Suppose we are given a directed network G $=($V$,$ E$)$ with a root node r and a set of terminals T $$ V $.$ We would like to disconnect many terminals from r$,$ while cutting relatively few edges. We make this tradeoff precise as follows. For a set of edges F $$ E$,$ let q$($F$)$ denote the number of nodes v in T such that there is no r $$ v path in the subgraph $($V$,$ E $$ F$).$ Give a polynomial time algorithm to find a set F of edges that maximizes the quantity q$($F$)|$F$|.($Note that setting F equal to the empty set is an option.$)$ Hint: How would you have solved the problem if there were only one terminal vertex? Now extend it to the case of multiple terminals $($sinks$).$ Visualize any cut properly