




"""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()











"""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__)





