#include <bits/stdc++.h>
using namespace std;
long long n, min1, min2, min3;
vector<long long> num;
void read() {
  cin >> n;
  num.resize(n);
  vector<long long> gg;
  gg.resize(n);
  for (long long i = 0; i < n; ++i) {
    cin >> num[i];
    gg[i] = num[i];
  }
  sort(gg.begin(), gg.end());
  min1 = gg[0];
  min2 = gg[1];
  min3 = gg[2];
  long long cnt1 = 0, cnt2 = 0, cnt3 = 0;
  for (long long i = 0; i < n; ++i) {
    if (num[i] == min1) {
      ++cnt1;
    }
    if (num[i] == min2) {
      ++cnt2;
    }
    if (num[i] == min3) {
      ++cnt3;
    }
  }
  if (min1 == min2 and min2 == min3) {
    cout << cnt1 * (cnt1 - 1) * (cnt1 - 2) / 6;
  } else if (min1 == min2) {
    cout << cnt1 * (cnt1 - 1) * cnt3 / 2;
  } else if (min1 == min3) {
    cout << cnt1 * cnt2 + (cnt1 - 1) / 2;
  } else if (min2 == min3) {
    cout << cnt1 * cnt2 * (cnt2 - 1) / 2;
  } else {
    cout << cnt1 * cnt2 * cnt3;
  }
}
int main() { read(); }

### Prompt

Please create a solution in cpp 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, min1, min2, min3;
vector<long long> num;
void read() {
  cin >> n;
  num.resize(n);
  vector<long long> gg;
  gg.resize(n);
  for (long long i = 0; i < n; ++i) {
    cin >> num[i];
    gg[i] = num[i];
  }
  sort(gg.begin(), gg.end());
  min1 = gg[0];
  min2 = gg[1];
  min3 = gg[2];
  long long cnt1 = 0, cnt2 = 0, cnt3 = 0;
  for (long long i = 0; i < n; ++i) {
    if (num[i] == min1) {
      ++cnt1;
    }
    if (num[i] == min2) {
      ++cnt2;
    }
    if (num[i] == min3) {
      ++cnt3;
    }
  }
  if (min1 == min2 and min2 == min3) {
    cout << cnt1 * (cnt1 - 1) * (cnt1 - 2) / 6;
  } else if (min1 == min2) {
    cout << cnt1 * (cnt1 - 1) * cnt3 / 2;
  } else if (min1 == min3) {
    cout << cnt1 * cnt2 + (cnt1 - 1) / 2;
  } else if (min2 == min3) {
    cout << cnt1 * cnt2 * (cnt2 - 1) / 2;
  } else {
    cout << cnt1 * cnt2 * cnt3;
  }
}
int main() { read(); }

```