





import warnings

from ...utils import logging
from .image_processing_owlvit import OwlViTImageProcessor


__lowercase       :Any       =  logging.get_logger(__name__)



class    _a     (				lowercase__							):






							"""simple docstring"""

							def __init__(      self				:     str							,	*a				:     Optional[Any]							,	**a				:     int    )	->None:
													warnings.warn(
													    "The class OwlViTFeatureExtractor is deprecated and will be removed in version 5 of Transformers. Please"
													    " use OwlViTImageProcessor instead."							,	a							,	)
													super().__init__(*a							,	**a    )






def       UpperCAmelCase							(     _lowerCamelCase      :  int			,   _lowerCamelCase      :  bool = 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_317_044_064_679_887_385_961_981 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__     :				List[str]   =					[
						    2_047,
						    1_373_653,
						    25_326_001,
						    3_215_031_751,
						    2_152_302_898_747,
						    3_474_749_660_383,
						    341_550_071_728_321,
						    1,
						    3_825_123_056_546_413_051,
						    1,
						    1,
						    318_665_857_834_031_151_167_461,
						    3_317_044_064_679_887_385_961_981,
						]

						SCREAMING_SNAKE_CASE__     :				Union[str, Any]   =					[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
						for idx, _p in enumerate(_lowerCamelCase			,   1     ):
												if n < _p:
																		# then we have our last prime to check
																		SCREAMING_SNAKE_CASE__     :				Dict   =					primes[:idx]
																		break
						SCREAMING_SNAKE_CASE__,							SCREAMING_SNAKE_CASE__     :				Dict   =					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__     :				str   =					False
												for r in range(_lowerCamelCase     ):
																		SCREAMING_SNAKE_CASE__     :				Optional[Any]   =					pow(_lowerCamelCase			,   d * 2**r			,   _lowerCamelCase     )
																		# see article for analysis explanation for m
																		if (r == 0 and m == 1) or ((m + 1) % n == 0):
																								SCREAMING_SNAKE_CASE__     :				str   =					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       UpperCAmelCase							(     ):





						'''simple docstring'''


						assert not miller_rabin(561     )
						assert miller_rabin(563     )
						# 2047

						assert not miller_rabin(838_201     )
						assert miller_rabin(838_207     )
						# 1_373_653

						assert not miller_rabin(17_316_001     )
						assert miller_rabin(17_316_017     )
						# 25_326_001

						assert not miller_rabin(3_078_386_641     )
						assert miller_rabin(3_078_386_653     )
						# 3_215_031_751

						assert not miller_rabin(1_713_045_574_801     )
						assert miller_rabin(1_713_045_574_819     )
						# 2_152_302_898_747

						assert not miller_rabin(2_779_799_728_307     )
						assert miller_rabin(2_779_799_728_327     )
						# 3_474_749_660_383

						assert not miller_rabin(113_850_023_909_441     )
						assert miller_rabin(113_850_023_909_527     )
						# 341_550_071_728_321

						assert not miller_rabin(1_275_041_018_848_804_351     )
						assert miller_rabin(1_275_041_018_848_804_391     )
						# 3_825_123_056_546_413_051

						assert not miller_rabin(79_666_464_458_507_787_791_867     )
						assert miller_rabin(79_666_464_458_507_787_791_951     )
						# 318_665_857_834_031_151_167_461

						assert not miller_rabin(552_840_677_446_647_897_660_333     )
						assert miller_rabin(552_840_677_446_647_897_660_359     )
						# 3_317_044_064_679_887_385_961_981
						# upper limit for probabilistic test


if __name__ == "__main__":
				test_miller_rabin()