


"""simple docstring"""





snake_case__		:  List[Any]     					=					{
    '''0''': 1,
    '''1''': 1,
    '''2''': 2,
    '''3''': 6,
    '''4''': 24,
    '''5''': 120,
    '''6''': 720,
    '''7''': 5_040,
    '''8''': 40_320,
    '''9''': 362_880,
}

snake_case__		:  Tuple     					=					{145: 145}

snake_case__		:  Optional[int]     					=					{
    145: 0,
    169: 3,
    36_301: 3,
    1_454: 3,
    871: 2,
    45_361: 2,
    872: 2,
}


def   _snake_case    (    _snake_case					:      Union[str, Any]      ):


      if n in CACHE_SUM_DIGIT_FACTORIALS:
            return CACHE_SUM_DIGIT_FACTORIALS[n]
      lowerCAmelCase       :						Dict							= sum(DIGIT_FACTORIALS[let] for let in str(_snake_case      )      )
      lowerCAmelCase       :						Tuple							= ret
      return ret


def   _snake_case    (    _snake_case					:      Dict			, _snake_case					:      Tuple = None      ):
      lowerCAmelCase       :						str							= previous or set()
      if n in CHAIN_LENGTH_CACHE:
            return CHAIN_LENGTH_CACHE[n]
      lowerCAmelCase       :						Optional[Any]							= sum_digit_factorials(_snake_case      )
      if next_number in previous:
            lowerCAmelCase       :						List[str]							= 0
            return 0
      else:
            previous.add(_snake_case      )
            lowerCAmelCase       :						int							= 1 + chain_length(_snake_case			, _snake_case      )
            lowerCAmelCase       :						Any							= ret
            return ret


def   _snake_case    (    _snake_case					:      str = 60			, _snake_case					:      Dict = 1000000      ):
      return sum(1 for i in range(1			, _snake_case      ) if chain_length(_snake_case      ) == num_terms      )


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








import copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging


UpperCamelCase__						=		logging.get_logger(__name__)

UpperCamelCase__						=		{}


class 							__SCREAMING_SNAKE_CASE				(						lowerCamelCase    ):
					_lowerCamelCase						    =					"""fsmt_decoder"""

					def __init__(							self					,			__lowercase=0					,			__lowercase=0   ):







						'''simple docstring'''




						super().__init__()
						lowerCamelCase_				:						Tuple				  =				vocab_size
						lowerCamelCase_				:						Union[str, Any]				  =				bos_token_id


class 							__SCREAMING_SNAKE_CASE				(						lowerCamelCase    ):
					_lowerCamelCase						    =					"""fsmt"""
					_lowerCamelCase						    =					{"""num_attention_heads""": """encoder_attention_heads""", """hidden_size""": """d_model"""}

					def __init__(							self					,			__lowercase=["en", "de"]					,			__lowercase=42_024					,			__lowercase=42_024					,			__lowercase="relu"					,			__lowercase=1_024					,			__lowercase=200					,			__lowercase=1_024					,			__lowercase=4_096					,			__lowercase=12					,			__lowercase=16					,			__lowercase=0.0					,			__lowercase=4_096					,			__lowercase=12					,			__lowercase=16					,			__lowercase=0.0					,			__lowercase=0.0					,			__lowercase=0.1					,			__lowercase=0.0					,			__lowercase=0.02					,			__lowercase=2					,			__lowercase=True					,			__lowercase=True					,			__lowercase=False					,			__lowercase=5					,			__lowercase=1.0					,			__lowercase=False					,			__lowercase=True					,			__lowercase=1					,			__lowercase=0					,			__lowercase=2					,			__lowercase=2					,			**__lowercase					,			):







						'''simple docstring'''




						lowerCamelCase_				:						Any				  =				langs
						lowerCamelCase_				:						Union[str, Any]				  =				src_vocab_size
						lowerCamelCase_				:						Tuple				  =				tgt_vocab_size
						lowerCamelCase_				:						List[Any]				  =				d_model  # encoder_embed_dim and decoder_embed_dim

						lowerCamelCase_				:						str				  =				encoder_ffn_dim
						lowerCamelCase_				:						str				  =				encoder_layers
						lowerCamelCase_				:						Dict				  =				encoder_attention_heads
						lowerCamelCase_				:						Any				  =				encoder_layerdrop
						lowerCamelCase_				:						Union[str, Any]				  =				decoder_layerdrop
						lowerCamelCase_				:						Optional[int]				  =				decoder_ffn_dim
						lowerCamelCase_				:						List[str]				  =				decoder_layers
						lowerCamelCase_				:						int				  =				decoder_attention_heads
						lowerCamelCase_				:						List[str]				  =				max_position_embeddings
						lowerCamelCase_				:						int				  =				init_std  # Normal(0, this parameter)
						lowerCamelCase_				:						Optional[Any]				  =				activation_function

						lowerCamelCase_				:						Union[str, Any]				  =				DecoderConfig(vocab_size=__lowercase					,			bos_token_id=__lowercase   )
						if "decoder" in common_kwargs:
							del common_kwargs["decoder"]

						lowerCamelCase_				:						int				  =				scale_embedding  # scale factor will be sqrt(d_model) if True

						# 3 Types of Dropout
						lowerCamelCase_				:						Optional[int]				  =				attention_dropout
						lowerCamelCase_				:						Union[str, Any]				  =				activation_dropout
						lowerCamelCase_				:						Dict				  =				dropout

						lowerCamelCase_				:						Optional[int]				  =				use_cache
						super().__init__(
						    pad_token_id=__lowercase					,			bos_token_id=__lowercase					,			eos_token_id=__lowercase					,			decoder_start_token_id=__lowercase					,			is_encoder_decoder=__lowercase					,			tie_word_embeddings=__lowercase					,			forced_eos_token_id=__lowercase					,			max_length=__lowercase					,			num_beams=__lowercase					,			length_penalty=__lowercase					,			early_stopping=__lowercase					,			**__lowercase					,			)





					def       lowercase_				(							self   ):







						'''simple docstring'''




						lowerCamelCase_				:						List[Any]				  =				copy.deepcopy(self.__dict__   )
						lowerCamelCase_				:						Optional[int]				  =				self.decoder.to_dict()
						lowerCamelCase_				:						Dict				  =				self.__class__.model_type
						return output
