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)

#region いつもの
#pragma warning disable
using System;
using System.Collections.Generic;
using System.Linq;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;
using TextReader = System.IO.TextReader;
using static AtCoderProject.Global;

namespace AtCoderProject
{
    static class Global
    {
        private class ComparerReverseImpl<T> : Comparer<T> where T : IComparable<T> { public override int Compare(T y, T x) => x.CompareTo(y); public override bool Equals(object obj) => obj != null && GetType() == obj.GetType(); public override int GetHashCode() => GetType().GetHashCode(); }
        public static IComparer<T> ComparerReverse<T>() where T : IComparable<T> => new ComparerReverseImpl<T>();
        public static BigInteger ParseBigInteger(string s)
        {
            // MonoのBigInteger.Parseが遅いので自前実装
            var res = BigInteger.Zero;
            var splited = new string[(s.Length + 7) / 8];
            for (int i = 0; i < splited.Length - 1; i++)
            {
                splited[i] = s.Substring(8 * i, 8);
            }
            splited[splited.Length - 1] = s.Substring(8 * (splited.Length - 1));
            foreach (var sp in splited)
            {
                res *= (int)Math.Pow(10, sp.Length);
                res += int.Parse(sp);
            }
            return res;
        }
        public static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
        public static string AllJoin<T>(IEnumerable<T> source) => string.Join(" ", source);
    }
    static class Ext
    {
        public static IComparer<T> Reverse<T>(this IComparer<T> comparer) => Comparer<T>.Create((x, y) => comparer.Compare(y, x));
        public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector) => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count());
        public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i);
    }
    public class ConsoleReader { private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries); private string[] line = Array.Empty<string>(); private int linePosition; private TextReader textReader; public ConsoleReader(TextReader tr) { textReader = tr; } public int Int => int.Parse(String); public int Int0 => Int - 1; public long Long => long.Parse(String); public double Double => double.Parse(String); public string String { get { if (linePosition >= line.Length) { linePosition = 0; line = ReadLineSplit(); } return line[linePosition++]; } } public class SplitLine { private string[] splited; public SplitLine(ConsoleReader cr) { splited = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); } public int[] Int => String.Select(x => int.Parse(x)).ToArray(); public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray(); public long[] Long => String.Select(x => long.Parse(x)).ToArray(); public double[] Double => String.Select(x => double.Parse(x)).ToArray(); public string[] String => splited; } public SplitLine Split => new SplitLine(this); public class RepeatReader : IEnumerable<ConsoleReader> { ConsoleReader cr; int count; public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; } public IEnumerator<ConsoleReader> GetEnumerator() => Enumerable.Repeat(cr, count).GetEnumerator(); System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator(); public IEnumerable<string> String => this.Select(cr => cr.String); public IEnumerable<int> Int => this.Select(cr => cr.Int); public IEnumerable<int> Int0 => this.Select(cr => cr.Int - 1); public IEnumerable<long> Long => this.Select(cr => cr.Long); public IEnumerable<double> Double => this.Select(cr => cr.Double); } public RepeatReader Repeat(int count) => new RepeatReader(this, count); }
    public class Program
    {
        [System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] private ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc());

        #endregion
        public object Calc()
        {
            var N = consoleReader.Int;
            result = new int[N - 1];
            {
                var sw = System.Diagnostics.Stopwatch.StartNew();
                var gb = new GraphBuilder(N);
                for (int i = 0; i < N - 1; i++)
                {
                    var cra = consoleReader.Int0;
                    var crb = consoleReader.Int0;
                    edges.Add(Tuple.Create(cra, crb), i);
                    gb.Add(cra, crb);
                    result[i] = -1;
                }
                sw.Stop();
                tree = gb.ToTree(0);
            }

            var queue = new Queue<int>(N);

            for (int i = 0; i < tree[0].children.Length; i++)
            {
                var child = tree[0].children[i];
                result[edges[Tuple.Create(0, child)]] = i + 1;
                queue.Enqueue(child);
            }

            while (queue.Count > 0)
            {
                var index = queue.Dequeue();
                var root = tree[index].root;
                int rootColor;
                {
                    if (root < index)
                        rootColor = result[edges[Tuple.Create(root, index)]];
                    else
                        rootColor = result[edges[Tuple.Create(index, root)]];
                }

                var color = 1;
                foreach (var child in tree[index].children)
                {
                    if (color == rootColor) ++color;
                    if (child < index)
                        result[edges[Tuple.Create(child, index)]] = color++;
                    else
                        result[edges[Tuple.Create(index, child)]] = color++;
                    queue.Enqueue(child);
                }
            }

