Random Walk With Rest Periods

A process evolves in rounds. Each round, independently, with probability 1/2 the walker rests (position unchanged) and with probability 1/2 it takes a step that is +1 or -1 with equal odds. The walker stops at the first round in which it completes its 8th actual (non-rest) step. Let S be the position at that stopping time. Find E[S^2].