






from __future__ import annotations

import math






def    __magic_name__    (	SCREAMING_SNAKE_CASE				)     ->    list[int]:

							if num <= 0:
														_lowercase							:   List[str] 							=   F"""{num}: Invalid input, please enter a positive integer."""
														raise ValueError(SCREAMING_SNAKE_CASE				)

							_lowercase							:   Union[str, Any] 							=   [True] * (num + 1)
							_lowercase							:   Union[str, Any] 							=   []
							_lowercase							:   Dict 							=   2
							_lowercase							:   Union[str, Any] 							=   int(math.sqrt(SCREAMING_SNAKE_CASE				)				)

							while start <= end:
														# If start is a prime
														if sieve[start] is True:
																					prime.append(SCREAMING_SNAKE_CASE				)

																					# Set multiples of start be False
																					for i in range(start * start     ,     num + 1     ,     SCREAMING_SNAKE_CASE				):
																												if sieve[i] is True:
																																			_lowercase							:   str 							=   False

														start += 1

							for j in range(end + 1     ,     num + 1				):
														if sieve[j] is True:
																					prime.append(SCREAMING_SNAKE_CASE				)

							return prime


if __name__ == "__main__":
							print(prime_sieve(int(input("Enter a positive integer: ").strip())))











from __future__ import annotations

import math
import random
from typing import Any


class       __lowerCAmelCase					:


	'''simple docstring'''





	def __init__(						self:						Dict			):
			lowercase__					:      list[Any]      =		[]
			lowercase__					:      int      =		0
			lowercase__					:      int      =		0

	def    snake_case__(						self:						Optional[int]			):
			return self.head == self.tail

	def    snake_case__(						self:						Any,					lowerCamelCase_:						Any			):
			self.data.append(lowerCamelCase_			)
			lowercase__					:      int      =		self.tail + 1

	def    snake_case__(						self:						Tuple			):
			lowercase__					:      Optional[Any]      =		self.data[self.head]
			lowercase__					:      Optional[int]      =		self.head + 1
			return ret

	def    snake_case__(						self:						List[Any]			):
			return self.tail - self.head





	def    snake_case__(						self:						List[Any]			):
			print(self.data			)
			print('**************'			)
			print(self.data[self.head : self.tail]			)


class       __lowerCAmelCase					:


	'''simple docstring'''





	def __init__(						self:						Union[str, Any],					lowerCamelCase_:						Any			):
			lowercase__					:      List[Any]      =		data
			lowercase__					:      MyNode | None      =		None
			lowercase__					:      MyNode | None      =		None
			lowercase__					:      int      =		1

	def    snake_case__(						self:						Optional[Any]			):
			return self.data

	def    snake_case__(						self:						List[str]			):
			return self.left

	def    snake_case__(						self:						Optional[int]			):
			return self.right

	def    snake_case__(						self:						Optional[Any]			):
			return self.height

	def    snake_case__(						self:						Optional[int],					lowerCamelCase_:						Any			):
			lowercase__					:      Tuple      =		data

	def    snake_case__(						self:						Optional[int],					lowerCamelCase_:						MyNode | None			):
			lowercase__					:      Dict      =		node

	def    snake_case__(						self:						Union[str, Any],					lowerCamelCase_:						MyNode | None			):
			lowercase__					:      Optional[Any]      =		node





	def    snake_case__(						self:						List[Any],					lowerCamelCase_:						int			):
			lowercase__					:      Union[str, Any]      =		height


def       SCREAMING_SNAKE_CASE__  (       _lowercase     : MyNode | None			)   ->							int:




		'''simple docstring'''
		if node is None:
				return 0
		return node.get_height()


def       SCREAMING_SNAKE_CASE__  (       _lowercase     : int   ,    _lowercase     : int			)   ->							int:




		'''simple docstring'''
		if a > b:
				return a
		return b


def       SCREAMING_SNAKE_CASE__  (       _lowercase     : MyNode			)   ->							MyNode:




