

'''simple docstring'''

from __future__ import annotations

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







class   UpperCamelCase__   (       lowercase__       ):


		"""simple docstring"""

		SCREAMING_SNAKE_CASE__  :     Optional[Any]       =							1
		SCREAMING_SNAKE_CASE__  :     Optional[int]       =							2
		SCREAMING_SNAKE_CASE__  :     Dict       =							3







		def __repr__(			self      ):


							'''simple docstring'''

							return f"{self.__class__.__name__}.{self.name}"





def 				lowercase (					__magic_name__			,   __magic_name__			,   __magic_name__							):



					'''simple docstring'''







					UpperCAmelCase ,			UpperCAmelCase		:							Any        =       point
					return degrees(atana(y - miny			,   x - minx							)							)





def 				lowercase (					__magic_name__			,   __magic_name__			,   __magic_name__							):



					'''simple docstring'''







					UpperCAmelCase ,			UpperCAmelCase		:							Optional[Any]        =       starting
					UpperCAmelCase ,			UpperCAmelCase		:							List[Any]        =       via
					UpperCAmelCase ,			UpperCAmelCase		:							List[str]        =       target
					UpperCAmelCase		:							Tuple        =       degrees(atana(ya - ya			,   xa - xa							)							)
					via_angle %= 360
					UpperCAmelCase		:							Optional[int]        =       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 				lowercase (					__magic_name__							):



					'''simple docstring'''







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

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

					UpperCAmelCase		:							Tuple        =       sorted(SCREAMING_SNAKE_CASE_			,   key=lambda __magic_name__							: angle_comparer(SCREAMING_SNAKE_CASE_			,   SCREAMING_SNAKE_CASE_			,   SCREAMING_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		:							List[str]        =       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		:							str        =       Direction.left

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

															if next_direction == Direction.left:
																				UpperCAmelCase		:							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(SCREAMING_SNAKE_CASE_							)



'''simple docstring'''

from ..utils import DummyObject, requires_backends







class   UpperCamelCase__   (       metaclass=lowercase__       ):


		"""simple docstring"""

		SCREAMING_SNAKE_CASE__  :     List[Any]       =							["torch", "transformers", "invisible_watermark"]







		def __init__(			self   ,      *snake_case   ,      **snake_case      ):


							'''simple docstring'''

							requires_backends(self   ,      ["torch", "transformers", "invisible_watermark"]      )







		@classmethod
		def 				A_	(			cls   ,      *snake_case   ,      **snake_case      ):


							'''simple docstring'''

							requires_backends(cls   ,      ["torch", "transformers", "invisible_watermark"]      )







		@classmethod
		def 				A_	(			cls   ,      *snake_case   ,      **snake_case      ):


							'''simple docstring'''

							requires_backends(cls   ,      ["torch", "transformers", "invisible_watermark"]      )







class   UpperCamelCase__   (       metaclass=lowercase__       ):


		"""simple docstring"""

		SCREAMING_SNAKE_CASE__  :     int       =							["torch", "transformers", "invisible_watermark"]







		def __init__(			self   ,      *snake_case   ,      **snake_case      ):


							'''simple docstring'''

							requires_backends(self   ,      ["torch", "transformers", "invisible_watermark"]      )







		@classmethod
		def 				A_	(			cls   ,      *snake_case   ,      **snake_case      ):


							'''simple docstring'''

							requires_backends(cls   ,      ["torch", "transformers", "invisible_watermark"]      )







		@classmethod
		def 				A_	(			cls   ,      *snake_case   ,      **snake_case      ):


							'''simple docstring'''

							requires_backends(cls   ,      ["torch", "transformers", "invisible_watermark"]      )
