#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class T, class U>
ostream& operator<<(ostream& o, const pair<T, U>& p) {
  o << "(" << p.first << "," << p.second << ")";
  return o;
}
template <class T>
ostream& operator<<(ostream& o, const vector<T>& v) {
  o << "[";
  for (T t : v) {
    o << t << ",";
  }
  o << "]";
  return o;
}
ll C(int n, int r) {
  ll x = 1;
  for (int(i) = 0; (i) < (int)(r); ++(i)) x *= n - i;
  for (int(i) = 0; (i) < (int)(r); ++(i)) x /= i + 1;
  return x;
}
int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int(i) = 0; (i) < (int)(n); ++(i)) cin >> a[i];
  vector<int> s(a);
  sort((s).begin(), (s).end());
  map<int, int> ct;
  for (int(i) = 0; (i) < (int)(n); ++(i)) ++ct[a[i]];
  ll ans = ct[s[2]];
  if (s[2] == s[1] && s[2] == s[0])
    ans = C(ct[s[2]], 3);
  else if (s[2] == s[1])
    ans = C(ct[s[2]], 2);
  cout << ans << endl;
  return 0;
}

### 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;
using ll = long long;
template <class T, class U>
ostream& operator<<(ostream& o, const pair<T, U>& p) {
  o << "(" << p.first << "," << p.second << ")";
  return o;
}
template <class T>
ostream& operator<<(ostream& o, const vector<T>& v) {
  o << "[";
  for (T t : v) {
    o << t << ",";
  }
  o << "]";
  return o;
}
ll C(int n, int r) {
  ll x = 1;
  for (int(i) = 0; (i) < (int)(r); ++(i)) x *= n - i;
  for (int(i) = 0; (i) < (int)(r); ++(i)) x /= i + 1;
  return x;
}
int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int(i) = 0; (i) < (int)(n); ++(i)) cin >> a[i];
  vector<int> s(a);
  sort((s).begin(), (s).end());
  map<int, int> ct;
  for (int(i) = 0; (i) < (int)(n); ++(i)) ++ct[a[i]];
  ll ans = ct[s[2]];
  if (s[2] == s[1] && s[2] == s[0])
    ans = C(ct[s[2]], 3);
  else if (s[2] == s[1])
    ans = C(ct[s[2]], 2);
  cout << ans << endl;
  return 0;
}

```