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
readline = sys.stdin.buffer.readline

def dfs(s):
    stack = [s]
    used = set(s)
    dist = [0]*N
    while stack:
        vn = stack.pop()
        for vf in Edge[vn]:
            if vf not in used:
                used.add(vf)
                dist[vf] = 1 + dist[vn]
                stack.append(vf)

N = int(readline())

zero = N//3
one = N//3 + int(N%3 >= 1)
two = N - zero - one



Edge = [[] for _ in range(N)]
for _ in range(N-1):
    a, b = map(int, readline().split())
    a -= 1
    b -= 1
    Edge[a].append(b)
    Edge[b].append(a)



root = 0
col = [0]*N

stack = [root]
used = set(stack)
while stack:
    vn = stack.pop()
    for vf in Edge[vn]:
        if vf not in used:
            used.add(vf)
            col[vf] = 1 - col[vn]
            stack.append(vf)

if 2*sum(col) < N:
    col = [1-c for c in col]
black = sum(col)
white = N - black

Ans = [None]*N
remain = set(range(1, N+1))
if N <= 3:
    Ans = list(range(1, N+1))

elif white <= zero:
    zb = [i for i in range(1, N+1) if i%3 == 0]
    rb = [i for i in range(1, N+1) if i%3 != 0]
    for i in range(N):
        if col[i] == 0:
            Ans[i] = zb.pop()
    rb += zb
    for i in range(N):
        if col[i] == 1:
            Ans[i] = rb.pop()

elif one <= black and two <= white:
    zb = [i for i in range(1, N+1) if i%3 == 0]
    ob = [i for i in range(1, N+1) if i%3 == 1]
    tb = [i for i in range(1, N+1) if i%3 == 2]
    for i in range(N):
        if col[i] == 1:
            if ob:
                Ans[i] = ob.pop()
            else:
                Ans[i] = zb.pop()
        else:
            if tb:
                Ans[i] = tb.pop()
            else:
                Ans[i] = zb.pop()
else:
    assert False,''
print(*Ans)