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)

use proconio::{fastout, input};
use std::cmp;

#[fastout]
fn main() {
    input! {
        n: usize,
        r#as: [f64; n],
    }

    let r#as = r#as
        .into_iter()
        .map(|a| {
            let mut a = (10f64.powi(9) * a + 0.1).floor() as u64;
            let e1 = a.trailing_zeros() as usize;
            let mut e2 = 0;
            while a % 5 == 0 {
                a /= 5;
                e2 += 1;
            }
            (e1, e2)
        })
        .collect::<Vec<_>>();

    let mut count = vec![vec![0; 19]; 19];
    for (e1, e2) in r#as {
        count[cmp::min(e1, 18)][cmp::min(e2, 18)] += 1u64;
    }

    let mut ans = 0;
    for i1 in 0..=18 {
        for i2 in 0..=18 {
            for j1 in 0..=18 {
                for j2 in 0..=18 {
                    if i1 + i2 >= 18 && j1 + j2 >= 18 {
                        ans += if (i1, j1) == (i2, j2) {
                            let count = count[i1][j1];
                            count * count.saturating_sub(1)
                        } else {
                            count[i1][j1] * count[i2][j2]
                        };
                    }
                }
            }
        }
    }

    debug_assert_eq!(ans % 2, 0);
    ans /= 2;

    println!("{}", ans);
}