"""simple docstring"""






from __future__ import annotations

from collections.abc import Iterable
class 							snake_case			:




					"""simple docstring"""

					def __init__(							self  :      Union[str, Any]       ,lowerCamelCase__  :      List[str]       ,lowerCamelCase__  :      Optional[int]     ):
									UpperCAmelCase__			 =				float(lowerCamelCase__     ), float(lowerCamelCase__     )







					def __eq__(							self  :      int       ,lowerCamelCase__  :      Tuple     ):
									return self.x == other.x and self.y == other.y







					def __ne__(							self  :      Optional[int]       ,lowerCamelCase__  :      Any     ):
									return not self == other







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







					def __lt__(							self  :      List[str]       ,lowerCamelCase__  :      Any     ):
									return not self > other







					def __ge__(							self  :      Dict       ,lowerCamelCase__  :      Optional[int]     ):
									if self.x > other.x:
													return True
									elif self.x == other.x:
													return self.y >= other.y
									return False







					def __le__(							self  :      List[Any]       ,lowerCamelCase__  :      Optional[Any]     ):
									if self.x < other.x:
													return True
									elif self.x == other.x:
													return self.y <= other.y
									return False







					def __repr__(							self  :      str     ):
									return f'''({self.x}, {self.y})'''







					def __hash__(							self  :      str     ):
									return hash(self.x     )






def     a_		(   lowerCamelCase   ,     ):
				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     a_		(   lowerCamelCase			):

				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     a_		(   lowerCamelCase   ,     lowerCamelCase   ,     lowerCamelCase			):
				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     a_		(   lowerCamelCase			):
				UpperCAmelCase__			 =				sorted(_validate_input(_lowercase			)			)
				UpperCAmelCase__			 =				len(_lowercase			)
				UpperCAmelCase__			 =				set()

				for i in range(n - 1			):
								for j in range(i + 1   ,     _lowercase			):
												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     a_		(   lowerCamelCase			):
				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     a_		(   lowerCamelCase   ,     lowerCamelCase   ,     lowerCamelCase   ,     lowerCamelCase			):
				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     a_		(   lowerCamelCase			):
				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     a_		(   ):
				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()








'''simple docstring'''




class      UpperCamelCase_					:





	def __init__(    self       )     ->     None:
								UpperCAmelCase	:						int					=						[0, 1]






	def 					_lowercase(    self						,						A       )     ->     list:
								if (difference := index - (len(self.sequence       ) - 2)) >= 1:
															for _ in range(A       ):
																						self.sequence.append(self.sequence[-1] + self.sequence[-2]       )
								return self.sequence[:index]




def  __lowerCamelCase    (   ) ->     None:
							print(
							    """Fibonacci Series Using Dynamic Programming\n"""      ,							"""Enter the index of the Fibonacci number you want to calculate """      ,							"""in the prompt below. (To exit enter exit or Ctrl-C)\n"""      ,							sep=""""""      ,							)
							UpperCAmelCase	:						Tuple					=						Fibonacci()

							while True:
														UpperCAmelCase	:						str					=						input(""">> """						)
														if prompt in {"exit", "quit"}:
																					break

														try:
																					UpperCAmelCase	:						int					=						int(_lowercase						)
														except ValueError:
																					print("""Enter a number or 'exit'"""						)
																					continue

														print(fibonacci.get(_lowercase						)						)


if __name__ == "__main__":
							main()

