"""simple docstring"""



from typing import TYPE_CHECKING

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


SCREAMING_SNAKE_CASE__:Union[str, Any]			=	{
    """configuration_m2m_100""": ["""M2M_100_PRETRAINED_CONFIG_ARCHIVE_MAP""", """M2M100Config""", """M2M100OnnxConfig"""],
    """tokenization_m2m_100""": ["""M2M100Tokenizer"""],
}


try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 SCREAMING_SNAKE_CASE__:Union[str, Any]			=	[
     """M2M_100_PRETRAINED_MODEL_ARCHIVE_LIST""",
     """M2M100ForConditionalGeneration""",
     """M2M100Model""",
     """M2M100PreTrainedModel""",
 ]


if TYPE_CHECKING:
 from .configuration_mam_aaa import M2M_100_PRETRAINED_CONFIG_ARCHIVE_MAP, MaMaaaConfig, MaMaaaOnnxConfig
 from .tokenization_mam_aaa import MaMaaaTokenizer

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_mam_aaa import (
      M2M_100_PRETRAINED_MODEL_ARCHIVE_LIST,
      MaMaaaForConditionalGeneration,
      MaMaaaModel,
      MaMaaaPreTrainedModel,
  )


else:
 import sys

 SCREAMING_SNAKE_CASE__:Tuple			=	_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)

"""simple docstring"""



from __future__ import annotations



def 					_lowerCamelCase(					a ,  a ,  a ,  a ,  a ,  ):
       __a     				=  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							):
       __a     				=  []
       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)
