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)

n = int(input())
p, count = 1, 0
an, bn = [], []
for i in range(n):
    a = float(input())
    if not a.is_integer():
        bn.append(a)
    else:
        an.append(a)

an, bn = list(set(an)), list(set(bn))

for i in range(len(an)):
    for j in range(len(bn)):
        if (an[i] * bn[j]).is_integer():
            count += 1

pl = len(an)
for i in range(len(an)):
    p *= pl
    pl -= 1

print(p+count)