State H1 H2 S 5 4 A 3 2 B 6 6 2 2 1 D 3 3 G 0 0 B 3 3 D A 1 3 1 1 2 G s 12 Consider the above heuristic values for the given graph. a) Is H1 a consistent heuristic? Show all the required steps. [2] b) Is H2 a consistent heuristic? Show all the required steps. [2] c) Check whether any of the heuristic is admissible or not. [2] d) Find out the path from S to G using A* tree search considering the admissible heuristic from H1 and H2. State how many nodes were expanded during the search process. Did you find out the optimal path? If not, then state which path would be optimal? (If there is a tie, expand the nodes in alphabetical