Problem: 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

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        String str = scan.next();
        int len = str.length();
        int[] p = new int[len + 1];
        int[] q = new int[len + 1];
        for (int i = 0; i < len; i++) {
            for (int a = i, b = i + 1; a >= 0 && b < len
                    && str.charAt(a) == str.charAt(b); a--, b++) {
                p[b]++;
                q[a]++;
            }
            for (int a = i, b = i; a >= 0 && b < len
                    && str.charAt(a) == str.charAt(b); a--, b++) {
                p[b]++;
                q[a]++;
            }
        }
        for (int i = len-1; i >= 0; i--)
            q[i] += q[i + 1];
        long ans = 0L;
        for (int i = 0; i < len; i++)
            ans += (long)p[i] * q[i + 1];
        System.out.println(ans);
    }
}