Uninity

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.

Examples

Input

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

Output

2

Input

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

Output

3

inputFormat

Input

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

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

outputFormat

Output

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

Examples

Input

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

Output

2

Input

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

Output

3

样例

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

3