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
sys.setrecursionlimit(10**6)
from collections import deque

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

# process
# 頂点を2グループに分類
group = [-1]*N
group[0] = False
def categorize2g(pi, i, g):
    for ci in Edges[i]:
        if ci == pi:
            continue
        group[ci] = not g
        categorize2g(i, ci, not g)

categorize2g(-1, 0, 0)

# 順列を求める
ans = [0]*N
mod0 = [x for x in range(1, N+1) if x%3 == 0]
mod1 = [x for x in range(1, N+1) if x%3 == 1]
mod2 = [x for x in range(1, N+1) if x%3 == 2]
gtnum = sum(group)
if gtnum <= N//3:
    dq = deque(mod1+mod2+mod0)
elif N-gtnum <= N//3:
    dq = deque(mod0+mod1+mod2)
else:
    dq = deque(mod1+mod0+mod2)

if len(ans) == N:
    for i, g in enumerate(group):
        if g:
            ans[i] = dq.pop()
        else:
            ans[i] = dq.popleft()

# output
# print(group)
print(" ".join(map(str, ans)))