Problem p02749 (python)

Fixed submission:
import sys
sys.setrecursionlimit(1000000000)
N = int(input())
AB = [list(map(int, input().split())) for _ in range(N - 1)]


class Tree:
    def __init__(self, v):
        self.v = v
        self.neighbors = []

    def set_rank(self, rank, parent):
        self.rank = rank
        for neighbor in self.neighbors:
            if neighbor is parent:
                continue
            neighbor.set_rank(rank=rank + 1, parent=self)


trees = {i: Tree(i) for i in range(1, N + 1)}

for a, b in AB:
    trees[a].neighbors.append(trees[b])
    trees[b].neighbors.append(trees[a])
try:
    trees[1].set_rank(1, None)
except:
    print(-1)
    exit()

group0 = [node.v for node in trees.values() if node.rank % 2 == 0]
group1 = [node.v for node in trees.values() if node.rank % 2]
x = [set(), set(), set()]
for i in range(1, N + 1):
    x[i % 3].add(i)
if len(group1) < len(group0):
    group1, group0 = group0, group1
result = {}
if len(group0) <= len(x[0]):
    while group0 and x[0]:
        result[group0.pop()] = x[0].pop()
    y = x[0] | x[1] | x[2]
    while group1 and y:
        result[group1.pop()] = y.pop()
else:
    while x[2] and group0:
        result[group0.pop()] = x[2].pop()
    while x[1] and group1:
        result[group1.pop()] = x[1].pop()
    while group0 and x[0]:
        result[group0.pop()] = x[0].pop()
    while group1 and x[0]:
        result[group1.pop()] = x[0].pop()
    if group0 or group1:
        print(-1)
        exit()

print(' '.join(str(result[i]) for i in range(1, N + 1)))

Buggy submission (verdict: Runtime Error):
import sys
sys.setrecursionlimit(1000000000000)
N = int(input())
AB = [list(map(int, input().split())) for _ in range(N - 1)]


class Tree:
    def __init__(self, v):
        self.v = v
        self.neighbors = []

    def set_rank(self, rank, parent):
        self.rank = rank
        for neighbor in self.neighbors:
            if neighbor is parent:
                continue
            neighbor.set_rank(rank=rank + 1, parent=self)


trees = {i: Tree(i) for i in range(1, N + 1)}

for a, b in AB:
    trees[a].neighbors.append(trees[b])
    trees[b].neighbors.append(trees[a])
try:
    trees[1].set_rank(1, None)
except:
    print(-1)
    exit()

group0 = [node.v for node in trees.values() if node.rank % 2 == 0]
group1 = [node.v for node in trees.values() if node.rank % 2]
x = [set(), set(), set()]
for i in range(1, N + 1):
    x[i % 3].add(i)
if len(group1) < len(group0):
    group1, group0 = group0, group1
result = {}
if len(group0) <= len(x[0]):
    while group0 and x[0]:
        result[group0.pop()] = x[0].pop()
    y = x[0] | x[1] | x[2]
    while group1 and y:
        result[group1.pop()] = y.pop()
else:
    while x[2] and group0:
        result[group0.pop()] = x[2].pop()
    while x[1] and group1:
        result[group1.pop()] = x[1].pop()
    while group0 and x[0]:
        result[group0.pop()] = x[0].pop()
    while group1 and x[0]:
        result[group1.pop()] = x[0].pop()
    if group0 or group1:
        print(-1)
        exit()

print(' '.join(str(result[i]) for i in range(1, N + 1)))

Buggy submission (verdict: Runtime Error):
N = int(input())
AB = [list(map(int, input().split())) for _ in range(N - 1)]


class Tree:
    def __init__(self, v):
        self.v = v
        self.neighbors = []

    def set_rank(self, rank, parent):
        self.rank = rank
        for neighbor in self.neighbors:
            if neighbor is parent:
                continue
            neighbor.set_rank(rank=rank + 1, parent=self)


trees = {i: Tree(i) for i in range(1, N + 1)}

for a, b in AB:
    trees[a].neighbors.append(trees[b])
    trees[b].neighbors.append(trees[a])
trees[2].set_rank(2, None)

group0 = [node.v for node in trees.values() if node.rank % 2 == 0]
group1 = [node.v for node in trees.values() if node.rank % 2]
x = [set(), set(), set()]
for i in range(1, N + 1):
    x[i % 3].add(i)
if len(group1) < len(group0):
    group1, group0 = group0, group1
result = {}
if len(group0) <= len(x[0]):
    while group0 and x[0]:
        result[group0.pop()] = x[0].pop()
    y = x[0] | x[1] | x[2]
    while group1 and y:
        result[group1.pop()] = y.pop()
else:
    while x[2] and group0:
        result[group0.pop()] = x[2].pop()
    while x[1] and group1:
        result[group1.pop()] = x[1].pop()
    while group0 and x[0]:
        result[group0.pop()] = x[0].pop()
    while group1 and x[0]:
        result[group1.pop()] = x[0].pop()
    if group0 or group1:
        print(-1)
        exit()

print(' '.join(str(result[i]) for i in range(1, N + 1)))

