



import random






def      __lowercase       (			a__       )    ->			bool:
							__SCREAMING_SNAKE_CASE									= num - 1
							__SCREAMING_SNAKE_CASE									= 0

							while s % 2 == 0:
														__SCREAMING_SNAKE_CASE									= s // 2
														t += 1

							for _ in range(5       ):
														__SCREAMING_SNAKE_CASE									= random.randrange(2							,       num - 1       )
														__SCREAMING_SNAKE_CASE									= pow(a__							,       a__							,       a__       )
														if v != 1:
																					__SCREAMING_SNAKE_CASE									= 0
																					while v != (num - 1):
																												if i == t - 1:
																																			return False
																												else:
																																			__SCREAMING_SNAKE_CASE									= i + 1
																																			__SCREAMING_SNAKE_CASE									= (v**2) % num
							return True






def      __lowercase       (			a__       )    ->			bool:
							if num < 2:
														return False

							__SCREAMING_SNAKE_CASE									= [
							    2,
							    3,
							    5,
							    7,
							    11,
							    13,
							    17,
							    19,
							    23,
							    29,
							    31,
							    37,
							    41,
							    43,
							    47,
							    53,
							    59,
							    61,
							    67,
							    71,
							    73,
							    79,
							    83,
							    89,
							    97,
							    1_01,
							    1_03,
							    1_07,
							    1_09,
							    1_13,
							    1_27,
							    1_31,
							    1_37,
							    1_39,
							    1_49,
							    1_51,
							    1_57,
							    1_63,
							    1_67,
							    1_73,
							    1_79,
							    1_81,
							    1_91,
							    1_93,
							    1_97,
							    1_99,
							    2_11,
							    2_23,
							    2_27,
							    2_29,
							    2_33,
							    2_39,
							    2_41,
							    2_51,
							    2_57,
							    2_63,
							    2_69,
							    2_71,
							    2_77,
							    2_81,
							    2_83,
							    2_93,
							    3_07,
							    3_11,
							    3_13,
							    3_17,
							    3_31,
							    3_37,
							    3_47,
							    3_49,
							    3_53,
							    3_59,
							    3_67,
							    3_73,
							    3_79,
							    3_83,
							    3_89,
							    3_97,
							    4_01,
							    4_09,
							    4_19,
							    4_21,
							    4_31,
							    4_33,
							    4_39,
							    4_43,
							    4_49,
							    4_57,
							    4_61,
							    4_63,
							    4_67,
							    4_79,
							    4_87,
							    4_91,
							    4_99,
							    5_03,
							    5_09,
							    5_21,
							    5_23,
							    5_41,
							    5_47,
							    5_57,
							    5_63,
							    5_69,
							    5_71,
							    5_77,
							    5_87,
							    5_93,
							    5_99,
							    6_01,
							    6_07,
							    6_13,
							    6_17,
							    6_19,
							    6_31,
							    6_41,
							    6_43,
							    6_47,
							    6_53,
							    6_59,
							    6_61,
							    6_73,
							    6_77,
							    6_83,
							    6_91,
							    7_01,
							    7_09,
							    7_19,
							    7_27,
							    7_33,
							    7_39,
							    7_43,
							    7_51,
							    7_57,
							    7_61,
							    7_69,
							    7_73,
							    7_87,
							    7_97,
							    8_09,
							    8_11,
							    8_21,
							    8_23,
							    8_27,
							    8_29,
							    8_39,
							    8_53,
							    8_57,
							    8_59,
							    8_63,
							    8_77,
							    8_81,
							    8_83,
							    8_87,
							    9_07,
							    9_11,
							    9_19,
							    9_29,
							    9_37,
							    9_41,
							    9_47,
							    9_53,
							    9_67,
							    9_71,
							    9_77,
							    9_83,
							    9_91,
							    9_97,
							]

							if num in low_primes:
														return True

							for prime in low_primes:
														if (num % prime) == 0:
																					return False

							return rabin_miller(a__       )






def      __lowercase       (			a__ = 10_24       )    ->			int:
							while True:
														__SCREAMING_SNAKE_CASE									= random.randrange(2 ** (keysize - 1)							,       2 ** (keysize)       )
														if is_prime_low_num(a__       ):
																					return num


if __name__ == "__main__":
			lowerCAmelCase__		:					Dict							=generate_large_prime()
			print(('''Prime number:''', num))
			print(('''is_prime_low_num:''', is_prime_low_num(num)))











from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_torch_available,
)


lowerCAmelCase__		:					str							={'''configuration_vit_mae''': ['''VIT_MAE_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''ViTMAEConfig''']}

try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			lowerCAmelCase__		:					Optional[int]							=[
			    '''VIT_MAE_PRETRAINED_MODEL_ARCHIVE_LIST''',
			    '''ViTMAEForPreTraining''',
			    '''ViTMAELayer''',
			    '''ViTMAEModel''',
			    '''ViTMAEPreTrainedModel''',
			]

try:
			if not is_tf_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			lowerCAmelCase__		:					List[str]							=[
			    '''TFViTMAEForPreTraining''',
			    '''TFViTMAEModel''',
			    '''TFViTMAEPreTrainedModel''',
			]

if TYPE_CHECKING:
			from .configuration_vit_mae import VIT_MAE_PRETRAINED_CONFIG_ARCHIVE_MAP, ViTMAEConfig

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_vit_mae import (
						    VIT_MAE_PRETRAINED_MODEL_ARCHIVE_LIST,
						    ViTMAEForPreTraining,
						    ViTMAELayer,
						    ViTMAEModel,
						    ViTMAEPreTrainedModel,
						)

			try:
						if not is_tf_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_tf_vit_mae import TFViTMAEForPreTraining, TFViTMAEModel, TFViTMAEPreTrainedModel


else:
			import sys

			lowerCAmelCase__		:					Optional[int]							=_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)






