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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

function main(input) {
  let args = input.split('\n');
  args.pop();
  let count = 0;
  for (let i = 0;i < args.length;i++) {
    for (let j = i + 1;j < args.length;j++) {
      let result = (args[i] * 10000000000) * (args[j] * 10000000000);
      if (result % (10000000000 * 10000000000) == 0 && args[i] !== args[j]) {
    	count++;
      }
    }
  }
  console.log(count);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));