Continuity of discrete homomorphisms of diffeomorphism groups

Let M and N be two closed C-infinity manifolds and let Diff(c)(M) denote the group of C-infinity diffeomorphisms isotopic to the identity. We prove that any (discrete) group homomorphism between Diff(c)(M) and Diff(c)(N) is continuous. We also show that a nontrivial group homomorphism Phi: Diff(c)(M) -> Diff(c)(N) implies that dim (M) <= dim (N) and give a classification of such homomorphisms when dim (M) = dim (N).