





from __future__ import annotations

from collections.abc import Iterable




class      UpperCamelCase_				:


							def __init__(							self			:List[str]							, __A			:int							, __A			:Optional[int]						)      ->      Optional[Any]:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__		,  SCREAMING_SNAKE_CASE__								=					float(__A						), float(__A						)


							def __eq__(							self			:Tuple							, __A			:Union[str, Any]						)      ->      Optional[Any]:



									"""simple docstring"""



									return self.x == other.x and self.y == other.y


							def __ne__(							self			:Union[str, Any]							, __A			:Optional[Any]						)      ->      Any:



									"""simple docstring"""



									return not self == other


							def __gt__(							self			:int							, __A			:Optional[Any]						)      ->      int:



									"""simple docstring"""



									if self.x > other.x:
											return True
									elif self.x == other.x:
											return self.y > other.y
									return False


							def __lt__(							self			:int							, __A			:List[Any]						)      ->      Optional[Any]:



									"""simple docstring"""



									return not self > other


							def __ge__(							self			:str							, __A			:Dict						)      ->      List[Any]:



									"""simple docstring"""



									if self.x > other.x:
											return True
									elif self.x == other.x:
											return self.y >= other.y
									return False


							def __le__(							self			:List[str]							, __A			:Tuple						)      ->      Union[str, Any]:



									"""simple docstring"""



									if self.x < other.x:
											return True
									elif self.x == other.x:
											return self.y <= other.y
									return False


							def __repr__(							self			:List[str]						)      ->      str:



									"""simple docstring"""



									return f'''({self.x}, {self.y})'''


							def __hash__(							self			:Any						)      ->      Any:



									"""simple docstring"""



									return hash(self.x						)






def  SCREAMING_SNAKE_CASE__							(				UpperCamelCase__:							list[Point] | list[list[float]] | Iterable[list[float]]    ,      ):
		SCREAMING_SNAKE_CASE__								=					[]
		if list_of_tuples:
				for p in list_of_tuples:
						if isinstance(UpperCamelCase__    ,      UpperCamelCase__			):
								points.append(UpperCamelCase__			)
						else:
								try:
										points.append(Point(p[0]    ,      p[1]			)			)
								except (IndexError, TypeError):
										print(
										    f'''Ignoring deformed point {p}. All points'''
										    """ must have at least 2 coordinates."""			)
		return points






def  SCREAMING_SNAKE_CASE__							(				UpperCamelCase__:							list[Point] | list[list[float]]			):

		if not hasattr(UpperCamelCase__    ,      """__iter__"""			):
				SCREAMING_SNAKE_CASE__								=					f'''Expecting an iterable object but got an non-iterable type {points}'''
				raise ValueError(UpperCamelCase__			)

		if not points:
				SCREAMING_SNAKE_CASE__								=					f'''Expecting a list of points but got {points}'''
				raise ValueError(UpperCamelCase__			)

		return _construct_points(UpperCamelCase__			)






def  SCREAMING_SNAKE_CASE__							(				UpperCamelCase__:							Point    ,      UpperCamelCase__:							Point    ,      UpperCamelCase__:							Point			):
		SCREAMING_SNAKE_CASE__								=					(a.x * b.y + b.x * c.y + c.x * a.y) - (a.y * b.x + b.y * c.x + c.y * a.x)
		return det






def  SCREAMING_SNAKE_CASE__							(				UpperCamelCase__:							list[Point]			):
		SCREAMING_SNAKE_CASE__								=					sorted(_validate_input(UpperCamelCase__			)			)
		SCREAMING_SNAKE_CASE__								=					len(UpperCamelCase__			)
		SCREAMING_SNAKE_CASE__								=					set()

		for i in range(n - 1			):
				for j in range(i + 1    ,      UpperCamelCase__			):
						SCREAMING_SNAKE_CASE__								=					SCREAMING_SNAKE_CASE__								=					False
						SCREAMING_SNAKE_CASE__								=					True
						for k in range(UpperCamelCase__			):
								if k != i and k != j:
										SCREAMING_SNAKE_CASE__								=					_det(points[i]    ,      points[j]    ,      points[k]			)

										if det_k > 0:
												SCREAMING_SNAKE_CASE__								=					True
										elif det_k < 0:
												SCREAMING_SNAKE_CASE__								=					True
										else:
												# point[i], point[j], point[k] all lie on a straight line
												# if point[k] is to the left of point[i] or it's to the
												# right of point[j], then point[i], point[j] cannot be
												# part of the convex hull of A
												if points[k] < points[i] or points[k] > points[j]:
														SCREAMING_SNAKE_CASE__								=					False
														break

								if points_left_of_ij and points_right_of_ij:
										SCREAMING_SNAKE_CASE__								=					False
										break

						if ij_part_of_convex_hull:
								convex_set.update([points[i], points[j]]			)

		return sorted(UpperCamelCase__			)






def  SCREAMING_SNAKE_CASE__							(				UpperCamelCase__:							list[Point]			):
		SCREAMING_SNAKE_CASE__								=					sorted(_validate_input(UpperCamelCase__			)			)
		SCREAMING_SNAKE_CASE__								=					len(UpperCamelCase__			)

		# divide all the points into an upper hull and a lower hull
		# the left most point and the right most point are definitely
		# members of the convex hull by definition.
		# use these two anchors to divide all the points into two hulls,
		# an upper hull and a lower hull.

