import java.util.*;

public class Solution 
{
    static int ascendingChainsComplete;
    static int descendingChainsComplete;
    static int standaloneCount;
    static String ticker="";
    static int ascendingCounter;
    static int descendingCounter;
    static boolean isStandalone=false;
    
    static int counter = 0;
    
    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
        
        //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
       
        //***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)
       
        //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,3.5f,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,3.35f,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,3f,3.2f,3.3f
        
        //used to test the ticker
        //3.5f,3.4f,3.35f,3.6f,3.7f,3.8f, 3.7f,3.5f,3.6f,3.7f,3.8f,3.7f
        // 3.5f,3.6f,3.7f,3.8f, 3.7f,  3.5f,  3.6f,3.7f,3.8f,  3.7f,3.6f,  3.5f
        //3.5f,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
        //40.1f,35.1f, 35.2f, 35.3f, 35.2f, 35.1f, 85.6f
        //3.5f,3.6f, 3.5f, 3.6f, 3.5f,3.4f,3.0f,2.9f,2.4f,2.5f
        //2.9f,2.8f,2.7f,2.6f,2.5f,2.4f,2.3f,2.4f,2.5f,2.6f,2.7f,2.8f,2.7f,4.0f
        //3.0f,3.1f,3.2f,3.3f,3.2f,3.1f,3.2f,4.0f
        
        //*****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
        //3.5f,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
        
        //3.5f,3.6f,3.5f   //it is worth focussing on most simplest example to understand
        
        
        //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
        //so need to configure variable 
        
       //3.5f,3.6f,3.5f,3.1f,3.0f,2.9f   //ascending descending descending
       //3.5f,3.6f,3.5f,3.6f   //ascending descending ascending 
       //3.5f,3.6f,3.5f,3.2f,3.1f   //ascending descending descending
       
       //Extreme late test case scenario
       // 0.1f,0.2f,0.1f
       
       //85.3f, 85.2f, 19.6f, 19.7f, 19.8f, 19.9f, 20.0f, 19.9f, 19.8f, 63.5f, 14.9f, 14.9f
       //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)
       //56.0f,96.0f, 96.1f,96.2f,96.3f, 40.1f, 40.3f,40.2f,40.2f,40.1f,40.3f,40.5f  //(does not write standalones at end due to skipping iteration)
       //28.6f, 28.5f, 28.4f, 28.3f, 28.2f, 28.1f, 28.0f, 39.0f, 33.6f, 33.7f, 33.8f,
       };
       
       int lengthNums = nums.length;
       
       System.out.println(summaryRanges(nums,lengthNums));
       
       System.out.println("Standalone numbers: " + standaloneCount + "   Ascending chains: " + ascendingChainsComplete + "   Descending chains: " + descendingChainsComplete);
    }
    
    public static String completeTicker(String start, String end, int k, int lengthNums)
    {
        if (!start.equals("END") && !end.equals("END"))
        {
            if (start.equals(end))
            {
                ticker=ticker+"S";
                standaloneCount++;
                isStandalone=true;
            }
            
            if(!isStandalone)
            {
                if (Float.valueOf(end)>Float.valueOf(start))
                {
                    if ((k==lengthNums-2))
                    {
                        ascendingCounter=ascendingCounter+1;
                    }
                    
                    ticker=ticker+"A"+"("+(ascendingCounter)+")";
                    ascendingChainsComplete++;
                    ascendingCounter=0;
                }
                else
                {
                    if (descendingCounter==0 || descendingCounter==1)
                    {
                        descendingCounter=2;
                    }
                    
                     if ((k==lengthNums-2) && descendingCounter!=2)
                    {
                        descendingCounter=descendingCounter+1;
                    }
                    
                    ticker=ticker+"D"+"("+(descendingCounter)+")";
                    descendingChainsComplete++;
                    descendingCounter=0;
                }
            }
        }
        
        isStandalone=false;
        
        return ticker;
    }
    
    public static List<String> summaryRanges(float[] nums, int lengthNums) 
    {
        boolean isPrevNumAscending=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)
        {
            start=String.valueOf(nums[0]);
            sm.add(start);
            System.out.println("1Writing Standalone: " + start);
            completeTicker(start, start,0,lengthNums);
            return sm;
        }

        for (int k=0; k<nums.length-1;k++)
        {
            if (k==0)
            {
                start=String.valueOf(nums[k]);
            }
            
