Problem:
Score : 300 points

Problem Statement

There are N integers, A_1, A_2, ..., A_N, written on the blackboard.

You will choose one of them and replace it with an integer of your choice between 1 and 10^9 (inclusive), possibly the same as the integer originally written.

Find the maximum possible greatest common divisor of the N integers on the blackboard after your move.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq A_i \leq 10^9

Output

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible greatest common divisor of the N integers on the blackboard after your move.

Sample Input 1

3
7 6 8

Sample Output 1

2

If we replace 7 with 4, the greatest common divisor of the three integers on the blackboard will be 2, which is the maximum possible value.

Sample Input 2

3
12 15 18

Sample Output 2

6

Sample Input 3

2
1000000000 1000000000

Sample Output 3

1000000000

We can replace an integer with itself.

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Time Limit Exceeded)

(defparameter *a* #())
(defparameter *ans* 0)
(defparameter *memo* '())

(defun gcd2(a b)
  (if (= b 0) a (gcd2 b (mod a b))))

(defun solve ()
  (loop :for i :from 0 :to (1- (length *a*))
        :if (not (find (aref *a* i) *memo*))
        :do
           (let ((value (aref *a* i)))
             (append *memo* (list value))
             (setf (aref *a* i) 0)
             (let ((gcd (reduce #'gcd2 *a*)))
               (setf *ans* (max *ans* gcd)))
             (setf (aref *a* i) value)))
  *ans*)

(defun main ()
  (let* ((n (read))
         (a (loop :repeat n :collect (read))))
    (setf *a* (make-array (length a) :initial-contents a))
    (format t "~A~%" (solve))))

(main)