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 PyPy3 (7.3.0) (judge verdict: Accepted)

def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))


X = INT()

def f(a, b):
    return a**4 + a**3*b + a**2*b**2 + a*b**3 + b**4

for alpha in range(1, int(X**0.5)+1):
    if X % alpha == 0:
        beta = X // alpha

        a = alpha // 2
        b = a - alpha

        while f(a, b) <= beta:
            if f(a, b) == beta:
                break
            a += 1
            b += 1
        
        else:
            continue
        break

print(a, b)