Buggy python submission (verdict: Runtime Error):
import sys
sys.setrecursionlimit(10**7)

n = int(input())
graph = {i : [] for i in range(n)}
ls = []
for i in range(n-1):
    a, b = [int(i) for i in sys.stdin.readline().split()]
    a -= 1
    b -= 1
    ls.append((a,b))
    graph[a].append(b)
    graph[b].append(a)
_max = 0
_max_node = None
for k, v in graph.items():
    if len(v) > _max:
        _max = len(v)
        _max_node = k
colors = [[0 for i in range(n)] for j in range(n)]
color_dict = {i : set(range(1,1+_max)) for i in range(n)}
candidate = set(range(1,_max+1))
def dfs(_from, ind, last):
    next_constain = []
    for _next in graph[ind]:
        if _next == _from:
            continue
        res = dfs(ind, _next, next_constain)
        last.append(res)
        next_constain.append(res)
    if _from == -1:
        return 0
    used = list(candidate - set(last))[0]
    colors[ind][_from] = used
    colors[_from][ind] = used
    return used

dfs(-1, _max_node, [])
print(_max)
for a, b in ls:
    print(colors[a][b])

Fixed submission:
import sys
from collections import deque
sys.setrecursionlimit(10**7)

n = int(input())
graph = {i : [] for i in range(n)}
ls = []
for i in range(n-1):
    a, b = [int(i) for i in sys.stdin.readline().split()]
    a -= 1
    b -= 1
    ls.append((a,b))
    graph[a].append(b)
    graph[b].append(a)
_max = 0
_max_node = None
for k, v in graph.items():
    if len(v) > _max:
        _max = len(v)
        _max_node = k

parent = [_max_node] * (n)
order = []
stack = [_max_node]
while stack:
    x = stack.pop()
    order.append(x)
    for y in graph[x]:
        if y == parent[x]:
            continue
        parent[y] = x
        stack.append(y)

colors = [-1 for i in range(n)]
for i in order:
    c = 1
    for _next in graph[i]:
        if _next == parent[i]:
            continue
        if c == colors[i]:
            c += 1
        colors[_next] = c
        c += 1
print(_max)
for a, b in ls:
    if parent[a] == b:
        print(colors[a])
    else:
        print(colors[b])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from collections import deque
sys.setrecursionlimit(10**7)

n = int(input())
graph = {i : [] for i in range(n)}
ls = []
for i in range(n-1):
    a, b = [int(i) for i in sys.stdin.readline().split()]
    a -= 1
    b -= 1
    ls.append((a,b))
    graph[a].append(b)
    graph[b].append(a)
_max = 0
_max_node = None
for k, v in graph.items():
    if len(v) > _max:
        _max = len(v)
        _max_node = k
colors = [[0 for i in range(n)] for j in range(n)]
que = deque()
color_dict = {i : set(range(1,1+_max)) for i in range(n)}
cur = _max_node
already = set()
while True:
    cnt = 1
    already.add(cur)
    for _next in graph[cur]:
        if colors[cur][_next] == 0:
            if _next not in already:
                que.append(_next)
                already.add(_next)
            candidate = color_dict[_next].intersection(color_dict[cur])
            cnt = list(candidate)[0]
            colors[cur][_next] = cnt
            colors[_next][cur] = cnt
            color_dict[cur].remove(cnt)
            color_dict[_next].remove(cnt)
    if len(que) == 0:
        break
    cur = que.popleft()
print(_max)
for a, b in ls:
    print(colors[a][b])

Fixed submission:
import sys
from collections import deque
sys.setrecursionlimit(10**7)

n = int(input())
graph = {i : [] for i in range(n)}
ls = []
for i in range(n-1):
    a, b = [int(i) for i in sys.stdin.readline().split()]
    a -= 1
    b -= 1
    ls.append((a,b))
    graph[a].append(b)
    graph[b].append(a)
_max = 0
_max_node = None
for k, v in graph.items():
    if len(v) > _max:
        _max = len(v)
        _max_node = k

parent = [_max_node] * (n)
order = []
stack = [_max_node]
while stack:
    x = stack.pop()
    order.append(x)
    for y in graph[x]:
        if y == parent[x]:
            continue
        parent[y] = x
        stack.append(y)

colors = [-1 for i in range(n)]
for i in order:
    c = 1
    for _next in graph[i]:
        if _next == parent[i]:
            continue
        if c == colors[i]:
            c += 1
        colors[_next] = c
        c += 1
print(_max)
for a, b in ls:
    if parent[a] == b:
        print(colors[a])
    else:
        print(colors[b])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from collections import deque
sys.setrecursionlimit(10**7)

n = int(input())
graph = {i : [] for i in range(n)}
ls = []
for i in range(n-1):
    a, b = [int(i) for i in sys.stdin.readline().split()]
    a -= 1
    b -= 1
    ls.append((a,b))
    graph[a].append(b)
    graph[b].append(a)
_max = 0
_max_node = None
for k, v in graph.items():
    if len(v) > _max:
        _max = len(v)
        _max_node = k
colors = [[0 for i in range(n)] for j in range(n)]
que = deque()
color_dict = {i : [] for i in range(n)}
cur = _max_node
while True:
    cnt = 1
    for _next in graph[cur]:
        if colors[cur][_next] == 0:
            if _next not in que:
                que.append(_next)
            candidate = color_dict[_next] + color_dict[cur]
            while cnt in candidate:
                cnt = cnt + 1 if cnt + 1 <= _max else 1
            colors[cur][_next] = cnt
            colors[_next][cur] = cnt
            color_dict[cur].append(cnt)
            color_dict[_next].append(cnt)
            cnt += 1
    if len(que) == 0:
        break
    cur = que.popleft()
print(_max)
for a, b in ls:
    print(colors[a][b])

