
Score : 1400 points
Problem StatementWe will recursively define uninity of a tree, as follows: (Uni is a Japanese word for sea urchins.)
A tree consisting of one vertex is a tree of uninity 0.
Suppose there are zero or more trees of uninity k, and a vertex v. If a vertex is selected from each tree of uninity k and connected to v with an edge, the resulting tree is a tree of uninity k+1.
It can be shown that a tree of uninity k is also a tree of uninity k+1,k+2,..., and so forth.
You are given a tree consisting of N vertices.
The vertices of the tree are numbered 1 through N, and the i-th of the N-1 edges connects vertices a_i and b_i.
Find the minimum k such that the given tree is a tree of uninity k.
Constraints
2 ≦ N ≦ 10^5
1 ≦ a_i, b_i ≦ N(1 ≦ i ≦ N-1)
The given graph is a tree.
InputThe input is given from Standard Input in the following format:
N
a_1 b_1
:
a_{N-1} b_{N-1}
OutputPrint the minimum k such that the given tree is a tree of uninity k.
Sample Input 17
1 2
2 3
2 4
4 6
6 7
7 5
Sample Output 12
A tree of uninity 1 consisting of vertices 1, 2, 3 and 4 can be constructed from the following: a tree of uninity 0 consisting of vertex 1, a tree of uninity 0 consisting of vertex 3, a tree of uninity 0 consisting of vertex 4, and vertex 2.
A tree of uninity 1 consisting of vertices 5 and 7 can be constructed from the following: a tree of uninity 1 consisting of vertex 5, and vertex 7.
A tree of uninity 2 consisting of vertices 1, 2, 3, 4, 5, 6 and 7 can be constructed from the following: a tree of uninity 1 consisting of vertex 1, 2, 3 and 4, a tree of uninity 1 consisting of vertex 5 and 7, and vertex 6.
Sample Input 212
1 2
2 3
2 4
4 5
5 6
6 7
7 8
5 9
9 10
10 11
11 12
Sample Output 23
