




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	(						_lowerCAmelCase	,  _lowerCAmelCase	,  _lowerCAmelCase						):
     """simple docstring"""

     @register_to_config
     def __init__(			self     :      str		,     A__     :      int		,     A__     :      int		,     A__     :      int		,     A__     :      float		,     A__     :      int		,     A__     :      int		,     A__     :      int		,     A__     :      int		,     A__     :      str		,     A__     :      bool = False		,     ) ->				Union[str, Any]:
           super().__init__()

           lowerCamelCase__					     = nn.Linear(A__		,     A__		,     bias=A__	)

           lowerCamelCase__					     = nn.Embedding(A__		,     A__	)
           lowerCamelCase__					     = False

           lowerCamelCase__					     = nn.Dropout(p=A__	)

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

           lowerCamelCase__					     = TaLayerNorm(A__	)
           lowerCamelCase__					     = nn.Dropout(p=A__	)




     def        __snake_case      (			self     :      Optional[Any]		,     A__     :      Optional[int]		,     A__     :      int	) ->				List[Any]:
           lowerCamelCase__					     = self.input_proj(A__	)

           # terminal relative positional encodings
           lowerCamelCase__					     = encoder_inputs.shape[1]
           lowerCamelCase__					     = torch.arange(A__		,     device=encoder_inputs.device	)

           lowerCamelCase__					     = encoder_inputs_mask.sum(-1	)
           lowerCamelCase__					     = torch.roll(input_positions.unsqueeze(0	)		,     tuple(seq_lens.tolist()	)		,     dims=0	)
           x += self.position_encoding(A__	)

           lowerCamelCase__					     = self.dropout_pre(A__	)

           # inverted the attention mask
           lowerCamelCase__					     = encoder_inputs.size()
           lowerCamelCase__					     = self.get_extended_attention_mask(A__		,     A__	)

           for lyr in self.encoders:
                 lowerCamelCase__					     = lyr(A__		,     A__	)[0]
           lowerCamelCase__					     = self.layer_norm(A__	)

           return self.dropout_post(A__	), encoder_inputs_mask





def 	lowerCAmelCase_	(     lowerCamelCase:				int  )    ->	int:


      '''simple docstring'''




      return n * (2 * n - 1)

def 	lowerCAmelCase_	(     lowerCamelCase:				int  )    ->	bool:


      '''simple docstring'''




      lowerCamelCase__					     = (1 + 24 * n) ** 0.5
      return ((1 + root) / 6) % 1 == 0

def 	lowerCAmelCase_	(     lowerCamelCase:				int = 1_44  )    ->	int:


      '''simple docstring'''




      lowerCamelCase__					     = start
      lowerCamelCase__					     = hexagonal_num(lowerCamelCase  )
      while not is_pentagonal(lowerCamelCase  ):
            n += 1
            lowerCamelCase__					     = hexagonal_num(lowerCamelCase  )
      return num


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