Buggy python submission (verdict: Runtime Error):
import collections
I = [int(_) for _ in open(0).read().split()]
N = I[0]
AB = I[1:]
G = collections.defaultdict(set)
for a, b in zip(AB[::2], AB[1::2]):
    G[a].add(b)
    G[b].add(a)
color = [None] * (N + 1)


def dfs(G, v, cur):
    color[v] = cur
    for w in G[v]:
        if color[w] is None:
            dfs(G, w, 1 - cur)


dfs(G, 1, 0)
c=collections.Counter(color[1:])

Fixed submission:
import collections
import sys
sys.setrecursionlimit(2*10**5)
I = [int(_) for _ in open(0).read().split()]
N = I[0]
AB = I[1:]
G = collections.defaultdict(set)
for a, b in zip(AB[::2], AB[1::2]):
    G[a].add(b)
    G[b].add(a)
color = [None] * (N + 1)


def dfs(G, v, cur):
    color[v] = cur
    for w in G[v]:
        if color[w] is None:
            dfs(G, w, 1 - cur)


dfs(G, 1, 0)
c=collections.Counter(color[1:])
cand1 = set(range(1, N + 1, 3))
cand2 = set(range(2, N + 1, 3))
cand3 = set(range(3, N + 1, 3))

i0, i1 = 0, 1
if c[0] > c[1]:
    i0, i1 = 1, 0

ans = [None] * (N + 1)
if c[i0] <= len(cand3):
    for i in range(1, N + 1):
        if color[i]==i0:
            ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand2:
                ans[i] = cand2.pop()
            elif cand3:
                ans[i] = cand3.pop()
else:
    for i in range(1, N + 1):
        if color[i] == i0:
            if cand2:
                ans[i] = cand2.pop()
            elif cand3:
                ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand3:
                ans[i] = cand3.pop()
print(*ans[1:])

Buggy python submission (verdict: Runtime Error):
import collections
I = [int(_) for _ in open(0).read().split()]
N = I[0]
AB = I[1:]
G = collections.defaultdict(set)
for a, b in zip(AB[::2], AB[1::2]):
    G[a].add(b)
    G[b].add(a)
color = [None] * (N + 1)


def dfs(G, v, cur):
    color[v] = cur
    for w in G[v]:
        if color[w] is None:
            dfs(G, w, 1 - cur)


dfs(G, 1, 0)
c=collections.Counter(color[1:])
cand1 = set(range(1, N + 1, 3))
cand2 = set(range(2, N + 1, 3))
cand3 = set(range(3, N + 1, 3))

i0, i1 = 0, 1
if c[0] > c[1]:
    i0, i1 = 1, 0

ans = [None] * (N + 1)
if c[i0] <= len(cand3):
    for i in range(1, N + 1):
        if color[i]==i0:
            ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand2:
                ans[i] = cand2.pop()
            elif cand3:
                ans[i] = cand3.pop()
else:
    for i in range(1, N + 1):
        if color[i] == i0:
            if cand2:
                ans[i] = cand2.pop()
            elif cand3:
                ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand3:
                ans[i] = cand3.pop()
print(*ans[1:])


Fixed submission:
import collections
import sys
sys.setrecursionlimit(2*10**5)
I = [int(_) for _ in open(0).read().split()]
N = I[0]
AB = I[1:]
G = collections.defaultdict(set)
for a, b in zip(AB[::2], AB[1::2]):
    G[a].add(b)
    G[b].add(a)
color = [None] * (N + 1)


def dfs(G, v, cur):
    color[v] = cur
    for w in G[v]:
        if color[w] is None:
            dfs(G, w, 1 - cur)


dfs(G, 1, 0)
c=collections.Counter(color[1:])
cand1 = set(range(1, N + 1, 3))
cand2 = set(range(2, N + 1, 3))
cand3 = set(range(3, N + 1, 3))

i0, i1 = 0, 1
if c[0] > c[1]:
    i0, i1 = 1, 0

ans = [None] * (N + 1)
if c[i0] <= len(cand3):
    for i in range(1, N + 1):
        if color[i]==i0:
            ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand2:
                ans[i] = cand2.pop()
            elif cand3:
                ans[i] = cand3.pop()
else:
    for i in range(1, N + 1):
        if color[i] == i0:
            if cand2:
                ans[i] = cand2.pop()
            elif cand3:
                ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand3:
                ans[i] = cand3.pop()
print(*ans[1:])

