Counting

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.