6. Suppose that you are trying to find a max flow in a directed graph. However, instead of having capacities on the edges, you have capacities on the nodes. In other words, each node can only accept a certain amount of total incoming flow. (Can you think of a real-life application for this kind of problem?) Show how to find a max flow in such a case. Hint: think about how to modify the graph, rather than the algorithm.

Treat single arithmetic operations (addition, subtraction, multiplication, and division) as constant time operations.