Let I be a finite set of colors, and G be a directed graph on which each arc is labeled with a color in E. An w-walk is an infinite path VO COU1C1U2.. on G such that, for each i, G has an arc from v; to Vi+1 with color cz. In particular, we say the walk starts from vo. The walk is fair if there are infinitely many prefixes of the walk on which the number of red arcs, the number of green arcs and the number of blue arcs are all the same. Prove that there is an algorithm to decide whether the graph G has a fair walk starting from a given node vo