CF1542D.Priority Queue

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题目描述

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 $998\,244\,353$ .

输入格式

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 $A$ .

输出格式

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

输入输出样例

输入#1
```
4
-
+ 1
+ 2
-
```
输出#1
```
16
```

输入#2

15
+ 2432543
-
+ 4567886
+ 65638788
-
+ 578943
-
-
+ 62356680
-
+ 711111
-
+ 998244352
-
-

输出#2

750759115

说明/提示

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 $16$ .

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