#include <bits/stdc++.h>
using namespace std;
const double pi = 3.141592653589793;
const int SZ = 1000005, mod = 1000000007;
int ara[SZ];
long long x;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> ara[i];
  sort(ara, ara + n);
  long long a = 1, b = 1, c = 1;
  x = ara[0];
  for (int i = 1; i < n; i++) {
    if (ara[i] == x)
      a++;
    else
      break;
  }
  if (a >= 3) {
    cout << a * (a - 1) * (a - 2) / 6 << endl;
    return 0;
  }
  x = ara[a];
  for (int i = a + 1; i < n; i++) {
    if (ara[i] == x)
      b++;
    else
      break;
  }
  if (a + b >= 3) {
    if (a == 1) {
      cout << b * (b - 1) / 2 << endl;
    } else
      cout << b << endl;
    return 0;
  }
  x = ara[a + b];
  for (int i = a + b + 1; i < n; i++) {
    if (ara[i] == x)
      c++;
    else
      break;
  }
  cout << c << endl;
  return 0;
}

### Prompt

Please create a solution in cpp 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 namespace std;
const double pi = 3.141592653589793;
const int SZ = 1000005, mod = 1000000007;
int ara[SZ];
long long x;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> ara[i];
  sort(ara, ara + n);
  long long a = 1, b = 1, c = 1;
  x = ara[0];
  for (int i = 1; i < n; i++) {
    if (ara[i] == x)
      a++;
    else
      break;
  }
  if (a >= 3) {
    cout << a * (a - 1) * (a - 2) / 6 << endl;
    return 0;
  }
  x = ara[a];
  for (int i = a + 1; i < n; i++) {
    if (ara[i] == x)
      b++;
    else
      break;
  }
  if (a + b >= 3) {
    if (a == 1) {
      cout << b * (b - 1) / 2 << endl;
    } else
      cout << b << endl;
    return 0;
  }
  x = ara[a + b];
  for (int i = a + b + 1; i < n; i++) {
    if (ara[i] == x)
      c++;
    else
      break;
  }
  cout << c << endl;
  return 0;
}

```