






from __future__ import annotations

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


class      __SCREAMING_SNAKE_CASE       ( _a):
						_SCREAMING_SNAKE_CASE						:							int				=       1
						_SCREAMING_SNAKE_CASE						:							Optional[int]				=       2
						_SCREAMING_SNAKE_CASE						:							Tuple				=       3






						def __repr__(						self ):






												"""simple docstring"""
												return F"{self.__class__.__name__}.{self.name}"







def 						_UpperCamelCase (     UpperCamelCase_							:       tuple[int, int]     ,							UpperCamelCase_							:       int     ,							UpperCamelCase_							:       int		)	-> Optional[Any]:

						"""simple docstring"""



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







def 						_UpperCamelCase (     UpperCamelCase_							:       tuple[int, int]     ,							UpperCamelCase_							:       tuple[int, int]     ,							UpperCamelCase_							:       tuple[int, int]		)	-> Optional[int]:

						"""simple docstring"""



						lowerCAmelCase__         =    starting
						lowerCAmelCase__         =    via
						lowerCAmelCase__         =    target
						lowerCAmelCase__         =    degrees(atana(ya - ya     ,							xa - xa		)		)
						via_angle %= 360
						lowerCAmelCase__         =    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 (     UpperCamelCase_							:       list[tuple[int, int]]		)	-> Dict:

						"""simple docstring"""



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

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

						lowerCAmelCase__         =    sorted(_lowercase     ,							key=lambda UpperCamelCase_		: angle_comparer(_lowercase     ,							_lowercase     ,							_lowercase		)		)
						# 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)		)

						lowerCAmelCase__         =    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.
						lowerCAmelCase__         =    Direction.left

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

																		if next_direction == Direction.left:
																								lowerCAmelCase__         =    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(_lowercase		)









'''simple docstring'''



import os
import unittest

import pytest
from parameterized import parameterized

from transformers.testing_utils import require_torch, require_torch_gpu, slow, torch_device


# skipping in unittest tests

__UpperCAmelCase     :Tuple												=  [(1,)]




def       _a      (		):





     '''simple docstring'''






     __UpperCAmelCase      :					Any    				=     bool(os.getenv('''RUN_SLOW'''     ,   0    )    )
     if run_slow:
          assert True
     else:
          assert False, "should have been skipped"




def       _a      (		):





     '''simple docstring'''






     __UpperCAmelCase      :					str    				=     bool(os.getenv('''RUN_SLOW'''     ,   0    )    )
     if run_slow and torch_device == "cuda":
          assert True
     else:
          assert False, "should have been skipped"



@require_torch
class       a							(						unittest.TestCase			):


     """simple docstring"""






     @slow
     @require_torch_gpu
     def 					lowerCamelCase__					(							self	:						Tuple     )		->				str:
          check_slow_torch_cuda()

     @require_torch_gpu
     @slow
     def 					lowerCamelCase__					(							self	:						Any     )		->				List[Any]:
          check_slow_torch_cuda()






     @parameterized.expand(snake_case     )
     @slow
     def 					lowerCamelCase__					(							self	:						Union[str, Any]				,					snake_case	:						int=None     )		->				Union[str, Any]:
          check_slow()




@slow
@require_torch_gpu
def       _a      (		):





     '''simple docstring'''






     check_slow_torch_cuda()




@require_torch_gpu
@slow
def       _a      (		):





     '''simple docstring'''






     check_slow_torch_cuda()




@slow
@pytest.mark.parametrize('''param'''     ,   [1]    )
def       _a      (		_lowercase   :      Union[str, Any]    ):





     '''simple docstring'''






     check_slow()




@pytest.mark.parametrize('''param'''     ,   [1]    )
@slow
def       _a      (		_lowercase   :      Dict    ):





     '''simple docstring'''






     check_slow()