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.*;

class Main {
	public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        List<BigDecimal> list = new ArrayList<BigDecimal>();
        for(int i = 0; i < N; i++) {
            BigDecimal t = sc.nextBigDecimal();
            list.add(t);
        }
        
        int ans = 0;
        for(int i = 0; i < list.size(); i++) {
            for(int j = i + 1; j < list.size(); j++) {
                BigDecimal t1 = list.get(i);
                BigDecimal t2 = list.get(j);
                // 掛け算
                BigDecimal t3 = t1.multiply(t2);
                // double型とlong型にキャストして差分を計算
                long t4 = t3.longValue();
                double t5 = t3.doubleValue();
                if (Math.abs(t5 - t4) < 1e-12) {
                    ans++;
                }
            }
        }
        System.out.println(ans);
		sc.close();
	}
}