these two sets si in SP were defined to partition the natural numbers so for any number any natural number like 6 you know which said it belongs to so you know that 6 belongs to s of B there's no and and so you know the last character that was encoded was B and then you can also recover the last state the previous state before he was encoded and the way you do that is just by looking at the position of six and S sub B a so you see that six is the fourth number and SOP so that's the previous day and you can just