Problem M
Rumor Mill

At the Benjamin Franklin School in Broken Fork Saskatchewan, the spreading of rumors is strictly regulated.

On Day 0, a student wishing to spread a rumor must notify the school office. No spreading of the rumor may occur that day.

On Day 1, the student must tell all of his or her friends the rumor before the end of the day. (Leaving out any friends causes hurt feelings, so this rule is strictly enforced.) No further spreading of the rumor is allowed that day.

On Day 2, each student who learned of the rumor the previous day must pass the rumor along to every friend who has not yet heard the rumor. No further spreading of the rumor is allowed that day.

The rumor must continue spreading in this fashion until the day comes that no more spreading of the rumor is possible under the rules. On that day, the school principal reads the rumor over the intercom, which guarantees that all students have heard the rumor.

Following the intercom announcement, the principal must file a report with the school board. In the report, the principal must list the student who started the rumor, followed by the students (in lexicographic order) who first learned of the rumor on Day 1, and so on, ending with the students (in lexicographic order) who first learned of the rumor over the intercom.

For example, suppose the student body consists of Cam, Art, Edy, Bea, and Dan, where Bea and Edy are friends, Dan and Bea are friends, and Art and Dan are friends.

• On Day 0, Dan notifies the office of his plan to start a rumor about the school lunches.

• On Day 1, Dan spreads the rumor to his two friends, Bea and Art.

• On Day 2, Bea tells her friend Edy. Bea’s other friend (Dan) already knows the rumor, as does Art’s only friend (also Dan).

• On Day 3, the rules don’t permit anyone else to be told the rumor, since Edy’s only friend (Bea) already knows. The principal reads the rumor over the intercom and invites everyone to lunch at McDonalds. Cam, who is new to the school and has no friends, finally learns what everyone else has been whispering about.

After lunch, the principal fires the lunchroom staff and files the rumor report, listing the students in this order: Dan, Art, Bea, Edy, Cam.

Your job is to help the principal prepare rumor reports.

Input

The first line contains the number $n$ of students at the school ($1 \le n \le 2\, 000$).

The next $n$ lines are student names. Each line contains a single unique name (maximum length $20$, no embedded white space).

The next line contains the number $f$ of friend pairs at the school ($0 \le f \le 10\, 000$.

The next $f$ lines identify friends. Each line contains the names of two students who are friends. No one is his or her own friend. A single friend pair never appears more than once.

The next line contains the number $r$ of reports that the principal needs to generate ($1 \le r \le 2\, 000$).

Each of the next $r$ lines is the name of a student who has started a rumor.

Output

For each student named in the final section of the input, print the list of students that the principal would need to put into a report concerning a rumor started by that student. The list should be a single line that contains, in the proper order, the names of all the students in the school. The names should be separated by spaces.

3
Cassandra
Alberforth
Buttrick
1
Cassandra Alberforth
1
Alberforth

Alberforth Cassandra Buttrick

5
Cam
Art
Edy
Bea
Dan
3
Bea Edy
Dan Bea
Art Dan
2
Dan
Cam

Dan Art Bea Edy Cam
Cam Art Bea Dan Edy