





from __future__ import annotations

def       A(__a:			Dict						,   __a:			Dict						,   __a:			Union[str, Any]						,   __a:			Tuple						,   __a:			Any						,   ):
		lowerCAmelCase_												=				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(__a:			Union[str, Any]				):
		lowerCAmelCase_												=				[]
		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()