import Control.Arrow ((&&&))

fibstep :: (Integer, Integer) -> (Integer, Integer)
fibstep (a, b) = (b, a + b)

fibnums :: [Integer]
fibnums = map fst $ iterate fibstep (0, 1)

fibN2 :: Integer -> (Integer, Integer)
fibN2 m
  | m < 10 = iterate fibstep (0, 1) !! fromIntegral m
fibN2 m = fibN2_next (n, r) (fibN2 n)
  where
    (n, r) = quotRem m 3

fibN2_next (n, r) (f, g)
  | r == 0 = (a, b) -- 3n  ,3n+1
  | r == 1 = (b, c) -- 3n+1,3n+2
  | r == 2 = (c, d) -- 3n+2,3n+3   (*)
  where
    a =
      5 * f ^ 3 +
      if even n
        then 3 * f
        else (-3 * f) -- 3n
    b = g ^ 3 + 3 * g * f ^ 2 - f ^ 3 -- 3n+1
    c = g ^ 3 + 3 * g ^ 2 * f + f ^ 3 -- 3n+2
    d =
      5 * g ^ 3 +
      if even n
        then (-3 * g)
        else 3 * g -- 3(n+1)   (*)

main :: IO ()
main = print $ (length &&& take 20) . show . fst $ fibN2 (10 ^ 2)