#include <bits/stdc++.h>
using namespace std;
const int N = 350001;
const int SQRTN = 320;
const int LOGN = 20;
const long double PI = acos(-1);
int n, a[N];
map<int, long long> mp;
signed main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    scanf("%d", a + i);
    mp[a[i]]++;
  }
  sort(a, a + n);
  long long ans = 0, t;
  if (a[0] == a[1] && a[1] != a[2])
    ans = mp[a[0]] * (mp[a[0]] - 1) * mp[a[2]] / 2;
  if (a[2] == a[1] && a[1] != a[0])
    ans = mp[a[2]] * (mp[a[2]] - 1) * mp[a[0]] / 2;
  if (a[0] != a[1] && a[1] != a[2]) ans = mp[a[0]] * mp[a[1]] * mp[a[2]];
  if (a[2] == a[1] && a[1] == a[0]) {
    ans = 1ll * mp[a[0]] * (mp[a[0]] - 1) * (mp[a[0]] - 2);
    ans /= 6;
  }
  cout << ans << endl;
}

### Prompt

Please provide a cpp coded solution 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;
const int N = 350001;
const int SQRTN = 320;
const int LOGN = 20;
const long double PI = acos(-1);
int n, a[N];
map<int, long long> mp;
signed main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    scanf("%d", a + i);
    mp[a[i]]++;
  }
  sort(a, a + n);
  long long ans = 0, t;
  if (a[0] == a[1] && a[1] != a[2])
    ans = mp[a[0]] * (mp[a[0]] - 1) * mp[a[2]] / 2;
  if (a[2] == a[1] && a[1] != a[0])
    ans = mp[a[2]] * (mp[a[2]] - 1) * mp[a[0]] / 2;
  if (a[0] != a[1] && a[1] != a[2]) ans = mp[a[0]] * mp[a[1]] * mp[a[2]];
  if (a[2] == a[1] && a[1] == a[0]) {
    ans = 1ll * mp[a[0]] * (mp[a[0]] - 1) * (mp[a[0]] - 2);
    ans /= 6;
  }
  cout << ans << endl;
}

```