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)

main = do
  line <- getLine
  let 
    x = read $ head $ words line :: Int
    power a b = power_ 1 a b 
    power_ p a b 
      | b > 0     = power_ (p*a) a (b-1)
      | otherwise = p
    func i j x 
      | x == 1          = 1
      | power i j <= x  = max (func (i+1) j x) (func i (j+1) x)
      | otherwise       = choice (power (i-1) j) (power i (j-1))
    choice a b
      | a <= x && b <= x  = max a b
      | otherwise         = min a b
    in
      putStrLn $ show $ func 2 2 x