Palindrome Counting
Count the number of palindromes that exist in a particular string. Duplicates are allowed so long as they cover distinct intervals of the string. Empty strings do not count towards this total.
Example 1:
Input: abab
Output: 6
Explanation:
The following intervals are palindromes(0-indexed), [0,0],[1,1],[2,2],[3,3],[0,2],[1,3]