

"""simple docstring"""




def 						A							(  snake_case__		,					snake_case__ = False     ):




			'''simple docstring'''


			if n == 2:
						return True
			if not n % 2 or n < 2:
						return False
			if n > 5 and n % 10 not in (1, 3, 7, 9):  # can quickly check last digit
						return False
			if n > 3_31_70_44_06_46_79_88_73_85_96_19_81 and not allow_probable:
						raise ValueError(
						    """Warning: upper bound of deterministic test is exceeded. """
						    """Pass allow_probable=True to allow probabilistic test. """
						    """A return value of True indicates a probable prime."""     )
			# array bounds provided by analysis
			SCREAMING_SNAKE_CASE__										=   [
			    20_47,
			    1_37_36_53,
			    25_32_60_01,
			    32_15_03_17_51,
			    2_15_23_02_89_87_47,
			    3_47_47_49_66_03_83,
			    3_41_55_00_71_72_83_21,
			    1,
			    3_82_51_23_05_65_46_41_30_51,
			    1,
			    1,
			    31_86_65_85_78_34_03_11_51_16_74_61,
			    3_31_70_44_06_46_79_88_73_85_96_19_81,
			]

			SCREAMING_SNAKE_CASE__										=   [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
			for idx, _p in enumerate(snake_case__		,					1     ):
						if n < _p:
									# then we have our last prime to check
									SCREAMING_SNAKE_CASE__										=   primes[:idx]
									break
			SCREAMING_SNAKE_CASE__				,		SCREAMING_SNAKE_CASE__										=   n - 1, 0
			# break up n -1 into a power of 2 (s) and
			# remaining odd component
			# essentially, solve for d * 2 ** s == n - 1
			while d % 2 == 0:
						d //= 2
						s += 1
			for prime in plist:
						SCREAMING_SNAKE_CASE__										=   False
						for r in range(snake_case__     ):
									SCREAMING_SNAKE_CASE__										=   pow(snake_case__		,					d * 2**r		,					snake_case__     )
									# see article for analysis explanation for m
									if (r == 0 and m == 1) or ((m + 1) % n == 0):
												SCREAMING_SNAKE_CASE__										=   True
												# this loop will not determine compositeness
												break
						if pr:
									continue
						# if pr is False, then the above loop never evaluated to true,
						# and the n MUST be composite
						return False
			return True

def 						A							(  ):




			'''simple docstring'''


			assert not miller_rabin(5_61     )
			assert miller_rabin(5_63     )
			# 2047

			assert not miller_rabin(83_82_01     )
			assert miller_rabin(83_82_07     )
			# 1_373_653

			assert not miller_rabin(17_31_60_01     )
			assert miller_rabin(17_31_60_17     )
			# 25_326_001

			assert not miller_rabin(30_78_38_66_41     )
			assert miller_rabin(30_78_38_66_53     )
			# 3_215_031_751

			assert not miller_rabin(1_71_30_45_57_48_01     )
			assert miller_rabin(1_71_30_45_57_48_19     )
			# 2_152_302_898_747

			assert not miller_rabin(2_77_97_99_72_83_07     )
			assert miller_rabin(2_77_97_99_72_83_27     )
			# 3_474_749_660_383

			assert not miller_rabin(1_13_85_00_23_90_94_41     )
			assert miller_rabin(1_13_85_00_23_90_95_27     )
			# 341_550_071_728_321

			assert not miller_rabin(1_27_50_41_01_88_48_80_43_51     )
			assert miller_rabin(1_27_50_41_01_88_48_80_43_91     )
			# 3_825_123_056_546_413_051

			assert not miller_rabin(7_96_66_46_44_58_50_77_87_79_18_67     )
			assert miller_rabin(7_96_66_46_44_58_50_77_87_79_19_51     )
			# 318_665_857_834_031_151_167_461

			assert not miller_rabin(55_28_40_67_74_46_64_78_97_66_03_33     )
			assert miller_rabin(55_28_40_67_74_46_64_78_97_66_03_59     )
			# 3_317_044_064_679_887_385_961_981
			# upper limit for probabilistic test


if __name__ == "__main__":
						test_miller_rabin()





"""simple docstring"""




from typing import List

from .keymap import KEYMAP, get_character

def 						A							(  snake_case__     ):




			'''simple docstring'''


			def decorator(snake_case__     ):
						SCREAMING_SNAKE_CASE__										=   getattr(snake_case__		,					"""handle_key"""		,					[]     )
						handle += [key]
						setattr(snake_case__		,					"""handle_key"""		,					snake_case__     )
						return func

			return decorator

def 						A							(  *snake_case__     ):




			'''simple docstring'''


			def decorator(snake_case__     ):
						SCREAMING_SNAKE_CASE__										=   getattr(snake_case__		,					"""handle_key"""		,					[]     )
						handle += keys
						setattr(snake_case__		,					"""handle_key"""		,					snake_case__     )
						return func

			return decorator





class  lowerCamelCase    (A__      ):

			def __new__(       cls					:    Dict     ,					__UpperCAmelCase					:    Tuple     ,					__UpperCAmelCase					:    Any     ,					__UpperCAmelCase					:    Optional[Any]							) ->     List[str]:
						SCREAMING_SNAKE_CASE__										=   super().__new__(cls     ,					__UpperCAmelCase     ,					__UpperCAmelCase     ,					__UpperCAmelCase							)
						if not hasattr(__UpperCAmelCase     ,					"""key_handler"""							):
									setattr(__UpperCAmelCase     ,					"""key_handler"""     ,					{}							)
						setattr(__UpperCAmelCase     ,					"""handle_input"""     ,					KeyHandler.handle_input							)

						for value in attrs.values():
									SCREAMING_SNAKE_CASE__										=   getattr(__UpperCAmelCase     ,					"""handle_key"""     ,					[]							)
									for key in handled_keys:
												SCREAMING_SNAKE_CASE__										=   value
						return new_cls





			@staticmethod
			def        SCREAMING_SNAKE_CASE					(       cls					:    Tuple							) ->     Dict:
						SCREAMING_SNAKE_CASE__										=   get_character()
						if char != KEYMAP["undefined"]:
									SCREAMING_SNAKE_CASE__										=   ord(__UpperCAmelCase							)
						SCREAMING_SNAKE_CASE__										=   cls.key_handler.get(__UpperCAmelCase							)
						if handler:
									SCREAMING_SNAKE_CASE__										=   char
									return handler(cls							)
						else:
									return None

def 						A							(  cls     ):




			'''simple docstring'''


			return KeyHandler(cls.__name__		,					cls.__bases__		,					cls.__dict__.copy()     )


