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.Windows;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Atcoder
{
    public class Program
    {
        private static List<List<Tuple<int, int>>> l = new List<List<Tuple<int, int>>>();
        private static List<int> ans = new List<int>();

        static void Main(string[] args)
        {
            var n = Read().ToInt32();
            for (int i = 0; i < n; i++)
            {
                l.Add(new List<Tuple<int,int>>());
                ans.Add(0);
            }
            for (int i = 0; i < n - 1 ; i++)
            {
                var r = ReadSplit();
                var a1 = r[0].ToInt32() - 1;
                var a2 = r[1].ToInt32() - 1;
                l[a1].Add(new Tuple<int, int>(i, a2));
                l[a2].Add(new Tuple<int, int>(i, a1));
            }
            
            Write(l.Max(x => x.Count));
            Dfs(0, -1, -1);
            for (int i = 0; i < ans.Count -1; i++)
            {
                Write(ans[i]);
            }
            Read();
        }

        private static void Dfs(int s ,int from, int color)
        {
            var d = l[s];
            var c = 1;
            if (color == c) c++;
            foreach (var item in d)
            {
                if (from == item.Item2) continue;
                ans[item.Item1] = c;
                Dfs(item.Item2, s, c);
                c++;
            }
        }

        public static string Read()
        {
            return Console.ReadLine();
        }

        public static string[] ReadSplit()
        {
            return Console.ReadLine().Split(' ');
        }

        public static void WriteRead(object str)
        {
            Console.WriteLine(str);
            Read();
        }

        public static void Write(object str)
        {
            Console.WriteLine(str);
        }
    }
}


public static class Extentions
{
    public static int ToInt32(this object obj)
    {
        return int.Parse(obj.ToString());
    }

    public static long ToInt64(this object obj)
    {
        return long.Parse(obj.ToString());
    }

    public static decimal ToDecimal(this object obj)
    {
        return decimal.Parse(obj.ToString());
    }

    public static double ToDouble(this object obj)
    {
        return double.Parse(obj.ToString());
    }

    public static T2 GetValueZero<T1, T2>(this Dictionary<T1, T2> d, T1 key) where T2 : struct
    {
        T2 value;
        if (d.TryGetValue(key, out value))


        {
            return value;
        }
        return new T2();
    }
}