Subset Min Max

For an array $A$ of length $N$ and a binary string $S$ of length $N$, define $f(S)$ as follows: * Create an array $B$ containing exactly those values $A_i$ such that $S_i = 1$. * If $B$ is empty, $f(S) = 0$. * Otherwise, $f(S) = \min(B) \cdot \max(B)$ --- You are given an array $A$ of length $N$, a binary string $S$ of length $N$, and a positive integer $X$. In one operation, you may toggle any