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 <stdio.h>
#include <string.h>
#include <math.h>

int main()
{
  int N, i, j, n, cnt = 0;
  double A[200000];
  double num;

  if (scanf("%d", &N) == 1)
    ;

  for (n = 0; n < N; n++)
  {
    if (scanf("%lf", &A[n]) == 1)
      ;
  }

  for (j = 1; j < N; j++)
  {
    for (i = 0; i < j; i++)
    {
      num = A[i] * A[j];
      if (ceil(num) != floor(num))
      {
      }
      else
      {
        cnt++;
      }
    }
  }

  printf("%d", cnt);

  return (0);
}