import Data.Ix
import Data.Maybe
import qualified Data.Set as S

main = do
  dat <- readFile "pixel.in"
  mapM_ (pp.solve) $ parse dat

parse dat = f $ lines dat where
  f (size:fs:rs) | size/="0" = let n = read size in (n, g n fs):f rs
  f _ = []
  g n fs = foldr (\w f -> fromJust (lookup w funcs) n . f) id $ words fs

  funcs =
    [ ("id"    ,\n -> id)
    , ("id-"   ,\n -> id)
    , ("rot"   ,\n (x,y) -> (y,n-1-x))
    , ("rot-"  ,\n (x,y) -> (n-1-y,x))
    , ("sym"   ,\n (x,y) -> (n-1-x,y))
    , ("sym-"  ,\n (x,y) -> (n-1-x,y))
    , ("bhsym" ,\n (x,y) -> if y<n`div`2 then (x,y) else (n-1-x,y))
    , ("bhsym-",\n (x,y) -> if y<n`div`2 then (x,y) else (n-1-x,y))
    , ("bvsym" ,\n (x,y) -> if y<n`div`2 then (x,y) else (x,3*n`div`2-1-y))
    , ("bvsym-",\n (x,y) -> if y<n`div`2 then (x,y) else (x,2*n`div`2-1-y))
    , ("div"   ,\n (x,y) -> (x,y`div`2 + n`div`2*(y`mod`2)))
    , ("div-"  ,\n (x,y) -> (x,(2*y`mod`n)+(2*y`div`n)))
    , ("mix"   ,\n (x,y) -> let (a,b) = (x`div`(n`div`2),y`mod`2) in (2*x-n*a+b,y+a-b))
    , ("mix-"  ,\n (x,y) -> (x`div`2+(y`mod`2)*n`div`2,y+x`mod`2-y`mod`2)) ]

solve (n,f) = inner S.empty (range ((0,0),(n-1,n-1))) where
  inner _ [] = 1
  inner s (p:ps)
    | p `S.member` s = inner s ps
    | otherwise = let (n,ns) = g s p in lcm n (inner ns ps)
    where
      g s p | p `S.member` s = (0,s)
            | otherwise = let (n,ns) = g (p `S.insert` s) (f p) in (1+n,ns)

pp n = print n