






__UpperCAmelCase      =				{
    "0": 1,
    "1": 1,
    "2": 2,
    "3": 6,
    "4": 2_4,
    "5": 1_2_0,
    "6": 7_2_0,
    "7": 5_0_4_0,
    "8": 4_0_3_2_0,
    "9": 3_6_2_8_8_0,
}

__UpperCAmelCase      =				{1_4_5: 1_4_5}

__UpperCAmelCase      =				{
    1_4_5: 0,
    1_6_9: 3,
    3_6_3_0_1: 3,
    1_4_5_4: 3,
    8_7_1: 2,
    4_5_3_6_1: 2,
    8_7_2: 2,
}





def 						A_					(						lowercase_			)				->int:







 """simple docstring"""

 if n in CACHE_SUM_DIGIT_FACTORIALS:
  return CACHE_SUM_DIGIT_FACTORIALS[n]
 SCREAMING_SNAKE_CASE				    =		sum(DIGIT_FACTORIALS[let] for let in str(lowercase_			)			)
 SCREAMING_SNAKE_CASE				    =		ret
 return ret





def 						A_					(						lowercase_	,  lowercase_ = None			)				->int:







 """simple docstring"""

 SCREAMING_SNAKE_CASE				    =		previous or set()
 if n in CHAIN_LENGTH_CACHE:
  return CHAIN_LENGTH_CACHE[n]
 SCREAMING_SNAKE_CASE				    =		sum_digit_factorials(lowercase_			)
 if next_number in previous:
  SCREAMING_SNAKE_CASE				    =		0
  return 0
 else:
  previous.add(lowercase_			)
  SCREAMING_SNAKE_CASE				    =		1 + chain_length(lowercase_	,  lowercase_			)
  SCREAMING_SNAKE_CASE				    =		ret
  return ret





def 						A_					(						lowercase_ = 6_0	,  lowercase_ = 1_0_0_0_0_0_0			)				->int:







 """simple docstring"""

 return sum(1 for i in range(1	,  lowercase_			) if chain_length(lowercase_			) == num_terms			)


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












import copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging
from ..auto.configuration_auto import AutoConfig


__UpperCAmelCase      =				logging.get_logger(__name__)
class 	a_(		lowercase__	):



     """simple docstring"""



     __snake_case		:				Union[str, Any]  					='''speech-encoder-decoder'''
     __snake_case		:				List[Any]  					=True





     def __init__(		self					:	Any  ,  **lowerCAmelCase__					:	List[Any])							->	Tuple:

      """simple docstring"""
      super().__init__(**lowerCAmelCase__)
      if "encoder" not in kwargs or "decoder" not in kwargs:
       raise ValueError(
           f'''A configuraton of type {self.model_type} cannot be instantiated because not both `encoder` and'''
           f''' `decoder` sub-configurations are passed, but only {kwargs}''')

      SCREAMING_SNAKE_CASE				    =		kwargs.pop('encoder')
      SCREAMING_SNAKE_CASE				    =		encoder_config.pop('model_type')
      SCREAMING_SNAKE_CASE				    =		kwargs.pop('decoder')
      SCREAMING_SNAKE_CASE				    =		decoder_config.pop('model_type')

      SCREAMING_SNAKE_CASE				    =		AutoConfig.for_model(lowerCAmelCase__  ,  **lowerCAmelCase__)
      SCREAMING_SNAKE_CASE				    =		AutoConfig.for_model(lowerCAmelCase__  ,  **lowerCAmelCase__)
      SCREAMING_SNAKE_CASE				    =		True





     @classmethod
     def     __UpperCamelCase						(		cls					:	str  ,  lowerCAmelCase__					:	PretrainedConfig  ,  lowerCAmelCase__					:	PretrainedConfig  ,  **lowerCAmelCase__					:	List[str])							->	PretrainedConfig:

      """simple docstring"""
      logger.info('Setting `config.is_decoder=True` and `config.add_cross_attention=True` for decoder_config')
      SCREAMING_SNAKE_CASE				    =		True
      SCREAMING_SNAKE_CASE				    =		True

      return cls(encoder=encoder_config.to_dict()  ,  decoder=decoder_config.to_dict()  ,  **lowerCAmelCase__)





     def     __UpperCamelCase						(		self					:	str)							->	Union[str, Any]:

      """simple docstring"""
      SCREAMING_SNAKE_CASE				    =		copy.deepcopy(self.__dict__)
      SCREAMING_SNAKE_CASE				    =		self.encoder.to_dict()
      SCREAMING_SNAKE_CASE				    =		self.decoder.to_dict()
      SCREAMING_SNAKE_CASE				    =		self.__class__.model_type
      return output




