->54.3, 11.5, 91.4->91.8]
       
     //34.1f,34.2f,34.3f,75.9f,75.9f,54.3f,54.2f,54.1f,54.0f,53.9f,54.0f,54.1f,54.2f,54.3f
       
       
       //focussing on 2-3 runs of ascending/descending and overlapping transition
       //*****************************************************
         
         //****PASS CASES*************************************************************************
          
         
           
          //3.5f,3.4f,3.0f,2.9f,2.5f,2.4f   //descending descending descending
          //3.5f,3.4f,3.0f,2.9f,4.5f,4.6f   //descending descending ascending
        
            //3.0f,2.7f,2.5f,2.4f,2.5f,2.6f  //changed last digit, want to see how it handles this  ****FAIL**************
            //3.5f,3.4f,3.5f,3.6f,32.1f,32.2f   //descending ascending ascending
       
            //5.0f,4.9f,4.8f  //most basic desecnding
           //47.3f, 47.4f,47.5f  //(RESOLVED)
           //47.3f, 47.4f
           //3.0f,2.7f,2.5f,2.4f,2.5f,2.6f  //(RESOLVED)
          //3.0f,2.7f,2.5f,2.4f,2.5f,4.0f  //exploring above scenario but the descend is slightly longer  ***FAIL**********  (RESOLVED)
         
          //2.5f,2.4f,2.5f
        
         //3.5f,3.6f, 3.5f, 3.6f, 3.5f,3.4f,3.0f,2.9f,2.5f,2.4f  //ascending descending ascending  descending descending descending
          //4.6f,3.5f,3.4f,3.5f,3.4f,6.7f,6.9f   //descending ascending descending        (NOW FAILS)-----------------------------
         
          //3.5f,3.6f,40.0f,40.1f   //it has not written  3.5f,3.6f,40.0f
        
        //new test cases exploring standalone repeat numbers
         
         //40.2f,40.2f,96.0f, 96.1f   //(standalone at front)
         //40.2f,40.2f,96.0f, 96.0f,33.4f   //(two standalones at front, repeat)
        //40.1f, 45.1f  //(it merges them, very basic error in my logic to resolve)
        
         //3.5f,3.6f,40.0f,40.1f   //(simple ascending, ascending)
         //3.5f,3.6f,40.0f,40.1f,56.2f   //(simple ascending, ascending, then standalone)
         //3.5f,3.6f,40.0f,40.1f,56.2f,56.3f  //ascending ascending ascending   (writing 3.5->40.1, 56.2->56.3)
         //3.5f,3.6f,40.1f,4.1f,40.0f   //ascending standalone  (it has only written standalone cases)
       
       //small extract from chatGPT2
       //75.0f, 75.0f, 95.6f, 95.7f, 95.8f, 95.9f, 96.0f, 96.1f, 40.1f, 40.1f,35.1f, 35.2f, 35.3f, 35.2f, 35.1f, 85.6f, 85.5f, 85.4f, 85.3f, 85.2f, 19.6f, 19.7f, 19.8f, 19.9f, 20.0f, 19.9f, 19.8f, 63.5f, 14.9f, 14.9f, 48.6f, 48.5f, 48.4f, 48.3f, 48.2f, 48.3f, 48.4f, 48.5f, 48.6f, 65.2f, 82.1f, 82.2f, 82.3f, 82.4f, 82.5f, 82.4f, 82.3f, 82.2f, 82.1f, 28.9f, 28.8f, 28.7f, 28.6f, 28.5f, 28.4f, 28.3f, 28.2f, 28.1f, 28.0f, 39.0f, 33.6f, 33.7f, 33.8f, 33.9f, 34.0f, 34.1f, 34.2f, 34.3f, 75.9f, 75.9f, 54.3f, 54.2f, 54.1f, 54.0f, 53.9f, 54.0f, 54.1f, 54.2f, 54.3f, 11.5f, 
       
       
       //this now fails, so it appears that it needs to perform 0000Write when k==1-
      
         //3.5f,3.6f,40.0f  // (simple ascending, then standalone)
        
        //3.0f,2.5f,2.4f,2.5f,2.8f,2.9f  //(This is fine, but the next example, it writes 2.4->2.5 twice).
        //3.0f,2.7f,2.5f,2.4f,2.5f,4.0f  //exploring above scenario but the descend is slightly longer  ***FAIL**********  (RESOLVED)
       //40.2f,40.2f,96.0f, 96.1f,3.0f,3.0f   //(standalone at end both not writteny)
       //47.3f,40.0f,40.1f,3.5f   //failing adding range twice
       //96.0f, 96.1f, 40.1f, 40.1f  //(does not write standalones at end)
       //56.0f,96.0f, 96.1f,96.2f,96.3f, 40.1f, 40.1f,40.2f,40.2f  //(does not write standalones at end due to skipping iteration)
        
