$n$-cluster tilting subcategories for radical square zero algebras

We give a characterization of radical square zero bound quiver algebras $\mathbf{k}Q\mathrm{/}{\mathcal{J}}^2$ that admit $n$-cluster tilting subcategories and $n\mathbb{Z}$-cluster tilting subcategories in terms of $Q$. We also show that if $Q$ is not of cyclically oriented extended Dynkin type $\tilde{A}$, then the poset of $n$-cluster tilting subcategories of $\mathbf{k}Q\mathrm{/}{\mathcal{J}}^2$ with relation given by inclusion forms a lattice isomorphic to the opposite of the lattice of divisors of an integer which depends on $Q$.