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,*L=map(int,open(0).read().split())
g=[[]for _ in range(n)]
for a,b in zip(*[iter(L)]*2):
	g[a-1].append(b-1)
	g[b-1].append(a-1)
b=[-1]*n
b[0]=0
q=__import__("collections").deque([0])
while q:
	c=q.pop()
	for x in g[c]:
		if b[x]<0:b[x]=1-b[c];q.append(x)
lab=[-1]*n
Z=[i for i,x in enumerate(b) if x==0]
O=[i for i,x in enumerate(b) if x]
z=len(Z)
if z<=n//3 or n-z<=n//3:
	(L,H)=(Z,O) if z<=n//3 else (O,Z)
	a,b=1,3
	for i in L:lab[i]=b;b+=3
	for i in H:
		if b<=n:lab[i]=b;b+=3
		else:lab[i]=a;a+=1 if a%3==1 else 2
else:
	a,b,c=1,2,3
	for i in Z:
		if a<=n:lab[i]=a;a+=3
		else:lab[i]=c;c+=3
	for i in O:
		if b<=n:lab[i]=b;b+=3
		else:lab[i]=c;c+=3
print(*lab)