Three noncontextual hidden variable models for the Peres-Mermin square

I will argue that the Peres-Mermin square does not necessarily rule out a value-definite (deterministic) noncontextual hidden variable model if operators are given physical interpretation satisfying following two requirements: (i) each operator is uniquely realized by single measurement; (ii) commuting simultaneous measurements. To underpin this claim, construct three models for different realizations of square: one violating (i), another (ii), and third both (ii).