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
import math

N = int(input())
side = [[]for i in range(N)]
for i in range(N-1):
    a,b = map(int,input().split())
    side[a-1].append(b-1)
    side[b-1].append(a-1)
ans = [0]*N
ans[0] = 1
queue = deque([0])
count = [0,1,0]
while queue:
    q = queue.popleft()
    for i in side[q]:
        if ans[i] == 0:
            ans[i] = ans[q]%2 + 1
            count[ans[i]] += 1
            queue.append(i)
if max(count) <=N - (N+1)//3:
    X = [3,2,2]
    X[count.index(max(count))] = 1
    for i in range(N):
        if X[ans[i]] <= N:
            X[ans[i]] += 3
            ans[i] = X[ans[i]]-3
        else:
            ans[i] = X[0]
            X[0] += 3
else:
    Y = 3 - count.index(max(count))
    Z = 3 - Y
    X = 3
    for i in range(N):
        if ans[i] == Y:
            ans[i] = X
            X += 3
    W = 1
    for i in range(N):
        if ans[i] == Z:
            ans[i] = W
            W += 1
            if W%3 == 0 and W < X:
                W += 1
print(*ans)