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: Time Limit Exceeded)

// 定数定義
static DEC_CONST: u64 = 1000000000;
static DEC_CONST_2: u64 = DEC_CONST * DEC_CONST;

fn main() {
    // 変数宣言
    let n: u32;
    let mut a_count_d: Vec<u64>; // "約数" 中の 小数部 の桁数
    let mut a_count_5: Vec<u64>; // "約数" 中の "5" の数
    let mut a_count_2: Vec<u64>; // "約数" 中の "2" の数

    // 入力の処理
    let mut buf: String = String::new();
    std::io::stdin().read_line(&mut buf).ok();
    n = buf.trim().parse().ok().unwrap();
    a_count_d = Vec::<u64>::with_capacity(n as usize);
    a_count_5 = Vec::<u64>::with_capacity(n as usize);
    a_count_2 = Vec::<u64>::with_capacity(n as usize);
    for _ in 0..n {
        buf = String::new();
        std::io::stdin().read_line(&mut buf).ok();
        // 最大14桁
        let tmp: Vec<&str> = buf.trim().split('.').collect();
        let mut tmp_d: u64 = 0;
        if tmp.len() > 1 && tmp[1].len() > 0 {
            tmp_d = tmp[1].len() as u64;
        }
        a_count_d.push(tmp_d);
        let mut tmp_d: u64 = format!("{}{}", tmp[0], if tmp.len() > 1 { tmp[1] } else { "" })
            .trim()
            .parse()
            .ok()
            .unwrap();
        let mut tmp_5: u64 = 0;
        while tmp_d % 5 == 0 {
            tmp_d = tmp_d / 5;
            tmp_5 += 1;
        }
        a_count_5.push(tmp_5);
        let mut tmp_2: u64 = 0;
        while tmp_d % 2 == 0 {
            tmp_d = tmp_d / 2;
            tmp_2 += 1;
        }
        a_count_2.push(tmp_2);
    }
    // 愚直カウント
    let mut counter: u32 = 0;
    for i in 0..n {
        for j in (i + 1)..n {
            let vd = a_count_d[i as usize] + a_count_d[j as usize];
            let v2 = a_count_2[i as usize] + a_count_2[j as usize];
            let v5 = a_count_5[i as usize] + a_count_5[j as usize];
            if vd <= v2 && vd <= v5 {
                counter += 1;
            }
        }
    }
    println!("{}", counter);
}