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 Python (3.4.3) (judge verdict: Accepted)

# -*- coding: utf-8 -*-

from collections import deque

n = int(input())
edges = [list(map(int, input().split())) for i in range(n-1)]

tree = {}
node_in = [0 for i in range(n)] # 頂点に入る辺は1つ
node_out = [[0] for i in range(n)] # 頂点から出る辺は1つ以上
for edge in sorted(edges):
    a = edge[0] # 頂点a
    b = edge[1] # 頂点b

    color = 0
    if node_out[a-1][-1] == 0:
        if node_in[a-1] <= 1: # node_in[a-1] == 0の時1、1の時2なのでまとめて
            color = node_in[a-1] + 1
        else: # node_in[a-1] >= 2
            color = 1
    else:
        color = node_out[a-1][-1] + 1
        if node_in[a-1] == color:
            color += 1
            
    tree[(a, b)] = color
    node_out[a-1].append(color)
    node_in[b-1] = color

print(max(tree.values()))
for edge in edges:
    a = edge[0] # 頂点a
    b = edge[1] # 頂点b
    print(tree[(a, b)])