#include <bits/stdc++.h>
using namespace std;
long long q[100010];
long long C(long long n1, long long n2) {
  long long temp = 1;
  for (long long i = 1; i <= n2; i++) {
    temp *= (n1 - i + 1);
  }
  for (long long i = 1; i <= n2; i++) {
    temp /= i;
  }
  return temp;
}
int main() {
  long long i, j, k, a, b, c, n;
  scanf("%I64d", &n);
  for (i = 0; i < n; i++) {
    scanf("%I64d", &q[i]);
  }
  sort(q, q + n);
  a = q[0];
  b = q[1];
  c = q[2];
  long long c1 = 0;
  long long c2 = 0;
  long long c3 = 0;
  for (i = 0; i < n; i++) {
    if (q[i] == a) c1++;
    if (q[i] == b) c2++;
    if (q[i] == c) c3++;
  }
  long long ans = 0;
  if (a == b && b == c) {
    ans = C(c1, 3);
  } else if (a == b && b != c) {
    ans = C(c1, 2) * c3;
  } else if (a != b && b == c) {
    ans = C(c2, 2) * c1;
  } else {
    ans = c1 * c2 * c3;
  }
  printf("%I64d\n", ans);
  return 0;
}

### Prompt

In cpp, your task is to solve 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 q[100010];
long long C(long long n1, long long n2) {
  long long temp = 1;
  for (long long i = 1; i <= n2; i++) {
    temp *= (n1 - i + 1);
  }
  for (long long i = 1; i <= n2; i++) {
    temp /= i;
  }
  return temp;
}
int main() {
  long long i, j, k, a, b, c, n;
  scanf("%I64d", &n);
  for (i = 0; i < n; i++) {
    scanf("%I64d", &q[i]);
  }
  sort(q, q + n);
  a = q[0];
  b = q[1];
  c = q[2];
  long long c1 = 0;
  long long c2 = 0;
  long long c3 = 0;
  for (i = 0; i < n; i++) {
    if (q[i] == a) c1++;
    if (q[i] == b) c2++;
    if (q[i] == c) c3++;
  }
  long long ans = 0;
  if (a == b && b == c) {
    ans = C(c1, 3);
  } else if (a == b && b != c) {
    ans = C(c1, 2) * c3;
  } else if (a != b && b == c) {
    ans = C(c2, 2) * c1;
  } else {
    ans = c1 * c2 * c3;
  }
  printf("%I64d\n", ans);
  return 0;
}

```