(30 points) We would like to use a genetic algorithm to solve the 8-Queens problem. Remember, this problem asks you to place 8 queens on an 8 x 8 chessboard such that no two queens can attack each other (i. e., share the same row, column, or diagonal). a)Propose a chromosome representation (i. e., a state representation) such that the string contains only numbers 1 through 8 and the state is valid. A valid state is one in which there is exactly one queen per column and one queen per row. Explain why your representation only encodes valid states. b)Propose a crossover operator that ensures that child states are valid and explain why your operator would help generate good results over other operators. Show (i. e., draw) an example of your crossover operator on two parent states to produce two child states.