#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  cin >> n;
  long long a[n + 1];
  map<long long, long long> m;
  int x;
  for (int i = 1; i <= n; i++) {
    cin >> x;
    a[i] = x;
    m[x]++;
  }
  a[0] = 0;
  sort(a, a + (n + 1));
  int ch1 = a[1];
  int ch2 = a[2];
  int ch3 = a[3];
  int how = 0;
  long long ans;
  if (a[1] == a[2] and a[1] == a[3])
    ans = (m[a[1]]) * (m[a[1]] - 1) * (m[a[1]] - 2) / 6;
  else if (a[1] == a[2])
    ans = (m[a[1]]) * (m[a[1]] - 1) / 2, ans *= m[a[3]];
  else if (a[1] == a[3])
    ans = (m[a[1]]) * (m[a[1]] - 1) / 2, ans *= m[a[2]];
  else if (a[2] == a[3])
    ans = (m[a[2]]) * (m[a[2]] - 1) / 2, ans *= m[a[1]];
  else
    ans = m[a[1]] * m[a[2]] * m[a[3]];
  cout << ans;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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;
  cin >> n;
  long long a[n + 1];
  map<long long, long long> m;
  int x;
  for (int i = 1; i <= n; i++) {
    cin >> x;
    a[i] = x;
    m[x]++;
  }
  a[0] = 0;
  sort(a, a + (n + 1));
  int ch1 = a[1];
  int ch2 = a[2];
  int ch3 = a[3];
  int how = 0;
  long long ans;
  if (a[1] == a[2] and a[1] == a[3])
    ans = (m[a[1]]) * (m[a[1]] - 1) * (m[a[1]] - 2) / 6;
  else if (a[1] == a[2])
    ans = (m[a[1]]) * (m[a[1]] - 1) / 2, ans *= m[a[3]];
  else if (a[1] == a[3])
    ans = (m[a[1]]) * (m[a[1]] - 1) / 2, ans *= m[a[2]];
  else if (a[2] == a[3])
    ans = (m[a[2]]) * (m[a[2]] - 1) / 2, ans *= m[a[1]];
  else
    ans = m[a[1]] * m[a[2]] * m[a[3]];
  cout << ans;
}

```