        
        //LATE TEST CASES**************************************************************************
        //***ISSUE WHEN 2 DESCENDING AT END*** (RESOLVED)
         //3.5f,3.6f,3.7f,3.8f,3.7f
         //3.5f,3.6f,3.7f,3.8f,3.7f,3.9f,4.0f
        //***ISSUE WHEN 4 DESCENDING AT END***
         //3.5f,3.6f,3.7f,3.8f,3.7f,45.5f,45.4f
        //*****NO ISSUE 2 ASCENDING AT END
        //3.5f,3.4f,3.3f,3.2f,3.3f
        //*****NO ISSUE 3 DESCENDING AT END
        //3.5f,3.6f,3.7f,3.8f,3.7f,3.6f
        //Now combining lots of these together...
         //3.5f,3.6f,3.7f,3.8f,3.7f,3.5f,3.6f,3.7f,3.8f,3.7f,3.6f,3.5f,3.6f,3.7f,3.8f,3.7f,3.9f,4.0f,3.5f,3.6f,3.7f,3.8f,3.7f,45.5f,45.4f
         //3.5f,3.6f,3.7f,3.5f,3.4f,3.3f,3.2f,25.0f,25.1f,49,3f,3.33f,3.7f,3.6f
         //3.5f,3.6f,3.7f,3.8f,3.7f,45.5f,45.4f
        //3.5f,3.6f,3.7f,3.8f,3.7f,3.8f
        
        
        
        
        };
       
        System.out.println(summaryRanges(nums));
    }
    
    public static List<String> summaryRanges(float[] nums) 
    {
        boolean IsstoreFirstNotEqualNumsk=false;
        boolean includeStandalone=false;
        final float epsilon = 0.0005f;
        boolean writtenPrevious=false;   
        boolean combineMerge=false;
        String potentialfurtherAscendingBeyondThisStart="";
        String potentialfurtherAscendingBeyondThisEnd="";
        
        boolean hasNotWrittenLastNumber=true;
        
        boolean isFirstOccurenceAscendingChain=false;
        boolean isFirstOccurenceAscendingChainNoTransition =false;
        
        List<String> sm = new ArrayList<>();
        int counter = 0;
        String start="";
        String end="";
        String temp="";
        String backupStart="";
        boolean hasTransition=false;
        String transitionNumber="";
        float difference=0.1f;

        if (nums.length==1)
        {
            sm.add(String.valueOf(nums[0]));
            System.out.println("1Writing Standalone: " + nums[0]);
            return sm;
        }

        for (int k=0; k<nums.length-1;k++)
        {
            //IsstoreFirstNotEqualNumsk=false;
            System.out.println("WHEN--------------------------------------------------------------------------------------------");
            if (k==0)
            {
                start=String.valueOf(nums[k]);
            }
            
            if (nums[k]!=nums[k+1])
            {
                System.out.println("CHECKING: " + nums[k] + " with " + nums[k+1]);
                System.out.println("START: "+ start);
                
                //if (includeStandalone)
                //{
                 //       start=String.valueOf(nums[k+1]);
                  //      sm.add(start);
                //        System.out.println("Including standalone due to configuration such as: " + "3.0f,2.7f,2.5f,2.4f,2.5f,4.0f");
                 //       System.out.println("5Writing standalone: " + start);
                  //      includeStandalone=false;
                //        break;
                //}
                
                //this will ensure that if data such as  3.5f,3.6f, (3.5f, 3.6f), 3.5f,3.4f,3.0f,2.9f,2.5f,2.4f
                //is stored..
                //otherwise it will get lost since following number 3.5f is lower....
                //we also need to perform comparison with potentialfurtherAscendingBeyondThisStart since its only way to ascertain
                //if nums[k+1] is deflecting opposite direction.... in which case activate this loop
                
                //this logic needs revising
                //it stores 53.9->54.0    when it performs the check 53.9 with 54.0 (this is ok)
                //when it performs 54.3->11.5...,   it writes stored, it writes  53.9->54.3  and it writes the standalone                
                //so we need to check that if potentialfurtherAscendingBeyondThisStart==start 
                //if (Math.abs(nums[k] - (nums[k+1] + difference)) <epsilon)
                //this is checking that in stored range it is ascending
                //we can discard stored value and perform potentialfurtherAscendingBeyondThisStart -> end
                //54.3f, 54.2f, 54.1f, 54.0f, 53.9f, 54.0f, 54.1f, 54.2f, 54.3f, 11.5f
                
                //in primciple, I would need to investigate if
                //54.0f, 54.1f, 54.0f, 53.9f, 53.8f, 53.7f, 53.6f
                //we know in storage would be (54.0f->54.1f)  and then it would have 54.1->53.6
                //we can see the stored is in the same range....
                //I would have to create this scenario to see if it causes issue on the original code
                  //fliiping the scenario... (no issues);
                //75.9f, 75.9f,54.0f, 54.1f, 54.0f, 53.9f, 53.8f, 53.7f, 53.6f,11.5f
                
                System.out.println(potentialfurtherAscendingBeyondThisStart);
                System.out.println(potentialfurtherAscendingBeyondThisEnd);
                System.out.println(start);
                
                        //this is guaranteed to break out of ascending sequence
                 if (!potentialfurtherAscendingBeyondThisStart.equals("") && !(potentialfurtherAscendingBeyondThisEnd.equals("")) && nums[k+1]<=Float.valueOf(potentialfurtherAscendingBeyondThisStart))
                
