{"raw_statement":[{"iden":"problem statement","content":"Consider rooted trees with $N$ vertices, where the vertices are labeled $1$ through $N$, and vertex $1$ is the root.  \nCount how many such rooted trees satisfy the following condition, and output the result modulo $998244353$.\n\n*   For every integer $i$ such that $1 \\leq i \\leq N$, the number of children of vertex $i$ is either $0$ or a prime number."},{"iden":"constraints","content":"*   $3 \\leq N \\leq 2.5 \\times 10^5$\n*   $N$ is an integer"},{"iden":"input","content":"The input is given from standard input in the following format:\n\n$N$"},{"iden":"sample input 1","content":"3"},{"iden":"sample output 1","content":"1\n\nFor example, consider the rooted tree where both vertex $2$ and vertex $3$ have parent $1$.  \nThis satisfies the condition because vertex $1$ has $2$ children (a prime number), and vertices $2$ and $3$ both have $0$ children.  \nThis is the only rooted tree that satisfies the condition."},{"iden":"sample input 2","content":"123456"},{"iden":"sample output 2","content":"607180670"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}