



'''simple docstring'''







from __future__ import annotations

from collections.abc import Iterable

class      lowerCamelCase__     :






	'''simple docstring'''

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




								'''simple docstring'''





								lowerCAmelCase__  ,lowerCAmelCase__  =   float(__a					), float(__a					)




	def __eq__(  self		:  str   ,		__A		:  str					)     ->			Optional[int]:




								'''simple docstring'''





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




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




								'''simple docstring'''





								return not self == other




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




								'''simple docstring'''





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




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




								'''simple docstring'''





								return not self > other




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




								'''simple docstring'''





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




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




								'''simple docstring'''





								return hash(self.x					)





def 			_lowerCAmelCase(      UpperCAmelCase_      :	List[Any]					, ) ->							int:
							lowerCAmelCase__  =   []
							if list_of_tuples:
														for p in list_of_tuples:
																					if isinstance(_SCREAMING_SNAKE_CASE					, _SCREAMING_SNAKE_CASE						):
																												points.append(_SCREAMING_SNAKE_CASE						)
																					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 			_lowerCAmelCase(      UpperCAmelCase_      :	List[Any]						) ->							str:


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

							if not points:
														lowerCAmelCase__  =   F'''Expecting a list of points but got {points}'''
														raise ValueError(_SCREAMING_SNAKE_CASE						)

							return _construct_points(_SCREAMING_SNAKE_CASE						)
def 			_lowerCAmelCase(      UpperCAmelCase_      :	Tuple					, UpperCAmelCase_      :	Any					, UpperCAmelCase_      :	Optional[int]						) ->							List[str]:
							lowerCAmelCase__  =   (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 			_lowerCAmelCase(      UpperCAmelCase_      :	Optional[Any]						) ->							Dict:
							lowerCAmelCase__  =   sorted(_validate_input(_SCREAMING_SNAKE_CASE						)						)
							lowerCAmelCase__  =   len(_SCREAMING_SNAKE_CASE						)
							lowerCAmelCase__  =   set()

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

																																			if det_k > 0:
																																										lowerCAmelCase__  =   True
																																			elif det_k < 0:
																																										lowerCAmelCase__  =   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]:
																																																	lowerCAmelCase__  =   False
																																																	break

																												if points_left_of_ij and points_right_of_ij:
																																			lowerCAmelCase__  =   False
																																			break

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

							return sorted(_SCREAMING_SNAKE_CASE						)
def 			_lowerCAmelCase(      UpperCAmelCase_      :	Union[str, Any]						) ->							Tuple:
							lowerCAmelCase__  =   sorted(_validate_input(_SCREAMING_SNAKE_CASE						)						)
							lowerCAmelCase__  =   len(_SCREAMING_SNAKE_CASE						)

							# 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

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

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

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

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

							_construct_hull(_SCREAMING_SNAKE_CASE					, _SCREAMING_SNAKE_CASE					, _SCREAMING_SNAKE_CASE					, _SCREAMING_SNAKE_CASE						)
							_construct_hull(_SCREAMING_SNAKE_CASE					, _SCREAMING_SNAKE_CASE					, _SCREAMING_SNAKE_CASE					, _SCREAMING_SNAKE_CASE						)

							return sorted(_SCREAMING_SNAKE_CASE						)
def 			_lowerCAmelCase(      UpperCAmelCase_      :	Any					, UpperCAmelCase_      :	List[Any]					, UpperCAmelCase_      :	Optional[Any]					, UpperCAmelCase_      :	Tuple						) ->							Dict:


							if points:
														lowerCAmelCase__  =   None
														lowerCAmelCase__  =   float("""-inf"""						)
														lowerCAmelCase__  =   []

														for p in points:
																					lowerCAmelCase__  =   _det(_SCREAMING_SNAKE_CASE					, _SCREAMING_SNAKE_CASE					, _SCREAMING_SNAKE_CASE						)

																					if det > 0:
																												candidate_points.append(_SCREAMING_SNAKE_CASE						)

