



from __future__ import annotations






def 			lowerCAmelCase__	(					lowerCamelCase_	:	list[int] ,lowerCamelCase_	:	list[int] ,lowerCamelCase_	:	list[int] ,lowerCamelCase_	:	list[list[str]] ,lowerCamelCase_	:	int ,):





				'''simple docstring'''

				lowerCAmelCase__  :       str				=  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 			lowerCAmelCase__	(					lowerCamelCase_	:	int):





				'''simple docstring'''

				lowerCAmelCase__  :       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)






from __future__ import annotations

from collections.abc import Iterable, Iterator
from dataclasses import dataclass

__snake_case       :	Optional[int]            =(3, 9, -1_1, 0, 7, 5, 1, -1)
__snake_case       :	str            =(4, 6, 2, 0, 8, 1_0, 3, -2)



@dataclass
class  lowerCamelCase__    :




		'''simple docstring'''



		snake_case_			=42
		snake_case_			=42



class  lowerCamelCase__    :




		'''simple docstring'''



		def __init__(self	,__lowerCamelCase				)  ->    None:

						"""simple docstring"""






						lowerCAmelCase__  :       Node | None				=  None
						for i in sorted(__lowerCamelCase	,reverse=__lowerCamelCase				):
										lowerCAmelCase__  :       Dict				=  Node(__lowerCamelCase	,self.head				)



		def __iter__(self				)  ->    Iterator[int]:

						"""simple docstring"""






						lowerCAmelCase__  :       Optional[Any]				=  self.head
						while node:
										yield node.data
										lowerCAmelCase__  :       Dict				=  node.next_node



		def __len__(self				)  ->    int:

						"""simple docstring"""






						return sum(1 for _ in self				)



		def __str__(self				)  ->    str:

						"""simple docstring"""






						return " -> ".join([str(__lowerCamelCase				) for node in self]				)






def 			lowerCAmelCase__	(					lowerCamelCase_	:	SortedLinkedList ,lowerCamelCase_	:	SortedLinkedList):





				'''simple docstring'''

				return SortedLinkedList(list(lowerCamelCase_) + list(lowerCamelCase_))


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							__snake_case       :	Any            =SortedLinkedList
							print(merge_lists(SSL(test_data_odd), SSL(test_data_even)))

