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 (3.4.3) (judge verdict: Wrong Answer)

X = int(input())

def han(n, k):
  if int(n**(1/k)) == n**(1/k):
    return True
  else:
    return False
  
while 1:
  if han(X, 2) or han(X, 3) or han(X, 5) or han(X, 7) or han(X, 4) or han(X, 6) or han(X, 8) or han(X, 9) or han(X, 10):
    print(X)
    break
  X -= 1