






from __future__ import annotations

from collections.abc import Iterable
class 	a_:



     """simple docstring"""



     def __init__(		self					:	List[Any]  ,  lowerCAmelCase__					:	Union[str, Any]  ,  lowerCAmelCase__					:	List[str])							->	Optional[Any]:

      """simple docstring"""
      SCREAMING_SNAKE_CASE    ,   SCREAMING_SNAKE_CASE				    =		float(_UpperCAmelCase), float(_UpperCAmelCase)





     def __eq__(		self					:	int  ,  lowerCAmelCase__					:	Optional[int])							->	Union[str, Any]:

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





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

      """simple docstring"""
      return not self == other





     def __gt__(		self					:	Optional[Any]  ,  lowerCAmelCase__					:	List[str])							->	Dict:

      """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]  ,  lowerCAmelCase__					:	int)							->	Dict:

      """simple docstring"""
      return not self > other





     def __ge__(		self					:	Dict  ,  lowerCAmelCase__					:	int)							->	List[str]:

      """simple docstring"""


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





     def __le__(		self					:	Dict  ,  lowerCAmelCase__					:	str)							->	Tuple:

      """simple docstring"""


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





     def __repr__(		self					:	str)							->	Optional[Any]:

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





     def __hash__(		self					:	Optional[int])							->	Any:

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





def 						A_					(						lowercase_	,  )				->list[Point]:







 """simple docstring"""

 SCREAMING_SNAKE_CASE				    =		[]
 if list_of_tuples:
  for p in list_of_tuples:
   if isinstance(lowercase_	,  lowercase_			):
    points.append(lowercase_			)
   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_					(						lowercase_			)				->list[Point]:







 """simple docstring"""

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

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

 return _construct_points(lowercase_			)





def 						A_					(						lowercase_	,  lowercase_	,  lowercase_			)				->float:







 """simple docstring"""

 SCREAMING_SNAKE_CASE				    =		(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_					(						lowercase_			)				->list[Point]:







 """simple docstring"""

 SCREAMING_SNAKE_CASE				    =		sorted(_validate_input(lowercase_			)			)
 SCREAMING_SNAKE_CASE				    =		len(lowercase_			)
 SCREAMING_SNAKE_CASE				    =		set()

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

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

    if points_left_of_ij and points_right_of_ij:
     SCREAMING_SNAKE_CASE				    =		False
     break

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

 return sorted(lowercase_			)





def 						A_					(						lowercase_			)				->list[Point]:







 """simple docstring"""

 SCREAMING_SNAKE_CASE				    =		sorted(_validate_input(lowercase_			)			)
 SCREAMING_SNAKE_CASE				    =		len(lowercase_			)

 # 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

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

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

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

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

 _construct_hull(lowercase_	,  lowercase_	,  lowercase_	,  lowercase_			)
 _construct_hull(lowercase_	,  lowercase_	,  lowercase_	,  lowercase_			)

 return sorted(lowercase_			)





def 						A_					(						lowercase_	,  lowercase_	,  lowercase_	,  lowercase_			)				->None:







 """simple docstring"""

 if points:
  SCREAMING_SNAKE_CASE				    =		None
  SCREAMING_SNAKE_CASE				    =		float('-inf'			)
  SCREAMING_SNAKE_CASE				    =		[]

  for p in points:
   SCREAMING_SNAKE_CASE				    =		_det(lowercase_	,  lowercase_	,  lowercase_			)

   if det > 0:
    candidate_points.append(lowercase_			)

    if det > extreme_point_distance:
     SCREAMING_SNAKE_CASE				    =		det
     SCREAMING_SNAKE_CASE				    =		p

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





def 						A_					(						lowercase_			)				->list[Point]:







 """simple docstring"""

 SCREAMING_SNAKE_CASE				    =		sorted(_validate_input(lowercase_			)			)
 SCREAMING_SNAKE_CASE				    =		len(lowercase_			)

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

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





def 						A_					(						)				->List[Any]:







 """simple docstring"""

 SCREAMING_SNAKE_CASE				    =		[
     (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)]
 SCREAMING_SNAKE_CASE				    =		convex_hull_bf(lowercase_			)

 SCREAMING_SNAKE_CASE				    =		convex_hull_recursive(lowercase_			)
 assert results_bf == results_recursive

 SCREAMING_SNAKE_CASE				    =		convex_hull_melkman(lowercase_			)
 assert results_bf == results_melkman

 print(lowercase_			)


if __name__ == "__main__":
      main()






from ctypes import c_float, sizeof
from enum import Enum
from typing import TYPE_CHECKING, Optional, Union


if TYPE_CHECKING:
							from .. import AutoFeatureExtractor, AutoProcessor, AutoTokenizer  # tests_ignore
class       A__  (		lowerCAmelCase__							):
							lowerCAmelCase__						:		Any            =				c_float





							@property
							def      a__					(					self    :  List[str]							)		->						int:



											"""simple docstring"""


											return sizeof(self.value							)






def 				__SCREAMING_SNAKE_CASE  (						SCREAMING_SNAKE_CASE			: int       ,				SCREAMING_SNAKE_CASE			: int       ,				SCREAMING_SNAKE_CASE			: int = 0     )	->		int:
				# < 0 is possible if using a dynamic axis
				if dimension <= 0:
								__lowercase								=   fixed_dimension

				dimension -= num_token_to_add
				return dimension




def 				__SCREAMING_SNAKE_CASE  (						SCREAMING_SNAKE_CASE			: int       ,				SCREAMING_SNAKE_CASE			: ParameterFormat     )	->		int:
				return num_parameters * dtype.size




def 				__SCREAMING_SNAKE_CASE  (						SCREAMING_SNAKE_CASE			: str     )	->		Optional[Union["AutoTokenizer", "AutoFeatureExtractor", "AutoProcessor"]]:
				from .. import AutoFeatureExtractor, AutoProcessor, AutoTokenizer  # tests_ignore

				try:
								return AutoProcessor.from_pretrained(SCREAMING_SNAKE_CASE     )
				except (ValueError, OSError, KeyError):
								__lowercase						,   __lowercase								=   None, None
								try:
												__lowercase								=   AutoTokenizer.from_pretrained(SCREAMING_SNAKE_CASE     )
								except (OSError, KeyError):
												pass
								try:
												__lowercase								=   AutoFeatureExtractor.from_pretrained(SCREAMING_SNAKE_CASE     )
								except (OSError, KeyError):
												pass

								if tokenizer is not None and feature_extractor is not None:
												raise ValueError(
												    F"""Couldn't auto-detect preprocessor for {model_name}. Found both a tokenizer and a feature extractor."""     )
								elif tokenizer is None and feature_extractor is None:
												return None
								elif tokenizer is not None:
												return tokenizer
								else:
												return feature_extractor





