You are a game designer working on a new video game, Outstandingly Captivating Platforming Challenge. The game consists of $$$n$$$ levels indexed $$$1 \ldots n$$$, which the player must complete in that order. In addition to the normal progression, the levels are also connected through $$$n$$$ one-way warp portals. A different team in your company has already completed the design of each level. They have placed one warp portal entrance and one warp portal exit in every level. Your task is to connect each entry portal to an exit portal on a different level such that each exit portal is also connected to only one entry portal.

However, there is an additional restriction: the player must not be able to skip ahead in the game. That is, the player must not be able to enter a portal, exit at a portal on a later level, and keep playing on that later level. In order to make this possible, the level designers have placed some exit portals in isolated locations from which the rest of the level is not accessible. That is: if an entry portal on level $$$u$$$ leads to an exit portal on some level $$$v \gt u$$$, then the exit portal on level $$$v$$$ must be in an isolated location.

You have already written a program to examine all allowed ways to connect each entry portal to an exit portal, in order to measure the predicted audience engagement. That program has been running for a while now, your boss is getting angry, and you want to know how long this program will take. Thus, calculate the number of allowed ways to connect each entry portal to an exit portal. Print the answer modulo $$$998\,244\,353$$$.