#include <bits/stdc++.h>
using namespace std;
const int MAX_N = 100000;
int n;
int a[MAX_N];
long long choose(int n, int k) {
  k = min(k, n - k);
  long long x = 1;
  for (long long i = n; i > n - k; i--) {
    x *= i;
  }
  for (int i = k; i >= 2; i--) {
    x /= i;
  }
  return x;
}
int main() {
  cin >> n;
  unordered_map<int, int> freq_map;
  vector<int> keys;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    if (freq_map.count(a[i]) == 0) {
      freq_map[a[i]] = 1;
      keys.push_back(a[i]);
    } else {
      freq_map[a[i]]++;
    }
  }
  sort(keys.begin(), keys.end());
  int left = 3;
  for (int i = 0; i < 3; i++) {
    if (freq_map[keys[i]] >= left) {
      cout << choose(freq_map[keys[i]], left) << endl;
      break;
    }
    left -= freq_map[keys[i]];
  }
}

### 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;
const int MAX_N = 100000;
int n;
int a[MAX_N];
long long choose(int n, int k) {
  k = min(k, n - k);
  long long x = 1;
  for (long long i = n; i > n - k; i--) {
    x *= i;
  }
  for (int i = k; i >= 2; i--) {
    x /= i;
  }
  return x;
}
int main() {
  cin >> n;
  unordered_map<int, int> freq_map;
  vector<int> keys;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    if (freq_map.count(a[i]) == 0) {
      freq_map[a[i]] = 1;
      keys.push_back(a[i]);
    } else {
      freq_map[a[i]]++;
    }
  }
  sort(keys.begin(), keys.end());
  int left = 3;
  for (int i = 0; i < 3; i++) {
    if (freq_map[keys[i]] >= left) {
      cout << choose(freq_map[keys[i]], left) << endl;
      break;
    }
    left -= freq_map[keys[i]];
  }
}

```