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);
        int n = sc.nextInt();
        int cnt = 0;
        BigDecimal[] array = new BigDecimal[n];
        for (int i = 0; i < n; i++) {
            array[i] = sc.nextBigDecimal();
        }

        for (int i = 0; i < n - 1; i++) {
            for (int j = i + 1; j < n; j++) {
                boolean flg = true;
                BigDecimal tmp1 = array[i];
                BigDecimal tmp2 = array[j];
                BigDecimal tmp = tmp1.multiply(tmp2);
                String tmpstr = String.valueOf(tmp);
                if (tmpstr.contains("E")) {
                    flg = false;
                } else if (!tmpstr.contains(".")) {
                    cnt++;
                    flg = false;
                }
                if (flg) {
                    int indexOfDecimal = tmpstr.indexOf(".");
                    String ans = tmpstr.substring(indexOfDecimal);
                    String aftans = ans.replaceAll("0", "");
                    if (".".equals(aftans)) {
                        cnt++;
                    }
                }
            }
        }
        System.out.println(cnt);
    }
}