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: Time Limit Exceeded)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Main main = new Main();
        main.solve();
    }
    public void solve() {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int N = scan.nextInt();
        Node[] nodes = new Node[N+1];
        Edge[] edges = new Edge[N-1];
        for (int i = 1; i <= N; i++) {
            nodes[i] = new Node(i);
        }
        for (int i = 0; i < N-1; i++){
            Edge edge = new Edge(i, scan.nextInt(), scan.nextInt());
            edges[i] = edge;
            nodes[edge.from].addEdge(edge);
            nodes[edge.to].addEdge(edge);
        }
        Node top = null;
        int max = 0;
        for (int i = 1; i <= N; i++) {
            Node node = nodes[i];
            int d = node.degree();
            if (max < d) {
                top = node;
                max = d;
            }
        }
        int K = top.degree();
        PriorityQueue<Node> deque = new PriorityQueue<>(new NodeComparator());
        deque.add(top);
        while(!deque.isEmpty()) {
            Node node = deque.poll();
            node.color(K);
            node.visited = true;
            for (int id : node.edges.keySet()) {
                Edge edge = node.edges.get(id);
                if (edge.from != node.no) {
                    Node next = nodes[edge.from];
                    if (!next.visited) {
                        deque.add(next);
                    }
                }
                if (edge.to != node.no) {
                    Node next = nodes[edge.to];
                    if (!next.visited) {
                        deque.add(next);
                    }
                }
            }
        }
        System.out.println(K);
        for (int i = 0; i < N-1; i++) {
            System.out.println(edges[i].color);
        }
    }
    class NodeComparator implements Comparator<Node> {
        @Override
        public int compare(Node o1, Node o2) {
            int d1 = o1.degree();
            int d2 = o2.degree();
            if (d1 != d2) {
                return -Integer.compare(d1, d2);
            }
            return Integer.compare(o1.no, o2.no);
        }
    }
    class Node {
        int no;
        boolean visited = false;
        HashMap<Integer, Edge> edges = new HashMap<>();
        Node(int no) {
            this.no = no;
        }
        void addEdge(Edge edge) {
            edges.put(edge.id, edge);
        }
        int degree() {
            return edges.size();
        }
        void color(int K) {
            boolean[] colors = new boolean[K+1];
            List<Integer> possible = new ArrayList<Integer>();
            for (Edge edge : edges.values()) {
                if (0 < edge.color) {
                    colors[edge.color] = true;
                }
            }
            for (int i = 1; i <= K; i++) {
                if (colors[i]) {
                    continue;
                }
                possible.add(i);
            }
            for (Edge edge : edges.values()) {
                if (0 < edge.color) {
                    continue;
                }
                edge.color = possible.remove(0);
            }
        }
    }
    class Edge {
        int id;
        int from;
        int to;
        int color;
        Edge(int id, int from, int to) {
            this.id = id;
            this.from = from;
            this.to = to;
            this.color = -1;
        }
    }
}