Orange mood#1749
Once, the president of the European-level club "Nadir" announced that from the next season, the Dutch coach, who had won the respect of fans, might be replaced by a less successful Italian. Hearing this, outraged fans of the club headed to the president's palace to stage an orange revolution (after the color of the Dutch national team's shirts) and bring back the coach. It turned out that the presidential guard also rooted for "Nadir"...
The president is in a palace consisting of many rooms and corridors connecting them. Any two different rooms can be connected by at most one corridor. At both ends of each corridor is a door. Some doors have a deadbolt that can be locked or unlocked from inside the room. A locked deadbolt blocks access to the room from the corridor. The palace can be entered from the outside through some rooms (these are entrances).
Initially, all doors are open. Your task is to determine whether the president can choose a room to hide from the outraged fans such that, starting from this room, he can walk through the palace corridors, lock some doors, and then return to his hideout so that access to him from outside the palace is blocked.
The first line contains three integers , , : the number of rooms in the palace, the number of corridors, and the number of entrances (1 \le N \le 10000, 0 \le M \le 1000000, 1 \le P \le N). The second line contains integers — the numbers of the rooms through which you can enter the palace. The next lines describe the corridors of the palace. Each corridor is defined by a pair of integers from to — the numbers of the rooms it connects.
Then follow lines describing the rooms: for each room, the first value is P_i — the number of doors (corridors) that can be locked from inside the room; then P_i integers follow — the numbers of the corridors whose doors can be locked from inside this room (0 \le P_i \le 100).
Rooms and corridors are numbered starting from in the order they appear in the input file.
Print a single integer — the number of the room in which the president can hide. If there are multiple such rooms, print the smallest one. If it is impossible for the president to hide, print Impossible (without quotes).
Example 1