





"""simple docstring"""
import os
from typing import Dict, List, Tuple, TypeVar, Union


__UpperCamelCase     :						int						       =  TypeVar('''T''')

__UpperCamelCase     :						Union[str, Any]						       =  Union[List[T], Tuple[T, ...]]
__UpperCamelCase     :						int						       =  Union[T, List[T], Dict[str, T]]
__UpperCamelCase     :						str						       =  Union[str, bytes, os.PathLike]












from __future__ import annotations






def 		lowerCAmelCase  (	UpperCamelCase__   :   list[int]       ,			UpperCamelCase__   :   list[int]       ,			UpperCamelCase__   :   list[int]       ,			UpperCamelCase__   :   list[list[str]]       ,			UpperCamelCase__   :   int       ,			)      ->    None:

						"""simple docstring"""





						__SCREAMING_SNAKE_CASE:				Any           =   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:

						"""simple docstring"""





						__SCREAMING_SNAKE_CASE:				list[list[str]]           =   []
						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)



