Yen-Jen loves loli very much!!!

Now, he is solving a problem with a cute, cat-eared loli. 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 $N - 1$ trials, the $i^{th}$ trial must contain exactly $i$ distinct edges. All edges must be decomposed in exactly one trial.

Input

The input contains only one line with one integer $N$, the number of vertices in the complete graph.

• $2 \leq N \leq 1000$

Output

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 $i^{th}$ trial. In the $i^{th}$ line, output $i + 1$ integers represents the $i^{th}$ trial. The neiboring integers in one line represents the edges!

Please, do not output trailing spaces in every line!

Sample Input

3

Sample Output

1 2
2 3 1