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 main () =
  let x = Scanf.scanf "%d\n" (fun a -> a) in
  let ans = BatArray.make (x+1) false in
  ans.(1) <- true;
  for i = 2 to x do
    let n = ref @@ i * i in
    while !n <= x do
      ans.(!n) <- true;
      n := !n * i;
    done;
  done;
  for i = x downto 1 do
    if ans.(i) then (print_int i; exit 0)
  done;;

let _ = main ()