Tree is a connected graph without cycles. A leaf of a tree is any vertex connected with exactly one other vertex.

You are given a tree with n vertices and a root in the vertex 1. There is an ant in each leaf of the tree. In one second some ants can simultaneously go to the parent vertex from the vertex they were in. No two ants can be in the same vertex simultaneously except for the root of the tree.

Find the minimal time required for all ants to be in the root of the tree. Note that at start the ants are only in the leaves of the tree.

Input

The first line contains integer n (2 ≤ n ≤ 5·105) — the number of vertices in the tree.

Each of the next n - 1 lines contains two integers xi, yi (1 ≤ xi, yi ≤ n) — the ends of the i-th edge. It is guaranteed that you are given the correct undirected tree.

Output

Print the only integer t — the minimal time required for all ants to be in the root of the tree.

Examples

Input

12
1 2
1 3
1 4
2 5
2 6
3 7
3 8
3 9
8 10
8 11
8 12


Output

6


Input

2
2 1


Output

1
import java.io.*;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.StringTokenizer;

/**
 * Created by vikas.k on 24/12/16.
 */
public class CFE7E {
    public static void main(String[] args){
        CFE7E gv = new CFE7E();
        gv.solve();
    }

    private List<List<Integer>> str;
    private List<Integer> dist;

    private void solve(){
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        int n = sc.nextInt();

        str = new ArrayList<>(n);
        for (int i=0;i<n;i++) str.add(new ArrayList<>());

        for(int i=0;i<n-1;i++){
            int x = sc.nextInt();
            int y = sc.nextInt();

            str.get(x-1).add(y-1);
            str.get(y-1).add(x-1);
        }

        int ans =0;
        for(int i:str.get(0)){
            ans = Math.max(ans, compute(i)+1);
        }
        out.println(ans);
        out.close();
    }

    private int compute(int v){
        dist = new ArrayList<>();
        doDfs(v,0,0);
        Collections.sort(dist);

        for(int i=0;i<dist.size();i++){
            if(i>0) dist.set(i ,Math.max(dist.get(i),dist.get(i-1)+1));
        }
        return dist.size()>0? dist.get(dist.size()-1):0;
    }

    private void doDfs(int v,int p,int d){
        int ch =0;
        for(int i:str.get(v)){
            if(i == p) continue;
            ch++;
            doDfs(i,v,d+1);
        }
        if(ch == 0) dist.add(d);
    }

    public static PrintWriter out;

    private static class MyScanner{
        BufferedReader bufferedReader;
        StringTokenizer stringTokenizer;

        private MyScanner(){
            bufferedReader = new BufferedReader(new InputStreamReader(System.in));
        }

        private String next(){
            if(stringTokenizer == null || !stringTokenizer.hasMoreElements()){
                try {
                    stringTokenizer = new StringTokenizer(bufferedReader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return stringTokenizer.nextToken();
        }

        private int nextInt(){
            return Integer.parseInt(next());
        }
        private String nextLine(){
            String ret= "";
            try {
                ret= bufferedReader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return ret;
        }
    }
}
