回文串的组合 DP

D. Palindrome pairs

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 С++. 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

题目大意：

回文串的组合

http://codeforces.com/contest/159/problem/D

思路:
虽然表示题解说的挺详细了，但是敲起来的时候还是遇到了各种问题

首先我们定义p[j][i]代表j到i是否是会问，然后用dp[i]来保存j<i的回文总数就好了