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 Python (3.8.2) (judge verdict: Accepted)

L=[1]
s=2
for i in range(2,32):
  while True:
    s=s*i
    if s<=1000:
      L.append(s)
    else:
      s=i+1
      break
L=sorted(list(set(L)))
N=int(input())
S=[i for i in L if i<=N]
print(S[-1])