To every negative definite plumbing, Nemethi associates a computable combinatorial object called graded root. In the case the plumbing is the resolution of an almost rational singularity, the corresponding graded root captures the Heegaard Floer homology of the boundary 3-manifold. In this talk, I'll demonstrate how to detect the contact Ozsvath-Szabo invariant inside a graded root when the contact structure is compatible with an almost rational plumbing. As an application, we obstruct the existence of a Stein cobordism between the canonical contact structures on links of singularities. This is a joint work with F. Ozturk.