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 Ruby (2.7.1) (judge verdict: Wrong Answer)

require 'prime'

X = gets.to_i

def calc(x, y) x**5 - y**5 end

def divisors(n)
  n.prime_division.inject([1]) do |ary, (p, e)|
    (0..e).map{ |e1| p ** e1 }.product(ary).map{ |a, b| a * b }
  end.sort
end

ans = [0, 0]
divisors(X).each{|n|
  (0..120).each{|i|
    wk = calc(i, i-n)
    break if wk > 10 ** 9
    if wk == X then
      ans = [i, i-n]
      break
    end
  }
  break if ans != [0, 0]
}

puts ans*?\s