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: Runtime Error)

using System;
 using System.Collections.Generic;
using System.ComponentModel.Design;
using System.Diagnostics;
using System.Linq;
using System.Runtime;
using System.Text;
using Microsoft.Win32;
using static System.Console;
 
 public static class Program
 {
     private static readonly long INF = long.MaxValue / 2;
     private static readonly int MOD = 1000000007;
 
     struct Pair<T, U> : IComparable<Pair<T, U>>
         where T : IComparable<T>
         where U : IComparable<U>
     {
         public T first;
         public U second;
         private bool CompWithFirst;
 
         public Pair(T f, U s, int comp)
         {
             first = f;
             second = s;
             CompWithFirst = comp == 1;
         }
 
         public int CompareTo(Pair<T, U> other)
         {
             return CompWithFirst ? first.CompareTo(other.first) : second.CompareTo(other.second);
         }
     }
 
     public class PriorityQueue<T> where T : IComparable<T>
     {
 
         private List<T> Q;
         private readonly int r;
 
         public PriorityQueue(bool ascending)
         {
             if (ascending)
             {
                 r = 1;
             }
             else
             {
                 r = -1;
             }
 
             Q = new List<T>();
         }
 
 
         private void PushHeap(List<T> list, T item)
         {
             int n = list.Count();
             list.Add(item);
 
             while (n != 0)
             {
                 int pIndex = (n - 1) / 2;
 
                 if (list[n].CompareTo(list[pIndex]) * r > 0)
                 {
                     Swap(Q, n, pIndex);
                 }
                 else
                 {
                     break;
                 }
 
                 n = pIndex;
             }
         }
 
         private void PopHeap(List<T> list)
         {
             int n = list.Count() - 1;
             list[0] = list[n];
             list.RemoveAt(n);
 
             int cur = 0;
             int comp;
 
             while (2 * cur + 1 <= n - 1)
             {
                 int c1 = 2 * cur + 1;
                 int c2 = 2 * (cur + 1);
                 if (c1 == n - 1)
                 {
                     comp = c1;
                 }
                 else
                 {
 
                     comp = list[c1].CompareTo(list[c2]) * r > 0 ? c1 : c2;
                 }
 
                 if (list[cur].CompareTo(list[comp]) * r < 0)
                 {
                     Swap(Q, cur, comp);
                 }
                 else
                 {
                     break;
                 }
 
                 cur = comp;
             }
         }
 
         private void Swap(List<T> list, int a, int b)
         {
             T keep = list[a];
             list[a] = list[b];
             list[b] = keep;
         }
 
 
 
         public void Enqueue(T value)
         {
             PushHeap(Q, value);
         }
 
         public T Dequeue()
         {
             T ret = Q[0];
             PopHeap(Q);
             return ret;
         }
 
         public T Peek()
         {
             return Q[0];
         }
 
         public int CountItem()
         {
             return Q.Count();
         }
 
         public bool IsEmpty()
         {
             return !Q.Any();
         }
     }
 
     static long ModInv(long a, long m)
     {
         long b = m, u = 1, v = 0;
         while (b != 0)
         {
             long t = a / b;
             a -= t * b;
             long tmp = a;
             a = b;
             b = tmp;
             u -= t * v;
             tmp = u;
             u = v;
             v = tmp;
         }
 
         u %= m;
         if (u < 0) u += m;
         return u;
     }
 
     public static long CalcComb(long n, long m)
     {
         //条件チェック
         if (n < m) return 0;
         if (n < 0 || m < 0) return 0;
 
         //nＣm ＝ nＣm-1 ×（n-m+1）/ m 
 //         return CalcFact(n) / (CalcFact(m) * CalcFact(n - m));
         //MODで割ってbの逆元を求める
         return CalcFact(n) * ModInv((CalcFact(m) * CalcFact(n - m)) % MOD, MOD) % MOD;
     }
 
     /// <summary>
     /// 階乗を計算する。
     /// </summary>
     /// <param name="n">n</param>
     /// <returns>nの階乗（n!）</returns>
     public static long CalcFact(long n)
     {
         if (n <= 0)
         {
             return 1;
         }
 
         return n * CalcFact(n - 1) % MOD;
     }
 
 
     struct Pos
     {
         public int x;
         public int y;
 
         public Pos(int x, int y)
         {
             this.x = x;
             this.y = y;
         }
         
         public static Pos operator +(Pos p1, Pos p2)
         {
             var result = new Pos();
             result.x = p2.x + p1.x;
             result.y = p2.y + p1.y;
             return result;
         }
 
         public static Pos operator -(Pos p1, Pos p2)
         {
             var result = new Pos();
             result.x = p2.x - p1.x;
             result.y = p2.y - p1.y;
             return result;
         }
     }
     
     class Modular
     {
         private const int M = 1000000007;
         private long value;
 