                //else
                {
                    //now if the value in potentialfurtherAscendingBeyondThisStart is same as start...
                    //we do not process this
                    
                    System.out.println("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5");
                    System.out.println(potentialfurtherAscendingBeyondThisStart);
                    System.out.println(start);
                    
                    if (potentialfurtherAscendingBeyondThisStart.equals(nums[k]))
                    {
                        System.out.println("Stored value also ascending and overlap, not storing");
                    System.out.println("NO storage required");
                    System.out.println("XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX");
                    //I think it makes logical sense to also clear these values out... since it will not be using it anymore
                    //for next nums[k]
                    potentialfurtherAscendingBeyondThisStart="";
                    potentialfurtherAscendingBeyondThisEnd="";
                        
                    }   
                    /*     REMOVED LAST MOMENT - CAREFUL
                    else  //the first number in store does not equal to k    
                    {
                    System.out.println("YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYy");
                    System.out.println("using stored start");
                        sm.add(potentialfurtherAscendingBeyondThisStart+"->"+potentialfurtherAscendingBeyondThisEnd);
                        System.out.println("19731Writing range: " +potentialfurtherAscendingBeyondThisStart+"->"+potentialfurtherAscendingBeyondThisEnd);
                        potentialfurtherAscendingBeyondThisEnd="";
                        potentialfurtherAscendingBeyondThisStart="";
                        System.out.println("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!CURRENT LIST:" + sm);
                        //IsstoreFirstNotEqualNumsk=true;
                    }
                    */
                }


            
                //useful to identify the epsilon based on the difference
                System.out.println(nums[k]+difference);
                System.out.println(nums[k]-difference);
                
                
                //in descending sequence
                if (Math.abs(nums[k] - (nums[k+1] + difference)) <epsilon)
                {
                    System.out.println("HEREEEEE");
                    if (counter==0)
                    {
                        backupStart=String.valueOf(nums[k]);
                    }
                    System.out.println("COUNTER IS 0-----------------------------------------------------------------------------------------");
                    if (counter==0 && (k==nums.length-2))
                    {
                        if(!(potentialfurtherAscendingBeyondThisStart=="") && !(potentialfurtherAscendingBeyondThisEnd=="") && isFirstOccurenceAscendingChain)
                        {
                            sm.add(potentialfurtherAscendingBeyondThisStart+"->"+nums[k]);
                            System.out.println("--------------------2322USING STORED TO WRITE RANGE");
                            System.out.println("9705Writing range: " + potentialfurtherAscendingBeyondThisStart + "-> " + nums[k]);
                            potentialfurtherAscendingBeyondThisStart="";
                            potentialfurtherAscendingBeyondThisEnd="";
                        }
                        
                        
                        start=String.valueOf(nums[k]);
                        end = String.valueOf(nums[k+1]);
                        sm.add(start+"->"+end);
                        System.out.println("5Writing range: " + start + "-> " + end);
                        isFirstOccurenceAscendingChain=false;
                        isFirstOccurenceAscendingChainNoTransition =false;
                        break;
                    }
                
                    if (counter!=0 && (k==nums.length-2))
                    {
                        end=String.valueOf(nums[k+1]);
                        sm.add(start +"->"+end);
                        System.out.println("6Writing range: " + start + "-> " + end); 
                    }
                    System.out.println("HERE!!!!");
                    if (counter==0)
                    {
                        if (isFirstOccurenceAscendingChainNoTransition || isFirstOccurenceAscendingChain)
                        {
                            end=String.valueOf(nums[k]);
                            sm.add(start+"->"+end);
                            System.out.println("28Writing range: " + start + "-> " + end);
                            isFirstOccurenceAscendingChain=false;
                            isFirstOccurenceAscendingChainNoTransition =false;
                        }
                        else
                        {
                            System.out.println("IN HERE!!!!");
                            //due to design of the code, this is a location for which it can make a decision here to perform a write (3.5->3.6) for 
                            //(3.5f,3.6f),3.5f,3.6f   by performing comparison of difference. However it would need to look two numbers ahead [k+2]
                            //this is something I have not done in my code at all..
                            //also I do not believe it will cause an exception anywhere... since if there were two numbers in the array,
                            //it would be handled in area where k=nums.length-2 and break...
                            //any longer numbers where ascending part is longer than two numbers will enter into area where
                            //isFirstOccurenceAscecndingChain and isFirstOccurenceAscendingChain are processed.
                        }
                        
                        start=String.valueOf(nums[k]);
                        System.out.println("Establishing start: " + start);
                    
                        if (k==nums.length-1)
                        {
                            System.out.println("2Writing Standalone: " + start);
                            sm.add(start);
                        }
                        
                    }
                    counter++; 
                }  
                else    //not descending sequence
                {
                     
