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)

use proconio::*;
use proconio::marker::*;
use std::collections::*;
use std::cmp::*;
use std::ops::Bound::*;
use num::integer::gcd;

/*
fn gcd(a: u64, b: u64) -> u64 {
    if b == 0 {
        a
    } else {
        gcd(b, a % b)
    }
}
*/

fn calc(n: u64) -> (u64, u64) {
    let mut n = n;
    let mut res = (0, 0);
    while n % 2 == 0 {
        res.0 += 1;
        n /= 2;
    }
    while n % 5 == 0 {
        res.1 += 1;
        n /= 5;
    }
    res
}

fn run() {
    input! {
        n: usize,
        a: [Chars; n],
    }
    let mut map = std::collections::BTreeMap::<((u64, u64), (u64, u64)), u64>::new();
    for s in a {
        let mut de = 0u64;
        let mut val = 0u64;
        for c in s {
            if c == '.' {
                de = 1;
            } else {
                val = 10 * val + c.to_digit(36).unwrap() as u64;
                de *= 10;
            }
        }
        if de == 0 {
            let p = calc(val);
            *map.entry((p, (0, 0))).or_insert(0) += 1;
        } else {
            let g = gcd(de, val);
            de /= g;
            val /= g;
            let (p, c) = (calc(val), calc(de));
            *map.entry((p, c)).or_insert(0) += 1;
        }
    }
    let mut val = vec![];
    for (a, cnt) in map {
        val.push((a, cnt));
    }
    let mut ans = 0;
    for (i, p) in val.iter().enumerate() {
        let ((nu, de), cnt) = *p;
        if de.0 == 0 && de.1 == 0 {
            ans += cnt * (cnt - 1) / 2;
        }
        for q in val.iter().take(i) {
            let ((x, y), z) = *q;
            if nu.0 + x.0 >= y.0 + de.0 && nu.1 + x.1 >= y.1 + de.1 {
                ans += z * cnt;
            }
        }
    }
    println!("{}", ans);
}

fn main() {
    run();
}