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: Accepted)

class Integer
  def divisor
    res = []
    1.upto((self**0.5)) do |i|
      if self % i == 0
        res.push i
        res.push self / i if i != self / i
      end
    end
    res.sort
  end
end

def answer_if_valid(x, a, d)
  b = a - d
  if x == a ** 5 - b ** 5
    puts "#{a} #{b}"
    exit
  end
end

x = gets.to_s.to_i

r = x % 5

divisors = x.divisor.select{|t| r == t % 5}

divisors.each do |d|
  
  left = (( x / d - d ** 4 ) / 5).abs
  
  if left == 0
    answer_if_valid(x,0,d)
    (d ** 3).abs.divisor.each do |a|
      answer_if_valid(x, a, d)
      answer_if_valid(x,-a, d)
    end
  end
  
  left.divisor.each do |a|
    answer_if_valid(x,  a, d)
    answer_if_valid(x, -a, d)
  end
end