Description

Kong belongs to a huge family. Recently he got a family name list which lists all men (no women) in his family over many generations. The list shows that the whole family has a common ancestor, let's call him Mr. X. Of course, everybody except Mr.X in the list is Mr. X's descendant. Everybody's father is shown in the list except that Mr. X's father is not recorded. We define that Mr. X's generation number is $0$. His son's generation number is $1$.His grandson's generation number is $2$, and so on. In a word, everybody's generation number is$1$ smaller than his son's generation number. Everybody's generation number is marked in some way in the list. Now Kong is willing to pay a lot of money for a program which can re-arrange the list as he requires ,and answer his questions such as how many brothers does a certain man have, etc. Please write this program for him.

Format

Input

There are no more than $15$ test cases. For each test case: The first line is an integer$N( 1 <= N <= 30,000)$, indicating the number of names in the list. The second line is the name of Mr. X. In the next $N-1$ lines, there is a man's name in each line. And if the man's generation number is $K$, there are $K$ dots( '.') before his name. Please note that : $1$) A name consists of only letters or digits( '$0$'-'$9$').$2$) All names are unique. $3$) Every line's length is no more than $60$ characters. $4$) In the list, a man M's father is the closest one above M whose generation number is $1$ less than M. $5$) For any $2$ adjacent lines in the list, if the above line's generation number is G1 and the lower line' s generation number is G2, than G2 <= G1 +1 is guaranteed. After the name list, a line containing an integer $Q(1<=Q<=30,000)$follows, meaning that there are $Q$ queries or operations below. In the Next $Q$lines, each line indicates a query or operation. It can be in the following 3 formats: 1) L Print the family list in the same format as the input, but in a sorted way. The sorted way means that: if $A$ and $B$ are brothers(cousins don’t count), and $A$'s name is alphabetically smaller than $B$'s name, then $A$ must appear earlier than $B$. 2) b name Print out how many brothers does "name" have, including "name" himself. 3) c name1 name2 Print out the closest common ancestor of "name1" and "name2". "Closest" means the generation number is the largest. Since Mr. X has no ancestor in the list, so it's guaranteed that there is no question asking about Mr. X's ancestor. The input ends with $N = 0$.

Output

Already mentioned in the input.

Samples

9
Kongs
.son1
..son1son2
..son1son1
...sonkson2son1
...son1son2son2
..son1son3
...son1son3son1
.son0	
7
L
b son1son3son1
b son1son2
b sonkson2son1
b son1
c sonkson2son1 son1son2son2
c son1son3son1 son1son2
0

Kongs
.son0
.son1
..son1son1
...son1son2son2
...sonkson2son1
..son1son2
..son1son3
...son1son3son1
1
3
2
2
son1son1
son1