Solve the following problems by reducing to the original max-flow problem. In other words, explain how to solve the new flow variant problem using an algorithm for solving max-flow as a black-box. Explain how to take an input for the new problem and define an input for the original max-flow problem. Then given a max-flow f to this input you just defined, explain how to get the solution to the new problem. (a) There are many sources and many sinks, and we wish to maximize the total flow from all sources to all sinks. (b) Each vertex also has a capacity on the maximum flow that can enter it.