#include <bits/stdc++.h>
using namespace std;
int a[111111];
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  if (n == 3) {
    cout << 1 << endl;
    return 0;
  }
  sort(a + 1, a + n + 1);
  int t = 4;
  while (t <= n and a[t] == a[t - 1]) t++;
  int tp[4] = {};
  tp[1] = 1;
  int cnt = 1;
  for (int i = 2; i < t; i++) {
    if (a[i] != a[i - 1]) {
      cnt++;
    }
    tp[cnt]++;
  }
  if (cnt == 3) {
    cout << tp[3] << endl;
  }
  if (cnt == 2) {
    if (tp[1] == 1) {
      cout << 1LL * tp[2] * (tp[2] - 1) / 2 << endl;
    } else {
      cout << tp[2] << endl;
    }
  }
  if (cnt == 1) {
    cout << 1LL * tp[1] * (tp[1] - 1) * (tp[1] - 2) / 6 << endl;
  }
  return 0;
}

### Prompt

Please formulate 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 a[111111];
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  if (n == 3) {
    cout << 1 << endl;
    return 0;
  }
  sort(a + 1, a + n + 1);
  int t = 4;
  while (t <= n and a[t] == a[t - 1]) t++;
  int tp[4] = {};
  tp[1] = 1;
  int cnt = 1;
  for (int i = 2; i < t; i++) {
    if (a[i] != a[i - 1]) {
      cnt++;
    }
    tp[cnt]++;
  }
  if (cnt == 3) {
    cout << tp[3] << endl;
  }
  if (cnt == 2) {
    if (tp[1] == 1) {
      cout << 1LL * tp[2] * (tp[2] - 1) / 2 << endl;
    } else {
      cout << tp[2] << endl;
    }
  }
  if (cnt == 1) {
    cout << 1LL * tp[1] * (tp[1] - 1) * (tp[1] - 2) / 6 << endl;
  }
  return 0;
}

```