


from __future__ import annotations

def       lowercase_		(		_A			:    Optional[Any]    ,					_A			:    Union[str, Any]    ,					_A			:    List[str]    ,					_A			:    Optional[Any]    ,					_A			:    List[str]    ,					):

      """simple docstring"""




      lowerCamelCase__		:				List[str]    =  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       lowercase_		(		_A			:    Optional[Any]						):

      """simple docstring"""




      lowerCamelCase__		:				Union[str, Any]    =  []
      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)






from typing import TYPE_CHECKING

from ..utils import _LazyModule


UpperCAmelCase__   	=							{
    '''config''': [
        '''EXTERNAL_DATA_FORMAT_SIZE_LIMIT''',
        '''OnnxConfig''',
        '''OnnxConfigWithPast''',
        '''OnnxSeq2SeqConfigWithPast''',
        '''PatchingSpec''',
    ],
    '''convert''': ['''export''', '''validate_model_outputs'''],
    '''features''': ['''FeaturesManager'''],
    '''utils''': ['''ParameterFormat''', '''compute_serialized_parameters_size'''],
}


if TYPE_CHECKING:
  from .config import (
      EXTERNAL_DATA_FORMAT_SIZE_LIMIT,
      OnnxConfig,
      OnnxConfigWithPast,
      OnnxSeqaSeqConfigWithPast,
      PatchingSpec,
  )
  from .convert import export, validate_model_outputs
  from .features import FeaturesManager
  from .utils import ParameterFormat, compute_serialized_parameters_size

else:
  import sys

  UpperCAmelCase__   	=							_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)

