
"""simple docstring"""





from __future__ import annotations
def 							A_     (__a				,   __a				,   __a				,   __a				,   __a				,   ):

					'''simple docstring'''





					A_				 =						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 							A_     (__a				):

					'''simple docstring'''





					A_				 =						[]
					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)






"""simple docstring"""





import baseaa
def 							A_     (__a				):

					'''simple docstring'''





					return baseaa.aaaencode(string.encode("utf-8"				)				)
def 							A_     (__a				):

					'''simple docstring'''





					return baseaa.aaadecode(__a				).decode("utf-8"				)


if __name__ == "__main__":
		import doctest

		doctest.testmod()




