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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)


import java.util.*;
public class Main {

	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);

			int n=sc.nextInt();
		double a[]=new double[n];
		ArrayList<Double> aa=new ArrayList<>();
		for(int i=0;i<n;i++) {
			a[i]=sc.nextDouble();
			if(Math.ceil(a[i])==Math.floor(a[i])||(int)Math.ceil(a[i]*10000)==(int)Math.floor(a[i]*10000)) {
				aa.add(a[i]);
			}
		
		}
		int count=0;
	
			s:for(int i=0;i<aa.size();i++) {
			
				for(int j=i+1;j<aa.size();j++) {
				
					if((int)Math.ceil((aa.get(i)*aa.get(j)))==(int)Math.floor(aa.get(i)*aa.get(j))) {
						count++;
						
					}
				}
			}
			System.out.println(count);
		
	}

}