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())
edge=[[] for i in range(n+1)]
for i in range(n-1):
    a,b=map(int,input().split())
    edge[a].append(b)
    edge[b].append(a)
ans=[0 for i in range(n+1)]
od=[1]
ev=[]
q=[1]
c=[1 for i in range(n+1)]
c[1]=0
t=0
while q:
    tl=q[:]
    q=[]
    for i in tl:
        for j in edge[i]:
            if c[j]:
                q.append(j)
                c[j]=0
                if t:
                    od.append(j)
                else:
                    ev.append(j)
    t^=1
if len(od)>len(ev):
    od,ev=ev,od
if len(od)<=n//3:
    t=3
    for i in od:
        ans[i]=t
        t+=3
    x=0
    for i,j in enumerate(ans):
        if j==0:
            ans[i]=x
            x+=1
            if x%3==0 and x<t:
                x+=1
else:
    t=0
    for i in range(1,n+1,3):
        ans[ev[t]]=i
        t+=1
    t=0
    for i in range(2,n+1,3):
        ans[od[t]]=i
        t+=1
    t=0
    for i,j in enumerate(ans):
        if j==0:
            ans[i]=t
            t+=3
print(" ".join(map(str,ans[1:])))