Suppose you need to solve a maximum flow problem on a directed network,

but in addition to capacities on edges, there are now capacities on vertices

as well; this means that each vertex $v$ cannot have more than $c_v$ units

of flow passing through it$.$ Show how to transform this problem into an

equivalent ordinary maximum flow problem that does not have capacities

on the vertices. $($Hint: the number of vertices could double$)$