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)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let n = read::<usize>();
    let mut numbers = vec![];
    'o: for i in 0..n {
        let s = read::<String>();
        let s = s.parse::<f64>().unwrap();
        // let s2 = (s * 10000.0).round() / 10000.0;
        let num = ((s * 10000000000.0).round() + 0.1) as i128;
        numbers.push(num);
    }
    // debug!(numbers);
    let max_idx = 20;
    let mut mutiples = vec![vec![0; max_idx + 1]; max_idx + 1];
    let mut ans = 0i128;
    for num in numbers {
        let mut num = num;
        let mut two_c = 0;
        for i in 0..max_idx {
            if num % 2 == 0 {
                two_c += 1;
                num /= 2;
            } else {
                break;
            }
        }

        let mut five_c = 0;
        for i in 0..max_idx {
            if num % 5 == 0 {
                five_c += 1;
                num /= 5;
            } else {
                break;
            }
        }
        //debug!(num, two_c, five_c);
        ans += mutiples[max_idx - two_c][max_idx - five_c];

        for i in 0..two_c + 1 {
            for j in 0..five_c + 1 {
                mutiples[i][j] += 1;
            }
        }
    }
    println!("{}", ans);
}

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()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}