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

### Prompt

Create a solution in CPP for 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 int n, x;
vector<int> a;
long long int tarkib(long long int r, long long int n) {
  long long int a = 1;
  for (long long int i = n; i > (n - r); i--) a = a * i;
  for (long long int i = 2; i < r + 1; i++) a = a / i;
  return a;
}
int main() {
  long long int r;
  cin >> n;
  for (long long int i = 0; i < n; i++) {
    cin >> x;
    a.push_back(x);
  }
  sort(a.begin(), a.end());
  long long int i;
  for (i = 3; i < n; i++) {
    if (a[i] > a[i - 1]) break;
  }
  i--;
  i--;
  if (a[0] == a[1]) {
    if (a[1] == a[2]) {
      r = 3;
      i += 2;
    } else {
      r = 1;
    }
  } else {
    if (a[1] == a[2]) {
      i++;
      r = 2;
    } else {
      r = 1;
    }
  }
  cout << tarkib(r, i);
  return 0;
}

```