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;
import java.util.Arrays;

public class Main {
  public static void main(String[] args) {
    Scanner s = new Scanner(System.in);
    char[] w = s.nextLine().trim().toCharArray();

    boolean[][] pals = new boolean[w.length][w.length];
    int[] nump = new int[w.length];
    for (int l = 1; l <= w.length; ++l) { 
     for (int k = 0; k < w.length - l + 1; ++k) {
       if (l == 1) pals[k][k] = true;
       else {
         if (w[k] != w[k+l-1]) pals[k][k+l-1] = false;
         else {
           if (l > 3) pals[k][k+l-1] = pals[k+1][k+l-2];
           else pals[k][k+l-1] = true;
         }
       }
       if (pals[k][k+l-1]) {
         for(int j = 0; j <= k; j++) nump[j]++;
       }
     }
    }
 
    long numTups = 0;
    for (int j = 0; j < w.length; j++) {
      for (int k = j; k < w.length-1; k++) {
        if (pals[j][k]) numTups += nump[k+1];
      }
    }
 
    System.out.println(numTups);
  }
}