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
from collections import deque, Counter

n = int(input())
es = [[] for _ in range(n + 1)]

for _ in range(n - 1): 
	a, b = list(map(int, input().split()))
	es[a].append(b)
	es[b].append(a)

depth = [-1 for _ in range(n + 1)]
dq = deque([1])
depth[1] = 0

while dq:
	v = dq.pop()
	for e in es[v]:
		if depth[e] != -1:
			continue
		depth[e] = depth[v] + 1
		dq.append(e)

ans = [-1 for _ in range(n + 1)]	
cnt_dict = Counter([x % 2 for x in depth[1:]])

nums = [[i for i in range(1, n + 1) if i % 3 == 1], [i for i in range(1, n + 1) if i % 3 == 2], [i for i in range(1, n + 1) if i % 3 == 0]]
if cnt_dict[0] <= n // 3:
	for i in range(1, n + 1):
		if depth[i] % 2 == 0:
			ans[i] = nums[2].pop()
		else:
			if nums[0]:
				ans[i] = nums[0].pop()
			elif nums[1]:
				ans[i] = nums[1].pop()
			else:
				ans[i] = nums[2].pop()
elif cnt_dict[1] <= n // 3:
	for i in range(1, n + 1):
		if depth[i] % 2 == 1:
			ans[i] = nums[2].pop()
		else:
			if nums[0]:
				ans[i] = nums[0].pop()
			elif nums[1]:
				ans[i] = nums[1].pop()
			else:
				ans[i] = nums[2].pop()
else:
	for i in range(1, n + 1):
		if depth[i] % 2 == 0:
			if nums[0]:
				ans[i] = nums[0].pop()
			else:
				ans[i] = nums[2].pop()
		else:
			if nums[1]:
				ans[i] = nums[1].pop()
			else:
				ans[i] = nums[2].pop()

print(*ans[1:])