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: Accepted)

(defun main ()
  (let* ((n (read))
         (a (make-array 0 :element-type 'integer
                          :adjustable t
                          :fill-pointer 0))
         (g (make-array (+ n 2) :element-type 'integer
                                :initial-element 0
                                :adjustable t))
         (gr (make-array (+ n 2) :element-type 'integer
                                 :initial-element 0
                                 :adjustable t))
         (ans 0))
    (dotimes (i n)
      (vector-push-extend (read) a))
    (setf (aref g 0) (aref a 0))
    (setf (aref gr (1+ n)) (aref a (1- n)))
    (loop for i from 1 upto n
          do (setf (aref g i) (gcd (aref g (1- i)) (aref a (1- i))))
             (setf (aref gr (1+ (- n i))) (gcd (aref gr (- n i -2)) (aref a (- n i)))))
;;    (format t "~A~%~A~%~A~%" a g gr)
    (loop for i from 2 below n
          do (setf ans (max ans (gcd (aref g (1- i)) (aref gr (1+ i))))))
    (format t "~A~%" (max ans (aref g (1- n)) (aref gr 2)))))

(main)