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: Accepted)

fn main() {
    let n: usize = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        buf.trim_end().parse().unwrap()
    };

    let mut a: Vec<i64> = Vec::with_capacity(n);
    for _ in 0..n {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        let n: f64 = buf.trim_end().parse().unwrap();
        let mut s = format!("{:.9}", n);
        s.retain(|c| c!= '.');
        a.push(s.parse().unwrap())
    }

    let mut map = std::collections::HashMap::new();
    for i in 0..n {
        let (mut two, mut five) = (0, 0);
        while a[i] % 2 == 0 {
            two += 1;
            a[i] /= 2;
        }
        while a[i] % 5 == 0 {
            five += 1;
            a[i] /= 5;
        }
        *map.entry((two, five)).or_insert(0i64) += 1;
    }

    let mut ans = 0;
    for (key1, val1) in &map {
        for (key2, val2) in &map {
            if key1.0 + key2.0 < 18 || key1.1 + key2.1 < 18 {
                continue;
            }
            if key1 == key2 {
                ans += val1 * (val1 - 1) / 2;
            } else if key1 < key2 {
                ans += val1 * val2;
            }
        }
    }
    println!("{}", ans);
}