P17740 [ICPC 2019 Xuzhou R] Loli, Yen-Jen, and a graph problem

Description

Now, Yen-Jen is solving a problem with a cute catgirl. But he drinks too much yesterday and his mind is not open yet, so he asked you to solve the following problem for him! There's a $N$ vertice complete graph. Please decompose the graph into $N - 1$ trails, the $i^{th}$ trail must contain exactly $i$ distinct edges. All edges must be decomposed in exactly one trail.

Input Format

The input contains only one line with one integer $N$, the number of vertices in the complete graph. - $2 \leq N \leq 1000$

Output Format

If there's no way to decompose the graph, output $-1$ in a single line. Otherwise, output $N - 1$ lines, the $i^{th}$ line is the description of the $i^{th}$ trail. In the $i^{th}$ line, output $i + 1$ integers represents the $i^{th}$ trail. The neiboring integers in one line represents the edges.