

from __future__ import annotations

import queue





class 		__SCREAMING_SNAKE_CASE       :







				def __init__(					self    :		Tuple		,				UpperCAmelCase__    :		int      ):
										'''simple docstring'''
										lowercase   :       int								=data
										lowercase   :       Tuple								=None
										lowercase   :       Dict								=None






def 							_lowerCAmelCase (      )							->     TreeNode:
						print('''\n********Press N to stop entering at any point of time********\n'''	)
						lowercase   :       Dict								=input('''Enter the value of the root node: '''	).strip().lower()
						lowercase   :       queue.Queue								=queue.Queue()
						lowercase   :       str								=TreeNode(int(__magic_name__	)	)
						q.put(__magic_name__	)
						while not q.empty():
												lowercase   :       List[Any]								=q.get()
												lowercase   :       Any								=f'''Enter the left node of {node_found.data}: '''
												lowercase   :       Dict								=input(__magic_name__	).strip().lower() or '''n'''
												if check == "n":
																		return tree_node
												lowercase   :       int								=TreeNode(int(__magic_name__	)	)
												lowercase   :       List[str]								=left_node
												q.put(__magic_name__	)
												lowercase   :       Union[str, Any]								=f'''Enter the right node of {node_found.data}: '''
												lowercase   :       str								=input(__magic_name__	).strip().lower() or '''n'''
												if check == "n":
																		return tree_node
												lowercase   :       List[Any]								=TreeNode(int(__magic_name__	)	)
												lowercase   :       Dict								=right_node
												q.put(__magic_name__	)
						raise






def 							_lowerCAmelCase (      __magic_name__	:    TreeNode	)							->     None:
						if not isinstance(__magic_name__      ,   __magic_name__	) or not node:
												return
						print(node.data      ,   end=''','''	)
						pre_order(node.left	)
						pre_order(node.right	)






def 							_lowerCAmelCase (      __magic_name__	:    TreeNode	)							->     None:
						if not isinstance(__magic_name__      ,   __magic_name__	) or not node:
												return
						in_order(node.left	)
						print(node.data      ,   end=''','''	)
						in_order(node.right	)






def 							_lowerCAmelCase (      __magic_name__	:    TreeNode	)							->     None:
						if not isinstance(__magic_name__      ,   __magic_name__	) or not node:
												return
						post_order(node.left	)
						post_order(node.right	)
						print(node.data      ,   end=''','''	)






def 							_lowerCAmelCase (      __magic_name__	:    TreeNode	)							->     None:
						if not isinstance(__magic_name__      ,   __magic_name__	) or not node:
												return
						lowercase   :       queue.Queue								=queue.Queue()
						q.put(__magic_name__	)
						while not q.empty():
												lowercase   :       Optional[int]								=q.get()
												print(node_dequeued.data      ,   end=''','''	)
												if node_dequeued.left:
																		q.put(node_dequeued.left	)
												if node_dequeued.right:
																		q.put(node_dequeued.right	)






def 							_lowerCAmelCase (      __magic_name__	:    TreeNode	)							->     None:
						if not isinstance(__magic_name__      ,   __magic_name__	) or not node:
												return
						lowercase   :       queue.Queue								=queue.Queue()
						q.put(__magic_name__	)
						while not q.empty():
												lowercase   :       Dict								=[]
												while not q.empty():
																		lowercase   :       Tuple								=q.get()
																		print(node_dequeued.data      ,   end=''','''	)
																		if node_dequeued.left:
																								list_.append(node_dequeued.left	)
																		if node_dequeued.right:
																								list_.append(node_dequeued.right	)
												print()
												for node in list_:
																		q.put(__magic_name__	)






def 							_lowerCAmelCase (      __magic_name__	:    TreeNode	)							->     None:
						if not isinstance(__magic_name__      ,   __magic_name__	) or not node:
												return
						lowercase   :       list[TreeNode]								=[]
						lowercase   :       Dict								=node
						while n or stack:
												while n:  # start from root node, find its left child
																		print(n.data      ,   end=''','''	)
																		stack.append(__magic_name__	)
																		lowercase   :       Optional[int]								=n.left
												# end of while means current node doesn't have left child
												lowercase   :       int								=stack.pop()
												# start to traverse its right child
												lowercase   :       str								=n.right






def 							_lowerCAmelCase (      __magic_name__	:    TreeNode	)							->     None:
						if not isinstance(__magic_name__      ,   __magic_name__	) or not node:
												return
						lowercase   :       list[TreeNode]								=[]
						lowercase   :       List[str]								=node
						while n or stack:
												while n:
																		stack.append(__magic_name__	)
																		lowercase   :       Dict								=n.left
												lowercase   :       Union[str, Any]								=stack.pop()
												print(n.data      ,   end=''','''	)
												lowercase   :       Tuple								=n.right






def 							_lowerCAmelCase (      __magic_name__	:    TreeNode	)							->     None:
						if not isinstance(__magic_name__      ,   __magic_name__	) or not node:
												return
						lowercase   :       Union[str, Any]								=[], []
						lowercase   :       Union[str, Any]								=node
						stacka.append(__magic_name__	)
						while stacka:  # to find the reversed order of post order, store it in stack2
												lowercase   :       List[Any]								=stacka.pop()
												if n.left:
																		stacka.append(n.left	)
												if n.right:
																		stacka.append(n.right	)
												stacka.append(__magic_name__	)
						while stacka:  # pop up from stack2 will be the post order
												print(stacka.pop().data      ,   end=''','''	)






def 							_lowerCAmelCase (      __magic_name__	:    str = ""      ,   __magic_name__	:    str=50      ,   __magic_name__	:    Dict="*"	)							->     str:
						if not s:
												return "\n" + width * char
						lowercase   :       List[str]								=divmod(width - len(__magic_name__	) - 2      ,   2	)
						return f'''{left * char} {s} {(left + extra) * char}'''


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							print(prompt("""Binary Tree Traversals"""))

							UpperCamelCase_							=					build_tree()
							print(prompt("""Pre Order Traversal"""))
							pre_order(node)
							print(prompt() + """\n""")

							print(prompt("""In Order Traversal"""))
							in_order(node)
							print(prompt() + """\n""")

							print(prompt("""Post Order Traversal"""))
							post_order(node)
							print(prompt() + """\n""")

							print(prompt("""Level Order Traversal"""))
							level_order(node)
							print(prompt() + """\n""")

							print(prompt("""Actual Level Order Traversal"""))
							level_order_actual(node)
							print("""*""" * 50 + """\n""")

							print(prompt("""Pre Order Traversal - Iteration Version"""))
							pre_order_iter(node)
							print(prompt() + """\n""")

							print(prompt("""In Order Traversal - Iteration Version"""))
							in_order_iter(node)
							print(prompt() + """\n""")

							print(prompt("""Post Order Traversal - Iteration Version"""))
							post_order_iter(node)
							print(prompt())








'''simple docstring'''





def 							_lowerCAmelCase (      __magic_name__	:    int = 1000000	)							->     int:
						lowercase   :       Dict								=set(range(3      ,   __magic_name__      ,   2	)	)
						primes.add(2	)
						for p in range(3      ,   __magic_name__      ,   2	):
												if p not in primes:
																		continue
												primes.difference_update(set(range(p * p      ,   __magic_name__      ,   __magic_name__	)	)	)

						lowercase   :       List[Any]								=[float(__magic_name__	) for n in range(limit + 1	)]

						for p in primes:
												for n in range(__magic_name__      ,   limit + 1      ,   __magic_name__	):
																		phi[n] *= 1 - 1 / p

						return int(sum(phi[2:]	)	)


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





