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: Wrong Answer)

#!/usr/bin/env python
def factorization(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 main():
    x = int(input())

    fact = factorization(x)
    fact = [[1]] + fact
    chk = 1
    for q in fact:
        p = q[0]
        a = p
        b = 0
        y = p ** 5
        while y <= x and chk == 1:
            y = a ** 5 - b ** 5
            if x == y and chk == 1:
                print(a, b)
                chk = 0
                break
            a += 1
            b += 1
        if chk == 0:
            break

        a = p
        b = 0
        while a >= b:
            z = a ** 5 + b ** 5
            if x == z and chk == 1:
                print(a, -b)
                chk = 0
                break
            a -= 1
            b += 1
        if chk == 0:
            break

if __name__ == '__main__':
    main()