


from __future__ import annotations


def      a	(							SCREAMING_SNAKE_CASE_      :		Dict							,			SCREAMING_SNAKE_CASE_      :		Any							,			SCREAMING_SNAKE_CASE_      :		Tuple							,			SCREAMING_SNAKE_CASE_      :		str							,			SCREAMING_SNAKE_CASE_      :		str							,			):






       """simple docstring"""





       UpperCamelCase    :	Union[str, Any]   	=		len(_snake_case       )

       # If row is equal to the size of the board it means there are a queen in each row in
       # the current board (possible_board)
       if row == n:
              # We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
              # this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
              boards.append(['''. ''' * i + '''Q ''' + '''. ''' * (n - 1 - i) for i in possible_board]       )
              return

       # We iterate each column in the row to find all possible results in each row
       for col in range(_snake_case       ):
              # We apply that we learned previously. First we check that in the current board
              # (possible_board) there are not other same value because if there is it means
              # that there are a collision in vertical. Then we apply the two formulas we
              # learned before:
              #
              # 45º: y - x = b or 45: row - col = b
              # 135º: y + x = b or row + col = b.
              #
              # And we verify if the results of this two formulas not exist in their variables
              # respectively.  (diagonal_right_collisions, diagonal_left_collisions)
              #
              # If any or these are True it means there is a collision so we continue to the
              # next value in the for loop.
              if (
                  col in possible_board
                  or row - col in diagonal_right_collisions
                  or row + col in diagonal_left_collisions
              ):
                     continue

              # If it is False we call dfs function again and we update the inputs
              depth_first_search(
                  [*possible_board, col]							,			[*diagonal_right_collisions, row - col]							,			[*diagonal_left_collisions, row + col]							,			_snake_case							,			_snake_case							,			)


def      a	(							SCREAMING_SNAKE_CASE_      :		List[str]       ):






       """simple docstring"""





       UpperCamelCase    :	List[str]   	=		[]
       depth_first_search([]							,			[]							,			[]							,			_snake_case							,			_snake_case       )

       # Print all the boards
       for board in boards:
              for column in board:
                     print(_snake_case       )
              print(''''''       )

       print(len(_snake_case       )							,			'''solutions were found.'''       )


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  n_queens_solution(4)





import torch

from transformers import AutoModel



class    UpperCAmelCase_	(							torch.nn.Module):
       '''simple docstring'''






       def __init__(     self ,					__SCREAMING_SNAKE_CASE="sayef/fsner-bert-base-uncased"						):




              """simple docstring"""




              super(__SCREAMING_SNAKE_CASE ,					self						).__init__()

              UpperCamelCase    :	List[str]   	=		AutoModel.from_pretrained(__SCREAMING_SNAKE_CASE ,					return_dict=__SCREAMING_SNAKE_CASE						)
              UpperCamelCase    :	Optional[int]   	=		torch.nn.CosineSimilarity(3 ,					1e-08						)
              UpperCamelCase    :	List[Any]   	=		torch.nn.Softmax(dim=1						)






       def  _lowercase   (     self ,					**__SCREAMING_SNAKE_CASE						):




              """simple docstring"""




              return self.bert(**__SCREAMING_SNAKE_CASE						).last_hidden_state






       def  _lowercase   (     self ,					__SCREAMING_SNAKE_CASE						):




              """simple docstring"""




              return token_embeddings.sum(2 ,					keepdim=__SCREAMING_SNAKE_CASE						)






       def  _lowercase   (     self ,					__SCREAMING_SNAKE_CASE ,					__SCREAMING_SNAKE_CASE ,					__SCREAMING_SNAKE_CASE=1						):




              """simple docstring"""




              return self.softmax(T * self.cos(__SCREAMING_SNAKE_CASE ,					__SCREAMING_SNAKE_CASE						)						)






       def  _lowercase   (     self ,					__SCREAMING_SNAKE_CASE ,					__SCREAMING_SNAKE_CASE						):




              """simple docstring"""




              UpperCamelCase    :	Any   	=		W_supports['''sizes'''].tolist()
              UpperCamelCase    :	Optional[int]   	=		W_supports['''start_token_id'''].item()
              UpperCamelCase    :	Any   	=		W_supports['''end_token_id'''].item()

              del W_supports["sizes"]
              del W_supports["start_token_id"]
              del W_supports["end_token_id"]

              UpperCamelCase    :	Union[str, Any]   	=		self.BERT(**__SCREAMING_SNAKE_CASE						)
              UpperCamelCase    :	List[str]   	=		self.BERT(**__SCREAMING_SNAKE_CASE						)

              UpperCamelCase    :	List[Any]   	=		None
              UpperCamelCase    :	Any   	=		None

              UpperCamelCase    :	Optional[Any]   	=		W_supports['''input_ids'''] == start_token_id
              UpperCamelCase    :	Any   	=		W_supports['''input_ids'''] == end_token_id

              for i, size in enumerate(__SCREAMING_SNAKE_CASE						):
                     if i == 0:
                            UpperCamelCase    :	Optional[int]   	=		0
                     else:
                            UpperCamelCase    :	Tuple   	=		support_sizes[i - 1]

                     UpperCamelCase    :	Tuple   	=		S[s : s + size][start_token_masks[s : s + size]]
                     UpperCamelCase    :	List[str]   	=		S[s : s + size][end_token_masks[s : s + size]]

                     UpperCamelCase    :	Dict   	=		torch.matmul(q[i] ,					s_start.T						).sum(1						).softmax(0						)
                     UpperCamelCase    :	Tuple   	=		torch.matmul(q[i] ,					s_end.T						).sum(1						).softmax(0						)

                     if p_starts is not None:
                            UpperCamelCase    :	List[str]   	=		torch.vstack((p_starts, p_start)						)
                            UpperCamelCase    :	Union[str, Any]   	=		torch.vstack((p_ends, p_end)						)
                     else:
                            UpperCamelCase    :	str   	=		p_start
                            UpperCamelCase    :	Optional[int]   	=		p_end

              return p_starts, p_ends

