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(clippy::needless_range_loop)]
#![allow(unused_macros)]
#![allow(dead_code)]
#![allow(unused_imports)]

use itertools::Itertools;
use num::integer::Integer;
use proconio::input;
use proconio::marker::*;

fn main() {
    input! {
        a: [String],
    }
    let mut cnt = [[0usize; 20]; 20];
    let tf: Vec<_> = a.iter().map(|x| {
        let mut q = if let Some(p) = x.find('.') {
            let mut a = x[0..p].parse::<usize>().unwrap() * 1000000000;
            let mut r = 100000000;
            for x in x[(p + 1)..].chars() {
                a += (x as u8 - b'0') as usize * r;
                r /= 10;
            }
            a
        } else {
            x.parse::<usize>().unwrap() * 1000000000
        };
        let mut two = 0;
        let mut five = 0;
        while q % 2 == 0 {
            q /= 2;
            two += 1;
        }
        while q % 5 == 0 {
            q /= 5;
            five += 1;
        }
        (std::cmp::min(two, 18), std::cmp::min(five, 18))
    }).collect();
    for &(two, five) in tf.iter() {
        for c in cnt[0..=two].iter_mut() {
            for item in c[0..=five].iter_mut() {
                *item += 1;
            }
        }
    }
    let mut s = 0;
    let mut t = 0;
    for &(two, five) in tf.iter() {
        if two >= 9 && five >= 9 {
            t += 1;
        }

        s += cnt[18 - two][18 - five];
    }
    let ans = (s - t) / 2;
    println!("{}", ans);
}