


"""simple docstring"""
from __future__ import annotations

from collections import defaultdict
from dataclasses import dataclass





@dataclass
class   __A  :





							'''simple docstring'''

							__lowercase:		int
							__lowercase:		TreeNode | None				   =     None
							__lowercase:		TreeNode | None				   =     None







def     _a					(   )     ->					TreeNode:
							return TreeNode(3					,			TreeNode(9					)					,			TreeNode(20					,			TreeNode(15					)					,			TreeNode(7					)					)					)







def     _a					(   _SCREAMING_SNAKE_CASE					)     ->					list[int]:

							def depth_first_search(
							    _SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					) -> None:
														if not root:
																					return

														if depth == len(_SCREAMING_SNAKE_CASE					):
																					right_view.append(root.val					)

														depth_first_search(root.right					,			depth + 1					,			_SCREAMING_SNAKE_CASE					)
														depth_first_search(root.left					,			depth + 1					,			_SCREAMING_SNAKE_CASE					)

							snake_case_     							=		[]
							if not root:
														return right_view

							depth_first_search(_SCREAMING_SNAKE_CASE					,			0					,			_SCREAMING_SNAKE_CASE					)
							return right_view







def     _a					(   _SCREAMING_SNAKE_CASE					)     ->					list[int]:

							def depth_first_search(
							    _SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					) -> None:
														if not root:
																					return

														if depth == len(_SCREAMING_SNAKE_CASE					):
																					left_view.append(root.val					)

														depth_first_search(root.left					,			depth + 1					,			_SCREAMING_SNAKE_CASE					)
														depth_first_search(root.right					,			depth + 1					,			_SCREAMING_SNAKE_CASE					)

							snake_case_     							=		[]
							if not root:
														return left_view

							depth_first_search(_SCREAMING_SNAKE_CASE					,			0					,			_SCREAMING_SNAKE_CASE					)
							return left_view







def     _a					(   _SCREAMING_SNAKE_CASE					)     ->					list[int]:

							def breadth_first_search(_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					) -> None:
														snake_case_     							=		[(root, 0)]
														snake_case_     							=		defaultdict(_SCREAMING_SNAKE_CASE					)

														while queue:
																					snake_case_     							=		queue.pop(0					)
																					snake_case_							,    snake_case_     							=		first

																					lookup[hd].append(node.val					)

																					if node.left:
																												queue.append((node.left, hd - 1)					)
																					if node.right:
																												queue.append((node.right, hd + 1)					)

														for pair in sorted(lookup.items()					,			key=lambda _SCREAMING_SNAKE_CASE					: each[0]					):
																					top_view.append(pair[1][0]					)

							snake_case_     							=		[]
							if not root:
														return top_view

							breadth_first_search(_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					)
							return top_view







def     _a					(   _SCREAMING_SNAKE_CASE					)     ->					list[int]:
							from collections import defaultdict

							def breadth_first_search(_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					) -> None:
														snake_case_     							=		[(root, 0)]
														snake_case_     							=		defaultdict(_SCREAMING_SNAKE_CASE					)

														while queue:
																					snake_case_     							=		queue.pop(0					)
																					snake_case_							,    snake_case_     							=		first
																					lookup[hd].append(node.val					)

																					if node.left:
																												queue.append((node.left, hd - 1)					)
																					if node.right:
																												queue.append((node.right, hd + 1)					)

														for pair in sorted(lookup.items()					,			key=lambda _SCREAMING_SNAKE_CASE					: each[0]					):
																					bottom_view.append(pair[1][-1]					)

							snake_case_     							=		[]
							if not root:
														return bottom_view

							breadth_first_search(_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					)
							return bottom_view


if __name__ == "__main__":
				import doctest

				doctest.testmod()







"""simple docstring"""
from __future__ import annotations

from collections import deque
from enum import Enum
from math import atana, degrees
from sys import maxsize





class   __A  (snake_case__):





