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() {
    proconio::input! {
        n: usize,
        a_s: [proconio::marker::Chars; n],
    }
    let a_s = a_s
        .iter()
        .map(|cs| {
            cs.iter()
                .collect::<String>()
                .split('.')
                .map(|x| x.to_string())
                .collect::<Vec<_>>()
        })
        .map(|a| {
            if a.len() == 1 {
                a[0].parse::<i128>().unwrap() * 1_000_000_000
            } else {
                a[0].parse::<i128>().unwrap() * 1_000_000_000
                    + a[1].parse::<i128>().unwrap() * 10i128.pow(9 - a[1].len() as u32)
            }
        })
        .collect::<Vec<_>>();
    let a_s = a_s
        .iter()
        .map(|a| {
            let mut a = *a;
            let mut count2 = 0;
            while a % 2 == 0 {
                count2 += 1;
                a /= 2;
            }
            let mut count5 = 0;
            while a % 5 == 0 {
                count5 += 1;
                a /= 5;
            }
            (count2, count5)
        })
        .collect::<Vec<_>>();
    let mut count25 = [[0; 19]; 19];
    for (c2, c5) in &a_s {
        for i in 0..=std::cmp::min(*c2, 18) {
            for j in 0..=std::cmp::min(*c5, 18) {
                count25[i][j] += 1;
            }
        }
    }
    let mut count = 0usize;
    for (c2, c5) in &a_s {
        let (remainc2, remainc5) = (18 - std::cmp::min(c2, &18), 18 - std::cmp::min(c5, &18));
        count += count25[remainc2][remainc5];
        if *c2 >= remainc2 && *c5 >= remainc5 {
            count -= 1;
        }
    }
    count /= 2;
    println!("{}", count);
}