

from __future__ import annotations

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





class 				lowerCamelCase  (A__     ):
			lowerCamelCase__				:						Optional[int]   						=							1
			lowerCamelCase__				:						List[Any]   						=							2
			lowerCamelCase__				:						List[str]   						=							3

			def __repr__(   self			:  Optional[Any]    )				->      Union[str, Any]:
						return F"""{self.__class__.__name__}.{self.name}"""

def 		A    (       snake_case__						,			snake_case__						,			snake_case__      ):




			'''simple docstring'''


			SCREAMING_SNAKE_CASE__							,						SCREAMING_SNAKE_CASE__									= point
			return degrees(atana(y - miny						,			x - minx      )      )

def 		A    (       snake_case__						,			snake_case__						,			snake_case__      ):




			'''simple docstring'''


			SCREAMING_SNAKE_CASE__							,						SCREAMING_SNAKE_CASE__									= starting
			SCREAMING_SNAKE_CASE__							,						SCREAMING_SNAKE_CASE__									= via
			SCREAMING_SNAKE_CASE__							,						SCREAMING_SNAKE_CASE__									= target
			SCREAMING_SNAKE_CASE__									= degrees(atana(ya - ya						,			xa - xa      )      )
			via_angle %= 3_60
			SCREAMING_SNAKE_CASE__									= 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 		A    (       snake_case__      ):




			'''simple docstring'''


			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
			SCREAMING_SNAKE_CASE__									= 0
			SCREAMING_SNAKE_CASE__							,						SCREAMING_SNAKE_CASE__									= maxsize, maxsize
			for i, point in enumerate(snake_case__      ):
						SCREAMING_SNAKE_CASE__									= point[0]
						SCREAMING_SNAKE_CASE__									= point[1]
						if y < miny:
									SCREAMING_SNAKE_CASE__									= y
									SCREAMING_SNAKE_CASE__									= x
									SCREAMING_SNAKE_CASE__									= i
						if y == miny and x < minx:
									SCREAMING_SNAKE_CASE__									= x
									SCREAMING_SNAKE_CASE__									= i

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

			SCREAMING_SNAKE_CASE__									= sorted(snake_case__						,			key=lambda snake_case__      : 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)      )

			SCREAMING_SNAKE_CASE__									= 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.
			SCREAMING_SNAKE_CASE__									= Direction.left

			for i in range(3						,			len(snake_case__      )      ):
						while True:
									SCREAMING_SNAKE_CASE__									= stack[-2]
									SCREAMING_SNAKE_CASE__									= stack[-1]
									SCREAMING_SNAKE_CASE__									= sorted_points[i]
									SCREAMING_SNAKE_CASE__									= check_direction(snake_case__						,			snake_case__						,			snake_case__      )

									if next_direction == Direction.left:
												SCREAMING_SNAKE_CASE__									= 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__      )





"""simple docstring"""




from .hash_table import HashTable





class 				lowerCamelCase  (A__     ):

			def __init__(   self			:  List[str]      ,			*__UpperCAmelCase			:  Union[str, Any]      ,			**__UpperCAmelCase			:  Any    )				->      Optional[int]:
						super().__init__(*__UpperCAmelCase      ,			**__UpperCAmelCase    )





			def    SCREAMING_SNAKE_CASE			(   self			:  List[str]      ,			__UpperCAmelCase			:  int      ,			__UpperCAmelCase			:  Union[str, Any]=None    )				->      Optional[int]:
						SCREAMING_SNAKE_CASE__									= 1
						SCREAMING_SNAKE_CASE__									= self.hash_function(key + i * i    )

						while self.values[new_key] is not None and self.values[new_key] != key:
									i += 1
									SCREAMING_SNAKE_CASE__									= (
									    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


