



"""simple docstring"""






def      _lowercase							(    __snake_case = 50      )		->  int:
			__lowerCAmelCase :    Optional[int]				=			[1] * (length + 1)

			for row_length in range(3   ,length + 1      ):
						for block_length in range(3   ,row_length + 1      ):
									for block_start in range(row_length - block_length      ):
												ways_number[row_length] += ways_number[
												    row_length - block_start - block_length - 1
												]

									ways_number[row_length] += 1

			return ways_number[length]


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




"""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				):




	'''simple docstring'''





	@register_to_config
	def __init__(	self:						List[str]			,     _SCREAMING_SNAKE_CASE:						int			,     _SCREAMING_SNAKE_CASE:						int			,     _SCREAMING_SNAKE_CASE:						int			,     _SCREAMING_SNAKE_CASE:						float			,     _SCREAMING_SNAKE_CASE:						int			,     _SCREAMING_SNAKE_CASE:						int			,     _SCREAMING_SNAKE_CASE:						int			,     _SCREAMING_SNAKE_CASE:						int			,     _SCREAMING_SNAKE_CASE:						str			,     _SCREAMING_SNAKE_CASE:						bool = False			,     )							->			Any:

				"""simple docstring"""

				super().__init__()

				__lowerCAmelCase :    str				=			nn.Embedding(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE)

				__lowerCAmelCase :    Dict				=			nn.Embedding(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE)
				__lowerCAmelCase :    str				=			False

				__lowerCAmelCase :    Optional[Any]				=			nn.Dropout(p=_SCREAMING_SNAKE_CASE)

				__lowerCAmelCase :    Dict				=			TaConfig(
				    vocab_size=_SCREAMING_SNAKE_CASE			,     d_model=_SCREAMING_SNAKE_CASE			,     num_heads=_SCREAMING_SNAKE_CASE			,     d_kv=_SCREAMING_SNAKE_CASE			,     d_ff=_SCREAMING_SNAKE_CASE			,     dropout_rate=_SCREAMING_SNAKE_CASE			,     feed_forward_proj=_SCREAMING_SNAKE_CASE			,     is_decoder=_SCREAMING_SNAKE_CASE			,     is_encoder_decoder=_SCREAMING_SNAKE_CASE			,     )

				__lowerCAmelCase :    str				=			nn.ModuleList()
				for lyr_num in range(_SCREAMING_SNAKE_CASE):
							__lowerCAmelCase :    int				=			TaBlock(_SCREAMING_SNAKE_CASE)
							self.encoders.append(_SCREAMING_SNAKE_CASE)

				__lowerCAmelCase :    Dict				=			TaLayerNorm(_SCREAMING_SNAKE_CASE)
				__lowerCAmelCase :    Any				=			nn.Dropout(p=_SCREAMING_SNAKE_CASE)







	def 				_SCREAMING_SNAKE_CASE  (	self:						Any			,     _SCREAMING_SNAKE_CASE:						Tuple			,     _SCREAMING_SNAKE_CASE:						str)							->			List[str]:

				"""simple docstring"""

				__lowerCAmelCase :    Union[str, Any]				=			self.token_embedder(_SCREAMING_SNAKE_CASE)

				__lowerCAmelCase :    Optional[Any]				=			encoder_input_tokens.shape[1]
				__lowerCAmelCase :    List[Any]				=			torch.arange(_SCREAMING_SNAKE_CASE			,     device=encoder_input_tokens.device)
				x += self.position_encoding(_SCREAMING_SNAKE_CASE)

				__lowerCAmelCase :    List[Any]				=			self.dropout_pre(_SCREAMING_SNAKE_CASE)

				# inverted the attention mask
				__lowerCAmelCase :    List[Any]				=			encoder_input_tokens.size()
				__lowerCAmelCase :    Any				=			self.get_extended_attention_mask(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE)

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

				return self.dropout_post(_SCREAMING_SNAKE_CASE), encoder_inputs_mask