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.BufferedInputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.StringJoiner;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;
import java.util.*;

public class Main {
    public static class Edge {
      int idx;
      int node;
      public Edge(int n, int i) {
        this.idx = i;
        this.node = n;
      }
    }
    static In in = new In();
    static Out out = new Out();
    static long mod = 1000000007;
    static long inf = 0xfffffffffffffffL;

    void solve() {
        int n = in.nextInt();

        Map<Integer, List<Edge>> graph = new HashMap<>();
        Map<Integer, Set<Integer>> usedColor = new HashMap<>();
        for(int i = 1; i <= n; i++) {
            graph.put(i, new ArrayList<>());
            usedColor.put(i, new HashSet<>());
        }

        for(int i = 0; i < n - 1; i++) {
            int v = in.nextInt();
            int u = in.nextInt();
            graph.get(v).add(new Edge(u, i));
            graph.get(u).add(new Edge(v, i));
        }

        int cnt = 0;
        for(List<Edge> adjs : graph.values())
            cnt = Math.max(cnt, adjs.size());
        out.println(cnt);
        
        int[] colors = new int[n-1];
        Queue<Integer> queue = new LinkedList<>();
        Set<Integer> visited = new HashSet<>();
        queue.offer(1);
        visited.add(1);
        while(!queue.isEmpty()) {
          int node = queue.poll();
          for(Edge e : graph.get(node)) {
            if(visited.contains(e.node)) continue;
            int c = 1;
            while(usedColor.get(node).contains(c) || usedColor.get(e.node).contains(c)) c++;
            if(colors[e.idx] == 0)
                colors[e.idx] = c;
            usedColor.get(node).add(c);
            usedColor.get(e.node).add(c);
            queue.offer(e.node);
            visited.add(e.node);
          }
        }
        for(int i = 0; i < colors.length; i++)
          out.println(colors[i]);
    }

    public static void main(String[]$) {
        new Main().solve();
        out.flush();
    }

    static public class In {
        private BufferedInputStream reader = new BufferedInputStream(System.in);
        private byte[] buffer = new byte[0x8000];
        private int i = 0;
        private int length = 0;

        private int read() {
            if (i == length) {
                i = 0;
                try {
                    length = reader.read(buffer);
                } catch (IOException ignored) {
                }
                if (length == -1) {
                    return -1;
                }
            }
            return buffer[i++];
        }

        String next() {
            StringBuilder builder = new StringBuilder();
            int b = read();
            while (b < '!' || '~' < b) {
                b = read();
            }
            while ('!' <= b && b <= '~') {
                builder.appendCodePoint(b);
                b = read();
            }
            return builder.toString();
        }

        int nextInt() {
            return (int)nextLong();
        }

        long nextLong() {
            int b = read();
            while (b < '!' || '~' < b) {
                b = read();
            }
            int i = 0;
            if (b == '-') {
                i = 1;
                b = read();
            }
            long n = 0;
            while ('0' <= b && b <= '9') {
                n = n * 10 + b - '0';
                b = read();
            }
            return i == 0 ? n : -n;
        }

        char[][] nextCharArray(int n, int m) {
            char[][] a = new char[n][m];
            for (int i = 0; i < n; i++) {
                a[i] = next().toCharArray();
            }
            return a;
        }

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        int[] nextIntArray(int n, IntUnaryOperator op) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = op.applyAsInt(nextInt());
            }
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextLong();
            }
            return a;
        }

        long[] nextLongArray(int n, LongUnaryOperator op) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = op.applyAsLong(nextLong());
            }
            return a;
        }
    }

  static class Out {
      private static PrintWriter out = new PrintWriter(System.out);

      void println(Object... a) {
          StringJoiner joiner = new StringJoiner(" ");
          for (Object obj : a) {
              joiner.add(String.valueOf(obj));
          }
          out.println(joiner);
      }

      void print(Object... a) {
          StringJoiner joiner = new StringJoiner(" ");
          for (Object obj : a) {
              joiner.add(String.valueOf(obj));
          }
          out.print(joiner);
      }

      void flush() {
          out.flush();
      }
  }
}