






UpperCAmelCase__            =	{
    "0": 1,
    "1": 1,
    "2": 2,
    "3": 6,
    "4": 24,
    "5": 120,
    "6": 720,
    "7": 5040,
    "8": 40320,
    "9": 362880,
}

UpperCAmelCase__            =	{145: 145}

UpperCAmelCase__            =	{
    145: 0,
    169: 3,
    36301: 3,
    1454: 3,
    871: 2,
    45361: 2,
    872: 2,
}
def 		_a					(   a				:int				)							->    int:
 if n in CACHE_SUM_DIGIT_FACTORIALS:
  return CACHE_SUM_DIGIT_FACTORIALS[n]
 a							=   sum(DIGIT_FACTORIALS[let] for let in str(a				)				)
 a							=   ret
 return ret
def 		_a					(   a				:int			,							a				:set | None = None				)							->    int:
 a							=   previous or set()
 if n in CHAIN_LENGTH_CACHE:
  return CHAIN_LENGTH_CACHE[n]
 a							=   sum_digit_factorials(a				)
 if next_number in previous:
  a							=   0
  return 0
 else:
  previous.add(a				)
  a							=   1 + chain_length(a			,							a				)
  a							=   ret
  return ret
def 		_a					(   a				:int = 60			,							a				:int = 1_000_000				)							->    int:
 return sum(1 for i in range(1			,							a				) if chain_length(a				) == num_terms				)


if __name__ == "__main__":
  print(f"""{solution() = }""")










import warnings

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding






class 	lowercase_      (			lowercase     ):






      '''simple docstring'''




      __snake_case  						=						['''image_processor''', '''tokenizer''']
      __snake_case  						=						'''AutoImageProcessor'''
      __snake_case  						=						'''AutoTokenizer'''







      def __init__(   self   :		Any				,      __UpperCAmelCase   :		Union[str, Any]=None				,      __UpperCAmelCase   :		int=None				,      **__UpperCAmelCase   :		Union[str, Any]						)					->Dict:




       """simple docstring"""


       a							=   None
       if "feature_extractor" in kwargs:
        warnings.warn(
            '''The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`'''
            ''' instead.'''				,      __UpperCAmelCase				,      )
        a							=   kwargs.pop('''feature_extractor'''						)

       a							=   image_processor if image_processor is not None else feature_extractor
       if image_processor is None:
        raise ValueError('''You have to specify an image_processor.'''						)
       if tokenizer is None:
        raise ValueError('''You have to specify a tokenizer.'''						)

       super().__init__(__UpperCAmelCase				,      __UpperCAmelCase						)
       a							=   self.image_processor







      def __call__(   self   :		List[Any]				,      __UpperCAmelCase   :		Optional[Any]=None				,      __UpperCAmelCase   :		Optional[int]=None				,      __UpperCAmelCase   :		str=None				,      **__UpperCAmelCase   :		List[Any]						)					->Dict:




       """simple docstring"""


       if text is None and images is None:
        raise ValueError('''You have to specify either text or images. Both cannot be none.'''						)

       if text is not None:
        a							=   self.tokenizer(__UpperCAmelCase				,      return_tensors=__UpperCAmelCase				,      **__UpperCAmelCase						)

       if images is not None:
        a							=   self.image_processor(__UpperCAmelCase				,      return_tensors=__UpperCAmelCase				,      **__UpperCAmelCase						)

       if text is not None and images is not None:
        a							=   image_features.pixel_values
        return encoding
       elif text is not None:
        return encoding
       else:
        return BatchEncoding(data=dict(**__UpperCAmelCase						)				,      tensor_type=__UpperCAmelCase						)







      def    __lowerCAmelCase      (   self   :		List[Any]				,      *__UpperCAmelCase   :		Optional[Any]				,      **__UpperCAmelCase   :		List[str]						)					->Optional[Any]:




       """simple docstring"""


       return self.tokenizer.batch_decode(*__UpperCAmelCase				,      **__UpperCAmelCase						)







      def    __lowerCAmelCase      (   self   :		str				,      *__UpperCAmelCase   :		List[Any]				,      **__UpperCAmelCase   :		Optional[Any]						)					->Union[str, Any]:




       """simple docstring"""


       return self.tokenizer.decode(*__UpperCAmelCase				,      **__UpperCAmelCase						)







      @property
      def    __lowerCAmelCase      (   self   :		str						)					->str:




       """simple docstring"""


       a							=   self.tokenizer.model_input_names
       a							=   self.image_processor.model_input_names
       return list(dict.fromkeys(tokenizer_input_names + image_processor_input_names						)						)







      @property
      def    __lowerCAmelCase      (   self   :		str						)					->Optional[Any]:




       """simple docstring"""


       warnings.warn(
           '''`feature_extractor_class` is deprecated and will be removed in v5. Use `image_processor_class` instead.'''				,      __UpperCAmelCase				,      )
       return self.image_processor_class







      @property
      def    __lowerCAmelCase      (   self   :		int						)					->Optional[Any]:




       """simple docstring"""


       warnings.warn(
           '''`feature_extractor` is deprecated and will be removed in v5. Use `image_processor` instead.'''				,      __UpperCAmelCase				,      )
       return self.image_processor


