7-Laboratoriya jumısı. Tema : Shuqırlıq boyınsha izlew algoritmı (dfs)

input
output
10 234 -1 12 234 13 234 14 234 15 234 16 234 17 234 18 234 19 234 233 19 5 234 233 233 12 233 13 233 15 233 19	1 0 0 0 2

6-topshiriq
The group of people consists of N members. Every member has one or more friends in the group. You are to write program that divides this group into two teams. Every member of each team must have friends in another team.

Input

The first line of input contains the only number N (N ≤ 100). Members are numbered from 1 to N. The second, the third,…and the (N+1)th line contain list of friends of the first, the second, …and the Nth member respectively. This list is finished by zero. Remember that friendship is always mutual in this group.

Output

The first line of output should contain the number of people in the first team or zero if it is impossible to divide people into two teams. If the solution exists you should write the list of the first group into the second line of output. Numbers should be divided by single space. If there are more than one solution you may find any of them.

Sample

input	output
7 2 3 0 3 1 0 1 2 4 5 0 3 0 3 0 7 0 6 0	4 2 4 5 6

7-topshiriq
Knife. Moonlit night. Rotten stump with a short black-handled knife in it. Those who know will understand. Disaster in the village. Werewolf.
There are no so many residents in the village. Many of them are each other's relatives. Only this may help to find the werewolf. The werewolf is merciless, but his descendants never become his victims. The werewolf can drown the village in blood, but he never kills his ancestors.
It is known about all the villagers who is the child of whom. Also, the sad list of the werewolf's victims is known. Your program should help to determine the suspects. It would be a hard task, if a very special condition would not hold. Namely, citizens of the village are not used to leave it. If some ancestor of some citizen lives in the village, then also his immediate ancestor does. It means, that, for example, if the father of the mother of some citizen still lives in the village, than also his mother still lives.

Input

The first line contains an integer N, 1 < N ≤ 1000, which is the number of the villagers. The villagers are assigned numbers from 1 to N. Further is the description of the relation "child-parent": a sequence of lines, each of which contains two numbers separated with a space; the first number in each line is the number of a child and the second number is the number of the child's parent. The data is correct: for each of the residents there are no more than two parents, and there are no cycles. The list is followed by the word "BLOOD" written with capital letters in a separate line. After this word there is the list of the werewolf's victims, one number in each line.

Output

The output should contain the numbers of the residents who may be the werewolf. The numbers must be in the ascending order and separated with a space. If there are no suspects, the output should contain the only number 0.

Samples

input	output
8 1 3 3 6 4 5 6 2 4 6 8 1 BLOOD 3 8	4 5 7
6 1 2 3 2 1 4 3 4 2 6 5 2 5 4 BLOOD 2 5	0