Buggy submission (verdict: Runtime Error):
N = int(input())
AB = [list(map(int, input().split())) for _ in range(N - 1)]


class Tree:
    def __init__(self, v):
        self.v = v
        self.neighbors = []

    def set_rank(self, rank, parent):
        self.rank = rank
        for neighbor in self.neighbors:
            if neighbor is parent:
                continue
            neighbor.set_rank(rank=rank + 1, parent=self)


trees = {i: Tree(i) for i in range(1, N + 1)}

for a, b in AB:
    trees[a].neighbors.append(trees[b])
    trees[b].neighbors.append(trees[a])
trees[1].set_rank(1, None)

exit()
group0 = [node.v for node in trees.values() if node.rank % 2 == 0]
group1 = [node.v for node in trees.values() if node.rank % 2]
x = [set(), set(), set()]
for i in range(1, N + 1):
    x[i % 3].add(i)
if len(group1) < len(group0):
    group1, group0 = group0, group1
result = {}
if len(group0) <= len(x[0]):
    while group0 and x[0]:
        result[group0.pop()] = x[0].pop()
    y = x[0] | x[1] | x[2]
    while group1 and y:
        result[group1.pop()] = y.pop()
else:
    while x[2] and group0:
        result[group0.pop()] = x[2].pop()
    while x[1] and group1:
        result[group1.pop()] = x[1].pop()
    while group0 and x[0]:
        result[group0.pop()] = x[0].pop()
    while group1 and x[0]:
        result[group1.pop()] = x[0].pop()
    if group0 or group1:
        print(-1)
        exit()

print(' '.join(str(result[i]) for i in range(1, N + 1)))

Buggy submission (verdict: Runtime Error):
N = int(input())
AB = [list(map(int, input().split())) for _ in range(N - 1)]


class Tree:
    def __init__(self, v):
        self.v = v
        self.neighbors = []

    def set_rank(self, rank, parent):
        self.rank = rank
        for neighbor in self.neighbors:
            if neighbor is parent:
                continue
            neighbor.set_rank(rank=rank + 1, parent=self)


trees = {i: Tree(i) for i in range(1, N + 1)}

for a, b in AB:
    trees[a].neighbors.append(trees[b])
    trees[b].neighbors.append(trees[a])
trees[1].set_rank(1, None)

group0 = [node.v for node in trees.values() if node.rank % 2 == 0]
group1 = [node.v for node in trees.values() if node.rank % 2]
x = [set(), set(), set()]
for i in range(1, N + 1):
    x[i % 3].add(i)
if len(group1) < len(group0):
    group1, group0 = group0, group1
exit()
result = {}
if len(group0) <= len(x[0]):
    while group0 and x[0]:
        result[group0.pop()] = x[0].pop()
    y = x[0] | x[1] | x[2]
    while group1 and y:
        result[group1.pop()] = y.pop()
else:
    while x[2] and group0:
        result[group0.pop()] = x[2].pop()
    while x[1] and group1:
        result[group1.pop()] = x[1].pop()
    while group0 and x[0]:
        result[group0.pop()] = x[0].pop()
    while group1 and x[0]:
        result[group1.pop()] = x[0].pop()
    if group0 or group1:
        print(-1)
        exit()

print(' '.join(str(result[i]) for i in range(1, N + 1)))

Buggy submission (verdict: Runtime Error):
N = int(input())
AB = [list(map(int, input().split())) for _ in range(N-1)]

class Tree:
    def __init__(self, v):
        self.v = v
        self.neighbors = []

    def set_rank(self,rank,parent):
        self.rank = rank
        for neighbor in self.neighbors:
            if neighbor is parent:
                continue
            neighbor.set_rank(rank=rank+1,parent=self)



trees = {i:Tree(i) for i in range(1,N+1)}

for a,b in AB:
    trees[a].neighbors.append(trees[b])
    trees[b].neighbors.append(trees[a])
trees[1].set_rank(1,None)

group0 = [node.v for node in  trees.values() if node.rank %2 ==0]
group1 = [node.v for node in  trees.values() if node.rank %2]
x = [set(),set(),set()]
for i in range(1,N+1):
    x[i%3].add(i)
if len(group1) < len(group0):
    group1,group0 = group0,group1

result = {}
if len(group0) <= len(x[0]):
    while group0 and x[0]:
        result[group0.pop()]= x[0].pop()
    y = x[0]|x[1]|x[2]
    while group1 and y:
        result[group1.pop()] = y.pop()
    if y:
        import time
        time.sleep(10)
else:
    while x[2] and group0:
        result[group0.pop()] = x[2].pop()
    while x[1] and group1:
        result[group1.pop()] = x[1].pop()
    while group0 and x[0]:
        result[group0.pop()] = x[0].pop()
    while group1 and x[0]:
        result[group1.pop()] = x[0].pop()
    if group0 or group1:
        print(-1)
        exit()


print(' '.join(str(result[i]) for i in range(1,N+1)))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict

