Sinkless orientation is hard also in the supported LOCAL model

We show that any algorithm that solves the sinkless orientation problem in the supported LOCAL model requires $\Omega(\log n)$ rounds, and this is tight. The supported LOCAL is at least as strong as the usual LOCAL model, and as a corollary this also gives a new, short and elementary proof that shows that the round complexity of the sinkless orientation problem in the deterministic LOCAL model is $\Omega(\log n)$.