"""simple docstring"""







from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_SCREAMING_SNAKE_CASE  :		List[str]        =      {'''configuration_umt5''': ['''UMT5Config''', '''UMT5OnnxConfig''']}


try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     _SCREAMING_SNAKE_CASE  :		Optional[Any]        =      [
         '''UMT5EncoderModel''',
         '''UMT5ForConditionalGeneration''',
         '''UMT5ForQuestionAnswering''',
         '''UMT5Model''',
         '''UMT5PreTrainedModel''',
     ]

if TYPE_CHECKING:
     from .configuration_umta import UMTaConfig, UMTaOnnxConfig

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_umta import (
              UMTaEncoderModel,
              UMTaForConditionalGeneration,
              UMTaForQuestionAnswering,
              UMTaModel,
              UMTaPreTrainedModel,
          )
else:
     import sys

     _SCREAMING_SNAKE_CASE  :		Optional[int]        =      _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)







"""simple docstring"""







from __future__ import annotations

from collections.abc import Iterable






class     _SCREAMING_SNAKE_CASE       :



   '''simple docstring'''



   def __init__(  self   ,							_SCREAMING_SNAKE_CASE   ,							_SCREAMING_SNAKE_CASE  ):


      '''simple docstring'''

      __lowerCamelCase		,__lowerCamelCase								=				float(_SCREAMING_SNAKE_CASE  ), float(_SCREAMING_SNAKE_CASE  )







   def __eq__(  self   ,							_SCREAMING_SNAKE_CASE  ):


      '''simple docstring'''

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







   def __ne__(  self   ,							_SCREAMING_SNAKE_CASE  ):


      '''simple docstring'''

      return not self == other







   def __gt__(  self   ,							_SCREAMING_SNAKE_CASE  ):


      '''simple docstring'''

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







   def __lt__(  self   ,							_SCREAMING_SNAKE_CASE  ):


      '''simple docstring'''

      return not self > other







   def __ge__(  self   ,							_SCREAMING_SNAKE_CASE  ):


      '''simple docstring'''

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







   def __le__(  self   ,							_SCREAMING_SNAKE_CASE  ):


      '''simple docstring'''

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







   def __repr__(  self  ):


      '''simple docstring'''

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







   def __hash__(  self  ):


      '''simple docstring'''

      return hash(self.x  )



def 			A__						(  lowercase_    :  list[Point] | list[list[float]] | Iterable[list[float]]			,   )     ->       list[Point]:
   __lowerCamelCase								=				[]
   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 			A__						(  lowercase_    :  list[Point] | list[list[float]]	)     ->       list[Point]:

   if not hasattr(lowercase_			,   '__iter__'	):
      __lowerCamelCase								=				F'''Expecting an iterable object but got an non-iterable type {points}'''
      raise ValueError(lowercase_	)

   if not points:
      __lowerCamelCase								=				F'''Expecting a list of points but got {points}'''
      raise ValueError(lowercase_	)

   return _construct_points(lowercase_	)



def 			A__						(  lowercase_    :  Point			,   lowercase_    :  Point			,   lowercase_    :  Point	)     ->       float:
   __lowerCamelCase								=				(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 			A__						(  lowercase_    :  list[Point]	)     ->       list[Point]:
   __lowerCamelCase								=				sorted(_validate_input(lowercase_	)	)
   __lowerCamelCase								=				len(lowercase_	)
   __lowerCamelCase								=				set()

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

               if det_k > 0:
                  __lowerCamelCase								=				True
               elif det_k < 0:
                  __lowerCamelCase								=				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]:
                     __lowerCamelCase								=				False
                     break

            if points_left_of_ij and points_right_of_ij:
               __lowerCamelCase								=				False
               break

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

   return sorted(lowercase_	)



def 			A__						(  lowercase_    :  list[Point]	)     ->       list[Point]:
   __lowerCamelCase								=				sorted(_validate_input(lowercase_	)	)
   __lowerCamelCase								=				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

   __lowerCamelCase								=				points[0]
   __lowerCamelCase								=				points[n - 1]

   __lowerCamelCase								=				{left_most_point, right_most_point}
   __lowerCamelCase								=				[]
   __lowerCamelCase								=				[]

   for i in range(1			,   n - 1	):
      __lowerCamelCase								=				_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 			A__						(  lowercase_    :  list[Point]			,   lowercase_    :  Point			,   lowercase_    :  Point			,   lowercase_    :  set[Point]	)     ->       None:
   if points:
      __lowerCamelCase								=				None
      __lowerCamelCase								=				float('-inf'	)
      __lowerCamelCase								=				[]

      for p in points:
         __lowerCamelCase								=				_det(lowercase_			,   lowercase_			,   lowercase_	)

         if det > 0:
            candidate_points.append(lowercase_	)

            if det > extreme_point_distance:
               __lowerCamelCase								=				det
               __lowerCamelCase								=				p

      if extreme_point:
         _construct_hull(lowercase_			,   lowercase_			,   lowercase_			,   lowercase_	)
         convex_set.add(lowercase_	)
         _construct_hull(lowercase_			,   lowercase_			,   lowercase_			,   lowercase_	)



def 			A__						(  lowercase_    :  list[Point]	)     ->       list[Point]:
   __lowerCamelCase								=				sorted(_validate_input(lowercase_	)	)
   __lowerCamelCase								=				len(lowercase_	)

   __lowerCamelCase								=				points[:2]
   for i in range(2			,   lowercase_	):
      __lowerCamelCase								=				_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:
         __lowerCamelCase								=				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 			A__						(  )     ->       List[Any]:
   __lowerCamelCase								=				[
       (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)]
   __lowerCamelCase								=				convex_hull_bf(lowercase_	)

   __lowerCamelCase								=				convex_hull_recursive(lowercase_	)
   assert results_bf == results_recursive

   __lowerCamelCase								=				convex_hull_melkman(lowercase_	)
   assert results_bf == results_melkman

   print(lowercase_	)


if __name__ == "__main__":
     main()






