Delegation (Platinum)

Farmer John's farm consists of $N$ pastures ($2 \leq N \leq 10^5$) connected by $N-1$ roads, so that any pasture is reachable from any other pasture. In other words, the farm is a tree. But after 28 years of dealing with the tricky algorithmic problems that inevitably arise from trees, FJ has decided that a farm shaped like a tree is too complex. He believes algorithmic problems are simpler on paths.

So he plans to partition the set of roads into several paths and delegate responsibility for these paths to his farm hands. He does not care about the number of paths. However, he wants every path to be as long as possible, so that no farm hand can get away with an asymptotically inefficient algorithm.

Help Farmer John find the largest positive integer $K$ such that the roads can be partitioned into paths of length at least $K$.

The first line contains a single integer $N$.

The next $N-1$ lines each contain two space-separated integers $a$ and $b$ describing an edge between vertices $a$ and $b$. Both $a$ and $b$ are in the range $1 \ldots N$.

Print $K$.

One possible set of paths is as follows: $2-1-6-7-8, 3-1-4-5$