Swag Subsets

Hussain really likes problems that involve summation over X, where X can be subsets, paths in a tree, intervals of numbers etc. You are given two integer sequences $A_1, A_2, A_3, \ldots, A_N$ and $B_1, B_2, B_3, \ldots, B_N$. Consider an arbitrary non-empty subset $S$ of the set $\{1, 2, \ldots, N\}$. Let's define the *swagness* of such a set as $$\left(\mathrm{max}_{(p \in S)} \; A_p\right) \cd