Jumping Frog on Vertical Side

A frog sitting at the point $(1, 2)$ begins a sequence of jumps, where each jump is parallel to one of the coordinate axes and has length $1$, and the direction of each jump (up, down, right, or left) is chosen at random. The sequence ends when the frog reaches a side of the square with vertices $(0,0), (0,4), (4,4),$ and $(4,0)$. What is the probability that the sequence of jumps ends on a vertical side of the square$?$ The answer is in the form $\frac{\alpha}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.