



from math import pi, sqrt
def  UpperCamelCase						(       _A			:				float    )->       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  UpperCamelCase						(       )->       None:





						"""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()
						UpperCAmelCase_							:      List[str]      =  1.0
						while num:
												UpperCAmelCase_							:      Tuple      =  float(input("Gamma of: "))
												print(F'''gamma({num}) = {gamma(num)}''')
												print("\nEnter 0 to exit...")










import math
from collections.abc import Iterator
from itertools import takewhile
def  UpperCamelCase						(       _A			:				int    )->       bool:





						"""simple docstring"""





						if 1 < number < 4:
												# 2 and 3 are primes
												return True
						elif number < 2 or number % 2 == 0 or number % 3 == 0:
												# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
												return False

						# All primes number are in format of 6k +/- 1
						for i in range(5			,							int(math.sqrt(_A    ) + 1    )			,							6    ):
												if number % i == 0 or number % (i + 2) == 0:
																		return False
						return True
def  UpperCamelCase						(       )->       Iterator[int]:





						"""simple docstring"""





						A__							=       2
						while True:
												if is_prime(_A    ):
																		yield num
												num += 1
def  UpperCamelCase						(       _A			:				int = 2000000    )->       int:





						"""simple docstring"""





						return sum(takewhile(lambda _A    : x < n			,							prime_generator()    )    )


if __name__ == "__main__":
						print(F'''{solution() = }''')





