


'''simple docstring'''

from __future__ import annotations

from collections.abc import Iterable







class 			UpperCAmelCase			:

 def __init__(			self			:						Optional[Any],       a_			:						Optional[int],       a_			:						List[Any]       ):





    """simple docstring"""



    UpperCamelCase__    ,		UpperCamelCase__			    =    float(lowerCamelCase__       ), float(lowerCamelCase__       )

 def __eq__(			self			:						int,       a_			:						Union[str, Any]       ):





    """simple docstring"""



    return self.x == other.x and self.y == other.y

 def __ne__(			self			:						Optional[int],       a_			:						int       ):





    """simple docstring"""



    return not self == other

 def __gt__(			self			:						Optional[Any],       a_			:						Optional[Any]       ):





    """simple docstring"""



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

 def __lt__(			self			:						Union[str, Any],       a_			:						Optional[Any]       ):





    """simple docstring"""



    return not self > other

 def __ge__(			self			:						Optional[Any],       a_			:						Tuple       ):





    """simple docstring"""



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

 def __le__(			self			:						Tuple,       a_			:						int       ):





    """simple docstring"""



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

 def __repr__(			self			:						Dict       ):





    """simple docstring"""



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

 def __hash__(			self			:						List[Any]       ):





    """simple docstring"""



    return hash(self.x       )







def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					Optional[int]     ,		)		->       list[Point]:





   '''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 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					int )		->       list[Point]:





   '''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 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					Optional[int]     ,		_UpperCamelCase   :					Optional[Any]     ,		_UpperCamelCase   :					int )		->       float:





   '''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 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					List[Any] )		->       list[Point]:





   '''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 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					str )		->       list[Point]:





   '''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 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					int     ,		_UpperCamelCase   :					Any     ,		_UpperCamelCase   :					Optional[Any]     ,		_UpperCamelCase   :					Dict )		->       None:





   '''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 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					Optional[Any] )		->       list[Point]:





   '''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 							SCREAMING_SNAKE_CASE__(		)		->       Any:





   '''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()






from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


SCREAMING_SNAKE_CASE_		  =			{
    """configuration_markuplm""": ["""MARKUPLM_PRETRAINED_CONFIG_ARCHIVE_MAP""", """MarkupLMConfig"""],
    """feature_extraction_markuplm""": ["""MarkupLMFeatureExtractor"""],
    """processing_markuplm""": ["""MarkupLMProcessor"""],
    """tokenization_markuplm""": ["""MarkupLMTokenizer"""],
}

try:
      if not is_tokenizers_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      SCREAMING_SNAKE_CASE_		  =			["""MarkupLMTokenizerFast"""]

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      SCREAMING_SNAKE_CASE_		  =			[
          """MARKUPLM_PRETRAINED_MODEL_ARCHIVE_LIST""",
          """MarkupLMForQuestionAnswering""",
          """MarkupLMForSequenceClassification""",
          """MarkupLMForTokenClassification""",
          """MarkupLMModel""",
          """MarkupLMPreTrainedModel""",
      ]


if TYPE_CHECKING:
      from .configuration_markuplm import MARKUPLM_PRETRAINED_CONFIG_ARCHIVE_MAP, MarkupLMConfig
      from .feature_extraction_markuplm import MarkupLMFeatureExtractor
      from .processing_markuplm import MarkupLMProcessor
      from .tokenization_markuplm import MarkupLMTokenizer

      try:
            if not is_tokenizers_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .tokenization_markuplm_fast import MarkupLMTokenizerFast

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_markuplm import (
                MARKUPLM_PRETRAINED_MODEL_ARCHIVE_LIST,
                MarkupLMForQuestionAnswering,
                MarkupLMForSequenceClassification,
                MarkupLMForTokenClassification,
                MarkupLMModel,
                MarkupLMPreTrainedModel,
            )


else:
      import sys

      SCREAMING_SNAKE_CASE_		  =			_LazyModule(__name__, globals()["""__file__"""], _import_structure)


