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.io.PrintWriter;
import java.util.Scanner;

public class N2D {

    Scanner in;
    PrintWriter out;

    void solve() {
        String s = in.next();
        int l = s.length();
        boolean[][] palindrome = new boolean[l + 1][l + 1];
        int[] left = new int[l];
        int[] right = new int[l];
        for (int i = l - 1; i >= 0; i--) {
            palindrome[i + 1][i] = palindrome[i][i] = true;
            left[i]++;
            right[i]++;
            for (int j = i + 1; j < l; j++) {
                if (palindrome[i + 1][j - 1] && s.charAt(i) == s.charAt(j)) {
                    palindrome[i][j] = true;
                    left[i]++;
                    right[j]++;
                }
            }
        }
        long k = 0, lsum = 0;
        for (int i = 1; i < l; i++) {
            lsum += right[i - 1];
            k += lsum * left[i];
        }
        System.out.println(k);
    }

    void run() {
        in = new Scanner(System.in);
        out = new PrintWriter(System.out);
        try {
            solve();
        } finally {
            out.close();
        }
    }

    public static void main(String[] args) {
        new N2D().run();
    }
}