CF159D 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 $1 \le a \le b < x \le y \le |s|$ 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

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.