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: Accepted)

X = int(input())

res = 0
if X <= 3:
    res = 1
else:
    for i in range(2,X):
        c = 2
        while 1:
            a = i**c
            if a <= X:
                if res < a:
                    res = a
                c += 1
            else:
                break
print(res)