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() {
    static PLANE_MAX: i64 = 101;
    static PLANE_OFFSET: i64 = PLANE_MAX / 2;
    // 変数宣言
    let n: u64;
    let mut a_count: Vec<Vec<i64>>; // "約数" 中の "5" と "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 = Vec::<Vec<i64>>::with_capacity(n as usize);
    let mut plane: Vec<Vec<i64>>;
    plane = Vec::<Vec<i64>>::with_capacity(PLANE_MAX as usize);
    for _ in 0..PLANE_MAX {
        let mut zero_vec: Vec<i64> = Vec::with_capacity(PLANE_MAX as usize);
        for _ in 0..PLANE_MAX {
            zero_vec.push(0);
        }
        plane.push(zero_vec.clone());
    }
    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;
        }
        let mut tmp_v: u64 = format!("{}{}", tmp[0], if tmp.len() > 1 { tmp[1] } else { "" })
            .trim()
            .parse()
            .ok()
            .unwrap();
        let mut tmp_5: u64 = 0;
        while tmp_v % 5 == 0 {
            tmp_v = tmp_v / 5;
            tmp_5 += 1;
        }
        let mut tmp_2: u64 = 0;
        while tmp_v % 2 == 0 {
            tmp_v = tmp_v / 2;
            tmp_2 += 1;
        }
        let tmp_vect: Vec<i64> = vec![tmp_5 as i64 - tmp_d as i64, tmp_2 as i64 - tmp_d as i64];
        a_count.push(tmp_vect)
    }
    // 平面上にマッピング
    for item in a_count.clone() {
        let vx1 = -item[0] as i64 + PLANE_OFFSET;
        let vx2 = -item[1] as i64 + PLANE_OFFSET;
        for i in vx1..PLANE_MAX {
            for j in vx2..PLANE_MAX {
                plane[i as usize][j as usize] += 1;
            }
        }
    }
    // カウント
    let mut counter: i64 = 0;
    for item in a_count.clone() {
        let vx1 = item[0] as i64 + PLANE_OFFSET;
        let vx2 = item[1] as i64 + PLANE_OFFSET;
        counter += plane[vx1 as usize][vx2 as usize];
        if item[0] >= 0 && item[1] >= 0 {
            counter -= 1;
        }
    }
    println!("{}", counter / 2);
}