Expected Absorption Time with Increasing Drift

A Markov chain on $\{0, 1, 2, 3, 4\}$ has absorbing states $0$ and $4$. The transition probabilities for transient states are: $$p(1,0) = \tfrac{1}{5}, \quad p(1,2) = \tfrac{4}{5}, \quad p(2,1) = \tfrac{2}{5}, \quad p(2,3) = \tfrac{3}{5}, \quad p(3,2) = \tfrac{3}{5}, \quad p(3,4) = \tfrac{2}{5}.$$

Compute $E[T \mid X_0 = 1]$ and $E[T \mid X_0 = 3]$, where $T = \inf\{n \ge 0 : X_n \in \{0, 4\}\}$.