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: Time Limit Exceeded)

import java.util.*;
import java.io.*;

class Main{
    static HashMap<Pair, Integer> colors;
    static ArrayList<Integer> edges[];
    public static void main(String[] args){
        FastScanner fsc=new FastScanner();
        int n=fsc.nextInt();
        edges=new ArrayList[n];
        for(int i=0;i<n;i++) edges[i]=new ArrayList<Integer>();
        Pair[] pairs=new Pair[n-1];
        int dim=0;
        for(int i=0;i<n-1;i++){
            int a=fsc.nextInt()-1, b=fsc.nextInt()-1;
            edges[a].add(b);
            edges[b].add(a);
            dim=Math.max(Math.max(dim, edges[a].size()), edges[b].size());
            pairs[i]=new Pair(a, b);
        }
        fsc.close();
        colors=new HashMap<>();
        coloring(0, -1, 0);
        StringBuilder sb=new StringBuilder();
        sb.append(dim+"\n");
        for(int i=0;i<n-1;i++) sb.append(colors.get(pairs[i])+"\n");
        System.out.print(sb);
    }
    static void coloring(int v, int parent, int color){
        int c=1;
        for(int u:edges[v]){
            Pair pair=new Pair(u, v);
            if(u!=parent){
                if(color==c) c++;
                colors.put(pair, c);
                coloring(u, v, c);
                c++;
            }
        }
    }
}
class Pair{
    int id1, id2;
    public Pair(int id1, int id2){this.id1=id1; this.id2=id2;}
    @Override public boolean equals(Object o){
        if(! (o instanceof Pair)) return false;
        Pair p=(Pair) o;
        if((p.id1==id1 && p.id2==id2) || (p.id1==id2 && p.id2==id1)) return true;
        else return false;
    }
    @Override public int hashCode(){return id1*id2;}
}
class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte(){
        if(ptr<buflen) return true;
        else{
            ptr = 0;
            try{
                buflen = in.read(buffer);
            }
            catch(IOException e){
                e.printStackTrace();
            }
            if(buflen<=0) return false;
        }
    return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) throw new NumberFormatException();
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }
            else if(b == -1 || !isPrintableChar(b)) return minus ? -n : n;
            else throw new NumberFormatException();
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
    public void close(){
        try{in.close();}
        catch(IOException e){e.printStackTrace();}
    }
}