#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, i;
  cin >> n;
  int a[n];
  for (i = 0; i < n; i++) cin >> a[i];
  int idx1 = -1, idx2 = -1, min1 = INT_MAX, min2 = INT_MAX, min3 = INT_MAX;
  for (i = 0; i < n; i++) {
    if (a[i] < min1) {
      min1 = a[i];
      idx1 = i;
    }
  }
  for (i = 0; i < n; i++) {
    if (i == idx1) continue;
    if (a[i] < min2) {
      min2 = a[i];
      idx2 = i;
    }
  }
  for (i = 0; i < n; i++) {
    if (i == idx1 || i == idx2) continue;
    if (a[i] < min3) {
      min3 = a[i];
    }
  }
  long long int count1 = 0, count2 = 0, count3 = 0;
  for (i = 0; i < n; i++) {
    if (a[i] == min1) ++count1;
    if (a[i] == min2) ++count2;
    if (a[i] == min3) ++count3;
  }
  bool b1 = min1 == min2;
  bool b2 = min2 == min3;
  long long int ans;
  if (b1) {
    if (b2)
      ans = count1 * (count1 - 1) * (count1 - 2) / 6;
    else
      ans = count3;
  } else {
    if (b2)
      ans = count2 * (count2 - 1) / 2;
    else
      ans = count3;
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Your challenge is to write 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() {
  int n, i;
  cin >> n;
  int a[n];
  for (i = 0; i < n; i++) cin >> a[i];
  int idx1 = -1, idx2 = -1, min1 = INT_MAX, min2 = INT_MAX, min3 = INT_MAX;
  for (i = 0; i < n; i++) {
    if (a[i] < min1) {
      min1 = a[i];
      idx1 = i;
    }
  }
  for (i = 0; i < n; i++) {
    if (i == idx1) continue;
    if (a[i] < min2) {
      min2 = a[i];
      idx2 = i;
    }
  }
  for (i = 0; i < n; i++) {
    if (i == idx1 || i == idx2) continue;
    if (a[i] < min3) {
      min3 = a[i];
    }
  }
  long long int count1 = 0, count2 = 0, count3 = 0;
  for (i = 0; i < n; i++) {
    if (a[i] == min1) ++count1;
    if (a[i] == min2) ++count2;
    if (a[i] == min3) ++count3;
  }
  bool b1 = min1 == min2;
  bool b2 = min2 == min3;
  long long int ans;
  if (b1) {
    if (b2)
      ans = count1 * (count1 - 1) * (count1 - 2) / 6;
    else
      ans = count3;
  } else {
    if (b2)
      ans = count2 * (count2 - 1) / 2;
    else
      ans = count3;
  }
  cout << ans << endl;
  return 0;
}

```