


from __future__ import annotations

def    lowercase_	(	_A    :					list[int]					,      _A    :					list[int]					,      _A    :					list[int]					,      _A    :					list[list[str]]					,      _A    :					int					,      ):

						"""simple docstring"""




						lowerCamelCase__	:       str					=						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    lowercase_	(	_A    :					int		):

						"""simple docstring"""




						lowerCamelCase__	:       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)






def    lowercase_	(	_A    :					int					,      _A    :					int		):

      """simple docstring"""




      if a < 0 or b < 0:
            raise ValueError("the value of both inputs must be positive"		)

      lowerCamelCase__	:       List[str]					=						str(bin(_A		)		)[2:]  # remove the leading "0b"
      lowerCamelCase__	:       List[Any]					=						str(bin(_A		)		)[2:]  # remove the leading "0b"

      lowerCamelCase__	:       List[Any]					=						max(len(_A		)					,      len(_A		)		)

      return "0b" + "".join(
          str(int(char_a != char_b		)		)
          for char_a, char_b in zip(a_binary.zfill(_A		)					,      b_binary.zfill(_A		)		)		)


if __name__ == "__main__":
    import doctest

    doctest.testmod()


