{-# LANGUAGE BangPatterns #-} import Control.Monad import Data.Bool import Data.Bits import qualified GHC.Integer.GMP.Internals as GMP import qualified Data.Array.ST as ArrST import qualified Data.Array.Unboxed as ArrU thirdRoot :: Float -> Float thirdRoot n = fst $ until (uncurry(==)) (\(_, x0) -> (x0,((n - 1.0) * x0 + 3.0 / x0 ** (n - 1.0)) / n)) (3.0, 3.0 / n) sieveUA :: Int -> ArrU.UArray Int Bool sieveUA top = ArrST.runSTUArray $ do let m = (top-1) `div` 2 r = floor . sqrt $ fromIntegral top + 1 sieve <- ArrST.newArray (1,m) True forM_ [1..r `div` 2] $ \i -> do isPrime <- ArrST.readArray sieve i when isPrime $ do forM_ [2*i*(i+1), 2*i*(i+2)+1..m] $ \j -> do ArrST.writeArray sieve j False return sieve primesToUA :: Int -> [Int] primesToUA top = 2 : [i*2+1 | (i,True) <- ArrU.assocs $ sieveUA top] main :: IO () main = readLn >>= putStrLn . solver solver :: Int -> String solver n = bool "NO" "YES" $ func1 n func1 :: Int -> Bool func1 n = iter n 0 ps where ps = primesToUA 40000 iter res p [] | p >= 3 || (p == 2 && millerRabin p) = True | p == 1 = not $ millerRabin res | res >= 10 ^ 12 = let xxx = round $ thirdRoot $ fromIntegral res in if even xxx then millerRabin $ xxx - 1 else millerRabin xxx | otherwise = False iter i j (l:ls) | i < 2 = j >= 3 | j >= 3 = True | i `mod` l == 0 = iter (func2 i l) (j + func3 i l) ls | otherwise = iter i j ls func2 :: Int -> Int -> Int func2 n mo | n `mod` mo == 0 = func2 (n `div` mo) mo | otherwise = n func3 :: Int -> Int -> Int func3 n mo = iter n mo 0 where iter i j k | i `mod` j == 0 = iter (i `div` j) j (k + 1) | otherwise = k millerRabin :: Int -> Bool millerRabin k | k <= 3 = k == 2 || k == 3 | even k = False | otherwise = mr k where mr :: Int -> Bool mr 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 powModInt :: Int -> Int -> Int -> Int powModInt !a !n !mo = fI $ GMP.powModInteger (fi a) (fi n) (fi mo) !m = n - 1 !s = ctz m !d = m .>>. s loop :: [Int] -> Bool loop [] = True loop (a:as) | powModInt a d n /= 1 && allok = False | otherwise = loop as where allok = all (\r -> (powModInt a ((1 .<<. r) * d) n) /= m) [0..(s - 1)] infixl 8 .<<., .>>. (.<<.) :: Bits b => b -> Int -> b (.<<.) = unsafeShiftL {-# INLINE (.<<.) #-} (.>>.) :: Bits b => b -> Int -> b (.>>.) = unsafeShiftR {-# INLINE (.>>.) #-} fi :: Int -> Integer fi = fromIntegral {-# INLINE fi #-} fI :: Integer -> Int fI = fromInteger {-# INLINE fI #-} ctz :: FiniteBits fb => fb -> Int ctz = countTrailingZeros {-# INLINE ctz #-}