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.*;
import java.math.BigInteger;
import java.util.*;

public class A {
    static MyScanner sc;
    static PrintWriter pw;

    public static void main(String[] args) throws Throwable {
        sc = new MyScanner();
        pw = new PrintWriter(System.out);

        char[] s = sc.next().toCharArray();
        int n = s.length;
        boolean[][] pal = new boolean[n][n];
        for (int i = 0; i < n; i++) {
            pal[i][i] = true;
            if (i < n - 1 && s[i + 1] == s[i])
                pal[i][i + 1] = true;
        }
        for (int l = 3; l <= n; l++)
            for (int i = 0; i + l - 1 < n; i++) {
                int j = i + l - 1;
                if (pal[i + 1][j - 1] && s[i] == s[j])
                    pal[i][j] = true;
            }
        long ans = 0;
        int cntL = 0;
        for (int i = 0; i < n; i++) {
            int cntR = 0;
            for (int j = i; j < n; j++)
                if (pal[i][j])
                    cntR++;
            ans += 1L * cntL * cntR;
            for (int j = i; j >= 0; j--)
                if (pal[j][i])
                    cntL++;
        }
        pw.println(ans);

        pw.flush();
        pw.close();
    }

    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}