






def 						snake_case      (UpperCAmelCase__			,					UpperCAmelCase__						) ->       int:
		if a < b:
				return gcd(__lowerCAmelCase			,					__lowerCAmelCase						)
		if a % b == 0:
				return b
		return gcd(__lowerCAmelCase			,					a % b						)

def 						snake_case      (UpperCAmelCase__			,					UpperCAmelCase__			,					UpperCAmelCase__						) ->       int:
		if y == 0:
				return 1
		UpperCamelCase_:      Tuple					   =       power(__lowerCAmelCase			,					y // 2			,					__lowerCAmelCase						) % mod
		UpperCamelCase_:      Tuple					   =       (temp * temp) % mod
		if y % 2 == 1:
				UpperCamelCase_:      int					   =       (temp * x) % mod
		return temp

def 						snake_case      (UpperCAmelCase__						) ->       bool:
		UpperCamelCase_:      str					   =       2
		while b < n:
				if gcd(__lowerCAmelCase			,					__lowerCAmelCase						) == 1 and power(__lowerCAmelCase			,					n - 1			,					__lowerCAmelCase						) != 1:
						return False
				b += 1
		return True


if __name__ == "__main__":
			A_	:	Any				=				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_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


A_	:	List[Any]				=				{
    'configuration_openai': ['OPENAI_GPT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'OpenAIGPTConfig'],
    'tokenization_openai': ['OpenAIGPTTokenizer'],
}

try:
   if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   A_	:	List[str]				=				['OpenAIGPTTokenizerFast']

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   A_	:	Any				=				[
       'OPENAI_GPT_PRETRAINED_MODEL_ARCHIVE_LIST',
       'OpenAIGPTDoubleHeadsModel',
       'OpenAIGPTForSequenceClassification',
       'OpenAIGPTLMHeadModel',
       'OpenAIGPTModel',
       'OpenAIGPTPreTrainedModel',
       'load_tf_weights_in_openai_gpt',
   ]

try:
   if not is_tf_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   A_	:	str				=				[
       'TF_OPENAI_GPT_PRETRAINED_MODEL_ARCHIVE_LIST',
       'TFOpenAIGPTDoubleHeadsModel',
       'TFOpenAIGPTForSequenceClassification',
       'TFOpenAIGPTLMHeadModel',
       'TFOpenAIGPTMainLayer',
       'TFOpenAIGPTModel',
       'TFOpenAIGPTPreTrainedModel',
   ]


if TYPE_CHECKING:
   from .configuration_openai import OPENAI_GPT_PRETRAINED_CONFIG_ARCHIVE_MAP, OpenAIGPTConfig
   from .tokenization_openai import OpenAIGPTTokenizer

   try:
      if not is_tokenizers_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_openai_fast import OpenAIGPTTokenizerFast

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_openai import (
          OPENAI_GPT_PRETRAINED_MODEL_ARCHIVE_LIST,
          OpenAIGPTDoubleHeadsModel,
          OpenAIGPTForSequenceClassification,
          OpenAIGPTLMHeadModel,
          OpenAIGPTModel,
          OpenAIGPTPreTrainedModel,
          load_tf_weights_in_openai_gpt,
      )

   try:
      if not is_tf_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_tf_openai import (
          TF_OPENAI_GPT_PRETRAINED_MODEL_ARCHIVE_LIST,
          TFOpenAIGPTDoubleHeadsModel,
          TFOpenAIGPTForSequenceClassification,
          TFOpenAIGPTLMHeadModel,
          TFOpenAIGPTMainLayer,
          TFOpenAIGPTModel,
          TFOpenAIGPTPreTrainedModel,
      )

else:
   import sys

   A_	:	str				=				_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)