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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var cin = new Scanner2();
			int n = cin.Int();
			Dictionary<int, int>[] to = new Dictionary<int, int>[n];
			Edge[] edge = new Edge[n - 1];
			for (int i = 0; i < n; i++) {
				to[i] = new Dictionary<int, int>();
			}

			int first = 0;
			for (int i = 0; i < n - 1; i++) {
				int a = cin.Int() - 1;
				int b = cin.Int() - 1;
				to[a].Add(b, -1);
				to[b].Add(a, -1);

				edge[i] = new Edge {
					From = a,
					To = b
				};

				if (i == 0) {
					first = a;
				}
			}

			int num = to.Max(x => x.Count);

			var q = new Queue<ToColor>();
			q.Enqueue(new ToColor { To = first, Color = -1 });
			while (q.Count > 0) {
				var next = q.Dequeue();
				int color = next.Color == -1 ? 0 : (next.Color + 1) % num;
				foreach (var nn in to[next.To].Keys.ToArray()) {
					if (to[next.To][nn] == -1) {
						to[next.To][nn] = color;
						to[nn][next.To] = color;
						q.Enqueue(new ToColor { To = nn, Color = color });
						color = (color + 1) % num;
					}
				}
			}

			var sb = new StringBuilder();
			sb.AppendLine(num.ToString());
			for (int i = 0; i < n - 1; i++) {
				sb.AppendLine((to[edge[i].From][edge[i].To] + 1).ToString());
			}

			Console.WriteLine(sb.ToString());
		}
	}

	public class Edge
	{
		public int From {get; set;}
		public int To { get; set; }
	}

	public class ToColor
	{
		public int To { get; set; }
		public int Color { get; set; }
	}


	public class Scanner2
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private readonly string filePath_;
		private string[] buf_;
		private int index_;
		Func<string> reader_;

		public Scanner2(string file = "")
		{
			if (string.IsNullOrWhiteSpace(file)) {
				reader_ = Console.ReadLine;
			} else {
				filePath_ = file;
				var fs = new StreamReader(file);
				reader_ = fs.ReadLine;
			}
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = reader_();
			while (st == "") {
				st = reader_();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int() => int.Parse(Next());
		public long Long() => long.Parse(Next());
		public double Double() => double.Parse(Next());

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}

		public void Save(string text)
		{
			if (string.IsNullOrWhiteSpace(filePath_)) {
				return;
			}

			File.WriteAllText(filePath_ + "_output.txt", text);
		}
	}
}