#include <bits/stdc++.h>
using namespace std;
long long nCr(long long x, long long y) {
  long long ans = 1;
  for (long long i = 1; i <= y; i++, x--) ans *= x;
  for (long long i = 2; i <= y; i++) ans /= i;
  return ans;
}
void solve() {
  long long n;
  cin >> n;
  vector<long long> a(n);
  map<long long, long long> f;
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
    f[a[i]]++;
  }
  sort(a.begin(), a.end());
  map<long long, long long> m;
  for (long long i = 0; i < 3; i++) m[a[i]]++;
  long long ans = 1;
  for (auto X : m) {
    ans *= nCr(f[X.first], X.second);
  }
  cout << ans << "\n";
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long t = 1;
  while (t--) {
    solve();
  }
}

### Prompt

Your challenge is to write 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 nCr(long long x, long long y) {
  long long ans = 1;
  for (long long i = 1; i <= y; i++, x--) ans *= x;
  for (long long i = 2; i <= y; i++) ans /= i;
  return ans;
}
void solve() {
  long long n;
  cin >> n;
  vector<long long> a(n);
  map<long long, long long> f;
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
    f[a[i]]++;
  }
  sort(a.begin(), a.end());
  map<long long, long long> m;
  for (long long i = 0; i < 3; i++) m[a[i]]++;
  long long ans = 1;
  for (auto X : m) {
    ans *= nCr(f[X.first], X.second);
  }
  cout << ans << "\n";
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long t = 1;
  while (t--) {
    solve();
  }
}

```