Div1 850's explanation is ready.
This was a great problem. Unfortunately it is also the kind of problem that has a trick that you either see or you don't. I would love to know what in the minds of target / red coders allows them to think of such creative ideas. But I don't.
My current plan is to finish the rest of the editorial tonight. Unfortunately my deteriorating health (I am not kidding) might get in the way and require me to add a whole day delay. But I will still try.