计数题 - 题目

#15978. 计数题

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题目描述

对于 $1 \sim n$ 的错排 $p$，定义无向图 $G(p) = (V, E)$ 如下：$V = \{1, 2, \dots, n\}$，$E = \{(i, p_i) \mid 1 \le i \le n\}$。

定义无向图 $G$ 的权值 $f(G)$ 为 $G$ 中所有连通块大小的平方和。对于 $1 \sim n$ 的所有错排 $p$，求 $f(G(p))$ 之和对 $998244353$ 取模后的结果。

输入格式

一行一个正整数 $n$，表示错排长度。

输出格式

对于每组测试数据：一行一个非负整数表示答案对 $998244353$ 取模后的结果。

样例数据

样例输入

样例输出

样例解释

子任务

对于所有测试数据，满足 $2 \le n < 998244353$。

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