Prime Prefixes

For any array $B$ of length $M$, define: - The prefix sum $S_i = \sum_{j=1}^{i} B_j$ for $1 \le i \le M$. - The value $f(B)$ as the number of indices $i$ such that $S_i$ is a **prime** number. --- You are given an array $A$ of length $N$, consisting only of the numbers $1$ and $2$. Let $M$ denote the maximum value of $f(B)$ among all arrays $B$ that can be obtained by **reordering** the element