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 $Y$, $\deg^{+}v\leq \deg^{-}v$
Problem
Source: Iranian National Olympiad (3rd Round) 2002
Tags: graph theory, combinatorics proposed, combinatorics