A frog is standing in a center of a $3 \times 3$ grid of lilypads. Each minute, the frog chooses a square that shares exactly one side with their current square uniformly at random, and jumps onto the lilypad on their 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?


[i]2021 CCA Math Bonanza Lightning Round #3.2[/i]