Consider the Hill Climbing Search algorithm for the $N-$Queens problem with $N=4.$ The image represents the start state. We want to reach a state i$.$e$.$

configuration of the board with $4$ queens such that no two queens attack each other. The objective function we consider is the number of pairs of queens that

attack each other and we want to minimise this objective function. The successor function we consider is moving a single queen along its column by one

square either directly up or directly down.

Let the objective function for the start state $=x,$ the number of neighbours of the start state $=y,$ the objective function of the neighbour of the start state with the

lowest objective function $=z,$ then what is the value of $2x+y+3z?$