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
input = sys.stdin.readline
n = int(input())
ab = [list(map(int,input().split())) for i in range(n-1)]
graph = [[] for i in range(n+1)]
for a,b in ab:
  graph[a].append(b)
  graph[b].append(a)
stack = [(1,1)]
color = [0]*(n+1)
while stack:
  x,c = stack.pop()
  color[x] = c
  for y in graph[x]:
    if color[y] == 0:
      stack.append((y,3-c))
ans = [0]*(n+1)
cnt1 = 1
cnt2 = 2
cnt3 = 3
if color.count(1) >= (n*2+2)//3:
  for i in range(1,n+1):
    if color[i] == 1:
      if cnt1 <= n:
        ans[i] = cnt1
        if cnt1%3 == 1:
          cnt1 += 1
        else:
          cnt1 += 2
      else:
        ans[i] = cnt3
        cnt3 += 3
    else:
      ans[i] = cnt3
      cnt3 += 3
elif color.count(2) >= (n*2+2)//3:
  for i in range(1,n+1):
    if color[i] == 2:
      if cnt1 <= n:
        ans[i] = cnt1
        if cnt1%3 == 1:
          cnt1 += 1
        else:
          cnt1 += 2
      else:
        ans[i] = cnt3
        cnt3 += 3
    else:
      ans[i] = cnt3
      cnt3 += 3
else:
  c1 = []
  c2 = []
  for i in range(1,n+1):
    if color[i] == 1:
      c1.append(i)
    else:
      c2.append(i)
  for x in c1:
    if cnt1 <= n:
      ans[x] = cnt1
      cnt1 += 3
    else:
      ans[x] = cnt3
      cnt3 += 3
  for x in c2:
    if cnt2 <= n:
      ans[x] = cnt2
      cnt2 += 3
    else:
      ans[x] = cnt3
      cnt3 += 3
ans = ans[1:]
print(*ans)