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:
from sys import stdin, setrecursionlimit
from collections import deque

setrecursionlimit(10 ** 9)

N = int(stdin.readline())
ab = [list(map(int, stdin.readline().split())) for i in range(N - 1)]

# 1 index
graph = [[] for i in range(N + 1)]

for a, b in ab:
    graph[a].append(b)
    graph[b].append(a)

q = deque([])

mod0 = deque([])
mod1 = deque([])
mod2 = deque([])

for k in range(1, N + 1):
    if k % 3 == 0:
        mod0.append(k)
    elif k % 3 == 1:
        mod1.append(k)
    else:
        mod2.append(k)

dist = [-1] * (N + 1)


def bfs(start):
    q.append(start)
    dist[start] = 0

    while q:
        now = q.popleft()

        for node in graph[now]:
            if dist[node] != -1:
                continue
            else:
                dist[node] = dist[now] + 1
                q.append(node)


node_p = [0] * (N + 1)


def modfit(i):
    if even <= N / 3:
        if dist[i] % 2 == 0:
            node_p[i] = mod0.pop()

        else:
            if mod1:
                node_p[i] = mod1.pop()
            elif mod2:
                node_p[i] = mod2.pop()
            else:
                node_p[i] = mod0.pop()

    elif odd <= N / 3:
        if dist[i] % 2 != 0:
            node_p[i] = mod0.pop()

        else:
            if mod1:
                node_p[i] = mod1.pop()
            elif mod2:
                node_p[i] = mod2.pop()
            else:
                node_p[i] = mod0.pop()

    else:
        if dist[i] % 2 == 0:
            if mod1:
                node_p[i] = mod1.pop()
            elif mod0:
                node_p[i] = mod0.pop()
            else:
                print(-1)
                exit(0)
        else:
            if mod2:
                node_p[i] = mod2.pop()
            elif mod0:
                node_p[i] = mod0.pop()
            else:
                print(-1)
                exit(0)

    print(node_p[i], end=" ")


odd = 0
even = 0

bfs(N)

for i in range (1,N + 1):
    if dist[i] % 2 == 0:
        even += 1
    else:
        odd += 1

for k in range(1, N + 1):
    modfit(k)

print()