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)

import sys

def debug(*args):
    print(*args, file=sys.stderr)

# https://www.themathpage.com/Alg/difference-two-squares-2.htm#fifth

# https://qiita.com/snow67675476/items/e87ddb9285e27ea555f8
def factorize(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr

def get_factors_of(a_number):
    factorized = factorize(a_number)
    return [factor for factor, _ in factorized]


x_diff_of_5th_factor = int(input())

factors_of_x = get_factors_of(x_diff_of_5th_factor)

# debug(factors_of_x)

for a_factor_of_x in factors_of_x:
    for a in range(a_factor_of_x//2+1):
        b = a - a_factor_of_x

        if a ** 5 - b ** 5 == x_diff_of_5th_factor:
            print('{} {}'.format(a, b))
            sys.exit(0)
print('0 0')
sys.exit(1)