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: Wrong Answer)

use text_io::*;
use std::process::exit;
use im_rc::HashMap;
use std::intrinsics::transmute;

fn main(){
    let mut n:usize = read!();
    let mut v = [[0;20];20];
    for i in 0..n {
        let mut aaa:f64 = read!();
        let mut aa:f64 = 1000000000.0*aaa;
        let mut a:usize = aa as usize;
        let mut ni:usize = 0;
        while a%2 == 0 && ni < 19{
            ni += 1;
            a /= 2;
        }
        let mut go:usize = 0;
        while a%5 == 0 && go < 19{
            go += 1;
            a /= 5;
        }
        *& mut v[ni][go] = *& mut v[ni][go]+1;
    }
    let mut sum:usize = 0;
    for i in 0..20 {
        for j in 0..20 {
            for k in 0..20 {
                for l in 0..20 {
                    if i+k>17 && i>=k{
                        if j+l>17 && j>=l{
                            if i == k && j == l && v[i][j] != 0 {
                                sum += v[i][j]*(v[i][j]-1)/2;
                            } else {
                                sum += v[i][j]*v[k][l];
                            }
                        }
                    }
                }
            }
        }
    }
    println!("{}",sum);
}