Partition of a directed bipartite graph into two directed cycles

Let D = (V1, V2; A) be a directed bipartite graph with |V1| = |V2| = n ⩾ 2. Suppose that dD(x) + dD(y) ⩾ 3n + 1 for all x ϵ V1 and y ϵ V2. Then D contains two vertex-disjoint directed cycles of lengths 2n1 and 2n2, respectively, for any positive integer partition n = n1 + n2. Moreover, the condition is sharp for even n and nearly sharp for odd n.