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
from collections import deque
sys.setrecursionlimit(10**6)
input = sys.stdin.readline
N = int(input())
G = [[] for _ in range(N)]
for i in range(N-1) :
    a, b = map(int,input().split())
    G[a-1].append(b-1)
    G[b-1].append(a-1)

col = [-1]*N
col[0] = 0
stack = deque([0])
while stack :
    now = stack.pop()
    for i in G[now] :
        if col[i] == -1 :
            col[i] = (col[now] + 1)%2
            stack.append(i)

mod0 = [x for x in range(1, N+1) if x%3 == 0]
mod1 = [x for x in range(1, N+1) if x%3 == 1]
mod2 = [x for x in range(1, N+1) if x%3 == 2]

ans = [0 for _ in range(N)]
if sum(col) <= N//3 :
    mods = deque(mod0 + mod1 + mod2)
    for i in range(N) :
        if col[i] == 1 :
            ans[i] = mods.popleft()
        else :
            ans[i] = mods.pop()
elif sum(col) >= 2*N//3 :
    mods = deque(mod0 + mod1 + mod2)
    for i in range(N) :
        if col[i] == 0 :
            ans[i] = mods.popleft()
        else :
            ans[i] = mods.pop()
else :
    mods = deque(mod1 + mod0 + mod2)
    for i in range(N) :
        if col[i] == 0 :
            ans[i] = mods.popleft()
        else :
            ans[i] = mods.pop()

print(*ans)