private boolean check() {
        if (N == 0) {
            if (first != null) return false;
        }
        else if (N == 1) {
            if (first == null)      return false;
            if (first.next != null) return false;
        }
        else {
            if (first.next == null) return false;
        }

        // check internal consistency of instance variable N
        int numberOfNodes = 0;
        for (Node x = first; x != null; x = x.next) {
            numberOfNodes++;
        }
        if (numberOfNodes != N) return false;

        return true;
    }