
def 						a_      (__A							,					__A			)							->	Optional[Any]:



					"""simple docstring"""
					if a < b:
										return gcd(__A							,					__A			)
					if a % b == 0:
										return b
					return gcd(__A							,					a % b			)







def 						a_      (__A							,					__A							,					__A			)							->	Optional[Any]:



					"""simple docstring"""
					if y == 0:
										return 1
					__a				:	Tuple			=				power(__A							,					y // 2							,					__A			) % mod
					__a				:	str			=				(temp * temp) % mod
					if y % 2 == 1:
										__a				:	int			=				(temp * x) % mod
					return temp







def 						a_      (__A			)							->	List[Any]:



					"""simple docstring"""
					__a				:	Optional[Any]			=				2
					while b < n:
										if gcd(__A							,					__A			) == 1 and power(__A							,					n - 1							,					__A			) != 1:
															return False
										b += 1
					return True


if __name__ == "__main__":
			UpperCAmelCase__			 =	int(input('''Enter number: ''').strip())
			if is_carmichael_number(number):
						print(F"{number} is a Carmichael Number.")
			else:
						print(F"{number} is not a Carmichael Number.")













from typing import TYPE_CHECKING

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


UpperCAmelCase__			 =	{'''configuration_pegasus''': ['''PEGASUS_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''PegasusConfig''']}

try:
			if not is_sentencepiece_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			UpperCAmelCase__			 =	['''PegasusTokenizer''']

try:
			if not is_tokenizers_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			UpperCAmelCase__			 =	['''PegasusTokenizerFast''']

try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			UpperCAmelCase__			 =	[
			    '''PEGASUS_PRETRAINED_MODEL_ARCHIVE_LIST''',
			    '''PegasusForCausalLM''',
			    '''PegasusForConditionalGeneration''',
			    '''PegasusModel''',
			    '''PegasusPreTrainedModel''',
			]

try:
			if not is_tf_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			UpperCAmelCase__			 =	[
			    '''TFPegasusForConditionalGeneration''',
			    '''TFPegasusModel''',
			    '''TFPegasusPreTrainedModel''',
			]

try:
			if not is_flax_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			UpperCAmelCase__			 =	[
			    '''FlaxPegasusForConditionalGeneration''',
			    '''FlaxPegasusModel''',
			    '''FlaxPegasusPreTrainedModel''',
			]


if TYPE_CHECKING:
			from .configuration_pegasus import PEGASUS_PRETRAINED_CONFIG_ARCHIVE_MAP, PegasusConfig

			try:
						if not is_sentencepiece_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .tokenization_pegasus import PegasusTokenizer

			try:
						if not is_tokenizers_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .tokenization_pegasus_fast import PegasusTokenizerFast

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_pegasus import (
						    PEGASUS_PRETRAINED_MODEL_ARCHIVE_LIST,
						    PegasusForCausalLM,
						    PegasusForConditionalGeneration,
						    PegasusModel,
						    PegasusPreTrainedModel,
						)

			try:
						if not is_tf_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_tf_pegasus import TFPegasusForConditionalGeneration, TFPegasusModel, TFPegasusPreTrainedModel

			try:
						if not is_flax_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_flax_pegasus import (
						    FlaxPegasusForConditionalGeneration,
						    FlaxPegasusModel,
						    FlaxPegasusPreTrainedModel,
						)

else:
			import sys

			UpperCAmelCase__			 =	_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)





