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.

Constraints

* 2\leq N\leq 2\times 10^5
* 1\leq a_i, b_i \leq N
* The given graph is a tree.

Input

Input is given from Standard Input in the following format:


N
a_1 b_1
a_2 b_2
\vdots
a_{N-1} b_{N-1}


Output

If no permutation satisfies the condition, print `-1`.

Otherwise, print a permutation satisfying the condition, with space in between. If there are multiple solutions, you can print any of them.

Example

Input

5
1 2
1 3
3 4
3 5


Output

1 2 5 4 3

Solution (in PYTHON3):

Solution:
import sys

input=sys.stdin.readline
sys.setrecursionlimit(10**7)

N=int(input())
edge=[[] for i in range(N)]
for i in range(N-1):
    a,b=map(int,input().split())
    edge[a-1].append(b-1)
    edge[b-1].append(a-1)

depth=[0]*N
def dfs(v,pv):
    for nv in edge[v]:
        if nv!=pv:
            depth[nv]=depth[v]+1
            dfs(nv,v)

dfs(0,-1)

even=0
odd=0
for i in range(N):
    if depth[i]%2==0:
        even+=1
    else:
        odd+=1

ans=[0 for i in range(N)]

if N%3==0:
    if min(even,odd)>=N//3:
        evencount=0
        oddcount=0
        allcount=0
        for i in range(N):
            if depth[i]%2==0:
                if N//3>evencount:
                    ans[i]=evencount*3+1
                    evencount+=1
                else:
                    ans[i]=(allcount+1)*3
                    allcount+=1
            else:
                if N//3>oddcount:
                    ans[i]=oddcount*3+2
                    oddcount+=1
                else:
                    ans[i]=(allcount+1)*3
                    allcount+=1
        print(*ans)
    elif N//3>even:
        allcount=0
        d=1
        for i in range(N):
            if depth[i]%2==0:
                ans[i]=3*allcount+3
                allcount+=1
        for i in range(N):
            if depth[i]%2==1:
                if N//3>allcount:
                    ans[i]=3*allcount+3
                    allcount+=1
                else:
                    ans[i]=d
                    if d%3==1:
                        d+=1
                    else:
                        d+=2
        print(*ans)
    else:
        allcount=0
        d=1
        for i in range(N):
            if depth[i]%2==1:
                ans[i]=3*allcount+3
                allcount+=1
        for i in range(N):
            if depth[i]%2==0:
                if N//3>allcount:
                    ans[i]=3*allcount+3
                    allcount+=1
                else:
                    ans[i]=d
                    if d%3==1:
                        d+=1
                    else:
                        d+=2
        print(*ans)
elif N%3==2:
    if min(even,odd)>=N//3+1:
        evencount=0
        oddcount=0
        allcount=0
        for i in range(N):
            if depth[i]%2==0:
                if N//3+1>evencount:
                    ans[i]=evencount*3+1
                    evencount+=1
                else:
                    ans[i]=(allcount+1)*3
                    allcount+=1
            else:
                if N//3+1>oddcount:
                    ans[i]=oddcount*3+2
                    oddcount+=1
                else:
                    ans[i]=(allcount+1)*3
                    allcount+=1
        print(*ans)
    elif N//3+1>even:
        allcount=0
        d=1
        for i in range(N):
            if depth[i]%2==0:
                ans[i]=3*allcount+3
                allcount+=1
        for i in range(N):
            if depth[i]%2==1:
                if N//3>allcount:
                    ans[i]=3*allcount+3
                    allcount+=1
                else:
                    ans[i]=d
                    if d%3==1:
                        d+=1
                    else:
                        d+=2
        print(*ans)
    else:
        allcount=0
        d=1
        for i in range(N):
            if depth[i]%2==1:
                ans[i]=3*allcount+3
                allcount+=1
        for i in range(N):
            if depth[i]%2==0:
                if N//3>allcount:
                    ans[i]=3*allcount+3
                    allcount+=1
                else:
                    ans[i]=d
                    if d%3==1:
                        d+=1
                    else:
                        d+=2
        print(*ans)
else:
    if even>=N//3+1 and odd>=N//3:
        evencount=0
        oddcount=0
        allcount=0
        for i in range(N):
            if depth[i]%2==0:
                if N//3+1>evencount:
                    ans[i]=evencount*3+1
                    evencount+=1
                else:
                    ans[i]=(allcount+1)*3
                    allcount+=1
            else:
                if N//3>oddcount:
                    ans[i]=oddcount*3+2
                    oddcount+=1
                else:
                    ans[i]=(allcount+1)*3
                    allcount+=1
        print(*ans)
    elif even>=N//3 and odd>=N//3+1:
        evencount=0
        oddcount=0
        allcount=0
        for i in range(N):
            if depth[i]%2==1:
                if N//3+1>evencount:
                    ans[i]=evencount*3+1
                    evencount+=1
                else:
                    ans[i]=(allcount+1)*3
                    allcount+=1
            else:
                if N//3>oddcount:
                    ans[i]=oddcount*3+2
                    oddcount+=1
                else:
                    ans[i]=(allcount+1)*3
                    allcount+=1
        print(*ans)
    elif N//3>=even:
        allcount=0
        d=1
        for i in range(N):
            if depth[i]%2==0:
                ans[i]=3*allcount+3
                allcount+=1
        for i in range(N):
            if depth[i]%2==1:
                if N//3>allcount:
                    ans[i]=3*allcount+3
                    allcount+=1
                else:
                    ans[i]=d
                    if d%3==1:
                        d+=1
                    else:
                        d+=2
        print(*ans)
    else:
        allcount=0
        d=1
        for i in range(N):
            if depth[i]%2==1:
                ans[i]=3*allcount+3
                allcount+=1
        for i in range(N):
            if depth[i]%2==0:
                if N//3>allcount:
                    ans[i]=3*allcount+3
                    allcount+=1
                else:
                    ans[i]=d
                    if d%3==1:
                        d+=1
                    else:
                        d+=2
        print(*ans)