Diameter of a Tree

Hard#trees #bfs #dfs· solved by 0 · time limit 2.0 s

A tree has $n$ nodes and $n-1$ edges. Its diameter is the number of edges on the longest path between any two nodes. Find it. (Trick: BFS from any node to the farthest node $a$ , then BFS from $a$ .)

Input

$n$ , then $n-1$ lines u v.

Output

The diameter.

Constraints

$1 \le n \le 10^5$

Sample 1

Input

Output