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)

X = int(input())
n = 1
if X<=3:
    print(1)
elif X==4:
    print(4)
else:
    n = 4
    for i in range(2,int(X**0.5)+1):
        b = i
        k = 1
        while b**k<=X:
            k += 1
        k -= 1
        if k>=2:
            n = max(n,b**k)
    print(n)