#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  scanf("%d", &n);
  long long a[n];
  for (int i = 0; i < n; i++) scanf("%lld", &a[i]);
  sort(a, a + n);
  long long count_a = 0, count_b = 0, count_c = 0;
  long long x, y, z, ans = 0;
  x = a[0], y = a[1], z = a[2];
  for (int i = 0; i < n; i++) {
    if (x == a[i]) count_a++;
    if (y == a[i]) count_b++;
    if (z == a[i]) count_c++;
  }
  if (x != y && y != z) {
    ans = count_a * count_b * count_c;
  } else if (x == y && y != z) {
    ans = count_a * (count_a - 1) / 2 * count_c;
  } else if (y == z && x != y) {
    ans = count_b * (count_b - 1) / 2 * count_a;
  } else if (x == y && y == z) {
    ans = count_a * (count_a - 1) * (count_a - 2) / 6;
  }
  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;
int main() {
  int n;
  scanf("%d", &n);
  long long a[n];
  for (int i = 0; i < n; i++) scanf("%lld", &a[i]);
  sort(a, a + n);
  long long count_a = 0, count_b = 0, count_c = 0;
  long long x, y, z, ans = 0;
  x = a[0], y = a[1], z = a[2];
  for (int i = 0; i < n; i++) {
    if (x == a[i]) count_a++;
    if (y == a[i]) count_b++;
    if (z == a[i]) count_c++;
  }
  if (x != y && y != z) {
    ans = count_a * count_b * count_c;
  } else if (x == y && y != z) {
    ans = count_a * (count_a - 1) / 2 * count_c;
  } else if (y == z && x != y) {
    ans = count_b * (count_b - 1) / 2 * count_a;
  } else if (x == y && y == z) {
    ans = count_a * (count_a - 1) * (count_a - 2) / 6;
  }
  printf("%lld\n", ans);
  return 0;
}

```