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)

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
X = int(input())
A = []
for i in factorization(X):
  for j in range(0,i[1]+1):
    a = i[0]**j
    b = X//a
    if(a<b):
      A.append([a,b])
    else:
      A.append([b,a])
 
A = list(map(list, set(map(tuple, A))))
flag = 0
for i in A:
  r = list(range(0,100000+1))
  for a in r:
    b = a - i[0]
    if a**4 + a**3 * b + a**2 * b**2 + a * b**3 + b**4 == i[1]:
      print(a,b)
      flag = 1
      break
  if flag==1:
    break
  r = list(range(0,100000+1))
  for a in r:
    b = a - i[1]
    if a**4 + a**3 * b + a**2 * b**2 + a * b**3 + b**4 == i[0]:
      print(a,b)
      flag = 1
      break
  if flag==1:
    break