         public Modular(long value)
         {
             this.value = value;
         }
 
         public static implicit operator Modular(long a)
         {
             var m = a % M;
             return new Modular((m < 0) ? m + M : m);
         }
 
         public static Modular operator +(Modular a, Modular b)
         {
             return a.value + b.value;
         }
 
         public static Modular operator -(Modular a, Modular b)
         {
             return a.value - b.value;
         }
 
         public static Modular operator *(Modular a, Modular b)
         {
             return a.value * b.value;
         }
 
         private static Modular Pow(Modular a, int n)
         {
             switch (n)
             {
                 case 0:
                     return 1;
                 case 1:
                     return a;
                 default:
                     var p = Pow(a, n / 2);
                     return p * p * Pow(a, n % 2);
             }
         }
 
         public static Modular operator /(Modular a, Modular b)
         {
             return a * Pow(b, M - 2);
         }
 
         private static readonly List<int> facs = new List<int> {1};
 
         private static Modular Fac(int n)
         {
             for (int i = facs.Count; i <= n; ++i)
             {
                 facs.Add((int) (Math.BigMul(facs.Last(), i) % M));
             }
 
             return facs[n];
         }
 
         public static Modular Ncr(int n, int r)
         {
             return (n < r) ? 0
                 : (n == r) ? 1
                 : Fac(n) / (Fac(r) * Fac(n - r));
         }
 
         public static explicit operator int(Modular a)
         {
             return (int) a.value;
         }
     }
     
     static class Permutation<T>
     {
         private static void Search(List<T[]> perms, Stack<T> stack, T[] a)
         {
             int N = a.Length;
             if (N == 0)
             {
                 perms.Add(stack.Reverse().ToArray());
             }
             else
             {
                 var b = new T[N - 1];
                 Array.Copy(a, 1, b, 0, N - 1);
                 for (int i = 0; i < a.Length; ++i)
                 {
                     stack.Push(a[i]);
                     Search(perms, stack, b);
                     if (i < b.Length) { b[i] = a[i]; }
                     stack.Pop();
                 }
             }
         }
         public static IEnumerable<T[]> All(IEnumerable<T> src)
         {
             var perms = new List<T[]>();
             Search(perms, new Stack<T>(), src.ToArray());
             return perms;
         }
     }
 
     public static int ReadLineToInt()
     {
         return int.Parse(ReadLine());
     }
     
     public static long ReadLineToLong()
     {
         return long.Parse(ReadLine());
     }
     
     public static int[] ReadLineToInts()
     {
         return ReadLine().Split(' ').Select(int.Parse).ToArray();
     }
     
     public static long[] ReadLineToLongs()
     {
         return ReadLine().Split(' ').Select(long.Parse).ToArray();
     }
     
     static int nibunn(int[] array, int target)
     {
         int L = 0;
         int R = array.Length; 
             
         while(R - L > 1)
         {
             int mid = (R + L) / 2;
             if (array[mid] > target) L = mid;
             else R = mid;
         }
         return L;
     }


     struct Testmony
     {
         public int To;
         public int IsHonest;

         public Testmony(int to, int isHonest)
         {
             To = to;
             IsHonest = isHonest;
         }
     }

     
     static void dfs(int v, int p = -1)
     {
         int color_count = 0;
         foreach (var c in _tree[v])
         {
             color_count++;
             if (p == c)
             {
                 continue;
             }
             int from = v < c ? v : c;
             int to = v < c ? c : v;
             
             _edges[from,to].Color = color_count;
             
             dfs(c, v);
         }
     }

     struct Edge
     {
         public int number;
         public int Color;
     }

     static List<int>[] _tree;
     static Edge[,] _edges;
     public static void Main(string[] args)
     {
         int n = ReadLineToInt();
         _tree = new List<int>[n];
         _edges = new Edge[n,n];
         for (int i = 0; i < n; i++)
         {
             _tree[i] = new List<int>();
         }

         for (int i = 0; i < n - 1; i++)
         {
             var input = ReadLineToInts();
             int a = input[0];
             int b = input[1];
             a--;
             b--;
             _tree[a].Add(b);
             _tree[b].Add(a);
             int from = a < b ? a : b;
             int to = a < b ? b : a;
             _edges[from, to] = new Edge{number = i,Color = 0};
         }
         dfs(0);
         int mx = 0;
         foreach (var e in _edges)
         {
             mx = Math.Max(mx, e.Color);
         }
         WriteLine(mx);
         List<Edge> ans = new List<Edge>();
         foreach (var e in _edges)
         {
             if (e.Color >= 1)
             {
                 ans.Add(e);
             }
         }

         ans.OrderBy(x => x.number);
         foreach (var e in ans)
         {
             WriteLine(e.Color);
         }
     }
 }