拓扑序计数 - 問題

#12037. 拓扑序计数

統計

给定 $n$，定义 $f(E)$ 表示一个边集为 $E$ 的 $n$ 个点的有向图的拓扑序个数。

一张 $n$ 个点的图的一个合法拓扑序是一个 $1..n$ 的排列 $p[1...n]$，满足对于该图的所有有向边 $(u,v)$，有$p[v]>p[u]$

现在给定 $m$ 条有向边，假设这 $m$ 条边构成的集合为 $T$，求 $\sum_{E \subseteq T}f(E)$

由于答案可能很大，你只需要输出答案对 $998244353$ 取模后的值

输入格式

第一行两个整数 $n,m$

接下来 $m$ 行，每行两个整数 $u,v~(1\leq u,v\leq n)$，表示一条有向边 $(u,v)$

保证没有重边和自环

输出格式

输出答案对 $998244353$ 取模后的值

样例数据

样例 1 输入

3 2
1 2
2 3

样例 1 输出

子任务

$Task1~(7pts)$：$1\leq n,m\leq 5$

$Task2~(12pts)$：$1\leq n+m\leq 20$

$Task3~(16pts)$：$1\leq n\leq 9$

$Task4~(17pts)$：保证 $E$ 中的边都是 $(i , i+1)$ 的形式

$Task5~(48pts)$：无特殊限制

对于所有数据，有 $1\leq n\leq 20$，$0\leq m\leq n(n-1)$

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