            if (nums[k]!=nums[k+1])
            {
                System.out.println("\nCHECKING: " + nums[k] + " with " + nums[k+1]);
                //System.out.println("---------------------------VALS d: " + descendingCounter);
                //System.out.println("---------------------------VALS a: " + ascendingCounter);
                //System.out.println("currently in list: " + sm);
                
                 if (!potentialfurtherAscendingBeyondThisStart.equals("") 
                 && !(potentialfurtherAscendingBeyondThisEnd.equals("")) 
                 && nums[k+1]<=Float.valueOf(potentialfurtherAscendingBeyondThisStart))
                {   
                    if (potentialfurtherAscendingBeyondThisStart.equals(nums[k]))
                    {
                        System.out.println("Stored value also ascending and overlap, not storing");
                        System.out.println("NO storage required");
                        potentialfurtherAscendingBeyondThisStart="";
                        potentialfurtherAscendingBeyondThisEnd="";
                    }
                }
                
                if (Math.abs(nums[k] - (nums[k+1] + difference)) <epsilon)
                {
                    System.out.println("Descending sequence (difference)");
                    descendingCounter++;
                    
                    if (k!=0)
                    {
                        if ((Math.abs(nums[k] - (nums[k-1] + difference)) <epsilon))
                        {
                        transitionNumber=String.valueOf(nums[k]);
                        System.out.println("Transition number:" + transitionNumber + " descending(difference) on either side");
                        }
                    }
                    
                    if (counter==0)
                    {
                        backupStart=String.valueOf(nums[k]);
                    }
                    
                    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]);
                            ascendingCounter++;
                            completeTicker(start,String. valueOf(nums[k]),k,lengthNums);
                            potentialfurtherAscendingBeyondThisStart="";
                            potentialfurtherAscendingBeyondThisEnd="";
                        }
                        
                        if (sm.isEmpty() && !isFirstOccurenceAscendingChain 
                        && !(potentialfurtherAscendingBeyondThisStart=="") 
                        && !(potentialfurtherAscendingBeyondThisEnd==""))
                        {
                            sm.add(potentialfurtherAscendingBeyondThisStart+"->"+nums[k]);
                            System.out.println("--------------------1980USING STORED TO WRITE RANGE");
                            System.out.println("43434Writing range: " + potentialfurtherAscendingBeyondThisStart + "-> " + potentialfurtherAscendingBeyondThisEnd);
                            potentialfurtherAscendingBeyondThisStart="";
                            potentialfurtherAscendingBeyondThisEnd="";
                        }
                        
                        start=String.valueOf(nums[k]);
                        end = String.valueOf(nums[k+1]);
                        sm.add(start+"->"+end);
                        System.out.println("5Writing range: " + start + "-> " + end);
                        descendingCounter++;
                        completeTicker(start,end,k,lengthNums);
                        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);
                        descendingCounter++;
                        completeTicker(start,end,k,lengthNums);
                    }
                   
                    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;
                            ascendingCounter++;
                            completeTicker(start,end,k,lengthNums);
                            potentialfurtherAscendingBeyondThisEnd="";
                            potentialfurtherAscendingBeyondThisStart="";
                        }
                        else
                        {
                            if (String.valueOf(nums[k+1]).equals(potentialfurtherAscendingBeyondThisStart))
                            {
                                System.out.println("123456using stored start");
                                sm.add(potentialfurtherAscendingBeyondThisStart+"->"+potentialfurtherAscendingBeyondThisEnd);
                                System.out.println("197618Writing range: " + potentialfurtherAscendingBeyondThisStart+"->"+potentialfurtherAscendingBeyondThisEnd);
                                ascendingCounter++;
                                completeTicker(potentialfurtherAscendingBeyondThisStart,potentialfurtherAscendingBeyondThisEnd,k,lengthNums);
                                potentialfurtherAscendingBeyondThisStart="";
                                potentialfurtherAscendingBeyondThisEnd="";
                            }
                        }
                        
                        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);
                            completeTicker(start, start,k,lengthNums);
                        }
                    }
                    counter++; 
                }  
                else
                {
                    if (k==nums.length-2)
                    {
                        System.out.println("k=nums.length-2");
                        
                        if (temp!="")
                        {
                            sm.add(temp);
                            System.out.println("9Writing range: " + temp);
                            isFirstOccurenceAscendingChain=false;
                            isFirstOccurenceAscendingChainNoTransition =false;
                        }
                        if (counter==0)
                        {    
                            if (Math.abs(nums[k] - (nums[k+1] + difference)) <epsilon)
                            {
                                System.out.println("next number descending (difference)");
                                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
                            {
                                end = String.valueOf(nums[k]);
                            
