32464번 - Graceful Triangles 스페셜 저지다국어

문제

Consider the following graph in the shape of $n$ equilateral triangles stitched together horizontally:

This graph has $n+2$ vertices and 2ドルn+1$ edges. The vertices are labeled in the order of increasing horizontal position, as in the image above.

In other words, the graph has $n+2$ vertices labeled from 1ドル$ through $n+2,ドル and 2ドルn+1$ edges connecting all pairs of vertices whose labels differ by at most 2ドル$.

A positive integer value is assigned to each vertex. Vertex $i$ has the value of $v_i$. The value of an edge that connects vertices $i$ and $j$ is $|v_i-v_j|$. Find a way to assign values to all vertices so that for every positive integer $k$ up to 2ドルn+1$ inclusive, exactly one edge has the value of $k$. The value of any vertex cannot exceed 10ドル^{18}$.

입력

The first line contains $n,ドル a positive integer.

출력

If a solution exists for the given $n,ドル print the values assigned to the vertices 1,2,ドル\ldots ,n+2$ in one line, separated by spaces. The values must be positive integers not exceeding 10ドル^{18}$. Otherwise, print $-1$.

제한

• 1ドル\le n\le 200,円 000$

노트