$12.(4$ pts$.)$ Consider the search space below, where S is the start node and G$1$ and G$2$ satisfy the goal test. Arcs are labeled with the cost of traversing them and the estimated cost to a goal is reported inside nodes. For each of the following search strategies, indicate which goal state is reached $($if any$)$ and list, in order, all the states popped off of the OPEN list. When all else is equal, nodes should be removed from OPEN in alphabetical order.

$($i$)$ Best$-$first search $($using $\backslash ($ f$=$h $\backslash ))$

Goal State reached:

States popped off:

$($ii$)$ Iterative Deepening

Goal State reached:

States popped off:

$($iii$)$ A$*$

Goal State reached:

States popped off:

please give the correct answer.I am giving this question second time but not giving the proper answer