N = int(input())
AB = [list(map(int, input().split())) for _ in range(N-1)]

d = defaultdict(list)
class Tree:
    def __init__(self, v):
        self.v = v
        self.neighbors = []

    def set_rank(self,rank,parent):
        self.rank = rank
        for neighbor in self.neighbors:
            if neighbor == parent:
                continue
            neighbor.set_rank(rank=rank+1,parent=self)



trees = {i:Tree(i) for i in range(1,N+1)}

for a,b in AB:
    trees[a].neighbors.append(trees[b])
    trees[b].neighbors.append(trees[a])
trees[1].set_rank(1,None)

group0 = [node.v for node in  trees.values() if node.rank %2 ==0]
group1 = [node.v for node in  trees.values() if node.rank %2]
x = [set(),set(),set()]
for i in range(1,N+1):
    x[i%3].add(i)
if len(group1) < len(group0):
    group1,group0 = group0,group1

result = {}
if len(group0) <= len(x[0]):
    while group0 and x[0]:
        result[group0.pop()]= x[0].pop()
    y = x[0]|x[1]|x[2]
    while group1 and y:
        result[group1.pop()] = y.pop()
    if y:
        import time
        time.sleep(10)
else:
    while x[2] and group0:
        result[group0.pop()] = x[2].pop()
    while x[1] and group1:
        result[group1.pop()] = x[1].pop()
    while group0 and x[0]:
        result[group0.pop()] = x[0].pop()
    while group1 and x[0]:
        result[group1.pop()] = x[0].pop()
    if group0 or group1:
        print(-1)
        exit()


print(' '.join(str(result[i]) for i in range(1,N+1)))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict

N = int(input())
AB = [list(map(int, input().split())) for _ in range(N-1)]

d = defaultdict(list)
class Tree:
    def __init__(self, v):
        self.v = v
        self.neighbors = []

    def set_rank(self,rank,parent):
        self.rank = rank
        for neighbor in self.neighbors:
            if neighbor == parent:
                continue
            neighbor.set_rank(rank=rank+1,parent=self)



trees = {i:Tree(i) for i in range(1,N+1)}

for a,b in AB:
    trees[a].neighbors.append(trees[b])
    trees[b].neighbors.append(trees[a])
trees[1].set_rank(1,None)

group0 = [node.v for node in  trees.values() if node.rank %2 ==0]
group1 = [node.v for node in  trees.values() if node.rank %2]
x = [set(),set(),set()]
for i in range(1,N+1):
    x[i%3].add(i)
if len(group1) < len(group0):
    group1,group0 = group0,group1

result = {}
if len(group0) <= len(x[0]):
    while group0 and x[0]:
        result[group0.pop()]= x[0].pop()
    y = x[0]|x[1]|x[2]
    while group1:
        result[group1.pop()] = y.pop()
else:
    while x[2] and group0:
        result[group0.pop()] = x[2].pop()
    while x[1] and group1:
        result[group1.pop()] = x[1].pop()
    while group0 and x[0]:
        result[group0.pop()] = x[0].pop()
    while group1 and x[0]:
        result[group1.pop()] = x[0].pop()
    if group0 or group1:
        print(-1)
        exit()


print(' '.join(str(result[i]) for i in range(1,N+1)))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict

N = int(input())
AB = [list(map(int, input().split())) for _ in range(N-1)]

d = defaultdict(list)
class Tree:
    def __init__(self, v):
        self.v = v
        self.neighbors = []

    def set_rank(self,rank,parent):
        self.rank = rank
        for neighbor in self.neighbors:
            if neighbor == parent:
                continue
            neighbor.set_rank(rank=rank+1,parent=self)



trees = {i:Tree(i) for i in range(1,N+1)}

for a,b in AB:
    trees[a].neighbors.append(trees[b])
    trees[b].neighbors.append(trees[a])
trees[1].set_rank(1,None)

group0 = [node.v for node in  trees.values() if node.rank %2 ==0]
group1 = [node.v for node in  trees.values() if node.rank %2]
x = [set(),set(),set()]
for i in range(1,N+1):
    x[i%3].add(i)
if len(group1) < len(group0):
    group1,group0 = group0,group1

result = {}
if len(group0) <= len(x[0]):
    while group0 and x[0]:
        result[group0.pop()]= x[0].pop()
    y = x[0]|x[1]|x[2]
    while group1:
        result[group1.pop()] = y.pop()
else:
    while x[2] and group0:
        result[group0.pop()] = x[2].pop()
    while x[1] and group1:
        result[group1.pop()] = x[1].pop()
    while group0 and x[0]:
        result[group0.pop()] = x[0].pop()
    while group1 and x[0]:
        result[group1.pop()] = x[0].pop()
    if group0 or group1:
        import time
        time.sleep(10)


print(' '.join(str(result[i]) for i in range(1,N+1)))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict

