



'''simple docstring'''






from __future__ import annotations

from collections import deque
from collections.abc import Sequence
from dataclasses import dataclass
from typing import Any

@dataclass
class        SCREAMING_SNAKE_CASE:







	"""simple docstring"""






	lowerCamelCase__    				= 42
	lowerCamelCase__    				= None
	lowerCamelCase__    				= None


def 				snake_case_  (      )   ->     Node | None:

							'''simple docstring'''





							UpperCAmelCase				: str											=	Node(1						)
							UpperCAmelCase				: Any											=	Node(2						)
							UpperCAmelCase				: Any											=	Node(3						)
							UpperCAmelCase				: Optional[int]											=	Node(4						)
							UpperCAmelCase				: Optional[Any]											=	Node(5						)
							return tree


def 				snake_case_  (      _lowerCAmelCase						:		Node | None						)   ->     list[int]:

							'''simple docstring'''





							return [root.data, *preorder(root.left						), *preorder(root.right						)] if root else []


def 				snake_case_  (      _lowerCAmelCase						:		Node | None						)   ->     list[int]:

							'''simple docstring'''





							return postorder(root.left						) + postorder(root.right						) + [root.data] if root else []


def 				snake_case_  (      _lowerCAmelCase						:		Node | None						)   ->     list[int]:

							'''simple docstring'''





							return [*inorder(root.left						), root.data, *inorder(root.right						)] if root else []


def 				snake_case_  (      _lowerCAmelCase						:		Node | None						)   ->     int:

							'''simple docstring'''





							return (max(height(root.left						)     ,   height(root.right						)						) + 1) if root else 0


def 				snake_case_  (      _lowerCAmelCase						:		Node | None						)   ->     Sequence[Node | None]:

							'''simple docstring'''





							UpperCAmelCase				: list[Any]											=	[]

							if root is None:
														return output

							UpperCAmelCase				: Tuple											=	deque([root]						)

							while process_queue:
														UpperCAmelCase				: int											=	process_queue.popleft()
														output.append(node.data						)

														if node.left:
																					process_queue.append(node.left						)
														if node.right:
																					process_queue.append(node.right						)
							return output


def 				snake_case_  (      _lowerCAmelCase						:		Node | None     ,   _lowerCAmelCase						:		int						)   ->     Sequence[Node | None]:

							'''simple docstring'''





							UpperCAmelCase				: list[Any]											=	[]

							def populate_output(_lowerCAmelCase						:		Node | None     ,   _lowerCAmelCase						:		int						) -> None:
														if not root:
																					return
														if level == 1:
																					output.append(root.data						)
														elif level > 1:
																					populate_output(root.left     ,   level - 1						)
																					populate_output(root.right     ,   level - 1						)

							populate_output(__snake_case     ,   __snake_case						)
							return output


def 				snake_case_  (      _lowerCAmelCase						:		Node | None     ,   _lowerCAmelCase						:		int						)   ->     Sequence[Node | None]:

							'''simple docstring'''





							UpperCAmelCase				: list[Any]											=	[]

							def populate_output(_lowerCAmelCase						:		Node | None     ,   _lowerCAmelCase						:		int						) -> None:
														if root is None:
																					return
														if level == 1:
																					output.append(root.data						)
														elif level > 1:
																					populate_output(root.right     ,   level - 1						)
																					populate_output(root.left     ,   level - 1						)

							populate_output(__snake_case     ,   __snake_case						)
							return output


def 				snake_case_  (      _lowerCAmelCase						:		Node | None						)   ->     Sequence[Node | None] | list[Any]:

							'''simple docstring'''





							if root is None:
														return []

							UpperCAmelCase				: list[Sequence[Node | None]]											=	[]

							UpperCAmelCase				: List[str]											=	0
							UpperCAmelCase				: List[Any]											=	height(__snake_case						)

							for h in range(1     ,   height_tree + 1						):
														if not flag:
																					output.append(get_nodes_from_left_to_right(__snake_case     ,   __snake_case						)						)
																					UpperCAmelCase				: str											=	1
														else:
																					output.append(get_nodes_from_right_to_left(__snake_case     ,   __snake_case						)						)
																					UpperCAmelCase				: Union[str, Any]											=	0

							return output


def 				snake_case_  (      )   ->     None:  # Main function for testing.

							'''simple docstring'''





							UpperCAmelCase				: Optional[Any]											=	make_tree()
							print(f"""In-order Traversal: {inorder(__snake_case						)}"""						)
							print(f"""Pre-order Traversal: {preorder(__snake_case						)}"""						)
							print(f"""Post-order Traversal: {postorder(__snake_case						)}"""     ,   '''\n'''						)

							print(f"""Height of Tree: {height(__snake_case						)}"""     ,   '''\n'''						)

							print('''Complete Level Order Traversal: '''						)
							print(level_order(__snake_case						)     ,   '''\n'''						)

							print('''Level-wise order Traversal: '''						)

							for level in range(1     ,   height(__snake_case						) + 1						):
														print(f"""Level {level}:"""     ,   get_nodes_from_left_to_right(__snake_case     ,   level=__snake_case						)						)

							print('''\nZigZag order Traversal: '''						)
							print(zigzag(__snake_case						)						)


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()










'''simple docstring'''






UpperCamelCase__:     dict[tuple[int, int, int], int]										=    {}


def 				snake_case_  (      _lowerCAmelCase						:		int     ,   _lowerCAmelCase						:		int     ,   _lowerCAmelCase						:		int						)   ->     int:

							# if we are absent twice, or late 3 consecutive days,
							# no further prize strings are possible
							if late == 3 or absent == 2:
														return 0

							# if we have no days left, and have not failed any other rules,
							# we have a prize string
							if days == 0:
														return 1

							# No easy solution, so now we need to do the recursive calculation

							# First, check if the combination is already in the cache, and
							# if yes, return the stored value from there since we already
							# know the number of possible prize strings from this point on
							UpperCAmelCase				: List[Any]											=	(days, absent, late)
							if key in cache:
														return cache[key]

							# now we calculate the three possible ways that can unfold from
							# this point on, depending on our attendance today

							# 1) if we are late (but not absent), the "absent" counter stays as
							# it is, but the "late" counter increases by one
							UpperCAmelCase				: int											=	_calculate(days - 1     ,   _lowerCAmelCase     ,   late + 1						)

							# 2) if we are absent, the "absent" counter increases by 1, and the
							# "late" counter resets to 0
							UpperCAmelCase				: Optional[Any]											=	_calculate(days - 1     ,   absent + 1     ,   0						)

							# 3) if we are on time, this resets the "late" counter and keeps the
							# absent counter
							UpperCAmelCase				: Tuple											=	_calculate(days - 1     ,   _lowerCAmelCase     ,   0						)

							UpperCAmelCase				: str											=	state_late + state_absent + state_ontime

							UpperCAmelCase				: List[Any]											=	prizestrings
							return prizestrings


def 				snake_case_  (      _lowerCAmelCase						:		int = 30						)   ->     int:
							return _calculate(_lowerCAmelCase     ,   absent=0     ,   late=0						)


if __name__ == "__main__":
						print(solution())