		'''simple docstring'''
		print('left rotation node:'   ,    node.get_data()			)
		lowercase__					:      Optional[int]      =		node.get_left()
		assert ret is not None
		node.set_left(ret.get_right()			)
		ret.set_right(_lowercase			)
		lowercase__					:      List[str]      =		my_max(get_height(node.get_right()			)   ,    get_height(node.get_left()			)			) + 1
		node.set_height(_lowercase			)
		lowercase__					:      Optional[Any]      =		my_max(get_height(ret.get_right()			)   ,    get_height(ret.get_left()			)			) + 1
		ret.set_height(_lowercase			)
		return ret


def       SCREAMING_SNAKE_CASE__  (       _lowercase     : MyNode			)   ->							MyNode:




		'''simple docstring'''
		print('right rotation node:'   ,    node.get_data()			)
		lowercase__					:      Union[str, Any]      =		node.get_right()
		assert ret is not None
		node.set_right(ret.get_left()			)
		ret.set_left(_lowercase			)
		lowercase__					:      str      =		my_max(get_height(node.get_right()			)   ,    get_height(node.get_left()			)			) + 1
		node.set_height(_lowercase			)
		lowercase__					:      List[str]      =		my_max(get_height(ret.get_right()			)   ,    get_height(ret.get_left()			)			) + 1
		ret.set_height(_lowercase			)
		return ret


def       SCREAMING_SNAKE_CASE__  (       _lowercase     : MyNode			)   ->							MyNode:




		'''simple docstring'''
		lowercase__					:      str      =		node.get_left()
		assert left_child is not None
		node.set_left(left_rotation(_lowercase			)			)
		return right_rotation(_lowercase			)


def       SCREAMING_SNAKE_CASE__  (       _lowercase     : MyNode			)   ->							MyNode:




		'''simple docstring'''
		lowercase__					:      Optional[Any]      =		node.get_right()
		assert right_child is not None
		node.set_right(right_rotation(_lowercase			)			)
		return left_rotation(_lowercase			)


def       SCREAMING_SNAKE_CASE__  (       _lowercase     : MyNode | None   ,    _lowercase     : Any			)   ->							MyNode | None:




		'''simple docstring'''
		if node is None:
				return MyNode(_lowercase			)
		if data < node.get_data():
				node.set_left(insert_node(node.get_left()   ,    _lowercase			)			)
				if (
				    get_height(node.get_left()			) - get_height(node.get_right()			) == 2
				):  # an unbalance detected
						lowercase__					:      Tuple      =		node.get_left()
						assert left_child is not None
						if (
						    data < left_child.get_data()
						):  # new node is the left child of the left child
								lowercase__					:      Optional[Any]      =		right_rotation(_lowercase			)
						else:
								lowercase__					:      List[str]      =		lr_rotation(_lowercase			)
		else:
				node.set_right(insert_node(node.get_right()   ,    _lowercase			)			)
				if get_height(node.get_right()			) - get_height(node.get_left()			) == 2:
						lowercase__					:      Dict      =		node.get_right()
						assert right_child is not None
						if data < right_child.get_data():
								lowercase__					:      Dict      =		rl_rotation(_lowercase			)
						else:
								lowercase__					:      Tuple      =		left_rotation(_lowercase			)
		lowercase__					:      List[Any]      =		my_max(get_height(node.get_right()			)   ,    get_height(node.get_left()			)			) + 1
		node.set_height(_lowercase			)
		return node


def       SCREAMING_SNAKE_CASE__  (       _lowercase     : MyNode			)   ->							Any:




		'''simple docstring'''
		while True:
				lowercase__					:      List[Any]      =		root.get_right()
				if right_child is None:
						break
				lowercase__					:      List[str]      =		right_child
		return root.get_data()


def       SCREAMING_SNAKE_CASE__  (       _lowercase     : MyNode			)   ->							Any:




		'''simple docstring'''
		while True:
				lowercase__					:      Any      =		root.get_left()
				if left_child is None:
						break
				lowercase__					:      List[str]      =		left_child
		return root.get_data()


def       SCREAMING_SNAKE_CASE__  (       _lowercase     : MyNode   ,    _lowercase     : Any			)   ->							MyNode | None:




