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 std::cmp::max;

const N_TWO: usize = 60;
const N_FIVE: usize = 30;

fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());

    let n: usize = sc.read();
    let mut map = [[0; N_FIVE]; N_TWO];
    let mut ans: i64 = 0;
    for _ in 0..n {
        let x: String = sc.read();
        let (mut x, add) = if !x.contains('.') {
            let add = 9;
            let x = x.parse::<i64>().unwrap();
            (x, add)
        } else {
            let add = 9 - x.split('.').skip(1).next().unwrap().len();
            let x = x
                .chars()
                .filter(|&c| c != '.')
                .collect::<String>()
                .parse::<i64>()
                .unwrap();
            (x, add)
        };
        let mut two = add;
        let mut five = add;
        while x % 2 == 0 {
            x /= 2;
            two += 1;
        }
        while x % 5 == 0 {
            x /= 5;
            five += 1;
        }

        let required_two = max(two, 18) - two;
        let required_five = max(five, 18) - five;

        let mut count = 0;
        for two in required_two..N_TWO {
            for five in required_five..N_FIVE {
                count += map[two][five];
            }
        }

        // eprintln!("{}", count);
        ans += count;

        map[two][five] += 1;
    }

    println!("{}", ans);
}
pub struct CumulativeSum<T> {
    ny: usize,
    nx: usize,
    sum: Vec<Vec<T>>,
}

impl<T> CumulativeSum<T>
where
    T: Copy + std::ops::Add<Output = T> + std::ops::Sub<Output = T>,
{
    pub fn new(a: &[Vec<T>], init: T) -> CumulativeSum<T> {
        assert!(!a.is_empty());
        let ny = a.len();
        let nx = a[0].len();
        let mut sum = vec![vec![init; nx + 1]; ny + 1];
        for i in 0..ny {
            for j in 0..nx {
                sum[i + 1][j + 1] = a[i][j] + sum[i][j + 1] + sum[i + 1][j] - sum[i][j];
            }
        }
        CumulativeSum { ny, nx, sum }
    }

    pub fn get_sum(&self, y1: usize, x1: usize, y2: usize, x2: usize) -> T {
        assert!(y1 <= y2 && x1 <= x2);
        assert!(y2 < self.ny);
        assert!(x2 < self.nx);
        self.sum[y2 + 1][x2 + 1] + self.sum[y1][x1] - self.sum[y1][x2 + 1] - self.sum[y2 + 1][x1]
    }
}
pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> Self {
        Self(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: ToString>(&mut self, s: S) {
        use std::io::Write;
        self.1.write_all(s.to_string().as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}