"""simple docstring"""







from __future__ import annotations

from collections.abc import Iterable

class 						UpperCamelCase     :



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



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



				def __ne__(self							: Optional[int]      ,    _A							: str)       ->      Optional[int]:
					return not self == other



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



				def __lt__(self							: Tuple      ,    _A							: int)       ->      Dict:
					return not self > other



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



				def __repr__(self							: str)       ->      List[Any]:
					return f"({self.x}, {self.y})"






				def __hash__(self							: List[str])       ->      str:
					return hash(self.x)







def     __UpperCAmelCase							(       UpperCAmelCase_       :							int     ,				)				->     Union[str, Any]:

	'''simple docstring'''





	__snake_case     :				Any 						=					[]
	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     __UpperCAmelCase							(       UpperCAmelCase_       :							Optional[Any]    )				->     Optional[Any]:

	'''simple docstring'''





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

	if not points:
		__snake_case     :				str 						=					F"Expecting a list of points but got {points}"
		raise ValueError(UpperCAmelCase_    )

	return _construct_points(UpperCAmelCase_    )
def     __UpperCAmelCase							(       UpperCAmelCase_       :							Optional[int]     ,				UpperCAmelCase_       :							Union[str, Any]     ,				UpperCAmelCase_       :							List[str]    )				->     str:

	'''simple docstring'''





	__snake_case     :				List[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     __UpperCAmelCase							(       UpperCAmelCase_       :							Any    )				->     List[str]:

	'''simple docstring'''





	__snake_case     :				Optional[int] 						=					sorted(_validate_input(UpperCAmelCase_    )    )
	__snake_case     :				List[str] 						=					len(UpperCAmelCase_    )
	__snake_case     :				Any 						=					set()

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

					if det_k > 0:
						__snake_case     :				List[Any] 						=					True
					elif det_k < 0:
						__snake_case     :				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]:
							__snake_case     :				Dict 						=					False
							break

				if points_left_of_ij and points_right_of_ij:
					__snake_case     :				List[str] 						=					False
					break

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

	return sorted(UpperCAmelCase_    )
def     __UpperCAmelCase							(       UpperCAmelCase_       :							List[str]    )				->     Optional[int]:

	'''simple docstring'''





	__snake_case     :				Tuple 						=					sorted(_validate_input(UpperCAmelCase_    )    )
	__snake_case     :				str 						=					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

	__snake_case     :				Dict 						=					points[0]
	__snake_case     :				Union[str, Any] 						=					points[n - 1]

	__snake_case     :				Any 						=					{left_most_point, right_most_point}
	__snake_case     :				List[str] 						=					[]
	__snake_case     :				Tuple 						=					[]

	for i in range(1     ,				n - 1    ):
		__snake_case     :				List[str] 						=					_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     __UpperCAmelCase							(       UpperCAmelCase_       :							List[Any]     ,				UpperCAmelCase_       :							Any     ,				UpperCAmelCase_       :							Tuple     ,				UpperCAmelCase_       :							Tuple    )				->     Dict:

	'''simple docstring'''





	if points:
		__snake_case     :				str 						=					None
		__snake_case     :				int 						=					float('-inf'    )
		__snake_case     :				Dict 						=					[]

		for p in points:
			__snake_case     :				str 						=					_det(UpperCAmelCase_     ,				UpperCAmelCase_     ,				UpperCAmelCase_    )

			if det > 0:
				candidate_points.append(UpperCAmelCase_    )

				if det > extreme_point_distance:
					__snake_case     :				Optional[Any] 						=					det
					__snake_case     :				Dict 						=					p

		if extreme_point:
			_construct_hull(UpperCAmelCase_     ,				UpperCAmelCase_     ,				UpperCAmelCase_     ,				UpperCAmelCase_    )
			convex_set.add(UpperCAmelCase_    )
			_construct_hull(UpperCAmelCase_     ,				UpperCAmelCase_     ,				UpperCAmelCase_     ,				UpperCAmelCase_    )
def     __UpperCAmelCase							(       UpperCAmelCase_       :							Optional[Any]    )				->     Optional[int]:

	'''simple docstring'''





	__snake_case     :				Dict 						=					sorted(_validate_input(UpperCAmelCase_    )    )
	__snake_case     :				Optional[Any] 						=					len(UpperCAmelCase_    )

	__snake_case     :				Optional[int] 						=					points[:2]
	for i in range(2     ,				UpperCAmelCase_    ):
		__snake_case     :				Any 						=					_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:
			__snake_case     :				Tuple 						=					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     __UpperCAmelCase							(       )				->     str:

	'''simple docstring'''





	__snake_case     :				int 						=					[
	    (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)]
	__snake_case     :				Dict 						=					convex_hull_bf(UpperCAmelCase_    )

	__snake_case     :				List[Any] 						=					convex_hull_recursive(UpperCAmelCase_    )
	assert results_bf == results_recursive

	__snake_case     :				List[str] 						=					convex_hull_melkman(UpperCAmelCase_    )
	assert results_bf == results_melkman

	print(UpperCAmelCase_    )


if __name__ == "__main__":
	main()









"""simple docstring"""







import torch
import torch.nn as nn
from transformers.modeling_utils import ModuleUtilsMixin
from transformers.models.ta.modeling_ta import (
    TaBlock,
    TaConfig,
    TaLayerNorm,
)

from ...configuration_utils import ConfigMixin, register_to_config
from ...models import ModelMixin






class  __A							(			_SCREAMING_SNAKE_CASE,       _SCREAMING_SNAKE_CASE,       _SCREAMING_SNAKE_CASE     ):






 """simple docstring"""




 @register_to_config
 def __init__(						self					,       __A					,       __A					,       __A					,       __A					,       __A					,       __A					,       __A					,       __A					,       __A					,       __A = False					,       )   ->	Optional[Any]:
     super().__init__()

     a											=nn.Linear(__A					,       __A					,       bias=__A		)

     a											=nn.Embedding(__A					,       __A		)
     a											=False

     a											=nn.Dropout(p=__A		)

     a											=TaConfig(
         d_model=__A					,       num_heads=__A					,       d_kv=__A					,       d_ff=__A					,       feed_forward_proj=__A					,       dropout_rate=__A					,       is_decoder=__A					,       is_encoder_decoder=__A					,       )
     a											=nn.ModuleList()
     for lyr_num in range(__A		):
         a											=TaBlock(__A		)
         self.encoders.append(__A		)

     a											=TaLayerNorm(__A		)
     a											=nn.Dropout(p=__A		)





 def  SCREAMING_SNAKE_CASE				(						self					,       __A					,       __A		)   ->	str:
     a											=self.input_proj(__A		)

     # terminal relative positional encodings
     a											=encoder_inputs.shape[1]
     a											=torch.arange(__A					,       device=encoder_inputs.device		)

     a											=encoder_inputs_mask.sum(-1		)
     a											=torch.roll(input_positions.unsqueeze(0		)					,       tuple(seq_lens.tolist()		)					,       dims=0		)
     x += self.position_encoding(__A		)

     a											=self.dropout_pre(__A		)

     # inverted the attention mask
     a											=encoder_inputs.size()
     a											=self.get_extended_attention_mask(__A					,       __A		)

     for lyr in self.encoders:
         a											=lyr(__A					,       __A		)[0]
     a											=self.layer_norm(__A		)

     return self.dropout_post(__A		), encoder_inputs_mask