






"""simple docstring"""
from __future__ import annotations






def 			__UpperCamelCase	(		snake_case__   ,   snake_case__   ,   snake_case__   ,   snake_case__   ,   snake_case__   ,   ):
	A_		:						Any	    =   len(snake_case__					)

	# 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(snake_case__					):
		# 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]   ,   snake_case__   ,   snake_case__   ,   )






def 			__UpperCamelCase	(		snake_case__					):
	A_		:						list[list[str]]	    =   []
	depth_first_search([]   ,   []   ,   []   ,   snake_case__   ,   snake_case__					)

	# Print all the boards
	for board in boards:
		for column in board:
			print(snake_case__					)
		print(""""""					)

	print(len(snake_case__					)   ,   """solutions were found."""					)


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							n_queens_solution(4)









"""simple docstring"""
_lowerCAmelCase         =							{"a": ["c", "b"], "b": ["d", "e"], "c": [], "d": [], "e": []}
_lowerCAmelCase         =							["a", "b", "c", "d", "e"]






def 			__UpperCamelCase	(		snake_case__   ,   snake_case__   ,   snake_case__					):
	A_		:						int	    =   start
	# add current to visited
	visited.append(snake_case__					)
	A_		:						Any	    =   edges[current]
	for neighbor in neighbors:
		# if neighbor not in visited, visit
		if neighbor not in visited:
			A_		:						Optional[Any]	    =   topological_sort(snake_case__   ,   snake_case__   ,   snake_case__					)
    # if all neighbors visited add current to sort
	sort.append(snake_case__					)
	# if all vertices haven't been visited select a new one to visit
	if len(snake_case__					) != len(snake_case__					):
		for vertice in vertices:
			if vertice not in visited:
				A_		:						Optional[Any]	    =   topological_sort(snake_case__   ,   snake_case__   ,   snake_case__					)
    # return sort
	return sort


if __name__ == "__main__":
							_lowerCAmelCase         =							topological_sort("a", [], [])
							print(sort)

