Hitting Time with Interior Reflecting Barrier

A Markov chain on $\{0, 1, 2, 3, 4\}$ has the following transitions:

• State $0$ is absorbing.
• From state $1$: $p(1, 0) = \tfrac{1}{2}$, $p(1, 2) = \tfrac{1}{2}$.
• From state $2$: $p(2, 1) = \tfrac{1}{3}$, $p(2, 3) = \tfrac{2}{3}$.
• From state $3$: $p(3, 2) = \tfrac{1}{2}$, $p(3, 4) = \tfrac{1}{2}$.
• From state $4$: $p(4, 3) = 1$ (reflecting barrier).

Compute $E[T_0 \mid X_0 = 3]$.