#include <bits/stdc++.h>
using namespace std;
long long n, i, a[100009], hasil, b[100009], d[4], cnt;
long long rek(long long x, long long y) {
  if (y == 1) {
    return x;
  } else if (y == 2) {
    return x * (x - 1) / 2;
  } else {
    return x * (x - 1) * (x - 2) / 6;
  }
}
int main() {
  cin >> n;
  for (i = 0; i < n; ++i) {
    cin >> a[i];
  }
  sort(a, a + n);
  cnt = 0;
  b[cnt] = 1;
  for (i = 1; i < n; ++i) {
    if (a[i] != a[i - 1]) {
      cnt++;
    }
    b[cnt]++;
  }
  d[0] = 1;
  d[1] = 0;
  d[2] = 0;
  if (a[1] == a[0]) {
    d[0] = 2;
    if (a[2] == a[1]) {
      d[0] = 3;
    } else {
      d[1] = 1;
    }
  } else {
    d[1] = 1;
    if (a[2] == a[1]) {
      d[1] = 2;
    } else {
      d[2] = 1;
    }
  }
  hasil = rek(b[0], d[0]);
  if (d[1] > 0) {
    hasil *= rek(b[1], d[1]);
  }
  if (d[2] > 0) {
    hasil *= rek(b[2], d[2]);
  }
  cout << hasil << endl;
}

### Prompt

Generate a Cpp solution 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 n, i, a[100009], hasil, b[100009], d[4], cnt;
long long rek(long long x, long long y) {
  if (y == 1) {
    return x;
  } else if (y == 2) {
    return x * (x - 1) / 2;
  } else {
    return x * (x - 1) * (x - 2) / 6;
  }
}
int main() {
  cin >> n;
  for (i = 0; i < n; ++i) {
    cin >> a[i];
  }
  sort(a, a + n);
  cnt = 0;
  b[cnt] = 1;
  for (i = 1; i < n; ++i) {
    if (a[i] != a[i - 1]) {
      cnt++;
    }
    b[cnt]++;
  }
  d[0] = 1;
  d[1] = 0;
  d[2] = 0;
  if (a[1] == a[0]) {
    d[0] = 2;
    if (a[2] == a[1]) {
      d[0] = 3;
    } else {
      d[1] = 1;
    }
  } else {
    d[1] = 1;
    if (a[2] == a[1]) {
      d[1] = 2;
    } else {
      d[2] = 1;
    }
  }
  hasil = rek(b[0], d[0]);
  if (d[1] > 0) {
    hasil *= rek(b[1], d[1]);
  }
  if (d[2] > 0) {
    hasil *= rek(b[2], d[2]);
  }
  cout << hasil << endl;
}

```