{"problem":{"name":"Rooted Tree","description":{"content":"Consider rooted trees with $N$ vertices, where the vertices are labeled $1$ through $N$, and vertex $1$ is the root.   Count how many such rooted trees satisfy the following condition, and output the ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"fps_24_o"},"statements":[{"statement_type":"Markdown","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.\n\n## Constraints\n\n*   $3 \\leq N \\leq 2.5 \\times 10^5$\n*   $N$ is an integer\n\n## Input\n\nThe input is given from standard input in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"fps_24_o","tags":[],"sample_group":[["3","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."],["123456","607180670"]],"created_at":"2026-03-03 11:01:14"}}