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)

let rec gcd n m =
  if m = 0 then n
  else gcd m (n mod m)
  
let () = Scanf.scanf "%d\n" @@ fun n ->
  let as_ = Array.init n @@ fun _ -> Scanf.scanf "%d " @@ fun a -> a in
  let acc = Array.make (n + 1) 0 in
  let acc' = Array.make (n + 1) 0 in
  for i = 0 to n - 1 do
    acc.(i + 1) <- gcd acc.(i) as_.(i)
  done;
  for i = n - 1 downto 0 do
    acc'.(i) <- gcd acc'.(i + 1) as_.(i)
  done;
  Printf.printf "%d\n" @@
  Array.fold_left max min_int @@
  Array.init n @@ fun i -> gcd acc.(i) acc'.(i + 1)