code: 
  
  
  
  
  """simple docstring"""
  
  
  
  from __future__ import annotations
  
  from collections.abc import Iterable
  
  
  
  
  class 			UpperCAmelCase_						:
  
  
  
  
      def __init__(					self		: Optional[Any]			,				snake_case_		: str			,				snake_case_		: Dict   )   ->							List[str]:
  
  
  
  
       '''simple docstring'''
  
       A__,   A__ =       float(snake_case_   ), float(snake_case_   )
  
  
  
  
      def __eq__(					self		: Optional[Any]			,				snake_case_		: Any   )   ->							List[str]:
  
  
  
  
       '''simple docstring'''
  
       return self.x == other.x and self.y == other.y
  
  
  
  
      def __ne__(					self		: List[Any]			,				snake_case_		: Union[str, Any]   )   ->							Any:
  
  
  
  
       '''simple docstring'''
  
       return not self == other
  
  
  
  
      def __gt__(					self		: str			,				snake_case_		: Dict   )   ->							Tuple:
  
  
  
  
       '''simple docstring'''
  
       if self.x > other.x:
        return True
       elif self.x == other.x:
        return self.y > other.y
       return False
  
  
  
  
      def __lt__(					self		: Tuple			,				snake_case_		: Union[str, Any]   )   ->							List[Any]:
  
  
  
  
       '''simple docstring'''
  
       return not self > other
  
  
  
  
      def __ge__(					self		: str			,				snake_case_		: List[Any]   )   ->							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		: str			,				snake_case_		: List[Any]   )   ->							List[Any]:
  
  
  
  
       '''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   )   ->							Optional[Any]:
  
  
  
  
       '''simple docstring'''
  
       return F"""({self.x}, {self.y})"""
  
  
  
  
      def __hash__(					self		: str   )   ->							Any:
  
  
  
  
       '''simple docstring'''
  
       return hash(self.x   )
  
  
  
  
  
  
  
  def 						_SCREAMING_SNAKE_CASE     (							lowercase_    ,				)		->	list[Point]:
   A__ =       []
   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 						_SCREAMING_SNAKE_CASE     (							lowercase_		)		->	list[Point]:
  
   if not hasattr(lowercase_    ,				"__iter__"		):
    A__ =       f"""Expecting an iterable object but got an non-iterable type {points}"""
    raise ValueError(lowercase_		)
  
   if not points:
    A__ =       f"""Expecting a list of points but got {points}"""
    raise ValueError(lowercase_		)
  
   return _construct_points(lowercase_		)
  
  
  
  
  
  
  
  def 						_SCREAMING_SNAKE_CASE     (							lowercase_    ,				lowercase_    ,				lowercase_		)		->	float:
   A__ =       (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     (							lowercase_		)		->	list[Point]:
   A__ =       sorted(_validate_input(lowercase_		)		)
   A__ =       len(lowercase_		)
   A__ =       set()
  
   for i in range(n - 1		):
    for j in range(i + 1    ,				lowercase_		):
     A__ =       A__ =       False
     A__ =       True
     for k in range(lowercase_		):
      if k != i and k != j:
       A__ =       _det(points[i]    ,				points[j]    ,				points[k]		)
  
       if det_k > 0:
        A__ =       True
       elif det_k < 0:
        A__ =       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]:
         A__ =       False
         break
  
      if points_left_of_ij and points_right_of_ij:
       A__ =       False
       break
  
     if ij_part_of_convex_hull:
      convex_set.update([points[i], points[j]]		)
  
   return sorted(lowercase_		)
  
  
  
  
  
  
  
  def 						_SCREAMING_SNAKE_CASE     (							lowercase_		)		->	list[Point]:
   A__ =       sorted(_validate_input(lowercase_		)		)
   A__ =       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
  
   A__ =       points[0]
   A__ =       points[n - 1]
  
   A__ =       {left_most_point, right_most_point}
   A__ =       []
   A__ =       []
  
   for i in range(1    ,				n - 1		):
    A__ =       _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 						_SCREAMING_SNAKE_CASE     (							lowercase_    ,				lowercase_    ,				lowercase_    ,				lowercase_		)		->	None:
   if points:
    A__ =       None
    A__ =       float("-inf"		)
    A__ =       []
  
    for p in points:
     A__ =       _det(lowercase_    ,				lowercase_    ,				lowercase_		)
  
     if det > 0:
      candidate_points.append(lowercase_		)
  
      if det > extreme_point_distance:
       A__ =       det
       A__ =       p
  
    if extreme_point:
     _construct_hull(lowercase_    ,				lowercase_    ,				lowercase_    ,				lowercase_		)
     convex_set.add(lowercase_		)
     _construct_hull(lowercase_    ,				lowercase_    ,				lowercase_    ,				lowercase_		)
  
  
  
  
  
  
  
  def 						_SCREAMING_SNAKE_CASE     (							lowercase_		)		->	list[Point]:
   A__ =       sorted(_validate_input(lowercase_		)		)
   A__ =       len(lowercase_		)
  
   A__ =       points[:2]
   for i in range(2    ,				lowercase_		):
    A__ =       _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:
     A__ =       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 						_SCREAMING_SNAKE_CASE     (							)		->	Optional[int]:
   A__ =       [
       (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)]
   A__ =       convex_hull_bf(lowercase_		)
  
   A__ =       convex_hull_recursive(lowercase_		)
   assert results_bf == results_recursive
  
   A__ =       convex_hull_melkman(lowercase_		)
   assert results_bf == results_melkman
  
   print(lowercase_		)
  
  
  if __name__ == "__main__":
        main()
  
  
  
  
  
  
style_context: 
  
  
  
  
  """simple docstring"""
  
  
  
  from typing import TYPE_CHECKING
  
  from ...utils import _LazyModule
  
  
  SCREAMING_SNAKE_CASE       = {"tokenization_bert_japanese": ["BertJapaneseTokenizer", "CharacterTokenizer", "MecabTokenizer"]}
  
  
  if TYPE_CHECKING:
        from .tokenization_bert_japanese import BertJapaneseTokenizer, CharacterTokenizer, MecabTokenizer
  
  else:
        import sys
  
        SCREAMING_SNAKE_CASE       = _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)
  
  
  
  
  
  