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 OCaml (4.02.3) (judge verdict: Accepted)

(* O(n log(max a_s)) *)
let n = Scanf.scanf " %d" @@ (+) 0
let a_s = Array.init n @@ fun _ -> Scanf.scanf " %d" @@ (+) 0
let gcds = Array.make_matrix 2 (n + 1) 0
let rec gcd a b = if b = 0 then a else gcd b (a mod b)
let ans = ref 0
let _ =
  Array.iteri (fun i a -> gcds.(0).(i + 1) <- gcd gcds.(0).(i) a) a_s;
  Array.iteri (fun i a -> gcds.(1).(n - i - 1) <- gcd gcds.(1).(n - i) a_s.(n - i - 1)) a_s;
  for i = 0 to n - 1 do
    ans := max !ans @@ gcd gcds.(0).(i) gcds.(1).(i + 1)
  done;
  Printf.printf "%d\n" !ans