{-# LANGUAGE MagicHash #-} import qualified Control.Arrow as Arrow import Data.Bool (bool) import Data.Bits import qualified Data.ByteString.Char8 as BSC8 import qualified Data.Vector.Unboxed as VU import GHC.Exts import GHC.Natural 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 [] = True loop (a:as) | (powModInt (a `mod` n) d n /= 1) && allok = False | otherwise = loop as where allok = all (\r -> (powModInt a ((1 `unsafeShiftL` r) * d) n) /= m) [0..(s - 1)] powModInteger :: Integer -> Integer -> Integer -> Integer powModInteger b e m = GMP.powModInteger (b `mod` m) e m {-# INLINE powModInteger #-} powModWord :: Word -> Word -> Word -> Word powModWord (W# x) (W# y) (W# m) = W# (GMP.powModWord x y m) {-# INLINE powModWord #-} powModInt :: Int -> Int -> Int -> Int powModInt x y m | m <= 0 = error "powModInt: non-positive modulo" | y < 0 = error "powModInt: negative exponent" | otherwise = wordToInt $ powModWord (intToWord (x `mod` m)) (intToWord y) (intToWord m) {-# INLINE powModInt #-} wordToInt :: Word -> Int wordToInt = fromIntegral {-# INLINE wordToInt #-} wordToInteger :: Word -> Integer wordToInteger = fromIntegral {-# INLINE wordToInteger #-} intToWord :: Int -> Word intToWord = fromIntegral {-# INLINE intToWord #-} intToInteger :: Int -> Integer intToInteger = fromIntegral {-# INLINE intToInteger #-} naturalToInteger :: Natural -> Integer naturalToInteger = fromIntegral {-# INLINE naturalToInteger #-} integerToNatural :: Integer -> Natural integerToNatural = fromIntegral {-# INLINE integerToNatural #-} integerToWord :: Integer -> Word integerToWord = fromIntegral {-# INLINE integerToWord #-} integerToInt :: Integer -> Int integerToInt = fromIntegral {-# INLINE integerToInt #-} 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 VU.mapM_ (BSC8.putStrLn . solve) xs solve :: Int -> BSC8.ByteString solve n = BSC8.pack $ bool (show n ++ " 0") (show n ++ " 1") (isPrime n) -------------------------------------------------------------------------------