Consider a $4$ queen problem where you are trying to place $4$ queens on each column of a $4$X$4$ board such that no two queen attacking another. Below is the current state where queens are placed in cells $(1,1),(2,2),(3,3)$ and $(4,4).$ Q Q Q Q You can move each queen only along the column arrive at a goal state. Assume that the heuristic function being used here is number of pairs of queens attacking each other. i$)$ ii$)$ iii$)$ What is the heuristic value of the current state. You are trying to solve this problem using the first choice hill climbing algorithm $($that is$,$ generate successors and accept the first successor which improves the state$).$ Show one step of this algorithm with all the necessary details. Consider that we decide to use simulated annealing in place of first choice hill climbing algorithm. Assume that the current temperature T is $0\mathrm{.}2.$ Given this, how likely the move that you suggested in the previous $($first choice hill climbing$)$ question is accepted? Provide details.