                    System.out.println("TRACK1");
                    //System.out.println("IN THIS SECTION IF THE NUM[k] and NUM[k+1] ARE ASCENDING SEQUENCE");
                    if (k==nums.length-2)
                    {
                        System.out.println("k=nums.length-2");
                        System.out.println("TRACK2");
                        if (temp!="")
                        {
                            sm.add(temp);
                            System.out.println("9Writing range: " + temp);
                            isFirstOccurenceAscendingChain=false;
                            isFirstOccurenceAscendingChainNoTransition =false;
                        }
                        if (counter==0)
                        {
                            System.out.println("TRACK BACK!!");
                            //descending
                            if (Math.abs(nums[k] - (nums[k+1] + difference)) <epsilon)
                            {
                                start=String.valueOf(nums[k]);
                                end = String.valueOf(nums[k+1]);
                                sm.add(start+"->"+end);
                                System.out.println("7Writing range: " + start + "-> " + end);
                                isFirstOccurenceAscendingChain=false;
                                isFirstOccurenceAscendingChainNoTransition =false;
                            }
                            else   //we know its definitely not descending
                            {
                                System.out.println("TRACK5");
                                end = String.valueOf(nums[k]);
                            
                                if (isFirstOccurenceAscendingChainNoTransition || isFirstOccurenceAscendingChain)
                                {
                                    System.out.println("TRACK6");
                                    if (Math.abs(nums[k] - (nums[k+1] - difference)) <epsilon)
                                    {
                                        end=String.valueOf(nums[k+1]);
                                        sm.add(start+"->"+end);
                                        System.out.println("35Writing range: " + start + "-> " + end); 
                                        hasNotWrittenLastNumber=false;
                                        isFirstOccurenceAscendingChain=false;
                                        isFirstOccurenceAscendingChainNoTransition =false;
                                    }
                                    else
                                    {
                                        System.out.println("TRACK7");
                                        end=String.valueOf(nums[k]);
                                        sm.add(start+"->"+end);
                                        System.out.println("27Writing range: " + start + "-> " + end); 
                                    }
                                }     
                                else  //it is here because neither of the key booleans are set to true...
                                {   System.out.println("TRACK8");
                                
                                    if (temp=="")
                                    {
                                        //                          prev number smaller
                                        System.out.println("TRACK9");
                                        //wide scope
                                        //we know this would be the case for  two ascending numbers only in array  47.3, 47.4 
                                        //but because we are here    (47.3),47.4 it will cause ArrayIndexOutOfBoundsException looking back..
                                        //so perhaps need something before here...
                                        //I do not want to introduce exception handling at all
                                        //we are in this section because k=nums.length-2
                                        //but it can also be k==nums.length-2 for other reason with longer array...
                                        //so need something here that specifically looks at the length of the array
                                        
                                        if (nums.length==2)
                                        {
                                            if ((Math.abs(nums[k] - (nums[k+1] + difference)) <epsilon) || (Math.abs(nums[k] - (nums[k+1] - difference)) <epsilon))
                                            {
                                                start=String.valueOf(nums[k]);
                                                end=String.valueOf(nums[k+1]);
                                                sm.add(start+"->"+end);
                                                System.out.println("2678Writing range, only two ascending numbers in array: " + start + "-> " + end);
                                                break;
                                            }
                                            else
                                            {
                                                start=String.valueOf(nums[k]);
                                                System.out.println("234Writing Standalone: " + start);
                                                sm.add(start);
                                                start=String.valueOf(nums[k+1]);
                                                sm.add(start);
                                                System.out.println("2348Writing Standalone: " + start);
                                                break;
                                            }
                                        }
                                        //3.0f,2.5f,2.4f,2.5f,2.8f,2.9f 
                                        //prev number descending
                                        if (Math.abs(nums[k] - (nums[k-1] + difference)) <epsilon)
                                        {
                                            System.out.println("TRACK9999");
                                            
                                            
                                            
                                            
                                            //next number is larger         4.0f
                                            if (Math.abs(nums[k] - (nums[k+1] - difference)) <epsilon)
                                            {
                                                 System.out.println("TRACK INSIDE");
                                                //this variable reflects scenario such as where it writes
                                                //2.5->2,4 and  2.4->2.5
                                                //it sets boolean to true
                                                
                                            
                                                if (writtenPrevious)
                                                {
                                                    System.out.println("WRITTEN PREVIOUS-------------------------------------------------------------");
                                                    //start would be at nums[k]
                                                    
                                                    //CRITICAL CHANGE IF SOMETHING GOES WRONG
                                                    start=potentialfurtherAscendingBeyondThisStart;
                                                    //start=String.valueOf(nums[k]);
                                                    
                                                    //we would capture next number in the range
                                                    end=String.valueOf(nums[k+1]);
                                                    sm.add(start+"->"+end);
                                                    System.out.println("6098Writing range: " + start + "-> " + end);
                                                    
                                                }
                                                                 //ST         EN
                                                //3.0f,2.7f,2.5f,(2.4f),2.5f,(4.0f)
                                                
                                                else  //we need to include previous number since state is !writtenPrevious
                                                      //we are still here because of ascending sequence
                                                {
                                                    start=String.valueOf(nums[k-1]);
                                                    end=String.valueOf(nums[k+1]);
                                                    sm.add(start+"->"+end);
                                                    System.out.println("9876Writing range: " + start + "-> " + end);
                                    
