Problem Statement

You are given a tree with $N$ vertices numbered $1$ through $N$. The $i$-th edge connects vertex $A_i$ and vertex $B_i$.

Find the minimum integer $K$ such that you can paint each vertex in a color so that the following two conditions are satisfied. You may use any number of colors.

• For each color, the set of vertices painted in the color is connected and forms a simple path.
• For all simple paths on the tree, there are at most $K$ distinct colors of the vertices in the path.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq A_i, B_i \leq N$
• The given graph is a tree.
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

N
A_1 B_1
\vdots
A_{N-1} B_{N-1}

Output

Print the answer.