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:
# -*- coding: utf-8 -*-

import sys

def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
sys.setrecursionlimit(10 ** 9)
INF = 10 ** 18
MOD = 10 ** 9 + 7

def dfs(nodes, src):
    """ DFS(木、スタック、重みなし) """

    N = len(nodes)
    stack = [(src, -1, 0)]
    dist = [-1] * N
    while stack:
        u, prev, c = stack.pop()
        dist[u] = c
        for v in nodes[u]:
            if v != prev:
                # 0,1を交互に入れて二部グラフを塗り分け
                stack.append((v, u, 1-c))
    return dist

N = INT()
nodes = [[] for i in range(N)]
for _ in range(N-1):
    a, b = MAP()
    a -= 1; b-= 1
    nodes[a].append(b)
    nodes[b].append(a)

res = dfs(nodes, 0)
cnt0 = res.count(0)
cnt1 = res.count(1)

ans = [0] * N
# グラフの偏りによって場合分け
if cnt0 <= N // 3 or cnt1 <= N // 3:
    if cnt0 > cnt1:
        cnt0, cnt1 = cnt1, cnt0
        res = [1-c for c in res]
    # 少ない方に全部0mod3入れて、多い方は残りを適当に入れる
    p12 = 1
    p3 = 3
    for i in range(N):
        if res[i] == 0:
            ans[i] = p3
            p3 += 3
    for i in range(N):
        if res[i] == 1:
            if p12 <= N:
                ans[i] = p12
                p12 += 1
                if p12 % 3 == 0:
                    p12 += 1
            else:
                ans[i] = p3
                p3 += 3

else:
    # それぞれに1mod3と2mod3を優先して入れて、なくなったら残りには0mod3を入れる
    p1 = 1
    p2 = 2
    p3 = 3
    for i in range(N):
        if res[i] == 0:
            if p1 <= N:
                ans[i] = p1
                p1 += 3
            else:
                ans[i] = p3
                p3 += 3
        else:
            if p2 <= N:
                ans[i] = p2
                p2 += 3
            else:
                ans[i] = p3
                p3 += 3
print(*ans)