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)


from itertools import permutations

def power(base, exp):
  """ Fast power calculation using repeated squaring """
  if exp < 0:
      return 1 / power(base, -exp)
  ans = 1
  while exp:
      if exp & 1:
          ans *= base
      exp >>= 1
      base *= base
  return ans

def parse():
  return int(input())

def main():
  X = parse()

  A = None
  B = None

  # Z = [i for i in range(0, 5)]
  # print(Z)
  # print(list(permutations(range(0, 5), 2)))
  # print(list(permutations(range(0, 5), 2)))
  # exit(0)

  max_val = 10
  signs = [[1, 1], [-1, 1], [1, -1], [-1, -1]]

  for i in range(0, max_val + 1):
    for j in range(0, max_val + 1):
      for sign in signs:
        # A5 = 
        # print(i * sign[0], j * sign[1])
        if power(i * sign[0], 5) - power(j * sign[1], 5) == X:
          A = i * sign[0]
          B = j * sign[1]
          break

  print(A, B)

if __name__ == "__main__":
  main()