Problem on Tree

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

inputFormat

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}

outputFormat

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

样例

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

8