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:
\begin{shortitems}
    \item ``\texttt{+ v}'' --- performs $A := A + v$;
    \item ``\texttt{= v}'' --- performs $A := v$.
\end{shortitems}

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.