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<cmath>
#include<cstring>
#include<algorithm>
using namespace std;
#define MAXN 100010
int Adj[MAXN],V[MAXN*2],nxt[MAXN*2],c;
void AddEdge(int u,int v)
{
	c++;V[c]=v,nxt[c]=Adj[u];Adj[u]=c;
}
int dp[MAXN][21],n,ans;
void dfs(int u,int p)
{
	for(int i=Adj[u];i;i=nxt[i])
		if(V[i]!=p)
		{
			int v=V[i];
			dfs(v,u);
			for(int j=0;j<=20;j++)
				dp[u][j]+=dp[v][j];
		}
	int k=0;
	for(int i=20;i>=0;i--)
		if(dp[u][i]>1)
		{
			k=i+1;
			break;
		}
	while(dp[u][k]) k++;
	dp[u][k]++;
	for(int i=0;i<k;i++)
		dp[u][i]=0;
	ans=max(ans,k);
}
int main()
{
	scanf("%d",&n);
	int u,v;
	for(int i=1;i<n;i++)
	{
		scanf("%d%d",&u,&v);
		AddEdge(u,v);
		AddEdge(v,u);
	}
	dfs(1,0);
	printf("%d\n",ans);
}
