ShellSort

He made each turtle stand on another one's back
And he piled them all up in a nine-turtle stack.
And then Yertle climbed up. He sat down on the pile.
What a wonderful view! He could see 'most a mile!

King Yertle wishes to rearrange his turtle throne to place his highest-ranking nobles and closest advisors nearer to the top. A single operation is available to change the order of the turtles in the stack: a turtle can crawl out of its position in the stack and climb up over the other turtles to sit on the top.

Given an original ordering of a turtle stack and a required ordering for the same turtle stack, your job is to determine a minimal sequence of operations that rearranges the original stack into the required stack.

Input Specification

The first line of the input consists of a single integer K, giving the number of test cases. Each test case consists of an integer n, giving the number of turtles in the stack. The next n lines specify the original ordering of the turtle stack. Each of the lines contains the name of a turtle, starting with the turtle on the top of the stack and working down to the turtle at the bottom of the stack. Turtles have unique names, each of which is a string of no more than eighty characters drawn from a character set consisting of the alphanumeric characters, the space character and the period (“.”). The next n lines in the input give the desired ordering of the stack, once again by naming turtles from top to bottom. Each test case consists of exactly 2n+1 lines in total. The number of turtles (n) will be less than or equal to two hundred.

Output Specification

For each test case, the output consists of a sequence of turtle names, one per line, indicating the order in which turtles are to leave their positions in the stack and crawl to the top. This sequence of operations should transform the original stack into the required stack and should be as short as possible. If more than one solution of shortest length is possible, any of the solutions may be reported. Print a blank line after each test case.

Sample Input

1. 2
2. 3
3. Yertle
4. Duke of Earl
5. Sir Lancelot
6. Duke of Earl
7. Yertle
8. Sir Lancelot
9. 9
10. Yertle
11. Duke of Earl
12. Sir Lancelot
13. Elizabeth Windsor
14. Michael Eisner
15. Richard M. Nixon
16. Mr. Rogers
17. Ford Perfect
18. Mack
19. Yertle
20. Richard M. Nixon
21. Sir Lancelot
22. Duke of Earl
23. Elizabeth Windsor
24. Michael Eisner
25. Mr. Rogers
26. Ford Perfect
27. Mack

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Output for Sample Input

1. Duke of Earl
3. Sir Lancelot
4. Richard M. Nixon
5. Yertle

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