






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 			snake_case__   (							lowercase_	,    lowercase_	,    lowercase_):

       '''simple docstring'''



       @register_to_config
       def __init__(							self			,						a__			,						a__			,						a__			,						a__			,						a__			,						a__			,						a__			,						a__			,						a__			,						a__ = False			,						) ->      Tuple:






            '''simple docstring'''





            super().__init__()

            __snake_case			:int          =						nn.Embedding(a__			,						a__    )

            __snake_case			:Any          =						nn.Embedding(a__			,						a__    )
            __snake_case			:Union[str, Any]          =						False

            __snake_case			:Any          =						nn.Dropout(p=a__    )

            __snake_case			:List[str]          =						TaConfig(
                vocab_size=a__			,						d_model=a__			,						num_heads=a__			,						d_kv=a__			,						d_ff=a__			,						dropout_rate=a__			,						feed_forward_proj=a__			,						is_decoder=a__			,						is_encoder_decoder=a__			,						)

            __snake_case			:str          =						nn.ModuleList()
            for lyr_num in range(a__    ):
                 __snake_case			:str          =						TaBlock(a__    )
                 self.encoders.append(a__    )

            __snake_case			:Any          =						TaLayerNorm(a__    )
            __snake_case			:Union[str, Any]          =						nn.Dropout(p=a__    )



       def 					__lowercase						(							self			,						a__			,						a__    ) ->      List[str]:






            '''simple docstring'''





            __snake_case			:Dict          =						self.token_embedder(a__    )

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

            __snake_case			:Optional[int]          =						self.dropout_pre(a__    )

            # inverted the attention mask
            __snake_case			:Tuple          =						encoder_input_tokens.size()
            __snake_case			:Union[str, Any]          =						self.get_extended_attention_mask(a__			,						a__    )

            for lyr in self.encoders:
                 __snake_case			:List[str]          =						lyr(a__			,						a__    )[0]
            __snake_case			:Dict          =						self.layer_norm(a__    )

            return self.dropout_post(a__    ), encoder_inputs_mask










from __future__ import annotations

lowerCamelCase__							=     list[list[int]]

# assigning initial values to the grid
lowerCamelCase__							=     [
    [3, 0, 6, 5, 0, 8, 4, 0, 0],
    [5, 2, 0, 0, 0, 0, 0, 0, 0],
    [0, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]

# a grid with no solution
lowerCamelCase__							=     [
    [5, 0, 6, 5, 0, 8, 4, 0, 3],
    [5, 2, 0, 0, 0, 0, 0, 0, 2],
    [1, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]






def   UpperCamelCase  (       snake_case__     :   Matrix	,snake_case__     :   int	,snake_case__     :   int	,snake_case__     :   int  ):




     '''simple docstring'''






     for i in range(9  ):
          if grid[row][i] == n or grid[i][column] == n:
               return False

     for i in range(3  ):
          for j in range(3  ):
               if grid[(row - row % 3) + i][(column - column % 3) + j] == n:
                    return False

     return True






def   UpperCamelCase  (       snake_case__     :   Matrix  ):




     '''simple docstring'''






     for i in range(9  ):
          for j in range(9  ):
               if grid[i][j] == 0:
                    return i, j
     return None






def   UpperCamelCase  (       snake_case__     :   Matrix  ):




     '''simple docstring'''






     if location := find_empty_location(snake_case__  ):
          __snake_case       , __snake_case			:Optional[int]          =						location
     else:
          # If the location is ``None``, then the grid is solved.
          return grid

     for digit in range(1	,10  ):
          if is_safe(snake_case__	,snake_case__	,snake_case__	,snake_case__  ):
               __snake_case			:Union[str, Any]          =						digit

               if sudoku(snake_case__  ) is not None:
                    return grid

               __snake_case			:Tuple          =						0

     return None






def   UpperCamelCase  (       snake_case__     :   Matrix  ):




     '''simple docstring'''






     for row in grid:
          for cell in row:
               print(snake_case__	,end=""" """  )
          print()


if __name__ == "__main__":
     # make a copy of grid so that you can compare with the unmodified grid
     for example_grid in (initial_grid, no_solution):
          print("""\nExample grid:\n""" + """=""" * 20)
          print_solution(example_grid)
          print("""\nExample grid solution:""")
          lowerCamelCase__							=     sudoku(example_grid)
          if solution is not None:
               print_solution(solution)
          else:
               print("""Cannot find a solution.""")


