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


colors = [-1] * N
stack = [(0, 0)]
while stack:
    n, color = stack.pop()
    colors[n] = color
    for to in T[n]:
        if colors[to] != -1:
            continue
        stack.append((to, color ^ 1))


# あまり１、あまり２、あまり０になるように並び替え
X = [[] for _ in range(3)]
for n in range(1, N + 1):
    X[n % 3].append(n)
X.append(X[0])
del X[0]


ans = []
x12, x3 = X[0] + X[1], X[2]
if colors.count(0) <= N // 3:
    for color in colors:
        if color == 0:
            ans.append(x3.pop())
        elif x12:
            ans.append(x12.pop())
        else:
            ans.append(x3.pop())

elif colors.count(1) <= N // 3:
    for color in colors:
        if color == 1:
            ans.append(x3.pop())
        elif x12:
            ans.append(x12.pop())
        else:
            ans.append(x3.pop())

else:
    for color in colors:
        if X[color]:
            ans.append(X[color].pop())
        else:
            ans.append(X[2].pop())

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