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)

/*
  agc047_a.rs
*/

use std::io::{self, Read};

fn run_puzzle(input: &str) {

  let all: Vec<f64> = input.trim().split('\n').map(|x| str::parse(x).unwrap()).collect();
  let nums = &all[1..];  // Ignore the first integer.

  // Decimal shit.
  let decimals = 1000000000;
  let decimal_product = decimals * decimals;

  let mut count = 0;

  for i in 0..(nums.len() - 1) {
    for j in (i + 1)..nums.len() {

      let a = nums[i];
      let b = nums[j];

      // Inflate the numbers until there are no more decimal
      let big_a = (a * decimals as f64) as u128;
      let big_b = (b * decimals as f64) as u128;

      // Get product.
      let p = big_a * big_b;

      // Check if the product has any decimal places.
      if p % decimal_product == 0 {
        count += 1;
      }
    }
  }

  println!("{}", count);

}

fn run_stdin() {

  // Get input.
  let mut buffer = String::new();
  let stdin = io::stdin();
  let mut handle = stdin.lock();
  handle.read_to_string(&mut buffer).unwrap();

  // Run puzzle.
  run_puzzle(&buffer);
}

fn main() {

  run_stdin();

}