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)]
use proconio::*;

fn main() {
    input! {
    n: usize,
    f: [f64; n],
    }

    // log2(10^4 * 10^9)
    const P_MAX: usize = 45;

    let mut dp = vec![vec![0u64; P_MAX]; P_MAX];
    let mut ans = 0;
    for i in 0..n {
        let mut num = (f[i] * 1_000_000_000f64).round() as u64;
        let mut two = 0;
        let mut five = 0;
        while num % 2 == 0 {
            num /= 2;
            two += 1;
        }
        while num % 5 == 0 {
            num /= 5;
            five += 1;
        }
        // println!("{:?}", (two, five));
        for i in 0..P_MAX {
            for j in 0..P_MAX {
                if i + two >= 18 && j + five >= 18 {
                    ans += dp[i][j];
                }
            }
        }
        dp[two][five] += 1;
    }
    println!("{}", ans);
}