#include <bits/stdc++.h>
using namespace std;
#pragma comment(linker, "/stack:200000000")
long long int ans, t, n, m, i, j, k, a, b, c, d, e, f, g;
string s, s2, s3, s4;
long long int ar[(int)(1e6 + 10)];
vector<long long int> v;
map<long long int, long long int> mp;
void brainfuck();
int main() {
  ios_base::sync_with_stdio(NULL);
  cin.tie(NULL);
  cout.tie(NULL);
  brainfuck();
  return 0;
}
void brainfuck() {
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> a;
    mp[a]++;
    v.push_back(a);
  }
  sort(v.begin(), v.end());
  if (v[0] != v[1] && v[2] != v[1]) {
    a = mp[v[0]];
    b = mp[v[1]];
    c = mp[v[2]];
    ans = a * b * c;
  } else if (v[0] == v[1] && v[1] == v[2]) {
    a = mp[v[0]];
    for (i = 1; i < a - 1; i++) {
      b = a - i;
      ans += b * (b - 1) / 2;
    }
  } else if (v[0] == v[1] && v[1] != v[2]) {
    c = mp[v[2]];
    a = mp[v[0]];
    ans = (a * (a - 1) / 2) * c;
  } else if (v[0] != v[1] && v[1] == v[2]) {
    a = mp[v[0]];
    b = mp[v[1]];
    ans = (b * (b - 1) / 2) * a;
  }
  cout << ans;
}

### 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;
#pragma comment(linker, "/stack:200000000")
long long int ans, t, n, m, i, j, k, a, b, c, d, e, f, g;
string s, s2, s3, s4;
long long int ar[(int)(1e6 + 10)];
vector<long long int> v;
map<long long int, long long int> mp;
void brainfuck();
int main() {
  ios_base::sync_with_stdio(NULL);
  cin.tie(NULL);
  cout.tie(NULL);
  brainfuck();
  return 0;
}
void brainfuck() {
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> a;
    mp[a]++;
    v.push_back(a);
  }
  sort(v.begin(), v.end());
  if (v[0] != v[1] && v[2] != v[1]) {
    a = mp[v[0]];
    b = mp[v[1]];
    c = mp[v[2]];
    ans = a * b * c;
  } else if (v[0] == v[1] && v[1] == v[2]) {
    a = mp[v[0]];
    for (i = 1; i < a - 1; i++) {
      b = a - i;
      ans += b * (b - 1) / 2;
    }
  } else if (v[0] == v[1] && v[1] != v[2]) {
    c = mp[v[2]];
    a = mp[v[0]];
    ans = (a * (a - 1) / 2) * c;
  } else if (v[0] != v[1] && v[1] == v[2]) {
    a = mp[v[0]];
    b = mp[v[1]];
    ans = (b * (b - 1) / 2) * a;
  }
  cout << ans;
}

```