#include <bits/stdc++.h>
using namespace std;
const double eps = 1e-10;
int matrix[2005][2005];
char st[2005];
vector<pair<int, int> > vct;
int is_pal(int s, int e) {
  if (s == e) return 1;
  if (e == s + 1) return st[s] == st[e];
  if (matrix[s][e] != -1) return matrix[s][e];
  if (st[s] != st[e]) return matrix[s][e] = 0;
  return matrix[s][e] = is_pal(s + 1, e - 1);
}
int main() {
  for (int i = 0; i < 2005; i++)
    for (int j = 0; j < 2005; j++) matrix[i][j] = -1;
  scanf("%s", st);
  int len = strlen(st);
  for (int i = 0; i < len; i++)
    for (int j = i; j < len; j++)
      if (is_pal(i, j)) vct.push_back(make_pair(i, j));
  long long res = 0;
  for (int i = 0; i < (int)vct.size(); i++) {
    res +=
        (long long)(vct.end() - upper_bound(vct.begin(), vct.end(),
                                            make_pair(vct[i].second + 1, -1)));
  }
  cout << res << "\n";
  return 0;
}

### Prompt

Please formulate a Cpp solution to the following 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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const double eps = 1e-10;
int matrix[2005][2005];
char st[2005];
vector<pair<int, int> > vct;
int is_pal(int s, int e) {
  if (s == e) return 1;
  if (e == s + 1) return st[s] == st[e];
  if (matrix[s][e] != -1) return matrix[s][e];
  if (st[s] != st[e]) return matrix[s][e] = 0;
  return matrix[s][e] = is_pal(s + 1, e - 1);
}
int main() {
  for (int i = 0; i < 2005; i++)
    for (int j = 0; j < 2005; j++) matrix[i][j] = -1;
  scanf("%s", st);
  int len = strlen(st);
  for (int i = 0; i < len; i++)
    for (int j = i; j < len; j++)
      if (is_pal(i, j)) vct.push_back(make_pair(i, j));
  long long res = 0;
  for (int i = 0; i < (int)vct.size(); i++) {
    res +=
        (long long)(vct.end() - upper_bound(vct.begin(), vct.end(),
                                            make_pair(vct[i].second + 1, -1)));
  }
  cout << res << "\n";
  return 0;
}

```