#include <bits/stdc++.h>
using namespace std;
template <typename T>
istream &operator>>(istream &in, vector<T> &a) {
  for (int i = 0; i < a.size(); ++i) in >> a[i];
  return in;
}
template <typename T>
ostream &operator<<(ostream &out, const vector<T> &a) {
  for (int i = 0; i < a.size(); ++i) out << a[i] << " ";
  return out;
}
int main() {
  int n;
  cin >> n;
  vector<int> arr(n);
  for (int i = 0; i < n; ++i) {
    cin >> arr[i];
  }
  sort(arr.begin(), arr.end());
  int x = arr[0], y = arr[1], z = arr[2];
  long long int answ_x = 0, answ_y = 0, answ_z = 0;
  for (int i = 0; i < n; ++i) {
    if (arr[i] == x) answ_x++;
    if (arr[i] == y) answ_y++;
    if (arr[i] == z) answ_z++;
  }
  if (x == y && y == z)
    cout << (answ_x) * (answ_x - 1) * (answ_x - 2) / 6;
  else if (x == y)
    cout << (answ_x) * (answ_x - 1) * answ_z / 2;
  else if (y == z)
    cout << (answ_y) * (answ_y - 1) * answ_x / 2;
  else
    cout << answ_x * answ_y * answ_z;
  cout << endl;
  return 0;
  ;
}

### 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;
template <typename T>
istream &operator>>(istream &in, vector<T> &a) {
  for (int i = 0; i < a.size(); ++i) in >> a[i];
  return in;
}
template <typename T>
ostream &operator<<(ostream &out, const vector<T> &a) {
  for (int i = 0; i < a.size(); ++i) out << a[i] << " ";
  return out;
}
int main() {
  int n;
  cin >> n;
  vector<int> arr(n);
  for (int i = 0; i < n; ++i) {
    cin >> arr[i];
  }
  sort(arr.begin(), arr.end());
  int x = arr[0], y = arr[1], z = arr[2];
  long long int answ_x = 0, answ_y = 0, answ_z = 0;
  for (int i = 0; i < n; ++i) {
    if (arr[i] == x) answ_x++;
    if (arr[i] == y) answ_y++;
    if (arr[i] == z) answ_z++;
  }
  if (x == y && y == z)
    cout << (answ_x) * (answ_x - 1) * (answ_x - 2) / 6;
  else if (x == y)
    cout << (answ_x) * (answ_x - 1) * answ_z / 2;
  else if (y == z)
    cout << (answ_y) * (answ_y - 1) * answ_x / 2;
  else
    cout << answ_x * answ_y * answ_z;
  cout << endl;
  return 0;
  ;
}

```