CSES - Finding a Centroid
• Time limit: 1.00 s
• Memory limit: 512 MB
Given a tree of $n$ nodes, your task is to find a centroid, i.e., a node such that when it is appointed the root of the tree, each subtree has at most $\lfloor n/2 \rfloor$ nodes.

Input

The first input line contains an integer $n$: the number of nodes. The nodes are numbered $1,2,…,n$.

Then there are $n-1$ lines describing the edges. Each line contains two integers $a$ and $b$: there is an edge between nodes $a$ and $b$.

Output

Print one integer: a centroid node. If there are several possibilities, you can choose any of them.

Constraints
• $1 \le n \le 2 \cdot 10^5$
• $1 \le a,b \le n$
Example

Input:
5 1 2 2 3 3 4 3 5

Output:
3