Problem:
Score : 400 points

Problem Statement

Give a pair of integers (A, B) such that A^5-B^5 = X.
It is guaranteed that there exists such a pair for the given integer X.

Constraints

1 \leq X \leq 10^9

X is an integer.

There exists a pair of integers (A, B) satisfying the condition in Problem Statement.

Input

Input is given from Standard Input in the following format:

X

Output

Print A and B, with space in between.
If there are multiple pairs of integers (A, B) satisfying the condition, you may print any of them.

A B

Sample Input 1

33

Sample Output 1

2 -1

For A=2 and B=-1, A^5-B^5 = 33.

Sample Input 2

1

Sample Output 2

0 -1

Solution in Haskell (GHC 8.8.3) (judge verdict: Runtime Error)

main = do
    x <- readInt <$> getLine
    let max = max' 0 x
        candidates = concat [[n, - n] | n <- [0..max]]
        answer = head [(a, b) | a <- candidates, b <- candidates, a ^ 5 - b ^ 5 == x]
    putStr $ show (fst answer) ++ " " ++ show (snd answer)

readInt :: String -> Integer
readInt = read

max' n m 
    | 2 * (n ^ 5) < m = max' (n + 1) m
    | otherwise     = n