






'''simple docstring'''







class 						SCREAMING_SNAKE_CASE       :






			def __init__(			self   :      int	,    __SCREAMING_SNAKE_CASE   :      int	,    __SCREAMING_SNAKE_CASE   :      Any=None	,    __SCREAMING_SNAKE_CASE   :      Optional[Any]=None       )      ->      Optional[int]:
							a_		:	Optional[int]									=   data
							a_		:	Optional[int]									=   previous
							a_		:	Union[str, Any]									=   next_node






			def __str__(			self   :      int       )      ->      str:
							return f'{self.data}'






			def       SCREAMING_SNAKE_CASE   (			self   :      Union[str, Any]       )      ->      int:
							return self.data






			def       SCREAMING_SNAKE_CASE   (			self   :      Dict       )      ->      List[str]:
							return self.next







			def       SCREAMING_SNAKE_CASE   (			self   :      Union[str, Any]       )      ->      int:
							return self.previous





class 						SCREAMING_SNAKE_CASE       :






			def __init__(			self   :      List[Any]	,    __SCREAMING_SNAKE_CASE   :      Optional[Any]       )      ->      Optional[Any]:
							a_		:	List[str]									=   head






			def __iter__(			self   :      Union[str, Any]       )      ->      Dict:
							return self







			def       SCREAMING_SNAKE_CASE   (			self   :      List[str]       )      ->      Any:
							if not self.current:
											raise StopIteration
							else:
											a_		:	List[str]									=   self.current.get_data()
											a_		:	Dict									=   self.current.get_next()
											return value





class 						SCREAMING_SNAKE_CASE       :






			def __init__(			self   :      int       )      ->      Union[str, Any]:
							a_		:	Any									=   None  # First node in list
							a_		:	Optional[int]									=   None  # Last node in list






			def __str__(			self   :      List[Any]       )      ->      Union[str, Any]:
							a_		:	Union[str, Any]									=   self.head
							a_		:	Union[str, Any]									=   []
							while current is not None:
											nodes.append(current.get_data()       )
											a_		:	str									=   current.get_next()
							return " ".join(str(__SCREAMING_SNAKE_CASE       ) for node in nodes       )






			def __contains__(			self   :      Tuple	,    __SCREAMING_SNAKE_CASE   :      int       )      ->      Optional[int]:
							a_		:	int									=   self.head
							while current:
											if current.get_data() == value:
															return True
											a_		:	int									=   current.get_next()
							return False






			def __iter__(			self   :      Optional[Any]       )      ->      str:
							return LinkedListIterator(self.head       )






			def       SCREAMING_SNAKE_CASE   (			self   :      int       )      ->      Optional[Any]:
							if self.head:
											return self.head.get_data()
							return None






			def       SCREAMING_SNAKE_CASE   (			self   :      str       )      ->      List[str]:
							if self.tail:
											return self.tail.get_data()
							return None






			def       SCREAMING_SNAKE_CASE   (			self   :      Any	,    __SCREAMING_SNAKE_CASE   :      Node       )      ->      None:
							if self.head is None:
											a_		:	Union[str, Any]									=   node
											a_		:	int									=   node
							else:
											self.insert_before_node(self.head	,    __SCREAMING_SNAKE_CASE       )






			def       SCREAMING_SNAKE_CASE   (			self   :      Optional[Any]	,    __SCREAMING_SNAKE_CASE   :      Node       )      ->      None:
							if self.head is None:
											self.set_head(__SCREAMING_SNAKE_CASE       )
							else:
											self.insert_after_node(self.tail	,    __SCREAMING_SNAKE_CASE       )






			def       SCREAMING_SNAKE_CASE   (			self   :      Tuple	,    __SCREAMING_SNAKE_CASE   :      int       )      ->      None:
							a_		:	Dict									=   Node(__SCREAMING_SNAKE_CASE       )
							if self.head is None:
											self.set_head(__SCREAMING_SNAKE_CASE       )
							else:
											self.set_tail(__SCREAMING_SNAKE_CASE       )






			def       SCREAMING_SNAKE_CASE   (			self   :      Union[str, Any]	,    __SCREAMING_SNAKE_CASE   :      Node	,    __SCREAMING_SNAKE_CASE   :      Node       )      ->      None:
							a_		:	Optional[Any]									=   node
							a_		:	Tuple									=   node.previous

