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 _ in range(n)]
for _ in range(n-1):
  a, b = map(int, input().split())
  edge[a-1].append(b-1)
  edge[b-1].append(a-1)
 
group = [False] * n
parent = list(range(n))
stack = [0]
while stack:
  v = stack.pop()
  while edge[v]:
    u = edge[v].pop()
    if parent[v] != u:
      group[u] = not group[v]
      parent[u] = v
      stack.append(u)
 
three = 3
p = [0] * n
if group.count(False) <= n // 3:
  other = 1
  for i in range(n):
    if group[i] and other <= n:
      p[i] = other
      other += other % 3
    else:
      p[i] = three
      three += 3
elif group.count(True) <= n // 3:
  other = 1
  for i in range(n):
    if not group[i] and other <= n:
      p[i] = other
      other += other % 3
    else:
      p[i] = three
      three += 3
else:
  one, two = 1, 2
  for i in range(n):
    if group[i] and one <= n:
      p[i] = one
      one += 3
    elif not group[i] and two <= n:
      p[i] = two
      two += 3
    else:
      p[i] = three
      three += 3
print(' '.join(map(str, p)))