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: Time Limit Exceeded)

N=int(input())
A=[]
for i in range(N):
  x=float(input())
  A+=[x]

AA={}  

def is_int(x,y):
  if x.is_integer() and y.is_integer():
    return True
  m=min(x,y)
  M=max(x,y)
  m=m*10000
  z=M/10000*m
  if (int(z)==z):
    return True
  else:
    return False

count=0
for i in range(N-1):
  for j in range(i+1,N):
    if is_int(A[i],A[j]):      
#      t=(A[i],A[j])
#      if not t in AA:
#        AA[t]=1
#      else:
#        AA[t]+=1
      count+=1

#for k in AA.keys():
#  print('AA[{}]={}'.format(k,AA[k]))
print(count)