{-# LANGUAGE BangPatterns #-} {-# LANGUAGE OverloadedLists #-} import Control.Monad import Control.Monad.Cont import Control.Monad.ST import Control.Monad.State import Data.Bits import Data.Bool import Data.STRef.Strict import System.IO import qualified Data.ByteString.Builder as BSB import qualified Data.ByteString.Char8 as BSC8 import qualified Data.ByteString.Lazy.Char8 as BSLC8 import qualified GHC.Integer.GMP.Internals as GMP import qualified Data.Vector.Fusion.Stream.Monadic as VFSM import qualified Data.Vector.Generic as VG import qualified Data.Vector.Unboxed as VU main :: IO () main = do q <- readLn :: IO Int xs <- VU.unfoldrN q (runStateT rInt) <$> BSLC8.getContents putBuilder $ v2BLinesWith (\b -> BSB.byteString $ BSC8.pack $ show b ++ bool " 0" " 1" (millerRabin b)) xs millerRabin :: Int -> Bool millerRabin k | k <= 3 = k == 2 || k == 3 | k .&. 1 == 0 = False | otherwise = _millerRabin k where _millerRabin :: Int -> Bool _millerRabin n | n < 2047 = loop [2] | n < 1373653 = loop [2,3] | n < 9080191 = loop [31,73] | n < 25326001 = loop [2,3,5] | n < 4759123141 = loop [2,7,61] | n < 1122004669633 = loop [2,13,23,1662803] | n < 2152302898747 = loop [2,3,5,7,11] | n < 3474749660383 = loop [2,3,5,7,11,13] | n < 341550071728321 = loop [2,3,5,7,11,13,17] | otherwise = loop [2,325,9375,28178,450775,9780504,1795265022] where !m = n - 1 !s = ctz m !d = m .>>. s loop :: VU.Vector Int -> Bool loop vec = runST $ do ret <- newSTRef True withBreakST $ \break1 -> do VU.forM_ vec $ \a -> do let check1 = powModInt a d n /= 1 check2 = all (\r -> powModInt a ((1 .<<. r) * d) n /= m) ([0..(s - 1)] :: [Int]) when (check1 && check2) $ do lift $ writeSTRef ret False break1 () readSTRef ret powModInt :: Int -> Int -> Int -> Int powModInt a n mo = fI $ GMP.powModInteger (fi a) (fi n) (fi mo) {-# INLINE powModInt #-} recipModInt :: Int -> Int -> Int recipModInt a mo = fI $ GMP.recipModInteger (fi a) (fi mo) {-# INLINE recipModInt #-} fi :: Int -> Integer fi = fromIntegral {-# INLINE fi #-} fI :: Integer -> Int fI = fromInteger {-# INLINE fI #-} clz :: FiniteBits fb => fb -> Int clz = countLeadingZeros {-# INLINE clz #-} ctz :: FiniteBits fb => fb -> Int ctz = countTrailingZeros {-# INLINE ctz #-} infixl 8 .<<., .>>. (.<<.) :: Bits b => b -> Int -> b (.<<.) = unsafeShiftL {-# INLINE (.<<.) #-} (.>>.) :: Bits b => b -> Int -> b (.>>.) = unsafeShiftR {-# INLINE (.