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.math.BigDecimal;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);

		Integer n = sc.nextInt();
		Integer n2 = 1;

		BigDecimal[] A = new BigDecimal[n];

		Integer count = 0;
		
		for (Integer i = 0; i < n; i++) {
			A[i] = new BigDecimal(sc.next());
		}

		for (Integer i = 0; i < n; i++) {
			for (Integer j = 0; j < n - n2; j++) {

				BigDecimal x = A[i].multiply(A[j + n2]);

				x.remainder(new BigDecimal(1));
				
				if (x.remainder(new BigDecimal(1)).compareTo(BigDecimal.ZERO) == 0) {
					count++;
				}
			}
			n2++;
		}

		System.out.println(count);

	}
}