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.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        long ans = 0;
        int n = scanner.nextInt();
        int[][] f = new int[20][20];
        for (int i = 0; i < n; i++) {
            double v = scanner.nextDouble();
            long vv = (long) (v * 1000000000);
            int p = 0, q = 0;
            while (vv % 2 == 0) {
                p++;
                vv = vv / 2;
            }
            while (vv % 5 == 0) {
                q++;
                vv = vv / 5;
            }
            for (int j = 18 - p; j <= 18; j++) {
                for (int k = 18 - q; k <= 18; k++) {
                    ans = ans + f[j][k];
                }
            }
            f[p][q]++;
        }
        System.out.println(ans);
    }
}