Quark the corgi has a bin full of balls, each of which has an integer written on it. The integers form a multiset $$$S=\{b_1,b_2,\dots,b_n\}$$$, and he wants to use it to generate a random sequence $$$A=a_1,a_2,\dots,a_n$$$, that he will later use to decide in what order to fetch the balls.

Initially, the sequence $$$A$$$ is empty. Quark performs the following operation exactly $$$n$$$ rounds:

For the $$$i$$$-th round, let $$$S_i$$$ be the multiset of the remaining numbers after previous rounds ($$$S_i=S$$$ if $$$i=1$$$). Let $$$sum_i$$$ be the sum of all elements in $$$S_i$$$. Quark will randomly select an element from $$$S_i$$$ with probability proportional to its value. Specifically, the probability of selecting $$$b_j\in S_i$$$ is $$$\frac{b_j}{sum_i}$$$. Then Quark will append the selected number to the end of the sequence $$$A$$$ and remove it from $$$S_i$$$.

After all $$$n$$$ rounds, Quark obtains a random sequence $$$A$$$. He is interested in the expected number of inversions in $$$A$$$, i.e., the expected number of index pairs $$$(i, j)$$$ such that $$$i \lt j$$$ and $$$a_i \gt a_j$$$.

Since corgis are known to dislike fractions, you only need to output the answer modulo $$$998244353$$$.