Devise an original consistent heuristic function for the Lights-On puzzle, justify it, and prove that it is consistent. (Recall that there is a difference between consistent heuristic and admis- sible heuristic. This problem is concerned with consistent heuristic.) You will be graded on the quality and originality of your heuristic and the strength of your argument. (a) (7 points) Describe how your heuristic works and your technique for calculating it, as clearly and concisely as possible. (b) (7 points) What features of the board does it attempt to capture? Justify your heuristie's design using example boards. (C) (5 points) Prove that your heuristic is consistent. Devise an original consistent heuristic function for the Lights-On puzzle, justify it, and prove that it is consistent. (Recall that there is a difference between consistent heuristic and admis- sible heuristic. This problem is concerned with consistent heuristic.) You will be graded on the quality and originality of your heuristic and the strength of your argument. (a) (7 points) Describe how your heuristic works and your technique for calculating it, as clearly and concisely as possible. (b) (7 points) What features of the board does it attempt to capture? Justify your heuristie's design using example boards. (C) (5 points) Prove that your heuristic is consistent