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)

import sys
input=sys.stdin.readline
sys.setrecursionlimit(10 ** 7)
from collections import defaultdict
from collections import Counter
import fractions
import math
from collections import deque
from bisect import bisect_left
from bisect import insort_left
import itertools
from heapq import heapify
from heapq import heappop
from heapq import heappush
import heapq
import numpy as np
INF = float("inf")
#d = defaultdict(int)
#d = defaultdict(list)
#N = int(input())
#A = list(map(int,input().split()))
#S = list(input())
#S.remove("\n")
#N,M = map(int,input().split())
#S,T = map(str,input().split())
#A = [int(input()) for _ in range(N)]
#S = [input() for _ in range(N)]
#A = [list(map(int,input().split())) for _ in range(N)]
N = int(input())
ab = [list(map(int,input().split())) for _ in range(N-1)]
tree = [[] for _ in range(N)]
for i in range(N-1):
    a,b = ab[i]
    tree[a-1].append(b-1)
    tree[b-1].append(a-1)
    index = -1
    MAX = 0
for i in range(N):
    li = tree[i]
    n = len(li)
    if n > MAX:
        MAX = n
        index = i
d = defaultdict(int)

def dfs(cur,parent,prevcolor):
    li = tree[cur]
    n = len(li)
    if n == 0:
        return
    flag = 0
    for i in range(n):
        chi = li[i]
        if chi == parent:
            flag = 1
            continue
        a = (prevcolor+1+i)%MAX
        if flag == 1:
            a -= 1
        d[(cur,chi)] = a
        d[(chi,cur)] = a
        dfs(chi,cur,a)
dfs(index,-1,0)
print(MAX)
for i in range(N-1):
    a,b = ab[i]
    ans = d[(a-1,b-1)]
    if ans == 0:
        ans += MAX
    print(1+ans%MAX)