Topological invariant of multilayer Haldane models with irregular stackings

We study multilayer Haldane models with irregular type of stacking, considering the nearest interlayer hopping. We prove that the value of the topological invariant is equal to the number of layers times the value of the topological invariant of monolayer Haldane model, regardless of stacking type, and interlayer hoppings do not induce gap closing and phase transitions.