






from math import pi, sqrt






def 			__UpperCamelCase	(		snake_case__					):
	if num <= 0:
		raise ValueError("""math domain error"""					)
	if num > 171.5:
		raise OverflowError("""math range error"""					)
	elif num - int(snake_case__					) not in (0, 0.5):
		raise NotImplementedError("""num must be an integer or a half-integer"""					)
	elif num == 0.5:
		return sqrt(snake_case__					)
	else:
		return 1.0 if num == 1 else (num - 1) * gamma(num - 1					)






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


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

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









"""simple docstring"""
from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors






def 			__UpperCamelCase	(		snake_case__					):
	A_		:						List[str]	    =   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()

