Score : 600 points
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:
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.
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}
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.
5 1 2 1 3 3 4 3 5
1 2 5 4 3
The distance between two vertices is 3 for the two pairs (2, 4) and (2, 5).
Thus, this permutation satisfies the condition.