Problem:
Score : 400 points

Problem Statement

Given is a tree G with N vertices.
The vertices are numbered 1 through N, and the i-th edge connects Vertex a_i and Vertex b_i.

Consider painting the edges in G with some number of colors.
We want to paint them so that, for each vertex, the colors of the edges incident to that vertex are all different.

Among the colorings satisfying the condition above, construct one that uses the minimum number of colors.

Constraints

2 \le N \le 10^5

1 \le a_i \lt b_i \le N

All values in input are integers.

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

N
a_1 b_1
a_2 b_2
\vdots
a_{N-1} b_{N-1}

Output

Print N lines.

The first line should contain K, the number of colors used.

The (i+1)-th line (1 \le i \le N-1) should contain c_i, the integer representing the color of the i-th edge, where 1 \le c_i \le K must hold.

If there are multiple colorings with the minimum number of colors that satisfy the condition, printing any of them will be accepted.

Sample Input 1

3
1 2
2 3

Sample Output 1

2
1
2

Sample Input 2

8
1 2
2 3
2 4
2 5
4 7
5 6
6 8

Sample Output 2

4
1
2
3
4
1
1
2

Sample Input 3

6
1 2
1 3
1 4
1 5
1 6

Sample Output 3

5
1
2
3
4
5

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.util.Map.Entry;

import javax.swing.text.Segment;
import javax.xml.ws.WebEndpoint;

import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;

import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;
 
public class Main //implements Runnable
{
//    static int dx[]={-1,0,1,0};
//    static int dy[]={0,-1,0,1};
	static double s;
	
    public static void main(String[] args)   throws Exception, IOException{        
//        long mod=1000000007;
        Reader sc = new Reader(System.in);
        PrintWriter out=new PrintWriter(System.out);

        int n=sc.nextInt();
        ArrayList<Long> ret[] = new ArrayList[n];
        for (int i = 0; i < ret.length; i++) {
            ret[i] = new ArrayList<>();
        }
        for (int i = 0; i < n-1; i++) {
            int a=sc.nextInt()-1;
            int b=sc.nextInt()-1;
            ret[a].add((long)1000000*b+i);
            ret[b].add((long)1000000*a+i);
        }

        int p[]=new int[n];
        int cn[]=new int[n];
        int c[]=new int[n-1];
        fill(p,-1);

        LinkedList<Integer> l=new LinkedList<>();
        long t=1000000,e,nm=1;
        l.add(0);
        while(!l.isEmpty()) {
        	int w=l.poll();
//        	db(w);
        	for (int i = 0,to,nc=1,ei; i < ret[w].size(); i++) {
        		e=ret[w].get(i);
        		to=(int)(e/t);
        		ei=(int)(e%t);
				if(to==p[w])continue;
				if(nc==cn[w])nc++;
				c[ei]=nc;
				p[to]=w;
				cn[to]=nc;
				nm=max(nc,nm);
				l.add(to);
				nc++;
			}
        }
        
        out.println(nm);
        for (int i = 0; i < c.length; i++) {
            out.println(c[i]);
		}

        out.println();
     	out.flush();
    }


    static void ret(String ans) {
    	System.out.println(ans);
    	System.exit(0);
    }
    
    static boolean validpos(int x,int y,int r, int c){
        return x<r && 0<=x && y<c && 0<=y;
    }

    static void db(Object... os){
        System.err.println(Arrays.deepToString(os));
    }
}

//
//class P {
//	int x, y, d;
//	P(int  x, int y, int d) {
//	  this.x=x;
//	  this.y=y;
//	  this.d=d;
//	}
//}

class P implements Comparable<P>{
    int a,b;
    P(int a, int b) {
    	this.b=b;
    	this.a=a;
    }

    public int compareTo(P p){
        return -p.a+a;//as
    }
}

class Reader
{ 
    private BufferedReader x;
    private StringTokenizer st;
    
    public Reader(InputStream in)
    {
        x = new BufferedReader(new InputStreamReader(in));
        st = null;
    }
    public String nextString() throws IOException
    {
        while( st==null || !st.hasMoreTokens() )
            st = new StringTokenizer(x.readLine());
        return st.nextToken();
    }
    public int nextInt() throws IOException
    {
        return Integer.parseInt(nextString());
    }
    public int[] nextIntArray(int size) throws IOException{
        int r[] = new int[size];
        for (int i = 0; i < size; i++) {
            r[i] = this.nextInt(); 
        }
        return r;
    }
    public long[] nextLongArray(int size) throws IOException{
        long r[] = new long[size];
        for (int i = 0; i < size; i++) {
            r[i] = this.nextLong(); 
        }
        return r;
    }
    public char[] getCharSet() throws IOException{
        return this.nextString().toCharArray();
    }    
    public long nextLong() throws IOException
    {
        return Long.parseLong(nextString());
    }
    public double nextDouble() throws IOException
    {
        return Double.parseDouble(nextString());
    }
}