



'''simple docstring'''





from math import pi, sqrt






def 			lowerCAmelCase__	(					lowerCamelCase_	:	float):





				'''simple docstring'''

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






def 			lowerCAmelCase__	(					):





				'''simple docstring'''

				assert gamma(0.5) == sqrt(_A)
				assert gamma(1) == 1.0
				assert gamma(2) == 1.0


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

							testmod()
							__snake_case       :	Dict            =1.0
							while num:
														__snake_case       :	List[str]            =float(input('Gamma of: '))
														print(f"""gamma({num}) = {gamma(num)}""")
														print('\nEnter 0 to exit...')






from bisect import bisect
from itertools import accumulate






def 			lowerCAmelCase__	(					lowerCamelCase_	:	List[str] ,lowerCamelCase_	:	Optional[Any] ,lowerCamelCase_	:	List[str] ,lowerCamelCase_	:	Optional[int]):





				'''simple docstring'''

				lowerCAmelCase__  :       Any				=  sorted(zip(lowerCamelCase_ ,lowerCamelCase_) ,key=lambda lowerCamelCase_: x[0] / x[1] ,reverse=lowerCamelCase_)
				lowerCAmelCase__		,	lowerCAmelCase__  :       List[str]				=  [i[0] for i in r], [i[1] for i in r]
				lowerCAmelCase__  :       Tuple				=  list(accumulate(lowerCamelCase_))
				lowerCAmelCase__  :       str				=  bisect(lowerCamelCase_ ,lowerCamelCase_)
				return (
				    0
				    if k == 0
				    else sum(vl[:k]) + (w - acc[k - 1]) * (vl[k]) / (wt[k])
				    if k != n
				    else sum(vl[:k])
				)


if __name__ == "__main__":
							import doctest

							doctest.testmod()

