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: Time Limit Exceeded)

import java.util.*;
class Main{
    public static void main(String[] args) {
        Scanner sc = new Scanner (System.in);
        int n = sc.nextInt();
        int x = 0;
        double [] a = new double [n];
        while(x<n){
            a[x] = sc.nextDouble();
            x++;
        }
        int count = 0;
        for(int i = 0; i<n-1;i++){
            for(int j =i+1;j<n;j++){
                double res = a[i]*a[j];
                if(res%1 ==0 && a[i]!=a[j]){
                    count++;
                }


            }
        }
        System.out.println(count);
    }
}