#include <bits/stdc++.h>
using namespace std;
long long n, a[100005];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  long i;
  for (i = 0; i <= n - 1; i++) cin >> a[i];
  sort(a, a + n);
  long long pc = 1, qc = 1, rc = 1;
  long long b[3];
  long long p = a[0], q = a[1], r = a[2];
  if (p == q && q == r) {
    long long c = 3;
    for (i = 3; i <= n - 1; i++)
      if (a[i] == p) c++;
    cout << c * (c - 1) * (c - 2) / 6;
  } else if (p == q) {
    long long pc = 2, rc = 1;
    for (i = 3; i <= n - 1; i++)
      if (a[i] == p)
        pc++;
      else if (a[i] == r)
        rc++;
    cout << pc * (pc - 1) * rc / 2;
  } else if (q == r) {
    long long pc = 1, rc = 2;
    for (i = 3; i <= n - 1; i++)
      if (a[i] == p)
        pc++;
      else if (a[i] == r)
        rc++;
    cout << rc * (rc - 1) * pc / 2;
  } else {
    long long rc = 1;
    for (i = 3; i <= n - 1; i++)
      if (a[i] == r) rc++;
    cout << rc;
  }
  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;
long long n, a[100005];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  long i;
  for (i = 0; i <= n - 1; i++) cin >> a[i];
  sort(a, a + n);
  long long pc = 1, qc = 1, rc = 1;
  long long b[3];
  long long p = a[0], q = a[1], r = a[2];
  if (p == q && q == r) {
    long long c = 3;
    for (i = 3; i <= n - 1; i++)
      if (a[i] == p) c++;
    cout << c * (c - 1) * (c - 2) / 6;
  } else if (p == q) {
    long long pc = 2, rc = 1;
    for (i = 3; i <= n - 1; i++)
      if (a[i] == p)
        pc++;
      else if (a[i] == r)
        rc++;
    cout << pc * (pc - 1) * rc / 2;
  } else if (q == r) {
    long long pc = 1, rc = 2;
    for (i = 3; i <= n - 1; i++)
      if (a[i] == p)
        pc++;
      else if (a[i] == r)
        rc++;
    cout << rc * (rc - 1) * pc / 2;
  } else {
    long long rc = 1;
    for (i = 3; i <= n - 1; i++)
      if (a[i] == r) rc++;
    cout << rc;
  }
  return 0;
}

```