





from __future__ import annotations





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     )							-> None:




    """simple docstring"""




    _A     =							len(_SCREAMING_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(_SCREAMING_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]							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     )





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> None:




    """simple docstring"""




    _A     =							[]
    depth_first_search([]							,     []							,     []							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)

    # Print all the boards
    for board in boards:
        for column in board:
            print(_SCREAMING_SNAKE_CASE				)
        print(''				)

    print(len(_SCREAMING_SNAKE_CASE				)							,     'solutions were found.'				)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 n_queens_solution(4)







def   lowerCamelCase__							(							__lowerCAmelCase    :    list							):




			"""simple docstring"""


			for i in range(len(__lowerCAmelCase							) - 1       ,				0       ,				-1							):
						lowerCAmelCase_         =      False

						for j in range(__lowerCAmelCase       ,				0       ,				-1							):
									if unsorted[j] < unsorted[j - 1]:
												lowerCAmelCase_      ,    lowerCAmelCase_         =      unsorted[j - 1], unsorted[j]
												lowerCAmelCase_         =      True

						for j in range(__lowerCAmelCase							):
									if unsorted[j] > unsorted[j + 1]:
												lowerCAmelCase_      ,    lowerCAmelCase_         =      unsorted[j + 1], unsorted[j]
												lowerCAmelCase_         =      True

						if not swapped:
									break
			return unsorted


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			_A  =	input("Enter numbers separated by a comma:\n").strip()
			_A  =	[int(item) for item in user_input.split(",")]
			print(f"""{cocktail_shaker_sort(unsorted) = }""")



