{-# LANGUAGE BangPatterns #-} module Main where import Control.Monad import Control.Monad.ST import Control.Monad.State import Data.Bits import Data.Bool import Data.Char import Data.Coerce import Data.Word import Unsafe.Coerce import qualified Data.ByteString.Char8 as BSC8 import qualified Data.Vector.Fusion.Stream.Monadic as VFSM import qualified Data.Vector.Generic as VG import qualified Data.Vector.Generic.Mutable as VGM import qualified Data.Vector.Unboxed as VU main :: IO () main = do xs <- seqInput 4 putStrLn $ bool "No" "Yes" (solve xs) solve :: VU.Vector Int -> Bool solve xs = runST $ do let ys = introSort xs a = ys VU.! 0 b = ys VU.! 1 c = ys VU.! 2 d = ys VU.! 3 return ((a + 1 == b) && (b + 1 == c) && (c + 1 == d)) type CParser a = StateT BSC8.ByteString Maybe a runCParser :: CParser a -> BSC8.ByteString -> Maybe (a, BSC8.ByteString) runCParser = runStateT {-# INLINE runCParser #-} int :: CParser Int int = coerce $ BSC8.readInt . BSC8.dropWhile isSpace {-# INLINE int #-} seqInput :: Int -> IO (VU.Vector Int) seqInput n = VU.unfoldrN n (runCParser int) <$> BSC8.getLine {-# INLINE seqInput #-} introSort :: (Ord a, VG.Vector v a) => v a -> v a introSort = introSortBy compare introSortBy :: VG.Vector v a => (a -> a -> Ordering) -> v a -> v a introSortBy cmp = VG.modify $ inplaceIntroSortBy cmp inplaceIntroSortBy :: VGM.MVector mv a => (a -> a -> Ordering) -> mv s a -> ST s () inplaceIntroSortBy cmp vec = do let depthLimit = 2 * floorLog2 (VGM.length vec) threshold = 16 fix `flip` depthLimit `flip` vec $ \loop !depth mv -> when (VGM.length mv > threshold) $ if depth > 0 then do pivot <- getMedian3Pivot cmp mv cut <- pivotPartition cmp mv pivot loop (depth - 1) (VGM.unsafeDrop cut mv) loop (depth - 1) (VGM.unsafeTake cut mv) else inplaceHeapSortBy cmp mv inplaceInsertionSortBy cmp vec where floorLog2 :: Int -> Int floorLog2 x = fromIntegral $ y .>>. 52 - 1023 where y :: Word64 y = unsafeCoerce (fromIntegral x :: Double) pivotPartition :: (VGM.MVector mv a) => (a -> a -> Ordering) -> mv s a -> a -> ST s Int pivotPartition cmp vec pivot = fix `flip` 0 `flip` VGM.length vec $ \loop !l !r -> do !l' <- flip fix l $ \loopL !i -> do x <- VGM.unsafeRead vec i case cmp x pivot of LT -> loopL (i + 1) _ -> return i !r' <- flip fix (r - 1) $ \loopR !i -> do x <- VGM.unsafeRead vec i case cmp pivot x of LT -> loopR (i - 1) _ -> return i if l' < r' then do VGM.unsafeSwap vec l' r' loop (l' + 1) r' else return l' {-# INLINE pivotPartition #-} getMedian3Pivot :: VGM.MVector mv a => (a -> a -> Ordering) -> mv s a -> ST s a getMedian3Pivot cmp vec = median cmp <$> VGM.unsafeRead vec 0 <*> VGM.unsafeRead vec (VGM.length vec `quot` 2) <*> VGM.unsafeRead vec (VGM.length vec - 1) {-# INLINE getMedian3Pivot #-} median :: (a -> a -> Ordering) -> a -> a -> a -> a median cmp x y z = case cmp x y of LT -> case cmp y z of LT -> y _ -> case cmp x z of LT -> z _ -> x _ -> case cmp x z of LT -> x _ -> case cmp y z of LT -> z _ -> y {-# INLINE median #-} inplaceInsertionSortBy :: VGM.MVector mv a => (a -> a -> Ordering) -> mv s a -> ST s () inplaceInsertionSortBy cmp vec = for 1 (VGM.length vec) $ \i -> do x <- VGM.unsafeRead vec i hd <- VGM.unsafeRead vec 0 case cmp hd x of LT -> flip fix i $ \loop !j -> do y <- VGM.unsafeRead vec (j - 1) case cmp x y of LT -> do VGM.unsafeWrite vec j y loop (j - 1) _ -> VGM.unsafeWrite vec j x _ -> flip fix i $ \loop !j -> if j > 0 then do VGM.unsafeRead vec (j - 1) >>= VGM.unsafeWrite vec j loop (j - 1) else VGM.unsafeWrite vec 0 x {-# INLINE inplaceInsertionSortBy #-} siftDown :: VGM.MVector mv a => (a -> a -> Ordering) -> Int -> mv s a -> ST s () siftDown cmp offset vec = do let !len = VGM.length vec flip fix offset $ \loop !parent -> do let !l = 2 * parent + 1 !r = l + 1 x <- VGM.unsafeRead vec parent when (l < len) $ do childL <- VGM.unsafeRead vec l if r < len then do childR <- VGM.unsafeRead vec r case cmp childL childR of LT -> when (cmp x childR == LT) $ do VGM.unsafeSwap vec parent r loop r _ -> when (cmp x childL == LT) $ do VGM.unsafeSwap vec parent l loop l else when (cmp x childL == LT) $ do VGM.unsafeSwap vec parent l loop l {-# INLINE siftDown #-} heapify :: VGM.MVector mv a => (a -> a -> Ordering) -> mv s a -> ST s () heapify cmp vec = rev (VGM.length vec `quot` 2) $ \i -> siftDown cmp i vec {-# INLINE heapify #-} inplaceHeapSortBy :: VGM.MVector mv a => (a -> a -> Ordering) -> mv s a -> ST s () inplaceHeapSortBy cmp vec = do heapify cmp vec flip fix (VGM.length vec - 1) $ \loop !i -> when (i > 0) $ do VGM.unsafeSwap vec 0 i siftDown cmp 0 $ VGM.unsafeTake i vec loop (i - 1) {-# INLINE inplaceHeapSortBy #-} stream :: Monad m => Int -> Int -> VFSM.Stream m Int stream !l !r = VFSM.Stream step l where step x | x < r = return $ VFSM.Yield x (x + 1) | otherwise = return $ VFSM.Done {-# INLINE [0] step #-} {-# INLINE [1] stream #-} streamR :: Monad m => Int -> Int -> VFSM.Stream m Int streamR !l !r = VFSM.Stream step (r - 1) where step x | x >= l = return $ VFSM.Yield x (x - 1) | otherwise = return $ VFSM.Done {-# INLINE [0] step #-} {-# INLINE [1] streamR #-} for :: Monad m => Int -> Int -> (Int -> m ()) -> m () for l r = flip VFSM.mapM_ (stream l r) {-# INLINE for #-} rep :: Monad m => Int -> (Int -> m ()) -> m () rep n = for 0 n {-# INLINE rep #-} rev :: Monad m => Int -> (Int -> m ()) -> m () rev n = flip VFSM.mapM_ (streamR 0 n) infixl 8 .<<., .>>. (.<<.) :: Bits b => b -> Int -> b (.<<.) = unsafeShiftL {-# INLINE (.<<.) #-} (.>>.) :: Bits b => b -> Int -> b (.>>.) = unsafeShiftR {-# INLINE (.>>.) #-}