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)

import Data.List
import Control.Monad

input_int :: IO Int
input_int = do
    a <- getLine
    return (read a)

test :: Int -> (Int, Int)
test x = 
    let ns = [(n^5, n) | n <- [1..100]]
        adds = [(an, bn) | (a, an) <- ns, (b, bn) <- ns, a > b, a - b == x]
        subs = [(an, (-bn)) | (a, an) <- ns, (b, bn) <- ns, a + b == x]
    in  head (adds ++ subs)
    
    
main = do
    x <- input_int
    let (a, b) = test x
    putStr ((show a) ++ " " ++ (show b))