Jorge, as a dedicated ICPC participant, was upsolving the problems from the 2026 ICPC Gran Premio de Mexico 1ra Fecha contest. The last problem he upsolved was $$$F(x,l,r)$$$, a problem that asks contestants to find the sum of a function over all subarrays of a given array. Immediately after he finished upsolving, he started thinking about more problems that ask for the sum of a function over all subarrays, and he came up with the following problem:

For a given array $$$A=[a_1,a_2,\dots,a_n]$$$, Jorge defines $$$F(l,r)$$$ as:

$$$$$$ F(l,r)=\prod_{i=l}^r a_i $$$$$$

Jorge defines the value of the array $$$A$$$ as the sum of $$$F(l,r)$$$ over all its subarrays:

$$$$$$ \sum_{l=1}^n \sum_{r=l}^n F(l,r) $$$$$$

Jorge immediately found the answer to this problem, so he thought that it was too easy. Then he thought, "What if we now find the sum of the values of all permutations of length $$$n$$$?" This problem is not as trivial as Jorge thought, so he asks you to solve it.

You are given an integer $$$n$$$. Help Jorge find the sum of the values of all permutations of the integers $$$1,2,\dots,n$$$. Since the answer might be huge, find it modulo $$$998244353$$$.