



from __future__ import annotations

def        __a			(   __lowerCAmelCase      ,	__lowerCAmelCase      ,	__lowerCAmelCase      ,	__lowerCAmelCase      ,	__lowerCAmelCase      ,	)     ->     None:
					SCREAMING_SNAKE_CASE							:     Optional[int]						=				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        __a			(   __lowerCAmelCase   )     ->     None:
					SCREAMING_SNAKE_CASE							:     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        __a			(   __lowerCAmelCase      ,	__lowerCAmelCase = 0   )     ->     list:
					SCREAMING_SNAKE_CASE							:     int						=				length or len(__lowerCAmelCase   )
					SCREAMING_SNAKE_CASE							:     Union[str, Any]						=				False
					for i in range(length - 1   ):
										if list_data[i] > list_data[i + 1]:
															SCREAMING_SNAKE_CASE					,  SCREAMING_SNAKE_CASE							:     List[Any]						=				list_data[i + 1], list_data[i]
															SCREAMING_SNAKE_CASE							:     Any						=				True

					return list_data if not swapped else bubble_sort(__lowerCAmelCase      ,	length - 1   )


if __name__ == "__main__":
			import doctest

			doctest.testmod()