Olympiad Geometry · Superchallenge problem

Let $A = (0, 0)$, $B = (8, 0)$, and $P = (1, 3)$. For a line $\ell$ through $P$, let $S$ be the sum of the perpendicular distances from $A$ and from $B$ to $\ell$. Find the largest possible value of $S$.