#include <bits/stdc++.h>
using namespace std;
const int MaxN = 1e5;
int a[MaxN + 5];
map<int, long long> cnt;
int n;
int main() {
  while (~scanf("%d", &n)) {
    int tot = 0;
    for (int i = 1; i <= n; i++) {
      int num;
      scanf("%d", &num);
      if (!cnt[num]) a[++tot] = num;
      cnt[num]++;
    }
    sort(a + 1, a + 1 + tot);
    long long ans = 0;
    if (cnt[a[1]] >= 3)
      ans = cnt[a[1]] * (cnt[a[1]] - 1LL) * (cnt[a[1]] - 2LL) / 6LL;
    else if (cnt[a[1]] == 2)
      ans = cnt[a[2]];
    else if (cnt[a[1]] == 1) {
      if (cnt[a[2]] >= 2)
        ans = cnt[a[2]] * (cnt[a[2]] - 1) / 2LL;
      else if (cnt[a[2]] == 1)
        ans = cnt[a[3]];
    }
    printf("%lld\n", ans);
  }
  return 0;
}

### Prompt

Please provide a CPP coded solution 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;
const int MaxN = 1e5;
int a[MaxN + 5];
map<int, long long> cnt;
int n;
int main() {
  while (~scanf("%d", &n)) {
    int tot = 0;
    for (int i = 1; i <= n; i++) {
      int num;
      scanf("%d", &num);
      if (!cnt[num]) a[++tot] = num;
      cnt[num]++;
    }
    sort(a + 1, a + 1 + tot);
    long long ans = 0;
    if (cnt[a[1]] >= 3)
      ans = cnt[a[1]] * (cnt[a[1]] - 1LL) * (cnt[a[1]] - 2LL) / 6LL;
    else if (cnt[a[1]] == 2)
      ans = cnt[a[2]];
    else if (cnt[a[1]] == 1) {
      if (cnt[a[2]] >= 2)
        ans = cnt[a[2]] * (cnt[a[2]] - 1) / 2LL;
      else if (cnt[a[2]] == 1)
        ans = cnt[a[3]];
    }
    printf("%lld\n", ans);
  }
  return 0;
}

```