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;

vector<int> ans;
int COLOR = 0;


class Edge{
public:
    int id;
    long from, to, cost;
    int color = 0;

    Edge(int i, long f, long t, long c){
        id=i;
        from = f; // 0-indexed
        to = t; // 0-indexed
        cost = c;
    }

    bool operator<(const Edge &e) const{
        if(cost < e.cost){
            return true;
        }
        return false;
    }

    bool operator==(const Edge &e) const{
        if(to == e.to && from == e.from && cost == e.cost){
            return true;
        }
        return false;
    }

    inline bool operator!=(const Edge& e) const{
        return !(*this == e);
    }
};

class Vertex{
public:
    int id; // 0-indexed
    long cost;
    bool visited;
    int from;

    bool operator<(const Vertex &v) const{
        if(cost < v.cost){
            return true;
        }
        return false;
    }

    bool operator==(const Vertex &v) const{
        if(id == v.id){
            return true;
        }
        return false;
    }

    inline bool operator!=(const Vertex& v) const{
        return !(*this == v);
    }

    void reset_vertex(){
        cost = 0;
        visited = false;
        from = 10000000;
    }
};

class Graph{
public:
    int N; // vertices
    int M; // edges
    vector<Vertex> vertex;
    vector < vector < Edge > > edge; // 隣接リスト

    void reset_vertex(){
        for(int i=0; i<N; ++i){
            vertex[i].reset_vertex();
        }
    }
};
Graph graph;

void dfs(Vertex start, int color){
    int l = graph.edge[start.id].size(); // 接続先
    int c = 0;
    for(int i=0; i<l; i++){
        int next = graph.edge[start.id][i].to; // next vertex id
        if(!graph.vertex[next].visited){
            graph.vertex[next].visited = true;
            graph.vertex[next].cost = graph.vertex[start.id].cost + graph.edge[start.id][i].cost;
            graph.vertex[next].from = graph.vertex[start.id].id;
            c++;
            if(c==color){
                c++;
            }
            if(COLOR<c){
                COLOR=c;
            }
            
            ans[graph.edge[start.id][i].id] = c;
            // cout<<"as "<<graph.edge[start.id][i].color<<" "<<graph.edge[start.id][i].id<<endl;
            dfs(graph.vertex[next], ans[graph.edge[start.id][i].id]);
        }
    }
}


int main(){
    
    int from, to;
    cin>>graph.N;
    graph.M = graph.N-1;
    graph.vertex.resize(graph.N);
    graph.edge.resize(graph.N);
    
    // edge init
    for(int i=0; i<graph.M; i++){
        cin>>from>>to;
        // 入力される値の範囲, 0-indexed ?
        from--;
        to--;
        
        graph.edge[from].push_back((Edge){i, from, to, 1});
        // graph.edge[to].push_back((Edge){to, from, 1}); // 無
    }



    // vertex init
    for(int i=0; i<graph.N; i++){
        // graph.vertex[i] = (Vertex){i, 0, false, 0};
        graph.vertex[i].id = i;
        graph.vertex[i].cost = 0;
        graph.vertex[i].visited = false;
        graph.vertex[i].from = 0;
    }
    graph.reset_vertex();

    ans.resize(graph.M);
    // dfs
    for(int i=0; i<graph.N; ++i){
        if(!graph.vertex[i].visited){
            graph.vertex[i].visited = true;
            // ans[i] = 1;
            dfs( graph.vertex[i], 0);
        }
    }
    
    /*
    for(int i=0; i<graph.N; i++){
        int l = graph.edge[i].size();
        for(int j=0; j<l; j++){
            ans[graph.edge[i][j].id] = graph.edge[i][j].color;
        }
    }
    */
    cout<<COLOR<<endl;
    for(int i=0; i<graph.M; ++i){
        cout<<ans[i]<<endl;
    }

    return 0;
}