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 Python (3.8.2) (judge verdict: Wrong Answer)

# -*- coding: utf-8 -*-

def is_integer(number):
    return float.is_integer(number)


def load():
    num = int(input())
    numbers = [float(input()) for _ in range(num)]

    return numbers


def get_pair(numbers):
    num = len(numbers)

    for i in range(num - 1):
        for j in range(i + 1, num):
            yield (numbers[i], numbers[j])


if __name__ == "__main__":
    numbers = load()
    counter = 0

    for A_i, A_j in get_pair(numbers):
        prod = A_i * A_j
        if is_integer(prod):
            counter += 1

    print(counter)