Fixed submission:
import sys
from collections import deque
sys.setrecursionlimit(10**7)

n = int(input())
graph = {i : [] for i in range(n)}
ls = []
for i in range(n-1):
    a, b = [int(i) for i in sys.stdin.readline().split()]
    a -= 1
    b -= 1
    ls.append((a,b))
    graph[a].append(b)
    graph[b].append(a)
_max = 0
_max_node = None
for k, v in graph.items():
    if len(v) > _max:
        _max = len(v)
        _max_node = k

parent = [_max_node] * (n)
order = []
stack = [_max_node]
while stack:
    x = stack.pop()
    order.append(x)
    for y in graph[x]:
        if y == parent[x]:
            continue
        parent[y] = x
        stack.append(y)

colors = [-1 for i in range(n)]
for i in order:
    c = 1
    for _next in graph[i]:
        if _next == parent[i]:
            continue
        if c == colors[i]:
            c += 1
        colors[_next] = c
        c += 1
print(_max)
for a, b in ls:
    if parent[a] == b:
        print(colors[a])
    else:
        print(colors[b])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from collections import deque
sys.setrecursionlimit(10**7)

n = int(input())
graph = {i : [] for i in range(n)}
ls = []
for i in range(n-1):
    a, b = [int(i) for i in sys.stdin.readline().split()]
    a -= 1
    b -= 1
    ls.append((a,b))
    graph[a].append(b)
    graph[b].append(a)
_max = 0
_max_node = None
for k, v in graph.items():
    if len(v) > _max:
        _max = len(v)
        _max_node = k
colors = [[0 for i in range(n)] for j in range(n)]
que = deque()
color_dict = {i : [] for i in range(n)}
cur = _max_node
while True:
    cnt = 1
    for _next in graph[cur]:
        if colors[cur][_next] == 0:
            que.append(_next)
            candidate = color_dict[_next] + color_dict[cur]
            while cnt in candidate:
                cnt = cnt + 1 if cnt + 1 <= _max else 1
            colors[cur][_next] = cnt
            colors[_next][cur] = cnt
            color_dict[cur].append(cnt)
            color_dict[_next].append(cnt)
            cnt += 1
    if len(que) == 0:
        break
    cur = que.popleft()
print(_max)
for a, b in ls:
    print(colors[a][b])

Fixed submission:
import sys
from collections import deque
sys.setrecursionlimit(10**7)

n = int(input())
graph = {i : [] for i in range(n)}
ls = []
for i in range(n-1):
    a, b = [int(i) for i in sys.stdin.readline().split()]
    a -= 1
    b -= 1
    ls.append((a,b))
    graph[a].append(b)
    graph[b].append(a)
_max = 0
_max_node = None
for k, v in graph.items():
    if len(v) > _max:
        _max = len(v)
        _max_node = k

parent = [_max_node] * (n)
order = []
stack = [_max_node]
while stack:
    x = stack.pop()
    order.append(x)
    for y in graph[x]:
        if y == parent[x]:
            continue
        parent[y] = x
        stack.append(y)

colors = [-1 for i in range(n)]
for i in order:
    c = 1
    for _next in graph[i]:
        if _next == parent[i]:
            continue
        if c == colors[i]:
            c += 1
        colors[_next] = c
        c += 1
print(_max)
for a, b in ls:
    if parent[a] == b:
        print(colors[a])
    else:
        print(colors[b])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from collections import deque
sys.setrecursionlimit(10**7)

n = int(input())
graph = {i : [] for i in range(n)}
ls = []
for i in range(n-1):
    a, b = [int(i) for i in sys.stdin.readline().split()]
    a -= 1
    b -= 1
    ls.append((a,b))
    graph[a].append(b)
    graph[b].append(a)
_max = 0
_max_node = None
for k, v in graph.items():
    if len(v) > _max:
        _max = len(v)
        _max_node = k

colors = [[0 for i in range(n)] for j in range(n)]

que = deque()
color_dict = {i : [] for i in range(n)}
cur = _max_node
while True:
    cnt = 1
    for _next in graph[cur]:
        if colors[cur][_next] == 0:
            que.append(_next)
            candidate = color_dict[_next] + color_dict[cur]
            while cnt in candidate:
                cnt = cnt + 1 if cnt + 1 <= _max else 1
            colors[cur][_next] = cnt
            colors[_next][cur] = cnt
            color_dict[cur].append(cnt)
            color_dict[_next].append(cnt)
            cnt += 1
    if len(que) == 0:
        break
    cur = que.popleft()
print(_max)
for a, b in ls:
    print(colors[a][b])

Fixed submission:
import sys
from collections import deque
sys.setrecursionlimit(10**7)

n = int(input())
graph = {i : [] for i in range(n)}
ls = []
for i in range(n-1):
    a, b = [int(i) for i in sys.stdin.readline().split()]
    a -= 1
    b -= 1
    ls.append((a,b))
    graph[a].append(b)
    graph[b].append(a)
_max = 0
_max_node = None
for k, v in graph.items():
    if len(v) > _max:
        _max = len(v)
        _max_node = k

parent = [_max_node] * (n)
order = []
stack = [_max_node]
while stack:
    x = stack.pop()
    order.append(x)
    for y in graph[x]:
        if y == parent[x]:
            continue
        parent[y] = x
        stack.append(y)

colors = [-1 for i in range(n)]
for i in order:
    c = 1
    for _next in graph[i]:
        if _next == parent[i]:
            continue
        if c == colors[i]:
            c += 1
        colors[_next] = c
        c += 1
print(_max)
for a, b in ls:
    if parent[a] == b:
        print(colors[a])
    else:
        print(colors[b])