		# all points to the left (above) the line joining the extreme points belong to the
		# upper hull
		# all points to the right (below) the line joining the extreme points below to the
		# lower hull
		# ignore all points on the line joining the extreme points since they cannot be
		# part of the convex hull

		SCREAMING_SNAKE_CASE__								=					points[0]
		SCREAMING_SNAKE_CASE__								=					points[n - 1]

		SCREAMING_SNAKE_CASE__								=					{left_most_point, right_most_point}
		SCREAMING_SNAKE_CASE__								=					[]
		SCREAMING_SNAKE_CASE__								=					[]

		for i in range(1    ,      n - 1			):
				SCREAMING_SNAKE_CASE__								=					_det(UpperCamelCase__    ,      UpperCamelCase__    ,      points[i]			)

				if det > 0:
						upper_hull.append(points[i]			)
				elif det < 0:
						lower_hull.append(points[i]			)

		_construct_hull(UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__			)
		_construct_hull(UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__			)

		return sorted(UpperCamelCase__			)






def  SCREAMING_SNAKE_CASE__							(				UpperCamelCase__:							list[Point]    ,      UpperCamelCase__:							Point    ,      UpperCamelCase__:							Point    ,      UpperCamelCase__:							set[Point]			):
		if points:
				SCREAMING_SNAKE_CASE__								=					None
				SCREAMING_SNAKE_CASE__								=					float("""-inf"""			)
				SCREAMING_SNAKE_CASE__								=					[]

				for p in points:
						SCREAMING_SNAKE_CASE__								=					_det(UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__			)

						if det > 0:
								candidate_points.append(UpperCamelCase__			)

								if det > extreme_point_distance:
										SCREAMING_SNAKE_CASE__								=					det
										SCREAMING_SNAKE_CASE__								=					p

				if extreme_point:
						_construct_hull(UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__			)
						convex_set.add(UpperCamelCase__			)
						_construct_hull(UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__			)






def  SCREAMING_SNAKE_CASE__							(				UpperCamelCase__:							list[Point]			):
		SCREAMING_SNAKE_CASE__								=					sorted(_validate_input(UpperCamelCase__			)			)
		SCREAMING_SNAKE_CASE__								=					len(UpperCamelCase__			)

		SCREAMING_SNAKE_CASE__								=					points[:2]
		for i in range(2    ,      UpperCamelCase__			):
				SCREAMING_SNAKE_CASE__								=					_det(convex_hull[1]    ,      convex_hull[0]    ,      points[i]			)
				if det > 0:
						convex_hull.insert(0    ,      points[i]			)
						break
				elif det < 0:
						convex_hull.append(points[i]			)
						break
				else:
						SCREAMING_SNAKE_CASE__								=					points[i]
		i += 1

		for j in range(UpperCamelCase__    ,      UpperCamelCase__			):
				if (
				    _det(convex_hull[0]    ,      convex_hull[-1]    ,      points[j]			) > 0
				    and _det(convex_hull[-1]    ,      convex_hull[0]    ,      points[1]			) < 0
				):
						# The point lies within the convex hull
						continue

				convex_hull.insert(0    ,      points[j]			)
				convex_hull.append(points[j]			)
				while _det(convex_hull[0]    ,      convex_hull[1]    ,      convex_hull[2]			) >= 0:
						del convex_hull[1]
				while _det(convex_hull[-1]    ,      convex_hull[-2]    ,      convex_hull[-3]			) <= 0:
						del convex_hull[-2]

    # `convex_hull` is contains the convex hull in circular order
		return sorted(convex_hull[1:] if len(UpperCamelCase__			) > 3 else convex_hull			)






def  SCREAMING_SNAKE_CASE__							(				):
		SCREAMING_SNAKE_CASE__								=					[
		    (0, 3),
		    (2, 2),
		    (1, 1),
		    (2, 1),
		    (3, 0),
		    (0, 0),
		    (3, 3),
		    (2, -1),
		    (2, -4),
		    (1, -3),
		]
		# the convex set of points is
		# [(0, 0), (0, 3), (1, -3), (2, -4), (3, 0), (3, 3)]
		SCREAMING_SNAKE_CASE__								=					convex_hull_bf(UpperCamelCase__			)

		SCREAMING_SNAKE_CASE__								=					convex_hull_recursive(UpperCamelCase__			)
		assert results_bf == results_recursive

		SCREAMING_SNAKE_CASE__								=					convex_hull_melkman(UpperCamelCase__			)
		assert results_bf == results_melkman

		print(UpperCamelCase__			)


if __name__ == "__main__":
	main()






# tests directory-specific settings - this file is run automatically
# by pytest before any tests are run

import sys
import warnings
from os.path import abspath, dirname, join


# allow having multiple repository checkouts and not needing to remember to rerun
# 'pip install -e .[dev]' when switching between checkouts and running tests.
_lowerCamelCase       =	abspath(join(dirname(dirname(dirname(__file__))), 'src'))
sys.path.insert(1, git_repo_path)


# silence FutureWarning warnings in tests since often we can't act on them until
# they become normal warnings - i.e. the tests still need to test the current functionality
warnings.simplefilter(action='ignore', category=FutureWarning)






def  SCREAMING_SNAKE_CASE__							(				UpperCamelCase__:							Tuple			):
		from transformers.testing_utils import pytest_addoption_shared

		pytest_addoption_shared(UpperCamelCase__			)






def  SCREAMING_SNAKE_CASE__							(				UpperCamelCase__:							Tuple			):
		from transformers.testing_utils import pytest_terminal_summary_main

		SCREAMING_SNAKE_CASE__								=					terminalreporter.config.getoption("""--make-reports"""			)
		if make_reports:
				pytest_terminal_summary_main(UpperCamelCase__    ,      id=UpperCamelCase__			)