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: Accepted)

import math
X = int(input())

if X == 1:
    print(1,0)
    exit()

def repeat_any_square( a,n ):
    if n == 1:
        return a
    x = repeat_any_square( a,n//2 )
    x *= x
    if n % 2 == 1:
        x *= a
    return x

ans = []
for i in range(-1000,1000):
    ans.append(repeat_any_square(i,5))

#print(ans)
for i in range(2000):
    if ((ans[i] - X) in ans) == True:
        flag_A = 1
        flag_B = 1
        if ans[i] < 0:
            flag_A = -1
        if ans[i] - X < 0:
            flag_B = -1
        print(flag_A*int(math.pow(flag_A*ans[i],1/5)),flag_B*int(math.pow(flag_B*(ans[i]-X),1/5)))

        exit()