Let $a_1, a_2, \cdots, a_n$ be a sequence of positive numbers, and $b_1, b_2, \cdots, b_n$ be any permutation of the first sequence. Prove that $$\frac{a_1}{b_1}+\frac{a_2}{b_2}+\cdots \frac{a_n}{b_n}\ge n$$