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)

{-# OPTIONS_GHC -O2 -funbox-strict-fields #-}

main :: IO ()
main = do
  x <- readLn
  print $ solve x

solve :: Int -> Int
solve x = head $ filter isExpNumber [x, x-1 ..]

isExpNumber :: Int -> Bool
isExpNumber 1 = True
isExpNumber x = any g [b | b <- [2 .. x], x `mod` b == 0] where
  g b = any (x ==) $ takeWhile (x >=) [b ^ p | p <- [2 ..]]