#include <bits/stdc++.h>
using namespace std;
int main() {
  long long int m, n, c = 0, x, t, d, ts, y, g, s = 0;
  cin >> n;
  long long int a[n + 10];
  map<long long int, long long int> p;
  map<long long int, long long int> q;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    p[a[i]]++;
  }
  sort(a, a + n);
  if (p[a[0]] == 1) {
    if (p[a[1]] >= 2) {
      x = p[a[1]] - 1;
      x = x * (x + 1);
      x /= 2;
      cout << x << endl;
    } else {
      cout << p[a[2]];
    }
  } else if (p[a[0]] == 2) {
    cout << p[a[2]] << endl;
  } else if (p[a[0]] >= 3) {
    x = p[a[0]] - 2;
    t = 1;
    for (int i = x; i >= 1; i--) {
      s += i * t;
      t++;
    }
    cout << s << endl;
  }
}

### Prompt

Develop a solution in Cpp to the problem described below:

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() {
  long long int m, n, c = 0, x, t, d, ts, y, g, s = 0;
  cin >> n;
  long long int a[n + 10];
  map<long long int, long long int> p;
  map<long long int, long long int> q;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    p[a[i]]++;
  }
  sort(a, a + n);
  if (p[a[0]] == 1) {
    if (p[a[1]] >= 2) {
      x = p[a[1]] - 1;
      x = x * (x + 1);
      x /= 2;
      cout << x << endl;
    } else {
      cout << p[a[2]];
    }
  } else if (p[a[0]] == 2) {
    cout << p[a[2]] << endl;
  } else if (p[a[0]] >= 3) {
    x = p[a[0]] - 2;
    t = 1;
    for (int i = x; i >= 1; i--) {
      s += i * t;
      t++;
    }
    cout << s << endl;
  }
}

```