



from __future__ import annotations

from collections.abc import Iterable


class 						lowerCamelCase__			:


						def __init__(			self    :	Union[str, Any]   ,							_a    :	Any   ,							_a    :	Tuple      ):
													a__				,      a__:							Tuple									=float(_UpperCamelCase      ), float(_UpperCamelCase      )


						def __eq__(			self    :	Union[str, Any]   ,							_a    :	List[Any]      ):
													return self.x == other.x and self.y == other.y


						def __ne__(			self    :	Optional[Any]   ,							_a    :	str      ):
													return not self == other


						def __gt__(			self    :	Optional[int]   ,							_a    :	Tuple      ):
													if self.x > other.x:
																				return True
													elif self.x == other.x:
																				return self.y > other.y
													return False


						def __lt__(			self    :	Optional[int]   ,							_a    :	List[str]      ):
													return not self > other


						def __ge__(			self    :	Tuple   ,							_a    :	Optional[Any]      ):
													if self.x > other.x:
																				return True
													elif self.x == other.x:
																				return self.y >= other.y
													return False


						def __le__(			self    :	str   ,							_a    :	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    :	int      ):
													return F"({self.x}, {self.y})"







						def __hash__(			self    :	List[Any]      ):
													return hash(self.x      )





def     __lowerCamelCase							(   __magic_name__						:	list[Point] | list[list[float]] | Iterable[list[float]]  ,			):
							a__:							Dict									=[]
							if list_of_tuples:
														for p in list_of_tuples:
																					if isinstance(__magic_name__  ,			__magic_name__    ):
																												points.append(__magic_name__    )
																					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							(   __magic_name__						:	list[Point] | list[list[float]]    ):






							if not hasattr(__magic_name__  ,			"__iter__"    ):
														a__:							List[Any]									=F"Expecting an iterable object but got an non-iterable type {points}"
														raise ValueError(__magic_name__    )

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

							return _construct_points(__magic_name__    )





def     __lowerCamelCase							(   __magic_name__						:	Point  ,			__magic_name__						:	Point  ,			__magic_name__						:	Point    ):
							a__:							Union[str, 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     __lowerCamelCase							(   __magic_name__						:	list[Point]    ):
							a__:							Optional[Any]									=sorted(_validate_input(__magic_name__    )    )
							a__:							str									=len(__magic_name__    )
							a__:							Union[str, Any]									=set()

							for i in range(n - 1    ):
														for j in range(i + 1  ,			__magic_name__    ):
																					a__:							str									=False
																					a__:							List[Any]									=True
																					for k in range(__magic_name__    ):
																												if k != i and k != j:
																																			a__:							Union[str, 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__:							Optional[int]									=False
																																			break

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

							return sorted(__magic_name__    )





def     __lowerCamelCase							(   __magic_name__						:	list[Point]    ):
							a__:							Dict									=sorted(_validate_input(__magic_name__    )    )
							a__:							int									=len(__magic_name__    )

							# 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__:							List[str]									=points[0]
							a__:							List[Any]									=points[n - 1]

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

							for i in range(1  ,			n - 1    ):
														a__:							Tuple									=_det(__magic_name__  ,			__magic_name__  ,			points[i]    )

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

							_construct_hull(__magic_name__  ,			__magic_name__  ,			__magic_name__  ,			__magic_name__    )
							_construct_hull(__magic_name__  ,			__magic_name__  ,			__magic_name__  ,			__magic_name__    )

							return sorted(__magic_name__    )





def     __lowerCamelCase							(   __magic_name__						:	list[Point]  ,			__magic_name__						:	Point  ,			__magic_name__						:	Point  ,			__magic_name__						:	set[Point]    ):






							if points:
														a__:							Optional[int]									=None
														a__:							List[Any]									=float("-inf"    )
														a__:							List[str]									=[]

														for p in points:
																					a__:							Dict									=_det(__magic_name__  ,			__magic_name__  ,			__magic_name__    )

																					if det > 0:
																												candidate_points.append(__magic_name__    )

																												if det > extreme_point_distance:
																																			a__:							Optional[int]									=det
																																			a__:							List[Any]									=p

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





def     __lowerCamelCase							(   __magic_name__						:	list[Point]    ):
							a__:							str									=sorted(_validate_input(__magic_name__    )    )
							a__:							List[Any]									=len(__magic_name__    )

							a__:							Any									=points[:2]
							for i in range(2  ,			__magic_name__    ):
														a__:							Union[str, 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:
																					a__:							Tuple									=points[i]
							i += 1

							for j in range(__magic_name__  ,			__magic_name__    ):
														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(__magic_name__    ) > 3 else convex_hull    )





def     __lowerCamelCase							(   ):
							a__:							Union[str, 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(__magic_name__    )

							a__:							Optional[Any]									=convex_hull_recursive(__magic_name__    )
							assert results_bf == results_recursive

							a__:							Tuple									=convex_hull_melkman(__magic_name__    )
							assert results_bf == results_melkman

							print(__magic_name__    )


if __name__ == "__main__":
		main()












def _a							(      lowerCamelCase:  List[Any]					)      ->		Optional[Any]:







      '''simple docstring'''






      __A			  =							[7_01, 3_01, 1_32, 57, 23, 10, 4, 1]
      for gap in gaps:
            for i in range(lowerCamelCase   ,							len(lowerCamelCase					)					):
                  __A			  =							collection[i]
                  __A			  =							i
                  while j >= gap and collection[j - gap] > insert_value:
                        __A			  =							collection[j - gap]
                        j -= gap
                  if j != i:
                        __A			  =							insert_value
      return collection


if __name__ == "__main__":
       from doctest import testmod

       testmod()
       snake_case__   :				Optional[int]						=	input('Enter numbers separated by a comma:\n').strip()
       snake_case__   :				int						=	[int(item) for item in user_input.split(',')]
       print(shell_sort(unsorted))





