def convert_simple_sub_commands_to_position(arr: list) -> tuple[int, int, int]:
    """
    Args:
        arr: list of strings including a simple command and magnitude separated by one space
    Returns:
        depth, horizontal, and depth * horizontal positions after parsing all simple sub commands
    """
    d = 0
    h = 0
    for elem in arr:
        command, magnitude = elem.split(' ', 1)
        if command == 'forward':
            h += int(magnitude)
        elif command == 'up':
            d -= int(magnitude)
        elif command == 'down':
            d += int(magnitude)

    return d, h, d * h