{"raw_statement":[{"iden":"problem statement","content":"Count the number of simple **connected** undirected graphs with $N$ vertices labeled $1$ through $N$.  \nOutput the result modulo $998244353$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 2.5 \\times 10^5$\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":"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 $4$."},{"iden":"sample input 2","content":"123456"},{"iden":"sample output 2","content":"317059543"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}