A8404. Palindrome pairs

You are given a non-empty string $s$ consisting of lowercase letters. Find the number of pairs of non-overlapping palindromic substrings of this string.

In a more formal way, you have to find the quantity of tuples $(a,b,x,y)$ such that $1<=a<=b<x<=y<=|s|$ and substrings $s[a...\ b]$ , $s[x...\ y]$ are palindromes.

A palindrome is a string that can be read the same way from left to right and from right to left. For example, "abacaba", "z", "abba" are palindromes.

A substring $s[i...\ j]$ ( $1<=i<=j<=|s|$ ) of string $s$ = $s_{1}s_{2}...\ s_{|s|}$ is a string $s_{i}s_{i+1}...\ s_{j}$ . For example, substring $s[2...4]$ of string $s$ = "abacaba" equals "bac".

The first line of input contains a non-empty string $s$ which consists of lowercase letters ('a'...'z'), $s$ contains at most $2000$ characters.

Output a single number — the quantity of pairs of non-overlapping palindromic substrings of $s$ .

Please do not use the %lld format specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d format specifier.