The 6-queen problem requires that you place 6 queens on a 6 6 chessboard, so as no queen attacks another one located in the same row, column or diagonal. We define the states to be any configuration of the board where we have one queen per column. The successor function moves a single queen to another square in the same column. For a state S, consider the evaluation function fitness(S), as the number of non-attacking pairs of queens in state S. (a) How many possible states are there in total? (b) How many successor states are there for each state? (c) What is the fitness function for the following state: