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

namespace AtCoder2 {
	class Program {
		static void Main(string[] args) {
		var inputArray = retreiveLongArray();
			var inputCount = 1;

			// 不正な入力は処理しない
			if (inputArray.Length != inputCount) {
				Console.WriteLine("invalid input");
				return;
			}
			var N = inputArray[0];

			var inputInfo = new List<long[]>();

			for (int i = 0; i < N-1; i++) {
				inputInfo.Add(retreiveLongArray());
			}

			//各頂点の起点と結ぶ色を記録する。最初の点は0と結ばれていることとする
			var kitenColorDic = new Dictionary<long, long> {
				{ 1, 0 }
			};
			//各頂点が、いま何色まで使ったか
			var CurrentColorDic = new Dictionary<long, long> {
				{ 1, 0 }
			};
			//辺の色を格納する
			var resultList = new List<long>();
			for (int i = 0; i < N-1; i++) {
				var start = inputInfo[i][0];
				var end = inputInfo[i][1];
				var baseColor = kitenColorDic[start];

				//初めて起点側に来る頂点の場合
				if (!CurrentColorDic.ContainsKey(start)) {
					//まず今回の辺の色を決める
					var color = baseColor == 1?2:1;
					CurrentColorDic.Add(start, color);
					resultList.Add(color);
					kitenColorDic.Add(end, color);

				}
				else {//2回目以外に起点に来る場合
					var currentColor = CurrentColorDic[start];
					var x = currentColor + 1 == baseColor ?  2 :  1;
					var color = currentColor + x;
					resultList.Add(color);
					kitenColorDic.Add(end, color);
					CurrentColorDic[start] = CurrentColorDic[start] + x;
				}

			}


			var K = resultList.Max();


			//答えの出力
			Console.WriteLine(K);
			for (int i = 0; i < N-1; i++) {
				Console.WriteLine(resultList[i]);
			}
		}

		/// <summary>
		/// スペースで区切られた文字列配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static string[] retreiveStringArray() {
			var inputArray = Console.ReadLine().Split(' ');
			return inputArray;
		}

		/// <summary>
		/// スペースで区切られた整数配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static long[] retreiveLongArray() {
			var inputArray = Console.ReadLine().Split(' ');
			var longArray = inputArray.Select(s => long.Parse(s));
			return longArray.ToArray();
		}
	}
}