et $=(,)$G$=($V$,$E$)$ be a graph and $$:$->+$c:E$$R $+$ be an edge cost function. We call an edge $$ in $$e in E $(1)$ necessary if $$e is contained in every minimum spanning tree; $(2)$ useless if no minimum spanning tree contains $$e; $(3)$ optional else. How many edges in the graph below are necessary