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.

Sample Input 1

7
3 4
1 5
4 5
1 2
7 4
1 6

Sample Output 1

3

If $K=3$, the conditions can be satisfied by painting vertices $1,2,3,4$, and $5$ in color $1$, vertex $6$ in color $2$, and vertex $7$ in color $3$. If $K \\leq 2$, there is no way to paint the vertices to satisfy the conditions, so the answer is $3$.

Sample Input 2

6
3 5
6 4
6 3
4 2
1 5

Sample Output 2

1

Sample Input 3

9
1 3
9 5
8 7
2 1
5 2
5 8
4 8
6 1

Sample Output 3

3