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
#include <iostream>
#include <cstdio>
#include <cctype>

using namespace std;

inline int read()
{
	int x=0,f=1;
	char ch=getchar();
	while (!isdigit(ch)) f=ch=='-'?-1:f,ch=getchar();
	while (isdigit(ch)) x=x*10+ch-'0',ch=getchar();
	return x*f;
}

const int N=100005;
const int E=N<<1;

int tov[E],nxt[E];
int last[N];
int n,tot,ans;

inline void insert(int x,int y){tov[++tot]=y,nxt[tot]=last[x],last[x]=tot;}

int dfs(int x,int fa=0)
{
	int ret=0,uni=0;
	for (int i=last[x],y,bit;i;i=nxt[i])
		if ((y=tov[i])!=fa) bit=dfs(y,x),uni|=bit&ret,ret|=bit;
	int d=1;
	for (int tmp=uni;tmp;d=tmp<<1,tmp-=tmp&-tmp);
	for (;ret&d;d<<=1);
	int res=0;
	for (int tmp=d;tmp;++res,tmp>>=1);
	ans=max(ans,res-1),ret=(ret^d)&((-1)^(d-1));
	return ret;
}

int main()
{
	//freopen("uninity.in","r",stdin),freopen("uninity.out","w",stdout);
	n=read();
	for (int i=1,x,y;i<n;++i) x=read(),y=read(),insert(x,y),insert(y,x);
	dfs(1),printf("%d\n",ans);
	//fclose(stdin),fclose(stdout);
	return 0;
}