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.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;

namespace AtCoder.D
{
    public class Program
    {
        public static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.Write(r); }

        private static object GetResult()
        {
            var N = ReadLong();
            var tree = Enumerable.Range(0, (int)N)
                .Select(x => new List<Node>())
                .ToArray();

            for (int i = 0; i < N - 1; i++)
            {
                var inputs = ReadLongs();

                // indexに変換
                var a = inputs[0] - 1;
                var b = inputs[1] - 1;

                var node = new Node
                {
                    Index = i,
                    A = a,
                    B = b,
                };

                tree[a].Add(node);
                tree[b].Add(node);
            }

            var nodeColors = new long[N - 1];
            var queue = new Queue<KeyValuePair<long, long>>();// valueが親Nodeの色とする
            queue.Enqueue(new KeyValuePair<long, long>(0, 0));
            while (queue.Count > 0)
            {
                var q = queue.Dequeue();
                var drawColor = 1;
                foreach (var node in tree[q.Key])
                {
                    if (nodeColors[node.Index] == drawColor || q.Value == drawColor) drawColor++;
                    nodeColors[node.Index] = drawColor;

                    var nextPoint = node.A == q.Key ? node.B : node.A;
                    // 二重カウントにならないように除外する
                    tree[nextPoint].RemoveAll(x => x.Index == node.Index);
                    queue.Enqueue(new KeyValuePair<long, long>(nextPoint, drawColor));

                    drawColor++;
                }
            }

            var colorCount = nodeColors.Max();
            var sb = new StringBuilder();
            sb.AppendLine(colorCount.ToString());
            foreach (var c in nodeColors)
            {
                sb.AppendLine(c.ToString());
            }

            return sb.ToString().Trim();
        }

        class Node
        {
            public long Index { get; set; }
            public long A { get; set; }
            public long B { get; set; }
        }

        #region Console

        public static string ReadText() { return Console.ReadLine(); }
        public static List<string> ReadTexts() { return Console.ReadLine().Split(' ').ToList(); }
        public static long ReadLong() { return long.Parse(Console.ReadLine()); }
        public static List<long> ReadLongs() { return Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList(); }

        #endregion
    }
}