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)

module Main where

import           Control.Monad
import           Data.List
import           Data.Ord
import           Data.List.Split
import           Data.Array.IO
import qualified Data.Vector.Unboxed as V

main :: IO ()
main = do
  x <- readLn :: IO Int
  print $ f x
  where
    f x | x == 1 = 1
        | otherwise = maximum [g x n (n * n) | n <- [2 .. x]]
    g x a aa | aa > x = 0
             | (aa * a) > x = aa
             | otherwise = g x a (aa * a)