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           Control.Monad

import           Data.List             (sortBy)

-- 1024 = 2 ^ 10
-- 1024 = 32 ^ 2

f :: Int -> [Int]
f n = sortBy (flip compare)
      (1 : [b ^ p | b <- [2 .. 32], p <- [2 .. 10], b ^ p <= n])

main :: IO ()
main = do
    n <- readLn :: IO Int
    print $ head (f n)