#include <bits/stdc++.h>
using namespace std;
string s;
set<pair<int, int> > my_s;
bool isPal(int i, int j) {
  if (i + 1 > j) return true;
  return my_s.find(make_pair(i, j)) != my_s.end();
}
void CalcPal(int i, int j) {
  if (s[i] != s[j]) return;
  if (isPal(i + 1, j - 1)) {
    my_s.insert(make_pair(i, j));
  }
}
int main() {
  cin >> s;
  vector<int> d(s.length(), 0);
  for (int len = 1; len < s.length(); ++len) {
    for (int i = 0; i + len - 1 < s.length(); ++i) {
      CalcPal(i, i + len - 1);
      if (isPal(i, i + len - 1)) ++d[i];
    }
  }
  vector<long long> sum(s.length() + 1, 0);
  for (int i = s.length() - 1; i >= 0; --i)
    sum[i] = (long long)d[i] + sum[i + 1];
  long long ans = 0;
  for (int i = 0; i < s.length(); ++i) {
    for (int j = i; j < s.length(); ++j) {
      if (isPal(i, j)) {
        ans += sum[j + 1];
      }
    }
  }
  cout << ans;
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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;
string s;
set<pair<int, int> > my_s;
bool isPal(int i, int j) {
  if (i + 1 > j) return true;
  return my_s.find(make_pair(i, j)) != my_s.end();
}
void CalcPal(int i, int j) {
  if (s[i] != s[j]) return;
  if (isPal(i + 1, j - 1)) {
    my_s.insert(make_pair(i, j));
  }
}
int main() {
  cin >> s;
  vector<int> d(s.length(), 0);
  for (int len = 1; len < s.length(); ++len) {
    for (int i = 0; i + len - 1 < s.length(); ++i) {
      CalcPal(i, i + len - 1);
      if (isPal(i, i + len - 1)) ++d[i];
    }
  }
  vector<long long> sum(s.length() + 1, 0);
  for (int i = s.length() - 1; i >= 0; --i)
    sum[i] = (long long)d[i] + sum[i + 1];
  long long ans = 0;
  for (int i = 0; i < s.length(); ++i) {
    for (int j = i; j < s.length(); ++j) {
      if (isPal(i, j)) {
        ans += sum[j + 1];
      }
    }
  }
  cout << ans;
  return 0;
}

```