




from __future__ import annotations



def       UpperCAmelCase__  (     lowerCamelCase,			lowerCamelCase,			lowerCamelCase,			lowerCamelCase,			lowerCamelCase,			):
  lowercase    :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       UpperCAmelCase__  (     lowerCamelCase   ):
  lowercase    :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)









from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


_UpperCAmelCase	:						Optional[int]			=     {
    "configuration_biogpt": ["BIOGPT_PRETRAINED_CONFIG_ARCHIVE_MAP", "BioGptConfig"],
    "tokenization_biogpt": ["BioGptTokenizer"],
}

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     _UpperCAmelCase	:						int			=     [
         "BIOGPT_PRETRAINED_MODEL_ARCHIVE_LIST",
         "BioGptForCausalLM",
         "BioGptForTokenClassification",
         "BioGptForSequenceClassification",
         "BioGptModel",
         "BioGptPreTrainedModel",
     ]


if TYPE_CHECKING:
     from .configuration_biogpt import BIOGPT_PRETRAINED_CONFIG_ARCHIVE_MAP, BioGptConfig
     from .tokenization_biogpt import BioGptTokenizer

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_biogpt import (
              BIOGPT_PRETRAINED_MODEL_ARCHIVE_LIST,
              BioGptForCausalLM,
              BioGptForSequenceClassification,
              BioGptForTokenClassification,
              BioGptModel,
              BioGptPreTrainedModel,
          )


else:
     import sys

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