Buggy python submission (verdict: Runtime Error):
import collections
I = [int(_) for _ in open(0).read().split()]
N = I[0]
AB = I[1:]
G = collections.defaultdict(set)
for a, b in zip(AB[::2], AB[1::2]):
    G[a].add(b)
    G[b].add(a)
color = [None] * (N + 1)


def dfs(G, v, cur):
    color[v] = cur
    for w in G[v]:
        if color[w] is None:
            dfs(G, w, 1 - cur)


dfs(G, 1, 0)
c=collections.Counter(color[1:])
cand1 = set(range(1, N + 1, 3))
cand2 = set(range(2, N + 1, 3))
cand3 = set(range(3, N + 1, 3))

i0, i1 = 0, 1
if c[0] > c[1]:
    i0, i1 = 1, 0

ans = [None] * (N + 1)
if c[i0] <= len(cand3):
    for i in range(1, N + 1):
        if color[i]==i0:
            ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand2:
                ans[i] = cand2.pop()
            else:
                ans[i] = cand3.pop()
else:
    for i in range(1, N + 1):
        if color[i] == i0:
            if cand2:
                ans[i] = cand2.pop()
            else:
                ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            else:
                ans[i] = cand3.pop()
print(*ans[1:])


Fixed submission:
import collections
import sys
sys.setrecursionlimit(2*10**5)
I = [int(_) for _ in open(0).read().split()]
N = I[0]
AB = I[1:]
G = collections.defaultdict(set)
for a, b in zip(AB[::2], AB[1::2]):
    G[a].add(b)
    G[b].add(a)
color = [None] * (N + 1)


def dfs(G, v, cur):
    color[v] = cur
    for w in G[v]:
        if color[w] is None:
            dfs(G, w, 1 - cur)


dfs(G, 1, 0)
c=collections.Counter(color[1:])
cand1 = set(range(1, N + 1, 3))
cand2 = set(range(2, N + 1, 3))
cand3 = set(range(3, N + 1, 3))

i0, i1 = 0, 1
if c[0] > c[1]:
    i0, i1 = 1, 0

ans = [None] * (N + 1)
if c[i0] <= len(cand3):
    for i in range(1, N + 1):
        if color[i]==i0:
            ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand2:
                ans[i] = cand2.pop()
            elif cand3:
                ans[i] = cand3.pop()
else:
    for i in range(1, N + 1):
        if color[i] == i0:
            if cand2:
                ans[i] = cand2.pop()
            elif cand3:
                ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand3:
                ans[i] = cand3.pop()
print(*ans[1:])

Buggy python submission (verdict: Runtime Error):
import collections
I = [int(_) for _ in open(0).read().split()]
N = I[0]
AB = I[1:]
G = collections.defaultdict(set)
for a, b in zip(AB[::2], AB[1::2]):
    G[a].add(b)
    G[b].add(a)
color = [None] * (N + 1)


def dfs(G, v, cur):
    color[v] = cur
    for w in G[v]:
        if color[w] is None:
            dfs(G, w, 1 - cur)


dfs(G, 1, 0)
c=collections.Counter(color[1:])
cand1 = set(range(1, N + 1, 3))
cand2 = set(range(2, N + 1, 3))
cand3 = set(range(3, N + 1, 3))

i0, i1 = 0, 1
if c[0] > c[1]:
    i0, i1 = 1, 0

ans = [None] * (N + 1)
if c[i0] <= len(cand3):
    for i in range(1, N + 1):
        if color[i]==i0:
            ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand2:
                ans[i] = cand2.pop()
            else:
                ans[i] = cand3.pop()
else:
    for i in range(1, N + 1):
        if color[i] == i0:
            if cand1:
                ans[i] = cand2.pop()
            else:
                ans[i] = cand3.pop()
        else:
            if cand2:
                ans[i] = cand1.pop()
            else:
                ans[i] = cand3.pop()
print(*ans[1:])


Fixed submission:
import collections
import sys
sys.setrecursionlimit(2*10**5)
I = [int(_) for _ in open(0).read().split()]
N = I[0]
AB = I[1:]
G = collections.defaultdict(set)
for a, b in zip(AB[::2], AB[1::2]):
    G[a].add(b)
    G[b].add(a)
color = [None] * (N + 1)


def dfs(G, v, cur):
    color[v] = cur
    for w in G[v]:
        if color[w] is None:
            dfs(G, w, 1 - cur)


dfs(G, 1, 0)
c=collections.Counter(color[1:])
cand1 = set(range(1, N + 1, 3))
cand2 = set(range(2, N + 1, 3))
cand3 = set(range(3, N + 1, 3))

i0, i1 = 0, 1
if c[0] > c[1]:
    i0, i1 = 1, 0

ans = [None] * (N + 1)
if c[i0] <= len(cand3):
    for i in range(1, N + 1):
        if color[i]==i0:
            ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand2:
                ans[i] = cand2.pop()
            elif cand3:
                ans[i] = cand3.pop()
else:
    for i in range(1, N + 1):
        if color[i] == i0:
            if cand2:
                ans[i] = cand2.pop()
            elif cand3:
                ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand3:
                ans[i] = cand3.pop()
print(*ans[1:])

