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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;

//----------------------------------------------------------------------------------------------------------------------
typedef signed long long ll;

#define FOR(x,to) for(x=0;x<(to);x++)
#define FORR(x,arr) for(auto& x:arr)
#define ITR(x,c) for(__typeof(c.begin()) x=c.begin();x!=c.end();x++)
#define ALL(a) (a.begin()),(a.end())
#define ZERO(a) memset(a,0,sizeof(a))
#define MINUS(a) memset(a,0xff,sizeof(a))
//----------------------------------------------------------------------------------------------------------------------
//----------------------------------------------------------------------------------------------------------------------
template<class T,class U>
ostream& operator<<(ostream& os,const pair<T,U>& p){
    os<<"("<<p.first<<": "<<p.second<<")";
    return os;
}

template<class T>
ostream& operator <<(ostream& os,const vector<T>& v){
    os<<"{";
    for(int i = 0;i < (int)v.size(); i++){
        if(i)os<<", ";
        os<<v[i];
    }
    os<<"}";
    return os;
}


//#define TRACE

#ifdef TRACE
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
    cerr << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
    const char* comma = strchr(names + 1, ',');cerr.write(names, comma - names) << " : " << arg1<<" | ";__f(comma+1, args...);
}
#else
#define trace(...)
#endif
//----------------------------------------------------------------------------------------------------------------------
//----------------------------------------------------------------------------------------------------------------------
//----------------------------------------------------------------------------------------------------------------------
//----------------------------------------------------------------------------------------------------------------------
//----------------------------------------------------------------------------------------------------------------------

void solve()
{
    
}

void colorEdges(int ptr, vector<vector<pair<int, int> > >& gra,
                vector<int>& edgeColors, bool isVisited[])
{
    queue<int> q;
    int c = 0;

    set<int> colored;

    // return if isVisited[ptr] is true
    if (isVisited[ptr])
        return;

    // Mark the current node visited
    isVisited[ptr] = 1;

    // Traverse all edges of current vertex
    for (int i = 0; i < gra[ptr].size(); i++) {
        // if already colored, insert it into the set
        if (edgeColors[gra[ptr][i].second] != -1)
            colored.insert(edgeColors[gra[ptr][i].second]);
    }

    for (int i = 0; i < gra[ptr].size(); i++) {
        // if not visited, inset into the queue
        if (!isVisited[gra[ptr][i].first])
            q.push(gra[ptr][i].first);

        if (edgeColors[gra[ptr][i].second] == -1) {
            // if col vector -> negative
            while (colored.find(c) != colored.end())

                // increment the color
                c++;

            // copy it in the vector
            edgeColors[gra[ptr][i].second] = c;

            // then add it to the set
            colored.insert(c);
            c++;
        }
    }

    // while queue's not empty
    while (!q.empty()) {
        int temp = q.front();
        q.pop();

        colorEdges(temp, gra, edgeColors, isVisited);
    }

    return;
}

int main()
{
    set<int> empty;

    // declaring vector of vector of pairs, to define Graph
    vector<vector<pair<int, int> > > gra;

    vector<int> edgeColors;

    bool isVisited[100009] = { 0 };

    // Enter the Number of Vertices
    // and the number of edges
    int ver = 4;
    int edge = 4;
    cin >> ver;
    edge = ver-1;

    gra.resize(ver);
    edgeColors.resize(edge, -1);

    // Enter edge & vertices of edge
    // x--; y--;
    // Since graph is undirected, push both pairs
    // (x, y) and (y, x)
    // graph[x].push_back(make_pair(y, i));
    // graph[y].push_back(make_pair(x, i));
    long x, y;
    for (long i = 0; i< edge; i++)
    {
        cin >> x >> y;
        gra[x-1].push_back(make_pair(y-1, i));
        gra[y-1].push_back(make_pair(x-1, i));
    }


    colorEdges(0, gra, edgeColors, isVisited);
    int ans= -1;
    // printing all the edge colors
    for (int i = 0; i < edge; i++)
        ans = max(ans, edgeColors[i] + 1);
    cout << ans<<'\n';
    for (int i = 0; i< edge; i++)
        cout << edgeColors[i] + 1 << '\n';
    return 0;
}