Starting with a single stick of unit length, a point $p \in (0, 1)$ is picked uniformly at random along the stick and the stick is snapped, producing two sticks of length $p$ and $1-p$.

At each next stage, a stick is picked uniformly at random, and a point is picked uniformly at random along the length of that stick, and it is snapped.

**Question:** After n snaps, what is the expected length of the longest remaining stick?