Every Tuesday, critic Ivor Smallbrain drinks a little too much, staggers out of the pub, and performs a kind of random walk towards his home. At each step of this walk, he stumbles either forwards or backwards, and the walk ends either when he collapses in a heap or when he reaches his front door (one of these always happens after a finite [possibly very large] number of steps). Ivor's Irish friend Gerry O'Laughing always accompanies him and records each random walk as a sequence of \(0 \mathrm{~s}\) and 1s: at each step he writes a 1 if the step is forwards and a 0 if it is backwards.

Prove that the set of all possible random walks is countable.