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 deque

N = int(input())
tree = [[] for i in range(N)]
for i in range(N-1):
  a, b = map(int, input().split())
  tree[a-1].append(b-1)
  tree[b-1].append(a-1)

d = deque([[0, -1]])
dist = [0] * N
while d:
  node, par = d.pop()
  children = tree[node]
  for child in children:
    if child == par:
      continue
    dist[child] = (dist[node] + 1) % 2
    d.appendleft([child, node])

count0 = dist.count(0)
count1 = N - count0
s = [set(), set(), set()]
for i in range(1, N+1):
  s[i%3].add(i)
if count0 > N//3:
  if count1 > N//3:
    for i in range(N):
      if dist[i]:
        if s[2]:
          dist[i] = s[2].pop()
        else:
          dist[i] = s[0].pop()
      else:
        if s[1]:
          dist[i] = s[1].pop()
        else:
          dist[i] = s[0].pop()
  else:
    for i in range(N):
      if dist[i]:
        dist[i] = s[0].pop()
      else:
        if s[2]:
          dist[i] = s[2].pop()
        elif s[1]:
          dist[i] = s[1].pop()
        else:
          dist[i] = s[0].pop()
else:
  for i in range(N):
    if dist[i]:
      if s[2]:
        dist[i] = s[2].pop()
      elif s[1]:
        dist[i] = s[1].pop()
      else:
        dist[i] = s[0].pop()
    else:
      dist[i] = s[0].pop()

print(*dist)