Wuhan University is one of the most beautiful universities in China, and there are many charming scenic spots in the campus. After observing for several years, iSea find an interesting phenomenon of those spots: many old spots were built organically and not according to some architecture plan, but, strangely, their growth exhibits a similar pattern: the cities started from three points of spots, with each pair being connected by a bidirectional street; then, gradually, new points of spots were added. Any new point of spot was connected by two new bidirectional streets to two different previous points of spots which were already directly connected by a street.
A tourist visiting our university would like to do a tour visiting as many points of spots as possible. The tour can start at any point of spot and must end at the same point of spot. The tour may visit each street at most once and each point of spot at most once except the first point of spot.
Searing in the library, iSea have known how the scenic spots grew. Now he want to find the largest number of different points of spots a single tour can visit.