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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {

    static class Edge {
        int from, to, id;

        public Edge(int from, int to, int id) {
            this.from = from;
            this.to = to;
            this.id = id;
        }
    }

    static class Pair implements Comparable<Pair> {
        int id, prevColor;

        public Pair(int id, int prevColor) {
            this.id = id;
            this.prevColor = prevColor;
        }

        @Override
        public int compareTo(Pair o) {
            return id - o.id;
        }
    }

    static void bfs(int at) {
        visited = new boolean[N];
        visited[at] = true;

        Deque<Pair> deq = new ArrayDeque<>();
        deq.offer(new Pair(0, -1));

        while(!deq.isEmpty()) {
            Pair node = deq.poll();
            int color = 1;
            if (color == node.prevColor) ++color;

            for (Edge edge : graph.get(node.id)) {
                if (visited[edge.to]) continue;
                deq.offer(new Pair(edge.to, color));
                visited[edge.to] = true;
                res[edge.id] = color;
                ++color;
                if (color == node.prevColor) ++color;
            }
        }
    }

    static int N;
    static int maxDeg = 0;
    static List<List<Edge>> graph;
    static int[] res;
    static boolean[] visited;
    static List<Pair> edges;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        N = Integer.parseInt(sc.next());
        graph = new ArrayList<>();
        res = new int[N-1];
        for (int i = 0; i < N; ++i) graph.add(new ArrayList<>());

        edges = new ArrayList<>();
        for (int i = 0; i < N-1; ++i) {
            int a = Integer.parseInt(sc.next()) - 1;
            int b = Integer.parseInt(sc.next()) - 1;
            graph.get(a).add(new Edge(a, b, i));
            graph.get(b).add(new Edge(b, a, i));
        }

        int maxColor = 0;
        for (int i = 0; i < N; ++i) {
            maxColor = Math.max(maxColor, graph.get(i).size());
        }

        for (int i = 0; i < N; ++i) {
            maxDeg = Math.max(maxDeg, graph.get(i).size());
        }


        bfs(0);

        System.out.println(maxColor);
        for (int i = 0; i < res.length; ++i) {
            System.out.println(res[i]);
        }
    }
}