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)

import sys
import os


def main():
    if os.getenv("LOCAL"):
        sys.stdin = open("input.txt", "r")

    N = int(sys.stdin.readline().rstrip())
    ret = 0
    for b in range(1, N):
        for p in range(2, N):
            if b ** p <= N:
                ret = b ** p

    print(ret)


if __name__ == '__main__':
    main()