							'''simple docstring'''

							__lowercase:		Dict				   =     1
							__lowercase:		List[str]				   =     2
							__lowercase:		int				   =     3



							def __repr__(					self				:   Optional[Any]							)       ->Optional[int]:



														"""simple docstring"""



														return F"""{self.__class__.__name__}.{self.name}"""







def     _a					(   _SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					)     ->					float:
							snake_case_							,    snake_case_     							=		point
							return degrees(atana(y - miny					,			x - minx					)					)







def     _a					(   _SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					)     ->					Direction:
							snake_case_							,    snake_case_     							=		starting
							snake_case_							,    snake_case_     							=		via
							snake_case_							,    snake_case_     							=		target
							snake_case_     							=		degrees(atana(ya - ya					,			xa - xa					)					)
							via_angle %= 360
							snake_case_     							=		degrees(atana(ya - ya					,			xa - xa					)					)
							target_angle %= 360
							# t-
							#  \ \
							#   \ v
							#    \|
							#     s
							# via_angle is always lower than target_angle, if direction is left.
							# If they are same, it means they are on a same line of convex hull.
							if target_angle > via_angle:
														return Direction.left
							elif target_angle == via_angle:
														return Direction.straight
							else:
														return Direction.right







def     _a					(   _SCREAMING_SNAKE_CASE					)     ->					list[tuple[int, int]]:

							if len(_SCREAMING_SNAKE_CASE					) <= 2:
														# There is no convex hull
														raise ValueError("""graham_scan: argument must contain more than 3 points."""					)
							if len(_SCREAMING_SNAKE_CASE					) == 3:
														return points
							# find the lowest and the most left point
							snake_case_     							=		0
							snake_case_							,    snake_case_     							=		maxsize, maxsize
							for i, point in enumerate(_SCREAMING_SNAKE_CASE					):
														snake_case_     							=		point[0]
														snake_case_     							=		point[1]
														if y < miny:
																					snake_case_     							=		y
																					snake_case_     							=		x
																					snake_case_     							=		i
														if y == miny and x < minx:
																					snake_case_     							=		x
																					snake_case_     							=		i

    # remove the lowest and the most left point from points for preparing for sort
							points.pop(_SCREAMING_SNAKE_CASE					)

							snake_case_     							=		sorted(_SCREAMING_SNAKE_CASE					,			key=lambda _SCREAMING_SNAKE_CASE					: angle_comparer(_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					)					)
							# This insert actually costs complexity,
							# and you should instead add (minx, miny) into stack later.
							# I'm using insert just for easy understanding.
							sorted_points.insert(0					,			(minx, miny)					)

							snake_case_     							=		deque()
							stack.append(sorted_points[0]					)
							stack.append(sorted_points[1]					)
							stack.append(sorted_points[2]					)
							# In any ways, the first 3 points line are towards left.
							# Because we sort them the angle from minx, miny.
							snake_case_     							=		Direction.left

							for i in range(3					,			len(_SCREAMING_SNAKE_CASE					)					):
														while True:
																					snake_case_     							=		stack[-2]
																					snake_case_     							=		stack[-1]
																					snake_case_     							=		sorted_points[i]
																					snake_case_     							=		check_direction(_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					)

																					if next_direction == Direction.left:
																												snake_case_     							=		Direction.left
																												break
																					if next_direction == Direction.straight:
																												if current_direction == Direction.left:
																																			# We keep current_direction as left.
																																			# Because if the straight line keeps as straight,
																																			# we want to know if this straight line is towards left.
																																			break
																												elif current_direction == Direction.right:
																																			# If the straight line is towards right,
																																			# every previous points on those straigh line is not convex hull.
																																			stack.pop()
																					if next_direction == Direction.right:
																												stack.pop()
														stack.append(sorted_points[i]					)
							return list(_SCREAMING_SNAKE_CASE					)



