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())
peer = [[] for _ in range(n)]
for _ in range(n-1):
  a,b = map(int,input().split())
  a -= 1
  b -= 1
  peer[a].append(b)
  peer[b].append(a)
seen = [0 for _ in range(n)]
clr = [2 for _ in range(n)]
seen[0] = 1
clr[0] = 0
now = [0]
while now:
  last = now
  now = []
  for x in last:
    for y in peer[x]:
      if seen[y] == 0:
        seen[y] = 1
        now.append(y)
        clr[y] = 1 - clr[x]
#print(seen)
#print(clr)
a = n - sum(clr)
b = sum(clr)
z1 = 1
z2 = 2
z3 = 3
g1 = (n+2)//3
g2 = (n+1)//3
g3 = n//3
#print(g1,g2,g3)
ans = [0 for _ in range(n)]
if a > g3 and b > g3:
  for i in range(n):
    if clr[i] == 0:
      if g1:
        ans[i] = z1
        z1 += 3
        g1 -= 1
      else:
        ans[i] = z3
        z3 += 3
    else:
      if g2:
        ans[i] = z2
        z2 += 3
        g2 -= 1
      else:
        ans[i] = z3
        z3 += 3
elif a <= g3:
  g3 -= a
  for i in range(n):
    if clr[i] == 0:
      ans[i] = z3
      z3 += 3
    else:
      if g3:
        ans[i] = z3
        z3 += 3
        g3 -= 1
      elif g1:
        ans[i] = z1
        z1 += 3
        g1 -= 1
      else:
        ans[i] = z2
        z2 += 3
elif b <= g3:
  g3 -= b
  for i in range(n):
    if clr[i] == 1:
      ans[i] = z3
      z3 += 3
    else:
      if g3:
        ans[i] = z3
        z3 += 3
        g3 -= 1
      elif g1:
        ans[i] = z1
        z1 += 3
        g1 -= 1
      else:
        ans[i] = z2
        z2 += 3
else:
  err
print(' '.join(map(str,ans)))