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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Applicative
import Data.List

a = [2..31]
f x = takeWhile (<=1000) $ map (x^) [2..]
c = sort $ nub (1:(concat (map f a)))
main = do
    x <- readLn
    print $ head (reverse (takeWhile (<=x) c))