



from dataclasses import dataclass
from typing import List, Optional, Union

import numpy as np
import PIL
from PIL import Image

from ...utils import BaseOutput, is_torch_available, is_transformers_available

@dataclass
# Copied from diffusers.pipelines.stable_diffusion.__init__.StableDiffusionPipelineOutput with Stable->Alt
class    _SCREAMING_SNAKE_CASE						(UpperCamelCase			):
     lowerCAmelCase       =      42
     lowerCAmelCase       =      42


if is_transformers_available() and is_torch_available():
      from .modeling_roberta_series import RobertaSeriesModelWithTransformation
      from .pipeline_alt_diffusion import AltDiffusionPipeline
      from .pipeline_alt_diffusion_imgaimg import AltDiffusionImgaImgPipeline












from __future__ import annotations

from collections.abc import Iterable





class        lowerCamelCase__:
      def __init__(							self:					Dict       ,			UpperCamelCase_:					int       ,			UpperCamelCase_:					str  ):
             __lowerCamelCase,  __lowerCamelCase  =		float(UpperCamelCase_  ), float(UpperCamelCase_  )
      def __eq__(							self:					List[Any]       ,			UpperCamelCase_:					List[str]  ):
             return self.x == other.x and self.y == other.y
      def __ne__(							self:					Tuple       ,			UpperCamelCase_:					Dict  ):
             return not self == other
      def __gt__(							self:					List[Any]       ,			UpperCamelCase_:					List[Any]  ):
             if self.x > other.x:
                    return True
             elif self.x == other.x:
                    return self.y > other.y
             return False
      def __lt__(							self:					str       ,			UpperCamelCase_:					int  ):
             return not self > other
      def __ge__(							self:					Dict       ,			UpperCamelCase_:					Any  ):
             if self.x > other.x:
                    return True
             elif self.x == other.x:
                    return self.y >= other.y
             return False
      def __le__(							self:					Union[str, Any]       ,			UpperCamelCase_:					Optional[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    lowerCamelCase__			(		A__			:   list[Point] | list[list[float]] | Iterable[list[float]]    ,     ):





       '''simple docstring'''



       __lowerCamelCase  =		[]
       if list_of_tuples:
              for p in list_of_tuples:
                     if isinstance(A__    ,     A__      ):
                            points.append(A__      )
                     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    lowerCamelCase__			(		A__			:   list[Point] | list[list[float]]      ):





       '''simple docstring'''



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

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

       return _construct_points(A__      )




def    lowerCamelCase__			(		A__			:   Point    ,     A__			:   Point    ,     A__			:   Point      ):





       '''simple docstring'''



       __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    lowerCamelCase__			(		A__			:   list[Point]      ):





       '''simple docstring'''



       __lowerCamelCase  =		sorted(_validate_input(A__      )      )
       __lowerCamelCase  =		len(A__      )
       __lowerCamelCase  =		set()

       for i in range(n - 1      ):
              for j in range(i + 1    ,     A__      ):
                     __lowerCamelCase  =		__lowerCamelCase  =		False
                     __lowerCamelCase  =		True
                     for k in range(A__      ):
                            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(A__      )




def    lowerCamelCase__			(		A__			:   list[Point]      ):





       '''simple docstring'''



       __lowerCamelCase  =		sorted(_validate_input(A__      )      )
       __lowerCamelCase  =		len(A__      )

       # 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(A__    ,     A__    ,     points[i]      )

              if det > 0:
                     upper_hull.append(points[i]      )
              elif det < 0:
                     lower_hull.append(points[i]      )

       _construct_hull(A__    ,     A__    ,     A__    ,     A__      )
       _construct_hull(A__    ,     A__    ,     A__    ,     A__      )

       return sorted(A__      )




def    lowerCamelCase__			(		A__			:   list[Point]    ,     A__			:   Point    ,     A__			:   Point    ,     A__			:   set[Point]      ):





       '''simple docstring'''



       if points:
              __lowerCamelCase  =		None
              __lowerCamelCase  =		float("""-inf"""      )
              __lowerCamelCase  =		[]

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

                     if det > 0:
                            candidate_points.append(A__      )

                            if det > extreme_point_distance:
                                   __lowerCamelCase  =		det
                                   __lowerCamelCase  =		p

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




def    lowerCamelCase__			(		A__			:   list[Point]      ):





       '''simple docstring'''



       __lowerCamelCase  =		sorted(_validate_input(A__      )      )
       __lowerCamelCase  =		len(A__      )

       __lowerCamelCase  =		points[:2]
       for i in range(2    ,     A__      ):
              __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(A__    ,     A__      ):
              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(A__      ) > 3 else convex_hull      )




def    lowerCamelCase__			(		):





       '''simple docstring'''



       __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(A__      )

       __lowerCamelCase  =		convex_hull_recursive(A__      )
       assert results_bf == results_recursive

       __lowerCamelCase  =		convex_hull_melkman(A__      )
       assert results_bf == results_melkman

       print(A__      )


if __name__ == "__main__":
       main()

