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)

#[allow(unused_imports)]
use proconio::{input, marker::*};

#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};

#[allow(unused_imports)]
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*).unwrap();
    }
}

fn main() {
    input! {
        n: usize,
        a: [String;n],
    }

    let a = a
        .into_iter()
        .map(|e| {
            let mut num = 0;
            let mut count = 0;
            let mut flag = false;
            for c in e.chars() {
                if c == '.' {
                    flag = true;
                    continue;
                }
                if flag {
                    count += 1;
                }
                num = num * 10 + c as usize - '0' as usize;
            }
            num * 10usize.saturating_pow(9 - count)
        })
        .collect::<Vec<_>>();

    let mut vec = vec![vec![0; 19]; 19];
    let mut sums = vec![vec![0; 20]; 20];
    let mut count = 0usize;
    for mut e in a {
        let mut twos = 0usize;
        let mut fives = 0usize;
        while e % 2 == 0 {
            e /= 2;
            twos += 1;
        }
        while e % 5 == 0 {
            e /= 5;
            fives += 1;
        }
        if twos > 18 {
            twos = 18;
        }

        if fives > 18 {
            fives = 18;
        }
        vec[twos][fives] += 1;

        count += sums[18 - twos][18 - fives];

        sums = vec![vec![0; 20]; 20];
        for i in 0..19 {
            for j in (0..19).rev() {
                sums[i][j] = sums[i][j + 1] + vec[i][j];
            }
        }
        for j in 0..19 {
            for i in (0..19).rev() {
                sums[i][j] += sums[i + 1][j];
            }
        }
    }
    println!("{}", count);
}