'''simple docstring'''




from __future__ import annotations

from collections.abc import Iterable


class    UpperCAmelCase__	:






   """simple docstring"""
   def __init__(self							,					_a							,					_a					)     ->  Union[str, Any]:
        lowercase_					,lowercase_       :							Any  					=       float(_a					), float(_a					)
   def __eq__(self							,					_a					)     ->  Union[str, Any]:
        return self.x == other.x and self.y == other.y
   def __ne__(self							,					_a					)     ->  Optional[int]:
        return not self == other
   def __gt__(self							,					_a					)     ->  Any:
        if self.x > other.x:
             return True
        elif self.x == other.x:
             return self.y > other.y
        return False
   def __lt__(self							,					_a					)     ->  List[Any]:
        return not self > other
   def __ge__(self							,					_a					)     ->  Any:
        if self.x > other.x:
             return True
        elif self.x == other.x:
             return self.y >= other.y
        return False
   def __le__(self							,					_a					)     ->  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					)     ->  List[Any]:
        return hash(self.x					)



def _UpperCamelCase (							SCREAMING_SNAKE_CASE_	,							):
     lowercase_       :							list[Point]  					=       []
     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 _UpperCamelCase (							SCREAMING_SNAKE_CASE_				):

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

     if not points:
          lowercase_       :							Union[str, Any]  					=       f'''Expecting a list of points but got {points}'''
          raise ValueError(SCREAMING_SNAKE_CASE_				)

     return _construct_points(SCREAMING_SNAKE_CASE_				)

def _UpperCamelCase (							SCREAMING_SNAKE_CASE_	,							SCREAMING_SNAKE_CASE_	,							SCREAMING_SNAKE_CASE_				):
     lowercase_       :							List[Any]  					=       (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 (							SCREAMING_SNAKE_CASE_				):
     lowercase_       :							Optional[Any]  					=       sorted(_validate_input(SCREAMING_SNAKE_CASE_				)				)
     lowercase_       :							Union[str, Any]  					=       len(SCREAMING_SNAKE_CASE_				)
     lowercase_       :							List[Any]  					=       set()

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

                         if det_k > 0:
                              lowercase_       :							Dict  					=       True
                         elif det_k < 0:
                              lowercase_       :							List[str]  					=       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]:
                                   lowercase_       :							str  					=       False
                                   break

                    if points_left_of_ij and points_right_of_ij:
                         lowercase_       :							Union[str, Any]  					=       False
                         break

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

     return sorted(SCREAMING_SNAKE_CASE_				)

def _UpperCamelCase (							SCREAMING_SNAKE_CASE_				):
     lowercase_       :							List[str]  					=       sorted(_validate_input(SCREAMING_SNAKE_CASE_				)				)
     lowercase_       :							Union[str, Any]  					=       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

     lowercase_       :							str  					=       points[0]
     lowercase_       :							List[Any]  					=       points[n - 1]

     lowercase_       :							Optional[Any]  					=       {left_most_point, right_most_point}
     lowercase_       :							str  					=       []
     lowercase_       :							Union[str, Any]  					=       []

     for i in range(1	,							n - 1				):
          lowercase_       :							Optional[int]  					=       _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 _UpperCamelCase (							SCREAMING_SNAKE_CASE_	,							SCREAMING_SNAKE_CASE_	,							SCREAMING_SNAKE_CASE_	,							SCREAMING_SNAKE_CASE_				):
     if points:
          lowercase_       :							Optional[int]  					=       None
          lowercase_       :							str  					=       float('-inf'				)
          lowercase_       :							Optional[int]  					=       []

          for p in points:
               lowercase_       :							List[str]  					=       _det(SCREAMING_SNAKE_CASE_	,							SCREAMING_SNAKE_CASE_	,							SCREAMING_SNAKE_CASE_				)

               if det > 0:
                    candidate_points.append(SCREAMING_SNAKE_CASE_				)

                    if det > extreme_point_distance:
                         lowercase_       :							int  					=       det
                         lowercase_       :							Any  					=       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 _UpperCamelCase (							SCREAMING_SNAKE_CASE_				):
     lowercase_       :							Optional[Any]  					=       sorted(_validate_input(SCREAMING_SNAKE_CASE_				)				)
     lowercase_       :							List[str]  					=       len(SCREAMING_SNAKE_CASE_				)

     lowercase_       :							List[str]  					=       points[:2]
     for i in range(2	,							SCREAMING_SNAKE_CASE_				):
          lowercase_       :							Optional[Any]  					=       _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:
               lowercase_       :							str  					=       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 _UpperCamelCase (							):
     lowercase_       :							Dict  					=       [
         (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)]
     lowercase_       :							Dict  					=       convex_hull_bf(SCREAMING_SNAKE_CASE_				)

     lowercase_       :							List[Any]  					=       convex_hull_recursive(SCREAMING_SNAKE_CASE_				)
     assert results_bf == results_recursive

     lowercase_       :							Dict  					=       convex_hull_melkman(SCREAMING_SNAKE_CASE_				)
     assert results_bf == results_melkman

     print(SCREAMING_SNAKE_CASE_				)


if __name__ == "__main__":
 main()





'''simple docstring'''




from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_torch_available,
)


_A										= {
    'configuration_rwkv': ['RWKV_PRETRAINED_CONFIG_ARCHIVE_MAP', 'RwkvConfig', 'RwkvOnnxConfig'],
}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _A										= [
     'RWKV_PRETRAINED_MODEL_ARCHIVE_LIST',
     'RwkvForCausalLM',
     'RwkvModel',
     'RwkvPreTrainedModel',
 ]


if TYPE_CHECKING:
 from .configuration_rwkv import RWKV_PRETRAINED_CONFIG_ARCHIVE_MAP, RwkvConfig, RwkvOnnxConfig

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_rwkv import (
      RWKV_PRETRAINED_MODEL_ARCHIVE_LIST,
      RwkvForCausalLM,
      RwkvModel,
      RwkvPreTrainedModel,
  )
else:
 import sys

 _A										= _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




