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#100. 四面体

Estadísticas

给定一个正四面体。它的每条棱都被 $n-1$ 个分点分成了 $n$ 条等长的线段。设 $M$ 为所有分点的集合。问以 $M$ 中的点为顶点的非退化四面体有多少个?

输入的第一行包含一个整数 $n$ ($2 \le n \le 4000$)。

在输出的第一行打印问题的答案。

样例

输入格式 1

2

输出格式 1

12

输入格式 2

37

输出格式 2

65561472

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