D - Uninity

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

• 1 頂点からなる木はウニ度 0 の木である。
• ウニ度 k の木を 0 個以上と、ひとつの頂点 v を用意する。用意した各ウニ度 k の木から頂点をひとつずつ選び、その選んだ頂点と v を辺で結ぶ。こうしてできた木はウニ度 k+1 の木である。

ウニ度 k の木はウニ度 k+1,k+2,... の木でもあることが証明できます。

N 頂点からなる木が与えられます。 この木の頂点には 1 から N までの番号がついており、N-1 本の辺のうちの i 本目は頂点 a_ib_i を結んでいます。

### 制約

• 2 ≦ N ≦ 10^5
• 1 ≦ a_i, b_i ≦ N(1 ≦ i ≦ N-1)
• 与えられるグラフは木である。

### 入力

N
a_1 b_1
:
a_{N-1} b_{N-1}


### 入力例 1

7
1 2
2 3
2 4
4 6
6 7
7 5


### 出力例 1

2


### 入力例 2

12
1 2
2 3
2 4
4 5
5 6
6 7
7 8
5 9
9 10
10 11
11 12


### 出力例 2

3


Score : 1400 points

### Problem Statement

We 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.

### Input

The input is given from Standard Input in the following format:

N
a_1 b_1
:
a_{N-1} b_{N-1}


### Output

Print the minimum k such that the given tree is a tree of uninity k.

### Sample Input 1

7
1 2
2 3
2 4
4 6
6 7
7 5


### Sample Output 1

2


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 2

12
1 2
2 3
2 4
4 5
5 6
6 7
7 8
5 9
9 10
10 11
11 12


### Sample Output 2

3