N = int(input())
AB = [list(map(int, input().split())) for _ in range(N-1)]

d = defaultdict(list)
class Tree:
    def __init__(self, v):
        self.v = v
        self.neighbors = []

    def set_rank(self,rank,parent):
        self.rank = rank
        for neighbor in self.neighbors:
            if neighbor == parent:
                continue
            neighbor.set_rank(rank=rank+1,parent=self)



trees = {i:Tree(i) for i in range(1,N+1)}

for a,b in AB:
    trees[a].neighbors.append(trees[b])
    trees[b].neighbors.append(trees[a])
trees[1].set_rank(1,None)

group0 = [node.v for node in  trees.values() if node.rank %2 ==0]
group1 = [node.v for node in  trees.values() if node.rank %2]
x = [set(),set(),set()]
for i in range(1,N+1):
    x[i%3].add(i)
if len(group1) < len(group0):
    group1,group0 = group0,group1

result = {}
if len(group0) <= len(x[0]):
    while group0 and x[0]:
        result[group0.pop()]= x[0].pop()
    if group0:
        import time
        time.sleep(100)
    y = x[0]|x[1]|x[2]
    while group1:
        result[group1.pop()] = y.pop()
else:
    while x[2] and group0:
        result[group0.pop()] = x[2].pop()
    while x[1] and group1:
        result[group1.pop()] = x[1].pop()
    while group0 and x[0]:
        result[group0.pop()] = x[0].pop()
    while group1 and x[0]:
        result[group1.pop()] = x[0].pop()

print(' '.join(str(result[i]) for i in range(1,N+1)))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict

N = int(input())
AB = [list(map(int, input().split())) for _ in range(N-1)]

d = defaultdict(list)
class Tree:
    def __init__(self, v):
        self.v = v
        self.neighbors = []

    def set_rank(self,rank,parent):
        self.rank = rank
        for neighbor in self.neighbors:
            if neighbor == parent:
                continue
            neighbor.set_rank(rank=rank+1,parent=self)



trees = {i:Tree(i) for i in range(1,N+1)}

for a,b in AB:
    trees[a].neighbors.append(trees[b])
    trees[b].neighbors.append(trees[a])
trees[1].set_rank(1,None)

group0 = [node.v for node in  trees.values() if node.rank %2 ==0]
group1 = [node.v for node in  trees.values() if node.rank %2]
x = [set(),set(),set()]
for i in range(1,N+1):
    x[i%3].add(i)
if len(group1) < len(group0):
    group1,group0 = group0,group1

result = {}
if len(group0) <= len(x[0]):
    while group0:
        result[group0.pop()]= x[0].pop()
    y = x[0]|x[1]|x[2]
    while group1:
        result[group1.pop()] = y.pop()
else:
    while x[2] and group0:
        result[group0.pop()] = x[2].pop()
    while x[1] and group1:
        result[group1.pop()] = x[1].pop()
    while group0:
        result[group0.pop()] = x[0].pop()
    while group1:
        result[group1.pop()] = x[0].pop()

print(' '.join(str(result[i]) for i in range(1,N+1)))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict

N = int(input())
AB = [list(map(int, input().split())) for _ in range(N-1)]

d = defaultdict(list)
class Tree:
    def __init__(self, v):
        self.v = v
        self.neighbors = []

    def set_rank(self,rank,parent):
        self.rank = rank
        for neighbor in self.neighbors:
            if neighbor == parent:
                continue
            neighbor.set_rank(rank=rank+1,parent=self)



trees = {i:Tree(i) for i in range(1,N+1)}

for a,b in AB:
    trees[a].neighbors.append(trees[b])
    trees[b].neighbors.append(trees[a])
trees[1].set_rank(1,None)

group0 = [node.v for node in  trees.values() if node.rank %2 ==0]
group1 = [node.v for node in  trees.values() if node.rank %2]
x = [set(),set(),set()]
for i in range(1,N+1):
    x[i%3].add(i)
if len(group1) < len(group0):
    group1,group0 = group0,group1

result = {}
if len(group0) <= len(x[0]):
    while group0:
        result[group0.pop()]= x[0].pop()
    y = x[0]|x[1]|x[2]
    while group1:
        result[group1.pop()] = y.pop()
else:
    while x[1] and group0:
        result[group0.pop()] = x[2].pop()
    while x[2] and group1:
        result[group1.pop()] = x[1].pop()
    while group0:
        result[group0.pop()] = x[0].pop()
    while group1:
        result[group1.pop()] = x[0].pop()

print(' '.join(str(result[i]) for i in range(1,N+1)))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict

