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.buffer.readline

N = int(input())

tree = [[] for _ in range(N)]
bip = [None for _ in range(N)]

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

stack = [0]
bip[0] = 0

while stack:
    node = stack.pop()
    for adj in tree[node]:
        if bip[adj] is not None:
            continue
        bip[adj] = not bip[node]
        stack.append(adj)

res = [None for _ in range(N)]

white = sum(bip)
black = N - white

p0 = []
p1 = []
p2 = []

for i in range(1, N + 1):
    if i % 3 == 0:
        p0.append(i)

for i in range(1, N + 1):
    if i % 3 == 1:
        p1.append(i)

for i in range(1, N + 1):
    if i % 3 == 2:
        p2.append(i)

if white <= N // 3:
    p = p0 + p1 + p2
    cnt = 0
    for i in range(N):
        if bip[i]:
            res[i] = p[cnt]
            cnt += 1
    for i in range(N):
        if not bip[i]:
            res[i] = p[cnt]
            cnt += 1
    print(*res)

elif black <= N // 3:
    p = p0 + p1 + p2
    cnt = 0
    for i in range(N):
        if not bip[i]:
            res[i] = p[cnt]
            cnt += 1
    for i in range(N):
        if bip[i]:
            res[i] = p[cnt]
            cnt += 1
    print(*res)

else:
    p = p1 + p0 + p2
    cnt = 0
    for i in range(N):
        if not bip[i]:
            res[i] = p[cnt]
            cnt += 1
    for i in range(N):
        if bip[i]:
            res[i] = p[cnt]
            cnt += 1
    print(*res)