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: A, B = map(int, input().split())
  
  prime_A = set()
  prime_B = set()
  
  curr = 2
  while A > 1:
      if A % curr == 0:
          prime_A.add(curr)
          A = A // curr
      elif curr * curr >= A:
          prime_A.add(A)
          A = 1
      else:
          curr += 1
  
  curr = 2
  while B > 1:
      if B % curr == 0:
          prime_B.add(curr)
          B = B // curr
      elif curr * curr >= B:
          prime_B.add(B)
          B /= B
      else:
          curr += 1
  print(len(prime_A & prime_B) + 1)
  
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."}]