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: Accepted)

def main():
    import math
    from itertools import product
    x = int(input())
    k = math.ceil(x ** .5)
    l = [1]

    for i, j in product(range(2, k), range(2, 10)):
        if i ** j <= 1000:
            l.append(i ** j)
    ans = max([i for i in l if i <= x])
    print(ans)


if __name__ == '__main__':
    main()