ThREE

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

inputFormat

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}

outputFormat

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

样例

5
1 2
1 3
3 4
3 5

1 2 5 4 3