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<cstdio>
#include<cstring>

int n,x,y,hd[100001],cnt,d[100001],f[100001],t[200001],v[100001],num[21],fa[100001],mx;

struct node
{
	int to,next,ans;
}e[200001];

void addedge(int x,int y)
{
	e[++cnt].next=hd[x];
	hd[x]=cnt;
	e[cnt].to=y;
	e[cnt].ans=0;
}

int calc(int x) {return ((x-1)^1)+1;}
int getmax(int a,int b) {return a>b?a:b;}

void dfs(int x)
{
	for (int i=hd[x]; i; i=e[i].next)
		if (e[i].to!=fa[x]) fa[e[i].to]=x,dfs(e[i].to);
	memset(num,0,sizeof(num));
	for (int i=hd[x]; i; i=e[i].next)
		if (e[i].to!=fa[x]) 
			for (int j=0; j<21; j++)
				if ((f[e[i].to]>>j)&1) num[j]++;
	mx=-1;
	for (int i=20; i>=0; i--) 
		if (num[i]>1) {mx=i; break;}
	v[x]=mx+1;
	while (num[v[x]]) v[x]++;
	f[x]=(1<<v[x]);
	for (int i=v[x]+1; i<=20; i++)
		if (num[i]) f[x]|=(1<<i);
}

int main()
{
	scanf("%d",&n); cnt=0;
	memset(hd,0,sizeof(hd));
	memset(d,0,sizeof(d));
	for (int i=1; i<n; i++) 
		scanf("%d%d",&x,&y),addedge(x,y),addedge(y,x),d[x]++,d[y]++;
	memset(f,0,sizeof(f));
	memset(fa,0,sizeof(fa));
	dfs(1); mx=0;
	for (int i=1; i<=n; i++) mx=getmax(mx,v[i]);
	printf("%d\n",mx);
	return 0;
}