Palindromic substrings count

Given a string, the task is to count all palindrome sub string in a given string. Length of palindrome sub string is greater than or equal to 2.

Examples:

Input : str = "abaab"
Output: 3
Explanation :
All palindrome substring are :
"aba" , "aa" , "baab"

Input : str = "abbaeae"
Output: 4
Explanation :
All palindrome substring are :
"bb" , "abba" ,"aea","eae"