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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
string s;
bool f[2005][2005];
int n, x;
long long res, g[2005];
int main() {
  if (0) {
    freopen("a.inp", "r", stdin);
  };
  cin >> s;
  n = s.length();
  for (int i = 0; i < n; i++) {
    f[i][i] = true;
    if (i != 0) f[i][i - 1] = true;
    g[i] = 1;
  }
  for (int i = n - 2; i >= 0; i--) g[i] += g[i + 1];
  for (int l = 2; l <= n; l++) {
    for (int i = 0; i <= n - l; i++) {
      int j = i + l - 1;
      f[i][j] = (s[i] == s[j] && f[i + 1][j - 1]);
    }
    x = 0;
    for (int i = n - l; i >= 0; i--) {
      g[i] += x;
      if (f[i][i + l - 1]) {
        g[i]++;
        x++;
      }
    }
  }
  for (int i = 0; i < n - 1; i++)
    for (int l = 1; l < n; l++)
      if (f[i][i + l - 1]) res += g[i + l];
  cout << res << endl;
}