

"""simple docstring"""





import copy

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


__UpperCamelCase						:   Any							   =	logging.get_logger(__name__)

__UpperCamelCase						:   Union[str, Any]							   =	{}







class        SCREAMING_SNAKE_CASE      (	a_ ):






					"""simple docstring"""



					lowercase__       				= 'fsmt_decoder'







					def __init__( self    :       Optional[Any]     ,lowercase_    :       Optional[Any]=0     ,lowercase_    :       Any=0	):
						super().__init__()
						lowerCAmelCase__			:		Optional[int]						       =			vocab_size
						lowerCAmelCase__			:		str						       =			bos_token_id







class        SCREAMING_SNAKE_CASE      (	a_ ):






					"""simple docstring"""



					lowercase__       				= 'fsmt'
					lowercase__       				= {'num_attention_heads': 'encoder_attention_heads', 'hidden_size': 'd_model'}







					def __init__( self    :       List[str]     ,lowercase_    :       List[Any]=["en", "de"]     ,lowercase_    :       List[str]=4_2_0_2_4     ,lowercase_    :       List[str]=4_2_0_2_4     ,lowercase_    :       Tuple="relu"     ,lowercase_    :       List[Any]=1_0_2_4     ,lowercase_    :       Union[str, Any]=2_0_0     ,lowercase_    :       Tuple=1_0_2_4     ,lowercase_    :       List[str]=4_0_9_6     ,lowercase_    :       Union[str, Any]=1_2     ,lowercase_    :       Optional[Any]=1_6     ,lowercase_    :       Optional[int]=0.0     ,lowercase_    :       Any=4_0_9_6     ,lowercase_    :       List[str]=1_2     ,lowercase_    :       Union[str, Any]=1_6     ,lowercase_    :       Any=0.0     ,lowercase_    :       int=0.0     ,lowercase_    :       Optional[Any]=0.1     ,lowercase_    :       Tuple=0.0     ,lowercase_    :       Any=0.02     ,lowercase_    :       List[str]=2     ,lowercase_    :       Any=True     ,lowercase_    :       Dict=True     ,lowercase_    :       Tuple=False     ,lowercase_    :       int=5     ,lowercase_    :       Union[str, Any]=1.0     ,lowercase_    :       Optional[Any]=False     ,lowercase_    :       Tuple=True     ,lowercase_    :       Tuple=1     ,lowercase_    :       Dict=0     ,lowercase_    :       Optional[Any]=2     ,lowercase_    :       int=2     ,**lowercase_    :       Optional[Any]     ,):
						lowerCAmelCase__			:		Any						       =			langs
						lowerCAmelCase__			:		Union[str, Any]						       =			src_vocab_size
						lowerCAmelCase__			:		Optional[Any]						       =			tgt_vocab_size
						lowerCAmelCase__			:		Optional[Any]						       =			d_model  # encoder_embed_dim and decoder_embed_dim

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

						lowerCAmelCase__			:		Dict						       =			DecoderConfig(vocab_size=lowercase_     ,bos_token_id=lowercase_	)
						if "decoder" in common_kwargs:
							del common_kwargs["decoder"]

						lowerCAmelCase__			:		Optional[int]						       =			scale_embedding  # scale factor will be sqrt(d_model) if True

						# 3 Types of Dropout
						lowerCAmelCase__			:		Optional[Any]						       =			attention_dropout
						lowerCAmelCase__			:		str						       =			activation_dropout
						lowerCAmelCase__			:		Optional[Any]						       =			dropout

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







"""simple docstring"""





from itertools import permutations

def 						__SCREAMING_SNAKE_CASE						(   A_ = 5				):
	if gon_side < 3 or gon_side > 5:
		raise ValueError('''gon_side must be in the range [3, 5]'''				)

	# Since it's 16, we know 10 is on the outer ring
	# Put the big numbers at the end so that they are never the first number
	lowerCAmelCase__			:		str						       =			list(range(gon_side + 1		,  0		,  -1				)				)
	lowerCAmelCase__			:		int						       =			list(range(gon_side + 2		,  gon_side * 2 + 1				)				)

	for perm in permutations(small_numbers + big_numbers				):
		lowerCAmelCase__			:		Optional[Any]						       =			generate_gon_ring(A_		,  list(A_				)				)
		if is_magic_gon(A_				):
			return int(''''''.join(str(A_				) for n in numbers				)				)

	lowerCAmelCase__			:		Tuple						       =			f'Magic {gon_side}-gon ring is impossible'
	raise ValueError(A_				)

def 						__SCREAMING_SNAKE_CASE						(   A_		,  A_				):
	lowerCAmelCase__			:		Dict						       =			[0] * (gon_side * 3)
	lowerCAmelCase__			:		Optional[int]						       =			perm[0:3]
	perm.append(perm[1]				)

	lowerCAmelCase__			:		int						       =			1 if gon_side < 5 else 2

	for i in range(1		,  len(A_				) // 3 + magic_number				):
		lowerCAmelCase__			:		List[str]						       =			perm[2 * i + 1]
		lowerCAmelCase__			:		Optional[int]						       =			result[3 * i - 1]
		lowerCAmelCase__			:		List[Any]						       =			perm[2 * i + 2]

	return result

def 						__SCREAMING_SNAKE_CASE						(   A_				):
	if len(A_				) % 3 != 0:
		raise ValueError('''a gon ring should have a length that is a multiple of 3'''				)

	if min(numbers[::3]				) != numbers[0]:
		return False

	lowerCAmelCase__			:		int						       =			sum(numbers[:3]				)

	return all(sum(numbers[i : i + 3]				) == total for i in range(3		,  len(A_				)		,  3				)				)


if __name__ == "__main__":
							print(solution())




