Stack-Queue Sort (Challenge)

There are $B$ blocks (numbered $1$ through $B$) distributed in $N$ containers (numbered $1$ through $N$). For each valid $i$, the weight of the $i$-th block is $W_i$ kilograms. For each container $i$, you should decide if it will be used like a *stack* or a *queue*. At any time, a container may contain any sequence of blocks (possibly the empty sequence); let's denote the number of the $j$-th b