Program $2$: Perform DFS $($Depth$-$First Search$)$ and output the heights of each tree in the search forest.

In both problems you will read a sequence of adjacency lists. Here we assume the lists are sorted to get well$-$defined answers. If your traversal algorithm needs to make a choice, then choose the first $($lowest index$)$ vertex available. Here, the first line for each digraph is an integer n indicating the order of the digraph. This is followed by n white space separated lists of $($out$-)$ adjacencies for nodes labeled $0$ to n $1.$ The last digraph of the sequence will be a digraph of order $0$ and this is noi processed, Input comes from stdin $($keyboard$)$ and output goes to stdout $($console$).$

Sample Input$/$Output

Adjacency Lists

$3$

$1$

$2$

$01$

$5$

$13$

$024$

$3$

$014$

$23$

$8$

$123$

$0$

$07$

$12$

$23$

$6$

$015$

$14$

$0$

DFS Sample Output

$2$

$4$

$41$