{-# LANGUAGE BangPatterns #-} import qualified Control.Arrow as Arrow import Data.Bits (Bits (unsafeShiftL, unsafeShiftR), FiniteBits (countTrailingZeros)) import Data.Bool (bool) import qualified Data.ByteString.Char8 as BSC8 import qualified Data.List as List import qualified Data.Vector.Unboxed as VU import qualified Data.Vector.Fusion.Stream.Monadic as MS import qualified GHC.Integer.GMP.Internals as GMP isPrime :: Int -> Bool isPrime k | k <= 3 = k == 2 || k == 3 | even k = 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 = countTrailingZeros m d = m `unsafeShiftR` s loop :: [Int] -> Bool loop = List.foldl (\acc x -> acc && (func1 x || func2 x)) True where func1 :: Int -> Bool func1 a = powModInt a d n == 1 func2 :: Int -> Bool func2 a = not $ all (\r -> (powModInt a ((1 `unsafeShiftL` r) * d) n) /= m) [0..(s-1)] powModInt :: Int -> Int -> Int -> Int powModInt a n mo = fromInteger $ GMP.powModInteger (fromIntegral a) (fromIntegral n) (fromIntegral mo) {-# INLINE powModInt #-} type Parser a = BSC8.ByteString -> Maybe (a, BSC8.ByteString) parseInt :: Parser Int parseInt = fmap (Arrow.second BSC8.tail) . BSC8.readInt parse1 :: IO Int parse1 = readLn parseN :: Int -> IO (VU.Vector Int) parseN n = VU.replicateM n parse1 ------------------------------------------------------------------------------- main :: IO () main = do n <- parse1 xs <- parseN n rep n (\i -> BSC8.putStrLn $ solve $ xs VU.! i) solve :: Int -> BSC8.ByteString solve n = BSC8.pack $ bool (show n ++ " 0") (show n ++ " 1") (isPrime n) ------------------------------------------------------------------------------- rep :: (Monad m) => Int -> (Int -> m ()) -> m () rep n = flip MS.mapM_ (stream 0 n) {-# INLINE rep #-} stream :: (Monad m) => Int -> Int -> MS.Stream m Int stream !l !r = MS.Stream step l where step x | x < r = return $ MS.Yield x (x + 1) | otherwise = return MS.Done {-# INLINE [0] step #-} {-# INLINE [1] stream #-}