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 collections
import sys
sys.setrecursionlimit(2*10**5)
I = [int(_) for _ in open(0).read().split()]
N = I[0]
AB = I[1:]
G = collections.defaultdict(set)
for a, b in zip(AB[::2], AB[1::2]):
    G[a].add(b)
    G[b].add(a)
color = [None] * (N + 1)


def dfs(G, v, cur):
    color[v] = cur
    for w in G[v]:
        if color[w] is None:
            dfs(G, w, 1 - cur)


dfs(G, 1, 0)
c=collections.Counter(color[1:])
cand1 = set(range(1, N + 1, 3))
cand2 = set(range(2, N + 1, 3))
cand3 = set(range(3, N + 1, 3))

i0, i1 = 0, 1
if c[0] > c[1]:
    i0, i1 = 1, 0

ans = [None] * (N + 1)
if c[i0] <= len(cand3):
    for i in range(1, N + 1):
        if color[i]==i0:
            ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand2:
                ans[i] = cand2.pop()
            elif cand3:
                ans[i] = cand3.pop()
else:
    for i in range(1, N + 1):
        if color[i] == i0:
            if cand2:
                ans[i] = cand2.pop()
            elif cand3:
                ans[i] = cand3.pop()
        else:
            if cand1:
                ans[i] = cand1.pop()
            elif cand3:
                ans[i] = cand3.pop()
print(*ans[1:])