Buggy python submission (verdict: Runtime Error):
import collections
I = [int(_) for _ in open(0).read().split()]
N = I[0]
AB = I[1:]
G = collections.defaultdict(set)
for a, b in zip(AB[::2], AB[1::2]):
    G[a].add(b)
    G[b].add(a)
color = [None] * (N + 1)


def dfs(G, v, cur):
    color[v] = cur
    for w in G[v]:
        if color[w] is None:
            dfs(G, w, 1 - cur)


dfs(G, 1, 0)
c=collections.Counter(color[1:])
cand1 = set(range(1, N + 1, 3))
cand2 = set(range(2, N + 1, 3))
cand3 = set(range(3, N + 1, 3))

i0, i1 = 0, 1
if c[0] > c[1]:
    i0, i1 = 1, 0

ans = [None] * (N + 1)
if c[i0] <= len(cand3):
    for i in range(1, N + 1):
        if color[i]==i0:
            ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand2:
                ans[i] = cand2.pop()
            else:
                ans[i] = cand3.pop()
else:
    for i in range(1, N + 1):
        if color[i]==i0:
            if cand1:
                ans[i] = cand1.pop()
            else:
                ans[i] = cand3.pop()
        else:
            if cand2:
                ans[i] = cand2.pop()
            else:
                ans[i] = cand3.pop()
print(*ans[1:])


Fixed submission:
import collections
import sys
sys.setrecursionlimit(2*10**5)
I = [int(_) for _ in open(0).read().split()]
N = I[0]
AB = I[1:]
G = collections.defaultdict(set)
for a, b in zip(AB[::2], AB[1::2]):
    G[a].add(b)
    G[b].add(a)
color = [None] * (N + 1)


def dfs(G, v, cur):
    color[v] = cur
    for w in G[v]:
        if color[w] is None:
            dfs(G, w, 1 - cur)


dfs(G, 1, 0)
c=collections.Counter(color[1:])
cand1 = set(range(1, N + 1, 3))
cand2 = set(range(2, N + 1, 3))
cand3 = set(range(3, N + 1, 3))

i0, i1 = 0, 1
if c[0] > c[1]:
    i0, i1 = 1, 0

ans = [None] * (N + 1)
if c[i0] <= len(cand3):
    for i in range(1, N + 1):
        if color[i]==i0:
            ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand2:
                ans[i] = cand2.pop()
            elif cand3:
                ans[i] = cand3.pop()
else:
    for i in range(1, N + 1):
        if color[i] == i0:
            if cand2:
                ans[i] = cand2.pop()
            elif cand3:
                ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand3:
                ans[i] = cand3.pop()
print(*ans[1:])

Buggy python submission (verdict: Runtime Error):
import collections
I = [int(_) for _ in open(0).read().split()]
N = I[0]
AB = I[1:]
G = collections.defaultdict(set)
for a, b in zip(AB[::2], AB[1::2]):
    G[a].add(b)
    G[b].add(a)
color = [None] * (N + 1)


def dfs(G, v, cur):
    color[v] = cur
    for w in G[v]:
        if color[w] is None:
            dfs(G, w, 1 - cur)


dfs(G, 1, 0)
cand1 = set(range(1, N + 1, 3))
cand2 = set(range(2, N + 1, 3))
cand3 = set(range(3, N + 1, 3))
ans = [None] * (N + 1)
for i in range(1, N + 1):
    if color[i]:
        if len(cand1):
            t = cand1.pop()
        else:
            t = cand3.pop()
    else:
        if len(cand2):
            t = cand2.pop()
        else:
            t = cand3.pop()
    ans[i] = t
print(*ans[1:])


Fixed submission:
import collections
import sys
sys.setrecursionlimit(2*10**5)
I = [int(_) for _ in open(0).read().split()]
N = I[0]
AB = I[1:]
G = collections.defaultdict(set)
for a, b in zip(AB[::2], AB[1::2]):
    G[a].add(b)
    G[b].add(a)
color = [None] * (N + 1)


def dfs(G, v, cur):
    color[v] = cur
    for w in G[v]:
        if color[w] is None:
            dfs(G, w, 1 - cur)


dfs(G, 1, 0)
c=collections.Counter(color[1:])
cand1 = set(range(1, N + 1, 3))
cand2 = set(range(2, N + 1, 3))
cand3 = set(range(3, N + 1, 3))

i0, i1 = 0, 1
if c[0] > c[1]:
    i0, i1 = 1, 0

ans = [None] * (N + 1)
if c[i0] <= len(cand3):
    for i in range(1, N + 1):
        if color[i]==i0:
            ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand2:
                ans[i] = cand2.pop()
            elif cand3:
                ans[i] = cand3.pop()
else:
    for i in range(1, N + 1):
        if color[i] == i0:
            if cand2:
                ans[i] = cand2.pop()
            elif cand3:
                ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand3:
                ans[i] = cand3.pop()
print(*ans[1:])