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: Time Limit Exceeded)

def Exponential(x):

    ans = 0
    if x == 1:
        ans = 1
    else:
        for i in range(1, x + 1):
            for w in range(2, x + 1):
                if i ** w <= x:
                    ans = max(ans, i ** w)

    return ans

def main():
    x = int(input())
    print(Exponential(x))

if __name__ == '__main__':
    main()