






from __future__ import annotations





def  _lowerCamelCase						(						__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase ,							__lowerCamelCase ,							) ->			None:

     '''simple docstring'''
     UpperCAmelCase__      :  Any				      =			len(__lowerCamelCase       )

     # 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(__lowerCamelCase       ):
          # 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] ,							__lowerCamelCase ,							__lowerCamelCase ,							)





def  _lowerCamelCase						(						__lowerCamelCase       ) ->			None:

     '''simple docstring'''
     UpperCAmelCase__      :  list[list[str]]				      =			[]
     depth_first_search([] ,							[] ,							[] ,							__lowerCamelCase ,							__lowerCamelCase       )

     # Print all the boards
     for board in boards:
          for column in board:
               print(__lowerCamelCase       )
          print(""""""       )

     print(len(__lowerCamelCase       ) ,							"""solutions were found."""       )


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      n_queens_solution(4)








'''simple docstring'''



from ...configuration_utils import PretrainedConfig
from ...utils import logging


_lowercase          =						logging.get_logger(__name__)

_lowercase          =						{
    """facebook/dpr-ctx_encoder-single-nq-base""": (
        """https://huggingface.co/facebook/dpr-ctx_encoder-single-nq-base/resolve/main/config.json"""
    ),
    """facebook/dpr-question_encoder-single-nq-base""": (
        """https://huggingface.co/facebook/dpr-question_encoder-single-nq-base/resolve/main/config.json"""
    ),
    """facebook/dpr-reader-single-nq-base""": (
        """https://huggingface.co/facebook/dpr-reader-single-nq-base/resolve/main/config.json"""
    ),
    """facebook/dpr-ctx_encoder-multiset-base""": (
        """https://huggingface.co/facebook/dpr-ctx_encoder-multiset-base/resolve/main/config.json"""
    ),
    """facebook/dpr-question_encoder-multiset-base""": (
        """https://huggingface.co/facebook/dpr-question_encoder-multiset-base/resolve/main/config.json"""
    ),
    """facebook/dpr-reader-multiset-base""": (
        """https://huggingface.co/facebook/dpr-reader-multiset-base/resolve/main/config.json"""
    ),
}




class     UpperCAmelCase_	(						_SCREAMING_SNAKE_CASE					):






						'''simple docstring'''






						_lowercase						: str										=  '''dpr'''




						def __init__(   self       ,  _lowercase=30_522       ,  _lowercase=768       ,  _lowercase=12       ,  _lowercase=12       ,  _lowercase=3_072       ,  _lowercase="gelu"       ,  _lowercase=0.1       ,  _lowercase=0.1       ,  _lowercase=512       ,  _lowercase=2       ,  _lowercase=0.02       ,  _lowercase=1e-12       ,  _lowercase=0       ,  _lowercase="absolute"       ,  _lowercase = 0       ,  **_lowercase       ,  ):

												"""simple docstring"""



												super().__init__(pad_token_id=_lowercase       ,  **_lowercase )

												_lowerCAmelCase    		=					vocab_size
												_lowerCAmelCase    		=					hidden_size
												_lowerCAmelCase    		=					num_hidden_layers
												_lowerCAmelCase    		=					num_attention_heads
												_lowerCAmelCase    		=					hidden_act
												_lowerCAmelCase    		=					intermediate_size
												_lowerCAmelCase    		=					hidden_dropout_prob
												_lowerCAmelCase    		=					attention_probs_dropout_prob
												_lowerCAmelCase    		=					max_position_embeddings
												_lowerCAmelCase    		=					type_vocab_size
												_lowerCAmelCase    		=					initializer_range
												_lowerCAmelCase    		=					layer_norm_eps
												_lowerCAmelCase    		=					projection_dim
												_lowerCAmelCase    		=					position_embedding_type
