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 \lt 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 \le i \le j \le |s|) of string s = s1s2... s|s| is a string sisi+1... sj. 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 C++. It is preferred to use cin, cout streams or the %I64d format specifier.