题目描述
There is a tree with N vertices, numbered 1 through N.
The i-th of the N-1 edges connects the vertices p_i and q_i.
Among the sequences of distinct vertices v_1, v_2, ..., v_M that satisfy the following condition, find the maximum value of M.
- For every $1 \leq i < M$, the path connecting the vertices v_i and v_{i+1} do not contain any vertex in v, except for v_i and v_{i+1}.
Constraints
- $2 \leq N \leq 10^5$
- $1 \leq p_i, q_i \leq N$
- The given graph is a tree.
Input
The input is given from Standard Input in the following format:
N
p_1 q_1
p_2 q_2
:
p_{N-1} q_{N-1}
Output
Print the maximum value of M, the number of elements, among the sequences of vertices that satisfy the condition.
Examples
Input
4
1 2
2 3
2 4
Output
3
Input
10
7 9
1 2
6 4
8 1
3 7
6 5
2 10
9 6
2 6
Output
8
输入格式
见题面
输出格式
见题面
样例输入
10
7 9
1 2
6 4
8 1
3 7
6 5
2 10
9 6
2 6
样例输出
8