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#9710. Loli, Yen-Jen, 和一个图论问题

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Yen-Jen 非常喜欢萝莉!!!

现在,他正在和一个可爱的猫耳萝莉一起解决一个问题。但他昨天喝得太多,脑子还没转过来,所以他请求你帮他解决以下问题!

有一个包含 $N$ 个顶点的完全图。请将该图分解为 $N - 1$ 条路径(trials),其中第 $i$ 条路径必须恰好包含 $i$ 条不同的边。所有的边都必须恰好被分解到一条路径中。

输入仅包含一行,为一个整数 $N$,表示完全图的顶点数。

  • $2 \leq N \leq 1000$

如果无法分解该图,请在单行内输出 -1

否则,输出 $N - 1$ 行,第 $i$ 行描述第 $i$ 条路径。在第 $i$ 行中,输出 $i + 1$ 个整数来表示第 $i$ 条路径。同一行中相邻的整数表示路径中的边!

请注意,每行末尾不要输出多余的空格!

样例

输入格式 1

3

输出格式 1

1 2
2 3 1

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