A Munchausen number is a natural number n the sum of whose digits (in base 10), each raised to the power of itself, equals n.

(Munchausen is also spelled: Münchhausen.)

For instance:    3435 = 33 + 44 + 33 + 55 



Task
Find all Munchausen numbers between   1   and   5000.



Also see

 The OEIS entry:  A046253
 The Wikipedia entry:  Perfect digit-to-digit invariant, redirected from Munchausen Number


import Control.Monad (join)
import Data.List (unfoldr)
 
isMunchausen :: Integer -> Bool
isMunchausen =
  (==)
    <*> (sum . map (join (^)) . unfoldr digit)
 
digit 0 = Nothing
digit n = Just (r, q) where (q, r) = n `divMod` 10
 
main :: IO ()
main = print $ filter isMunchausen [1 .. 5000]