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:
from collections import deque, defaultdict
import sys
input = sys.stdin.readline
sys.setrecursionlimit(100000000)

n = int(input())
edges = defaultdict(lambda : defaultdict(lambda: False))
for i in range(n-1):
    a, b = map(int, input().split())
    edges[a][b] = True
    edges[b][a] = True

nums = [deque() for _ in range(3)]
for i in range(1, n+1):
    nums[i%3].append(i)

color = [-1 for _ in range(n)]
cnts = [0 for _ in range(2)]
def coloring(num, pre_color):
    if pre_color:
        col = 0
    else:
        col = 1
    color[num-1] = col
    cnts[col] += 1
    for k in edges[num].keys():
        if color[k-1] == -1:
            coloring(k, col)

coloring(1, 1)

ans = [0 for _ in range(n)]
def solve(v):
    for i in range(n):
        if color[i] == v:
            ans[i] = nums[0].pop()
        else:
            for j in [1, 2, 0]:
                if len(nums[j]) > 0:
                    ans[i] = nums[j].pop()
                    break

if cnts[0] <= n // 3:
    # print("A")
    solve(0)
elif cnts[1] <= n // 3:
    # print("B")
    solve(1)
else:
    # print("C")
    for i in range(n):
        if color[i]:
            if len(nums[1]) > 0:
                ans[i] = nums[1].pop()
            else:
                ans[i] = nums[0].pop()
        else:
            if len(nums[2]) > 0:
                ans[i] = nums[2].pop()
            else:
                ans[i] = nums[0].pop()

print(" ".join(list(map(str, ans))))