An undirected graph $G$ is shown below. We assume that we are using adjacency lists as the graph representation. We further assume that the vertices on the adjacency lists are listed alphabetically. For example, if both $x$ and $Y$ are on the adjacency list of vertex $Z,$ then $x$ is ahead of $Y$ on the list of $Z.$

Apply breadth$-$first search $($FFS$)$ on the graph, starting with vertex $s=A.$ During the computation, the algorithm computes values v$.$d and $v$:$$ for each vertex in the graph, where v$.$d is the current distance from $s$ to vertex $v$ and $v.$ is the predecessor of vertex $v,$ respectively. After the $BFS,$ answer the following questions.

$($a$)$ After BFS$,$ what is B$.$d$?$

$($c$)$ After BFS$,$ what is C$.$d$?$

$($d$)$ After BFS$,$ what is $C.?$

$($e$)$ After BFS$,$ what is D$.$d$?$

$($f$)$ After BFS$,$ what is $D*?$