from .hash_table import HashTable
from .number_theory.prime_numbers import is_prime, next_prime




class 					_snake_case						(						_lowercase				):
					def __init__(  self:				Any	,  *__lowerCamelCase:				Any	,  **__lowerCamelCase:				Tuple     )    ->				List[str]:
												super().__init__(*__lowerCamelCase	,  **__lowerCamelCase     )
					def    _lowerCamelCase (  self:				Tuple	,  __lowerCamelCase:				str	,  __lowerCamelCase:				Dict     )    ->				int:
												__UpperCAmelCase						:			Union[str, Any]         =   (
												    next_prime(value % self.size_table     )
												    if not is_prime(value % self.size_table     )
												    else value % self.size_table
												)  # gt = bigger than
												return next_prime_gt - (data % next_prime_gt)
					def    _lowerCamelCase (  self:				str	,  __lowerCamelCase:				Optional[Any]	,  __lowerCamelCase:				int	,  __lowerCamelCase:				List[Any]     )    ->				str:
												return (increment * self.__hash_function_a(__lowerCamelCase	,  __lowerCamelCase     )) % self.size_table





					def    _lowerCamelCase (  self:				Optional[int]	,  __lowerCamelCase:				int	,  __lowerCamelCase:				str=None     )    ->				List[str]:
												__UpperCAmelCase						:			Optional[int]         =   1
												__UpperCAmelCase						:			Optional[int]         =   self.hash_function(__lowerCamelCase     )

												while self.values[new_key] is not None and self.values[new_key] != key:
																			__UpperCAmelCase						:			Tuple         =   (
																			    self.__hash_double_function(__lowerCamelCase	,  __lowerCamelCase	,  __lowerCamelCase     )
																			    if self.balanced_factor() >= self.lim_charge
																			    else None
																			)
																			if new_key is None:
																										break
																			else:
																										i += 1

												return new_key





from __future__ import annotations

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




class 					_snake_case						(						_lowercase				):
					lowerCamelCase__:		Tuple  =     1
					lowerCamelCase__:		Dict  =     2
					lowerCamelCase__:		List[str]  =     3
					def __repr__(  self:				List[Any]     )    ->				int:
												return f'''{self.__class__.__name__}.{self.name}'''




def   _UpperCamelCase   (			snake_case__,    snake_case__,    snake_case__							)						->   float:
							__UpperCAmelCase    ,	__UpperCAmelCase						:			Optional[Any]         =   point
							return degrees(atana(y - miny,    x - minx							)							)




def   _UpperCamelCase   (			snake_case__,    snake_case__,    snake_case__							)						->   Direction:
							__UpperCAmelCase    ,	__UpperCAmelCase						:			List[Any]         =   starting
							__UpperCAmelCase    ,	__UpperCAmelCase						:			Optional[int]         =   via
							__UpperCAmelCase    ,	__UpperCAmelCase						:			List[str]         =   target
							__UpperCAmelCase						:			Tuple         =   degrees(atana(ya - ya,    xa - xa							)							)
							via_angle %= 360
							__UpperCAmelCase						:			str         =   degrees(atana(ya - ya,    xa - xa							)							)
							target_angle %= 360
							# 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   _UpperCamelCase   (			snake_case__							)						->   list[tuple[int, int]]:

							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
							__UpperCAmelCase						:			str         =   0
							__UpperCAmelCase    ,	__UpperCAmelCase						:			Any         =   maxsize, maxsize
							for i, point in enumerate(snake_case__							):
														__UpperCAmelCase						:			str         =   point[0]
														__UpperCAmelCase						:			Any         =   point[1]
														if y < miny:
																					__UpperCAmelCase						:			Tuple         =   y
																					__UpperCAmelCase						:			int         =   x
																					__UpperCAmelCase						:			str         =   i
														if y == miny and x < minx:
																					__UpperCAmelCase						:			Any         =   x
																					__UpperCAmelCase						:			Dict         =   i

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

							__UpperCAmelCase						:			Any         =   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)							)

							__UpperCAmelCase						:			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.
							__UpperCAmelCase						:			Any         =   Direction.left

							for i in range(3,    len(snake_case__							)							):
														while True:
																					__UpperCAmelCase						:			List[Any]         =   stack[-2]
																					__UpperCAmelCase						:			Tuple         =   stack[-1]
																					__UpperCAmelCase						:			Any         =   sorted_points[i]
																					__UpperCAmelCase						:			Optional[Any]         =   check_direction(snake_case__,    snake_case__,    snake_case__							)

																					if next_direction == Direction.left:
																												__UpperCAmelCase						:			Optional[int]         =   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__							)