N = int(input())
AB = [list(map(int, input().split())) for _ in range(N-1)]

d = defaultdict(list)
class Tree:
    def __init__(self, v):
        self.v = v
        self.neighbors = []

    def set_rank(self,rank,parent):
        self.rank = rank
        for neighbor in self.neighbors:
            if neighbor == parent:
                continue
            neighbor.set_rank(rank=rank+1,parent=self)



trees = {i:Tree(i) for i in range(1,N+1)}

for a,b in AB:
    trees[a].neighbors.append(trees[b])
    trees[b].neighbors.append(trees[a])
trees[1].set_rank(1,None)

group0 = [node.v for node in  trees.values() if node.rank %2 ==0]
group1 = [node.v for node in  trees.values() if node.rank %2]
x = [set(),set(),set()]
for i in range(1,N+1):
    x[i%3].add(i)
if len(group1) < len(group0):
    group1,group0 = group0,group1

result = {}
if len(group0) <= len(x[0]):
    while group0:
        result[group0.pop()]= x[0].pop()
    y = x[0]|x[1]|x[2]
    while group1:
        result[group1.pop()] = y.pop()
else:
    while x[1] and group0:
        result[group0.pop()] = x[1].pop()
    while x[2] and group1:
        result[group1.pop()] = x[2].pop()
    while group0:
        result[group0.pop()] = x[0].pop()
    while group1:
        result[group1.pop()] = x[0].pop()

print(' '.join(str(result[i]) for i in range(1,N+1)))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict

N = int(input())
AB = [list(map(int, input().split())) for _ in range(N-1)]

d = defaultdict(list)
class Tree:
    def __init__(self, v):
        self.v = v
        self.neighbors = []

    def set_rank(self,rank,parent):
        self.rank = rank
        for neighbor in self.neighbors:
            if neighbor == parent:
                continue
            neighbor.set_rank(rank=rank+1,parent=self)



trees = {i:Tree(i) for i in range(1,N+1)}

for a,b in AB:
    trees[a].neighbors.append(trees[b])
    trees[b].neighbors.append(trees[a])
trees[1].set_rank(1,None)

group0 = [node.v for node in  trees.values() if node.rank %2 ==0]
group1 = [node.v for node in  trees.values() if node.rank %2]
x = [set(),set(),set()]
for i in range(1,N+1):
    x[i%3].add(i)
if len(group1) < len(group0):
    group1,group0 = group0,group1

result = {}
if len(group0) <= N//3:
    while group0:
        result[group0.pop()]= x[0].pop()
    y = x[0]|x[1]|x[2]
    while group1:
        result[group1.pop()] = y.pop()
else:
    while x[1] and group0:
        result[group0.pop()] = x[1].pop()
    while x[2] and group1:
        result[group1.pop()] = x[2].pop()
    while group0:
        result[group0.pop()] = x[0].pop()
    while group1:
        result[group1.pop()] = x[0].pop()

print(' '.join(str(result[i]) for i in range(1,N+1)))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict

N = int(input())
AB = [list(map(int, input().split())) for _ in range(N-1)]

d = defaultdict(list)
class Tree:
    def __init__(self, v):
        self.v = v
        self.neighbors = []

    def set_rank(self,rank,parent):
        self.rank = rank
        for neighbor in self.neighbors:
            if neighbor == parent:
                continue
            neighbor.set_rank(rank=rank+1,parent=self)



trees = {i:Tree(i) for i in range(1,N+1)}

for a,b in AB:
    trees[a].neighbors.append(trees[b])
    trees[b].neighbors.append(trees[a])
trees[1].set_rank(1,None)

group0 = [node.v for node in  trees.values() if node.rank %2 ==0]
group1 = [node.v for node in  trees.values() if node.rank %2]
x = [set(),set(),set()]
for i in range(1,N+1):
    x[i%3].add(i)
if len(group1) < len(group0):
    group1,group0 = group0,group1

result = {}
if len(group0) <= N//3:
    while group0:
        result[group0.pop()]= x[0].pop()
    y = x[0]|x[1]|x[2]
    while group1:
        result[group1.pop()] = y.pop()
else:
    while x[1] and group0:
        result[group0.pop()] = x[1].pop()
    while x[2] and group1:
        result[group1.pop()] = x[2].pop()
    while group0:
        result[group0.pop()] = x[0].pop()
    while group1:
        result[group1.pop()] = x[0].pop()

print(' '.join(str(result[i]) for i in range(1,N+1)))

Buggy submission (verdict: Runtime Error):
N = int(input())
AB = [list(map(int, input().split())) for _ in range(N - 1)]
# N = 9
# AB = [[1, 2], [2, 3], [9, 8], [8, 3], [3, 4], [4, 5], [3, 6], [6, 7]]
if N == 2:
    print(1, 2)
    exit()


class Node:
    def __init__(self, v):
        self.linked = set()
        self.v = v

    def add_node(self, node):
        self.linked.add(node)

    def set_rank(self, parent, rank):
        self.rank = rank
        for node in self.linked:
            if node is parent:
                continue
            node.set_rank(parent=self, rank=rank + 1)

    def __repr__(self):
        return '{}'.format(self.rank)


nodes = {v: Node(v) for v in range(1, N + 1)}
for a, b in AB:
    nodes[a].add_node(nodes[b])
    nodes[b].add_node(nodes[a])

