
from __future__ import annotations



def      __lowerCAmelCase						(							UpperCAmelCase__				:      list[int]			,				UpperCAmelCase__				:      list[int]			,				UpperCAmelCase__				:      list[int]			,				UpperCAmelCase__				:      list[list[str]]			,				UpperCAmelCase__				:      int			,				)  ->    None:
							lowerCamelCase_							  =					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       )  ->    None:
							lowerCamelCase_							  =					[]
							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)







from abc import ABC, abstractmethod
from argparse import ArgumentParser





class       __A(				UpperCAmelCase       ):

					@staticmethod
					@abstractmethod
					def    lowercase__      (	__UpperCamelCase					:     ArgumentParser   ):
												raise NotImplementedError()



					@abstractmethod
					def    lowercase__      (	self					:     Any   ):
												raise NotImplementedError()





