Let S be a string consisting only of letters. Count the number of tuples (i,j,k,t) such that 1≤i≤j<k≤t≤|S| and S[i..j]+S[k...t] is a palindrome.
### Input
- Only line contains a string S.
### Output
- Print the number of quadruples that satisfy the conditions.
### Constraints
|S|≤5000
### Example
Input:
aaca
Output:
14