Problem Statement

You are given a tree with $N$ vertices. The vertices of the tree are numbered from $1$ to $N$, and the edges are numbered from $1$ to $N-1$.

Edge $i \ (1 \leq i \leq N-1)$ connects vertices $u_i, v_i$.

Now, perform the following operation.

• Remove $1$ of the undirected edges of the given tree. The number of connected components of the graph becomes $2$.

  For each connected component of the graph, choose $1$ vertex belonging to that component, and connect those $2$ vertices with an undirected edge.

The graph remains a tree after this operation. Find the minimum possible diameter of the tree after the operation.

Here, the diameter of a tree is defined as the maximum number of edges contained in a path connecting $2$ vertices in the tree.

Constraints

• $\displaystyle 2 \leq N \leq 10^5$
• $\displaystyle 1 \leq u_i, v_i \leq N$
• $\displaystyle u_i \neq v_i$
• All inputs are integers.
• The graph represented by the input is a tree.

Input

The input is given from standard input in the following format.

$N$
$u_1\ \ v_1$
$u_2\ \ v_2$
$:$
$u_{N-1}\ \ v_{N-1}$

Output

Output the value you found, followed by a newline.

Sample

5
1 2
2 3
3 4
4 5

3

2
1 2

1