                                                    //START IS PREVIOUS NUMBER
                                                    //END IS NEXT NUMBER
                                                    potentialfurtherAscendingBeyondThisStart="";
                                                    potentialfurtherAscendingBeyondThisStart="";
                                                }
                                                
                                                System.out.println("TRACK12");
                                            //3.0f,2.7f,2.5f,2.4f,(2.5f),4.0f
                                            writtenPrevious=false;
                                            
                                            System.out.println("K " + k);
                                            System.out.println(nums.length);
                                            
                                            
                                            
                                            
                                                }
                                                
                                                
                                            //i think I need logic here for situation such as
                                            //3.0f,2.7f,2.5f,2.4f,(2.5f),4.0f
                                            //checking  2.5f with 4.0f
                                            //since it would realise 2.store 2.5f -> 2.4f
                                            //it would need to add this
                                            //it would perform this operation as an else to the below loop
                                            //we have to remember if the chain ended with 
                                            //3.0f,2.7f,2.5f,2.4f,(2.3.f) or //3.0f,2.7f,2.5f,2.4f,(2.6.f)
                                            //it would qualify to be in the else statement...
                                            //we would of course need to pay consideration if 
                                            //3.0f,2.7f,2.5f,2.4f,(2.6.f) since 2.6f becomes standalone
                                            
                                            //prev number is lower and next number is not greater than difference
                                            //3.0f,2.7f,2.5f,2.4f,(2.5f),4.0f
                                            else
                                            {
                                                if (writtenPrevious)
                                                {
                                                    System.out.println("6111using stored start");
                                                    sm.add(potentialfurtherAscendingBeyondThisStart+"->"+potentialfurtherAscendingBeyondThisEnd);
                                                    System.out.println("197618Writing range: " + potentialfurtherAscendingBeyondThisStart+"->"+potentialfurtherAscendingBeyondThisEnd);
                                                    writtenPrevious=false;
                                                    potentialfurtherAscendingBeyondThisStart="";
                                                    potentialfurtherAscendingBeyondThisEnd="";
                                                }
                                                //now we need to write for 2.4->2.5
                                                //3.0f,2.7f,2.5f,2.4f,(2.5f),4.0f
                                                
                                                //MASSIVE CODE CHANGE, I AM JUST GETTING RID OF THIS AREA
                                                System.out.println("NUMSK: " + nums[k]);
                                                
                                                if (k==1 && nums.length>=3 /*&& !IsstoreFirstNotEqualNumsk*/)
                                                {
                                                start=String.valueOf(nums[k-1]);
                                                end=String.valueOf(nums[k]);
                                                
                                                //CAREFUL HERE, I HAD MISSED THOSE WHOLE LINE OUT ALTOGETHER..
                                                //NO IDEA IMPACT
                                                sm.add(start+"->"+end);    
                                                
                                                System.out.println("00000Writing range: " + start+"->"+end);
                                                }
                                                
                                                
                                                    //writtenPrevious=false;
                                                    //potentialfurtherAscendingBeyondThisStart="";
                                                    //potentialfurtherAscendingBeyondThisEnd="";
                                                    
                                                    //now we are left with standalone... But I am unsure if it will always be
                                                    //single number left
                                                    //so will approach this with calculation
                                                    
                                                    if (k+1==nums.length-1)
                                                    {
                                                        start=String.valueOf(nums[k+1]);
                                                        sm.add(start);
                                                        System.out.println("0241Writing Standalone: " + start);
                                                        System.out.println("This should be last number");
                                                        break;
                                                        
                                                    }
                                                
                                            }
                                                
                                                
                                                
                                        }
                                        
                                        
                                        
                                        else  //the previously number is not smaller
                                        {
                                                 //next number is not bigger                                           //prev number is not smaller 
                                            if (!(Math.abs(nums[k] - (nums[k+1] - difference)) <epsilon))
                                            {
                                              //EXTREMELY CAREFUL THIS DOES NOT IMPACT ELSEWHERE IN ANY TESTS
                                              System.out.println("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%");
                                            start=String.valueOf(nums[k]);
                                            sm.add(start);
                                            System.out.println("009Writing Standalone: " + start);
                                            
                                            start=String.valueOf(nums[k+1]);
                                            sm.add(start);
                                            System.out.println("0089Writing Standalone: " + start);
                                            }
                                            else  //need to assume last two numbers and are ascending sequence....
                                                 //based on analysis of descending descending ascending
                                            {
                                                if(!(potentialfurtherAscendingBeyondThisStart=="") && !(potentialfurtherAscendingBeyondThisEnd=="") && isFirstOccurenceAscendingChain)
                                                {
                                                    sm.add(potentialfurtherAscendingBeyondThisStart+"->"+potentialfurtherAscendingBeyondThisEnd);
                                                    System.out.println("--------------------2322USING STORED");
                                                System.out.println("2025Writing range: " + potentialfurtherAscendingBeyondThisStart + "-> " + potentialfurtherAscendingBeyondThisEnd);
                                                }
                                                
