D. Priority Queue
combinatorics; dp; implementation; math; ternary search
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 \(998\,244\,353\).
In the first example, the following are all possible pairs of \(B\) and \(f(B)\): \(B=\) {}, \(f(B)=0\). \(B=\) {-}, \(f(B)=0\). \(B=\) {+ 1, -}, \(f(B)=0\). \(B=\) {-, + 1, -}, \(f(B)=0\). \(B=\) {+ 2, -}, \(f(B)=0\). \(B=\) {-, + 2, -}, \(f(B)=0\). \(B=\) {-}, \(f(B)=0\). \(B=\) {-, -}, \(f(B)=0\). \(B=\) {+ 1, + 2}, \(f(B)=3\). \(B=\) {+ 1, + 2, -}, \(f(B)=2\). \(B=\) {-, + 1, + 2}, \(f(B)=3\). \(B=\) {-, + 1, + 2, -}, \(f(B)=2\). \(B=\) {-, + 1}, \(f(B)=1\). \(B=\) {+ 1}, \(f(B)=1\). \(B=\) {-, + 2}, \(f(B)=2\). \(B=\) {+ 2}, \(f(B)=2\). The sum of these values is \(16\).