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: Runtime Error)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.nio.charset.StandardCharsets;

public class Main {
	public static void main (String[] args) throws IOException{
	    InputStreamReader reader = new InputStreamReader(System.in, StandardCharsets.UTF_8);
	    BufferedReader in = new BufferedReader(reader);
	    int cnt = 0;
		int size = Integer.parseInt(in.readLine());
		float[] num =  new float[size];

		for(int i=0; i < size; i++) {
			num[i] = Float.parseFloat(in.readLine());
		}

		for(int i=0; i < size-1; i++) {
			for(int j = 1; j < size; j++) {
				j += i;
				if(num[i]*num[j] == Math.floor(num[i]*num[j])) {
					cnt++;
				}
			}
		}
		System.out.println(cnt);
	}
}