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 Common Lisp (SBCL 2.0.3) (judge verdict: Accepted)

(defun factorize (N)
  (loop for x from 1 to (isqrt N) with q and r
        do (multiple-value-setq (q r) (floor N x))
        if (zerop r) collect x
        if (and (zerop r) (/= x q)) collect q))

(defvar N (read))

(loop named outer for x in (factorize N) do
      (loop for a from (floor x 2)
            for b from (- (floor x 2) x)
            with y = (/ N x) with z
            do (setf z (+ (* a a a a)
                          (* a a a b)
                          (* a a b b)
                          (* a b b b)
                          (* b b b b)))
            if (= y z)
            do (return-from outer (format t "~A ~A" a b))
            if (< y z)
            return nil))