One day, you woke up in a huge maze. You did not remember why you are here, but you do remember that you have an important exam this morning! Thus you would like to get out of this maze as soon as possible. You found a map of this maze on the wall, but unfortunately the map did not show where you are. You have to mark yourself on the map first.

According to the map, this maze is formed by rooms and passages. Each passage connects two rooms, and does not intersect with other passages. These passages may form cycles. Each passage belongs to at most 1 cycle, and each room belongs to at most 2 cycles. Also, a room is connected by no more than 2+k passages where k is the number of cycles that this room belongs to. Further more, the i-th cycle may have a common point with a_i cycles and there are b_i passages which do not belong to any cycle but connect to exactly 1 room in this cycle. a_i + b_i <= 2.

You walked around for a while, starting from a room and ending in another room. During your walk, you drew a local map of the rooms and passages that you just walked through. You are sure that if a passage on your local map is in a cycle, then all passages in that cycle are also on the local map.

Now, you have the map of whole maze as well as your local map. Can you write a program to determine all the possible locations that you are in?