Study the Demo code for 8-puzzle problem and answer the following questions: 1. Modify the DLS to simulate depth-first search. Find the best depth-limit prove that this is indeed the best depth-limit. Find the worst depth-limit based on your experiments. Provide a log of all experiments and the results to support you answer. 2. Compare the performance of A* and recursive best-first search on a set of randomly generated problems with Manhattan distance heuristic. Discuss your results. 3. Compare the performance of A* with Manhattan distance and A* with Misplaced tiles Heuristic on randomly generated problems. Explain the differences.