																												if det > extreme_point_distance:
																																			lowerCAmelCase__  =   det
																																			lowerCAmelCase__  =   p

														if extreme_point:
																					_construct_hull(_SCREAMING_SNAKE_CASE					, _SCREAMING_SNAKE_CASE					, _SCREAMING_SNAKE_CASE					, _SCREAMING_SNAKE_CASE						)
																					convex_set.add(_SCREAMING_SNAKE_CASE						)
																					_construct_hull(_SCREAMING_SNAKE_CASE					, _SCREAMING_SNAKE_CASE					, _SCREAMING_SNAKE_CASE					, _SCREAMING_SNAKE_CASE						)
def 			_lowerCAmelCase(      UpperCAmelCase_      :	List[Any]						) ->							List[Any]:
							lowerCAmelCase__  =   sorted(_validate_input(_SCREAMING_SNAKE_CASE						)						)
							lowerCAmelCase__  =   len(_SCREAMING_SNAKE_CASE						)

							lowerCAmelCase__  =   points[:2]
							for i in range(2					, _SCREAMING_SNAKE_CASE						):
														lowerCAmelCase__  =   _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:
																					lowerCAmelCase__  =   points[i]
							i += 1

							for j in range(_SCREAMING_SNAKE_CASE					, _SCREAMING_SNAKE_CASE						):
														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(_SCREAMING_SNAKE_CASE						) > 3 else convex_hull						)
def 			_lowerCAmelCase(      ) ->							Union[str, Any]:
							lowerCAmelCase__  =   [
							    (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)]
							lowerCAmelCase__  =   convex_hull_bf(_SCREAMING_SNAKE_CASE						)

							lowerCAmelCase__  =   convex_hull_recursive(_SCREAMING_SNAKE_CASE						)
							assert results_bf == results_recursive

							lowerCAmelCase__  =   convex_hull_melkman(_SCREAMING_SNAKE_CASE						)
							assert results_bf == results_melkman

							print(_SCREAMING_SNAKE_CASE						)


if __name__ == "__main__":
		main()












"""simple docstring"""





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


lowerCAmelCase__        =      {
    '''configuration_deberta_v2''': ['''DEBERTA_V2_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''DebertaV2Config''', '''DebertaV2OnnxConfig'''],
    '''tokenization_deberta_v2''': ['''DebertaV2Tokenizer'''],
}

try:
						if not is_tokenizers_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCAmelCase__        =      ['''DebertaV2TokenizerFast''']

try:
						if not is_tf_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCAmelCase__        =      [
						    '''TF_DEBERTA_V2_PRETRAINED_MODEL_ARCHIVE_LIST''',
						    '''TFDebertaV2ForMaskedLM''',
						    '''TFDebertaV2ForQuestionAnswering''',
						    '''TFDebertaV2ForSequenceClassification''',
						    '''TFDebertaV2ForTokenClassification''',
						    '''TFDebertaV2Model''',
						    '''TFDebertaV2PreTrainedModel''',
						]

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCAmelCase__        =      [
						    '''DEBERTA_V2_PRETRAINED_MODEL_ARCHIVE_LIST''',
						    '''DebertaV2ForMaskedLM''',
						    '''DebertaV2ForMultipleChoice''',
						    '''DebertaV2ForQuestionAnswering''',
						    '''DebertaV2ForSequenceClassification''',
						    '''DebertaV2ForTokenClassification''',
						    '''DebertaV2Model''',
						    '''DebertaV2PreTrainedModel''',
						]


if TYPE_CHECKING:
						from .configuration_deberta_va import (
						    DEBERTA_V2_PRETRAINED_CONFIG_ARCHIVE_MAP,
						    DebertaVaConfig,
						    DebertaVaOnnxConfig,
						)
						from .tokenization_deberta_va import DebertaVaTokenizer

						try:
												if not is_tokenizers_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .tokenization_deberta_va_fast import DebertaVaTokenizerFast

						try:
												if not is_tf_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_tf_deberta_va import (
												    TF_DEBERTA_V2_PRETRAINED_MODEL_ARCHIVE_LIST,
												    TFDebertaVaForMaskedLM,
												    TFDebertaVaForQuestionAnswering,
												    TFDebertaVaForSequenceClassification,
												    TFDebertaVaForTokenClassification,
												    TFDebertaVaModel,
												    TFDebertaVaPreTrainedModel,
												)

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_deberta_va import (
												    DEBERTA_V2_PRETRAINED_MODEL_ARCHIVE_LIST,
												    DebertaVaForMaskedLM,
												    DebertaVaForMultipleChoice,
												    DebertaVaForQuestionAnswering,
												    DebertaVaForSequenceClassification,
												    DebertaVaForTokenClassification,
												    DebertaVaModel,
												    DebertaVaPreTrainedModel,
												)

else:
						import sys

						lowerCAmelCase__        =      _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)






