




"""simple docstring"""




import math



def 					a__				(       snake_case__       )		->      bool:
			assert isinstance(snake_case__ ,				snake_case__       ) and (
			    number >= 0
			), "'number' must been an int and positive"

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

			lowerCamelCase       =      range(3 ,				int(math.sqrt(snake_case__       ) + 1       ) ,				2       )
			return not any(not number % i for i in odd_numbers       )



def 					a__				(       snake_case__ ,				snake_case__=1 ,				**snake_case__       )		->      Optional[Any]:
			lowerCamelCase       =      factor * value
			lowerCamelCase       =      value

			while not is_prime(snake_case__       ):
						value += 1 if not ("desc" in kwargs and kwargs["desc"] is True) else -1

			if value == first_value_val:
						return next_prime(value + 1 ,				**snake_case__       )
			return value









"""simple docstring"""




from __future__ import annotations



def 					a__				(       snake_case__ ,				snake_case__ = None ,				snake_case__ = None       )		->      None:
			if start is None:
						lowerCamelCase       =      0

			if end is None:
						lowerCamelCase       =      len(snake_case__       ) - 1

			if start >= end:
						return

			lowerCamelCase       =      (start + end) // 2

			slowsort(snake_case__ ,				snake_case__ ,				snake_case__       )
			slowsort(snake_case__ ,				mid + 1 ,				snake_case__       )

			if sequence[end] < sequence[mid]:
						lowerCamelCase   ,     lowerCamelCase       =      sequence[mid], sequence[end]

			slowsort(snake_case__ ,				snake_case__ ,				end - 1       )


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

					testmod()



