(44 points) It is known that 5 chess queens can dominate the whole chess board which has 8 columns and 8 rows if the queens are strategically placed on the chess board. Consider this board game as a state space search problem to search a sequence of states, on each state of the sequence a queen will be added and the queens placed will together dominate certain numbers of board places. A best-first search will be used for find the sequence of states that dominate as much places as possible on the board. a) (6 points) Design a computer data structure for representing states. b) (18 points) Design an A algorithm (not necessary A*) for searching this state space. Give and describe your heuristic evaluation function. c) (20 points) Describe a production system or a rule based Knowledge-Based system (indicate the rule set and the inference engine), which solves this game problem.