





"""simple docstring"""





from __future__ import annotations

from collections.abc import Iterable





class 							_lowerCamelCase   :


						def __init__(self ,				__a ,				__a		)			-> int:
								UpperCamelCase ,					UpperCamelCase =						float(__a		), float(__a		)


						def __eq__(self ,				__a		)			-> Optional[int]:
								return self.x == other.x and self.y == other.y


						def __ne__(self ,				__a		)			-> Optional[Any]:
								return not self == other


						def __gt__(self ,				__a		)			-> List[Any]:
								if self.x > other.x:
										return True
								elif self.x == other.x:
										return self.y > other.y
								return False


						def __lt__(self ,				__a		)			-> List[str]:
								return not self > other


						def __ge__(self ,				__a		)			-> Dict:
								if self.x > other.x:
										return True
								elif self.x == other.x:
										return self.y >= other.y
								return False


						def __le__(self ,				__a		)			-> List[Any]:
								if self.x < other.x:
										return True
								elif self.x == other.x:
										return self.y <= other.y
								return False


						def __repr__(self		)			-> str:
								return F"({self.x}, {self.y})"




						def __hash__(self		)			-> int:
								return hash(self.x		)



def    a__       (       _SCREAMING_SNAKE_CASE	,						):




		"""simple docstring"""


		UpperCamelCase =						[]
		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    a__       (       _SCREAMING_SNAKE_CASE     ):




		"""simple docstring"""


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

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

		return _construct_points(_SCREAMING_SNAKE_CASE     )


def    a__       (       _SCREAMING_SNAKE_CASE	,						_SCREAMING_SNAKE_CASE	,						_SCREAMING_SNAKE_CASE     ):




		"""simple docstring"""


		UpperCamelCase =						(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    a__       (       _SCREAMING_SNAKE_CASE     ):




		"""simple docstring"""


		UpperCamelCase =						sorted(_validate_input(_SCREAMING_SNAKE_CASE     )     )
		UpperCamelCase =						len(_SCREAMING_SNAKE_CASE     )
		UpperCamelCase =						set()

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

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

								if points_left_of_ij and points_right_of_ij:
										UpperCamelCase =						False
										break

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

		return sorted(_SCREAMING_SNAKE_CASE     )


def    a__       (       _SCREAMING_SNAKE_CASE     ):




		"""simple docstring"""


		UpperCamelCase =						sorted(_validate_input(_SCREAMING_SNAKE_CASE     )     )
		UpperCamelCase =						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

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

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

		for i in range(1	,						n - 1     ):
				UpperCamelCase =						_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    a__       (       _SCREAMING_SNAKE_CASE	,						_SCREAMING_SNAKE_CASE	,						_SCREAMING_SNAKE_CASE	,						_SCREAMING_SNAKE_CASE     ):




		"""simple docstring"""


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

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

						if det > 0:
								candidate_points.append(_SCREAMING_SNAKE_CASE     )

								if det > extreme_point_distance:
										UpperCamelCase =						det
										UpperCamelCase =						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    a__       (       _SCREAMING_SNAKE_CASE     ):




		"""simple docstring"""


		UpperCamelCase =						sorted(_validate_input(_SCREAMING_SNAKE_CASE     )     )
		UpperCamelCase =						len(_SCREAMING_SNAKE_CASE     )

		UpperCamelCase =						points[:2]
		for i in range(2	,						_SCREAMING_SNAKE_CASE     ):
				UpperCamelCase =						_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:
						UpperCamelCase =						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    a__       (       ):




		"""simple docstring"""


		UpperCamelCase =						[
		    (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)]
		UpperCamelCase =						convex_hull_bf(_SCREAMING_SNAKE_CASE     )

		UpperCamelCase =						convex_hull_recursive(_SCREAMING_SNAKE_CASE     )
		assert results_bf == results_recursive

		UpperCamelCase =						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__)






