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;

class Program
{
    static void Main(string[] args)
    {
        var waaaa = new waaaa();
        waaaa.Solve();
    }
}

public class waaaa
{
    const int MOD = 1000000007;
    const int INF = 1 << 20;
    const long INFL = 1 << 62;
    const int MOD2 = 998244353;

    myinout IO = new myinout();
    Math2 mmath = new Math2();




    public void Solve()
    {
        //ここから
        var n = IO.int1;
        var edge = Enumerable.Repeat(0, n).Select(_ => new List<int>()).ToArray();　//頂点vにつながる辺list
        var e = new Tuple<int, int>[n];　//from to
        for (int i = 0; i < n - 1; ++i)
        {
            var o = IO.intm;
            e[i] = new Tuple<int, int>(o[0]--, o[1]--);  
            edge[e[i].Item1].Add(i);  
            edge[e[i].Item2].Add(i);
        }

        var col = new int[n - 1];
        var q = new Queue<int>();
        q.Enqueue(0);
        while (q.Any())
        {
            int p = q.Dequeue();
            int pcol = 0;
            foreach (var item in edge[p]) //頂点につながる辺
            {
                if (col[item] > 0) //すでに彩色なら
                {
                    pcol = col[item];　//頂点pの色にする
                    break;
                }
            }
            int c = 1;
            foreach (var item in edge[p])
            {
                if (col[item] > 0) continue; //彩色してない辺について
                if (c == pcol) c++;　   //頂点と同じ色なら違う色にする
                col[item] = c;
                c++;
                q.Enqueue(e[item].Item1 + e[item].Item2 - p); //辺itemのfromの頂点+toの頂点-今の頂点(いま見てない方向に行きたい)
            }
        }

        int k = col.Max();
        foreach(var item in col) IO.wri(item);



    }



}

//b-aで降順

public class Math2
{
    public long[] fact;  //Nまでの階乗
    public long[] invfact;  //階乗の逆元

    //Nまでの階乗をセットしておく
    public void factoricalmodset(long N, long MOD = 1000000007)
    {
        fact = new long[N + 1];
        invfact = new long[N + 1];
        fact[0] = 1;

        for (long i = 1; i <= N; ++i)
        {
            fact[i] = fact[i - 1] * i % MOD;
        }
        invfact[N] = pow(fact[N], MOD - 2);

        for (long i = N; i > 0; --i)
        {
            invfact[i - 1] = invfact[i] * i % MOD;
        }

    }

    //nCr 引数:n r (mod)
    public long nCr(long n, long r, long MOD = 1000000007)
    {
        return (fact[n] * invfact[r] % MOD * invfact[n - r] % MOD);
    }

    //階乗(O(logN)) 引数:底x n乗　(MOD)
    public long pow(long i, long n, long MOD = 1000000007)
    {
        long res = 1;
        while (n > 0)
        {
            if ((n & 1) != 0) res = res * i % MOD;
            i = i * i % MOD;
            n >>= 1;
        }
        return res;
    }

    //最大公約数 引数:整数x,y
    public long gcd(long i, long y)
    {
        while (y != 0)
        {
            var r = i % y;
            i = y;
            y = r;
        }
        return i;
    }

    //最小公倍数 引数:整数x,y
    public long lcm(long i, long y)
    {
        return i * y / gcd(i, y);
    }

    //素因数分解 引数:整数N
    public Dictionary<long, int> primefactorization(long N)
    {
        var ret = new Dictionary<long, int>();

        for (long i = 2; i * i <= N; ++i)
        {
            int cnt = 0;
            while (N % i == 0)
            {
                cnt++;
                N /= i;
            }
            if (cnt != 0) ret[i] = cnt;

        }
        if (N >= 2) ret[N] = 1;

        return ret;

    }

    //約数列挙
    public List<long> divisorenumrate(long N)
    {
        var ret = new List<long>();

        for (long i = 1; i * i <= N; ++i)
        {

            if (N % i == 0)
            {
                ret.Add(i);
                ret.Add(N / i);
            }

        }

        return ret;

    }

    public void swap<T>(ref T a, ref T b)
    {
        var i = a;
        a = b;
        b = i;
    }

}

class myinout
{
    //in
    public string str => Console.ReadLine();

    public string[] strm => str.Split(' ');

    public long[] longm => strm.Select(long.Parse).ToArray();
    public int[] intm => strm.Select(int.Parse).ToArray();
    public char[] charm => str.ToArray();
    public long long1 => longm[0];
    public int int1 => intm[0];
    public char char1 => charm[0];

    //out
    public void wri<T>(T i)
    {
        Console.WriteLine(i);
    }

    public void yn(bool i)
    {
        if (i) wri("Yes");
        else wri("No");
    }

}