


"""simple docstring"""


from __future__ import annotations







def  __snake_case       (   UpperCamelCase__ ,			UpperCamelCase__ ,			UpperCamelCase__ ,			UpperCamelCase__ ,			UpperCamelCase__ ,			)      ->		None:







		"""simple docstring"""





		A					       = 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  __snake_case       (   UpperCamelCase__	)      ->		None:







		"""simple docstring"""





		A					       = []
		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)









"""simple docstring"""


from __future__ import annotations







def  __snake_case       (   UpperCamelCase__	)      ->		int:







		"""simple docstring"""





		if not nums:
				return 0
		A					       = nums[0]
		A					       = 0
		for num in nums[1:]:
				A       , A					       = (
				    max_excluding + num,
				    max(UpperCamelCase__ ,			UpperCamelCase__	),
				)
		return max(UpperCamelCase__ ,			UpperCamelCase__	)


if __name__ == "__main__":
	import doctest

	doctest.testmod()





