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.Arrays;

public class Main {

  private static void solve() {
    int n = ni();
    int[] from = new int[n - 1];
    int[] to = new int[n - 1];
    int[] w = new int[n - 1];

    int[] cnt = new int[n];
    for (int i = 0; i < n - 1; i++) {
      from[i] = ni() - 1;
      to[i] = ni() - 1;
      w[i] = i;
      cnt[from[i]]++;
      cnt[to[i]]++;

    }
    int[][][] g = packWU(n, from, to, w);
    int[] ret = new int[n - 1];
    dfs(0, -1, -1, g, ret);

    int deg = Arrays.stream(cnt).max().getAsInt();
    out.println(deg);
    for (int v : ret) {
      out.println(v);
    }
  }

  private static void dfs(int now, int pre, int pare, int[][][] g, int[] ret) {
    int c = 0;

    for (int[] v : g[now]) {
      int nex = v[0];
      int e = v[1];

      if (nex == pre)
        continue;

      c++;
      if (pare >= 0 && c == ret[pare]) {
        c++;
      }
      ret[e] = c;
      dfs(nex, now, e, g, ret);
    }
  }


  public static int[][][] packWU(int n, int[] from, int[] to, int[] w) {
    int[][][] g = new int[n][][];
    int[] p = new int[n];
    for (int f : from)
      p[f]++;
    for (int t : to)
      p[t]++;
    for (int i = 0; i < n; i++)
      g[i] = new int[p[i]][2];
    for (int i = 0; i < from.length; i++) {
      --p[from[i]];
      g[from[i]][p[from[i]]][0] = to[i];
      g[from[i]][p[from[i]]][1] = w[i];
      --p[to[i]];
      g[to[i]][p[to[i]]][0] = from[i];
      g[to[i]][p[to[i]]][1] = w[i];
    }
    return g;
  }


  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}