Problem3932--Palindrome pairs

3932: Palindrome pairs

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 = s1s2... s|s| is a string sisi+1... sj. For example, substring s[2...4] of string s = "abacaba" equals "bac".

Input

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

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.

Examples
Input
aa
Output
1
Input
aaa
Output
5
Input
abacaba
Output
36

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