Before revision:  We  show that the hard instances from this earlier work have the propertythat in every partition of the hypergraph formed by the constraints into small blocks, most of the hyperedges are incident on vertices from distinct blocks .
After revision:  We design a family of appropriate CSPs (one for every q) from any given OCSP, and apply their work to this family of CSPs. We show that the hard instances from this earlier work have the propertythat in every partition of the hypergraph formed by the constraints into small blocks, most of the hyperedges are incident on vertices from distinct blocks .