AT_fps_24_m 連結グラフ

Count the number of simple **connected** undirected graphs with $ N $ vertices labeled $ 1 $ through $ N $ . Output the result modulo $ 998244353 $ .

The input is given from standard input in the following format: > $ N $

Print the answer.

### Sample Explanation 1 For $ N=3 $ , the simple connected undirected graphs are: - $ 3 $ graphs with $ 2 $ edges, - $ 1 $ graph with $ 3 $ edges, for a total of $ 4 $ . ### Constraints - $ 1 \leq N \leq 2.5 \times 10^5 $ - $ N $ is an integer