{"raw_statement":[{"iden":"problem statement","content":"Consider a directed graph $G$ with $N$ vertices numbered $1$ to $N$ that satisfies all of the following conditions.\n\n*   $G$ is a tournament. In other words, $G$ has no multi-edges or self-loops, and for any two vertices $u,v$ of $G$, exactly one of the edges $u \\rightarrow v$ and $v \\rightarrow u$ exists.\n    \n*   Among the edges of $G$, exactly $M$ are directed from a vertex with a smaller number to a vertex with a larger number.\n    \n\nFind the total number of strongly connected components over all such directed graphs $G$, modulo $998244353$."},{"iden":"constraints","content":"*   $1 \\le N \\le 30$\n*   $0 \\le M \\le \\frac{N(N-1)}{2}$"},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $M$"},{"iden":"sample input 1","content":"3 1"},{"iden":"sample output 1","content":"7\n\nBelow are the three directed graphs $G$ that satisfy the conditions. The numbers of their strongly connected components are $3,1,3$ from left to right, so the answer is $7$.\n![image](https://img.atcoder.jp/arc163/ee8acabc2a7d48164b3cc568e88f0840.png)"},{"iden":"sample input 2","content":"6 2"},{"iden":"sample output 2","content":"300"},{"iden":"sample input 3","content":"25 156"},{"iden":"sample output 3","content":"902739687"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}