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
from collections import *

def bfs():
    q = deque([0])
    color = [0]*N
    color[0] = 1
    
    while q:
        v = q.popleft()
        
        for nv in G[v]:
            if color[nv]==0:
                color[nv] = -color[v]
                q.append(nv)
    
    return color

N = int(input())
G = [[] for _ in range(N)]

for _ in range(N-1):
    a, b = map(int, input().split())
    G[a-1].append(b-1)
    G[b-1].append(a-1)
    
cnt = [0]*3

for i in range(1, N+1):
    cnt[i%3] += 1

color = bfs()
m = color.count(1)
ans = [-1]*N

if m<=cnt[0]:
    c0, c1, c2 = 3, 1, 2
    
    for i in range(N):
        if color[i]==1:
            ans[i] = c0
            c0 += 3
    
    for i in range(N):
        if color[i]==-1:
            if c0<=N:
                ans[i] = c0
                c0 += 3
            else:
                if c1<=N:
                    ans[i] = c1
                    c1 += 3
                else:
                    ans[i] = c2
                    c2 += 3
elif m>=N-cnt[0]:
    c0, c1, c2 = 3, 1, 2
    
    for i in range(N):
        if color[i]==-1:
            ans[i] = c0
            c0 += 3
    
    for i in range(N):
        if color[i]==1:
            if c0<=N:
                ans[i] = c0
                c0 += 3
            else:
                if c1<=N:
                    ans[i] = c1
                    c1 += 3
                else:
                    ans[i] = c2
                    c2 += 3
else:
    c0, c1, c2 = 3, 1, 2
    
    for i in range(N):
        if color[i]==1:
            if c1<=N:
                ans[i] = c1
                c1 += 3
            else:
                ans[i] = c0
                c0 += 3
        
    for i in range(N):
        if color[i]==-1:
            if c0<=N:
                ans[i] = c0
                c0 += 3
            else:
                ans[i] = c2
                c2 += 3

print(*ans)