Buggy python submission (verdict: Runtime Error):
import collections
n = int(input())
one = collections.deque([1])
two = collections.deque([])
three = collections.deque([])
graph = [[] for _ in range(n)]

for i in range(n - 1):
    a, b = map(int, input().split())
    graph[a - 1].append(b - 1)
    graph[b - 1].append(a - 1)
    if i % 3 == 0: two.append(i + 2)
    elif i % 3 == 1: three.append(i + 2)
    else: one.append(i + 2)

que = collections.deque([0])
num = [0] * n
dist = [-1] * n
parity = [0] * 2
dist[0] = 0
flag = True
while len(que) != 0:
    i = que.popleft()
    parity[dist[i] % 2] += 1
    for j in graph[i]:
        if dist[j] != -1: continue
        dist[j] = dist[i] + 1
        que.append(j)

if parity[0] <= n // 3 or parity[1] <= n // 3:
    rem = 0 if parity[0] < parity[1] else 1
    for i, v in enumerate(dist):
        if v % 2 == rem:
            num[i] = str(three.popleft())
        else:
            if len(one) != 0: str(one.popleft())
            elif len(two) != 0: str(two.popleft())
            else: str(three.popleft())
else:
    for i, v in enumerate(dist):
        if v % 2 == 0:
            if len(one) != 0: num[i] = str(one.popleft())
            elif len(three) != 0: num[i] = str(three.popleft())
            else:
                flag = False
                break
        else:
            if len(two) != 0: num[i] = str(two.popleft())
            elif len(three) != 0: num[i] = str(three.popleft())
            else:
                flag = False
                break

print(' '.join(num))


Fixed submission:
import collections
n = int(input())
one = collections.deque([1])
two = collections.deque([])
three = collections.deque([])
graph = [[] for _ in range(n)]

for i in range(n - 1):
    a, b = map(int, input().split())
    graph[a - 1].append(b - 1)
    graph[b - 1].append(a - 1)
    if i % 3 == 0: two.append(i + 2)
    elif i % 3 == 1: three.append(i + 2)
    else: one.append(i + 2)

que = collections.deque([0])
num = [0] * n
dist = [-1] * n
parity = [0] * 2
dist[0] = 0
flag = True
while len(que) != 0:
    i = que.popleft()
    parity[dist[i] % 2] += 1
    for j in graph[i]:
        if dist[j] != -1: continue
        dist[j] = dist[i] + 1
        que.append(j)

if parity[0] <= n // 3 or parity[1] <= n // 3:
    rem = 0 if parity[0] < parity[1] else 1
    for i, v in enumerate(dist):
        if v % 2 == rem:
            num[i] = str(three.popleft())
        else:
            if len(one) != 0: num[i] = str(one.popleft())
            elif len(two) != 0: num[i] = str(two.popleft())
            else: num[i] = str(three.popleft())
else:
    for i, v in enumerate(dist):
        if v % 2 == 0:
            if len(one) != 0: num[i] = str(one.popleft())
            elif len(three) != 0: num[i] = str(three.popleft())
            else:
                flag = False
                break
        else:
            if len(two) != 0: num[i] = str(two.popleft())
            elif len(three) != 0: num[i] = str(three.popleft())
            else:
                flag = False
                break

print(' '.join(num))

Buggy python submission (verdict: Runtime Error):
import collections
n = int(input())
one = collections.deque([1])
two = collections.deque([])
three = collections.deque([])
graph = [[] for _ in range(n)]

for i in range(n - 1):
    a, b = map(int, input().split())
    graph[a - 1].append(b - 1)
    graph[b - 1].append(a - 1)
    if i % 3 == 0: two.append(i + 2)
    elif i % 3 == 1: three.append(i + 2)
    else: one.append(i + 2)

que = collections.deque([0])
num = [0] * n
dist = [-1] * n
parity = [0] * 2
dist[0] = 0
flag = True
while len(que) != 0:
    i = que.popleft()
    parity[dist[i] % 2] += 1
    for j in graph[i]:
        if dist[j] != -1: continue
        dist[j] = dist[i] + 1
        que.append(j)

if parity[0] <= n // 3 or parity[1] <= n // 3:
    rem = 0 if parity[0] < parity[1] else 1
    for i, v in enumerate(dist):
        if v % 2 == rem: num[i] = str(three.popleft())
    else:
        if len(one) != 0: str(one.popleft())
        elif len(two) != 0: str(two.popleft())
        else: str(three.popleft())
else:
    for i, v in enumerate(dist):
        if v % 2 == 0:
            if len(one) != 0: num[i] = str(one.popleft())
            elif len(three) != 0: num[i] = str(three.popleft())
            else:
                flag = False
                break
        else:
            if len(two) != 0: num[i] = str(two.popleft())
            elif len(three) != 0: num[i] = str(three.popleft())
            else:
                flag = False
                break

print(' '.join(num))


Fixed submission:
import collections
n = int(input())
one = collections.deque([1])
two = collections.deque([])
three = collections.deque([])
graph = [[] for _ in range(n)]

for i in range(n - 1):
    a, b = map(int, input().split())
    graph[a - 1].append(b - 1)
    graph[b - 1].append(a - 1)
    if i % 3 == 0: two.append(i + 2)
    elif i % 3 == 1: three.append(i + 2)
    else: one.append(i + 2)

que = collections.deque([0])
num = [0] * n
dist = [-1] * n
parity = [0] * 2
dist[0] = 0
flag = True
while len(que) != 0:
    i = que.popleft()
    parity[dist[i] % 2] += 1
    for j in graph[i]:
        if dist[j] != -1: continue
        dist[j] = dist[i] + 1
        que.append(j)

if parity[0] <= n // 3 or parity[1] <= n // 3:
    rem = 0 if parity[0] < parity[1] else 1
    for i, v in enumerate(dist):
        if v % 2 == rem:
            num[i] = str(three.popleft())
        else:
            if len(one) != 0: num[i] = str(one.popleft())
            elif len(two) != 0: num[i] = str(two.popleft())
            else: num[i] = str(three.popleft())
else:
    for i, v in enumerate(dist):
        if v % 2 == 0:
            if len(one) != 0: num[i] = str(one.popleft())
            elif len(three) != 0: num[i] = str(three.popleft())
            else:
                flag = False
                break
        else:
            if len(two) != 0: num[i] = str(two.popleft())
            elif len(three) != 0: num[i] = str(three.popleft())
            else:
                flag = False
                break

print(' '.join(num))