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())
e = [[] for _ in range(N + 1)]
for _ in range(N - 1):
  u, v = map(int, input().split())
  e[u].append(v)
  e[v].append(u)

a = [1]
b = []
s = [1]
vis = [0] * (N + 1)
table = [-1] * (N + 1)
table[1] = 1
vis[1] = 1
while len(s):
  x = s.pop()
  for y in e[x]:
    if vis[y]: continue
    vis[y] = 1
    table[y] = table[x] ^ 1
    if table[y]: a.append(y)
    else: b.append(y)
    s.append(y)
if len(a) > len(b): a, b = b, a
res = [0] * (N + 1)
if len(a) <= N // 3:
  ss = set([x for x in range(1, N + 1)])
  x = 3
  for y in a:
    res[y] = x
    ss.discard(x)
    x += 3
  ss = list(ss)
  for i in range(1, N + 1):
    if res[i]: continue
    res[i] = ss.pop()
  print(*res[1: ])
else:
  ss = set([x for x in range(1, N + 1)])
  x = 2
  for y in a:
    res[y] = x
    ss.discard(x)
    x += 3
    if x > N: break
  x = 3
  for y in a:
    if res[y]: continue
    res[y] = x
    ss.discard(x)
    x += 3
  ss = list(ss)
  for i in range(1, N + 1):
    if res[i]: continue
    res[i] = ss.pop()
  print(*res[1: ])