A frog is standing in the center of a $3 \times 3$ grid of lilypads. Each minute, the frog chooses a square that shares exactly one side with its current square uniformly at random and jumps onto the lilypad on the chosen square. The frog stops jumping once it reaches a lilypad on a corner of the grid. What is the expected number of times the frog jumps?

Let's think step by step and output the final answer within \boxed{}.
user