


from __future__ import annotations

from collections.abc import Iterable







class 					lowerCAmelCase__	:




     '''simple docstring'''


     def __init__(						self			,						__lowerCamelCase			,						__lowerCamelCase)      ->    Optional[Any]:
            _A   ,      _A				:	Dict       =			float(__lowerCamelCase), float(__lowerCamelCase)


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


     def __ne__(						self			,						__lowerCamelCase)      ->    Any:
            return not self == other


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


     def __lt__(						self			,						__lowerCamelCase)      ->    Optional[int]:
            return not self > other


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


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


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




def 							_UpperCAmelCase    (UpperCamelCase__					:  list[Point] | list[list[float]] | Iterable[list[float]]    ,							):
       _A				:	list[Point]       =			[]
       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__					:  list[Point] | list[list[float]]						):

       if not hasattr(UpperCamelCase__    ,							"__iter__"						):
              _A				:	Any       =			f"Expecting an iterable object but got an non-iterable type {points}"
              raise ValueError(UpperCamelCase__						)

       if not points:
              _A				:	Tuple       =			f"Expecting a list of points but got {points}"
              raise ValueError(UpperCamelCase__						)

       return _construct_points(UpperCamelCase__						)
def 							_UpperCAmelCase    (UpperCamelCase__					:  Point    ,							UpperCamelCase__					:  Point    ,							UpperCamelCase__					:  Point						):
       _A				:	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__					:  list[Point]						):
       _A				:	Tuple       =			sorted(_validate_input(UpperCamelCase__						)						)
       _A				:	Union[str, Any]       =			len(UpperCamelCase__						)
       _A				:	Any       =			set()

       for i in range(n - 1						):
              for j in range(i + 1    ,							UpperCamelCase__						):
                     _A				:	Optional[int]       =			False
                     _A				:	Any       =			True
                     for k in range(UpperCamelCase__						):
                            if k != i and k != j:
                                   _A				:	Any       =			_det(points[i]    ,							points[j]    ,							points[k]						)

                                   if det_k > 0:
                                          _A				:	int       =			True
                                   elif det_k < 0:
                                          _A				:	Union[str, 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]:
                                                 _A				:	Optional[int]       =			False
                                                 break

                            if points_left_of_ij and points_right_of_ij:
                                   _A				:	Any       =			False
                                   break

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

       return sorted(UpperCamelCase__						)
def 							_UpperCAmelCase    (UpperCamelCase__					:  list[Point]						):
       _A				:	Dict       =			sorted(_validate_input(UpperCamelCase__						)						)
       _A				:	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

       _A				:	Any       =			points[0]
       _A				:	int       =			points[n - 1]

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

       for i in range(1    ,							n - 1						):
              _A				:	Union[str, Any]       =			_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[Point]    ,							UpperCamelCase__					:  Point    ,							UpperCamelCase__					:  Point    ,							UpperCamelCase__					:  set[Point]						):
       if points:
              _A				:	Union[str, Any]       =			None
              _A				:	Union[str, Any]       =			float("-inf"						)
              _A				:	str       =			[]

              for p in points:
                     _A				:	Tuple       =			_det(UpperCamelCase__    ,							UpperCamelCase__    ,							UpperCamelCase__						)

                     if det > 0:
                            candidate_points.append(UpperCamelCase__						)

                            if det > extreme_point_distance:
                                   _A				:	List[str]       =			det
                                   _A				:	Optional[Any]       =			p

              if extreme_point:
                     _construct_hull(UpperCamelCase__    ,							UpperCamelCase__    ,							UpperCamelCase__    ,							UpperCamelCase__						)
                     convex_set.add(UpperCamelCase__						)
                     _construct_hull(UpperCamelCase__    ,							UpperCamelCase__    ,							UpperCamelCase__    ,							UpperCamelCase__						)
def 							_UpperCAmelCase    (UpperCamelCase__					:  list[Point]						):
       _A				:	Any       =			sorted(_validate_input(UpperCamelCase__						)						)
       _A				:	Any       =			len(UpperCamelCase__						)

       _A				:	Union[str, Any]       =			points[:2]
       for i in range(2    ,							UpperCamelCase__						):
              _A				:	Optional[int]       =			_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				:	Union[str, Any]       =			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    ():
       _A				:	List[Any]       =			[
           (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				:	Dict       =			convex_hull_bf(UpperCamelCase__						)

       _A				:	List[Any]       =			convex_hull_recursive(UpperCamelCase__						)
       assert results_bf == results_recursive

       _A				:	str       =			convex_hull_melkman(UpperCamelCase__						)
       assert results_bf == results_melkman

       print(UpperCamelCase__						)


if __name__ == "__main__":
    main()




import warnings

from .generation import FlaxGenerationMixin







class 					lowerCAmelCase__	(    a):




     '''simple docstring'''
     # warning at import time
     warnings.warn(
         "Importing `FlaxGenerationMixin` from `src/transformers/generation_flax_utils.py` is deprecated and will "
         "be removed in Transformers v5. Import as `from transformers import FlaxGenerationMixin` instead."					,   a					,   )
