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 Counter
def main():
    N=int(input())
    AB=[list(map(int, input().split())) for _ in range(N-1)]
    G=[[]for _ in range(N)]
    cnt=[0]*N
    for a,b in AB:
        G[a-1].append(b-1)
        G[b-1].append(a-1)
        cnt[a-1]+=1
        cnt[b-1]+=1
    CI=sorted(((c,i) for i,c in enumerate(cnt)), reverse=True)
    ans=[0]*N
    C=[0]*N
    stack=[(0,-1,0)]
    while stack:
        u,p,d=stack.pop()
        for v in G[u]:
            if v!=p:
                stack.append((v,u,d^1))
                C[v]=d^1
    X=sum(C)
    if X<=N//3:
        D=[[i for i in range(1,N+1,3)]+[i for i in range(2,N+1,3)],[i for i in range(3,N+1,3)]]
        for i in range(N):
            if D[C[i]]:
                ans[i]=D[C[i]].pop()
            else:
                ans[i]=D[C[i]^1].pop()
    elif N-X<=N//3:
        D=[[i for i in range(3,N+1,3)],[i for i in range(1,N+1,3)]+[i for i in range(2,N+1,3)]]
        for i in range(N):
            if D[C[i]]:
                ans[i]=D[C[i]].pop()
            else:
                ans[i]=D[C[i]^1].pop()
    else:
        D=[[i for i in range(1,N+1,3)],[i for i in range(2,N+1,3)],[i for i in range(3,N+1,3)]]
        for i in range(N):
            if D[C[i]]:
                ans[i]=D[C[i]].pop()
            else:
                ans[i]=D[2].pop()
    print(*ans)

if __name__ == "__main__":
    main()