Problem:
Score : 200 points

Problem Statement

You are given a positive integer X.
Find the largest perfect power that is at most X.
Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.

Constraints

1 ≤ X ≤ 1000

X is an integer.

Input

Input is given from Standard Input in the following format:

X

Output

Print the largest perfect power that is at most X.

Sample Input 1

10

Sample Output 1

9

There are four perfect powers that are at most 10: 1, 4, 8 and 9.
We should print the largest among them, 9.

Sample Input 2

1

Sample Output 2

1

Sample Input 3

999

Sample Output 3

961

Solution in PyPy3 (2.4.0) (judge verdict: Wrong Answer)

X = int(input())
fact = [1]
for i in range(2, 40):
  p = i
  while(p <= 1000):
    fact.append(p)
    p = p*i
fact.sort()
ans = 0
for n in fact:
  if(n <= X):
    ans = n
  else:
    break
print(ans)