#include <bits/stdc++.h>
using std::int64_t;
constexpr inline int64_t Combinations(int64_t N, int64_t M) {
  switch (M) {
    case 0:
      return 1;
    case 1:
      return N;
    case 2:
      return N * (N - 1) / 2;
    case 3:
      return N * (N - 1) * (N - 2) / 6;
    default:
      std::abort();
  }
}
int main() {
  using namespace std;
  ios_base::sync_with_stdio(false);
  map<int, int> Nodes;
  int N;
  cin >> N;
  while (N-- > 0) {
    int A;
    cin >> A;
    Nodes[A]++;
  }
  int RequiredNumCount = 3;
  int64_t Answer = 0;
  for (auto &Node : Nodes) {
    if (Node.second >= RequiredNumCount) {
      Answer = Combinations(Node.second, RequiredNumCount);
      break;
    } else {
      RequiredNumCount -= Node.second;
    }
  }
  cout << Answer << endl;
}

### 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 std::int64_t;
constexpr inline int64_t Combinations(int64_t N, int64_t M) {
  switch (M) {
    case 0:
      return 1;
    case 1:
      return N;
    case 2:
      return N * (N - 1) / 2;
    case 3:
      return N * (N - 1) * (N - 2) / 6;
    default:
      std::abort();
  }
}
int main() {
  using namespace std;
  ios_base::sync_with_stdio(false);
  map<int, int> Nodes;
  int N;
  cin >> N;
  while (N-- > 0) {
    int A;
    cin >> A;
    Nodes[A]++;
  }
  int RequiredNumCount = 3;
  int64_t Answer = 0;
  for (auto &Node : Nodes) {
    if (Node.second >= RequiredNumCount) {
      Answer = Combinations(Node.second, RequiredNumCount);
      break;
    } else {
      RequiredNumCount -= Node.second;
    }
  }
  cout << Answer << endl;
}

```