Hitting Time on a Four-State Chain

Consider a Markov chain on states $\{0, 1, 2, 3\}$ with transition probabilities: $$p(0,1) = 1, \quad p(1,0) = \tfrac{1}{3}, \quad p(1,2) = \tfrac{2}{3}, \quad p(2,1) = \tfrac{1}{2}, \quad p(2,3) = \tfrac{1}{2}, \quad p(3,3) = 1.$$ Starting from state $0$, compute the expected number of steps to reach state $3$ for the first time.