





from __future__ import annotations

from collections import deque
from enum import Enum
from math import atana, degrees
from sys import maxsize





class 						_A( SCREAMING_SNAKE_CASE__       ):


				"""simple docstring"""


				UpperCamelCase   :  Any    =     1
				UpperCamelCase   :  Any    =     2
				UpperCamelCase   :  int    =     3



				def __repr__(      self					):
									return F"""{self.__class__.__name__}.{self.name}"""







def 			_SCREAMING_SNAKE_CASE    (       a ,						a ,						a  )				->				Dict:
					__A     :						Dict          =    point
					return degrees(atana(y - miny ,						x - minx  )  )







def 			_SCREAMING_SNAKE_CASE    (       a ,						a ,						a  )				->				Optional[Any]:
					__A     :						Dict          =    starting
					__A     :						List[str]          =    via
					__A     :						Dict          =    target
					__A     :						List[Any]          =    degrees(atana(ya - ya ,						xa - xa  )  )
					via_angle %= 3_60
					__A     :						Optional[Any]          =    degrees(atana(ya - ya ,						xa - xa  )  )
					target_angle %= 3_60
					# t-
					#  \ \
					#   \ v
					#    \|
					#     s
					# via_angle is always lower than target_angle, if direction is left.
					# If they are same, it means they are on a same line of convex hull.
					if target_angle > via_angle:
										return Direction.left
					elif target_angle == via_angle:
										return Direction.straight
					else:
										return Direction.right







def 			_SCREAMING_SNAKE_CASE    (       a  )				->				List[Any]:

					if len(snake_case__  ) <= 2:
										# There is no convex hull
										raise ValueError('graham_scan: argument must contain more than 3 points.'  )
					if len(snake_case__  ) == 3:
										return points
					# find the lowest and the most left point
					__A     :						Any          =    0
					__A     :						Optional[Any]          =    maxsize, maxsize
					for i, point in enumerate(snake_case__  ):
										__A     :						Union[str, Any]          =    point[0]
										__A     :						Optional[Any]          =    point[1]
										if y < miny:
															__A     :						List[Any]          =    y
															__A     :						List[str]          =    x
															__A     :						Optional[int]          =    i
										if y == miny and x < minx:
															__A     :						List[Any]          =    x
															__A     :						Any          =    i

    # remove the lowest and the most left point from points for preparing for sort
					points.pop(snake_case__  )

					__A     :						Any          =    sorted(snake_case__ ,						key=lambda a  : angle_comparer(snake_case__ ,						snake_case__ ,						snake_case__  )  )
					# This insert actually costs complexity,
					# and you should instead add (minx, miny) into stack later.
					# I'm using insert just for easy understanding.
					sorted_points.insert(0 ,						(minx, miny)  )

					__A     :						deque[tuple[int, int]]          =    deque()
					stack.append(sorted_points[0]  )
					stack.append(sorted_points[1]  )
					stack.append(sorted_points[2]  )
					# In any ways, the first 3 points line are towards left.
					# Because we sort them the angle from minx, miny.
					__A     :						Tuple          =    Direction.left

					for i in range(3 ,						len(snake_case__  )  ):
										while True:
															__A     :						Dict          =    stack[-2]
															__A     :						Union[str, Any]          =    stack[-1]
															__A     :						int          =    sorted_points[i]
															__A     :						Tuple          =    check_direction(snake_case__ ,						snake_case__ ,						snake_case__  )

															if next_direction == Direction.left:
																				__A     :						Dict          =    Direction.left
																				break
															if next_direction == Direction.straight:
																				if current_direction == Direction.left:
																									# We keep current_direction as left.
																									# Because if the straight line keeps as straight,
																									# we want to know if this straight line is towards left.
																									break
																				elif current_direction == Direction.right:
																									# If the straight line is towards right,
																									# every previous points on those straigh line is not convex hull.
																									stack.pop()
															if next_direction == Direction.right:
																				stack.pop()
										stack.append(sorted_points[i]  )
					return list(snake_case__  )











from .hash_table import HashTable





class 						_A( snake_case__       ):


				"""simple docstring"""


				def __init__(      self					, *_A					, **_A					):
									super().__init__(*_A					, **_A					)





				def  UpperCAmelCase_		(      self					, _A					, _A=None					):
									__A     :						Optional[int]          =    1
									__A     :						Union[str, Any]          =    self.hash_function(key + i * i					)

									while self.values[new_key] is not None and self.values[new_key] != key:
														i += 1
														__A     :						Tuple          =    (
														    self.hash_function(key + i * i					)
														    if not self.balanced_factor() >= self.lim_charge
														    else None
														)

														if new_key is None:
																			break

									return new_key




