#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 10;
const int maxm = 1e6;
long long a[maxn];
map<long long, long long> w;
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%I64d", &a[i]);
    w[a[i]]++;
  }
  sort(a + 1, a + 1 + n);
  if (a[1] == a[2] && a[2] == a[3]) {
    long long ans = w[a[1]];
    cout << ((ans - 1) * (ans - 2) * ans) / 6 << endl;
  } else if (a[1] == a[2] && a[1] != a[3]) {
    long long ans1 = w[a[1]];
    long long ans2 = w[a[3]];
    cout << (ans1 * (ans1 - 1) / 2) * ans2 << endl;
  } else if (a[1] != a[2] && a[2] == a[3]) {
    long long ans1 = w[a[2]];
    long long ans2 = w[a[1]];
    cout << (ans1 * (ans1 - 1) / 2) * ans2 << endl;
  } else {
    long long ans1 = w[a[1]];
    long long ans2 = w[a[2]];
    long long ans3 = w[a[3]];
    cout << ans1 * ans2 * ans3 << endl;
  }
}

### Prompt

Generate 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 namespace std;
const int maxn = 1e5 + 10;
const int maxm = 1e6;
long long a[maxn];
map<long long, long long> w;
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%I64d", &a[i]);
    w[a[i]]++;
  }
  sort(a + 1, a + 1 + n);
  if (a[1] == a[2] && a[2] == a[3]) {
    long long ans = w[a[1]];
    cout << ((ans - 1) * (ans - 2) * ans) / 6 << endl;
  } else if (a[1] == a[2] && a[1] != a[3]) {
    long long ans1 = w[a[1]];
    long long ans2 = w[a[3]];
    cout << (ans1 * (ans1 - 1) / 2) * ans2 << endl;
  } else if (a[1] != a[2] && a[2] == a[3]) {
    long long ans1 = w[a[2]];
    long long ans2 = w[a[1]];
    cout << (ans1 * (ans1 - 1) / 2) * ans2 << endl;
  } else {
    long long ans1 = w[a[1]];
    long long ans2 = w[a[2]];
    long long ans3 = w[a[3]];
    cout << ans1 * ans2 * ans3 << endl;
  }
}

```