11.3 The procedure depth_first_iterative_deepening/2 in this section may get into an indefinite loop if there is no solution path in the state space. It keeps searching for longer solution paths even when it is obvious that there do not exist any longer paths than those already searched. The same problem may occur when the user requests alternative solutions after all the solutions have already been found. Write an iterative deepening search program that will look for paths of length i+1 only if there was at least one path found of length i.