>>.) #-} rep :: Monad m => Int -> (Int -> m ()) -> m () rep n = flip VFSM.mapM_ (streamG 0 (n - 1) const 0 (+) 1) {-# INLINE rep #-} rep' :: Monad m => Int -> (Int -> m ()) -> m () rep' n = flip VFSM.mapM_ (streamG 0 n const 0 (+) 1) {-# INLINE rep' #-} rep1 :: Monad m => Int -> (Int -> m ()) -> m () rep1 n = flip VFSM.mapM_ (streamG 1 (n - 1) const 0 (+) 1) {-# INLINE rep1 #-} rep1' :: Monad m => Int -> (Int -> m ()) -> m () rep1' n = flip VFSM.mapM_ (streamG 1 n const 0 (+) 1) {-# INLINE rep1' #-} rev :: Monad m => Int -> (Int -> m ()) -> m () rev n = flip VFSM.mapM_ (streamRG (n - 1) 0 const 0 (-) 1) {-# INLINE rev #-} rev' :: Monad m => Int -> (Int -> m ()) -> m () rev' n = flip VFSM.mapM_ (streamRG n 0 const 0 (-) 1) {-# INLINE rev' #-} rev1 :: Monad m => Int -> (Int -> m ()) -> m () rev1 n = flip VFSM.mapM_ (streamRG (n - 1) 1 const 0 (-) 1) {-# INLINE rev1 #-} rev1' :: Monad m => Int -> (Int -> m ()) -> m () rev1' n = flip VFSM.mapM_ (streamRG n 1 const 0 (-) 1) {-# INLINE rev1' #-} range :: Monad m => Int -> Int -> (Int -> m ()) -> m () range l r = flip VFSM.mapM_ (streamG l r const 0 (+) 1) {-# INLINE range #-} rangeR :: Monad m => Int -> Int -> (Int -> m ()) -> m () rangeR r l = flip VFSM.mapM_ (streamRG r l const 0 (-) 1) {-# INLINE rangeR #-} forP :: Monad m => Int -> (Int -> m ()) -> m () forP p = flip VFSM.mapM_ (streamG 2 (p - 1) (^) 2 (+) 1) {-# INLINE forP #-} forG :: Monad m => Int -> Int -> (Int -> Int -> Int) -> Int -> (Int -> Int -> Int) -> Int -> (Int -> m ()) -> m () forG l r f p g d = flip VFSM.mapM_ (streamG l r f p g d) {-# INLINE forG #-} forRG :: Monad m => Int -> Int -> (Int -> Int -> Int) -> Int -> (Int -> Int -> Int) -> Int -> (Int -> m ()) -> m () forRG r l f p g d = flip VFSM.mapM_ (streamRG r l f p g d) {-# INLINE forRG #-} streamG :: Monad m => Int -> Int -> (Int -> Int -> Int) -> Int -> (Int -> Int -> Int) -> Int -> VFSM.Stream m Int streamG !l !r !f !p !g !d = VFSM.Stream step l where step x | f x p <= r = return $ VFSM.Yield x (g x d) | otherwise = return VFSM.Done {-# INLINE [0] step #-} {-# INLINE [1] streamG #-} streamRG :: Monad m => Int -> Int -> (Int -> Int -> Int) -> Int -> (Int -> Int -> Int) -> Int -> VFSM.Stream m Int streamRG !r !l !f !p !g !d = VFSM.Stream step r where step x | f x p >= l = return $ VFSM.Yield x (g x d) | otherwise = return VFSM.Done {-# INLINE [0] step #-} {-# INLINE [1] streamRG #-} withBreakIO :: ((r -> ContT r IO b) -> ContT r IO r) -> IO r withBreakIO = flip runContT pure . callCC {-# INLINE withBreakIO #-} withBreakST :: ((r -> ContT r (ST s) b) -> ContT r (ST s) r) -> (ST s) r withBreakST = flip runContT pure . callCC {-# INLINE withBreakST #-} v2BLinesWith :: VG.Vector v t => (t -> BSB.Builder) -> v t -> BSB.Builder v2BLinesWith showFct = VG.foldr (\ a -> (showFct a <>) . (BSB.char7 '\n' <>)) mempty {-# INLINE v2BLinesWith #-} putBuilder :: BSB.Builder -> IO () putBuilder = BSB.hPutBuilder stdout {-# INLINE putBuilder #-} rInt :: StateT BSLC8.ByteString Maybe Int rInt = StateT $ BSLC8.readInt . BSLC8.dropWhile (<'!') {-# INLINE rInt #-}