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




def        __UpperCamelCase					(    lowerCAmelCase__							:    int  ):






 """simple docstring"""




 __a			:  Optional[Any]		    =  prime_factors(snake_case__  )
 if is_square_free(snake_case__  ):
  return -1 if len(snake_case__  ) % 2 else 1
 return 0


if __name__ == "__main__":
      import doctest

      doctest.testmod()


from math import pi, sqrt




def        __UpperCamelCase					(    lowerCAmelCase__							:    float  ):
 if num <= 0:
  raise ValueError('''math domain error'''  )
 if num > 1_71.5:
  raise OverflowError('''math range error'''  )
 elif num - int(lowerCAmelCase__  ) not in (0, 0.5):
  raise NotImplementedError('''num must be an integer or a half-integer'''  )
 elif num == 0.5:
  return sqrt(lowerCAmelCase__  )
 else:
  return 1.0 if num == 1 else (num - 1) * gamma(num - 1  )




def        __UpperCamelCase					(    ):
 assert gamma(0.5  ) == sqrt(lowerCAmelCase__  )
 assert gamma(1  ) == 1.0
 assert gamma(2  ) == 1.0


if __name__ == "__main__":
      from doctest import testmod

      testmod()
      lowercase__          =1.0
      while num:
            lowercase__          =float(input('Gamma of: '))
            print(F"""gamma({num}) = {gamma(num)}""")
            print('\nEnter 0 to exit...')
