+826 Xavier and Yvonne meet one day at a cafe. For any day that Xavier goes to the cafe, the probability that Xavier goes the next day is $\frac{1}{2},$ and the probability that Xavier returns in two days is $\frac{1}{2}.$ For any day that Yvonne goes to the cafe, the probability that Yvonne goes the next day is $\frac{1}{2},$ and the probability that Yvonne returns in two days is $\frac{1}{2}.$ Find the expected number of days until both Xavier and Yvonne both visit the cafe again.
