import math
def 					UpperCamelCase__		(							A__       )  ->   list[int]:
				if not isinstance(_SCREAMING_SNAKE_CASE     ,					_SCREAMING_SNAKE_CASE       ):
								snake_case__   :      Optional[int]   				= F"""Input value of [number={number}] must be an integer"""
								raise TypeError(_SCREAMING_SNAKE_CASE       )
				if number < 1:
								snake_case__   :      str   				= F"""Input value of [number={number}] must be a positive integer"""
								raise ValueError(_SCREAMING_SNAKE_CASE       )
				snake_case__   :      Union[str, Any]   				= [number]
				while number != 1:
								if number % 2 == 0:
												snake_case__   :      int   				= math.floor(math.sqrt(_SCREAMING_SNAKE_CASE       )       )
								else:
												snake_case__   :      Dict   				= math.floor(
												    math.sqrt(_SCREAMING_SNAKE_CASE       ) * math.sqrt(_SCREAMING_SNAKE_CASE       ) * math.sqrt(_SCREAMING_SNAKE_CASE       )       )
								sequence.append(_SCREAMING_SNAKE_CASE       )
				return sequence


if __name__ == "__main__":
				import doctest

				doctest.testmod()






"""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  (snake_case__    ,		snake_case__    ,		snake_case__):





							'''simple docstring'''

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



														"""simple docstring"""



														super().__init__()

														snake_case_     							=		nn.Linear(UpperCAmelCase_		,							UpperCAmelCase_		,							bias=UpperCAmelCase_							)

														snake_case_     							=		nn.Embedding(UpperCAmelCase_		,							UpperCAmelCase_							)
														snake_case_     							=		False

														snake_case_     							=		nn.Dropout(p=UpperCAmelCase_							)

														snake_case_     							=		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_		,							)
														snake_case_     							=		nn.ModuleList()
														for lyr_num in range(UpperCAmelCase_							):
																					snake_case_     							=		TaBlock(UpperCAmelCase_							)
																					self.encoders.append(UpperCAmelCase_							)

														snake_case_     							=		TaLayerNorm(UpperCAmelCase_							)
														snake_case_     							=		nn.Dropout(p=UpperCAmelCase_							)



							def 		lowerCAmelCase							(					self				:   Optional[Any]		,							UpperCAmelCase_				:   Any		,							UpperCAmelCase_				:   List[str]							)       ->List[Any]:



														"""simple docstring"""



														snake_case_     							=		self.input_proj(UpperCAmelCase_							)

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

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

														snake_case_     							=		self.dropout_pre(UpperCAmelCase_							)

														# inverted the attention mask
														snake_case_     							=		encoder_inputs.size()
														snake_case_     							=		self.get_extended_attention_mask(UpperCAmelCase_		,							UpperCAmelCase_							)

														for lyr in self.encoders:
																					snake_case_     							=		lyr(UpperCAmelCase_		,							UpperCAmelCase_							)[0]
														snake_case_     							=		self.layer_norm(UpperCAmelCase_							)

														return self.dropout_post(UpperCAmelCase_							), encoder_inputs_mask