		'''simple docstring'''
		lowercase__					:      List[Any]      =		root.get_left()
		lowercase__					:      List[Any]      =		root.get_right()
		if root.get_data() == data:
				if left_child is not None and right_child is not None:
						lowercase__					:      Dict      =		get_left_most(_lowercase			)
						root.set_data(_lowercase			)
						root.set_right(del_node(_lowercase   ,    _lowercase			)			)
				elif left_child is not None:
						lowercase__					:      List[Any]      =		left_child
				elif right_child is not None:
						lowercase__					:      Dict      =		right_child
				else:
						return None
		elif root.get_data() > data:
				if left_child is None:
						print('No such data'			)
						return root
				else:
						root.set_left(del_node(_lowercase   ,    _lowercase			)			)
		else:  # root.get_data() < data
				if right_child is None:
						return root
				else:
						root.set_right(del_node(_lowercase   ,    _lowercase			)			)

		if get_height(_lowercase			) - get_height(_lowercase			) == 2:
				assert right_child is not None
				if get_height(right_child.get_right()			) > get_height(right_child.get_left()			):
						lowercase__					:      List[Any]      =		left_rotation(_lowercase			)
				else:
						lowercase__					:      Optional[Any]      =		rl_rotation(_lowercase			)
		elif get_height(_lowercase			) - get_height(_lowercase			) == -2:
				assert left_child is not None
				if get_height(left_child.get_left()			) > get_height(left_child.get_right()			):
						lowercase__					:      Optional[int]      =		right_rotation(_lowercase			)
				else:
						lowercase__					:      Dict      =		lr_rotation(_lowercase			)
		lowercase__					:      Any      =		my_max(get_height(root.get_right()			)   ,    get_height(root.get_left()			)			) + 1
		root.set_height(_lowercase			)
		return root


class       __lowerCAmelCase					:


	'''simple docstring'''





	def __init__(						self:						str			):
			lowercase__					:      MyNode | None      =		None

	def    snake_case__(						self:						Optional[Any]			):
			return get_height(self.root			)

	def    snake_case__(						self:						List[Any],					lowerCamelCase_:						Any			):
			print('insert:' + str(lowerCamelCase_			)			)
			lowercase__					:      int      =		insert_node(self.root,					lowerCamelCase_			)

	def    snake_case__(						self:						Tuple,					lowerCamelCase_:						Any			):
			print('delete:' + str(lowerCamelCase_			)			)
			if self.root is None:
					print('Tree is empty!'			)
					return
			lowercase__					:      int      =		del_node(self.root,					lowerCamelCase_			)





	def __str__(						self:						str,					):  # a level traversale, gives a more intuitive look on the tree
			lowercase__					:      Optional[int]      =		''
			lowercase__					:      Any      =		MyQueue()
			q.push(self.root			)
			lowercase__					:      Dict      =		self.get_height()
			if layer == 0:
					return output
			lowercase__					:      Optional[int]      =		0
			while not q.is_empty():
					lowercase__					:      Dict      =		q.pop()
					lowercase__					:      Optional[Any]      =		' ' * int(math.pow(2,					layer - 1			)			)
					output += space
					if node is None:
							output += "*"
							q.push(lowerCamelCase_			)
							q.push(lowerCamelCase_			)
					else:
							output += str(node.get_data()			)
							q.push(node.get_left()			)
							q.push(node.get_right()			)
					output += space
					lowercase__					:      Union[str, Any]      =		cnt + 1
					for i in range(100			):
							if cnt == math.pow(2,					lowerCamelCase_			) - 1:
									lowercase__					:      Optional[int]      =		layer - 1
									if layer == 0:
											output += "\n*************************************"
											return output
									output += "\n"
									break
			output += "\n*************************************"
			return output


def       SCREAMING_SNAKE_CASE__  (       )   ->							None:




		'''simple docstring'''
		import doctest

		doctest.testmod()


if __name__ == "__main__":
			_test()
			__UpperCamelCase:	int = AVLtree()
			__UpperCamelCase:	int = list(range(1_0))
			random.shuffle(lst)
			for i in lst:
						t.insert(i)
						print(str(t))
			random.shuffle(lst)
			for i in lst:
						t.del_node(i)
						print(str(t))


