

'''simple docstring'''
def 					_A		(	snake_case     )			->	list[list]:
   _lowercase			:      Any			     =   current_set.copy()
   for row_index, row in enumerate(A__     ):
      _lowercase			:      str			     =   row[0]
      for column_index, column in enumerate(A__     ):
         if magnitude == 0:
            _lowercase			:      Union[str, Any]			     =   column
            continue
         _lowercase			:      int			     =   column / magnitude
    # Subtract to cancel term
   _lowercase			:      Optional[int]			     =   current_set[0]
   _lowercase			:      int			     =   [first_row]
   _lowercase			:      Union[str, Any]			     =   current_set[1::]
   for row in current_set:
      _lowercase			:      Union[str, Any]			     =   []
      # If first term is 0, it is already in form we want, so we preserve it
      if row[0] == 0:
         final_set.append(A__     )
         continue
      for column_index in range(len(A__     )     ):
         temp_row.append(first_row[column_index] - row[column_index]     )
      final_set.append(A__     )
   # Create next recursion iteration set
   if len(final_set[0]     ) != 3:
      _lowercase			:      Optional[int]			     =   final_set[0]
      _lowercase			:      Optional[int]			     =   []
      _lowercase			:      Optional[int]			     =   []
      for row in final_set[1::]:
         current_first_column.append(row[0]     )
         next_iteration.append(row[1::]     )
      _lowercase			:      Union[str, Any]			     =   simplify(A__     )
      for i in range(len(A__     )     ):
         resultant[i].insert(0		,							current_first_column[i]     )
      resultant.insert(0		,							A__     )
      _lowercase			:      str			     =   resultant
   return final_set







def 					_A		(	snake_case     )			->	list:



   if len(A__     ) == 0:
      raise IndexError("solve_simultaneous() requires n lists of length n+1"     )
   _lowercase			:      Dict			     =   len(A__     ) + 1
   if any(len(A__     ) != _length for item in equations     ):
      raise IndexError("solve_simultaneous() requires n lists of length n+1"     )
   for row in equations:
      if any(not isinstance(A__		,							(int, float)     ) for column in row     ):
         raise ValueError("solve_simultaneous() requires lists of integers"     )
   if len(A__     ) == 1:
      return [equations[0][-1] / equations[0][0]]
   _lowercase			:      Tuple			     =   equations.copy()
   if any(0 in row for row in data_set     ):
      _lowercase			:      str			     =   data_set.copy()
      _lowercase			:      Union[str, Any]			     =   []
      for row_index, row in enumerate(A__     ):
         if 0 not in row:
            _lowercase			:      Dict			     =   data_set.pop(A__     )
            break
      if not full_row:
         raise ValueError("solve_simultaneous() requires at least 1 full equation"     )
      data_set.insert(0		,							A__     )
   _lowercase			:      Dict			     =   data_set.copy()
   _lowercase			:      Any			     =   simplify(A__     )
   _lowercase			:      List[Any]			     =   simplified[::-1]
   _lowercase			:      List[Any]			     =   []
   for row in simplified:
      _lowercase			:      str			     =   row[-1]
      if not solutions:
         if row[-2] == 0:
            solutions.append(0     )
            continue
         solutions.append(current_solution / row[-2]     )
         continue
      _lowercase			:      Optional[int]			     =   row.copy()[: len(A__     ) - 1 :]
      while temp_row[0] == 0:
         temp_row.pop(0     )
      if len(A__     ) == 0:
         solutions.append(0     )
         continue
      _lowercase			:      Union[str, Any]			     =   temp_row[1::]
      _lowercase			:      Tuple			     =   temp_row[::-1]
      for column_index, column in enumerate(A__     ):
         current_solution -= column * solutions[column_index]
      solutions.append(A__     )
   _lowercase			:      str			     =   []
   for item in solutions:
      final.append(float(round(A__		,							5     )     )     )
   return final[::-1]


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    _snake_case     =  [
        [2, 1, 1, 1, 1, 4],
        [1, 2, 1, 1, 1, 5],
        [1, 1, 2, 1, 1, 6],
        [1, 1, 1, 2, 1, 7],
        [1, 1, 1, 1, 2, 8],
    ]
    print(solve_simultaneous(eq))
    print(solve_simultaneous([[4, 2]]))









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  __lowerCAmelCase     (					SCREAMING_SNAKE_CASE			,			SCREAMING_SNAKE_CASE			,			SCREAMING_SNAKE_CASE							):




  @register_to_config
  def __init__(				self							,   lowerCAmelCase							,   lowerCAmelCase							,   lowerCAmelCase							,   lowerCAmelCase							,   lowerCAmelCase							,   lowerCAmelCase							,   lowerCAmelCase							,   lowerCAmelCase							,   lowerCAmelCase							,   lowerCAmelCase = False							,   )  -> Tuple:
        '''simple docstring'''






        super().__init__()

        _lowercase	       =nn.Embedding(lowerCAmelCase							,   lowerCAmelCase					)

        _lowercase	       =nn.Embedding(lowerCAmelCase							,   lowerCAmelCase					)
        _lowercase	       =False

        _lowercase	       =nn.Dropout(p=lowerCAmelCase					)

        _lowercase	       =TaConfig(
            vocab_size=lowerCAmelCase							,   d_model=lowerCAmelCase							,   num_heads=lowerCAmelCase							,   d_kv=lowerCAmelCase							,   d_ff=lowerCAmelCase							,   dropout_rate=lowerCAmelCase							,   feed_forward_proj=lowerCAmelCase							,   is_decoder=lowerCAmelCase							,   is_encoder_decoder=lowerCAmelCase							,   )

        _lowercase	       =nn.ModuleList()
        for lyr_num in range(lowerCAmelCase					):
              _lowercase	       =TaBlock(lowerCAmelCase					)
              self.encoders.append(lowerCAmelCase					)

        _lowercase	       =TaLayerNorm(lowerCAmelCase					)
        _lowercase	       =nn.Dropout(p=lowerCAmelCase					)




  def   A__     (				self							,   lowerCAmelCase							,   lowerCAmelCase					)  -> Dict:
        '''simple docstring'''






        _lowercase	       =self.token_embedder(lowerCAmelCase					)

        _lowercase	       =encoder_input_tokens.shape[1]
        _lowercase	       =torch.arange(lowerCAmelCase							,   device=encoder_input_tokens.device					)
        x += self.position_encoding(lowerCAmelCase					)

        _lowercase	       =self.dropout_pre(lowerCAmelCase					)

        # inverted the attention mask
        _lowercase	       =encoder_input_tokens.size()
        _lowercase	       =self.get_extended_attention_mask(lowerCAmelCase							,   lowerCAmelCase					)

        for lyr in self.encoders:
              _lowercase	       =lyr(lowerCAmelCase							,   lowerCAmelCase					)[0]
        _lowercase	       =self.layer_norm(lowerCAmelCase					)

        return self.dropout_post(lowerCAmelCase					), encoder_inputs_mask


