





from __future__ import annotations


def      lowerCamelCase_						(   lowerCAmelCase:						Dict     ,				lowerCAmelCase:						List[Any]     ,				lowerCAmelCase:						Union[str, Any]     ,				lowerCAmelCase:						int     ,				lowerCAmelCase:						Optional[int]     ,				)->		Union[str, Any]:
  _snake_case :					Tuple								=						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_						(   lowerCAmelCase:						Tuple					)->		List[Any]:
  _snake_case :					Union[str, Any]								=						[]
  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)









a__   :					Tuple 						=      "Tobias Carryer"

from time import time



class    UpperCAmelCase__:

   '''simple docstring'''




   def __init__(    self	:      str      ,					lowerCAmelCase	:      List[str]      ,					lowerCAmelCase	:      Any      ,					lowerCAmelCase	:      str      ,					lowerCAmelCase	:      str=int(time()))						->					List[Any]:  # noqa: B008




         """simple docstring"""

         lowercase__  =	multiplier
         lowercase__  =	increment
         lowercase__  =	modulo
         lowercase__  =	seed



   def       UpperCAmelCase		(    self	:      int)						->					Tuple:




         """simple docstring"""

         lowercase__  =	(self.multiplier * self.seed + self.increment) % self.modulo
         return self.seed


if __name__ == "__main__":
       # Show the LCG in action.
       a__   :					str 						=      LinearCongruentialGenerator(1_66_45_25, 10_13_90_42_23, 2 << 31)
       while True:
              print(lcg.next_number())
