Given a tree with ~N~ nodes which are numbered from ~0~ to ~N-1~. Root of tree is node numbered by ~0~. Caculate height of the tree.

Input

• The first line is an integer ~N~ ~(1 \le N \le 10^5)~.
• Each line in the next ~N - 1~ lines contains ~2~ integers ~u, v~, represeting an edge connecting vertex ~u~ and vertex ~v~.

Output

• An integer which is height of the given tree.

Sample Input

3
0 1
1 2

Sample Output

2