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

def solve():
    input = sys.stdin.readline
    N = int(input())
    Edge = [[] for _ in range(N)]
    Par = [0 for _ in range(N)]
    Son = [[] for _ in range(N)]
    for _ in range(N - 1):
        a, b = map(int, input().split())
        Edge[a-1].append(b-1)
        Edge[b-1].append(a-1)
    Dist = [0] * N
    DistType = [0, 0]
    q = deque()
    q.append((0, 0, 0)) #(now, pre, dist)
    modCount = [N // 3, N // 3, N // 3]
    if N % 3 == 1: modCount[1] += 1
    elif N % 3 == 2:
        modCount[1] += 1
        modCount[2] += 1
    modIndex = [0, 0, 0]
    search = deque()
    while q:
        nowNode, preNode, dist = q.popleft()
        Dist[nowNode] = dist
        Par[nowNode] = preNode
        Son[preNode].append(nowNode)
        search.append(nowNode)
        DistType[dist % 2] += 1
        for nextNode in Edge[nowNode]:
            if nextNode != preNode: q.append((nextNode, nowNode, dist + 1))
    Ans = [-1] * N
    if DistType[0] <= modCount[0]:
        for i, d in enumerate(Dist):
            if d % 2 == 0:
                Ans[i] = 3 * modIndex[0] + 3
                modIndex[0] += 1
            else:
                if modIndex[1] < modCount[1]:
                    Ans[i] = 3 * modIndex[1] + 1
                    modIndex[1] += 1
                elif modIndex[2] < modCount[2]:
                    Ans[i] = 3 * modIndex[2] + 2
                    modIndex[2] += 1
                else:
                    Ans[i] = 3 * modIndex[0] + 3
                    modIndex[0] += 1
    elif DistType[1] <= modCount[0]:
        for i, d in enumerate(Dist):
            if d % 2 == 1:
                Ans[i] = 3 * modIndex[0] + 3
                modIndex[0] += 1
            else:
                if modIndex[1] < modCount[1]:
                    Ans[i] = 3 * modIndex[1] + 1
                    modIndex[1] += 1
                elif modIndex[2] < modCount[2]:
                    Ans[i] = 3 * modIndex[2] + 2
                    modIndex[2] += 1
                else:
                    Ans[i] = 3 * modIndex[0] + 3
                    modIndex[0] += 1
    else:
        for i, d in enumerate(Dist):
            if d % 2 == 0:
                if modIndex[1] < modCount[1]:
                    Ans[i] = 3 * modIndex[1] + 1
                    modIndex[1] += 1
                else:
                    Ans[i] = 3 * modIndex[0] + 3
                    modIndex[0] += 1
            else:
                if modIndex[2] < modCount[2]:
                    Ans[i] = 3 * modIndex[2] + 2
                    modIndex[2] += 1
                else:
                    Ans[i] = 3 * modIndex[0] + 3
                    modIndex[0] += 1
    print(" ".join(map(str, Ans)))

    return 0

if __name__ == "__main__":
    solve()