We have two urns A and B. Urn A has 2 green balls and 3 red balls. Urn B has 2 green balls and 3 blue balls. We first draw two balls without replacement from urn A and put them into urn B. We then draw two balls without replacement from urn B and put them into urn A. Let N be the number of green balls in urn A after the above operations. Compute the probability mass function of N. Simplify your answer to a fraction.