#include <bits/stdc++.h>
using namespace std;
int MAX = numeric_limits<int>::max();
const int N = 1e6 + 10;
long long a[N];
int n;
int main() {
  scanf("%d", &n);
  for (int i = 1; i < n + 1; i++) {
    scanf("%lld", &a[i]);
  }
  sort(a + 1, a + n + 1);
  long long d = 1;
  long long p = 3;
  long long ans = 1;
  for (int i = 2; i < n + 1; i++) {
    if (a[i] != a[i - 1]) {
      if (p > 0) {
        long long x = 1;
        if (d >= p) {
          long long num = d;
          for (int j = 0; j < p; j++) {
            x = x * (num);
            num--;
          }
          num = p;
          for (int j = 1; j < p; j++) {
            x /= num;
            num--;
          }
          ans *= x;
        }
        p -= d;
      }
      d = 1;
    } else {
      d++;
    }
  }
  if (p > 0) {
    long long x = 1;
    if (d >= p) {
      long long num = d;
      for (int j = 0; j < p; j++) {
        x = x * (num);
        num--;
      }
      num = p;
      for (int j = 1; j < p; j++) {
        x /= num;
        num--;
      }
      ans *= x;
    }
  }
  cout << ans << "\n";
}

### Prompt

Generate a Cpp solution to the following problem:

After returning from the army Makes received a gift — an array a consisting of n positive integer numbers. He hadn't been solving problems for a long time, so he became interested to answer a particular question: how many triples of indices (i, j, k) (i < j < k), such that ai·aj·ak is minimum possible, are there in the array? Help him with it!

Input

The first line of input contains a positive integer number n (3 ≤ n ≤ 105) — the number of elements in array a. The second line contains n positive integer numbers ai (1 ≤ ai ≤ 109) — the elements of a given array.

Output

Print one number — the quantity of triples (i, j, k) such that i, j and k are pairwise distinct and ai·aj·ak is minimum possible.

Examples

Input

4
1 1 1 1


Output

4


Input

5
1 3 2 3 4


Output

2


Input

6
1 3 3 1 3 2


Output

1

Note

In the first example Makes always chooses three ones out of four, and the number of ways to choose them is 4.

In the second example a triple of numbers (1, 2, 3) is chosen (numbers, not indices). Since there are two ways to choose an element 3, then the answer is 2.

In the third example a triple of numbers (1, 1, 2) is chosen, and there's only one way to choose indices.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int MAX = numeric_limits<int>::max();
const int N = 1e6 + 10;
long long a[N];
int n;
int main() {
  scanf("%d", &n);
  for (int i = 1; i < n + 1; i++) {
    scanf("%lld", &a[i]);
  }
  sort(a + 1, a + n + 1);
  long long d = 1;
  long long p = 3;
  long long ans = 1;
  for (int i = 2; i < n + 1; i++) {
    if (a[i] != a[i - 1]) {
      if (p > 0) {
        long long x = 1;
        if (d >= p) {
          long long num = d;
          for (int j = 0; j < p; j++) {
            x = x * (num);
            num--;
          }
          num = p;
          for (int j = 1; j < p; j++) {
            x /= num;
            num--;
          }
          ans *= x;
        }
        p -= d;
      }
      d = 1;
    } else {
      d++;
    }
  }
  if (p > 0) {
    long long x = 1;
    if (d >= p) {
      long long num = d;
      for (int j = 0; j < p; j++) {
        x = x * (num);
        num--;
      }
      num = p;
      for (int j = 1; j < p; j++) {
        x /= num;
        num--;
      }
      ans *= x;
    }
  }
  cout << ans << "\n";
}

```