							if node.get_previous() is None:
											a_		:	int									=   node_to_insert
							else:
											a_		:	Optional[Any]									=   node_to_insert

							a_		:	Any									=   node_to_insert






			def       SCREAMING_SNAKE_CASE   (			self   :      Union[str, Any]	,    __SCREAMING_SNAKE_CASE   :      Node	,    __SCREAMING_SNAKE_CASE   :      Node       )      ->      None:
							a_		:	Union[str, Any]									=   node
							a_		:	int									=   node.next

							if node.get_next() is None:
											a_		:	List[str]									=   node_to_insert
							else:
											a_		:	Tuple									=   node_to_insert

							a_		:	Dict									=   node_to_insert






			def       SCREAMING_SNAKE_CASE   (			self   :      str	,    __SCREAMING_SNAKE_CASE   :      int	,    __SCREAMING_SNAKE_CASE   :      int       )      ->      None:
							a_		:	str									=   1
							a_		:	List[str]									=   Node(__SCREAMING_SNAKE_CASE       )
							a_		:	Optional[int]									=   self.head
							while node:
											if current_position == position:
															self.insert_before_node(__SCREAMING_SNAKE_CASE	,    __SCREAMING_SNAKE_CASE       )
															return
											current_position += 1
											a_		:	Union[str, Any]									=   node.next
							self.insert_after_node(self.tail	,    __SCREAMING_SNAKE_CASE       )






			def       SCREAMING_SNAKE_CASE   (			self   :      List[str]	,    __SCREAMING_SNAKE_CASE   :      int       )      ->      Node:
							a_		:	int									=   self.head
							while node:
											if node.get_data() == item:
															return node
											a_		:	Union[str, Any]									=   node.get_next()
							raise Exception('''Node not found'''       )






			def       SCREAMING_SNAKE_CASE   (			self   :      List[str]	,    __SCREAMING_SNAKE_CASE   :      Dict       )      ->      List[str]:
							if (node := self.get_node(__SCREAMING_SNAKE_CASE       )) is not None:
											if node == self.head:
															a_		:	Optional[int]									=   self.head.get_next()

											if node == self.tail:
															a_		:	List[str]									=   self.tail.get_previous()

											self.remove_node_pointers(__SCREAMING_SNAKE_CASE       )






			@staticmethod
			def       SCREAMING_SNAKE_CASE   (			__SCREAMING_SNAKE_CASE   :      Node       )      ->      None:
							if node.get_next():
											a_		:	Tuple									=   node.previous

							if node.get_previous():
											a_		:	Union[str, Any]									=   node.next

							a_		:	Tuple									=   None
							a_		:	List[Any]									=   None







			def       SCREAMING_SNAKE_CASE   (			self   :      Optional[int]       )      ->      str:
							return self.head is None





def 		_UpperCAmelCase (				):
				pass


if __name__ == "__main__":
		import doctest

		doctest.testmod()












'''simple docstring'''







import math





def 		_UpperCAmelCase (				__A				: int   ):
				a_		:	str									=   []
				a_		:	Tuple									=   2
				a_		:	Optional[Any]									=   int(math.sqrt(__A   )   )  # Size of every segment
				a_		:	Optional[Any]									=   [True] * (end + 1)
				a_		:	Union[str, Any]									=   []

				while start <= end:
								if temp[start] is True:
												in_prime.append(__A   )
												for i in range(start * start    ,		end + 1    ,		__A   ):
																a_		:	List[Any]									=   False
								start += 1
				prime += in_prime

				a_		:	Any									=   end + 1
				a_		:	Optional[Any]									=   min(2 * end    ,		__A   )

				while low <= n:
								a_		:	Optional[Any]									=   [True] * (high - low + 1)
								for each in in_prime:
												a_		:	Any									=   math.floor(low / each   ) * each
												if t < low:
																t += each

												for j in range(__A    ,		high + 1    ,		__A   ):
																a_		:	Union[str, Any]									=   False

								for j in range(len(__A   )   ):
												if temp[j] is True:
																prime.append(j + low   )

								a_		:	Tuple									=   high + 1
								a_		:	str									=   min(high + end    ,		__A   )

				return prime




print(sieve(10**6))




