Buggy python submission (verdict: Time Limit Exceeded):
from math import ceil,floor,factorial,gcd,sqrt,log2,cos,sin,tan,acos,asin,atan,degrees,radians,pi,inf
from itertools import accumulate,groupby,permutations,combinations,product,combinations_with_replacement
from collections import deque,defaultdict,Counter
from bisect import bisect_left,bisect_right
from operator import itemgetter
from heapq import heapify,heappop,heappush
from queue import Queue,LifoQueue,PriorityQueue
from copy import deepcopy
from time import time
from functools import reduce
import string
import sys
sys.setrecursionlimit(10 ** 7)
def input() : return sys.stdin.readline().strip()
def INT()   : return int(input())
def MAP()   : return map(int,input().split())
def LIST()  : return list(MAP())

def bfs(k):
    c = [[0]*n for i in range(n)]
    dist = [-1]*n
    que = deque([0])
    dist[0] = 0
    v_prev = 0
    while que:
        v = que.popleft()
        d = dist[v]
        color = set(range(1, k+1))
        used = []
        for w in g[v]:
            if dist[w] > -1:
                used.append(c[v][w])
        color.difference_update(used)
        color = deque(color)
        for w in g[v]:
            if dist[w] > -1:
                continue
            c[v][w] = c[w][v] = color.popleft()
            dist[w] = d + 1            
            que.append(w)
    return c

n = INT()
a = [0]*(n-1)
b = [0]*(n-1)
g = [[] for i in range(n)]
for i in range(n-1):
    a[i], b[i] = MAP()
    a[i] -= 1
    b[i] -= 1
    g[a[i]].append(b[i])
    g[b[i]].append(a[i])
k = 0
for x in g:
    k = max(k, len(x))
print(k)
c = bfs(k)
for i in range(n-1):
    print(c[a[i]][b[i]])

Fixed submission:
from math import ceil,floor,factorial,gcd,sqrt,log2,cos,sin,tan,acos,asin,atan,degrees,radians,pi,inf
from itertools import accumulate,groupby,permutations,combinations,product,combinations_with_replacement
from collections import deque,defaultdict,Counter
from bisect import bisect_left,bisect_right
from operator import itemgetter
from heapq import heapify,heappop,heappush
from queue import Queue,LifoQueue,PriorityQueue
from copy import deepcopy
from time import time
from functools import reduce
import string
import sys
sys.setrecursionlimit(10 ** 7)
def input() : return sys.stdin.readline().strip()
def INT()   : return int(input())
def MAP()   : return map(int,input().split())
def MAP1()  : return map(lambda x:int(x)-1,input().split())
def LIST()  : return list(MAP())

def solve():
    n = INT()
    Q = [tuple(MAP1()) for _ in range(n-1)]

    deg = [0]*n
    adj = [[] for _ in range(n)]
    color = dict()

    for a, b in Q:
        deg[a] += 1
        deg[b] += 1
        adj[a].append(b)
        adj[b].append(a)

    def dfs(s, p):
        nouse = -1
        if p > -1:
            nouse = color[(min(s,p),max(s,p))]
        c = 1
        for t in adj[s]:
            if t == p:
                continue
            if c == nouse:
                c += 1
            color[(min(s,t),max(s,t))] = c
            dfs(t,s)
            c += 1
    
    dfs(1,-1)
    
    print(max(deg))
    for a, b in Q:
        print(color[(a, b)])

if __name__ == '__main__':
    solve()

Buggy python submission (verdict: Time Limit Exceeded):
from math import ceil,floor,factorial,gcd,sqrt,log2,cos,sin,tan,acos,asin,atan,degrees,radians,pi,inf
from itertools import accumulate,groupby,permutations,combinations,product,combinations_with_replacement
from collections import deque,defaultdict,Counter
from bisect import bisect_left,bisect_right
from operator import itemgetter
from heapq import heapify,heappop,heappush
from queue import Queue,LifoQueue,PriorityQueue
from copy import deepcopy
from time import time
from functools import reduce
import string
import sys
sys.setrecursionlimit(10 ** 7)
def input() : return sys.stdin.readline().strip()
def INT()   : return int(input())
def MAP()   : return map(int,input().split())
def LIST()  : return list(MAP())

def bfs():
    c = [[0]*n for i in range(n)]
    dist = [-1]*n
    que = deque([0])
    dist[0] = 0
    v_prev = 0
    k = 0
    while que:
        v = que.popleft()
        d = dist[v]
        color = set(range(1, n))
        used = []
        for w in g[v]:
            if dist[w] > -1:
                used.append(c[v][w])
        color.difference_update(used)
        color = deque(color)
        for w in g[v]:
            if dist[w] > -1:
                continue
            c[v][w] = c[w][v] = color.popleft()
            k = max(k, c[v][w])
            dist[w] = d + 1            
            que.append(w)
    return k, c

n = INT()
a = [0]*(n-1)
b = [0]*(n-1)
g = [[] for i in range(n)]
for i in range(n-1):
    a[i], b[i] = MAP()
    a[i] -= 1
    b[i] -= 1
    g[a[i]].append(b[i])
    g[b[i]].append(a[i])
k, c = bfs()
print(k)
for i in range(n-1):
    print(c[a[i]][b[i]])

