SE-SKOLORNAS 1969 Problem 3

$a_1 \le a_2 \le ... \le a_n$ is a sequence of reals $b_1, _b2, b_3,..., b_n$ is any rearrangement of the sequence $B_1 \le B_2 \le ...\le B_n$ . Show that $\sum a_ib_i \le \sum a_i B_i$ .