



"""simple docstring"""


from __future__ import annotations

from collections.abc import Iterable







class  A_     :



						"""simple docstring"""






						def __init__(   self					:Union[str, Any]  ,    lowercase_					:Union[str, Any]  ,    lowercase_					:Optional[int]   )							->     Dict:
												UpperCAmelCase ,       UpperCAmelCase			 =					float(lowercase_   ), float(lowercase_   )






						def __eq__(   self					:List[str]  ,    lowercase_					:Optional[int]   )							->     str:
												return self.x == other.x and self.y == other.y






						def __ne__(   self					:Optional[int]  ,    lowercase_					:Tuple   )							->     Any:
												return not self == other






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






						def __lt__(   self					:List[Any]  ,    lowercase_					:Dict   )							->     int:
												return not self > other






						def __ge__(   self					:List[Any]  ,    lowercase_					:Union[str, Any]   )							->     List[Any]:
												if self.x > other.x:
																		return True
												elif self.x == other.x:
																		return self.y >= other.y
												return False






						def __le__(   self					:str  ,    lowercase_					:Union[str, Any]   )							->     List[Any]:
												if self.x < other.x:
																		return True
												elif self.x == other.x:
																		return self.y <= other.y
												return False






						def __repr__(   self					:int   )							->     int:
												return f"""({self.x}, {self.y})"""






						def __hash__(   self					:Union[str, Any]   )							->     List[str]:
												return hash(self.x   )


def 					_lowerCAmelCase (  lowercase_						,      ):
						UpperCAmelCase			 =					[]
						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 					_lowerCAmelCase (  lowercase_		):

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

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

						return _construct_points(lowercase_		)

def 					_lowerCAmelCase (  lowercase_						,      lowercase_						,      lowercase_		):
						UpperCAmelCase			 =					(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 (  lowercase_		):
						UpperCAmelCase			 =					sorted(_validate_input(lowercase_		)		)
						UpperCAmelCase			 =					len(lowercase_		)
						UpperCAmelCase			 =					set()

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

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

																								if points_left_of_ij and points_right_of_ij:
																														UpperCAmelCase			 =					False
																														break

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

						return sorted(lowercase_		)

def 					_lowerCAmelCase (  lowercase_		):
						UpperCAmelCase			 =					sorted(_validate_input(lowercase_		)		)
						UpperCAmelCase			 =					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

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

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

						for i in range(1						,      n - 1		):
												UpperCAmelCase			 =					_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 					_lowerCAmelCase (  lowercase_						,      lowercase_						,      lowercase_						,      lowercase_		):
						if points:
												UpperCAmelCase			 =					None
												UpperCAmelCase			 =					float('-inf'		)
												UpperCAmelCase			 =					[]

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

																		if det > 0:
																								candidate_points.append(lowercase_		)

																								if det > extreme_point_distance:
																														UpperCAmelCase			 =					det
																														UpperCAmelCase			 =					p

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

def 					_lowerCAmelCase (  lowercase_		):
						UpperCAmelCase			 =					sorted(_validate_input(lowercase_		)		)
						UpperCAmelCase			 =					len(lowercase_		)

						UpperCAmelCase			 =					points[:2]
						for i in range(2						,      lowercase_		):
												UpperCAmelCase			 =					_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:
																		UpperCAmelCase			 =					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 					_lowerCAmelCase (  ):
						UpperCAmelCase			 =					[
						    (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)]
						UpperCAmelCase			 =					convex_hull_bf(lowercase_		)

						UpperCAmelCase			 =					convex_hull_recursive(lowercase_		)
						assert results_bf == results_recursive

						UpperCAmelCase			 =					convex_hull_melkman(lowercase_		)
						assert results_bf == results_melkman

						print(lowercase_		)


if __name__ == "__main__":
				main()







from __future__ import annotations

import math
import random

def    UpperCamelCase_ (	a_  ,				a_  ,				a_		)     ->list[int]:
		A				=d * e - 1
		A				=0
		A				=0
		while p == 0:
				A				=random.randint(2  ,				n - 1		)
				A				=k
				while True:
						if t % 2 == 0:
								A				=t // 2
								A				=(g**t) % n
								A				=math.gcd(x - 1  ,				a_		)
								if x > 1 and y > 1:
										A				=y
										A				=n // y
										break  # find the correct factors
						else:
								break  # t is not divisible by 2, break and choose another g
		return sorted([p, q]		)


if __name__ == "__main__":
	import doctest

	doctest.testmod()




