Sums of Digit Factorials (Euler, 254)

-- ### Project Euler, problem 254 ### --
import Data.List (find)
import Data.Maybe (fromJust)

fact :: Integer -> Integer
fact n | n > 1            = n * fact (n-1)
       | n == 0 || n == 1 = 1
       | otherwise        = 0

intToLStr :: Integer -> [String]
intToLStr = map (\x -> [x]) . show

digsSum :: Integer -> Integer
digsSum = sum . map read . intToLStr

f :: Integer -> Integer
f = sum . map (fact . read) . intToLStr

sf :: Integer -> Integer
sf = digsSum . f

g :: Integer -> Integer
g i = fromJust $ find ((== i) . sf) [1..]

sg :: Integer -> Integer
sg = digsSum . g

solveit :: Integer -> Integer
solveit n = sum $ map sg [1..n]

main = do
  putStrLn . show $ solveit 20   -- control-case
  putStrLn . show $ solveit 150  -- problem