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 OCaml (4.02.3) (judge verdict: Accepted)

let rec iter a b f = if a >= b then () else (f a; iter (a+1) b f)
let () =
  Scanf.scanf "%d" @@ fun x ->
  let a = Array.make (x+1) false in
  a.(1) <- true;
  iter 2 (x+1) (fun b ->
    let rec loop v =
      if v > x then ()
      else (a.(v) <- true; loop (v*b))
    in loop (b*b));
  Array.mapi (fun i e -> i,e) a
  |> Array.fold_left (fun v (i,t) -> if t then i else v) 1
  |> Printf.printf "%d\n"