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:
N = int(input())
data = [[] for i in range(N)]

for i in range(N-1):
    a,b = map(int,input().split())
    a -= 1
    b -= 1
    data[a].append(b)
    data[b].append(a)

stack = [0]
d = [-1] * N
d[0] = 0

while stack:
    x = stack.pop()
    for y in data[x]:
        if d[y] != -1:
            continue
        d[y] = d[x] + 1
        stack.append(y)

mod = [[],[]]
for i in range(N):
    mod[d[i]%2].append(i)

ans = [0]*N

p = 1
q = 2
r = 3
if len(mod[0]) > N//3 and len(mod[1]) > N//3:
    for k in mod[0]:
        if p <= N:
            ans[k] = p
            p += 3
        else:
            ans[k] = r
            r += 3
    for l in mod[1]:
        if q <= N:
            ans[l] = q
            q += 3
        else:
            ans[l] = r
            r += 3
    
elif len(mod[0]) > N//3:
    for k in mod[0]:
        if p <= N:
            ans[k] = p
            p += 3
        elif q <= N:
            ans[k] = q
            q += 3
        else:
            ans[k] = r
            r += 3
    for l in mod[1]:
        ans[l] = r
        r += 3

else:
    for k in mod[1]:
        if p <= N:
            ans[k] = p
            p += 3
        elif q <= N:
            ans[k] = q
            q += 3
        else:
            ans[k] = r
            r += 3
    for l in mod[0]:
        ans[l] = r
        r += 3

print(" ".join(map(str,ans)))