#include <bits/stdc++.h>
using namespace std;
const int N = 100100;
int val[N], cnt[N];
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", val + i);
  vector<int> vec;
  for (int i = 1; i <= n; i++) vec.push_back(val[i]);
  sort(vec.begin(), vec.end());
  vec.resize((unique(vec.begin(), vec.end()) - vec.begin()));
  for (int i = 1; i <= n; i++)
    cnt[lower_bound(vec.begin(), vec.end(), val[i]) - vec.begin()]++;
  if (cnt[0] >= 3) {
    printf("%I64d\n", (long long)cnt[0] * (cnt[0] - 1) * (cnt[0] - 2) / 6);
  } else if (cnt[0] + cnt[1] >= 3) {
    if (cnt[0] == 1) {
      printf("%I64d\n", (long long)cnt[1] * (cnt[1] - 1) / 2);
    } else {
      printf("%d\n", cnt[1]);
    }
  } else {
    printf("%d\n", cnt[2]);
  }
  return 0;
}

### Prompt

Create a solution in cpp for 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 N = 100100;
int val[N], cnt[N];
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", val + i);
  vector<int> vec;
  for (int i = 1; i <= n; i++) vec.push_back(val[i]);
  sort(vec.begin(), vec.end());
  vec.resize((unique(vec.begin(), vec.end()) - vec.begin()));
  for (int i = 1; i <= n; i++)
    cnt[lower_bound(vec.begin(), vec.end(), val[i]) - vec.begin()]++;
  if (cnt[0] >= 3) {
    printf("%I64d\n", (long long)cnt[0] * (cnt[0] - 1) * (cnt[0] - 2) / 6);
  } else if (cnt[0] + cnt[1] >= 3) {
    if (cnt[0] == 1) {
      printf("%I64d\n", (long long)cnt[1] * (cnt[1] - 1) / 2);
    } else {
      printf("%d\n", cnt[1]);
    }
  } else {
    printf("%d\n", cnt[2]);
  }
  return 0;
}

```