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::*;
use std::collections::*;

fn run() {
    input! {
        n: usize,
        a: [f64; n],
    }
    let mut map = BTreeMap::new();
    for a in a {
        let mut a = (a * 1_000_000_000f64).round() as u64;
        let mut cnt = (0, 0);
        while a % 2 == 0 {
            a /= 2;
            cnt.0 += 1;
        }
        while a % 5 == 0 {
            a /= 5;
            cnt.1 += 1;
        }
        *map.entry(cnt).or_insert(0) += 1;
    }
    let a = map.into_iter().collect::<Vec<_>>();
    let mut ans = 0u64;
    let v = 18;
    for (i, &(x, p)) in a.iter().enumerate() {
        if 2 * x.0 >= v && 2 * x.1 >= v {
            ans += p * (p - 1) / 2;
        }
        for &(y, q) in a.iter().take(i) {
            if x.0 + y.0 >= v && x.1 + y.1 >= v {
                ans += p * q;
            }
        }
    }
    println!("{}", ans);
}

fn main() {
    run();
}