Priority Queue

3000ms

524288K

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 $$$998\,244\,353$$$.

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 $$$998\,244\,353$$$.

Sample Input:

4
-
+ 1
+ 2
-

Sample Output:

Sample Input:

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

Sample Output:

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 $$$16$$$.

Informação

Provedor Codeforces

Código CF1542D