import Text.Read (readMaybe)
import System.Exit (exitSuccess)


main :: IO ()
main = do
    n <- askNumber
    let (d, root) = findIntegerSqrt n
        q = (root - d)
        p = (root + d)
    putStrLn ("n = " ++ show n)
    putStrLn ("Found d = " ++ show d ++ ", sqrt(n + d^2) = " ++ show root)
    putStrLn ("q = " ++ show q ++ ", p = " ++ show p)


askNumber :: IO Int
askNumber = do
    putStrLn "Enter an integer:"
    input <- getLine
    case readMaybe input :: Maybe Int of
        Just n  -> return n
        Nothing -> do
            putStrLn "Not a valid integer!"
            exitSuccess

-- Find the smallest integer d >= 0 such that sqrt(n + d^2) is an integer
findIntegerSqrt :: Int -> (Int, Int)
findIntegerSqrt n = go 0
  where
    go d =
        let val  = n + d*d
            root = floor (sqrt (fromIntegral val))
        in if root * root == val
           then (d, root)
           else go (d + 1)