#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  sort(a.begin(), a.end());
  map<int, long long> m;
  m[a[0]] = 0;
  m[a[1]] = 0;
  m[a[2]] = 0;
  for (int i = 0; i < n; i++) {
    if ((m.find(a[i])) != m.end()) {
      m[a[i]]++;
    }
  }
  long long ans = 1;
  if (m.size() == 1) {
    ans = ((m[a[0]]) * (m[a[0]] - 1) * (m[a[0]] - 2)) / 6;
  } else if (m.size() == 2) {
    if (a[0] == a[1]) {
      ans = (((m[a[0]]) * (m[a[0]] - 1)) / 2) * m[a[2]];
    } else {
      ans = (((m[a[1]]) * (m[a[1]] - 1)) / 2) * (m[a[0]]);
    }
  } else {
    ans = m[a[0]] * m[a[1]] * m[a[2]];
  }
  cout << ans;
  return 0;
}

### Prompt

Your task is to create 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 main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  sort(a.begin(), a.end());
  map<int, long long> m;
  m[a[0]] = 0;
  m[a[1]] = 0;
  m[a[2]] = 0;
  for (int i = 0; i < n; i++) {
    if ((m.find(a[i])) != m.end()) {
      m[a[i]]++;
    }
  }
  long long ans = 1;
  if (m.size() == 1) {
    ans = ((m[a[0]]) * (m[a[0]] - 1) * (m[a[0]] - 2)) / 6;
  } else if (m.size() == 2) {
    if (a[0] == a[1]) {
      ans = (((m[a[0]]) * (m[a[0]] - 1)) / 2) * m[a[2]];
    } else {
      ans = (((m[a[1]]) * (m[a[1]] - 1)) / 2) * (m[a[0]]);
    }
  } else {
    ans = m[a[0]] * m[a[1]] * m[a[2]];
  }
  cout << ans;
  return 0;
}

```