Markov Chains & Long-Run Behavior · Hard problem

A $5$-state Markov chain has this rule: state $1$ always moves to state $2$, and state $2$ always moves back to state $1$; state $3$ is absorbing; state $4$ moves to state $1$ or to state $5$, each with probability $1/2$; state $5$ moves to state $3$ or to state $4$, each with probability $1/2$. How many of the $5$ states are recurrent (that is, once the chain is in one of them, it is certain to return to it)?