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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

public class MainClass
{
	public const long Giri = 1000000007;

	public class Node 
	{
		public int Index{get;set;}
		//public List<int> Connections {get;set;}
		public List<int> Edges {get;set;}
		public bool Seen {get;set;}
	}
	public class Edge
	{
		public int Color{get;set;}
		public int Connect1 {get;set;}
		public int Connect2 {get;set;}
		public bool Seen {get;set;}
		
	}
	
	public static void Main(string[] args)
	{
		var n = Console.ReadLine().ToInt();
		var nodes = new Node[n];
		var edges = new Edge[n-1];
		for(int i = 0; i < n; i++)
		{
			nodes[i] = new Node() { Index = i, Edges = new List<int>()};
		}
		for(int i = 0; i < n-1; i++)
		{
			var p = Input().ToInt();
			var a = p[0]-1;
			var b = p[1]-1;
			//nodes[a].Connections.Add(b);
			//nodes[b].Connections.Add(a);
			nodes[a].Edges.Add(i);
			nodes[b].Edges.Add(i);
			edges[i] = new Edge() { Color=-1, Connect1 = a, Connect2 = b};
		}
		//Array.Sort(nodes, (s, t) => t.Edges.Count - s.Edges.Count);
		
		int colorSize = nodes[0].Edges.Count;
		Check(nodes, edges, nodes[0], null, -1);
		Array.Sort(nodes, (s, t) => t.Edges.Count - s.Edges.Count);
		Console.WriteLine(colorSize);
		
		foreach(var ed in edges)
		{
			Console.WriteLine(ed.Color+1);
		}
	}
	
	public static void Check(Node[] nodes, Edge[] edges, Node n, Node parent, int color)
	{
		if(n.Seen)
			return;
		n.Seen=true;
		int col = 0;
		foreach(var e in n.Edges)
		{
		//	Console.WriteLine(e);
		//	Console.WriteLine("{0}, {1}", edges[e].Connect1, edges[e].Connect2);
			if(edges[e].Seen)
				continue;
			edges[e].Seen=true;
			if(edges[e].Color != -1)
			{
				var text = nodes[edges[e].Connect2];
				if(text == n)
					text = nodes[edges[e].Connect1];
		//		
				Console.WriteLine("Fill {0}->{1} X", n.Index, text.Index);
				continue;
			}
				
			if(col == color)
				col++;
			edges[e].Color = col;
			var next = nodes[edges[e].Connect2];
			if(next == n)
				next = nodes[edges[e].Connect1];
			
			if(next != parent)
			{
				Check(nodes, edges, next, n, edges[e].Color);
			}
			else
			{
				//Console.Writ
			}
		//	Console.WriteLine("Fill {2}->{3} {0} {1}", col, e, n.Index, next.Index);
			
			col++;
			
		}
		
	}

	
	static long GCD(long a, long b)
	{
		var v = new[] { a, b };
		while (v[1] != 0) { v = new[] { v[1], v[0] % v[1] }; }
		return v[0];
	}
	public static string[] Input() { return Console.ReadLine().Split(' '); }
	public static int Clamp(int val, int max, int min = 0) { return Math.Min(max, Math.Max(min, val)); }
}

public static class Smarter
{
	public static int ToInt(this string str) { return int.Parse(str); }
	public static long ToLong(this string str) { return long.Parse(str); }
	public static int[] ToInt(this string[] str)
	{
		var r = new int[str.Length];
		for(int i = 0; i < str.Length; i++) r[i] = str[i].ToInt();
		return r;
	 }
}