P14600 [NWRRC 2025] Asynchronous Processor

You are given a program consisting of $n$ instructions executed by a processor with a single integer register $A$, initially equal to $0$. Each instruction is one of two types: - $\texttt{+ v}$ --- performs $A := A + v$; - $\texttt{= v}$ --- performs $A := v$. The instructions in the program are numbered from $1$ to $n$. Each instruction $i$ initially has timestamp $i$. Some instructions are marked as $\textit{asynchronous}$. If instruction $i$ is asynchronous, its timestamp can be changed to any $\textbf{real}$ number greater than $i$. After all timestamp adjustments, all timestamps must be distinct. The processor then executes the instructions in order of increasing timestamp. Determine the number of distinct final values of $A$ that can be obtained after all instructions have been executed, considering all possible choices of asynchronous instruction timestamps.

The first line contains an integer $n$, denoting the number of instructions in the program ($1 \le n \le 2000$). The $i$-th of the following $n$ lines describes instruction $i$ and contains three tokens. The first token is either $\texttt{+}$ or $\texttt{=}$, denoting the type of the instruction. The second token is an integer $v$, denoting the argument of the instruction ($1 \le v \le 500$). Finally, the third token is either $\texttt{async}$ if the instruction is marked as asynchronous, or $\texttt{sync}$ otherwise.

Print the number of distinct final values $A$ can take after executing the program.

In the first test, the program execution starts with instruction $1$ setting $A$ to $1$. Then, instructions $2$ and $3$ are executed in one of the two orders: - if $\texttt{= 2}$ is executed before $\texttt{+ 3}$, $A$ will be equal to $5$; - if $\texttt{+ 3}$ is executed before $\texttt{= 2}$, $A$ will be equal to $2$. Thus, there are two possible values of $A$ at the end: $5$ and $2$.