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;
const int MAX = 2016;
bool palindrome[MAX][MAX];
long long sum[MAX];
long long DP[MAX];
bool checkP(string str, int i, int j) {
  while (str[i - 1] == str[j - 1] && i < j) {
    i++;
    j--;
  }
  if (i < j) {
    return false;
  } else {
    return true;
  }
}
int main() {
  string str;
  cin >> str;
  for (int i = 1; i <= str.length(); i++) {
    for (int j = i; j <= str.length(); j++) {
      palindrome[i][j] = checkP(str, i, j);
    }
  }
  for (int i = 1; i <= str.length(); i++) {
    sum[i] = sum[i - 1];
    for (int k = i; k > 0; k--) {
      sum[i] += palindrome[k][i];
    }
  }
  for (int i = 1; i <= str.length(); i++) {
    long long summ = 0;
    for (int j = i; j > 0; j--) {
      summ += (sum[j - 1] * palindrome[j][i]);
    }
    DP[i] = DP[i - 1] + summ;
  }
  cout << DP[str.length()] << endl;
  return 0;
}