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.

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.

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.

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

见题面 Input 部分

见题面 Output 部分