import qualified Control.Arrow as Arrow import qualified Data.ByteString.Char8 as BSC8 import qualified Data.Vector.Unboxed as VU import Data.Bits import GHC.Integer.GMP.Internals import Data.Bool fi :: Int -> Integer fi = fromIntegral fI :: Integer -> Int fI = fromInteger powModInt :: Int -> Int -> Int -> Int powModInt a n mo = fI $ powModInteger (fi a) (fi n) (fi mo) millerRabin :: Int -> Bool millerRabin n | n <= 1 = False | n == 2 || n == 3 || n == 5 || n == 7 = True | even n = False | otherwise = mrCheck n mrCheck :: Int -> Bool mrCheck n | n < 2047 = loop [2] | n < 9080191 = loop [31,73] | n < 4759123141 = loop [2,7,61] | n < 2152302898747 = loop [2,3,5,7,11] | 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 d n /= 1) && allok = False | otherwise = loop as where allok = all (\r -> (powModInt a ((1 `unsafeShiftL` r) * d) n) /= m) [0..(s - 1)] 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_ (putStr . solve) xs solve :: Int -> String solve n = bool (show n ++ " 0\n") (show n ++ " 1\n") (millerRabin n)