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:
//package codeforces;

import java.io.BufferedReader;
import java.io.Closeable;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class D implements Closeable {
    BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter writer = new PrintWriter(System.out);
    StringTokenizer stringTokenizer;

    D() throws IOException {
//        reader = new BufferedReader(new FileReader("input.txt"));
//        writer = new PrintWriter(new FileWriter("output.txt"));
    }


    String next() throws IOException {
        while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
            stringTokenizer = new StringTokenizer(reader.readLine());
        }
        return stringTokenizer.nextToken();
    }

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

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

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

    int MOD = 1000 * 1000 * 1000 + 7;

    int sum(int a, int b) {
        a += b;
        return a >= MOD ? a - MOD : a;
    }

    int product(int a, int b) {
        return (int) (1l * a * b % MOD);
    }

    @SuppressWarnings("unchecked")
    void solve() throws IOException {
        char[] s = next().toCharArray();
        boolean[][] isPalindrome = new boolean[s.length][s.length + 1];
        for(int i = 0; i < s.length; i++) {
            isPalindrome[i][i] = true;
            isPalindrome[i][i + 1] = true;
        }
        long[] suffixSum = new long[s.length + 1];
        long answer = 0;
        for(int i = s.length - 1; i >= 0; i--) {
            int palindromesStart = 0;
            for(int j = i + 1; j <= s.length; j++) {
                boolean ok = isPalindrome[i][j] || s[i] == s[j - 1] && isPalindrome[i + 1][j - 1];
                isPalindrome[i][j] = ok;
                if(ok) {
                    palindromesStart++;
                    answer += suffixSum[j];
                }
            }
            suffixSum[i] = suffixSum[i + 1] + palindromesStart;
        }
        writer.println(answer);
    }

    public static void main(String[] args) throws IOException, InterruptedException {
        try (D d = new D()) {
            d.solve();
        }
    }

    @Override
    public void close() throws IOException {
        reader.close();
        writer.close();
    }
}