In this problem, the goal is to stack the blocks alphabetically from a given initial configuration. The agent has a limited number of movements to accomplish this task:

move a block from the current stack and put on the table

move a block from the current stack onto another stack

Each configuration of the current stack is a state in the search space and can be given a heuristic value. This is how you compute the heuristics value of a state:

Add a point for every block that is positioned on the block it should be on$.$

Subtract a point for every block that is resting on the wrong block.

Using this function, the goal state has a score of $8$ because every block is in the right position so we add one point for each block as follows

$A(+1),B(+1),C(+1),D(+1),E(+1),F(+1),G(+1),$ and $H(+1)$ giving a total of $8.$

The initial state has a score of $4(+1$ for blocks C$,$ D$,$ E$,$ F$,$ G$,$ H and $-1$ for A and B$).$

In the example above, there's one move from the initial state: move $A$ to the table.

Figure $2.$ The Initial $($left$)$ and the only state reachable from it $($right$)$: state$2$

From this new state $($state$2),$ there are $3$ possible moves shown below from left to right:

place $A$ on $H($back to the original stack$)$

move $H$ to the table

place $H$ on $A$

What are the scores of these three states?

In every step and as discussed in class, Hill Climbing $(HC)$ will move in the direction of the higher score $($towards the goal with the maximum score of $8).$ If the scores of the states reachable from the current state are not higher than the score of the current state, then $HC$ will halt. At this point, $HC$ will have reached a local optimum. Give ne python implementation of this problem