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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use competitive::prelude::*;

fn main() {
    input! {
        n: usize,
        a: [f64; n],
    }

    let a = a
        .into_iter()
        .map(|a| (a * 1e10).round() as i128)
        .collect_vec();

    let b = a
        .into_iter()
        .map(|a| {
            let mut a = a;

            let mut two = 0;
            let mut five = 0;

            while a % 2 == 0 {
                a /= 2;
                two += 1;
            }
            while a % 5 == 0 {
                a /= 5;
                five += 1;
            }

            (min(two, 20), min(five, 20))
        })
        .collect_vec();

    let mut mm = BTreeMap::<(i32, i32), usize>::new();

    for r in b.iter() {
        *mm.entry(*r).or_default() += 1;
    }

    let mm = mm.into_iter().collect_vec();
    let mut ans = 0;

    for (two, five) in b {
        for &((t, f), c) in mm.iter() {
            if two + t >= 20 && five + f >= 20 {
                ans += if two == t && five == f { c - 1 } else { c };
            }
        }
    }

    echo!(ans / 2);
}
*/

fn main() {
    let exe = "/tmp/bin8E1F2DEB";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";