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)

// -*- coding:utf-8-unix -*-

use proconio::{fastout, input};

#[fastout]
fn main() {
    input! {
        n: usize,
        a: [f64; n],
    }
    let mut a_list = vec![vec![0; 19]; 44];
    let mut ans: u64 = 0;
    for &ai in &a {
        let mut aa = (ai * 10f64.powi(9)).round() as usize;
        let mut count2 = 0;
        while aa % 2 == 0 {
            aa /= 2;
            count2 += 1;
        }
        let mut count5 = 0;
        while aa % 5 == 0 {
            aa /= 5;
            count5 += 1;
        }
        for i in 0..=43 {
            if i + count2 < 18 {
                continue;
            }
            for j in 0..=18 {
                if j + count5 < 18 {
                    continue;
                }
                ans += a_list[i][j];
            }
        }
        a_list[count2][count5] += 1;
    }
    println!("{}", ans);
}