"""simple docstring"""







from __future__ import annotations

from collections.abc import Iterable


class       _lowercase		:

				def __init__(  self							:     int							,     _lowercase							:     Tuple							,     _lowercase							:     Optional[Any]  ):


										'''simple docstring'''
										UpperCAmelCase__						,   UpperCAmelCase__       						=		float(_lowercase  ), float(_lowercase  )

				def __eq__(  self							:     int							,     _lowercase							:     int  ):


										'''simple docstring'''
										return self.x == other.x and self.y == other.y

				def __ne__(  self							:     Any							,     _lowercase							:     Tuple  ):


										'''simple docstring'''
										return not self == other

				def __gt__(  self							:     Optional[Any]							,     _lowercase							:     List[str]  ):


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

				def __lt__(  self							:     List[str]							,     _lowercase							:     Dict  ):


										'''simple docstring'''
										return not self > other

				def __ge__(  self							:     Tuple							,     _lowercase							:     Optional[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[Any]							,     _lowercase							:     List[str]  ):


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

				def __repr__(  self							:     int  ):


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

				def __hash__(  self							:     List[str]  ):


										'''simple docstring'''
										return hash(self.x  )


def 	a__   (		UpperCAmelCase__							:      list[Point] | list[list[float]] | Iterable[list[float]]		,      )->						list[Point]:
						UpperCAmelCase__       						=		[]
						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 	a__   (		UpperCAmelCase__							:      list[Point] | list[list[float]]      )->						list[Point]:

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

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

						return _construct_points(UpperCAmelCase__      )


def 	a__   (		UpperCAmelCase__							:      Point		,      UpperCAmelCase__							:      Point		,      UpperCAmelCase__							:      Point      )->						float:
						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__   (		UpperCAmelCase__							:      list[Point]      )->						list[Point]:
						UpperCAmelCase__       						=		sorted(_validate_input(UpperCAmelCase__      )      )
						UpperCAmelCase__       						=		len(UpperCAmelCase__      )
						UpperCAmelCase__       						=		set()

						for i in range(n - 1      ):
												for j in range(i + 1		,      UpperCAmelCase__      ):
																		UpperCAmelCase__       						=		UpperCAmelCase__       						=		False
																		UpperCAmelCase__       						=		True
																		for k in range(UpperCAmelCase__      ):
																								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(UpperCAmelCase__      )


def 	a__   (		UpperCAmelCase__							:      list[Point]      )->						list[Point]:
						UpperCAmelCase__       						=		sorted(_validate_input(UpperCAmelCase__      )      )
						UpperCAmelCase__       						=		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

						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(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 	a__   (		UpperCAmelCase__							:      list[Point]		,      UpperCAmelCase__							:      Point		,      UpperCAmelCase__							:      Point		,      UpperCAmelCase__							:      set[Point]      )->						None:
						if points:
												UpperCAmelCase__       						=		None
												UpperCAmelCase__       						=		float("""-inf"""      )
												UpperCAmelCase__       						=		[]

												for p in points:
																		UpperCAmelCase__       						=		_det(UpperCAmelCase__		,      UpperCAmelCase__		,      UpperCAmelCase__      )

																		if det > 0:
																								candidate_points.append(UpperCAmelCase__      )

																								if det > extreme_point_distance:
																														UpperCAmelCase__       						=		det
																														UpperCAmelCase__       						=		p

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


def 	a__   (		UpperCAmelCase__							:      list[Point]      )->						list[Point]:
						UpperCAmelCase__       						=		sorted(_validate_input(UpperCAmelCase__      )      )
						UpperCAmelCase__       						=		len(UpperCAmelCase__      )

						UpperCAmelCase__       						=		points[:2]
						for i in range(2		,      UpperCAmelCase__      ):
												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(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 	a__   (		)->						List[str]:
						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(UpperCAmelCase__      )

						UpperCAmelCase__       						=		convex_hull_recursive(UpperCAmelCase__      )
						assert results_bf == results_recursive

						UpperCAmelCase__       						=		convex_hull_melkman(UpperCAmelCase__      )
						assert results_bf == results_melkman

						print(UpperCAmelCase__      )


if __name__ == "__main__":
						main()


"""simple docstring"""







from ...utils import (
    OptionalDependencyNotAvailable,
    is_torch_available,
    is_transformers_available,
    is_transformers_version,
)


try:
						if not (is_transformers_available() and is_torch_available() and is_transformers_version(""">=""", """4.27.0""")):
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						from ...utils.dummy_torch_and_transformers_objects import (
						    AudioLDMPipeline,
						)
else:
						from .pipeline_audioldm import AudioLDMPipeline

