Tree Diameter

A tree consisting of $n$ vertices is given.

The diameter of a tree is the maximum distance between two vertices. Find the diameter of the given tree.

Input

The first line contains an integer $n(1\le n\le 2\cdot 10^5)$ — the number of vertices in the tree. The vertices are numbered from $1$ to $n$.

Each of the following $n-1$ lines describes an edge and contains two integers $a$ and $b(1\le a,b\le n)$, indicating that there is an edge between vertices $a$ and $b$.

Output

Print one integer — the diameter of the tree.

Examples