


from __future__ import annotations







class   __lowercase						:





							"""simple docstring"""







							def __init__(			self ,	lowerCAmelCase__					):





										"""simple docstring"""




										SCREAMING_SNAKE_CASE_		:    Optional[int] 		=				value
										SCREAMING_SNAKE_CASE_		:    Node | None 		=				None
										SCREAMING_SNAKE_CASE_		:    Node | None 		=				None







class   __lowercase						:





							"""simple docstring"""







							_UpperCAmelCase						     =	4_2






							def __init__(			self					):





										"""simple docstring"""




										SCREAMING_SNAKE_CASE_		:    Dict 		=				0






							def 				UpperCamelCase__    (			self ,	lowerCAmelCase__ ,	lowerCAmelCase__					):





										"""simple docstring"""




										if node is None:
													return

										if path_sum == self.target:
													self.paths += 1

										if node.left:
													self.depth_first_search(node.left ,	path_sum + node.left.value					)
										if node.right:
													self.depth_first_search(node.right ,	path_sum + node.right.value					)






							def 				UpperCamelCase__    (			self ,	lowerCAmelCase__ ,	lowerCAmelCase__ = None					):





										"""simple docstring"""




										if node is None:
													return 0
										if target is not None:
													SCREAMING_SNAKE_CASE_		:    Union[str, Any] 		=				target

										self.depth_first_search(lowerCAmelCase__ ,	node.value					)
										self.path_sum(node.left					)
										self.path_sum(node.right					)

										return self.paths


if __name__ == "__main__":
				import doctest

				doctest.testmod()



from itertools import compress, repeat
from math import ceil, sqrt






def 	a__ (							A__							):

			if num <= 2:
						return []
			if num == 3:
						return [2]

			# Odd sieve for numbers in range [3, num - 1]
			SCREAMING_SNAKE_CASE_		:    Any 		=				bytearray(B'\x01'							) * ((num >> 1) - 1)

			for i in range(3,			int(sqrt(A__							)							) + 1,			2							):
						if sieve[(i >> 1) - 1]:
									SCREAMING_SNAKE_CASE_		:    Optional[int] 		=				i**2
									SCREAMING_SNAKE_CASE_		:    List[str] 		=				repeat(
									    0,			ceil((num - i_squared) / (i << 1)							)							)

			return [2] + list(compress(range(3,			A__,			2							),			A__							)							)


if __name__ == "__main__":
				import doctest

				doctest.testmod()





