#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 50;
struct node {
  int val, id;
} arr[maxn];
bool cmp(node a, node b) { return a.val < b.val; }
int main() {
  int n;
  while (~scanf("%d", &n)) {
    for (int i = 1; i <= n; ++i) {
      scanf("%d", &arr[i].val);
      arr[i].id = i;
    }
    sort(arr + 1, arr + n + 1, cmp);
    int i = 1, j = 1;
    long long a = 0, b = 0, c = 0, ans = 0;
    while (arr[j].val == arr[i].val && j <= n) a++, j++;
    i = j;
    while (arr[j].val == arr[i].val && j <= n) b++, j++;
    i = j;
    while (arr[j].val == arr[i].val && j <= n) c++, j++;
    if (a == 1) {
      if (b == 1)
        ans = c;
      else
        ans = b * (b - 1) / 2;
    } else if (a == 2)
      ans = b;
    else if (a == 3)
      ans = 1;
    else
      ans = a * (a - 1) * (a - 2) / 6;
    printf("%lld\n", ans);
  }
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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 + 50;
struct node {
  int val, id;
} arr[maxn];
bool cmp(node a, node b) { return a.val < b.val; }
int main() {
  int n;
  while (~scanf("%d", &n)) {
    for (int i = 1; i <= n; ++i) {
      scanf("%d", &arr[i].val);
      arr[i].id = i;
    }
    sort(arr + 1, arr + n + 1, cmp);
    int i = 1, j = 1;
    long long a = 0, b = 0, c = 0, ans = 0;
    while (arr[j].val == arr[i].val && j <= n) a++, j++;
    i = j;
    while (arr[j].val == arr[i].val && j <= n) b++, j++;
    i = j;
    while (arr[j].val == arr[i].val && j <= n) c++, j++;
    if (a == 1) {
      if (b == 1)
        ans = c;
      else
        ans = b * (b - 1) / 2;
    } else if (a == 2)
      ans = b;
    else if (a == 3)
      ans = 1;
    else
      ans = a * (a - 1) * (a - 2) / 6;
    printf("%lld\n", ans);
  }
  return 0;
}

```