#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1000000007;
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long n;
  cin >> n;
  long long arr[n];
  for (long long i = 0; i < n; i++) cin >> arr[i];
  sort(arr, arr + n);
  long long a, b, c;
  long long flag = 0;
  a = arr[0];
  b = arr[1];
  c = arr[2];
  long long ca = 1;
  long long cb, cc = 1;
  for (long long i = 3; i < n; i++) {
    if (arr[i] == c)
      cc++;
    else
      break;
  }
  if (a == b && b == c) {
    cout << ((cc + 2) * (cc + 1) * cc) / 6;
  } else if (b == c) {
    cout << ((cc + 1) * cc) / 2;
  } else {
    cout << cc;
  }
  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 long long MOD = 1000000007;
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long n;
  cin >> n;
  long long arr[n];
  for (long long i = 0; i < n; i++) cin >> arr[i];
  sort(arr, arr + n);
  long long a, b, c;
  long long flag = 0;
  a = arr[0];
  b = arr[1];
  c = arr[2];
  long long ca = 1;
  long long cb, cc = 1;
  for (long long i = 3; i < n; i++) {
    if (arr[i] == c)
      cc++;
    else
      break;
  }
  if (a == b && b == c) {
    cout << ((cc + 2) * (cc + 1) * cc) / 6;
  } else if (b == c) {
    cout << ((cc + 1) * cc) / 2;
  } else {
    cout << cc;
  }
  return 0;
}

```