                                                start=String.valueOf(nums[k]);
                                                end=String.valueOf(nums[k+1]);
                                                sm.add(start+"->"+end);
                                                System.out.println("1992Writing range: " + start + "-> " + end);
                                                isFirstOccurenceAscendingChain=false;
                                                isFirstOccurenceAscendingChainNoTransition=false;
                                            }
                                            
                                        }
                                        combineMerge=true;
                                    }
                                }
                            
                                if (hasNotWrittenLastNumber && !combineMerge)
                                {
                                    start=String.valueOf(nums[k+1]);
                                    System.out.println("4Writing Standalone: " + start);
                                    sm.add(start);
                                    hasNotWrittenLastNumber=false;
                                }
                            }
                        }
                        else   
                        {
                            end=String.valueOf(nums[k]);
                            sm.add(start+"->"+end);
                            System.out.println("3Writing range: " + start + "-> " + end);
                        
                            if ( (Math.abs(nums[k] - (nums[k+1] - difference)) <epsilon)   ||   (Math.abs(nums[k] - (nums[k+1] + difference)) <epsilon))
                            {
                                start=String.valueOf(nums[k]);
                                end=String.valueOf(nums[k+1]);
                                sm.add(start+"->"+end);
                                System.out.println("49Writing range: " + start + "-> " + end);
                                isFirstOccurenceAscendingChain=false;
                                isFirstOccurenceAscendingChainNoTransition =false;
                            }
                            else
                            {
                                start=String.valueOf(nums[k+1]);
                                sm.add(start);
                                System.out.println("599Writing standalone: " + start);
                            }
                        }
                    }
                    else   //k!=nums.length-2
                    {
                        System.out.println("K!=nums.length-2");
                        if (Math.abs(nums[k] - (nums[k+1] + difference)) <epsilon)
                        {
                            end=String.valueOf(nums[k+1]);
                        }
                        else
                        {
                            
                            end=String.valueOf(nums[k]);
                            System.out.println("********WRITTEN END--------------------------------------------------------------------: " + end);
                        }
                        
                        System.out.println("This is counter at the moment:  " + counter);
                        System.out.println("It is not possible to trigger hasTransition if counter is 0 since can not see transition in opposite direction");
                        
                        if (counter==0)
                        {
                            if(k==0)
                            {
                                //if it is going into descending, we need to make a decision here
                                //if there is something in the store
                                
                                //desc
                                if (Math.abs(nums[k] - (nums[k+1] + difference)) <epsilon)
                                {
                                    System.out.println("0000000000000000000000000000000000000");
                                    if (writtenPrevious)
                                    {
                                    System.out.println("7777using stored start");
                                                        sm.add(potentialfurtherAscendingBeyondThisStart+"->"+end);
                                                        System.out.println("197617Writing range: " + start+"->"+end);
                                                        writtenPrevious=false;
                                                        potentialfurtherAscendingBeyondThisStart="";
                                                        potentialfurtherAscendingBeyondThisEnd="";
                                                        
                                    }
                                
                                    start=String.valueOf(nums[k]);
                                    counter++;
                                }
                                
                                
                                else
                                {
                                    //ascendency, this is simply used on the basis of consecutive ascending numbers
                                    if (Math.abs(nums[k] - (nums[k+1] - difference)) <epsilon)
                                    {
                                        System.out.println("CURRENT START: " + start);
                                        start=String.valueOf(nums[k]);
                                        end=String.valueOf(nums[k+1]);
                                        
                                        potentialfurtherAscendingBeyondThisStart = start; 
                                        potentialfurtherAscendingBeyondThisEnd = end;
                                        System.out.println("--------------------------------------Stored start -> end: " + start + "->" + end);
                                        
                                        System.out.println("$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$CURRENT list: " + sm);
                                        //writtenPrevious=true;
                                        System.out.println("CURRENT START: " + start);
                                        
                                        //sm.add(start+"->"+end);
                                        //System.out.println("58Writing range: " + start + "-> " + end);
                                        isFirstOccurenceAscendingChain=false;
                                        isFirstOccurenceAscendingChainNoTransition =false;
                                    }
                                    else
                                    {
                                        System.out.println("5Writing standalone: " + start);
                                        sm.add(start);
                                    }
                                }
                            }
                            else
                            {
                                System.out.println("COUNTER NOT EQUAL TO 0");
                                
                                if (Math.abs(nums[k] - (nums[k+1] + difference)) <epsilon)
                                {
                                    if (temp=="")
                                    {
                                        if (Math.abs(nums[k] - (nums[k-1] + difference)) <epsilon)
                                        {
                                            backupStart=String.valueOf(nums[k-1]);
                                        }
                                        else
                                        {
                                            backupStart=String.valueOf(nums[k]);
                                        }
                                    
