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 input (n)
  (let ((a (make-array (1+ n))))
    (loop for i from 1 to n do (setf (aref a i) (read)))
    a)) 
(let* ((n (read))
       (a (input n))
       (r (make-array (+ n 2)))
       (l (make-array (+ n 2))))
  (setf (aref l n) (aref a n))
  (loop for i from 1 below n
    do (setf (aref r i) (gcd (aref r (1- i)) (aref a i))))
  (loop for i from n downto 1
    do (setf (aref l (1- i)) (gcd (aref l i) (aref a (1- i)))))
  (format t "~A~%"
          (loop for i from 1 to n
                maximize (gcd (aref r (1- i)) (aref l (1+ i))))))