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: Time Limit Exceeded)

use num_bigint::{BigInt, ToBigInt};
#[allow(unused_imports)]
use proconio::{fastout, input};

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

    let aaa = 1000000000.0;
    let bbb = 1000000000000000000usize.to_bigint().unwrap();
    let mut vvv = Vec::new();
    for v in a {
        vvv.push(((v * aaa) as u64).to_bigint().unwrap());
    }

    let mut count = 0;
    for i in 0..n {
        for j in i + 1..n {
            if (&vvv[i] * &vvv[j]) % &bbb == 0.to_bigint().unwrap() {
                count += 1;
            }
        }
    }

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