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import Control.Monad.Trans.State
import Data.Foldable (foldrM)
import Data.HashMap.Lazy as HM hiding (filter, mapMaybe, map, null)
import Data.List (nub)
import Data.Maybe (mapMaybe)
import Debug.Trace
type S = HashMap String [String]
-- Return Nothing if no match; unmatched remainder (can be []) if
-- match.
match :: String -> String -> Maybe String
match xs [] = Just xs
match (x:xs) (y:ys) | x == y = match xs ys
| otherwise = Nothing
match [] _ = Nothing
matchAny :: [String] -> String -> State S [String]
matchAny yss xs = do
s <- get
case HM.lookup xs s of
Nothing -> let r = mapMaybe (match xs) yss
in put (HM.insert xs r s) >> return r
Just x -> return x
check :: [String] -> String -> State S Bool
check yss xs = do
zss <- nub <$> matchAny yss xs
if [] `elem` zss
then return True
else anyM (check yss) zss
anyM :: Monad m => (a -> m Bool) -> [a] -> m Bool
anyM p = foldrM f False
where
f a b = (b ||) <$> p a
parseTowels :: String -> [String]
parseTowels = map init . words
parse :: String -> ([String],[String])
parse s = let yss = filter (not . null) . drop 2 $ lines s
xss = parseTowels . head $ lines s
in (xss, yss)
main :: IO ()
main = do
input <- getContents
let (xss, yss) = parse input
print . length . filter id $ evalState (mapM (check xss) yss) HM.empty
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