The British Informatics Olympiad is the computing competition for schools and colleges. We are proud to present BIO'99.

The 1999 British Informatics Olympiad Final
Spy vs Spy - Part Two

You have just heard from your two spies that the budget problems extended to their sophisticated equipment; apparently both pieces of chalk broke. The upshot of the equipment failure is that the spies were unable to know for certain when they entered a room they had been in before. In other words some rooms might occur on a map more than once with different labels. The spies are conscientious, so each version of a room will have the correct number of corridors leading from it.

Write a program that reads in the details of the two maps and determines if they might represent the same complex. The first line will be a pair of integers, 1<=n<=100 then 1<=m<=100, specifying the rooms on each map. The next n lines will contain the first spy's map, and the following m lines the second spy's map. The format for these lines is the same as the previous part.

If the two maps might represent the same complex you should output n lines. The jth line should be a list of all room labels on the second spy's map that correspond to label j on the first spy's map. If there are multiple solutions you only need to print one. If the two maps cannot represent the same complex you should just output Different.

```4 6
a 2 x 4
b 3
c 1
a 2 x 1
a 2 x 1
b 3
c 4
a 5 x 4
b 6
c 1
```

### Sample Output

```1 4
2 5
3 6
1 4```

The simplest map representing this complex would be defined by:

```a 2 x 1
b 3
c 1```

In other words, either of the two maps in the sample input can be compared wih this map and shown to be equivalent.