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 Rust (1.42.0) (judge verdict: Wrong Answer)

fn main() {
    let n: i32 = read();
    let mut inputs: Vec<f64> = Vec::new();

    for _ in 0..n {
        let a: f64 = read();
        inputs.push(a);
    }

    let mut count = 0;

    for i in 0..(n - 1) {
        for j in (i + 1)..n {
            let a = inputs[i as usize] * inputs[j as usize];
            
            // aの整数判定
            let is_int = a % 1.0 == 0.0;

            if is_int {
                count += 1;
            }
        }
    }

    println!("{}", count);
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}