Priority Queue
Description
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 $998\,244\,353$.
Input
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 $A$.
Output
Print one integer, which is the answer to the problem, modulo $998\,244\,353$.
Samples
4
-
+ 1
+ 2
-
16
15
+ 2432543
-
+ 4567886
+ 65638788
-
+ 578943
-
-
+ 62356680
-
+ 711111
-
+ 998244352
-
-
750759115
Note
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 $16$.