Let \(q_n\) (\(n=1,2,\dots,N\)) be a set of positive numbers, not necessarily in ascending order of magnitude. For any real \(x\) denote by \(Q(x)\) the number of \(n\) for which \(q_n \le x\). Show that \[ \sum_{n=1}^N \frac{1}{nq_n} \le 1 \] provided that \(Q(x) \le x-1\) for all \(x \ge 1\).