Problem G

I want to be a good teacher, so at least I need to remember all the student names. However, there are too many students, so I failed. It is a shame, so I don't want my students to know this. Whenever I need to call someone, I call his CLOSEST student instead. For example, there are 10 students:

A ? ? D ? ? ? H ? ?

Then, to call each student, I use this table:

Input

There is only one test case. The first line contains n, the number of students (1<=n<=100). The next line contains n space-separated names. Each name is either ? or a string of no more than 3 English letters. There will be at least one name not equal to ?. The next line contains q, the number of queries (1<=q<=100). Then each of the next q lines contains the position p (1<=p<=n) of a student (counting from left).

Output

Print q lines, each for a student. Note that "middle of X and Y" is only used when X and Y are both closest of the student, and X is always to his left.

Sample Input

10
A ? ? D ? ? ? H ? ?
4
3
8
6
10

Output for the Sample Input

left of D
H
middle of D and H
right of right of H