


"""simple docstring"""

from __future__ import annotations


def lowerCAmelCase_   (					UpperCamelCase__						:			list[int]					, UpperCamelCase__						:			list[int]					, UpperCamelCase__						:			list[int]					, UpperCamelCase__						:			list[list[str]]					, UpperCamelCase__						:			int					, ):






 """simple docstring"""







 __lowercase						=						len(UpperCamelCase__			)

 # 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(UpperCamelCase__			):
  # 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]					, UpperCamelCase__					, UpperCamelCase__					, )


def lowerCAmelCase_   (					UpperCamelCase__						:			int			):






 """simple docstring"""







 __lowercase						=						[]
 depth_first_search([]					, []					, []					, UpperCamelCase__					, UpperCamelCase__			)

 # Print all the boards
 for board in boards:
  for column in board:
   print(UpperCamelCase__			)
  print(""""""			)

 print(len(UpperCamelCase__			)					, """solutions were found."""			)


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       n_queens_solution(4)




"""simple docstring"""

def lowerCAmelCase_   (					UpperCamelCase__						:			int			):






 """simple docstring"""







 assert (
     isinstance(UpperCamelCase__					, UpperCamelCase__			) and number_of_steps > 0
 ), f'''number_of_steps needs to be positive integer, your input {number_of_steps}'''
 if number_of_steps == 1:
  return 1
 __lowercase				,		__lowercase						=						1, 1
 for _ in range(number_of_steps - 1			):
  __lowercase				,		__lowercase						=						current + previous, current
 return current


if __name__ == "__main__":
       import doctest

       doctest.testmod()
