Input:  a = [13, 5604, 31, 2, 13, 4560, 546, 654, 456]
Output: 5 
Explanation:

      

      There are 5 cyclic pairs of numbers - pairs which are equal to each other after cyclic shifts.
      
      

        
a[0] = 13 and a[4] = 13 (i = 0 and j = 4)
        
a[0] = 13 and a[4] = 13 (i = 0 and j = 4)
        
a[1] = 5604 and a[5] = 4560 (i = 1 and j = 5)
        
a[2] = 31 and a[4] = 13 (i = 2 and j = 4)
        
a[6] = 546 and a[7] = 654 (i = 6 and j = 7)
      
      

      Note that a[6] = 546 and a[8] = 456 are not cyclic pairs - 546 can only be paired with cyclic shift of 546, 465 and 654.
      
      

      Also, note that a[5] = 4560 and a[8] = 456 are not cyclic pairs because they have different number of digits.