# usokaihou
import random

root = nodes[random.randint(1, N)]
root.set_rank(None, 1)

group = [[], []]
for node in nodes.values():
    group[node.rank % 2].append(node)
group.sort(key=len)
result = {}
x1 = set()
x2 = set()
x3 = set()

for i in range(1, N + 1):
    if i % 3 == 1:
        x1.add(i)
    elif i % 3 == 2:
        x2.add(i)
    else:
        x3.add(i)

for node in group[0]:
    if x1:
        result[node.v] = x1.pop()
    else:
        result[node.v] = x3.pop()

for node in group[1]:
    if x2:
        result[node.v] = x2.pop()
    else :
        result[node.v] = x3.pop()


print(' '.join(str(result[i]) for i in range(1, N + 1)))

Buggy submission (verdict: Runtime Error):
N = int(input())
AB = [list(map(int, input().split())) for _ in range(N - 1)]
# N = 9
# AB = [[1, 2], [2, 3], [9, 8], [8, 3], [3, 4], [4, 5], [3, 6], [6, 7]]
if N == 2:
    print(1, 2)
if N == 3:
    print(1, 2, 3)

x1 = set()
x2 = set()
x3 = set()

for i in range(1, N + 1):
    if i % 3 == 1:
        x1.add(i)
    elif i % 3 == 2:
        x2.add(i)
    else:
        x3.add(i)
x = [x1, x2, x3]

result = {}


class Node:
    def __init__(self, v):
        self.linked = set()
        self.v = v

    def add_node(self, node):
        self.linked.add(node)

    def set_rank(self, parent, rank):
        self.rank = rank
        if parent == None:
            result[self.v] = x1.pop()
        else:
            if x[(result[parent.v] + 1) % 3]:
                result[self.v] = x[(result[parent.v] + 1) % 3].pop()
            elif x1:
                result[self.v] =  x1.pop()
            elif x2:
                result[self.v] =  x2.pop()
            else:
                result[self.v] =  x3.pop()
        for node in self.linked:
            if node == parent:
                continue
            node.set_rank(parent=self, rank=rank + 1)

    def __repr__(self):
        return '{}'.format(self.rank)


nodes = {v: Node(v) for v in range(1, N + 1)}
for a, b in AB:
    nodes[a].add_node(nodes[b])
    nodes[b].add_node(nodes[a])

# usokaihou
root = nodes[1]
root.set_rank(None, 0)
print(' '.join(str(result[i]) for i in range(1, N + 1)))

exit()

Buggy submission (verdict: Runtime Error):
N = int(input())
AB = [list(map(int, input().split())) for _ in range(N - 1)]
# N = 9
# AB = [[1, 2], [2, 3], [9, 8], [8, 3], [3, 4], [4, 5], [3, 6], [6, 7]]
if N == 2:
    print(1, 2)
if N == 3:
    print(1, 2, 3)

x1 = set()
x2 = set()
x3 = set()

for i in range(1, N + 1):
    if i % 3 == 1:
        x1.add(i)
    elif i % 3 == 2:
        x2.add(i)
    else:
        x3.add(i)
x = [x1, x2, x3]

result = {}


class Node:
    def __init__(self, v):
        self.linked = set()
        self.v = v

    def add_node(self, node):
        self.linked.add(node)

    def set_rank(self, parent, rank):
        self.rank = rank
        if parent == None:
            result[self.v] = x1.pop()
        else:
            if x[(result[self.parent.v] + 1) % 3]:
                result[self.v] = x[(result[self.parent.v] + 1) % 3].pop()
            elif x1:
                x1.pop()
            elif x2:
                x2.pop()
            else:
                x3.pop()
        for node in self.linked:
            if node == parent:
                continue
            node.set_rank(parent=self, rank=rank + 1)

    def __repr__(self):
        return '{}'.format(self.rank)


nodes = {v: Node(v) for v in range(1, N + 1)}
for a, b in AB:
    nodes[a].add_node(nodes[b])
    nodes[b].add_node(nodes[a])

# usokaihou
root = nodes[1]
root.set_rank(None, 0)
print(' '.join(str(result[i]) for i in range(1, N + 1)))

exit()

Buggy submission (verdict: Runtime Error):
N = int(input())
AB = [list(map(int, input().split())) for _ in range(N - 1)]
# N = 9
# AB = [[1, 2], [2, 3], [9, 8], [8, 3], [3, 4], [4, 5], [3, 6], [6, 7]]
if N == 2:
    print(1, 2)
    exit()


class Node:
    def __init__(self, v):
        self.linked = set()
        self.v = v

    def add_node(self, node):
        self.linked.add(node)

    def set_rank(self, parent, rank):
        self.rank = rank
        for node in self.linked:
            if node is parent:
                continue
            node.set_rank(parent=self, rank=rank + 1)

    def __repr__(self):
        return '{}'.format(self.rank)


nodes = {v: Node(v) for v in range(1, N + 1)}
for a, b in AB:
    nodes[a].add_node(nodes[b])
    nodes[b].add_node(nodes[a])