                                        temp=backupStart+"->"+end;
                                        hasTransition=false;
                                        System.out.println(" 1hasTransition set back to false");
                                    }
                                    else
                                    {
                                        end=String.valueOf(nums[k+1]);
                                        temp=backupStart+"->"+end;
                                        hasTransition=false;
                                        System.out.println(" 2hasTransition set back to false");
                                    }
                                    System.out.println("8Storing range: " + temp);
                                }
                                else
                                {
                                    System.out.println("NOT DESCENDING SEQUENCE------");
                                    if(temp!="")
                                    {
                                        sm.add(temp);
                                        System.out.println("8Writing range: " + temp);
                                        temp="";
                                        backupStart="";
                                        isFirstOccurenceAscendingChain=false;
                                        isFirstOccurenceAscendingChainNoTransition =false;
                                    }
                                    else
                                    {
                                        System.out.println("TEMP IS BLANK");
                                        
                    if ((Math.abs(nums[k] - (nums[k-1] + difference)) <epsilon) ||   (Math.abs(nums[k] - (nums[k+1] - difference)) <epsilon))
                                        {
                                            System.out.println("LAST ITEM SMALLER OR NEXT ITEM BIGGER");
                                            end = String.valueOf(nums[k]);
                                            
                                            //ascending sequence
                                            if  (Math.abs(nums[k] - (nums[k+1] - difference))<epsilon)
                                            {
                                                System.out.println("NEXT ITEM IS BIGGER");
                                                if (!isFirstOccurenceAscendingChainNoTransition)
                                                {
                                                    System.out.println("NOT isFirstOccurenceAscendingChainNoTransition");
                                                    start=String.valueOf(nums[k]);
                                                    
                                                    isFirstOccurenceAscendingChainNoTransition=true;
                                                }
                if ((Math.abs(nums[k] - (nums[k-1] + difference)) <epsilon) &&   (Math.abs(nums[k] - (nums[k+1] - difference))<epsilon))
                                                    {  System.out.println("Previous number less, next number greater");
                                                        if (!isFirstOccurenceAscendingChain)
                                                        {
                                                            start=String.valueOf(nums[k-1]);
                                                            
                                                            isFirstOccurenceAscendingChain=true;
                                                        }
                                                    }
                                            }  // its here because sequence is not ascending  (3.6 with 40.0)
                                            else
                                            {
                                                System.out.println("next item is not larger");  //HERE
                                                //if (isFirstOccurenceAscendingChainNoTransition || isFirstOccurenceAscendingChain)
                                                //{
                                                    System.out.println("One of deflection booleans are set");
                                                    
                                                    if (!potentialfurtherAscendingBeyondThisStart.equals("") && !(potentialfurtherAscendingBeyondThisEnd.equals("")))
                                                    {
                                                        System.out.println("using stored start");
                                                        sm.add(start+"->"+end);
                                                        System.out.println("197619Writing range: " + start+"->"+end);
                                                    }
                                                    else
                                                    {
                                                        sm.add(start+"->"+end);
                                                        System.out.println("1541Writing range: " + start+"->"+end);
                                                    }
                                                    
                                                    potentialfurtherAscendingBeyondThisEnd="";
                                                    potentialfurtherAscendingBeyondThisStart="";
                                                    
                                        
                                                isFirstOccurenceAscendingChain=false;
                                                isFirstOccurenceAscendingChainNoTransition=false;
                                                isFirstOccurenceAscendingChain=false;
                                                isFirstOccurenceAscendingChainNoTransition =false;
                                                //}
                                            }
                                        }
                                        else  //it is here because one before is not smaller by difference
                                              // or the one in front is not bigger by difference
                                              //ie not an ascending sequence
                                        {
                                            System.out.println("NOT IN SEQUENCE WITH PREVIOUS OR AFTER");
                                            
                                            if (potentialfurtherAscendingBeyondThisStart!="" && potentialfurtherAscendingBeyondThisEnd!="")
                                            {
                                                //we need to add this first
                                                 System.out.println("using stored start");
                                                sm.add(potentialfurtherAscendingBeyondThisStart+"->"+potentialfurtherAscendingBeyondThisEnd);
                        System.out.println("888881Writing range: " +potentialfurtherAscendingBeyondThisStart+"->"+potentialfurtherAscendingBeyondThisEnd);
                        potentialfurtherAscendingBeyondThisEnd="";
                        potentialfurtherAscendingBeyondThisStart="";
                        System.out.println("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!CURRENT LIST:" + sm);
                                            }
                                            else
                                            {
                                                start = String.valueOf(nums[k]);
                                            sm.add(start);
                                            System.out.println("6Writing Standalone: " + start);
                                            isFirstOccurenceAscendingChain=false;
                                            isFirstOccurenceAscendingChainNoTransition=false;
                                            }
                                            
                                        }
                                    }  
                                }
                            }
                        }
                        else    //counter!=0              3.5, (3.4),  3.5   //we can see there is not a transition here since we are accustomed to seeing 
                                                          // the following sequence would qualify in here   3.3, 3.4, 3.3
                                                          //So we must handle the additional logic of the sequence 3.5, (3.4), 3.5 in area of code
                                                          //where 3.4f makes decision with next number.. this is in section 2writing range
                                                          //whatever happens, it has to remember to place  3.5f->3.4f first
                                                          //3.5f,(3.4f),3.5f,3.4f
                                                          
