Problem D
Busiest Ant Level

Illustration of Ant colony

Deep under the forest, an ant colony is built as a network of tunnels and chambers. It is possible to reach every chamber from every chamber using a unique path. Chamber $0$ is the queen’s chamber and is at level $0$. The level of a chamber is its distance from the queen’s chamber, counted in terms of how many tunnels must be taken to reach it from the queen’s chamber.

Your task: find the level that contains the most chambers. If multiple levels have the same maximum number of chambers, print the lowest-numbered level.

Input

The first line contains one integer $n$ ($1 \le n \le 100\, 000$), which stands for the number of chambers in the ant colony.

The next $n-1$ lines each contain two integers $u$ and $v$ ($0 \leq u, v < n$) meaning there is a tunnel between chambers $u$ and $v$.

Output

The level that contains the maximum number of chambers. If there is a tie, print the smallest such level.

3
0 1
0 2

1

16
0 1
0 2
0 3
1 4
1 5
2 6
2 7
3 8
3 9
4 10
5 11
5 12
8 13
8 14
8 15

2