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)

fn main() {
	let mut s = String::new();
	use std::io::Read;
	std::io::stdin().read_to_string(&mut s).unwrap();
	let mut s = s.split_whitespace();
	let _n: usize = s.next().unwrap().parse().unwrap();

	let mut cnt = vec![vec![0i64; 128]; 128];

	for s in s {
		let neg = if let Some(i) = s.find(".") {
			(s.len() - 1) - i
		} else {
			0
		};

		let s = s.replace(".", "");
		let n: i64 = s.parse().unwrap();
		let e2 = {
			let mut m = n;
			let mut r = 0;
			while m % 2 == 0 {
				r += 1;
				m /= 2;
			}
			r
		};
		let e5 = {
			let mut m = n;
			let mut r = 0;
			while m % 5 == 0 {
				r += 1;
				m /= 5;
			}
			r
		};
		cnt[64 + e2 - neg][64 + e5 - neg] += 1;
	}

	let mut ansid = 0;
	let mut ansdis = 0;
	for e2 in -63..64 {
		for e5 in -63..64 {
			for f2 in -63..64 {
				for f5 in -63..64 {
					if e2 + f2 >= 0 && e5 + f5 >= 0 && (e2, e5) != (f2, f5) {
						ansdis += cnt[(64 + e2) as usize][(64 + e5) as usize] * cnt[(64 + f2) as usize][(64 + f5) as usize];
					}
				}
			}
			if e2 >= 0 && e5 >= 0 {
				ansid += cnt[(64 + e2) as usize][(64 + e5) as usize] * (cnt[(64 + e2) as usize][(64 + e5) as usize] - 1) / 2;
			}
		}
	}
	println!("{}", ansdis / 2 + ansid);
}