                                if (isFirstOccurenceAscendingChainNoTransition || isFirstOccurenceAscendingChain)
                                {
                                    if (Math.abs(nums[k] - (nums[k+1] - difference)) <epsilon)
                                    {
                                        System.out.println("next number ascending (difference)");
                                        end=String.valueOf(nums[k+1]);
                                        sm.add(start+"->"+end);
                                        System.out.println("35Writing range: " + start + "-> " + end);
                                         ascendingCounter++;
                                         completeTicker(start,end,k,lengthNums);
                                        hasNotWrittenLastNumber=false;
                                        isFirstOccurenceAscendingChain=false;
                                        isFirstOccurenceAscendingChainNoTransition =false;
                                         ascendingCounter++;
                                    }
                                    else
                                    {
                                        end=String.valueOf(nums[k]);
                                        sm.add(start+"->"+end);
                                        System.out.println("27Writing range: " + start + "-> " + end); 
                                    }
                                }     
                                else 
                                {   
                                    if (temp=="")
                                    {
                                        if (nums.length==2)
                                        {
                                            if ((Math.abs(nums[k] - (nums[k+1] + difference)) <epsilon) 
                                            || (Math.abs(nums[k] - (nums[k+1] - difference)) <epsilon))
                                            {
                                                System.out.println("next number ascending AND/OR descending within difference");
                                                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
                                            {
                                                System.out.println("next number NOT within difference");
                                                start=String.valueOf(nums[k]);
                                                System.out.println("234Writing Standalone: " + start);
                                                completeTicker(start, start,k,lengthNums);
                                                sm.add(start);
                                                start=String.valueOf(nums[k+1]);
                                                sm.add(start);
                                                System.out.println("2348Writing Standalone: " + start);
                                                completeTicker(start, start,k,lengthNums);
                                                break;
                                            }
                                        }
                                        
                                        if (Math.abs(nums[k] - (nums[k-1] + difference)) <epsilon)
                                        {
                                            System.out.println("previous number descending (difference)");
                                            if (Math.abs(nums[k] - (nums[k+1] - difference)) <epsilon)
                                            {
                                                System.out.println("next number ascending (difference)");
                                                 ascendingCounter++;
                                                if (writtenPrevious)
                                                {
                                                    start=potentialfurtherAscendingBeyondThisStart;
                                                    
                                                    end=String.valueOf(nums[k+1]);
                                                    sm.add(start+"->"+end);
                                                    System.out.println("6098Writing range: " + start + "-> " + end);
                                                }
                                                else
                                                {
                                                    start=String.valueOf(nums[k-1]);
                                                    end=String.valueOf(nums[k+1]);
                                                    sm.add(start+"->"+end);
                                                    System.out.println("9876Writing range: " + start + "-> " + end);
                                    
                                                    potentialfurtherAscendingBeyondThisStart="";
                                                    potentialfurtherAscendingBeyondThisStart="";
                                                }
                                                
                                                writtenPrevious=false;
                                            }
                                            
                                            else
                                            {
                                                if (writtenPrevious)
                                                {
                                                    System.out.println("6111using stored start");
                                                    sm.add(potentialfurtherAscendingBeyondThisStart+"->"+potentialfurtherAscendingBeyondThisEnd);
                                                    System.out.println("197618Writing range: " + potentialfurtherAscendingBeyondThisStart+"->"+potentialfurtherAscendingBeyondThisEnd);
                                                    writtenPrevious=false;
                                                    potentialfurtherAscendingBeyondThisStart="";
                                                    potentialfurtherAscendingBeyondThisEnd="";
                                                }
                                                
                                                if (k==1 && nums.length>=3)
                                                {
                                                    start=String.valueOf(nums[k-1]);
                                                    end=String.valueOf(nums[k]);
                                                    sm.add(start+"->"+end);    
                                                
                                                    System.out.println("00000Writing range: " + start+"->"+end);
                                                }
                                                
                                                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");
                                                    completeTicker(start, start,k,lengthNums);
                                                    break;
                                                }
                                            }
                                        }
                                        else
                                        {
                                            if (!(Math.abs(nums[k] - (nums[k+1] - difference)) <epsilon))
                                            {
                                                System.out.println("previous number not descending (difference)");
                                                System.out.println("next number ascending (difference)");
                                                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);
                                                completeTicker(start, start,k,lengthNums);
                                            }
                                            else
                                            {
                                                System.out.println("previous number not within difference, next number within difference");
                                                
