#include <bits/stdc++.h>
using namespace std;
long long a[100001];
map<long long, long long> mp;
inline long long Cnm(long long n, long long m) {
  long long cha = n - m + 1, shang = 1, xia = 1, ans;
  for (long long i = n; i >= cha; i--) shang *= i;
  for (long long i = 1; i <= m; i++) xia *= i;
  ans = shang / xia;
  return ans;
}
int main() {
  register long long n;
  scanf("%lld", &n);
  for (register int i = 1; i <= n; i++) {
    scanf("%lld", &a[i]);
    mp[a[i]]++;
  }
  sort(a + 1, a + n + 1);
  if (a[1] == a[2] && a[2] == a[3]) {
    printf("%lld\n", Cnm(mp[a[1]], 3));
  } else if (a[1] < a[2] && a[2] < a[3]) {
    printf("%lld\n", mp[a[1]] * mp[a[2]] * mp[a[3]]);
  } else if (a[1] == a[2] && a[2] < a[3]) {
    printf("%lld\n", Cnm(mp[a[1]], 2) * mp[a[3]]);
  } else if (a[1] < a[2] && a[2] == a[3]) {
    printf("%lld\n", mp[a[1]] * Cnm(mp[a[2]], 2));
  }
  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;
long long a[100001];
map<long long, long long> mp;
inline long long Cnm(long long n, long long m) {
  long long cha = n - m + 1, shang = 1, xia = 1, ans;
  for (long long i = n; i >= cha; i--) shang *= i;
  for (long long i = 1; i <= m; i++) xia *= i;
  ans = shang / xia;
  return ans;
}
int main() {
  register long long n;
  scanf("%lld", &n);
  for (register int i = 1; i <= n; i++) {
    scanf("%lld", &a[i]);
    mp[a[i]]++;
  }
  sort(a + 1, a + n + 1);
  if (a[1] == a[2] && a[2] == a[3]) {
    printf("%lld\n", Cnm(mp[a[1]], 3));
  } else if (a[1] < a[2] && a[2] < a[3]) {
    printf("%lld\n", mp[a[1]] * mp[a[2]] * mp[a[3]]);
  } else if (a[1] == a[2] && a[2] < a[3]) {
    printf("%lld\n", Cnm(mp[a[1]], 2) * mp[a[3]]);
  } else if (a[1] < a[2] && a[2] == a[3]) {
    printf("%lld\n", mp[a[1]] * Cnm(mp[a[2]], 2));
  }
  return 0;
}

```