




"""simple docstring"""




from math import pi, sqrt







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







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


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

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











def  a__ (__lowercase							:str					,  __lowercase							:str   )		-> float:

				def get_matched_characters(__lowercase							:str					,  __lowercase							:str   ) -> str:
								_A	:				Union[str, Any]   =      []
								_A	:				Dict   =      min(len(_stra   )					,  len(_stra   )   ) // 2
								for i, l in enumerate(_stra   ):
												_A	:				Tuple   =      int(max(0					,  i - limit   )   )
												_A	:				Union[str, Any]   =      int(min(i + limit + 1					,  len(_stra   )   )   )
												if l in _stra[left:right]:
																matched.append(__lowercase   )
																_A	:				List[Any]   =      f"""{_stra[0:_stra.index(__lowercase   )]} {_stra[_stra.index(__lowercase   ) + 1:]}"""

								return "".join(__lowercase   )

				# matching characters
				_A	:				str   =      get_matched_characters(__lowercase					,  __lowercase   )
				_A	:				Optional[Any]   =      get_matched_characters(__lowercase					,  __lowercase   )
				_A	:				Any   =      len(__lowercase   )

				# transposition
				_A	:				str   =      (
				    len([(ca, ca) for ca, ca in zip(__lowercase					,  __lowercase   ) if ca != ca]   ) // 2
				)

				if not match_count:
								_A	:				Optional[int]   =      0.0
				else:
								_A	:				str   =      (
								    1
								    / 3
								    * (
								        match_count / len(__lowercase   )
								        + match_count / len(__lowercase   )
								        + (match_count - transpositions) / match_count
								    )
								)

				# common prefix up to 4 characters
				_A	:				Any   =      0
				for ca, ca in zip(stra[:4]					,  stra[:4]   ):
								if ca == ca:
												prefix_len += 1
								else:
												break

				return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	print(jaro_winkler('hello', 'world'))



