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 Python (3.8.2) (judge verdict: Runtime Error)

x=int(input())

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

a=prime_factorize(x)

a.append(1)
a=list(set(a))
len=len(a)
for i in range(len):
    if a[i]>11:
        a[i]=0
a=list(set(a))
if (0 in a)=1:
    a.remove(0)
    
t=-100
ansx=0
ansy=0
while True:
    if not ansx== 0 or not ansy== 0:
        break
    for i in range(len):
        if ((t+a[i])**5-t**5)-x==0:
            ansx=t+a[i]
            ansy=t
            break
        else:
            t+=1
print(ansx,ansy)