Give a complete problem formulation, in terms of (1) initial state, (2) goal test, (3) successor function and (4) cost function, for each of the following a) and b). Choose a formulation that is precise enough to be implemented. a) Using only four colors, you have to color a planar map in such a way that no two adjacent regions have the same color; b) You have a program that outputs the message illegal input record when fed a certain file of input records. You know that processing of each record is independent of the other record. You want to discover what record is illegal.