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::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::f64::consts::*;

#[allow(unused)]
const INF: usize = std::usize::MAX / 4;
#[allow(unused)]
const M: usize = 1000000007;

fn main() {
    input! {
        n: usize,
        a: [String; n],
    }
    let mut a = a
        .into_iter()
        .map(|ai| {
            let s = ai.split('.').collect::<Vec<_>>();
            if s.len() == 1 {
                (s[0].parse::<usize>().ok().unwrap(), 0)
            } else {
                (
                    format!("{}{}", s[0], s[1]).parse::<usize>().ok().unwrap(),
                    s[1].len(),
                )
            }
        })
        .collect::<Vec<_>>();
    a.sort_by_key(|&(_, k)| k);
    // eprintln!("{:?}", a);

    let mut factors = HashMap::new();
    for i in 0..n {
        let (mut x, k) = a[i];
        let mut two = 0;
        while x % 2 == 0 {
            two += 1;
            x /= 2;
        }
        let mut five = 0;
        while x % 5 == 0 {
            five += 1;
            x /= 5;
        }
        *factors.entry((two, five, k)).or_insert(0) += 1;
    }

    let factors = factors.into_iter().collect::<Vec<_>>();
    eprintln!("{:?}", factors);
    let m = factors.len();
    let mut result = 0usize;
    for i in 0..m {
        let ((fi, gi, ki), ci) = factors[i];
        if fi >= ki && gi >= ki {
            result += ci * (ci - 1) / 2;
        }
    }
    for i in 0..m {
        let ((fi, gi, ki), ci) = factors[i];
        for j in 0..i {
            let ((fj, gj, kj), cj) = factors[j];
            if fi + fj >= ki + kj && gi + gj >= ki + kj {
                result += ci * cj
            }
        }
    }
    println!("{}", result);
}