$7\mathrm{.}24($Eight Queens$)$ Another puzzler for chess buffs is the Eight Queens problem, which asks the following: Is it possible to place eight queens on an empty chessboard so that no queen is "attacking" any other $($i$.$e$.,$ no two queens are in the same row, in the same column or along the same diagonal$)?$ Use the thinking developed in Exercise $7\mathrm{.}22$ to formulate a heuristic for solving the Eight Queens problem. Run your application. $[$Hint: It's possible to assign a value to each square of the chessboard to indicate how many squares of an empty chessboard are "eliminated" if a queen is placed in that square. Each of the corners would be assigned the value $22,$ as demonstrated by Fig. $7\mathrm{.}31.$ Once these "elimination numbers" are placed in all $64$ squares, an appropriate heuristic might be as follows: Place the next queen in the square with the smallest elimination number. Why is this strategy intuitively appealing?$]$