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:
N=int(input())
AB=[list(map(int,input().split())) for i in range(N-1)]
c=[[] for i in range(N)]
v=[0]*N
x=[0]*N
for i,j in AB:
    c[i-1].append(j-1)
    c[j-1].append(i-1)
import sys
sys.setrecursionlimit(10**9)
def dfs(p):
    y=1 if x[p]==2 else 2
    for n in c[p]:
        if v[n]==0:
            v[n]=1
            x[n]=y
            dfs(n)
v[0]=x[0]=1
dfs(0)
def f(x,a,b):
    p,q,r=0,0,1
    for i in range(N):
        if x[i]==a and p*3+1<=N:
            x[i]=p*3+1
            p+=1
        elif x[i]==b and q*3+2<=N:
            x[i]=q*3+2
            q+=1
        else:
            x[i]=r*3
            r+=1
if x.count(1)<=N//3:
    f(x,2,2)
elif x.count(2)<=N//3:
    f(x,1,1)
else:
    f(x,1,2)
print(*x)