Non-loose Legendrian spheres with trivial Contact Homology DGA

Loose Legendrian n-submanifolds, for n at least 2, were introduced by Murphy and proved to be flexible in the h-principle sense: any two loose Legendrian submanifolds that are formally Legendrian isotopic are also actually Legendrian isotopic. Legendrian contact homology is a Floer theoretic invariant that associates a differential graded algebra (DGA) to a Legendrian submanifold. The DGA of a loose Legendrian submanifold is trivial.