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 defaultdict
import sys
input = sys.stdin.readline


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

colors = [-1] * n

colors[0] = 0

todo = []
for to in edges[0]:
    todo.append([to, 1])

while todo:
    node, color = todo.pop()

    if colors[node] != -1:
        continue

    colors[node] = color
    new_color = 1 - color
    for to in edges[node]:
        if colors[to] != -1:
            continue
        todo.append([to, new_color])

red_count = sum(colors)  # 1
blue_count = n - red_count  # 0

ans = [0] * n

num3s = list(range(3, n+1, 3))
nums = [num for num in range(1, n+1) if num % 3 != 0]

if red_count <= n // 3:
    for node in range(n):
        if colors[node] == 1:
            ans[node] = num3s.pop()

        else:
            if nums:
                num = nums.pop()
            else:
                num = num3s.pop()
            ans[node] = num


elif blue_count <= n // 3:
    for node in range(n):
        if colors[node] == 0:
            ans[node] = num3s.pop()

        else:
            if nums:
                num = nums.pop()
            else:
                num = num3s.pop()
            ans[node] = num

else:
    num1s = list(range(1, n+1, 3))
    num2s = list(range(2, n+1, 3))

    for node in range(n):
        if colors[node] == 1:
            if num1s:
                num = num1s.pop()
            else:
                num = num3s.pop()
            ans[node] = num

        else:
            if num2s:
                num = num2s.pop()
            else:
                num = num3s.pop()
            ans[node] = num

print(*ans)