To celebrate National Party with your Bear Day, the school is going to hold a Bear-themed Poetry Festival all day on each of November 15, 16, and 17. Several poetry sessions have been planned, and a large number of poets have been invited to read their work during the event. You need to select presenting poets, subject to the following constraints:

Exactly k poetry readings must be performed each day, and thus 3k altogether.

Each reading will be one poets work in one particular type (limericks, haiku, ballad, etc).

Each type of poem may be presented at most once per day.

Each candidate poet has given you a list of types he or she is willing to present.

Each poet can read for at most three presentations during the entire event. Suppose you have a list of the n candidate poets and g different types of poems. You are also given k, the number of readings each day. Use network flow techniques to design a polynomial-time algorithm that either assigns a poet and a style to each of the 3k readings, or correctly reports that no such assignment is possible.