#include <bits/stdc++.h>
using namespace std;
template <class c>
struct rge {
  c b, e;
};
template <class c>
rge<c> range(c i, c j) {
  return rge<c>{i, j};
}
template <class c>
auto dud(c* x) -> decltype(cerr << *x, 0);
template <class c>
char dud(...);
struct debug {
  template <class c>
  debug& operator<<(const c&) {
    return *this;
  }
};
long long answer(long long n, long long r) {
  debug() << " ["
          << "n"
             ": "
          << (n)
          << "] "
             " ["
          << "r"
             ": "
          << (r) << "] ";
  long long deno = 1;
  long long num = 1;
  for (int i = 1; i <= r; i++) {
    deno *= i;
    num *= (n - i + 1);
  }
  debug() << " ["
          << "num"
             ": "
          << (num)
          << "] "
             " ["
          << "deno"
             ": "
          << (deno) << "] ";
  return num / deno;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  set<int> a;
  map<int, int> cnt;
  for (int i = 0; i < n; i++) {
    int tmp;
    cin >> tmp;
    a.insert(tmp);
    cnt[tmp]++;
  }
  debug() << " ["
          << "cnt"
             ": "
          << (cnt) << "] ";
  int c = 3;
  for (auto u : a) {
    debug() << " ["
            << "c"
               ": "
            << (c) << "] ";
    if (c - cnt[u] <= 0) {
      cout << answer(cnt[u], c);
      exit(0);
    }
    c -= cnt[u];
  }
}

### Prompt

Please formulate 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;
template <class c>
struct rge {
  c b, e;
};
template <class c>
rge<c> range(c i, c j) {
  return rge<c>{i, j};
}
template <class c>
auto dud(c* x) -> decltype(cerr << *x, 0);
template <class c>
char dud(...);
struct debug {
  template <class c>
  debug& operator<<(const c&) {
    return *this;
  }
};
long long answer(long long n, long long r) {
  debug() << " ["
          << "n"
             ": "
          << (n)
          << "] "
             " ["
          << "r"
             ": "
          << (r) << "] ";
  long long deno = 1;
  long long num = 1;
  for (int i = 1; i <= r; i++) {
    deno *= i;
    num *= (n - i + 1);
  }
  debug() << " ["
          << "num"
             ": "
          << (num)
          << "] "
             " ["
          << "deno"
             ": "
          << (deno) << "] ";
  return num / deno;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  set<int> a;
  map<int, int> cnt;
  for (int i = 0; i < n; i++) {
    int tmp;
    cin >> tmp;
    a.insert(tmp);
    cnt[tmp]++;
  }
  debug() << " ["
          << "cnt"
             ": "
          << (cnt) << "] ";
  int c = 3;
  for (auto u : a) {
    debug() << " ["
            << "c"
               ": "
            << (c) << "] ";
    if (c - cnt[u] <= 0) {
      cout << answer(cnt[u], c);
      exit(0);
    }
    c -= cnt[u];
  }
}

```