            Console.WriteLine(result.Max());
            return AllLines(result);
        }

        TreeNode[] tree;
        int[] result;
        Dictionary<Tuple<int, int>, int> edges = new Dictionary<Tuple<int, int>, int>(1000000);


        struct Edge : IEquatable<Edge>, IComparable<Edge>
        {
            public int x;
            public int y;
            public Edge(int[] arr) : this(arr[0], arr[1]) { }
            public Edge(int x, int y)
            {
                this.x = x;
                this.y = y;
            }

            public int CompareTo(Edge other) => this.x.CompareTo(other.x);

            public bool Equals(Edge other) => this.x == other.x && this.y == other.y;
            public override bool Equals(object obj)
            {
                if (obj is Edge) return Equals((Edge)obj);
                return false;
            }
            public override int GetHashCode() => x ^ y;
            public override string ToString() => $"({x}, {y})";
        }


        class GraphBuilder
        {
            private List<int>[] roots;
            private List<int>[] children;
            public GraphBuilder(int count, bool isOriented = true)
            {
                this.roots = new List<int>[count];
                this.children = new List<int>[count];
                for (int i = 0; i < count; i++)
                {
                    if (isOriented)
                    {
                        this.roots[i] = new List<int>();
                        this.children[i] = new List<int>();
                    }
                    else
                    {
                        this.roots[i] = this.children[i] = new List<int>();
                    }
                }
            }
            public GraphBuilder(int count, ConsoleReader cr, int edgeCount, bool isOriented = true) : this(count, isOriented)
            {
                for (int i = 0; i < edgeCount; i++)
                    this.Add(cr.Int - 1, cr.Int - 1);
            }
            public void Add(int from, int to)
            {
                children[from].Add(to);
                roots[to].Add(from);
            }
            public TreeNode[] ToTree(int root)
            {
                var res = new TreeNode[this.children.Length];
                res[root] = new TreeNode(root, -1, this.children[root].ToArray());

                var queue = new Queue<int>();
                foreach (var child in res[root].children)
                {
                    res[child] = new TreeNode(child, root, null);
                    queue.Enqueue(child);
                }

                while (queue.Count > 0)
                {
                    var from = queue.Dequeue();
                    if (res[from].root == -1)
                        res[from].children = this.children[from].ToArray();
                    else
                    {
                        var children = new List<int>(this.children[from].Count);
                        foreach (var c in this.children[from])
                            if (c != res[from].root)
                                children.Add(c);

                        res[from].children = children.ToArray();
                    }

                    foreach (var child in res[from].children)
                    {
                        res[child] = new TreeNode(child, from, null);
                        queue.Enqueue(child);
                    }
                }

                return res;
            }

            public Node[] ToArray() =>
                Enumerable
                .Zip(roots, children, (r, c) => Tuple.Create(r, c))
                .Select((t, i) => new Node(i, t.Item1.ToArray(), t.Item2.ToArray()))
                .ToArray();
        }
        public class TreeNode : IEquatable<TreeNode>
        {
            public TreeNode(int i, int root, int[] children)
            {
                this.index = i;
                this.root = root;
                this.children = children;
            }
            public int index;
            public int root;
            public int[] children;

            public override string ToString() => $"children: {string.Join(",", children)}";
            public override bool Equals(object obj)
            {
                if (obj is TreeNode)
                    return this.Equals((TreeNode)obj);
                else
                    return false;
            }
            public bool Equals(TreeNode other) => this.index == other.index;
            public override int GetHashCode() => this.index;
        }
        public class Node : IEquatable<Node>
        {
            public Node(int i, int[] roots, int[] children)
            {
                this.index = i;
                this.roots = roots;
                this.children = children;
            }
            public int index;
            public int[] roots;
            public int[] children;

            public override string ToString() => $"children: {string.Join(",", children)}";
            public override bool Equals(object obj)
            {
                if (obj is Node)
                    return this.Equals((Node)obj);
                else
                    return false;
            }
            public bool Equals(Node other) => this.index == other.index;
            public override int GetHashCode() => this.index;
        }



    }
}