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 Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)



import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public final class Main {

    public static void main(String[] args) {
        final Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        final int x = in.nextInt();
        int t = 0;
        final Map<Integer, Integer> map = new HashMap<>();
        while (Math.pow(t, 5) < x + 10) {
            map.put((int) Math.pow(t, 5), t);
            map.put((int) Math.pow(-t, 5), -t);
            t++;
        }
        int[] res = twoSum(x, map);
        System.out.println(res[0] + " " + res[1]);
    }

    public static int[] twoSum(int target, Map<Integer, Integer> map) {
        for (int num : map.keySet()) {
            if (map.containsKey(target + num)) {
                return new int[] { map.get(target + num), map.get(num) };
            }
        }
        return null;
    }
}