



'''simple docstring'''
import torch
import torch.nn as nn
from transformers.modeling_utils import ModuleUtilsMixin
from transformers.models.ta.modeling_ta import (
    TaBlock,
    TaConfig,
    TaLayerNorm,
)

from ...configuration_utils import ConfigMixin, register_to_config
from ...models import ModelMixin



class _A  (    __SCREAMING_SNAKE_CASE	,				__SCREAMING_SNAKE_CASE	,				__SCREAMING_SNAKE_CASE    ):





		@register_to_config
		def __init__(     self ,       __UpperCAmelCase ,       __UpperCAmelCase ,       __UpperCAmelCase ,       __UpperCAmelCase ,       __UpperCAmelCase ,       __UpperCAmelCase ,       __UpperCAmelCase ,       __UpperCAmelCase ,       __UpperCAmelCase ,       __UpperCAmelCase = False ,       )       ->     List[str]:

					'''simple docstring'''
					super().__init__()

					__UpperCAmelCase   :      Optional[Any]										=     nn.Linear(__UpperCAmelCase ,       __UpperCAmelCase ,       bias=__UpperCAmelCase				)

					__UpperCAmelCase   :      List[Any]										=     nn.Embedding(__UpperCAmelCase ,       __UpperCAmelCase				)
					__UpperCAmelCase   :      Any										=     False

					__UpperCAmelCase   :      Union[str, Any]										=     nn.Dropout(p=__UpperCAmelCase				)

					__UpperCAmelCase   :      int										=     TaConfig(
					    d_model=__UpperCAmelCase ,       num_heads=__UpperCAmelCase ,       d_kv=__UpperCAmelCase ,       d_ff=__UpperCAmelCase ,       feed_forward_proj=__UpperCAmelCase ,       dropout_rate=__UpperCAmelCase ,       is_decoder=__UpperCAmelCase ,       is_encoder_decoder=__UpperCAmelCase ,       )
					__UpperCAmelCase   :      Any										=     nn.ModuleList()
					for lyr_num in range(__UpperCAmelCase				):
								__UpperCAmelCase   :      str										=     TaBlock(__UpperCAmelCase				)
								self.encoders.append(__UpperCAmelCase				)

					__UpperCAmelCase   :      int										=     TaLayerNorm(__UpperCAmelCase				)
					__UpperCAmelCase   :      Union[str, Any]										=     nn.Dropout(p=__UpperCAmelCase				)





		def 							__A       (     self ,       __UpperCAmelCase ,       __UpperCAmelCase				)       ->     str:

					'''simple docstring'''
					__UpperCAmelCase   :      Any										=     self.input_proj(__UpperCAmelCase				)

					# terminal relative positional encodings
					__UpperCAmelCase   :      int										=     encoder_inputs.shape[1]
					__UpperCAmelCase   :      Dict										=     torch.arange(__UpperCAmelCase ,       device=encoder_inputs.device				)

					__UpperCAmelCase   :      Dict										=     encoder_inputs_mask.sum(-1				)
					__UpperCAmelCase   :      Union[str, Any]										=     torch.roll(input_positions.unsqueeze(0				) ,       tuple(seq_lens.tolist()				) ,       dims=0				)
					x += self.position_encoding(__UpperCAmelCase				)

					__UpperCAmelCase   :      Tuple										=     self.dropout_pre(__UpperCAmelCase				)

					# inverted the attention mask
					__UpperCAmelCase   :      List[Any]										=     encoder_inputs.size()
					__UpperCAmelCase   :      Dict										=     self.get_extended_attention_mask(__UpperCAmelCase ,       __UpperCAmelCase				)

					for lyr in self.encoders:
								__UpperCAmelCase   :      Union[str, Any]										=     lyr(__UpperCAmelCase ,       __UpperCAmelCase				)[0]
					__UpperCAmelCase   :      Any										=     self.layer_norm(__UpperCAmelCase				)

					return self.dropout_post(__UpperCAmelCase				), encoder_inputs_mask









'''simple docstring'''
from itertools import permutations


def   lowercase_	(   lowerCAmelCase__	:  int = 5 ):

			"""simple docstring"""





			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
			__UpperCAmelCase   :      int										=     list(range(gon_side + 1			,							0			,							-1 ) )
			__UpperCAmelCase   :      int										=     list(range(gon_side + 2			,							gon_side * 2 + 1 ) )

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

			__UpperCAmelCase   :      Optional[int]										=     f'Magic {gon_side}-gon ring is impossible'
			raise ValueError(lowerCAmelCase__ )


def   lowercase_	(   lowerCAmelCase__	:  int			,							lowerCAmelCase__	:  list[int] ):

			"""simple docstring"""





			__UpperCAmelCase   :      Tuple										=     [0] * (gon_side * 3)
			__UpperCAmelCase   :      Optional[Any]										=     perm[0:3]
			perm.append(perm[1] )

			__UpperCAmelCase   :      Union[str, Any]										=     1 if gon_side < 5 else 2

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

			return result


def   lowercase_	(   lowerCAmelCase__	:  list[int] ):

			"""simple docstring"""





			if len(lowerCAmelCase__ ) % 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

			__UpperCAmelCase   :      Optional[int]										=     sum(numbers[:3] )

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


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




