Degeneracy of holomorphic curves in surfaces

LetX be a complex projective algebraic manifold of dimension 2 and let D₁, ..., D_u be distinct irreducible divisors onX such that no three of them share a common point. Let(f:{mathbb{C}} to Xbackslash ( cup _{1 leqslant i leqslant u} D_i )) be a holomorphic map. Assume thatu ? 4 and that there exist positive integers n₁, ... ,n_u,c such that n_in_J D _i.D_j) =c for all pairsi,j. Thenf is algebraically degenerate, i.e. its image is contained in an algebraic curve onX.