Hitting Time on the Ladder Graph (2×3 Grid)

Consider the $2 \times 3$ grid graph (ladder graph) with vertices arranged as: $$\begin{matrix} 1 & - & 2 & - & 3 \\ | & & | & & | \\ 4 & - & 5 & - & 6 \end{matrix}$$ Edges connect horizontal and vertical neighbors. A simple random walk moves at each step to a uniformly random neighbor. Starting at corner vertex $1$ (degree $2$), what is the expected number of steps to reach the opposite corner vertex $6$ (degree $2$)?