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.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;

public class D2 {
    static byte[][] dp;
    static String s;

    public static byte isPalindrome(int i, int j) {
        if (j + 1 == i || i == j)
            return 1;
        if (dp[i][j] != -1)
            return dp[i][j];
        if (s.charAt(i) == s.charAt(j))
            return dp[i][j] = isPalindrome(i + 1, j - 1);
        return 0;
    }

    static class Pair implements Comparable<Pair> {
        int a, b;

        public Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(Pair o) {
            if (a == o.a)
                return b - o.b;
            return a - o.a;
        }
    }

    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        s = in.readLine();
        dp = new byte[s.length()][s.length()];
        for (byte[] a : dp)
            Arrays.fill(a, (byte) -1);
        int[] starts = new int[s.length()];
        Pair[] palindromes = new Pair[s.length() * s.length()];
        int top = 0;
        for (int i = 0; i < s.length(); i++)
            for (int j = i; j < s.length(); j++)
                if (isPalindrome(i, j) == 1) {
                    palindromes[top++] = new Pair(i, j - i + 1);
                    starts[i]++;
                }
        Pair[] palindromes2 = new Pair[top];
        for (int i = 0; i < palindromes2.length; i++)
            palindromes2[i] = palindromes[i];
        Arrays.sort(palindromes2);
        for (int i = s.length() - 2; i >= 0; i--)
            starts[i] += starts[i + 1];
        long total = 0;
        for (Pair p : palindromes2)
            if (p.a + p.b < s.length())
                total = total + starts[p.a + p.b];
        System.out.println(total);
    }
}