so, if any two coordinates are 2, then flying into any position with two 1 coordinates is death, in the 2d sense
however, if you fly from 3,3,3 to 2,2,2 then your next move must be a two-one-coordinate position
so, my question is whether 3,3,3 to 2,2,2 is a death move
all three possible two-axis diversions are functionally equivalent, so considering just one...
3,3,3 to 2,2,2 is a north/west/down move. if you turn to just down then you end up at 2,2,1 where you can turn to east/down for 2,3,0 and then just east for 2,4,0
so, 3,3,3 to 2,2,2 is escapable
however, not ALL paths after 3,3,3 to 2,2,2 with two future moves have a third future move
if you're at 2,2,2 moving NWD then your algorithm will say that NWD is a valid move, because 1,1,1 and 0,0,0 can be reached from there
also, that's a LOT of computation
just having a lookup table of suicide moves would save a lot of cpu time on the judge