$1.$ In the graph below, nodes can be expanded based on different search strategies. The first node is labeled $"$S$"($Start$),$ and edges between nodes are numbered according to their path cost $($i$.$e$.$ distance to the next node$).$ Additionally, each node is associated with a heuristic value, denoted as $"$h$($n$),"$ representing an estimate of the effort that needs to be made to reach the next node from that node. The heuristic values are provided below:

$-\backslash ($ h$($S$)=7\backslash )$

$-\backslash ($ h$($A$)=6\backslash$cdot h$($B$)=4\backslash$cdot h$($C$)=5\backslash )$

$-\backslash ($ h$($D$)=2\backslash )$

$-\backslash ($ h$($E$)=3\backslash )$

$-\backslash ($ h$($F$)=1\backslash )$

The graph structure is as follows:

If you apply the following search strategies, what node will be expanded next? Show your calculations for each node when needed or you will not receive credit for your solution.

A$)$ A$*[10$ Points$]$ S$,$ A

B$)$ Greedy Best$-$First Search $[5$ Points$]$

C$)$ Depth$-$First Search $[5$ Points$]$