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.Monad
import Data.List
import Data.Bits
import Debug.Trace
import Data.Maybe
import qualified Data.ByteString.Char8 as C

main :: IO ()
main = do
  [x] <- readInts
  print $ solve x

solve :: Int -> Int
solve x = maximum (map (maxExp x) [1 .. maxRoot x])

maxRoot :: Int -> Int 
maxRoot = floor . sqrt . fromIntegral

maxExp :: Int -> Int -> Int
maxExp x r = if r == 1 then 1 else maxExpIter x r r
  where
    maxExpIter x r a =
      if next > x
        then a
        else maxExpIter x r next
      where next = r * a

-- 以下ライブラリ

readInts :: IO [Int]
readInts = map (fst . fromJust . C.readInt) . C.words <$> C.getLine

readNInts :: Int -> IO [[Int]]
readNInts = flip replicateM readInts

readIntegers :: IO [Integer]
readIntegers = map (fst . fromJust . C.readInteger) . C.words <$> C.getLine

readNIntegers :: Int -> IO [[Integer]]
readNIntegers = flip replicateM readIntegers

getNLns :: Int -> IO [String]
getNLns = flip replicateM getLine

toTup2 :: [[a]] -> [(a, a)]
toTup2 = map (\ys -> case ys of y : z : zs -> (y, z))

encIdx2 :: Int -> (Int, Int) -> Int
encIdx2 mx (y, x) = y * mx + x

decIdx2 :: Int -> Int -> (Int, Int)
decIdx2 mx idx = (idx `div` mx, idx `mod` mx)

encIdx3 :: (Int, Int) -> (Int, Int, Int) -> Int
encIdx3 (my, mx) (z, y, x) = z * my * mx + y * mx + x

decIdx3 :: (Int, Int) -> Int -> (Int, Int, Int)
decIdx3 (my, mx) idx = (z, y, x)
  where
    basez = my * mx
    z = idx `div` basez
    y = (idx `mod` basez) `div` mx
    x = idx `mod` mx

while :: Monad m => m Bool -> m () -> m ()
while cond body = do
  b <- cond
  when b $ do
    body
    while cond body