Problem:
We have a tree with N vertices. The vertices are numbered 1 to N, and the i-th edge connects Vertex a_i and Vertex b_i.  Takahashi loves the number 3. He is seeking a permutation p_1, p_2, \ldots , p_N of integers from 1 to N satisfying the following condition:    * For every pair of vertices (i, j), if the distance between Vertex i and Vertex j is 3, the sum or product of p_i and p_j is a multiple of 3.  Here the distance between Vertex i and Vertex j is the number of edges contained in the shortest path from Vertex i to Vertex j.  Help Takahashi by finding a permutation that satisfies the condition.

Incorrect submission (verdict: Wrong Answer):
import sys
sys.setrecursionlimit(10**9)
N=int(input())

tree=[[] for _ in range(N+1)]
occur_list=[0]*(N+1)
for _ in range(N-1):
  a,b=map(int,input().split())
  tree[a].append(b)
  tree[b].append(a)
  occur_list[a]+=1
  occur_list[b]+=1
#print(tree)
#print(occur_list)

leaf=0
for i in range(1,N+1):
  if occur_list[i]==1:
    leaf=i
    break
#print(leaf)

def dfs(u,p1,p2,p3):
  global min_3m0
  global min_3m1
  global min_3m2
  
  if p3==0:
    if min_3m0<=N:
      mark_list[u]=min_3m0
      min_3m0+=3
    elif min_3m1<=N:
      mark_list[u]=min_3m1
      min_3m1+=3
    elif min_3m2<=N:
      mark_list[u]=min_3m2
      min_3m2+=3
    else:
      print(-1)
      sys.exit(0)
  elif mark_list[p3]%3==0:
    if min_3m1<=N:
      mark_list[u]=min_3m1
      min_3m1+=3
    elif min_3m2<=N:
      mark_list[u]=min_3m2
      min_3m2+=3
    elif min_3m0<=N:
      mark_list[u]=min_3m0
      min_3m0+=3
    else:
      print(-1)
      sys.exit(0)
  elif mark_list[p3]%3==1:
    if min_3m2<=N:
      mark_list[u]=min_3m2
      min_3m2+=3
    elif min_3m0<=N:
      mark_list[u]=min_3m0
      min_3m0+=3
    else:
      print(-1)
      sys.exit(0)
  elif mark_list[p3]%3==2:
    if min_3m1<=N:
      mark_list[u]=min_3m1
      min_3m1+=3
    elif min_3m0<=N:
      mark_list[u]=min_3m0
      min_3m0+=3
    else:
      print(-1)
      sys.exit(0)
    
  for v in tree[u]:
    if mark_list[v]==0:
      dfs(v,u,p1,p2)

mark_list=[0]*(N+1)
min_3m0=3
min_3m1=1
min_3m2=2
dfs(leaf,0,0,0)

print(*mark_list[1:])

Fixed, accepted submission:
import sys
sys.setrecursionlimit(10**9)
N=int(input())

tree=[[] for _ in range(N+1)]
for _ in range(N-1):
  a,b=map(int,input().split())
  tree[a].append(b)
  tree[b].append(a)
#print(tree)

def dfs(u,par,depth):
  dist_list[u]=depth
  for v in tree[u]:
    if v!=par:
      dfs(v,u,depth+1)
  
dist_list=[-1]*(N+1)
dfs(1,0,0)
#print(dist_list)

num_even=num_odd=0
for i in range(1,N+1):
  if dist_list[i]%2==0:
    num_even+=1
  else:
    num_odd+=1
#print(num_even,num_odd)

num_3m0=3
num_3m1=1
num_3m2=2
answer_list=[0]*(N+1)
if num_even<=N//3:
  for i in range(1,N+1):
    if dist_list[i]%2==0:
      answer_list[i]=num_3m0
      num_3m0+=3
    else:
      if num_3m1<=N:
        answer_list[i]=num_3m1
        num_3m1+=3
      elif num_3m2<=N:
        answer_list[i]=num_3m2
        num_3m2+=3
      else:
        answer_list[i]=num_3m0
        num_3m0+=3
elif num_odd<=N//3:
  for i in range(1,N+1):
    if dist_list[i]%2==1:
      answer_list[i]=num_3m0
      num_3m0+=3
    else:
      if num_3m1<=N:
        answer_list[i]=num_3m1
        num_3m1+=3
      elif num_3m2<=N:
        answer_list[i]=num_3m2
        num_3m2+=3
      else:
        answer_list[i]=num_3m0
        num_3m0+=3
else:
  for i in range(1,N+1):
    if dist_list[i]%2==0:
      if num_3m1<=N:
        answer_list[i]=num_3m1
        num_3m1+=3
      else:
        answer_list[i]=num_3m0
        num_3m0+=3
    else:
      if num_3m2<=N:
        answer_list[i]=num_3m2
        num_3m2+=3
      else:
        answer_list[i]=num_3m0
        num_3m0+=3
        
print(*answer_list[1:])