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: Runtime Error)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Deque;
import java.util.List;
import java.util.regex.Pattern;

public class Main {
    public void solve(BufferedReader stdin, PrintWriter stdout) throws NumberFormatException, IOException {
        Pattern space = Pattern.compile(" ");
        int n = Integer.parseInt(stdin.readLine());
        int[] a = new int[n];
        int[] b = new int[n];
        for (int i = 0; i < n - 1; i++) {
            int[] line = space.splitAsStream(stdin.readLine()).mapToInt(Integer::parseInt).toArray();
            a[i] = line[0] - 1;
            b[i] = line[1] - 1;
        }

        int[] used = new int[n];
        int[][] colors = new int[n][n];
        Deque<Integer> queue = new ArrayDeque<>();
        queue.addLast(0);
        while (!queue.isEmpty()) {
            int current = queue.removeFirst();
            List<Integer> nexts = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                if (a[i] == current) nexts.add(b[i]);
                if (b[i] == current) nexts.add(a[i]);
            }

            int color = 1;
            for (int next : nexts) {
                if (colors[current][next] != 0) continue;
                if (used[current] == color) color++;
                colors[current][next] = color;
                colors[next][current] = color;
                used[next] = color;
                color++;
                queue.add(next);
            }
        }

        int max = 0;
        for (int i = 0; i < n - 1; i++) {
            max = Math.max(max, colors[a[i]][b[i]]);
        }

        stdout.println(max);
        for (int i = 0; i < n - 1; i++) {
            stdout.println(colors[a[i]][b[i]]);
        }
    }


    public static void main(String[] args) throws NumberFormatException, IOException {
        BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter stdout = new PrintWriter(System.out, false);
        new Main().solve(stdin, stdout);
        stdout.flush();
    }
}