Разложение на два квадрата

import Data.List

getExactDiff :: Int -> Int -> [Int]
getExactDiff n quad = [floor d, ceiling d]
    where
        d = fromIntegral ( abs (n - quad*quad) ) ** 0.5

compareVar :: (Int, Int, Int) -> (Int, Int, Int) -> Ordering
compareVar (_, q1, a1) (_, q2, a2)
    | abs(a1) /= abs(a2) = compare (abs a1) (abs a2)
    | otherwise = compare q1 q2

getPairs :: Int -> [(Int, Int, Int)]
getPairs n =
    sortBy compareVar [(p, q, p*p+q*q-n) | p <- [1..n_root], q <- (getExactDiff n p), p <= q, q > 0]
    where
        n_root = ceiling (fromIntegral n ** 0.5)

getVariant :: Int -> (Int, Int, Int)
getVariant = head . getPairs

main = do
    putStrLn "Enter number:"
    num <- getLine
    let result = getVariant (read num)
    putStrLn (show result)