



from __future__ import annotations

def   _lowerCAmelCase   (						A__						,  A__						,  A__						,  A__						,  A__						,  ):
      lowercase__     =  len(A__	)

      # 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(A__	):
            # 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]						,  A__						,  A__						,  )

def   _lowerCAmelCase   (						A__	):
      lowercase__     =  []
      depth_first_search([]						,  []						,  []						,  A__						,  A__	)

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

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


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       n_queens_solution(4)





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


a__      :				Optional[int]   	=			{
    "configuration_blenderbot": [
        "BLENDERBOT_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "BlenderbotConfig",
        "BlenderbotOnnxConfig",
    ],
    "tokenization_blenderbot": ["BlenderbotTokenizer"],
}

try:
       if not is_tokenizers_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       a__      :				Any   	=			["BlenderbotTokenizerFast"]

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       a__      :				Dict   	=			[
           "BLENDERBOT_PRETRAINED_MODEL_ARCHIVE_LIST",
           "BlenderbotForCausalLM",
           "BlenderbotForConditionalGeneration",
           "BlenderbotModel",
           "BlenderbotPreTrainedModel",
       ]


try:
       if not is_tf_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       a__      :				List[str]   	=			[
           "TFBlenderbotForConditionalGeneration",
           "TFBlenderbotModel",
           "TFBlenderbotPreTrainedModel",
       ]


try:
       if not is_flax_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       a__      :				int   	=			[
           "FlaxBlenderbotForConditionalGeneration",
           "FlaxBlenderbotModel",
           "FlaxBlenderbotPreTrainedModel",
       ]


if TYPE_CHECKING:
       from .configuration_blenderbot import (
           BLENDERBOT_PRETRAINED_CONFIG_ARCHIVE_MAP,
           BlenderbotConfig,
           BlenderbotOnnxConfig,
       )
       from .tokenization_blenderbot import BlenderbotTokenizer

       try:
              if not is_tokenizers_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .tokenization_blenderbot_fast import BlenderbotTokenizerFast

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_blenderbot import (
                  BLENDERBOT_PRETRAINED_MODEL_ARCHIVE_LIST,
                  BlenderbotForCausalLM,
                  BlenderbotForConditionalGeneration,
                  BlenderbotModel,
                  BlenderbotPreTrainedModel,
              )

       try:
              if not is_tf_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_tf_blenderbot import (
                  TFBlenderbotForConditionalGeneration,
                  TFBlenderbotModel,
                  TFBlenderbotPreTrainedModel,
              )

       try:
              if not is_flax_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_flax_blenderbot import (
                  FlaxBlenderbotForConditionalGeneration,
                  FlaxBlenderbotModel,
                  FlaxBlenderbotPreTrainedModel,
              )

else:
       import sys

       a__      :				Optional[Any]   	=			_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)
