Write the state space of the $8-$puzzle using the following:

The diagonal of initial state contains the first unique numbers of your university number, and the rest numbers are random, avoid the $"9"$ if it is found in your number.

The Goal state is $[1,2,3$;$4,5,6$;$7,8,n\}$

Use Greedy best first search with the heuristic number of misplaced tiles $($minimize$)$

Do the same using $A^{**}$ algorithm,