output_description: Print the maximum number of divisors that can be chosen to satisfy the
  condition.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      A B
attempt: ##D - Disjoint Set of Common Divisors
  A, B = map(int, input().split())
  
  from fractions import gcd
  
  vPrime = gcd(A, B)
  box = []
  for i in range(1, vPrime + 1, 2):
      if vPrime % (i) == 0:
          box.append(i)
  
  check = []
  for x in box:
      for y in box:
          if x < y:  # or (x != y and x % y == 0):
              break
          elif x > y:
              if x % y == 0:
                  break
          else:  # x == y
              check.append(x)
  print(len(check))
  
problem_description: Statement
  
  Given are positive integers A and B.
  
  Let us choose some number of positive common divisors of A and B.
  
  Here, any two of the chosen divisors must be coprime.
  
  At most, how many divisors can we choose?
  
  Definition of common divisor
  
  An integer d is said to be a common divisor of integers x and y when d divides
  both x and y.
  
  Definition of being coprime
  
  Integers x and y are said to be coprime when x and y have no positive common
  divisors other than 1.
  
  Definition of dividing
  
  An integer x is said to divide another integer y when there exists an integer
  \alpha such that y = \alpha x.
samples: [{"input": "12 18", "output": "3\n    \n\n12 and 18 have the following positive common divisors: 1, 2, 3, and 6.\n\n1 and 2 are coprime, 2 and 3 are coprime, and 3 and 1 are coprime, so we can\nchoose 1, 2, and 3, which achieve the maximum result.\n\n* * *"}, {"input": "420 660", "output": "4\n    \n\n* * *"}, {"input": "1 2019", "output": "1\n    \n\n1 and 2019 have no positive common divisors other than 1."}]