Minimum cost maximum flow algorithm with custom cost function
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What kind of cost functions can be used in minimum cost maximum flow algorithm?

Is it possible to have a cost function similar to:

 - if flow on an edge is between [1, X], cost = FixedCost + C1 + flow * cost_per_flow[C1]
 - if flow on an edge is between [X + 1, Y], cost = FixedCost + C2 + flow * cost_per_flow[C2]
 - etc.

Does this change the algorithm in any way?