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
sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline

n = int(input())

g = [[] for _ in range(n)]
for _ in range(n-1):
    a, b = map(int, input().split())
    g[a-1].append(b-1)
    g[b-1].append(a-1)

lst = [[], [], []]
for i in range(1, n+1):
    lst[i % 3].append(i)

p = [0]*n

depth = [-1]*n
depth[0] = 0

q = [0]

cnt = [1, 0]

while q:
    v = q.pop()
    for w in g[v]:
        if depth[w] != -1:
            continue
        depth[w] = depth[v] + 1
        cnt[depth[w] % 2] += 1
        q.append(w)


ans = [0]*n

if cnt[0] <= n//3:
    ans[0] = lst[0].pop()
    q = [0]
    while q:
        v = q.pop()
        for w in g[v]:
            if ans[w] != 0:
                continue
            if depth[w] % 2 == 0:
                ans[w] = lst[0].pop()
            else:
                if lst[1]:
                    ans[w] = lst[1].pop()
                elif lst[2]:
                    ans[w] = lst[2].pop()
                else:
                    ans[w] = lst[0].pop()
            q.append(w)
elif cnt[1] <= n//3:
    ans[0] = lst[1].pop()
    q = [0]
    while q:
        v = q.pop()
        for w in g[v]:
            if ans[w] != 0:
                continue
            if depth[w] % 2 != 0:
                ans[w] = lst[0].pop()
            else:
                if lst[1]:
                    ans[w] = lst[1].pop()
                elif lst[2]:
                    ans[w] = lst[2].pop()
                else:
                    ans[w] = lst[0].pop()
            q.append(w)
else:
    ans[0] = lst[2].pop()
    q = [0]
    while q:
        v = q.pop()
        for w in g[v]:
            if ans[w] != 0:
                continue
            if depth[w] % 2 != 0:
                if lst[1]:
                    ans[w] = lst[1].pop()
                else:
                    ans[w] = lst[0].pop()
            else:
                if lst[2]:
                    ans[w] = lst[2].pop()
                else:
                    ans[w] = lst[0].pop()
            q.append(w)

print(*ans)