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 $k$.