


from __future__ import annotations

from collections.abc import Iterable





class    _a				:




	def __init__(   self		:						int						,   _SCREAMING_SNAKE_CASE		:						int						,   _SCREAMING_SNAKE_CASE		:						str						)->			str:
			lowerCAmelCase__	,      lowerCAmelCase__  :     int       	=   float(_SCREAMING_SNAKE_CASE						), float(_SCREAMING_SNAKE_CASE						)




	def __eq__(   self		:						List[str]						,   _SCREAMING_SNAKE_CASE		:						str						)->			str:
			return self.x == other.x and self.y == other.y




	def __ne__(   self		:						int						,   _SCREAMING_SNAKE_CASE		:						List[Any]						)->			Tuple:
			return not self == other




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




	def __lt__(   self		:						Dict						,   _SCREAMING_SNAKE_CASE		:						Optional[int]						)->			Dict:
			return not self > other




	def __ge__(   self		:						List[Any]						,   _SCREAMING_SNAKE_CASE		:						Tuple						)->			Union[str, Any]:
			if self.x > other.x:
					return True
			elif self.x == other.x:
					return self.y >= other.y
			return False




	def __le__(   self		:						Optional[Any]						,   _SCREAMING_SNAKE_CASE		:						Optional[int]						)->			str:
			if self.x < other.x:
					return True
			elif self.x == other.x:
					return self.y <= other.y
			return False




	def __repr__(   self		:						str						)->			Optional[int]:
			return F'({self.x}, {self.y})'




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






def 	lowerCamelCase_       (			_a      ,  ):




		"""simple docstring"""






		lowerCAmelCase__  :     list[Point]       	=   []
		if list_of_tuples:
				for p in list_of_tuples:
						if isinstance(_a      ,  _a			):
								points.append(_a			)
						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_       (			_a			):




		"""simple docstring"""






		if not hasattr(_a      ,  '''__iter__'''			):
				lowerCAmelCase__  :     Optional[int]       	=   f'Expecting an iterable object but got an non-iterable type {points}'
				raise ValueError(_a			)

		if not points:
				lowerCAmelCase__  :     Optional[int]       	=   f'Expecting a list of points but got {points}'
				raise ValueError(_a			)

		return _construct_points(_a			)






def 	lowerCamelCase_       (			_a      ,  _a      ,  _a			):




		"""simple docstring"""






		lowerCAmelCase__  :     str       	=   (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_       (			_a			):




		"""simple docstring"""






		lowerCAmelCase__  :     Any       	=   sorted(_validate_input(_a			)			)
		lowerCAmelCase__  :     int       	=   len(_a			)
		lowerCAmelCase__  :     List[str]       	=   set()

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

										if det_k > 0:
												lowerCAmelCase__  :     int       	=   True
										elif det_k < 0:
												lowerCAmelCase__  :     List[Any]       	=   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__  :     Optional[Any]       	=   False
														break

								if points_left_of_ij and points_right_of_ij:
										lowerCAmelCase__  :     int       	=   False
										break

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

		return sorted(_a			)






def 	lowerCamelCase_       (			_a			):




		"""simple docstring"""






		lowerCAmelCase__  :     List[str]       	=   sorted(_validate_input(_a			)			)
		lowerCAmelCase__  :     Optional[int]       	=   len(_a			)

		# 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__  :     Union[str, Any]       	=   points[0]
		lowerCAmelCase__  :     str       	=   points[n - 1]

		lowerCAmelCase__  :     int       	=   {left_most_point, right_most_point}
		lowerCAmelCase__  :     List[str]       	=   []
		lowerCAmelCase__  :     Optional[Any]       	=   []

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

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

		_construct_hull(_a      ,  _a      ,  _a      ,  _a			)
		_construct_hull(_a      ,  _a      ,  _a      ,  _a			)

		return sorted(_a			)






def 	lowerCamelCase_       (			_a      ,  _a      ,  _a      ,  _a			):




		"""simple docstring"""






		if points:
				lowerCAmelCase__  :     List[str]       	=   None
				lowerCAmelCase__  :     Optional[Any]       	=   float('''-inf'''			)
				lowerCAmelCase__  :     Union[str, Any]       	=   []

				for p in points:
						lowerCAmelCase__  :     Optional[Any]       	=   _det(_a      ,  _a      ,  _a			)

						if det > 0:
								candidate_points.append(_a			)

								if det > extreme_point_distance:
										lowerCAmelCase__  :     str       	=   det
										lowerCAmelCase__  :     Any       	=   p

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






def 	lowerCamelCase_       (			_a			):




		"""simple docstring"""






		lowerCAmelCase__  :     Optional[Any]       	=   sorted(_validate_input(_a			)			)
		lowerCAmelCase__  :     str       	=   len(_a			)

		lowerCAmelCase__  :     Optional[int]       	=   points[:2]
		for i in range(2      ,  _a			):
				lowerCAmelCase__  :     Optional[int]       	=   _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__  :     Any       	=   points[i]
		i += 1

		for j in range(_a      ,  _a			):
				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(_a			) > 3 else convex_hull			)






def 	lowerCamelCase_       (			):




		"""simple docstring"""






		lowerCAmelCase__  :     Any       	=   [
		    (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__  :     Any       	=   convex_hull_bf(_a			)

		lowerCAmelCase__  :     Union[str, Any]       	=   convex_hull_recursive(_a			)
		assert results_bf == results_recursive

		lowerCAmelCase__  :     List[str]       	=   convex_hull_melkman(_a			)
		assert results_bf == results_melkman

		print(_a			)


if __name__ == "__main__":
		main()








from .chunk_utils import chunk_layer
from .data_transforms import make_atomaa_masks
from .feats import atomaa_to_atomaa, frames_and_literature_positions_to_atomaa_pos, torsion_angles_to_frames
from .loss import compute_predicted_aligned_error, compute_tm
from .protein import Protein as OFProtein
from .protein import to_pdb
from .rigid_utils import Rigid, Rotation
from .tensor_utils import dict_multimap, flatten_final_dims, permute_final_dims