# usokaihou
import random

root = nodes[random.randint(1, N)]
root.set_rank(None, 1)

group = [[], [], []]
for node in nodes.values():
    group[node.rank % 3].append(node)
group.sort(key=len)
result = {}
x1 = set()
x2 = set()
x3 = set()

for i in range(1, N + 1):
    if i % 3 == 1:
        x1.add(i)
    elif i % 3 == 2:
        x2.add(i)
    else:
        x3.add(i)

for node in group[0]:
    if x3:
        result[node.v] = x3.pop()
    else:
        import time
        time.sleep(10)
for node in group[1]:
    if x2:
        result[node.v] = x2.pop()
    elif x3:
        result[node.v] = x3.pop()
    else:
        result[node.v] = x1.pop()

for node in group[2]:
    if x1:
        result[node.v] = x1.pop()
    elif x2:
        result[node.v] = x2.pop()
    else:
        result[node.v] = x3.pop()

print(' '.join(str(result[i]) for i in range(1, N + 1)))

Buggy submission (verdict: Runtime Error):
N = int(input())
AB = [list(map(int, input().split())) for _ in range(N - 1)]
# N = 9
# AB = [[1, 2], [2, 3], [9, 8], [8, 3], [3, 4], [4, 5], [3, 6], [6, 7]]
if N == 2:
    print(1, 2)
    exit()


class Node:
    def __init__(self, v):
        self.linked = set()
        self.v = v

    def add_node(self, node):
        self.linked.add(node)

    def set_rank(self, parent, rank):
        self.rank = rank
        for node in self.linked:
            if node is parent:
                continue
            node.set_rank(parent=self, rank=rank + 1)

    def __repr__(self):
        return '{}'.format(self.rank)


nodes = {v: Node(v) for v in range(1, N + 1)}
for a, b in AB:
    nodes[a].add_node(nodes[b])
    nodes[b].add_node(nodes[a])

# usokaihou
import random

root = nodes[random.randint(1, N)]
root.set_rank(None, 0)

group = [[], [], []]
for node in nodes.values():
    group[node.rank % 3].append(node)
group.sort(key=len)
result = {}
x1 = set()
x2 = set()
x3 = set()

for i in range(1, N + 1):
    if i % 3 == 1:
        x1.add(i)
    elif i % 3 == 2:
        x2.add(i)
    else:
        x3.add(i)

for node in group[0]:
    result[node.v] = x3.pop()

for node in group[1]:
    if x2:
        result[node.v] = x2.pop()
    elif x3:
        result[node.v] = x3.pop()
    else:
        result[node.v] = x1.pop()

for node in group[2]:
    if x1:
        result[node.v] = x1.pop()
    elif x2:
        result[node.v] = x2.pop()
    else:
        result[node.v] = x3.pop()

print(' '.join(str(result[i]) for i in range(1, N + 1)))

Buggy submission (verdict: Runtime Error):
N = int(input())
AB = [list(map(int, input().split())) for _ in range(N - 1)]
# N = 9
# AB = [[1, 2], [2, 3], [9, 8], [8, 3], [3, 4], [4, 5], [3, 6], [6, 7]]
if N == 2:
    print(1, 2)
    exit()
if N == 3:
    print(1, 2, 3)
    exit()


class Node:
    def __init__(self, v):
        self.linked = set()
        self.v = v

    def add_node(self, node):
        self.linked.add(node)

    def set_rank(self, parent, rank):
        self.rank = rank
        for node in self.linked:
            if node == parent:
                continue
            node.set_rank(parent=self, rank=rank + 1)

    def __repr__(self):
        return '{}'.format(self.rank)


nodes = {v: Node(v) for v in range(1, N + 1)}
for a, b in AB:
    nodes[a].add_node(nodes[b])
    nodes[b].add_node(nodes[a])

# usokaihou
import random

root = nodes[random.randint(1, N)]
root.set_rank(None, 0)

group = [[], [], []]
for node in nodes.values():
    group[node.rank % 3].append(node)
group.sort(key=len)
result = {}
x1 = set()
x2 = set()
x3 = set()

for i in range(1, N + 1):
    if i % 3 == 1:
        x1.add(i)
    elif i % 3 == 2:
        x2.add(i)
    else:
        x3.add(i)

for node in group[0]:
    result[node.v] = x3.pop()

for node in group[1]:
    if x2:
        result[node.v] = x2.pop()
    elif x3:
        result[node.v] = x3.pop()
    else:
        result[node.v] = x1.pop()

for node in group[2]:
    if x1:
        result[node.v] = x1.pop()
    elif x2:
        result[node.v] = x2.pop()
    else:
        result[node.v] = x3.pop()

print(' '.join(str(result[i]) for i in range(1, N + 1)))

Buggy submission (verdict: Runtime Error):
N = int(input())
AB = [list(map(int, input().split())) for _ in range(N - 1)]
# N = 9
# AB = [[1, 2], [2, 3], [9, 8], [8, 3], [3, 4], [4, 5], [3, 6], [6, 7]]
if N == 2:
    print(1, 2)
if N == 3:
    print(1, 2, 3)


class Node:
    def __init__(self, v):
        self.linked = set()
        self.v = v

    def add_node(self, node):
        self.linked.add(node)

    def set_rank(self, parent, rank):
        self.rank = rank
        for node in self.linked:
            if node == parent:
                continue
            node.set_rank(parent=self, rank=rank + 1)

    def __repr__(self):
        return '{}'.format(self.rank)


nodes = {v: Node(v) for v in range(1, N + 1)}
for a, b in AB:
    nodes[a].add_node(nodes[b])
    nodes[b].add_node(nodes[a])

