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)

(defun input (n)
  (let ((a (make-array n)))
    (loop for i below n do (setf (aref a i) (read)))
    a)) 
(let* ((n (read))
       (a (input n)))
  (format t "~A~%"
          (loop for i below n
                maximize (let ((x 0))
                           (loop for j below n
                                 when (not (= i j))
                                 do (setf x (gcd x (aref a j))))
                           x))))