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.*;
import java.math.*;

public class Main {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int N = s.nextInt();
        BigDecimal[] A = new BigDecimal[N];
        for (int i = 0; i < N; i++) {
            A[i] = s.nextBigDecimal();
        }

        int count = 0;
        for (int i = 0; i < N; i++) {
            for (int j = i + 1; j < N; j++) {
                BigDecimal x = A[i].multiply(A[j]);
                if (x.compareTo(BigDecimal.valueOf(x.intValue())) == 0) {
                    count++;
                }
            }
        }
        System.out.println(count);
    }
}