Lie subalgebras of $ L = \mathfrak{g}(\!(x)\!) \times \mathfrak{g}[x]/x^n\mathfrak{g}[x] $, complementary to the diagonal embedding $\Delta$ \mathfrak{g}[\![x]\!] and Lagrangian with respect some particular form, are in bijection formal classical $r$-matrices topological bialgebra structures on algebra power series $. In this work we consider arbitrary subspaces associate them so-called type (n...