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 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;
 
public class Main {
  public static void main(String[] args ) {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    int k = 0;
    Double[] kazu = new Double[N];
    for (int i=0; i<N; i++) {
    	kazu[i]=sc.nextDouble();
    }
    for (int i=0; i<N; i++){
      int j=i+1;
      while (j<N){
        Double seki=kazu[i]*kazu[j];
        if ((seki == Math.floor(seki)) && !Double.isInfinite(seki)) {
            k=k+1;
        }
        j=j+1;
      }
    }
    System.out.println(k);
  }
}