Problem:
Score : 300 points

Problem Statement

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).

Sample Input 1

5
7.5
2.4
17.000000001
17
16.000000000

Sample Output 1

3

There are 3 pairs with integer product:

7.5 \cdot 2.4 = 18

7.5 \cdot 16 = 120

17 \cdot 16 = 272

Sample Input 2

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

Sample Output 2

8

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <cmath>
using namespace std;
bool is_integer(long double x)
{
  return floor(x) == x;
}
int main()
{
  int n;
  cin >> n;
  long double A[200000];
  for (int i = 0; i < n; i++)
  {
    cin >> A[i];
  }

  int cnt = 0;
  for (int i = 0; i < n; i++)
  {
    for (int j = i + 1; j < n; j++)
    {
      if (is_integer(A[i] * A[j]))
      {
        cnt++;
      }
    }
  }
  cout << cnt << endl;
}