


'''simple docstring'''


from __future__ import annotations




def      lowerCamelCase					(      lowerCamelCase  :      list[int]							,						lowerCamelCase  :      list[int]							,						lowerCamelCase  :      list[int]							,						lowerCamelCase  :      list[list[str]]							,						lowerCamelCase  :      int							,						):

      '''simple docstring'''





      A_						:  Dict          =				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  :      int):

      '''simple docstring'''





      A_						:  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 typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tf_available,
    is_torch_available,
    is_vision_available,
)


__magic_name__			=      {
    'configuration_convnext': ['CONVNEXT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'ConvNextConfig', 'ConvNextOnnxConfig']
}

try:
     if not is_vision_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     __magic_name__			=      ['ConvNextFeatureExtractor']
     __magic_name__			=      ['ConvNextImageProcessor']

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     __magic_name__			=      [
         'CONVNEXT_PRETRAINED_MODEL_ARCHIVE_LIST',
         'ConvNextForImageClassification',
         'ConvNextModel',
         'ConvNextPreTrainedModel',
         'ConvNextBackbone',
     ]

try:
     if not is_tf_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     __magic_name__			=      [
         'TFConvNextForImageClassification',
         'TFConvNextModel',
         'TFConvNextPreTrainedModel',
     ]

if TYPE_CHECKING:
     from .configuration_convnext import CONVNEXT_PRETRAINED_CONFIG_ARCHIVE_MAP, ConvNextConfig, ConvNextOnnxConfig

     try:
          if not is_vision_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .feature_extraction_convnext import ConvNextFeatureExtractor
          from .image_processing_convnext import ConvNextImageProcessor

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_convnext import (
              CONVNEXT_PRETRAINED_MODEL_ARCHIVE_LIST,
              ConvNextBackbone,
              ConvNextForImageClassification,
              ConvNextModel,
              ConvNextPreTrainedModel,
          )

     try:
          if not is_tf_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_tf_convnext import TFConvNextForImageClassification, TFConvNextModel, TFConvNextPreTrainedModel


else:
     import sys

     __magic_name__			=      _LazyModule(__name__, globals()['__file__'], _import_structure)
