Prof. Ramish is working on the problem called The 196-Problem

Prof. Ramish is working on the problem called The 196-Problem. The problem is as follows:

 

Step 1: Take any number with atmost 3 digits.

Step 2: Form a mirror of the number choosen in step 1 by reversing it. Step 3: Add the number of step 1 and its mirror derived in step 2.

 

It may happen that the sum calculated in step 3 is palindromic number. A number N is palindromic if by reversing the digits of N we get the same number N. If the sum calculated in step 3 is not palindromic number then take the mirror of the sum and add it into the sum. Perhaps the now the new sum may be palindromic number. If it is not then repeat the process again.

 

At the end nearly all numbers lead to a palindromic number. There may be some numbers which may not lead to a palindromic number.

 

-  Can you help Prof. Ramish by writing a program which takes a number with atmost 3 digits as an argument and find whether the input number leads to a palindromic number or not?  - If input number leads to a palindromic number then also display in how many iteration it leads to a palindromic number?

-  If input number does not lead to palindromic number after 7 iteration then display

"Number does not lead to palindromic number"

-  If user does not provide any number then display "Missing required inputs" - If user provides a number with more than 3 digits long or less than 2 digits long then display "Invalid number"

-  If user does not provide a valid number then also display "Invald number"

  

Input

Command Line Argument: <<A number with 3 digits>>         

Output

[Number leads to palindromic number in X iterations] or [Number does not lead to palindromic number] or [Invalid number] or [Missing required inputs] 

Example

Example 1: 

    Inputs: Command Line Argument: 88           

    Output:  Number leads to palindromic number in 6 iterations           

            /* Here the original number is 88.

            Iteration 1:   88 + 88 = 176 

            Iteration 2:   176 + 671 = 847  

           Iteration 3:   847 + 748 = 1595

            Iteration 4:   1595 + 5951 = 7546

              Iteration 5:   7546 + 6457 = 14003     

             Iteration 6:   14003 + 30041 = 44044            

              44044 is a palindromic number.

            /*

Example 2:

            Inputs: Command Line Argument: 196          

            Output:  Number does not lead to palindromic number

            /* Here the original number is 196

            Iteration 1:   196 + 691 = 887 

            Iteration 2:   887 + 788 = 1675 

            Iteration 3:   1675 + 5761 = 7436

            Iteration 4:   7436 + 6347 = 13783

            Iteration 5:   13783 + 38731 = 94039 

            Iteration 6:   94039 + 93049 = 187088

            Iteration 7:   187088 + 880781 = 1067869

             

 Hence, even after 7 iteration number does not lead to palindromic number.

            */

             

             

   solution          

                        

under construction