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())
a=[float(input()) for i in range(n)]
cou=0
for i in range(n):
  for j in range(i+1,n):
      # if a[i]==int(a[i]) and a[j]==int(a[j]):
        
      #   cou+=1
      # elif a[i]==int(a[i]):
      #   aj=a[j]-int(a[j])
      #   b=aj*a[i]
      #   c=b-int(b)
      #   if c==0:
      #     cou+=1
      # elif a[j]==int(a[j]):
      #   ai=a[i]-int(a[i])
      #   b=ai*a[j]
      #   c=b-int(b)
      #   if c==0:
      #     cou+=1  

      # else:

        b=a[i]*a[j]
        # c=b-int(b)
        if b.is_integer():
          
          cou+=1
print(cou)