Olympiad Number Theory · Superchallenge problem

By the rearrangement inequality, the maximum of $a_1b_1 + a_2b_2 + a_3b_3 + a_4b_4$ over all orderings of $\{a_i\} = \{1, 2, 3, 4\}$ and $\{b_i\} = \{2, 3, 5, 7\}$ is achieved by pairing them in the same order, and the minimum by opposite orders. Compute the maximum minus the minimum.