






'''simple docstring'''

def    lowercase__			(				__UpperCamelCase		,						__UpperCamelCase   )->			str:
      if a < 0 or b < 0:
            raise ValueError("""the value of both inputs must be positive"""   )
      UpperCamelCase      = str(bin(__UpperCamelCase   )   )[2:]  # remove the leading "0b"
      UpperCamelCase      = str(bin(__UpperCamelCase   )   )[2:]
      UpperCamelCase      = max(len(__UpperCamelCase   )		,						len(__UpperCamelCase   )   )
      return "0b" + "".join(
          str(int("""1""" in (char_a, char_b)   )   )
          for char_a, char_b in zip(a_binary.zfill(__UpperCamelCase   )		,						b_binary.zfill(__UpperCamelCase   )   )   )


if __name__ == "__main__":
 import doctest

 doctest.testmod()








'''simple docstring'''

from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors







def    lowercase__			(				__UpperCamelCase   )->			int:
      UpperCamelCase      = prime_factors(__UpperCamelCase   )
      if is_square_free(__UpperCamelCase   ):
            return -1 if len(__UpperCamelCase   ) % 2 else 1
      return 0


if __name__ == "__main__":
     import doctest

     doctest.testmod()
