Contest Duration: ~ (local time)
K - 木の問題 / Problem on Tree

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

• 全ての 1 \leq i < M について、v_iv_{i+1} を結ぶ経路の上に、v の他の頂点が存在しない。

### 制約

• 2 \leq N \leq 10^5
• 1 \leq p_i, q_i \leq N
• 与えられるグラフは木である。

### 入力

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


### 入力例 1

4
1 2
2 3
2 4


### 出力例 1

3


### 入力例 2

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


### 出力例 2

8


Score : 100 points

### Problem Statement

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.

### 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