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 Python (3.8.2) (judge verdict: Wrong Answer)

X = int(input())

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr

def search():
    for b in range(10**10):
        #B^5 = A^5-X
        #A^5 = B^5+X
        for sign in [1,-1]:
            a_5 = (sign*b)**5 + X
            #print(a_5, sign*b, a_5 - b**5, X)
            candidate = factorization(abs(a_5))
            if len(candidate) == 1 and candidate[0][1]%5 == 0:
                #print(a_5 ** 0.2, b)
                print(candidate[0][0]**(candidate[0][1]//5), b)
                return
            

            

search()