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)

x = int(input())
if x == 1:
  print(0,-1)
  exit()
  
def divisorize(fct):
    b, e = fct.pop()  # base, exponent
    pre_div = divisorize(fct) if fct else [[]]
    suf_div = [[(b, k)] for k in range(e + 1)]
    return [pre + suf for pre in pre_div for suf in suf_div]


def factorize(n):
    fct = []  # prime factor
    b, e = 2, 0  # base, exponent
    while b * b <= n:
        while n % b == 0:
            n = n // b
            e = e + 1
        if e > 0:
            fct.append((b, e))
        b, e = b + 1, 0
    if n > 1:
        fct.append((n, 1))
    return fct


def num(fct):
    a = 1
    for base, exponent in fct:
        a = a * base**exponent
    return a

c = []
fct = factorize(x)
for div in divisorize(fct):
    c.append(num(div))
    
chk = False
for s in c:
  if chk:
    break
  for i in range(1000):
    if (i+s)**5-i**5 > x:
      break
    if (i+s)**5-i**5 == x:
      ans = (i+s,i)
      chk = True
      break
  if s <1000:    
    for p in range(s,1000):
      j = -1*p
      #print(s,(j+s)**5-j**5)
      if (j+s)**5-j**5 > x:
        break 
      if (j+s)**5-j**5 == x:
        ans = (j+s,j)
        chk = True
        break 
  for ww in range(1,(s+1)//2)[::-1]:
    jj = -1*ww
    if (jj+s)**5-jj**5 > x:
      break    
    if (jj+s)**5-jj**5 == x:
      ans = (jj+s,jj)
      chk = True
      break 
print(*ans)