IR-MO 2002 Problem 12

We have a bipartite graph $G$ (with parts $X$ and $Y$ ). We orient each edge arbitrarily. Hessam chooses a vertex at each turn and reverse the orientation of all edges that $v$ is one of their endpoint. Prove that with these steps we can reach to a graph that for each vertex $v$ in part $X$ , $\deg^{+}(v)\geq \deg^{-}(v)$ and for each vertex in part $Y$ , $\deg^{+}v\leq \deg^{-}v$