d'Alembertian of Ricci tensor

What is the d’Alembertian of the Ricci tensor $square R_{munu}$?

I know that for a scalar $square := g^{munu} nabla_mu nabla_nu$ and I can use the fact that $nabla_mu nabla_nu F = left( partial_mu partial_nu – Gamma^X_{munu} partial_X right) F$ for a scalar function $F$.

How does this work for tensors?