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.Vector.Unboxed as VU 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 = (not allok) && loop as | otherwise = loop as where allok = 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 VU.mapM_ (BSC8.putStrLn . solve) xs solve :: Int -> BSC8.ByteString solve n = BSC8.pack $ bool (show n ++ " 0") (show n ++ " 1") (isPrime n) -------------------------------------------------------------------------------