Fixed submission:
from math import ceil,floor,factorial,gcd,sqrt,log2,cos,sin,tan,acos,asin,atan,degrees,radians,pi,inf
from itertools import accumulate,groupby,permutations,combinations,product,combinations_with_replacement
from collections import deque,defaultdict,Counter
from bisect import bisect_left,bisect_right
from operator import itemgetter
from heapq import heapify,heappop,heappush
from queue import Queue,LifoQueue,PriorityQueue
from copy import deepcopy
from time import time
from functools import reduce
import string
import sys
sys.setrecursionlimit(10 ** 7)
def input() : return sys.stdin.readline().strip()
def INT()   : return int(input())
def MAP()   : return map(int,input().split())
def MAP1()  : return map(lambda x:int(x)-1,input().split())
def LIST()  : return list(MAP())

def solve():
    n = INT()
    Q = [tuple(MAP1()) for _ in range(n-1)]

    deg = [0]*n
    adj = [[] for _ in range(n)]
    color = dict()

    for a, b in Q:
        deg[a] += 1
        deg[b] += 1
        adj[a].append(b)
        adj[b].append(a)

    def dfs(s, p):
        nouse = -1
        if p > -1:
            nouse = color[(min(s,p),max(s,p))]
        c = 1
        for t in adj[s]:
            if t == p:
                continue
            if c == nouse:
                c += 1
            color[(min(s,t),max(s,t))] = c
            dfs(t,s)
            c += 1
    
    dfs(1,-1)
    
    print(max(deg))
    for a, b in Q:
        print(color[(a, b)])

if __name__ == '__main__':
    solve()

Buggy python submission (verdict: Time Limit Exceeded):
from math import ceil,floor,factorial,gcd,sqrt,log2,cos,sin,tan,acos,asin,atan,degrees,radians,pi,inf
from itertools import accumulate,groupby,permutations,combinations,product,combinations_with_replacement
from collections import deque,defaultdict,Counter
from bisect import bisect_left,bisect_right
from operator import itemgetter
from heapq import heapify,heappop,heappush
from queue import Queue,LifoQueue,PriorityQueue
from copy import deepcopy
from time import time
from functools import reduce
import string
import sys
sys.setrecursionlimit(10 ** 7)
def input() : return sys.stdin.readline().strip()
def INT()   : return int(input())
def MAP()   : return map(int,input().split())
def LIST()  : return list(MAP())

def bfs():
    c = [[0]*n for i in range(n)]
    dist = [-1]*n
    que = deque([0])
    dist[0] = 0
    v_prev = 0
    k = 0
    while que:
        v = que.popleft()
        d = dist[v]
        color = 1
        used = []
        for w in g[v]:
            if dist[w] > -1:
                used.append(c[v][w])
        for w in g[v]:
            if dist[w] > -1:
                continue
            while color in used:
                color += 1
            c[v][w] = c[w][v] = color
            k = max(k, color)
            dist[w] = d + 1            
            que.append(w)
            color += 1
    return k, c

n = INT()
a = [0]*(n-1)
b = [0]*(n-1)
g = [[] for i in range(n)]
for i in range(n-1):
    a[i], b[i] = MAP()
    a[i] -= 1
    b[i] -= 1
    g[a[i]].append(b[i])
    g[b[i]].append(a[i])
k, c = bfs()
print(k)
for i in range(n-1):
    print(c[a[i]][b[i]])

Fixed submission:
from math import ceil,floor,factorial,gcd,sqrt,log2,cos,sin,tan,acos,asin,atan,degrees,radians,pi,inf
from itertools import accumulate,groupby,permutations,combinations,product,combinations_with_replacement
from collections import deque,defaultdict,Counter
from bisect import bisect_left,bisect_right
from operator import itemgetter
from heapq import heapify,heappop,heappush
from queue import Queue,LifoQueue,PriorityQueue
from copy import deepcopy
from time import time
from functools import reduce
import string
import sys
sys.setrecursionlimit(10 ** 7)
def input() : return sys.stdin.readline().strip()
def INT()   : return int(input())
def MAP()   : return map(int,input().split())
def MAP1()  : return map(lambda x:int(x)-1,input().split())
def LIST()  : return list(MAP())

def solve():
    n = INT()
    Q = [tuple(MAP1()) for _ in range(n-1)]

    deg = [0]*n
    adj = [[] for _ in range(n)]
    color = dict()

    for a, b in Q:
        deg[a] += 1
        deg[b] += 1
        adj[a].append(b)
        adj[b].append(a)

    def dfs(s, p):
        nouse = -1
        if p > -1:
            nouse = color[(min(s,p),max(s,p))]
        c = 1
        for t in adj[s]:
            if t == p:
                continue
            if c == nouse:
                c += 1
            color[(min(s,t),max(s,t))] = c
            dfs(t,s)
            c += 1
    
    dfs(1,-1)
    
    print(max(deg))
    for a, b in Q:
        print(color[(a, b)])

if __name__ == '__main__':
    solve()