
'''simple docstring'''
def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE = False				):
							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_3170_4406_4679_8873_8596_1981 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
							_snake_case       =  [
							    2047,
							    137_3653,
							    2532_6001,
							    32_1503_1751,
							    2_1523_0289_8747,
							    3_4747_4966_0383,
							    341_5500_7172_8321,
							    1,
							    382_5123_0565_4641_3051,
							    1,
							    1,
							    3186_6585_7834_0311_5116_7461,
							    3_3170_4406_4679_8873_8596_1981,
							]

							_snake_case       =  [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
							for idx, _p in enumerate(UpperCAmelCase_							, 1				):
														if n < _p:
																					# then we have our last prime to check
																					_snake_case       =  primes[:idx]
																					break
							_snake_case,							_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:
														_snake_case       =  False
														for r in range(UpperCAmelCase_				):
																					_snake_case       =  pow(UpperCAmelCase_							, d * 2**r							, UpperCAmelCase_				)
																					# see article for analysis explanation for m
																					if (r == 0 and m == 1) or ((m + 1) % n == 0):
																												_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  __SCREAMING_SNAKE_CASE				(  ):
							assert not miller_rabin(561				)
							assert miller_rabin(563				)
							# 2047

							assert not miller_rabin(83_8201				)
							assert miller_rabin(83_8207				)
							# 1_373_653

							assert not miller_rabin(1731_6001				)
							assert miller_rabin(1731_6017				)
							# 25_326_001

							assert not miller_rabin(30_7838_6641				)
							assert miller_rabin(30_7838_6653				)
							# 3_215_031_751

							assert not miller_rabin(1_7130_4557_4801				)
							assert miller_rabin(1_7130_4557_4819				)
							# 2_152_302_898_747

							assert not miller_rabin(2_7797_9972_8307				)
							assert miller_rabin(2_7797_9972_8327				)
							# 3_474_749_660_383

							assert not miller_rabin(113_8500_2390_9441				)
							assert miller_rabin(113_8500_2390_9527				)
							# 341_550_071_728_321

							assert not miller_rabin(127_5041_0188_4880_4351				)
							assert miller_rabin(127_5041_0188_4880_4391				)
							# 3_825_123_056_546_413_051

							assert not miller_rabin(796_6646_4458_5077_8779_1867				)
							assert miller_rabin(796_6646_4458_5077_8779_1951				)
							# 318_665_857_834_031_151_167_461

							assert not miller_rabin(5528_4067_7446_6478_9766_0333				)
							assert miller_rabin(5528_4067_7446_6478_9766_0359				)
							# 3_317_044_064_679_887_385_961_981
							# upper limit for probabilistic test


if __name__ == "__main__":
				test_miller_rabin()








'''simple docstring'''
import warnings

from diffusers import StableDiffusionInpaintPipeline as StableDiffusionInpaintPipeline  # noqa F401


warnings.warn(
    'The `inpainting.py` script is outdated. Please use directly `from diffusers import'
    ' StableDiffusionInpaintPipeline` instead.'
)