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

class Program
{
    #region Lib

    static int Gcd(int a, int b)
    {
        if (a % b == 0)
            return b;
        else
            return Gcd(b, a % b);
    }

    #endregion

    static void Main()
    {
        var tree = new Tree(ReadInts()[0]);

        for (int i = 0; i < tree.NodeNum - 1; i++)
        {
            var nums = ReadInts();
            tree.Add(nums[0], nums[1]);
        }

        tree.Coloring();
        var colors = tree.Colors.ToArray();
        Console.WriteLine(colors.Max());
        foreach (var item in colors)
        {
            Console.WriteLine(item);
        }
    }

    #region Utils
    public static int[] ReadInts()
    {
        return Console.ReadLine().Split().Select(int.Parse).ToArray();
    }
    #endregion



}

class Tree
{

    private readonly TreeNode[] _nodes;

    private readonly List<Bar> _bars = new List<Bar>();

    public Tree(int nodeNum)
    {
        NodeNum = nodeNum;
        _nodes = Enumerable.Range(1, nodeNum).Select(_ => new TreeNode()).ToArray();
    }

    public int NodeNum { get; }


    public void Add(int a, int b)
    {
        var bar = new Bar(_bars.Count, a, b);
        _bars.Add(bar);
        _nodes[a-1].Bars.Add(bar);
        _nodes[b-1].Bars.Add(bar);
    }

    class TreeNode
    {
        public List<Bar> Bars { get; } = new List<Bar>();
    }


    public void Coloring()
    {
        foreach (var item in _nodes)
        {
            Coloring(item);
        }
    }

    private void Coloring(TreeNode node)
    {
        var bars = node.Bars;
        var nums = Enumerable.Range(1, bars.Count).Except
            (bars.Select(p => p.Color)).ToArray();

        var stack = new Queue<int>(nums);

        foreach (var item in bars.Where(p=>p.Color == 0))
        {
            item.Color = stack.Dequeue();
        }
    }

    public IEnumerable<int> Colors => _bars.Select(p => p.Color);

}

class Bar
{
    public Bar(int index, int a, int b)
    {
        Index = index;
        A = a;
        B = b;
    }

    public int Index { get; }
    public int A { get; }
    public int B { get; }

    public int Color { get; set; }


    //public List<Bar> AFriends { get; } = new List<Bar>();
    //public List<Bar> BFriends { get; } = new List<Bar>();

}