module Exercise_12 where

import Data.List (nub,permutations,sortOn)
import Data.Function

{-H12-}
isPrime :: Int -> Bool
isPrime n
  | n <= 1 = False
  | otherwise = primeAux (n-1)
  where
    primeAux 1 = True
    primeAux i = n `mod` i /= 0 && primeAux (i-1)

-- returns all primes up to the passed number
primes :: Int -> [Int]
primes n = [i | i<-[2..n], isPrime i]

{-WETT-}
f = map fst . nub
theMaster = [1..]
encrypt :: String -> String
encrypt s = f $ filter (isPrime.snd) str  ++ str
  where str = zip s theMaster
decrypt :: String -> String
decrypt s = f $ sortOn snd $ zip s $ nub $ primes (length s) ++ theMaster
{-TTEW-}