Diffeomorphism-invariant covariant hamiltonians of a linear frame and a linear connection

Let π : FN → N (resp. p : CN → N) be the bundle of linear frames (resp. the bundle of linear connections) of a C∞ manifold N. The Ehresmann connections on FN ×NCN for which the covariant Hamiltonian of every DiffN-invariant Lagrangian density is also DiffN-invariant, are determined.