#include <bits/stdc++.h>
using namespace std;
long long n, a[200001], c = 0;
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  sort(a, a + n);
  if (a[2] == a[0]) {
    c = 3;
    for (int i = 3; i < n; i++) {
      if (a[i] == a[i - 1]) {
        c++;
      } else {
        break;
      }
    }
    cout << c * (c - 1) * (c - 2) / 6;
  } else {
    if (a[1] == a[2]) {
      c = 2;
      for (int i = 3; i < n; i++) {
        if (a[i] == a[i - 1]) {
          c++;
        } else {
          break;
        }
      }
      cout << c * (c - 1) / 2;
    } else {
      c = 1;
      for (int i = 3; i < n; i++) {
        if (a[i] == a[i - 1]) {
          c++;
        } else {
          break;
        }
      }
      cout << c;
    }
  }
  return 0;
}

### Prompt

Please create a solution in cpp 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;
long long n, a[200001], c = 0;
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  sort(a, a + n);
  if (a[2] == a[0]) {
    c = 3;
    for (int i = 3; i < n; i++) {
      if (a[i] == a[i - 1]) {
        c++;
      } else {
        break;
      }
    }
    cout << c * (c - 1) * (c - 2) / 6;
  } else {
    if (a[1] == a[2]) {
      c = 2;
      for (int i = 3; i < n; i++) {
        if (a[i] == a[i - 1]) {
          c++;
        } else {
          break;
        }
      }
      cout << c * (c - 1) / 2;
    } else {
      c = 1;
      for (int i = 3; i < n; i++) {
        if (a[i] == a[i - 1]) {
          c++;
        } else {
          break;
        }
      }
      cout << c;
    }
  }
  return 0;
}

```