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: Runtime Error)

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

double a[10010];
bool check[10010];

int main() {
    int n = 0;
    cin >> n;

    for (int i=0; i < n;i++)
    {
      cin >> a[i];
    }
    int dCount = 0;
    for (int k=0; k < n;k++)
    {
      for (int s = k + 1; s < n; s++)
      {
        if(a[k] == a[s]){
          dCount++;
        }
      }
    }
    int count = 0;

    for (int k=0; k < n;k++)
    {
      for (int s = k + 1; s < n; s++)
      {

          if(std::floor(a[k]) == a[k] &&
            std::floor(a[s]) == a[s] ){

            count++;
 
          }else{
            double data = a[k] * a[s];

            if(std::floor(data) == data){
              count++;

            }
          }
      }
    }


    cout << count - dCount;

    return 0;
}