                                                        
                        {           System.out.println("counter is not zero");                         
                                            //prev number is less                                         //next number is less         
                            if ((Math.abs(nums[k] - (nums[k-1] + difference)) <epsilon)  && (Math.abs(nums[k] - (nums[k+1] + difference)) <epsilon))
                            {
                                end=String.valueOf(nums[k]);
                                sm.add(backupStart+"->"+end);
                                System.out.println("10Writing range: " + backupStart+"->"+end);
                                hasTransition=true;
                                System.out.println(" 12hasTransition set to true");
                                transitionNumber=String.valueOf(nums[k]);
                                isFirstOccurenceAscendingChain=false;
                                isFirstOccurenceAscendingChainNoTransition =false;
                            }
                            if (!hasTransition)
                            {
                                System.out.println("NO TRANSITION");
                                if (temp!="")
                                {
                                    System.out.println("TEMP!=blank");
                                    end=String.valueOf(nums[k+1]);
                                    sm.add(start+"->"+end);
                                }
                                else
                                {
                                    System.out.println("TEMP is blank");
                                    //it would be processing these at this point. It is also due to counter!=0
                                    //since it has performed (3.5f,3.4f)
                                    //We can see above that it states !hasTransition.
                                    //we can see there is transition but because the transition has happened on second number.
                                    //However looking at code above, it enters hasTransition=true when the counter!=0
                                    //so unfortunately this leaves an issue since (3.5f),3.4f is still when counter ==0
                                    //I will verify this also with output of the counter value
                                    
                                    System.out.println("COUNTER VALUE: " + counter);
                                    
                                    //3.5f,(3.4f,3.5f),3.4f 
                                    
                                    //this is going to be massively improvised
                                    //And if my chatGPT test case begins to fail, I will visit here to undo this change
                                    //basically to undo the change, I will need to remove the if
                                    //and change the else with the if
                                    //if previous number is greater, we need to write start=nums[k] and end = nums[k-1]
                                    //3.5f, (3.4f), 3.5f, 3.4f 
                                    
                                    //3.0f, (2.5f,2.4f,2.5f),2.8f,2.9f 
                                    //3.0f,2.7f,(2.5f,2.4f,2.5f),4.0f
                                    
                                    System.out.println("&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&");
                                    System.out.println("-------------------------------------------");
                                    
                                    
                                    //prev number greater                                                    //next number greater                         
                                    if ((Math.abs(nums[k] - (nums[k-1] - difference)) <epsilon) && (Math.abs(nums[k] - (nums[k+1] - difference)) <epsilon))
                                    {
                                        //I will now write the existing start ->  end  (3.5f, 3.4f)
                                        System.out.println("3121Writing range: " + start + "-> " + end);
                                        sm.add(start+"->"+end);
                                        end=String.valueOf(nums[k+1]);
                                        start=String.valueOf(nums[k]);
                                        
                                        //perhaps need to store value in variable start->end
                                        //in event that next k is greater again
                                        //3.5f,3.4f,3.5f,(3.6f),32.1f,32.2f
                                        //otherwise it will write 3.4->3.5
                                        //3.4->3.6
                                        //the chain could go on ascending long time, so no point checking for difference
                                        //such as [k+2].......
                                        
                                        potentialfurtherAscendingBeyondThisStart = start; 
                                        potentialfurtherAscendingBeyondThisEnd = end;
                                        System.out.println("--------------------------------------Stored start -> end: " + start + "->" + end);
                                        //System.out.println("9846Writing range: " + start + "-> " + end);
                                        //sm.add(start+"->"+end);
                                        System.out.println("$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$CURRENT list: " + sm);
                                        
                                        writtenPrevious=true;
                                        System.out.println("value of next k: "+ (k+1));
                                        System.out.println("last index array: "+ (nums.length-1));
                                        System.out.println("CURRENT START: " + start);
                                        //we know we have included k+1 as the end.
                                        //so if there is one number left in the array, we can set a flag
                                        if (((nums.length-1)-(k+1))==1)
                                        {
                                            includeStandalone=true;
                                        }
                                    }
                                    else
                                    {
                                    System.out.println("2Writing range: " + start + "-> " + end);
                                    
                                    sm.add(start+"->"+end);
                                    }
                                    
                                    isFirstOccurenceAscendingChain=false;
                                    isFirstOccurenceAscendingChainNoTransition =false;
                                    
                                }
                            }
                            counter=0;
                            temp="";
                            backupStart="";
                            hasTransition=false;
                            System.out.println(" 3hasTransition set back to false");
                        }
                    }
                }
            }
            
            else   //this will ensure we preserve duplicate standalone numbers
                   //need to remember that it will process up to <nums.length-1
                   //so on a sequence 40.2f,40.2f,96.0f, 96.1f,3.0f,3.0f
                   //it will reach here when 3.0f follows 3.0f
                   //it will write standalone
                   //then it will iterate...
                   //but the last 3.0f is at nums.length-1
                   //so on a specific instance when the last two are same of the entire array
                   //we need to perform action twice
            {
                if (k==(nums.length-2))
                {
                    start = String.valueOf(nums[k]);
                    sm.add(start);
                    System.out.println("07774544Writing Standalone: " + start);
                }
                start = String.valueOf(nums[k]);
                sm.add(start);
                System.out.println("019238475Writing Standalone: " + start);
            }
        }
            return sm;
    }
}