A14461 | Priority Queue

You are given a sequence $A$ , where its elements are either in the form + x or -, where $x$ is an integer.

For such a sequence $S$ where its elements are either in the form + x or -, define $f(S)$ as follows:

- iterate through $S$ 's elements from the first one to the last one, and maintain a multiset $T$ as you iterate through it.
- for each element, if it's in the form + x, add $x$ to $T$ ; otherwise, erase the smallest element from $T$ (if $T$ is empty, do nothing).
- after iterating through all $S$ 's elements, compute the sum of all elements in $T$ . $f(S)$ is defined as the sum.

The sequence $b$ is a subsequence of the sequence $a$ if $b$ can be derived from $a$ by removing zero or more elements without changing the order of the remaining elements. For all $A$ 's subsequences $B$ , compute the sum of $f(B)$ , modulo $998\,244\,353$ .

The first line contains an integer $n$ ( $1\leq n\leq 500$ ) — the length of $A$ .

Each of the next $n$ lines begins with an operator + or -. If the operator is +, then it's followed by an integer $x$ ( $1\le x<998\,244\,353$ ). The $i$ -th line of those $n$ lines describes the $i$ -th element in $A$ .

Print one integer, which is the answer to the problem, modulo $998\,244\,353$ .