





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


__lowerCAmelCase :Dict     =    logging.get_logger(__name__)

__lowerCAmelCase :Optional[Any]     =    {
    "facebook/nllb-moe-54B": "https://huggingface.co/facebook/nllb-moe-54b/resolve/main/config.json",
}






class        _a(    __lowerCAmelCase    ):
		lowerCamelCase__     :Dict   				=		"nllb-moe"
		lowerCamelCase__     :Any   				=		["past_key_values"]
		lowerCamelCase__     :Optional[int]   				=		{"num_attention_heads": "encoder_attention_heads", "hidden_size": "d_model"}







		def __init__(    self ,						__snake_case=1_2_8_1_1_2 ,						__snake_case=1_0_2_4 ,						__snake_case=1_2 ,						__snake_case=4_0_9_6 ,						__snake_case=1_6 ,						__snake_case=1_2 ,						__snake_case=4_0_9_6 ,						__snake_case=1_6 ,						__snake_case=0.05 ,						__snake_case=0.05 ,						__snake_case=True ,						__snake_case=True ,						__snake_case="relu" ,						__snake_case=1_0_2_4 ,						__snake_case=0.1 ,						__snake_case=0.1 ,						__snake_case=0.0 ,						__snake_case=0.02 ,						__snake_case=2 ,						__snake_case=True ,						__snake_case=False ,						__snake_case="float32" ,						__snake_case=False ,						__snake_case=1_2_8 ,						__snake_case=6_4 ,						__snake_case=4 ,						__snake_case=4 ,						__snake_case=0.0_01 ,						__snake_case=0.0_01 ,						__snake_case="all" ,						__snake_case=False ,						__snake_case=False ,						__snake_case=1.0 ,						__snake_case=0.2 ,						__snake_case=1 ,						__snake_case=0 ,						__snake_case=2 ,						__snake_case=False ,						**__snake_case ,						)      ->      Tuple:


							'''simple docstring'''

							_snake_case       :					Optional[int]				       =   vocab_size
							_snake_case       :					List[Any]				       =   max_position_embeddings
							_snake_case       :					str				       =   d_model
							_snake_case       :					Union[str, Any]				       =   encoder_ffn_dim
							_snake_case       :					Optional[int]				       =   encoder_layers
							_snake_case       :					Tuple				       =   encoder_attention_heads
							_snake_case       :					Union[str, Any]				       =   decoder_ffn_dim
							_snake_case       :					Optional[int]				       =   decoder_layers
							_snake_case       :					List[str]				       =   decoder_attention_heads
							_snake_case       :					Union[str, Any]				       =   dropout
							_snake_case       :					Union[str, Any]				       =   attention_dropout
							_snake_case       :					Tuple				       =   activation_dropout
							_snake_case       :					List[str]				       =   activation_function
							_snake_case       :					int				       =   init_std
							_snake_case       :					str				       =   encoder_layerdrop
							_snake_case       :					Any				       =   decoder_layerdrop
							_snake_case       :					str				       =   use_cache
							_snake_case       :					str				       =   encoder_layers
							_snake_case       :					List[Any]				       =   scale_embedding  # scale factor will be sqrt(d_model) if True
							_snake_case       :					Optional[Any]				       =   router_z_loss_coef
							_snake_case       :					List[str]				       =   router_aux_loss_coef
							_snake_case       :					Optional[int]				       =   decoder_sparse_step
							_snake_case       :					List[str]				       =   encoder_sparse_step
							_snake_case       :					Any				       =   num_experts
							_snake_case       :					int				       =   expert_capacity
							_snake_case       :					Optional[int]				       =   router_bias
							if router_dtype not in ["float32", "float16", "bfloat16"]:
												raise ValueError(f"""`router_dtype` must be one of 'float32', 'float16' or 'bfloat16', got {router_dtype}"""				)
							_snake_case       :					Tuple				       =   router_dtype

							_snake_case       :					Optional[Any]				       =   router_ignore_padding_tokens
							_snake_case       :					Dict				       =   batch_prioritized_routing
							_snake_case       :					Union[str, Any]				       =   second_expert_policy
							_snake_case       :					Dict				       =   normalize_router_prob_before_dropping
							_snake_case       :					List[str]				       =   moe_eval_capacity_token_fraction
							_snake_case       :					Dict				       =   moe_token_dropout
							_snake_case       :					Any				       =   output_router_logits
							super().__init__(
							    pad_token_id=lowerCamelCase__ ,						bos_token_id=lowerCamelCase__ ,						eos_token_id=lowerCamelCase__ ,						is_encoder_decoder=lowerCamelCase__ ,						decoder_start_token_id=lowerCamelCase__ ,						**lowerCamelCase__ ,						)






from math import factorial

__lowerCAmelCase :dict[str, int]     =    {str(digit): factorial(digit) for digit in range(10)}







def    A				(							UpperCAmelCase				):
					if not isinstance(UpperCAmelCase  ,  UpperCAmelCase				):
										raise TypeError("Parameter number must be int"				)

					if number < 0:
										raise ValueError("Parameter number must be greater than or equal to 0"				)

					# Converts number in string to iterate on its digits and adds its factorial.
					return sum(DIGIT_FACTORIAL[digit] for digit in str(UpperCAmelCase				)				)







def    A				(							UpperCAmelCase = 60  ,  UpperCAmelCase = 1_000_000				):

					if not isinstance(UpperCAmelCase  ,  UpperCAmelCase				) or not isinstance(UpperCAmelCase  ,  UpperCAmelCase				):
										raise TypeError("Parameters chain_length and number_limit must be int"				)

					if chain_length <= 0 or number_limit <= 0:
										raise ValueError(
										    "Parameters chain_length and number_limit must be greater than 0"				)

					# the counter for the chains with the exact desired length
					_snake_case       :					Optional[int]				       =   0
					# the cached sizes of the previous chains
					_snake_case       :					dict[int, int]				       =   {}

					for start_chain_element in range(1  ,  UpperCAmelCase				):
										# The temporary set will contain the elements of the chain
										_snake_case       :					Union[str, Any]				       =   set()
										_snake_case       :					Tuple				       =   0

										# Stop computing the chain when you find a cached size, a repeating item or the
										# length is greater then the desired one.
										_snake_case       :					str				       =   start_chain_element
										while (
										    chain_element not in chain_sets_lengths
										    and chain_element not in chain_set
										    and chain_set_length <= chain_length
										):
															chain_set.add(UpperCAmelCase				)
															chain_set_length += 1
															_snake_case       :					Optional[Any]				       =   digit_factorial_sum(UpperCAmelCase				)

										if chain_element in chain_sets_lengths:
															chain_set_length += chain_sets_lengths[chain_element]

										_snake_case       :					List[Any]				       =   chain_set_length

										# If chain contains the exact amount of elements increase the counter
										if chain_set_length == chain_length:
															chains_counter += 1

					return chains_counter


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							print(F'''{solution()}''')