import Data.List (sort, length)
import Data.Array.Unboxed


containsEveryDigitOnce :: Int -> Bool
containsEveryDigitOnce number = sortedDigits == [0..9]
    where
        digits = map (`mod` 10) $ takeWhile (> 0) $ iterate (`div` 10) number
        sortedDigits = sort digits


primesToNA :: Int -> [Int]
primesToNA n = 2 : [i | i <- [3, 5..n], ar ! i]
  where
    ar = f 5 $ accumArray (\a b -> False) True (3, n)
      [(i, ()) | i <- [9, 15..n]]
    f p a
      | q > n = a
      | otherwise = if null x then a2 else f (head x) a2
      where
        q = p * p
        a2 :: UArray Int Bool
        a2 = a // [(i, False) | i <- [q, q + 2 * p..n]]
        x = [i | i <- [p + 2, p + 4..n], a2 ! i]


findPairs :: [(Int, Int)]
findPairs = [(p, q) | p <- primesToNA 100000, q <- primesToNA 2200, (p^2 + q^3) <= 98765432100, containsEveryDigitOnce (p^2 + q^3)]

main :: IO ()
main = print (length findPairs)