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QOJ

Limite de temps : 1 s Limite de mémoire : 262144 MB Points totaux : 100 Hackable ✓

#13128. 野格利口酒

Statistiques

无向图的围长(girth)定义为其最短简单环的长度。 如果一个图的每个顶点的度数都等于 $k$,则称该图为 $k$-正则图。 给定一个素数 $p$。请构造一个 $(p + 1)$-正则图,使其围长不小于 6,且顶点数尽可能少。

输入格式

输入仅一行,包含一个素数 $p$ ($2 \le p \le 47$)。

输出格式

第一行输出一个整数 $N$,表示图中的顶点数。 接下来的 $N$ 行,每行输出 $p + 1$ 个以空格分隔的整数。第 $i$ 行必须包含顶点 $i$ 的邻居列表。顶点编号从 1 开始。

所描述的图必须满足围长至少为 6,且不包含任何自环或重边。$N$ 的值必须在所有满足条件的图中尽可能小。如果存在多种可能的答案,输出其中任意一个即可。

样例

输入 1

2

输出 1

14
7 10 11
5 6 10
5 7 14
9 10 14
2 3 12
2 8 13
1 3 8
6 7 9
4 8 12
1 2 4
1 12 13
5 9 11
6 11 14
3 4 13

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