A frog sitting at the point $(1,1)$ 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 independently 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?