#include <bits/stdc++.h>
using namespace std;

int main() {
  int N;
  cin >> N;
  map<pair<int, int>, int> MA;
  long ans = 0;
  for (double A; cin >> A;) {
    long a = round(A * 1e9);
    int x = 0, y = 0;
    while (a % 2 == 0) a /= 2, x++;
    while (a % 5 == 0) a /= 5, y++;
    for (auto [xy, cnt] : MA) {
      if (x + xy.first >= 18 && y + xy.second >= 18) ans += cnt;
    }
    MA[{x, y}]++;
  }
  cout << ans << "\n";
}
### Prompt

Construct a CPP code solution to the problem outlined:

You are given N real values A_1, A_2, \ldots, A_N. Compute the number of pairs of indices (i, j) such that i < j and the product A_i \cdot A_j is integer.

Constraints

* 2 \leq N \leq 200\,000
* 0 < A_i < 10^4
* A_i is given with at most 9 digits after the decimal.

Input

Input is given from Standard Input in the following format.


N
A_1
A_2
\vdots
A_N


Output

Print the number of pairs with integer product A_i \cdot A_j (and i < j).

Examples

Input

5
7.5
2.4
17.000000001
17
16.000000000


Output

3


Input

11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001


Output

8

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

int main() {
  int N;
  cin >> N;
  map<pair<int, int>, int> MA;
  long ans = 0;
  for (double A; cin >> A;) {
    long a = round(A * 1e9);
    int x = 0, y = 0;
    while (a % 2 == 0) a /= 2, x++;
    while (a % 5 == 0) a /= 5, y++;
    for (auto [xy, cnt] : MA) {
      if (x + xy.first >= 18 && y + xy.second >= 18) ans += cnt;
    }
    MA[{x, y}]++;
  }
  cout << ans << "\n";
}
```