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
def divisor(n):
    ans = []
    sqr = int(math.sqrt(n))
    for x in range(1, sqr+1):
        if n % x == 0:
            ans.append(x)
            y = n//x
            if x != y:
                ans.append(y)
    ans.sort()
    return ans

x = int(input())
div = divisor(x)
flag = False
for i in div:
    if flag:
        break
    a = i // 2
    j = x // i
    b = a - i
    jj = a**4+a**3*b+a**2*b**2+a*b**3+b**4
    #print('a = {0}, b = {1}'.format(a, b))
    #print('i = {0},  j = {1}, jj = {2}'.format(i, j, jj))
    while(jj <= j):
        b = a - i
        jj = a**4+a**3*b+a**2*b**2+a*b**3+b**4
        #print('a = {0}, b = {1}'.format(a, b))
        #print('i = {0}, j = {1}, jj = {2}'.format(i, j, jj))
        if j == jj:
            print('{0} {1}'.format(a, b))
            flag = True
            break
        a += 1