                                                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);
                                                ascendingCounter++;
                                                completeTicker(start,end,k,lengthNums);
                                                isFirstOccurenceAscendingChain=false;
                                                isFirstOccurenceAscendingChainNoTransition=false;
                                            }
                                        }
                                        combineMerge=true;
                                    }
                                }
                            
                                if (hasNotWrittenLastNumber && !combineMerge)
                                {
                                    start=String.valueOf(nums[k+1]);
                                    System.out.println("4Writing Standalone: " + start);
                                    sm.add(start);
                                    completeTicker(start, start,k,lengthNums);
                                    hasNotWrittenLastNumber=false;
                                }
                            }
                        }
                        else   
                        {
                            end=String.valueOf(nums[k]);
                            sm.add(start+"->"+end);
                            System.out.println("3Writing range: " + start + "-> " + end);
                            //descendingCounter++;
                            completeTicker(start,end,k,lengthNums);
                        
                            if ( (Math.abs(nums[k] - (nums[k+1] - difference)) <epsilon)   
                            ||   (Math.abs(nums[k] - (nums[k+1] + difference)) <epsilon))
                            {
                                System.out.println("ascending/descending - next number within diffference");
                                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
                            {
                                System.out.println("Next number not within difference");
                                start=String.valueOf(nums[k+1]);
                                sm.add(start);
                                System.out.println("599Writing standalone: " + start);
                                completeTicker(start, start,k,lengthNums);
                            }
                        }
                    }
                    else
                    {
                        System.out.println("K!=nums.length-2");
                            
                        if (Math.abs(nums[k] - (nums[k+1] + difference)) <epsilon)
                        {
                             System.out.println("next number descending (difference)");
                            end=String.valueOf(nums[k+1]);
                        }
                        else
                        {
                            System.out.println("next number not descending (difference)");
                            end=String.valueOf(nums[k]);
                        }
                        
                        System.out.println("This is counter at the moment:  " + counter);
                        
                        if (counter==0)
                        {
                            if(k==0)
                            {
                                if (Math.abs(nums[k] - (nums[k+1] + difference)) <epsilon)
                                {
                                    System.out.println("next number descending (difference)");
                                    
                                    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
                                {
                                    if (Math.abs(nums[k] - (nums[k+1] - difference)) <epsilon)
                                    {
                                        System.out.println("next number ascending (difference)");
                                        ascendingCounter++;
                                        start=String.valueOf(nums[k]);
                                        end=String.valueOf(nums[k+1]);
                                        
                                        potentialfurtherAscendingBeyondThisStart = start; 
                                        potentialfurtherAscendingBeyondThisEnd = end;
                                        System.out.println("--------------------------------------Stored start -> end: " + start + "->" + end);
                                        
                                        isFirstOccurenceAscendingChain=false;
                                        isFirstOccurenceAscendingChainNoTransition =false;
                                    }
                                    else
                                    {
                                        System.out.println("2next number NOT within difference");
                                        System.out.println("5Writing standalone: " + start);
                                        sm.add(start);
                                        completeTicker(start, start,k,lengthNums);
                                    }
                                }
                            }
                            else
                            {
                                System.out.println("COUNTER NOT EQUAL TO 0");
                                
                                if (Math.abs(nums[k] - (nums[k+1] + difference)) <epsilon)
                                {
                                    System.out.println("next number descending (difference)");
                                    if (temp=="")
                                    {
                                        if (Math.abs(nums[k] - (nums[k-1] + difference)) <epsilon)
                                        {
                                            System.out.println("previous number descending (difference)");
                                            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("next number not descending (difference)");
                                        
                                    if(temp!="")
                                    {
                                        sm.add(temp);
                                        System.out.println("8Writing range: " + temp);
                                        temp="";
                                        backupStart="";
                                        isFirstOccurenceAscendingChain=false;
                                        isFirstOccurenceAscendingChainNoTransition =false;
                                    }
                                    else
                                    {
                                        if ((Math.abs(nums[k] - (nums[k-1] + difference)) <epsilon) ||   
                                        (Math.abs(nums[k] - (nums[k+1] - difference)) <epsilon))
                                        {
                                            System.out.println("previous number descending AND/OR next number ascending (difference)");
                                            end = String.valueOf(nums[k]);
                                                
