Description

SDNU ACM-ICPC Association is in a mess. If you join it, you should be in the shadow of a person. This person, we call him "dalao".

For example, there are two rookies, $C$ and $D$, rely on $A$. We can say that $A$ is the closest dalao of rookies $C$ and $D$.

For another example, $A$ have two heelers $C$ and $D$, $D$ have two heelers $E$ and $F$.We can know that $A$ is the closest dalao of $E$ and $C$.

But with the growth of Association, we cannot find the closest dalao between two rookies. So we need your help.

Format

Input

There will be a series of examples.

For each input, the first line contains two integers $N$. $N$ means the number of people.

Followed by the $N-1$ lines, each line contains two integers $A$ and $B$. It means that $A$ is a dalao of $B$.

Then the next line, contains two integers $A$ and $B$. It means that we want to know who is the closest dalao between $A$ and $B$.

Output

For each input, you should output the name of the closest dalao.If you cannot find this dalao, you should output "I am so bad."

Samples

7
1 2
1 3
2 5
2 6
6 7
6 8
3 5

1

Hints

Remember that a rookie is also a dalao of itself
For example:
Input

3  
1 2  
2 3  
2 3

Output

2