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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;
public class Main
{
	int n;
	ArrayList<Integer> list[];
	final int inf=(int)(1e9+1);
	private void solve()throws IOException
	{
		n=nextInt();
		list=new ArrayList[n+1];
		for(int i=1;i<=n;i++)
			list[i]=new ArrayList<>();
		for(int i=1;i<n;i++)
		{
			int a=nextInt();
			int b=nextInt();
			list[a].add(b);
			list[b].add(a);
		}
		int dia=farthest(farthest(1).first).second;
		int ans=0;
		while(dia>0)
		{
			dia=(dia-1)/2;
			ans++;
		}
		out.println(ans);
	}
	Pair farthest(int v)
	{
		Queue<Integer> queue=new LinkedList<>();
		queue.add(v);
		Pair max=new Pair(v,0);
		int dist[]=new int[n+1];
		Arrays.fill(dist,inf);
		dist[v]=0;
		while(!queue.isEmpty())
		{
			int curr=queue.remove();
			for(int next:list[curr])
				if(dist[next]>dist[curr]+1)
				{
					dist[next]=dist[curr]+1;
					if(dist[next]>max.second)
						max=new Pair(next,dist[next]);
					queue.add(next);
				}
		}
		return max;
	}
	class Pair{
	    int first,second;
	    Pair(int a,int b){
	        first=a;
	        second=b;
	    }
	}

	 
	///////////////////////////////////////////////////////////

	public void run()throws IOException
	{
		br=new BufferedReader(new InputStreamReader(System.in));
		st=null;
		out=new PrintWriter(System.out);

		solve();
		
		br.close();
		out.close();
	}
	public static void main(String args[])throws IOException{
		new Main().run();
	}
	BufferedReader br;
	StringTokenizer st;
	PrintWriter out;
	String nextToken()throws IOException{
		while(st==null || !st.hasMoreTokens())
		st=new StringTokenizer(br.readLine());
		return st.nextToken();
	}
	String nextLine()throws IOException{
		return br.readLine();
	}
	int nextInt()throws IOException{
		return Integer.parseInt(nextToken());
	}
	long nextLong()throws IOException{
		return Long.parseLong(nextToken());
	}
	double nextDouble()throws IOException{
		return Double.parseDouble(nextToken());
	}
}