                                            if  (Math.abs(nums[k] - (nums[k+1] - difference))<epsilon)
                                            {
                                                System.out.println("Next number ascending");
                                                 ascendingCounter++;
                                                    
                                                if (!isFirstOccurenceAscendingChainNoTransition)
                                                {
                                                    System.out.println("NOT isFirstOccurenceAscendingChainNoTransition");
                                                    start=String.valueOf(nums[k]);
                                                    
                                                    isFirstOccurenceAscendingChainNoTransition=true;
                                                }
                                                    
                                                if (isFirstOccurenceAscendingChainNoTransition 
                                                && potentialfurtherAscendingBeyondThisStart.equals("") 
                                                && potentialfurtherAscendingBeyondThisEnd.equals(""))
                                                {
                                                    start=String.valueOf(nums[k]);
                                                    end=String.valueOf(nums[k+1]);
                                        
                                                    potentialfurtherAscendingBeyondThisStart = start; 
                                                    potentialfurtherAscendingBeyondThisEnd = end;
                                                   
                                                    System.out.println("--------------------------------------22Stored start -> end: " + start + "->" + end);
                                                }
                                                    
                                                if ((Math.abs(nums[k] - (nums[k-1] + difference)) <epsilon) 
                                                &&   (Math.abs(nums[k] - (nums[k+1] - difference))<epsilon))
                                                {
                                                    System.out.println("Previous number descending (difference) AND next number ascending (difference)");
                                                        
                                                    if (!isFirstOccurenceAscendingChain)
                                                    {
                                                        start=String.valueOf(nums[k-1]);
                                                            
                                                        isFirstOccurenceAscendingChain=true;
                                                    }
                                                }
                                            }
                                            else
                                            {
                                                System.out.println("next item is not larger (difference)");
                                                
                                                if (!potentialfurtherAscendingBeyondThisStart.equals("") 
                                                && !(potentialfurtherAscendingBeyondThisEnd.equals("")))
                                                {
                                                    System.out.println("using stored start");
                                                        sm.add(start+"->"+end);
                                                        System.out.println("197619Writing range: " + start+"->"+end);
                                                        ascendingCounter++;
                                                        completeTicker(start,end,k,lengthNums);
                                                }
                                                else
                                                {
                                                    sm.add(start+"->"+end);
                                                    System.out.println("1541Writing range: " + start+"->"+end);
                                                }
                                                    
                                                potentialfurtherAscendingBeyondThisEnd="";
                                                potentialfurtherAscendingBeyondThisStart="";
                                                    
                                                isFirstOccurenceAscendingChain=false;
                                                isFirstOccurenceAscendingChainNoTransition=false;
                                                isFirstOccurenceAscendingChain=false;
                                                isFirstOccurenceAscendingChainNoTransition =false;
                                            }
                                        }
                                        else  
                                        {
                                            System.out.println("previous number ascending OR next number descending");
                                            
                                            if (potentialfurtherAscendingBeyondThisStart!="" && potentialfurtherAscendingBeyondThisEnd!="")
                                            {
                                                System.out.println("using stored start");
                                                sm.add(potentialfurtherAscendingBeyondThisStart+"->"+potentialfurtherAscendingBeyondThisEnd);
                    System.out.println("888881Writing range: " +potentialfurtherAscendingBeyondThisStart+"->"+potentialfurtherAscendingBeyondThisEnd);
                                                potentialfurtherAscendingBeyondThisEnd="";
                                                potentialfurtherAscendingBeyondThisStart="";
                                            }
                                            else
                                            {
                                                start = String.valueOf(nums[k]);
                                                sm.add(start);
                                                System.out.println("6Writing Standalone: " + start);
                                                completeTicker(start, start,k,lengthNums);
                                                isFirstOccurenceAscendingChain=false;
                                                isFirstOccurenceAscendingChainNoTransition=false;
                                            }
                                        }
                                    }  
                                }
                            }
                        }
                        else                        
                        {
                            System.out.println("counter is not zero");                         
                                
                            if ((Math.abs(nums[k] - (nums[k-1] + difference)) <epsilon)  
                            && (Math.abs(nums[k] - (nums[k+1] + difference)) <epsilon))
                            {
                                System.out.println("next number descending (difference) AND previous number descending (difference)");
                                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]);
                                System.out.println("Transition number:" + transitionNumber + " descending(difference) on either side");
                                
