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)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};

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

    let mut b = vec![0i128; n];
    for i in 0..n {
        b[i] = (a[i] * 1e9 + eps) as i128;
    }
    let mut c = vec![];
    let mut tfs = vec![vec![0i64; 37]; 37];
    for &x in b.iter() {
        let mut pf = prime_factor(x);
        let two = *pf.entry(2).or_insert(0);
        let five = *pf.entry(5).or_insert(0);
        c.push((two, five));
        tfs[two as usize][five as usize] += 1i64;
    }
    c.sort();
    let mut ans = 0i64;
    for &(two, five) in c.clone().iter() {
        for i in 18 - two as usize..37 {
            for j in 18 - five as usize..37 {
                ans += tfs[i][j];
            }
        }
        if two + two >= 18 && five + five >= 18 {
            ans -= 1;
        }
    }
    println!("{}", ans / 2);
}

const eps: f64 = 1e-12;
pub trait BinarySearch<T> {
    fn lower_bound_by<F: Fn(&T) -> bool>(&self, f: F) -> usize;
    fn lower_bound(&self, x: &T) -> usize;
    fn upper_bound(&self, x: &T) -> usize;
}
impl<T: Ord> BinarySearch<T> for [T] {
    fn lower_bound_by<F: Fn(&T) -> bool>(&self, f: F) -> usize {
        let mut ng = -1;
        let mut ok = self.len() as i64;
        while (ok as i32 - ng as i32).abs() > 1 {
            let mid = (ok + ng) / 2;
            if f(&self[mid as usize]) {
                ok = mid;
            } else {
                ng = mid;
            }
        }
        ok as usize
    }
    fn lower_bound(&self, x: &T) -> usize {
        self.lower_bound_by(|y| y >= x)
    }
    fn upper_bound(&self, x: &T) -> usize {
        self.lower_bound_by(|y| y > x)
    }
}
fn prime_factor(mut n: i128) -> std::collections::HashMap<i128, i128> {
    let mut res: std::collections::HashMap<i128, i128> = std::collections::HashMap::new();
    let mut i = 2;
    while i * i <= n {
        while n % i == 0 {
            let v = match res.get(&i) {
                Some(v) => *v + 1,
                None => 1,
            };
            res.insert(i, v);
            n /= i;
        }
        i += 1;
    }
    if n != 1 {
        res.insert(n, 1);
    }
    res
}