
"""simple docstring"""


import numpy as np
import PIL
import torch
import torchvision.transforms as T
import torchvision.transforms.functional as TF
from PIL import Image



def        _lowerCamelCase(__UpperCamelCase       ,					__UpperCamelCase=256			)							->					List[Any]:
	_lowerCAmelCase								=min(img.size			)

	if s < target_image_size:
		raise ValueError(F'''min dim for image {s} < {target_image_size}'''			)

	_lowerCAmelCase								=target_image_size / s
	_lowerCAmelCase								=(round(r * img.size[1]			), round(r * img.size[0]			))
	_lowerCAmelCase								=TF.resize(lowerCAmelCase__       ,					lowerCAmelCase__       ,					interpolation=PIL.Image.LANCZOS			)
	_lowerCAmelCase								=TF.center_crop(lowerCAmelCase__       ,					output_size=2 * [target_image_size]			)
	_lowerCAmelCase								=torch.unsqueeze(T.ToTensor()(lowerCAmelCase__			)       ,					0			)
	return img



def        _lowerCamelCase(__UpperCamelCase			)							->					str:
	_lowerCAmelCase								=2.0 * x - 1.0
	return x



def        _lowerCamelCase(__UpperCamelCase       ,					__UpperCamelCase=True       ,					__UpperCamelCase="RGB"			)							->					Any:
	_lowerCAmelCase								=x.detach().cpu()
	if process:
		_lowerCAmelCase								=post_process_tensor(lowerCAmelCase__			)
	_lowerCAmelCase								=x.numpy()
	if process:
		_lowerCAmelCase								=(255 * x).astype(np.uinta			)
	_lowerCAmelCase								=Image.fromarray(lowerCAmelCase__			)
	if not x.mode == mode:
		_lowerCAmelCase								=x.convert(lowerCAmelCase__			)
	return x



def        _lowerCamelCase(__UpperCamelCase			)							->					Optional[int]:
	_lowerCAmelCase								=torch.clamp(lowerCAmelCase__       ,					-1.0       ,					1.0			)
	_lowerCAmelCase								=(x + 1.0) / 2.0
	_lowerCAmelCase								=x.permute(1       ,					2       ,					0			)
	return x



def        _lowerCamelCase(__UpperCamelCase			)							->					int:
	_lowerCAmelCase								=post_process_tensor(x.squeeze()			)
	return x.permute(2       ,					0       ,					1			).unsqueeze(0			)




from __future__ import annotations

from collections.abc import Iterable
class 							a_					:






 '''simple docstring'''






 def __init__(     self   :    int     ,       lowercase__   :    Optional[int]     ,       lowercase__   :    List[str]):







        '''simple docstring'''



        lowerCAmelCase__      ,   lowerCAmelCase__	      =   float(lowercase__), float(lowercase__)




 def __eq__(     self   :    int     ,       lowercase__   :    int):







        '''simple docstring'''



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




 def __ne__(     self   :    Tuple     ,       lowercase__   :    List[Any]):







        '''simple docstring'''



        return not self == other




 def __gt__(     self   :    Optional[Any]     ,       lowercase__   :    List[Any]):







        '''simple docstring'''



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




 def __lt__(     self   :    str     ,       lowercase__   :    List[str]):







        '''simple docstring'''



        return not self > other




 def __ge__(     self   :    List[Any]     ,       lowercase__   :    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   :    Dict     ,       lowercase__   :    str):







        '''simple docstring'''



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




 def __repr__(     self   :    List[str]):







        '''simple docstring'''



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




 def __hash__(     self   :    Dict):







        '''simple docstring'''



        return hash(self.x)






def  __lowerCamelCase						(		lowerCAmelCase__      ,    ):
       lowerCAmelCase__	      =   []
       if list_of_tuples:
              for p in list_of_tuples:
                     if isinstance(lowerCAmelCase__      ,    lowerCAmelCase__      ):
                            points.append(lowerCAmelCase__      )
                     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						(		lowerCAmelCase__      ):

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

       if not points:
              lowerCAmelCase__	      =   F"""Expecting a list of points but got {points}"""
              raise ValueError(lowerCAmelCase__      )

       return _construct_points(lowerCAmelCase__      )






def  __lowerCamelCase						(		lowerCAmelCase__      ,    lowerCAmelCase__      ,    lowerCAmelCase__      ):
       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						(		lowerCAmelCase__      ):
       lowerCAmelCase__	      =   sorted(_validate_input(lowerCAmelCase__      )      )
       lowerCAmelCase__	      =   len(lowerCAmelCase__      )
       lowerCAmelCase__	      =   set()

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






def  __lowerCamelCase						(		lowerCAmelCase__      ):
       lowerCAmelCase__	      =   sorted(_validate_input(lowerCAmelCase__      )      )
       lowerCAmelCase__	      =   len(lowerCAmelCase__      )

       # 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(lowerCAmelCase__      ,    lowerCAmelCase__      ,    points[i]      )

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

       _construct_hull(lowerCAmelCase__      ,    lowerCAmelCase__      ,    lowerCAmelCase__      ,    lowerCAmelCase__      )
       _construct_hull(lowerCAmelCase__      ,    lowerCAmelCase__      ,    lowerCAmelCase__      ,    lowerCAmelCase__      )

       return sorted(lowerCAmelCase__      )






def  __lowerCamelCase						(		lowerCAmelCase__      ,    lowerCAmelCase__      ,    lowerCAmelCase__      ,    lowerCAmelCase__      ):
       if points:
              lowerCAmelCase__	      =   None
              lowerCAmelCase__	      =   float('-inf'      )
              lowerCAmelCase__	      =   []

              for p in points:
                     lowerCAmelCase__	      =   _det(lowerCAmelCase__      ,    lowerCAmelCase__      ,    lowerCAmelCase__      )

                     if det > 0:
                            candidate_points.append(lowerCAmelCase__      )

                            if det > extreme_point_distance:
                                   lowerCAmelCase__	      =   det
                                   lowerCAmelCase__	      =   p

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






def  __lowerCamelCase						(		lowerCAmelCase__      ):
       lowerCAmelCase__	      =   sorted(_validate_input(lowerCAmelCase__      )      )
       lowerCAmelCase__	      =   len(lowerCAmelCase__      )

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






def  __lowerCamelCase						(		):
       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(lowerCAmelCase__      )

       lowerCAmelCase__	      =   convex_hull_recursive(lowerCAmelCase__      )
       assert results_bf == results_recursive

       lowerCAmelCase__	      =   convex_hull_melkman(lowerCAmelCase__      )
       assert results_bf == results_melkman

       print(lowerCAmelCase__      )


if __name__ == "__main__":
    main()