# usokaihou
root = nodes[1]
root.set_rank(None, 0)

group = [[], [], []]
for node in nodes.values():
    group[node.rank % 3].append(node)
group.sort(key=len)
result = {}
x1 = set()
x2 = set()
x3 = set()

for i in range(1, N + 1):
    if i % 3 == 1:
        x1.add(i)
    elif i % 3 == 2:
        x2.add(i)
    else:
        x3.add(i)

for node in group[0]:
    result[node.v] = x3.pop()

for node in group[1]:
    if x2:
        result[node.v] = x2.pop()
    else:
        result[node.v] = x3.pop()

for node in group[2]:
    if x1:
        result[node.v] = x1.pop()
    elif x2:
        result[node.v] = x2.pop()
    else:
        result[node.v] = x3.pop()

print(' '.join(str(result[i]) for i in range(1, N + 1)))

Buggy submission (verdict: Runtime Error):
N = int(input())
AB = [list(map(int, input().split())) for _ in range(N - 1)]
# N = 9
# AB = [[1, 2], [2, 3], [9, 8], [8, 3], [3, 4], [4, 5], [3, 6], [6, 7]]
if N == 2:
    print(1, 2)
if N == 3:
    print(1, 2, 3)

last = set(range(1, N + 1))
result = {}


class Node:
    def __init__(self, v):
        self.linked = set()
        self.v = v

    def add_node(self, node):
        self.linked.add(node)

    def set_rank(self, parent, rank):
        self.rank = rank
        result[self.v] = last.pop()
        for node in self.linked:
            if node == parent:
                continue
            node.set_rank(parent=self, rank=rank + 1)

    def __repr__(self):
        return '{}'.format(self.rank)


nodes = {v: Node(v) for v in range(1, N + 1)}
for a, b in AB:
    nodes[a].add_node(nodes[b])
    nodes[b].add_node(nodes[a])

# usokaihou
root = nodes[1]
root.set_rank(None, 0)
print(' '.join(str(result[i]) for i in range(1, N + 1)))

exit()

# ---
group = [[], [], []]
for node in nodes.values():
    group[node.rank % 3].append(node)
group.sort(key=len)
indexes = [0] * 3
result = {}
for node in group[0]:
    indexes[0] += 1
    result[node.v] = indexes[0] * 3
    last.remove(indexes[0] * 3)
for node in group[1]:
    if indexes[1] >= N // 3 + ((N % 3) >= 1):
        indexes[0] += 1
        result[node.v] = indexes[0] * 3
        last.remove(indexes[0] * 3)
    else:
        result[node.v] = indexes[1] * 3 + 1
        last.remove(indexes[1] * 3 + 1)
        indexes[1] += 1
for node in group[2]:
    result[node.v] = last.pop()
#
#     result[node.v] = indexes[2] * 3 + 2
#     indexes[2] += 1

Buggy submission (verdict: Runtime Error):
N = int(input())
AB = [list(map(int, input().split())) for _ in range(N-1)]
# N = 9
# AB = [[1, 2], [2, 3], [9, 8], [8, 3], [3, 4], [4, 5], [3, 6], [6, 7]]
if N == 2:
    print(1, 2)
if N == 3:
    print(1, 2, 3)


class Node:
    def __init__(self, v):
        self.linked = set()
        self.v = v

    def add_node(self, node):
        self.linked.add(node)

    def set_rank(self, parent, rank):
        self.rank = rank
        for node in self.linked:
            if node == parent:
                continue
            node.set_rank(parent=self, rank=rank + 1)

    def __repr__(self):
        return '{}'.format(self.rank)


nodes = {v: Node(v) for v in range(1, N + 1)}
for a, b in AB:
    nodes[a].add_node(nodes[b])
    nodes[b].add_node(nodes[a])

root = nodes[1]
root.set_rank(None, 0)

group = [[], [], []]
for node in nodes.values():
    group[node.rank % 3].append(node)
group.sort(key=len)
indexes = [0] * 3
result = {}
last = set(range(1, N + 1))
for node in group[0]:
    indexes[0] += 1
    result[node.v] = indexes[0] * 3
    last.remove(indexes[0] * 3)
for node in group[1]:
    if indexes[1] >= N // 3 + ((N % 3) >= 1):
        indexes[0] += 1
        result[node.v] = indexes[0] * 3
        last.remove(indexes[0] * 3)
    else:
        result[node.v] = indexes[1] * 3 + 1
        last.remove(indexes[1] * 3 + 1)
        indexes[1] += 1
for node in group[2]:
    result[node.v] = last.pop()
#
#     result[node.v] = indexes[2] * 3 + 2
#     indexes[2] += 1
print(' '.join(str(result[i]) for i in range(1, N + 1)))