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;

class Program
{
    static void Main(string[] args)
    {
        var N = sc.ReadInt();
        var AB = new Tuple<int, int>[N - 1];
        for (int i = 0; i < N - 1; i++)
        {
            AB[i] = Tuple.Create(sc.ReadInt() - 1, sc.ReadInt() - 1);
        }
        var tree = new HashMap<int, int>[(int)1e5];
        for (int i = 0; i < tree.Length; i++)
        {
            tree[i] = new HashMap<int, int>();
        }
        var max = 0;
        for (int i = 0; i < N - 1; i++)
        {
            max = Math.Max(max, tree[i].Count);
        }
        var q = new Queue<Tuple<int, int>>();
        q.Enqueue(Tuple.Create(0, 0));
        while (q.Count > 0)
        {
            var t = q.Dequeue();
            var from = t.Item1;
            var c = t.Item2;
            var now = 0;
            var keys = tree[from].Keys.ToArray();
            for (int i = 0; i < keys.Length; i++)
            {
                now++;
                if (now == t.Item2) now++;
                var to = keys[i];
                if (tree[from][to] > 0) continue;
                tree[from][to] = now;
                tree[to][from] = now;
                q.Enqueue(Tuple.Create(to, now));
            }
        }

        Console.WriteLine(max);
        for (int i = 0; i < N - 1; i++)
        {
            var a = AB[i].Item1;
            var b = AB[i].Item2;
            Console.WriteLine(tree[a][b]);
        }
    }

    class HashMap<K, V> : Dictionary<K, V> where V : new()
    {
        private V DefaltValue = new V();
        public HashMap() { }
        public HashMap(V defaultValue)
        {
            this.DefaltValue = new V();
        }
        new public V this[K i]
        {
            get
            {
                V v;
                return TryGetValue(i, out v) ? v : base[i] = this.DefaltValue;
            }
            set { base[i] = value; }
        }
    }
    static Scanner sc = new Scanner();
}

class Scanner
{
    string[] S = new string[0];
    int Index = 0;
    char[] Separators = new char[] { ' ' };

    public string Next()
    {
        if (this.Index < this.S.Length) return this.S[this.Index++];
        var line = "";
        while (line == "") line = Console.ReadLine();
        this.S = line.Split(this.Separators, StringSplitOptions.RemoveEmptyEntries);
        if (this.S.Length == 0) return this.Next();
        this.Index = 0;
        return this.S[this.Index++];
    }
    public string ReadStr()
    {
        return this.Next();
    }
    public char ReadChar()
    {
        return this.Next()[0];
    }
    public int ReadInt()
    {
        return int.Parse(this.Next());
    }
    public uint ReadUInt()
    {
        return uint.Parse(this.Next());
    }
    public long ReadLong()
    {
        return long.Parse(this.Next());
    }
    public double ReadDouble()
    {
        return double.Parse(this.Next());
    }
    public Tuple<int, int> ReadTup()
    {
        return Tuple.Create(this.ReadInt(), this.ReadInt());
    }
    public Tuple<long, long> ReadTupLong()
    {
        return Tuple.Create(this.ReadLong(), this.ReadLong());
    }
    public Tuple<int, int, int> ReadTup3()
    {
        return Tuple.Create(this.ReadInt(), this.ReadInt(), this.ReadInt());
    }
    public Tuple<int, int, int, int> ReadTup4()
    {
        return Tuple.Create(this.ReadInt(), this.ReadInt(), this.ReadInt(), this.ReadInt());
    }
    public int[] ReadIntArray(int n)
    {
        var array = new int[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadInt();
        }
        return array;
    }
    public long[] ReadLongArray(int n)
    {
        var array = new long[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadLong();
        }
        return array;
    }
    public double[] ReadDoubleArray(int n)
    {
        var array = new double[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadDouble();
        }
        return array;
    }
    public char[] ReadCharArray(int n)
    {
        var array = new char[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadChar();
        }
        return array;
    }
    public string[] ReadStrArray(int n)
    {
        var array = new string[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadStr();
        }
        return array;
    }
    public Tuple<long, long>[] ReadTupLongArray(int n)
    {
        var array = new Tuple<long, long>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTupLong();
        }
        return array;
    }
    public Tuple<int, int>[] ReadTupArray(int n)
    {
        var array = new Tuple<int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup();
        }
        return array;
    }
    public Tuple<int, int, int>[] ReadTup3Array(int n)
    {
        var array = new Tuple<int, int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup3();
        }
        return array;
    }
    public Tuple<int, int, int, int>[] ReadTup4Array(int n)
    {
        var array = new Tuple<int, int, int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup4();
        }
        return array;
    }
}