

'''simple docstring'''






from __future__ import annotations




def        _SCREAMING_SNAKE_CASE  (				A  :       list[int]  ,		A  :       list[int]  ,		A  :       list[int]  ,		A  :       list[list[str]]  ,		A  :       int  ,		)    -> None:







   """simple docstring"""
   __snake_case				:      str     							= 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        _SCREAMING_SNAKE_CASE  (				A  :       int  )    -> None:







   """simple docstring"""
   __snake_case				:      list[list[str]]     							= []
   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)







'''simple docstring'''






from typing import TYPE_CHECKING

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


__A    	=   {
    '''configuration_distilbert''': [
        '''DISTILBERT_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''DistilBertConfig''',
        '''DistilBertOnnxConfig''',
    ],
    '''tokenization_distilbert''': ['''DistilBertTokenizer'''],
}

try:
      if not is_tokenizers_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      __A    	=   ['''DistilBertTokenizerFast''']

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      __A    	=   [
          '''DISTILBERT_PRETRAINED_MODEL_ARCHIVE_LIST''',
          '''DistilBertForMaskedLM''',
          '''DistilBertForMultipleChoice''',
          '''DistilBertForQuestionAnswering''',
          '''DistilBertForSequenceClassification''',
          '''DistilBertForTokenClassification''',
          '''DistilBertModel''',
          '''DistilBertPreTrainedModel''',
      ]

try:
      if not is_tf_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      __A    	=   [
          '''TF_DISTILBERT_PRETRAINED_MODEL_ARCHIVE_LIST''',
          '''TFDistilBertForMaskedLM''',
          '''TFDistilBertForMultipleChoice''',
          '''TFDistilBertForQuestionAnswering''',
          '''TFDistilBertForSequenceClassification''',
          '''TFDistilBertForTokenClassification''',
          '''TFDistilBertMainLayer''',
          '''TFDistilBertModel''',
          '''TFDistilBertPreTrainedModel''',
      ]

try:
      if not is_flax_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      __A    	=   [
          '''FlaxDistilBertForMaskedLM''',
          '''FlaxDistilBertForMultipleChoice''',
          '''FlaxDistilBertForQuestionAnswering''',
          '''FlaxDistilBertForSequenceClassification''',
          '''FlaxDistilBertForTokenClassification''',
          '''FlaxDistilBertModel''',
          '''FlaxDistilBertPreTrainedModel''',
      ]


if TYPE_CHECKING:
      from .configuration_distilbert import (
          DISTILBERT_PRETRAINED_CONFIG_ARCHIVE_MAP,
          DistilBertConfig,
          DistilBertOnnxConfig,
      )
      from .tokenization_distilbert import DistilBertTokenizer

      try:
            if not is_tokenizers_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .tokenization_distilbert_fast import DistilBertTokenizerFast

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_distilbert import (
                DISTILBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
                DistilBertForMaskedLM,
                DistilBertForMultipleChoice,
                DistilBertForQuestionAnswering,
                DistilBertForSequenceClassification,
                DistilBertForTokenClassification,
                DistilBertModel,
                DistilBertPreTrainedModel,
            )

      try:
            if not is_tf_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_tf_distilbert import (
                TF_DISTILBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
                TFDistilBertForMaskedLM,
                TFDistilBertForMultipleChoice,
                TFDistilBertForQuestionAnswering,
                TFDistilBertForSequenceClassification,
                TFDistilBertForTokenClassification,
                TFDistilBertMainLayer,
                TFDistilBertModel,
                TFDistilBertPreTrainedModel,
            )

      try:
            if not is_flax_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_flax_distilbert import (
                FlaxDistilBertForMaskedLM,
                FlaxDistilBertForMultipleChoice,
                FlaxDistilBertForQuestionAnswering,
                FlaxDistilBertForSequenceClassification,
                FlaxDistilBertForTokenClassification,
                FlaxDistilBertModel,
                FlaxDistilBertPreTrainedModel,
            )

else:
      import sys

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