The spider stalking a fly on a line of leaves

Leaves are strung in a line and numbered $0,1,2,3,4$. A spider sits on leaf $0$ and a fly on leaf $4$. Each second, only the fly moves: it hops to an adjacent leaf, toward the spider or away, with probability $\tfrac12$ each. If the fly ever reaches leaf $0$ it is caught. Leaf $4$ is the far wall, from leaf $4$ the fly can only move to leaf $3$ (it cannot go past the wall).

What is the expected number of seconds until the spider catches the fly?