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;

namespace abc146_d
{
  class Program
  {
    static void Main(string[] args)
    {
      var n = CIn.ReadInt();
      var nodes = new Node[n];
      var paths = new Path[n - 1];

      for (var i = 0; i < n; i++)
      {
        nodes[i] = new Node(i);
      }

      for (var i = 0; i < n - 1; i++)
      {

        var a = CIn.ReadInt() - 1;
        var b = CIn.ReadInt() - 1;

        paths[i] = new Path(i, nodes[a], nodes[b]);

        nodes[a].Paths.Add(paths[i]);
        nodes[b].Paths.Add(paths[i]);
      }

      Array.Sort(nodes);
      Console.WriteLine(nodes[n - 1].Paths.Count);

      for (var i = n - 1; i >= 0; i--)
      {
        foreach (var p in nodes[i].Paths)
        {
          for (var j = 1; j <= nodes[n - 1].Paths.Count; j++)
          {
            if (!p.NodeA.UsedColor.Contains(j) && !p.NodeB.UsedColor.Contains(j))
            {
              p.Color = j;
              p.NodeA.UsedColor.Add(j);
              p.NodeB.UsedColor.Add(j);
              break;
            }
          }
        }
      }

      for (var i = 0; i < n - 1; i++)
      {
        Console.WriteLine(paths[i].Color);
      }
    }
  }

  class Node : IComparable<Node>
  {
    public int Num { get; }
    public List<Path> Paths { get; } = new List<Path>();
    public HashSet<int> UsedColor { get; } = new HashSet<int>();

    public Node(int num)
    {
      Num = num;
    }

    public int CompareTo(Node other)
    {
      return Paths.Count.CompareTo(other.Paths.Count);
    }
  }

  class Path
  {
    public int Num { get; }
    public Node NodeA { get; }
    public Node NodeB { get; }
    public int Color { get; set; }

    public Path(int num, Node a, Node b)
    {
      Num = num;
      NodeA = a;
      NodeB = b;
    }
  }

  class CIn
  {
    private static readonly Queue<string> fieldBuffer = new Queue<string>();

    public static string Read()
    {
      if (fieldBuffer.Count == 0)
      {
        foreach (var field in Console.ReadLine().Split())
        {
          fieldBuffer.Enqueue(field);
        }
      }
      return fieldBuffer.Dequeue();
    }

    public static int ReadInt() => int.Parse(Read());
    public static long ReadLong() => long.Parse(Read());
    public static double ReadDouble() => double.Parse(Read());

    public static string[] ReadStringArray(long n)
    {
      var array = new string[n];
      for (var i = 0; i < n; i++)
      {
        array[i] = Read();
      }
      return array;
    }

    public static int[] ReadIntArray(long n)
    {
      var array = new int[n];
      for (var i = 0; i < n; i++)
      {
        array[i] = ReadInt();
      }
      return array;
    }

    public static long[] ReadLongArray(long n)
    {
      var array = new long[n];
      for (var i = 0; i < n; i++)
      {
        array[i] = ReadLong();
      }
      return array;
    }

    public static double[] ReadDoubleArray(long n)
    {
      var array = new double[n];
      for (var i = 0; i < n; i++)
      {
        array[i] = ReadDouble();
      }
      return array;
    }
  }
}