Costly Swapping

$X$ and $Y$ are binary sequences of length $N$, i.e. $0 \le X_i, Y_i \le 1$. There are $4$ positive integer parameters $A$, $B$, $C$, and $D$. You can do the following set of operations any number of times: - Choose $2$ indices $i$ and $j$ such that $1 \le i < j \le N$. - Perform **exactly** one of the following actions: - Swap $X_i$ and $X_j$, paying a cost of $A$ if $X_i = 1$ (after the sw