A uniform solid prism with a regular $N$-gon cross-section ($N > 2$), side length $s$, and total mass $m$ rests on one of its rectangular faces on a horizontal floor. It is set rolling toward an adjacent face by being given an initial angular velocity about the edge shared by the two faces, with friction sufficient to prevent slipping. What minimum initial kinetic energy is required for the prism to come to rest on the adjacent face rather than fall back?