Problem Description

There is a tree with $ N $ vertices. Each vertex in the tree is numbered from $ 1 $ to $ N $.

There are $ N-1 $ edges, and the $ i $-th edge connects vertex $ p_i $ and vertex $ q_i $.

Find the maximum $ M $ of a sequence of distinct vertices $ v_1, v_2, ..., v_M $ that satisfies the following condition:

• For all $1 \leq i < M$, there is no other vertex on the path connecting $ v_i $ and $ v_{i+1} $.

Input Format

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

$ N $ $ p_1 $ $ q_1 $ $ p_2 $ $ q_2 $ $ : $ $ p_{N-1} $ $ q_{N-1} $

Output Format

Output the maximum $ M $ of the sequence of distinct vertices that satisfies the condition.

Sample Input and Output

Sample Input #1

4
1 2
2 3
2 4

Sample Output #1

3

Sample Input #2

10
7 9
1 2
6 4
8 1
3 7
6 5
2 10
9 6
2 6

Sample Output #2

8

Notes/Hints

Constraints

• $2 \leq N \leq 10^5$
• $1 \leq p_i, q_i \leq N$
• The given graph is a tree.

见题面 Input 部分

见题面 Output 部分