Problem:
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

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

//by yjz
#include<bits/stdc++.h>
using namespace std;
#define FF first
#define SS second
#define PB push_back
#define MP make_pair
#define bged(v) (v).begin(),(v).end()
#define foreach(it,s) for(__typeof((s).begin()) it=(s).begin();it!=(s).end();it++)
typedef long long ll;
const int Imx=2147483647;
const ll Lbig=2e18;
const int mod=1e9+7;
//My i/o stream
struct fastio
{
	char s[100000];
	int it,len;
	fastio(){it=len=0;}
	inline char get()
	{
		if(it<len)return s[it++];it=0;
		len=fread(s,1,100000,stdin);
		if(len==0)return EOF;else return s[it++];
	}
	bool notend()
	{
		char c=get();
		while(c==' '||c=='\n')c=get();
		if(it>0)it--;
		return c!=EOF;
	}
}_buff;
#define geti(x) x=getnum()
#define getii(x,y) geti(x),geti(y)
#define getiii(x,y,z) getii(x,y),geti(z)
#define puti(x) putnum(x),putchar(' ')
#define putii(x,y) puti(x),puti(y)
#define putiii(x,y,z) putii(x,y),puti(z)
#define putsi(x) putnum(x),putchar('\n')
#define putsii(x,y) puti(x),putsi(y)
#define putsiii(x,y,z) putii(x,y),putsi(z)
inline ll getnum()
{
	ll r=0;bool ng=0;char c;c=_buff.get();
	while(c!='-'&&(c<'0'||c>'9'))c=_buff.get();
	if(c=='-')ng=1,c=_buff.get();
	while(c>='0'&&c<='9')r=r*10+c-'0',c=_buff.get();
	return ng?-r:r;
}
template<class T> inline void putnum(T x)
{
	if(x<0)putchar('-'),x=-x;
	register short a[20]={},sz=0;
	while(x)a[sz++]=x%10,x/=10;
	if(sz==0)putchar('0');
	for(int i=sz-1;i>=0;i--)putchar('0'+a[i]);
}
inline char getreal(){char c=_buff.get();while(c==' '||c=='\n')c=_buff.get();return c;}
int n;
vector<int>con[100111];
int dfs(int x,int pre=-1)
{
	int ret=0;
	for(int i=0;i<con[x].size();i++)
	{
		int u=con[x][i];
		if(u==pre)continue;
		ret|=dfs(u,x);
	}
	return ret+1;
}
int main()
{
	geti(n);
	for(int i=1;i<n;i++)
	{
		int x,y;
		getii(x,y);
		con[x].PB(y);
		con[y].PB(x);
	}
	int tmp=dfs(1);
	for(int i=30;i>=0;i--)if(tmp>>i&1)
	{
		cout<<i<<endl;
		return 0;
	}
	return 0;
}