Three identical long blocks, each of mass $m$, are stacked on top of each other on a frictionless horizontal floor. The coefficient of kinetic friction between the top and middle blocks is $\mu$, and the coefficient of kinetic friction between the middle and bottom blocks is also $\mu$. The middle block is given an initial horizontal velocity $v_0$, while the top and bottom blocks are initially at rest. Assume the blocks are long enough that they do not fall off each other. After a long time, all three blocks move together at the same speed. How far has the top block moved relative to the middle block by the time they are all moving together? (Answer in terms of $v_0$, $\mu$, $g$.)