  We introduce a new invariant, the \textit{positive idempotent group}, for
strongly asymptotically dynamically convex contact manifolds. This invariant
can be used to distinguish different contact structures. As an application, for
any complex dimension $n>8$ and any positive integer $k$, we can construct
$n-$dimensional Stein manifolds $V_0,V_1,\cdots,V_k$ such that
$\tilde{H}_j(V_i)=0, j\neq n-1,n$, $V_i's$ are almost symplectomorphic, their
boundaries are in the same almost contact class but not contactomorphic.
