$,$ Consider the search space below, where S is the start node and G$1$ and G$2$ satisfy the

goal test. Ares 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 $f=h)$

Goal State reached:

States popped off:

$($ii$)$ Iterative Deepening

Goal State reached:

States popped off:

$($iii$)A^{**}$

Goal State reached:

States popped off: