Complete the code for the dfs$\_$visit function below.

To do so$,$ please read the rest of the code provided and the surrounding comments very carefully.

Please ensure that the following rules are followed:

When visiting a node i$,$ consider the set of adjacent nodes in increasing order.

This is automatically done for you when you get self.adj$\_$list$[$i$]$ which is implemented as a python set.

Use the DFSTimeCounter class provided to keep track of DFS time.

The timer should be incremented just before we return from dfs$\_$visit and record the finish time for a node.

Recall that a back edge in a DFS is encountered whenever we visit a node i and encounter adjacent node j such that j has been discovered but not finished.

If this happens, add $($i$,$j$)$ to the set of back edges.

The dfs$\_$visit code does not return anything but updates the arguments discovery$\_$times, finish$\_$times, dfs$\_$tree$\_$parent and dfs$\_$back$\_$edges in place.