{"problem":{"name":"Connected Graph","description":{"content":"Count the number of simple **connected** undirected graphs with $N$ vertices labeled $1$ through $N$.   Output the result modulo $998244353$.","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"fps_24_m"},"statements":[{"statement_type":"Markdown","content":"Count the number of simple **connected** undirected graphs with $N$ vertices labeled $1$ through $N$.  \nOutput the result modulo $998244353$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2.5 \\times 10^5$\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_m","tags":[],"sample_group":[["3","4\n\nFor $N=3$, the simple connected undirected graphs are:\n\n*   $3$ graphs with $2$ edges,\n*   $1$ graph with $3$ edges,\n\nfor a total of $4$."],["123456","317059543"]],"created_at":"2026-03-03 11:01:14"}}