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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import sys
from math import ceil, sqrt
def input(): return sys.stdin.readline().strip()


def main():
    X = int(input())
    x = int(X ** (1/5))
    if x == X ** (1/5):
        print("{} {}".format(x, 0))
        return
    
    for B in range(1, x + 1):
        A = (X - B**5) ** (1/5)
        if A < B: break
        if int(A) == A:
            print("{} {}".format(int(A), -B))
            return
    
    y = sqrt(X)
    if int(y) == y:
        upper = int(y) + 1
    else:
        upper = ceil(y)

    for d in range(1, upper):
        #print("d={}".format(d))
        if X % d == 0:
            B = 1
            while (B + d) ** 5  < B ** 5 + X:
                B += 1
            if (B + d) ** 5 == B ** 5 + X:
                print("{} {}".format(B + d, B))
                return
            
            d = X // d
            while (B + d) ** 5  < B ** 5 + X:
                B += 1
            if (B + d) ** 5 == B ** 5 + X:
                print("{} {}".format(B + d, B))
                return



if __name__ == "__main__":
    main()