Problem 7 [10 points]. Consider the 8puzzle problem and the two heuristics i and h2 from class. Recall that hi counts the number of misplaced tiles and h2 counts the total Manhattan distance of the tiles to their target locations. Prove that both heuristics are admissible. Problem 8 [10 bonus points]. For hi and h2 in the previous problem, show that they are consistent. Note that if you are sure you can prove consistency, you answer also works for the previous