code: '''simple docstring'''
  
  def        SCREAMING_SNAKE_CASE__(		_UpperCamelCase      :				Optional[int]    ,		_UpperCamelCase      :				Dict   )		->					int:
  
  
  
  
  
     '''simple docstring'''
  
  
  
  
  
  
  
     if a < b:
        return gcd(__lowerCAmelCase    ,		__lowerCAmelCase   )
     if a % b == 0:
        return b
     return gcd(__lowerCAmelCase    ,		a % b   )
  
  
  
  def        SCREAMING_SNAKE_CASE__(		_UpperCamelCase      :				Optional[Any]    ,		_UpperCamelCase      :				Optional[Any]    ,		_UpperCamelCase      :				Optional[int]   )		->					int:
  
  
  
  
  
     '''simple docstring'''
  
  
  
  
  
  
  
     if y == 0:
        return 1
     UpperCamelCase__ 						=						power(__lowerCAmelCase    ,		y // 2    ,		__lowerCAmelCase   ) % mod
     UpperCamelCase__ 						=						(temp * temp) % mod
     if y % 2 == 1:
        UpperCamelCase__ 						=						(temp * x) % mod
     return temp
  
  
  
  def        SCREAMING_SNAKE_CASE__(		_UpperCamelCase      :				Union[str, Any]   )		->					bool:
  
  
  
  
  
     '''simple docstring'''
  
  
  
  
  
  
  
     UpperCamelCase__ 						=						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__":
         __lowercase:		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.""")
style_context: 
  
  
  '''simple docstring'''
  
  from typing import TYPE_CHECKING
  
  from ...utils import (
      OptionalDependencyNotAvailable,
      _LazyModule,
      is_sentencepiece_available,
      is_tokenizers_available,
      is_torch_available,
  )
  
  
  __lowercase:		int							=     {
      "configuration_open_llama": ["OPEN_LLAMA_PRETRAINED_CONFIG_ARCHIVE_MAP", "OpenLlamaConfig"],
  }
  
  try:
         if not is_sentencepiece_available():
                raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
         pass
  else:
         __lowercase:		str							=     ["LlamaTokenizer"]
  
  try:
         if not is_tokenizers_available():
                raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
         pass
  else:
         __lowercase:		List[Any]							=     ["LlamaTokenizerFast"]
  
  try:
         if not is_torch_available():
                raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
         pass
  else:
         __lowercase:		Union[str, Any]							=     [
             "OpenLlamaForCausalLM",
             "OpenLlamaModel",
             "OpenLlamaPreTrainedModel",
             "OpenLlamaForSequenceClassification",
         ]
  
  
  if TYPE_CHECKING:
         from .configuration_open_llama import OPEN_LLAMA_PRETRAINED_CONFIG_ARCHIVE_MAP, OpenLlamaConfig
  
         try:
                if not is_sentencepiece_available():
                       raise OptionalDependencyNotAvailable()
         except OptionalDependencyNotAvailable:
                pass
         else:
                from transformers import LlamaTokenizer
  
         try:
                if not is_tokenizers_available():
                       raise OptionalDependencyNotAvailable()
         except OptionalDependencyNotAvailable:
                pass
         else:
                from transformers import LlamaTokenizerFast
  
         try:
                if not is_torch_available():
                       raise OptionalDependencyNotAvailable()
         except OptionalDependencyNotAvailable:
                pass
         else:
                from .modeling_open_llama import (
                    OpenLlamaForCausalLM,
                    OpenLlamaForSequenceClassification,
                    OpenLlamaModel,
                    OpenLlamaPreTrainedModel,
                )
  
  
  else:
         import sys
  
         __lowercase:		Tuple							=     _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)