                                isFirstOccurenceAscendingChain=false;
                                isFirstOccurenceAscendingChainNoTransition =false;
                            }
                            
                            if ((Math.abs(nums[k] - (nums[k-1] - difference)) <epsilon)  
                            && (Math.abs(nums[k] - (nums[k+1] - difference)) <epsilon))
                            {
                                transitionNumber=String.valueOf(nums[k]);
                                System.out.println("Transition number:" + transitionNumber + " ascending(difference) on either side");
                                System.out.println("next number ascending (difference) AND next number descending (difference");
                            }
                            
                            if (!hasTransition)
                            {
                                if (temp!="")
                                {
                                    System.out.println("TEMP!=blank");
                                    end=String.valueOf(nums[k+1]);
                                    sm.add(start+"->"+end);
                                }
                                else
                                {
                                    System.out.println("COUNTER VALUE: " + counter);
                                                     
                                    if ((Math.abs(nums[k] - (nums[k-1] - difference)) <epsilon) 
                                    && (Math.abs(nums[k] - (nums[k+1] - difference)) <epsilon))
                                    {
                                        System.out.println("previous number ascending (difference) AND next number ascending (difference)");
                                        System.out.println("3121Writing range: " + start + "-> " + end);
                                        sm.add(start+"->"+end);
                                        end=String.valueOf(nums[k+1]);
                                        start=String.valueOf(nums[k]);
                                        descendingCounter++;
                                        completeTicker(end,start,k,lengthNums);
                                        ascendingCounter++;
                                        
                                        potentialfurtherAscendingBeyondThisStart = start; 
                                        potentialfurtherAscendingBeyondThisEnd = end;
                                        System.out.println("--------------------------------------Stored start -> end: " + start + "->" + end);
                                            
                                        writtenPrevious=true;
                                     
                                        if (((nums.length-1)-(k+1))==1)
                                        {
                                            
                                        }
                                    }
                                    else
                                    {
                                        System.out.println("previous number AND/OR next number not ascending(difference)");
                                        System.out.println("2Writing range: " + start + "-> " + end);
                                    
                                        sm.add(start+"->"+end);
                                        completeTicker(start,end,k,lengthNums);
                                    }
                                    
                                    isFirstOccurenceAscendingChain=false;
                                    isFirstOccurenceAscendingChainNoTransition =false;
                                }
                            }
                            counter=0;
                            temp="";
                            backupStart="";
                            hasTransition=false;
                        }
                    }
                }
            }
            else
            {
                if (k==(nums.length-2))
                {
                    if ((Math.abs(nums[k] - (nums[k-1] - difference)) <epsilon) 
                    && potentialfurtherAscendingBeyondThisStart.equals("")  
                    && potentialfurtherAscendingBeyondThisEnd.equals(""))
                    {
                        System.out.println("Previous number ascending (difference)");
                        System.out.println("CURRENT START: " + start);
                        start=String.valueOf(nums[k-1]);
                        end=String.valueOf(nums[k]);
                                
                        System.out.println("9705Writing range: " + start + "-> " + end);
                        sm.add(start+"->"+end);
                        isPrevNumAscending=true;
                    }
                    
                    if (!potentialfurtherAscendingBeyondThisStart.equals("") 
                    && !(potentialfurtherAscendingBeyondThisEnd.equals("")))
                    {
                        sm.add(potentialfurtherAscendingBeyondThisStart+"->"+nums[k]);
                        System.out.println("--------------------23229USING STORED TO WRITE RANGE");
                        System.out.println("9705Writing range: " + potentialfurtherAscendingBeyondThisStart + "-> " + potentialfurtherAscendingBeyondThisEnd);
                        potentialfurtherAscendingBeyondThisStart="";
                        potentialfurtherAscendingBeyondThisEnd="";
                        System.out.println("CURRENT LIST: " + sm);
                    }
                    else
                    {
                        start = String.valueOf(nums[k]);
                        sm.add(start);
                        System.out.println("07774544Writing Standalone: " + start);
                        completeTicker(start, start,k,lengthNums);
                    }
                }
                
                if (!isPrevNumAscending)
                {
                    start = String.valueOf(nums[k]);
                    sm.add(start);
                    System.out.println("019238475Writing Standalone: " + start);
                    completeTicker(start, start,k,lengthNums);
                }
            }
            isPrevNumAscending=false;
        }
        System.out.println("\nTICKER: " + completeTicker("END","END",0,lengthNums));
        return sm;
    }
}