// prefix order traversal
    public void printPre () {
        if (root != null) printPre (root);
        StdOut.println ();
    }
    private static void printPre (Node n) {
        StdOut.print (n.val + " ");
        for (Node child : n.children) {
            printPre (child);
        }
    }

    // level order traversal
    public void printLevel () {
        Queue<Node> queue = new Queue<>();
        if (root != null) queue.enqueue(root);
        while (!queue.isEmpty()) {
            Node n = queue.dequeue();
            StdOut.print (n.val + " ");
            for (Node child : n.children) {
                queue.enqueue(child);
            }
        }
        StdOut.println ();
    }