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:
import sys
sys.setrecursionlimit(10**6)

n = int(input())
ed = [tuple(map(int, input().split())) for _ in range(n-1)]
g = [list() for _ in range(n)]
for a,b in ed:
  g[a-1].append(b-1)
  g[b-1].append(a-1)
bi = [0]*n

def dfs(v, p):
  for x in g[v]:
    if x == p: continue
    bi[x] = 1 - bi[v]
    dfs(x, v)
  return


dfs(0,-1)
one = sum(bi)
two = n - one
if one < two:
  one, two = two, one
  bi = [1-x for x in bi]
# print(bi)
on = 1
tw = 2
th = 3
ans = [0]*n
if two <= n//3:
  for i in range(n):
    if bi[i]:
      if on > n and tw > n:
        ans[i] = th
        th += 3
      elif on > n:
        ans[i] = tw
        tw += 3
      else:
        ans[i] = on
        on += 3
    else:
      ans[i] = th
      th += 3
  print(*ans)
  exit(0)

for i in range(n):
  if bi[i]:
    if on > n:
      ans[i] = th
      th += 3
    else:
      ans[i] = on
      on += 3
  else:
    if tw > n:
      ans[i] = th
      th += 3
    else:
      ans[i] = tw
      tw += 3
print(*ans)