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 ith 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≤N≤1000
Output
If there's no way to decompose the graph, output -1 in a single line.
Otherwise, output N−1 lines, the ith line is the description of the ith trial. In the ith line, output i+1 integers represents the ith 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