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 C (Clang 10.0.0) (judge verdict: Time Limit Exceeded)

#include <inttypes.h>
#include <math.h>
#include <stdbool.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int main(void)
{
    intmax_t X;
    intmax_t A = 0, B = 0, factor = 2;

    scanf("%jd", &X);

    if (X == 1) {
        puts("0 -1");
        return 0;
    }

    while (1) {
        while (X % factor)
            factor++;

        for (size_t i = 0; i < (int)100; i++) {
            A = i + factor;
            B = i;
            if (A * A * A * A * A - B * B * B * B * B == X) {
                printf("%jd %jd\n", A, B);
                return 0;
            }

            A = -i + factor;
            B = -i;
            if (A * A * A * A * A - B * B * B * B * B == X) {
                printf("%jd %jd\n", A, B);
                return 0;
            }
        }
        factor++;
    }

    return 0;
}