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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(defun f (n a b)
  (cond ((or (= a 1) (= n 1)) b)
    ((= (rem n a) 0) (f (/ n a) a (1+ b)))
    (t 0)))

(let ((n (read))
      (flg t))
     (loop for i from n downto 1 while flg do
           (loop for j from i downto 1 while flg do
                 (if (< 1 (f i j 0)) (progn (princ i)
                                            (setf flg nil)))))
     (if flg (princ 1)))