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;
using System.Text.RegularExpressions;
using static System.Console;
using static System.Math;
using static MyIO;
using static MyUtil;

public class D
{
	public static void Main() => (new Solver()).Solve();
}

public struct Edge
{
	public int I;
	public int To;

	public Edge(int i, int t)
	{
		I = i;
		To = t;
	}
}

public class Solver
{
	public void Solve()
	{
		int N = GetInt();
		int[] a = new int[N - 1];
		int[] b = new int[N - 1];
		int[] deg = new int[N];
		var adj = Enumerable.Range(0, N).Select(_ => new List<Edge>()).ToArray();
		for(int i = 0; i < N - 1; i++)
		{
			a[i] = GetInt() - 1;
			b[i] = GetInt() - 1;
			adj[a[i]].Add(new Edge(i, b[i]));
			adj[b[i]].Add(new Edge(i, b[i]));
			deg[a[i]]++;
			deg[b[i]]++;
		}

		int K = deg.Max();
		int[] color = new int[N - 1];
		int r = Array.FindIndex(deg, x => (x == K));
		int c = 1;
		foreach(var edge in adj[r])
		{
			color[edge.I] = c;
			dfs(adj, edge.To, K, c, color);
			c++;
		}

		WriteLine(K);
		WriteLine(string.Join("\n", color));
	}

	private void dfs(List<Edge>[] adj, int v, int K, int x, int[] color)
	{
		int c = 1;
		foreach(var edge in adj[v])
		{
			if(color[edge.I] != 0)
				continue;

			if(c == x)
				c++;

			color[edge.I] = c;
			dfs(adj, edge.To, K, c, color);		
			c++;
		}
	}
}

public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(int N) => Enumerable.Range(0, N).Select(_ => GetInt()).ToArray();
	public static long[] GetLongs(int N) => Enumerable.Range(0, N).Select(_ => GetLong()).ToArray();
	public static double[] GetDoubles(int N) => Enumerable.Range(0, N).Select(_ => GetDouble()).ToArray();
	public static string[] GetStrings(int N) => Enumerable.Range(0, N).Select(_ => GetString()).ToArray();
}

public static class MyUtil
{
	public static void chmax<T>(ref T x, T y) where T : IComparable<T>
	{
		if(x.CompareTo(y) < 0)
			x = y;
	}

	public static void chmin<T>(ref T x, T y) where T : IComparable<T>
	{
		if(x.CompareTo(y) > 0)
			x = y;
	}

	public static void swap<T>(ref T x, ref T y)
	{
		T tmp = x;
		x = y;
		y = tmp;
	}
}